46 BIRKELAND. THE NORWEGIAN AURORA POLARIS EXPEDITION, 19021903. 



A simple mechanical reflection then shows that 



d = - 8 Ht = aid Hf. 

 180 . 60 r 



If we resolve to reckon P d positive towards the west, we obtain the following rule for the sign of f d . 

 e d is positive when increasing ordinate corresponds to increasing westerly, or decreasing easterly, 

 declination. 



In taking out the ordinate-difterences, a purely graphic method has been adopted, the normal line 

 being drawn upon the magnetogram itself, and the ordinate-differences taken out directly by measurement. 



One thing which here often causes some difficulty, is the placing of the normal line. It may 

 sometimes happen, especially when the perturbation is of long duration, that doubt may arise with 

 regard to its situation, and in this way a corresponding fault may arise in the determination of the 

 perturbing force. 



In a series of perturbations, however, this doubtful territory is small, so that the position of the 

 normal line is decided almost without question. 



It will immediately be seen that the strong, brief perturbations, which appear somewhat suddenly 

 on an otherwise calm day, will be particularly favorable in this respect. Here the normal line will be 

 a line that connects the calm districts before and after, in such a manner that its further course is ruled 

 by the curve on the nearest calm days. Perturbations such as these, in which the situation of the 

 normal line can be easily fixed, will be indicated as well-defined perturbations. The study of these short, 

 well-defined perturbations will also, as already remarked, be advantageous for the reason that we are 

 here possibly face to face with elementary phenomena, which together may form the multiplicity of the 

 perturbations. 



If the perturbation is of long duration, if it extends over the whole magnetogram, which generally 

 represents 24 hours, there will very likely be some uncertainty. If, for instance, there is a part of the 

 curve that is normal, part of the normal line will thereby also be determined. Its absolute distance 

 from the base-line will then be ascertained, and its further course over the perturbed region must be 

 determined by the form of the curve on the nearest calm days. We must here notice whether, if the 

 temperature has varied during the period under consideration, it has approximately varied in the same 

 manner throughout the day; should this not be the case, we should have to find, by the aid of the tem- 

 perature coefficient, the form for the neighbouring curves, that corresponds to the temperature on the 

 day under consideration. 



If there is no part of the magnetogram calm, the normal line must be determined, both as to its 

 form and to its absolute distance from the base-line, by the aid of the curves on the nearest calm days. 

 And here regard must be paid to differences in temperature. If we are to avoid corrections for tem- 

 perature, it will not be sufficient that the temperature-curve has the same course during the two days; 

 the temperature must also have the same absolute value at the same hour. As a rule, the temperature 

 in the observatory will be fairly constant, so that in most cases by this method there will be no need 

 of correction for temperature, unless it were actually to affect the sensibility. 



As the curves from day to day in other respects -- presupposing the same circumstances - do 

 not repeat themselves altogether congruently, there is liable to be some arbitrariness in their situation. 

 If therefore we are to be able to count upon obtaining values for the perturbing force with a reasonable 

 error-percentage, these protracted perturbations must also be strong, if the calculation is to yield any 

 return; and it will frequently happen that in such cases the direction and strength of the perturbing 

 force cannot be greatly relied upon, when the magnitude of the force is small. 



