TtTXIKO-FORK. 



TUNNEL. 



411 



lowering of the tenor o from 538 to 522. A decree of the Emperor 

 actioocd thi standard, and nude it compuUtory on all musical 

 Ubluhmenu in any way supported by the state to adopt this stan- 

 dard at Paris from the 1st of July, 1859,and in the province* from the 

 1st of December following. 



The preliminary meeting of the Society of Arts was held on the 3rd 

 of June, 1859. A large number of musical gentlemen and one lady, 

 Madame Goldschmidt (Jenny Lind), attended, together with a few 

 scientific men. It was agreed that the pitch bad gradually risen, was 

 still ruing, that it ought to be checked, and that the settlement of a 

 definite standard, once for all, was very desirable. Madame Gold- 

 schuiidt stated that within the short space of twelve years the pitch 

 had risen sufficiently to make the change painful to the singers of 

 soprano music. A committee was appointed to examine and report on 

 the question : the deliberations lasted twelve months. It is worthy of 

 remark that Sir John Herschel addressed a letter to the committee, in 

 which he expressed his astonishment that the French commission 

 should have fixed upon the number 870 for their A fork, or 522 for c ; 

 and he expressed his conviction that sooner or later the mathemati- 

 cally simple and easily calculated 512 must be adopted. His proposal 

 was to re-form the pitch effectually, and once for all, by the adoption 

 of that number. The instrument-makers, he remarks, would be some- 

 what puzzled by any change, but that the embarrassment would not 

 be increased by making the full required alteration at onco. The 

 committee, however, reported in favour of a number between the two 

 namely, 528, or the pitch established by the Stuttgard 



in 1834. Tbe instrumental performers stated to the com 

 mittee that they could lower the Opera pitch of 546 down to 5L"*, but 

 if they had to lower it to 512 some of them would bare to purchase 

 new instruments. On the other hand, the vocalists who would have 

 preferred 512 were content to accept 528 as a compromise in the right 

 direction. Besides this, 528 was recommended as A good number for 

 the fundamental note of the octave, since it admits of the other notes 

 of the scale being expressed in whole numbers without fractions. At 

 the presentation of the report a strong attempt was made to obtain a 

 vote in favour of 512, but without success ; so that for some time to 

 this number will probably only reign in Professor Hulkh's 



) scientific process by which the number of vibrations per second 

 is determined, consists in the use of one of three or four methods. 

 The first is by means of the monochord, a string of known length and 

 diameter, stretched by a known weight usually in a horizontal position. 

 The length of the string is the vibrating portion between two well-defined 

 edge* or bridges, and the weight is guided over a very small pulley. 

 Fischer was, we believe, the first to point out a source of error in this 

 arrangement, namely, that in the horizontal position the string is 

 prevented by friction from experiencing the full effect of the weight, 

 and the calculation will give the number of vibrations in excess of 

 the true value. The string must therefore be in a vertical position. 

 The formula convenient for calculation results from the mathematical 

 theory of the vibrations of a stretched cord : 



Let I = the length in inches of the cord or wire. 



c = the length aim in inchei, whose weight would be equal to 

 that by which it is stretched. 



Then the number of vibrations per second will be 

 N = ^fx 9-8257, 



in which 9-825* is 4 V0. ff being the accelerative force of the gravity 

 of the earth at its surface, expressed in inches. 



Mr. Woolhouae ('Essay on Musical Intervals') took a piece of the 

 stoutest plain string of the pianoforte, weighing very nearly 2 grains 

 to the inch : 272 inches weighed just 9 drams or 540 grains. A length 

 of 7'23 inches, stretched in a vertical position by a weight of 28 Ibs. 

 avoir., sounded the common pitch-note A : hence, according to the 

 preceding formula, c= 88726 inches; v'c= 314 2 inches ; Vcx9-8257 



= 8087-2 inches; and n = !2!L?.= 424. " We therefore conclude that 



7*28 



the pitch-note A vibrates about 424 tiroes in one second. This may 

 differ one or two vibrations from the truth, on account of the 

 unavoidable small defects of the materials used in the experiment." 

 According to this determination the notes of the octave have the 

 following values : c 254, D 286, S 318, r 339, o 382, A 424, B 477, and 

 O 609 vibrations per second respectively. 



Tbe second mode of determining the pitch of a given note is by 

 means of the STRE*. and the method of doing so is briefly, but perhaps 

 sufficiently, described under that head. For the method of BEATS. 

 we may refer to that bead, and likewise to the articles ACOUSTICS, and 

 TEMPERAMENT and TcNi.tn. But the most rapid and striking method 

 of defc-rmininR the number of vibrations in a given note is that 

 recently introduced by M. Lissajoux [NODAL POINTS AND LINES]. By 

 means of an electro-magnetic machine a disc one metre in circumference 

 moves with utrict uniformity, and makes one revolution in one second. 

 Thi disc is covered with a tain layer of copperplate printer's ink, and 

 the fork is furnished with a small ivory point. On vibrating the fork 

 and bringing the point up to the rotating disc, it will engrave a number 



of tooth -like waves, which have only to be counted in order to deter- 

 mine the number of vibrations per second of the fork. 



