496 



RICE 



ART. K 



+ 2 



av 



v9r9r 



-, ) [(?'2 - ro) (rs - ro) + (rj - r^ (n - ro) 



+ {n — To) (fi — ro)] > + higher powers, 

 and similarly 



X = Xo + f — j (ri + r2 + rs - 3ro) 



,1 f/9^X 

 "^ 2! 



+ 



/ 9^ X \ 

 2 \7^f) K^2 - ro) (rg - ro) + (rg - ro) (n - n) 



+ (ri — ro) (r2 — ro)] > + higher powers. 



Hence (f)(t, E, F, H) and x{t, E, F, H), the true and the 

 approximative expansions of ^l/v agree to the terms of the second 

 degree inclusive. The remaining statements on page 212 can 

 be deduced similarly. 



The equations 



r^ + ra^ + rg^ = On^ + a^^ + a^^ + a^i^ + 022' + 023^ 



+ agi^ + aga^ + agg^, 



ra^rg^ + rgV^^ + nVa^ = ^u^ + An^ + An'' + ^21' + ^22^ 



+ ^23' + ^31^ + A322 + ^3g2, 



an ^12 ^13 

 rir2rg = 021 ^22 0,23 



dzi Cli-i ^33 



are equations [432], [434], [437] of the text. By partial differ- 

 entiation with respect to an, we can, as Gibbs points out, 



