176 HISTORY OF PHYSICAL ASTRONOMY. 



motion of the nodes and its inequalities, the change 

 of inclination of the orbit, are full of beautiful 

 and efficacious artifices. But Newton's inventive 

 faculty was exercised to an 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 eccentricity of the moon's orbit upon 

 the motion of the apogee, he says 10 , "The computa- 

 tions, as too intricate and embarrassed with approx- 

 imations, 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, whether New- 

 ton's reasoning was sufficient to establish this part 

 of his theory; namely, that her actual motions arise 

 from her gravitation to the sun. And to this we 

 may reply, that it was sufficient for that purpose, 

 since it showed that, from Newton's hypothesis, 

 inequalities must result, following the laws which 

 the moon's inequalities were known to follow; 

 since the amount of the inequalities given by the 

 theory agreed nearly with the rules which astrono- 

 10 Schol. to Prop 35, first edit. 



