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CELESTIAL, OR STELLAR , 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
sixth
Ptolemy
indicating thereby an order of magnitude brighter than the average of a fourth, but inferior to that of a thirdand 3.4 for 6, e, and so on; but it was not till the year 1?96 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., 'gob). 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 method which might lead him to more definite results. In the year when Sir John Herschel concluded his photo-metric 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
equator was published in 1886.Dr B. A. Gould (18241896), 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 question. 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 mkt-ore 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 Pkkering's the polar star selected, whether Polaris, with which Meridian the brighter stars were compared, or a Ursae Photometer. 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 re-marked 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 may 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 Zollner 's instrument an artificial star is taken as the standard of comparison. There is only one telescope, and inside the tubenear the eye end is a plate of glass placed at an angle Zoiiner's of 45 with the axis, so that the rays from a lamp which Photometer. 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 being arranged that the lamp 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 object glass, and reading the graduated circle. Professor Pritchard's (18081893) wedge photometer is con- structed on the principle that the absorption of light in passing The Wedge through a uniform medium depends, caeteris paribus, photometer. 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 observa- tion, 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 substi- tute 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, 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 been of great interest
either the wedge itself should be of a greenish hue, or green light should be used in finding the scale-value (the constant B in the formula m=A+Bw). In the second, star magnitudes obtained by extinction with the wedge will agree better with those obtained by photography than those obtained with other visual photo-meters, since photographic action is chiefly produced by rays from E to G in the spectrum, and the E light of ultimate importance with the wedge photometer is nearer this light in character than the D light with which other photometers are chiefly concerned. It would also appear that results obtained with the wedge photometer are independent of the aperture of telescope employed, which is not the case with other photometers. Passing now to the consideration of photographic methods, it is found that when a plate is exposed to the stars, the images Photo- of the brighter stars are larger and blacker than graphic those of the fainter ones, and as the exposure is Photo- prolonged the increase in size and blackness contin- metry. ues. Much of the light is brought to an accurate focus, but, owing to the impossibility of perfect achromatism in the case of refractors, and to uncorrected aberration, diffraction, and possibly a slight diffusion in both refractors and reflectors, there are rays which do not come to accurate focus, grouped in rings of intensity gradually diminishing outwards from the focus. As the brightness of the star increases, or as the time of exposure is prolonged, outer and fainter rings make their impression on the plate, while the impression on the -inner rings becomes deeper. Hence the increase in both diameter and blackness of the star disks. As these increase concurrently, we can estimate the magnitude of the star by noting either the increase in diameter or in blackness, or in both. There is consequently a variety in the methods proposed for determining star magnitudes by photography. But before 'considering these different methods, there is one point affecting them all which is of fundamental importance. In photography a new variable comes in which does not affect eye-observations, viz., the time of exposure, and it. is necessary to consider how to make due allowance for it. There is a simple law which is true in the case of bright lights and rapid plates, that by doubling the exposure the same photographic effect is produced as by. increasing the intensity of a source of light twofold, and so far as this law holds it gives us a simple method of comparing magnitudes. Unfortunately this law breaks down for faint lights. Sir W. Abney, who had been a vigorous advocate for the complete accuracy of this law up till 1893, in that year read a paper to the Royal Society on the failure of the law, finding that it fails when exposures to an amyl-acetate lamp at r ft. are reduced to o'.00i, and " signally fails " for feeble intensities of light; indeed, it seems possible that there is a limiting intensity beyond which no length of exposure would produce any sensible effect. This was had news for astronomers who have to deal with faint lights, for a.simple law of this kind would have been of great value