22 PROF. JULIUS MACLEOD ON TEN 
biological significance, is something VERY VARIABLE and therefore rather 
vague. 
When we want to construct, for instance, a mean interval curve of a 
certain character of a group of specimens (see § 7), we need to find the 
relative value of the ten ordinates. As the variation of the character within 
the limits of a given interval depends (almost entirely) on chance, the mean 
value in an interval a is approximately the most probable (the most frequent) 
value of the character in the middle of a. Taking the mean values of the 
ten intervals, we eliminate as much as possible the influence of chance; 
the differences between the ten figures depend (almost entirely) on the 
influence of gradation. The construction of a mean interval curve (in 
which the ten mean values are used) is thus justified ; such a curve gives 
us, by the relative values of its ordinates, an adequate representation of the 
variation of the character along the axis. But the absolute values of the 
mean values (ordinates) are of secondary importance, because those absolute 
values vary from one patch to another. (See the construction of percentage 
interval curves, in which the absolute values are eliminated, § 8.) 
We see from this example that, when we want to use mean values, their 
real significance ought to be exactly defined in each peculiar case. 
What is, for instance, the significance of the mean length 7:38 mm., 
calculated by means of the eight figures in §13? As the variation of these 
eight figures depends merely on chance, the calculation of a mean value is 
justified from a mathematical standpoint. But its significance is limited to 
the patch to which the eight stems belong; similar values may be useful 
‘for the comparison of several patches with each other *, but they are not 
characteristic for the species. 
It is, in fact, IMPOSSIBLE to establish the mean value of a variable character 
of a species. In the above example (M. spinosum, § 13) the mean length of 
the leaves was calculated by means of specimens belonging to one patch. 
But when we collect several patches of the same species in different localities, 
each patch gives a different mean value ; when we bring these values together 
and try to calculate in that way the mean value of the species, the result is, 
of course, an ARTIFICIAL one and will be modified again and again by each 
new observation. 
Moreover, even if we succeeded in establishing a specific mean value f, this 
would give us little help, if any help at all, for the identification of a given 
specimen.— Example : We have found for the length of the longest leaf of 
Mnium spinosum the value 7°38; in a similar way we found for Maium 
cuspidatum the value 4:63 mm. Let us suppose that those values were really 
* For instance, with reference to the influence of different conditions of existence. 
+ For instance, by cultivating the species under certain conditions of existence defined 
by convention—a method which is practicable only in exceptional cases. 
