256 PROFESSOR A. O. OREENHTLL ON THE 



and DARBOUX'S equations (DESPEYROUS, ' Cours de mecanique,' II., note 17). 



O n o > O O 



r+? + r^ ?>+?+- = ! (9)> 



a b c a? W c- 



are identified with our notation by putting 



A = B& = Cc = DA (10), 



and 



A.p* + B? 2 + Or 2 = D/?, 2 (11), 



+ BY + cv 3 = D 2 /> 2 (12), 



are two integrals of EULKR'S equations 



A^ = (B-C)^... (13), 



or, as they may be written, 



Then 



2 = / 4- 



_ ^B - - A 



A T> I 



- C '> ( - A) (A - B) ^ __ n 



ABC yfc jfc^ 



supposing 



P/ > p~> p,~ > > p, 2 (17), 



and inverting the integral, 



p s = /o 2 2 sn a (K - m) + Ps W (K - i), -= \/ P * 7*^ (18). 



11 \r A* 



Again, projecting on the invariable plane the areas swept out on the co-ordinate 

 planes 



o dnr Ax I dz o 



and 



dz _ z dy _ n /'A_ JB ^ fl _,_ A^- C 

 dt dt 



