Imagini ale paginilor
PDF
ePub

ANNUAL RECORD

OF

SCIENCE AND INDUSTRY.

1875.

A. MATHEMATICS AND ASTRONOMY.

THE EARLY USE OF THE DECIMAL POINT.

Mr. J. W. L. Glaisher, in some remarks on the history of the introduction of the decimal point into arithmetic, concludes that this invention must be attributed to Napier, the immortal inventor of logarithms. The earliest work in which the decimal separator was employed seems to be Napier's posthumous work in 1619, at which time it appears that he was aware of all the attributes that enable the decimal point to complete systematically our method of notation. About the same time Briggs employed a bent or curved line, for which, in printing, he substituted merely a horizontal bar drawn under the figures that were to be considered as decimals; but Napier himself has left so many instances of the actual use of the decimal point as to render it pretty certain that he thoroughly appreciated its use.-Rep. Brit. Assoc., 1873, 12.

TABLES OF ELLIPTIC INTEGRALS.

The committee of the British Association, which has for some years had in hand the preparation of a list of tables and the calculation of new mathematical tables, report the completion of the tables of the elliptic functions, on which six or seven computers have been constantly engaged for two years past, under the superintendence of the Messrs. Glaisher.

A

These tables give the four theta functions which form the numerators and denominators of the three elliptic functions. The calculations relating to these functions have been carried to ten decimal places, and the printed results will occupy about four hundred pages.-12 A, X., 372.

NEW FORMULA FOR DETERMINING THE ALTITUDE FROM BARO-
METRIC OBSERVATIONS.

M. St. Robert, of France, has published the concluding volume of his memoirs, among which we notice a new formula for determining the altitude for barometric observations. This formula embodies the results of Glaisher's balloon observations.

THE REDUCTION OF ELLIPTIC INTEGRALS.

From a mathematical paper by Meissel, Professor in Kiel, we take the following theorem, whose enunciation will be of interest to mathematicians. He states that in a great number of cases he has been able to represent the complete elliptic integral of the second order by means of algebraic formulæ, and demonstrates, in general, that the complete integral of the second order can be converted into a complete integral of the first order.-Archiv der Mathematik, LVI., 337.

THE TRISECTION OF AN ANGLE.

The problem of the trisection of a circular are has lately been solved by Dr. Hippauf in a simple manner by means of an auxiliary curve, which may be designated as the conchoid on a circular base. This circular conchoid is the locus of a series of points found by drawing through one extremity of the diameter of a circle a series of lines, and finding, upon each, that point which is at a distance from the circumference of the circle equal to the radius. Having described such a circular conchoid for the circle an arc of which we wish to trisect, we draw the chord belonging to the latter arc, and then through the origin of the conchoid a parallel chord; this latter is equal to the chord of the third part of the arc to be trisected. Three other methods of effecting this trisection are also given by Hippauf by the aid of the same curve; and many other curious properties are found by Professor Sidler, who has shown that this conchoid may also be

[merged small][merged small][ocr errors]

described as the locus of the feet of a series of perpendiculars let fall upon all possible tangents to a circle, from a point outside the circle, and at a distance from the centre thereof equal to its diameter. The conchoid is likewise easily described graphically by a point fastened to a given circle which rolls around a fixed circle, provided that the two circles have the same diameter, and that the point be fastened to the rolling circle at a distance from its centre equal to the diameter thereof.-Mitth. der Naturf. Gesell., Berne, 1873, 31.

STANDARD TIME IN PITTSBURGH.

The question of the regular distribution throughout the community of standard uniform time has been well tested by Professor Langley, of Pittsburgh, who, during the past five years, has steadily extended the system of telegraphic connections between the astronomical observatory of that city and the railroads that centre therein. The magnificent new City Hall has in its turret a large tower clock, built by the Messrs. Howard of Boston, which by electrical connections is made to beat, second by second, in perfect unison with the standard clock at the observatory. A person at the latter building can, if necessary, even adjust the tower clock by telegraph, and can at any moment ascertain whether its indications are correct or not. The large bell of the tower is struck with the utmost accuracy at noon, and at every third hour throughout the day and night, and the public appreciation of the convenience and utility of the general system of absolutely accurate time is noticed in the universal comparison of watches daily at the stroke of noon. This ordinarily causes a movement so general and simultaneous throughout the city as on the one hand to amuse a stranger, and on the other hand to demonstrate how nervously anxious Americans are to secure the highest attainable accuracy in the timekeepers on which they depend for the regulation of private as well as public business. During nearly two years that the system has been in operation it is stated that there has not been any interruption from the failure of electric mechanism, and the utility of the system certainly more than justifies the expense which the city has been to in establishing this now recognized public necessity, which can not hereafter be dispensed with. In fact, the amount of time wasted

« ÎnapoiContinuă »