1911 Encyclopædia Britannica/Photometry

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PHOTOMETRY (from Gr. φῶς, φωτός, light, μέτρον, a measure), the art and science of comparing the intensities or illuminating powers of two or more sources of light. As in all scientific measurements, its methods are attempts to give quantitative accuracy to the crude comparisons made by the eye itself. The necessity for this accuracy in practical affairs of life has arisen because of the great development of artificial lighting in recent times. The eye soon learns to associate with any particular source of light a quality of brightness or power of illumination which diminishes with increase of distance of the source from the eye or from the surface illuminated. This quality depends upon an intrinsic property of the source of light itself, generally known as its “candle power.” The aim of photometry is to measure this candle power; and whatever be the experimental means adopted the eye must in all cases be the final judge.

In the photometric comparison of artificial lights, which frequently vary both in size and colour, direct observation of the sources themselves does not yield satisfactory results. It is found to be much better to compare the illuminations produced on dead white surfaces from which no regular reflection takes place, or through colourless translucent material uniformly illuminated by the light placed on the further side. By such processes there is always loss of light, and we must be certain that the various coloured constituents of the light are reduced in the same proportion. This necessary condition is practically satisfied by the use of white diffusing screens.

Two principles of radiation underlie many photometric applications, namely, the inverse square distance law, and J. H. Lambert’s “cosine law.” Both can be established on theoretical grounds, certain conditions being fulfilled. But as these conditions are never absolutely satisfied, the applicability of the two laws Inverse Square Distance Law. must in the end be tested by experiment. Since we find that within the errors of observation four candles, placed together at a distance of 2 ft. from a diffusing screen, produce the same illumination as one candle at a distance of 1 ft., we may regard the inverse square distance law as satisfied. Thus if two lights of intensities A and B produce equal illuminations on a screen when their distances from the screen are respectively a and b, we at once write down the relation between the two intensities in the form A : B=a2 : b2. The theoretical basis of the law follows at once from the universally accepted view that light is energy radiating outwards in all directions from the source. If we assume that there is no loss of energy in the transmitting medium, then the whole amount of radiant energy passing in one second across any closed surface completely surrounding the source of light must be the same whatever the size or form of the surface. Imagine for simplicity a point source of light, or its equivalent, a uniformly radiating spherical surface with the point at its centre, and draw round this point a spherical surface of unit radius. Across this surface there will pass a definite amount of radiant energy, in other words a definite total luminous flux, E, which will be the same for all concentric spherical surfaces. Since the area of a spherical surface of radius r is 4 π r2, the flux which crosses unit area is E/4 π r2. This quantity is the “illumination.” It is measured in terms of the unit called the lux, which is defined as the illumination produced by a light of unit intensity on a perfectly white surface at a distance of 1 ft. In the great majority of photometers the illuminations are compared, and the intensities are deduced by applying the law of the squared distances.

Lambert’s cosine law has to do with the way in which a luminous surface sends off its radiations in various directions. It is a matter of common observation that the disk of the sun appears equally bright all over the surface. Careful measurements show that this is not strictly true; but it is sufficiently near the truth Lambert’s cosine Law. |to suggest that under certain definable conditions the law would hold accurately. Again, when a glowing surface is viewed through a small hole in an opaque plate, the brightness is very approximately independent of the angular position of the incandescent surface. This is the same phenomenon as the first mentioned, and shows that the more oblique, and therefore larger, element of surface sends the same amount of radiation through the hole. Hence the amount per unit surface sent off at a given angle with the normal must be less than that sent off in the direction of the normal in the inverse ratio of the areas of the corresponding normal and oblique elements, that is, as the cosine of the given angle to unity. For most practical purposes, and so long as the obliquity is not great, Lambert’s law may be assumed to hold.

