Computation of certain Harmonic Components. 73 



a yearly period of 365 days, which could be transformed by interpola- 

 tion into a series of 360 days, each term of which would correspond 

 to fff days = 1+yV days. But the irregularities of a series of daily 

 quantities, in meteorological discussions, would be so great, even when 

 dealing with the mean of many years, that no practical advantage 

 would be obtained by employing such a series ; the computations 

 would be more troublesome, and the five-day means will be pre- 

 ferable. 



10. 



The annexed Forms are proposed as supplying methods of computa- 

 tion from the formulae contained in the foregoing discussion, which 

 shall involve the least practicable quantity of arithmetical operations. 



Form 1 differs little from what is believed to be the ordinary 

 method at present. It requires tables of multiples of the sines of 

 15°, 45°, 60° and 75°. 



Form 2 is for the proposed new method of computation. It 

 requires tables of multiples of the special multipliers applicable to the 

 several orders of harmonic coefficients. 



Form 3 requires no comment except to mention that the value of 

 the angles which correspond to the hours of maximum fi will facilitate 

 the graphic representation of the several components, and appear to 

 characterise them better than the angles T. 



Forms 4 and 5 call for no special remark. But they indicate the 

 degree of divergence that exists between the approximate values of 

 coefficients obtained from them, and those got by the more exact 

 methods. The figures employed are the mean hourly temperatures 

 for one year for the month of June, at Greenwich. If the mean 

 values for a series of years had been dealt with, the results would not 

 have differed one with another by so much as one-tenth of a degree 

 Fahrenheit. 



Form 6 shows the method of computation from 73 five-day mean 

 values. The figures employed are mean temperatures at Konigsberg 

 for 24 years (taken from Bessel's paper, the translation of which is 

 given in the ' Quarterly Weather Report ' of the Meteorological Office, 

 Part IV, 1870, page [29]), which were selected in order to test the 

 agreement of the results with those given by Bessel, calculated by 

 the method of least squares. The values of the coefficients by the 

 two methods are virtually identical with the exception of p s , in which 

 I feel satisfied that some error has been committed in Bessel's calcu- 

 lation ; to verify this, however, would involve a very tedious com- 

 putation which I have not thought it worth while to undertake. It 

 should be observed that Bessel's coefficients, being calculated with 

 reference to a period commencing with the first of the five-day means, 

 that is noon on the 3rd day of the year, have to be modified to adjust 



