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experiment is complicated: the wave was not deducted; Resistance
I.
II.
III.

IV. ids.

and it was not a plane, but a cube.

of Fluids. 180

10000 168

Don George d'Ulloa found the impulse of a stream of 9899 9893

+3
156 9568

9578
+10

square,
sea-water, running two feet per second, on a foot

to be 151 pounds English measure. This greatly ex-
144
9045 9084

+39

ceeds all the values given by others.
132
8346 8446
+100

35
From these experiments we learn, in the first place, Conseqpen.
7500
7710

+210 108

that the direct resistance to a motion of a plane surface ces from 6545 6925

+389 96

through water, is very nearly equal to the weight of a 5523 6148

+625
84

column of water baving that surface for its base, and
4478
5433

+955

for its height the fall producing the velocity of the mo-
72
3455 4800 +1345

tion. This is but one half of the resistance determined
60
2500
4404
+ 1904

by the preceding theory. It agrees, however, very well
4240
+2586

with the best experiments made by other philosophers
955
4142
+3187

on bodies totally immersed or surrounded by the fluid;
24
432 4063 +3631

and sufficiently shows, that there must be some fallacy
109
3999
+3890

in the principles or reasoning by which this result of
The resistance to i square foot, French measure, mo-

the theory is supposed to be deduced. We shall have ving with the velocity of 2,56 feet per second, was very

occasion to return to this again. nearly 7,625 pounds French.

But we see that the effects of the obliquity of inciReducing these to English measures, we have the sur dence deviate enormously from the theory, and that this face = 1,1363 feet, the velocity of the motion equal

deviation increases rapidly as the acuteness of the prow to 2,7263 feet per second, and the resistance equal to increases. In the prow of 60° the deviation is nearly 8,234 pounds avoirdupois. The weight of a column equal to the whole resistance pointed out by the theory, of fresh water of this base, and baving for its height

and in the prow of 1 2° it is nearly 40 times greater than the fall necessary for communicating this velocity, is

the theoretical resistance. 8,264 pounds avoirdupois. The resistances to other The resistance of the prow of 90° should be one-half velocities were accurately proportional to the squares of

the resistance of the base. We bave not such a prow; the velocities.

but the medium between the resistance of the

prow

of There is great diversity in the value wbich different 96 and 84 is 5790, instead of 500. authors have deduced for the absolute resistance of wa Tliese experiments are very conform to those of other ter from their experiments. In the value now given authors on plane surfaces. Mr Robins found the resistnothing is taken into account but the inertia of the wa ance of the air to a pyramid of 45°, with its apex fore. ter. The accumulation against the fore part of the box

most, was to that of its base as 1000 to 1411, instead was carefully noted, and the statical pressure backwards,

of one to two. Chevalier Borda fouud the resistance of arising from this cause, was subtracted from the whole a cube, moving in water in the direction of the side, resistance to the drag. There had not been a sufficient was to the oblique resistance, when it was moved in the variety of experiments for discovering the share which

direction of the diagonal, in the proportion of 5 to 7; tenacity and friction produced, so that the number of

whereas it should have been that of v 2 to 1, or of 10 pounds set down here may be considered as somewhat to 7 nearly. He also found, that a wedge whose angle superior to the mere effects of the inertia of the water. was 90°, moving in air, gave for the proportion of the We think, upon the whole, that it is the most accurate

resistances of the edge and base 7281 : icoco, instead determination yet given of the resistance to a body in of 5000 : 10000. Also, when the angle of the wedge motion : but we shall afterwards see reason for believing,

was 60°, the resistances of the edge and base were 52 that the inpulse of a running stream having the same and 100, instead of 25 and 100. velocity is somewhat greater; and this is the form in

In short, in all the cases of oblique plane surfaces, the which most of the experiments have been made. resistances were greater than those which are assigned

Also observe, that the resistance here given is that by the theory: The theoretical law agrees tolerably to a vessel two feet broad and deep and four feet long. with observation in large angles of incidence, that is,

