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Vol.UMa 27, NvMasR 2

APRn. , 1955

:5'em Ana. .ysis oI': t.xe ..nterI.'erometer 0;&servations
oI: .3ay1:on C. er .V. .i....
R. S. SHANKLAND) S. W. MCCUSKEY) F. C. LEONE) AND G. KUERTI
Case Institute of Technology, Cleoetand, Ohio
For nearly thirty years the results of the Michelson-Morley experiment obtained by Dayton C. Miller on Mount Wilson have stood at variance with all other trials of this experiment. As interest in Miller's results has continued to the present time, and since the original data sheets are available to the present writers, it has
seemed appropriate that the observations be subjected to a new analysis. It is now shown that the small
periodic fringe displacements found by Miller are due in part to statistical fluctuations in the readings of the fringe positions in a very difficult experiment. The remaining systematic effects are ascribed to local temperature conditions. These were much more troublesome at Mount Wilson than those encountered by experimenters elsewhere, including Miller himself in his work done at Case in Cleveland. As interpreted in the present study, Miller's extensive Mount Wilson data contain no effect of the kind predicted by the aether theory and, within the limitations imposed by local disturbances, are entirely consistent with a null result at all epochs during a year.

INTRODUCTION

that the earth's orbital velocity at one epoch might

HK null result obtained in the Michelson-Morley experiment at Cleveland in 1887' was the culmi-
nation of the long nineteenth-century search for an aether and proved to be a major incentive for the theoretical developments made by Lorentz, FitzGerald, Larmor, Poincare, and especially Einstein. The crucial significance of the Michelson-Morley result stimulated
many repetitions of this experiment during the next fifty years, especially as the implications of the theory of relativity unfolded. All trials of this experiment except
those carried out at Mount Wilson by Dayton C. Miller yielded a null result within the accuracy of the observa-
tions. Miller's observed fringe displacements also were very small, being on the average only about 1/'13 of those predicted by the aether theory for the 30 km/sec velocity of the earth in its orbit. However, as these small
residuals have received no adequate explanation, and
since interest in them has continued, it has seemed desirable to make a rather detailed analysis of the
observational material. 2 Michelson and Morley had originally planned to re-
peat their experiment at intervals of about three month. s throughout a year and thus to allow for any possibility
' A. A. Michelson and E. W. Morley, Am. J, Sci. 34, 333 (1887).
s A rather complete report on the early experiments was made in this journal, hence the present analysis of the data is published
here. See D. C. Miller, Revs. Modern Phys. S, 203 (1933).

~ fortuitously combine with the motion of the entire solar
system through space and give a small resultant velocity to their apparatus. However, after completing the July, 1887 observations, they did not return to this problem, and the completion of the aether-drift experiment for all
epochs was finally carried out by Miller during the years
from 1921 through 1926 in Cleveland and at Mount
Wilson. Miller's Mount Wilson experiments' were con-
ducted at intervals from April, 1921, through February,
1926, being interspersed with and followed by extensive trials at Cleveland.
In February, 1921, the interferometer was set up at
Mount Wilson, and Miller made numerous observations during the period April 8—21, 1921.These data indicated a possible small periodic eGect, with an average second-
harmonic amplitude of about 0.04 fringe, but Miller suspected that temperature eGects or magnetostriction in the steel base of the interferometer as it rotated in the
earth's magnetic field might be the cause. Accordingly
he had designed a concrete base for the interferometer, which was cast at Mount Wilson in October of 1921. Undoubtedly the greatest incentive to continue the experiments came from Professor Albert Einstein who visited Miller at Case on May 25, 1921, and urged that

s
(b)

D. C.
Science

Miller: 61, 617

(a) Proc. Natl. (1923); (c) 63,

Acad. Sci. 433 (1926);

(1d)1,A3s0tr6oph(y1s9. 23J).;

6&, 341 (1928); (e) see reference 2; (f) Nature 133, 162 (1934).

167

168

SHAN KLAN D, Mc CUSKE Y, LEONE, AN D KUE RTI

TABLE I. Trials of the Michelson-Morley experiment.

Observer

Michelson~
Michelson and Morley Morley and Miller' Miller" Miller'
Miller (sunlight) ' Tomaschek (starlight)'
Miller h Kennedy'

Illingwor th j

Piccard and Michelson,

Stahelk
et al. '

Joos

Year
1881 1887 1902-04 1921 1923-24 1924 1924 1925-26 1926
1927 1927 1929 1930

Place
Potsdam Cleveland Cleveland Mt. Wilson Cleveland Cleveland Heidelb erg Mt. Wilson Pasadena and
Mt. Wilson Pasadena Mt. Rigi Mt. Wilson Jena

120 cm 1100 3220 3200 3200 3200 860 3200 200
200 280 2590 2100

2D/X (v/c) 2
0.04 fringe 0.40 1.13 1.12 1.12 1.12 0.3 1.12 0.07
0.07 0.13 0.9 0.75

0.01 fringe 0.005 0.0073 0.04 0.015 0.007 0.01 0.044 0.001 0.0002 0.003 0.005 0.001

a A. A. Michelson, b A. A. Michelson

aAndm.EJ..WSc. iM. 2o2r,le1y2, 0A(m18. 8J1.)S; Pcih.il3.4,M3a3g3.

'3, 236 (1882).
(1887); Phil. Mag.

24,

449

(1887).

e E. W. Morley and D. C. Miller, Phil. Mag. 9, 680 (1905); Proc. Am. Acad. Arts Sci. 41, 321 (1905).

d D. C. Miller, Data sheets of Observations December 9 to 11, 1921 (unpublished).

" e D. C. Miller, Observations, August 23 to September 4, 1923; J»ne 27 to July 26, 1924 (unpublished).
D. C. Miller, "Observations with Sunlight on July 8 to 9, 1924, Proc. Natl. Acad. Sci. 11, 311 (1925).

g R. Tomaschek, Ann. d. Physik 73, 105 (1924).

h i

D. R.

JC..KMenilnleerd,y,RePvrso. cM. Nodaetrl.n

Phys. Acad.

5, 203 (1933). Sci. 12, 621 (1926);

Astrophys.

J. 68, 367 (1928).

& K. K. Illingworth, Phys. Rev. 30, 692 (1927).

~ A. Piccard 1 Michelson,

and E. Stahel, Compt. rend.
Pease, and Pearson, Nature

112833, ,84820(1(912992)6; J);.1O8p4t,.

152, 451 (1927); 185, 1198 Soc. Am. 18, 181 (1929).

(1927);

J.

phys.

radium

m G. Joos, Ann. Physik 7, 385 (1930); Naturwiss. 38, 784 (1931).

8, 56 (1927).

Ratio
2
40 80 15 40 80 15 13 35
175 20 90 375

further trials be made to remove any possible doubts

concerning the earlier results obtained in this experiment.

