[471 ] 
ncceHity of ufing eight figures for the fame purpofc 
thus, the logarithm fine of 89° o' o'Ms 9-9999338, the 
fame feven figures as for the logarithm fine of 89° o' i". 
From this confideration it follows, that the analogies 
commonly laid dow n and ufed for the fblutions of fpheri- 
cal triangles are not in all cafes equally convenient, and 
I might fay, equally accurate ; and that it would be more 
eafy and exadt in calculations to find what was required, 
by means of fines of arcs, which, being fmail, require 
the ufe of only a few places of figures. Now the cafes 
which often occur in afironomy, where fpherical trigo- 
nometry can only be of ufe, are generally of fuch a na- 
ture that we know nearly, or at leaft wdthin a few de- 
grees, what the required fide or angle is, there is nothing 
therefore wanted but to find how" much this quantity, or 
firfl approximation, differs from the true value of the 
fide or angle. Thus in calculating the right afeenfion of 
any point of the ecliptic, whofe longitude and declina^ 
tion are known, inflead of finding the right afeenfion im- 
mediately, it will be more convenient to feek for the dif^ 
ference between the longitude and right afeenfion, which 
as it never exceeds 2j four or five places of figures will 
always be fufficient to determine it within a fecond. And 
in other fimilar cafes, rules might be made agreeable to 
the exigency of each particular cafe, which would be bet- 
ter than the application of the general method of folu- 
tion. Some examples of which fhall be fhewn in the 
VoL. LXV. R r r followdng 
