SECT. 2] AND WEIGHT 427 



development (very steep slope), 36 from the 8th to the 13th day 

 (less steep slope), 24 from the 13th to the i8th day (still less steep), 

 and 25 from then onwards. The higher numerically the constant k, 

 the steeper the slope, and consequently the greater the instantaneous 

 growth-rate. In Figs. 53 a, b and Table 55 are shown most of the 

 weights and processes in the hen's egg whose constants have been 

 calculated by Brody. Each system grows at a rate peculiar to itself. 



Murray, as we have seen, also plotted log. weight against age, but 

 he did not get a straight-line relationship ; on the contrary, the resulting 

 curve was concave to the age (abscissa) . McDowell, again, got a similar 

 concave curve for the pre-natal growth of the mouse, and there is much 

 point in his criticism of Brody 's work: "Brody draws a series of 

 straight lines through corresponding exponential curves and concludes 

 that growth-rate does not decline continuously but by abrupt drops 

 between periods of uniform rate. Since any curve can be approxi- 

 mated by a series of straight lines, the critical significance, both of 

 the specific number of straight lines, and of his general conclusions, 

 seems somewhat questionable"*. 



Table 55 includes also a column in which the time taken for 

 the embryo or a corresponding entity to double its weight or amount 

 is shown. For, when the instantaneous percentage growth-rate is 

 constant, the time intervals between doubling of weights are con- 

 stant; therefore, from the expression 



W - Ae^\ 

 at a certain time 



logs _ 0-695 

 k ~ k ' 



and, as k is found to be for the rat embryo 0-53 or 53 per cent., the 



time required for it to double its weight must be — ^ or 1-3 days. 

 ^ 0-53 



Further, if growth in weight can be taken as a measure of the in- 

 crease in the population of cells in the body, a new cell-generation 

 is produced every 1-3 days on an average, and the cell-division 

 frequency is 1/1-3, i-^- 0-77 times per day. It is thus possible to 

 determine, as Brody says, the mean life of a mother cell before it 

 divides into two daughter cells. 



* Nevertheless, McDowell himself admits a discontinuity between pre-axial and axial 

 growth, as we have seen on pp. 394 and 396. 



