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NATURE

[APRIL I8, I925

Letters to the Editor.
[The Ed#or does not hold himself responsible for opinions expressed by his correspondents. Neither can he undertake to return, nor to correspond witlt the wn"ters of, rejected manuscripts intended for this or any other part of NATURE. No notice is taken ofanonymous communications.]

The Effect of the Earth's Rotation on the Velocity of Light.

IN the Philosophical Magazine (6), 8, 716, 1904, an experiment was described, designed to test the effect of the earth's rotation on the velocity of light. In consequence of atmospheric disturbances, it was quite impossible to measure the interference fringes in the open air. Accordingly a twelve-inch water-pipe was laid on the surface of the ground in the form of a
rectangle, 2010 ft. by 1I I3 ft. The residual pressure was reduced to about one-half an inch by means of a fifty horse-power pump. One of the ends was double, as shown in Fig. r. At A, light from a carbon arc

D c

£

A 8

F

FIG. I.

was divided by a plane parallel plate, thinly covered with gold, into two beams, one traversing the circuit in a clockwise, the other in a counter-clockwise direction.
Observations showed that the beam going in the counter-clockwise direction was retarded with respect
to the other by 0·230 of a fringe.
TABLE I.

Displacement in Fringes.

Number of Observations.

Deviation from Mean.

I

0·252

2

•255

3

•193

4

•246

5

•235

6

•207

7

•232

8

·230

9

•2!7

IO

·Ig8

II

•252

12

•237

- -13

0·230

Mean 0·230

20 20 20 20 20 26 20 20 20 20 20 20 23
Total26g

0•022

·025

•037

•0!6

•005

·023

•002

•000 ·OI3

I

•032

•022

•007

0•000

Av. dev. from mean o·or6

Observations I-6 inclusive, without collimator; 7·I3 inclusi:ve, with collimator.

Displacement

Obs.

Calc.

. 0·23oto·oo5 0·236±o·oo2

The theoretical value,1 on the assumption of a
stagnant ether, is given by the formula Ll. = 4Aw sin (J
'Ac I This is twice the value given in the original article. Attention was directed to this correction by L. Silberstein in the Journal of the Optical Society of America, 5, .291, rgzr.
NO. 2894, VOL. I IS]

With the actual dimensions of the apparatus, the
calculated displacement is 0·236 of a fringe. In this formula the latitude, IJ, is 4I 0 46', and the wavelength, w, as measured by comparison with sodium light, is 5700 A.D.; w is the angular velocity of the earth's rotation, and c the velocity of light.
Two hundred and sixty-nine observations were
made, and averaged, usually in groups of twenty, in the order taken. Thirteen such means are given in Table I.
The results are interpreted to mean that the calculated and observed displacements agree to
within the limits of observational error.

University of Chicago, March 21.

A. A. MICHELSON. HENRY G. GALE.

Atmospheric Electric Transmission.

IT appears to be of interest and value, in relatio11 to current investigations on the circumstances of wireless transmission at short ranges, to note the intensity of reflection of electric waves that might be expected at the sharp boundary of an ionised layer, high in the atmosphere. The term sharp here implies practically that the transition is completed in, say, not less than one-tenth or, for nearly direct incidence, onefifth of a wave-length. The relative amplitudes in the reflected waves are then, for the two polarised components, given sufficiently by the Fresnel expres-

sions

_sin (i- r) and

rl

sin (i +r) tan (i+rf

When the index of refraction I" is I - v where v is small, they become

v

d v cos 2i.

- 2 cos2 i an 2 cos2 i ·

e.g. for rays inclined at 30° to the horizontal they are - 2v and - v.
For the most favourable case (NATURE, November I, I924, p. 650,' or Phil. Mag., December, p. 1031), that of free ions, N per cubic em., unhampered by collisions, therefore high up, the value of v is
2
1f'm
whichis i x I o-3N for free electrons and for wave-length
of one kilometre. To ensure a reflection of roper cent. in amplitude (or I per cent. in energy) of rays inclined at 30° as above, N would have to be about 300 electrons or else 5 x ro5 hydrogen ions per cubic em. If the wave-length is IO times smaller, namely, IOO metres, these numbers have to be multiplied by Io2•
At the other extreme, if a gradual transition is to bend round the complete ray through the same angle of 6o0 in traversing a curve of whatever length, the difference of the values of N at the top and bottom of this curved path figures out (cf. loc. cit.) of the order of 300 electrons per cubic em. when ·ft. is one kilometre, much the same density of ions being thus necessary in the two cases.
For the first case, however, that of transition practically sharp, a layer a few wave-lengths in thickness would play the part of Newton's thin plate in optics, by reflecting from both its faces : thus as the wave-length is gradually changed, there would be regular fluctuations at th_e receiver. . Ionic ?lauds drifting across the sky m1ght cause 1rregulanty of
' At top of column 2 read 1x ro· 3 watts per square em.

© 1925 Nature Publishing Group