Prof. Clausing on the Conduction of Heat by Gases. 529 



denotes the temperature reckoned from the freezing-point. If 

 we further represent the coefficient of expansion of the perma- 

 nent gases, namely ^-^, by a, as is usually done, we can write 



„ 5 #mN n w n 3 e , dt 



Lastly, if we introduce here the symbol K with the value 



our equation reads 



5 kmN UQ 6 ? Y 



K= 24~273~' (XV - 



g=-k*/ft^£ (xvi.) 



§ 25. The factor K contains only magnitudes which relate to 

 the normal condition of the gas, and is therefore only a constant 

 dependent on the nature of the gas under consideration. Accord- 

 ingly, the form of the last equation enables us at once to draw 

 two general conclusions. 



First. For a given value of-y, the conduction of heai increases 



with the temperature which the gas has at the place under consi- 

 deration. This increase takes place in the same ratio as the 

 increase in the velocity of sound by rise of temperature, namely, 

 proportionally to the quantity \/l-\-ctt. 



Secondly. The conduction of heat is not affected by the pressure 

 to which the gas is exposed. This is explained by the circum- 

 stance that, although the number of molecules which can convey 

 the heat is greater in a gas which is rendered more dense by in- 

 creased pressure, the distances traversed by the individual mole- 

 cules are smaller. This latter conclusion might lead to absur- 

 dity if it were assumed to be applicable to the gas under every 

 conceivable condition of compression or expansion. It must, 

 however, be borne in mind that there are obvious limits to the 

 application of it to conditions of the gas which depart very much 

 from the mean condition : on the one hand, the gas must not be 

 so much compressed as to produce a too great departure from 

 the laws of permanent gases which have been taken as the foun- 

 dation for the whole course of reasoning; and on the other 

 hand, it must not be so much expanded that the mean length of 

 excursion of the molecules becomes so great that its higher 

 powers cannot be disregarded. 



§ 26. It will be necessary, for the numerical calculation of the 

 above formula, to return once more to the point mentioned in 

 § 7, namely, the accidental variations of the velocity of the mole- 

 * Phil. Mag. S. 4. No. 157. SuppL Vol. 23. 2 N 



