396 
MR. J. A. BROUN ON THE VARIATIONS OF THE 
It will be remembered that these variations are those about the means in each case ; 
it has been considered a sufficiently near approximation to the mean horizontal intensity 
for each day, and for each of these periods, to take the means for four weeks, two weeks 
preceding and two weeks following each day. The observed means for each civil day 
having then been projected and connected with black lines, the curve of four-weekly 
means was formed by a dark dotted line (see Plate 38); from this line the sums of the 
three variations were set o ft jolus or minus , and connected by red lines drawn from point 
to point. 
It requires only a glance at these projections to see with how much fidelity the 
calculated represents the observed curve, in spite of the effects of the larger irregular 
variations on the means for each period, and on the appearance of the observed curves 
for the periods in which they occur. 
The conclusions drawn are as follows : — 
1st. The increase of amplitude of the oscillations which appears in February and 
March, and in September to November, 1844, is explained by the occurrence, near the 
same time, of the maximum actions of the sun and moon. In order to show this fact 
more distinctly, the separate actions of each body are projected above the oscillation for 
February 1844 (Plate 38). 
2nd. The diminution and apparent disappearance of the oscillations in June and 
July, which seemed so inexplicable when only one cause of variation was supposed to 
exist, are explained by the opposing actions of the two causes, the maximum of the one 
occurring at the same time as the minimum of the other. The independent actions of 
each body are shown in the projections below the movement for June (Plate 38). 
3rd. The variation of the time of single oscillations is explained in a similar manner 
by the combinations of the different variations. 
4th. Since the agreement between the observed and calculated results is so consi- 
derable, we are entitled to conclude that during a period of twelve months the solar and 
lunar actions remained nearly constant for the same positions of these bodies relatively 
to the earth and to each other. 
Had it been sought merely to establish the fact that the variations of the daily mean 
horizontal force of the earth’s magnetism may be represented very nearly in years of 
small magnetic irregularity by the computed variations due to three causes having 
periods of 26, 27’3, and 29 - 5 days, the investigation might have stopped here. It 
seemed to me, however, desirable to examine to what extent the same process would 
succeed in a year for which the movements appeared more irregular. The variations 
for 1845 were therefore calculated from the means in the last columns of Tables I., II., 
and III., in the same way as has been explained for 1844, commencing January 1, 1845, 
with the 3rd day of the solar, the 9th of the lunar synodical, and the 10th of the lunar 
tropical period. 
The sums of variations for each day having been obtained, they were set off from the 
curve of four-weekly means as before (see Plate 38). 
