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but, on the other hand, it will not do to leave it long enough to become sensibly moist. Something will probably depend on the particular sample of collodio-chloride.

The exposure required is about five or seven minutes to the autumn sun. On a hazy day something more may be required; but if there are many clouds about, the experimenter, unless naturally of a good temper, will do well to postpone his operations.

On removal from the frame, the plates may be placed in a dish of water until it is convenient to finish them. They are fixed, without any toning, in a dilute solution of hyposulphite of soda, such as is used for paper prints, and then carefully washed. The most effective washing is a combination of rinsing and soaking. My practice is to rinse the plates under the tap for half a minute in order to remove the greater part of the hyposulphite of soda, and then to allow them to soak for an hour or two in water changed two or three times. After a final rinsing the plates may be set up to dry.

Gratings finished in this way give excellent definition, but the spectra are rather deficient in brilliancy. This defect is of less importance than might be supposed; for in order to see the finer fixed lines, sunlight is in any case indispensable, and with sunlight there is usually illumination to spare. Nevertheless, as gratings are likely to be largely used for the purpose of popular illustration under circumstances where artificial light must be employed, I am glad to be in a position to recommend a simple mode of treatment by means of which the brilliancy of the spectra may be materially enhanced. For this purpose it is only necessary to treat the fixed and washed impression with a solution of corrosive sublimate. When the whitening effect is complete, the plate must be again washed and then set up to dry. Considered as a photographic transparency, the grating is reduced rather than heightened in intensity by this process. The cause of the improvement of the spectra will be touched upon presently. These mercury-treated gratings cannot be varnished without sacrificing most of the advantage of the method. I have occasionally applied the same treatment successfully to tannin plates.

When not in use, the finished gratings should be kept in a dry place and protected from dust and other atmospheric deposit. For this purpose they may be put away wrapped in paper. For a short time there is no objection to leaving them standing, face inwards, against a wall; but a better plan is to place them, face downwards, on a flat and thoroughly clean piece of plate glass.

The originals from which I have hitherto taken copies are three in number. Two are by Nobert, and contain respectively 3000 and 6000 lines, in each case covering a square inch (Paris),

On a casual inspection the second, apart from the greater number of its lines, would be preferred as presenting a more even appearance. The 3000-line grating is divided into three parts, giving spectra of differing degrees of brightness, corresponding no doubt to a variation in the cut of the diamond or other stone employed, a peculiarity which is faithfully preserved in the copies. But on actual trial it is found that the spectra of the 3000-line grating are much the best in respect of definition; and the same difference is observed in the copies. The superior brilliancy of the closer-ruled grating is thus of little or no advantage for the investigation of the solar spectrum. In order to make good use of it, a higher degree of magnifying-power would be necessary than the definition of the spectra will bear.

The other original grating was engraved by Mr. Rutherford, of New York, and was kindly lent me by Mr. Browning; it contains 6000 lines to the inch. Owing to a change of residence, I have not hitherto had an opportunity of testing either the original or the copies on the solar spectrum; but I may observe that in respect of brightness they fall far short of Nobert's. This, as I have already remarked, is not always an objection; and the accuracy of division, on which definition depends, is said to be very superior*.

In testing gratings I prefer to work in a dark room. The slit is fastened in the window-shutter, outside which is placed the heliostat or porte-lumière. As slits are frequently required in optical experiments, and as usually made are rather expensive, I may be allowed to mention a very simple method by which serviceable slits may often be obtained. A piece of glass is covered with tinfoil, which must be made to adhere well; I have found a weak shellac-varnish a suitable cement. The alcohol is allowed to evaporate, and the thin layer of shellac softened by heat. In order to make a slit, it is only necessary to lay a staight edge on the tinfoil and draw a line with a sharp knife, afterwards wiping the line of the cut with a rag moistened with alcohol. The width and regularity of the slit may be judged of by holding it close to the eye, and observing the appearance presented by a distant candle. The narrower the aperture the more dilated (in the direction of the width of the slit) the image will appear. Broader slits may be made by removing the foil between two parallel cuts.

At a distance of 12 feet or more from the shutter are placed the grating and the object-glass of the observing-telescope. In making the preliminary adjustments, it is convenient to use a slit so wide that the spectra and the light reflected from the Draper, "On Diffraction Spectrum Photography," Phil. Mag. Dec. 1873, p. 419.

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grating can be seen on a screen. By the second the aspect of the plane of the grating can be judged of; and when the line of spectra is horizontal, it will be known that the lines of the grating are vertical and parallel to the slit. As object-glass, I am in the habit of using a single lens of about 24 inches solar focus. The eyepiece is a high-power achromatic, supplied by Mr. Browning, and forms, with the object-glass, a telescope of much higher magnifying-power than is ordinarily used in spectroscopes. Without a high power it is impossible to bring out the full value of the grating. In order to obtain the best definition, it is necessary to adjust carefully the aspect of the object-glass; and I find that the best aspect is not always the same. It is possible that the performance of other optical instruments might occasionally be improved if means were provided for a slight alteration in the direction of the optic axis of one of the lenses employed. The grating itself I usually place approximately in the position of minimum deviation.

