^94 ikIAIXE AGRICULTURAL EXPERIMEXT STATIOX. I915. 



goes on, have increasing need to be able to handle these curve- 

 easily and critically. 



Up to the present time the only available method of fittin:^ 

 logarithmic curves was that of least squares. Several years ag^.- 

 Pearl and McPheters published a set of tables intended u> 

 lighten materially the labor of fitting such curves by the least- 

 squares method. For a long time, however, the writer has felt 

 that it would be highly desirable to bring this class of curves 

 into the general system of curve fitting worked out by Pearson 

 and known as the "method of moments." The theory of the 

 method is extremely simple, involving as it does only the as- 

 sumption that if we equate the area and moments of a theoreti- 

 cal curve to the area and moments of a series of observations 

 we shall get a reasonable fit of the curve to the observations. 

 Experience with the method in the hands of different workers 

 in England and America has abundantly demonstrated that this 

 assumption is entirely justified in the fact. 



In the papers cited, and in others also, Pearson has given the 

 equations for the calculation of the constants from the moments 

 in the case of (a) skew frequency curves in general, (b) sine 

 curves, (c) parabolas of all orders, (d) the point binomial, (,? ) 

 hypergeometrical series, etc. There has been lacking, however, 

 the determination of the equations connecting moments an'i 

 constants for the general family of logarithmic curves of the 

 type. 



j=a-|-fc.r-f-c.r'-|-(ilog(.r-|-g) 

 and its modifications. The necessary equations are given in- the 

 paper here abstracted. 



INTERPOLATION AS A MEANS OF APPROXIMATTOX 

 TO THE GAMMA FUNCTION FOR HIGH VALUES 

 OF w* 



This paper is purely mathematical in subject matter and in- 

 terest. The question discussed is whether a degree of approxi- 

 mation, sufficient for statistical purposes, to the value of ic.^r 

 gamma n can be had by interpolating in a table of log factorial 

 n. 



*This is an abstract of a paper by Raymond Pearl, having the same- 

 title and published in Science N. S. Vol. XLI, pp 506-507. 



