Chapter XLIII: Section XXXVII (3)

NOTE 189, pp. 138, 153, 156. _Reflection and Refraction._ Let P C p, fig. 48, be perpendicular to a surface of glass or water A B. When a ray of light, passing through the air, falls on this surface in any direction I C, part of it is reflected in the direction C S, and the other part is bent at C, and passes through the glass or water in the direction C R. I C is called the incident ray, and I C P the angle of incidence; C S is the reflected ray, and P C S the angle of reflection; C R is the refracted ray, and p C R the angle of refraction. The plane passing through S C and I C is the plane of reflection, and the plane passing through I C and C R is the plane of refraction. In ordinary cases, C I, C S, C R, are all in the same plane. We see the surface by means of the reflected light, which would otherwise be invisible. Whatever the reflecting surface may be, and however obliquely the light may fall upon it, the angle of reflection is always equal to the angle of incidence. Thus I C, Iʹ C, being rays incident on the surface at C, they will be reflected into C S, C Sʹ, so that the angle S C P will be equal to the angle I C P, and Sʹ C P equal to Iʹ C P. That is by no means the case with the refracted rays. The incident rays I C, Iʹ C, are bent at C towards the perpendicular, in the direction C R, C Rʹ; and the law of refraction is such, that the sine of the angle of incidence has a constant ratio to the sine of the angle of refraction; that is to say, the number expressing the length of I m, the sine of I C P, divided by the number expressing the length of R n, the sine of R C p, is the same for all the rays of light that can fall upon the surface of any one substance, and is called its index of refraction. Though the index of refraction be the same for any one substance, it is not the same for all substances. For water it is 1·336; for crown-glass it is 1·535; for flint-glass, 1·6; for diamond, 2·487; and for chromate of lead it is 3, which substance has a higher refractive power than any other known. Light falling perpendicularly on a surface passes through it without being refracted. If the light be now supposed to pass from a dense into a rare medium, as from glass or water into air, then R C, Rʹ C, become the incident rays; and in this case the refracted rays, C I, C Iʹ, are bent from the perpendicular instead of towards it. When the incidence is very oblique, as r C, the light never passes into the air at all, but it is _totally_ reflected in the direction C rʹ, so that the angle p C r is equal to p C rʹ; that frequently happens at the second surface of glass. When a ray I C falls from air upon a piece of glass A B, it is in general refracted at each surface. At C it is bent towards the perpendicular, and at R from it, and the ray emerges parallel to I C; but, when the ray is very oblique to the second surface, it is totally reflected. An object seen by total reflection is nearly as vivid as when seen by direct vision, because no part of the light is refracted. When light falls upon a plate of crown-glass, at an angle of 4° 32ʹ counted from the surface, the glass reflects 4 times more light than it transmits. At an angle of 7° 1ʹ the reflected light is double of the transmitted; at an angle of 11° 8ʹ the light reflected is equal to that transmitted; at 17° 17ʹ the reflected is equal to 1/2 the transmitted light; at 26° 38ʹ it is equal to 1/4, the variation, according to Arago, being as the square of the cosine.

NOTE 189, p. 154. _Atmospheric refraction._ Let a b, a b, &c., fig. 49, be strata, or extremely thin layers, of the atmosphere, which increase in density towards m n, the surface of the earth. A ray coming from a star meeting the surface of the atmosphere at S would be refracted at the surface of each layer, and would consequently move in the curved line S v v v A; and as an object is seen in the direction of the ray that meets the eye, the star, which really is in the direction A S, would seem to a person at A to be in s. So that refraction, which always acts in a vertical direction, raises objects above their true place. For that reason, a body at Sʹ, below the horizon H A O, would be raised, and would be seen in sʹ. The sun is frequently visible by refraction after he is set, or before he is risen. There is no refraction in the zenith at Z. It increases all the way to the horizon, where it is greatest, the variation being proportional to the tangent of the angles Z A S, Z A Sʹ, the distances of the bodies S Sʹ from the zenith. The more obliquely the rays fall, the greater the refraction.

