Universal impulse là gì

Page 2

Refidual the Residual Analysis. The first book of the analysis most fragrant balsams. It exudes from the bark spon- Refer, 1

appeared in 1764, which contained an explanation of taneously, but more readily if incifions are made. The Rebitare. Relin.

the principles of the new calculus, with its application colour of it is yellow, and at first it is fluid; but after io problems of the direct method of fluxions, and the fe- being inspiffated in the fun, it becomes folid. When cond book folved several problems of the inverse me- burnt on hot coals, it smells like a mixture of balsam ihod, but it was never published.

of Tolu and benzoin, approaching somewhat to ttorax. If we estimate the value of this analysis by its prac- “ It is perfectly soluble in spirit of wine, but not in wa-

Htite's rical utility, it may be faid to poffefs no great merit

. ter, nor even in essential

of turpentine, unlefs it be

Voyage,

Appendice Its principles are much less easily apprehended than the digefted in a strong heat. The varnish which it makes fluxionary calculus; they are not so luminous, and less with either is very weak, and of little use. With redirect in their application, as well as inferior to it for spect to its medicinal qualities, Mr White has found enlarging the boundaries of mathematical science. it, in many cases, a good pectoral medicine, and very

RESIDU.11. Figure, in Geometry, the figure remaining balsamic. It is not obtainable in so great abundance as after the fubtraction of the less from the greater.

the red gum produced by the eucalyptus refinifera.
RESIDUAL Root, is a root composed of two members The plant which produces the yellow gum seems to be
only connected by the fign or minus. Thus, a-b, perfectly unknown to botanists, but Mr White has com- or 5–3, is a residual root; and is so called, because its municated no specimens by which its genus or even class true value is no more than the residue, or difference be- could be determined."

tween the parts a and b or 5 and 3, which in this cafe RESINOUS ELECTRICITY, is that kind of electric

city which is produced by exciting bodies of the resin- RESIDUE, the remainder or balance of an account, ous kind, and which is generally negative. See ELEC- debt, or obligation.

TRICITY pasim.
RESIGNATION, in general, signifies the implicit RESISTANCE, or RESISTING Force, in Philosophy, fubmiffion of ourselves, or of fomething we potless, to denotes, in general, any power which acts in an oppo- the will of another. In a religious sense it fignifies a fite direction to another, so as to destroy or diminish its perfect submission, without discontent, to the will of effect. See MECHANICS, HYDRODYNAMICS, and PNEU- God. See MORAL PHILOSOPHY, No 119.

RESIN, in Natural History, a viscid juice cozing Of all the resistances of bodies to each, there is un- Importar e either spontanoously, or by incision, from several trees, doubtedly none of greater importance than the re- of the lub-

as the pine, fir, &c.- A premium for several years has fistance or reaction of fluids. It is here that we multject.

the water which must be overcome, that the ship may Elallic RESIN. See CAOUTCHOUC, CHEMISTRY proceed in her course ; and this must also be modified Index.

to our purpose, that the ship may not drive like a log to Gum RESIN, a mixture of gum and resin. See CHE- leeward, but on the contrary may ply to windward, MISTRY and MATERIA MEDICA Index.

that she may answer her helm briskly, and that fhe may Red Gum RESIN, is procured from the red gum tree, be easy in all her motions on the surface of the troubled or eucalyptus resinifera ; a tree so large and lofty as to

The impulse of wind and water makes them exceed in size the English oak. The wood of the tree ready and indefatigable servants in a thousand shapes for is brittle, and of little use but for firewood, from the driving our machines; and we should lose much of their large quantity of refinous gum it contains. The tree service did we remain ignorant of the laws of their acis distinguished by having pedunculated flowers, and an tion : they would sometimes become terrible masters, if acute or pointed conical calyptra. To obtain the juice we did not fall upon methods of eluding or softening from this tree incisions are made in the trunk of it, their attacks.

and sometimes upwards of 60 gallons of red refinous We cannot refuse the ancients a considerable know- The 23White's juice have been obtained from one of m. “ When ledge of this subject. It was equally interesting to them cients were Voyage, this juice is dried, it becomes a very powerful astrin- as to us; and we cannot read the accounts of the naval tolerab'y Appendi.

gent guin-refin, of a red colour, much resembling that exertions of Phoenicia, Carthage, and of Rome, exertions qu-inted
known in the shops by the name of kino, and, for all which have not been surpassed by any thing of modern with it. medical purposes, fully as efficacious. Mr White ad- date, without believing that they poffeffed much prac- ministered it to a great number of patients in the dy- tical and experimental knowledge of this fubje&t. It sentery, which prevailed much foon after the landing was not, perhaps, poffeffed by them in a ftrict and of ihe convicts, and in no one instance found it to faił. systematic form, as it is now taught by our mathema- This gum-relin diffolves almost entirely in spirit of ticians ; but the master builders, in their dockyards, did wine, to which it gives a blood-red tincture. Water undoubtedly exercise their genius in comparing the diffolves about one-fixth part only, and the watery folu- forms of their fineft ships, and in marking those cir-

tion is of a bright red. Both these solutions are power- cumstances of form and dimension which were in fact

accompanied with the desirable properties of a thip,
Yellow Gum Resin, is procured from the yellow re- and thus framing to themselves maxims of naval archi- sin tree, which is, as large as the English walnut tree. tecture in the fame manner as we do now. For we The properties of this resin are equal to those of the believe that our naval architects are not disposed to

grant

Page 3

Rhiance. For, when GH represents the direct impulse of a par- mated in the direction GH of the stream ; and GH is Resistance,

ticle, GI is the absolute oblique impulfe, and GO is the to GQ as GH to GI”, that is, as rad.' to fin.’i.
effective impulse in the direction GO: Now GI is to Cor. 1. The effective impulse in the direction of the
GO as radius to the line of GIO, and GIO is the com- stream on any plane surface BC, is to the direct impulse
plement of IGO, and is therefore equal to CGO, the on its bale BR or SE, as the square of the fine of the angle of obliquity.

angle of incidence to the fquare of the radius.
Therefcre 1:=R : Sin. O.

2. If an isosceles wedge ACB (fig. 3.) be exposed to Fig. 3. But F:f-R: Sin.' i

a stream of tluid moving in the direction of its height Therefore F : P=R3 : Sin. ix Sin. O. and . CD, the impulle on the sides is to the direct' impulse on OT x Sin.? i x Sin. 0.

the base as the square of half the base AD to the square

of the side AC, or as the square of the fine of half the Proportion

Cor.-- The direct impulse on any furface is to the ef- angle of the wedge to the square of the radius. For it of the di- fective oblique impulse in the direction of the stream, as is evident, that in this case the two transverse impulses, rect im

the cube of radios to the cube of the fine of incidence. such as GP in fig. s. balance each other, and the only pulse to the

For draw and GP perpendicular to GH, and IP impulse which can be oblerved is the sum of the two effective

oblique im- perpendicular to GP; then the absolute impulse GI is impulses, fuch as GQ of fig. 1. which are to be compar-

stream, and GP, which may be called the transverse im- base, Now AC : AB = rad. : fin. ACD, and ACD is pulse. The angle GIQ is evidently equal to the angle equal to the angle of incidence. GHI; or FGC, the angle of incidence.

Therefore, if the angle ACB is a right angle, and 2

ACD is half a right angle, the square of AC is twice
Therefore f : Q =GI: GQ,ER : Sin. i.
But F:f=

R? : Sin.'i.

the square of AD, and the impulse on the sides of a
Therefore F:0=

N3 : Sin.3;; rectangular wedge is half the impulse on its base. And Q = F X Sin.3 i.

Alo, if a cube ACBE (fig. 4.) be exposed to a Fig. 4.

stream moving in a direction perpendicular to one of its Impulse on

Before we proceed further, we all consider the im- fides, and then to a Itream moving in a direction pera tarface in pulte on a furface which is also in motion. This is evi- pendicular to one of its diagonal planes, the impulse in

dently a frequent and an important case. It is perhaps the first case will be to the impulse in the second as v2 the most frequent and important : It is the case of a ship to 1.

Call the perpendicular impulse on a fide F, and under fail, and of a wind or water-mill at work.

the perpendicular impulse on its diagonal plane f, and Therefore, let a stream of fluid, moving with the di

the effective oblique iinpulse on its lides 0 ;-we have Fig.

rection and velocity DE, meet a plane Lc, (fig. 2.) which is moving parallel to itself in the direction

F:f = AC : AB =1:12, and
and with the velocity DF: It is required to determine

f:9= AC": AD = 2:1. Therefore
the impulse?

