BRITISH SPECIES OF THE GENUS MNIUM. 5 
PARTE 
GRADATION. 
Variation of a Given Character along a Given A«is.— Variation within 
the Limits of One Specimen. 
$1. DrrricuLTIES.— When we try to apply the quantitative method to 
the description of an animal or a vegetable species, we meet two serious 
difficulties. 
The FIRST DIFFICULTY depends on the individual variation. The great 
majority of the characters of animals and plants are variable within the 
limits of each species, and the differences between several individuals of 
the same species are often great. When we measure, for instance, the 
length and the breadth of the pronotum (prothoraz) and the elytra of a 
dozen Beetles (Coleoptera) between which there is no specific difference, 
we see that they are all different from each other in the four characters 
under consideration ; and one who makes for the first time such a series 
of measurements is astonished by the importance of the observed differ- 
ences, although the measured specimens seemed to be, at first sight, almost 
identical. The figures seem to vary in a most capricious way, and to be 
useless for the description of a species or the identification of a specimen. 
In the description of living beings, quantitative data have been used 
only in those rather exceptional cases in which a character is not (or 
only very slightly) variable (examples: number of teeth of the peristome 
of the Mosses, number of stamens and styles in many flowers, etc.). We 
shall see further (Part II.) how it is possible to use even such VARIABLE 
figures for description and identification. 
The SECOND DIFFICULTY occurs especially in the Vegetable Kingdom and 
in polypiform animals; also to a certain degree in other animals. It is 
the result of a peculiar sort of variation which is quite distinct from the 
individual variation (or variation properly so-called), and may be called 
GRADATION. 
Example: Let us suppose that we want to compare the length of the 
leaves 1n two species of plants, A and B. Enormous differences are almost 
always observed between the leaves of each specimen. In one fertile stem 
of Mnium orthorrhynchum, with 53 leaves, the shortest leaf had a length of 
046 mm., the length of the longest leaf was 3:91 mm. In a similar stem 
of M. undulatum, with 51 leaves, the length of the longest leaf was 
8:97 mm., that of the shortest leaf 1:06 mm.* What answer can be given 
* In a branch of Ulmus montana with seven leaves the length of the longest leaf 
(petiole +limb) was 15:5 cm., that of the shortest leaf 6 cm. 
