298 
DR. S. CHAPMAN ON THE LUNAR DIURNAL VARIATION OF THE 
group of 28 to 31 equal solar hours in like degree. If, then, we subtract from each 
hourly value the monthly mean value for that hour, the remainders will be due to 
causes not regularly solar, i.e., to irregular disturbances from whatever cause, and to 
any lunar action which may be at work. These remainders, when re-grouped, in 
sufficient quantity, according to their lunar time, enable the magnetic variations 
depending on lunar time to be determined either for whole lunations, or for any 
particular lunar phase, since the regular solar variations are already eliminated, and 
the accidental irregularities, independent of lunar time, average out.* 
In eliminating the solar variation it is too troublesome to subtract from the hourly 
values on each day the monthly mean values for the twenty-nine days exactly centred 
at that day, yet, on the other hand, it is perhaps hardly accurate enough to assume 
that the monthly mean values for the ordinary calendar month properly represent the 
solar variation for all the days in that month—especially during seasons of rapid 
change in the solar variation. The simple plan which I have adopted is to take the days 
of a calendar month in six groups each containing five days (except that the last 
group contains the days from the 26th to the end of the month), and to take the same 
monthly mean hourly values for all the days in each group ; these hourly values are 
interpolated according to simple rules (embodied in a table for the computer’s 
convenience) from the monthly mean hourly values of the given calendar month and 
of those preceding and following it, each set being assumed to apply to the centre of 
its respective month. The differences “ actual—mean ” are written down on the sheets 
containing the printed hourly values, alongside the latter ; it is convenient, where 
possible, to place positive differences to the left, and negative differences to the right 
of the printed values. These differences need not be written down more accurately 
than to one-tenth of a minute of arc in the case of declination, or to ly (O'OOOOl C.G.S. 
unit) in the case of force. 
The re-grouping of these differences according to their lunar time is effected by 
copying them on to “ lunar ’ sheets ruled into 27 columns and 40 or 45 rows, on 
which have been written out, in the second column, the local civil times of upper 
transit of the moon (lunar hour 0) for the successive days in the calendar month to 
which each sheet is devoted. The times of lunar hour 0 will not generally fall at an 
exact solar hour, and the nearest solar hour to the correct time must be used instead; 
the resulting error will generally be small, and is assumed to disappear in the mean 
from a large number of days. These times, for the meridian of Greenwich, can be 
taken from the Nautical Almanac or, perhaps, more conveniently, from the “ Companion 
to The Observatory” (I2 h must be added to obtain civil instead of astronomical time). 
They may be corrected for difference of longitude for an observatory on another 
meridian, but I have found it convenient not to do so, using the same civil times of 
* It may be noted here that in the computation of the lunar magnetic variation many small errors of 
solar diurnal periodicity which occasionally occur in magnetic observations, such as those arising from a 
faulty temperature correction, are eliminated from the observations with the regular solar variation. 
