29't^ D*s Reply to C,*s Observations [April, 



by Bacon, and supported by Newton ; namely, that heal; consists 

 in motion. What a wonderful discovery ! " a discovery," to use 

 the words Sir H. Davy has employed on another occasion, " that 

 seems to have been reserved for C. and the year 1821 ; " a disco- 

 very, it is plain, that makes it " as self-evident as that two and 

 two make five ;" that Bacon and Newton, as well as Mr. Hera- 

 path, " have in truth quite mistaken the road to philosophical 

 science." 



Having proved the importance of C.'s discovery, let us consi- 

 der a little more attentively whether it be really a consequence 

 of Mr. Herapath's theory, or of C.'s " invincible " mathematics. 

 Mr. H.'s Prop. 4, in the Annals for April, 1821, stands thus : 

 ** If a hard body overtake and strike another hard body, moving 

 with a less velocity in the same right line, the first body will, 

 after the stroke, continue its course with the same velocity which 

 the other body had before it ; and the second body will acquire 

 from the stroke a momentum equal to the difference of the 

 velocities of the bodies previous to the contact, drawn into the 

 mass of the first body ; that is, if A B represent the two bodies, 

 and a b their velocities before collision, the motion of A after- 

 wards will be A by and that of B, B /> 4- (a — ^) A." Hence 

 Conceiving that the particles of each body move uniformly and 

 respectively with their mean velocities, which is the precise case 

 C. has considered, it follows in the case of A overtaking B, that 

 B will return to its body with the motion 2 B /; — /> A ; and A, 

 instead of returning to its proper body, will continue to move 

 towards the other body with the motion A /;, until it meet with 

 B, or some other particle, in its exit from the body. For A 

 cannot now overtake another particle, because its velocity from 

 the last collision is reduced to the same as that of the particles 

 of the other body; nor can it return to its own body, because the 

 collision did not give it an inward, but merely diminished its 

 outward, motion. Now the outward particle which A next 

 strikes must evidently meet it with the mean motion B b of the 

 particles to which it belongs. By Mr. H.'s Prop. 5, of his first 

 paper, an exchange of motion between A and the second struck 

 particle will take place ; A will return to its body with the 

 motion B /> or A «, and the particle struck to its body with the 

 motion A b. The motion, therefore, which is communicated to 

 the body to which A belongs by the return of this particle, under 

 the view in which C. would consider it, is A a ; that is, the same 

 as the proper motion of the particles of the body ; and the total 

 motion with which the two particles struck return to their body 

 is2B^ — A^ + A6= 2B^; that is, precisely the same as 

 the sum of the mean motions of any two of its particles. Conse- 

 quently the temperature of the body, which C. says ought to be 

 augmented, is neither augmented nordiminished, by being in con- 

 tact with a body of an equal temperature having particles less ia 

 size. 



