KAUTH'S MAGNETISM PRODUCED BY THE MOON AND SUN. 2B5 



conductivity, and is most naturally interpreted in that way. Moos, however, seems 

 in >t to have thought of the matter in this simple light, hut speaks of changes in the 

 radio-activity of the, earth's crust, due to a tidal action, as possibly responsible for the 

 luni-solar changes, perhaps by ionizing the atmosphere indirectly; and also of the 

 reflection by the moon of ionizing radiation from the sun.* 



10. Since the mean variation of any element over a whole lunation is almost 

 exactly a semi-diurnal wave, Moos'tf expression is equivalent to 



'2 COS (2<-M )[l + COS (< + ;)] = C08(t + t -)+2cOB(2t + t ) + C08(3t + t + v), . (A) 



though he did not himself write it out formally thus. The examination of the data 

 by harmonic analysis, which is effected in the third part of this paper, is the best 

 means of numerically testing Moos's suggestion, being preferable to a mere comparison 

 of two sets of curves by eye. The desire to apply this test partly occasioned the 

 present re-examination of the existing data, which also has in view the comparison 

 of the results of these past determinations of the lunar magnetic variation (on which 

 enormous lalxnir has been spent) to see how far they confirm one another, and gauge 

 the possibility of obtaining accurate information from them. 



Moos's suggestion implies the presence, in the lunar diurnal variation at a 

 particular lunar phase, of first and third harmo'nic components of amplitude equal 

 to half that of the semi-diurnal component, and with phase angles which respectively 

 decrease and increase by 45 with each change of lunar phase, the epoch of the 

 second component remaining constant. No other relations or components would 

 satisfy the above equation. 



11. The calculations from the observational data show that while first and third 

 harmonic components possessing the alxrve phase relations are present, the amplitudes 

 are not generally in accordance with Moos's equation. Moreover, a fourth harmonic 

 component, which was calculated in the first instance merely because to do so involved 

 scarcely any trouble after the other components had been computed, was also found 

 to be present, of quite appreciable amount, and obeying an unexpected phase law ; 

 its phase angle increases during each lunation by 4?r, twice the amount of change in 

 the phases of the first and third components. 



There is considerable accidental error in the determinations of the phase angles and 

 amplitudes at each lunar phase, as, of course, the material is much subdivided. While, 

 however, the phase angles go through an easily recognizable monthly cycle, the 

 amplitudes show no regular variation with lunar phase (the mean of a number of 

 lunations is dealt with, of course, so that perigee and apogee occur at different phases 

 during the period). The mean of the amplitudes at the separate phases gives, 

 therefore, the best determination of the amplitudes of the first, third, and fourth 



* 'Bombay Magnetical Observations,' 1846-1905, vol. II., 527. It may be mentioned that earlier 

 investigators had regarded the lunar variations as possibly due to the direct or indirect action of induced 

 magnetism in the moon, arising from solar or terrestrial magnetism, or both. 



