AND ITS CHANGE WITH LUNAE DISTANCE. 167 



These mean results may be compared with individual results from the quoted 

 memoirs by BEGUN and FIGEE. The values from BEOUN'S paper are 



Degrees. 



,' October-April .... P -<9 A = 21 

 Trevandrum declination 



tion-< 



May-September. . . . P A = 14 



These differences (on which BEGUN made no remark) confirm the phase change 

 indicated in Table IV., though the amount is larger than the value there determined. 



FIGEE gives the phase angles at perigee and apogee only for declination (winter), 

 dividing his sixteen years' data into various groups as follows : 



Degrees. 



Nine maximum sunspot years Qi-Q\ = 42 



Seven minimum sunspot years 33 



Eight odd year's of the series 54 



Eight even years of the series 11 



Whole sixteen years 37 



He remarked : " The first formula) reveal the remarkable property that the occurrence 

 of the maximum of the semi-diurnal wave was accelerated by the increasing magnetic 

 force exercised by the moon from apogee to perigee, the amount of the acceleration 

 being more than one hour, with a striking accordance in the two periods chosen 

 (maximum and minimum). It was to be expected that a subdivision in two other 

 series (odd and even years) should show a similar accordance, which unfortunately 

 was not the case, as may be seen from the above figures. By this the reality of an 

 acceleration of the occurrence of the maximum with decreasing distance of the moon 

 from the earth is made less probable, though certainly suggested by the above 

 figures." 



Discussion. 



The whole body of evidence here collected makes clear the reality of this 

 remarkable phase change, so that the differences between FIGEE'S various results 

 would seem to be only accidental, large though some of them are. The magnitude 

 of the phase change is not very exactly determined, but it appears to be approxi- 

 mately 30 degrees between perigee and apogee. The value of (0 P A )/(#i> #A)> if 

 accurately known, should afford information as to how the phase varies between 

 these epochs. If the phase angle is harmonically periodic during a lunation, so that 

 the formula for the lunar variation is 



sin (2t + c cospt + a + /3) 



(where l/p is the number of days in a lunation), then the mean phase angle during a 

 half lunation should be 2/Tr times the phase angle at the middle point of this period, 



