MESSKS. A. SCHUSTER AND G. BDEMSALECH (>.\ 



and the velocity of the film being everywhere at right angles to the image of the slit, 

 the interpretation of the photographs was obvious. But with the film on the 

 face of the disc, as in our final experiments, the linear velocity is not the same for 

 different portions of the slit image, or different parts of the spectrum, nor is it every- 

 where perpendicular to the slit image. The following investigation shows how the 

 velocity of the particles may be deduced from the measurement of the photographs. 



Fig. 9. 



H 



/ 



Let AA' (fig. 9) represent the upper, and BB' the lower, edge of the spectrum, as 

 it would be formed on a stationary film. KH represents the monochromatic image of 

 the slit at the instant of the beginning of the discharge, and KB,, HS the curved 

 edges of a spectroscopic line as they appear on a photograph taken with a moving 

 slit. The displacements are most easily determined by measuring the coordinates 

 PC = y and NC = x parallel and at right angles to HK. If be the centre of the 

 disc, a point, C', of the slit image will describe a circular arc, C'C, on the moving film, 

 and the time taken by the moving particle to go from K to C' is the same as that . 

 which the point C of the disc takes to describe the arc CO', which may for our purpose 

 be taken as equal to the length of the chord. From the middle point of CO' draw 

 the lines MQ perpendicular to HK, and QO parallel to HK. Then 



C'N : NC = MQ : OQ, 



or if KG' = 2, OF = a, FK = b, and if the squares of y and z and their products 

 are neglected, compared to a", 



z y = bx/a. 



For the line HS we should similarly find z y = bx/a. Also from the figure 



CC' : CN = OM : OQ, 



