MR. C. CHAMBERS ON LUNI-SOLAR VARIATIONS OF 
1G 
9. Considering now the typical variation curves (figs. 1 to 16), we see that those 
which are the most definite and systematic in character, and have the largest range, 
whether of declination or horizontal force, are for the winter season ; and, in the case 
of each type, the curves for the other seasons are definitely related to these. Thus, 
as to declination, between winter and summer there is an inversion of the types of 
both figs. 1 and 5 ; and the type-curves of the transition period, the spring season, 
have but a small range, and in them the prominent features of the winter curves are 
all but obliterated. Necessarily there is also a return inversion of the type in another 
season, and it occurs between mid-autumn and mid-winter. On the other hand, the 
horizontal force types (figs. 9 to 16), although of largest range in winter, are never 
reversed in character, but contract only to a minimum range, which is reached in the 
summer season. 
The typical diurnal variation for November to January of horizontal force at new 
moon (fig. 9), and that of declination at the one-eighth phase reversed to correspond 
to the seven-eighths phase (fig. 5 reversed), have generally a maximum about three 
hours before noon, a minimum about three hours after noon, and are nearly nil for 
three or four hours before and after midnight; those of declination at new moon 
(fig. l) and of horizontal force at the one-eighth phase (fig. 13) have a principal 
upward inflexion with a turning point about noon, two nearly equal downward 
inflexions with turning points about five or six hours before and after noon, and little 
or no departure from the mean line for three or four hours before and after midnight. 
For the summer and autumn seasons similar descriptions of the typical diurnal 
variations would apply, providing due allowance were made for the double reversal in 
the course of the year of the declination types. 
Comparing figs. 3 and 4 with 1, and figs. 7 and 8 with 5, all declination curves, it 
may be noted, as a minor characteristic, that the principal inflexions occur generally 
somewhat earlier in summer and autumn than in winter. 
10. The general similarity of character of figs. 1 and 13, representing the f c . 2 (K) and 
fs°(h ) data of our formula for the declination and horizontal force respectively, and the 
opposition of character of figs. 5 and 9, representing conversely the f s _ 2 (h) and f c . 2 (h) data 
for the elements taken in the same order, call for further consideration. These rela¬ 
tions may be translated into a statement that, in the winter season, the luni-solar 
variation of declination due to new moon is similar to the luni-solar variation of 
horizontal force due to the one-eighth phase ; and the luni-solar variation of horizontal 
force due to new moon is similar to the luni-solar variation of declination due to the 
seven-eighths phase. In other words, the luni-solar variation of declination due to 
any phase of the moon is similar to the luni-solar variation of horizontal force due to a 
phase later by one-eighth of a lunation. In the summer and autumn seasons it is, on 
the other hand, the luni-solar variations of horizontal force that precede by one-eighth 
of a lunation the similar variations of declination ; this will be seen by comparing 
figs. 11 and 12 with figs. 7 and 8, and figs 15 and 16 with figs. 3 and 4 reversed. 
