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THE PHILOSOPHICAL
HISTORY
रा
AND
37
MEMOIRS
OF THE
Royal Academy of Sciences at Paris:
O.R,
An ABRIDGMENT of all the PAPERS relating
to Natural Philofophy, which have been
publiſh'd by the Members of that Illuſtrious
Society.
Illuftrated with COPPER PLATES.
The Whole Tranflated and Abridged,
By JOHN MARTY N, F. R. S.
Profeffor of Botany in the Univerſity of Cambridge;
AND
EPHRAIM CHAMBERS, F. R. S.
Author of the Univerſal Dictionary of Arts and Sciences.
VOL. I.
LONDON:
Printed for JOHN and PAUL KNAPTON, in Ludgate-frect;
and FRANCIS COGAN, and JOHN NOURSE, near Temple-
Bar. M.DCC.XLII.
To the READER.
T
HE Bookfellers having been in-
formed, fince the Publication of
this Abridgment, that the late Mr. Cham-
bers, Author of the Cyclopædia, or Univer-
fal Dictionary of Arts and Sciences, had
made fome Progrefs in the fame Defign,
were defirous to make uſe of the Papers
left by an Author fo well efteemed by the
Publick. In the Courfe therefore of this
Work, fuch Papers of Mr. Chambers will
be inferted, as come within the preſent
Defign. But as I am unwilling to affume
to myſelf the Labours or Merit of another,
Care will be taken to diſtinguiſh each Pa-
per, which was written by Mr. Chambers:
which I believe will be acceptable to the
Reader; as he will be able by this means
to know, which Parts were compoſed by
that ingenious Author, and which by
Chelfea, Nov. 30,
1741.
John Martyn.
THE PHILOSOPHICAL
HISTORY
AND
MEMOIRS
OF THE
Royal Academy of Sciences at Paris:
OR,
An ABRIDGMENT of all the PAPERS relating
to Natural Philofophy, which have been
publiſh'd by the Members of that Illuftrious
Society.
CONTAINING
Many Remarkable ACCOUNTS of the NATURE
and PROPERTIES of the
Thunder,
Lightning,
Loadſtone,
Magnetical Needle,
Flux and Reflux of &c.
the Sea,
The feveral Improvements and Diſcoveries in
Air,
Winds,
Rains,
Earthquakes,
Opticks,
Mechanicks,
Hydrostaticks,
Hydraulicks,
1
Geography,
Navigation.
With many Curious OBSERVATIONS relating to the
Natural Hiſtory and Anatomy of Animals, &c.
The Whole Tranſlated and Abridged,
By JOHN MARTY N, F. R. S.
Profeffor of Botany in the Univerſity of Cambridge.
VOL. I.
LONDON:
Printed for FRANCIS COGAN, and JOHN NOURSE,
near Temple-Bar. M.DCC.XLII.
THE
PREFACE.
T
HE knowledge of nature
affords fo great a delight to
the mind of man, and is of fo
much importance to the well being
of fociety; that there is hardly any
confiderable ſtate in Europe, where
it has not been thought neceffary to
affemble a body of learned men,
whoſe chief employment it ſhould be
to improve natural hiſtory and phi-
lofophy. The ROYAL SOCIETY of
London was founded for this pur-
poſe, about fourſcore years ago, by
King Charles the Second: and what
improvements have been made by
that learned body, not only with
relation to fpeculative knowledge,
but even to the common ufes of life,
may be ſeen in thoſe excellent pa-
pers, publiſhed from time to time
under
A 2
iv
PREFACE.
under the title of Philofophical
Tranfactions. Soon after the foun-
dation of the Royal Society, the late
King of France, who was unwilling
to omit any thing which might con-
tribute to his glory, affembled a
confiderable number of the moſt
able men in his kingdom, to whom
he gave the title of the ROYAL ACA-
DEMY OF SCIENCES ; and engaged
them in the purfuit of natural and
mathematical knowledge. But this
learned affembly was not eſtabliſh-
ed, as a regular fociety, till that
monarch, in the beginning of the
year 1699, thought fit to give them
new eſtabliſhment, and to regu-
late their conduct by a body of laws
framed for that purpoſe.
From the time of this new efta-
bliſhment of the Royal Academy of
Sciences, a volume of their difco-
veries and obfervations has been pub-
liſhed every year, under the title of
A Hiftory of the Royal Academy of
Sciences,
PREFACE.
A
Sciences, by their perpetual fecre-
tary, the celebrated M. Fontenelle.
This Hiftory confifts of two parts:
the firſt is what is particularly called
the Hiftory. In this part, M. Fonte-
nelle gives a fhort account of every
remarkable tranfaction, either in
writing or by word of mouth, that
has paffed in the academy. The
other part contains the Memoirs, or
pieces that have been read in the
academy, fuch as have been judged
to be of the greateſt importance, and
the moſt worthy of being communi-
cated to the publick at full length.
The papers contained in this cu-
rious Hiftory are ranged under feve-
ral heads: the firft of which com-
prehends thoſe which relate to natu-
ral philofophy in general. Under
this head the reader will find many
remarkable accounts of the nature
and properties of the air, obferva-
tions on the thermometer, barometer,
&c. difcourfes on the cauſes and ef-
fects of winds, on the flux and reflux
of
vi
PREFACE.
of the ſea, relations of the effects of
thunder, lightning, &c. confidera-
tions on the aurora borealis, and
other remarkable appearances in the
heavens; curious difcoveries of the
various and furprifing properties of
the loadſtone; inquiries into the na-
ture of the magnetical needle; and
many other entertaining as well as
inftructing particulars, which we ſhall
not here detain him with enumerating.
To thefe papers on natural philo-
Sophy in general, we have added many
others, which we thought would be
efteemed to be moſt uſeful and en-
tertaining to the generality of readers.
Theſe contain the natural hiſtory
and anatomy of animals, many uſe-
ful diſcoveries relating to geography
and navigation, a great variety of
optical, dioptrical, and mechanical
diſcoveries and obfervations, with
many other mathematical papers,
which relate to common ufes of life,
paffing over thoſe, which are merely
fpeculative, or of leſs general uſe.
The
PREFA C E.
vii
The Abridgment of the Philofophi-
cal Tranfactions has been fo well re-
ceived by the publick, that we flat-
ter ourſelves the preſent work, which
is fo nearly allied to it, will meet
with a no lefs favourable reception.
It is an Abridgment of all the Me-
moirs of the Royal Academy of
Sciences, which relate to natural
philofophy in general, to the natural
hiftory of animals, and to the practi-
cal parts of the mathematicks; to
which we have prefixed fuch accounts
in M. Fontenelle's Hiftory, as are
not to be found in the Memoirs
themſelves.
As for thofe accounts in the Hi-
ftory, which are found more at large
in the Memoirs, we have thought
proper wholly to omit them; be-
cauſe they are generally no more
than a hiftorical account of what is
contained in the Memoirs themſelves.
And as we have contracted each of
thofe Memoirs, into as narrow a
compaſs as we could, without injur-
ing
vin
PREFA CE.
ing their ſenſe, we thought it would
be unneceffary to add the hiftorical
account of them too, which would
fwell the bulk of theſe volumes too
much; it being our defign to lay
before the reader the philofophical
difcoveries and obfervations of the
Royal Academy of Sciences, with re-
lation to the particulars above-men-
tioned, in as concife a manner as we
could, without diminiſhing any part
which really conduces to that end.
If the prefent undertaking meets
with the fuccefs which we hope for, it
will be an encouragement to us to
proceed in abridging the other papers,
which, tho' they are of lefs general
uſe than theſe now publiſhed, will,
however, be of the greateſt ſervice to
fuch as are engaged in thoſe parti-
cular ftudies.
A
A
TABLE
OF THE
PAPERS contained in the ABRIDGMENT
of the HISTORY and MEMOIRS of the
ROYAL ACADEMY of SCIENCES at
PARIS, for the Year MDCXCIX.
I.
In the HISTORY.
Comparisons ma
Omparisons of the obfervations made in
different places on the barometer, the
winds, and quantity of rain.
II. Obfervations on the fingularities of the natural
history of France.
III. Of infects.
IV. On the feathers of birds.
V. Of the tigers in China.
VI. The pofition of fome towns in Turkey, China,
and Armenia.
VII. The effects of burning glaffes three or four
feet in diameter.
VIII. On a machine made to prove the proportion
of the fall of bodies.
In the MEMOIRS.
1. Reflections on light and colours, and on the ge-
neration of fire, by Father Mallebranche.
II. A defcription of a new fort of flood-gate uſed
in the undertaking of the new navigation ef
the Seine, by M. Des Billettes.
VOL. I. No. 1.
B
III.
X
A TABLE, &c.
III. An explanation of fome fingular effects, which
happen to plain glaffes, fuch as looking-glaffes,
by M. de la Hire, at the obfervatory.
IV. A commodious way of fubftituting the action of
fire, instead of the force of men and horſes, to
move machines, by M. Amontons.
L
V. A defcription of a level, which is used by
M. Couplet, more exact in this fecond edition.
VI. A method to centre telescope glaſſes in working
them, by M. de la Hire at the obfervatory.
VII. Obſervations on the infects called adder-bolts,
by M. Homberg.
VIII. An inquiry into the ftrength of man to move
burdens, either by lifting, carrying, or draw-
ing, confidered abfolutely and with comparison
to that of animals which carry and draw, as
borfes, by M. de la Hire at the obfervatory.
IX. Two forts of wheels to draw water, by M.Des
Billettes.
X. Of the refiftance caused in machines, both by
the frictions of the parts of which they are
compofed, and by the stiffness of the cords em-
ployed in them; and the manner of calculating
both of them, by M. Amontons.
XI. A defcription of the heart of the tortoife,
and of fome other animals, by M. du Vernay.
AN
AN
ABRIDGMENT
OF THE
Philofophical Diſcoveries
AND
OBSERVATIONS
IN THE
HISTORY of the ROYAL ACADEMY of
SCIENCES at Paris for the Year 1699.
I. Comparisons of the obfervations made in
different places, on the barometer, the winds,
and quantity of rain.
M.
MARALDI having feen the ob-
ſervations made by Dr. Derham on
the barometer and on the winds at
Upminster, in England, during the
years 1697 and 1698, compared them with
thoſe which were made at the obfervatory during
the fame years; and this is the reſult of the com-
parifon.
Tho' the winds which reign at Paris, and at
Upminster, are commonly different, yet there are
many days in the different feafons of the year, in
which the winds have been the fame in both theſe
places. When the wind has been the fame in
B 2
Both
12 The HISTORY and MEMOIRS of the
both, it has uſually been violent, and of fome
continuance; tho' even theſe have fometimes
varied.
There is found alfo fome conformity in the
conftitution of the air, and it hath often happened
to rain, or fnow, or to be fair weather in both
theſe places on the fame days.
There is a great agreement between the varia-
tion of the height of the barometer obferved at
Paris and at Upminster. We generally find it to
riſe or fall at Paris, when it rifes or falls at Up-
minster; tho' theſe variations are not always
equal. In each month the days on which the
quickfilver has been higheft or loweſt, have been
the fame both at Paris and Upminster; but com-
monly when it has been loweft, it has been 3 or
4 lines lower at Paris than at Upminster, the
Engliſh meaſure being reduced to that of Paris.
It appears by the obfervations:
1. That the quickfilver riſes ſometimes, when
the wind is N. N. E. or N. W. and that it falls
with a S. S. E. and S. W. wind. It has how-
ever rifen and fallen at the fame time in both
thefe places, tho' the winds have often been dif-
ferent, and fometimes even oppoſite.
2. In theſe two laft years, when the quick-
filver was at the loweſt in both places, there fell
fome fnow; it fometimes alfo fnowed, tho' the
quickfilver did not fall more than ufual.
3. When the quickfilver rofe, it was often fair
weather, and it fell when it was rainy weather;
it was often fair weather alfo when the quickfilver
was low, and cloudy when it was high.
4. When the quickfilver fell at the fame time
in both places, and it rained in one and was
fair in the other, the quickfilver often fell in pro-
portion where it rained. In like manner when
I
it
ROYAL ACADEMY of SCIENCES. 13
it roſe in both places, it roſe higher in proportion
where it was fair.
Laſtly, it appears, that the quickfilver rofe
in one when it fell in the other, and that it fell in
like manner, whether the wind and weather were
the fame in both places, or different.
M. de Vauban having fent the academy a memoir
on the quantity of rain that fell in the citadel of
Lille for 10 years, from 1685 to 1694, M. de la
Hire has compared the 6 laſt years of the obfer-
vation at Lille with the fame years, which he has
obſerved very exactly at Paris.
Years, At Lille.
At Paris.
Inches. Lines.
Inches. Lines.
1689
18 9
18
I I
1690
24 8/2/2
23
1691 15 2
14
1692 25 42
I
22
1693
30 32
22
35790
2
8
1694 19 3
19
9
121
9
6 Years 133 6/2/2
By the compariſon of theſe 6 years we fee in
general, that it rains rather more at Lille than at
Paris; and that the mean year at Lille will be
22 inches, 3 lines, and at Paris 20 inches, 3
lines.
But M. de la Hire has found in 1695, 19 in-
ches, 7 lines; in 1696, 19 inches, 5 lines;
in 1697, 20 inches, 3 lines; in 1698, 21 in-
ches, 9 lines; and taking a mean year for thefe
10, we find 20 inches, 3 lines for each of the
6 firft; whereas at Lille the 6 laft give for a
mean
14
The HISTORY and MEMOIRS of the
mean 22 inches, 3 lines, and the 10 together
give 23 inches, 3 lines.
II. Obfervations on the fingularities of the
natural history of France.
The academy having a deſign to examine the
wonders of France, has begun with Dauphiny,
and with a very famous burning fountain in that
province, four hours diftant from Grenoble.
Saint Auguftin* has mention'd it, and feems to
treat it as a ſupernatural miracle. But as it is good
to be well affured of our facts, and not to feek for
the reafon of what does not exift; M. de la Hire
wrote to M. Dieulamant, the king's engineer in
the department of Grenoble, from whom he re-
ceived an information, as well circumftanced as
could be wiſhed. M. Dieulamant went upon the
fpot, and examined it with a philofophical eye.
It is no fountain; but a fmall fpot of ground,
6 feet long, and 3 or four broad, where may be
feen a light, wandering flame, like that of brandy,
fixt to a dead rock, of a fort of rotten flate,
which crumbles in the air. This fpot is upon a
pretty ſteep declivity; about 12 feet below it,
and as much on one fide, there falls from the neigh-
bouring mountains a little rivulet or torrent,
which perhaps may formerly have flowed more
high, and near the burning earth, which might
have given room to think that the water burned.
'The flame is not obſerved to come out of any
hole or cleft in the rock, by which it might be
ſuſpected to have a communication with fome
lower cavern that might be inflamed. There is
no matter found which may ferve as nouriſhment
to the flame, and it is only perceived to have a
ftrong
* De civitate Dei, lib. xi. cap. 7.
ROYAL ACADEMY of SCIENCES. 15
ftrong ſmell of fulphur; and it leaves no afhes.
There is a very hot, white fort of ſalt petre about
the place where the fire appears.
M. Dieulamant has been affured, that this fire
burns moft in winter, and in moift weather, that
it diminiſhes gradually in great heats, and often
goes out near the end of fummer, after which it
rekindles of itſelf. It is very eafy alſo to make it
kindle by another fire, which it does readily with
a noiſe.
M. Dieulamant obferved in the laſt place, that
about the fire the earth cleaves, gives way, and
finks down. He does not afcribe this however
to the fire, but to the waters which flow among
the dead rocks, and hollow the earth, or carry it
away. This effect is fo confiderable in Dauphiny,
and eſpecially in the country called le Chanfeaux,
that fometimes two villages fituated upon two
different mountains, which could not be feen from
each other, becauſe other higher mountains were
between them, have begun at once to be ſeen,
from the finking of the interpofed mountains.
III. Of infects.
Infects appear contemptible to the vulgar, who
neither know how to place their admiration nor
their contempt. They are moft commonly treated
as imperfect animals, but philofophy judges them
fo much more worthy of her attention, as they
feem to have been formed by nature on a quite
particular idea.
None but they, for example, change their
fpecies, and after having crept on the ground rife
up into the air, and take a new and more noble
life. What M. Homberg * has obſerved of the
* See the memoirs for this year, Art. vii.
odd
16
The HISTORY and MEMOIRS of the
odd copulation of adder-bolts will fhew how fruit-
ful and unexhauftible nature is in mechanical in-
ventions, to obtain her ends.
To be of both fexes at once, and to perform
the functions of both at the fame time, is another
circumſtance peculiar to infects. M. Poupart has
enumerated all the fpecies in which he is fure of
this particularity. They are the earth worms,
the round worms in the human inteſtines, thoſe
in the inteſtines of horſes, the flugs or fnails with-
out ſhells both of the land and the freſh waters, all
the fpecies of fnails with fhells, all the fpecies of
leeches. And as all theſe infects are reptile and
without bones, M. Poupart concludes, that pro-
bably the reſt, which have theſe two characters,
are alſo hermaphrodites; for nature, which varies
fo much from one kind of animals to another, ob-
ferves uniformity enough between the fpecies of
the fame kind, as to their principal characters.
Not but that there are reptiles without bones,
which are not hermaphrodites, as the worms
which change to flies, filk-worms, and other ani-
mals. But far from being hermaphrodites they
are of no fex at all; and, to fpeak properly,
are not animals, being nothing but cafes or masks
that wrap up and hide real animals, which after-
wards come out with wings. And tho' theſe
worms may ſeem to be fenfible, yet perhaps
their fenfibility belongs only to the concealed
animal, and not to that which appears. But,
however, the worm which is to change to a fly or
to a butterfly, is neither male nor female, and
does not engender fo long as it is a worm; but
itays till it is metamorphofed.
To give an example of the obſervations that
may be made on the hermaphrodite animals, fee
how M. Poupart has made his on the copulation
of
ROYAL ACADEMY of SCIENCES.
17
of earth-worms. Thefe little ferpents flide by
pairs into a hole that fuits them, there they ad-
juft themſelves in fuch a manner, that the head of
one is turned towards the tail of another; they
apply themſelves to each other in a right line,
and a little button of one in form of a little cone
is inferted into a little aperture of the other reci-
procally. The mutual infertion of thefe little but-
tons is eaſily ſeen, by taking the two worms gently,
drawing them gradually in the space between the
buttons, and furveying them in a full light. They
are found in copulation in the fpring; and you
muſt look for them in fat and moift paftures, if
you defire the biggeſt.
As theſe animals are male at one extremity of
the body, and female at the other, and as they
can eaſily bend, M. Homberg does not think it
impoffible, but that an earth-worm may couple
with itſelf, and be both father and mother of the
fame animal. This would be a ſtrange fort of
generation; but what is ftrange may perhaps be
fo only through our ignorance; and do we know
the bounds of the diverfity with which nature
has thought fit to adorn her works?
IV. On the feathers of birds.
M. Poupart has obferved, that feathers are
nouriſhed by blood and by lymph. We may be
fure of this by diffecting with a little ſkill a great
feather of a young bird before it has loft its down;
but it is ftill more eaſy to prefs this feather length-
wife, and ſee the lymph and the blood come out
of it. It must be a young bird, as it muſt always
be a young animal, when one would obferve how
the nouriſhment of the bones is formed. Feathers.
and bones are parts whofe veffels diſappear, and
VOL. I. No. 1,
whoſe
C
18 The HISTORY and MEMOIRS of the
whoſe mechaniſm grows lefs vifible as they become
more perfect. At the end of the quill there is a
little hole, by which the blood-veſſels enter, juſt
as they enter into a tooth by a little hole that is
at the extremity of the root. The pith, which is
taken from the infide of a quill when we cut it to
make a pen, in young birds is a great fleſhy ca-
nal, juſt like a vein filled with lymph, about
which the blood veffels, which entred at the end
of the quill, ſpread themſelves and divide into a
thouſand little branches,
But if we would know what this great fleſhy
canal is, we muſt not examine it in young birds,
but in ſuch as are full grown; the point of view
in which it is to be placed being no longer the
fame.
An explanation of the figures.
Plate I. Fig. 1. The great feather of the wing
of a large young bird, which has not loft its
down, being almoft wholly inclofed in the long
cartilaginous tube a b, which preferves the vanes
of the feather, which at prefent are only a fort
of pap.
Fig. 2. Reprefents the fame feather, with the
quill opened lengthwife, to fhew in its cavity a
large and long cavernous fleshy body, cd, upon
which are ſpread an infinite number of ſmall blood-
veffels, which enter by the lower hole d, to pour
their lymph into the caverns of this body, to be
carried into all the parts of the feather to nouriſh
them.
Fig. 3. The pith taken out of the quill of a
large young bird, to fhew them more cafily and
diftinctly.
Fig. 4. Cavernous bodies compofed of funnels
towards the upper part, and cups in the reft,
I
which
ROYAL ACADEMY of SCIENCES.
19
which are feen in the great quills of young birds,
when they begin to dry and become tranſparent.
Fig. 5. Three funnels boxed into one another,
which are taken out of the canal a of Fig. 4, to
fhew how the canals of theſe funnels enter after-
wards into their pavilions, to carry the lymph
into the veins and pith of the feather Fig. 2. to
which the canal e is faftened at the place c.
Fig. 6. Little bags or cups of which the body
repreſented in Fig. 4. is chiefly compofed.
We fee then in grown birds, that this canal
is compofed of feveral little tranſparent cups, pla-
ced one above another, and difpofed in fuch a
manner, that the bottom of the lower one is ar-
ticulated, or faftened into the opening of the up-
per one, and fo upwards on to the top of the
quill. But when we come near to the vanes of
the feather, theſe little cups become like funnels,
at leaſt in ſome fpecies of birds, as in turkeys.
The tube of the lower funnel enters into the pa-
vilion of the upper one, and faftens itſelf to the
bottom of it, and the tube of the laft funnel enters
into the pith of the feather.
The blood-veffels pour their lymph into theſe
little cups, and thence it is filtred to the top of
the quill, whence it enters into the pith of the
feather, which being only a fpongy ſubſtance ea-
fily imbibes it, and diftributes it on both fides
into the vanes.
In turkeys this pith is nothing but an affemblage
of an infinite number of pretty fenfible canals;
for the parts of the organs of an animal are
themſelves organifed, and the complication of the
mechanifm is infinite; and there is hardly any
room to queſtion, but that the other birds whofe
canals of the pith of the feather are not vifible,
C 2
are
20 The HISTORY and MEMOIRS of the
are found there only in fmall, and perform the
fame functions.
M. Poupart has obferved that one fingle fea-
ther of a young vultur, with the down ftill on,
weighed more than fix other feathers of the fame
bignefs that were in their perfection, it was fo
loaded with nutritious juices; and thence he con-
cludes, that as feathers are inftruments abfolutely
neceffary for birds to feek their ſubſiſtance, nature
makes hafte to bring them to perfection, and la-
bours about them with more diligence than fhe
does in moſt of her other works.
One might be contented with ſeeing that the
cavity of the quill had been wrought by nature,
to reconcile at once ftrength, fupplenefs and
lightneſs; but we fee befides that this void ferves
for a magazine to the nourishment which is to be
diftributed thro' the whole feather, and that the
fame mean anſwers to feveral views at once.
It is another curiofity, to obſerve the care that
nature takes to preferve the fprouting feathers of
young birds. The vanes of thefe feathers are at
firſt ſo tender and delicate, that they ſeem to be
meer pap. They are alfo rolled up in a long
cartilaginous tube, full of moisture, that they may
not be expoſed to the air, which would fo dry
them and ſhut up their pores, that they could not
receive any nouriſhment.
But when they are
ſtrong enough to be no longer afraid of the action
of the air, the cafe, in which they were rolled up,
becoming no longer neceffary, dries up and falls
off of itſelf in ſcales.
V. Of the tigers in China.
F. Gouye has communicated an anatomical de-
fcription of a friped tiger, made at China by
the
ROYAL ACADEMY of SCIENCES.
21
the Jefuits. We hardly know in Europe any
tigers, but fuch as have their ſkin marked with
fpots; but in Tartary and China they have a fort
which is marked with black ſtripes; and in thoſe
countries it is pretended that they are two diffe-
rent fpecies, tho' they do not ſeem to have any
other difference. The ftriped tiger, which the
Jefuits of China diffected, had been killed in
hunting by the emperor, together with four
others: It weighed but 265 pounds, fo that it was
none of the biggeft; one of the others weigh'd
400 pounds. That which was diffected, had of
its ftomach full of worms, and it could not be
faid to be corrupted: One of the company faid
he had found the fame thing in another tiger,
which he had feen opened at Macao.
Y M
3
VI. The pofition of fome towns in China,
Turkey, and Armenia.
F. Gouye having collected the obfervations
made by the Jefuits in theſe countries, has calcu-
lated them all, and drawn from them the pofi-
tions of ſeveral towns: He has chofen the leaft
doubtful operations, has had regard to the error
which may be fufpected in the inftruments, he
has taken the mean numbers between the greateſt
differences, which refult from different obferva-
tions made for the fame end.
We fhall not give here either the obfervations
of the Jefuits, or the calculations of F. Gouye,
but only the reſults of them.
The longitudes were taken from the immerſions
or emerfions of the fatellites of Jupiter, which
F. Gouye has reduced to the meridian of Paris,
by M. Caffini's tables, and by the neareft obfer-
vations
22
The HISTORY and MEMOIRS of the
vations which he has found to have been made at
the obſervatory.
The pofitions of fome towns in China.
Pekim.
Lat. N. at the houfe of the Jefuits
Longitude
It muſt be obſerved, that we here
fuppofe, and always fhall here-
after ſuppoſe the longitude of Pa-
ris to be
39 54
136 46 30
22
3
Ning-po or Liampo, in the province of Chekiam.
Lat. N.
Longitude
The cape of Ning-po is about 5
leagues more to the E. than Ning-
po, which gives almoſt 15′ of a
degree in longitude.
The Cape-Vert is more W. than
Paris by
Which gives the difference in lon-
29 56
141 18
} 19 30
gitude between Cape Vert and 138 33
Ning-po
However F. Coronelli in his great 1163 37
globe makes it
1
Kiam-Cheu, a town of the firſt rank in the province
Lat. N.
Longitude
Lat. N.
Longitude
of Xanfi.
Nan Kim.
1
"}
35 37
131 39 15
32
4
139
Xambay,
ROYAL ACADEMY of SCIENCES. 23
Xambay, a town of the third order on the E. coaft
of China, and upon a great river named Ho-
ampou, 4 leagues from the fea,
Lat. N.
The obfervations from which this
latitude was taken, are not abſo-
lutely certain. There may be 2
minutes difference.
Longitude
1
31 16
141 41 45
Sing-ghan-fu, capital of the province of Xenfi.
Latitude N.
Longitude
34 16 45
129 6 45
Nam-cham-fu, capital of the province of Kiamfi.
Latitude.
28 40
Kam-cheu-fu of Kiamfi.
Latitude
28 49 54
Nan-ghan-fu of Kiamfi.
Latitude
25 27 31
$
Xoacheu.
Latitude
24 44 10
It is doubtful.
}
Canton.
Latitude
Longitude
23 746
133 13 15
}
!
Tho' the latitude is different from all thoſe that
have hitherto been affigned to this city, yet we
may depend more upon this, becauſe it is drawn
from the moſt exact and numerous obfervations.
Su-cheu-fu, in the province of Namkim.
Latitude
Longitude
( 11
1 1
O
1
31 17 50
140 16 15
The
24 The HISTORY and MEMOIRS of the
The obfervations, from which F. Gouye has
concluded theſe latitudes and longitudes, which will
ſerve to rectify the map of China, are received
from the Fathers de Fontanay, le Comte, Bouvet,
Gerbillon, and Vifdelou.
!
The academy received alfo in June a letter from
F. de Fontenay, dated Nov. 8. 1697, at Tchaot-
cheou, a city of the first order in the province of
Canton. He gave an account of an obſervation
he had made of mercury in the fun at Tchaotcheou,
Nov. 3, 1697, Tho' he did not think it himſelf
entirely exact, F. Gouye calculated it, in order to
compare it with the obſervation at Paris. He
found by this compariſon, that the total emerfion
of mercury from the difk of the fun, which was
feen at Tchaotcheou at 3 48 44 afternoon, was
h
1
h
ſeen at Paris at 8 10 24 in the morning, and that
confequently the difference of the meridians of
h
Tchaotcheou and Paris, is 7 38 20, which be-
ing valued in degrees, and added to the longi-
tude of Paris, gives the longitude of Tchaotcheou
F. Fontenay judges alfo by efti-
mation, that Tchaotcheou is more
eafterly than Canton
Whence the longitude of Canton
would refult
It has been found by the Satellites
to be
137 5 30
3 30
} 133 35 30
}:
$133 13 15
//
Which is a fufficient conformity for fuch great
diſtances, and in fuch nice operations.
The
ROYAL ACADEMY of SCIENCES. 25
The pofitions of fome towns of Turkey and
Armenia,
Smyrna.
Latitude
38 12 39
Coronelli makes it
39 15
L
Trebifonde.
Latitude
Riccioli makes it
Longitude
41 3 54
43 11
65 0 45
o
Coronelli makes it
71 30
Erzeron.
Latitude
Longitude
39 56 35
68 45 45
Eruan.
40 19 33
· Latitude
F. Gouye has drawn thefe conclufions from the
obfervations of F. de Beze.
VI. The effects of burning glaſſes of three or
four feet in diameter.
M. Tfchirnhaus has cut fome burning glaffes,
the effects of which are above all that has yet
been feen. What he has communicated to us
is as follows.
1. You muſt place the glaſs ab, * ſo that it
may receive the rays of the fun full, which may
be known by the focus or image of the fun E,
appearing perfectly round on the plank cd, which
muſt be parellel to the glafs a b; and if this fi-
gure fhould be oval, you must bend and turn the
glaſs till it arrives at this perfect roundneſs; and
then wood will catch fire in a moment, lead will
*Plate I. Fig. 7.
VOL. I. No. 1.
Fiz. D
melt,
26 The HISTORY and MEMOIRS of the
melt, flates will vitrify, &c. and this at the dif-
tance of 12 feet, the focus being 1 inch in dia-
meter.
To render this focus more vivid, you muſt
contract it by means of a fecond lens, which muſt
be placed at fg, parallel to the firſt glaſs a b,
and then the focus, which was at E, will be at
H, and whereas it had a diameter of 1 inch, it
will have one of 8 lines; but its force will be
much augmented, fo that the fubftances, which
were not fufible at E, will melt at H.
I
3. This glaſs muſt be mounted on a foot like
that which bears the great burning mirrour of the
obfervatory, that it may be turned every way,
and placed in a convenient fituation to receive the
rays of the fun always full upon the glafs. Thefe
rays are always ftrongeſt from 9 in the morning
to 3 in the afternoon, both in fummer and win-
ter. It muſt be obſerved alſo to expoſe leſs mat-
ter in winter than in fummer, and that the ef-
fects are a little flower in winter. Theſe effects
are:
1. Every fort of wood, let it be ever ſo hard,
or ever fo green, nay, tho' it be foaked in water,
will catch fire in a moment.
2. Water in a ſmall veffel will boil in a mo-
ment.
3. Bits of metal being of a proportionate big-
nefs will melt, not in a moment, but immedi-
ately after the whole bit of metal has attained to
a certain degree of heat. For example, a bit of
lead, if it is too big, will not melt at all, but be-
ing of a proportionate bignefs, it muſt be held a
little while in the focus; and when it begins to
melt in one place, all the reft will continue to
melt. The iron muſt be in very thin flakes, and
then
ROYAL ACADEMY of SCIENCES. 27
then it will grow red in a moment, and after-
wards melt alfo.
4. Tiles, flates, pumice-ftones, earthen ware,
&c. of any bignefs whatſoever, grow red in a
moment and vitrify.
5. Sulphur, pitch, and all forts of refins melt
under water.
6 When you expofe to it in fummer any ten-
der wood, fuch as fir, under water, it does not
ſeem to change it on the outfide; but when it is
cleft in two, it is found burnt within to a coal.
7. If you make a hollow in a coal of hard
wood, and put the fubftances into it that you
would expofe to the fun, the effect will be infi-
nitely more violent.
8. Any metal whatſoever put into the hollow
of a charcoal melts in a moment, and fire fparkles
in it as in a forge; and if you keep the metals in
this manner in fufion for fome time, they fly
quite away, which happens particularly and very
readily to lead and tin.
9. The afhes of wood, herbs, paper, linnen,
&c. turn to a tranfparent glafs in a moment.
10. If any fubftances will not melt when they
are in pieces, you muſt expoſe them in powder;
and if they do not melt in powder, you muſt add
fome falt, and the whole will melt.
11. The fubftances, which are moſt altered by
this fire, are fuch as are black, and remain
black in melting; the more difficult are fuch as
are white and become black in melting; ftill
more difficult are thofe which are black and
become white in melting; the moſt difficult
of all are the white fubftances, which remain
white in melting, fuch as flints, Engliſh chalk,
lime, &c.
12. All
D 2
28 The HISTORY and MEMOIRS of the
12. All metals vitrify on a China plate, pro-
vided it is thick enough not to melt itſelf, and the
fire is given it by degrees that it may not crackle.
Gold receives a fine purple colour in its vitrifi-
cation.
13. If you put in a great receiver a b c fome
fubftances in which melt eafily, fuch as herbs,
fulphur, antimony, zink, biſmuth, &c. by ap-
plying a fingle burning glafs, you may obſerve
very curious effects in the receiver; but you muſt
take care that the part of the receiver a b, which
gives paffage to the rays of the fun, may not be
near enough to the focus c, for the heat to break
the receiver.
14. Salt petre in a fuitable dofe volatiliſes en-
rely, and goes off in fmoke; fo that by this
means one might make ſpirit of nitre readily in a
great receiver.
15. To melt the greateft quantity of matter at
once, you muſt put but a little at a time, and when
it is melted, add a little more, and fo on. In this
manner, you may keep 4 ounces of filver in fu-
fion at once.
16. A ſolid ſubſtance which is eaſily put in
fufion, may ſerve as a flux to another, which is
melted with difficulty, if you expoſe them to the
focus together, even tho' there might be but a
little of that which is eafily fufible.
17. It is obfervable alfo, that two fubftances,
each of which is difficult to melt feparately, when
they are expoſed together in a certain dofe, melt
very eaſily, as flints and English chalk.
18. A little copper melted in this manner, and
thrown quickly into cold water, produces fo vio-
lent a ftroak in this water, that the ftrongeſt
earthen veffels break, and the copper flies away
divided into fuch fmall parts, that there cannot
I
the
ROYAL ACADEMY of SCIENCES. 29
the leaft grain be found, which does not happen
to any other metal.
19. As metals evaporate in the fufion, fome
fooner than others, fome of them may thereby
purify others; for example, filver may be puri-
fied by lead, as well as by the ordinary cuppel.
20. You may make by it all forts of coloured
glaſs.
21. All bodies, except metals, loſe their co-
lours in this fire, and even precious ftones are
quickly deprived of theirs; fo that an oriental
ruby lofes all its colour in a moment.
22. Some bodies vitrify immediately, and be-
come as tranſparent as cryftal, and when cool
they become as white as milk, and loſe all their
transparence.
23. Some bodies on the contrary, which are
opake in the fufion, become finely tranfparent
when they are cold.
24. Some fubftances are very tranfparent in the
fufion, and remain fo when cold; but fome days
after they become opake.
25. Some ſubſtances, which the fire changes
into a glaſs, that is tranfparent at firſt, and after-
wards becomes opake, being melted with other
fubftances that are always opake, will produce a
fine glaſs, which will always remain tranfparent.
26. Thoſe bodies, which change into a tranf
parent glaſs, become much more beautiful, if they
are left a little longer in the focus.
27. Some ſubſtances turn to fo hard a glaſs,
that being cut in facets, it cuts common glaſs.
28. When you melt lead and tin together on a
thick plate of copper, there comes out a great
deal of imoke; but if there is only one of them,
and they do not go off entirely in fmoke, there
remains always a vitrified fcorium.
29. You
30 The HISTORY and MEMOIRS of the
29. You may concentrate the rays of the
moon by theſe glaffes, but they will give no fen-
fible heat, tho' they make a great brightneſs.
30. You may make alfo with thefe glaffes
curious reprefentations in opticks, and better than
with the concave mirrours; and you may make
alfo glaffes for teleſcopes and microſcopes, much
better than any that have hitherto been feen.
VII. On a machine made to prove the pro-
portion of the fall of bodies.
The ingenious hypothefis of Galileo, on the
proportion according to which the quickness of
falling bodies increaſes, is from henceforth efta-
bliſhed in phyficks. By dividing into equal parts
the time of the fall of a body, we know that in
the ſecond moment it
goes thro' 3 times more
ſpace than in the firft, 5 times more in the third,
and fo on, according to the odd numbers. But
this hypotheſis, ſo convenient for calculation, and
fo probable in reafoning, is however not good at
the bottom, any other wife than as it agrees with
experience, and this is not very eafy to prove in
a great degree of exactnefs.
For this purpoſe, F. Sebastien has conceived
and very exactly executed a machine, which
feemed to him more fit to prove the fyftem of
Galileo, than the other experiments which have
been made with the fame defign.
This machine is compofed of 2 or 4 equal pa-
rabolas, which interfect at their top by making
equal angles, and have a common axis perpen-
dicular to the horizon. This forms a para-
boloid, about which there turns a fpiral, com-
pofed of two parallel brafs wires, which make
a very narrow inclined plane, and fo dif
pofed,
ROYAL ACADEMY of SCIENCES. 31
pofed, that the firſt turn of the ſpiral being I inch
in diameter, the fecond is 3, the third 5, the fourth
7, &c. Thefe turns of the fpiral, which are to each
other as their diameters, are the unequal spaces
which the falling bodies muft go thro' in equal
times. We fee therefore, that if we let a little ivo-
ry ball of 6 inches in diameter fall from the top of
the paraboloid, and paſs thro' the whole inclined
fpiral plane, it will pafs thro' all the turns in the
fame time; and this will appear ftill better, if 2
equal balls turn about a paraboloid at the fame
time, and at fome diftance from each other; for
when one has ſeen them pafs in the fame inftant
over the fame arch of one of the parabolas, one
fees that they continue to go always together, and
to be found at the fame inftant over every other
arch whatſoever, tho' being at different heights
they go through very unequal turns of the fpiral.
୮
ΑΝ
ΑΝ
ABRIDGMENT
OF THE
Philofophical Memoirs
OF THE
HISTORY of the ROYAL ACADEMY of
SCIENCES at Paris for the Year 1699*.
1. Reflections on light and colours, and on the
generation of fire, by F. Mallebranche.
IN
N order to explain my notion of the natural
cauſes of light and colours, let us imagine a
great ball preffed on the outfide by an infinite
force, and filled with a fluid matter, the motion
of which is fo rapid, that not only the whole
turns with a great deal of quickneſs, about a
common centre, but alſo, that each part, to ful-
fil its whole motion, that is, to move as much as
it has force to do fo, is obliged either to turn
upon the centre of an infinite number of little
vortices, or elfe to flow among them, and all this
with an extraordinary rapidity. In a word, let
us imagine the matter contained in this ball to be
nearly fuch, as M. Defcartes has affigned to our
vortex; excepting that the globules of his fecond
element, which he ſuppoſes to be hard, are them-
felves only little vortices, or at leaſt that they
have no hardneſs, but by the compreffion of the
*
April 4. 169
matter
ROYAL ACADEMY of SCIENCES.
33
1
matter which furrounds them. For if theſe globules
were hard of themſelves, which I think I have
fufficiently proved * to be falſe, they could not, as
we fhall fee hereafter, tranfmit the light and dif-
ferent colours thro' the fame point, where the
rays croſs. But if this fuppofition meets with
any difficulty, it is fufficient at prefent to imagine
a ball full of water, or rather of a matter infi-
nitely fluid, and extremely compreffed on the
outſide. The circle ABC† is the ſection of
this ball thro' the centre.
This being fuppofed, if we make a little hole.
in this ball, as at A, I fay, that all the parts of
water, as thoſe, for inftance, at R, S, T, V, will
tend towards the point A, in right lines RA, SA,
TA, VA. For all theſe parts, which were equally
preffed, ceafing to be fo on the fide which an-
fwers to the hole A, they muſt tend thither; fince
every body that is preffed muft tend to move it-
felf by the fide where it finds the leaſt reſiſtance:
But if we put a pifton to the aperture A, and
drive it quickly in, the fame parts R, S, T, V,
&c. will all endeavour to remove from the hole
by the fame right lines A R, A S, &c. becauſe
when the pifton advances, they are more preffed
by the fide which anfwers to them directly, than
by any other.
In fine, if we conceive that the pifton advances
and retires very quickly, then all the parts of the
fluid matter which fills the ball exactly, the elaf-
ticity of which I fuppofe to be very great, or
that it ſtretches or extends itfelf with great diffi-
culty, will receive an infinite number of fhocks,
which I call vibrations of preffure.
Ch. Dernier de la Recherche de la Verite,
Plate II. Fig. 1.
VOL. I. No. 1.
E
As
34 The HISTORY and MEMOIRS of the
As every thing is full, our eyes are actually
preffed, tho' fhut or in the dark. But this com-
preffion of the optic nerve does not excite any fenfa-
tion of colours, becauſe this nerve is always equally
compreffed: for the fame reafon that we do not
feel the weight of the air which furrounds us,
tho' as heavy as 28 inches of quickfilver. But,
if we imagine an eye at T, or elſewhere, turned
towards a flambeau at A; the parts of the flame
being in a continual motion, will prefs without
ceafing more ſtrongly than in the dark, and by
very quick ſhakes or vibrations, the fubtile mat-
ter on all fides, and confequently becauſe of the
plenum, quite to the end of the eye; and the op-
tic nerve, being more preffed than ufual, and
fhaken by thefe vibrations, will excite in the
mind a fenfation of light, and of a lively and
glaring whiteneſs.
If we ſuppoſe at S, a black body M; the ſub-
tile matter not being reflected towards the eye
turned that way, and not fhaking the optic nerve,
we ſhall fee black, as when we look into the
mouth of a cave, or the hole of the fight of an
eye.
If the body M is fuch, that the fubtile matter,
which the flambeau fhakes, is reflected from this
body towards the eye, without the quicknefs of
the vibrations diminishing, this body will appear
white, and fo much the more white, as there are
more rays reflected. It will alfo appear luminous
like the flame, if the body M being polifhed,
the rays are all reflected, or a great part of them,
in the fame order, becaufe the brightneſs comes
from the force of the vibrations, and the colour
from their quickneſs.
But if the body M is fuch, that the ſubtile
matter being reflected has its vibrations lefs quick
in
ROYAL ACADEMY of SCIENCES. 35
in certain degrees, which I do not think we can
determine exactly; we fhall have fome one of
the colours which are called primitive, yellow,
red, or blue, if all the parts of the body M
equally diminish the vibrations caufed by the
flame in the fubtile matter. And we fhall fee all
the other colours which are formed by the mixture
of the primitive, according as the parts of the
body M fhall unequally diminish the quicknefs of
the vibrations of the light. This is what I meant,
when I advanced in fome of my books, that light
and colours confifted only in different fakes or
vibrations of the etherial matter, or in † more or
lefs quick vibrations of preffure, which the fubtile
matter produced on the retina.
*
at
This plain difcovery of my opinion will per-
haps make it appear fomething probable;
leaſt to thoſe who are acquainted with the philo-
fophy of M. Defcartes, and are not contented
with the explication which that learned man has
given of colours. But that a more folid judgment
may be formed of my opinion, it will be necef-
fary to give fome proof of it; and therefore we
fhall obferve:
1. That found is heard only by the medium of
the vibrations of the air, which fhakes the audi-
tory nerve: for when we have drawn the air as
much as we can out of the pneumatic engine, the
found does not pafs thro' it, but is louder as the
air is condenfed, and lefs in proportion as it is
rarefied.
2. That the difference of tones does not come
from the force of the vibrations of the air, but
from their greater or lefs quicknefs, as all the
world knows.
* Recherche de la Verite, tom. 2. pag. 364.
Entretiens fur la Metaph 12. Entr. n. 1.
E 2
3. Thar
f
36 The HISTORY and MEMOIRS of the
3. That tho' the impreffions, which objects
make on the organs of our fenfes, differ fometimes
only as to more and lefs, yet the fentiments, which
the mind receives from them, differ effentially.
There are no fenfations more oppofite than pleaſure
and pain; yet he that fcratches with pleaſure,
will feel pain if he fcratches a little harder: be-
cauſe the greater or lefs motion in our fibres dif
fers effentially with refpect to the well being of
the body, and our fenfes inform us only of this
relation. It is very probable, that ſweet and bit-
ter, which caufe fuch oppofite fenfations, often
differ only as to more and lefs; for there are fome
who think bitter what others think fweet. There
are fome fruits which to-day are fweet, and to-
morrow will be bitter. A little difference there-
fore in the bodies renders them capable of caufing
very oppofite fenfations. In a word, the laws of
the union of the foul and body are arbitrary, and
there is nothing in the objects like the fenfations
that we have of them.
It is certain, that colours depend naturally on
the ſhaking of the organ of the fight. Now this
fhaking can be only ſtrong and weak, or quick
and flow. But experience fhows, that the more
or leſs ſtrength or weakneſs of the fhaking of the
optic nerve does not alter the fpecies of the co-
lour; fince the more or lefs light, on which de-
pends the more or lefs of this force, does not
ufually fhew the colours of a different and quite
oppofite fpecies. It is therefore neceffary to con-
clude, that it is the more or lefs quickneſs in the
vibrations of the optic nerve, or of the fhocks of
the fpirits contained in them, that changes the
fpecies of colours, and confequently that the
cauſe of theſe fenfations comes primitively from
the
ROYAL ACADEMY of SCIENCES. 37
the more or less quick vibrations of the fubtile
matter, which compreffes the retina.
Thus it is with light and different colours, as
it is with found and different tones. The great-
ness of the found comes from the more or less force
of the vibrations of the grofs air, and the diver-
fity of the tones from the more or lefs quickness
of the fame vibrations, as all agree. The force or
brightnefs of the colours comes therefore alfo from
the more or lefs force of the vibrations, not of
the air, but of the fubtile matter, and the diffe-
rent fpecies of colours from the more or lefs quick-
ness of the fame vibrations.
When one has looked at the fun, and the optic
nerve has been very much fhaken by the bright-
nefs of its light, becauſe the fibres of this nerve
are fituated in the focus of the tranſparent humours
of the eye; then if one fhuts the eyes, or enters
into a dark place, the fhaking of the optic nerve
will alter only as to more and lefs. However,
we fhall fee different colours, white at firft, yel-
low, red, blue, and fome of thofe which are
formed by the mixture of the primitives, and in
the laft place black. Whence we may conclude,
that the vibrations of the retina, which are very
quick at first, become flower by degrees. For
once more, it is not the greatness or force of thefe
vibrations, but their quickness that changes the
fpecies of the colours; fince red, for example, ap-
pears red to a weak as well as to a ſtrong light. We
might therefore judge perhaps by the feries of
thefe colours, if it was very conftant, that the
vibrations of the yellow are more quick than thofe
of the red, and of the red than of the blue, and
fo of the other colours that fucceed. But it feems
to me impoffible to difcover precifely by this
means, or even by any other, the exact relations
of
38
The HISTORY and MEMOIRS of the
of the quickneſs of theſe vibrations, as they have
been diſcovered in the confonances of mufick.
We can therefore only conjecture, and have re-
courfe to the probable.
As the air is compreffed only by the weight of
the atmoſphere, there must be fome little time
allowed for every particle of air to remove the
next to it. Therefore found tranfmits itſelf pretty
flowly. It travels no more than about 180 toifes
in a fecond. But it is otherwife with light, be-
caufe all the parts of the ethereal light touch one
another, and are very fluid, and especially, be-
cauſe they are compreffed by the weight, if I
may ſo ſpeak of all the vortices. So that the
vibrations of preffure, or the action of the lumi-
nous body, muft communicate from a great dif-
tance in a very little time. And if the compref-
fion of the parts, which compofe our vortex, was
infinite, then the vibrations of preffure muſt be
made in an inſtant.
M. Huygens, in his treatife of light *, concludes
from the eclipfes of the Satellites of Jupiter, that
light tranfmits itſelf about 600,000 times fafter
than found. Thus the weight or preffure of the
whole celeftial matter is without comparifon
greater than that which is produced on the earth
by the weight of the atmofphere. I think I have
fufficiently proved elſewhere †, that the hardneſs
of bodies can come only from the preffure of the
fubtile matter. And if this is fo, it must be ex-
tremely great, feeing fome bodies are fo hard, as
to require a very great force to feparate the leaft
parts of them. It appears to me, that the pro-
portion of the weight of the ather to that of the
atmoſphere, is yet greater than that of 600,000
* Page 9.
+ Recherches de la Ferite, Ch. dernier.
to
t
ROYAL ACADEMY of SCIENCES. 39
+
to 1, and that we may even look upon it as in-
finite.
Let us therefore now fuppofe, that all the parts
of the ather, or fubtile and invifible matter of
our vortex are compreffed with an infinite force
by thoſe which encompass it, and that each of its
parts is very fluid, and has no hardneſs but by
the motion of thoſe which encompaſs or compreſs
it on all fides. And let us fee how it is poffible
in the fyftem that I propofe, that the impreffions
of an infinite number of rays, or of different co-
lours, communicate without confounding each
other. Let us fee how 10,000 rays, which croſs
each other in a phyfical, or fenfible point, tranf-
mit all their different vibrations thro' the fame.
point, fince I have juſt proved, that the difference
of colours cannot come but from the more or
Jefs quickness of the fame vibrations. Probably
the fyftem of the world, which
may clear up this
grand difficulty, will be conformable to the
truth.
Let* APE N be the fection of a chamber
painted with an infinite variety of colours, and
let them be the moſt diftinct that can poffibly be
that is, let there be at A white next to the black
n; blue b next the red r; yellow i next to the
violet v. If from all theſe points A, n, b, r, i, v,
there be drawn right lines interfecting each other
as in Q, and the eye be placed beyond as at E, c,
d, f, g, h, we fhall fee all thefe different colours
by the intermiffion of the point of interfection Q:
and as this figure reprefents only one row of co-
lours, whereas we ought to imagine as many as
there are parts that the eye can diftinguifi in a
ſphere, the point of interfection Q muft receive
Fig. 2.
and
40 The HISTORY and MEMOIRS of the
and tranfmit a very great number of different in
preffions, without their deſtroying each other.
If the phyſical point, or the globule Q was a
hard body, as M. Defcartes fuppofes, it would
be impoffible for the eye at E to fee the white at
A, and another eye at c to fee the black at n.
For when a body is perfectly hard, if fome part
of this body advances a little, or tends directly
towards the optic nerve, as from A towards E,
it is neceffary that all the other parts tend thither
alfo. Then we fhall not be able to fee the black
and the white at the fame time by the rays that in-
terfect in Q.
M. Defcartes pretends again, that the red is
formed by the turning of little globules, which
communicate together in the whole ray from the
object to the eye. This opinion is infupportable
for many reafons. But it is enough to overthrow
it, if we do but confider, that if the globule Q
turns upon the axis P N from r where there is
red, toƒ where the eye is, it will not be able to
turn at the fame time upon the axis rf, from N
where I again fuppofe red, to P where I fuppofe
another eye.
I
Moreover, when I fay that the rays interfect
in the globule, or vortex Q, I do not pretend
that theſe little vortices are exactly fpherical, nor
that the viſible rays have the fame thickneſs with
a globule of the fecond element or a vortex,
do not determine what muſt be the bignefs of
theſe rays, for them to be able to fhake the optic
nerve fufficiently to fhew the colours. But what
I have faid of one fingle globule, must be under-
ſtood of a thouſand, or a million, if one ray, in
order to be fenfible, muft be extended as far as a
thouſand or a million of globules.
It
ROYAL ACADEMY of SCIENCES. 41
It is not therefore poffible, that the globule Q,
or its like, can tranſmit the action of the light
proper to fhew all forts of colours, fuppofing theſe
globules to be hard. But if we conceive them in-
finitely fluid or foft, fo that the fimple idea of
the matter reprefents all the bodies, fince reft has
no force, and it is indifferent to each part of a
body to be or not to be near its neighbour, and
it muft part from it eafily, if fome force, that is,
fome motion does not reftrain it; for we do not
conceive in the bodies any other force than their
motion: if, I fay, we imagine theſe globules very
foft, or rather, which I think is the truth, like
little vortices, compoſed of a matter almoſt infi-
nitely fluid, or extremely agitated, they will be
fufceptible of an infinite number of different im-
preffions, which they may communicate to others
on which they reſt, and with which they are al-
moft infinitely compreffed. This I muſt endea-
vour to explain and prove.
In order to this, it is neceffary perfectly to
comprehend, that the re-action, which like the
action communicates itſelf at firft in a right line,
is here neceffarily equal to the action by this rea-
fon effential to the effect in queftion, that our
vortex is almoſt infinitely compreffed, and that
confequently it cannot have any vacuum in it. If,
for example, I was to push my cane againſt an
immoveable wall, my hand and cane would be
repelled with the fame force which I puſhed with.
The reaction will be equal to the action. Now,
tho' the rays are not hard like fticks, the fame
thing happens with regard to the reaction, be-
cauſe of the preffure and plenitude of our vortex.
For if we ſuppoſe a barrel full of water, or the
ball of the first figure full of air, and that having
adapted a pipe to it, we pufh a pifton into the
VOL. I. N° 2.
F
pipe,
42 The HISTORY and MEMOIRS of the
pipe, this piſton will be as much repelled as it is
puſhed forward. And if we make beſides in this
piſton a little hole, for the water to get out of the
barrel, and puſh this pifton, all the water, that
fhall be compreffed by it, will tend at the fame
time, becauſe of its fluidity, to remove itſelf from
each point of this pifton by the action, and by
the reaction it will approach the hole in the mid-
dle. For if the pifton was puſhed with fufficient
force and quicknefs, the barrel would burft in the
weakest place, wherefoever it was, a certain mark,
that by the action of the pifton, the water would
prefs the barrel every where, and if the piſton is
puſhed ever ſo little, the water will immediately
fpout out of the little hole in confequence of the
reaction. And all this, becauſe the reaction is
equal to the action in the plenum, and the water
or fubtile matter is foft enough or fluid enough
for each part to form itſelf in fuch a manner as to
anſwer all forts of impreffions.
It muſt be obſerved, that the more ftrongly we
puſh the piston that is let into the barrel, by fo
much more is the water, tho' driven toward the
concave furface of the barrel, ftrongly repelled
toward the piſton, and ſpouts at its aperture with
the more force. Whence it is eaſy to judge, that
a black point on a white paper muſt be more vi-
fible than on a blue paper: becauſe the white re-
turning the light more ftrongly than any other
colour, not only fhakes the optic nerve very
much, but is the caufe that the fubtile matter tends
by the reaction toward the black point with more
force; but if the ethereal matter was not infi-
nitely foft or fluid, it is clear, that the globules
which tranfmit the impreffion of the white, being
hard, muſt hinder that of the black; becauſe
thefe globules fuftaining each other, could not
terd
ROYAL ACADEMY of SCIENCES. 43
۲
tend toward the black point: and if this ethereal
matter was not compreffed, there would be no
reaction.
What I have juſt ſaid of the white and black,
may be applied to the other colours. But it
would be very difficult to do it particularly, and
to anſwer the difficulties which many people might
form on this fubject; for it is eaſy to make ob-
jections on obfcure fubjects. I think however,
that I have clearly proved, that the different co-
lours confift only in the different quickness of the
vibrations of preffure of the fubtile matter; as the
different tones of mufick come only from the dif-
ferent quickness of the vibrations of the grofs air,
as we learn from experience, which vibrations
alfo crofs without deftroying each other.
It ought not to be imagined, that what I have
faid of the globules of the ſecond element, which
far from thinking hard, I rather look upon as
little vortices of a fluid matter, can overthrow
the philofophy of M. Defcartes. On the con-
trary, if my opinion is true, it perfects what is
general in his fyftem. For if my opinion may
ferve to explain light and colours, it feems to me
alfo very proper to refolve, conformably to the
principles of this philofopher, other general quef-
tions in natural philofophy; as for example, to ex-
plain the generation and furprifing effects of fire,
which I fhall now endeavour to do.
On the generation of fire:
As bodies cannot naturally acquire any motion,
unless it is communicated to them by fome others,
it is plain, that fire cannot be kindled without the
communication of the motion of the fubtile matter
to the groffer bodies. M. Defcartes, we know,
ſuppoſes, that it is only the firft element that com-
municates
F 2
44 The HISTORY and MEMOIRS of the
1
く
​municates its motion to the third, of which the
groffer bodies are compofed, and which by agi-
tating them fets them on fire. According to him,
when we let off a gun, we forcibly detach a little
part
of the flint. (I ſhould rather it was a part
torn from the fteel that kindled; for when we
examine with a microſcope the fparks of fire ga-
thered together, we fee that it is the fteel that has
been diffolved and reduced to globules, or little
ferpents; and I have not obſerved any alteration
to be made in the fparks detached from the flint.)
This little part being detached from the iron
whirling round with force, drives the globules of
the ſecond element, and makes the first flow back
upon it, which encompaffing it on all fides, com-
municates to it a part of its rapid motion which
makes it appear in fire. This is pretty nearly
the opinion of M. Defcartes on the generation of
fire. But if the globules are hard, and all of them
touch, as he ſuppoſes for the explication of co-
lours; it is difficult to comprehend how the firſt
element could flow back towards the part detached
from the iron; and that with a fufficient abun-
dance to encompaſs it and fet it on fire; and not
only it, but all the powder of a cannon or of a
mine, the effects of which are violent. For the
firſt element that can flow back can be at moſt
but a very ſmall portion of the fubtile matter,
which fills the little triangular and hollow ſpaces,
which the globules leave between them.
I fhall therefore thus explain the generation of
fire and its violent effects, on the fuppofition that
the globules of the fecond element are in effect
only little vortices, of a fluid matter very much
agitated.
But it muſt firſt be obſerved, that tho' the air
is not neceffary to excite any little ſpark of fire, yet
without
ROYAL ACADEMY of SCIENCES. 45
without air the fire foon goes out, and cannot fo
much as communicate itſelf to the gun-powder,
which is fo ready to catch fire. When we dif
charge in vacuo a piftol well primed, we learn by
experience, that for want of air the prime does
not take, and that it is very difficult to fee fo
much as one ſpark from it. In fhort, every one
knows that fire goes out for want of air, and
kindles by blowing. This being fuppofed, I ex-
plain the generation of fire, and its quick effect
in mines after the following manner.
If one lets off a firelock in vacuo, the force of
the ftroke beats off a ſmall part of the iron or
fteel. This little part whirling round, and ſtrik-
ing quickly on fome little vortices of the fecond
element, breaks them, and confequently deter-
mines their parts to encompaſs, and afterwards to
agitate it and fet it on fire. But the matter of
theſe vortices, which we cannot imagine too much
agitated, after having had in an inſtant a great
number of irregular motions, partly replaces itſelf
quickly in new vortices, and partly eſcapes into
the intervals of the furrounding vortices, which
intervals become greater, when theſe vortices ap-
proach the detached part of the iron: and theſe
laft vortices are not broken, becauſe the part of
the iron which is rounded or almoft cylindrical,
turning upon its centre or length, does not ſhock
the encompaffed vortices in a manner fit to break
them. All this is done, as it were in an inftant,
when the iron and flint fhock each other in a place
void of air, and the ſpark is then hardly viſible
and does not continue.
But when we let off the firelock in the open
air, the part torn from the iron, by whirling
ſtrongly, not only meets and ſhakes fome little
ortices, but a great many parts of air, which
were
46 The HISTORY and MEMOIRS of the
were branched, meet, and confequently break bý
their motion many more vortices, than the little
part of the iron could by itſelf. So that the fub-
tile matter of theſe vortices, coming to encompaſs
the fire and the air, it gives them a fufficient num-
ber of different motions, to repel the other vor-
tices ftrongly. Thus the fparks muſt be much
brighter in the air than in vacuo: they muft alfo
continue longer, and have force enough to fet
fire to the gun-powder. And this powder cannot
want fubtile matter to ſet it on fire, what quantity
of powder foever there is, fince it is not only the
matter of the first element, as M. Defcartes be-
lieved, but much more that of the fecond, or of
the ſmall broken vortices, that produces the ex-
traordinary motion of the fire in the mines. If we
reflect upon what happens to the fire, when a
great deal of air is driven againſt it, we fhall not
queftion but that the parts of air are very fit to
break a great many of the vortices of the ſecond
element, and confequently to determine the fub-
tile matter to communicate a part of its motion to
the fire. For it is only from this matter, that
the fire can draw its force or its motion; fince it
is certain, that a body cannot move but by the
action of thoſe which encompafs or fhock it. The
prodigious effects of the great burning mirrours
fufficiently prove, that the fubtile matter is the
true cauſe of fire. The rays of light croffing each
other at the focus of theſe mirrours, the little
vortices of the ethereal matter of which theſe rays
are compofed, muft change their circular motion
different ways, and tend to move themſelves all
the fame way, that is, according to the axis of
the cone of reflected light, and to pierce alfo and
ſhake the parts of the body which they meet, and
to inflame them.
II.
ROYAL ACADEMY of SCIENCES. 47
II. A defcription of a new fort of flood-gate,
ufed in the undertaking of the new navi-
gation of the Seine, by M. des Billettes *.
This gate is quite fingular, and has no relation
to any that has been ſeen in any of the other na-
vigations, The principal properties of it are:
1. It faves at leaſt a foot of excavation, which
is known to be a great advantage in this fort of
works.
2. It is of extraordinary ftrength, and in a
manner invincible.
3. It is not faſtened to the piles, and confe-
quently independent on the inconveniences of all
thoſe that are fo.
4. A fingle man can open it with ſo much eaſe
and quickneſs, that a mariner, when he is within
a hundred toifes above or below, need only blow
a horn, and he finds it open before he gets to it.
Thus the navigation is never interrupted, as it
uſually happens at other gates, where whole hours
are often loft whilft they are opening them.
5. If there are any repairs to be made, two
men can get it out of the water in of an hour;
and as ſoon as it is mended, they replace it in an
inftant.
6. There can be no gathering of fand or other
things, to hinder the opening of it, but what may
be taken away in a moment.
7. Tho' it is very fimple, and more certain than
any that has been made till now, it cofts much
lefs, and is not ſubject to the accidents of other
conftructions.
It was invented by the late duke of Rouanez.
* May 2, 1699.
2
The
48 The HISTORY and MEMOIRS of the
The construction.
We fhall here only give a geometrical plan of
this gate, with a profile of one of its arms, with-
out entering into the explication of thoſe parts,
which are neceffary to all forts of fluices.
گرام
Having therefore fuppofed the excavation to be
as it ought, and the two floors above and below
proper for the emplacement of this gate, whether
open or fhut, with all the conditions requifite to
hinder the water from paffing underneath, or da-
maging the piles of the canal, we fhall content
ourfelves with obferving here, that theſe two
floors are in a manner made into one, being joined
by a platform common to both, and making
part of them.
*
This platform is here reprefented by 4 pricked
lines, and marked A. B. B. A. It is made of 4
pieces of crooked wood, placed end to end, and
making together 48 feet in length, and 18 inches
in breadth. Its bend is 2 portions of a circle,
which meet in the middle of the canal at the points
B. B. the centres of which are about 30 feet be-
low, and a little without its alinement. This
canal is here marked by the 2 parallel pricked
lines c. c. c. €.
Into each of theſe two centres is driven a great
ftake 15 or 16 feet long, and 18 or 20 inches
thick, of which there remains out of the ground.
only the length of about 2 feet, rounded into a
trunnion of 10 inches diameter. Theſe two
ſtakes are the pivots of the gate, and marked
P. P. It has fince been found more proper (in-
ſtead of making this trunnion out of the thickneſs
of the wood) to cut the head of the ftake quite
Plate II. Fig. 3:
fmooth,
ROYAL ACADEMY of SCIENCES. 49
Imooth, and place in the centre of it a pin of iron
about 4 inches in diameter or a little more.
We ſhall now fhew in what the gate alone
confifts.
It has 2 leaves, each of which is compoſed of
2 great arms and 2 fmall ones.
The great arms marked D. D. D. D. are pieces
of wood, 30 feet long, and 10 or 12 inches
fquare, joined and bound together with great
ferrels and iron pins at the lower end, and fepa-
rated at the upper end by a diſtance of 5 or 6
feet. At a little above the diſtance of a foot from
the extremity of their union, they are cut in fuch
a manner as to form a round hole, into which the
trunnions of the pivots enter. At their feparated
ends they are mortifed into 2 curbs of wood, 12
or 13 feet long to 7 inches fquare, marked E E,
which are arched like the platform, and meet in
like manner at the points B. B. when the
gate is
fhut. And on both fides they are faftened to the
curbs by mortifed binders F.
At 10 feet from the curbs, the arms are faf-
tened by croſs quarters GG; and in like man-
ner alfo at about 8 or 9 feet from the extremity of
their lower ends.
At about 6 feet from their lower extremity,
there arife alfo 2 other ſmaller arms of which
the tenons below enter into the mortifes H; and
feparating afterwards by a very acute angle, rife
at their other end about 4 feet higher, and are
mortifed into another curb raiſed parallel above
the firft. They are again fupported by upright
poſts, mortifed into the great arms at the places I.
One of thefe little arms joined to the great one,
and at once to the upper and lower curbs, may
be ſeen in the profile mentioned afterwards.
VOL. I. No. 2.
G
As
50
The HISTORY and MEMOIRS of the
As the great arms are faſtened by binders to the
lower curbs which reft on the platform, the fmall
ones are likewife faſtened by like binders, to curbs
4 feet higher than theſe, and are likewife held
by a cross quarter like that at G.
Theſe upper and lower curbs are connected
with upright pofts, and binders mortifed into each.
The place of theſe mortifes may be ſeen in 12
places of thefe lower curbs.
Against thefe curbs are faftened vertically, on
the fide of their convexity, fome planks, which
make a kind of fection of a portal and it is
thereby that the water is kept up on the floors
above and below. They are allowed to be 6 or
7 feet high or more, according as there is water
to fuftain in proportion to the piles and cham-
bords of the canal.
One of theſe planks is marked in the profile,
at** e e.
The two upright pofts, which are at the extre-
mity of each curb, bear at the bottom each of
them on a roller, or cylinder, 10 inches in dia-
meter, and 7 long. And it is by thefe 4 rollers.
that the gate turns upon the platform: one of
thefe rollers is in the profile marked j.
At the bottom of the planks in the fore part, or
above the ſtream, there are little boards applied
refting on the chant, and faſtened by hinges, fo
that they play like the lid of a box againſt the
tringle of wood raiſed and nailed along the whole
bend of the platform. So that by this means the
water cannot enter under the gate by the intervals
of the rollers; and yet when any weeds, fand,
wood, or other fubftances ftop before or above
theſe boards, they are let under the gate in a mo-
Fig. 4.
ment,
ROYAL ACADEMY of SCIENCES. 51
ment, by raiſing theſe little boards with a chain
or hook.
