4-36 Introduction to the Sixth Section 



no means to find this out, as the direction of the axis cannot 

 be observed independently of the telescope. 



The determination of /3, on the contrary, is necessary, and 

 may be obtained either by repeating the observations after re- 

 versing the instrument, or by comparing the image of the pole- 

 star reflected from a horizontal plane, with that seen by direct 

 vision. The latter method appears to me to be far more ad- 

 vantageous, on account of the slow motion of this star, of its 

 being independent of other errors, and on account of the great- 

 ness of the quantity by which the effect of /3 shows itself, es- 

 pecially in our high latitudes. 



The observation of reflected images of stars has, as far as 

 I know, been first employed by Tralles for finding the errors 

 of collimation of his instrument, when measuring the height 

 of mountains in Switzerland : it likewise affords very valuable 

 methods for examining astronomical instruments, and is there- 

 fore frequently used in the Konigsberg observatory. I have 

 used water to obtain the horizontal plane ; at first in a vessel 

 18 inches long and 12 broad ; but this was found too small, 

 as it did not always with perfect distinctness represent the 

 images of stars when viewed with the highest power, while 

 the telescope was fixed, — the distinctness of the images in a 

 telescope of such aperture and power being the surest sign of 

 a level surface. In a vessel of three feet diameter, from the 

 middle of which the reflexion takes place, 1 found no such de- 

 viation from a plane, and have therefore, ever since the 12th 

 of April, used such a vessel. 



If the zenith distance of a star be z = f — 8, it is for its re- 

 fleeted image = ISO — z = 180 — p + 8; therefore the devia- 

 tion of the instrument from the meridian for this image of the 

 star = 



15 (a + a) sin (f - 8) — 15 (4+ /3) cos (<p — 8) + 15 c 

 and 15 (a + a ) sin (<p — 8) - 15 (b' —. /3) cos (<p — 8) + 15 C 



If the times of transit of a star over the middle wire have 

 been observed by direct vision and by reflexion = t and t', we 

 have, the circle being to the east, 



t+{a + a) &i£=» + (b +/3) ^L ( ^ + X = 



1 V ' / cos J ' \ r- 1 cos J cos I 



.. , , I N sin (p — I) ,, , a s cos (<p — Z) I c 



f + [a fa) -£} (b + fi —£j- + coT* 



and when the circle is to the west, 



. , , < i \ sin (<p — <M n i flx cos tip — 5) i o' 



t + (a + a) *V~ (b — p) — rr— + Z^\~ 



1 v ' cos I v ~ ' cos i cos i 



t +(« + *)-,; s -j--(6-^)--^- + — 



therefore 



