Note 199, pp. 171, 200. Fig. 58 shows Newton’s rings, of which there are seven, formed by screwing two lenses of glass together. Provided the incident light be white, they always succeed each other in the following order:—

1st ring, or 1st order of colours: Black, very faint blue, brilliant white, yellow, orange, red.

2nd ring: Dark purple, or rather violet, blue, a very imperfect yellow green, vivid yellow, crimson red.

3rd ring: Purple, blue, rich grass green, fine yellow, pink, crimson.

4th ring: Dull blueish green, pale yellowish pink, red.

5th ring: Pale blueish green, white, pink.

6th ring: Pale blue green, pale pink.

7th ring: Very pale blueish green, very pale pink.

After the seventh order the colours become too faint to be distinguished. The rings decrease in breadth, and the colours become more crowded together, as they recede from the centre. When the light is homogeneous, the rings are broadest in the red, and decrease in breadth with every successive colour of the spectrum to the violet.

Note 200, p. 172. The absolute thickness of the film of air between the glasses is found as follows:—Let A F B C, fig. 59, be the section of a lens lying on a plane surface or plate of glass P Pʹ, seen edgewise, and let E C be the diameter of the sphere of which the lens is a segment. If A B be the diameter of any one of Newton’s rings, and B D parallel to C E, then B D or C F is the thickness of the air producing it. E C is a known quantity; and when A B, the diameter, is measured with compasses, B D or F C can be computed. Newton found that the length of B D, corresponding to the darkest part of the first ring, is the 98,000th part of an inch when the rays fall perpendicularly on the lens, and from this he deduced the thickness corresponding to each colour in the system of rings. By passing each colour of the solar spectrum in succession over the lenses, Newton also determined the thickness of the film of air corresponding to each colour, from the breadth of the rings, which are always of the same colour with the homogeneous light.

Note 201, p. 174. The focal length or distance of a lens is the distance from its centre to the point F, fig. 60, in which the refracted rays meet. Let L Lʹ be a lens of very short focal distance fixed in the window-shutter of a dark room. A sunbeam S L Lʹ passing through the lens will be brought to a focus in F, whence it will diverge in lines F C, F D, and will form a circular image of light on the opposite wall. Suppose a sheet of lead, having a small pin-hole pierced through it, to be placed in this beam; when the pin-hole is viewed from behind with a lens at E, it is surrounded with a series of coloured rings, which vary in appearance with the relative positions of the pin-hole and eye with regard to the point F. When the hole is the 30th of an inch in diameter and at the distance of 6¹⁄₂ feet from F, when viewed at the distance of 24 inches, there are seven rings of the following colours:—

1st order: White, pale yellow, yellow, orange, dull red.

2nd order: Violet, blue, whitish, greenish yellow, fine yellow, orange red.

3rd order: Purple, indigo blue, greenish blue, brilliant green, yellow green, red.

4th order: Blueish green, blueish white, red.

5th order: Dull green, faint blueish white, faint red.

6th order: Very faint green, very faint red.

7th order: A trace of green and red.

Note 202, p. 175. Let L Lʹ, fig. 61, be the section of a lens placed in a window-shutter, through which a very small beam of light S L Lʹ passes into a dark room, and comes to a focus in F. If the edge of a knife K N be held in the beam, the rays bend away from it in hyperbolic curves K r, K rʹ, &c., instead of coming directly to the screen in the straight line K E, which is the boundary of the shadow. As these bending rays arrive at the screen in different states of undulation, they interfere, and form a series of coloured fringes, r rʹ, &c., along the edge of the shadow K E S N of the knife. The fringes vary in breadth with the relative distances of the knife-edge and screen from F.

Note 203, p. 177. Fig. 43 represents the phenomena in question, where S S is the surface, and I the centre of incident waves. The reflected waves are the dark lines returning towards I, which are the same as if they had originated in C on the other side of the surface.

Note 204, p. 180. Fig. 62 represents a prismatic crystal of tourmaline, whose axis is A X. The slices that are used for polarising light are cut parallel to A X.

Note 205, p. 181. Double refraction. If a pencil of light R r, fig. 63, falls upon a rhombohedron of Iceland spar A B X C, it is separated into two equal pencils of light at r, which are refracted in the directions r O, r E: when these arrive at O and E they are again refracted, and pass into the air in the directions O o, E o, parallel to one another and to the incident ray R r. The ray r O is refracted according to the ordinary law, which is, that the sines of the angles of incidence and refraction bear a constant ratio to one another (see Note 184), and the rays R r, r O, O o, are all in the same plane. The pencil r E, on the contrary, is bent aside out of that plane, and its refraction does not follow the constant ratio of the sines; r E is therefore called the extraordinary ray, and r O the ordinary ray. In consequence of this bisection of the light, a spot of ink at O is seen double at O and E, when viewed from r I; and when the crystal is turned round, the image E revolves about O, which remains stationary.

