343 Mr. J. J. Waterston on the Integral of Gravitation, 



§14. 

 On the Transfusion of vis viva across a system that simultane- 

 ously revolves and progresses. 



Perhaps the most difficult point to realize to the mind con- 

 sistently with the causal relation of dependent action, is the 

 periodical ebbing and flowing of vis viva from and to each part 

 of a system endowed with a rectiUneal as well as a rotatory 

 movement. In the simple example of two equal globes, given in 

 § 11, as often as they are in a line perpendicular to the line de- 

 scribed by the common centre of gravity, the vis viva of one (A) 

 is 49, and of the other (B) 1. Setting out from this, A loses 

 and B gains vis viva until they come to the line in which the 

 common centre of gravity moves, when A is found reduced to 25 

 and B has risen to the same amount, having in the quarter revo- 

 lution gained 24 parts of square velocity which has been trans- 

 ferred to it from A. During the next quarter another 24 parts 

 have passed over. The ebb of force from A here ceases, and is 

 succeeded in the next quarter revolution by a flow of vis viva 

 from B to A, which continues until the revolution is completed, 

 when the same circle of changes is repeated. This transference 

 of force from one part of a system to another being unaccom- 

 panied with any appearance of action, may be termed transfusion, 

 as in the heading of this paragraph ; it is nevertheless as real a 

 transference of force as what takes place on a billiard table. 



How are we to present such phsenomena to our minds in 

 conformity with Newton's second law of motion, viz. " The 

 alteration of ^notion is ever proportional to the motive force im- 

 j)ressed, and is made in the direction of the right line in which that 

 force is impressed""^ 



Let us take, for example, the system formed by the earth and 

 the moon. At full moon the absolute motion of our satellite con- 

 siderably exceeds the amount it contains when at the opposite 

 point of its orbit, and in the earth it is vice versa. How may 

 we conceive this flux and reflux to take place ? 



In § 6 a dynamic arrangement was suggested, which repre^ 

 sented the peculiarity in the development of mechanical force, 

 specified in §§ 4 and 5, as a physical characteristic deduced from 

 the law of elastic impact : is it possible to deduce transfusion 

 from the same primary mode of action ? 



Let there be two perfectly elastic plates of equal surface and 

 mass placed opposite and parallel to each other ; on the exterior 

 surface of each, let a current of perfectly elastic particles be sup- 

 posed to impinge continually ; the minuteness as well as velo- 

 city of these particles being excessive. The eff"ect of the current 

 would be to drive the plates towards each other with an accele? 



