334 Mr. J. J. Watei-stou on the Integral of Gravitation, 



The following dynamic arrangement will serve perhaps to 

 convey a distinct idea of this : — 



Let there be two perfectly elastic plates presenting the same 

 siu'face, but unequal in mass, say in the ratio of 1 to 10. On 

 one side of each let a current of perfectly elastic particles be 

 supposed to impinge continually, — the minuteness as well as 

 velocity of these particles being excessive. Whether these plates 

 are at rest or moving in a direction perpendicular to the plane of 

 their surface, the number of particles that impinge in an element 

 of time must be constant so long as the velocity of the particles 

 is incomparably greater than the velocity of the plates. If the 

 plates are kept at rest by an interposed obstacle, the impinging 

 particles are reflected without change of velocity, and no motion 

 is transferred from them to the plate, or from the plate to them. 

 If the plates move in the same direction as the particles with 

 velocity 1, the particles at impact lose one decrement of squai'e 

 velocity, and if with velocity 10, then the particles lose ten de- 

 crements of square velocity. These decrements being transferred 

 to the plates, become collectively increments of motion having 

 the character of an accelerating force. 



While the plates are prevented from moving by resting on an 

 interposed obstacle, the current of impinging particles forms a 

 pressure or tendency to put the plates in motion, which is equal in 

 both plates, but the faculty of taking motion from the current de- 

 pends on the plates being in a state of motion and increases with 

 their velocity. The heavier plate, by its greater mass being con- 

 fuTcd in its velocity to one-tenth, has its ability to take force from 

 the curi'ent reduced in this proportion. 



Gravitation as an impulse. 



If the fact of the integral of gravitation as a force generator, 

 being a function of space, is admitted as an argument for the 

 existence of the force in space before it is communicated to the 

 falling body, it realizes the idea or impression which Newton has 

 expressed in the introduction to Section 11 of the first Book of 

 the ' Principia,' viz. " I shall therefore at present go on to treat 

 of the motion of bodies mutually attracting each other, consi- 

 dering the centripetal forces as attractions, though perhaps in a 

 physical strictness they may more truly be called impulses. But 

 these propositions ai-e to be considered as purely mathematical, and 

 therefore laying aside all physical considerations, I make use of a 

 familiar way of speaking to make myself more easily understood." 

 Considered as an impulse, gi-avitation has several character* 

 istics,-;-statical, dynamical, and directive. 

 -J, It is au impulse the statical magnitude of which upon au 



