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THE UNIVERSITY
() F ILLING)IS
LIBRARY
Q.535 C5
JO
v. Go

NOTICE: Return or renew all Library Materials! The Minimum Fee for each lost Book is $50.00.
The person charging this material is responsible for -
its return to the library from which it was withdrawn on or before the Latest Date stamped below.
Theft, mutilation, and underlining of books are reasons for discipli nary action and may result in dismissal from the University. To renew call Telephone Center, 333-6400 UNIVERSITY OF ILLINOIS LIBRARY AT URBANA-CHAMPAIGN
00I 24 1940
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OCI 13 E. mirrauðrúR£50%
*IERLIBRARY than
L161-O-1096

Journal
of the

Optical Society of America
and

Review of Scientific Instruments

EDITOR-IN-CHIEF: PAUL D. FOOTE BUREAU of STANDARDs, WASHINGTON, D.C. ASSISTANT EDITOR-IN-CHIEF AND BUSINESS MANAGER: F. K. RICHTMYER
CoRNELL UNIVERSITY, ITHACA, N. Y. CoNSULTING BUSINESS MANAGER, M. E. LEEDs, Philadelphia, Pa.

Term Ending Dec. 31, 1923
H. D. CURTIS E. P. HYDE PAUL E. KLOPSTEG L. SILBERSTEIN L. T. TROLAND F. E. WRIGHT

Associate Editors:
Term Ending Dec. 31, 1925
G. K. BURGESS K. T. COMPTON L. R. INGERSOLL C. E. K. MEES C. E. MENDENHALL D. C. MILLER

Term Ending Dec. 31, 1927
W. T. BOWIE H. G. GALE HERBERT E. IVES W. B. LANCASTER P. G. NUTTING J. P. C. SOUTHALL

Volume VI, Numbers 1 to 10, 1922

OFFICE OF PUBLICATION: GEORGE BANTA PUBLISHING COMPANY
MENASHA, WISCONSIN

Q5 2. S. & S.

-Yo

v. 6

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TABLE OF CONTENTS

Volume VI

JANUARY, 1922
Announcement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Brilliance and Chroma in Relation to Zone Theories of Vision. . . . . . . . . . . . .
LEONARD THOMPSON TROLAND Measurement of the Color Temperature of the More Efficient Artificial
Light Sources by the Method of Rotatory Disperson . . . . . . . . . . . . . . . . 27 IRWIN G. PRIEST
The Blue Glow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 E. L. NICHOLS AND H. L. Howe's
The Significance of the 3% Terms in Spectral Series Formulae. . . . . . . . . . . . . 54
PAUL D. FOOTE AND F. L. MOHLER The Dispersion of Glass. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
T. SMITH
INSTRUMENT SECTION
The Crystelliptometer, an Instrument for the Polariscopic Analysis of Very Slender Beams of Light. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
LE ROY D. WELD Reviews and Notices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
MARCH, 1922
Report on Atmospheric Scattering, Sky Polarization and Allied Phenomena F. E. FOWLE
Note on Mr. F. E. Wright's Article for Determining Prism Angle Errors. . . . 108 WALTER F. C. FERGUsoN
Invariant Ratios and Functions in Glass Dispersion. . . . . . . . . . . . . . . . . . . . . 109 P. G. NUTTING
The Propagation of Light in Rotating Systems. . . . . . . . . . . . . . . . . . . . . . . . . . 112 A. C. LUNN
Observations on the Rare Earths, XI: The Arc Spectrum of Yttrium . . . . . . . 121 L. F. YNTEMA WITH B. S. HOPKINS
1921 Report of Committee on Standard Wave-Lengths. . . . . . . . . . . . . . . . . . 135 W. F. MEGGERS
The Gloss Characteristics of Photographic Papers. . . . . . . . . . . . . . . . . . . . . . 140 L. A. JoNES
INSTRUMENT SECTION
Standard Radio Wavemeter, Bureau of Standards Type R 70B . . . . . . . . . . . . 162 R. T. COX
Mercury Lubricated Resistance Box Plugs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 J. R. ROEBUCK
III

TABLE OF CONTENTS –Continued

A High-Voltage Storage Battery for Use with Electron Tube Generators of Radio-Frequency Currents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 E. L. HALL AND J. L. PRESTON

A Method of Testing Plates from Piezo-Electric Crystals. . . . . . . . . . . . . . . 18 W. G. CADY

An Electron Tube Amplifier for Amplifying Direct Current . . . . . . . . . . . . . . 18 H. A. S.Now

A Simple Form of Laboratory Potentiometer . . . . . . . . . . . . . . . . . . . . . . . . . . 19 H. W. FARWELL

Photography of Moving Interference Fringes. . . . . . . . . . . . . . . . . . . . . . . . . 19 AUGUSTU's TRow BRIDGE

A High Speed Precision Relay. .

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CARL KINSLEY

Notices. . . . . . . . . . . . . . . . . . . .

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MAY, 1922
Review of the Present Status of the Two Forms of Quantum Theory. . . . . . . 21 RICHARD C. TolMAN
Mathematical Aspects of Quantum Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . 22 H. B. PHILLIPs
Some Recent Applications of the Quantum Theory to Spectral Series. . . . . . 23 SAUL DUSHMAN
The Evaluation of Quantum Integrals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Critical Frequency Relations in Scotopic Vision . . . . . . . . . . . . . . . . . . . . . . . 25 HERBERT E. Ives

INSTRUMENT SECTION

A Pocket Size Range Estimator. . . . . . . . .

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A New Form of Electrostatic Voltmeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 J. E. SHRADER

The Phonelescope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

A Differential Electrodynamometer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

A Precision X-Ray Spectrometer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 H. M. TERRILL
Notices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

JUNE, 1922 The Beginnings of Optical Science. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
JAMES P. C. SouTHALL
IV

TABLE OF CONTENTS–Continued
Helmholtz on the Doctrine of Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 HENRY CREw
Helmholtz's Contributions to Physiological Optics. . . . . . . . . . . . . . . . . . . . . 327 LEONARD THOMPsoN TROLAND
Reminiscences of Hermann von Helmholtz. . . . . . . . . . . . . . . . . . . . . . . . . . . 336 M. I. PUPIN
A Theory of Intermittent Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 HERBERT E. Ives
The Visibility Function and Visibility Thresholds for Color-Defectives. . . . . 362 MARGARET C. SHIELDS
Recalescence in Antimony. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369 ENOCH KARRER
INSTRUMENT SECTION
Three-plane Orientation Clamp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 W. R. MILES
Note on a Method of Increasing the Carrying Capacity of a Rheostat. . . . . . . 376 W. E. FORSYTHE
Constructional Data for a Cemented Objective of Barium Crown and Flint. . 379 I. C. GARDNER
An Apparatus for Studying the Motion of Relays. . . . . . . . . . . . . . . . . . . . . . . . 391 HERBERT E. Iv ES AND T. L. Dow EY
Infra Red Telegraphy and Telephony . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398 T. W. CASE
Notices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
JULY, 1922
False Spectra from Diffraction Gratings I. Secondary Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417 W. F. MEGGERS AND C. C. KIESS II. Theory of Lyman Ghosts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429 CARL RUNGE
III. Periodic Errors in Ruling Machines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 J. A. ANDERSON
On the Propagation of Light in Rotating Systems, A Rejoinder to Dr. A. C. Lunn. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443 LUDWIK SILBERSTEIN
On the Optical Constants of Selenium in the form of Isolated Crystals. . . . . . 448 L. P. SIEG
Huygens' Contributions to Dioptrics, with Notes. . . . . . . . . . . . . . . . . . . . . . . 461 JAMES P. C. SouTHALL
Accuracy in Color Matching of Incandescent Light Sources. . . . . . . . . . . . 476
W. E. FORSYTHE
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V

TABLE OF CONTENTS-Continued
INSTRUMENT SECTION
Cooperation Between the Makers and the Users of Apparatus in America. . . 4. F. K. RICHTMYER
A Field Telemeter for Approximate Surveying. . . . . . . . . . . . . . . . . . . . . . . . . I. C. GARDNER
On the Characteristics of Optical Systems for Reading Small Mirror De
flections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Contact Resistance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IRVING B. SMITH
An Apparatus for Demonstrating the Electrical Properties of Conducting
Gases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . John ZELENY
Reviews and Notices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
AUGUST, 1922
Report of Committee on Colorimetry for 1920-21. . . . . . . . . . . . . . . . . . . . . . L. T. TROLAND
Heteromorphies Due to Variation of Effective Aperture and Visual Acuity. . K. HoRovITZ
The Absorption of the Eye for Ultra-Violet Radiation. . . . . . . . . . . . . . . . . . . WINIFRED P. GRAHAM
INSTRUMENT SECTION
A New Principle and Its Application to the Lummer-Brodhun Photometer . . E. P. HYDE AND F. E. CADY
An Electromagnetic Method of Detecting Minute Irregularities in Curvature of Spheres and Cylinders and of Controlling the Oscillations of a Mass of Metal Suspended by Means of a Torsion Fibre. . . . . . . . . . . . . . . . . ALEXANDER MARCUS
An Improved Form of Nichols Radiometer. . . . . . . . . . . . . . . . . . . . . . . . . . . . B. J. SPENCE
A Portable Seismometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P. G. NUTTING
An Instrument for the Gamma Ray Measurement of the Radium Content of Weakly Active Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
N. ERNEST DORSEY The Effect of a Photo-electric Material on the Thermo-electric Current in
High Vacuum Audion Bulbs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . THEODORE W. CASE
Direct Capacity Measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GEORGE A. CAMPBELL
Notices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c
VI

TABLE OF CONTENTS –Continued

SEPTEMBER, 1922
Magnetic Rotation in Various Liquids in the Short Infra-red Spectrum. . . . . 663 L. R. INGERSOLL

INSTRUMENT SECTION

The Classification of Optical Instruments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 682 T. SMITH
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Summary of the Literature Relative to the Formation of Film on Polished
Glass Surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 688 GEORGE W. MoREY
A Suspension to Eliminate Mechanical Disturbances. . . . . . . . . . . . . . . . . . . 694 ALBERT P. CARMAN
A Form of Iron Clad Thomson Astatic Galvanometer. . . . . . . . . . . . . . . . . . . 696 B. J. SPENCE
A Low Voltage Cathode Ray Oscillograph . . . . . . . . . . . . . . . . . . . . . . . . . . . . 701
J. B. JOHNSON

Specifications for Recording Vapor-Pressure Thermometers and for Pres sure Gages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713 FREDERICK J. SCHLINK

Sieve Testing Apparatus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 719 L. V. JUDSON AND R. E. Gould

The Film Method of Measuring Surface and Interfacial Tension . . . . . . . . 722 A. W. FAHRENWALD

The Passage of Hydrogen Through Quartz Glass. . . . . . . . . . . . . . . . . . . . . . 734 J. B. JoHNSON AND R. C. BURT

A Simple Apparatus for Comparing Thermal Conductivity of Metals and Very Thin Specimens of Poor Conductors. . . . . . . . . . . . . . . . . . . . . . . . . 739 M. S. WAN DUSEN

Aeronautic Instruments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

744

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FRANKLIN L. HUNT

Reviews. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 812

OCTOBER, 1922 A Photo-Electric Theory of Color Vision. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 813
JANET H. CLARK Pioneers in Physiological Optics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 827
JAMES P. C. SouTHALL
INSTRUMENT SECTION The Mechanics of Optical Polishing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 843
ELIHU THOMSON A Variable Resistor of Low Value. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 848
C. N. HICKMAN
VII

TABLE OF CONTENTS –Continued

A Rotary Slide-Wire for Producing Uniform Variation in Potential Differ

€11Ce . . . . . . . . . . . . . . . . . . . . . . . . . . .

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A Simple Direct-Reading Potentiometer for Standard Cell Comparisons. . . MARION EPPLEY AND WILLIAM R. GRAY

On Construction of Platinum Thermometers and of Resistance Coils . . . . . J. R. ROEBUCK

The Drainage Error in the Bingham Viscometer. . . . . . . . . . . . . . . . . . . . . . . WINSLow H. HERSCHEL

Specifications for Bourdon Tube Pressure Gages for Air, Steam, and Water Pressures, and for Use as Reference Standards. . . . . . . . . . . . . . . . . . . . FREDERICK J. SCHLINK

A Method of Maintaining Small Objects at any Temperature Between -180° and +20° C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P. P. CIOFFI AND L. S. TAYLOR

A Tungsten Furnace for Experiments on Dissociation and Ionization . . . . . K. T. COMPTON

NOVEMBER, 1922

Note on the Energy Exchanges in the Formation of the Latent Image of a Photographic Emulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. E. SHEPPARD AND E. P. WIGHTMAN

The Optical Constants of Isolated Tellurium Crystals. . . . . . . . . . . . . . . . . . GEORGE DEw EY WAN DYKE

The Study of Visual Processes by Means of Momentary Retinal Shadows. .

FREDERICK W. ELLIS

A Comparison of the Fechner and Munsell Scales of Luminous Sensation

Value. . . . . . . . . . . . . . . . . . . . . . . .

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INSTRUMENT SECTION
The Measurement and Specification of Optical Characteristics in Projector
Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G. W. MOFFITT
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An Electron Tube Tuning Fork Drive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. A. ECKHARDT, J. C. KARCHER AND M. KEISER
A Laboratory Hypsometer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. F. MUELLER AND T. S. SLIGH, JR.
A High Temperature Regulator for Use with Alternating Current. . . . . . . . HowARD S. Rob ERTS
An Integraph Based on Parallel Double Tongs. . . . . . . . - - - -- -- - - - -- -- - VLADIMIR KARAPETOFF
Reviews and Notices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
VIII

TABLE OF CONTENTS—Continued
DECEMBER, 1922 Extraordinary Diffraction of X-Rays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 989
L. W. McKEEHAN
On the Quantity of Light Energy Required to Render Developable a Grain of Silver Bromide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 998 P. S. HELMICK
Recent Measurements of Stellar and Planetary Radiation. . . . . . . . . . . . . . 1016 W. W. COBLENTZ
INSTRUMENT SECTION The Lensometer, An Instrument for the Measurement of the Effective or
Vertex Power of Ophthalmic Lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1030 CHARLEs SHEARD AND E. D. TILLYER
A Hemispherical Photometric Integrator. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1040 FRANK BENFORD
Telephone Receiver and Transmitter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1059 C. W. HEWLETT
A Small High Intensity Mercury Arc in Quartz-glass. . . . . . . . . . . . . . . . . . . 1066 L. J. BUTTOLPH
Correlation of Elementary Proofs of the Fundamental Properties of Oblique Deviation by Prisms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1072 H. S. UHLER
Index to Volume VI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1077
IX

OFFICERS
OF THE
OPTICAL SOCIETY OF AMERICA
FOR THE YEAR 1922

President: L. T. TROLAND
Vice-Pres: HERBERT E. Ives
•
Secretary: IRwiN G. PRIEST
Treasurer: ADOLPH LOMB

Harvard University, Cambridge, Mass.
Western Electric Co.
#"
Bureau of S
£"
Rochester, N.Y.

The Council consists of the above officers, the Editor-in-Chief and the Assistant Editor-in-Chief and Business Manager of the JoURNAL, the past President, James P. C. Southall, Columbia University, and the following elected members: Adelbert Ames, Dartmouth College, H. G. Gale, University of Chicago, Ernest Merritt, Cornell University and W. E. Forsythe, Nela Research
Laboratories.
The object of the Optical Society of America is to serve the interests of all who are engaged in any branch of optics from fundamental research to the manufacture of optical goods.
The Constitution provides that anyone who has contributed materially to the advancement of optics shall be eligible to regular membership in the Society, with the privilege of voting and holding office. Anyone interested in optics is eligible to associate membership.

****
2-)

Journal
of the

Optical Society of America
and
Review of Scientific Instruments

Vol. VI

JANUARY, 1922

Number 1

ANNOUNCEMENT
The Optical Society of America announces the addition to its JOURNAL of a section on “Scientific Instruments” beginning with the March, 1922 number. The Journal will henceforth be known as the JourNAL of THE GPTICAL SocIETY of AMERICA AND RE
VIEW OF SCIENTIFIC INSTRUMENTS.
For several years the question of establishing an Instrument Journal in this country has been agitated. Practically no source of publicity has existed for the presentation of articles describing new laboratory and scientific instruments. There has been no question as to the need for and desirability of such a journal; the problem has been as to the means whereby it might be estab
lished.
Some time past the National Research Council suggested that the JourNAL OF THE OPTICAL SOCIETY might enlarge its field to include papers on instrument design of all kinds, as well as optical. After careful consideration on the part of the Council of the Society it was decided that such an arrangement was in the best interest of the readers of the JourNAL.
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By cooperation with the Association of Scientific Apparatus Makers of the United States of America, especially through the efforts of its president, Mr. M. E. Leeds, by cooperation with the National Research Council, and through the agency of certain generous patrons, the Optical Society has been able to launch the
1

2

OPTICAL SOCIETY

|J.O.S.A. & R.S.I., VI

combined “JourNAL of THE OPTICAL SocIETY of AMERICA AND REVIEW OF SCIENTIFIC INSTRUMENTs” on a strong financial basis.
The March and succeeding issues of the new Journal will
devote approximately 38 of the reading matter to material on instruments other than optical. Beginning May 1922 the JoURNAL will be issued monthly instead of bi-monthly, so that the total for each year will contain as much material in pure optics as formerly and in addition some 400 or 500 pages on design of instruments of every description. The rate of subscrip tion probably will be increased sometime during the current year, but for the immediate present the same rate will be maintained as
formerly. The success of any journal is largely determined by the length
of the subscription list. While the JourNAL OF THE OPTICAL SoCIETY has been very fortunate in this respect, its circulation having doubled twice in the past two years, it nevertheless, from the specialized nature of the material presented, must have a direct appeal to a comparatively limited number of readers.
The new JourNAL should interest a very large group of readers. It is believed that this enterprise will meet with the approval and cooperation of all engaged in scientific work from the manu facture of apparatus to fundamental research. The permanent
success of the venture rests with the readers and contributors.
Let each reader and member of the Society cooperate to make this JournAL one of high scientific merit and large circulation. Let us place 2500 subscriptions as a conservative goal for 1923.

