B extra current at break during the motion outwards. The balance с w FIG. 18.-Diagram of Helmholtz's Electrically-maintained Tuning-Fork, generally used as an Interrupter. NS, adjustable pole-pieces of an electro-magnet, excited by a current from battery B, which passes up through the mercury cup C, the wire w, and the upper prong of the fork back to the battery. The wire w just dips into the mercury, so that the circuit is broken when the electro-magnet is excited. T FIG. 19.-Common Form of Electrically-maintained Fork. The wire w just touches the contact block b, when the electro-magnet NS is unexcited. If the wire w is removed, and an interrupted current of nearly the frequency of the fork is sent through the electro-magnet, the fork is kept in vibration with the frequency of the current. to supply the energy of sound radiated out by the fork and the Another common form of electric maintenance is represented by Fig. 19, where the electro-magnet is placed between the prongs, and the contact breaker is a platinum wire pressing lightly against an adjustable contact block. The self-induction is here again, doubtless, aided in increasing the balance of energy supplied over energy withdrawn, by the manner in which the wire makes contact. If the interrupted current from a fork, like either of those just described, be sent through the coil of an electro-magnet placed, as in Fig. 19, between the prongs of a fork of nearly the same period (the second fork now having no contact breaker), then this fork will be set in vibration, not in its own period, but in that of the interrupting fork; and the nearer the two are in frequency, the greater is the vibration of the second fork. But it is not necessary that the second fork shall be nearly of the same frequency. It is sufficient that it is very near to one of the multiples of the frequency of the interrupter. For, as we shall see in Chapter V., a vibration of given period may, in general, be regarded as a compound, made up of a number of simple constituents or "harmonics; " the first, of the actual period and frequency; the second, of half the period and twice the frequency; the third, of one-third the period and thrice the frequency; and so on. If the dependent fork is very near in period to any one of these harmonics which is prominent in the vibration of the interrupter, it will vibrate in the period of that harmonic. Stroboscopic Methods.-There is an old experiment in which a rapidly revolving wheel is made to appear at rest, by viewing it only by intermittent flashes of light, so timed that during each interval of darkness one spoke moves exactly into the position of the next. If the wheel goes at rather less than this speed, it appears to travel slowly back; and if at rather more, it appears to travel slowly forward; for, in the first case, each spoke just falls short of the position of the next for which it is mistaken, and in the second case it just exceeds it. This principle has been adopted in several forms to determine frequency. The Experiments of M'Leod and Clarke.—The tuningfork to be tested is fixed with its prongs (Fig. 20) between a revolving drum and a microscope. Lengthwise on the drum are ruled equidistant white lines, and an image of these is thrown, by a short focus lens, into a plane in which the fork is fixed. The image of the lines as interrupted by the fork is viewed by the microscope. When both drum and fork are at rest, the appearance is as represented in Fig. 21, a. If the drum is now revolved, the right-hand side of the field will appear grey. If the fork is also set vibrating, and if the time of one vibration is just equal to the time taken by one line to move into the place of the next, the division between the two parts of the field will appear waved, as in Fig. 21, в, for whenever a white line is in 1 Phil. Trans., 1880, vol. 171, p. 1. a given position, the prong of the fork is in a definite position, and cuts off a definite part of it,-most when the prong is at one FIG. 20.-Diagram of M'Leod and Clarke's Apparatus for Determining the A revolving drum, having a graduated strip round it ruled in white lines, revolves at a known rate. A lens throws an image of the strip at the side of a vibrating fork. The image is examined by the microscope. end, and least when it is at the other end of its swing. If the drum turns at rather less than this speed, the white lines have FIG. 21.-Appearance in Microscope. A, when fork and drum are at rest; B, when fork is vibrating in time taken by each line to pass into position of next. not moved quite so far when the same amount is cut off, and the waves appear to travel slowly backward. If the drum is too rapid, the motion appears to be in the direction of rotation. The speed of the drum is under control, and a counter gives the total number of revolutions during a time exactly determined by electric signals from a pendulum. When the waves are quite stationary, the number of lines passing the centre of the field in any time is equal to the number of vibrations of the fork in the same time. If the waves are not stationary, the number of waves passing must be added or subtracted according to their direction of motion. Lord Rayleigh's Method.1-If two light metal plates are so fixed on to the ends of the prongs of a fork that at the extremity of the outward swing they just draw apart and leave a gap, an eye looking through the gap will have a view really made up of a rapid succession of views, one for each vibration of the fork. By electric maintenance the swing may be kept of constant amplitude, so as to make the gap every swing. If the eye looks at a pendulum through the gap, the eye will see as many positions of the pendulum as there are vibrations of the fork in one vibration of the pendulum. If the period of one is an exact multiple of that of the other, the positions will appear stationary; but if the accordance is not exact, the position will appear to change slowly, moving forward if the pendulum gains, backward if it loses. This was adopted as the principle of a method devised by Lord Rayleigh to determine exactly the frequency of a certain fork marked as having frequency 128, the correctness of the marking being open to doubt. A fork of frequency about 125 was electrically maintained by an interrupter fork of frequency about 121. On this last the thin metal plates were fixed to form the intermittent gap, and a seconds pendulum (making one complete vibration in two seconds), having an illuminated bead on it, was viewed through the gap; there were, therefore, twenty-five positions of the bead. To enable one of these positions to be studied, a narrow vertical slit was fixed in front of it. The position of the bright spot at successive flashes appeared to move slowly back across the slit, showing that the pendulum lost on the fork. After a short time the bright spot disappeared altogether, and eighty seconds from its first appearance the next position had retreated so as to come into view. It passed across the slit, disappeared, and so on every eighty seconds. The fork, therefore, made one more than 80 × 123, or 1001 vibrations in eighty seconds. This gave a frequency of 12.5125. The dependent fork, having naturally very nearly ten times this frequency, was made to vibrate 125 125 times per second. The fork to be tested made with it 180 beats in sixty seconds, or three beats per second, whence its frequeney was 128.1. A further development of the method is described in the Philosophical Transactions.2 21 1 Nature, xvii. p. 12. 2 Pt. i., 1883, p. 316 Koenig's Manometric Flames.-Manometric flames, or flames showing variations of pressure, are especially suitable for comparing the relative frequencies of pipes. A manometric flame is arranged as shown in Fig. 22, a. The gas, on its way to a pinhole burner, passes through a small chamber closed on one side by a membrane three or four centimetres across. If there are rapid variations of pressure on the left-hand side of the membrane, it moves in and out, and checks or aids the flow of gas to the burner. The flame is thus made variable, and jumps up and down with a frequency the same as that of the membrane. If, for instance, a note be sung into a mouthpiece connected with the lefthand compartment, the flame is affected. But in general the vibrations are too rapid to be seen separately, and the only direct indication of their existence consists in the peculiar drawn-out appearance of the flame, as shown in Fig. 23, where a shows its shape with steady pressure and b its shape when jumping up and down. If the eye be rapidly carried past the flame, (a) (6) FIG. 23.—Manometric Flame. (u) pressure steady; (b) pressure intermittent. |