The resistance to a plane of two feet broad and deep in incidences noc differing very far from the perpendiwould probably have exceeded this in the proportion of cular; but in more acute prows the resistances are more 15,22 to 14,54, for reasons we shall see afterwards. nearly proportional to tbe eines of incidence than to

From the experiments of Chevalier Buat, it appears that a body of one foot square, French measure, and

The academicians deduced from these experiments two feet long, having its centre 15 inches under water,

an expression of the general value of the resistance, moving three French feet per second, sustained a pres which corresponds tolerably well with observation. Thus sure of 1454 French pounds, or 15,63 English. This

let z be the complement of the half angle of the prow, reduced in the proportion of 3 to 2,569 gives 11,43

and let P be the direct pressure or resistance, with an pounds, considerably exceeding the 8,24.

incidence of 90°, and p the effective oblique pressure : Mr Bouguer, in his Maneuvre des Vaisseaux, says,

tlien p=Px cosine x+3,153

3,2 that be found the resistance of sea-water to a velocity

This gives of one foot to be 23 ounces poids de Marc.

for a prow of 12° an error in defect about roo, and in The chevalier Borda found the resistance of sea-water larger angles it is much nearer the truth; and this is to the face of a cubic foot, moving against the water exact enough for any practice. one foot per second, to be 21 ounces nearly. But this. This is an abundantly simple formula; but if we in.

troduce

r.

their squares.

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Re-i-tance'troduce it in our calculations of the resistances of curvis the most proper obliquity in a thousand important cases. Resistan of Fluids. lineal protvs, it renders them so complicated as to be al By appealing to them, we can tell what is the proper of Pad

nost useless; and what is worse, when the calculation angle of the sail for producing the greatest impulse in the is completed for a curvilineal prow, the resistance wbich direction of the ship's course; or the best inclination of results is found to differ widely froni experiment. This the sail of a wind-mill, or the best inclination of the shows that the motion of the fluid is so modified by the float of a water-wheel, &c. &c. These deductions will action of the niost prominent part of the prow, that its be made in their proper places in the course of this impulse on what succeeds is greatly affected, so that we work. We see also, that the deviation from the simple are not allowed to consider the prow as composed of a theory is not very considerable till the obliquity is number of parts, each of which is affected as if it were great; and that, in the inclinations which other cir. detached from all the rest.

cumstances would induce us to give to the floats of waAs the very nature of naval architecture seems to re ter-wheels, the sails of wind-mills, and the like, the quire curvilineal forms, in order to give the necessary results of the theory are sufficiently agreeable to experistrengtlı, it seemed of importance to examine more par ment, for rendering this theory of very great use in the ticularly the deviations of the resistances of such prows construction of machines. Its great defect is in the imfrom the resistances assigned by the theory. The aca pulsions on curved surfaces, which puts a stop to our demicians therefore made vessels with prows of a cylin improvement of the science of naval architecture, and drical shape; one of these was a half cylinder, and the the working of ships. other was one-third of a cylinder, both having the same But it is not enough to detect the faults of the theobreadth, viz. two feet, the same depth, also two feet, ry: we should try to amend it, or to substitute anand the same length, four feet. The resistance of the other. It is a pity that so much ingenuity should have half cylinder was to the resistance of the perpendicular been thrown away in the application of a theory so deprow in the proportion of 13 to 25, instead of being as fective. Mathematicians were seduced, as bas been al13 to 19.5. The chevalier Borda found nearly the ready observed, by the opportunity which it gave for same ratio of the resistances of the balf cylinder, and its exercising their calculus, which was a new thing at the diametrical plane when moved in air. He also compa time of publishing this theory. Newton saw clearly red the resistances of two prisms or wedges, of the same the defects of it, and makes no use of any part of it breadth and height. The first had its sides plane, in- in bis subsequent discussions, and plainly has used it clined to the base in angles of 60°: the second had its merely as an introduction, in order to give some genesides portions of cylinders, of which the planes were the ral notions in a subject quite new, and to give a demonchords, that is, their sections were arches of circles of stration of one leading truth, viz. the proportionality of 60°. Their resistances were as 133 to ico, instead of the impulsions to the squares of the velocities. While we being as 133 to 220, as required by the theory; and as profess the highest respect for the talents and labours the resistance of the first was greater in proportion to of the great mathematicians who have followed Newthat of the base than the thcory allows, the resistance of ton in this most difficult research, we cannot belp being the last was less.

