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 would be absolutely fixed and would constantly reflect the light of this star down the axis of its telescope; in practice a slight motion

can be given to the mirror so as to keep in view the polar star selected, whether Polaris, with which the brighter stars were compared, or Ursae Minoris, which was used for fainter stars. The second mirror (which projects a little beyond the first so as to get an unobstructed view of the meridian) can be rotated round the axis of the telescope by means of a toothed-wheel gearing, and can thus be made to reflect any star on the meridian down the second telescope; it is also provided with a small motion in the perpendicular direction, so as to command a degree or two on each side of the meridian. Near the common eyepiece of the telescopes there is a double image prism which separates the light received from each into two pencils; the pencil of ordinary rays from one object glass is made to coincide with that of extraordinary rays from the other, and the two remaining pencils are excluded by a stop. The two coincident pencils then pass through a Nicol prism to the eye of the observer, who by rotating the prism round its axis can equalize them at a definite reading depending on their relative intensities. This reading gives in fact the difference of magnitude between the two stars selected for comparison. It may be remarked that the position of the double image prism is important. It should be just within, not at, the common focus: this position prevents any noticeable colour in the images, and gives the ordinary and extraordinary pencils a sufficient separation at the eye-stop to permit the entire exclusion of one without the loss of any part of the other. If the prism were exactly at the focus, and any part of the superfluous images were admitted, the resulting secondary images would coincide with the others and thus lead to errors in observing. But in the actual construction of the instrument the secondary images would appear, if at all, only as additional stars near those under observation, and too faint to produce any inconvenience. It is worthy of note that Professor Pickering has extended his survey into the southern hemisphere, so that the Harvard photometry is the most complete of all. Each observation consists of four comparisons; after the first two the observer reverses the position of the star images in the field, and also reverses the double-image prism. The former precaution is necessary in order to eliminate a curious error depending on the relative position of the images, which ma amount to several tenths of a magnitude. Errors of this kind affect all estimations of the relative brightness of two stars in the same field, as has been repeatedly shown; a striking instance is given by A. W. Roberts, of Lovedale, South Africa (Mon. Not. R.A.S. April 1897), who found that his eye-estimations of the brightness of variable stars required a correction depending on the position-angle of the comparison star ranging over nearly two magnitudes.

In Zöllner’s instrument an artificial star is taken as the standard of comparison. There is only one telescope, and inside the tube near the eye end is a plate of glass placed at an angle of 45° with the axis, so that the rays from a lamp which enter the tube from the side are reflected down the tube to the eyepiece, while the light from the star passes

through the plate unobstructed. The lamplight passes through a Nicol prism and a plate of rock crystal, which give control over the colour; through two Nicols which can be rotated round the axis of the beam to definite positions read off on a graduated circle; and then through a convex lens which forms an image reflected by the glass plate to focus alongside the star. The whole of this apparatus is carried in a compact form on the eye end of the telescope, it e1ng arranged that the amp shall always stand upright. The measures are made by rotating the Nicols until the brightness of the artificial star is equal to that of the star viewed through the ob]ect glass, and reading the graduated circle.

Professor Pritchard’s (1808–1893) wedge photometer is constructed on the principle that the absorption of light in passing through a uniform medium depends, caeteris paribus, upon the thickness. On this principle a thin wedge is constructed of homogeneous and nearly neutral tinted glass, through which the images of stars formed in the

focus of a telescope are viewed. Simple means are contrived for measuring with great exactness the several thicknesses at which the light of these telescopic star-images is extinguished. In this way the light of any star can be readily compared with that of Polaris (or any other selected star) at the moment of observation, and thus a catalogue of star-magnitudes can be formed. Two material improvements suggested by Dr E. J. Spitta are worthy of notice. The first (Proc. Roy. Soc., 1889, 47, 15) corrects a slight defect in the form of the instrument. If a pencil of rays passes through a thin wedge of tinted glass, the rays do not all pass through the same thickness of glass. Dr Spitta proposes to substitute a pair of wedges with their thicknesses increasing in opposite directions. By sliding one over the other we obtain a parallel plate of glass of varying thickness, and a uniform beam of light of sensible dimensions can then be extinguished satisfactorily. He has also pointed out a source of error in the method of “evaluating” the wedge and shown how to correct it. The scale value was determined by Professor Pritchard by the use of a doubly refracting prism of quartz and a Nicol prism. Using this method subsequently, Pk:kering's