Miller conducted a series of observations with the concrete base interferometer from December 4—11, 1921,

but with rather discouraging results. Much of the time

the interferometer behaved poorly, the fringes were

often unsteady, temperature variations near the instru-

ment were troublesome, and vibrations caused by high

winds often made observation entirely impossible. How-
ever, at last on December 9—11, 1921, thirteen sets of

readings comprising 153 complete turns of the inter-

" ferometer were made under favorable conditions, some
with "excellent seeing. These data gave an average

periodic amplitude of only 0.04 fringe, nearly the same

as the April, 1921 results with the steel base interferometer, and Miller concluded that "all effects are probably due to the instrument. This is the endt'" So,

shortly thereafter he dismounted his apparatus for its

return to Cleveland where it was reassembled in a base-

ment room of the Case Physics Laboratory.

Since the 1921 experiments with both the steel and

the concrete bases for the interferometer gave essentially

the same results, Miller concluded that magnetostriction

was not the cause of the small periodic effects observed.

However, since the mechanical rigidity of the concrete

base instrument was less than that for the steel, a

conclusive argument could not be made. The magnitude

of the magnetostriction effect is marginal. Nevertheless

it cannot
harmonic

be ignored, in the fringe

since it would
displacements.

produce Professor

aG.sJeocoonsd, '

in his repetition of these experiments in 1930 at Jena,

used a fused quartz base for his interferometer because

4 D. C. Miller, Research Notebook, December 11, 1921. 5 G. Joos, Ann. phys. 7, 385 (1930) and personal communication in a letter of May, 1954.

he concluded that magnetostriction in a steel or Invar base would be excessive for the precision he expected to attain.
After the 1921 trials at Mount Wilson, Miller probably
would have abandoned further work on the problem except for a visit to Case made by H. A. Lorentz during the following spring. During his visit he discussed the Mount Wilson observations and encouraged Miller to
continue the experiments.
From the time the steel base interferometer was set up again at Case in 1922 until it was returned to Mount Wilson near the end of the summer of 1924, Miller carried out many experiments designed to test and improve, the performance of the apparatus. He established the order of magnitude of the fringe shifts produced by unequal heating of the air in the optical paths of the interferometer, by varying the speed and reversing the direction of rotation of the instrument, and by various adjustments of the centering pin. He also used different
light sources, including sunlight.
In many of the Cleveland trials of 1923 and 1924, especially those for which the data sheets record the best "seeing" of the interference fringes, the periodic effects are very small. These data were not analyzed in detail by Miller as he considered them only preliminary to the later work at Mount Wilson. However, 19 sets of observations made from August 23 to September 4, 1923, and 42 sets of data taken from June 27 to July 26, 1924, including those made with sunlight, for which the
" interferometer was in the best adjustment and the
fringes were often noted as "good" or "excellent, constitute some of the best data obtained with Miller's interferometer. These 1923—1924 Cleveland results are
included in Table I which summarizes the important
trials of the Michelson-Morley experiment.

NEW ANALYSIS OF THE INTERFEROMETER OBSERVATIONS

169

After completion of the July, 1924 trials, the appa-

ratus was returned to Mount Wilson where it was again

set up in the observation hut, which was moved back

some distance from the canyon edge to reduce the eGects

of wind. After a considerable number of preliminary

trials, extensive series of observations were made by
Miller at four epochs: March 27—April 10, 1925; July 24—August 8, 1925; September 10—23, 1925; and February 3—12, 1926.

The readings of fringe position were taken at 16

azimuth positions starting from the north and measured

clockwise. A data sheet usually contained readings for

20 turns of the interferometer, although some contained

a greater or lesser amount of data. For his analyses

Miller averaged the 20 readings at each azimuth and

then applied a linear correction for fringe pattern drift

so that the averages closed as a periodic function in the 360' rotation. Furthermore, a constant was then sub-

tracted from these averages so that their mean was zero.

These adjusted means were plotted in azimuth and con-

nected by straight lines to give a graph for harmonic

analysis with the Henrici machine. A sample data sheet

which presents details of his reduction method is

published in Miller's paper in reference 2.

Miller's harmonic analyses of these curves yielded

amplitudes and phases for the first five harmonics. The

second harmonic provides the parameters needed for

computing the presumed aether drift. The phases ob-

tained from these analyses were never capable of being

fitted into a logical relationship corresponding to an

oscillation about sidereal day. As

rtehpeornteodrthbypoMinitlledru, r'intghe

the course axes were

of a dis-

placed from the meridian as follows: "for February 10'

" to the west of north; for April the displacement is 40'
east; for August 10' east; and for September 55' east.

This azimuth anomaly has been the greatest obstacle to

the acceptance of the small periodic amplitudes re-

ported by Miller as having relevance to an aether-drift

effect. Synge and Gardner' developed a theory of the

Michelson-Morley experiment, including the e6ects of

acceleration, which was not inconsistent with the oc-

currence of azimuth anomalies, such as found by Miller,

but further predictions of this theory have been dis-

proved in experiments by Ditchburn. 7

STATISTICAL ANALYSIS OF MILLER'S DATA

The data collected by Miller have recently been reexamined with a view to establishing the relative im-
portance of statistical fluctuations and physical causes
in the small periodic effects which he obtained.
Consider first the individual data sheets. It is gener-
ally agreed that an experienced observer with keen eyesight, such as Miller had, can estimate the fringe position to 0.05 fringe, which may be regarded as the least count of the instrument. This personal factor will

'I. L. Synge and G. H. F. Gardner, Nature 170, 245 (1952);

als'o

Proc. R. W.

Royal Dublin Ditchburn and

Soc. 26, 45 (1952). O. S. Heavens, Nature

170, 705 (1952).

introduce variations in the data in addition to those arising from other causes. Prominent among the latter possibilities are mechanical vibrations and bending as the interferometer rotates, temperature disturbances producing both a drift of the fringes and periodic changes, and magnetostriction which also would cause a periodic effect.
A typical data sheet contains entries in 16 columns for the azimuth points of the instrument, and 20 rows, one for each complete turn of the interferometer. Under ideal conditions with no aether drift nor other systematic or random eGects present, all entries in a table should be identical. In a few sets of data taken at Cleveland in 1924, this is nearly the case. Usually, however, the readings show considerable variation, having the general character of random Auctuations superimposed on an irregular drift. A standard analysis of variance technique may be used to examine the degree of randomness in the entries on a data sheet.
Let x be a reading of fringe position and let x, (i= 1, 2,
16) be the average of the ith column of data (azimuth position on the interferometer); furthermore, let x be
the average of all 320 entries, x;;, on a data sheet, where the x;;, and hence the averages, have already been freed
of the linear drift of the whole fringe system in the same
manner as Miller did it. Suppose that these 320 values be considered as random sample values drawn from a
normal population. Furthermore, suppose the arrangement into columns and rows is a random one. Then statistical theory shows that the variance of x may be resolved into a contribution due to variation of the individual entries in the columns about the column means and a contribution due to differences between column means and the mean of the whole assembly. A
measure of the relative significance of these js the
statistic Ii defined by
— 16 P (x, x)'
320y19 ' 1
Under the hypotheses of randomness and normality
of population, the probability that F for a given sample
will exceed a given value has been tabulated. For the number of degrees of freedom involved in the present data, theory shows that the probability of obtaining by
F) pure sampling fluctuation an 1.71 is only 0.05; the
J") probability of obtaining an 2.21 is only 0.01. These
probabilities are accepted limits for rejecting the hypothesis that the array could have arisen by sampling fluctuations in a normally distributed population. When a large number of data sheets are analyzed, one would
expect only one out of twenty to exhibit an J &1.71 if
the population of which the sheets are samples consists
only of randomly fluctuating data. If many of the data
sheets lead to an P-value greater than the limits quoted,

