PART I. ON MAGNETIC STORMS. CHAPT. I. 45 



It need hardly be said that instances will necessarily occur in which it will be difficult to decide 

 whether the curve is normal or not. No exact definition of a perturbation can therefore be given; but 

 we shall always try to keep to cases in which there is no doubt about the matter. 



We will call the magnetic force that is actually found at a given moment, Ft, and the force we 

 should have had at the time, without perturbation, F n . 



The perturbing force P is the force which, together with /", has F t as its resultant. 



We resolve all the forces along 3 axes at right angles to one another -- one vertical, one along 

 the magnetic meridian, and one perpendicular to these, and we designate 



the components of Ft as F Ul , F u , F lv 

 /' F n h, F n t, F m 

 P , P h , P d , P,. 



We thus obtain 



Pk = Ftk-F* =//-// ) 



Pd = F id ~F, ld = F u ( W 



P, = F tv - F,= V t - V n , 



introducing the customary denotations for the horizontal and vertical components of terrestrial magnetism. 

 We will call the horizontal component of the perturbing force /-*,, and we have 



PI =1 Pk* + Pi* and 



P = !/>, *-)-/>, a. 



It appears from equations (i), that it is only necessary to know the difference between the 

 components of FI and F,,, and not their absolute value; and this difference is found by the curves, a 

 "normal line" being drawn upon the magnetogram, which gives the course of the curve, if no perturba- 

 tion has taken place. 



If we denote the ordinate from the base-line to the curve and to the normal line at a given 

 moment, as Of, and O n , and if a deviation of one length-unit on the magnetogram answers to a magnetic 

 force , then 



Ph = tk (Oft Ort) = t h 4 

 Pa = td (Otd O nd ) d l d 

 P, = e, (O t , O m ) = e v /, 



the differences of the ordinate being denoted by // 4 and /, 



According to our definition-equations (i), we shall have P k and P, becoming positive in the same 

 direction as the corresponding total forces. H is positive towards the north, and V is assumed to be 

 positive downwards. We hereby obtain the following rule for the sign of ;, and ,. 



(i, is positive when increasing ordinate corresponds to increasing horizontal intensity. 



For we obtain 



(1) In the northern hemisphere, 



e v positive, when increasing ordinate corresponds to increasing numerical value of V. 



(2) In the southern hemisphere. 



e, positive, when increasing ordinate corresponds to decreasing numerical value of V. 



With regard to d it should be noted that in general it is not directly given. On the other hand, 

 the number of minutes of arc, (i, that the declination is altered by oscillations of one length-unit 

 is given. 



