Nov. 19, 1885] 



NA TURE 



55 



of Sciences, U.S.' Briefly this last method consists, first, 

 of making the tuning-fork itself, by means of an added 

 style of extreme tenuity, scribe its vibrations as sinuosities 

 in a curve on a revolving cylinder of smoked paper, an 

 old conception ; and, secondly, of determining the exact 

 number of such sinuosities as occurred in a second, by 

 means of electricity, which was entirely new, and in which 

 lies the pith and difficulty of the method. 



When in 1S79 the writer was collecting materials for 

 his "History of Musical Pitch" {Joitrn. of Soc. Arts, 

 March 5 and April 2, 1S80, and January 7, 1881), it 

 became necessary to verify Scheibler's forks, and to do so 

 he had five large forks constructed, giving the pitches of 

 certain forks preserved in the Conservatoire at Paris. 

 These forks he measured with great care by Scheibler's 

 tonometer, and then Prof. MacLeod measured them by 

 his process, after which they were sent to .America to be 

 measured by Prof. Mayer (the particulars of his measure- 

 ments of these forks are given in his paper cited above), 

 and on their return they were remeasured by the writer 

 with the scribing-points on, and by Prof. MacLeod with 

 the scribing-points on and oft', in order to ascertain the 

 flattening caused by the scribing-points, and also any 

 losses that might have been occasioned by the journey. 

 The sum of the two affected only the second place of 

 decimals, except in one fork, where they amounted to 

 02 vibrations. By adding these, and also correcting for 

 temperature, the result was an agreement of all the three 

 methods within o'l vibrations.'^ 



But Prof. Mayer's results are given to three places of 

 decimals, which it would be extremely difficult to check, 

 not only because of the delicacy of the measurement, but 

 on account of the alteration of pitch by temperature, and 

 the uncertainty which prevails over the coefficient of 

 alteration. Thus for 1° F. Prof. Mayer considers this 

 coefficient to be '00004638, or i in 21 561 ; Prof. MacLeod 

 takes I in 20,490, and Dr. Koenig as i in 16,097, or in 

 i6,ii2, or 16,000. The writer's own experiments, between 

 59° and 175° F., gave i in 18,280. For all ordinary 

 purposes i in 20,000 may be conveniently used. But the 

 coefficient certainly alters with the size, shape, and 

 quality of the fork observed, and hence it is necessary to 

 correct each observation for temperature separately, 

 . before taking the mean, as Prof. Mayer has done. Under 

 these circumstances, at most 2 places of decimals (per- 

 haps only i) out of 3 of Prof. Mayer's means can be 

 trusted. That is, it is doubtful whether his process for 

 measuring the frequency of tuning-forks is superior to 

 Scheibler's, properly carried out. 



The difficulties of the process, which caused Prof. 

 Mayer much trouble to overcome, may now be referred 

 to. The kernel of the method consists in a very exact 

 assignment of the beginning and end of each second on 

 the sinuous curve of vibrations. This is obtained from a 

 clock, the rate of which has to be ascertained. Its pendu- 

 lum is armed with a point which cuts through a globule 

 of mercury in a cup, screwed up to be small and rigid, 

 and, as this globule rapidly becomes oxidised, by the 

 passage of electricity, it must be renewed for each experi- 

 ment. The spark from the inductorium at every contact 

 of the pendulum and mercury, must make a single per- 

 foration of the smoked paper covering the cylinder. To 

 effect this the strength of the current must be carefully 

 regulated, as otherwise a great number of holes may be 

 made. The paper is very interesting on this point, which 

 is well illustrated by experiments and a diagram. Other 



' " On a method of precisely Measuring the Vibratory Periods of 'J'uning- 

 Forks, and the determination of the Laws of the Vibrations of Forks ; with 

 special reference of these Facts and Laws to the Action of a Simple Clirono- 

 scope." 



'^ Prof Mayer measured, at temperalures varying from63'3 F. to 69*25 F. 

