CELESTIAL PHOTOMETRY. 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 A.D.), 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 peyedos or " magnitude " ; the brightest he designates as being of the first magnitude, and so down-wards till he comes to the minimum visibile, to which he assigns the sixth. These magnitudes he still further divides each into three. To those stars which, though ranged in any particular order of brightness, nevertheless exceed the average of that order in lustre he attaches the letter p, the initial letter in /j,£i(wv (greater), and to those in the same order which exhibit a lustre inferior to that of the average he affixes the letter e, the initial letter of eAdWwv. 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 esti-mated, but the principle involved is obvious. The eye was here made the natural photometer, and it is certain that even in the instances where modern instrumental ap-pliances are called into requisition the ultimate appeal is made to perception by the eye. Moreover, 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 by any of Ptolemy's numerous successors in this field of re-search. Flamsteed was the first astronomer who extended the estimation of magnitude to stars visible only by the telescope, and he improved Ptolemy's notation by writing 4'3 instead of S, JX—indicating thereby an order of mag-nitude brighter than the average of a fourth, but inferior to that of a third—and 3-4 for 8, e, and so on. Later astronomers have sometimes adopted a more precise nomen-clature by subdividing the several orders decimally, but it does not appear that by any immediate and unaided effort the eye can estimate subdivisions of lustre exceeding the thirds adopted by the Greek philosopher.
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, pub-lished in catalogues scattered through the Philosophical Transactions from 1796 to 1799; but he discontinued the work before its conclusion. It might be urged that such a work touches on no human interests, but it rightly seemed otherwise to the philosophic mind of the great astronomer. He remarked that the sun is, after all, only one among the stars, and that what befalls them in the way of varying light as time proceeds may also befall the sun. He puts the question, " Who would not wish to know what degree of permanency we ought to ascribe to the lustre of our sun? Not only tne stability of our climates, but the very exist-ence of the whole animal and vegetable creation itself, is involved in the question. Where can we hope to receive information upon the subject but from astronomical observa-tions?" 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 magni-tudes 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 con-tinuous effort, but the effects of ever-varying meteoro-logical conditions greatly impede it. Moreover, there is an unsatisfactory indefiniteness attending all estimations made by the unaided eye; numerical or quantitative com-parisons are out of the question, and hence we find Sir John, in the very midst of establishing his "sequences," adopting also an instrumental method which might lead him to more definite results.
In the year when Sir John Herschel concluded his photometric work at the Cape (1838) Dr Argelander com-menced, 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 instru-mental photometry it must ever remain a monument of intelligent patience. Argelander's labours were confined to stars visible to the naked eye; by the aid of his assist-ants, Dr Schonfeld and Dr Kriiger, a catalogue of magni tudes and celestial coordinates was ultimately published in their well-known Durchmusterung, extending to the enormous number of 324,000 stars.
Dr Gould also, in his Uranometria Argentina, has done similar work for stars visible only in the southern hemi-sphere, and with the aid of his colleagues has attained to an exactness and precision in his estimations of stellar lustre certainly not hitherto surpassed. There have been other worthy labourers in the same field, each of whom has rendered efficient service, such as Dr Heis and M. Houzeau; but it is chiefly to the labours of Argelander and Gould that astronomers at present make their appeal.
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. By the aid of appliances of the simplest kind he deflected the light of the moon (by means of the internal reflexion of a rectangular prism) through a small lens 0T2 inches in diameter and of very short focus, 0"2253 inches, so as to form a sort of artificial star in its focus. By the instrumentality of strings and a wooden pole he could move this artificial star of compari-son 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 this microscopic lunar image to such a distance from the eye that its light was adjudged to be sensibly the same as that of the star compared. The dis-tance of the short focused lens with the image contiguous to it was measured by a graduated tape, and the inverse squares of these distances afforded relative numerical mea-sures of the brightness of the several stars thus brought into ocular juxtaposition with the equalized light of the tiny lunar image. In this way he proceeded with the ob-servations of a considerable number of stars, and these, by appropriate methods, were reduced so as to afford the means of the comparison of their relative brightness when set side by side with results obtained by means of his " sequences," and with the estimated magnitudes of preceding astro-nomers. Sir John, however, did not go on to the formation of a complete " uranometria." While he was thus busy at the Cape of Good Hope, Steinheil at Munich had com-pleted for Dr 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 the intervention of prismatic reflexion, nearly in the same line of sight, and one of the lenses was then moved until the light of the two stars near the respective foci of the semi-lenses seemed equal to the judgment of the observer's eye. The distance through which it was neces-sary to bring the movable lens furnished the data for com-paring the relative lustre of the two stars in question. A large amount of work was thus achieved by Seidel, which for a considerable time has been, with greater or less reason, regarded as worthy of confidence in regard to precision (Trans. Mun. Acad., vol. ii.). Dr Zöllner substituted the deflected and reduced image of a lamp for one of Steinheil's stars, and the intensity of this light, or artificial star, he could by means of double refraction reduce in any measur-able proportion he pleased according to the well-known relations of polarized light. In this way he could equalize the light of the artificial lamp-star with that of the real star with which he compared it; and the division of the lens was thus dispensed with, but a new difficulty was intro-duced in the impossibility of maintaining the constancy of the flame. Dr' Zöllner also availed himself of the effects of double refraction in altering at will the colour of his artificial star of comparison. This ingenious form of photometer has enjoyed considerable reputation, but no astronomer has yet persevered in producing a complete " uranometria " by its aid. The most recent and probably the most successful device for a stellar photometer on the principle of equalizing lights is that invented by Professor Pickering of Harvard College. He deflects the light of Polaris, or of some other star such as A Ursse Minoris, by means of prismatic reflexion, and he contrives to form an image of it contiguous to the image of any other star selected on the meridian. The equalization of the lights is then effected by the intervention of a polarizing appa-ratus, such as that adopted by Zöllner. Thus the artificial and in many respects objectionable lamp-star of Zöllner is dispensed with. Professor Pickering, with singular invent-ive power, has devised many other forms of stellar photo-meters on virtually the same principle; for a detailed account of these labours the reader is referred to the Annals of the Harvard College Observatory (vol. xi.). Unlike his eminent predecessors, the American astronomer is persever-ing in the formation of a complete catalogue of star-magnitudes.
