On Aquatic Carnivorous Coleoptera or Dytiscide. 185 
matter of subordinate importance. And it seems to me that a numerical linear 
arrangement might here be of assistance. If genera were numbered consecutively, 
and the number habitually quoted, we should recognize the position of the genus 
much more easily by means of the number than we do by means of a name; for 
instance if we have the knowledge that there are about 700 genera of Longicorns 
and have an idea of the method on which they are arranged, and if we knew that 
in a numerical arrangement of the Coleoptera the Longicorns begin at 3,000, and run 
on to 3,700, it is clear that we shall at once recognize any number between the tivo 
just named as indicating a genus of Longicorns: and further that we shall be able to 
recall in a more or less vague manner, what part of the Longicorn family it belongs 
to; whether it comes near the beginning or end of the family and consequently 
some ally with which we are specially familiar. There is a further advantage in 
a numerical expression of classification, inasmuch as it gives us a prospect of being 
able in the future to indicate in an exact manner, by means of a numerical formula 
the true systematic value of any aggregate we are required to deal with, and thus 
to ascertain for instance the true difference between the faunze of two countries we 
might wish to compare in this respect. A numerical system applied in the way I 
have indicated, can however express only a linear arrangement, and as this can 
never be more than an approximation to a natural classification, it is clear that a 
simple numerical system can never do more than express feebly the complex 
relations existing between animals; moreover, it could only be of full service 
when applied systematically to all the animal kingdom; and I have accordingly 
adopted it here as an adjunct of my classification without attaching to it any 
considerable, present importance; but still it seems possible that it is in the 
direction of numerical expression of classification that we may hope for real 
improvement. 
In the second synthesis the genera are treated as units to be arranged into 
groups; and in the third synthesis these groups become the units of which tribes 
are formed ; and this method of proveeding from the simpler to the more complex 
ageregates is carried on till ultimately such questions would come to be considered 
as whether there really exists an isolation or division of organic beings into 
vegetable and animal kingdoms. In the present memoir this method of classifica- 
tion is carried only to the extent of a synthesis of the fifth degree. 
I have already mentioned that during the progress of the work I have had my 
attention frequently directed to those problems as to evolution and descent in 
which naturalists at present are so greatly interested, and the points I have more 
particularly kept in view were these two. First, are the structures of these 
creatures of such a kind as to make one believe they may have arisen by gradual 
modification of a precedent different structure? and second, are the various re 
semblances, or affinities as they are called, among the different species such as tu 
make it appear probable they are the results of genetic community of descent 