2:17, =V2:1, or Nothing is more easy : The mutual actions of bodies depend on their relative motions only. The motion,

very nearly as 10 to 7. DE of the fluid relative to BC, which is also in motion,

The fame reasoning will apply to a pyramid whose is compounded of the real motion of the fluid and the

base is a regular polygon, and whose axis is perpendicu- opposite to the real motion of the body. Therefore pro-

duce FD till Df=DF, and complete the parallelogram stream of Huid moving in the direction of the axis, the

lar to the base. If such a pyramid is exposed to a
Dfe E, and draw the diagonal De. The impulse on

direct impulse on the base is to the effective impulse on
the plane is the same as if the plane were at reit, and every particle of the fluid impelled it in the direction

the pyramid, as the square of the radius to the square of and with the velocity De; and may therefore be de-

the tine of the angle which the axis makes with the sides

of the pyramid. termined by the foregoing proposition. This proposition

And, in like manner, the direct impulsion on the base applies to every possible cafe ; and we shall not beitow

of a right cone is to the effective impulsion on the conimore time on it, but reserve the important modification

cal surface, as the square of the radius to the square of of the general proposition for the cases which shall oc.

the fine of half the angle at the vertex of the cone. cur in the practical applications of the whole doctrine

This is demonstrated, by supposing the cone to be a py-. of the impulse and resistance of Auids.

ramid of an infinite number of sides. roportion Prop. IV. The direct impulse of a fiream of fluid, We may in this manner compare the impulse on any

the di. whose breadth is given, is to its oblique effective im- polygonal surface with the impulse on its bale, by comEftim

pulse in the direction of the stream, as the square of paring apart the impulses on each plane with those in ilie of

radius to the square of the fine of the angle of incin their corresponding bases, and taking their sum. given dence.

And we may compare the impulfe on a curved surface e effec. e oblique For the number of filaments which occupy the ob

with that on its bale, by resolving the curved surface

into elementary planes, each of which is impelled by an pulse in lique plane BC, would occupy the portion NC of a e fume perpendicular plane, and therefore we have only to elementary filament of the stream. rection. compare the perpendicular impulse on any point V with

The following beautiful propofition, given by Le the effective impulse made by the fame filament FV on

Seur and Jaquier, in their Commentary on the second the oblique plane at G. Now GH represents the im- book of Newton's Principia, with a few examples of its pulse which this filament would make at V; and GQ application, will fuffice for any further account of this is the effective impulse of the fame filament at G, elti theory,

PROF,

Page 4

Refiftance.

I. II.

experiment is complicated : the wave was not deducted; Resistance, III,

IV.

and it was not a plane, but a cube. 180 10000

10000 168

Don Gcorge d'Ulloa found the impulse of a stream of 9890 9893

+3

fea-water, running two feet per fecond on a foot square, 156 9568 9578

+10

to be 154 pounds English measure. This greatly ex144 9045

9084

+39

cceds all the values given by others. 132 83.46 8446 +100

35 From these experiments we learn, in the first place, Consequen- I 20 7500 7710

-+-210 108

that the direct resistance to a motion of a plane surface ces from 6925 +383

through water, is very nearly equal to the weight of a them. 5523 6148 +625

column of water having that surface for its bale, and 54.33 +955

for its height the fall producing the velocity of the mos 72 3455 4800

+1345

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

by the preceding theory. It agrees, however, very well 4240 + 2;86

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

bodies totally immersed or surrounded by the Puid ; and 24 432 4063 . +3631

fufficiently shows, that there muit be some fallacy in the 109 3999 +3890

principles or reasoning by which this result of the theory The resistance to i square foot, French measure, mo- is fupposed to be deduced. We shall have occafion to ving with the velocity of 2,56 feet per second, was very return to this again. nearly 7,625 pounds French.

But we see that the effects of the obliquity of inci- Reducing these to English measures, we have the fur- dence deviate enormoully 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 refiitance pointed out by the theory, of fresh water of this base, and having for its height and in the prow of 12° it is nearly 40 times greater than the fall neceflary for communicating this velocity, is the theoretical resistance. 8,264 pounds avoirdupois. The refittances to other ve- The resistance of the

prow 90° should be one half locities were accurately proportional to the squares of the the resistance of the base. We have not such a prow; velocities.

but the medium between the resistance of the prow of There is great diversity in the value which different 86 and 84 is 5790, instead of 500. authors have deduced for the absolute resistance of wa- These 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 rehtt. nothing is taken into account but the inertia of the wa- ance of the air to a pyramid of 45°, with its apex foreter. The accumulation against the forepart 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 found the resistance of arising from this cause, was fubtracted from the whole a cube, moving in water in the direction of the fide, 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 si to 7 ;. tenacity and friction produced ; so that the number of whereas it should have been that of v 2 to 1, or of ro to y pounds fet down here may be considered as fomewhat nearly. He also found, that a wedge whose angle was fuperior to the mere effects of the inertia of the water. 90°, moving in air, gave for the proportion of the refiftWe think, upon the whole, that it is the most accurate ances of the edge and base 7281 : 10000, instead of determination yet given of the resistance to a body in 5000 : 10000.. Also, when the angle of the wedge motion : but we shall afterwards fee reason for believing, Was 60°, the resistances of the edge and base were 52 that the impulse 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 moft of the experiments have been made. refistances were greater than those which are asigned by

Allo observe, that the resistance here given is that to the theory. The theoretical law agrees tolerably with a veffel two feet broad and deep and four feet long. observation in large angles of incidence, that is, in inciThe resistance to a plane of two feet broad and deep dences not differing very far from the perpendicular ;

would probably have exceeded this in the proportion of but in more acute prow's the rehitances are more nearly 34 15,22 to 14,54, for reasons we shall see afierwards. - proportional to the fines of incidence than to their and others. From the experiments of Chevalier Buat, it appears fquares:

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 relittance, moving three French feet per second, sustained a pressure which corresponds tolerably well with obfervation. Thus of 1454 French pounds, or 15,63 English. This redu- let x be the complement of the half ar, le of the prow, ced in the proportion of za to 2,562 gives 11,43 pounds, and let P he the direct preffure or relittance, with an confiderably exceeding the 8,24.

incidence of 90°, and p the effective oblique preffure :
Mr Bouguer, in his Mancuvre des Vaisseaux, says, that he found the resistance of sea-water to a velocity of one

p?

3,25 foot to be 23 ounces poids des Marc.

for a prow of 12o an error in defect about thi 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 rwarly. But this This is an abundantly Imple formula; but if we in

Page 5

Refiftance.

Such is the demonstration which Mr Bernoulli has uncertain and vague as it was sure and precise in the for. Refiltance. given of this propofition. Limited as it is, it is highly mer case. valuable, because derived from the true principles of hy- It is therefore without proper authority that the draulics.

absolute impulse of a vein of fluid on a plane which reHe hoped to render it more extensive and applicable ceives it wholly, is aflerted to be proportional to the to oblique impulses, when the axis AC of the vein sine of incidence. If indeed we suppose the velocity (fig. 15.) is inclined to the plane in an angle ACN. in G and H are equal to that at A, then b=l, =a, and But here all the simplicity of the cale is gone, and we the whole impulse is 2a VI-?, as is commonly supare now obliged to ascertain the motion of each fila- posed. But this cannot be. Both the velocity and

ment. It might not perhaps be impossible to deter- quantity at H are less than those at G. Nay, frequent- His theory

attempted mine what must happen in the plane of the figure, ly there is no efHux on the fide H when the obliquity

a greater proportion than that of the line of incidence
much of the fluid will go in the direction EKG, and to radius. If the whole water escapes at G, and none what will go in the path FLH, and to ascertain the form of each filament, and the velocity in its different goes off laterally, the pressure will be 20+202—2bc x points. But in the real state of the case, the water Vic? The experiments of the Abbé Boffut show will dissipate from the centre C on every side ; and we

in the plainest manner that the pressure of a vein, ftri- cannot tell in what proportions. Let us however con-

king obliquely on a plane which receives it wholly, di- fider a little what happens in the plane of the figure, minishes faster than in the ratio of the square of the

and suppose that all the water goes either in the course fine of incidence; whereas, when the oblique plane is

Nor will this proposition determine the impulse of a
at H. ACG and ACH are the two changes of di- impulse is perpendicular to the plane. The circum-
rection, of which let c and -c be the cofines. Then, stance is now wanting on which we can establish a adopting the former reasoning, we have the pressure of calculation, namely, the angle of final defection. Could the watery plate GKEACM on the plane in the di-

this be ascertained for each filament, and the velocity
rection AC=_P

of the filament, the principles are completely adequate
x 20—2cb, and the pressure of the
P+11

to an accurate solution of the problem. In the expe

riments which we mentioned to have been made under plate HLFACN=

x 2a + 203, and their sum the inspection of Sir Charles Knowles, a cylinder of

P+
PX 21---20 +11 x 20 + 203

fix inches diameter was exposed to the action of a ; which being multiplied stream moving precisely one foot per second; and when

