OUTLINES OF NATURAL PHILOSOPHY. 



exact, and gives only a first approximation to the 

 quantities sought ; but being far simpler than the 

 other, it is much better suited to the elements of 

 science. It is also the original method, and that 

 which was first applied by Sir ISAAC NEWTON to , 

 explain the irregularities of the Moon's motion. 

 The same has been followed and improved by CA- 

 LENDRINI, in his Commentary on the third Book of 

 the Principia ; by FRISI in his Cosmographia ; and 

 by VINCE, in the second volume of his Astronomy. 



The other method was not invented till several years 

 later, when it occurred nearly about the same time 

 to the three first geometers of the age, CLAIRAUT, 

 EULER, and D'ALEMBERT. It was followed also 

 by MAYER, and several others, but particularly by 

 LA PLACE, who, in the Mecanique Celeste, has gi- 

 ven a complete investigation of the inequalities 

 both of the primary and secondary planets. 



I shall explain the resolution of the forces that is 

 in some measure common to both methods ; and 

 shall shew how their effects are to be estimated in 

 some simple instances, going from thence to the 

 enumeration of the results. I begin with the 

 Moon's irregularities, as the easiest case of the 

 problem. 



249. The Moon, in her motion round the 

 Earth, is disturbed by the action of the Sun ; 

 her gravity to the Earth is increased near the 



quadratures, 



