ARTES
18176
SCIENTIA
LIBRARY
VERITAS
OF THE
UNIVERSITY OF MICHIGAN
SPLURIBUS UNDI
上
​за
TUENOR
I:QUÆRIS-PENINSULAM AHŒNA!
CIRCUMSPICE
♡
An Eafy and Pleafant
INTRODUCTION
ΤΟ
SIR ISAAC NEWTON's
PHILOSOPHY:
CONTAINING THE
FIRST PRINCIPLES
OF
MECHANICS, TRIGONOMETRY,
OPTICS, and ASTRONOMY.
By a Fellow of the Royal Society.
WITH
An ESSAY on the ADVANCEMENT of
LEARNING,
In various Modes of Recreation.
By JOHN RYLAND, A. M. of Northampton.
THE SECOND EDITION.
To this New Edition
An APPENDIX is added, to render the Book
more uſeful to Schools.
LONDON:
Printed for EDWARD and CHARLES DILLY, in the
Poultry. 17720
3
"Q
(157
R99
1772
1
ور نام نگم نکلوار قرن 25-22
History of Scrince
Bowers
10-20-31
24455
(iii)
ADVERTISEMENT.
THE
HE APPENDIX, which I have now
added, is taken, by the confent of my
intimate and ingenious friend Mr. JAMES
FERGUSON, F. R. S. from his excellent
Lectures; and I am happy in having his per-
miffion for this purpoſe: No perſon can write
with greater fimplicity and clearness of
thought on theſe ſubjects.—I have, after
many years experience and labour, en-
deavoured to propoſe his thoughts and words
in the eaſieſt manner, knowing that young
people are apt to be terrified with imaginary
difficulties, at their firft fetting out in the
ſtudy of the Newtonian Philofophy. I know,
if we can but prevail on them to get the firſt
principles in their heads, the power and
beauty of Truth will irrefiftibly charrn them
to go on with admiration and incredible
delight: And I would earneſtly perfuade the
ingenious
(IV)
ingenious and virtuous Youth of Great
Britain and our Colonies to diſdain fenfual
pleaſures, and fordid purſuits, and make a
trial of theſe rational and manly entertain-
ments. If once they come to tafte that
ſweetneſs there is in the natural truths of
GEOMETRY*, MECHANICS, and the
other branches of PHILOSOPHY, they
will find their underſtandings fo ftrengthened
and improved, as to aftoniſh even them-
felves; and they will be thereby fo prepared
for all other kinds of ftudies, and important
employments of life, and fee fuch folly and
mifery attending ignorant Libertines, as will
produce a rich abundance of happy con-
fequences to themſelves, their parents, and
their country.
Northampton,
January 1. 1772.
JOHN RYLAND.
* EUCLID'S ELEMENTS contain the greateft num-
ber of natural truths of any book in the Pagan world,
and is moſt wifely adapted to habituate the underſtand-
ing to the contemplation of TRUTH. In this view it
is far fuperior to any other production of the Greeks or
Romans.
THE
!
}
PREF A Ċ E.
THIS ſhort treatiſe was drawn up, at my
houſe, by a judicious friend, who is
well acquainted with thefe fciences, and has
a happy talent for communicating know-
ledge in the moft clear and eafy manner.
I am not at liberty to mention his name,
which would do me honour-excite the at-
tention of the public-and very much pro-
mote the fale of the book.
I had long wanted an eaſy and familiar
treatiſe of this fort, for the ufe of my
ſcholars, and it gave me a móſt ſenſible
pleaſure, when I had prevailed on my friend
to execute it.
The book with all the drawings, was
begun and finiſhed in leſs than fix weeks. It
is not defigned for the learned; it was writ-
ten for the uſe of boys, and, with no de-
fign to go any farther than my own ſchool;
but
a 2
[ i ]
but the trouble of tranfcribing, with ex-
actneſs, by each youth that wanted it, would
be fo great, as to prevent the eaſy commu-
nication of this kind of knowledge.
I am convinced, by more than nineteen
years experience in the province of inftructing
youth, that much more may be done, than
has been done, towards furniſhing and-
adorning the human mind, in the early part
of life. It is a grievous thing to confider,
how we are fuffered to waſte ſeven or ten
years, in learning little more than meer
words, whilft the improvement of the un-
derſtanding and the reafon, is almoſt en-
tirely neglected in moft fchools, through
this kingdom.
The minds of youth are happily vacant
of the cares and buſineſs of life; they are
very receptive of ideas of all kinds, pro-
vided you propoſe them in a fimple and
familiar manner, and avoid every thing that
is abftracted and remote from fenfe.
Logic, and metaphyfics, though ex-
tremely uſeful to perfons of riper under-
ſtanding, are, by no means proper for young
minds; almoſt every other branch of ici-
ence, in the whole circle of learning, may
be
[iii]
1
be propoſed and communicated to ingeni-
ous youth, from ten to fixteen years of age.
The natural hiſtory of the air, the waters,
minerals, plants, and animals, which is what
we call fenfible knowledge, may be infuſed
with eaſe and pleaſure into the infant mind,
and certainly we have fome of the beſt
books for this purpoſe that can be well ima-
gined.-I mean Mr. Pluche's beautiful
work intitled Spectacle de la Nature, in 7
vol. 12mo. Dr. Brookes's System of Natu-
ral Hiſtory, in 6 volumes, 12mo, with the
beautiful ſketches of every part of the
creation in Mr. Hervey's works; as we
never had a more paffionate admirer of the
beauties of nature, fo ro man perhaps in
our nation had a richer imagination, or a
better talent of ftrong and delicate expref-
fion than himſelf.
Arithmetic, and, geometry, are exceed-
ingly uſeful and important fciences for
youth, and they may be taught in a more
pleafing and infinuating manner than they
ufually are. Every thing fhould be mixed
with pleaſure, and familiarity, that belongs
to youth.
a 3
Arith-
[ iv ]
Arithmetic can never be enough taught;
it deferves more attention than is given to
it; we have two authors, who have made
the ſcience more eaſy and pleaſant than ever
-the one is the Rev. Mr. Stephen Adding-
ton of Market Harborough, in Leicester-
ſhire, the other is Mr. Daniel Fenning of
London, their books in my opinion are the
beft adapted for the inſtruction of youth.-
I beg leave to infert here a general canon
for the rule of proportion, which I con-
ftantly uſe in my own fchool, and I would
recommend it to mafters of the younger
clafs to infift upon it, that their fcholars
work every queftion in fingle proportion,
in four different ftatings, this will ftrength-
en the mind, and is the firſt and beſt method
of teaching them the uſe of their reafoning
powers that I am acquainted with.
GENERAL CANON OR RULE FOR
SINGLE PROPORTION TRANS-
POSED FOUR WAYS.
If four numbers or quantities are pro-
portional, their order may be fo tranfpofed
that each of thofe numbers or quantities.
may be laſt in proportion. And fo of any
four proportional numbers or quantities of
liquids
[ v ]
liquids or folids, if three be given the other
that is wanting may be found thus.
FIRST
AS FIRST
1
SECOND
4
: 8
THIRD
8:
FOURTH
32
AS SECOND
FOURTH
THIRD
32
: 8
AS THIRD
8
FOURTH
FIRST
SECOND
4 : 1 ::
1 :: 32
: 32 :: I : 4
AS FOURTH
32
THIRD
SECOND FIRST
: 8 :: 4 : I
Geometry, or the doctrine of extended
or continuous quantity, including the con-
fideration of lines, fuperfices and folids.-
Next to divinity and hiſtory, this is certainly
the very best ſcience in which youth can
be inftructed.
It has a prodigious tendency to fix the
attention, to ſtrengthen and enlarge the
mind, to improve the memory, to teach
clear ideas, and an habit of juſt reafoning.
It is furely the best logic that ever was in-
vented for the ufe of mankind.
a 4
The
[vi]
The firſt fix books of Euclid's Elements
may be taught to fchool boys, in a way
of play, by working all the problems,
and moſt of the theorems, in the fand. Let
a young mafter of a ſchool provide himſelf
with a large pair of compaffes, and a long
ruler. Let him firft take Le Clerc's Prac-
tical Geometry printed for Meffrs. John and
Carington Bowles, work one or two pro-
pofitions, in the court yard, or playing
place of his ſchool every day, and in about
fix weeks, or two months, his ſcholars will
be able to enter upon Euclid's Elements in
the fame manner. In a year's time, he may
have twenty or thirty boys able to give a
good account of the firft principles of geo-
metry, and plain trigonometry, without lofs
of time, or interrupting the buſineſs of
their ſchool hours.
I ſhould reckon it a great honour to my
ſchool, to have it juſtly faid, "that the boys
are taught geometry, as a recreation,
and, that Euclid's Elements were as familiar
as the Latin accidence, or the numeration
table. I am very fure, that all the parts of
philofophy may be taught in the moſt eaſy
and familiar manner, if ſchool mafters had
but public ſpirit, good humour and con-
defcention. In a word, if they had but a
fatherly
[vii]
1
fatherly heart, and as much concern for the
pleaſure and improvement of their ſcholars,
as they have for their own private gratifica-
tion, and the inferior amufements of life.
For inftance-a fire fhovel, tongs, and po-
ker, will fhew the foundation of the me-
chanic powers; eſpecially the nature of
levers. A fpinning wheel, will clearly fhew
the power of the wheel and axle-A brick
bat on a table, will fhew the advantage of
broad above narrow wheels.-marbles, will
teach a ſchool boy the nature of percuffion,
and the laws of motion.-By the whipping
and ſpinning of tops, we may fhew the di-
urnal and annual motion of the earth.-
The twirling of a chamber maids mop, will
ſhew the nature of the centrifugal force of
the planets. The fall of a farthing ball,
teaches the doctrine of gravitation, and
the laws of falling bodies.-A pennyworth
of quick filver, divided on a table, and fome
bits of cork in a bafon of water, will fhew
you the attraction of coheſion.-A fpunge
will teach the rife of water in capillary
tubes. A fyringe, or a fquib, or fucking
with a reed, or a wheaten ftraw, will fhew
the nature of pump work.-A fchool boy's
jews harp, will ferve to teach us, thofe
tremulous motions, which are the cauſe of
founds;
a 5
[ viij. ]
founds; and a glafs prifm, and foap bub-
bles *, a looking glafs, and an oxe's
eye, from the butchers will be a happy
foundation for optics.-A few hoops, from
the cooper's fhop, placed with ſkill, will
fhew the grand circles of the ſphere, viz.
the horizon, the meridian, and equinoctial
line, the ecliptic or fun's path, the two
tropics, and the polar circles.
A fmall pillar, of the fame fize which
is uſed for a barber's block, with a few
rings of leather, or of horn, with fome
wires and wooden balls, will make a tole-
rable good orrery, to fhew the fituation,
the diſtances, the motions, and magnitudes
of the heavenly bodies, in the Newtonian
ſyſtem of aſtronomy. Thus, I have given
a few brief hints, how younger mafters may
purſue the moſt popular methods, with lit-
tle expence, for the inftruction, pleaſure,
and vaft profit of their pupils, which would
iffue in their own honour and temporal ad-
vantage, and be an unfpeakable fatisfaction
to the parents who entruſt them with their
deareſt earthly treaſure.
* Note, Let the man that laughs at this; be told
that Sir Ifaac Newton made a fine improvement in
optics by feeing fome boys blow up foap bubbles in
the air.
I
[ix]
I will, (now I am on the head of teach-
ing the fciences, by way of recreation) ad-
vance this affértion, that all the branches.
of knowledge may be taught by cards.
The method of teaching the fciences, by
the uſe of cards, is fuch as, perhaps in no
other way can be fo eafy, fo popular, fo
pleaſant, and fuccefsful.
By cards I do not mean the common
playing ones for gaming, which were firſt
invented for the ufe of a lunatic French
king, and continued in vogue to this day
by millions of mankind, infected with a
worfe fpecies of lunacy;, nothing but the
height of raging madneſs could ever fpred
fuch a foolish diverfion fo wide, or continue
it ſo long, to the deftruction of the peace
of the mind, the pleafures of friendſhip,
the health of the body, and the horrible
ruin of thouſands of fine eftates and fami-
lies. But to fuch a height of infanity are
multitudes arrived, as to render all means
for their cure ineffectual; I therefore dif-
;.
mifs them in defpair, with this one reflec-
tion; that, were I capable of wishing the
greateſt mifery, to the worst enemy upon
earth, and that he might be one of the
moft uſeleſs and contemptible animals in
the
[ x ]
ទ
:
'
the world, I would with him to be a con-
ſtant and infatuated card-player.
But whilſt common fenfe, and the love
of one's country can defpife and abhor fo
fooliſh and infipid a diverfion, this fame
common fenfe, and public fpirit can in-
vent a thouſand ways by which cards, that
is to fay, the fame kind of blank papers,
which are ufed for cards, may with very
different kind of furniture and application,
be promotive of the glorious purpoſes of
fcience and virtue, fome of theſe pleaſant
ufes we will now explain.
FIRST, GEOGRAPHICAL CARDS.
Take a pack of blank or meffage cards,
write on them the principal cities of Eu-
rope, Afia, Africa, and America, one city
on each card, with the latitude, longitude,
number of inhabitants, and their religion.
When you have compleated the furniture
of theſe cards, the manner of playing with
them is as follows. In a rainy day, or a
winter evening, when the weather does not
permit them to play in the open air, let
iwo, three or four boys, agree to play at a
game
[ xi ]
game of geography; deal out the cards and
let the firſt boy begin, draw a card, inſpect
it, name only the city, and turn it's face
downward on the table. The ſecond boy
muſt anſwer, thus for example. Suppoſe
it was London. London (replies the ſecond)
is the capital city of the kingdom of Eng-
land, it's north latitude is 51 degrees, and
32 minutes, it's longitude is nothing, be-
cauſe the firſt. degree of longitude, or the
firſt meridian, begins at London. The
number of inhabitants in the city and fu-
burbs, are reckoned near a million, or ten
hundred thouſand; and the people profeſs
the proteftant religion,
If the fecond boy, gives a true account
of what is upon the firft card, he has a right
to play one of his, and the third boy muſt
anfwer. But if the fecond boy miffes, and
the third boy anſwers truly, then he fits
above him, or takes his place, plays his card,
and the ſecond boy is obliged to anſwer, if
he miſtakes again, and the fourth boy names
right, he takes his place, and the fecond
boy is put lower with difgrace. And thus
let the boys go on, till their cards are all
played out; and let him that has made the
feweft blunders, be called the captain for
that day.
II. CARDS
[ xii]
II. CARDS OF ANTIENT HISTORY,
WITH THE
ANNEXED.
CHRONOLOGY
The furniture of a pack of blank cards
with antient hiſtory muſt be thus ordered.
On the firſt card write on it thus:
FIRST EPOCH.
ADAM, OR THE CREATION,
FIRST AGE OF THE WORLD.
ANNO MUNDI,
YEAR OF THE WORLD,
O
ANTE CHRISTUM.
BEFORE CHRIST,
4004
On the fecond card write, Second epoch,
Noah, or the deluge, with the year of the
world, and the years before Chrift.-Third
epoch, the call of Abraham.-Fourthepoch,
Mofes, or the written law. - Fifth epoch,
the deſtruction of Troy. Sixth epoch,
Solomon, or the temple finiſhed. Seventh
epoch, Romulus, or Rome founded.
Eighth epoch, Cyrus, or the Jews reſtored.
Ninth epoch, Scipio, or the conqueſt
of Carthage. Tenth epoch, the birth of
1
Jefus
[ xiii]
Jefus Chrift; which is the feventh age of
the world
ANNO MUNDI ANNO ROMÆ
4004
754
ANNO CHRISTI
I
Let every young perfon, according to
his ability, after he has placed the above
furniture on one fide of his cards, write fome
peculiar felect facts which happened in each
period, on the other fide. By this means
he will have many of the moſt beautiful
and delicate parts of antient hiftory at an
eafy rate within his power; and fchool-boys
may play at cards of this fort with as much
pleaſure and profit, as, with the geographi-
cal ones firſt mentioned.
III. CARDS OF MODERN HISTORY,
WITH THE
ANNEXED.
CHRONOLOGY
The beſt way of treating modern hiſtory,
is to divide it into centuries, beginning with
the birth of Jeſus Chriſt, and to denominate
every century according to the principal
facts tranfacted in that century. And I can
think of nothing better than the epithets
of that learned hiftorian, Dr. William
Cave, viz.
He
[ xiv ]
He ftiles
Century I.
Sæculum Apoftolicum.
Century II.
Sæculum Gnofticum.
Century III.
Sæculum Novatianum.
Century IV.
Sæculum Arianum
Century V.
Sæculum Neftorianum.
Century VI.
Sæculum Eutychicum.
Century VII.
Sæculum Monotheliticum.
Century VIII.
Sæculum Eiconiclafticum.
Century IX.
Sæculum Photianum.
Century X.
Sæculum Obſcurum.
Century XI.
Sæculum Hildebrandinum.
Century XII.
Sæculum Waldenfe.
Century XIII. Sæculum Scholafticum.
Century XIV. Sæculum Wicklevianum.
Century XV. Sæculum Synodale.
Century XVI. Sæculum Reformatum.
Century XVII. Sæculum Doctiffimum.
I add to Dr. Cave,
Century XVIII. Sæculum Luxuriofum.
IV. GEOMETRICAL CARDS.
The firſt and eaſy principles of geometry
may be placed on cards in the following
fimple manner, and a figure ſhould at-
tend each definition to make it more eaſily
understood. On the first card fix a point.-
On
[ xv. ]
On the fecond, a fecant point. On the
third, a central point. -a right line-
a circular line curve line a mixed
line-a plumb line a perpendicular
line-horizontal line oblique line-
parallel lines a baſe-line
finite lines
a
infinite lines apparent line occult
line diagonal line diameter line
ipiral line chord line an arc
tangent linea fecant line-a right lined
angle a curve lined angle a mixed
angle - a right angle an acute angle
-an obtufe angle - and from thence pro-
ceed to all forts of furfaces. This will lay a
fure foundation for plain geometry, and pre-
pare the ingenious boy for reading Euclid's
Elements with pleaſure and fuccefs.
V. OPTICAL CARDS.
Optics, or the confideration of the na-
ture of light, and the human eye, is one
of the moſt fublime ſciences in the world.
Its first principles may be infuſed into
fchool-boys in the following eafy manner:
take fome blank cards, let any ingenious
man draw the figures, and write under-
neath, the eaſieſt definitions, from Dr. Ru-
therforth's Syftem of Philofophy, viz. -
a ray
[xvi ]
the inflexion of a ray
of
a ray of light
light-the refraction of a ray of light-the
reflexion of a ray of light the angle of in-
cidence the refracted angle the angle
of refraction --the angle of reflection
diverging rays of light-converging rays
of light parallel rays of light-a radiant
point - a focus a focus changed into a
radiant a double convex lensa plano
convex lens a double concave lens-a
plano-concave lens - a menifcus, or con-
cavo-convex lens a plane glaſs - a flat
convex glafs — a priſm the axis of lens
glaffes the poles or vertexes of a lens
diverging rays falling on a lens form a cone,
whofe apex is the radiant point, and the lens
is its baſe the axis of a beam of light-
direct rays upon a lens-oblique rays upon
a lens a pencil of rays the human eye
-the outer coat of the eye, called the
Sclerotica- the middle or black coat of the
eye, called the Choroïdes the inner coat
of the eye, or net work, called the Retina
the three humours of the eye, viz. the
Aqueous, or watry humour of the eye-
the Chryſtalline, or brighteft humour of the
eye, in the form of a double convex lens —
the Vitreous, or glaffy humour of the eye.
N. B. When theſe firſt principles and defi-
nitions are clearly underſtood and well re-
membered, it will be eaſy and pleaſant to
proceed
[ xvii ]
proceed even to Sir Ifaac Newton's moſt
beautiful and incomparable Treatife on
Optics, which is much more within the
power of good common fenfe than is uſually
imagined.
VI. CARDS OF ANATOMY.
The ſtructure and beauty of the human
body ought to be ftudied with delight
and admiration by every man; and the
knowledge of this elegant fabric may be
conveyed into the minds of youth, with great
eaſe and pleaſure, by the uſe of cards. I
fhall only exemplify it a little with regard
to the bones, and refer my ingenious young
friends to that moſt exquifitely delicate and
alluring defcription of a human body,
which he will find in Mr. Hervey's Theron
and Afpafio, Dialog. XII.
Let an ingenious young man take Chef-
elden's Anatomy, or the Tables of Anatomy
engraved by Mr. Tinney, in Fleet-ftrect,
on folio fheets; with his pencil copy on a
blank card one bone, with its name; and
thus proceed with his cards through the
principal bones of the human body. And
left I ſhould not be thoroughly underſtood,
ar
[ xviii ]
}
or the minds of young perfons be too indo-
lent to purfue my advice, I will lead him
farther, and mention the names of the bones,
which are thefe: Os frontisos bregmatis
-os temporis - os occiptis -os jugale
clavicula, or collar bone- fternum, or
breaſt bone-feven vertebræ of the neck
twelve vertebræ, or joints of the back
bone five vertebræ of the loins, in all
twenty-four joints-feven true ribs of a fide
five falſe ribs the fcapula, or ſhoulder-
blade — os humeri, or bone of the arm
above the elbow the radius and ulna,
the two bones of the arm below the elbow
bones of the carpus or wrift-bones of
the metacarpus or hand bones of the
fingers -the os facrumos coccygis
os iliumos pubis os femoris, or bone
of the thigh-the patella, or knee-pan
the tibia, or largeſt bone of the leg
fibula, or leaſt bone of the leg
the foot
–
the
os calcis,
or bone of the heel- the tarfus, or fix
inſtep bones the metatarfus, or bones of
laftly, the bones of the toes.
Thefe, with the fmaller bones, may be
numbered thus: about fixty in the head
and neck; fixty in the arms and hands;
fixty in the trunk of the body; and, fixty
in the thighs, legs, and feet; in all, about
two hundred and forty. And with thefe
the
[ xix ]
the all-wife and powerful God has built the
ftructure of the human body; and for
which he deſerves eternal love and adora-
tion. I do not adviſe young men to ſtudy
this ſcience with the accuracy of anatomiſts,
but as a profitable and rational recreation,
in order to increaſe their veneration for our
omnipotent and good creator; and, I can
affure them, after more than twenty years
experience, that the pleaſure and profit of
this ſtudy will richly reward them for their
labour.
VII. CARDS OF ASTRONOMY, AND
A LIVING ORRERY, MADE WITH
SIXTEEN SCHOOL-BOYS.
Aſtronomy is a moft fublime and deli-
cious ſcience: To form a juft idea of the
magnitude, motions, and diftances of the
heavenly bodies, has a powerful and happy
tendency to enlarge and elevate the foul,
and to give us ftriking thoughts of the
wiſdom, goodneſs, and univerfal agency of
God. But can any notion of this fcience
be conveyed into the minds of ſchool-boys?
Will it not rather puzzle and confound
their brains, and unfit them for the more
important employment of ftudying dry-
words
[ xx ]
words for ſeven years together? I anſwer,
No. It may be taught them in their play
hours with as much pleaſure as they learn
to play at marbles, or drive a hoop for an
hour or two; and this may be done in
manner and form following:
Take fixteen blank cards; write on one,
the fun, a ſeventeenth boy of a large fize
muſt be uſed for the fun in the center,
with his diameter, which is feven hun-
dred thousand miles. On another card
write mercury, with his period, eighty-eight
days, diſtance from the fun thirty-two mil-
lion, diameter two thouſand fix hundred
miles, and hourly motion, which is one
hundred thousand miles. So go on to ve-
nus, our earth, mars, jupiter, and faturn.
Then write on your other cards the names
and periods of the ten moons in our ſyſtem.
