FROM SELECTED DAYS DURING THE SEVEN YEARS 1898 TO 1904. 
.‘300 
conspicuous minimum in the three months November to January, the night fall a 
conspicuous maximum from December to March. The regular causes, whatever they 
are, to which the clay and night falls are due, are at Kew nearly equal in intensity 
in the average month both of equinox and summer. 
The daily range when considered absolutely is, as we have already seen, greater in 
winter than summer; but relative to the mean value of P for the day, the day and 
night falls and the range all show a decided minimum in November, December and 
January. If the potential gradient is due to a negative charge on the earth, the 
density of that charge is on the average greater in winter than in summer, but the 
diminished charge of summer is, relatively considered, more influenced by the causes 
to which the regular diurnal inequality is due. 
The figures in the last column of Table IV. are shown graphically in the dotted 
curve of fig. 1. 
Analysis of Diurnal Inequality in Fourier Series. 
§ 8. The diurnal inequalities in Table III. have been analysed in Fourier series 
c x sin (t + a x ) + c 2 sin (2 t-\-a 2 ) + c z sin (3£ + a 3 ) + c 4 sin (4 t + af), 
where t represents time counted from midnight (G.M.T.), one hour being taken as 
equivalent to 15°. The amplitudes c l5 &c., and the phase angles a x , &c., for the 
individual months, the year, and the three seasons are shown in Table V. In the 
case of the amplitudes, unity represents, as before, a potential gradient of one volt 
per metre. The variation of c x and c 2 throughout the year is illustrated by the 
heavier full and dotted line curves respectively of fig. 3. The ordinates represent the 
ratios borne by the monthly values to their arithmetic mean. 
The annual variation of c x is of a most unusual character. The mid-winter 
maximum and mid-summer minimum are extraordinarily pronounced. The phase 
angle a x also shows a remarkable annual variation, the times of maximum in 
‘summer and “ winter” differing by nearly 8 hours. In July and December the 
24-hour waves are nearly in opposite phases. 
The 12-hour term presents very different features. Its amplitude, c 2 , is slightly less 
for winter than for summer, and there are maxima at the equinoxes, but the annual 
variation is comparatively small. The variation shown by the phase angle a 2 is also 
comparatively small, the difference between the times of maximum in winter and 
equinox being little over half an hour. 
The 8-hour and 6-hour terms are so small that considerable uncertainty must 
attach to the results for individual months. Still, there is a regularity about the 
figures, especially those for the 8-hour term, which seems to justify our acceptance 
of at least the general features. The annual variation of c 3 is somewhat similar to 
