On the Computation of certain Harmonic Components. 61 



"On the Computation of the Harmonic Components of a 

 Series representing a Phenomenon recurring in Daily and 

 Yearly Periods." By Lieut.-General R. Strachey, R.E., 

 F.R.S. Received April 15 —Read May 13, 1886. 



1. 



Following the notation commonly used, the general expression for 

 the harmonic components of the successive terms of a series repre- 

 senting a periodically recurring phenomenon, observed at equal 

 intervals of time, is — 



a u = Pq+%>i cos nz + q x sin nz +p 2 cos 2nz + q 2 sin 2nz + &c, 



where a n is the observed value of any term in question ; 



z is the angular equivalent of the time interval between the 

 observations ; 



n is the number of intervals from the commencement of the 



period to the time when the term a n occurs ; 

 p Q is the mean value of all the terms for the whole period. 



Then if A» represents the sum of the terms in the above series which 

 involve nz, 

 B M the sum of the terms involving 2nz, 

 C» „ „ Snz, &c, 



d n = p + A n + B n + C n + &C. 



Computation for a Daily Period. 

 9. 



For a daily period of 24 hourly intervals z = 15°, and consequently, 









A M+ i2 ; 









— B«+i2 — 



B K+6 = 



— R«+18 5 







= C w+ i6 — 



— C n +i — 



C M+ i2 = — C M +2o ; 



D M =D w+6 = 





— = 



— D«+3 — - 





whence, disregarding the terms involving multiples of z greater than4w£, 



d n — a n — tt»+i2 — 2(A M + C»), 

 and 



n — + = 2(A„— A H +4 + A u+S ) + 2(C«— M+ 4 + C M+8 ) ; 



but 



