( 29 ) 

 The sum of R roAvs is then : 



To 



sin lla 



A — ^ cos 



sin a 



■2.T dV" 



— TJr-~T-C-\{ll- 1) 



When (f is small this expression can he siiii|tlilie(l hy [»iillin<^ 



r = T 



T — 



in tlie second term under the cosine. Tlie sum of' the first, second 

 etc. f2:roup of R rows is then: 



sin Ra /2jr 



.4 -^ cos — T — C ^ lla 



sin a \ ni 



sin Ra /2jt 



A — cos I T — r -^3 Ra 1 etc, 



sin a V >'f 



(H) 



If tlie oscillation is of a purely periodical description andoferpial 

 amplitudes the sum will show a principal maximum, /i .1, for « = 0, 

 and further secondary maxima for all values of (( which satisfy tlic 

 equation : 



R ta/Kj a = tan(/ Ra 



i.e., when R = 51(), for values of a corresponding with periods of: 



^ 25.872^^ [ 25.925^ 



( 25.728 i 25.G75 



but the amplitudes of these maxima will he resp. 5 and ^ times 

 smaller than the principal maximum. 

 The amplitude will vanish whenever 



Ra = rr, 2,t, ojt e,tc. 

 i.e. for periods of 



^ 25.850^^ ( 25.900^ 



/ 25.750 I 25.790 



The upper curve of fig. 2 gi\'es an image of the fluctnations of 

 these theoretical amplitudes. 

 If we put: 



T = 25.8 T' == 25.8 ± ,/■ 



the amount of shifting to be given to each gi-oup corresponding 

 with 0.01 day, is: 



80 ..I.J 



•60 a — 



2°.094, 



.r, in the denominator being neglected. 



The variation has been carried on, as ntmost allowable limit, to 



