TEERESTRIAL MAGNETISM AT KEW OBSERVATORY. 
115 
where Rq denotes the range in an ideal year of no sunspots and S is Wolfee’s 
sunspot frequency. 
A rise of 100 in S would increase R by 107 per cent, of R„. Hitherto, in the 
present paper, we have been employing as unit not Ry but what is practically the 
mean value of R for the period concerned. Taking, for instance, the whole 11 years, 
for which the mean value of S was 41'7, and representing by R the mean value of R 
for the period, we may replace (l) by 
R = R(l + l-07x 10-'S) ^(1 + 1 •07x0-417) 
= R(l + l-07x 10-'S)/l-446 .(2) 
In the case of the 11 years in Table IV. the difference between the extreme values 
of the Greenwich spot areas during the 31 days was 150 per cent, of the mean value. 
No serious error will arise in regarding Greenwich areas and Wolfee’s frequencies as 
standing to one another in a constant ratio, or in assuming the mean value of the 
frequency for the representative 31 days to be exactly 41‘7. If, then, the variation 
in absolute ranges on individual days followed, except for a lag, the same law as that 
of inequality ranges in individual years, the anticipated variation of H ranges in 
Table V. would have been 
R (1-07 x0-626)/l-446, 
and the change expressed as a percentage of the mean value would thus have 
been 46'3. 
The percentage change actually seen in the H ranges was 
111-6-93-5 = 18-1, 
or only 0'39 of that just deduced from the formula. 
Again, taking the data of Table XVIII., in columns n, we have a percentage 
change of 8’2 in the absolute range, corresponding to a difference of 25‘9 per cent, in 
sunspot frequency. 
If the change in the absolute range had, in this case, followed the law embodied 
in (2), its amplitude as a percentage of its mean value would have been 
r07 X 25-9/1-446 = 19-2. 
The ratio of the observed to the calculated value in this case is 
8-2/19-2 = 0-43. 
A still larger value for this ratio is obtainable from the H range data in Table V. 
for the years 1892 to 1894. The range of sunspot areas in the representative 31 days 
was 135 per cent, of the mean value, and the mean value of Wolfee’s frequency for 
the 3 years was 78-6. 
