When the spark was received on the ice, it lost its flaming character, and became thin and wiry, spreading out in all directions. If the discharging-wires were tipped with ice, the spark was always flaming when any thickness of air intervened between them. Even over the ice, if the spark passed a fraction of an inch above the surface, it was always a flaming one, but changed to the thin spark when the point of the discharging-wire was thrust into the ice. If one of the discharging-wires of the great coil is brought to the centre of a large swing looking-glass and the other wire connected with the amalgam at the back, the sparks are thin and wiry, arborescent, and very bright (see figure, p. 69), the crackling noise of these discharges being quite different from that of the heavy thud or blow delivered by the flaming spark. When the discharging-wire is brought close to the frame of the lookingglass, or if a sufficient thickness of air intervenes, the spark again becomes flaming; or, as sometimes occurs, if the discharging wire is placed about 5 inches from the frame, the spark is partly flaming and partly wiry, i. e. when it impinges on the glass. The examination of the flaming spark with the spectroscope has not as yet settled anything definitely. The spectrum is a continuous one with the sodium-line. When the blast of air is used, and the wiry sparks made apparent, then the nitrogen line appears. The flaming spark has been ascribed by some experienced observers to the incandescence of the dust in the air, and especially sodium chloride. If the salt &c. is thus made hot, can the air in which it is mechanically diffused remain cool? Is not the salt &c. in the same condition as a platinum-wire held in the non-luminous part of the hot burnt gas escaping from the chimney of an Argand burner? Will gaseous elements when combining (and in this case the nitrogen and oxygen do unite, as proved by the formation of nitric acid) give a continuous spectrum? To ascertain whether the "flaming spark" could be obtained with a small number of cells, the large Bunsen's battery was reduced to 3 cells; and it was found that no appreciable spark could be produced when the whole primary wire was used with less than 5 cells. By reducing the length of the primary wire, and using the 4 divisions. separately, the following results were arrived at : : If the two wires from the secondary coil are placed in water, no spark is perceptible, even when they are brought very close together, until they touch. If the negative wire is passed through a cork, on which a glass tube (a lamp-glass) is fixed containing a depth of 5 inches of water, and the positive wire is brought within half an inch of the surface of the water in the tube, it becomes red-hot; and if drawn further away from the surface, the upper part of the tube is filled with a peculiar glow or light abounding in Stokes's rays. The experiments with the vacuum-tubes, and especially Gassiot's cascade, are, as might be expected, very beautiful. When a coal-gas vacuum-tube of considerable diameter, and conveying the full discharge from the secondary coil, is supported over a powerful electromagnet axially, the discharge is condensed and heat is produced. If placed equatorially, the heat increases greatly; the discharge is condensed and impinges upon the sides of the glass tube, which becomes too hot to touch; and if the experiment had been continued too long, no doubt the tube would have cracked. The enormous quantity of electricity of high tension which the coil evolves when connected with a battery of 40 cells, is shown by the rapidity with which it will charge a Leyden battery. Under favourable circumstances, three contacts with the mercurial break will charge 40 square feet of glass. Mr. Gassiot was present on one occasion, and particularly observed with myself the rapidity with which a series of 12 large Leyden jars arranged in cascade were discharged. The noise was great; and each time the spark (which was very condensed and brilliant) struck the metallic disk, the latter emitted a ringing sound, as if it had received a sharp blow from a small hammer. The discharges were made from a point to a metallic disk; and when the former was positive the dense spark measured from 18 to 18 inches, and fell to 8 inches when the metallic plate was positive and the point negative. A variations of the Leyden-jar experiments was tried, by connecting the coil worked by a quantity battery of 25+25 cells with six Leyden jars arranged in cascade; and the spark obtained measured 8 inches. The same six jars connected with the coil when the 50 cells were arranged continuously for intensity gave a spark of 12 inches of very great density and brilliancy. Other experiments are being tried with the great coil, the results of which will be duly brought before the Society if thought of sufficient importance. XXVIII. "On the Mechanical Description of Curves." Received June 17, 