DIURNAL INEQUALITIES, 



89 



23. Tables XII to XXII (pp. 90 to 99) give the results obtained for the diurnal inequalities. In the 

 case of the Declination two sets of results are given, the one derived from all clays available, the other from 

 the quieter only of these days. Table XII gives the all-days' Declination results for individual months. 

 Table XIII gives the corresponding results for the twelve months of the year, taking a mean from 1902 

 and 1903 in cases when data from both years were available ; it also gives diurnal inequalities for the year 

 as a whole and for three seasons, Midwinter (May to July), Equinox (March, April, September, and October), 

 and Midsummer (November to January). Tables XIV and XV give corresponding results from the 

 quieter days. For November, 1902, an additional inequality is added in T;ihle XIV which excludes only the 

 five most highly disturbed days, and so is intermediate between the inequalities based on " all " and on 

 " quieter " days. Midwinter was limited to three months, so as to include only days throughout the whole 

 of which the sun was below the horizon ; in Midsummer, on the other hand, the sun never set. The 

 Horizontal Force and Vertical-Force data were treated similarly to the Declination, except that no quieter 

 days' inequalities were formed. Tables XVI and XVII relate to the Horizontal Force, Tables XVIII 

 and XIX to the Vertical Force. In the case of the Inclination, inequalities have to be calculated from 

 the corresponding Horizontal-Force and Vertical-Force inequalities. It appeared sufficient to give a single 

 table, Table XX, containing results for the twelve months of the year, and the three seasons, employing 

 data from both 1902 and 1903 when available. Tables XXI and XXII give the diurnal inequalities 

 of the components of the Horizontal Force, respectively in and perpendicular to the astronomical 

 Meridian ; results are given only for the three seasons and the year. These were calculated from the 

 corresponding inequalities AD and AH in Declination and Horizontal Force by means of the formulae 



AS = cos <AH + sin <AD, AW = cos <AD - sin 



where < is the supplement of the easterly Declination, and A denotes the departure at any given hour 

 from the mean value of the day. The mean values accepted for < and for H, and the force equivalent 

 to 1' in Declination, were as follows : 



The working equations thence actually deduced, AH, AS, and AW, being measured in terms of ly as 

 unit, and AD in terms of 1', were as follows : 



24. In all the diurnal inequality tables the algebraically largest and least of the hourly values are in 

 heavy type. The tables also contain the ranges as derived from the largest and least of the hourly 

 readings, and the sum of the 24-hourly differences from the mean for the day. 



In calculating the diurnal inequalities use was made in general only of days in which the record was 

 complete from midnight to midnight. In some months, where the number of days of complete record was 

 small, hourly values were interpolated when a gap of only an hour or two occurred in the record during a 

 relatively quiet day. In some cases where material was scanty, use was made of periods of 24 successive 

 hours which commenced at hours other than local midnight. This happened, for instance, with the 

 Vertical Force in November and December, 1903. In the latter month the record extended from 2 p.m. 

 on the 12th to 1 p.m. on the 16th, and by making the day start at 2 p.m. four complete days' record 

 were obtained. 



Particulars of the days employed for the various inequalities are given in the table on pp. 71 and 72. 



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