Mathematical Conditions of the Formation of Nebulæ.

91. It can be shown, that if two gaseous suns impact completely, the suns having had no original proper motion, and that were the whole of the motion converted into heat, and this heat into the potential energy of expansion, then the new sun would have a diameter the sum of the diameters of the original suns. It can also be shown that such a condition is one of molecular equilibrium.

92. Consequently the complete impact of two gaseous suns not possessing much original motion, and brought together by gravitation, does not make a nebula of them; but as soon as page 29 the paroxysm of the encounter is over they are of the same temperature as before, having used up all their energy in increasing to the sum of their original diameters. This is a remarkable and unexpected result.

93. Were there great original proper motion, they might become a nebula by complete impact; but were the original velocity of the two bodies very high, and the impact of very great energy, then an indefinitely-defused nebula would result. Such a nebula, if hot, would be unstable, and would indefinitely expand. Croll's theory to account in this way for an increase in the age of the sun's heat is therefore umtenable.