PROTEIN REQUIREMENTS OF CATTLE: MITCHELL 45 



curve in the area of decreasing growth rate. According to Brody, the 

 following equations describe the a^e-weight relations of these cattle : 



Holstein-Friesian, females, W = 1215-1775e--°''«°* (22) 



Ayrshire, females, W = 1014- 1468e--"^°°' (23) 



Jersey, females, W= 926-1499e--°=*''* (24) 



In all of these equations W is the weight of the heifer in pounds at 

 age t, expressed in months from conception. The mature weights of the 

 cows are estimated at 1215, 1014, and 926 pounds, respectively, and the 

 percentage monthly declines in the velocity of growth with age are, in 

 order, 4.5, 5.0, and 5.4. 



If it may be assumed that dairy heifers retain daily per 1000 pounds 

 live weight as much nitrogen for growth as Hereford-Shorthorn steers 

 of " equivalent ages," then the nitrogen requirements of these cattle may 

 be readily estimated. 



According to Brody (*8), the equivalence of age among different spe- 

 cies of animals may be computed from the value k in equation (1) 

 describing growth in weight beyond the point of inflection of the growth 

 curve. This constant k measures the fractional decline in the weight 

 increment per unit of time. The greater the fractional decline, k, the 

 more rapidly will the limiting or mature weight. A, be approached. 

 " Indeed," according to Brody, '^ the rapidity of approach to the mature 

 weight, A, is directly proportional to the numerical value of k, . . . . 

 and the relative duration of the periods of growth of two animals is, 

 therefore, inversely proportional to the numerical values of their k's. 

 These facts give us a basis for computing the equivalence of growth age 

 in different animals." 



For example, the numerical value of k for the Hereford-Shorthorn 



steer is .0303 (Equation (3) ) and that found by Brody for Jersey heifers 



is .0540. Therefore, one month for the Jersey heifer is equivalent, during 



the phase of growth following the point of inflection of the growth 



.0540 

 curve, to ' • = 1.T8 months for the Hereford-Shorthorn steer. As 

 .OoUo 



Brody points out, this relation may or may not hold true for the phase 

 of growth preceding the point of inflection, characterized by a positive 

 acceleration of growth. 



Thus, neither conception nor birth can be taken as points of reference 

 in computing age equivalence according to this method. Instead, Brody 

 takes the age when the curve of Equation (1) cuts the age axis, corres- 

 ponding to zero body weight. This age is termed t* and may be readily 

 obtained for any equation of this type by putting W = and solving 

 for t. 



