370 Jstrotiomical and Nautical Colleclioiis. 



For q we have A" - A' = 3°.53'.26", und A'" — A" = 

 3°.53'.49", hence 



Log R' 0.003132 Log R'" 0.002184 



+ Logsin(A'-A')8.831555 + Log sin (A"'-A")8.832267 



8.834687 L(R"'sin[A"'-A"]) 8.8344.51 

 -L(R' sin [A— A']) 8.834687 



Log .99946 9.999764 



conseqyently (j ~ — .0005U. New in order to find _— , we 



have (7 — p) = — .00114. Hence 



Log 11' sin (A' - A') 8.834687 



Log (q - }>)[ -] 7.056905 



Log m 9.648938 



5.540530 

 — Log .12210, the denom. §. 46 9.086716 

 _ Log (?) 9.541829 



Log -0.00082 6.911985 



We have therefore H = 1 +p— + -\- = .99978, and 



t (^)M 



Log H = 9.999904 ; and in order to obtain the corrected co- 

 efficients in the equations for r" and k", we have only to sub- 

 tract 96 from the logarithms of the terms containing M, and 192 

 from those which contain M' : they will then become 

 /" = V (1.01011 - 1.21455^' + .90829^'^) 

 r = V ( -01868 - .10958^' + .49694/0 

 These equations differ so httle from the former, that it is not 

 worth while to recalculate / from them, especially as the calcu- 

 lation would only be a repetition of the former. It is obvious 

 from this example, how nearly accurate the supposition, that the 

 chords are divided in tlie proportion of the times, proves to be 

 for an interval of eight days. I must however observe, that the 

 value of M, and that of the small arcs c-, r, A" — A', A"' — A", 

 must be computed with great care, in order that the correction 

 deduced from them may not be erroneous. 



