298 Prof. 0. W. Richardson on 



This would require M to vary as T _3/2 . Using equation (6) 

 to find the value of M we get 



M = 



k ^ X / k Je-^ (7) 



i V w 



2 vA 



In the case of tungsten at 2000° K, taking K. K. Smith's * 

 values for i and w, and putting c -1 = 6 xlO 4 E.M.U., it 

 appears that 



M = 4'65 x 10- 28 E.M.U. x cm. 



If the moment is due to charges +e separated by a distance 

 S the value of the distance is 



S=2-92xl0- 8 cm. 



This is of the order of the linear dimensions of a tungsten 

 atom, and is therefore of the order to be expected from 

 general considerations. Langmuir's data for tungsten would 

 give values of M and 8 about 10 times as large as those 

 above. It seems doubtful, however, if the value of M 

 can be much greater ^ than 5xl0~ 28 without making the 

 emitting particles larger than atoms, and this would conflict 

 with the theory in other directions. 



A knowledge of M helps towards an estimation of the 

 number of " free " electrons present at any instant on this 

 theory. The number ejected from atoms in unit volume 

 per second is Np. If the electrons travel on the average a 

 distance d 1 with velocity V before recombining, they will be 

 free for a time t~djY. The number instantaneously 

 present in the free state is thus 



U ~ V ~eMVd C ~ve.M.Vd °> ' ' ( " 



where v is the number of molecules in 1 c.c. of a gas under 

 standard conditions. Putting 



c -i = 6 x 10 4 E.M.U., T = 2000° K, 



vA- = 3'711xl0 8 ergdeg- 1 , ^='4327 E.M.U., 

 M = 4-65x 10- 28 E.M.U.,andV = 3xl0 7 cm./sec, 



n' = 62 xlO 22 ^ 1 (9) 



The number of atoms per c.c. of tungsten is 6*16 x 10 22 . 

 The agreement of this number with the numerical factor in 



* Phil. Mag. vol. xxix. p. 802 (1915). 



