Note. Such is the inconvenience resulting from the use of a variety of metre scales, and such a number of methods of measurement, frequently taking quite different points for measures bearing the same name, as in the case of the skull especially, that the distinguished Professor Von Bær, of St. Petersburg, has just proposed a Congress of Anthropologists, to determine upon one uniform scale and to establish one system. By this means, all the results of measurements of the human body would be rendered of universal applicability.-Nachrichten über die ethnog. craniol. Sammlung zu St. Petersburg. S. 81. ART. XXIX.-Report of Assistant Charles A. Schott, on the latest results of the Discussion of the Secular Change of the Magnetic Declination, accompanied by tables showing the declination (variation of the needle) for every tenth year from the date of the earliest reliable observations, for twenty-six stations on the Atlantic, Gulf, and Pacific coasts of the United States. [Published in this Journal by permission of the Treasury Department, and communicated by Prof. A. D. BACHE, Superintendent U. S. Coast Survey.] IN accordance with the Superintendent's letter of January 21, 1859, I have prepared a set of tables for practical use, giving the secular change of the magnetic declination and showing for every tenth year, from the date of the earliest reliable observations to the present time, the magnetic declination (commonly called the variation of the magnetic needle) for stations on or near the northeastern coast of the United States and also for some stations on our southern and western coasts-as derived from my several discussions of the secular change in which have been included the latest data in possession of the Coast Survey. For the eastern and southern coasts, the following papers may be referred to: Coast Survey report for 1855, Appendix No. 48, pp. 306-337; Coast Survey report for 1858, Appendix No. 25, pp. 192-195, and Appendix No. 26, pp. 195– 197. For the western coast, Coast Survey report for 1856, Appendix No. 31, pp. 228-235 may be consulted. In general the secular change of the declination appears to be of a periodic character, but in no instance has a whole cycle been completed on either coast. Its length therefore remains necessarily in a great measure uncertain, and the tentative analytical process so far followed has for its main object the proper representation of all reliable observations made at any one station, so as to furnish the means of interpolation and also to enable us to calculate the magnetic declination for any required place and date, within the limits of the discussion. In the in vestigation of 1855 a linear function was used in the discussion which does not involve the duration of the period, and on this account the results were, in regard to time, of rather limited extent (see remark on p. 337 of Report for 1855). For the western coast stations, I still prefer to retain this form of the discussion. Subsequently, by means of the knowledge gained in that discussion, an attempt was made to substitute a circular function, directly involving a period or periods, the length of which, as well as all other numerical co-efficients in the formula for the secular change, has been determined by applying the method of least squares. The use of a circular function-commenced in 1858 with two stations, is now extended to eighteen, within the limits stated above, and it has been applied to some stations in Canada, the southern coast of the United States and Central America, in order to furnish material for the generalization of the law, so far as ascertained, in reference to epochs and rates of change. A secondary period within the first was traced at several stations, its length, however, being much more variable and uncertain, was found fluctuating between one-half and one-fifth of the primary period, while its amplitude was on the average fifteen times smaller than that of the primary wave for stations forming group 1, or within the geographical limits of Portland, Burlington and Williamsburg. This smaller amplitude was found nearly constant and equal to 0°.4. To make the present paper more complete it contains also the record of all observations used in the discussion not heretofore published in the Coast Survey reports. As long as the cause producing the secular change remains altogether unknown, it is not safe to trust too far to the continuation of the law thus empirically derived, and in the following tables no value, deduced by the formula, has been inserted antecedent to the first observation by more than ten years. The tabular values may therefore be regarded in the light of a strict interpolation between actual observations, and since the analytical treatment will equalize and remove, in a measure, accidental errors of observation, they may be considered as certainly more trustworthy than any single observation, particularly in cases where the number of observations available for the discussion exceeds half a dozen, properly distributed in relation to time. The probable error of any single representation will be found in the second table. For all ordinary use by the surveyor (or navigator) the tabular values are sufficiently precise, when greater accuracy is required the annual inequality of the declination and the diurnal variation for the time required must be taken into account; the former correction will probably not exceed, in any case, one minute, and the latter may amount in summer, in maximo, to minus or plus six minutes, and in winter to 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 considerably 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. Formule 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. 14 27 73 10 D +1155-410 cos (1-30n+36)+021 cos 43 39 70 16 D=+10·70-2·63 cos (1·33n+87) (20.7n+220°) 8 Providence, R. L. 41 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=+ 8.60−3·59 cos (1·25n+45) 10 07 75 08 D=+5·23-3-28 cos (1·54n+47)+022 cos 39 16 76 35 D + 2·70-2.25 cos (1.5n+49) 17 Washington, D. C. 38 53 77 00 D=+ 18 Williamsburg, Va. 37 15 76 40 D= 2·42–20 cos (1·5n+49) (4°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 23 96 Epoch of min. Least Annual change. v1850 v1860 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. 1860 +10-30 +12·3|+11·2] +99 +...........+10·8 +1056 +968 +81 | +26 +1.2 1860 +746 +83 +5·95 | +701 +5·19 +5·32 +2.9 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 |