It has been already stated that mere estimations of relative brightness by the unaided eye are inadequate to the production of numerical quantitative results. In the instrumental devices explained, whether by means of the alteration of distances or by the known alteration of planes of polarization, no such defect exists. By their means it is possible to obtain a fairly exact numerical expression for the ratio of the intensities of the two lights measured. On applying a photometric measurement it is found that the ratio of the intensities of the lights in passing from one magnitude to the next, even in the conventional magni-tudes of Argelander and Gould, is not by any means con-stant, and even hardly definite. At the suggestion of Mr Pogson it is now generally accepted by astronomers that the adopted and conventional ratio of the intensity of light in passing from one magnitude to another shall be 2'512, a convenient number because its logarithm is "4, which is easily remembered, and still more so because on the whole it agrees better than any other number with the varying light-ratio existing among the hitherto received orders of magnitude obtained by eye-estimation alone.
There remains still another principle on which a stellar photometer may be successfully formed, and which has been recently largely applied to the determination of star-magnitudes at the university observatory, Oxford. It is constructed on the principle that the absorption of light in passing through a uniform medium depends, cseteris 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 con-trived 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. This method has been already applied by Professor Pritchard to all the brighter stars north of the equator; the results are published in the forty-seventh volume of the Memoirs of the Royal Astronomical Society, and are to be speedily followed by a complete catalogue, extending to all the stars in Argelander's Uranometria Nova north of the equator, and to a few others beyond. Por the details of the processes adopted the reader must here, as in all other cases, consult the original researches.
Even in a rapid sketch of so extensive a subject some notice must be taken of the application of photometry to the determination of the relative amount of light received on the earth from the sun, the moon, and the planets. The methods by which these ratios have been obtained are as simple as they are ingenious ; and for them we are mainly indebted to the labours of Bouguer and Bond. The former philosopher compared the light received from the sun with that from the moon in the following fashion in 1725. A hole one-twelfth of a Paris inch was made in the shutter of a darkened room ; close to it was placed a concave lens, and in this way an image of the sun 9 inches in diameter was received on a screen. Bouguer found that this light was equal to that of a candle viewed at 16 nches from his eye. A similar experiment was repeated with the light of the full moon. The image now formed was only two-thirds of an inch in diameter, and he found that the light of this image was comparable with that of the same candle viewed at a distance of 50 feet. From these data and a very simple calculation it followed that the light of the sun was about 256,289 times that of the moon. Other experiments followed, and the average of all the results was that the light of the sun was about 300,000 times the average light of a full moon, both being viewed in the heavens at the same altitudes. The details will be found in Bouguer's Traite d'Optique. Wollaston in 1829 tried a series of experiments in which the ratio 801,072 was obtained; but the omission of certain necessary pre-cautions vitiates the result (Phil. Trans., 1829). Bond (Mem. Amer. Acad., 1851, p. 295) adopted a different process. He formed the image of the sun on a silvered globe of some 10 inches diameter; the light of this image was reflected on to a small mercurial thermometer bulb; and then this second image was compared with a Bengal light so moved that the lights appeared to be equal. The same process was adopted with the full moon instead of with the sun. The result was that the sun's light was 470,980 times that of the moon. Seidel long before this date had compared the light of the mean full moon with that of Jupiter in mean opposition; his result is 6430. So also this light of Jupiter was found to be '4864 times that of Venus at her brightest; and Jupiter was found to give 8-2 times the light of a Lyras. If, then, these numbers could be accepted with confidence, we should have the means of comparing the light received from the sun with that received from any of the stars. Adopting these pre-carious numbers on the authorities of Bond and SeidePwe have the following results—
Sun's light = 470,980 that of the full moon.
,, = 622,600,000 ,, Venus at her brightest.
,, = 302,835,000 ,, Jupiter at mean opposition. = 5,970,500,000 ,, Sirius.
Lastly, Bouguer, by comparing the light of the full moon viewed at different altitudes with an artificial light, found that the atmosphere absorbs T877 of the light incident on
it at the zenith of any place. Professor Pritchard, from photometric measures taken at Cairo, found this number to be T57. At Oxford it was -209. Thus Bouguer's determination indicates an absorptive capacity in the atmosphere of Brittany just midway between those of
Oxford and Cairo. Seidel at Munich expresses "surprise " at finding his own results so nearly accordant with Bouguer's. These numbers, therefore, may be regarded as close approximations to fact.1 (o. P.)
Footnote
840-1 Phil. Trans., 1796, p. \U.
The above article was written by: Rev. Prof. Charles Pritchard, D.D., University Laboratory, Oxford.