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pear whether the disturbed or undisturbed depth is Compared to be taken. The analysis of Mr Airy seems to show with theory that a depth somewhat greater than that due to the by Mr Kelutmost effect of disturbance is to be preferred. land and Mr Airy. Russell also made experiments on the propagation of waves in channels of different forms of section. Professor Kelland has given a very simple expression for the velocity of the wave in this case, which on the whole agrees with experiment.

(422.) Peculiar effect of

Sometime about the year 1830, attention was drawn to a singular fact connected with the resistwave trans-ance of water in the case of canal navigation. It mission on was first noticed I believe in Scotland, probably on canal navi- the Forth and Clyde Canal. It amounted to this, gation. that whereas at moderate or rather slow velocities, the resistance to a boat increases with the square of the velocity, after a certain point, not differing very much from 7 miles an hour, the resistances not only cease to increase according to the same rapid law, but actually diminish to some extent when the speed is greater. Different experiments were made by the canal proprietors with a view to meet in some degree the active competition by railways, then commencing. Mr Russell was employed by the directors of the Forth and Clyde Canal, and to his experiments we now refer. It appears from his tables that the resistances increased on the whole faster than the squares of the velocities up to 7 miles an hour, when they suddenly diminished between 7 and 8 miles an hour by one-fifth part in one experiment, and by no less than one-third in another. It was not until about 12 miles an hour, that the resistance reached the same amount as at 7 miles.

(423.) Practical results.

In

The occurrence of this singular transition was attended with a phenomenon easily noticeable. every ordinary case a boat in a canal drives a wave before it, which is in fact a heap of water resisting the boat by increasing the pressure against its bows, which wave may be called a forced wave, having this peculiarity that it travels with the speed of the boat and never quits it; whilst a free wave, by whatever cause excited, is propagated at a rate depending only on the dimensions of the canal, particularly its depth. Now the diminished resistance takes place when the boat is by the force of traction partly drawn out of the water, and lifted up upon the wave to which its own motion gives rise. It is said to ride upon the wave, and the head of water pressing against its bows is visibly diminished. The most advantageous rate of transport was found to be about one-third greater than that required merely to mount the wave, which last depends principally on the depth of the canal. Thus on three different canals, 31, 51, and 9 feet deep, the most advantageous velocities were 8, 11, and 15 miles an hour. The actual velocities of the free wave were ascertained by Mr Russell in an in

A

When the boat is

genious and satisfactory manner.
dragged to most advantage, the draught of water is
less at the stem and stern than in the centre. All
these circumstances have been very ingeniously and
satisfactorily explained by Mr Airy in his paper on
Tides and Waves, articles (404–411).

Many persons (amongst whom are Colonel Henry (424.) Beaufoy, Mr Scott Russell, and the American ship- Forms of ships. builders) have bestowed much attention on the forms of vessels for ensuring speed, especially by the avoidance of waves of various kinds generated by steamvessels in motion. Every one who can compare the performance of such vessels during the last twenty years, and the still surface which waters navigated by steam vessels now present, as if they were merely cut open and closed again before and after the passage of the ship, instead of being tossed into dangerous billows consuming uselessly the propelling force, will readily admit that, however imperfect the theory, practical art has made real progress in this direction.

(425.)

machine

III. Improved Hydraulic Machines-Turbine.Before concluding this section, I will refer to the Improved most considerable improvement made of late years hydraulic in the application of hydraulic pressure to motive the Turpurposes, and I shall couple it with the names bine. of two French engineers, MM. FOURNEYRON and PONCELET, the former the inventor of the Turbine (the machine referred to), at least in its improved practical form; the latter an important contributor to the useful application of hydraulics, an accomplished mathematician, and the author of several standard works connected with industrial mechanics.

