182L] Observations on Mr. Ilerapatlis Theory. 421 



atoms of the body B. The communication of motion from the 

 atoms of A to the atoms of B will not be compensated ; for the 

 atoms of B having less velocity than the atoms of A will never 

 overtake them. The motion of the atoms of the whole body 

 B, therefore, will be increased ; so that if one body A have atoms 

 of a less magnitude than the atoms of a body B with which it is 

 in contact, but with a velocity inversely greater ; that is, accord- 

 ing to Mr. H. the bodies A and B being of the same temperature, 

 the momentum of the atoms ; that is, the temperature of the 

 body B shall continually increase. But this we know is con- 

 trary to the real fact; therefore the temperature of bodies is not 

 the same as the momentum of their atoms moving among each 

 other with different velocities. 



I could hardly claim room in your pages to trace out all the 

 contradictions to known facts which will be the necessary result 

 of Mr. Herapath's theory : it will be probably more obedient to 

 his wish that I should examine the mathematical demonstration. 



Almost the whole of this theory is founded upon Prop. 2 and 

 its corollaries (Annals of Philosophy, April, p. 284.) The propo- 

 sition is, " If a hard spherical body impinge perpendicularly on 

 a hard fixed plane, the body will, after the stroke, remain at 

 rest." This will not be disputed. Mr. H. states in support of 

 it, " that action and reaction are equal." " The force, there- 

 fore, with which the ball is acted on by the plane at the time of 

 the contact in a direction opposite to its motion is just equal to its 

 momentum ; consequently the motion and action destroy one 

 another, and the ball, having no other tendency, continues at 

 rest." This reasoning is I admit indisputable, and being so, it 

 follows that whenever a hard spherical body shall be acted on 

 by a force " in a direction opposite to its motion " ''just equal 

 to its momentum," that force and momentum " destroy each 

 other." 



Let A be a hard ball having a given momentum ; now bodies 

 act with a force equal to their momentum, and so it is assumed 

 of the ball in the foregoing proposition. But if there be another 

 body B similar, and having similar velocity to the body A, the 

 momentum of B shall be equal to the momentum of A ; and, 

 consequently, the force with which B acts shall be equal to the 

 momentum of A. If, therefore, B moving in an opposite direc- 

 tion to A meet A, it will act upon it " with a force in a direction 

 opposite to its motion just equal to its momentum," and conse- 

 quently the momentum of A and the action of B, " being equal 

 and opposite, destroyed each other." This would seem to be 

 necessarily deducible from Mr. Herapath's own proposition and 

 reasoning. But no, says Mr. H. " If two hard and equal balls 

 come in contact with equal and opposite momenta, they will 

 separate with the same velocity with which they met." Let us 

 examine the reasoning. u Suppose a hard plane, or other body, 

 be held against a fixed hard body, unci in this way receive the 



