Now, plotting this acceleration curve from the date of the first measurement made three days after the amputation of the tail (Fig. 36), we see that it has no point of inflection, but falls steadily, only more and more slowly, till at last it comes down nearly to the base-line. The velocities of growth are continually diminishing. As regards the missing portion at the beginning of the curve, we cannot be sure whether it bent round and came down to zero, or whether, as in our ordinary acceleration curves of growth from birth onwards, it started from a maximum. The former is, in this case, obviously the more probable, but we cannot be sure.
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, apôÙproxôÙiôÙmateôÙly, 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 25ô¯, of which the tangent is ôñ46, or in round numbers ô§.
Had the angle been 45ô¯ (tanã₤45ô¯ =ã₤1), the curve would have been actually a rectangular hyperbola, with VãT =ã₤constant. As it is, we may assume, provisionally, that it belongs to the same family of curves, so that V ÿ£¢ m ã T ÿ£¢ n ã₤, or V ÿ£¢ mã₤ãã₤n ã T , or VãT ÿ£¢ nã₤ãã₤m ã₤, 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 VãT ÿ£¢ 2 =ã₤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