170

SHANKLAND, McCUSKEY, LEONE, AND KUERTI

100-

O C
Ol
U
CP L
u
50-

5% Point l% Point
I

S

6

7

Va lue

FIG. 1.The distribution of F-values for 216 sets of Mount Wil=on
data. The smooth theoretical curve is normalized so that the area
under this curve is equal to the area of the histogram.

it is highly probable that some systematic effects are

present in the data. Figure 1 shows the frequency distribution of the Ii-

values computed from the data sheets together with a
theoretical distribution of F appropriate to the number of degrees of freedom involved. It is apparent immedi-

ately that the observed number of large F-values far

exceeds the number to be expected on the basis of a

random sampling from a normal population. In fact,

36.5 percent of the J -values exceed the critical value

1.71, and 25.3 percent exceed the value 2.21. The

analysis indicates that the fluctuations in the column

means cannot be attributed entirely to random effects,

but that systematic effects are present to an appreciable

degree.

A second method also shows that the periodic eGects

observed by Miller cannot be accounted for entirely by random statistical fluctuations in the basic data. Five

representative were subjected

sheets to an

with original autocorrelation

unapnraolcyessisse. d'

data These

sheets were selected as typical of the Mount Wilson

data. Miller had deduced for them. second-harmonic

amplitudes of 0.021, 0.045, 0.059, 0.082, and 0.123

fringe respectively. Thus they embrace nearly the entire

range of the second-harmonic effect which is under

examination.

In three sets of data (Nos. 42, 75, and 79 in Table II)

a strong period of 8 (second harmonic) was found rela-

tive to those of periods 4 through 12. However, in the

We are indebted to R. L. Stearns, Dr. E. F. Shrader, and Dr. L. L. Foldy for making the autocorrelation analysis; the MS thesis of R. L. Stearns, Case Institute of Technology, 1952, gives details
of the analysis and description of machine used.

other two sets of data analyzed by this method, the period of 8 was no more prominent than the other periodic components. This indicates that the true magnitude of the systematic eGect varies greatly with the conditions of observation, as would be the case if caused by local disturbances. A summary of the pertinent re-
sults regarding the period of 8 is given in Table II. The
units in the table are fringes.
Column 2 gives the amplitude of the second harmonic
as obtained from the Henrici machine by harmonic analysis; column 3 gives the amplitude deduced from
the correlogram and contains whatever random Quctua-
tions are in the data; column 4 gives the amplitude with
the random effects removed. It is again apparent that
random statistical processes contribute considerably to the periodic eGect when it is small but that the larger amplitudes are relatively unaffected and cannot be
explained in this manner.
Consider next the actual harmonic analyses of the Mount Wilson data. Miller's harmonic analysis records
give amplitude distributions for the first five harmonics for which the relevant statistical parameters are sum-
marized in Table III. The values of the mean amplitude Aq(k=1, 2, . 5) and the standard deviation s(AI) have
been computed directly from his data cards. Altogether, for the four seasons, 306 sets of data were used. There is
no significant seasonal variation in the mean amplitude
of the second harmonic, the values of 32 being 0.042, 0.049, 0.038, and 0.045 fringes for April, 1925, July,
1925, September, 1925, and February, 1926 epochs
respectively.
Table III indicates clearly the dominance of the first
and second harmonics over the others in the harmonic
analyses. While the third, fourth, and fifth harmonics
have an order of magnitude equal to the standard
deviations, the first and second harmonics are con-
siderably larger. However, the average A2 here is only 1/13 of the value to be expected on the basis of the usual
aether-drift hypothesis. It is interesting to note that
among the trials which yielded unusually large ampli-
tudes of the second harmonic (A2) 0.08 fringe), 14 out of 17 were made either at the beginning or the end of a
series of observations, or were made under adverse
conditions noted on the data sheets. The question now is, "What part of the observed
average amplitude for the second harmonic, deduced by harmonic analysis, may reasonably be attributed to
random statistical fluctuations in the data)" I.et sets of

TABLE II. Summary of autocorrelation analysis.

Sheet
15 23 79 75 42

Miller's observed
A2
0.021 0.045 0.059 0.082 0.123

Correlogram

Uncorrected A2

Corrected for random eÃects

0.032 0.054 0.062 0.079 0.129

0.013 0.043 0.060 0.078 0.126

NEW ANALYSIS OF THE INTERFEROMETER OBSERVATIONS

observations be selected at random from a population

which is normally distributed and be plotted as ordinates

with the order numbers of drawing as abscissae. Suppose

a harmonic analysis is made of each set. Then the

probability that an amplitude of a kth harmonic, AI„

chosen at random among the sets, will lie between A and

A+dA

is
P(A)dA

=nh'

exp( —h'nA'/2)AdA,

where e is the number of observations analyzed and h is
the measure of precision of the population. From this,
the mean amplitude Ai, often designated M(AI, ), and
the standard deviation o-(A~) are found to be, re-
spectively,

(2nh')

(4-~q &
and o(A~)=l

independent of k.
A tabulation of the values of S; irrespective of the azimuth i from which Miller made his harmonic analyses
indicates an approximately normal population with a standard deviation 0.05 fringe. Thus in this extreme case, if all of the variation in the data used for analysis were attributable to random Quctuations, one would expect
A~ —0.023 fringe and o-(Aq) =0.012 fringe.
On the usual assumption that the squares of the random and systematic contributions to amplitude add to pro-
duce the observed (A,)', it appears that not more than
15 percent of the second-harmonic amplitude can be due to statistical causes. This is in accord with the result of the autocorrelation analysis and leaves an average
residual amplitude of A2=0.038 fringe to be explained
in other ways. Thus there can be little doubt that statistical Auctua-
tions alone cannot account for the periodic fringe shifts observed by Miller. On the other hand, the presence of a
periodic e6'ect in the column means x; may be clearly
demonstrated in a way which again exposes the incompatibility between the phase anomalies already noted and the usual kinematic accounting in aether-drift experiments.
When the x; for twenty sheets of the July —August,
1925 Mount Wilson data are plotted as a function of
azimuth index i, the result is as shown in Fig. 2. These
sheets have been chosen so as to span the Z4 hours of the sidereal day. There is obviously considerable scatter in
— TAsrz III. Summary of harmonic analyses Mount Wilson data.

