PRINCIPLES OF THE MECHANICAL THEORY OF HEAT. 255 



In all these writing's tlic raeclianical theory of heat is developed, as it needs 

 must be when a general and complete solution of tlie pro1)leni is contemplated, 

 through a certain amount of the higher mathematical analysis. In what follows, 

 however, I shall endeavor to set forth at least the most important principles 

 thereof in an elementary form, and, bj- the application of these principles to 

 saturated vapors, to show some material consequences of their action. I shall 

 hope, thereby, not only to communicate a right idea of the nature and significa- 

 tion of the theory in question to, those who are deficient in a knowledge of the 

 difierential and integral calculus, but also to supply to those who may be provided 

 with that learning, a sort of introduction or preparation for the more thorough 

 stutly of those doctrinal difficulties which are apt to oppose themselves at the 

 entrance upon such an investigation. But before proceeding to a nearer consid- 

 eration of the grounds of the mechanical theory of heat, we will examine more 

 definitely the loss ofhcaf, corresponding, in some particular cases, to t\io 2J€r/orm- 

 ancc of work. 



Y. — DISAPPEARANCE OF HEAT THROTTGH THE PERFORMANCE OF WORK. 



By a large number of experiments directed to the subject under consideration, 

 Hirn has shown that in steam-engines a quantity of heat disappears directly 

 corresponding to the work executed, he having emjdoyed with that view engines 

 of from 90 to 150 horse-power. The machines with which he experimented were 

 of the expansion order, in which the steam, after it had operated, passed (^ff into 

 a condenser. In order to avoid errors which might arise from water beiu"- 

 mechanically carried over by the engine from the boiler, or steam already con- 

 densed in the expansion, Hirn caused the machinery to work with overheated 

 steam, which he procured by means of an appropriate apparatus, whereby the 

 vapors proceeding from the boilt-r were heated, before their entrance into the 

 cylinder, to a definite temperature ascertained by a thermometer. 



The quantity of water j; which entered, in a second, the vessel for evapora- 

 tion, and arrived through the machine in the condenser, was ascertained by exact 

 measurement of the quantity ot water which, during the space of a whole day, 

 was conveyed by the feed-pump into the boiler, under a uniform working of the 

 machine, and with an unchanged height of water in the boiler. In like manner 

 the quantity of water P immitted each second into the condenser was ascertained 

 by the determination of the quantity of water of condensation discharged during 

 a whole day under a miiform influx. 



The quantity of heat given up by the steam condensed during each second, 

 was found in the following manner: If t be the tem[)erature at which the steam 

 is formed in the boiler, then according to Ilegnault's experiments, the whole 

 quantity of heat which is contained in one kilogram of steam at this tem})erature 

 more than that contained in one kilogram of water at 0°, is qi=iG0G.5-\-O.305t 

 units of heat. But this steam, l)ef'ore its entrance into the cylinder of the steam 

 engine, is heated to the degree of T, whence there is further necessary for each 

 kilogram of steam (/2=0..'3 (T — t) units of heat, if we take, as may be done with 

 approximative correctness, 0.5 as the specific heat of the steam. 



The ([uantity of heat which this kilogram of steam loses, until it is condensed 

 and cooled to the temperature of/ degrees, with which the water of condensation 

 leaves the condenser, is thus qi-{-q2 — -f, and hence the whole quantity of heat, 

 which the quantity of steam jjj traversing the engine every second gives up, is 



:=p [GUG.5+ 0.305 /+0.5 (T— /)—/]. 



If, now, no heat were consumed by the performance of work in the cylinder 

 the whole quantity of heat Qi must be carried over to the condenser, and lien 

 serve to raise the temperature of the condensation-water. If i be the temperature, 

 at which that water enters the condenser, but/ the temperature at which it issues 

 therefrom, i\\cnf- — i is the quantity of lieat which each kilogram of condensation- 



