AT the close of the memoir published in the Proceedings of the Royal Society, Mr. W. D. Niven, referring to Maxwell’s scientific work, says:—

It will probably be many years before an approximate estimate can be formed of the value of Maxwell’s work. In the following pages no attempt has been made to give more than a brief account of a few of his principal contributions to science. The chief subjects referred to have, for convenience, been arranged in the following order:—

1. Experiments on Colour Vision and other contributions to Optics.

2. Investigations respecting Elastic Solids.

3. Pure Geometry.

4. Mechanics.

5. Saturn’s Rings.

6. Faraday’s Lines of Force, and Maxwell’s Theory of the Electro-magnetic Field, including the Electro-magnetic Theory of Light and other investigations in Electricity.

7. Molecular Physics.

1. The subject of colour-vision attracted Clerk Maxwell’s attention at an early period. In dealing with phenomena of this class, we must remember that it is necessary to distinguish between the sensation itself and its physical cause, or between the subjective and objective aspects of the same phenomenon. Thus a pure musical tone consists of a regular succession of similar vibrations, and two tones may differ in the extent of these vibrations, and in the number which take place in a second. Corresponding to these physical differences, are experienced differences in the intensity or loudness, and the pitch of the note. Light, like sound, consists objectively of certain periodic disturbances or vibrations of a medium, but differs from sound in the character of the motion, the nature of the medium which transmits it, and the number of vibrations which take place in a second. The simplest kind of light consists, like a pure tone in sound, of a regular succession of similar vibrations, the extent of which determines the intensity of the light, while their rapidity corresponds to the colour sensation produced. The constitution of ordinary white light is much more complicated. Newton allowed a beam of sunlight to pass through a prism, and then to fall upon a screen, when, instead of a white patch of light, he obtained a spectrum, or continuous band of colour, varying from crimson through scarlet, orange, yellow, green, blue, to violet. Rays corresponding to this infinite variety of colour must, therefore, exist together in white solar light, and these rays differ physically from one another in the rapidity of the vibrations of which they consist; the deep crimson corresponding to less than 400,000,000,000,000 vibrations per second, and the extreme violet to more than 700,000,000,000,000, the length of a wave in air being, in the first case, about StartFraction 1 Over 39 comma 000 EndFraction of an inch, and, in the second case, about StartFraction 1 Over 68 comma 000 EndFraction of an inch.

But white light is not necessarily of so complex a nature as sunlight; thus it may consist of a mixture of red, green, and blue lights simply, or of yellow and blue, or greenish-yellow and violet, or of other mixtures of two or more kinds of light, each in itself homogeneous. When this is the case, the constitution of the light is revealed when it is allowed to pass through a prism, for it is then separated into its simple constituents which, on emerging from the prism, pursue different paths. Similarly, various kinds of homogeneous light may be matched by means of a mixture of lights of other colours appropriately chosen. Thus orange light of a particular hue may be the homogeneous light of the spectrum, or it may be a mixture of red and yellow or of red and green lights, which is chromatically identical with the homogeneous orange, but optically different, inasmuch as the mixture can be resolved into its constituents by means of a prism, while the homogeneous orange light may be passed through any number of prisms and yet retain its perfect homogeneity.

These results were accounted for by Thomas Young (1801), on the supposition that there are three separate sensations which are excited to different degrees—the proportion in which each is excited depending on the nature of the light. He was of opinion that these three sensations were red, green, and violet, and that all other hues were compound colours, though they might correspond to a simple kind of light. “The quality of any colour depends, according to this theory, on the ratio of the intensities of the three sensations which it excites, and its brightness depends on the sum of these three intensities.”

Young’s colour diagram was a triangle, at the angular points of which he placed the three colours corresponding, according to his theory, with the primary sensations; along the sides of the triangle were placed the colours formed by mixing these two and two together, while within the triangle were to be found the colours resulting from mixtures of all three in different proportions. The position of each colour was determined by finding the centre of gravity, of two or three heavy particles placed at the angular points of the triangle, the weight of each particle being proportional to the quantity of the corresponding light employed in the mixture.