Having thus furniſhed your cards, then
provide the orbits for thefe fham planets,
go into any plain field, or place, where boys
can play, draw a circle of two hundred feet
diameter, which you may eaſily do with a
cord and a broomstick, ordering one boy
to hold the cord in the center, while you
defcribe the circle with the ftick at the
other end of the ftring. When you have
formed your circle, divide the femi-diame-
ter into a hundred parts; if you chuſe exact-
nefs,
[ xxi ]
nefs, take five of theſe parts from the cen-
ter and deſcribe a circle for mercury's or-
bit, take ſeven parts for the orbit of ve-
nus; ten parts for our earth's orbit;
fifteen parts for the orbit of mars; fifty-
two parts, that is fifty-two feet for the or-
bit of jupiter. And let the outward circle
of a hundred feet reprefent the orbit of fa-
turn, which is the boundary of the New-
tonian ſyſtem. After this draw your circles
for our moon round the earth, for jupiter's
moons round him, and laft of all for faturn's
five moons. There is no occafion to be
fcrupulouſly exact till the boys are well
verfed in theſe firſt eaſy notions, reduce
them to accuracy by degrees. Mr. Whif
ton's Aftronomical Principles of Religion,
andMr. Ferguſon's Aftronomy will furniſh
you with ample materials for all your pur-
pofes. Now begin your play, fix your boys
in their circles, each with his card in his
hand, and then put your orrery in motion,
giving each boy a direction to move from
weft to eaft, mercury to move fwifteft,
and the others in proportion to their diftan-
ces, and each boy repeating in his turn
the contents of his card, concerning his
diſtance, magnitude, period, and hourly-
motion. Half an hour ſpent in this play
once a week will in the compafs of a year
fix fuch clear and fure ideas of the folar
fyftem
1
[ xxii ]
fyftem as they can never forget to the
laft hour of life. And probably rouze
fome fparks of genius, which will kindle
into a bright and beautiful flame in the
manly part of life.
· AN ADDRESS TO THE INGENU-
OUS YOUTH OF GREAT BRI-
TAIN.
Young Gentlemen,
The defign of this addrefs to you is to
give you a few brief hints concerning fome
fome felect books on the principal branches
of ſcience in order to fhorten your path to
good learning and ftrew it with flowers.
I know by the painful experience of above
thirty years what it is to pant for know-
ledge and books, fometimes without any
guide, fometimes with infufficient and ig-
norant ones, fometimes with men of learn-
ing without genius, fometimes with men
of genius and furniture, but too lazy
and indifferent, or fwelled with pride
and a haughty ſtiffneſs, or poffeſt of no ta-
lent for the communication of knowledge,or
no
[ xxiii]
no inclination or condefcenfion to accom-
modate themſelves to the capacity and
taſte of enquirers after truth.
But the greatft defect I have ever found
in learned men is a want of public fpirit,
and a fervent love to the rifing generation:
this is the worst part of their temper, and
an indelible ſtain in their character; for
which they deſerve the ſevereſt rebuke.
We have in this nation men well verſed
in all the ſciences, and all the branches of
learning were never better underſtood than
at prefent. But if every learned man had
a true love to the rifing generation and a
condeſcending temper, I will venture to
aver that in feven years time, where we
have one man of real knowledge now, we
night have an hundred, or perhaps five
hundred then. We ſhould not fee fuch ig-
norance in thouſands of our minifters of
religion nor fuch wretched and ſhameful
unacquaintance with the hiſtory, laws,
- and government of their country, as hath
fully appeared in multitudes of our young
nobility, and I am forry and grieved
to fay it, in the majority of the reprefenta-
tives of a brave and powerful people.
b
Now
[ xxiv ]
Now my dear ingenious youths, let me
offer you a little affiftance, give me your
hand, and let me lead you into a moft
beautiful and pleafant path, which I my-
felf have trod. I do not pretend to write
for men, nor for thoſe young perfons who
have ſkilful tutors always to attend them.
I write for all thoſe who have a good na-
tural taſte, and a paffionate fondneſs for
real knowledge, but want an experienced
guide, to fuch the following hints will
not be unwelcome, nor unferviceable.
Do you in the firſt place wiſh for two
or three excellent books to guard you from
errors in ftudy, and to be your faithful
guides in the purfuit of folid learning
then my dear boys read above all authors
Dr. Watts's Improvement of the Mind,
8vo. Mr. Locke's Conduct of the Under-
ſtanding, izmo. and John Clarke's Effay
on Study, 12mo.
Would you gain clear and beautiful
ideas of the works of creation, read Plu-
che's Nature Difplayed, 4 vols. 12mo.
Dr. Brooks's Natural Hiftory, 6 vols. 12mo.
Ray on the Wifdom of God in Creati-
on,
12mo. Wefley's Compendium of
Natural Philofophy, 2 vols. 12mo.
Dr.
Cotton
[ XXV
]
Cotton Mather's Chriftian Philofopher, 8vo.
1721. Dr. Derham's Phyfico Theology,
2 vols. 8vo. Cambray on the Exiſtence
of God, 12mo. a new beautiful edition of
which is juſt publiſhing. Martin on the
Exiſtence of a Deity, from Sixteen Fountains
of Evidence, and his Young Gentleman's
and Lady's Philofophy, 2 vols. 8vo.
Theſe are the best books, and the
eafieft to introduce you to Voltaire's Ele-
ments of Sir Ifaac Newton's Philofophy,
tranflated from the French, 8vo. 1738.
an excellent book. Algarotti's Six Dia-
logues on Sir Ifaac Newton's Philoſophy,
2 vols. 12mo. 1739. Rowning's Com-
pendious Syſtem of Natural Philofophy,
2 vols. 8vo. Martins xii Lectures on all
the Branches of Experimental Philofophy,
intitled Philofophia Britannica, 2 vols.
8vo. and to crown all, Dr. Rutherforth's
Syſtem of Natural Philofophy, 2 vols. 4to.
1748. If your inclination ſhould lead you
to enquire farther after books on natural
philoſophy, you may be directed to the
utmoſt of your wiſhes, in Johnſon's Quæf-
tiones Philofophicæ, 12mo. Cambridge,
1735.
b 2
If
[ xxvi ]
If ever your genius fhould grow ſtrong
enough to taſte the pleaſures of ſcience,
abſtracted from fenfe, and the rational
entertainments arifing from the confidera-
tion of the doctrine of being and of fpi-
rits, I adviſe you to read but a few ſelect
books, the beſt I am acquainted with are Dr.
Watts's Scheme of Ontology, at the end
of his philofophical effays, and Dr. Dod-.
dridge's Pneumatology in his Lectures, 4to.
1762. I have in MS. Mr. Henry Grove's
beautiful Syſtem of Pneumatology. I wiſh
from my heart that fome bookfeller would
venture to print it, on the footing of a
fubfcription from the learned world. This
ingenious writer certainly was one of the
cleareſt thinkers on metaphyfical fubjects
that our age has produced.
Have you a tafte for the knowledge
of numbers and quantity? Read and
ſtudy theſe books, Mr. Addington's
Syftem of Arithmetic, 8vo. Le Clerc's
Geometry, 12mo. Dechale's Euclid,
12mo. Whifton's Edition of Euclid,
8vo. 1714. Theſe two editors of Euclid,
fhew the practical ufes of the problems
and theorems; and will remarkably
ftrengthen your habit of attention, teach
you to fift and compare your ideas, and
enlarge
[ xxvii ]
enlarge your reafoning powers in a re-
markable manner.
Do you defire to form a familiar ac-
quaintance with the firft principles of na-
tural religion, and moral philofophy?
Read Sir Richard Blackmore's Natural
Theology, 8vo. 1728. Wollafton's Reli-
gion of Nature Delineated, 4to. Reima-
rus on Natural Religion, 8vo. Fordyce's
Elements of Moral Philofophy, 12mo. 17.
and to compleat your ftudies on this
head, read Grove's Syftem of Moral Philo-
ſophy, 2 vols. 8vo. I freely own I prefer
this for the favour of piety and delicate
compofition, beyond Dr. Hutchenſon's
Syſtem, 2 vols. 4to.
Do you love the grand fcience of fo-
ciety, government, and the laws of your
country? This is indeed a moft noble and
important object of the human underſtand-
ing: it gives an amplitude to the foul, and
leads to a moft exalted idea of the divine
government of the univerſe. I am ſo far
from advifing you not to study politics,
that on the other hand, I counſel you to
employ your powers very often on the
glorious ftructure and excellence of the
Britiſh conftitution; and to affift you in
your
b 3
[ xxviii]
your views, read the beſt books that were
ever written, fince Britain exiſted, Mil-
ton, Sydney, Locke and Dr. Campbell,
Sydney's Treatife on Government, folio,
1696. Locke on Government, 8vo.
Dr. Campbell's Prefent State of Europe,
8vo. 5th edition, and his excellent Sketch
of Laws and Government publiſhed in the
Preceptor, vol. 2. to thefe books add
Dr. Blackstone's Commentaries on the Laws
of England, 2 vols. 4to.-Theſe are cer-
tainly ſuperior to every work of the kind,
that have appeared in our language.
Above all things my dear young friends,
ſtudy the evidences and contents of the
CHRISTIAN RELIGION. The greateſt and
beſt ſtep you can take for this purpoſe, is
to confider deeply and accurately, the in-
fufficiency of human reafon to lead you to
eternal happineſs, in the full fruition of
the fupreme good; ſtudy this ſubject to
the utmoſt of your capacity, I can affure
you after twenty-two years inceffant labour
and thought on this moſt important and
momentous point, that nothing does more
mortify our native pride, and conceit of
our ſtrength of reaſon than a juft and im-
partial view of its infufficiency, to conduct
us to the higheſt end of man. If you do
not
[ xxix ]
#
not believe me, try what you can do with-
out your bible; fummon up your beſt pow-
ers, and exert the utmoft force of your
genius to attain a clear and extenſive
knowledge, of the attributes and provi-
dence of God; find out the true way of
worshipping God; tell me in the moſt
convincing manner, wherein conſiſts the
folid happineſs of human nature; declare
to me and the world, the chief good of the
foul; draw out a fyftem of true morality
without any defect; explain every duty we
owe to God and mankind, produce the
richeſt, and moft perfuafive motives to
excite to the exerciſe of every virtue; dif-
play fuch powerful reafons, as fhall pre-
vail with every man, to diſcharge the
whole of moral obligation, and perfevere
in virtue and goodneſs to the laſt moment
of his life; give me a moſt fatisfying ac-
count of the origin of moral evil, which has
ever raged with fuch dreadful power and
malignity all over the rational world; and
fhew me how this may be pardoned fo as to
fatisfy a ferious enquirer, and calm a guilty
confcience; demonftrate to me by the
ftrength of your reafon, how one finner,
how millions of finners, may be introduc-
ed into the favour and friendship of God,
notwithſtanding all their paft offences,
b 4
and
[ xxx ]
and be happy in him for ever; affure me
of an effectual means to curb every licen-
tious paſſion, every vile appetite, every
vicious inclination, every impure imagi-
nation and tafte; fhew me a fufficient fund
of moral and proximate power, to raiſe me
above the wicked ſpirit and polluted man-
ners of the whole world, and to perfiſt in
virtue and goodneſs in ſpite of all temp-
tations, to my last hour.
If you think the powers of reafon are
fufficient to conduct you to the fupreme
good and final happineſs of man; try your
utmoſt ſtrength to fupport yourſelf under
the troubles of life, and the vexations and
croffes, you meet with in mind body, and
eftate; fortify yourſelf againſt all the ter-
tors and ftings of death; act a courageous
part, when that ghaftly monarch, who is
ftiled by an ancient and very acute philo-
fopher* the terrible of all terribles, fhall
come to ſeparate your foul and body; to
turn the mortal part of your nature into
corruption and duft, and fix your charac-
ter and ftate in another world, which
you muſt enter into with all your thinking
powers, and moft lively conſciouſneſs for
evermore. Now if you have fortitude
enough,
* Ariftotle.
[ xxxi ]
enough, meet this king of terrors, and
without the affiſtance of divine revelation,
addreſs him boldly. O! death, where is
thy fting? O! grave, where is thy victory?
This method of proceeding in order to
prepare you, for ftudying the evidences
and contents of the chriftian religion, is
the beſt that can be thought of; becauſe it
has a direct tendency to humble the pride
of your nature, to abaſe the high conceit
which every man forms of his own ftrength
and goodneſs of heart; and fuch confide-
rations as thefe, will bring you to the duſt
as a guilty ruined creature; utterly infuf-
ficient to conduct yourſelf to the final per-
fection of your faculties, and the ulti-
mate happineſs of your immortal ſpirit.
In this temper of mind fet yourſelf to
examine the evidences of the truth and
divine authority of the chriftian religion.
To affift you in this affair of infinite
moment, I recommend to your perufal
Dr. David Jennings's two difcourfes intite-
led, An Appeal to common Senfe for
the Truth of the Scriptures, and Dr.
Doddridge's three fermons on the
Evidences of Chriſtianity, 12mo.
price 8d. Theſe are perhaps the moſt
b 5
clear
[ xxxii ]
clear and convincing of any fermons in our
language; but the moſt extenfive view of
the whole fubject, in all its parts and con-
nexions, that has appeared in our world,
you will find in Dr. Doddridge's Courſe of
Divinity, 4to. 1763. including LIII. lec-
tures (viz.) from lect. CI. to lect.
CLIV. It is an act of juſtice to acknow-
ledge, that no one fingle book of a theo-
logical nature has equalled this in our
land and it is an honour to the good
fenſe and candour of fome gentlemen, in
public feminaries, that they have paid a
proper attention to this excellent courfe
of lectures on pneumatology, ethics and
divinity *
In order to make your enquiries more
eafy, pleaſant and fucceſsful, I will lead
you on a little farther. Our moſt learned
and judicious divines have a thouſand
times obferved, that revelation ſtands on
four principal pillars, or, in other words,
is fupported and confirmed by four ca-
pital arguments, viz. the fulfilment of
prophecies the working of miracles-
*This celebrated work was the refult of thirty
years accurate ftudy and labour, with the revifal of
all his best friends and correfpondents.
the
[ xxxiii]
the goodneſs of the doctrine- and the
moral character of the pen-men,-efpeci-
ally the divine character of the great foun-
der of the chriſtian religion.
I. FULFILMENT OF PROPHECIES.
This is a glorious argument to demon-
ſtrate the divine truth and authority of the
holy fcriptures; and it has this excellence,
that its evidence is ever growing by the ac-
compliſhment of many prophecies now in
the world. No age or country has been
bleſſed with a brighter diſplay of this evi-
dence in its vaft extent and connexion
than our own. It is enough to name Dr.
Newton's 3 vols. of Differtations on Pro-
phecy; it would be an affront to common
fenſe to ſay any thing in favour of a work
which is fo generally known and efteemed,
and which furpaffes all commendation.
However, it will be no difparagement to that
incomparable work, to mention Dr. Gill's
Treatife on the Prophecies fulfilled in the
Meffiah, 8vo. 1728. The judicious Mr.
Robert Fleming's Treatife on the fulfiling
of the Scripture, a fmall folio. And the
excellent Mr. Benjamin Bennett's Diſcour-
fes on the Fulfilment of Scripture, towards
good
[ xxxiv ]
good and bad Men, in his Sermons on In-
fpiration, 8vo. 1730. Let me adviſe you
to ftudy this argument throughly: make
yourſelf maſter of the fubject in all its parts.
Nothing ftrikes a wife man's mind fo
ftrongly as facts, and it muſt give you un-
utterable pleaſure to obferve how the
biſhop of Bristol confirms and illuſtrates
the prophecies and facts of fcripture, by
a judicious and moft happy application of
paffages felected from antient hiſtory.
It is no difhonour to this great man to fay,
that our learned Dr. Prideaux, and an au-
thor who is the glory of the kingdom
of France, and whofe naine and writings
will ever be dear to me, paved the way
for Dr. Newton and pointed out the
method which he has fo well purfued.
Would you know this laſt author? He is
the amiable, I had almoſt faid the
DIVINE, ROLLin.
II. THE WORKING OF MIRACLES.
This is another excellent and moft con-
vincing argument to prove the divine in-
fpiration of the holy fcriptures; and taken
in connexion with the fulfilment of pro-
phecies on the one hand, and with the
goodneſs
[ XXXV ]
goodness of the doctrine on the other, it
rifes up almoſt to irrefiftable demonſtra-
tion.
I will not mention a thouſandth part of
what has been faid for or againſt this head
of argument; but will fhew you the plain-
eſt and moſt pleaſing method of beginning
your confiderations upon it, fo as to pro-
duce the moſt ſtriking conviction of its
glory and evidence, only remarking, by the
way, that the Deifts have of late, as well
as in former days, employed their utmoſt
art and force to overthrow this argument,
particularly David Hume, and Rouffeau.
The former has been fully anſwered by
the late Dr. Leland, in his View of the
Deiſtical Writers, Vol. II. 8vo. and by
the Rev. Mr. Richard Price, F. R. S. in
his Differtations juft publiſhed. The latter
i. e. Rouffeau has been effectually con-
futed by one of his own country men and
fellow citizens, Dr. Claparede, profeffor of
divinity at Geneva, whofe work has been
tranſlated from the French, and printed this
year in London for Mr. Newbery, 8vo.-I
would adviſe you to read this little treatiſe
on miracles with attention, as it is written
with remarkable clearnefs and precifion and
contains
[ xxxvi ]
contains the ſubſtance of what you will
find in larger volumes.
But fuppofe you had no book on mira-
cles except your bible, what would you
do in order to have a clear and extenfive
view of this fubject, and anſwer your great
end, which is a full and compleat con-
viction that the facred fcriptures are in-
fpired from heaven? I will fatisfy you, my
dear young friend; I will point out to you
the moſt eaſy and effectual method of ftu-
dying this fubject.
The first thing I adviſe you to do is
this, endeavour to attain the cleareft idea
of a MIRACLE.
The learned and judicious Mr. John
Hurrion* defines a miracle thus "Mi-
racles are extraordinary works of God,
above, beyond or contrary to the courſe
* His fixteen excellent fermons, p. 436, intitled,
The ſcripture doctrine of the proper divinity real
perfonality, and the external and extraordinary
works of the Holy Spirit, ftated and defended at
Pinners-hall, 1729, 1730, 1731. 8vo. Ofwald
in the Poultry, 1734.-Note. Few people in the
world know the worth of thefe fermons. On the
fubject they have no equal.
of
[ xxxvii ]
of nature, or the power of fecond cauſes,
done to confirm the truth."
Dr. Doddridge * defines a miracle thus,
"When ſuch effects are produced as
(cæteris paribus) are ufually produced,
God is faid to operate according to the
common course of nature: but when fuch
effects are produced as are (cæt. par.) con-
trary to, or different from that common
course, they are faid to be MIRACULOUS."
Dr. Claparede's definition is the
ſhorteſt and moſt eaſy to be underſtood,
"A miracle is a fenfible change in the
order of nature." Nature is the affem-
blage of created beings.
Theſe beings act upon each, other, or
by each other, agreeable to certain laws;
the refult of which is what we call the or-
der of nature.
Theſe laws, being a confequence of the
nature of theſe beings, and of the relati-
ons which they bear to each other, are
* See his lectures, part V. lect. CI. definition
LXVII.
Read his confiderations upon the miracles of
the gofpel, 8vo. 2s. 6d. Newbery, 1767.
invariable:
[ xxxviii]
invariable: it is by them God governs the
world. He alone eſtabliſhed them. He
alone therefore can fufpend them.
The proper effect then of miracles is to
mark clearly the divine interpofition, and
the fcriptures fuppofe that fuch too is
their defign. Hence I draw this confe-
quence, that he who performs a miracle.
performs it in the name of God and on
his behalf, that is to fay, in proof of a
divine miffion.
But what are the characters of true mi-
racles? How may we know that the maf-
ter of nature hath been pleaſed to modify
or fufpend its laws? A queſtion of the
higheſt importance!
We have a clue to guide us in this re-
fearch fince the end of miracles is to
mark the divine interpofition, the miracle
muſt have characters proper to mark this in-
terpoſition. 1ſt. It muſt have an end impor-
tant and worthy of its author. 2. Be
fenfible and eaſy to be obferved. 3. Be in-
dependent of fecond cauſes. 4. Be inftan-
taneouſly performed.
Now, my young friend, proceed to take
afurvey of the miracles in what I would call
A
[ xxxix ]
A COMPENDIOUS VIEW OF THE
MIRACLES RECORDED IN THE
BIBLE.
Deluge
confufion of languages-fire
burning bufh-rod turned
rivers made blood - the
duft turned into lice -
fwarms of flies-murrain on the cattle-
boils on man and beaſt-hail mingled
with fire locufts- darknefs to be felt
death of the first born red fea divid-
on Sodom-burning buſh
into a ferpent
plague of frogs
ed - bitter waters of Marah fweetened
-rock gufhes out with water-law gi-
ven at Sinai with thunder, fire, and earth- -
quake. quails given to eat for 600,000
men-manna given every morning for
40 years - Nadab and Abihu burnt with
fire-earth opens to fwallow up Korah,
Dathan, and Abiram-brazen ferpent cur-
ing-a dumb aſs fpeaking with an human
voice Jordan divided
fun and moon
ſtanding ſtill for a whole day Gideon's
fleece-powers of Sampfon-water flowing
from a jawbone-meal and oil multiplied-
widow's fon raiſed-no rain for three years
Shunamites fon raiſed the wonders
of Elijah and Elifha Naaman's leprofy
cured
[ x ]
3
ค
cured-Gehazi made a leper for life-
one hundred fourfcore and five thoufand
Affyrians killed in one night
the fun on
the dial of Ahaz going ten degrees back-
ward three heroes in the fiery furnance
-a man's hand writing on the wall-lions
refufing to devour Daniel in the den—a fiſh
fwallowing Jonah, and after three days and
three nights vomiting him up alive upon
the dry land!
MIRACLES OF THE NEW TES-
TAMENT.
The man Jefus born without an earthly
father-water turned into wine-a noble-
man's fon reſtored- leper cleanſed - cen-
turion's fervant healed burning fever in
Peter's wife's mother removed a raging
tempeft calmed-legion of devils driven out
-palfy cured with a word-Jairus's dead
daughter raiſed-iffue of blood of twelve
years ſtanding effectually removed-dumb
man made to ſpeak-two blind men made.
to ſee
withered hand reſtored a man,
made blind and dumb by the devil, reftor-
ed to fight and ſpeech-five thousand fed
with a few loaves and fishes-Jefus walk-
ing
[ xli ]
ing on the watry world
a poor woman
cured by touching the hem of his garment-
Syrophoenician woman's daughter reftored
a man by the devil made a lunatick
cured a fish bringing the tribute money
in his mouth fig tree withering away-
deaf and ſtammerer reſtored to hearing
and free fpeech four thousand fed
wonderful draught of fiſhes-widow's dead
fon raifed-feven devils caft out of Mary
Magdalen a woman crooked for eigh-
teen years made ſtraight ten lepers
cleanfed a man impotent for thirty-
eight years healed a man blind from his
birth made to fee buyers and fellers
whipt out of the temple,-(this is thought
the greateſt miracle)- Lazarus dead and
putrified reſtored to life darkneſs at
Christ's death-Chrift's own refurrection,
a glorious miracle !-the Saints arifing with
Jefus-a net full of great fifhes, (one hun-
dred and fifty three) yet the net not
broken.
Note.
1. Explain the precife circum-
ftances of each miracle. 2. Make perti-
nent and ſtriking reflections on each.
III. GOOD.
[ xlii ]
III. GOODNESS OF THE DOC-
TRINE.
This is the moſt popular, convincing
and attractive argument, to prove the di-
vine infpiration of the fcriptures.
Good, in its moft fimple idea, fignifies
any thing that is fuited to pleaſe our taſte
or promote our happineſs-natural good,
is any thing that is fitted to anſwer its
end metaphyfical good is whatever is
agreeable to the intention of the great and
wife creator natural good, as confidered
with relation to fenfible or rational and intel-
ligent beings, fignifies what is pleaſant, or that
which tends to procure pleaſure or happineſs.
Good, in a rational fenfe fignifies any
being or thing that is poffeft of fuch per-
fections as are proper for any valuable
and important end.
The goodneſs of a thing is its fitnefs to
produce any particular end that is valuable
and important to a reaſonable creature.