water

The defects of common vertical water-wheels, (426.) whether overshot or undershot, are so great and Defects of so notorious, that only their simplicity, and the common fact that in very many cases water-power costs wheelsnext to nothing, and may be squandered with im- Barker's punity, could justify their use. The advantage of mill. using the simple pressure of a fluid as a moving power had been foreseen in that application of re-action called Barker's Mill, which, though well known in models, was seldom if ever applied in practice. Mathematicians were, however, aware that it offered important advantages. Of late years a patent has been taken out in Scotland for a modification of it, which is found, I believe, to work well. But the Turbine or horizontal water-wheel imagined by Burdin and Fourneyron, and brought to a high state of perfection by the latter about the year 1833, appears to exhaust all that is valuable in this mode of applying water.

ron's tur

bine.

Referring to other parts of the Encyclopædia (427.) for the details, I may here explain generally that Fourneythe Turbine consists of two parts, one a fixed cylinder or drum of small height compared to its diameter; the other a portion of a cylinder exterior to the former, and moveable round it, so that

1 Velocity=√1; where A is the area of section of the canal, b the breadth of the water at the surface, and g the accelerating effect of gravity. Edinburgh Trans. vol. xiv.

2 Edin. Trans., vol. xiv., p. 48.

VOL. I.

50

(428.)

of greatest

in waterwheels.

the inner surface of the moveable cylinder is all but
in contact with the circumference of the fixed cylin-
der. Further, water under a greater or less hydro-
static pressure, and moving with the consequent velo-
city, is introduced at the centre of the fixed cylinder,
and conveyed to its circumference by channels of a
peculiar form constructed by means of vertical parti-
tions or guides of continuous curvature, from which
the water is discharged against float boards within
the external cylinder, which are also curved, but the
curvature is turned the other way so that the parti-
tions in the first cylinder are where they terminate
nearly perpendicular to the internal surface of the
moveable or second cylinder where they commence.
These latter partitions or float-boards terminate ex-
teriorly in a direction nearly tangential to the outer
cylindric surface where the water emerges.

The hydraulic principle of greatest possible advanPrinciple tage to which these Turbines are made as nearly as advantage possible to approximate is this, that the water shall enter the moveable apparatus without shock, and shall quit it without velocity, being simply left behind by the wheel as it escapes from it. Since both these conditions cannot absolutely be fulfilled, the first part of the condition is left imperfect. Some secrecy is, I believe, still maintained as to the forms and dimensions of these machines; but their actual efficiency has been most thoroughly tested by means of De Prony's Friction Dynamometer1 by Colonel Morin, a most competent authority. His experiments leave no doubt of the admirable qualities of these machines. In particular, the useful effect compared to the theoretical effect represented by the fall of water expended rises higher than probably in any other hydraulic machine, being under favourable circumstances about eighty per cent. Now water-wheels moved principally by the shock of the fall seldom, in the most advantageous conditions, realize thirty-five per cent., often not seven per cent. This superiority of action of the Turbine is due entirely to the approximation which it gives to the theoretic condition above mentioned of perfect efficiency.

of the turbine.

(429.) But what is not less striking in the performance Power of of this machine, is the variety of circumstances under adaptation which it acts advantageously; however great may be the variation in the size and velocity of the wheel, the height of fall, and the power disposable. Turbines have been made of as small diameter as 2 feet with the enormous fall of 350 feet, making 2300 revolutions per minute. They work with nearly equal advantage (relatively to the power expended) whether the supply of water be small or great. They may be completely

drowned or buried under water to a considerable
depth without any sensible variation in their effi-
ciency, thus preventing any inconvenience from floods.
It is remarkable that, with these manifest advan- (430.)
tages, the Turbine has been so sparingly introduced at
least in this country. No doubt the first establish-
ment of it is attended with considerable expense.