Although the light of the spectrum which corresponds to any particular spectral colour is simple in its constitution, consisting of a definite number of waves per second, and ordinary white light is a combination of an infinite number of such rays, varying in rapidity of vibration from the extreme red to the extreme violet, yet the mechanism of vision appears to be of a threefold character, so organised that light of each particular wave-length affects in different proportions the three colour senses, the hue depending on the relative amounts to which they are severally excited, as explained by Young. An analogy may help to make this distinction, clearer; thus, it has been customary to speak of the heating power, the illuminating power, and the photographic power, of any particular kind of light; and in the solar spectrum formed by a glass prism the greatest heating power is possessed by the ultra red rays, the greatest illuminating power (judged by normal eyes) by the greenish yellow rays, and the greatest photographic power (in relation to silver salts) by the ultra-violet rays; but we do not thereby imply that there are three separate classes of rays in solar light, consisting respectively of heating rays, illuminating rays, and chemical rays: we simply mean that any particular homogeneous ray possesses each of these three powers to a certain extent. Similarly any ray of the spectrum may be capable of stimulating each of three independent colour sensations, but it does not follow that it consists physically of three different kinds of light.

In the Philosophical Magazine for 1852 there is an account of an experiment by Helmholtz, which consisted in mixing the colours of the spectrum by forming two spectra from slits at right angles to each other. It is obvious that if the breadth of each spectrum be equal to its length, every pair of colours in the whole spectrum will in this way be superposed. In Helmholtz’s experiment it appeared that a mixture of yellow and indigo produced white.

Maxwell’s first published experiments on the mixture of coloured lights, executed while he was a B.A. at Cambridge, had reference to the mixtures of coloured lights obtained from coloured papers. One of the best accounts of these experiments will be found in the paper read before the Royal Society of Edinburgh by Clerk Maxwell on 19th March 1855.

The instrument first employed was a top, constructed by Maxwell himself; but he afterwards had tops made by Mr. Bryson of Edinburgh. The coloured papers were cut into circular discs, with a small hole in the centre to admit the spindle of the top, and were slit along a radius from the circumference to the central hole. By this means two or more discs could be placed together, and by turning one relatively to the others, more or less of any particular disc could be made visible from above. The top consisted of a disc of metal, covered with white paper and mounted on a suitable spindle, the circumference of which was divided into 100 equal parts. Two sizes of discs were employed; the larger discs having been adjusted as required, were placed on the graduated plate, and the smaller discs above them. The plate then presented an appearance similar to that sketched in the adjoining figure. The employment of the apparatus depends on the fact, observed by Hartley the psychologist, that visual impressions remain for some time on the retina even after the source of light has been removed. Thus, suppose that the larger discs are respectively red, green, and blue, and suppose that we look at the middle of the red sector and then spin the top. If the spinning is sufficiently rapid the impression produced by the red light will not have diminished sensibly before the green paper takes the place of the red, and the green light produces its effect on the same portion of the retina, and this again is followed by blue before either the red or the green sensations have sensibly diminished, and then the whole process is repeated many times in a second. The impressions due to the three coloured lights are therefore blended on the retina, and it can be shown experimentally that the tint observed is the same as when the three kinds of light in the same relative proportions are allowed to fall simultaneously upon the eye. The colour top, therefore, enables us to mix together, in any definite proportions, which can be changed at will, the lights from differently coloured papers, and to observe the effect produced by the mixing.

Suppose that the colours of the larger discs are red, green, and blue, and that these are arranged so that the coloured lights may be mixed in the proportions necessary to form white light. Then the colour of the ring exhibited by the larger discs when the top revolves can differ from that of white paper only in respect of illumination. If, therefore, we can diminish the apparent brightness of the central circle at will, we may produce a complete match. This may be effected by combining a black disc, which emits very little light indeed, with the white disc, so that the amount of light received from the central circle is approximately proportional to the angle of the white sector. On spinning the top, the central circle appears of a neutral gray, which is the same as a dull white, and the darkness of the gray increases with the amount of the black sector introduced. If, now, the outer circle appears yellow compared with the central gray when the top is spinning, it is found that, by increasing the amount of blue and diminishing the red and green, the circles may be matched in hue. Similarly, if it appears too green we must diminish the green and increase the red and blue, while if it appears purple we must increase the amount of green. After a little experience it is easy to recognise the character of the change required.

