BRITISH SPECIES OF THE GENUS MNIUM. 2L 
The second and the third method will be useful, especially in those cases in 
which it is impossible to measure a great number of characters (for instance, 
in many Fungi, Algæ, and lower animals). 
Finally, the three methods may be used at the same time. 
For more than a century innumerable species have been described in 
several instances under different names, because the available descriptions 
did not allow an exact identification. The result has been an enormous 
waste of time and a prejudicial disorder in the synonymy. We are still 
going on in the same way, and it is to be feared that in the future more 
labour will be wasted and more disorder will arise. 
‘Would it be too much to hope that the state of things will be improved by 
the exact measurement of characters and the construction of limit-tables ? 
PART: III. 
THE MEASUREMENT OF THE CHARACTERS OF THE LEAVES IN THE 
GENUS Mxriua. 
$21. EXACT MEASUREMENTS. POSSIBLE ERROR.—The exact expression by 
measurement of the characters of a living being is only possible if each 
character is strictly determined. When we want to measure, for instance, 
the length of the leaves of a certain plant, we must know exactly which 
leaves are to be measured, and we must determine the significance which we 
ascribe to the word length and even to the word leaf. 
There is something elusive in the variation of animals and plants. This 
variation is so great that one might be tempted to content himself with 
more or less approximate measurements, This would be a grievous mistake, 
by which the use of the quantitative method might be seriously endangered. 
As soon as we use the quantitative method we discover how many of our 
notions are rather superficial; and, as we proceed, we become more and 
more aware of the necessity of reaching the highest possible degree of 
exactitude. Errors are unavoidable, but even the limits of error ought to be 
as much as possible determined. 
In order to obtain an estimate of the possible errors, I measure a given 
character p of an object several times ; after a few days I repeat the same 
measurement with the same object several times. The difference between 
the highest and the lowest figure divided by 2 is the possible (positive or 
negative) error with reference to the character p. 
All the figures given iu this paper were verified at least by a second 
measurement. 
