164 DE. S. CHAPMAN ON THE LUNAR DIUENAL MAGNETIC VARIATION, 



nearly, we see that the mean ranges of the curves, as well as the mean areas, for the 

 two distances are in the approximate ratios of the inverse cubes of the moon's distance 

 from the earth, as in the theory of the tides " (loc. cit., 405). 



FIGEE did not determine the ratio of the mean amplitudes over half lunations, but 

 only over periods of three days centred at apogee and perigee ; hence his results 

 should be compared with 1'39 and not with 1'23. This point seems to have been 

 overlooked by him, for on comparing his figures with BROUN'S, he remarked that 

 BROUN'S value of the perigee-apogee amplitude ratio (l'24) "is much smaller than 

 that found for Batavia, 1'68, and therefore the conclusion drawn by BROUN is not 

 allowed here ' that the mean ranges of the curves, as well as the mean areas, for the 

 two distances, are in the approximate ratios of the inverse cubes of the moon's 

 distance from the earth, as in the theory of the tides ' " (loc. cit., 23). The figure 

 1'68, here referred to, is the ratio of the areas of the variation curves at perigee and 

 apogee for declination (winter), the element chiefly affected by the moon at Batavia. 

 The ratios for the other elements and seasons were also determined, however, though 

 in some cases (especially that of vertical force) the whole lunar variation is so small 

 that any effect of the kind sought for would be liable to be masked by accidental error. 

 But in the case of horizontal force the total amplitudes, while smaller than that 

 of declination in winter, seem to be sufficiently large to entitle the perigee-apogee 

 ratios derived from them to some weight. The three values of this ratio which 

 appear to be the most reliable, amongst FIGEE'S results, are consequently : 



Declination (winter) 1'68. 



Horizontal force (summer) 1'40. 



Horizontal force (winter) I'OO. 



The mean of these results* is 1'36, which is very nearly equal to the theoretical ratio 

 1'39 ; hence, we may conclude that, while it is subject to considerable accidental error, 

 the mean result from Batavia tends, like that from Trevandrum, to the support of the 

 tidal hypothesis as to the origin of the lunar magnetic variations. 



The newly computed results, next to be described, are derived from the hourly 

 values of the magnetic elements at five observatories, Pavlovsk, Pola, Zi-Ka-Wei, 

 Manila, and Batavia (in each case for seven magnetically " quiet" years), treated in 

 the manner explained in a recent paper on the lunar magnetic variations at Pavlovsk 

 and Pola.t The amplitude ratio has been determined both from short periods of three 



t The other results obtained by FIGEE are as follows : declination (summer) 1 -09, vertical force (summer) 

 1-97, vertical force (winter) 089. The mean of these values is 1'32, but on account of the smaller 

 amplitude of these variations, not much weight can be given to this mean value. 



t CHAPMAN, 'Phil. Trans.,' A, 214, pp. 295-317 (1914). For the purpose of the perigee-apogee 

 investigation the work described in that paper is useful up to the end of 4. 



The seven years dealt with are 1897-1903, except in the case of Batavia, where on account of interrup- 

 tions in the observations the years 1899-1901 were replaced by the correspondingly quiet years of the 

 previous sunspot cycle, 1888-1890, 



