steps. In the newest of all the sciences, therefore, which enables us to regard matter wheresoever situate from an entirely new point of view, the investigator's caution must be redoubled, and those who would follow him must be careful to secure firm foothold at every step. Fortunately for us the laws and phenomena of nature have such a oneness in their diversity, and are so exquisitely intertwined, that it is possible for us in the consideration of any new branch of Science to aid our conceptions by mental images derived from the older sciences or ordinary phenomena, and this is especially true for that science now under consideration.

We can thus begin by some elementary notions which, when fully comprehended, will enable us to build on them conclusions which will be so many further steps.

By means of post-offices, railways, and electric telegraphs, we have the idea perpetually brought before us that in one place a man or a thing sends; that somewhere else, it may be near or it may be far off, we have a man or a thing which receives; and that between the man or the thing which sends, and the man or the thing which receives, there is a something which enables the thing sent to pass from one place to the other. There does not seem to be any deep science in this, nor is there; but these considerations enable us to make an important distinction. In the case of two boys playing at ball, one boy throwing the ball to the other, we have also a sender and a receiver, and the thing sent goes bodily from the one who sends to the one who receives.

So in a parcel sent by train, but not so in the case of a telegraphic message. In the electric telegraph office two instruments may be seen-one the receiving instrument, the other the sender. Between the office in which we may be and the office with which communication is being made, there is a wire. We know that a thing is not sent bodily along that wire in the same way as the boy sends the ball to his fellow, or as the goods train carries the parcel. We have there in fact a condition of motion with which science at present is not absolutely familiar; but we picture what happens by supposing that we have a state of things which travels. The wire must be there to carry the message, and yet the wire does not carry the message in the same way as a train carries a parcel.

Take another case. I burn my foot, I instantly raise it. To make me conscious that my foot had been burnt, a message (as we know now) must have gone from my foot to my brain, and a return message must have gone from my brain to my foot, to tell it to change its position so as not to be burnt any more. Now it is generally held that this internal transit of messages is not managed by electricity, but that although electricity is not here at work, still that there is something which behaves very much after the manner of electricity. No one imagines that the pain travels up the leg and then back again; it is, in fact, a state of things which travels up from the nerve of the foot to the brain; and then there is another state of things which travels back again from the brain to the

foot, along another set of nerves. A rope will here afford us a useful mental image. By shaking a rope we can send that state of things we call a wave along it without the rope itself travelling as a whole; this will help to give us an idea of what is meant when we say that a state of things travels along a wire or along a nerve, and brings about either those electrical disturbances which result in the conveyance of a message, or that nerve action which generates the action of the brain.

§2. Water Waves.

Next to dwell more especially upon the word wave, and the idea which that word most generally calls forth. Let us find a piece of tranquil water and drop a stone into it. What happens?-a most beautiful thing, full of the most precious teachings. The place where the stone fell in is immediately surrounded by what we all recognize as a wave of water travelling outwards, and then another is generated, and then another, until at length an exquisite series of concentric waves is seen, all apparently travelling outwards—not with uncertain speed, but so regularly that all the waves all round are all parts of circles and of concentric circles.

Let us drop two stones in at some little distance apart. What happens then? We have two similar systems each working its way outwards, to all appearance independently of the other. We get what is represented in Fig. 1.

Now these appearances are as if there were an actual outpouring of water from the cavity made by the stone; but if we strew small pieces of paper or other light material on the water surface before we drop the stone, we find that it is not the water which moves outwards,

but only the state of things-the wave. Each particle of water moves in a circular or elliptic path in a vertical plane lying along the direction of the wave, and so comes again to its original place. Hence it is that only

the phase goes on-how it goes on will easily be gathered from Fig. 2.

FIG. 2.-Showing the formation of waves by the circular motion of each particle of water in a vertical plane. Eight positions in each revolution are shown.

I. One particle in motion.-II. Two particles in motion.-III. Three particles in motion.— IV. Complete wave and motion of its elements.

3. Sound Waves.

Let us now pass to a disturbance of another kind, from two dimensions to three, from the surface of water to air.

We hear the report of a gun or the screech of a railway whistle, or any other noise which strikes the How comes it that the ear is struck? Certainly no one will imagine that the sound comes from the

ear.