HOW THE EARTH IS WEIGHED. 



745 



A S and B S', representing the direction of the star S, as seen from the 

 points A and B, may, in consequence of the immense distance of the 

 star from the earth, be regarded as parallel. On account of the prox- 

 imity of the mountain G, the plumb-line does not take the direction 



Fig. 1. 



A Z, but is deflected toward the mountain, so that it gives the direc- 

 tion A Z' as the apparent vertical, and Z' as the apparent zenith. On 

 this account, the zenith-distance of the star is increased by the angle a, 

 to a degree that is represented by the angle m. The prolonged plumb- 

 lines B Z" and A Z' consequently do not form the angle x at the center 

 of the earth, but another angle, y, which differs from x by the magni- 

 tude a, wherefore, a = xi/. If, now, we imagine the line of direction 

 A S prolonged backward, an equivalent of the angle u is formed at T, 

 and by the lines A C and A T the angle m, equal to the observed 

 zenith-distance at A. But u being the external angle of a triangle, 

 = m 2/, or i/ = mu; and since a is equal to a- y, if we substitute 

 for y the difference m u, a = x + u m. The angles n and ni have 

 been obtained b}^ observation as zenith-distances of the fixed star S S', 

 and we have only to obtain the value of the angle x, which is deduced 

 from a trigonometrical measurement of the arc A B. The mass of the 



