12 Colorado College Studies. 



(5) 1 \-r cot normal to r sin 0<](f dr. 



do r 



(6) — 2 cos Oh' normal to rdo dr, 



sin 0(J<s 



(7) r sin f-2 sin ^lo normal to r sin Ode do, 



dr 



(8) sin f-2cos<'?r normal to r sin Od(f dr. 



do 



dir 2ii 



(9) ^H f-2cot^?' normal to rr/0 r/r. 



d<p r 



Among the expressions above, (2), (4) and (7) are simi- 

 lar to c (1), page 10, in that the losses within the element are 

 affected by the increase of the opposite faces in one dimension. 

 In the case of (2) the changing dimension to be considered 

 is rsinOd<f; of (4), r sin Od<f^ and of (7), rdO. Taking this 

 into account, we obtain the following expressions for the losses 

 within the element: 



.'>/<rii 2dii 2ii\ „ . , 



( 1 ) 1 ) r sin 0(1 <s do dr, 



f>\dr' r r"^ J 



!>.( d-u. du cot 2dv 2r \ ., . 



(2) -( cot r sm Ode dO dr, 



^ ,"\r'dO' rhlO rdO r J 



(3) -( ]r amOdc do dr, 



f>\r^ sin'- Od(p'^ rdc J 



(4) ^Yr'^ + 4 — +— ^ r sin Ody dO dr, 

 l> \ dr dr r / 



,^s fj/(Pr , 2dn , , ^ dr r \ ., . ^ , ,^ , 



(o) 1 1- cot r-sin^(/v- do dr, 



fVdO' r-do rdO rsm'oj 



!>.( f/'r 2cos0dw\., . 



(6) —I ; : ]' sm Ode do dr, 



f> \r sin 0'\](p- r sin Od<f J 



,r,v ■" / ■ ^<^'ii' , A ■ ^<^>'^ , «sin 0%c\ ., . ,, , ,^ , 



(7) - r sin^ 1-4 sin f-2 — '"" sin Od<s do dr, 



l> \ dr'^ dr r J 



,,,, !j/s\\\Od'n' , H con Odw 2 sin ^^/r\ ., . „ , ,. , 



(8) ]r- sin Od<,^ do (h\ 



f\ rdo' rdO r J 



^_, /Y <r,r , 2d II ^2 cot Odr\., . 



(9) h — — ^ 1 : /•" sin Od(f dO dr. 



f>\r sin Ode' r' sin Ode r sin Ode j 