The goodneſs of the doctrine of revealed
religion is its fuitableness to increaſe our
pleaſure,
[ xliii ]
pleaſure, diminiſh our pain, continue the
prefence of good, and to remove the pref-
fures of evil.
Goodneſs, in the ſenſe in which we uſe
it on this occafion, fignifies fuch a revelati-
on or diſcovery of God, as hath an exqui-
fite tendency to pleaſe a rational taſte, ele-
vate and extend our perceptions, remove
the preffures of guilt, fupport under a fenfe
of pain, and particularly affift and animate
us, in the purſuit of the nobleſt ends of
our exiſtence, and carry us on to the final
deftination of our nature, in its reft in the
fupreme and eternal good, who is the final
cauſe of our immortal fpirits. That which
has the fitteſt tendency to carry us with
the fureft fuccefs to the higheft end, muft
be eſteemed the richeft and moſt abundant
good to man.
In order to know the chief good of the
human kind, we muſt confider what we are;
what are our chief ſprings of action; what
are our principles of fruition; and what is
the last end of man.
We find that there are three conſtituent
principles, or properties, which diftinguiſh
human nature from the beafts that periſh.
Man has a perception of a firſt cauſe,
whom
[ xliv ]
whom we callGod-he has a moral ſenſe, or
perception, of the difference between moral
and a lively appre-
henfion of immortality in a future world.
good and moral evil
But in fpite of human pride man is a
guilty creature; he has fwerved from his
trueft and nobleft end; and has infinite
need of a divine revelation, to reftore him
to his original ſtate, and raiſe him to an
immortal dignity.
The gofpel is adapted to this end, with
the moſt exquifite delicacy and wiſdom. It
teaches us to confefs the depravity of our
own nature, and the rectitude and beauty
of the divine; to acknowledge the holi-
nefs of the law, and cover ourſelves with
fhame, for all our deviations from the wife
and excellent order of heaven-it infpires
us with fentiments of veneration for the
excellencies of God; and obliges us to fee
and own the tranfcendent beauty of his
perfections, as the object of our choiceſt
thoughts and higheſt eſteem.
This bleffed revelation perfuades us to
truft in the fupreme mind, and commit all
our concerns in life and death into the
hands of that God, who is a Being of infi-
nite tenderneſs and fidelity; it animates us
to
1
[ xlv ]
to a generous zeal for the honour of his
perfections, when they are denied or de-
graded by the tongues and actions of in-
fidels, who fet themſelves againſt him.
It teaches us to improve all our talents
of nature, literature and goodneſs, all
our power, wealth and reputation for the
divine honour; and to produce the glori-
ous fruits of knowledge and benevolence,
proportionable to the advantage we enjoy;
and thus to reprefent the beauty of God's
moral perfections to mankind.
}
This excellent religion perfuades and
affifts us to acknowledge our infinite dif
tance from God, our utter unworthineſs
before him, and univerfal dependence on
his vital prefence, and inceffant energy to
preſerve, enlighten and extend our pow-
ers; it teaches us to give him the higheſt
glory, as the generous author of all our
good, the fource of all our bleffings; to ex-
prefs the utmoſt gratitude for his benefi-
cence; to fet an extreme value on all his
bleffings of nature and grace; and to pre-
ferve a deep fenfe of the precious benefits
of health, wealth, and happineſs.
* See Dr. Ridgley's body of divinity, p. 1-7.
This
[ xlvi ]
This generous religion pours a torrent
of pleaſure through all the mind and foul
of man; it breathes eternal chearfulneſs into
the diftreffed confcience; it recommends
God's fervice as moſt agreeable to our fa-
culties, moſt ſuitable to our rational pow-
ers, promotive of our beft intereft, full of
folid fatisfaction; and it ſweetly conſtrains
us to avow in the face of the whole world,
that we do not repent of engaging in the
ſervice of our adorable mafter; that we
do not wish we had purfued the paths of
vice, and pleaſed the grand apoftate, the
firſt rebel in the world, rather than our
omnipotent and good Creator, the ever
bleffed and immortal GOD.
A MINIATURE PICTURE OF THE
CHRISTIAN RELIGION, OR A
VIEW OF THE BEAUTIFUL
PERFECTIONS OF CHRISTIAN-
ITY.
The goſpel is a bright diſcovery of a
benevolent provifion of happineſs for man;
-a provifion of happinefs confiftent
with eternal rectitude, and founded upon
the invariable juftice of the divine nature;
a provifion replete with wonder ani-
mated
[ xlvii ]
mated by love, made effectual in its inten-
tions by omnipotence, and carried on to its
final iffue under the conduct of the moſt
exquiſite wiſdom and prudence.
This revelation gives us the best ideas.
of God's perfections, it unfolds God's full
character, it diſcovers all of God at once,
as far as man in his prefent ftate can appre-
hend.-This glorious inftitution teaches us
the feveral relations of God to our world,
as its almighty creator, proper owner, wife
governor, generous benefactor, and im-
partial judge.
This divine religion afferts the original
dignity and happineſs of human nature,
it shows the revolt of all mankind from
God, and their deviation from the eternal
order of beings and the beautiful fitneſs
which the will of God has crdained to run
through his univerfal empire.-It opens to
our admiring eyes, God's infinite compaf-
fions to miferable man, and the harmoni-
ous affemblage of the divine perfections
to recover us from ruin and raife us to
final felicity. It gives a wonderful view of
commanding authority to awe the mind,
and of love to allure the heart to obedience.
Chriſtianity
€
[ xlviii]
Chriſtianity throws open the moſt ſub-
lime truths to aſtoniſh and yet improve
the human underſtanding, and elevate
the mind to its higheſt perfection; it draws
the moſt beautiful image of God upon
the foul, preſcribes the moſt intenfe ado-
ration of man to his creator, and trains him
"p to the moſt generous devotion and the
pleaſures of angels.
This lovely ſcheme of religion prefents
us with the moſt perfect ſtandard of beauti-
ful and found morals, it holds up to our
view the beſt ſyſtem of true virtue that ever
appeared in the world, a fyftem without
redundancy, without defect; a ſyſtem ad-
jufted to the nature, the powers and the
connections of man, and that is calculat-
edfor the perfect felicity, as well as the per-
fect rectitude of human nature. It like-
wife provides the beſt fuccours for our
feeble powers, and gives the fureſt aids,
the richest affiftances to attain the glorious
holinefs it preſcribes, and thus equally
prevents a bold prefumption of indepen-
dence, and a cowardly indolence and
dreaming inactivity, arifing from a want of
ftrength, or a confcioufnefs of weaknefs.
This
[ xlix ]
This chriſtian revelation difcovers un-
utterable encouragement to diftreffed fin-
ners in the divine obedience of the Lord
Jefus Chrift; it opens a ſcene of the moſt
glorious actions performed by the fon of
God in the nature of man; or in other
words,it fhews us the bleffed Jefus filled with
heavenly dignity, and greatnefs of mind,
animated by the moſt burning love to God
and mankind, performing a regular courfe
of the moſt beautiful actions and fervices;
or you may view his whole life as one entire
grand action performed for the honour
of God's moral attributes, fuffering a death
the moſt terrible and alarming with in-
vincible refolution and fortitude, and fol-
lowed with the most precious confequences
to man, for it ſhews us that this one grand
action and ſuffering compleated in death, it
fhews us I fay all this terminating upon us,
as made rich by theſe meritorious actions
and divine fervices which entitle us to the
full fruition of God!
What a contrivance of God's fuperla-
tive wiſdom is this? to give us all the
infinite benefits arifing from the glorious
obedience, and moft agonizing death of the
higheſt perfonage in the world! Thus by
reaſon of our relation to him and his con-
nexion
C 2
[ 1 ]
nexion with us, we are made rich with his
riches, and heirs of all God's empire by
virtue of our relation to him who is the
heir of all things.
This divine inftitution humbles the
finner and exalts the redeemer. It teach-
es us to form a very low opinion of the
extent of our own knowledge and good-
neſs, and to feel a deep ſenſe of our con-
ftant and abfolute dependance on God's
univerfal agency, and a conſciouſneſs of
our guilt: that we have offended the
infinite majeſty of heaven, and deferved
his contempt and indignation. That we
ought to be treated with abhorrence, and
puniſhed with the lofs of all poffible
and infinite good through an eternal du-
ration. In a word, this religion plainly
fhews us that fin is an infinite evil, as it
ftrikes at an infinite God, expofes us to
infinite lofs, fixes a ftain in the foul
through an infinite duration. Such views
of fin lay the foul in the duft at the foot of
God, and teaches us to adore and love
that Saviour who with almighty power and
boundleſs love hath reſcued us from eter-
nal and overwhelming deftruction.
Our
[i]
Our bleffed religion ordains the moſt
excellent buſineſs and uſeful employment
for every day of our fhort life upon earth,
it teaches us to fill up every hour with fuch
generous deeds as fhall follow us with
honour into eternity and enlarge our glory
and felicity for ever. Upon the chriftian
plan of principles and actions, we are
taught that a contemplation of the moral
perfections of God, devotion to him
through Chrift, and unwearied bene-
volence to man, are the only ends for
which life is worth a wifh or a rational
thought. Confequently
This divine fyftem propofes to us the
nobleft fprings of action, and directs us to
the moft exalted ends of our exiſtence, it
teaches us that God is the father and au-
thor of our being, that we fprang from his
breath, fhould refemble his virtues, and
tend towards him as our final reſt
and infinite good. This bleffed gofpel
raifes us to a daily correfpondence with
heaven, a fublime converfe with the great
father of reafon, and the fountain of im-
mortal fpirits.
This precious fcheme of falvation, is ex-
cellently adapted to the welfare of the fouls
of individual perfons, to ftrengthen the
understanding;
}
[ lii]
ftanding; to brighten our genius; re-
fine our reaſon; to enlarge the heart with
benevolence; fortify the foul with cou-
rage; and ſweeten all the devout and fo-
cial affections.
This divine religion, gloriously pro-
motes the good of all civil focieties, unites
all ranks of men in one bleffed band of
fathers, brothers, fons and fubjects; it
teaches the rich to be generous parents to
the poor, and the poor to be dutiful,
grateful children to the rich; it teaches
kings to be fathers, and ſubjects to be
fons, and turns all mankind into one ge-
neral family of friendſhip and love.
NORTHAMPTON,
Jan. 1. 1768.
JOHN RYLAND.
Note, This difplay of the beautiful perfections of
the CHRISTIAN religion will be continued in the
SECOND ESSAY on the ADVANCEMENT OF LEARN-
ING, and prefixed to a book now printing, entitl-
ed a Compendiun of Natural Philofophy, contain-
ing Mechanics, Hydrostatics, Pneumatics, Optics and
Aftronomy. By John Horfley, A. M. adapted to a
courfe of Experiments performed in Glafgow, 12mo,
PART
1
PART THE FIRST,
OF
MECHANICS.
CONCERNING THE
?
MECHANICAL POWERS.
A
NY machine or engine by which
a man can raiſe a greater weight,
or overcome a greater reſiſtance,
than he could do by his natural ftrength
without it, is called a mechanical power:
To every machine of this fort, a power
is applied, in order to raiſe a weight or
overcome a refiftance. And the ma-
chine is fo contrived, that the power
which works it, fhall move through a
greater ſpace in the fame time, than the
weight or reſiſtance moves through :
for without this, no advantage can be
gained by it.
*
B 2
1
The
?
[ 4 ]
The power or advantage gained by
any machine, let it be ever ſo ſimple
or ever fo compound, is as great, as
the ſpace moved through by the work-
ing power is greater than the ſpace
through which the weight or reſiſtance
moves, during the time of working.
Thus, if that part of the machine to
which the working power is applied,
moves through 5, 10, 20, or (if you
will) 1000 times as much space as the
weight moves through in the fame time;
a man who has juft ftrength enough to
work the machine will raife 5, 10, 20,
or 1000 times as much by it as he could
do by his mere natural ftrength with-
out it. But then, the time loft will be
always as great as the power gained.
For it will take 5, 10, 20, or 1000 times as
much time for the power to move through
that number of feet or inches, as it would
do to move through one foot or one inch.
The
[ 5 ]
The fimple machines called mecha-
nical powers, are fix in number, viz.
the lever, the wheel and axle, the pul-
leys, the inclined plane, the wedge,
and the ſcrew.
And of thefe, all the
moſt compound engines do confiſt.
J
4
{
१
B 3
THE
PLATE I.
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Fig. 1.
E
4
6
MECHANICS.
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B
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Fig. 2.
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Fig.3.
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nce page
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3
Fig. 8.
3
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Fig. 7.
4
J.Mynde foulp.
•
THE
1
さ
​L
E V
VER,
OR FIRST
MECHANICAL POWER.
A
LEVER is a bar of iron or
wood, made uſe of for raifing
great weights a little way from the
ground, and fupporting them until ropes
be put under them, to raiſe them higher
by other machines, if required.
Fig. 1. ABC is fuch a bar, placed
upon'a ftone D in the ground E. The
ftone muſt be firm in the ground, to
fupport the lever or bar; and is called
the prop.
The parts AB and BC, on different
fides of the prop, are called the arm's
¡
B
of
4
[ 8 ]
of the lever.
The end of the ſhorteſt
arm AB is put below the weight F,
and the hand (which is called the
working power) is applied to the end
C of the longeſt arm BC.
Here it is plain, that if the hand at
C either pulls or puſhes down the end
C of the arm of the lever BC, the end
A of the arm AB will raiſe the weight
F.
And, by means of this fimple ma-
chine, a man will be able to raife as
much more weight at F than he could
raiſe by his natural ſtrength without
any fuch machine, as the arm BC is
longer than the arm AB: and the
power or hand at C will move through
as much more ſpace than the weight
F moves through, as BC is longer than
AB. Hence, the power or advantage
gained by this lever, or added to the
natural ſtrength of a man, is as great
as
[ 9 ]
}
as the arm BC is longer than the arm
AB.
To prove this by experiment, provide
fuch a bar as ABC (fig. 2.) and divide
its length into any number of equal
parts, as fuppofe 7, of which AB hall
be one part, and BC the other fix.
Let the part AB be made fo thick and
heavy, as juft to balance the part BC,
when the bar reft on the prop D, having
the part AB on the left fide of the
prop, and the part BC on the right
fide. Then hang the weight E of one
ounce, on the end of the arm BC at 6,
and hang the weight F of fix ounces at
A on the end of the arm AB; and the
weight E will juſt balance and ſupport
the weight F which is fix times as
heavy. Here, E may be called the
power, and F the weight. F being as
much nearer the prop than E is, as E
is lighter than F.
B 5
There
[ 10 ]
1
There are four different kinds of
ĺevers: the one here referred to is called
a lever of the first kind, in which, the
prop is between the power and the
weight. The deſcription of the other
three kinds follow in order.
THE SECOND KIND OF LEVER.
In this machine, the weight is be-
tween the prop and the power. Thus,
the bar ABC is fupported at the end
A by the table D, a weight as E is
hung any where upon the bar, as at B,
and the power or hand is applied to
the other end C of the bar, to lift
up that end, and raiſe the weight.
The power or advantage gained
by this machine is as great as the
diſtance of the hand from the table
or prop D exceeds the diſtance of
the
[
1 ]
if
the weight from it.
Thus, if the
power or hand at C be feven times as
far from D as the point B of the bar is,
on which the weight E is hung, a power
equal to the feventh part of the weight
will fupport it. So that a man, taking
hold of the end C of the bar or lever
ABC, and pulling upward, could fup-
port ſeven times as much weight hang-
ing for the point B as he could carry
in his arms without fuch a machine;
and he muſt raiſe the end C feven in-
ches, in order to raiſe the weight E
one inch.
To confirm this by experiment, di-
vide the length of the bar ABC (fig.4.)
into feven equal parts, and place the
end A on the prop D: then tie the
ftring dd to the other end C of the bar,
and put the ſtring over the pulley e
which turns freely round its axis ƒ;
the ſaid axis being ſuppoſed to be fixed
in
[ 12 ]
in the wall of the room.
This done,
hang a weight F of one ounce to the
end of the ſtring at I; and hang a
weight of 7 ounces on the point B of
the bar AB, at a feventh part of the
length of the bar from the prop D;
and the weight F by endeavouring to
defcend, and raife the end C of the
bar, will ſuſtain the weight E; fo that,
between theſe weights, the bar or lever
will remain immoveable.
THE THIRD KIND OF LEVER.
In this machine, the power is be-
tween the prop and the weight. It
cannot properly be reckoned a mecha-
nical power, but rather the reverſe
thereof; becauſe a man can lift as
much more by his natural ſtrength than
he can by this lever, as the diftance of
the
[ 13 ]
the weight from the prop is greater
than the diſtance of the power from
the prop. So that it is the lever of the
fecond kind reverfed.
For, if the end A of the bar ABC
(fig. 5.) be placed below the table D,
and the bar be divided into feven equal
parts, from A to C; and there be a
weight of one ounce, as E hung upon
the end C of this lever, and a man
takes hold of the lever at B, which is
only a ſeventh part of the whole length
from the end A, and pulls upward, he
muſt pull with a power or force of
feven ounces at B to fupport one ounce
at the end C; and then, if he raifes
his hand one inch higher, the weight
C will be raiſed ſeven inches.
To prove this, divide the bar ABC
(fig. 6.) into feven equal parts, put the
end A under the table D, and tie one
end
[ 14 ]
end of the ftring dd to the divifion 1 at
B, and tie the other end of the ftring
at 7 to a weight F of feven ounces.
Then, tie the weight E of one ounce
to the ſeventh divifion at the end C of
the bar, and put the ftring over the
pulley e which is at liberty to turn
'round its axis f; and the weight F
which acts as a power of 7 ounces to
pull the lever upward, will be balanced
by the weight E which is but one
ounce, and pulls the lever downward
with the force of one ounce. So that,
if the part AB be made thick enough
to balance the part BC without any
weights, and the weights E and F be
hung on as in the figure, they will just
balance and ſupport each other. And
if the weight F be pulled one inch
downward, it will raiſe the weight E
feven inches.
THE
[ 15 ]
THE FOURTH KIND OF LEVER.
This lever differs in nothing but its
form, from the lever of the firſt kind :
its power is the fame, and its ſhape is
reprefented in fig. 8. and is applicable
to that of drawing a. nail out of wood
by a hammer.
Suppoſe the ſhaft AB (fig. 7.) of the
hammer ABC to be five times as long
as the iron part BC, which draws the
nail D; the part B of the hammer
reſting on the point 5 of the board as
a prop. Then, by pulling backward
the end of the ſhaft at A, a man will
draw the nail D with a fifth part of the
power that he could pull it out with
pincers, in which caſe, the nail would
move as faft as his hand does; but with
this hammer, the hand moves through
five
[ 16 ]
five times the length of the nail by.
the time the nail is drawn out of the
wood.
ነ
To confirm this, make AB (fig. 8.)
five times as long as BC, bending the
bar ABC to the form of a carpenter's
fquare. Then let the heel B turn on a
pin b, as a fixt axis or prop, driven in-
to the wainſcot of a room, and let a
ftring fixt at A go over the pulley D
which turns on the pin d alſo fixt into
the wainſcot. Then hang a weight E
of one ounce to the lower end of the
ftring, and a weight of five ounces as
F, to the end C of the bended lever;
and theſe weights will balance each
other. Here the axis or prop b is be-
tween the weight F and the power E,
(whofe action is at A) as in the lever
of the first kind.
All fciffars, pincers, and fnuffers,
are levers of the firſt kind, and the nail
which
[ 17 ]
which holds them together is the ful-
crum or prop.
Bakers knives, which are fixed by a
ſtaple at the point of the blade, act as
levers of the ſecond kind, in cutting
loaves. Rudders of fhips, and doors
turning on hinges are levers of the
fecond kind, and fo are oars of boats.
The bones of a man's leg or arm act
as levers of the third kind, and ſo do
the pinions and wheels of clocks and
watches.
<
THE
THE
WHEEL AND AXLE,
}
OR SECOND
MECHANICAL POWER.
C
N this machine a cord C goes round
IN
the wheel A, and another cord E
goes round the axle B, which is fixt
into the wheel; ſo that for every time
the wheel is turned round, the axle
muft turn round alfo.
A weight F (fig. 9.) is fixt to the
cord E that goes round the axle, and
a power is applied at D to the cord C
that goes round the wheel. If the
power D bears the fame proportián to
the weight F that the diameter of the
axle bears to the diameter of the wheel,
}
the
་་་་
I'LATE II,
Fig.9.
8
E
H
MECHANICS.
Fig.10!
A
a
лъ
D
Fig.15.
To face page 19.
1 D
8
F
10D
D
Fig.16.
B
G
Frig.13・
D
D
É
E
4
Fig.11.
4
F
B
C
Fig 12.
I
Fig.14.
F
A
!
8
K
}
}
B
D
E
B
D
B
Fig.17.
:
E
J. Mynde fculp
[ 19 ]
the power and weight will balance each
other. Thus, fuppofe the diameter of
the wheel to be eight inches, and the
diameter of the axle to be orie inch; then,
one ounce acting as a power at D will
balance eight ounces of weight at F;
and a ſmall additional power at D will
cauſe it to deſcend, and turn the wheel
and its axle, and fo raife the weight F.
And for every inch that Frifes, D`will
fall eight inches: fo that the velocity of
the power D will exceed the velocity of
the weight F as the circumference of the
wheel exceeds the circumference of the
axle, which we here fuppofe to be eight
times. And by fuch a machine a man
pulling the cord C at D would be able
to raife eight times as much weight at
Fhung to the cord E as he could raife
by his natural ſtrength without ſuch a
machine. Hence, the power and ad-
vantage gained by this machine is as
great
[ 20 ]
great as the diameter or circumference
of the wheel exceeds the diameter or cir-
cumference of the axle.
It is eaſy to conceive that the power
of the wheel and axle is the ſame with
that of a lever of the firft kind. For,
(in fig. 10.) let HC be a wheel, and
Ab its axle. Draw the ftraight line
ABC; then, as B is the center of the
wheel, AB is the femi-diameter of the
axle, and BC the femi-diameter of the
wheel; and here, AB may be confi-
dered as the ſhorter arm of the lever
ABC, BC as its longer arm, and a
the prop. Now, if BC be eight times
as long as AB, a weight D of one
ounce hanging from C will balance a
weight F of eight ounces hanging from
A.
THE
THE
PULLEY,
OR THIRD
MECHANICAL POWER.
A
Single pulley as AB (fig. 11.)
that turns round its axis in a
fixt block as C, and does not move out
of its place, ferves only to change the
direction of the power, but gives no
mechanical advantage thereto. So that
a man can raiſe no more weight by
means of this pulley than he could lift
by his natural ſtrength without it.
For, if a rope DE goes over this
pulley, and has the two equal weights
F and G (ſuppoſe four ounces each)
hung to its ends, they will balance
each
"""
[ 22 ]
each other; and if either of them be
pulled down, through any given ſpace,
the other will rife through juſt as much
ſpace in the fame time: and therefore
as the velocity of the weight is equal
to the velocity of the
power, the po-
wer muſt be as great as the weight to
balance it.
But if (as in fig. 12.) one end of
the rope ABC be tied to a fixt hook
D, and the rope goes under the pulley
E which turns in the moveable block
F, and over the pulley G which turns
in the fixed block H, a power equal
to one ounce at the end of the rope C
at I will balance a weight K of two
ounces hung at the moveable block F.
So that, where a pulley is ufed that
will rife with the weight, a power
equal to half the weight will balance'it.
For the weight K of eight ounces
hangs by a double rope AB, and there-
fore,
[ 23 ]
*
fore, the part A of the rope fuftains
one half of the weight, and the part B
the other. And therefore, if a man
was to take hold of the rope at B, and
pull upward, he would only feel half
the weight K, becauſe the other half
hangs by the part of the rope at A.
But as it is more convenient to pull
downward than upward, if the rope
be put over the pulley G, which turns
in the fixt block H, and ferves only to
change the direction of the pull; a man
pulling by the rope at C will raiſe twice
as much weight at K as he could lift
by his natural ſtrength without any
machine.