P+11

certain deductions were made for the water which was by the line of ACM or VT-", gives the pressure per. held adhering to the posterior base (as will be noticed pendicular to the plane MIN = PX 20—2cb+11 x 24 afterwards), the impulse was found equal to 3; ounces

avoirdupois. There were 36 coloured filaments distri.
P+11

buted on the stream, in such fituations as to give the most +2013

VI.

useful indications of their curvature. It was found ne- But there remains a prelture in the direction perpen- some above it; for the form of these filaments, at the

cesary to have some which passed under the body and dicular to the axis of the vein, which is not balanced, fame dilance from the axis of the cylinder, was consider- as in the former case, by the equality on opposite sides ably different : and those filaments which were situated

of the axis. The pressure arising from the water

in planes neither horizontal nor vertical took a double

pro-
duced by the water which escapes at H., When this great care, and the defecting forces were computed for

curvature. In short, the curves were all traced with is taken into account, we shall find that their joint ef- each, and reduced to the direction of the axis; and forts perpendicular to AC are?--- x za vi=e", which,

they were fummed up in such a manner as to give the p+11

impulse of the whole stream. The detiections were. being multiplied by the cofine of ACM, gives the ac

marked as far ahead of the cylinder as they could be

assuredly observed. By this method the impulse was tion perpendicular to MN-1--11

x 29Viac

computed to be 27. ounces, differing from observation

i'r of an ounce, or about i' of the whole ; a difference The sum or joint effort of all these pressures is which may most reasonably be ascribed to the adhesion PX 20—206+ 11 x 204 203

of the waier, wbich must be most sensible in such fmall 1 ---(?+ X 2 ac velocities. These experiments may therefore be confi-

Pt11

P +11 VI-a?.

dered as giving all the confirmation that can be desired

of the juftness of the principles. This indeed hardly adThus, from this case, which is much simpler than mits of a doubt: but, alas! it gives us but small asliftcan happen in nature, seeing that there will always be ance; for all this is empirical, in as far as it leaves us in a latcral cux, the determination of the impulse is as every case the talk of observing the form of the curves

and

Page 6

Resistance. curvature will be insensible, and the fluid included in be, draw b m (fig. 20.) perpendicular to bF, and the Reliezas

the space ZYHQ will move uniformly as if the solid parallel nq infinitely near it. The part bn of the Huid
body were not there. The motions on the other fide contained in the canal bngm would fuftain some pref- Fig.za
of the axis AC will be the same ; and we need only at- fure from b towards », or from n towards b. Therefore tend to one half, and we all consider these as in a llate fince the fluid in this itagnant canal should be in equili- of permanency.

brio, there must also be some action, at lealt in one of
No body changes either its direction or velocity other- the paris b m, m7,9, to counterbalance the action on
wise than by intensible degrees: therefore the particle the part b 11. But the thuid is stagnant in the space which is moving in the axis will not reach the vertex FAM (in consequence of the law of continuity).

A of the body, where it behoved to detect instantane- Therefore there is no force which can act on b m, m9,

dy in M; and then, gliding along the body, will quit pressure in the canal FM, except what proceeds from

The vclocity therefore in the canal FM is constant Let a be the velocity of a particle of the fluid in if finite, or infinitely small if variable : for, in the first any inftant, and d' its velocity in the next instant. The case, the force be would be absolutely nothing; and in velocity a may be considered as compounded of a' and the second case, it would be an infinitesimal of the sea a'. If the particles tended to move with the velocities cond order, and may be considered as nothing in comall only, the whole fluid would be in equilibrio (general parison with the velocity, which is of the first order. principle), and the pressure of the fluid would be the We Shall see by and by that the lalt is the real state of fame as if all were stagnant, and each particle were the case. Therefore the Huid, before it begins to urged by a force , expressing an indefinitely small in forne point y a-head of F, and by the time that it

change its direction in F, begins to change its velocity

reaches F its velocity is as it were annihilated. moment of time. (N. B. is the proper expression of

Cor. 1. Therefore the pressure in any point D arifes the accelerating force, which, by acting durir.g the mo.

both from the retardations in the party F, and from ment t*, would generate the velocity a"; and a" is fup

the particles which are in the canal MD: as these lalt posed an indeterminate quantity, different perhaps for move along the surface of the body, the force , deeach particle). Now let a be supposed constant, or a=d'. In this case a' =o. That is to say, no preffure ftroyed in every particle, is compounded of two others, whatever will be exerted on the solid body unless there one in the direction of the surface, and the other perhappen changes in the velocities or directions of the pare pendicular to it; call these p and p. The point D is ticles.

pressed perpendicularly to the surface MD; ist, by-all Let a and a' then be the motions of the particles in the forces p in the curve MD; 2d, by the force packtwo consecutive inftants. They would be in equilibrio ing on the single point D. This may be neglected in

comparison of the indefinite number of the others : if urged only by the forces Therefore if y be the therefore taking in the arch MD, an infinitely small point where the particles which describe the curve FM portion Nm, s, the pressure on D, perpendicular to begin to change their velocity, the pressure in D would

the surface of the body, will be = S; and this flu. be equal to the pressure which the fluid contained in the canal , FMD would exert, if each particle were solicited ent must be so taken as to be = o in the point M.

a" by its force

Cor, 2. Therefore, to find the pressure on D, we The question is therefore reduced to

must find the force p on any point N. Let u be the the finding the curvature in the canal , FMD, and the velocity of the particle N, in the direction Nm in any

a' accelerating forces in its different parts.

inftant, and utu its velocity in the following inftant; It in the first place, that no pressure is ex- appears,

we must have

Therefore the whole question

p= erted by any of the particles along the curve FM : for Fig. 19.

fuppose that the particle a (fig. 19.) describes the in- is reduced to finding the velocity u in every point n, in
definitely small straight line ab in the firft inftant, and the direction Nm.
be in the second instant; produce ab till bd=ab, and And this is the aim of a series of propositions which His finai
joining dc, the motion ab or bd may be considered as follow, in which the author displays the most accurate equatiom composed of bc, which the particle really takes in the and precise conception of the subject, and great address trus is.

next instant, and a motion dc which should be destroy- and elegance in his mathematical analysis. He at length blem,

no accelerating or retarding force at b; for if there even exhibit the final equation ; for it is conceived in

Page 7

Resistance, even 'rebound, as is frequently observed. This actual tion of water above the body which was exposed to the Reflance.

Tebounding is here prevented by the surrounding wa- stream. ter, which is moving with the same velocity but Since the pressures are as the squares of the veloci,

the preffure may be almost annibilated by the tendency ties, or as the heights h which produce the velocities,

25.5 Part (and perhaps a confiderable part) of this appa-

we may express this pressure by the symbol h, or

21.5
rent non-pression is undoubtedly produced by the tena- 1.186h, or mh, the value of m being 1.186. This city of the water, which licks off with it the water

exceeds confiderably the result of the experiments of lying in the hole. But, at any rate, this is an im- the French academy. In these it does not appear that

portant fact, and gives great value to these experiments. m fenfibly excecds unity. Note, that in these experi-

It gives a key to many curious phenomena in the re72

ments the body was moved through still water ; here Substance filtance of fluids ; and the theory of Mr Buat deserves a it is exposed to a stream. These are generally supposed very serious consideration. It is all contained in the two

to be equivalent, on the authority of the third law of theory. following propositions.

motion, which makes every action depend on the rela- ; 1." If, by any cause whatever, a column of fluid, whe- tive motions. We shall by and by see some causes of ther making part of an indefinite fluid, or contained in folid difference.

74 canals, come to move with a given velocity, the pressure

The writers on this subject seem to think their talk The action which-it exerted laterally before its motion, either on the

completed when they have considered the action of the on the hina adjoining fluid or on the sides of the canal, is diminished " fluid on the anterior part of the body, or that part of des part of by the weight of a column having the height necesary for it which is before the broadest section, and have paid thip equal. communicating the velocity of the motion.

little or no attention to the hinder part. Yet those wholy impor2. “ The pressure on the centre of a plane surface per- are most interested in the subject, the naval architects, tant with pendicular to the stream, and wholly immersed in it, is } of seem convinced that it is of no less importance to at that parthe the weight of a column having ihe height necessary for tend to the form of the hinder part of a thip. And fore-part.

communicating the velocity. For 33 is } of 217." Experi.

