( 274 ) 



2 r(/,3 4- 1/2 „2) 0^ _^. (2 a h sin 0^ + '/o a" sin 0^ cos ö,)] • 



If we now call the angle CM A, point C lying on the sphei'e A, 

 2 ip, we have evidently, O^ being ^ 180 — g) — 2 ip: 



sin Oi ■=■ sin (go -j- 2 j/y) = sin (f cos 2 ip -\- cos cp sin 2 ip , 



cos Oi=i — cos [ff ~\- 2 ijj) ■=. — cos (f cos2 \p ■\- sin cf sin 2 ip ) 



or as 



sin 7= cos (fi =^ — tan cp = — ; — 



a a h 



sin ip = -^— sin 2 U/ = — i/a^ — V4 ^^ cos 2 ip z= — (a^— V3 ^^j . 



a «^ ö"* 



also sin Oi^j [V2 '• («' - V3 R') + h R [/a^ - \, R"- ] 



cos ^1 = 4 I" - /' («' - Vs-K') + V2 r ii ^/«2 _ 1/4 /1:' 1 ; 

 «'* L - 



so, taking into consideration the relation 



h- = a" — Vj, r", 

 after reduction, we find : 



2ah sin Oy + 1/3 "2 «>' ^1 CO-' ^i = 7^^. [Vs »• l/«2 — 1/4 «-^ (3 a^ - V3 «*) 4- 

 + R y/a^ - 1/4 /i""- (3 a* + 1/3 «=^ (R' - '■■') - V4. R'' '■')] • • (1 ) 



^1 being equal to (180 — c/i) — 2 <// . 

 Now the form to be integrated is 



471 i^ 1 Y^^ + ^-)] ^ part of segment y^dh. 



