Sbction III., 1906. [ 3 ] Trans. 11. S. C. 



I. — Abacus of the Altitude and Azimuth of the Pole Star. 

 By E. Deville, LL.D. 



(Read May 23rd, 1906.) 



The boundaries of soctions in the land surveys of the Dominion 

 being north and south or east and west lines, it is essential that surveyors 

 who subdivide townships should ascertain frequently the direction 

 of the astronomical meridian, so that they may know the exact bearings 

 of the lines which they are running. The method prescribed for this 

 determination is the observation of the Pole Star in day light. The Star 

 is readily seen an hour after sunrise or before sunset with the telescope 

 of 11/2 in. aperture supplied to the Dominion Land Surveyors, provided 

 it is adjusted to bring the Star approximately in the centre of the field. 

 The direction in azimuth is given from the survey lines or by means of 

 the magnetic needle, after which the telescope is set to the altitude of 

 the Pole Star. Sidereal time is given by a common watch, regulated to 

 gain 3 m. 56 s. per day; its error is ascertained from time to time by 

 meridian transits of the sun or stars. To facilitate matters, astronomical 

 field tables are supplied to surveyors. Among other data the tables give 

 tlie bearing of the Pole Star for every ten minutes and for townships 

 0, 20, 40, 60 and 80 : the bearing at any other time and for any otheï 

 to^Tiship is obtained by interpolation. The distance of the Star above or 

 below the pole is also given for calculating the altitude. Although the 

 interpolation for the bearing and the calculation of the altitude are very 

 simple, some surveyors prefer to have no calculation whatever : this con- 

 dition is fulfilled by the abacus. 



Graphic Representation of Equations. 



Before explaining the theory of this abacus, it is necessary to recall 

 a few of the principles of the graphic representation of equations. An 

 exhaustive investigation of the subject has been made by d'Ocacrne;! 

 what is needed for our purpose ma}' be briefly summed up as follows : 



If, in the equation of a curve : 



(1) ^1 (.r, y, o'l) = o 



Buccessive increments are griven to the parameter a-,, to each of thepe 

 increments corresponds a different curve : the equation thus defines a 

 system of curves (a^). 



* Traité de Nomographie by Maurice d'Ocagne, Paris — Gauthier — Villars. 



