a Problem in physical Astronomy. 
which, when y = i, becomes 
&c. which is 
the value of v in Art. 12. of the foregoing paper. 
These three examples, I conceive, are sufficient to illustrate 
this method of summing the slowly converging numerical series 
which arose in the solution of the problem in the preceding 
paper. The three series of which the sums are now investi- 
gated are, as was before observed, the most difficult to sum of 
all that arose in that solution ; so that, whoever understands 
what is done here, may, with great ease, compute the sums of 
the rest of the series which are found there, and of many others 
of this kind, which arise in the solution of problems. 
II. Observations , tending to facilitate and abridge the numerical 
Computations of hand B in the preceding Paper. 
6, The radical factor \/(i — cc), in the literal expressions of 
the values of A and B, may be taken away, by multiplying the 
other factors by its equivalent 1 — — — £ — — i n con- 
2 o IO 
sequence of which, other expressions will be obtained, better 
adapted to the purpose of numerical calculation. This will ap- 
pear by the following operations. 
The product of v /(i — cc) x the other factor in the ex- 
pression of the value of A, in Art. 9. of the preceding paper, 
will be 
