iOS HISTORY OF PHYSICAL ASTRONOMY. 



any impression on this problem, or course of problems. No one fol 

 sixty years after the publication of the Principia,, and, with Newton's 

 methods, no cue up to the present day, had added any thing of any 

 value to his deductions. AVe know that he calculated all the prin- 

 cipal lunar inequalities; in many of the cases, he has given us his 

 processes ; in others, only his results. But who has presented, in his 

 beautiful geometry, or deduced from his simple principles, any of the 

 inequalities which he left untouched? The ponderous instrument of 

 synthesis, so effective in his hands, has never since been grasped by 

 one who could use it for such purposes ; and we gaze at it with 

 admiring curiosity, as on some gigantic implement of war, which 

 stands idle among the memorials of ancient days, and makes us wonder 

 what manner of man he was who could wield as a weapon what we 

 can hardly lift as a burden. 



It is not necessary to point out in detail the sagacity and skill 

 which mark this part of the Principia. The mode in which the 

 author obtains the effect of a disturbing force in producing a motion 

 of the apse of an elliptical orbit (the ninth Section of the first Book), 

 has always been admired for its ingenuity and elegance. The general 

 statement of the nature of the principal inequalities produced by the 

 sun in the motion of a satellite, given in the sixty-sixth Proposition, is, 

 even yet, one of the best explanations of such action ; and the calcu- 

 lations of the quantity of the effects in the third Book, for instance, 

 the variation of the moon, the motion of the nodes and its inequalities, 

 the change of inclination of the orbit, are full of beautiful and effica- 

 cious artifices. But Newton's inventive faculty was exercised to au 

 extent greater than these published investigations show. In several 

 cases he has suppressed the demonstration of his method, and given 

 us the result only ; either from haste or from mere weariness, which 

 might well overtake one who, while he was struggling with facts and 

 numbers, with difficulties of conception and practice, was aiming also 

 at that geometrical elegance of exposition, which he considered as 

 alone fit for the public eye. Thus, in stating the effect of the eccen- 

 tricity of the moon's orbit upon the motion of the apogee, he says, 9 

 "The computations, as too intricate and embarrassed with approxima- 

 tions, I do not choose to introduce." 



The computations of the theoretical motion of the moon being thus 

 difficult, and its irregularities numerous and complex, we may ask 



9 Schol. to Prop. 35, first edit. 



