Prof. Thomson on the Dissipation of Mechanical Energy. 305 



vegetatiou, or in chemical action, there is a dissipation of me- 

 chanical energy, and perfect restoration is impossible. 



In connexion with the second proposition, the question. How 

 far is the loss of poiver experienced by steam in rushing through 

 narrow steam-jnpes compensated, as regards the ceconomy of the 

 engine, by the heat (containing an exact equivalent of mechanical 

 energy) created by the friction ? is considered, and the following 

 conclusion is arrived at : — 



Let S denote the temperature of the steam (which is nearly 

 the same in the boiler and steam-pipe, and in the cylinder till 

 the expansion within it commences) ; T the temperature of the 

 condenser; //, the value of Carnot's function for any tempera- 

 ture t ; and K the value of 



1 /"s 



Then (1 — R) w expresses the greatest amount of mechanical effect 

 that can be (Economized in the circumstances from a quantity 



jw of heat produced by the expenditure of a quantity w of 



work in friction, whether of the steam in the pipes and entrance 

 ports, or of any solids or fluids in motion in any part of the 

 engine ; and the remainder, Rio, is absolutely and irrecoverably 

 wasted, unless some use is made of the heat discharged from the 

 condenser. The value of 1 — R has been shown to be not more 

 than about ;|^ for the best steam-engines, and we may infer that 

 in them at least three-fourths of the work spent in any kind of 

 friction is utterly wasted. 



In connexion with the third proposition, the quantity of work 

 that could be got by equalizing the temperature of all parts of a 

 soHd body possessing initially a given non-uniform distribution 

 of heat, if this could be done by means of perfect thermo-dyna- 

 mic engines without any conduction of heat, is investigated. If 

 / be the initial temperature (estimated according to any arbitrary 

 system) at any point xyz of the solid, T the final uniform tem- 

 perature, and c the thermal capacity of unity of volume of the 

 solid, the required mechanical effect is of course equal to 



^Jjyc{t-T)dxdydz, 



being simply the mechanical equivalent of the amount of heat 

 put out (jf existence. Hence the problem becomes reduced to 

 that of the determination of T. The following solution is ob- 

 tained : — 



ffjrrf?\ 



, , , ctdxdydz 



fff-y> 



c dx dy dz 

 Vhd. Mag. S. 4. 'Vol."4. No. 25. Oct. 1852. 



