Computation of certain Harmonic Components, GO 



from 21 hours to 23 hours, be laid down graphically, and to the right 

 of them the mean values from hours to 2 hours, the ordinate of 

 hours being made coincident with that of 24 hours, the curves drawn 

 through the points thus fixed would, if prolonged to meet one 

 another, be continuous if there were no non-periodic disturbance. If 

 they are not thus continuous half the distance between them measured 

 on the ordinate of hours will be the quantity c. 



The value may be obtained by calculation, perhaps with less 

 trouble. Assuming that the third differences of the quantities (a) 

 will vanish, when freed from the non-periodical variation ; and that 

 the corrected series of observed values immediately before and after 

 midnight is a n — \%c, a^—\\c, (a^—c) or (a + c), c^+^c, o 2 -Hfc; 

 and 



a u = £ ( a 23 + a i) — 3 ( a 22 + a d ~ a 0i 

 a u + a o = %c = i(%3+ — 3(^22+^2) — - 2a o> 

 c = £{2(028 + Oi) - \{a n + o 2 ) } - a . 



It may also be noticed that when a series of mean values for several 

 days is being dealt with, the quantity 2c will be the difference between 

 the first observed value and the value for the hour immediately 

 following the last of the series, divided by the number of complete days 

 in the series. 



Computation for a Yearly Period. 



• " * 9. 



The computation of the harmonic components of a yearly series of 

 305 daily values, or of 73 five-day mean values, such as are now usually 

 calculated for the principal meteorological elements, would be 

 extremely laborious if conducted in the usual manner, and it is there- 

 fore desirable to contrive some approximate method which shall not 

 involve excessive arithmetical operations. For meteorological pur- 

 poses the following mode of procedure will, it is believed, supply what 

 is needed, and it may possibly be employed conveniently in other 

 cases. 



When the number of the terms of a series is exactly divisible by 

 2, 4, 6, and 8, it will be readily seen that the new method of computa- 

 tion proposed in the case of a daily series of 24 hourly terms, will be 

 applicable in its general form ; all that is necessary by way of modi- 

 fication being the introduction of suitable changes in the combination 

 of the terms, and the adoption of other multipliers in place of those 

 given in the equations (3). 



The series of five-day means for a year consists of 73 terms, and 

 the above-mentioned condition is therefore not directly complied with 

 by it. It may, however, be easily transformed by interpolation into 



