should act, nor even that the curve of photographic intensity should admit of two distinct maxima within the spectrum. Suppose that rays of all refrangibilities lying within certain limits pass through the crystal and fall on the plate. For the sake of obtaining an expression which admits of being worked out numerically without too much trouble, and yet results from a hypothesis not very remote from the circumstances of actual experiment, I will suppose the total photographic power of the rays whose parameters lie between m and m + dm to be proportional to sin mdm between the limits m= 2π and m 3π, and to vanish beyond those limits. Since m is very nearly proportional to the reciprocal of the wave-length, and the ratio 37 to 2π or 3 to 2 is nearly that of the wave-lengths of the fixed lines D, H, this assumption corresponds to the supposition that the rays less refrangible than D are inefficient, that the action there commences, then increases according to a certain law, attains a maximum, decreases, and finally vanishes at H. The action would really terminate at H if a bath of a solution of sulphate of quinine of a certain strength were used. On this assumption, and supposing, as before, that the rays of different refrangibilities act independently of each other, we have On working out this expression, and writing a for 2r2, we find As the full discussion of this formula presents no difficulty it may be left to the reader. The last factor in the numerator of the fraction is that where fluctuations correspond to the rings. Whenever passes through an odd integer greater than 1 the first factor changes sign, and there is a dislocation or displacement of half an order, but when a passes through the value 1 the denominator changes sign along with both factors of the numerator, and there is no dislocation. When a becomes considerable the denominator 2-1 becomes very large, and the fluctuations of intensity become insensible. The following table contains the values of I calculated from the formula (3) for 16 values of x in each of the first 7 orders of rings. In passing from one ring to its consecutive the angle π increases by 27, and therefore x by 0.8. The sixteenth part of this, or 0.05, is the increment of x in the table. Each vertical column corresponds to one order. The value of a corresponding to any number in the table will be found by adding together the numbers in the top and left-hand columns. A curve of intensity might easily be constructed from this table by taking ordinates proportional to the numbers in the table, and abscissæ proportional to the values of r, and therefore to the square roots of the numbers 0, 1, 2, 3, 4, etc. But the form of the curve will be understood well enough either from the formula (3), or from an inspection of the numbers in the table. It will be seen that in the first three columns the numbers lying between the horizontal lines beginning 20 and 60 correspond to bright rings, and the remainder of each column, together with the beginning of the next, corresponds to a dark ring. But the dark ring, which would regularly follow the fourth bright ring, is converted, by the change of sign of the factor cos (πx), into a bright ring, forming with the former one broad bright ring having a minimum corresponding to x=3, where however the intensity falls only down to its mean value unity. A similar displacement occurs in the seventh column, but here the whole variation of intensity is comparatively small. In the case of calcareous spar the character of the rings is the same all the way round, but in the photographs of the rings of nitre a new feature presents itself. Mr Crookes's figure of the abnormal rings of nitre is rather too small to be clear, but with the assistance of his description there is no difficulty in imagining what takes place. With reference to these photographs he observes, “But here a remarkable dislocation presented itself; each quadrant of the interior rings, instead of retaining its usual regular figure, appeared as if broken in half, the halves being alternately raised and depressed towards the neighbouring rings." This effect admits of easy explanation as a result of the superposition of systems of rings which separately are perfectly regular, when we consider that the poles of the lemniscates of the several elementary systems do not coincide, since in nitre the angle between the optic axes increases from the red to the blue. Now the change of character which may be described as a displacement of half an order is due to the circumstance that the smaller rings corresponding to the more refrangible rays are, as it were, overtaken by the larger rings corresponding to the less refrangible. It is plain that the variation of position of the poles of the lemniscates would tend to retard this effect in directions lying outside the optic axes, and to accelerate it in directions lying between those axes. Hence what was a bright ring in one part of its course would become a dark ring in another part, so that each quadrant would exhibit a dislocation of half an order in the rings. In order to show this dislocation to the greatest advantage, a crystal of a certain thickness should be used. With a very thin crystal there would be no dislocation of this nature, but only a displacement like that which takes place with calcareous spar. With a very thick crystal the effect of the chromatic variation of position of the optic axes would be too much exaggerated. It appears then that all the leading features of the abnormal rings are perfectly explicable as a result of the superposition of separately regular systems. But if known causes suffice for the explanation of phenomena, we must by no means resort to agents whose existence is purely hypothetical, such for example as invisible rays accompanying, but distinct from, visible rays of the same refrangibility. Some of the minor details of the abnormal rings may require further explanation or more precise calculation; but such calculations are of no particular interest unless the phenomena offered grounds for suspecting the agency of hitherto unrecognized causes. The difference between the photographs taken with iodide and bromide of silver is easily explained, when we consider the manner in which those substances are respectively affected by the rays of the spectrum. With iodide of silver there is such a concentration of photographic power extending from about the fixed line G of Fraunhofer to a little beyond H, that even when white light is employed we may approximately consider that we are dealing with homogeneous rays. On this account, and not because the rays of high refrangibility are capable of producing a more extended system of rings than those of low refrangibility, the rings visible on the photograph are much more numerous than those seen directly by the eye with the same white light. Moreover, the rings do not exhibit the same abnormal character as with bromide of silver, in relation to which substance the photographic power of the rays is more diffused over the spectrum. It is not possible to place the eye and a sensitive plate prepared with bromide of silver under the same circumstances with regard to the formation of abnormal rings. It would be easy, theoretically at least, to place the eye and the plate in the same circumstances as regards rings, by using homogeneous light; but then, I feel no doubt, the rings visible on the plate would be as regular as those seen by the eye. On the other hand, if differences of colour exist in the figure viewed by the eye, they inevitably arrest the attention, and it is impossible to get rid of them without at the same time rendering the light so nearly homogeneous that on that account nothing abnormal would be shown. Hence Mr Crookes's abnormal rings afford a very curious. example of the creation, so to speak, by photography of forms which do not exist in the object as viewed by the eye. ON THE METALLIC REFLEXION EXHIBITED BY CERTAIN NON-METALLIC SUBSTANCES. [From the Philosophical Magazine, VI, Dec. 1853, pp. 393-403. Also Pogg. Ann., xCI, 1854, pp. 300—14; Ann. de Chimie, XLVI, 1856, pp. 504-8.] IN the October Number of the Philosophical Magazine is a translation of a paper by M. Haidinger of Vienna, containing an account of his observations relating to the optical properties of Herapathite. In this paper he refers to a communication which I made to the British Association at the meeting at Belfast*; and indeed one great object of his examination of this salt was to see whether a law which he had discovered, and already extensively verified, relating to the connexion between the reflected and transmitted tints of bodies which have the property of reflecting a different tint from that which they transmit, would be verified in this case. The report of my communication published in the Abbé Moigno's Cosmos† had led him to suppose observations were at variance with his law. that my My attention was first directed to this subject while engaged in some observations on safflower-red (carthamine), which I was led to examine with reference to its fluorescence. In following out the connexion which I had observed to exist between the absorbing power of a medium and its fluorescence, I was induced to notice particularly the composition of the light transmitted by the powder; and I found that the medium, while it acted powerfully on all the more refrangible rays of the visible spectrum, absorbed green light with remarkable energy. I need not now describe the mode of absorption more particularly. During these experiments I was struck with the metallic yellowish-green reflexion which this substance exhibits. It occurred to me that the almost metallic opacity of the medium with respect to green light [* p. 18, ante.] |