Prof. Encke o?i HacUey's Sextant. 89 



sitive if its pole is above the plane perpendicular to the axis 

 of rotation). We then have this equation : 



sin S = sin ^. cos y + cos I sin y cos {u—a). 

 For determining the quantities 8, y, u, it is necessary to know 

 three values of /, with the corresponding values of u, and the 

 problem will then agree with the determination of the rotation 

 of the sun from the spots on its disk, or with the problem of 

 determining time, latitude and altitude, from three unknown 

 but equal altitudes, of which Prof. Gauss has given an elegant 

 solution in the " Monthly Correspondence " by M. de Zach, 

 Oct. 1808. In the present case the smallness of the quantities 

 y and S, and the possibility of ascertaining the different values 

 of « very exactly, allow an abbreviation. 



Almost all sextants are capable of measuring 120°. If the 

 sextant is therefore placed in the three positions in which the 

 angles read off are 0°, 60°, 120°, and if the corresponding 

 value of I is read off in every situation, we shall have 

 a = 0° I = lo 

 a = 30^ I = h 

 a = 60° I z= h 

 and thence with abundant accuracy 



8 = (2/, - 3/, + 2k) + (/,- 21, + lo)x/3 

 ysmti={ l^—2l,+ k) + {h- h )V'3 

 yCOSM= ( l^ — 3^, + 2lo) +{lo— 21, + h)'/^ 

 For prismatic mirrors the relative situation of the two planes 

 might be hereby determined, if it were possible to distinguish 

 the two images. The formulae here given will only have an 

 application in practice, if we have the particular purpose and 

 adequate means to determine every thing in the most exact 

 manner. For the use of the sextant approximate methods will 

 be sufficient. In most sextants of recent construction the 

 screws for adjusting the position of the large mirror are omit- 

 ted. It is to be supposed that the artist will have taken all 

 possible pains to render the axis of rotation perpendicular to 

 the plane, so that in the equation / = 8 — y cos (w — «) the last 

 term may be neglected, or that at least the variation of it may 

 be neglected, the influence of I being besides very small in 

 itself. Tiie most simple adjustment which may be performed 

 with the greatest accuracy, is the parallel position of the two 

 mirrors by bringing the two images of the same teiucstrial ob- 

 ject to coincidence in a position for which a. is about 0. If we 

 suppose this adjustment to have been made, we have k = /, and 

 / may be considered as constant. The fornuila (A) will then be: 



. . , , 4siriW'' r — sin /' (cos « -f siiW- i^in 1 «-') 



Sm(« — «)— -;;i;;-(7:f:7)|_(.os,-»cos/'(tanf;/cos(i^— (3)— tang.cosi*)* 



If we now call the angle read oft" on the sextant s, so tiiat 

 N. S. Vol. G. No. 32. Attjr. 1829. N s = 



