The Intensity of Transmitted Light, 163 



succeeding letters Ag.^g &c., may be found in terms of the 

 letters Ui, U2, U3 &c. These values of Ai, A2 &c., being 

 substituted in the expressions previously obtained for the 

 various powers of x, we obtain the following results 



coefficient of x = ^^ 



^ = 



x" 



3U3_2U22 



1/1 2U4 ISUgUa^SUa' 



1/]2U4_ 18U3U2 SUa^ 



1/20U6 _ 32U4U-2 _ 18U3^ 48U3W _ 16 W \ 



g _ 1 /SOUe _ o OUsUa _ 6OUJJ3 8OU4W 



"^ "5V U; W Ui^ ^ W 



QOU/Ua _ I2OU3W 323^ 



) 



by a continuation of the process the coefficients of the other 

 powers of x may be determined. 

 If we expand 



log^^ or log( W + 2U2^^ + 3U3V + &c. 



in powers of x, the result will differ from the result already 

 obtained in this respect only, for the letters Ui, U2, U3, &c. 

 the accented letters 13}, Ug^, \}}, %lq., must be used ; hence 

 we shall have the equation — 



'%S - '°s| = logU.' - logU. + «2(g - ^^) 



+ nKuf' ~ u J " K(W " u?)} "" t r\w " u!) 



-^^(U.')2 "u?7 V(u.'f u/;/ + 4V"Ui' uj 



