AND ITS CHANGE WITH LUNAR DISTANCE. 163 



FIGEE'S data alone being insufficient to resolve the doubt, I have made an attempt 

 in the present paper to decide the question, with the aid of newly computed data. 

 The result is not so decisive as could be desired, owing to the considerable accidental 

 errors affecting the determinations of the minute quantities concerned ; but the 

 evidence, on the whole, is confirmatory of the tidal hypothesis. It can certainly be 

 stated that, if the amplitude of the lunar magnetic variation is inversely proportional 

 to an integral power of the lunar distance, this power is the cube and not the square 

 or the fourth power. 



This conclusion, while important, cannot be called surprising. The investigation 

 very clearly revealed, however, another phenomenon of a remarkable and quite 

 unexpected nature, viz., that the phase of the lunar magnetic variation at perigee is 

 considerably in advance of that at apogee (i.e., by about 30 degrees). On referring 

 back to BROW'S and FIGEE'S papers, it appeared that their data confirmed this result, 

 though BROUN, not unnaturally, made no remark on what seemed to be nothing more 

 than an accidental feature of the observations. FIGEE, on the other hand, noticed 

 and commented on it, but on account of variations in its amount, as determined from 

 different portions of his material, he expressed doubt as to its reality. He appears to 

 have gone no further with it, not even examining BROUN'S data for confirmation or 

 otherwise. The body of evidence in its support, which is here brought forward, 

 establishes this remarkable phenomenon beyond question. 



The Change with Lunar Distance of the Amplitude of the Lunar Magnetic 



Variation. 



If the amplitude of the lunar magnetic variation varies continuously between a 

 maximum value at perigee and a minimum at apogee, the ratio of the mean amplitudes 

 during two periods centred at these epochs must obviously depend on the length of 

 the periods. The mean eccentricity of the lunar orbit being 0'055, the extreme ratio 

 of the amplitudes (at exact perigee and apogee) on the tidal theory should be 1'39, 

 which is the cube of (l'055 -r- 0'945) : for periods of four days centred at perigee and 

 apogee the ratio should be 1'38, while if the periods each extend over half a lunation 

 the ratio is 1'23. 



BROUN divided his material into the perigee and apogee half lunations, thus utilizing 

 all his material, but diminishing the magnitude of the quantity to be determined. 

 His data were ten years' hourly observations of declination at Trevandrum, in India, 

 and he treated the summer and winter half years separately. The mean inequalities 

 derived from the four groups of data (summer and winter, perigee and apogee) were 

 compared according to their mean ranges, mean areas, and harmonic amplitude 

 coefficients. The perigee-apogee ratios so obtained varied between 1'15 and 1'34, with 

 a mean value of 1'24 from the whole material. BROUN summed up his result thus : 

 " The ratio of the moon's mean distance from the earth in the half orbit about apogee 

 is to that in the half orbit about perigee nearly as 1'07 to 1 ; as the cube of 1'07 = 1'23 



y 2 