Now, suppose that we have three and only three colour sensations, and that, for the sake of argument, these correspond respectively to red, green, and blue. Then if two colours contain the same amount of red, the same amount of green, and the same amount of blue, they must be in every respect identical. There are, therefore, three conditions to satisfy in order that two colours may match. But in the case of the top, two other conditions must be also fulfilled, for the portions of the smaller discs employed must exactly fill up the circle, and the same must be true of the larger discs. Hence there are in all five conditions to be fulfilled in order to make a colour match, and in general five discs will have to be employed and matched, two against three or three against two. If there had been four primary colour sensations, we should have required in general to employ six discs to ensure a match, and so on for any other number. Maxwell showed that with a normal eye a match could always be obtained with five discs, but that with a colour-blind person a match could always be obtained with four discs, thus demonstrating that the normal eye possesses three independent colour sensations, while the eye of the colour-blind possesses only two. This conclusion will appear more evident from the experiments with the colour box, which will be described presently.

The result of each experiment was first expressed by an equation in which the colours in the outer circle, with their respective quantities as coefficients, appeared on the left of the equation, and those in the inner circle on the right side. Thus, employing normal upper V for vermilion, normal upper U for ultramarine, and upper E upper G for emerald green, upper S upper W for snow-white, and upper B k for black, the equation dot 37 normal upper V plus dot 27 normal upper U plus dot 36 upper E upper G equals dot 28 upper S upper W plus dot 72 upper B k means that a sector of vermilion occupying 37 divisions of the outer circle, combined with a sector of ultramarine occupying 27 divisions, and a sector of emerald green occupying 36 divisions, produced, on spinning, a colour which matched that obtained by a sector of white paper occupying 28 divisons, and a sector of black occupying 72 divisions. The sum of the coefficients on each side of the equation is of course 1.

The mode of conducting an experiment is best described in Maxwell’s own words:—

In a similar way matches were obtained in which the resulting tint was a decided colour and not a neutral gray. Thus on the 5th of March 1855 a match was obtained as follows— dot 39 upper P upper C plus dot 21 normal upper U plus dot 40 upper B k equals dot 59 normal upper V plus dot 41 upper E upper G comma where upper P upper C represents pale chrome. The resulting tint in this case is an impure yellow.

Mixtures which appear to make perfect matches by one kind of light are far from matching one another when viewed by a different light. Thus, normal upper C representing carmine, the following match was obtained by daylight, viz.— dot 44 normal upper C plus dot 22 normal upper U plus dot 34 upper E upper G equals dot 17 upper S upper W plus dot 83 upper B k while by gaslight the match was dot 47 normal upper C plus dot 08 normal upper U plus dot 45 upper E upper G equals dot 25 upper S upper W plus dot 75 upper B k which shows that the yellowing effect of the gaslight tells more on the white than on the combination of colours.”

Maxwell, following Young, represented the results of his experiments graphically by means of a triangle, at the angular points of which he placed the three colours which he believed to most nearly correspond with the primary sensations. (See Plate I.) The colours he selected for these positions were vermilion, ultramarine, and emerald green, of such strength that, when mixed in equal proportions, they produced a neutral gray which therefore appeared at the centre of the triangle. In the paper published in the Edinburgh Transactions the reason alleged for selecting green in preference to yellow is the fact that it was found possible to produce a distinct yellow from a mixture of emerald green and vermilion, but impossible to produce a green from a mixture of blue and yellow. Any colour which can be produced by a mixture of all the three primary tints will lie within the triangle; but a colour which must be mixed with one of the primary tints in order to match a mixture of the other two will lie without the triangle. Thus the pale chrome referred to above must be mixed with blue in order to match a mixture of red and green, and it must therefore be placed in such a position that the centre of gravity of the yellow and blue taken in proper proportions may be on the line joining the red and green, and may divide this line in the inverse ratio of the amounts of red and green respectively required. A copy of Maxwell’s diagram, showing the chromatic relations of coloured papers, is given in the accompanying plate (Plate II.) The original is in the Cavendish Laboratory.