If there are two pullies in the lower
block F, there must also be two in the
upper block H; and then, as the rope
will be twice doubled in going over
and under all theſe pullies, the weight
will hang by four parts of the rope,
and
[ 24 ]
and a power equal to a fourth part of
the weight will balance it. Hence,
the power of this machine is as the
number of parts of the rope by which
the lower block F hangs; and this will
be always equal to twice the number
of pullies in that block.→
THE
THE
INCLINED PLANE,
OR FOURTH
MECHANICAL POWER.
I'
F a wedge ABC (fig. 13.) be cut
lengthwife through its middle
AED, it will be divided into two equal-
ly inclined planes, one of which is
ABC (fig. 14.) whofe acting fide is
AEDB. The power of this machine
is as great as the length AB of the act-
ing fide exceeds the thickneſs or height
of the back BCED where the blow is
given.
For (fig. 15.) if a moulding D was
to be ſplit off from a thick plank E,
by driving the inclined plane ABC be-
C
tween
[ 26 ]
tween the plank and moulding, the
moulding will be as much eaſier fepe-
rated from the plank by this means,
than it could be pulled off by a cord
fixed to a ſtaple in the moulding at D,
as BC is longer than AC.
To prove this by experiment, let
the inclined plane A (fig. 16.) run
upon
wheels, and be drawn forwards
by means of a weight G, to which the
line EE is fixed, and alſo to the in-
clined plane at B;
the fixed pulley F.
the line going over
Let one end of
the line D be fixed to a hook in the
wall, at five or fix feet from the in-
clined plane, in fuch a manner, that
when the other end of the line is tied
to the frame of the roller C the line,
may be parallel to the acting fide A of
the plane. Now, if the weight G be
as much lighter than the roller C and
its frame, as the height or thickneſs a,
of
[ 27 ]
t
of the plane is less than the length of
the fideA,the plane will reft under the
Load C, fo as the load can neither make
it run back, nor can the weight G
draw it forward. So that, if the length
of the fide A be four times as great as
the perpendicular height a, a power
at G equal to one fourth part of the
weight of the load C will balance the
plane under it.
If you
fet the inclined plane (fig.
17.) againſt the piece A to keep it
from moving backward,, and let the
roller be drawn by the line BB go-
ing over the fixed pulley D-by
means of the weight C. If C be as
much lighter than the roller as the in-
clined fide of the machine is longer
than the machine is thick at A, the
load will be fupported on the plane by
the power of the weight C.
C. And
thus we find, that in drawing a cart
C 2
or
[ 28 ]
}
or waggon up-hill, if the power of
the horſes be proportioned to the
weight of the waggon as the perpen-
dicular height of the hill is to the
length of its fide, the waggon will be
kept from running back. And as
much additional power as will over-
come the friction of the axles, will
draw the waggon up the hill.
1
t
THE
PLATE II.
B
Fig.18.
L
1
"
Fig.19.
d
C
Frig:20.
M
A
Fig. 24
K
A
MECHANICS
Fig.21
A
A
C
Fig.23
B
d
EC
B
IP
d
b a
B
B
D
Fig.
22.
•
To face page 29.
A
E
F
B
G
H
h
E
M
N
L
Fig.25.
0
J. Mynde fails.
THE
14
WEDGE,
OK FIFTH
MECHANICAL POWER.
I
F two inclined planes (fig. 18.)
which are equal and fimilar, aṣ
ABd and CBd be joined together at
their bafes Bd, they will become a
wedge as ABC.
Therefore, in cleaving wood, the
power of the wedge will be to, the re-
fiftance of the wood on the fide BC
as the length of that fide is to the half
back Cd of the wedge; and as the
refiftance of the wood againſt the fide
BC is to the half back Ad. That is,
the power or advantage gained by the
C 3
wedge
[ 30 ]
wedge is as great as the fide BC or,
BA exceeds the half back Ad or Cd.
Or, putting the whole together, as
great as the length of both the fides
AB and BC exceeds the length of the
back AC where the blow is ftruck by
the hammer or mallet.
For, in fig. 19, before the wedge
ABC enters the wood EHG that is in-
tended to be cloven, the parts EF and
GF are in contact; but when the
wedge is driven into the wood, the
part G is removed as from a to C, and
the part E is removed as from a to A:
d
fo that, the velocity of E or G (go-
ing off obliquely) is to the velocity of
the wedge, as the length of the fide
of the wedge BA or BC is to the half
back dA or dC. And, in this, as well
as in all the foregoing mechanical
powers, the power or advantage gained
is
[ 31 ]
is as great as the velocity of the power
exceeds the velocity of the refiſtance.
To prove this by experiment, let
the two pieces of wood (fig. 20.) EH
and GH be joined at HH by band or
hinge, and be drawn together by the
fmall cords Efgf and Ghi, going over
the pullies g and i, and having weights
as K at the lower ends of the cords,
(the weight on the line Ghi, equal to
the weight K, being hid from fight by
the table M) and let the light wedge
ABC be drawn into the wood EHHG
by means of the weight L hanging at
the cord DDB, faftened to the wedge
at B, and going over the pulley e. If
the weight L be in the fame propor-
tion to the weight K as the half back
Ad of the wedge is to either of its
fides AB or CB, the weight L which
acts as a power for making the wedge
go into the wood, will balance the
C 4
weight
[ 32 ]
weight K which pulls the fide EH of
the cleft EHHG, as a refiftance,
againſt the fide AB of the wedge; and
will alfo balance a weight equal to K
hanging at the cord Ghi, and pulling
the fide GH of the cleft as a reſiſtance
againſt the other fide BC of the wedge.
{
THE
THE
L
SCREW,
OR SIXTH
MECHANICAL POWER.
F
IE a piece of paper be cut into the
ſhape of an inclined plane ABC
(fig.21.) and wrapped round and round
the cylinder AB (fig.22.) from the per-
pendicular AC to the point B, the fide
CB being ſtill kept upon itſelf in wrap-
ping, the inclined fide AB will form a
fpiral or fcrew as abcd around the
cylinder AB.
If theſe ſpirals be cut deep into the
wood, as at abcd, as in fig. 23, and the
gudgeons g and b of the wood do
turn in a frame; if the cylinder AB
C 5
be
[ 34 ]
be turned round and round by the
winch W, the ſpirals or threads of the
fcrew abcd will have a progreffive mo-
tion, as from A toward B, advancing
through the ſpace ab, or bc, or cd,
always in being once turned round.
And, if the top of the ſtrong ſpring
D (whofe foot is fixed into the heavy
and immoveable block F) be put be-
tween any two of the fcrew-threads,
as at e, and then if the fcrew be turned
once round, the top of the fpring will
be moved from e to f, through a ſpace
equal to the diſtance between any two
of the threads ab or bc; and the
fpring, which acts as a refiftance againſt
the power that turns the ſcrew, will be
bent into the form GEƒ.
Now, fince the refiftance moves only
from e to f, in the time that the ſcrew
is turned once round, it is plain, that
the power or force gained by the fcrew
is
[ 35 ]
is as great as the circumference of the
cylinder AB on which the fpirals are
cut, exceeds the diſtance or ſpace be-
tween the neighbouring ſpirals, if the
ſcrew be turned round by hand, taking
hold of the end of the cylinder at B.
But, as the fcrew is never turned in
that manner, but by means of a lever
or winch W, the power of the ſcrew
is increaſed as much as the length of
the lever from / to the handle W ex-
ceeds the ſemi-diameter of the cylin-
der AB.
Thus, in fig. 24. the weight G is
fixt to the end of the rack F whofe
teeth work in the fcrew E belonging
to the axis CD, on the top of which is
the handle or winch AB, which being
turned once round, will turn the ſcrew
one round, and lift the rack and weight
through the ſpace of one tooth, as
from F to f. Now, fuppofe this ſpace
to
[ 36 ]
•
to be one inch, which is lifted at one
turn, and the length AB of the handle
to be feven inches; then the circle de-
ſcribed by the power that moves the
handle will be forty-four inches in
circumference. So that, as the velo-
city of the power is forty-two times.
as great as the velocity of the weight,
a man could raiſe forty-two times as
much weight [allowing for friction]
by this engine as he could do by his
natural ſtrength without it,
A
A
POWERFUL ENGINE
FOR
RAISING VERY GREAT WEIGHTS.
C
N the axis C of the winch AB
is a pinion Ð turning the wheel
E, on whofe axis is a pinion F turn-
ing the wheel G, on whoſe axis is a
pinion H turning the wheel I, on whoſe
axis is a pinion K turning the wheel
L, on whofe axis M the rope N coils or
winds (as the machine is turned by the
winch) and draws up the weight O.
Now, fuppofe each pinion to have
eight leaves (fometimes called teeth)
and each wheel to have eighty teeth,
it is plain that the pinion turns ten
times
[ 38 ]
times round for once that the wheel
can turn round in which the pinion
works. Therefore, the pinion D will
make ten revolutions for one of the
wheel E and pinion F; the pinion F
will make ten revolutions for one revo-
lution of the wheel G, which wheel,
together with the pinion H will make
ten revolutions for one of the wheel I
and pinion K, and the pinion K will
make ten revolutions for one revolution
of the wheel L and its axle M.
theſe four tens being multiplied into
one another give a product of 10000.
So that the winch AB muſt be turned
round ten thouſand times, in order to
make the wheel L turn once round,
which will only raise the weight O
through as much space as it takes
length of the
N to go once round
the axle M.
rope
And
Hence,
[ 39 ]
1
Hence, if the axle C was to be turned
round by hand, without a winch, a
man could raiſe ten thousand times as
much weight by the rope coiling round
the axle M as he could do if it coiled
round the axle C. But if he makes
ufe of a winch as AB, of which the
length AB is ten times as great as the
femidiameter of the axle C, the power
of the engine will become ten times
as great as before; and ten times ten
thouſand is an hundred thoufand: fo
that, by this engine a man could raiſe
an hundred times as much weight as
he could do by his natural ftrength
without it: and, for every inch that
the weight rifes the handle B of the
winch would move through an hun-
dred thouſand inches, or almoft 2778
yards.
Suppofing all the axles equally big
as the winch ufed, the rope going
round
[ 40 ]
round the axle C would enable the
man to raiſe ten times as much as he
would do without it: round the axle
d 100 times as much; round e 1000
times; round f 10000 times, and round
M 100000 times. So that the power
may be increaſed at pleaſure by ma-
chinery; but we fee it may be made
fo great as to be ufelefs, on account of
the time that would be loft in working
it for the time loft is always as great
as the power gained.
•
PART
PART THE SECON D.
GEOMETRY,
BY SCALE AND COMPASSES.
TRIGONOMETRY,
MEASURING OF HEIGHTS AND
DISTANCES.
}
;
GEOMETRY.
K
PLATE IV.
Fig. 2.
Fig.3.
፣
A
OF
60
B
A
8,0
B*
00%
8'0
5'0
Line of Chords
Fig. 1.
70:
θα
Line of Kines
10
90
H
B
40
Line of Fangents
20
60
160.
230
260
190
220
120
250
150
180
210 240
Fig.4.
50 80 110 140 170 200 23
H
b face page 43.
160 190
220
130
100
210
180
170
150
50
200
120
170
40
90
140
190
160
110
180
60
130
.80
150
170
100
-40°
120
140160
30
50 70
99 Ito 130 150.
The Line of Chords
50
140
30
120
80
100
90
6a
130
11.0
40
90
20
260
120 80.
100
20
50
8.0
110
60
70
100
-10
30
80
Go
40
190
50
60
D
70 80
50.
10
40 30
30
40 50
50 60
40
Bo
50
20
10
40/30
པ།བ
?
60
40.
30
50
20
40
30
10
20
30
10
20
20
20
10
10
10
سلسل
A
10
15
•
O
CED
DEF
20
30
35
of blot
1253##121
10.
Ch
:
K
50
I
J. Mynde foulp
THE
CONSTRUCTION
f
t
O F
ANGLES, SINES, TANGENTS,
AND CHORDS.
FIĠ. I. EXPLAINED.
E's divided
A
14
VERY circle, great or fmall,
is divided (or ſuppoſed to be di-
vided) into 360 equal parts, called
degrees. Thus, the quadrant DE of
the large circle ABDE contains go
degrees, and fo do the ſmaller quadrants
G, H, I: and 4 times 90 is 360.
An angle is the ſpace intercepted by
two lines, as CD and CF, meeting
one another in the center of the circle
at
f
[ 44 ]
→
at C and its meafure is the number
of degrees contained in the arc DF,
(as fuppofe 45) which is the fame
number as is contained in the arc G, or
H, or I, bounded by the lines CD and
CF. So that, the angular point C
where theſe lines meet, is always fup-
poſed to be in the center of a circle;
and the meaſure or quantity of the an-
gle is the number of degrees in the
circumference of the circle intercepted
between the two points (as D and F)
where theſe lines meet or cut the
circle.
The diameter of a circle is a ftraight
line, as ACD, paffing through the
center C of the circle, and meeting
its periphery in two oppofite points, as
A and D.
The radius of a circle is half its
diameter, as CA or CD.
The
[ 45 ]
The chord of an arc is a ſtraight
line drawn from one extremity of the
arc to the other. Thus, AbB is the
chord of the arc AeB: and as the arc
AeB contains 90 degrees, its chord
AbB contains the fame. number alſo.
And if one foot of the compaſſes be
conſtantly kept in the point A, where
the arc and chord meet at one end,
and the other foot be opened fuccef-
fively to all the 90 degrees of the arc,
and theſe diſtances of opening be tranf-
ferred from the arc to the chord line,
as in the figure, the chord line will be
divided into 90 degrees.
N. B. Sixty degrees on the chord
line, taken from A to b, are equal to
the radius of the circle from which the
Thus, Ab is
line of chords is made.
equal to AC.
The right line of an arc is half the
chord of double that arc. Thus, df
is
[ 46 ]
is the right fine of the arc Dd; and is
half of Dfg, which is the chord of
the arc dDg. To make a line of fines
as for the go degrees of the arc AE,
draw ftraight lines, parallel to the ra-
dius AC, from every degree of the arc
AE to the radius or femidiameter CE,
and they will divide CE into a line of
fines, as in the figure.
A tangent is a ſtraight line as DK,
touching the circle into any given
point as D. It may be divided into
degrees by ſtraight lines drawn from
the center C through the degrees of
the arc DB, as in the figure. But you
can never get to the goth degree on
the line DK, becauſe it is parallel to
the radius CB. So that the tangent
of 90 degrees is infinite.
:
1
PROBLEM
[ 47 ]
PROBLEM I.
To lay down an angle of any given
number of degrees lefs than 90, as
ſuppoſe of 25 degrees, fig. 2.
Draw the ſtraight line AB, and let
the angular point be at the end A.
Open your compaffes from A to b (fig.
1.) that is, from the beginning of the
line of chords to the 60th degree
thereof and with that extent, fetting
one foot of the compaffes in the end
of the line at A (fig. 2.) with the
other foot deſcribe the arc def. Then,
ſetting one foot of the compaffes in
the beginning of the line of chords,
extend the other foot to 25, the given
number of degrees thereon: and, with
that extent, fet one foot in the end of
the arc at d (fig. 2.) in the line AB,
and
[ 48 ]
1
and make a mark with the other foot
as at e, in the arc def. Laftly, from
A, draw the ſtraight line AeC, through
the mark e; and the line AC will
make an angle of 25 degrees with the
line AB as was required.
N. B. Where an angle is marked
by three letters, as CAB, the middle
letter A always denotes the angular
point, or meeting of the lines which
make the angle.
PROBLEM II.
To meaſure the quantity of an angle (as
CAB in fig. 3.) by the line of chords.
With the chord of 60 degrees (that
is, by taking 60 degrees of the line of
chords in your compaffes) fet one foot
in the angular point A, and with the
other
[ 49 ]
other foot defcribe the arc de from one
leg (or fide) of the angle to the other:
then, fetting one foot in the end d of
the arc, in the line AB, extend the
other foot to the other end of the arc
at e, in the line AC. Laſtly, apply
that extent to the line of chords, from
the beginning of the line toward 90 ;
and the number of degrees in the
chord line that are intercepted between
the points of the compaffes will be the
meaſure of the angle CAB, as was
required. Which meaſure, in fig.3.will
be found to be twenty-eight degrees.
!
D
PROBLEM
[ 50 ]
PROBLEM III.
To make ſcales of equal parts, for
meaſuring lines; or for laying down
lines which ſhall repreſent given dif-
tances taken in feet, or yards, or
miles, &c. fig. 4.
Draw feveral ſtraight lines on a flat
fmooth piece of box-wood, and, at
one end, place the numbers 10, 15,
20, 25, 30, 35, 40, as in the figure.
Set off a whole inch at A, two-
thirds of an inch at B, half an inch at
C, four tenths of an inch at D, one
third of an inch at E, three tenths of,
an inch at F, and one quarter of an
inch at G ; and divide the ſeveral lines
ABC, &c. into as many of theſe ſpaces
as they will contain. Then divide each
of the firſt ſpaces as ABC, &c. into
ten
[
51 ]
ten equal parts, and put the numeral
figures to them. So fhall the lines or
fcales ABC, &c. be divided in fuch
a manner, as that one inch ſhall be
contained in ten parts or divifions of A,
in 15 of B, in 20 of C, in 25 of D, in
C,in
30 of E, in 35 of F, and 40 of G.
The line of chords may be taken from
fig. 1. and inſerted on this ſcale.
The equal divifions either of the
lines A, B, C, D, E, F, G, may be
taken for feet, or yards, or miles, in
plotting or meaſuring of any figure.
And as the first space at each of the
above letters contains ten equal parts,
all the other ſpaces being equally large
in each particular line, is fuppofed to
contain ten equal parts alfo.
To take off any given number of
parts with your compaffes, from either
of theſe ſcales, as fuppofe 26 from the
fcale A, which contains ten parts in an
D 2
inch
[ 52 ]
inch, fet one foot of the compaffes in
20 on that ſcale, and extend the other
towards A, fo far, as till it reaches the
fixth divifion counted from o to a, and
then you will have the given number
of parts between the points of the
compaffes.
In plotting maps or
figures fo that
up a large fhare
of room on paper, the ſcales A or B
may be uſed; but where a great deal
is intended to be put in little room,
the ſcales For G are to be made uſe of.
Thus, fuppofe I wanted to lay down
a ſmall part may take
50
feet of diſtance, and had about as
much ſpace allowed for it as from H to
I I take that extent in the compaffes,
and find by trial that it will agree with
50 parts of the ſcale A. But if I had
no more ſpace than KL for repreſent-
ing that diſtance, I find by trial, that
I muſt lay it down from the ſcale G.
and
PLATE V.
A
M
OF
CH
A
3
Fig.5.
h .
Fig. 6.
A
}
C
B
49 Deg.
}
!
GEOMETRY. - very set of
To face page 53
Fig. 7.
go Deg
114 Feet
75 Feet
A
30
7
Frig. 8.
81
49-
Deg
a
104
:
41 Deg
100
Deg
go Deg
86 Feet
B
20
AD
:
50
B
Fug: 9.
F
OD
-D
40 50 60 70 80
Fig.10
F
E
J.Minde/culp.
Ї
]
Ï 5353 ]
and which-ever fcale is begun with,
the whole map or figure muſt be drawn
by that fcale.
PROBLEM IV.
To raiſe a perpendicular BC on the
end of B of a given ſtraight line AB
fig. 5.
Open the compaffes to any con-
venient width, and fetting one foot in
the end B of the line AB, let the
other foot fall any where above the
line (no matter where, in reaſon,) as
at d, and make a mark there. Then,
without altering the compaffes, fet one
foot in the point d, with the other
foot defcribe the circle efgh; and, lay-
ing the edge of a ruler to the interfec-
- tione (of the circle with the line AB)
D 3
and
[ 54 ]
and thro' the point d, draw the diame-
ter edg. Laftly, laying a ruler to B, at
the end of the line AB, and to the end
g of the faid diameter, draw the right
line BgC, which fhall be perpedicular
to the line AB, as was required.
DESCRIPTION OF A RIGHT
ANGLED PLAIN TRIANGLE.
The fide AB (fig. 6.) is called the
bafe, the fide BC the perpendicular,
and the longeſt or oblique fide AC
the hypothenufe.
The angle at B is called a right an-
gle, which contains 90 degrees; for as
BC is perpendicular to AB, the point
B may be made the centre of a quad-
rant def, or quarter of a circle, con-
taining 90 degrees. The angles at A
and C are called acute angles, becauſe
each of them is lefs than 90 degrees:
for
[ 55 ]
for, if they be made the centres of the
arcs klm and ghi, neither of theſe arcs
contain 90 degrees; but both of them
taken together always do.
3 I
Thus, if the angle at A contains
degrees, the angle at C contains 59,
which being added together make 90.
And as the right angle at B contains
90, all the three angles taken together
contain 180 degrees.
And hence it is, that if either of the
acute angles of a right angled triangle
be given, if its quantity be ſubſtracted
from 90 degrees, the remainder will
be the quantity or number of degrees
in the other acute angle.
D4
SOLU-
[ 56 ]
SOLUTION OF THE SEVERAL
CASES OF RIGHT ANGLED
PLAIN TRIANGLES.
N. B. In all the following feven cafes,
we ſhall keep by the ſcale C (fig.
4.) in meaſuring the fides of the
triangle; and by the line of chords
(fig. 4.) in meaſuring the angles;
and ſhall make the triangle (fig. 7-)
ferve for all the cafes.
CASE I.
FIG. 7.
The two acute angles at A and C,
and the baſe AB, being given, to find
the perpendicular BC.
In the triangle ABC the given angle
at A is 49 degrees, and the given an-
gle
1
[ 57 }
gle at C is 41 degrees, and the baſe
AB is 75 feet. Quef. The number of
feet in the perpendicular BC ?
Make AB equal to 75 parts of the
fcale C (fig. 4.) and make BC per-
pendicular to AB by Prob. IV. Then,
fetting one foot of the compaffes in
the beginning of the line of chords,
extend the other foot to 60 degrees
(which is called the radius, or chord of
60) and with that extent, fetting one
foot in A (fig. 7.) fweep the arc ab
with the other foot, and taking 49
degrees from the line of chords in
your compaffes, fet that extent from
b to a, and through the point b, from
A, draw the line AaC, meeting the
perpendicular at C. Then, taking the
line BC between the points of your
compaffes, apply that extent of the
compaffes to the fcale C (fig. 4.) and
you will find it to be 86 parts or divi-
D 5
fions
•
[ 58 ]
fions of that ſcale. And as the bafe
AB is reckoned in feet, fo muſt the
perpendicular BC be. Hence, the
perpendicular is 86 feet; which was
required to be found. Quod erat
demonftrandum.
CASE II. FIG. 7.
The two acute angles at A and C,
and the baſe AB being given (as in
cafe I.) to find the hypothenuſe AC.
Project the triangle ABC, as taught
in cafe I. Then take the hypothe-
nuſe AC in your compaffes, and apply-
ing that extent to the ſcale C in fig.4.
you will find it to be 114 parts, which
are feet if the bafe AB be taken in feet,
or yards if the baſe AB be taken in
yards.
CASE
[ 59 ]
CA SE III. FIG. 7.
The two acute angles A and B being
given, viz. A 49 degrees, and C 41;
and alfo the hypothenufe AC 114 feet.
Quef. The number of feet in the baſe
AB?
The triangle ABC being projected
(as fhewn in cafe I.) take the baſe AB
in your compaffes, and by meaſuring
it on the fame ſcale (C, fig. 4.) as
above, it will be found to contain 75
feet.
CASE IV. F 1 G. 7.
The baſe AB being given, viz. 75
feet, and the perpendicular BC 86 feet.
Quef. The number of feet in the hypo-
thenuſe AC?
Make
[ 60 ]
Make AB equal to 75 parts of the
above fcale, and draw, BC perpen-
dicular to AB, by Prob. IV. mak-
ing BC 86 parts of the fcale. Then
draw the hypothenuſe AC, and mea-
fure its length by your compaffes on
the fame ſcale, which length will be
found to be 114 parts, which are feet,
becauſe AB is reckoned in feet.
