48 BIRKELAND. THE NORWEGIAN AURORA POLARIS EXPEDITION, lgO2 1903. 



It should at once be remarked that it is the total force that can be calculated almost after an 

 objective method. The components, or partial forces, as we will call them, will as a rule be less exact. 

 A decomposition will nevertheless be of value in throwing light upon the development of the perturbations. 



CALCULATION OF THE SCALE-VALUES FOR THE REGISTERINGS 

 AT THE NORWEGIAN STATIONS. 



16. A. Determination of the Scale-Values for the Declinometer. The declinometer consists 

 principally of a magnet suspended by a quartz thread. Fixed to the magnet is a mirror. Light from a 

 fixed source is reflected in the mirror, and is focussed by a lens into a spot of light upon the photo- 

 graphic paper. If the fibre had no torsion, the turning of the mirror would give directly the change 

 of declination. 



But the fibre has torsion, and its effect must be determined. 



The effect of the torsion is found by twisting a certain angle a minutes of arc, and measuring the 

 corresponding deviation on the paper. 



The scale-value, or the angle in absolute measurement, which answers to a length-unit in deviation, 

 is determined by the following formula: 



-f x) 



' d 



where / is given by the equation 



/ =- 



x 



r<i is the distance from the mirror of the declinometer to the cylinder with the photographic paper. 

 ka is the angle in radians about which the twisting is done. 

 .v is the deviation on paper, answering to the torsion. 



When the angle in the equation for y. is measured in minutes, and .v in millimetres, we can put 

 for our apparatuses for the numerical calculation, approximately, 



2 krd = i, and 



y. = 



For the calculation of the perturbing force perpendicular to the meridian, we obtain the following 

 scale-value : 



H t is the horizontal component actually existing at the moment. 



17. B. Determination of the Sensibility of the Variometers for the horizontal and vertical 

 Intensity. The main principle here consists in seeking the deflection corresponding to a known mag- 

 netic force /. 