As above mentioned, Maxwell found that in the case of colour-blind persons only four discs (including black) were required instead of five to ensure a match. The following is an example of a colour-blind equation:— dot 19 normal upper G plus dot 05 normal upper B plus dot 76 upper B k equals 1 dot 00 normal upper R comma where normal upper G, normal upper B, and normal upper R represent green, blue, and red respectively. To a normal eye the outer circle represented by the left-hand side of the equation appears of a dark blue green, but to the colour blind this matches the full red of the smaller circle.

By comparing different colour matches, it is possible to determine the position on the colour diagram of the tint corresponding to the missing sensation in the colour-blind. Thus, if two colours appear to a colour-blind person to match, they can only differ in their effect upon a normal eye by the degree in which they excite the sensation which is missing in the colour-blind, and they must therefore lie upon a line passing through the position of this missing sensation. By determining two such lines, the position of the pure sensation is located.

A line drawn through this point and the position of white is, to a colour-blind person, a neutral line for its whole length (see Plate II.) The position corresponding to the pure sensation which is missing in the colour-blind is near the red, but outside the triangle, and hence corresponds to a purer red than any in the solar spectrum (see p. 480).

The colour-blind generally class all tints as yellows or blues. According to Maxwell’s theory, their sensations correspond to green and blue; but the reason why they regard yellow as brighter than green lies in the fact that although to the normal eye the sensation of yellow is a combination of the sensations of red and green, yet yellows are so much brighter than greens that light from them generally excites the green sensation more powerfully than that from green objects themselves, and hence yellows are more conspicuous than greens to the colour-blind, but only in virtue of the green they contain.

To enable colour-blind persons to distinguish between red and green, Maxwell had a pair of spectacles constructed, one eye-glass of which was red and the other green, so that the object appeared differently to the two eyes. These spectacles cause objects to appear to possess a metallic lustre on account of the different ways in which they are presented to the eyes. To the colour-blind a red object would appear brighter when seen through the red glass, while a green object would appear brighter through the green glass.

There are colour-blind persons whose vision is very different from that described by Maxwell in his early papers, but to these we shall again refer presently (p. 482).

It would occupy too much space to describe the different methods adopted by Maxwell for the purpose of mixing light of different colours, but his colour box demands a special notice, both on account of the perfection with which it is adapted to the object in view and the extreme beauty of its arrangement. The first two boxes constructed were of inconveniently large dimensions. The form we shall describe is that finally adopted, and the shell, as well as the principal optical apparatus of the box, are still at the Cavendish Laboratory. The description is taken from Maxwell's paper in the Phil. Trans. for 1860.

Fig. 2 represents the instrument. At normal upper A normal upper B is placed the apparatus represented in Fig. 3, in which normal upper A prime normal upper B prime represents a rectangular frame of brass, having a rectangular aperture of 6 times 1 inches.

On this frame are placed six brass sliders, normal upper X normal upper Y normal upper Z. Each of these carries a knife-edge of brass in the plane of the surface of the frame.

At normal upper E (Fig. 2) is a fine vertical slit. At e, normal upper M prime and normal upper M are three plane mirrors, each inclined at 45 Superscript ring to the sides of the box. normal upper P normal upper P prime are two prisms (angles 45 Superscript ring), and normal upper S is a concave silvered glass of radius, 34 inches.

If light enter the box at normal upper E, it will be reflected at e, and a portion of the pencil, after passing through the prisms, will be reflected from normal upper S, and after again traversing the prisms will form a spectrum at normal upper A normal upper B.

The six movable knife edges above referred to form three slits, normal upper X normal upper Y normal upper Z, which may be so adjusted as to coincide with any three portions of the pure spectrum formed by light from normal upper E. The intervals between the sliders are closed with hinged shutters, which allow the sliders to move without letting light pass between them.

The inner edge of the brass frame is graduated to twentieths of an inch, so that the position of any slit can be read off. The breadth of the slit is ascertained by means of a wedge-shaped piece of metal, 6 inches long, and tapering to a point from a breadth of half an inch. This is gently inserted into each slit, and the breadth is determined by the distance to which it enters, the divisions on the wedge corresponding to the 200th of an inch difference in breadth, so that the unit of breadth is ·005 inch. The gauge is balanced on one finger, and inserted into the slit till the pressure just causes it to slide on the finger. This (on the same principle as in Whitworth’s Millionth Measurer) ensures uniformity in the pressure in different measurements.

