ADAMS: A USEFUL TYPE OF FORMULA 471 



gated (0-6000 atm.) As a first step in the search for a suitable 

 equation it is advantageous to plot the data and to consider the 

 general form of the graph, especially its limiting characteristics. 

 As an illustration let us consider the e.m.f. of a copper-con- 

 stantan thermoelement as a function of temperature. If we plot 

 e.m.f. against temperature we obtain a curve of the type shown 

 in figure 1. 



The most important characteristic of this curve is its property 

 of becoming more nearly linear the farther it departs from the 

 origin. That is, the curve is asymptotic to a straight line (such 

 as the dotted line shown in the figure), which does not pass 



Fig. 2 



thru the origin. It is apparent that neither a parabola nor a 

 cubic equation (nor any power series with a reasonable number 

 of terms) can conform over a wide range to this essential con- 

 dition, namely, that of steadily increasing linearity with increas- 

 ing values of E or t. A power series can be made to approximate 

 only to a greater or smaller portion of the whole curve, the de- 

 gree of approximation being better the greater the number of 

 terms included in the series and the smaller the portion of the 

 curve dealt with. 



On the other hand there are a number of possible functions 

 which have the desired general form. To derive one let us con- 

 sider the course of the slope dE/dt of the curve given in figure 



