30 



Art. 7. — K. Terazawa: 





r- — a' 



a-ya- 



+-~-r^-— ^^77^U'^i-^<(«) • (71) 



a-ra^ (? (v) l i 



a'ra' Jr'( 



The other integrals in (62) are found without the knowledge 

 of elliptic functions. 



/'^ a—rcosd -la 71 , 



/ do = lor r <; a, 



•/ R- a 







= „ ?• > a ; 



./- 





-dd = -^ „ r <: a, 

 2a' 



(72) 



(73) 



?r-' 



'A) 



„ r > a, 



§23. Substituting these values of integrals in (öS) we obtain 

 the following expressions for the displacement: 



2a~'/2 I '2 J 



// 



2a7T(X + fjL) ] a 



2a 



(r < a) 



2r 



-(r > a) 



orz 



+ ^r>[-^i-^'^i(W+e.)] 



2;: 



+ 



^ [^^ (V-.J . [^^ (.)-..J ^^-^-f >Ö^} , (74) 



?/. = 



Hz 



2a7T[x 



— (r <; a) 

 a 



{r>a) 



azcoi , z(r' — a-) v/]^ — co^^[v) 

 2a>T 2(2-V>T 



2a7t[j.{k-\- [I.) 



~{r < a) 

 (r>a)_ 



S='(^) 



, 2 ,■ , >, ?•- — a^ 

 ««TT za'va- 



+ ^(f^ [W-e,] ^^^^If^l • (75) 



7ra ra'' i^ iv) ) 



