LAW OF GRAVITATION.

OUR readers will remember, that in reporting on Captain FORMAN'S pamphlet, we begged that some of the scientific authorities of the day would put him out of his misery, by answering him ; and, lest his pains should be longer protracted, we even offered a portion of our space for that charitable object. Hitherto, mathematicians have held aloof ; on one point—a specimen point—Mr. WOODS, of Dulwich, has now favoured us with a refutation.

TO THE EDITOR OF THE SPECTATOR.

East Dulwich, 19th November 1132.

SIR—I avail myself of your invitation of the 27th October last, none wor- thier having done so, and send a few remarks on the subject of the Tides.

Suppose the Earth not revolving, and to be attracted to any point, as the centre of the Moon ; and that the attraction be invariable, whatever be the dis- tance; then the form of the Earth would be spherical, from the mutual attraction of its own atoms, and from the absence of any external power to change it : and such would be the result, whether the Earth were moving in a direct line to- wards the Moon without projectile force, or in a circle round their common centre of gravity. Thus, the attraction of the Sun or Moon, however great either might be, would, so long as it acted equally on every part of the Earth, produce no change of figure; and in case of the Earth's revolution on its axis, consequently no tide. But if gravitation should increase as the distance decreased, then the action of the Moon on the nearest part of the Earth would be greater than that on the fur- thest part. The figure would become a prolate spheroid, and if moving in a direct line towards the Moon, more and more prolate as the bodies approached ; because the nearer to each other, the greater would be the difference of attrac- tion between their nearest and their furthest sides.

A power of gravitation, varying inversely as the square of the distance, is found to correspond with all the phenomena of our system ; and therefore this is considered to be the true law. On this principle is made the following calcu- lation of the relative powers of the Sun and of the Moon to change the figure of the Earth, and thus produce tides.

Put the mass of the Sun = 23,074,100 = 1211.

Ditto Moon =

Distance from the Sun to the nearest part of the Earth 93,722,044 miles = a.

Ditto ditto furthest ditto

93,760,ts5 i = b.

ditto

Ditto Moon nearest 2313,18S — = c.

Ditto ditto furthest ditto 244,100 — = d. Then Al M — — — = power of the Sun to produce a tide = .000000000000345. a- 7,2

m ne — — ditto Moon ditto = .000000000001143.

cs d2

The power of the Sun to change the figure of the Earth, being thus, to that of the Moon to do so, as 345 1140.

I am, Sir, your obedient Servant, GEORGE WOODS.