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NOTE 162, p. 106. Analytical formula or expression. A combination of symbols or signs expressing or representing a series of calculation, and including every particular case that can arise from a general law.
NOTE 163, p. 106. Fig. 38 is a perfect octahedron. Sometimes its angles, A, X, a, a, &c., are truncated, or cut off. Sometimes a slice is cut off its edges A a, X a, a a, &c. Occasionally both these modifications take, place.
NOTE 164, p. 107. Prismatic crystals of sulphate of nickel are somewhat like fig. 62, only that they are thin, like a hair.
Note 165, p. 108. Zinc, a metal either found as an ore or mixed with other metals. It is used in making brass.
NOTE 166, p. 108. A cube is a solid contained by six plane square surfaces, as fig. 39. Fig. 39.
NOTE 167, p. 108. A tetrahedron is a solid contained by four triangular surfaces, as fig. 40 : of this solid there are many varieties.
NOTE 168, p. 108. There are many varieties of the octahedron. In that mentioned in the text, the base a a a a, fig. 38, is a square, but the base may be a rhomb; this solid may also be elongated in the direction
of its axis A X, or it may be depressed. NOTE 169, pp. 109, 192, 273. A rhombohedron is a solid contained by six plane surfaces, as in fig. 63, the opposite planes being equal and similar rhombs parallel to one another; but all the planes are not necessarily equal or similar, nor are its angles right angles. In carbonate of lime the angle CAB is 1050.55, and the angle B or C is 750.05.
NOTE 170, p. 109. Sublimation. Bodies raised into vapour which is again condensed into a solid state.
NOTE 171, p. 112. Platinum. The heaviest of metals; its colour is between that of silver and lead.
NOTE 172, p. 113. The surface of a column of water, or spirit of Note 174, p. 114. In fig. 41 the line cd shows the direction of the resulting force in the two cases.
wine, in a capillary tube, is hollow ; and that of a column of quicksilver is convex, or rounded, as in fig. 41.
NOTE, 173, p. 113. Inverse ratio, &c. The elevation of the liquid is greater in proportion as the internal diameter of the tube is less.
NOTE 175, p. 115. When two plates of glass are brought near to one another in water, the liquid rises between them ; and, if the plates touch each other at one of their upright edges, the outline of the water will become an hyperbola.
NOTE 176, p. 115. Let A A’, fig. 42, be two plates, both of which are wet, and B B'two that are dry. When partly immersed in a liquid, its
surface will be curved close to them, but will be of its usual level for the rest of the distance. At such a distance they will neither attract nor repel one another. But, as soon as they are brought near enough to have the whole of the liquid surface between them curved, as in a d', bb', they will rush together. If one be wet and another dry, as C C', they will repel one another at a certain distance ; but, as soon as they are brought very near, they will rush together, as in the former cases.
NOTE 177, p. 123. In a paper on the atmospheric changes that produce rain and wind, by Thomas Hopkins, Esq., in the Geographical Journal, it is shown that, when vapour is condensed and falls in rain, a partial vacuum is formed, and that heavier air presses in as a current of wind. Thus the vacuum arising from the great precipitation at the tropics causes the polar winds to descend from the upper regions of the atmosphere and blow along the surface to the equator as trade winds to supply the place of the hot currents that are continually raising them into the higher regions. This circumstance removes the only difficulty in Lieutenant Maury's theory of the winds.
NOTE 178, p. 134.. Latent or absorbed heat. There is a certain quantity of heat in all bodies, which cannot be detected by the ther. mometer, but which may become sensible by compression.
Note 179, p. 137. Reflected waves. A series of waves of light, sound, cr water, diverge in all directions from their origin I, fig. 43, as from a
centre. When they meet with an obstacle SS, they strike against it, and are reflected or turned back by it in the same form as if they had proceeded from the centre C, at an equal distance on the other side of the surface SS.
