300 Royal Astrofwmical Society. 



tremities of his arc of meridian parallel to the Baltic. Whatever be 

 the construction of the transit instrument used, the proper method 

 of observation is the following : — The error of level of the axis being 

 ascertained, the instrument is directed to the star, while it is yet 

 north of the eastern prime vertical, and the transit of the star is ob- 

 served over each of the wires preceding the middle of the field ; the 

 position of the instrument being continually changed, so that the 

 oblique transit is observed over the centre of each wire. When the 

 star has passed the wire next before the middle, the instrument is 

 reversed ; and the passage of the star, now on the south side of the 

 eastern prime vertical, is observed over the same wires as before, 

 but in the opposite order. The error of level of the axis is then 

 ascertained. Then, when the star is approaching the western prime 

 vertical from the south, the instrument being still in its second 

 position, the error of level of the axis is again ascertained ; then the 

 transit of the star is observed again over the same wires ; before it 

 passes the middle of the field, the instrument is reversed to its first 

 position ; then the transit of the star, now on the north side of the 

 west prime vertical, is observed again over the same wires. Finally, 

 the error of level of the axis is ascertained in this position. 



The reduction of the observations is made in the following form, 

 each wire being treated separately. The projection of each wire on 

 the sky is a small circle whose pole is in the north point N of the 

 horizon ; and if a be the angular distance of that wire from the line 

 of coUimation, 90° — a will be the radius of the small circle when 

 the star is seen on it north of the prime vertical, and 90° + a when 

 the star is south of the prime vertical. Form the spherical triangle 

 NFS ; let A be the hour-angle from the meridian, or the supplement 

 of the angle at P ; / the latitude of place ; ij the star's north polar 

 distance. Then when the star is north of the prime vertical, 



cos (90° — «)= cos /.cos 5— sin /.sin 5. cos A, ; 

 and when the star is south of the prime vertical, 



cos (90° + a)= cos /.cos 5'— sin /.sin J. cos Ao. 

 Adding these two equations, we obtain 



cot /.cot ^= cos— lit — ?.cos — ! -. 



2 2 



Aj is half the interval between the first transit east and the second 

 transit west, and Ag is half the interval between the second transit 

 east and the first transit west, in both cases converted into arc. 

 Thus by the observations on each wire we determine with great 

 facility / from J, or J from /, without any knowledge of the distance 

 of that wire from the line of coUimation. 



The mean error of level of the instrument may be applied to I 

 before forming the logarithm of cot / (supposing that it is the object 

 of the observation to determine (J). Or a correction may be applied 

 for it (which will be different for different stars) to the result ob- 

 tained with a constant value of /. The latter is the course followed 

 by M. Struve in reducing the observations of which I shall shortly 

 speak. 



