INVESTIGATION

OF THE

INFLUENCE OF THE MOON ON THE MAGNETIC DECLINATION.

THE existence of a sensible lunar effect on the magnetic declination has already been established by the labors of Broun, Kreil, Sabine, and others. It is nevertheless important to add the weight of new numerical results to those already obtained.

In the discussions of the Philadelphia observations of magnetic declination, already presented to the Association, I have shown how the influence of magnetic disturbances, of the eleven year period of the solar diurnal variation and its annual inequality, of the secular change, and of the annual variation may be severally eliminated, leaving residuals from which the lunar influence is to be studied. Each observation was marked with its corresponding lunar hour and the hourly normals used for comparison.

This method of treatment of the subject is that followed by General Sabine in his discussion of the results of the British observations.1

The details of the method will be better understood by an example.

The time of the moon's passage over the meridian of Philadelphia (upper transit) was obtained from the American Almanac, the small correction for the difference

1 In reference to methods and results, in general, on this subject, the following papers may be consulted: Observations in Magnetism and Meteorology made at Makerstown, in Scotland, in the observatory of General Sir Thomas M. Brisbane, Bart., in 1845 and 1846, forming vol. xix., part i. of the Trans. Royal Society of Edinburgh. By John Allan Broun. Edinburgh, 1849; also vol. xix. part ii., containing the general results (1850).

Einfluss des Mondes auf die magnetische Declination by Carl Kreil. Vol. iii. of the Proceedings of the Mathematical and Physical Section of the Imperial Academy of Sciences of Vienna, 1852; also, vol. v., ibid., 1853.

Philosophical Trans. Royal Society, art. xix., 1853: On the Influence of the Moon on the Magnetic Declination at Toronto, St. Helena, and Hobarton. By Col. E. Sabine.

Phil. Trans. Royal Society, art. xxii., 1856: On the Lunar-diurnal Magnetic Variation at Toronto. By Major General E. Sabine. And

Phil. Trans. Royal Society, art. i., 1857: On the evidence of the Existence of the Decennial Inequality in the Solar-diurnal Magnetic Variations and its Non-existence in the Lunar-diurnal Variation, of the Declination at Hobarton. By Major General E. Sabine.

of longitude being neglected. The observation nearest to the local mean solar time of the moon's transit was marked with a zero, signifying Oh of lunar time. The time of the inferior transit was next obtained; and the observation nearest to it in time was marked 12h. The greatest difference in interval between the moon's transit and the time of observation could in no instance exceed half an hour. In the bi-hourly series, the observations nearest the moon's transit, or to either hour angle, one hour before or one hour after the transit was marked. The mean of a number of differences for the same hours thus gave a result corresponding nearly enough with the hour. The number of observations intermediate between those marked Oh and 12h were marked with the corresponding hour angle by interpolation, care being taken to note the nearest full hour against each observation in the bi-hourly series. The hourly series begins with October, 1843. In the case of thirteen observations within twelve lunar hours, the one nearest midway between the two consecutive lunar hours was omitted.

In the month of March, 1842, which is selected as an example of the details of working the bi-hourly series, the number of observations available is 298, of which 148 correspond to western and 150 to eastern hour angles. In the abstract which follows indicates a deviation of the north end of the magnet to the west, and

a deviation to the east of the respective normal position for the hour. The hourly normals are given in the first part of the discussion. No difference exceeds eight divisions, this being the limit in number indicated by the criterion.

LUNAR-DIURNAL VARIATION FROM OBSERVATIONS AT PHILADELPHIA IN MARCH, 1842.
Differences from the hourly normals.

+6.4 +1.0 +3.6
+1.7 +3.3 +1.6

-0.7 +0.2 -3.2
+0.8 -5.1 +3.0
+2.9 -2.7 +3.1

-1.3
+1.9
-0.9
-0.9
0.0

+1.8

-1.7

+2.8 -1.3 +2.2

-3.0

+4.1 +6.1 -0.1 -5.0
+1.3
-0.9 -0.1 +1.0 +2.5 +3.1 +0.9 -4.1
-2.5 -4.2 +2.0 +1.0 +7.2 +0.2 +7.8 0.0 +1.2 -2.0 +2.1 -1.8
+3.1 -1.4 +4.6 +6.1 +1.4 +0.9 -0.6 -0.5 +4.2 -2.7 +1.6 -6.8
-4.3 +4.3 -0.7 +1.8 +0.3 +1.2 +2.3 -3.0 +1.0 +5.2 -0.4 -2.0
-1.9 -0.5 +3.9
-0.6 -2.9 -0.5 +1.4 +0.7 -1.8 -1.1 -5.2
-4.8 +1.3 -0.1 +2.1 -3.3 +7.0 +1.7 +5.6
+3.1 -2.3 -1.6 -6.2 +2.3 -1.1
+6.5 +6.6
+2.9 -3.8 -3.8 -3.1 -4.5 -5.5
-7.2 -6.3 -5.9
-3.7 -2.4 -4.6 -0.8
+0.5 +0.5 -5.1 -0.9

