SAMUEL BRODY AND ARTHUR C. RAGSDALE 629 



where x, the weight of the animal, is expressed as a function of its 

 age, t. Equation (2) is the form used by Robertson.^ If desired, 

 equation (2), a weight-age equation, may be changed to a velocity-age 

 equation by differentiating it after some simplification and obtaining^ 



dx Ke^' 



dt (H-e^O' 



doc 

 where — is the velocity, t and K have the same significance as in 

 dt 



equation (2), e = 2.718, the base of natural logarithms. Equation 

 (2) will, however, be used on account of the relative simplicity of its 

 application to the data. 



In equation (2), x is the weight gained from the beginning of any 

 cycle up to any age, t, of that cycle; while A is the total growth made 

 in that cycle which is equivalent to the limiting growth substance 

 present at the beginning of the cycle. If the cycle under considera- 

 tion is preceded by one or more other cycles, then the growth of the 

 preceding cycles must be subtracted from the weight of the animal 

 at the age / in order to obtain x. Let w be the weight gained up to 

 the beginning of the cycle under consideration and Xi the weight of 

 the animal at the age /; then equation (2) becomes 



Xi — w 



log -—7 r =K{t- h) (3) 



A — \xi — w) 



The simplest method of applying equation (2) or (3) is first to plot 

 the experimental data on growth in terms of monthly gains as was 

 done in Figs. 2 and 3. The highest point of the velocity curve cor- 

 responds by definition to the age h. Having thus evaluated h, a 

 reasonable beginning or end of the cycle is chosen by inspection; 

 the growth made between the ages h and the beginning or end of the 

 cycle is the value of ^A, since h is in the center of the growth cycle. 

 If the values of h and ^A are properly chosen, the values of K for 

 different values of x should be nearly constant. If the value of K 

 deviates systematically then a slightly smaller or slightly larger 

 value of ^A is chosen until the systematic deviations disappear; the 



^ Cf. Lewis, G. N., Z. physikal. Chem., 1905, lii, 310; Dept. Interior, Bureau 

 Gov. Lab., Chem. Lab., No. 30, 1905. 