Harmonic

Mean amp.'itude Ag, (fringes)
0.046 0.044 0.011 0.007 0.005

Standard deviation s(Ah) (fringes)
0.033 0.022 0.008 0.005 0.004

;10-
Xi
~~~
~g0
0—
~I
~~
—I. O—

~~

I~

I

~

~

~ss~~
iI~

I
~

'w
I

+ I

I

j~ ~

~ 'I

~ ~

~

g

I

s
~

~
I

~

!

~

~

~

~ ~

g

l

1

I

I

I

I

6

8

IO

l2

l4

l6

Azimuth index i

FIG. 2. The individual column means ii are plotted as a function
of azimuth pcsition for the July, 1925 observational data. Large circles and the connecting curve show the second harmonic effect exhibited by the averages, (z;), due to ordering in azimuth. Units
for the ordinate are fringes.

the x; at each azimuth position, but the average values

(x,), calculated for each index, shone a marked second harmonic effect The lar.ge filled circles represent the (x;).
Similar results have been found for the other three

epochs of the Mount Wilson observations.

Now let the aged with those

values
for i=

of 1,

(x,) 2, 3

for i=9, 10 .
8. When this

16 be averis done and

a smooth curve is drawn through the points, the result
is the curve labelled "July" in Fig. 3. Similar curves for

the other epochs are also shown in the figure. Twenty

data sheets, representative of all sidereal times, were

used for each sample.

Note that all of the resulting periodic functions have
amplitudes between 0.02 and 0.03 fringe, but that they
differ in phase. Particularly striking is the difference be-

tween the February, 1926 result and the others.
It is, on the other hand, possible to caLculate in a

rather straightforward way the fringe shift pattern,

averaged o~er all sidereal times, to be expected on the

assumption of an absolute motion of the earth through

an aether on the basis of the usual kinematic considera-

tions. Let V be the vector velocity of the earth at a

given epoch toward an apex whose celestial coordinates
are rr, 8; let V„be the projection of V in the plane of the

interferometer, q be the latitude of the observer, and P
be the azimuth of the telescope arm of the interferome-

ter measured from the north point through the east.

Then calculation shows that the value (hn)A, of the

fringe shift, averaged over all sidereal times, is given by

(hn)A. = V'F(5, q) cos2$.

(1)

Since q is constant and 8 is axed at a specified epoch,

an average fringe sults. Clearly, the

shift angle

of P

seeqcuoanlsd-h2azr.m(io—nic1)/1n6ataunrde

rethe

computed (An)A, corresponds to the observational
—'[, (x,)+(x;+s)7. Thus there is a direct correspondence

between the curves of Fig. 3 and Eq. (1), and no phase

172

SHANKLAND, McCUSKEY, LEONE, AND KUERTI

-a

a

o~~

IX

~x X

0

XX

e~ ~

0

~IVX'

-IoI

FEB JULY
x SEPT. APRI I.

4 Azimuth Index

I

I

8

9

Fro. 3. Second harmonics in the —',[(a,)+(z;~)] for the four epochs
of the Mount Wilson data.

anomalies of the kind observed in Fig. 3 are permissible. The four curves should have a conTTnon maximum (or
minimum) at s= 1; only the amplitude may be different
at diGerent epochs.
" This criticism is, of course, only different in form from
the objections raised by v. Laue' and Thirring. Both authors point out that the Lorentz criterion, which requires the mean value of V„over a sidereal day to be a vector in the meridian, is not satisfied by the results of the Mount Wilson observations of 1921 and 1925, and Thirring shows for a single daily pattern of these observations that it cannot be made to coincide with
any one of the daily patterns derivable from the usual kinematic theory upon variation of 8. The present form of the criterion, if it may be so designated, is perhaps more convenient when a large amount of data is to be
checked for consistency. In the interpretation of his observations, Miller
hypothesized that, for unknown reasons, the daily swing of the vector V„might be symmetric about some line other than the meridian, the angular deviation from the meridian being permitted to vary from epoch to epoch. In terms of Fig. 3, this is simply the deviation of the 6rst
UP, „; mfAigcautxuriemalluydm,itf)f=eMrfsriioldclmeeorrnesatdihldreeewtriamnboletryh)tehfocfpurroroevmianecsth,thAobofusteIttshe0ftho(feuAonuda=rngebalpzyeoismcMhuisntihllaeonruo.drf'
determined his anomalies from what he called the "own axis" of the plot. The meaning of that term is obscure. Contrary to expectation, it does rot designate the hori-
zontal axis through the centroid of the observational
curve, since the ratio of the upper to the lower area is
found to be 1.3, 1.7, 1.4, and 0.6 respectively for the four
epochs.
Under these circumstances, little significance can be
attached to the remarkable agreement between the
values of o. and 6, computed from the V„vs 8 curves on
the one hand and from the A vs 0 curves on the other
hand, as presented in Tables I and II in reference 2, p.
230. The second method of computing uses the 0 values
at which A passes "its own axis" and the quantity
, both taken from the curves. Both parameters

" depend, of course, on the choice of the "own axis, but

the first of them is extremely sensitive to that choice and,

furthermore, is directly equal to the right ascension of

the apex, 0,. Hence, even if one were to accept the

azimuth anomalies as an unknown effect to be explained

by a more re6ned theory, any numerical results based on

the A vs 0 curves should be accepted with reservation.

Whether a reliable determination of the other pair of
, parameters, U„, /UP, ;„and f)v„, ;„,from the U„TIs 0
curves is at all possible has not been decided. The

method of averaging small groups of U„-values (each U„

corresponding to one set of twenty turns) in order to

obtain twenty V„-averages roughly equidistant in 0, and

the use of these twenty points as true representatives of

the curve sought cannot be considered statistically

satisfactory because of the enormous scatter of the

observational results. However, a more refined rede-

termination of these parameters that enter the 6rst

method of computation did not seem justi6ed to us for

the following reasons.

If the azimuth anomalies are accepted, then Eq. (1)

establishes the simple connection,

. (An) A.. ——U'F (fi, ioII)

(2)

between the maximum of the fringe shift average ob-
served during the epoch and the function F(o, yII), whose
derivative with respect to 5 can be shown to vanish for
, fi = 90'. Now, (An)&„, „changes only slightly from epoch
to epoch (cf. Fig. 3), which makes it feasible to satisfy
(2) approximately by the same constant vector V for all epochs. However, the vector V must contain the variable
contribution of the orbital motion of the earth. This
difficulty may be overcome by choosing a cosmic VII such
that Vp)) V„b;~„i and bp is not far from 90'; but a further obstacle arises here, namely, at 8= 90', F (8, pII) becomes
simply a' cos'pp, where u' is a constant completely determined by the geometry and wavelength of the interferometer. Thus, the magnitude of Vs+ V„b;~,t cannot be chosen freely. A reduction factor becomes
, necessary so as to make (An)A, , ——k U'F(b, ipII) where k
is about 1/20 in Miller's cosmic solution.
It seems to us on the basis of this discussion that the
internal consistency of the cosmic solution is not so
great a surprise as it appears at 6rst glance. It certainly
is not cogent enough to serve as a logical support of the claim that the half-period effect observed is a true aether-drift effect. We therefore did not embark on a
statistically sound recomputation of the cosmic solution,
but rather concentrated our eGorts on an interpretation of Miller's observations in terms of systematic local
disturbances such as may be caused by mechanical effects or by nonuniform temperature distributions in the observation hut.

POSSIBLE MECHANICAL EFFECTS

-' M. v. Laue, Handbuch d. Experimenta/physik (1926), Vol.

XVIII, 's H.

pp. 95, 101. Thirring, Z.

Physik

35, 723 (1926); Nature

118, 81

(1926).

The question may be raised whether some of the local causes which are responsible for Miller's results can be
