It was for these researches that Maxwell received the Rumford Medal of the Royal Society in 1860.

The only cases of colour-blindness which Maxwell met with in the course of his earlier experiments were those of persons blind to red rays. This, however, is not the only kind of colour-blindness known. Some appear to be deficient in the blue (or violet) sensation. To these persons bright yellow appears white, and the neutral line is a line drawn through the yellow and the point corresponding to the pure blue (or violet) sensation. In a valuable paper published in the Proceedings of the Royal Society, vol. XXXI. p. 302, M. Frithiof Holmgren, Professor of Physiology in the University of Upsala, gave an account of a case of red blindness, and a case of violet-blindness in each of which only one eye was really colour-blind, the vision of the other being nearly normal. This peculiarity enabled the observer to compare the experience of colours gained through one eye with that gained by the other, and thus to state in the language of those possessing normal vision, how colours really appear to the colour-blind. His results agree in their general character with Maxwell’s, but Holmgren (with many others) makes the third sensation correspond to violet instead of blue, while, according to him, the violet-blind class colours as red and yellow instead of red and green.

Though the largest and most important, Maxwell’s theory of compound colours was by no means his only, or even his earliest, contribution to Optics. While a bachelor-scholar at Trinity, at the request of Messrs. Macmillan he wrote a considerable portion of a text-book on geometrical optics. The work was never finished, but the MS. is still extant. The mode of treating the subject, as stated by Professor Maxwell in one of his letters to his father,[248] is decidedly novel, and calculated to bring down a storm of abuse upon the author. He starts by postulating the possibility of obtaining perfect images, and then investigates the laws of reflection and refraction necessary for this.

Perhaps the most remarkable of Maxwell’s contributions to Optics was his identification of the velocity of light with the ratio of two quantities, each of which is capable of being measured electrically; but this subject will be again referred to in describing his electrical researches. A paper on a general theory of optical instruments was published by Maxwell in the Quarterly Journal of Mathematics in 1858, and another on the same subject in the Proceedings of the Cambridge Philosophical Society, 1866. A paper on the best mode of projecting a spectrum on a screen appeared in the Proceedings of the Royal Society of Edinburgh in 1869. We may also refer to the papers on “The Focal Lines of a refracted Pencil,” in the Proceedings of the Mathematical Society of London for 1871-3; on a “Bow seen on the surface of ice,” in the Proceedings of the Royal Society of Edinburgh for 1872; on “The Spectra of Polarised Light,” the subject which had interested him so much in 1847 (see Part I., p. 84), in the Transactions of the Royal Society of Edinburgh for 1872; and on “Double Refraction in a Viscous Fluid in Motion,” in the Proceedings of the Royal Society for 1873, and the Ann. de Phys. and Chimie, 1874.

Among the many optical contrivances designed by Professor Maxwell, we ought not to omit to mention the real-image stereoscope. This instrument, in which ordinary stereoscopic slides are employed, consists essentially of two convex lenses of short focal length, say 4 inches, placed side by side in a wooden frame at a distance from the pictures, equal to twice their focal length, while the distance between the centres of the lenses is half the distance between the centres of the pictures. The result of this arrangement is that real images of the two pictures of the same size as the pictures themselves, formed one by one lens, and the other by the other, are superposed on the axis of the instrument at a distance in front of the lenses equal to twice their focal length, that is, as far in front of the lenses as the pictures are behind them. The double, or stereographic image so formed is viewed through a large lens at a suitable distance in front of it, the observer standing at a distance of three or four feet. Many persons[249] who cannot appreciate the ordinary box stereoscopes obtain very satisfactory effects with this instrument.

Professor Maxwell prepared a large number of stereoscope slides of geometrical figures. Among them may be mentioned the surface of centres of an ellipsoid, lines of curvature on an ellipsoid, and on elliptic and hyperbolic paraboloids, the parabolic cyclide, the horned cyclide, and the spindle cyclide, a twisted cubic with three asymptotes, a Gordian knot, etc. The wood blocks from which these slides were printed are now in the Cavendish Laboratory.

