The Use of Graphs in Paleontology. 361 
be expressed as a percentage of the total possible range. In the latter 
case the extremes of each series are taken as 0 per cent and 100 per 
cent respectively. The former method will be illustrated later, only 
the latter will be used here. 
These two items, the series as a whole and the percentage of 
change within each series, are placed along the co-ordinate (Fig. 2). 
If in a specimen a, one of a group of organisms which is being 
studied, series A has advanced to 40 per cent of the possible range, 
B to 20 per cent, C to 60 per cent, D to 20 per cent, and E to 25 per 
cent, then the line a (Fig. 2,1) will represent the specimen a. 
Similarly the line £ will represent the specimen fp. 
| 00); Bg----p----F == Foyt 1O0p-yoreperere ay 
SO at re SOae ee 
@ Ob-4----$----b---F === 
05 cece inetnOn MeN aN 
AQ seer pea ae 
(00--+----! TE 10 0}-4---- AT 
‘ 
‘ 
j=4-oNc rec cosrn 
Fic. 2.—Diagrams illustrating the types of relationship that morphological 
graphs of organisms may have to one another. 
Considering first a group of organisms belonging to the same 
lineage, two hypothetical cases may be taken :— 
Case 1.—In this the rate of change is the same for all series. This 
implies that the series are intimately related with one another, so 
that the amount of change in one is, of necessity, accompanied by 
a proportional amount of change in each of the others. In this 
case the graphs, representing members of the lineage, will be parallel 
with one another. If each series started at zero, or at the same per- 
centage level, then the graphs would be straight (Fig. 2, II). If 
each had its own starting point, the graphs would be crooked 
(Fig. 2, III). Y 
Case 2.—In this the rate of change is different for the several 
series. This implies that the series are to some extent independent 
of one another, and not intimately correlated. The graphs, though 
they will not be parallel with one another, will develop out of, and 
will not cross one another (Fig. 2, IV). 