CASE V. F1 G. 7.
The baſe AB and perpendicular
BC being given (as above) to the two
acute angles at A and C.
Conſtruct the triangle as directed in
cafe IV. Then, with the chord of 60
degrees taken in the compaffes (fee
cafe I.) fet one foot in the angular
point A, and with the other foot de-
ſcribe the arc ab; then, without alter-
ing
[61]
ing the compaffes, fet one foot in the
angular point C, and with the other
foot deſcribe the arc cd. Lastly, take
theſe arcs at their extremities in your
compaffes, and by meaſuring them on
the line of chords (fee Prob. II.) you
will find ab (the meaſure of the angle
at A) to be 49 degrees, and cd (the
meaſure of the angle at C) to be 41
degrees. Or, having found either of
theſe angles, ſubſtract it from 90 de-
grees, and the remainder will be the
meaſure of the other.
CASE VI. FIG. 7.
The baſe AB and the hypothenufe
AC being given, the former being 75
feet, and the latter 114, to find the
acute angles A and C.
Make
[ 62 ]
Make AB equal to 75 parts of the
above-mentioned fcale, and from the
end B draw BC (long enough, be fure)
perpendicular to AB. Then, taking
114 parts from the fame ſcale in your
compaffes, fet one foot in the end A
of the baſe AB, and with the other
foot cross the perpendicular BC in C,
and draw AC. Then meaſure the
angles at Aand C, as directed in cafeV;
and you will find that the former con-
tains 49 degrees, and the latter 41.
CASE VII. F I G. 7.
The baſe AB and hypothenufe AC
being given (as fuppofe of the above
meaſures) to find the acute angles A
and C, and the perpendicular BC.
Project the triangle ABC as directed
in cafe VI. Then meaſure the angles
A and
[63]
A and C, as in that cafe; and the for-
mer will be found to be 49 degrees,
and the latter 41. And by taking the
length of the perpendicular BC in
your compaſſes, and applying that ex-
tent to the ſcale C (fig. 4.) it will be
found to be 86 parts, which are feet,
as the bafe is taken in feet.
HERE ENDETH ALL THE CASES OF
RIGHT ANGLED PLAIN TRIANGLES.
SOLU-
[ 64 ]
SOLUTION OF THE SEVERAL
CASES OF OBLIQUE ANGLED
PLAIN TRIANGLES.
In all theſe cafes we ſhall keep by
the fame ſcales of equal parts and
chords which were uſed in the folu-
tion of right angled plain triangles.
N. B. In every oblique angled plain
triangle (as ABC, fig. 8.) the fum of
all the angles make 180 degrees, which
is equal to two right angles, or twice
90 degrees.
CASE I. FIG. 8.
Two fides and an angle oppofite to
one of them being given, to find the
angle oppofite to the other fide.
In
[ 65 ]
In the triangle ABC there are given
the fide AB 104 feet, the fide BC 53
feet, and the angle at A 30 degrees.
Quef. The number of degrees in the
angle at C?
Take 60 degrees from the line of
chords (fee Prob. II.) and, with that
extent, fetting one foot of the com-
paſſes in the angular point C, with the
other foot deſcribe the arc efg; then
fetting one foot in the extremity e of
the arc, extend the other foot to the
other extremity g thereof, and apply
that extent to the line of chords. But,
as it happens at prefent, this extent is
greater than 90 degrees, which is the
whole length of the chord line, and
confequently the angle at C is greater
than a right angle. Therefore, tak-
ing the whole length of the line of
chords in your compaffes, fet that ex-
tent from e to ƒ on the arc efg; and
then,
[ 66 ]
then, taking the remainding part fg of
the arc in your compaffes, meaſure it
on the line of chords from the begin-
ning thereof, and it will be found to
be ten degrees; which added to the
former 90 makes 100. So that the
angle C contains 100 degrees: which
was to be found.
CASE II. FIG. 8.
The three angles and one of the
fides being given, to find either of the
other fides.
B
In the triangle ABC there are given
the angle at A 30 degrees, the angle at
50, the angle at C 100 degrees, and
the fide AC 81 feet (by the ſcale C in
fig. 4.) Quef. The number of feet
contained in the fide AB?
Take
[ 67 }
Take the line AB in your compaf-
fes, and meaſure its length on the ſcale
C in fig. 4, and it will be found to
contain 104 of the equal parts of that
ſcale, which are to be eſteemed fo ma-
ny feet, becauſe the given fide AC is
reckoned feet.
CASE III. F 1 G. 8.
Two fides and an angle oppofite to
one of them being given, to find the
other fide.
t
In the triangle ABC there are given,
the fide AB 104 feet, the fide AC 81
feet, and the angle at 30 degrees.
Quef. The length of the fide BC in
feet?
Take BC in your compaffes, and
meaſure its length on the aforefaid
ſcale, and you will find it to be 53
parts or feet: which was required.
CASE
[ 68 ]
CASE IV. F I G. 8.
Two fides and the angle included
between them being given, to find the
other angles.
In the triangle ABC there are given,
the fide AC 81 feet, the fide BC 53
feet, and the included angle at C 100
degrees.
and B ?
Quef. The angles at A
Meaſure theſe angles as fhewn in
prob. II. and you will find the angle
A to be 30 degrees and the angle B
50: which was to be done.
CASE V. FIG. 8.
Two fides and their included angle
being given, to find the third fide.
In
[ 69 ]
In the triangle ABC the fame things
are given as in cafe 1V. And it is
required to find the third fide BC.
Take BC in your compaffes, and
meaſure it on the fame ſcale as you
have hitherto uſed for this triangle,
and you will find it to be 53 feet.
CASE VI. FIG. 8.
The three fides being given, to find
the three angles.
In the triangle ABC are given, the
fide AB 104 feet, the fide AC 81
feet, and the fide BC 53.
Ques
The number of degrees in each of
the angles AB and C ?
Meaſure the angles as taught in
Prob. II. (anfwering to fig. 3.) and
will find the angle at A (fig. 8.)
you
to
[ 70 ]
to be 30 degrees, the angle at B 50,
and the angle at C 100: which was
to be done.
HERE ENDETH ALL THE CASES OF OB-
LIQUE ANGLED PLAIN TRIANGLES.
We ſhall next defcribe the quadrant,
and then fhew the method of finding
inacceffible heights and diſtances; in
which, fome of the foregoing cafes
will be found uſeful.
PRO-
[ 71 ]
PROBLEM
V.
A QUADRAN T.
FIGURE 9, 10.
This is a fourth part of a circular
plate, divided into 90 equal parts
or degrees, which is a fourth part of
the number contained in a circle. A
thread Cd hangs from its centre C;
and the end d of the thread is fixt to
a little weight D, called the plummet.
The thread is called the plumb-line,
and the general ufe of the quadrant,
thus fitted up, is to take the angular
height of objects above the level of the
center C of the quadrant, or their de-
preffion below it.
Let GCE (fig. 9.) be an horizon-
tal Fine, and EF an upright object.
It
[ 72 ]
}
It is plain, that if a man puts his eye
to the corner A of the quadrant, and
holds its face perpendicular to the ho-
rizon, ſo that the plumb-line may
hang freely and perpendicularly on
the face of the quadrant, and hold the
quadrant ſo as that looking along the
fide AC he may juſt ſee the top of the
object at F, the plumb-line will ſhew
the angle of the object's height above
the horizon, which will be equal to
the number of degrees counted from
B in the arc Bd. For, juft as many
degrees as the corner A of the quad-
rant is depreffed below the horizontal
line GCE in the arc GA, fo many de-
grees will the fide CB of the quadrant
deviate from the perpendicular Cd.
And fince ACƒF and GCeE are ſtrait
lines, the angle fCe muſt be equal to
the oppofite angle GCA; and there-
fore the arc ef muft contain the fame
number
[ 73 ]
number of degrees as AG does; which
is equal to the number of degrees in
the arc Bd of the quadrant, namely 20.
So that the angle of the height of
the object EF above the level of the
center C of the quadrant is 20 degrees.
The depreffion of any part of a vi-
fible object below the level of the ob-
ferver's eye may be eaſily found by
the quadrant, thus. If the obſerver
be on the top or fide of a hill (fig. 10.)
as at C, and fees an upright object as
EF at the foot of the hill, and wants
to know the angle of its depreffion be-
low the line СbD which is on a level
with his eye at C. Let him hold the
quadrant fo, as that by looking along
the edge CB, he may juft fee the foot
of the object at F, if he wants the
depreffion of the foot; and the plumb
line hanging freely on the face of the
quadrant will fhew the angle of de-
preffion,
E
[ 74 ]
preffion, by the number of degrees it
hangs upon, counted from A in the
arc Ad (which is here reprefented to
be 29 1-half) for the arc of depreffion
is bB, which is equal to the arc Ad;
as is plain to fight by the figure. The
quadrant has generally two thin braſs
plates with holes in them (called the
fights) to look through at the object.
And a line drawn through theſe holes
is parallel to the ftraight edge of the
quadrant.
PROBLEM VI.
To find the height of a houſe or tower,
provided it ſtands on level ground.
Fig. 11.
Retire to fome convenient diſtance
from the tower, on level ground, as fup-
poſe
PLATE VI.
A
30 Degrees
70 Yards
By the Scale B (Plate IV) of
15 parts in an Inch.
Fig.11
TRIGONOMETRY.
A
3 Yards
40
B
By the Scale B (Plately)
of 15 parts in an Inch.
h
d
!
رماس
By the Scale Plate NV) of
35 parts in an Inch
Fig. 13.
A
30 Degrees
1
* 15 Feet
convenient
To find the Height of the Obelisk D C The Observer measures off any
distance, as suppofe 75 feet from the middle of the foundation (at D) of the Obelisk, &.
C
placing himself at A, he observes the top of the Obelisk through the Sights of
his Quadrant, and writes down the Angle of its height above the level of his Eye.
which we shall suppose to be 30 Degrees, as in the Figure. Then, working according.
to the Directions in Prob.NI, he finds the real height of the Obelisk above the point B
which is on a level with his Eye,to be 43 feet, to which he adds the height of his Eye
above the Ground, which is equal to BD.and then he knows the whole height of the
Obelisk
A
29 Degrees
100 feet
D
Sa Degrees
Fig.14
By the ScaleFPlate of
35 parts in an Inch.
28 Degrees.
:
75 Yards
D
40 Degrees
77 feet
100 feet
700 Yards
100 Yards
C
To face page 75
Fig. 12
12.
:
[ 75 ]
1
pofe feventy yards, and ſtanding there,
obſerve the top of the tower through
the fights (or along the edge) of the
quadrant, and take the angle of its
height, as ſuppoſe thirty degrees, above
the level of your eye, as directed in
the laſt problem (page 73.) Then go
home, and project the triangle ABC,
(fig. 11.) as follows: the larger the
better.
Suppoſe the given diſtance AB from
the tower to be feventy yards, and the
angle A of the height of the tower to
be thirty degrees. Quef. The height
of the tower BC in yards?
From either of the ſcales of equal
parts, B, C, or D, (fig. 4. page 50.)
as fuppofe from the ſcale B, take
feventy parts in your compaffes, and
make the line of diſtance AB equal
thereto. Then draw the line AC,
making an angle of thirty degrees with
E 2
the
[ 76 ]
the line AB, and raiſe the line BC
(for the tower) perpendicular to AB,
drawing it on from B till it meets the
line AC. Laftly, take the length of
the line BC in your compaffes, and
meaſure it on the fame fcale from
which you laid down the line AB, and
you will find it to be forty parts and
about two-thirds of the forty-firſt part,
which is to be eſteemed fo many yards,
fince the diſtance was taken in yards.
So that the height of the tower, above
the level of the obſerver's eye, is forty
yards and 2-thirds; to which add the
height of the obferver's eye above the
ground, and the whole will be the
height of the tower BC.
When larger diftances are taken,
fome of the fmaller fcales, as C, D,
or E, &c. muſt be uſed, that the
figure may come within the compafs
of the paper.
This
[ 77 ]
This problem anfwers to cafe I. of
right angled plain triangles, page 47.
PROBLEM VII.
To take the height of a tower ftand-
ing at the foot of a hill, where no
level ground can be had to obferve
it by.
In fig. 12, let AB be part of the
fide of a hill, and Bk a tower ſtanding.
at the foot of the hill; the height of
which tower is wanted to be known in
yards.
Meaſure any
convenient diſtance, as
fuppofe eighty yards, from B to A, up
the fide of the hill, which may be
eafily done if the flope is even, as
Abcd B. But if it has hollows in it,
as at e, g, i, poſts muſt be fet up in
E 3
them,
[ 78 ]
them, fo that their tops may be in a
ftraight line with the little rifings be-
tween them, and the ſtraight diftances
nd, db, kc, &c. meaſured all the way
from B to A.
Standing at A, take the angle of
depreffion (by Prob. V. page 73.) of B,
the foot of the tower, by means of the
quadrant, and alfo the angle of de-
preffion of the top of the tower at k,
both below the horizontal line AC:
and write them down. Now let us
ſuppoſe that the angle BAC of depref-
fion of the foot of the tower at B was
twenty-nine degrees 1-half, and the
angle of depreffion CAk, of the top
of the tower was three degrees 1-quar-
ter; which being fubftracted from
twenty-nine and an half, leaves twen-
ty-fix degrees 1-quarter for the angle
of the tower's height.
Draw
[ 79 ]
Draw the ftraight lines AB and AC,
making an angle of twenty-nine de-
grees 1-half (Prob. I. page 47.) Then,
from any convenient fcale of equal
parts (as the ſcale B, page 50.) take
off eighty equal parts for the yards of
the obſerver's diſtance from the foot of
the tower, and fet them off with your
compaffes from A to B, and draw
BkC perpendicular to AC. This done,
take twenty-fix degrees 1-quarter from
the line of chords, with your com-
paffes, and fet them off from c to m,
in the arc cml which meaſures the an-
gle CAB: and, from A draw the
ftrait line Amk through the point m;
and it will cut the upright line BC in
the point k: fo that the line Bk will
repreſent the height of the tower.
Laſtly, take Bk in your compaffes, and
meaſure its length on the fame ſcale
of equal parts by which you fet off
'
E 4
the
[ 80 ]
the eighty yards of diſtance from A to
B; and you will find the height of
the tower Bk to be thirty-fix yards.
PROBLEM VIII.
To find the height of a tower as BC
when the diſtance from it cannot be
meaſured, on account of an inter-
vening river as BD; and alfo to find
the breadth of the river, Fig. 13.
On the farther fide of the river,
(at D) from the tower, take the an-
gular height of the tower, by the
quadrant, which angular height we
ſhall ſuppoſe to be fifty-two degrees.
Then, from D (the fide of the
river BD) meaſure off any convenient
number of feet, as fuppofe one hun-
dred, to A and ftanding at A, take
again
[ 81 ]
again the angular height of the tower;
which we ſhall fuppofe to be twenty-
nine degrees
fields is done
and your work in the
;
Draw the ftrait line ADB ; and from
any of the ſmaller fcales (as from the
ſcale F, page 50, of thirty-five parts
in an inch) fet one hundred parts
which you are to reckon fo many feet.
Then from A draw the ftrait. line
AC, making an angle of twenty-nine
degrees with the line ADB; and from
D draw the line DC, making an angle
of fifty-two degrees with DB; and
the two obſerved angles of altitude
will be projected.
Now, as it is plain, that the top of
the tower at C muſt be the oint C
where the lines AC and DC interfect
each other; therefore, from the
point C let fall the perpendicular CB
on the line ADB and taking CB in
E
5
your
[ 82 ]
your compaffes, meaſure its length on
the ſcale F (page 50.) and you will
find it to be one hundred parts, which
are to be reckoned fo many feet for
the height of the tower above the le-
vel of the obferver's eye.
Laſtly, take DB (the breadth of the
river) in your compaffes, and by mea-
furing it on the fame fcale, you will
find it to be ſeventy-ſeven feet.
The following problem for find-
ing the perpendicular height of a hill,
and alfo for finding the breadth of
that part of the baſe which is between
the perpendicular and the obferver, is
exactly of the fame nature with this
problem.
PROBLEM
[83]
PROBLEM IX.
To find the perpendicular height of a
hill, Fig. 14.
$
Let E be a hill whofe perpendicular
height BC is to be found.
Place yourſelf as near to the foot of
the hill (fuppofe at D) as you can,
fee its top; and ſtanding at D, take
the angular height of the hill by your
quadrant, which we fhall fuppofe to be
forty-two degrees and an half.
Then meafure off any convenient
diſtance, as ſeventy-five yards, towards
A; and ſtanding at A, obferve again
the angular height of the hill, which
we fhall fuppofe to be twenty-eight
degrees; and your work in the field is
done.
$
Draw
[ 84 ]
Draw the ſtrait line ADB, and taking
feventy-five parts from fome of the
fore-mentioned ſcales, as fuppofe from
the ſcale F, fet theſe parts with your
compaffes from A to D. Then draw
the ftrait line AC, making an angle
of twenty-eight degrees with ADB;
and draw the ſtraight line DC, making
an angle of forty-two degrees and an
half with DB. And thus, having
projected the two obferved angles, the
top of the hill muſt be at the interſec-
tion C of the line AC and DC.
Therefore, from the point C draw
CB perpendicular to DB; and taking
CB in your compaffes, meaſure its
length on the fame fcale from which
you ſet off the feventy-five parts from
A to D, and you will find it to con-
tain one hundred parts, which are to
be eſteemed fo many yards for the
perpendicular height of the hill.
By
M
:
PLATE VIL
Ъ
By the Scale G (PLI) of 40 parts in anInch
202 Poles
A106 Deg,
BC
394 Deg.
150 Poles
43 Deg.
B1084 Deg.
70
86
:
285 Poles
TRIGONOMETRY,
لعبة
10
20
40
Tä
Fig.15.
OK
60
70
80
910
Fig.17
265 Poles
By the Scale G(P1.IV of 40
parts in an Inch
468 Poles
180 Poles
734 Deg.
m
,
276 Fathoms ·
h
Fig.16.
964 Fathoms
120 Fathoms fromatВ e
To face page 8
266 Fathoms
8 Deg.
The
B
Myndefculp.
[ 85 ]
By the fame kind of meaſurement,
the part Be of the baſe of the hill,
from the perpendicular BC, to the
place where the hill begins to riſe, on
the fide next the obſerver, will be
found to be one hundred and two
yards.
Thefe examples being fufficient to
fhew the method of finding inacceffi-
ble heights, we fhall next fhew how
to find inacceffible diſtances.
PROBLEM X.
To find the diſtance of an inacceffible
object, as fuppofe a fhip at ſea,
Fig. 16.
Provide a quadrant with two fights
(fig. 15.) on each of its ftraight edges,
as
[ 86 ]
as a, b, and c, d; and alfo with a
moveable index as CD, turning on
the center C, and having two fights
as e and f, whofe holes for looking
through are in a ſtraight line with the
center C and the fiducial edge g
which marks the degrees in the quad-
rant.
In fig. 16, at any convenient place
as A on the fhore, lay the quadrant
flat on a table, and from A meaſure
off a convenient diftance, along the
fhore, as fuppofe one hundred and
twenty fathoms, to B, and fet up a
mark at B. Then direct the edge Ab
of the quadrant toward the mark at B,
fo as you may ſee the mark through
the fight-holes; this done, keep the
quadrant fteady, and move the index
Ad till you ſee the ſhip at C through
the fight-holes of the index, and write
down the number of degrees cut by
the
[ 87 ]
the index on the quadrant, reckoning
from b tod; which we fhall fuppofe
to be ſeventy-one degrees and an half.
Then remove the quadrant to B,
having left a mark where it ſtood at
A; and placing it flat on the table,
ſet it ſo as you may ſee the mark at Á
through the fight-holes on the fide Be..
This done, move the index till you
fee the ſhip at C through the fight-
holes of the index, and write down
the number of degrees cut by the
index in the quadrant reckoning from
e to g, which number we ſhall fuppofe
to be eighty-two. And you have done
the
part of
your work without doors.
Draw the ſtraight line AB for part
of the ſhore, and taking one hundred
and twenty parts, for ſo many fathoms,
from the ſcale G, fet them with your
compaffes from A to B. Then, from
A, draw the ſtraight line AC, making
an
[ 88 ]
1
an angle of ſeventy-two degrees and
an half with the line AB; and from
B, draw the ftraight line BC; making
an angle of eighty-two degrees with
the line BA. This done, take the
lines AC and BC feparately in your
compaffes, and meaſure them on the
fcale G: the former will be found to
be two hundred and feventy-fix parts,
for the number of fathoms that the
ſhip is diſtant from A and the latter
will be found to be two hundred and
fixty-fix fathoms for the diſtance of the
ſhip from B. The ſhip being fuppofed
to be lying at anchor. Laftly draw Ce
perpendicular to AB, and its length
meaſured by the compaffes on the fcale,
will be found to be two hundred and
fixty-four fathoms and an half from
that point of the fhore to which the
is neareſt.
;
In
'
[ 89 ]
In the fame manner may the breadth
of a river be found, by ufing C as a
mark or object on the farther bank of
the river.
If your ſcale be too fhort, fet its
whole length as from A to b, and then
meaſure the remaining part hC.
PROBLEM XI.
To find the diſtances of two inaccef-
fible objects as C and D (fig. 17.)
from two given points asA and B, and
likewiſe the diſtance of theſe objects
from one another.
For this purpoſe, inftead of a quad-
rant (as in the laft problem) you muſt
have a femi-circle, devided into one
hundred and eighty degrees, with a
moveable
[ 90 ]
moveable index, and fights, as in the
quadrant.
Pitch on two places, as A and B,
from each of which you may fee the
inacceffible objects C and D, and mea-
fure the diſtance from A to B, which
we ſhall ſuppoſe to be one hundred and
fifty poles *.
Place the femi-circle on a table at A,
in fuch a manner as that looking
through the fights on its edge bc you
may ſee a mark fet up at B. Then
move the index till through the fights
on it
you can fee the inacceffible ob-
ject D, and write down the number of
degrees cut by the index, reckoned
from c; which number we fhall fup-
pofe to be thirty-nine 1-quarter. Then
move on the index till through its
fights you perceive the other inacceffi-
* A pole or perch is five yards and an half, which
makes fixteen feet and an half.
ble
[ 91 ]
ble object C, and write down the
number of degrees cut by the index
from c, which we fhall fuppofe to be
one hundred and fix.
Set up a mark at A, and remove the
femi-circle to B, and placing it there
on the table, ſet it fo as you can perceive
the mark at A through the fights on
the edge de; and then, moving the in-
dex till you can firft fee the inacceffible
object C through the fights of the in-
dex, and then till you can fee the other
object D through them; write down
the number of degrees cut by the in-
dex at both theſe times, counting from
d; as ſuppoſe forty-three degrees for
C, and an hundred and eight 1-quarter
for D, and your work in the field is
done.
From either of the ſmall ſcales (as
from G, page 50.) take an hundred
and fifty parts, for fo many poles, and
fet
[ 92 ]
fet them with your compaffes from A
to B, and draw the line AB. Then
draw AD making an angle of thirty-
nine degrees 1-quarter with AB, and
draw AC making an angle of one
hundred and fix degrees with AB.
Draw alfo BC making an angle of
forty-three degrees with BA and BD
making an angle of one hundred and
eight degrees 1-quarter with BA.
The interfections of theſe lines at
C and D are the places of the above-
mentioned inacceffible objects, whofe
diſtances from each other, and from
the places of obſervation at A and B,
are found by meaſuring the lines CD,
AC, AD, BC, BD, on the ſcale
G with the compaffes; which dif-
tances will be found, from C to D
two hundred and fixty-five poles,
from A to C two hundred and two,
from
[ 93 ]
from A to D two hundred and fixty-
eight, from B to C two hundred and
eighty-five, and from B to D one
hundred and eighty, as in the fi-
gure.
}
PART
P
PART THE THIRD.
