2 Cady — On the Energy of the Cathode Rays. 



[gr.] their mass, we have for the amount of heat given up to 

 the conductor 



Q=N-hnv 1 (1) 



(ergs per second). 



If the charge on each particle be e, we shall have flowing to 

 earth through the galvanometer a "cathode-current" of inten- 

 sity 



i=N-B (2) 



Now the kinetic energy of each particle is 



V-e = hnv\ (3) 



Hence 



Q = N- V-e = i'V, 



or 



?->■ 



According to Starke's investigations,* a part of the cathode 

 rays are reflected. This can have no effect upon the above, 

 provided that after reflection the velocity of the rays remains 

 unchanged ; and indeed the measurements made by Merrittf 

 upon the deflection of reflected cathode rays seem to show this 

 to be the case. We will, however, assume for the present that 

 upon reflection the energy of each particle is diminished in the 

 ratio r' : 1, while the charge remains unchanged. Then if the 

 fraction r of the rays be reflected, we have 



Q = N(l—r)-hmv" + N'r(l—r')'^mv 2 — %Nmv*(l—rr') (la) 



i = Ne(\—r) (2a) 



Ve = {mv" (3a) 



iV \—r ,. . 



Q 1-rr' v ' 



If r' = 1 (Merritt), we have still i V/Q = 1. If in the limit- 

 ing case r' — 0, then i V/Q = 1— r. 



These relations were investigated experimentally as described 

 in the following paragraphs. 



Apparatus. 



Fig. 1 shows the arrangement of apparatus at first used. 

 For measuring the energy Q a thermo-element was here em- 

 ployed ; it was later displaced by a bolometer (see below.) 

 The thermo-element, S, was of the Melloni type, consisting of 

 49 bismuth-antimony couples each 25 mm long; the exposed sur- 

 face of the junctions was 196 mm \ It was placed inside the 



* H. Starke, Wied. Ann., lxvi, p. 49, 1899. 

 fE. Merritt, Phys. Rev., vii, p. 217, 1898. 



