418 



Reports on Special Researches 



curve is the fact that the early morning minimum is not so sharp as is usually the case with 

 the land observations. When allowance is made for the difference in the absolute values 

 of the potential-gradient, the land curve to which the ocean curve most closely corresponds 

 is that for Potsdam. The relation comes out strongly when the Fourier amplitudes of the 

 different harmonics are considered. If the potential-gradient be expressed in the usual 

 form X = ao+ai sin i<pi+x)+a2 sin {,p2+2x)+ . . . etc., where the a's are ampUtudes 

 and the <p's phase angles, Table 94 gives for the first 3 Fourier "waves" the values of the 

 a's and <p's for the curves plotted in Figure 27. 



Table 94. — Amplitudes and Phase Angles for Diurnal-Variation Curve of the Potential-Gradient. 



It will thus be seen that the curve for the ocean values partakes of the properties of the 

 curves for Potsdam and Kew in showing, for the 12-hour "wave," an amplitude which is 

 greater than that for the 24-hour "wave." A similar result was obtained by Simpson and 

 Wright^ in their observations over the Atlantic and Indian Oceans. The preponderance of 

 the 12-hour term over the ocean is of special interest when it is recalled that over land the 

 ampUtude of this term appears to diminish very rapidly with altitude. Thus the ratio oi/aj 

 is very much larger at the top of the Eiffel tower than at a point on a level with the base. 

 It has been customary to attribute the 12-hour term to dust carried up by convection 

 currents during the hotter part of the day, but the preponderance of this term in ocean 

 observations, where the air is very pure, would appear to cast some doubt on such an 

 explanation, a point to which Simpson and Wright have also called attention. 



The diurnal-variation curve of the ionic content shows a flat maximum extending 

 over about 8 hours from 6 a. m. to 2 p. m., and a minimum about midnight, the ampUtudes 

 and phase angles of the first 3 Fourier "waves" being Oo = 810, Oi = 41.8, 02 = 3.3, 03 = 8.2, 

 <Pi = 278°, <P2 = 90°, <p3 = 156°. The diurnal range forms, in the case of the ionic content, only 

 about 10 per cent of the whole. If this were all attributable to a change in the rate of 

 production of ions, we should expect a diurnal range of about 20 per cent in the latter 

 quantity; but we have seen that the observations give no evidence of any appreciable 

 diurnal variation in R. Since the value of X controls, to some extent, the values of the 

 ionic densities near the Earth's surface,^ we may expect a diurnal variation in X to be 

 accompanied by a diurnal variation in n+ ; increase of X should be accompanied by decrease 

 of n+. On referring to Figure 26, we indeed find that the midnight maximum for X cor- 

 responds to a minimum for n+, and although the early morning maximum of X is not 

 accompanied by a distinct minimum of n+, there is an indication of a tendency in this 

 direction. There is, however, a further cause which contributes to the diurnal variation of 

 the ionic content, for a, the rate of recombination of the ions, is known to decrease with 

 increase of temperature, the decrease amounting, according to Erikson,' to about 1 per 

 cent per degree at ordinary temperatures. The diurnal variation of the temperature, as 



'Proc. R. Soc. A, vol. 85, p. 181, 1911. 



'See E. von Schweidler, Wien. Ber., vol. 117, p. 653, 1908; also W. F. G. Swann, Terr. Mag-, vol. 18, p. 163, 1913. 



*Phil. Mag., vol. 18, pp. 328-366, 1909. 



