if qQ be the equinoctial, and NmS 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 153. p. 118. 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 154. pp. 120. 150. fig. 37. Shows the propagation of waves from two points C and C', where stones are supposed to have fallen. Those points in Fig. 37.

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 155. p. 121. The centrifugal force may, &c. The centrifugal force acts in a direction at right angles, to NS, the axis of rotation, fig. 30. Its effects are equivalent to two forces, one of which is in the direction b m perpendicular to the surface Qm 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 towards the equator.

NOTE 156. p. 127. 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 157. p. 131. Platina. The heaviest of metals; its colour is between that of silver and lead.

⚫ NOTE 158. p. 132. 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, Xa, a a, &c. Occasionally both these modifications take place.

Fig 38.

a

X

NOTE 159. p. 133. Prismatic crystals of sulphate of nickel are somewhat like fig. 62., only that they are thin, like a hair.

NOTE 160. p. 134. Zinc, a metal either found as an ore, or mixed with other metals. It is used in making brass.

NOTE 161. p. 135. A cube is a solid contained by six plane square surfaces as fig. 39.

Fig. 39.

•A

Fig. 40.

C

B

NOTE 162. p. 135. surfaces, as fig. 40.

A tetrahedron is a solid contained by four triangular of this solid there are many varieties.

NOTE 163. p. 135. There are many varieties of the octahedron. In tha mentioned in the text, the base a aa 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 164. pp. 136. 229. 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 165. p. 136. Sublimation. Bodies raised into vapour which is again condensed into a solid state.

NOTE 166. p. 137. 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 167. p. 137. Inverse ratio, &c. The elevation of the liquid is greater, in proportion as the internal diameter of the tube is less.

NOTE 168. p. 139. In fig. 41., the line c d shows the direction of the resulting force in the two cases.

NOTE 169. p. 139. 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 170. p. 140. 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, b b, 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 171. p. 155.

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.

Nore 172. p. 159. Reflected waves. A series of waves of light, sound, or water, diverge in all directions from their origin I, fig. 43., as from a centre.

When they meet with an obstacle S S, 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 S S.

NOTE 173. p. 160. 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.

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 harmonies; that is, the

octave and the 12th above C, nnn being the points of rest; and the fourth figure shows the real motion when compounded of all three.

NOTE 175. p. 167. 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 176. p. 169. 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 bb.

NOTE 177. p. 170. 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 178. p. 171. 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. 6. when united. The fig. 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 b, b. Figs. 1, 2. and 3. plate 4. represent forms which the sand takes, in conse quence 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 supermposed simple modes of vibration. These complicated figures are de

termined by computation independent of experiment.

NOTE 179. p. 171.

The long cross lines of fig. 46. show the two systems of nodal lines given by M. Savart's lamina.