MAGNETIC DECLINATION AND HORIZONTAL FORCE. 
13 
and last quarter are inverted in comparison with the force scales for new moon and 
full moon. With the curves thus arranged, the four, occupying each vertical curve- 
form, and of which the fifth curve is, in each case, the type (or average), can be taken 
into view at a single glance, and the degree of their similarity is thus easily recognised. 
But similarity in these curves means the same thing as the second characteristic of 
the curves of lunar diurnal variations, which is expressed in words in the last para¬ 
graph as follows—the curves, regarded as solar diurnal curves, have generally the 
same form and range at intervals of half a lunation, and opposite forms at intervals of 
a quarter of a lunation. The similarity is very pronounced in all seasons except the 
transition one—February to April—in which the inversion of character of the varia¬ 
tions is in progress.—23rd September, 1886.] 
8. It now became an object to adapt the results already obtained, which have 
reference to the lunar day, to the determination of the data f c .%(h) and of the 
formula ; for this purpose the following process was adopted. 
As the lunar day roughly approximates to the same length as the solar day, we 
suppose the observed lunar diurnal variation at new moon to imply with rough 
approximation a solar diurnal variation of the same character; and we enter the 
hourly excesses in a Table having solar hours, from 0 to 23, marked at the top of the 
columns; under these numbers we enter the excesses of full moon, placing the 
number belonging to the Oth hour of lunar time under the 12th hour of solar time, 
and we then take the sums of the two sets of numbers. Again, we enter the 
excesses of first quarter, placing the number belonging to the Oth hour of lunar time 
under the 6th hour of solar time; and under these we enter the excesses of last 
quarter, placing the number of the Oth hour of lunar time under the 18th hour of 
solar time, and we then take the sum of these two sets of numbers ; next, we subtract 
the latter sums from the former, and divide the results by 4, calling the series of 
quotients the typical variation for the quarters of the moon, that is f c , 2 (h). Similarly, 
substituting the hourly excesses of the phases one-eighth, three-eighths, five-eighths, 
and seven-eighths for those of new moon, first quarter, full moon, and last quarter 
respectively, we obtain the typical variation for the eighths phases, that is 
In this way, of which an example will now be given, have been obtained the typical 
variations shown in Tables 9 and 10, using as data the numbers in Column 2 of 
Tables 1 to 4 for the first line of Table 9, in Column 3 of Tables 1 to 4 for the second 
line of Table 9, and so on. 
