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To Find the Meridian from "Polaris." 



The north star, Polaris, being out of the pole of the equator, is in the meridian but 

 twice in a stellar day once above and once below the pole called the upper and 

 lower transits, or culminations. 



It is also at its extreme distance, east and west, twice in a stellar day, called 

 greatest elongations, east or west. 



At the time of a culmination, it would be only necessary to get the bearing of the 

 star to have the place of the true meridian. But this would require an exact knowl- 

 edge of the time, an element not usually possessed by surveyors. Moreover, the 

 observation must be made with certainty, at the instant, which is not always practi- 

 cable. On this account, this method is not in favor with surveyors. 



At elongation, the apparent motion of the star is tangent to the vertical, and 

 therefore, for a few minutes, with regard to azimuth, it appears to stand still, thereby 

 ^fording ample time for deliberate observation. 



The distance of this star from the pole called its polar distance, was 1 18' 16" 

 on January 1, 1885, and is diminishing at the rate of about 19.06" per year, whence 

 its distance in following years may be known.* 



The azimuth of the star, corresponding to any polar distance, is variable with the 

 latitude. Thus, an observer at the equator would see this star say at eastern 

 elongation in the horizon, and at the distance of 1 18' 16" to the right of the pole, 

 or true meridian. 



If now the observer should go north, the azimuth of the star would increase with 

 Its altitude, till he should arrive at a latitude equal to the complement of the polar 

 distance, when it would be N. 90 E. Between these limits, the bearing of the star, 

 at elongation from the pole, would vary according to the following equation, in which 

 Z = the azimuth, or bearing : 



. _ sin Polar Distance 

 ; cosine Latitude 



As the telescope of the surveyor's transit is not usually of sufficient power to show 

 the star in the daytime, the observation must be made at night, in which case the 

 cross-wires of the telescope must be illuminated by light reflected into the tube. A 

 piece of stiff white paper, with an opening large enough to admit of seeing the star 

 through it, and held obliquely in front of the telescope, will make a good reflector. 



As generally but one of the elongations can be seen, on the same night, it is im- 

 portant to know, which one is observed. Also the latitude must be known, at least 

 approximately. 



The pole is nearly in line between Polaris and the star Mizar, which is at the bend 

 in the handle of the Dipper, so that when these two stars are nearly in a horizontal line 



and the dipper is east . f of the pole, Polaris is at his greatest elongation ^ 



In sighting to the star, the observer must be careful to keep his transit level 

 transversely, for the star is so high that inattention to this might introduce a serious 

 error into the resulting azimuth. 



A satisfactory sight having been obtained, the telescope should be brought down 

 to fix a mark on the ground, at a distance of 300 to 400 yards from the transit. 



This mark should be something clear and definite, like a nail set in a hub, driven 

 into the ground, which may be located by means of a plummet lamp, or by means 

 of a common lamp in a box, having a vertical slit in one side of say J or an inch in 

 thickness, with a plumb-line suspended from the slit, and manipulated by an 

 assistant. 



The direction of the star being satisfactorily marked, compute the azimuth from 



the above equation, and set the resulting angle off to the f 1 ? 11 * \ of the mark for 





It may happen, that the resulting azimuth may have an odd number of seconds, 

 or fraction of a minute, not convenient to be set off with a vernier graduated to 



* Small corrections to the distances thus calculated are needed, but do not amount to more than 30" in 

 all; see a Nautical Almanac. 



