MAGNETIC DECLINATION AND HORIZONTAL FORCE. 
43 
no trace of that idea in any of Broun’s writings. Neither does he find in Broun’s 
writings any of the following results that are described in the present paper, viz. :— 
(1.) The discovery of relations subsisting between the lunar diurnal variation of 
declination as a whole at one phase of a lunation with the same at other phases in 
each season of the year [this as distinguished from the movements that occur near 
sunrise, and the nature of which was described by Broun]. 
(2.) The discovery that a part, being the bulk of the whole, of the lunar diurnal 
variation runs through a cycle of change in a lunation ; to this part the name of the 
luni-solar variation is given. 
(3.) A hypothesis is advanced—a hypothesis of phenomenal relations and not of 
physical causation—that the luni-solar variation of a given season is a combination of 
solar diurnal variations of constant types that go through cycles of wave-like change 
of amplitude in the periods of a lunation, half a lunation, &c., &c., and a formula is 
found to give expression to this hypothesis. 
(4.) Following up this hypothesis, the observations of declination for the quarter 
November to January of the years 1846 to 1870 are divided into categories of solar 
days according to the age of the moon ; and the excess solar diurnal variation—the 
excess over the mean solar diurnal variation for the approximate full lunation—is 
entered in the Tables for each day, and the mean value is calculated for each category. 
Curves representing these mean excess solar diurnal variations for each day of the 
moon’s age are found to agree fairly well with the formula expressing the luni-solar 
variation of the quarter November to January, a result which tends to confirm the 
hypothesis. 
(5.) The mode of change, from season to season, of the character of the elements of 
the luni-solar variations is described. 
(6.) All the results, without exception, of the investigation with reference to the 
lunar variations of horizontal force must be placed on this list. 
(7.) That the luni-solar variations of declination are related to those of the hori¬ 
zontal force in the following manner, viz. :—(«) In the winter season 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 ; and 
( b ) in the summer and autumn seasons it is, on the other hand, the luni-solar varia¬ 
tions of horizontal force that precede by an eighth of a lunation the similar variations 
of declination. 
(8.) It is shown that, when the Bombay observations have pointed the way, 
Broun’s determinations of the lunar diurnal variations of declination at Trevandrum 
for the four quarters of the moon in each month of the year, when properly treated, 
support the hypothesis of result (3). 
