Prof. Encke on Hadley's Sextant. 181 



any other state than as a definite compound with carbon, re- 

 quiring twice its vohnne of oxygen for saturation. The pro- 

 cess of Dr.Bache is not competent to inform us what the gases 

 are; but enables us, when their nature is known, to discover 

 their proportions. 



XXVII. On Hadley's Sexlaiit. 

 [From Prof. Encke's Ephemeris for 1830, J5. 285.) 

 [Continued from p. 92.] 

 TN thus using the sextant as a heliotrope, the angle between 

 -■- the sun and the object must not much exceed 90° ; but this 

 defect may be easily remedied by using a large mirror for re- 

 flecting the image of the sun. It will perhaps be useful to 

 mention in this place a circumstance which at first sight may 

 appear strange. If we measure the angles between objects in 

 which parallel lines are visible, and whose angular distance is 

 not very small, these parallel lines will intersect each other at 

 very sensible angles while bringing the images to coincidence 

 whenever the plane of the sextant must be considerably in- 

 clined to these lines. The doubly reflected image retains the 

 same inclination towards the plane of the sextant taken in the 

 same sense, after the double reflexion ; but for this very reason 

 the lines lose their parallelism. Let us designate, for brevity, 

 the plane which the parallel lines intersect at right angles, by 

 the name of horizon (from the case which most frequently 

 occurs), and let us call the elevations of the objects above the 

 horizon h and //', and next form the triangle between the zenith 

 and the two objects. In this triangle, let the angle at the 

 zenith = A, the interior angle at the direct image = C, and 

 the exterior angle at the doubly reflected image = B ; and the 

 angle at which the vertical images will intersect each other 

 will be = B — C. By Napier's analogies, or Gauss's formulae, 

 we obtain 



tang i (B-C) == ~||^Jj- tang \ A and introducing 

 the measuretl angle s 



tang i(B-C)= tang i. s-. tang i(/^ '+//)./ f^^^^-^^'-^% 



'i'he quantity under the radical sign will seldom much diiler 

 fiom 1, so that the first two factors will be suflicient. 



WJioever possesses the proper astronomical apparatus will 

 liave no difficulty in determining the constants here required. 

 Let it suflicc here to suggest a method which requires only 

 such sinqile apjiaratus as every body may easily procure. 



An iiishunient for dctcrniiiiing the position oithe plane of 

 the sextant is indisj)en.'>abiy requisite. I'or llif use of the 



sextant 



