COMSTOCK — STUDIES IN ASTRONOMY 81 



V. — DETERMINATION OF TIME AND AZIMUTH FEOM TRAN- 

 SITS OVER THE VERTICAL. OF THE POLE STAR. 



In a development of the formulao for determining the 

 time from transits over the vertical of a circum-polar star, 

 published in 1828, Bessel says by way of introduction: 

 " That this may not appear futile I remark, what Hansteen 

 and Schumacher have properly noted, that the most ap- 

 propriate use of a portable transit instrument for a time 

 determination consists in mounting it, not in the meridian, 

 but in an azimuth which admits of an observation of one of 

 the polar stars, wherever this may be with respect to the 

 meridian, closely followed or preceded by a transit of a 

 fundamental star." 



The obvious advantage which this mode of observing 

 possesses lies in the shorter period of time during which 

 the observer depends upon the stability of his instru- 

 mental constants. For meridian observations this period 

 is rarely much less than half an hour, while by the method 

 suggested it need never exceed five minutes. Nevertheless, 

 the general opinion of two generations of field astronomers 

 seems fairly represented by the words of Chauvenet, who, 

 after devoting a score of pages to a discussion of the 

 method, remarks in closing: "The methods which have 

 here been given * * * are intended for the use of ob- 

 servers in the field who have but little time to adjust their 

 instruments and wish to collect all the data possible, re- 

 serving their reduction for a future time. The greater 

 labor of these reductions, compared with those of meridian 

 observations, is often more than compensated by the saving 

 of time in the field. " This greater labor of reduction is 

 now obviated through the simplifications introduced into 

 the method by the Russian astronomer, Dollen, who main- 

 tains with equal zeal and cogency the greater precision and 



