NOTES. 



411 



A , a small part of the meridian, is determined. Again, if D be a point 

 visible from the extremities of the known line BC, two of the angles of 

 the triangle BCD may be measured, and the length of the sides CD, 

 BD, computed. Then if the angle Emm' he measured, all the angles 

 and the side B m of the triangle Emm' are known, whence the length of 

 the line m m' may lie computed, so that the portion A m' of the meridian 

 is determined, and in the same manner it may be prolonged indefinitely. 



NOTE 126, pp. 47. 48. The square of the sine of the latitude. Q. b m, fig. 

 30. being the latitude ofm,em is the sine, and b e the cosine. Then the 

 number expressing the length of em, multiplied by itself, is the square of 

 the sine of the latitude ; and the number expressing the length of A , 

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



NOTE 127, p. 49. A pendulum is that part of a clock which swings to 

 and fro. 



NOTK 128, p. 51. Parallax. The angle aSft, 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 the radius of the earth 

 would lie seen under, if viewed from that object. Let E, fig. 32, be the 



Fig. 32. 



center of the earth. E H .ts radius, and m H O the horizon of an observer 

 at H. Then H m E is the parallax of a body m, the moon for example. 

 As TO rises higher and higher in the heavens to the points m', m", &c., 

 the parallax H m' E, H m" E, &c. decreases. At Z, the zenith, or point 

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

 the body is in the horizon, the angle H m E is the greatest possible, and 

 is called the horizontal parallax. It is clear that with regard to celestial 

 bodies the whole effect of parallax is in the vertical, or in the direction 

 m m' Z ; and as a person at H sees m' in the direction H m' A, when it 

 really is in the direction E m' B, it makes celestial objects appear to be 

 lower than they really are. The distance of the moon from the earth 

 has been determined from her horizontal parallax. The angle E m H 

 can be measured. EH m is a right angle, and EH, the radius of the 

 earth, is known in miles ; whence the distance of the moon E m is easily 

 found. Annual parallax is the angle under which the diameter of the 

 earth's orbit would be seen, if viewed from a star. 



NOTE 129, p. 52. The radii n B, n G, &c., fig. 3, are equal in any one 



