392 
MR. J. A. BROUN ON THE VARIATIONS OE THE 
Hence, in 1844, 4" has to be subtracted from the lunar synodical and 2"' from the 
lunar tropical corrections of the solar period, while in the corrections of the former for 
the latter 4' and 2' respectively must be added. In 1845 the corresponding changes are 
+ 6" and +7'" in the first cases, and —6' and — 7' in the last. 
Tables I., II., and III. contain the mean variations for each of the three periods in 
the years 1844 and 1845 as derived from the means of 24 hourly observations in each 
civil day , together with the corrections obtained by the preceding expressions and the 
corrected means. It should be remarked that the quantities represented by 1', 2', 
1", 2", I"', 2"', have each been supposed unaffected by the actions of other 
periods ; in seeking these corrections, however, the uncorrected means as derived from 
14, 12, and 13 of the respective periods were employed. Any error due to this cause 
might have been avoided by a repetition of the corrections ; the error, however, was 
found to be negligible in this investigation. 
If we could assume not only that the variations found are those produced by the sun 
and moon in each period of their respective rotations or revolutions during twelve months, 
but also that there are no other causes of variation, we might then construct the observed 
results by the addition of the three variations due to the positions of a given solar meri- 
dian and of the moon relatively to the earth and sun on each day of the year. All 
notice, however, has been omitted of other regular or irregular causes of variation ; and 
we have only to look at the projections of the observed means to see that great changes 
of the mean horizontal force occur within the space of one or two days, at intervals 
which cannot be connected with any continuous law. Frequent disturbances appear, 
especially in the means for the year 1845 (see Plate 38). It might be allowable, then, to 
omit these means in the investigation, or to employ interpolated quantities in their 
stead. It is difficult, however, to fix on the limit beyond which means should be 
excluded, without giving some grounds for the idea that the results obtained might not 
have been the same had all the observations been included. I have thought it best 
under these circumstances to employ all the observations in obtaining the variations 
given in Tables I., II., and III., and to make no attempt to “ improve ” the appearance 
of the results by any artifice. The year 1844 was one of minimum magnetic 
disturbance, and on this account the better fitted to show any law which is independent 
of these apparently irregular variations ; I shall for this reason consider the results for 
that year first. 
Having entered the variations belonging to the solar period in columns corresponding 
to each day of the year, the first quantity (column 5, Table I.) appeared opposite 
January 1, January 27, February 22, and so on, repeated 14 times; the quantities in 
column 5 of Table II. were placed in the next column, so that the first was opposite 
January 5, February 4 (days of full moon), the remaining quantities following in 
order for each synodical revolution. Similarly the first variation (column 5 of Table III.) 
was entered opposite January 3, 30, February 27 ... . (days for which the moon’s north 
declination was greatest), the other variations following in their order. The sums of 
the three quantities were then taken for each day of the year. 
