ERA OF NEWTON, HALLEY, AND HERSCHEL. 39 



were true, the planets might be supposed to gravitate towards the sun, and to be restrained 

 thereby from flying off under the action of the centrifugal force. Sixteen years rolled 

 away before this beautiful hypothesis was verified, and difficulties arose in testing it which 

 seemed to disprove it altogether. It was necessary to calculate the force of gravity at 

 the surface of the earth ; to estimate its diminished energy at an increased distance ; and, 

 after having found the law of the diminution, to ascertain whether the phenomena of the 

 lunar motions corresponded proportionably with those of falling bodies at the terrestrial 

 surface. Assuming the force of gravity to vary inversely as the square of the distance, 

 it followed that, at the distance of the moon, it would be about 3600 times less than 

 at the surface of the earth. The problem, therefore, to be solved was, whether the 

 versed sine of an arc described by the moon, which measures the space through which in 

 the same time she would fall to the earth, if abandoned to the action of gravity, would 

 be 3600 times less than the space through which in the same time a heavy body falls, at 

 the earth's surface, A B being the arc of the moon's orbit, c d the 

 sine of the arc, and ef the versed sine. After a careful study of 

 the lunar observations supplied by Flamstead, and a series of cal 

 culations displaying unexampled originality and industry, New 

 ton fully demonstrated that the versed sine of an arc described by 

 the moon in one minute was equal to the space traversed in de 

 scent by a heavy body at the surface of the earth in one second 

 the exact proportion that ought to exist, according to the mo 

 dification to which the intensity of gravity is subject by variation 

 of distance. 



The first certain gleam of this grand conclusion obtained by Newton, is said so to have 

 overpowered him, that he Avas obliged to suspend his calculations, and call in the aid of a 

 friend to finish the last few arithmetical computations. He saw the important relations 

 of the demonstration the planets wheeling round the sun the satellites round the 

 planets the far-wandering comets returning to the source of light in obedience to the 

 law of gravitation: a result sufficient to throw the successful discoverer into nervous 

 excitement. It is clear that, if a body be projected into space, it will proceed in the 

 direction of the original impulse and with a uniform velocity for ever, supposing no 

 obstacle to impede its course. But the combination of two antagonistic forces will 

 produce a resulting motion in a diagonal direction. 



Suppose the straight lines A B to represent the direction in which the earth would travel 

 under the influence of the projectile force which launched it into 

 universal space : the straight lines A s are those it would describe 

 at any point of its orbit if surrendered to the influence of the sun's 

 attraction. The primitive impulse is, however, checked by the solar 

 attraction, and the latter by the former ; so that while the earth, if 

 abandoned to either, would describe A B or A s, the effect of their 

 joint influence incessantly acting is to deflect it from both, and pro 

 duce a curved path. The cause perpetually operating, the effect is 

 constant ; and hence the formation of the terrestrial orbit, and the cause extending to the 

 other bodies in the system, the planetary orbs are deflected from their natural rectilinear 

 paths, and pursue a circuit round the common centre. The force of attraction is, however, 

 proportional to the quantity of matter, and the proximity of the attracting body. Like 

 light, the power of gravitation is weakened by diffusion, and diminishes as the square of 

 the distance increases. This square is the product of a number multiplied by itself. A 

 planet, therefore, twice our distance from the sun, will gravitate four times less than we 

 do, the product of two multiplied by itself being four. Such is the great LAW OF 



