passes through the same phases of growth23. In all cases growth begins slowly; it attains a maximum velocity early in its course, and afterwards slows down (subject to temporary accelerations) towards a point where growth ceases altogether. But especially in the cold-blooded animals, such as fishes, the slowing-down period is very greatly protracted, and the size of the creature would seem never actually to reach, but only to approach asymptotically, to a maximal limit.
The size ultimately attained is a resultant of the rate, and of {72} the duration, of growth. It is in the main true, as Minot has said, that the rabbit is bigger than the guinea-pig because he grows the faster; but that man is bigger than the rabbit because he goes on growing for a longer time.
In ordinary physical investigations dealing with velocities, as for instance with the course of a projectile, we pass at once from the study of acceleration to that of momentum and so to that of force; for change of momentum, which is proportional to force, is the product of the mass of a body into its acceleration or change of velocity. But we can take no such easy road of kinematical inôÙvesôÙtiôÙgaôÙtion in this case. The ãvelocityã of growth is a very different thing from the ãvelocityã of the projectile. The forces at work in our case are not susceptible of direct and easy treatment; they are too varied in their nature and too indirect in their action for us to be justified in equating them directly with the mass of the growing structure.
It was apparently from a feeling that the velocity of growth ought in some way to be equated with the mass of the growing structure that Minot24 introduced a curious, and (as it seems to me) an unhappy method of representing growth, in the form of what he called ãpercentage-curvesã; a method which has been followed by a number of other writers and experimenters. Minotãs method was to deal, not with the actual increments added in