K. Pkarson 



lü 



curve, the fit is purely artififiul : a little beyond the ränge of the actiial 

 observutions, the parabela will diverge iniiiien.sely from the sort of result tliat we 

 could possibly reach it" we inultiplicd (lur observatioiis so as to get, say, the 

 frequeucy at ;b = 5, or x = 2'i. Tlie ie])resentation is artificial, the parabolic curve 

 cannot give the limited rauge, or tlie high coutact at its terminals, — well-known 

 characters of such frequency distributions — which can be provided by other curves 



Flu. 9. Exauiple of fittiiiK parabolas (Thiele's frequeucy observations). 



with, perhaps, a qnarter the number of constants. Heuce the sort of statenient 

 so frequently heard, — " Yes, of course, more constants make better fits," — is oiily 

 a half truth, and the manner in which engineers, physicists and actuaries so 

 readily use parabolic curves is open to consideral)le criticisin. There are offen 

 considerations, hing outside the actual data, which suffice to iudicate that 

 trigonometrical, exponential or other types of curves will give better results than 

 parabolas. A parabt)la which passes even through all the observations ma}' indoed 



3—2 



