1 68 PHYSICAL GEOGRAPHY. 



trouble of adjusting a light for this purpose. With a theodolite having 

 a vertical circle, which has been previously adjusted with care and firmly 

 set (as in all these observations the instrument should be), take the star 

 at least three hours before its culmination, recording its altitude and the 

 angle it makes with the mark ; reverse the telescope, and observe in the 

 same way again. Note, also, the time of each observation with sufficient 

 accuracy to be ready for the star at the same altitude after culmination. 

 Before the star descends to this altitude, set the vertical circle to that 

 altitude, with the telescope in the same position (direct or reverse) as 

 when the observation at the same altitude was made before culmination, 

 and, as soon as it can be done, bring the star into the field by turning 

 only the horizontal circle ; put the vertical line upon the star, and follow 

 it till it comes to the intersection; read both circles, and observe the 

 mark ; reverse the telescope, set to the other altitude, and observe the 

 star, and mark again in the same manner. Find the mean angle between 

 the star and mark by the first set of observations taken before culmina- 

 tion, and, also, by those taken after ; and the half difference of these two 

 angles will be the angle between the mark and meridian. By this method 

 of equal altitudes, all trouble of finding the exact local time, and of 

 computations, is avoided. 



It remains only to give the formulae for computing the azimuth of the 

 pole star, i. When taken at its elongation ; and, 2. When taken at any 

 other time. 



1. Let p = the polar distance of the star. 



/ =z the latitude of the observer. 



z = the required azimuth. 



Then we have 



sin# 



sin,? = ~^^ 



sin/ 



when taken at the elongation. 



2. Using the same notation as above, with the addition of t = the 

 time since the last culmination reduced to degrees, &c, of arc, we have 



cos (/ -)- k) cot t 



cot z = r y , 



sin k 



in which 



tan k = tan / cos/, 



when the observation is not at the elongation. 



Note. Inasmuch as this chapter explains satisfactorily the proper way of using the magnetic needle, I take 

 occasion here to say that all the courses mentioned subsequently in this report may be understood as referring 

 to the true meridian. They were taken with pocket compasses originally, and have been corrected according 

 to the principles stated so lucidly by Prof. Quimby. C. H. H. 