NOTE 190, p. 154. _Bradley’s method of ascertaining the amount of refraction._ Let Z, fig. 50, be the zenith or point immediately above an observer at A; let H O be his horizon, and P the pole of the equinoctial A Q. Hence P A Q is a right angle. A star as near to the pole as s would appear to revolve about it, in consequence of the rotation of the earth. At noon, for example, it would be at s above the pole, and at midnight it would be in sʹ below it. The sum of the true zenith distances, Z A s, Z A sʹ, is equal to twice the angle Z A P. Again, S and Sʹ being the sun at his greatest distances from the equinoctial A Q when in the solstices, the sum of his true zenith distances, Z A S, Z A Sʹ, is equal to twice the angle Z A Q. Consequently, the four true zenith distances, when added together, are equal to twice the right angle Q A P; that is, they are equal to 180°. But the observed or apparent zenith distances are less than the true on account of refraction; therefore the sum of the four apparent zenith distances is less than 180° by the whole amount of the four refractions.

NOTE 191, p. 155. _Terrestrial refraction._ Let C, fig. 51, be the centre of the earth, A an observer at its surface, A H his horizon, and B some distant point, as the top of a hill. Let the arc B A be the path of a ray coming from B to A; E B, E A, tangents to its extremities; and A G, B F, perpendicular to C B. However high the hill B may be, it is nothing when compared with C A, the radius of the earth; consequently, A B differs so little from A D that the angles A E B and A C B are supplementary to one another; that is, the two taken together are equal to 180°. A C B is called the horizontal angle. Now B A H is the real height of B, and E A H its apparent height; hence refraction raises the object B, by the angle E A B, above its real place. Again, the real depression of A, when viewed from B, is F B A, whereas its apparent depression is F B E, so E B A is due to refraction. The angle F B A is equal to the sum of the angles B A H and A C B; that is, the true elevation is equal to the true depression and the horizontal angle. But the true elevation is equal to the apparent elevation diminished by the refraction; and the true depression is equal to the apparent depression increased by refraction. Hence twice the refraction is equal to the horizontal angle augmented by the difference between the apparent elevation and the apparent depression.

NOTE 192, p. 155. Fig. 52 represents the phenomenon in question. S P is the real ship, with its inverted and direct images seen in the air. Were there no refraction, the rays would come from the ship S P to the eye E in the direction of the straight lines; but, on account of the variable density of the inferior strata of the atmosphere, the rays are bent in the curved lines P c E, P d E, S m E, S n E. Since an object is seen in the direction of the tangent to that point of the ray which meets the eye, the point P of the real ship is seen at p and pʹ, and the point S seems to be in s and sʹ; and, as all the other points are transferred in the same manner, direct and inverted images of the ship are formed in the air above it.

NOTE 193, p. 156. Fig. 53 represents the section of a poker, with the refraction produced by the hot air surrounding it.

NOTE 194, p. 156. _The solar spectrum._ A ray from the sun at S, fig. 54, admitted into a dark room, through a small round hole H in a window-shutter, proceeds in a straight line to a screen D, on which it forms a bright circular spot of white light, of nearly the same diameter with the hole H. But when the refracting angle B A C of a glass prism is interposed, so that the sunbeam falls on A C the first surface of the prism, and emerges from the second surface A B at equal angles, it causes the rays to deviate from the straight path S D, and bends them to the screen M N, where they form a coloured image V R of the sun, of the same breadth with the diameter of the hole H, but much longer. The space V R consists of seven colours—violet, indigo, blue, green, yellow, orange, and red. The violet and red, being the most and least refrangible rays, are at the extremities, and the green occupy the middle part at G. The angle D g G is called the mean _deviation_, and the spreading of the coloured rays over the angle V g R the _dispersion_. The deviation and dispersion vary with the refracting angle B A C of the prism, and with the substance of which it is made.