To open and ſhut the gate eafily, there is placed
on each fide a vertical windlafs, or capftan, near
the edge of the canal. About this windlafs is an
iron chain, the two ends of which are faftened
near each other on the curb above, after having
made a turn on a roller or pully faftened to the
pile; and by this means one man alone turning
the capftan, by a lever, one way opens the gate,
and the other way fhuts it in a very little time.
Each leaf of the gate, when it is open, places
itſelf in an excavation as low as the floors, repre-
fented by the triangles of pricked lines * A. K. L.
This emplacement is called the étang, or pond,
becauſe the water has no courſe.
To keep the boats from ftriking against the
pivots, there are two ftakes Q. Q. placed before
them, which are called pieux de garde, or pieux
de defenfe; that is, guarding ftakes.
It
This gate may be made fimple, and has fome-
times been made fo; that is, of one leaf only,
which bars the whole breadth of the canal.
has only 2 great arms at the extremities, that is,
to right and left, and two others fhorter between
them, butting only on a croſs quarter which holds
the first; and very little different alfo in its con-
ſtruction, wherefore it is not neceffary to ſpeak
of it here, becauſe the former is much better.
This fimple one has but one leaf, which extends
over the whole breadth of the canal; it turns alfo
on a ſingle pivot, and has need only of one pond
to place itſelf when it is open. But tho' this fingle
pivot muſt ſuſtain the whole effort of the water
of the canal; whereas the two-leaved gate has 2
pivots, each of which fuftains but half this effort,
Fig. 3.
G 2
yet
52
The HISTORY and MEMOIRS of the
yet the fimple one is however very excellent, and
may be neceſſary on fome occafions, where we
can have the pond but on one fide.
An explanation of the profile of one of the leaves,
which muſt be imagined to be elevated on the
geometrical plan of the others.
a a DDIR is the affemblage of the great
and little arm, with one of the upright pofts of
the gate, which is marked R.
H is the place of the mortife marked in the
plan of the gate: I one of the upright pofts
which holds the upper and lower arms together.
P is one of the great ftakes ferving for pivots
to the gate T is the trunnion.
M is a brace of 2 large pieces joined together
to hold the trunnion.
N is one of the ſtakes which hold the brace in
notches, and ferve together with the brace to
make the pivot ftronger againſt the force of the
water ſuſtained by the gate.
j is one of the 4 rollers. They are faftened to
the bottom of the upright pofts by blocks and
gudgeons.
ee is one of the planks which form the leaf of
the gate.
III. An explanation of fome fingular effects
which happen to plain glaffes, fuch as look-
ing-glaffes, by M. de la Hire, at the ob-
fervatory.
When we look at an object thro' a plain glaſs,
that is well poliſhed on both fides, as a looking-
glafs, we do not perceive that it is multiplied fe-
*Fig. 4.
1
veral
ROYAL ACADEMY of SCIENCES. 53
veral times but if it is in darknefs, and the ob-
ject is a luminous body as a candle, we may fee
it multiplied at leaſt 4 times; and the multiplied
object appears ſo much the more diftinctly, as the
glafs is more oblique to the line drawn from the
eye to the object.
This repetition of the object feems fometimes.
on one fide and fometimes on the other of the
luminous body, and thefe appearances diminiſh a
little in vivacity, in proportion as they are far-
ther diftant; and at laft they become fo weak as
to be no longer perceived. But there is an oblique
pofition of the glaſs in which the candle does not
feem multiplied; and there are ſome glaffes alfo,
thro' which we cannot fee any multiplication of
the object, tho' it is very much inclined.
I firſt obſerve, that this appearance is fenfible
only when the glafs, tho' plain, is unequal in
thickness. And as looking-glaffes generally have
their furfaces undulated, which comes from the
manner of poliſhing them, for they are generally
well wrought and fmoothed, by rubbing them a-
gainſt one another; which fhews the object mul-
tiplied in ſome poſitions of the glaſs, ſometimes
on one fide, fometimes on another, and in ſome
pofitions there does not appear a ſenſible, if any,
multiplication.
17
I fay now, that the most diftinct multiplication
of the luminous object is made in the line, which
is the ſection or meeting of a plane, which paf-
fing thro' the eye and thro' the object, is perpen-
dicular to both the furfaces of the glafs together,
and that this multiplication is made by the diffe-
rent reflections of the light within the glafs, and
by the refractions in coming in and going out, as
I fhall demonftrate.
bi
In
54 The HISTORY and MEMOIRS of the
In the first place, it is eafily known, that the
luminous rays cannot make feveral turns and re-
turns both within and without the glafs, unleſs it
be in plain furfaces, perpendicular to each furface
of the glafs, and which pafs thro' the ray within
the glaſs, feeing all thefe turns, both in reflection
and refraction, are always in a plane which paffes
thro' the perpendicular to the furface, which
makes the reflection or refraction; and fince there
are two furfaces, there will be alfo two perpendicu-
lars; and if thefe perpendiculars are in the fame
plane, all the rays, both refracted and reflected,
will be in the fame plane, and they will make
angles with each other more obtufe, than if they
were on different planes, and inclined to each
other; which must be understood only of the
rays, which coming from the object may meet
the eye.
I ſay now, that if the glafs was all over of
equal thickness, or if the fection of its furfaces
was two lines parallel to each other on a plane per-
pendicular to the glafs which paffes thro' the eye
and the luminous object, this object could not
appear fenfibly multiplied, provided it was at a
confiderable diftance from the glafs.
*
A SALE
CALGA
Let the fection of the glafs be EMBD, of
which the 2 lines E M, B D are parallel; let the
luminous point be C, and the eye O. It is evi-
dent, that all the rays, as CA, which coming
from the object C, meet on the furface of the glaſs
EM, are refracted and turn as at A B, as they
approach the perpendicular within the glafs, ac-
cording to the rules of refraction, and come out
afterwards at BO; in fuch a manner that the an-
gle of incidence CAE is equal to that of the
exit D BO, feeing the refracted angle EA B is
* Plate III. Fig. 1.
equal
ROYAL ACADEMY of SCIENCES. 55
equal to DBA, becauſe of the parallel ſurfaces.
Thus the eye being at O, will fee the luminous
point C, by the ray O B parallel to CA.
If the furfaces are not parallel, but the ſection
EM, GD is two parallel lines, it will be almoft
the fame thing, feeing the whole difference will
lie only in the reflected rays, which will not be on
one furface, by which this demonftration is not
affected.
But for the fame reafon, if another ray CF,
which may be confidered as parallel to CA, if the
point C is at a confiderable diftance from the
glaſs, tho' the ſpace A F is large enough, falls on
the part A E of the furface E. M of the glafs, it
will have its refracted ray F G within the glaſs,
which will alfo be parallel to A B; and that as
GH which fhall go out of the glafs, being alfo
parallel to BO, will not be able to enter the eye
O, unless it is very near to BO, which I do not
ſuppoſe here. It would be the fame with another
ray, which ſhould meet the furface of the glaſs on
the other fide of A towards M. But if one part
of the ray F G is reflected at I by the laws of ca-
toptricks, and if another part of the fame ray GI
is reflected at IK, which will alfo be parallel to
A B, becauſe of the parallel furfaces EM, BD,
goes out of the glafs at K, being refracted at KL,
it is as evident, that this ray KL will either meet
the eye at O, or not at all; and if it does meet
it, it will not make a different image from that
of the ray BO, ſeeing it enters the pupil with the
fame direction as BO, wherefore in this cafe the
object will not appear multiplied. But if we fup-
poſe, that CF makes the angle CF E much more
obtufe than the angle CA E, then it may be that
the ray KL, which will alfo make the angle
DKL equal to CFE, will meet the eye in O,
under
2
56 The HISTORY and MEMOIRS of the
under another direction than BQ whicho willį
form an image of the luminous point, different
from that made by the ray BQ Niw and I
But this fecond image formed by K.L, will be
a little weak, becauſe the greateſt part of the rays
will be loft in coming out of the glafs at Giand
at I.
3:
It muſt be obſerved, that if the glafs is not
very thick, or the object not far enough off the
ray K L will be very near BO, and confequently
the image formed by KL will be fo much the
more eaſily confounded, as it is more weak, with
that which is formed by BO; and that fo the ob-
ject will not appear fenfibly multiplied.
It is not neceffary to demonftrate that the ray,
which coming from the point C would fall upon
the part A M of the furface of the glafs, would
make a more obtufe angle than CA M, and could
never meet the eye after one or more reflections,
feeing it would always feparate more and more
from BO,
Now if the glafs is fuppofed to be of un-
equal thickness, and to be thicker towards the
object C than towards the eys O; 1 The
ray CABO, which will come to the eye after two
refractions, will come to the line BO, which be-
ing prolonged will meet the incident ray CA
for the ray A B refracted within the glafs, being
more perpendicular on B D, than A M, the ray
alfo OB will make with AB a more obtufe an-
gle than CA with the fame A B, wherefore OB
being prolonged will meet CA towards the object
C. And if the bignefs of the glaſs does not
hinder the rays immediately, from the object Citos
wards the eye O, we fhall fee the object C fims
址
​*
196
ply
Fig 2.
ROYAL ACADEMY of SCIENCES.
57
ply out of the glaſs, and on the fide the object
thro' the glass by the ray OB.
יו
2. There will be other rays as CR, which
coming from the object C, after a refraction
RN and two reflections N M, M P, and a re-
fraction PO, may come to the eye O. For fup-
pofing CR as parallel to CA, R N will be alfo
parallel to A B. But the furface B D being able
to meet the furface A M in D, the ray N M will
be more perpendicular to the furface A M than
the ray N R, which does not merit demonftra-
tion; and the ray M P making the angle PMD
equal to the angle NMA, the angle MPD will
be lefs obtufe than the angle RND or ABD:
wherefore the refracted ray PO making the an-
gle D P O greater than the angle DBO, it may
meet BO at the point O, which is the eye.
We fhall find alfo other incident rays at C R,
which meeting the furface A D beyond R towards
D and after two refractions both in coming in and
going out, and 4 or 6 or 8 reflections within the
glafs, may fall on the fame point Ơ, which will
fhew the object as many times multiplied as there
are different rays, which come to the eye O. And
thefe rays will come to the eye in the fame man-
ner as if the luminous object was placed in the
rays OP, prolonged to a diftance from the point
O equal to the fun of all the rays OP, PN, MN,
NR, RC; for they will enter the eye with the
fame direction, as if they came effectively from a
point placed at this diftance.
It is known by what I have juſt demonſtrated,
that the laſt images of the object, which are thofe
that come to the eye after a greater number of re-
flections, and confequently after a longer way,
will appear fmaller than thoſe which are nearer
the firſt O B, becauſe coming as it were from a
Vol. I. N°.2.
H
greater
58 The HISTORY and MEMOIRS of the
greater diſtance, the rays enter the eye more pa-
rallel to each other, which makes the object feen
16285120 oe of the
farther off; and the faintnefs of the image
objects moſt diſtant from OB, contributes alſo
very much to make them appear fmaller.
3127
It is eafy to fee, that the rays which come to
the eye, after a greater number of reflections
within the glafs, muft appear much fainter than
thofe which come thither after a lefs number:
feeing at each meeting which the ray makes with
one of the inner fürfaces, the greateft part of the
rays comes out of the glafs, and as very few are
reflected, fo the laft that come out and make only
part of thoſe which are reflected, muſt be very
faint: it is for this reafon alfo, that if the body
was not luminous, and, if it was not in the dark,
we fhould not perceive any multiplication.
JAE S
It muft now be demonftrated, why there ap-
pears a greater diftance between each multiplied
object, when the glafs is more oblique to the ray
which goes from the object to the eye, than when
it is lefs oblique.
100
ان
in,
Let there be the ray CABO, which meets the
eye in O after two refractions, one in coming
and the other in going out of the glaſs, and ano-
ther ray CRN MPO, which comes alfo to the
eye in O after two refractions and two reflections.
in the glafs. Let there be alſo another ray Ko,
of another luminous point K, more inclined to the
glafs than CA, and paffing thro' Ka B, and ano-
ther Ke Nur, which coming alfo from K after
two refractions and two reflections, meets B in
where the eye would be I fay that the angle B
is greater than the angle BOP, and confequently
the two images which come to the eye by the rays
OB, OP, and their ordinates, will appear lefs fe-
Fig. 3. T
H
}
M
a
parated
ROYAL ACADEMY of SCIENCES. 59
parated from each other, than thofe which fhall be
formed by the rays wB, wπ.
a
མ
}
The ray B in the glaſs makes with AB the
the angle &BA, fmaller than the angle BO formed
by the fame refracted rays in coming out of the
glafs, which is known by dioptricks; for the rays
as BO which are the refracted of the incidents
AB, approaching much quicker to the furface of
the glafs BD, than the incidents in the fame glafs
do to the fame furface HB. But the line N be-
ing as a parallel to aB, becaufe we fuppofe the
rays K, Ke as parallels, it follows that the an-
gle NR will be equal to the angle MN; and
confequently the difference of the angles DMP,
D will be alfo equal to the angle «BA.
AY
But the rays MP, 7, being more perpendicu-
lar to the furface BD than AB and aB, the re-
fracted rays PO and T will make between them
a fmaller angle that OB, and if we draw I pa-
rallel to PO, the angle I will be equal to that
which is contained by the rays PO and Tw,
πω, which
will be ſmaller than the angle OB which is
plain from the reafon juſt given.
πω
Now becaufe the external angles are equal to
the two internal oppofite ones in the triangles,
the angle Dr minus the angle DB will be equal
to the angle B; and the angle DPO minus the
angle DBO will be equal to the angle POB: but
the difference between the angle D and DPO,
or its equal DI, which is the angle I was de-
monftrated above to be fmaller than the angle
OB: wherefore if from the angle Dre we take
away the angle DB; and if from the fame angle
Dow plus the angle I, we take away the angle
DB, and the BO, which is greater than I, as
has been demonftrated, it follows that the firft re-
mainder is greater than the fecond, feeing in the
fecond
છે.
ய
A
H 2
1.
60 The HISTORY and MEMOIRS of the
fecond there is more taken away than added g but
the firſt remainder is equal to the angle B and
the fecond-equal to POB; therefore the angle B
is greater than the angle POB, Q. En D. en sy
It will be the fame with the other angles made
as TB by incident rays which will fall towards D.
"
こ
​E
Experience confirms what I have juſt démon-
ftrated of the images which appear by the rays
OB, OP, OQ, &c. which are formed by the
incident rays CA, CR, CS, and thoſe which are
of the fame ordinance, or which coming from the
fame point of the luminous object, can enter the
pupil: for if a paper is applied to the furface of
the glaſs AD, and it is drawn forward from D
towards A, when the paper hall cover the place
S of the incident ray CS the luminous image in
Qwill diſappear. Afterwards when it is come
to R, the light in P will diſappear in its turn,
and fo on. And it will be obferved, that no re-
gard is to be had to the image of the paper, which
is feen doubled becauſe of the refraction, which
is not ſeen out of the darkneſs but it is a parti-
cular cafe which I fhall explain afterwards.
し
​The diſtances between the images BPQ appear
almoft equal among themfelves for thefe images
are formed by reflected rays, which furpafs one
another by a feries of two, and the incident rays
CA, CR, CS, which form them, are very near
to each other but this appearance can only be
when the furfaces of the glafs are almoft planes;
for if one or both of them are curves, the diſtances
between the images will appear very unequal;
which is eafy to know by the difpofition of the
rays which can come to the eye w
I have already demonftrated, that the images
appear more faint in proportion as they are far-
ther removed from thofe which are neareſt the lu-
minous
ROYAL ACADEMY of SCIENCES.
61
$1
8
minous object, by the quantity of rays which
elcape out of the glafs and I have faid alfo, that
they appear ſmaller, becauſe they come to the
eye as if they were farther off but I demonftrate
at prefent, that they appear larger in proportion
as they are farther feparated from the luminous
object, which must always be underſtood of the
images multiplied in the plane, which paffing
thro' the object and thro' the eye is perpendicular
to the two furfaces of the glafs.
We fhall explain this phenomenon, as we did
the preceding. For the rays, which come to the
*eye
*O from the two points CK, which are on
the two fides of the luminous body, after two re-
fractions only, are more inclined to the furface of
the glafs which is turned towards the eye, than
thofe which come thither after two refractions and
two reflections within the glass, which appears
by the figure, and by what has been already de-
monftrated. But fince the rays more inclined to
the furface BD make angles much more acute in
proportion, as they approach to the furface of the
glafs, than thofe of inclination are, becauſe the
refractions follow the proportion of the fines of
the angles of inclination; it follows that the rays
OB, O3 will make an angle BQ3 much more
acute in proportion than the rays OP, Or, which
comprehend the angle POT. For the ray 03
muſt be more inclined with regard to its incident
ray, than the ray Or with regard to its incident:
thus the angle BO3 will be more acute in propor-
tion to the length of the ray which goes to the
object by the point B, and by its turns within the
glafs, than the angle PO in proportion to the
length of the ray which goes to the object by the
ray
OP and by all its turns. Therefore, laftly,
Je doule
Fig. 4.
}
the
62 The HISTORY and MEMOIRS of the
the image repreſented to the eye by the angle PO,
will appear larger than that which is reprefented by
the angle BO3, in proportion to the height of
thefe images. For the height of the image of
the body, which I have fuppofed to be a candle,
muft diminiſh only in proportion to the ways
which the rays take both within and without the
glaſs to come to the eye, feeing the ſection of the
glafs, which determines the greateſt indlination of
its furfaces, is fuppofed horizontal.
It muſt be obferved, that in all which is here
explained of the rays that come from the points
of an object as CK, I fpeak only of the principal
rays; tho' we muſt always conceive an ordinance
of the rays of thefe fame points, which come all to
the eye to enter the aperture of the pupil, which
make a fort of cones or pencils as fome call them,
which affemble on the retina to make the pic-
ture of the object; for it is demonftrated in diop-
tricks, that the point, where they affemble after
their refractions in the eye, is always upon one of
theſe rays called the principal.
* As for the paper which hides the multiplied
images as faft as it advances, as I have faid before,
it is certain that we could not fee its edge MN
multiplied, if it was not the luminous body that
makes it appear. For if the paper MN begins to
hide the incident rays VT, which fhew the breadth
of the image D of the candle, the edge of the pa-
per, which will appear at OP will hide alfo a
part of this image; but if the fame edge of the
paper MN hides the greatest part of the rays SR,
which fhew the image Q, it is evident that only
a fmall part of this image will be ſeen as at Q,
where we may perceive the image of the edge of
Fig. 5.
the
ROYAL ACADEMY of SCIENCES. 63
1
the paper that hides it, which one could not per-
ceive without the light which appears at Q.
Joam now to demonftrate how the multiplica-
tion of the object is made, when the angle of
the fection of the glafs is turned towards the lu-
minous object; but after what has been faid a-
bove, the figure may be fufficient to explain what
ought to happen.
7
Let the fection of the glaſs therefore be
EDB, of which let the concurrence of the fur-
faces in D be turned towards the object C, and
let the eye be placed oppofite towards O. Firſt
let the incident ray be CA, which being refracted
in the glafs at AB, in going into it, and refracted
again at BO in coming out of it, comes to the
eye O; I fay, that if the glafs fhould be cut in
B, and the part BD taken away; we could not
then fee the object Cause 2 and t
JA
י
!
}
For the ray AB within the glafs, being more
inclined on the furface DB than on DAE, the
angle ABO will be lefs obtufe than the angle
BAC; wherefore the ray CA will concur with
the ray OB towards O, and confequently there
can be no direct ray which comes from the object
C to the eye Of de pesona chaud i
s
But it is as evident, that all the rays which com-
ing from the luminous object C, and meeting the
furface of the glafs towards E, can never come to
the eye, which we fuppofe placed in the ray BO,
after two or more reflections in the glafs, feeing
they will be always more and more inclined to
the furface DB, and confequently they will come out
of the glafs in parting from the ray BO. The rays
therefore which fall upon AD towards the con-
currence of the furfaces of the glafs, will be
gba na tu gemi pale using
Fig. 6.
thofe
64 The HISTORY and MEMOIRS of the
thoſe which make the multiplication of the ob
ject.
For in the fecond place, let the incident ray be
CR, which coming from the luminous object C
as parallel to CA, meets the furface DA in R,
the refracted ray RN will therefore be alfo as
parallel to the refracted ray AB; but the reflected
ray NM will be more inclined to the ſurface DA
than NR, and placed counter to the quantity of
the angle P of the two furfaces of the glaſs, as I
have demonftrated in the firft cafe: wherefore the
reflected ray MP will make the angle EMP
more acute then the angle ERN or its equal
EAB; therefore the ray MP in coming out of the
glaſs by PO will make the angle XPO more acute
than XBO; and confequently PO may meet BO
at the point O, where the eye is in the ray BO.
It will be the fame thing with the other rays
which coming alfo from the object, may meet
the eye after two refractions of 4 or 6 reflections
within the glafs, which it is not worth the while
to explain more at length.
1
If we draw a paper on the furface of the glafs
from the part E towards A, we fhall fee that the
ftrongeſt image formed by the ray CA will difap-
pear first, and the reft afterwards, as faft as the
edge of the paper fhall advance towards D; and
we fhall fee the image alfo of the paper multi-
plied as in the preceding cafe. For in the fame
figure, if the edge of the paper MN covers the
greateft part of the fpace SR, which compre-
hends the rays which form the image Q. alfo the
image XY of the edge of the paper will appear to
hide the greateſt part of the image Q of the lu-
ninous body. And if the fame edge of the pa-
per MN in the fame pofition covers alſo a great
part of VT, by which the rays enter that form the
}
image
ROYAL ACADEMY of SCIENCES. 65
image D, we shall fee alfo the edge of the paper
repreſented in OP, which will cover a part of the
image P, which is eafy to underſtand.
By means of this multiplication of the objects,
we may know the different thickneffes of a piece
of looking-glafs which is uſed in working the great
teleſcope glaffes, and in a much more fure and
juſt manner, than by all the meaſures that can be
taken for it:
But to make this explanation more complete,
we muſt ſtill examine how the multiplication of
the object is made, when it is placed on the fame
fide with the eye, with regard to the fame fur-
face of the glaſs.
Every body knows, that when we look at a
candle placed near a looking-glafs which has been
tinned, the eye being alfo near the glafs, we fee
the image of the candle multiplied feveral times.
It is very eafy to fee the reafon of it; for the
anterior furface of the glaſs reflects the firſt image,
and the other fends back the fecond, after two
refractions of the rays in coming in and going out
of the glafs, and a reflection on the tin. But
what is more difficult to be known, is the reafon
why there appear more than two images. This
experiment and its explanation ferve no doubt for
a proof of what I have already advanced concern-
ing the luminous rays which are reflected within
the glafs in meeting its furfaces, tho' they are not
tinned. It is eafy to fee, that if the glass is tin-
ned, all the rays, which fhall enter the glafs, can-
not go out of it, and that they muſt all be reflect-
ed, and confequently the image which fhall be
formed by this reflection and after two refractions,
will be much more vivid than that which is made
by the reflection alone on the anterior furface, be-
caufe in this the greatest part of the rays having
VOL. I. N°. 2.
I
pene-
1
66 The HISTORY and MEMOIRS of the
penetrated within the glaſs, cannot meet the pupil
of the eye in going out, if the reflected only have
met it, and eſpecially if the glafs has a little thick-
nefs. But as the fame thing happens to a glaſs
which is not tinned, as to one that is, and as fome
particular obfervations may be made on that
which is not, that are not found in that which is,
I fhall here explain only what happens to a glafs
which is not tinned.
As the different images of the fame object may
be formed by rays which have different inclina-
tions to the eye, thefe rays muft neceffarily come
from different parts of the furface of the glafs,
which cannot be without the firft incident rays of
one point being different from each other, we
ſuppoſe the ſurfaces of the glafs to be planes,
and parallel to one another; and theſe different
inclinations of the rays cannot meet the pupil,
which is as a point, till after feveral reflections
within the glass. But if thefe rays which come
out of the glaſs, are, as it were, parallel to each
other, which happens when the object is far enough
from the eye, and the glafs is of equal thicknefs,
or when they are on the fame plane, which be-
ing equally inclined on each fide to the furfaces of
the glaſs, and paffing thro' the eye and the ob-
ject, makes parallel fections, it is evident, as I
have already demonftrated, that the rays of the
fame point having fuffered feveral reflections.
within the glafs, cannot meet the eye; there will
then in this cafe be only one image formed by
thefe forts of rays. But if in the fame cafe of
parallel furfaces, the object is near the eye and
the glafs, there may fall on the furface of the
glafs fome rays from one and the fame point of
the object differently inclined to form feveral
images, as is fhewn by experience.
I
If
ROYAL ACADEMY of SCIENCES. 67
If the glaſs is of unequal thickneſs, and the
right lines which are the fection of the glafs by a
plane perpendicular to its furfaces paffing thro' the
eye and the object, concur on both fides, we
fhall fee ſeveral images of the object, at least if it
is luminous, and in the night; fince at whatſoever
diftance from the eye the object is placed, there
will be found feveral rays which coming as pa-
rallels from the fame point of the object, and
having ſuffered ſeveral reflections within the glafs,
will come out of it with different inclinations,
which will form different images, which has no
need to be explained after what I have faid already;
and thefe images will be found fometimes on one
fide, fometimes on the other, with regard to that
which is made by one ſingle reflection, according
as the angle of inclination of the glafs fhall be
either towards the eye or towards the object.
We may alſo by this means know with a very
great exactnefs, whether the glaffes poliſhed on
both fides are of the fame thickneſs, tho' in a
very ſmall ſpace; which it would not be poffible
to obferve any other way. For if we obſerve on
the furface of a glafs the image of a bright line
in the dark, or of a black line in the light, and
if it is at a. pretty confiderable diftance, and if
the eye and the object are on the fame fide of the
furface, and alſo if in turning the piece of glaſs
different ways, we fee this image only fingle, in
one fingle pofition, we may be fure that the piece
of glafs is of equal thickness according to the
difpofition of the bright or dark line, and that it
is of unequal thicknefs every other way, the
greateft angle of which will be in the fection,
which fhall cut the image of this line perpendi-
cularly. Alfo in every other pofition of the
glafs but that where the image of the line is fingle,
I 2
it
68 The HISTORY and MEMOIRS of the
it will be feen double; and they will appear far-
ther diſtant from each other, when they fhall cut
at right angles the pofition where it appeared
fingle.
It will alſo be obſerved, that one of the two
images of the line appears much more vivid than
the other, and that it is this which is made by re-
flection, becauſe there are more rays that come to
the eye.
بازد
It will not therefore be difficult to know by
this means, what place of the glafs, will be the
thickeſt. For if the fainteft, image appears to-
wards the object, I fay, that the part of the glafs
which is turned towards the object is the thinneft;
and if the fainteft image is towards the eye, that
part of the glafs will alſo be the thinneft.
For if the object is * B, and the eye O, and
a luminous ray BD meeting the ſurface of the
glafs HE in D is reflected towards the eye at O,
it is eaſy to fee, that if another incident ray com-
ing alfo from the point B, and as it were parallel
to BD, meeting the furface of the glafs in F, is
on either fide of D, and penetrating on the infide
to K, meets the other furface KI, which concurs
towards the firft in M, on the fide of the object,
the greateſt part of this refracted ray FK will go
out of the glaſs; and a very fmall part only being
reflected in K, will return towards the furface HE
in H, or being refracted in HL, it can never meet
the eye in O. For the ray KH, being more in-
clined to the ſurface HE than the ray KF, alfo
the ray HL will be more inclined to the fame
furface than the incident ray FB; and confe-
quently this ray HL, which parts more and more
from the ray DO, can never meet the point O,
* Fig. 7.
if
ROYAL ACADEMY of SCIENCES. 69
if the point H is farther from the top of the angle
M than the point D.
It will not be the fame with another ray as BE,
which having fuffered a refraction in E, a reflec-
tion in I, and a fecond refraction in G, comes
out at the point G between D and M; for this
ray refracted in G may meet the eye in O, becauſe
the inclination HGO is always greater than BEM,
or BDM, or ODH, as has juſt been demon-
ftrated; wherefore the fainteft image which is
formed by the ray OG, which has fuffered two
refractions and pne reflection, will appear in G
towards the part M, which is the thinneft of the
glafs.
The demonſtration will be the fame, if the
thinnest part of the glafs is turned towards the eye.
IV. A commodious way of fubftituting the
action of fire, instead of the force of men
and horfes to move machines, by M. Amon-
tons*.
Experiment I. Of the rarefaction of the air by
the beat of boiling water.
}
4
Wet immerged in a kettle full of water, the
balls of three glafs tubes ACD, ACD, ACD, of
equal length, each open at A, bent at. C, and
ending in a ball D; the capacities of the balls
were to each other as the numbers 1, 2, 3, as
well as thofe of the tubes AB, which befides were
pretty narrow, the mean one being but half a line
diameter within; there was in each glafs fome
quick filver from the entrance E of the balls up to
B, where the quickfilver was three inches higher
than at E, becauſe the air of which the balls were
* June 20, 1699.
+ Plate IV. Fig. 1.
7
full,
70
The HISTORY and MEMOIRS of the
full, having found no out-let when the quickfilver
was poured in by the apertures A, fuftained it by
its fpring, and hindered it from going down to
the level of that of the entrance of the balls.
The whole was fet on the fire, and the quick-
filver at B rofe equally in equal times in all the
three glaffes; ſo that when the water began to
fimper, it was 9 inches higher than B, and 9 in-
ches 10 lines, when it boiled out, after which it
entirely ceaſed to rife. From this experiment it
follows:
1. That the heat of boiling water has bounds
which it cannot pafs.
2. That unequal maffes of air increaſe equally
the force of their fpring by equal degrees of heat,
and on the contrary.
3. That the heat of boiling waterdoes not increaſe
the force of the fpring of the air any more than to
make it fuftain the weight of about 10 inches in
height of quickfilver, or 11 feet 8 inches of wa-
ter more than the weight of the atmoſphere*.
For the quantity by which the air diminishes its
fpring in dilating itfelf to replace the quickfilver
which rifes from В to F, equals almoft the two
lines which are wanting to the 10 inches in this
experiment.
4. That if the air has the liberty of extending
itſelf, being preffed only by the weight of the
atmoſphere, it will not increafe its bulk by the
heat of the boiling water by any more than about
of its mafs; for according to M. Mariotte's ex-
periments, the air making an equilibrium by its
fpring to weights proportioned to the bulks, to
which thefe weights are reduced by their preffure,
and the bulks being to each other in an inverted
*The weight of water is fuppofed to be to that of quickfilver
as I to 14.
ratio
ROYAL ACADEMY of SCIENCES. 71
ratio of theſe weights, if the height of the quick-
filver is fuppofed at 41 inches, as indeed it may
be in this experiment, and if the bulk of air is ex-
preffed by the number 3; when the height of the
quickfilver fhall be no more than 31 inches, the
bulk will be 3 31.
30
But as the weight of the atmoſphere is here fup-
pofed equal to 31 inches of quickfilver, which it
really is not, this weight being hardly equal to more
than 28 inches of quickfilver, the fraction ought
to be reckoned as an integer; becauſe the air
lofing the force of its fpring lefs when it is but
little loaded, than when it is more, it must not
augment its bulk fo much to reduce itfelf from
the preffure of 41 inches to that of 31 inches, as
it muſt in reducing itſelf from the preffure of 38
inches to that of 28 inches.
Ι
5. That if the air, being rarified by the heat of
the boiling water, has not the liberty of augment-
ing its bulk fo far as to be bigger, the force of
its fpring will always be equivalent to a greater
weight than that of the atmoſphere, and this
weight will always be to that of the atmoſphere
in an inverted ratio to that of the bulks; and if
the bulk of this air is expreffed, for example, by
the number 7, and the height of the quickfilver
which refifts the force of its fpring is 41 inches
when this bulk fhall be augmented by, that is,
ſhall be expreffed by the number 8, the force of
the fpring of the air will be equivalent to 353
of quickfilver, and what it has loft will be equi-
valent only to 5 inches of quickfilver, or 5 feet
II inches of water, and only 5 feet 6 inches,
6 lines, the calculation being made upon 38 in-
ches, inſtead of 41 inches.
3
+
;
Experiment
72 The HISTORY and MEMOIRS of the
Experiment II.
Another time the thermometer being almoft at
temperate; we immerged in cold water the balls
of the 3 tubes of the preceding experiment, and
the quickfilver fell but to about a line below B,
in the glafs which had the biggeſt ball, to two
lines in the next, and to three in the leaft; after
which it left falling entirely in all the three glaffes;
they were afterwards taken out of the water, and
the quickfilver continued to fall about a line in
the glafs with the ſmalleſt ball, two lines in the
next, and about three lines in the glafs with the
biggeſt ball; ſo that the quickfilver remained for
a time in all the three glaffes about 4 lines lower
than B, and roſe again by degrees as fast as the
balls dried.
This experiment being conformable to ano-
ther which I made 12 years ago in August, when
the heats are very great, with the zymofimeter;
the ball of which was immerged in cold water,
and yet the air did not diminiſh any more the
force of its fpring, it follows:
1. That the air immerged in the water dimi-
niſhes the force of its fpring only in fuftaining but
one line in height of quickfilver leſs than the at-
moſphere.
2. That the air diminishes its fpring by the
coldness of the water in proportion to its bulk;
but that the greateſt loſe leſs than the ſmalleſt.
3. That the water, which is ready to evapo-
rate, diminiſhes the force of the fpring of the air
more than when it is in a fufficient quantity to
encompaſs it on all fides, which is confirmed by
this other experiment of the zymofimeter: for
having immerged the ball in the fpirit of wine,
the spring of the air diminifhed and fuftained
the
ROYAL ACADEMY of SCIENCES. 73
the weight of 4 ounces in height of water lefs than
the weight of the atmofphere; being withdrawn
from the fpirit of wine, it ftill diminiſhed fo as
to fuftain 5 inches of water lefs, which made in
all g'inches of water lefs than the weight of the
atmoſphere; being put again into the fpirit of
wine, the fpring of the air increafed the 5 inches
which it had loft out of it; and being put again
out of the fpirit of wine, it loft the 5 inches again.
This experiment was made at the fame time of
the year with that mentioned above, that is, during
the heats of fummer.
4. That this fecond diminution of the force of
the fpring of the air is made alfo in proportion
to its bulk; and that it is greater in the biggeft,
and fmaller in the leaft.
Experiment III.
We cauſed a cube to be conftructed of tin *
ABCD, exactly cloſe on all fides, and divided
equally into two, by the feparation EF; the lower
part EBCF has no communication with the upper
AEFD; but by the tube GH. incloſed in a big
ger IL, fhut at L, and ftopped and foldered at I,
to the upper part of the cube. MN is another
tube, which penetrates into the upper part, and
reaches near the bottom EF, and is foldered to
this part in O, and ftopped and foldered by its
extremity N to a little bucket or refervoir P;
there is alſo towards A, a little cock to give air
to the upper part. This cock being opened, we
poured fome water into the little bucket P, this
water defcended by the canal NM, into the up-
per part of the cube; when this part of it was
quite full, we fhut the cock, and immerged for 6
feconds the lower part of the cube in boiling wa-
*Plate IV. Fig 2.
VOL I. N°. 2.
K
ter,
74 The HISTORY and MEMOIRS of the
We
ter, and a confiderable part of the water contained
in the upper part of the cube being driven by the
force of the fpring of the air, rofe with precipi-
tation into the bucket P. At the end of 6 fe-
conds, having taken it out of the boiling water,
the water of the bucket began to go down again;
but in the ſpace of 300 feconds, it was not yet
reduced to the ſtate in which it was before.
afterwards put this lower part into cold water to
finiſh the reducing of the air to its firft bulk, after
which we put it into boiling water during 6 fe-
conds more, and the water rofe again, as before,
into the bucket P; after which it was immerged
into cold water, and the air refumed its former
bulk in 18 or 20 feconds, which was repeated
ſeveral times; and very near the fame thing hap-
pened always, whether this lower part of the cube
was always kept during 18 or 20 feconds in cold
water, or whether after having been dipped in
it, it was taken into the air. It follows from this
experiment:
1. That the hard bodies which are not very
thick, as tin, receive very readily the heat of the
boiling water.
2. That it is not always the cold alone of the
medium that destroys the action of the heat, feeing
by the preceding experiments, the air and the
water are of almoft the fame temperature.
3. That theſe thin bodies are three or four times.
as long in lofing in the cold water the heat received
in the boiling water, as they were in receiving it.
I call that water cold, which is almoft of equal
temperature with the air.
Experiment IV.
In the preceding experiment, the tubes NMGH
were but a foot in height, but afterwards they
were
ROYAL ACADEMY of SCIENCES. 75
were prolonged to eight; and having repeated
the fame experiments, they produced the fame
effect again, excepting that the water did not rife
in altogether fo large a quantity, which muft ne-
ceffarily happen, becauſe of the greater height or
load of water, which by its weight oppofed the
dilatation of the bulk of air inclofed in the lower
part of the cube.
After this, we put the part BC upon burning
coals, which made the water rife into the bucket
P, juft as the boiling water had done, but it did
not riſe ſo quickly, becauſe the heat was imme-
diately applied only to the bottom BC, whereas in
the boiling water it was immediately applied to
the four fides BE, BF, FC, CE, which made to-
gether a double furface BC. We could not therefore
well obſerve the time which the water took in
rifing into the bucket P, becauſe we were not
careful enough, that the folder fhould not melt,
which happened at laft, but the water was then in
the bucket, at leaſt as high as it had been by the
effect of the boiling water, and would have rifen
higher without it.
It follows from this experiment, that we may,
by the heat of fire applied immediately to the
capacity which inclofes the air, increaſe the force
of its spring much more confiderably than by
boiling water, provided what inclofes the air is
able to refift the action of the fire; and that effect
of it is fo much more quick, as the action is made
in a greater extent.
Experiment V.
Five men were applied to the motion of a ma-
chine, who in pufhing by the levers to which
horſes are uſed to be faftened, employed their
whole force to make it move.
K 2
Suppofing
76 The HISTORY and MEMOIRS of the
Suppofing the force of each man to be 200 lb.
the total is 1000 lb.
1
1
Horfes were afterwards put to work at this
machine, they laboured for three months; and
tho' 4 horfes were put to at a time, and they were
relieved every three hours, and afterwards every
hour and half, fo that each horfe laboured but 6
hours in 24, and went all this time no more than
about 6 leagues, yet they were not able to under-
go this fatigue, and died under it.
From this experiment it follows, that to con-
tinue a like labour night and day, there was need
of 16 horfes; and that we cannot reckon that a
a horſe ſupplies the place of a continual power of
60 lb. making one league an hour.
Experiment VI.
The workmen who poliſh glaffes, to press their
poliſhers make uſe of an arrow or bow of wood,
one of the ends of which being rounded refts upon
the middle of the poliſher; and the other, which
is an iron point, preffes againſt a ſtrong oaken
plank refted upon their work: the fimplicity of
this machine caufes the whole force of the work-
man to be folely employed in difpatching his
work. The polishers moſt commonly uſed are
of three bigneffes, and require three different
degrees of ſtrength, of which the mean quantity
is about 25 lb. now thefe operators ufually begin
their work at 5 in the morning, and finish it at 7
in the evening, taking two hours at three times
for their meals; fo that in 24 hours they regularly
work 12, interrupted every 3 hours by their
meals; the flight of their arrow, or the way that
their poliſher makes every time they pufh it, or
draw it back, is uſually a foot and half, and the
time employed at each flight half a ſecond; but as
they
ROYAL ACADEMY of SCIENCES. 77
they ftop from time to time to look at their work,
and to brush their polifhers, and befides as they
employ fome time in turning their glaſſes, about
of the time is to be fubftracted from their work,
fo that out of the 12 hours we can hardly reckon
above 10, during which their labour is equivalent
to the continual elevation of a burthen of 25 lb.
at 3 feet in a fecond.
It follows from this experiment: that to keep
up a like labour for 24 hours would require two
men; and therefore that a fingle man is in lieu
only of a continual weight of 12 lb. 1, making i
of a league an hour; that is, about part of the
&
labour of a horfe.
The following experiments were made with
poliſhers of different bigneffes, preffed by at-
rows of different forces.
A poliſher 6 inches in ſurface preffed by 28 lb.
was drawn by 23 in its fort, that is, when the
arrow was plumb, or in the middle of its flight,
and by 20 lb. in its feeble.
The fame preffed by 30 lb. was drawn by 26 lb.
in its feeble.
Another poliſher 11 inches in furface, preffed
by 28 lb. was drawn by 25 lb. in its fort, and by
23 lb. in its feeble.
Another poliſher 24 inches in furface, preffed
by 28 lb. was drawn by 25 lb. in its fort, and by
23 lb. in its feeble.
The fame loaded with 30 lb. was drawn by
28 lb. in its fort, and by 25 lb. in its feeble.
From theſe experiments we may obſerve, by
the by, that it is an error to think, that the fric-
tions in machines increaſe or diminiſh in propor-
tion, as the parts which rub are more or lefs ex-
tended; and that the wheels, for example of a
mill turn fo much the more eafily as the gudgeons
2
are
78 The HISTORY and MEMOIRS of the
are fhorter, which befides is a faulty conftruction,
becauſe they continually eat the boxes, in which
they turn. But that theſe frictions augment or
diminiſh in proportion to the burthens which are
moved, and to the ratio of the length of the
levers, which ferve to move them, to the length
of thoſe by which they are fupported.
Problem.
Any number of equal weights being given
B, G, H, I, L, on the femicircumference of a
vertical wheel, from the plumb line which paffes
thro' the centre of the wheel, to find the refifting
force, which being applied to the circumference
of the wheel, fhall make an equilibrium to the
given weights.
The folution demonftrated.
Let the horizontal diameter be AB, becaufe
of the equal rays AC, CB, an equal weight to B,
being applied at A, will make an equilibrium
to the weight B.
Befides, the weights which hang at the extre-
mities of a balance being between them, as is
demonftrated in the mechanicks, in a reciprocal
ratio of their diſtance to the point of ſupport, a
weight which fhall be at the weight B, as CD,
equal to the right fine of the angle GCL, to the
ray CB, will make an equilibrium to the weight G.
By the fame reafon a weight which fhall be to
the weight B, as CE to CB, will make an equi-
librium to the weight H; another weight which
fhall be to B, as CF to CB, will make an equi-
librium to the weight I, and fo of the reft in any
quantity whatſoever; if the weight L, being in
the plumb line, has no need of any weight in A,
* Plate IV. Fig. 3.
to
ROYAL ACADEMY of SCIENCES.
79
"
to make an equilibrium to it. Now as in what-
foever place of the circumference of the wheel the
refifting force is applied, it is always thought to
act by the direction of a tangent to the extremity
of a ray equal to AC, it follows, that the refift-
ing force, or the fum of the weights which being
applied at A, make the equilibrium to the given
weights is to theſe fame weights as the fum of
the right fines of the angles, by which thefe
weights are removed from the plumb of the cen-
tre of the wheel, to the total fine multiplied by
the number of the weights. QE. D.
6
A defcription of the commodious way of making
ufe of fire to move machines.
All that is faid above being fuppofed, if *
A, B, C, D, E, F, and 1, 2, 3, 4, 5, 6, &.
are two circular and concentric ranges of cells
diſpoſed about a horizontal and moveable axis.
G, and exactly clofed on all fides, excepting
that each of the cells A, B, C, D, E, F, &. may
communicate with each of the cells, 1, 2, 3, 4, 5,6,
&. by means of the tubes, HI, LM, NO, PQ
RS,TV,&. and that the cells 1, 2, 3, 4, 5, 6, &
have communication with each other by the valves
7, 8, 9, 10, 11, 12, &. which are all placed and
open the fame way, fo that they permit the wa-
ter to enter out of the first into the fecond cell,
out of the ſecond into the third, and fo on to the
laft, and again from this laft to the firft; but
refuſe it entrance the contrary way.
1
If moreover the cells A, B, C, D, E, F, &.
have no communication directly with one another,
and 2 of the cells 1, 2, 3, 4, &. have 2 aper-
tures, as X, T, by which they have been filled
with water, and thefe apertures have afterwards.
*Plate IV. Fig. 4.
been
80 The HISTORY and MEMOIRS, of the
been cloſed exactly, if the capacity of each of
thefe cells, 1, 2, 3, 4, 5, 6, &. is near of
that of the cells A, B, C, D, E, F, &. and if
the refifting force is fuppofed to make an equi
librium with the water of the cells, 1, 2; if laftly.
we apply at BB, the flame coming out of the
furnace AA, driven by the air which enters by
the grate of the furnace, and if the bottom, of
the barrel made of the cells ABCDEF, &.
dips in the cold water of the refervoir, &.&. I
fay:
1. That the air of the cell B, will increaſe its
fpring fufficiently to fuftain not only the height of
water Ir, but alfo to make the water pafs out
of the cell into the cell 3, if this height Ir is
but near 5 feet.
2. That the weight of this water will make
all this conftruction turn the way BAF, about
the centre G, if the refifting force is lefs than this
weight.
3. That as faſt as by the motion about the
centre G, the water in , aims to defcend, new
cells prefent themfelves at BB, and new air aug-
ments its fpring to repel it, and fuftain it at the
fufficient height, that its weight may be continually
fuperior to the refifting force; during which the
air that had been dilated refumes its former bulk,
as faſt as the cells which contain it, pafs thro' the
water of the back, &. &. and from thence
thro' the air, where it ceafes to reduce itfelf, to
be anew dilated every time thefe cells return to
BB; for by the firſt and fourth experiment, the
air increaſes its ſpring by a quantity equivalent to
a load of 11 feet 8 inches in height of water::
Now of thefe 11 feet 8 inches, according to Mi
Mariotte's rule for the preffure of the air, there
are but 10 inches and employed in the preffure
1
neceffary
ROYAL ACADEMY of SCIENCES. 81
neceffary to make place for the augmentation of
the bulks of air, dilated by the heat of the fire,
which added to 5 feet 6 inches, which this
augmentation makes the fpring of the dilated air
to fofe, by Exp. I. Cor. 5. make in all 6 feet, 4
inches, 10 lines, which being taken from 11 feet,
8 inches, there remain 5 feet, 3 inches, 2 lines
in height, to which the fpring of the air dilated
by a heat equal to that of boiling water can ſuf-
tain the water in Y.
Now by the preceding problem, the refifting
force being applied in any place of the circumfe-
rence, which paffes thro' the middle of the cells
I, 2, 3, 4, 5, 6, &. is to the weight of this wa-
ter, almoſt as 11 to 14; and if this weight is
12000, this refifting force will be 9428. Now
in allowing 12 feet of diameter to the barrel
made of the cells 1, 2, 3, 4, 5, 6, &. to a like
length of 12 feet, and 2 feet of depth taken on
the fide of the centre of the wheel, thefe cells
contain a space of 754 cubical feet of which
is 188, which being multiplied by 70 lb. weight
of a cubical foot of water, make 13200 lb. But
as in machines the moving force ought to be fu-,
perior to the refifting force, and as there is al-
ways fome friction to furmount, the 1200 lb.
muſt be counted for that; fo that the effect of
this motion may be reputed 9428‡, which would
be equivalent at leaft by Exp. V. to the force
of 157 horfes, if the refifting force made a league
of way in an hour; but as to do this, the con-
ftruction had need to make 400 revolutions in
an hour, that is, employ but 9 feconds in each,
whereas by Exp. III. it cannot employ less than
36, it follows that this mean would at leaft be in-
ſtead of 39 horfes, or of 234 men, by Exp. VI;
which fuppofes the degree of heat, equal to that
VOL. I. N° 3. L
of
82 The HISTORY and MEMOIRS of the
of boiling water, for otherwife the effect would
become fo much more confiderable, as this de-
gree of heat would be greater; and the profit in
making uſe of this fort of fire-mill, would be fo
much the more confiderable, as the price of
wood would be less than that of labour; and be-
fides the furnaces might be alfo applied to other
purpoſes, as vitrifications, founding of metals,
and other chymical operations, or mechanical
works, that demand the affiftance of fire.
I fhall not enter into a farther detail of the
conftruction of this machine, only I fhall juſt
mention, that it would be proper to make the
cells which contain the air of great plates of cop-
per rivetted and luted; and that all the reft, ex-
cept the tubes of communication, may be of
wood.
The advantages of this way are:
1. That we can ftop and refume the labour at
pleaſure, without being encumber'd with the care
and feeding of the horfes, and without being
fubjected to the danger of lofing them.
2. That we have always an equal and uninter-
rupted power, when we pleafe, which cannot be
had in wind-mills and water-mills, the firft being
often ſtopped for want of wind, and the others
by the ice and inundations of the water.
3. That we are not confined to any places,
becauſe combuftible materials are found almoſt
every where.
The defcription of Fig. 4.
The fire at BB dilates the air inclofed in A,
and making it pals thro' the canal HI, preffing
the furface of the water in, makes the valve or
fucker 18 cloſe itſelf, and the valves, 7, 8, and 9
open to let the water rife towards Y, and charge
2
this
ROYAL ACADEMY of SCIENCES. 83
this fide, which makes the wheel move on its
centre G, and the cell B fucceed the cell A,
whilft this laft enters the water, &. to make the
air which it contains return to its firſt ſtate.
And it has been demonftrated, that in making
Q19 of 8 feet, 20, 21 of 12, 22 L of 18
and 23, 24 of 30, the whole on a depth of 12
feet, and that the heat at BB is equal to that of
boiling water; it will answer to 39 horſes.
V. A defcription of a level which is used by
M. Couplet, more exact in this fecond
edition.*
This level is compofed of a teleſcope AB,
of 2 veffels CD, joined together by one or two
tubes 00, which I call the canal; of 2 other
veffels o b, o c, called callebaffes, becauſe they
carry the teleſcope, and float in the water with
which this canal is filled. The teleſcope is 2 feet
8 inches long; its tube fhould be of tin, tho' the
reft is made of copper: in one end A of this tube,
as in all the other tubes of teleſcopes, the object
glafs is placed; and in the other end 3 eye glaffes
are placed, if we would have the teleſcope confift
of 4 lens's. One eye-glafs alone would be fuffi-
cient here, becauſe it does not fignify whether
the object is inverted or not. The opticians
ufually put the 3 eye-glaffes into little fcrew-boxes,
which they glue and fit in a tube of paſtboard
called porte oculaire, and they puſh it into the end
B of the teleſcope.
However the teleſcope of the level differs from
the others only in having a bar on the infide,
which traverſes it diametrically and horizontally.
This bar is nothing but a hair ftretched in fuch
a place c, that he who looks thro' the teleſcope
June 27. 1699. + Plate V. Fig. 1.
L 2
Fig. 2.
fees
84 The HISTORY and MEMOIRS of the
fees it very plainly on the objects to which he
points it.
J
This hair is ſtretched in the middle of a ring
or crown of tin 4, the greateſt diameter of which
is equal to that of the eye-glaffes of the teleſcope,
that it may be put into a ſcrew-box as each eye-
glafs. On the edge of this crown are made two
little incifions, which are covered with fome drops
of wax, after having twifted the ends of the hair.
But becauſe we muſt ſometimes turn and return
the porte-oculaire to place the horizontal hair, and
this turning would divide or unglue the boxes -5, I
put this porte-oculaire into one end of a tin tube
6, which I call foureau du porte-oculaire; and at
the end of this foureau, I folder a fort of funnel
which may be fqueezed to turn the porte-oculaire
juft as one will; and I put this foureau with the
porte-oculaire in the end B of the teleſcope.
It is eafy to conclude, that the end B of the te-
leſcope is much heavier than the end A; to coun-
terbalance this greater weight, a leaden ring is
foldered at the end A.
At CD is a vertical fection of the two veffels
+ CD. Thefe veffels, a little above the middle
of each of their ſquare faces, have points entering
within, about a line, and a little foftened; the
water, with which, thefe veffels are filled, has a
communication, with both of them by two tubes
too, the ends of which are foldered above the
joining of their fquare parts with their truncated
pyramidal parts; one tube might fuffice, but two
maintain thefe veffels better.
The calebaffes ob, in their cylindrical
part, are less by three or four lines than each fide
of the fquares CD, that they may float at liberty
between the points, of each of thefe veffels. Their
Fig. 3. + Fig. 2.
+ Fig. 3.
Fig. 1.
height,
ROYAL ACADEMY of SCIENCES. 85
да
height, to the edge of their lid, (which must be a
very flat dome, without being enough fo to fee
the water reft upon it) is lefs by about two inches
than the depth of the veffels CD: thefe calebaf-
fes must be fo well foldered, that not a drop of
water can get into them; and to be fure of this
abfolutely neceffary condition, they muſt be tinned
on the infide before they are covered with their
domes das al bebas, go
#
When they are covered, the canal is filled with
water; they are pur in; and to make them float
even, fome lead must be drop'd thro' a little hole
in their domes, and then thefe holes muſt be cloſed
with wax. I have chofen this fort of ballaſt,
becauſe notwithſtanding any bruiſe, or other acci-
dent that might happen to theſe calebaffes, they
might be made to float always even by fhaking
them, to make the too great quantity of lead on
one fide roll to the other, which could not be
done, if they were charged with any liquor. If
they were found from any flight caufes to leave
floating even, they might be immerged deeper by
dropping in more lead.
}
The tube of the teleſcope AB, which is placed
on the domes of the calebaffes, muft be, as we
have faid, of tin, which is much lighter than cop-
per, to have their greateſt weight below the centre
of gravity of thefe calebaffes; and thereby to ren-
der them more capable of refifting what would
hinder them from floating even.
To feat the tube of the teleſcope on the domes
ob, oc of the calebaffes, you muſt endeavour to
hold it there for a moment, whilft you mark the
place where the hooks are to be foldered, as may
be feen under A, B, and better in 8. Thefe
hooks have an opening of about a line, which is
Fig. 7.
*
pro-
26 The HISTORY and MEMOIRS of the
L
prolonged to fome lines near the domes and it
is near the foldering of thefe hooks upon the
domes that the holes are, by which thefe cale
baffes are filled.
* la.
The hooks being foldered, the teleſcope being
put in, its end B being fet as far diftant from the
end of the canal as is neceffary to put the eye to the
eye-glaſs of this teleſcope, and having obferved
that this pofition of the teleſcope does not hinder
the calebaffes from floating even and very freely
among the four entering points, there are made
thro' the flits of thefe hooks four repairs on the
tube of the teleſcope;, on theſe repairs are foldered
wings 7, filed and adjuſted in fuch a manner,
that they may enter freely to the very bottom of
the flits of the hooks, and bear the telescope
equally to fome lines above the bottom of theſe
hooks. Theſe four wings are formed with a
fharp bottom, and the bottom of the four flits is
fmoothed with a fine-toothed file: thefe wings
ferve to hold the teleſcope in the fame pofition on
the calebaffes.
}
M+ is the ſection of a portion of a ſphere taken
in a trunk of afh, or other proper wood. Under
this portion of a ſphere, or in the ſection repre-
fented by 0, p, q, the diameter of which fhould
not exceed the height of the canal, three branches
of wrought iron are faftened together, having at
each of their ends a hinge and a fcrew; theſe fcrews
P, o, q, enter into three fockets at the ends of
the three fupporters of the fphere M. As for the
other ends, there is no neceffity that they ſhould
be ſcrewed...
>
1
This pedeſtal being placed almoſt horizontally,
which is done by moving one of the legs nearer
or farther off, the fupport ESE of the canal is
+ Fig. 6.
* Fig. 3.
|| Fig. 4 :
to
ROYAL ACADEMY of SCIENCES. 87
to be placed upon them. It was at firſt a plank
about two inches thick, equal in breadth to the
diameter of the portion of the fphere M; its plan
ESF, and its profile Gr K/H fhew how this
plank has been finiſhed by hollowing the fquares
7 E, F, or G, H, for the veffels ** C, D to go
exactly in, up to o, os The fides of thefe fquares,
which are at the two ends of the fupport, are only
locked with an iron ring, put about the ends of
the fupport, not fo much to ftrengthen theſe ends,
as to keep the fupport from being longer than the
canal which it bears! This profile fhews alfo,
that this fupport is rendered flighter, by making
in its thickneſs a cavity r, K, t, fo deep, that
only the edge r, t, of its circumference rubs a-
gainst the convexity of the portion of a ſphere ++
M, that it may not have any more frictions to
overcome, when the inftrument ſhall be turued to
either fide upon this fupport; there are other
parts of this fupport ſcooped away alſo from ‡G
tor, and from to H, to give it the better
play.
}
Before the three branches of irono, p, q, are
faſtened under the portion of a fphere M, it is
traverſed by a great iron pin long enough to go
thro' the thickness of the fupport, and the hole *†
KorS is made larger than is neceffary for the
thickneſs of this pin, that the fupport may be
drawn to either fide on its pedeſtal* M, to hin-
der the water, with which the canal is filled, from
being ſpilt over either of its fides) {
•
The inftrument is then prepared in a conve-
nient place to diſcover feveral very diſtant objects,
* Fig. 5.
tt Fig. 6.
* Fig. 6.
+ † Fig. 4b
}
| |Fig.50** Fig. t.
Fig. 5Big Fig. 5. Fig 4-
't
6.
but
1
88 The HISTORY and MEMOIRS of the
*
but not fo far off that we cannot well diftinguifh
whether the hair in the teleſcope refts upon the
top 5 of fome building, upon the funnel 7 of
fome chimney, upon fome crowning of a work
8; or laftly, upon fome elevation well limited
and diftinguiſhed; for wherefoever the hair refts,
it has always little vibrations, which leave a little
thread of light between it and the greateſt height.
of the objects to which it is pointed, whereby we may
judge the better whether the hair exactly reft up-
on them. Theſe objects thus chofen are ſo much
the more neceffary, as a hair which is but of
a line in thickneſs covers about a foot of the ob-
ject, which is near 3000 toifes from the obferver.
24
To fee whether the hair conftantly touches the
fame object, its reft is interrupted by gently fhak-
ing the canal, and obferving whether it refumes
the fame place; or for a ftronger proof, the tele-
fcope is taken out of its hooks and put in again.
Care must be taken that there be no wa-
ter on the domes of the calebaffes, or any thing
that hinders the wings † 7 from refting on the
bottoms of the hooks; that the water in the canal
is high enough, that there may be no danger of
the calebaffes touching at the bottom, or either
end of the teleſcope on either edge of the canal.
If one ſhould fee, that among feveral obſerva-
tions there was one where the hair did not return
exactly on the fame object, one might fufpect
that the difference came from the refractions,
which differ often and from one moment to another;
eſpecially when it rains, when it is very hot or
very cold, when the viſual ray, which parts from
the inftrument, paffes from a place where there is
a fog, to one where there is not.
* Fig. 8.
+ Fig. 3.
Tho'
ROYAL ACADEMY of SCIENCES. 8g
Tho' the hair fhould return conſtantly to the fame
object, yet we cannot conclude, that this object is
in a level with the eye of the obſerver; but only
that the viſual rays* H 9 directed by this inftru-
ment always make equal angles 9HO, with a
plumb line HO, which is imagined to defcend
from the eye of the obferver to the centre of the
earth.
With this inftrument put in the ftate juft men-
tioned, we may find as many true points of level
between them as we defire, provided the places
to which the teleſcope is pointed, are equally dif
tant from the inftrument.
To have only two, which we ſhall mention
how all the perfection may be given that can be
defired, plant upright a ftaff c4, at 300 or 400
toifes from the inftrument, on the bank of a ri-
ver, a lake, or a canal, along which your affif-
tant ſhall preſent you a fignal, or a little fquare of
iron, white on one fide, and black on the other;
for in any fituation whatfoever the black is feen
more eaſily than the white: let him raife or lower
this fignal, till the hair of your teleſcope juft
touches its upper edge 4, and reckon how many
feet, inches, and lines there are from the edge 4
to the baſe of the ftaff c; then let the affiftant
preſent in like manner in another place e, as far
diftant from the inftrument as c, another fignal 5;
and knowing by your fign that the hair of your
teleſcope touches the edge of his fignal, he writes
how many feet, inches, and lines there are from
this edge 5 to the bafe e of his ſtaff.
By means of theſe points 4 and 5, which it is
eafy to find by all forts of levels, how defective
foever they may be, the inftrument may be ad-
juſted in the following manner, and difengaged
* Fig 8.
VOL. I. No. 3.
M®
from
90 The HISTORY and MEMOIRS of the
from the troubleſome neceffity of always chooſing
points equally diſtant from it.
Cauſe the inftrument to be carried near one of
the ftaves c 4, or e 5, and count how many feet,
inches, and lines there are from the upper edge of
the fignal 4 to p, where you fhall have obferved
the centre of the object-glafs of your teleſcope to
be, or the hair to be cut by the ftaff c 4: let your
affiftant then go and place upon the ſtaff e 5 a fig-
nal q, as much below 5 as p is below 4: then turn
the object-glafs of the teleſcope of your inftrument
towards q, without making any alteration in the
pedeſtal of this inftrument.
We ſee that the proper places to plant theſe
two ſtaves, ſhould be chofen along a river, that
their baſes may not be far from being upon a le-
vel. Having thus on each of theſe ftaves two o-
ther points p, q, on a true level, as the points 4
and 5 are, obſerve whether the hair of the tele-
fcope, which is at p, touches the upper edge of
the fignal q. If it touches it, the inftrument is
perfect; but it is a great chance. If the hair
refts higher than q, take fome of the lead out of
the calebafs oc; or if it did not feem too much
immerged in the water of the canal, put fome in
the calebafs ob, which bears the object-glafs.
In short, take out of one, or put into the other,
till the hair of the teleſcope approaches the fignal
9; then begin again to obferve where the hair of
the teleſcope is cut by the ſtaff c 4; reckon, as in
the preceding operation, how many feet, inches,
and lines there are from the fignal 4 to this point,
and place on the ftaff e 5 a fignal as much below
5, as the centre of the teleſcope is found to be
below 4; and if you obferve the hair to touch the
edge of this fignal, you may conclude this inftru-
ment to be perfect; if not, leffen by degrees
with
ROYAL ACADEMY of SCIENCES. 91
with a knife, and not with a file, the leaden
ring foldered at * A; charge or diſcharge the
calebaffes, and repeat theſe operations, till the
meaſure of the point of the level † 4, in the centre
of the teleſcope, is equal to the meaſure of the
point of level 5, where its hair cuts the ſtaff e 5;
and then you will be fure, that the viſual rays
which the inftrument directs, whether long or
fhort, make right angles with lines HO, ima-
gined to defcend from the eye of the obferver to
the centre of the earth. This is all that can be
required in the moſt juſt inftrument that ever was
feen.
The ſcale || gives the meaſures of each part of
this level. If the length of the fupport, and that
of its three feet are reduced to the length of the
canal, and if the diameter of the portion of a
fphere is reduced to the breadth of the fupport,
and to the height of the two veffels of the canal,
it is only to incloſe the whole in one caſe,
VI. A method to centre telescope-glaſſes in
working them, by M. de la Hire ‡, at
the obfervatory.
After what I have faid on the manner of know-
ing the inequality of the thickneſs of the glaffes,
ufed to make the object-glaffes of teleſcopes, it
will not be difficult to centre them in working;
that is, to caufe the greateſt thickneſs of the glaſs
to be found in the centre of the figure, when it
fhall be wrought.
First, the piece of glaſs, of which an object-
glafs is to be made, being cut in a circular figure,
*Fig. 1 and 2.
‡ July 22, 1699.
+ Fig. 8.
M 2
Fig. 9.
mark
92 The HISTORY and MEMOIRS of the
mark the centre as at * C: and by the method
which I have given, and as I fhall afterwards ex-
plain, trace upon this circle the diameter AB,
which will determine its greateſt thickneſs in B,
and its leaſt in A.
Secondly, begin to form the glafs according to
the figure which you would give it, by gradually
diminishing the part B, fo much as you can guefs
it to be thicker than the part A; and this fide of
the glaſs being at laſt entirely finiſhed and poliſh-
ed, unglue it, and fearch again for the thickeſt
part, if it is not equal every where. But as it is
cut on one fide, the centre may be determined by
the ſame method; that is, mark the point where
the greateſt thickneſs of this glafs is. This will
be done by tracing a diameter firſt, as I have juſt
fhewed, in which a clear or black line does not
appear multiplied, which may always be found;
and if this line does not appear doubled in all the
diameters, we are fure that the glaſs is well cen-
tered, and that we may work it equally on the
other fide to give it its entire perfection. But if
we trace on the glafs another diameter DE, per-
pendicular to AB, which is that where the image
of the clear or black line does not appear multi-
plied, and the image of the fame line does appear
multiplied in the diameter DE, we ſhall know that the
glafs is not centered. We muft then make the image
of the line on the glafs, which is parallel to the
diameter DE, appear, and make it move thereon
till it no longer appears doubled, which we may
always find and this line must be marked as at
FG on the furface of the glafs, which will cut at
right angles the diameter AB at the point H,
which will be then the centre of this glafs. Now
tranſport the magnitude CH to CI on the other fide
Plate VI. Fig. 1.
of
ROYAL ACADEMY of SCIENCES. 93
of the centre of the diameter AB, and having
faſtened the glaſs with maftick as before, begin
to cut it on the fide which is ftill flat, and wear
away gradually its part towards B, more than that
towards A; fo that being almoſt cut all ſpherically,
there remains only the little point I, which is not
cut on the furface. Then this fide of the glafs
may be finiſhed, and you may be fure that it will
be well centered.
On the ſurface of the glafs, which is firft cut,
a little bit of white paper may be pafted, where
the point I is marked, that this point may always
be known when you cut the other ſide.
The demonſtration of this practice is not diffi-
cult: for let * ABMN be the ſection of the glafs by
the diameter AB of its figure, and perpendicu-
larly to the plain furface AB, if we imagine a
plane parallel to this furface, which touches it in O
the fide NOM of the glaſs which is wrought, it
is evident that the point O will be the centre of
the glaſs, or its oppofite point H; and feeing the
point C is in the middle of the diameter AB, if
we take CI equal to CH, and make the point I be
the place where the curve PIQ equal and fimilar
to NOM, touches the plane AB, the line IO be-
ing bifected at K, will give the point K, for the
centre of this glaſs. Q. E. D.
Now as for the manner of finding the greateſt
thickneſs of the glafs, as it depends only on one
multiplication, you must only make uſe of the
reflection of a bright line in the dark, or of a
black one in a ſtrong light. We must therefore
expoſe one fide of the glafs + AB to the black or
bright line RS, fo that it may be perpendicular
to the plane, which paffes through the eye O,
and the line RS, and that this furface of the glafs
* Fig. 2.
+ Fig. 3.
may
94
The HISTORY and MEMOIRS of the
may be alſo very little inclined to this line to be
able to perceive the image of it more eaſily;
and when the image AB of the line RS appears
fingle, you will know that the diameter AB of
the circular piece of glaſs will thereby determine
its greateſt and leaft thickneſs. But if the image
AB appears double, and the moſt vivid is towards
X, and the fainteft towards Y, then the part X
will be thicker than the part Y, as I have already
demonftrated.
VII. Obfervations on the infects called adder-
bolts or dragon-flies, by M. Homberg.*
As my obſervations were made only on one
fpecies of adder-bolts, I fhall endeavour to di-
ſtinguiſh it from the reft in the firſt place, and
defcribe the parts which principally belong to my
obfervation.
