THE THEORY OF FISHER. 181 



leaving the constants p^, q to be adjusted according to observation and thus 

 determine h indirectly. 



Formulas for the principal variables are, then,^ 



^(sin/3-/3cos/3) (26) 



(27) 



m= , 

 g3 



_^nkpQ sin ^—^ cos /? 



also 

 whence 



k k 



^^ m, An , , T^ 47r Oq /sin ^9 ^ \ 



(29) 



For comparison of the variables p, p, e, with their values at the center, there 



are the ratios 



p sin j9 



^0 /? 



(30) 



^=4^ (31) 



Po iOo^-^'i' 



while the mean density is 



ep (p-prY (32) 



\P<s-pJ 



or in form of power series: 



sin ^1-/?^ cos ^x .oox 



p^ p,A 3! 5! '^ 7! / 



The expressions for E and (P take particular forms readily reduced to 



c/ 



^^8n|^= /" |j|-?i^-cosft(sm^-;Jcos;3)}d^ 



♦Z 



giving for these total energy values: 



q' 



^^,[l+2sin^._4(^i^^)V^ (34) 



* Most of these formulas occur in Fisher's paper, or in antecedent writings where the 

 Laplacian law is used. 



