300 
DE. S. CHAPMAN ON THE LUNAE DIUENAL VAEIATION OF THE 
of days. The average total number of days rejected for each element at each 
observatory, out of nearly 2500 lunar days (7 years) was 50 or 60 # , or about 2 per 
cent, of the whole. The rejected days were not always the same for different elements 
and observatories. At first a still smaller number, hardly more than a dozen days 
were deleted ; the further rejection of another 40 days improved the accordance of the 
results from the several lunar phases, and was therefore considered to be worth while, 
although it hardly altered the final means from all the phases. 
The number of days thus rejected is very much smaller than was customary 
amongst those previous investigators who adopted Sabine’s method of “ separating 
values”; Chambers,! for example, in treating 25 years’ Bombay observations, rejected 
about 20 per cent, of all the days, instead of 2 per cent, as here. Figee,J at Batavia, 
has stated that this procedure may seriously affect the values derived for the lunar 
magnetic variation, and it seems desirable, therefore, for definiteness and uniformity, 
to restrict the number of rejected days within very close limits. 
The disturbed days, chosen according to the principles thus laid down, were ruled 
out on the lunar sheets, as also any lunar days with incomplete record. The monthly 
sums were then formed at the foot of the several columns of hourly differences—the 
corresponding number of days used being written in the second column of the same 
row. Further, by reference to the Nautical Almanac, each month was divided up into 
eight groups of days (there being from three to five days in each group), these being 
distributed as evenly as possible around the times§ of new moon, one-eighth phase, first 
quarter, and so on, as centres. In eight rows, below the monthly sums, should be written 
down the sums of the hourly differences for each of these groups of days in order (new 
moon being phase 1, first-eighth phase 2, and so on), the number of days in each group 
being set down in the second column. The sum of the eight group sums in any 
column should equal the monthly sum in that column, and the additions should be 
checked by verifying that this is the case. 
§ 5. At this stage the utmost freedom is possible in the choice of further grouping 
of the results for discussion. In general, several months must be grouped together in 
order to obtain an accurate determination of the variation under any given conditions, 
as its total amount is always very small. The groups of days taken together should 
therefore be as large as is consistent with the exhibition of those features of the 
variation which it is desired to bring out. For the present purpose the eight lunar 
* As an indication of the sort of criterion which serves to separate about 60 days for rejection, in the 
three elements declination, horizontal force, and vertical force at Pola, the separating values were 
respectively 10' - 0 of arc, lOOy, and 50y in the total range of the hourly differences on any day. These 
limits might be different at other places and times. 
t Chambers, ‘Phil. Trans.,’ A, vol. 178, pp. 1-48 (1887). 
j Figee, ‘Batavian Observations,’ vol. 26 (1903). 
§ If the Greenwich civil times of lunar hour 0 are written in the second column of the lunar sheets, 
instead of the local civil times, the Greenwich civil times of the lunar phases should also be used in 
dividing up the months. This plan is recommended. 
