PRELIMINARY AND MINOR PAPERS 



FITTING LOGARITHMIC CURVES BY THE METHOD OF 



MOMENTS ' 



By John Rtce Miner, 

 Computer, Maine Agricultural Experiment Station 



WITH AN INTRODUCTORY STATEMENT ON THE USE OF LOGARITHMIC CURVES IN BIO- 

 LOGICAL AND AGRICULTIRAL INVESTIGATIONS BV RAYMOND PEARL, BIOLOGIST, 

 MAINE AGRICULTURAL EXPERIMENT STATION 



INTRODUCTORY STATEMENT 



The use of logarithmic curves in the analysis of various kinds of 

 biological and agricultural data is rapidly becoming widespread and 

 general. It was first shown by Lewenz and Pearson (13, 22) ^ that the 

 growth of children followed a logarithmic curve. The present writer 

 (17) demonstrated that the phenomena of growth and differentiation in 

 Ceratophyllum also followed a logarithmic curve. Donaldson (2, 3, 4, 

 5, 6) and Hatai (8, 9, 10) in a series of papers dealing with the growth 

 and quantitative relations of the whole organism and its various parts 

 in the white rat and the frog have shown that the same law holds for 

 growth in those forms. 



Other biological phenomena than growth follow a logarithmic law. 

 Pearl (14), in a case of regulation of the shape of abnormal eggs, and 

 later Curtis (i) for normal eggs, have shown that the changes in size and 

 shape of successively laid eggs are graduated with a logarithmic curve. 

 Work now in progress in the Biological Laboratory, Maine Experiment 

 Station, of which only a preliminary notice has yet been published (15), 

 shows that generally the change in milk flow with age in dairy cattle is 

 logarithmic. !3everal years ago Holtsmark (12) pointed out that the 

 relation between the number of food units required and the milk yields 

 of different animals was logarithmic. 



From this incomplete review of the literature recording the use of 

 logarithmic curves in biological and agricultural investigations it is clear 

 that the workers in these fields will, as time goes on, have increasing 

 need to be able to handle these curves easily and critically. 



Up to the present time the only available method of fitting logarithmic 

 curves was that of least scjuares. Several years ago Pearl and Mc- 

 Pheters (16) published a set of tables intended to 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 {18, 19, 20, 21, 23), and known as the "method of 

 moments." The theory of the method is extremely simple, involving as 



^ Papers from the Biological laboratory of the Maine Agricultural Experiinent Station. No. 78. 

 > Reference is made by number to " Literature cited," p. 4aa. 



Journal of Aericultural Research, Vol. Ill, No. s 



Dcpt. of Agriculture. Washincton. I). C Feb. ij, rgis 



Maine — 2 



(411) 



