30 



PROTEIN REQUIREMENTS OF CATTLE: MITCHELL 



Since the weight of a steer is a better indication of its stage of growth 

 than is the age, the same sort of data may be obtained for equal intervals 

 of weight rather than of time. From Equations (3), (3), and (4) the 

 average age of each group of steers at weights of 100, 200, 300, etc., 

 pounds in weight may be computed, and the composition of the steers at 

 these ages determined as were the values in Table 13. The percentage 

 composition, derived directly from such estimates, for the steers at equal 

 intervals of weight has been summarized in Table 15. 



The rate of deposition of nutrients and the percentage composition of 

 gains at different ages and iveiglits. — The ultimate purpose of this math- 

 ematical analysis of the Missouri data on steers is to secure satisfactory 

 estimates of the rate of deposition of each of the body constituents at 

 different times and at different weights. This information may be readily 

 obtained from equations obtained by differentiating Equations (9) to 

 (20) inclusive, in accordance with the general Equation (5). The linear 

 equation used in fitting the age-fat content data of Group I (see foot- 

 note to page 19) gives a constant, upon differentiation, of 7.932 kgms. 

 of fat per month. For this group, therefore, the rate of deposition of fat 

 was constant.* 



Obtained in this manner, the rate of gain per day by the steers of each 

 of the three groups in each of the constituents will be found, for equal 

 intervals of time in Table 16, and for equal intervals of weight in Table 

 17. The energy increments in these tables are obtained by assuming a 

 gross energy value for protein (Nx6.25) of 5.7 cals. per gram, and for 

 fat a value of 9.5 cals. per gram. 



^The differential equations obtained, from which the rate of deposition of the 

 constituent in question per month ( , j at any time t may be calculated are 

 as follows: 



Water content: 



Fat content: 



dt 



= sr-see-""'" 



= 35.006-""" 



— is.oee-"''" 



= 2.8096-'"'" 

 = 1.1496-"*^" 

 = 0.4486-"="" 



Ash content: 



dW 

 dt 



dW 

 dt 



dW 

 dt 



dW 

 dt 



dW 

 dt 



dW 

 dt 



= 7.932 



= 2.5116-'""*"' 

 = 1.0136-""'"' 



z= 2.5686-"="'' 

 = 1.1966-"='"' 

 = 0.8406-""^' 



