306 
DR. S. CHAPMAN ON THE LUNAR DIURNAL VARIATION OF THE 
First considering the phase angles, a general tendency to equality is evident 
between the values of 6 for the four components of a single element and season ; this 
result is obscured to some extent by irregularities, which are probably mainly 
accidental; it is what would be expected on the grounds of general theory (cf. § 23 of 
my former paper already cited). A comparison of corresponding phase angles at the 
two observatories reveals considerable similarity, though by no means exact agreement 
between the two sets of values. Both exhibit the more or less partial inversion, during 
the winter, of the variations in the horizontal force components, which does not appear 
in the case of vertical force (the vertical force variations for Pavlovsk are so small in 
amplitude that but little reliance can be placed upon the phase angles). 
As regards the amplitudes, the second harmonic is generally the greatest, though 
the first harmonic (which is usually the next greatest) sometimes equals or even 
exceeds it. The fourth harmonic is generally the smallest of all, often being quite 
inappreciable. The first three harmonics are as a rule much greater in summer than 
in the other seasons, the winter values usually being the smallest. A remarkable 
feature, however, brought out by Table VIa. is that the fourth harmonic is always 
greatest at the equinoxes, both absolutely and (a fortiori) in proportion to the other 
components ; this is shown even in the case of Pavlovsk vertical force. The equinoctial 
amplitude is frequently one-third that of the second harmonic, and sometimes 
greater. As I have previously shown (§ 25, p. 306, loc. cit.), the fact that the 
fourth harmonic is appreciable at all indicates that the diurnal variation in the 
atmospheric electrical conductivity cannot be represented by a simple diurnal wave 
a + b cos t, but that terms of higher frequency in the solar day must be present. 
The occurrence of these large values of C 4 at the equinoxes should therefore have an 
interesting physical bearing ; as yet, however, I have not entered into these theoretical 
questions, pending the acquisition of data from further observatories, and also the 
completion of an extension, by improved methods, of the mathematical theory of my 
former paper, both of which are now in hand. 
In conclusion it is a pleasure to acknowledge the assistance which has been placed at 
my disposal in carrying out the computations of this paper by the Government Grant 
Committee of the Poyal Society, by the Astronomer Royal, and by Dr. Schuster. 
The calculations have been performed mainly by Miss A. M. Palmer, and by Messrs. 
D. J. R. Edney and H. Furner ; their careful and accurate work has materially 
lightened my task of supervision. 
