450 SENESCENCE AND REJUVENESCENCE 



increments in grams for each period as determined from the differ- 

 ences in weight, and the fourth column the percentage increments, 

 i.e., the increments expressed as percentages of the total weight at 

 the beginning of each interval. It is evident at once that the 

 absolute increments in the third column increase during the first 

 seven months of the embryonic period, and that after birth there 

 is at first an increase and then a decrease, with slight irregularities. 

 But the percentage increments show an increase only from the 

 third to the fourth month and afterward a decrease. In comparing 

 the increments before and after birth it must be remembered that 

 the time intervals from birth to two years are three times and those 

 from two to four years twelve times as long as those before birth, 

 so that we must divide the increments given in the table for these 

 periods by three and by twelve respectively to make them com- 

 parable to the increments for the embryonic period. 



If from the growth-increments we plot a curve of growth, using 

 the time intervals as abcissae and the increments as ordinates, the 

 form and direction of the curve will be very different, according 

 as we use the absolute or the percentage increments. The curve 

 which results when the absolute increments are used is shown in 

 Fig. 199. This is an S-shaped curve and is similar to the curve of 

 an autocatalytic chemical reaction. Ostwald and Robertson have 

 used the absolute increments in their studies of growth and have 

 obtained similar curves for a variety of data. 



But if we use the percentage increments the curve is of the kind 

 shown in Figs. 200 and 201. Fig. 200 is the curve for the embry- 

 onic period and Fig. 201 for the period after birth, the former being 

 on a larger scale than the latter in order to show its character 

 more clearly. This method of graphic presentation of the data 

 gives a descending curve, which expresses the fact that the rate of 

 increase in weight as a percentage of total weight decreases from a 

 very early period on. The other data of growth used by Ostwald 

 and Robertson give essentially similar results, with here and there 

 shght irregularities resulting from larval moultings, changes in 

 relation to environment, etc. Donaldson's and Minot's curves of 

 rate of growth were also drawn from percentage in crements.^ 



' See Donaldson, '95; Minot, '91, '08; and also pp. 274-77 above. 



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