The males and females are of the fame bignefs,
being about 20 lines long: the body of each of
them is equally flender; except that the end of
the tail, or extremity of the belly in the female †
b is a little bigger than that of the male ‡ a.
They are both very lively, and keep ufually on
the banks of rivers.
The males are of a fhining violet colour all
over their bodies; their 4 wings are tranfparent,
a little gilded, with a great fpot almoft in the
middle of each wing e, of the fame violet colour
with their whole body, which makes this part
of the wings opake.
The females are all over their body of a fhin-
ing gilded grey, approaching to green. Their 4
wings f are transparent, of the fame colour, and
without any (pot.
*Aug. 22, 1659
Fig. 4.
+ Plate VI. Fig. 5.
|| Fig. 4.
Fig 5.
I
When
ROYAL ACADEMY of SCIENCES.
95
When they are at reft, or do not fly, their 4
wings draw cloſe to each other, fo as to feem
but one, whereas ſeveral other ſpecies of adder-
bolts keep their wings always extended, as well
when they are at reft as when they fly.
The head of this animal, which is very big in
compariſon of its body, joins to the breaſt only
by a very flender thread: its belly * a c, or that
part which reaches from the place where its wings
are planted, to the other extremity, is divided
into 10 joints, the motion of which is only up
and down, and from fide to fide.
The place, on which the wings are planted, I
fhall call the breaft.
It has its lungs about the middle of the belly
towards, which appears by this part's heaving
continually at fmall intervals, as the parts of re-
ſpiration commonly do.
The extremity of the belly of the male || a, or
the tenth joint of its belly, is a fimple ring,
which makes its anus; it is furniſhed with
4 little
hooks, 2 large above, about a line in length,
and 2 fmaller below, which it can open and fhut,
juſt as lobſters do their claws.
The extremity of the belly of the female † b,
I
feems to confift of 2 tubes placed one below the
other. The upper one is the anus, which is placed
as in the males, and the lower one is the female
organ, or entrance into the matrix. This laft
is about a line long; and rifes from the lower
part of the eighth joint of the belly: each of
theſe tubes are furniſhed at the end with 2 very
fmall points; whereas the anus of the male has
4 hooks. The 2 ends of the tube, being placed
one above the other, make the extremity of the
female's belly bigger, and not to be fo much
pointed as in the male.
* Fig 4•
I
+ Fig. 4.
Fig. 5.
Fig. 5.
96 The HISTORY and MEMOIRS of the
I have ſeen theſe animals perform an action,
which has apppeared to me very extraordinary,
and has raiſed a curiofity in me to examine them
attentively; the male finding the female fitting
on fome leaf or branch by the water-fide, took
her as he flew, with the hooks of his anus, by the
neck between the head and breaſt, and ſo carried
her off hanging by the head at the end of his tail.
I thought at firft, they had been two different
fpecies of animals, and that they were quarrelling ;
but as I faw no refiftance made by one of them
againſt its being carried off, but on the contrary,
that one of them preſented itſelf, and feemed to
expect the other, to be carried off more commo-
diouſly, I thought quite otherwife.
I followed them, and faw that the male feated
himſelf not far off, on a leaf of a ruſh, and at the
fame time he raiſed his tail, with which he held
the female by the neck, to place her on the fame
leaf where he was. The female being thus feated
behind the male, bent her belly, turning it be-
tween her legs, and with the end of her belly, fhe
thruſt her parts againſt the breaſt of the male,
whofe genital parts are in that place*: the male
fupporting the head of the female with his tail,
during this whole action.
They continued in this poſture for about three
minutes, and then the male lifted up his breaft
ftrongly, and the genital parts of theſe two ani-
mals ſeparated, as if they had been forced afun-
der the male alfo let the head of the female go
at the fame time, and flew away immediately.
The female being at liberty, put herſelf in order
again, and remained without motion in the fame
place for a full half quarter of an hour, and then
The flew away alſo.
*Fig. 6.
I
ROYAL ACADEMY of SCIENCES: 97
4
I have caught feveral of thefe animals, to exa-
mine their genital parts; and this is what I have
found. The upper part of the belly, in both
lexes, is convex thro' its whole length. The un-
der part of the belly is folded and bent inwards,
and forms a gutter, lengthwife, almoft like the
inner part of a feather between its vanes. This
gutter begins in the males at the third joint, and
is continued quite to the anus. The first joint of
its belly, next the breaft, is only a round and
very narrow ring, about the breadth of a large
pin; and it does not feem to have any other ufe,
than to give a more free and large motion to the
reſt of the belly.
}
The fecond joint in the males**
C, is two lines
long, very much, hollowed in the fore part under-
neath, making a fort of a bag, the edges of which
are fet with hair, and the bottom is towards the
breaſt.
}
"
From the bottom of this bag proceeds a ſmall
hard and black body, of the fize of a hog's briſtle,
two lines long, with a hard and very fmall white
pearl at the end. This little body feems to be im-
planted into the breaſt of the male, and to per-
form the office of a penis. It is lodged length-
wife in the bag, in fuch a manner, that the little
white pearl is always vifible when we prefs the
end of a feather into, this bag, the penis comes
out of itſelf, about a line in length; which hap-
pens alſo when the anus is preffed. I have cut the
breaſt of the male tranfverfly with fciffars above
the wings, and found in the fleshy part within
the breaſt a hollow cone, the bafe of which was
towards the head of the animal, and its vortex
bordered within on the root of the penis; I have
driven a little needle into the vertex of this hol-
*
Fig. 4.
VOL. I. N°. 3.
N
low
98 The HISTORY and MEMOIRS of the
low cone, which has made the whole length of
the penis come out of the bag.
I have opened the breaft in feveral males to ex-
amine this cavity, but I have found it only in
two; all the reſt had their breafts full. One of
theſe had juſt done coupling when I took him,
and the other I took at hazard. This difference
made me think, that this cavity might be the re-
fervoir of the feed of this animal, which being
but juſt emptied, made the cavity ftill viſible
but before the copulation, this place being full, or
fometime after it, the fides of this veffel being fal-
len, there would not appear any ſenſible mark of it.
;
The bag, in which the penis is lodged, is only
â continuation of the gutter which runs along the
whole belly almoſt underneath, with the diffe-
rence, that in this place the gutter is deeper and
wider, than in all the reft of its extent, and that
it is hairy, whereas all the reſt is ſmooth.
The under part of the belly of the females is
in like manner folded into a gutter, which begins
at the ſecond joint of the belly * d, which is not
hairy, like the males, and continues along the
6 following joints :
The two laft joints but one of the female hold
its external genital parts b underneath. They
are formed after the following manner the ninth
joint underneath has an aperture furniſhed on each
fide with a light grey little wing. Theſe two
little wings cover this aperture, and have a mo-
tion of opening and fhutting; and when they are
fhut, they ſeem to form a little tube i.
At the root of the eighth joint, there arifes a
little bunch, up to the root of the ninth joint.
On the extremity of this bunch are planted two
little crooked horns, black, very hard, a little
above a line long, fhaped almoft like the fangs of
Fig, 5.
#
ROYAL ACADEMY of SCIENCES. 99
a viper, but a little more crooked, and its points
are turned towards the anus. They are articula
ted, and have a motion every way; they are u-
ſually lodged under the little wings juſt deſcribed,
and are entirely hidden by them; they are laid fo
near each other, that they appear like one fingle
hook.
I believe theſe two little horns may have the
two following uſfes. Firſt, as they are couched
between the two little wings, which cover the
female parts, and as they have a motion every
way, they can, by parting from each other, open
the two little wings, and thereby diſcover the a-
perture of theſe parts.
The ſecond uſe may be, to direct the parts of
the female in copulation towards thofe of the
male, and that in the following manner :
We have ſeen that the parts of the male are
very near its breaft, whereas thofe of the female
are placed at the other extremity of the belly, fo
that the female is obliged, in copulation, to bend
her belly and bring it between her legs and under
her breaſt, to reach the parts of the male, as is
reprefented in Fig. 6. which is a very uneafy
poſture, in which fhe might often miss the parts
of the male, without the affiftance of thefe two
horns but when theſe horns rife under the little
wings, they prefent their convexity to the gutter,
which poffeffes the whole under part of the belly
of the male, in which they very easily engage
themſelves; and after they are entered into this
gutter, they ferve for an infallible guide to the
parts of the female, to arrive furely to thofe of
the male.
I have fhut up feveral of thefe females, to fee
if they would produce any eggs; but as they
flood in need of nourishment, which they would
}
N 2
not
100 The HISTORY and MEMOIRS of the
not take in their prifon, they all died, fo that
I could not extend my obſervation any farther.
$
•
I never found any eggs in them on diffection,
which makes me believe the females hide them-
felves foon after copulation, to lay their eggs,
and that they perifh afterwards. The males alfo
muſt perish foon after copulation; which I gueſs,
becauſe I have found a great many wings of males
in feveral places, where it is probable, that they
died; and as I found no bodies, it is probable,
that they were eaten by other infects.
1
I obferved, that the firft, of theſe animals,
which I took about the 18th of July this year,
particularly the males, were longer and ftronger
than thole which I took a fortnight afterwards,
that there were hardly any three weeks after, and
that theſe few were very poor ones; which makes
me believe, that theſe animals could not all hatch
at the fame time, and that the first fight is better
than the last.
VIII. An inquiry into the strength of man to
move burdens, either by lifting, carrying,
or drawing, confidered abfolutely, and with
comparison to that of animals which carry
and draw, as horfes, by M. de la Hire,
at the obfervatory *
في
I fuppofe, in the first place, that a ſtrong
man of a midling ftature weighs 140 lb. of our
weight.
บุ )
}
I confider firft, that fuch a man, having his
knees on the ground, can raife himſelf, by reft-
ing only on the point of the feet, and the two
knees being continually joined together; and as
*Nov. 10, 1699.
AN
"
this
ROYAL ACADEMY of SCIENCES. 101
"
this effort is made by means of the mufcles of the
legs and thighs, it is evident, by the fuppofition
juft made of his weight, that the mufcles of the
legs and thighs will have ftrength to raife 140 lb.
But a man having the hams a little bent, can
recover himſelf, tho' loaded with a weight of
150 lb. together with the weight of his body
which he raiſes at the fame time; fo that the
force of the mufcles of the legs and thighs can
raiſe a weight of 290 lb. that is, 150 lb. of the
weight with which it is loaded, and 140 lb. of the
weight of his body, when the elevation is but two
or three inches.
Such a man, as we have already fuppofed and
confidered, can alfo raiſe from the earth a weight
of 100 ib. which fhall be placed between his
legs, by only bending the body, and taking this
weight with the hands as with two hooks, and
then recovering himſelf. Whence it follows, that
the muſcles of the loins alone have ftrength to
raiſe a weight of 170 lb. that is, 100 lb. of the
weight, and 70 lb. which is half his own weight;
for he must not only raife the weight of 100 lb.
but all the upper part of his body, which I efti-
mate at 707. feeing he bent down to lift the
weight.
As for the force of the arms in drawing, or
raiſing a burden, it may be reckoned at 160 lb.
which depends on the force of the mufcles of the
fhoulders and arms. For if a man takes with
both his hands any fixt body, placed above his
head, he can eaſily enough, by the fole effort of
his arms, raiſe his whole body, and 20 lb. beſides,
as if he was loaded with the weight of 20 lb. The
experiment of this may eaſily be made, if there is
a weight of 160 lb. which is faftened to the ex-
tremity of a cord, which paffes over a pully;
2
and
102 The HISTORY and MEMOIRS of the
and if a man who weighs but 140 lb. draws the
other extremity of this cord, it is evident that he
can never raile the weight of 160 lb. feeing all
that he can do is to hang upon this cord, and the
weight at the other extremity, weighing more
than he, will keep him fufpended; for the pully
is nothing but a continued ballance with equal
arms but if this man is loaded with a weight of
20 lb. he will then make an equilibrium with the
weight on the other fide; and if we add to this
20 lb. then he will raiſe the weight, for the muſ-
cles of his fhoulders and arms have ftrength
enough to raiſe all this weight.
Altho' the muſcles of each part of the body,
are able to make fuch great efforts to raiſe burdens,
yet we must not compute the ftrength of a
man by that of all his muſcles together, tho’
the fpirits which ſwell the muſcles ferving to mo-
tion in general, by contracting themfelves, and
drawing the tendons of their extremities, could
diftribute themſelves equally into all theſe parts,
and in the fame manner with a feparated part,
ſeeing each part ufually ferves for a fupport to
that which is joined to it. For example, the
muſcles of the arms and fhoulders contracting
themſelves, can raiſe a weight of 160 lb. But
if the body is bent, the arms cannot ſuſtain this
weight, unleſs the mufcles of the loins have ſtrength
at the fame time, to fuftain the upper part of
the body with the weight with which it is loaded;
and if the hams were alfo bent, then the muſcles
of the legs and thighs, muſt ſtill make a greater
effort, as they muft fuftain the weight of 160 lb.
and at the fame time that of the whole body.
Whence it happens, that in this difpofition of the
whole body, the ftrength is divided by the diftri-
bution of the fpirits into all the parts, which is
the
ROYAL ACADEMY of SCIENCES. 103
the cauſe that a man cannot raiſe from the ground
a weight of 160 lb.
Not but that there may be fome men, whoſe
fpirits flow in fuch abundance, and with ſo much
rapidity into their muſcles, that they make efforts
triple and quadruple of what is ufual; and this
feems to me the natural reafon of the ſurpriſing
force that we ſee in fome men who carry and
lift fuch burdens, as 2 or 3, men together would
be at a loſs to ſupport; tho' thefe men are fome-
times of a moderate fize, and feem outwardly ra-
ther weak than ftrong. There was one not long
ago, in this country, who was faid to carry a
great fmith's anvil, and of whom ſeveral won-
derful actions were related: but I faw another at
Venice, who was young; and did not feem to be
able to carry above 40 or 50 lb. with all poffible
advantages, who getting upon a little table raiſed
an afs from the ground, and held it up in the air,
by a large girt that went under the belly, and was
faſtened at each end to hooks, which hung at the
end of 2 little twiſts made of ſmall cords, and a
few hairs on each fide of the head of this young
fellow and all this great ftrength depended only
on the muſcles of the ſhoulders and loins; for he
ftooped at firft whilft the hooks were faſtened to
the girt; and afterwards he lifted the animal off
the ground, leaning his hands upon his knees.
He again raifed in the fame manner other bur-
dens, which feemed heavier than this animal,
and ſaid he found lefs difficulty in it, becauſe the
afs ftruggled when it was off the ground.
I now examine the effort of a man to carry
a burden on his fhoulders; and I fay the weight
of this burden may be 150 lb. and that he can walk,
with this load eafily enough on a horizontal plane,
provided he does not make great ftrides; but he
cannot
104 The HISTORY and MEMOIRS of the
cannot go up a hill or a ladder with the fame
weight. For the action of walking with a bur-
den on the fhoulders, muft be confidered as the
circular motion of the centre of gravity of the
body, and of the weight joined together, on the
foot which advances as centre of the arch of
motion; the effort of the mufcles of the other
.
leg ferving only to push this centre forwards;
and if the arch defcribed by this centre is fmall,
the effort of the hinder leg muſt not be great,
to make it be defcribed, feeing the whole burden
of the body, and of the weight, is not to be raiſed
by more than the quantity of the verfed fine of
half the arch; which is not confiderable in this
çafe, with regard to the arch which is the path
in which the whole burden advances.
Thus we fee that a man well loaded can walk
the more eaſily, as he makes lefs ftrides, feeing
the fine will be ſo much the leſs, and that he could
not advance by making fuch large ftrides, that the
effort of the hinder leg could not raife the bur-
den of the body, and of the weight by the quan-
tity of the verfed fine of the arch, which would
be half the ftep.
It is eafy alfo to fee that the fame man cannot
go up a ladder, or ſteep hill with this load, feeing
according to what we have already explained, the
effort of the mufcles of his legs being able to
raife a weight of 150 lb. only to the height of ?
or 3 inches, he could not raife it to 5 inches which
is the height of the ufual ſteps, nor go up a hill
without making fuch fhort fteps, as to rife but 2
or 3 inches at each.
+
It therefore now remains for me only to confider
the effort of a man to draw or puſh horizontally.
But to render this explication more clear and in-
telligible, I confider his ftrength applied to the
handle
f
ROYAL ACADEMY of SCIENCES. 105
handle of a roller the axis of which is horizontal,
and over which a cord is turned which fuftains a
weight, having fuppofed the diftance from the
centre of the roller to the elbow of the handle,
equal to the femi-diameter of the roller, that the
force may be compared being applied without
any augmentation on the fide of the machine, I
have alſo had no regard to the frictions of the
axis of the roller, nor to the difficulty which the
cord may have to bend.
Firft it is evident, that if the elbow of the
handle is placed horizontally, and that it is about
the height of the knees, the effort of the man
who raifes it in drawing, may at the fame time
lift the weight of 150 lb. which fhall be faftened
to the extremity of the cord, taking all poffible
advantages, feeing it is the fame as to raife the
weight, as I have already explained. But if it is
to deprefs the handle, his effort can be no more
than 140 lb. which is the weight of his whole
body, that he can apply by bearing upon it, un-
lefs he is loaded; for then he could make a much
greater effort.
Secondly, if the elbow of the handle is placed
vertically, and is at the height of the fhoulders,
it is certain that a man can make no effort to turn
it, by drawing it or pufhing it with his hands,
if the 2 feet are against each other, and the body
trait, which is reprefented by the line AP, and
if the line of the arms reprefented by AM is ho-
rizontal, and makes a right angle with AP, fince
in this pofition, neither the force of the whole
body or if its parts, nor its weight, can make any
effort to push or draw, which is known by me-
chanicks, for I confider the breadth of the feet
only as a fingle point. P. Bat if the handle is
* Plate -VI. Fig: 7.
VOL. I. N°. 3.
O
higher
106 The HISTORY and MEMOIRS of the
higher or lower than the height of the ſhoulders,
then the line which goes from the fhoulders to the
hands, which is AM, and that which goes from
the fhoulders to the end of the feet, which here
is AP, will make an obtuſe or an acute angle,
and the man may have fome force to draw or puſh
the handle; and this force depends wholly on the
weight of the body, as is eafy to know and
demonſtrate; and this weight or this force
muſt be confidered as reunited in his centre of
gravity, which is near the navel within the body,
fay that regard muſt be had only to the weight
of the body to determine the equilibrium, for
the effort of the muſcles of the legs and thighs
ferves only to preſerve this equilibrium in walking.
* Let the handle D be at the height of the
ſhoulders A, and let the centre of gravity of the
body be at C, the body being very much inclined
towards the handle; but let the end of the feet be
at P: we muſt confider 1ft this point P as the
fulcrum of a lever or ftrait rod PCH, which
paffing thro' the centre of gravity C of the
whole body, meets the line of the arms MA at
the point H; 2. That this point C of the lever
being loaded with the weight of all the body
140 lb. with its natural direction, its extremity H
is fuftained with the horizontal direction MAH;
whence it will be eaſy to conclude by mechanicks,
what effort the weight of the body at C with its
natural direction, can make on the handle ac-
"ording to the horizontal direction DH.
For first, let PH be of 240 parts and PC of
80; fince the effort of all the body at the point
C is 140 lb. it will be but 80 lb. at the point H,
as if at the point H there was a weight of 80 lb.
fufpended with its natural direction, which must be,
Fig. 8.
in
ROYAL ACADEMY of SCIENCES. 107
in the fuppofitions that we have made, perpendicular
to MA. Wherefore if we draw from the point of
fupport P the line PF perpendicular to MAF, the
weight of 80 lb. at H with its natural direction,
will be to the effort of the fame according to
the horizontal direction MAH on the handle, in
the ratio of PF to HF, which very much dimi-
niſhes the effort of the 80 lb. in a moderate incli-
nation of the body ACB. And if we fuppofe
for inftance, that the line PCH makes with MAF
the angle PHF of 70 degrees, the line of the
body ACB will then be inclined to the horizon,
or with MF, an angle of more than 60 degrees,
which is at moſt the inclination in which the
body can be to be able to walk; and the fine of
70 degrees which is PF, will be to the fine of
its complement which is HF, very near as 3 to 1;
and confequently the effort of the 80 lb. at H ac-
cording to the natural direction, will be to that
which they make according to the horizontal di-
rection, only of 80 lb. which is a little lefs
than 27 16.
1
Thoſe who have not made the experiment of
the ſtrength of a man, to puſh horizontally with
the arms, or to draw a horizontal cord in walking,
the body being inclined forwards, whether the
cord be faftened towards the fhoulders or about
the middle of the body, for the effort will be no
greater in the fame inclination of the body, fince
the fines of inclination and its complement are al-
ways in the fame ratio, cannot perfuade them-
felves that the whole ftrength of a man, is reduced
to draw only 27 lb. with a horizontal direction.
Not but that a man being bent can ſuſtain a
much greater weight than 27 lb. ſeeing if the line
PH made with HF an angle of 45 degrees, it is
certain that the weight of the body would fiftain
O 2
;ך י !
7
108 The HISTORY and MEMOIRS of the
70 lb. but as he would be bent according to a
line as AB, which would be much more inclined
to the horizon than 45 degrees, it is certain that
far from being able to walk, he would hardly be
able to fuftain it.
The fame demonftration ferves alfo to fhew,
that a man will have much more ftrength to draw
in walking backwards than forwards. For in
this fituation of the body, the line* PCH which
paffes from the end of the feet P thro' the centre
of gravity C, and whereon depends the augmen-
tation of the force, will be always more inclined
to the horizon, than the line of the body ACB,
quite contrary to what it was in the preceding
pofition.
But this manner of drawing could not be put
in practice, unless it was only to draw a cord,
the man continuing always in the fame place;
and one ſhould not fail of putting one's felf in this
poſture in ſuch a cafe, for nature and experience
have taught us to take always all poffible advan-
tages in common operations.
It is for the fame reafon alfo that our mariners,
and in general all who row on the fea, always
pull their oars from before backwards, for they
have much more force than if they puſhed them
forwards, as the gondeliers of Venice do, for
which I fee no other reafon than that of feeing
before them; which is much more neceffary for
them than great force, becaufe of the frequent
turns they are obliged to make in the canals,
and to avoid running againſt one another.
It remains for me in the laft place to compare
the ſtrength of men with that of horfes in draw-
ing which are the ftrongest of all drawing ani-
mal but as it does not entirely depend upon
Fig. 9.
their
ROYAL ACADEMY of SCIENCES. 109
their weight, as that of men does, but princi-
pally on the muſcles of their body, and on the
general difpofition of its parts, which have a
very great advantage in pufhing forwards, we
muit be contented with the common experiment,
that a horfe draws horizontally as much as feven
men; and thus a horfe can draw horizontally
only a little less than 200 lb. Not but that, when
loaded, he can draw a little more; but it is
but little in proportion to our idea of the great
ſtrength of this animal. But as it is ufually con-
fidered as being applied to fome wheel-carriage,
fuch as carts, we cannot make fuch a juft eftima-
tion of it, becauſe on a fmooth and horizontal
plain they need no more force than is neceffary
to overcome the frictions of the axle-trees.
We may obferve again, that three men will do
more than a horfe in carrying a burden up a ſteep
hill; for three men loaded with 100 lb. each, will
rife more quickly and eafily than a horſe loaded
with 300 lb; which comes from the difpofition of
the parts of the human body, which are better
adapted to afcend than thofe of a horſe.
We fee alfo by this demonftration, that thofe
who have thought to obtain a very great advan-
tage from the weight of the horſe, by applying
it to a ſwipe, to move the piftons of a pump,
have not found in the execution all that they had
concluded by the calculation of the weight of this
animal, fince at each ftep it muſt be obliged to
go up a fort of ladder.
瞥
​IX.
110 The HISTORY and MEMOIRS of the
IX. Two forts of wheels to draw water, by
M. des Billettes *.
The first. It is quite clofed on one fide by a
circle of eight feet in diameter, made of planks
1 inch thick, faſtened on a crofs of eight pieces
of wood, which in the centre of their affemblage
leave a hole eight inches fquare, in which the end
of an arbor of like bignefs is inferted, which
turning round makes the wheel turn with it. The
oppofite fide is void from the centre to about 13
inches from the circumference. This fpace of 13
inches is occupied by 14 buckets nailed on the
planks, being on the infide 15 inches long, 14
high, and 11 broad. The length is underſtood
of the fpace, which they poffefs on the turn of
the circumference, the height of their perpendi-
cular elevation on the plane, and the breadth of
their ſpace from the circumference to the centre.
The outer plank of their length is cut fome in-
ches, and confequently leaves an opening to give
entrance to the water, every time each bucket im-
merges, all the other five fides being exactly
clofed. That which covers their height confifts
of two pieces; one of which is immoveable; the
other is faftened by two pair of hinges; fo that
it can open and fhut like the lid of a box. On
this lid is alſo faſtened a latch, made alfo like the
common latches of doors, and which being pref-
fed by a ſpring placed on the fame lid, engages
itſelf under an iron catch faſtened to the plank on
the fide of the bucket towards the centre, or the
void of the wheel. And thus the water, which
has entered the bucket by its aperture, remains
fhut up as long as the latch holds the lid. But as
• December 9, 1699.
foon
1
ROYAL ACADEMY of SCIENCES. III
}
foon as it unlatches, the weight of the water
makes it immediately difgorge into a trough un-
derneath. This trough is a foot high, and two
broad, and has an iron hook ſtrongly fixed, cal-
led the decrochoir; becauſe, as the wheel turns,
this hook catches at the latches of the buckets fuc-
ceffively, and forcing their fpring, difengages or
unhooks them, from below the catches which
held the lids cloſe down. Then as the wheel
continues to immerge, the lids fhut, both becauſe
of the lofs of their own weight, and becauſe of the
water which ſtrikes them on the outfide, and gives
liberty to the play of the fprings, which hook the
latches under the catches again.
The fecond: It is lefs compound than the other.
For it is formed of two hoops which cloſe it pa-
rallelly, and contain between them an arbitrary
number of volets, clofed at the bottom, fides, and
ends but quite open at the circumference of the
wheel. What is moſt particular, is a curve-trough,
which embraces both its planes by a fegment of a
circle of about 100 degrees, fo that below it riſes
a little above the horizontal ſpoke of the wheel,
and confequently conducts all the water that it
draws to a place above, where it has a ſpout, at
which the water difgorges itſelf into a gutter pre-
pared for the voidance.
D
-
The advantage of the fecond wheel above the
other is its having a little more fimplicity in its
conftruction; but it has alfo a great deal more
friction, becauſe the trough muft touch the fides
exactly, or elſe there will be a great lofs of wa-
ter. And this friction is much more confider-
able, when towards the end of the drawing, the
water having funk very confiderably, the wheels
must be inclined to the horizon. But the first
has neither friction nor lofs of water, and fo is in
all
112 The HISTORY and MEMOIRS of the
all poins the beft. With both of them one may
draw 5000 muids of water in an hour..
F
X. Of the refiftance caufed in machines, both
by the frictions of the parts of which they
are compofed, and by the stiffness of the cords
employed in them, by M. Amontons *
Experiment.
*.
We put upon fome planes † AA, of copper,
iron, lead, and wood, anointed with old lard,
other planes BB of like materials, and different
bigneffes they were preffed one upon another
differently by ſprings, like that repreſented by
CCC, of which the quantity of preffure was
known. Theſe planes were changed all poffible
ways, putting ſometimes thoſe of iron on thoſe of
copper, lead, and wood, and ſometimes thefe laſt
on thofe of iron; and at each time we obferved
with a fpring balance D, the quantities of force
neceſſary to make them move, and we found,
1. That the refiftance caufed by the friction
increaſes and diminishes only in proportion to the
greater or lefs preffures, according as the parts
which rub have more or lefs extent.
2. That the refiftance caufed by the frictions is
nearly the fame in the iron, the copper, the lead,
and the wood, let them be varied how you will,
when theſe fubftances are anointed with old lard.
3. That this refiftance is nearly equal to of
the preffure. To thefe remarks we may add a
fourth, that thefe refiftances are between themfelves
in a ratio compounded of the weights or pref
fures of the parts which rub, of the times and of
the velocities of their motion.
* Dec. 19, 1699. + Plate VII. Fig. 1.
For
ROYAL ACADEMY of SCIENCES. 113
For if, for inftance, the plane * A is preffed
on the horizontal plane BBBB by a quantity
equal to 30 lb. according to the third remark it
muſt have a power equal to 10 lb. to move it,
whether this plane is moved according to any
right line whatſoever as AD, or according to a
circular line as AE; for we may fuppofe this
plane A fo fmall, that the determination about
the centre C does not produce an effect which fen-
fibly differs from that which it would produce ac-
cording to the determination of a right line. Now
it is evident, that if inftead of applying the power
at A, or any place of the radius CA, we apply
it at F, or any place of the radius FC, as far
diftant from the point C, as the place where this
power ſhould have been applied towards A or to-
wards F, provided it is at an equal diſtance from
thefe points, or from the centre C. But as it is
demonftrated in mechanicks, that two forces do
not act equally, but when they are between them-
ſelves in a reciprocal ratio from the centre of fup-
port, it follows that if the power, which being
applied at A was equal to the refiftance cauſed by
the friction of the plane A, was 10 lb. it muſt be
20 lb. equal to the refiftance, when this power is
applied at G, fo that GC is to AC as one to
two: on the contrary, fuppofing the refiftance at
G, and the power at A, this power needs be no
more than 5 lb. to equal this refiftance; and if
both at A and G, we fuppofe a preffure equal
to that of the plane A, the power which ſhall be
applied at A or F, needs be no more than 15 lb.
to equal theſe two refiftances caufed by the two
preffures, each of 30 lb. whence we fee that thefe
reſiſtances are between themſelves, when the pref-
fures are equal, in proportion to the ſpaces run
* Fig. 2.
VOL. I. N°. 3.
P
thro'
114 The HISTORY and MEMOIRS of the
thro' at the fame time, and confequently that they
are alſo between themſelves in an inverfe ratio of
the times of their motions, when the ſpaces run
thro' are equal; whence it follows, that if a plane
is doubly preffed, and runs thro' a double ſpace
in half the time that another plane does, the
friction of the firft will equal eight times that of
the laſt.
It is by reaſoning according to the above prin-
ciples, that we know that the friction in the fledge
makes a reſiſtance at leaft equal to of the weight
of the fledge, and of the burden with which it is
loaded; that in the waggon, this refiftance is lefs
than in the fledge, according to the ratio of the
circumference of the wheel to the hole of the nave
which receives the axle; and that if this ratio is
as 18 to 1, the refiftance cauſed by the friction,
is in the waggon equal to part of the weight
of the body of the waggon, and of the burden
with which it is loaded.
I
5+
It is in ſhort by theſe principles, that we know
why in all machines, and in all weights which are
moved horizontally on a pivot, the friction is fo
inconfiderable, as well as in ballances, let the
weight be ever fo heavy; for the ratio of the
bigness of that part of the pivot which rubs, to
the length of the lever by which the power acts,
is fo fmall, that it is almoft infenfible.
But tho' all the experiments above related ſeem to
prove fufficiently, that the refiftance cauſed by the
friction of the furfaces which rub, increaſes or
diminiſhes according to the greater or lefs pref
fures, and not according to the greater or lefs ex-
tent of theſe ſurfaces; as this does not always fuf-
fice to convince a reaſonable mind, it is good
however to eſtabliſh this truth by demonftrating
Now,
it.
ROYAL ACADEMY of SCIENCES. 115
Now if we meditate carefully on the nature of
friction, we fhall find it is nothing but the action
by which a body which is prefed against another,
is moved on the furface of that which it touches;
and that as the furfaces, which rub againſt one ano-
ther, cannot be confidered either as rugged and un-
equal, or as perfectly fmooth, and as it is impoffible
in the firft cafe that thefe inequalities fhould be
partly convex and partly concave, and that the
firſt entring into the laft they fhould not pro-
duce a certain refiftance when we would make
them move, fince to do that they muft remove
what preffes them against one another, and that
the action of theſe inequalities or otherwiſe the ef-
fect which they may produce, is the fame with that
of the inclined planes, which are uſed to raiſe bur-
dens; it follows, that the greater the preffure,
the more confiderable is the refiftance to the mo-
tion: beſides, in the cafe before us, we muſt fup-
poſe the preffure to be equally diftributed in the
whole extent of the furfaces: it follows alfo, that
of different furfaces of different extents loaded
with equal weights, each of the parts which com-
pofe the great ones is lefs loaded than each of the
parts of the fame extent which compoſe the ſmall
ones, and this according to the ratio between
their furfaces, and that fo, for example, if a fur
face of a foot fquare or 144 inches, is loaded
with a weight of 144 lb. each fquare inch will be
loaded only with 1 lb. whereas the fame weight
of 144 lb. being fupported by a furface of foot,
or 36 fquare inches, each fquare inch will ſupport
4lb. and as it is the fame thing to raiſe to a cer-
tain height in a certain time 36 times 4 lb. or to
raife in the fame time 144 . to the fame height,
it follows alfo that the refiftance cauſed by the
friction of the furfaces of different extents is
always
P 2
4
116 The HISTORY and MEMOIRS of the
always the fame when they are loaded with equal
weights, or, which is the fame thing, when the
preffures are equal; and as when the preffures are
unequal, the forces which they muſt have to raiſe
different weights to the fame height in a certain
time are between themſelves as theſe weights or
theſe preſſures, it follows alfo, that the refiftances
cauſed by different preffures are among themſelves
as theſe preffures.
First remark.
This demonftration always fubfifts, whether
thefe inequalities are fuppofed rigid, or whether
they are ſuppoſed capable of elaſticity, fince the
power which would furmount the ftiffnefs of a
ſpring, and would make it move, for example,
from A to B, does not differ from that which
would raiſe to an equal height, a weight equal to
the force of this fpring.
Second remark.
But if we fuppofe that the furfaces which rub.
are without any inequalities, and confider them
as mere mathematical planes, we ſhall find alſo,
that this propofition is true, fince how eaſy ſo ever
the lateral motion may be of heavy bodies, which
are not removed from the centre of the earth, the
laws of motion inform us, that the more gra-
vity theſe bodies have, the more refiftance they
make againſt being moved; add, that it is not
true abfolutely fpeaking, that two mathematical
planes can be moved upon one another, in
in any fi-
tuation that they are put, without one of them re-
moving from the centre of the earth more or lefs,
according to the fituation of thefe planes, and
that fo the greater the weights are with which
• Fig. 3.
they
ROYAL ACADEMY of SCIENCES. 117
they are loaded, the more force they require to
move them, which has no need of demonſtration.
Third remark.
Tho' it has juſt been demonftrated, that the
refiſtance cauſed by the frictions augments ac-
cording to the preffure, and not according to the
extent of the ſurfaces which rub, here is however
a very particular cafe; in which, if we attend
fufficiently to it, it appears to be the quite con-
trary. Let there be as many planes as you pleaſe,
* AAAA, preffed between others BBBB, by the
weight C taken at will. If the planes as AAAA,
can be drawn all together by the fame power D,
without the planes BBBB being able to move
otherwife, than to tranſport the preffure of the
weight C to all the planes AA and BB, ſuppo-
fing befides all theſe planes without any gravity,
and that we know the refiftance cauſed by the
friction of one of the planes A, againſt one of
the planes B, by the preffure of the weight C;
the power at D, which will furmount the refift-
ance caufed by the friction of all theſe planes,
will be to the weight C multiplied by the number
of all the planes ÃA BB, minus 1, as the refift-
ance cauſed by the friction of 2 planes A and B,
preffed by the weight C, is to the fame weight C;
and if the particular refiftance caufed by the
friction of 2 of thefe planes, is, for inftance,
as 1 to 1, let the number of the planes be 11,
the power at D muſt be decuple of the weight
C, whence it follows, that a very little preffure
may make a reſiſtance, greater and greater to in-
finity, by augmenting alfo the number of the
planes which rub against one another; which
feems at firſt a meer paradox, but the truth of
*Fig. 4.
it
118 The HISTORY and MEMOIRS of the
it is eafily known, by confidering that if to over-
come the particular refiftance caufed by the
friction of 2 planes as A and B, the power,
which draws one of the planes, muft raiſe the
weight C by a certain quantity, then the power,
which fhall make a greater number of thefe planes
move, rnuft raiſe this weight by a quantity, double,
triple, quadruple, and fo thefe powers must be
among themſelves as the heights to which they
raiſe the weight. Now as it is the fame thing to
raife a certain weight to a height double, triple,
quadruple of another height, or to raiſe the
double, the triple, the quadruple of this weight
to this height at the fame time, it follows that
the great elevation of the weight C, in the cafe.
in queftion, ferves inftead of gravity, and fo
that it is always true to fay, that the refiftance.
cauſed by the friction. changes in proportion to
the greater or lefs preffures, and not according to
the extent of the furfaces that rub.
What we have juft faid of the great refiftance
cauſed by ſeveral planes engaged one in another,
tho' preffed by a very fmall weight, may ferve
exceedingly well to explain the caufe of the hard-
nefs of the bodies called hard, and by oppofition
that of the fluidity, or liquidity of thoſe which
are called fluid or liquid; but we referve the dif
courfing on it for another time.
After having fufficiently eſtabliſhed what fric-
tion is, its nature and its laws, there remains
only to fay fomething of the rules by which we
may reduce it to calculation, to know the quan-
tity of it in the most compound machines.
First rule.
In machines where there are feveral frictions,
we must examine them in order one after another
beginning
ROYAL ACADEMY of SCIENCES. I10
beginning with the neareft to the moving force,
comparing the firft with the moving force, and
afterwards all the reft with the firſt, to know the
value of each in particular.
This order is fo much the more natural, as the
parts, which tranfmit the motion to the reft,
are nearer to the moving force, and as there is
no friction, where there is no motion, as has
been already obſerved.
Second rule.
We ſhall have the value of the firft friction
of a machine, by comparing the ſpace run thro'
by the part which rubs, to the ſpace run thro'
by the moving force, in the fame time, and tak-
ing the fuitable proportional part in the of the
moving force.
2
We shall eaſily conceive the reafon of this, if
we confider, that in the experiment of the frictions
above related, the power was immediately applied
to the part which caufed the friction, and that
the ſpaces run thro' by this part, and by the
power in the fame times, were confequently equal;
and that in the calculation of a friction, we muſt
neceffarily have regard to this circumftance; it
being very evident, that if the fpace run thro'
by the part which rubs, is for inftance, but of
that which fhall be run thro' by the power in the
fame time, the friction alfo will be but of what
it ſhould have been, if it had run thro' an equal
fpace, by this axiom, that every effect is propor-
tioned to the caufe from which it refults; and that
fo a friction by a ſpace leſs than another in the
fame time, is an effect lefs than the other,
which has been alfo demonſtrated in another man-
ner, in confequence of the 4th maxim of the
above mentioned experiment. Now by the third
I
maxim
120 The HISTORY and MEMOIRS of the
maxim of this experiment, the friction of the
parts which rub is equal to of their preffure, and
this preffure in the part of a machine the
neareſt to the moving force, being always double
of this force, becauſe the refiftance makes a like.
effort with the moving force upon this part, it
follows that the firft friction of a machine is al-
ways equal to of this moving force, when the
ſpace run thro' by it, is equal to the ſpace run
thro' by the part which rubs in the fame time;
and that this friction is lefs than the of this
force, in proportion as the firſt ſpace is lefs than
the fecond, and on the contrary; and that ac-
cording to the ratio of the ſpaces run thro' by
both in the fame times.
3
Third rule.
3
We ſhall have the value of the moving force,
when only the reſiſtance is given, by calculating
aud comparing according to the principles of
mechanicks, the ſpace which this force has to
run thro' by the difpofition of the machine, with
the ſpace which the weight, or the refifting force
ought to run thro' in the fame time; upon which
it is to be obferved, that when the refifting force,
or the moving force is a weight, the ſpace, which
they muſt run thro', is always meafur'd by a
plumb line, whereas, when there are other
powers, this ſpace is meaſured according to the
determination of the motion of theſe powers.
Fourth rule.
We fhall have the total frictions of a machine,
when after having compared each friction with
the firſt and neareft to the moving force, we add
all theſe particular frictions in a fum; but we
muft not expect that in augmenting the moving.
force
ROYAL ACADEMY of SCIENCES. 121
er
force by a quantity equal to this value, it ſhould
be fufficient to furmount the refifting force; for
this addition to the moving force immediately pro-
duces a new friction, of which we muſt find the
value, and afterwards that of the augmentation of
it, and that till this quantity of friction proceed-
ing from the augmentation made each time to the
power is ſo ſmall that we muſt have no farther
regard to it; for example, if the refifting force
was 100, the moving force 64, the total value of
the frictions 16, this addition would produce alſo
a new friction, the value of which would be 4,
and upon this another friction, the value of which
would be 1, if in order to furmount the refifting
force, and all the frictions of the machine, the
moving force ought to be equal to 64 plus 16,
plus 4, plus 1, that is, equal to 85 and plus.
Experiment on the stiffness of cords.
We faftened to a fixt body, as to the floor of a
chamber, the extremities *A, A of two cords
AC, AC, 5 or 6 inches diftant from each other;
the ends of theſe cords hanging freely at the bot-
tom, bore the bafon D of a ballance.
We engaged in thefe cords a cylinder of wood
BB, making each cord take a turn the fame way
about each end of the cylinder in the manner re-
prefented in Fig. 6. we afterwards put at Da
pretty conderable weight, and twitted about the
middle of the cylinder, the contrary way to the
cord AEFG, that is, the way EGF, a very
flexible tape, at the end of which was another
little fcale hanging freely at H, in which we put
a fufficient quantity of weights, to make the cy-
linder BB defcend notwithstanding the refiftance
cauſed by the ſtiffneſs of the cords AC, AC.
Fig. 5:
+ Fig. 5.
‡ Fig. 6.
VOL. I. No. 4.
Q
We
122 The HISTORY and MEMOIRS of the
We made theſe experiments with cylinders and
cords of different bigneffes, charged with different
weights, and after having reduced the action of the
weight H to an equal diſtance from the point of
contact E, in all the cylinders, having regard to
the weight of each cylinder, and of the bafons H
and D, we found that at inch diſtance from the
point E,
45 ounces furmounted the refiftance of two cords,
each three lines diameter, loaded with
a weight of 20 lb. and turned about a
a cylinder of inch; that
90 ounces furmounted this refiftance, the weight
being 40 lb. and
135 ounces, the weight being 60 lb.
Whence it follows, that the reſiſtance cauſed
by the ſtiffneſs of the cords about the fame or equal
pullies, increaſes in proportion to the weights
which hang at the ends of the cords,
Continuing the experiment, we always found
that at inch from the point E,
30 ounces furmounted the refiftance of two cords,
each of two lines diameter, loaded at
D, with a weight of 20 lb. and turned
about the fame cylinder.
15 ounces furmounted the refiftance of two cords
of one line diameter, loaded in like
manner at D, with a weight of 20 lb.
and turned about the fame cylinder.
Whence it follows, that the reſiſtance cauſed
by the ſtiffneſs of the cords increaſes not only in
proportion to the weights, which hang at the ex-
tremities of theſe cords, but alſo in proportion
to the thicknefs of thefe cords, and that fo upon
equal pullies theſe refiftances are between them-
felves in a ratio, compounded of thoſe of the
weights and of the thickneſs of the cords.
It
ROYAL ACADEMY of SCIENCES. 123
It muſt be obſerved, that the reſiſtance cauſed
by the thickneſs of the cords, proceeds only from
this thickness removing or bringing nearer the ac-
tion of the weights to the point of fupport, and not
from their containing more or leſs matter; for if
it was fo, theſe refiftances would increaſe or di-
miniſh according to the fquares of the diameters.
Continuing the experiment, we always found
that at inch from the point E,
90 ounces furmounted the refiftance of two cords
of three lines diameter, loaded at D
with a weight of 60 lb. and turned
about a cylinder 1 inch in diameter
I
that
14
;
114 ounces furmounted this refiftance with the
fame weights and cords, turned about
a cylinder of one inch in diameter, and
135 ounces, the cords turned about a cylinder
inch in diameter.
Whence it follows, that the refiftance caufed
by the ſtiffneſs of cords of equal bignefs, loaded
with equal weights, increaſes as the diameter of
the pullies, about which they are turned, dimi-
niſhes, but not according to the fame proportion;
for in the cafe now under confideration, tho' the
diameters of the pullies are between themſelves as
the numbers 1, 2, 3, yet the refiftances increaſe
only according to the numbers 90, 114, 135,
whereas they ought to increaſe according to the
numbers 90, 180, and 270, if they followed the
proportion of the pullies.
We fhall find the overplus of the experiment
in the following table.
Q 2
The
124
The HISTORY and MEMOIRS of the
The weight with
which the two
cords were loaded.
The refiftance of
the cords about a
cylinder of inch
diameter.
The refiftance of the
cords about a cy-
linder of 1 inch
diameter.
The refiftance of the
cords about a cy-
linder of 1 inch
diameter.
Thickness of
the cords.
135 ounces.
114 ounces.
60 lb.
90 ounces.
90
76
60
45
38
30
324
3 lines.
40 lb.
{
90
76
60
60
503
40
30
2535
20
29 16.
{
45
30
15
32
∞ 52
38
25
123/3
30
20
I
327f
10
321
I
It
ROYAL ACADEMY of SCIENCES. 125
It were to be wifhed, in order to determine
well the proportion of the reſiſtance cauſed by the
ſtiffneſs of cords of equal thicknefs, loaded with
equal weights, about pullies of unequal bignefs,
that we had a greater number of experiments than
thofe here related; but in the mean time, in or-
der to find theſe reſiſtances, as well as to find all
the others already mentioned, we may make uſe
of the following rules.
Rules for the calculation of the stiffness of cords
in machines.
32
In the examination and compariſon which fhall
be made of the reſiſtance cauſed by the ſtiffneſs of
the cords of a machine, we fhall follow the fame
order as in the frictions, and make uſe of the 1ſt,
3d, and 4th rules related above, which ferve
equally for both, and which it would be needleſs
here to repeat but to have the firſt reſiſtance
cauſed by the ſtiffneſs of the cords of a machine,
we fhall divide the moving force by 10, and
multiply the quotient by the quantity of lines con-
tained by the diameter of the cord, then we fhall
take the of the product, if the diameter of
the pully is but 6 lines, the if it is 12, and the
if it is 18, and upwards; we ſhall divide this
laft product by the quantity of inches contained
in the diameter of the pully, and the quotient of
the divifion will be what is fought; the reafon
of which is, that the reſiſtance cauſed by the ſtiff-
nefs of the cords augmenting according to the
ratio of the weights with which they are loaded,
and according to that of the diameter of thefe
cords, and that, according to the above experi-
ment, the weight hanging to the extremity of a
cord 1 line in diameter, being 10 lb. when the
16
48
re-
126 The HISTORY and MEMOIRS of the
refiſtance is 7 inches on a cylinder of an inch,
6 ounces on a cylinder of one inch, and only 5
ounces of a cylinder of 1 inch and upwards, it
follows that dividing by this weight of 10 lb. the
weight equal to the moving force, we have the
ratio of this weight to the weight of the experi-
ment, and afterwards the ratio compounded of
theſe weights and of the thickneffes of the cords,
by multiplying the quotient by the number of
lines contained by the diameter of the cord; fo
that the product of this multiplication expreffes
the augmentation of the refiftance caused by the
ſtiffneſs of the cords, which are above a line in
diameter, and are loaded with more than 10%.
And as by the above experiment this refiftance is
7 ounces, on a pully of inch, 6 ounces on a
pully of 1 inch, and only 5 ounces on a pully of
1 inch and upwards; it follows, that according
to the diameter of the pully, we need only mul-
tiply either of theſe quantities by this product, or,
which is the fame thing, take either the or
the or the of it, to have the quantity of
this refiftance; but as in this experiment the dif-
tance of the action of this reſiſtance from the point
of fupport, or the length of the lever by which it
refifts is inch, it is proper alfo to have regard
to that of the pully; and if its radius or lever is
more than inch, that is, if the pully is more
than an inch in diameter; divide alfo the laft pro-
duct by the number of inches contained in the
femidiameter, or, which is the fame, by the
number of inches contained in the whole diameter.
12
48
1
2
%
I 6
32
But if neither the divifion of the weight equal
to the moving force, by 10 lb. which is the leaſt
weight, as a line is the leaft thicknefs of the cord,
in the experiment which ferves for a foundation
to this calculation, nor the multiplication of
the
ROYAL ACADEMY of SCIENCES. 127
I
3
the quotient by the lines of the diameter of the
cord have place, becauſe both of them, or one
only may be lefs, we ſhould need only to take
the proportionate part of the leaft refiftance which
is found in the table of the above experiment;
for example, if we would know the refiftance
cauſed by a cord of a line in diameter, and
loaded only with of 10 lb. we need but take
or 7 ounces, if the diameter of the pully was
inch, or of 6 ounces of this diameter was I
inch, or only of 5 ounces, if this diameter was
1 inch and upwards; having alfo regard to the
diameter of the pullies, that is, dividing alſo the
quotient by the number of inches contained in the
diameter of the pully about which the cord
fhould be thrown; and if the weight, not only
was less than 10 lb. but alfo the cord was lefs
than a line in diameter, we muſt alſo, after having
taken the proportional part for the weight as
above, without having regard to the diminution
of the cord, take alfo from the quotient another
proportional part for the diminution of the
cord: for example, if the cord being loaded
only with 3 lb. was but line thick, after
1
butline
having taken or 7 ounces, or 6 ounces
3
or 5 ounces as before, we muſt alſo take the
one or other of theſe quantities, and divide it by
the number of inches, contained in the diameter
of the pully, to have the refiftance caufed by the
ſtiffneſs of this cord about this pully.
1
3>
of
To facilitate the calculation of the reſiſtance
cauſed by the ſtiffneſs of the cords in machines,
I have drawn up the following table, wherein you
may find thefe refiftances for all fizes of cords
from 1 line to 30 lines, loaded with all forts of
weights from 1 lb. to 100,000.
I
The
128 The HISTORY and MEMOIRS of the
The ufe of the following table.
Seek in the margin of this table the diameter
or bigness of the cord expreffed in lines, and at
the top of the table the weights fupported by this
cord; of what you fhall find under each weight,
over-againſt the diameter of the cord, make a
fum, and divide it by the quantity of inches con-
tained in the diameter of the pully; the quotient
of the divifion will be the reſiſtance cauſed by the
ftiffneſs of this cord.
Example.
Seek the refiftance caufed by the ſtiffneſs of a
cord of 18 lines in diameter, loaded with a weight
of 12393 lb. and paffing about a pully 2 inches
in diameter.
For 10,000 lb. you will find over-
againſt 18 lines
5625
2,000
300
90
3
1125
168 12
50 10
I II
All theſe fums added together make
I
6971 1
diameter of
Which being divided by 2 inches
the pully give 3485 lb. 8 ounces for the re-
fiftance fought.
2
Moreover, when the fame cord is not equally
flexible throughout, we must not expect that the cal-
culation will always agree exactly with experience,
this not being morally poffible, but only very
near we may fay as much of the frictions, be-
caufe the different confiftences of the greafe,
which
វ
ROYAL ACADEMY of SCIENCES. 129
A
which is more or leſs thick, and the parts which
rub intercepting more or lefs, make theſe refif-
tances vary; this does not hinder the uſe of theſe
rules from fhewing pretty exactly the effect to be
expected from a machine, to reckon certainly
upon it, this extreme exactneſs being other wife of
no uſe; and we may make uſe of the prefent,
till more ample experiments give us room to
eſtabliſh ſome that are more certain.
The uſe of pullies being very common, it will
not be improper, before I finish this difcourfe,
and to make trial of our rules, to compare the re-
fiſtances cauſed, both by the friction of the
rundles, and by the ſtiffneſs of the cords in pullies
of different bigneffes; and the rather becauſe thoſe,
who do not uſually attend to theſe reſiſtances, will
fee by the calculation, that it is not fo indiffe-
rent a thing as they imagine to prefer ſmall pul-
lies to great ones, becauſe of the fmall ſpace that
they occupy. Let it be propofed therefore to
raife a load of 800 lb. with a pully of 24 inches,
or with one of 3 inches only in the first place,
it is evident, that in both thefe pullies the rundles
muſt be of equal ftrength, as well as the cords,
fince they have an equal weight to fupport: let the
rundle therefore of each pully be one inch in dia-
meter, and the cord 20 lines; we fhall find by
making the calculation according to the above
rules, that in the pulley of 24 inches, befides the
800 lb. which is wanted to equal the weight of
the load propofed to be raifed, the mov-
ing force muft alfo be augmented by
that of
21 lb. to furmount the refiftance cauſed by the
ſtiffneſs of the cord, by that of
R
VOL. I. N° 4.
22
130 The HISTORY and MEMOIRS of the
22 lb. to furmount the reſiſtance cauſed by the
friction of the rundle, and alfo by that of
1 lb. to furmount the refiftance cauſed by the
ſtiffneſs of the cord, becauſe of the aug-
mentation of 21 lb. and 22 lb. and laftly
by that of
1 lb. to furmount the refiftance caufed by the
friction of the rundle, becauſe of the ſaid
augmentation of 21 lb. and 22 lb. all
theſe weights together making that of
845 lb. ſo that a moving force fuperior to this
weight will raife with the pully of 24 in-
ches diameter, the weight propofed of
800 lb.
But with the pulley of 3 inches, the fame cal-
culation fhews us, that befides the weight of
800 lb. neceffary to equal the load, there muſt
alſo be that of
167 lb. to furmount the refiftance caufed by the
ftiffneſs of the cord; that of
178 lb. to furmount the refiftance caufed by the
friction of the rundle; that of
37 lb. to furmount the refiftance caufed by the
ſtiffneſs of the cord, becaufe of the aug-
mentation of the 167 lb. and 178 lb.
3816
38 lb.
I
that of
to furmount the refiftance caufed by the
friction of the rundle, becaufe of the faid
augmentation; that of
8 lb. to furmount the refiftance caufed by the
ftiffneſs of the cord, becauſe of the aug-
mentation of the 37 lb. and 38 lb. };
}; and
laftly, that of
8
ROYAL ACADEMY of SCIENCES. 131
8 lb. to furmount the refiftance cauſed by the
friction of the rundle, becauſe of the aug-
mentation of the faid 37 lb. and 38 lb. 3.
2
All which weights together make that of
1236 lb., that is, 391 lb. more than with the
pully of 24 inches, in which the cord and the
rundle do not make a refiftance equal to of the
I 6
burden, whereas in that of 3 inches the fame re-
fiſtance is more than the fame load.
플
​R 2
Weights
Uork
Diameters of the cords.
*.
132
Weights ſupported by the cords.
lb.
lb.
lb.
lb.
Ib.
Ib.
lb.
Jb.
1b.
lb.
6
7
8
9
10
I 2 3 4 5
oun, dr 1. oun,'l. oun. dr. l. oun. I. oun. dr. \l. oun. 1. oun, dr.\l. oun. ¡l. oun, dr.\l. oun.
I
4
I 1 4
2
24
3
34
4
4 4 5
2
1 O
ลง
2
3 0
3 I 4
3
4 4
46
5 0
6
7 0
8
9 이 ​10
7 4
9
10 4
12
13 4 15
4 20
4
60
8
10 O
12
14 01
ΟΙ
2 ΟΙ
524
5
7 4
10
12 4
151
I 41
630
6
90
12
15 01
21
5 01
+18
4I
6
41 9
81 II OI 14
7 3 4
7
10 4
141
1 4
I
840
8
12 OI
OI
4 OI
500
51
8 41 121
15 42
81 12 02
02
40
4 02 8
944
9
13 4
I
21 6 41 111 15 42
42
8
42 13
10 5 0
IO
15 01
41
II 5 4
III 04 I
61
12 60
13
6
14 7 0
15 7 4
40
131
121 2 OI 81
3 41 102
141 5 01 122
9 01 142 3 02
1142
112 6 42
14 02 42 10 03
82
13 03 2
123
1 43 7
013
6 03 12
042 72 13 43
302 103 1 03
43 10 44 1 I
15
I 6 41
16 8 01 ΟΙ
17
8 41
18 9 01
19 941
II
94
21 11 0:2
2
142
802 O'2
22 10 43 33 11 44
42 13 03 6
3 15 04
5 42 133 4 43
8 03 013 8 04
83 15 04
04
3 44 11
805
0
44 12 45 5
85
I 05 10
124
44
31
12 4
2
62 15 43 94
2 44 125
LA LA
5 45 5
2010 01
4
1 14 02
83
2 03 124
605
015
5 10 06
2110 41
5
I 15
5 42 103
2211 OI 62
N
4 43 154 9 45 45 14 46 91
1 02 123 7 014 24 13 05
86
306 14
2311 41
72
2 4
2 143 9 44
2412 01 82
4 03
03 12 04
Ln00
55 0 45
126
7 47 3
85
4 06
06
12 0
07
8
25
12 41 9/2
6 03 44
26 13 01 102
5 43 23 14 445
603
2713 41 112 7 43
28 14 01 122 903
2914 41 132 10 43 104
104 145 11 06
3 415 15 14 4
7 4
47
0 47 13
6
++
87 508
4
6 127
127
94
9 48 7
84
6015
4
16 2 07
07 14 0812
8 45
76
5 47 4 4'8 249
3015 01 14/2 12 03
124
11 05 106
9 07
88 709
Weights
Weights fupported by the cords.
133
lb.
lb.
Jb.
lb.
lb.
1h,
lb.
lb.
lb.
IO 20
30
40 50
60 70
80 90
lb.
100
I
5
ΙΟ
I
I
4
2
ΙΟ Ι
4-
1. oun§ 1. oun.] 1. ouu. 1. cun. 1. oun.] 1. oun. 1.
15
9
I 14 2 83 23 124
oun. 1. cun. 1. oun.
1.1.
1. oun
3 2 8 2 13 3
I 14 2
2
6 5 05
106
10 6 4
3
15
I 14
42
+8
2 13 3
12 4 11 5 10 6
9788
79 6
46
8 3 12 5
5
93
61 14 3 12 5 10 7
24 116
o 6
4 7 13 9
47
8 8
1210 011
412
co
8
610 1512 84
115 10
89 611
2
7 34
82 8 5
9
2 13 5
10 8
66 9
O 7 8:10
711
8
OI 2
413
1210 1513 215 517 819 1121 14
8,15 0,17 820 022
215 016 1418 12
825 о
II
103
216
49
113
6
7 14/10
123 12 7
811
415
3'4
14:4
++
1 8
212
در
3
16
4,20
ΟΙΟ
681213
4 119
165
217
821 1426
414 116 1419 1122 825
612
815 1018 12 21 1425 028
513 1217 320 1024
018 1222 826
524 628
430 1035 039
528
2
231
4
127 830 1534
430 032 1237 8
732 836
940 10
43 12
614
015 020
118 1223
7 28
232 1337 842
346 14
025
030 035
040 045
050
17.5 5
185 1011
5:10
10 15 15 21
426
931 1437
342 847 1353
2
19.5 15
20'6
21
6
4.
913
237
416 1422
11 1417 1323 1229 1135 1041
I 2 818 1225
031
219 1126
22 6 14 13 12 20 1027
3.14 6/21
828
233 1239
45 050 1056
947 857
759
759 6
437 843 1250 056
432 1239 645 1552 859
834 641
928 1235 1543
462 8
165 10
448
255 061 1468 12
250
557 864 1171 14
2417
815 022
830 037
8,45 0,52
860 067 875
Diameters of the cords.
2
27
8
7
116 14/25
8 40 1046 1256 1465 073
533 1242
348 1059
288 12,17 826 435 043 12 50 861
O
25 7 13 15 1023 731 439 144 1454 1162 870 578 2
2618 16 424 632
281
4
167 875 1584 6
470 078 1287 8
2919
118 227 336
309 618 12/28
237
445 552
552 663
846 1454 465 1075 084
772 881 990 10
695 12
Weights
134
16.
lb.
lb.
Jb.
lb.
lb.
100
200
Weights ſupported by the cords.
Ib.
Ib.
Ib.
300 400 500 600 700 800 900 1000
lb.
1. oun. 1.
oun. 1.
oun. 1. oui.
ound 1.
oun. 1. oun. 1. 1. oun. 1. oun.
13 2
26 4 12
8
18
12 25 0
319
6 18 12
28
237 8 46
14 56
412 825
037
850062
8
75
0 87
465 10 75 84 6
8100112 8125
O
-
515 10 31
4 46
14
62 8 78
2 93
12 109
6125140 10155 4
618 12 37
8 56
4
75
75093
121 12
8131
4150168 12187 8
721 14 43 12 65
10
87 8109
6131
4153
2175196 14218 12
8125 9 50 o 75
0100 0125
0150 0175
0 200 225
0250
O
928
103!
2 56 4 84
893
113 L 61 68 12 103
462
Diameters of the cords.
1237
8
75
0112
6112 8140 10168 12196 14225253
12125 0156 4187 8218 12250281
2137 8171 14206
14206
8,150 0187 8225
2281
4312
48
0262
4240 10275309
8300337
6343 12
8375
O
13:40 10 81
14162 8203 2243 12284
4175 0218 12262
10187 8234 6281 4328
4121
1443 12 87 8131
46 14 93 12140
2375421 14468 12
1650
0100 0150 0200 0250 0300 0350 0400 450 9500
753 2106 4159
6212 8265 10318 12371 14425478
1856 4112 8168 12.225 0281 4337 8393 12450506
1959 6118 12178 2237 8296 14356 4415 10 475534
2062
8125 0187 8250 0312
8375 0437
2165 10131 4196 14262 8328
6325 365 10406 4
8306
8306
4350393 12437 8
O
2531 4
4562
+8
8
6593 12
8500562 8625 O
2393 12459
6 525590 10656 4
22
26181
2784
68 12137
8,206 4,275 0353
2371 14143 12215 10 287 8369
2475 0150
0300 0385
2578 2156
6312 8400 10468 12546 14625703
4162
0225
4234
8243 12325 0416 4487 8568 12 650731
6168 12253
2337 8431 14506 4590 10675759
2887
8175 0262
8350 0447 8515 0612
2990 10181
14 362 8463 2533 12634
4375 0478 12552 8656
4271
3095 12 187 8/281
8700787 8876 0
6725815 10907 4
47501843 12938
8
Weights
12412
8481
4550618 12687 8
6431
4503
0450
450 0525
2575646 14718 13
600675 0750
O
2781 4
4812
*100
8
6844 12
Diameters of the cords.
2
3
I
135
Weights fupported by the cords.
lt.
lb.
7000 8000 9000
Ib.
lb.
Ib.
lb.
lb.
Ib.
lb.
6000
”. 1.
oun. 1 1.
oun.
1.
1.
oun.
1. gun.
1000 2000
3000 4000 5000
1. oun. 1. oun. 1. oun.
lb.
10000
1. oun.
0 750 01125
13406 4 812 81218
4 312 8 468
4/125 이 ​250 이
​5156
6187 8 375
12
562
8 750
7218 12 437 8 656
9281
8250 이 ​500 이 ​750
4 562 8 843
10312 8 625 0937
12 687 81031
11343
12375
4 875 1093
121125 1406
812501562 81875 02187
12
0 1000 1250
01500 0
41687 81968
812501562
122250
825002812
83125
0
41375 1718
122062 82406
427503093 123437
015001875
015001875
02250 02625
02250 02625
030003375
03750 0
1216252031
42437 82843
1232503656
44062 S
16500
14437 8 875 01312
5468 12 937 81406
01000 01500
0 2000 2500
03000 3500
17531
41062 81593 1221252656 43187 83718
18562 81125 01687 822502812 83375 3937
19593 12 1187 81781 423752968 123562 84156
20625 01250 01875 025003125 03750 04375
21656 41312 81968 1226253281
22687 81375 02062
81375 02062 827503337 84125 04812
81750 2187
81750 2187
82625 03062
82625 03062
835003937
84375 0
418752343
122812 83281
437504218
124687 8
4000 4500
1242504781
05000 0
45312 8
43937 84593
845005062 85625
447505343 125937
050005625 05250 0
1252505906 4 6552 8
855006187 86875
23718 121437 82156 428753493 124312 85031
457506468
127187 8
24750
01500 02249
030003650 04500 05250
06000 6750
07500 0
25781
1562 82342
123125 3806
231253806
44687 85468
1262507031
47812 8
26812
81625 2436
832503962 84875 05687
865007312
88135 0
27844 12 1687 82530
28 876 01750 02624 35004275 05259 06125
291907 4 1812 82717 1236254431
30938
81874 02811 837504587
433754118 12 5062 85906
467507593
128447 8
07000 7874
08759 0
45437 86343
1272508155
49071 8
85625 06562 8750c8436. 89384
Weights
136
-
I
2
3
4
Diameters of the cords.
56
2
Weights fupported by the cords.
1b.
10000
lb.
20000
lb.
30000
lb.
Ib.
lb.
Ib.
40000 50000
60000
70000
lb.
80000
lb.
lb.
90000
100000!
1.
oun
7.
1,
oun.
1.
oun.
1.
ount.
1.
01419.
1.
7
720
8
9
10 3125 0
11 3437 8
12,3750
7500
134062 8 8125
1443750 8750
54687 8 9375 14072 8
5000 010000 15000 0
175312 81062515937 8
185825 01125016875 022500
19 5937 81187517812 823750
206250 01250018750 025000
216562 81312519687 8 2625032812 8
226875 01375020624 027500 34375 0
23 7187 81437521561 82875035937 842125
24 7500 01500022498 030000 37500 044000
257812 815625 23435 83125039062 84587554687 8
26 8135 016250 24473 032500 40624 04775056875 0
27 8447 816875 25410 833750 42186 849625 59062 8,67500
3375042186
288759 017500 26348 0 35000 44749
5150061250 070000
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XI
ROYAL ACADEMY of SCIENCES. 137
XI.A defcription of the heart of the tortoiſe,and
of fome other animals, by M. du Verney*
Part. 1. Sect. I. The structure of the heart of
the tortoife.
Before I opened the heart of the great tortoife,
I obſerved, that the fcale, which cover'd it, was
2 feet, 3 inches long, to 2 feet 1 inch broad,
and its under fcale 1 foot 5 inches long, to 1 foot
2 inches broad; whereas the upper fcale of our
common tortoifes is but 6 or 7 inches long to 5
broad, and the under one 3 inches broad, to 5
or 6 inches long.
The pericardium of thefe animals is a mem-
brane of a very cloſe texture. Thro' all its cir-
cumference, it is clofely united with the perito-
neum, and its capacity is very large in
tion to the bulk of the heart †.
propor-
This heart is fituated in the upper part of the
thorax, above the liver: there is no mediaftinum.
In the ſmall tortoifes, there is a ligament, which
goes from the apex of the heart, and is faſtened
to the bottom of the pericardium; there is none
in the American tortoife. This ligament is a
prolongation of the membrane which wraps the
fibres of the heart ‡.
The figure of the heart of the great tortoife is
hemiſpherical; its lower part being convex, and
the upper plain, but a little dented in the middle,
which is the place where the auricles and arteries
are implanted, fo that this heart pretty much re-
fembles the kidney of a fheep; but in our imal
tortoifes it is drawn out a little into a point .
* Dec. 23. 1699.