NOTE 195, pp. 159, 164. Under the same circumstances, and where the refracting angles of the two prisms are equal, the angles D g G and V g R, fig. 54, are greater for flint-glass than for crown-glass. But, as they vary with the angle of the prism, it is only necessary to augment the refracting angle of the crown-glass prism by a certain quantity, to produce nearly the same deviation and dispersion with the flint-glass prism. Hence, when the two prisms are placed with their refracting angles in opposite directions, as in fig. 54, they nearly neutralize each other’s effects, and refract a beam of light without resolving it into its elementary coloured rays. Sir David Brewster has come to the conclusion that there may be refraction without colour by means of two prisms, or two lenses, when properly adjusted, even though they be made of the same kind of glass.

NOTE 196, p. 165. The object glass of the achromatic telescope consists of a convex lens A B, fig. 55, of crown-glass placed on the outside, towards the object, and of a concave-convex lens C D of flint-glass, placed towards the eye. The focal length of a lens is the distance of its centre from the point in which the rays converge, as F, fig. 60. If, then, the lenses A B and C D be so constructed that their focal lengths are in the same proportion as their dispersive powers, they will refract rays of light without colour.

NOTE 197, p. 165. If the mean refracting angle of the prism D g G, fig. 54, were the same for all substances, then the difference D g V - D g R would be the dispersion. But the angle of the prism being the same, all these angles are different in each substance, so that in order to obtain the dispersion of any substance the angle D g V - D g R must be divided by the angle D g G or its excess above unity, to which the mean refraction is always proportional. According to Mr. Fraunhofer the refraction of the extreme violet and red rays in crown-glass is 1·5466 and 1·5258; so D g V - D g R = 1·5466 - 1·5258 = ·0208, and half the sum of the excess of each above unity is = ·5362; consequently

(D g V - D g R)/D g G = ·0208/·5362 = 0·03879; for diamond

(D g V - D g R)/D g G = (2·467 - 2·411)/1·439 = 0·0389;

so that the dispersive power of diamond is a little less than that of crown-glass; hence the splendid refracted colours which distinguish diamond from every other precious stone are not owing to its high dispersive power, but to its great mean refraction.—SIR DAVID BREWSTER.

NOTE 198, p. 168. When a sunbeam, after having passed through a coloured glass V Vʹ, fig. 56, enters a dark room by two small slits O Oʹ in a card, or piece of tin, they produce alternate bright and black bands on a screen S Sʹ at a little distance. When either one or other of the slits O or Oʹ is stopped, the dark bands vanish, and the screen is illuminated by a uniform light, proving that the dark bands are produced by the interference of the two sets of rays. Again, let H m, fig. 57, be a beam of white light passing through a hole at H, made with a fine needle in a piece of lead or a card, and received on a screen S Sʹ. When a hair, or a small slip of card h hʹ, about the 30th of an inch in breadth, is held in the beam, the rays bend round on each side of it, and, arriving at the screen in different states of vibration, interfere and form a series of coloured fringes on each side of a central white band m. When a piece of card is interposed at C, so as to intercept the light which passes on one side of the hair, the coloured fringes vanish. When homogeneous light is used, the fringes are broadest in red, and become narrower for each colour of the spectrum progressively to the violet, which gives the narrowest and most crowded fringes. These very elegant experiments are due to Dr. Thomas Young.

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 6-1/2 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.

Name of Star. Proper Motion. Parallax. Observers and Computers.

α Centauri 3ʺ·764 0ʺ·92 Maclear. „ .. 1ʺ Henderson. 61 Cygni 5ʺ·123 0ʺ·374 Bessel. α Lyræ 0ʺ·364 0ʺ·207 Peters. Sirius 1ʺ·234 0ʺ·230 Henderson. Arcturus 2ʺ·269 0ʺ·127 Peters. Pole Star 0ʺ·035 0ʺ·106 Peters. Capella .. 0ʺ·046 Peters. La Chevre 0ʺ·461 0ʺ·046 Peters. ι Great Bear 0ʺ·746 0ʺ·133 Peters.

