SOME BIOLOGICAL PROBLEMS.
7
which appears as if lying on a rectangular network or grid. If
now we imagine all the lines to be connected and also elastic
and capable of any desired contraction, expansion and inclina-
tion, it is evident that although the network of crossing lines
can be altered in an almost endless variety of ways, owing to
their connection the lines will always have a definite relation
to one another coresponding to the kind of deformation to
which the whole system has been subjected. It follows naturally
that the outline of the animal will be modified accordingly. It
is found that these modified outlines often correspond very
closely to those of some related species or, vice versa, that the
network of lines obtained by plotting the outline of a related
species is one which can be produced by some simple deformation
of the original rectangular grid. Prof. D'Arcy Thompson shows
that the correlation between the shapes of related forms which
can be brought to light by the application of this method of
co-ordinates leads to important conclusions. In his own words:
"If . . . 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 compre-
"hensive 'law of growth' has pervaded the whole structure
"in its integrity, and that some more or less simple and recog-
"nisable 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 independent or localised variations
"must often be considered." Numerous examples of this
correlation are given from various classes of the animal kingdom
among them being two Copepod Entomostraca, one an elongated
form, Oithona, and the other a broad form, Sapphirina.
As a further example of the correlation of form among the
Entomostraca I have prepared the accompanying four figures
(fig. 1). The first (upper to left) shows in outline a very common
form of Daphnia pulex placed in a system of regular rectangular
co-ordinates. The second (below) shows how, by a reduction