ON SDNSPOTS AND TERRESTRIAL PHENOMENA. 449 



netic declination was coincident with that of sunspot frequency, and 

 that its daily range increased and decreased with that of the spots. 

 The increase of the amplitude is approximately proportional to the 

 variation at different places of the earth's surface, so that on the average 

 the daily oscillation is from 15 to V7 times as large at times of snnspot 

 maxima as at times of snnspot minima. If we compare together the 

 curves of snnspot frequency and those of the daily range, we find that not 

 only do the maxima and minima correspond with each other, but that the 

 shape of the curves is throughout very similar, the irregularities of one 

 being generally repeated in the other. The connection seems so close that 

 Wolf has attempted to represent it by means of a mathematical formula. 

 Denoting by M the daily range of declination, and by w Wolf's number 

 for snnspot frequency, the following equation is found to hold very 

 nearly : M = a + b\\. a and b are two constants, which depend on 

 the place of observation. Wolf has determined them for thirty places, but 

 the question of the constancy of these factors can only be settled by 

 further observations. According to Ellis and Balfour Stewart, the curves 

 of daily declination range lag rather behind those of sunspot frequency; 

 even sudden outbursts of solar disturbance seem to be represented in the 

 magnetic curves by an increase in the daily range, which takes place 

 nearly simultaneously. 



The intensity of the horizontal component of the earth's magnetism 

 has a daily range, showing an oscillation which is larger at times of sun- 

 spot maxima than at times of sunspot minima. 



Hansteen ' has investigated the changes in the daily average of magnetic 

 declination and of dip, and has found that they present a period corre- 

 sponding to that of sunspot frequency ; the horizontal intensity is larger, 

 and the dip less at times of fewer sunspots ; and these two elements vary 

 together in such a way as to suggest the probability that the vertical 

 force remains comparatively unaltered, so that the change in the dip seems 

 produced by a change in the horizontal force only. At Kew, 2 however, 

 the change in the horizontal force seems inappreciable, while the dip 

 is increased at times of numerous sunspots, which latter result agrees 

 with that of the Munich observers, and seems to point to a change in the 

 vertical force. At Toronto, 2 on the other hand, both the dip and the 

 horizontal force seem to increase simultaneously with increase of sun- 

 spots, so that here the vertical force seems to alter more rapidly than the 

 horizontal component. But it must be remembered that changes in the 

 dip and in the horizontal force cannot be determined to the same degree 

 of accuracy as change of declination, and these last- mentioned results are 

 therefore not established with certainty. Fritz has investigated the ques- 

 tion whether the state of the sun's surface affects the rate at which the 

 secular change of declination takes place, and has found that at Paris, 

 Brussels, and Munich the secular change takes place most quickly when 

 there are many spots on the sun. The Kew results show, however, an 

 increase in declination at times of many spots, which denotes a retardation 

 in the secular change. The increase which is given by the Toronto 

 measurements, on the other hand, supports the view expressed by Fritz, 

 as the declination at Toronto at the present time increases. 



1 Ast. Nachr. No. 1069 (1857). 



2 See the article 'Terrestrial Magnetism ' in the Encycl. Brit. (Balfour Stewart), 

 p. 24. 



1884. g g 