the universal practice of all nations has been to make He attempted to ascertain the medium pressure on

the hinder part more acute than the fore-part. This which it is the whole furface, by opening 625 holes dispersed all

has undoubtedly been deduced from experience ; for it confirmed. over it. With the fame velocity of current, he found

is in direct opposition to any notions which a person the height in the tube to be 29 lines, or 7 more than would naturally form on this subject. Mr Buat therethe height neceffary for producing the velocity. But

fore thought it very neceffary to examine the action of he justly concluded this to be too great a measure, be- the water on the hinder part of a body by the same cause the holes were of an inch from the edge : had method. And, previous to this examination, in order ment on there been holes at the very edge, they would have sul- to acquire some scientific notions of the subject, he made this subject tained a non-pression, which would have diminished the

the following very curious and instructive experiment. by Buai, height in the tube very confiderably. He exposed to Two little conical pipes AB (fig. 24.) were inserted Fig. 24, the same stream a conical funnel, which raised the wa- into the upright side of a prismatic vefiel. They were ter to 34 lines. But this could not be considered as

an inch long, and their diameters at the inner and outer a measure of the pressure on a plane solid surface; for

ends were five and four lines. A was 57 lines under the central water was undoubtedly scooped out, as it the surface, and B was 73. A glass fyphon was made were, and the filaments much more deflected than they

of the shape represented in the figure, and its internal would have been by a plane surface. Perhaps something diameter was I lines. It was placed with its mouth ! of this happened even in every small hole in the for

in the axis, and even with the base of the conical pipe. mer experiments. And this suggests fome doubt as to The pipes being shut, the vessel was filled with water, the accuracy of the measurement of the pressure and of

and it was made to stand on a level in the two legs of the velocity of a current by Mr Pitot's tube. It surely renders fome corrections absolutely necessary. It is a

the fyphon, the upper part being full of air. When

this fyphon was applied to the pipe A, and the water fact, that when exposed to a vein of Auid coming running freely, it rose 32 lines in the short leg, and sunk through a short paffage, the water in the tube stands on as much in the other. When it was applied to the a level with that in the reservoir. Now we know that

pipe B, the water rose 41 lines in the one leg of the
the velocity of this stream does not exceed what would fyphon, and lunk as much in the other.

76 be produced by a fall equal to soo of the head of wa

He reasons in this manner from the experiment. The and his ter in the reservoir. Mr Buat made many valuable ob

ring comprehended between the end of the fyphon and reasoning servations and improvements on this most useful inftru

upon it,

the sides of the conical tube being the narrowest part ment, which will be taken notice of in the articles Ri.

of the orifice, the water issued with the velocity corVERS and WATER-Works.

responding to the height of the water in the vessel Mr Buat, by a fcrupulous attention to all the circum

above the orifice, diminished for the contraction. -- If , stances, concludes, that the medium of pressure on the therefore the cylinder of water immediately before the whole furface is equal to 25.5 of the weight of a co

mouth of the syphon issued with the same velocity the 21.5

tube would be emptied through a height equal to this lumn, having the surface for its base, and the produc- HEAD OF WATER (charge). If, on the contrary, this tive fall for its height. But we think that there is an cylinder of water, immediately before the mouth of the uncertainty in this conclusion ; becaufe the height of the fýphon, were stagnant, the water in it would exert its water in the vertical tube was undoubtedly augmented full pressure on the mouth of the syphon, and the water by an hydrostatical pressure arising from the accumula- in the syphon would be level with the water in the veffel.

Between

Page 8

Iefuitance. unity, to be determined by experiment. The mals in ve could say nothing fufficiently precise on the subject. Relillance.

nction is no longer P +, but P + np, while its Persons not accustomed to the difcusions in the physico- weight in the fluid is still p. Therefore we muit have mathematical sciences, are apt to entertain doubis or

P
ap Ia

falle notions connected with this circumilance, which and n=

n Ptp=nP

we hall attempt to remove; and with this we shall con- +1

clude this dissertation.

If a fluid were perfectly incompreftible, and were Explained, A prodigious number of experiments made by M.

contained in a velfel incapable of extension, it is im-
Buat on spheres vibrating in water gave values of 1,
wbich were very contiant, namely, from 1.5 10 1.7;

poslible that any void could be formed behind the body; and by considering the circumstances which accompa-

and in this case it is not very easy to see how motion

could be performed in it. A sphere moved in such a
nied the variations of n (which he found to arise chief-

medium could not advance the smallest distance, unless ly from the curvature of the path described by the

ball), he states the mean value of the number n at some particles of the fluid, in filling up the space left

by it, moved with a velocity next to infinite. Some 1.583. So that a tphere in motion drags along with it about is of its own bulk of tluid with a velocity degree of compresibility, however small, seems necef-

fary. If this be intensible, it may be rigidly demon- equal to its own.

lie made fimilar experiments with prisms, pyramids, strated, that an external force of compreffion will make and other bodies, and found a complete confirmation of

no sensible change in the internal motions, or in the re- his affertion, that priims of equal lengths and sections,

fittances. This indeed is not obvious, but is an imme. though ditlimilar, dragged equal quantities of fluid ; that

diate consequence of the quaquaver, um pressure of Huids. fimilar priims and priims not limilar

, but whose lengths compressions in one side of a body, fo much is it aug

As much as the pressure is augmented by the external were as the square root of their tections, dragged quan- tities proportional to their bulks.

mented on the other side ; and the same must be said of He found a general value of a for prismatic bodies, every particle. Nothing more is necessary for securing

the same motions by the lame partial and internal forces; which alone may be considered as a valuable truth;

and this is fully verified by experiment. Water renamely, that n = 0.705 V+1.13

mains equally fluid under any compreffions. In some

of Sir Isaac Newton's experiments balls of four inches From all these circumstances, we see an intimate con- diameter were made fo light as to preponderate in wa- nection between the preffures, non-pressures, and the fluid ter only three grains. These balls defcended in the dragged along with the body. Indeed this is immedi- fame manner as they would have descended in a fluid ately deducible from the first principles; for what Mr where the resistance was equal in every part; yet, when

Buat calls the dragged fluid is in fact a certain portion they were near the bottom of a veslel nine feet deep,

moving force; whereas, when near the top of the vessel, It was found, that with respect to thin planes, spheres, it was not above 50 or 60 times. and pyramidal bodies of equal bases, the resistances were But in a fluid sensibly compressible, or which is not inversely as the quantities of fluid dragged along. confined, a void may be left behind the body. Its mo- The intelligent reader will readily observe, that these tion

may

be so swift that the surrounding pressure may 'views of the Chevalier Buat are not so much discoveries not suffice for filling up the deserted spacers and, in of new principles as they are classifications of conse- this case, a statical pressure will be added to the resist. quences, which may all be deduced from the general prin-

This may be the case in a vesel or pond of wa- ciples employed by D'Alembert and other matheinati- ter having an open surface exposed to the finite or limi- cians. But they greatly assist us in forming notions of ted preffure of the atmosphere. The question now is, different parts of the procedure of nature in the mutual whether the resistance will be increased by an increase of action of fluids and solids on each other. This muft be external prefiure? Supposing a sphere moving near the very acceptable in a subject which it is by no means surface of water, and another moving equally fast at probable that we shall be able to investigate with ma- four times the depth. If the motion be so swift that a thematical precision. We have given an account of void is formed in both cases, there is no doubt but that these laft observations, that we may omit nothing of the sphere which moves at the greatest depth is most *consequence that has been written on the subject ; and refitted by the pressure of the water. If there is

we take this opportunity of recommending the Hydrau- void in either case, then, because the quadruple depth

trine of the principle of uniform motion of fluids in pipes a double velocity produces a quadruple non-pressure.

questions which at present they are hardly able to guess some experiments of Chevalier de Borda. The effect, 89 at. See Rivers and WATER Works.

therefore, of greater immersion, or of greater comprefChange of

The only circumstance which we have not noticed in fion, in an elaitic fluid, does not follow a precise ratio roduced detail, is the change of resistance produced by the void, of the preffure, but depends partly on absolute quanto

y the void or tendency to a void, which obtains behind the body; ties. It cannot, therefore, be stated by any very simple ehind a and we omitted a particular discussion, merely because formula what increase or diminution of resistance will rody. Vol. XVII. Part II.

Page 9

Resurrec- new-modelled by the ever active imagination; and at And softer curs, that lie and sleep at home,

Resurrec. lait many absurd and fantastic circumstances would Do often rouse, and walk about the room, doubtlefs' be combined with the original truth, that And bark, as if they saw some strangers come. death puts not an end to human existence.

And birds will fart, and seek the woods, by night, But though we are firmly convinced that the first Whene'er the fancy'd hawk appears in light, principles of useful knowledge, and among them the Whene'er they fee his wing or hear him fight. doctrine of a future state, were cominunicated to man

CREECH. by his Maker; and though this doctrine, in large and permanent societies, might certainly be conveyed more

These powers of fancy extend wide over animal crea

tio ; and it is on this general principle that necroman- or less pure to late pofterity through the channel of tra- dition--we are far from attributing so much to tradition

cers and dreamers have in all ages established their trade, as fome writers are disposed to do, or thinking it the that the ftories of goblins have at all times fo very easily only fource from which mankind could derive the belief procured belief, and that of their existence beyo: d the grave. In Imall tribes of The village matron, round the blazing hearth, favages such a tradition could hardly be preserved ; and Suspends the infant audience with her tales, yet some indistinct notio: $ of a future itate have been Breathing astonishment! Of witching rhymes found among tribes u 'o are laid to have lost all tradi- And evil spirits ; of the deathbed call tionary notions even of the being of a God.

