24.2 M^^' Herschel 071 the 



field of view of a telefcope is a cone, we fliall have its (o- 

 lidity to that of the great cone of flars, formed by the above 

 conftrufllon as the fquare of the diameter of the bafe of the 

 fic-d of view, to the fquare of the diameter of the bafe of the 

 great cone, the height of both being the fame ; and the flars iii 

 each cone being in the ratio of the foUdity, as being equally fcat- 

 tered (^), we have 72= v^B'S. And the length of the vilual 

 ray = « - i, which was to be determined. 



(/) We o\ight to remark, that the periphery and bafe of the cone of the field 

 of vicv, in g'Tgint,', would ir» all probability feldom fall exaftly on fuch ftars as 

 would produce a perfecl e(pi:'.lity of fituation between the ilars contained in the 

 fmall and the great cone; and that, confequer.tly, the folution of this problem,, 

 where we fu-ppoie the flars of one cone to be to thofe of the other in the ratio' 

 of the folidity on account of their being equally fcattered, will not be flriAly 

 true. But it fliould be remembered, that in fmall numbers, where the different 

 terminations of the fields would moll affev^ this folution, the ftars in view havci 

 always been afcertained from gages that were often repeated, and each of vvhich^ 

 confiilcd of no lefs than ten fields fucceffively taken, fo that the different deviations 

 at the periphery and bafe of the cone would certainly compenfate- each other 

 fufficienrly for the purpofe of this calculation. And that, on the other hand, in- 

 higli gages, which could not have the advantage of being fo often repeated, thefc 

 deviations would bear a much fmaller proportion to the great number of liars ia 

 a field of view j and therefore, on this account, fuch gages may very juflly be 

 admitted in a folution where praftical truth rather than mathematical precifion 

 is the end we have in vicvv. It is moreover not to be fuppofed that we imagine 

 the flars to be actually arranged in this regular manner, and, returning therefor© 

 to our general hypothefis of their being equally fcattered, any one field of view 

 pfomifcuoufly taken may, in this general fenfe, be fuppofed to contain a due 

 proportion of them ; fo that the principle on which this folution is founded may 

 therefore be faid to be even more rigoroufly true than we have occafion to mfift 

 upon in an argument of this kind, ^ 



the 