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

α Centauri 5 leagues Henderson and Maclear.
61 Cygni 10 leagues Bessel.
α Lyræ 2 leagues Struve and Peters.
Sirius 6 leagues Henderson and Maclear.
Arcturus 22 leagues Peters.
Pole Star ½ league Lindenau and Struve.
La Chevre 12 leagues Peters.
ι Great Bear 7 leagues Peters.

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:—

Name of Star. Period in Perihelion By whom Computed.
Years. Passage.

ζ Herculis 30·216 1831·41 Madler.

η Coronæ 42·500 1807·21 Madler.

ζ Cancri 58·910 1853·37 Madler.

ξ Ursæ Majoris 58·262 1817·25 Savary.

ω Leonis 82·533 1849·76 Villarceaux.

ρ Ophiuchi 73·862 1806·83 Encke.

3062 in Dorpat 94·765 1837·41 Madler.
Catalogue

ξ Bootis 117·140 1779·88 Sir J. Herschel.

δ Cygni 178·700 1862·87 Hind.

γ Virginis 182·120 1836·43 Sir J. Herschel.

Castor 252·660 1855·83 Sir J. Herschel.

ς Coronæ 736·880 1826·48 Hind.

γ Virginis 632·270 1699 Hind.

α Centauri 77·000 1851·50 Jacob.

Orbit of γ Virginis.

Perihelion passage 1836·40

Inclination 27° 36ʹ

Position of ascending Node 19 7

Angle between line of Nodes and 295° 13
Apsides

Excentricity 0·8794

Period in years 184·53

Orbit of ζ Herculis.

Perihelion passage 1830·56
Inclination 140° 39ʹ
Position of ascending Node 217° 14ʹ
Angle between line of Nodes and Apsides 266·53
Eccentricity 0·4381
Period in years 37·21

_Computed by J. Fletcher, Esq._, 1853.

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.

INDEX.

Aberdeen, high water at, 94.

Absorption, influence of, on temperature, 239;
difference of sea and land in power of, 242;
gradually decreasing, in transmission of radiant heat, 259;
of radiant heat, varying with substances, 268;
a transfer of force, 275, 276.

Acceleration of the moon’s mean motion, 37, 38.

Adams, Mr., perturbation in Uranus’s motion computed by, 22;
discovery of Neptune, 62.

Aërolites, theory of, 420, 423.

Africa, tidal wave passing, 94;
mean annual equatorial temperature in, 245;
indigenous productions of, 249, 250.

Air, comparative velocity of light in water and, 202.
_See_ Atmosphere.

Airy, Professor, periodic inequality in the solar system worked out by,
26;
phenomenon observed by, during an eclipse, 41;
mass of Jupiter ascertained by, 55;
experiments ascertaining its density, 57;
astronomical tables improved by, 63;
discoveries in polarization of light, 192, 193.

Aldebaran, an optically double star, 401.

Aleutian Islands, the, vegetation of, 252.

Alexandria, arc of the meridian measured between Syene and, 49.

Algæ, districts of distinct species of, 252;
banks of, in the Atlantic, 253.

Algol, fluctuations in lustre of, 390, 391.

Alhazen, effects of refraction observed by, 155.

Alkalies, resolved into metallic oxides, 307.

Alpha Antaris, “Coal Sacks” between α Centauri and, 386.

Alpha Aquilæ, an optically double star, 401.

—— Centauri, the parallax of, 54;
its rank, 384;
the Milky Way near, 386;
parallax, as determined by Henderson and Maclear, 387;
distance from the sun, 388;
orbit and mass of, 399, 400;
colour, 401;
amount of light emitted by, 404;
rate of its proper motion, 404, 405;
globular nebulous cluster, 414.

—— Crucis, zone of stars passing through, 385;
zone between η Argûs and, 390;
nebulous cluster round, 415.

—— Lyræ, the polar star of the northern hemisphere, 82;
parallax of, 388;
distance from the sun, 389;
an optically double star, 400;
amount of light emitted by, 404.

