ISH.] On the Anlilunar Tide. 129 



of gravity, and to the more matured opinions of Mr. M'Lauria 

 himself. 



The discussion of the question will be much simplified, and the 

 results rendered more satisfactory, by a previous examination of the 

 effects of tlie general principles which regulate the moon's orbit 

 round the centre common to the moon and the eartli, the eccentri- 

 city of that orbit being explained on the same principles as the 

 phenomena of the tides, and these cfl'ects being so much greater 

 than those produced on the figure of the earth. 



For the explanation of these effects upon the moon's orbit, we 

 shall again taka iVIr. M'Laurin as our guide. " Let us suppose," 

 says he, " that the projectile motions of the earth and m.oon were 

 destroyed, and that they were allowed to fall freely towards the sun. 

 If the moon was in conjunction with the sun, or in that part of her 

 orbit which is nearest to him, the moon would be more attracted 

 than the earth, and fall with greater velocity towards the sun, so 

 that the distance of the moon from the earth would he increased in 

 the fall. If the moon was in opposition, or in the part of her orbit 

 which is farthest from the sun, she would be less attracted than the 

 earth by the sun, and would fall with a less velocity towards the sun 

 than the earth, and the moon would be left behind by the earth, so 

 that tiie distance of the moon from the earth would be increased in 

 this case also. If the moon was in one of the quarters, then the 

 earth and moon l)cing both attracted towards tiie centre of the sun, 

 they would both directly descend towards tliat centre ; and by ap- 

 proaching to the same centre, they would necessarily approach at 

 the same time to each other ; and their distance from one another 

 would be diminished in this case. Now, wherever the action of 

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

 towards the sun, there we may be sure the sun's action, by endea- 

 vouring to separate them, diminishes their gravity to each other; 

 wherever the action of the sun would diminish their distance, then 

 the sun's action, by endeavouring to make them approach to one 

 another, increases their gravity to each other ; tliat is, in the con- 

 junction and opposition their gravity towards each other is dimir 

 nishcd by the action of the sun, but in the two quarters it is in- 

 creased by the action of the sun. In corjsidering, therefore, the 

 effects of the sun's action on the motions of the earth and moon, 

 with respect to each other, we need only attend to the excess of its 

 action on the earth in their conjunction, and we must consider this 

 excess as drawing the moon from the earth towards the sun in that 

 place. In the opposition we need only consider the excess of the 

 action of the sun on the earth above its action on the moon, and we 

 must consider this excess as drawing the wooti from tlie earth in 

 this place in a direction opfjoule to t\i(t J or mcr', that is, to the place 

 opposite to where the sun is, because we consider the earth as 

 quicscent,and refer the motion and all its irregularities to the moon."* 



* Accordin-; to I.nplacc — " Daiit i>eii cuiijonctioiis avec le solcil, lalune eii est 



Vol.. III. N°ll. 1 