found in the mechanical performance of his apparatus.

NFL ANALYSIS OF THE INTERFEROMETER OBSERVATIONS

Miller's papers and notebooks do not offer much perti-

nent material but information from

it
his

hraespobret,en'

possible from the

to extract some originals of the

photographs published there, and from interviews with

former co-workers. These data make it possible to

investigate the motion and deformation of the steel

cross carrying the optics of the interferometer.

The cross consists of four arms bolted together, each

arm being a box structure held together by rivets. The

central portion of the cross rests squarely on a wooden

support which Aoats on mercury.

Consider the beams B» and B2, each formed by one
pair of opposite arms. If the supporting Goat is hori-

zontal, the ends of the beams will sag under the inhuence

of gravity somewhat below the level of the supported

central portion. Now let the cross turn about the beam

B2 through a small angle n». This will cause the beam B»

to unbend slightly, since only t1;e component of gravity

normal to the beam contributes tv- the bending moment.

The mirrors rigidly connected to the ends of B» will

therefore suffer small additional ro,"ations in opposite

directions about axes parallel to B2. A:,~cry small change

in the length of the light path will be th» consequence of

this change in the relative position of the mirrors on B».

In reference 2, p. 215, Miller supplies direct evidence

of the effect of bending, when he states that an end load

" of 282 g placed on one end of the four arms produces a
shift of one fringe. We may reasonably assume that
half this load, 8=141 g, placed simultaneously on two
opposite arms would have produced the same effect; a

simple argument now gives the fringe shift due to an

angular rotation e» about B2 in units of one fringe as

— rci = (1 coscc,)q/6,

(3)

where q depends on the weight of the beam and on its distribution, and the analogous formula holds for a
rotation o.2 about B». We obtained" for q the value
48X10' g. From Eq. (3) we can find the angle czi necessary to
produce a total fringe shift e»=2X0.044, which is the
mean of the observations on Mount Wilson. The result
is e» —1.3', which seems too large to permit an interpre-
tation of the observed fringe shifts in terms of a wobbling
motion of the slowly rotating cross (one turn in 50 sec). But smaller libratory irregularities, perhaps of the order of a few tenths of a degree, must undoubtedly have been present in Miller's experiments. In order to find out
about their possible contributions to the results, the
dynamic constants of the apparatus in rotation were
determined, and a simple analysis of its motion was
made.
"This figure is not strictly a constant; according to a check on
"It February 4, 1926, it is 313 g. will be noticed that the quantity 8 is determined when the structural properties of the cross, the geometry of the light path, and the wavelength are known. The calculated 5 came out about twice as large as 8 given by Miller, but an overestimation of the stiffness was to be expected, since no correction for incomplete fixity of rivets and bolts was made. We wish to thank F, Krasnoff for his assistance in these computatioi»s.

Assuming the apparatus strictly symmetrical about the vertical, one obtains for the moments of inertia C and A about the vertical symmetry axis and about a horizontal axis through the center of mass, respectively,
C= 1.67X10"g-cm', A = 9.05X10' g-cm'.

The center of mass is 48.5 cm above the centroid of the displaced mercury, and the metacenter is 210.5 cm above the center of mass. The restoring moment produced by a small angle 0 between the symmetry axis of the apparatus and the vertical is OD, where
D = 2.48 X 10" dyne-cm.

The period of roll about a horizontal axis through the

center of mass is therefore only 1.20 sec.

The motion of the system may be considered as that

of a (hanging) top. The restoring couple is 0D. Depend-

ing on the fixity of the centering pin (which was not the

same in all experiments), the fixed point may be

identi6ed either with the center of mass itself or with the

bearing of the pin, which is about 51.5 cm below the

center of mass. The equatorial moment of inertia is in
this latter case A=1.22X10" g-cm', C and D are, of

course, unchanged.

Let us consider the motion in the neighborhood of

steady rotation about the vertical axis of symmetry.

The values of the constants A, C, D, together with the very small spin r = 2'/50 sec ', are such as to preclude

" regular precession, whichever fixed point is chosen. The
motion is of the "rosette-type, the instantaneous

position of the symmetry axis being given by"

8 =rt sincuit, cubi —L(C'r'+4AD)/4A']'*

f=cezt,

coz —(C/2A)r.

(4)

Here 0 and P are the polar coordinates of the axis of symmetry, and q is an amplitude constant characteristic of the asymmetry of the initial impulse.
It is now possible to 6nd an approximate expression
for the fringe shift due to angles n» and o,2 subtended
simultaneously by B» and B2 with the horizontal plane,
when the symmetry axis moves according to Eq. (4).
One obtains
t) e= ei —rtz —(pW/25)rP sin'[e~it] cosL2 (r —arz) t]. (5)

The circular frequency cubi is very close to (D/A)' and corresponds to the roll period mentioned before. Thus Dn oscillates with twice the roll frequency, the ampli-
— tude being modulated with the circular frequency
2(r coz). The value of coi is not very sensitive to a change of the 6xed point; the roll period increases from 1.20 sec to 1.40 sec if the fixed point is assumed at the pin bearing. The period of modulation, however, decreases from 39 sec to 10 sec if, instead of the center of
mass, the pin bearing is assumed fixed. Obviously, these rapid oscillations cannot account for
"F. Klein and A. Sommerfeld, Ueber die Theoric des Ereisels
(Leipzig, 1898), p. 331.

SHANKLAND, McCUSKEY, LEONE, AND KUERTI

the true second-harmonic period (25 'sec) which strongly

dominates such runs as shown by sheets 79, 75, and 42 in
Table II. Beyond that, one may in general expect the

contributions of these oscillations to cancel each other in

the average throughout a set of 20 runs. In order to

estimate the efFiciency of the averaging process, assign

to the amplitude constant ti the (improbably large)

value of 0.5'; compute a table of 20 rows according to

Eq. (5) by setting 3 = 50k/16, where k = 1, 2, 320; and

determine the column averages (its)A, , ;. It turns out

that the maximum value of (its)«, ; stays well below

~

~

0.005 fringe.

These conclusions would not be strongly affected by a

slight asymmetry of the apparatus about its vertical

axis as must undoubtedly have been present.

EFFECTS OF TEMPERATURE
Miller's 1923 laboratory tests of the eGects of thermal variations on the interference fringes have been studied with the view of establishing their relationship to his
Mount Wilson observations, where temperature eGects due to intense sunlight during the day and to canyon air currents at night were often troublesome. Miller's own suspicions that thermal eGects might be important are shown by the entry in his laboratory notebook for April
14, 1921:"Sun shining full on side of house, There was a
very large drift which seems to be in the direction of the sun; indicating possibility that the entire effect is due to temperature I"
In the laboratory tests, electric heaters were placed at
the level of the mirrors and about three feet from the circle travelled by them. The altered refractive index of the heated air and the thermal effects on the mirror supports change the optical path lengths of the interferometer, and when these are affected unequally in the two arms, the fringes shift in position. On the assumption that the four arms of the interferometer all have the same thermal insulation, a localized temperature anomaly or a temperature gradient across the room will produce a second-harmonic term in the fringe positions as the interferometer rotates, similar to that anticipated for an aether drift.
