404 Oa Dlamagnetism and the Concentration of Energy. 



but the passage of heat may take place either by conduction 

 or radiation. The simplest case is obtained by supposing that 

 there are only two external bodies with which the system can 

 exchange heat. It was then assumed by Carnofc that, in 

 a complete cycle, it will be impossible, without an expenditure 

 of mechanical work, to transfer heat by means of the system 

 from the colder of the two bodies to the hotter. Mechanical 

 work can therefore only be obtained from the system, during 

 a complete cycle of operations, when it absorbs heat from the 

 hotter of the two bodies and gives out heat to the colder. 

 Consequently, if the energy of a material system consist 

 entirely of heat of uniform temperature, it will be impossible 

 to transform any of it into work. 



Now it is found that all kinds of energy tend to pass into 

 heat, and the passage of heat from a hot body to a colder 

 (without the production of work) is an everyday occurrence. 

 It has therefore been predicted with confidence that our uni- 

 verse is approaching a state in which the whole of its energy 

 will be in the form of heat of uniform temperature, and all 

 kinds of mechanical action impossible. 



The following consideration, however, appears to offer a 

 serious difficulty to the universal application of Carnot's 

 principle. Thus, let A be a piece of permanently magnetized 

 hard steel ; and let B be a piece of a soft diamagnetic sub- 

 stance, as bismuth, which, when brought within the influence 

 of A, becomes magnetized by induction and is repelled by A. 

 Then suppose that the following cycles of operations are per- 

 formed at constant temperature : — 



(a) Let B be removed from a position P, remote from A, 

 to a second position Q, near A, so slowly that at every instant 

 the magnetization of B has its maximum value ; and let the 

 work expended be called W. Then let B return slowly to its 

 original position P by the former path reversed. The work W, 

 which had been expended, will be recovered ; so that, on the 

 whole, there will be neither gain nor loss of mechanical 

 work. 



{h) Let B be removed from P to Q so rapidly that the 

 magnetization of B has not time to alter sensibly. The work 

 done on B will be less than W. After allowing B to remain 

 long enough in the position Q to attain its permanent mag- 

 netic state, let it return rapidly from Q to P by the first path 

 reversed. The work restored by B will be greater than W. 

 There is therefore a gain of work in this cycle performed at 

 constant temperature, contrary to Carnot's principle. 



There are three ways of looking at this difficulty : — 



(1) We may suppose that the work which has been obtained 



