Method of practically determining the index of refraction and the curvature of the surfaces of any given convex or concave lens.

26. It is frequently convenient for a practical optician to be enabled to determine the radii of curvature of a given lens, and I am not aware of any rule being given for this purpose; the following therefore may be acceptable. The method of measuring the radii of a given concave lens is very well known it is simply to measure the reflected solar focus of each of the two surfaces; then double these numbers will be the radii sought.

The same simplicity of calculation does not present itself in the convex lens; still, however, the following method of deducing the radii will be found by no means difficult.

Obtain, as in the case of the concave lens, the focus by reflection from the back surface of the convex lens, exposing first one surface and then the other to the solar rays; measure also accurately the solar focal length of the lens by refraction; and then by means of these three quantities, equations may be formed which will give the radii of curvature and index of refraction.

Let r, r' be the radii of curvature of the two surfaces, and 1 + x the index of refraction let the lens be exposed to the sun's rays, so that the latter are first received upon the surface r. Then by known optical principles the refracted focus at the first surface will be

We may now therefore (disregarding the thickness of the

lens, consider these rays as converging towards the back surface to a focus f; and from this surface a part of them will be reflected to a focus f'; which will be expressed by

fr

= 2 f— pl

This, by substituting for f, its preceding value, and making

These rays will be refracted at the first surface to a focus which we suppose to have been measured. Let this measured distance be m; then by known principles for expressing the refraction at the surface of a rarer medium, we have

And of course by simply inverting the lens, or changing

r to r', we have (calling the other measured focus n)

Let be the measured solar focus by refraction; then Φ

1 + being the index, we have

x(+) = ÷÷
¤ (÷ + ÷.)

ᄒ

From which three equations, and the known relation between y and x, and x, the three required quantities x, r, and r' may be obtained.

Substituting for r' and r in the two former, we have (ob

And substituting the last two values in the equation pre

And since here q = — 1 is obviously one of the roots, the

27. In order to determine the index of a given concave lens, we must combine it with any proper convex lens to produce a compound focus. Let this focus be 4, that of the convex lens f, and the required focus of the concave x, then by known principles

=

I

ᄒ+ᄒ.

Whence x becomes known. Having then measured the radii of curvature as already stated, and calling them r, r', and index 1a, we have

a' ( ÷ + ÷ ) = ÷ ›

and since r, r', and x are known, a' and 1 + d' will of course be known also.

XVII.

On the change in the plumage of some Hen-Pheasants. By WILLIAM YARRELL, Esq. F. L. S. Communicated by WILLIAM MORGAN, Esq. F. R. S., March 19, 1827.

Read May 10, 1827.

THE latter part of the last shooting season has been unusually productive of those hen-pheasants which assume, more or less, the appearance of the male, and considerable discussion has, in consequence, arisen as to the cause of this change in the plumage.

Chance, rather than design, having supplied me with many opportunities of observation both on pheasants and the common domestic fowl, I am induced to notice the internal peculiarities that have been observed invariably to accompany this change of feather, and such other circumstances as appear connected with this subject, some of which I think will be found new and interesting.

A Paper on this subject, by Mr. JOHN HUNTER, published in the 70th Volume of the Philosophical Transactions, and afterwards reprinted in his "Animal Economy," details the appearance of several female birds having the feathers of the male, in which account he is led to observe," that this change of character takes place at an advanced age of the animal's life, and does not grow up with it from the beginning.”

In the Third Volume of the Memoirs of the Wernerian Society, Mr. JOHN BUTTER devotes a Paper to a consideration of the change which takes place in certain hen-birds at an