trial-work, divided by the total population of the country, will give the measures of correction to be applied to the assumed point, in order to deduce the true center from it. In the case of a population so extensively and diversely scattered as that of the United States, there is room for any amount of refinement in the details of the calculation. The larger cities arc treated as special centers. Leaving them out, the population of the country is grouped by square degrees—that is, by the spaces, included between two consecutive degrees of latitude and of longitude, the centers of which, except where there are reasons for exception, are taken as the local centers of population. By this process, the center of population of the United States for 1880 is placed in latitude 39° 4' 8" and longitude 84° 39' 40", or at a point in Kenton County, Kentucky, one mile south of the Ohio River, and eight miles west by south from the heart of the city of Cincinnati. This location is, after all, only approximate, and extreme accuracy is hardly attainable under ordinary modes of calculation. In fixing it, the surface of the country has been assumed to be plane, whereas it is spherical or spheroidal, and a parallel of latitude has been made one of the axes, whereas the arc of a great circle should have been taken. Then there are differences in the kind of map-makers' projections that are used, all distorting the spheroidal surface in attempting to represent it as a plane, but some giving worse distortions than others. Mr. Carpenter believes that if it were practicable to make an absolutely correct calculation, the actual center would be found about thirty miles to the north and a trifle to the east of the present estimated location, or in Butler County, Ohio. The center is thrown so near the northern boundary, by the fact that our country in general shape is the segment of a zone; and the case is supposable, if the segment were extended far enough in longitude, in which the center of population would be situated entirely outside of the country.
Movements of Plants.—Mr. Thomas Meehan, of Philadelphia, has recently noticed some apparent irregularities in the motility of various plants which have not been adequately accounted for. The expansion and closing of the petals of Draba verna, which take place in connection with the diurnal erection and drooping of the pedicle, appear to require a clear light; yet while at one time the expansion seemed to be prevented by a cloudiness that hardly dimmed the Bun's rays, it was at another time not at all interfered with during a densely cloudy, warm, and moist day that followed a thundershower. The earliest flowers of Lamium amplexicaule are the largest ones in the Isle of Wight; here the case is reversed: the flowers never expand; and plants alongside of each other under the same conditions and external influences vary a week in the time of their flowering. The drooping branches of the Kilmarnock willow have grown from the upward branching Salix caprea without any known external influence to determine a different direction of growth, and they bear erect catkins, while erect branches bear pendulous ones. Such facts should teach us that external causes have but little influence with motility, and that in many cases a combination of circumstances controls the influences attributed to one. The facts will vary with various observations—those of one observer seeming rather to conflict with than to confirm another—and it is too soon to form any conclusion as to the motive cause.
Inscriptions of the Mound-Builders.—Major William S. Beebe, of Brooklyn, gave an interesting account, at the recent meeting of the American Association, of his efforts to decipher the inscriptions that have been found in the mounds at Davenport, Iowa, and Piqua, Ohio. Two pieces of slate were found in a mound at Davenport, one of which was inscribed on one side, the other on both. The stone inscribed on but one side bore on its surface a series of concentric circles, between the outer two of which were twelve equidistant signs, presumably the zodiacal signs. About two years after these slates were found, two terra-cotta tablets were dug up at Piqua, Ohio, bearing series similar to each other of characters, "evidently letters," ranged in horizontal lines, on four of which the letters were in each case six in number. In the fifth and remaining instance there were five lines,