Nov. 1, 1877] 



NATURE 



13 



vation which seems to prove that it cannot be left out of 

 account. If two sounds of nearly the same pitch are 

 going on together, slow beats are heard as the result of the 

 superposition of vibrations. Suppose now that a third 

 sound supervenes whose pitch is such that it gives rapid 

 beats with the other two. It is evident that these rapid 

 beats will be subject to a cycle of changes whose fre- 

 quency is the same as that of the slow beat of the first 

 two sounds. For example, in the case of equal inten- 

 sities of two sounds there is a moment of silence due 

 to the superposition, of equal and opposite vibrations, 

 and at this moment a third sound would be heard 

 alone and could not give rise to beats. The experiment 

 may be made with tuning-forks, and the period of the 

 cycle will be found to be sensibly the same whether it be 

 determined from the slow beat of the two forks nearly in 

 uniFon or from the rattle caused by the simultaneous 

 sounding of a third fork giving from four to ten beats per 

 second with the other two. In the case of forks there is 

 no fear of sensible mutual action, but if it were possible 

 for the third sound to affect the pitch of one of the others 

 the equality of the periods would be disturbed. The 

 observation on Appunn's instrument was as follows : — 

 The reeds numbered o and 64 being adjusted to an exact 

 octave, it was found that the beats arising from the simul- 

 taneous sounding of reeds o, 63, and 64 were by no 

 means steady, but passed through a cycle of changes in a 

 period no greater than about' five seconds. In order to work 

 with greater certainty a resonator of pitch corresponding 

 to reed 64 was connected with the ear by a flexible tube 

 and adjusted to such a position that the beats between 

 reeds o and 64 (when put slightly out of tune) were 

 as distinct as possible, indicating that the gravest tone of 

 reed 64 and the octave over-tone of reed o were of equal 

 intensity. 'Qy flatteniiis: reed 64 (which can be done very 

 readily by partially cutting ofT the wind) the beats of the 

 three sounds could be made nearly steady, and then when 

 reed 63 was put out of operation, beats having a 5 

 seconds' period were heard, indicating that reeds o and 

 64 were in tune no longer. It would appear, therefore, 

 that when reed 63 sounds the pitch of reed 64 is raised, 

 but in interpreting the experiment a difficulty arises from 

 the amount of the disturbance being much in excess of 

 what would be expected from the performance of the 

 instrument when tested in other ways.' 



I come now to an independent determination of abso- 

 lute pitch, which it is the principal object of the present 

 communication to describe. The method employed may 

 be regarded as new, and it appears to be capable of giving 

 excellent results. 



The standard fork, whose frequency was to be measured, 

 is one of Konig's, and is supposed to execute 128 com- 

 plete vibrations in a second. When placed on its stand 

 (which does not include a resonance box) and excited by 

 a violin bow, it vibrates for a minute with intensity suffi- 

 cient for the counting of beats. The problem is to 

 compare the frequency of this fork with that of the 

 pendulum of a clock keeping good time. In my experi- 

 ments two clocks were employed, of which one had a 

 pendulum making about li^ complete vibrations per second, 

 and the other a so-called seconds' pendulum, making 

 half a vibration per second. Contrary to expectation, 

 the slower pendulum was found the more convenient in use, 

 and the numerical results about to be given refer to it 

 alone. The rate of the clock at the time of the experi- 

 ments was determined by comparison with a watch that 



' The value of my instrument has been greatly enhanced by the valuable 

 assistance of Mr. Ellis, who was good enough to count the entire series of 

 beats, and to compare the pitch with that of the tuning-forVs employed by 

 him in previous investigations. Mr. EUis, however, is not responsible for 

 the facts and opinions here expressed. It may be worth mentioning that 

 the steadiness or unsteadiness of the beats heard when three consecutive 

 reeds are sounding simultaneously is a convenient test of the equality of the 

 consecutive intervals. The frequency of the cycle of the four a second 

 beats is equal to the difference of the frequencies of either of the actual 



•extreme notes and that which, in conjunction with the other two, would 



'make the intervals exactly equal. 



was keeping good time, but the difference was found to 

 be too small to be worth considering. In what follows it 

 will be supposed for the sake of simplicity of explanation 

 that the vibrations of the pendulum really occupied two 

 seconds of time exactly. 



