206 
MR. J. H. JEANS ON THE CONFIGURATIONS 
certainly below the critical value (about 2'2), so that as the rotation increases matter 
will be thrown off from the equator before the ellipsoidal shape can be reached. No 
matter how much material is ejected in this way, the central mass remains a mass of 
helium with y = if-, and so can never attain the ellipsoidal form. The mass will 
disintegrate completely by loss of matter from its equator, and there can be no fission 
into separate masses—unless, of course, the helium ultimately so changes its character 
that the average value of y becomes greater than about 2'2. 
Contrast this with the behaviour of the mass of iron and hydrogen already 
considered. The mass will lose matter by equatorial ejection, but the matter lost 
will consist entirely of hydrogen, and so this process will continually diminish the 
ratio of hydrogen to iron, and as the process continues the mass will continually 
approximate to a mass of incompressible iron. As soon as the ratio of hydrogen to 
iron is reduced to about one-third, the pseudo-spheroidal form becomes unstable, and 
the mass will assume a pseudo-ellipsoidal form. 
53. We are now in a position to follow the changes in a mass of gas whose rotation 
continually increases through shrinkage. At first we may assume the gas to obey 
the ideal laws, so that y will be less than if, and, as the rotation increases, a stage 
will be reached at which matter is ejected from the equator. Some of this matter 
will perhaps fall back on to the rotating mass, but some must also pass to infinity, 
this latter representing a real loss of mass and of angular momentum to the rotating 
body. The loss must be at such a rate that the figure of the rotating body always 
remains a pseudo-spheroid with a sharp edge, and the velocity of rotation remains 
always exactly equal to the critical velocity corresponding to this critical figure. 
When y is equal to If, the critical angular velocity is given by equation (180), so 
that w 2 = 0'36 x 271-/5. For the greatest value of y for which the pseudo-spheroidal 
figure is possible (about y = 2'2), the value of the critical angular velocity is given 
by equation (178), and this seems to be converging to a value not far from 
w 2 = 0'36 x 27 rp. We may perhaps conjecture that for all masses of gas which are 
throwing off matter equatorially the value of w 2 is nearly equal to 0'36 x 27rjo. 
As the mass shrinks p becomes greater, so that rotation becomes more and more 
rapid. A stage is reached in time in which the ideal gas laws no longer hold, owing 
to the distance apart of the molecules having become comparable with their diameters. 
The value of y now increases beyond its value for an ideal gas, and values of y 
greater than if become possible. When a value of y is reached which is about 
equal to 2‘2 if the mass of gas is perfectly mixed, but may be greater if the mixing is 
imperfect, the pseudo-spheroidal form becomes unstable, the mass assumes the pseudo- 
ellipsoidal form and the process probably ends by fission into two detached masses. 
54. The value y = 2'21 has been found by Koch for air at a pressure of 100 atmo¬ 
spheres and a temperature of — 79°'3 C., the corresponding density being 0‘23. 
Partly from this observational material, and partly from general theoretical 
principles, we may anticipate that the value y = 2’2 will be attained at a density 
