NOTES. 



451 



base A B makes with the meridian, be measured, the length of the sides 

 B m, Am, may be obtained by computation, so that A. m, a small part of 



Fig. 31. 



the meridian, is determined. Again, if D be a point visible from the ex- 

 tremities of the known line B C, two of the angles of the triangle BCD 

 may be measured, and the length of the sides C D, B D, computed. Then, 

 if the angle B m m' be measured, all the angles and the side B m of the 

 triangle B m m' are known, whence the length of the line m m' may be 

 computed, so that the portion A m' of the meridian is determined, and in 

 the same manner it may be prolonged indefinitely. 



- NOTE 127, pp. 47, 49. The square of the sine of the latitude. Q 6 m, 

 fig. 30, being the latitude of m, em is the sine and b e the cosine. Then 

 the number expressing the length of e m, multiplied by itself, is the square 

 of the sine of the latitude ; and the number expressing the length of 6 e, 

 multiplied by itself, is the square of the cosine of the latitude. 



NOTE 128, p. 48. The polar diameter of the earth determined by the 

 survey of Great Britain is 7900 miles ; the equatorial is 7926, which gives 

 a compression of 595.53. 



NOTE 129, p. 50. A pendulum is that part of a clock which swings to 

 and fro. 



NOTE 130, p. 52. Parallax. The angle S6, fig. 29, under which 

 we view an object a b : it therefore diminishes as the distance increases. 

 The parallax of a celestial 



object is the angle which *V- 62 " 



the radius of the earth 

 would be seen under, if 

 viewed from that object. 

 Let E, fig. 32, be the 

 centre of the earth, E H 

 its radius, and m H the 

 horizon of an observer at 

 H. Then HmE is the 

 parallax of a body m, the 

 moon for example. As m 

 rises higher and higher in 

 the heavens to the points 

 m', m", &c., the parallax 

 H m' E, H m" E, &c., de- 

 creases. At Z, the zenith, 

 or point immediately above 

 the head of the observer, it is zero ; and at m, where the body is 