Of hiin who robb'd the widow and devour'd Others ima. Others, therefore, are inclined to believe that, in- The orphan's portion ; of unquiet fouls

dependent of any traditions, mankind might be led by Ris’n from the grave to ease the heavy guilt notion

certain phenomena to form fome conjectures of a future Of deeds in life conceal'd; of thapes that walk I might be conjectured state. They obferve, that although a few individuals At dead of night, and clank their chains and wave from natu- perhaps may, yet it feldoin happens that the whole in- The torch of hell around the murderer's head. * ral pheno. dividuals of any nation are exempted from dreaming :

AIKENSIDE. mena; They observe, too, and this observation is founded on

Mankind in general would willingly dispense with as from experience, that the inayes of the dead are from the

these troublesome visits of the dead. To prevent the dreaming, remaining impressions of memory frequently fummoned up in the fancy; and that it appears from all the lan

return of the zumbi or the ghost, fome nations of Afriof rude nations, who pay the greatest attention that the frighted Hottentots leave in the hut where a Congo and

ca use many fuperititious riles *; and Kolben tells us, * Voyage to guages their vitions, that these images (A) have always been person has died all the utensils and furniture, left the Angola, taken by them for reali ies; nay, fone of the learned, them in their dreams, and infest them in the night.

angry ghost, incensed at their avarice, should haunt Churchillos

Voyages. and the celebrated Bax'er is of the number, are dispo- Divines and moralists have laboured to show that these fed to doubt whether these appearances be not fomcthing more than illusions of the brain : But whether

are merely imaginary terrors : but God and nature seem

to have determined that they shall produce the same they readily be so or not, one thing is certain, that all effects upon certain minds as if they were real; and nations in all countries, in the darheft ages and the ru-

that while there is any sensibility in the heart, while dett pcriols, are accuiloned to dream; and whether there is any reinembrance of the pait, and any conjuring ileeping or waking, in the itillaels of the night, in the gloom of folitude, in the fondness of friendinnip, in the timid, hall often meet with the goblins of darkness

, the

power in the fancy; the ignorant, the benighted, the rovings of love, the delirium of fever, and the anguish spectres of the tomb, the apparitions that hover round

of remorse, to see and converfe with the modes of the the grave, and the forms of the dead in the middle * Lucret. departed; and Lucretius * has remarked, that even the

dream. See SPECTRE. inferior animals are not exempted from such illusions of a restless fancy.

From these phenomena, which have been so common Probable

in all countries and in all ages, what would mankind inferences For often fleeping racers pant and sweat,

naturally infer? Would they not infer, that there is from Breathe short, as if they ran their second heat;

fomething in the nature of man that survives death, and dreams,&c. As if the barrier down with eager pace

that there is a future Itate of existence beyond the They ftretch'd, as when contending for the race.

grave ? Are not still many specimens of this reasoning And often hounds, when fleep hath closd their eyes,

preferved in the ancient poets? and is it not thus that They to', and tumble, and attempt to rise ;

Achilles + reasons after imagining that he faw the ghof Hom liiad.

of luis friend Patroelus? They open often, often snuff the air, As if they preft the footsteps of the deer ;

'Tis true, 'tis certain, man, thoughi dead, retains And sometimes wakid, pursue their fancy'd prey, Part of himself; th’immortal mind remains: The fancy'd deer, that seem to run away,

The form fubfifts without the body's aid, Till quite awak'd, the follow'd shapes decay.

Aerial femblance, and an empty shade.

This

(1) These images were called by the Grecks Eidws Oxvolwv; and

among

the Romans they had various names, as umbre, lemures, manes, larvæ, and were sometimes called occursacula noctium, bufforum formidamina, fepulchro. rum terriculamento, animae errantes, which are all comprehended under the species mortuorum.

Page 10

Resurrec. of superior merit, but because he had married the daugh- The conscious wretch must all his acts reveal,?

Relorrec ter of Jove.

Loth to confess, unable to conceal, 33

Even long after a future state had become the scene From the first moment of his vital breath, Becuines a of rewards and punishments, there for the most part To the last hour of unrepenting death. place or re- were distributed, not according to moral, but physical wards and distinctions. With the Greeks and Romans, the foul

The spirits of the dead no longer mingle together as punuh.

was condemned to many calamities for a number of in the less enlightened period of Homer; the vicious. years, if the body was not honoured with funeral rites. are disinissed to a place of torments, the virtuous sent to Among the Scandinavians, a natural death was attend regions of bliss : indifferent characters are confined to a

ed with infamy, while a violent death, pàrticularly in limbus *; and those who are too virtuous for hell, but * Or para.

Among the

ven without preparation, are for some time detained in a Tla calans, it was only the great that were permitted purgatory. to animate birds and the nobler quadrupeds; the lower For there are various penances enjoin'd,

35 ranks were transformed into weasels, into paultry.

Virgil's 33

And fome are hung to bleach upon the wind ; There at beetles, and such mean animals. Among the Mexicans,

purgatory.

Some plung'd in waters, others purg'd in fires, firk distri- those who were drowned, who died of a dropsy, tu,

Till all the dregs are drain'd, and ruft expires; cording to

mors, or wounds, or such like diseases, went along with physical the children that had been sacrificed to the god of wa

Till nothing's left of their habitual stains,

But the pure ether of the foul remains. distinc- ter, and in a cool and delightful place were allowed to tions ; indulge in delicious repasts and varieties of pleasures : When thus purified, they become fitted to receive

those who died of other diseases, were sent to the north the rewards of their paft virtues, and now enter into or centre of the earth, and were under the dominion of those regions of happiness and joy. the gods of darkness. “ The soldiers who died in battle, or in captivity among their enemies, and the

With ether vested, and a purple sky,

His hca women who died in labour, went to the house of the

The blissful seats of happy souls below, fun, who was considered as the prince of glory. In his

Stars of their own, and their own suns they know ; manfions they led a life of endless delight. Every day

Where patriots live, who, for their country's good, the soldiers, on the first appearance of his rays,

hailed

In fighting fields were prodigal of blood. his birth with rejoicings and with dancings, and the

Prielts of unblemish'd lives here make abode, music of instruments and voices. At his meridian they

And poets worthy their inspiring god; met with the women, and in like festivity accompanied And searching wits, of more mechanic parts, him to his setting. After four years of this glorious life,

Who grac'd their age with new-invented arts : they went to animate clouds, and birds of beautiful fea-

Those who to worth their bounty did extend ; thers and of sweet fong; but always at liberty to rise

And those who knew that bounty to commend. again, if they pleased, to heaven, or descend to the # Clavige.

These good men are engaged in various amusements, ro's Hift. of

earth, to warble their songs, and to suck flowers *.” Mexico, These sentiments of a future state, conceived in a fa- according to the taste and genius of each. Orpheus is vol. vi, vage and a rude period, could not long prevail among lighted with their chariots, their horses, and their

still playing on his harp, and the warriors are still deP: 136.

an enlightened and civilized people. When the times 34 and afterof rapine and violence therefore began to cease ; when

The place of torment is at some distance. wards ac

societies regulated by certain laws began to be etablithcording to ed; when martial prowess was less requisite, and the A gaping gulf, which to the centre lies,

His hell. moral di- qualities of the heart had begun to give an importance And twice as deep as earth is distant from the skies; tinctions.

to the character, the future state was also modelled on From hence are heard the groans of ghosts, the pains a different plan. In the Æneid of Virgiờ, an author Of sounding lashes, and of dragging chains. of a highly cultivated mind, and of polithed manners, Here, those who brother's better claim disown, it becomes a place of the most impartial and unerring Expel their parents, and usurp the throne; justice ; every one now receives a sentence suited to the Defraud their clients, and, to lucre sold, actions of his past life, and a god is made to preside in Sit brooding on unprofitable gold. judgement;

Who dare not give, and even refuse to lend,

To their poor kindred, or a wanting friend. Who hears and judges each committed crime, Vaft is the throng of these ; nor less the train Inquires into the manner, place and time,

Of luftful youths for foul adult'ry llain.

Hofts

in the skies. One foul of the hero is therefore repining with the ghosts of mortals in the regions belowy, while
the other is enjoying all the happiness of the gods above. (See Odysey, book ii. near the end). Philosophers fince have improved on this hint of the poet; and men have now got rational, animal, and vegetable fouls, to which fometimes a fourth one is added, as properly belonging to matter in general. Homer infinuates, that

Menelaus was to be translated to Elyfium without tasting death. This Elyfium is the habitation of men, and

Page 11

Refurrec. Hofts of deserters, who their honour fold,

conscience; and support their opinion by observing, that Resurrec. And bafely broke their faith for bribes of gold : matter cannot act upon spirit; forgetting, perhaps, that All these within the dungeon's depth remain,

at the resurrection the spirit is to be clothed with a bo- Delpairing pardon, and expecting pain.

dy, and, at any rate, that it is not for man vainly to prescribe bounds to Omnipotence.

