274 Prof. Encke on Tfansifs. 



or Niagara Rivers. (G. S. p. 98.) It is to be remarked, that 

 no coal has been found between the " millstone grit " and the 

 new red sandstone, although they have been frequently seen 



in contact. 



[To be continued.] 



XLIL Oti Transits. 

 (From Prof. Encke's Astronom.Jahrbuchfor 1830, p. 305.) 



THE excellent papers by M. Hansen and Prof. Bessel in 

 the late Numbers of the Astron. Nachr., have rendered 

 superfluous the explanation of the use of the transit for deter- 

 mining time and latitude which was intended for this volume ; 

 and the only part which I deem it proper, therefore, to insert 

 in this place, is the rigorous derivation of the formula; for de- 

 termining the former of these elements. This subject has al- 

 ready been treated by Prof. Bohnenberger in the Journal of 

 Astronomy. I have endeavoured to render the rigorous for- 

 mulae as nearly similar to the approximate ones as possible. 

 On the supposition of the true figure of the pivots, the line of 

 vision of a transit will in every position describe a great circle, 

 if placed at right angles to the axis of rotation. If the instru- 

 ment has what is called an error in coUimation ( = c), the line 

 of vision describes a small circle parallel to the great circle, 

 the distance of which from the other in parts of the great cir- 

 cle is everywhere = c. If we suppose that the axis of rotation 

 is produced to the sphere, and call the points in which it in- 

 tersects the surface of the sphere its polesy nothing will be re- 

 quired in order to have a perfect knowledge of every position of 

 the instrument, but the position of one of these poles with 

 regard to known planes and points and the quantity c. For 

 the purpose of determining time, the most proper plane to which 

 the position of the pole can be referred will be the meridian. 

 We may assume for the fixed point in this plane from which 

 the angles are counted, either the pole or the zenith, or both at 

 the same time. The first assumption gives the formula which 

 M. Bessel has introduced, the second the formula of Mayer, 

 and the third that which M. Hansen has used at Heligoland. 



Let PZA be the meridian, P the pole, Z the zenith, A 

 the point of intersection of the equator, O the east point, j) 

 the eastern pole of the axis of rotation, S^)' the great circle, 

 which the instrument would describe if c = o, the dotted circle 

 the one which it actually does desci'ibe in the case of a given 

 Cf and let its distance from 7/8 = c be positive if eastern. In 



order 