In almost all accurate methods of photometry the aim is to bring the illuminating powers of the two sources to equality. This may be effected by altering the distance of either light from the illuminated surface. Or we may use polarized light and diminish the intensity of the stronger beam by suitable rotation of a Nicol prism, a method particularly useful in spectrophotometer’s. The same result may also be effected by interposing absorbent disks, the precise absorbing powers of which must, however, be known with great accuracy. Another useful Talbot’s Law.method is that first described by H. Fox Talbot in 1834, and used with effect by Professor William Swan (1849), and more recently by Sir W. de W. Abney. Talbot’s law is thus enunciated by H. von Helmholtz: “When any part of the retina is excited by regularly periodic intermittent light, and when the period is sufficiently short, the resulting impression will be continuous, and will be the same as that which would be produced if the whole light were distributed uniformly throughout the whole period.” Talbot deduced the principle from the well-known experiment in which a continuous luminous line is produced by rapid rotation of a luminous point. If the principle be granted, it is obvious that any mechanism by which a ray of light is obstructed in a regularly rhythmic manner during definite intervals t ′, separated by intervals t, during which the light is allowed to pass, will have the effect of reducing the apparent brightness of the ray in the ratio t/(t + t ′) This is frequently accomplished by placing in the ray a rotating disk perforated by radial sectors, the so-called Talbot disk.

If photometric results are to be of general value it is essential to have a unit in which to express all other intensities. For example, electric lights are classified according to their “candle-power.” The candle, in terms of whose brightness the brightness of other sources of Standards
of Light.
light is to be expressed, must, of course, fulfil the conditions demanded of all standards. It must give under definite and easily realizable conditions a definite and constant luminous effect, and it must be easily reproducible. The earlier attempts to get a candle of constant brightness were not very satisfactory. The British standard is a sperm candle which weighs 1/6 ℔, and loses in burning 120 grains per hour. It is found that these conditions are not sufficient to determine the luminous power of the candle, since the length and shape of the wick, the height of the flame, and the composition, temperature and humidity of the atmosphere all have an effect upon its brightness. The same is true of other similar sources of light—for example, the German standard candle, which is made of paraffin, has a diameter of 2 cm, and has its wick cut until the flame is 5 cm. high, but which with all precautions suffers continual alterations in brightness. For ordinary practical purposes, however, these candles are steady enough. Other kinds of flame have also been used as a standard source of light. The oldest of these is the French Carcel lamp, which is provided with a cylindrical Argand burner, and gives the standard brightness Vernon-Harcourt Pentane Standard. when 42 grammes of colza oil are consumed per hour. The supply and draught are regulated by clockwork. A. G. Vernon-Harcourt’s pentane standard, in which a mixture of gaseous pentane and air is burnt so as to maintain a flame 2.5 in. high at ordinary barometric pressure, gives good results, and is readily adjustable to suit varied conditions. Several forms of this standard have been constructed, one of the most important being the 10 candle-power pentane lamp, in which air saturated with pentane vapour is burnt in a specially-designed burner resembling an Argand burner. For photometric purposes a definite length of the lower part of the flame is used, the upper part being hidden within an opaque tube. The amyl-acetate lamp designed by H. von Hefner-Alteneck has been elaborately studied by the German authorities, and at present is probably more used than any other flame for photometry. It is of simple construction, and gives the standard Hefner Lamp. brightness when it burns with a flame 4 cms. in height in still air of humidity 0.88% and free of carbon dioxide. The presence of carbon dioxide and increase in the humidity have a marked effect in diminishing the brilliancy of the flame. If the vapour pressure is e and the barometric pressure p, the strength of the flame, when all other conditions are fulfilled, is given by the formula

1.049 − 5.5e/(pe)

One disadvantage for photometric purposes is the reddish colour of the flame as compared with the whiter artificial lights in general use.

For an interesting account of the various experimental investigations into the properties of the Hefner flame see E. L. Nichols, “Standards of Light,” Transactions of the International Electrical Congress, vol. ii. (St Louis, 1904). Ångstrom’s determination of the radiation of the flame in absolute energy units is also of special interest.

Attempts have been made, but hitherto with limited success, to construct a convenient standard with acetylene flame. Could a satisfactory burner be devised, so that a steady brilliancy could be easily maintained, acetylene would, because of its intense white light, soon displace all other flames as standards.

