ASTRONOMY. J5 



The distances of bodies having different horizontal 

 parallaxes, are therefore inversely as the sines of 

 those parallaxes, or, when the parallaxes are small, 

 inversely as the parallaxes themselves. 



76. If two observers, under the same meridian, 

 but at a great distance from one another, ob- 

 serve the zenith distances of the same star, 

 when it passes the meridian on the same day, 

 they can from thence determine the horizontal 

 parallax. 



If the amplitude of the arch of the meridian inter- 

 cepted between the zeniths of the observers, be 

 called a, and if <p and <p' be the zenith distances ob- 

 served, making one of them negative in respect of 

 the other, if the star be between the two zeniths, 



thenP= 



sm <p sin <p' 



a. If A and B (fig. 7.) be the places of the observers, 

 Z, Z' their zeniths, and C the centre of the earth ; 

 S the star, of which the parallax is to be found ; 

 if SA, SB, SC be drawn, 



ang. Z AS = ang. ACS -f ang. ASC; 

 ang. Z'BS = ang. BCS + ang. BSC ; 



subtracting the lower equation from that above it, 



ang. Z AS ang. Z'BS = ang. ACB + ang. ASB ; 

 r ang. Z AS ang. Z'BS ang. ACB = ang. ASB ,- 



or & <?' a = ang. ASB. 



If 



