242 Mr, Herschel on the 
field of view of a telefcope is a cone, we (hall have its fo- 
il cl it y to that of the great cone of ftars, formed by the above 
conflruflion as the fquare of the diameter of the bafe of the 
field of view, to the fquare of the diameter of the bafe of the 
great cone, the height of both being the fame ; and the flats in 
each cone being in the ratio of the folidity, as being equally feat- 
tered (£), we have n — vAETS. And the length of the vifual 
ray = n - i, which was to be determined. 
(/;) We ought to remark, that the periphery and bafe of the cone of the field 
of view, in gaging, would in all probability feldom fall exaftly on fuch liars as 
would produce a perfect equality of fituation between the liars contained in the 
fmall and the great cone; and that, confequently, the folution of this problem, 
where we fuppofe the liars 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 ftridtly 
true. But it Ihould be remembered, that in fmall numbers, where the different 
terminations of the fields would moll affeft this folution, the liars in view have 
always been afeertained from gages that were often repeated, and each of which 
confifled 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 
fufficiently for the purpofe of this calculation. And that, on the other hand, in. 
high 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 in 
a field of view; and therefore, on this account, fuch gages may very juflly be 
admitted in a folution where practical truth rather than mathematical precifiom 
is the end we have in view. It is moreover not to be fnppofed that we imagine 
the liars to be a&ually arranged in this regular manner, and, returning therefore- 
to our general hypo thefts of their being equally fcattered, any one field- of view 
promifeuoufly 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 r.ig.oroufly true than we have occafion to infift 
upon in an argument of this kind. 
