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6 PROF. JULIUS MACLEOD ON TEN 
when we are asked what is the length of the leaves of a specimen of Mnium 
orthorrhynchum or Mn. undulatum? To find the answer, we want to 
establish the conditions under which the measurements are to be made 
in order to obtain comparable figures. In other words, when we have 
measured a leaf / belonging to a specimen of the species A, we want 
to find in a specimen of the species B a leaf which is comparable 
with l. 
§ 2. Grapation.—The way in which it is possible to solve this problem 
may be indicated by the study of an example. 
We take the Mosses of the genus Mnium. All the species belong to the 
ordinary type of the Acrocarpie Mosses. In a complete specimen we find 
fertile stems (which bear a fruit) and, according to the species, erect and 
horizontal sterile branches, male branches, ete. The leaves of all those 
branches are more or less different from each other in all the specimens of a 
given species. We agree, therefore, to limit our measurements to certain 
definite and restricted features, in the same way as we do when we measure 
the properties of inorganic objects. We select the fertile stem, and exclude 
all the other parts of the plant. The fertile stems may be considered as 
comparable in all the specimens and all the species. 
When we measure, for instance, the length of all the successive leaves of 
such a stem from the base to the summit, we see that the character length 
increases up to a maximum and then diminishes (see Table I.). 
TABLE I. 
Mnium punctatum, Hedw. : a fertile stem with 10 leaves ; length of the 
successive leaves in mm. 
Leaves: 1. 2: B: 4. 5. 6. rA 8. 9. 10. 
Length .... 0°97 1:31 QAUM ID. OUI. 0OUA TIS - :12- 689 246 
Here we have a first simple example of gradation. GRADATION IS THE 
VARIATION OF A GIVEN PROPERTY ALONG A GIVEN AXIS. In this case 
the axis of gradation or line of gradation is the longitudinal axis of the 
stem which bears the measured leaves. We know that those leaves have 
been developed successively in acropetal order ; therefore the whole system 
of ten leaves represents a period of growth, and at the same time a period of 
gradation of the character under consideration. 
By means of the figures in Table I. we may construct the Gradation 
Curve of one specimen (specimen curve), in which the axis is represented by 
a horizonial line, the length of the successive leaves being represented 
by equidistant vertical ordinates (fig. 1). A specimen curve is merely a 
graphic representation of facts, without any calculation. 
