470 



ADAMS : A USEFUL TYPE OF FORMULA 



the most suitable equation to be fitted to a given set of experi- 

 mental results there is usually considerable latitude; but among 

 the host of mathematical functions there will often be certain 

 ones which from their peculiar characteristics or general shape 

 are especially adapted to the data in hand. Nevertheless most 

 chemists and physicists, who desire to fit their experimental re- 

 sults to some equation, turn blindly to the familiar power series. 

 When the graph representing the 

 results is obviously non-linear, 

 the quadratic or parabola, y = 

 A -\- Bx + Cx^, is first tried; if 

 a satisfactory fit is not obtained 

 another term is added, and so 

 on until there is sufficiently close 

 agreement between the calcu- 

 lated and observed values thru- 

 out the range of observation. 



Now it happens that in some 

 cases a parabolic equation repre- 

 sents the relation between two 

 physical quantities with great 

 exactness. A notable example is 

 the resistance of pure platinum, 

 which is a quadratic function 

 of the temperature between 0° 

 and 1000° to within 0.05 per cent 

 or better. Such accidents, how- 

 ever, are rare. More often than 

 not a cubic or a fourth power 



equation is necessary especially for experimental observations of 

 high precision. For instance, according to Bridgman^ a power 

 series of at least five terms — and probably more — ^would be re- 

 quired to represent the resistance of mercury as a function of 

 pressure, with an accuracy of iV per cent, the degree of accuracy 

 of the experimental work thruout the range of pressures investi- 



Fig. 1 



Proc. Am. Acad. 44: 237, (1909). 