42 The souls of babes, of unhappy lovers, and some What seems to have tortured the genius of divines of the mid-

others, seem to be placed in a paradise of fools residing much more than heaven or hell, is a middle state. On die ftate, fools.

and diffein a quarter distinct from Elysian Tartarus and Purga- this subject there being little revealed in Scripture,

rent opi. tory.

many kave thought it incumbent upon them to supply nions about It is curious to observe, how much these ideas of a the defect; which they feem to have done in different it. future state differ from the vague and simple conjectures ways. From the Scriptures speaking frequently of the of rude nations; and yet from their simple and rude con- dead as sleeping in their graves, those who imagine that jectures, we can easily trace the successive changes in the powers of the mind are dependent on the body, fupthe writings of Homer, Plato, and Virgil; and may ea- pose that they sleep till the resurrection, when they are fily show, that those laws which different nations have to be awakened by the trump of God, reunited to their prescribed for their dead, have always borne the strong bodies, have their faculties rehored, and their sentence eft analogy to their state of improvement, their system awarded. of opinions, and their moral attainments. Some na- This opinion they fupport by what St Peter says in tions, as those of India, have fancied a number of hea. the Acts, that David is not ascended into heaven ; and vens and hells, corresponding to some of their principal that this patriarch could not possibly be fpeaking of shades in virtue and vice; and have filled each of these himself when he said, “ Thou wilt not leave my foui in

43 places respectively with all the scenes of happiness and hell, i.e. the place of the dead." They observe, too, According misery, which friendship and hatred, admiration, con- that the victory of Christ over death and the grave

to some a

ftate of tempt, or rancour, could suggeit. But having already seems to imply, that our souls are subject to their power;

Пleep ; observed the progress of the human mind in forming the that accordingly the Scripture fpeaks frequently of the grand and leading ideas of a future state, we mean not soul's drawing near to, of its being redeemed from, and to descend to the modifications which may have occurred of its descending into, the grave ; that the Psalmist, to particular nations, fects, or individuals.

however, declares plainly, that when the breath of man The belief of Christians respecting futurity demands goeth forth, he returneth to his earth, and that very of the dead our attention, as being founded on a different principle, day his thoughts perish. And should any one choose to as revealed

namely, on express revelations from heaven. From in Scrip

cenfult Ecclefiaftes, he will find, that the living know many express declarations in Scripture - all Christians that they shall die, but that the dead know not any seem to be agreed, that there is a heaven appointed for thing: that their love, and their hatred, and their en- the good and a hell for the wicked. In this heaven vy, are perished ; and that there is no work, nor de the saints dwell in the presence of God and the uninter- vice, nor wisdom, nor knowledge, in the grave, whi- . rupted fplendors of day. Those who have been wise ther they are gone.

44 shine as the firmament, and those who have converted Those who believe that the soul is not for the exercise According

many to righteousness as the stars. Their bodies are of its faculties dependent on the body, are upon its se. to others, aa 40 glorious, immortal, incorruptible, not subject to disease, paration at death obliged to dispose of it some other way.

conscious The nature to pain, or to death. Their minds are strangers to sor- In establishing their theory, they usually begin with at- existence.. of heaven. row, to crying, to disappointment; all their desires are tempting to prove, from Scripture or tradition, both its

presently satisfied; while they are calling, they are an- active and separate existence; but with proofs from tra- fwered ; while they are speaking, they are beard. Their dition we intend not to meddle. Their arguments from mental faculties are also enlarged; they no more fee Scripture being of more value, deserve our serious confi- things obscurely, and as through a cloud, but continual. deration; and are nearly as follow. ly beholding new wonders and beauties in creation, are Abraham, they fay, Isaac, and Jacob, are ftill living, constantly exclaiming, “ Holy, holy, holy ! is the Lord because Jehovah is their God, and he, it is allowed, is of Hofts, worthy is he to receive glory, and honour, and not the God of the dead, but of the living. But their thanksgiving; and to him be ascribed wisdom, and opponents reply, That this is the argument which our power, and might; for great and marvellous are his Saviour brought from the writings of Mofes to prove a

works, and the whole universe is filled with his glory." future resurrection of the dead; and that any perfor Of hell. Their notions of hell differ considerably. Some un who looks into the context, will see it was not meant of

derstanding the Scriptures literally, have plunged the a middle state. From the dead living unto God, our wicked into an abyss without any bottom ; have made Saviour infers nothing more than that they fall live at. this gulf darker than night ; have filled it with ranco. the resurrection, and that these gentlemen would do rous and malignant spirits, that are worse than furies ; well in future to make a distinction between simply liv- and have described it as full of sulphur, burning for ing and living unto God : For though Abraham, Ifaac,

This frightful gulf has by fome been placed in and Jacob, be living unto God, our Saviour has assured the bowels of the earth; by some in the sun ; by fome us that Abraham is dead, and the prophets dead.

in the moon; and by some in a comet : but as the Scrip- A fecond argument is that glimpse which St Paul

his Second Epiftle to the Corinthians. To this argu- Others imagine, that the fire and sulphur are here to ment their opponents reply, That as St Paul could not be taken in a figurative sense. These suppose the tor- tell whether, on that occasion, he was out of the body ments of hell to be troubles of mind and remorses of or in the body, it is more than probable that the whole

was

Page 12

Retire. every fide No exertion is necessary. Objects pour

nor will it indurate so as to endanger the breaking the Retracts themselves into the lenses, and it would be difficult to necks of the vefsels when teken off.",

# Retort.

prevent their admittance. But, in retirement, there RETRACTS, among horfemen, pricks in a horse's mult be a spirit of philosophy and a store of learning, feet

, arifing from the fault of the farrier in driving nails or else the fancied scenes of bliss

aoith like the co- that are weak, or in driving them ill-pointed, or otherlours of the rainbow. Poor Cowley might be faid to be wise amiss. melancholy mad, He languished for folitude; and wish- RETREAT, in a military senfe. -An army or body ed to hide himself in the wilds of America, But, alasd+ of men are said to retreat when they turn their backs he was not able to support the folitude of a country vil upon the enemy, or are retiring from the ground they lage within a few miles of the metropolis!

occupied : hence every march in withdrawing from the “ With a virtuous and cheerful family, with a few enemy is called a retreal. faithful and good-humoured friends, with a well-select- That which is done in sight of an active enemy, whor ed collection of elegant books, and with a competency, pursues with a fuperior force, is the most important part one may enjoy comforts even in the deserted village, of the subject ; and is, with reason, looked upon as the which the city, with all its diversions, cannot fupply glory of the profession. It is a manouvre the most des

RETORT, in Chemistry, an oblong or globular vef- licate, and the propereft to display the prudence, genius, fel of glals or porcelain, with its neck bent, proper for courage, and address, of an officer who commands 5, distillation.

0598 ? 19 ore 4: the historians of all ages testify it; and historians have 1 p. In the fifth volume of the Transactions of the Lon- never been so lavifh of culogiums as on the subject of

Society for the Encouragement of Arts, p. 96. we the brilliant retreats of our heroes. If it is important, find a paper containing a method for preventing-stone it is no less difficult to regulate, on account of the raretorts from breaking; or stopping them when crack. riety of circumstances, each of which demands differents ed, during any chemical operation, without losing any principles, and an almost endless detail. Hence a goodo of the contained subject. -- I have always found it ne- retreat is esteemed, by experienced officers, the waiter's ceffary (says the writer) ito ufe a previous coating for piece of a general

. He hould therefore be well acab filling up the interfices of the earth or stone, which is quainted with the fituation of the country through made by dissolving two ounces of borax in a pint of which he intends to make it, and careful that nothing is boiling water, and adding to the folution as much la- omitted to make it safe and honourable., See WAR.? ked lime as will make it into a thin paste; this, with a RETREAT, is also a beat of the drum, at the firing common painter's brush, may be spread over several se- of the evening gun, at which the drum-major, with all torts, which when dry are then ready for the proper the drums of the battalion, except such as are upon dupreserving oqating. The intention of this first coating ty, beats from the camp.colours on the right to those is, that the fubftances

, thus spread over, readily vitrify- i on the left, on the parade of encampment, the drums ing in the fire, prevent any of the distilling matters from: of all the guards beat allo; the trumpets at the fame> peryading the retort, but do in nowile prevent it from time founding at the head of their respective troops.c cracking time

