JOURNAL 



OF THE 



WASHINGTON ACADEMY OF SCIENCES 



Vol. Ill NOVEMBER 19, 1913 No. 19 



MATHEMATICS. — A useful type of formula for the interpolation 

 and representation of experimental results. L. H. Adams. 

 Geophysical Laboratory. 



Mellor, in his Higher Mathematics,^ remarks, ''The reader will 

 perhaps have been impressed with the frequency with which ex- 

 perimental results are referred to a series formula of the type: 



y = A -\- Bx + Cx- + Bx^ H , 



in physical or chemical text books. For instance, I have counted 

 over thirty examples in the first volume of Mendeleeff's The 

 Principles of Chemistry and more than this number in Preston's 

 Theory of Heat^ It is well known that for the representation 

 of experimental results limited power series often leave much to 

 be desu'ed, and that such formulae adequately represent the data 

 only in comparatively few instances or over short ranges; and 

 yet as indicated by the above quotation this fact is seldom ap- 

 preciated. It is the purpose of this note to point out the ad- 

 vantage of functions other than power series and to advocate 

 their more general employment in cases where power series ob- 

 viously do not conform to the known general form of curve given 

 by the measurements. 



By far the larger number of physical changes follow laws as 

 yet unknown, and so, until the precise theoretical function is 

 ascertained, the experimental results in question can be repre- 

 sented only by some sort of empirical formula. In the choice of 



1 J. W. Mellor, Higher mathematics for students of physics and chemistry, p. 

 273. 



469 