BRILLIANCE AND CHROMA IN RELATION TO ZONE THEORIES OF VISION*
BY
LEONARD THOMPSON TROLAND
I. INTRODUCTION
Ophthalmologists draw a clear line of demarcation between three functions of vision which they call the light sense, the form sense, and the color sense respectively. They find that in visual derangements these three functions may be disturbed more or less independently. However, theorists in the field of physiological optics have not been able to agree that these three functions rest upon separate mechanisms. From some points of view and by certain tests they appear to be distinct, but from other angles they appear to be simply different aspects of an integral process. It is my purpose in the present paper to discuss certain problems relating to the separateness of the mechanisms underlying two of these functions, viz., those of the light sense and the color sense. I shall review and attempt to synthesize certain data previously established by others, but in addition shall present new data of my own bearing upon the problem.
It will be necessary in the beginning to define clearly certain of the terms to be used in the ensuing discussion. A great deal of confusion exists in arguments over visual problems as a result of the absence of a definitely established nomenclature. In the major ity of discussions in this field there is a failure to distinguish clearly between psychological, or subjective conceptions, and physical conceptions which relate only to the stimulus. The Colorimetry Committee of the Optical Society in its forthcoming report has worked out what it deems to be a consistent terminol ogy, and I shall make an endeavor to employ this in the present paper. You have been accustomed to hear the two aspects of visual experience, which I am to consider, described by the terms
* Paper presented to the Rochester Section of the Optical Society of America, October 10, 1921.
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"To appear in a later number of this Journal.
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“brightness” and “color.” However, the word “brightness” has a distinct meaning in photometry which should not be confused with that dimension of visual sensation which is defined by the terminal qualities black and white. The preferred term for this dimension, or attribute, of visual sensation is the word “bril
liance.” A careful consideration of all of the circumstances bear
ing upon the problem, moreover, seems to make it advisable to employ the word “color” to designate any visual sensation what soever, including the neutral, or achromatic, qualities as well as the chromatic ones. In order to distinguish the latter from the former, therefore, we must employ a different word, for which the term “chroma” appears to be appropriate. I may therefore define my problem succinctly as that of the interrelation between the physio logical mechanisms underlying brilliance and chroma vision.
II. FACTS INDICATING THE INDEPENDENCE OF BRILLIANCE AND CHROMA
There is a considerable array of facts which strongly suggest
that these mechanisms are distinct from one another. The first
consideration which comes to mind is naturally that of the evolu tion of color vision. Experiments in the field of comparative physiology, such as those carried out by the indefatigable Carl von Hess,” indicate clearly that the invertebrates are totally lacking in chroma vision. Their reactions to radiation are wholly in terms of different degrees in a single dimension which we may suppose to be that of brilliance or apparent brightness. Their
vision is achromatic. The consensus of evidence also is that the
lower vertebrates, such as fish, are incapable of chromatic dis crimination, their differentiated responses to various colors being based wholly upon differences in the brightness effects of the latter.” Many birds and mammals, however, seem to possess the power of true chromatic differentiation between stimuli. The visual capacities of the higher primates are apparently practically
* See, for example, Hess C. v. Beiträge zur Kenntnis des Lichtsinnes bei Wir bellosen. Arch. f. d. ges. Physiol., 177, 57-109; 1920.
* See, for example, Schnurmann, F. Untersuchungen an Elritzen über Farben wechsel und Lichtsinn der Fische. Zeitsch. f. Biol., 71, 69–98; 1920.

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the same as those of man. It appears probable, therefore, that brilliance vision appeared in the course of evolution long before chromatic vision, the latter being superposed upon the former by a process of accretion or of differentiation.
Facts of visual pathology and anomaly also suggest strongly
that brilliance vision is more fundamental than chromatic vision.
Disease or injury of the nervous mechanisms connected with vision more readily disturbs chromatic discrimination than it does discrimination in terms of brilliance. Congenital partial or total “color blindness” involves a loss or impairment of the capacity for differentiation of chromas without necessarily bring ing with it a similar disorder of brilliance judgment. The different types of chromatic blindness can, in fact, be arranged in an evolu tionary series ranging from anomalous trichromatism through deuteranopia, or green blindness, and protanopia, or red blind ness, to the complete absence of chromatic response which is commonly known as “total color blindness.” In these various forms of chromatic blindness it would appear that successively laid down strata of visual mechanism have been destroyed by accidents to the germ plasm, these accidents representing various degrees of atavism. The resulting visual types may be taken to represent actual stages in the evolution of human vision.
However, we do not have to look to pathological or rare cases for evidence that chromatic vision is something superposed upon a more fundamental brilliance vision. In the distribution of the
capacity for chromatic discrimination between the center and the periphery of the visual field we seem to discover a replica of the
evolutionary process. In the extreme periphery of the visual field
chromatic vision appears to be practically in abeyance, all objects, except under conditions of very high illumination, being perceived
as neutral in color." As the stimulus is moved from the periphery
towards the center, chromatic discrimination in terms of blueness * See Hess, C. v. Die Rotgrünblindheiten. Arch. f. d. ges. Physiol., 185, 147–164,
1920.
* Ferree and Rand find that red, yellow and blue, but not green, can be perceived as chromatic at the extreme periphery with a sufficient intensity of light. See Ferree,
C. E. and Rand, G. The Absolute Limit of Color Sensitivity and the Effect of Inten sity of Light on the Apparent Limit. Psychol. Rev., 27, 1–23, 1920.

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or yellowness first becomes possible, this being succeeded at a more central position by an added power of discrimination in terms of redness and greenness. In the center of the field for the normal individual we find complete color vision. It is a very significant fact that in spite of these wide differences which exist between the chromatic perception of various portions of the retina, under con ditions of daylight adaptation, the visibility curves representing the brilliance responses of these various portions are practically
identical."
Another very impressive group of facts which indicate the separability of the mechanisms underlying brilliance and chroma is to be found in a considerable number of laws of visual response in which the effects produced by lights of different color are sub stantially independent of the chromatic aspect and rest almost wholly upon the brilliance factor. One of the most familiar of these laws is to be found in the logarithmic function which con nects visual acuity with luminosity. This function, which repre sents the threshold of the form sense, is seemingly determined, to the first order at least, by the brilliance value of any stimulus independently of its hue or saturation effects.” There are, of course, second order dependencies upon wave-length, as has been demonstrated by Luckiesh,” but these latter dependencies are

*See Parsons, J. H. An Introduction to the Study of Color Vision, p. 71, 1915. * The proposition that the acuity index depends upon the brightness value of a stimulus, independently of its color, was clearly enunciated by Helmholtz in several places, and had been assumed by previous workers such as Macé de Lapinay and Nicati who employed equality of acuity as a criterion of equality of brightness. Repeated attempts have been made to employ an acuity test as a basis for heterochromatic photometry. König regarded his very systematic work on this subject as clearly sub stantiating Helmholtz's original conjecture. See König, A. Die Abhangigkeit der Sehscharfe von der Beleutungsintensität, Gesammelte Abhandlungen zur Physiologi schen Optik. 1903, p. 391. However, the problem is much complicated by uncertainty in the conditions or method of observation; the proportions of rod and cone vision: involved, the exact visibility curves of the observers, and the exact importance of the purely physical chromatic aberration effects within the eye. Dr. Ferree finds a very considerable dependence of acuity upon chroma even when rod vision is excluded. Whether his results, in common with those of Luckiesh, can be explained in terms of the refractive properties of the eye or whether they will require a retinal basis is at present uncertain. • Luckiesh, M. Color and Its Applications, pp. 130-137, 1915.

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directly traceable to the chromatic aberration of the eye which forms a sharper image upon the retina for the mid wave-lengths of the spectrum than for the extreme wave-lengths. Given equally sharp retinal pictures, it would seem that the resolving power of the optical mechanism is determined wholly by the brilliance response without reference to chroma.
Another well known law of this character is that which links
critical flicker frequency with the brightness of the stimulus. T. C. Porter found that this frequency, the rate of alternation of a color with black which is required just to eliminate flicker, is strictly proportional to the logarithm of the brightness through out a range of from 1 to 12800 units of intensity and that the pro portionality factor is strictly independent of wave-length.” Here again, as shown later by Ives," there are secondary dependencies upon chroma, but these seem to rest upon the fact that there are two kinds of flicker, one a brilliance flicker and the other a chro matic flicker, which are not quite separable at low intensities and rates of alternation. Moreover, the situation is complicated by the different degrees of participation of rod and cone vision in the process as aroused by stimuli of different wave-lengths at low brightnesses, the brilliance response of the rods being much more sluggish than that of the cones. The substantial independence of critical flicker frequency upon chroma is, of course, the basis of the critical frequency method of heterochromatic photometry.
Another function of brilliance which shows very little con comitant dependence upon chroma is the time required for the brilliance sensation to reach its maximum after the first applica tion of the stimulus. McDougall's investigation" indicated that this so-called action time was quite independent of chroma. The much discussed experiments of Broca and Sulzer,” however,
* Parsons, J. H., op. cit., p. 96. * Ives, H. E. Studies in the Photometry of Lights of Different Colors. II. Spectral Luminosity Curves by the Method of Critical Flicker Frequency. Phil. Mag., 24, p. 357-362, 1912. * McDougall, W. The Variation of the Intensity of Visual Sensation with the Duration of the Stimulus. British Jour. of Psychol, 1, p. 189, 1904 *See Nutting, P. G. The Luminous Equivalent of Radiation. Bull. of the Bur. of Stands., 5, p. 293, 1908,

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showed a considerable difference in the rates of rise of sensation
due to stimuli of different wave-length compositions. The recent very elaborate measurements of Bills” also show an appreciable difference between colors of the same brilliance but differing hue. However, neither of these investigations, apparently, were made under conditions which insure equal degrees of participation of rod and cone vision for all of the stimuli employed, and the close
affiliation which exists between rates of rise and fall, for various
stimuli, and flicker frequency, suggests that causes of error in the investigations in question may exist.
A further very important visual function which rests exclusively upon the luminosity of the stimulus is the brightness discrimina tion threshold. The elaborate measurements made by König" with a wide range of spectral stimuli demonstrate that for cone vision Weber's constant, and Fechner's law, which is derived from it, are practically independent of chroma. It is probable also that the brilliance contrast effects between color fields of differing brilliance are independent of concomitant chroma or chroma differences. I gather this from qualitative observations of my own, although I have not been able to find any published accurate data on the subject. The investigations of Ives" and others have made it clear that the separate brightnesses of different colors which are mixed additively summate arithmetically without
reference to their differences in chroma.
All of the above discussed facts, which indicate that brilliance can act as an independent variable determining other visual functions almost without reference to the accompanying chroma, may perhaps be regarded as somewhat lacking in significance because, to a certain extent at least, they may be considered as definitory of the nature of brilliance. It has been suggested, for example, that brilliance be defined in terms of equal flicker frequencies or in terms of equal acuity results. I do not regard

*Bills, M.A. The Lag of Visual Sensation and Its Relation to Wave-Length and Intensity of Light. Psychological Review Monographs, 28, No. 5.
*See Nutting, P. G. loc. cit., p. 286. *Ives, H. E. Studies in the Photometry of Lights of Different Colors. IV. The Addition of Luminosity to Different Colors. Phil. Mag. 24, pp. 845–853, 1912. .

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this objection as actually capable of substantiation, but, on the other hand, it is significant that most of the laws which we have above considered involve processes of discrimination as essential factors. These discrimination processes undoubtedly depend upon cortical mechanisms which are especially adapted to deal exclu sively with brilliance or its underlying physiological correlate, and hence the lack of dependence which the resulting reactions show with respect to chroma might be considered as indicative merely of a highly efficient selective response of these discriminative activities. However, there are other facts to which we can yet appeal which are not subject even to this last objection.
It is a common conviction among students of physiological optics that negative after-image phenomena depend upon retinal rather than upon central changes. These phenomena are usually explained in terms of general or differential retinal fatigue, that is, as results of reduction in the sensitivity of the retinal mechanism to stimuli, this sensitivity being supposedly represented by the concentration of some chemical substance. Negative after-image effects may be divided into brilliance and chromatic aspects. I have personally made a very large number of observations and measurements upon the brilliance aspects of negative after-images produced by spectral or other highly chromatic stimuli. Except under special conditions which I shall discuss in more detail later on I have found these effects to be practically independent of chroma. For example, the duration of negative after images produced by spectral colors and projected upon a reacting field or background of the same spectral color as produced the image are practically the same for all wave-lengths of the stimulus." It is true that there is a slightly less duration for stimuli lying at the ends of the spectrum than for those lying in the middle, and also that the red after-image has a somewhat longer life than the violet one. However, it seems probable that these secondary differences are due to differences in the sharpness of the primary stimulus images which produce the after-effects, such sharpness

"Troland, L. T. Apparent Brightness; Its Conditions and Properties. Trans. of the Illum. Eng. Soc. 5, p. 954; 1916.

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discrepancies being referable to the chromatic aberration of the eye, which influences the distinctness of the retinal picture in the
several cases. I have made careful measurements of the time
required for brilliance fatigue, or minuthesis, as I have proposed to call it, to reach an equilibrium condition for different spectral stimuli, and find that for colors of equal brilliance this time is practically independent of chroma. Similar statements apply to the degree of reduction of the sensitivity of the visual system which is brought about by this minuthetic process in any specified time or at equilibrium with stimuli of equal brightness. The gen eral laws of brilliance minuthesis, in other words, are substantially independent of chroma. I shall return to a consideration of such further special laws later on.

III. THE PROBLEM IN THE LIGHT OF CLASSICAL THEORIES
Having reviewed the above facts bearing upon our problem, let us now turn to a discussion of the most important theoretical treatments dealing with the interrelation of brilliance and chroma vision. The two salient theories of vision, those of Hering and of Young and Helmholtz," involve radically distinct conceptions of the relation holding between brilliance and chroma. Hering, in the original formulation of his theory, regarded brilliance as identical with whiteness and, therefore, as proportional to the degree of excitation of the white process, in his theory, or of lack of excitation of the black process. Later on, however, he intro duced the conception of the specific brightness of colors according to which the red and yellow processes of his theory possess a brilliance-producing power while the green and blue processes have a negative capacity in this respect, or are “specifically dark.” The total brilliance effect according to Hering's view, therefore, represents the algebraic sum of contributions made by all six processes, the white, red, and yellow adding to, while the black, blue, and green subtract from the total. Even in accord ance with this specific brightness theory, however, the preponder ant contribution appears to be made by the black-white process,
"For expositions of these two theories see Parsons, J. H., op. cit., Part III.

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so that Hering's hypothesis seems consistent with the existence of a very considerable independence of brilliance function with respect to chroma. A residual dependence, however, should be expected, and this should be of the order of magnitude of the difference between cone and rod vision luminosity distribution over the spectrum, or between the photopic and scotopic visibility curves. It was in order to explain these differences that Hering originally introduced the specific brightness theory.
The Young-Helmholtz theory, being characterized in general by a less subtle psychological analysis, than that which governed Hering's conjectures, makes assumptions concerning the interre lations of the brightness and chroma mechanisms which are far simpler and more naive. Helmholtz himself and also his followers, König and Dieterici, paid relatively little attention to the relations of photometric measures to color-mixture data. The latter two investigators, for example, although their determinations of the three color sensation curves are probably the most thorough on record, provide us with no measures whatsoever of the relative photometric values of the unit in which their sensation curves are expressed. This criticism, however, does not apply to Abney," whose recent death robs us of one of the most painstaking investi gators of visual phenomena in the light of the Helmholtz Theory. This theory, as is well known, makes the chromatic aspects of color vision depend upon the proportions of excitation of three elementary mechanisms. It is very natural to hold that the brilliance accompanying any complex or simple excitation is simply the sum of the excitation values of the components which
are involved.
The treatment of brilliance or luminosity value as the sum of the color excitation values is not only a theoretically obvious hypothesis, but is a straightforward development of the data involved in the case; although in spite of this fact these data cannot be regarded as proving the physiological identity of the brilliance and chroma mechanisms. When a spectrum having a characteristic luminosity distribution,-for example one possessing
*See Abney, W. de W. Researches in Color Vision and the Trichromatic Theory,
1913.

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equal energy values, for all wave-lengths, in which case the luminosity distribution would be proportional to the visibility curve, -is matched by varying mixtures of three elementary stimuli it is of course a necessary consequence of the additive
property of luminosities that the sum of the luminosity distribu
tions of the three elementaries should yield the original luminosity distribution of the spectrum which was matched. However, this same result should be expected if the luminosity values of the elementaries do not represent integral aspects of the color excita tion processes, but simply more or less accidental associates of these excitation values the magnitudes of which are determined by the exact point in the spectrum from which the three elementary stimuli are picked. The brilliance process necessarily has a charac teristic distribution over the spectrum, represented approximately at least by the visibility curve. Similarly, the three chromatic processes also have their own characteristic distributions, and a stimulus taken at any point in the spectrum will naturally pick up the chromatic and the brilliance activities in a fixed ratio, and this ratio will enter as a constant in all subsequent color-mixture operations. These experimental facts, therefore, provide us with no basis for distinguishing between the inherent brilliance assump tion and the idea that brilliance depends upon a mechanism distinct from that governing chroma.
It does seem to me, however, that the relative magnitudes of the three coefficients which are empirically found to represent the above mentioned proportionality between the brilliance and chromatic powers of any stimulus, do have some bearing upon the probability of the inherent brilliance assumption. When the elementaries to be mixed are red, green and blue, practically all of the luminosity of the spectrum appears to depend upon the red and green, the blue contributing only about one per cent. of the total. Depending upon the exact elementaries which are selected, either the red or the green may greatly preponderate over the other. Such large discrepancies between the chromatic and the brilliance powers of the elementaries would suggest that the underlying mechanisms of the two functions are actually distinct, these coefficients representing an arbitrary association of the two.

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Another consideration which points in the direction of an independence between the brilliance and chromatic mechanisms is to be found in the very perfect symmetry of the retinal visi bility curve." This latter curve is obtained by correcting the ordinary normal visibility curve for the selective absorption of the ocular media, and should be regarded as representing the spectral sensitivity of the brilliance process by itself. It is improb able that independent spectral distributions having maxima in different portions of the spectrum, such as those of the three fundamental chromatic excitations, should be capable of sum mating to yield the very perfect, symmetrical curve which represents the retinal visibility function. It is true that the empirically obtained chromatic excitation curves do actually summate in this manner, but it seems probable that their exact form is dictated by the relations between a symmetrical bril liance function and chromatic response curves which in their true physiological forms do not actually summate to yield a sym
metrical curve.
IV. STUDIES ON THE “ABNEY EFFECT"
Although a direct analysis of the color-mixture system does not permit us to differentiate between the two hypotheses which we have under consideration, it is far from being impossible to find a means of testing between them. It would seem likely, a priori, that there must be some way by which the casual association of a chromatic and a brilliance process, such as that which a theory of the Hering type supposes to exist for a stimulus of any given wave-length, could be broken down. A method of actually dissolving this association presents itself in experiments
of brilliance fatigue with lights of different color. Exposure of
the retina to continued stimulation by radiation of any wave length composition brings about a radical reduction in both the chromatic and the brilliance responses of the eye. In the course of the exposure the apparent brightness of the color is reduced by an asymptotic process to a level which is lower the higher the
”See Troland, L. T. loc. cit., p. 955–957.

