504 RICE 



ABT, K 



The function ^v of t, Xx', Xy', . . . Zz', Ta, T^, etc., defined 



by 



will give the second set of [473], and a function x^. of t, Xx'> 

 Xy', . . . Zz', tJ-a, y^b, etc., defined by 



will yield the first group of [473]. 



The function tv gives us the equation [471], viz.. 



or 



I.e., 



dan dQv 



and so on, which is the first group of [474]. 

 The function ypv' gives us 



dr]v' dXx' 



dan dt 



i.e., 



dQv' dXx' dXx' 



dan dt d log t 



and so on, which is the second group of [475]. 

 The function 



€v' — 22Ax'flu 



regarded as a function of rjv', Xx', Xy', • • ■ Zz', Ta, Tb', etc. 

 will yield, when treated similarly, the second group of [474]; 

 while the first group of [475] can be derived from the function 

 ^v in a similar manner. 