J. Violle has proposed to use as standard the light emitted by a square centimetre of surface of platinum at its melting-point, but there are obvious practical difficulties in the way of realizing this suggested standard. J. E. Petavel, who carefully examined the necessary conditions Violle’s Platinum Standard. for producing it (Proc. Roy. Soc. 1899), finds that the platinum must be chemically pure, that the crucible must be made of pure lime, that the fusion must be by means of the oxy-hydrogen blow-pipe, that the gases must be thoroughly mixed in the proportion of 4 volumes of hydrogen to 3 of oxygen, and that the hydrogen must contain no hydro-carbons. Under these conditions the variation in the light emitted by the molten platinum would probably not exceed 1%. O. Lummer and F. Kurlbaum have proposed as a standard a strip of platinum foil 25 mm. wide and .015 mm. thick brought to incandescence by an electric current of about 80 amperes. The temperature is gradually increased until 1/10th of the total radiation is transmitted through a water trough 2 cm. in width. This ratio is determined by means of a bolometer, and so long as it is adjusted to 1/10th the light is practically constant.

For comparative photometric work the incandescent electric light is very convenient, having the one great advantage over candles and flames that it is not affected by atmospheric changes. But it does not satisfy the requirements of a primary standard. It ages with use, and when run at constant voltage gradually loses in brilliancy, partly because of changes in the filament itself, partly because of the deposit of carbon on the interior of the bulb. Professor J. A. Fleming has shown that very good results can be obtained if carbon filaments carefully selected Fleming’s Incandescent Lamp Standard. and run in ordinary bulbs for a definite time at a little above their normal voltage are remounted in large clear glass bulbs 6 or 8 in. in diameter. If used sparingly, and never above their marked voltage, these large incandescent bulbs have been found to remain constant for years, and therefore to be eminently suitable as secondary standards. In his Handbook for the Electrical Laboratory and Testing Room (vol. ii) Fleming concludes that the best primary standards are the Violle incandescent platinum and the Vernon-Harcourt pentane one-candle flame; and that the most convenient practical standards are the Hefner lamp, the ten-candle pentane lamp, and the Fleming large bulb incandescent electric lamp. Comparisons of the intensities of these various standards do not give quite concordant results. Thus three different authorities have estimated the 10-candle pentane lamp as being equal to 10.75, 11.0, 11.4 Hefner lamps.

A specially constructed instrument or piece of apparatus for comparing light intensities or illuminations is called a photometer The earlier forms of photometers were very simple and not capable of giving very precise results. The principles of construction are, Photometers.however, the same in all the recognized forms down to the most elaborate of recent inventions Two of the earliest forms were described by P. Bouguer and W. Ritchie. The Ritchie wedge constitutes the basis of many varieties of type. The two lights to be compared illuminate the sides of the wedge, which is Ritchie’s Wedge.placed between them, so that the eye set in front of the wedge sees the two sides illuminated each by one of the lights. The edge should be as sharp as possible so that the two illuminated surfaces are in close contact. The illuminations are made equal either by shifting the Wedge along the line joining the lights or by moving one of the lights nearer to or farther from the wedge as may be required The lights given out by the sources are then as the squares of the distances from the matched parts of the surfaces. Count Rumford suggested the comparison of the intensity of the shadows of the same object thrown side by side on a screen by the two lights to be compared. In this Rumford’s Photometers.case the shadow due to one source is lit up by the other alone; and here again the amounts of light given out by the sources are as the squares of their distances from the screen when the shadows are equally intense. The shadow-casting object should be near the screen, so as to avoid penumbra as much as possible; yet not too near, so that the shadows may not overlap.

R. Bunsen suggested the very simple expedient of making a grease-spot on white paper for photometric purposes. When Bunsen’s the paper is equally illuminated from both sides the grease-spot cannot be seen except by very close inspection. In using this photometer, the sources are placed in one line with the grease-spot, which liesBunsen’s Photometers. between them and can be moved towards one or other. To make the most accurate determinations with this arrangement the adjustment should first be made from the side on which one source lies, then the screen turned round and the adjustment made from the side of the other source-in both cases, therefore, from the same side of the paper screen. Take the mean of these positions (which are usually very close together), and the amounts of light are as the squares of the distances of the sources from this point The efficiency of the Bunsen photometer has been improved by using two inclined mirrors so that the eye views both sides of the paper simultaneously.

Sir Charles Wheatstone suggested a hollow glass bead, silvered internally, and made to describe very rapidly a closed path, for When" use as a photometer. When it is placed between two sources we see two parallel curves of reflected light, one due to each source. Make these, by trial, equally bright; and the amountsWheatstone’s Photometer. of light from the sources are, again, as the squares of the distances.