in the complex department of photometry. But it seems possible that a certain modification or equivalent of the law may be used in practice. Professor H. H. Turner found that for plates taken at Greenwich, when the time of exposure is prolonged in the ratio of five star magnitudes the photographic gain is four magnitudes (Mon. Not. R.A.S. lxv. 775), and a closely similar result has been obtained by Dr Schwarzschild using the method presently to be mentioned. Stars of different magnitudes impress on the plate images differing both in size and blackness. To determine the magni-Diatneterastude from the character of the image, the easiest Test of quantity to measure is the diameter of the image, magnitude. and when measurements of position are being made with a micrometer, it is a simple matter to record the diameter as well, in spite of the indefiniteness of the border. Accordingly we find that various laws have been proposed for representing the magnitude of a star by the diameter of its image, though these have usually been expressed, as a preliminary, as relations between the diameter and time of exposure. Thus G. P. Bond found the diameter to increase as the square ofthe exposure, Turner as the cube, Pritchard as the fourth power; while W. H. M. Christie has found the law that the diameter varies as the square of the logarithm of the exposure within certain limits. There is clearly no universal law--it varies with the instrument and the platebut for a given instrument and plate an empirical law may be deduced. Or, without deducing any law at all, a series of images may be produced of stars of known brightness and known exposures, and, using this as a scale of reference, the magnitudes of other images may be inferred by interpolation. A most important piece of systematic work has been carried out by the measurement of diameters in the Cape Photographic Durchmusterung (Ann. Cape Obser. vols, iii., iv. and v.) of stars to the tenth magnitude in the south-ern hemisphere. The measurements were made by Professor J. C. Kapteyn of Groningen, on photographs taken at the Cape of Good Hope Observatory; he adopts as his purely empirical formula magnitude = B/(diameter+ C), where B and C are obtained independently for every plate, from comparison with visual magnitudes. C varies from ro to 28,, and B from 90 to 260. The part of the sky photographed was found to have an important bearing on the value of these constants, and it was in the course of this work that Kapteyn found a systematic difference between stars near the Milky Way and those far from it, which may be briefly expressed in the law, the stars of the Milky Way are in general bluer than the stars in other regions of the sky. It is intended, however, in the present article to discuss methods rather than results, and we cannot here further notice this most interesting discovery. Of methods which choose the blackness of the image rather than the diameter for measurement, the most interesting is that initiated independently by Pickering at Harvard Images out and C. Schwarzschild at Vienna, which consists of Focus. in taking star images considerably out of focus. The result is that these images no longer vary appreciably in size, but only in blackness or density; and that this gradation of density is recognizable through a wide range of magnitudes. On a plate taken in good focus in the ordinary way there is a gradation of the same kind for the faintest stars; the smallest images are all of approximately the same size, but vary in tone from grey to black. But once the image becomes black it increases in size, and the change in density is not easy to follow. The images-out-of-focus method seems very promising, to judge by the published results of Dr Schwarzschild, who used a pre-pared comparison scale of densities, and interpolated for any given star from it. The most satisfactory photographic method would certainly be to take account of both size and blackness, i.e. to measure the total deposit in the film; as, for instance, by interposing the whole image in a given beam of light, and measuring the diminution of the beam caused by the obstruction. But no considerable piece of work has as yet been attempted on these lines. 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 Light of the earth from the sun, the moon and the planets. sun, moon The methods by which these ratios have beenanaPPanets. obtained are as simple as they are ingenious; and for them we are mainly indebted to the labours of P. Bouguer and W. C. Bond (1789-1859). The former 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 con-'cave lens, and in this way an image of the sun 9 in. in diameter was received on a screen. Bouguer found that this light was equal to that of a candle viewed at 16 in. 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 5o ft. 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. W. H. Wollaston in 1829 tried a series of experiments in which the ratio 801,072 was obtained; but the omission of certain necessary precautions vitiates the result (Phil. Trans. 1829). Bond (Mem. Amer. Acad. 1861, p. 295) adopted a different process. He formed the image of the sun on a silvered globe of some 10 in. 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 Lyrae. 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 precarious
