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SITY.

or law.

Proclamations, are binding upon the subject, where they tained the title of illustrious, and was made pretor of Procopius Proclama

Constantinople.

ll do not either contradict the old laws, or tend to estation

blish new ones ; but only enforce the execution of such PROCREATION, the begetting and bringing forth Prolile. Procopius, laws as are already in being, in such manner as the young. See GENERATION and SEMEN.

king shall judge necessary. Thus the established law PROCTOR, a person commissioned to manage an-
is, that the king may prohibit any of bis subjects froin other person's cause in any court of the civil or eccle-
leaving the realm: a proclamation therefore forbidding siastical law.
this in general for three weeks, by laying an embargo Proctor, in the English universities. See UNIVER-
upon all shipping in time of war, will be equally bind.
ing as an act of parliament, because founded upon a pri PROCURATION, an act or instrument by wbich a

a
But a proclamation to lay an embargo in time person is empowered to treat, transact, receive, &c. in
of peace upon all vessels laden with wheat, (though in

another person's name.
the time of a public scarcity), being contrary to law, PROCURATOR. See PROCTOR.
and particularly to statute 22 Car. II. c. 13. the ad. PROCYON, in Astronomy, a fixed star of the second
visers of such a proclamation, and all persons acting magnitude, situated in canis minor, or the little dog.
under it, found it necessary to be indemnified by a spe-

PRODIGALITY, means extravagance, profusion,
cial act of parliament, 7 Geo. III. c. 7. A proclama- waste, or excessive liberality, and is the opposite ex-
tion for disarming Papists is also binding, being only treme to the vice of parsimony. By the Roman law, if
in execution of what the legislature has first ordained : a man by notorious prodigality was in danger of wasting
but a proclamation for allowing arms to Papists, or for his estate, he was looked upon as non compos, and com-.
disarming any Protestant subjects, will not bind; be mitted to the care of curators, or tutors, by the prætor.
cause the first would be to assume a dispensing power, And by the laws of Solon, such prodigals were branded:
the latter a legislative one ; to the vesting of either of with perpetual infamy.
which in any single person the laws of England are ab PRODUCT, in Arithmetic and Geometry, the factum
solutely strangers. Indeed, by the stat. 31 Hen. VIII, of two or more numbers, or lines, &c. into one another:.
c. 8. it was enacted, that the king's proclamations thus 5 X 4=20 the product required.
should bave the force of acts of parliament; a statute, PROEDRI, among the Athenians, were magistrates,
which was calculated to introduce the most despotic ty who had the first seats in the public assemblies, and whose
ranny: and which must have proved fatal to the liber office it was to propose at each assembly the things to be
ties of this kingdom, had it not been luckily repealed deliberated upon and determined. Their office always
in the minority of his successor, about five years after. ended with the meeting. Their vumber was vine, so
By a late act of parliament the king is empowered to long as the tribes were ten in number.
raise regiments of Roman Catholics to serve in the pre PROFANATION, the acting disrespectfully to sa--
sent war.

cred things.
PROCLUS, surnamed DIADocus, a Greek philo PROFANE, a term used in opposition to holy ; aud
sopher and mathematician, was born in Lycia, and lived in general is applied to all persons who have not the sa-
about the year 500. He was the disciple of Syrianus, cred character, and to things which do not belong to the
and had a great share in the friendship of the emperor

service of religion.
Anastasis. It is said, that when Vitalian laid siege to PROFESSION means a calling, vocation, or known
Constantinople, Proclus burnt his ships with large bra employment. In Knox's Essays, vol. i. page 234, we
zen speculums. This philosopher was a Pagan, and find an excellent paper on the choice of a profession,
wrote against the Christian religion. There are still ex which that elegant writer concludes thus : “All the
tant his Commentaries on some of Plato's books, and occupations of life (says he) are found to have their ad-
other of his works written in Greek.

vantages and disadvantages admirably adapted to preserve
PROCONSUL, a Roman magistrate, sent to govern the just equilibrium of happiness. This we may confi-
a province with consular authority.

dently assert, that, whatever are the inconveniencey of
The proconsuls were appointed out of the body of any of them, they are all preferable to a life of inac-
the senate ; and usually as the year

of
any
one's con-

tion; to that wretched listlessness, which is constrained
sulate expired, be was sent proconsul into some pro to pursue pleasure as a business, and by rendering it the
vince.