sorry that some of the greatest of them continued to Mr Robins found the resistance of a sphere moving attach themselves to a theory which be neglected, mere. in air to be to the resistance of its great circle as i to ly because it afforded an opportunity of displaying their 2.27 ; whereas theory requires them to be as 1 to 2. profound knowledge of the new calculus, of which they He found, at the same time, that the absolute resistance were willing to ascribe the discovery to Leibnitz. It was greater than the weight of a cylinder of air of the has been in a great measure owing to this that we have same diameter, and having the height necessary for ac been so late in discovering our ignorance of the subquiring the velocity. It was greater in the proportion ject. Newton had himself pointed out all the defects to de of 49 to 40 nearly

of this theory; and he set himself to work to discover painted at Borda found the resistance of the sphere moving in another which should be more conformable to the pawater to be to that of its great circle as roco to 2508, ture of things, retaining only such deductions from the and it was one-ninth greater than the weight of the co other as his great sagacity assured him would stand the lumn of water whose height was that necessary

for

pro test of experiment. Even in this he seems to have been ducing the velocity. He also found the resistance of air mistaken by bis followers. He retained the proporto the sphere was to its resistance to its great circle as I tionality of the resistance to the square of the relocity. to 2.45

This they have endeavoured to demonstrate in a man. 36 The theory

It appears, on the whole, that the theory gives the ner conformable to Newton's determination of the gives some

resistance of oblique plane surfaces too small, and that oblique impulses of fluids; and under the cover of the resistances of curved surfaces too great ; and that it is quite unfit agreement of this proposition with experiment, they intoo small for ascertaining the modifications of resistance arising troduced into mechanics a mode of expression, and even and others from the figure of the body. The most prominent part of conception, which is inconsistent with all accurate 100 great. of the prow changes the action of the fluid on the suc notions of these subjects. Newton's proposition was,

ceeding parts, rendering it totally different from what it that the motions communicated to the fluid, and therewould be were that part detached from the rest, and ex fore the motions lost ly the body, in equal times, were posed to the stream with the same obliquity. It is of no as the squares of the velocitics, and he conceived these consequence, therefore, to deduce any formula from the

as proper measures of the resistances. It is a matter of valuable experiments of the French academy. The ex experience, that the forces or pressures by which a body periments themselves are of great importance, because must be eupported in opposition to the impulses of They give us the impulses on plane surfuces with every fuils, are in this very proportion. In determining the obliquity. They there!ore put it in our power to select proportion of the direct and oblique resistances of plane 5

surfaces,

by Net

tos.

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of iberoan appeared from time to time in defence of the common

tance surfaces, he considers the resistances to arise from mu. or impulse, Jolin Bernoulli and others were at last obli- Resistance newyds to al collisions of the surface and liaid, repeated at inter- ged to assert that there were no perfectly hard bodies of fluido

