In looking through a telescope the officer will see the enemy much more distinctly than with his unaided eye, but he cannot tell how far off the enemy is. If you have tried the experiment with two pins which I have suggested in the last chapter, you will know how difficult it is to judge even a small distance unless you can use both eyes.

I think every boy and girl will know what a triangle is, and those who get geometry at school can imagine one straight line drawn from the distant object to one eye, and another straight line drawn from the object to the other eye, and then, by drawing another short line from one eye to the other, we have, in our imagination, formed a great triangle. Those who know some geometry will tell you that every triangle must have three angles and three sides, and if you tell them the length of one side of a triangle, and the sizes of two of the angles, they will complete the triangle for you, and tell you all its other measurements. Now suppose we were able to draw a great triangle with its point or apex where the enemy is, and the base of the triangle where our gunners are.

It is evident that we could not measure the angle at the apex, as it is far beyond our reach, nor could we measure the length of the long sides of the triangle, which reach out to the enemy, but we could measure the base of this great imaginary triangle, as it is beside our own gunners, and we could also measure the two angles which are formed at the ends of this base line. Perhaps some boys and girls have thought geometry to be a very useless sort of thing. If so, they have been greatly mistaken, for by our knowledge of geometry we can calculate the lengths of those long sides of the triangle that reach out to the enemy. We can tell the exact distance to the enemy. I am quite sure that there is some boy or girl wondering how you can measure the angles of an imaginary triangle which does not really exist. Where the gunners are you could draw a straight line of any desired length to form the base line of a great triangle, but the straight lines which are to form the sides of the triangle which reach out to the enemy cannot exist. If I say that they can exist, you may think that I am either joking or meaning that they can exist in imagination in our minds, but I mean that they can exist in real life and not in imagination only. What then forms the sides of this great triangle? Suppose you place a telescope at each end of the base line which you have drawn beside the gunners, or let us suppose that we are on board a great battleship, and we wish to measure the distance to an enemy ship. We take the length of the ship to be the base line of our triangle, and we fix one telescope at the bow and another at the stern of the ship. If we now fix the telescopes so that they are both looking straight at one of the masts of the enemy ship, are there not straight lines between the enemy mast and the telescope? You admit that you imagine straight lines drawn between these points. I am speaking of real things; I am thinking of the light that travels in straight lines. Of course you cannot see these æther waves which we call light, but they are none the less real. But how are these straight lines of light going to help us to tell the distance to the enemy mast?

Suppose that the enemy ship is very near, or if you cannot imagine an enemy ship being near to one of our battleships, you must imagine that you are focusing the telescope on the mast of a friendly vessel quite close at hand. If this ship should happen to be at the centre of our battleship, then the two telescopes will point inwards. If the friendly ship should happen to be opposite the stern while we are turned broadside on to the ship, then the stern telescope will point straight out, and the bow one would point very much inwards. The position of the friendly ship will determine the angles at which the telescopes are placed. The length of the ship is the base line of our triangle, and the straight lines of light entering each telescope form the sides of the triangle, while the point or apex of the triangle is at the mast of the friendly ship. Having measured the length of our base line, which is the distance between the telescopes, and having measured the angles formed between the telescopes and this base line, we have sufficient figures to enable us to calculate by geometry the lengths of the sides of the triangle, and thus we may find out the distance to the friendly ship.

All this arrangement of telescopes and measuring of angles would take time, and perhaps before we had got to the end of our calculations the observed ship might have changed her position. It is here that our war invention comes in. Instead of using two telescopes and going through the actual measuring of angles, we have a single telescope arrangement which we call a "range-finder." The reason for this name is that its purpose is to find out the range at which our large guns have to fire to be sure of hitting the enemy. If you knew nothing about range-finders and you chanced to come upon a man using one, you might think that he was acting in a very strange manner. He has a long telescope mounted on a stand, but instead of looking in at one end in the usual way, he is looking in at the centre of the long telescope tube. You ask him what he is measuring, and he points to a small object at a great distance in front of him. This is strange, as the telescope is not pointing in that direction, but is lying broadside on to the object. A range-finder being used on board a ship to measure the distance to a ship right opposite the centre of our ship would be pointing towards the bow and stern, and not out from the side of the ship, as one might expect. If it were an ordinary telescope you could only look either to the bow or to the stern, and you could never see a distant ship which is at the side. But when you take a look at the range-finder you see that the two ends of the telescope are closed up, and if you go round to the front you find that the light enters at two apertures or holes, one placed near each end of the long tube. Now we see why the man is looking in through holes at the centre placed at the back of the tube. It is quite evident that the light entering at the holes in the front is being sent by mirrors along the tube to the centre, and that when it reaches the centre it is being reflected to pass out at the back of the instrument.

Instead of mirrors the range-finder has little glass prisms. The construction of a range-finder is very ingenious, but we are not going to worry about the details except to notice that when the observer looks through the range-finder he sees the distant object cut in two, and by moving a thumbscrew he can make the two images overlap to form one image. In moving the thumbscrew he is altering the position of a small prism within the tube, and when this prism has bent the light so that the two images overlap, the position of the prism is made to indicate the actual distance of the object.

I remember the first occasion on which I saw through a range-finder. It was at the works where range-finders were being made. The instrument was directed at a distant church spire, and then I was asked to measure the distance to the spire. Looking at the spire I saw it as if it were split into two separate portions; I turned the thumb-screw till the two portions exactly overlapped. Then it was the instrument and not I who did the actual measuring. The indicator pointed to the distance on a scale. Of course it was the inventor of this instrument who arranged this scale and made range-finding so simple.