Williams.] CORRELATION OF THE FAUNA. 77 
difficult to form, from a study of the figures and descriptions, a clear 
notion of what particular combination of characters the author had in 
mind when sorting out and labeling" the figures and applying specific 
names to them. 
The specimens referred to by Billings as "like R. bialveata" are 
represented in the collection and evidently belong to this species. At 
least one of the specimens agrees fairly well with Hall's description, 
though the figures are poor and do not convey a correct idea of the 
true form and characters. The plications and the boundary plications 
of the sinus and fold are very sharp and distinct, even close up to the 
beak region. The two plications of the fold of the dorsal valve begin 
very close up to the beak, but they are depressed below the surface in 
a groove, and as they run out toward the front they come up even with 
the surface about midway and constitute a prominent fold at the front. 
This constitutes a well-differentiated specific group in the Square Lake 
fauna, the individuals of which evidently were naturally small. The 
narrow form, the abrupt sides, the sharply angular plications, and the 
mode of development of fold and sinus are dissimilar to the young 
stages of the other rhynchonellas of the fauna. These two species, 
R. aspasia and R. bialveata, correlate the fauna with the Delthyris 
Shaly limestone stage of the Lower Helderberg. 
Applying this method of determining the stages of evolution of a 
series to the correlation of the Square Lake fauna, the results point to 
a stage of mutation corresponding to that of the Delthyris Shaly lime- 
stone of New York, but not in its full expression. The Square Lake 
forms are nearer to the Lower Pentamerus than to the Upper Pentam- 
erus stage. This is indicated by the fact that the dominant form, 
named R. mainensis by Billings, 1 is nearer to R. abrupta of the Del- 
thyris Shaly limestone series than to the side forms R. ventricosa and 
R. nobilis, which are the dominant types of the Upper Pentamerus. 
In plications and form the Square Lake forms are thus nearer the R. 
mutabilis stage of evolution. The state of mutation may be expressed 
by saying that the mature stage of R. mutabilis dominates the first 
half of the development of R. mainensis, whereas it dominates but a 
quarter of the R. abrupta form; and in the second half of growth of 
R. mainensis we have represented the three-quarters adult growth of 
R. abrupta. The result, in form, is a greater convexity of the beak 
part, with broadening of the median area, whereas the dominant char- 
acteristic of R. abrupta is the square-built form of the main body, with 
only moderately gibbous umbonal region. The gibbous form of the 
Delthyris Shaly limestone, R. nucleolata, shows its advance upon 
R. mutabilis by its fewer ribs at a corresponding stage of growth and 
size, and, when compared with R. mutabilis, shows an acceleration of 
the lateral superficial over the forward growth. 
1 See PI. II, figs. 11, 14, 17, which is the typical form of R mainensis Bill., and PI. I, figs. 9-24, and 
PI. II, figs. 2, 5, 8, 11, 14, 17. 
