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Rh practical needs. Spectrophotometric observations are necessary to determine the position in the spectrum of the particular monochromatic ray, but when it has been determined a coloured glass may be made which allows light in the neighbourhood of this ray to pass, and the photometric comparison may then be effected by looking through this glass.

This article has been confined strictly to the methods of visual photometry, with very little reference to the results. Comparison of intensities of radiation by photographic means or by methods depending on the effects of heat introduces considerations quite distinct from those which lie at the basis of photometry in its usual sigrufication.

The earliest records that have come down to us regarding the relative positions of the stars in the heavens have always been accompanied with estimations of their relative brightness. With this brightness was naturally associated the thought of the relative magnitudes of the luminous bodies from whence the light was assumed to proceed. Hence in the grand catalogue of stars published by Ptolemy (c. 150 ), but which had probably been formed three hundred years before his day by Hipparchus, the 1200 stars readily visible to the naked eye at Alexandria were divided into six classes according to their lustre, though instead of that term he uses the word or “magnitude”; the brightest he designates as being of the first magnitude, and so downwards till he comes to the minimum visible, to which he assigns the sixth. These magnitudes he still further divides each into three. To those stars which, though not ranged in any particular order of brightness, nevertheless exceed the average of that order in lustre he attaches the letter,, the initial letter in (greater), and to those in the same order which exhibit a lustre inferior to that of the average he affixes the letter, the initial letter of . With this sort of subdivision he passes through all the six orders of magnitude. He does not, indeed, tell us the precise process by which these divisions were estimated, but the principle involved is obvious. It is one of the many remarkable instances of the acuteness and precision of the Greek mind that for upwards of 1500 years no real improvement was made in these estimations of lustre. J. Flamsteed extended the estimation of magnitude of stars visible only by the telescope, and he improved Ptolemy’s notation by writing 4·3 instead of ,—indicating thereby an order of magnitude brighter than the average of a fourth, but inferior to that of a third—and 3·4 for , and so on; but it was not till the year 1796 that any real advance was made in stellar photometry. Sir W. Herschel, instead of assigning a particular magnitude to stars, arranged them in small groups of three or four or five, indicating the order in which they differed from each other in lustre at the time of observation. This method was admirably adapted to the discovery of any variations in brightness which might occur in the lapse of time among the members of the group. Sir William observed in this way some 1400 stars, published in four catalogues in the Philosophical Transactions from 1796 to 1799; and two additional catalogues were discovered among his papers in 1883 by Professor E. C. Pickering of Harvard (see Harvard Annals, xiv. 345), and have recently been published by Colonel J. Herschel (Phil. Trans., 1906). These researches of the elder Herschel were in due time followed by those of his son, Sir John, about the year 1836 at the Cape of Good Hope. He both extended and improved the methods adopted by his father at Slough, and by a method of estimated sequences of magnitude he hoped to arrange all the stars visible to the naked eye at the Cape or in England in the order of their relative lustre, and then to reduce his results into the equivalent magnitudes adopted by the universal consent of astronomers. Sir John, however, like his father, left this important labour incomplete. Not only is the work one of great and continuous effort, but the effects of ever-varying meteorological conditions greatly impede it. Moreover, there is an unsatisfactory indefiniteness attending all estimations made by the unaided eye; numerical or quantitative comparisons are out of the question, and hence we find

Sir John, in the very midst of establishing his “sequences,” adopting also an instrumental metl1od which might lead him to more definite results.

In the year when Sir John Herschel concluded his photometric work at the Cape (1838) Dr F. W. A. Argelander commenced, and in 1843 completed, his Uranometria nova, in which the magnitudes of all stars visible to the unaided eye in central Europe are catalogued with a precision and completeness previously unknown. It contains 3256 stars, and although it will probably be superseded by instrumental photometry it must ever remain a monument of intelligent patience. Argelander’s labours were not confined to stars visible to the naked eye; by the aid of his assistants, Dr E. Schonfeld and Dr A. Kruger, three catalogues of magnitudes and celestial co-ordinates were ultimately published (1859–1862) as the Bonn Durchmusterung, including the enormous number of 324,188 stars, and an additional volume containing 133,659 stars south of the equator was published in 1886.

Dr B. A. Gould (1824–1896), in his Uranometria Argentina (1879), has done similar work for 7756 stars visible only in the southern hemisphere, and his successor at Cordoba, J. M. Thome, has published (1904) three volumes of the Argentine (Cordoba) Durchmusterung containing 489,662 stars between declination −22° to −52°. There have been other worthy labourers in the same field, each of whom has rendered efficient service, such as Dr E. Heis and M. J. C. Houzeau.

It is to Sir John Herschel that we are indebted for the first successful attempt at stellar photometry by what may be termed “artificial” means. He deflected the light of the moon (by means of the internal reflection of a rectangular prism) through a small lens 0·12 in. in diameter and of very short focus (0·23 in.) so as to form a sort of artificial star in its focus. With strings and a wooden pole he could move this artificial star of comparison so as to be in the same line of sight with any actual star whose light he proposed to measure. Other strings enabled him to remove it to such a distance from the eye that its light was adjudged to be sensibly the same as that of the star compared; and the distance was measured by a graduated tape. While he was thus busy at the Cape of Good Hope, K. A. Steinheil at Munich had completed for Dr P. L. Seidel an instrument nearly the same in principle but more manageable in form. He divided the small object-glass of a telescope into two halves, one of which was movable in the direction of its axis. The images of two stars whose light he desired to compare were formed by prismatic reflection, nearly in the same line of sight, and one of the lenses was then moved until the light of the two images seemed equal. The distance through which it was necessary to bring the movable lens furnished the data for comparing the relative lustre of the two stars in qucstion. More recently other photometers have been devised, and descriptions of three of them, with which considerable researches have been conducted will now be given. With the first mentioned below Professor Pickering of Harvard has made more than a million measures with his own eyes. The results of his observations, and of those of his assistants, will be found in the Harvard Annals especially in vol. xlv. published in 1901, which contains a general catalogue of about 24,000 stars brighter than magnitude 7·5, north of declination −40°. With the Zollner photometer Drs Gustav Muller and P. Kempf of Potsdam have recently completed a similar piece of work, their catalogue of stars north of the equator brighter than 7·5 containing 14,199 stars (Potsdam Publications, 1907, vol. xvii.). The catalogue of Professor C. Pritchard was smaller, containing 2784 stars brighter than magnitude about 6·5 and north of declination −10°; but it was published in 1886, when very little had yet been done towards the systematic measurement of the brightness of the stars (Uranometria nova oxoniensis, vol. ii. of the Oxford University Observatory publications).

Pickering’s meridian photometer (Ann. Astron. Obs. Harv. vols. xiv. and xxiii.) consists of two telescopes placed side by side pointing due east, the light from the stars on the meridian being reflected into them by two mirrors inclined at an angle of 45° to this direction. If there were a star exactly at the Pole, one of these mirrors 