1822.] on Mr, HerapaWs Theory, 295 



The circumstance under which I have considered this, corre- 

 sponds to the mean circumstances of the case. I have omitted 

 to consider the unequal motions of the particles arising from, 

 their mutual attraction, which will sometimes make them strike 

 with a less, and sometimes with a greater, than their mean force ; 

 but which ultimately come to the same thing, as if they were all 

 mutually moving among one another within prescribed paths, with 

 a velocity uniform for the particles of each body. However, 

 though this omission will make no difference on the mean com- 

 munication of motion from one body to the other, it will, how- 

 ever, make a considerable difference in one case on which C. 

 has ventured to dehver his opinion. C. says, "the greater 

 atoms having less velocity than the less will never overtake 

 them." This is not universally the case. In consequence of 

 the mutual action of the particles, they move both in their 

 goings and returnings swifter at some parts of their paths than 

 at others. Generally speaking, in the exterior particles, which 

 are those of the two bodies that come in contact, their velocities 

 are the swiftest immediately before and after the collision ; and 

 the slowest immediately preceding and following the exterior 

 extremity of their path. Hence, therefore, the greater particles 

 may often move much swifter than the less; and consequently 

 may frequently overtake and strike them, notwithstanding C 

 asserts the contrary. This httle circumstance will, perhaps, help 

 to show C. that his haste in this attack on Mr. H. exceeds his 

 judgment, and his temerity his depth. 



From the views I have just taken, it follows that if two bodies 

 be brought into contact, having unequal temperatures, and 

 nothing foreign interferes, they will ultimately have the same 

 temperature ; the particles of the body with the higher temper- 

 ature communicating just so much of their excess of motion, as 

 will give to the particles of the other body, individually, a momen- 

 tum equal to their own reduced momentum. For as the parti- 

 cles strike one another in all directions, the differences of 

 temperature which are momentarily communicated to each body 

 by the contact, are distributed as soon, or almost as soon, as 

 communicated, by the successive particles in every direc- 

 tion. By this means, the motion of the particles which first 

 received the difference of temperature becomes presently 

 affected in the very opposite direction to that in which the dif- 

 ference was first communicated ; and consequently the differ- 

 ence between the communicated motions from body to body 

 becomes less. And thus this difference continually diminishes 

 until the two bodies attain a common temperature. This very 

 simple and obvious consequence I should not have taken the- 

 trouble to explain, had not C. drawn conclusions on this subject 

 too absurd to be entertained by any other person, I apprehend, 

 but himself. Because by Mr. H.'s theory of coUision, when two 

 perfectly hard bodies meet moving in opposite directions, aa 



