TRANSACTIONS OF SECTION A. 567 



and 



whence, when sin d is very small, 



? = 52-8.10''(l-^/') 



Let now, for example, .t;, = 3-09.10'" kilometrei^, and '^'' = 10'; and, therefore, 



sin(9 = ^ = 3'16.10-* ; -whence, w = 291,000 kilometres per second, and 

 i = T - 7,080 seconds = T - 2 hours approximately. 



By these results it is most interesting to know that our supposed sphere of 

 perfectly compressible fluid, beginning at rest with density 1-61.10--' of that of 

 water, and of any magnitude large or small, and left unclogged by ether to shrink 

 under the influence of mutual gravitation of its parts, would take nearly seventeen 

 million years to reach -0161 of the density of water, and about two hours longer 

 to shrink to infinite density at its centre. It is interesting also to know that if 

 the initial radius is 3-09.10"' kilometres, the inward velocity of the surface is 

 291,000 kilometres per second at the instant when its radius is 3-09,10'-' and its 

 density -0161 of that of water. If now, instead of an ideal conipressible fluid, we 

 "■0 back to atoms of ordinary matter of all kinds as the immitive occupants of 

 our sphere of 3-09.10"' kilometres radius, all these conclusions, provided all the 

 velocities are less than the velocity of light, would still hold, notwitlistanding the 

 ether occupying the space through which the atoms move. This would, I believe,' 

 exercise no resistance whatever to uniform motion of an atom througli it; but it 

 would certainly add quasi-inertia to the intrinsic Newtonian inertia of the atom 

 itself moving through ideal space void of ether; which, according to the New- 

 tonian law, would be exactly in proportion to the amount of its gravitational 

 quality. The additional quasi-inertia must be exceedingly small in comparison 

 with the Newtonian inertia, as is demonstrated by the Newtonian proofs, includ- 

 ing that founded on Kepler's laws for the groups of atoms constituting the planets, 

 and movable bodies experimented on at the earth's surface. 



In one thousand seconds of time after the density -OlOl of the density of water 

 is reached, the inward surface velocity -n-ould be 305,000 kilometres per second, 

 or greater than the velocity of light ; and the whole surface of our condensing 

 globe of gas or vapour or crowd of atoms would begin to glow, shedding light 

 inwards and outwards. All this is absolutely realistic, except the assumption of 

 uniform distribution through a sphere of the enormous radius of 3-09.10'" kilo- 

 metres, which we adopted temporarily for illustrational purpose. The enormously 

 o-reat velocity (291,000 kilometres per second) and rate of acceleration (13-7 kilo- 

 metres per second per second) of the boundary inwards, which we found at the 

 instant of density -0161 of that of water, are' due to greatness of the primitive 

 radius, and the uniformity of density in the primitive distribution. 



To come to reality, according to the most probable judgment present know- 

 ledge allows us to form, suppose at many millions, or thousands of millions, or 

 millions of millions of years ago, all the matter in the universe to have been 

 atoms very nearly at rest" or quite at rest; more densely distributed in some 

 places than in others, of infinitely small average density through the wliole of 

 infinite space. In regions where the density was then greater than in neighbour- 

 ing regions, the density would become greater still ; in places of less density, the 



' ' On the Motion produced in an Infinite Elastic Solid by the Motion through 

 the Space occupied by it of a Body acting on ij;^only by Attract^ion or Repulsion,' 

 Cong - - _- ■ ^ x^ , -- ^ 



Part _, ^w„^, „„.... _ -- , 



Kelvin's Collected Math, and Phjs. Pa2'crs, vol. ii. art. Isix. 



P P 



