with reference to the Measure and Transfer of Force. 343^ 



rative force (§ 6). Let the velocity acquired at the end of nine 

 seconds be 9, aud in the next second 10 ; the square velocity- 

 increases in one second from 81 to 100, the augmentation in 

 each being 19, or 38 in the sum of both. Let us now suppose 

 the plates, before the respective currents set upon them, to have 

 had a uniform velocity of 20 feet in the direction AB, In nine 

 seconds after the currents commenced to act, the velocity of A 

 has become 29, and that of B 11. In the next second, A is up 

 to 30 and B down to 10, and in one second the square velocity 

 in A has increased from 841 to 900, and that of B decreased 

 from 121 to 100. The sum of both has during this second in- 

 creased from 962 to 1000 ; the augmentation being 38, as before, 

 when the common centre of gravity was at rest. It will be re- 

 marked that the relative motion of A and B, as well as the in- 

 crease of their united vis viva, is the same in this last case as in 

 the former ; nevertheless there has been a transfusion of force 

 from B to A, the amount of which is 40, being equal to twice 

 the velocity of the common centre of gravity. If A had received 

 no greater augmentation of square velocity than in the former 

 case, the amount at the end of the tenth second would be 

 841 + 19 = 860, but it is actually 900. Again, if B had received 

 an augmentation the same as in the previous case, the amount 

 at the end of the tenth second would be 121 + 19 = 140, but it 

 is ] 00. Hence 40 has been transfused from B to A. 



If the motion of the common centre of gravity had been in a 

 direction perpendicular to AB, the relative motion and augmen- 

 tation of united vis viva would be the same, but there would be 

 no transfusion ; it is only when the current acts in the direction 

 of or contrary to the absolute motion. 



Suppose the plates A, B to revolve around their common 

 centre of gravity with such velocity that the centrifugal tendency 

 just equilibriates the effect of the currents. So long as the 

 centre of gravity is at rest, no force is given to or taken from the 

 impinging currents or particles ; but when rectilineal motion is 

 given to the system, transfusion takes place. The greatest rate 

 at which this takes place is when A and B are in the line of 

 their absolute motion. At other parts of the revolution, when 

 A >nd B have a position oblique to the direction of absolute 

 motion, the rate of transfusion is diminished in the ratio of the 

 cosine of the contained angle. During one half of a revolution 

 the absolute motion resolved in the direction of the current goes 

 with the current upon one of the plates and against it on the other 

 so that the flux and reflux of the force upon each plate alternates 

 positive and negative to exactly the same amount. 



It is thus that we may obtain a clear conception of transfu- 

 sion aa a necessary sequent to the mode of action of the forces of 



