Principles of the Nebular Theory. 265 



presented by dots on our outer circle (fig. 1) all around, may 

 be regarded as so many comets approaching the sun at the 

 centre S, and they must counteract one another's influence in 

 the same maimer. While they move forward and downward 

 more and more rapidly, they produce no upward or backward 

 motion. Moreover they do not, like a rolling ball, press on 

 an inclined surface, but on the level equatorial zone. 



Having shown that the particles on the surface of a con- 

 tracting and rotating nebula must move like a comet approach- 

 ing the sun with a velocity always accelerated by the force of 

 gravity, let us now attend to the method by which this velo- 

 city of rotation may be calculated. Evidently the velocity of 

 rotation gained in contracting from the outer to the inner circle 

 (fig. 1) must be the same as the velocity gained by a fall from 

 one circle to the other in a direct line toward the centre. As 

 gravity, the force causing both the fall and the rotation, varies 

 its power inversely as the squares of the distances, therefore 

 a mass which would be attracted with a power or weight of 

 409,000,000 pounds at the sun's surface would be attracted 

 with only 9020 pounds at the earth's orbit, with only 10 

 pounds at the orbit of Neptune, and with only the tenth part 

 of an ounce at forty times the distance of Neptune. We 

 need not inquire how far the ancient nebulas extended in prder 

 to find the beginnings of their falls toward their centres, 

 because the force of gravity was so feeble on their surfaces 

 that we may reject its precise amount, and assume as tanta- 

 mount all the velocity which could be acquired by a fall from 

 infinite distance toward their centres. If the velocity acquired 

 by a fall from infinite distance to the outer circle be repre- 

 sented by a, and the same to the inner circle be represented 

 by b, then the velocity acquired by a fall from the outer to the 

 inner circle would be b — a. The velocity (V) of these falls 

 from infinite distance may be computed by the following for- 

 mula, Y = \/2gr. Here r stands for the radius of the nebula 

 (of our sun, for instance, when in a nebulous condition), and g 

 stands for the velocity per second acquired by a fall during 

 one second on the surface of the nebula. This velocity on the 

 surface of our nebulous sun may be found from that on our 

 earth's surface, which is 32*16 feet per second, by comparing 

 the mass and radius of our nebulous sun with the mass and 

 radius of our earth. By using this formula, it appears that 

 the velocity of a fall from the orbit of Neptune to that of 

 Uranus becomes a mile and a quarter per second, deci- 

 mally 1*244. This, added to the actual velocity of Nep- 

 tune, 3*491, gives a velocity for Uranus of 4*735 miles per 

 second. But the actual velocity of Uranus is 4*369, showing 



