1898-1902. No. 6.] TERRESTRIAL MAGNETISM. 27 



C. HORIZONTAL INTENSITY. 



For the determination of the absolute value of the horizontal inten- 

 sity, both vibration and deflection observations were made with the two 

 magnets belonging to the apparatus, V and VI, whose length was 

 respectively 99 mm. and 98 mm. 



In the regions explored by the Expedition, it must be presupposed 

 that while the observations were being made, the magnetic conditions 

 were always disturbed, and cannot be taken into account, as the Ex- 

 pediton had not taken variation instruments with them. I have there- 

 fore endeavoured to calculate the horizontal intensity separately from 

 vibrations and from deflections, by means of the two following formulae^: 



C^l 



sin cp ' 



For deflections, H = 4^^ [1 - (3/J + a) t^\ {\ ) 



For vibrations, 1? = - • ^^ fl + W + «) «J (2) 



The symbols employed in these formulae are as follows: 



H = absolute horizontal intensity. 



q> = angle of deflection. 



7= time of vibration, corrected for rate of chronometer, arc of 

 vibration and torsion force of the suspended thread. 



f = temperature of magnet during the deflections. 



t^ = temperature of magnet during the vibrations. 



a — temperature coefficient. 



/? = coefficient of dilatation for brass (0.0000180). 



/S' = coefficient of dilatation for steel (0.0000124). 



^i and G are two constants, of which the first, f.i, is proportional to 

 the magnetic moment of the magnet, while C is the constant employed 

 when the horizontal intensity is to be calculated from simultaneous 

 vibrations and deflections, according to the following well-known formula^: 



G_ 

 ^■j/sin cp I 



H=^^[l + fi't,-lpt^ + '%^ (3) 



' Nansen Expedition. T. M. p. 64. 



2 I will take this opportunity of drawing attention to the fact that in the Report 

 on the Nansen Expedition, T. M., p. 62, this formula has been incorrectly given as 