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 1877 of the light incident on it at the zenith of any place. Professor Pritchard, from photo-metric measures taken at Cairo, found this number to be 157. 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. Although rather outside the domain of photometry in the strict sense, a word or two may be said here about recent attempts to measure the heat received from the stars, the first being made with the " radio-micrometer " of C. V. Boys. (Proc. Roy. Soc. 1890). This is an extremely delicate instrument for Very little measuring radiant heat, and consists of a very light Heat from thermo-electric circuit (two tiny bars of antimony the Stars. and bismuth soldered together at one edge, the outer edges being connected by a hoop of copper wire) suspended by a quartz fibre (a torsion fibre of the very greatest sensitiveness) in a strong magnetic field. A minute quantity of radiant heat falling on one of the junctions of the circuit sets up a current in the circuit, which thus rotates in the magnetic field until brought to rest by the torsion of the fibre. For use on the heavenly bodies the radiant heat is collected to focus by a reflecting telescope (an object-glass would absorb it), and when the telescope is pointed to the moon the varying radiation from different parts of the disk is beautifully shown. No heat comes from the unlit portion, and of the illuminated portion the maximum is obtained from near the limb. But when pointed to the brightest stars no indications were obtained, although the instrument is sensitive enough to detect the heat from a candle more than a mile off. It seems certain that indications of heat from the stars obtained by previous observers must be spurious. It is also manifest that to obtain satisfactory results even more sensitive apparatus must be devised, and by using a radiometer and the powerful resources of the Yerkes Observatory E. F. Nichols
sixth
1. PHRAATES I., son of Priapatius, reigned c. `175170 B.C. He subdued the Mardi, a mountainous tribe in the Elburz (Justin xli. 5; Isid. Charac. 7). He died young, and appointed as his successor not one of his sons, but his brother Mithradates I. (Justin xli. 5). 2. PHRAATES II., son of Mithradates I., the conqueror of Babylonia, reigned 138127. He was attacked in 130 by Antiochus VII. Sidetes, who, however, in 129 was defeated and killed in a great battle in Media, which ended the Seleucid rule east of the Euphrates (see SELEUCID DYNASTY). Meanwhile the kingdom was invaded by the Scythians (the Tochari of Bactria), who had helped Antiochus. Phraates marched against them, but was defeated and killed (Justin xlii. 1; Johannes Antioch, fr. 66). 3. PHRAATES III., " the God " (Phlegon, fr. 12 ap. Photius cod. 97 and on some of his coins), succeeded his father, Sanatruces, in 70 B.C., at the time when Lucullus was preparing to attack Tigranes of Armenia, who was supreme in western Asia and had wrested Mesopotamia and several vassal states from the Parthian kingdom. Naturally, Phraates declined to assist Mithradates of Pontus and Tigranes against the Romans (see TIGRANES). He supported his son-in-law, the younger Tigranes, when he rebelled against his father, and invaded Armenia (65 B.C.) in alliance with Pompey, who abandoned Mesopotamia to the Parthians (Dio. Cass. xxxvi. 45, 51; Appian, Mithr. 104; Liv. Epit. loo). But Pompey soon overrode the treaty; he acknowledged the elder Tigranes, took his son prisoner, occupied the vassal states Gordyene and Osroene for the Romans, and denied the title of " king of kings, which Phraates had adopted again, to the Parthian king (Plut. Pomp. 33, 38; Dio. Cass. xxxvii. 5 seq.). About 57 Phraates was murdered by his two sons, Orodes I. and Mithradates III. 4. PHRAATES IV., son of Orodes I., by whom he was appointed successor in 37 B.C., after the death of Pacorus. He soon murdered his father and all his thirty brothers (Justin xlii. 5; Plut. Crass. 33; Dio Cass. xlix. 23). He was attacked in 36 by Antonius (Mark Antony), who marched through Armenia into Media Atropatene, and was defeated and lost the greater part of his army. Believing himself betrayed by Artavasdes, king of Armenia, he invaded his kingdom in 34, took him prisoner, and concluded a treaty with another Artavasdes, king of Atropatene. But when the war with Octavianus Augustus
Augustus
5. PHRAATES V., or PHRAATACES, the younger son of Phraates IV. and the " goddess Musa," with whom he is associated on his coins. Under him a war threatened to break out with Rome about the supremacy in Armenia and Media. But when Augustus sent his adopted son Gaius Caesar into the east in order to invade Parthia, the Parthians preferred to conclude a treaty (A.D. 1), by which once again Armenia was recognized as in the Roman sphere (Dio. Cass. lv. ro; Velleius ii. rot). Soon after Phraataces and his mother were slain by the Parthians, about A.D. 5 (Joseph. Ant. xviii. 2, 4). (ED. M.) End of Article: CELESTIAL, OR STELLAR If you wish, you can link directly to this article.
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