let-efflux

M. PONCELET, an active and intelligent officer of (431.) Génie, and member of the Institut, is favourably M. Ponceknown by his hydraulic observations and inventions, of fluidsas well as by his skilful investigation of the effects breastof machines, and his excellent works and memoirs wheels. on several subjects. He has investigated with much patience and geometrical nicety the form and discharges of spouting fluids, and was one of the first to improve materially the ordinary water-wheels, by introducing a kind of breast-wheel (which thirty-five years ago was scarcely known in France) in which the water is conveyed without shock into compartments on the descending side, from which again it was allowed to escape with all its acquired velocity spent, or nearly so. The efficiency of these wheels is equal to about two-thirds of the power expended. Before the Turbine had been finally improved by M. Fourneyron, M. Poucelet had invented an engine on the same principle, in which the water enters at the circumference of the horizontal wheel, and is delivered at the centre.

I am aware how imperfect this section remains as (432.)
a history of Hydrodynamics. But I must again Capillary
refer to special articles on the subject, the plan of attraction
-Young
the Dissertation not admitting of farther detail. As and La
nothing material has been added to the doctrine of place.
Capillary Attraction since the publications alluded
to in Sir John Leslie's Dissertation (although M.
Poisson has written a treatise on the subject), I will
for the sake of compression not enlarge upon it. I
do so with the less regret, because I cannot regard
the excessive mathematical illustration which it has
received as altogether justified by the certainty and
due appreciation of the physical principles involved,
such as can alone give to applied mathematics their
distinctive value. The theory of Laplace, so far
as it was based on novel grounds, was anticipated
by Dr Young, and gave rise to several controversial
articles by that most eminent philosopher, of which
an account will be found in Dr Peacock's Life of
Young, pages 199-210, as well as a most excellent
review of the subject of Capillary Attraction, which,
indeed, by its candour and completeness, supersedes
anything which I should have felt disposed to say
on the subject.

1 Gaspard de Prony, born in 1755, was an eminent engineer, especially in the department of hydraulics, and the author of a
voluminous work entitled Nouvelle Architecture Hydraulique; but his originality was not great enough to authorize his being
placed among the leaders of his age. His simple invention of the Frein Dynamometrique, or friction dynamometer, is the one
by which perhaps he will be longest remembered. It consists of an iron collar with tightening screw, which may be clasped
on a horizontal wooden arbor connected with uniformly revolving machinery. A lever, to which a weight may be applied, is
attached so as to form part of the collar. The clasping screw being moderately tightened, the collar and lever are of course
carried round by the machinery until a weight is applied sufficient to check the velocity, and to generate an amount of friction
which is in fact the useful effect of the machine for that velocity, and which is determined by the momentum of the weight over-
come in one second. De Prony was a most amiable man, and died in 1839, in the 84th year of his age,

of the pro

§ 7. Progress of Acoustics. CHLADNI-SAVART. Laplace's Correction of the Theory of Sound.
Vibrating Plates and Acoustic Figures. Cagniard de la Tour's "Sirène.”

(433.) The mathematical theory of the propagation of
Mathema- sound, considered as a branch of analytical mecha-
tical theory nics, made far greater progress during the eighteenth
pagation century, in harmony with the general character of
of sound. the science of that period, than the inductive doc-
trines of acoustics. Newton here, as in other de-
partments, overstepping the limits of knowledge of
his day, left a legacy of toil to his immediate suc-
cessors. Lagrange had the most distinguished good
fortune in reducing the theory of aërial tremors under
their most general conditions to the laws of mecha-
nics by the calculus of partial differentials; and La-
place supplied the link which was wanting to recon-
cile the result with the known mechanical properties
of air. As the former of these matters belongs more
properly to the period of the previous Dissertation,
Laplace's and as the beautiful discovery of Laplace has been
correction more especially touched upon by Sir John Leslie,
of the
it will be sufficient here to recall the fact that the
theory.
spring of air, or the effort by which it tends to re-
expand under sudden compression or to contract to
its former bulk when suddenly dilated, is increased
by the heat extricated in the former case, as well as
by its absorption in the latter. And as sonorous
pulsations are held to consist of a series of com-
pressed and rarified waves whose velocity is affected
by the recoil of air, it appears certain that the velo-
city must be increased by this circumstance, though
it is difficult to determine experimentally the exact

(434.)

the reviver

mental

amount.

