838 THE POPULAR SCIENCE MONTHLY. 



the absolute scale we wish to determine. We have as above Tt : T 

 :: H-h : II, and Tt' : T :: H-h' : h', if h! is the heat rejected 

 at the temperature t'. Hence Tt : Tt' :: II h : H h! . But 

 Hh is the heat converted into work by an engine working between 

 the temperatures T and t, and is proportional to the area B C D A. 

 Also Hli' is the heat converted into work by an engine working 

 between the temperatures T and t' , and is proportional to the area 

 B Cm n. Therefore T-t : Tt' :: area B C B A : area B Cmn ; 

 or 180 : T-t' :: area BCBA: area B Cm n. 



Having the data for constructing the isothermal and adiabatic 

 lines, the areas BCBA and B C m n can be computed, and hence 

 t' determined. The divisions of an absolute scale so constructed are 

 found to correspond very closely with the divisions of the air-ther- 

 mometer, and to differ but little from the divisions of the Fahrenheit 

 scale. We are led, then, to the conclusion that to convert all the en- 

 ergy of a given amount of heat into mechanical effect, a refrigerator 

 at a temperature of 491 Fahrenheit degrees below the melting-point 

 of ice, or 459 below zero Fahr., is necessary. 



Let us recapitulate briefly the points of this argument. 



1. It is impossible for any heat-engine, of whatever construction, 

 to convert into mechanical effect a larger proportion of the heat de- 

 rived from a given source than can be done under the same condi- 

 tions by a reversible engine. This proposition can not be denied with- 

 out involving a denial of two physical axioms which are founded uj)on 

 the results of all past experience, viz. : That the perpetual motion is 

 impossible, and that " it is impossible by means of inanimate material 

 agency to derive mechanical effect from any portion of matter by 

 cooling it below the temperature of the coldest of surrounding ob- 

 jects." 



2. That all reversible engines, whatever the working substance, 

 have the same efficiency ; that is, taking from the source the same 

 quantity of heat H, they will transfer to the refrigerator the same 

 quantity h, and convert into mechanical effect the same quantity Hh. 

 Hence whatever results are derived from a discussion of any one form 

 of reversible engine will be true of all others. 



3. If a scale of temperature be constructed such that the tem- 

 perature of the source is to the temperature of the refrigerator of a 

 reversible engine as the heat derived from the source is to the heat 

 given to the refrigerator, the scale divisions will differ but little from 

 the divisions of the scales in common use. The efficiency of an engine 



Tt t 



will then be = 1 . 



T T 



4. Upon such a scale, if there are, as in the Fahrenheit scale, 

 180 between the freezing and the boiling points of water, the for- 

 mer point would be numbered 491*4 and the latter 671 '4. The pos- 



