But the chief advantage that this subject possesses appears to me to be the middle position which it holds between the purely theoretical and the purely experimental. It contains sufficient of physical interest to give reality, and the easy and certain experiments by which it can be illustrated are convincing evidences of the correctness of the results, whilst the analysis which is requisite to obtain these results is sufficient to afford the reader, who up till now has been studying Algebra and Euclid, a proof that the said Algebra and Euclid have really some distinct use in explaining the phænomena of common life.

When the idea of writing such a book was first suggested to me by my old master, Professor Drew of King's College, I was afraid that there was hardly room, under the present system, for the subject in the course of a boy's school-work: I therefore, after making some progress in it, wrote to obtain the opinion of the head mathematical masters of two or three of our best schools; and I cannot sufficiently acknowledge the courtesy with which these gentlemen gave me the information I required. While acknowledging that the doubt which I had expressed existed in their own minds, they urged me strongly to continue my work, as they fully agreed in recognizing the great use of introducing a subject into school-work which should combine new ideas with practice in former knowledge.

The familiar use of the subject of Geometrical Optics by all who have received any but a very slight mathematical training precludes the possibility of originality in the facts themselves, and admits of but small originality in their treatment. At the same time it is hoped that it will be found that this book is not merely a rescript of any existing work.

It might be thought that it would be an easy task to adapt a subject of simple principles to the comprehension of boys possessing mathematical knowledge of the standard usually found in the higher classes of our schools. I imagined so myself, and during the course of my working I have been gradually learning my error. I can only wish that what I consider to be an object of the highest importance had been approached by some one more fitted both by mathematical knowledge and experience than by one whose sole qualifications are considerable fondness of the subject and a great desire to afford to beginners some glimpse of one of the steps to science to which their daily mathematics are leading. I have endeavoured as much as possible to avoid the example of those popular lecturers who explain difficulties by ignoring them. But as the nature of my design necessitated brevity, I have omitted entirely one or two portions of the subject which I considered unnecessary to a clear understanding of the rest, and which appear to me better learnt at a more advanced stage,—such

are the subjects of Illumination of Surfaces and Achromatism.

I need not say that I shall feel most thankful for notices of corrections that are needed, and for any suggestions as to the improvement of the book. O. AIRY.

WELLINGTON College,
April 2, 1870.

THERE are certain ideas connected with light and vision which are familiar to us all from the moment that our powers of observation exist. We know, for instance, that some bodies send out light of their own, such as the sun, or a gas-flame, or a red-hot coal; whereas others send out only light which they have received from something else, as, for instance, the bright spots on the polished back of a chair which come from the light of the gas-flame, or the fire, or the moon, who sends us the light which she gets from the sun. Then again, we cannot but feel sure that light comes from the object to our eye in straight lines. As an illustration of this there is the fact that if a small round hole be made in a sheet of paper, and a steady candleflame held before it, the light which passes through the hole will make an image of the flame upside down on another sheet of paper held parallel to the first. But this is only true so long as we suppose the light to be passing

through the same "medium," as it is called, that is, for instance, so long as it is passing through the same kind of air. If in its course it come to a surface of water, the same thing would happen to it as happens to a ball passing through the air which is suddenly struck by another ball thrown from the side; i.e. its course is instantly changed from the straight line in which it was travelling to another straight line.

2.

Before going any further we will give the definition of some terms which we shall often have to use :

(i) Any point of a luminous body is sending out light
in every direction in straight lines. It is therefore
called a 66
centre of light," or a luminous point."

66

(ii) And any one of such straight lines is called a "Ray.”

(iii) Any number of consecutive Rays form a "pencil."

The most convenient form in which to imagine a pencil is a solid cone of rays, of which the centre of light is the vertex.

(iv) The middle ray, or axis of the cone of rays, is called the "Axis" of the pencil *.

(v) When the rays forming a pencil of light come from a point, or as if from a point, the pencil is called a "divergent" pencil. When they come to a point, or as if to a point, it is called "convergent."

The ancients used to assume that the rays of a pencil were not close together, but separated like the fingers of the hand spread. By this they accounted for the fact that occasionally, in looking for a small object, like a needle, we cannot see it when it is under our nose.