O F
OPTICS,
OR,
THE CONSIDERATION OF THE
HUMAN EYE AND THE NA-
TURE OF LIGHT.
}
O F
LIGHT.
HE diſtance of the earth from
TH
the fun is upwards of 81 mil-
lions of miles; and it is demonftrable
that light comes from the fun to the
earth in 8 minutes. Hence, the ve-
locity of light is fo great, that it moves
upwards of 10 millions of miles in a
minute of time.
A cannon ball could not move from
the earth to the fun in lefs than 20
years. So that, light travels as far
in 8 minutes as a cannon ball could
travel in 20 years.
But there are 10,512,000 minutes
in 20 years. And this number be-
F
ing
[ 98 ]
ing divided by 8 minutes, quotes
1,314,000, for the number of times
that light moves fwifter than a cannon
ball.
Now, fuppofe we fay (for the fake
of round numbers) that light moves
only one million of times as ſwift as a
cannon ball moves; it is plain, that
if a million of particles of light put
together were as big as a fingle grain
of fand, we could no more open our
eyes to receive the impulſe of light,
than we durft to have fand ſhot point
blank againſt them from a cannon.
When any object is illuminated,
either by the fun or a candle, every
illuminated point of the object reflects
the light in all manner of directions.
And it is by this reflection of the light
that objects become viſible.
Thus, fuppofe the object ABC (fig.
1.) to be illuminated by the fun on
the
+
PLATE VIII.
B
"
OPTICS.
Fig.1.
>
1
H
E
F
A
m
B
D
୯
e
B
g
80
Hig⋅ 3·
C
A
+
Fig. 2.
B
b
a
Y
To face page 98
T
с
-R.
?
J.Mynde fouly
હૂ
OF
[ 99 ]
}
the right-hand fide, the points A, B,
and C, reflect the rays of light every
way through the hemifphere DEFG;
and therefore, theſe three points will
be viſible to an eye placed any where
in that hemifphere. But all the inter-
mediate points of the object reflect the
light in the fame manner: and there-
fore the whole object will be viſible
to an eye placed any where on the
enlightened fide.
The left-hand fide, on which the
fun fhines not, would be altogether
invifible, if it were not for the rays
of light reflected upon it from the
terreſtrial objects on that fide. But
as the left fide is much dimmer than
the right, we fee how much stronger
the direct light of the fun is than the
reflection of light from rough and un-
poliſhed objects.
Every object would
F 2
be
+
>
[ 100 ]
be dark, and confequently invifible,
if it reflected none of the light.
CONCERNING THE REFRAN-
GIBILITY OF LIGHT.
The rays of light proceeding from
a luminous body go on in ftraight
lines, whilft they continue in any
medium of an equal and uniform
denfity or compactneſs. But when
they pafs out of one medium obliquely
into another, they are refracted or bent
out of their rectilineal courſe at their
entrance into the different medium.
Let AB (fig. 2.) be a glafs cup, and
Ca board fet up between the cup and
a candle at D. The fhadow bilk of
the board will fall into the cup, and if
there be no water in it, the fhadow
will reach to i. So that if a thread be
ſtretched from i, ftraight over the top
of
[ 101 ]
of the board, and continued to the
candle, it will come into the flame
thereof; which fhews, that the ray
Dghi goes on from the candle in a
ſtraight line. Moreover, if a perfon
places his eye below the bottom of the
cup, at i, and looks over the top of the
board C, he will fee the flame of the
candle even with the top of the board.
Now let water be poured into the
cup, fo as to fill it up almoft to the
brim, and you will perceive the fha-
dow move from i to k; which fhews
that the ray Dghi is bent from its rec-
tilineal courfe, into the form Dglk,
and that the bended part is at the fur-
face of the water at b. So that, if a
perfon now places his eye under the
glaſs bottom at k, he will ſee the can-
dle D juft over the board; and the
candle will feem to him to be raiſed
from D to E, becauſe it will appear
F 3
to
[ 102 ]
to him to be in the right line khE, in
direction of the bended part bk of the
now refracted ray.
When a ray of light falls perpendi-
cularly on the ſurface of water, or any
other medium, the ray goes on in the
fame perpendicular direction. Thus,
the ray Ffm, falling perpendicularly
on the furface of the water at f, goes
on in the fame direction fm, without
fuffering any refraction at all. Which
fhews, that the rays of light muſt en-
ter obliquely into a medium, if they
are refracted by it.
The rays of light come ſtraight from
the fun, in the open ſpace, till they fall
upon the earth's atmoſphere, and then
they are refracted by the denfer medium
of the atmoſphere, fo as to bring the fun
in view every day, before he rifes in our
horizon; and to keep him in view for
fome time after he is really fet below it.
And
[ 103 ]
And by means of this refraction, we
have about a whole fummer's more fun-
ſhine in 100 years than we would have
if there were no atmoſphere.
Let ABC (fig.3.) be a portion of the
earth, whofe convex furface is gOh, and
let debt be the top of the atmoſphere.
Let alfo HOR be the horizon of an
obferver on the earth's furface at O,
and let S be the fun,
below the hori-
zon. A ray of light Sab comes all
the way ftrait from the fun till it falls
obliquely on the top of the atmoſphere,
as at b, where it is turned out of its
rectilineal courfe and fo, inſtead of
going on in the fame direction be, it
goes in the direction bo, to the obfer-
ver's place at O, and therefore, to this
obferver, the fun, even before he riſes
in the horizon HOR, will appear a-
bove the horizon at T; becauſe he will
be feen in the direction of Ob, the re-
fracted
F 4
[104]
and Ob
fracted part of the ray ObaS
produced ftrait outwards, will be in
the rectilineal direction ObcT.
If a ray of light Sikl falls obliquely
upon
the furface of a plane glaſs ABCD
at / (fee the lower part of fig. 3.) the
ray will not paſs through the glaſs` in
direction ikl, but will be refracted in
the direction Im in the glafs: and if the
glafs be equally thick, that is, if the
fide AD be parallel to the fide (or fur-
face) BC, the ray leaving the glafs at
m will be refracted the contrary way,
and go on in the direction of mn, pa-
rallel to the direction ikl in which it
came to the glaſs. And, an eye at n
will fee the fun S, not in his true place
at S, but higher, in direction of the
line must. If a ray op falls perpendi-
cularly on the furface of the glaſs, as
at p, it will ſuffer no refraction in
paffing through the glafs, but will go
on
PLATE IX.
F
Fig. 4.
A
B
Ꭰ .
E
Fig.5
Fig. 6.
B
b
OPTICS.
G
Ꮐ
Fig. 7.
B
D
D
H
1
:
B
To face page205-
A
Fig. 8.
I
3
a
b
k
F
k
A
fo
ed
Β'
do
B
Frig⋅ 9.
E
F
J.Mynde foulp.
[ 105 ]
on in the ftrait line pqr continued:
and an eye at r will ſee the fun in his
true place at U.
Fig. 4. fhews five forts of ground
glaffes edgewife. A, is called a plano-
convex glaſs, becauſe it is plane on one
fide and convex on the other. Bis
called a double convex glaſs, becauſe
it is convex on both fides. Cis called
a plano-concave glafs, because it is
plane on one fide and concave on the
other. D is a double-concave glafs,
being concave on both fides. And E
is called a meniſcus glaſs, which is con-
cave on both fides; but more fo on
one fide than the other. All theſe
forts of glaffes are called lenfes, and
the right line FG is their axis.
The funs rays may be reckoned pa-
rallel at the earth, as ABCD (fig. 5,
6.) at the earth's furface, on account
F 5
of
[ 106 ]
of the fun's vaft diftance from the
earth.
If parallel rays, ABCD (fig. 5.):
fall on a plano-convex glafs BDe, ſo
as the middle ray def be perpendicular
to the plane furface of the glafs, they
will be fo refracted in paffing through
the glafs, that they will meet in a
point F, in the further fide of a circle
BDkFiB, of which the convex fide of
the glaſs BC is a part of a ſphere or
globe whofe diameter is equal to the
diameter of the circle. The point F
where the rays meet, is called the
principal focus of the glaſs; and, if
the rays are not ftopt at the focus, but
are fuffered to pafs on, they will di-
verge from the focus toward the con-
trary fides. Thus, the ray CDF will
go on from the focus in the direction
Fc, and the Fay ABF will
go on
from the focus in the direction Fb.
The
[ 107 ]
The middle ray def is not refracted at
all, becauſe it falls perpendicularly on
the glaſs. Whatever fide of the glafs
is turned toward the fun, the diſtance
of the focus F will be the fame from
the plane fide e of the glaſs.
If parallel rays, ABCD (fig. 6.)
fall upon a double convex glafs BDe,
they will be fo refracted as to meet
and croſs one another in a point F,
which is the center of a circle BDkfiB,
equal to the diameter of a ſphere, of
which either of the convex fides BD
or BeD is a portion. And the rays,
after croffing, will diverge to the con-
trary fides, in the ſpace Fgh, juſt as
much as they converged in the ſpace
BFD; and would continue to go on
in this diverging ſtate. But if ſuch
another double-convex glafs, gfb be
placed in the fide of the circle oppo-
fite to BeD, the rays, after paffing
through
}
[ 108 ]
through the glafs gfb will go on pa-
rallel to one another, in the ſpace
ghbc, continued in the fame manner as
they came parallel to one another in
the ſpace ACBD, to the glaſs BeD.
But, becauſe they crofs in the focus F,
they change fides afterward. Thus,
the parcel of rays ABdeF, which are
on the left fide of the middle ray deF,
after meeting at F, cross over to the
right fide of the middle ray, and
in the ſpace Fbbff.
dCDeF croſs the middle ray at F, and
then go on in the ſpace FgcfF. So
that, ABFbb is one of the outfide rays,
and CDFge is another.
go on
And the rays
A raidant point of any object is a
point from which rays of light pro-
ceed, as F, in fig. 7. And theſe rays
CDE continually diverge in ftraight
lines every way from that point.
If
راد
[ 109 ]
If the radiant point be in the focus
F of a convex glafs AB, all the rays
that fall upon the glafs will be rc-
fracted in paffing through it, and af-
ter leaving it they will go on in paral-
lel lines in the ſpace GABH.
If the radiant point R (fig. 8.) be
further from the convex glafs than its
focus F, the diverging rays RA, RB,
&c. which fall upon the glafs AB,
will converge after paffing through
the glaſs, in the ſpace ABIA; and
will all meet in a point I, where they
will form the image of the radiant
point R.
If the focal diſtance aF is known,
and alfo the diftance aR of the radiant
point, from the glafs AB; the dif
tance of the image J, of the radiant
from the other fide of the glaſs, may
be found by this rule: multiply the
diſtance aR of the radiant by the fo-
cal
[ 110 ]
cal diſtance aF, and divide the product
by their difference of diſtance; and
the quotient will be the diſtance bI of
the image of the radiant from the glafs.
Thus fuppofe the focal diftance aF to
be two inches, and the diſtance of the
radiant R fix inches; thefe being mul-
tiplied together make 12. But the
difference between two inches and fix
inches is four; by which, divide the
product 12, and the quotient is 3
in-
ches for the diſtance of the image I
of the radiant point R from the glaſs.
If three radiant points (fig. 9.) as
D, E, F, (or any other number) be
placed at any diſtance, as AD, AE,
AF from the glaſs AB, greater than
its focal diſtance; all the rays which
flow from theſe points through the
glafs will form the images of theſe
points in an inverted order, as d, e, f,
behind the glafs. Thus, the rays
DA,
[ 111 I
DA, DC, DB from the radiant D are
converged in the directions Ad, Cd,
Bd; and from the image of the point
Dat d. The rays EA, EC, EB from
the radiant E pafs through the glaſs
and go on in the directions Ae, Ce,
Be, and by meeting at e they form the
image of the radiant E. And the rays
FA, FC, FB from the radiant F, af-
ter paffing through the glaſs, go on
in the directions Af, Cf, Bf, meet in
the point f, where they form the image
of the radiant F.
If more radiant points are placed
between D and E, and between E
and F, their rays will meet behind
the glaſs, and form their refpective
images between d and e, and between
e and f.
Hence we may eaſily apprehend how
the images of objects are formed by
the rays which flow from the object
through a convex glaſs, and fall on a
piece
[ 112 ]
piece of white paper held upright at a
proper diſtance behind the glaſs. For,
let ACB (fig. 10.) be a convex glaſs,
and DEF an object farther from the
glafs than its focal diſtance. The rays
which flow from the extremities D
and F, and middle point E of the ob-
ject, and paſs through the glaſs, will
be collected into points at d, f, and e
behind the glaſs, where they will form
the images of the extreme and mid-
dle points of the object. But, as
every intermediate point of the object
between D and E, and between E
and F, fend out rays in the fame
manner, theſe rays which pafs through
the glafs will be collected into all the
intermediate points between d and e,
and between e and f; and confe-
quently, a perfect image def will be
formed of the object DEF; but in an
inverted form and the image will be¬
as
2
}
PLATE X
:
OPTICS.
fi
Fig. 10.
D
>
E
Fig. 11
a
充
​Fig.12.
E
a
E
E
a
B
C
}
E
Fig.24.
P
Fig 15
F
AD
Fig. 13.
B
45
C
To face page 2.
B
C
B
JMynde fail
ง
M
H.
[ 113 ]
}
1
}
as much leſs than the object, as the
diſtance of the object from the glaſs is
greater than the diſtance of the image
from the glaſs.:
*
OF THE EYE, AND MANNER
OF VISION.
OF
Fig. 11. repreſents a ſection of the
eye, very much magnified, and cut
quite through the middle from the vi-
fible or fore part, to the back part
which is concealed from fight in the
head. The eye confifts of three coats
and three humours. The outer coat
A is called the fclerotica, the middle
coat B the choroides, and the inner-
moſt coat C the retina, which is only
a continuation of the fibres of the
tic nerve K, ſpread over the choroides
like a fine net-work; and on this, the
images of all viſible objects are formed.
op-
The
[ 14 ]
eye.
The fore-part EEE of the fclerotica is
tranfparent like fine thin clear horn,
and is therefore called the cornea.
The choroides B has a round hole in
the fore part of it at F, and this hole
is called the pupil, or fight of the
Behind the pupil lies the cryftalline
humour G, which is perfectly tranf-
parent, and of the form of a double-
convex glaſs or lens. From the edge
of the chryſtalline humour, all around,
there proceeds a membrane HH, cal-
led the ciliary ligament, whofe outer-
moft edge adheres to the choroides B,
and keeps the chryftalline humour G
in its proper place. Under the cornea
EEE is a fine tranfparent fluid aaaa,
called the aqueous humour, which
alfo fills the pupil F, and the ſpace be-
tween the choroides B and the chry-
ftalline humour G and ciliary ligament
HH; at the back of which is the
vitrious
}
[ 15 ]
vitrious humour HIII, which is tranf-
parent, but of a confiftence as thick as
jelly, and fomewhat of a greeniſh co-
lour like glaſs.
When an object, as ABC (fig. 12.)
is before the eye, fome of the rays
which flow from every point of the
object on the fide next the eye (as Ac,
AP, Ae, &c.) will pafs through the
pupil P, and chryftalline humour G,
by which they will be collected into
as many points, a, b, c, and every
where between, from a to b, and from
b to c; and will form an inverted
image abc of the object upon the retina
or bottom of the eye: for the chry-
ftalline humour G acts like a lens, or
double-convex glafs (as in fig. 10.)
and by this means the object ABC
comes to be perceived; and the judg-
ment tracing the rays back toward the
object, in the direction they came
from
[ 116 ]
from it, the object appears not in-
verted, but direct.
If the object ABC (fig. 13.) be
brought nearer the eye, or the eye ap-
proaches nearer the object, the object
will appear fo much the bigger. For,
the object ABC in fig. 12. is juſt equal
to the object ABC in fig. 13. But the
latter being twice as near the eye as
the former, its image abc is twice as
big on the retina.
Let P (fig. 14.) be the pupil of
the eye, and fdbace the retina. Now,
it is evident by the figure, that the
image of the object AB is limited to
the ſpace ba on the retina: but if AB
be brought nearer to the eye, as fup-
pofe to CD, its image on the retina
will fill the larger ſpace dbac: and if
it be brought ſtill nearer, as to EF,
its image will take up the yet larger
fpace fdbace. So that, the greater the
angle
[ 117 ]
angle be under which the object is
ſeen, the larger the object will appear
to the eye.
In order that vifion may be quite
perfect or diſtinct, it is neceffary that
the which flow from every parti-
rays
cular point of the object ſhould be col-
lected upon each particular part of
the retina in fo many points of the
image; otherwiſe the image will ap-
pear confufed or indiftinct. Thus
(fig. 12.) the rays Ac, AP, Ae which
flow from the upper extremity of the
object ABC through the pupil P, muſt
be collected in a point a on the retina
to form the image of the extremity A
of the object and fo of all the rays
which flow from every other point of
the object. ´When the object is nearer
the eye, as in fig. 13. the ciliary liga-
ment contracts, and brings the chry-
ftalline humour forwarder in the eye,
and
[ 118 ]
#
and farther from the retina; other-
wife we could fee objects diftinctly at
only one diſtance. But the author of
nature has ſo ordered it, that by means
of this ligament, the chryftalline hu-
mour ſhall be ſo adjuſted (in young
eyes where the fibres are not rigid) as
to advance backward or forward as the
objects are farther or nearer, and fo
bring their rays to points on the
retina.
When people grow old, the aqueous
and chryſtalline humours of their eyes
grow too flat (fig. 15.) and therefore
the rays flowing from an object, as
ABC, are not converged into points
on the retina abc, but form broad fur-
faces thereon; which renders vifion
imperfect and confufed: for, if the
rays could penetrate the retina and
other coats of the eye, they would
from
PLATE XI.
M
Ħ
G
E-
M
Fig.16.
1
1
OPTICS
B
Frig. 18
Fig
•
20.
D
R
0
N
K
Fig. 21.
H
1
Fig. 17.
G
E
D
m
H.
D
H
Fig.19.
F
E
To face page ng.
E
:
B
A
B
C
Tillynde faitp.
[ 119 ]
form the true image of the object be-
hind the eye; as at def.
This defect of the eye is helped by
convex glaffes or fpectacles, which
caufe the rays, after paffing through
them, to come lefs diverging to the
eye, or parallel, or a little converg-
ing if the cafe requires it: and fo,
being helped a little towards a con-
verging ftate before they enter the
eye, by means of a convex glafs at
DE (fig. 16.) the humours of the
eye converge them fufficiently after-
ward, fo as to cauſe them to unite in
points on the retina; and therein to
form the perfect image abc of the ob-
ject ABC.
Although every point of an object
AB (fig. 17.) reflects the rays of light
in all manner of rectilineal directions,
yet only thoſe which come in the
fpace def from the point A can enter
the
[ 120 ]
the pupil P of the eye, and be con-
verged to a point for forming the ex-
tremity a of the image AB. The
like may be faid of the rays which
flow from the point B by reflection;
for only thoſe which come in the
ſpace ghi can enter the pupil P, and
be converged to a point at b, for form-
ing the image of the point B of the
object AB. And the like is true with
reſpect to the rays which flow from
every intermediate point of the object
AB: but theſe are left out, to avoid
confufion in the figure.
If a double convex glafs as CD be
placed between the eye F and the ob-
ject AB, the object will appear to be
magnified. Thus, all the rays that
flow from the top A of the object
AB, in the ſpace klm, and through
the glaſs between C and d, will enter
the pupil P of the eye, and be con-
verged
←
[121]
verged into a point a on the retina,
where they will form the image of
the top of the object at A. And all
the rays which flow from the lower
point B of the object AB, in the ſpace
nop, and paſs through the glafs be-
tween D and e, will enter the pupil P
and be converged in the point 6 where
they form the image of the lower ex-
tremity B of the object. And as the
object is feen through the glafs under
the angle GPH, equal to the oppofite
angle bРa, the object AB will appear
ſo magnified as to fill up the whole
fpace GABH. The diſtances of the
eyes E and F from the object are
equal; but by means of the glaſs, the
image ab on the retina of the eye F,
is double the fize of the image ab on
the retina of the eye E; and therefore,
the object AB will appear to be twice
G
as
[122]
f
as long and twice as broad to the eye
F as it does to the eye E.
The fimple microſcope is only a
finall double convex glaſs or ſens, as
CD (fig. 18.) beyond which, at a
little leſs ſpace than the focal diſtance
of the glaſs, is placed a ſmall object,
as ab, from which the rays, flowing
through the glaſs, and through the
humours of the eye, are converged
into points on the retina, where they
form the image AB, greatly magni-
fied, of the minute object ab. Since
the rays diverge from every point of
every viſible object, and fall upon the
eye in a diverging ſtate, which (efpe-
cially in young eyes) is neceffary for
diftinct vifion, the object is always
placed a little within the focal diſtance
of this microſcope glaſs, which occą-
fions the rays that flow through the
glafs, from each point of the object, to
diverge
[ 123 ].
diverge a little between the glaſs and
the eye. If the rays come parallel
from the glafs to a common found
eye, they would converge to points
before they reached the retina, and
would render the image indiſtinct
thereon; much more ſo if they came
from the glaſs to the eye in a con-
verging ſtate.
In the compound microfcope,
(fig. 19.) the fmall object AB is
placed a little farther from the con-
vex lens than its focal diſtance, in
order that the rays flowing from each
particular point of the object may con-
verge into each particular point be-
tween C and D, in which ſpace they
will form the image CD of the object.
And if the focal diſtance of the other
convex lens GH from the image, or
rather a little within that diſtance, is
the lens GH placed. Then, as the
G 2
rays
[ 124 ]
rays flow from each point of this
image, through the glafs GH, they
will pass on to the eye in a ſtate of ſmall
divergency; and entering the eye in
that ſtate, they will be converged into
points on the retina, by paffing through
the humours of the eye; and ſo they
will form the image de of the image
GH of the obje& AB.
Sound and perfect eyes perceive
objects best, without glaffes, at ten
or twelve inches diftance. But fmall
microſcope objects are too minute to
be ſeen by the bare eye at fuch a dif-
tance. The magnifying power of the
fingle microſcope is as great as the
focal diſtance of the glafs CD (fig. 18.)
is less than ten or twelve inches. The
magnifying power of the compound
microſcope (fig 19.) is compounded of
the proportion which the diftance of the
image from the object glafs EF bears
to
[ 125 ]
to its diſtance from the eye glaſs GH,
and of that which the diſtance of the
object from the eye bears to its dif-
tance from the object glaſs.
The aftronomical teleſcope confiſts
of an object glafs DE (fig. 20.) and
an eye glaſs IK, placed at ſuch a dif-
tance from each other, that their fo-
cufes, or centers of double convexi-
ties, may meet in a point as at G:
and the pupil P of the eye is placed in
the other focus of the eye glaſs. ABC
is an object, fuppofed to be placed at a
great diſtance from the teleſcope. The
rays which flow from each point of
the object ABC through the object
glafs DE, are by means of that glaſs
converged and crofs each other in all
the points between H and F, in which
ſpace an inverted image FGH of the
object ABC is formed in the focus of
the object glaſs DE; and thefe rays
going
G 3
[ 126 ]
going on through the eye glaſs IK,
will become parallel to one another
between the eye glafs and the eye.
That is, the rays from the point H
will be parallel between I and P, the
rays from the point G will be parallel
between n and P, and the rays from
the point F will be parallel between
K and P; becauſe they flow from the
image in the focus of the glafs IK;
and croffing in the pupil P, they will
be converged into all the points on
the retina between L and N, where
they will form the image of the object
ABC. And this image being feen by
the eye under the angle IPK, it will
appear to be ſo much magnified, as to
fill the whole ſpace OHGFO.
To find the magnifying power of
this teleſcope, divide the focal length
Gm of the object glaſs by the focal
length Gn of the eye glafs, and the
quotient
[ 127 ]
quotient will exprefs the magnifying
power. But this teleſcope fhews the
object in an inverted pofition, becauſe
it has only one eye glaſs.
