NOTE on ART. 2. Let a tax be imposed on wages which is a fraction k of the whole. Let the labourer's consumption of manufactured goods be a fraction m of his whole consumption; and let the portion of the value of goods which depends on wages be a fraction n of the whole. Let a be the fraction by which wages rise in consequence of the tax. Now goods before the tax consist in value of m wages, and 1m raw produce. When wages are increased in the ratio 1+ 1, the value of goods will therefore be increased in the ratio (1 + x) m + 1 − m: 1, or 1 + mx : 1. Also before the tax the labourer's consumption is n in goods and 1-n in produce. And if it continue the same in each article, (which is supposed) its parts will be n (1 + mx) and 1-n: and these, together with the tax, which is k (1+x) make up the whole new wages. Therefore The result given in Art. 2, is inaccurate on the supposition of a tax of one tenth on wages; for the first step of the effect of such a tax would be to increase wages by one ninth, in order that when one tenth of the increased wages was deducted, the part remaining to the labourer, might be the same as before. It is to be noticed, that the reasoning of the preceding pages differs from that of Mr. Thompson's Theory of Rent, only in the introduction of mathematical processes. CORRECTIONS. Page 192, line 5 for or read and. 18 I have accidentally misstated Mr. Ricardo's object in the argument which I have quoted. The purpose which he has in view when he adduces it, is to shew that taxes on wages must fall on profits. This mistake however does not affect the use of the argument for illustrating the observation which I have founded upon it. Page 192, line 23 for limits read limit. ... 195 .... ...... 196 ... ... 8 for And this read And it. 25 dele comma after one. ...... 198 ... 16 dele comma after superimposed. .... 199, AXIOм 3. The object of this Axiom is to assert that there will always be a limiting soil; and the clauses which precede this assertion are not necessarily and universally true. It might happen from some cause, for instance, from improvements in agriculture, that the produce of land should increase, and yet that the same soil as before should be the limiting soil; no new land being taken into cultivation. This correction of what is asserted, will not affect its application in any of the cases where it is introduced into the calculation; since the only use of the Axiom in the investigations is to furnish the equation which represents the condition of there being a limiting soil. Page 201, AXIOM 4. This Axiom comprehends only one of the elements of a change of price, the alteration of the supply. Any causes which affect demand directly, affect price through it; but such causes are not here considered. Page 205, line 13 for profits read return to capital with profits. In several places the word profits is used instead of the return to capital with profits. The reader who attends to the reasoning will easily make this correction. Page 205, line 18 for Taxes read Partial Taxes. Page 207, line 9, &c. Instead of (aa), we ought to have in the formulæ at-at This correction will not affect what follows. Page 212, line 3, the part acqo of the tax is said "to fall on profits." Agreeably to what has just been said, the expression should have been that it falls on the returns to capital. But even with this correction of the phrase, this portion of the tax cannot be considered as lost to the capitalist, because the diminution of the return here spoken of, arises from the capital being no longer employed in the same way. The term acqu may be conceived to be compensated to the capitalist by some new employment of the displaced capital. But it was necessary to give some explanation of this term, and so far as agriculture is concerned, the description which I have given of it suggests the true nature of the alteration. Page 213, line 2. The last soil is supposed to have less capital employed upon it than the richer ones; which will be true if the richer soils are capable of having dose after dose employed upon them, till we come to a dose which gives a return the same as the return of the poorer soils; and this is the theoretical supposition. If however the richer soils have less capital on them than the poorer ones, we shall have c less than c1, and in p. 217 will be less than 1. In this case the rent will be a considerable portion of the produce. Page 213, line 17 for r read r1. 