Fig. 2. 



CB 



L 



264 Mr. J. Ennis on the Physical and Mathematical 



every particle would float on the level surface ; still the motions 

 of all the particles would be in the direction of an inclined 

 plane, and subject to calculation as inclined- 

 plane motions. In fig. 2, a ball rolling down 

 the incline from A to C must gain the same 

 velocity as if it fell from A to B through the 

 same height. And in fig. 1 the same truth 

 is illustrated by its triangle ABC. If the 

 outer circle represent the surface of our solar nebula when 

 expanded to the orbit of Neptune, and the inner when expanded 

 to Uranus, then the velocity of rotation gained in contracting 

 from the outer to the inner must be the same as the velocity 

 gained by a fall directly toward the centre from orbit to orbit ; 

 that is, the particle at A moving by rotation and contraction 

 to C would acquire the same velocity as if it fell from A to B, — 

 friction always excepted. 



Because action and reaction are equal and in opposite direc- 

 tions, it follows in our terrestrial inclined planes that, as the 

 ball rolls downward and forward, the plane must move upward 

 and backward with the same momentum. But this upward 

 and backward motion cannot occur in the nebula. This may 

 be illustrated by the movements of comets. A comet in its 

 aphelion at A (fig. 3) must gain the same velocity in moving 

 to C as if it fell in a direct 

 line to B, equally near to the 

 sun at S ; the distance B S 

 = C S, and B' S = C S &c. 

 Also when the comet arrives 

 at C, 6", C'Vand 0"'< re- 

 spectively, it must have the 

 same velocity as if it fell to 

 the points B', B", B /;/ , and 

 W" in a direct line, equally 

 near the sun in the focus S. 

 At every step the sun, in- 

 versely in proportion to its 

 mass, moves in the direction 

 opposite to that of the comet. 

 But if there were many comets 

 equally large and distant, and 

 moving in the same plane and 

 direction all around the sun, 

 then they would counteract 

 one another's influence on the 

 sun, and the sun would not 

 be moved. The particles on 

 the surface of the nebula, re- 