Another extremely pretty optical toy of his construction, at present in the possession of Mrs. Maxwell, is a Zoëtrope, or “Wheel of Life.” In the ordinary instrument, on looking through the slits in the revolving cylinder the figures are seen moving on the opposite side of the cylinder. Maxwell inserted concave lenses in place of the slits, the lenses being of such focal length that the virtual image of the object at the opposite extremity of the diameter of the cylinder was formed on the axis of the cylinder, and consequently appeared stationary as the cylinder revolved.[250]

In ordinary light the vibrations take place in all directions at right angles to that in which the light is being transmitted. A beam of ordinary light is therefore symmetrical on all sides. But it is possible in various ways to confine all the vibrations to one plane. Thus, if a ray be reflected from the surface of polished glass at a particular angle, all the vibrations take place in one plane, and it is generally believed that this plane is parallel to the surface of the glass, and therefore perpendicular to the plane of incidence. Since all the vibrations are now taking place in one plane, the beam of light has acquired, as it were, sides or poles, and is said to be plane polarised. There are other contrivances by which the movements may be made all to take place in regular succession in a circle about the direction of the ray as axis, and the light is then said to be circularly polarised. This may be effected by passing a beam of plane polarised light through a sheet of mica (or some other crystals) of a particular thickness.

The velocity with which waves are transmitted through a substance depends not only on the density but on the elasticity of the substance in the direction in which the vibrations take place. How, many crystals have different elasticities in different directions, and a similar condition may be induced by mechanical means in other bodies. In such substances the velocity of light depends on the direction in which the vibrations take place; and, generally, if a beam of ordinary light fall upon such a crystal it will be separated into two, one of which will consist of vibrations in the direction in which the elasticity is greatest (of all the directions which it can select), and the other in that in which the elasticity is least. These rays, being transmitted with different velocities, will be differently refracted, and part company in the crystal; and since in each ray the vibrations are in one direction only, each ray will be plane polarised, the vibrations taking place in the two rays in planes perpendicular to one another.

A Nicol’s prism consists of a long prism of Iceland spar cut into two along a diagonal plane, the segments being cemented together again by Canada balsam. The effect of the balsam is to reflect one of the polarised rays out at the side of the prism while it allows the other to pass through. Consequently, if common light fall on a Nicol’s prism, only half of it will pass through, and this will be plane-polarised in a particular plane. If another prism be placed in the path of the ray and be situated similarly to the first, the light will pass through it, but if it be turned around its axis through a right angle, the light falling on it corresponds to that which is reflected out of the prism by the balsam, and no light passes through the second prism. Under these circumstances the Nicols are said to be crossed. Such an arrangement of two Nicol’s prisms or any equivalent arrangement which may be made with glass reflectors or crystals of tourmaline, constitutes a polariscope; the first Nicol is called the polariser, the second the analyser.

Fresnel first pointed out that by mechanical stress it is possible to impart to glass a property analogous to that of doubly refracting crystals, making its elasticity (for light) different in different directions. Sir David Brewster showed that a piece of glass heated and then suddenly cooled, i.e. unannealed, possesses similar properties. If it be placed between the polariser and analyser of a polariscope and examined by white light, a gorgeous display of colour is observed. The reason is that the plane-polarised light from the polariser on entering the glass is generally split into two rays vibrating in planes at right angles to one another, and these pass through the glass with different velocities.

When they reach the analyser only that component of each set of vibrations can pass through which takes place in the plane corresponding to transmission through the analyser. Then it may happen that the two rays of light of one particular colour are so vibrating that the waves interfere and destroy one another, so that this colour is completely absent in the transmitted light while other colours are partially destroyed. The result is that the combination of colours which passes through produces a particular tint, and this will be different according to the obliquity of the ray, the thickness of the glass, and the amount of strain it has experienced, for on the latter depends the difference of velocity of the two rays, and consequently the particular colour destroyed in the case of glass of a given thickness.

