rate of 1800 in twelve hours, which is the time included between the passages of the moon at the upper and under meridian.

NOTE 153, p. 99.-If S be the earth, fig. 14, d the sun, and CQOD the orbit of the moon, then C and O are the syzygies. When the moon is new she is at C, and when full she is at O; and as both sun and moon are then on the same meridian, it occasions the spring-tides, it being high water at places under C and O, while it is low water at those under Q and D. The neap-tides happen when the moon is in quadrature at Q or D, for then she is distant from the sun by the angle d SQ, or d SD, each of which is 900.

NOTE 154, pp. 89, 90.-Declination. If the earth be in C, fig. 11, and if q TQ be the equinoctial, and N m S a meridian, then m Cn is the declination of a body at n. Therefore the cosine of that angle is the cosine of the declination.

NOTE 155, p. 91.-Moon s southing. The time when the moon is on the meridian of any place, which happens about forty-eight minutes later every day.

NOTE 156, pp. 93, 124.-Fig. 37 shows the propagation of waves from

Fig. 37.

C

two points C and C', where stones are supposed to have fallen. Those points in which the waves cross each other, are the places where they counteract each other's effects, so that the water is smooth there, while it is agitated in the intermediate spaces.

NOTE 157, p. 94.-The centrifugal force may, &c. The centrifugal force acts in a direction at right angles to N S, the axis of rotation, fig. 30. Its effects are equivalent to two forces, one of which is in the direction bm perpendicular to the surface Q m n of the earth, and diminishes the force of gravity at m. The other acts in the direction of the tangent m T, which makes the fluid particles tend toward the equator.

NOTE 158, p. 101.--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 159, p. 104.-Platina. The heaviest of metals; its color is between that of silver and lead.

NOTE 160, p. 105.-Fig. 38 is a perfect octahedron. Sometimes 'ts angles, A, X, a, a, &c., are truncated, or cut off. Sometimes a slice is cut

off its edges A a, Xa, a a, &c. Occasionally both these modifications take place.

NOTE 161, p. 106.

X

Prismatic crystals of sulphate of nickel are some

what like fig. 62, only that they are thin, like a hair.

NOTE 162, p. 106. Zinc, a metal either found as an ore or mixed with other metals. It is used in making brass.

NOTE 164, p. 107.-A tetrahedron is a solid contained by four triangular surfaces, as fig. 40: of this solid there are many varieties.

NOTE 165, p. 107. 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 AX, or it may be depressed.

NOTE 166, pp. 108, 186.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 C A B is 1050-55, and the angle B or C is 750.05.

NOTE 167, p. 108. — Sublimation. Bodies raised into vapor which i again condensed into a solid state.

NOTE 168, p. 109. The surface of a column of water, or spirit of wine, in a capillary tube, is hollow; and that of a column of quicksilver is convex, or rounded, as in fig. 41.

Fig. 41.

NOTE 169, p. 109.-Inverse ratio, &c. The elevation of the liquid is greater in proportion as the internal diameter of the tube is less.

NOTE 170, p. 110.-In fig. 41, the line cd shows the direction of the resulting force in the two cases.

NOTE 171, p. 110.-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 a hyperbola.

NOTE 172, p. 111.-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 a, bb', they will rush together. If one be wet and another dry, as CC', 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 173, p. 128.-Latent heat. There is a certain quantity of heat in all bodies, which cannot be detected by the thermometer, but which may become sensible by compression.

NOTE 174, p. 131.-Reflected waves. A series of waves of light, sound,

or water, diverge in all directions from their origin I, fig. 43, as from a center. When they meet with an obstacle 8 S, they strike against it, and are reflected or turned back by it in the same form, as if they had proceeded from the center C, at an equal distance on the other side of the surface SS.

NOTE 175, p. 132.-Elliptical shell. If fig. 6 be a section of an eilip tical 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 TmS is equal to tm F. In a spherical hollow shell, a sound diverging from the center is reflected back to the center again.

NOTE 176, p. 136. Fig. 44 represents musical strings in vibration; the Fig. 44.

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 of rest; the fourth figure shows the real motion when compounded of all three.

NOTE 177, p. 137. 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 in the divisions

or nodes n n', &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 178, p. 139. 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 179, p. 140. 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 180, p. 140. 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 of fig. 6 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 experi

ment.

NOTE 181, p. 140.-The long cross-lines of fig. 46 show the two systems of nodal lines given by M. Savart's laminæ.

[Fig. 46.

NOTE 182, p. 141.-The short lines on fig. 46 show the positions of the nodal lines on the other sides of the same laminæ.

NOTE 183, p. 141.-Fig. 47 gives the nodal lines on a cylinder, with the paper rings that mark the quiescent points.

Fig. 47.

149.-Reflection and refraction. Let PC p, fig. 48, be perpendicular to a surface of glass or water AB. When a ray of light, passing through the air, falls on this surface in any direction IC, 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 C R. IC is called the incident ray, and ICP the angle of incidence; CS is the reflected ray, and PCS the angle of reflection: CR is the refracted ray, and PCR the angle of refraction. The plane passing through S C and IC is the plane of reflection, and the plane passing through IC and CR is the plane of refraction. In ordinary cases, CI, CS, CR, are all