520 



NA TURE 



{Oct. 1 8, 1877 



eastern monsoon yields only three inches, and with Bangalore, 

 where it yields only six or seven. I may add that he also com- 

 pares it with Bellary, which derives only three inches from the 

 north-east monsoon. It must be evident that any cyclic period- 

 icity in the Madras rainfall which is chiefly derived from the 

 north-eastern monsoon, cannot possibly be common to such 

 stations as Bangalore, Bellary, and Secunderabad, which are 

 scarcely reached by the north-east monsoon, and which derive 

 an altogether insignificant rainfall from it. 



I have only quoted three instances, but the paper is full of simi- 

 lar absurdities. The Government of India should not be surprised 

 that we Madrasfees are jealous of its interference and distrustful 

 with regard to its ability to inteifere for good, so long as it puts 

 its official inipiimatur on papers such as this. I do not suppose 

 that Mr. Blanford, the meteorological reporter, is personally 

 responsible for it. The explanrtion no doubt consists in the 

 fact that the paper has been drawn up by some ignorant native 

 clerk, and signed pro forma by his official superior. Any sub- 

 altern in a marching regiment who has crossed the Ghauts knows 

 that the north-east monscon cannot possibly exert a common 

 influence upon the coast where it breaks in its first fury, and the 

 walled-in plateau of Hyderabad or Bellary, where it scarcely 

 reaches at all. Old Madrassee 



Potential Energy 



Wherever the fault may lie, your correspondent, " P. M.," 

 has quite misapprehended John O'Toole, whose amanuensis I 

 am, in every point on which he, "P. M ," touches, but one, viz., 

 John's wish to place the potential energy in the force instead of 

 in the body to be moved. X. 



Dublin, October 12 



In the capacity of poor P. I have suffered much at the hands 

 of the doctors, and am glad to find in jour correspondent " X." 

 so competent an exponent of many of the difficulties with which 

 the subject of energy, ns generally taught, is beset. But while 

 in the main I agree with the criticisms of "X." there are two or 

 three points with refeience to which I may perhaps venture an 

 opinion. 



It seems to be admitted (NATt;RE, vol. xvi. p. 459) by your 

 correspondent that in the case of a moving body " the kinetic 

 energy is undeniably in the body." This appears to me to lie at 

 the root of the chief difficulty, for, as far as I can see, we have 

 no more right to assert that a cannon shot possesses kinetic E. 

 when it leaves the muzzle of the gun than to say that a clock 

 weight possesses potential E. when it has been wound up ; for it 

 may happen that the shot is at rest relative (shall we say) to the 

 centre of giavity of the physical universe. At any rate we are 

 well assured that of itself it can do no work. Suppose the shot 

 to find a home in the side of a ship ; in entering the ship it does 

 work, but the amount done depends u|)on the original motion of 

 the sliip, being gieater if the ship were moving to meet the shot 

 than if it were at rest ; it also depends on the mass of the ship, 

 for if the shot sensibly change the motion of the ship its own 

 motion will be less altered by the inij^act. When a shot strikes 

 a target, which we assume to be rigidly connected with the earth, 

 the mass of the latter is so great that we may consider the target 

 as fixed, and thus we have only to contemplate the mass and 

 velocity of the shot. Simple problems of this nature werg of 

 course more inviting than those in which the m.ass pnd velocity 

 of both the colliding bodies had to be taken into account ; and 

 thus it came to pass that the kinetic E. was altiibuted to the shot 

 alone instead of being considei cd an attribute of the system consist- 

 ing of the earth and shot togeiher and due to the relative velocity of 

 the two. Adopting this latter mode of expression, we may, if we 

 please, suppose the shot to be at rest and tlie earth moving rela- 

 tive to it with the velocity of (say) i,4CO feet per second, and 

 the energy of the system will be unaltered by our convention ; 

 but where should we be if in this case we supposed the kinetic E. 

 of a rigid moving body to be an attribute of it alone ? 



Again, when we say that the kinetic E. of m units of mass 

 moving with z' units of velocity is 4 ti'v", this velocity must be 

 measured with reference to some point or other which we for the 

 time consider fixed. In order to obtain 4. m v"- units of work 

 from the body, we must bring it to rest relative to our point of 

 reference, but in so doing we must lake care that no motion is 

 imparted to the point of reference itself, for if this be the case 

 the body will come to rest relative to it wilhjut losing v units of 

 velocity, and therefore without d ing \m'J- units of work. If 



our system consist only of two bodies, and work is to be done by 

 bringing them finally to relative rest, this condition will be ful- 

 filled only when the body which we choose to consider at rest 

 is indefinitely great compared with the other, and only then may 

 we represent the kinetic energy of the system by \ m v~, m being 

 the mass of the smaller body and v its velocity relative to the 

 other. 



