A C H R O M A TIC — ACID maximum efficiency for the purpose to which it is to be applied. Thus, for visual use the value of corresponding to a wave-length of about 5600 is best, while for photography with ordinary sensitive plates that for a wavelength of about 4300, a materially larger value, should be substituted. The variability in the dispersive ratio for different regions of the spectrum gives rise to an imperfection in achromatic combinations, which, immaterial in small lenses, becomes of serious consequence in large telescopes and in spectroscopes. In astronomical telescopes the defect appears as a fringe of colour, properly violet, about bright objects; it also renders such instruments quite unavailable for photography. In spectroscopes it necessitates a continuous change in adjustment from one end of the spectrum to the other. As it constitutes the gravest error in the modern telescope, many efforts have been made during more than a century for its elimination. A review of the success attained necessitates a consideration of other defects to which objectives are subject. These may be tabulated as follows :— 1. Chromatic differences of focal length, or secondary colour. 2. Chromatic differences of spherical aberration. 3. Chromatic differences of magnification. 4. Zonal differences of magnification. 5. Images by reflections which illuminate the field. All of these are inherent in refracting objectives, and no maker, however skilful, is able wholly to eliminate them. The highest success in designing an objective is only attainable by a due regard to the relative importance of these errors, and an adjustment of them to the purpose to which the instrument is to be applied. In the table of errors the first is that already considered and shown to be dependent on the optical properties of the materials employed; 3 is not distinguishable from this except in cases where the members of the optical system are separated, as in microscopes and camera objectives, and in some forms of telescope; 5, known as “ ghosts ” to opticians, is fixed as to number, but the positions of the images can be advantageously restricted. To explain the errors 2 and 4, especially important for our present purpose, another term must be first defined. When a single lens is used for forming an image of a remote object, it is found that the power of the lens always increases continuously with the distance of the portion used from the axis; in other words, the focal lengths of the concentric zones, into which the lens may be regarded as divided, continuously decrease with their diameters. This phenomenon, whose magnitude depends upon the shape as well as upon the power of the lens, is called spherical aberration. It is easy to see that it would be possible to combine a positive lens of such a shape as to yield a small degree of spherical aberration with a properly formed negative lens, even numerically less in power, so as to give a combination free from aberration for light of a chosen refrangibility. An achromatic combination which meets this condition for remote sources of light is a telescope objective. If free from spherical aberration for yellow light it will still possess aberration for light of less refrangibility, while for shorter wave-lengths it will be oyer-corrected, or have negative aberration. This property, given as 2 in the table, is quite negligible in telescope objectives constructed of ordinary materials, but in microscopic objectives of high efficiency it becomes by far the most serious error. The error 4 is illustrated in the preceding paragraph as accompanying spherical aberration. In a combined system it may exist independently of such aberration,
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and it is especially to be avoided in all instruments in which precision of images at even moderate distances from the axis is desired, such as meridian instruments, heliometers, and in all photographic objectives. The analytical condition for this end is that the sine of the angle of deviation of the light of each zone, in the production of an axial image, shall bear a constant ratio to the diameter of the zone. The extent of secondary colour error (1 of the table) is pretty nearly independent of the kinds of glass employed, provided that only silicic acid, soda, potash, lime, or oxide of lead enter into the composition of the materials. Fraunhofer seems to have experimented with boracic acid as a partial substitute for silica, but without satisfactory results. The experiments of the eminent Jena glassmakers with phosphate crowns and borate flints are optically highly successful, but unfortunately none of these materials is permanent. Recent experiments by the same makers with a very light flint and a dense crown are more promising, but the chromatic differences of spherical aberration are so great, even when the ratio of focal length to aperture is unduly increased over the customary value, that the gain for astronomical use is problematical. Doubtless the Jena potash crown and a boro-silicate flint make the best binary combination for visual telescopes, although the crown has the great disadvantage of being strongly hygroscopic. A triple combination of ordinary crown and flint with a boro-silicate flint has been used with success, but the necessary increase of focal length, together with the fact that the number of harmful reflections is increased from six, the number of the binary lens, to fifteen, renders the advantage in telescopes of large size questionable. A quadruple cemented combination of ordinary crown and flint with potash crown and borosilicate flint, is practically perfect for small telescopes, and can be unhesitatingly recommended for spectroscopic use. In microscope objectives the unrecognized error of chromatic differences of spherical aberration rendered all advance in the improvement of that important aid to scientific research nearly stationary for a third of a century, until Abbe made the brilliant discovery that it is possible to eliminate it by a proper separation of the parts of the optical system. Very summarily stated, his method is this—a front, often quite complex in construction, strongly under-corrected for both colour and sphericity, is increased in power by a back system over-corrected in both particulars to the requisite degree. The character of the image produced is found to vary greatly with the separation of the two systems, so that with successive trials a solution may ultimately be discovered in which the defect in question disappears. It is true that this process necessarily introduces the error 3 in a very marked degree, but this may be practically compensated by employing an ocular with equivalent errors of an opposite sign. The proper method of designing an objective, after finding the optical constants of the materials which are to be employed, is to deduce the values of A and B from the equations above, and then, assuming a ratio for the two radii of the first lens which experience has shown to approximate to the form desired, find by successive trigonometrical computations (not neglecting thicknesses and separations) the remaining constants of construction which adjust the various errors to the best values for the purposes to which the objective is to be applied. (c. s. h.) Acid and Alkali Manufacture. — We comprise under this heading the manufacture of the three great mineral acids (sulphuric, hydrochloric, and nitric), and that of the carbonate and hydrate of sodium, from which, however, the manufacture of chlorine and its comS. I. — 6
