186 Prof. Encke on Hadley's Sextant. 



which direction the object (neglecting the parallax) is situated. 

 If at the same time the doubly reflected image of another ob- 

 ject is observed on the lateral wire whose distance is ?«', this 

 object lies with regard to O in the direction 2 a + /3— to' ; and 

 if in this position of the sextant the reading is = s, we have 



s — Co = 2 a ; 

 the difference of these two directions is the real angular di- 

 stance of the two objects. If this distance is now actually 

 measured with the sextant, the reading of which must then be 

 = 5', we shall have this equation : 



s'— Co = 180°— (/3— to) — (s— Co + |3— ?«') whence 

 2|S = 180°— (s + s*- TO— to'— 2Co). 

 In this case to must always be negative. Should the construc- 

 tion of the sextant and the brightness of the images permit 

 their being bi'ought into contact on the same wire, which like- 

 wise depends on the number of objects from which a selection 

 is to be made, we shall have, calling the absolute distance of 

 the wire ?«, 2 /3 = 180° — (s + s'+ 2to — 2 c^). 



The process is therefore as follows : Near the left side of 

 the field of vision a wire is to be fixed, the absolute distance 

 of which, TO, is to be determined as shown above. On this, if 

 possible, two objects are brought into contact after single and 

 double reflexion, as near as possible to the horizontal wire of 

 the cross wires, and the sextant read off; let the reading be s. 

 Then the real angle of the objects is to be measured, and if 

 the reading of the sextant in this measurement is = s', and c^ 

 the index-error, we shall have the angle /3 by the preceding 

 formula. It is clear that all adjustments of the sextant are 

 here supposed to have been made. The former of these ope- 

 rations cannot well be performed without a stand. 



In Troughton's sextant the distances of the two lateral 

 wires from the middle one were nearly equal, each 33'. With 

 / = +8', which is a sufficiently accurate mean value, we ob- 

 tain, 



To the lower lateral wii-e corresponds / = -f 33', to the upper 



one 