Fig. 1.

William Swan’s prism photometer, invented in 1859, is a beautiful application of the principle embodied in Bunsen’s grease-spot photometer (see Trans. Roy. Soc. Ed. vol. xxi) The essential part of the instrument is fundamentally the same as that described by O. Lummer and E Brodhun in 1889. It consists of two equal right-angled isosceles glass Swan’s Double Prism.prisms placed with their diagonal faces together so as to form a cube (fig. 1), and cemented together by a small patch of Canada balsam, which spreads out into a circle when the prisms are pressed together. In the figure, which represents a central section of the bi-prism, the Canada balsam is represented by the letter N. The light from two illuminated surfaces, PQ, RS, is allowed to fall perpendicularly on the faces AB, AD. In each case that part of the light falling internally on the portion of the diagonal face which is not backed with the Canada balsam is totally reflected. On the other hand, the light which falls on the portion backed by the Canada balsam is almost wholly transmitted. Thus an eye placed in the position qtp receives light from both sources, the surface RS supplying nearly all the light that seems to come from the patch N, and the surface PQ supplying all the light which seems to come from the region immediately surrounding N. The patch N will in general be visible; but it will quite disappear when the luminosity of the ray Tt, which traverses the Canada balsam, is exactly equal to the luminosity of the rays Pp, Qq, which have come after total reflection from the surface PQ. This condition of invisibility of N is arrived at by adjusting the positions of the sources of light which illuminate the surfaces PQ, RS. The brightnesses of the two sources will then be as the squares of their distances from their respective screens.

The essential part of Lummer and Brodhun’s photometer is a combination of prisms very similar to Swan’s. In its most improved form the bi-prism or "optical cube" has one of its component prisms cut in a peculiar manner The diagonal face is partly cut away, so that the central part only of this face can be brought into contact with the Lummer and Brodhun’s Photometer.diagonal face of the other prism. The Canada balsam is dispensed with, the surfaces being pressed closely together so that no layer of air is left between them. In order to make the instrument convenient for use with an optical bench, Lummer and Brodhun make the illuminated surfaces which are to be compared the opposite sides of an opaque screen set in the continuation of the diagonal (CA) of the bi-prism, the rays being brought by reflection from symmetrically situated mirrors so as to enter the sides AB and AD perpendicularly. An important modification, due also to Lummer and Brodhun, is the fallowing By means of a sand-blast a portion which may be called r, is removed from one half of the diagonal face of the one prism, and from the other half of the same prism there is removed in like manner all but a part l corresponding to the part r. The portions which have not been removed are pressed close to the diagonal face of the other prism, and become the parts through which light is freely transmitted. On the other hand, the light which enters the second prism and falls on the portions of surface backed by the layers of air filling the cut-out parts is totally reflected. The general result is the production of two similar luminous patches l and r, each of which is surrounded by a field of the same intensity as the other patch. When the photometric match is made the whole region will be uniformly bright But, by insertion of strips of glass so as to weaken equally the intensity in the surrounding fields, the match will be obtained when these fields are made of equal intensity and when at the same time the two patches differ equally in intensity from them. Under these conditions the eye is abale to judge more certainly as to the equality of intensity of the two patches, and an untrained observer is able to effect a comparison with an accuracy which is impossible with most forms of photometer.

J. Joly’s diffusion photometer consists of two equal rectangular parallelepiped’s of a translucent substance like paraffin separated by a thin opaque disk. It is set between the sources of light to be compared in such a way that each paraffin block is illuminated by one only of the sources, and is adjusted until the two blocks appear to be of the same brightness.Joly’s Photometer. The method is made more sensitive by mounting the photometer on an elastic vibrator so as to render it capable of a slight to-and-fro oscillation about a mean position.

A form of photometer which is well adapted for measuring the illumination in a region is that due to L. Weber. It consists of a horizontal tube across one end of which is fitted another, tube at right angles. This second tube can be rotated into any position perpendicular to the horizontal tube. Where the axes of the two tubes meet is placed in the later forms of Weber’s Photometer.the instrument one of Lummer and Brodhun’s modified Swan cubes. At the other end of the horizontal tube a standard flame is set illuminating a piece of ground glass which may be moved to any convenient position in the tube. The eye looks along the cross tube, at the farther end of which is placed another piece of ground glass illuminated from the outside. The illuminations of the two pieces of ground glass as viewed through the photometer double prism are brought to equality, either by shift of the ground glass to or from the standard light, or by means of two Nicol prisms placed in the cross tube. One advantage of the instrument is its portability.