vals of time too small to be perceived. But in making in nature, nor could be, but that all bodies were elastic;
this comparison, he has no occasion whatever to cousi and that in the communication of motion by percussion,
der this repetition; and when he assigns the proportion the velocities of both bodies were gradually changed by
between the resistance of a cone and of its base, he, in their mutual elasticity acting during the finite but im-
fact, assigns the proportion between two simultuneous perceptible time of the collision. This was, in fact, gi-
and instantaneous impulses. But the mathematicians ving up the whole argument, and banishing percussion,
who followed him have considered this repetition as while their aim was to get rid of pressure. For what is
equivalent to an augmentation of the initial or first im- elasticity but a pressure? and how shall it be produced?
pulse ; and in this way have attempted to demonstrate To act in this instance, must it arise from a still small-
that the resistances are as the squares of the velocities. er impulse ? But this will require another elasticity,
When the velocity is double, each impulse is double, and so on without end.
and the number in a given time is double; therefore, These are all legitimate consequences of this attempt
say they, the resistance, and the force which will with to state a comparison between percussion and pressure.
stand it, is quadruple ; and observation confirms their Numberless experiments have been made to confirm the
deduction : yet nothing is more gratuitous and illogi. statement; and there is hardly an itinerant lecturing
cal. It is very true that the resistance, conceived as showman who does not exhibit among his apparatus
Nerrion conceives it, the loss of motion sustained by a Gravesande's machine (Vol. I. plate xxxv. fig. 4.).
body moving in the fluid, is quadruple ; but the instan But nothing affords so specious an argument as the ex-
taneous impulse, and the force which can withstand it, perimented proportionality of the impulse of fluids to
is, by all the laws of mechanics, only double. What is the square of the velocity. Here is every appearance

the force which can withstand a double impulse ? No of the accumulation of an infinity of minute impulses,
pa- thing but a double impulse. Nothing but impulse can in the known ratio of the velocity, each to each, pre-

be opposed to impulse; and it is a gross misconception ducing pressures which are in the ratio of the squares of P32- to think of stating any kind of comparison between im the velocities.

pulse and pressure. It is this which has given rise to The pressures are observed; but the impulses or per-
much jargon and false reasoning about the force of cussions, whose accumulation produces these pressures,
percussion. This is stated as infinitely greater than are only supposed. The rare fluid, introduced by New-
any pressure, and as equivalent to a pressure infinitely ton for the purposc already mentioned, either does not
repeated. It forced the abettors of these doctrines at exist in bature, or does not act in the manner we have
last to deny the existence of all pressure whatever, and said, the particles making their impulse, and then esca-
to assert that all motion, and tendency to motion, was ping through among the rest without affecting their mo-
the result of impulse. The celebrated Euler, perhaps tion. We cannot indeed say what may be the proportion
the first mathematician, and the lowest philosopher, of between the diameter and the distance of the particles.
this century, says, "since motion and impulse are seen The first may be incomparably smaller than the second,
to exist, and since we see that by means of motion pres even in mercury, the densest fluid which we are familia
sure may be produced, as when a body in motion strikes arly acquainted with : but although they do not touch
another, or as when a body noved in a curved channel each other, they act nearly as if they did, in conse-
presses upon it, merely in consequence of its curvilineal quence of their mutual attractions and repulsions. We
motion, and the exertion of a centrifugal force; and since have seen air a thousand times rarer in some experi-
Nature is most wisely economical in all her operations; ments than in others, and therefore the distance of the
it is absurd to suppose that pressure, or tendency to mo particles at least ten times greater than their diameters;
tion, bas any other origin ; and it is the business of a and yet, in this rare state, it propagates all pressures or
pbilosopher to discover by wbat motion any observed impulses made on any part of it to a great distance, al-
pressure is produced.” Whenever any pressure is ob most in an instant. It cannot be, therefore, that fluids
served, such as the pressure of gravity, of magnetism, act on bodies by impulse. It is very possible to con.
of electricity, condensed air, nay, of a spring, and of ceive a fluid advancing with a flat surface against the
elasticity and cohesion themselves, however disparate, flat surface of a solid. The very first and superficial par-
way, opposite, the philosopher must immediately cast ticles may make an impulse ; and if they were annibi-
about, and contrive a set of motions (creating pro re lated, the next might do the same : and if the velocity
natá the movers) which will produce a pressure like were double, these impulses would be double, and would
the one observed. Having pleased his fancy with this, be withstool by a double force, and not a quarlruple,
he crits out iveras " this will produce the pressure;" as is observed : and this very circumstance that a qua-
et frustra fit per plura quod fieri potest per pauciora, druple force is necessary, should have made us conclude
“therefore in this way the pressure is produced.” that it was not to impulse that this force was opposed.
Thus the vortices of Descartes are brought back in The first particles having made their stroke, and not
triumph, and have produced vortices without number, being annihilated, must escapc laterally. In their es- Bul a very
which fill the universe with motion and pressure. caping they effectually prevent every farther impulse, 'mall part
Such bold attempts to overturn long-recrived doc because they come in the way of those filaments which of a fluid

can make trines in mechanics, could not be reccived without much would bave struck the body. The whole process seems

any impuise criticism and opposition ; and inany able dissertations to be somewhat as follows:

