As regards that large portion of the curve which we are acquainted with, we see that it resembles the curve known as a rectangular hyperbola, which is the form assumed when two variables (in this case _V_ and _T_) vary inversely as one another. If we take the logarithms of the velocities (as given in the table) and plot them against time (Fig. 37), we see that they fall, approximately, into a straight line; and if this curve be plotted on the {143} proper scale we shall find that the angle which it makes with the base is about 25°, of which the tangent is ·46, or in round numbers ½. Had the angle been 45° (tan 45° = 1), the curve would have been actually a rectangular hyperbola, with _V_ _T_ = constant. As it is, we may assume, provisionally, that it belongs to the same family of curves, so that _V_^{_m_} _T_^{_n_}, or _V_^{_m_/_n_} _T_, or _V_ _T_^{_n_/_m_}, are all severally constant. In other words, the velocity varies inversely as some power of the time, or _vice versa_. And in this particular case, the equation _V_ _T_^2 = constant, holds very nearly true; that is to say the velocity varies, or tends to vary, inversely as the square of the time. If some general law akin to this could be established as a general law, or even as a common rule, it would be of great importance. [Illustration: Fig. 38. Rate of regenerative growth in larger tadpoles.] But though neither in this case nor in any other can the minute increments of growth during the first few hours, or the first couple of days, after injury, be directly measured, yet the most important point is quite capable of solution. What the foregoing curve leaves us in ignorance of, is simply whether growth starts at zero, with zero velocity, and works up quickly to a maximum velocity from which it afterwards gradually falls away; or whether after a latent period, it begins, so to speak, in full force. The answer {144} to this question-depends on whether, in the days following the first actual measurement, we can or cannot detect a daily _increment_ in velocity, before that velocity begins its normal course of diminution. Now this preliminary ascent to a maximum, or point of inflection of the curve, though not shewn in the above-quoted experiment, has been often observed: as for instance, in another similar experiment by the author of the former, the tadpoles being in this case of larger size (average 49·1 mm.)[188]. Days 3 5 7 10 12 14 17 24 28 31 Increment 0·86 2·15 3·66 5·20 5·95 6·38 7·10 7·60 8·20 8·40 Or, by graphic interpolation,