526 Mr. 0. J. Lodge on a Mechanical Illustration 



short period and very small amplitude. Eacli button will by 

 its friction tend to move the cord with it. Being all exactly 

 alike, their vibrations will all be isochronous ; but they will be 

 in all manner of phases at any one instant ; so on the average 

 they will neutralize each other's effect on the cord, and the 

 cord will remain stationary without oscillation. 



The hypothesis just made, viz. that the molecules of a solid 

 are oscillating, and that the oscillation of any one exerts a cer- 

 tain electromotive force, capable of producing a current except 

 for the circumstance that it is exerted equally in opposite di- 

 rections in rapid succession, and moreover that it is in general 

 neutralized by the similar but ill-timed action of its neighbours, 

 is the hypothesis whose consequences it is the object of the 

 present paper to trace. 



§ 22. First of all, then, there is some energy lost in this 

 motion ; for the buttons are sliding backwards and forwards 

 on the cord, and, though they are tolerably smooth, the friction 

 must ultimately bring them to rest, unless the loss of energy 

 is made up to the body from other portions of the same body 

 or from external sources. The energy which is thus continu- 

 ally being wasted in warming the cord must, I think, be held 

 to correspond to the heat lost by radiation into space ; the loss 

 being compensated, in cases of equilibrium of temperature, by 

 equivalent receipts from neighbouring bodies. But if a set of 

 molecules, or a finite mass of any substance, be isolated from 

 all other bodies and left to itself in free space, the molecules 

 will gradually deliver up their motion to the interpenetrating 

 medium, and will ultimately come to rest. If, then, we calcu- 

 late the work done in unit time by a button sliding to and fro 

 on the cord, we shall get the rate at which a body cools under 

 these circumstances; and from this the rate under any other 

 circumstances can be obtained at once by simply subtracting 

 the rate at which it gains heat from the enclosure. 



Since we have no data regarding the actual motion of a 

 button, we may as well for the present consider it as simply 

 harmonic; any other sort of motion will give very nearly the 

 same result. Let the period of the simple harmonic motion 



2-Tj- 



of a button be 2t= — — , and let its amplitude be a, so that 2a 



V K 



is the whole length of a button's excursion from right to left. 

 Its velocity at any distance x from its mean position is 

 v= \/fc(d 2 —x 2 ), and its maximum velocity is Y = a^/ k. Now 

 we remember that the retarding force acting between a button 

 and the cord is proportional to r the specific resistance of the 

 substance or the coefficient of " friction," and to v the velocity 