Maxwell’s first serious experiments on light appear to have had their origin in his visit to Mr. Wm. Nicol in April 1847. After this visit he constructed a polariscope of cardboard, employing blackened glass mirrors as polariser and analyser. This was supplied with lenses for use when a conical beam of polarised light was required. The lenses were mounted in cardboard frames. A very similar instrument constructed by him shortly afterwards, but of wood instead of cardboard, together with the lenses mounted as before on cards, is still preserved in the Cavendish Laboratory. Maxwell, after returning from Mr. Nicol’s, prepared some samples of unannealed glass by heating pieces of thick plate glass to redness and allowing them to cool rapidly. By means of a camera lucida adapted to the cardboard polariscope he observed and faithfully copied in water-colours some of the chromatic effects exhibited by these plates of glass, showing the manner in which the glass was strained by the rapid cooling. Some of these figures are shown in Plate III., and will be again referred to.[251] As mentioned in the previous part of this work, of these water-colour drawings he sent some to Nicol, who presented him in return with a pair of Nicol prisms of his own construction, which are now, with the original colour-top, polariscope, specimens of unannealed glass, etc., in the Cavendish Laboratory. His experiments on the passage of light through solids exposed to strain suggested to Maxwell the employment of polarised light as an analyser of the strains in the different portions of an elastic solid when exposed to mechanical stress, and led to the production of the paper on “Elastic Solids” read before the Royal Society of Edinburgh in February 1850; but before giving an account of this paper we must mention another investigation connected with the physiology of vision.

There are some persons who, when they look at a point in the sky distant 90 Superscript ring from the sun, at once observe two conspicuous yellow brushes with their axis in a plane passing through the sun, while the space between exhibits the complementary violet colour. This phenomenon was first noticed by Haidinger in 1844, and is known as Haidinger’s Brushes. The appearance is only transitory, and disappears in a very short time if the eye he kept directed to the same point in the heavens. The same appearance is produced whenever “plane-polarised” light enters the eye; as, for example, when light is reflected from a polished surface of glass at a particular angle. But there are some persons, on the other hand, who are apparently incapable of seeing Haidinger’s Brushes, or only see them with difficulty. Generally it is persons of a dark complexion who see Haidinger’s Brushes more readily than others, and in such persons the yellow spot appears to be peculiarly insensitive to blue light. A paper on this subject was read before the mathematical and physical section of the British Association by Professor Maxwell in 1866 (Report, Part II.) He found that on looking through a solution of chrome alum, the centre of the field of view appears distinctly pink and much paler than the rest of the solution on account of this peculiarity of the foramen centrale. The effect decreases if the observer continue to look. Maxwell’s attention was first called to this peculiarity of his own eye by noticing a black hand in the blue portion of the spectrum whenever he directed his eye straight to that portion. The hand never appeared in any other part of the spectrum, but followed the eye up and down the spectrum in the blue, vanishing as soon as the optic axis passed out of the blue into other colours.

The following account of Maxwell’s explanation of Haidinger’s Brushes, and the personal reminiscences which accompany it, have been kindly contributed by Professor William Swan:—

2. In the paper read before the Royal Society of Edinburgh on Feb. 18, 1850, Maxwell describes the mathematical results of the application of Stokes’s theory of elasticity to a number of cases of the deformation of elastic solids, which results, when possible, he tested experimentally by subjecting the strained solid to analysis by polarised light. The first, and perhaps the most interesting, example given in this paper, refers “to the case of a hollow cylinder, of which the outer surface is fixed, while the inner surface is made to turn through a small angle.” The conclusions derived we give in Maxwell's own words:—

Some pieces of gutta-percha mounted in this way by Professor Maxwell are still preserved in the Cavendish Laboratory; as are also the original plates of isinglass above referred to. The interior cylinder employed for twisting these plates was a cork, and in one of the plates two corks were placed with their circumferences about three eighths in. apart, and were twisted equally in the same direction. The result of this operation is described as case XIII. in the paper in question, and is determined geometrically by the superposition of the two conditions of strain due to the two twists independently.

The isochromatic curves thus obtained are represented in Fig. 4, which is taken from that in the Edinburgh Transactions. The points normal upper B 1, normal upper B 2, correspond to no retardation. These curves completely agree with those obtained when the plate of isinglass is examined with circularly polarised light. The advantage of employing circularly polarised light lies in the fact that whatever may be the direction of the lines of stress in the isinglass the two component rays into which the light may be supposed separated on entering the medium are of equal intensity, and the colour therefore depends only on the state of strain and not on the position of the plane of primitive polarisation.