object of severe and unvaried attention, destroys its very
The proconsuls decided cases of equity and justice, essence.”
either privately in their pretorium or palace, where they Among the Romanists profession denotes the entering
received petitions, heard complaints, granted writs un into a religious order, wherely a person offers himself
der their seal, and the like; or else publicly, in the com to God by a vow of inviolably observing obedience, cha-
mon hall, with the usual formalities observed in the court stity, and poverty.
of judicature at Rome. They bad besides, hy virtue of PROFESSOR, in the universities, a person who
their edicts, the power of ordering all things relating teaches or reads public lectures in some art or science
to the tributes, taxes, contributions, and provisions of from a chair for that purpose.
corn and money, &c. Their office lasted only a year. PROFILE, in Architecture, the draught of a build-
See ConsuL.

ing, fortification, &c. wherein are expressed the several
PROCOPIUS, a famous Greek historian, born in heights, widths, and thicknesses, such as they would ap-.
Cæsaria, acquired great reputation by his works in the pear were the building cut down perpendicularly from
reign of Justinian, and was secretary to Belisarius du- the roof to the foundation. Whence the profile is also
ring all the wars carried on by that general in Persia, called the section, sometimes orthugreprical section, ard:
Africa, and Italy. He at length became senator, ob- by Vitruvius also sciagraphy,

Profle,

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argue

ner.

Profile, in this sense, amounts to the same with eleva ment concerning the event of a disease; as whether it progeste tion ; and stands opposed to plan or ichnography. shall end in life or death, be short or long, mild or ma

PROFILE is also used for the contour or outline of a lignant, &c. figure, building, member of architecture, or the like; PROGRAMMA, anciently signified a letter sealed as a base, a cornice, &c. Hence profiling is sometimes with the king's seal. used for designing, or describing the member with rule, Programma is also an university term for a billet or compass, &c.

advertisement, posted up or given into the band, by way PROFILE, in sculpture and painting.--A head, a por of invitation to an oration, &c. containing the trait, &c. are said to be in profile, when they are repre ment, or so much as is necessary for understanding thereof. sented sidewise, or in a side-view; as, when in a portrait PROGRESSION, in general, denotes a regular adthere is but one side of the face, one eye, one cheek, vancing, or going forwards, in the same course and man&c. shown, and nothing of the other.-On almost all medals, the faces are represented in profile.

PROGRESSION, in Mathematics, is either arithmetical PROFLUVIUM, in Medicine, denotes a flux, or li or geometrical. Continued arithmetic proportion is, quid evacuation of any thing.

where the terms do increase and decrease by eqnal difPROGNOSTIC, among physicians, signifies a judge- ferences, and is called arithmetic progression : Thusa, atd, a +2d, a+3d, &c. increasing 2

by the difference d. In numbers

§ 2, 4, 6, 8, 10, &c. increasing

710, 8, 6, 4, 2, &c. decreasing by the difference 2.
Geometric Progression, or Continued Geometric Proportion, is when the terms do increase or decrease by equal
ratios : thus,
a, ar, arr, arrr, &c. increasing
from a continual multiplication

byr
a,
que
&c. decreasing

{ division
2, 4, 8, 16, 32, 64, increasing

from a continual
s multiplication

by 2.
64, 32, 16, 8, 4, 2, decreasing

2 division See the articles Fluxions, GEOMETRY, and SERIES.

a, =, &

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the science.

2

bodies,

theory.

Object of THIS is the name for that part of mechanical philo that it would be ridiculous affectation to pay any regard sophy which treats of the notion of bodies any to the deviations from equality and parallelism. A bul

. how projected from the surface of this earth, and influ let rising a mile above the surface of the earth loses only enced by the action of terrestrial gravity.

Toto of its weight, and a horizontal range of 4 miles
Effect of It is demonstrated in the physical part of astronomy, makes only 4' of deviation from parallelism.
gravity on that a body so projected must describe a conic section, Let us therefore assume gravitation as equal and pa-
projected having the centre of the earth in one focus ; and that it rallel. The errors arising from this assumption are

will describe round that focus areas proportional to the quite insensible in all the uses which can be made of this
times. And it follows from the principles of that sci-
ence, that if the velocity of projection exceeds 36700 The theory itself will ever be regarded with some ve-
feet in a scond, the body (if not resisted by the air) neration and affection by the learned.

