2()8 



Mr. J. Ennis on the Physical and Mathematical 



The harmony between gravity as the only projectile force, 

 and the velocities of all the planets and asteroids, is further 

 confirmed by the satellites. By taking into account the masses 

 of the planets in our five planetary systems, I found that in 

 all cases the force of gravity was strong enough to produce in 

 the planetary nebulae a velocity of rotation such that the cen- 

 trifugal equalled the centripetal force, and therefore equatorial 

 rings were necessarily abandoned to form satellites. By cal- 

 culation I found that in the cases of Mars, Venus, and Mercury 

 their nebular expansions were not far enough, and their force 

 of gravity was not strong enough, to produce a rotation that 

 could abandon equatorial rings. Our earth, from want of 

 mass and want of nebular expansion, came very near to having 

 no satellite, no friendly, softly shining moon. 



Having compared the power of gravity as the only projec- 

 tile force with the actual velocities of the planets, asteroids, 

 and satellites, we may advance an important step and prove 

 the general abstract proposition, that, in all greatly expanded 

 nebulae, after rotation has once begun, and during a slow con- 

 traction, the force _ of gravity is sufficient to cause a velocity 

 such that the centrifugal must equal the centripetal force — in 

 other words, that the falls toward their centres from infinite 

 space will be more rapid than the velocities required in their 

 planets when formed. This demonstration is aided by the 

 following diagram (fig. 5). The notation is the same as that 

 in the formula Y = \/2gr, already given. Fig-. 5. 



Let ABE be the orbit of 

 a planet. E B an arc passed 

 through by a planet in 1 

 second. 'Then ED = BF 

 = distance fallen toward the 

 sun in 1 second = \ g. A E 

 = twice the distance of a 

 planet = 2r. BE (very 

 nearly are BE) = the velo- 

 city of planet in orbit = v. 



EA : BE : : BE : DE, 



2r : v : : v 



iffi 



v= s/gr. 



But the velocity acquired by a fall from infinite distance 

 = 2gr\ .*. planet's velocity in orbit : velocity of fall from 

 infinite distance : : 1 : v 2. 



We may now pass on to the demonstration that in a very 

 large nebula, whose rotation pervades the interior throughout 

 as well as the exterior, the velocity of rotation may become 

 sufficient to abandon all its material by centrifugal force, 



