NOTE 140. p. 85. Inversely proportional, &c. That is, the total amount of solar radiation becomes less as the minor axis C C', fig. 20., of the earth's orbit becomes greater.

NOTE 141. p. 87. Fig. 35. represents the position of the apparent orbit of the sun as it is at present, the earth being in E. The sun is nearer to the earth in moving through PY, than in moving through YA, but its motion through PY is more rapid than its motion through YA; and as the swiftness of the motion and the quantity of heat received vary in the same proportion, a compensation takes place.

A

Fig. 35.

S

W

P

NOTE 142. p. 88. In an ellipsoid of revolution, fig. 1., the polar diameter N S and every diameter in the equator q E Qe are permanent axes of rotation, but the rotation would be unstable about any other. Were the earth to begin to rotate about C a, the angular distance from a to the equator at q would no longer be ninety degrees, which would be immediately detected by the change it would occasion in the latitudes.

NOTE 143. pp. 62. 93. Let q Y Q, and EY e, fig. 11., be the planes of the equator and ecliptic. The angle e Y Q, which separates them, called the obliquity of the ecliptic, varies in consequence of the action of the sun and moon upon the protuberant matter at the earth's equator. That action brings the point Q towards e, and tends to make the plane q Y Q coincide with the ecliptic EY e, which causes the equinoctial points, Y and , to move slowly backwards on the plane e E at the rate of 5041 annually. This part of the motion, which depends upon the form of the earth, is called luni-solar precession. Another part, totally independent of the form of the earth, arises from the mutual action of the earth, planets, and sun, which, altering the position of the plane of the ecliptic e E, causes the equinoctial points Y and to advance at the rate of 031 annually; but as this motion is much less than the former, the equinoctial points recede on the plane of the ecliptic at the rate of 50" 1 annually. This motion is called the precession of the equinoxes.

NOTE 144. pp. 76. 95. Let qYQ,e Y E, fig. 56., be the planes of the equinoctial or celestial equator and ecliptic, and p, P, their poles. Then suppose p, the pole of the equator, to revolve with a tremulous or wavy motion in the little ellipse pc db in about 19 years, both motions being very small, while the point a is carried round in the circle a A B in 25,868 years. The tremulous motion may represent the half-yearly variation, the motion in the ellipse gives an idea of the nutation discovered by Bradley, and the motion in the circle a A B arises from the

greater axis p d of the small ellipse is 18" 5, its minor axis b c is 1374. These motions are so small, that they have very little effect on the parallelism of the axis of the earth's rotation during its revolution round the sun, as represented in fig. 20. As the stars are fixed, this real motion in the pole of the earth must cause an apparent change in their places.

NOTE 145. p. 97. Let N be the pole, fig. 11., e E the ecliptic, and Q q the equator. Then N n m S being a meridian, and at right angles to the equator, the arc Ym is less than the arc Y n.

NOTE 146. p. 99. Heliacal rising of Sirius. When the star appears in the morning, in the horizon, a little before the rising of the sun.

NOTE 147. p. 101. Let PYA, fig. 35., be the apparent orbit or path of the sun, the earth being in E. Its major axis, A P, is at present situate as in the figure, where the solar perigee P is between the solstice of winter and the equinox of spring. So that the time of the sun's passage through the arcY A is greater than the time he takes to go through the arc PY. The major axis A P coincided with Y, the line of the equinoxes, 4000 years before the Christian era; at that time P was in the point Y. In 6468 of the Christian era, the perigee P will coincide with . In 1234 A.D. the major axis was perpendicular to Y, and then P was in the winter solstice.

NOTE 148. p. 102. At the solstices, &c. Since the declination of a celestial object is its angular distance from the equinoctial, the declination of the sun at the solstice is equal to the arc Q e, fig. 11., which measures the obliquity of the ecliptic, or angular distance of the plane Ye from the plane.

NOTE 149. p. 102. Zenith distance is the angular distance of a celestial object from the point immediately over the head of an observer.

NOTE 150. p. 104. Reduced to the level of the sea. The force of gravitation decreases as the square of the height above the surface of the earth increases, so that a pendulum vibrates slower on high ground; and in order to have a standard independent of local circumstances, it is necessary to reduce it to the length that would exactly make 86,400_vibrations in a mean solar day at the level of the sea.

NOTE 151. p. 104. A quadrant of the meridian is a fourth part of a meridian, or an arc of a meridian containing 90°, as N Q, fig. 11.

NOTE 152. p. 107. The angular velocity of the earth's rotation is at the rate of 180° in twelve hours, which is the time included between the passages of the moon at the upper and under meridian.

NOTE 153. p. 109. If S be the earth, fig. 14., d the sun, and CQ O D 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 S Q, or d S D, each of which is 900.

NOTE 154. pp. 110, 111. Declination. If the earth be in C, fig. 11., and if qYQ 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. 112. 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. 115. 148. Fig. 37. shows the propagation of waves from 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. 116. 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 Qmn 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 158. p. 125. 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. 128. Platina. The heaviest of metals; its colour is between that of silver and lead.

NOTE 162. p. 131. Zinc, a metal either found as an ore, or mixed with other metals. It is used in making brass.

NOTE 163. p. 131. A cube is a solid contained by six plane square surfaces, as fig. 39.

Fig. 39.

Fig. 40.

B

NOTE 164. p. 132. A tetrahedron is a solid contained by four triangular surfaces, as fig. 40.: of this solid there are many varieties.

In that

NOTE 165. p. 132. There are many varieties of the octahedron. 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 166. p. 133. 221. 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 75°.05.

NOTE 167. p. 133. Sublimation. Bodies raised into vapour which is again condensed into a solid state.

Fig. 41.

NOTE 168. p. 134. 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.

Note 169. p. 134. Inverse ratio, &c. The elevation of the liquid is greater in proportion as the internal diameter of the tube is less.

NOTE 170. p. 136. In fig. 41. the line cd shows the direction of the resulting force in the two cases.

NOTE 171. p. 156. 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 172. p. 137. 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 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 173. p. 153. 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. 156. 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.

S