HORIZONTAL FORCE OE THE EARTH’S MAGNETISM. 
389 
of the solar meridian producing the maximum after certain intervals, or to superposed 
regular or irregular causes, I hoped, and hope yet, to determine.” 
One of the most marked objections to the constancy of the solar action for given solar 
meridians for any considerable period was to be found in the middle of the series of 
well-marked oscillations for 1844. In the months of January to April there were four 
successive movements with periods of from 25 to 29 days, each having amplitudes of 
about one thousandth of the whole horizontal force; in the months of May, June, and 
July the oscillation may be said to have disappeared, while in the following months 
the movement reappeared as distinctly as in the first months of the year. It is the 
principal object of the present communication to show that this apparently anomalous 
result is due to the joint actions of the sun and moon. 
Solar and Lunar Actions. 
On a reconsideration lately of the results obtained by me previously for the moon’s 
synodical revolution from four successive years’ observations at Makerstoun, it seemed 
extremely improbable that they could be wholly explained by an action having a period 
of 26 days. Since in a discussion of a year’s observations nearly 14 periods of 26 days 
and 12 of 29’53 days are employed, if the solar action remains the same for each period 
the maximum must have happened at nearly all the positions of the moon, and should 
have an equal effect at all epochs in the discussions relatively to the revolution of our 
satellite. If the moon’s position had no effect on the magnetic variation, any result 
which might be obtained could be due only, as was supposed in this case, to irregu- 
larity in the solar action, and would certainly be different in the discussion of observa- 
tions made in successive years. Some difference there was without doubt ; but a recon- 
sideration of the whole results has induced me to conclude that the agreement was too 
great to be explained by any other hypothesis than that of a conjoint action of the sun 
and moon. 
The simplest method of determining the truth of this supposition was the following : — 
To obtain from the observations for a given time the mean variations due to each of 
three periods (namely, that of 26 days supposed due to the solar rotation, and those of 
29 - 53 and 27'3 days due to the lunar synodical and tropical revolutions), to assume 
that these mean results represent the solar and lunar actions during each period (or 
that the action of each body remains constant for the same position) throughout the 
whole number of periods included in the investigation, and to obtain the variations of 
horizontal force for each day of the year by their addition. Such a construction will 
show to what extent the assumption is well founded. 
In order, however, that this construction may be as accurate as possible, the mean 
results obtained for each body must be free from the effects due to the others. For 
this investigation we have the following equalities : — 
