Elastic Efjuilibrium of Semi-Infinite Solid. 31 



§24. For purposes of calculation, it will be very convenient 

 to have the forniuhe expressed in terms of Jacobi's ç-series. q is 

 defined by 



CO, 



After Weierstrass, if we put 



then q can be computed from 



of which the ftrst two or three terms are usually sufficient. The 

 ç'-series of the functions needed here are as follows: — 



2 \ 2 ' "^ ^ 



■&l'{o) 



and 



'' V2co, ' â,{o) ' 



â,{o) = 2q^(i + q' + (f+q''+ ), 



ä["(o) = -27rY(l-3Y- + 5V-7V-+ ), 



â/(o) = 2;rg^(]-3gH5g«-7gi^+ ), 



ê:{o) = -2>T'g'(l + 3V + 5V + 7V--^+ ). 



§25. The calculation of the term vy], — io,^(v) requires a little 

 explanation. By the fermula 



e • (t{v) = Ico,- 



we have 



