of Natural Philosophy. 151 
given to one of them alone, the common rier 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 iba which remains 
at rest, or has a uniform rectilineal motio 
Prop. 162. This theorem, as it ee in Rowning, was 
inverse duplicate ratio of the distance. As nothing analo- 
gous to this investigation has fovea retained by Enfield, the 
assertion that when the fo! in the inverse 
move forward, and vice versa, made in the course of the. 
demonstration, is wholly gratuitous. © se 
Prop. 163. The demonstration i is not oily irrelevant to 
peal nearer to ‘ah earth” than it would ot rise “Od; 
“and describe a portion of an orbit inaedbenviovers or near- 
eracircte.” The former statement is correct; but it con- 
tradicts the latter. So in the corollary we are told that 
“when the gravity of the moon towards the earth decreas- 
es — the excentricity of the orbit will increase; and 
when her gravity towards tie earth increases too fast, the 
excentricity will decrease.” ~The fact is, that in both cases 
alike the excentricity will increase. It is when the gra wi 
increases or diminishes too slow, that the excentricity \ 
decrease. Those who will give themselves the trou 
consulting the prop. as it stands in Rowning, will find no 
difficulty in perceiving how a amen abeldger mie etch 
conditions of the demonstra ue ts 
Props. 164 and 166. 6. Why. two propositions so “ely 
identical should find a place i in this ene we can _— no 
account,—unless ome had fox t he 
had given a theorem on the motion of iehots Rows 
ning, and ‘theft reat for one in some putes author. 
So much at least is certain—that prop. 166, and this - 
