in cycles,(296) each cycle being merely the repetition of bd, but the vowels becoming less distinct in each successive cycle. The distance of any given vowel from its respective centre points, a, c, being always the same in all.

No. 2. IEA OU UO AEI IEA OU UOAEI IEA OU.

"If another reed be tried, whose wave is equal to a, c, (No. 2), the centres of the cycles a, c, e, &c., will be at the distance of the sonorous wave of the new reed from each other, but the vowel distances exactly the same as before; so that, generally, if the reed wave ac be twice r inches long, and the length of the pipe producing any given vowel measured from a be v inches, the same vowel will always be produced by a pipe whose length" is found thus: multiply twice the number of inches (r) in the reed wave by any whole number, and add (or subtract at pleasure) to (or from) the result the number of inches (v) which the pipe must consist of, when measured from a, in order to produce the given vowel, or, in mathematical symbols, the length of the pipe "equal 2 nr+v, or 2 nr-v (inches,) n being any whole number.

"When the pitch of the reed is high, some of the vowels become impossible. For instance, let the wave of the reed be ac (No. 3), where half of ac is less than the wave producing U.

"In this case, it would be found that the series would never reach higher than O; that, on passing b, instead of coming to U, we should begin with O again, and go through the inverse series. In like manner, if still higher notes be taken for the reed, more vowels will be cut off. This is exactly the case in the human voice; female singers are unable to pronounce U and O on the higher notes of their voice. For example, the proper length of pipe for O, is that which corresponds to the note c;" (30) and beyond this note in singing, it will be found impossible to pronounce a distinct O.

(296). A cycle is properly a circle, Greek núnλos (kiuklos, or kiklos in M. G.), and is hence used for phenomena which recur in regular order.

(30.) "In speaking of musical notes, I shall denote their place in the scale by the German tablature. The octave from the tenor e to b on the third line of the

"The short and long U, however, are indefinite in their lengths; the the short U (as in but:31)) seems to be the natural vowel of the reed,(32) and as this is but little affected by the pipe except in loudness, between O and b (No. 1) this vowel will be found to prevail through a long space, and, upon approaching b, to change gradually into the long U (as in boot), which always appears more perfect the longer ab can be made. *

* *

“The vowel distances in the first series, that is, those measured from a (No. 1), are always rather less than those measured from the centre points c, e, &c. This diminution varies with different reeds, and appears to be due to some disturbing effect of the reed itself, or the short pipe annexed to it, which I have not been enabled as yet to examine so satisfactorily as I could wish. For this reason, I have preferred, in the following table, obtaining the vowel lengths from the second and third series, by bisecting (326) their respective distances from each other measured across c, which appears liable to no such alterations. These lengths, in inches, occupy the third column. For want of a definite notation, I have given, in the second column, the English word containing the vowel in question. The fourth contains the actual note of the musical scale corresponding to a stopped pipe of the vowel length, supposing O to yield c", which it does as nearly as possible. In effect, its length is 4 inches, which, with Bernouilli's (33) correction,(34) gives four inches for the length of the pitch pipe, and this will be found to give c".

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treble is marked once, thus, c', the next above, twice, c", and so on. As a standard for pitch, I use a pitch pipe, which is made to sound by a small pair of attached bellows, yielding a constant pressure of 25 in. The internal dimensions are by in, and 1 foot long. Lumière 16 in. An attached scale is graduated to shew the actual length of the pipe (that is, the distance from the bottom of the pipe to the bottom of the piston) in English inches and decimals."

(31.) It will be shewn, in Chap. 5, sections 2 and 3, that it is better not to call the vowel in but, "short ;" the name proposed for this species of vowel is "stopped." A stopped vowel cannot be prolonged, as a short vowel can, without entirely losing its character. We presume that Prof. Willis means to indicate the vowel sound in burr, which may be indefinitely prolonged, and which by almost all writers is confused with the vowel in but. The words "cur, curry," serve to shew the resemblance and the difference.

(32.) The vowel sound in burr is by many persons termed the natural vowel. It is the nearest approach to the unmodified voice; but voice can no more be produced in an absolutely unmodified state, than matter can exist without form.

(32 b.) Or, halving.

(33.) "Bernuilyi," or "Bernuiyi," in the Parisian pronunciation.

(34.)

"Mem. Ac. Par., 1762, p. 460. Biot, Phys. II., p. 134.”

"I have found this table as correct a general standard as I could well expect; for vowels, it must be considered, are not definite sounds, like the different harmonics of a note, but, on the contrary, glide into each other by almost imperceptible gradations, so that it becomes extremely difficult to find the exact length of pipe belonging to each, confused as we are by the difference of quality between the artificial (?) and natural vowels. Future experiments, in more able hands than mine, will, I trust, determine this matter with greater accuracy, and I should not even despair of their eventually furnishing philologists with a correct measure for the shades of difference in the pronunciation of the vowels by different nations." "One source of fallacious decision, however, it must be remarked,” says Sir John Herschell, (35) after citing this table and paragraph, “will subsist in its application, in the effect of contrast, on which much of the difference between vowels depends. Its influence, indeed, may be traced in the above table itself. Thus, Mr. Willis, assisted, no doubt, by the contrast arising from frequent and rapid transition, has been able to discriminate between the vowel sounds yielded by pipes of the lengths 3750 and 3, though the sounds in the exemplifying words paw and nought, which he has chosen, are so closely allied that we confess our own inability to detect any shade of difference."(36)

There are other points in which the above table appears to us to be defective, but we think it best to defer our remarks for the present, as they will be better understood at a subsequent period.