The last example of stress in an elastic solid is that of a triangle of unannealed glass, in which “the lines of equal intensity of the action on light are seen without interruption by using circularly polarised light.” They are represented in Plate III. In Figs. 5 and 6 normal upper A, upper B upper B upper B, upper D upper D upper D, are the neutral points, or points of no action on light, and upper C upper C upper C, upper E upper E upper E, are the points where the action is greatest; and the intensity of the action at any other point is determined by its position with respect to the isochromatic curves.

“The direction of the principal axes of pressure at any point is found by transmitting plane polarised light, and analysing it in the plane perpendicular to that of polarisation. The light is then restored in every part of the triangle, except in those points at which one of the principal axes is parallel to the plane of polarisation. A dark band formed of all these points is seen, which shifts its position as the triangle is turned round in its own plane.

Fig. 5 represents these curves for every fifteenth degree of inclination. They correspond to the lines of equal variation of the needle in a magnetic chart.

“From these curves others may be formed which shall indicate, by their own direction, the direction of the principal axes at any point. These curves of direction of compression and dilatation are represented in Fig. 6; the curves whose direction corresponds to that of compression, are concave toward the centre of the triangle, and intersect at right angles the curves of dilatation.”

The figures on Plate III. are copies of water-colour sketches made by Professor Maxwell in the very early periods of these investigations, and show the isochromatic lines in unannealed glass in the case of a pentagon and a triangle.

The remainder of the paper on elastic solids is taken up with a discussion of a number of examples of great importance to the engineer, such as the flexure of beams, the torsion of cylinders, and the like. To these engineering problems Maxwell again returned many years later, and his paper “On Reciprocal Figures, Frames, and Diagrams of Force,” read before the Royal Society of Edinburgh, 7th February 1870, received the award of the Keith Medal. The Theory of Oërsted’s Piezometer, given in the paper of 1850, is, however, of great scientific value. In it Maxwell points out that the behaviour of a vessel exposed to equal pressures within and without depends only on its cubic compressibility, while the relation between the cubic compressibility and the rigidity in solids, so far from being constant, as Poisson supposed, may be almost any whatever, cork having great rigidity in comparison with its power to resist compression, while caoutchouc, on the other hand, has extremely little.

3. While a bachelor-scholar of Trinity College, on March 13, 1854, Clerk Maxwell read a paper before the Cambridge Philosophical Society “On the Transformation of Surfaces by Bending.” This paper, which embodies a great deal of thought, and indicates that its author possessed an extensive acquaintance with the geometrical works of Gauss, Monge, Liouville, and others, is of more interest to the pure mathematician than to the general reader, but in connection with it we may mention a surface which was prepared for Professor Maxwell many years afterwards, and coated by his own hands, as described below, and now preserved in the Cavendish Laboratory. If a heavy uniform string be suspended from two points, and allowed to hang freely, it assumes the form of a curve called a catenary. If a board be cut out in this shape, and the string be stretched around its edge, then cut at the lowest point and one-half of the string unwrapped so as always to be kept stretched, and therefore the free portion of the string a tangent to the board at the point where it leaves it, the extremity of the string will describe a curve called a tractory, because it is the curve traced by a particle lying on a rough horizontal plane, when the end of a string attached to it describes a straight line on the plane, the particle starting from a point outside the straight line. As we go farther along the curve traced by the particle, we of course continually approach the straight line described by the end of the string, but never reach it. This straight line is the “asymptote” of the tractory, and is also the “directrix” of the catenary above referred to. If the tractory be made to revolve about its asymptote it will trace out a surface which has the peculiarity that the intrinsic curvature is the same at every point of the surface and is negative, the two principal radii of curvature being opposite in direction and inversely proportional the one to the other. If a flexible surface be constructed so as to fit a portion of the surface of the solid, thus forming a coat, it will be found to fit equally well at every part of the surface, and it may be inverted or turned through any angle whatever, and it will continue to fit every portion of the solid equally well. By weaving together curved strips of parchment paper and pasting them, Professor Maxwell constructed a coat which fitted every portion of the solid, however it might be placed upon it.

