ON COMPAHISON AND REDUCTION OF MAGNETIC OBSERVATIONS. 213 



Sabine termed ' disturbed ' observations included only some 10 per cent. 

 of the entire number ; so that, even supposing the years to which his 

 results and the present results applied had been the same, it would hardly 

 have been possible to utilise his results in framing a better hypothesis. 

 Some light might have been thrown on the subject by taking measure- 

 ments at each hour of every day immediately preceding or succeeding a 

 'quiet' day, and examining the magnitude of the non-cyclic element for 

 each combination of twenty-four consecutive hours. The fact that this 

 would have entailed some 12,000 additional measurements put it out of 

 court so far as the present inquiry was concerned. 



I have thus decided to regard the variation of an element throughout 

 the typical ' quiet ' day of a given month as composed of first a non-cyclic 

 part, consisting in a uniform increase or decrease throughout the twenty- 

 four hours, second a truly cyclic part spoken of as the diurnal inequality. 



Thus suppose an increment 24 I to occur during the twenty -four hours ; 

 then the diurnal inequality is what remains of the observed hourly departures 

 from the mean for the day after the correction (12 — ^)1 has been applied, 

 t denoting the number of hours elapsed .since midnight. This correction 

 raises the values throughout one half of the day and depresses them 

 throughout the other. It of course leaves unchanged the mean value 



{K[0] + [24]) + [l]+ .. . +[23j}/24, 



and after its application 



[0]=[24]. 



The size of the correction applied to each month's results for declination 

 and horizontal force is obvious from Table II., so that the uncorrected 

 values can easily be reproduced from the corrected ones recorded pre- 

 sently. 



Tables of Diurnal Inequality and their Discussion. 



§ 7. The following tables. III. and IV., give the diurnal inequality 

 in the several months and quarters of the year, as well as for winter, 

 summer, and the entire year. The values given under each month are 

 the arithmetic means from the data of the five years. The numerically 

 largest maxima and minima ai-e distinguished by heavy type. The hours 

 are numbered continuously from midnight, so that 13 and higher numbers 

 refer to the afternoon. The results for hour 24, being the same as for 

 hour 0, are omitted. 



A graphical illustration of the diurnal inequality for the year ; for 

 winter, for summer, for midwinter (December and January), and for 

 midsummer (June and July), is afforded in Plate V. by the curves 1, 2, 3, 4, 5 

 for the declination, and by the curves 6, 7, 8, 9, 10 for the horizontal force. 

 The curves will facilitate the comprehension of the principal phenomena. 

 A comparison of the declination table and curves with the corresponding 

 results at Kew during the epoch 1858-62, as given by General Sabine in 

 the 'Phil. Trans.' for 1863, will be found of interest. 



§ 8. In both tables the results proceed one figure further than the 

 actual measurements, the extra figure ai'ising in the process of taking the 

 means. No smoothing process has been applied to the original data, and 

 no correction other than the elimination of the non-cyclic element. That 

 the results are trustworthy, as measurements of magnetic variation, to 



