Prof. Encke on Hadley's Sextant. 185 



from 30", as on the one hand its magnitude determines that of 

 the greatest angle which it is possible to measure, and on the 

 other is limited again by the dimensions and the distance of 

 the two mirrors. The small correction of |3 arising from the 

 inclination of the large mirror is entirely to be neglected. 



By means of this operation we obtain likewise the index- 

 error of the instrument. It seems that it is erroneously sup- 

 posed, that this error cannot be as accurately determined by 

 terrestrial objects as by the sun. In most cases it is easy to 

 obtain with sufficient accuracy the data requisite for the small 

 correction, which is to be applied in the former case. If the 

 object is projected on the sky, we have the advantage of a per- 

 fectly quiet observation, while the sextant is firmly at rest, and 

 the contact of the images maj' be made with greater accuracy 

 than the sextant can be read off. We have at the same time 

 a means of determining the errors of the coloured glasses by 

 comparing the index-error thus determined with that obtained 

 by each coloured glass. The correction is the same for all 

 angles, as the path of the rays through the coloured glasses is 

 under all circumstances the same. 



There is another method of determining the angle /3 with 

 the sextant only, by a process with which Prof. Gauss made 

 me acquainted when showing me the use of the sextant for 

 heliotropical purposes. If the great mirror is turned back as 

 far as is requisite for nearly the greatest angle which the sex- 

 tant is capable of measuring, an image will be obtained, after a 

 single reflexion from the small mirror of such luminous ob- 

 jects as send their rays closely past the frame of the large 

 mirror directly to the small mirror. These images will only be 

 visible on the left side of the field of view, as the light to the 

 middle of it is intercepted by the large mirror. It will be ad- 

 vantageous to cover the back of the small mirror by the co- 

 loured glasses or otherwise, in order to pievent the direct rays 

 from rendering invisible the images produced by single and 

 double reflexion. 



In order to compare the paths of these two rays, let us sup- 

 pose that the sextant is placed in the plane of the objects whose 

 images are thus seen by single and double reflexion. The 

 line of vision we suppose to be fixed ; let its direction be A, 

 (fig. 1. p. 85.) If we now suppose that the image seen by one 

 reflexion is observed on one of the lateral wires whose jiositive 

 distance, according to the above-stated assuni{)tion in deter- 

 mining the distances of the wires, is = tn ; and if we count the 

 angles from /) to A, the first path of the once reflected ray from 

 the eye will be in the direction /3 — m, and after the reflexion 

 its direction from O is through the point lH0'^ — [j3 — vi), in 



N. 6'. Vol. G. No. 33. Sept. 1829. 2 B which 