Maxwell’s fondness for geometry has already been alluded to more than once, and not unfrequently he would take up geometrical questions of a very generalised character. A simple and very good illustration of some of his investigations in this department is to be found in a paper “On Hills and Dales,” published in the Philosophical Magazine for December 1870. In this paper, having described the general character of contour-lines, or the lines in which the surface of the earth is cut by level surfaces. Maxwell proceeds to show[252] that the number of summits, or regions of elevation reduced to points, exceeds by one the number of passes, a pass being the point where two regions of elevation unite. Similarly, the number of Bottoms, or regions of depression, exceeds by one the number of Bars, a Bar being the boundary between two regions of depression. Lines of slope are defined as lines everywhere perpendicular to the contour lines. By following lines of slope we generally reach a Summit or a Bottom, but we may reach a Pass or Bar. “Districts whose lines of slope run to the same bottom are called Basins or Dales. Those whose lines of slope come from the same summit may be called, for want of a better name, Hills.” “Dales are divided from each other by Watersheds, and Hills by Watercourses.” “Lines of Watershed are the only lines of slope which do not reach a bottom, and lines of Watercourse are the only lines of slope which do not reach a summit.” These extracts indicate Maxwell’s anxiety that definite meanings should be assigned to all scientific terms, and that they should be used only in the senses so defined. A further illustration of this trait in his character is found in his paper “On the Mathematical Classification of Physical Quantities,” published in The Proceedings of the London Mathematical Society, vol. III. No. 34. We give one other example, taken from Matter and Motion, a little work published by the S. P. C. K., and a model of scientific accuracy and philosophic thought. “When the simultaneous values of a quantity for different bodies or places are equal, the quantity is said to be uniformly distributed in space.” “When the successive values of a quantity for successive instants of time are equal, the quantity is said to be constant.” Such examples might be multiplied almost indefinitely from Maxwell’s published writings. The more elementary the work the greater need did he see for exactness in definitions and accuracy in the use of words; and perhaps no one has done more than Maxwell in giving accuracy to the expression of scientific thought. His influence in this respect has especially been felt by all who have attended the Physical School in Cambridge. On one occasion he remarked, in his half-humorous way, that spheres are inclusive figures but circles are exclusive:—people are always trying to get into other circles, but to do so they must get out of their own spheres.

4. The keystone as well as the foundation of physical science is dynamics—a subject to which Maxwell was greatly attracted in early days, and to which, even in its most elementary principles, he constantly reverted in after life. We have already referred to his Dynamical Theory of the Electromagnetic field; the sections of his Treatise on Electricity and Magnetism, which are devoted to dynamical principles and the general equations of motion, form a most valuable compendium of dynamics; while for those who require less strong meat, his treatment of the subject in the Theory of Heat leaves little to be desired; and last, but not least, under the comprehensive title of Matter and Motion, we have a treatise on dynamics written for children in the higher grade schools, so simple that the most casual reader will think that he understands it, while it is the admiration of professed mathematicians, and by no means easy reading for those who expect, or have gained, high places in the mathematical tripos: but as the book is well within the reach of every reader, it is unnecessary here to attempt any detailed account of it.

But Maxwell’s investigations in dynamics were not confined to paper. Of the problems suggested to him by the devil on two sticks we have no account. During his residence in Cambridge he endeavoured to investigate the process by which a cat is enabled invariably to alight on her feet. The mode of conducting the experiments and the impression they left on the mind of the College will appear from the following extract from a letter written to Mrs. Maxwell, from Trinity, on January 3d, 1870, when Professor Maxwell was examining for the Mathematical Tripos:—

The “Dynamical Top,” which wag invented by Maxwell to illustrate dynamical propositions, technically so-called, was, in its final form, constructed of brass by Mr. Ramage of Aberdeen. It was this top which Maxwell brought with him to Cambridge when he came up for his M.A. degree in the summer of 1857, and exhibited to a tea-party in his room in the evening. His friends left it spinning, and next morning Maxwell, noticing one of them coming across the court, leapt out of bed, started the top, and retired between the sheets. It is needless to say that the spinning power of the top commanded as great respect as its power of illustrating Poinsot’s Theorie Nouvelle de la Rotation des Corps.