Localized heating will also produce a first harmonic in the fringe displacements when one of the four interferometer arms, for example that containing the observing telescope, has difIerent thermal insulation properties from the others. The effects of heat on the 3rd, 4th, 5th, and higher harmonics of the fringe displacements should be small for any temperature conditions likely to be encountered.
The laboratory tests of 1923 were conducted with various amounts of thermal insulation protecting the light paths and mirror supports. In some trials the air was directly exposed to the heaters; in many cases the
glass and wood casing that served at Mount Wilson as
insulation for the light path was employed; and in certain experiments additional corrugated paper was placed over the vertical glass walls of the casing, the

TAnLE IV. Laboratory heating trials (unit: fringes).

Periodic amplitudes
AI
Ag A3 A4 Ae

Controls

Set 17

Set 28

0.006 0.015 0.006 0.004 0.001

0.006 0.010 0.005 0.003 0.001

Heat

Set 18

Set 29

0.010 0.049 0.009 0.006 0.003

0.021 0.05Z 0.005 0.011 0.002

mirror mountings, and in some cases over the steel base of the interferometer as well. In the experiments where the air in the optical paths was directly exposed to heat,
large second harmonics (As=0.35 fringe for one heater,
and about twice this value for two heaters) were always observed in the fringe displacements, and with the expected phase. Shifting the heaters to a diGerent azimuth produced a corresponding change in the phase of the second harmonic. When the optical paths and mirror supports were thermally insulated, the second harmonics were greatly reduced; for example, with the
glass coverings as used at Mount Wilson in place, the amplitudes were reduced to about 0.07 fringe.
Among the laboratory trials made by Miller at Case in 1923 are four sets of observations which reveal rather clearly the character of the temperature effects. In these
sets the optical paths of the interferometer were en-
closed with the glass thermal insulation as used at
Mount Wilson, and, in addition, corrugated paper was placed over all arms of the interferometer. In two of these trials no artificial heating was used, but in each of the two sets immediately following these controls, the heater, in the position mentioned above, was in operation. The results of these experiments are given in
Table IV. It is evident that the heater produced dis-
turbances which increased the amplitudes of all five harmonic components. However, the egect on the second harmonic A~ is much the largest, as is to be expected on physical grounds. Furthermore, the phases of the second harmonic in sets 18 and 29 have values consistent with the position of the heater. The first harmonic A1 "-'=. somewhat increased by heat, and for this also there is some physical justification. The increases in the ampli-
tudes A3, A4, and A5 are much smaller.
It must be emphasized that the foregoing analysis of
these tests reveals small but certain temperature eGects, in contrast to Miller's statement that he had shown the
absence of periodic eA'ects caused by artificial heating when the light path was thermally insulated as previ-
ously described. ' Similar conclusions regarding .the danger of spurious second harmonics due to thermal conditions were reached by Joos in his elaborate preparations for a repetition of the Michelson-Morley experiment at Jena. In fact, Joos concluded from his labora-
tory trials that temperature disturbances would be so serious that photographic recording of fringe positions
"See reference 2, p. 220.

NEW ANALYSIS OF THE I NTE RF E ROM ETE R OBSERVATIONS

" would be impossible except in a well-insulated basement
laboratory.

tion with ridge at 20 to the N—S direction, and with its under side only a few feet above the thin wooden cover

Thus Miller's experiments in 1923 do not rule out the of the casing of the light paths. We conclude from the

possibility of attributing the remaining systematic foregoing estimate that an interpretation of the system-

egects in the Mount Wilson data, which are most atic e8ects in terms of the radiation field established by

prominent in the second harmonic A2, and to a lesser the nonuniform temperatures of the roof, the walls and

degree in the first harmonic A~, to temperature causes. the Boor of the observation hut is not in quantitative

In what follows, we shall interpret the systematic eGects contradiction with the physical conditions of the

on this basis, but must admit that a direct and general experiment.

quantitative correlation between amplitude and phase

In view of the local factors affecting the temperature

of the observed second harmonic on the one hand and conditions of the interferometer, we may now ask

the thermal conditions in the observation hut on the whether the epoch averages shown in Fig. 3 should not

other hand could not be established. The reason for this in some way correlate with what is known about the

failure lies in the inherent inadequacy, for our purpose, mean temperature conditions at the several epochs.

of the temperature data available.

Thus it has been noted that in Fig. 3 the curve of the

I.et us first discuss the physical consequences of the February, 1926 observations differs considerably in

weak radiation field maintained across the hut by the phase from those for the other epochs. We believe this

temperature differences of the walls. Since periodic
temperature variations of only 0.001'C in the air of the
" optical arms would produce fringe shifts as large as the
average eGects observed at Mount Wilson, a very

behavior is correlated with the fact that throughout the February experiments the thermometers on the north and west walls of the house consistently registered
temperatures from 1'C to 2'C lower than the south and

conservative estimate was made of the wall temperature east wall thermometers. This situation resulted pri-

differences necessary to produce temperature oscillations marily from a blanket of snow which covered the ground of that magnitude. For this purpose it was assumed that on the N —W side of the hut. Furthermore, the west wall

(1) the ambient air temperature in the hut was es- of the hut was water-soaked throughout the February

— sentially constant, (2) radiation was absorbed only by runs. As a result the average temperature gradient
the vertical glass plates of the casing, and (3) heat through the hut was in the general SE &NW direction in

" transfer from the glass to the air inside the casing was by
conduction only. The resulting wall temperature differences are about ten times as large as those usually

February, in contrast to that in July and September, 1925 when the temperature gradient averaged throughout a day was more nearly along the N—S line.

recorded by the four thermometers located on the walls of the observation hut. There is no doubt, however, that
this factor ten would be very considerably reduced if

Turning now to single sets of observations, we may first try to correlate the smallest fluctuations
f occurring" in the Mount Wilson sets with the ther-

convection of th'e air inside the casing were taken into mometer readings. There are eleven sets with f-values

account and if the contribution of the cover of this casing, facing the roof of the hut, could be evaluated.
In reality, however, the effects of temperature on the apparatus must have been very complex, being mixed contributions of changes in density of the air in the

smaller
=av.

than
T; T~

0.015 fringe.
(i=1, 2, 3, 4)

—asIf

we an

introduce indicator

(DT)A, of uni-

~

formity in temperature conditions, where T, denotes a

thermometer reading, then (AT)A„ranges from 0.02'C to

0.25'C with a mean value of 0.11'C for these ob-

optical paths, angular deflection of the mirror supports, servations.

and thermal expansion of the steel frame, the latter
