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reflected light is variable (and equal to the sum of c=3.101o cm. and the component of the velocity of the image in the direction of the ray) we shall have

c=c+2kv cos 0.

And since c'n'λ' and c=nλ we have λ=λ. It remains then to see by experiment whether or not we can observe, in addition to the Doppler effect, a variation in the value of A; from this we can ascertain whether c remains constant or not on reflexion from a moving mirror. I have not proceeded to the observation of the Doppler effect in these researches since there is no doubt about its existence, already proved experimentally by the authors quoted; I have rather sought to find out whether and in what way A varies when the velocity of the moving mirrors changes.

Belopolski's arrangement for the study of the Doppler effect was inconvenient on account of the excessive subtility of the luminous ray necessary to obtain multiple reflexions from the same mirrors; for this reason the author mentioned was unable to observe the displacement of the rays except by photography. I prefer to adopt the arrangement shown diagrammatically in fig. 2. A horizontal brass wheel R, 35 cm.

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in diameter (6 mm. thick), which can be made to revolve with a maximum velocity of 80 turns per second, bears on its periphery ten mirrors similar to M, rectangular, plane, vertical, of glass silvered at the back. The velocity of the centres of the mirrors, corresponding to the greatest velocity of rotation, amounts therefore to more than 100 metres per

second. The number of revolutions of the wheel was determined acoustically in each experiment. The mirrors, at equal intervals on the periphery of the wheel, are inclined to the radius from R passing through the centre of each of them at an angle a=29°. They are fixed solidly to R by screw movements capable of permitting a rigorous adjustment. The support for the bearings of the axle of R carries also fixed mirrors F, vertical like M, of which the number in the figure is three; but this number may, at will, be reduced, or increased up to nine. The position of the F's and M's is such that a parallel beam of light L, after a certain number of reflexions from the F's and M's (seven in the figure), may be received at L' when R has deterininate angular positions. Naturally the intensity of L' is much weaker than that of L, and this enfeeblement is much more marked if R is in rotation, because in this case the light arrives at L' only during certain very short instants (ten times per revolution). I have observed in practice, however, that the four moving and three fixed reflexions of the figure allow of experimenting with light sufficiently intense at L' even if R is in motion: that is to say, that direct observation (without photography) suffices to establish the luminous phenomenon of which we have spoken above.

To study the value of λ the light L' was examined with. the well-known interferometer of Michelson, shown diagrammatically in the figure. It is known that if the distances. SS, and SS, are exactly equal fringes are observed with the telescope C even if the light is not monochromatic ; these fringes then have the coloration of Newton's rings. As soon as a difference of path occurs (even if only of a few microns) observation with white light is no longer possible. Monochromatic light must then be used, and the order of the interference fringes increases with this difference. Their visibility is greater, the simpler the luminous vibrations. From the researches of Michelson it is known that from this point of view the line that gives the greatest visibility of the fringes with the greatest difference in path is the green one of mercury (546μμ). In this case numberless circular fringes are visible even for a difference of path 1=2(S1S2-S2S3)=40 cm. I have therefore employed as source La mercury arc in vacuo the light of which is conveniently filtered by solutions of chromate of potassium and chloride of nickel to absorb the violet and yellow rays;

*Travaux et Mémoires, Bur. Int. de poids et mésures, xi. p. 146 (1895).

in this manner I have been able to observe with the telescope C, with sufficient clearness, countless circular fringes, even for 1=32 cm. But for these researches I have limited the difference of path to l=13 cm., or still less.

The disposition described above is particularly suitable for detecting very small differences in the value of the incident wave-length; in fact, the value of being large a very great number of wave-lengths is comprised in this length (e. g., 200,000 if λ=0·5μ, and l=10 cm.), and correspondingly for the same variations very sensible displacements can be observed in the position of a fringe.

With the apparatus disposed as above, let us note with the micrometer wire of the telescope the position of a fringe, for instance the first central bright one, when R is in the position shown in the figure, or, still better, when it revolves. with a negligible velocity (one turn per second). If, now, this velocity be increased to sixty turns per second a displacement of the fringe under observation is distinctly visible; if the mirrors are moving against the incident ray this displacement indicates a diminution of A, and it changes sign when the direction of rotation of the wheel is reversed, and this indicates an increase of λ. In order to define the sense of the displacement, I will say that on examining the system of circular fringes with the telescope focussed for infinite distance the diameter of each of these increases when the mirrors move against the incident ray, and the fringes themselves crowd together as those of large diameter are very little displaced; at the same time some new fringes come out from the centre of the system. On the other hand, when the mirrors are moving in the sense of propagation of the incident light the diameter of each fringe diminishes; they become more widely separated, and some of them are as it were swallowed up by the centre.

