14 PROTEIN REQUIREMENTS OF CATTLE: MITCHELL 



fat in the adipose tissue is impossible. Certainly this is true of what we 

 understand by normal growth. On the other hand, it is quite probable 

 that during fattening the filling of the adipose tissues with fat involves 

 cellular proliferation in those tissues and hence a simultaneous deposi- 

 tion of protein and other protoplasmic constituents. 



A mathematical analysis of the Missouri investigations on growing 

 and fattening steers. — In this difficult situation, it is well to study in 

 some detail the results of an investigation of the growth of cattle involv- 

 ing the chemical analysis of cattle of different ages growing and fatten- 

 ing at different rates. For this purpose the investigations on growing 

 and fattening steers published by the Missouri Agricultural Experiment 

 Station (3^' ^^' 3'- ^^) will serve admirably. The data presented in Bulletin 

 55 of this station are particularly pertinent to this discussion. 



The cattle in this comprehensive investigation were raised upon the 

 same ration, consisting, except in the first few weeks of feeding, of a 

 grain mixture and alfalfa hay, but were given different amounts of feed 

 in accordance with a definite plan. The cattle in Group I were fed as 

 much of this ration as they would consume. The cattle in Group II were 

 fed to secure " maximum growth without the storage of surplus fat," 

 as judged by the animal husbandmen in charge. The cattle in Group III 

 were fed to induce a distinctly retarded growth, at a rate approximately 

 half that shown by Group II. The cattle used were of the Hereford- 

 Shorthorn cross and were all unsexed males. 



The average monthly body weights of these three groups of animals 

 up to and including the fourth year of age are given in Research Bulletin 

 63 of the Missouri Station (^^). The numbers of animals averaged at any 

 one time were not large, never exceeding 19 and in the later months 

 tapering down to 1 or 2, so that the weight-age curves are somewhat 

 irregular, particularly those for Group II. In using these data to the best 

 advantage, therefore, it is necessary to obtain a satisfactory mathematical 

 description of them by fitting to them a suitable algebraic equation. 



The weight-age relation. — The weight-age relation for growing ani- 

 mals under approximately constant conditions of feeding and manage- 

 ment assumes the shape of a sigmoid curve. However, no simple 

 equation for a sigmoid curve that has thus far been suggested will fit the 

 entire growth curve of an animal. Robertson's (*°) growth curve, rep- 

 resenting the course of an autocatalytic monomolecular reaction, is 

 sigmoid in shape, but it is symmetrical about its point of infiection, 

 whereas the weight-age curve of animals possesses a point of inflection 

 much nearer birth than maturity. Brody(*^) has suggested a mathe- 

 matical function to describe animal growth from this point of inflection 

 to maturity, based upon the assumption that following this point the 