Prof. Wheatstone, after giving a very brief abstract of that portion of

(35.) SOUND, par. 375.

(36.) "Let the reader pronounce slowly and distinctly the words paw, gnaw, naughty, nought, for his own satisfaction."

Prof. Willis's paper, which we have taken the liberty of printing almost at length, proceeds thus: (37)

"Mr. Willis further states that cylinders of the same length give the same vowel, whatever be their diameter and figure; and that so far as he has tried, he has always found that any two cavities yielding the identical note when applied to the embouchure(38) of an organ pipe, will impart the same vowel quality to a given reed, or indeed to any reed, provided its note be flatter than that of the cavity.

"From these experiments it is evident that the forms stated by Kratzenstein, as producing different vowels, are perfectly arbitrary. The entire series of vowels can be produced from tubes of either" (any one) " of his forms by merely changing its dimensions.

"Mr. Willis finally concludes, from his experiments, that the vowel quality, added to any sound, is merely the co-existence of its peculiar note with that sound; this accompanying note being excited by the successive reflections of the original wave of the reed at the extremities of the added tube.

"This view of the matter naturally associates the phenomena of vowel sounds with those of multiple resonance, a subject first investigated by Prof. Wheatstone.

"The phenomena of simple or unisonant resonance are so well known that we need only call attention to one or two of the most striking facts. If a vibrating body be brought near a column or volume of air, which would be capable of producing the same sound were it immediately caused to sound as an organ-pipe or otherwise, then the sound of the vibrating body is greatly reinforced, as when an harmonica glass is brought before a unisonant cavity, or when a tuning fork is placed at the embouchure of a flute, the apertures of which are stopped, so that if blown into, the flute would sound the same note; in the latter case the experiment is more remarkable, as the sound of the tuning fork is scarcely itself audible. The same effect takes place when the cavity of the mouth is adjusted so as to be in unison with the tuning fork.

"We now come to the new facts of resonance: a column of air will not only enter into vibration, when it is capable of producing the same sound as the vibrating body which causes the resonance, but also, when the number of the vibrations which it is capable of making" (in a given time; say one second,) "is any simple multiple of that of the original sounding body," the time for which the number of vibrations is reckoned

(37.) London and Westminster Review, Oct., 1837, pp. 34–37. (38.) "Anbushúr," opening, or mouth-piece.

being of course the same in either case, "or, in other words, if the sound to which the tube is fitted is any harmonic of the original sound.

"For instance, if a tube closed at one end by a moveable piston is taken, and its length adjusted to six inches, it will resound as an unison to a C tuning fork; and if we shorten the length of the tube to three inches, the unison will no longer be reciprocated, but its octave will be heard. The same effect is produced by altering the cavity of the mouth.

"By placing a vibrating lamina(39) which produces a lower sound than can be obtained from a tuning fork, the tongue of a Jew's harp, for instance, and successively adjusting the column of air so as to be one-half, one-fourth, one-fifth, &c., of the column reciprocating the fundamental sound, the octave, twelfth, double octave, seventeenth, &c., will be produced. The relative numbers, considering the vibrations of the tongue" of the Jew's harp, as unity, are 1, 2, 3, 4, 5, &c. The mouth produces precisely the same effect as this changeable tube does, and all the beautiful sounds which Mr. Eulenstein(40) manages with so much skill are pro

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(39.) Lamine," or thin plate, as a metallic spring, &c.

(40.) Karl Eulenstein (=Karl Oil-ǝnshtain) was born in the year 1802, at Heilbronn (=Hailbron), in the kingdom of Würtemberg (=Vúrtǝmberg). His parents were engaged in business on a small scale, but he lost his father while still a child. At seven, he was put to school, where he received instruction in music as a chorister. His mother was opposed to his devoting himself to music, a passion for which was very early developed, and apprenticed him to be prepared for the office of clerk, and subsequently to a bookbinder, in neither of which places did he stop many weeks. Finally, he was apprenticed to a dealer in hardware goods, whose wife (that soon became sole mistress, by the death of her husband) had a great distaste for music, and insisted upon his giving up all his instruments, violin, flageolet, French horn. Among other hardware articles, however, this lady dealt in Jew's harps, and Eulenstein tried to solace himself, for the want of other instruments, by performing upon this, which he did at night, and frequently under the bed clothes, for fear of his mistress discovering him. "One night, he fell asleep with a Jew's harp in his mouth, and was awakened by a scratch in the face from the point of the spring. To remedy this inconvenience in future, he covered it with a little sealing-wax. This he found altered the pitch; and, by means of loading the end of the tongue more or less heavily, he tuned a series of harps with the greatest nicety, and was thus enabled to command a very extensive scale, and to modulate, with surprising truth and accuracy, into every variety of key." At length, his mother permitted him to go and seek his fortunes as a musician. For a long time he met with little or no encouragement, and in Paris was reduced to great distress, till M. Stockhausen (=Shtokhau zən), "the husband of the celebrated singer, 'talked him about,' and succeeded in procuring him several profitable engagements with his Jew's harp, and fairly set him afloat again." He then came to London, but had again no success, till patronized by the Duke of Gordon, (then Marquis of Huntley.) After a successful season, he returned to Heilbronn, where he studied music, and labored diligently at the guitar. In 1828,