. DENSITY. 
by dbfervation the planet is found to produce in difturbing 
the motions of the other planets.’ For the determination of 
the denfity of eae La Place prefers deducing it from 
analogy, by obferving the law of the set sata a en 
of the planets relatively to their diftances fr 
it muft a acknow wledged, that fuch een is ele 
better t 
The firtt of ~ above "methods? is founded ae a theo- 
rem, derived from the dodtrine of central] forces 
Let F reprefent the attraGtive force of the fun 
T the Aanour time of the planet, whofe inafs we wilh 
to deter 
the radius of sire obit of the plane 
? the radius of the iulegl - the Tatelit 
F’, the attra€tive force e planet ae its fatellite. 
Ts the periodic time of the fatellite. 
M, the mafs of the fun 
M, the mafs of the planet. 
5 
It will then appear that M : M’:: 
For by the principles of central forces 
xy’ 
F; FE’; oe a : Ts , 
and fince we fuppofe the attractive force of the planet upon 
its fatellite to vary antes as the {quare of the diftance 
r?, 
Multiplying thefe two op sportionk: and dividing by F’, 
: 73 
F: if T? * 1h Ts 3 
bot F: f, are the attraGtive forces of the fun and planet, 
upon a particle of matter, placed at equal diftances, and 
are aa et to the maffes. Therefore, 
M: M’: a : aa 
Example.—To | the mafs of Jupiter. 
rir: are 7s 
fey ar soni: 16.689 
, (63662)% (798 +2) ave . I 
Therefore M : M (365.256) ' 6.089) * PTT APT 
fr) 
But, as the force | retains Jupiter i in its orbit, is the 
of the attra@ions of Jupiter and the fun, the deno- 
minator muit be increafed by unity, and the mafs of Jupi- 
. I 
ter will be 7067.08" 
In the fame manner, La Place finds Saturn 7 : 
3359-4 
The Georgian 
1950 
The fecond method confifts in determining the diftance 
which a planet (as the earth) deflcéts from its tangent in one 
fecond, by comparing its angular velocity, with the mean ra- 
by experiment the 
dius of its orbit; ard having foun 
the 
{pace which a heavy body defcribes in one fecond by 
force of gr the furface of the planet, we can co 
pute the {pace it would fall through in the fame time, if re 
moved to the di f the fun, and fince at equal diftances 
forces. By this method the mafs of the earth is found to 
be hae of the fun. 
329630 
the mafies of Venus and Mars - been eftimated by 
the fecular variation which thofe bodies produce on the fo- 
La Place concludes the mafs of Mars —— 
18460825 
—, the fun being unity. Thefe 
lar fyftem. 
and that of Venus 
aE 37 
quantities were obtained by the fecular dimioution of the 
ey cu me oo and from the acceleration of the 
mean mo 
he denfitics of he erical bodies ake as their mafles, die 
vided by the cubes of their femi-dia 
The diameters of the planets bane found by obfervation, 
and their maffes by the above methods, the deniities of 
the planets appear to be as follows 
un 1.0000 
Earth 3.9393 
Jupiter 0.8601 
aturn 0.4951 
Georgian 1.1376 
r. Vince, in his Aftronomy, a us the following me 
thod ‘of finding the denfities of the planets : 
ut d = the denfity of the central body, 
m = its diameter. 
.@ = its quantity "of m 
P = the alge time cot ties evolving body, 
D = the me ates ee of the revolving body from 
its cen 
S = the fine of ie ete under which m appears at 
the diftance D, to radius unity. 
Then a varies as dm, but P? varies as 3 which varies 
D: 
as Ta hence d varies as aa But s= D? ; hence d vae 
ries as x 3 we will therefore aflume d= ra oy 
oe the fun.—If we take the earth as the revolving body, 
= 365, 25639 days, according to M. de la Caille 5 = 
©. — 155 = hin. 32’, 1", 5, the mean apparent diameter 
of the fun, hence d = —_—_— 
0.0993155° x 365. 25639" 
9. 
For the earth.—Here we muft take the moon for the res 
= —— = 36.7569. 
0.0331553 x 27. saa 
For Jupiter und has obferved the greateft elon- 
gation of its fourth, fatellite to be 8’ 1 d the corre- 
{ponding diameter of Jupiter to be 39”, ie the fine S of 
the angle under which the diameter of Jupiter appeared 
at that fatellite at that time was 0.0 : lfo P= 
16.68898- aoe according to M. Wargentin; hence 
= 7-3857- 
oO. eee x 16.6! 68898" 
For Saturn.—According to Mr. Pound, the greateft 
esti OF i its fourth fatellite i . . “58 and the correfpond- 
ing diameter of Saturn = 18”; eS = 0.10112. Allo. 
P15 9454 days, according : "Dr. Halley, hence d = 
=o <==, = 3.8038. 
O.1OTI23 X 15 ey.,54? 
For the Gat. —If we take the fecond fatellite, we- 
have, according to Dr. Herfchel, its greateft elon aie 
= 44".23, and the cerrefponding diameter of the p 
= 3” 
