234 



Mr. Nultjiread a paper "On the Determination of Azimuths 

 in a Geodesical Survey, from a Series of Observations of Po- 

 laris." 



This star, when towards its maximum elongation from the meri- 

 dian of a station, has been found to give more consistent and uniform 

 results than observations of the sun, and should therefore be exclu- 

 sively preferred at all geodesical stations, which require a high de- 

 gree of accuracy in their respective bearings. The principal data 

 employed in the computation of an azimuth, chiefly depend on the 

 instrument used by the observer. With the repeating circle, a num- 

 ber of angular distances forming a series may be taken vertically, 

 between the star, near its greatest eastern or western elongation, and 

 a corresponding signal placed in the horizon ; or a like series of ho- 

 rizontal angles may be observed by means of a theodolite. Both 

 modes of observation will lead to accurate results; but when the star 

 is viewed successively near its greatest eastern and also near its 

 greatest western elongation from the meridian of the station, so as to 

 guard against imperfection in the instrument, the latter is preferred 

 as having superior advantages. This mode of observing Polaris 

 has been lately adopted in the U. S. Coast Survey, by its present 

 superintendent. It must give to the azimuthal bearings of that ex- 

 tensive work every requisite precision. The brief notice here taken 

 will enable the mathematician to form a sufficient idea of the problem 

 of azimuths by Polaris, as considered by the author of the paper now 

 under report. The several instants of observation with the elonga- 

 tions of the star, and the known latitude of the station, are the essen- 

 tial elements of solution ; but, instead of introducing them into the 

 usual general expressions for azimuths, which in case of one or seve- 

 ral series would be attended with excessive labour, the author em- 

 ploys special formulae immediately bearing on the observed positions 

 of the star, and by which the practical computation of azimuths by 

 Polaris, is reduced to almost the same facility as that of latitude. It 

 is hardly necessary, in a summarj^ of this nature, to describe mi- 

 nutely the character of the formulae investigated in the paper. They 

 correspond in general to three positions of Polaris, taken as an origin 

 or mean instant of a series; the first being the time of maximum 

 elongation, the second involving a horary angle of six hours from the 

 meridional passages at the station, and the third referring to a more 

 general position of the star, not, however, far distant from its plane 

 at greatest elongation. In a mathematical sense, they have each 