 The standard temperature of the writer was 59° F. = 15° C , the temperature 

 at which the Diapason Normal in Paris has been settled. It may Ije men- 

 tioned that in Prof. Mayer's tables .\iii. and xiv. of this paper, the titles have 

 been transposed ; the first related to the Tuileries fork, 434 vib., and the 

 second to the Feydeau fork. 422 8 vib., and not conversely as printed. 



precautions are necessary, but the above two are the most 

 important. The primary coil of the inductorium and the 

 clock (through the pendulum and globule of mercury) are 

 placed in the circuit of a voltaic cell. The fork and 

 cylinder (separated from the style by the thickness of the 

 smoked paper) are placed in the secondary circuit of the 

 inductorium. The work of the for'ic on the paper in scribing 

 was found not to flatten by more than '004 vib. The flatten- 

 ing from the appended scribing-point was shown by Prof. 

 MacLeod's measurements of the writer's forks to vary 

 from '02 1 to '0475 vib. It therefore always sensibly 

 affected the second place of decimals, showing that the 

 results for determining the frequency of an unarmed fork, 

 when the effect of the arming could not be determined (as 

 it cannot be by Prof. Mayer's method), could not be 

 trusted beyond one decimal place. This limit can be 

 reached very simply without all this apparatus and these 

 precautions, by simply counting the beats of good forks 

 within ideating distance of each other. Prof. Mayer's 

 method, therefore, does not surpass Scheibler's for simply 

 determining the frequency of tuning-forks, but is fully 

 equal to it, provided the forks are sufficiently large. 

 Neither Prof. Mayer's nor Prof. MacLeod's process is 

 applicable to small forks. The writer is doubtful whether 

 the passing of a current through one prong of the fork 

 and not the other may not affect the period of the fork. 

 The necessity of screwing the fork on to a block (as 

 indeed .of screwing it into a resonance box) is always 

 dangerous from the possibility of twisting the prongs. 

 The writer has known of a fork which was tlrus consider- 

 ably altered. The frequency of a fork screwed on to 

 block in this way is not the same as that of a fork on a 

 resonance box. Prof. Mayer has himself, in his paper, 

 determined that the amount of correction for support and 

 scrape may amount to - '026 vib. Prof. Mayer does not 

 renew the excitation with a bow during the same obser- 

 vation, as Prof. MacLeod had to do, and he has shown 

 that the frequency is practically independent of the 

 amplitude of vibration. 



Prof. Mayer did not himself apply his instrument to 

 determine the frequency of forks generally, but, as he 

 states in the title of his paper, specially as a chronoscope. 

 In that case the above difficulties disappear. What is 

 wanted to know is the exact number of vibrations of the 

 scribing-fork as it scribes, affected by all the circum- 

 stances mentioned — screwing, scribing, passage of elec- 

 tricity, &c. We are not in the least concerned to discover 

 the frequency of the unscrewed, unarmed, unelectrified 

 fork. Even temperature is of no conseciuence, provided 

 it be uniform during the experiment. The velocity of 

 rotation of the cylinder is also immaterial, provided it be 

 constant for one doulole vibration, which can hardly help 

 being the case for such a small fraction of a second. 

 There is only one source of error, the inecjuality of the 

 seconds' penduhim, arising from the globule of mercury 

 being of a sensible magnitude, so that an appreciable 

 time is occupied in traversing it (eliminated by counting 

 the sinuosities for every two seconds instead of everv 

 second), and the inevitable want of true centering of the 

 globule and pendulum (eliminated by taking a mean). 

 Prof. Mayer's arrangement then becomes an extremely 

 simple and also an extremely accurate means of measur- 

 ing short intervals of time within, to a certainty, one- 

 hundredth of a vibration of the fork. Thus, if the 

 fork gives 400 vibrations in a second, the measure- 

 ment would be correct to one-forty-thousandth part of 

 a second ! 



Prof. Mayer concludes his very valuable and interesting 

 paper — which is recommended to the attention of all ex- 

 perimenters requiring accurate chronoscopic observations 

 — with showing the arrangement for experimenting with 

 this chronoscope " on the velocities of fowling-piece shot 

 of various sizes projected with various charges of powder 

 from 12- and lo-gaugc guns," with a diagram giving the 



