416 



NOTES. 



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. 99. 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 a 

 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 dSQ,, or tfSD, 

 each of which is 90. 



NOTE 154, pp. 89, 90. Declination. If the earth be in C, fig. 11, and 

 if q T Q, be the equinoctial, and N m S a meridian, then in C n is the de- 

 clination of a body at n. Therefore the cosine of that angle is the cosine 

 of the declination. 



NOTE 155, p. 91. 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. 93, 124. Fig. 37 shows the propagation of waves from 



Fig. 37. 



1 



C- C' 



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. 94. The centrifugal force may, 8,-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 

 bm perpendicular to the surface Q,m?t of the earth, and diminishes the 

 force of gravity at m. The other acts in the direction of the tangent mT, 

 which makes the fluid particles tend toward the equator. 



NOTE 158, p. 101. 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. 104. Platina. The heaviest of metals; its color is be- 

 ; of silv* 



tween that 



ver and lead. 



NOTE 160, p. 105. Fig. 38 is a perfect octahedron. Sometimes ! ts an- 

 gles, A,X, a, a, &c., are truncated, or cut off. Sometimes a slice is cut 