The copies on worked glass by the ordinary photographic processes and by the modification of the collodio-chloride last described rarely fail in definition. With the original (3000) grating, or with the copies, I can make out nearly, but not quite, all that is shown in Ångström's map. With this grating the third spectrum is generally the most serviceable. When the picked patent plate is employed, there will generally be a proportion whose performance is less satisfactory, though few which would not give very fair results when tested by a low power only. Some cannot be considered inferior to the worked glass, at least when the object-glass is specially adjusted for them. In many cases the definition may be considerably improved by the use of a diaphragm in the form of a horizontal slit, so placed that only the central parts of the lines of the grating are operative. In respect of brilliancy, gratings may be more quickly judged of; it is sufficient merely to examine the spectra of a candle placed in a dark room.

The lines themselves are of course too close to be seen without a microscope; but their presence may be detected, and even the interval between them measured, without optical aid, by a method not depending on the production of spectra or requiring a knowledge of the wave-length of light. If two photographic copies containing the same number of lines to the inch be placed in contact, film to film, in such a manner that the lines are nearly parallel in the two gratings, a system of parallel bars develops itself, whose direction bisects the external angle between the directions of the original lines, and whose distance increases as the angle of inclination diminishes. The cause of the phenomenon will be readily understood by drawing on paper two

sets of equally distant and not too thin bars inclined at a small angle. Where the opaque and tranparent parts severally overlap, the obstruction of light is, on the average, less than the double of that due to each set separately*, and consequently these places appear by comparison bright. The interval between the bars is evidently half the long diagonal of the rhombus formed by two pairs of consecutive lines, and is expressed by a cos 0÷sin 0, or approximately a÷0, where a is the interval between the primary lines, and the mutual inclination of the two sets.

When parallelism is very closely approached, the bars become irregular, in consequence of the imperfection of the ruling. This phenomenon might perhaps be made useful as a test.

If the planes of the films be not quite parallel, bars parallel to the original lines may appear when the line of intersection of the planes is in the same direction. This arises from foreshortening of one of the sets, making it equivalent to a grating of a somewhat higher degree of fineness.

When examined under the microscope, the opaque bar on the copy, which corresponds to the shadow of the groove of the original, is seen to be composite, being not unfrequently traversed along its length by several fine lines of transparency. In one case, where the copy was on common glass, this effect went so far that at certain parts of the grating the periodicity was altered by each line splitting into two, the first spectrum altogether disappearing. In order to make this observation, the eye should be placed at the point where the pure spectra are formed and be focused on the grating. The places in question will then appear as irregular dark bands.

The disappearance of the first spectrum is very unusual; but it is common for bands to appear when the eye is placed in the place of the fourth and higher spectra. When the order is high, the bands will not be black, but coloured with light belonging to one of the other spectra. There is no difficulty in understanding how this occurs. In the process of copying, the groove of the original is widened into a bar, whose width depends on the closeness of contact, an element which necessarily varies at different parts of the plate. The dark bands are the locus of points at which the relation of the alternate parts is such as to destroy the spectrum in question.

I have not had an opportunity of trying the method of copying on lines closer than 6000 to the inch; but I have no doubt that the limit of fineness was not attained. I should expect to find no difficulty with lines 10,000 or 12,000 to the inch; but beyond that point it is possible that the method would fail,

The mathematical reader will easily prove this from the law of absorption.

or require special precautions, such as the use of extra-flat glass and greater pressure to ensure close contact in the printing. For preliminary experiments I should be inclined to try mica as a support, whose flexibility would facilitate a close contact. I may mention that I have done copies of the 3000line grating on sheets of mica, which may be obtained very thin and smooth from the photographic dealers. For more convenient manipulation in the preliminary stages of preparation, the mica should be mounted on a sheet of glass of the same size as itself. A small drop of water interposed will ensure a sufficiently close adhesion.

I have tried to take copies of copies, but with indifferent success, even when the performance of the first was not perceptibly inferior to that of the original.

Gratings may be copied without the aid of photography by simply taking a cast. Following Brewster, I have obtained a fair result by allowing filtered gelatine to dry after being poured on the 3000 Nobert. This method, however, is attended with much more risk to the original, and is besides open to other objections, sufficient, I think, to prevent its competing with photography.

[To be continued.]

XIII. On Wheatstone's Bridge.

To the Editors of the Philosophical Magazine and Journal.



January 11, 1874.

R. BROUGH, in the last Number of this Journal, has called attention to the fact that, in a paper "On the best Arrangement of Wheatstone's Bridge," in the Philosophical Magazine for February 1873, I did not start from the general equation for the strength of the current through the galvanometer irrespective of a balance, but took that form which the expression assumes when at a balance. In fact I assumed (ad-bc) to be indefinitely small. My reason for doing so was, that the question was to find the best arrangement at a balance, the great object of resistance-measuring being to get a balance; besides which, the course I adopted led to much greater simplicity and no less accuracy.

To take the special case upon which Mr. Brough dwells, viz. to find the best resistance for the galvanometer. This amounts to finding the resistance external to the galvanometer; and when a balance is obtained, as the galvanometer and battery are conju

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