Prof. Clausius on the Conduction of Heat by Gases, 419 



In answer to the objection that so great a mobility as I assume 

 their molecules to possess must cause two gases which are in 

 contact with each other to mix very quickly, I have shown in a 

 former paper that the space moved through by each individual 

 molecule must be exceedingly small. In reference to this, Joch- 

 mann says (p. 156), "Even if we consider this as disposing of 

 the objection derived from the mixture of gases, it by no means 

 disposes of the other, namely, that local variations in the tem- 

 perature of a gas would be impossible, but that a uniform mean 

 velocity must very soon be established throughout the mass. 

 Seeing that the irregular motions of the gaseous atoms cannot be 

 easily presented to the mind, let us make use of a simple analogy 

 in order to assure ourselves that the two points are essentially 

 different. Suppose a row of similar, perfectly elastic balls placed 

 at equal distances from one another in a straight line. If a certain 

 velocity be imparted to the first ball so as to cause it to strike the 

 second centrally, it is true that, the movement propagating itself 

 through the whole row, each ball will only alter its position as 

 much as the distance between two balls ; but the velocity im- 

 parted to the first will propagate itself through the whole series 

 about as quickly as if the first ball had continued to move onward 

 without encountering any obstruction.'''' 



Jochmann thus does not take the matter as it is into consi- 

 deration, but gets over the difficulty which the consideration of 

 it certainly does offer, by selecting as analogous a very much 

 simpler case. This case is, however, so entirely different from 

 the one it is supposed to represent, that no inference whatever 

 can be drawn from the one respecting the other. If we wish to 

 arrive at really reliable con elusions concerning this and other 

 allied subjects, we must not be afraid of the somewhat trouble- 

 some consideration of the irregular motions. Of course this 

 does not preclude the use here and there of assumptions which 

 help us to avoid useless complication in calculations; but these 

 assumptions ought always to be of such a kind that we see clearly 

 that they cannot affect the result*. 



The Philosophical Magazine for 1860 (vol. xix. p. 19, and 

 vol. xx. p. 21) contains an interesting memoir by Prof. Maxwell, 



* Hoppe has also made the same objection, on essentially similar 

 grounds, in two papers, the last of which (Pogg. Ann. vol. ex. p. 598) is a 

 reply to a note published by myself. He says expressly, p. 603, " The cases 

 in which two molecules that meet each other are unequal, or do not strike 

 centrally, can plainly cause no alteration in the general result." The word 

 plainly appears to me to be by no means in place here ; on the contrary, I 

 believe that the inaccuracy of the opinion which has been quoted will be 

 made clearly evident by what follows. I leave the reader to form his own 

 opinion of the other remarks occurring in Hoppe's reply, for I am unwilling 

 to inflict upon the scientific public a mere dispute about words. 



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