275 



over, tliat wlien you have taken the first observation, yon 

 cannot get a favourable opportunity for tbe second. 



The third method is by observing a single circumpolar star 

 at its greatest elongation. This is a very accurate method 

 and recognised as one of the best, still it requires a knowledge 

 of the latitude. 



The fourth method is by observing two circumpolar stars at 

 their greatest elongation, and taking the difference of their 

 azimuths at the time of observation. From the observed 

 difference of azimuths of the two stars, and their declinations 

 as given in the almanac, the azimuth of each star can be 

 obtained. From either azimuth the position of the true 

 meridian can be ascertained at once. 



Two stars can be selected which do not differ much in the 

 time of their elongations, consequently there need not be 

 much time spent in observing. 



A knowledge of the latitude is not required, and as the 

 only angle observed is horizontal, there is no error from re- 

 fractions, and the method suits the theodolite. 



The formula to be used is given below, and an example is 

 worked out, but I shall not trespass further on your time by 

 reading them. 



Let the stars observed be X and Y, X at its greatest 



eastern elongation, and Y at its greatest western elongation. 



Let the azimuth of X be A 



,, azimuth of Y ,, B 



Declination of X ,, D 



Declination of Y „ E. 



Then it may be j^i'oved that — 



Tan. i (A— B) = — Tan. H^ + E) Tan. f (D— E) Tan. 

 J (A + B), which is a formula adapted to logarithmic compu- 

 tation from which A — B can be obtained. 



A + B is the difference of readings of the theodolite ob- 

 tained by directing the telescope first to the star X, and 

 then turning it round to Y, supposing X to come into 

 position first. 



When we know A + B and A — B, it is easy to deter- 

 mine the separate values of A and B. 



If the stars X and Y are both on the same side of the 

 meridian, the observed angle is A — B, and the same formula 

 may be used by making A + B and A — B change places as 

 follows : — 

 Tan. h (A + B) = Tan. h (A— B) Cot. M^ + E) Cot. i (D— E) 



To illustrate this formula an example is added, which has 

 been worked out by Mr. A. G. Tofft : — 



The following stars were observed at their greatest elongation on the 

 evening of October 11, 1884 : — A Trianguli over its western elongation at 