Now suppose light to enter at normal upper E, and to be refracted by the two prisms normal upper P and normal upper P prime, and after reflection at normal upper S, to again pass through the prisms. A pure spectrum, showing Fraunhofer’s lines, is formed at normal upper A normal upper B, but only that part is allowed to pass which falls on the three slits normal upper X normal upper Y normal upper Z. The rest is stopped by the shutters. Suppose that the portion falling on normal upper X belongs to the red part of the spectrum: then, of the white light entering at normal upper E, only the red will come through the slit normal upper X. If we were to admit red light at normal upper X, it would be refracted to normal upper E by the principle in optics that the course of any ray may be reversed. If, instead of red light we were to admit white light at normal upper X, still only red light would come to normal upper E, for all other light would be refracted more or less than the red, and would not reach the slit at normal upper E. Applying the eye at the slit normal upper E, we should see the prism normal upper P uniformly illuminated with red light of the kind corresponding to the part of the spectrum which falls on the slit normal upper X when white light is admitted at normal upper E.

Let the slit normal upper Y correspond to another portion of the spectrum, say the green: then, if white light be admitted at normal upper Y, the prism, as seen by an eye at normal upper E, will be uniformly illuminated with green light; and if white light be admitted at normal upper X and normal upper Y simultaneously, the colour seen at normal upper E will be a compound of red and green, the proportions depending on the breadth of the slits and the intensity of the light which enters them. The third slit normal upper Z enables us to add a third colour, and thus to combine any three kinds of light in any given proportions, so that an eye at normal upper E shall see the face of the prism at normal upper P uniformly illuminated with the colour resulting from the combination of the three. The position of these three rays in the spectrum is found by admitting the light at normal upper E, and comparing the position of the slits with the position of the principal fixed lines.

At the same time, another portion of the light from the source (generally a sheet of white paper) enters the instrument at upper B upper C, is reflected at the mirror normal upper M, passes through the lens normal upper L, is reflected at the mirror normal upper M prime, passes close to the edge of the prism normal upper P, and is reflected along with the coloured light at e, to the eye-slit at normal upper E.

In this way the compound colour is compared with a constant white light in optical juxtaposition with it. The mirror normal upper M is made of silvered glass, that at normal upper M prime is made of glass roughened and blackened at the back, to reduce the intensity of the constant light to a convenient value for the experiments. By adjusting the slits properly the two portions of the field may be made equal both in colour and brightness, so that the edge of the prism becomes almost invisible. When light enters at normal upper E, the instrument gives a spectrum in which Fraunhofer’s lines are very distinct, and the length of the spectrum between Fraunhofer’s lines normal upper A and normal upper H is 3·6 inches. The outside measure of the box is 3 feet 6 inches, by 11 inches, by 4 inches, and it can be carried about, and set up in any position, without readjustment.

In making an observation the centres of the slits normal upper X normal upper Y normal upper Z are placed opposite the divisions of the scale corresponding to the colours to be mixed, the breadth of each slit being varied till the resultant light cannot be distinguished from the white light reflected from normal upper M and normal upper M prime. If the mixture differs from the standard white light only by being too bright or too dull, all the slits normal upper X normal upper Y normal upper Z must be opened or closed in the same proportion. The result of any observation is expressed by an equation in which each particular colour employed is represented by the corresponding division of the scale placed in brackets, while the breadth of the slit is written as the coefficient of this colour. Thus, the equation 18 dot 5 left parenthesis 24 right parenthesis plus 27 left parenthesis 44 right parenthesis plus 37 left parenthesis 68 right parenthesis equals normal upper W means that the breadth of the slit normal upper X was 18·5, as measured by the wedge, while its centre was at the division (24) of the scale; that the breadths of normal upper Y and normal upper Z were 27 and 37, and their positions (44) and (68); and that the illumination produced by these slits was exactly equal, in the estimation of the observer, to the constant white normal upper W.

In the first instance, recorded in the paper above referred to, the observations were made by Professor Maxwell himself (J), and by Mrs. Maxwell (K). Professor Maxwell’s complexion was dark and his hair black; Mrs. Maxwell was extremely fair. The observations of each exhibited very small errors from the mean, far less than would have been expected, but there was always a difference apparent between the two observers, and this always in the same direction. A difference of this character was found by Maxwell to be general between dark and fair persons, especially when the light fell on the centre of the retina (the fovea centralis or macula lutea). To this point reference will again be made.

