14 Sir William Thomson [Jan. 21, 



the sun have his present slow rotation when shrunk to his present 

 dimensions. This exceedingly exact aiming of the one body at the 

 other, so to speak, is, on the dry theory of probability, exceedingly 

 improbable. On the other hand, there is certainty that the two bodies 

 A and B at rest in space if left to themselves undisturbed by other 

 bodies and only influenced by their mutual gravitation, shall collide with 

 direct impact, and therefore with no notion of their centre of inertia, 

 and no rotational momentum of the compound body after the collision. 

 Thus we see that the dry probability of collision between two neigh- 

 bours of a vast number of mutually attracting bodies widely scat- 

 tered through space is much greater if the bodies be all given a 

 rest, than if they be given moving in any random directions and with 

 any velocities considerable in comparison with the velocities which 

 they would acquire in falling from rest into collision. In this con- 

 nection it is most interesting to know from stellar astronomy, aided 

 so splendidly as it has recently been by the spectroscope, that the 

 relative motions of the visible stars and our sun are generally very 

 small in comparison with the velocity (612 kilometers per second) 

 which a body would acquire in falling into the sun, and are compar- 

 able with the moderate little velocity (29-5 kilometres per second) of 

 the earth in her orbit round the sun. 



To fix the ideas, think of two cool solid globes, each of the same 

 mean density as the earth, and of half the sun's diameter ; given at 

 rest, or nearly at rest, at a distance asunder equal to twice the earth's 

 distance from the sun. They will fall together and collide in exactly 

 half a year. The collision will last for about half an hour, in the 

 course of which they will be transformed into a violently agitated 

 incandescent fluid mass flying outward from the line of the motion 

 before the collision, and swelling to a bulk several times greater than 

 the sum of the original bulks of the two globes.* How far the fluid 

 mass will fly out all round from the line of collision it is impossible 

 to say. The motion is too complicated to be fully investigated by 

 any known mathematical method ; but with sufficient patience a 

 mathematician might be able to calculate it with some fair approxima- 

 tion to the truth. The distance reached by the extreme circular 



introduced within the last sixty years (by scientists speaking as now, each his 

 own vernacular) to signify the importance of the special subject referred to in 

 each case. The expression moment of momentum is highly valuable and con- 

 venient in dynamical science, and it constitutes a curious philological monument 

 of scientific history. 



* Such incidents seem to happen occasionally in the universe. Laplace says 

 some stars " have suddenly appeared, and then disappeared, after having shone 

 for several months with the most brilliant splendour. Such was the star observed 

 by Tycho Brahe in the year 1572, in the constellation Cassiopeia. In a short 

 time it surpassed the most brilliant stars, and even Jupiter itself. Its light then 

 waned away, and finally disappeared sixteen months after its discovery. Its colour 

 underwent several changes ; it was at first of a brilliant white, then of a reddish 

 vellow, and finally of a lead-coloured white, like to Saturn." (Harte's translation 

 of Laplace's ' System of the World.' Dublin, 1830.) 