1 Fig. 3:
VOL. I. No. 4.
S
+ Plate VIII. Fig. 1.
Fig. 2 and 3.
In
138 The HISTORY and MEMOIRS of the
In the great tortoife, the heart being meaſured
from the middle of the basis to the apex is inch
5 lines; and about 3 inches from one of the fides
of the bafis to the other; but in one of the parts,
the diſtance from the middle of the bafis to the apex
is but 6 lines, and 9 lines from one of the fides
of the basis to the other.
A
›
-
We fee under the right auricle of the heart
of theſe animals, a fort of refervoir of an oblong.
figure, and pretty like that of a blown up blad-
der; it is formed by the concourfe of feveral
veins. The right axillary, and the vena cava
inferior open into the right fide of this refervoir,
one at top and the other at bottom. On the other
fide we fee in a like fituation the left axillary, and
a vein which returns the blood from the left part
of the liver. The coronary vein and fome other
veffels, which proceed from the neighbouring
parts, empty themfelves alfo into it; and as the
jugulars difcharge themfelves into the axillaries,
this caufes the blood of all the veins to be brought
back into this refervoir, except that of the veins
of the lungs*.
1
This refervoir is furnished on the infide with
ſeveral fleſhy fibres, which croſs and interlace one
another, almoſt like thofe on the inſide of the au-
ricles of the human heart. All the veins, which
ſerve to form this refervoir are alfo furniſhed
with fibres, which are interlaced in the fame
manner +.
da, quivi dans
>
This refervoir alfo towards its middle, opens
into the right auricle, on the fide towards the up-
per fcale.
.
The 2 pulmonary veins rife along the lower
fide of each branch of the trachea
Mel'i box..
* Plate IX. Fig. 3. and Plate X. Fig. 2.
the right,
+ Plate IX. Fig. 4.
Fig. 1 and 2.
having
ROYAL ACADEMY of SCIENCES. 139
having run thro' the pericardium, paffes behind
the refervoir, and advances to the left auricle.
The left pulmonary vein having alfo run thro'
the pericardium, hides itfelf behind the axillary
on the fame fide, and unites with the right pulmo-
nary, to the pofterior part of the left auricle, near
its neck, where they form a fort of refervoir*.
#
At the opening of the great refervoir into the
right auricle, there are 2 valves fituated ſomething
obliquely with regard to the right auricle. They
refemble 2 eye-lids, and are compofed af flefhy
fibres produced by thofe of the auricle. At their
exterior angle, they are faftened by a bundle of
fibres, which rifing a little obliquely towards the
bottom of the auricle, expand themfelves and
are loft in it.aduh the
The lower valve has a little more extent than
the upper one, and when they join, they fhut
this aperture exactly
The bafon of the little refervoir, is alfo furnifhed
on the infide with fleshy fibres, but in leſs quan-
tity than that of the great refervoir. In the fmall
tortoifes. (which I have not feen in the great one)
there is at its outlet a fleshy valve in form of a
half moon, turned fo that the angles are towards
the right auricle. It is like that which is found
in birds that have the opening of the trunk of
the pulmonary vein into the auricle ||.
The auricles are of different bignefs; the right
has a greater capacity than the left: they refemble
two purfes, which lying fide by fide, are joined
together at their aperture, that is, at the fhorteſt
part they are, feparated from each other at this
place by a membrane: this feparation is a little
{
*Fig. 1 and 5
08 903 20
1
"
Plate XI, Fig. 1.
Plate IX. Fig. 2. and Plate VIII. Fig. 3.
S 2
ཨཱཝཱ
leaning
1
140 The HISTORY and MEMOIRS of the
leaning towards the middle of the basis of the
heart, bur more to the left fide than the right.
This membrane ooteared in its greatest part
with flefhy fibres, which are continuations of
thofe of the auricles: the bafi of it is quite ten-
dinous, and fo thin that yousmay fee thro? it; it
is faſtened between the 2 valves, which are at
the outlets of the auricles, and of which we fhall
fpeak afterwards*.
1
The bottom of thefe auricles is fpherical, and
much bigger than the place where they join: they
contract themſelves towards the basis of the heart,
and form a fort of neck, which is divided into
two by the membranous partition fpoken of
abovet.
1
L
All the infide of thefe auricles is furnished
with mufcular fibres, which are interlaced fo many
different ways, that they compofe, efpecially in
the ſmall tortoifes, a very spongy texture; which
makes them, when fwoln and dried, in fome mea-
fure reſemble the fubftance of the dungs: the mem-
brane, which ſeparates them, is quite fimooth.
At the outlet of each auricle there is a valve,
and thefe 2 valves are joined together by one of
their extremities, and covered with flefby fibres,
directed from one fide of the baffs of the heartto
the othe:. The membrane between the au icles,
is faftened on the outfide to the middle of thefe 2
valves, as has been faid, and thus makes the fepa-
ration in this place. By the fide, which they
have at liberty, they may, by falling and be-
coming concave, let the blood paſs from the au-
ricles into the heart, and on the other they hinder
the return of it by rifingio Thus we fee, that
tho' theſe 2 valves joined together make a fort of
*Plate VIII. Fig. z. Plate X. Fig 3 and Plate XI.
Fig. 1 and 2. Plate X. Fig. 2 and 3.
+ Plate X. Fig. 2 and 3. Plate XI. Fig. 1.
I
long
ROYAL ACADEMY of SCIENCES. 141
long ſquare, when they are applied againſt the
apertures of the auricles, yet, when the blood
paffes thither, each reprefents feparately the
ter of a concave oval, oppofed and joined to ano-
ther by the fummit*.
quar.
Thefe valves have this in common with that of
the foramen ovale of the fetus, that, when they
open the paffage to the blood, they become hol-
low like gutters, and when they cloſe and apply
themſelves against the hole, they become flat.
Two things alſo contribute to apply them againſt
the hole: the firft is the impulfe of the blood;
the ſecond is the action of the fleſhy fibres, which
compofe them: theſe fibres from crooked becoming
ftrait, and the blood which ſtrikes againſt theſe
valves thus flatted, and applied againſt their
holes, maintaining them in this ftate.
There are 3 cavities in the heart of this animal,
one is in the right fide of the part which I call
the anterior, which is that towards the under
ſcale; the 2 others occupy the part which I call
the pofterior, which is towards the upper fcalet.
Of the 2 cavities in the pofterior part of the
heart, I fhall hereafter call the first cavity, that
which receives the blood from the right auricle;
the fecond cavity, that which occupies the whole
left part, and receives the blood from the left
auricle; and the third cavity, that which is to-
wards the right fide of the anterior part of the
heart, and into which the pulmonary artery
- opens.
t
The texture of the infide of the heart, is fur-
miſhed with fleshy columns of different fizes, in-
terlaced with each other
09
There are ſeveral which rifing from the mid-
dle of the pofterior face, up to the bafis on the
Plate XI. Fig. 1and5. † Fig, 1, and 2.
fume
142 The HISTORY and MEMOIRS of the
fame fide, leave under the valves of the auricles
a paffage, by which the first and fecond cavity
communicate together; for that we may truly
fay it is but one. As the first cavity communi-
cates likewife with the third, we muſt alſo fay
that all the 3 make but one the blood which is
emptied into the heart by the right and left auricle,
being able to mix eafily, and to enter from one
cavity into the other.vt star wars
ล
}
The valve of the outlet of the right auricle is
fo difpofed, that the blood which paffes into it
flowing from left to right tends, only to fill the
first cavity; which communicating with the third,
the blood enters at the fame time: but the valve
of the left auricle being turned from right to left,
the blood, which comes from it, fills at firſt
only the fecond cavity *.
6
We have faid that the texture of fleshy fibres,
which feparates the first cavity from the fecond,
leaves a paffage for the blood to go from one to
the other. This paffage is of the fame length
with the basis of the valves, and is about 3 lines
in diameter; ſo that the valves being depreffed,,
there always remains an aperture, and the com-
munication of the first and fecond cavity is not
entirely hindred by it*.
It must be obſerved in this place, that the com-
munication of the firft cavity, with the third, is
made by an arched aperture, compofed of fleshy
fibres about 2 lines in diameter. This aperture is
on the right fide of the anterior face of the
heart, near the outlet of the artery, which I fhall
call the left branch of the defcending aorta,
The furface of the heart appears all over of an
equal thickneſs: thence it comes that there being
2 cavities one upon the other in its right part,
Plate XI. Fig 5.
T
L
their
ROYAL ACADEMY, of SCIENCES. 143
their fides are lefs thick than thofe of the fecond
cavity; but the fides of the firſt are alfo thicker
than thofe of the third *
A
7.
ご
​This heart is confpofed of feveral orders of fi-
bres; the exterior ones defcribe curve lines, and
appear to be directed from left to right; the in-
terior ones form feveral columns, as has been
faid, whence arife thefe forts of partitions, which
ſeparate the cavities of the heart; and being inter-
laced various ways leave as it were fo many little
cells, which communicate with each other; which
makes the heart when fwoln and dry to appear
all over spongy amictals in ogn
?
Towards the right part of the anterior face of
the baſis of the heart there proceed 3 confiderable
arteries: 2 of thefe arteries compofe the aorta,
and open into the first cavity of the heart. The
orifices of this are placed between the outlet of
the right auricle, and the aperture which makes
the communication of the firft cavity with the
third, and they are fo near as to touch one
another t
mine payl
1
The third artery which is that of the lungs,
proceeds immediately from the third cavity of the
heart t..
10
The outlets of thefe 3 veffels are fupported by
an almoſt femicircular cartilage, to which alfo
their valves are faftened
and at each of thefe
outlets there are 2 figmoidal valves, which have
the fame ufe as in other animals t
Thefe arteries are cloſely united; two of them
are almsoft in front, namely that which I call the
left branch of the deſpending dorta, and the pul-
V
Fig Land 2.
of Plate VI Fig. 2. Plate IX.
Fig. 1. Plate X. Fig. 1. and Plate XI. Fig. 5.
↑
Fig 2, 3, and 4.
monary
144
The HISTORY and MEMOIRS of the
monary artery, and behind thefe is that which I
call the first trunk of the aorta*.
In our fmall land tortoifes, theſe arteries are
embraced at their origin by a ring of fleſhy fi-
bres: there was none in the heart of the American
tortoise +.
Thefe 3 veffels, after having rifen to a certain
height, are bent back again.
This artery, which makes the first trunk of the
aorta, foon after its origin divides into 2 branches,
one of which rifes, and diftributes itſelf to the
fore parts, and to all the upper parts, I fhall
call it the afcending aorta; the other defcends
bending under the ventricle, without making any
branch, and joins itſelf to the left branch of the
deſcending aorta, I fhall call it the right branch
of the deſcending aorta ‡.
The left branch of rhe defcending aorta bends
alfo on the left fide of the heart, and without
making any branch, it defcends alfo under the
ventricle, and in this place furniſhes 2 arteries,
the fuperior of which is in the room of the cœ-
liac, and the inferior in the room of the mef-
enteric; afterwards it is united with the right
branch of the defcending aorta, and theſe 2
branches thus re-united form the trunk of the
defcending aorta, which is diftributed into the
parts of the lower belly, and all the lower extre-
mities t
The pulmonary artery, which immediately
touches the left branch of the defcending aorte,
arifes, as has been faid, from the third cavity of
the heart: this artery is very big, and is as much
in diameter as the first trunk of the aorta: after
having rifen a little, it divides into two branches,
*Plate X. Fig. 1.
Plate VIII. Fig. 3.
Fig. 2. and Plate IX. Fig. 1.
which
d
ROYAL ACADEMY of SCIENCES. 145
which are bent alfo, one of which goes to the left
part of the lungs, and the other to the right*.
The coronary artery is compofed of one fingle
trunk, which proceeds from the first trunk of
the aorta, a little above the figmoid valves, and
it is diftributed to the heart and auricles .
1
Sect. II. The ftructure of the beart of the frog.
The heart of the frog is of a conical figure,
like that of moft animals, and incloſed in a peri-
cardium, which has lefs capacity in proportion,
than that of the tortoife..
2
There is under this heart, a fort of round reſer-
voir, about three lines in diameter.
7:1
The vena cava inferior, proceeding from the
liver, receives a great vein on each fide; one be-
longing to the right and the other to the left part
of this bowel.
The concourſe of theſe three veffels ferves prin-
cipally to form this refervoir, which receives the
axillaries on each fide: the coronary vein is alfo
diſcharged into it †.
This refervoir opens above and towards the
right fide of the auricle: its outlet is furnifhed
with two valves, fituated obliquely with regard to
the auricle: they form together as it were two
eye-lids: the upper is larger than the lower, as
well as in the tortoife, and they have the fame
ufe f.
To each part of the lungs towards the back, is
faftened the trunk of the vein which returns the
blood from it; both, thefe veins, in quitting the
Jungs, proceed about two lines, inclining to-
wards each other; and uniting form but one
Fig. 2. Plate IX Fig. 1. and Plate X.
Plate X. Fig. 3 and 4, + Plate XII.
↑ Fig 2.
*Plate VIII.
Fig. 1.
Fig. 1.
VOL. I. N°. 4.
T
trunk,
146 The HISTORY and MEMOIRS of the
trunk, which is ftuck to the upper part of
the refervoir. This trunk alfo opens into the au-
ricle immediately above the outlet of the refer-
voir into the auricle .
There is but one auricle in the heart of this: it
is fpherical, and it not only covers the whole
bafis of the heart, but has a great deal more ex-
tent.
Its outlet is very large, and furniſhed with two
valves, one of which is faftened to that part of
the basis of the heart towards the fpine, and the
other to the oppoſite part of the fame baſis: they
are femicircular, fhaped almoſt like thoſe which
we call figmoid; fo that the blood being driven
upwards in the contraction of the heart fwells
them, and brings the two edges exactly toge-
ther *.
In this heart there is only one ventricle, and
the fides of it are very thin; the flcfhy fibres of
its inner part interlace in fo many different man-
ners, that they compoſe a very ſpongy texture.
There is alfo but one artery which proceeds
immediately from the right bafis of the heart:
this veffel from its origin lies on the right
fide of the auricle, of which it covers almoſt };
and it goes obliquely to the length of about two
or three lines; and afterwards divides into two
branches, one of which goes to the right, and the
other to the left, bending a little each of theſe
branches is fubdivided into three others †.
Of theſe three the upper one towards the head
is divided into two branches, one of which is
diſtributed to all the parts under the throat, and
the other rifes to the brain.
Plate XII. Fig. 3.
* Fig. 4.
+ Fig. 5.
The
ROYAL ACADEMY of SCIENCES. 147
1
The branch of the middle one, which is the
biggeft, bends, and forms the defcending aorta.
Over-againſt the arm-pit it is divided into two
great branches, the ſmalleſt of which is diſtributed
to the muſcles under the fhoulder, upon the back
and on the head; the other, which is much big-
ger, forms the axillary. Afterwards this branch.
defcends below the heart, throwing off ſeveral
branches, which go to the fpine; and uniting
with that on the oppofite fide, they form but one
trunk, whence proceeds a great branch, which
is inftead of the coeliac and mefenteric: this
trunk is afterwards diftributed to all the lower
parts.
The third branch, which is the lower, divides
alfo into two others, the fmalleft of which is di-
vided into two branches, which diftribute them-
felves among the muſcles, ferving for the motions.
of the head: the other branch is divided into
three or four confiderable branches, which at
their origin are faftened to the lungs, and make
an infinite number of other ſmall branches, which
communicate together, and embrace on all fides
above and below *.
This corta has two figmoidal valves at its open-
ing into the heart; and, as we have faid, it rifes
obliquely the fpace of about three lines, and in
this place it is covered again with circular fleshy.
fibres. Within this veffel, there is in the middle
a cartilaginous lamina, faftened only to the part
of the canal towards the fpine, and turned fpi-
rally from left to right.
This lamina is terminated in a figmoidal valve,
and on the fide there are two others of the farme
figure, each fuftained by a little cartilaginous but-
ton: they are all three fituated at the place where
*Plate XII Fig. 5.
T 2
this
148
The HISTORY and MEMOIRS of the
this veffel begins to divide; and when they are
raiſed, they cloſe the entrance very exactly †.
This mechanifm, which is very fingular, has
however a great fimilitude with that of the aorta
of fome fishes. For in the ſkate, and feveral o-
thers, the aorta, at its origin, is alfo cloathed
with very thick circular fleſhy fibres, to the
length of about an inch; and there appear on
the infide four rows of cartilaginous tubercles, be-
tween which the blood flows which comes out of
the heart each of theſe tubercles fupports a
valve, and theſe valves being open, hinder the
return of the blood: thofe of the meſt diſtant
row from the heart are the biggeft. The figure
of theſe tubercles is fo irregular, and the Lignefs
of the valves fo different, that it would be te-
dious to enumerate them particularly *.
Sect. III. The ſtructure of the heart of the viper.
The heart of the viper is formed like that of the
Frog; but is more flat, and the left fide is more
elevated than the right: it is placed at about fix
inches diſtance from the head, and one inch
above the liver .
The pericardium is of a great capacity, and fo
thin, that the heart may eaſily be feen thro' it.
There are three vena cave, one inferior and two
ſuperior. The vena cava inferior is the big-
geft; the Superior on the right, fide inofculates
with the inferior, and in this place, each of theſe
veffels is a little bent t..
A
99701
The fuperior on the left fide paffing above the
defcending aorta, fticks to the left auricle; and
making a little elbow, defcends under the bafis of
+ Fig. 6.
Fig. 9.
* Fig. 7.
||Fig. 8.
the
ROYAL ACADEMY of SCIENCES. 149
the heart, to open into the vena cava inferior
near its outlet +.
The trunk formed by the union of theſe three
veffels has its outlet towards the middle of the right
fide of the right auricle, and this outlet is fur-
niſhed with two valves formed like eye-lids, as
in the tortoife and frog, fituated obliquely with
regard to the auricle 1.
•
The pulmonary vein is compofed of two
branches, one which returns the blood from the
upper part of the lungs, and is the biggeft; and
the other which returns it from the lower part.
Theſe two veins meet on the left fide of the left
auricle, and the trunk formed by their union goes
obliquely above the lower part of the auricle, to
which it is cloſely ſtuck, to open itſelf into the
fame auricle by a very oblique infertion*
The two auricles of the heart of the viper do
not differ from thoſe of the ſmall land-tortoife,
except in being longer and narrower; they are
feparated by a partition of the fame figure.
At the opening of each auricle into the heart,
there is a valve, and thefe valves have exactly
the fame conformation with thofe in the heart of
the tortoise.
Lastly, there are three cavities in this heart,
the inner configuration of which is entirely like
that of the cavities of the heart of the tortoife;
and they have the fame communication with each
other.
Three arteries proceed from the right fide of
the basis of the heart: there are two in front, and
a third behind them, and of theſe three, there
are two likewife, which form the aorta.
The first trunk of the aorta rifes to the height
of four or five lines, and is divided into two
+ Fig. 10. ‡ Fig. 11. * Fig. 10.
Fig. 8.
branches,
150 The HISTORY and MEMOIRS of the
branches, of which the biggeſt that is on the
right fide bends, and deſcending about three lines,
throws off a branch, which makes the right ca-
rotid; it then defcends, and having furnished
fome branches to the fpine, it receives the aorta,
which is on the oppofite fide. The other branch
produces the left carotid. We may call this firſt
trunk of the aorta, as in the tortoife, the afcend-
ing aorta, becauſe it furniſhes blood to all he
upper parts .
The fecond trunk of the aorta rifes to the
height of about three lines, croffing the two o-
thers it bends afterwards and defcends about
inch below the heart, to unite itſelf with the
aorta on the oppofite fide. In defcending it
throws off a branch, which goes to the ven-
tricle. This branch of the artery may alſo be
called the defcending aorta, becauſe it diftributes
itfelf only to the lower parts *.
The third artery, which is that of the lungs,
rifes to the height of four lines: it lies on the
middle part of the lungs, and is there divided
into two branches: this divifion is immediately
under the afcending aorta.
The branch which is intended for the upper
part of the lungs, is much bigger than the other;
and accompanies the vein thro' its whole extent.
Sect. IV. The ftructure of the heart of files.
Being about to defcribe the heart of fiſhes, I
have made choice of the cap, becauſe it is eaſily
procured.
The heart of this fish is fituated below the
fauces, which are above the ears, at the bottom
of the mouth. The cavity, in which the heart
is incloſed, is covered with a very ſmooth mem-
* Fig 8.
Fig 8.
+ Fig. 8.
brane,
ROYAL ACADEMY of SCIENCES. 151
brane, which is in the place of the pericardium
in feveral other fifhes, but cannot be called fo
here, becauſe the heart is alfo incloſed in a very
thin pellicle, which is properly its pericardium 1.
The basis of this cavity is clofed by a mem-
brane, which feparates the heart from all the o-
ther vifcera, and is a continuation of the pre-
ceding.
Under the heart there is a refervoir formed by
the concourfe of feveral veins, three of which
proceed from the liver, and ferve only to return.
the blood from the vena porte, and from one part
of the ovaries of theſe three there are two, which
open on each ſide into the bottom of this refer-
voir, and the third diſcharges itſelf into it alfo by
a very large outlet. Two other veins rife on each
fide of the fpine, accompanying the aorta; and
unite an each fide of the refervoir with the veins
which proceed from the fides of the liver: thus
theſe two veffels have on each fide, in this place,
but one outlet. The trunk of the vein, which
returns the blood from the gills, lies above the
acrta: it defcends on the right fide of the heart,
it is ſtuck to the fides of the cavity where the
heart is incloſed, and making a turn, it opens into
the right fide of the reſervoir *
This refervoir opens above towards the middle.
of the lower part of the auricle: at its outlet it
has two valves, in form of eye-lids, like thofe of
the animals already defcribed, and thofe which
are at the outlet of the vena cava inferior of birds,
of which we ſhall fay nothing, becauſe it is fo fo-
reign to the ſubject we are treating on †.
}
This heart has but one auricle, but of a great
capacity. It is applied to the left fide; and in its
upper part it forms on each fide a procefs or
Plate XIII. Fig. 1.
*Fig. 2.
↑ Fig. 3.
horn,
152 The HISTORY and MEMOIRS of the
horn, of which the left is bigger than the right:
its outlet is in the upper part of the left fide of
the heart*
There are two valves at the opening of the au-
ricle into the heart, the one above, and the other
below, faftened by all the femicircle which they
form, and open on the fide of the apex of the
heart; which caufes the blood, that flows back
by the contraction of the heart, to raiſe them, and
join them to each other, as in the frog †.
This heart is of a femicircular figure, and flatted
pretty much like a chefnut: it is placed in fuch
a manner with regard to the head, that the two flat
fides are towards their gills: its bafis is articulated
with the aorta by a fort of gynglimus; thefe two
parts having eminences and cavities, which re-
ceive each other mutually .
The fides of this heart are very thick, in pro-
portion to its bulk, and its fibres are of a very
compact texture.
To have the diftribution of the veffels in this
fish well understood, we muſt have fome notion.
of the ſtructure of the gills. Wherefore we ſhall
fay, that the gills, which are known to ſerve for
lungs to fishes, are, as I may fay, divided into
two lobes, each of which is compofed of four
lamina, placed near one another, and fuftained
by four bony arches. We fhall call that the firſt
arch on each fide, which is neareſt the heart.
The convex part of theſe arches is hollow like
a gutter, along which the veffels flow, which I
fhall fpeak of afterwards. The lamina fuftained
by thefe arches occupy the whole ſpace between
the maxilla and the fauces; they are compofed of
a double row of offeous lamella. Each of theſe
lamella is formed like a little fcythe; and at its
+ Fig. 5.
*Fig. 4.
I
|| Fig. 6.
origin
ROYAL ACADEMY of SCIENCES. 153'
origin has a little fort of foot, which is thicker
than the reft, and hollow underneath in form of.
a gutter: this foot leans only by its extremity upon
the edge of the arch, to which it is faftened only
by means of the very thick membrane which
covers the arch: the convex fide of this lamina is
furnished quite to the point with threads, which
diminish in length as they approach this point;
and the concave fide has them much fhorter, and is
furniſhed with them only as far as the middle *.
Theſe threads are bound together on each fide,
by a very fine bony membrane, which gathers
them by the middle almoſt thro' their whole
length; but as the extremities are not joined, they
repreſent the teeth of a faw †.
We have faid that each lamina is compoſed of
a double row of lamella; we muft add, that the
concave of each of thefe lamelle is applied to the
convex of that which is oppofite to it, and that
they are all bound together by a membrane, which
reaches from their origin to the middle of their
height, where becoming thicker it forms a fort
of ligament, above which it is faftened to the
lamella by the ends, of as many lunula, as there
are ſpaces between them. The reft of the lamelle
is free, and ends in a very fine and fupple point ‡.
The refting of thefe lamelle on the edges of
the arch, being by the extremity of their foot, as
has been faid, there remains in the middle a little
void in form of a triangular canal, which reaches
the whole length of the arch, and ferves to lodge
the veffels .
Thefe lamella are covered with a very fine
membrane, and ferve only to fupport the ramifi-
cations of all the veffels of the gills. Thefe vef-
*
Fig. 7, 8. + Fig. 8.
VOL. I No. 4.
‡ Fig. 9..
Fig. ro.
U
fels,
154 The HISTORY and MEMOIRS of the
,
fels, which run in the gutter of each arch, are an
artery, à vein,yand a nerve.ng an
&
I
Before we fpeak of the diftribution of the ar-
teries, we fhall obferve that the part of the aorta
which riſes from the heart, and has 2 figmoidal
valves, like that of the tortoife, is of no great
bulk, in proportion to that which it has a little
above; for at firft it fpreads fo as to cover the
whole bafis of the heart, then contracting by de-
grees it forms a fort of cone, from the point of
which proceeds the veffel which is the continuation
of the aorta. The infide of its dilated part is
filled with feveral fleshy columns, which diminish
continually towards the top; and they have be-
tween their baſes fome interſtices, which form ca-
vities, where the refluent blood is received; which
ſtrengthens the action of the valves juſt mentioned,
and produces the fame effect with the valves in
the mufculous part of the aorta of the ſkate and
frog *.
The canal, which comes out of the point of
the cone of the aorta, runs between the two
lobes of the gills. Over againft the first pair of
arches of thefe lobes, it makes on each fide a
great branch, which is fubdivided again into 2
others, the first of which runs on each fide in the
gutter of this first pair of arches, and the fecond
in the gutter of the fecond pair. The fame trunk,
in its courfe, divides again into 2 branches, each
of which goes on its own fide to the third pair;
and more forward into 2 others, which go to the
laft pair of theſe arches.
Each artery running along the baſe of each
lamina, throws off as many pairs of branches as
there are pairs of lamellas and lofes itſelf entirely
in the extremity of the laminato that the aorta
Fig. 11.
}
and
ROYAL ACADEMY of SCIENCES. 155
and its branches mmonly from the heart to the
extremity of the gills, where they end. For
the diftribution of each pair of arteries, fee
15h an
Fige014, and 115, ***
L
?
j
1.
wide but I
On the edge of each lamella there is a vein,
and each vein difcharges itſelf into a trunk, which
runs in the gutter of each arch, the ramifications
of which are plainly feen in the figures. Theſe
veins coming from the extremity of each arch,
which is towards the basis of the eranium, take
the confiftence of arteries; and are reunited by
pairs on each file.to This, for inftance, which
comes out of the fourth arch, after having fur-
niſhed branches, which diftribute the blood to the
organs of fenfation, to the brain, and to all the
other parts of the heads joins itſelf with that of
the third arch. Thus they make but one branch:
This branch, after having gone about 2 lines is
united with that on the oppofite fide, and both
form but one trunk, which running under the
bafis of the cranium, receives alfo foon after on
each fide another branch, formed by the reunion
of the veins of the fecond and firft pair of arches.
This trunk continues its courfe along the vertebre,
and diftributing the blood to all the other parts,
performs the office of a defcending aorta. Thefe
veins, by their other extremity, which is to-
wards the origin of the arches, difcharge them-
felves into a trunk which is inferted into the re-
fervoit
J
*
33 947
1
The conformity, which is found in the ſtructure
of the heart of thefe animals, has obliged us to
defcribe them at the fame time. pos
But before I explain the ufes of them, it will
not be amiſs to obferve, that by the term refer-
voir, I mean nothing but a trunk of veins formed
* Fig. 12, 13.
+ Fig. 16, 17.
U 2
by
156 The HISTORY and MEMOIRS of the
by the concourſe of ſeveral others, which is in-
ftead of the upper and lower vena cava in the
tortoife and carp; and in the frog, it is nothing
but the trunk of the vena cava inferior, which
receives the 2 axillaries; for tho' this reſervoir or
trunk is furniſhed with fleshy fibres, we do not
pretend to fay that it is not of the kind of veins,
feeing thofe, which open into the auricles and ca-
vities of the heart of other animals, are alfo
covered in this place with like fibres.
Part II. The uses of the heart of the tortoife.
In the deſcription which we have made of the
ftructure of the heart of the tortoife, it may be
obſerved, that it differs in many things from that
of most other animals.
The firft difference is that of the ventricles:
for tho' the three cavities of the heart of the tor-
toiſe are ſeparated by partitions, yet there being
openings of communications between them, they
make properly but one ventricle; whereas there
are two in men, quadrupeds, and birds; becauſe
the partition between thefe ventricles feparates
them entirely. We cannot give the cavities of
the heart of the tortoife, the name of right and
left ventricle, fixing the ufual ideas to thefe 2
words; becaufe on one fide, if we confider them
with regard to the auricles, and the courſe of the
venal blood, one of them might really be called
the right ventricle, and the other the left; but if
we confider them with regard to the origin of the
arteries, the fame cavity, which we call the right
ventricle, fhould alfo be called the left ventricle, be-
cauſe it gives rife to the 2 arteries which fupply
the place of the aorta; that which we call the
left ventricle would then have no arteries, and
what
ROYAL ACADEMY of SCIENCES. 157
'
what we call the third ventricle would have nei-
ther auricles nor veins, which is contrary to the
conformation of the heart of man, and of moſt
animals.
The ſecond difference regards the circulation of
the blood in the cavities of the heart; for in
men, quadrupeds and birds, all the blood, which
is returned by the vena cava, paffes thro' the
right ventricle, and from thence into the pulmo-
nary artery; and all that returns from the lungs
enters again into the left ventricle, and from
thence into the 2 arteries which ſupply the place
of the aorta.
But in the tortoife, the blood which is returned
from all parts of the body, except the lungs, en-
ters' into the right auricle, by the great refervoir,
which contracting itſelf by the action of the
fleſhy fibres, with which it is lined on the infide
drives it into the auricle; and as the valve, which
is at the opening of this auricle into the heart, is
fo difpofed that the blood which it drives by con-
tracting itfelf, runs from left to right, it is ma-
nifeſt that every time the auricle empties itſelf,
it fills not only the first cavity, but alſo the
third which is only a continuation of it.
There are 2 valves in form of eye-lids, at the
outlet of this reſervoir, which in the contraction
of the auricle join together, and clofing this
aperture exactly, hinder the blood with which
this auricle is filled, from returning into this re-
fervoir; which obliges it to flow entirely into
the ventricle of the heart.
We find in birds fuch like valves at the
opening of the vena cava into the auricle; and
in quadrupeds, inftead of valves, we fee between
the 2 vene cave and within their opening, fome
returns formed by bundles of fleshy fibres, which
difengage
158 The HISTORY and MEMOIRS of the
A
difengage themſelves in fuch a manner about
thefe veffels, that they form as it were fo many
fplinters, feeing they embrace not only the space
between the vena cave, but alfo their outlet, and
they cannot contract, without binding in a manner
thefe 2 veins at their entrance into the auricle.
In man thefe returns are lefs diftinct.
V
We fee by this, that theſe ſphincters and theſe
valves have the fame ufe: for as thefe valves per-
mit the blood to enter from the refervoir into
the auricle, and hinder the return of it; in like
manner theſe ſphincters being relaxed, permit the
blood of the veins to fill the auricle; but when
they contract, they clofe the apertures of thefe
veffels, and hinder the return of the blood.
The blood, which is brought back by the
pulmonary vein, fills the left auricle. In the
fmall tortoifes, and in birds, there is a fleshy
valve at the outlet of this vein," which hinders the
return of the blood: and afterwards the left auri-
cle contracting, tends only to fill the fecond ca-
vity, becauſe of the valve being turned from
right to left, which is at its outlet.
"
"
By the compreffion of the heart, all the blood
contained in the fecond cavity is forced to enter
again into the firſt, this cavity having no arteries,
by which it may difcharge itfelf. At the fame
time that the heart contracting itſelf drives the
blood out of the fecond cavity into the first, it
drives alfo into the principal trunk of the aorta,
and the left Branch of the defcending aorta, the
blood which was contained in this firft cavity to
diftribute it into all its parts laftly in the time
that the first cavity empties itself, the blood of
the third cavity is alfo driven into the artery,
which goes to the lungs, and diftributes itself
into their whole fubftance. We fee thereby, that
(
thefe
ROYAL ACADEMY of SCIENCES. 159
thefe 3 cavities empty themfelves at the farne time,
and concur to drive the blood into the arteries.
The ring or ſphincter at the origin of the
aorta in the fmall tortoife, clofing itself imme-
diately after the contraction of the heart, gives
room to believe, that its principal ufe is to acce-
lerate and augment the motion of the blood to-
wards the extremities.
In frogs and ſeveral fishes, this circular ring
occupies a confiderable part of the aorta; which
makes us judge, that by its contraction it drives
the blood alfo with more force towards all the
parts of the body; and it ſeems that the valves,
which are found in greater number in this part of
the aorta, are intended to hinder the reflux of it.
The third difference is in the manner in which
the blood is mixed in the cavities of the heart.
In man, all the blood, which is deprived of its
active parts, enters into the right ventricle, to be
carried thence into the lungs, where it muſt receive
all the preparations neceffary to animate and vi-
vify the parts; and it is afterwards carried into
the left ventricle, and into the aorta, which di-
ſtributes it thro' the whole body.
?
In the tortoiſe, at each circulation, a little more
than of the blood paffes into the lungs, where
13
it receives all the preparations neceffary for its
ufes; and the blood, which flows into them, is
principally that which is inclofed in the third ca-
vity, and is almoft wholly venal: the other por-
tion of the blood of the veins, which is in the
first cavity, mixes itſelf with that of the
fecond cavity, which is returned from the lungs;
and by this mixture it is gradually impregnated with
the active parts, with which the first was charged
in the lungs, as much as is neceffary for the oc-
cafions of the animals; thus all the blood, which
2
returns
160 The HISTORY and MEMOIRS of the
returns from the lungs, is mixed in the cavities
of the heart of the tortoife with that of the veinss
but in the ventricle of the human heart, there is
no fuch mixture made; and all the blood, which
returns from the lungs, paffes from the left ven-
tricle into the aorta.
Let us here make fome reflections, in order
to perceive the differences better, which are be-
tween the heart of the tortoife, and that of the
other animals, of which we have ſpoken.
Three things particularly eſtabliſh this diffe-
rence: the firft is the communication between
theſe cavities: the fecond is, that the aorta de-
rives its origin from the right cavity: and the
third is, that the left has no arteries.
To diſcover the reafon of this difference, we
muft obferve, that the body of man, and of the
animals which we have fpoken of, fuffers a diffi.
pation and a confiderable lofs of fubftance, by
all the functions performed when awake, and by
the rapid motion of the blood and fpirits; and
this lofs cannot be fufficiently repaired, unlefs the
whole blood difcharged by the vena cave into
the right ventricle circulates thro' the lungs, in
order to go into the left ventricle, and from thence
into the aorta; becauſe it is in the lungs that the
air communicates to the blood fome parts fo ac-
tive and fo penetrating, that its heat, fluidity,
and fermentation depend upon them; it is by
this mixture that it is rendered fit for nourish-
ment, and that it can, by circulating in the brain,
furnish it with thefe quick and fubtile parts,
called animal fpirits, and ferve in fhort for all
the other uſes.
We muſt not therefore be furprized, if man
(who ſtands in need of abundance of nourishment,
and of a prodigious quantity of fpirits, to furnish
fo
ROYAL ACADEMY of SCIENCES. 161
I
ſo many different fenfations, and all the motions
of a perfon awake, which are fo violent, and of
fo long a continuance) has need alſo, that all the
blood furniſhed by each of the vena cava fhould
circulate alfo thro' the lungs; but it is fufficient
for the tortoife, which fpends the whole winter
in reſt and in a fort of numbnefs, which can alſo
live feveral months during the greatest heats of
fummer, incloſed in a vetfel, without taking any
nouriſhment, which has but very flow motions,
and but feldom pulfations of the heart, and
which hardly perfpires at all: it is fufficient, I
fay, that of the blood, which comes out of
the heart, ſhould be carried into the lungs, there
to receive the preparations neceffary for the life of
the animal, and that this portion of blood ſhould
be mixed again, with that which is to be driven
thro' the aorta into all the parts of the body. In
frogs the 2 pulmonary veins diſcharge themſelves
into the auricle: in falamanders they are emptied
into the vena cava inferior near its opening into
the heart thus in all thefe animals the mixture is
made, before the blood enters into the heart;
but in tortoifes, ferpents, and vipers, the 2 pul-
monary veins empty themfelves into the fecond
cavity, and thus this mixture is made in the
heart. We may therefore fay that it was necel-
fary, that theſe cavities fhould have a communi-
cation, that the blood, which returns from the
lungs, might mix itfelf with that of the veins;
and the aorta was to derive its origin from the
first cavity, which is the place where this mixture
is made, becauſe it is to diftribute the blood im-
pregnated with thefe active particles to the whole
body. Tho' fishes have a great analogy to thefe
animals, yet the circulation is performed in them
after a different manner, feeing the blood, which
VOL. I. N°. 5.
X
comes
162 The HISTORY and MEMOIRS of the
comes out of the heart at each pulfation, is dif
tributed into the gills by an infinite number of
fmall arteries, which cover the furfaces of all
the lamella, of which they are compoſed; and
ſince the veins, which bring back this blood, dif-
tribute it to all the parts, after the manner of ar-
teries. The reafon of this difference is, that the
fmall quantity of air engaged between the parts
of the water, which feparates from it only with
difficulty, and by the compreffion, which it re-
ceives between the lamella of the gills, muſt be
applied to a greater furface of blood, to furnish
fufficiently thefe active particles to the occafions
of theſe animals.
Altho' the 3 cavities of the heart of the tor-
toiſe muſt be confidered as one fingle ventricle,
yet there is room to believe, that all the blood
which is brought thither by the rena cava and
pulmonary vein, is not exactly mixed there; the
forts of partitions which diftinguiſh the'e cavities,
hinder the perfect mixture of it; and the blood,
which comes from the lungs, emptying itfelf by
the contraction of the heart into the cavity, whence
the acrta derive their origin is probably deter
mined to fill theſe veffels, and above all the prin-
cipal trunk of the aorta, the aperture of which
is the largeſt, and the moſt expoſed to the di-
rection of this vivified blood; and it is this,
which fupplies the head, and the upper parts,
where there is need of a greater abundance of
active parts. But the pulmonary artery being de-
rived from the third cavity, which could be fil-
led only with the blood of the firſt cavity, which
is almoſt all venal, brings into this bowel only
fuch blood as has been deprived of the active
parts, with which it muft there be impregnated.
An
ROYAL ACADEMY of SCIENCES. 163
An explanation of the figures.
Plate VIII. Fig. 1. reprefents the heart of the
tortoife inclofed in its pericardium, and ferves
only to fhew the great capacity of the pericar-
diu, in proportion to the bulk of the heart.
All that appears thro' it will be explained in the
next figure.
Fig. 2. repreſents the heart, its auricles, and
veffels, in their natural bignefs; and we have ad-
ded to it a portion of the trachea, and of the
branches of the pulmonary arteries and veins.
A. The great refervoir formed by the con-
courfe of the following veins.
B. The vena cava inferior.
C. The right axillary.
D. The jugular on the fame fide.
E. A vein which brings back the blood from
the left part of the liver.
F. The left axillary.
G. The jugular on the fame fide.
H. H. Two veins which come out of the two
partition lobes.
I. The heart.
K. The right auricle.
L. The left auricle.
M. The pulmonary artery.
N. The left branch of the defcending aorta;
behind thefe 2 veffels is hidden that which I call
the principal trunk of the aorta.
O. The bend of the right branch of the de-
fcending aorta.
P. The branch which rifes a little before it
makes a bend; it is divided on each fide into 2
others, which are,
Q. The right axillary.
1
1
X 2
R.
164 The HISTORY and MEMOIRS of the
R. The carotid on the fame fide.
S. The left axillary.
T. The carotid on the fame fide.
b. b. Two little arteries which proceed from
the carotids, and diftribute themfelves into a gland
which fills the ſpace left between them.
V. The right branch of the defcending aorta,
which after having made a bend defcends into the
lower belly, to unite itfelf with the aorta on the
left fide.
X. The left bend of the defcending aorta.
Y. The fame veffel, which having defcended
below the ventricle throws off
d. The branch which ferves for a coeliack.
e. That which ferves for a mefenterick.
Z. The place where the 2 branches of the de-
fcending aorta are again united.
2. The place where the pulmonary artery goes
off.
3. The right bend of this veffel, which paffes
behind the 2 trunks of the aorta, and is inclofed
under the bend of the deſcending aorta.
The fame veffel which defcends on the ex-
terior fide of the bronchia, to be implanted at
e into the lungs.
5. The left bend of the pulmonary artery
placed under the left branch of the defcending
corta.
6. The fame veffel which defcends to the left
fide of the lungs.
7. 7. The pulmonary veins, which rife again
to the interior fide of the bronchia.
Fig. 3. reprefents the heart of a fmall land
tortoife.
A. The heart.
B. B. Its auricles.
C. C. The arteries with their bends.
D.
ROYAL ACADEMY of SCIENCES. 165
D. A ring of fleshy fibres, which embraces
theſe arteries at their coming out of the heart.
E. A ligament which parts from the apex of
the heart, and faftens it to the bottom of the
pericardium.
F. A fmall gland placed between the carotids.
Fig. 4. reprefents the 2 auricles cut from top
to bottom, to fhew the outlet of each refervoir,
with their valves.
A. The heart.
B. B. The auricles opened.
C. C. The valves, which are at the outlet of
the great refervoir.
D. The femilunar valve, at the outlet of the
fmall refervoir, which is the third particularity
contained in the fmall land tortoife.
E. The partition, which feparates the auricles.
Plate IX. Fig. 1. reprefents the refervoirs,
the veins which compofe them, and the arteries:
the whole feen thro' the upper fcale, as the ani-
mal is in the poſture of walking.
A. The right auricle.
B. The left.
C. The great reſervoir.
D. The vena cava inferior.
E. The right axillary.
F. The vein which brings back the blood from
the left part of the liver.
G. The left axillary.
H. The place where the great reſervoir is im-
planted into the right auricle.
II. The two pulmonary veins.
K. Their refervoir.
L. The place where it is implanted into the
left auricle.
M. The principal trunk of the aorta, which
did not appear in the preceding figures, which
reprefent
166 The HISTORY and MEMOIRS of the
repreſent the animal reverfed, becauſe it is then
hidden by the two other arteries.
The reft of the diftribution of thefe veffels was
defcribed in Plate VIII. Fig. 2.
Fig. 2. reprefents the great and fmall refer-
voirs.
A. The great refervoir.
B. Its union with the right auricle.
C. The outlet of the ſmall refervoir opened.
Fig. 3. reprefents the great refet voir naked,
and fhews nothing new but
A. The form of its outlet, and
E. The infertion of the coronary vein.
Fig. 4. repreſents the fame refervoir opened,
to fhew the fleshy fibres, with which it is lined
on the infide.
Fig. 5. reprefents the little refervoir formed
by the concourfe of the pulmonary veins, and its
outlet.
Plate X. Fg. 1. reprefents the three arteries
already defcribed, cut at the bafis of the heart,
to fhew their origin and connection.
A. The principal trunk of the aorta.
B. The left branch of the defcending aorta.
C. The pulmonary artery.
Fig. 2. reprefents the heart reverſed on its auri-
cles, to fhew the diftribution of the coronary
vein.
A. The heart.
B. B. Its auricles.
C. The trunk of the coronary vein.
D. Its infertion into the great refervoir.
E. E. Its ramifications.
Fig. 3. reprefents the heart, the three arteries
of which are cut at their origin, with its auricles
fwoln; it ferves principally to fhew how each
auricle, in contracting itfelf, makes a fort of
canal,
ROYAL ACADEMY of SCIENCES. 167
canal, which inofculates with the cavities of the
heart. It diſcovers alfo the origin of the coro-
nary artery.
A. The heart.
B. B. B. Its three arteries cut.
C. C. The auricles fwoln.
D. D. The place where they contract them-
felves, and make a canal.
E. The origin of the coronary artery, which
comes out of the principal trunk of the defcend-
ing aorta, immediately upon the basis of the
heart.
Fig. 4. reprefents the heart in the fame view,
the tract of the auricles, and the aperture of their
infertions into the heart with the partition laid
down, becauſe being in front it is hardly feen.
Plate XI. Fig. 1. reprefents the auricles, a
part of which has been removed to fhew their in-
ner texture, the partition that feparates them,
and the valve at the outlet of the great refervoir.
It repreſents the heart alfo with three pieces re-
moved, one on the right fide to fhew the third
cavity, and its hole of communication with the
firft; the other on the left fide, to difcover the
fecond cavity. Theſe fections at the fame time
fhew the different thickneſs of the fides of theſe
cavities. The third piece is removed from the
bafis of the heart, to difcover as much as poffible.
the fituation of the valves of the auricles, the
fleſhy fibres which compofe them, and the faften-
ing of their partition to the middle of thefe
valves.
A. The right auricle.
B. B. The two valves in form of eye-lids, at
the outlet of the great refervoir. They are fhewn
more diftinctly above this figure, at the place
marked B B.
I
C.
168 The HISTORY and MEMOIRS of the
C. The partition which feparates the auricles.
D. The outlet of the fmall refervoir.
E. The heart.
F. The third cavity.
G. Its hole of communication with the firft.
H. The ſecond cavity,
II. The two valves of the auricles: they are
ſeen more eaſily under this figure, marked with
the fame letters.
Fig. 2. reprefents the third cavity of the heart,
and the pulmonary artery, half of which has been
removed, from the place of its origin to its divi-
fion.
A. The heart.
B. The third cavity opened.
C. The pulmonary artery, which opens im-
mediately into this cavity.
D. One of the two figmoidal valves, which
are at its outlet. They may be feen better in
Fig. 3 and 4, under the fame letter. In Fig. 3,
one of theſe valves is placed on, one fide, and in
Fig. 4, they are both in their fituation and blown
up.
Fig. 5. reprefents the heart feen thro' the upper
fcale, and opened fo as to fhew under its bafis
the two valves at the outlets of the auricles; and
a fmall part of the fame outlets. The orifices
alfo are diſcovered of the two trunks of the aorta,
and a little on one fide, and above the hole of
communication of the firft cavity with the third.
In the laft place are fhewn the firft and fecond
cavity of the heart in their whole extent, and the
paffage of communication between them.
A. A. A. A. The fides of the heart which
have been ſeparated.
B. B. The two valves of the auricles.
C. C.
ROYAL ACADEMY of SCIENCES. 169
C. C. A part of their outlets, which appears
under theſe valves.
D. The orifice of the principal trunk ofthe aorta.
E. That of the left branch of the deſcending
aorta.
F. The hole of communication of the firft ca-
vity with the third, which is altogether on the
right fide.
G. The firft cavity.
H. The fecond.
IIII, The pillars of fleſh which in rifing make
a fort of partition, and have been ſeparated from
the upper part of the heart.
K. K. The paffage of communication.
L. The cartilage, which is faſtened to the
outlet of the arteries. It has been deprived of a
portion of the membrane which covers it, and
only one part of it is fhewn.
Fig. 6. fhews the two valves of the auricles in
particular, marked B. B.
Fig. 7. repreſents the fame valves, with the
outlets of the auricles, and of the two aorta, and
alfo the cartilage partly divefted, and its mem-
brane reverſed.
Plate XII. The heart of the frog
Fig. 1. A. The refervoir.
B. The vena cava inferior.
C. C. The veins which return from the liver.
D. D. The axillaries.
E. The coronary vein.
F. The outlet of the refervoir into the auricle.
Fig. 2. reprefents the outlet of the reſervoir in-
to the auricle.
A. The refervoir.
B. Its outlet.
C. C. Two valves in form of eye-lids.
VOL. I. No.
5.
Y
Fig.
170 The HISTORY and MEMOIRS of the
Fig. 3. A. The reſervoir ſeen on the fide of
the fpine.
B. B. The pulmonary veins.
C. Their trunk.
D. Its outlet into the auricle.
E. The auricle.
Fig. 3. reprefents alfo the fame parts feen on
the fide of the belly, with the auricle, one half
of which is cut down from top to bottom.
A. The refervoir.
B. B. The two pulmonary veins.
C. The outlet of the trunk of the pulmonary
vein above the ſuperior valve of the refervoir.
D. D. The half of the auricle towards the fpine.
E. E. The two valves of the refervoir.
Fig. 4. A. The heart opened.
B. B. The two valves, which are at the outlet
of the auricle.
C. The auricle opened.
Fig. 5. repreſents the heart, the auricle, its re-
fervoir, the aorta, with its principal branches,
and the lungs, of which the right lobe is drawn
very faint, to fhew the veffels that paſs under-
neath.
A. The heart.
B. The reſervoir.
C. C. The auricle.
'D. The trunk of the aorta.
EE. Its two branches, which diftributing
themſelves equally to right and left, are fubdivi-
ded into three others.
F. The fuperior branch, which divides itſelf
into two, of which the exterior makes the carotid.
G. The carotid.
The interior goes to the mufcles which are under
the throat.
H. The interior.
I.
ROYAL ACADEMY of SCIENCES. 171
I. The branch of the middle, which is the
biggeft. In defcending it throws off three con-
fiderable branches, of which the firft marked K
makes the axillary. The fecond marked L,
running under the arm-pit thro' the muſcles of
the back divides into two branches, of which the
firſt marked M rifes again, and diftributes itſelf
to the muſcles which cover the fhoulders, and
the head. The fecond marked N defcending
behind the tranfverfe apophyses of the verte-
bra, throws off fome branches to right and left;
fome of which go to the mufcles of the back and
loins, and the reft entering by the holes of the
vertebra, go to the ſpinal marrow. We muſt
thus correct this part in the defcription, where
theſe laſt veffels are not juftly deſcribed. The
third marked O goes to the cefophagus.
P. The meeting of the two branches of the aorta,
Q. The artery which fupplies the place of the
cœliack and mefenterick.
R. R. The third branch of the aorta. It di-
vides into two others. The fmalleft marked R
diftributes itſelf into the mufcles of the head. The
biggeſt marked S is the pulmonary artery, which
is divided into feveral branches.
Fig. 6. A. The heart.
E. The fleshy fibres of the aorta.
Fig. 6. A. The aorta opened.
B. The cartilaginous lamella in the middle of
the canal.
C. C. The figmoidal valves at the origin of
the aorta.
D. The valve at the extremity of the lamella.
E.E. Two other valves, which occupy the
reſt of the canal.
Fig. 7. A. The aorte opened.
B. B. The circular flefhy fibres.
Y 2
C.C.C.C.
172 The HISTORY and MEMOIRS of the
C. C. C. C. The four rows of valves, with the
tubercles which fuftain them. Thofe of the laſt
row are much bigger than the reſt.
Fig. 8. A. The heart of the viper, the veins
of which have been taken out, to avoid confuſion.
a. a. The auricles.
B. The defcending aorta.
C. C. The afcending aorta.
D. D. The pulmonary artery.
E. A branch which goes to the ſtomach, and
comes from the defcending aortar
F. The reunion of the two dorte.
G. The left carotid
H. The right carotid.
st
I. A branch of the afcending aorta, which
goes to the ſpine.
17
від
K. K. The branches which go to the lungs, of
which the upper one is the biggeſt.
By the fide of this figure are fhewn the heart
and its auricles difengaged from all the veffels.
A. The heart.
B. B. Its two auricles.
ال الاسلام
Fig. 9. reprefents the heart a little reverfed on
the left fide.
A. The vena cava fuperiori
B. The inferior.
C. Their union.
D. The right auricle.
E. The left.
F. The heart.
ご
​)
Fig. 10. repreſents the heart reverſed on the
right fide, to fhew the left vena cava fuperior,
and the pulmonary veins.
A. The right vena cava fuperior.
B. The inferior.
C. The left auricle feen fidewiſe.
D. The left vena cava fuperior.
ROYAL ACADEMY of SCIENCES. 173
3. Its outlet into the vena cava inferior.
E. The vein of the upper part of the lungs.
F. That of the lower part.
G. The trunk formed by their meeting, and
its infertion into the left auricle.
H. The heart.
Fig. 11. A. The right auricle opened.
B. The meeting of the two vena cave on the
right fide.
C. C. The two valves which are at the open-
ing of this vein into the auricle.
Plate XIII. The heart of the carp.
Fig. 1. A. The pericardium.
B. The aperture, at which the aorta goes out.
Fig. 2. AA. The refervoir.
B.B. Two veins, which fupply the place of
the vena cava inferiores,
C. C. The two vena cava fuperiores.
D. D. D. The three veins, which return from
the liver.
E. A vein which brings back a part of the
blood from the gills, and neighbouring parts,
F. The auricle.
On the fide of this figure are the two vena cava,
and thoſe of the liver, reunited at ſome diſtance
from the refervoir.
Fig. 3. repreſents the auricle cut from top to
bottom, to fhew the outlet of the reſervoir.
A. The refervoir.
B. The auricle cut.
C. C. The valves in form of eye-lids.
Fig. 4. reprefents the heart reverſed on the
right fide, to fhew the form of the auricle.
A. The auricle.
B. The heart.
C. The aorta dilated.
Fig. 5. A. The heart.
B.B.
174 The HISTORY and MEMOIRS of the
•
B. B. The two valves which are at the outlet
of the auricle.
C. The aperture which is between theſe valves.
Fig. 6. reprefents the heart reverſed on the left
fide, to fhew its form better, and in what man-
ner the aorta, which is very much dilated at its
origin, reſts upon its baſe.
A. The heart.
B. The dilatation of the aorta.
Fig. 7. repreſents one of the arches feen above,
to fhew the gutter, and the two parts which com-
poſe it.
A. The first part of the arch.
B. The fecond part.
C. The gutter.
Fig. 8. reprefents one of the lamella in parti-
cular, we fpeak of it here before the veffels, be-
cauſe they are made to fupport their ramifications.
A. The ftalk of the lamella.
B. The threads of the convex part. We fee
that they are tied together by a very fine mem-
brane, but that their extremities are not joined.
C. Thoſe of the concave part.
D. The foot with its gutter.
Fig. 9. repreſents two lamella feen in front,
and furniſhed with their threads.
A. The lamella, which makes the convex fide
of the lamina.
B. The lamella, which makes the concave
fide of the fame lamina.
We fee by this, that the bony threads are lon-
ger in the concave fide of the lamella A, and
fhorter in the convex fide of the lamella B. So
that theſe two lamella always have their ſhorteſt
threads towards each other. This is what has not
been fufficiently explained in the defeription,
where we have ſpoken only of the lamella, which
make the convex fide of the lamina,
Fig.
ROYAL ACADEMY of SCIENCES. 175
Fig. 9. reprefents the lamella feen fidewife,
and parted, to fhew the membrane which con-
nects them, and cord which terminates it.
A. A. A. The membrane, which connects the
lamella.
1
B. The cord which terminates it. We fee how
this cord forms as many lunula, as there are
ſpaces between the lamella.
Fig. 10. reprefents the canal formed by the
meeting of the gutter with the two feet of the
lamellæ.
Fig. 11. repreſents the aorta opened, to fhew
the fleshy columns, with which it is furniſhed on
the infide, which makes it very much fwoln in
this place.
Fig. 12. repreſents the diftribution of the
corta.
A. The heart.
B. The auricle,
C. The aorta dilated.
D. Its divifion into four branches on each fide.
We fee that each of theſe branches running thro'
the whole length of the lamina terminates entirely
in its extremity.
E. E. E. E. Four twigs which detach them-
felves from each branch about an inch from their
origin, and diſtribute themſelves to the beginning
of each lamina. The fame figure fhews how each
branch is divided into as many twigs as there are
lamellæ.
Fig. 13. reprefents a portion of a lamina de-
tached from one of the fides of the gutter, and
a little reverfed, to fhew how the artery is inclofed
in the middle of the void, which the feet of the
lamella leave between them. It is difengaged
from the vein which covers it, and a little drawn
downwards,
176 The HISTORY and MEMOIRS of the
downwards, for the better difcovery of the pairs
of branches which it gives to the lamella.
A. A. The gutter.
B. A portion of the lamina.
C. The artery with its branches.
Fig. 14. A. A. repreſents a pair of lamina de-
prived of their veffels.
Fig. 14. A. The trunk of the artery incloſed
in the gutter of the arch.
B. B. The two branches of the fame artery,
which rife along the inner edge of each lamella.
C. The place where the two branches make an
anaſtomoſis.
D. D. D. Their little tranfverfal arteries, which
cover the flat of each lamella.
E. E. The tube which ferves for a vein, and
is depreſſed on the exterior edge of each lamella,
in which alſo their little tranfverfal arteries imme-
diately inofculate.
F. The trunk of the vein incloſed in the gut-
ter of the arch.
Fig. 15. reprefents the fame arteries detached
from the lamella.
Fig. 16 and 17. reprefent the diftribution of
the veins of the gills.
We there fee, that the vein incloſed in each arch
receives almoſt of the distance from each of its
extremities two branches, each of which returns
from each row of the lamina to which it is ap-
plied, whereas it is the middle of this vein that
furniſhes itſelf to the part of the middle of this
lamina, under which it is couched. This diſtri-
bution is made thus differently, only to make the
courſe of the veffels, which go to the lamella,
more fure and eaſy.
A. A. A. The trunk of the vein of the gills,
which is couched above the aorta.
B. B. B. B.
ROYAL ACADEMY of SCIENCES. 177
B. B. B. B. The place where each vein divides
into three.
C. C. C. C. The place where theſe veins are
inferted into the trunk marked A.
D. D. D. D. The place where each of theſe
veins fubdivides into three more; of which there
are two alfo, which return from the lamella.
E. E. The place, where thefe veins are re-
united by pairs on each fide.
F. The trunk formed by their meeting. It is
to be obſerved, that as foon as each of theſe veins
comes out of the extremity of the gutter of the
arch, the fides of their canal become thicker, and
take the fame confiftence with the arteries, where-
as all the reft of thefe veins is as thin and fine as
the finest lymphatic veffel.
G. The branch of the laft arch, which before
the reunion cafts off feveral branches, which go to
the eye, the noſe, the brain, and to all the neigh-
bouring parts of the head.
It fupplies the place of the afcending aorta,
and the trunk formed by the meeting of thefe
veins, which are become arteries, ferves for a
defcending aorta.
VOL. I. Nº. 5.
N
A
A
TABLE
OF THE
PAPERS contained in the ABRIDGMENT
of the HISTORY and MEMOIRS of the
ROYAL ACADEMY of SCIENCES at
PARIS, for the Year MDCC.
In 'the HISTORY.
11. ON Some fingularities of France.
II.
On the apparent largeness of the hori
zontal moon.
III. On a body of fire feen in Normandy.
IV. On the yellow amber.
V. On a change made in the texture of bodies by
exterior motion only.
VI. Of the trembling of the nerves of a frog after
death.
VII. Of a stone found in the bladder of a mare.
VIII. Of a monftrous double leveret.
IX. On a new telescope-glass.
X. On the centres of converfion, and on frictions.
XI. On the bodies which fwim in liquors.
XII. A falſe report of the perpetual motion being
difcovered, and the impoffibility of it demon-
ſtrated.
In the MEMOIRS.
I. An obfervation on the barometer, thermometer,
and quantity of rain and fnow-water, that
fell at Paris in the royal obfervatory, during
the year 1699, by M. de la Hire.
་་
2
II.
180
A TABLE, &c.
II. A new manner of rendering barometers lumi-
nous, by M. Bernoully, profeffor at Gro-
ninguen.
III. Remarks on the construction of pendulum
clocks, by M, de la Hire.
IV. An extract of fome letters written from Por-
tugal and Brazil, by M. Couplet the fon, to
the Abbé Bignon, prefident of the Royal Aca-
demy of Sciences.
V. A general method of throwing bombs, in all
cafes propofed, with an univerfal inftrument
for this purpofe, by M. de la Hire.
AN
A N
ABRIDGMENT
OF THE
PHILOSOPHICAL DISCOVERIES and OB-
SERVATIONS, in the HISTORY of the
ROYAL ACADEMY of SCIENCES at
Paris, for the Year 1700.
A
•
I. On fome fingularities of France.
S the academy continues its defign of ex-
amining all the wonders of the natural
hiftory of France, there has been mention made
of the Montagne de l'Aiguille in Dauphiny, other-
wife called the inacceffible mountain. The fitu-
ation of it is reverfe, and it is pitched if I may
fo ſpeak, on its fummit and point, for it is but
1000 paces round at its baſe, and yet is 2000 at
top. Hence it obtains the name inacceffible:
However when Charles VIII. went into Italy in
1492, he fent fome perfons of fufficient courage
and dexterity, to climb up to the top of this
mountain. They found only Chamois upon it,
and it is not eaſy to comprehend, how theſe ani-
mals, which had ufed no induftry, could get thi-
ther. There were no trees feen upon it, there
being only a meadow. The way that they took
to go up might be about half a league. Upon
the platform of this mountain there is a pointed
elevation, on which account it is called Montagne
de l'Aiguille, or the needle mountain.
Another fingularity of Dauphiny is the grotto
of Notre Dame de la Balme near Grenoble. It
opens with a pretty high arch; and leads to a
lake
182 The HISTORY and MEMOIRS of the
lake incloſed under the mountain, and ſeeming
to be a league broad. When Francis I. was in
Dauphiny, he fent thither fome people in a boat,
who went above 2 leagues upon the lake, but be-
ginning to hear a great noiſe they were afraid, and
proceeded no farther, and placed fome lighted
torches upon planks, which they faw diſappear
in a certain place, which probably was a whirl-
pool. A clergyman of that country went thi-
ther a few years afterwards, and whether he took
another way in the grotto, or was lefs eaſily
frighted, or had an imagination lefs difpofed to
the marvellous, he has left a very different, and
much more fimple relation of this voyage. He
faw fome falls of water, he found fome places
that were dry, and others where the arch was fo
low, that there was no paffing without lying down
flat in the boat. This laft circumftance may give
us fome trouble, but in fhort the marvellous finks
confiderably in the fecond relation.
This is what has been related in books con-
cerning this grotto, and the inacceffible moun-
tain. But M. Dieulamant has given himſelf the
trouble to fend the academy a relation of the
grotto, which he has examined with his own eyes,
and it preferves no farther remains of its ancient
wonders. It is irregularly hollowed in the rock,
and its entrance may be 4 or 5 toifes in breadth,
and 5 or 8 in height. At the bottom of this
entrance, there comes out a little rivulet which
flows into the Rhone: This rivulet was almoſt
dry in August, when M. Dieulamant went to fee
the grotto, but he judged by the channel, that
it was always very fmall. The grotto is forked.
In the part on the right hand, there are a great
many congelations of the water that diftills thro'
the rocks. In the part on the left hand, fome
I
waters
ROYAL ACADEMY of SCIENCES. 183
waters diftil, which make part of the rivulet.
They fall at firſt into a pretty large natural baſon,
below which there are feveral other fmall ones,
which make a pretty agreeable cafcade. At the
end of this grotto is a fort of opening hollowed
alfo in the rock, at the bafe of which is the wa-
ter that forms the greateft part of the rivulet.
This is what is called the lake, becauſe the water
is dormant. It is half a foot, or at moſt a foot
in depth. The alley, where this fort of lake is,
appeared to M. Dieulamant to be not above 29
toifes in length, contracting itſelf a little; for
from the beginning where he was, he thought he
faw the end with torches. The people of the
country affirmed that there was nothing beyond.
This however is the abyfs where the torches were
fwallowed.
If M. Dieulamant had examined the inac-
ceffible mountain, perhaps that alfo might have
been reduced.
The floating islands in a lake near St. Omer,
have alfo been reviewed, and found to be lefs
wonderful. They are properly nothing but tufts
of the roots of grafs mixt with a little fat earth.
II. On the apparent largeneſs of the hori-
zontal moon.
1
It ſhould ſeem that the apparent largenefs of
an object, muft depend on the largeneſs of the
image that it traces on the bottom of the eyes
and yet fometimes the contrary happens, and the
moon of which our eye receives a fmaller object
at the horizon than at the meridian, becauſe it is
then farther from us, appears much larger at the
horizon,
A
This
184 The HISTORY and MEMOIRS of the
This Phenomenon has very much embaraffed
the greatest philofophers among the moderns,
as it often happens that when we give very diffe-
rent explications of one and the fame thing, none
of them is true. F. Gouye has not been contented
with what has hitherto been imagined on this
fubject: Descartes fays that when the moon rifes
or fets, a long feries of objects oppofed between
us, and the extremity of the fenfible horizon,
make us imagine. it farther off than when it
is in the meridian, where our eye fees nothing
between it and ourfelves, that this appearance of a
greater diftance makes us imagine the moon larger,
becauſe an object that we fee under a certain angle,
and think at the fame time to be very far off, na-
turally makes us judge it to be very large, to ap-
pear fo far off under that angle, and thus a mere,
tho' neceffary judgment of our mind, which is
common to all men, makes us fee the moon lar-
ger at the horizon, in fpite of the fmaller image
that is painted on the bottom of the eye. But
F. Gouye at once deftroys this fo ingenious an
explication, by affirming that the more the hori-
zon is bounded, the more large the moon appears
to us. M. Gaffendi pretends that the pupil of
the eye, which is conftantly moft open in the
dark, being more fo in the morning and evening,
becauſe thicker vapours are commonly fpread
over the earth, and becauſe it muſt alfo traverle
a longer way to look at the horizon, the image
of the moon enters the eye under a greater an-
gle, and paints itfelf really larger. But notwith-
ſtanding this dilatation of the pupil caufed by
the darkneſs, if we look at the moon thro' a
little tube of paper, we fhall fee it fmaller at the
horizon,
To
1
ROYAL ACADEMY of SCIENCES. 185
{
}
To find any reafon therefore for fo odd a
Phænomenon, F. Gouye conjectures that when the
moon is in the horizon near the earth, the thicker
vapours, with which this planet is then encompaſſed
with regard to us, have the fame effect with a
wall placed behind a column, which then appears
much bigger than if it ftood by itſelf, and was
encompaffed on all fides by an enlightened air.
Befides a fluted column appears bigger than a
plain one, becauſe the flutings make fo many par-
ticular objects, which by their multitude give
room to imagine, that the total object which
they compofe is of a greater bulk. It is much
the fame with all the objects that are ſpread on
that part of the horizon, with which the moon
correfponds when it is near them; which caufes
it to appear greater when it rifes behind trees, the
intervals between which being cloſer and more
obſervable, have almoft the fame effect on the
apparent diameter of this planet, as a greater num-
ber of flutings would have on the body of a
pillar.