The photometry of incandescent electric lamps has led to several special modifications and devices. The candle power varies distinctly in different horizontal directions, and one measurement in any particular direction is not sufficient. Sometimes the lamp is rotated about three times a second about a vertical axis and Incandescent Electric Lamp.an average value thus obtained. But there is always a risk of the filament breaking; and in all cases the effect of centrifugal force must alter the form of the filament and therefore the distances of the different parts from the screen. Accuracy demands either the measurement of the radiation intensity in a number of directions all round the lamp, or one combined measurement of as many rays as can be conveniently combined. One of the best methods of effecting this is by means of C. P. Matthews's integrating photometer. By the use of twelve mirrors arranged in a semicircle whose diameter coincides with the axis of the lamp, twelve rays are caught and reflected outward to a second set of twelve mirrors which throw the rays on to the surface of a photometric screen. This combined effect is balanced by the illumination produced by a standard lamp on the other side of the screen (see Trans. Amer. Inst. Elect. Eng., 1902, vol. xix.).

So long as the lights to be compared are of the same or nearly the same tint. the photometric match obtained by different observers is practically the same. If, however, they are of distinctly different colours, not only do different observers obtain different results but those obtained by the same observer at different times are not always in agreement. Helmholtz was of opinion that photometric comparison of the intensities of different coloured lights possessed no real intrinsic value. There can be little doubt that in a rigorous sense this is true. Nevertheless it is possible under certain conditions to effect a comparison which has some practical value. For example, when the intensities of two differently coloured lights differ considerably there is no difficulty in judging which is the stronger. By making the one light pass through a fairly large range of brightness we may easily assign limits outside which the intensities are undoubtedly different. After some experience these limits get close; and many experimenters find it possible, by taking proper precautions, not only to effect a match, but to effect practically the same match time after time. According to Abney,Abney’s Experiments. whose memoirs on colour photometry (Phil. Trans., 1886, 1892) form a most important contribution to the subject, the observer in making his judgment as to the equality of luminosity of two patches of colour placed side by side must not begin to think about it, but must let the eye act as unconsciously as possible. His method was to compare the coloured patch with white light given by a particular standard and cut down to the proper intensity by use of a Talbot's rotating sector, which could be adjusted by means of a suitable mechanism while it was rotating.

At the same time, although the eye may be able to effect a definite matching of two patches of colour of a particular luminosity, it has been long known that a change in the luminosity will destroy the apparent equality. This depends upon a physiological property of the retina discovered by J. E. Purkinje in 1825 (see below, Celestial Photometry). In virtue of this property the blue and violet end of the spectrum is more stimulating to the eye than the red end when the general luminosity is low, whereas at high luminosities the red gains relatively in brightness until it becomes more stimulating than the blue. Unless therefore account is taken in some definite measurable manner of the absolute brightness, there must always be some uncertainty in the photometric comparison of the intensities of differently coloured sources of light.

Instead, however, of trying to effect a photometric match in any of the ways which have been found sufficient when the sources are of the same or nearly the same tint, we may effect important practical comparisons in what is called hetero chromatic photometry by an appeal to other physiological properties of the eye. For example, the power of clearly discriminating patterns in differently coloured lights of various intensities is obviously of great practical importance; and this power of detailed discrimination may be made the basis of a method of photometry. According to this method two lights are arranged so as to illuminate two exactly similar patterns of lines drawn, for example, on the sides of a Ritchie wedge, and their distances are adjusted until the patterns are seen equally distinct on the two sides. Application of the usual distance law will then give the relation between the two lights. A discrimination photometer constructed on this principle has been designed by J. A. Fleming. Its results do not agree with the indications of an ordinary luminosity photometer; for it is found that the eye can discriminate detail better with yellow than with blue light of the same apparent luminous intensity.

