24 
PROFESSOR G. H. DARWIN ON THE MECHANICAL CONDITIONS OF 
Finding x ‘^ 7 } for these four values and combining them bj the rules of integration, 
I find 
_ 2-1767, when 2-786 a.(35) 
CtoO 
We thus see that the mass of the whole system is 2-1767 times the mass of the 
isothermal nucleus, and its radius is 2-786 times the radius of the nucleus. 
The mass of the isothermal nucleus is thus 46 per cent, of the whole. M. Fitter, 
taking the ratio of the specific heats as instead of f, says that the proportion is 
about 40 per cent. 
§ 6. On a Gaseous Sphere in “ Isothermal-Adiabatic” Equilibrium. 
M. Fitter calls a sphere, with isothermal nucleus and a layer in convective 
equilibrium above it, a case of isothermal-adiabatic equilibrium. Since the height of 
an atmosphere in convective equilibrium depends only on the temperature at the base, 
and since the isothermal nucleus in our numerical example is at minimum temperature, 
the thickness of the adiabatic layer is a minimum, and the isothermal nucleus a 
maximum. 
We are now in a position to collect together all the numerical results of the last 
two sections in a form appropriate for our subsequent investigation. It will be 
convenient to refer all the densities and masses to the roean density and mass of the 
isothermal nucleus. Gravity may also be referred to gravity G at the limit of the 
isothermal nucleus, and velocity to v^, the mean square of velocity of agitation in the 
isothermal nucleus. 