III. On a body of fire feen in Normandy.
The 7th of Jan. an hour before day, there ap-
peared to the inhabitants of la Hague in lower
Normandy, a body of fire fo bright that it eclip-
fed the light of the moon, and that the inhabi-
tants of S. Germain des Vaux, and of Auderville,
two great villages fituated on the banks of the
fea, thought it at firft to have been day, and
were much frightened at fuch a prodigious light.
The figure of this fire was like a great tree, and
ran from W. N. W. to E. S. E. it did not fall till
an hour after day-light, and then with fo great a
noife, that the houfes of thofe two villages fhook
VOL. I. No. 5.
A a
with
186 The HISTORY and MEMOIRS of the
with it. They who were 12 leagues from Cher-
bourg, thought it had fallen on Valognes, and they
of Valognes thought it had been on Cherbourg.
But as the inhabitants of la Hague were the only
ones who heard the noife, and felt the fhock caufed
by its fall, they are the more credible, witneffes in
this point, It appear'd to them as if this flame
was loft in the fea, near the little ifle of Origni,
and this appearance was not much unlike that of a
great ſhip on fire. The academy was obliged to M.
de Seneffey a gentleman of lower Normandy for
the information they received of this phænomenon.
IV. On the yellow amber.
It is commonly thought that yellow amber,
which is found in the Dantzick fea, is a gum which
is produced, and falls from certain trees fituated
on the banks of this fea. But M. Tournefort re-
ceived an account from Aix, that yellow amber
is to be found in the moft bare and barren cliffs
of the rocks of Provence; which fhould incline.
us to believe that this gum is mineral and not
vegetable; and that the amber which is in the
fea of Dantzick, did not fall therein from trees,
but was conveyed thither by land floods.
V. On a change made in the texture of bodies
by exterior motion only.
It is well known what force an inward motion
hath, when diffufed thro' all the infenfible parts
of a body to change the texture of it, and pro-
duce great alterations. But that a meer outward
motion, which feems to terminate in the whole
mafs without agitating the parts, fhould produce
the fame effects, is fomething more furprizing,
B A
#,
at
ROYAL ACADEMY of SCIENCES. 187
at leaſt to a natural philofopher. M. Homberg
fays, that having tied a bottle of wine to the
clapper of a mill, he found that the motion of
this clapper alone had changed the wine into
very good vinegar in the fpace of three days; and
that a pound of quickfilver had by the fame
means in three months time, given 4 or 5 ounces
of a blackish powder.
VI. Of the trembling of the nerves of a
frog after death.
M. Du Verney fhewed a frog juft dead, which
in taking the nerves of the belly of this animal
which go to the thighs and legs, and irritating
them a little with a fcalpel, trembled and fuf-
fered a fort of convulfion. Afterwards he cut
theſe nerves in the belly, and holding them a
little ſtretched with his hand, he made them do
fo again by the fame motion of the fcalpel. If
the frog had been longer dead, this would not
have happened, in all probability there yet re-
mained fome liquor in thefe nerves, the undula-
tion of which caufed the trembling of the parts
where they correfponded, and confequently the
nerves are only pipes, the effect whereof depends
upon the liquor which they contain,
VII. Of a stone found in the bladder of a
•
mare.
The academy has feen in the hands of M. Le-
mery, a ftone found in the bladder of a mare,
which weighed 23 ounces 7 drams. It is 4 in-
ches in diameter one way, and 4 the other.
It is the fize of a midling melon, covered with
a lot of fmooth and fhining fkin. Its fubftance
A & 2
is
188 The HISTORY and MEMOIRS of the
is afh-colour, and it is hardened fince it has been
drawn from the animal, altho it is ſtill very fri-
able. It has alſo loft in drying a very ſtrong ſmell
of urine, which it had at firft.
ment.
VIII. Of a monftrous double leveret,
-
M. Lemery brought alfo to.the affembly a mon-
ftrous leveret, or rather two leverets joined toge-
ther from the head to the breaft. They had but
one head and one face, tho' they had four ears.
In the place for the mouth there was only a little.
cavity without any opening to receive the nouriſh-
Nevertheleſs they lived, and even out of
their mother's belly; for they were taken with
the hand by a huntſman. This double animal
was walking in a wood, but one of the leverets
drew one way, and the other another way, ſọ
that they did not get forward at all. They told
M. Lemery, that in opening them, they had
found in each a heart, lungs, and ftomach, all
found,
IX. On a new telescope-glass.
M.Tfchirnhaus has informed the learned of the
effects of a new glafs, which he has made.
This glaſs is convex on both fides, and 32 feet
of focus, but it is extraordinary by the largeneſs of
its diameter; for as the greateſt glaffes of the fame
focus, which have hitherto been uſed are only 4
or 5 inches in diameter, this is more than a Rhe-
nish foot, and at first it had two feet, but it was
injur'd by accident. From hence we may judge
what the machine, muft, be that M. Tchirnhaus
has invented to cut fuch great glaffes.
>
ROYAL ACADEMY of SCIENCES, 189
1
All dioptricks feem to be reverfed by the ef-
fects which it produces. For example, the com-
mon object glaffes of teleſcopes, tho' fmall enough
already, have very little aperture left them, and
yet M. Tfchirnbaus leaves his quite open, not-
withſtanding it is fo large.
!
To underſtand the reafon of the common prac-
tice, and the particularity of this of M. Tfchirn-
baus; you muſt know exactly how the image of a
luminous point, the rays of which have traverfed
it, is made in the focus of a convex glaſs. Let us
fuppofe this glaſs to be an entire hemifphere. The
rays that the luminous point fends upon the fur-
face of this hemifphere, do not reunite them-
felves, after having croffed it, upon one fingle
point of its axis, as we might imagine, from the
rules of the focus, and of the reunion commonly
ufed in this fubject. On the contrary they have a
pretty large space, but much less than the furface
of the hemifphere on which they were before
fpread. Thus altho' they are not exactly reunited,
they are more clofe one to the other than they
were. Moreover, in the extent of the fpace
which they fill, they are unequally cloſe, leſs fo
toward the extremities, and much more toward
the middle, that is toward the axis of the hemi-
fphere, and there one would think they were en-
tirely united in one point. Theſe rays nearly
united upon the axis, are thofe which are entered
toward the axis, that is, towards the middle of
the hemifphere, and as all the others, which fall
upon the reft of the furface, unite very ill, they
take away all this remainder of the hemifphere,
and preferve only the middle of it to make the
objects. But there is alſo another obfervation to
be made. The rays which have heen refracted,
}
森
​•
natu-
190 The HISTORY and MEMOIRS of the
naturally form colours and Iris's, unless they are
not reunited by the refraction, or at leaft extremely
locked against each other. Thus an object glafs,
which is only a little remnant of the hemifphere,
is nevertheless commonly very large, becauſe it
receives rays towards its edges, which after being
refracted do not again cloſe themſelves enough,
and make Iris's very inconvenient to the obfer-
vers. It is for this reafon they cover the edge of
the object glaſs, and that they leave only a little
round extent about its axis.
M. Tfchirnbaus difapproves of this practice, in
all appearance ſo well founded, and ſuppoſes there
are many other errors in opticks, which fhould be
rooted out. He does not leffen at all the great furface
of his object glafs, but he has fome fecret about it,
which he has not yet difcovered. It is always cer-
tain, that it would be advantageous to leave a
larger aperture to the object glaffes provided
there is no other inconveniencies, becaufe there
would come more rays to the fame point.
M.
M. Tfchirnhaus's object glafs may be uſed
without an eye-glafs, which is a very great ad-
vantage, for the more glaffes there are in a te-
leſcope, the more rays there are reflected upon
their furfaces which are loft to the obſervers.
Tſchirnbaus alſo affures us, that the objects fhew
themſelves more clear with his fingle glafs, than
they have yet been feen with teleſcopes. He af-
firms alfo, that they appear more clear, than to
the naked eye, altho? fome reflections of rays are
neceffarily made upon this glafs, but this lofs is
probably more than recompenfed by the great
number of rays in the fame point, which the great
extent of its ſurface and focus caufes to enter into
the eye.
This
ROYAL ACADEMY of SCIENCES. 191
This glafs may be uſed without a tube, and in
another manner than that which M. Huygens men-
tions in his aftrofcopy. For the object fhews it-
felf always diftinctly, notwithstanding the rays
of the fun which pass between it and the eye.
《 The fpace which may be feen at once with this
glafs, is of an incredible fize. M. Tfchirnhaus
affirms, thats without tube or eye-glafs, he has
feen very diftinctly at noon, an entire town at the
diſtance of a German mile and half.ss
So many fingularities of M. Tchirnbaus's glafs
foretel great and happy novelties in dioptricks.
mua bsbuzo. is
C
'
X. On the centres of converfion, and on
५
frictions.
DIAL
{
}
If a ſtick be laid upon a ftagnant water, and
drawn by a thread fixed to it, fo that the thread
makes always the fame angle with the ftick, for
example, always a right angle, the ſtick will be
found to turn upon one of its points which will
be immoveable, which M. Parent calls the centre
of converfion. We may fuppofe for the greater
eafe, that the thread be faftened to one end of
the ſtick.
COIN.
This effect arifes from the refiftance of the
fluid, and from the manner wherein it divides.
For let us imagine the first moment of the traction;
it is certain, that the refiftance of the parts of the
fluid which are to be difplaced, tends to make
the flick turn about the point where the thread is
faſtened, as about a centre, fo that in the prefent
fuppofition, the ſtick defcribes exactly a quadrant
of a circle, after which the fluid would no longer
refift the ftick lengthwife. But if this circular
motion is executed, the free end of the ſtick, and
the
192 The HISTORY and MEMOIRS of the
the parts which are nearest to it, would defcribe
longer arches of circles than the others, and have
a greater velocity. The refiftance therefore of the
fluid, which tends to imprefs a circular motion on
the ſtick about the point where the thread is tied,
tends to imprefs a greater velocity on the parts,
which are towards the other extremity, or, which
comes to the fame thing, theſe parts have need of
a greater velocity, to furmount the refiftance of
the fluid, fo that the ftick does not take this cir-
cular motion about the point where the thread is,
or the refiftance of the fluid is greater towards
the free end of the ſtick, and ftill leffens from
thence towards the other end. Now we muſt
fuppofe, that all the columns or threads of water,
which refift the ftick, are of the fame length, or of
the fame mafs. Therefore we may find upon the
ftick fuch a point, that taking a greater number
of theſe threads on the fide where they refift leaſt,
and a lefs number on the fide where they refift
moſt, there will be an exact compenfation, and
the forces will be equal on both fides. It is this
point which is the centre of converfion, and ast
the fame reaſoning has place in all moments of
the traction, which is made always in the fame
manner, this centre is always the fame point.
If the angle of the thread with the ſtick fhould
ceaſe to be a right one, and become obtufe, the
centre of converfion would nevertheleſs be always
at the fame point, becauſe the refiftance of the
fluid, altho lefs in itſelf, is always according to
the fame proportion, greater towards the free
end of the ſtick, and lefs towards the other end,
which appears vifibly by the circular motion
which it always tends to imprefs on the ſtick, al-
tho' this motion need not be an entire quadrant of
a circle. But if, after having drawn the ſtick by
its
ROYAL ACADEMY of SCIENCES. 193
its thread under a right angle, we draw it under
an obtufe one, the centre of converfion, which
would not change its place upon the ſtick, would
change it in the fluid, becauſe the whole ſtick
would make a motion, and we fhould not fee it
turn any longer upon the fame immoveable
point.
15
The grand queftion is to know precifely at
what point the centre of converfion is to be found,
and it is this, which M. Parent has determined
by an algebraical calculation, adding fome other
general confiderations of mechanicks, befides.
thoſe which are particular to this phænomenon,
and which are the only ones that we have related ;
he finds that if the ftick drawn by one extremity
be a fingle line, divided into 20 parts counting
from the thread, the centre of converfion will be
nearly on the 13th. If it be not any more a line,
but a furface, or a folid that is drawn, there will
be fome change in the fituation of the centre of
converfion, according to the furface or the folid.
All this requires a great detail of algebraical cal-
culations, into which M. Parent has entered.
If inſtead of fuppofing here that the body drawn
fwims upon a fluid, we fuppofe it upon a rough
uneven plane, the refiftance of the plane to the
motion of the body will always divide itſelf in
the fame manner, and determine the fame centre
of converfion.
This refiftance is exactly what they call the
friction, fo prejudicial to the effect of all ma-
chines; and the theory of centres of converfion
which might appear at firſt very little uſeful,
has been of fervice to M. Parent, in the inqui-
ries and determination of the force of frictions.
To confine in certain bounds this queftion,
which makes innumerable and confequently in-
VOL. I. No. 5.
B b
folvable
}
194
The HISTORY and MEMOIRS of the
folvable, the endless differences of furfaces which
may rub together, M. Parent confiders only one
body perfectly hard, which rubs either upon a
very hard body, or a very foft one, that is, a'
fluid. Theſe two extremes being once known,
we fhall judge pretty nearly of all thofe which
are between them.
Each of theſe two cafes divides again in two,
for it is a queſtion to know the neceffary effort
either to move the leaft that is poffible, that is
to begin to move one body upon another, or to
move them with a certain given quickness.
If the body, upon which the very hard body
muſt move, is fluid, experiment alone can de-
termine the fize of the firſt effort, but this firſt
effort being once found, thoſe which will be necef-
fary to impreſs fuch velocity as we would, will
be between themſelves as the fquares of theſe ve-
locities, for the refiftance of the fluid does not
increaſe only, becauſe the body, which is moved
upon it, is moved fafter, but alſo becauſe being
moved fafter, it meets and fhocks many more
particles of the fluid, which makes a double
ratio, or fquares.
If the body upon which the very hard body is
moved, be alfo very hard, M. Parent confiders
the two ſurfaces of them as quite fet round with
equal hemifpheres, fo that the hemifpheres of the
upper bodies are engaged in thofe of the lower.
They muſt be difengaged and raiſed to begin the
motion. This figure helps M. Parent to make a
calculation, and he finds by pure geometry that
in this fuppofition, to raiſe a weight of 20 lb.
there would be required a force which was either
14 lb. when one of the hemifpheres of the upper
body muſt be raifed above two of the lower, or,
only 7 lb. when it was to be raiſed above one.
I
Now
ROYAL ACADEMY of SCIENCES. 195
Now as theſe two cafes meet at once with regard
to the different parts of the fame furface, there
is then required a mean force between 14 and 7,
or between 11 and 10. This proportion is ex-
actly that which M. Amontons has determined by
the experiment of glaffes and their polifhers, which
are very hard bodies, and which wear very little
by one fingle friction, which brings them very
near the fuppofition of M. Parent,
When the lower body is covered with any fat
fubftance, the intervals of the hemifpheres of its
furface are filled in fuch a manner, that thofe of
the upper body do not engage themſelves any
more, and may begin to move themſelves with-
out being fenfibly raiſed. Then in this caſe, the
force, which moves the weight of 20 lb. muſt be
lefs than the fmalleft which can move in the cafe
where it fhould raife the hemifpheres to their
whole height; that is, this force muſt be lefs
than 7 lb. M. Amontons has found by the expe-
riments related in the memoirs of 1699*, that it is
the third part of the weight, and confequently in
the preſent fuppofition 6 lb. which is under 7.
M. Parent's geometry, altho' in a matter which
ſeems to have eſcaped geometry, has conducted
him to the fame point where M. Amontons is ar-
rived by experiment.
3
The compariſon of different velocities with
which we would move one of theſe bodies upon
the other, always according to the hypothefis of
the hemifpheres, has thrown M. Parent into a
yet more complicated and delicate geometry. All
that we can here gather which is clear and and fen-
fible enough, is, that the refiftance of the lower
bodies to the motion of the upper does not increaſe
in the fame ratio with the velocity of the upper
Pag. 69. of this abridgment.
*
Bb 2
one
196 The HISTORY and MEMOIRS of the
one, and even does not increaſe more fenfibly be-
yond a certain point, altho this velocity increaſes
alfo as much as you will br
-
{
Let us imagine with M. Parent, the upper
body entirely reduced to only one of the hemi-
ſpheres of its furface, without lofing any of its
weight, and that this hemifphere paffes fucceffively,
and with a horizontal motion, upon a row of
lower hemiſpheres, equal to it, falling at each
moment between their intervals, and raiſing it
felf continually. If the weight of this upper
hemifphere be fuch, that it muft in a fecond make
it run over a vertical ſpace equal to the height or
depth of the intervals, which are between the
lower hemiſpheres, and if the horizontal motion
of the upper hemifphere is fuch, that it makes
in a ſecond but one interval of two lower hemi-
fpheres, it is certain that at each fecond it will
fink entirely into one of theſe intervals, that is,
it will infert it felf as much as poffible. But if
by its horizontal motion, it can run over two in-
tervals in one fecond, it will enter into each but
half of its depth, becauſe theſe two halves put
together will make all the height, which its weight
ought to cauſe to fall in one fecond. It is then
viſible that the more the horizontal motion,
(which may increaſe without end) is great with
reſpect to the vertical motion of the weights,
which cannot change, fo much the lefs will the
upper hemifphere fink and infert itſelf into the
lower ones, and in fine the horizontal velocity
may be fuch, that the upper hemifphere will not
touch the lower one but by their fummits, after
which the friction will not encreaſe more fenfibly
by the increaſe of the velocity. But it muſt be
well obferved, that the friction will never be null,
becauſe let the horizontal velocity be ever fo great,
TE
?
as
ROYAL ACADEMY of SCIENCES. 197
as it cannot but be finite and determined, that
of the vertical motion of the weight is always
fomething with regard to it.
The more quick a body moves in a fluid, the
more parts it meets, the multitude of which is a
greater obftacle; and on the contrary the more
quick a body moves upon a very hard body, the
lefs it is engaged in the intervals of its parts, and
confequently is lefs detained by them.
XI. On the bodies which fwim in liquors.
It is well known, that a body of the fame
fpecific gravity with a liquid in which it is im-
merged, remains in whatfoever place it is put;
but if it is lighter than the liquid, it ſwims upon
it, having one part immerged more or lefs, ac-
cording to the proportion of its gravity, to that
of the liquid, and if it is heavier, it goes to the
bottom. All mathematicians have demonſtrated
the neceffity of thefe effects.
་
This is only with regard to the place of a
body in a liquid, but the fituation of this body
in the fame liquid, is different from the place
which it there occupies. For example, a ſphere
which there makes a half turn upon its centre,
would change its fituation, becauſe the upper
part would become the lower, but it would not
change its place.
1.
Let us imagine a body compofed of two dif
ferent parts immerged in water, one lighter, and
the other heavier than the water, as of wood and
lead, fuppofe alfo the quantity of theſe two parts
fo proportioned, that the whole together weighs
exactly as much as an equal bulk of water. Ima-
gine laftly the body to be ſpherical. It is plain
that more than the fphere will be wood.
This
198 The HISTORY and MEMOIRS of the
}
}
This body will have two centres; one, its
centre of figure and extent, that is, the point
of the middle of the fphere: the other, its cen-
tre of gravity, that is, the point of a horizontal
diameter by which it fhould be fufpended, that
the two parts of wood and lead, of unequal
weight, may remain in equilibrio. Now we
know that to put them in equilibrio the point
of fupport, or which is the fame thing, the cen-
tre of gravity, muſt be neareſt to the heavieft,
and confequently the centre of gravity of this
fphere, heterogeneous in its parts would be more
toward the fide of the lead, and would not be
the fame point with the centre of the figure.
1
This fphere being immerged in water, fo that
its centre of gravity be above it, it is afked
what will happen to it.
It is certain that a body which has liberty to
move itſelf, cannot reft till its centre of gravity
is funk as low as it is poffible. The centre of
gravity of the fphere, that is, the fphere itſelf
must then fink, fince it can.
On the other fide, fince it is of the fame fpe-
cific weight with the water, it ought neither to
rife nor fall, but remain exactly in the fame.
place where it was laid.
To reconcile thefe two things, M. Borelli in
his excellent treatife of the motion of animals,*
determines, that the ſphere will turn upon its cen-
tre of figure, until its centre of gravity be funk
to the lower part, and toward the earth, pro-
vided the body changes the fituation, and not
the place.
This decifion of fo great an author, and in
appearance fo convincing, has not however
feemed fo to M. Parent and he has not been
*Part I. Cap. 3. Prop. 207.
$
afraid
ROYAL ACADEMY of SCIENCES. 199
afraid to advance this paradox; that the body,
notwithſtanding the equality of its fpecific weight
with that of the water, would defcend to a cer-
tain point, and what will appear yet more fur-
prizing, that the figure of the body would rife,
while the body it felf deſcended.
That two equal forces, acting by lines parallel
to each other, draw a rod by one end two oppo-
fite ways, is certain, fince we do not fuppofe
any fixed point of this rod, that it will turn upon
one of its points, and that this point will be the
middle, becauſe theſe two oppofite forces are
equal. If they were not, it would turn upon ano-
ther point, as much nearer the greater force, as
this greater force fhould exceed the other.
The ſphere immerged in water is driven down-
ward by its own weight, of which all the action.
is united again in the centre of gravity. It is at
the fame time driven upward, by the weight of
a bulk of water equal to it, which always endea-
vours to defcend, and take its place, and all the
action of this equal body of water, muſt be con-
ceived as reunited in the centre of figure of the
ſphere; for we are confidering the extent of the
bulk, and it is this which determines the quantity
of water of which we are confidering the action.
Here are two oppofite forces which act parallel,
as theſe are two weights, they are equal by the
fuppofition, they are applied at two different
points taken on the fame diameter of the ſphere.
The ſphere therefore muft turn upon a middle
point, between thefe two, and it muſt be equally
diſtant from them.
As the centre of gravity of the fphere had
been placed above, it cannot turn upon this
middle point, without the centre of gravity
defcending, and at laft when it has defcended to
+
the
200 The HISTORY and MEMOIRS of the
the vertical line, its action ceaſes becauſe it
cannot defcend any more, and the ſphere ftops.
On the other fide, it is plain, that in this dif
pofition the centre of the figure which was below
the centre of gravity, rofe, and from thence M.
Parent concludes, that the body, which is confi-
dered as entirely gathered together in its centre
of gravity, defcended, while the figure of the fame
body rofe.
The ſpherical figure was only taken for an ex-
ample, and it is clear, that the fame reafoning
fubfifts with all other figures.
It fubfifts again when the two forces are une-
qual.
If the weight of the heterogeneous body im-
merged in water, is greater than that of an equal
bulk of water, and its centre of gravity has been
placed above, not only this body muft immerge
itſelf in the liquid, but it muſt make a half turn
in immerging, becauſe its centre of gravity muft
defcend as low as is poffible; after which the body
continues to immerge, but without turning any
more. It turns round upon a point which is not
equally diſtant from the centres of gravity and of
figure, becauſe the two forces which are applied
to it are unequal.
Hence it comes, that cats, and many other
animals of the fame kind, as martins, pole-cats,
foxes, tigers, &c. when they fall from a high
place, generally fall upon their feet, altho' at
firſt they were uppermoft, and confequently they
fhould have falled upon their heads. It is very
certain, they could not turn themſelves thus of
their own accord in the air, where they have no
fixed point to help themſelves. But the fear with
which they are ſeized makes them bend the ſpine
of their back, fo that their entrails are driven
upwards
ROYAL ACADEMY of SCIENCES. 201
upwards at the ſame time they ſtretch out the head
and legs toward the place from whence they-
are fallen, as if to find it again, which gives to
thefe parts a greater action to raiſe themfelves.
Thus their centre of gravity comes to be different
from the centre of figure, and placed above it,
from whence it follows by the demonftration of
M. Parent, that theſe animals muft make a half
turn in the air, and turn their legs again down-
wards, which commonly faves their lives. The
niceft knowledge of mechanicks would not do bet-
ter on this occafion, than this confufed and blind
fenſe of fear does.
If the weight of the body is lefs than that of the
water, only one part will be immerged, and we
muft confider only the part immerged as a centre
of figure, becauſe it is that alone which tries and
receives the action of the water, one of the two
unequal and oppofite forces. As for the centre
of gravity, it is always that of the entire body,
becauſe it is always the whole weight that acts.
After this, it is eafy to judge by what has been
faid how it turns round.
While the body makes its half turn, if we ſup-
poſe the centre of turning fixed, as it is naturally
and by itſelf, the part immerged in the water will
be always equal, if this body be a ſphere; but if
it be of any other figure, the action of turning
will cauſe this part immerged to be fometimes
greater and fometimes lefs. On the other fide,
the equilibrium of the body with a certain deter-
minate bulk of water requires, that its part im-
merged fhould always fill the place of it, which
is always of the fame fize. Thus the action of
turning round appears contrary to what the equi-
librium would, but what fettles all is, that when by
the turning round the part immerged is too little,
VOL. I. No. 6.
C c
this
202 The HISTORY and MEMOIRS of the
this equilibrium makes the body fink more, and
confequently its centre of turning defcends in a
vertical line. If the part immerged be too great,
the body raiſes itſelf, and alfo its centre of turn-
ing.
It is manifeft, that in both thefe motions, the
centre of the whole figure rifes or falls in a right
line, and at the fame time turns circularly, and
confequently deſcribes a cycloid, for it is formed
by a direct and circular motion mixed in this
manner.
To theſe proofs, which fhew plainly enough
that in all theſe cafes the bodies turn, not upon
their centre of figure, but on a mean point be-
tween this centre and that of gravity, M. Parent
adds another, as convincing, but falling into a
greater geometrical difcuffion. The principle is,
that the common centre of gravity, both of the
liquid and of the body immerged, muſt always
be as low as is poffible, after which M. Parent
demonſtrates, that it has this ſituation only in his
ſyſtem.
He finds by the fame ways, what fituation
heterogeneous bodies immerged at the fame time.
in feveral liquors of different weights, muft take.
The principals do not change at all, but the ap-
plication of them becomes more difficult.
The different figures which we may imagine
of this body, throw alfo this problem into a greater
detail of geometry; Archimedes has refolved it
for the right paraboloid placed only in a liquid.
But M. Parent refolves it for all the conoids fitu-
ated in ever ſo many liquors.
XII.
ROYAL ACADEMY of SCIENCES. 203
XII. A falſe report of the perpetual motion
being difcovered, and the impoffibility of it
demonftrated.
There was in this year a report ſpread, that the
perpetual motion was found. It was feen in a
place where the difficulty of the thing was not
well known, where the invention was not ex-
amined, as it would have been in an academy,
where an air of ſcience fucceeds fometimes, and
the air of confidence almoſt always. M. Sauveur
explained the invention to the academy, who
were very much furprized at it. A little while
after the noiſe that this difcovery made, the per-
petual motion difappeared with its author. On
this occafion, M. Parent proved the impoffibi-
lity of it by this fingle reaſon, that all the
parts
of a machine have a common centre of gravity,
that while they turn round an axis or fixed point,
which ever it be, this common centre of gravity
finds itſelf neceffarily in one fituation, where it is
lower than in any other, and that preſently all
muſt ſtop. For fince there is a point where the
force, which many bodies have to defcend, is
entirely reunited, as foon as this point cannot de-
ſcend any more, all theſe bodies must remain
fixed. M. Parent determined in general, that
there must inevitably be this point of reft for all
the machines poffible,
Cc 2
ΑΝ
;
A N
ABRIDGMENT
OF THE
PHILOSOPHICAL MEMOIRS of the ROYAL
ACADEMY of SCIENCES at Paris for
the year 1700.
1. An obfervation on the barometer, ther-
mometer, and quantity of rain and fnow-
water, that fell at Paris in the royal ob-
fervatory, during the year 1699.
year 1699. By M.
de la Hire *
AH E obfervations on the quantity of rain
THE
water which fell in the obfervatory, have
been made in the fame manner with thoſe of the
preceding years. For this purpoſe, they placed
in the open tower a veffel of tin, whofe furface
was 4 feet, and which was furrounded with a
rim 6 inches high. This veffel is a little bent
near one of its angles, where there is a little hole
with an end of a pipe, which conveys all the wa
ter which falls in the veffel, into an earthen pot
placed underneath; and as foon as it has rained,
great care is taken to meaſure exactly all the wa-
ter which is gathered in this earthen veffel, of
which a particular regiſter is kept. This mea-
fure is made in a little veffel of a cubical figure,
whoſe fides were three inches, ſo that 32 lines
heighth of water in this little veffel, are anfwer-
able to half a line's heighth on the furface of the
great tin veffel wherefore there is drawn near
the brim of this cubical veffel, which has no
* Jan. 16. 1700.
+
cover
ROYAL ACADEMY of SCIENCES. 205
cover, a line within 4 lines diſtance of the brim,
that in filling this little veffel to the height of this
line, there may be the value of half a line's
heighth of the water which falls. This is the
ftate of what fell in each month of this year.
Jan.
Feb.
Lines.
11 /
Lines.
Mar.
I I
11
I I
I
July
Aug.
I I
I
Apr.
36
Sept.
Octob.
3-
5 2
May
June
22 +
Nov.
18 21/20
35
12
9
29 4
Dec.
15 A
~+~+~+
1
+
The fum of the height of the water which fell in
the whole year, is 224 lines, or 18 inches 8 7.4
Though this year appeared to be extremely dry,
we ſee nevertheleſs that the quantity of rain-wa-
ter is but little lefs than what falls in the mean
years but it muſt be obſerved, that commonly
the greateſt rains happen in the months of July
and August; whereas this year they happened in
the months of April, May, June, and September;
and that the greateſt did not exceed 36 lines in a
month, which is but little in compariſon of what
frequently falls in fummer. But, in fhort, the
three firſt months and the three laft of this year
together, have only given very near as much as
the months of April and of September together.
We may obferve, that the moft plentiful rains
this year happened in one and the fame day, and
were not continual, and that very confiderable
intervals of time paffed without rain.
As to the barometer, which is placed at the
top of the great hall of the obfervatory, and
near 20 toifes above the river, the greateſt height
of the quickfilver therein was but 28 inches 3
lines,
3
206 The HISTORY and MEMOIRS of the
lines, the 21 of Nov. and the 31 of December;
and its loweſt was but 26 inches 9 lines, on the
14 of Jan. and the 14 of December; and con-
fequently the difference of the heights of the quick-
filver between the greateſt and leaft height was 18
lines.
The thermometer, which I uſe to make obfer-
vations of heat and cold, is placed in the E. tower
of the obfervatory, which is uncovered in fuch a
manner as to be fheltered from the wind, and
that the fun never fhines either on the ball nor on
the tube. All the obfervations which I daily
make are a little before fun-rifing, which is the
time wherein the air is commonly the moſt cool.
I have made obfervations on this thermometer to
determine its mean height, and after having left
it fome days in the bottom of the cave of the ob-
fervatory, I found that the ſpirit of wine therein
remained at the height of 38 parts, which I take
for a mean height; fo that when it is of this
height in a place where it is expofed, I judge
that the temper of the air is between cold and
hot. I have found that during this year from
the first day of Jan. to the 5th of June, there has
but little variation happened in the height of the
liquor, and that theſe two days it was the fame.
from 42 to 43 parts, and that it froze very little,
and that only in the beginning of Feb. the ther-
mometer not falling lower than 29 parts, which
is commonly the time when it is moft cold, as
the greateſt heat happens at the beginning of
July. But the 11 of Dec. the thermometer fell
to 25 parts, which was the coldeft of the year;
and the 25th of July, which was the hotteft, the
thermometer rofe to 63 parts: by which we
fee that the heat of the fummer, compared to the
mean ftate of the air, was near double the cold.
compared
ROYAL ACADEMY of SCIENCES. 207
compared even with this mean ftate, though the
obfervation of the heat of the air was made only
before the fun-rifing.
I alſo obſerved the 23d day of Ocher the
declination of the needle to be 8° 10' in the fame
place, and with the fame needle with which I
uſed to obferve. This needle is 8 inches long,
and is one of the beſt which was ever made;
but though it was very lightly hung, I do not
find in the obfervations of the fubfequent years,
the fame progreffion of declination; whether it
be that the declination does not keep an equal
motion, or that there may be any other caufe of
irregularity, which may alſo proceed from the ob-
fervation, though I ufe all the precautions I am ca-
pable of: but it is always difficult to obferve the
minutes on an inftrument, whofe degree is but
one line at the moft; it will be much more diffi-
cult to obferve them, when the degree has but
half a line, fuch as are the common compaffes of
three or four inches diameter. All that can be
done in this caſe, is to take a long ſeries of obſer-
vations, as of ten or twelve years, made with
the fame needle, and in the fame place, and di-
vide the difference by the number of years, and
then they muſt be alfo certain, that the declination
does not either diminiſh or increafe. Example.
At the end of the year 1686, I found that the
declination of the needle was 4°. 30′ towards the
W, and that at the end of last year 1699, it
was 8°. 10', -and confequently the diffe-
rence was 3°. 40'. or 220'. for 13 years, which
gives for each year 17. motion from N to W.
II.
Jean Bemontli
1700
208 The HISTORY and MEMOIRS of the
II. A new manner of rendering barometers
luminous, by M. Bernoully, profeffor at
Groninguen, extracted from one of his
letters written from Groninguen, June
19, 1707.
After having read in a little book, entitled, A
treatiſe of barometers and notiometers, or hygro-
meters, the extraordinary phænomenon which hap-
pened in 1675, to the barometer of the late
M. Picard, which was that interrupted light
which he perceived by chance in the motion of
the quickfilver, by carrying the barometer from
one place to another, when it was very dark, I
judged it worthy to make fome reflections upon
it; and the more, becauſe the author of this
treatiſe, invites the curious to perfect this difco-
very; and fays, that in thofe experiments which
have been already made of it, on many other
barometers, to fee if the fame thing would happen,
there was but one found which came near that of
M. Picard: probably it might be that of M.
Caffini, in which M. du Hamel fays there had
been obſerved the fame effect, tho' lefs vifible than
in the other. I have therefore applyed my felf
to it; and after having made fome obfervations
on this fubject, accompanied with, neceffary ex-
periments, the fuccefs of which anſwered to my
defires, and conformable to the reaſoning which
I had made à priori, I feem to have diſcovered
the true caufe of this phenomenon, and a way of
making a very lively light appear in all barome-
ters without diftinction, at all times and in all
places: fo that here is a new kind of perpe-
tual Phosphorus, which does not confume like
thofe made by the chymifts.
Before
ROYAL ACADEMY of SCIENCES. 209
Before I explain my reafoning to you, I will
tell you that the fame evening on which I read
this phenomenon in this little treatife, I would
make a tryal of it on my barometer, which had
been tried about a month: I carried it then into the
dark, I balanced it lightly at firft, but without
any fuccefs, not obferving in it the leaft light:
but at last having balanced it violently (which I
can do without danger of breaking the tube or
fpilling the quickfilver, the tube being fet in a
piece of wood, as in a frame, and the quick-
filver at the bottom fhut up in a wooden box
fixed to the board, and cloſe every where, fo that
it is only through the pores of the wood, that the
air enters to prefs upon the quickfilver) I obfer-
ved that when the quickfilver (rifing and falling
with great quickneſs through a long part of the
tube) was quite at the bottom, it caft a very
weak light, which vaniſhed as ſoon as the quick
filver began to re-aſcend. This made me think, that
thofe conjectures which the author of the treatife
alledges, to give the reafon why this light had
not yet appeared in any but in one barometer
only, which was, that as to the others, they had
not perhaps been long enough tried, could have
no weight, fince my barometer had been tried
but four weeks or thereabouts.
After this experiment, I would try, whether
the other conjectures of the author were to be
admitted: he fays, that the other barometers
had not the fame effect, whether it was that
they were not fufficiently cleared of the air, or
that the quickfilver was not pure enough. To
be certain of this, atter having carefully cleaned
the quickfilver, by forcing it to pafs through the
pares of a bit of leather, I put it again into the
receiver, from which I drew out the air, and left
VOL. I. No. 6.
D d
it
210 The HISTORY and MEMOIRS of the
par-
it therein 24 hours, to give it time to let the
ticles of air which were mixed with the quick-
filver evaporate. After having thus purified it, I
filled a tube with it in the common manner, with
all the precaution poffible to hinder any fmall
bubbles of air from remaining; but the baro-
meter thus mounted had not any better effect, for
let me balance the quickfilver never fo violently,
hardly could I draw that weak glimmering which
fhewed it felf, and vanifhed away almoft in the
fame inſtant.
:
A
ť
I left the barometer in this ftate for common
ufe, having thought it a pity to take it to pieces,
after having taken fo much trouble and care in
putting it together fo exactly, that I am certain,
neither in the empty part of the tube, nor among
the quickfilver, there was not the leaft particle of
grols air.
I then concluded from this fecond experiment,
that the other conjectures of the author of the
treatiſe, were no more valid than this; or at
leaft, that neither the purifying of the quick-
filver, nor the perfect vacuum of the upper part
of the tube, were the principal caufe of the ap-
pearance of this light.
I therefore fought for the true cauſe of it, and
thus I reafoned. As the light does not appear
every time that it is balanced, but when the va
cuum is made, that is, only in the defcent of the
quick filver, I comprehended that when the quick-
filver defcends there must go out of it, and reaf
cend at the fame inftant, a very thin and fubtile
matter to occupy, and fill part of that ſpace of the
tube, which the quickfilver leaves I fay a part,
becauſe we may well believe, that the pores of the
glais being without doubt larger than thofe of the
quickfilver (as it appears by the lightneſs of the
{
one,
1
ROYAL ACADEMY of SCIENCES. 211
L
one, and the great heaviness of the other) there
enters at the fame time thro' the pores of the
tube, another matter much more fubtile than the
grofs air, but much lefs fo than that which goes
out of the quickfilver and thefe two matters
mixing together immediately, fill the space which
the quickfilver by its defcent leaves to them; it
is of no confequence what names you give to
theſe two matters: you may if you pleafe, call
with M. Descartes, that which penetrates through
the pores of the tube, the matter of the fecond
element, or celeftial, globules; and, that which
is fo fine, that it efcapes from the quickfilver,
the matter of the first element.. In effect, M.
Defcartes has well enough fhewn in his principles
of philofophy, part the 4th art. 58. that the
particles of quickfilver leave among them fuch
acute angles, that they cannot be filled except by
the fineſt matter, that is, by that of the firft
element.
#t
10 201
Now you know how M. Defcartes explains
the production of light,, making it confift in the
moſt rapid motion of the matter of the firft ele-
ment, affembled only in fome fpace, and in the
effort which it makes on the celeftial globules. I
fay, therefore, that while the particles of the firſt
element are diſperfed in theſe little interſtices, and
parts
in a manner opprefs'd by the terreſtrial of
the quickfilver, they cannot acquire this rapid
motion, or act or make joint efforts to produce
the light, but as foon as by the defcent of the
quickfilver, theſe go plentifully out of it, they
unite together; and being thus at once difengaged
from all other matter, they take that rapid
courfe, which is common to them when they are
free; and by the effort, which they make on the
celeftial globules which meet them, they produce
Dd 2
#
this
212 The HISTORY and MEMOIRS of the
A
this light; from thence the reafon is feen why
this light is only obferved in the defcent of the
quickfilver . for when it rettfcends, the matter of
the firft barnent is fo far from going out, that
there rather enters again, apart of that which
went out at yes preceding fall; and the rest is
abits
driven away with the celeftial globules, out of
the tube, through the pores of the glass. This is
alfo the reaſon why this light always accompa-
nies the top of the defcending quickfilver, and is
in a manner fixed to its upper furface; why the
light produced in a defcent is not lafling; and
why on the finishing of cach defcent, this light
is at an end, and immediately vanishes alfo.
This proceeds from the particles of the firft
element, which were united at the going out
of the quickfilver, and having made a very lit-
the way in getting diftant from the furface of the
quickfilver, being immediately fcatter'd and dif
perfed by the crowd of celeftial globules, which
with their impetuofity bear them down, and thus
take from them the force of producing this effect
of light fo that it cannot laft but in proportion,
as there comes out of the quickfilver a continual
and new matter of the firft element, to fucceed
that which is alfo continually wafting, not much
unlike the fame manner which a flame of a
candle waeg and rettews each moment. It is
therefore manifefty that the light in queftion can-
not at the moſt laft any longer than each defcent
of the quickfilver lafts.
1
"i
A
$
I muſt now fhew the principal, which is,
why this light does not fhew it felf in all barome-
ters and why it has not been obſerved till now
except in two or three as alfo, the way of reme-
dying this, and making it infallibly appear in
all barometers at all times, and with a furprizing
vivacity,
2
ROYAL ACADEMY of SCIENCES. 213
vivacity, provided they do it in a very dark place,
both theſe will ſtrengthen and confirm perfectly
well the reaſons which I have made ufe of in
the explanation which I have juft made of the
caufe of this phenomenon.
Α
I have obferved, that if we expofe quickfilver
in any veffel to the open air, we fhall find at
the end of fome time. the furface, where the air
touches it, quite difturbed and covered with a
very thin pellicle, which being taken away with
a clean feather, the primitive brightneſs returns
on the furface, and it will be again poliſhed like
a looking-glats; but if we leave the quickfilver
expoſed to the air, another pellice immediately
like a cobweb, which thickens by time, will fpread
over it. And if this is well examined with the
microſcope, we fhall fee that it very much refem-
bles leaf filver: and indeed, it is nothing but a
very fine texture of a kind of mofs or moffy
hair, which is formed of little filaments, which
having been feparated from the quickfilver, by
the continual agitation of the air, and yet being
not able to follow its motion, fall again with
other impurities which it finds in the air, on the
furface of the quickfilver; and intermingling by
degrees, compoſe this pellicle. We obferve the
fame thing in all kinds of liquors, which, if we
let them ftand, fo that the air may dry the top of
them, will at laſt be covered with a ſkin more
or lefs thick, according to the conftitution of the
corpufcles, which exhale from, and afterwards
fall back on the liquors. All this being well
confidered, I fay, that it is this pellicle which hin-
ders the appearing of the light in thofe barome-
ters, which have been filled in the common man-
ner. In this manner I conceive the thing. When
they make the barometer, they take a tube her-
metrically
214 The HISTORY and MEMOIRS of the
{
:
}
fealed at one end, and into the other they pour
quickfilver, which falls drop by drop along the
tube, fo that each drop by penetrating and di-
viding the air from the top to the bottom,
wipes it, if I may fo fay, and draws away with
it all the impurities; which is the cauſe that in
this moment employed in running along the
tube, the quickfilver is more loaded with this
mofs, than it would be in two or three days, if
fimply expofed to the air. What I have here
faid is fo true, that if you let only one drop of
quickfilver, cleanted and purifyed as much as
poffible, fall from the height of one foot only
into a veffel, wherein there is more of it, which
has alſo been fo well purified that the furface
thereof is fmooth, and polifhed like a looking-
glafs; you fhall fee that the drop falling on this
poliſhed ſurface, will obfcure the luftre of it
in that part where it fhall enter into the mafs of
the quickfilver, and leave there a viſible ſpot, which
is a certain mark that the drop, clean as it was,
had been infected by the impurity of the air.
It is thus that the drops of quickfilver poured
into the tube, while they are running are covered
with this pellicle; but by the fall of the drops
one upon another, and by the preffure of the
quickfilver, thefe particular pellicles easily break
to permit a continuity in the quickfilver; and
thefe impurities not being able to agree with the
motions, nor with the figure of the particles of
the quickfilver, are obliged, as excrements, to
retire out of the inner fubftance of the quick-
filver, and place themſelves on every fide between
the concave furface of the tube and the convex of
the quickfilver. Thus then is the whole mer-
curial column involved in this very thin ſkin as
with a cuticle. Surely, there is great appearance
:
2
that
ROYAL ACADEMY of SCIENCES. 215
that the thing is, as I have faid; for the tube be-
ing filled in this manner, if it is inverted to make
the barometer by ftopping the aperture with the
end of the fingen, till it is immerged in the
quickfilver contained in the veffel; it will be
obferved by taking away the finger, that the
quickfilver defcending in the rube, will leave be-
hind fome remains of this cuticle adhering to the
fides of the glafs on the empty parts of the tube,
like the fcum of melted lead.
It is not therefore difficult to conceive, that the
barometer being made, the horizontal and upper
furface of the mercurial cylinder may be covered
with a thicker palliole than any other part of the
furface of this cylinder, becauſe it thickens partly
by thoſe remainders which may continue ad-
hered to the empty part of the tube, and which
are at the laſt laofened; and fall again on the top
of the mercurial columns and partly by thofe
which are below and are thruft up by the weight
of the quickfilversport
}
Therefore, for a laft conclufion, it is fufficient
for me to fay, that this pellicle which occupies
the upper part of the quickfilver, as thin as it ap-
pears to our eyes, covers fo well the pores of the
furface of the quickfilver, that it fhuts up either
wholly, or in a great part, the paffage to the
matter of the firft element, which by its violent
motion alone can produce light; whence it fol-
lows, that in barometers which are filled in the
common manner there will appear none, or very
little, and that with great balancings, as in mine,
which I have fpaken of above, it muſt not be
thought ſtrange that fo fmall and delicate a pel-
licle can hinder the particles of the firft cle-
ment from going out of the pores of the quick
filver, or at leaft from going out in fuch abon-
dance.
?
216 The HISTORY and MEMOIRS of the
[
dance, and with fo much vehemence; fince we
fee daily that the quick filver itfelf paffes eafily
through the pores of the fkin of almoſt all ani-
mals; but that the paffage fhould be entirely
clofed, if they do not feparate that tender web,
which the phyſicians call Epidermis, or Cuticula.
What contradiction is there then, that fuch a
thing may not happen in the ſubject we are
upon?
Thus have I reafoned on the cauſe of ſo ſtrange
an effect. But as we are very apt to be deceived
in reaſoning on phyfical fubjects, unless they are
confirmed by experiments, I have contrived two
ways of hindering the mercurial column from being
covered with this cuticle, both which have fuc-
ceeded very well.
1. I took a glafs tube 3 feet long, open at
both ends, which I took care to fcour and cleanſe
well on the infide, that I might leave therein
neither filth nor moisture, having plung'd one
end thereof a little way in quickfilver, contained
in a large veffel the moft obliquely that the rim of
the veffel would permit; fo that the angle which
the tube made with the horizon, contained about
18 or 20 degrees; which having done, I ap-
plied my mouth to the other end of the tube,
and began to fuck; in this manner, I eafily made
the quickfilver afcend to the top, and having even
drawn fome drops of it into my mouth, I made a
fign to one of my fcholars, whom I had inftructed
for this purpoſe, to ftop quickly with his finger
the lower end which was dipped in the quick-
filver. I muſt tell you here by the way, that I
finiſhed raiſing the quickfilver by what I fucked
with one breath alone, lett had I fetched my breath
and fucked again, there might have entered into
the tube a little breath or fpittle. The tube be-
ing
ROYAL ACADEMY of SCIENCES. 217
ing then filled in this manner, while my fcholar
held the lower end ftopped with his finger, I after-
wards cloſed the upper end with the cement, which
I make uſe of to confolidate broken cups or glaffes.
After having cloſed it well, I bid this fcholar
take away his finger from the end which was yet
dipped in the quickfilver; I then raiſed the tube
perpendicular, and the quickfilver defcended to
its equilibrium as ufual; but I had the pleaſure to
fee that it left no fcum adhering to the empty
part of the tube, as in tubes which are filled in
the common manner which I immediately took
for a good fign. Indeed I forefaw that this would
be the confequence; for in the manner with
which the tube had been filled, it is well feen
that the air could not touch the quickfilver in
aſcending in the tube, except at the first drop
which was a kind of fhield, by the help of which
all the remainder of the mercurial column could
aſcend without fuffering the leaſt approach of air;
but this one drop, befides that it could not be
much infected, having not divided and penetrated
the air with violence, like a drop which falls,
did not remain in the tube: for, as I have faid, I
drew fome of the firft drops of the quickfilver
into my mouth.
Thus was I fure of having a barometer whoſe
mercurial column was entirely diveſted of this cu-
ticle fo fatal to others. Mean while to make the
experiment more conveniently without running
the hazard of fpilling the quickfilver by the re-
moving or balancing of it, I took the tube out of
the large veffel, keeping the lower end of it clofed
with my finger, and put it into a narrower and
deeper veffel, which was half filled with quick-
filver; all being finiſhed, I impatiently waited for
night, which being come, I took my barometer
VOL. I. No.6.
E e
thus
218 The HISTORY and MEMOIRS of the
thus prepared, the tube in my left hand, and the
veffel in which the lower end of it was dipped in
my right hand; as foon as I was in the dark, I
already perceived, without having yet balanced
the barometer, very vivid lights, which were
cauſed by a little fhaking, impreffed on the mer-
curial column by the motion of removing it:
but when I began, tho' very gently, to balance
the barometer, that I might give to the quick-
filver a more confiderable reciprocation than it had
by the fole motion of removing it, there appeared
at each defcent fuch an exquifite light, that it il-
luminated the neareſt objects, in fuch a manner
that I could well enough difcern, by the help of
this light, letters of a moderate fize at a foot dif
tance. I own to you, that I was very much contented
to ſee the event anfwered fo well to my expecta-
tion, and fo much the more as it was an experi-
ment not made by chance, but a deliberate act
founded on the principles of my own reafoning.
I muſt alfo fay, that this light appeared fo eafily,
that the most infenfible balancings, which hardly
made the quickfilver rife and fall the thicknefs of
a knife, produced nevertheleſs the most vivid
lights. The following days I repeated this ex-
periment with 3 or 4 other tubes, which I filled
in the fame manner; but all performed their ef
fect equally with much vivacity, and never failed;
which makes me boldly advance, that all baro-
meters thus prepared as I have faid, will fhew
at all times the phænomenon, which happened in
that of M. Picard, and perhaps much more vi-
gorously
}
The fecond way which I contrived to fill the
tube with quickfilver, without the mercurial co-
Jumn being covered with the abovefaid pellicle,
was this in few words. I took a very clean tube,
I
open
ROYAL ACADEMY of SCIENCES. 219
open at one end only, which I plunged into quick-
filver contained in a veffel, which I erected per-
pendicularly; fo that there was yet nothing but air
in the tube. To draw the air out of the tube, I
covered the tube and the veffel in which the open
end of the tube was dipped, with a glafs receiver
made in the form of a bell, the top of which
was extended into a long tail hollow on the infide,
to contain the tube, as the fheath contains the
blade of the fword (this receiver is made pur-
pofely to make thefe forts of experiments with the
barometer.) I then applied the receiver with the
tube, and the veffel within it on the copper plate of
the air-pump; by means of which I drew the air
out of the receiver, and thus at the fame time out
of the tube, which not being able to go out by
the upper end which was ftopped, went out with
a little bubbling thro' the end which was dipped
in the quickfilver. After having drawn the air
from the receiver and from the tube, the moſt
exactly I could poffibly, I let it again enter into
the receiver; but being not able to make it again
enter into the tube, becaufe of the qnickſilver in
the veffel which hindered it, by its preffure it
thruft the quickfilver into the tube to the height
of 24 or 25 inches; fo that it wanted but little
of afcending to the common height of the baro-
meter; which fhewed that the air had been with
care enough drawn out of the receiver. The
quickfilver being thus raifed, I judged that it
muſt be quite ſtripped of its cuticle, fince the very
top of the mercurial column could not touch the
air, except by that little which remained in the
tube, but which by reafon of its extreme rarefac-
tion, could not alter the top of the quickfilver,
and much leſs the remainder of the mercurial co
lumn, the leaft part of which had not been ex-
}
Eez
P
pofed
i.
220 The HISTORY and MEMOIRS of the
poſed to the air in afcending. In effect, when I
made the experiment the night following, the
light appeared in this tube with the fame ftrength,
and in like manner as in the other which had
been prepared in the preceding method. By
which may be alfo feen, that the air which re-
mained in the empty part of the tube could not at
all hinder the light from appearing; and thus,
if it does not appear in the barometers filled in the
common manner, it is not becauſe they are not
cleanfed from the air, but only becauſe the quick-
filver contained in the tube is fo wrapped up in
this pellicle, as to stop the paffage of the matter
of the first element.
A
Mean while I have found by experience, that
there is nothing fo prejudicial to the appearing
of this light, as humidity; for after having con-
tinued fome weeks to balance every evening one
of theſe barometers prepared according to the first
method, to ſee if there was any difference, either
in the vivacity, or in other circumftances; and
being not able to obferve the leaft difference to
my great fatisfaction, I contrived to pour a little.
water into the veffel below, to cover therewith
the furface of the quickfilver contained therein,
and then I lifted up the tube gently, till the
lower end coming out of the quickfilver in the
veffel reached the water; but as foon as a few
drops of water were entered into the tube, I
dipped it again into the quickfilver, and thefe
drops afcending to the top, covered the fummit
of the mercurial column. I was then curious to fee
if this little water would not hinder the appearance
of the light, and indeed it hindered it fo much,
that with the moſt violent balancings, there was
no way to produce the leaft trace of light. I
after that tried the fame thing with rectified fpirit
of
I
ROYAL ACADEMY of SCIENCES. 221
J
of wine, thinking that being of itſelf inflammable,
it would perhaps rather help to produce our light
then to deftroy it: but in vain; for a few drops
of ſpirit of wine had no fooner occupied the fum-
mit of the mercurial column, but the light which
had before appeared with all poffible vivacity at
the leaſt ſhaking of the tube, ceafed to appear
even with the greateft balancing: from whence
I conclude, that all moisture and heterogeneous
matter may either ftop the pores of the quick-
filver, and hinder the violent motion of the mat-
ter of the firſt element, as the pellicle does; or
at least partly ftop the great rapidity with which
the firſt element ought to be moved in order to
excite the light for it is vifible, that a foreign
matter occupying already a little fpace, directly
above the mercurial column, where the matter of
the firſt element is to affemble, it is, I fay, vi-
fible, that it cannot move in conjunction, nor
confequently with the rapidity which is common.
to it when it is alone, without paffing through
the pores of a groffer matter.
III. Remarks on the construction of pendulum
clocks, by M. de la Hire *.
Altho' it does not feem poffible to add any
thing to the conftruction of the great pendulum
clocks as they are at prefent, to make them more
perfect and juft in the meaſure of time; yet we
may make fome remarks, which may ferve to
correct fome inequalities that are found in them.
Firſt, it feems that the rod of the pendulum
might be fufpended to a little fine fpring inſtead
of filk, to avoid the inconveniencies which hap-
pen to the filk, as of its lengthening by the
*
May 22, 1700.
heaviness
222 The HISTORY and MEMOIRS of the
heaviness of the weight, which is hung to it, and
chiefly when the weather is dry; and on the con-
trary, of its ſhortening when the weather is moiſt,
as it is with all threads and ftrings compofed of
many threads twiſted together: for the ſhortening
or lengthening of the filk, fhortening or ftretching
out the length of the pendulum, will make the
clock go fafter or flower. We might alſo add,
that at each vibration, the filk makes a little twiſt
at the place where it is tied to the rod of the pen-
dulum, by the effort which the fourchette makes
to entertain the motion of the pendulum. But
the experiment which I have made for fome years,
of a ſpring applied to the rod of the pendulum
inftead of filk, has convinced me, that there are
more confiderable irregularities with that than
with the filk, which I can attribute only to the
different alterations of the fpring by cold and
heat, which making elaftic bodies more or lefs
ftiff, cauſe in them very confiderable alterations;
for the ſtiffer a ſpring is, the more frequent vi-
brations it makes; on the contrary, when it is
limber, it makes them flower. I was then obliged
to take from a great pendulum of feconds, the
fpring which fupports the rod of the pendulum, to
put a filk to it, and I did not afterwards find all
the irregularities which I had obferved before,
which convinced me entirely, that theſe inequalities
were caufed only by the fpring.
Secondly, I confidered, that if in the pendulum
of half feconds, when the irregularities were not
fenfible, the little fpring * A was fixed very faft
to the rod of the pendulum, thefe forts of clocks
might be rendered more portable than they com-
monly are with filk, in long voyages by fea,
which may perhaps be of ufe in the knowing of
+ Plate XIV. Fig. 1
the
ROYAL ACADEMY of SCIENCES. 223
the longitudes; for in the common motion of a
veffel, the pendulum fupports itſelf, and will not be
fo much interrupted in its vibrations as when it is
only fufpended by a filk.
But if inſtead of a fpring A, which is applyed
by its breadth according to the length of the
arbor, the pendulum was fufpended to a ſtiff and
firm rod, the breadth of which fhould cut the
axis of the arbor perpendicularly, and it fhould be
ſtopped by the arbor, then the motion of the pendu-
lum would entirely govern the motion of the clock.
*
In ſhort, if in the pendulums of feconds, to
avoid the accidents of the filk and the fprings,
the pendulum was fufpended, as I have juft faid,
to a firm and ftiff rod, which was engaged and
held faſt in a little particular arbor A, which
moves itſelf freely upon its pivots, the arbor of
the pallet which would bear the fourchette, would
give the motion to the pendulum by the means
of this fourchette, which being governed by the
vibrations of the pendulum, would rectify the
motion of the clock. I am perfuaded that this
manner of applying the pendulum to the clocks,
will be better than thofe which are in ufe. The
axis of the pivot A muſt be in the fame right
line, with that of the arbor which bears the pal-
let to avoid the friction of the fourchette, along
the rod of the pendulum, which muft neceffarily
happen to the pendulums, which have cycloids;
and this friction caufes a confiderable inequality
in the motion of the pendulum, when the oil
in this place thickens, or it gathers a little ruft.
It might be objected, that the vibrations of the
pendulum, which might be of unequal lengths,
would not be reduced all to equality, there be-
ing no cycloid in this conftruction. To this I
anfwer
Fig. 2.
1
!
224 The HISTORY and MEMOIRS of the
anſwer, that thoſe who have a great while ma-
naged with care the great pendulum clocks, know
well that theſe vibrations are fo equal, that they
have no need of cycloids, and eſpecially if theſe
vibrations are not of a long extent: but when we
would have regard to the inequalities of the vi-
brations of the pendulum in this conftruction, I
fhall explain hereafter the manner in which they
muſt be corrcted.
Some pendulums have been made, the four-
chette of which was placed above the pallets,
and met the rod of the pendulum below the
weight of the pendulum, in a part of the rod
which paffes beyond the weight: but this con-
ftruction is faulty, and cannot ferve for great
clocks to make obfervations; for the vibrations
being very fhort, the weight of the pendulum
has but little motion, and it may be ftopped and
turned very eaſily by a very weak power; thus
the unequal motions of the fourchette, communi-
cating with the motions of the pendulum, it cannot
be rectified, nor the clock be juft, as fome of
our academicians then obferved, in comparing
thefe clocks with thofe we commonly uſe. But
after the great clocks, which ſerve for celeſtial
obſervations, were reduced to a point of per-
fection, to which one would not have believed
they could ever arrive, fince we often' fee for
ſeveral days together, that they do not vary from
the equal motion which they mark, one fingle
fecond of time; there only wanted to be found
the invention of reducing to a regularity, thofe
which are commonly carried in the pocket; and
to regulate the motion of the balance, which is
generally very unequal, a way was thought on to
apply a little fpring, which in bending and un-
bending might rectify the motions of it. This
principle
ROYAL ACADEMY of SCIENCES. 225
principle of regularity is founded upon this, that
the vibrations of the fprings put into motion aré
nearly equal; at leaft when thefe vibrations are
very near of equal extent.
At firſt they applied to thefe clocks a little
fpring quite ftrait, which being held faft by one
of its extremities, bore at the other extremity
which was free, a little fourchette which governed
one of the radii of the balance meeting it in a
mean diſtance from its centre; and by this means
the motion of the balance, was reduced to a fort
of equality by the regularity of the vibrations of
the fpring. But as the length of this little ſpring
could not be at moſt above of the diameter
of the watch, it muſt needs be extremely weak
to have its vibrations nearly equal to thofe of the
balance, and if it was fo weak, it could not re-
gulate the inequalities of the balance, which muft
make about four vibrations in a fecond of time.
They have therefore quitted this ftrait ſpring, to
ſubſtitute one of a ſpiral figure, which takes
but little room, tho' it is of a confiderable length.
The extremity the fartheft diftant from the eye
of this fpiral is held faft in two places to be there
fupported, and the other extremity toward the
eye, is alfo fixed in the arbor, which bears the
pallets and the balance, that the motion of the
fpring, which is entertained by the motion of the
balance, may at the fame time communicate its
regularities to it; but when we carefully examine
the motion of this balance regulated by the motion
of the fpiral plate, we perceive that there yet re-
mains a great deal of inequality in it, fo much
that the motions of the pallets acting against the
extremity of the fpiral plate, and there making
an effort in proportion to the length of the femi-
diameter of the arbor, at the place where this
VOL. I. N°. 6.
fpring
Ff
226 The HISTORY and MEMOIRS of the
fpring is engaged, they fubdue the fpring, which
yields and gives way to the inequality, becaufe
it is weak and flight, and cannot refift the mo-
tion of the balance; which is eafy to underſtand,
by what I have already explained above in fpeak-
ing of the great pendulums fufpended to a ſpring.
I then confidered that the motion of the fpring
muft neceffarily be applied at a distance fome-
thing confiderable from the centre of the balance,
to be able to govern its unequal motions with
more force, and not to receive the inequalities
of it. It was neceffary therefore to cut the fpi-
ral ſpring pretty far from the eye, and to apply a
little fourchette to this extremity, which was en-
gaged in one of the radii of the balance, at about
a quarter part from the circumference of the
centre; and the balance was to be placed in fuch
a manner, that when the fpiral is at reft, and not
conſtrained by the balance, the radius where the
fourchette is engaged, was already perpendicular
to the line traced by the point where the four-
chette is applied, when the fpring bends and
unbends, that the fourchette might have lefs
friction along the radius of the balance, as may
be ſeen in Fig. 3.
*But here is yet another way to apply a ſpring
to the balance of a common watch. This fpring
muft, be thin and broad as the common fpirals are,
but its figure is waving with the waves very
cloſe, by this means we have a great fpring
which takes up but little room in length, fo that
its vibrations may be flow, without filling a
great pace. The waves are formed according to
the breadth of the plate, which is placed upon
the third wheel, which makes it fupport its
great length eaſily; one might even give it much
Fig. 4.
xd
**
d
more
ROYAL ACADEMY of SCIENCES. 227
more breadth than to the common ſpirals, that it
may ſupport itſelf more eafily. I have proved
that theſe fort of fprings bent into waves, have
very great advantages above the other fprings,
in their being very foft, very long, and making
but little effort in each of their parts. They
have yet a very great advantage above the wire-
fprings, which have alfo length in a little ſpace,
in this, that thefe fprings in their prolongations
and contractions, cannot extend this fpire without
the wire of which they are compoſed, or made,
twifting or untwifting, which foon fpoils them in
a continued motion, which does not happen tò
the waved fprings, even when they are made
with a wire inſtead of a plate, as I have here
fuppofed.
To make application of this waved fpring to
the balance of the watch, it muſt be held faft by
one of its extremities.to the upper plate of the
watch, in the fame manner with the fpiral fprings;
and by the other extremity where the waves end,
it bears a little fourchette, which paffes into one
of the radii of the balance near a quarter part
of the diftance from the centre, as may be feen
in fig. 4.
As for the manner of fhortring for lengthening
this fpring, that it may make its vibrations ei-
ther longer or fhorter, it must be done as in the
fpiral fprings, by the means of a little bridle faft-
ened to a piece which runs in a groove, to draw
it nearer or farther from the place where the
fpring is fixed to the plate of the watch.
1
We may make this fpring long or short, ac
cording to themdmber aid fize of its waves, to
make its vibrations agree with the alternate moz
tion of the balanced for thefe two motions must
Fig. 4.
Ff 2
1
be
A
228 The HISTORY and MEMOIRS of the
be very nearly equal, that the one may entertain
the other more eaſily.
See now how we may rectify the motion of
the pendulum, when there is no filk to fuftain
it, and the rod which fuftains the pendulum is
held faſt in the pivot upon which it is moved, as
I have before propoſed.
Let * AB be the length of the pendulum,
from its point of ſuſpenſion A, to the centre
B the total weight, which I fuppofe to be that
of ofcillation, whofe motion must be made by a
cycloid, as M. Huygens has laid down. From
the centre B with the radius BA, I defcribe the
circle AD, and having bifed AB in E, I
draw EF perpendicular to AB, which may be
the baſe of a cycloid AGF, which has for a
diameter of its generating circle the magnitude
EA, which will be the axis of it.
Now let there be AH the curve defcribed by
the evolution of the cycloid, beginning the evo-
lution at the top A, and let there be the cycloid
BIF deſcribed by the evolution of the cycloid
AGF, beginning the evolution upon the bafe
at F.
I fay that the pivot, which must fuftain the
rod of the pendulum, muſt be hollow under the
circular figure AD, and that it must move upon
the convex part of the curve AH. I fay nothing
of the manner of applying this pivor, and that
which fupports it, for there is no difficulty in it,
and it does not fignify whether the concave part
rolls or flides upon the convex AH, fince the
point B will always be found in the cycloid BIF.
The demonftration of this conftruction depends
upon the nature of the curves defcribed by evo-
lution. For it is certain, that if the right line AB
* Fig. 5.
roils
ROYAL ACADEMY of SCIENCES. 229
rolls in applying itfelf upon the cycloid AGF,
its extremity B will defcribe the cycloid BIF, and
its extremity A the curve AH, and that this line
AB will be different in all its pofitions, as IGH
perpendicular on both fides to each curve BIF
and AH.
But when any point as D, of the circle AD,
fhall be applied upon the curve AH at the point.
H, the circle and the curve will touch in the fame
point H, and the line HGI drawn from this point
H for a tangent of the cycloid in G, being per-
pendicular to the curve AH and to the circle, will
be equal to BA by the defcribing of the circle;
and confequently the extremity I of this line will
agree with the point B, placed in I upon the cy-
cloid, altho' the rod AB is found in fome other
pofition, as AR; for it is no matter what point
D of the circle AD with refpect to the point A,
where the rod of the pendulum is applied, is
found in H upon the curve AH, fince all theſe
lines are radii of the fame circle.
But as this fort of hollow pivot may ſeem dif-
ficult to be excuted, I fay that it may be made
of an infinite number of different figures convex
or concave, and fuch as you will, which deter-
mines at the fame time the figure of the curve of
the hole, or fupport, on which it moves, which
will be eafy to do, by the methods that I have
explained in my treatife of epicycloids.
{
+
}
1
t
XI.
' '
230 The HISTORY and MEMOIRS of the
IV. An extract of fome letters written from
Portugal and Brazil, by M. Couplet the jon,
Abbot Bignon, prefident of the royal aca-
demy of Sciences.
The longitude of Lisbon.
Among many obfervations of the fatellites of
Jupiter, which I made at Lisbon in 1698, there
was one, which was likewife obferved at Paris,
in the royal obfervatory by M. Caffini. It was
an immerſion of the firft fatellite into the fhadow
of Jupiter on May 7, 1698, as follows.
It is well to obſerve beforehand, that I placed
myſelf upon St. Katherine's mount, fituated to
the S. S. W. of the town, in a convenient place.
for theſe fort of obfervations; that I was per-
fectly affured of the ſtate of my pendulum, and
that I made my obfervation with a teleſcope of
17 feet, and exactly of the fame force with that
which M. Caffini ufed at Paris for his.
