September 11, 1885.] 



SCIENCE. 



213 



tional to r; and calculation shows us that the press- 

 ure, which they will then produce hy rebounding 

 from the piston, will be proportional to this amount. 

 It will also, for any increased volume, be inversely 

 proportional to that volume. In the ordinary formula 

 connecting the volume pressure and temperature of 

 a perfect gas, pv=Et, we have only to suitably change 

 the value of B to be able to write pv)=B'W' where W 

 is the converter quantity of energy referred to in the 

 law, which we have stored up in the molecules to act 

 as the agent or instrument for the conversion of heat 

 into work, or vice versa. 



We wish to emphasize this point, — just as the 

 animal cannot perform its functions without life, so 

 it is this stored-up energy which is the real agent in 

 the engine. Eankine says, '' The effect of the pres- 

 ence in a substance of a quantity of actual energy 

 in causing transformation of energy, is the sum of 

 the effects of all its parts." Here he distinctly rep- 

 resents energy as the agent for the transformation of 

 energy. 



I believe that nothing but energy can thus act, and 

 that the general law underlying transformations of 

 energy may perhaps be thus stated: " Every conver- 

 sion of energy from a form A into a form B can be 

 effected only through the agency of a quantity of 

 energy," (and I venture to add) and this agent or con- 

 verter quantity must possess at once the characteris- 

 tics of A and B. 



In the engine the agent possesses temperature and 

 pressure, — the characteristics of heat and work: in 

 the dynamo the field is characterized by both elec- 

 trical and mechanical tension. 



Now our agent-quantity of heat must act without 

 expense to itself, for this is the peculiarity of agents ; 

 therefore the expansion must be isothermal : a source 

 of heat at the temperature r + dr being applied to 

 the conducting bottom, the gas will then expand 

 without loss of energy from the volume unity to the 

 volume V, thereby converting a quantity of heat into 

 work, which will be infinite for an infinite volume. 

 For any given change of volume, the amount of work 

 will be proportional to the pressure ; that is, to the 

 amount of agent-energy : so that for such a change 

 the truth of the law is seen. 



Let us look now at the behavior of the molecules : 

 as each rebounds from the hot bottom, its stock of 

 agent-energy receives into itself a portion of the heat 

 W which is to be converted into work; i.e., the 

 molecule is driven away with an increased velocity by 

 the hotter molecules of the bottom; it carries this 

 portion to the piston, to which it gives it up in the 

 form of work, because if the piston be moving with 

 a velocity V, the molecule will rebound from it with 

 its velocity reduced by 2 V. As the volume in- 

 creases, the pressure must fall, on account of the re- 

 bounds becoming less frequent, and the heat will be 

 converted into work more slowly; but for any and all 

 particular changes of volume, the rate of conversion 

 will be in proportion to the amount of agent-energy, 

 and, therefore, to the temperature of the gas. It is 

 interesting, also, to notice that the distance (from the 

 bottom to the piston), over which the heat-energy W 



must be carried, increases directly with the volume; 

 and therefore the time required to carry a certain 

 amount will be proportionately increased, the only 

 way to obtain a more rapid conversion being evidently 

 to increase the velocity of the molecules; i.e. the 

 amount of agent-energy. 



Let us turn now to Eankine: he is most easily 

 understood if we commence with his ' general law for 

 the transformation of energy,' already quoted, and 

 proceed backward ; and we come first to a graphical 

 representation of the second law. After explaining 

 the quantities in his diagram, and the known relations 

 between them, he asks us to suppose the temperature 

 r to be divided into n equal parts. Should this 

 supposition be difficult to make, we have only to 

 remember that r is the temperature of the agent, 

 and, therefore, the amount of agent -energy in 

 terms of a suitable unit; in fact, the statement that 

 a unit mass of gas possesses a temperature r, is 

 equivalent to saying that it possesses r units of 

 energy, the unit being the energy required to raise 

 this amount of gas one degree in temperature. We 

 are to suppose, then, the agent-energy divided into n 

 equal parts ; and we are afterward told that these parts 

 are ' similar and similarly circumstanced.' Now let us 

 suppose a molecule, at the temperature r=0, to be 

 heated to the temperature r by the addition of n 

 equal increments of energy; once added, all distinc- 

 tion between these parts vanishes, and there re- 

 mains only the conception of the whole amount of 

 energy as consisting necessarily of n smaller amounts ; 

 and the effects of all these amounts will be the same, 

 and the sum of their effects the effect of the whole. 

 It is only upon the thermometer-scale that degrees of 

 temperature have special places, and that the last one 

 added, and the first subtracted, must be the top one : 

 we cannot, however, see any way in which the energy 

 last added must be the same as the first subtracted. 



In Rankine's graphical treatment he shows iso- 

 thermal expansion; and it should be emphasized that 

 it is the only expansion suitable for the conversion 

 of heat into work, or vice versa. With adiabatic 

 expansion we have nothing to do: its only use is to 

 alter the amount of agent-energy, and it need not be 

 used until we come to engines working in a cycle. 



Rankine's next statement of his law is the second 

 one criticised by Maxwell, and it supposes nothing 

 more than the division of the absolute temperature 

 already discussed. The first formula should, how- 

 ever, read 



d _ d 



dr 



Q 



dQ' 



Proceeding backward, we come to a seemingly more 

 general and ^comprehensible statement of the law, 

 which speaks of 'the total actual heat.' jS'ow, Ran- 

 kine has, I think, sufficiently defined this; and it is 

 simply the kinetic energy of the molecules, or that 

 portion of the heat furnished which remains as heat. 



Inasmuch as the first statement of the law seems 

 more general, insomuch has it led, as I believe, to a 

 false comprehension of its meaning. It may seem 

 more general in this way: — 