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intensity of the stimulus and which at moderately low intensities may amount to the elimination of ninety per cent. of the original value. At the same time the color, if it be chromatic, changes in saturation and usually also in hue. A careful study of the laws governing these simultaneous brilliance and chromatic fatigue processes, or as I have proposed to call them, minutheses, ought to throw a clear light upon the question as to the fundamental dependence or independence of the two.
I am not acquainted with any exact data bearing on the ques tion as to the identity of the laws of minuthesis for brilliance and chroma. Qualitative observations of my own indicate that the two processes do not occur at the same rate or exhibit the same constants. I hope in the near future to make some careful quan
titative measurements on the simultaneous courses of these two
processes. It ought to be particularly instructive to carry the minuthesis to its asymptotic limit both for the brilliance and chromatic aspects of the sensation, and then to observe the course of recovery of these two attributes. Qualitative observations indi cate that they do not recover at the same rate.
One very obvious method, resting upon the facts of minuthesis, of attacking our problem is as follows. Suppose that we fatigue the retina by a spectral red of given intensity and that we measure the diminution in apparent brightness brought about by this minuthetic process. Let us then throw upon this fatigued area a spectral green stimulus and again measure the reduction in ap parent brightness which has been produced for this second stimulus. Since the spectral red should be expected to fatigue the elementary red sensation mechanism much more than the elementary green mechanism we should anticipate on the Abney Helmholtz assumption that the luminosity reduction for the green stimulus would be much less than for the red one. On the other hand, if brilliance and chroma depend upon distinct mechan isms the factors involved, so far as brilliance is concerned, should be the same in the case of the green as in that of the red, and consequently the percentage reduction of the two should be identical. Another way of stating the proposition in a very general form is to say that fatigue with colored stimuli should be

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expected on the Abney-Helmholtz hypothesis to modify the form of the visibility curve, whereas on the alternative theory this
should not occur.
Abney himself carried out experiments of this general charac ter, and his results indicate clearly that a modification in the form of the visibility curve actually does occur.” Moreover, according to Abney’s analysis, the change in question is exactly such as would be expected in accordance with his own hypothesis. His results, so far as they go, are clearly in the direction of sub stantiating the idea that brilliance and chroma depend upon the same mechanism. However, Abney’s conditions of experimenta
tion were such as still to leave some doubt in our minds as to the
exact significance of his results. In the first place, the size of field which he employed was evidently such as to permit a con siderable amount of rod vision to be involved. Different degrees of participation of rod and cone vision accompanying the applica tion of various spectral stimuli yield results very similar to those obtained in Abney’s experiments. The effects obtained by Abney were apparently small, although the smoothness of his curves indicates a precision which is astonishing for heterochromatic comparisons of the type involved in such investigations. More over, the contrasts in color saturation which appear in such experi ments may readily be confused with brilliance contrasts, provided the latter are small. However, the most serious objection to Abney’s work lies in the fact that he neglected, in his experiments, to determine the absolute degree of fatigue, his data giving simply the proportionality between the two compared colors. Although his results may indicate some degree of interdependence of bril liance and chroma, we cannot from his data determine whether the relation is of the exact magnitude which is required by his own theory or not.
-
I have particularly been led to doubt the significance of Abney’s results because of the outcome of certain experiments of my own. Several years ago at Nela Park I carried through a series of minuthesis measurements” with spectral colors the conclusions
* Abney, W. de W. op.cit., pp. 371-380. * As yet unpublished.

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of which were that the brilliance minuthesis brought about by one spectral color carried over without change to any other such color, or in other words, that the minuthetic effects of different spectral colors of the same brightness are identical as tested by all colors. Large saturation contrasts existing in my experiment, however, would have made impossible the reliable detection of apparent brightness contrasts much less than twenty per cent in magnitude, although I employed the constant error technique and was able to compute statistical differences less than the threshold. The upshot of my measurements was that if any Abney effect, —as we may call it, -existed, it was smaller than the photometric threshold in my comparisons. More recently Mr. C. H. Langford and I have taken up this problem anew in the Harvard Psychological Laboratory. Mr. Langford has made preliminary observations of a qualitative nature employing a considerable number of subjects to determine whether or not the Abney effect is observed. He finds that the majority of persons experience such an effect, although it is so small that the observer often has difficulty in determining whether the contrast is one of brilliance or of saturation. At the same time there are some per sons who report a reversed Abney effect. I have observed the latter myself quite strongly with certain combinations of stimuli. This reversed effect, so far as it goes, would point in the direction of the Hering theory of specific brightnesses combined with the doctrine of antagonistic colors. It is quite probable, however, that the reverse phenomenon is attributable to a failure exactly to balance photometrically the two stimuli of different color which are utilized in the fatigue phase of the experiment.
Since one of the principal difficulties which is encountered in experiments of the type just described consists in the existence of a very large saturation contrast superposed upon the brightness contrast which it is desired to study, it occurred to me that a flicker method might be applied to the problem, the saturation contrast being eliminated by fusion in accordance with the well known principle of the flicker photometer. Mr. Langford and I have carried through a systematic series of observations employ ing this method, the two color stimuli which were used being an

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extreme spectral red or its equivalent, and a minus red obtained by use of the Wratten No. 44 filter. The procedure was as follows. The retina of one eye was first fatigued for three minutes to a two degree field of the red, fixation being kept constant on the
center of the field. The red stimulus was now alternated with the
minus red, or green, in the same field, and the intensity of one or
the other of the two stimuli was varied until the minimum or zero
flicker point was found. The intensity of the variable stimulus required for this flicker match was recorded. At another time a
similar flicker match was established in the absence of minuthesis
by the red stimulus. Two photometric values were thus obtained, the one standing for the brilliance of the red relative to the green with minuthesis, and the other for the same relationship substan tially without minuthesis. In parallel with these two measure ments, determinations were made of the degree of minuthesis which resulted from the three minute fatigue exposure, this being accomplished by fatiguing a semicircular field and matching this in brilliance by variations in the intensity of a stimulus projected upon the adjacent semicircle at the termination of the fatigue
exposure.
From the data thus obtained, using Abney’s color sensation curves and the known spectral distributions of the stimuli which were employed, it was possible to compute not only the intensity of the Abney effect which actually appeared to two observers, but also that which should be expected theoretically in accordance with the Young-Helmholtz assumptions. This latter value is ap proximately 75 per cent., representing the depression of the appar ent brightness of the red relative to that of the green. The values actually found, hewever, were for one observer only 3 per cent. and for the other 5 per cent. The empirical results, therefore, are in radical disagreement with the Young-Helmholtz assumptions as interpreted by Abney. They indicate that the linkage between brilliance and chroma is far less thorough-going than is supposed by these latter theoretical interpretations. Indeed the Abney effect is so small as to suggest that there is actually no affiliation whatsoever between the two functions, on the supposition that the values for the effect actually found are simply due to errors of

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observation. However, considerable care was taken in the experi ments to eliminate all asymmetries in the technique, and compu tation of the probable error of the average results indicates that the magnitudes actually found probably have some significance. The results would seem more consistent with an hypothesis of Hering's type in which the main body of brilliance sensations is attributed to a single process independent of the chromatic excitations although there is a slight residual contribution of brilliance due to the latter. It is possible, however, to reconcile the results with the Young-Helmholtz Theory if we suppose that the three chromatic spectral distribution curves overlap in the spectrum much more extensively than has been assumed by Abney and other interpreters of the Young-Helmholtz Theory. This overlap, however, in order to explain our results, would necessarily be so great that all three of the chromatic curves would differ only slightly from the visibility curve. There are other data which indicate that the actual overlap is greater than assumed by Abney, and on this hypothesis our data could be employed to compute the magnitude of this overlap.

V. THE DIMMING EFFECT AND THE ASSOCIATION OF BRILLIANCE WITH CHROMA
In the foregoing discussion I have supported the thesis that the mechanisms underlying brilliance and chromatic vision are distinct, and have attempted to refute the doctrine of the Young Helmholtz Theory which identifies these mechanisms. I wish to turn now to certain phenomena which, I believe, are quite new and which point in the opposite direction, indicating a very strong affiliation between the brilliance and chromatic functions. These phenomena appear under the influence of sudden changes in the brightness of the stimulus field. The fundamental processes which are involved are probably identical with those of effects which I have previously described elsewhere in conjunction with such brightness changes.”

* Troland, L. T. Preliminary Note; The Influence of Changes of Illumination upon After-Images. Amer. Jour. of Psychol., 28, pp. 497–503; 1917.

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The conditions for the observation of the phenomena in ques tion, in relation to our present problem, may be described as fol lows. The retina is first fatigued by exposure to a bipartite field consisting of two semicircular areas of different color, for exam ple a red and a green, of equal brilliance. Fixation is constantly directed to the center of the dividing line of this field. At the end of the fatigue phase of the experiment the entire circular field is converted into a single color, ordinarily that of one of the fatigue phase stimuli. This is an ordinary procedure for the study of the Abney effect, and this effect, if it manifests itself at all, should be visible on the homogeneous field at the moment of the removal of the additional color which was present in the first phase. In my own experience, as previously stated, however, practically no
brilliance difference exists between the two halves of the field.
The Abney effect, if it appears, will be of the order of magnitude of five per cent. If now the stimulus field be suddenly darkened or dimmed in intensity, say to about one quarter of its initial value, a very strong brilliance contrast will often appear. The degree of this contrast depends upon that of the dimming as well as upon the absolute brightnesses of the stimuli, and it is furthermore dependent in a very important way upon the exact color pairs which were employed in producing the original minuthesis. For some color pairs the contrast is practically absent, but for others it is very high, amounting often, I should estimate, to a difference of ninety per cent. In other words this dimming technique, or test, brings out an Abney effect, or analogous phenomenon, which is of the magnitude which should actually be expected from theory for the case of stimuli not varied in intensity. These results seem to indicate inevitably that there is a fundamental linkage between the brilliance and chromatic mechanisms, which linkage manifests itself, however, only under these special conditions.
I have made some preliminary experiments on the influence of various combinations of spectral colors upon the effect in ques tion. Four spectral colors, representing red, yellow, green and blue, were selected and each of these were made up into a pair with each other and in successive series of observations the minu thetic effects of all of these pairs were projected upon each of the

20

LEONARD TRoland [J.O.S.A. & R.S.I., VI

four spectral stimuli as reacting excitations. The results form a rather complex system but in practically every case in which a red was involved a strong brightness contrast appeared during the dim phase of the experiment. The indications, therefore, are
that the red chromatic excitation is affiliated with the brilliance
process in a unique manner.” The brilliance contrasts in the case of the red in comparison with other stimuli were in the direction coinciding with an expected Abney effect. However, the bril liance contrasts appearing in the case of the blue stimulus in com parison with certain others were in an opposite direction.
It is not my purpose in the present paper to attempt a thorough explanation of these complicated relationships. It will be neces sary to accumulate a considerable mass of quantitative data before this can be accomplished with any degree of satisfaction. However, it is necessary as a portion of the argument here to consider briefly a certain general hypothesis concerning the mechanism underlying these dimming effects. I have previously studied experimentally in great detail similar phenomena which appear upon dimming a homogeneous circular stimulus field upon one half of which is projected a negative after-image produced by
the same stimulus but of lesser area. Under such conditions a
a very strong initial brilliance contrast exists between the two halves of the field, since one half has been fatigued to brilliance
and the other has suffered no minuthesis whatsoever. In the
course of a minute or so, depending upon the length of the fatigue exposure, this brilliance contrast disappears, owing to the reduc tion of the fresh area to a level of sensitivity substantially similar to that of the other half of the field. If now, however, the field be dimmed, the brilliance contrast returns with great vividness. On maintaining the field at the dimmed intensity, this brilliance contrast rapidly disappears. If, next, the intensity be restored to its original value a brilliance contrast reappears, but this time in the opposite direction from that which characterized the original effect and also that obtained by dimming. In other
* In the Young-Helmholtz Theory, as interpreted by the majority of its expo nents, this uniqueness of the red would probably consist in its being the only chromatic process which is capable of being excited in isolation from others.

Jan., 1922]

ZONE THEORIES OF COLOR

21

words there is a reversal of the brilliance contrast during brighten ing of the field. If the bright state is maintained, the brilliance contrast again fades out. This process of dimming and brighten ing with rejuvenation of the brilliance contrast can be carried out over and over again.
-
On account of the fact that these brilliance contrasts which re
sult from changes in the brightness of the stimuli are ephemeral in character the most reasonable conception of their nature would regard them as dependent upon differences between the rates of fall and rise of the excitations in the two halves of the field. Upon or during dimming the brilliance in the more minuthesized half of the field drops more rapidly than in the less minuthesized half, while upon or during brightening the rise is more rapid in the former than in the latter. This principle can be stated in
terms of resistance of the excitations in the two halves of the field
to change in their magnitudes. The resistance to change, whether in decrease or increase, is apparently less in the more minuthesized field than in the less minuthesized one. Given sufficient time, both sides of the field reach the same asymptotic limit either in the process of increase or of decrease, but during the course of their change a difference appears between them due to the greater speed of change of one as compared with the other.
If we turn now from an abstract consideration of the experi mental results to the neural mechanism which is responsible for them we find that the most plausible portion of this mechanism in which to look for the resistance changes above considered consist in the so-called synapses, or nerve junctions, which enter into the conductional processes of the optic nerve and tract. Physiologists are accustomed to regard there synapses as seats of a variable resistance or conductance. In general, exercise, or the passage of a nerve current, through the synapses, reduces their resistance. This principle is obviously in harmony with the relationship of our dimming and brightening phenomena, since it is always the more fatigued, or more exercised, portion of the retinal field which exhibits the greater facility of change; which, in other words, darkens or brightens the faster with the corresponding changes in the stimulus intensity. We are therefore led to suppose that the

22

LEONARD TRolAND J.O.S.A. & R.S.I., VI

mechanisms underlying these dimming and brightening phenom ena are localized in the nerve synapses rather than in the retinal
receptors.
VI. EXPLANATION IN TERMS OF A ZONE THEORY OF VISION
In the considerations of the last paragraph we find an indica tion of the manner in which we may hope to resove the paradox established in the present paper. This paradox is the outcome of two sets of data, one of which seems to indicate the complete, or at least the very approximate, independence of brilliance function with respect to chromatic function. The other system of data, centering around effects resulting from intensity changes in the stimulus, point in exactly the opposite direction, necessitating the supposition that the brilliance and chromatic mechanisms are very closely affiliated. Even a cursory examination of the mechan ism underlying visual sensation and perception reveals its extreme intricacy. The prevailing theories of visual processes err in many respects, but fundamentally in their tacit assumption that the visual mechanism is simple, or can be so regarded. The first step in the analytic description of the complex mechanism which we find in the eye and its nervous appendages would appear to be to divide up the propagational or conductional system in which it consists into successive stages or zones. The first of these may be considered to be the object in space before the eye, the second the radiation which is sent off from the object to impinge upon the cornea, the third stage would consist in the refractive adventures of the radiation in the ocular media, the fourth the photochemical changes occurring in the retinal receptors, and the fifth the reac tion of the photochemical end products with the optic nerve fibers to initiate the visual impulses. Following thereafter comes a series of nerve conduction stages or zones involving successive synaptic and nerve fibre activities leading finally through the sub ordinate ocular motor nuclei of the corpora quadrigemina and other lower visual centers, to the visual projection areas of the cerebral cortex. Finally there are the complicated connections of the visual projection areas with various association areas of the cortex. It is probably only in conjunction with processes

Jan., 1922]

ZoNE THEORIES OF COLOR

23

occurring in these latter association areas that chroma and bril liance as aspects of visual consciousness are aroused.
It is clear that visual effects observed in consciousness may depend upon any one or any combination of the mechanisms lying in these successive zones of the visual conduction apparatus. One criterion, or test, such as flicker, may bring out the peculiarities of the mechanism in a certain zone such as, for example, the cor tex, whereas another test, such as our dimming procedure, may
emphasize the characteristics of some other zonal mechanism, say for example the mechanism of certain synaptic regions which lie afferent to the cortex. Other phenomena, such as the three color sensation curves, may rest principally upon the characteris tics of retinal mechanisms. By a proper selection of tests or procedures we might hope to be able to isolate the characteristics and internal relationships of any one of these visual zones. The resolution of our paradox concerning the interrelations of brilliance and chroma would therefore seem to lie in the suggestion that the retinal mechanisms underlying brilliance and chroma respectively are nearly or quite independent of one another, but that the synaptic or certain nerve conduction mechanisms which are sub sequent to the retinal processes involve a very definite linkage of
the factors which transmit the values of these distinct retinal excitations to the cerebrum.
This doctrine of the existence of zones in the visual mechanism is
by no means a new one. It has been recognized by practically all visual theorists, although very few of them have made any use of it since they have tended to suppose that, although the mechanisms involved in the separate zones were separate, they were neverthe less quite similar in character to one another and connected by a point to point correspondence. The theory of Donders,” however, is a definite exception to this rule. Von Kries has also advocated a zone theory which makes the retinal apparatus different in
character from that of the cerebrum. The most serious of all
theories of this type which has yet appeared, however, is that of

* Cf. Parsons, J. H., op.cit., p. 270.

