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DR. C. CHREE: DISCUSSION OF KEW MAGNETIC DATA 
small, and the general accordance of individual H observations and curve measure¬ 
ments seems, to preclude the possibility of any large percentage error in the value 
accepted. 
There is, in short, no direct evidence of the existence of uncorrected temperature 
effects, while there is a good deal in favour of the substantial accuracy of the 
allowances made. At the same time, direct experiment, if possible without undue 
risk of interfering with the records, would be desirable. 
Fourier Coefficients. 
§ 19. The analysis of the diurnal inequalities into series of harmonic terms whose 
periods are 24, 12, &c., hours is part of the regular routine at some observatories. To 
some people circular functions seem on a wholly superior plane to all others, and the 
analysis of diurnal inequalities according to any other type of function would appear 
almost inconceivable. Others may argue that the employment of circular functions 
for the representation of magnetic diurnal inequalities may hide rather than reveal 
what is of real physical importance. There are several common-sense arguments in 
favour of the analysis in series of sines and cosines. The use of these is so very 
general that for the intercomparison of results at different stations there is really no 
competing series. Again, it is found that as a rule 4 Fourier waves— i.e., terms with 
periods of 24, 12, 8 and 6 hours—suffice to give a very close approximation to the 
observed diurnal inequality, and the 8-hour and 6-hour waves are usually small 
compared with the first two. There is thus a good deal to be said for the argument 
that the Fourier analysis is a natural one. This argument of course would lose much 
of its force if a single function of the time, of a not unduly complicated form, with only 
2 or 3 parameters sufficed to represent the diurnal inequality adequately at a number 
of stations. But until such a function has been proved to exist, the course which is 
followed here of employing ordinary Fourier series is likely to commend itself to the 
majority. 
The diurnal inequality is usually expressed in one of the alternative forms 
«! cos t + b x sin t + a 2 cos 2 1 + b 2 sin 2 1 +... 
Cl sin (t + ai) + c 2 sin (2 t + a. 2 ) + ... , 
where t represents time counted from midnight, one hour in t being taken as the 
equivalent of 15°. The constants a, b of the first series, or c, a of the second, are 
generally called Fourier coefficients, c representing the amplitude and a the phase 
angle. The usual process is to calculate the a, b constants from the hourly values 
in the diurnal inequality, and then deduce the c, a constants from the equations 
tan a = a/b, c EE \/a 2 + b' 2 — af sin a = b/ cos a. 
If a, b coefficients have been calculated for three magnetic elements, they can be 
deduced at once for any other element, through the formula expressing it in terms of 