By considering the errors in the several, observations between the standard colours, Maxwell showed that greater accuracy is attainable in the case of red light than in that of green or blue, and that variations in colour are more easily detected than variations in brightness.

One result of the observations is especially worthy of notice. It follows from a comparison of the equations obtained in the several parts of the spectrum that any tint in the spectrum lying between the divisions (24) and (46) of the scale could be exactly imitated by mixing in proper proportions the red of (24) and the green of (46), while every tint lying between (48) and (64) could be produced by a proper mixture of the green of (48) and the blue of (64). Hence if a colour diagram be constructed as explained on page 473, the whole of the spectrum between the red of (24) and the green of (46) will lie in a straight line, forming one side of the triangle, while that lying between (48) and (64) forms another side (the included angle being not quite closed). It was also found that the violet beyond (68) lay very nearly on the line joining (68) and (24), so that the spectrum exhibited in this diagram “forms two sides of a triangle, with doubtful fragments of the third side.” Thus “all the colours of the spectrum may be compounded of those which lie at the angles of this triangle.” A diminished copy of one of Maxwell's lecture diagrams, painted with his own hand and deduced (it is believed) from experiments with the colour top, is given in Plate I.[246]

By studying Plate I., it will be seen that a mixture of yellow and blue lights produces varying shades of dirty yellow and pink, as the relative amount of blue is increased, and by properly selecting the yellow and blue a neutral gray (or white) may be obtained.

The pink tint produced by mixing blue and yellow lights had been previously noticed by Helmholtz and others. The well-known fact that an admixture of blue and yellow pigments produces generally a green was explained by Helmholtz on other grounds. Suppose, for instance, that we are provided with properly chosen blue and yellow glasses: let sunlight shine through the blue glass and fall upon a screen, and allow a second beam of sunlight, after reflection at a mirror, to pass through the yellow glass and fall on the same portion of the screen as the blue light. If the two colours are properly selected, the illuminated portion of the screen will appear white or pink. Now place the pieces of glass together, so that the same light passes through both, and the light transmitted will be green. This is explained if we examine with the prism the light transmitted by each glass. That which has passed through the blue glass will show, in addition to blue light, a certain amount of violet and green, while that which has passed through the yellow glass will comprehend, in addition to yellow light, a certain quantity of orange (perhaps red) and green. Now the only light capable of passing through both glasses is green, and this, therefore, is the colour observed on looking through the two together. Similarly, when blue and yellow pigments are ground together, the light penetrates a little way into the substance of the pigment, is reflected, and emerges, some of its constituents being absorbed by one pigment and some by the other, and the only light which both pigments transmit is green, which is consequently the colour of the emergent light, and therefore the hue of the mixture.

The set of colour equations given above, and the diagram of colours there described, were obtained from the observations of Mrs. Maxwell (K). The diagram obtained from Professor Maxwell’s (J’s) own observations was slightly different, as before mentioned.[247] The chief differences were that (J) saw more green in the orange and yellow portions of the spectrum than (K), so that in the diagram obtained from his observations these colours appeared nearer the green than in the other, while the colours between green and blue appeared more blue to (J) than to (K), and were therefore placed higher up in his diagram. Thus, when the instrument was adjusted to suit (K), one of the selected colours being (32), (36), or (40), then (J) saw the mixture too green; but if (48), (52), (56), or (60) were the selected colour when adjusted for (K), it appeared too blue to (J), “showing that there was a real difference in the eyes of these two individuals, producing constant and measurable differences in the apparent colour of objects.”

With those colour-blind persons whom Maxwell first examined only two slits were required to produce a colour chromatically identical with white; while the spectrum, a little on the red side of the line F, appeared to be identical with white. “From this point to the more refrangible end the spectrum appears to them ‘blue.' The colours on the less refrangible side appear all of the same quality, but of different degrees of brightness; and when any of them are made sufficiently bright they are called ‘yellow.'” Thus a colour-blind or dichromic person, in speaking of red, green, orange, and brown, refers to different degrees of brightness or purity of a single colour, and not to different colours. This colour he calls yellow.