862 D'AKCY WENTWORTH THOMPSON ON 



If, in the evolution of a fish, for instance, it be the case that its several and con- 

 stituent 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 separate com- 

 I unisons, 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." If he is from time to time con- 

 strained 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 descrip- 

 tions, point by point, and character by character. 



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 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 local independent variations 

 must often be considered. 



If we begin by drawing a net of rectangular equidistant co-ordinates (about the 

 axes x and y), we may alter or deform this network in various ways, several of which 

 are very simple indeed. Thus (l) we may alter the dimensions of our system, extend- 

 ing it along one or other axis, and so converting each little square into a correspond- 

 ing and directly proportionate oblong (figs. 1, 2). It follows that any figure which 

 we may have inscribed in the original net, and which we transfer to the new, will 

 thereby be deformed in strict proportion to the deformation of the entire confign ra- 

 tion, being still defined by corresponding points in the network and being through- 

 out in conformity with the original figure. For instance, a circle inscribed in the 

 original "Cartesian" net will now, after extension in the ^/-direction, be found 

 elongated into an ellipse. In elementary mathematical language, for the original 



