Till; CONSTITUTION OF THE ELECTRIC SPARK. 197 



or writing s for CC' and r for OM, 



Again neglecting the square of small quantities, 



a : x = r : a -f y. 



It is convenient to introduce in place of a the distance (c) between O and the centre 

 of the spectrum, so that a = c h, where h represents half the width of the spectrum. 

 To the required degree of accuracy it is then found that 



x ~ ~c ( l ^ ~ ) ' 



C V \ C I 



where the minus sign refers to measurements taken along HS. 



The time (t) taken for the description of the arc CC' is s/rta, at denoting the angular 

 velocity of the disc, and if v be the linear velocity at the centre of the spectrum 



TO 



As y and x are obtained by measurement of photographs, and h and c have been 

 practically constant in the experiments (though also measured in each case), the above 

 equations allow us to calculate 



h 



If a,, y,, and x?, y 2 are the measured coordinates of two points lying near each other 

 on the curved images of the spectroscopic lines, the velocity of the luminous particles 



at the corresponding point of the spark will be K . -* , where K is the ratio of the 



l t r, 



length of the spark gap to that of its image on the film, which in our can 

 was simply the ratio of the focal lengths of the camera and collimator lenses, 

 i.e., 1'16. If both poles are made of the same material, so that both the lines which 

 appear at the top and bottom of spectrum can be measured and the mean taken, the 



correction disappears, and the velocity of the particles is given directly by Kw' J -'. 



j~ t x t 



Even when a line can only be measured on one side, this may approximately be taken 

 to be the velocity, for in our experiments c was equal to 14, the distance b was seldom 

 greater than 1 and never greater than 2, while the ratio x/y was always less than , 

 so that z and y oiJy differed at the maximum by 5 per cent, from each other. The 

 uncertainty of our experiments, for reasons which will be given, was greater than that 



amount. Similarly may the quantity be neglected for the present. 



