36 
MR. C. CHAMBERS OX LUNI-SOLAR VARIATIONS OF 
21. The numbers of Table 26 are curved in dotted lines in fig. 48. The general 
correspondence of fact, as indicated by the thin-line curve, with our formula, as 
indicated by the dotted curves, cannot fail to arrest the attention of the reader; and, 
whatever be the physical conditions lying behind the phenomena, it cannot but be 
helpful towards their discovery that a compact mental grasp of the phenomena, such 
as the formula affords, should take the place of such notions of disconnected variations 
as are the first outcome of a study of the observations. 
22. The numbers of Table 27 are curved in dotted lines in fig. 49, and on the same 
form are curved, in thin lines, the observed lunar diurnal variations of horizontal 
force, taken from Column 2 of Tables 5 to 8, for each of the eight phases of the moon. 
Here again the comparison of observation, as indicated by the thin-line curves, with the 
formula, through its representative dotted curves, shows remarkably close agreement. 
23. That in their more prominent inflexions the dotted curves of fig. 48 are generally 
of smaller range than the thin-line curves is sufficiently explained by the fact that 
the typical variations for each phase are averages for three or four consecutive days, 
whilst the thin-line curves represent variations for first days, second days, third days, 
&c., after new moon—all single days of the moon’s age. Indeed, it is easy to 
show that the typical variations f c .i{h), f s , l {h) should have been multiplied by 
47r 
29TS3 
sin 
47r 
2!b53 
= 1*031 when derived from the observed variations at the quarters, and by 
3-39 
7T 
29-53 
sm 
—= 1*022 when derived from the observed variations at the eighths phases; 
29*53' 
and similarly that jC 2 (/i), should have been multiplied by 
877 
2¥5S 
sm 
877 
29 t 53 
= 1*132 and 
by 
6*7877 
29*53 
sm 
6*7877 
29*53 
— 1*092 in the same two cases respectively. The inadvertent omission to 
apply these factors is most influential in respect of the larger of them (1*132 and 
1*092), since the range of the °{h) variations is much greater than that of the 
fc.i(h) and /^(h). 
24. In the case of the horizontal force curves (fig. 49) the factors would, if applied, 
affect both the thick-line and the thin-line curves alike, the latter representing the 
data from which the former were constructed ; here, accordingly, the two sets of curves 
approach more nearly to identity of range. 