May 7, 1698. The total immerfion of the firft
fatellite into the shadow of Jupiter, obferved
At Paris at
At Lisbon at
}
L
The difference of the merid. is-
Which comes to
h
1
"1
I I 9 21 P.M.
10 17 30
0 51 51
12 57 45
by which Lisbon is more easterly than Paris.
{}
Suppofing the longitude of Paris 21° only, as
there are ftrong prefumptions to make it, that of
Lisbon will be
8 2 15
This difference of the meridians between Paris
and Lisbon, is much greater in Sanfon's maps,
which have paffed without contradiction for the
bef
ROYAL ACADEMY of SCIENCES. 231
beſt theſe thirty years. Lisbon appears in them
more wefterly than by our obfervations by 52 15
of degrees, which are equivalent to 16 or 17
leagues in this parallel.
On the contrary the new fea-charts, printed by
order of the king fix years ago, make Lisbon
lefs wefterly than our obfervations by 27 45 of
degrees, which is above 9 leagues. Thus the
diſtance between the meridians of Paris and
Lisbon, marked in the new fea charts, is diffe-
1 "}
rent from that of Sanfon's maps i 20; which is
confiderable, being more than of their true
diſtance which refults from our obfervations.
The latitude of Liſbon.
As there is no great difficulty in obferving the
latitude, it is not fo eafy to miſtake it, provided
one has inftruments of a reaſonable fize. The ob-
fervations that I have made of the latitude of
Lisbon, will ferve to confirm that which is
marked in the new fea-charts. As for the lati-
tude of Lisbon, marked by Sanfon in his parti-
1
11
cular map of Portugal in 1654, at 38 27, it is
fo far from truth, that I do not believe any.
body can be miſtaken in it; alfo in a general
map of Spain which he has made fince, he has
increaſed it all at once, 23.
1
I obferved the polar ftar at the end of
ber 1697, with an inftrument of 1 foot
furniſhed with glaffes with threads,
found at Lisbon,
Decem-
radius,
and I
The
232 The HISTORY and MEMOIRS of the
The greateſt meridian height of the
polar ſtar
The leaft height of the fame
The difference of the two heights is
The half of this difference is
Adding this half difference, with the
leaft height of the polar ftar, we
fhall have for the apparent height
of the pole
From which fubftracting the fuitable
refraction
There remains
© } 4°
1
41 5 40
36 28
4 37 40
2 18 50
38 46 50
}
0 1 25
38 45 25
for the true height of the pole at Lisbon.
The declination of the needle at Lisbon.
Dec. 26, 1697. I obferved at Lisbon the de-
clination of a magnetical needle 6 inches long by
the means of a meridian line, which I had drawn
fome days before with great exactnefs, and I
found it to be 4 18 N. W.
1
The difference of the length of the pendulum at
Liſbon and at Paris.
Before I left Paris, I had regulated my clock
at the royal obfervatory in July and the begin-
ning of Aug. 1697, and I had put it to the mean
motion, where it had remained a confiderable
time to be affured of it. Having left it in the
fame ftate, I fet it a going at Lisbon the Nov.
following, and I obferved, that it loft 2 13 in
24 hours. As I had found that in raifing the
little weight as high as it could, it did not acce-
lerate the motion of the pendulum an entire mi-
nute, which was not fufficient; I determined to
fhorten
ROYAL ACADEMY of SCIENCES. 233
fhorten the pendulum, and after many attempts,
I found that the pendulum of the clock fhould
be fhorter at Lisbon than at Paris by 2 lines 4.
The latitude of Paraiba.
As the fky was often cloudy, I was above a
month in regulating my clock, becauſe there
wanted a great many obfervations to have the
length of the pendulum, and during this I took
the height of the fun ſeveral times; from whence
658
I conclude, that this town is at
fouthern latitude.
11
6 58 18 of
The declination of the needle at Paraiba.
May 20, 1698, having firſt carefully drawn a
meridian line, which I uſed for aftronomical ob-
ſervations, I obſerved the declination of the mag-
0
netical needle to be 5 35 N. E.
The difference of the length of the pendulum at
Paraiba and at Paris.
When I arrived at Paraiba in March 1698,
my firſt care was to regulate my clock, and to put
it exactly into mean motion, as well to know the
difference of the length of the pendulum, as to
prepare myſelf to make the obfervations of the
fatellites of Jupiter for determining the longitude.
of this town. At firſt, I put the pendulum again
into the ſtate where it was when I left Paris, and
fet it a going, I found that it loft of its mean
motion 4 12 in 24 hours. I then ſhortened the
pendulum feveral times, and at laft having re-
gulated it upon the mean motion, I found that
the pendulum muſt be ſhorter at Paraiba than at
Paris by 3 lines.
VOL. I. No. 6.
G g
العمر
234 The HISTORY and MEMOIRS of the
I afterwards put the fame clock in the ſtate
where it was, when I uſed it to make my obfer-
vations at Lisbon, where I had regulated it upon
the mean motion, and I obſerved that in this
ſtate it loft at Paraiba 2 5 in 24 hours.
1
Altho' the difference which is found between
the two pendulums of feconds taken at Paraiba
and at Paris, is, as we have obferved, but 3
lines, which is not confiderable in a length of
3 or 4 feet, as were thoſe which we compared ;
nevertheleſs it caufed a fenfible error, (as it is eafy
to fee, fince we know that the times employed in
the vibrations of the pendulums are between them-
felves as the roots of their heights) by which we
fee, that if at Paraiba we made ufe of a pendulum
of feconds, like that at Paris, that is, 3 feet
8 lines, inſtead of 3 feet 4 lines 2. which
it ſhould have in this part of Brazil to fwing the
feconds. Then its motion would be flackened,
that in the ſpace of an hour it would not give
more than about 3585 ofcillations inftead of
3600, which it gave at Paris, which is near
6
69
15
difference in an hour; and on the contrary,
if the pendulum of feconds of Paraiba, that is
3 feet, 4 lines & was put into motion at Paris,
where it ought to be 3 feet, 8 lines, it would
accelerate and give 3615 vibrations in an hour,
inſtead of only 3600 which it gave at Paraiba.
Theſe obſervations, added to thoſe which have
been made by many of the learned, fufficiently
confirm, that the nearer we are to the equator,
the more we muſt ſhorten the pendulum; but
the relation between thefe different contractions,
which do not follow the proportion of the diffe-
rent latitudes, with which they agree, is hitherto
unknown to us; altho' many able philofophers
have
ROYAL ACADEMY of SCIENCES. 235
have endeavoured to explain it to us; and to ar-
rive at it, there must be yet a great number of
obfervations on this fubject, which altogether may
perhaps at laſt, by their numerous compariſons,
diſcover to us the true caufe which has been long
fought for.
The attention that we muſt have to know the
true length of the pendulum, proper for the place
where we obferve it, is not confined to aftrono-
inical obfervations, but is alfo effential in an in-
finite number of things; as for example, in the
gauging of current waters, in the practice of which
we commonly uſe the fimple pendulum, whofe
length is meaſured, as we know from the centre
of the ball to the point of fufpenfion, and this
length of the pendulum, proper for the place
where we are to make obfervations, muft be
meaſured with exactnefs, fince, that ſpring, for
example, which at Paris would ſupply 3600 in-
ches of water in one hour, determined by the mean
of the pendulum of the true length, that is, of 3 feet,
8 lines would feem to fupply 3615 inches, if
14
we uſe there a pendulum of 3 feet, 4 lines &
fuch as we muſt at Paraiba, thus we fhall be
miſtaken 15 inches of the running in each hour.
69
I cannot caft my eyes upon thefe aftronomical
obſervations that I made at Paraiba, without re-
collecting an accident which happened to me at
the fame time. As I do not believe any author
has ever ſpoken of the fame thing, it will perhaps
be agreeable to find it here. There is in Brazil
a fort of ferpent, about 2 feet long, and 3 or 4
inches round, called by the Portugueſe cobra de
los cabeças, or two headed ferpent; not that it
really has two heads, as I found after having ex-
amined it carefully, for it has only at the end of
the tail a thickneſs, which has at a distance the
G g 2
ap-
236 The HISTOLY and MEMOIKS of the
appearances of a head. The Brazilians or Ma-
zombes, and after them the Portugueze, have
taken it for a head fo much the more eafily, be-
caufe they extremely feared this fort of ferpent,
for they fuppofe there is no cure for the fting of
it. They know even that it is dangerous to
touch it after it is dead, and probably it is this
which has kept them from examining it. They
told me, that only the touching of it would bring
the itch; I neglected this wholefome advice,
which I looked upon as an effect of their fear,
but I was puniſhed for my boldness; for having
killed feveral of theſe ferpents, I flayed fome of
them to examine them, and preferve the fkin;
and 2 or 3 days after, I faw myfelf really covered
with puftules, which were filled with a red wa-
ter they remained a long while, and even three
months after, I was not entirely free from them.
There are in the country ferpents of an extra-
ordinary fize, I killed one with a gun in the
woods between Paraiba and Pernambouc, which
was above 15 feet long, and 16 or 18 inches
round; it was all covered with fcales, black,
white, grey, and yellow, which altogether made
a very beautiful appearance: the bite of theſe
ferpents is venemous, nevertheleſs the Brazilians
and Blacks made no difficulty of eating the flesh.
This ought not to appear more ftrange, than that
which is obferved in the manibot, the meal of
which is the most common food in Brazil, and
the juice is a poiſon, as I have tried upon a dog,
which I made drink lefs than half a tavern-glaſs
of it at eight o'clock at night. I obferved him
for fome time, without perceiving any fenfible
alteration. I ſhut him up that night, and the
next morning I found him dead.
*
ROYAL ACADEMY of SCIENCES. 237
V. A general method of throwing bombs in all
cafes propofed, with an univerfal inftrument
for this purpofe, by M. de la Hire *
This + inftrument confifts only of a femicircular
plate ABD, which has a rule or tail BE fixed
upon the edge of the circle, which anſwers to the
centre C, and of which the fide BE being pro-
longed, meets the centre C of the circle, and is
perpendicular to the diameter ACD of the femi-
circle. The femidiameter CD of the femicircle
is divided into 9 equal parts, and upon CE there
are alſo marked the fame divifions, as upon CD.
Each of theſe divifions reprefents 100 toiſes, and
they may be fubdivided by little points into o-
ther leffer parts; but it will be eafy to judge by
the eye alone, which is fufficient for thefe forts of
operations. Through the divifions of the dia-
meter 7, 8 and 9, draw femicircles with their
centre in C.
To the centre C of the inftrument, is fixed a
rule CF, which is flit in the middle, that it may
let the pin G run in it, with the head turned to-
ward the plate; the middle of this flit anfwers to
the centre C of the femicircle. This pin G paffes
alfo into the flit of another rule IH like the firft,
ſo that theſe two rules may be held faft by the
fame pin, with a little fcrew with ears, to what
length, and in what angle you pleaſe.
At the extremity H of the rule IH, there is a
little round plate, the breadth of the rule, which
fhould be of fome white metal, as filver, upon
which is marked a black point, which anfwers to
the middle of the flit of the rule. Upon this
* July 24, 1700.
+ Plate XIV. Fig. 6.
1
rule
238 The HISTORY and MEMOIRS of the
rule IH, from the centre H of the filver pin are
alſo marked the magnitudes C7, C8, C 9.
The rule CF, which may turn freely upon its
pin C, which is placed in the centre of the femi-
circle, may be held faft in what pofition you
pleaſe, upon the plate of the femicircle, by the
means of a ſcrew at the end of the pin, which locks
the plate and rule together, it muſt be obſerved,
that theſe pins C and G muſt be pointed at their
ends, and raiſed a little above their ſcrew.
Along the femidiameter CD, there is upon the
plate a flit, into which paffes or runs a fliding
piece O, with a pointed head, to which is faf-
tened the thread of a plummet: the middle of
this flit muſt be upon the diameter ACD of the
femicircle.
As for the uſe of this inftrument, it may ferve
at firft to determine the diftance from the ſtation
where the mortar is, to the mark, without its being
neceffary to know the number of toifes of this diſtance.
This is done by taking ſome baſe of 3 or 4 hun-
dred toifes on the fide of the place where one is,
and aiming at fome known object at this diſtance,
by the pin C and the fliding piece G; aim alfo at
the mark by the pins C and G, fix the rule CF,
in this poſition on the plate, by means of the
fcrew at C. Afterwards remove the inftrument
to the ſtation where you aimed at firſt, and then
place the ſliding piece O at the number of toifes
from the point C to the other ſtation and aiming
alfo by the ſliding piece and by the pin C,make the
pin G run upon the rule CG, till you fee by the
fliding piece O and the pin G, the mark you
aim at then ftop the pin G in this pofition, and
the diſtance CG will be in the parts of CO the
number of toifes from the ſtation where you ſhoot,
to the mark; which is not neceffary to know,
3
pro-
ROYAL ACADEMY of SCIENCES. 239
provided the pin G is ftopped upon the rule CF
in this pofition. But if this diftance was given,
you need only place the rule CF upon the line
CE, and ſtop the pin G in the number of toiſes
there marked.
To have the elevation or depreffion of the
mark, with relation to the horizon of the place
from whence you are to fhoot, the plate muſt be
held faft in fuch a fituation, that the thread of the
plummet P be applied to the point A, or upon
the diameter AD, and move the rule CF, fo
that you may ſee the mark by the point of the
pins C, G. You muſt then ſtop the rule CF very
faſt upon the plate of the femicircle. Theſe are
the two things we muſt always know, together
with the force of the powder in whatſoever me-
thod it be.
As for the force of any certain quantity of
powder, or of the height to which the caft can
be raiſed in aiming toward the zenith; as it can-
not be known by experiment, we know by the
demonſtration that the point of the horizon where
the bomb may come, when it is caft in an angle
of 45°, or half a right one, is alway diftant from
the place where you aim, double the elevation of
the vertical caft; this is what is called the am-
plitude of the caft; wherefore one fingle obfer-
vation made in this manner, and with its con-
veniencies, may
ferve for all forts of cafes.
For example, if the caft is 1600 toifes, the ver-
tical or perpendicular caft will be raiſed to 800
toifes. This inftrument may alſo ſerve to make
this caft, as will be feen hereafter.
Now for the practice of cafts, and the ufe of
the inftrument, you muſt place the fliding
piece O upon the number of toiles of the vertical
caft, as in the figure, upon the point of goo
toules,
240 The HISTORY and MEMOIRS of the
toiſes, if the vertical caft is 900 toifes, or elſe if
the amplitude of the caft be 45°, 1800 toifes. Af
terwards move the rule IH in its groove upon the
pin G immoveable upon CF, till the fame divi-
fion of goo toifes of this rule HI meet upon
CE, when IH will be pretty near parallel to
AD, or IH perpendicular to CE; which will be
known by turning the rule IH, if its divifion of
900 touches the line CE. Then if you turn the
rule IH upon the pin G, the length GH re-
maining always the fame, that you found it.
When the centre of the plate H fhall touch the
circle OLL of goo toifes, ftop the rule IH very
faft to the rule CF with the fcrew which is at G.
Now if you apply one of the fides of the tail
BE, which we fuppofe of equal breadth every
where, within the mortar or cannon, and after-
wards raiſe or deprefs it as much as is neceffary
to make the thread of the plummet P pafs by
the point L, the caft will fall at the mark
defigned.
If the point H cannot meet its circle but in
one point, there is but one fingle caft, which can
go to the mark; but if it can meet it in 2
points, theſe 2 points, as L, will ferve to make
2 different cafts in the fame manner, that we
have explained for one, which will both go to
the fame mark. If the point H cannot meet
its circle, there is not any caft which can go to
the mark.
The demonftration.
*The demonftration of this practice depends
upon a propoſition of the parabola, which I have
demonftrated, and which M. Blondel relates from
me in Chap. 7. of part III. of his treatife. For
the point G being the mark aimed at, and by
*Fig. 7.
my
ROYAL ACADEMY of SCIENCES. 24
1
my conſtruction GH being equal to the difference,
between the height of the vertical caſt CO, and
the height of the mark G above the horizon,
which paffes by C, or elfe the fum of the fame,
if the point G is below the horizon; or under
the level of the point C, that is, if GH is per-
pendicular to the horizon, the line OH will be
the level therefore the points of interfection
LL of the two circles OL, HL, are the foci of
the parabola's, which will pafs by C. and G, and
it is this figure which M. Blondel has only re-
verfed in his fquare inftrument, which does not
alter the conſtruction.
Now I fay that the line OL being vertical or
perpendicular, will make with OH or CE of my
inftrument, which is parallel to it, the angle that
the direction of the caft muft make to the point
C, without there being need to make a new
operation, and it is in this chiefly that the fim-
plicity of this practice confifts.
For if you draw LM perpendicular upon
OH, and bifect it in S, the point S muſt be the
fummit of the parabola of the caft. But alfo
by the properties of the parabola, we know
that the line LC being drawn, and OC being a
diameter, the tangent CN of the parabola at
the point C, will bifect the angle OCL, and con-
fequently the angle OCN determines the angle
of the caft, if OC is confidered as vertical. But
I fay alſo that the angle HOL is equal to the
angle OCN, which is evident, fince the 2 rect-
angular triangles CON, OLM, have one equal
angle CON, OLM, the two lines CO, LM,
being parallel, and cut by the fame OL: there-
fore in the inftrument, if the thread of the plum-
met paffes by OL, it is plain that OH or CE,
VOL. I. N°. 7.
Ꮋ h
er
242 The HISTORY and MEMOIRS of the
or any other which is parallel to them, will give
the inclination of the mortar, or the line by which
the caft muſt be made.
It may be obſerved by the cafts of bombs or
bullets, that as there are in almoſt all cafts 2 points
as LL, there will be alfo 2 different cafts which
go to the fame mark, but the upper one will be
more fit, to make its effort againſt bodies which
are placed in a level, and the other caft will have
more effect againſt bodies that are perpendicular,
as walls.
A
TABLE
OF THE
PAPERS contained in the ABRIDGMENT
of the HISTORY and MEMOIRS of the
ROYAL ACADEMY of SCIENCES at
PARIS, for the Year MDCCI.
I.
II.
In the HISTORY.
N the declination of the needle.
ON
A method propofed for obferving the flu
and reflux of the fea in the ports.
III. On the continuation of motion.
IV of an extraordinary fort of ants in Surinam,
V. Of a black fand found in Italy.
VI. Of another fort of fand found in the mountain
of Pifaro, which being viewed by the mi-
croſcope, appears like precious stones.
VII. Of the fatal effects of the damps in a well
at Rennes.
VIII. An improvement in the art of dialling.
IX. On the pofition of the axis of windmills, with
regard to the wind.
In the MEMOIRS.
I. Of the new phofphorus, by M. Bernoully,
profeffor at Groninguen, Extracted from
one of his letters written at Groninguen,
Nov. 6, 1700.
II. Obfervations on the rain-water, which fell at
the royal obfervatory in 1700; with some
remarks on the thermometer and barometer
by M. de la Hire.
Hh2
III
244
A TABLE, &c.
20.
III. A letter from M. Bernoully, profeſſor at Gro-
ninguen, concerning his new phofphorus.
IV. Remarks on the measure and weight of water,
by M. de la Hire.
¿
V. Anatomical obfervations made on the ovaries
of cows and sheep, by M. du Verney, jun.
VI. On the circulation of the blood of thofe fishes,
which have gills, and on their refpiration, by
M. du Verney, fėn.
;
*
AN
AN
ABRIDGMENT
OF THE
PHILOSOPHICAL DISCOVERIES and OB-
SERVATIONS, in the HISTORY of the
ROYAL ACADEMY of SCIENCES at
Paris, for the Year 1701.
1. On the declination of the needle; tranflated
by Mr. Chambers.
R. Halley, a learned English philofopher,
D'having made a voyage to the fouthern.
parts, has, among other philofophical treaſures,
brought with him a general theory of the varia-
tion of the loadftone.
In the vaſt fea which feparates Europe and A
frica from America, he finds four feveral places
wherein the needle does not decline at all.
First, In 18
2º of northern latitude.
Secondly, In 4°
2
and 379 1/
Thirdly, In 10°1
and 169A
Fourthly, In 64°.
and 31°1
of western longitude and
of western longitude.
of fouth latitude.
of weſtern longitude,
of western longitude,
of fouth latitude.
of north latitude.
The longitudes being all reckoned from the
meridian of London.
Having theſe four points, he imagined that
they might be comprehended in a curve-line,
which ſhould furround the terreftrial globe, and
under which the needle fhould have no variation,
but in all places on one fide of the variation
fhould
246 The HISTORY and MEMOIRS of the
fhould be eaſtern, and in all thofe of the other
weſtern.
This notion, fo new and pleafing to the mind,on
account of that order which it introduces into a
matter, whereof there was before no appearance,
would be ftill further defirable for the improve-
ment of navigation in long voyages, where it is
very inconvenient to be in a perpetual diftruft of
the needle, and not to dare intirely to credit any
calculus depending thereon.
Dr. Halley had the fatisfaction to find, that all
the other obfervations in his whole voyage agreed
with and confirmed this fyftem, the declination
being always found eaſtern or weftern, and greater
or lefs, according as the places whereon this or
that fide of the curve line exempt of all varia,
tion, and as they were more or lefs diftant there-
from.
But M. Caffini the younger, being employed
in continuing the meridian of Paris thro' the
fouthern provinces of France, and obferving at
the fame time the ſeveral declinations of the load-
ftone in the ſeveral places, did not find them al-
together fuch as they fhould have been by Dr.
Halley's fyftem; for continuing the lines, which that
author had drawn on the ocean thro' the inter-
mediate lands and Mediterranean fea into the
continent of Europe, it appeared, that the decli-
nation, for inſtance, in the gulph of Lyons is 2°
greater than it fhould be by the new doctrine-
But the reafon may be, that the laws of variation
undergo fome change between the ocean and fuch
diftant continents, and it would be well worth our
attention to obferve this defect of uniformity, and
find the meafure and quantity thereof; the leaft
we can do is to favour, as far as nature will allow
us,
ROYAL ACADEMY of SCIENCES. 247
us, fo beautiful a diſcovery, and never to give it
up till we can no longer hold it.
If it be true, that the line of no variation will
be movable on the furface of the earth, fince the
variation changes in the fame places at the rate
of 11 or 12 minutes in a year; but it may be
added, that this variation feems confined within
certain bounds, for in the whole courfe of time
that the needle has been known to point towards
the north, it has altered fo little as to leave the ob-
fervers till of late in the error of believing it di-
rected precifely to the north; and upon the
whole, 'tis not improbable, but that the motion of
the line of no variation is included between a kind
of tropicks.
II. A method for obferving the flux or re-
flux of the fea in the ports, tranflated by
Mr. Chambers.
Tho' the tides have pafs'd for a myſtery al-
moſt impenetrable to the human mind, yet the
cauſe thereof ſeems at length diſcover'd; but
what will appear furprizing, we have more room
to flatter ourſelves upon having the true ſyſtem,
than upon exact obfervations of its phænomenon.
The academy therefore bethought themſelves of
procuring fuch obfervations from different places,
and accordingly a memoir was drawn up by Fa-
ther Gouye and M. de la Hire, upon the hints
and fuggeftions of the whole company, and pre-
fented to the co untde Pontchartrane, who having
the direction of marine matters, fent it into all
the ports of France; its tenor is as follows:
A
248 The HISTORY and MEMOIRS of the
A method of obferving the flux and reflux of the
Sea in Sea ports.
i. A place is to be pitch'd on well fhelter'd;
where the fea has no other motion befides its flux
and reflux;here a ftake is to be planted, fur-
paffing the greateſt height to which the water
rifes in fuch place.
2. This take to be divided into inches,
reckoning from the furface of the ground, and
parallel lines to be drawn thro' each divifion.
3. At each tide it is to be noted in a journal,
what divifion. of the ftake the fea was at, when
either higheft or loweſt, and if this happen to
fall between 2 divifions, the interval to be eſti-
mated as nearly as may be.
4. The hour and minute when the fea appear'd
either higheſt or loweſt on the ſtake, is likewife
to be obferved by a well regulated watch.
5. If the fea at low-water retire from the ſtake,
it may fuffice to mark, the divifion it is at when
higheft, and the time thereof.
6. Let it be obſerved, as often as may be, at
what preciſe time the fea arrives at the fame de-
vifion both rifing and falling.
7. Obferve what winds blow while the fea
rifes and falls, and in what direction the tide
drives both rifing and falling.
8. Obferve the crofs wind of the road, as alfo
that which ranges the entrance of the port;
Laftly obferve a few times in a year, whether
there be not a little reft between the times, when
the fea rifes and falls, in order hereto it will be
proper to moor a floop in the road in calm wea-
ther, and a-crofs the edges of the floop to place
a little wooden axis fitted to turn readily, at each
end, whereof may be a little turn-pike whofe
arms
ROYAL ACADEMY of SCIENCES. 249
arms to enter 5 or 6 inches in the water, between
the 2 contrary motions of the fea, it will be eaſy
to obſerve whether this machine do not remain
fome time, without turning, and in caſe it do,
how long ſuch ceffation continues.
III. On the continuation of motion; tranflated
by Mr. Chambers.
The first notions of phyficks, for instance, the
effence of matter, and the nature of motion, tho'
the moft fimple in themſelves, are not yet the
cleareft, and thofe principals which it feems ought
to be perfectly known before we go farther, re-
mains ftill in great meaſure unknown, and we
advance nevertheleſs.
Why a ftone thrown upwards by a hand, con-
tinues to move after the hand has quitted it, is no
eafy queftion, and perhaps may be longer e'er it
be folved, than the caufe of the ebbing and flow-
ing of the tide.
Descartes maintains, that motion is a kind of
being, which by its nature ſhould always continue
as well as reft, and that the ftone once put in mo-
tion, would always perfift therein, if it did not
communicate its motion to other bodies it meets
withal, and ceas'd at length to have any motion
itſelf, by this continual communication of it to
others.
An author whoſe differtation on the fubject is
printed in the memoirs of Trevoux, difapproves
this fyftem of M. Defcartes, and after combating
it very ingeniouſly, fubftitutes another in its place.
He alledges, that at the time when the hand
moves, and raiſes itſelf with the ftone, a column
of air defcends to take the place of the lifted
hand, that the motion of this defcending column
VOL. I. No. 7.
I i
muft
1
250 The HISTORY and MEMOIRS of the
muſt be accelerated like that of all other bodies,
that this acceleration of motion, continues after
the cauſe of the motion has ceas'd acting, and
confequently, that the ſtone when it has quitted
the hand, continues rifing not by vertue of its
being impell'd by the hand, but by the reafon
the air which takes its place continues to defcend.
But M. de la Hire hereupon obferved, that a
heavy body only weighs in a fluid it floats in, by
reafon fuch fluid is lighter than the body, con-
fequently that a maſs of air does not weigh in
air of the fame nature, that if it move and fall
therein 'tis by the impulfe of fome foreign power;
that it is no fooner abandon'd thereby than it
ceaſes to move; and laſtly, that there is no room
for acceleration, fince it is not the weight that
acts.
M. Parent likewife attack'd the new fyftem,
by a great number of difficulties, which arife
from it. What for inftance ſhould be the cauſe
of horizontal motion, fince here is no acceleration
of falling air? and why, when the motion is
both horizontal and circular, as when a bowl,
faſten'd to a horizontal rod, is ftruck perpen-
dicularly to the rod, why here does the bowl
turn round, fince the air is not moved circularly,
but only in a right line; if the ball come of
the rod it would continue moving according to
the tangent, to the point of the circular circumfe-
rence where it was then found; did the air defcribe
this tangent or rather all the poffible tangents, in
which the bowl would continue moving if it
came off, and what fhould be the cauſe of re-
flection on this hypothefis? The air you will
fay, which goes before the moving body, being
reflected upon meeting the obftacle, carries the
body back with it; but if the obſtacle were
removed
ROYAL ACADEMY of SCIENCES. 251
removed as foon as the air has made its impulfe,
ere the body be arrived, would it be reflected not-
withſtanding?
IV. Of an extraordinary fort of ants in
Surinam.
M. Homberg received a letter dated Jan. 24.
1701, from Paramaribo, a Dutch fettlement in
the province of Surinam, on the N. coaft of S.
America. This letter relates, that there are in
that country a fort of ants, which are called by
the Portugueze vifiting ants, and with good rea-
fon. They march in troops, and like a great
army. When they fee them appear, they open
all the boxes and cabinets in their houſes; they
enter and extirpate rats, mice, cackerlacs, which
are infects of the country, and in fhort, all the
noxious animals, as if they had a particular mif-
fion from nature, to punifh them and deliver men
from them. If any one is ungrateful enough to
anger them, they fall upon him, and tear in pieces
his ſhoes and ſtockings. The misfortune is, that
they do not make their proceffions often enough.
They would be glad to fee them every month, and
they are fometimes three years without appearing.
{
V. Of a black fand found in Italy.
M. Geoffroy being in Italy obferved a black
fand, which they commonly ufe for writing. It
is very much mixed with little flat, and fhining
particles, like enamel, all the others which com-
poſe it are without any glofs. In putting fome of
this fand near a loadftone, M. Geoffroy faw, that
it had only the little obfcure particles which fixed
themfelves to it; from which he judges, that they
I i2
are
252
The HISTORY and MEMOIRS of the
are iron or loadftone; but he is fure they are not
loadſtone, becauſe iron does not draw them at all.
As for the fhining particles, he believes them to
be a black talky powder, and indeed they find
talc in many places in Italy; and M. Geoffroy has
obſerved, that about Rome, when the fun begins
to appear after rain, all thefe little atoms of talc,
which have juft been waſhed, glitter, and have a
very agreeable effect.
The ferruginous particles of the black fand
thrown into the fire, do not flame at all, as file-
ings of iron do. This comes from their being
half vitrified, and cloathed with a very earthy
bitumen, which ferves them for a varniſh, and
defends them from the action of the fire.
The great quantity of black fand which they
find in Italy, is upon the furface of the earth as a
fort of indication of its compofition within, and
the volcanos which make fuch ravages there, de-
pend on the fame caufe with thefe ferruginous
particles, mixed with a little bitumen, and half
vitrified.
VI. Of another fort of fand, found on the
mountain of Pefaro, which being viewed
by the microscope appears like precious
fones.
Another fand heaped upon the mountain of Pe-
faro, crew alfo the curiofity of M. Geoffroy. It
is by its extreme hardneſs very fit for working
perfpective-glaffes, for it refifts a great while at
this work, whereas the other fand turns very
foon to a powder fo fine, that it does not grind
any longer upon the glafs, and they are obliged
to change it very often. This fand of Pefaro is
mixed with little particles, fome as clear as cryf-
tal,
ROYAL ACADEMY of SCIENCES. 253
*
tal, others as green as emeralds, others like ame-
thyfts, topazes and jacinths; and when we view
this duft with a microſcope, it is a furprizing col-
lection of precious ftones. There is however a
confiderable quantity of particles of iron, as in
the black fand of Rome.
VII. Of the fatal effects of the damps in a
well at Rennes.
1
There is in the city of Rennes, near the gate
Morlaix, a well made three or four years ago,
into which a maſon let fall his hammer. A la-
bourer, who would fetch it up again, going
down, was fuffocated in approaching to the wa-
ter. A fecond, who went thither to draw up the
dead body, had the fame fate; and likewife a
third. At laft, they let down a fourth, half
drunk, and well tied, whom they had charged to
cry as foon as he perceived any diforder. He
cried as foon as he was near the water, and they
drew him up quickly; but he died three days
after. They let down a dog, which cried at the
fame place, and died three days after having been
drawn up.
When they threw water upon the dog
while it was dying, he recovered, like thofe which
are thrown into the famous Grotti di Cane near
Naples. The three bodies were drawn up with
hooks and opened; but they could not find any
caufe of their death. What is very furprizing is,
that this is not new ftirred earth, which is the
cauſe of theſe fatal accidents; and that they drink
every day the water of this well without incon-
veniency. F. Louvard, a benedictin of the abbey
of St. Denys, received this account from Rennes,
and communicated it to M. Varignon.
VIII.
254 The HISTORY and MEMOIRS of the
VIII. An improvement in the art of dialling.
When we make a dial, we muſt begin by find-
ing what the pofition of the plane is, for example,
of the wall where we would make it, with regard
to the fun, and the principal circles of the heavens.
At firſt the compaſs prefents itſelf for this ufe;
but experience foon undeceives us. The iron
which is almoſt every where in buildings turns the
magnetick needle irregularly, and gives it ano-
ther declination than that which we know it ought
to have, and upon which we reckon ; and if it had
only its natural declination, the compafs is too
fmall an inftrument, to give exactly the divi-
fions and the parts of a degree, which will be
neceffary to the juftnefs of the operation.
We had then recourfe to 2 or 3 points of fha-
dow taken upon the plane of the dial. They ferve
to determine the poſition of it, and to find after-
wards by the theory of gnomonicks all the lines
that we would reprefent. It is upon them that
all the juſtneſs of the dial depends. They are
taken in the fame day at 3 or 4 hours frorn one
another. They muſt be taken as diftant as pof-
fible, becauſe all the other points, and the inter-
mediate lines are afterward orè difintangled.
To have theſe points as diftant as they can,
there muſt be two things: 1. They muſt be taken
in the folftices, or within 10 or 12 days of them
at most, becauſe the farther the fun is diftant from
the equator, which is commonly repreſented upon
the dial by a right line, the more the lines which
repreſent the circles parallel to the equator, are
fenfibly curves, and confequently their points
which answer to the fame hours, are farther dif
tant from one another.
I
2.
ROYAL ACADEMY of SCIENCES. 255
2. The ftile muſt be long, for the ſhadow of its
extremity makes fo much the more way, and the
points which mark the fame hours are much far-
ther diſtant.
But the ſeaſon of the folftices, and the length of
the ftile, have their inconveniences.
It is very troubleſome to work in the air in
either folftice. The fun does not often appear
long enough, or often enough in a day; and in-
deed it is a great confinement to have but theſe
two very fhort times to make a good dial in.
It is exactly the extremity of the fhadow of the
ftile that muſt be had, that is, the fhadow of a
fingle point. But it is very difficult to have it
exactly, becauſe the extremities of a fhadow are
always ill terminated, and uncertain, and beſides
light has a certain trembling, which becomes
more fenfible at the extremity of the fhadow of a
greater body. Therefore the late M. Picard, and
M. de la Hire have each invented a different
plate, to take more exactly the end of the
fhadow of the ftile. The defcription of it may
be ſeen in M. de la Hire's treatiſe of gnomo-
nicks, printed in 1698.
But however ingenious thefe methods may be,
M. Parent has obferved, that with their help, it
is yet difficult to have the fhadow of the end of
the ſtile very juſt, and he has thought of another
method, which gives this fhadow very exactly,
and at the fame time renders the conftruction of
the dial independant of the folftice. Beſides, the
points of fhadow, which by the common method
are obliged to be taken in the fame day, may be
taken at very diftant times, even at fix months,
* M. Parent's method confifts in the ufe of an
inftrument DBHFG, which is a kind of frame,
Plate XV. Fig. 1.
*
of
256 The HISTORY and MEMOIRS of the
of which the two fides BH, FG, are ſtrongly
joined and parallel between themſelves. FG muft
be about two feet long, and there put a teleſcope
which has two threads croffed at its focus. Upon
the fide HBD, in its whole length BD, it muſt
have at the face oppofite to the teleſcope a groove,
exactly parallel to the axis of the teleſcope. BD
muſt end in a point D, which muſt be in a right
line with the groove.
Chooſe in the night any fixed ftar. The ob-
ſerver ſees it with the teleſcope FG, and at the
fame time carries the inftrument DBHFG upon
his fhoulder, the fide HBD being that which
lies upon the ſhoulder, which determines the dif-
tance of two parallel fides of the inftrument to be
only one foot at moſt. The obferver muſt have
engaged in the groove the end of the ftile that he
deſigns for the dial, and at the fame time turn his
back to the wall where he would draw it. Con-
fequently the point D will be in the air, and in
this fituation, not lofing fight of the ftar, which
he fees at the interfection of the threads, he walks
by degrees backward toward the wall, till he
ftrikes it with the point D. It is vifible, by the
conſtruction of the inftrument, and by the nature
of the operation, that this point D marked upon
the wall, is the very exact extremity of a ray
conducted from the ftar to the wall by the end of
the ftile, and we fee at the fame time by this prac-
tice what are the principal attentions required,
both by the conftruction of the inftrument and
the operation.
In like manner we take a fecond or third point
of fhadow of the fame ftar, but at as diftant
hours as we can. It does not in the leaft fignify
that it be in the fame night, becauſe the motion
of the fixed ftars being very flow, in proportion
to
ROYAL ACADEMY of SCIENCES. 257
to that of the fun, we fhall find it again at the
end of fix months, in the fame fenfible pofition,
whereas we ſhall not find the fun again from
one day to another.
The ftar muſt be taken as near the equator
as it can; it is plain that the points of fhadow
at different hours will be moſt diftant.
1
To be more fure of the operation, you may
take with different ftars the points of fhadow
that you have occaſion for.
have occafion for. If the lines that are
to be drawn by the means of theſe points, are
found to be the fame in ufing the points of dif-
ferent ftars, the operation has been made with
all poffible juftnefs. If they are not the fame,
there muſt be others drawn which keep exactly
the middle.
In adding to the inftrument upon BD, a groove
oppofite and parallel to that which is abfolutely
neceffary, we ſhall put it in a ſtate of proving
itſelf. For you may turn it upon the two oppo-
fite faces of the fide BD, and in theſe two fitu-
ations fee the fame ftar, the end of the ftile be-
ing always engaged in one or other of the grooves.
And if you find always the fame point upon the
wall, the two fides HBD, GF, are in an exact
paralleliſm, which is all the perfection of the
inftrument.
To this new invention, which is only for the
practice of dials, M. Parent has added two others
which regard the theory.
There is a portable dial very ingenious, and
very ufual in compaffes, invented by M. de
Vaulefard. It is an azimuthal one joined with a
horizontal. It has very great advantages, but it
is always determined to a certain height of the
pole, and is ufelefs out of that. M. Parent
having ftudied a great while to remove this
VOL. L. N°. 7. Kk
fault,
4
258 The HISTORY and MEMOIRS of the
fault, and to render it univerſal, is at length ar-
rived at it. M. Parent's new dial has alfo the
convenience of not having need of any foreign
meridian, and to find out the eaft itſelf.
But it is true that it is charged with a great
number of lines, of which many are curves, and
difficult to defcribe. M. Parent has therefore.
thought of another, which preferves all the ad-
vantages of the firft, is univerfal and finds the
eaft itſelf, and with all this is only rectilineal.
VIII. On the poſition of the axis of windmills,
with regard to the wind.
A windmill, confidering merely the 4 fails
which turn by the impulfe which they receive
from the wind, is a more ingenious machine,
depending upon much finer principles than we
think, and whoever fhall reflect upon them for
the firſt time, will fee that it is not very eaſy to
fay why the mill turns.
In order to this, we muſt fuppofe the theory
of compound motions. A body which moves.
perpendicularly against any furface, ftrikes it
with all the force that is in it; if it moves pa-
rallel to this furface, it does not ftrike it at all;
in fine, if it moves and meets it obliquely, this
motion which partakes both of the perpendicular
and the parallel, and is compounded of them,
has no effect upon the furface, but fo far as it is
perpendicular, and according to the proportion
of what perpendicularity it has to what it has of
parallelifin, and drives the furface only according
to the perpendicular direction, which enters into
its compofition. Thus every oblique direction
of a motion, is the diagonal of a parallelogram,
1
of
ROYAL ACADEMY of SCIENCES. 259
of which the perpendicular and parallel directions
are the two fides.
Again, when a furface, which being obliquely
ftruck, has received only the perpendicular im-
preffion, is faftened to fome other body, in fuch a
manner that it cannot follow this perpendicular
direction, but ſome other which approaches more
or lefs to it, then the perpendicular itſelf becomes
the diagonal of a new parallelogram, one of
whofe fides is the direction, that the furface
ftruck may follow, and the other fide that which
it cannot follow. Thus, when a rudder faſtened
obliquely to the keel of a veffel, is ftruck by
the current of water parallel to this keel, and
confequently it is ftruck obliquely by it, we fee
that in drawing upon the furface the line of the
perpendicular impreffion, that it tends to dif
engage itſelf from the keel, and to get from it,
and that this direction perpendicular to the rudder,
is oblique to the keel. It would get from it then
by an oblique motion: but as it cannot difengage it
felf,nor confequently get from it, it muſt only take,
in this oblique motion, that of the two directions
which compoſe it, by which it may be moved
without getting from the keel, and leave as uſeleſs
that which would have removed it. Now the
direction, according to which it may move with-
out getting from the keel, is that which makes
it move circularly about its extremity as a centre;
then all the effect of the oblique ftroke of the
water upon the rudder is reduced at firft to a per-
pendicular impreffion, which is again reduced to
make the rudder turn, or, if the rudder is im-
moveable, to make the veffel turn.
In an oblique and compound motion, where
only one of the directions is ufeful, the greater
ratio the other has to it, the lefs effect will the
Kk 2
motion.
260 The HISTORY and MEMOIRS of the
motion have, and on the contrary. In examining the
compound motions of the rudder, we fee that the
more oblique it is to the keel, the ratio of the
direction, which ſerves to turn it on the other, is
the greater; but, on the other fide, the more
oblique it is to the keel, and confequently to the
courfe of the water, which is fuppofed to be pa-
rallel to it, the weaker it is ftruck. The obli-
quity of the rudder has then at the fame time an
advantage and a difadvantage: but as they are not
equal, and as each of them is always varying with
every different pofition of the rudder, they are
differently complicated; fo that it is fometimes
one, and fometimes the other which prevails, and
that more or lefs; it has been a queftion to find
the poſition of the rudder, where the advantage
ſhould be greater than in any other pofition. M.
Renau, in his famous theory of the working of
fhips, has found, that the rudder, to be in its
beſt ſituation, muſt make an angle of almoft 55
degrees with the keel.
If a windmill, expofed directly to the wind,
fhould have its four fails perpendicular to the com-
mon axis to which they are fitted, they would
receive the wind perpendicularly, and it is vifible
that this impreffion would tend only to overturn
them. It was therefore neceffary to make them
oblique to their common axis, that they might re-
ceive the wind obliquely. Let us confider only one
vertical fail. The oblique impreffion of the wind
upon
this fail is reducible to a perpendicular direc-
tion. This direction, which cannot be intirely fol-
lowed by the fail, is compofed of two, one of which
tends to make it turn upon the axis, and the other
to fall backwards. But only this first direction can
be followed, and confequently all the impulfe of
the wind upon the fail has no other effect, than
to
ROYAL ACADEMY of SCIENCES. 261
to make it turn from right to left, or from left to
right, according as its acute angle turns either
way. And the invention of this machine is fo
happy, that by the ſame reaſons the other three
fails are determined to turn the fame way.
The obliquity of the fails with refpect to their
axis, has exactly the fame advantage and difad-
vantage, with the obliquity of the rudder to the
keel; and M. Parent having ftudied by the ana-
lyfis the moft advantageous inclination of the
fails upon the axis, found it to be exactly the
fame angle of almoft 55 degrees. Probably the
experience of thofe who have invented mills
made them find this angle after long trying:
but as experience teaches us, that theſe common
and grofs practices are by no means infallible,
and that they often are wide of the mark, it is
well to examine them by geometry, and be affured
if what we do is the beſt that can be done.
M. Parent has even fearched if there was no-
thing to correct in the common practice of putting
the axis of the mill exactly in the direction of
the wind. Theſe are not eafy inquiries. We
muft find, by mechanicks, the proportion of all
the different forces, which enter into the motion
of a machine, according to all its different difpo-
fitions poffible, and having given them algebraic
or analytic expreffions, we muſt by the fame
analyfis find of all theſe expreffions that which de-
termines the greateſt force. By this learned cir-
cuit, M. Parent has arrived only to juftify the
common practice. The axis of the mill muft be
put in the direction of the wind; and they were
put fo before we were fure that it was right.
}
ΑΝ
Jean Bernoulli
A N
ABRIDGMENT
OF THE
PHILOSOPHICAL MEMOIRS of the ROYAL
ACADEMY of SCIENCES at Paris for
the year 1701.
I. Of the new phofphorus, by M. Bernoully,
profeffor at Groninguen. Extracted from
one of his letters, written at Groninguen,
Nov. 6, 1700.
TH
HE objections, which fome gentlemen of
the academy have made to my diſcovery of
the light of the barometer, have been the occa-
fion of my making a new one, of much greater
importance and curiofity: it confifts in making
of the quickfilver a portable and perpetual phof-
phorus, which I can carry about, and fend con-
veniently and without danger wherefoever I will,
and at all times; for it will laft for ever, and yet
its light, to the ftrength of which that of the ba-
rometer is not to be compared, never diminiſhes.
As this diſcovery, tho' very cafy, as you will fee
hereafter, has been drawn from the principles by
which I have believed, and ftill believe, that I
have explained the light of the barometer.
verily perfuaded, that I am not fo much miſtaken
in my judgment, as you may perhaps think, with
thofe gentlemen, who attribute the light of my
barometer to the nature of my own quickfilver;
for
you faid not a word upon the explication which
I have given; it is apparent, that you have ta-
ken it for a conceit, feeing that my experiment
I am
done
1
ROYAL ACADEMY of SCIENCES. 263
my
done again by fome of your gentlemen, had not
the wiſhed fuccefs; and that on the contrary,
the barometer of M. le Marechal de Villeroy, that
Lord Portland gave him, produced light even
after having been filled with his quickfilver in the
common manner. Theſe are objections I own,
which feem to deftroy all my reafonings. I ought
then to anſwer them, if I would fupport my in-
vention: but what fhould I fay, if I had been
preſent at theſe experiments: I fhould perhaps
have taken notice of a hundred circumſtances, in
which they had not well obferved my method of
filling the tube: for example, the manner of
filling it by the means of a leathern purfe, which
you fay is equivalent to mine, has however this
difference, that here it is the quickfilver that muſt
drive the air before it, which in making fome.
little refiftance, may let fome little remains or
bubbles of air fix themſelves to the fide of the
glafs, which will already fuffice to engender the
pellicle of the quickfilver, which I have faid hin-
ders the light; whereas by the fuction it is the
outward air, which drives the quickfilver up, and
which confequently only follows the motion of the
air within, which by its rarefaction goes out of
the tube, as I may fay, voluntarily. It is not
that I would abfolutely difapprove this manner of
filling the barometer by the means of a leathern
purfe, I imagine it must be proper enough
for the exciting of the light. This is then ano-
ther fault in the circumstances; it may be that the
tube which they uſed was not dry nor clean
enough; for the leaft moifture or greaſe hinders
the appearance of the light. This tube was alfo
too flender, not being, as you fay, above a line
and half diameter within; the largeſt tubes are
the beſt for this purpofe, as I have known by
I
expe-
264 The HISTORY and MEMOIRS of the
experience. The reafon of it is evident; for be-
fides, that the quickfilver in a large tube balances
more freely than in a narrow one, where the
Friction of the quickfilver againſt the glafs leffens
the quickneſs of the defcent: the pellicle which
covers the quickfilver, if it makes any, muſt be
more thick in a narrow tube than in a wide one,
becauſe not being able to extend itſelf in breadth,
it thickens in height.
7
8
As for the other experiment, I queftion whe-
ther they were able to fill the tube of quickfilver
with the mouth as I do, without fuffering a little
breath or ſpittle to get in, it being very difficult to
hinder it, feeing others have not fucceeded there-
in. It requires a particular dexterity; for my
part, it is not difficult for me to do it, being able be-
fides by a fort of habit to draw with my mouth out
of a little receiver of the air which it contains;
fo that there remains only part, and without
ftraining myſelf too much. I have yet other con-
jectures, which make me fufpect the experiments
you mention, but as I was not prefent, I can fay
nothing for certain: I hope nevertheless, that if
the gentlemen will make a fecond trial of my ex-
periment, in obferving well what I have juft now
faid, they will have better fuccefs. But I had
rather that they would do it at night than in the
day, altho' in the dark; for you know, that if
in the day one goes 'fuddenly into a dark place,
the eyes being dazzled with the too great bright-
nefs of the day, do not fo well perceive a faint
light, fuch as is that of the barometer, tho' other-
wife it may be brifk enough in the night.
M. de Villeroy's barometer, which you fay
made the light, after having been filled in the
common way, throws me I own into fome diffi-
culty but I fhould have been glad to have feen
it
ROYAL ACADEMY of SCIENCES. 265
it filled; and then I do not doubt but that I
ſhould have been able to find ſome anſwer; per-
haps when they threw in the quickfilver, they
held the tube very obliquely to the horizon, to
let the drops of quickfilver run foftly, as in a
channel, which must have hindered the air from
affecting it ſo much as it would have done, if
they had let the drops fall in vertically with im-
petuofity. In effect, after having filled a tube in
this manner with my quickfilver, I have perceived
the light more than ordinary; but always much
lefs than by the manner of fuction, or of the air-
pump. In all cafes, why may I not fay, that
the quickfilver of M. de Villeroy is fo exceeding
well purified, that there is no more heterogenous
matter of which the contact of the air can form
a pellicle; and thus my manner of explaining the
cauſe of the light of the barometer, will be rather
confirmed than deftroyed.
nary
Befides, if my explanation was not the true
one, and it was to the particular nature of the
quickfilver, and not to the manner of my having
filled the tube, that the production of the light
ſhould be afcribed, pray tell me, why my ordi-
barometer filled in the common manner, al-
tho' very much fhaken, makes little or no light;
whereas the other tubes, filled in my manner
with the fame quickfilver, make an excellent
light with the leaft balancing? I made again
for the fecond time, many experiments upon it,
as foon as I received your letter. And to con-
vince myſelf entirely, that this light was not the
effect of a fingular property of my quickfilver,
which all other has not, I borrowed fome other,
with which I made the fame experiments again,
and with the fame fuccefs as with my own. Now
it is morally impoffible, that the fecond quick-
VOL. I. N°. 7.
filver
L. 1
266 The HISTORY and MEMOIRS of the
filver fhould be exactly of the fame nature with
my firft; fince, as they pretend, it must be of fo
extraordinary a quality, that among a hundred
forts of quickfilver, they fhall not perhaps find
one which makes a like effect.
To come now to the diſcovery of my new
phosphorus, I thought that one of the principal
reaſons, by which the pelliclè hindered the ap-
pearance of the light in the barometer, might be
the two great uniformity of the motion of the
quickfilver in fo uniform a tube. For in rifing
and falling thus the length of a cylindrical tube,
its pellicle muſt never change its thickneſs, nor
break, but on the contrary, remain always fixed
to the upper furface, with which it rifes and falls
without ever quitting it; in fuch a manner, that
it makes no opening, by which the matter of the
firſt element, as I call it with M. Defcartes,
may get out of the pores of the quickfilver, after
the manner mentioned in my laft letter. But it
being fo difficult to avoid this pellicle in a full
barometer, even according to my manner, I con-
clude, that notwithſtanding this pellicle, provided
it is not too thick, the like muft always ap-
pear, if by any means I could make it burft,
or difperfe in pieces by the motion of the quick-
filver, which makes me judge that nothing would
be more proper for this purpoſe, than a very violent,
irregular, and not uniform motion of the quick-
filver, inclofed in a glafs a little bigger, and of
an unequal figure, from which the air has been
emptied as well as poffible. This reafoning was
confirmed by the following lucky experiment,
which makes the fubject of my difcovery.
1
I took a clean fair phial, which held about
half a pint, and ſtrong enough to fuftain the agi-
tation of the quick filver; I put into it 5 or 6
ounces
ROYAL ACADEMY of SCIENCES. 267
ounces of quickfilver well purified; after that, I
cemented on the neck of the phial with great ex-
actneſs, a cock, which I afterwards applied to the
air-pump, to draw the air out of the phial; hav-
ing done this as carefully as I could poffibly, I
fhut the cock to hinder the air from entering into
the phial again, when it was feparated from the
air-pump: this is all the artifice.
To try then if I had reafoned juftly, I carried
the phial the fame night into the dark, and hold-
ing it faft by the neck, I began to ſhake it ſtrong-
ly, as they do in rinfing a bottle, to give a great
agitation to the quickfilver. And prefently the
phial appeared full of a fire, the light of which
was not interrupted, nor intercepted, like that of
the barometer; but lafted as long as the quick-
filver was in agitation, and with fo much vivaci-
ty, that I could eafily fee the faces of the fpectators
enough for to know them: I repeated this expe-
riment many times, with more than one fort of
quickfilver, and always with the fame fuccefs;
except when I had not been exact enough in draw-
ing the air out of the phial, or that I had let a
little get in again; for then not only the light ap-
peared much fainter, but it leffened by degrees,
notwithſtanding the continual fhaking of the
phial, till it diſappeared intirely. After that,
there was no way to make it appear again, with-
out drawing the new air out of the phial.
Having examined by day, what was the caufe
of the faintnefs of the light, I found all the fur-
face of the quick filver covered with a pellicle,
not only visible, but fo thick, that it was like a
paſte made of dirt: notwithflanding before the agi-
tation the phial was very clean within, and the
furface of the quickfilver polfhed like a looking-
glaſs. From whence I judge, that the air being
L12
agitated,
268 The HISTORY and MEMOIRS of the
1
agitated, altho in a fmall quantity, might ex-
tremely infect the quickfilver, and that for this
reaſon, as fast as this pafte formed itſelf, the
light grew fainter, and intirely difappeared, when
this paſte acquired fuch a confiftence, as not to
be broken in pieces by any violent agitations that
were given the quickfilver. It is alfo by this, that
you may know whether the air is well taken out
of the phial or not; for if it is well emptied, not
only the light does not leffen, and the quickfilver
does not cover itſelf with dirt, but the light itſelf
becomes more excellent in time; and the pellicle
of the quickfilver, if it had any at the firſt, dif-
perfes intirely, in fuch a manner, that the quick-
filver polishes itſelf fo well at last, by frequent
ufe, that there does not remain any fpot; and
when this happens, then the light is in the higheſt
degree of vivacity, and appears always with the
fame force every time that you shake the phial
in the dark.
à
I do not believe, that they have found till now
the perpetual phosphorus, that is, which does not
confume by time, or at leaft which does not in
the end lofe its virtue; but here is one which
muſt laft as long as you will without lofing any
of its own, provided the phial remains always
well ſtopped, and that the air does not enter; for
the quickfilver inclofed in the vacuum is not fub-
ject to any alteration, fo that there is no reafon
why it ſhould not have its effect at all times.
It is true, that the cock which I had cemented
upon the phial, with which I made the firft ex-
periment, began to fpoil by the quickfilver, be-
cauſe it was of brafs; but I have fince found the
fecret of ftopping the phial after having drawn
out the air, without having occafion for the cock.
Among many ways which I thought on, the
moſt
ROYAL ACADEMY of SCIENCES. 269
>
moft fure and expeditious is, firft to ſtop the
phial before you draw out the air, with a cork
and a proper wax over it, and then to make a little
hole with a pin through the wax and cork, to
give an opening to the air which you are going
to draw out of the phial; this being done inclofe
the phial in a receiver, out of which the air muſt
afterwards be drawn, as exactly as poffible, to get
it at the fame time out of the phial by the aper-
ture of the little hole: the greateft difficulty is
how to cloſe this little hole, before you let any
air get into the receiver. To perform this eafily,
you muſt expoſe the receiver thus empty to the
fun, and with a convex-glafs melt the edges of
the wax about the hole, in this manner the hole is
filled with the melted wax, and ftops itſelf per-
fectly well of its own accord. This being done,
you may ex abundanti, apply the receiver again
to the air-pump, to fee, if during the operation,
there has not a little air flipped into the receiver
by fome invifible aperture: the fureſt way is dur-
ing the operation to hold all the parts of the re-
ceiver, by which the air can flip in, under water.
Being thus affured, that all is done well, let the
air enter again into the receiver to take out the
phial, which being thus prepared, ferves then for
a phosphorus whenever you will take the pains to
ſhake the phial in the dark. I kept 5 or 6 weeks
two of theſe phials filled with two different forts of
quickfilver, which had their effect admirably
well. The curious, to whom I have fhewn
them, have declared, that they have feen nothing
more wonderful. In fhort, the whole phial is in
a flame, and the quickfilver like a burning li
quor.
If you have a mind to make one of them, you
muſt carefully obferve thefe three things
1
That
3
the
270 The HISTORY and MEMOIRS of the
the phial be very clean and dry within; and if
you doubt of its being fo, it would be better to
take a quite new one, as it comes from the glaſs-
houſe. 2. That you do not ftir the quickfilver
much before the air is drawn out of the phial.
3. That you empty the air out of the phial as
carefully as is poffible. This third point muſt be
obferved with all the exactnefs imaginable, or
elſe it will not make any phofphorus, or if it does,
it will be faint, and not last long. The air-
pump muſt be very good; mine, which was
made in Holland, is fo nice, that the piston, be-
ing drawn from the bottom of the cylinder to the
mouth, and remaining fo for 24 hours, does not
let in the 1000oth part of air into the cavity of
the cylinder, as I have known by experience, a
certain fign of very great exactneſs.
II. Obfervations on the rain-water which fell
at the royal obfervatory in 1700; with
Some remarks on the thermometer and baro-
meter, by M. de la Hire *
During the whole year 1700,
inches of water at the obfervatory,
mean quantity that falls every year.
There fell in
there fell 20
which is the
Lines.
Jan.
Feb.
4
Mar.
13
Apr.
27
~+~+~+~t
11 1 July
13 Aug.
Lines.
35 4
9
3
May
17
June
I
44 4
Sept.
Octob.
Nov.
Dec.
1 1/
24
2.5
16
++++
2 2
456
1
* Jan. 8, 1700.
We
7
ROYAL ACADEMY of SCIENCES. 271
→
>
We may obferve, that in the two months of
June and July alone there fell 80 lines, which is
of that which fell in the whole year: but the
month of August gave only 9 lines altho' there
are generally the greatest rains in it, as I have
obferved for many years fince I have made
theſe obſervations. What is alfo remarkable in
the rains of this year is, that there fell but I
line in September, whence the drought was very
44
great towards the end of fummer.
The thermometer fhewed us, that the greatest
cold of the months of January and February,
was on the 9th of February, when my thermo-
meter fell only to 28 parts, the mean ſtate of
heat or cold being at 48 parts, as I have proved
for fome time in the bottom of the caves of the
obfervatory, where my thermometer always re-
mained at this height. This thermometer falls
ſometimes in the winter below 15 parts. It is
expoſed to the air, but fhelter'd from great winds.
and the fun. All the reft of theſe two months it
was commonly at 40 parts; we muſt take notice,
that all the obſervations that I made every day,
were about fun rifing, when the air is commonly
the coldeft. But on the 19th of December the
thermometer fell to 25 parts, a little lower
than it did at the beginning of February, which
is generally the coldest time. By theſe obferva-
tions it appears, that the cold has not been very
confiderable during all this year.
As for the heat, it was the greatest on the 21st
of July, the thermometer marking 61 parts 4.
We ought not to judge of the coldnets of the
air, by the impreffion which it makes on our
bodies; for a great wind makes the air always
appear colder to us, than it really is, becauſe it
makes the air pafs through the cloaths, and drives
away
272 The HISTORY and MEMOIRS of the
away
that which is about the fkin, and which is
warmed by it. This experiment proves that the
violence of the wind does not augment the cold
of the air. I blowed with a pair of bellows
againſt the ball of a thermometer for fome mi-
nutes, and I did not obferve any fenfible altera-
tion in the height of the fpirit of wine. This
experiment would have been more juſt, if it had
been made with one of Santorius's thermometers,
where the impreffion of heat and cold is made
on the air it felf.
For the barometer, that which I ufe is fixed at
the top at the great hall of the obfervatory. The
greateft height was on the first day of Jan. at 28 in-
ches 4 lines and more than 3, with a gentle wind at
ENE, and it always kept very high during this
month, altho' the wind was often toward the
W. but always inclining a little to the N. yet
it was not then cold, for the air was commonly
in a temperate ftate, and fometimes hotter, the
barometer at the loweſt was at 26 inches 8 lines
1, November 26 with a high S. wind and a
little fnow, which foon melted, the air not being
cold. Thus the difference between the greateſt
heights, and the greateft falling of the quick-
filver during this year, was 1 inch and a little
more than 8 lines.
I found the declination of the needle 8° 12' to-
ward the W. November 20, of the last year
1700. This obfervation was made against the
S. wall of the terrafs of the obfervatory, which
I found was placed exactly according to the me-
ridian line, and the needle which I ufed was 8
inches long, and very well hung.
}
III.
ROYAL ACADEMY of SCIENCES. 273
III. A letter from M. Bernoulli profeſſor at
Groninguen, concerning his new phosphorus.*
I read the paper which you fent me, but I do
not know whether I ought to be forry for the
bad fuccefs, which it contains of the experiments
upon the light of the quickfilver; I think I
have rather reafon to be glad myſelf, that no
body can yet effect that which I do very easily,
either by my fkill, if I have any, or by the
goodneſs of my pieumatic machine. For is it
not ſurpriſing, that the experiments of the aca-
demy have never fucceeded, and that mine have
never failed? you ſend word, that it is ſome par-
ticular accident, which happens to fome quick-
filver, which may render it capable of light in a
place void of air; but pray confider that I have
made my phosphorus with 5 or 6 forts of quick-
filver, which I have known were brought here
from different places and at different times, which
nevertheleſs have fucceeded very well with me, ex-
cept one only which did not give light at the
firft, but which I rendered luminous by washing,
it, as I fhall mention hereafter.
I do not find it neceffary to anſwer in order
to the experiments in this paper, nor to the re-
flections and confequences which are drawn from
them. To end the difpute, I defire the academy
to fend me fome of the fame quickfilyer, which
they have uſed without fuccefs. I engage to make
a phofpborus with it as good as thoſe which I
have already made hitherto. And that the aça-
demy may be affur'd that it is the fame quick-
filver that they ſend me, with which I make the
phosphorus; I will do it in the prefence of au-"
thentick witneffes, and fend it again to the aca-
* July 5.1701.
VOL. 1. N°. 7.
M m
demy
填
​50
274 The HISTORY and MEMOIRS of the
$
demy. What makes me thus bold is, that I fee
fome circumftances that the paper mentions,
which makes me believe, that theſe experimeuts
have not been made exact enough, and that con-
fequently the ill fuccefs of it muſt be imputed en-
tirely, either to the machine of the academy,
which perhaps may not be the most juft, or to
fome miſtake. One of thefe circumftances is.
that the quickfilver in a phial emptied of air
being very much fhaken, really gives a little
light very faint, that it was ftrong at the begin-
ning, that it diminiſhed by little and little, but
without any air entering again into the veffel,
and that after having let the air in again, and
then emptying the machine immediately a fecond
time, this quickfilver had not given any more
light, altho' very much fhaken. I fee by this,
that the quickfilver had not been purified as it
cught from the heterogeneous matter, of which
had been formed that pellicle which I spoke of
in my preceding, by the gathering of the air
which was left in the phial, which was thought
to have been emptied enough; it was by this
that the light was fo weak and vaniſhed by de-
grees, whereas it would have been very lively
and lafting, if the phial had been well emptied,
and the quickfilver well purified; for I have
tried more than once, that the quickfilver in-
clofed in a veffel void of air, where it fhone very
much for a long time with an equal force, has
ceafed to fhine by lofing its light by degrees, as
foon as I have let a little air into it. However,
we may conclude from the experiments which
they object to me, that the quick filver, which
was not fhining in the barometers, for as the pa-
per does not mention that they had different
quickfilver, I believe that they uſed only the
4.1 *
}
fame
3
ROYAL ACADEMY of SCIENCES. 275
fame, was at leaſt ſo in a phial emptied of the
air: if they had then made this experiment with
the barometer alone, and had declared that the
quickfilver was not luminous, would they not
have been miſtaken, fince it really was fo? It is
the fame with the fecond experiment, by which
they did not fee any more light in the fame phial,
after having emptied the air a fecond time, becaufe
that, according to the paper, perhaps in letting
the air again into the veffel, a little of the moif-
ture of the air had faſtened itſelf to the fides of
this veffel, which they know, as well as I, to be
prejudicial to the light of quickfilver." Let us
fee then what would have happened, if from the
first time there flipped fome moiſture infenfibly
into the phial; there is no doubt, that the light
not appearing at all from this firſt time, it would
have been faid, that this quickfilver was not at all
luminous, altho' it had been the fault of him
who had made the experiment, and not that of
the quickfilver. I fay this, that you may obferve
that the experiments which did not fucceed, prove
nothing to fuftain a negative propofition'; becauſe
it may always be 'doubted in making of theſe
experiments, that fome miſtake has been com-
mitted.
I fhall fay nothing concerning the experiments
upon the barometer, both becauſe I have already
anſwered to theſe objections in my fecond letter,
and becauſe I entirely neglect making of other
obfervations upon the light of the barometer, fince
I have found the way to render the quickfilver
luminous in a phial; which, in my opinion, is
far more curious, as it furniſhes a fort of perpe-
tual phosphorus, and convenient to carry about,
befides that the light of it is much more lively
than that of the barometer: I fhall only fay fome-
M'm 2
thing
276 The HISTORY and MEMOIRS of the
thing upon the ſecond barometer, made in the
pneumatic machine of the academy. They
may reaſonably ſay, that the quickfilver was not
rifen to the fame height in this laſt barometer, as
it is commonly in a barometer well made, it not
being poffible to empty in this manner all the air
out of the tube; becauſe the weight of the quick-
filver, preffing upon the open end of the tube,
hinders the going out of the air. I fee by this,
that they have let the open end of the tube dip
too deep into the quickfilver; whereas when I
made this experiment, I placed the tube in fuch
a manner, that its end was near the furface of the
quickfilver, and very little dipped. For this pur-
pofe I took a veffel, broad and a little flat, to
the end that in letting in the air again, which by
its preffure had made the quickfilver riſe in the
tube, this quickfilver might not fail; by this
means, I raiſed the quickfilver to the height of
26 inches, fo that it wanted but little of the com-
mon height. Altho' it be true, that it is not ab-
folutely neceffary that the quickfilver be in a place
perfectly void of air to become luminous, as they
have very well obſerved in the paper in queſtion;
however, it muſt be known that there did not remain
fo much air in the tube, as they perhaps thought:
and befides that the light, altho' very brifk the
firſt night, was very much weakened the nights
following, without doubt becaufe of this little air
which remained in the tube, which I had not ob-
ferved till after my laft letter. From whence it
follows, that the more perfect the vacuum is, the
more excellent and durable the light will be; fo
that the quickfilver in a phial perfectly emptied
of air (or at leaft if it be fo to the tenth thou-
fandth part or more, for it is impoffible to draw
the air intirely out of any veffel) fhines as lively
as
ROYAL ACADEMY of SCIENCES. 277
as poffible; and very far from the lights growing
fainter, it increaſes to certain degrees, and then
it continues and fhews itſelf with equal force every
time that you ſhake the phial, provided alſo that
the quickfilver be well purified from its dirt; I
own that it is a conjecture, which appears true to
me, when they fufpected that my firſt quickfilver,
which the moment it was expofed to the air, co-
vered itſelf with a pellicle, which became like
duft if it was fhaken, was not fo clean as it might
be: I will agree, that this pellicle formed itſelf of
a foreign matter, either metallick or other, which
came from the quickfilver rather than from the
air, nevertheleſs that does not at all invalidate
the general explication, which I give of the pro-
duction of the light of the quickfilver, nor even
deſtroy my idea of the generation of the faid pel-
licle; for it is always conftant, as I have obfer-
ved in my preceding, that the air, if it is not al-
ways the material caufe, is at leaft the efficient
cauſe, ſeeing that the fame quickfilver, when it
is incloſed in the vacuum, remains always bright
and poliſhed, altho' very much fhaken; and as
foon as you have admitted the air, it grows thick
as uſual. But I have found the ſecret of purifying
it fo well from all its dirt, that it does not thicken
any more, even when it is expofed to the air, and
fhaken very ſtrongly. I put 4 or 6 ounces of
quickfilver into a phial, and pour common wa-
ter upon it, till it covers the quickfilver to the
thickneſs of two fingers or thereabouts; then I
ſhake the phial ſtrongly for a great while, as in
rinfing it, I empty the water out, which is quite
black and dirty, at the top of the quick filver,
and put freſh upon it, and begin again to fhake
the phial, till the water becomes dirty again; I
then change the water a fecond time, and do the
#
!
fame
278 The HISTORY and MEMOIRS of the
fame thing; which being repeated till the water
is no longer black, or very little, I dry the quick-
filver by paffing it feveral times through a clean
cloth if you uſe fpirit of wine inftead of water,
you will fooner have cleaned the quickfilver. By
this means I took all the dirt out of it, fo that be-
ing fhaken in the open air, as much as you would,
it does not leave any traces of pellicle or of duft,
only it tarnishes a little in fome days, as if it was
by the team that apparently comes from the
touching of the air, which is always a little in-
fected with humidity. The phofphorus made with
the quickfilver thus cleanfed, was much finer
than thofe made before; which confirms my
explication of the production of this light,
which I have faid was hindered by the hetero-
geneous matter, poffeffing the top of the quick-
filver.
