the Foundations of Dynamics . 33 



being limited only by tbe arrangement of the molecules; and 

 the component of the blow or thrust transmitted in any di- 

 rection is diminished in accordance with the suitable cosine 

 law. The process is notoriously not an easy one to follow 

 into detail, even in a simple case, partly for lack of data ; and 

 there is some uncertainty as to the disposal of the energy for 

 the case of a blow, though even in that case there is no un- 

 certainty about the momentum ; while for a steady force the 

 body, however essentially elastic, gets rapidly into a practi- 

 cally rigid state, and the molecules then merely act as trans- 

 mitters t of the energy. They are, as it were, connected by 

 massless struts and ties, and along these the energy is trans- 

 mitted, partitioning itself off into several directions, much as 

 it did in the case of impact, and producing local velocities 

 determined by the arrangement of the particles, that is, by 

 the shape and other circumstances of the body*. 



The conception of a rigid body, to which a couple can be 

 applied, and which moves as a whole without dislocation of 

 parts, every portion instantaneously feeling whatever force 

 there is to reach it, simplifies problems enormously ; and it 

 may be said that just as a moving body retains its kinetic 

 energy and carries it through space without transfer or trans- 

 formation, so a rigid body conveys thrust or potential energy 

 through space, receiving it at one point, delivering it up at 

 other points, and transmitting it instantaneously without 

 transfer or transformation. The thrust of a connecting-rod, 

 the torque of a shaft, the tension of a belt, and the tangential 

 stress of a cog-wheel, are typical instances of this practically 

 instantaneous communication, or locomotion of potential 

 energy, caused by a rigid body. 



The simplest way to think of the ordinary case of gearing 

 and shafting is thus to ignore its molecular structure and treat 

 it as a linkage of entirely rigid bodies, where the potential 

 energy communicated to one point is conveyed elsewhere as 

 a simple flux without transfer or transformation, as kinetic 

 is conveyed when a bullet is shot across an empty space. 



But that this blindfold treatment • does not exhaust the 

 matter can be seen at once by thinking of a moving fly-wheel 

 suddenly geared on to a stationary cog-wheel, so as to transmit 

 a portion of its kinetic energy to machinery. The stress 

 necessary to effect the transfer is too gigantic, and results in 

 damage unless some elasticity is provided in shaft or spokes 

 wherewith to store it temporarily and subsequently give it 



* In Thomson and Tait, vol. i. part 1, §§ 311-318, the effect of an 

 impact on a number of elastically connected particles is treated. So it is 

 partly in a review in ' Nature,' vol. xlvii. p. 601 (April 27, 1893). 



Phil. Mag. S. 5. Vol. 36. No. 218. July 1893. D 



