572 Dr. A. C. Crehore on an Atomic Model 



To find the scalar value of R from this, square the coefficients 

 and add, giving 



R' = ,»(l + M ), (13) 



where 5 8 = r 2 + a 1 2 + a 2 2 , a constant, . . . (14) 



2 



and u — -g [ — rtui'Si — ciiyGi — a 2 zS 2 sin a + cl 2 i/C 2 



+ « 2 ''S 2 cosa — a 1 a 2 SiS 2 cosa — a 1 ^ 2 C 1 C 2 ]. (15) 



For substitution in the Saha equation (3) the vector 

 velocities q l and q 2 are required. These may be found by 

 differentiating (4) and (5) with respect to the time, but at 

 this point a very important difference arises between the use 

 of the Saha theory and such a theory as" that of Larnior- 

 Lorentz. Saha states in the paper referred to " But in 

 performing differentiations with regard to (jc ! , y' , z', I') we 

 here assume that they are quite independent of (&*, y, z, I). 

 I am not quite definite as to which of these two standpoints 

 is correct, but I am inclined to think that my standpoint is 

 more in accordance with Minkowski's ideas of time and 

 space. However, it is preferable to keep an open mind on 

 this point." We shall here adopt Saba's view and differen- 

 titiate (4) to find q 1? giving 



q 1 = a 1 ft) 1 (C 1 i-S 1 ;> . . . . (15 a) 



To find q 2 differentiate (10) with respect to t' as though the 

 observer were at the position of the second charge, giving 



q 2 = a 2 co 2 (C 2 cos ai~ S 2< ; + C 2 sin otk). . . (16) 



For the ponderomotive force equation, the several required 

 quantities may now be found. From (15 a) and (16) we 

 find 



qi-Wc^AAECAcosa+SiS,]. . . (17) 



From the definition of 



A^l-q^R/cR, (18) 



we find 



RA,/c=R/c-^[a J? S 1 C s -a 2 S,C 1 c6s«-C J *-t S^]. (19) 

 The complete form of the ponderomotive force in terms- 