The common telefcope (fig. 21.)
which fhews objects (as ABC) in
their true pofition, confifts of an ob-
ject glafs DE, and three eye glaffes
IK, MN, and QR, fo placed, that
the focuffes of DE and IK may meet
in G; thofe of IK and MN may mect
in L; and thoſe of MN and QR may
meet in g. Then, the image of the
object will be formed in an inverted
pofition between H and F in the focus
of DE; then the rays flowing through
IK will become parallel which belong
to each point of the image, and crof-
fing at L, and going on, will pafs
through the glafs MN, which will
converge them into points in its focus,
and will there form the ſecond image
G 4
fgh
1
[ 128 ]
fgh erect; which image will be viewed
by the eye in the focus P of the eye
glafs QR. And as this laft image
will be feen under the angle QPR, it
will appear for magnified, as to fill the
whole ſpace OfghO.
All the three eye glaffes, QR, MN,
and IK, are of equal focal diftances;
and to find the magnifying power of
this teleſcope, divide the focal length
Gm of the object glaſs DE by the fo-
cal length gn of the eye glaſs QR,
and the quotient will exprefs the mag-
nifying power of the teleſcope.
THE
}
PART THE FOURTH
O F
ASTRONOMY.
OF THE
1
SOLAR SYSTE M.
T
HE folar fyftem confifts of the
fun, fix primary planets, ten
moons, and ſeveral comets, of which
the number is not yet certainly known.
The fun is placed in the center of
the fyftem, and all the planets move
round him, in different times, and at
different diftances from him. One
moon moves round the earth, four
moons round Jupiter, and five round
Saturn.
The planets are moved by a pro-
jectile force impreffed upon them by
the deity at the beginning, which
force would for ever have cauſed them
to move in ſtraight lines: but the fun
being endued with an attractive
power
1
[ 132 ]
power (no ways inherent in matter,
or peculiar to` it) this power draws
the planets toward the fun juft as much
as the projectile force
them off from the fun;
would carry
and fo com-
pels them to revolve about the fun,
in the fame orbits, over and over
again, as they did at the beginning.
Their periods round the fun compleat
their years, and their rotations on their
axes compleat their days and nights.
The times in which the planets make
their annual periods round the fun are
found by obſervation; and their com
parative diſtances from the fun have
been alſo aſcertained by obfervation.
And it is found, that the fquales of
the periodical times bear the fame
proportion to one another as the cubes
of their diſtances from the fun do bear
to each other. And hence it comes
out, that the fun's attractive power,
which
[ 133 ]
which retains all the planets in their
orbits, decreaſes as the fquare of their
diſtances increaſe from the fun.
The times in which the planets per-
form their revolutions about the fun,
and their relative or comparative dif-
tances from the fun, are as follows,
fuppofing the earth's mean diſtance
from the fun to be divided into 10000
equal parts.
Periodical. Times. Comp. dift. as in the fcale
days. hours.
parts.
of equal parts,
Mercury 87 23
3871
in fig. I. where
Venus 224 17
7233
each divifion
The earth 365
6
10000
is fuppofed to
Mars
686
23
15237
be fub-divided
52009
into one hun-
dred.
Jupiter 4332 12
Saturn 10759. 7 95400
Having found the comparative dif
tance of the planets from the fun, in
fuch parts as the earth's diſtance from
the
[ 134 ]
the fun contains 10000, if we can
find the real diſtance of either of the
planets from the fun in miles, we may
find thereby the real diſtances of all the
reft.
By obfervations of the late tranfit of
of Venus (A. D. 1761. June 6.) the
earth's diſtance from the fun is found
to be 95,173,000 English miles.
Therefore,
As 10,000 is to 95,173,000, ſo is
387, Mercury's diſtance from the fun
in parts, to 36,841,468 his diſtance
from the fun in miles. And,
As 10,000 is to 95,173,000, fo is
7233, Venus's diſtance from the fun
in parts, to 68,891,486, her diſtance
from the fun in miles. Again,
As 10,000 is to 95,173,000, fo is
15237, Mars's diſtance from the fun
in parts, to 145,014,148, his diſtance
from the fun in miles. Likewife,
As
[ 135 ]
As 10,000 is to 95,173,000, fo is
52009, Jupiter's diſtance from the fun
in
parts, to 494,990,976, his diſtance
from the fun in miles. Once more,
As 10,000 is to 95,173,000, fo is
95400, Saturn's diſtance from the fun
in parts, to 907,956,130, his diſtance
from the fun in miles.
As 7 is to 22, fo is the diameter of
a circle to its circumference. Hence,
from the above diftances of the pla-
nets from the fun, the circumference
of their orbits are as follows.
Mercury's, 231,574,940 Engliſh
miles; Venus's 433,032,198 miles ;
the earth's 598,230,286; Mars's
911,517,502, Jupiter's 3,111,371,849
miles; and Saturn's 5,707,152,817.
Dividing the circumference of each
planet's orbit by the number of hours
contained in the planet's periodical
revolution round its orbit, we have the
number
[136]
number of miles which each planet
moves in an hour. And they are as
follows.
A
Mercury, 109,699 miles; Venus
80,295; the Earth 68,243;
Mars 55,287; Jupiter 29,0830';
and Saturn 22, 101 miles.
6 4
Venus turns round her axis in 24
days 8 hours, the earth turns round its
axis in 24 hours, Mars in 24 hours
40 minutes, and Jupiter in 9 hours 56
minutes. The times in which Mer-
cury and Saturn turn round their axes
are unknown to us.
To bring all theſe things together
in view, the following table is con-
ftructed.
A TABLE
ધ
C
H
PLATE XII.
9500
Saturn
L
}
TO OF
8,500
8000+
MA
1.
E
7500-
7000+
T
N
6500+
6000+
Figs. The comparative Distances of the Planets from the Sun.
5500-
5000+
4500
Jupiter
S
4000
P
3500
3000-
2500
Fig.5.
1500
1000-
Mars
500
TheEarth
Venus
Mercury
!
1
H
ASTRONOMY
N
G
\R
K
n
H
Fig.
2.
Aug. 23
Sep 23
Oct.23
n
11
n
9 E
n
M
9
་
Es Anf
le suns
ARIE S
TAURUS
Nov.29
GEMINI
CANCER
i
To face page 137
Fig. 4.
LEO
VIRGO
LIBRA
Apr.20
Mar,20
Dec.22
Jan.20
Figs.
Feb.19
S
B
册
​J.Myndefalp
A TABLE fhewing the times in which the planets defcribe their annual periods round the
fun, and their diurnal rotations on their own axes; their diſtances from the fun, their circumferences of their
orbits, and the number of miles they advance every hour thereîn.
Compara- Real Diſtances
the Planets. al Periods. InalRotations fr. theSun
Names of Their Annu- Their Diur-tive Dift. from the Sun in
in Parts. English Miles.
Circumference of Hourly Moti-
their Orbits in ons in their
English Miles. Orbits.
Mercury.
87 23 Unknown 3871 36,841,468
Days. Hou.
231,574,940 109,699
1 6
TOU
Venus.
224 17 24
Hou.
8 7233 68,891,486
433,032,198 80,295
24
Min.
Earth.
365 6 24
'0
* 1000
10000 95,173,000
598,230,286 68,243
Mars.
686 23 24
Jupiter.
Saturn.
Hou. Min.
40 15237 145,014,148
Hou. Min.
4332 12 9 56 52009 494,990,976 3,111,371,849 29,0830
10759 7 Unknown 95400 907,956,130 5,707,152,817 22,101
6 4
T
911,517,502 55,287 T80
[ 138 ]
The moon is the earth's fatellite ;
her diſtance from the earth is 240,000
miles; and the goes round her orbit
from change to change in 29 days 12
hours 44 minutes 3 feconds. Jupiter
has four moons, and Saturn five.
As the ſquare of the earth's period
round the fun (viz. 365 days 6 hours)
is to the cube of its diftance from the
fun, ſo is the ſquare of any other pla-
net's period round the fun to the cube
of its diſtance from him.
6
The fun's parallex, as deduced
from the tranfit of Venus, is 8,5
feconds of a minute of a degree,
which ſhews by calculations of a plain
right angled triangle, that the fun's
mean diſtance from the earth is
95,173,000 Engliſh miles.
For, the logarithmic fine (or tan-
gent) of 8
6 5
feconds is 5,6219140;
which being fubftracted from the
radius
[ 139 ]
radius 10,0000000, leaves remaining
the logarithm 4,3780860, whoſe
number is 2388284; which is the
number of femidiameters of the earth
that the fun is diftant from it. And
this laſt number, 23388284 being
multiplied by 3985, the number of
Engliſh miles contained in the earth's
femidiameter, gives 95,173,117 miles
for the earth's mean diſtance from
the fun. But, becauſe it is impoffible,
from the niceft obfervations of the
fun's parallex, to be fure of his true
diſtance from the earth within 100
miles, we do at prefent, for the fake
of round numbers, ftate the earth's
mean diſtance from the fun at
95,173,000 Engliſh miles.
6
In ſo ſmall an arc as 8,5% feconds of
fo
a degree, the fine and tangent are fo
nearly equal, that we may without
any fenfible error confider them as
equal.
[ 140 ]
equal. And there is no difference
between them in the logarithmie
tables.
OF SIDEREAL AND SOLAR
TIME.
In fig. 2, let S be the fun, npqr
the earth, turning round its axis ac-
cording to the order of the letters,
from weſt, by fouth to eaſt; let ʼn be
any given place on the earth's furface,
whoſe meridian is naq, and let N be
a fixt ftar, at fuch an immenfe diſtance,
that the whole orbit of the earth
ABCDEFGHIKLMA is but a point
in compariſon to that diſtance. Then
let the earth be in any part whatever
of its orbit, as at b, c, d, e, f, &c.
when the faid meridian is in the poſi-
tion bn, cn, dn, en, fn, &c. its plane
will
[ 141 }
1
will pass through the ftar; that is,
whenever the meridian becomes pa-
rallel to its pofition an, the ftar will
be upon that meridian, let the earth
be in any part of its orbit whatever.
When the meridian, on any day,
becomes parallel to the fituation that
it had at any given inftant on the day
before, the earth has made a compleat
revolution about its axis; and this it
always does, when any given meri-
dian has revolved from any ftar to the
ſame ſtar again; and the time of ſuch
a revolution is in 24 fidereal hours,
which is called a fidereal day.
If the earth were always to remain
at a, the meridian an would always
revolve from the fun to the fun again
in the fame time that it does from the
ftar N to the fame ftar again; and
then 24 fiderial hours would be the
fame as 24 folar hours: for the plane
of
[ 142 ]
of the meridian an continued, would
paſs through the fun's center S, at the
fame inſtant of its paffing through the
ftar N.
But as the earth has a progreffive
motion in its orbit through ABCD, ſo
as to go round its orbit in a year, ac-
cording to the order of the letters, the
faid meridian will revolve fooner and
fooner every day to the ftar than to the
fun; and fo much fooner every day,
that in 365 days, as meaſured by the
fun, the meridian will have revolved
366 times to the ftar. So that, what-
ever the number of folar days in the
year be, the number of fiderial days
will exceed it by one.
Thus, when the earth is at a, the
point n has both the fun and the ftar
on its meridian; but in a month after-
ward, when the earth has advanced to
b, the meridian will have made a cer-
tain
[ 143 ]
་
tain number of revolutions to the ftar,
as often as it has been in the pofition
of bn, parallel to an; but then when
it is at bn, the point n (or place on
the meridian) muft revolve from n to
o before it has the fun on its meridian;
and the arc no is a twelfth part of the
earth's circumference, which is equal
to two hours revolution. And there-
fore, the number of folar days in a
month is (among them all) two hours
longer than the number of fiderial
days in that time.
When the earth is at C, the point n
will be directed to the ftar four hours
fooner than it can revolve through the
arc no to the fun. At d fix hours
fooner; at e eight hours; at ften hours;
and at g the point n will have the ſtar
N on its meridian at midnight; or 12
hours before it revolves half round,
through the arc n to the the fun S.
At
[ 144 ]
At b the accompliment of the
fiderial day will be 14 hours ſooner
than the folar, at i 16, at k 18, at /20,
at m 22, and at a 24; for at a, one
turn of the earth on its axis will be
loft with regard to the number of days
and nights in the year, on account of
the earth's motion round the fun.
OF THE DIFFERENT SEASONS.
8",
In fig. 3 let S be the fun,
&c. the earth's annual orbit repre-
fented in a very oblique view; a,b,c,
d, e, f, &c. the earth in twelve diffe-
rent parts of its orbit; and ns the
earth's axis, of which n is the north-
pole and s the fouth pole. In the
earth's whole annual courſe round the
fun, its axis ns is 23 degrees in-
clined from a perpendicular to its orbit;
and
[ 145 ]
the figns ry
and
பத
m
and its axis ſtill keeps the fame ob-
lique direction. Therefore, it is plain,
that whilft the earth moves through
the north
pole of its axis conftantly inclines
more or leſs toward the fun, and moſt
of all when the earth is at d; as the
earth moves through mand x
its north pole n inclines more or leſs
from the fun; and moſt of all from
him when the earth is at k. This
obliquity is the cauſe of all the vicif-
fitudes of the feafons.
In fig. 4, the obferver is fuppofed
to be placed at a great diſtance above
the center of the earth's orbit
8
where he fees the
a m m I bom
northern half of the earth, of which
N is the north pole (fee the earth at
March 20) where all the meridians
meet. P is the north polar circle, T
the tropic of cancer, and E the equa-
H
tor.
[ 146 ]
tor. The fide of the earth that is at
any time turned toward the fun S has
day, whilſt the fide that is the turned
from him has night.
On the 20th of March, when the earth
enters the beginning of Libra, and the
fun as feen from the earth, appears to be
at the beginning of the fign Aries,
the boundary of light and darkneſs cuts
the earth in its north pole; and then
all the places on the earth go equally
through the light and the dark, which
makes day and night then equal. In
April the north pole is confiderably in
the light, and the day is longer than
the night; in May more fo, and on
the 21st of June moft of all; the
whole north polar circle being `then in
the light, and the days at the longeſt
in the northern half of the earth.
From that time the days fhorten and
nights lengthen, till September 23,
when
[ 147 ]
when they are again equal as on the
zoth of March. From September 23
to March 20, the north pole is con-
tinually in the dark, but moſt ſo on
the 22d of December, when the
whole polar circle is in the dark, and
the days at the ſhorteſt and nights at
the longeſt, all the way between the
equator and polar circle. At each pole
there is but one day and one night in
the whole year.
{
This figure fhews the pofition of the
earth at the time of its entrance into
each fign of the ecliptic, and how it is
then enlightened by the fun. Its mo-
tion round its axis being the cauſe of
days and nights, and its motion round
the fun on its oblique axis the cauſe of
the different lengths of days and
nights, and of all the variety of the
feafons.
H 2
When
[ 148 ]
When the earth enters any fign of
the ecliptic, the fun then feen from the
earth appears to enter the oppofite
fign.
OF THE MOTIONS AND PHA-
SES OF THE MOON.
Which ever fide of the moon is to-
ward the fun S at any time, will
then be enlightened by the fun; and
the other half will be in the dark.
And as the moon goes round the earth,
ſhe will appear to be more or leſs en-
lightened, as the enlightened fide of
her is more or lefs turned toward the
earth. See fig. 5.
Let OPQR be the annual orbit of
the earth E, and T the orbit of the
moon, in which he goes round the
earth from change to change, in 29
days,
149 ]
days, 12 hours, 44 minutes, 3 ſeconds,
according to the order of the letters
fghiklmn. When the moon is at f,
her dark fide is toward the earth, and
ſhe becomes invifible, becauſe ſhe can
then reflect none of the fun's light to
the earth ; and has no light of her
own to ſhine by. When fhe is at g,
a little of her enlightened fide will be
toward the earth; and he will ap-
pear horned as at G.
When ſhe is at
b, half her enlightened fide will be
toward the earth; and he will appear
half full, as at H, when we fay fhe is
in her first quarter, encreafing. When
ſhe is at i, fhe will appear gibbous, as
at 1, the greateſt part of her enlighten-
fide being then toward the earth. When
ſhe is at k, the whole of her enlighten-
ed fide will be toward the earth;
and ſhe will appear quite full, as at
K.
When ſhe is at /, her whole en-
H 3
lightened
[ 150 ]
lightened fide cannot be feen from the
earth; and fhe will appear gibbous,
on the decreaſe, as at L. When the
is at m, half her enlightened fide will
be toward the earth, and the appears
half decreaſed, as at M; when we
fay ſhe is in her third quarter. When
fhe is at n, the greateft part of her
enlightened fide is turned from the
earth, and ſhe appears horned, not far
from the change. And when ſhe comes
to f, fhe is all dark toward the earth,
as at F; and then ſhe is quite inviſible;
at which time we fay it is new moon.
Both the earth and moon caft fha-
dows directly outward from their dark
fides. And hence, it is plain, that if
the moon's orbit lay even (or in the
fame plane) with the earth's orbit,
the moon's fhadow would fall on
the earth at every change, and the
earth's fhadow would fall on the moon
at
[ 151 ]
at every full.
there would always be an eclipfe of the
fun, and in the latter cafe an eclipſe
of the moon. But one half of the
moon's orbit is on the north fide of
the earth's orbit, and the other half
on the fouth fide thereof. So that the
moon's orbit croffes the earth's orbit
in two oppofite points, which are cal-
led the moon's nodes. And there
can be no eclipfe of the fun but
when the moon changes in or near
either of the nodes; nor can the
moon be eclipfed but when he is
full, in or about
or about either of her
In the former cafe
nodes.
The moon's orbit is elliptical, and
the earth's center is in one of its fo-
cufes.
OBSERVA-
H 4
[ 152 ]
OBSERVATIONS ON THE AS-
TRONOMICAL
PART OF
THIS WORK.
I. If the earth were fixed immove-
able in its orbit, fo as to have no pro-
greffive motion therein, and to turn
round its axis with the fame velocity
it does at prefent; its axis being fup-
poſed to be perpendicular to the plane
of its orbit: and the moon were to re-
volve in her orbit with her preſent
velocity, her orbit being fuppofed to
be circular, and fhe to be of the ap-
parent bulk of the fun: In this cafe,
the folar or natural day would be of
the ſame length with the fiderial day;
namely, 23 hours 56 minutes 4 feconds:
the fun would always appear to revolve
in the plane of the equator, and the
days and nights would be always of
an
[ 153 ]
an equal length. The moon would
likewiſe revolve in the plane of the
equator, from the fun to the fun again,
or from change to change, in the time
ſhe now goes round her orbit; namely,
in 27 days 7 hours 43 minutes. The
diameters or breadths of the fun and
moon would always appear to be equal.
The moon would eclipſe the ſun to-
tally, but without any continuance
of total darkneſs, at the time of every
new moon. Theſe eclipfes would be
no where total but at the equator;
and partial every where elſe, ſo far as
they extended, which would be about
2400 miles on each fide of the equator;
beyond which, farther north or fouth,
the fun would never be eclipſed at all.
The moon would be eclipfed by the
earth's fhadow every time ſhe was full;
and the eclipfe would be total, as feen
from
any part of the earth.
II. If
[ 154 ]
II. If the moon's orbit acquired an
elliptical form, and all the other cir-
cumftances remained the fame as above.
The length of days and nights, and of
the lunations would be as above men-
tioned. Whatever part of the moon's
orbit was once between the earth and
the fun would always be fo. If it was
the apogeal point, the moon would
be too far from the earth at the change
to hide the whole body of the fun,
even at the equator; at which all
the fun's eclipfes would be annular.
If the perigeal point of the moon's
orbit was toward the earth, all the
fun's eclipfes would be total at the
equator, and the darkneſs would con-
tinue about four minutes. If the
middle point between the apogee and
perigee were toward the fun, his eclip-
fes would be total at the equator with-
out
[ 155 ]
1
out any continuance of darknefs.
The lunar eclipfes total, as above.
III. With thefe circumftances, fup-
pofe now that the earth fhould revolve
about the fun, with its preſent annual
velocity, but in the plane of the equi-
noctial. The days and nights would
always be of equal length, only the
24 folar hours would be 3 minutes 56
feconds longer than if the earth had
no annual motion: but there would
be no difference of feafons. The
lunations would be 29 days 12 hours
44 minutes 3 ſeconds in length. The
eclipſes of the fun would be ſometimes
total with continuance, at the equator,
fometimes total without continuance,
and at other times annular. Thofe of the
moon would be as above mentioned.
IV. If now, the earth fhould go
round the fun in the plane of the
ecliptic, and the moon go round the
earth
[ 156 ]
earth in the plane of the ecliptic;
and the earth's axis fhould become in-
clined to the ecliptic as it is at prefent.
This would bring on all the inequality
of days and nights, and all the viciffi-
tudes of feafons we now enjoy: but ftill
the fun would be eclipfed at the time
of every new moon, and the moon at
the time of every full. But the cen-
tral éclipfes of the fun would not be
confined to the equator; for, in our
fummer, the center of the moon's
fhadow would take the earth at the
equator, where the general eclipſe
would begin at the middle of the
general eclipfe the center of the fha-
dow would fall on the northern tropic,
and thence it would move obliquely
fouthward, and would go off the
earth at the equator. In fpring, the
center of the moons fhadow would
go obliquely over the earth, from the
fouthern
[ 157 ]
fouthern tropic to the northern: in
autumn it would go obliquely over the
earth from the northern tropic to the
fouthern. And in winter it would
first touch the earth at the equator,
then bend fouthward to the ſouthern
tropic; from thence toward the equa-
tor again, and would at laft leave the
earth at the equator. All the eclipfes
of the moon would be total and cen-
tral (as above) let them be feen from
any part of the earth whatever.
V. If the moon's orbit fhould be-
come inclined to the ecliptic, as it now
is, and all the other circumſtances re-
main as above; the nodes of the moon's
orbit having no motion, but always to
keep in the fame oppofite points of
the ecliptic; there could never then
be above fix eclipſes in the year; and
when there were that number, four
of them would be of the fun and
two
[ 158 ]
two of them of the moon. At other
times, as the moon might happen to
change in or near the nodes, there
would only be three eclipſes; of which
there would be two of the fun and
only one of the moon. And the time
between theſe eclipfes about the dif-
ferent nodes would be half a year.
So that, in whatever feaſons the eclipfes
once fell, they would always do fo
again. The moon's eclipfes would
fometimes be total and at other times
partial.
VI. If the moon's nodes ſhould af-
terwards acquire a retrograde motion,
fuch as they now have, and every
thing elſe continue as above: this
would occafion all the variety of eclipfes
of the fun and moon that we now
have: to explain which, would require
the writing of a large volume.
TO
[ با
159 ]
1
TO REPRESENT THE MOON's
ORBIT ON A CELESTIAL
GLOBE.
Tie a filk thread round the ball of
the globe on the ecliptic, and then find
the place of the moon's afcending
node in the ecliptic by an ephemeris.
This done mark the place of the
aſcending node in the ecliptic with a
chalk, and alſo the oppofite points of
the ecliptic for the place of the deſ-
cending node: mark alſo the two points
of the ecliptic which are half way be
tween the nodes, or 90 degrees from
each.
Then, reckoning 90 degrees from
the afcending node, according to the
order of the figns, fet the filk thread
5 degrees northward there, or half
way between the nodes; and on the
oppofite
[ 160 ]
3
4
oppofite fide of the globe ſet the thread
5 degrees fouth of the ecliptic: and
laftly adjuſting the thread by hand to
be like a great circle on the globe croſ-
fing the ecliptic at an angle of 5 3
degrees in the nodes, the thread will
truly repreſent the moon's orbit in the
heavens for that time, and ſhew what
ftars it paffes either through, or near
to. And finding the moon's place by
an ephemeris for the given time look
for the fame place in the ecliptic, and
right againſt it; under the thread, will
be the moon's place in her orbit for
that time.
The diameter of the moon is to that
of the earth as roo, to 365.-The
moon's velocity is about 2200 miles
an hour.
Note, In 24 hours the moon moves
13 degrees, 10 minutes of a degree
and
35 ſeconds; and every minute of
a degree
[ 161 ]
a degree in the moon's orbit is equal
to a whole degree on the earth's
furface.
