the velocity of shot is, notwithstanding, of great service to the thoughtful sportsman. In these experiments, the time of flight was such as to permit the shot to fall about four inches in going one hundred feet, a distance which is of little importance in comparison with the distance traversed by the bird while the shot is in the air. In the case of most double guns the elevation of the rib at the breech is more than sufficient to compensate for the distance through which the shot will fall in going forty yards. A sight one-tenth of an inch in height, at thirty inches from the eye, will exactly cover a line four inches in length at a distance of one hundred feet. The elevation of the rib of most double guns is greater than one-tenth of an inch." U. S. Naval Academy, July, 1875. J. M. RICE. [From the "Rod and Gun," July 31, 1875.] A NEW METHOD OF OBTAINING A PERMANENT TRACE OF THE PLANE OF OSCILLATION OF A FOUCAULT-pendulum. ALFRED M. MAYER, of Hoboken, N. J. [ABSTRACT.] By LAST year, in the month of October, I mounted, in the physical laboratory of the Stevens Institute of Technology, a Foucaultpendulum formed of a cannon ball suspended by a steel wire. By floating the ball in mercury, I determined the point on the ball to which the wire should be attached, so that this point and the centre of gravity of the ball should be in the same vertical line. This line, having been prolonged as a diameter of the ball, determined the spot into which I screwed a pointed index. The point of this index, when the ball was stationary, was about 1-49 of an inch above a piece of smoked paper placed on a plate of metal which had been carefully brought into a horizontal plane. The pendulum was now drawn from the vertical by the tension of a delicate cord, one end of which was attached to the ball, the other fastened to a fixed support. The pendulum was started in the usual manner by burning this string. After a few oscillations, a current of electric sparks from an induction coil were passed through the suspending wire, and from the point of the index of the pendulum through the smoked paper to the metal plate, and thus was obtained a trace of the path of oscillation of the pendulum. At successive and known intervals of time I obtained similar traces, which were rendered permanent by passing the smoked paper through spirit varnish. The intersection of these traces gives the centre around which the angles are measured. The advantages of the method are: 1st, There is no friction of a tracing point; 2nd, The traces give the centre around which the angles are measured; 3d, The traces are permanent; and 4th, The angles of inclination of the traces can be leisurely and accurately measured. Last May I described this experiment to Professor Cross of the Massachusetts Institute of Technology, and he then informed me that the same idea had occurred to him, though he had not put it in practice, and also that he had recently mentioned this plan of experimenting before the American Academy of Arts and Sciences in Boston; therefore his name and mine should be always associated in designating this method of obtaining a permanent trace from the Foucault-pendulum. ON A SIMPLE MEANS OF MEASURING THE ANGLE OF INCLINATION OF THE MIRRORS USED IN FRESNEL'S EXPERIMENT ON THE INTERFERENCE OF LIGHT. By ALFRED M. MAYER, of Hoboken, N. J. [ABSTRACT.] THE inclination of the Fresnel mirrors is measured by pasting a disk of known size on a window pane, and then ascertaining the distance at which the disk, when viewed by reflection from the mirrors, appears double and the two disks are tangential to cach other. From the known diameter of the disk, and the distance of the disk from the line of intersection of the planes of the mirrors, the angle of inclination of the mirrors is readily calculated. NEW PLANETARY NEBULE. BY EDWARD C. PICKERING, of Cambridge, Mass. [ABSTRACT.] DURING the past year, a search has been made for new planetary nebula with the large telescope of the Harvard College Observatory. A direct vision prism, placed between the objective and eyepiece, converts the image of a star into a colored line of light. A planetary nebula, on the other hand, being nearly monochromatic, appears as a point of light, and is distinguished at a glance from a star. Many thousand stars may be quickly examined in this way, and a single nebula selected from among them. Two new nebula have thus been found, having the positions, R.A. 18h 25m 10', Dec., 25° 13', and R.A. 18h 4m 19', Dec., 28° 12'. Either of these objects would be mistaken for a star if examined in the usual way. On the evening of August 28, an object was found with a very singular spectrum. The light consists mainly of two bright bands, one in the yellow, a little more refrangible than the D line, the other in the green or blue. The approximate wave lengths are from 5,800 to 5,830, and from 4,670 to 4,730. There is also a faint continuous spectrum. This object cannot in other ways be distinguished from an ordinary star, and in fact, has been observed as one, by Argelander, and at the Washington Observatory, about thirty years ago. It does not seem to have changed since then in position or magnitude. It is designated as Eltzen, 17681, and its position for 1880 is, R.A. 18h 1m 17', Dec., 21° 16'. The comparative faintness of the continuous spectrum makes it more nearly resemble a planetary nebula than a star, but since the bands are differently placed, the material must be different. NEW METHOD FOR FINDING THE NUMERICAL ROOTS OF EQUATIONS BELOW THE FOURTH Degree. By JAMES D. WARNER, of Brooklyn, N. Y. [ABSTRACT.] THIS method is new for complete equations, and for those cubic equations where x appears in more than one term. For others it is not wholly new, but the arrangement is claimed as an improvement. For finding the roots of the incomplete quadratic, the following rule is given, viz. : Under the number write the figures of the root, commencing under the first figure of the last half, or of the larger latter part when divided as nearly as possible into two equal portions. Having ascertained the first figure of the root, take its square from the number, writing all of the different figures of the remainder over the number, in their proper numerical places.1 Under the figure of the root, write its double, and with this as a trial divisor, find the next figure of the root. The square of this, together with the product of itself into the trial divisor, taken from the remainder, gives the next remainder. Adding the double of the last found figure of the root, to the line of the double of the root previously found, will give a new trial divisor, by which the next figure of the root can be ascertained. The same process pursued with this and each succeeding figure found, will finally evolve the whole roct. EXAMPLE. 2531441: or extraction of the square root of 531441, 1 531441 729 144 Observe, that when any figure in the lines of remainders has been used, and there is no figure over it, or over a succeeding figure, to cancel it, by either striking a line through it or over it; also, whenever in doubling the root, there is anything to carry, to put it as a subscript to the previous figure, and use the sum ot the two thereafter. Any remainder can be set off, by a long cancelling line through or over the next preceding figure on the upper 1In subtracting, add a unit to amount to be carried when the unit figure of the subtrahend exceeds the figure from which it is subtracted. line of the remainders, or a dash with the remainder written after it, may be used. The same method answers for finding the roots of the complete quadratic, by adding in the coefficient of the first power of x to the first trial divisor. If the coefficient of a2 is other than unity, multiply each figure of the root by it, before every multiplication of the figures of the root. EXAMPLE. 2x2+3x=6, 5 12862 6. 1.138 526 742 5 A nearly similar method is applicable for finding the roots of 23a, or extracting the cube root. RULE. In extracting the cube root, the first figure of the root is placed under the first figure of the last part of the number, when the number of the figures have been divided as nearly as possible into three equal parts. The first line of figures under the root is three times the root, and is formed continuously from the root as found, just before obtaining the true divisor, and may be desig |