282 Mr, Herapath on the Causes, Laws, andprincipal [Aprilv. 



In the fifth postulatum I have given the liuid of Newton for 

 explaining the cause of gravitation. This illustrious philosopher 

 has so clearly developed his ideas of the nature and action of 

 this etherial fluid, that I have had scarcely any thing to do but 

 to confirm them with the application of the principles of our 

 third and fourth postulata. It is true that the novelty of the 

 views I have been obliged to take, and the unbeatenness of the 

 track, have rendered even this a task of some difficulty ; but 

 the results I have obtained will, I presume, convince the Royal 

 Society that my efforts have not been wholly unsuccessful ; and 

 that this idea of Newton, which has, from the uniform want of 

 success to demonstrate it, often been placed to the account of 

 this great man's foibles, was not adopted upon light grounds, or 

 without mature consideration. 



Of the Collision of perfectly hard Bodies. 



Dejinitions of Hardness^ Softness, and Elasticity, 



DeJ". 1. — That body is perfectly hard whose figure cannot be 

 altered by any weight, or percussion. 



Corollari/. — Hence a perfectly hard body must also be per- 

 fectly entire ; for if it be composed of parts, there may be a 

 force sufficient to separate them, and then the figure would be 

 changed, which is against the definition. By a hard body, I 

 mean one without parts, unchangeable, and indivisible, such as, 

 perhaps, the primary particles of matter are. 



Def. 2. — The figure of a soft body yields to pressure, or per- 

 cussion, without recovering itself again. 



Cor. — Hence a soft body cannot be entire, but must be com- 

 posed of parts, which, being displaced, retain whatever situation 

 18 given them. 



Def. 3.— A perfectly elastic body, like a soft one, suffers its 

 figure to be changed by force, but recovers it again with an 

 energy equal to the force by which it was changed. 



Cor. 1. — Therefore an elastic body does likewise consist of 

 particles, which, like the particles of a soft body, may be 

 deranged ; but as soon as the power is overcome by which they 

 were disturbed, they exert as much force in recovering their 

 situation, as was used in depriving them of it. 



Cor. 2. — Because an elastic body recovers its figure with the 

 same force by which it was changed, as much motion is gene- 

 rated in the recovery as was destroyed in the loss of the figure. 



Prop. I. 



If two bodies absolutely hard impinge on one another, 

 the duration, or smartness, of the stroke, is independent of. 

 the velocity of the contact ; that is, it is neither augmented nor 

 diminished by any increase or diminution of the relative velocityi 

 of the bodies. 



