DIUKNAL INEQUALITIES. 87 



CHAPTER III. 

 DIURNAL INEQUALITIES. 



20. The questions of secular change and annual inequality have been treated out of their natural 

 order because they appeared so closely connected with instrumental questions that it was desirable to 

 discuss them in that connection. Before passing to the diurnal inequalities, it will be convenient to deal 

 with some points relating to the measurement of the curves and the construction of the tables of 

 observational data (pp. 8-70). After examining the curves, I came to the conclusion that if the value 

 assigned to a particular element at a definite hour were derived as usual from a single measurement of the 

 curve ordinate at the exact hour, the irregularities arising from " accidental " disturbances would probably 

 conceal the regular diurnal inequality altogether, or at least in great measure. To meet this difficulty, 

 it is customary at some places to smooth curves by drawing a pencil trace, giving the general trend, as 

 distinguished from "accidental " irregularities. An alternative plan, which has been sometimes suggested, 

 is to determine mean ordinates for successive hourly intervals of time by planimeter measurements. 

 Owing to the excessively disturbed character of the Antarctic Declination and Horizontal-Force curves, 

 neither of these alternatives appeared feasible. Eventually I decided not to smooth the curves in any 

 way, but to take as the ordinate at any hour the arithmetic mean of three ordinates, one exactly at the 

 hour, the others at 20 minutes before and after. This necessitated the measurement of the curves at 

 20-minute intervals throughout the day. A suitable glass scale was constructed by Mr. FOSTER, one of 

 the senior assistants in the Observatory Department. The ordinates on the scale were divided at 

 millimetre intervals and, when reading, 1 mm. was usually aimed at, though this degree of accuracy 

 is not claimed in the results. Headings were in all, or nearly all, cases repeated, usually by a different 

 observer, and in the event of serious discrepancy a third measurement was made. Owing to the time 

 occupied in changing papers, it was a frequent occurrence for one of the 20-minute readings to be lost, 

 and, at some seasons, intervals exceeding 20 minutes were not unusual. The way of dealing with these 

 gaps varied according to circumstances. Supposing, for instance, the reading at an exact hour missing, 

 the value assigned to that hour was usually the mean from the readings at 20 minutes before and after ; 

 but if a gap commenced or ended within a few minutes of an exact hour, the readings taken 20 minutes 

 before and after the hour might be combined with an interpolated value, intended to represent the 

 missing reading. The precise procedure to be adopted was determined by myself with the curves 

 before me. In the case more particularly of the Horizontal Force, the limits of registration were exceeded 

 rather frequently, especially in Summer. If this happened at, say, 20 minutes before the hour, the curve 

 coming on the sheet at, say, 10 minutes to the hour and continuing on for some time, the value given 

 in the table of hourly values was the mean from three readings which corresponded to the exact hour 

 and to 10 minutes before and after. If, however, a limit of registration were exceeded for an appreciable 

 time at the exact hour, the entry in the tables normally indicated an excess of the limit, precisely as it 

 would have done if the limit had been exceeded not merely at the hour but at 20 minutes before and 

 after as well. 



21. In the case of the Declination, measurements were always taken to - 1 mm. answering to 0''15 

 but decimals are discarded in the hourly values in the tables as not really warranted by the accuracy 

 attainable. In the case, however, of the diurnal inequalities (pp. 90-99), the data being means from 

 a number of readings are given to the nearest 0' - 1. 



In the Horizontal-Force tables hourly values are given to ly, and diurnal-inequality data (pp. 94 and 95) 

 to O'ly. This degree of accuracy was fairly warranted, so far as mere uncertainties of reading are 

 concerned, owing to the very open scale. It is, however, I freely admit, open to criticism on the ground 

 that no temperature correction has been applied. What the exact degree of uncertainty on this ground 

 may be it is difficult to say. None of the suspensions used in the Antarctic survived, and no inference 

 seemed capable of being drawn by application of the method employed in the case of the Vertical Force. 

 All that inspection showed was that the temperature coefficient was small, its sign even not being disclosed. 

 Even if it had been large, the continually disturbed state of the Horizontal Force would have rendered 

 any high accuracy in its determination impossible. We know that the rigidity of the quartz suspension 



