PROTEIN REQUIREMENTS OF CATTLE: MITCHELL 15 



velocity of growth (gain in weight per iinit time) declines with age in geo- 

 metrical progression. The body weight is thus supposed to increase by 

 successively decreasing gains in weight, in such a way that the ratio 

 of the gain in weight during any month (or other interval of time) to 

 the gain during the preceding month will be constant. The equation is as 

 follows : 



W^A-Be-*^' (1) 



in which W equals body weight at time t, A is a constant representing 

 the maximum weight attained at maturity, B is a second constant whose 

 magnitude depends upon A and upon the length of the growth period 

 preceding the point of inflection, and k is a third constant equal to the 

 ratio of the gain in weight per unit time to the growth yet to be made 

 (A — W) ; e is the base of the natural system of logarithms. 



Brody(*^) has calculated the constants of this equation applied to the 

 growth data of the Missouri cattle in Group I. For the other groups of 

 cattle, B and k have been calculated by the method of averages for a 

 series of values for A, the final selection being that combination of con- 

 stants giving a sum of residuals approximating closest to algebraically. 

 The equations thus obtained are as follows : 



Group I W = 2425-3530e--°='-'^' (2) 



Group II W = 1600-2057e--°3°3t (3) 



Group III W=1300-1481e--o-2Tt (4) 



By these equations W is computed in pounds for any age t, expressed 

 as months from conception. For cattle the conceptional age at birth is 

 taken to be 9.4 months. The closeness of fit of these equations to the 

 Missouri data for the three groups of cattle is indicated by the compu- 

 tations in Tables 3, 4 and 5. 



For Group I, the agreement is poor between observed and calculated 

 weights until a conceptional age of 15.4 to 16.4 months (6 to 7 months 

 from birth) is reached. This area of bad fit represents the area before 

 the point of inflection in the curve of growth, when the acceleration of 

 growth changes from positive to negative in sign. An area of retarded 

 growth from the 32nd to the 30th month is smoothed out and towards 

 the upper end of the range the fit again becomes less good, but the per- 

 centage difference does not become great even to the final observation. 



For Group II, the agreement between calculated and observed weights 

 becomes satisfactory much earlier than for Group I. A serious depres- 

 sion of the observed growth in this group between the 36th and the 53rd 

 month from conception is smoothed out, as it probably should be, since 

 it possesses no evident biological significance. 



