of Natural Philosophy. 151 



given to one of them alone, the common centre of gravity of 

 the two will not continue at rest. Nor does this contradict 

 the proposition referred to in the Mechanics ; for the com- 

 mon centre will move uniformly in a right line. The propo- 

 sition should have stood thus : " The sun and any planet 

 revolve round a common centre of gravity, which remains 

 at rest, or has a uniform rectilineal motion." 



Prop. 162. This theorem, as it stood in Rowning, was 

 preceded by an investigation of the motion of the apses 

 produced by a force varying in a greater or less than the 

 inverse duplicate ratio of the distance. As nothing analo- 

 gous to this investigation has been retained by Enfield, the 

 assertion that when the force varies faster than in the inverse 

 duplicate ratio of the distance the line of the apses will 

 move forward, and vice versa, made in the course of the 

 demonstration, is wholly gratuitous. 



Prop. 163. The demonstration is not only irrelevant to 

 the proposition, but from an inadvertent change in the con- 

 ditions as laid down by Rowning, a blunder is carried 

 through it and the annexed corollary. The demonstration 

 affirms that if the moon is passing from the higher to the 

 lower apsis and its gravity increases too fast, " it will ap- 

 proach nearer to the earth" than it would otherwise do, 

 " and describe a portion of an orbit less excentric, or near- 

 er a circle." The former statement is correct ; but it con- 

 tradicts the latter. So in the corollary we are told that 

 " when the gravity of the raoon towards the earth decreas- 

 es too fast, the excentricity of the orbit will increase ; and 

 when her gravity towards the earth increases too fast, the 

 excentricity will decrease." The fact is, that in both cases 

 alike the excentricity will increase. It is when the gravity 

 increases or diminishes too slotv, that the excentricity will 

 decrease. Those who will give themselves the trouble of 

 consulting the prop, as it stands in Rowning, will find no 

 difficulty in perceiving how a hasty abridger might shift the 

 Conditions of the demonstration. 



Props. 164 and 166. Why two propositions so near)}'" 

 identical should find a place in this chapter we can give no 

 account, — unless that the compiler had forgotten that he 

 had given a theorem on the motion of the nodes from Row- 

 ning, and therefore looked for one in some other author. 

 So much at least is certain, — that prop. 166, and this only, 



