and the Sun's Distance. 529 



has shifted its position, and the returning rays do not strike at the 

 same angle of incidence as when they left it. Hence the image is 

 displaced in the direction of the rotation, and this displacement in- 

 creases with the velocity of rotation ; it also increases with the 

 length of the route passed over by the rays, and with the distance of 

 the mark from the plane mirror. 



" If we call V the velocity of light, n the number of times the 

 mirror turns in a second, I the distance between the plane mirror 

 and the last concave mirror, r the distance of the mark from the 



turning mirror, and d the observed displacement, we have V= — - — ; 



an expression which gives the velocity of light when the other quan- 

 tities are separately measured. The distances / and r are measured 

 directly by a rule. The deviation is observed micrometrically ; it 

 remains to show how the number of turns (n) of the mirror is found. 



" Let us describe first how a constant velocity is imparted to the 

 mirror. This mirror, of silvered glass, and 14 millims. in diameter, 

 is mounted directly upon the axis of a small air-turbine, of a well- 

 known model, admirably constructed by Froment. The air is sup- 

 plied by a high-pressure bellows of Cavaille-Colle, justly distin- 

 guished for the manufacture of large organs. As it is important 

 that the pressure should be very constant, the air after leaving the 

 bellows traverses a regulator, recently contrived by Cavaille, in which 

 the pressure does not vary by one-fifth of a millimetre in a column 

 of water of thirty centimetres. The fluid flowing through the orifices 

 of the turbine represents a motive power of remarkable constancy. 

 On the other hand, the mirror, when accelerated, soon encounters in 

 the surrounding air a resistance which for a given velocity is also 

 perfectly constant. The moving body placed between these two 

 forces, which tend to equilibrium, cannot fail to receive and to pre- 

 serve a uniform velocity. Any check whatever, acting upon the flow 

 of the water, allows this velocity to be regulated within very exten- 

 sive limits. 



" It remains to estimate the number of turns, or rather to impress 

 on the moving body a determined velocity. This problem has been 

 completely solved in the following manner. Between the micro- 

 scope and the reflecting glass a circular disc is placed, the edge of 

 which, cut in fine teeth, encroaches upon the mark and partly inter- 

 cepts it. The disc turns uniformly on itself, so that, if the image 

 shines steadily, the teeth at its circumference escape detection from 

 the rapidity of the motion. But the image is not permanent : it 

 results from a series of discontinuous appearances equal in number 

 to the revolutions of the mirror ; and whenever the teeth of the 

 screen succeed one another with the same frequency, there is pro- 

 duced on the eye an illusion easily explained, which makes the teeth 

 appear immoveable. Suppose then that the disc, with n teeth in its 

 circumference, turns once in a second, and that the turbine starts 

 up. If, by regulating the flow of air, the teeth are made to appear 

 fixed, we are certain that the mirror makes n turns in a second. 

 - "Froment, who made the turbine, wished to invent and construct 



