7@ OUTLINES OF NATURAL PHILOSOPHY. 



If P be the horizontal parallax, 



ang. ASC = P X sin &AS, and 

 ang. BSC = P X sin Z'BS ; whence 

 ang. ASB = P (sin ZAS sin Z'BS) 

 == P (sin <p sin <p'). But ang. ASB r 

 <p $>' a ; therefore P = 



Hence, also, 



sn <p - sn 



2 cos 



<p' must be supposed negative, if the star is between 

 the zeniths. 



b. If the star does not change its declination, this 

 formula will give the horizontal parallax, though 

 the observer be not on the same meridian, because 

 the meridian altitude of such a star, is the same at 

 all places in the same latitude. 



c. If there is a change of declination, and if the ob- 

 servers are not under the same meridian, then, by 

 repeated observations of the zenith distance at any 

 of the places, the star's change of declination for a 

 given interval of time, may be found ; and so, from 

 the observed altitude at that place, the altitude at 

 any other place, under the same parallel, may be 

 found, if the difference of longitude is known. 

 Hence the altitude is known at the place where the 



meridian 



