M. Achille Cazin on Internal Work in Gases. 277 



necessary to combine equation (11) with formula (6), and the 

 following simple formula is obtained : — 



C P (T 1 -T0=! A ^»(l-i r ) ) . . . (12) 



from which we can deduce v n . 



I shall use equation (12) in order to verify the calculation 

 made of T' by means of equations (9). 



To this end I introduce in formula (6) the values 1^=283° 

 and p'= 751*63 millims., and from it deduce 



z/'=0*527296 cub. m., //t*" = 396-33. 



Having v n , we introduce its value into equation (12); and 

 putting C p = 0-216, I find 



which is just the value deduced from formulae (9). 



The identity of the numbers evidently depends on the value 

 of C p • but the value which I have chosen is rather too great, so 

 that it leads us to take 3°*56 as a minimum. The smallest value 

 of C p observed by M. Regnault is 0*187; this number leads to 



T,-T'=4 ll, 



and we must regard this value as a maximum. Messrs. Joule 

 and Thomson have made use of the formula (12) by expressing 

 2*j and v n as functions of p x and// by means of the law of Ma- 

 riotte. In fact putting 



<n v — T ^P, 

 1 o 



p'v'^T^, 



In 



we have 



T.-T'^^^-y). ..... (13) 



In this formula the pressures are expressed in units of weight 

 on the unit of surface ; if we wish to express them in atmo- 

 spheres, we shall take 



T,-T'= 3Aa ^° T2 10334 (»,-«') atmosphere. (14) 



P 1 



Such is the formula employed by the English physicists, 

 p. 337 of their memoir*. Let us examine if it agrees with 



* Philosophical Transactions of the Royal Society of London, vol. cxliv. 

 part 2. 



There is a mistake in the printing of the last formula of page 337 ; the 



p p 



factor — 2 is omitted. 