I have faid above, that I have tried 5 or 6
forts of quickfilver, which all fucceeded with me,
of which fome were alfo infected with duft by
the motion, like my firft, and the others remained
clear and polifhed, like thofe of the academy.
Among theſe there was one, which, at firſt, gave
no light but I fufpected that, even before I
made the trial; for it feemed to be more thick,
or leſs fluid than the others, fince, when it was agi-
tated, it made no bubbles upon the furface, as I
obferved in the others, which I'attributed to its
vifcidity, which hindered the feparation of its
parts. This made me fufpect, that there was
perhaps in that quickfilver fome oily or fulphu-
rous matter, which becaufe of its vifcofity, did
not fhew itfelf upon the furface, as the other im-
purities did, which more eafily feparated them-
felves from the little parts of the quickfilver to be
thrown out: thus this oily matter remaining al-
ways
7. 1.
ROYAL ACADEMY of SCIENCES. 279
ways mixed within the quickfilver, is taken to be
very pure, tho' it is by no means fo; and much
lefs fo, than that which covers itſelf at firſt with a
viſible pellicle. Then having well waſhed it in
the above manner with ſpirit of wine, rather than
with water, becauſe I thought it better than wa-
ter to take our the vifcocity, the quickfilver,
which was not at all luminous, became as fhining
as any other but what is ftill more wonderful,
the firſt quickfilver, which grew thick with the
leaft motion, became fo pure with waſhing, al-
tho' with water alone, that I have ſeen it make
light even in a phial full of natural air, without
its having any drawn away. It is true, that the
light was not fo lively as that which was made in
the vacuum, and it appeared only like ſeparate
fparks, which arofe fucceſsfully, and perifhed
almoſt at the fame time; whereas the light in
the vacuum is like a continual flame which lafts
inceffantly while the quickfilver is in agitation, I
conclude from thefe experiments, that the quick-
filver, if it is perfectly purified, may let the fub-
tile matter (which I call with M. Descartes, by
the name of the firft element) go out of its pores
in fuch a quantity at once, that for all the re-
fiftance of the air, it has ftill motion enough to
produce fome light. If they then take the pains
to wash the quickfilver well, which they fay is
not luminous, and after having well dried it (for
the leaſt moiſture will occafion bad fuccefs) pour,
it into a clean and dry phial; if they then draw
out the air carefully, I am fure they will fucceed,
Tho' this quickfilver is thought to be perfectly
pure, becauſe it remains clear after the agitation:
I have nevertheleſs obferved, that it may be in-
fected with a concealed glutinous matter, which
fhutting up intirely the pores of it, or at leaft
TO
14
making-
280 The HISTORY and MEMOIRS of the
making them ftiff, hinders or keeps back the
particles, which ought to cauſe the light, from
going out. I fay, that the ſtiffneſs of the pores
may hinder or keep back theſe particles from go-
ing out; for it is very vifible, that altho' the
quickfilver be in very great agitation, if never-
theleſs the pores of its particles are not flexible
enough to change their fhape, the matter of the
firſt element cannot be driven away from it, for
the pores muſt often fhrink that this matter may
go out.
It is therefore very likely, that the
quickfilver, which is faid to become luminous by
the diſtillation through quicklime, is one of thofe
whofe pores are thus ftiff, becauſe of fome ful-
phurous or glutinous matter. And therefore
very far from being of the opinion with thofe who
believe they are igneous particles, that the quick-
lime has given to the quickfilver in paffing thro'
it, which produce the. light; I am ſtrongly per
fuaded on the contrary, that the true reafon of it
is the purification alone, fo that the lime has con-
tributed nothing to it but its pores, thro' which
the quickfilver paffing has left behind all the fo-
reign and glutinous matter, and is thus delivered
from it there is then nothing done by the diftil-
lation than what I have done by washing alone.
In fhort, thefe igneous particles appear to me
great paradoxes for many reafons, of which I fhall
only mention fome.
1. This new phosphorus muſt at laſt loſe its
virtue, becauſe theſe igneous particles become at
laft of no fervice by frequent ufe, as you fee by
other phosphori which are luminous, by the means
of fuch igneous particles.
2. If thefe igneous particles are fo fine, that
they can lodge in the little fpaces of the quick-
filver, and pals through them, as is pretended,
without
ROYAL ACADEMY of SCIENCES. 281
without doubt they could pafs much more eaſily
through the pores of the glafs, which are much
larger then thoſe of quickfilver, how comes it
then that in fhaking the phial, they do not dif
perſe themſelves immediately by flying off thro'
the pores of the glafs, let them be in ever fo
great quantity in the quickfilver?
3. We can no more explain why the light in
the barometer appears only in the defcent of the
quickfilver: for if it is caufed by theſe igneous
particles, which fwim upon the furface, why have
they not their effect when the quickfilver riſes,
as well as when it falls, if there wanted nothing
but motion to make them fucceffively upon the
furface of the quickfilver.
Now all thefe difficulties are avoided by my
way of explaining this light; for in faying that
it is produced by a very fine matter, which being
univerfal and found every where, never fails, we
fhall fhew that this phosphorus muft laft perpetu-
ally, the quickfilver only lending its pores, which
are very narrow, aud ferve as a fieve to the
matter of the firſt element, to feparate it from the
fecond and third, (I make uſe of thefe terms be-
cauſe they are convenient to explain myſelf) from
which being delivered, and afterward driven out
of the quickfilver by the agitation which is given
it, it takes at firft its rapid motion, which is ufual
with it, when it is alone and difengaged from all
other matter, and fo produces in our eyes the ef-
fect which caufes in us the fenfation of light.
Therefore this luminific matter, altho' it is dif
perfed in a moment, yet is immediately followed
by another which has the fame effect, and fo on,
which will always continue. This explication
proved itſelf alfo by one of theſe phofpkori, with
which I have made the experiment almoft every
VOL. I. No. 8.
N n
night
282 The HISTORY and MEMOIRS of the
night for about a year, and I can truly fay, that
I have never obferved any fenfible change in
it, but quite on the contrary, that the light
was always equally bright, as it ftill is; and
very far from its having fuffered any diminu-
tion, it ſeems at prefent to be a little more
lively than it was at the beginning, perhaps be-
cauſe the quickfilver is become more fluid by
the frequent agitations, and the reft of its dirt is
ſeparated from it by degrees, and is fixed to the
fides of the glaſs, as the glafs being a little thick
within, plainly fhows; fo that the quickfilver
being entirely purified, gives light for the future
to the higheſt degree of vivacity. My explica-
tion appears to me in other refpects fo plaufible,
that I am fully perfuaded, that another pure liquor
as heavy as the quickfilver, if there was one, would
make without doubt the fame effect; fo that I
believe gold would be the fittest to make the like
phosphori, if we knew the way of rendering it
fluid, without lofing any of its ſpecifick gravity:
for as I make this effect depend on the ſmallneſs
and flexibility of the pores, it is certain, that
gold having the ſmalleſt of any body, it wants
only the flexibility of its pores, which we cannot
procure it but by a perfect fluidity of its mafs.
Perhaps melted lead put into a vacuum, would
give alſo a light, at leaſt if the dirt, with which it
is always infected, does not hinder it.
As for the quickfilver, which is faid to be
made luminous by the artificial liquid phosphorus,
I believe that it was not the quickfilver which was
luminous, but the particles themſelves of the ar-
tificial phosphorus. Now that would have hap-
pened to many other bodies, which we fee fhine
by the friction alone of folid phosphorus; and
as the light of it does not laft long, I imagine
alfo that the quickfilver bere mentioned, has not
always
ROYAL ACADEMY of SCIENCES. 283
always kept this light borrowed from the artifi-
cial liquid phosphorus; fo neither does that light
belong to our fubject.
1
By all theſe reaſonings, joined to the obferva-
tions which I have alledged, it appears that the
three confequences which they have drawn from
it cannot fubfift. For, 1. we fee that the quick-
filver is not only capable of becoming luminous.
in a place emptied of air; but that it is in effect
already luminous, provided its light be not hin-
dered by fome foreign caufe either internal or
external.
2. Alfo all quickfilvers are equally luminous,
provided again their lights are not hindered in
fome more than in others, by any caufe whatfo-
ever, I made a remarkable obfervation upon
this fubject: I took two phials both alike, and
equal, into which I put an equal quantity of
quickfilver taken from the fame mafs; I drew
the air equally and in the fame hour from each
phial. Would one not fay, that the light ought
to appear equally ftrong in both phials, fince in
all appearance every thing was perfectly equal
and alike? but the effect fhewed quite the con-
trary, for one of thefe phials made the light very
lively with the leaft motion, but the other did
not till after much fhaking, and then having once
began to fhine, it wanted only the leaft motion
to make the light appear again, and after ha-
ving let this phial reft for two or three hours, it
wanted to be ſtrongly fhaken before the light
began to appear again; whereas the firſt phial al-
ways gave light without any trouble. What can
we fay to this? unleſs that perhaps there entered
a little moiſture into one of the phials, altho'
imperceptible to my eyes, either from the breath,
or from the fweat of the hands in touching it;
Nn 2
4
which
284 The HISTORY and MEMOIRS of the
which was fufficient to cauſe ſo great a difference
in the light. It does not then follow from hence,
if one quickfilver gives more light than another,
that it is more capable of giving it than the other;
for here where the quickfilvers were taken from
the fame maſs, and confequently equally capable
of fhining, yet they fhined differently.
3. Laſtly, we ſee that the fame quickfilver, if
it be well prepared, muſt always be equally lumi-
nous, and that if it is fometimes much, fometimes
little, fometimes not at all, it is a fign that there
is an alteration happened to it, which augments,
diminiſhes, or hinders the appearance of the light,
which without that, would be always the fame:
witneſs the phosphorus which I have mentioned
above, that gave light a year without any fen-
fible alteration. I can confirm what I have faid
by another obſervation, which I made not long
ago: I had a phial prepared with phosphorus,
which fhone equally for about 6 weeks; without
opening or letting the air into the phial, I burned
with the fun by a convex glafs, a little bit of
cork that had been ſeparated from the reft, and
fwam upon the quickfilver. It made a little
fmoak in the phial, which otherwife remained in
its firft ftate, without being at all changed. One
would not believe how much this little fmoak
diminiſhed the vivacity of the light, befides that
it wanted to be fhaken much more ftrongly
than before to make it appear; which fhews the
alteration of the light obferved at the academy,
muſt not be taken for an effential quality, but
for the effect of an accidental cauſe.
I agree that all common quickfilver is perfectly
alike, as all gold and all filver is alike, from
whatſoever part of the world it comes, provided
skat it be pure: for this is the foundation of
my
ROYAL ACADEMY of SCIENCES. 285
3
$
my explication of this light, to maintain that
it is general, and that it comes only from
the quickfilver which gives way to the matter
of the firft element, to the exclufion of another
more grofs matter. I agree alfo, that it fol-
lows from my explication, that all quickfilver
muſt be luminous, and at all times; it is alſo
both, as I have now proved, provided the light
be not hindered by fome foreign caufe, as the fun is
always luminous, although its light may be taken
from us by an eclipfe or other caufe. I conclude
then, that it is not, as is believed, a particular acci-
dent happened to fome quickfilver, which can
render it capable of fhining in a place emptied
of air; but on the contrary, that it is natural
and effential to all quickfilver, as to all other li-
quids equally heavy, if we had any fuch, to be
luminous and it would be rather a particular acci-
dent happened to the quickfilver, which hindered
the appearance of its light. That if after all this
they ftill find difficulties, without being able to
fucceed in making my new phosphorus as perfectly
as I have done it; I only wish to have the fame
quickfilver, which ſo obftinately darkens itſelf; I
hope to diſperſe the darkneſs, and that I fhall
have the good luck to fupport this quickfilver
in the greek title of phosphorus, with as much
juſtice as the planet Venus bears the Latin title
of Lucifer.
IV. Remarks on the measure and weight of
water, by M. de la Hire. *
Extract of the memoirs of M. Picard.
171 inches of water of Arcueil weigh 6 lb.
14 oun. 4 dr. 2 gr.
* September 2. 1701.
Hence
286 The HISTORY and MEMOIRS of the
Hence I find that the cubical foot of water of
Arcueil weighs 1113 oun. 3 dr. 20 gr. or 69 lib.
9 oun. 3 dr. 20 gr.
M. Picard adds that the Paris pinte of the
meaſure of the Hotel de ville contains 47 inches .
But that the Chopine of the Hotel de ville con-
tains almost 24 inches.
And if we fuppofe that the pinte contains 47
inches, it will weigh of the fame water 30 oun.
3 dr. 1, or 1' lib. 14 oun. 3 dr. 1
But if we fuppofe it to contain 48 inches, in
proportion to the chopine, then we fhall find it to
weigh 30 oun. 7 dr. 1, or 1 lb. 14 oun. 7 dr. §.
I
Aug. 5, 1701, at M. Boulduc's, we weighed a
pinte of river water in a quite new pewter pinte
pot.
42
The water being warm weighed 31 oun. 4 dr.
Being cold it weighed
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31
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Aug. 20, 1701, at the Hotel de Ville, with
M. Boulduc, we meaſured in the braſs ſtandard a
pinte of river water; and having weighed it ex-
actly with a good balance, after different man-
ners, it weighed 1 lb. 14 oun. 3 dr. 2 gr. The
water was neither cold nor hot
1
This meaſure agrees exactly with that which I
had concluded from M. Picard's obfervations;
for the difference of a few grains may come from
the water of Arcueil, which M. Picard ufed,
weighing a little more than the river water, and
perhaps it might be a little colder than the river
water, which we made ufe of the last time.
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V.
ROYAL ACADEMY of SCIENCES. 287
V. Anatomical obfervations made on the ova-
ries of cows and keep, by M. du Verney
junior *
Having met with the uterus of a cow, which
incloſed a fœtus of about a fortnight or three
weeks, which however had all the parts very di-
ftinct, I applied myſelf with care to diſcover
where this fetus had got out of the ovary. The
tubes and their expanfions appeared a little more.
fwoln and ſpongy than ufual, one of the ovaries
was about the bignefs of a wallnut, a little pointed
at the end, and the fides were of a hard ſubſtance,
fet with veficles and fome whitish points. All the
reft of the ovary was of a ſpongy nature, covered
with a ſmooth and very thin membrane, inter-
mixed with ſeveral blood-veffels. On one of the
fides of the veficular fubftance, there appeared a
dark yellow fpot, of the fize of a lentil, and I
thought it might be the place where the fatus got
out. I blowed into it with a pipe, the air got in,
and fwelled the whole ovary, I preffed it to make
the air go out, and drove in freſh. Not only the
ovary fwelled up like a veficular texture, but alſo
a number of veffels, which feemed to come out
of it. I found them to be blood-veffels. I made
ufe of this aperture to enter into the ovary. I
there found feveral cavities, very fmooth, which
appeared like little bafons. I blowed into them
as faft as they prefented themſelves, and all the
veifels, which I had ſeen before, fwelled in like
manner. The whole middle of this ovary was a
ſpongy body, which was very eafily detached; it
received veffels at its bafe, and fome at its point.
Sept. 7, 1701.
There
288 The HISTORY and MEMOIRS of the
There ufually appears at this place a little dent,
fo difpofed, that one would always expect to find
an aperture. At laft, being willing to be fure
that I was not deceived, and thinking of a good
way to difcover the ova without breaking their
outer covering, and how this membrane grows thin,
and opens where the point of the egg is, I faw
two fits at fome diftance from each other, very
exactly cloſed by the membrane itſelf, one edge
of which paffed under the other in form of the
fcale of a fifh.
To know whether thefe apertures are always
found, I took another ovary, which feemed to
me to be much of the fame nature, and not being
able to find them either with the pipe or probe, I
made one myſelf with the lancet. But it was in
vain to blow into it, for the air did not paſs either
in the ovary or its veffels. I pierced other ovaries
in ſeveral places, and always in vain, which made
me judge that theſe apertures are not always found
and at all times. However, I have found them
fince in ſeveral ſubjects, as I fhall mention after-
wards.
To demonſtrate the ova without breaking their
outer covering, the ovary muſt be parted into two
by degrees, at the place where the veffels enter
it. Then moſt of the ova prefent themſelves, and
we have the pleaſure of feeing and obferving in
what manner the membrane is thinned, the places
where it is opened; and to conceive eafily how it
may be opened at the time of maturity. This did
not ſeem to me more difficult to comprehend,
than the manner in which moſt pods open, to
let out their feeds.
Having opened an ovary, the bignefs of which
depending on that of the fpongy body, I found
in the inner membrane a fit covered by a tuin
of
3
ROYAL ACADEMY of SCIENCES. 289
of the fame coat in form of a fcale, and on blow-
ing into it, I obferved that the air raiſed the
outer membrane, and made it play.
Jo
Continuing to labour on the fame fubject, I
found an ovary, in which the membrane of the
point of the spongy body was open again. I
was willing to be fure whether this aperture com-
municated with the blood-veffels, as in the pre-
ceding obfervation. I blowed in at the fpermatic
vein, the whole ovary fwelled, and I faw the
wind get out at this aperture. The ſpongy body
juſt mentioned feems to rife from the extremity
of the veffels, juft as fome muſhrooms grow upon
trees, the fponges upon briars, and the galls upon
oaks, by the aperture made by the puncture of
fome infect in fome veffel of thefe trees: we
may fay alſo, that the little bafon-like cavities
were like cups, or the lodges of fome ova, which
had gotten out, with the mouths of their veffels
remaining open; perhaps at laft they were recep-
tacles, which were to be filled with air and fpi-
rits, at certain times, to give more play to theſe
parts in the time of enjoyment, and to facilitate
in others the exit of the ova. Thefe facts, not-
withſtanding their being fo manifeft, were con-
teſted at the academy by part of the anatomiſts,
and they were defirous to fee them upon new
fubjects. Happily I met with three uteri of cows,
one of which inclofed a fatus of about 3 weeks
or a month. In another, I found each ovary co-
vered with the hood, and embraced by the ex-
panſions of the tube; but there did not appear
any thing particular in the third.
The ovaries of the portion, which inclofed a
fatus, were very different from each other.
VOL .I. No. 8.
! '
That
290 The HISTORY and MEMOIRS of the
That on the fide where the fetus was, feemed
withered, and not very veficular, and the upper
part was even, ſmooth, and of a dark yellow.
The other ovary was ftretched, entirely vefi-
cular, and in a manner tranfparent.
There was obferved at the point of the firſt o-
vary a little aperture, fhaped like a half crefcent,
of which one return fell upon the other; I drove
fome air into it, but it did not fwell the ovary.
ap-
At the lower part of this ovary, we perceived
near an ovum, a little red cicatrix, the fkin
peared thinned, and we difcovered a little aper-
ture in it, which was alfo fhaped like a half cre-
fcent. The wind, which was driven into it,
made one of the edges rife, but it did not pene-
trate quite into the ovary.
As this little aperture was at the place of the
egg, where the skin is ufually found thinned, and
as the air did not penetrate, I opened the ovary
into two parts, at the place where the veffels en-
tered, and the ovum ftill half covered with its
cup, remained faftened only to the place where
it appeared externally tranfparent.
After having emptied the liquor, I drove in
fome air, the membrane rofe, and the air got
out from between the cup and the ovum, by the
exterior aperture, which I have defcribed, and
the wind filled the membrane of the ovum.
To confirm myfelt in this experiment, I re-
peated it feveral times, and it always fucceeded.
I afterwards examined the ovaries wrapped up
in the expanfions of the tube, I blowed into it, and
the hood rofe. Having opened one of thefe o-
varies, I found a great many fibres in it, fo clofe-
ly faftened to its membrane, that, when we would
have feparated them, they tore in feveral places,
which made me fufpect this difpofition not to be
3
natural.
ROYAL ACADEMY of SCIENCES. 291
natural. This ovary incloſed a ſpongious body,
and a great number of veficles, the greateſt part
of which feemed half come out of their cups; and
when I blowed, the aimpaffed between the mem-
brane of the ovum and the cup. I afterwards
opened the covering of the other ovary; on
one of its fides, the point appeared red, like a
fruit of the winter cherry in its bladder; it was
the ſpongy body, the point of which was ex-
tremely foft, and open on one of its fides. Very
near to a ſmall red cicatrix there was an ovum
raiſed, which prefented itſelf like the point of an
acorn, when it begins to come out of its cup.
When we blowed againft the little cicatrix,
we faw a fmall membrane, fhaped like a half
creſcent, which paffed over the place. of the
ovum, that was ftill in the ovary. This ovary
being kept for fome days, the eggs grew wither-
ed, and when we went to prefs them, they rofe
again, and partly came out of the membrane.
On the other edge of the ovary there appeared
alfo two other eggs raiſed.
1
There were ſeveral fibres of the expansion of
the tube about the bafe of the fpongy body; fo
that we could fee but one half of them.
After having found feveral other ovaries,
opened at the point of the fpongy body, I drove
fome air into them, which made them fwell, and
came out either by the blood-veffels or spermatic
veffels.
There was in one of the biggeft ovaries that
could be found, a red procefs, the point of which
rofe out of the furface, when it was preffed on
the fides; it was the membrane that covers the
ovum before its getting out. It was alfo to
empty, that, when we blowed againſt it, it was
O02
im-
292 The HISTORY and MEMOIRS of the
immerged in the ovary, and eafily fhewed the
whole cavity of the ovum which had got out.
L
In another large ovary, which I had preſerved
in brandy, I obferved that the ova were all wi-
thered, and that the exterior membrane funk in-
wards, in fuch a manner that we could eafily
count them. Having dipped this ovary in wa-
ter, I blowed by the fpermatic vein, and faw
that not only the ovary fwelled, but that there
was alfo two large ova among others, which
fwelled as far as their coverings could extend,
thefe eggs feemed externally diftinguished from
the reft, by their figure and by their circum-
ference,
as long, ph
All that I have faid here has been obferved by
me alfo in theep, in the beginning of their preg-
nancy.
conor
}
An explanation of the figures.
Plate XV. Fig. 2. A. The ovary, upon which
are fhewn ova of different fizes, which are known
by their tranfparence.
h
B. The extremity, or the point of the ſpongy
body,"open at its upper part marked C.
D. D. The aperture of the expanfion of the
tube. wods m
0.0.0.0. Flefhy fibres about the expan-
fion of the tube.
گی۔
E. The expanſion of the tube, as it appeared
when it was blown into, fupported by the mem-
brane, which forms the hood.
F. F. F: The tube
al
G. The infertion, or entrance of the tube into
the cornu uteri.
}
H. One end of this horn.
I. I. I. I. I. I. I. I.' The fpermatic veins blown
up by the air driven in by the natural aperture
1
C;
ROYAL ACADEMY of SCIENCES. 293
C; which I have difcovered and demonftrated
upon ſeveral ſubjects.
K. The fpermatic artery.
Fig. 3. A. The extremity of the cornu uteri.
B. B. B. The tube.
F
C. The expanfion of the tube raiſed to fhew
the aperture, the flefhy fibres, and other neigh-
bouring parts, faſtened to the ovary marked
0.0.
D. D. D. D. D. Fleſhy fibres, feveral of which
are faſtened to the ovary marked O. O.
E. E. Two ova, a part of which was on the
outfide, the membrane of the ovary and the other
part on the infide, appearing like the point of
an acorn out of its cup.
1,
}
F. An aperture fhaped like a half crefcent,
which has been mentioned feveral times.
Fig. 4. Is an ovary uncovered.
A. A. A. A great fpongy body, of which,
I. I. Is the point.
R. The aperture, which is found fometimes,
and almoſt always at certain ſeaſons.
N. The entrance of a cavity, which leads to
the outer part, which is feen only by blowing.
P. P. Half the ovary, wherein are feen fe-
veral eggs, almoſt detached from their cup.
Fig. 5. Is an ovary feparated at the place
where the veffels enter, where eggs of different
fizes are ſeen.
ار
T. T. Is an ovum emptied of liquor, to fhew
how much the membrane of the ovary is thinned,
at the place where the egg muft go out.
Fig. 6, A. A. A. A. A. A. A part of the cornu
uteri.
S. S. S. S. S. The hood, which exactly em-
braces the ovary on all fides.
1
0. 0. 0. O. Q. Q. The tube, of which the ex-
panſion is hidden by the hood.
Fig.
294 The HISTORY and MEMOIRS of the
1
Fig. 7. fhews another ovary, which was alſo
embraced and hidden by the hood.
A. A. A. A. Part of the cornu uteri.
B. B. B. B. The hood opened.
C. C. C. The ovary, upon which are feen fe-
veral eggs, one of which appeared to be raiſed.
D. The fpongy body.
I. The place where it was opened.
X. An aperture ſhaped like a half creſcent, of
which the edge was raifed, which paffes over the
egg when it is blown into thro' a pipe.
Fig. VIII. and IX. reprefent an ovary on the
outfide and infide.
Fig. VIII. A. A. The fpongy body feparated
from the veficular membrane or ovary.
B. B. The part of the ovary, where the ova
were.
C. C. The two apertures fhaped like a half
crefcent.
Fig. IX. A. A. The fame ovary feen on the
infide, in which feveral ova are difcovered.
B. B. An egg emptied of the liquor, which
fhews by blowing in with a pipe the neareſt ex-
ternal aperture to the fpongy body.
VI. On the circulation of the blood in those
fishes which have gills, and on their refpi-
ration, by M. du Verney ſenior*
It is known by every body, that the heart of
all fishes, which do not breath air, has but one
cavity, and confequently but one auricle, at the
outlet of the veffel which returns the blood.
That of the heart of the carp is applied to the
left fide.
The flesh of the heart is very thick in
Nov. 29, 1701.
propor-
tion
ROYAL ACADEMY of SCIENCES. 295
tion to its bulk, and its fibres are very compact:
thus it has need of a very strong action for the cir-
culation, as we ſhall fee hereafter.
Every one knows what gills are; but every
one does not know, that theſe parts ſerve for
lungs to fifhes. Their fabrick is compofed of 4
ribs on each fide, which move upon themſelves
in opening and ſhutting, and alfo with regard to
their upper and lower fupports, in receding from
and approaching towards each other. The con-
vex fide of each rib is charged on both its edges
with two forts of lamina, each of which is com-
poſed of a row of narrow lamella, ranged and
locked againſt each other, which form as it were
fo many beards or fringes, like the vanes of a
feather; and thefe fringes are properly called the
lungs of the fishes.
Here is a very extraordinary, and very fingu-
lar fituation of the parts.
The thorax, as well as
the lungs, is in the mouth: the ribs bear the
lungs, and the animal breaths water.
The extremities of thefe ribs, which are to-
wards the throat, are joined together by feveral
little bones, which form a fort of fternum'; in
fuch fort however, that the ribs have a much
freer play upon the fternum, and can recede from
each other much more eaſily than thoſe of men,
and that the sternum can be raiſed and depreſſed.
The other extremities, which are towards the
baſe of the ſkull, are alfo joined by fome little
bones, which are articulated with this bafe, and
can recede from it, or approach to it.
Each rib is compofed of two pieces, joined by
a very fupple cartilage, which in each of thefe
parts is what the hinges are in mechanical works.
The first piece is bent into an arch, and its
length
296 The HISTORY and MEMOIRS of the
length is about a fixth portion of the circle of
which it would be a part.
The fecond almoft defcribes a capital Roman S.
The convex part of each rib is hollowed like a
gutter, and the veffels, which I fhall mention
afterwards, run along this gutter.
Each of the lamine, of which the lamelle are
compofed, is of the figure of a fcythe, and at
its origin it has a foot, which refts only by its
extremity on the edge of the rib.
Each of thefe lamine is compofed of 135
lamelle, thus the 16 contain 8,640 furfaces,
which I reckon here, becauſe the 2 furfaces of
each lamella are cloathed all over with a very
fine membrane, upon which are made almoſt
innumerable ramifications of the capillary veffels
of thefe forts of lungs.
I have fhewed the company, that there are
46 mufcles employed in the motions of theſe
ribs; 8 of them dilate the interval, and 16 con-
tract it, 6 inlarge the arch of each rib, and 12
contract it, and at the fame time deprefs the
fternum; and the other 4 raife it up.
The gills have a large aperture, upon which
is placed a cover compofed of an affemblage of
feveral pieces; it has the ufe of the leather of a
pair of bellows, and each cover is formed with
fuch artifice, that, in feparating from each other,
they bend outwards to augment the capacity of
the mouth, whilft cne of their pieces, which
plays on a fort of knee, keeps the apertures
of
the gills clofe, and opens them only to give
paffage to the water which the animal has re-
fpired, which is done at the fame time that the
cover is deprefied and contracted.
There are 2 muſcles, which ferve to raiſe this
cover,
ROYAL ACADEMY of SCIENCES. 297
cover, and 3 which ferve to deprefs and con-
tract it.
I have juft faid, that the affemblage, which
compoſes the ſtructure of the covers, makes
I fhall
them capable of bending outwards.
add 2 other circumftances. 1. That the
That the part of
this cover, which affifts in forming the under
part of the throat, is plaited like a fan upon lit-
tle bony lamella, to ferve, as it unfolds, for the
dilatation of the throat in the infpiration of the
water. 2. That each cover is cloathed both
within and without by a ſkin which adheres
very cloſely to it. Thefe 2 fkins joining together,
are prolonged to about 2 or 3 lines beyond the
circumference of the cover, and diminifh con-
tinually in thickneſs. This prolongation is much
larger under the throat, than towards the top of
the head. It is very fupple, that it may be ap-
plied the more exactly to the aperture upon
which it refts, and to keep it ſhut at the firſt
moment of the dilatation of the mouth for
refpiration.
The artery, which comes out of the heart,
dilates itſelf in fuch a manner, as to cover the
whole basis of it; and then contracting gradu-
ally it forms a fort of cone. At the place where
it is thus dilated, it is furniſhed on the infide
with feveral fleshy columns, which may be con-
fidered as fo many mufcles, which make of this
part of the aorta a fort of fecond heart, or at
leaft a fort of fecond ventricle, which joining its
preffure to that of the heart, doubles the force ne-
ceffary for the diftribution of the blood, in order
to the circulation.
This artery rifing by the interval between the
gills, makes over against each pair of ribs on
each fide, a great branch, which runs in the
VOL. I. No. 8.
Pp
gutter
258 The HISTORY and MEMOIRS of the
A
تم ؟
gutter hollowed on the outer furface of each
rib, from one extremity of the lamina to the
other. This is the courfe of the aorta in the
animals of this kind. The aorta, which in other
animals, carries the blood from the centre to
the circumference of the whole body, runs in
thefe, no farther than from the heart to the ex-
tremity of the gills, where it ends.
2
"
This branch furniſhes as many twigs, as there
are lamelle on each edge of the rib. The great
branch ends at the extremity of the rib, as has
been faid, and the twigs end at the extremity
of the lamelle, to which each of them is diftri
buted, selan
J
{
←
Each twig of an artery, rifes along the inner
edge of each lamella of the 2 lamine placed upon
each rib, that is, along both edges of the lamella,
which are towards each other, thefe 2 twigs in-
ofculate in the middle of their length; and con-
tinuing their courfe, reach as I have faid, to the
point of each lamella. There each twig of the
extremity of the artery, finds the mouth of a
vein; and thefe 2 mouths being immediately ap-
plied to each other, and making but one canal,
notwithstanding the differefft confiftence of the 2
veffels, the vein goes down upon the exterior
"edge of tach lamella, and being come to the
bottom of the lamella, it pours its blood into a
great venal veffel, couched near the branch of the
artery, in the whole extent of the gutter of the
rib, But it is not only by this immediate inof
Culation of the extremities of the artery and
the vein, that the artery difcharges itſelf into the
vein, But alfo by its whole courfe; in the fol-
Towing manffer! upon quind
The twig of the attery upon the edge of each
tamelle throws off, thro its whole courfe, upon
the
ROYAL ACADEMY of SCIENCES, 299
I
the flat of each lamella on both fides an infi-
nite number of veffels; which parting by pairs
from this twig, one on one fide, and the other
on the other, each of them on its own fide goes
ftrait to the yein, which defcends upon the op-
pofite edge of the lamella, and inofculates, with
it by an immediate contact. It is thus that the
blood paffes in this kind of animals, from their
pulmonary arteries into their veins from one end
to the other Their arteries are true arteries,
both by their structure, and by their carrying
the blood. Their veins are true veins, both by
their receiving the blood from the arteries, and
by the extreme delicacy of their confiftence. Thus
far there is nothing but what is in the ufual ceco-
nomy. But the fingularities are the imme-
diate inofculation of the arteries with the veins,
which is found indeed in the lungs of other ani-
mals, eſpecially in thofe of frogs and tortoifes,
but is not fo manifeft as in the gills of fishes.
2. The regularity of the diftribution, which ren-
ders this inofculation more visible in this kind of
animals; for all the branches of arteries, rifing
along the lamelle upon the ribs, are as ftrait, and
as equally diftant, from each other, as the lamella.
The tranfverfe capillary twigs, which part from
theſe branches at right angles, are equally diftant
from each other; fo that the direction and the in-
tervals of thefe veffels, both the upright and the
tranfverfe, being as regular, as if they had been
drawn by rule and compass, we follow them with
the eye and with the microfcope. We fee.there-
fore that the tranfverfe, arteries end immediately
in the body of the defcending vein, and each of
theſe veins, having received the blood from the
tranverſe capillary arteries on each fids of the
W
PP2you lamella,
to y
}
1300 The HISTORY and MEMOIRS of the
lamella, inofculates directly with the trunk of the
vein couched in the gutter.i
W
ons
¿
J
It muſt be confeffed, that this diftribution is
very fingular: but what follows is more fo.
Theſe trunks of veins, full of arterial blood,
coming out on each fide by their extrernity,
which is towards the basis of the cranium, take
the confiftence and thickness of arteries, and unite
themfelves again by pairs on each fide. That of
the firft rib furniſhes, before its reunion, fome
branches, which diftribute the blood to the or-
gans of fenfation, the brain, and neighbouring
parts, and by this means performs the functions,
which belong to the afcending aorta in quadrupeds,
then it joins itſelf again to that of the ſecond rib,
and theſe two together make but one trunk, which
running along the bafis of the cranium, receives
again on each fide another branch formed by the
reunion of the veins of the third and fourth parts
of the ribs, and altogther make but one trunk.
་
Afterwards this trunk, all the roots of which
were veins in the lungs, becoming an artery, by
its coat and office, continues its courfe along the
vertebra and diftributing the arterial blood to
all the other parts, performs the function of a
defcending aorta, and the arterial blood is by
this means equally diftributed to all the parts, to
nourish and animate them and there are roots
of veins every where, which take up the refidue
again, and carry it back by feveral trunks formed
by the union of all theſe roots, to the common
refervoir, which must return it to the heart; thus
the circulation is finiſhed in thefe animals.
But what increales the fingularity, is that theſe
very pulmonary veins coming out of the gutter
of the ribs by their extremity towards the throat,
proferve the coat and function of veins, by bring-
ing
ROYAL ACÁDEMY of SCIENCES. 301
ing back, into the recepticle of all the venal
blood, a portion of the arterial blood, which
they have received from the pulmonary arteries.
As the motion of the jaws contributes alfo to
the refpiration of fiſhes, it will not be amifs to
obferve, that the upper one is moveable, that.
it is compofed of feveral pieces, which are
naturally engaged in each other, in fuch a man-
ner, that they may, by unfolding, dilate and pro-
long the upper jaw.
All the parts, which ferve for the refpiration
of the carp, amount to fo furprifing a number,
that it cannot be amifs to enumerate them in this
place.
کرار
The bony parts are in number 4386 and
there are 69 mufcles.
The arteries of the gills, befides their eight
principal branches, divide into 4320 twigs; and
each twig makes on each fide, on the flat of each
lamella, an infinite number of tranfverfe capil-
lary arteries, the counting of which will not be
difficult, and will much exceed num-
all thefe
bers together.
I
There are as many nerves as arteries, the rami-
fications of the firft exactly following thofe of the
reft.
The veins, as well as the arteries, befides their
eight principal branches, make 4320 twigs,
which are mere tubes, and differ from the twigs
of the arteries, in not forming any tranfverfe ca-
pillary veffels.
The blood, which is brought back from all
the parts of the body of fiflies, enters the recep-
tacle, into which all the veins empty themselves
into the auricle, and thence into the heart; which,
by its contraction, drives it into the aorta, and
into all the ramifications, which it makes upon
the
302 The HISTORY and MEMOIRS of the
the lamelle of the gills: and as at its origin it is
furniſhed with feveral very thick fleshy columns,
which contract immediately afterwards; it fe-
conds and fortifies by its compreffion the action
of the heart, which is to drive the blood with much
more force into the tranfverfe capillary twigs, fi-
tuated on each ſide, upon all the lamella of the
gills.was quq o pengad
1
ก
It has been obferved, that this artery and its
branches run only from the heart to the extre-
mity of the gills. Thus this redoubled ſtroke of
a pifton muſt fuffice to drive the blood, with
inpetuolity, into this infinite number of little ar-
réries, fo ftrait and fo regular where the blood
finds no other dbftacle than meer contact; and
not the fhock and the reflections,pas in other ani-
mals, where the tarteries are ramified a thoufand
ways, efpecially in their luft fubdivificns.
So much for the paffage of the blood into the
lungs it remains for me now to fpeak of the
preparation of litur subɔem smet sé
I fuppofey that the particles of air, which are in
water as water is in a fpongedare able to dif
engage themselves from it feveral ways.. 1. By
heat, as we fee in boiling water. 2. By the
weakening of the ſpring of the air, which preffes
the water, in which thefe particles of air are en-
gaged, as we feed in the air pump. 3. By the
agitation and extreme divifion of the water, when it
has any degree of deaths eg, mode
*/\ We cannot queftion there being a great deal of
air in the bodies of fishes, and that this air is very
neceffary for them. Both thefe dre fhewn by the
air-pump÷mos 67 ingud nos silo s
Kliput a very brifk tench into a veffel full of
water, which was placed under angeceiver; and
after having given 5 or 6 furoaks of the pifton,
3
We
ROYAL ACADEMY of SCIENCES. 303
A
L
we obſerved that this tench was quite covered,
with an infinite number of little bubbles of air,
which got out from between the fcales; fo that
the whole body feemed fet with pearls. There
alſo got out a very great number by the gills,
much bigger than thofe on the furface of the
body. At last fome came out by the mouth, but
in lefs quantity. Beginning to pump anew two
or three times fucceffively, we obſerved that the
fiſh was agitated and tormented in an extraordinary
manner, and that it breathed more frequently.
After having ſpent a full quarter of an hour in
this condition, it grew languid, the whole body
and even the gills having no longer any fenfible
motion. Then taking the veffel from under the
receiver, we threw the fish into common water.
where it began to breath and fwim, but faintly,
and it was a long time in returning to its natural
ftate.
H
I made the fame experiment on a carp..
I
put it into the fame machine, and having pumped
the air 3 or 4 times, as we had done from the
tench, the fish began at firft to be agitated; the
whole furface of the body became pearled, there
came out of the mouth and gills an infinite num-
ber of very large bubbles of air, and the region
of the air-bladder fwelled very mucha gydy
Tho' this carp was bigger than the tench, the
beating of the gills ceafed fooners When we be-
gan to pump again, the gills began to beat again,
but only for a little while, and very faintly At
laft it continued without any motion); and, the
region of the bladder became fo foln and fo
ftretched, that the row began to come out at the
anus. This dafted about Biofdan hour, when it
died, being growthmary flat, Having we penesh, it
we found the bladder burb. novig prived 2006
We
304 The HISTORY and MEMOIRS of the
We also found by experiment, that a fish be-
ing put into water purged of air, cannot live there
long.
Befides thefe experiments, which may be made
in the air-pump, here are others, which prove
alfo that the air, which is mixed in the water,
has the principal fhare in the reſpiration of fishes.
If you inclofe fome fifhes in a glafs-veffel
full of water, they live for fome time, provided
the water is renewed: but if you cover the veffel,
and ſtop it, fo that the air cannot get in, the
fifhes will be ftifled. This proves that the water
ferves for their refpiration, only fo far as it has
liberty to be impregnated with air.
Put feveral fishes into a veffel, which is not
entirely filled with water, if you cloſe it, theſe
fishes, which before fwam at full liberty, and
were brifk, will be agitated, and prefs towards
the upper part, to refpire that portion of the wa-
ter, which is nearest to the air.
We obferve alfo, that when the furface of the
ponds is frozen, the fifhes die fooner or later, ac-
cording as the pond is of greater or lefs extent
and depth; and we obferve, that when the ice is
broken any where, the fishes preſent themſelves
haftily to breathe this water impregnated with
new air. Thefe experiments manifeftly prove
the neceffity of air for the refpiration of fifhes.
Let us fee now what paffes in the time of this re-
ſpiration.
The mouth opens, and the lips advance, and
thereby the cavity of the mouth is prolonged, the
throat fwells, the coverings of the gills, which
have the fame motion with the leathers of a pair
of bellows, feparating from each other, arch out-
wards by their midille only, whilft one of their
pieces, which plays upon a fort of knee, keeps
the
ROYAL ACADEMY of SCIENCES. 305
the apertures of the gills fhut, continually raiſing
themſelves a little, without permitting the water
to enter; becauſe the little fkin, which edges
each covering, clofes the aperture of the gills ex-
actly.
All this increaſes and inlarges every way the
capacity of the mouth, and determines the wa-
ter to enter into its cavity, juſt as the air enters by
the mouth and noftrils, into the trachea and lungs,
by the dilatation of the breaſt. At the fame
time the ribs of the gills open, by feparating from
each other; their arch is enlarged, the fternum is
withdrawn from the palate; and fo every thing
confpires to make the water enter the mouth in
greater quantity. Thus the infpiration of fiſhes is
performed. Afterwards the mouth fhuts; the
lips, which before were prolonged, contract them-
felves, eſpecially the upper one, which folds like
a fan, the lower lip fticks to the upper one by
means of a little fkin in form of a crefcent, which
falls down like a curtain, and hinders the water
from getting out. The cover is flatted upon the
aperture of the gills. At the fame time the ribs
cloſe againſt one another, their arch is contracted,
and the sternum finks upon the palate.
All this contributes to comprefs the water which
is entered into the mouth. It then prefents itfelf
to get out by all the intervals of the ribs, and by
thoſe of their lamella, and it paffes like fo many
wires; and by this motion the membranous bor-
der of the covers is raiſed, and the water being
preffed eſcapes by this aperture. Thus the ex-
piration is performed in filhes. We here fee, that
the water goes in at the mouth, and out at the
gills by a fort of circulation, quite contrary to
what happens in quadrupeds, in which the air goes
VOL. I. No. 8.
Q.9
in
306 The HISTORY and MEMOIRS of the
in and out alternately by the fame aperture of the
trachea.
This is all that concerns the motions of the re-
fpiration of fishes. Let us now purfue the courfe
of the blood in the gills, and fee what preparation
it there receives.
The blood, which comes out of the heart of
the carp, fpreads itfelf in fuch a manner upon all
the lamella, of which the gills are compofed,
that a very ſmall quantity of blood preſents it
felf to the water under a very great furface; that
by this means each of its parts may more eafily
and in lefs time be penetrated by the particles of
air, which are difengaged from the water, by the
extreme divifion that it fuffers between theſe la-
mella. It is for this that it was neceffary not only
that each lamina fhonld have fo great a number
of them, but alſo that all their furfaces fhould be
covered with tranfverfe capillary branches of the
aorta.
We obferve in fome meaſure the fame mecha-
nifm in the lungs of other animals; for they are
formed of a prodigious number of fmall mem-
branous veficles, which fupply the place of la-
melle, they are interwoven with an infinite num-
ber of ſmall veffels, which make the blood
ſpread itſelf in the fubftance of the lungs in fuch
a manner, as to prefent itfelf to the air under a
very great furface.
But the number of thefe veffels in the veficles of
the lungs does not come near the number of thofe
of the lamelle. It is alfo more difficult to draw air
from water, than to breathe pure air, fuch as en-
ters into the veficular lungs.
If we confider the extraordinary concuffion and
livifion, which the parts of air fuffer in the time
of expiration, we fhall be apt to believe, that it
1
3
is
ROYAL ACADEMY of SCIENCES. 307
is then that the air enters into the capillary veffels
of the gills. It is therefore probable, that the
fame thing happens in the lungs of other animals;
for as the air muſt have fome force to infinuate
itſelf into the veffels, it does not appear that it
can enter them in the time of infpiration, that is,
when it enters naturally into the lungs. On the
contrary, when it is repelled by the expiration,
it endeavours to eſcape on all fides; and forcing
all the obftacles that it meets, it paffes through
the thin and fine membranes, which compofe
the veffels, whilft the greateſt part of this air goes
out again by the trachea.
The difficulty, with which theſe fmall parts of
air paſs through the pores of thefe veffels, com-
preffes their ſpring; whence it follows, that when
they are entered, this fpring muft diſcharge with
impetuofity against the particles of the blood,
which are then depreffed, agitated, and pounded
with violence; which makes them fhock toge-
ther every way; and it is by this that they ac-
quire a new motion of liquidity and heat.
If this is true in the animals that breath air, it
muſt be ftill more true in the animals that breath
water; becauſe here the air is otherwife compref-
fed, than the free air is which they firtt refpire; fo
that the great feparation of theſe particles of air
fo compreffed, muft in fome meafure fupply the
lefs quantity of air, which enters into the veffels
of the gills.
When we confider that the blood of the veins.
of the gills is of a more vermillion red, than that
of the aorta, we eafily judge, that it is there
charged with fome particles of air. We obſerve
in other animals the fame difference between the
blood of the pulmonary artery, which is always
Q ૧ 2
of
308 The HISTORY and MEMOIRS of the
í
1
of a dark red, and that of the pulmonary vein,
which is always of a very bright red.
The blood thus impregnated with particles of
air, and thereby become truly arterial, enters
into the veins of the gills; and theſe veins com-
'ing out of the gutter of the ribs by the extremity,
which is towards the bafis of the cranium, take
the confiftence of arteries, and diftribute this blood
to all the parts. It is afterwards taken up again
by the veins which carry it to the heart.
It muſt not be forgot, that the artery which
proceeds from the heart, has a pulfation, whereas
the veffels, which perform the function of the
aorta, have none at all, or at leaft none that is
fenfible. 1. Becauſe they have no immediate
communication with the heart. 2. Becauſe the
blood paffes from a fmall tube into a great one,
But it muſt alſo be confidered, that the throwing
of the blood is not neceffary for the nutrition
of the parts, for which it is fufficient that the
blood flows with a gentle courfe; as it is al-
fo neceffary, that it fhould flow otherwife for
its diftribution and circulation, eſpecially in thoſe
animals, where it is much flower, which perfpire
but little, and can live a long time without any
nouriſhment!
i
It is eafy to judge by all that has been juſt ſaid,
that the fituation and conformation of the lungs
"and their commerce with the heart, are very dif-
ferent in the different fpecies of animals, which
was not unknown to Malpighi.
4
In the fetus, there are particular ducts, which
have fo near a communication with the ventri-
cles of the heart, and the head of the veffels of
the lungs, that they make almoſt all the nutri-
tious juices of the mother pafs immediately into
the aortay which diftributes them to all the reft
of
ROYAL ACADEMY of SCIENCES. 309
of the body: whereas, after the birth, all the
blood of the veins enters into the right ventricle,
which drives it immediately into the lungs; from
whence, after it has in a long circuit been im-
pregnated with particles of air, it paffes into the
left ventricle, which ſpreads it immediately by
the aorta into all the parts.
کلمه
14
HOWE
In tortoifes, frogs, and other animals analo-
gous to them, of the blood paffes through the
lungs at each circulation, and there receives all
the preparations neceffary for the functions of
life. This blood, which returns from the lungs,
mixes afterwards with that of the veins in the ca-
vity of the heart, where this laft being impreg-
nated with the active parts of the air, which the
firſt received in the lungs, is afterwards diftribu-
ted by the aorta to the whole body.
In fifhes, all the blood, which comes out of
the heart, paffes through the lungs, where being
alſo impregnated with the active parts of the air,
it afterwards diftributes itſelf through the whole
body, and fo far this circulation is conformable
to that of man. Fishes however have but one
fingle ventricle but this fingular circulation is
occafioned by the aorta, performing the office of
the pulmonary artery, and by the pulmonary
veins becoming arteries and performing the office
of the aorta.
In infects, the trachea, which ferve them for
lungs, are fpread through all the parts, where
they are ramified after the manner of the bran-
chia in the veficular lungs, fo that whereas in
other animals the air borrowed from the branchia
is diftributed into all the parts by the arteries, it is
here immediately diftributed into the juices which
are actually in each part.
to avort moin
The reafon of fo furpriſing a diſtribution comes
from
310 The HISTORY and MEMOIRS of the
from the nature of the liquors contained in the
tubes of theſe animals, which, that they may
be extremely glutinous and vifcid, and confequently
very fit to be connected together, and ftuck to the
furface of their veffels, ought to be impregnated,
in their whole courſe, with the active parts of
air, to facilitate their circulation, and render them
fit for nutrition,
We fee by this enumeration, that the functions
of the lungs have not always a cloſe connection
with thoſe of the heart, and that each of theſe
parts have very different ufes, with regard to the
blood.
The heart is only for the motion, which we
call circulation. The lungs favour it by the in-
troduction of the particles of air, and alfo by the
impulſe of the water into the animals in queſtion.
But its principal office is to impregnate the blood
with air, and thereby to render it capable of car-
rying the aliment, life, and heat all over. It is
for this reaſon, that we have juft fhewn, 1. That
in all animals, except infects, the blood never
paffes from the heart into the aorta, without hav-
ing paffed through the lungs, even in the fatus,
in the manner that we have explained. 2. That
in moſt it muſt neceffarily pass thither entire, as
in men, quadrupeds, birds, and fishes. 3. Or
that it paffes thither in part, as in tortoifes, frogs,
&c. And it is neceffary, that at leaſt of the
blood ſhould paſs through the lungs of thefe ani-
mals, to be vivified as much as their functions re-
quire.
3
Laſtly, we have fhewn, that if in infects there
are no lungs for the blood to pafs through, it is
becauſe the air is neceffarily mixed in all their
parts with the nutritious juices; fo that by this
mechanifm each part ferves for lungs to itſelf.
A
STAP.
A
damian stode to
TABL
AB LEVE
OF THE
ttt le annual
1
aludy usb ME
PAPERS contained in the ABRIDGMENT
of the HISTORY and MEMOIRS of the
ROYAL ACADEMY of SCIENCES at
PARIS, for the Year MDCCII.
I.
**
In the HISTORY.
...
N the effects of the elasticity of the air in
gunpowder and thunder.
II. On the cause of refraction.
III. Of the tarantula, and the cure of its bite by
mufick.
1
aj
IV. Of a very valuable loadſtone.
V. Of a pyramid of falt formed in a cryftalliſa-
nales?
tion.
VI. Of a woman delivered of four children at a
birth.
wlady gets ling
VII. Of the tides on the coast of Bretagne and
t
2967
Aura »
Normandy.
VIII. Of the making of allum, fine u.
IX. Microfcopical obfervations on a cheese-mite."
X. Of two kittens joined together from the bead
to the naveli,
+
* 2 * ba A
XI. On an ancient communication of the Medi
terranean with the Red Sea. V
r
XII. On the manner of cutting moulds for hyper-
bolical glaſſes, and for turning all conoids in
general.
*
L
at tỏi gnul on zuz
XIII. Of the reduction of the motions of animals
to the laws of mechanicks
X
uw ring
vy algo milum XIV.
312
A TABLE, &c.
XIV. Of the refiftance of hollow and folid cylin-
ders.
XV. Of machine invented by F. Sebaſtien,
In the MEMOIRS.
I. Obfervations on the quantity of rain, which fell
at the royal obfervatory in 1701, with fome
remarks on the thermometer and barometer,
by M. de la Hire.
II. A difcourfe on fome properties of the air, and
the means of knowing the temperature of it,
in all the climates of the earth, by M. A-
montons.
III. A comparison of the ancient itinerary mea-
fures with the modern, by M. Caſſini.
IV. Reflections on the measure of the earth, re-
lated by Snellius, in his book intitled, Era-
teſthenes Batavus, by M. Caffini the fon.
V. Remarks on the different manner of managing
the common oars, aud the turning oars,
lately proposed by the Sieur du Guet, by M.
Chazelles.
VI. An obfervation on a column of light feen at
the obfervatory, May 11, 1702, in the
morning, by M. de la Hire.
VII. Obfervations made by means of the burning-
glass, by M. Homberg.
VIII. A deſcription of the labyrinth of Candy,
:
with fome obfervations on the growth and ge
neration of ftones, by M. Tournefort.
IX. An estimate of the power neceſſary to move
boats, both in ftagnant and running waters,
either by a rope or by oars, or any other ma-
chine, by M. de la Hire.
AN
AN
ABRIDGMENT
OF THE
PHILOSOPHICAL DISCOVERIES and OB-
SERVATIONS, in the HISTORY of the
ROYAL ACADEMY of SCIENCES at
Paris, for the Year 1702.
I. On the effects of the elasticity of the air
in gunpowder and thunder, tranflated by
Mr. Chambers.
HE air, which, till of late, appeared a
TH
fluid almoſt void of action, is now found
one of the moſt violent and univerfal agents in all
nature. The force, for inftance, of gunpowder,
how furpriſing foever, is only the force of the
air. There is air inclofed, or rather crowded
and impriſoned, in each grain of the powder;
and there is likewife air in all the intervals be-
tween the grains, and when the powder takes fire,
the fprings of all theſe little portions of air open
and unbend themſelves all at once. Thefe fprings
are the only caufe of fuch prodigious effects, the
powder only ferving to light a fire to put the air
in action; after which 'tis the air alone that is
to do all.
+
?
Hence M. de la Hire has ventured to afcribe *!
all the phenomena of gunpowder to the proper-
ties of elasticity, the principal whereof, or at
leaft thoſe of moft importance in his enquiry, are
as follow.
A fpring, for inſtance, a bended leaf, or la-
mella of fteel, tends to unbend itſelf on the two
VOL. I. No. 8. Rr
op
314 The HISTORY and MEMOIRS of the
AL
2:
Re
bas
oppofite fides with equal violence, it requires as
certain refiftance to enable it to exercife its whole
force, and it acts fo much the lefs, as the body it
acts againſt yields or gives way more eafily. A
fpring, in fine, has a greater effect on one fide,
when it meets with a refiftance on the oppofite
one.
On theſe fuppofitions, M. de la Hire firft con-
fiders all the ſprings of the air put in action by
the fire which lights the powder in the barrel of
a gun fome philofophers have imagined, that
when lighted fucceffively, its effort is greater in
the part where it was firft kindled, by reafon its
violence is here augmented by that which kindles
afterwards: but this muft be a mistake; for ac-
cording to the remark of M. de la Hire, a fpring
refting upon another equal fpring, and refifted
by it, has all the force it is capable of, nor will
receive any addition by any number of other
fprings fucceeding each other, either to ſuſtain it,
or to fuftain thoſe it bears upon. On the contrary,
the force of the firft may perhaps be diminiſhed,
while the others are put in motion; and if during
this fpace of time, the body againſt which they
are to act begins to give way, their action of con-
fequence will be fo much the weaker.
'Tis better therefore that the fprings all unbend
together, even though one would only have them
act in the place where the powder firft begins to
take fire 'tis evident befides, that if the powder
kindle all at once, a greater heat will arife, and
confequently the ſprings be put in a greater ten-
fion; and that as they will hereby fuftain each
other at the fame time, they will be capable of
the greater effort towards every fide, all we have
to be apprehenfive of is the cannon's burfting, by
a too hafty and fudden inflamation of the whole
powder;
ROYAL ACADEMY of SCIENCES. 315
powder; on which account it has been found pro-
per to have it a little diminished. de
The cannon being fuppofed thick enough to
refift all the impulfe.directed from the axis of the
barrel towards its circumference, there only re-
mains that which is in the direction of the breech
and mouth, the fprings drive equally in thofe two
contrary ways, and hence it happens, that the
cannon rebounds or flies backwards, while the
ball iffues the other way. ·
量
​T
The force therefore, which caufes the rebound,
is the fame as that which caufes the motion of
the ball, whence then does it proceed, that the
motion of the ball is of fo great an extent, and
that of the rebound fo little? The reafon is,
that the cannon finds much more oppofition to its
moving backwards, than the ball to its moving
forwards; and as the two effects arife from an
equal power, the way paffed over by the ball, is
fo much greater, than that paffed by the cannon,
as the difficulty of its moving backwards furpaffes
that of the ball's moving forwards.
}
Hence there muſt be a great refiftance made to
the rebound of the cannon. This reſiſtance we
ſeem to have from the friction of fo heavy a ma-
chine, as a cannon with its carriage against the
ground; but this is not all, for the refiftance of a
motion is ſo much the greater, as this motion is
quicker; and when its quickneſs is fuch, as that
the refifting power has no time to give way in
this cafe, a body very weak of itſelf may do the
office of any movable obftacle. Thus it is, that
the air and water, when ftruck fo haftily, and
with fuch nimblenefs, that they have not time to
recede, become fixed points; one of them for
the flight of birds, and the other for the action of
oars; ſo a ſtaff fufpended at the two ends, by
Rr
J <
✓ flor
w
(
two
316 The HISTORY and MEMOIRS of the
1
Canto
7
two flender threads, may be ftrnck in the middle
with fo quick a motion, as to break it in two
without injuring the threads it was fuftained by;
for the fibres of fuch threads require a certain time
to be lengthened and extended, fo as to feparate,
which time is not here allowed them; befides,
that the air not having been able to efcape quick
enough from behind the ftaff, fuftained it as it
were, and thus expofed it to receive the whole im-
preffion of the ftroke, the extreme velocity there-
fore, or as I would rather call it, the extreme
fuddennefs of the motion, which the powder
gives the cannon, muft augment the refiftance
made to its rebounding, either by the ground,
or even by the air, if a cannon were fufpended,
experience fhews us, that the rebound would be
very great.
A rocket, whofe conftruction I here fuppofe
known, is only a little light cannon, which by
the impulfe of the lighted matter it contains, re-
bounds upwards in the direction of its breech,
and this with the fame velocity, as that where-
with the combuflible matter ftreams out at its
mouth, which looks downwards in effect; this
rebound is the rife of the rocket.
When the rocket is charged with all its matter,
if its centre of gravity were above the centre of
its figure, with regard to the clofe end, which
is what goes foremoft, it would follow from fome
reafons, laid down in the hiftory of 1700*,
that as foon as the rocket began to rife, it
would defcribe a femicircle in the air, till it
became upfide down, and after this would fall
back again, by reafon the clofe end which makes
the rebound, would be turned towards the earth;
now it being impoffible in the practice to deter-
mine the precife place of the centre of gravity and
Pag. 191. of this abridgment.
· its
ROVAL ACADEMY of SCIENCES. 317
?
chussult jobrol of
MORDIY
102970n
77
ex-
its poſition, with regard to its centre of magni-
tude, recourſe is had to a fhorter and eafier ex
pedient, a ftick is tied to one end of the rocket,
whoſe weight is fuch, as that the centre of gra-
vity of the rocket and ftick taken together, falls
a little below the aperture of the rocket; if this
centre be below that aperture when the rocket is
intire, it will be more below it ftill when it rifes,
fince it is continually difcharging its combustible
matters, and thus becomes lighterand lighter. This
centre therefore is always defcending in proportion
as the rocket rifes, and thus makes it preferve a
direct motion.
K.
ud bas
M. de la Hire confeffes to the glory of that
vague and inaccurate experience, which produced
the arts, that he believes the moft fubtil fpecula-
tion cannot add any thing to the conftruction of
rockets; only he obferves, that the ftick being
faſtened to one of the fides, the centre of gravity
of the whole cannot be in the axis of the rocket,
and confequently that it can never rife quite ver-
tically; but that in order to give it this direction,
it would be better to faften two flicks to the two
fides, both of them only weighing the fame as
one ſhould have done.'
'Tis eafy to apply the principles which obtain
in cannons and rockets to petards. To augment
the effect of a petard against a gate or wall, it is
faſtened to, M. de la Hire propofes, that it be
rendered perfectly firm and immovable on the
oppofite fide; this will prevent its rebounding, and
redouble its violence on that fide it is to act on..
1
Thunder itſelf is only a kind of lighted gun-
powder, and men may without prefumption
boaft they have imitated it. 'Tis a mixture of
fulphur and ſalt petre, or other matters, near a-
kin to them, and the air dilated, and its fprings
put
318 The HISTORY and MEMOIRS of the
1
}
put in action by the inflammation thereof, pro-
u ces the principal phenomena of thunder.
'
If this air, when it dilates and unbends, meet
with nothing to refift it, we find lightening pro-
duced, but hear no noiſe; if it meet with clouds,
which oppofe its motion, there arifes a friction or
collifion of the air, which occafions the noiſe,
and this noife is fo much the greater, as thefe
clouds being formed of little particles of ice, are
lefs difpofed to receive motion from an inflamed
air, when the fire produced by thunder moves
with fo much violence, as to compreſs and ftrain
the fprings of the grofs air around it, this air be-
comes capable hereby of refifting and driving it
back again, which happening feveral times to-
gether, makes the lightning appear like waving
darts of fire.
The air neareſt the earth being the groffeft,
muſt make the moft refiftance to the motion of
thunder,that is,muft tend moft to make it reafcend;
and hence the flame must be frequently repelled
towards the place it arofe from, and thus fpend
itſelf without effect.
We fometimes find water fpout through the
adjutage of a fountain, three or four times higher
than the height of the refervoir can occafion, tho
it quickly returns again to the regular height; if it
be enquired how it came to exceed it, M. de la
Hire attributes it to the air incloſed in the pipe,
which having been compreffed by the water con-
tinually defcending, unbended itſelf againſt that
which was afcending, and gave it this momen-
tary velocity; fo he alfo imagines, that the vio-
lence of thunder may fometimes be increaſed by
the air, which after a ftrong compreffion, occa-
fioned by the fire of the thunder, itfelf refumes
its natural extenfion: were one to purfue all the
effects
ROYAL ACADEMY of SCIENCES. 319
SOUTH
effects of the air, it would be found, as it were,
the only foul of the world, if by world we mean
that which we inhabit, and which furrounds us
neareſt.
II. On the cauſe of refraction, tranflated by
Mr. Chambers.
The difpute about refraction between Meff.
Defcartes and Fermat is famous; they had each
of them their way of demonftrating, that an
oblique ray paffing out of air into water, muſt be
refracted towards the perpendicular. But in Def
cartes's demonftration, it was fuppofed, that the
rays penetrate water more eaſily than air. Where-
as it followed from that of Fermat, that the rays
penetrate air more eafily than water; this was
the chief point in difpute between thoſe two
great men, and it afterwards divided the otherphi-
lofophers.
;
M. Carré has efpoufed Defcartes's fide, affert-
ing, that the air makes more oppofition to the
paffage of light than water does, notwithſtand-
ing that it receives a much greater quantity
thereof, and reflects it lefs; for thoſe two things
may be eaſily ſeparated. According to this author,
air is the only body penetrable by light, all other
bodies are folid with refpect thereto, and reflect
it; and when light paffes through water, or glafs,
it only paffes through the air contained in their
pores, the proper particles of the glafs or water
reflecting it back again; and hence that multi-
tude of reflections in tranfparent bodies, the par-
ticles of that fpacious fluid, which we properly
call air, have a liberty of moving beyond all
compariſon greater than thofe of air inclofed and
imprifoned in water or glafs, now the extreme
mobi-
320 The HISTORY and MEMOIRS of the
mobility of the particles of free or open air, and
their continual agitation every way, proves a
great impediment to the motion of a ray of light,
diſturbing, interrupting, and confequently weak-
ning and diminiſhing its velocity; whereas the
air incloſed in tranfparent bodies, being lefs mova-
ble, proves leís detrimental to the motion of the
rays; and hence it follows, that of all bodies pe-
netrable by light, free air is the most difficultly
penetrable, and that all other give it the eafier
paffage, as they contain lefs air and are more
denſe.
•
Accordingly glafs, which contains lefs air than
water, is more favourable to the paffage of light,
and refracts it more; fo boiling water, which
has emitted a great quantity of air, occafions a
greater refraction than cold water, and the re-
fraction of oil is but little different from that of
glaſs, by reaſon it only contains little air, as we
find by putting it in vacuo; 'tis true fpirit of
wine in thoſe circumftances bubbles extremely,
and confequently feems to contain a deal of air,
yet its refraction is equal to that of oil; but this
ebullition is of no continuance, and the air which
arifes from it all at once is but fmall in quantity.
To eſtabliſh this fyftem of M. Carré, a greater
number of experiments fhould be made
upon the
magnitude of refraction, in refpect of the weight
and the quantity of air contained in fluids, and
the denſity of folid bodies which are tranfparent.
In the mean time it is fome prejudice in behalf of
this opinion, that a mufket-ball fhot off lightly
upon the water, feems to be refracted from the
perpendicular; now 'tis certain, that water being
more difficult to divide, makes more refiftance
to the motion of the ball than air does; if it like-
wife made more refiftances to the motion of a
ray,
I
ROYAL ACADEMY of SCIENCES. 321
ray, this too would be refracted from the per-
pendicular, whereas it is really refracted towards it.