24

LEONARD TRoLAND J.O.S.A. & R.S.I., VI

Schjelderup,” a very recent, and apparently a very important, addition to our vast collection of visual speculations. Schjelder up’s theory is worthy of careful study by all students of the visual
mechanism.
Schjelderup divides the visual apparatus into three successive zones; those of the retina, the cerebral cortex, and an intermediate stage (Zwischenprozesse). He recognizes the correctness of Hering's analysis of the visual qualities into the six psychological primaries, white, black, red, yellow, green, and blue. In the cere bral zones there are, according to his view, six distinct activities which are in one to one correspondence with these six psychologi cal primaries. There is no element of linkage or identity between
these six cerebral mechanisms in and for themselves. In the
intermediate zone, however, the activities which correspond with the six psychological primaries, although still in a one-to-one relation with the latter via the cortical elements, are arranged in antagonistic pairs. The black- and white-representing activities are linked together and one of them cannot be affected without influencing the other. The same consideration holds true for the pairs red and green, as well as for blue and yellow. In cases of color blindness due to the dropping out of any one of these inter mediate zone processes the antagonistic activities must disappear together. However, in the case of color blindness due to cortical derangement an independent dropping out of elementaries corre sponding to antagonists in the intermediate zones is possible. In the third or retinal zone three separate mechanisms are sup posed to exist, each having a characteristic response curve to different wave-lengths in the spectrum. One of the retinal mech anisms responds by a process of oxidation to all of the wave lengths of the spectrum but to a varying degree which is repre sented approximately by the visibility curve. The activities of this mechanism are transmitted exclusively to the white-repre senting process of the intermediate zone. A second retinal mechanism responds by an oxidative process to the long waves of the spectrum but by an opposed or reductive process to shorter
* Schjelderup, H. K. Zur Theorie der Farbenempfindungen. Zeits. für Sinnes physiol. 51, 19–45; 1920.

-- 1:

Jan., 1922]

ZoNE THEORIES OF COLOR

25

waves, ending approximately at the blue of the spectrum. The oxidative phase of this mechanism transmits its energy not merely to the red-representing process of the intermediate zone but also to a certain extent to the white- and yellow-representing factors of the latter zone. The reductive phase of the same retinal activity also transmits its response not merely to the green-representing
element of the intermediate zone but also to a certain extent to
the black and blue components of the latter. A third retinal mechanism also shows opposed oxidative and reductive reactions to different wave-lengths with maxima for these respective phases of its activity localized approximately at the yellow and blue, the energies of the oxidative response being transmitted to the green and yellow factors in the intermediate zone activity while the reductive response influences the blue and red components of the intermediate stage. The relation between the retinal zone and the intermediate zone is obviously not a plain one-to-one correspon dence but a far more complicated arrangement.
By means of the mechanism thus sketched, which in my opinion is by no means too complicated to represent the actual system of visual response, Schjelderup is able to explain all known forms of color blindness, including not only the common types which are considered by the Hering and Young-Helmholtz Theories but also the rarer forms for which these latter theories are powerless to account. The general nature of the interrelation which Schjelder up’s hypothesis postulates as existing between the chromatic and brilliance producing mechanisms promises to be of assistance in the attempt to explain many of the facts which we have consid ered in the present paper. The retinal mechanism which is asso ciated most closely with the red chromatic process is also linked with the brilliance producing activity, a fact which suggests a possible rationale of the brilliance contrasts which are brought out by the dimming procedure whenever a red enters into a compari
son with other colors. The association of the retinal mechanism
which is most intimately connected with the green chromatic pro cess with the black producing excitation also suggests a possible explanation of the reversed brilliance contrast which appears in the dimming experiment when blue is contrasted with green or

26

LEONARD TROLAND J.O.S.A. & R.S.I., VI

yellow. However, it is not my purpose in the present paper to attempt a detailed development of these possibilities.
The moral of the foregoing discussion is that to arrive at a thorough understanding of the mechanism or theory of visual response, it is absolutely necessary to take into consideration the
zonal structure of the mechanism which is involved. The three
zones of Schjelderup's hypothesis are not too many to account for the actual maze of facts which we encounter. Anatomical analysis shows that many more than three are inevitably concerned in the total process. All of the many visual theories which have been propounded probably have some truth in reference to some zone of the visual process, and it is possible that a sufficient number of zones actually exist to permit each of these multudinous theories to be substantially true for at least one of the zones, leaving other zones open for its opponents.
HARVARD UNIVERSITY CAMBRIDGE, MAss.

-I-
MEASUREMENT OF THE COLOR TEMPERATURE OF THE MORE EFFICIENT ARTIFICIAL LIGHT SOURCES BY THE METHOD OF ROTATORY DISPERSION*
BY
IRWIN G. PRIEST
I. INTRODUCTION
The color temperatures of a number of sources of comparatively low or medium efficiency have been published some years ago. Forsythe has recently communicated results on various lamps including gas-filled tungsten lamps at several efficiencies up to 27.3 lumens per watt.” So far as the author knows there are no data extant for higher temperatures than those given by Forsythe and no data duplicating the higher temperatures given by him. Also so far as we know, no attempt has heretofore been made to determine the color temperature of the carbon arc by direct
observation.
The author has previously described an apparatus which may be readily adapted to the measurement of very high color tem peratures” by the rotatory dispersion method.
The purposes of the present paper are: (1) To illustrate the practical applicability of the rotatory dispersion method to the measurement of color temperatures
between 3000° and 4000°K.
(2) To present some data on the precision and accuracy of meas urements of color temperature at about 2850°K.
* Published by permission of the Director, Bureau of Standards. This paper was first presented at the Rochester Meeting of the Optical Society of America, Oct. 25, 1921.
The author is indebted to Dr. K. S. Gibson, Mr. E. P. T. Tyndall and Mr. H. J. McNicholas for their assistance in obtaining the data on precision and accuracy shown in Tables I and II, and to Dr. M. Katherine Frehafer and Dr. Gibson for much assistance in computing.
* Hyde and Forsythe: J. Frank. Inst., 183, pp. 353–354; 1917. E. F. Kingsbury: J. Frank. Inst., 183, pp. 781-782; 1917.
* Meeting of American Physical Society, Washington, April, 1921; Phy. Rev. (2) 18, p. 147; Aug., 1921.
*J. Op. Soc. Am., 5, pp. 178–183; March, 1921. Cf. also Phy. Rev. (2), 10, pp. 208-212; 1917, particularly the closing paragraph.
-
27

28

IRwiN G. PRIEST [J.O.S.A. & R.S.I., VI

(3) To present an independent confirmation of Forsythe's data on the color temperature of gas-filled lamps.
(4) To present new data on the color temperature of the gas filled lamp (Mazda C) up to efficiencies of about 39 lumens per watt, which corresponds very nearly to the melting point of tung sten and the consequent failure of the filament.
(5) To present some data on the color temperature of the crater
of the carbon arc.
II. DEFINITION OF COLOR TEMPERATURE
In this paper, color temperature is understood to mean the temperature at which a hypothetical Planckian radiator (“black body”) would emit light competent to evoke a color of the same quality (hue and saturation) as the light from the lamp under
test.
The value 14350 micron-degrees is assumed for the Planckian constant c2 throughout this paper."
III. THE PRECISION AND ACCURACY OF MEASUREMENTS OF COLOR TEMPERATURE
Before proceeding further it is pertinent to introduce some data on the precision and accuracy of temperature measurements of lamps by the method of color matching in general, and quite aside from the particular features of the method to be described in this paper.
These data were obtained under the following conditions:— (1) Type of photometric field: Circular and divided along a diameter, (Martens photometer). (2) Angular size of whole field: 6°. (3) Absolute temperature, 2850°K. (4) Method: The observer adjusts lamp voltage to color match while an assistant records the voltages thus set. The differences between single settings and averages are computed and these residuals translated into temperature by means of the known relation between voltage and temperature. Data on precision are shown in Table I.
* Coblentz, B. S. Sci. Pap. No. 248; p.470; 1916. Forsythe, J. Op. Soc. Am., 4, p. 332; 1920.
-

Jan., 1922]

COLOR TEMPERATURE

29

TABLE 1

AV E R A G E D E V IAT I O N S

FROM MEANS OF TEN OBSERVATIQNS Average|PROBABLE PR

(Degrees, Centigrade)

of

ERROR E OF

->

Average OF

MEAN

et No || || 2 || 3 4 || 5 || 6 || 7 || 8 |DeViations ONE

OF

4Obs.

OBSERVATIO TEN

I G P |3.6|9.8||0.8||5.9 |6.7|7.5|5.3|6.9| 7.1°C + 6.3°C + 2.0°C
KS G |6.7| 6.9 5.5|4.5 |8.6|4.8 |5.8 || 6.9 || 6.2 + 5.5 + 1 .. 7

E P T T || |.O. 5.3 6.5. 4.3 |4.2|7. |8.8|6. O. 6.6 |+ 5.9 |+ 1 .. 8

H J M 4.2|5.O 5.7| 7.9 |3.4|5. | |4.2|6. || 5.2 |+ 4.6 |+ [.. 3

Average->

6.3

5.6

I.T

Precision of color matching lamps at about 2850°K. Circular photometric field divided on a diame ter. Angular diameter of whole field about 6° (Martens Photometer). Observer sets voltage on test lamp to color match comparison standard. Assistant records voltages. Observed deviations in volts have been reduced to corresponding deviations in temperature.
Data from four gas-filled 500-watt lamps, June 29–30, 1921.

Data on the agreement among the final results of determinations by different observers on the same lamps are shown in Table II. The systematic differences between observers shown in this table is probably due to the fact that for each observer a constant set ting of the comparison lamp was used.
TABLE 2

DE VIATION S. degrees C mp!o 325 3 2 55 || 3 2 56 | 3 2 5 7 |Average
Obs.
I G P | - 3.2 | - 4.9 | – | . T | - 7.O || - 4.2
KSG | + 9.4 | + 7.4 | + 6. T | + | O. 2 || + 8.4 E P T T | – 9. 2 | – 4. | | – 6.9 | - 5.6 || - 6.4
H J M | + 3. O | + | . 8 || + | . 9 || + 2. 5 || + 2.3
Average with out regard to sign || 5.3

Departure of individual observer's means (20 observations) from mean of four observers. Substitution method. Circular photometric field divided on a diameter. Angular diameter of whole field about 6° (Martens Photometer). Data from four gas-filled 500-watt lamps, June 29–30, 1921.

30

IRwiN G. PRIEST [J.O.S.A. & R.S.I., VI

IV. STANDARD SOURCE

1. Description of Lamp

The fundamental reference standard on which the temperature scale in this paper is based is embodied in a particular 500 watt gas-filled concentrated-filament tungsten stereopticon lamp,

Fig. 1

20, 40- 60-80

40 6

|.
1.7
|.
31.5
D
#14
|.3
Lu
= 12
< 1.1
L
a 1.
0.
0.8
0.7
0.6

0. O
0.2

-
DTI
-

• * * B.S. Lamp 1717 at 118.0 volts
- Planckian Radiator for C-14350 micron degrees

V25"25"50 80500

WAVE LENGTH millimicrons

Spectral distribution of energy, B. S. Lamp No. 1717 and Planckian radiator at 2820° and 2850°

designated as B. S. Lamp No. 1717, operated at 118.0 volts. 'The
efficiency of this lamp as found by the photometric section, Bureau of Standards, was:—
On April 3, 1917 at 118.0 v, 4.06 a, 15.6 l.p.w. On June 17–18, 1921 at 118.0 v, 4.05 a, 15.75l.p.w.

Jan., 1922]

COLOR TEMPERATURE

31

2. Standardization by Spectral Distribution
The spectral distribution of energy from this standard lamp as determined radiometrically by Dr. W. W. Coblentz of the Bureau of Standards in April 1917 is shown by the circles in Fig. 1. The continuous curves in the same figure show the theoretical spectral distribution of energy from a Planckian radiator at 2820° and 2850°K. It may be inferred from this figure that the color temperature of this lamp is approximately 2840 to 2850°K but from mere inspection of the figure this conclusion is subject to considerable uncertainty." A more precise value has been derived from the same data by the following procedure:
(1) The wave-length of the center of gravity of a spectral distribution of light is defined as
_JV:Exi, fV.Ed).
where \ =wave-length; E = energy per unit wave-length for wave-length, \; V = visibility of radiant energy for wave-length, A.
(The graphic significance of this definition may be explained by reference to Fig. 2. X is plotted as abscissa. VE is plotted as ordinate. The different curves represent spectral distributions of light from a Planckian radiator at different temperatures. For any temperature, \ is the X-coordinate of the center of gravity of a thin template of uniform density bounded by the X-axis and the distribution curve for that temperature.)"
(2) A has been computed for a Planckian radiator at various temperatures and plotted as a function of temperature as shown

* In previous papers (J. Op. Soc. Am., 5, pp. 178–183; March 1921 and B. S. Sci. Pap. No. 417, Vol. 17, pp. 231-265; 1921), the color temperature 2830°K was inferred from these same data. This value was merely a rough approximation as inferred from plotting the data on a small scale and is not accurate enough for the present purpose. The revised value given in the present paper results from a more careful examination of the data, and a more precise and reliable method of reducing it.
* Compare also:—Jour. Op. Soc. Am., 4, pp. 389-401; 1920. B. S. Sci. Pap. No. 417, Vol. 17, p. 234; 1921.

32

IRwIN G. PRIEST [J.O.S.A. & R.S.I., VI

in Fig. 3. These computations have been made by arithmetic
throughout by the formula
XV.E.X. X =-
>V.E

taking values of V, E and X at intervals of 10 millimicrons, and

are more accurate than the graphic integrations used in previous

papers.”

Fig. 2

|OO

so SPECTRAL DISTRIBUTION
of

80

LIGHT

|

from

|A compu-ETE DADATOR

O

at

ADIOUS TEMDE

60

:

420 440 460 480 500 520 540 560 - 580 600 620 640 860 680 TOO T20 WAVE LENGTH raillimicrons
Spectral distribution of light, Planckian radiator at various temperatures. Energy by Planck's Formula (C1=14350). Visibility:
X, 560-650 H. E. Ives, Phil. Mag. Dec. 1912, p. 859. X, 410–550 and 660–710 Hyde, Forsythe & Cady, Jour. Frank. Inst. 48, p. 87. Numbers attached to curves indicate temperatures in degrees K.
(3) A has likewise been computed in the same way for the original experimental data on the spectral distribution of energy from the lamp, and this value of \e used to derive the color tem
J. Op. Soc. Am., 4, pp. 389-401; 1920. B. S. Sci. Pap. 417, Vol. 17, pp. 234 235; 1921.

Jan., 1922]

COLOR TEMPERATURE

33

perature from the relation between A. and color temperature shown in Fig. 3. The color temperature so derived is"
2848°K

38O

Fig. 3
5 RELATION BETWEEN
TEMPERATURE AND WAVE - LENGTH OF CENTER OF GRAVITY OF LIGHT FOR

36

PLANCK1AN RADIATOR

3400 3200

c2 = 14350 micron degrees
Visibilitu :
X 400-550 & 660-710 m
Hude et al. £rce''': p.87
A 560 - 650 m
£ag. Dec.1912.e.859
(\e computed by formula I L-x
at intervals of 10 mM. Oct. 1921)

24

5

5

574 5

578

c millimicrons

Relation between temperature and wave-length of center of gravity, Planckian radiator

This value is the weighted mean of three separate computa tions, and from their agreement, it is estimated that the uncer

* It is to be observed that while the visibility of energy enters into the formulas used, it does not enter in such a way as to affect the temperature found so long as the same values of visibility known to be approximately correct, are used in determining all values of Ac considered and the spectral distribution approximates Planck's for mula. The values of visibility actually used throughout the present paper are shown by the solid curve in Fig. 8, J. Op. Soc. Am., 4, p. 471.

34

IRwIN G. PRIEST J.O.S.A. & R.S.I., VI

tainty of this result due to approximations in computation is less
than 3°.
The sensibility and accuracy of this method are clearly demon strated by the consistency of the several points determining the curve at about 2850°K, Fig. 3. Judging from this, the uncer tainty is less than 5°.
3. Standardization by Color Match with Planckian Radiator (Nela Laboratory)
In order to compare this standard with the color temperature scale of the Nela Research Laboratory, a 500-watt gas-filled lamp of the type now used as photometric standards was accurately color matched with B. S. Lamp 1717, at 118.0 volts by a substi tution method. The voltage for color match was determined by 20 settings by each of four observers. The resulting mean voltage was 101.0 v, for which the current was 4.097 a. The lamp was then sent to the Nela Research Laboratory and its color tempera ture by color match with a “black body” was found to be”
2848°K at 101.0 v, 4.099 a.

4. Conclusion as to Standard
On the basis of the good agreement between the color tempera ture derived from Coblentz's isothermal data and that indepen dently found by color matching with a “black body” at the Nela Research Laboratory, we may define our standard for future reference in a more fundamental way than by referring to a partic ular lamp, as we have at the beginning of this discussion.
Our standard source is accordingly a source closely approximating the Planckian spectral distribution in the visible spectrum and having a color temperature of 2848°K.

V. ExPERIMENTAL METHOD
The essential feature of the rotatory dispersion method is this: A quartz plate between nicol prisms, serving as a light filter of adjustable spectral transmission," is used to modify the color of
* Letter, W. E. Forsythe, Nela Lab., to I. G. Priest, Aug. 11, 1921.

Jan., 1922]

COLOR TEMPERATURE

35

a comparison source so as to match the unknown, the constants of the apparatus being chosen so that the spectral distribution of the light emerging from the quartz-nicol train is always repre sented by the Planckian formula. Colorimetrically, the experi ment is equivalent to varying the temperature of a “black body” until it is color matched with the lamp in question and then noting the temperature. The essential parts and arrangement of the apparatus are shown in Fig. 4. The experimental procedure is
Fig. 4

g" |

..

1

£-><|B23-[2-(E >< t >~~~ |------ Optic Axis of Quartz

| L rn
i
Comparison Source

| O.5OO X mm

><s"
Screen

Position of Standard Lamp
or Test Lamp

Essential parts of apparatus

then as follows: The standard lamp of known spectral distribu tion is placed at X so as to illuminate part of the photometric field. The quartz plate being removed, the current in the com parison lamps in the box is adjusted to give a color match in the photometric field. This current is thenceforth maintained con stant. The source whose color temperature is to be measured is then substituted for the standard lamp; the quartz plate is inserted between the nicols and nicol No. 2 is rotated (angle, b) to produce a match of color quality. (A brilliance match is of course simul taneously made by other nicols, not shown in Fig. 4.)
The actual apparatus used was the Arons Chromoscope."
The Lummer-Brodhun cube is set so that the field has the form
shown in Fig. 5. The visual angle of the circle (comparison light) is about 3.5°. This form of field appeared to be somewhat more sensitive than the concentric field for matching of color quality, although its particular odd shape is not to be recommended.