e6ect introducing a long time lag. It is practically im-
possible to carry through calculations which would

Thus small f-values usually go with small (AT)„„ values, but the correlation is very incomplete, as (AT)A„
values of 0.2'C are very often found in the Mount

predict the over-all behavior of the interferometer due Wilson sets. Furthermore, sets with small f-values

to temperature anomalies, since hardly any of the usually do not compose a normal population. For ex-
necessary data for such calculations exist. In fact, the ample, if (S;+x,+s)/2 is computed for half of one of

readings of the four thermometers constitute all of the these sets, then usually a much larger f-value results.

available information about the temperature (and This agrees with the existence of periods other than 8

radiation) pattern in the hut. They give essentially the found in the autocorrelation analysis of the two samples
air temperature along the wall (but not the wall having small A~ shown in Table II and indicates that

temperature), and say nothing about the temperature many of the small f-values observed are the result of

distribution along the roof, itself a low-gable construc-

'5 According to the personal communication from Professor G.

Joos (1954); see also reference S.

'6 This figure is in agreement with similar estimates made by

R. J. Kennedy, Proc. Natl Acad. Sci. 12., 621 (1926); and by G.

Joo"sW, Pehyasr.e

Rev. 45, indebted

114 (1934). to our colleague

Dr. H. G. Klrod

for these

calculations.

chance cancellations.

()0. If, on the other hand, the largest f-values

08

fringe) are considered, one is left, after elimination of

"I.et averages x; be calculated as on p. 169 and consider

(g;+g;+s)/2 as an approximation to the amplitude of the second

f harmonic. The maximum absolute difference between m~r of these

numbers will be denoted by 2f, where the fluctuation

now

correspondS to Aq.

176

SHANKLAND, McCUSKEY, LEONE, AND KUERTI

sets where remarks such as "sun shines on interferome-

ter" occur, with a selection that appears to consist of

two different groups. In one group, including sets 103

and 106 of March 28 around 5:00 P.M. ; 128 of April 8, 5:00 P.M. ; 135 of April 9, 3:00 P.M. ; 45 and 47 of
September 17, before noon, 68 and 69 of September 19,

around 8:00 A.M. ; and sets 4, 5, 6 of February 4, around

()0. 3:00 P.M. ; and 12 and 13 of February 5, around noon,

(AT)~„ is large

4'C). In the other group, which

includes sets 72 to 75 of August 6, around noon; sets 80

to 82, soon after sunrise on August 7; 88 to 90 near

midnight of August 7 and 8; and 91 to 94 following sunrise on August 8, (AT)A„ is about 0.2'C or smaller.

Thus in the April, September, and February epochs

the largest occurring f-values are associated with large

(AT)&„values, but not so in the July epoch. We have no

certain explanation for the existence of large eGects

when the wall thermometers give reasonably small

(AT)~„values, but would point out that no temperature

data are available to reveal thermal conditions at the

roof, which may be responsible for the large fringe

displacements at the times of highest altitude of the sun.

Although the thermometer readings cannot be used to

describe the thermal conditions in the observation hut

in all cases, they should nevertheless provide an indica-

tion of the stability of the thermal pattern in the hut

affecting the fringe positions, particularly during the night hours. Accordingly the Mount Wilson data for

each of the four epochs of observation have been

searched for sets of readings taken during this part of

the day and which exhibit "similar" temperature

patterns.

Ideal observing conditions could obtain if all four

thermometers read the same and remained constant

throughout a series of observations. Departures from

the ideal always occur, and the extent to which tempera-

ture disturbances are revealed by the recordings of the

thermometers may be estimated by applying the

following criteria:

1. The magnitude
ture difference(AT)Av

of the
((T;

average absolute T))Ay(i=1, 2, 3,

4)te.—mpera-

2. The time rate of change of the temperature pattern

in the room as indicated by the readings of the four

thermometers.

3. The drift in mean temperature, T, with the time.

4. The linearity of the drift of the fringe pattern and

the nonreversal of sign of this drift during a series of

observations.

The last two criteria are particularly important because of the complex time lag in the thermal behavior of the heavy steel interferometer base and the mirror supports.
Thus, on the hypothesis that the second harmonics of the fringe displacements are due primarily to temperature conditions, the observed fringe behavior throughout a set of midnight-dawn experiments should be the same within t,ice experimental uncertainties on nights when the temperature conditions remained rather constant, as

I

I

I

I

I

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.ps—
EO
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a p—
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s (4'-

Op
p 4
l9—

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2 34 56 7 89

AZIMUTH INDEX

Fz( . 4, The temperature pattern in the observation hut and the

observed fringe shift is shown here for three dates: Fig. 4(A),

August 30, 1927 (Cleveland); 4(B), September 23, 1925 (Mount

Wilson); 4(C), July 30, 1925 (Mount Wilson). Each group of four

points in the upper parts of the figures represents the thermometer

readings on the four walls of the hut at a given time between

midnight and
Arrows at the

dawn (a range of about left of the temperature

s5calheosurisndiincatseidearea1l '

time). range.

The lower part of each 6gure shows the fringe shift as a function of

azimuth index for the times corresponding to the temperature

patterns. The lower part of each figure shows the fringe shift as a function of azimuth index for the times corresponding to the

temperature patterns. The dashed curve in Fig. 4(C) shows the

fringe displacement when direct sunlight fell on the interferometer

at dawn.

defined by the criteria above. This, in fact, is the case. Figure 4 illustrates the observed inhuence of several
temperature conditions on the second harmonics of the
fringe displacements. Figure 4(A) shows ten sets of observations, Nos. 31 to 40 inclusive, made in the hut on
the Case campus between midnight and 5:00 A.M. on August 30, 1927. During this entire interval the readings
of the four thermometers were remarkably constant, the
average temperature changing by only 0.4'C. Likewise

NEW ANALYSIS OF THE INTERFEROMETER OBSERVATIONS

177

the second harmonics are almost identical in both phase and amplitude throughout the entire series. This be-
havior persists throughout almost five hours of sidereal time as the earth makes nearly ~ of a revolution and would be extremely unlikely if the fringe shifts were due to any cosmic eI'.-ect. On the contrary, it strongly supports our hypothesis that local temperature conditions are the dominant factor producing the observed second
harmonics.
Similar correlations between the observed second
harmonics and the temperature conditions existing from midnight to dawn can also be made in each of the four epochs during the Mount Wilson experiments. In all but one case where the criteria given above indicated good temperature conditions, the second harmonics were
nearly alike during the time interval encompassed by the observations. A typical example of Mount Wilson results taken under rather good temperature conditions
is shown in Fig. 4(B) for runs 75 to 83 inclusive taken from 12:18 A.M. to 6:00 A.M. on September 23, 1925. Figure 4(C) will be discussed later.
Other sets of Mount Wilson data taken under steady temperature conditions and which show constancy of both amplitude and phase in the second harmonics of the fringe displacements are the following: April 2, 1925,
