1893.] on Economies in the Utilisation of Energy. 85 



possible on the left-hand side of the diagram which is impossible 

 on the right — inrpossible, that is, because it has already been attained. 

 Half of our possibilities — indeed, far more than half our possibilities 

 — are of improving up to the best ; it is infinitely harder to improve 

 up from the best. 



When any one tells us that he has invented something, or some 

 method, by which one ton of coal goes as far as two, we may know 

 for certain one of two things ; either he has made a mistake (which is 

 possible enough) or else his standard of comparison has been unfor- 

 tunately chosen. Hundreds of thousands of pounds have been thrown 

 away on elaborate schemes which, at best, could do no more than 

 bring bad and careless practice up to a level passed every day in 

 places where care and common sense have been expended on the same 

 matter. Plenty of room exists for raising the general average 

 efficiency of boiler work ; for, if the average working all over the 

 country were brought up to the standard of the best, there would, 

 probably, be one-third less coal used every year than is now actually 

 burnt. 



The process which we have discussed is, perhaps, really rather to 

 be called a transference than a transformation ; at any rate, it falls 

 into the category of transformation whose theoretical maximum 

 efficiency is 100 per cent., or, allowing for absolutely inevitable 

 losses, perhaps 90 per cent. But with many processes with which we 

 have to do, unfortunately, our maximum theoretical efficiency is only 

 25 per cent., and instead of attaining 80 per cent, even of this we are 

 often happy enough with half as much. 



In the very great majority of instances the mechanical energy 

 which we utilise is originally obtained from the heat of combustion, 

 transferred to some liquid or gaseous body, and by it made to cause 

 certain parts in a machine to move, and to do mechanical work for us. 



Now the actual cycle of physical process, isothermal, adiabatic, 

 isodynamic or what not, which the steam or air or gas may go through 

 is often a very complicated one, sometimes so complicated that it is a 

 matter of considerable difficulty to say beforehand exactly what the 

 maximum theoretical efficiency is. We always, however, know two 

 things about it : first, that it is always far less than 100 per cent. ; 

 second, that it cannot exceed — and in all practical cases must fall 

 considerably short of — a certain known limiting value much less 

 than 100 per cent. This limiting value is the very familiar one 



T — T 



which is written — 7p — -• Here T x stands for the highest tempera- 



1 



ture, measured above absolute zero, at which the working fluid receives 



heat. T 2 stands for the lowest temperature at which the fluid parts 

 with its heat. The difference between the two temperatures, T 1 - T 2 , 

 is the working difference of temperature. The value of the ratio 

 which I have just given is always much less than unity, and must 

 always be so. In the case of a modern steam engine its value is 



