Elastic Equiftliriimi of Seuii-Infinite Solid. 



17 



"' 'o ""■ 



zr = -^ /e-<^+^'^V,(A7-)/rV/A-, 







To = 0, d): = 0. 



These integrals can he expressed in terms of zonal liarmonics 

 and the associated functions. If Pn (x) denotes the zonal harmonic 

 of ?üh order and 



X X 



then 



fK-JjMä^ = -J-+») 



dx" 



.p: 



n). 



By making use of these formula?, we have 



,, _ // / z{z + a) , ;> + 2/. 1 \. 



4-Ü I (r- + iz + a)'-^)^''- / + // * (r- + (^ + a)- )i'" / ' 



(42) 



(43) 



and 



-__/// a {r- + {z + of) + 3^r- _ jj. F 1 _ ;g + a ~|| 



' 2;r I (r- + (^ + a) J"" T+ /^ " L >•-' t%7^ + (;? + a)^^ J / ' 



fa_ ft [ ^ ,« r^__ z + a ~\ 



~~ YA (rH(;J + «)-)^'- T+TT L r- r'V + C? + a)7^J 



_ ^ z+a \ 



7+y 7^+(^ + a)T- )' 



2- ■ (r^ + (,, + ,,/)-v2 ' 



(44) 



1) See K. Terazawa, Proc. Eoy. Soc. London, A. vol. 92 (1915) p. 57—. 



