11 Regula Tertia Philosojihandi." 23 



action of gravity, and, what is much more, the parabolic motion 

 of a projectile. The latter fact is indicative of the law that the 

 acceleration in the direction in which gravity acts is the same 

 whatever from other causes may be the movement of the body 

 acted upon. It is here proper to remark that experimental 

 determinations may be classed under two different heads, 

 some being necessary as foundations of theoretical research, 

 and others serving to verify and extend theoretically calcu- 

 lated results. Of the former class are Galileo's theorems re- 

 specting the acceleration of falling bodies and the parabolic 

 motion of a projectile. All that Newton and Laplace wrote 

 on physical astronomy depends on hypothetically adopting 

 these two theorems. Newton, in his First Book, repeatedly 

 expresses his indebtedness to the second, calling it " Galileo's 

 Theorem." Kepler's observations belong to the other class ; 

 and his name occurs in the Third Book, where Newton speci- 

 ally refers to the law of the planetary distances as a phenome- 

 non to be accounted for by the theory of gravitation. The 

 laws of the lunar and planetary motions being determinable 

 since Newton's time by theoretical investigation, there was no 

 more occasion to employ for that purpose such observations 

 as those of Kepler, it being the particular province of theory 

 to demonstrate laws, while observations are required for as- 

 certaining the numerical values of the constants which the 

 theoretical formulae involve. The astronomical observer of 

 the present day simply determines as accurately as he can the 

 celestial places of the sun, moon, and planets, and gives his 

 results to the theoretical computer to be dealt with accord- 

 ing to his requirements. Flamsteed, from not understand- 

 ing what he considered to be Newton's crotchets, attempted to 

 discover the laws of the lunar inequalities solely by observa- 

 tion. There is reason to think that something like Flam- 

 steed's misapprehension of the relation between the respec- 

 tive provinces of theory and experiment exists at the present 

 time. 



After these preliminaries, I am prepared to enunciate the 

 parts (I.), (IT)? (III.) of Physical Astronomy. The differen- 

 tial calculus satisfies the demands of physical astronomy so 

 far as regards the operations which calculation has to perform. 

 Part (I.) consists in making these three hypotheses : — (1) 

 that every particle of matter attracts by the force of gravity 

 every other particle; (2) that the action varies with the dis- 

 tance between the particles according to the law of the inverse 

 square ; (3) that the action conforms to the law of Galileo's 

 Theorem. Part (II.) consists in deducing from these hypo- 

 theses what is equivalent in modern analysis to forming a 



