MAGNETIC DECLINATION AND HORIZONTAL FORCE. 
3 
use of was F'4 or its equivalent ’204 scale divisions. The separating value adopted 
for the horizontal force was the equivalent in scale reading of '000334 of a C.G.S. 
unit of force. 
5. Continuing now the extract—from the monthly Tables already described in it, 
“ all observations having been thrown out which deviated from the ‘ Final Normal ’ of 
each hour by more than the amount of the separating value, new Tables were formed 
in which each observation was substituted by its excess above the Final Normal of its 
own hour ; or rather, by that excess, plus a constant round number. Practically, the 
Final Normal was diminished by the round number, and the difference being then 
taken between the number found and each observation in the same hour column, all 
the differences have the positive sign, and thus the inconvenience of dealing with 
positive and negative numbers is avoided. On the new Tables the observation at the 
solar hour of each day which was nearest to the time of the moon’s crossing the 
meridian of Bombay (from East to West) was marked with a figure 0 to indicate that 
that observation must be placed to the 0th hour of the lunar day in Tables having the 
lunar hours, from 0 to 23, marked in consecutive order at the top of the several 
columns. If only twenty-three observations intervened between two marked ones, 
they were entered in the Table consecutively as forming a complete lunar day ; but, as 
twenty-four observations generally intervened, the two which were in the nearest 
correspondence to the same lunar hour were combined together, and the mean of the 
two treated as a single observation.” The times of New Moon, First Quarter, Full 
Moon, and Last Quarter—taken from the Nautical Almanac, and duly corrected for 
difference of longitude between Greenwich and Bombay, or Gottingen^—were also 
marked on the margin of the sheet opposite to the several corresponding solar days ; 
for the groups of days, two before and two after these times respectively, the moon 
was regarded as at the several quarters; and during the intervening days the desig¬ 
nations of the moon’s phases were one-eighth, three-eighths, five-eighths, and seven- 
eighths respectively. The entries in the Tables of lunar differences, thus marked, were 
now distributed, in full lunar days, amongst thirty-two new Tables, called lunar 
abstracts, of which there was one for each eighth of a cycle of the moon’s phases in 
each quarter of the year. The whole of a lunar day’s differences were entered in the 
lunar abstracts under that variety of phase to which the greater half of the day 
belonged. Whenever the number of undisturbed observations on a lunar day was less 
than twelve the whole day’s differences were rejected. When all the differences of 
each category had been entered on their respective lunar Tables, the hourly means 
were taken on these Tables, and the excess was then found of each of these means 
above the mean of all the hours ; finally, these excesses were converted into force 
equivalents. The series of hourly excesses thus found may, in a sufficiently extended 
inquiry, be taken to represent the lunar diurnal variation of declination or horizontal 
force when the sun and moon have the positions indicated by that particular Table. 
6. The following Tables show, for each magnetic element, the converted hourly 
excesses found on each of the thirty-two lunar abstracts :—t 
* Until 1866-0 the records were made at hours of Gottingen Astronomical time; since that date, at 
hours of Bombay Civil time. All the results tabulated or graphically represented in this paper have 
reference, however, to the lunar day or the solar astronomical day at the place of observation. 
t The calculations having been made also for the summer and winter half-years, and for the full year, 
their results for these periods are also shown in the Tables. 
B 2 
