224 Remarks upon Mr. Herapath's Theory. [Sept. 



principal step on which his proof depends is, that the elasticity- 

 varies as the momentum of the particles x the number of 

 returns. We may certainly grant that the elasticity varies as the 

 action of the particles against a given portion of the surface con- 

 taining he gas, but it may fairly be questioned whether this 

 action can be measured by the momentum x the number of 

 returns. The momentum must be the mass x the velocity, and 

 the velocity and the number of returns seem to be the same 

 thing; so that the same factor is introduced twice ; and hence 

 the square of the temperature, instead of the simple temperature, 

 results. 



In Prop. IX. and its cors. which depend upon the last, he 

 asserts, in a somewhat positive manner, that MM. Dulong and 

 Petit are mistaken in the result drawn from their experiments ; 

 but without entering upon any examination of their reasoning, 

 and solely on the authority of his own theory. Thus even 

 granting the validity of the proof above considered, he is assum- 

 ing an hypothesis producing a result at variance with experi- 

 ments (by his own confession), and in consequence rejecting the 

 experiments. 



The third cor. to Prop. IX. appears to contain an expression 

 which stands much in need of elucidation. Mr. H. says, that 

 the ratio of the temperature of freezing water to that of boiling is 

 as 6 to 7 nearly. In a former paper on this subject, published 

 in the Annals for July, 1816, he has warned his readers that he 

 does not use the word " temperature " in its usual sense, 

 though he by no means makes it clear in what sense he does use 

 it. The only sense which the expression seems to me to admit 

 in this place is, the heat which has been communicated to a 

 body above that which can be conceived an absolutely cold 

 state ; and then the proposition must imply, that the gas has 

 gone on expanding by successive communications of heat from 

 a state in which it had no heat at all ; because it is only esta- 

 blished on the ground of that theorem which asserts tempera- 

 ture to be in a certain ratio to volume ; and this is deduced only 

 from experiments made within the limits at which heat expands 

 the bodies employed ; but both from the law laid down by Mr. 

 H. and because heat is the cause which keeps atoms asunder, it 

 follows, that when the temperature is 0, the volume must be 

 also ; or, in other words, the gas must then not have existed. 

 Thus by temperature we are to understand a certain degree of 

 heat above that which thrown into a nonentity shall expand it 

 into existence. 



Mr. H.'s theoiy certainly affords a good explanation of the 

 cause why all gases have a tendency to mix ; but it appears to 

 me that the explanation of their mixture on common principles 

 does not necessarily involve the contradiction which he points 

 out. If the gaseous state of a body be owing to the repulsion 

 of its particles, and if we suppose the surfaces of two different 



