No. 7.] HORIZONTAL INTENSITY. 63 



where C is a constant quantity of the following form: 



' (2) 



As already mentioned, there are two magnets belonging to the apparatus, 

 designated V and VI, respectively 99'0 mm. and 98'0 mm. in length. 



The temperature coefficient a was determined for both of them in Hamburg 

 on June 8th, 1893, by a long series of observations, after they had been 

 placed, on June 3rd and 4th, in steam of 100 C., and kept there for 12 

 consecutive hours, in order to ensure them against loss of permanent mag- 

 netism afterwards. 



The following values were found: 



a 



For magnet V . . . . 0-000307 



VI . . . 0-000638 (?). 



The moment of inertia of the magnets, K, was also determined on 

 June 9th, 1893, from several series of vibration observations, alternately 

 with and without the addition to the magnet of a ring of known weight 

 and dimensions, with the following result, which, however, does not lay 



claim to any great accuracy: 



K 

 For magnet V . . . . 99'47 



VI .... 200-22 



The induction coefficient cannot be directly determined with this in- 

 strument. 



The total constant, C, in which both the moment of inertia and the 

 induction coefficient are included, may, however, be inferred by means of 

 equation (1), if combined vibration and deflection observations are taken with 

 the instrument, in a place where the horizontal intensity is known, as the 

 following equation is then obtained: 



log C = log H + log T+ i log sin <p - log [1+pt - /?*' + a(t - 1')} (3) 



The observations for the calculation of the constant C were made in 

 Hamburg before the departure of the expedition, and in Wilhelmshaven after 

 its return. 



As it was to be expected that there might often be occasions during the 

 Fram Expedition, when there was no opportunity of observing simultaneous 



