166 DE. S. CHAPMAN ON THE LUNAR DIURNAL MAGNETIC VARIATION, 



not be unreasonable to conclude from the present data that the effect of lunar 

 distance may be a little less than the tidal theory would indicate ;* but, at any rate, 

 it seems clear that we may conclude that if the amplitude of the lunar magnetic 

 variation is inversely proportional to the w ih power of the moon's distance, where n 

 is integral, then n can have no other value than three, t 



The, Change with Lunar Distance of the Phase of the Lunar Magnetic Variation. 



In the computations by which the lunar magnetic variation data, discussed here 

 and in a former paper, were determined, the hourly values of the magnetic elements, 

 after being freed from the solar diurnal variation, were written out in rows of twenty- 

 five, the first value on each row corresponding to the civil hour nearest to the moon's 

 meridian transit on that day.J Hence the origin of lunar time is, in the mean, at 

 the hour of lunar transit and is independent of the longitude of the moon in its orbit. 

 We shall represent the lunar magnetic variation by sin (2t + 9), where t, measured 

 from the origin just mentioned, increases by 2x in a lunar day : then 9 is the phase 

 of the variation, which is found to vary with the longitude of the moon. We shall 

 denote its values at perigee and apogee by P and $ A) and its mean values during the 



half lunations centred at these epochs by P and A . The differences 6 P A and 9 P # A 

 corresponding to the various observatories, elements, and seasons dealt with in 

 Tables I. and II. are given in Tables III. and IV. respectively ; in practically every 

 case they are positive, indicating an acceleration of phase at perigee. As a slight guide 

 to the probable reliability of the determined phase angles, the mean of the amplitudes 

 given in Tables I. and II. are tabulated in Tables III. and IV. respectively. 



The mean values of 6 v 6\ from Tables III. (a), (b), and (c), which, being derived 

 from short periods, should show practically the whole phase change between these 



epochs, are 



Degrees. 



Declination (six determinations) +26 



Horizontal force (five determinations) .... +30 

 Vertical force (four determinations) +18 



Similarly the mean value of 6 P A are, from Table IV., 



Degrees. 



Declination (six determinations) + 8 '2 



Horizontal force (six determinations) +9'8 



Vertical force (four determinations) +8'9 



* A possible explanation of such a conclusion, if it were substantiated, might be framed along the lines 

 indicated on p. 168, last paragraph. 



t The amplitude ratios for "short periods " if n had the values 2, 4 would be 1'23, 1-51 respectively, 

 and for half lunations, T14 and 1-31 respectively, which seem to be outside the probable limits of error 

 of the observed results. 



I Of. ' Phil. Trans.,' A, vol. 214, 3. 