"J. Op. Soc. Am.4, pp. 485-486. " Ann, der Phy. (4)39, pp. 545–568; 1912.

36
160

IRwiN G. PRIEST J.O.S.A. & R.S.I., VI
Fig. 5
Comparison
:g
I'orm of photomeric field

8
| 5öö "EAD"SSG"S50"OU">O"
VA/AME LENGTH rrillirrhicroris Spectral distributions of energy, Planckian radiator at various temperatures compared with distributions obtained by rotatory dispersion. The solid black curves represent Planck's formula with C1–14350. The numbers attached to these curves indicate temperatures in degrees K. The various circles represent distributions obtained by the arrangement shown in Fig. 4. Each different style and size of circle refers to a particular value of p, and the numbers attached to the circles indicate values of qi in circular degrees. In all cases, energy=100.0 at wave-length 590 (arbitrary convention).

Jan., 1922]

COLOR TEMPERATURE

37
-

VI. METHOD OF CONSTRUCTING THE TEMPERATURE SCALE

Let q (measured from extinction position with quartz removed,

and in same direction as the rotation by the quartz) be the angle

through which nicol No. 2 is rotated to obtain a color match.

The method of constructing the temperature scale correspond

ing to the instrument reading (b) is a refinement and extension of

that previously published.” The spectral distributions of energy corresponding to different
values of q are shown in Fig. 6, together with the spectral dis tributions of a Planckian radiator at various temperatures.

Inspection of this figure shows:

(1) The distributions obtained by rotatory dispersion approxi mate very closely to the theoretical distributions by the Planckian
formula.

(2) The temperature corresponding to any value of p can be inferred approximately from simple inspection of this figure,

although this method of establishing the relation between p and

temperature is not sufficiently precise for our present purpose." The precise relation between p and temperature has been ob
tained as follows:

(1) A has been computed for the spectral distributions corre sponding to different values of p (Fig. 6) in the same way as for

the standard lamp and the Planckian radiator as described above.

(2) Temperatures corresponding to these values of X. have been read from Fig. 3 and plotted as a function of p in Fig. 7.

Figure 7 thus obtained now serves as a calibration curve for deriving

color temperature from experimentally observed values" of p.

VII. CHECK MEASUREMENTs
1. Check of the Method with Radiometric Determinations

The color temperature of B. S. Lamp 1716 (a 500-watt gas

filled stereopticon lamp, like 1717) at 22.0 l.p.w.., has been found

by this method to be

3082°K

(mean of 30 observations)

*J. OP. Soc. Am., 5, pp. 178–183; March, 1921. *The curve shown in Fig. 6, J. OP. Soc. Am., 5, p. 182, was obtained by this simple process of inspection. "Cf. “Experimental Method” above.

38

IRWIN G. PRIEST |J.O.S.A. & R.S.I., VI

###########

5

#

#

3

s

## # # # # # # # # # # 3 #

#

#

#

3

s

6 ep - 19 @

Jan., 1922]

COLOR TEMPERATURE

39

The temperature derived by means" of A. from the spectral energy distribution determined by Coblentz" is
3086°K
2. Check of the Method with Color Temperature Determinations by the Nela Research Laboratory
The color temperature of a 900-watt gas-filled “Movie” Lamp at 22.7 l.p.w.., has been independently determined by Forsythe at the Nela Research Laboratory, using their methods, and by the author at the Bureau of Standards, using the present method.
The results follow." before B. S. Measurement. . . . . . . . . . . . . . . . . . . . . 3091°K
Nela after B. S. Measurement. . . . . . . . . . . . . . . . . . . . . .3083
Mean. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3087
Bureau of Standards (Each value is mean of 10 observa tions). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3090°K
3095 3067 3087 3093 3079
Mean. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3085
VIII. THE COLOR TEMPERATURE OF THE GAS-FILLED TUNGSTEN LAMPAS A FUNCTION OF EFFICIENCY
The data shown by the small open circles in Fig. 8 refer to a 500-watt gas-filled lamp (Mazda C National Lamp Works) of the type now used as a photometric standard at the Bureau of Stand
ards.
These data were obtained in the following way: (1). Two lamps of nearly identical characteristics (equal effi ciencies at equal voltages) were selected.
(2) One of these (B.S. 3261) was used to determine efficiency
as a function of voltage for increasing voltage until the filament
* By the same method as described above for deriving the color temperature of the standard lamp No. 1717 from the radiometric data.
* Coblentz's determinations of Lamp 1717 were made in April 1917. His deter minations on Lamp 1716 were made in December 1918, after readjusting his appara
tus.
* Letter, Forsythe to Priest, July 29, 1921.

40

IRwiN G. PRIEST J.O.S.A. & R.S.I., VI

failed." This filament failed at 200 volts, the efficiency at 195 v.
being 38.2 1.p.w.
(3) The other (B.S. 3260) was used to determine color tempera
ture as a function of voltage at increasing voltages until the fila
ment failed, at 206 volts.
(4) Correlating the data on the two lamps, color temperature
is shown as a function of efficiency, in Fig. 8.
Fig. 8
37oo

360

35
Y
3 4O

3.30

320

3

3. O

MAZDA C LAMP

B S. Data

2

O Me an of Lamps 3254,2255

3.256, a257

OO Lamp 3260. Data by

28

July 26, |

Ne la Data For
© e-

l

20

25

3O

E F F | C | ENCY

lpw

Color temperature of 500-watt gas-filled photometric standard lamp as a function of efficiency

Some of Forsythe's previously published data” are also plotted
in this figure. The agreement is as good as could be expected
considering the different lamps involved.
In order to avoid burning the lamp longer than absolutely
necessary at any one voltage (which would have shortened its life
and forestalled observations at the highest temperatures), accuracy
was sacrificed for speed in these observations. The observations of
temperature were made as rapidly as possible and only five at

*These determinations were made by Ben S. Willis, Photometric Section, Bureau
of Standards.
"Phy. Rev. (2) 18, p. 147; Aug. 1921.

Jan., 1922]

COLOR TEMPERATURE

41

each voltage. On this account the points (Fig. 8) depart from a
smooth curve. It is believed nevertheless that the curve which
has been drawn through them is not in error, on this account, by more than 10° at any point. These data are, however, pre sented as a preliminary roughing out of the color temperature— efficiency relation rather than a precision determination.
At the highest efficiency attained (39.2 1.p.w.) the color tem perature observed was 3644°K. The accepted value” for the true temperature of the melting point of tungsten is 3673°K. No precise relation between the true temperature and the color tem perature of gas-filled lamps can be stated; it appears, however, that the present determination is in as close accord with the accepted melting point as could be expected.”
IX. THE COLOR TEMPERATURE OF THE CRATER OF THE CARBON ARC
Previous work has shown” that the temperature of the crater of the arc varies by nearly 200°C, dependent upon the carbons particularly, and upon the current and other conditions to a less
extent.
The most reliable of our data by the rotatory dispersion method indicate color temperatures as follows for the crater of a 65-volt, 10-ampere arc:
Solid carbons 3780°K (mean of 50 observations) Cored carbons 3420°K (mean of 50 observations) These means are considered uncertain by about 50°. So far as we know there are no previous determinations of “color temperature” of the arc with which to compare these results. Waidmer and Burgess” give 3680° to 3720° as “black body brightness temperature.”
-
The method described would be convenient and suitable to use
in an extensive determination of the temperature of the arc under
various conditions. NATIONAL BUREAU of STANDARDs NovEMBER 4, 1921.
*Worthing, Phys. Rev. (2) 10, p. 392; 1917. "Cf. Forsythe, Phy. Rev. (2), 18, p. 147; 1921. *Waidner and Burgess, B. S. Bulletin, 1, pp. 109–124; 1904. * B. S. Bulletin, 1, p. 123.

THE BLUE GLOW
BY
E. L. NICHOLS AND H. L. Howe's
Certain oxides when heated to incandescence emit light of a distinctly bluish cast at temperatures corresponding to the dull
red heat of non-selective radiators.
To this effect, which is particularly well marked when the heating is done with a hydrogen flame sufficiently reinforced with oxygen to secure the desired temperature, we have given the name of the blue glow. It is a special case of the luminescence of incandescent solids, a topic upon which we are now engaged and which, in its broader aspects, will form the subject of a forth coming paper. In our study of the blue glow it was desired to determine (1) the temperature of the glowing oxide; (2) the brightness of its temperature-radiation proper; and (3) the bright ness of the blue glow itself which may be regarded as superimposed upon the temperature-radiation.
For this purpose we used an optical pyrometer of the type based upon the well known Morse gauge, in which the filament of an incandescent lamp in the eyepiece of the instrumentis superimposed upon the image of the glowing surface the temperature of which is
to be measured. To mount the oxide for observation an annular
groove about 1 cm in outer diameter, 1 mm deep and 2 mm wide was ground in a bed of alundum. Fragments of thick walled alun dum tubing of large diameter, of which an abundance chanced to be available, answered admirably for this purpose. The annular groove was pressed full of the black oxide of uranium, a substance which affords an excellent approximation to the ideal black body
and which withstands the direct contact of the H-O flame better
than any black powder which we have thus far found. The disk of alundum within this ring of uranium oxide was then covered with the oxide to be studied, the two surfaces of powder being carefully pressed down to the same level. Especial care was taken to have a sharp boundary line between the white oxide within and the ring of black powder surrounding it. Upon the surface thus prepared a flame of hydrogen from a blast lamp, with just
42

Jan., 1922.

THE BLUE GLOW

43

sufficient oxygen to give it direction and stability, played verti cally and concentrically from above. It was found that when the two surfaces were at the same level, neither being sensibly elevated or depressed with reference to the other, and when the flame was large enough to cover them fully and was properly centered, they attained the same temperature.
TABLE I
The Blue Glow of Magnesium and Beryllium Oxides

Mg O

Be O

Temp. Ibb
C.

Io

Io/Ibb

.65u .45u .65u .45u

Io

Io/Ibb

.65u .45u | .65u .45u

665° |.00013||.00000018, .0202|.00140|156.7 ||.000000025 .0563 .000195|437.

735° |.001.23||.0000026 .0320|.00214. 45.0 ||.0000016 .0795 .000.867. 65.8

837° |.0246 ||.00033 .423 |.0135 | 17.2 ||.00067

.295 .0271 12.0

960° .419 ||.0202

3.63|.0482 8.77 ||.038

1.44 .0832 3.14

1037° 1.95||. 165

8.91.0847 || 4.57 || .213

1.95 . 109

1.00

1097° 5.93 1.077 16.1 .182 2.72

1.00

3.31. . 169

561

1145° 13.2ll. . . . . . . . . . . . . . . . . . . . . . . . . . .

2.46

6.37 - 186

.511

1190° 26.6 9.77 26.4 .367 1.04

6.75

13.0 .252

423

1228° 45.7ll. . . . . . . . . . . . . . . . . . . . . . . . . . . 72.5

110.2|1.58

2.44

1263° 76.7|| 26.6

36.7 .347

.479|| 146.

179.9|1.91

2.35

1294° | 156. ||. . . . . . . . . . . . . . . . . . . . . . . . . . . 229.

230. 1.98

1.99

1328° 178. 55.6

72.0 .312 .404|| 295.

254. | 1.66

1.43

1394° 389. 62.0

139. .357

.356|| 513.

316. | 1.32

.813

1429° 582. || 182.

194. |. 313

.333ll. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1462° 828. || 285.

277. .344 .334|| 767.

513. .927

.621

1488° 1097. || . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 910.

600. .830

.535

1527° 1602. || 745.

525. .460 .324|1181.

773. . 728

.477

1580° 2690. || 1614.

1012. .600

.375||1641.

1052. . . 610

.391

1606° 3420. ||2309.

1387. |. 675

.406||1928.

1282. .564

.375

Seen through the pyrometer, with the usual red screen in the eye-piece the field of view at about 700°C appeared as a red ring with dark center. Through a blue screen it consisted of a blue central patch, the blue and violet rays from the red hot uranium oxide not being of sufficient brightness to render the surrounding ring visible.
To express these conditions and their changes with rising temperature in quantitative form the following cycle of readings

44

NICHOLS AND How ES J.O.S.A. & R.S.I., VI

was made at intervals of about fifty degrees between 600°C and 1600°C, or up to the point of fusion of the oxide under observa
tion:—

(a) A setting on the outer ring through the red screen (equivalent wave-length .65u). This gave the actual black body temperature of the black surface which was the same as
that of the oxide of the central disk.

(b) A setting on the central disk through the red screen. This gave the black body temperature corresponding to the
red radiation from the oxide of the central disk.

TABLE 2
The Blue Glow of Calcium and Aluminum Oxides

CaO

Al2O3

Temp. Ibb
C.

Io

Jo/Ibb

.65u .45u .65u .45u

Io

Jo/Ibb

.65u .45u .65u .45u

665° |.00013||.00000055 .0276 .00432. 216 || 000000051 0794. .00039 ||617.

735° || 00123| .0000159 .0632 .0128 |52.2 .0000036 .144. .00287 (117.

837° .0246 .00292 .336 .114 13.7

.000209 .422 .00851 |17.2

960° . 419

..100 | 1.46 .240 £3.49

.0121 : 733. .0287 | 1.74

1037° | 1.95

.802 | 7.31 .411 |3.75

. 159 | 1.66 .0813

.852

1097° 5.93

2.62 25.0 | .453 (4.19

.912 || 3.76 | . 154

.634

1145° 13.2

6.92 || 41.7 | .522 |3.11

2.72 7.41 .206

.573

1190° 26.6

17.5 || 58.2 | . 656 2.18

7.76 24.5 .292

.923

1228° 45.7

33.1 87.5 | . 725 1.91 || . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

126.3° | 76.7

40.7 |151.

. 531 (1.97

32.2 103.5 .420

1.35

1294° 156.

61.7 |254.

.535 2.20

64. 6 1155.

.595

1.34

1328° 178.

120. |351.

.671 |1.97 133.4 |195. . 748

1.09

1362° 266.

264. |310.

.994 |1.17 251.0 |298. .944

1.12

1394° 389.

345. 226.

.887 | .582|| 408.

582. 1.048

1.49

1429° 528.

422. 190.

.725 .326||. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1462° |828.

507. 226.

. 613 .274|| 1000.

1084. | 1.21

1.31

1488° 1097. 624. 126.

.570 | . 115||. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1527° 1602. 871. 327.

.536 .202|| 2370.

1863. | 1.46 1.15

1580° 2690. || 1225. 578.

.455 .215||. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1606° 3420. || 1429. 794.

.381 .232||. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Since, as has aready been mentioned, the oxides in question are exceedingly feeble temperature radiators and since the blue glow is of too short wave-lengths to pass the red screen, these measurements, for the lower portion of our range

Jan., 1922]

THE BLUE GLOW

45

of temperature, i.e., below 1000°C, gave black body tempera tures far below the actual temperature of the surface.
(c) A setting upon the central disk seen through a solution of ammonio-sulphate of copper which cut out all red and yellow rays and practically all of the green of the spectrum. The equivalent wave-length for this screen was about .45u. It trans mitted the greater part of the radiation constituting the “blue glow” and since for the lower range, from 800° downwards, the temperature-radiation of these wave-lengths was almost too small to measure, this setting, with a very close approximation, gave the blue glow alone. At higher temperatures where the ordinary temperature-radiation became appreciable, this setting gave the sum of temperature-radiation and blue glow.
TABLE 3 The Blue Glow of Silicon and Zirconium Oxides

SiO2

Z2O2

Temp. Ibb C.

Io

Io/Ibb

.65u .45u .65u .45u

Io

Io/Ibb

65u .45u .65u .45u

665° |.00013||.000000076 .0382|.00059|195

.0000026 .0068 .0204 |53.1

735° |.00123| .0000026 .0708.00210 57.3 .000077| .0382 .0621 |30.9

837° .0246

.00059 .341 .0239| 13.9

.0039 .403 1.61 |16.4

960° .419

.0275| 1.65 .0600 3.59

. 121 3.41

.288 8.15

1037° | 1.95

. 191| 4.42 .0977| 2.26

1.20 | 69.1

.617| 3.50

1097° 5.93

1.10

11.0 .186 1.86

6.34 19.2

1.07 | 3.25

1190° 26.6

8.51

35.3 .316 1.33 24.5

87.5

.923 3.29

126.3° 76.7

41.2 89.1 .537| 1.16 59.0 ||146.

. 770 1.91

1294° 156.

100.0 [167.

.865| 1.44 ||. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1328° 178.

233.

316. 1.31 | 1.77 155. 233.

.870| 1.31

1362° 266. ||. . . . . . . . . . . . . . . . . . . . . . . . . . . . 254. 317.

979| 1.19

1394° 389.

614.

631. 1.58 3.09 419. 397.

1.07 | 1.00

1429° 528. ||. . . . . . . . . . . . . . . . . . . . . . . . . . . . 769. 610.

1.32 | 1.04

1462° 1828. 1390.

1902. 1.68 2.30 || 1150. 798.

1. 38 990

1527° 1602. || 2500.

2566. 1.54 | 1.55 || 1950. 1102.

1.20

679

1580° 2690. || . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2620. 1500.

97.3 .427

By measurements of this sort on the oxides of calcium, magne sium, zirconium, beryllium, silicon, aluminum, etc., some of the results of which are given in the following tables and figures, we are able to describe the blue glow in fairly definite terms.

46

NICHOLS AND Howe's [J.O.S.A. & R.S.I., VI

The blue glow is essentially a phenomenon of the lower stages of incandescence. Its upper limit cannot be given definitely in degrees since it depends upon the state of activity of the oxide,
but it lies between 1000° and 1200° in the cases thus far studied.
If, as in Fig. 1, we plot the brightness of the blue of the spectrum (.45 u) of one of these oxides (MgO) between 900° and 1200° and for comparison the brightness curve (B.B.) for the corresponding region of the spectrum of a black body we see that the oxide remains brighter than the black body until a temperature of about
1200° is reached. It is this excess of radiation above what even
a perfect radiator such as the ideal black body is capable of produc ing by virtue of its temperature alone which constitutes the effect in question.

?oo"

wood"

//do”

*200"

Fig. 1. Blue glow of magnesium oxide, 900° to 1200°C

The lower limit of the blue glow is the temperature threshold of visibility. For the lowest temperature at which we can observe we get the maximum value of the ratio between the brightness of the glow and that of a black body of the same temperature. This ratio may be denoted as I./I".

