Note 153, [p. 88]. Zenith distance is the angular distance of a celestial object from the point immediately over the head of an observer.
Note 154, [p. 89]. 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 155, [p. 90]. 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 156, [p. 93]. 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 157, [p. 96]. 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 158, [p. 96]. If S be the earth, fig. 14, d the sun, and C Q 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 90°.
Note 159, [p. 97]. Declination. If the earth be in C, fig. 11, and if q ♈ Q be the equinoctial, and N m S a meridian, then m C n is the declination of a body at n. Therefore the cosine of that angle is the cosine of the declination.
Note 160, pp. [99], [131]. Fig 37 shows the propagation of waves from two points C and Cʹ, 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 161, [p. 100]. 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 b m 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 towards the equator.