Another and very promising method of photometry depends upon the duration of luminous impressions on the retina. J. A. F. Plateau observed in 1829 that the blending into homogeneous impression of a pattern of alternate sectors of black and some other colour marked on a diskFlicker Photometry. when that disk was rotated occurred for rates of rotation which depended on the colour used. A form of experiment suggested in Professor O. N. Rood’s Modern Chromatics seems to have been first carried out by E. L. Nichols (Amer. Journ. of Science, 1881). A black disk with four narrow open sectors was rotated in front of the slit of a spectroscope. When the rotation was not too quick the yellow part of the spectrum appeared as a succession of flashes of light separated by intervals of darkness of appreciable length, whereas towards both the red and violet ends no apparent interruption in the steady luminosity could be observed. As the rate of rotation increased the part of the spectrum in which flickering appeared contracted to a smaller length extending on each side of the yellow, and finally with sufficiently rapid alternation the yellow itself became steady This seems to show that the retinal image persists for a shorter time with yellow light than with light of any other colour; for with it the intervals of darkness must be shorter before 8. continuous impression can be obtained. Now yellow is the most luminous part of the spectrum as it affects the normal human eye; and E. S. Ferry (Amer. Journ. of Science, 1892) has shown that the duration of luminous impression is mostly, if not entirely, determined by the luminosity of the ray. Hence the determination of the minimum rate of intermittence at which a particular colour of light becomes continuous may be regarded as a measure of the luminosity, the slower rate corresponding to the lower luminosity. Although in the experiment just described the red part of the ordinary solar spectrum becomes continuous for a slower rate of intermittence than the yellow part, yet we have simply to make a red ray as luminous as the yellow ray to find that they become continuous for the same rate of intermittence. It is, however, highly improbable that the duration of impression depends only on the luminosity of the light and not to some extent upon the wave-length. There are indeed phenomena which require for their explanation the assumption that the duration of luminous impression does depend on the colour as well as on the brightness.

Nevertheless the luminosity is by far the more important factor, as shown by Ogden N. Rood’s experiments. He found (Amer. Journ. of Science, 1893) that, when a disk whose halves differ in tint but not in luminosity is rotated rather slowly, the eye of the observer sees no flickering such as is at once apparent when the halves differ slightly in luminosity. Rood himself suggested various forms of photometer based on this principle. In his latest form (Amer. Journ. of Science, Sept. 1899) the differently coloured beams of light which are to be compared photometrically are made to illuminate the two surfaces of a Ritchie wedge set facing the eye. Between the wedge and the eye is placed a cylindrical concave lens, which can be set in oscillation by means of a motor in such a way that first the one illuminated surface of the wedge and then the other is presented to the eye in sufficiently rapid alternation. The one source of light is kept fixed, while the other is moved about until the sensation of flicker disappears. From work with this form of instrument Rood concluded that “the accuracy attainable with the flicker photometer, as at present constructed, and using light of different colours almost spectral in hue, is about the same as with ordinary photometers using plain white light, or light of exactly the same colour.”

Various modifications of Rood’s forms have been constructed from time to time by different experimenters. The Simmance and Abady flicker photometer is an ingenious and yet mechanically simple method by which (as it were) the wedge itself is made to oscillate so as to throwSimmance and Abady’s Photometer. on the eye in rapid succession, first the one side and then the other. The rim of a wheel of white material is bevelled in a peculiar manner. The sharp edge, which passes slightly obliquely across the rim from one side of tie wheel to the other and back again, is the meeting of two exactly similar conical surfaces facing different ways and having their axes parallel to, but on opposite sides of, the axis of rotation of the wheel. As the wheel rotates with its rim facing the eye, the intersection of the two surfaces crosses and recrosses the line of vision during each revolution. Hence first the one illuminated side and then the other are presented to the eye in rapid alternation. The inventors of this instrument claim that their instrument can gauge accurately and easily the relative intensities of two lights, whether of the same or of different colour (Phil. Mag., 1904). There is no doubt that results obtained by different observers with a flicker photometer are in better agreement than with any other form of photometer. The comparative ease with which the balance is obtained even when the tints are markedly different shows that its action depends upon a visual distinction which the eye can readily appreciate, and this distinction is mainly one of brightness.

