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sidered to give the size of the bird), from the shortest to the longest, and the same number of vertical lines are drawn, numbered from one to twenty. In this case (and wherever practicable) the body-length is measured from the lower line of the diagram, so that the actual length of the bird is exhibited as well as the actual variations of length. These can be well estimated by means of the horizontal line drawn at the mean between the two extremes, and it will be seen that one-fifth of the total number of specimens taken on either side exhibits a very large amount of variation, which would of course be very much greater if a hundred or more specimens were compared. The lengths of the wing, tail, and other parts are then laid down, and the diagram thus exhibits at a glance the comparative variation of these parts in every specimen as well as the actual amount of variation in the twenty specimens ; and we are thus enabled to arrive at some important conclusions.

We note, first, that the variations of none of the parts follow the variations of the body, but are sometimes almost in an opposite direction. Thus the longest wing corresponds to a rather small body, the longest tail to a medium body, while the longest leg and toes belong to only a moderately large body. Again, even related parts do not constantly vary together but present many instances of independent variation, as shown by the want of parallelism in their respective variation-lines. In No. 5 (see Fig. 4) the wing is very long, the tail moderately so; while in No. 6 the wing is much shorter while the tail is considerably longer. The tarsus presents comparatively little variation; and although the three toes may be said to vary in general together, there are many divergencies; thus, in passing from No. 9 to No. 10, the outer toe becomes longer, while the hind toe becomes considerably shorter; while in Nos. 3 and 4 the middle toe varies in an opposite way to the outer and the hind toes.

In the next diagram (Fig. 5) we have the variations in forty males of the Red-winged Blackbird (Agelæus phæniceus), and here we see the same general features. One-fifth of the whole number of specimens offer a large amount of variation either below or above the mean ; while the wings, tail, and head vary quite independently of the body. The wing and tail too,

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though showing some amount of correlated variation, yet in no less than nine cases vary in opposite directions as compared with the preceding species.

The next diagram (Fig. 6), showing the variations of thirtyone males of the Cardinal bird (Cardinalis virginianus), exhibits these features much more strongly. The amount of variation in proportion to the size of the bird is very much greater; while the variations of the wing and tail not only have no correspondence with that of the body but very little with each other. In no less than twelve or thirteen instances they vary in opposite directions, while even where they correspond in direction the amount of the variation is often very disproportionate.

As the proportions of the tarsi and toes of birds have great influence on their mode of life and habits and are often used as specific or even generic characters, I have prepared a diagram (Fig. 7) to show the variation in these parts only, among twenty specimens of each of four species of birds, four or five of the most variable alone being given. The extreme divergence of each of the lines in a vertical direction shows the actual amount of variation; and if we consider the small length of the toes of these small birds, averaging about three-quarters of an inch, we shall see that the variation is really very large ; while the diverging curves and angles show that each part varies, to a great extent, independently. It is evident that if we compared some thousands of individuals instead of only twenty, we should have an amount of independent variation occurring each year which would enable almost any modification of these important organs to be rapidly effected.

In order to meet the objection that the large amount of variability here shown depends chiefly on the observations of one person and on the birds of a single country, I have examined Professor Schlegel's Catalogue of the Birds in the Leyden Museum, in which he usually gives the range of variation of the specimens in the museum (which are commonly less than a dozen and rarely over twenty) as regards some of their more important dimensions. These fully support the statement of Mr. Allen, since they show an equal amount of variability when the numbers compared are

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