When the flat surface of the fluid has come into con- face. doctrines. In consequence of the many objections to tact with the plane surface AD (fig. 7.) perpendicular Fig 7the comparison of pure pressure with pure percussion to the direction DC of their motion, they must deflect

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1

Resistance to both sides equally, and in equal portions, because no sured by the pressure of gravity. We are not compá- Resistant of Fluids. reason can be assigned why more should go to either ring forces of different kinds, percussions with pres- of Finita

side. By this means the filament EF, which would sures, but pressures with each other. Let us see whe-
bave struck the surface in G, is deflected before it arrives ther this view of the subject will alford us any method
at the surface, and describes a curved path EFIHK, of comparison or absolute measurement.
continuing its rectilineal motion to I, where it is inter When a filament of fluid, that is, a row of corpuscles,
cepted by a filament immediately adjoining to EF, on are turned out of their course EF (fig. 7.), and forced Pis 7.
the side of the middle filament DC. The different par to take another course IH, force is required to produce
ticles of DC may be supposed to impirige in succession this change of direction. The filament is prevented
at C, and to be deflected at right angles ; and gliding from proceeding by other filaments which lie between it
along CB, to escape at B. Each filament in succession, and the body, and which deflect it in the same manner
outwards from DC, is deflected in its turn; and being as if it were contained in a bended tube, and it will
hindered from even touching the surface CB, it glides press on the concave filament next to it as it would press
off in a direction parallel to it; and thus EF is deflect on the concave side of the tube. Soppose such a bended
ed in I, moves parallel to CB from I to H, and is again tube ABE (fig. 10.), and that a ball A is projected Fig.no
deflected at right angles, and describes HK parallel to along it with any velocity, and moves in it without fric-
DC. The same thing may be supposed to happen on tion: it is demonstrated, in elementary mechanics, that
the other side of DC.

the ball will move with undiminished velocity, and will
And thus it would appear, that except two filaments press on every point, such as B, of the concave side of
immediately adjoining to the line DC, which bisects the tube, in a direction BF perpendicnlar to the plane
the surface at right angles, no part of the fluid makes CBD, which touches the tube in the point B. This
any impulse on the surface AB. All the other fila- pressure on the adjoining filament, on the concave side
ments are merely pressed against it by the lateral fila- of its path, must be withstood by that filament which
ments without them, which they turn aside, and pre- deflects it; and it must be propagated across that fila-

ment to the next, and thus augment the pressure upon 40

vent from striking the surface. No impulse In like manner, when the fluid strikes the edge of a that next filament already pressed by the deflection of on the

prism or wedge ACB (fig. 8.), it cannot be said that the intermediate filament; and thus there is a pressure edge of a

any real impulse is made. Nothing binders us from towards the middle filament, and towards the body, ari-
prism.
Fig. 3.

supposing C a mathematical angle or indivisible point, sing from the deflection of all the outer filaments; and
not susceptible of any impulse, and serving merely to their accumulated som must be conceived as immediate-
divide the stream. Each filament EF is effectually pre- ly exerted on the middle filaments and on the body, be-
vented from impinging at G in the line of its direction, cause a perfect fluid transmits every pressure undimi-
and with the obliquity of incidence EGC, by the fila- nished.
ments between EF and DC, which glide along the sur The pressure BF is equivalent to the two BH, BG, Pressure
face CA; and it may be supposed to be deflected when one of which is perpendicular, and the other parallel, the activa
it comes to the line CF which bisects the angle DCA, to the direction of the original motion. By the first of inics
and again deflected and rendered parallel to DC at I. taken in any point of the curvilineal motion of any fi-
The same thing happens on the other side of DC; and lament), the two halves of the stream are pressed toge-