The revival of experimental acoustics is due to Chladni ERNST CHLADNI a native of Saxony, but of Hungarian of experi- extraction, born in 1756. Little had been done in this department since the time of Sauveur, who asacoustics. certained the nature of the harmonic vibrations of strings, and that of Daniel Bernouilli, who considered the analogous case of organ pipes. We are indebted to Chladni for two classes of original experiments his measure of the velocity of sound in a variety of bodies by peculiar and ingenious methods; and his observations on the vibrations of plates by means of the ingenious expedient of strewing them with sand and other powders.

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of different gases with respect to heat, by ascertain-
ing from experiment the co-efficient in Laplace's
correction for the velocity of sound.
also probably the first to notice the longitudinal os-
cillations of strings and rods which always yield a
note immensely sharper than the lateral vibrations.
By means of the former he ascertained the velocity
of sound in a variety of woods and metals, in some
of which it is no less than seventeen times greater
than in air. These observations are not only inte-
resting in themselves, but as throwing light on the
constitution of solid bodies. To Chaldni we like-
wise owe a knowledge of the twisting vibrations of
rods, which exhausts the modes of vibration of such
bodies. To connect theoretically the periods of these
different kinds of movement, has been a favourite
problem with recent mathematicians, but has not even
yet been quite successfully performed.

In water.

The determination of the velocity of sound in (436.) water, an experiment by no means difficult, was reserved for MM. Colladon and Sturm, who observed it on the Lake of Geneva, and found it to be 4708 English feet per second, a result closely conforming to the theoretical amount deduced from Oersted's observation on the compressibility of water.

the vibra

II. But Chladni's experiments on the vibrations (437.) of plates are of still greater interest and originality. Chladni on Though it has been affirmed that Galileo strewed tion of sand or light substances upon the sounding boards plates. of musical instruments,1 Chladni deserves the entire credit of rendering this an exact method of ascertaining the nodal lines or points of rest in bodies vibrating in a stable or permanent manner. He first applied it to plates round, square, or of different figures, supported horizontally and caused to vibrate by applying a violin bow to their edges. Dust or fine sand strewed or sifted uniformly over such a plate, arranges itself in a variety of beautiful figures, being Acoustic tilted from the greater part of the surface, and heaped figures. up on those parts which are at rest in consequence of the vibratory motion of adjacent parts taking place simultaneously in opposite directions; just as the nodal points of a string vibrating harmonically are without motion on the same account. The number and variety of figures thus producible in the same plate is very great, and corresponds, as Chladni clearly saw, to different simple harmonical vibrations of the elastic plate, being accompanied by their appropriate notes; or by the superposition of several such modes of vibration, and of the corresponding sounds. The tract published by him in 1787 entituled, Entdeckungen über die Theorie des Klanges, contains numerous figures of these appearances, which,

1 This, however, is very doubtful. See Dove, Repertorium, iii. 106.

more recently, Savart found the means of preserving by transferring them to sheets of gummed paper. There are few experiments in physics of a more striking character, or which so plainly reveal minute and complex motions so small and so rapid as to be difficultly appreciated otherwise. Mr Faraday and Mr Wheatstone have pursued the same enquiry experimentally, and the latter has satisfactorily deduced the figures of Chladni's square plates from the mechanical superposition of simple modes of vibration which are symmetrical and isochronous. (Phil. Trans. 1833.) By so doing he has succeeded better than the mathematicians, whose results on this subject have been very little practical.

