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



Table of five columns be formed, the first column denoting abso- 

 lute temperatures from 246° to 506°, the second column denoting 

 values of log P, the third column denoting values of A log P, 

 the fourth column denoting values of log A log P, and the fifth 

 column denoting values of A log A log P, it will be found that 

 the quantities in the fifth column are the reciprocals of the 

 numbers in the first column nearly. In other words, it is found 



that A log A log P = nearly. Even when intervals so 



great as 10° C. are taken, the differences are very small between 

 the numbers in the fifth column and the reciprocals of the abso- 

 lute temperature. In order to form by the use of logarithms a 

 Table of elastic forces of steam of maximum density for intervals 

 of one degree Centigrade, or one degree Fahrenheit, nothing is 

 required beyond, 1st, a Table of reciprocals of numbers repre- 

 senting absolute temperatures ; 2ndly, the value of A log P for 

 any one specific interval of temperature ; and 3rdly, the value 

 of log P for any one specified temperature. 



The remarkable property just mentioned is consequent on the 

 form of the differential coefficient of log Y ti which is 



either T or a f 1 + - ) 



/ t\r ^ a ' 



Calling this u t , and taking the ratio of two consecutive coefficients 

 at unit intervals, we get 



"t+i^ dAogVt+^ / a + t+i yl^fa 1 \4, 

 a t d.logP* \ a + t ) \ a-\-t) 

 which becomes, when the intervals of temperature are indefinitely 

 diminished, 



* t+dt . A . At \-\ _^_ x i ^-J» 



^ = f 1+ JLH=,-lb^=io- 



u t \ a + t) 



a+t. 



Taking common logarithms of both sides of the former of the 

 above two equations, we get 



, ut+i 1 i a + t + 1 



com i og _=_ pCom i og ___ r) 



or, which is the same thing, 



(com log ctt+i — com log a t ) 



= - (hyp log (a + t+ 1) -hyp log {a + *)). 



That is to say, the differences between the common logarithms 

 of the rates of increment of the elastic forces are equal to the 

 differences of the hyperbolic logarithms of the corresponding ab- 

 solute temperatures. This is another way of expressing the essen- 

 tial principle involved in the law of steam of maximum density. 



