206 On the Antilunar Tide. [March, 



action be indicated hy 10,000, and be confined to tlie earth ; then 

 the moon would still be affected by the same force, 400; the earth 

 by the sun's force, 10,000, and the moon's force, 10; and being 

 supposed at the period of opposition, the effect on the earth would 

 be 10,000 —10= 9990. Let the smi's attraction, still taken at 

 10,000, be now extended to the moon, all the bodies remaining 

 fixed ; then, while the earth continues to be aftected with the same 

 forces as before, that is, the difference of the attracting forces, the 

 moon will be affected by the sum of these, or 10,000 + 400 = 

 ■ 10,400, and these forces will not be affected by any changes in- 

 duced on these bodies, as long as they continue in the same direc- 

 tion, other than that produced by difference of distance. Let the 

 earth and moon revolve round the sun, with a projectile force, 

 respectively, such as shall exactly i)alance their gravitating forces : 

 they will then describe circular' orbits, and being each of thera 

 thereby kept at their original distance from tlie sun and each other, 

 their mutual gravities will remain unaltered. But if this would 

 really be the case in these circumstances, then there can be no 

 truth in the position, " tiiat, wherever the action of the sun would, 

 increase their distance, if they were allowed to fall towards the sun, 

 there the siur''- action, by endeavouring to separate them, diminishes 

 their gravity tn each other.'" And the theory founded on such a 

 position must be erroneous also. It is olivious, that the additional 

 movement of the moon in its orbit round the earth cannot affect 

 tlie question ; because if the sun's action would not diminish the 

 gravity of the moon to the earth, were they moving in concentric 

 circles round the sun (in wiiich case the earth would, if allowed to 

 fall freel}-, be separated from the moon, with an accelerating velo- 

 city,) there. can be no law, which gives the tendency to such sepa- 

 ration, the effects of ac/"?/a/ separation. It must hold good in every 

 case, or in none. It may be safely held, therefore, that the eccen- 

 tricity of the moon's orbit is like the eccentricity of the orbits of 

 the other satellites and planets, to be ascribed to the combination 

 of forces and velocities, which increase and diminish in difierent 

 ratios. 



These objections to tlie principle on which the Newtonian tlieory 

 is founded i.^ equally strong, wlielher the application be made to 

 the moon's orbit, or the swclliiig of the waters on the earth ; per- 

 haps therefore enough has been slated to warrant the rejection of 

 the principle altogetlier; but as it is the foundation of a great 

 fabric, it deserves more llian ordinary consideration. 



\\. may b^ remarked that considerable obscurity hangs ovgr the 

 principle itself. It is a plain and now an acknowledged "law, that 

 gravity decreases inversely as the square of thcdistance. It would 

 be also easily ninderstood, were \rc informed, that of two bodies 

 falling from unequal distances tovv'ards the sun, tiie one nearest and 

 most attracted would leave bcl)ind it the one least attracted ; and 

 that tlie action of gravity between these tuo bodies would be 

 diminiu-cd by this separation in tiic ratio of the squares of their 



