414 



Journal of Agricultural Research 



Vol. HI. No. s 



(/ + g) (^log.o i - logi„ / + (7 j + (^/ + 5' - ^ /og,„ < j J 



W+q? 



-c\{l + q)log,„ (l + q) 



-^ log,(, '- -(^l + q-^yog,o cjj 



SPECIAL CASES 



In the preceding section the simplest form of logarithmic cur\'e in 

 practical biometric use is considered. Extended experience in the Bio- 

 logical Laboratory of the Maine Experiment Station has shown that this 

 simple form of the curve is only rarely adequate in the fitting of biological 

 data. Usually one or the other, or both, of two modifications is found to 

 be necessary before a suitable logarithmic curv^e is found. One of these, 

 first used in biometric work by Pearl (17), in his studies of the growth of 

 Ceratophyllum, later by Hatai (8) and others, is to add another constant, 

 «, so that the equation then becomes 



' y = a + hx+c \og(x+o(). 



The second modification is made by adding a term in x- to the equation. 

 This modification is necessary in the wide range of cases where, after 

 reaching a maximum, the values of the ordinates decrease with increasing 

 values of x. This curve with the x^ term was first used by Pearl to 

 describe the change in shape of successively laid eggs of a particular hen 

 (14). A logarithmic curve of this type 



y=a + bx + cx^ + d log x 



appears, from rather extensive experience in this laboratory, to be the 

 general form of expression of the quantitative changes in an organism 

 throughout its life — that is, including both growth and setiescence. 

 The equations for determining the constants of the curve 



are as follows 



d= 



y = a + bx + cx^ + d logio* 

 2oM3-3o(/+9 + 0M, + 3[4(/ + </)2 + 6(/ + 9)+i]M, 



l\_il + <!)\{l+qy+l(l + q) + ^ 



, , log,o--logi„(/ + 9) 

 4) I 2 



+2(i+qy- 



^jj(/+#+i4(/ + 9) + ^ 



MlogiocJ 



(xi) 