1869. Let A, B, C be three wheels rolling in one another (fig. 1); they may of course be supposed to describe simultaneously the angles mo, no, ro, when m, n, and r are constant. Let a, ß, y be three nuts situated on A, B, C respectively, at distances a, b, c from their centres. Then if these nuts work in horizontal bars (as exemplified in many sewing-machines), the bars will descend vertically 29 39 through the spaces a sin mo, b sin no, e sin re respectively. We may combine all these vertical motions together; for if vertical rods be attached to the horizontal bars, and a cord fixed at Q pass over the pulleys a1, A,, a, b1, B2, b1, C1, C2, C, as shown in the figure, the other extremity Q, will describe the space a sin m0+b sin n0+c sin r0. By this contrivance we are able to combine any number of vertical descents, so that it is readily seen that a sin (mo+a)+b sin (no+ẞ)+ &c. may be described mechanically. A machine on the same principle as this had been previously invented by Mr. Bashforth. I soon perceived that in order to describe the general equation of the rth order by continued motion, it was necessary to make a wheel revolve through an angle equal to the sum and difference of the angles described in the same time by two given wheels; to effect this I invented the apparatus shown in fig. 2. In fig. 2 let A be a vertical wheel working truly in a horizontal rack R1, which propels the horizontal frame a, ß, y, d. On this frame stand the wheels B and D parallel to the plane of the paper. The wheel C, supposed perpendicular to the plane of the paper, works by teeth in the wheels B and D, and the four wheels A, B, C, D are precisely equal. To the centre of C is attached a square axis, which passes through the centre of the wheel E, so that the wheel E in revolving may, without changing its plane, communicate motion to C as the frame moves forward. Two horizontal racks, R., R,, parallel to the plane of the paper, are urged by the wheels B and D; and these, again, work in the fixed wheels F and G, equal to A, B, C, D in all respects. Then if the wheel A describe in a given time the angle 0, and the wheel E in the same time the angle o, the wheels F and G will revolve respectively in the same time through the angles 0+ and 0-4. We shall call the wheel A an abscissa wheel, the wheel E, an ordinate wheel, for reasons which will appear directly, also F an addition wheel, and G a subtraction wheel. Let xa sin 0, y=a sin p, then the general equation of the rth order may be written a sin (m0+np)+a' sin (m'0—n'p)+a" sin (m"0+n'q) +... =a sin 0. Let a number of machines like the foregoing be placed side by side with their ordinate wheels rolling in one another, and their abscissa wheels duly connected. Let one abscissa wheel describe an angle me, and the corresponding ordinate wheel the angle no, then a nut placed on the corresponding addition wheel, at a distance a from its centre, will cause a horizontal bar to descend vertically through a space a sin (m0+ng). In the same way a nut properly placed on the subtraction wheel will cause a horizontal bar to descend vertically through a space a sin (mo-no). By means of the adjacent machines we may in like manner cause bars to descend through the vertical spaces, a" sin (m'0+n'o), a" sin (m'0-n'p), &c. Now let motion be communicated to the ordinate wheels, and let all the vertical motions due to the addition and subtraction wheels be combined together and made to act vertically upon a nut in one of the abscissa wheels; then the angles 0, 4, will satisfy the equation a sin (m0+no)+a' sin (m0—no)+a" sin (m'0+n'q) ... =a sin 0, which is the general equation of the rth order. Therefore two bars moved respectively horizontally and vertically by nuts in the wheels describing the angles 0 and will trace by their intersection the required curve. COMMUNICATIONS RECEIVED SINCE THE END OF THE SESSION. I. "Spectroscopic Observations of the Sun."-No. V. By J. NORMAN LOCKYER, F.R.S. Received July 8, 1869. Since the date of my last communication under the above title the weather has, if possible, been worse for telescopic work than during the winter and spring; my opportunities of observation, therefore, have been very limited : still the sun has occasionally been in such a disturbed state, and our atmosphere has at times been so pure, that several new facts of importance have come out. I will state them here as briefly as possible, reserving a discussion of them and my detailed observations for a future occasion. I. The extreme rates of movement in the chromosphere observed the present time are :— Vertical movement.... 40 miles a second Horizontal or cyclonic movement. 120 up to II. I have carefully observed the chromosphere when spots have been near the limb. The spots have sometimes been accompanied by prominences, at other times they have not been so accompanied. Such observations show that we may have spots visible without prominences in the same region, |