1821.] Observations on Mr. Herapath's Theory. 425 



There is, however, one advantage in this mode of reasoning 

 which of course I ought not omit to mention. It is well known 

 that any one who publishes a theory is frequently attacked on 

 opposite sides. For instance, while 1 am endeavouring to show 

 that this proposition is not founded in truth, another person may 

 attempt to prove that if it were, the consequences would be such 

 as directly to contradict the supposition that heat is motion; for 

 it may be said, that if it be true, " that when one hard body 

 strikes another in the line of the centies of gravity, an exchange 

 of state will take place " then if a body the particles of which 

 have any degree of momentum (that is, a heated body), were 

 brought into contact with a body, the particles of which had no 

 motion (that is, an absolutely cold body), an exchange of state 

 would take place ; but the effect, which would be absolute in 

 the extreme, would be proportionate in the mean. If one body, 

 therefore, were brought into contact Avith another whose parti- 

 cles had individually a less degree of momentum, a chano-e of 

 state would take place in proportion to the difference in the 

 momentum of their particles ; that is, if one body were brought 

 in contact with another body having a less temperature, an 

 exchange of state would take place. This, however, is contrary 

 to the fact ; the surplus temperature would actually be divided 

 by them. But here a distinguished excellence of Mr. H.'s 

 reasoning comes into use ; for in order to meet this opposite 

 argument, it is only to change the terms, and the same reason- 

 ing may be made to prove exactly the contrary to what it proved 

 before ; like the newly-invented steam-vessels, which can sail 

 backwards or forwards with equal ease. Thus let the body, B 

 (the quiescent body), be supposed to have a ratio to A (the mov- 

 ing body), less than any assignable ratio instead of the reverse, 

 and, mutatis mutaiidis, the argument will stand thus : ' If we 

 suppose B so small as to have a ratio to A less than any assign- 

 able ratio, the ratio of the loss of the motion of A by the stroke, 

 to the motion of A before the stroke, will also be less than any 

 assignable ratio ; the difference in the motion of A, therefore, 

 before and after the stroke, will be unassignably small ; that is, 

 they will be just the same !' It will be easily seen that the whole 

 argument may thus be reversed, so that, in a manner most feli- 

 citous, the same course of reasoning which proved that an 

 exchange of state between the balls will take place, may be made 

 to prove that such an exchange of state will not take place. 



But the proposition is in itself worthy of being repeated. " If 

 a hard balk" (for example, one foot in diameter) " strike another 

 hard ball," (of the magnitude of a pin's head,) " at rest in the 

 line of their centres of gravity, an exchange of state will take 

 place, the former," (the large ball,) " will remain at rest after 

 the stroke, and the latter," (the pin's head ball,) " will proceed 

 in the same direction in which the first was moving, and with 

 the game momentum." 



