The problem is closely akin to that of the cartographer who transfers identical data to one projection or another; and whose object is to secure (if it be possible) a complete correspondence, in each small unit of area, between the one representation and the other. The morphologist will not seek to draw his organic forms in a new and artificial projection; but, in the converse aspect of the problem, he will inquire whether two different but more or less obviously related forms can be so analysed and interpreted that each may be shown to be a transformed representation of the other. This once demonstrated, it will be a comparatively easy task (in all probability) to postulate the direction and magnitude of the force capable of effecting the required transformation. Again, if such a simple alteration of the system of forces can be proved adequate to meet the case, we may find ourselves able to dispense with many widely current and more complicated hypotheses of biological causation. For it is a maxim in physics that an effect ought not to be ascribed to {725} the joint operation of many causes if few are adequate to the production of it: Frustra fit per plura, quod fieri potest per pauciora.
It is evident that by the combined action of appropriate forces any material form can be transformed into any other: just as out of a “shapeless” mass of clay the potter or the sculptor models his artistic product; or just as we attribute to Nature herself the power to effect the gradual and successive transformation of the simplest into the most complex organism. In like manner it is possible, at least theoretically, to cause the outline of any closed curve to appear as a projection of any other whatsoever. But we need not let these theoretical considerations deter us from our method of comparison of related forms. We shall strictly limit ourselves to cases where the transformation necessary to effect a comparison shall be of a simple kind, and where the transformed, as well as the original, co-ordinates shall constitute an harmonious and more or less symmetrical system. We should fall into deserved and inevitable confusion if, whether by the mathematical or any other method, we attempted to compare organisms separated far apart in Nature and in zoological classification. We are limited, not by the nature of our method, but by the whole nature of the case, to the comparison of organisms such as are manifestly related to one another and belong to the same zoological class.
Our inquiry lies, in short, just within the limits which Aristotle himself laid down when, in defining a “genus,” he showed that (apart from those superficial characters, such as colour, which he called “accidents”) the essential differences between one “species” and another are merely differences of proportion, of relative magnitude, or (as he phrased it) of “excess and defect.” “Save 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 ‘genus’ I mean, for instance, Bird or Fish.” And again: “Within the limits of the same genus, as a general rule, most of the parts exhibit differences ... in the way of multitude or fewness, magnitude or parvitude, in short, in the way of excess or defect. For ‘the more’ and ‘the less’ may be represented as {726} ‘excess’ and ‘defect[644].’ ” It is precisely this difference of relative magnitudes, this Aristotelian “excess and defect” 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 “specific” differences.
The applicability of our method to particular cases will depend upon, or be further limited by, certain practical considerations or qualifications. Of these the chief, and indeed the essential, condition is, that the form of the entire structure under investigation should be found to vary in a more or less uniform manner, after the fashion of an approximately homogeneous and isotropic body. But an imperfect isotropy, provided always that some “principle of continuity” 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 “independent variants” should be relatively few. That independent variations occur, that localised centres of diminished or exaggerated growth will now and then be found, is not only probable but manifest; and they may even be so pronounced as to appear to constitute new formations altogether. Such independent variants as these Aristotle himself clearly recognised: “It happens further that some have parts that others have not; for instance, some [birds] have spurs and others not, some have crests, or combs, and others not; but, as a general rule, most parts and those that go to make up the bulk of the body are either identical with one another, or differ from one another in the way of contrast and of excess and defect. For ‘the more’ and ‘the less’ may be represented as ‘excess’ or ‘defect.’ ”
If, in the evolution of a fish, for instance, it be the case that its several and constituent parts—head, body, and tail, or this fin and that fin—represent so many independent variants, then our co-ordinate system will at once become too complex to be intelligible; we shall be making not one comparison but several {727} separate comparisons, and our general method will be found inapplicable. Now precisely this independent variability of parts and organs—here, there, and everywhere within the organism—would appear to be implicit in our ordinary accepted notions regarding variation; and, unless I am greatly mistaken, it is precisely on such a conception of the easy, frequent, and normal independent variability of parts that our conception of the process of natural selection is fundamentally based. For the morphologist, when comparing one organism with another, describes the differences between them point by point, and “character” by “character[645].” If he is from time to time constrained to admit the existence of “correlation” between characters (as a hundred years ago Cuvier first showed the way), yet all the while he recognises this fact of correlation somewhat vaguely, as a phenomenon due to causes which, except in rare instances, he can hardly hope to trace; and he falls readily into the habit of thinking and talking of evolution as though it had proceeded on the lines of his own descriptions, point by point, and character by character[646].
But if, on the other hand, diverse and dissimilar fishes can be referred as a whole to identical functions of very different co-ordinate systems, this fact will of itself constitute a proof that variation has proceeded on definite and orderly lines, that a comprehensive “law of growth” has pervaded the whole structure in its integrity, and that some more or less simple and recognisable system of forces has been at work. It will not only show how real and deep-seated is the phenomenon of “correlation,” in regard to form, but it will also demonstrate the fact that a correlation which had seemed too complex for analysis or {728} comprehension is, in many cases, capable of very simple graphic expression. This, after many trials, I believe to be in general the case, bearing always in mind that the occurrence of independent or localised variations must often be considered.
We are dealing in this chapter with the forms of related organisms, in order to shew that the differences between them are as a general rule simple and symmetrical, and just such as might have been brought about by a slight and simple change in the system of forces to which the living and growing organism was exposed. Mathematically speaking, the phenomenon is identical with one met with by the geologist, when he finds a bed of fossils squeezed flat or otherwise symmetrically deformed by the pressures to which they, and the strata which contain them, have been subjected. In the first step towards fossilisation, when the body of a fish or shellfish is silted over and buried, we may take it that the wet sand or mud exercises, approximately, a hydrostatic pressure—that is to say a pressure which is uniform in all directions, and by which the form of the buried object will not be appreciably changed. As the strata consolidate and accumulate, the fossil organisms which they contain will tend to be flattened by the vast superincumbent load, just as the stratum which contains them will also be compressed and will have its molecular arrangement more or less modified[647]. But the deformation due to direct vertical pressure in a horizontal stratum is not nearly so striking as are the deformations produced by the oblique or shearing stresses to which inclined and folded strata have been exposed, and by which their various “dislocations” have been brought about. And especially in mountain regions, where these dislocations are especially numerous and complicated, the contained fossils are apt to be so curiously and yet so symmetrically deformed (usually by a simple shear) that they may easily be interpreted as so many distinct and separate “species[648].” A great number of described species, and here and there a new genus (as the genus Ellipsolithes for an obliquely deformed Goniatite or Nautilus) are said to rest on no other foundation[649].