50 



GROWTH 



Figure 31 shows some of 

 the linear measurements that 

 were taken on dairy cattle in 

 the Dairy Department of the 

 University of Missouri, and 

 Figure 32 shows typical 

 growth curves thus obtained. 

 The smooth curves passing 

 through the circles, etc., were 

 plotted according to the 

 formula 



W — A-Be" kt (2) 



in which W represents the 

 value of the linear measure- 

 ment, or weight, at the age t. 

 A is the value of linear meas- 

 urement, or weight, at ma- 

 turity and e is the natural base 

 of logarithms, k is the frac- 

 tional decline in the monthly 

 gains. Thus, if the gain in a 

 certain measurement is 100 

 units during one month, and 

 90 units during the following month, then clearly the fractional 



decline per month is or 0.1 or 10 per cent. The agreement 



100 



between observed values and the curve computed from this 

 formula is evidently satisfactory. 



The agreement between the circles, which represent the ob- 

 served values, and the smooth curves which were derived from 

 the formula, indicates that the fundamental characteristic of 

 linear growth in dairy cattle is that the gains or increments per 

 unit time decline at a constant ratio, or relative rate, repre- 

 sented by the value k in the formula, and the formula is thus 

 an elegant descriptive statement of the time relations of linear 



16 20 24 28 32 36 40 44 



Age 



Figure 32. Growth in linear dimensions of 

 Jersey cattle. The smooth curves passing 

 through the observed values represent equa- 

 tion (2). The numerals refer to the meas- 

 urements as indicated in Figure 31, as fol- 

 lows: 18 heart girth, 15 from point of 

 shoulder to ischium, 1 height at withers, 

 14 from point of shoulder to a point of hips, 

 12 from highest point of withers to a line 

 between hips, 4 depth of chest just behind 

 elbow joint, 8 length from poll to point of 

 muzzle, 6 width of hips, 10 circumference 

 of muzzle at opening of mouth, 5 width of 

 chest just behind the elbow joint, and 9 

 width of forehead, k represents the frac- 

 tional decline in growth in successive 

 months. 



