( 'orrespondence 
281 
these 55 specific- values is a puzzle to which the identification of Juras- 
sic Ammonites or recenl unios is but play. Nevertheless, no more in- 
structive series of variations of a single generic type has ever been de- 
scribed among Palaeozoic fossils. The firsi onset a1 such a group is 
certain to lay the student low with acute brain-fag, and leave upon his 
mind a ha/.y conviction thai all the alleged species are pretty much one 
and the same thing. The beauty of the series and the persistence of its 
variations or species dawns upon the mind gradually but invincibly. 
Having attained this point in the stud) of the original specimens of 
these fossils, the attempt was made by the process of superposition to 
ascertain a standard or radicle outline for the entire generic group. In 
the making of this composite figure, which is here reproduced, it was. 
of course, necessary to fix upon two points or one dimension as a base to 
which all the elements could he reduced or elevated; just as in compos- 
ite portraiture, the eyes, or some other indices, of all faces in the com- 
posite must be coincident. In this case the standard to which all have 
been made to conform has been the distance between the anterior car- 
dinal extremity and the deepest posterior incurvature of the valve: a 
purely arbitrary dimension; probably any other would serve as well. 
The figure represents superposed 
outlines of the left valve of 36 of these 
species of Leptodesma. It will be ob- 
served that notable differences of out- 
line in the components of this figure 
are obscured by the coincidence of 
the lines for a greater or less portion 
of their length, while the riding out- 
line or type stands out conspicuously 
like a, coarsely shaded drawing of the 
valve. Of all the component outlines 
this interwoven valve approaches nearest to that of /,. royerri, as shown 
in the adjoining figure. It will naturally he understood that /,. rogerd 
enters into t his combination no more than the other 35 species, nor are 
there other shells whose outline is so nearly 
similar to that of /.. royerri as to produce a suc- 
cession of parallel lines, which thus become 
intensified. The depth and predominance of 
the L. roger&i outline is wholly i\wr to the coin- 
cidence of parts of outlines of species which 
vary greatly in this respect, as witness the 
four following silh ties of elements in this 
(•imposition, shown on page 288. 
As already remarked, what is here done for the outline of t he valves 
can he done with equal facility for convexity or other specific variations, 
either by this method of superposition or In the expression of such dif- 
ferences by a series of co-ordinates or mat hematical curves. 
One interesting fact in regard to the type or fundamentum expressed 
in this composite is that /.. rogemi (the silhouette of which, here 
Leptodesma rogersi. 