This is to warn the soldiers to forbear firing, and the - Whenever I want to use any of the above coated : centinels to challenge, till the break of day that the retorts; after I have charged them with the substance, reveille is beat. The retreat is likewise called setting the to be distilled, I prepare a thin parte, made with com- watch. mon linseed oil and Naked lime well mixed, and perfecta, RETRENCHMENT literally signifies something ly, plastic, that it may be easily spread : with this let» cut off or taken from a thing; in which fenfe it is the the retorts be covered all over except that part of the same with fubtraction, diminution, &c. neck which is to be inserted into the receiver ; this is RETRENCHMENT, in the art of war, any kind of readily done with a painter's brolhs: the coating will work raised to cover a poft, and fortify it against the be sufficiently dry in a day or two, and they will then enemy, such as fascines loaded with earth, gambions, be fit for ulçh With this coating 1 bave for several barrels of earth, fand-bags, and generally all things that years worked my stone retorts, without any danger of can cover the men and ftop the enemy. See FORTIFI. their breaking, and have frequently used the same re- CATION and WAR.O gia tort four or five times ; observing particularly to coat RETRIBUTION, a handsome present, gratuity, or it over with the laft mentioned, composition every time acknowledgement, given instead of a formal falary of it is charged with fresh materials : Before I made use hire, to persons employed in affairs that do not so immeof this expedient, it was an even chance, in conducting diately fall under estimation, nor within the ordinary operations in stone and earthen retorts, whether they commerce in

money. did not crack every time; by which means great lois RETROMINGENTS, in Natural Hisory, a class has been suftained. If at any time during the opera- or division of animals, whose characterific is, that they tion the retorts should crack, spread some of the oil ftale or make water backwards, both male and fee compofition thick on the party and sprinkle fome pow- male. der of Aaked lime on it, and it immediately stops the RETURN (retarna or retorna), in Law, is used in

and prevents any of the difilling matter from divers senses. 1. Return of writs by sheriffs and bailiffs. pervading, even that fubtile penetrating substance the is a certificate made by them to the court, of what they Lolid phosphorus will not penetrate through it. It may have done in relation to the execution of the writ di

. be applied without any danger, even when the retort is rected to them. This is wrote on the back of the writ sed

it is made a little ftiffer, is more by the officer, who thus fends the writ back to the proper for luting,.vessels than any other I ever have court from whence it iflued, in order that it may be tried; because if properly mixed it will never crack, filed. 2. Return of a commission, is a certificate or an

fwer

Page 13

Revenue improvident panagement, is fent molt to nothing ; ber of the fe lepo rate funds, by uniling and blencirlz Revetia

and the cafual profits, 'arifing from the other branches them together; fuperadding the faith of jarliement for
of the cenfus regalis, are likewise almost all of them the general security of the whole. So that there are
alienated from the crown. In order to fupply the de- now only three capital funds of any account, the argit.
' ficiencies of wlich, we are now obliged to have recourse gate fund, and the general fund, called from lucia
i to new methods of railing money, unknown to our early union and addition ; and the South fea fund, being the ancestors; which methods constitute,

produce of the taxes appropriated to pay the interest of
II. The king's extraordinary revenue. For, the 'pub- fuch part of the national debt as was advanced by that lic patrimony being got into the hands of private fub- company and its annuitants: - Whereby' the de párate jeets, it is but reasonable that private contributions funds, which were thus united, are become mutual fe- ihould supply the public service. Which, though it curities for each other; and the whole produce of them, 1 may perhaps fall harder upon fome individuals, whose thus aggregated, liable to pay fuch interest or annuities

ancellors have had no share in the general plunder, as were formerly charged upon each distinct fund: the than upon others, yet, taking the nation throughout, it faith of the legilature being moreover engaged to lup- amounts to nearly the fame'; provided the gain by the ply any calual deficiencies. extraordinary lould appear to be no greater than the The customs, exciles, and other taxes, which are to lofs by the ordinarý revenue. And perhaps, if every support these funds, depending on contigencies, upon gentleman in the kingdom was to be stripped of such of exports, imports, and confumptions, muit neceisarily his lands as were formerly the property of the crown ; be of a very uncertain amount ; but they have always tras to be again subject to the inconveniences of pur- been considerably more than was sufficient to answer the veyance and pre-emption, the oppretlion of forest-laws, charge upon them. The surplusses, therefore, of the and the livery of feodal-lenures; and was to resign in- three greaç national funds, the aggregate, general, and to the king's hands all his royal franchises of waifs

, South-lea funds, over and above the interest and an- - wrecks, eltrays, treasure-trove, mires, deodands, forfei- nuities charged upon them, are directed by statute

tures, and the like; he would find himself a greater 3 Geo. I. c. 7.; to be carried together, and to attend
loler than by paying his quota to such taxes as are ne- the disposition of parliament, and are usually denomi-
ceffary to the support of government. The thing, there- nated the finking fund, because originally dellined to fink fore, to be withed and aimed at in a land of liberty, is and lower the national debt. To this have been fince by no means the total abolition of taxes, which would added many other entire daties, granted in fubsequent draw after it very pernicious consequences, and the very years ; and the annual interest of the sums borrowed on fuppoftion of rwhich is the height of political absurdity. their respective credits is charged 0nt, and payables out

For as the true idea of government and magistraçy will of, the produce of the finking fund. However, the nett • be found to confist in this, that fome few men are de- furplusses and savings, after all deductions paid, amount

puted by many others to preside over public affairs, so annually to a very considerable. fum, For as the in- that individuals may the better be enabled to attend terest on the national debt has been at leveral times re- their private concerns; it is necessary that those indivi- duced (by the consent of the proprietors, who had their duals should be bound to contribute a portion of their option either to lower their intereft or be paid their private gains, in order to support that government, and principal), the savings from the appropriated revenues reward that magistracy, which prote&s them in the on- muit needs be extremely large. joyment of their respective properties. But the things But, before any part of the aggregate fund (the, sur- to be aimed at are wisdom and moderation, not only in plusses whereof are one of the chief ingredients that granting, but also in the method of raising, the necessary form the sinking fund) can be applied to diminish the fupplies ; by contriving to do both in such a manner as principal of the public debt, it ftands mortgaged by may be most conducive to the national welfare, and at parliament to raise an annual fum for the maintenance - the same time molt confistent with economy and the li- of the king's household and the civil lift. For this pur-

berty of the subjeet ; who, when properly taxed, contri. pose, in the late reigns, the produce of certain branches butes only, as was before observed, some part of his pro- of the excise and culloms, the polt-office, the duty on perty in order to enjoy the rest...

wine licences, the revenues of the remaining, crown- These extraordinary grants are usually called by the lands, the profits arising from courts of justice, (which

Tynonymous names of aids, fulfidies, and Supplies; and articles include all the hereditary revenues of the crown),

The clear nett produce of the several branches of jesty's household, and the honour and dignity of the the revenue, after all charges of collecting and ma- crown. And, as the amount of these several branches

Tagement paid, amounted in the year 1786, to about was uncertain, (though in the last reign they were com-

tional debt. See NATIONAL Debi and Funds. nified his consent that his own hereditary revenues might

The respective produces of the several taxes were ori- be fo disposed of as might best conduce to the utility ginally separate and distinct funds; being securities for and satisfaction of the public, and having graciously the fums advanced on each several tax, and for them cepted a linnited sum, the said hereditary and other re. only. But at last it became neceffary, in order to avoid venues are now carried into, and made a part of, the ag-

confusion, as they multiplied yearly, to reduce the num- gregate fund; and the aggregate fund is charged with

5
G

the

Page 14

Reversion, number of years not exceeding 40 ; discounting at the to be received 19 years hence, and the rate of interest Reveifez

, rate of 5, 4, and 3 per cent. compound interesi. 5 per cent. is equal to ,6139 X 19,000 = 6139.00001. Revivirca.

or 61391. Again, the present value of 10,000l. due

in ten years, the rate of interest being 3 per cent. is Value at Value at Value ail 6 per ct. 4 perct. 3 per ct.

.7441 X 10,000=7441.

REVERSION of Series, in Algebra, a kind of reversed 1.9524 1.9615 .9709

operation of an infinite feries. See SERIES.

REVETEMENT, in Fortification, a strong wall 21.9070 1.9245 1:9426

built on the outside of the rampart and parapet to fup31.8638 1.88989151 .8227.8548.8385

port the earth, and prevent its rolling into the ditch,

REVIVIFICATION, in Chemisiry, a term general5-7835 1.8219 1.8626

ly applied to the distillation of quicklilver from cinna

bar, 6-7462 7903.8375

REVIVIFICATION, in Physiology, the recalling of ans71.7107 1.75998131 84.6768 173071-7894

mals apparently dead, to lite. There are many kinds of

insects which may be revivificd, after all the powers of 9.6446-7026 -7664 10.6139 .6756-7441

animation have been suspended for a considerable time.

