Theory of Heat to the Steam-engine, 339 



the volume and the temperature, or the volume and the pressure 

 of steam at a maximum density, Pambour applied, secondly, 

 Mariotte's and Gay-Lussac^s laws to the same. If, with Gay- 

 Lussac, we assume the volume of a kilogramme of steam at 

 100° C, and at its maximum density, to be 1696 cubic metres, 

 and reflect that the corresponding pressure of one atmosphere 

 amounts to 10,333 kilogrammes on every square metre, then from 

 the above law we obtain the equation M * 



' " , ^_ 10333 273 + ^ ,^Q, 



, = 1.696.-^.^-^3-^, .... (28) 



where, with reference to the same units, v and jo represent the 

 volume and the pressure corresponding to any other tempera- 

 ture t. Herein it is only necessary to substitute in place of ^ 

 the values given in the tension series in order to have, according 

 to the above assumption, the proper volume for each temperature. 

 29. In order, however, to be able conveniently to calculate the 

 value of the integral 



Jpdt 



which plays an important part in the formula for the work done 

 by a steam-engine, it was necessary to find the simplest possible 

 formula between v and p alone. 



If, by means of the ordinary empirical formulae for jt?, the tem- 

 perature t were eliminated from the above equation, the results 

 would prove to be too complicated; hence Pambour preferred 

 forming a special empirical formula for this purpose, to which, 

 according to the process of Navier, he gave the following general 

 form : — 



b+p ^ ' 



wherein B and b are constants. He then sought to determine 

 these constants, so that the volumes calculated from this formula 

 might agree as nearly as possible with those calculated from the 

 foregoing one. As this could not be done with sufficient accu- 

 racy, however, for all the pressures which occur in steam-engines, 

 he established two different formulae for machines with and with- 

 out condenser. 



The first of these was 



20000 .^^ . 



^=i200T^' (^^^) 



which agrees best with the above formula (28) between f and 3^ 

 atmospheres ; but is also applicable for a somewhat wider interval, 

 from about ^ to 5 atmospheres. ■ >. . ; 



