Fig. 15.—The pipistrelle (Vesperugo pipistrellus).
Fig. 16.—The whiskered bat (Vespertilio mystacinus).
The other curves in these four tables are drawn in exactly the same way. The mean length is stated; and the amount by which a bone in any bat exceeds or falls short of the mean can be seen and readily estimated by means of the horizontal lines of the table. Any one can reconvert the tables into figures representing our actual measurements.
Now, it may be said that, since some bats run larger than others, such variation is only to be expected. That is true. But if the bones of the wing all varied equally, all the curves would be similar. That is clearly not the case. The second metacarpal is the same length in 5 and 6. But the third metacarpal is two millimetres shorter in 6 than in 5. In 10 the radius and ulna are longer than in 11; but the second metacarpal is shorter in 10 than in 11. A simple inspection of the table as a whole will show that there is a good deal of independent variation among the bones.
The amount of variation is itself variable, and in some cases is not inconsiderable. In the long-eared bats 4 and 5 in [Fig. 14], the phalanges of the third digit measured 26.5 millimetres in 4, and 34 millimetres in 5—a difference of more than 28 per cent. This is unusually large, and it is possible that there may have been some slight error in the measurements.[P] A difference of 10 or 12 per cent. is, however, not uncommon.
In any case, the observations here tabulated show (1) that variations of not inconsiderable amount occur among the related bones of the bat's wing; and (2) that these variations are to a considerable extent independent of each other.
So far we have compared a series of individuals of the same species of bat, each table in Figs. 13-16 dealing with a distinct species. Let us now compare the different species with each other. To effect such a comparison, we must take some one bone as our standard, and we must level up our bats for the purposes of tabulation. I have selected the radius and ulna as the standard. In both the noctule and the greater horseshoe bats the mean length of this bone is 51.5 millimetres. The bones of each of the other bats have been multiplied by such a number as will bring them up to the level of size in these two species. Mr. Galton, in his investigations on the variations of human stature, had to take into consideration the fact that men are normally taller than women. He found, however, that the relation of man to woman, so far as height is concerned, is represented by the proportion 108 to 100. By multiplying female measurements by 1.08, they were brought up to the male standard, and could be used for purposes of comparison. In the same way, by multiplying in each case by the appropriate number, I have brought all the species in the table ([Fig. 17]) up to the standard of the noctule. When so multiplied, the radius and ulna (selected as the standard of comparison) has the same length in all the species, and is hence represented by the horizontal line in the table.