we cannot in that case assert that there is any impulse. ther; and in the case of fig. 7. and 8. exactly balance The ordi. We now see plainly how the ordinary theory must be each other. But the pressures, such as BG, must be nary theo- totally unfit for furnishing principles of naval architec ultimately withstood by the surface ACB; and it is by ry of no

ture, even although a formula could be deduced from these accumulated pressures that the solid body is urged Use in naval archi

such a series of experiments as those of the French Aca- down the stream; and it is these accumulated pressures tecture. demy. Although we should know precisely the impulse, which we observe and measure in our experiments. We

or, to speak now more cautiously, the action, of the fluid shall anticipate a little, and say that it is most easily de-
on a surface GL (fig. 9.) of any obliquity, when it is monstrated, that when a ball A (fig. 10.) moves with
alone, detached from all others, we cannot in the small. undiminished velocity in a tube so incurrated that its
est degree tell what will be the action of part of a stream axis at E is at right angles to its axis at A, the accu-
or fluid advancing towards it, with the same obliquity, mulated action of the pressures, such as BG, taken for
when it is preceded by an adjoining surface CG, having every point of the path, is precisely equal to the force
a different inclination ; for the fluid will not glide along which would produce or extinguish the original motion.
GL in the same manner as if it made part of a more ex This being the case, it follows most obviously, that if
tensive surface having the same inclination. The pre the two motions of the filaments are such as we have de-
vious deflections are extremely different in these two scribed and represented by fig. 7. the whole pressure in
cases; and the previous deflections are the only changes the direction of the stream, that is, the whole pressure
which we can observe in the motions of the fluid, and which can be observed on the surface, is equal to the

Wetber
the only causes of that pressure which we observe the weight of a column of fluid having the surface for its
body to sustain, and which we call the impulse on it. base, and twice the fall productive of the velocity for eastie or
This theory must, therefore, be quite unfit for ascer its height, precisely as Newton deduced it from other not
taining the action on a curved surface, which may be considerations; and it seems to make no odds wberber
considered as made up of an indefinite number of suc the fluid be elastic or unelastic, if the deflections and
cessive planes.

velocities are the same. Now it is a fact, that no difWe now see with equal evidence bow it happens that ference in this respect can be observed in the actions of the action of fluids on solid bodies may and must be op- air and water; and this had always appeared a great posed by pressures, and may be compared with and mea defect in Newton's theory : but it was only a defect of

41

Fig. 9.

they be

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the theory attributed to him. But it is also true, that greater than that of the body ; and the sensible deflec. Resistance ds. the observed action is but one-half of what is just now tion began at a considerable distance up the stream, es- of r luids.

deduced from this improved view of the subject. Whence pecially in the outer filaments.
arises this difference? The reason is this : We have gi. Lastly, the form of the curves was greatly influenced
ven a very erroneous account of the motions of the fila by the proportion between the width of the trough and
ments. A filament EF does not move as represented in that of the body. The curvature was always less when

fig. 7. with two rectangular inflections at I and at H, the trough was very wide in proportion to the body.
I came B. and a path IH between them parallel to CB. The pro Great varieties were also observed in the motion or

cess of nature is more like what is represented in fig. 11. velocity of the filaments, In general, the filaments
It is observed, that at the anterior part of the body AB, increased in velocity outwards from the body to a cer-
there remains a quantity of fluid ADB, almost, if not tain small distance, which was nearly the same in all
altogether stagnant, of a singular shape, having two cur cases, and then diminished all the

way

outward. Tuis ncarebanyak ved concave sides A a D, B 6 D, along which the mid was observed by inequalities in the colour of the fila

dle filaments glide. This fluid is very slowly changed. ments, by which one could be observed to outstrip anat The late Sir Charles Knowles, an officer of the British other. The retardation of those next the body seemed

navy, equally eminent for his scientific professional to proceed from friction; and it was imagined that

knowledge and for bis military talents, made many without this tbe velocity there would always bave been
les
beautitul experiments for ascertaining the paths of the greatest.