Note 180, p. 138. Elliptical shell. If fig. 6 be a section of an elliptical shell, then all sounds coming from the focus S to different points on the surface, as m, are reflected back to F, because the angle Tm S is equal to tm F. In a spherical hollow shell, a sound diverging from the centre is reflected back to the centre again.
NOTE 181, p. 142. Fig 44 represents musical strings in vibration ; the straight lines are the strings when at rest. The first figure of the four
would give the fundamental note, as, for example, the low C. The second and third figures would give the first and second harmonics ; that is, the octave and the 12th above C, nnn being the points at rest; the fourth figure shows the real motion when compounded of all three.
NOTE 182, p. 143. Fig. 45 represents sections of an open and of a shut pipe, and of a pipe open at one end. When sounded, the air spontaneously divides itself into segments. It remains at rest
Fig. 45. in the divisions or nodes nn', &c., but vibrates between them in the direction of the arrow-heads. The undulations of the whole column of air give the fundamental note, while the vibrations of the divisions give the harmonics.
NOTE 183, p. 144. Fig. 1, plate 1, shows the vibrating surface when the sand divides it into squares, and fig. 2 represents the same when the nodal lines divide it into triangles. The portions marked a a are in different states of vibration from those marked b b.
NOTE 184, p. 145. Plates 1 and 2 contain a few of Chladni's figures. The white lines are the forms assumed by the sand, from different modes of vibration, corresponding to musical notes of different degrees of pitch. Plate 3 contains six of Chladni's circular figures.
Note 185, p. 145. Mr. Wheatstone's principle is, that when vibrations producing the forms of figs. 1 and 2, plate 3, are united in the same surface, they make the sand assume the form of fig. 3. In the same manner, the vibrations which would separately cause the sand to take the forms of figs. 4 and 5, would make it assume the form in fig. when united. The figure 9 results from the modes of vibration of 7 and 8 combined. The parts marked a a are in different states of vibration from those marked bb. Figs. 1, 2, and 3, plate 4, represent forms which the sand takes in consequence of simple modes of vibration ; 4 and 5 are those arising from two combined modes of vibration; and the last six figures arise from four superimposed simple modes of vibration. These complicated figures are determined by computation independent of experiment.
NOTE 186, p. 146. The long cross-lines of fig. 46 show the two systems of nodal lines given by M. Savart's laminæ.
NOTE 187, p. 146. The short lines on fig. 46 show the positions of the nodal lines on the other sides of the same laminæ.
NOTE 188, p. 146. Fig. 47 gives the nodal lines on a cylinder, with the paper rings that mark the quiescent points.
NOTE 189, pp. 138, 153, 156. Reflection and Refraction. Let PCp, 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 CS, and the other part is bent at C, and passes through the glass or water in the
direction CR. I Cis called the incident $' ray, and ICP the angle of incidence ;
CS is the reflected ray, and PCS the A
angle of reflection ; C R is the refracted ray, and PCR the angle of refraction. The plane passing through SC and IC is the plane of reflection, and the plane passing through I C and CR is the plane of refraction. In ordinary cases, C I,
CS, CR, 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, I'C, being rays incident on the surface at C, they will be reflected into CS, CS, so that the angle SCP will be equal to the angle IC P, and S'C P equal to IC P. That is by no means the case with the refracted rays. The incident rays I C, IC, are bent at C towards the perpendicular, in the direction CR, CR'; 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 Im, the sine of ICP, divided by the number expressing the length of Rn, the sine of RC 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, 2487; 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 RC, R'C, become the incident rays; and in this case the refracted rays, CI,CI', 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 m', so that the angle p Cr is equal to p Cr'; that frequently happens at the second surface of glass. When a ray IC 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 IC; 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° 32' counted from the surface, the glass reflects 4 times more light than it transmits. At an angle of 7° 1' the reflected light is double of the transmitted ; at an angle of 11° 8' the light reflected is equal to that transmitted ; at 17° 17' the reflected is