NOTES. 



457 



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 neces- 

 sary 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 D 

 the orbit of the moon, then C and are the syzygies. When the moon is 

 new, she is at C, and when full she is at ; 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 0, 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 cyo 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 C', where 



stones are supposed to have **9* ^- 



fallen. Those points in which 

 the waves cross each other 

 are the places where they 

 counteract each other's ef- 

 fects, so that the water is 

 smooth there, while it is 

 agitated in the intermediate 

 spaces. 



NOTE 161, p. 100. The 

 centrifugal force may, tyc. 

 The centrifugal force acts in 

 a direction at right angles to 

 N S, the axis of rotation, 

 fig. 30. Its effects are equi- 

 valent to two forces, one of 



which is in the direction bm 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. 



X 



