renis ibr tiiuliiig Fluxions per Saltuiu. Tlie method will be 

 easily undeislood without the theorems. These and important 

 applications thereof it is intended soon to give in a separate 

 volume. 



In order to simplify the computation as much as possible, the 

 plane of the lunar orbit has been supposed coincident with the 

 plane of the ecliptic, the orbit of the earth without excentricity, 

 and the approximation has been only carried to the first power 

 of the excentricity of the lunar orbit. These circumstances have 

 little effect on the quantity of the mean motion of the Lunar 

 Perigee. 



The quantity of the motion found is expressed in terms of 

 the quotient of the periodic time of the moon by the periodic time 

 of the earth, and thereby are satisfactorily shewn the erroneous 

 conclusions of Machin, Walmsley, Frisi and Matthew Stewart, 

 Avho imagined that the mean motion of the apsids could be in- 

 vestigated by considering the moon acted on only by a centripetal 

 force, the mean tangential force being = o. This is of some im- 

 portance, as authors have recently referred to these solutions as 

 exact. Professor Playfair, indeed, in his outlines of Natural Philo- 

 sophy, published in 1814, speaks (vol. 2. p. 26 1) with some doubt 

 on the subject. After giving Dr. Stewart's result, and referring to 

 those of the others, he says, " The result of these investigations, 

 " therefore, agrees nearly with observation, but it cannot be 

 '• denied that the principle on which they are founded is liable 

 " to some objections, so that if it Avere not for the information 

 " derived from the direct solution of the problem of the three 

 " bodies, it might still be doubted, whether the principle of gravity 

 " accounted exactly for the motion of the Moon's apsids." 