(438.) Chladni was the first to make experiments on the In bodies vibrations of bodies whose elasticity varies in difpossessing ferent directions. Thus he cut plates out of different unequal elasticity. kinds of wood, and found the nodal curves unsymmetrical in different directions depending on the course of the fibres. The experiments were naturally afterwards employed to illustrate the theory of ellipsoidal waves on the undulatory hypothesis of Optics. (439.) The experiments of Chladni procured for him the Chaldni on especial notice of Napoleon, by whose wish one of his works was translated into French. He died in 1827, and besides his acoustical discoveries, he will be remembered by the sagacity and boldness with which he maintained the popular opinion of the fall of heavy meteors from the sky, contrary to the prevalent scepticism of philosophers. Chaldni's success in establishing this important fact in natural history is due, like his other physical inductions, to the constancy and simple-mindedness with which he attached himself to a strictly definite enquiry.

meteoric bodies.

Robison.

(440.) We must not here enlarge upon the ingenious and Young- important investigations of Dr Thomas Young connected with acoustics. Being chiefly connected with his admirable Theory of Light, they will be noticed in the chapter on Optics. The peculiarly practical and sagacious views of Dr Robison connected with the Theory of Musical Instruments and Acoustics generally, must also be passed over.

(441.) Savart.

In FELIX SAVART we find a man like Chladni who was especially devoted to a single and circumscribed branch of science-acoustics. His published researches are almost all detached notices in the Annales de Chimie, with a few memoirs in the publications of the Institute; and whilst they are very interesting, exact, and instructive, I doubt whether it would be possible to place the results in a connected and comprehensive view before the reader. They are therefore rather to be sought in the special articles of the Encyclopædia devoted to the subject. In general they may Propaga- be stated to refer to the following topics :-(1.) To the manner of propagation of sound through the air and through liquids, with an attempt to explore the manner in which sounds spread in apartments of different forms; an enquiry as difficult as it is important; (2.) To the generation and audibility of

tion of sound in masses of air, &c.

musical

ard de la

musical notes. Previous authors (for example, On the proChladni, Biot, and Wollaston) having differed mate- duction of rially as to the range of audibility of repeated equi- notes. distant impressions which affect the human ear as musical notes, Savart used a simple method, no doubt original to him, but anticipated I believe by Robison, in which a card is held near or touching a revolving wheel, and the number of impulses (each double) given to the air by every tooth as it passes the card, is readily measured. He thus found that a note occasioned by 24,000 double vibrations in a second is perfectly audible; and, at the other limit of the musical scale, from seven to eight equidistant beats constitutes a sound having a distinct pitch. According to Savart, two consecutive double impulses of whatever duration are sufficient to convey to the ear the sensation of pitch. But a more elegant and accurate instrument for the numeration of sonorous pulsations is the Sirène Sirène of of M. CAGNIARD DE LA TOUR, unquestionably one of M. Cagnithe most exact and satisfactory additions lately made to our experimental apparatus. In it a current of air is repeatedly interrupted and renewed, giving rise to a series of impulses similar to those of the toothed wheel; and this apparatus is ingeniously contrived, so as to maintain its own motion, and record its indications. It is by far the most accurate known method of ascertaining the pitch of a given note. It may also be worked with water. Robison had also the merit of the primary idea of the Sirene, by making a stopcock revolve rapidly whilst applied to a tube emitting a blast of air. (3.) Savart extended the researches of Chladni by means Savart on of sand to many new cases, and with interesting tion of results; in particular he exhibited the effects of the solids. unequal mechanical elasticity of crystals cut in different directions. He has also examined with great care and ingenuity, the nature of the vibrations which occasion the accumulations of sand on the nodal lines of plates, and he comes to the conclusion that they are determined by simultaneous transverse and longitudinal movements (the latter of which are parallel to the surface of the plate). In proof of this he shows that in long rods or hollow cylinders, the position of the nodes is intermediate and opposed upon the contrary sides of the rod or hollow cylinder. Savart made many experiments on the communication of vibrations from one body to another; showing that the molecular movements generally preserve their parallelism, so that a longitudinal vibration of one body may give rise to transversal movements in another; and he applies this to the theory of musical instruments.

the vibra

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§ 1. THOMAS YOUNG.-The Undulatory Theory of Light.-Its history from the time of Hooke
and Huygens.-The Law of Interference.-Its application to Diffraction-to the Rainbow
-and to other subjects.-The Theory of Polarization referred to another section.