Common flies, small beetles, spiders, moths, bugs, &c. 11.5847 1.6496 -7224

after being drowned in fpirit of wine, and continuing 12.5568 .6246 -7014

apparently dead for upwards of 15 minutes, have been

reitored to life merely by being thrown among wood13-5303 .6006 1.6839

alhes Dighlly warm. 14:5051:5775.661 15-4810.5553 .6419

While Dr Franklin was in France, he received a

quantity of Madeira wine from America, which had 116-4581.4339 .6232

been bottled in Virginia. He found a few dead flies in

fome of the bottles, which he exposed to the fun in the 171.4363-5134 1.6050

month of July; and in less than three hours thefe seem181.4155 .4936 1.5874 191.3957.4746 -5703

ingly dead animals recovered life which had been fo

long suspended. At firit they appeared as if convulsed; 20-3769-4564 -5537

they then raised themselves on their legs, walled their 217-3589 -4388 -5375

eyes with their fore feet, dressed their wings with thote

behind, and in a thort time began to fly about. 221-3418-4219 1.5219

But the most remarkable imitance of revivification we 1231.3255 1.4057.5067

have heard of, is the following. In the warmer pails 124.3100 1.3901:4919

of France there is an infect very pernicious to the rye, 251.2953-3757 1:4776

apparently beginning its operations at the root of ike 26.2812-3607-4637

plant, and gradually proceeding towards the car, If 27.26781-3468-4502

the plant be thoroughly dried while the insect is in the

root or ftem, the animal is irrecoverably killed; but af28.2551 1.3335 .4371

ter it has reached the grain, the cale is very different. 2914229 1-32064243

There have been instances of these insects being brought 30.2314-3003 1:4120

to life in 15 minutes, by a little warm water, after the 31.2204 .2965 1:4000

grains, in which they were lodged, had been kept dry 132.2099 1.2851 -3883

What is the metaphysician to think of these plena33.1999-2741 1:3779

mena, or what conclusion is he to draw from them se(34.1903.2636 -3660 1351.1813 .2534 3554

specting the mind? If he be a sober man he will draw

no conclufion, for this reason, that he knows nothing of 1361.1726 .2437-3450

the fentient principle of insects, or of any animal but

He is conscious that it is the same individual be371.1644 -2343 -3350

ing which in himself, thinks, and wills, and feels; he 38.1566-2253 -3252

knows that part of his thought is not in one place, and 39.1491 .2166 -3158

part of it in another; and therefore he concludes that 40.1420 .2083 -3066

this thinking being is not matter, while experience

teaches him that it quits the material system, when that The use of the preceding table.- To find the present becomes unfit to discharge its funcțions, and cannot be value of any sum to be received at the end of a given recalled. Experience teaches him, on the other hand, terma of years, discounting at the rate of 3, 4, or 5 per that the fentient principle of these inse&s does not quit cent, compound interest. Find by the above table the the syften when unfit for its functions, and hence he present value of il. to be received at the end of the ought to inser, that the minds of men and of insects are. given term; which multiply by the number of pounds very different, and that the bond which unites the maproposed, (cutting off four figures from the product on terial and immaterial parts of an insect, is certainly difaccount of the decimals), then the result will be the ferent from that which unites the mind and body of man, įue fougbt: For example, the present value of 10,000l. This is the only inference which can be fairly drawn,

from

Page 15

It has been said, that the Rhapsodi were peer

of France. It is about four miles in circumference, Rheias clothed in red when they sung the Iliad, and in blue and contains several fine squares, well-built houses, and

Rheum, when they sung the Odyssey. They performed on the magnificent churches. It had a mint, an university, theatres, and sometimes firove for prizes in contests of and five abbeys, the most famous of which is that of St poetry, singing, &c. After the two antagonists had Remy. There are also several triumphal arches and finithed their parts, the two pieces or papers they were other monuments of the Romans. It is feated on the written in were soon joined together again : whence the river Velie, on a plain surrounded by hills, which proname, viz, from

PXT7W f10, and wôn canticum : but there duce excellent wine. E. Long. 4. 8. N. Lat. 49. 14. seem to have been other Rhaplodi of more antiquiiy RHENISH WINE, that produced on the hills about than these people, who composed heroic poems or

Rheims. This wine is much used in medicine as a fongs in praise of heroes and great men, and sung their solvent of iron, for which it is well calculated on accan compositions from town to town for a livelihood; count of its acidity. Dr Percival observes, that it is of which profellion Homer himself is said to have been the best solvent of Peruvian bark ; in which, howSce BARD.

ever, he thinks its acidity has no share, because an adRHAPSODOMANCY, an ancient kind of divina- dition of vinegar to water does not augment its solvent tion performed by pitching on a passage of a poet at power. hazard, and reckoning on it as a prediction of what was RHETORES, amongst the Athenians, were ten to come to pass. There were various ways of practi- in number, elected by lot to plead public causes in the fir.g this rhapsodomancy. Sometimes tbey wrote feve- senate-house or aflembly. For every cause in which ral papers or sentences of a poet on so many pieces of they were retained, they received a drachm out of the wood, paper, or the like, shook them together in an public money. They were sometimes called Eumjegur, urn, and drew out one which was accounted the lot : and their fee to Euryogixoy. No man was admitted to fometimes they cast dice on a table whereon verses were this office before he was 40 years of age, though others written, and that whereon the die lodged contained the fay 30. Valour in war, piety to their parents, pruprediction. A third manner was by opening a book,

dence in their affairs, frugality, and temperance, were and pitching on fome verse at firit fight. This method necessary qualifications for this office, and every candithey particularly called the fortes Præneftina ; and af- date underwent an examination concerning these vir. terwards, according to the poet, made use of fortes Ho- lues, previous to the election. The orators at Rome mericæ, fortes Virgilianæ, &c. See SORTES.

were not unlike the Athenian rhetores. See ORATOR. RHAPSODY, in Antiquity, a discourse in verse fung RHETORIANS, a fect of heretics in Egypt, fo or rehearsed by a rhapsodift. Others will have rhapsody denominated from Rhetorius their leader. The distinto fignify a collection of verses, especially those of Ho- guishing tenets of this heresiarch, as represented by Phi. mer, which having been a long time dispersed in pieces laftrius, was, that he approved of all the heresies before and fragments, were at length by Pisistratus's order di- him, and taught that they were all in the right. gelted into books called rhapsodies, from gantw/wo, and RHETORIC, the art of speaking copiously on any won canticum. Hence, among moderns, rhapsody is also subject, with all the advantages of beauty and force. uled for an affemblage of palages, thoughts, and autho- See ORATORY. rities, raked together from divers authors, to compose RHEUM, a thin ferous humour, occasionally oozing fome new piece.

out of the glands about the mouth and throat, RHE, or REE, a little island in the bay of Biscay, RHEUM, Rhubarb; a genus of plants of the enneandria near the coast of Aunis in France. It was taken during class, and in the ratural method ranking under the 12th the war with France which ended in 1763, in the expe- order, Holoraceæ. See BOTANY and MATERIA MEdition commanded by Hawke and Mordaunt.

DICA Index. Here, after enumerating the species, we RHEA AMERICANA.

The American oftrich of au. thall introduce what has been said on the cultivation of Thors has been frequently mentioned, but till of late this valuable plant. There are five species, viz. 1. The years very imperfectly known.

See ORNITHOLOGY rhaponticum, or common rhubarb, has a large, thick, Index.

fleshy, branching, deeply-striking root, yellowish withRHEEDIA, a genus of plants belonging to the poly. in; crowned by very largę, roundish, heart-Thaped nadria clafs, and in the natural method ranking with those smooth leaves, on thick, slightly-furrowed foot-stalks ; of which the order is doubtful. See BOTANY Index. and an upright strong stem, two or three feet high,

RHEGIUM, in Ancient Geography, so very ancient adorned with leaves fingly, and terminated by thick a city as to be supposed to take its name from the violent close spikes of white flowers. It grows in Thrace and bursting of the coast of Italy from Sicily, thought to Scythia, but has been long in the English gardens. Its have been formerly conjoined (Mela, Virgil). A city root affords a gentle, purge. It is, however, of inferior of the Bruttii, a colony of Chalcidians from Euræa: quality to some of the following forts; but the plant bea strong barrier opposed to Sicily (Strabo); mentioned ing astringent, its young stalks in spring, being cut and by Luke; surnamed Julium (Ptolemy), from a fresh peeled, are used for tarts. 2. The palmatum, palmafupply of inhabitants sent hither by Auguftus, after ted-leaved true Chinese rhubarb, hath a thick fleshy root, driving Sextus Pompeius out of Sicily (Strabo); and yellow within ; crowned with very large palmated leaves, thus was in part a colony, retaining still the right of a being deeply divided into acuminated segments, exmunicipium (Inscription). The city is now called Reg- panded like an open hand; upright {tems, five or fix gio, in the Farther Calabria.

feet high or more, terminated by large spikes of flowers. RHEIMS, a city of France, in the department of This is now proved to be the true foreign rhubarb, the Marne, and capital of Rhemois. It is one of the most purgative quality of which is well known. ancient, celebrated, and largest places in the kingdom, compactum, or Tartarian rhubarb, hath a large, felhy, had an archbishop's see, whose archbishop was a duke and branched root, yellow within; crowned by very large,

Page 16