It is a very general rule, though apparently not a universal one, that regeneration tends to fall somewhat short of a complete restoration of the lost part; a certain percentage only of the lost tissues is restored. This fact was well known to some of those old investigators, who, like the Abbé Trembley and like Voltaire, found a fascination in the study of artificial injury and the regeneration which followed it. Sir John Graham Dalyell, for instance, says, in the course of an admirable paragraph on regeneration[190]: “The reproductive faculty ... is not confined to one portion, but may extend over many; and it may ensue even in relation to the regenerated portion more than once. Nevertheless, the faculty gradually weakens, so that in general every successive regeneration is smaller and more imperfect than the organisation preceding it; and at length it is exhausted.”
In certain minute animals, such as the Infusoria, in which the capacity for “regeneration” is so great that the entire animal may be restored from the merest fragment, it becomes of great interest to discover whether there be some definite size at which the fragment ceases to display this power. This question has {147} been studied by Lillie[191], who found that in Stentor, while still smaller fragments were capable of surviving for days, the smallest portions capable of regeneration were of a size equal to a sphere of about 80 µ in diameter, that is to say of a volume equal to about one twenty-seventh of the average entire animal. He arrives at the remarkable conclusion that for this, and for all other species of animals, there is a “minimal organisation mass,” that is to say a “minimal mass of definite size consisting of nucleus and cytoplasm within which the organisation of the species can just find its latent expression.” And in like manner, Boveri[192] has shewn that the fragment of a sea-urchin’s egg capable of growing up into a new embryo, and so discharging the complete functions of an entire and uninjured ovum, reaches its limit at about one-twentieth of the original egg,—other writers having found a limit at about one-fourth. These magnitudes, small as they are, represent objects easily visible under a low power of the microscope, and so stand in a very different category to the minimal magnitudes in which life itself can be manifested, and which we have discussed in chapter II.
A number of phenomena connected with the linear rate of regeneration are illustrated and epitomised in the accompanying diagram (Fig. [40]), which I have constructed from certain data given by Ellis in a paper on the relation of the amount of tail regenerated to the amount removed, in Tadpoles. These data are summarised in the next Table. The tadpoles were all very much of a size, about 40 mm.; the average length of tail was very near to 26 mm., or 65 per cent. of the whole body-length; and in four series of experiments about 10, 20, 40 and 60 per cent. of the tail were severally removed. The amount regenerated in successive intervals of three days is shewn in our table. By plotting the actual amounts regenerated against these three-day intervals of time, we may interpolate values for the time taken to regenerate definite percentage amounts, 5 per cent., 10 per cent., etc. of the {148}
| Series† | Body length mm. | Tail length mm. | Amount removed mm. | Per cent. of tail removed | % amount regenerated in days | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 3 | 6 | 9 | 12 | 15 | 18 | 32 | |||||
| O | 39·575 | 25·895 | 3·2 | 12·36 | 13 | 31 | 44 | 44 | 44 | 44 | 44 |
| P | 40·21 | 26·13 | 5·28 | 20·20 | 10 | 29 | 40 | 44 | 44 | 44 | 44 |
| R | 39·86 | 25·70 | 10·4 | 40·50 | 6 | 20 | 31 | 40 | 48 | 48 | 48 |
| S | 40·34 | 26·11 | 14·8 | 56·7 | 0 | 16 | 33 | 39 | 45 | 48 | 48 |
† Each series gives the mean of 20 experiments.
Fig. 40. Relation between the percentage amount of tail removed, the percentage restored, and the time required for its restoration. (From M. M. Ellis’s data.)
amount removed; and my diagram is constructed from the four sets of values thus obtained, that is to say from the four sets of experiments which differed from one another in the amount of tail amputated. To these we have to add the general result of a fifth series of experiments, which shewed that when as much as 75 per cent. of the tail was cut off, no regeneration took place at all, but the animal presently died. In our diagram, then, each {149} curve indicates the time taken to regenerate n per cent. of the amount removed. All the curves converge towards infinity, when the amount removed (as shewn by the ordinate) approaches 75 per cent.; and all of the curves start from zero, for nothing is regenerated where nothing had been removed. Each curve approximates in form to a cubic parabola.
The amount regenerated varies also with the age of the tadpole and with other factors, such as temperature; in other words, for any given age, or size, of tadpole and also for various specific temperatures, a similar diagram might be constructed.