Jan., 1922]

THE BLUE GLOW

47

In Fig. 2 are plotted curves for this ratio for several oxides. Such a diagram, to this scale, indicates nothing of the phenomena occurring above 1000° where the values approach and often fall
A.

(**)
al

44, o,
de O
:& 2.
Cao
At a d"

7co"

foo"

#22'

/doo"

Fig. 2. Ratios of luminescence to black body radiation for several oxides below 1000°C

below unity. Still less can the ratio for the red of the spectrum be thus depicted. The figure shows, however, that:—
(1) The curves for the various oxides are similar as to type. (2) In no case is there an indication of an approaching maxi mum in the direction of lower temperatures. (3) The temperature range within which the brightness of the blue end of the spectrum, to which these curves apply, falls to values of the same order as the corresponding intensity of black body radiation is nearly the same for all these oxides.

48 -

Nichols AND Howes [J.O.S.A. & R.S.I., VI

With logarithms of the intensity ratios as ordinates, we can bring the entire range of temperatures over which measurements were made into one plot and compare the changes occurring in the intensity of the red end of the spectrum with those in the blue.
Figure 3 contains such curves for magnesium oxide and these are quite typical of all the substances thus far investigated.
f 4just Xa7:37.
A, o, 44. 4.--

F's
4.5/

--/

*>. **~~~~...~"-------
/
A.

-/

/ /*
/
%

%r
x/ %

-2

/

/

/ /

Z.

/

Sco"

/odd"

/zoo"

/*00°

*
|-|--|--|--|

Fig. 3. Logarithmic curves for blue glow (.45u) and temperature-radiation (.65u) of Mg O

The characteristics common to all are as follows:–
(1) The luminescent outburst, with certain exceptions to be considered later, does not involve the longer wave lengths.
(2) The radiation in the red which, at the lower temperatures, is probably all temperature-radiation, rises from very small inten sities and approaches the falling values for the radiation in the

Jan., 1922]

THE BLUE GLOW

49

blue. Thus the oxide in passing from .600° to 1200° goes over from a body exhibiting blue luminescence and almost no tempera ture-radiation (for MgO less than a thousandth of that of a black body) to a body radiating almost nonselectively by temperature alone with a radiating power of the same order as that of the black body.
(3) The logarithmic curve is approximately linear up to the point where temperature-radiation supplants luminescence (1000°
# to 1200°). The curves for the ratio in Fig. 2 are, then, exponen
bb
tial curves, warped sometimes by changes due to fatigue during the run and rendered more or less irregular by failures to com pletely control the conditions.
(4) When temperature radiation has supplanted luminescence (at from 1000° to 1200°) the logarithmic curve tends to become horizontal; indicating that the effect of temperature is now that expressed by the usual equation for black-body radiation.
(5) The knee of the logarithmic curve affords a criterion for the change to temperature-radiation and thus serves to locate the upper limit of the blue glow. Comparing Figs. 1 and 3 we should conclude that luminescence did not altogether cease at the crossing of the curves at 1200° but continued slightly beyond to a point at which the normal radiating power by temperature had been reached. (Say at 1260° for MgO in the experiment which these curves illustrate.)
-
The foregoing paragraphs describe the blue glow as though it were the only form of luminescence occurring above the red heat. More frequently than not there are, however, other manifestations of luminescence within the range covered by our experiments. These either modify or supplant the blue glow at temperatures
below 1200° or succeed it when the oxide is still further heated.
Outbursts of luminescence at higher temperatures characterize several of the oxides already described notably, CaO, BeO and SiO2. In silica, as may be seen from Fig. 4, in which the ratio curves for .45u and .65u between 1000° and 1600° are plotted,
we have such an outburst. In this cut ordinates are magnified
one hundred times as compared with those in Fig. 2. The hori

50

NiCHols AND Howes J.O.S.A. & R.S.I., VI

zontal line, of intensity equal to unity, represents the brightness of the black body at the wave length and temperatures in ques
tion.
This luminescence, expressed in terms of ratios, appears quite insignificant when compared with the blue glow of silica which at 600° is represented by a value for I./I, of over 400 as against

%4. 444 % (0.446.-#4 asoo..”)

-3–

f

\

\

2-\ -*. \$5/-

l /

// | \
I
*
/
/ 45/
Af a

/2 co"
1* |

/400°
*

Fig. 4. Luminescence of SiO, at 1400°C

3. 1 for the outburst at 1400°. Since, however, the intensity of the black body radiation which forms the denominator of this ra tio increases according to the usual radiation law, we find the luminescence at 1400 degrees to be about 300,000 times as bright as the blue glow at 600 degrees and nearly 40,000 as great as the latter at 700 degrees. This high temperature outburst differs

Jan., 1922]

THE BLUE GLOW

51

from the blue glow also in that a greater portion of the spectrum is involved. That the red end at .65 u is considerably affected is evident from the curve for that wave length.
Modifications of the blue glow itself occur in several of the sub
stances which we have examined. When cerium oxide for exam
ple is heated and its spectrum studied, we find excess radiation at

Z
%
Jo/-
M

&e 0. 4-44-4-2'

soo'
—1–1

*
\ -*
/oco" --~, aco"
l * >|--

zoo.
*A l

Fig. 5. Luminescence of cerium oxide below 1000°C

the lowest stages of incandescence. The phenomenon differs from the blue glow in that the red and green become visible before the blue and in that the ratio I./I, rises in value to a maximum, at about 800 degrees. (See Table 4 and Fig. 5.) The blue is less strongly involved than either red or green and the brightness of the red instead of starting with almost infinitesimal values is

52

Nichols AND Howes J.O.S.A. & R.S.I., VI

nearly nine times great at 700 degrees as the corresponding region in the spectrum of the black body.
TABLE 4 Modified Blue Glow in Cerium Oxide

Temp. Ibb
C

Brightness at Various Temperatures

-

Io

Io/Ibb

.65u

.50u

.45u .65u

.50w .45u

702° 735° 837° O60° 1037° 1097° 1145° 1190° 126.3° 1328° 1394° 1462° 1527° 1580°

.00045

.0040

.0017. . . . . . . . 8.95 4.72 |. . . . . . . . .

001.23

().349

.0403 . . . . . . . . 28.3

32.6

. .... ... .

.0246

692

1.21

370 28.2

49.5

15.2

.419

4.92

6.53

3.02 || 17.7 15.6

7.21

1.95

13.9

15.3

13.7

7. 12

7.85

3.09

5.93

28.3

21.4

15.2

4.78

3.63

2.55

13.2

69.5

53.2

25.4

5.25

4.02

1.91

26.6

13.3.

133.

11.7

5.02

5.02

0.44

76.7

3.34.

304.

11.1

4.34

3.95

.144

178.

596.

519.

25.4 3.34 2.91

. 142

389.

653.

695.

87.9

1.58

1.69

.227

828.

783.

887.

113.

0.95

1.07

. 136

1602.

1319.

1109.

423.

. 813 || 0.684

, 260

2600.

3304.

1514.

656.

1.23

0. 562

.244

Here then is a luminescent glow which at 800 degrees is com posed approximately of one part blue, two parts red and three parts green, not in energy units but relatively to a nonselective radiator of the like temperature.
Without going further into details in the present paper it may be stated that the blue glow and other similar instances of lumi nescence at high temperatures occur in bodies which have the following characteristics.
(1) They are inactive under excitation by light or by the X-rays. (2) They are, however, in general, excited to luminescence in the kathode tube. (3) In many cases they are sensitive to flame
excitation.
(4) Like other luminescent substances they are white, or nearly so, i.e. transparent to most portions of the visible spectrum.
(5) They are of necessity highly refractory.

Jan., 1922]

THE BLUE GLOW

53

The luminescence of incandescent bodies is subject to fatigue. It is in the highest degree affected by previous heat treatment of the material; it is in some cases destroyed by fusion of the oxide; it is dependent on the mode of heating, being much more intense where an excess of oxygen is present than where there is a defi ciency.
Finally it appears to be a phenomenon of instability associated with and perhaps dependent upon changes of the conditions of equilibrium. Thus all the oxides which exhibit the blue glow are in transition, within the temperature range in question from a
condition of almost infinite electric resistance to one of semi
metallic conductivity and this change is accompanied by the well known profound modifications in optical properties, radiating power etc. Again the outburst of luminescence in silica at 1400 degrees occurs at the transformation point of quartz and is pre sumably intimately related to that change.
The most promising view at the present moment would seem to be that this form of luminesence like many well known forms at lower temperatures is the result of oxidation.
During these transitional conditions it would appear that a partial reduction takes place through the agency of the hydrogen of the flame and that this is immediately followed by oxidation, the two opposing processes going on in rapid alternation.
PHYSICAL LABORATORY OF CoRNELL UNIVERSITY, October, 1921.

THE SIGNIFICANCE OF THE 14 TERMS IN SPECTRAL
SERIES FORMULAE

BY
PAUL D. Foote and F. L. MoHLER"

Sommerfeld' from his mathematical derivation of the empirical Ritz equation concluded that the ratio of the constant a* for the enhanced spectrum of an alkali earth to the constant a for the arc spectrum of the alkali of next lower atomic number should be a"/a = 2.
Fues” showed that this relation was approximately true only when to m were assigned the values 1.5, 2.5 etc. in the ms and m & terms. The ratios thereby obtained for the elements Mg/Na, Ca/K, Sr/Rb, Ba/Cs, are 2.9, 2.2, 2.6, 2.1 respectively. The mean value is 2.45+12% average deviation, or a positive average deviation from 2 of 22%.
In spite of these large variations Sommerfeld” later affirms that the “atomic field constants gives the deviation from half numbers
rather than from whole numbers.”
The constant a by Sommerfeld's derivation takes the following form, to terms of the first order.
4.222
a_(27)'m', ................... (1)
m3/14

1

-#2 C1

-k)e^al”. . . . . . . . . . . . . . . . . . . (2)

where k = 1 for arc spectra, k = 2 for spark spectra, an is the diameter of the ring of electrons surrounding the nucleus, and n the azimuthal quantum number. Sommerfeld assumed that c. remained constant for any pair of elements. However, with the same number of electrons in a ring, the diameter of the ring decreases when the charge on the nucleus is increased. If this
* Published by permission of the Director, Bureau of Standards.
Nk2
Sommerfeld Atombau, 2nd Ed. p. 506. (m, a) = [m+a+a(m, a) |*
* Ann. d. Phys. 63, p. 1, 1920. * Ann. d. Phys. 63, p. 238, 1920.

Jan., 1922]

SPECTRAL SERIES FORMULA

55

factor is considered we no longer obtain a” = 2a, although the ap proximation is closer when a large number of electrons are as sumed in the same ring. For 50 electrons in a ring a” = 1.8a.
As a little better representation, however, of actual atomic conditions we shall consider two coplanar rings, the inner ring containing p electrons, the outer ring q electrons and around the whole the quantized coplanar orbit of the single remain ing valence electron. The azimuthal quantum number for the inner ring is 1 and for the outer ring 2. On carrying through the derivation for the case of two rings, exactly as Sommer feld’s except that we consider the effect of the nuclear charge on the radii ai and a2 of the rings, as follows:"

(11 = 1*a,
'Tz-s,

(12 =

22 (l),

* (z-p-s)

we obtain eq (3) for the general relation between a” and a.

p

16q

sk

* - N2 +

2

a"-2(Z'-se) (q+2-st)'

Ol

p

16q

(Z-s) + (7+1-s):

. . . . . . . . . . . . (3)
-

Here Z” and Z are the atomic numbers of the alkali earth and al
kali respectively and s, and so are the nuclear defects of the rings. The following table gives the values a” = & and a =s, as far as
known, for the alkali earths and the alkalis, empirically deter

© and s terms for integral m

Q

Element a' = & Element a =s

a"/a

obs.

comp.

8

Mg

.93

Na

.65

1.43

1.48

8

Ca

1.20

K

.82

1.46

1.49

18

Sr

1.32

Rb

. 81

1.63

1.66

18

Ba

1.43

Cs

.95

1.50

1.66

Av. dev. =4%

* Sommerfeld Atombau, p. 258. ah= radius of hydrogen atom.

56

Foot E AND MoHLER [J.O.S.A. & R.S.I., VI

mined for integral values of m. They accordingly contain the

quantity 3 ordinarily considered as belonging to m. Column 6

gives the ratio a”/a obtained from these data and column 7 the

ratio computed by eq (3).

The average deviation of the computed values of this ratio

from the observed is only 4% in contrast with 22% found by

Fues. This fact would seem to indicate that to m should be

assigned integers for the ms and me terms, as is the case with the

mp, md and mb terms. To an approximation (3) may be written

:k

2

"-2 (7+1=9

| (4)

(l

(q+2–s,)* .

It may be noted that by assigning various integers to q and in some cases by using more rings, these equations may be manipulated to give fairly close values of a and a” as well as of their ratio. In the above, however, we have employed the generally accepted numbers for q, and the distribution of inner rings does not mate rially affect the ratio a”/a.
Conclusion: The frequently expressed opinion that the half integral values of m in the ms terms have some mysterious signifi cance is not founded upon sufficient reason. The simple physical conceptions of the quantum theory suggest that m should be an integer and in the present note as good evidence is offered con firming this viewpoint as has been advocated to the contrary. .
BUREAU of STANDARDs, DEC. 6, 1921.

THE DISPERSION OF GLASS

BY

T. SMITH

The circumstances during the war which forced America to manufacture the optical glass needed for her own use have led to the appearance of a number of interesting papers in which the properties of glass are discussed. Among these are some con cerned with dispersive relations, for the representation of which various formulas have been proposed. In these discussions a very . satisfactory expression due to Conrady has been overlooked, though less good suggestions have been considered. According to Conrady' the dispersion may be regarded as a linear function of A- and A-" 2. A graphical demonstration shows that there is little room for improvement on this formula. In an investiga tion” based on the figures of the Jena catalogues the indices – 0.91 and -3.4 have been found by the present writer. The final
formula is

N"-X'." u-up-226(up-ac)+8(up-1)}. WWI-'I
X: “ — AC

X* –Niš'

+47:10,-no-Son-D'E:

(1)

-- - - - - --- --

where 8 is .0062 for normal glasses, and assumes a slightly lower value for telescope crowns, and a slightly higher value for tele scope flints. Neglecting variations in 8 the formula may be regarded as a special case of the type
-
| = a(up-uc)+bup+c, . . . . . . . . . . . . . . . . . . . . . (2)

the particular assumption being b-H c = 1. Another member of the same class has been investigated by Wright" whose assump tion is b = 1. . As these two cases lead to divergent conclusions on the possible properties of achromatic lenses it is hardly super fluous to investigate the matter closely and particularly to deter mine which assumption fits the facts most closely as far as these
are known.

Monthly Notices R.A.S. 64, p. 458. *Trans. Opt. Soc., 27, p. 99. *Jour. OPT. Soc. AMER, 5, p. 389.
57

58

T. SMITH

[J.O.S.A. & R.S.I., VI

If a number of glasses satisfy (2) with the same values of a, b, c for given lines of the spectrum, a thin lens built up of such glasses

will satisfy the relation

k – kD = a(ke – sc)+(b–1)KD+(b+c-1)R

where k is the power of the complete lens and R the sum of the total curvatures of its components. If the lens is achromatic for C and F complete achromatism (absence of secondary spec trum) may be attained in one of three ways

(I) b = 1, (II) b = 1,

C=0 R=0

R

b–1

(III) ...--, E-1

Of these (I) may be ruled out at once since if these conditions fitted the actual facts the removal of the ordinary chromatic aber ration would necessarily eliminate the secondary spectrum also. According to (II) if Wright's assumption is correct the secondary spectrum can be removed by a suitable choice of glasses, the cri terion being that if these are arranged to form a thin cemented system the curvatures of the first and last surface should be equal. This condition can be readily attained with three normal glasses provided they do not in addition to (2) satisfy a common relation of the type
A u = us - uc=d up-He

a relation which will certainly not be satisfied if the choice falls upon a crown and a flint of the ordinary silicate series together
with a dense barium crown. For if an achromatic combination
of three such glasses of given focal length is constituted of ele ments of powers ki, K2, K3, another combination having these same properties may be built from

./ 1 1

.. / 1 1

. (1 1

k1 +j , , ). k2+j , , ). K3+j ". .

and the change in the total curvature due to the alteration is (u2- us)Aul-H(us- ul)Aus+(u- u2)Aus (ul - 1) (u2-1) (us-1)

Jan., 1922]

THE DISPERSION OF GLASS

59

which must be finite under the condition just given. A value may be given to j which will enable the known total curvature of the original system to be removed, and the system should then be free from secondary spectrum. That reasonable powers may thus be secured for the components may be seen from a rough example. If the crown has an index 1.5, and the other two lenses the common value 1.625, the dispersions will be approximately in the ratios 7: 11: 17. The three conditions are obviously satisfied if the powers are given by

Kl

K2

K3

(a-1) (Aus–Aus) T (a-1) (Aus–Aa) T (a-1) (Aal-Aws)

K
-
"(Al-Aws)+P(A×Aw)+...(Au-Ags)
or in this case

values by no means unattractive for an apochromatic objective

constructed from normal glasses. As an actual example using typical glasses from the Jena list

of the three types mentioned let numbers 0.2188, 0.5799 and
0.93 be chosen. For k = 1 the total curvatures of the elements

are

– 8.3734

14.3648

– 5.9914

giving for the various spectrum lines the following powers for the

complete lens
A’

0.9990

C

0.9997

D

1.0000

F

0.9997

G'

0.997.5

The differences here are of the same order of magnitude as those

of an ordinary doublet, and the conclusions to which Wright's
formula would lead are not realized.

