of JVatural Philosophij. 149 



should be assigned each to its proper cause ; that in lati- 

 tude to the obhquity of the axis to the plane of the orbit, 

 and that in longitude to the excentric form of the orbit, — 

 instead of blending the explanations of both under the 

 loose proposition, " the libraiions of the moon may be ex- 

 plained on the supposition that the moon has a revolution 

 on its axis." In prop. 81, the equality of the times of ro- 

 tation and revolution is inferred from the librations ; while it 

 is in fact a matter of direct observation, and must be pre- 

 supposed in explaining the librations themselves. In prop. 

 82, the elliptical form of the moon's orbit is inferred from 

 the libration in longitude. We very much doubt whether 

 the species of oval to which the moon's orbit most nearly 

 approaches could have been determined from direct ob- 

 servations on so tritiing a change of phase. The proper 

 mode of presenting this part of the subject would be, to 

 infer the elliptical form of the orbit from the observed rela- 

 tion between the anomaly and the apparent diameter; and 

 then to employ this conclusion for the explanation of the 

 libration in longitude. 



Prop. 83. Schol. In stating the results of Dr. Hers- 

 chel's observations on the altitude of the lunar mountains, ic 

 is mentioned that " one was found to be about a mile in 

 height ; but none of the others which he measured proved 

 to be more than half that altitude." By consulting the orig- 

 inal memoir in the Philos. Trans, and another which he 

 has published since, it will be seen that Dr. Herschel's re- 

 sults differ much less from the estimates of the older As- 

 tronomers, and from the recent and accurate measurements 

 of Schroter, than is here represented. Dr. H. makes 

 several over a mile, and one, nearly two miles in height. 



Prop. 106. " If the moon, when new, is in one of its 

 nodes, the eclipse of the sun will be central. It should be, 

 — " to the inhabitants of some part of the earth it will be 

 centrally eclipsed in the zenith." To those parts of the 

 earth at which the moon js never vertical, a central eclipse 

 can happen only when the moon is not in its node, at the 

 the time of conjunction. 



Prop. 113, which affirms a motion "w antecedentin^^' 

 of the satellites of the superior planets while passing from 

 one elongation to the next tlirough their inferior conjunc- 

 tion, is RO less erroHeou? than the propositiens of former 



