336 Prof. G. H. Darwin. [June 19, 



Then H, = ^-^, 



whence, with log Z7 already found in (q) as (V0464, and, reducing 

 inches to feet, 



H, = 1-60 ft. 



Again *, = & + = 9- 71 - 6-40 = 3-31, 



where the value of is-taken from (q). 

 Lastly, 



H" = 0-272H, = 0-44 ft., and " = , = 3. 



The factor 0'272 is an absolute constant. 



(u.) Final Evaluation of K 1? 0, F. 

 Taking the values of l(WZ), |(X + Y) from (p), 

 TH' sin (' + i f ) = (W Z) = 1176, 

 TR'cos(^+i\^~)= J(X+Y) = 6-47; 

 g' + i Y~ lies in third quadrant, and 



J = 241-2. 



Then since, from (q), ^ = 18'35, we have ' + i = 222'8 ; and 

 since from (q) { = 6'52, therefore ' = 216'3 ; whence 



K ' = f + t*' = 216-3 + 196-9 = 53-2, 

 where the value of u is taken from (q). 



Then H' = ~ cosec 



whence, with log T already found in (q) as 9'9241, and reducing from 

 inches to feet, 



H' = 1-33 ft. 



Also H, = O331H' = 0-44, and *,= *' = 53. 



The factor 0'331 is an absolute constant. 

 We now have to compute 



L = (X+Y) tan ^e+f'H' cos (?' + tan ^, 

 M = (W Z) tan |e-f H' sin (?'+ i) tan ^e, 



