On Growth and Form

by D'Arcy Wentworth Thompson

Put in math­e­mat­i­cal form, the equations are as follows:

(m = the mass of air thrust downwards; V its velocity, proportional to that of the bird; M its momentum; l a linear dimension of the bird; w its weight; W the work done in moving itself forward.)

M = w = l³ .

But

M = m V, and m = l² V.

Therefore

M = l² V² , and

l² V² = l³ , or

V = √l.

But, again,