OF ARTS AND SCIENCES : APRIL 14, 1863. 119 



formation of a last image of the mai'k on the surface of the last concave 

 mirror of an odd number. I have been able to use 5 mirrors, which 

 furnish a line 20 metres long for the ray to travel. 



" The last of these mirrors, separated from the preceding one which 

 faces it by a distance of 4 metres, (equal to its radius of curvature,) 

 returns the pencil back on itself; a condition surely fulfilled, when the 

 returning image and the original image on the last mirror but one 

 coalesce. Then we are sure that the pencil retraces its steps, returns 

 in full to the plane mirror, and all the rays go back through the mai'k, 

 point for point as they went forth. 



" This return of the pencil may be proved on an accessible image 

 by reflecting the pencil to one side by a surface of glass at an an- 

 gle of 45°, and examining it through a microscope of small power. 

 The latter, resembling in all respects the micrometric microscopes in 

 use for astronomical observations, forms with the mark and the inchned 

 glass one solid piece of apparatus. 



" The real image sent into the microscope, and formed by the return- 

 ing rays, partially reflected, occupies a definite position in relation to 

 the glass and the mark itself. This position is precisely that of the 

 virtual image of the mark, seen by reflection in the glass. At least 

 this is true when the plane rotating mirror is at rest. But when this 

 mirror turns, the image changes its place ; for while the light is going 

 and returning between the mirrors, the plane mirror has shifted its 

 position, and the retui'ning rays do not strike at the same angle of inci- 

 dence as when they left it. Hence the image is displaced in the direc- 

 tion of the rotation ; and this displacement increases 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 



TT 8 TT n I r 



^ — '~d ' 



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

 ties are separately measured. The distances I and r are measured 

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

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



