to those who are engaged in drawing and studying the clouds.-Bulletin Hebdomadaire, XVI., 25.

ON THE ERRORS OF MICROMETRIC MEASUREMENTS.

In the course of an excellent series of measurements of the relative positions of the stars in the cluster of Sobieski's Shield, Professor Helmert has made a determination of the so-called personal errors in micrometric measurement of position angles. As Otto Struve and Dembowski are the only astronomers who have as yet thoroughly investigated this important source of error, the results of Helmert's observations are especially valuable. The apparatus used by the latter can easily be applied to any telescope, and will, it is hoped, be frequently applied by others. Helmert concludes that there was possibly in his case a gradual change in his method of observation, and that when this is eliminated there still remains a periodical error in his measurements of angles, which, although much smaller than that of Otto Struve, is quite similar to it in its general features.— Publications of the Hamburg Observatory, No. 1, p. 19.

ASTRONOMICAL

WORK WITH THE GREAT

TELESCOPE.

MELBOURNE

From the proceedings of the Royal Society of Victoria we learn that during the past five years Mr. Ellery, of the Melbourne Observatory, has examined the positions of 38,000 stars. The great reflecting telescope, of four feet aperture and forty feet focal length, has been employed in examining the star Eta Argus and its surrounding nebula. The spectrum of this star is found to be crossed by bright lines, which seem to indicate that hydrogen, nitrogen, sodium, and magnesium are present-no dark lines having been seen with certainty, though they were suspected. Considerable changes have, however, occurred in the spectrum, if we may judge from a comparison of the records of 1869 and 1874, since in the latter year no bright lines were to be detected, while a distinct nebulosity surrounded the star, which had formerly appeared projected on the black background. The nebula surrounding this star is evidently subject to great changes. In the spectrum of Jupiter absorption lines constantly appear. An examination of the small stars near

Sirius shows, besides Alvan Clark's companion and that of Lassell, eight others within a distance of one minute of arc. −12 4, XI., 90.

THE GERMAN NAUTICAL OBSERVATORY.

It may be known to some of our readers that since 1868 there has existed in Hamburg a private institution representing the combined nautical and meteorological interest of that city. The control and support of this institution has lately been assumed by the German Government under the following regulations, among others: By the name “Deutsche Seewarte" an institution is established whose problem shall be to further the knowledge of the ocean, so far as this is of interest to navigation, as also that of the phenomena of the weather on the German coasts, and to utilize this knowledge for the safety and expedition of navigation. The Seewarte is located at Hamburg, and has under it nine observ ing stations and forty-five signal stations along the German coast. The annual appropriation for the entire establishment and its dependencies is 75,000 marks.-7 C, XI., 130.

THE FIXED HORIZONTAL TELESCOPE OF LAUSSEDAT.

The Siderostat is the name given by Foucault to the perfected form of the apparatus originally used by Laussedat for photographing the sun. It consists essentially of a clock-work by means of which rotation is given to a mirror, and so uniform and smooth is the movement that for hours together it follows the diurnal movement of the stars with such perfect accuracy that an observer looking into it sees reflected any sidereal object, which latter appears stationary to him while the mirror is moving. Great labor has been spent upon this instrument by Foucault, who has designed it, and by Eichens, who has recently finished its construction. This instrument, as mounted at the Paris Observatory, has been in constant use in experiments in photographing the sun; in fact, it ought to be the indispensable auxiliary of physical astronomy, since it allows the observer to direct his spectroscope or photometer, or other apparatus, steadily in the same direction, viz., toward the mirror, which latter only moves and reflects the sun's rays directly into the optical apparatus.-12 A, X., 358.

t

1

DIVISIBILITY BY SEVEN.

Professor Brooks, of Millersville, Pennsylvania, presents a number of curious rules relating to the divisibility of numbers by 7, of which the most general expressions are as follows: Any number divided by 7, 11, or 13 leaves the same remainder as is obtained when the sum of the odd numerical periods, minus the sum of the even numerical periods, is divided by these numbers. The converse of which is that any number is divisible by 7, 11, or 13 when the difference between the sum of the odd and even numerical periods is divisible by these numbers.-The Analyst, July, 1875, II., 129.

THE VARIABILITY OF TERRESTRIAL LATITUDES.

