184 Prof. Encke on Hadley's Sextant. 



mirror, / will = 0. If this be not possible, observe the ob- 

 jects to which the telescope points, with the sextant's telescope, 

 and the known distance of the lateral wires will afford means 

 of estimation suflicientlV accurate for the present purjiose. If 

 the angular distance of this point (positive if north) from the 

 one formerly determined be = q, we obtain by the solution of 

 the right-angled triangle whose hypothennse is bisected, 



. iiii q 



2 cos \p . V'Ccos iq- + sin J 9- tsxug^p"-) 



for which we may always put 



I = ^ q . sec -J ]). 

 Accordingly as the index has been placed on 0°, 60°, 120^, or 

 other angles, L, l„ h will be found ; and hence it will be seen 

 whether it is necessary to introduce the cjuantities S, y, 11. For 

 any good sextant this will hardly ever be necessary. 

 For the sextant above referred to, it was found that 

 p being 89^ 25' and s = 0°,q was = + IV 20" 

 = 60 = -f- 11 20 



= 120 = -t- 12 



whence h = 7' 58" 



/, = 7 58 

 Zo = 8 27 

 These differences cannot be ascribed to the instrument. They 

 arise partly from the inequality of the different opeiations of 

 levelling, partly from the impossibility of obtahiing a firm po- 

 sition for the detached telescope on the unsteadj'^ floor of our 

 observatory : at any rate, their influence is entirely evanescent. 

 The small jnirror is now to be replaced, and the sextant, in a 

 firm position, directed to an object the images of which are 

 made to coincide on .the intersection of the wires by means of 

 the adjusting screws of the small mirror. By this process the 

 small mirror is made parallel to the large one, and the reading 

 off will give c,. Next let us look with the detached telescope 

 into the large mirror, and let the intersection of the wires be 

 directed to the image of the same object once reflected. If we 

 then measure with the sextant the angle between this inter- 

 section and the object, we shall have 



s~Co = 2^ — -{- sin 2 /3, but as 



o = c, + -7- sin 2 |3, we have 



2 /3 = 5 — c, 

 In Troughton's sextant 2 |S was found = 33° 46' 40"; in one 

 made by Ramsden, in the observatory of Seeberg, = 31° 30'; 

 in the one by Gary, in the observatory at Giittingen, accord- 

 ing to Bohnenberger, = 30°. In general it will not differ nmch 



from 



