130 AKSEL S. STEEN. TERRESTRIAL MAGNETISM. [NORW. POL. EXP. 



The material is thus insufficient for a direct calculation of the three 

 constants, and I therefore hesitated at first in considering the entire index- 

 error as approximately constant, with the mean value 17' for needle B, 

 and 23' for needle B 1 . This is a serious matter, however, when it 

 is a question of observations in the polar regions where the inclination is 

 not far from 90, and the total intensity, or the horizontal intensity, has to 

 be calculated by the formula 



-" /m\ 



W = 



cos I' 



It therefore occurred to me that it ought perhaps to be possible to make 

 use of some of the observations made during the expedition with the Fox 

 apparatus for the determination of the total intensity, as a check upon, or 

 for the eventual improvement of, the value of the index-error, if we had 

 simultaneous, reliable determinations of the horizontal intensity. 



The apparatus was accompanied by the two already-mentioned cylin- 

 drical deflectors for the determination of the total intensity, as also by a set 

 of accurately corrected weights. On only one occasion, however, was an 

 attempt made to use these weights; and the observation-result obtained does 

 not admit of criticism, as there is no material for the calculation of a table 

 for equivalent weights. The employment of weights, moreover, is not very 

 practical in the severe cold of the polar regions, on account of the repeated 

 opening of the door of the apparatus. The deflectors, on the contrary, were 

 regularly used for intensity determinations in connection with the inclination 

 observations, generally, however, only one deflector, both deflectors together 

 having been used only 5 times. 



If we call the inclination-needle's angle of deflection produced by the 

 employment of both deflectors simultaneously, i// 2 , and the total intensity W, 

 we have the following condition for equilibrium: 



W sin V 2 =JSa(l + 0. (3) 



where R 2 is a constant quantity dependent upon the magnetic moment of 

 both deflectors and the needle employed, is the temperature-coefficient, and 

 t the temperature observed during the deflection-observations. _R 2 ana< may 

 then be determined by taking a series of observations of i// 2 under the 

 greatest possible differences of temperature, at one or more places where 



