254 
DR. C. CHREE: DISCUSSION OF KEW MAGNETIC DATA 
being thus 237/11 or 2‘2y. This expressed as a percentage of the range is 
237 x 100/11 x 177, or 12'2. 
There is obviously a good deal that is “ accidental ” in the results obtained for 
individual months, especially in V. The values of b/a, it will be seen, are decidedly 
larger for H than for Y, implying that relatively considered the sunspot influence has 
more effect on the range of the former element than on that of the latter. 
The differences between observed and calculated values naturally tend to increase 
in size with the extent of the variation of R during the 11 years, and so are largest in 
summer. The fairest way, however, to compare the accuracy of the formula at 
different seasons, or for different elements, is to take as criterion the percentage which 
the mean difference between observed and calculated values is of the difference between 
the largest and least observed values of R. In H these percentages show no marked 
variation with the season. There are considerably greater variations in Y, but they 
probably represent in the main the smaller accuracy of observed values in that 
element, as the largest and smallest values for individual months both fall in 
summer. 
If we exclude the equinoctial value in Y, the agreement between observed and 
calculated values is decidedly closer for the seasons than for individual months, and in 
the case of H it is still closer, to a marked degree, for the year. 
One’s estimate of the suitability of a formula, while mainly determined by the size 
of the mean difference between observed and calculated values, is partly determined by 
the mode of grouping of the plus and minus signs. For instance, if the plus signs all 
occurred together, there would be reason to suspect a sensible secular change in the 
amplitude of the diurnal inequality, quite apart from sunspot variation. Table 
XXXIY. accordingly records for each year the actual differences between the observed 
Table XXXIY.—Observed less Calculated Ranges in mean Diurnal Inequality 
for the Year. 
Element. 
1890. 
1891. 
1892. 
1893. 
1894. 
1895. 
1896. 
1897. 
1898. 
1899. 
1900. 
H 
Y 
I 
+ 0 - ly 
— 1 ’ 7y 
+ 0' • 05 
+ 0 - 6y 
+ 1 ■ 2y 
+ 0' • 05 
+ 0' 5y 
0-0y 
+ 0'-08 
— 0 • 3y 
- l-6y 
+ 0'*01 
+ 0 ■ 4y 
+ 0 ’ 4y 
O'-00 
— 0-5y 
0-0y 
-O'-06 
— 0" ly 
+ 1 ■ 0y 
- O'-07 
1 + 
Poo 
O CO o 
— 
— 1 • 4y 
+ 1" ly 
- O'-13 
+1" 3y 
0-0y 
+ 0' • 13 
— 0 • 6y 
i * iy 
— 0 - 03 
and calculated values. The calculated values for H and V were derived from the 
values of a and b assigned in Table XXXIII. to the mean diurnal inequality for the 
year. The results for I were calculated from 
a = Cf'8648, b = (COllll, 
these being the values obtained by the aid of least squares from the observed I range, 
m the mean diurnal inequalities for the eleven years. The corresponding value of 
