a Problem in physical Astronomy , 547 
because they would have detained him too long from the im- 
mediate subject of this paper, if they had been inserted in it, 
are given in the following Appendix. 
AN APPENDIX TO THE FOREGOING PAPER: 
In which the Method of obtaining the Sums of the very slowly 
converging numerical Series which are used therein, and of 
many others of that Kind which arise in the Fluents of Bino- 
mial Surds, is explained and illustrated ; and some Observa- 
tions, tending to facilitate and abridge the Computations of 
the Coefficients A and B, are added. 
i 
1. As the sums of the very slowly converging numerical 
series, which arose in Art. ^,11, and 16, of the preceding paper, 
are not exhibited in any book that has come to my hands, and 
as series of that kind frequently occur, I conceive that the fol- 
lowing method of obtaining their sums will be acceptable to 
the lovers of mathematics in general, and particularly to those 
who have frequent occasion to use the sums of such series. 
And, having observed, while considering the literal expressions 
in the preceding paper for the values of A and B, that others, 
no less accurate, might be derived from them, by which the 
arithmetical operations would be facilitated and abridged, I 
thought these observations might likewise be acceptable to those 
who are engaged in the theory of astronomy, and have inserted 
them also in this paper; which, therefore, consists of two prin- 
cipal parts, the summation of the slowly converging series, and 
the observations now mentioned. 
4 As 
