A black surface is here divided into compartments for more convenient demonstration: let the spectator imagine five white squares between the parallel lines _a, b,_ and _c, d_. The square No. 1, is presented to the naked eye unmoved from its place. 294. But let the square No. 2, seen through a crown-glass prism _g_, be supposed to be displaced by refraction three compartments, exhibiting the coloured borders to a certain extent; again, let the square No. 3, seen through a flint glass prism _h_, in like manner be moved downwards three compartments, when it will exhibit the coloured borders by about a third wider than No. 2. 295. Again, let us suppose that the square No. 4, has, like No. 2, been moved downwards three compartments by a prism of crown-glass, and that then by an oppositely placed prism _h_, of flint-glass, it has been again raised to its former situation, where it now stands. 296. Here, it is true, the refraction is done away with by the opposition of the two; but as the prism _h_, in displacing the square by refraction through three compartments, produces coloured borders wider by a third than those produced by the prism _g_, so, notwithstanding the refraction is neutralised, there must be an excess of coloured border remaining. (The position of this colour, as usual, depends on the direction of the apparent motion (204) communicated to the square by the prism _h_, and, consequently, it is the reverse of the appearance in the two squares 2 and 3, which have been moved in an opposite direction.) This excess of colour we have called Hyperchromatism, and from this the achromatic state may be immediately arrived at. 297. For assuming that it was the square No. 5 which was removed three compartments from its first supposed place, like No. 2, by a prism of crown-glass _g_, it would only be necessary to reduce the angle of a prism of flint-glass _h_, and to connect it, reversed, to the prism _g_, in order to raise the square No. 5 two degrees or compartments; by which means the Hyperchromatism of the first case would cease, the figure would not quite return to its first position, and yet be already colourless. The prolonged lines of the united prisms, under No. 5, show that a single complete prism remains: again, we have only to suppose the lines curved, and an object-glass presents itself. Such is the principle of the achromatic telescopes. 298. For these experiments, a small prism composed of three different prisms, as prepared in England, is extremely well adapted. It is to be hoped our own opticians will in future enable every friend of science to provide himself with this necessary instrument. XX. ADVANTAGES OF SUBJECTIVE EXPERIMENTS.--TRANSITION TO THE OBJECTIVE. 299.