ã₤, and the equation to our original circle, x ÿ£¢ 2 ã₤+ã₤ y ÿ£¢ 2 =ã₤ a ÿ£¢ 2 ã₤, becomes that of the ellipse, x ÿ£¢ 1 ÿ£¢ 2 ã₤+ã₤ c ÿ£¢ 2 ã₤ y ÿ£¢ 1 ÿ£¢ 2 =ã₤ a ÿ£¢ 2 ã₤.
If I draw the cannon-bone of an ox (Fig. 354, A), for instance, within a system of rectangular co-ordinates, and then transfer the same drawing, point for point, to a system in which for the x of the original diagram we substitute xÿ£¢ãý =ã₤2xã₤ãã₤3, we obtain a drawing (B) which is a very close approximation to the cannon-bone of the sheep. In other words, the main (and perhaps the only) difference between the two bones is simply that that of the sheep is elongated, along the vertical axis, as compared with that of the ox in the relation of 3ã₤ãã₤2. And similarly, the long slender cannon-bone of the giraffe (C) is referable to the same identical type, subject to a reduction of breadth, or increase of length, corôÙreôÙsponôÙding to xÿ£¢ã° =ã₤xã₤ãã₤3.
(2) The second type is that where extension is not equal or uniform at all distances from the origin: but grows greater or less, as, for instance, when we stretch a tapering elastic band. In such cases, as I have represented it in Fig. 355, the ordinate increases logarithmically, and for y we substitute öçÿ£¢yã₤. It is obvious that this logarithmic extension may involve both abscissae and ordinates, x becoming öçÿ£¢xã₤, while y becomes öçÿ£¢yã₤. The circle in our original figure is now deformed into some such shape as that of Fig. 356. This method of deformation is a common one, and will often be of use to us in our comparison of organic forms.
(3) Our third type is the ãsimple shear,ã where the rectangular co-ordinates become ãoblique,ã their axes being inclined to one another at a certain angle ü. Our original rectangle now