The spectrophotometer is an instrument which enables us to make photometric comparisons between the similarly coloured portions of the spectra of two different sources of light, or of two parts of the same original source after they have passed through different absorbing media. WhenSpectrophotometry. it is desired to compare the intensities of the spectra from two different sources a convenient form is the one described by E. L. Nichols. A direct vision spectroscope mounted upon a carriage travels along a track between the two sources. In front of the slit two right-angled triangular prisms are set so that the light from each source enters the one side of one prism perpendicularly and is totally reflected into the spectroscope. The two spectra are then seen side by side. Attention being fixed on some chosen narrow portion, say, in the green, the instrument is moved along the track between the sources until the two portions appear of the same intensity. The process is then repeated until the whole spectrum has been explored.

Fig. 2.

In Lummer and Brodhun's form of spectrophotometer the rays to be compared pass in perpendicular lines through the modified Swan double prism, and then together side by side through a spectroscope. By means of a simple modification in the form of the two prisms, Professor D. B.Bruce's Spectrophotometer. Brace (Phil. Mag., 1899) made the combined prism serve to produce the spectra as well as to effect the desired comparison. In this arrangement the compound prism ABC (fig 2) is made up of two equal right-angled prisms ADB and ADC placed with their longer sides in contact, so that the whole forms an equilateral prism with three polished faces. Bart of the interface AD is silvered, the silvering forming a narrow central strip running parallel to AD. Along the rest of the interface the two prisms are cemented together with Canada balsam or other material having as nearly as possible the same refractive index as the glass. When two rays R S enter symmetrically from opposite sides of the base of the compound prism as shown in the diagram, the ray R will pass through the prism except where the silver strip intercepts it, and) will form a part of a spectrum visible to the eye place at R', while to the same eye there will be visible the similarly dispersed ray SS' reflected from the silvered surface. Thus two systems of incident parallel rays of white light will form on emergence two spectra with corresponding rays exactly parallel. Wit these and other forms of instrument the aim of the experimenter is to make the two spectra of equal intensity by a method which enables him to compare the original intensities of the sources. In most cases the relative intensities of the portions of the spectra being compared cannot conveniently be altered by varying the distances of the sources. Recourse is therefore generally ha to one of the other methods already mentioned, such as the use of polarizing prisms or of rotating sectors. Under certain conditions K. Vierordt's method of allowing the two rays to pass through slits of different width leads to good results, but too great confidence cannot be placed upon it.

In other types of spectrophotometer, such as t ose associated with the names of H Trannin, A. Crova, H. Wild, G. Hufner, J. Konigsberger, A. Konig, F F. Martens and others, the equalization in brightness of two rays is effected by using polarized light, which can be cut down at pleasure by rotation of a Nicol prism. For example, in the Konig-Martens instrument the two rays which are to be compared enter the upper and lower halves of a divided slit. After passing through a lens they pass in succession through (1) a dispersing prism, (2) a Wollaston prism, (3) a bi-prism, and are finally focused where the eight spectra so produced can be viewed by the eve. Of these only twoKonig-Martens's Spectrophotometer. are made use of, the others being cut out. These two are polarized in perpendicular planes, so that if between the spectrum images and the eye a Nicol prism is introduced the intensities of any two narrow corresponding portions of the two spectra can be readily equalized. In terms of the angle of rotation of the Nicol the relative intensities of the original rays can be calculated. An important application of the spectrophotometer is to measure the absorptive powers and extinction coefficients of transparent substances for the differently coloured rays of light. By appropriate means the intensities of chosen corresponding parts of the two contiguous spectra are made equal-in other words, a match is established. Into the path of the rays of one of the spectra the absorbent substance is then introduced, and a match is again established. A measure of the loss of luminosity due to the interposition of the absorbent substance is thus obtained.

