to the Antarctic Regions. 239 



tical difficulties ; and it seems safer to deduce this result indirectly. 

 From the formulae given in page 224, we have 



Y = X tan ; 

 so that if the inclination 6 be known, and the horizontal intensity X 

 determined in absolute measure, the vertical intensity Y is inferred. 

 For the purpose of observing the element d, each observatory is 

 furnished with an inclination instrument, the circle of which is 

 9| inches in diameter. The observation should be made in an open 

 space, sufficiently remote from the magnets of the observatory, and 

 from other disturbing influences ; and a series of measures should 

 be taken simultaneously with the two intensity magnetometers, for 

 the purpose of eliminating the changes of the inclination which may 

 occur in the course of the observation. As to the mode of observa- 

 tion, the best seems to be the usual one, the plane of the circle coin- 

 ciding with the magnetic meridian ; but for the purpose of testing 

 the axles of the needles, and the divided limb of the instrument, it 

 is desirable that some observations should be made in various azimuths, 

 — for example, every 30° of the azimuth circle commencing with the 

 magnetic meridian. The inclination is then inferred, from each 

 pair of corresponding results, by the formula 



cotan2 d = cotan2 4" -f cotan« ^' ; 

 '^ and ^' being the observed angles of inclination in two planes at right 

 angles to one another. Where the inclination is great (as at Mon- 

 treal), this method will serve to test only a limited portion of the 

 circumference of the axle and limb. In this case the best course 

 appears to be that pointed out by Major Sabine*, namely, to con- 

 vert one of the needles, temporarily, into a needle on Mayer's prin- 

 ciple, by loading it with sealing-wax ; and to deduce the inclination, 

 from the angles of position of the loaded needle, by the known for- 

 mula of Mayer. The observations here suggested having been very 

 carefully made, and the inclination changes eliminated in the manner 

 above explained, the observed difference between the mean and the 

 result obtained in the magnetic meridian, should be applied as a cor- 

 rection for the errors of axle and limb to all future observations made 

 in the meridian. 



These observations should be made at the same periods as those of 

 the absolute horizontal intensity. 



Variation of the Elements. 



The variations of the magnetic elements are, 1 . Those variations 

 whose amount! s a function of the hour angle of the sun, or of his 

 longitude; and which return to their original values at the same 

 hour in successive days, or the same season in successive years. 

 These, from their analogy to the corresponding planetary inequal- 

 ities, may be denominated j9enoc?«ea/. 2. The variations, which are 

 either continually progressive, or else return to their former values 

 in long and unknown periods ; these may in like manner be deno- 

 minated secular. 3. The irregular variations, whose amount changes 



* Reports of the British Association, vol. vii. p. 55. 



