7S 



AT A rURE 



[May 28, 1903 



Prok. MiNciiiN raises the question of the desirability, or 

 undesirability, of the use of adjectives with regard to 

 physical principles. If the noun deserve the adjective, and 

 if the meaning- of the adjective be clear, it is not easy to 

 see why the word should be omitted. Prof. Tait is cited, 

 rather unfortun ttely, as the leader of those who apply the 

 word " grand ' to the principle of conservation of energy, 

 while refraining from its application to certain other 

 physical principles. Whether or not it be the case that 

 *' following his lead, all but the most sober mathematicians 

 use the laudatory adjective when they write, about this 

 particular physical principle," it is certain that all but the 

 least sober physicists will see a very real reason for the 

 use of the term — precisely the reason which led Tait to 

 adopt jt. 



Prof. Tait's use of adjectives is instructive. He made 

 a very characteristic use of the term " mere," a word which 

 Prof. Minchin would abolish along with " grand." He 

 spoke of the mere mathematician, that is, a mathematical 

 machine not possessed by the soul of a physicist. 



But Tait did not refuse glorification to the principle of 

 conservation of matter. He placed it, in that respect, on 

 the same high level as the principle of conservation of 

 energy. And he glorified Newton's laws, so glorifying the 

 principle of conservation of momentum and the other 

 principles alluded to by Prof. Minchin. 



Tait also knew that it' was possible so to state the 

 principle of conservation of energy in a dynamical system 

 as to make it include that of conservation of momentum. 

 This was pointed out in an early chapter of a text-book on 

 dynamics which he never completed. 



Assume an origin and axes of reference. Let the (con- 

 served) energy of a system be Ej, so that 



•2.{mv"') = 2E,. 

 Assume that the energy is also constant ( = £3) when the 

 motions are referred to an origin moving uniformly with 

 speed 02 in a direction making an angle ^ with the line 

 of motion of the mass m, and we get 



a./2(w) - 2a.p.{mv COS &) = 2(E2 - Ej). 

 Similarly 



Oj^SCw) - 2ast(mv cos 0) = 2(E3 - E^) 

 if we refer to an origin moving with uniform speed a, in 

 the same direction. Hence 



2{w) =^ o, ^2{wv cos e) = o. 



The latter equation asserts conservation of momentum, the 

 former asserts conservation of matter. 



In the same way, if we postulate that momentum, found 

 to be conserved when referred to certain axes and a given 

 origin, is also conserved when referred to an origin moving 

 uniformly with regard to this reference system, we can 

 deduce the principle of conservation of matter. 



It is impossible that all three — matter, momentum, and 

 energy — can be in general found to be conserved simul- 

 taneously when referred to an origin in varying motion. 

 If matter be conserved, and if we could measure, from our 

 standpoint on the earth, the momentum and energy of the 

 universe, we should find one or both to be subject to at 

 least yearly, rnonthly, daily, &c., periodic variations. If 

 the origin move with the centre of inertia, as in all cases 

 ■directly experimented upon, all three principles hold if two 

 hold, while the energy is found to be constant in at least 

 •one state of motion of the centre of inertia, say zero. The 

 discussion of absolute conservation is as futile as the dis- 

 cussion of absolute motion. 



It may be that energy, or momentum, is only conserved 

 on the average as to space and time, the departures being 

 on an ultra-measurable scale and yet sufficient to account 

 for " guidance " action in living beings. But we do not 

 require to postulate this in order to account for guidance 

 action. Such action might occur and yet be in accordance 

 with conservation of both momentum and energy. Max- 

 well's demons could bring it about. Suppose that the mass 

 of a demon is zero, that he is perfectly elastic, and that his 

 parts are capable of rapid relative motion. Let an army 

 of such demons receive orders to abstract heat from one 

 portion of a body and give it to an adjacent portion, so as 

 to establish a diiTerence of temperature while keeping the 

 itotal energy constant. Because of his zero mass, each 



demon must adjust himself, in acting upon molecules, so 

 as to produce zero change of momentum at any instant. 