To facilitate experiments of this nature Dr J. R. Milne has devised a spectrophotometer which presents some novelties of construction (see Proceedings of the Optical Convention, 1905, vol. i.). The light from a bright flame is suitably projected by a lens so as to illuminate a small hole in theMilne's Spectrophotometer. end of the collimator. The rays from this point-source are made parallel by the collimator, and then pass, partly through the absorbing medium, partly through the space above it: These two parts of the original beam are transmitted through a dispersing prism and then fall upon a screen with two similar rectangular openings, the upper one allowing the unabsorbed part of the beam to pass, the lower that part which has been transmitted through the absorbing medium. The objective of the observing telescope converges the rays suitably upon a Wollaston prism, so that two spectra are seen side by side, having their light polarized in perpendicular planes. A Nicol prism is placed between the Wollaston prism and the eye-piece of the telescope, and by its rotation in the manner already described the intensities of any two corresponding portions of the two spectra can be brought to equality. By careful attention to all necessary details Milne shows that his instrument satisfies the requirements of a good spectrophotometer; for (1) the rays through the absorbing medium can be made strictly parallel; (2), the two spectra can be brought with ease accurately edge to edge without any diffraction effects; (3) the plane of the delimiting screen can be made conjugate to the retina of the observer's eye; (4) not only do the two spectra touch accurately along their common edge, but the two fans of rays which proceed from every point of the common edtge lie in one and the same plane; (5) the eye is called upon to ju ge the relative intensities not of two narrow slits but o two broad uniformly illuminated areas. Milne also points out that this instrument can be used as a spectropolarimeter.

E. L. Nichols considers that spectrophotometer's which depend for their action upon the properties of polarized light are necessarily open to serious objections, such as: selective absorption in the calcspar, altering the relative intensities of the constituents in the original rays; selective losses by reflection of polarized rays at the various optical surfaces; and the necessarily imperfect performance of all forms of polarizing media. To eliminate these defects as far as possible great care in construction and arrangement is needed, otherwise corrections must be applied.

It is evident that if the successive parts of two spectra are compared photometrically we may by a process of summation obtain a comparison of the total luminosities of the lights which form the spectra. This process is far too tedious to be of any practical value, but sufficiently accurate results may in certain cases be obtained by comparison of two or more particular parts of the spectra, for example, strips in the red, green and blue. Similar in principle is the method suggested by J. Macé de Lepinay, who matches his lights by looking first through a red glass of a particular tint and then through a chosen green. If R and G represent the corresponding ratios of the intensities, the required comparison is calculated from the formula I = R/1 + 0.208 (1 − GR) A. Crova, one of the earliest workers in this subject, effects the photometric comparison of differently coloured lights by matching those monochromatic rays from the two sources which have the same ratio of intensities as the whole collected rays that make up the lights. Careful experiment alone can determine this particular ray, but were it once ascertained for the various sources of light in use the method would have the merits of rapidity and accuracy sufficient for 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.  (C. G. K.) 

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 (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 μέγεθος 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, μ, the initial letter in μείζων (greater), and to those in the same order which exhibit a lustre inferior to that of the average he affixes the letter ε, the initial letter of ελάσσων. 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 δ, μ,—indicating thereby an order of magnitude brighter than the average of a fourth, but inferior to that of a third—and 3·4 for δ, ε, 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 would be absolutely fixed and would constantly reflect the light of this star down the axis of its telescope; in practice a slight motion Pickering’s Meridian Photometer. 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 λ 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 Zöllner’s Photometer. 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 The Wedge Photometer. 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 Purkinje Phenomenon. 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, 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 photometers, 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 of the brighter stars are larger and blacker than graphic those of the fainter ones, and as the exposure is prolonged the increase in size and blackness continues. 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 bo 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 1 ft. are reduced to 0s·001, 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 bad 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 magnitude from the character of the image, the easiest quantity to measure is the diameter of the image, 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, m relations between the diameter and time of exposure. Thus G. P. Bond found the diameter to increase as the square of the 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 plate-but 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 southern 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


where B and C are obtained independently for every plate, from comparison with visual magnitudes. C varies from 10 to 28, and B from go 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 and C. Schwarzschild at Vienna, which consists 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 prepared 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 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 Light of the Sun. Moon and Planets. 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 concave 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 50 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 Traité 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 α 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 numbers on the authorities of Bond and Seidel we 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 ⋅1877 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 ·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 Heat from the Stars. measuring radiant heat, and consists of a very light thermo-electric circuit (two tiny bars of antimony 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 succeeded in 1898 and 1900 in obtaining indications of heat from Arcturus and Vega, as well as from Jupiter and Saturn (Astrophysical Journ. xiii., 101), the heat received being comparable with that from a candle 6 m. away We may place alongside this result that obtained by W. J. Dibdin (Proc. Roy. Soc. April 1892), who compared candlelight with twenty-one stars ranging to the sixth magnitude, and found the light of a second magnitude star equal to that of a candle at 1260 ft.  (H. H. T.)