minus or plus three minutes, numbers which were derived from Prof. Bache's discussion of the Philadelphia observations. The tables will also answer for intermediate places, for which they furnish the necessary data of interpolation.

It is proper to state that the present formulæ should be considered as liable to future changes and improvements depending on the accumulation of additional observations, and it is hardly necessary to state that their number also may hereafter be con siderably increased by the accession of new material. The utility of a publication of tables showing the declination for every tenth year was suggested by Mr. T. B. Brooks. In the numerical calculations I was assisted by Mr. G. Rumpf of the Computing Division.

Formula expressing the secular change of the magnetic declination (commonly called variation of the magnetic needle) used for calculating the tabular values.-Group 1. Stations between Portland, Me., and Williamsburg, Va.

A positive sign of D indicates west declination, a negative sign, east declination. n equals the number of years (and fraction of a year) from 1830; positive for years after and negative for years before this epoch. Longitudes are reckoned from Greenwich.

Lat. Long.

41 27 73 10D +1155-410 cos (130n+36)+021 cos
(70·2n+290°)

43 39 70 16 D=+1070-2·63 cos (1:33n+87)
13 05 70 43 D=+10-20-245 cos (1:37n+72)
13 36 72 55 D=989-366 cos (1·5n+45)
12 23 71 07|D=+ 9·65−2·78 cos (1·30n+71)+0.22 cos
(20.7n+220°)

12 48 70 49 D=+ 955-256 cos (1·4n+78)
42 20 71 02 D=+9·16−2·55 cos (1·39n+76)+0·22 cos

8 Providence, R. I. 11 50 71 24 D=

9 Hartford, Conn. 10 New Haven, Conn. 11 Albany, N. Y. 12 Oxford, N. Y. 13 New York, 14 Philadelphia, 15 Hatboro, Pa.

16 Baltimore,

41 46 72 40 D=+
1 17 72 55 D=+
42 39 73 43 D=+
42 27 75 42 D)=+
40 43 74 00 D=+
39 58 75 10 D=+

(3o·6n+222°)

911-299 cos (1·45n+58)+0.19 cos
(70·2n+246°)

8·60−3·59 cos (1·25n+45)
8·13-3·49 cos (1·33n+39)
765-274 cos (1·42n+62)
6·65−3·69 cos (1·3n+40)
647-232 cos (1·6n+55)
537-344 cos (1 6n+39)

40 07 75 08 D=+5·23-3-28 cos (1·54n+47)+0·22 cos

39 16 76 35 D+ 2·70−2·25 cos (1·5n+49) 17 Washington, D. C. 3S 53 77 00 D + 242-20 cos (15n+49) 18 Williamsburg, Va. 37 15 76 40 D=+ 2·22-26 cos (1·5n+22)

(40·1n+347°)

The following table contains the number (n) of observations (single or combined) upon which each formula is based; the probable error (E) of an observation expressed in minutes, as a measure of the degree of accuracy with which the observations are represented; the epoch of the last minimum of west declination (or of maximum east declination) together with the least. west declination (greatest east), and lastly, the annual variation

SECOND SERIES, VOL. XXIX, No. 87.-MAY, 1860.

for the years 1840, 1850, and 1860, expressed in minutes. The positive sign expresses west declination increasing (east diminishing).

Locality.

Burlington, Vt.

H

954+

Cambridge, Mass.

22

12

1782

Newburyport, Mass.

Boston,

Table of magnetic declinations for eighteen stations forming group 1, on or near the northeastern coast of the United States, between the years 1680 and 1860. West declination is indicated by a plus sign, east declination by a minus sign, and is expressed in degrees and fractions of a degree,

+29

+26

+1.2

1860 +746 +8.3 +5.95 +701 +519 +5:32

Note.-At Cambridge, Mass., the observations after 1855 require farther examination. At Williamsburg, the values between 1700 and 1770 were not considered sufficiently reliable for insertion. The expression for Baltimore depends for length of period and time of minimum on the Washington formula.

The total number of observations upon which the tabular values and the formulæ are based is 180, the average number of any one station is 10, and the average probable error of any single representation is +11'.

If we arrange the stations geographically, we find that at the eastern stations the minimum (west) declination occurred earlier than at the more western and southern stations; thus, from six stations between Portland and Providence it occurred about the year 1777; in the Connecticut and Hudson valleys and along the sea-coast as far south as Washington, the year of the minimum does not differ much from 1797; Williamsburg in Virginia gives 1815. The transition as we pass from the New England states is somewhat abrupt, but too well marked to be accidental. Extending the investigation farther north, I find for Quebec, Canada, the year of the minimum 1769; going farther west we find that at Toronto it must have occurred before the year 1842, and at York Fort, Hudson Bay, I find the year 1842 (as already ascertained by General Sabine, after the receipt of Capt. Blakiston's observations of 1857). This latter station is nearly halfway across the continent, and if we proceed to the western coast we find that the eastern declination there has not yet reached its maximum (equivalent to a western minimum), but it is highly probable that it will reach it before the close of the

Baltimore.

Washington,
D. C.

Williamsburg,

Va.

present century. The present reverse or western motion of the isogonic lines in our eastern states which commenced about the year 1777 will gradually be communicated to the more westerly stations, and will, it is highly probable, be participated in our western coast before or at the close of the present century, the direction of the motion in this latter locality being at present still to the eastward and southward, though with a diminishing rate (see p. 235 of C. S. report of 1856).

The following equations constructed for the two northernmost stations may be added here:

York Fort, Hudson Bay, D=+ 5°1 -14°2 cos (1o·6n+340°) Quebec, Canada, D=+12 ·84 3 7 cos (1 6n+97)

The second group comprises the stations on the southern portion of the Atlantic coast and Gulf coast; only three in number, to which have been added some stations located further south.

Proceeding in a southerly direction the next station discussed outside of the boundaries of the United States is Havana, Cuba, lat. 23° 09', long. 82° 22', for which place I found D=-4°·82 -1.45 cos (1.3n+26°) with 1810 as the year of maximum east declination. The values collected for Jamaica were not discussed, but the nine values I was able to obtain, will be found in the appended record. For Panama, New Granada, lat. +8° 57', long. 79° 29', the southernmost station discussed, I find D=-6°9-1°·04 cos (1·2n+74°), an equation satisfying the observations, but not considered as preferable to the following expression, D=-5°•57-2°.21 cos (1·2n+34°), which supposes the maximum to occur in 1802.

Going westward and northward I found for Vera Cruz, Mexico, lat. 19° 12', long. 96° 09', D=-4°2-5'04 cos (1·1n+7°), with the maximum east declination in 1824.

The following table has been calculated from the preceding equations:

The following formula for stations of the western coast, between San Diego and Cape Disappointment, forming group 3, have been copied from p. 234 of the report for 1856.

The total number of observations used for the construction of the above formulæ is 21, the greatest number for any one station being 6, the least 3, the average probable error of any single representation is 12'. The annual change (increasing east declination) may be taken the same for all stations, viz., in 1840, -1'6, in 1850, -12, in 1860, -0'8.

The next station discussed, south of California, is San Blas, Mexico, lat. 21° 32′ N., long. 105° 16' W. of Gr., which gave the following expression (see p. 234, C. S. report for 1856),

D——8°.63-0·042n−0·00031n2,

which equation, when compared with those above, shows a reversal in the sign of the coefficient of n2 or an opposite curvature. The annual easterly increase at San Blas in 1850 according to the above formula was 3'3. This station, however, is already within the area of the peculiar form of the isogonic lines, which position may possibly render an immediate compar

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