ASTRONOMY. 
225 
of one law out of thousands which might equally have 
taken place, we see no less in the figures of the planetary 
orbits. It was not enough to fix the law of the centripetal 
force, though by the wisest choice; for even under that 
law, it was still competent to the planets to have moved in 
paths possessing so great a degree of eccentricity, as, in 
the course of every revolution, to be brought very near to 
the sun, and carried away to immense distances from him. 
The comets actually move in orbits of this sort; and had 
the planets done so, instead of going round in orbits near¬ 
ly circular, the change from one extremity of temperature 
to another must, in ours at least, have destroyed every ani¬ 
mal and plant upon its surface. Now, the distance from 
the centre at which a planet sets off, and the absolute 
force of attraction at that distance, being fixed, the figure 
of his orbit, its being a circle, or nearer to, or farther off 
from a circle, viz. a rounder or a longer oval, depends 
upon two things, the velocity with which, and the direction 
in which, the planet is projected. And these, in order to 
produce a right result, must be both brought within certain 
narrow limits. One, and only one, velocity united with 
one, and only one, direction, will produce a perfect circle. 
And the velocity must be near to this velocity, and the di¬ 
rection also near to this direction, to produce orbits, such 
as the planetary orbits are, nearly circular; that is, ellipses 
with small eccentricities. The velocity and the direction 
must both be right. If the velocity be wrong, no direction 
will cure the error; if the direction be in any considerable 
degree oblique, no velocity will produce the orbit required. 
Take for example the attraction of gravity at the surface of 
the earth. The force of that attraction being what it is, out 
of all the degrees of velocity, swift and slow, with which a 
ball might be shot off, none would answer the purpose of 
which we are speaking, but what was nearly that of five 
miles in a second.* If it were less than that, the body 
* The moon describes in one second of time nearly two-thirds of a 
mile in its orbit round the earth: and if its distance were diminished it 
might still continue to revolve nearly in a circle round the same centre, 
if its velocity were increased so as to compensate for the greater attrac¬ 
tion, which would now draw it constantly out of the rectilinear direc¬ 
tion, in which it would otherwise move. This distance may be supposed 
to be diminished till the moon is brought near to the earth’s surface, and 
t would, under these circumstances, still continue to complete its revolu¬ 
tion, if its velocity were increased to about five miles in a second. Now 
for the description of such a revolution, there is no difference between 
the moon and any other mateiial substance at the same distance; for they 
would both be drawn down through the same space in the same time by 