It was the first
would describe a hyperbola; if it be just 36700, it would fruits of mathematical philosophy. Galileo was the first
describe a parabola ; and if it be less than this, it would who applied mathematical knowledge to the motions of
describe an ellipsis. If projected directly upwards, in the free bodies, and this was the subject on which he exer-
first case, it would never return, but proceed for ever; cised his fine genius.
its velocity continually diminishing, but never becoming Gravity must be considered hy us as a constant or u.
less than an assignablé portion of the excess of the initial niform accelerating or retarding force, according as it is to
velocity above 36700 feet in a second; in the second produces the descent, or retards the ascent, of a body.
case, it would never return, its velocity would diminish A constant or invariable accelerating force is one which
without end, but never be extinguished. In the third produces an uniform acceleration ; that is, which in
case, it would proceed till its velocity was reduced to an equal times produces equal increments of velocity, and
assignable portion of the difference between 36700 and therefore produces increments of velocity proportional
its initial velocity; and would then return, regaining its to the times in which they are produced. Forces are of
velocity by the same degrees, and in the same places, as themselves imperceptible, and are seen only in their ef-
it lost it

. These are necessary consequences of a gravity fects; and they have no measure but the effect, or what directed to the centre of the earth, and inversely propor measures the eflect; and every thing which we can distional to the square of the distance. But in the greatest cover with regard to those measures, we must aflirm with projections that we are able to make, the gravitations regard to the things of which we assume them as the are so nearly equal, and in directions so nearly parallel, measures. Therefore,

The

4

The space

7

The motion of a falling body, or of a body projected half the length of the pendulum, as the circumference Conse. directly downwards, is uniformly accelerated, and that of a circle is to its diameter. The length of a penduquences of

of a body projected directly upwards is uniformly re lum can be ascertained with great precision ; and it can this fact.

tarded : ihat is, the acquired velocities are as the times be lengthened or shortened till it makes just 86,403
in which they are acquired by falling, and the extin vibrations in a day: and this is the way in which the
guished velocities are as the times in wbich they are space fallen through in a second has been accurately as-
extinguished.

certained.
Corollaries Cor. 1. If bodies simply fall, not being projected As all other forces are ascertained by the accelera-
drawn front downwards by an external force, the times of the falls tions which they produce, they are convenienty mea-
it.

are proportional to the final velocities ; and the times of sured by comparing their accelerations with the accele-
ascents, which terminate by the action af gravity alone, ration of gravity. This therefore has been assumed by
are proportional to the initial velocities.

all the later and best writeis on mechanical philosophy,
2. The spaces described by a heavy body falling from as the unit by which every other force is measured. It
rest are as the squares of the acquired velocities; and gives us a perfectly distinct notion of the force which
the differences of these spaces are as the differences of retains the moon in its orbit, when we say it is the
the squares of the acquired velocities: and, on the other 36octh part of the weight of the moon at the surface of
hand, the heights to which bodies projected upwards the earth. We niean by this, that it a bullet were bere
will rise, before their motions be extinguished, are as weighed by a spring steelyard, and pulled it out to the
the squares of the initial velocities.

mark 3600; if it were then taken to the distance of the 3. The spaces described by falling bodies are propor moon, it would pull it out only to the mark 1. And tional to the souares of the times from the beginning of the we make this assertion on the authority of our having fall; and the spaces described by bodies projected directly observed that a body at the distance of the moon falls upsards are as the squares of the times of the ascents. from that distance zoro part of 16 feet in a second.

4. space described by a body falling from rest is We do not, therefore, compare the forces, which are one half of the space which the body would have uni- imperceptible things; we compare the accelerations, formly described in the same time, with the velocity ac which are their indications, effects, and measures. quired by the fall.--And the height to which a body This las made philosophers so anxious to determine Two modes will rise, in opposition to the action of gravity, is one with precision, the fall of beavy bodies, in order to bave of deterbalf of the space which it would uniformly describe in an exact value of the accelerating porser of terrestrial mining the the same time with the initial velocitv.

gravity. Now we must here observe, that this measure

vy bodies. In like manner the difierence of the spaces which a may be taken in two ways: we may take the space falling or rising body describes in any equal successive through which the heavy body falls in a second; or we parts of its fall or risc, is one half of the space which it may take the velocity which it acquires in consequence would uniformly describe in the same time with the of gravity having acted on it during a second. The difference of the initial and final velociues.

