18 



STATEMENT AND EXPOSITION OF 



the solar equator, these molecules would, by their attraction, be brought closer to 

 the atmosphere, in the progress of its condensation, and would not cease to belong 



to it until, in consequence of this 

 Fig. 3. motion, they were brought nearer 



to the platte of the equator.^ 



(26) The description proceeds, 

 saying of these "zones of vapor" 

 (or rather nebulous zones) succes- 

 sively abandoned, that these zones, 

 must, in all probability, form by 

 their condensation and the mutual 

 attraction of their molecules, diverse concentric nebulous rings circulating around 

 the Sun. The mutual friction of the molecules of every ring must accelerate some 



and retard others, until all had acquired the same 

 angular motion. And (when all this went round 

 together) the actual velocity of molecules further 

 from the centre would be greater than that of 

 those nearer; the parts near the outside of the 

 ring going imiformly round in a large circuit, in 

 the same time in which those nearer, also moving 

 uniformly, described a smaller circuit. Thus, 

 Avith time the same, the angle ACB being the 

 same for both, the part, such as AB, is greater 

 than the similar part ah of the smaller circuit;^ 

 and the jiart of AB described in a unit (say a 

 second) of time, greater than the similar part of 

 ah; i.e. the actual velocity in AB is great eY. 



(27) Besides all this, in the progress inward of the particles forming the nebul- 

 ous rings, the actual velocity of rotation of those particles would be increased confor- 

 mably to the principle of the conservation of areas; which requires that an area 

 such as ACB, in the figure, should continue to be passed over, by the rotation of 

 GB, in the same time; so that if ^C and BG he shortened, the figure must be 

 hroader to preserve its size, or the distance BA, traversed in the same time must be 

 greater than before ; *. e, the particle must move faster along BA ; while the par- 

 ticles attracted toward the others outioard, and then forming the inner part of the 

 ring, would, in obedience to the same principle, have tlieir actual velocity of rota- 

 tion diminished. 



(28) Then if all the molecules of the nebulous ring continued to condense with- 

 out being disunited, they Avould at length form a liquid or a solid ring.^ But the 

 regularity requisite in such a case, in every part of the ring and also in its cooling, 

 must make this a very rare phenomenon. Accordingly the solar system affords but 

 a single example of this kind — that of the rings of Saturn. 



' The diagrams are our own. M. Laplace employs none in his Exposition du Systfeme du Monde. 



^ The difference being = Be. 



^ Or a ring of small solids closely arranged, as seems to be actually true of the rings of Saturn. 



