358 DE. C. CHEEE; ANAEYSIS OF EESULTS FEOM THE KEY’ MAGXETOGEAPHS 
where SN, for instance, represents the honrly value in the diurnal inequality ol X, 
wliich corresponds to the values SH and SD, answering to the same hour, in the 
inequalities of H and D. I’o the necessary degree of accuracy, we may ascribe to L), 
11, and I in these formulae their mean values for the period considered, and tlie 
formulae actually used were (see Table 11.) :•— 
SN = -955 SH - 1-58 SD, 
SW = -298 SH + 5-08 SD, 
ST = -385 SH + -923 SAh 
Here SD is supposed to ])e measured in minutes of arc. In the case of N, and T, 
inequalities are given for only tliree months of the year, selected one from each of the 
three seasons ; in the case of N and W mean inequalities are given for two groups of 
years, as well as for the whole 11 years. 
In a good many cases there are two distinct maxima and two distinct minima in 
the inequalities. xAll maxima and minima wliose existence seems absolutely unmis- 
takalde are indicated by heavy type, hut in cases where the second maximum and 
minimum am missing or doubtfully represented only the extreme values for the day 
are so marked. In the case of D the terms “ maximum ” and “ minimum ” are 
a]iplied respectively to an extreme westerly and an extreme easterly position of the 
magnet. This is of course purely arbitrary, and is opposed to the practice of a good 
many ^vriters, wlio measure declination positively to the east. As a mathematician, 
I am perfectly alive to the weight of the arguments advanced in support of this 
practice, which has its conveniences whien mathematical calculations are being made 
involving the use of Cartesian co-ordinates. At a station, however, such as Kew, 
where the declination is westerly, and tlie prominent feature is the rapid forenoon 
movement of the needle to the west, it is much more convenient for descriptive 
pui'poses to take the west as the + direction. If one 'wishes to emplov co-ordinate 
axes, witli the east as positive direction, it is a simple matter to change the sign. 
§ 21. In addition to the hourly values, the tables give the Range of the inequality, 
defined as the dilierence between the algebraically greatest and least of the mean 
hourly values. They also give the sum of the dilierences of the 24 hourlv ^'alues 
from their arithmetic mean— i.e., from the mean for the day—taken numerically. 
The meaning assigned to the term “ range ” is carefully to be borne in mind, 
because there are a variety of usages, some of which are technically more exact. If 
we suppose for simplicity that the phenomena are absolutely identical lor each dav of 
a month, then the maximum and minimum for each day will occur at fixed times, 
which will also be the times of occurrence of the maximum and minimum in the mean 
diurnal inequality for the month. And if it happen in addition that the times of 
occurrence of the maximum and minimum each coincides with an exact hour G.H.T., 
then the meaning to he assigned to the term range ” has no ambiguity, in practice, 
