180 THE AMERICAN NATURALIST. [VoL. XXXV. 
posterior laterals in each valve, Bernard’s formula would be as 
follows, — the anterior end of the hinge being at the left end 
of the formula. 
Right valve LA I : HI :| Ca3a:1:3p: RILPELHI: 
wert ave LÆT- IV | Cas ba pep Ap | RÍLP:H:IV 
The Steinmann formula for the same shell is: 
Rlolo:1orororlolo 
Lolol-orototrrolol. 
Ordinarily this formula is written in the opposite direction, 
bringing the left valve above the line, but I have reversed it 
here to make the formule more comparable. In the Steinmann 
formula we put l for a lateral and 1 for a cardinal ; o for a socket, 
and a period to set off the anterior laterals from the cardinals. 
In this formula nothing is left to theory: the figures symbolize 
exactly the number and relative position of the parts of the 
hinge and a diagram could hardly do it better; of course it is 
capable of enlargement : for instance, bifid teeth may be sym- 
bolized by a fraction %, instead of a single digit ; the amor- 
phous irregularities which occur on such a hinge as that of 
Venus mercenaria may be symbolized by an X, and the solder- 
ing of adjacent teeth by the insertion between their symbols 
of a+sign. All the facts of the hinge of an adult shell can 
be indicated by this formula. It is only when the facts of the 
development of any particular hinge have been ascertained 
that we can use the Bernard formula with equal confidence 
and accuracy. 
The initiation of denticulations on the hinge plate by 
external sculpture, as pointed out by Neumayr, is illustrated 
in many of the curious Paleozoic bivalves which he called 
Paleoconchs. These forms, though not in themselves the 
oldest known pelecypods, or prototypes, doubtless illustrate 
the method by which in prototypic forms the organs in ques- 
tion were evolved. Moreover, in the living Mytilidze, especially 
the more minute and deep-water forms, the same process in 
various stages can be directly observed. In some of them, as, 
for instance, Dacrydium, the development of hinge teeth stops 
