The Use of Graphs 1n Paleontology. 399 
Many lamelle are in reality the central continuation of the septa, 
from which they often become separated at the edge of the tabellar 
zone. New lamelle, having no relationship to the septa, often arise 
between the old ones. The total number may be counted and 
recorded. 
Not uncommonly the lamelle and the central ends of the septa 
become curved in various degrees, and may even become strongly 
spiral or even crumpled. These differences, which may form one or 
more series of changes, do not admit of easy measurement. In such 
cases the method of procedure is to represent the main steps in the 
series from one extreme to the other by five or ten diagrams. The 
extremes are then taken to be 0 and 100 respectively, and thus the 
stages in the development of curvature, represented by the diagrams, 
can be expressed as percentages of the maximum curvature. 
(Ss : 
CC 
Fic. 6.—Diagrams representing some of the stages in the serial reduction of 
the fossule in Carboniferous corals. c. cardinal fossula, cc. counter- 
cardinal fossula, a. alar fossule. 
This method of using a series of diagrams may be applied to 
differences exhibited by the columella. In some corals this unit 
is merely the central portion of a median partition, which stretches 
across the coral (Fig. 4 col.). In others this septum is broken on the 
cardinal side of the centre. In others, again, it is broken on the 
counter-cardinal side also. The columella also exhibits various 
degrees of thickening. The history of the columella, however, is not 
simple, and requires more discussion than the scope of this paper 
will allow. 
The passage from bilateral to radial symmetry is an important 
direction of change which undoubtedly takes place in numerous 
quite separate lines of descent, and expresses itself with the help 
of several structural units, such as the major and minor septa and the 
fossulee or depressions in the tabule. 
The changes, in so far as they involve the fossule, range from the 
presence of four fossule (Fig. 6) in bilaterally symmetrical corals, 
through various stages in the reduction first of the counter-cardinal, 
and then of the alar, and finally of the cardinal fossule, to the 
complete absence of all four in the radially symmetrical corals. 
Along some lines the alar fossule go before the counter-cardinal 
one does. In either case diagrams, representing stages at different 
percentage intervals from one extreme to the other, may be drawn. 
Of the major septa only four or six approximate to a radial 