Condition (III) gives a solution only if c is a constant multiple,

as the colour changes, of 1–b. . The value of a solution depends

60

T. SMITH

|J.O.S.A. & R.S.I., VI

upon the sign and upon the magnitude of the constant multiplier. In the special case, b + c = 1, the removal of the secondary spec trum becomes impossible. A decisive contradiction is therefore involved in the apparently small difference between the two cases b = 1 and b + c = 1, and an appeal to known reliable measurements must be invoked to decide which is more closely in accordance with the facts. It seems preferable under the circumstances to quote figures compiled by independent observers, and the com parison below is based on the figures of Jena catalogues. The gen eral experience of manufacturers who have relied on these values for the construction of apochromatic as well as of ordinary achro matic systems affords an indication of their accuracy. The cor rections which must be applied in the fifth decimal place to the indices calculated by each formula to give the catalogued figures are given in Table 1.
A glance at these figures indicates that on the whole the resid uals in the columns headed b-H c = 1 are distinctly the smaller. The distribution of these residuals is given in Table 2. In com piling the latter table the last four glasses, which have indices exceeding 1.7, are left out of account as they are of no interest for the construction of optical instruments such as are now con
sidered. The most notable differences in the two sets of correc
tions are in those applicable to the G’ line. While the corrections for the case in which b + c = 1 form a reasonably compact group, those for b = 1 are widely spread, and the figures relating to the extreme barium crowns form a detached group at one end. From the figures summarising the whole position at the end of the table it appears that each formula is a good fit of its kind, and that while in the central region of the spectrum and at the red end the assumption b+c = 1 leads only to slightly greater accuracy, the superiority of this formula over the alternative b = 1 becomes very pronounced at the blue end. In particular Wright's formula
fails for the dense barium crowns.
When glasses too unstable to be listed as general types are con sidered, it is found that one formula is better in some cases, the other for other types. Phosphate crowns and dense borate flints are better represented by b + c = 1, while barium phosphate

Jan., 1922]

THE DISPERSION OF GLASS

61

TABLE 1

Fifth Place Corrections Required to the Calculated Indices for Schott Glasses, List Dated
1913

Spectrum Line

A'

C and F

G'

Formula

b = 1 b+-c = 1 b = 1 b+-c = 1 b = 1 b+-c = 1

Glass Descrip Type No. tion

6781

FC

+4

–1

+2

0

+11

+3

6500

**

+6

–2

+2

–1

+13

-1

2188

B Sic

+3

–1

+2

0

+10

+2

7185

FC

+7

–2

+3

0

+15

0

802 B Sic

0

–5

-1

–3

+2

–6

3199 38.32
144 3848
599

UV c B Sic
** ** **

3512 57
3390 6367 2122

**
c
B Sic
**
Ba c

337 4817 6223 3453
546

C
*. ** 44
Z Sic

–2 –1 +3 –4 +2
–5 +7 +5 -1 –2
+2 +7 +3 +7
+2

–5 –3
0 –5 –2
–5 +3 +1 –6 +5
0 +1
0 +4
-1

–1 +1 +1 -1 –1
+1 +1 +3 +1 –1
+1 +2 +1 +1
+2

–2 0
–1 –2 –2
+1 -1 +1 –1
0
0 0 0 0
0

–1

–6

–1

–2

+7

–2

+3

–1

+5

–2

+1

–2

+7

0

+10

+3

+3

–5

–9

–1

+8

+2

+9

0

+6

-1

+5

–1

+6

-1

60

C

138

44

4125

44

66.34

**

567

**

+4

+1

+1

+4

+2

+1

+3

+1

+1

+3

–1

+1

+3

–1

+2

0

+6

0

0

+5

+1

0

+5

+1

0

+6

0

0

+9

+1

227 Ba Sic

+3

+3

0

–1

0

–3

2118

C

-1

–5

+1

0

+11

+4

3712 Bac

–7

+1

–2

0

– 11

0

203

C

+3

0

–1

–2

+5

-1

2071

Ba c

–8

+1

–3

-1

– 11

0

2164 15

C
Z Sic

+6

+1

+1

–1

+3

+1

0.

-1

+12

+4

+2

–2

62

T. SMITH

|J.O.S.A. & R.S.I., VI

TABLE 1—Continued

Spectrum Line Formula

A'

b=

b+c = 1

C and F b = 1 b+-c = 1

G' b = 1 b+c = 1

Glass || Descrip Type No. tion

211

Ba Sic

+2

+7

-1

0

–4

+1

3376

C

+4

0

+2

+1

+7

0

3551

Z Sic

+1

–3

+1

–1

+8

0

1209 5970
114 2994 1615

Bac
44
C Bac
-

–6

+3

–3

–6

+4

–3

0

-12

0.

0

-14

–2

+9

+4

+2

0

+8

0

+2

+11

–1

+1

– 12

-1

–5

+3

–2

0

-11

0

7.550 3961 7336 3248
463

Baf Bac Baf UV f Baf

5878 608
46.79 722
5799

Bac C
Bac Baf Bac

602 846
3439 381 583

Ba f
44
Tf C
Baf

0

+1

0

0

–3

-1

+2

+10

–2

+1

-12

-1

+1

+3

0

0

-4

–2

+4

+2

0

-1

+3

–2

0

+1

0

0

-1

0

–5

+3

–1

+1

-11

0

+10

+4

+2

0

+8

0

–5

+4

-1

+1

-11

0

-1

+2

–2

-1

–7

–2

–5

+4

–2

+1

–13

–1

+1

+2

+1

-1

–2

–2

+2

+3

0

+1

+1

–2

–3

–8

-1

–2

0

–7

+7

+2

+2

+1

+7

0

+2

+3

0

0

–3

–2

152 543 527
3.338 2015

Sig
Baf
44
Tf Bac

+4

+1

+2

0

+6

0

+2

+2

0

0

0

0

+4

+6

+1

0

-1

0

–2

–5

-1

–2

–3

–7

–3

+3

0

+1

–8

–2

575

Baf

+2

+3

+1

+1

-1

0

522

-

+4

+2

+2

+1

+4

+1

7821

B Sif

-4

–4

0

-1

–3

–4

726

f

+4

0

+1

0

+3

–4

6241

**

0

–2

+1

0

+2

-2

Jan., 1922]

THE DISPERSION OF GLASS

63

TABLE 1—Continued

Spectrum Line
Formula

A' b+1 b+c = 1

G and F
b = 1 b+-c = 1

Glass Descrip Type No. tion

578 378 6296 1266 154
376 276
569 340 184

Baf f
**
Baf f
44
** ** 444

+2

+3

0

0

+5

+1

+1

0

+2

-1

+1

0

-1

+1

–2

0

0

–2

-1

-1

0

–2

+1

0

0

–2

0

–1

-1

–4

0

0

+1

–1

0

0

0

-1

–3

–3

G'
b = 1 b+-c = 1

–3

–2

+5

-1

+1

–2

–6

-1

+1

0

+4

0

+7

+6

+4

+1

+2

0

–5

–4

748 318 118
167
3269

Baf
f
4-
**
Ba f

103

f

93

-

6131

44

919

4.

355

44

102

44

192

**

41

4-

113

--

165

**

198

**

+6

+9

0

+1

–3

+1

-1

–2

0

0

-1

-1

+1

–1

–2

–2

–3

–2

–2

–3

–3

–2

–3

–2

–3

+1

+1

+2

+1

+8

-1

–1

–2

-1

–2

0

0

0

–4

–3

–4

–2

+3

+2

+1

+1

+2

+3

+5

+5

0

+1

+4

+7

+4

+3

–3

–2

-1

+3

-1

0

–3

–2

–2

+3

0

+2

–3

-1

–2

+5

+1

+5

–1

+2

+2

+13

+8

+11

+8

+11

0

+3

+4

+16

0

+3

+8

+21

+5

+11

+1

+5

+-16

+-32

crowns and light borate crowns leave smaller residuals with b = 1. In the case of very dense flints neither formula is satisfactory; which is better depends upon the presence or absence of boric acid
as a constituent of the glass.

64
Spectrum line
Formula

T. SMITH

|J.O.S.A. & R.S.I., VI

TABLE 2

Analysis of Residual Corrections

A'

C and F

b = 1 b+c = 1 b = 1 b+c = 1

G’
b = 1 b+c = 1

Value of correction

15

0

0

0.

0

14

0

0

0

0

13

0

0

0

0

12

0

0

0

0

11

0

1

0

0

10

1

1

0

0

9

1

1

0

0

8

0

0

0

0

7

5

1

0

0

6

3

1

0

0

5

3

2

0

0

4

10

6

0

0

3

Q

12

3

0

2

11

9

12

1

1

6

13

24

17

() –1 –2 –3 —4

10

8

18

40

9

11

13

16

5

8

8

10

3

3

8

3

2

2

1

0

–5 –6 –7 –8 –9

5

6

0

0

2

1

0

0

1

0

0

0

1

1

0

0

0

0

0

0

– 10
– 11 – 12 – 13 – 14

0

0

0

0

0

0

0

()

0

0

0

0

0

0

0

0

0

0

0

0

1

0

0

0

1

O

1

0

2

0

2

0

2

0

4

1

5

1

5

1

6

1

4

2

4

5

5

2

5

7

3

25

7

14

4

19

8

1

3

3

1

1

1

2

1

2

1

0

1

0

0

0

5

0

3

0

1

0

1

0

Mean Mean of absolute
values
Root mean square
error

1.08 3.10 4.40

.64 2.67 3.95

0

– .30

1.31

.74

1.86

1.25

.41 - .44

5.10

1.82

7.72

3.01

Jan., 1922]

THE DISPERSION OF GLASS

65

A formula suggested by Nutting requires less detailed con sideration. He proposes a particular case of the type
1
- = A +BA" A -1

It is easy to show that no such formula can be applicable to glasses in general. For it involves among other relations the particular
relations

Ha *A

-

uc *c.

us *

-1 *

=f,

a constant

plc - up uA - 1

and

l, - us uc-1
-- =g, a constant ac- up ug - 1

If the three partial ratios

A - Ap Ad - H "f Ag:
ac-ur' ac- up ue-",
which are quoted in manufacturers’ lists are denoted by p1, p. and p3 respectively the above relations may be expressed as

v– pi
p1+p2–1 "VF,

and
v-Hpa-H p3 3 = g v-Hp2–1

Now normal clear glasses vary regularly in their partial dispersions
from the fluor crowns with values such as

w = 69.9, p1 = . 662, p2 = .700,
to the dense flints with such values as

p8 = .552

w = 32.0, p1 = .597, p2 = .717, p3 = , 615.

Over this range

p1+p2–1 decreases by 13%
and

ps increases by 11%

‘Jour. OPT. Soc. AMER., 2 and 3, p. 61.

66

T. SMITH

|J.O.S.A. & R.S.I., VI

#p’ -

On the other hand

falls from .981 to .960, just over 2%,

1/

2

# +-p2+p3 .

and

rises from 1.022 to 1.065, rather more than 3%.

2

It is clear from these figures that no formula of this class is of gen eral interest in connection with optical glass.

OPTICs DEPARTMENT,
NATIONAL PHYSICAL LABORATORY.

INSTRUMENT SECTION
THE CRYSTELLIPTOMETER
AN INSTRUMENT FOR THE POLARISCOPIC ANALYSIS OF VERY SLENDER BEAMS OF LIGHT
BY
LE ROY D. WELD
I. INTRODUCTORY
The determination of the elements of elliptic vibration of light, which has been transformed from a condition of plane to one of elliptical polarization, is found to reveal so much concerning the optical nature of the agencies effecting the transformation that it becomes a matter of considerable importance to be able to make such measurements with reasonable accuracy. It so happens that the ordinary methods, which are employed for the elliptical analy sis, and most of which are too well known to need setting forth here, require a fair breadth of field, and would therefore not easily apply, for example, to a ray passing through a pin-hole.
The research presented in this paper had its origin in a problem suggested to the writer some years ago by Dr. L. P. Sieg, and was begun in 1915. It has been carried out at Coe College by means of apparatus, much of which was kindly loaned for the purpose by the University of Iowa.
Various investigators have attempted to obtain the optical constants of metals and other opaque substances by reflection methods, with indifferent success. It appears certain from the research of Tate that the difficulty has been due, not to lack of precision in the analysis of the elliptically polarized light reflected from the opaque surfaces, but to the variation in surface condi tions, brought about by the polishing process, which modified the nature of that light. Thus it was found impossible to prepare two mirrors of the same kind of metal, even by the same process, which would give consistent results, while different measure ments, and even different kinds of reflection measurements, on
* Tate, Phys. Rev., 34, p. 321, 1912.
67

68

LE Roy D. WELD [J.O.S.A. & R.S.I., VI

the same fresh surface, gave good agreement. Dr. Sieg's suggestion was that opaque crystals, with their natural, unpolished facets, might be prepared of such surface purity as to obviate this diffi culty, and at the same time furnish material for an interesting experimental research in crystal optics.
Comparatively few large opaque crystals can be obtained in perfect form. Drude made some experiments long since with lead sulphide, and Müller" subsequently, with antimony sulphide, freshly exposed by cleavage, employing ordinary polariscopic methods. In 1916 the writer made a preliminary report" on the present research, which had already given unmistakable evidence of strong double refraction in minute hexagonal selenium crystals, and at the same meeting,” Dr. Sieg reported having found by direct photometric measurements that the selenium crystal has two different reflecting powers in the two principal directions. Mr. C. H. Skinner has given an account" of his interesting observations on selenium, using the ordinary Babinet compensator method, from which he concluded that the crystals, like artificially prepared surfaces, have in some respects their individual peculiarities, espe cially in the longitudinal direction.
The method adopted by the writer was presented to the Physical Society in 1917 but was published only in abstract" at that time, the research being then still in progress. It is applicable not only to the polariscopic analysis of light reflected from polished plane surfaces of any sort, however small (such as minute spikelets or flakes of selenium, tellurium, cadmium, etc.), but to light in slen der beams from any source. Its application has recently been suggested, for example, to the comparison, from point to point, of the optical properties of metal film-deposits of non-uniform thickness. Furthermore, being a photographic method, it is adaptable to the ultra-violet, and the apparatus was designed with this in view. Its original application to crystal-reflected,
* Drude, Ann. d. Physik, 36, p. 532, 1889. * Müller, Neues Jahrbuch für Mineralogie, 17, p. 187, 1903. * Weld, Proc. Iowa Acad. Sci., 1916, p. 233. * Sieg, Proc. Iowa Acad. Sci., 1916, p. 179. • Skinner, Phys. Rev., N.S. 9, p. 148, 1917. 7 Weld, Phys. Rev., N.S. 11, p. 249, 1918.

Jan., 1922]

THE CRYSTELLIPTOMETER

69

elliptically polarized light is what suggested to the writer the name “crystelliptometer” for the distinctive apparatus employed.
II. PRINCIPLE OF THE POLARISCOPIC METHOD
As regards the polariscopic analysis itself, the method employed
is a modification of that used by Voigt for the study of polarized ultra-violet. The principle is stated in Voigt's original articles and a more detailed account given by Mr. R. S. Minor" who applied it to artificially polished mirrors of steel, copper, silver, etc. A non-mathematical statement of the original method will first be given.
Let us have a uniform parallel beam of elliptically polarized monochromatic light; to determine the two elements of the elliptic
(l
of vibration, which may be taken as the ratio r = the X to the Y

amplitude, and the phase advance V of the X ahead of the Y

harmonic component (either positive or negative)."

R

C

Y

Fig. 1
Cross hairs and quartz wedge systems. X Y. reticule. C, compensator. R, rotator
This beam first passes through a pair of quartz wedges similar to a Babinet compensator, except that they are fixed with refer ence to each other (C, Fig. 1). The edges are, let us say, vertical, that is, parallel to the Y direction. As we now face the oncoming
* Voigt, Physik. Zeitschr, 2, p. 203, 1901. * Minor, Ann, d. Physik, 10, p. 581, 1903. * The reason for here using the inverted V instead of the customary A will appear later (Sec. VII).

70

LE Roy D. WELD [J.O.S.A. & R.S.I., VI

light and move across the emergent beam from left to right, we

encounter a steady increase in the phase advance, so that, whereas

the light through the center of the compensator has phase

difference V (the same as the original light), that at distance x

from the center has phase difference V+sa, where s is the com

pensator constant in degrees of phase per millimeter. Periodically,

therefore, we shall come to regions of light plane polarized at some

angle, viz., where V +sa = 0, r, 2T, . . . .

Y

~

\.

|v

/

•

-H

~

\

|v /

–5–

N.
\ !v /
...” -H -
\
|v

Fig. 2
Showing action of rotator on a strip of plane-polarized light

The next optical member is another pair of wedges, which will be called a rotator (R, Fig. 1). This consists of a wedge D of right handed, and one L of left-handed, quartz, the optic axis of each being along the path of the light. It is easily seen that if the light entering the rotator be plane-polarized, it will suffer a net rotation of plane which will be the greater, the higher the point at which it traverses the two wedges. This rotation may be designated by qy, q being the rotator constant in degrees of azi muth per millimeter.
To an observer facing the light as it comes from the rotator, any one of the periodic vertical ribbons of plane-polarized light from the compensator will have been acted upon by the rotator as

Jan., 1922]

THE CRYSTELLIPTOMETER

71

shown in Fig. 2. Therefore as we traverse this emergent beam vertically along any one of these plane-polarized regions, we shall encounter, at intervals, light vibrating vertically, and half way between these, light vibrating horizontally (V and H, Fig. 2).
Finally, let the beam be passed through a Nicol set so as to extinguish, say, the vertical component. Obviously, wherever we had in one of these plane-polarized strips a point of vertical vibration, we shall now have a black spot. The field will then be covered with black spots arranged in a regular pattern of vertical columns and horizontal rows, the exact design of which will depend upon the elements of the original elliptic vibration. Con versely, these elements may be easily deduced from the observed arrangement of the spot-pattern. There is introduced into the

Fig. 3 Spot-pattern for elliptically polarized light reflected from nickel. (Enlarged.)
field a pair of cross hairs corresponding to X and Y axes and coinciding with the neutral lines of rotator and compensator, respectively. This reticule is photographed along with the spot pattern and the coordinates of the spots determined by subsequent measurements on the plate. Such a spot-pattern, with the cross hairs, is shown, enlarged, in Fig. 3, in which the elliptic polariza tion was produced by reflection from nickel.
The equations relating to the processes just described, and the practical deduction of the elliptic elements therefrom, will be worked out in subsequent sections of the paper.

72

LE Roy D. WELD [J.O.S.A. & R.S.I., VI

III. ADAPTATION OF THE METHOD To SLENDER BEAMs
The above procedure, as followed by Voigt and others, ob
viously requires a beam of light whose cross section is large enough to cover the entire spot-pattern, and hence would not be adapted at all, for example, to light reflected from one facet of a small crystal. The writer's modification of it consists simply in keeping the very slender parallel beam, so reflected, stationary, and mov ing the whole analyzing system of quartz wedges, cross hairs, Nicol and camera back and forth perpendicularly across it, with
Azi Mu Thi clace"?

e CIRCLE
Fig. 4
Diagrammatic layout of apparatus. S, source. M, monochromator. L., N1, collimator and polarizer. K, reflecting surface mounted in front of drum D. X to E, crystelliptometer
a sort of weaving motion, until the whole spot-pattern has been
covered. The effect is the same as if the beam had a cross section
as large as the field thus traced out. Whenever any point of the analyzing system corresponding to one of the dark spots arrives at the beam, the latter is extinguished thereby, and the spot is left on the plate. In practice it is not necessary to cover the whole pattern, but only the regions of it in which the rows of spots are known approximately to lie; and this fact saves much time.

