There is another point in lighthouse optics which demands explanation. This is the term “divergence,” which plays an important part in the duration of the flash. In speaking about focus, the engineer follows somewhat in Euclid’s footsteps in regard to the definition of a point; in a way it is equally imaginary. The focal point does not mean the whole of the flame, but the centre of the luminous source, and, as is obvious, it is impossible to secure a flame without dimensions. It may be an attenuated, round, oval, or fan-shaped light--the result is the same. The focal point is the theoretical centre of the luminous source, and the rays, coming from the top, sides, and bottom of the flame cannot come from the true focus. If they did, all the light from one panel would be emitted in absolutely parallel lines, and therefore in a revolving apparatus the beam would pass any given point on the horizon in an infinitely short period of time--to be precise, instantaneously. But the ex-focal rays of the flame, in passing through the lens, emerge at an angle to those coming from the absolute centre, so that the whole beam becomes “diverged,” and throws a cone of light from the lens. Consequently the beam occupies an appreciable period of time in passing a given point on the horizon. As may be supposed, the intricate character of the lenses constituting the optical apparatus of the modern lighthouse demands the highest skill and infinite care in their preparation, while the composition of the glass itself is a closely guarded secret. There are less than half a dozen firms in the world engaged in this delicate and highly specialized work, of which France claims three, Germany one, and Great Britain one. All the lighthouse authorities of the various nations have to secure their requirements from one or other of these organizations. The industry commenced in France, and for many years the French reigned supreme. Then it contrived to make its entrance into England, and was taken up by the family of Chance in Birmingham, who soon proved themselves equal to their French leaders. [Illustration: FIG. 11.--RED AND WHITE FLASHING APPARATUS. (_By permission of Messrs. Chance Bros. and Co., Ltd._)]