Before stating the measure of the displacement observed we will see what it should amount to, making the hypothesis that the velocity of the light reflected from a mirror is the same as that of the incident light. Let g be the number of revolutions of R per second and d its diameter, reckoned between the centres of two opposite mirrors M, then πdg will be the instantaneous velocity of translation of the latter. Since the mirrors are inclined at an angle a to the radius of the wheel passing through each of them, the component of the given velocity in the direction normal to the plane of each mirror will be

v = πdg cos a.

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and, by the hypothesis of the invariability of c,

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If is the difference of path of two interfering rays in Michelson's apparatus, the number of fringes which are seen to cross the micrometer thread of the telescope when becomes (that is to say when the velocity of rotation varies between zero and g turns per second) is

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If the observation is made by noting the position of the fringes when the wheel turns in one sense with the velocity g, and that corresponding to an equal and contrary velocity, the number of fringes crossing the micrometer thread will be 2f.

Now, in my apparatus d=38 cm., a=29°, 0=27°, k=4 (as in the figure); if λ is put equal to 0.546μ (green mercury line), l=13 cm., c=3.1010 cm., and g=60 (turns of R per second in one sense and afterwards in the other), we may expect, according to the preceding formula, a fringe displacement 2f 0.71.

Experiment gives, for the case mentioned, a displacement of between 0.7 and 0.8 fringes; and it is not possible, for reasons of visibility, to carry the precision of the observations further. But, as is seen, the agreement between the predicted result and observation is sufficient; this agreement is confirmed by observations made by choosing other convenient values of 1 and g, of which for brevity's sake I shall not speak here.

Experiment, therefore, authorizes the conclusion that reflexion of light by a moving metallic mirror does not alter the velocity of propagation of the light itself, in air, and consequently, with great probability, also in vacuo; at least, in the conditions of the experiment above described. This experimental result, as to which no doubt can be entertained, is contrary to the hypothesis of some physicists who, like Stewart, basing themselves upon the electromagnetic emission theory of Thomson, maintain the possibility that * Phys. Rev. xxxii. p. 418 (1911). Phil. Mag. S. 6. Vol. 35. No. 206. Feb. 1918.

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light, after reflexion, is propagated with the velocity c+v, where v is the component of the velocity of the image in the direction of the reflected ray.

To complete these researches I intend, as I have said above, to investigate further with the same interferential arrangements, the velocity of propagation of light from a source set in motion artificially; but of these, and of the general conclusions to be drawn from these investigations, I reserve mention for a future occasion.

THE

XIX. The Visibility of Radiation.
By PRENTICE REEVES

In

HE theory of this subject has been given previously by Nutting and Ives, and in those papers may be found a thorough treatment of the early literature. this paper the writer wishes to present further data obtained. by a method similar to that employed by the above writers but using a different apparatus. The writer has data from thirteen subjects, five of whom were also used as observers by Nutting in his list of twenty-one subjects. The values for the spectral energy distribution of acetylene were those offered by Nutting, and were obtained by weighting the data accessible up to that time as well as his own results in this laboratory. By using these values the writer was able to directly compare results with those of the other writers, and by using the values offered by Coblentz § and revised by Coblentz and Emerson, we can see the effect of various values for the spectral energy distribution of acetylene. The variations in the acetylene values are probably due to the different kinds of burners used, as Coblentz has shown that the spectral energy distribution in the longer wavelengths is affected by the thickness of the radiating layer of incandescent particles in the flame.

The apparatus represented in fig. 1 is a modification of the Nutting monochromatic colorimeter¶ as manufactured

*Communicated by Dr. C. E. Kennett Mees, being communication No. 55 from the Research Laboratory of the Eastman Kodak Company. † P. G. Nutting, Phil. Mag. xxix. p. 301 (1915); Trans. Illum. Eng. Soc. ix. p. 633 (1914).

H. E. Ives, Phil. Mag. xxiv. p. 149 (1912).

W. W. Coblentz, Bull. Bur. Stds. vii. p. 243 (1911); reprinted, ix. p. 109 (1912).

|| W. W. Coblentz and W. B. Emerson, Bull. Bur. Stds. xiii. p. 1 (1916).

P. G. Nutting, Bull. Bur. Stds. ix. p. 1 (1913); Zsch. f. Instrumentenkund., xxxiii. p. 20 (1913).

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