Diftance, Magnitude, &c. of the Fixed Stars, &c. 39° 
fub-duplicate ratio of theilé reCtangles, it will be in the fub- 
duplicate ratio of the lines CD, Cd inverfely. Accordingly the 
velocities of comets revolving in parabolic orbits are always in 
the fub-duplicate ratio of their diftances from the fun in- 
verlely ; and the velocities of the planets, at their mean dif- 
‘tances (being always in a given ratio to the velocity of fuch 
comets, viz. in the fub-duplicate ratio of 1 to 2) mutt neceffa- 
rily obferve'the fame law likewule. 
g. Cor. 2. The magnitude of the central body remaining 
the fame, the velocity of a body falling towards it from an 
infinite height will always be, at the fame diftance. from the 
point C, taken any where without the central body, in the 
dub-duplicate ratio of its denfity ; for in this cafe the diftance 
Cd will remain the fame, the line rd only being increafed or 
diminithed in the proportion of the denfity, and the rectangle 
r€ confequently increafed or diminifhed in the fame proportion. 
 to.;Cor. 3. The denfity of the central body remaiuing the 
fame, the velocity of a body falling towards it from an infinite 
height will always be as its femi-diameter, when it arrives at 
the fame. proportional diftance from the point Cs for the 
weights, at the furfaces of different {pheres of the fame denfity 
are as their refpective femi-diameters ; and therefore the fides 
RD and CD, or any other fides rd and Ca, which are in a 
given ratio to thofe femi-diameters, being both increafed or 
diminithed in ‘the fame propertion, the re@angles RC or rC 
will be increafed or diminifhed in the duplicate, ratio of the 
femi-diameter CD, and — the velogey in the,fimple 
ratio of CD. 
11. Cor. 4. If the salocitin of a body falling from an ake 
height towards different central bodies is the Gunes when it ar- 
rives at their furfaces, the denfity of thofe central bodies muft be 
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