(1) When the diameter of the umbilicus of an ammonite is plotted against the diameter of the whole shell, or the whorl-thickness plotted against the whorl-height, the curves obtained are very commonly straight lines for the greater part of their courses.
(2) If, as is usually the case, these lines do not pass through the origin, the formula for the ammonite spiral is of the form r + c = eβθ and not r = eβθ.
(3) If the straight lines do not pass through the origin, it is useless to express one dimension as a percentage of the other and compare these percentages in different shells.
(4) There is no way of foreseeing, before the measurements are made, whether the dimensions of a species will plot accurately on a single curve or whether they will show a considerable amount of scatter. If, however, they do fall accurately on a single curve, this fact is an argument for the validity of the species, and the curve is a useful aid in the identification of other specimens.