284 I 'If- S. CHAPMAN ON THE DIURNAL VARIATIONS OF THE 



phases, but (rather strangely) this has only once been done hitherto, and then 

 without result.* CHAMBERS! obtained an analytical expression for the variation and 

 its dependence on phase, which satisfactorily represents the observations, but it is 

 not of a simple character. His formula was 



/,,(*.) cos 2 +/..,* sn 



where h is the hour of the solar day, P is the mean period of a lunation in solar days, 

 and t is the age of the moon in solar days; f e . 2 (h) and f,, 2 (h) are the observed 

 variations at new moon and one-eighth phase respectively. This formula, it will be 

 noticed, expresses the lunar variation as, in reality, a solar diurnal variation (h, the 

 solar time, being the variable) which merely runs through a cycle of change depending 

 oil the age of the moon. This, in fact, was CHAMBERS' view he termed the variation 

 " luni-solar." It will be seen later, however, that there is a true lunar semi-diurnal 

 variation which remains unchanged throughout the course of ar lunation, as well as 

 luni-solar components governed by the position of both bodies. As to CHAMBERS' 

 expression for the variation, while it is numerically correct, it does not aid in 

 interpreting the phenomenon, because it depends on two complex curves f c ,- 2 (ti) and 

 f,,t(h\ for which no analytical expression was obtained; these two curves are not 

 independent, as will appear later. 



8. FIOEE determined the harmonic coefficients of the diurnal and semi-diurnal 

 components of the variation at each lunar phase, and came to the conclusion that " a 

 regular variation of the movement of the magnetic needle with the moon's phases is 

 not indicated by the observations at Batavia."J It will be shown, on the contrary, 

 that the Batavian observations agree with those made at other places in manifesting 

 considerable regularity of change with lunar phase. 



9. Moos has made the valuable suggestion that the luni-solar variation may be 

 regarded as a simple lunar variation the amplitude of " part of which goes through 

 a series of wave-like changes in the course of a lunation." He multiplies each hourly 

 value of the mean lunar variation determined from a whole month by 1 + cos (t + ), 

 where t is the lunar time reckoned from upper culmination (one hour equalling 

 15), and v is the angular measure of the moon's age, reckoned as at new moon, and 

 changing through 360 in the course of a month. Curves showing the results of this 

 calculation are exhibited for comparison with the observed curves, for the eight lunar 

 phases, for the element of declination. The general similarity of the two sets of 

 curves is sufficiently striking to show that the suggestion is in the right direction. 

 It will be seen that this idea is, formally, much akin to SCHUSTER'S idea of variable 



* ' Batavian Observations,' XXVI., Appendix, p. 195, 44. 



t CHAMBERS, 'Phil. Trans.,' A, vol. 178 (1887). 



t ' Batavian Observations,' XXVL, Appendix, 44. 



'Bombay Magnetical Observations,' 1846-1905, vol. II., 526. 