Dr Spitta found that internal reflections within the Nicol prism interfered with the accuracy of the result, but that this error could be eliminated by using a suitable diaphragm (Mon. Not. R.A.S. March 1890; Abney, ibid., June 1890).

Since 1885 systematic catalogues of stellar brightness have been constructed with all these instruments, and it has great interest to compare the results. The comparison has in general shown a satisfactory agreement, but there are small differences which are almost certainly systematic, due to the difference of method

and instrument. One cause of such differences, the reality of which is undoubted, but the effects of which have as yet not been perhaps fully worked out, is the “Purkinje phenomenon” (Pflügers Archiv. lxx. 297). If a blue source of light and a red source appear equally bright to the eye, and if the intensity of each be diminished in the same ratio, they will no longer appear equally bright, the blue now appearing the brighter; in more general terms, the equalizing of two differently coloured lights by the eye depends upon their intensity. It is clear that this phenomenon must affect all photometric work unless the stars are all exactly of the same colour, which we know they are not. For let us suppose that both the comparison star of the meridian photometer and the artificial star of the Zöllner photometer were equalized with a bright star A, and that they could be also compared inter se and found equally bright. Then when a faint star B comes under observation and the intensities of the comparison stars are both reduced to equality with B, they will no longer appear equal to one another unless they are exactly the same in colour. In other words, the observed ratio of intensities of A and B will vary with the colour of the comparison star, and similarly it will also vary with the aperture of the telescope employed. Now it is one of the merits of the Potsdam catalogue above mentioned that it gives estimates of the colours of the stars as well as of their magnitudes—so that we now for the first time have this systematic information. In a most interesting section of their introduction it is shown that two of the Harvard photometric catalogues show systematic differences, due to colour, and amounting to nearly half a magnitude: and that the Purkinje phenomenon is a satisfactory explanation of these differences. This is the first instance in which the effect of this phenomenon has been measured in the case of the stars, though it was known to be sensible. But there is a set of numerical results obtained in the laboratory which is of importance for all such works, viz. those obtained by Sir W. Abney (Proc. Roy. Soc. May 1891; and Mon. Not. R.A.S. April 1892), giving the limiting intensity at which each pure colour vanishes. If we start with lights C D E F G of the colours usually denoted by these letters in the spectrum, and each so bright that it appears to the eye as bright as an amyl-acetate lamp at 1 ft., and if then the intensity of each be gradually diminished, the C light will disappear when the original intensity has been reduced to 22,000 ten-millionths of the original value. The other colours will disappear at the following intensities, all expressed in ten-millionths of the original: D at 350, E at 35, F at 17, and G at 15. If then we had a mixture of two lights, one of C colour as bright as before, and the other of G colour 1000 times fainter (a combination in which the eye would be unable to distinguish the G light at all), and if we continually reduced the combined intensity, the luminosity of the C light would diminish so much more rapidly than that of the G that the latter would begin to assert itself, and when the combined intensities were reduced to 22,000 ten-millionths of the original value, the C light would have all disappeared, while the G light would not. Hence the colour of the light would appear pure violet, though it was originally deep red. This extreme case shows that the “last ray to disappear” when a light is gradually extinguished may be very different in colour from that of the original light, and when more usual light-mixtures are considered, such as those of sunlight and starlight, which appear nearly white to the eye, the “ last ray to disappear ” is found to be in the green, very near E in the spectrum. This result has two important bearings on the use of the wedge photometer. In the first place,