Jast is the proper measure ; for the last is the immediate This proposition will be more conveniently expressed effect on the body. The action of gravity has changed for our purpose thus:

the state of the body--in what way? By giving it a deA body moving uniformly during the time of any termination to notion downwards, this both points out fall with the velocity acquired thereby, will in that time the kind and the degree or intensity of the force of describe a space double of that fall; and a body pro gravity. The space described in a second by falling, jected directly upwards will rise to a height which is is not an invariable measure; for, in the successive se. one balf of the space which it would, uniformly con conds, the body falls through 16, 48, 80, 112, &c. tinued, describe in the time of its ascent with the initial feet, but the changes of the body's state in each second velocity of projection.

is the same. At the beginning it bad no determination These theorems liave been already demonstrated in a to move with any appreciable velocity; at the end of popular way, in the article GUNNERY. But we would the first second it had a determination by which it recommend to our readers the 39th prop. of the first would have gone on for ever (had no subsequent force book of Newton's Principia, as giving the most general acted on it) it the rate of 32 feet per second. At the investigation of this subject ; equally easy with these end of the second second, it had a determination by more loose methods of demonstration, and infinitely su which it would have moved for ever, at the rate of 64 perior to them, by being equally applicable to every feet per second. At the end of the third second, it variation of the accelerating force. See an excellent bad a determination by which it wonld have moved application of this proposition by Mr Robins, for defin for ever, at the rate of g6 feet per second, &c. &c. ing the motion of a ball discharged from a cannon, in The difference of these determinations is a deiermination the article GUNNERY, N° 15.

to the rate of 32 feet per second. This is therefore The force

5. It is a matter of observation and experience, that constant, and the indication and proper measure of the of gravity a heavy body falls 16 feet and an inch English measure constant or invariable force of gravity. The space falin falling in a second of time ; and therefore acquires the velocity len through in the first second is of use only as it is Bodies can of 32 feet 2 inches per second. This cannot be ascer one half of the measure of this determination ; and as tained.

tained directly, with the precision that is necessary. A halves have the proportion of their wholes, different ac-
second is too small a portion of time to be exactly mea celerating forces may be safely affirmed to be in the pro-
sured and compared with the space described; but it portion of the spaces through which they uniformly im 8
is done with the greatest accuracy by comparing the pel bodies in the same time. But we should always re- Mistakes of
motion of a falling body with that of a pendulum. The collect, that this is but one half of the true measure of matheme-

ticians on time of a vibration is to the time of falling through the accelerating force. Mathematicians of the first rank this subject Vol. XVII. Part I.

+
3 D

bave

6

10

have committed great mistakes by not attending to this ; Leibnitz is one of the most obscure of his obscure witand it is necessary to notice it just now, because cases will ings, but deserves the attention of an intelligent and occur in the prosecution of this subject, where we shall be curious reader, and cannot fail of making an indelible very apt to confound our reasonings by a confusion in the impression on his mind, with relation to the modesty, use of those measures. Those mathematicians who are candour, and probity of the author. It is preceded accustomed to the geometrical consideration of curvili- by a dissertation on the subject which we are now enneal motions, are generally disposed to take the actual de- tering upon, the motion of projectiles in a resisting meflection from the tangent as the measure of the deflecting dium. Newton's Principiu had been published a few force; while those who treat the same subject algebrai- years before, and bad been reviewed in a manner shamecally, by the assistance of fluxions, take the change of fully slight, in the Leipsic Acts. Both these subjects

velocity, which is measured by twice the deflection. The make the capital articles of that immortal work. Mr Plate reason is this: when a body passes through the point B Leibnitz published these dissertations, without (says be) CCCCXLI. of a curve ABC, fig. 1. if the deflecting force were to having seen Newton's book, in order to show the world fig. 1.

cease at that instant, the body would describe the tan that he had, some years before, discovered the same
gent BD in the same time in which it describes the arch theorens. Mr Nicholas Fatio carried a copy of the
BC of the curve, and DC is the deflection, and is Principia from the author to Hanover in 1686, where
therefore taken for the measure of the deflecting force. he expected to find Mr Leibnitz; he was then absent,
But the algebraist is accustomed to consider the curve but Fatio saw him often before his return to France in
by means of an equation between the abscissä Ha, 1687, and does not say that the book was not given him.
Hb, Hc, and their respective ordinates Aa, Bb, Cc; Read along with these dissertations Dr Keill's letter to
and he measures the deflections by the changes made on John Bernoulli and others, published in the Journal Lite-
the increments of the ordinates. Thus the increment of raire de la Huyeé 1714, and to John Bernoulli in 1719.
the ordinate A a, while the body describes the arch AB Newton has been accused of a similar oversight by Newter as
of the curve, is BG. If the deflecting force were to John Bernoulli, (who indeed calls it a mistake in prin- cused d's
cease when the body is at B, the next increment would ciple) in his Proposition x. book 2. on the very sub- simlar mais
have been equal to BG, that is, it would have been EF; ject we are now considering. But Dr Keill has shown

take by J.

