70 
DR. S. CHAPMAN ON THE SOLAR AND LUNAR 
§ 27. The Residual Variations, and the Terms not Dependent Solely on 
Local Time. 
Our discussion of the magnetic variations has so far related entirely to the simple 
analytical representation of the observed data which has been described in §§ 10, 13. 
In this representation the only terms considered were those dependent on local time. 
It remains, therefore, to discuss the residuals in Tables III. and VI., and to examine 
how far they are to be attributed to the presence of variations not’ depending solely 
on local time (cf. § 22). 
In order to abbreviate this investigation, certain general features exhibited by the 
residuals will be described without setting out the detailed figures. In the first 
place, the mean residuals for any of the nine groups of observatories are generally 
similar for the years 1905 and 1902, and, in the case of the “annual’ residuals in 
Tables III. ( a) and III. ( (3 ), for the equinoxes and solstices. They are, however, 
greater for 1905 than for 1902, and greater at the equinoxes than at the solstices. 
If all the nine group mean residuals from any Table are combined numerically 
(counting all signs positive), the ratio of the 1905 and 1902 sums, or of the 
equinoctial and solstitial sums, can readily be determined. The former ratio is 
rather less than those of Table ft, being approximately 1'2, for the “annual’ 
residuals. The increase, such as it is, confirms the view that the residuals are a real 
part of the phenomenon, and do not merely represent accidental errors of 
observations. 
The ratio of the equinoctial to the solstitial “ annual ” residuals is greater, being 
about 1'4. This is shown in the case of all three magnetic elements, and all four 
periodic components, the separate mean ratios for these (n = 1, 2, 3, 4) being 1 *4, 1‘2, 
1'5 and 1‘6. These increases roughly correspond to those shown by the Q H n+] 
harmonics already discussed. 
The group-mean residuals, in the mean of equinox and solstice and of 1905 and 
1902, taken from Tables III. (a) and (/ 3 ), are collected in Table T. The “ seasonal ” 
residuals from Tables III. (y) and (S) will not be considered. 
The largest residuals in Table T occur in the column relating to the 24-hour 
component variation of North force. The corresponding residuals for the West force 
are small and may well represent merely local peculiarities at the various observatories. 
If the variations indicated by the North force residuals have a potential of simple 
form, this must be of type Q m °, since this is the only type which yields North force 
terms without contributing also to the West force variations. In § 22 it was shown 
that the inclination of the magnet to the geographical axis of the earth could give 
rise in the current function to the variation 
(no) 
6K 2 a CK tan </». r m °Q m ° sin (t — \ — a) 
