286 Mi\ Herapath on the Causes, Laws, andprincipal [April^ 



bodies, but to one whose nature is so very different, as to be 

 almost the very opposite. Hardness and softness are diametri- 

 cally opposite properties, and elasticity is nothing but an active 

 kind of softness ; for elasticity consists in a vigorous restoration 

 of an altered figure; and no body can have its figure altered 

 .which is not more or less soft. To argue, therefore, that two hard 

 ibodies which meet each other with equal and contrary momenta 

 •cannot separate after collision, because they have no elasticity, 

 .is evidently to abandon the definition of hardness, and to adopt 

 that of elasticity, which has no connexion whatever with it, and 

 consequently ought, in such a case, to be excluded. It is no 

 matter of surprise, therefore, with such incongruous ideas, that 

 mathematicians have hitherto had erroneous views of the theory 

 of collision of hard bodies. Probably the apparent sterility, if 

 not inutility of the subject, has occasioned an apathy towards a 

 scrupulous investigation, which the slightest idea of its import- 

 ance would have easily removed. Had it been imagined that 

 the collision of hard bodies was connected with the develop- 

 ment of the cause of heat, gravitation, light, magnetism, electri- 

 -city,&c. itwould have been scrutinized with a care which nothing 

 could have escaped; and with a rigorous investigation, I am 

 persuaded our ideas of the subject would have been very differ- 

 ent to what they are. 



If there be any method of classification which should have a 

 preference, it appears to me it should be to rank all those bodies 

 under one head which have mutable, and those under another 

 which have immutable figures. To the latter class will belong 

 hard bodies, and to the former every variety of soft and elastic 

 bodies ; the one will give their strokes instantaneously, and with- 

 out the lapse of time ; the other, gradually and with time. In 

 each particular case, the physical nature of the impulse should 

 be considered, and a theory of collision framed accordingly. 

 With such views, our theories of collision would be made to rest 

 on their true and veritable principles, the physical nature of the 

 bodies and of the strokes which they give. 



Many simple experiments might easily be devised to prove 

 the truth of our second cor. ; for it is immaterial on what bodies 

 we experiment : we can draw the same inference for any. The 

 thing, however, is so obvious that I have generally considered it 

 in the fight of an axiom ; and have often ascertained the opinion 

 of other people on the same subject by the following question : 

 " Suppose a hard sphere, moving freely with a given velocity, 

 strike directly upon a hard fixed body, it would strike with a 

 certain intensity : but now suppose that instead of the fixed 

 body the moving sphere strike upon another hard equal body, 

 moving with an equal velocity, in an opposite direction, what 

 would be the relative intensities of these two strokes?" The 

 answer has invariably been, that the latter would be the double 

 of the former. This, it must be allowed, is not a mathematical, 