Burnoulli but in consequence of the deflection, it is only CF: there it to be only an oversight, in drawing the tangent on fore he takes EC for the measure of the deflection, and of the wrong side of the ordinate. For in this very prothe deflecting force. Now EC is ultimately twice DC; position Newton exhibits, in the strictest and most beauand thus the measure of the algebraist (derived solely tiful manner, the difference between the geometrical from the nature of the differential method, and without and algebraical manner of considering the subject; and any regard to physical considerations) happens to coin- expressly warns the reader, that his algebraical symbol cide with the true physical measure. There is therefore expresses the deflection only, and not the variation of great danger of mixing these measures. Of this we can the increment of the ordinate. It is therefore in the Bat felse's

. Particular- not give a more remarkable instance than Leibnitz's at last degree improbable that he would make this misly of Leib- tempt to demonstrate the elliptical motion of the planets take. He most expressly does not; and as to the real

in the Leipsic Acts, 1689. He first considers the sub- mistake, which he corrected in the second edition, tbe
ject mechanically, and takes the deflection or DC for writer of this article has in his possession a manuscript
the measure of the deflecting force. He then intro copy of notes and illustrations on the whole Principia,
duces bis differential calculus, where he takes the dif written in 1693 by Dr David Gregory, Savilian professor
ference of the increments for the measure ; and thus of astronomy at Oxford, at the desire of Mr Newton,
brings bimself into a confusion, which luckily compen. as preparatory for a new edition, where he has rectified
sates for the false reasoning in the preceding part of this and several other mistakes in that work, and says
his paper, and gives bis result the appearance of a that Mr Newton had seen and approved of the amend-
demonstration of Newton's great discovery, while, in ments. We mention these particulars, because Mr Insincerity
fact, it is a confused jumble of assumptions, self-con- Bernoulli published an elegant dissertation on this sub- of Berne.
tradictory, and inconsistent with the very laws of me ject in the Leipsic Acts in 1713; in which be charges wilde te
chanics which are used by bim in the investigation. Newton (though with many protestations of admiration
Seventeen years after this, in 1706, having been cri. and respect) with this mistake in principle; and says,
ticised for his band reasoning, or rather accused of an that he communicated his correction to Mr Newton, by
envious and unsuccessful attempt to appropriate New his nephew Nicholas Bernoulli, that it might be cor-
ton's invention to himself, he gives a correction of his rected in the new edition, which he heard was in the
paralogism, which he calls a correction of language. press,

And he afterwards adds, that it appears by But he either had not observed where the paralogism some sheets being cancelled, and new ones substituted lay, or would not let himself down by acknowledging in this part of the work, that the mistake would have a mistake in what he wisbed the world to think his own continued, had be not corrected it. We would desire calculus (fluxions); he applied the correction where no our readers to consult this dissertation, which is ex. fault had been committed, for he had measured both tremely elegant, and will be of service to us in this artithe centrifugal force and the solicitation of gravity in the cle; and let them compare the civil things which is bere same way, but had applied the fluxionary expression to said of the vir incomparabilis, the omni laude major, the last and not to the first, and, by so doing, he com the summus Newtonus, with what the same author, in pletely destroyed all coincidence between his result and the same year, in the Leipsic Acts, but under a borthe planetary motions. We mention this instance, not rowed name, says of him. Our readers will have only as a caution to our mathematical readers, but also no hesitation in ascribing this letter to this author. as a very curious literary anecdote. This dissertation of For, after praising John Bernoulli as summus geometra,

natus

(1

spect to

Newton.

v=56. =,=Vh.7°=h, =49 feet.

3029

13

18

natus ad summorum geometarum paralogismos corrigen- or the height through which a body must fall to acquire 16

In bolies dos, summi candoris ut et modestiæ, he betrays himself this velocity.

projected by an unguarded warmth, when defending J. B.'s de

66

upwards, monstration of the inverse problem of centripetal forces, by calling it MEAM demonstrationem. Let our readers now consider the scope and inten

or 56*=3136. tion of this dissertation on projectiles, and judge whether

=49

feet.

