A very pretty experiment can be shown by fitting into the trough an oval band of metal bent into the form of an ellipse. If two pins are stuck into a sheet of card, and a loop of thread fitted loosely round them, and a pencil employed to trace out a curve by using it to strain the loop of thread tight and moving it round the pin, we obtain a closed curve called an _ellipse_ (see Fig. 19). The positions of the two pins A and B are called the _foci_. It is a property of the ellipse that the two lines AP and BP, called _radii vectores_, drawn from the foci to any point P on the curve, make equal angles with a line TT′ called a tangent, drawn to touch the selected point on the ellipse. If we draw the tangent TT′ to the ellipse at P, then it needs only a small knowledge of geometry to see that the line PB is in the same position and direction as if it were drawn through P from a false focus A′, which is as far behind the tangent TT′ as the real focus A is in front of it. Accordingly, it follows that circular ripples diverging from one focus A of an ellipse must, after reflection at the elliptical boundary, be converged to the other focus B. This can be shown by the use of the above described apparatus in a pretty manner. [Illustration: FIG. 19.] A strip of thin metal is bent into an elliptical band and placed in the lantern trough. The band is so wide that the water in the trough is about halfway up it. At a point corresponding to one focus of the ellipse, drops of water are then allowed to fall on the water-surface and start a series of divergent ripples. When the stroboscopic disc is set in revolution and its speed properly adjusted, we see that the divergent ripples proceeding from one focus of the ellipse are all converged or concentrated to the other focus. In fact, the ripples seem to set out from one focus, and to be, as it were, swallowed up at the other. When, in a later chapter, we are discussing the production and reflection of sound waves in the air, you will be able to bring this statement to mind, and it will be clear to you that if, instead of dealing with waves on water, we were to create waves in air in the interior of a similar elliptically shaped room, the waves being created at one focus, they would all be collected at the other focus, and the tick of a watch or a whisper would be heard at the point corresponding to the other focus, though it might not be heard elsewhere in the room.