32 Prof. Oliver Lodge on 



Appendix 2. — More detailed Discussion of the Transmission 

 of Energy in difficult cases. 



When I say (as I do on pp. 14, 15, and 20) that acting bodies 

 have the same velocity, I of course mean their action to be 

 immediate. If indirect action is contemplated, it is too obvious 

 that a clock-weight has not the same speed as the tip of the 

 second-hand or the hammer of its bell ; but at the contact of 

 every cog, two wheels, driver and driven, are moving at the 

 same pace. But now, it may be asked, if all action is contact- 

 action, if all action is direct, how is it possible ever to get a 

 variation in speed ? This is a question worth answering. 



It is done and only done by means of rotation. The type 

 of all such actions is a rotating wheel propelled by an 

 uncentral force. In such a wheel, regarded as a single rigid 

 body, we have every gradation of speed from a maximum to 

 nothing, and we can make use of or transmit elsewhere what 

 speed we like. This is the essence of levers, and mechanism 

 in general : without rotation the speed of all parts is the 

 same,, and therefore the same as the point to which the driving 

 force is applied. 



But now, treating the wheel as what it is — an assemblage 

 of particles — how comes it that they can act on each other so 

 as to generate differences of speed ? How can a force applied 

 tangentially to the face of a sphere cause part of the opposite 

 hemisphere to move backwards ? 



If we accept the sphere as a rigid body, nothing is easier 

 than to equate the momentum generated to the impulse of the 

 applied force, and its moment of momentum to the moment 

 of the impulse ; but if we treat it as an assemblage of con- 

 nected particles it is not so easy to tackle the problem. As 

 is well known it did historically give trouble ; until it was 

 realised, on the ground of Newton's third law (or D'Alem- 

 bert\s Principle as it was called), that all internal stresses 

 balanced each other, and might therefore be ignored for the 

 purpose of deducing the final result. 



There is now no controversy as to final result ; the only 

 question is how universal contact-action, with equal velocity 

 between agent and patient, or driver and driven, can account 

 for the ultimate result of all grades of velocity through zero 

 even to minus. 



There is no need to take refuge behind any such blinkers 

 as D'Alembert's Principle : an assemblage of connected par- 

 ticles can be directly contemplated. Let one of them receive 

 a blow, it is passed on to the others and the momentum 

 spreads laterally by oblique impacts, the amount of obliquity 



