u4%lionumktd and Nautical Vollections. 369 



r sin a t 



P = -r-- - -T 



r sin T t 



R"' sin (A'" — A") t" , 



q =: 1 L — — , and 



R' sin (A" — A) t' 



h = R'sin.(A"-A')(9-^)m . ^^^ ^^^^ 

 tang B" — ni sin (A" — a.' ') 



H = 1 + Ip + -A_. 



But since in the last member of the equation for H, the k is 

 divided by M, the expressions for these quantities having 



nearly the same denominators, we may take at once =: 



R' sin (A" — A')(o — p) mt' , .,, ,,. , ^ ., 



^^ -H LS , and with this value of H we 



(^) ( 7n sin (A" — a') — tang /3') t" 



may proceed to correct the coefficients. We shall then obtain 



two new equations for r" and k" very little different from the 



former, from which the corrected value of §' will be found so 



much the more easily, as its limits are so nearly ascertained by 



the previous determination of (5). Two new hypotheses for j', 



and an easy interpolation, will be fully sufficient for the purpose. 



§.62. 



In order to illustrate the mode of computation still more 

 completely, I shall return to the example of the comet of 1769, 

 §. 46, 47. We have already found (§. 51) \P =r 138®.19'.55", and 

 we had (p = 135°.52'.24", x = 4°.27'.46", consequently <r = 

 2°.27'.31 ", T = 2°.0'.15" ; we had also r' = 1.02367, and /•"'= 

 0.83504 ; consequently for p we have 



Log r' 0.010160 Log r'" 9.921707 



+ Log sin T 8.543722 + Log sin a- 8.632433 



8.553882 = L(r"' sin<7)8.554140 

 — L(r'sin t) 8.553882 



= L. 1000.60 0,000258 

 t" 



And in this case -j being = 1, we have p = .00060. 



