1814.] ' On tlie Antilunar Tide. ' «05 



quire laborious investigation to determine which is entitled to pre- 

 ference. 



The general laws of gravitation need not be explained here. It 

 seems to admit of no controversy, that coincident attractions, (at^ 

 tractions on the same side and in the same direction) however 

 multiplied and varied as to motion or rest, do act with a force equal 

 to the sum or aggregate of their attractions. * For, it is the general 

 law of gravity, that every particle of matter gravitates towards every 

 other particle of matter ; that it is obstructed by no intervening 

 body, or obstacle, and admits of no variation in the same matter, 

 but from its different distances only, from that to which it gravi- 

 tates. This general law, obviously determines the point where the 

 bodies are at rest ; for if two bodies, A and B, do act upon a third 

 body, C, without any variation, in consequence of their relative 

 attractions to each other, they must act on C with with the sum, at 

 aggregate of their attractions, that is, inversely, by their respective 

 quantities of matter multiplied by the squares of their respective 

 distances. But it also determines the point where the bodies are in, 

 motion : for, supposing them approaching or receding from each 

 other, if any point in their path be taken, it is the same thing as tq 

 the bodies at that point, as if they were at rest, and the law will 

 be there found to apply ; but if this will hold, where any point 

 soever is taken, it must hold in every point, and therefore the 

 law, that bodies on the same side and in the same direction, act 

 with the sum of their attractions, applies equally to bodies in mo- 

 tion as to bodies at rest. Let us apply these principles to the sun, 

 the earth, and the moon. Let the earth, and the moon, at the 

 period of opposition, be supposed mutually to attract each other, 

 but the sun's attraction to affect the earth only, if the earth remain 

 stationary, the mutual attraction of the earth and moon will not 

 be affected by tiie superadded attraction of the sun on the earth. 

 If the eartii in these circumstances, be allowed to fall to the 

 sun, then the attraction of the earth and moon will decrease as 

 the squares of their distance shall increase ; but if the moon be 

 also projected in the same direction, and accelerated in the same 

 proportion as the earth, their mutual attractions will remain un- 

 altered. For, the gravitation of the different particles of matter 

 to each other is independent of their relations to any other par- 

 ticles, and remains the same in all cases, except in as far as affected 

 by difference oi' distance. " (iravity," as formerly stated, " is 

 obstructed in its action by no intervening body, or obstacle, and 

 admits of no k'nd of variation in the same matter, but from its 

 different distances only from that to which it gravitates." To 

 illustrate this, let us take the gravities of the sun, moon, and 

 earth, at arbitrary values. Let the gravitation of »iie moon to- 

 wards the earth, be indicated by the number 400; that of the 

 earth towards the moon by 10, hnd let the force of the sun's 



• M'Laurin'i Exprrimrnls, 4lo. p. S76. 