(444.)
THE history of Optics in the eighteenth century is
Small pro- one of the blankest pages of scientific story; at least
gress of
if we allow Bradley's discovery of aberration to be (as
optics in
it really is) rather an astronomical than an optical
the 18th
century.
discovery. The most notable advance was unques-
tionably the invention of the achromatic telescope
as narrated in the Fifth Dissertation, founded on
the proof of Newton's oversight in the matter of dis-
persion. The construction of refracting telescopes
made rapid advancement in the workshop of Dollond,
whilst reflecting telescopes, in the hands first of Short,
but far more conspicuously, of Sir William Herschel,
were shown to be capable of making unimagined dis-
coveries. The geometrical theory of optical instru-
ments was also greatly improved; but all this led
to little increased knowledge concerning Light itself.
If we except the valuable though imperfect treatises
of Bouguer and Lambert on the subject of photo-
metry, and a paper by Mr (now Lord) Brougham in
the last years of the century, recalling attention to
the inflexion of light, the history of Physical Optics
(as that part of the science touching more imme-
diately the nature and qualities of light is now usu-
ally termed) is almost a blank from the publication
of the Optics of Newton in 1704 to that of Young's
papers almost one hundred years later.

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with a man altogether beyond the common standard,
one in whom natural endowment and sedulous cul-
tivation rivalled each other in the production of a
true philosopher; nor do we hesitate to state our
belief that since Newton, THOMAS YOUNG stands un-
rivalled in the annals of British science.

education

and attain

He was born at Milverton in Somersetshire on the (446.) 13th June 1773, and his biographers dwell with com- His early placency on the prodigies of his youth, uncertain as such attainments confessedly are in stamping the ments. greatness of the future character. At the age of fourteen he had learned (principally for amusement) seven languages besides his own, and besides had made a point of mastering every subject, whether in science or miscellaneous knowledge, which he had once determined upon prosecuting. Thus, whilst studying botany he resolved to learn how to make a microscope, but finding in Martin's Optics the notation of fluxions, he became his own preceptor in that branch of analysis. "He acquired a great facility in writing Latin. He composed Greek verses which stood the test of the criticism of the first scholars of the day, and read a good deal of the higher mathematics. His amusements were the studies of botany and zoology, and to entomology, in particular, he at that time paid great attention."3 Dr Young's education was almost completely private. Having been brought up according to the tenets of the Society of Friends, he had not thought of going to Cambridge

1 See also Herschel on Sound (Encyc. Metrop.); and Whewell's History of the Inductive Sciences, vol. ii.

2 It may be mentioned, however, that the credit usually ascribed to Dollond must be divided, at least, with Mr Hall, a pri-
vate gentleman of Worcestershire, who not only imagined but constructed achromatic telescopes as early as 1733 (Gentleman's
Magazine, 1790, and Phil. Mag., vol. ii.) The improvement by Dr Blair of Edinburgh has been alluded to in Sir John Leslie's
Dissertation. It consisted in enclosing fluids in the object glass, of such composition as to disperse the several rays of the spec-
trum in the same proportion to one another (though not to the same absolute amount) as the glass with which it was combined;
thus rendering the achromatism more perfect.

3 Memoir of the Life of Thomas Young, M.D. 8vo, 1831. The present section of the Dissertation was written shortly be-
fore the publication of the Life and Miscellaneous Works of Dr Thomas Young, for which the public is indebted to Dr Peacock,
Dean of Ely, the possession of which would have materially facilitated my task. Wherever Dr Peacock's information has

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