340 Mr. A. M. Worthington on the 



each side of that section above and below it. If there is no 

 tension, the position of equilibrium of the molecules is such 

 that the attractive cohesion-forces and the repulsive force of 

 heat across the section are equal. In my own mind the con- 

 ception of what is going on is rendered more vivid by thinking 

 of the analogy with two men who compress a spring placed 

 between them by pulling each other together. The force 

 with which they draw each other together is equal and oppo- 

 site to the reaction of the spring by which they are thrust 

 apart. 



Now let the bar be stretched: the intramolecular distance 

 is increased, and, by what we have seen, the repulsive forces 

 are on this account diminished, while of the cohesion-forces 

 we as yet only know that they must now be greater than the 

 repulsive forces ; and the equilibrium is now of a different 

 kind : the resultant action across the section is now attrac- 

 tive ; and since there is equilibrium, the molecules at either 

 side of the section must be pulled apart by the action of 

 molecules further away. The analogy which in my own 

 mind gives vividness to the conception, is that of two men 

 endeavouring by pulling at each other to compress a spring 

 (now weaker than before) which is placed between them, while 

 they themselves are somewhat pulled apart by others exerting 

 less power than themselves. It is necessary for equilibrium 

 that the cohesive force exerted across the section shall be 

 equal to the sum of the tension and the repulsive heat-force; 

 and the fact that we can increase the tension up to a certain 

 value, the " breaking-stress," and not beyond, shows that 

 after a certain point this condition ceases to he fulfilled. 



If we write T for the tension per unit of area across the 

 section, C for the cohesion per unit of area, and E for the 

 repulsive action per unit of area, then C = T + E or T=C— E 

 is an equation which holds for all values of T between and 

 the breaking-stress; but for an extension of the body greater 

 than that corresponding to the breaking-strain, C — E is less 

 than the breaking-stress. In other words, with an increase of 

 molecular distance the quantity (C — E) increases up to a 

 certain maximal value, beyond which an increase of the mole- 

 cular distance is attended by a decrease in (C — E). 



Also we have seen that E diminishes with the extension; 

 and that for extensions less than that corresponding to the 

 breaking-strain its diminution is more rapid than that of C. 

 Now it is evident that no maximal value could be attained by 

 (C — E) if C continually increased, remained constant, or 

 continually diminished less rapidly than E ; but that there 

 would be a maximal value if C, after increasing, remaining 