—— Orionis, a variable star, 393, 394.

Alum, experiments on the crystallization of, 106, 107;
heat transmitted through, 261, 262.

Amazons, the river of, distance from its mouth where tides are
perceptible, 98;
area occupied by forests on, 243.

America, course of the tidal wave along its coasts, 93, 94;
mean annual equatorial temperature in, 245;
separation of isothermal lines in high latitudes, _ib._;
number of known species of plants indigenous in, 249;
number of species of trees, 252;
shooting stars over the continent of, 421.

——, South, area of country raised by an earthquake in, 234.

Ampère, M., his discovery in electricity, 316;
theory of magnetism, 317, 318;
experiment testing his theory, 319, 320.

Analysis, boundless dominion of, 427, 428.

Andes, the, proportion of, to the earth’s mass, 6;
increasing rarity of the air experienced in ascending, 118.

Andromeda, nebula in, 413;
nebulous region of, 417.

Angström, the electric spark defined by, 303.

Animals, specific diversity of, laws regulating their distribution,
254, 255.

Annual equation, the, of the moon, 35, 36.

—— variations in mean values of the magnetic elements, 343.

Annular nebulæ, 409;
in the northern hemisphere, 410, 411.

Antarctic Ocean, tidal wave rising in 93;
period of its passage to the Thames, 94;
depth of the stratum of constant temperature in, 101;
depression of the barometer observed in, 120.

Antilles Islands, hurricanes beginning at, 126.

Antinori, Cav., experiments of, in electricity, 333.

Antinous, comet observed in the constellation of, 372;
the Milky Way between Orion and, 386.

Antithesis, the general character of magnetism, 339.

Aphelion of a planet’s path defined, 16.

Apogee, solar, its coincidence with the solstices, 86, 87.

April, 1833, disappearance of Saturn’s rings, 67;
apparent and mean time coinciding in, 84.

Apsides of an axis defined, 9;
direct, variable motion of, 14;
cause of their advance, or recession, 16.

Apures, the mission of the, Humboldt’s observations on sound at, 135.

Aqueous vapour, proportion of, in the atmosphere, 117.

Ara, nebula in, 414.

Arabian Gulf, the, monsoons blowing over, 124.

Arabs, the, their observations on planetary irregularities, 26;
lunar eclipses observed by, 38;
their division of time, 85;
the pendulum used as a measure of time by, 90.

Arago, François, experiment by, in proof of the undulatory theory of
light, 200;
decisive experiment suggested by, 202;
observations in photography, 213;
observations on the moon’s atmosphere, 226;
increase of temperature below the earth’s surface calculated by, 230;
slow communication of temperature from the earth, observed, 244;
source of magnetism discovered, 330;
theory of his magnetic experiments, 332;
divergent flames of a comet described by, 364;
his treatise on comets, 368;
nature of comet’s light determined by, 380, 381;
numbers of comets computed, 381, 382;
remark of, on _fixed_ stars, 405.

Arc, the Voltaic, 303-305.

Arcet, M. d’, vibration of fibres of the retina according to, 178.

Archer, Scott, stimulus given to photography by, 207.

Arcs of the meridian, mode of measuring, 47.

Arctic Sea, depth of the zone of constant temperature, 101.

—— regions, vegetation found in, 249.

Arcturus, comet bearing comparison with, 379;
rank of, 384.

Areas, described by the radii vectores of planets, a test of disturbing
forces, 10;
unequable description of, 15.

Argelander, M., period of a comet calculated by, 370;
his mode of estimating distance of fixed stars, 389;
periods of fluctuation in stars computed by, 390, 391;
sun’s motion proved, 405.

Argentine preparations in photography, chemical energy varying with,
207, 208;
changes effected by washing with alkalies, 210, 211.

Argo, variable star in, 393.

Aries, season of the sun’s entrance into, in Hipparchus’ age, 80.

Arseniate of soda, its crystals, 109.

Artesian wells, mode of sinking, origin of the name, 230.

