94 BULLETIN OF THE UNIVERSITY OF WISCONSIN 



VI.— DETERMINATION OF LATITUDE AND TIME FROM 

 EQUAL ALTITUDES OF STARS. 



The simultaneous determination of time and latitude from 

 the observed instants at which three different stars reach the 

 same (unknown) altitude is discussed in the principal text 

 books of spherical astronomy, but the laborious character 

 of the reduction of the observations there developed has 

 prevented the method from coming into general use, al- 

 though from theoretical considerations and from experi- 

 ence it has been abundantly shown to furnish a very 

 accurate determination of both time and latitude. In the 

 following pages an attempt is made to simplify the method 

 by substituting for the observation of three stars separated 

 by considerable intervals of time the observation of the 

 time at which a single star transits over the almucantar of 

 a close circum-polar star, usually Polaris, the elapsed time 

 between the pointing of the instrument upon the polar 

 star and the observed transits of the clock star being 

 made as short as possible, e. g. five minutes, or less. 



Such a comparison of one clock star with one jDolar fur- 

 nishes a single relation between the latitude and the clock 

 correction, and a similar comparison of another star fur- 

 nishes a second relation which suffices for the determina- 

 tion of both quantities. It should be noted that these two 

 sets of observations are entirely independent of each other 

 and require no assumption with regard to the stability of 

 the instrumental constants, save for the brief interval be- 

 tween pointing upon Polaris and observing the southern 

 star. 



The almucantar and the zenith telescope are the instru- 

 ments best adapted to observations of this kind, but any 

 instrument which possesses a telescope rotating about a 

 horizontal and a vertical axis and provided with a level 

 whose plane is perpendicular to the horizontal axis, may be 



