2882.1 -^-^^ [Hagen. 



If thus b is found for any azimuth, J A may be computed from (4') . 



Yet b varies with the azimuth and is represented by the formula 



b = i — i„ cos (^ — Ao)- 



The constant i is already known from the equations (9) and hence it is 



enough to find b for any two azimuths in order to find i„ and Ao- If we 



choose the two azimuths A and A + ^0°, we find 



bi — i = — i„ cos (A — Ao) 

 bj — i = -}- i„ sin {A — A^), 

 by which equations the two quantities i,, and A^ are fully determined. 

 Thus we are able to compute b for any azimuth by the formula 



b = i — i„ cos {A — A„). 

 But from (7) we have the equations 



ii sin Ai = + io cos A^ — 12 cos A^ ^ .. 



ij cos Jj = — i„ cos .4^ + i^ sin ^2 i 

 by which we finally find ij and Ai, i- e., the constant inclination of the ap- 

 parent to the true horizon, as far as it is caused by irregularities in the sur- 

 face of the Earth, and the azimuth of its direction. This constant inclina- 

 tion ij however, is not yet the total inclination Z Z^, since large iastru- 

 ments together with their piers may cause an inclination of the artificial 

 horizon variable with the zenith distance of the observed object, as will 

 be seen in Part II. 



Finally, attention must be called to two things. First, if the observa- 

 tions mentioned above are made on different days, the positions of the 

 stars are to be reduced to a common epoch, best to the beginning of the 

 year. Secondly, though we have found the formulas for finding the con- 

 stant inclination of the apparent to the true horizon as to magnitude and 

 direction, we are not to forget, that these formulas suppose the perfect 

 knowledge of the latitude and time of the place. 



3. The Transit instrument in the Meridian. 

 The correction of the hour-angle for observations by reflection 



has the meaning, that in the moment, when the reflected image of any ob- 

 ject passes over the middle thread of this instrument its actual hour-angle 

 is dt for upper transits and 180^ + dtfor loicer transits, if b is reckoned 

 positive right-hand of the observer. Yet for these instruments the inclina- 

 tion ^ of the apparent horizon remaining always on the same side, it will 

 be found more convenient to take /? positive towards west and conse- 

 quently to write the corrections for lower transits as follows : 



cos z 



while dt always denotes the increment of the hour-angle, which is reckoned 

 in the usual way from south to west. 