Asia, indigenous productions of, 249.

Assyrians, the, division of time by, 85.

Astronomers, fruits of their labours, 3;
question still to be resolved by, 24;
terrestrial orbit differently measured by, 36.

Astronomical distances, method of measuring, 43;
tables, method of forming, 58-64.

Astronomy, its rank in the physical sciences, an important office of,
1;
studies necessary to the study of, 2;
the key to divers problems in physical science, 3;
the two greatest discoveries in, 23;
the three departments of, 58;
standards for measurement afforded by, 83;
application of, to chronology, 87-89;
furnishing standards of weights and measures, 89, 90;
atmospheric effects connecting the laws of molecular attraction with,
102;
progress lately made by, 419, 420.

Atalanta, diameter of, 56.

Atlantic Ocean, direction of tidal waves in, 93;
conditions modifying tides, 94;
depth of, 96;
currents, 100;
origin of hurricanes, 126;
superficial temperature of, 244;
distinct vegetation of the polar basin, 252;
beds of algæ in, 253;
meteors falling in, 421.

—— telegraph, 325, 326;
terrestrial magnetism disturbing, 346.

Atmosphere of nebulous stars, 411, 412.

—— of planets, 226, 227.

—— of the sun, its constitution, 42;
indications of an absorptive surrounding the luminous, 213;
the true, 224.

—— terrestrial, solar rays bent by, in lunar eclipses, 40;
influence of, in solar eclipses, 41;
its analysis, pressure on the surface of the globe, 117;
form of, gradual decrease in density of its strata, 117, 118;
influence of temperature on its density, 119;
mean pressure of, variable, 120;
the medium conveying sound, 129;
sympathetic vibrations transmitted by, 147, 148;
its action on light, falsifying vision, 153;
phenomena produced by accidental
changes in its strata, 155-156;
effects of increased density in the stratum in the horizon, 157, 158;
lunar heat absorbed by, 227;
cause of the cooler air in higher regions of, 240, 241;
sun’s heat modified by, 244;
action of electricity in, 284;
transmission of electricity by induction, 286;
periodical variations of electricity in, 291;
accidental developments of electricity, 291, 292;
cause of variations in its magnetism, 344, 345;
nebulous bodies made visible by, 421-423.

Atmospheric air, extreme elasticity of, 105.

—— pressure, effect of, on electricity, 288.

Atomic constitution determining crystalline forms, 109.

Atoms, qualities of, determining the nature of substances, 110;
differences in weight of, 111.

Attraction, modes of, in spheres, in the celestial bodies, 4;
determining the forms of planets, 6;
determining the motions of planets, 7;
solar, compelling the elliptical revolutions of planets, 8;
mutual, of planets, complicating their motions, 10;
interference of, disturbing the motions of heavenly bodies, 11;
disturbances from the operation of reciprocal, 13;
disturbances from inequality of, 14;
of satellites to primaries, little disturbed, 26;
disturbing force of, in spheroids, 27;
its effects on Jupiter’s satellites, 28;
sun’s, of the moon, 34;
principle modifying the earth’s, 37;
local, affecting the plumb-line, 48;
comparative force of the sun’s, 57;
of an external body affecting a spheroid, 79;
producing tides, 91, 92;
of particles of matter, 103;
capillary, 113;
producing annual atmospheric undulations, 121;
the lunar atmosphere affected by, 226;
expansive force of heat overcoming, 271;
of electricities, 283;
destruction of, producing electricity, 284;
laws of electrical, 286-288;
modes of, in static and in voltaic electricity, 317;
action of planetary, on comet’s orbits, 361-363;
range of solar, 365.

Aurora, the, affecting the compass, 312.

Australia, evidence of deserts in the interior of, 124;
species of plants common to Europe and, 251.

Auvergne, temperature of hot springs in, 231.

Axes, change in form of masses revolving round, 6.

