10 



Art. 7.— K. Terazawa 



§11. To generalize the above so that the sokition may be 

 suitable to discuss the effect of any given normal pressure at the 

 boundary surface, suppose that Z and Z are functions of h of the 

 form Zm{k)dk and ZmQcJdk respectively, and superpose the 

 corresponding solutions for all positive values of h, then add them 

 together for all integral values of m. Thus, corresponding to the 

 boundary conditions 



zz= 2 /* ^ {^-(^'■'>-) COS m 6 + Z,„ (k) sill m 6 \j.,Xh-) dl:. 

 7r=0, 7ti = 



at z=0, we have 



CO 



■i'r = ^ ~J lz„,[l-)cosmß + Z,,,(k)mi)nd\e-''J' ,,,{l:r)dl: 



CO 



an 



«Ö = y -^f{z,XJc)co^md-ZJl-)smmd]e-'^T,,lkr) 



(22) 



dk 

 k 



dk^ 

 k 



y. = 



-> \,;7 , /"{z„^(Ä;)cos;;.^-Z„,(^-)siii;;.4«''^^"'(^-'')4^r ' 

 ^-t^3 2(/ + /ij/-,/ I J ^- 



= - ^—-1 [ZrX'k) COS ;^i ^ + X,„(Ä;) sin m e\e-''J,Xky)dk 



7)1= f^ Q 



^ CO • _ 



«;eo2/<;. +/.)./ I ' -^ ^ • i "^ ^ k 



(23) 



and 



^^ = |] /(l + Ä.-^4^.,(Ä:)cosmÖ + Z„XÄ-)si]i;;;^l'-*^/„,|A,7>ZA-, 

 ^ = -J ^/Ä;{z,„(/>;)cos;;i^ + Z„,,(A;)sinwöje-V'„,(A7-)f?Ä;, 



CO 



7d = -^JI^/ iz,Xk)coHmd-Z,Xk)mim.d\e-''J,,Xkr]dk, 

 etc. 



(24) 



