31 1 Prof. Cliallis on the Principles of Theoretical Physics. 



and the success with which new facts are elicited and new laws 

 established. In consequence, perhaps, of the striking character 

 of these achievements, compared with the slow and uncertain 

 steps with which theoretical physics have of late advanced, the 

 idea seems to be gaining ground that theory may be dispensed 

 with, and that the domain of natural philosophy includes only 

 the discovery of facts and educing laws out of them. On this 

 point I beg to offer a few observations. 



Natural philosophy, as the history of its progressive steps 

 seems clearly to point out, consists of two parts, related but di- 

 stinct — viz. the experimental and theoretical. The kind of rela- 

 tion existing between them may be illustrated by reference to 

 the history of physical astronomy. The labours of Kepler are 

 exclusively in the province of experiment, or observation ; those 

 of Newton in the province of theory. The former do not in- 

 volve the idea of force, while in the latter this idea is funda- 

 mental. By observations, carried on with wonderful patience 

 and perseverance, Kepler established three laws relating to the 

 motions of the planets about the sun. The knowledge of these 

 laws was not necessary for the discovery of the principle of 

 gravitation : Newton, in fact, did not use them for that purpose. 

 They were rather problems for solution, which Newton succeeded 

 in solving by differential calculation applied to the hypothesis of 

 a gravitating force varying according to the law of the inverse 

 square of the distance. It may, however, be doubted whether 

 the reasoning by which the solutions were effected would ever 

 have been discovered if the problems had not been proposed. 

 But as soon as the proper calculation was employed and the 

 proper hypothesis made, a few steps of symbolic reasoning 

 sufficed for the demonstration of the laws which it cost Kepler 

 so many laborious years to arrive at by observation. From 

 Newton's time, with the exception perhaps of some futile at- 

 tempts of Flamsteed, astronomical observation has not been 

 directed towards the investigation of laws, but has almost ex- 

 clusively been employed in furnishing the data indispensable for 

 making theoretical calculations applicable to actual bodies and 

 actual instances of motion, and in giving the means of correcting 

 previous data by comparisons of observed with calculated celes- 

 tial positions. The general result of the combination of obser- 

 vation with theory is the demonstration of the law of gravity. 

 This law could not be shown to be a physical reality either by 

 observation alone, or by theory alone. 



From this survey it would appear that in Kepler's time astro- 

 nomical observation was in advance of theoretical calculation, 

 and was occupied with the investigation of laws because the 

 means of doing so by theory, to which such investigation pro- 



