Page:Encyclopædia Britannica, Ninth Edition, v. 1.djvu/125

Rh ACOUSTICS 109 If, for the single toothed wheel, be substituted a set of four with a common axis, in which the teeth are in the ratios 4:5:6:8, and if the card be rapidly passed along their edges, we shall hear distinctly produced the fundamental chord C, E, G, C^ and shall thus satisfy our selves that the intervals C, E; Cj G, and C Cj are (as they 5 3 ought to be) -, -, and 2 respectively. 48. The syren of Seebeck is the simplest form of appa ratus thus designated, and consists of a large circular disc of pasteboard mounted on a central axis, about which it may be made to revolve with moderate rapidity. This disc is perforated with small round holes arranged in circles about the centre of the disc. In the first series of circles, reckoning from the centre, the openings are so made as to divide the respective circumferences, on which they are found, in aliquot parts bearing to each other the ratios of the numbers 2, 4, 5, G, 8, 10, 12, 1C, 20, 24, 32, 40, 48, 04. The second series consists of circles each of which is formed of two sets of perforations, in the first circle arranged as 4 : 5, in the next as 3 : 4, then as 2 : 3, 3 : 5, 4 : 7. In the outer series is a circle divided by perforations into four sets, the numbers of aliquot parts being as 3 : 4 : 5 : 6, followed by others which we need not further refer to. The disc being started, then by means of a tube held at one end between the lips, and applied near to the disc at the other, or more easily with a common bellows, a blast of air is made to fall on the part of the disc which con tains any one of the above circles. The current being alternately transmitted and shut off, as a hole passes on and off the aperture of the tube or bellows, causes a vibra tory motion of the air, whose rapidity depends on the number of times per second that a perforation passes the mouth of the tube. Hence the note produced with any given circle of holes rises in pitch as the disc revolves more rapidly; and if, the revolution of the disc being kept as steady as possible, the tube be passed rapidly across the circles of the first series, the notes heard are found to pro duce on the ear, as required by theory, the exact impres sion corresponding to the ratios 2:4: &c., i.e., of a series of notes, which, if the lowest be denoted by C, form the sequence C C t E x Gj C, &c., &c. In like manner, the first circle in which we have two sets of holes dividing the circum ference, the one into say 8 parts, and the other into 10, or in ratio 4:5, the note produced is a compound one, such as would be obtained by striking on the piano two notes . Similar results, all agreeing with the theory, are obtainable by means of the remaining perforations. A still simpler form of syren may be constituted with a good spinning top, a perforated card disc, and a tube for blowing with. 49. The syren of Cagnard de la Tour is founded on the same principle as the preceding. It consists of a cylindrical chest of brass, the base of which is pierced at its centre with an opening in which is fixed a brass tube projecting outwards, and intended for supplying the cavity of the cylinder with compressed air or other gas, or even liquid. The top of the cylinder is formed of a plate perforated near its edge by holes distributed uniformly in a circle concen tric with the plate, and which are cut obliquely through the thickness of the plate. Immediately above this fixed plate, and almost in contact with it, is another of the same dimensions, and furnished with the same number, n, of openings similarly placed, but passing obliquely through in an opposite direction from those in the fixed plate, the one set Fig. 10. b-jing inclined to the left, the other to the right. This second plate is capable of rotation about a steel axis perpendicular to its plane and passing through its centre. Now, let the movable plate be at any time in a position such that its holes are immediately above those in the fixed plate, and let the bellows by which air is forced into the cylinder (air, for simplicity, being supposed to be the fluid employed) be put in action ; then the air in its passage will strike the side of each opening in the mov able plate in an oblique direction (as shown in fig. 10), and will therefore urge the latter to rotation round its centre. After -th of a revolution, the two sets of perforations will again coincide, the lateral impulse of the air repeated, and hence the rapidity of rotation increased. This will go on continually as long as air is supplied to the cylinder, and the velocity of rotation of the upper plate will be accelerated up to a certain maximum, at which it may be maintained by keeping the force of the current constant. Now, it is evident that each coincidence of the perfora tions in the two plates is followed by a non-coincidence, during which the air-current is shut off, and that con sequently, during each revolution of the upper plate, there occur n alternate passages and interceptions of the current. Hence arises the same number of successive impulses of the external air immediately in contact with the movable plate, which is thus thrown into a state of vibration at the rate of n for every revolution of the plate. The result is a note whose pitch rises as the velocity of rotation increases, and becomes steady when that velocity reaches its constant value. If, then, we can determine the number m of revolu tions performed by the plate in every second, we shall at once have the number of vibrations per second correspond ing to the audible note by multiplying m by n. For this purpose the steel axis is furnished at its upper part with a screw working into a toothed wheel, and driv ing it round, during each revolution of the plate, through a space equal to the interval between two teeth. An index resembling the hand of a watch partakes of this motion, and points successively to the divisions of a graduated dial. On the completion of each revolution of this toothed wheel (which, if the number of its teeth be 100, will comprise 100 revolutions of the movable plate), a projecting pin fixed to it catches a tooth of another toothed wheel and turns it round, and with it a correspond ing index which thus records the number of turns of the first toothed wheel. As an example of the application of this syren, suppose that the number of revolutions of the plate, as shown by the indices, amounts to 5400 in a minute of time, that is, to 90 per second, then the number of vibrations per second of the note heard amounts to 90/i, or (if number of holes in each plate = 8) to 720. 50. Dove, of Berlin, has produced a modification of the Dove s syren by which the relations of different musical notes s &amp;gt; ren - may be more readily ascertained. In it the fixed and movable plates are each furnished with four concentric series of perforations, dividing the circumferences into different aliquot parts, as p. ex., 8, 10, 12, 1G. Beneath the lower or fixed plate are four metallic rings furnished with holes corresponding to those in the plates, and which may be pushed round by projecting pins, so as to admit the air-current through any one or more of the series of perforations in the fixed plate. Thus, may be obtained, either separately or in various combinations, the four notes whose vibrations are in the ratios of the above numbers, and which therefore form the fundamental chord (CEGCj). The invenvor has given to this instrument the name of the many-voiced syren. 51. Heknholtz has further adapted the syren for more j 10 c lt &quot;~ extensive use, by the addition to Dove s instrument of ( i fn ,i,i ( , another chest containing its own fixed and movable per- syren.