364 
COLONEL SABINE ON PERIODICAL LAWS DISCOVERABLE 
element in the five years, divided by 5, gives the mean annual value of that element, 
which we may take in each case, for the purpose of comparison with the actual 
aggregate values in the different years, as equal to I'OO; we have then the ratios of 
the disturbances of the different elements in the different years as follows : — 
Year ending June 30, 1844 
Table I. 
Declin. 
0-52 
Hor. Force. 
0-35 
Vert. Force. 
0-65* 
Mean. 
0-44 
Year ending June 30, 1845 
0-64 
0-47 
0-58 
0*57 
Year ending June 30, 1846 
0-82 
0-55 
073 
070 
Year ending June 30, 1847 
1-39 
1T4 
1-23 
1-25 
Year ending June 30, 1848 
1-63 
2-49 
1-80 
1*97 
The final column has been added to show the mean ratio of disturbance in each 
year as derived from the three elements, measured by the aggregate value in each 
year and in each element of all the disturbances which exceeded a certain definite 
magnitude, that magnitude being taken the same throughout the five years. 
It is seen by this Table, that in the year ending June 1847 the ratio of disturbance 
is above twice as great, and in the year ending June 1848 nearly four times as great 
as in either of the years ending June 1844 or June 1845. In the year ending June 
1848, which is the year of maximum, the proportion is nearly five times as great as 
in the year ending June 1844, which is the year of minimum. The evidence of the 
existence of a decennial period borne by the disturbances of the Declination, and 
announced to the Royal Society in March 1852, receives therefore the fullest confir- 
mation, from the variations in different years of the disturbances of the Horizontal 
and Vertical forces. 
Fig. 1, Plate X • has been drawn in illustration of the progressive increase of disturb- 
ance in each of the three elements between the year ending June 1844 and the year 
ending June 1848. The broken horizontal line represents the mean or average annual 
disturbance in each element, and is the zero-line, or the unit, with which the actual 
aggregate values of the disturbance of each element in each year are compared ; the 
Declination is represented by a dark continuous line, the Horizontal Force by a light 
continuous line, and the Vertical Force by a dotted line. The rate of increase of 
disturbance is seen to be much slower in the first half than in the second half of the 
five years. 
Annual Period . — The sum of the aggregate values of the disturbances of each 
element in the five years, divided by 12, gives the average monthly disturbance-value 
* In the deduction of this number, five months of the preceding year have been substituted for five months 
of the year ending June 1844 ; it has not been included therefore in the final column showing the mean ratios 
in each year. 
