from a Cylindrical Wall. 361 



In II., taking OAB = «, 



DA = a cos 0— b cos a, 

 DB=acos0 + />eosa, 

 and &sirfa=asin #. 



DA = ^ cos 0- v/^^in 7 ^ 

 and DB = r« cos (9 + vA 7 "-^ 2 sin" 6. 



Jit I., cos <£> = - = /= _^=— sin (i — — ^== = . 



' // / "J i 2 ' ' / 2 i 2 



" V •' + i" v ts +■ r* 



Hence (1) becomes 



2 f ^ c** r in « r DJ ' ncosa..^ 2 ^.^.^.^ 



Jo J, Jo Jda/ (tf 2 + r 2 ) 2 



Integrating with respect to c and then to ?' we get 



rC x * 7 f sin _l7 ' cos Or .DB T DA 



I 1 #tf#l fan -1 — tan 



J.r, Jo loc L a? a? 



J,, Jo l'# L 



-isin2tan-^ + i sin2(tan-^)" 



r/0. 



Using the above values for DA and DB we get after 

 reduction 



, _ X DB ,DA 2tf\A 2 -a 2 sin 2 



tan 1 — -tan" 1 — = tan , 2 , , M — : 



therefore as part of the integral with respect to we get 

 _i» 



cos tan v - ,/0 



Jo <Tt" + <r — /r 



\ b 

 f 8in « Aa 2 sin 2 6>cos(9 _ rf 



~ Jo vA 2 — a 2 sin 2 f 1 + A 2 (6 2 -.a 2 sin 2 0) } 



by integration by parts, 



ere A = . — - , 

 ^ 2 + a 2 — h' 



