PRINCIPLES OF THE MECUANICAL THEORY OF HEAT. 269 



well adopt tins equation as tlie true expression of tlie relations between p, ic, 

 and t Again, the values of u, as stated in tlie 7tli column, are not those calcu- 

 lated in the wa,y above given, but those very nearly the same, which are obtained 

 by a division of the values of Ajjm, given in column 10, by the corresponding 

 values of Aj). 



Let us now briefly consider the signification of the magnitudes represented in 

 the table. 



Q, as already said, is the total quantity of heat which is expended in order 

 first to heat one kilogram of water at 0° to t°, and then to convert the water of 

 t°, under the con-esponding pressure p, into saturated vapor of t°. 



A part of this quantity Q, namely, Ajm, is spent in external work ; it is, 

 therefore, no longer contained in the saturated vapor at t° ; the total quantity of 

 heat contained in the vapor (excepting that already in the water at 0°) is 

 only J=Q— A j; ii. The values of J are represented in the 11th column of our 

 table. 



In order to transform water at t° into saturated vapor at t°, the quantity of 

 heat r is necessary, whose values are exhibited in the 6th vertical series of the 

 table. It is this magnitude r which is usually designated as Jatoit heat; an 

 incorrect expression, however, if we mean thereby to indicate the quantity of heat 

 employed in aboUsJiing the cohesion of the particles of water, and hence spent in 

 an external work, for a part of the quantity r, namely, Apu, is consumed by 

 that external work. Only the remainder, p=^r—A2ni, can be regarded as the 

 internal latent heat of vapor, while the magnitude r might, according to Clausius, 

 be designated as evaporation-heat. 



It is evident that for a correct calculation of the effects of steam-engines the 

 values of v must be taken into account as they are set forth in our table, and not 

 hose reckoned after M. Gay-Lussac's law. It is to be observed, however, 

 tn a comparison of the values of V and v, given in two preceding pages, that 

 in the last the volume of one gram of vapor is expressed in cubic centimetres, 

 iwhile in the first it is stated in cubic metres. 



From a consideration of the numbers grouped together in the table it will bo 

 seen that of tlie quantity of heat conveyed to the water in the boiler only a very 

 small part is expended in mechanical work; for the quantity Apu employed in 

 such work is but an inconsiderable fraction even of the evaporation-heat r, about 

 J3 for 100°, and -^j for 1G0°. Tlie internal latent va;M)r-heat /> abides with the 

 vapor at its exit from the machine, and hence can do no work. This quantity 

 of heat fi can only be in part regained. 



This circumstance occasioned the constructing of i)ower machines, in which the 

 elasticity of heated air might operate instead of steam. fSuch machines, con- 

 structed particularly after Ericsson's designs, and known l)y the name of caloric 

 engines, have been repeatedly introduced into practice with high expectations, 

 but have been as often abandoned because their performance fell far short of 

 that of the steam-engine. 



Till. — ACTIOX OF SATUKATED STEAM DUKING EXPANSION. 



The results thus far obtained enable us to form a correct idea of the action 

 of steam in our expansion steam-engines. As we cannot, however, here develop 

 the equations necessary for the general solution of this problem, we nnist content 

 ourselves with the consideration of special cases. 



If, under the piston of a steam-cylinder, there be just one kilogram of saturated 

 steam of IGO^ C, we find for this steam by our talde, 



i = 0.:3002 cubic metre. 

 ^=03243.4 kilograms. 

 J = 610.53 units of heat. 



