No. 411.] HINGE TEETH OF BIVALVES. 179 
For those who may be interested to look into this subject it 
will be useful to explain the formulz proposed by Bernard and 
Steinmann, with their subsequent modifications. 
In Bernard's scheme the teeth are numerals, — those of the 
right valve with odd, and of the left valve with even numerals ; 
the cardinals have Arabic, the laterals Roman numerals. The 
character of the teeth is further indicated by capital letters, and 
their origin by lower case italic letters corresponding to the 
primitive lamina from which they are supposed to have been 
detached in the course of development. Bernard begins with 
the median cardinal and numbers both ways. In most pele- 
cypods the cardinals are all anterior, though the laterals are 
either anterior or posterior. He begins with the ventral lat- 
erals and numbers upwards. One of the interesting points 
made by Noetling is that the ventral lateral laminae are some- 
times the younger, and therefore the homologies which may be 
inferred from the numeration beginning below are liable to be 
disturbed, whereas if the numeration of the laterals began from 
. above, the dorsal laminz being, as he contends, the older, this 
source of error would be eliminated. 
In our opinion liability to error is inherent in the system 
which attempts to. combine theoretical assumptions as to age 
and origin with a numerical indication of facts. Laterals may 
undoubtedly be added above as well as below in the course of 
growth, for the dorsal margin of the hinge plate is added to as 
well as the ventral; the hinge, when the ligament is opistho- 
detic, or posterior to the beaks of the valves, increases at both 
edges as long as the shell continues to.grow. 
Bernard indicates the sockets by a colon and uses the letter 
L between vertical bars to indicate the place of the ligament. 
The portion of the ligament which is internal is (so far as 
known) always the resilium, so it would be better to use R as 
a symbol, the letter L being already appropriated to symbolize 
the lateral lamina. Vertical bars are also used to separate the 
anterior laterals from the cardinal series, though, as the index 
letter L or C is already in use as an indicator, the bars do not 
seem to be needed. If we take as an example the case of 
a bivalve having three cardinal teeth and two anterior and 