In the work just referred to, Poinsot shows that a body supported at its centre of gravity and rotating freely about it will move in the same manner as an ellipsoid whose centre is fixed, but which rolls in such a way as always to rest against a fixed plane (the invariable plane), which is, of course, a tangent plane at the point of contact. The line from the centre to the point of contact is the axis about which the body is at the instant rotating, and this line will, unless the plane touch the ellipsoid at the extremity of one of the principal axes, move both in space and in the body. The curve which the extremity of the axis of rotation describes on the invariable plane is called a herpolhode, while that which it describes on the surface of the ellipsoid is called a polhode. If at any instant the axis of rotation be very near either to the greatest or least axis of the ellipsoid, it will always remain very near that axis, and the polhode will be a small closed curve and the rotation will be stable; but if the axis of rotation be near to the mean axis of the ellipsoid, the polhode will be a very large curve, the axis of rotation will in time deviate very widely from its original position in the body, and the motion will be unstable.

Maxwell’s top consisted of a brass bell, a long screw passing through the top of the bell and terminating in a steel point “finished without emery and afterwards hardened,” serving as the axle. The point rested in an agate cup on the top of a pillar. A heavy nut could be screwed up and down on the axle for coarse adjustments, and the axle could be screwed through the top of the bell, to bring the point to coincide with the centre of gravity of the mass. The moments of inertia could be altered by means of the nut above referred to, and by nine screws with massive milled heads, six of which screwed horizontally into the rim of the bell, while three were arranged symmetrically around the top of the rim, and admitted of a vertical motion. By means of these screws the axle could be made the axis of greatest, least, or mean moment of inertia, or not a principal axis at all. The axle terminated in a point, by which a coloured disc could be fixed upon it. “The best arrangement, for general observations, is to have the disc of card divided into four quadrants, coloured with vermilion, chrome yellow, emerald green, and ultramarine. These are bright colours, and if the vermilion is good they combine into a grayish tint when the revolution is about the axle, and burst into brilliant colours when the axis is disturbed. It is useful to have some concentric circles, drawn with ink, over the colours, and about twelve radii drawn in strong pencil lines. It is easy to distinguish the ink from the pencil lines, as they cross the invariable axis, by their want of lustre. In this way the path of the invariable axis may be identified with great accuracy, and compared with theory.” If the top revolve about its axle, the whole disc will appear gray, but when the axle moves, the quadrants in which the “invariable axis” lies will be indicated by a circle of the corresponding colour appearing in full purity. Whenever the invariable line crosses an ink or pencil line, a dark ink dot or lustrous pencil dot will appear at the centre of the circle, and when it passes into another quadrant the circle will contract, then change its colour, and expand again. The use of the nine screws is thus indicated by Professor Maxwell:—“There must be three adjustments to regulate the position of the centre of gravity, three for the magnitude of the moments of inertia, and three for the directions of the principal axes—nine independent adjustments, which may be distributed as we please among the screws of the instrument.” A full account of the top and the mode of using it, together with a note on the rotation of the earth, will be found in the Transactions of the Royal Society of Edinburgh, vol. XXI., from which the above quotations have been taken.

5. In 1610 Galileo turning his telescope to Saturn, observed a projection on each side of the planet, which led him to conclude that “Saturn consists of three stars in contact with one another.” In 1659 Huygens discovered the true nature of these appendages, which, by their continually varying forms, had puzzled previous astronomers, and concluded that Saturn is girded with a thin flat ring inclined to the ecliptic; its external diameter being about 2 and one fourth times that of the planet itself. In 1665 William Bell observed a dark line running round the northern surface of the ring. In 1675 Cassini noticed the same on the other surface, and concluded that the ring consists of two concentric rings, of which the inner is the brighter. Hadley observed the shadow of the planet thrown upon the surface of the ring, and the shadow of the ring on the planet, and showed that Saturn rotates in the same plane with the rings. In 1714 Moradi observed a want of symmetry in the ring on opposite sides of the planet, and found that when it had disappeared on the eastern side it was still visible on the western, but he did not discover the cause of the phenomena. The observations of Sir William Herschel, published in 1790, corroborated the opinion of Cassini respecting the division. By observing certain spots on the surface of the planet, Herschel found that it rotated on its axis in 10 hours 29 minutes 16·8 seconds in the same direction as the rotation of the earth. In 1789, as the earth passed through the plane of Saturn’s ring, Herschel noticed some bright spots on the edge of the ring which were carried almost to the end of the diameter, and appeared to rotate about Saturn in about 10 hours 32 and one fourth minutes.

