Jan. 9, 1879] 



NATURE 



219 



And the more complicated the system be, the larger the number 

 of possible combinations of three bodies within it, the greater is 

 the number of experiments or observations we can make to 

 prove that the conservation of momentum is a general physical 

 fact. The larger the number of such observations becomes, the 

 further removed is the doctrine of the conservation of momentum 

 from the character of a logical deduction from definitions. 



Still, of course, the doctrine has only to do with relative 

 velocities and relative accelerations of velocities. It loses, how- 

 ever, none of its reality and truthfulness on account of this. 

 Why should not relations be capable of being real, even if not 

 permanent ? We are indeed incapable of conceiving anything as 

 real which does not owe its reality in our conception simply to 

 its relations to other things. If objective reality is in any way 

 the opposite of relativity, then, certainly, so far as our knowledge 

 goes, there is no such thing as objective reality. Our notions of 

 momentum and of force, then, are relative to three bodies, and not 

 to two bodies, and this seems to me to be an important point. The 

 ELEMENTARY notion of momentum derived from definition is 

 relative to Twobodies only ; but the practical notion derived from 

 EXPERIENCE is relative to three bodies at least, or to a complicated 

 system of bodies. It should not be forgotten that the physical 

 realities among which we live owe their existence to the com- 

 plexity of nature. Throughout the complexity there are certain 

 simple invariable relations, and these are the physical laws of 

 nature. The law of conservation of momentum is this : the 

 momentum of one system relative to another system remains un- 

 changed by exchanges of momentum between the parts of the 

 former system. Otherwise stated it is : exchanges of momentum 

 may and do take place between the parts of a system without 

 these exchanges being necessarily accompanied by an exchange 

 of momentum between this system and any other system. 



Energy is, of course, a quantity of as relative a character as 

 momentum, although its relativity is not of just the same kind. 

 Energy in general is usually defined as the power of doing work. 

 Curiously enough this definition is frequently followed closely 

 by the statement that a system may possess a very large amount 

 of energy, and yet if there are no differences of potential within 

 it no work can be done by it. The correct statement of what is 

 meant by this last has often been given, viz., that in this case 

 no work can be done by one part of the system upon another 

 part of the same system. But still more often is the inaccuracy 

 indulged in of saying that energy of one kind or another may 

 be transformed into work. Now work is not energy and has no 

 kind of smiilarity to energy, and therefore energy can never be 

 converted into work. When energy is transferred from one 

 body to another the first does work upon the second, the amount 

 of work done being measured by the amount of energy trans- 

 ferred. The rate at which energy is transferred is the rate of 

 doing work, or the horse-power. The doing of work or more 

 shortly work, is the transference of energy from one body to 

 another, but is not the energy itself. The confusion has never 

 entered into the practical use of the word "work," which has 

 always really been applied in the sense here explained, although 

 very probably a good deal of confusion of ideas among both 

 practical and theoretical men, may have been caused by the 

 above noted incorrect statement that energy and work are con- 

 vertible. The confusion is of the same sort as if we were to 

 use the word force in the sense I have advocated and confuse it 

 -wath acceleration of momentum. During some transferences of 

 energy there is an invariable transformation of energy. If 

 during the transference, the whole of the energy transferred is 

 also simultaneously transformed, then the rate of doing work is 

 also equal to the rate of transformation, and the amount of 

 work done is numerically equal to the amount of energy trans- 

 formed. But the phrase "work done" is only used when 

 transference takes place. When a portion of one kind of enercry 

 m a body is converted into energy of another kind without any 

 energy leaving the body, it is not the custom to say that work 

 has been done. Work is only done by one body upon another 

 so that work is the transference, not the transformation of 

 energy. To say that so much energy has been spent in doin<r an 

 equivalent amount of work is a convenient and quite allowable 

 mode of saying that this amount of energy has been transferred 

 from the working body without specifying what has become of 

 the energy j that is, without specifying into what other body the 

 enei^ has been transferred, and without specifying in what 



When a body possesses in two parts of it two quantities of 

 heat at two different temperatures, the amount of work which 

 the one part has the power of doing on the other in consequence 

 of this difference of temperature is not nearly equal to the whole 

 amount of heat energy in the two parts. Thus the energy in a 

 body is not the power meastired quantitatively, possessed by its 

 parts of doing work on each other. 