I think we shall avoid all difficulty if we define the kinetic 

 energy of a system as tlw ntcrgy uthich the syitcin possesses in 

 virtue of the relative motions 0/ its parts ; we shall then never 

 hear of the kinetic E. of a shot or other rigid body, except as 

 an abbrevia'ion for the kinetic E. of the system consisting of the 

 earth and the shot, &c. 



A precisely similar line of argument may be foUcrwed with 

 reference to potential E. or the K. of position. The potential 

 E. of a rigid body, whatever its position may be, is an absurdity. 

 The very notion of position implies relatioir to other bodies, as 

 we have no fixed points in space, and thus it is necessary, if only 

 for this reason, that in speaking of potential E., at least two por- 

 tions of matter which are capable of changing their po-iiion 

 relative to one another should be taken into account. In the 

 case of a raised weight, the system consisting of the earth and 

 the weight possesses energy in virtue of the separat on of its 

 parts, and the system can be made to do an amount of work 

 equivalent to this energy by keeping the earth fixed and letting 

 the weight fall, or by keeping the weight fixed and letting the 

 earth m jve up to it, or by letting each move to the other, as in 

 nature. In any case the work done will be the same, though 

 the time required may be very different ; but according to the 

 modes of cx[)re;sion complained of by your correspondent, I 

 suppose that in the first case the potential E. belongs to the 

 weight, in the second to the earth, and in the third it is divided 

 between the two. Should we not avoid all difficulty by defining 

 the potential energy of a system as t/ie energy 70/iieh the system 

 possesses in virtue of its confi^iiratieii ' We should then never 

 speak of the potential E. of a single rigid body, such as a rai^'ed 

 weight, except as an abbreviation for the potential E. of the 

 system consisting of the body and the earth. A strained elastic 

 body, such as a bent bow, of course possesses potential E., for 

 in this case the particles of the body have been moved relative 

 to one anothtr from their jwsition of rest, and thus the configura- 

 tion of the system has been changed. 



Of course I agree with your correspondent that the potential 

 energy of a system is just as truly energy as is its kinetic energy, 

 and this brings me to the last point I proposed touching upon, 

 viz., the terra "energy of tension." Perhaps energy of stress 

 might avoid some objections, since tension and its antithesi.=, 

 pressure, have very special meanings ; but surely in adopting 

 such a phrase we can hardly say that the designation implies an 

 " essential characteristic," while the term E. of configuration 

 refers only to a "condition." In the case of two attracting 

 bodies the potential E. is greatest when the attraction is least 

 on account of the increased distance, and it depends not upon 

 the actual attraction between the bodies in their existing con- 

 figuration, but upon the attractions which are called into play 

 in all the configurations assumed by the system as the bodies 

 approach each other, and which therefore belong in potentiality 

 only, to the system in its initial condition. If we define the 

 potential of a point in the tteighbourhood of a system of bodies 

 as the amount by which the energy of the system would be 

 iircreascd by the introduction of the unit mass at this point, then 

 so long as the mass is absent, the energy due to it can be only 

 potential, but when the mass is placed there the energy is actual. 

 In strictness, then, we ought not to apply the term potential to 

 the energy thus introduced into the system. We, however, 

 require some mark to distinguish this energy from kinetic energy, 

 and the word potential serves to remind us of the condition of 

 affairs before the mass was introduced. Again, we may have a stress 

 as great as we please actirrg between the parts of a system without 

 any consequent potential energy, so that the space " condition " 

 seems to be at least as important as the stress "characteristic." 

 On the whole I think the phrase potential energy preferable to 

 enei'gy of tension, stress, or configuration, although it is applied 

 to energy which is as truly actual, and belonging to the material 

 system, as is that of a sh.aft-impelled-against-an-ironclad. 



Cambridge W. G. 



With reference to the question concerning the bricks, in 

 Nature, vol. xvi. p. 477, it is obvious that if a man lifts a 

 brick down from a wall and places it on the ground, the vis viva 



