AND ITS CHANGE WITH LUNAR DISTANCE. 165 



or four days centred at apogee and perigee, and also from half lunations, as in BROUN'S 

 investigation. In order not to waste labour on computations which were not likely 

 to afford an accurate result, owing to the relative magnitude of the amplitude change 

 and the accidental errors, only those elements have been dealt with (and during those 

 seasons*) for which the range of the semi-diurnal lunar magnetic variation 

 approximated to at least 2y (2. 10"~ 5 C.G.S.). 



The results as regards amplitude are given in Tables I. and II., the former applying 

 to the shorter periods about apogee and perigee, and the latter to the half lunations. 

 The number of days contributing to each individual value of the semi-amplitude 

 in Table I. was approximately 100, and in Table II., approximately 400. The 

 theoretical value of the amplitude ratio in the former case is 1'38, and in tin; latter, 



1'23. The means of the observed values are as follows : 



Theoretical value, 

 r Declination (six determinations) . . . 1'33~] 



Short periods . < Horizontal force (five determinations) . 1'43 f- 1'38 



I Vertical force (four determinations) . 



* 



f Declination (six determinations) . 



Half lunations < Horizontal force (six determinations) . 0'98 ^ 1'23 



I Vertical force (four determinations) . . 



The individual results in Tables I. arid II., on which these means are based, show 

 considerable discordances, and better data are much to be desired. The accidental 

 errors in the determination of the minute lunar magnetic variations, especially from a 

 comparatively small number of days, are considerable ; in one or two cases, indeed, 

 some of the computed semi-amplitudes are palpably erroneous, and have been discarded 

 in taking the means from the tables. The discordance (including even the rather 

 surprising discordance of the second horizontal force mean value, 0'98) must, I think, 

 be attributed to the fortuitous effect of magnetic disturbances, and this can be 

 eliminated only by determining the lunar variation over the average of a considerably 

 longer period of time. It would be well if observatories would undertake such a 

 reduction of their own observations, but meanwhile the only available data are those 

 here communicated. 



Apart, then, from the fifth mean value tabulated above, t the present results, 

 taken in conjunction with BROUN'S and FIGEE'S data as previously discussed, may be 

 said to confirm with reasonable probability the hypothesis of tidal action. The 

 material is certainly not sufficient to determine the magnitude of the ratio of 

 amplitudes at perigee and apogee to within a few per cent., as is desirable. It would 



* The year was divided up into three parts, summer, winter, and equinox, comprising May- August, 

 November-February, and the intervening months, respectively. 



t It does not seem probable that the smallness of this result for horizontal force represents a 

 real phenomenon, especially as the second of the above mean values (1 43) would tend to the opposite 

 conclusion. 