If in a collection of bodies there be a certain one body with 

 a certain amount of kinetic energy, calculated from its velocity, 

 relative to the centre of inertia of the group, that one body 

 might deliver up the whole of this kinetic energy by direct 

 impact upon another body which had zero velocity relative to 

 that centre of inertia, provided these two bodies were exactly 

 alike in certain particulars as to mass and shape. Eut if there 

 did not exist in the group any body which had this particular 

 relation of shape and velocity to the fir^t, then this first could 

 not possibly deliver up all its kinetic energy, so as to get its 

 velocity relative to the centre of inertia of the whole group 

 reduced to zero. It is thus clear that the internal kinetic energy 

 of a collection of masses is not measured by* the amount of 

 kinetic energy calculated from the velocities relative to the centre 

 of inertia of the collection that can be transferred from one part 

 to another. 



Also, if another body, or another group of bodies, existed 

 apart from this first group, and possessed a velocity of centre of 

 inertia either zero, or of any other value, relative to the centre 

 of inertia of the first group, the kinetic energy of this first group, 

 measured either relatively to its own centre of inertia, or to that 

 of the other group, or to the centre of inertia of the two com- 

 bined, could only be wholly transferred to this second group, 

 provided that this second group had very special and very in- 

 geniously contrived relations with regard to mass and configura- 

 tion to the first group. Thus the kinetic energy of any collec- 

 tion is not measured by the power it may possibly have of doing 

 work upon bodies outside the collection. And quite evidently 

 the same may be said of any other kind of energy possessed by 

 the body. 



For each kind of energy we have more or less accurate means 

 of comparing quantitatively different amounts of that kind of 

 energy, and thus of measuring the amount of that kind of energy 

 possessed by a body in terms of the quantity which is adopted 

 as unit of that kind of energy. We have also means of convert- 

 ing different amounts of any one kind into most other kinds of 

 energy ; and since in several carefully-made experiments upon 

 the conversion of different kinds of energy there has on the 

 whole been a very fair agreement in the ratios furnished by 

 these experiments between the adopted units of the different 

 kinds, we have come to believe in the truth of the law of con- 

 servation of energy — the more especially since this belief is sup- 

 ported by theoretical reasoning based on the hypothesis of the 

 truth of the conservation of momentum. This latter theoretical 

 reasoning, however, we have, hitherto, at any rate succeeded in 

 applying only to transferences of kinetic energy of visible 

 motion, and to the thermodynamics of perfect gases. 



But taking this principle of conservation of energy for granted 

 as true, we have the means of measuring the amount of energy 

 of any kind possessed by a body in terms of the adopted unit 

 for kinetic energy of visible motion. 



Robert H. Smith 



{To be continued.^ 



tormthe energy has appeared in the other body. But to say 

 tJiat the energy is converted into work is qui'.e a different thino- 

 and altogether WTong. " 



The Unseen Universe — Paradoxical Philosophy 



W^ILL you permit me to ask through your columns how the 

 idea of the authors — that the present universe is developed out 

 of our unseen universe, which unseen universe is itself developed 

 out of another, and so on in an endless vista up to the un- 

 conditioned — works when applied to the present universe as 

 itself developing a lower imiverse ? 



The present imiver>e must be a conditioning as well as a con- 

 ditioned universe, or there would be a breach of the principle of 

 continuity, and there must, on the same principle, be an endless 

 vista of such lower universes. 



Have we any hint of any lower universe ? Ought we not to 

 have more than a hint? Ought we not to be fully conscious that 

 our own universe is developing and sustaining such a lower 

 universe, to the living intelligent beings in which we are, in fact, 

 supernatural agents, as the angels in the universe above tis are to 

 ourselves ? 