Therefore in 24 hours the moon
moves 47435 miles.
FÌN IS.
ERRAT A.
Page v. (Preface) 1. 6. for, 31, r. 32.
xx. (Preface) 1. 8, 9. A feventeenth boy of a
large fize must be uſed for the fun in the center.
This fhould have been printed as a note.
10. 1. 11. after, table D, add (fig. 3.)
11. 1. 10. for, hanging for, r. hanging on.
29. 1. 16. for, BC, ». BA.
36. 1. 7. for, forty-four, r. forty-two.
37. 1. 5. after, AB, add, (fig. 25.)
39. 1. 14. after, hundred, add, thoufand.
45. 1. 21. for, right line, r. right fine.
46. 1. 2. for, Dfg,,r. dfg.
77. 1. 2. for, +7, r. 56.
103. 1: 7. for, debt, r. debf.
138. 1. 13. for, parallex, r. parallax.
144. 1. 10. for, ¤‰, r. I‰¤N ™.
1.
A¹
Shortly will be published,
N Eafy and Pleafant COMPENDIUM of almoſt
the whole HEBREW BIBLE. Containing in
Select Verſes, a Quarter Part of the Book of
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of principal and frequent Ufe, with an Engliſh
Tranflation of each Root.
II. A COMPENDIUM of the GREEK TESTAMENT.
Containing in near Two Thousand Select Verfes,
a Quarter Part of that Sacred Book, including
near Five Thoufand Primitive Words, with an
English Tranflation of each Word.
Both by
JOHN RYLAND of Northampton.
III. One Hundred and Forty Four Familiar Latin
Dialogues, on the moft Common Subjects of Con-
verfation, and on the Firft Parts of the Roman
Hiftory. By Dr. Lange of Hall, in Saxony.
Printed for E. and C. DILLY, in the Poultry,
IV. Geography made a Recreation on Meffage Cards.
V. Cards of Ancient Hiſtory in X. Periods.
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VIII. Optical Cards.
IX. Cards of Anatomy.
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with fixteen School Boys. By JOHN RYLAND of
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Printed for and fold by CARINGTON BOWLES,
at Nº. 69. in St. Paul's Church Yard.
3
EXPERIMENTAL
PHILOSOPHY
FOR
SCHOOL-BOYS:
OR, AN
APPENDIX
TO THE
Introduction to the NEWTONIAN
PHILOSOPHY.
In two or three fhort and eaſy Lectures.
The general Principles of MECHANICS have their
valuable and excellent USES, not only for the Exer-
cife and Improvement of the Mind, but the Subjects
themſelves are very well worth our Knowledge, and
are often made of admirable Service to human Life.
Dr. WATTS's Improvement of the Mind,
Part I. p. 327.
* X 5 3 * 6 € / 2 X 5 3€ 253
LECTURE I
The true Foundation
IF
Of all Mechanic Powers.
On one eaſy Principle.
}
The whole of Mechanic's depends;
Which we thus explain:
we confider bodies in motion,
And compare them together,
We may do this either with refpect
To the quantities of matter they contain,
Or the velocities with which they are moved.
The heavier any body is,
The greater is the power required
Either to move it or to top its motion.
And again, the fwifter it moves
The greater is it force.
So that the whole momentum,
Or quantity of force
Of a moving body,
Is the refult of its quantity of matter,
Multiplied by the velocity
With which it is moved:
And when the products arifing
From the multiplication
Of the particular quantities of matter
In any two bodies
By their reſpective velocities are equal;
The momenta, or entire forces are ſo too.
An
(-3)=
}
An example to explain this Law.
HUS, fuppofe a body
THUS,
(Which we fhall call A)
To weigh forty pounds (40)
And to move at the rate of two miles in a minute *
And another body (which we shall call B)
To weigh only four pounds (4)
And to move twenty miles in a minute;
The intire forces
With which theſe two bodies
Would ſtrike against any obstacle,
Will be equal to each other:
And therefore it would require
Equal powers to ſtop them.
༨.
The Reafon of this
FOR 40 multiplied by z gives 88,
(The force of the body A)
And 20 multiplied by 4 gives 80,
(The force of the body B)
Upon this eafy Principle
depends the whole of Mechanics.
AND it holds univerfally true
That when two bodies are fufpended
By any machine,
So as to act contrary to each other,
If the machine be put into motion,
And the perpendicular afcent of one body
Multiplied into its weight,
Be equal to the perpendicular defcent of the other body
Multiplied into its weight;
Theſe bodies, how unequal foever
In their weights,
Will balance one another in all fituations;,
For, as the whole afcent of one
A 2
Is
( 4 )
Is performed in the fame time
With the whole defcent of the other,
Their reſpective velocities
Must be directly as the spaces
They move through;
And the excefs of weight in one body
Is compenfated by the excefs
Of velocity in the other.
Upon this eaſy principle,
It is eafy to compute
The power of any mechanical engine,
Whether fimple or compound;
For it is but only enquiring
How much fwifter the power moves
Than the weight does (i. e,)
How much farther in the fame time;
And juſt ſo much
Is the power increaſed
By the help of the engine.
REM À R. K.
+
IN the theory of this fcience, we fuppofe
All planes perfectly even,
All boites perfectly finooth,
Levers to have no weight,
Cords to be extremely pliable,
Machines to have no friction,
And, in fhort, all imperfections
Must be fet afide
Until the theory be eftabliſhed;
And then proper allowances are to be made.
**
#
}
Mechanic
( 5 )
Mechanic Powers.
(f
THE fimple MACHINES, ufually called
MECHANICAL POWERS, are fix in number, viz.
the wheel and axle-the pulley-
The lever
The inclined plane
the wedge--and the ſcrew.
They are called mechanical powers,.
Because they help us to raife weights,
Move heavy bodies,
And overcome refiitances,
Which we could not effect without them.
1
First MECHANIC POWER.
A
The LEVER.
Lever is a bar turning upon a prop
Or centre of motion,
And is uſed either to raiſe weights
Or to overcome refiftances.
There are three kinds of levels,
And in each of them the velocity
Of each point or end
$
Is directly as its diſtance from the prop.
AUS
A lever is faid to be of the firſt kind,
When the prop is between the weight
And the power :
Here the power and weight
Ballance each other, .
When the power is in proportion
To the weight,
As the distance of the weight from the prop
Is to the diſtance of the power from the prop.
Of this fort are our iron crows, fciffars,
Pincers, fnuffeis, and the like.
A 3.
Second.
( 6 )
A
10c
Second Kind of LEVER. ·
Lever is faid to be of the fecond kind,
When the weight is between the prop
And the power:
Here the power and weight
Ballance each other,
When the power is in proportion to the weight,
As the distance of the weight from the prop
Is to the distance of the power from the prop.
Of this fort are deers turning upon hinges,
Rudders of flips, oars, and fuch cutting knives.
As are fixed at the points.
Third Kind of LEVER.
A Lever is faid to be of the third kind,
When the power is between
The weight and the prop:
In this the power and the weight
Ballance each other,
When the power is in proportion to the weight
As the distance of the weight from the prop
Is to the distance of the power from the prop.
Of this fort are the bones of our legs and arms,
And the wheels of clocks and watches.
The bended lever differs in nothing but its form:
From a lever of the first kind;
Its power is the fame, and is fimilar
To that of an hammer drawing a nail.
Example of the third Kind of Lever,
HUS, when the power is applied
the
z
To a lever (of 24 inches long, weighing 2 oz.)
At the diftance of fix inches from the prop,
It will require four ounces to fupport the bare lever.
If the power be applied at four inches from the prop,
It will require fix ounces to fupport it ;
Or if at two inches, it will then require
No less than twelve ounces to balance it.
And if at the fame time
I put
{
( 7 )
+
:"
I put on a weight of one ounce,
At 24 inches diſtant from the prop,
It will then require 12 ounces moreo né
That is, 24 ounces in all,
Twelve to ballance the lever.
} {
And 12 more to ballance the weight."
*********
Second MECHANIC POWER.
The WHEEL and AXLE,
N the wheel and axle
IN
su is
The velocity of the power is
To the velocity of the weight,
As the circumference of the wheel
Is to the circumference of the axle;
And the advantage gained by this machine
Is directly in the fame proportion ;
For the power and weight balfance each other,
When the power is in proportion to the weight
As the circumference of the axle
Is to the circumference of the wheel.
This machine is the principal part
Of a common crane.
An Example to explain this Power.
Suppofe the circumference of a wheel
To be eight times as great
As the circumference of the axle:
Then a power equal to one pound,
Hanging by a cord
Which goes round the wheel,
Will-ballance a weight of eight pounds.
Hanging by a rope
Which goes round the axle.
[To be continued in feveral Lectures.]
EXPE
( 8 )
Ak kebettet tect tokekekeketek tetek
EXPERIMENTAL
PHILOSOPHY
FOR
SCHOOL - BOYS.
LECTURE IL
Third MECHANIC POWER.
The PULLEY.
A Pulley that only turns on its axis,
And does not rife with the weight,
Serves only to change the direction of the power ;,
For it gives no mechanical advantage thereto.
When, befides the upper pullies,
Which run round in a fixed block,
There is a block of pullies
Moving equally with the weight;.
The velocity of the weight is
To the velocity of the power,
As one is to twice the number of pullies
In the moveable block;
And the power and weight ballance each other
When the power is in proportion to the weight,,
As one is to twice the number of pullies
In the moveable block,
Or as one is to the whole number of cords.
I.
3
A's.
:
1
1
(9)
As for EXAMPLE,
SUPPOSE a weight of eight ounces,
Be hung at the lower end of a moveable block,
Which contains two pullies in it
And another weight of two ounces,
Hung unto the end of a cord
Which goes round the pullies,
H
And two other pullies in a fixed block
(To which the other end of the cord is faftened)
Theſe weights will ballance one another
In all fituations;
And the weight of two ounces
Will move through four times the ſpace,
And with four times the velocity
In the fame time that the other weight does.
Fourth MECHANIC POWER.
The INCLINED PLANE.
A Weight raifed, or a refiſtance moved
By an inclined plane,
Moves only through a ſpace equal ›
To the height or thickneſs of that plane,
In the time that the power drives
The plane through a ſpace
Equal to its whole length.
Hence the velocity of the power
Is in proportion to the velocity of the weight,
As the length of the plane
Is to its thickness or height;
And the power and weight ballance each other
When the power is in proportion to the weight,
As the thickness of the plane is to the length.
All edge-tools which are chamfered
Only on one fide,
Are inclined planes,
As far as the chamfer goes from the edge.
EX-
( 10 )
EXAMPLE.
SUPPOSE a load or roller of thirty-two ounces
To be ſtayed upon an inclined plane,
Whofe height is half its length;
Then it will require aweight of fixteen ounces,
Acting contrary to the load,
To ſupport it, and keep it from deſcending.
}
00000000000:0000000000
Fifth MECHANIC POWER.
The WEDGE.
A Wedge, in the common form,
Is like two inclined planes
Joined together at their bafes,
And the thickneſs or height of theſe planes
Makes the back of the wedge,
To which the power is applied in cleaving of wood,
When two equal refiftances act perpendicularly
Againſt the oppofite fides of the wedge,
And a power acts perpendicularly against
The back of the wedge,
The velocity of the power is in proportion
To the velocity of the reſiſtance
On each fide,
As the length of the wedge is
To half the thickneſs of its back,
And the power ballances the reſiſtance
Of the wood,
When the power is
In proportion to the refiftance,
As half the thickneſs of the back
Of the wedge is to its whole length,
If the harp edge go to the bottom
Of the cleft in the wood;
But when the wood ſplits before the wedge-
4
(As
( I )
(As it generally does)
The velocity of the refiftance on each fide is
To the velocity of the power acting on the wedge,
As half the thickness of the wedge is
To the whole length of the cleft;
}
And in this cafe the power and refiſtance'
Ballance each other,
When the power is to the refiftance,
As half the thickness of the wedge
(When it is driven quite into the wood)
Is to the whole length of the cleft
Below the back of the wedge.
"
EXAMPLE of the Law of the Wedge.
THUS, fixteen ounces of refiftance,
That is, eight ounces on each fide,
Will ballance, or be equal to
Eight ounces of power
At the back of the wedge,
When the back of the wedge
Is equal to one of the fides.
But when the back of the wedge
Is but half the length
Of one of the fides,
Then four ounces of power
Will be equal to
Sixteen ounces of reſiſtance
On both the fides.
}
-
1
1
bbbbbbbb
Sixth MECHANIC POWER.
The SCREW.
HE Screw may be confidered as if it were
Tan inclined plane wrapt round a cylinder;
An inclined
Hence the power muft turn the cylinder
Quite round in the time that the weight
Moves
( 12 )
Moves through a ſpace equal to the diſtance
Between the fpirals or threads of the ſcrew;
Therefore the velocity of the power is
In proportion to the velocity of the weight,
As the circumference of a circle
Deſcribed by the power,
In one turn of the ferew,
Is to the diſtance between the fpirals of the ſcrew,
And the power and refiftance ballance
Each other when the former is to the latter,
As the distance between the fpirals is
To the circumference of the circle
Defcribed by the power.
This machine, befides the advantage
Proper to itſelf,
Has generally the benefit of the wheel
And axle, on account of the handle
Or lever whereby it is turned.
1
The Law of the Screw made eafy.
THE power and refiftance ballance each other,
When the power is to the reſiſtance
As the diſtance between the ſpirals is
To the circumference of the circle,
Deſcribed by the power, cylinder, wheel, or lever,
EXAMPLE.
Thus if the lever which turns the fcrew
Does in one rotation defcribe a circle
'That meaſures thirty times the diſtance
Contained between any two fpirals,
It will then gain thirty degrees of power.
墨
​}
>
ነ
蒜​餅
​All
( 13 )
All the MECHANIC POWER S
combined together..
A
S the fcrew includes the inclined plane,
And two equally inclined planes make the wedge,
We have all the mechanical powers combined
Together in a common jack,
If it be turned by the fly, for then wề
Have alfo the lever, the wheel, and axle,
And the pullies. If this machine,
Be uſed for raiſing a weight,
By means of a power applied to the fly,
The power will ballance the weight,
If it be in proportion,to, the weight,
As the velocity of the weight is..,
To the velocity of the fly.
Now confidering how fast the fly moves,
(With respect to the motion of the weight).
It is evident, that a crane,
Constructed in the manner of a common jack,
Would be an engine of very great power:;
But then the time loft
Would alſo be very great
For, in all engines, the time loft
In working them is
As the power gained by them.
If machines could be made without friction,
The leaft degree of power added to that
Which ballances the weight,
Would be fufficient to raiſe it.
In the lever the friction
Is next to nothing.;
In the wheel and axle it is but ſmall¿
In the pullies it is very confiderable;
And in the inclined plane, wedge,
-And forew, it is very great.
B
Sir
( 14 )
Sir IS AAC NEWTON's
}
2.
LAWS of MOTION.
10 AC
LA W. I.
ALL bodies continue their ſtate of reft,
Or uniform motion, in a right-line,
'Till they are made to change that ſtate
By fome external force impreſſed upon them.
LAW II.
THE change of motion produced in any body.
Is always proportionable to the force
Whereby, it is effected;
And in the fame direction wherein the force acts,
}
2 13
+
LAW
III.
RE-ACTION is always contrary and equal to action,
Or the actions of two bodies upon each other
Are equal, and in contrary direction.
LAW IV.
BODIES mutually attract each other
1
In proportion to their respective quantities of matter,
And their attractions diminiſh
In-proportion as the fquare of the distance between them
increaſes.
}
See Dr. Cheyne's Philofophical Principles of Religion, and
Dr. Cotton Mather's Chriftian Philofopher, 8vo.
༣
}
A
ASTRO-
( 15 )
ASTRONOMY for School-Boys;
T
OR,
An INTRODUCTION to the Uſe of the
WHIRLING TABLE.
puit as se
LECTURE
ร่าง
37.05 £ 731.45 SE
The Excellence and Uſefulneſs of Aftronomy.
I'
TO 10 C
་
F we look upward with DAVID to the world's above us,
we confider the heavens as the work of the finger of
GOD, and the moon and ftaus which he hath 'ordained."
what amazing glories difcover themſelves to our fight! What
wonders of wiſdom are feen in the exact regularity of their
revolutions! nor was there ever any thing that has contri-
buted to enlarge my apprehenſions of the IMMENSE POWER
OF GOD, THE MAGNIFICENCE OF HIS CREATION, AND
HIS OWN TRANSCENDENT GRANDEUR, fo much as that
little portion of ASTRONOMY which I have been able to at
tain. And I would not only recommend it to YOUNG
STUDENTS for the fame purpoſes, but I would perfuade
ALL MANKIND (if it were poffible) to gain fome degrees of
acquaintance with the vaftneſs-the diſtances—and the
motions of the planetary worlds on the fame account. It
gives an unknown enlargement to the understanding, and af-
fords a divine entertainment to the foul and its better powers.
With what pleafure and rich profit would men furvey
thoſe aſtoniſhing SPACES in which the planets revolve, the
hugeneſs of their BULK, and the almoft incredible ſwiftneſs
of their MOTIONS: and yet all theſe govern'd and adjuſted
B 2
by
( 16 )
by fuch unerring rules, that they never mistake their way,
nor loſe a minute of their time, or change their appointed
circuits for feveral thouſands of years!
WHEN we mufe on theſe things we may lofe ourſelves in
holy wonder, and, cry out with the pfalmift, "LORD, what
“is man that thou art mindful of him, and the fon of man
"that thou ſhould'ſt viſit him!"
Dr. Watts's Aftronomy, Preface, p. 7.
THE immortal SIR ISAAC NEWTON, befides his other
innumerable and wonderful inventions, has difcovered the
fountain and Ipring of all the celestial motions, and the
GREAT LAW which is univerfally diffuſed thro’- the whole
fyſtem of nature, which the Almighty and wife CREATOR,
has commanded alt bodies to obferve, viz. THAT EVERY
PARTICLE OF MÁTTER ATRACTS EACH OTHER IN A
RECIPROCAL, DUPLICATE PROPORTION OF ITS DIS-
TANCE.
THIS law is, as it were, the cement of nature, and the
principle of union by which all things remain in their proper
state and order; it detains not only the planets, but the
comets within their due bounds, and hinders them from
making excurſions into the immenfe regions of ſpace, which
they would do, if they were only actuated by motion once
implanted in them, which naturally they would always pre-
ferve according to the firſt and principal law of motion.
We are alſo obliged to the ſaid gentleman for the diſcovery
of the law that regulates all the heavenly motions, ſets bounds
to the planets orbs, determines their greatest excurfions from
the fun, and their neareſt approaches to him.-To this fub-
lime GENIUS we owe, that now we know the cauſe why
fuch a conſtant and regular proportion is obſerved, by both
primary and fecondary planets, in their circulations round
their central bodies, IN COMPARING THEIR DISTANCES
WITH THEIR PERIODS; and why all the celeftial motions
are ſtill continued in ſuch a wonderful regularity, harmony,
and order.
Barrow's Dict. Aftronomy.
Twelve
( 17 )
>
Twelve Capital EXPERIMENTS on the
WHIRLING TABLE.'
2
EXPERIMENT. Í,
I
be to,.
fhew the propensity of matter to keep the ftate it is
in, whether motion or reût, for ever.
Tin, whether
+
# 7. 814 st dard འཏྭཱ{ ། 1
EX
Y
TO ſhew that bodies moving in orbits, have a tendency to
Ay out of theſe orbits.
EX P. II.
་
TO fhew that bodies move fafter in small orbits than in
large ones.
EX P. IV.
On centrifugal forces.
A
TO fhew that when bodies of EQUAL quantities of matter
revolve in EQUAL circles with EQUAL velocities, their cen-
trifugal forces are EQUAL.
6
E X P. V.
TO fhew that the centrifugal forces of revolving bodies
are in a direct proportion to their quantities of matter multi-
plied into their respective velocities, or into their diſtances
from the centres of their reſpective circles.
EX P. VI.
TÒ fhew that a double velocity in the fame circle is a bal-
lance to a quadruple power of gravity.
5
EXP.
( 18 )
E X P. VII.
TO fhew, that if one body moves round another, both of
them must move round their common center of gravity.
Here introduce the demi-globe of two pounds
weight, connected by a wire to a little, ball of one ounce :
This ſmall ball, in a rapid motion, will carry off the demi-
globe from the table.
EXP. VIII.
专
​TO demonftrate the abfundity of the Cartefian doctrine of
the planets moving round the fun in vortexes.
0
MEX P.
Maker
IX.
TO fhew the reafon why the tides rife at the ſame time
on oppofie fides of the earth,.
[This is the beautiful experiment invented by
Mr. Ferguſon.]
E X P. X.
>
<
TO fhew that the diameter of our earth is longer at the
equator than at the poles
[This must be done on the whirling-fphere.]
E X P. XI.
Kepler's Grand Problem illuftrated, viz.
}
THAT the fquares of the periodical times of the planets
round the fun are in proportion to the cubes of their diflances
from him: and that the fun's attraction is inverſely as the
fquare of the distance from his centre; that is, at twice the
diſtance his attraction,is four times leſs-at flirice the dif-
tance nine times lefs-at four times the distance fixteen
times lefs, and—at five times, twenty-five times lefs, &c.
E X P. XII.
J
}
THE earth's motion round the fun demonſtrated from all
the foregoing experiments.
$
}
"
Exrt-
( 19 )
EXPERIMENT VI. p. 17. Explained.
IF bodies af equal weights
Revolve in equal circles
With unequal velocities;
Their centrifugal forces are
As the fquares of the velocities.
To prove this law by experiment,
Let two balls, A. and B. of equal weight,
Be fixed on their cords at equal distances
+
From their respective centres of motion;
Then let the cat-gut ftring be put round the wheel,
Whofe circumference is only one half
· ˆ Of the circumference of the other wheel,
And let four times as much weight
Be put into the tower B
As in the tower A ;
Then turn the winch,
Jul.
And the ball B will revolve twice as faft'
As the ball A in a circle of the fame diameter,
Becauſe they are equidiſtant from the centers
Of the circles in which they revolve ;
And the weights in the towers
Will both rife at the fame inftant;
Which ſhews that a double velocity
In the fame circle,
Will exactly ballance
A quadruple, or fourfold power of attraction,
In the centre of the circle;
For the weights in the towers
May be confidered as the attractive forces
In the centers,
Acting upon the revolving balls;
Which, moving in equal circles,
Is the fame thing as if they both moved
In one and the fame circle.
See all theſe Experiments explained at length in Mr. Ferguſon's lar
La&tures, 410.
SELEC
( 20 )
མ
2
SELECT and EASY BOOKS for a
YOUNG PHILOSOPHER.
I
.NEWTONIAN Philofophy, for Boys and Girls, by Tom
Teleſcope, A. M. Twenty-fours Newberry..
2. Martin's Lectures on all the Sciences, in his Introduc-
tion to the English Language, 12mó.
3. Ferguſon's Analyſis of his XII, Lectures. 8vo. 6d, with
his Lectures on felect Subjects, 8vo. 78.
4. Locke's Elements of Natural Philofophy, 12mo. 6d.
5. Martin's Familiar Introduction to the Newtonian Philo-
ſophy, 8vo. 2s. 6d.
6. Martin's Philofophical Grammar, 8vo. 3d Edit.
7. Young Gentlemen and Ladies Philofophy, 2 Vols. 8vo.
in Dialogues. In 'Martin's Magazine of Arts and Sci-
ences.
8. Matho. 2 Vols 8vo, by Mr. Baxter.
incomparable Strength and Beauty.
{
A Work of
9. Nature displayed; by Mr. Plache. 4 Vols. izmo.
10. Ray's Wiſdom of God in the Creation. 8vo.
11. Dr. Derham's Phyfico Theology. 2 Vols. 24.
*
*
་
12. Dr. Cotton Mather's Chriftian Philofopher. 8vo. 1725.
13. Above all read Monf. Nollett's Laft Legacy to`young
Philofophers. 3 Vols. 12mo,
A
138 APR 6
6