46 Mr. Micuexr on the Means of difeovering the 
23. But though there is not the leaft probability that this 
element, fo eflential to be known, in order to determine with 
precifion the exact diftance and magnitude of a ftar, can wer 6b 
obtained, where it is in the fame circumftances, or nearly the 
fame, with thofe above fuppofed, yet the other elements, fuch 
as perhaps may be obtained, are fufficient to determine the dif- 
tance, &c. with a goad deal of probability, within {ome mode- 
ate limits; for in whatever ratio the real diftance of the two 
ftars may be greater or lefs than the diftance fuppofed, the den- 
fity of the central {tar muft be greater or lefs in the fixth 
power of that ratio inverfely ; for the periodic time of the re- 
volving body being given, the quantity of matter contained in 
the central body muft be as the cube of their diftance from each 
other. See Sir I. Newron’s Prin. b. 3d. pr. 8th. cor 3d. But 
the quantity of matter in different bodies, at whofe furfaces the 
velocity acquired by falling from an infinite height is the fame, 
muft be, according to art.12, dire€tly as their femi-diameters ; 
the femi-diameters therefore of {uch bodies muft be in the tri- 
plicate ratio of the diftance of the revolving body ; and confe- 
quently their denfities, by art. 11, being in the inverfe dupli- 
cate ratio of their femi-diameters, muft be in the inverfe fex- 
tuplicate ratio of the diftance of the revolving body. Hence 
if the real diftance fhould be greater or lefs than that fuppofed, 
an the proportion of two or three to one, the denfity of the cen- 
tral body muft be lefs or greater, in the firft cafe, in the pro~ 
portion of 64, or in the latter of 729 to 1. 
ecliptic, would be 215 times its apparent diametcr ; and as the bright ftar in 
Lyra appeared to Mr. Herscuer about a third part of a fecond in diameter, if this 
was its real difc, and it was no bigger than the fun, it would confequently have 
sn @nnual parallax in-the pole of the ecliptic of about 72’. 
24. There 
