Quantities occurring in the Mechanical Theory of Heat. 257 



tion ? Nearly every molecule has an altered position, velocity, 

 and acceleration ; those only have meanwhile continued in the 

 same place and situation whose velocity happened previously 

 to be : here the molecules have become scattered; there 

 they have moved closer to one another ; here is rarefaction, 

 there condensation perceptible. This is apparent not merely 

 in the interior, but also at the surface of the body ; there also 

 some of the molecules have moved further apart, while others 

 have come closer together. At the next moment again 

 another grouping shows itself; and so it goes on in constant 

 change. 



Now what is the consequence of this continual variation ? 

 As the number of the molecules, though very great, is not in- 

 finite, and we will provisionally suppose that no unparalyzed 

 external forces cooperate which could disturb the spontaneous 

 variation, there is just as much probability that, at any moment 

 previously selected, the partial rarefactions will predominate, 

 as that the reverse will be the case ; and therefore that in an 

 indefinitely short period chosen the sum of the expansions or 

 that of the contractions will predominate is equally probable — 

 supposing, I repeat, that no unparalyzed external forces act 

 on the body. Let us assume that at the moment chosen ex- 

 pansion predominates, so that in that element of time the 

 volume becomes greater. Let us then consider the body 

 again after a while ; it may just as well happen that now the 

 contractions predominate and therefore the space occupied 

 is diminishing. As, however, the successive changes can never 

 take place abruptly, all the gradations of both expansion and 

 contraction must occur, and in a continuous series, between 

 the limits determined by the given ratios. Accordingly the 

 volume will during a certain time continually increase until 

 it reaches an extreme limit of expansion corresponding to the 

 circumstances; it then remains an instant unaltered, and 

 thenceforward diminishes uninterruptedly till it reaches the 

 limit of condensation, when it again remains a moment un- 

 changed, to expand again and repeat the performance we have 

 described. It would certainly be a very remarkable and ex- 

 tremely rare chance, if the partial expansions and contractions 

 were at every moment to exactly compensate one another. It 

 is far more likely that the volume is subject to a continual varia- 

 tion, a constant pulsation. These oscillations are as little per- 

 ceptible to the senses as the motions of the molecules by which 

 they are brought about. After each complete oscillation the 

 body returns again to its previous phase. If we denote by i 

 the period of a complete oscillation, and by dv the actual 

 variation of volume in the time dt, then the total change of 



Phil. Mag. g. 5. Vol. 2. No. 11. Oct. 1876. S 



