12 
MR. C. CHAMBERS ON LUNI-SOLAR VARIATIONS OE 
7. Curves were now constructed to represent the variations otherwise expressed by 
the hourly excesses for the several seasons and phases, and a consideration of them 
led to the formation of the hypothesis that the bulk of the phenomenon dealt with 
is, properly speaking, not a lunar diurnal variation, but a solar diurnal variation that 
depends on the relative positions of the sun and moon, a variation such that it may 
be expressed, for any one season, by the formula 
fcM cos 2 (^) +/*»W sin 2 
where li is the hour .of the solar day, P the mean period of a lunation in mean solar 
days, and t the age of the moon in mean solar days ; and f 0 . 2 (h),/ 3 . 2 (h), are the observed 
variations at new moon and when the moon has the age one-eighth of a lunation 
respectively. It will presently be seen that, though the typical variations { /(h )} of 
one season differ from those of another, this hypothesis holds good generally in each 
quarter of the year separately. 
Of the two characteristics of the curves that pointed in the direction of the formula, 
the first was the general fact that the great movements occur in them, as in curves of 
tire mean solar diurnal variations for full lunations, in the solar day hours, and the 
night hours are relatively quiescent; or, viewed in another aspect, the significant 
movements occur at all hours of the lunar day in the course of a lunation, and appear 
earlier and earlier as the a^e of the moon increases. And the second characteristic 
was that 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 ; and this with reference separately to each of the two magnetic elements 
and to each season of the year. 
[7a. It may be explained here that in the first reductions of the Bombay declina¬ 
tion observations the categories into which the days were divided had reference 
(1) to the four seasons of the year, (2) to four positions of the moon in decimation, 
and (3) to the four quarters of the moon —not to eight phases as in the later reduc¬ 
tions. A short account of a first instalment of the results of these reductions, dealing 
with the observations of the years 1861 to 1863, was read before the Royal Society on 
the 2nd February, 1872 ; but it was the results of these earlier reductions for the full 
period of twenty-five years that suggested the idea of the luni-solar variation as 
expressed by the formula given in the last paragraph, and the computation and curving 
of the lunar diurnal variations of each category for that period were not completed till 
the 4th March, 1873. How very definite the suggestion was may be seen from the 
curves of figs. 50 to 53, 55 to 58, 60 to 63, and 65 to 68, which represent the lunar 
diurnal variations for the sixteen principal categories. To facilitate comparison, the 
curves for the different phases of the same season are placed under one another, the 
lunar time scales are arranged so that the beginning and end of the curves should 
correspond approximately to the same solar time, and the force scales for first quarter 
