SECT. 2.] OF WHICH TWO ONLY ARE COMPLETE. 245 



b = 11.009449, x = 1.083306, log A = 0.0728800, log/* = 9.7139702w 

 j&quot; = _ 2.082036, x* = + 6.322006, log Jl &quot;= 0.0798512ra log/*&quot;= 9.8387061 



MD= 3717 51&quot;.50, A&quot;D = 89 24 11&quot;.84, = 95 5&quot;.48 



D = 25 513.38, #7) = 11 20 49 .56. 



These preliminary calculations completed, we enter upon the first hypothesis. 

 From the intervals of the times we obtain 



log & (f t] 9.9153666 

 log k (t&quot; 0=9.9765359 

 log k (t&quot; f O = 0.0054651, 

 and hence the first approximate values 



log P = 0.06117, log (1 -f P ) 0.33269, log Qt = 9.59087 

 logP&quot;= 9.97107, log (1 + P&quot;) 0.28681, log Q&quot;= 9.67997, 

 hence, further, 



c = 7.68361, log d = 0.04666 n 

 c&quot;= + 2.20771, logrf&quot;= 0.12552. 



With these values the following solution of equations I., II., is obtained, after a 

 few trials : 



x = 2.04856, z = 23 38 17&quot;, log r = 0.34951 

 x&quot;= 1.95745, s&quot;=27 2 0, logr&quot;^ 0.34194. 

 From , / and e, we get 



C C&quot; = i/ i/ = ir r 5&quot;: 



hence v v, r, v &quot; v&quot;, r&quot;, will be determinable by the following equations : 

 log r sin (v v}= 9.74942, log r sin (v v + 17 7 5&quot;) = 0.07500 

 log/- &quot; sm(v &quot;v&quot;)= 9.84729, log/&quot; sin (z/&quot; v&quot;+ 17 7 5&quot;) = 0.10733 

 whence we derive 



v __ v 14 14 32&quot;, log r = 0.35865 

 v &quot; v&quot;= 18 48 33, log/&quot;=: 0.33887. 

 Lastly, is found 



log (H 01) = 0.00426, log (n 12) = 0.00599, log (n 23) = 0.00711, 

 and hence the corrected values of P , P&quot;, Q , Q&quot;, 



