176 SOUND which the disk was connected with the counter, we have the number of vibrations per second corresponding to the given sound. 2. The number of vibrations per second of a tuning fork, or of any rod or plate, can be determined very precisely by the following plan. The tuning fork or rod has attached to it a piece of delicate foil, which just touches the smoked surface of paper covering a metallic cylinder. If the cylinder is turned while the fork vibrates, it is evident that the point attached to the fork will trace a sinuous line on the cylinder. Now, if by any means we can mark off seconds of time on this sinuous trace, we shall have only to count the number of sinuosities between two successive second marks to have the num- ber of swings ma4e by the fork in a second. The above conditions are attained in the follow- ing manner : A break-circuit clock is placed in the primary or battery circuit of an induction coil ; one of the terminal wires of the secon- dary circuit of this induction coil is connect- ed with the tuning fork, while the other ter- minal wire is connected with the revolving cylinder. At each second the break-circuit clock sends a spark from the point attached to the vibrating point, through the smoked paper, to the revolving metallic cylinder. It is evi- dent that on counting the number of flexures contained between two successive spark holes in the fork's trace we have the number of half vibrations made by the fork in a second. When we have thus determined the exact num- ber of vibrations, at a known temperature, given by a tuning fork, we may use the num- ber of vibrations of this fork as a point of departure in determining the number of vibra- tions of any rod, plate, chord, or membrane, by means of a very simple and ingenious meth- od recently devised by Prof. O. N. Rood, and described by him in the "American Jour- nal of Science," August, 1874. Let us sup- pose that it is required to ascertain whether two tuning forks are in unison, or to deter- mine the difference in the number of vibra- ^^^^^^^^^ tions executed by ^^^^^^^ them in a second. _ JMHHBHBB^^ For this purpose a d short piece of fine steel wire is at- tached to each of the forks, and they are supported in positions so that their vibrations J shall be at right angles to each oth- er, as indicated in FIG. 8. % <*. The wires may have a diam- eter of one or two tenths of a millimetre, or even less, and are to be attached with the least possible amount of soft wax or varnish. They may be brought quite near to each other, or may if necessary be several inches apart. If the forks are now set into vibration and the intersection of the wires viewed against a bright background with a small telescope, it will be seen that an optical figure is developed, which is partly due to the same well known conditions that give rise to the acoustic figures of Lissajous, and partly to the circumstance FIG. 4. FIG. 5. that the wires move with less velocity when near their maximum deviation from the line of rest. Hence, if the difference in phase is zero, an appearance like fig. 4 is produced, which changes into fig. 5 when the difference in phase has increased to one half a complete vibration. Fainter indications of the same figures are shown in all cases, except when the difference in phase is one fourth, three fourths, &c., of a vibration, or nearly so. This figure is char- acteristic then of forks in unison, and the fact of its constancy will be the evidence of per- fect unison. If the forks are not exactly in unison, fig. 4 will after some time change into fig. 6, and the number of seconds necessary for this change will measure the interval re- quired by one of the forks in gaining or losing half of a complete vibration. The focal length of the object glass of the telescope used was 120 millimetres for parallel rays, and when the aperture was reduced to two millimetres, suffi- ciently distinct vision of both wires could be obtained, even when their distance apart was several centimetres. "With this limited aper- ture, the light from a white cloud answered quite well. If the forks differ by an octave, an almost equally distinct and well marked figure will be produced, such as is seen in figs. 6 and 7, which represent the characteristic appear- ances in this case. This figure is quite as useful for purposes of investigation as for that of unison. Somewhat less distinct and more complicated figures are given by the quint, the duodecime, and the double octave. From the foregoing it is evidently easy with this method to bring a vibrating string into fik w FIG. 6. FIG. 7. unison with a given tuning fork, or to adjust it so that the interval shall be a quint, octave, twelfth, or double octave, above or below. It is also easy to ascertain the number of vibra- tions made by a string in a given case, by the aid of a bridge and a properly selected fork making a known number of vibrations, the string being shortened till it furnishes one of the above mentioned figures, and therefore