In a memoir on the determination of the latitude of the Royal Observatory of Capodimonte, at Naples, Fergola, after calling attention to a source of error in the instrument used by Brioschi in 1820, as in fact had previously been done by Peters, states that he has employed in his own more recent determinations one of the instruments employed by Brioschi himself, but has used it in an entirely different manner; and has, in fact, employed it only for determining the differences of the zenith distances of stars in the meridian north and south of the zenith. He states, as is so frequently done nowadays, that this method is originally due to Captain Talcott, of the United States Army; in which statement, however, Fergola has fallen into an error, as Horrebow and Hell had already applied this method over a hundred years ago, as have also numerous European astronomers since that time. The special interest that attaches to Fergola's new determination of the latitude of Naples consists in this, that his result is over one second smaller than that of Brioschi; and he calls attention to the fact that quite similar differences will be found in the latitudes determined at various times at the observatories of Greenwich, Washington, Milan, and Rome. -Vierteljahrssch. Astron. Gesellsch., April, 1875, X., 60.

SIMPLE METHOD OF DETERMINING LATITUDE.

A method of determining latitude without instruments, and with a considerable degree of approximation, is given by D'Avout; and, as it may sometimes be useful to travelers, we

repeat it with some detail. Given a horizontal plane; above this plane, upon the same vertical and at known distances, are placed two points, whose shadows upon the horizontal plane can be followed. Around the common projection of these points, as a centre, two arcs of circles are described, whose radii are such that they can intersect the traces of the shadows of the points themselves before and after the meridian passage of the sun. The observation consists in measuring the chords of the arcs obtained by joining the intersections of the traces of the shadows with the circles; knowing the length of the chords, the radii of the arcs, and the heights of the points whose shadows are observed, we can, by a simple formula, calculate the latitude of a place. Either the two points whose shadows are projected may be two spheres, fixed upon the same vertical thread which traverses their centres, or we may use small circular openings pierced in metallic plates, and placed so that their centres are found on the same vertical. The shadows of these objects are small ellipses, whose centres may easily be found. The variation in the declination of the sun, between the afternoon and morning observations, occasions only a very small error, its effect being, in great part, eliminated from the final formula. The errors that may be made in measuring the various data above enumerated can occasion very small errors in latitude. The principal source of error is a possible want of exact horizontality in the plane on which the shadow is cast. In fact, an error of about two degrees in the inclination of this plane may produce an error of one degree in latitude. If, however, the plane be horizontal in a north and south direction, but incline in an east and west direction, the effect of the latter inclination may be neglected. The elimination of this latter source of error is due in part to the adoption of two points and shadows. The same advantages do not inhere in the employment of one point and one shadow.-Bulletin Hebdomadaire, XV., 578.

DETERMINATION OF LATITUDE AND TIME.

In a communication on the method of determining the time by means of two observed altitudes of any celestial body, Vice-admiral Von Wullerstorff-Urbair states that the method of determining the latitude by means of observations

of stars, at equal zenith distances, was proposed and applied by him in 1848, at the Naval Observatory in Venice, but has in later times been widely adopted, and is known in America as Talcott's method. Admiral Von Wullerstorff-Urbair shows that the same system may be applied with accuracy to the determination of time; and quotes a note from Palissa, at the Naval Observatory at Pola, who says that this method was applied by him in December, 1873, and gives results whose value is equal to those deduced from the transit instruments. The method is specially to be recommended to travelers, since by means of the same theodolite both time and latitude may be accurately determined. The formulæ given by Von Wullerstorff-Urbair seem scarcely so convenient in practice as those taught for many years past by Dollen and the Russian geographers, and which were published in full some years ago by Smysloff-"Mitth." Austrian Hydrogr. Off., II., 129.

THE COMPUTATION OF THE AREAS OF IRREGULAR FIGURES.

There often occurs a necessity for determining from a drawing the superficial contents of planes bounded by curved lines. This is the case, for instance, in the determination of the superficial contents of the water-lines of vessels. In such computations, ordinarily, we employ somewhat rude approximations, as in Simpson's or Stirling's methods. The latter author has given two methods: the first depending upon the principle that the portion of a curved line, between any two ordinates, may be considered as a portion of a parabola of the second degree. In the second method, given by the same author, the curve is considered as a portion of a parabola of the third degree. These three methods may be supplemented by other methods depending upon formule, developed by Gauss, Cotes, and others. But in general all these methods are somewhat more difficult of application than that known as Simpson's, which is far more frequently employed than any other. A very decidedly better way has been proposed by the Russian mathematician, Tchebitcheff, whose method is simpler than either of those just mentioned, and, although less accurate than that of Gauss, is more accurate than those of Cotes, Stirling, and others. Indeed, a greater simplicity of application than this method offers is scarcely to be demanded, and its accuracy surpasses the ordinary