174 Mr. T. R. Edmonds on the Elastic Force of 



very simple relation to one another, which is that of (-)* to 



( -r. The quantities a and a-\-t represent temperatures 



measured from an ideal fixed point which has been called the 

 absolute zero of temperature. The quantity a represents the 

 absolute temperature of the point adopted as the zero of the 

 thermometrical scale in use. The quantity t represents the 

 number of degrees in either direction measured on such scale. 



The exponent -r is the hyperbolic logarithm of 10, and is equal 



to 2-302585. 



From what has preceded, it ensues that if a be the hyper- 

 bolic logarithm representing the ratio of increment of the elastic 

 force P at the absolute temperature a, then the hyperbolic 

 logarithm representing the rate of increment of elastic force at 

 any other absolute temperature (a + /) will be 



Using differentials, we may say that if -p- = -, then will 



The above differential of log P* yields on integration the equa- 

 tion following, by which is expressed in logarithms the ratio of 

 elastic force of steam of maximum density at any thermometric 

 temperature t to the elastic force at absolute temperature a, 

 whence t is measured ; - 



hy P io g P,= f{i-(i + 3-"}. 



The quantity n is put for (t —l) = 1*302585. The above 

 equation, otherwise expressed, is 



™h-(i+t)- n i ^Mi_(i+_')-n 



T>* n t \ a J ) ~l(\ n . 



The quantity e is the base of the hyperbolic system of loga- 

 rithms, and is equal to 2*7182818, and k is the modulus of 

 the common or decimal system of logarithms, and equal to 

 •4342945. 



By means of the formulas above given, the values of (P*) the 

 elastic force, and [a t ) the rate of increment per degree of such 



