as colour, which he called ãaccidentsã) the essential differences between one ãspeciesã and another are merely differences of proportion, of relative magnitude, or (as he phrased it) of ãexcess and defect.ã ãSave only for a difference in the way of excess or defect, the parts are identical in the case of such animals as are of one and the same genus; and by ãgenusã I mean, for instance, Bird or Fish.ã And again: ãWithin the limits of the same genus, as a general rule, most of the parts exhibit differencesã...ãin the way of multitude or fewness, magnitude or parvitude, in short, in the way of excess or defect. For ãthe moreã and ãthe lessã may be represented as {726} ãexcessã and ãdefect3.ããã It is precisely this difference of relative magnitudes, this Aristotelian ãexcess and defectã in the case of form, which our co-ordinate method is especially adapted to analyse, and to reveal and demonstrate as the main cause of what (again in the Aristotelian sense) we term ãspecificã differences.
The applicability of our method to particular cases will depend upon, or be further limited by, certain practical conôÙsiôÙdeôÙraôÙtions or qualifications. Of these the chief, and indeed the essential, condition is, that the form of the entire structure under inôÙvesôÙtiôÙgaôÙtion should be found to vary in a more or less uniform manner, after the fashion of an apôÙproxôÙiôÙmateôÙly homogeneous and isotropic body. But an imperfect isotropy, provided always that some ãprinciple of continuityã run through its variations, will not seriously interfere with our method; it will only cause our transformed co-ordinates to be somewhat less regular and harmonious than are those, for instance, by which the physicist depicts the motions of a perfect fluid or a theoretic field of force in a uniform medium.
Again, it is essential that our structure vary in its entirety, or at least that ãindependent variantsã should be relatively few. That independent variations occur, that localised centres of diminished or exaggerated growth will now and then be