——, major, length of, in orbits, invariable, 20;
of the orbits of Jupiter’s satellites, cause of the direct motion
observed in, 28;
position of, in the solar system, 65;
a nutation in planetary, 66;
of the moon, 68, 69;
mechanical law affecting, 76.

——, optic, of crystals, 183.

Axis, greater, of the earth’s orbit, period of its revolution, 38;
period of the earth’s revolution, 58;
excess of Jupiter’s equatorial over his polar, 66;
of rotation, proof of its being invariable, 76, 77.

——, major, of a planet’s orbit, distance from the sun measured by, 8;
designation of its extremities, 9;
length of, determining the form of the orbit, 10;
periods of its revolutions, 17;
length of, not permanently changed, 20;
Jupiter’s periodically diminished, Saturn’s increased, 26;
of the solar ellipse, period of its revolution, 86.

——, magnecrystallic, 349.

Azores, the, icebergs reaching, 100.

Babbage, Charles, his theory of volcanic action, 235-237;
quotation from, on the nature of force, 353.

Babinet, M., his theory of dark lines observed in the solar spectrum,
163;
comet’s light computed by, 359.

Babylon, eclipse observed at, 36.

Bacon, Francis, anticipation of discovery by, 32.

Baily, Mr., compression of the terrestrial spheroid calculated by, 50;
density of the earth determined, 57;
fictitious antiquity ascribed to Indian astronomical observations,
88.

Bali, volcanic eruption in, 233.

Balloon, rarity of the air felt in a, 118;
observations made from, 119.

Baltic, the, a tideless sea, 98;
decreased atmospheric pressure on the shores of, 120.

Barlow, Mr., observations supporting his theory of electric currents,
346.

Barometer, the, principles of cohesion and attraction applied to the
construction of, 113;
density of the atmosphere measured by, 117;
mean heights of, varying with atmospheric densities, 118;
mountain heights measured by, 119, 120;
atmospheric phenomena affecting, 120;
used to trace the course of atmospheric waves, 121;
cause of sudden fall in, before hurricanes, 127;
refraction varying with, 154.

Barrow, Cape, observations on magnetic storms at, 345, 346.

Battery, voltaic, construction of, 298, 299;
Professor Daniell’s improvements, 299, 300;
action of, charged with water, 300;
constant flow of electricity obtained by means of, 312.

——, magnetic, constructed by Dr. Faraday, 324, 325;
Mr. Henley’s magneto-electric, 325;
Atlantic telegraph, 326;
structure of, for land telegraphs, 328;
relation of heat to power of, 329;
thermo-electric, 333.

Batsha, port of, tides neutralised in, 99.

Bayle, comparative density of the atmosphere in interplanetary space
according to his law, 356.

Bear, Little, the, the polar star in, 82.

Becquerel, M. E., unexplained photographic phenomenon observed by, 213;
phosphorescent property in the solar spectrum discovered, 216;
cause of phosphorescence, 217;
electricity excited by pressure, 283;
light attributed to electricity by, 284;
cause of phosphorescence investigated, 296;
instrument comparing intensities of electricities invented, 300;
crystals formed by agency of electricity, 308;
thermo-electric battery constructed by, 333;
effect of atmospheric on terrestrial magnetism estimated, 345.

Beehive, the, a nebulous star, 415.

Berard, M., experiments of, in polarizing heat, 264.

Berlin, line of coincidence in temperature passing through, 238.

Berne, increasing temperature of a deserted mine in, 230.

Berre, Dr., photographic pictures perfected by, 205.

Bessel, M., his calculations from measurements of arcs of the meridian,
48;
calculation of the sun’s mean apparent diameter, 56;
his computation of the mass of Saturn’s ring, 68;
diminished obliquity of the ecliptic observed by, 81;
parallax calculated, 389;
his theory of Sirius’s irregular motions, 392;
catalogue of double stars, 396;
mass of 61 Cygni found by, 404.

Beta Lyræ, a variable star, 391;
nebula between γ Lyræ and, 410.

Benzenberg, M., velocities of falling stars computed by, 423.