VELOCITY.— III. 581 



the radius of the Sun r, the Earth's distance is 2i4r, whose square =^45972. 

 Then — 2I4-^•45972=.o46638 whose square root=. 06829X382.956=26.15 miles 

 iper second velocity acquired by the mass at the orbit of the Earth on arrival from 

 a distance that is infinite. Solar gravity acts on all ©osmical bodies, which would 

 move toward the Sun unless restrained by an opponent able to counteract attrac- 

 tion. Such energy is centrifugal tendency, a tendency generated by velocity. 

 It is known how great orbital motion is required to evolve centrifugal tendency 

 equal to gravity at any distance ; hence the ratio of such velocity to velocity de- 

 rived from fall from infinite distance can be ascertained. 



Having found this ratio, it can be extended to any depth of space, and motion 

 computed. If a body revolve around the Sun with velocity sufficient to cause 

 centrifugal tendency to equal centripetal, such velocity is equal to G multiplied 

 by the square root of the quotient obtained by dividing the distance at which it 

 revolves by twice its square. We have for the motion of the Earth — twice the 

 square of 214=91945, when 214-^91945=. 002332 whose square root =.0483X 

 282.956=18.49 miles per second orbital velocity necessary to keep it from fall- 

 toward the Sun. But, 26.15-^18.49=1.414213, hence the sought for ratio of 

 orbital velocity at a distance of revolution where such motion evolves centrifugal 

 tendency equal to gravity, is to velocity of fall ot the same distance from the Suh 

 of a falling body that begun its fall at an infinite distance as i is to 1.4 142 13. 



Now, 1.414213 is the square root of 2, hence this ratio of velocities must be 

 correct, for if we take the square roots of quotients derived from dividing a num- 

 ber by the square and twice the square of another, this relation of roots must 

 inevitably obtain. This ratio may be said to be a characteristic of gravity and 

 motion and exists wherever matter does, or is at liberty to move in obedience to 

 gravitation. Let us again note from I and II the properties of this square 

 root of 2. If we should dig a well from the surface to the centre of the Sun 

 and drop in a stone, it would reach the centre with a velocity of 270. 79 miles 

 per second. But this is equal to 382.956-f-2.4i42i3, whence a mass falling from 

 the surface to the centre of the Sun will acqure seventy per cent of the velocity 

 attained on reaching the solar surface had it been falling since the " beginning." 

 Again — a body taken into space distant i radius of the Sun and let fall, will make 

 impact with this same velocity— 270.79 miles per second. Or, — a stone a few 

 miles above the Sun's surface (in absence of retarding matter) having orbital 

 velocity=27o.79 miles per second, will not fall but make revolution like a satel- 

 lite; or should the Sun's equator revolve with that rate, masses lying upon the 

 surface would be without weight. If a comet move with velocity equal to the 

 square root of 2, — velocity of a planet at same distance where centrifugal tend- 

 ency and gravity balance, being equal to i, then will the comet pass round the 

 Sun and retire never to return. Should its motion be less, say 1.38 or similar 

 ■velocity, then it will fall on some form of ellipse and make future circuits. In 

 short— velocity on closed is to velocity on open conies ; or orbital velocity at finite 

 is to velocity of fall from infinite distance as i is to 1.414213. We extend this 

 principle to the sidereal heavens seeking to learn what rate of motion solar gravity 



