AND ANNUAL VARIATION OF THE TERRESTRIAL MAGNETIC FORCE. 207 
Table I. 
1845. 
1846. 
1847. 
1848. 
1849. 
January 
3-5377 
3-5378 
3-5337 
3-5222 
3-5213 
February 
3-5376 
3-5313 
3-5320 
3-5255 
3-5210 
March 
3-5375 
3-5341 
3-5284 
3-5270 
3-5240 
April 
3-5351 
3-5323 
3-5249 
3-5261 
3-5260 
May 
3-5388 
3-5317 
3-5283 
3-5286 
June 
3-5421 
3-5367 
3-5302 
3-5274 
July 
3-5413 
3-5365 
3-5287 
3-5305 
August 
3-5383 
3-5313 
3-5335 
3-5279 
September 
3-5373 
3-5303 
3-5257 
3-5239 
October 
3-5363 
3-5290 
3-5251 
3-5223 
November 
3-5360 
3-5278 
3-5266 
3-5184 
December 
3-5379 
3-5334 
3-5237 
3-5214 
Regarding each monthly determination as entitled to equal weight, and taking the 
arithmetical mean of all the observed values as the most probable mean value, we 
find the mean value to be 3'53043 with a probable error of +‘00055 ; and the pro- 
bable error of a single monthly determination +*0040. 
This is on the most simple hypothesis, in which neither secular change nor annual 
variation is supposed to exist. If we call X the arithmetical mean as above derived, 
and X'l, X 2 , X' 3 . . . X '52 the several observed monthly results, we shall have the several 
errors remaining over, Xj— X, X 2 — X, X 52 — X, as follows ; — 
Table II. 
1845. 
1846. 
1847. 
1848. 
1849. 
January 
+ -OO 73 
+ •0074 
+ •0033 
-•0082 
-•0091 
February 
+ -OO 72 
+ •0009 
+ •0016 
—•0049 
— •0094 
March 
+ -OO 7 I 
+ •0037 
— •0020 
—•0034 
-•0064 
April 
+ •0047 
+ •0019 
—•0055 
-•0043 
-•0044 
May 
+ •0084 
+ •0013 
— •0021 
— •0018 
June 
+ •0117 
+ •0063 
— •0002 
— 0030 
July 
•0109 
+ •0061 
— •0017 
+ •0001 
August 
+ •0079 
+ •0009 
+ •0031 
-•0025 
September 
+ •0069 
-•0001 
-•0047 
— •0065 
October 
+ •0059 
-•0014 
-•0053 
-•0081 
November 
+ •0056 
-•0026 
-•0038 
—•0120 
December 
+ •0075 
+ •0030 
+ •0067 
-•0090 
The prevalence of + signs in the earlier portion of the period, and of — signs in 
the later portion, points obviously to the existence of secular change, viz. to a de- 
crease of the horizontal force in successive years during the period of observation. 
For the purpose of obtaining the mean annual value of this decrease, we may derive 
an equation from each of the monthly determinations of the form X'=X+ay, in which 
X is the most probable value of the horizontal force in the middle period of the series, 
i. e. on the 1 st of March, 1847, X' the observed horizontal force in any other month, 