The law which regulates the vibrations of a tongue of metal fixed at 

 one extremity, and free to vibrate at the other, is that the number of 

 vibrations of similar tongues, but of different lengths, are in the inverse 

 ratio of the squares of those lengths. Thus if one tongue be twice as 

 long as the other, the shorter will perform four times as many vibra- 

 tions in a given time as the longer. The method of tuning a fork by 

 a standard is to sound the fork with that standard, and if it agree* 

 with it, the two notes will sound in unison as one ; if it do not agree, 

 a system of beats will be heard more or less rapid according to the 

 divergence. The tuner then adopts one of two methods : by mean* of 

 a flat file he rubs off a portion from the ends of the prongs, thus 

 reducing them in length, and making them vibrate quicker; or he 

 introduce* a rat's tail file and removes a portion from between the 

 prongs, thus increasing their effective length and causing them to 

 vibrate slower. 



It is undoubtedly true, that the pitch even of the tuning-fork is 

 liable to slight variations from change of temperature. While writing 

 this article we have performed the following experiment 

 were sounded together and found to be strictly in tin . them 



was plunged into hot water for a few seconils, thru wi|>ed dry, .,n.l 

 again sounded with the other fork, when a very painful beat was 

 evident. 



On striking a tuning-fork briskly on a hard substance, other notes 

 besides the fundamental note may sometimes be heard. This arises 

 from nodal divisions in each limb, after the manner of strings and tubes 

 [PIPE], but not following quite the same laws. Where there is one 

 node it is at a distance from the fixed point, a little greater than two- 

 thirds the length of the prong; the note then given by this, which is 

 called the second mode, is much sharper than when there is no node 

 (or by the first mode), and the relative number of vibrations is V- A 

 still higher note corresponds to two nodes (third mode), and one still 

 higher to three nodes (fourth mode). These subdivisions of vibrating 

 rods may also be produced in tubes. The squares of the odd number* 

 3, 5, 7, 9, &c., represent with sufficient exactness the relations of the 

 number of vibrations corresponding to the second mode, third mode, 

 fourth mode, &c. Under all these circumstances it may be stated : 

 1. That the number of vibrations of similar springs of different length* 

 is in the inverse ratio of the squares of the lengths; 2. That the 

 number of vibrations of springs of the same length, but of different 

 thicknesses, is proportional to their thicknesses ; 3. That the width of 

 a spring has no influence on the number of its vibrations, provide. 1 it 

 be small with respect to its length, and that it vibrates after the first 

 mode ; 4. That springs of equal size, but of different material, such as 

 wood, glass, steel, &c , do not give the same note, because the number 

 of the vibrations depends upon the density and rigidity of matter. 



A tuning-fork may be mule to furnish several beautiful illustrations 

 of interference. [I.NTEiui HIM i .J If a vibrating tuning-fork 1 . 

 to the ear and turned gradually round, the sound will increase and 

 diminish in a remarkable manner ; when the prongs are presented at 

 an angle of 45 the sound is scarcely if at all percept ilile. In such 

 cases, when the prongs coincide, or are equally distant from the ear, the 

 waves of sound combine their effects, whilst in intermediate p< 

 they reach the ear in different phases, and interfere and produce total 

 or partial silence. A similar effect is produced by fixing the fork to 

 the mandril of a lathe, the length of the fork coinciding with the axis 

 of motion; if the fork be vibrated no sound will be heard while it is 

 rotating. If a vibrating tuning-fork be held with its handle obliquely 

 in contact with the table, the resonance of the table is heard while the 

 fork is at rest ; but if the fork be moved parallel to itself along the 

 surface of the table, the resonance ceases, from the interference of the 

 planes of vibration with each other. The moment the handle is 

 brought to rest, the resonance is again heard. If the tuning-fork be 

 held vertically, the resonance is not interrupted by moving it about, 

 since the planes of vibration coincide. If a vibrating tuning-fork be 

 held over a cylindrical glass vessel of suitable length, the air in the 

 glass will be made to vibrate and produce a tone. If a second glass 

 cylinder be held at right angles to the first, so that the re| 

 openings of the two vessels form a right angle, the musical tone pre- 

 viously heard will cease, but will sound again on removing the -- 

 vessel, on effect which arises from the interference of the vibrations of 

 the air in the two vessels. 



TUNNEL, in civil engineering, an arched passage formed under 

 ground to conduct a canal or road on a lower level than the natural 

 surface. The derivation of this word, which, in the sense above given, 

 is unnoticed by most lexicographers, is rather tun viuin. Kich.inlson 

 places it among the derivative* of tun, and defines it as " any inclosnre, 

 inclosed way or passage;" as a chimney tunnel, or [uissage for M 

 in hieh sense the word Inanri or tonnttl is used by Spenser and other 

 early Englir-h writers ; a passage for liquor, in which sense, as well as 

 in that last mentioned, it is convertible with /KM nr/,- or a net shaped 

 like a tunnel for liquid*, wide at the mouth, and diminishing to a pn.nt. 

 He also observes that "Tooke thinks tun and its diminutive I,',,,,,/ 

 (Anglo-Saxon, Tanrl, tent/) ore the past participles of the [Anglo- 

 Saxon] verb tyn-an, to enclose, to encompass." 



Long tunnels are usually made through hills in order to avoid the 

 inconvenience and loss of power occasioned by conducting a canal, road, 