" sets 113, 114, 115, 116, 117, and 118, taken between 1:52
A.mr. and 4:58 A.M. On August 8, 1925, sets 88, 89, 90, 91, 92, and 93 were made between midnight and 6:26
A.M. and with similar room temperature patterns
throughout, and again the amplitudes and phases of the second harmonics are nearly alike. A final example is
provided by data taken between 2:30 A.M. and 6:38 A.M. on February 11, 1926, in sets 84 to 91 inclusive. Here
again the temperature patterns during all runs are
similar, and within the experimental errors, all the
second harmonics are alike. The April 2 and September 23 runs show another im-
portant property, namely that the maxima of the second harmonic curves are definitely removed from the north
point (the maxima of the other two night runs being
close to it). This behavior throughout nearly six hours
of sidereal time coecllsively rules out cosmic eGects. It
also removes magnetostriction as the possible cause of
the fringe displacements, since the interferometer steel
cross was not dismantled during the four epochs of the
Mount Wilson observations; hence any magnetostriction effect should not change its directional character during
the four epochs. In addition to the night runs cited above, daytime
conditions occasionally gave steady temperature conditions as judged by the aforementioned criteria for three or more consecutive sets, which then usually showed similar second harmonics. When temperature conditions
departed markedly from the ideal as defined by our
"This run was followed by sets 119 and 120 taken after sunrise, '
when the temperature pattern in the room had changed due to heating of the east wall of the hut. These latter sets exhibit considerably increased amplitudes and different phases in the second harmonics.

criteria, widely varying second harmonics, both as
regards amplitude and phase, were observed in consecutive sets.
Particularly remarkable among the daytime observa-
tions are sets 56, 57, and 58, made in 1924 in a basement room of the Case physics laboratory between noon and
6:00 p.M. on July 8, which give almost identical null results. In fact, throughout most of the turns of the
interferometer the fringes showed no change in position whatever. The temperature conditions were ideal; all four thermometers gave identical readings throughout
each set of observations, and the drift in average room
temperature was only 0.1'C throughout the entire afternoon. If our hypothesis is correct, then this group
of observations is the best ever made with Miller's
" interferometer and shows the zero eGect consistent with
the results of other experimenters.
Among the Mount Wilson night sets there is, however, ore unusual series of observations, Nos. 21 to 28 in-
clusive, made between 1:43 A.M. and 6:04 A.M. on July 30, 1925. Here the temperature criteria are in part
violated (but not very strongly), and in part satisfied, yet the run shows an extremely erratic behavior
LFig. 4(C)]. We have no ready explanation for this
" apparent departure from the four other night runs with
"steady thermometric conditions. Perhaps the fact that the canvas over the roof was not yet installed is the reason; or again canyon winds may have been unusually
troublesome. It is certainly not possible to blame the
lack of regularity of this run on the statistical incom-
pleteness of its single sets. If one reduces half of a set by
Miller's method, one obtains essentially the same result as that obtained by reduction of the whole set, the agreement between the two results becoming pro-
" gressively closer during the course of the night' s
observations.
The run of Fig. 4(C) differs in the following respect from the other night runs. One may define some measure of the "noise" of a set of observations by taking the average, for the whole set, of the absolute values of the first differences of the single readings. In the run shown in Fig. 4(A), one so finds 0.079 and 0.063 fringe for sets 31 and 32 around midnight, and this figure drops steadily to 0.035 for No. 40 at 5:00 A.M. In the Mount
Wilson night runs, with the exception of that of Fig. 4(C), the corresponding "noise" drops from about 0.110 to about 0.060 fringe, while it decreases from 0.190 to
~ Sets 57 and 58 were made with sunlight, rather than the usual acetylene source employed in set 56. The null results obtained with sunlight are of especial interest in that they disprove the Ritz
emission theory of light. Trials of the Michelson-Morley experiment with sunlight or starlight had been urged by Tolman and
al&~ 'u~ aRosa to test this point, see R. C. Tolman, Phys. Rev. 35, 136 (1912); M. LaRosa, Nuovo cimento 3, 343 (1912); Phys. Z. 13, 1129 (1912).
2' T'.:i" holds for all of these night runs; in particular, the sets
sho~vn in Fig. 4(A) from No. 33 on have a surprisingly high degree of statistical completeness in the above sense. Together with the
autocorrelation results of Table II for sets 42, 75, and 79, this seems
t ~ justify Miller's method of correcting for drift by assuming it to
be linear.

SHAN KLAN D, Mc CUSKE Y, LEONE, AND K(JERTE

0is.1o0m0iitntedth. e'

night This

run of Fig. 4(C), if the last set, No. 28,
indicates an irregularity in the condi-

tions of the exceptional run which is not present in the

other night runs and is hardly rejected in the ther-

mometer readings.

CONCLUSIONS
We believe that this discussion of the eGect of temperature permits the following inference: Under the most favorable experimental circumstances the second harmonics in the Mount Wilson data remain essentially constant in phase and amplitude through periods of several hours and are then associated with a constant temperature pattern in the observation hut. This, together with the statistical and mechanical analyses,
"Set 28 (indicated by the dashed line) was taken at sunrise,
" and Miller noted, "Sun shines on interferometer; fringes becoming
unsteady. The very large increase in the second harmonic in this set clearly reveals the eGect of radiant heat on the interferometer, and similar effects occur at dawn in other sets. In judging the sensitivity of the interferometer toward radiation, it should be kept in mind that it was exposed to the direct sun rays only through cracks in the beaverboard wall of the hut or leaks around windows and the door. On July 31, a large canvas cover was put over the roof (apparently at some distance above it) and over most of the walls of the hut in order to protect the interferometer from light leaking through and to get rid of the effects of the direct irradiation of roof and walls. The canvas cover was at least partly in place also in the September and February epochs.

forces us to conclude that the observed harmonics in the fringe displacements are not due to a cosmic phenomenon (aether drift), nor to magnetostriction, nor to mechanical causes, but rather to temperature effects on the interferometer. These disturbances were much more severe at Mount Wilson than those encountered by other observers in their repetitions of the Michelson-
Morley experiment performed in laboratory rooms.
Table I summarizes the results of the significant trials
of the Michelson-Morley experiment. The first three columns of the table record the experimenter, year, and place of observation, The fourth column gives the optical path length D of an interferometer arm, as used in each of the several experiments. Column 5 gives the maximum anticipated fringe displacement corresponding to a 30-Km/sec aether drift velocity when the
apparatus is rotated through 90' in its optical plane.
Column 6 lists the amplitude A of the second harmonic of the fringe shifts actually found by each observer. In every case the observed double amplitudes 2A are much smaller than the expected fringe displacements listed in column 5. To provide a basis for comparison of the several trials of the experiment, the ratios of the expected fringe displacements in column 5 to the values of 2A actually found in each experiment are listed in the last column.