64 the author's aim was to instruct the world, or to acquire

17

5. Suppose a body projected directly downwards with and directfame, by correcting Newton. The dissertation does

the velocity of 10 feet per second; what will be its ve-ly downnot contain one theorem, one corollary, nor one step

of argument, which is not to be found in Newton's first locity after four seconds ? In four seconds it will bave wards. edition ; nor has he gone farther than Newton's single acquired, by the action of gravity, the velocity of 4 x 32,

or 128 feet, and therefore its whole velocity will be 138 proposition the xth. To us it appears an exact com

feet per second.
panion to his proposition on centripetal forces, which he

6. To find how far it will have moved, compound its
boasts of having first demonstrated, although it is in
every step a transcript of the 42d of the first Book of conds, with the motion which gravity alone would have

motion of projection, which will be 40 feet in four se-
Newton's Principia, the geometrical language of New- given it in that time, which is 256 feet ; and the whole
ton being changed into algebraic, as he has in the pre- motion will be 296 feet.
sent case changed Newton's algebraic analysis into a

7. Suppose the body projected as already mentioned,
very elegant geometrical one.

and that it is required to determine the time it will take We hope to be forgiven for this long digression. It

to go 296 feet downwards, and the velocity it will have is a very curious piece of literary history, and shows

acquired. tbe combination which envy and want of honourable

Find the height x, through which it must fall to acprinciple had formed against the reputation of our illu- quire the velocity of projection, 10 feet, and the time strious countryman ; and we think it our duty to em

y of falling from this height. Then find the time % of brace any opportunity of doing it justice.To return

falling through the height 296+x, and the velocity v to our subject : Accurate The accurate measure of the accelerative power of acquired by this fall. The time of describing the 296

zy, v measure of gravity, is the fall 161, feet, if we measure it by the From such examples, it is easy to see the way of an. the accele- space, or the velocity of 325 feet per second, if we take er or pow. the velocity. It will greatly facilitate calculation, and swering every question of the kind.

Writers on the higher parts of mechanics always More geneer of gravi-will be sufficiently exact for all our purposes, if we take compute the actions of other accelerating and retarding al forma16 and 32, supposing that a body falls 16 feet in a se

forces by comparing them with the acceleration of gra-læ cond, and acquires the velocity of 32 feet per second.vity, and in order to render their expressions more geneThen, because the heights are as the squares of the ral, use a symbol, such as g for gravity, leaving the reatimes, and as the squares of the acquired velocities, a

der to convert it into numbers. Agreeably to this body will fall one foot in one fourth of a second, and view, the general formulæ will stand thus : General

will acquire the velocity of eight feet per second. Now formula de let h express the height in feet, and call it the PRO I. v=v2gh, i. e. v2V&V h, =g ?, DUCING HEIGHT; v the velocity in feet per second, and

47 47 2h call it the PRODUCED VELOCITY, the velocity DUE ;

2

II. t= and t the time in seconds. We shall have the follow

28

28 ing formulæ, which are of easy recollection, and will

IIII. h=
serve, without tables, to answer all questions relative to

28
projectiles.
I. v=8h,= 8 x 41,=320

In all these equations, gravity, or its accelerating

power, is estimated, as it ought to be, by the cbange
II. (=
. 22

of velocity which it generates in a particle of matter in
4 32

an unit of time. But many mathematicians, in tbeir

investigations of curvilineal and other varied motions, III. vh==4

measure it by the deflection which it produces in this

time from the tangent of the curve, or by the increIV. h=

ment by which the space described in an unit of time 64

exceeds the space described in the preceding unit. This To give some examples of their use, let it be requi- have produced, had the body moved throngh the whole

is but one balf of the increment which gravity would 1. To find the time of falling through 256 feet.

moment with the acquired addition of velocity. In this 16

sense of the symbol g, the equations stand thus :
Here h=256, 256=16, and -2=4. Answer 4".

I. v=2Vg7l=25
2. To find the velocity acquired by falling four se-
conds. 1=4:32X4=128 feet per second.

II. t=

31:26
3. To find the velocity acquired by falling 625 feet.
h=625. Vh=25.8 [h=200 feet per second.

IV.h> =gt, and wh=
4. To find the height to which a boily will rise

2V8
wben projected with the velocity of 56 feet per second, It is also very usual to consider the accelerating force

of

14

duced.

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2

=161.

15 Examples of their use red, in falling bodies.

4

3 D 2

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