Note 206, p. 182. Both of the parallel rays O o and E o, fig. 63, are polarised on leaving the doubly refracting crystal, and in both the particles of light make their vibrations at right angles to the lines O o, E o. In the one, however, these vibrations lie, for example, in the plane of the horizon, while the vibrations of the other lie in the vertical plane perpendicular to the horizon.

Note 207, p. 183. If light be made to fall in various directions on the natural faces of a crystal of Iceland spar, or on faces cut and polished artificially, one direction A X, fig. 63, will be found, along which the light passes without being separated into two pencils. A X is the optic axis. In some substances there are two optic axes forming an angle with each other. The optic axis is not a fixed line, it only has a fixed direction; for if a crystal of Iceland spar be divided into smaller crystals, each will have its optic axis; but if all these pieces be put together again, their optic axes will be parallel to A X. Every line, therefore, within the crystal parallel to A X is an optic axis; but as these lines have all the same direction, the crystal is still said to have but one optic axis.

Note 208, p. 184. If I C, fig. 48, be the incident and C S the reflected rays, then the particles of polarised light make their vibrations at right angles to the plane of the paper.

Note 209, p. 184. Let A A, fig. 48, be the surface of the reflector, I C the incident and C S the reflected rays; then, when the angle S C B is 57°, and consequently the angle P C S equal to 33°, the black spot will be seen at C by an eye at S.

Note 210, p. 185. Let A B, fig. 48, be a reflecting surface, I C the incident and C S the reflected rays; then, if the surface be plate-glass, the angle S C B must be 57°, in order that C S may be polarised. If the surface be crown-glass or water, the angle S C B must be 56° 55ʹ for the first, and 53° 11ʹ for the second, in order to give a polarised ray.

Note 211, p. 186. A polarising apparatus is represented in fig. 64, where R r is a ray of light falling on a piece of glass r at an angle of 57°: the reflected ray r s is then polarised, and may be viewed through a piece of tourmaline in s, or it may be received on another plate of glass, B, whose surface is at right angles to the surface of r. The ray r s is again reflected in s, and comes to the eye in the direction s E. The plate of mica, M I, or of any substance that is to be examined, is placed between the points r and s.

Note 212, p. 187. In order to see these figures, the polarised ray r s, fig. 64, must pass through the optic axis of the crystal, which must be held as near as possible to s on one side, and the eye placed as near as possible to s on the other. Fig. 65 shows the image formed by a crystal of Iceland spar which has one optic axis. The colours in the rings are exactly the same with those of Newton’s rings given in Note 199, and the cross is black. If the spar be turned round its axis, the rings suffer no change; but if the tourmaline through which it is viewed, or the plate of glass, B, be turned round, this figure will be seen at the angles 0°, 90°, 180°, and 270° of its revolution. But in the intermediate points, that is, at the angles 45°, 135°, 225°, and 315°, another system will appear, such as represented in fig. 66, where all the colours of the rings are complementary to those of fig. 65, and the cross is white. The two systems of rings, if superposed, would produce white light.

Note 213, p. 188. Saltpetre, or nitre, crystallises in six-sided prisms having two optic axes inclined to one another at an angle of 5°. A slice of this substance about the 6th or 8th of an inch thick, cut perpendicularly to the axis of the prism, and placed very near to s, fig. 64, so that the polarised ray r s may pass through it, exhibits the system of rings represented in fig. 67, where the points C and C mark the position of the optic axes. When the plate B, fig. 64, is turned round, the image changes successively to those given in figs. 68, 69, and 70. The colours of the rings are the same with those of thin plates, but they vary with the thickness of the nitre. Their breadth enlarges or diminishes also with the colour, when homogeneous light is used.

Note 214, p. 189. Fig. 71 represents the appearance produced by placing a slice of rock crystal in the polarised ray r s, fig. 64. The uniform colour in the interior of the image depends upon the thickness of the slice; but whatever that colour may be, it will alternately attain a maximum brightness and vanish with the revolution of the glass B. It may be observed, that the two kinds of quartz, or rock crystal, mentioned in the text, are combined in the amethyst, which consists of alternate layers of right-handed and left-handed quartz, whose planes are parallel to the axis of the crystal.

Note 215, p. 193. Suppose the major axis A P of an ellipse, fig. 18, to be invariable, but the excentricity C S continually to diminish, the ellipse would bulge more and more; and when C S vanished, it would become a circle whose diameter is A P. Again, if the excentricity were continually to increase, the ellipse would be more and more flattened till C S was equal to C P, when it would become a straight line A P. The circle and straight line are therefore the limits of the ellipse.

