28 
DR. S. CHAPMAN ON THE SOLAR AND LUNAR 
As regards the reliability of the results in Table F, this is, of course, greater for 
the annual (i.e., mean equinoctial and mean solstitial) terms than for the seasonal 
terms (solstitial and equinoctial inequalities). In the latter case the harmonics Q n( ”> 
where m = n, are fairly well determined, but the higher harmonics m = n + 2 are 
much less certainly evaluated. Among the components of different periods the 
semi-diurnal one is probably most free from accidental error, but the agreements in 
phase and amplitude for the other periods in the various parallel cases seem to 
indicate that the harmonics Q” n+1 and Q„” for all four periodic terms have definite 
terrestrial significance. It should be remembered that Q m n contains a numerical 
factor which increases rapidly with m (cf Table B), so that the small amplitudes 
E m n , I m n for the higher harmonics represent magnetic variations much less small, in 
proportion to the diurnal and semi-diurnal terms, than their numerical values suggest 
at first sight. 
This completes the actual analysis of the solar diurnal magnetic variation field, 
although the original data, and the residuals between these and the values of a n and 
b n calculated from the analytical representation, will be discussed later in connection 
with the possible existence of a portion varying with the longitude. Before dis¬ 
cussing the relation between the external and internal variation fields already 
determined, a similar analysis of the lunar diurnal magnetic variation will be 
described in order that the results of the two analyses may be considered together. 
Part III.— A New Analysis of the Lunar Diurnal Magnetic Variation. 
§ 12. Description of the Data and of the Method of Analysis. 
The data used in this analysis consist of the a n , h n Fourier coefficients in the 
analysis of the lunar diurnal magnetic variation according to the formula (l). But the 
time t in (l) is now local mean lunar time, reckoned at the rate of 15 degrees per mean 
lunar hour, which is approximately ff times as long as a mean solar hour. The time of 
origin is the local time of upper culmination of the moon, at the epoch of new moon. 
The conventions as regards the signs of the three geographical components of force 
are the same as in § 7. The unit of force in which the Fourier coefficients are expressed 
is 10~ 7 C.G.S., or O'Oly, only one-tenth as large as the unit used in Part II. 
The lunar diurnal magnetic variation is of very small amount, and it can be 
computed with any approach to accuracy only by the use of a long series of 
observations, so as to eliminate accidental errors arising from fortuitous disturbances 
of much larger magnitude than the variation itself. In the present case seven years' 
observations at each observatory have been used, and the years chosen were “ quiet ” 
as regards solar and magnetic activity. Except in the case of Batavia, the same 
seven years (1897 to 1903) were used for each station. Owing to the reorganization 
of the Batavian observatory during this period the years 1899 to 1901 had in this 
instance to be replaced by the correspondingly quiet years 1888 to 1890 of a previous 
