No. 411.] HINGE TEETH OF BIVALVES. 177 
comprise five or six lines of difficultly intelligible letters and 
figures, requiring three or four times as much more space 
devoted to * Erklärung der Formel," and, when all is said and 
done, hinder rather than help. How long will it be before it 
is universally understood that symbolization which has not the 
merit of brevity is not only a foolish waste of ingenuity and 
time but is absolutely without any chance of acceptation ? 
In this connection it may be noted that Munier-Chalmas 
proposed a system of notation for the hinge of bivalves which 
erred not only by involving much purely hypothetical assump- 
tion but also by inordinate length. A better was proposed by 
Bernard, of which some modification is suggested by Dr. Fritz 
Noetling! in an interesting and suggestive paper which has 
lately reached us. Bernard began work on the teleodont 
forms (Heterodonta of Neumayr) and under the influence of 
Munier-Chalmas. As many of the Teleodesmacea have com- 
parable hinges, it was natural that Bernard should suppose that 
all hinges were comparable and that the formula he proposed 
should be based on the assumption that from the mere position 
on the hinge plate the homologies of the individual teeth could 
be taken for granted, which we believe to be a very mistaken 
idea. Bernard in his later work realized that error, but unfortu- 
nately was not spared to consider the revision of his symbols. 
As a matter of fact even in the Teleodesmacea Bernard showed 
before his death that several distinct systems of tooth develop- 
ment can be recognized which cannot be interchangeably homol- 
ogized. Much more is it impracticable to homologize teeth of 
such groups as the Prionodesmacea and Teleodesmacea. In 
groups where it is practicable, — to be determined by observa- 
tion and not by theory, — Bernard's system will doubtless, with 
some modification, continue to be used. It is, however, very 
liable to lead the student unacquainted with its pitfalls into an 
unprofitable wilderness of theory, when, for the present, facts, 
and again facts, are imperatively demanded. If we eliminate 
theory, it still remains important that there should be some 
symbolical way of presenting the facts to the eye without 
1Notes on the Morphology of the Pelecypoda, Paleontologia Indica, N-S. 
vol. i (1899), pp- 1-43, No. 2. Calcutta. 
