BRITISH SPECIES QF THE GENUS MNIUM. 13 
interval curves to such a form that the absolute values are eliminated, only 
the relative values (proportions) being retained. This method enables us to 
reduce all the curves to the same scale; this makes the comparisons much 
easier. 
In all the interval curves we suppose the mean value of the 10th interval 
— 100, and calculate the value of the other intervals in hundreds of the 10th 
one. We call such eurves percentage interval eurves or percentage curves 
(°/) curves). 
Example: We want to compare a mean interval curve of a group of 
specimens with the curve of one of the specimens. In Table VII. we give 
the mean curve of the length of the leaves * of eight stems of Mniwm hornum 
(belonging to the same patch) and the individual curve of one of those stems 
taken at random, with the corresponding percentage curves. 
TABLE VII. 
Mnium hornum, Linn.—Length of the leaves : mean curve of eight stems 
and one individual eurve, with the corresponding percentage curves. 
Intervals: — 1. 2. 5: 0M Ub. 6. 7. 8. Oe 105 
8 stems: length, in mm. .. 200 251 290 3:28 375 423 465 5:204 601 679 
Percentage ...... 80 820014100 MS 55 - 02-69 - 77 89 100 
l stem: length, in mm. .. 2°05 253 281 339 413 445 494 564 643 7:16 
Percentage ...... 29 0OMENOON Qn e 58 02. GB “990; - 100 
Comparing the percentage curves, we see that the individual eurve does not 
deviate much from the mean curve. This is an ordinary rule : in the great 
majority of the cases the gradation of a given character in a stem follows 
more or less approximately the mean curve of the group of stems to which it 
belongs. Therefore we may admit that a mean curve is not the result of an 
arbitrary method of computation, but that it has a real significance. A 
mean curve represents the most probable (approximately the most frequent) 
gradation in a group of stems. The differences between the specimen 
curves are very likely produced by chance—in the same way as the ordinary 
individual variation. 
$9. PERCENTAGE CURVES (continued).— Comparison between two species 
with reference to the gradation of the same property. Let us compare, for 
instance, the mean percentage curve in Table VII. CM. hornum) with the 
similar curve in Table VI. (M. punctatum). The difference between both 
curves is obvious—too great to be explained by chance. In the intervals 
7, 8, 9 the percentage values are much higher in punctatum than in hornum : 
the result is that the summit (interval 10) is distinctly more prominent in 
hornum. (See also Table IX.) 
* 340 leaves distributed among 10 intervals. 
