III] REGENERATION, OR GROWTH AND REPAIR 139 



(11-5 mm.) was cut o&, and the amounts regenerated in successive 

 periods are shewn as follows : 



Days after operation 



(1) Amount regenerated in mm. 



(2) Increment during each period 

 (3)(?) Rate per day during 



each period 0-46 0-50 0-30 0-25 0-07 0-12 0-05 



The first line of numbers in this table, if plotted as a curve 

 against the number of days, will give us a very satisfactory view 

 of the "curve of growth" within the period of the observations: 

 that is to say, of the successive relations of length to time, or the 

 velocity of the process. But the third line is not so satisfactory, 

 and must not be plotted directly as an acceleration curve. For 

 it is evident that the "rates" here determined do not correspond 

 to velocities at the dates to which they are referred, but are the 

 mean velocities over a preceding period ; and moreover the periods 

 over which these means are taken are here of very unequal length. 

 But we may draw a good deal more information from this experi- 

 ment, if we begin by drawing a smooth curve, as nearly as possible 

 through the points corresponding to the amounts regenerated 

 (according to the first line of the table) ; and if we then interpolate 

 from this smooth curve the actual lengths attained, day by 

 day, and derive from these, by subtraction, the successive daily 

 increments, which are the measure of the daily mean velocities 

 (Table, p. 141). (The more accurate and strictly correct method 

 would be to draw successive tangents to the curve.) 



In our curve of growth (Fig. 35) we cannot safely interpolate 

 values for the first three days, that is to say for the dates between 

 amputation and the first actual measurement of the regenerated 

 part. What goes on in these three days is very important; but 

 we know nothing about it, save that our curve descended to zero 

 somewhere or other within that period. As we have already 

 learned, we can more or less safely interpolate between known 

 points, or actual observations; but here we have no known 

 starting-point. In short, for all that the observations tell us, 

 and for all that the appearance of the curve can suggest, the 

 curve of growth may have descended evenly to the base-hne, 

 which it would then have reached about the end of the second 



