182 THE PRINCIPLES OF SCIENCE. 



and C may usually be made to produce a consequent of 

 the nature of A inverted in direction. When we apply 

 heat to a gas it tends to expand ; hence if we allow the 

 gas to expand by its own elastic force, cold is the result ; 

 that is B (air) and C (expansion) produce the negative of 

 A (heat). Or again, B (air) and compression, the nega- 

 tive of C, produce A (heat). Similar results may be ex- 

 pected in a multitude of cases. It is a most familiar law 

 that heat expands iron and nearly all solid bodies. What 

 may be expected, then, if instead of increasing the length 

 of an iron bar by heat we use mechanical force and stretch 

 the bar "? Having the bar and the former consequent, ex- 

 pansion, we should expect the negative of the former 

 antecedent, namely cold. The truth of this inference was 

 proved by Dr. Joule, who investigated the amount of the 

 effect with his usual skill f . 



This inversion of cause and effect in the case of heat 

 may be itself again inverted in a highly curious manner. 

 It happens that there are a few substances which are un- 

 explained exceptions to the general law of expansion by 

 heat. India-rubber especially is remarkable for contracting 

 when heated. Since, then, iron and india-rubber are oppo- 

 sitely related to heat, we may expect that as distension 

 of the iron produced cold, distension of the india-rubber 

 will produce heat. This is actually found to be the case, 

 and any one may detect the effect by suddenly stretching 

 an india-rubber band while the middle part is in the mouth. 

 Whenever stretched it will be found to grow slightly warm, 

 and when relaxed cold. 



The reader will readily see that many of the scientific 

 predictions mentioned in preceding sections were due to 

 the principle of inversion ; for instance, Professor Thomp- 

 son's speculations on the relation of pressure and the 

 melting-point. But many other illustrations could be 



f ' Philosophical Transactions,' (1855) vol. cxlv. pp. 100, &c. 



