﻿240 Mr. Bernard Cavanagh on 



order of magnitude ^ we obtain : 



log^+woO^aiO-iajC + JaaC 8 , . . (31) 

 | J^log(l+mC)=C(l-ia 1 C + ia 2 C 2 -ia 3 C 3 ), (32) 



c=o 



where a 1 = ?w (l — 0), 



a 2 = m 2 [l-2(<9-7 7 )], ... (33) 



a 3 = m o 3 [l-3(0-77 + f 



it being clear that, as stated above, £ can be neglected 

 altogether if no greater than about fa 

 We get then the equations 



( W =^ M +RC[i-KC+^ 2 c 2 -ia 3 ^] + g m j 

 IV - U*° (34) 



|i- =^-R[log<; s -a 1 C + ia 2 C 2 -ia i) C 3 ]+G s 



and thence the successive stages : — 



U=<£ M +RC[Wmo(l-0)C + ; WC 2 ] +G M ) 

 U/° (35) 



^=* M + RC[l-^ O] + G M 



and 



at 



,3M, 

 II. . .- .... (36) 



||£ = *.-R[logc.-m C]+G, 



and 



(|±=^ + RC + G M j 

 I. * M ° ....... (37) 



f|£ =^-Rlogc, + G, 



\ 0^9 J 



I. and II. being the first and second approximations 



obtained by the preliminary treatment in the previous paper. 



Taking I per cent, as the " probable experimental error," 



