i:\HTIIS MAUNETISM PRODrci-.l UY THE MOON AND SUN. 309 



disappearance of th(> corn-sponding harmonic components from the lunar variation, 

 as (I'-ti-i -inined from the mean of a whole number of months. It is found, indeed, 

 that any such component still remaining is of purely accidental character. 



As to the amplitude of the various components, this appears to be independent of 

 the lunar phase, the irregularities l>eing accidental. The mean of the amplitudes at 

 the separate phases has therefore been taken as the best value of the true amplitude, 

 except that a correction has l>een applied to allow for the fact that the instantaneous 

 amplitude is greater than that deduced from the mean of a few days, during which 

 the phase is varying. Thus, if we tabulate a function c cos(n6 + kv), where Q is the 

 lunar hour angle (one hour = 15) and v the age of the moon in angular measure, in 

 lunar hours for successive days over an interval of the month t> l to i/ 2 , the mean result 

 may be taktm as 



c (cos nd cos kv sin nd sin kv) 



where cos kv, sin kv are the mean values of these functions over the range v l to v. 2 . 

 This equals 



showing that the phase of the mean wave is equal to the true phase at the mean 

 time, but that the amplitude is reduced in the ratio 



sin 



2 ("-"*) 



The corresponding factors to counterbalance this are for Trevaudrum, where v a v t 

 is one-quarter of a month, or ^, 



and l'57(C 4 ), 



and at other stations, where v a v t = -", 



4 



1'02(C,, C,) and l'll(C 4 ). 



The values of the mean amplitudes, thus corrected, and of the phases of the 

 four components, reduced to new moon, for all the stations, are summarized in 

 Tables XI.-XIII. 



Tin* resolved parts of the amplitudes in the direction of the mean phase (where 

 the separate values of tf depart much from the mean) might have been taken, but 

 this would not have altered the mean amplitude greatly, and seemed hardly worth 



