638 
LIEUT.-COLONEL SABINE ON THE ANNUAL VARIATION OF THE 
MM had a constant value at the station to which the figure in the Plate referred, and 
would apply to any other year as well as to the one in which it represents the “ sum 
of all the observations in the year divided by their number.” This, however, is not 
the case : the line MM prolonged into other years would not be found to correspond 
with the mean declination in adjoining years, or in any other year than the one 
represented. Both at Toronto and at Hobarton the line MM would have a less 
westerly declination-value in years preceding, and a greater westerly declination- 
value in years succeeding those represented in the Plate. This Variation, since the 
observatories have been established, has at each station been progressive from year to 
year ; its period, if it has a period, is unknown ; it has therefore been called “ secular,” 
to distinguish it from those variations which have known periods. Its value for par- 
ticular years (as for example, for the three years at Toronto, and the five years at 
Hobarton, which are under present notice) may be satisfactorily determined by 
comparing the mean declination of one year with that of succeeding years, or of 
particular portions of the year with that of the same portions of succeeding years. 
At the Colonial Observatories it has been obtained by intercomparison in different 
years of the mean declinations corresponding to foi^tnightly periods ; and the small 
amount of the probable errors of these determinations shows their satisfactory cha- 
racter. The amount of the secular variation is comparatively small at Toronto, 
Hobarton and the Cape of Good Hope ; but it is large at St. Helena, being an 
annual increase of nearly eight minutes of west declination. This large amount at 
St. Helena has proved, however, in one respect, an advantage, by the opportunity it 
has afforded of examining the character of the progression according to which the 
secular change takes place, and of ascertaining by the concurrent evidence of several 
years, that the progression is equable and uniform in all parts of the year. 
The mean secular change during the years represented in Plate XXVII. being thus 
known, the mean declinations of each of the months at each of the observation- 
hours have received a correction, previous to their insertion in Plate XXVI., for the 
purpose of eliminating the influence of secular change on their actual positions in the 
annual range. This correction is in each case the proportional part of the secular 
change due to the interval of time occurring between the month in question and the 
middle period of the year. At Toronto, Hobarton and the Cape, the correction is 
small and little significant, even in the months most distant from the middle of the 
year ; and the Annual Variation is consequently very little different at these stations 
from the annual range, either in magnitude or in the relative position of the several 
months. But it is otherwise at St. Helena, where the secular change is large, and 
its elimination therefore is indispensable, even to an approximate knowledge of the 
phenomena of the Annual Variation. Happily at St. Helena the hypothesis of an uni- 
form and equable distribution of the secular change throughout the year, upon which 
the elimination is based, has been shown by the series of fortnightly mean declina- 
tions continued for several years, to be a correet representation of the facts of nature. 