Note 216, p. 194. The coloured rings are produced by the interference of two polarised rays in different states of undulation, on the principle explained for common light.

Note 217, p. 225. According to Mr. Joule, that heat is produced by motion, and that it is equivalent to it, Mr. Thompson of Glasgow investigates from whence the sun derives his heat, since he shows that neither combustion nor his primitive heat could have supplied the waste during 6000 years. He concludes that the solar heat is maintained by myriads of minute bodies that are revolving at the edge of his dense nebulosity or atmosphere, some of which are often seen by us as falling stars. These, vaporized by his heat, and drawn by his attraction, meet with intense resistance on entering the solar atmosphere as a shower of meteoric rain; through it they descend in spiral lines to the sun’s surface, producing enormous heat by friction during their fall, and serving for fuel on their arrival.

Note 218, p. 252. The class Cryptogamia contains the ferns, mosses, funguses, and sea-weeds; in all of which the parts of the flowers are in general too minute to be evident.

Note 219, p. 254. Zoophytes are the animals which form madrepores, corals, sponges, &c.

Note 220, p. 254. The Saurian tribe are creatures of the crocodile and lizard kind.

Note 221, p. 266. If heat from a non-luminous source be polarised by reflection or refraction at r, fig. 64, the polarised ray r s will be stopped or transmitted by a plate of mica M I, under the same circumstances that it would stop or transmit light; and if heat were visible, images analogous to those of figs. 65, 67, &c., would be seen at the point s.

Note 222, pp. 275, 329, 357. The foot-pound, or unit of mechanical force established by Mr. Joule, is the force that would raise one pound weight of matter to the height of one foot; or it is the impetus or force generated by a body of one pound weight falling by its gravitation through the height of one foot.

Impetus, vis viva, or living force, is equal to the mass of a body multiplied by the square of the velocity with which it is moving, and is the true measure of work or labour. For if a weight be raised 10 feet, it will require four times the labour to raise an equal weight 40 feet. If both these weights be allowed to descend freely by their gravitation, at the end of their fall their velocities will be as 1 to 2; that is, as the square roots of their heights; but the effect produced will be as their masses multiplied by 1 and 4; but these are the squares of their velocities: hence the impetus or vis viva is as the mass into the square of the velocity.

Thus impetus is the true measure of the labour employed to raise the weights, and of the effect of their descent, and is entirely independent of time. Now heat is proportional to impetus, and impetus is the true measure of labour. In percussion the heat evolved is in proportion to the force of the impetus, and is thus measured by labour.

Travail is a word used in mechanics, to express that work done is equal to the labouring force employed. The work done may be resistance overcome or any other effect produced, while the labouring force may be a horse, a steam-engine, wind, falling water, &c.

Note 223, p. 313. When a stream of positive electricity descends from P to n, fig. 72, in a vertical wire at right angles to the plane of the horizontal circle A B, the negative electricity ascends from n to P, and the force exerted by the current makes the north pole of a magnet revolve about the wire in the direction of the arrow-heads in the circumference, and it makes the south pole revolve in the opposite direction. When the current of positive electricity flows upwards from n to P, these effects are reversed.

Note 224, p. 314. Fig. 73 represents a helix or coil of copper wire, terminated by two cups containing a little quicksilver. When the positive wire of a Voltaic battery is immersed in the cup p, and the negative wire in the cup n, the circuit is completed. The quicksilver ensures the connection between the battery and the helix, by conveying the electricity from the one to the other. While the electricity flows through the helix, the magnet S N remains suspended within it, but falls down the moment it ceases. The magnet always turns its south pole S towards P, the positive wire of the battery, and its north pole towards the negative wire.

Note 225, p. 316. A copper wire coiled in the form represented in fig. 73 was the first and most simple form of the electro-dynamic cylinder. When its extremities P and n are connected with the positive and negative poles of a Voltaic battery, it becomes a perfect magnet during the time that a current of electricity is flowing through it, P and n being its north and south poles.

Note 226, p. 344. It is to Halley we are indebted for the first declination chart and the theory of 4 poles of maximum magnetic intensity, since confirmed by observation, as well as the earliest authentic values of the magnetic elements in London and St. Helena, where he went on purpose to make observations on terrestrial magnetism. Since that time M. Gauss has formed charts of the magnetic lines, and published a theory which very nearly represents the magnetic state of the globe. The mass of observations daily making by our cruizers and our Government surveys in every part of the earth is enormous.

