Hagen.] 



220 



[Feb. 3, 



Let now the rotation axis of tlie instrument be reversed so that the gradua- 

 tion runs in the contrary direction and z" be the I'eading of a direct obser- 

 vation and we shall have 



z" -j- a^ cos z 4- a" cos 2 z -f a"* cos 3 z -f . . . 



— b^ sin z — b" sin 2 z — b"^ sin 3 z — . . . 



— (N -f- 180O — ai + a" — a^" -j- , . .) — «„= 360° — ^ 

 Let finally z"^ be the reading of an observation by reflection in the same 



position of the instrument, and we shall have 

 ziii — a' cos z -f a" cos 2 z — a"* cos 3 z -f- . . 



— b sin z + b" sin 2 z — b"* sin 3 z + . . 



— (N + 180O — ai + a" — a"i + ...)_ a„ = 180° -f ^ — 3 a 

 But from the explanations in the first part, it is evident, that with obser- 



FI6.2 



vations by reflection a star is observed out of the vertical plane of the in- 

 strument, so that the azimuth of the star is by 



d ^ =;:2/5COtZ 



greater than the azimuth of the reading. Hence, if we want to compare with 

 each other the four equations given above, we are to reduce all the zenith 

 distances to the same azimuth. This may be effected by the well-known 

 formula 



dz =^ tan p sin z d A, 

 which by substituting the above value of d A becomes 



dz = 2 /? tan p cos z. (17) 



Here, as in Part I, p denotes the pai'allactic angle. Tlie meaning of 

 formula (17) is not, as if the inclination fi of the artificial horizon could pre- 

 vent the observer from reading the actual zenith distance of the star, 

 it means that the actual zenith distance is by dz greater, than it 

 would be, if the star were still in the azimuth of the instrument. 