45 filaments of water. At a distance up the stream, be These observations give us considerable information With infeallowed small jets of a coloured fluid, which did not respecting the mechanism of these mution-, aud the ac

rences from

them. mix with water, to make part of the stream; and the tion of fluids upon solids. The pressure in the duplicate experiments were made in troughs with sides and bottom ratio of the velocities comes here again into vir w. We of plate-glass. A small taper was placed at a considers found, that although the velocities were very different, -able height above, by which the shadows of the colour the curves were precisely the same. Now the observed ed filaments were most distinctly projected on a white pressures arise from the transverse forces by which each plane held below the trough, so that they were particle of a filament is retained in its curvilineal path; rately drawn with a pencil. A few important particu- and we know that the force by which a body is retainlars may be here mentioned.

ed in any curve is directly as the square of the velocity, The still water ADC, fig. 1 1. lasted for a long while and inversely as the radius of curvature. The curvature, before it was renewed; and it seemed to be gradually therefore, remaining the same, the transverse forces, and wasted by abrasion, by the adhesion of the surrounding consequently the pressure on the body, must be as the * water, which gradually licked a way the outer parts from square of the velocity : and, on the other hand, we can D to A and B ; and it seemed to renew itself in the di see pretty clearly (mdeed it is rigorou-ly demonstrated rection CD, opposite to the motion of the stream. There by D'Alembert), that wiratever be the veiorities, the was, however, a considerable intricacy and eddy in this curves will be the same. For it is known in hydraulics, motion. Some (seemingly superficial) water was conti. that it requires a fourfold or ninefold pres-ure to pronually, but slowly, flowing outward from the line DC, duce a double or triple velocity. And as all pressures while other water was seen within and below it, coming are propagated through a perfect fluid without diminginwards and going backwards.

tion, this fourfold pressure, while it produces a double The coloured lateral filaments were most constant in velocity, produces also fourfold transverse pressures, their form, while the body was the same, although the which will retain the particles, moving twice as fast, in velocity was in some cases quadrupled. Any change the same curvilincal paths. And thus we see that the which this produced seemed confined to the superficial impulses, as they are called, and resistances of finids, filaments.

have a certain relation to the weight of a column of As the filaments were deflected, they were also con fluid, whose beight is the height necessary for producing stipated, that is, the curved parts of the filaments were the velocity. How it happens that a plane surface, imnearer each other than the parallel straight blaments up mersed in an extended fluid, sustains just half the presthe stream; and this constipation was more considerable sure which it would have sustained had the motions been as the prow was more obtuse and the deflexion greater. such as are sketched in fig. 7th, is a matter of more

The inner filaments were ultimately more dellected curious and difficult investigation. But we see evidently than those without them; that is, if a line be drawn that the pressure must be less than what is there a-signtouching the curve EFIH in the point H of contrary ed; for the stagnant water a-head of the body greatly flexure, where the concavity begins to be on the side diminishes the ultimate deflections of the filaments : next the body, the angle HKC, contained between And it may be demonstrated, that when the part BE of the axis and the tangent line, is so much the greater as the canal, fig. 10. is inclined to the part AB in an the filament is nearer the axis.

angle less than 90°, the pressures BG along the whole
When the body exposed to the stream was a box of canal are as the versed sine of the uliimate angle of de-
upright sides, flat bottom, and angular prow, like a H«ction, or the vessed sine of the angle which the part.
wedge, having its edge also upright, the filaments were BE makes with the part AB. Therefore, since the
not all deflected laterally, as theory would make us ex deflections resenible more the sketch given in fig. II.
pect ; but the filaments near the bottom were also de the accumulated sum of all these forces BG of fig. 10.
flected downwards as well as laterally, and glided along must be less than the similar sum corresponding to
at some distance under the bottom, forming lines of fig. 7. that is, less than the weight of the column of
double curvature.

fluid, having twice the productive height for its height.
The breadth of the stream that was deflected was much How it is just one half, shall be our next inquiry.
Vol. XVII. Part II.
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