219, last line but one for t read t. X. On the Vowel Sounds, and on Reed Organ-Pipes. BY ROBERT WILLIS, M. A. FELLOW OF CAIUS COLlege, and OF THE PHILOSOPHICAL SOCIETY. [Read Nov. 24, 1828, and March 16, 1829.] THE generality of writers who have treated on the vowel sounds appear never to have looked beyond the vocal organs for their origin. Apparently assuming the actual forms of these organs to be essential to their production, they have contented themselves with describing with minute precision the relative positions of the tongue, palate and teeth, peculiar to each vowel, or with giving accurate measurements of the corresponding separation of the lips, and of the tongue and uvula, considering vowels in fact more in the light of physiological functions of the human body than as a branch of acoustics. Some attempts, it is true, have been made at various times to imitate by mechanical means the sounds of the human voice. Friar Bacon, Albertus Magnus, and others, are said to have constructed machines of this kind, but they were probably mere deceptions, like some contrivances which may be found in the works of Kircher and other writers of the same description*, * Kircher. Musurgia, p. 303. Bp. Wilkins. Dædalus, p. 104. Schottus. Mechanica. Hyd. Pneum. p. 240, and Magia Univ. II. 155. B. Porta. Magia Nat. p. 287. The Invisible Girl was a contrivance of this kind. See Nich. Journ. 1802, p. 56, 1807, p. 69. The abbè Mical (according to Rivarol)* made two colossal heads which were capable of pronouncing entire sentences, but the artist having destroyed them in a fit of disappointment at not receiving his expected reward from the government, and having left no trace of their construction, we are left completely in the dark, as to the means employed by him to produce the different sounds. He died about the year 1786. The only attempts which have a claim to a scientific character, are those of Kratzenstein and Kempelen; these gentlemen were both occupied about the year 1770, in the mechanical imitation of the voice, and have both in the most candid manner disclosed the means employed by them, and the results of their experiments, the first in a prize Essay presented to the Academy of Petersburgh in 1780†, the second in a separate treatise ‡. Kratzenstein's attempts were limited to the production of the vowels a, e, o, u, i, by means of a reed of a novel and ingenious construction attached to certain pipes, some of them of most grotesque and complicated figure, for which no reason is offered, save that experience had shewn these forms to be the best adapted to the production of the sounds in question. Kempelen's treatise abounds with original and happy illustrations, and the author is no less remarkable for his ingenuity and success, than for the very lively and amusing way in which he has treated his subject. None of these writers, however, have succeeded in deducing any general principles. * Rivarol. Discours sur l'universalitè de la langue françoise. Borgnis. Traitè des machines imitatives, p. 160. The abstract of this Essay will be found in the Act. Acad. Petrop. for 1780, and the whole Essay in the Journal de Physique, Vol. XXI. See also Young's Nat. Phil. I. p. 783. Le Mecanisme de la parole suivi de la description d'une Machine parlante, par M. de Kempelen. Vienne 1791. Dr. Darwin must also be reckoned among the mechanical imitators of speech. See Darwin's Temple of Nature 1803, Note XI. Kempelen's mistake, like that of every other writer on this subject, appears to lie in the tacit assumption, that every illustration is to be sought for in the form and action of the organs of speech themselves*, which, however paradoxical the assertion may appear, can never, I contend, lead to any accurate knowledge of the subject. It is admitted by these writers†, that the mouth and its apparatus, was constructed for other purposes besides the production of vowels, which appear to be merely an incidental use of it, every part of its structure being adapted to further the first great want of the creature, his nourishment. Besides, the vowels are mere affections of sound, which are not at all beyond the reach of human imitation in many ways, and not inseparably connected with the human organs, although they are most perfectly produced by them: just so, musical notes are formed in the larynx in the highest possible purity and perfection, and our best musical instruments offer mere humble imitations of them; but who ever dreamed of seeking from the larynx, an explanation of the laws by which musical notes are governed. These considerations soon induced me, upon entering on this investigation, to lay down a different plan of operations; namely, neglecting entirely the organs of speech, to determine, if possible, by experiments upon the usual acoustic instruments, what forms of cavities or other conditions, are essential to the production of these sounds, after which, by comparing these with the various positions of the human organs, it might be possible, not only to deduce the explanation and reason of their various positions, but to separate those parts and motions which are Kempelen's definition of a vowel, for instance, is deduced entirely from the organs of speech, "Une voyelle est donc un son de la voix qui est conduit par la langue aux lèvres, qui "le laissent sortir par leur ouverture. La différence d'une voyelle à l'autre n'est produite que "par le passage plus ou moins large que la langue ou les lèvres, ou bien ces deux parties. "ensemble accordent à la voix.” §. 106. |