Matter and Force in Theoretical Physics. 465 



the hypotheses, after all, rests on a comparison of consequences 

 mathematically deduced from them with actual phenomena, and 

 on their capability of explaining the phenomena. For the sake 

 of illustration I shall first show how the hypotheses of the Theory 

 of Gravitation satisfy the above conditions, before I proceed to 

 consider whether they are satisfied by the hypotheses of my 

 Physical Theory. 



In the Theory of Gravitation it is supposed that all bodies 

 attract each other with forces which at a given distance are pro- 

 portional to their masses, and at different distances vary inversely 

 as the squares of the distances. This law of the variation of 

 gravity, although it might have been suggested by calculating, 

 from data furnished by observation, as Newton did, the deflec- 

 tion of the moon from a tangent to her orbit, is still strictly an 

 hypothesis, on which the theoretical calculation of the motions 

 and paths of bodies acted upon by gravity is founded. Another 

 hypothesis respecting the force of gravity is, that whatever it 

 may be intrinsically, it is the same thing in kind as the force 

 which draws towards the earth a terrestrial body free to obey its 

 attraction. Now, with respect to this effect of the earth's attrac- 

 tion, observation and experiment have established the law that 

 whether the motion be rectilinear or curvilinear, the increments 

 of velocity estimated in the direction of the action of the force 

 are proportional to the increments of time, whatever be the 

 amount and direction of the actual velocity. This experimental 

 law of accelerative force is a fundamental hypothesis of the 

 Theory of Gravitation. The experiments of Galileo were neces- 

 sary antecedents of the calculations of Newton. It is true that 

 this law is established experimentally only for a constant force, 

 whilst the forces in the Theory of Gravitation are variable func- 

 tions of time and space. But the new order of calculation 

 which Newton discovered, which, whatever be the mode of repre- ' 

 senting it, amounts to the formation and solution of a differen- 

 tial equation, gave the means of passing from the case of the 

 constant to that of the variable force, after furnishing a sym- 

 bolic expression for the latter, founded on the axiom that during 

 an indefinitely short time a variable force acts as if it were a 

 constant force. There is still another hypothesis of the Theory 

 of Gravitation, viz. that the attractions of several bodies on the 

 same body at the same instant take effect without mutual inter- 

 ference. This law, which might be suggested by the observed 

 movements of the moon nnder the simultaneous influences of 

 the earth and the sun, is proved to be exactly true by compari- 

 sons of the results of calculations founded upon it with results 

 deduced from observation. The above are the only necessary 

 hypotheses of the Theory of Gravitation ; and perhaps the fore- 