The observations of the present century show that the outer of the two bright rings is permanently divided into two concentric rings by a very narrow gap, and when their plane is inclined to the line of sight at a considerable angle, so that the rings are widely open, a series of dark elliptic curves near the extremities of the major axis of the elliptic projection indicates that each ring is still further broken up into a number of thin concentric rings, the gaps between them being apparently filled by the edges of the inner rings except near the extremity of the major axis of the projections.

In 1850 a dark ring encircling Saturn within the other two rings was discovered independently by three astronomers in England and America. The distance between the outer edge of the dark ring and the inner edge of the adjoining bright ring appeared to vary between narrow limits, the rings sometimes appearing to be in contact. This innermost ring is transparent, so that the edge of the planet can be seen through it, and as it is seen in all positions without distortion it seems that the ring cannot consist of a transparent gas or liquid. The rings appear to be much thicker near the planet than at their outer edges. A comparison of measurements of the diameters of the rings at different times seems to indicate a rapid change in their breadths, the circumference of the outer ring extending outwards, while the inner bright ring appears to be approaching the planet, so that the whole breadth of the ring system is increasing. At least this is the conclusion to which Struve arrived from a comparison of his measurements with those of Huygens and Herschel.[253] According to Hind the exterior diameter of the outer ring is about 170,000 miles, its interior diameter 150,000; the exterior diameter of the inner bright ring is 147,000 miles, its interior diameter 114,000 miles; and the equatorial diameter of the planet 75,500 miles; but, as above stated, the breadth of the rings appears to be increasing. Sir John Herschel was of opinion that the thickness of the rings did not exceed 100 miles, and Bessel calculated that their mass, as determined by the disturbance they produced in one of Saturn’s satellites, did not exceed StartFraction 1 Over 118 EndFractionth the mass of the planet.

If Saturn’s rings were solid and at rest, but of course subject to the attraction of the planet, the stress upon them would be such that we can conceive of no material capable of sustaining it. Maxwell remarked that iron would not only be plastic but semi-fluid under such stresses. By allowing the rings to rotate, the attraction of the planet might expend itself in producing the necessary acceleration towards the centre, or, as is generally stated, might be balanced by the centrifugal force, and the stress might be thus relieved to a great extent; but if the rings rotated with the velocity proper to the interior of the inner ring, the rest would tend to fly off into space, while if they rotated with the velocity proper to the exterior of the outer ring, the inner portions would tend to fall towards the planet; and even if they rotated with the velocity proper to any intermediate portion of the system, the parts beyond would tend to fly outwards, and the parts within would tend to fall towards the planet, unless this tendency were compensated by the attraction of the ring itself. But there is another objection to the hypothesis of the rings being uniform solids, viz. the instability of the motion. If the motion of the ring were slightly disturbed, as is always the case, it would not return to its original orbit, but its deviation would increase until it came in contact with the planet itself.

Laplace was the first to investigate the conditions of stability of Saturn’s ring system. He concluded that if the rings are solid, they must consist of a great number of very small concentric rings, each rotating independently with its proper velocity about the planet. The velocity calculated by Laplace for the circumference of the outer ring agreed with that determined, as above mentioned, by Herschel. Laplace avoided the difficulty of the instability of the rings above alluded to by supposing that they were not homogeneous, but that their centres of gravity were at some distance from their geometrical centres. Laplace also showed that, for the attraction of the ring to neutralise its tendency to split up, it is necessary that its density should be StartFraction 10 Over 13 EndFraction that of the planet. In 1851 Professor Pierce showed that the number of rings in the system must be very much greater than Laplace had supposed. This was the position of the question when it was taken up by Maxwell.

On March 23d, 1855, the Examiners announced the subject for the Adams Prize in the following terms:—