ATTRACTION. 
can system, yet acknowledged an attractive 
power in matter. 
In France also, we find Ferinat and Ro- 
berval, mathematicians of great eminence, 
maintaining the same opinion. The latter, 
in particular, made it the fundamental prin- 
ciple of his system of physical astronomy, 
w hich he published in 1644, under the title 
of “ Arist. Samii de Mundi Systema.” 
Dr. Hooke, however, was the person who 
conceived the most just and clear notions 
of the doctrine of gravitation, of any before 
Newton ; in his work called “ An Attempt 
to prove the Motion of the Earth 1674. 
He observes that the hypothesis on which 
he explains the system of the world, is in 
many respects different from all others; and 
that it is founded on the following princi- 
ples: 1. That all the heavenly bodies have 
not only an attraction or gravitation to- 
wards their own centres, but that they mu- 
tually attract each other within the sphere 
of their activity. 2. That all bodies which 
have a simple or direct motion, continue to 
move in a right line, if some force operating 
without incessantly does not constrain them 
to describe a circle, an ellipse, or some 
other more complicated curve. 3. That at- 
traction is so much the more powerful, as the 
attracting bodies are nearer to each other. 
But the precise determination of the laws 
and limits of the doctrine of attraction, w'as 
reserved for the genius of Newton: in the 
year 1666, he first began to turn his atten- 
tion to this subject, when, to avoid the 
plague, he had retired from London into 
the country; but, on account of the incor- 
rectness of the measures of the terrestrial 
meridian, made before this period, he was 
unable to bring his calculations on the sub- 
ject to perfection at first. 
Some years afterwards his attention was 
again called to attraction by a letter of Dr. 
Hooke’s; and Picard, having about this 
time measured a degree of the earth, in 
France, with great exactness, he employed 
this measure in his calculations, instead of 
the one he had before used, and found, by 
that means, that the moon is retained in 
her orbit by the sole power of gravity, sup- 
posed to be reciprocally proportional to 
the squares of the distances. 
According to this law, he also found, that 
the line described by bodies in their des- 
cent is an ellipse, of which the centre of the 
earth occupies one of the foci ; and consi- 
dering afterwards, that the orbits of the pla- 
nets are in like manner ellipses, having the 
centre of the siui in one of their foci, he 
had the satisfaction to perceive, that the so- 
lution which he had undertaken only from 
curiosity, was applicable to some of the 
most sublime objects in nature. These dis- 
coveries gave birth to his celebrated work, 
which has justly immortalized his name, en- 
titled “ Philosophic® Naturalis Principia 
Mathematica.” 
In generalising these researches, he shew- 
ed that a projectile may describe any conic 
section whatsoever, by virtue of a force di- 
rected towards its focus, and acting in pro- 
portion to the reciprocal squares of the dis- 
tances. He also developed the various pro- 
perties of motion in these kinds of curves, 
and determined the necessary conditions, 
so that the section should be a circle, an el- 
lipse, or an hyperbola, which depend only' 
upon the velocity and primitive position of 
the body, assigning in each case the conic 
section which the body would describe. 
He also applied these researches to the 
motion of the satellites and comets, shewing 
that the former move, round their primaries, 
and the latter round the sun, according to 
the same law; and he pointed out the 
means of determining by observation the 
elements of these ellipses. 
He also discovered the gravitation of the 
satellites towards the sun, as well as to- 
wards the planets ; and that the sun gravi- 
tates towards the planets and satellites, as 
well as that these gravitate towards each 
other : and afterwards extending, by ana- 
logy, this property to all bodies, he esta- 
blished the principle, that every molecule 
of matter attracts every body in proportion 
to its mass, and reciprocally as the square 
of the distance from the body attracted. 
Having ascertained this principle, he from 
it determined, that the attractive force of a 
body on a point placed without it is the 
same as if the whole mass were united at 
the centre. He also proved that the rotation 
of the earth upon its axis must occasion a 
flattening of it about the poles ; which has 
since been verified by actual measurement : 
and determined the law of the variation of 
the degrees in different latitudes, upon the 
supposition that the matter of the earth was 
homogeneous. 
But, with the exception of what concerns 
the elliptical motions of the planets and co- 
mets, and the attractions of the heavenly 
bodies, these discoveries were not wholly 
completed by Newton. His theory of the 
figures of the planets is limited by the sup- 
position of their homogeneity ; and his solu- 
tion of the problem of the precession of the 
