Feb. 15, 191S 



Fitting Logarithmic Curves 



417 



From the foregoing it is evident thai since the ;'s involve only /, and 

 with equal intervals for the ordinates / will always be some integer, the 

 values of the j's for a series of values of / can be tabled once for all, and 

 in this way a great deal of labor saved in the ordinary fitting of logarithmic 



curves. Accordingly tables of the ;'sand of P + sl+1.5, -15' and-^have 



been prepared and are given in an appendix at the end of the paper. 

 For the curve y = a + bx + c log,o (*+«): 



6[M,-(l+ i)M,]+ (P+3l+i.5)M, 



(xxv) 



a'(l+2a'){/+a'){log,,{l+a')~]og,„a'}—^{P+i2a'l+i2a'%g^,e 

 b = ^{jM, - (/ + I ) M„ - c{«' (/ + a') (log.oa' - log.„/+^') 

 -(j + ^'ipogjj 



+ ( 



a= jM^--^b-c-j-[(l+o!')logi„{l+n')-a'\og^„a'-nog^„e] (xxvii) 

 where 'i'' = n' + K- 



/" 



ILLUSTRATIONS OF THE USE OF LOGARITHMIC EQUATIONS 



In order to make clear the use of the above equations, some numerical 

 illustrations will be given. 



Let us first consider the data contained in Table I. These give the 

 mean milk production in pounds over a 7-day period of Holstein-Friesian 

 cattle at different ages. The data are taken from the official 7-day A. R. 

 O. record of the Holstein-Friesian Association (11). The laborious task 

 of extracting and tabulating these records and calculating the means was 

 carried through by Mr. John W. Gowen, with the assistance of Mr. S. W. 

 Patterson and Miss Anna B. Perkins, all of the Maine Experiment Station. 

 In future publications from this laboratory these figures will be further 

 dealt with, but here they are used solely for purposes of illustrating the 

 method. 



The problem now is to fit by the method of moments a logarithmic 

 curve of the form 



>■ = a -f bx -I- cx^ ■\- d log * 



to these milk production means. 



