486 



NOTES. 



NOTE 150, p. 100. 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. 101. 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. 103. 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. 105. 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 154, pp. 105, 107. Declination. If the earth be in C, fig. 11, and if 

 q Y> 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 declina- 



NOTE 155, p. 108. 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. 110, 145. Fig. 37 shows the propagation of waves from two 

 Fig. 37. 



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 



