its immediate relation to growth105.
Regeneration, like growth in other cases, proceeds with a velocity which varies according to a definite law; the rate varies with the time, and we may study it as velocity and as acceleration.
Let us take, as an instance, Miss M. L. Durbinãs measurements of the rate of regeneration of tadpolesã tails: the rate being here measured in terms, not of mass, but of length, or longitudinal increment106.
From a number of tadpoles, whose average length was 34ôñ2 mm., their tails being on an average 21ôñ2 mm. long, about half the tail {139} (11ôñ5 mm.) was cut off, and the amounts regenerated in successive periods are shewn as follows:
| Days after operation | 3 | 7 | 10 | 14 | 18 | 24 | 30 |
|---|---|---|---|---|---|---|---|
| (1) Amount regenerated in mm. | 1ôñ4ã | 3ôñ4ã | 4ôñ3ã | 5ôñ2ã | 5ôñ5ã | 6ôñ2ã | 6ôñ5ã |
| (2) Increment during each period | 1ôñ4ã | 2ôñ0ã | 0ôñ9ã | 0ôñ9ã | 0ôñ3ã | 0ôñ7ã | 0ôñ3ã |
| (3)(?) Rate per day during each period | 0ôñ46 | 0ôñ50 | 0ôñ30 | 0ôñ25 | 0ôñ07 | 0ôñ12 | 0ôñ05 |
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 ãcurve of growthã 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 ãratesã 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 experiment, if we begin by drawing a smooth curve, as nearly as possible through the points corôÙreôÙsponôÙding 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