396 MISCELLANEOUS STUDIES 



tures are required k can be put equal to k, then k 2 will equal k 2 . 

 From the value of ff (equation 24) and equation (163) we have for 

 the value of A0' 8 = ff (6 + A<') 



__ 1 _ ) _ rw Bb^(a -f- a g a: ) j cos c 4 i"a cos <i + k z sin ci"[ 

 " y^*, 1 ) '+V (~2fcT'~L a2 +** 2 J 



, + ^2 si n 3~l 

 -' + *.') J 



cos c, a sin e,~\ , F2a cos e 



sm " - 



sin (2a0 + . : " cos (2c() r- (169) 



Leaving w and therefore & 2 and e, undetermined for the present" 

 equation (169) can be reduced to the form 



.560 i 

 , cos(30* c 2 ) cos (30* 69) | .0155w> ( 



i J-* i , _ _ . - ccr\ i i 



-560 ' (.274 + V) 



( f.506 + .259A-,~| . , r.966fc, .1361 



| L .274 + Vj Sm at + [ .274 + V J C S at 



fl.046 cos s -f k* sin c,"] . _ ^ , ffc, cos c 3 1.046 sin e 3 "j 

 2(1.096 + ft>) " 2(1.096 + *,) J 



cos2af I (170) 



using the following values of the remaining constants : a,^ = .318, 

 a 2 = -.0166, Be- 3 ^=5.9, Cl = 195, c = 69, e3 =( l +e 2 ), c 4 =(e 2 ej, 

 r=.2, a =.523, &, = .0365, (pp. 347, 351, 376), k = .2, k 2 = 



.2 .0365w , tan e 2 =T-(p. 394). Assume w equals 3, then 



K 2 



A^.= .448 3.78 cos (30* 60) + 3.48 cos (30< 69) 



- .113 j 1.58 sin 30* + .441 cos 30* i =.448 .69 cos 30* .18 sin 30* 



(171) 



The values of the temperatures and their reductions are given in 

 table 12. 



