256 PEINCIPLES OF THE MECHANICAL THEORY OF HEAT. 



water takes up in tlie condenser, whence the quantity of heat Q2 which is taken 

 up, in each second, by the condensation-water is Qa^P (/ — i,) and thus must 

 Qi=:Q3 if no heat be expended for the work. But experiment shows in fact that 

 Qi — Q2 is in nowise equivalent to nothing. In such an experiment, for example, in 

 which the ratio of expansion was 1 : 2, the tension of the steam in the boiler 

 gave a result equal to 4.5 atmospheres, and thus ^=148°. 3. Also, 

 T— f=91°.7 



jj=0. 34554 kilograms. Pk=5. 84004 kilograms. 



/=37°.28 «=:5°.l 



whence results, 



Qi=228.16 Q2=187.82 



Qi — Q3=40.34 units of heat. 

 There had, consequently, been 40.34 units of heat expended for the work 

 done, while the net efiect of the machine was found, by Prony's dynamometer 

 equal to 11250 metre-kilograms, and hence there results for one unit of heat 

 consumed 



=278 metre-kilograms, 



40.34 ^ ' 



as the practical or net effect. 



By another experiment with the same machine, in which the ratio of expan- 

 sion was 1 : 6, the following values were given : 



^=152°.2 T— ^=93° 



j;=0. 23548 kilograms. P=5.8718 kilograms. 



/=2°.605 ■ *=3°.2 



whence there results 



Qi — Q2=158.81 — 123.3=30.51 units of heat, 



■while the net effect of the machine was found equal to 8700 metre-kilograms, and 

 thus, for one unit of heat consumed, there results 



S'^OO „„^ .1-1 



^285 metre-kilograms, 



30.51 "^ 



Thus it will be seen from these premises that not only is there really a con- 

 sumption of heat for mechanical work, but also that the practical effect of steam- 

 engines is very nearly proportional to the loss of heat. 



We might, from these investigations alone, calculate the mechanical equivalent 

 of heat, if the practical effect measured were equal to the whole work done 

 by the steam. Let us suppose now that the net effect of the machine amounted 

 to about 70 per cent, of the entire work done by the steam, and we shall 

 have, as the mean of the two above experiments, the mechanical equivalent of 

 heat equal to 400 metre-kilograms. 



In like manner Clausius derived from a great number of experiments, which 

 were conducted with steam-engines by Hirn, the number 413 as the mean value 

 for the mechanical equivalent of heat. Now, if we assume the mechanical 

 equivalent of heat equal to 424, it would result from the two experiments, whose 

 details have been given above, that the practical effect of these machines amounts 

 to about 66 per cent, of the whole work done by the steam. 



Every process which is of a nature to produce heat can also perform mechani- 

 cal work ; but such work is always attended by a corresponding consump- 

 tion of heat, or, in other words, the quantity of heat produced by a definite 

 process suffers a corresponding diminution, it" together with the generation of 

 heat mechanical effect is produced. This proposition is well illustrated by the 

 electro-magnetic motor. When an electric current traverses the metallic coils of 

 a magnetizing spiral, the wire is heated, and the heat produced, in a given time, 

 in the whole circuit is expressed by the equation 



