418 report — 1884. 



where/ is the number of groups of sunspots seen on the day, a solitary 

 spot counting as a group ; g is the total number of spots, and K is coefficient, 

 depending on the instrument used. Putting k equal to one, for instance, 

 a group of two spots would give a number 12, while two single spots 

 would count as 22. The applicability of Wolf's equation is shown by the 

 fact that all the results deduced, from it agree well with those deduced 

 "from the direct measure of spotted area, and that especially the parallel 

 behaviour of the sunspot curve with that of the daily variation of the 

 magnetic needle becomes very apparent by using Wolf's number. Even 

 for the later observations, for which we possess the sunspot areas, it is- 

 a matter open to discussion whether an empirical formula like that of 

 Wolf may not give a more correct representation of solar activity than 

 the actual measure of the area. Thus it is very plausible, as shown in 

 the above example, that two spots, though covering the same area, should 

 represent a greater total solar activity if they are situated at the different 

 parts of the solar surface than if they are close together, forming one 

 group. But, at the same time, there is something arbitrary in Wolf's 

 number, each spot counting alike, whether it is large or small. We are- 

 forced at present to use Wolf's numbers, as giving us the most complete 

 and homogeneous series ; but we ought not to remain satisfied in future 

 observations with the mere counting of groups and spots without esti- 

 mation of their areas. Wolf has, in order to equalise the irregular varia- 

 tions, taken as a sunspot number for a given month the mean of the 

 number deduced from that month, the six preceding months and the six 

 following months, giving half the weight to the most distant month on 

 either side. The numbers thus obtained he calls compensated sunspot 

 numbers. He has calculated the numbers for each month from July 

 1749 to June 1876. 1 I shall adopt these numbers here as the measure 

 for solar activity. 



Connection between Sunspots and Terrestrial Magnetism. 



It is a well-known fact that the magnetical needle, in addition to its 

 more irregular displacements, shows each day a periodical movement. 

 Towards seven or eight o'clock in the morning the needle begins to travel 

 west ; at about one in the afternoon it has reached its greatest deflection ; 

 it then begins to travel east until about eleven at night. During the 

 night it is pretty stationary, moving, however, more quickly again in the 

 early hours of the morning. 



The hour at which the needle turns, as well as the extent of its daily 

 period, depends on the season. The range of this diurnal variation is 

 greater in summer than in winter. At Kew, for instance, the greatest 

 western deflection during the winter months averages nearly seven 

 minutes and a half, while the average deflection between October and 

 March is only about five minutes of arc. In the Southern Hemisphere 

 the motion of the needle is reversed, and in the equatorial regions there is 

 consequently a belt, shifting with the seasons, at which the variation- 

 vanishes. 



Rudolf Wolf, General Sabine, and Alfred Gautier pointed out almost 

 simultaneously, in the year 1852, that this daily variation of the mag- 



1 Memoirs 17. Aslr. Soc, vol. xliii. p. 200 (1875-1877). 



