If M be the total mass and a the radius of the nebula always supposed homogeneous
M´ = M (r3/a3),
and therefore
dM´ = 3 M (r2/a3) dr.
Hence the work done in the contraction is
(ε/r) M (r3/a3) · 3 M (r2/a3) dr = (3 ε/a6) M2 r4 dr.
Integrating, therefore, the total work of contraction is
⅗ (ε M2/a)
At the present moment a mass of 1 lb. at the surface of the sun would weigh 27 lbs. if tested by a spring balance. Hence
ε M/a2 = 27.