 He can allow quickly moving molecules to pass in one direc- 

 tion, slowly moving molecules in the other, while he prevents 

 to some extent the reverse process. He might thus work 

 railway points with no expenditure of energy on the whole, 

 and with no change of momentum on the whole. The onlv 

 principle temporarily interfered with is the principle o'f 

 dissipation of energy ; and that is temporarily interfered 

 with constantly in nature. 



Such speculations are of no value except as showing that 

 guidance action may occur without overthrowing accepted 

 dynamical principles. Further discussion lies outside 

 physics. As Tait said, " human science has its limits, and 

 there are^ realities with which it is altogether incompetent 

 to deal." A sufficiently wide Monism is scientific and 

 good._ '^v Peddie. 



university, Edinburgh. 



NO. 1752, VOL. 68] 



In his letter on the conservation of energy (p. 31), Prof. 

 Minchin holds that, while energy might be conserved in 

 the physical universe acted on in some way by mind, yet 

 neither force nor momentum would be. " They "' (the 

 causes altering the configuration of a system) " infallibly 

 alter its total momentum and total force in every direction.'' 

 Even for changes produced by physical causes, e.g. the 

 pressure of a smooth rail, this may not be the case. It 

 IS true the rail will not guide a moving body along 

 It unless It exerts pressure, and then it will generally alter 

 the momentum of the system, to which the rail itself is 

 not supposed to belong. It may happen, however, that 

 the pressure from without is exerted in equal amount in 

 opposite directions. Further, if it were true that the total 

 momentum would be infallibly altered by a physical cause 

 this would prove nothing for psychophysical action, unless 

 we beg the whole question, and assume at the outset thai 

 the motion of matter can only be affected by what i« 

 material. 



The constant use of physical analogy in this connection 

 soon leads to obscurity. The only resemblance that can at 

 present be said to exist between the action of mind and that 

 of an ideal immovable rail is that both do no work. To 

 explain how mind acts on matter, such analogies are use- 

 less. At most, in the case under discussion, they can only 

 serve to show that there are possible causes of change which 

 do not afTect the energy. It is only, I think, an undue us» 

 of physical analogy— the action of the mind, for instance 

 being thought of as pressure— that can prompt the state- 

 ment that any cause of change must alter the total 

 momentum in some direction. 



The laws of mechanics are merely regulative, and are 

 not of themselves sufficient to account for the motion of 

 a dynamical system with given initial conditions unless it 

 IS stipulated that all action is mechanical, or at least unless 

 t^he action on, or interference with, the motion is exactly 

 defined. This is proved by the simple fact that we can 

 solve examples in dynamics in which we suppose arbitrary 

 known interference to take place. In such examples as 'a 

 rule, the momentum of the system would be altered but 

 that IS not at all necessary. ' 



In conclusion, then, it may be agreed that the action of 

 mmd does not violate the laws of mechanics, but that no 

 more prevents mind producing changes than it prevents 

 those produced by ordinary mechanical action. 



The University, Birmingham. C. T. Preece. 



Extension of Kelvin's Thermoelectric Theory. 

 Lord Kelvin's thermoelectric theory has always seemed to 

 me to be one of his best works. Since its enunciation the scope 

 of the electric current has been extended, as in Maxwell's theory 

 It IS now the curl of the magnetic force of the field always and 

 everywhere. A corresponding extension of the thermoelectric 

 theory is needed. I do not know whether it has been done, but 

 it may be shortly stated, and contains some .striking results ' As 

 regards the necessity, the following case will show it plainly 

 Make up a circuit of two parallel wires of different materials^ 

 both thermoelectrically neutral, say one of lead, the other of one 

 of Tait's alloys. The places of thermoelectric force in the 

 circuit are then the terminals. Now send short waves along the 

 circuit, in the way so often done of late years. There need be 

 no current at all in the circuit at one end to pair with that at 



