upon the lens, L, through one of the holes in K, and R’ goes free toward some distant point, O. Those that impinge on the lens will be brought to a focus on S, where a bright speck of light might be seen.  This speck radiates light in all direction; some of the rays, proceeding from it, impinge on the lens at the other hole in the shade K, as shown in fig. 2, and are reduced by its agency to parallelism with r’ and R’, that is, with the rays that originally left the mirror:  consequently E, looking partly at the edge of the lens, and partly into space, sees a bright speck of light in the former, coincident with the point O in the latter.

[Fig 1 and Fig 2, as described in the text].

What is true for one point in the sun’s disc, is true for every point in it.  Accordingly, the signaller sees an image of the sun, and not a mere speck of light, in the lens; and the part of the landscape which that image appears to overlay, is precisely that part of it over which the flash from his mirror extends; or, in other words, it is that from any point of which a distant spectator may see some part or other of the sun’s disc reflected in the mirror.  There is no difficulty in signalling when the sun is far behind the back, if the eye-tubes are made to pull out to a total length of five inches, otherwise the shadow of the head interferes.  For want of space, the drawing represents the tubes as only partly drawn out.  The instrument is perfectly easy to manage, and letters can be signalled by flashes.  Its power is perfectly marvellous.  On a day so hazy that colours on the largest scale—­such as green fields and white houses—­are barely distinguishable at seven miles’ distance, a looking-glass no larger than the finger-nail transmits its signals clearly visible to the naked eye.

I have made a makeshift arrangement on the principle of my heliostat, using the object glass of an opera-glass for the lens, and an ordinary looking-glass:  the great size and short focus of the object glass is a great convenience when using a mirror with a wide frame.

Professor W. H. Miller, the Foreign Secretary of the Royal Society, has since invented a yet more compact method of directing the flash, which he has described in the Proceedings of the Royal Society for 1865.  It consists of a plate of silvered glass, one of whose rectangular corners is accurately ground and polished.  On looking into the corner when the glass is properly held an image of the sun is seen, which overlays the actual flash.  Beautifully simple as this instrument is, I do not like it so much as my own, for the very fact of its requiring no “setting” is its drawback.  With mine, when the image of the sun is lost it is immediately found again by simply rotating the instrument on its axis; but with Professor Miller’s the image must be felt for wholly anew.

Fire Signals.—­Fire-beacons, hanging up a lantern, or setting fire to an old nest high up in a tree, serve as night-signals; but they are never to be depended on without previous concert, as bushes and undulations of the ground will often hide them entirely.  The sparks from a well-struck flint and steel can be seen for much more than a mile.