242 Prof. Thomson's Elementary Demonstrations of 



them being curved in the same direction, the arrow head on each 

 indicating the way a north pole would be urged. Let AC, BD 

 be lines drawn perpendicular to all the lines of component force 

 between these two. Because of the curvature of these lines, the 

 lines AC and BD (whether straight or curved) must be so in- 

 clined to one another that the portion CD cut off from the last 

 shall be less than the portion AB cut off from the first. Let a 

 north pole of an infinitely thin, uniformly and longitudinally 

 magnetized bar, of which the south pole is at a great distance 

 from the magnets, be carried from D to C along the line of com- 

 ponent force through these points, from C to A perpendicular 

 to all the lines of force traversed, from A to B again along a line 

 of force, and lastly, from B to D perpendicular to the lines of 

 force. Work must be spent on it in carrying it from C to D, 

 and work is gained in passing it from A to B. Then, because no 

 work is either gained or spent in carrying it from C to A or from 

 B to D, the work gained in moving along AB cannot exceed the 

 work spent in the first part of the motion, or else we should 

 have a perpetual development of energy from no source*, by 

 simply letting the cycle of motion be repeated over and over 



again : and the work spent along DC cannot exceed that gained 

 from A to B, or else we might have a perpetual development of 

 energy from no source, merely by reversing the motion described, 

 and so repeating. The work spent and gained in the motions 

 along DC and AB respectively must therefore be exactly equal. 

 Hence the mean intensity of the force along CD, which is the 



* [Note added March 26, 1855.] — It might he objected, that perhaps 

 the magnet, in the motion carried on as described, would absorb heat, and 

 convert it into mechanical effect, and therefore that there would be no 

 absurdity in admitting the hypothesis of a continued development of energy. 

 This objection, which has occurred to me since the present paper was 

 written, is perfectly valid against the reason assigned in the text for reject- 

 ing that hypothesis ; but the second law of the dynamical theory of heat 

 (the principle discovered by Carnot, and introduced by Clausiusand myself 

 into the dynamical theory, of which, after Joule's law, it completes the 

 foundation) shows the true reason for rejecting it, and establishes the vali- 

 dity of the remainder of the reasoning in the text. In fact, the only ab- 

 surdity that would be involved in admitting the hypothesis that there is 

 either more or less work spent in one part of the motion than lost in the 



