354 D, Trowbridge on the Nebular Hypothesis. 
But equation (5) gives 
Me? —Mit= Safe De iti—tida se 
From (8) and (9) we have 
B[M’A? —Ma*] = * af¢ Dalas(1—2) Wa oe 
Differentiating (10), A being a constant, we have 
sBMat= = mpD,[as(1—e). . . . - + (1) 
We do not know the relation between a and e, and we might 
assume any abapete relation that would cause e to become 0 at 
the centre; but it will be sufficient for our purpose to suppose & 
constant. ‘This 5s. will cause (11) to assume the form 
= == Ha 3 . ° ° * * (12) 
From this equation, we see that the gukevold increased in 
density very rapidly near the centre. If the density at the 
mean distance es we earth from the sun be called unity, then 
=a=H=1; and the density at the mean distance of the sev- 
eral planets will Pa as given in the following table. 
TABLE ITI, 
Name. Density. 
Mercury, Oe eas) STF opine 
Venus, - - - - - 31070000 
Earth, - - - - - T-oD0oC000 
M - - . - 0-23440000 
perils - - - - 019760 
Jupiter, - - - - 000311300 
Saturn, . - - - 0-000387310 
Uranus, - - - - 000003234 
N ees + eS - 000001485 
above nutnbers, however, must be considered as vale a very 
rough approximation to abe true density. 
2. I Sr ES es the angular motion of all parts of the solar 
: wMk? — A = constant, or pene =oA, .. ~ (18) 
= =e principle of the vis viva gives 
“ iy a Seelam = W suppose . . (14) 
legitimate ; 
nue k. 