-1.9 -1.8

-2.9

-3.0

+2.6 +1.1

+4.4

Means

+0d..72 +0.38 +1.78 +0.30 +1.35 -1.15-0.53 -2.15 -0.05 -0.29 +0.46 -0d..84

13h.
15h.
-2.7 -0.5 -2.9 +0.5 +5.6 +0.5 +0.6 -4.1 +1.6 -4.9 +4.4 -4.2
-0.2 -2.4 -1.9 -0.4 -3.4 -1.7 -2.8 +1.3 +6.5 -5.4 -0.3 +0.6
-1.7 +3.0 +2.9 -0.6 -2.0 -0.6 -1.6 +2.5 -5.1 -0.4 +6.9
-1.0 -0.6 +0.5 -7.2
-3.2 -1.0 -0.6 -0.6 +04
+3.2 -0.2 -5.2 -0.5 -2.3
-6.0 +0.3 +0.6 +0.7
+0.9 +2.7 +3.4 -1.1 +1.4 +2.2 -3.3 -4.2 +0.2
+0.1 -1.1 +1.7
+2.4 +2.6 +4.5 +3.4 +1.0 +1.4 -3.8 -3.3 -0.7 -0.4 -2.8 +1.6
+1.9 +4.9 +5.4 +4.7 -1.0 +2.3 +2.9 -0.3
-3.6 -2.2 -1.5 -3.5
+7.4 -0.7 -1.1 +7.6 +5.8 -0.1 -0.7 -2.0 +5.9 +1.5 +1.4 -4.0
+0.3 -4.6 +6.4 +3.4 +3.0 -0.5 -3.0 +3.6 -1.0 +1.2 +3.0 -3.3
+5.3 -3.5 +1.6 -0.1
-0.3
-3.0 +2.5 -6.6 -1.6 -0.8 -0.4 +0.6
-1.2 -0.3 +1.5
-1.0
-0.7 -3.7 +3.4 +5.6 -3.4 +5.1
+4.9
-6.5 +2.8

18h.

-1.5

+0.6 -1.1

+1d..22 +0.20 +1.25 +0.88 +0.44 -0.34 -0.92-1.43 +0.47-0.39 +0.03

-Od..35

Number of observations or differences at western hour-angles

148

The following table contains the number of observations used in the discussion of the lunar-diurnal variation :

If divided into western and eastern hour-angles, the annual numbers stand as

The preceding mean results will be found inserted in their proper place in the following abstract of the mean monthly values for each observing month between 1840 and 1845.

Proceeding in this way the following results are obtained for the different months discussed.

June'

-0.23 -0.25 -1.28 +0.95 -1.09 +0.11 -0.21 +0.30 -1.12 +1.60 -0.02 +0.55 July 2 +0.52 +1.87 -0.56 +2.04-1.98 +1.60 -1.34 0.40 -0.21 0.47 +0.11 +0.75 August -0.71 0.10 +1.41 +0.73 +1.05 1.20-0.50 -0.44 +0.10 +0.86 +0.20 +0.75 September3 +1.74 -0.52 +1.05 -0.87 0.40-2.05 -0.67-1.18 +0.49 +0.28 +0.52 +1.53 October +0.77-1.13 +0.37 +0.98 +0.25 +1.23 -0.01 +0.71 -0.78 -0.01 +0.71 -0.78 -0.63 0.68 -3.61 November+1.11 +1.04 +1.21 +0.77 +1.07 +1.44 -0.39 -0.53 -1.44 -2.03 -0.08 -1.61 December -1.43 1.14 0.37 +0.37 +0.16 0.90 -0.73 -1.44 -1.03 +1.01 -0.81 +1.24

d.

June1 +0.50 +0.75 +0.38 +0.86 +0.19 +1.65 -0.72 +0.68-1.35 +0.69 -2.30 +0.98 July2 +1.15 -1.08 -0.41 +0.32 -1.71 +1.03 +0.15 -0.18 -0.37 +1.00 -1.38 -0.03 August +0.18 -1.56 -0.91 -0.65 -1.15 -0.03 0.06 -2.61 +1.50 -1.30 -1.27 -0.50 September3 +0.64 +0.38 +0.63 +2.25 +0.84 +1.26-0.61-0.01 -1.05 -0.61-0.23 +0.20 October +0.53-0.59 +0.30 +1.18 -1.19 +0.63 -0.31-0.99 -0.40 -0.40 +1.51 +1.05 November1 +0.75 -0.62 0.02 -0.82 -0.49 +0.01 -0.02 +1.09 +0.88 +0.57 +0.14 +0.18 December +0.91 -0.78 -0.67 -1.82 -0.06 -0.70-2.57 +1.21 +0.63 +0.86 +0.64 +1.48

1 The tabular values for this month are expressed in parts of the new or observatory scale, the quantities having been converted from parts of the old or college scale into parts of the new scale.

2 The tabular numbers refer to the new scale, the values for the first eighteen days of the month having been converted as above.

3 Attention was paid to the half-monthly normals for the hour 8h. 191m. (mean observatory time).

+ The index correction, on and after the twenty-third day of the month, was applied before the differences were taken.