82 BULLETIN OF THE UNIVERSITY OF WISCONSIN 



at least equal convenience of his method for all purposes 

 of field astronomy. Under Dollen's influence the method 

 has, within the last quarter century, come into consider- 

 able use in eastern and central Europe, and from an ex- 

 tended practical aj)plication of it the writer of these pages 

 is satisfied of the justice of the claims made in its behalf. 

 This section of the present paper is an attempt to bring to 

 the attention of American teachers of practical astronomy, 

 in substance, the theory of Dollen's method, but it cannot 

 be considered a substitute for the precepts and discussion 

 contained in the elaborate introduction to the Stern Ephem- 

 eriden zur Bestimmung von Zeit und Azimut, published annu- 

 ally by Dollen since 1886. 



As indicated by the above title, the observations for 

 time are equally available for a determination of azimuth, 

 and reduced to their simplest terms these observations are 

 as follows: Let the transit (universal instrument, or the- 

 odolite, in case a determination of azimuth is also desired) 

 be pointed at Polaris, and the chronometer time, S', at 

 which the star appears bisected by the middle vertical 

 thread, noted. Then revolve the telescope about the hori- 

 zontal axis without disturbing the azimuth of the instru- 

 ment and observe the time of transit, ^S', of a clock star over 

 all of the threads, and measure the inclination of the axis, 

 &, with a spirit level, if possible both before the observa- 

 tion of Polaris and after that of the southern star. Reverse 

 the instrument, point again upon Polaris, and observe it 

 and a clock star, as before. If the instrument possess a 

 graduated horizontal circle, which is read in connection 

 with the observations of the stars, these data will deter- 

 mine the zero point of the circle, i. e. its reading when the 

 telescope points north, and the azimuth of any terrestrial 

 point toward which the telescope may be directed. 



We proceed to consider the theory of the method and 

 adopt as a basis for the investigation the fundamental 

 equation of the transit instrument,' 



1 Chauveuet. Vol. II, Eq. (79). 



