Prof. Encke on Hadley's Sextant. 91 



It serves likewise to correct the index error if determined by 

 terrestrial objects. If we understand by index error always 

 that quantity which is to be subtracted from every angle read 

 oft; in order to obtain the correct value, an assumption by which 

 the arc of excess is to be considered as negative, and then 

 draw the triangle between the two mirrors and the object, and 

 call the distance of the object from the small mirror d, the di- 

 stance of the two mirrors /, the angle read off" at the coinci- 

 dence of the two images C|,and the true index error Cq, we have 



this equation: tang (c„-c,) = 7^" J^ : and therefore, 



c^z=c^ + -^ sin 2 (3 — -^ sin 4 |3. The angle (3 is likewise 



requisite if it is thought worth while to ascertain the point to 

 which the angle measured really belongs. In the case of a 

 positive reading, the rays of light will intersect in the prolon- 

 gation of the line of collimation, taken in the direction from 

 the small mirror to the telescope. If we call the distance of 

 the point of intersection from the small mirror, assumed as po- 

 sitive in this direction g, and if we denote the angle read off" 

 uncorrected by the error of the index by 5, we shall have 



sin(.-c„ + 2p) ^.^^,2,3+/-^^, whence 



*=> J sin (s-co) -^ -^ tang (s-c^ 



results the possibility of determining the distance of a near 

 object provided /and c^ could be ascertained with sufficient 

 accuracy. 



Lastly, the angle (3 is of use when the sextant is to be em- 

 ployed as a heliotrope. If the second object c (fig. 1.) were 

 the sun, the object which lies in the direction O B would re- 

 ceive the reflected rays of the sun. If the object A is to re- 

 ceive them, the pole P is to be moved forward in the order of 

 the divisions by the cjuantity |3, or, as on the sextant the double 

 angles are read off; the index must be advanced 2/3. The 

 operations are thereibre as follows : Place the plane of the sex- 

 tant into the plane of tiie object which is to receive the rays 

 of the sun by reflexion anil the sun, measure the angle as 

 usual, and advance the index 2 /3 beyond the division read off" 

 without changing the plane of the instrument. 



It is clear that a stand is indispensably necc.'k-.ary for this 

 operation. As long as any part of the sun's disk illuniinutes the 

 intersection of the cross wires, for whicli the angle /3 has been 

 determined, the object will receive light; tliis lime will amount 

 to about two minutes. The measurement ol' the angle is, there- 

 fore, lo be repealed every two or three miimtes, and that point 

 is lo be taken which by llie motion of the sun first passes the 

 cross wires. 11 the sun is the object directly seen, tiie innne- 



N 2 diate 



