On the Periodical Variations of Terrestrial Magnetism* 



all these curves conceal simple periods, which being superim- 

 posed give complicated results. 



That such periods being superimposed upon each other may 

 produce curves of irregular appearance, will not be doubted by 

 any one who may have once seen the multifarious curves, obtained 

 by the superim position of one or two waves, in the little machine 

 invented by "Wheatstone for representing the interferences of 

 luminous undulations ; and it is just the application of these 

 principles to the theory of terrestrial magnetism which reduces 

 these facts, in themselves highly intricate, to a surprising degree 

 of simplicity. In order to render more intelligible what we are 

 about to say, it will not be without its use if we conceive a wave 

 of which the elementary curve is the ordinary one of simple sines, 

 having for its equation 



y=k sin [x-\-a)f 

 and a second wave of double period, and of the equation 

 y = k sin (2^ + fl). 



If we superimpose these two forms, we shall have a figure 

 distinct from either. We here suppose the two components to 

 have equal excursions ; but by giving different values to the con- 

 stants which enter into the curve, we may get the share belonging 

 to the minor diurnal inflexions to be almost sensibly rectilinear ; 

 and vice versa we may have more exaggerated inflexions. 



In the equations of these curves we will distinguish the con- 

 stants by special names for the sake of brevity and clearness, call- 

 ing k the modulus, the arc x the argument, and a the parameter. 



This being premised, we come to the demonstration of the 

 law which has been enounced, which will be no other than a 

 corollary of the observed facts. 



And first, from an extended and comparative analysis of all 

 the magnetic observations, the sun is seen to be the principal 

 cause, not only of the diurnal, but also of the annual variations ; 

 and we have only to form to ourselves a clear idea of the manner 

 in which it operates. Colonel Sabine, in vol. ii. of the Toronto 

 Observations, p. 20, briefly sums up the fundamental points, 

 comparing the curves which we have cited, and calls attention to 

 two things, — 1st, the opposition of the movements of the needle 

 in the two observatories situated beyond the tropics in the two 

 opposite hemispheres (i, e. at Toronto and at Hobarton) ; and 

 2nd, the opposite direction induced by the sun^s passage of the 

 equator in the declination of the needle at St. Helena and at the 

 Cape of Good Hope, which phases place beyond doubt the in- 

 fluence of the sun's declination. He does not however proceed 

 further with the analysis. Now it seemed to me that this germ 

 :might be considerably more developed, and might become fer- 

 tile in very important consequences. It seemed to me strange 



