The Use of Graphs in Paleontology. 357 
The Use of Graphs in Palaeontology 
By H. H. Swinnerton, D.8c., F.G.8., F.Z.8., Professor of Geology, 
University College, Nottingham. 
(Gunes ane methods for the comparative study of numerous 
observations and facts have long been in use in the exact 
sciences. They have also been used to some extent in those branches 
of the descriptive sciences which deal more particularly with the 
problems of heredity and variation. The purpose of the present paper 
is to sketch in outline a way in which they may be used in the 
morphological and systematic study of fossils. 
It is necessary at the outset to recall the precise nature of the 
material with which the paleontologist has to deal. In studying 
living organisms it is customary to think in terms of species, genera, 
and the like, either individually or distributed in space. Thisis the 
practice also in the study of fossils, but in this case the element of 
time must also be taken into account. The paleontologist con- 
sequently pictures species as merely members of a long, probably 
continuous, series, which he calls a line of descent or a lineage. He 
is fortunate indeed if his collection of specimens is so complete that 
he is able to reconstruct such a lineage in all its stages. Hven when 
he has done this with the best fossil material available, the fact 
remains that his results are based upon incomplete evidence ; for all 
the softer parts of the animal—the nervous system, musculature, 
vascular system—perished long ago. Even the hard parts which are 
preserved for his use are frequently fragmentary, and consist merely 
of a bone, a spine, a thecal plate, or a spicule. To these he may 
give generic and specific names, which have a use and value ; but it 
must not be forgotten that such fragments cannot constitute 
a species, they are only a few of the many structures which together 
make up a species. Names or no names, the paleontologist is usually 
concerned with isolated or small groups of structural elements, or 
units, and never with the complete animal. 
All this may seem trite ; but it is necessary to remind ourselves 
occasionally that our so-called lineages are usually little more than 
studies in series of changes undergone by a small proportion of the 
structural units which make up the living organism, and that 
absolute phylogeny is an almost unattainable ideal. The greater 
the number of units studied, the closer will be the approach to a 
true conception of the lineage, or line of descent, of the species, and 
therefore to the realization of the ideal. 
The ever-accumulating fossil material makes it increasingly 
difficult to keep in mind all the peculiarities exhibited by each 
structure in all the genera, species, and varieties with which the 
investigator has to deal. For this and other reasons it seems 
desirable to seek for some method of expressing the morphological 
features of several types concisely, and in such a way that their 
evolutionary significance may be easily grasped. In setting forth 