The remainder of the apparatus consists of an elec- 

 trically maintained fork interrupter, with adjustable 

 weights, making about 12.V vibrations per second, and a 

 dependent fork, whose frequency is about 125. The 

 current from a Grove cell is rendered intermittent by the 

 interrupter, and, as in Helmholtz's vowel experiments, 

 excites the vibrations of the second fork, whose period is 

 as nearly as possible an exact submultiple of its own. 

 When the apparatus is in steady operation, the sound 

 emitted from a resonator associated with the higher fork 

 has a frequency which is determined by that of the 

 interrupter, and not by that of the higher fork itself; 

 nevertheless, an accurate tuning is necessary in order to 

 obtain vibrations of sufficient intensity} By counting the 

 beats during a minute of time it is easy to compare the 

 higher fork and the standard with the necessary accuracy, 

 and all that remains is to compare the frequencies of the 

 interrupter and of the pendulum. For this purpose the 

 prongs of the interrupter are provided with small plates 

 of tin so arranged as to afford an intermittent view of a 

 small silvered bead carried by the pendulum and suitably 

 illuminated. Under the actual circumstances of the 

 experiment the bright point of light is visible in general 

 in twenty-five positions, which would remain fixed, if the 

 frequency of the interrupter were exactly twenty-five 

 times that of the pendulum. In accordance, however, 

 with a well-known principle, these twenty-five positions 

 are not easily observed when the pendulum is simply 

 looked at ; for the motion then appears to be continuous. 

 The difficulty thence arising is readily evaded by the 

 interposition of a somewhat narrow vertical slit, through 

 which only one of the twenty-five positions is visible. In 

 practice it is not necessary to adjust the slit to any par- 

 ticular position, since a slight departure from exactness 

 in the ratio of frequencies brings all the visible positions 

 into the field of view in turn. 



In making an experiment the interrupter is tuned, at 

 first by sliding the weights and afterwards by soft wax, 

 until the interval between successive appearances of the 

 bright spot is sufficiently long to be conveniently ob- 

 served. With a slow pendulum there is no difficulty in 

 distinguishing in which direction the pendulum is vibrat- 

 ing at the moment when the spot appears on the slit, and 

 it is best to attend only to those appearances which 

 correspond to one direction of the pendulum's motion. 

 This will be best understood by considering the case of a 

 conical pendulum whose rhotion, really circular, appears 

 to be rectilinear to an eye situated in the plane of motion. 

 The restriction just spoken of then amounts to supposing 

 the hinder half of the circular path to be invisible. On 

 this understanding the interval between successive ap- 

 pearances is the time required by the fork to gain or lose 

 one complete vibration as compared with the pendulum. 

 Whether the difTerence is a loss or a gain is easily deter- 

 mined in any particular case by observing whether the 

 apparent motion of the spot across the slit (which should 

 have a visible breadth) is in the same or in the opposite 

 direction to that of the pendulum's motion. 



In my experiment the interrupter ^<z/«tv/ one vibration on 

 the clock in about eighty seconds, so that the frequency of 

 the fork was a thousandth part greater than 12-5 or 12-51. 

 The dependent fork gave the ninth harmonic, with a 

 frequency of 125T. The beats between this fork and the 

 standard (whose pitch was the higher) were 180 in sixty 

 seconds, so that the frequency of the standard was as 

 nearly as possible I28-I,agreeingvery closely with Konig's 



I This tuning is effected by prolonging as much as possible the period of 

 the beat heard when the dependent fork starts from rest This beat may be 

 regarded as due to an interference of the forced and natural notes. 