Note 227, p. 360. In fig. 74 the hyperbola H P Y, the parabola p P R, and the ellipse A E P L, have the focal distance S P, and coincide through a small space on each side of the perihelion P; and, as a comet is only visible when near P, it is difficult to ascertain which of the three curves it moves in.

Note 228, p. 363. In fig. 75, E A represents the orbit of Halley’s comet, E T the orbit of the earth, and S the sun. The proportions are very nearly exact.

Note 229, p. 382. Fig. 74 represents the curves in question. It is evident that, for the same focal distance S P, there can be but one circle and one parabola p P R, but that there may be an infinity of ellipses between the circle and the parabola, and an infinity of hyperbolas H P Y exterior to the parabola p P R.

Note 230, p. 387. Let A B, fig. 26, be the diameter of the earth’s orbit, and suppose a star to be seen in the direction A Sʹ from the earth when at A. Six months afterwards, the earth, having moved through half of its orbit, would arrive at B, and then the star would appear in the direction B Sʹ, if the diameter A B, as seen from Sʹ, had any sensible magnitude. But A B, which is 190,000,000 of miles, does not appear to be greater than the thickness of a spider’s thread, as seen from 61 Cygni, supposed to be the nearest of the fixed stars.

Note 231, p. 389. Stars whose parallax and proper motions are known.

The space run through in one second by these stars is therefore—

There are three great discrepancies in the parallax of the star Argelander or 1830 Groombridge. M. Otto Struve makes it 0ʺ·034, which gives it a velocity of 251 leagues per second, while M. Faye finds the parallax to be between 0ʺ·03 and 0ʺ·01, which makes its velocity from 30 to 85 leagues per second.

These are all minimum velocities, because we can only determine on the celestial vault a projection perhaps much foreshortened of the real motions of the stars.

Note 232, pp. 398, 401. The following are the binary systems whose orbits have been accurately determined:—

Note 233, p. 403. The mass is found in the manner explained in the text; but the method of computing the distance of the star may be made more clear by what follows. Though the orbit of the satellite star is really and apparently elliptical, let it be represented by C D O, fig. 14, for the sake of illustration, the earth being in d. It is clear that, when the star moves through C D O, its light will take longer in coming to the earth from O than from C, by the whole time it employs in passing through O C, the breadth of its orbit. When that time is known by observation, reduced to seconds, and multiplied by 190,000, which is the number of miles light darts through in a second, the product will be the breadth of the orbit in miles. From this the dimensions of the ellipse will be obtained by the aid of observation; the length and position of any diameter as S p may be found; and as all the angles of the triangle d S p can be determined by observation, the distance of the star from the earth may be computed.

Note 234, p. 405. The mean results of MM. Argelander, Otto Struve, and Luhndahl for stars in the northern hemisphere and the epoch 1790, places the point to which the sun is tending in 259° 5ʹ of right ascension and 55° 23ʹ of north polar distance. Mr. Gallaway computed from stars in the southern hemisphere, at the same epoch, the point to have been in 260° 1ʹ right ascension and 55° 37ʹ north polar distance, results nearly identical, though from very different data.

Note 235, p. 414. One of the globular clusters mentioned in the text is represented in fig. 1, plate 8. The stars are gradually condensed towards the centre, where they run together in a blaze. The more condensed part is projected on a ground of irregularly scattered stars, which fills the whole field of the telescope. There are few stars near this cluster.

Note 236, p. 420. Plate 8 shows five nebulæ as seen in Sir John Herschel’s 20-feet telescope.

1. An enormous ring seen obliquely with a dark centre and a small star at each extremity.

2. The ring in the constellation Lyra.

3. The dumb-bell nebula in Vulpicula.

4. The spiral nebula or brother system in the 20-feet telescope.

5. A spindle-shaped nebula.

Plate 9 represents some of the same objects as seen by Lord Rosse.

1. Nebula in the girdle of Andromeda.

2. The circular nebula of Lyra.

3. The dumb-bell nebula in Vulpicula.

The spiral nebulæ of 51 Messier, as seen by Lord Rosse, 1 in plate 10, represents fig. 4 of plate 8; and fig. 2 in the same plate is part of the great nebula in Orion, for the whole has never been seen, on account of extreme remoteness.

Note 237, pp. 32, 427. The motion of the earth is visibly proved by M. Foucault’s experiments. If a pendulum be left to oscillate quite freely, the forces producing the oscillations being in the vertical plane, there is no cause that can produce an absolute change in its position with regard to space; but the motion of the earth changes the position of a spectator with respect to the vertical plane, and he refers his own motion to it, which seems gradually to turn away from its position, precisely as a person in a boat refers his own motion to that of the land, and thus the motion of the earth is truly and visibly proved.