ö ART. ?,. — AICHT AND TANAKADATE : THEORY OF 



— 7— =0 , -T-^ = Unite, 



dy (fr 



i.e. £ is of tlie order r, or ;- is of the order of d-^. 

 Thus, if we again neglect 6^ as compared with unity, i.e. ß^ com- 

 pared with d, we have 



a = const, r 

 In the case of the circular cylinder, we have simply 



a = con«t. 

 Thus, putting da = dxdz and taking tlie limit of the integration 

 from — 00 to + oc 



V^ = — '^;r^ I I COS ^^o dxdz, V,— ■ — ^— ^ I I sin .^ddxdz 



kri J J X ' Iq J J À 



— ce— CO — 3;-x 



where cos —j- o =cos -j—{o, + o,,) 



2;r > 27r , . 2;r . . 2r . 



= cos — ^ — 0, COS — - — 0., — sin — - — o, sin — - — a, . 

 / À - I ?. - 



Therefore 



^7- const. C 2;: ^ , f 27r ^ , 



In the first part of these integrals put 



then I cos — j^ d^ dx = ( — - — J^ | cos ~^{u^ — xdu)du , 



and in the second part 



z^=^^v'^ 



+« 



then I cos -:^d.idz = ^ -^ j cos ^v'^dv=^-^ 



Hence Y^ = -^l--f — ^j» j co.s-|-(?/-xÖ«)r?M , 



