14 



5 



OS 



o 



6 , 



O -^ 



1^ 

 ■< 

 o 



l-H 



Q 



H-l 

 1^ 

 X 



Colorado College Studies. 

 dp 



■^ I X--^^ = — -vV, 



as 



CO ^ 



Y- 



fjdr St 

 dp '-r 



,»rdo of 

 dp ow 

 pdz fit 



Z--^ = 



X- 



dp 'In , r-fd'ii , (III II , '/■" 2dr , d u\ 

 — ^= ,-ir 1 \ \ — ^ — \ \ 



I'dr St p \dr rdr r' r'do' rdO dz' ) 



dp '''■,, III d'r . Hdr , d'^r . 2du . rd^v 

 -^— = r \-2 in: ( '"-7^ + 



dp ow ."/(I'll 



dr ' dr ' rdO' rdO ' dz' 



I b's 



dw (I'lC (i'lC 

 I'dz lit f>\dr' rdr r'-dO' dz' 



Z 'J^^J^-l:, 



■^ X--^^ = 



dp 



/'dr '5/ 



rr—r sin^^ w', 



^ -; Y- 

 - z- 



= r f- I iiv—r sin ^'cos ic . 



(>r do 

 dp 



o( 



ow 



^ C 



•A 



< 



Q 



O ^ 

 6 

 Q 



PS 



<! 



O 





-=r sin (-2 sin ^ uic + l r cos ^ i"if. 



I'V sin ^^c/c' o7 



(^//) oil , . .,„ ., !Jfd-u , 2di( 2ti , d'u , 

 — rr— ?-sin^u- (— H ■ \-- — - + 



odr ot 



du .^, 2dv 2r . ^, 



cot^' cot ('-{ 



rdO rdo r r' sin '-Od<s- 



P\dr rdr r' rdO' 

 (I'll 2 dw' 



rdc 



f'v , , dv 



dp '^v , f. . ^, ,. .. !' f d-v .dv 



i— =7' 1-2 uv—v sin cos w r [-4 h 



f>rdO St /'\ dr dr 



2c , d'v . 2 du , . ^ dr 

 + cot p- 



d'r 



tl 



I ■ L 



r rdo 

 2 cos dm 



r sin ^^r/cr 



dp 

 f>r sin 6'd<r 



(/^^ 



rdo r sin 'V^ ?• sin '"^'tZc:'- 



= r smO- — f-2 sin Otiir + 2 r cos Oviv ( r sin 



lit f 



dSo , . . (liv , 2 sin Ow , . aI'w , .. jlw 



1-4 sin 1 \-s\n0 1-3 cos 



dr' dr r rdo- rdO 



2 w sin 



+ 



d'H) 



+ 



2dn 2coi0dv 



rs\nOd(f'- r'-s\i\Od<f r sin Odf 



