404 
linear orbits. A stone, whirled about in a sling, endeavours to recede from 
the hand that turns it, and by that endeavour distends the sling, and that with 
so much the greater force, as it is revolved with the greater velocity, and as soon 
as ever it is let go, flies away. That force which opposes itself to this endea- 
vour, and by which the string perpetually draws back the stone towards the 
hand, as the centre of the orbit, I call the centripetal force. And the same 
thing is to be understood of all bodies revolved in any orbits,” &c. 
“ If a leaden ball projected from the top of a mountain by the force of gun- 
powder with a given velocity, and in a direction parallel to the horizon, is 
carried in a curve-line to the distance of two miles before it falls to the ground, 
the same, if the resistance of the air was taken away, with a double or decuple 
velocity, would fly twice or ten times as far. And by increasing the velocity 
we may at pleasure increase the distance to which it might be projected, and 
diminish the curvature of the line which it might describe, till at last it 
should fall at the distance of 10, 30, or 90 degrees, or even might go quite 
round the whole earth before it falls ; or, lastly, so that it might never fall to 
the earth, but go forward into the Celestial Spheres, and proceed in its motion 
ad infinitum .” 
Now, in these two brief citations you have, in Sir Isaac 
Newtaufis own words, the sum and substance of his arguments 
in support of the theory that the heavenly bodies could be 
held in their orbits and made to revolve by gravitation. As 
regards the first illustration of “ a stone whirled about in a 
sling,” I can only ask (as I did in my Cambridge paper), — 
Does the string, in the case supposed, “ draw back 33 the 
stone towards the hand, or merely restrain it, or hold it, at a 
certain distance from the centre ? And, could a force like 
gravity act as the string does ? Let a rod of wood or iron be 
substituted for the string, and it must be self-evident that the 
rod does not and cannot “ draw back 33 the stone attached to 
it. But I equally maintain that the string does not draw back 
the stone, but only holds or restrains it ; and that a positive 
and, if I may so say, elastic force like gravity could not act as 
the string or rod does.* Now this illustration is of more con- 
sequence than might at first be thought possible ; for, when 
well considered, and when you once fully realize the fact that 
the string does not in the least draw back the revolving 
stone, but only holds or restrains it from flying away, you will 
find it impossible to accept any kind of ^ns^-demonstration 
that might seem to prove the contrary. 
38. But the popular notion is, that there can be a kind of 
balance between the force of gravity and a projectile force, 
that would enable bodies to revolve in a perfect circle ; or, in 
* Vide Mech. of the Heavens , §§ 41 — 44. 