Jan., 1922]

THE CRYSTELLIPTOMETER

73

The assemblage of optical parts, which is given the lateral motion just described, together with its mountings, considered as a single instrument, is what has been referred to as the “crystelliptometer.”
The arrangement of the writer's apparatus for the study of crystals is shown in Fig. 4. Light from the source S is focused by the quartz lens L1 on the inlet slit of the monochromator M, from whose outlet slit the monochromatic light diverges and is collimated by the quartz lens L2. (In the earlier work, color filters were used instead of the monochromator, and the filtered light focused by Li directly upon the slit of the collimator.) The parallel beam from L2 is plane-polarized in any desired azimuth by N1, a large polarizing prism with square ends and a glycerine
film.

| || || ||
19.
Fig. 5
A, spot-pattern for light reflected for selenium in parallel position. B, in perpendicular position
The crystal or other small reflector K is mounted on a spectrom eter, by means of whose telescope T and verniers V any desired angle of incidence may be secured. The mounting can be rotated so that it is very easy to exhibit the double refraction of selenium, tellurium, etc., the spot-patterns obtained with axis horizontal and with axis vertical being quite visibly different, as seen in Fig. 5.
The slender reflected beam, in general elliptically polarized, now enters the analyzing system X, C, R, N2 of the crystelliptom eter. X represents the cross hairs, which the writer has found it necessary to place in front of the compensator C. (See Sec. VI.)

74

LE ROY D. WELD |J.O.S.A. & R.S.I., VI

The compensator wedges have an angle of 52', which gives a relative phase change of about 144° per horizontal millimeter with sodium light. R is the rotator, with wedge angle 24°, which gives a rotation in azimuth of about 16° per vertical millimeter with sodium light. The dimensions of the field are about 15 x 30 mm. The wedge system and cross hairs are mounted adjustably in a brass tube which screws upon the tube containing the analyzing prism N2.
N2 is a duplicate of N1, the two being interchangeable. They are rectangular prisms 15 x 30 x 30 mm consisting of Iceland spar wedges separated by glycerine, the angle of incidence on the inter face being 65°. The emergent (extraordinary) light vibrates parallel to the 15 mm dimension.
The spot-pattern and cross hairs are photographed together, by means of the quartz lens L3, upon the plate P. Behind the plate is an eyepiece E, used in adjusting the focus and alignment before the plate is inserted. The plates are 1 x 1% inch, with emulsion adapted to the wave-length, and are held in a diminutive plate holder.
The whole crystelliptometer, from cross hairs X to eyepiece E, is contained in a tube about 85 cm long, so mounted on two pairs of guides at right angles that it can be given the weaving motion referred to in order to trace out the spot-pattern. This is accom plished by means of two micrometer screws perpendicular to each other. One of these screws is driven by a worm-gear electric motor mechanism so as to move the instrument slowly across,
along a line determined by the other screw, the speed varying
with the exposure required. Furthermore, the whole tube, with its micrometer mountings, can be rotated about its longitudinal axis through any desired angle, thus varying the relative inclina tion of the elliptic vibration to be analyzed, with respect to the coordinate axes of the analyzing system. The extinction plane of the analyzer N2, which coincides with the Y axis, being first verti cal, one spot-pattern is produced. On rotating the instrument through an angle 6 another is obtained, and so on; without, how ever, modifying in any way the actual nature of the elliptic light under analysis. The equations used in the subsequent

Jan., 1922]

THE CRYSTELLIPTOMETER

75

theory make provision for this arbitrary angle 6, the advantage of which will then appear.
The source of light at first employed was an open Nernst fila ment, which has later been replaced by a special low-voltage tungsten ribbon lamp. In some preliminary work with ultra violet, an iron arc was employed.
A general view of the apparatus is shown in Fig. 6.

Fig. 6
General view of crystelliptometer and accessory apparatus
The spot-patterns are measured upon a micrometer comparator
to one-hundredth of a millimeter. The lenses were removed from
the microscope, and a pin-hole and hair-line substituted, a device suggested to the writer by Dr. Elmer Dershem. Not a little of the routine work consists of the plate measurements and their reduction. It has been found possible, with good, clear plates, to locate a spot by a single measurement with a probable error of less than one-hundredth of a millimeter. A selenium spot-pattern and the corresponding "comparison plate” (see Sec.VI) are shown

76

LE Roy D. WELD [J.O.S.A. & R.S.I., VI

together as A, B in Fig. 7, and another similar pair, with greater wave-length, as C, D.
The quartz lenses and wedges and the Iceland spar wedges for the Nicols, designed by the writer, were made by Hilger of London, as was also the monochromator; the comparator by Gaertner of Chicago. The remainder of the special apparatus, including the driving mechanism, was built at the University of Iowa by Messrs. M. H. Teeuwen and J. B. Dempster, assisted by the writer.

A. selenium spot-pattern. B, corresponding comparison plate. C, D, same, with greater wave-length. Note the greater spot-intervals
IV. OUTLINE OF THE MATHEMATICAL THEORY OF THE ANALYZING SYSTEM
The mathematical theory of the action of the analyzing system, as used in the writer's method, and of the determination of the elliptic elements, will now be briefly given." In the notation here used, X and Y are components of the vibration displacement of the light, while x and y are coordinates of points of the field with
reference to the axes.
* This is necessary for the reason that the present method departs in certain essen tial particulars from the original and gives rise to a different set of equations. Minor did not, for example, rotate the quartz wedge system through the arbitrary angle 6 which makes possible the least square adjustment of the observations, and which, as will be easily seen, also provides automatically for any difficulty due to the azimuth of the light under examination happening to be very small, without altering that light in any way.
-

Jan., 1922]

THE CRYSTELLIPTOMETER

77

Let the harmonic components of the elliptic vibration to be an alyzed, as viewed by one facing the oncoming waves, be given by the equations
X = a cos (wt-HV). . . . . . . . . . . . . . . . . . . . . (1) Y = b cos at . . . . . . . . . . . . . . . . . . . . . . . . . (2)

If the analyzing system by now rotated through an angle+6, these equations are transformed, with reference to the new axes,
into

X' = a cos 6 cos (ot-HV)+b sin 6 cos at . . . . . . . . . . . (3) Y' = b cos 6 cos ot— a sin 6 cos (at-HV). . . . . . . . . (4)

Upon passage through the compensator, the Y-component receives an advance of phase, varying with the abscissa x of the point where it passes through, and equal to six. (3) and (4) then
become

X" = a cos 6 cos (alt+V)+b sin 6 cos ot, . . . . . . . (5) Y’’=b cos 6 cos (aut--sa) — a sin 6 cos (ot-HV +sa)(6)

Upon passage through the rotator, there is a simple rotation of the axes of the ellipse, without further change, through an angle qy, which corresponds to a rotation —qy of the coordinate axes, so that the components of the finally emergent light are

X" = a cos 6 cos qy cos (alt+V)+b sin 6 cos qy cos at -b cos 6 sin qy cos (ot--six)+a sin 6 sin qy cos (ot-HV+sa). (7)
---------- - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - -
Y''' = (a corresponding long expression which we shall not need). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (8)

The light now passes through the Nicol N2, which shuts off

the Y-component all over the field; hence (8) is not needed.

Only X" gets through, and this will vanish, leaving the dark

spots, at every point where x and y have such values as to render

the expression (7) equal to zero all the time, that is, independently

of the value of t. To fulfill this condition, dividing (7) by b cos 6,

. Cl -

•

-

letting 5 =r, expanding the parentheses containing at and group

ing the terms in sin at and cos at separately, we have [-r tan 6 sin gy sin (V+sa)+sin qy sin sy —r cos qy sin V] sin ot

78

LE Roy D. WELD J.O.S.A. & R.S.I., VI

+[tan 6 cos gy-Hr cos gy cos V-sin qy cossa +r tan 6 sin qy cos (V+sa)] cos alt=0.

That this may be true independently of t, the coefficients must

separately vanish, giving

—r tan 6 sin qy sin (V+sa)+sin qy sin sa-r cos qy sin V = 0. . (9) tan 6 [cos qy+r sin qy cos (V+sa)] +r cos qy cos V -sin gy cossa
=0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (10)

Letting tan 6 = m, expanding the functions of W+six, and collect

ing, these become

[m sin qy cossa +cos qy]r sin V+m sin qy sin sac. r cos V =sin qy sinsz. . . . . . . . . . . . . (11)
m sin qy sin sa, r sin V+[m sin qy cossa-Hcos qy]r cos V =sin qy cossa-m cos qy. . . . . . . . . . . . . (12)

In these equations, x and y are the measured coordinates of

any dark spot, s and q are the compensator and rotator constants, determined from the spot intervals, and m is the tangent of the

known angle 6. Hence everything is known except r and V.

Letting

m sin qy cossa-H cos qy = H,

m sin qy sin six

= K,

(13)

sin qy sin sa

=L, . . . . . . . . . . . . . . . . .

sin qy cos s.r-m cos qy = P, (11) and (12) become
H. r sin V+ K-r cos W = L. . . . . . . . . . . . . . . . . . . . . . . . (14) K. r sin V +H: r cos W = P. . . . . . . . . . . . . . . . . . . . . . . . (15)

the solution of which, as simultaneous equations, gives the re

quired elliptic elements

_V(L*-P") (H2+K*)–4 LHPK

.(16)

r=

H2 – K2

-- - - - - - - - - - - - - -

LH –PK
W = — . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (17)
tan Y "PHILK
It is thus theoretically possible to deduce the elements from
the measured coordinates of any single spot.

Jan., 1922]

THE CRYSTELLIPTOMETER

79

V. APPLICATION TO SPOT-PATTERNS
If we place under examination light which is plane-polarized at azimuth 45°, so that r = 1 and V = 0, it will be seen from the manner of their formation, as described in Sec. II, that the spots will be symmetrically arranged with respect to the Y-axis in equally spaced horizontal rows. This is the condition of things on the comparison plate, Fig. 7 B (see Sec. VI). Let the distance apart of the spots in the rows be d, and in the vertical columns, 6 (Fig. 8). These are easily measured (see Sec. VI). The com
'' pensator constant s is equal to and the rotator constant q

# equals in degrees per millimeter (see Sec. II).

-
Y -a-- () () () ( t ) •2

Y #**

'F4 " " ' "

**

S

30 0 0

0 0 0+ 1

*
w A.

-- 0 0 Q || 0 0 0 - 1

8

":

S

4 M M | || 4 || *
X
-
*******

-

-*

() ()

-2

* . . . . . . . . . . ."

8 4. 4. 4. 4. ! -2
-7 - 6 -5 -4 -3 -2 -r o */ •2 •3 ** *s

Fig. 8
Diagram of spots on a comparison plate, taken with plane-polarized light at 45° azimuth

Fig. 9
Diagram of spots on a pattern taken with light elliptically polarized at phase difference 202° and azimuth 29°

If now we introduce by any means a phase difference V between the X- and Y-components, there will be a uniform lateral dis placement a of the whole spot system, so that the coordinates of
#. 6 -
the spot S, which in Fig. 8 are 0, now become a, 4. Then, again,
if a change is produced in the azimuth of the incident light, the alternate rows +1, -2, etc. will be displaced vertically one way,

80

LE ROY D. WELD |J.O.S.A. & R.S.I., VI

and rows +2, -1, etc., the other way, through a certain amount
6
*
a, so that now the coordinates of S are x = a, y = 4 +a (a being neg

ative). These changes are shown in Fig. 9.” Introducing the above values of s, q, x, and y into (13), and
resuming m = tan 6, we get
H = tan 6 sin ['s+'lso ko-'do- +co.['s + : isol |

[**'. lso K = tan 6 sin in [*]

|

L =sin [*:: *]in'" |

-

P -***: isoko-'or' – tan 6 co's + : isol |

While the attention is, indeed, fixed on one particular spot S,

6

-

•

-

•

-

Fig. 9, whose coordinates are a and 4. +a, yet in actual practice it

is expedient to make measurements on a number of spots, usually twenty or more, and deduce the position of S from them. Refer ring to Fig. 9, it is clear that the abscissa of any spot in the nth vertical column (numbered along the bottom of the figure) is

which gives

*=a+n,

a-a-'d

(19)

- -- - - - - - - - - - - - - - - - - -

By measuring the abscissas of several spots in different rows, thus varying x and n, we obtain as many independent observa tions upon a.

* If the azimuth is made 90°, rows +1, +2, rows -1, -2, etc., will merge or dove-tail together in pairs forming continuous horizontal dark stripes. If it is made 0, the pairs of rows +1, -1, etc., will similarly coincide. This affords a good means of adjusting the quartz wedge system with respect to the previously adjusted analyzing Nicol (see Sec. VI).

Jan., 1922]

THE CRYSTELLIPTOMETER

81

Again, the ordinate of any spot in the wth horizontal row (counted upward or downward from the X-axis) may be seen to be

-1)* y = + (

a–

+ 14– 2"

6
*

[**** *] + 1 –
Or a- +(–1)"

(20)
--- - - - - - - - - - -

(+ according as the row is above or below the X-axis), and we shall have, therefore, as many observations upon a as there are spots measured.
The averages from these observations on a and a are easily obtained by means of formulas depending upon the particular selection of spots made. If the selection consists of an equal num
ber of vertical columns on each side of the Y-axis and of horizontal rows above and below the X-axis (as should be the case for other
reasons), these averaging formulas become quite simple. a, a, d and ö being thus determined from the measurements on the plate, substitution of their values in (18) gives the necessary constants H, K, L, P, appearing in the expressions for r and tan V, Eqs. (16), (17), and the problem is solved so far as is possible from a sin gle experiment.
We may, however, expose other plates with different values of 6, obtained by rotating the crystelliptometer tube about its own axis. This does not alter the elliptic elements, but it gives new values of H, K, L, P. In such case, (14) and (15) may be used as observation equations of the first degree with r sin V and r cos V as unknowns, and we may obtain as many different pairs of them as there are measured plates, finally adjusting them by the method of least squares. It shas been the writer's practice to assign a weight to each measured plate by means of the grading method,” each plate characteristic, such as clearness, symmetry of spots, etc., being graded separately.
It should be stated that, except in cases where the number of spots on a plate available for measurement is too limited for precision, a
* Weld, A Method of Assigning Weights to Original Observations, Science, 50, p. 461, 1919.

82

LE ROY D. WELD |J.O.S.A. & R.S.I., VI

single plate, with 6=0, is sufficient, and a vast amount of labor

ious calculation is thus avoided. For with 6=0 in (18), the elliptic

elements, given by (16) and (17), reduce at once to

r = tan [*#1so.

(21)

----- - - - - - - - - - - -

-3(.1 360o

(22)

--- - - - - - - - - - - - - - - - - - - - - - - -

It is only with light of very large wave-length that the number of spots in the field is likely to be so few as to require the repeated
exposures.

VI. MISCELLANEOUS DETAILS AND SOURCES OF ERROR
The general arrangement of the apparatus as employed for the study of opaque crystals was explained in Sec. III. In order to adjust all the parts in proper relation to each other, use is made of a sensitive cathetometer set with reference to the pier on which the apparatus stands. By this means is secured the horizontality of the monochromator, the collimator, the polarized incident beam, the reflected beam from the crystal, and the crystelliptometer tube, taken in the order named. The plane of incidence and reflection is thus strictly horizontal, and the azi muth of polarization, the arbitrary angle 6, and the vibration com ponents X and Y are reckoned with reference to it. The crystal is mounted on the end of a small rod in front of the dark opening into a hollow drum, -a black body, so to speak, which makes a perfectly dead back-ground. The mounting may be turned in a vertical plane, and is provided with a graduated circle, so as to give the crystal any desired angle from 0° to 180° with the plane of reflection. The drum (D, Fig. 4) is placed on a spectrometer prism table for adjusting the angle of incidence, as previously explained.
Considerable trouble has been experienced with the mono chromator, inasmuch as no reliance can apparently be placed upon the wave-lengths indicated by it; and furthermore, the wave length corresponding to any given setting is found to vary from day to day. In all final work it has therefore been customary to

Jan., 1922]

THE CRYSTELLIPTOMETER

83

divert the light emerging from the monochromator into a separate grating spectrometer (not shown in Fig. 4) and compare it with the sodium standard just before making each exposure. Another and more serious difficulty with the monochromator is the impur ity of the light furnished, especially in the shorter wave-lengths.
The accurate adjustment of the focus of the collimating and camera lenses is a matter of some importance, especially the latter. These quartz lenses are, of course, not achromatic, and the focus must be calibrated for wave-length. In the case of the collimator, it has sufficed to measure the focal length for one wave-length on an optical bench and calibrate the tube from the known dispersion of quartz. But any inaccuracy in the focus of the camera lens will result in displacements of the spot images and resultant errors in the elliptic elements, so that this requires greater precision. The method here employed is one devised by the writer and referred to as the “offset” or “broken prism” method.” The proper focus for a given wave-length may be thus obtained with a probable error of only one or two tenths of a millimeter, and it is easy to calibrate the focus tube accordingly.
The need for a special precaution arises from the fact that the spot-pattern in the crystelliptometer appears to be a sort of virtual image lying in a definite plane. It is necessary to get the cross hairs accurately into that plane, otherwise there will be an apparent parallax between cross hairs and spots, and the results will be seriously affected if the light happens to be not strictly parallel to the crystelliptometer axis. Furthermore, the position of this virtual plane is found to vary systematically with the wave-length, so that the adjustment has to be made for each wave-length used. This is accomplished by mounting the cross hairs in a ring having a longitudinal micrometer movement in the tube. The crystelliptometer is turned a little to right and left with respect to the beam of light and the reticule moved forward or backward until the parallax disappears. It has always been found necessary, in the visible spectrum, to place the reticule in front of the compensator, as in Fig. 4.
* Weld, Some Precise Methods of Focusing Lenses, School Science and Mathe
matics, 18, p. 547, 1918.