J
III. Of the tarantula, and the cure of its
bite by mufick, tranflated by Mr. Chambers.
M. Geoffroy, being returned from a journey to
Italy, has fhewn the academy fome dead taran-
tulas he brought with him. The tarantula is a
large fpider, with eight eyes and as many legs;
but what is moft fingular in it, are two horns or
trunks, which it is continually moving, efpeci-
ally when in fearch of food; whence M. Geof-
froy conjectures them to be movable noſtrils.
The tarantula is not only found about Taren-
tum, from whence its name is taken, and through-
out Apulea, but alfo in feveral other parts of
Italy, and in the iſland of Corfica; only thofe of
Apulea are the moſt dangerous, tho' none are
much fo but thofe on the plains, where the air
is confiderably hotter than on the mountains;
and ſome even affert, that the animal is never ve-
nemous, except in coupling time.
Soon after a perfon has been bitten by a ta-
rantula, there enfues a very acute pain in the
part, and fome hours after a numbnefs; then he
falls into a profound fadneſs, refpiration grows
difficult, the pulfe weakens, the fight becomes
dim, and the eyes look wild; at length all fenfe
and motion are loft, and the patient dies unleſs
he be relieved.
嗤
​All the help phyfick affords confifts in a few
operations on the wound, with the ufe of cor-
dials and fudorifficks; but another much furer
and more efficacious remedy, which reafoning
and art would never have attained to, as being
accidentally difcovered, viz. mufick::
VOL. I. N°.9.
Sf
1
When
*.
322 The HISTORY and MEMOIRS of the
When the perſon bitten is left without ſenſe
and motion, a muſician tries different tunes, till
he meets with that whofe notes and modulation
fuit the patient; upon which a flight motion or
tremor appears in his body, then his fingers be-
gin to move in cadence, then his arms, legs, and
by degrees his whole body, till at laſt he rifes on
his feet, and falls a dancing, in which he con-
tinues, ftill increafing both in activity and ftrength.
Some will even dance fix hours together without
refting; after this the perfon is put to bed, and
when he is judged fufficiently recovered from
his firſt dance, they draw him out of bed by the
fame tune for a new dance. This exercife holds
feveral days, fix or ſeven at moſt, till fuch time
as the patient finds himſelf fatigued, and unable
to dance any longer, which is the indication 'of
his cure; for fo long as the poifon acts on him,
he would dance if they would let him, without
any diſcontinuance, till his ftrength being utterly
exhauſted, he ſhould die on the ſpot. When the
patient begins to find himſelf a weary, he comes
a little to his fenfes, and recovers as from a pro-
found fleep, without remembering any thing
of what paft during his accefs, not even his
dancing.
The patient thus recovered from his first acceſs,
is ſometimes intirely cured; if he be not, there
remains a black melancholly and alienation
of mind upon him; he fhuns the fight of man,
and feeks for water; and if he be not carefully
watched, throws himfelf into the firft river that
falls in his way. To the other fymptoms of this
difeafe muſt be added an averfion for black and
blue; and on the contrary, an affection for white,
red, and green.
If
ROYAL ACADEMY of SCIENCES. 323
If the perfon do not die, the fit returns at the
year's end, much about the time when he was
bitten; fo that he muft go to dancing again;
fome have had thefe periodical returns for 20
or 30 years running.
Each patient has his peculiar and fpecifick
tune; but all the airs or tunes in general are of
very briſk meaſure.
Thus much is attefted by perfons of the utmoſt
veracity; and was alfo confirmed to the academy,
not only by what informations M. Geoffroy could
procure in Italy, but alfo by the letters of a Jefuit
of Toulon to F. Gouye, who related, that he had
feen an Italian foldier bitten by a tarantula danced
feveral days together.
To facts fo very extraordinary, 'tis no won-
der if a few fables be added; fuch, for inſtance,
as this, that the patient is only affected fo long
as the tarantula that bit him is alive; and that
the tarantula itſelf dances to the fame tune.
'Tis not unreaſonable to ſuppoſe with M. Geof-
froy, that the poifon of the tarantula may occa-
fion an extraordinary tenfion of the nerves,
much greater than is fuited to their reſpective
functions, and hence the lofs of memory and
motion; but at the fame time, this tenfion being
equal to that of fome ftrings of an inftrument,
puts the nerves in motion to a certain tone, and
obliges them to vibrate when ftruck by the un-
dulations peculiar to that tone; and hence the
cure by mufick; for motion being thus reftored
to the nerves, by a proper mode, the fpirits are
recalled, which before had almoft intirely aban-
doned them.
It may perhaps be added, with fome proba-
bility, and pretty much on the fame principles,
if the patient's averfion for certain colours arifes
Sf2
324 The HISTORY and MEMOIRS of the
from this, that the tenfion of his nerves, even
out of the accefs, being ftill different from its
natural ſtate, the vibrations thofe colours occafion
in the fibres of the brain, are too contrary to
their difpofition, and make a kind of diffonance
therein, which is pain.
*
IV. Of a very valuable loadftone.
M. Carré read a letter written from Holland,
wherein mention was made of a loadftone, which
weighs 11 ounces, and lifts 28 pounds of iron,
that is above 40 times its own weight. They afk
5000 livres for it.
V. Of a pyramid of falt formed in a cryf
tallifation.
M. Homberg fhewed a little pyramid of falt,
which had formed itſelf in a cryftalliſation. It
was not very high in proportion to its bafe; it was
hollow within, and in forming itfelf, had its baſe
turned upwards. M. Homberg explained the fact
thus. At first, there was formed on the furface
of the falted water a little cube of falt, which is
the figure naturally affected by falt. This cube,
tho' heavier than the falted water, did not fink,
any more than a needle would do, if laid on
gently, and for the fame reafon; for when a
needle is thus laid on the water, there is a little.
hollow formed about it, filled only with air, where
it is, as it were, in a little boat, becauſe the bulk
of the little hollow, and of the needle together, is
lighter than a like bulk of water. There was
formed a like hollow about the cube of falt,
which plunged a little in the water without fink-
ing fo that its upper furface being not fo high
as
ROYAL ACADEMY of SCIENCES. 325
as that of the water, it continued dry. Along the
four fides of this dry furface, other cubes of falt
were cryftalliſed, which began by forming a lit-
tle hollow fquare, of which the firſt cube formed
the baſe. All theſe little cubes together, being
heavier than the first fingle one, and being en-
compaffed with lefs air in proportion, becauſe
they joined the firſt by their inner fides, plunged
a little more in the water, that is, to the upper
furface of the little cubes which touched the firft.
About thefe, other cubes were cryftallifed, which
plunged ftill deeper in the water. This conti-
nuing for fome time, as the hollow fquare grew
bigger, fo it plunged more and more, and formed
the inverted pyramid, which growing at laſt too
heavy, precipitated itſelf down to the bottom of
the water, where it left increafing.
A
VI. Of a woman delivered of four children
at a birth.
M. Lemery has related, that on the 19th of
June, a young woman of Lyons, aged 23, at her
firſt lying in, at the end of 7 months, was de-
livered of 3 boys and girl, all of them 14 in-
ches and fix lines in length, and they lived long
enough to be baptifed.
VII. Of the tides on the coast of Bretagne
and Normandy.
M. Carré had a queftion fent him from Bre-
tagne, why on the N. coaft of that province the
tides continually increaſe from Breft to St. Malo,
where they are fo high at the new and full moons,
as to rife 60 and 80 feet; and why from St. Malo
they
326 The HISTORY and MEMOIRS of the
they continually diminiſh along the coafts of Nor-
mandy?
1
M. Carré anſwered this queſtion by the figure
only of the coafts and ftraits. The tide, which
from the great extent of the Atlantic ocean, ſpreads
itſelf on the N. coaft of Bretagne, meets at the
fame time the outlet of la Manche, which is a
much narrower fpace than that from which it
comes. It muft fwell therefore at the entrance of
this channel, and take in height what the channel
wants in breadth, to contain the water that it
brings. The channel is afterwards more con-
tracted, and confequently the water rifes ftill
more. The town of St. Malo is ſituated in a fort
of returning angle, formed by the coaft of Bre-
tagne and Normandy, the tide is obliged to take
the fame direction with the N. coaft of Bretagne,
that is, a S. W. direction; having this courfe, it
goes directly againſt the English coaſt of Corn-
wall; whence it is ftrongly beat back exactly to
the corner where St. Malo is. There the waters.
being retained, and in a manner fhut up, muft
neceffarily rife. But beyond St. Malo the tide muft
find more liberty in its courfe along the coafts of
Normandy.
VIII. Of the making of allum.
M. Geoffroy informed himſelf exactly in Italy
of the manner of making roch allum at Civita
Vecchia. There are near that city fome quarries
of a greyish or reddiſh ſtone, pretty hard, and
like the Travertin. They calcine it in ovens,
and then diffolve the lime in water over a great
fire, the water gets all the falt out of it, and this
falt is allum'; there feparates an uſeleſs earth from
it, and at laft they leave this water to reft im-
pregnated
ROYAL ACADEMY of SCIENCES. 327
pregnated with a falt, which for fome days cryf-
tallifes of itſelf, as tartar does about the cafks,
and makes what is called roch allum. This is
only a general account of the operation; but M.
Geoffroy relates all the particulars.
Allum is made alfo at Solfatara near Puzzoli,
in the kingdom of Naples. Solfatara was for-
merly a burning mountain, of which there now
remains nothing but ruins, and a crown or cinc-
ture of white, yellowish, dry, half burnt and
calcined rocks, from which there comes out a very
thick fmoak in ſeveral places. The tradition of
the country is, that the earth between thefe rocks,
which made the top of the mountain, funk down
to a certain height. They go up over burning
rocks to go down again into a little low plain,
which muſt have been the top. It is almoft oval,
1246 feet long in its greateft extent, and 1000
feet broad. The foil of this plain is a yellow and
white fubftance, very falt, and fo hot in fome
places, that one cannot hold ones hand long upon
it. In fummer, there arifes on the furface of this
earth a falt flower or duft, which they need only
ſweep, and fhove into fome pits of water, which
are at the bottom of the plain; after which, to
evaporate this water, being well loaded with falt
and purified from the earth, there needs no other
fire than that which burns under the mountain;
the water is put into cauldrons funk into the
ground, without any other trouble. This allum
is not fo much efteemed as that of Civita Vecchia.
They make fulphur alfo at Solfatara, and thence
the place has obtained its name.
M. Geoffroy, to render his hiſtory of allum
more complete, has added the manner of making
it in England, in Yorkshire and Lancashire, and
alfo in Sweden.
It
328 The HISTORY and MEMOIRS of the
€
It appears by all the preparations of allum,
that the fame mine which affords it, does alfo,
or may at leaſt afford fulphur, nitre, and vitriol.
Perhaps theſe different minerals are at the bottom
only one principle, difguifed under theſe four
falts, according as it has been mixed by nature
with certain fubftances, or according as it has
been managed by men. M. Geoffroy thinks, that
the English and Swedish allums may partake more
of vitriol, and the Italian of ſea falt, which may
cauſe a variation in fome nice operations, or
change the effect of fome medicines, which re-
quire a great exactnefs.
IX. Microfcopical obfervations on a cheeſe-
lvos pal
f
}
mite.
M. Sauveur imparted to the company a fact
that M. Farger had writ to him from Breft. M.
Mollard, chief engineer, had fhut up in a little
common microſcope, a cheeſe-mite to ſee what
would become of it. This worm lived above feven
months without taking any nouriſhment, unleſs
the little air, which was in the microſcope, fupplied
it with any. It always moved. fenfibly, chiefly
when it was expofed to the fun; then it turned
and agitated itſelf a hundred different ways. At
laft it died, and from day to day, from white,
it became redo This little carcafs dried like a
chrysalis of filk worm, and at the end of 12
days, there came out of it a fly as big as the
worm. It was not at all made like the common
Alies, butallinle longer, cand. of the figure of thofe
which we forbetimes fee about neceffary houſes.
It neverytda any nouriſhment, unless it was that
of the abryfalis which it came out of. It died
at
3
ROYAL ACADEMY of SCIENCES. 329
at the end of ten days, and afterward dried and
wafted.
X. Of two kittens joined together from the
head to the navel.
M. Mery fhewed to the company two kittens,
which were united in the belly of their mother
They were joined from the head to the navel, and
made in all this extent but one fingle body; but in
all the reft, they were two very diftinct, and well
feparated. We fhall not enter into a more parti-
cular detail of this monſter; it is eaſy to imagine in
general, that two ova, or if they are not admitted
to be ova, two little fætus's in their firſt formation,
finding themſelves of equal ftrength, and alfo
meeting too near in the uterus, may faften and
ftick together, after which the liquors that ought
to nouriſh and ſtrengthen them, being become
common to them, they intirely quit, in one or
other, certain courfes in which they would flow
with difficulty, which abfolutely makes certain
parts in one of the fetus's periſh, and renders
them fingle for both, while thefe liquors flowing
in the other parts of the two fetus's with equal
eafe, keeps them always double. The meeting
of the 2 fætus's is only chance, and from certain
directions of the veſſel more or leſs favourable to
the courſe of the liquors, which makes them quit
certain ways, and always follow others; and as
this chance is fufceptible of an infinity of diffe-
rent combinations, the double monsters are infi-
nite.
M. Mery's two kittens are in another reſpect
more worthy of the attention and furprize of
philofophers. They had but one oefophagus and
one trachea; but theſe two canals were joined in
VOL. I. N°. 9.
T:
fuch
330 The HISTORY and MEMOIRS of the
907 J
Not nopu
J00
ſuch a manner, that they made but one, and this
fingle canal had no communication but with the
ſtomach, and no ways with the lungs, and confe-
quently was only one fimple oefophagus. The
monſter could not therefore take in any air; and
yet it lived about an hour after being out of the
mother's belly.
M
Hardw
dbirlw dono
JiiИ adi
XI. On an ancient communication of the Me-
diterranean with the Red-fea.
M. le Comte de Pontchartrain, making uſe of
his authority to affift the progreſs of the fciences,
had fent into Egypt fome memoirs made by M.
Delifle, which pointed out what was to be wifhed,
in order to rectify the map of that country. Theſe
memoirs were accompanied with very ftrong re-
commendations to the confuls and vice-confuls.
It was in the execution of thefe orders of M. de
Pontchartrain, that M. Boutier travelled over the
whole Delta, and fent to that minifter a map of
it, with a little account which explained it. M.
Delifle, to whom M. le Comte de Pontchartrain
had done the honour to fend the whole, fpake of
it to the academy.
The modern Egypt is but little known, altho'
fufficiently near and frequented; and we may
reckon, that it is the fame with all countries,
where the inhabitants are in ignorance, and where
learned ftrangers feldom travel, at leaft to make
obfervations. Altho' M. Boutier has not tra-
velled over the Lower Egypt, fo much as it would
be neceffary, he has neverthelefs, in M. Delife's
account, confiderably reftored the map, which
was very much disfigured. He begins with con-
fidering the Delta of the ancients, thofe mouths
which they have afcribed to the Nile, the greateſt
7
god
part
ROYAL ACADEMY of SCIENCES. 331
part
of which had been loft by the ignorance of
the modern geographers, a great number of
towns, whoſe names are not yet much altered; for
example, Samanout, or according to the Coptes,
Sebennetu, which is the ancient Sebennitus, Ab-
boutfier, or Butfir, which is Bufiris, &c. But
what is moſt remarkable in this map, is an ex-
tremity of a canal, which goes out of the moft
eaftern arm of the Nile, and which M. Delifle
judges to have been a part of that which formerly
made the communication of the Nile and the
Mediterranean with the Red-fea.
A
As this ancient communication, which M. De-
lifle eſtabliſhed for an indubitable fact, is unknown
at this time, even by many of the learned, we
were glad to fee the proofs which he had of it ;
he gave them fo plainly, and took the greateſt
part of them in places fo well known, that all
the difficulty that remains is, to know how they
have eſcaped the obfervation of every body.
Herodotus, in his fecond book, fays, there was
in the plain of Egypt, a canal drawn from the
Nile, a little above the town of Bubafte, and
below a mountain, which went on the fide of
Memphis, that this canal was extended very far
from Weft to Eaft, that afterwards it turned to
the South, and flowed into the Red-fea; that
Nechus, fon of Pfammiticus, was the firft that
undertook this work, where 120,000 men had
perifhed, that they had quitted it upon the an-
fwer of an oracle; but that Darius, fon of Hyf-
tafpes, had finiſhed it; that it was four days na-
vigation and that two gallies might paſs abreaft
in it.
Diodorus fpeaks of it in the firft book of his
Bibliotheca, and agrees with Herodotus, except
in this, that he makes the canal to be left unfi
Tţ 2
nished
332 The HISTORY and MEMOIRS of the
i
nished by Darius, to whom very bad engineers
had reprefented, that the Red-fea, being higher
than Egypt, would overflow it; and in this, that
he does not make the work to be finiſhed but by
Ptolomeus Philadelphus. He adds, that this
canal had been called the river of Ptolomy, that
this prince had caufed a town to be built at its
outlet into the Red-fea, which he had named Ar-
finoe, from one of his fifters that he loved, and
that the canal might be opened or fhut, according
as it was neceffary for navigation.
*
Strabo, lib. 17. of his geography, agrees with
Diodorus, in every thing, it only remains to
reconcile Herodotus, who makes the work to
be finiſhed by Darius, with Strabo and Dio-
dorus, who give that honour only to Ptolomy;
but there might happen to a work of this nature,
as foon as it was finished, an infinite number of
inconveniencies, which rendered it ufelefs, till a
new work was made.
}
At the point of the gulf, which they have
called the Red-fea, were two cities, Hernopolis
and Arfinoe, which, according to Strabo, was
alfo named by fome Cleopatris. Befides Strabo,
ſpeaking of the expedition made into Arabia by
Alius Gallus, the firft Roman governour of
Egypt, fays, that Gallus caufed veffels to be built
at Cleopatris, near an ancient canal derived from
the Nile. In another place, he fays alfo, that
Heroopolis was upon the Ne, and at the extre-
mity of the Red-fed.u
After this, we may pals over fome other autho-
tities, which were alfo related by M, Delifle. E-
very body knows the defign that, fome princes
had of making this communication; every body
knows, that it was croffed by the chimerical fear
of the inundation of the Red-fea; and as if the
greateſt
ROYAL ACADEMY of Sarences. 333
greatest part of readers had been ftruck with the
fame fear, they have not feen bin authors the in-
tire execution of the canal.o binow Aque and
3
M. Delifle has carried his inquiries even to the
Arabian authors Elmacin, lib.. capuge fays,
that under the Caliph Omar, toward the year
635 of the chriftianæra, Amr cauſed a canal to
be made to tranfport the corn from Egypt into
Arabia; probablys he only renewed the old one,
the navigation of which might cally have been
neglected in the decline of the Roman empire.
But in the year 150 of the Hegira, which agrees
with the year 775 of Chrift, Abugiafar Alman-
zor, 2d caliph of the Abboffides, cauſed this canal
to be ſtopped on the fide of the feat If ever this
union ſhould be renewed, the world would change
its face; China and France, for example, would
become neighbours, and our poſterity would la-
ment the fate of the barbarous ages, when the
Europeans were obliged to go round Africa to
get into Afia
30
m2
M
!
XII. Of the manner of cutting moulds
for hyperbolical glaffes, and for turning all
conoids in general
$
The rays coming from a diftant point, as the
centre of the fun, and for this reafon thought to be
parallel, having paffed through a glafs, which is
a portion of a ſphere, do not retinite at all in a
fingle point. Their foci have fo much more ex-
tent as the glaffes are portions of greater fpheres,
and as they are greater portions of them."
It would not be the fame with glaffes, that
ſhould be portions of folids, either conoid, ellip-
tical or hyperbolical, provided nevertheless that
the ellipfes or hyperbolas, of which thefe folids
!!
fhould
334 The HISTORY and MEMOIRS of the
fhould be formed, had a certain condition, that
is, that the ratio of the great axis of the ellipfis
to the diſtance of its foci, or the ratio of the dif
tance of the two foci of the hyperbola to its deter-
mined diameter, was the fame, with the conftant
ratio of the fine of incidence of a ray upon the
furface of the glafs, to its fine of refraction in the
glafs. Then the rays of a diftant point, which
had paffed through the elliptical or hyperbolical
glafs, would gather together in a fingle point,
which would be one of the foci of the ellipfis, or
of the hyperbola.
*
11 2002
A
4
Է
This confiderable advantage of reuniting into
a fingle point the rays from a fingle point, has
made M. Descartes prefer the elliptes and hyper-
bolas to circles, and other particular reafons have
made him prefer the hyperbolas to the ellipfes.
He had even given the defign of a machine for
fhaping glaffes into hyperbolas; but it did not
appear convenient for practice, and we have con-
tented ourſelves with fpherical glaffes, of which
we only take fuch a portion as reunites more rays
in the fame ſpace than any other portion, and re-
unites them in a ſpace fo fmall, as not to be fen-
fibly more than one point. It is partly for this
realon, that in the uſe of the great teleſcopes,
we do not leave the furface of the object-glafs en-
tirely uncovered; we had rather receive fewer
rays from the fame point, and have them more
exactly reunited In the hyperbolical figure, a
greater furface will not reunite the rays lefs exact
into a ſingle point, than a lefs furface, and confe-
quently we fhall have at the fame time a perfect
reunion, and as great a light as we pleaſe.
$
But it is well to obferve, that the hyperbola
would reunite in one point, only the rays from
the fingle point of the object, which would be in
its
ROYAL ACADEMY of SCIENCES. 335
its axis, and that all the rays from all the other
points of the fame object, would be ſo much leſs
exactly reunited, as theſe points would be diſtant
from the axis.On the contrary, circles which
do not reunite exactly into a point the rays which
come from any point of the object, reunite into
an equal extent, and exactly in the fame manner
the rays which come from all the different points.
of the object, and confequently the image of the
object formed by the hyperbola, will be moſt
lively and moſt perfect in the middle point; but
in the other points it will be fo confufed, that it
will not perhaps be any more an image, whereas
thoſe which are formed by the circles, lefs lively
and lefs perfect in the middle, are at leaſt equal
in all their parts. Thus the fpherical glaffes are
probably beſt for fight, but the hyperbolical ones
would have the advantage in burning; for one
fingle point is fufficient for this effect.
However, as M. Defcartes was defirous to ap-
ply hyperbolical glaffes to teleſcopes, and as the
hyperbola has at leaft the advantage in burning,
M. Parent was not willing to leave the proper-
ties of this figure ufelefs, and thought of a way
of bringing them into practice. In the first
place, there muſt be hyperbolical moulds, fome
convex and other concave, against which the
pieces of glafs must be ground, which will take
one of theſe figures..
But firſt, it is not eafy to fhape thefe moulds into
hyperbolas at one fingle ftroke; for if this figure is
given them only by trying, and placing one point
after another, we fhould make a work not very ex-
act, but uneven and irregularly curved. 2. As we
are accuſtomed to hyperbolas, of which the de-
termined diameter has to the diſtance of the foci,
the ratio of the fines of refraction to thoſe of in-
cidence,
336 The HISTORY and MEMOIRS of the
cidence, the moulds must be made fo, that the
conftruction may preferve this proportion with
extreme exactneſs. 3. We muſt take care, that
the figure of the moulds do not alter by the fame
motion, and by the friction, which we ufe to grind
the glaffes, which fhall be applied to them.
M. Parent has fhewn what method he took to
overcome theſe difficulties, he has alſo done more
than his defign obliged him to do, he has found
a practice for turning upon the cominon turn,
and without a model, all forts of conoids, that is
of folids, formed by the revolution of fome conic
fection about an axis, which embraces the hyper-
bolical mould as a fort of fpecies. But without
taking the round of the general method, that
which is for the hyperbolical moulds in particular
is reduced to holding against the furface of the
mould a folid rule, which makes with the axis an
angle of which the tangent is to the whole fine,
as the great axis of the hyperbola fought is to the
fmall ones.
XIII. Of the reduction of the motions of ani-
mals, to the laws of mechanicks, tranflated
by Mr. Chambers.
The fame laws reign every where. The works
of nature turn on the fame principles as thofe of
art; and when I barely lift up my arm, there is
a power raiſing a weight by means of a lever.
This mechanifm, tho' concealed from the eyes,
and rendered ſtill more infenfible by the facility of
natural motions, is not the lefs real. When my
arm, or rather that part thereof between the el-
bow and the wrift, having before been pendant,
comes to be raiſed on high, it moves circularly
about the elbow, or rather about a point to be
2
conceived
ROYAL ACADEMY of SCIENCES. 337
conceived in the centre of the articulation of the
upper jomt of the arm with the lower. This
motion is effected by means of a muſcle arifing
out of the former, inferted into the latter; which
fwelling, and confequently fhortning, raifes up
the arm, and thus overcomes not only the weight
of the arm, but that of the hand likewife; which
we compute at 616.0
?
If the arm and hand were a mere right line,
they would only make a lever, whofe fixed point
might be fuppofed in the centre of the elbow:
but as they have a fenfible bulk or thickneſs, they
are at the fame time a weight to be fuftained.
On this fuppofition, if their weight or thick-
nefs be every where equal, their centre of gra-
vity will be in the middle of their bulk, that is
about 8 inches diftance from the elbow: fo that
here we are to confider a weight of 6 pounds,
fufpended at 8 inches diftance from the fixed
point.
If the muſcle that acts be fixed to the arm an
inch below the elbow, and pull perpendicularly
upwards, while the weight draws perpendicularly
downwards, the power is only one inch diftant
from the fixed point, while the weight is diftant
8 inches. And as this weight is 646. the power
muſt be 48 lb. to fuftain it, and more to raile it.
But the power does not pull perpendicularly.
The muſcle is fixed very obliquely to the arm,
and confequently retains the fame obliquity of
direction. when vit ads and as the diftance of a
power from the fixed point is meaſured, by a per-
pendicular, drawn from the fixed point to the di
rection of the power;pand this perpendicularis:
ſo much ſhortor, as the direction is more, obo
lique; the ftrength of the mufele will be required
confiderably to exceed 48 lb. If the perpendicu-
VOL. I. No. 9.
9.9.
U u
lar,
•
338 The HISTORY and MEMOIRS of the
lar, drawn from the fixed point to the direction,
be only equal to the diſtance from the infertion,
that is, be only an inch, the force muſt be
96 lb. Who would imagine, that in only lifting
up the arm, we employ a force of 96 lb.
What furprizes moft is, that nature, notwith-
ſtanding her ufual oeconomy, which never fails to
take all poffible advantages, fhould here, contrary
to the rules of mechanicks, place the power be-
tween the fixed point and the weight; and thus
make it draw obliquely: which gives it the ut-
moſt diſadvantages, and obliges it to be incom-
parably greater than the weight. -Which fame
fuppofition being that moft ufually in muſcles
would almoſt feem at firft fight, that the fove-
reign wiſdom had here forgot itſelf.
But let it be confidered, that a fmall power
applied advantageouſly to a lever to raiſe a great
weight, muft have a great velocity, and pafs
over a deal of ſpace, while the weight only raiſed.
a little and flowly. On the contrary, a great
power applied to its lever difadvantageously, and
having only a fmall weight to fuftain, travels over
a fmall ſpace, while the weight travels a deal.
If now a large bell, for inftance, be to be
raiſed to the top of a fteeple, 'tis enough gene-
rally it be raiſed thither, nor matters it much in
what time. And as any powers we have to uſe are
ſmall and inconfiderable, compared to the large-
nefs of the weight, 'tis a fine advantage to have
the bell riſe fome 20 or 30 fathom in a day,
while e. g. the men who raiſe it travel perhaps fome
leagues. But if my hand, confiderered as a weight,
be to move for fonie office ufeful or neceffary for
the prefervation of life; the great buſineſs uſually
is to have it move quickly not to fpare ftrength;
which confifting in the contraction of a muſcle,
and
ROYAL ACADEMY of SCIENCES. 339
and the quantity of fpirits that fwell it, is always
greater than needs for the ordinary motions.
'Tis true, nature might have given the fame
velocity to the weight, by having the mufcle faf-
tened at the fame diſtance from the fixed point;
and yet have faved fomething in the ftrength of
the muſcle, by giving it a perpendicular direc-
tion. But 'tis clear, that in this direction, it would
have required a deal more room, than when
couched or laid, as it now is, along the bone it
is to pull. Now an animal being an aſſemblage
of an infinite number of different machines, the
faving of room is a very material confideration.
Befides, the ſtrength of a mufcle depends on
the quantity of fpirits, whereby it is put in con-
traction, ſo that the advantageous direction of a
muſcle, could in reality have only ferved to fave
fomething in the quantity of fpirits. Now a
great quantity of this juice was indifpenfibly ne-
ceffary on other accounts, particularly for the
offices of fenfation; fo that the excefs of ftrength
is provided for without any particular expence.
From the whole, it appears, that tho' the me-
chaniſm of animal motion departs fomewhat from
the common mechanicks, in reſpect of the poſi-
tion of the moving power, yet it is finally redu.
cible to the fame laws: and the ftrength of a
mufcle may be exactly computed, provided we
know the weight it is able to fuftain, the fixed
point on which it moves, and the divifion where-
in it acts.
gol al
Now the weight a mufcle fuftains is either the
mere weight of the part it draws, eg that weight
with fome foreign load fuperadded thereto.
Thus by the weight fuftained by, the mufcle,
which bends the arm, we either mean the natural
weight of the hand, and the first joint of the
#
Uu2
arm;
340 The HISTORY and MEMOIRS of the
arm; or befide this weight, the greateſt foreign
weight which can be bore in that action. And
take which way you will, 'tis experiment only,
tho' an experiment eafy made, that muft deter
mine what this weight is.
}
But there is fome difficulty in finding the fixed
points, and directions. The mechaniſm of theſe
motions is fo complicated, that the application of
rules thereto become very precarious, or at
leaft difficult; the intelligence which directed
thefe works, not having confined itſelf to thofe
fimple cafes, which we are accuſtomed to.
The celebrated Borelli was the firſt that engaged
in enquiries of this kind, in his treatife De Mo-
tibus Animalium; a work truly laudible, both
for the merit of being the firft, and for the many
curious truths difcovered therein. Yet M. Pa-
rent hath ventured to charge it with want of exact-
nefs in certain points, and even gives us a new
general theory, whereby a further degree of light
is brought into the whole matter; a little fketch
whereof we here fubjoin.
When the concave end of one bone, receives
the convex end of another, and this fecond being
pulled by a muſcle, moves upon the firſt, if their
figures be fuch, that during the whole motion the
fecond only bears upon the firſt by a fingle point:
it is evident, that in cafe of an equilibrium produ-
ced by an equality of two oppofite powers, their
common direction would pals through this point,
which therefore is the fixed point. And it is evi-
'dent withal, that in the motion of the bone, this
point is continually changing place, which is one
of the peculiarities of thefe mechanicks.
If the concavity and convexity of the two
bones were perfectly fpherical and concentrical,
they would touch in all their points; and yet
ftrictly
ROYAL ACADEMY of SCIENCES. 341
ftrictly speaking, the two furfaces would reſt or
bear on each other only in one point of their cir-"
cumferences, which point would be the fame, as
if, having been neither fpherical nor concentrical,
they were rendered fo in fome inftant of their
motion, it being viſible, that this would make
no alteration in the point of fupport. Accord-
ingly, tho' the common centre of two concentric
fpheres, be really immovable, during their mo-
tion, it is not properly and abfolutely the point
of fupport, but that which is a point of the circum-
ference, which is continually fhifting every mo-
ment of motion. Tis therefore from this point
that we are to meaſure the diſtances of the mufcle,
and of the weight which pull against each other.
'Tis true, in meaſuring them from the common
centre of the 2 fpheres, as Borelli has done, we
come at the fame conclufion, by reafon this com-
mon or compound direction does alfo pafs thro'
the centre but this is only by accident, which
would not obtain in other figures and it is necef-
ſary to know precifely and univerfally where the
real point of fupport is found.
This being had, the directions of the weight
and the muſcle muft likewife be found, in order
to draw perpendiculars to the fame from the point
of fupport.
As to the weight, its direction
of courſe is the vertical line, whereby it tends
downwards. But the mufcle being frequently tra
verſed by other mufcles, its direction in fuch caſes
is compounded of its own, and that of the others,
fuppofing them to act at the fame time. How-
ever, as they terminate in the fame tendon, which
is their common cord whereby they pull; this
tendon naturally reprefents their compound di-
rection, which therefore is eaſily found.
་
}
Thus
342 The HISTORY and MEMOIRS of the
Thus much only regards the fimple articulations,
that is where only two bones are joined together to
perform fome motion. When there are ſeveral bones,
as for inftance, the vertebræ of the fpina dorfi,
which confpire to bend the back inwards, the ar-
ticulation is compounded: and the application of
the rules may be faid to be fo likewife, tho' at
bottom they amount to the fame.- When the
back is bent, we may fuppofe that too contiguous
vertebræ, which before touched in the whole fur-
face of one of their fides, begin to feparate or
open outwards, and continue to widen further and
further, as their difpofition will admit; and dur-
ing fuch motion, only touch by a fingle line which
remains common to them in their baſe, in the
middle of which is the fixed point.
But in fact, the cafe is not fo fimple. The
bones which move by withdrawing them before
contiguous furfaces, leave no vacancy between
them. They are bound together by cartilages,
which may be conceived as adhering, on both
fides, to their whole furface. Thefe cartilages,
being dilatable and compreffible, neceffarily di-
late as the bones tend to divaricate. And for as
much as this dilatation requires a certain force,
the muſcle which produces the whole motion,
muft have this over and above what is required.
merely to raiſe the weight.
To eſtimate the power neceffary to dilate the
cartilage, M. Parent is obliged to confider the re-
fiftance which the cartilage makes to a dilatation,
as a power applied at a certain diftance from
the fixed point, and pulling against the mufcle.
And by reafon the dilatation is greater in different
parts of the fame cartilage, in proportion as they
are farther diſtant from the fixed point; the di-
latation may be confidered as velocities, and be
taken
ROYAL ACADEMY of ,
SCIENCES: 345
taken for the point where the whole force is u
ted; which would be the centre of agitation of
the plane of the cartilage.
**
If two or more bones be fo difpofed, that upon
opening them, or their upper fide, they approach
on the lower; and of confequence dilate one half
the cartilage, which binds them, and comprefs the
other; the fixed point will be in the middle of
the cartilage and the points whereon the refi-
ſtances of the cartilages both to their being com-
preffed and dilated unite, would be found in each
of their halves, after the fame manner as the point
of union of a ſingle refiftance would have been in
the whole.
A compound articulation having feveral fixed
points, there must be the fame number of per-
pendiculars drawn from each, both to the di-
rection of the weight, the direction of the muſcles.
whether fimple or compound, and thoſe of the
cartilages.
M. Parent divides the compound articulations
into confecrative, where all the motions tend the
fame way, alternate, where they are by turns diffe-
rent ways: Thefe laft motions are eafily reduced
to the laws of the firft.
From this theory may the ftrength of that pro-
digious number of machines, which are played
either feparately or together in the body of an
animal, be computed, and the relation of one to
another, either precifely or pretty nearly, be
found. If we could but likewife enter into all
the views which required fuch different relations
powers, and the advantages arifing from them,
what intelligence would not be confounded there-
with?
of
"
XIV.
384 The HISTORY and MEMOIRS of the
}
XIV. Of the refiftance of hollow and folid
cylinders.
If this queſtion was propofed, which of two
ticks equal in length, and cylindrical, is the
eafieft to break upon the knee, that which is en-
tirely folid, or that which is hollow, having the
fame quantity of matter with the other, moſt
people would not hefitate at all to decide that the
hollow ftick would be the eafieft to break.
Nevertheless it is quite the contrary, as foon as
we confult the principles of mechanicks. When
we reſt a ſtick upon the knee to break it, we reft
it by fome one of its points, and it is the point
diametrically oppofite, which will take a circular
motion about the point of fupport, while the
fracture is made. Here then is a lever, and this
point which moves circularly, defcribes an arch
fo much the greater, as it is farther diftant from
the point of Tupport, or from the fixed point,
and confequently it has fo much more force to
refift the power, which tends to make the frac-
ture. A thicker cylinder full is then more dif-
ficult to break, not only becaufe it contains more
matter, upon which we must act, but alſo becauſe
the diameter of its bafe is greater, and the extre-
mity of its diameter, which moves in the fracture,
is farther diftant from the fixed point. If this
cylinder preferving the fame quantity of matter,
became hollow, it is vifible, that its total diame-
ter, that is, th diameter, as well of the hollow
part, as of the folid, would necellarily increafe,
and confequently ali one of the caufes, which
made its force, and its refiftance againſt being
broken.
}
Every
ROYAL ACADEMY of SCIENCES. 345
{
Every hollow cylinder is then ſtronger than a
full cylinder, which has only the fame quantity.
of matter; and this, according to all appearance,
is one of the reafons why the bones of animals and
the culms of corn and grafs are hollow.
Galileo, the firft author of theſe forts of in-
quiries, has confidered in the full and hollow cy-
linders, having their bafes formed of the fame
quantity of matter, only the inequality of their
diameters, and confequently he has eftablifhed,
that the refiftance of a hollow cylinder, is to that
of a full cylinder, as the total diameter of the
hollow one is to the diameter of the full one. :
But this confideration is imperfect in this, that
the extenfions of the fibres of which the cylinders
are compofed, are not taken in. Thefe exten-
fions, and confequently the refiftances of all the
particular fibres; continually increaſe from the
fixed point to the moſt diftant fibre, which muſt
break the firft, and which we may fuppofe in the
greateſt extenfion that it can fuffer. It is the fum
of all theſe unequal refiftances that makes the re-
fiftance, which all the fibres together oppofe to
the power, which tends to break them.
Thus the total refiftance of the cylinder. de-
pends upon three things; on the quantity of
matter that compofes the bafe; on the refiftance
that all theſe fibres together bring to their exten-
fion, and on the magnitude of the diameter of the
cylinder.
There remains to determine and exprefs geo-
metrically thefe magnitudes; and it is this that
M. Parent has done. The circles of the baſe. of
the full cylinders must be made equal, to the full
bands or zones of the hollow cylinders, and we
muft find the infinite fum of the unequal re-
VOL. I. No. 9.
Xx
fiftances
346 The HISTORY and MEMOIRS of the
fiſtances of all the fibres, which is a particular cafe
of the general method of M. Varignon.
...M. Parent being arrived to a general formula,
which contains all the poffible refiftances of hol-
low cylinders, compared to the full, has calcula-
ted upon this formula, a table, where he fup-
pofes that the total femi-diameter of a hollow cy-
linder is always 100 parts; and that the refiftance
of the full cylinder, which contains in its bafe as
much matter as the other, is alfo divided into 100
parts. We fee by the table,
1. That in proportion as the hollow cylinder,
of which the radius can have but 100 parts of a
certain determinate magnitude, has more void,
and confequently lefs matter, it makes a greater
refiftance than the correfpondent full cylinder.
2. That this inequality of refiftance always di-
miniſhes in proportion as the hollow cylinder is
lefs hollow, and contains more matter; that, for
example, a cylinder, of which the void is 99 ra-
dius, and 1 in thickness, and to which confe-
quently a full cylinder anfwers, which is only 14
radius, has a refiftance, which is to that of the
full cylinder, as 848 to 100, that is, as 8 to
1; and that the cylinder, which has 50 in void
and 50 in thickneſs, and to which a full cylinder
of 87 radius anſwers, has a refiftance, which is
to that of the full one, only as 121 to 100.
That the hollow cylinder of 99 void, the refiftance
of which, compared to that of the full one, which
is 14 radius, would be, according to Galileo,
7 times greater, has one 8 12 times greater ac-
cording to the hypothefis, of M. Parent, which
sis alſo that of M. Mariotte.
bonspyd dordw
# 1
7
12
2 j
3.
XV.
'ROYAL ACADEMY of SCIENCES. 347
>
XV. Of a machine invented by F. Sebaſtien
This machine, invented by F: Sebastien, was
only made to try if the fall of bodies followed the
proportion of Galileo, or rather to fhew by expe-
riment, that it did follow it, for the machine was
folely conftructed upon this hypothefis it was
formed by the revolution of a parabola about its
axis, and the circumferences of circles of fmall
fpiral planes, which were the different ſpaces run
over by the falling bodies, reprefented the "feries
of uneven numbers.*
*
did for my fuel
3
But as it is not abfolutely impoffible to eſta-
bliſh, or at leaſt to be willing to try fome other
hypothefis than that of Galileo, upon the fall of
bodies, M. Varignon found the thought of F. Se-
baftien too ingenious not to extend it to all the
hypotheſes imaginable.
3 1
Whatfoever hypothefis therefore we take upon
the fall of bodies, M. Varignon requires us to ex-
prefs by the ordinates of a curve, the different
velocities acquired at each inftant, that afterward
we cauſe this curve to make a revolution about
its axis perpendicular to the horizon, like that
which the parabola makes in the hypothefis of
Galileo; and lastly, that round the folid, formed
by this revolution, we direct from the top to
the bottom an inclined plane, which makes always
the fame angle with the curve, that it always
meets after it has formed the folid; after that, he
demonftrates that if the hypothefis that we have
taken is the true one, a body that ſhall fall from
the top of this machine, by the inclined plane,
will make all its revolutions round the machine,
altho' unequal, in equal times, which happened
at leaft fenfibly, in that of F. Sebaftien.
*See pag. 30 of this abridgment.
Xx 2
The
348 The HISTORY and MEMOIRS of the
1
The effential principle of this property of the
machine is the perpetual equality of the angles of
the inclined plane with the generating curve.
From this equality all geometricians will very
eafily conclude, that all the different portions of
the inclined plane, taken between the fame arches
of the folid, and if we may ufe the expreffion,
between the fame meridians, are always between
themſelves as the ordinates of the curve which
anfwers to them. Now thefe ordinates exprefs
the acquired velocities, and the portions of the
inclined plane are the fpaces run over by the
means of theſe velocities; therefore the fpaces are
always as the velocities, therefore different ſpaces
are run over in the fame time.
In F. Sebafien's machine, all the angles of the
inclined plane, and of the arches of the curve,
were very near right ones, which was fufficient for
the fenfible equality of the time of the fall.
M. Varignon eafily found, that in his general
machine, the length of the inclined plane will al
ways be to that of the general curve, as the total
fine to the fine of the complement of the angle
of the inclined plane.
t
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ABRIDGMENT
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裔
​HOF THE shufanos fire
PHILOSOPHICAL MEMOIRS of the ROYAL
ACADEMY OF SCIENCES at Parts for
amilion ound adi mowied
the year 1702rade en ze zavlátnads
:
Rede word nor of mawine
1. Obfervations on the quantity of rain which
fell at the royal obfervatory in go with
Jome remarks on the thermometer and baro-
meter. By M. de la Hire
TH
ちょ
​di a zpowie
I O! 1970 MEN SIC
HE year 1701 feemed extraordinary for
the dryness of the fpring; it was however
in general one of the moft rainy years that we have
had a long time. For there fell in the months of
1
1
for nongren? N
Ernest bgnol ada Liñėstion
- 113 4
Jan.
Feb.
4
Mar.
22
Sept.
Apr.
I
Octob.
May
20
Nov.
June
38
Dec.
*** 17292 July Jadi Cad
119 Aug. 0 en
94500 and
24
19
10
+10 + 11f þes
The fum total is 256 lines, or 21 inches 4
lines.
We find hereby that there was no rain in April,
and that this might have rendered the year very
unfruitful, if the earth had not been moiftened by
the rains of the three preceding months. For
the fnows which ufually fall in winter, and remain
upon the ground in this feafon, hardly penetrate
* Jan. 7, 1702.
it
350 The HISTORY and MEMOIRS of the
baloqxe jon
1
it at all, and there would be need of a very great
quantity to fupply as much water as fell in the
three firft months of this year for the 5 inches
of water of thefe months muft have been fupplied
by 2 feet of ſnow, which would have been very
extraordinary, without reckoning, that the great-
eft part of the fnow dries before it is melted, ef-
pecially in winter when the air is very dry; and
this is what cannot happen to the water, which
has entered into the earth, and has, penetrated it
long before.
The three months of June, July, and August,
have commonly fupplied almost as much water as
all the rest of the year; but thefe great fummer
rains are quickly diffipated by the great heat of
the air, and by the drynefs of the ground.
The cold was not confiderable; for it hardly
froze. My thermometer marks the beginning of
the froft, when it is at 30 degrees, and it fell at
the loweſt but to 28, whereas, in a great cold,
fuch as we have fometimes in this country, it falls
to 7 degrees, as it was in Feb. 1695.
Towards the end of Jan, and beginning of Feb.
1701, which was the coldeft feafon, my ther-
mometer was often at 40 degrees, which is not
very diftant from the mean ftate of the air, as I
have found upon leaving the fame thermometer
at the bottom of the cave of the obfervatory for
fome days, where the liquor always kept at 48
degrees. We may alfo obferve, that on the laft
day of Nov. the heat was as great as on the 12th
of June.
}
The heats of the months of July and Aug, were
extraordinary for the fame thermometer rofe
pretty often to 65 degrees, and Sept. 1. it was at
65 degrees at the higheft. This thermometer
is always expofed to the air, but in a place much
2
fheltered,
ROYAL ACADEMY OF SCIENCES, 351
!
heltered, and not expofed either to the wind or
fun and all the obfervations that I have made
on it, are always about the riling of the fun,
which is the time of the day when the air is moft
cool: for the hottelt time is generally at 3 in the
afternoon. Wherefore to know the greateſt heat
of the air, in a place not affected by the fun, I
have obferved, that my thermometer rofe to 77
degrees with a ſtrong S. E. wind, Aug. 17. at
3 in the afternoon, which is a mark of extreme
heat. This thermometer is very long, and may
be expofed to the hot fummer fun, without the
liquor's rifing' to the top of the tube, that I may
mark the more eafily upon it the degrees of heat
and cold, even when it is expofed to the fun.
We may hence conclude, that the cold of the
air in this country is in general greater than the
heat in the abſence of the fun. For the mean ftate
of the air being 48 degrees on my thermometer,
and the greateſt heat 77, there are but 29 degrees
of difference, which being taken from 48, there
would remain 19 degrees for the mark of a cold
at the fame degree below the mean that the heat
is above it; and yet it fometimes happens here,
that the fame thermometer falls to 7 degrees.
We may obferve, that the greatest heat of the
day does not always follow the heat of the morn-
ing, as may be feen in thefe obfervations t for the
greatest heat of the morning was Sept. 1. the ther-
mometer marking 65 degrees, and that of the
afternoon Aug. 17, and on that very day it was in
the morning a little lefs than on Sept. 1. for the
thermometer marked but 63 degrees, which may
happen from feveral particular caufes.
The barometer which I ufe is fimple, as ufual,
having a tube of moderate thickneſs, that the
quickfilver may have the more liberty to move
in
352 The HISTORY and MEMOIRS of the`
in it; the bottle at the bottom is proportioned to
the bigness of the tube, fo that the falling or rifing
of the quickfilver of i inch in the tube, is not
fenfible in the bottle. This barometer is always
placed at the height of the great hall of the obfer-
vatory, which is near 22 toifes above the level of
the furface of the river in a mean ftate. I ob-
ferved it was at the lowest this year at 26 inches,
10 lines March 6. and the higheſt at 28 inches,
2 lines Feb. 9. The difference therefore be-
tween the higheſt and the loweſt was but 1 inch,
lines, which is fomething lefs than the com-
mon, which is 1 inch, 6 lines.
4
But the moſt confideráble thing that has hap-
pened this year is the hurricane of Feb. 2. the
wind was very violent, and the barometer was in
an almoſt mean ſtate at 27 inches, 4 lines, and
there was but I line of rain, which may be ob-
ferved as an extraordinary thing; for in great mo-
tions of the air, the barometer falls very low.
I-found the declination of the needle to be 3°
48′-Sept: 22. W. variation. I made ufe alfo of
the fame compafs, of which the needle is 8 inches
long, and very well fupported on a very flender
pivot. I always make the obfervations againft
one of the pillars of the lower terrafs of the ob-
fervatory, by applying the fide of the box to it,
wherein the needle is inclofed, and by this means
I avoid all the errors that could happen from the
pofition of the compafs on the meridian. I have
formerly proved the pofition of the fide of this
pillar, by the fun's pafling the meridian, applying
a great rule to it, which had at its extremities two
fights for the rays of the fun to paſs thro'; the
aperture of the objective fight, and the tract
marked on the other, were in a line exactly pa-
!
rallel
ROYAL ACADEMY of SCIENCES. 353
rallel to the fide of this rule, which was applied
againſt the face of the pillar.
II. A difcourfe on fome properties of the air,
and the means of knowing the temperature
of it in all the climates of the earth. By
M. Amontons *.
The experiments, which I have made three
years ago on the dilatation of the air by the heat of
boiling water, fhewed me, that uneqtral maffes
of air loaded with the fame or equal weights,
augmented equally the force of their fpring by
equal degrees of heat; and as my principal end
in theſe experiments was to know, how much the
heat of the boiling water increafed the fpring of
the air above what it has in the water, which we
call cold, theſe experiments led me at that time to
think, that it was but in a quantity capable of
fuftaining to inches of quickfilver in height be-
yond the weight of the atmoſphere but having
fince carried my experiments farther, I have
found, that the fpring of the air augmented
by the heat of boiling water, was not fixed to fuf-
tain no more than 10 inches of quickfilver, be-
fides the weight of the atmofphere; but that it
fuftained more or lefs in proportion to the weights
with which it was loaded, and that this augmen-
tation was always about the third part of thefe
weights, when the air is at firft in the ftate which;
we here call temperate, and lefs than a third part
when the air is hotter; and on the contrary, more
than a third part when it is colder. För inftance,
if, when it is temperate, a maſs of air loaded with
30 inches of quickfilver, comprehending the load
of the atmoſphere, has augmented its fpring by
* june 28, 1702.
VOL. I. N°. 9.
Y Y
the
354 The HISTORY and MEMOIRS of the
}
the heat of boiling water, fo as to fuftain 10 in-
ches of quickfilver, befides the load equal to 30
inches of quickfilver when this mafs fhall be
loaded with 66 inches, it will augment its fpring
20 inches and 30 inches when it fhall be loaded
with gay and fo of the rettWhence in feems,
that we may draw this confequence, that the fame
degree of heat, let it beeders fo little, may conti-
nually increaſe the force of the spring of the air, if
this air is continually loadedy with a greater and
greater weight. And as we have already obfer-
ved, that, unequal maffes of air equally augment
the force of their fpring by equal degrees of heat,
we may draw this other confequence, that a very
fmall parcel of air, let it be ever fo little, may ac-
quire a greater elafticforces and greater and greater
continually by a very small degree of heat, if this
little parcel is continually loaded more and more.
Theſe properties of the air may perhaps hereafter
ferve us, to explain feveral phyfical effects, of
which we do not at prefent know the caufes.
J
A
{
I have juft now faid that experience had taught
me, that unequal maffes of air, loaded with equal
weights augmented the force of their fpring equally
by equal degrees of heat, and that the elaftic forces.
which they acquired, were fo much more confi-
derable, as the weights with which they were
preffed were great; the reafon of which is, that
the maffes of air, either being in the fame medium,
or confidered as fuch, and loaded with equal
weights, there is no nepfomwhy one fhould ac-
quitel atomorenoonfiderable élaftic force than the
other. ey Forghofit is trueochat if thefe maffes of
air had the liberty of extending themfelves, the
greater would increase their bulk more than the
Impller this ought not hatever to take place in
the hugmentation of theirdpring, fince, accord-
ibropor
2.7
کرم
L
ing
ROYAL ACADEMY of SCIENCES. 355
J
{
ing to M. Mariott's rules unequal maffes of air
equally loaded mufti reduce themſelves to bulks
proportioned to their first maffes, to ncquire new
equal degrees of elaſtic force and that, by the
reverſe of this very tuleprif equalmaffes of air
unequally loaded have a liberty of extending
themſelves they will really poffefs ſpaces pro-.
portioned to the weights with which they are
loaded; but not being able to extend themfelves,
they muſt neceffarily acquire elaftic forces pro-
portioned to the fame weights.
}
17
!
!
і
When I had difcovered thefe truths, I endea-
voured to apply them; and thought I could make
an advantageous ufe of them in bringing ther-
mometers to perfection.
·
'
Few perfons are ignorant, that the first ther-
mometers made with air acted not only by the
heat and cold of the external air, but ftill more
by its greater or lefs weight, and that the motion
of thefe thermometers, caufed by the weight of
the air, was at leaſt as fenfible as that which was
cauſed by the heat, which rendered the obferva-
tions on them uncertain, and confequently of no
ufe. It is true, that there have fince been inven-
ted thermometers of fpirit of wine, fealed herme-
tically, which feem to act only by the alterations
of the air, as to cold or heat; but befide the fpirit
of wine's not receiving the impreffionsfo quickly
as the air, and the great imaffes receiving it more
flowly than the lefferrones, it is almoſt impoffible
for their tubes to be equal from one end to the
other; whereby the fame quantity of liquor,
which towards the bottom might perhaps poffefs
no more than 40 parts of their graduation, when
driven up towards the top may fometimes poffefs
45 or 50 more or lefs. Whence it comes to pats,
that if thefe thermometers were regulated only
according
i
Y y 2
356; The HISTORY and MEMOIRS of the
t
according to the greatest heat and greateſt cold of a
climate, the temperate degrees of the thermometers
would be all different from each other, tho' they
ought to be exactly the fame. But farther, let
us fuppofe, what is not true, that theſe thermo-
meters have none of the above-mentioned defects;
what is a degree of heat of thefe thermometers?
what knowledge do thefe degrees give us of the
temperature of our climated It is certain, that
they give us none, the first of thefe thermome-
ters were graduated, just as it happened, on the
greateſt heat and cold of fome years, and can only
ferve at most to fhew us, that fome are hotter or
colder than others: which is of no great ufe, as
we cannot certainly know the difference, and thefe
inftruments are not at all proper to tranfmit to
poſterity the obfervations, that may be made on
the different temperature of the climates: for to
fay, for example, that laft year the thermometer
rofe 7 or 8 parts more than the preceding, is giv-
ing no better intelligence how much this year was
hotter than the other, than if one fhould tell a
perfon, who is folicitous about knowing the
length of a pendulum that fwings feconds, that it-
is as long as fuch a ſtick, of which he does not
know the length but if one fhould tell him,
that the length of this pendulum is 3 feet, 8 lines;
then as thele meafures are known and fixt by ufe,
and by the comparison that may be made of them
to all forts of dimenfions; he has no longer any
reaſonable doubt, that may require to be cleared
upon It is not fo with a degree of the thermome-
ters that have hitherto appeared; we cannot fay
that there is, for example, the 100th part of the
difference between the greateſt heat and the great-
edcold of one year, feeing theſe differences are
hardly ever equal; and if they were fo, it would
"
J
ܬܵܐ
be
ROYAL ACADEMY of SCIENCES. 357
be at moft but for a certain climate; thus la de-
gree of the thermometer cannot be compared to
any degree of heat, and confequently cannot be
the meaſure of it. On the contrary, if fay the
greateſt heat of laft fummer was, for example,
of that of boiling water, this degree of hear
being known by thoufands of daily effects, that
which I would have known becomes for alfo, and
I can draw all the confequences from it that I
want. We must then agree upon a certain degree
of heat, conftant and invariable, khown by every
body, to which we may compare, and which
comprehends all the other degrees of heat that can
be in the air which we breathe. This is proba
bly what the late M. Colbert intended, when he
had a project of having a confiderable number of
thermometers conftructed, and to fend them into
different parts of the world for obfervations to be
made upon them but probably that great mi-
nifter gave over the defign, only becauſe he juftly
thought, that the fpirit of wine thermometers,
fuch as they had then, were improper for the
purpoſe, and that it would have been almoſt im-
poffible to eftablifh a fufficient uniformity in thefe
thermometers. wy w na dovi un gi
The degree of heat, neceffary to eftablish an
uniformity in the conftruction of thermometers,
might be that ofwcommon boiling water, expe-
rience having fhewn me, that it cannot acquire a
greater degree of heat, let it bebever ſo long on
the fire, and let the fire be ever ſoftongda olson
* ABCD is one of the glass tubes which I
made ufe of forfome former experiments, 27tb
know the increase of the spring of the air by the
heat of boiling water sopen at Awbenar land
ending in a balbDgaThe bigüe of this be is
* Plate XVI. P. Yadu i bas loups tɔve ylbint
about
358 The HISTORY and MEMOIRS of the
C
about line within, that lofinthe ball g inches,
a little more or less withoutp confequence; and
herein theſe thermometers Have a great advantage
above others, by the equality of their motion, fo
eafy to find in thefe new thermometers, fo. diffi-
cult to find in the old ones the length of this
tube from AftoB fhall be 46 linoles, that the to-
tal AC may be about 48worLetthere be quick-
filver from the entrance Eof the ball, and in all
the rest of the tube quite to the aperture A; fo
that the balbDbeing in the boiling water, the air
which it inclofes may fuftain by its elafticity 73
inches of quickfilver, comprehending the weight
of the atmosphere, whichisoalways. fuppofed
equal to 28 inches, and only 148 inches without
comprehending it, beginning at the level of the
quickfilvers which fhall beat Eg then the furface
of the quickfilver in the tube AB, near the aper-
ture A, fhall be the term from whence we may
begin to reckon all the other degrees of heat,
which fhall be lefs than that of boiling water:
for as there is no climate upon the earth, that can
be fuppoſed to be as hot as boiling water, we
fhall confequently have as high a degree of heat,
as is known in any country, which will compre-
hend all below it, and from which we may be-
gin to reckon. So that to exprefs the greater or
lefs degree of heat of any climate, we need only
count the number of inches and lines, by which
the furface of the quickfilver towards A, fhall be
fower than the place to which the heat of the
boiling water had made it rife, having a regard alfo
to the weight of the atmoſphere at the time of the
obfervation, whether it is more or lefs heavy
than 28 inches of quickfilvery becauſe the furface
of the quick filver towards A will be too low by
the quantity by which the weight of the atmo-
fphere
J
ROYAL ACADEMY of SCIENCES. 359
ſphere ſhall exceed that of 28 inches of quickfilver,
or too high by the quantity which fhalle fall fhort
of thoſe 28 inches. Wherefore, in the first cafe,
we muſt fubftract this excefs of inches and lines,
contained from the degree of the heat of the boil-
ing water; and, in the fecond cafe, we niuft add it.
It will be eafy therefore, by the affiftance of thefe
thermometers, totskhow the temperature of all
the climates of the earth, and to conftruct other
thermometers with fpirit of wine for each climate
which may be compared with thefe bewcair ther
mometers. The degrees marked on them will be
no longer unknown, and we may tranſmit your
knowledge to pofterity, to obtain the advan
tageous ufes from them, which there, is room
to promife, not only for all philofophical
ufes, but alfo for our own prefervation: The
thermometer must be prepared after the following
manner.
mor
শ
ས་
T
f
1
11
* ABCD is a little bit of afh, walnut, or any
other wood of like nature, about an inch fquare,
and inch in thickness; in the thickneſs of which
44
holes muſt be bored from fide to fide, as EF a-
bout 3 or 3 lines in bignefs, and another of
like bignefs as GH, to communicate only with
the firft, and no farther. Then apply with fome
maftick at G a glafs tube + ILG, about 4 feet
long, open at both ends IG, and bent at L, a-
bout an inch from the extremity Guapply after-
wards at F another tube as FMNO, open alfo at
the two extremities F and O, fwóin toward F
into a ball M, of about two inches in diameters
at inch from the extremity Fobent at N s
near the ball M as poffible, and defcending)da
gain towards O with 6 or 7 inches apply at
another end of a tube only 2 or 3 inches long:
* Plate XVI. Fig. 2.
}
7
Fige 3.
1
*
LUN
小
​all
360 The HISTORY and MEMOIRS of the
all theſe tubes must be but about a line or two
on the infide, except the extremity O, which
muſt be a little widened to receive the other tubes
more eaſily that are to be applied to it. Theſe
3
tubes muſt be fo applied to the little piece of
wood with maftick, that the quickfilver let in
with a funnel at I may flow freely towards F and
E, and may pafs, according as it fhall be necef
fary, either thro' the tube FMNO, or the tube
EP. Obferve to cover this whole piece of wood
well with maftick, for fear the quickfilver fhould
get thro' its pores.
This little machine being thus prepared, apply
it against a wall, making the ball M reft upon
two nails, and tying the tube * IL loofely, a little
below its extremity I, with a piece of packthread
to another nail faftened alfo in the wall. Apply
alfo with fome mattick at O the extremity A of
the thermometer, into which you would introduce
the quickfilver, making the bottom of it lean
upon fomething folid, as at C, after which clofe
the extremity P with maftick, and then with a
funnel pour the quickfilver in at the extremity I,
which will gradually fill the ball M, and pro-
portionably condenfe the air of the ball D. When
the ball M is quite full, and the quickfilver be
gins to pafs by the bending N, and go down to
C, leave off pouring in the quickfilver, and open
the extremity P by heating it with the flame of a
candle, driven thro' a little pipe, as when we
feal hermetically, then withdraw the quickfilver
from the ball M by the extremity P; and if the
quickfilver in the tube AC is about 27 inches a-
bove Et, when the heat of the air is the fame
with that of temperate of the eighth climate, and
f Fig. 1.
*
Fig. 4.
the
ROYAL ACADEMY of SCIENCES, 361
the weight of the atmoſphere is equal to 28 in-
ches of quickfilver, then you need only loofen the
tube of the thermometer from the tube NO, by
heating the maftick as before but if the quick-
filver was not 27 inches above E, the aperture P
muſt be cloſed again with maftick, and the
quickfilver poured again by I, till you judge
there is fome air, entered into the ball D, fuffi-
cient to fuftain the quickfilver in the tube AC,
27 inches above E, which may eafily be known
by the height which the quickfilver will keep in
the tube L1; if on the other fide the quickfilver
in the tube AC fhould be found the first time"
much above the 27 inches, it would be a fign
that the capacity of the ball M is too large;
then the glafs of the thermometer above the ma-,-
chine muſt be taken away, and emptied, to be-
gin to fill it anew, obferving, before you put the
maftick again on the tube NO, to put into the
ball M a fufficient quantity of quickfilver, to
diminiſh its capacity by about the quantity that
may have been thought too great. If there were any
perfons who had the mufcles of refpiration strong
enough to reduce the air in D, by blowing thro
A, into the fame ftate of condenfation with thefe
27 inches of quickfilver, they need only make
the machine ILMNO, and after having intro-
duced a little quickfilver into the ball D with a
funnel, blow itrongly thro' the aperture A, till
the quickfilver could rife in the tube AG 27 in-
ches above E: but few, if any, are capable of fo
much force, and the fureft way is to make ule of..
the machine above-mentioned..
In the laft place, to finish the preparation of::
the thermometer, obferve with a fingle barome...
ter, what is then the weight of the atmoſphere,
and what height of quicksilver it will fuftaine
VOL. I. N°. 10.
fubftract
Z z
362 The HISTORY and MEMOIRS of the
fubftract it from 73 inches, and mark with ſome
colour on the tube * CA, beginning over-againft
E, the number of inches and lines remaining from
the fubftraction. Afterwards dip the ball D in
a kéttle full of cold water, and fetting the whole
over a pretty good fire, keeping the tube AC
always even, leave it till the water boils very
brifkly; as faſt as the water heats, you will fee
the quickfilver rife, fo that when the water is
ready to boil, it will begin to difgorge by the
aperture A, if the weight of the 'atmofphere does
not then exceed 28 inches of quickfilver; and
when it is quite boiling, and there comes out no
more quickfilver, it must be inclined a little at
feveral times, to make it come out again, and
reduce it to the mark made towards A, that is,
to the neceffary height, to equal with the weight
of the atmoſphere a load of 73 inches of quick-
filver. Then this thermometer will be finiſhed,
and there is no more to do but to take it gradually
out of the boiling water, for fear the too great
cold of the external air fhould break the glaſs.
'
J
I have obſerved with thefe thermometers, that
the air, which we call temperate, fupports about
19 inches of quickfilver lefs than that which is
driven by a degree of heat equal to that of boil-
ing water. I have faid, that which we call tem-
perate, becaufe we are not fure that it is true,
this knowledge prefuppofing that of extreme heat
and cold, which we do not know yet: but in the
mean while, till we can eftabliſh the neceffary
correfpondences, thofe who have a mind to know
more on this fubject, may with thefe thermome-
ters make feveral experiments to carry their con-
jectures farther.
Fig. 1.
#
#
1
Obfer
فات
ROYAL ACADEMY of SCIENCES. 363
1.
Obfervations.
3
June 16, 1702. I expoſed to the fun at noon one
of thoſe ſpirit of wine thermometers, which being fet
out in the open air, without being always in the
fun, extend 33 inches from the greatest cold to
the greateſt heat experimented at Paris. I ex-
pofed near it at the fame time the new thermo-
meter, which I have juft defcribed, and obfer-
ved that the degree of the fun's heat fuftained 13
inches, 2 lines of quickfilver leſs than that of
boiling water, and 5 inches, 9 lines more than
that of the temperate air of our climate. During
the obſervation, there was a fmall N. E wind,
which made the quickfilver fometimes fall and
fometimes rife half an inch, whilft the ſpirit of
the other thermometer always rofe in a pretty e-
qual motion; fo that being arrived to the very
top of the glaſs, I was obliged to take it away
from the fun, for fear it fhould break; the
weight of the atmoſphere at that time was equal
to about 28 inches of quickfilver. I placed this
new thermometer another time in water, where
there was a good quantity of ice, and the quick-
filver fell but 2 inches below temperate; that is,
21 inches below the degree of heat of boiling
water; whence we may probably conjecture, that
there ſtill remains in the ice a very confiderablė
degree of heat; which we may eafily know, if
we confider, that after the firft frofts the common
thermometers fink very confiderably,
>
When the quickfilver rifes into the tube BA,
the capacity poffeffed by the air in the ball D,
is greater in ftrictnefs than when the quickfilver
falls from this tube, which it fhould not be, ab-
folutely speaking, if the different fizes of the
balls
Z z 2
364 The HISTORY and MEMOIRS of the
$
balls did not hinder the motion of the quick-
filver in theſe thermometers from being exactly
equal in all. Wherefore in the following expe-
riments, which were made with lefs balls than
that already mentioned, and with tubes of a pretty
large aperture, which had no proportion to their
balls, we muſt not be furprised if the motion of
the quickfilver is not exactly fuch as has been men-
tioned; for the inequalities of thefe very experi-
ments have ſhewn the neceffity of determining
more exactly the proportion of the tubes to the
balls. We muft not expect, however, that the
differences which proceed from the different fizes
of the balls are very confiderable, much leſs that
thofe differences follow thofe of the balls; fince
fuppofing balls of thermometers, one of 3,
and the other of 2 inches in diameter, and that
the ball of 3 inches is applied to a tube of an
aperture lefs by half than that of the tube applied
to the ball of 2 inches, if the quickfilver defcends
in the firft 19 inches below the place to which the
boiling water had made it rife, it will defcend in
the fecond at leaſt 18 inches whereas, according
to the proportion of the balls and tubes, it muſt
have defcended only 3 inches in this laft.
(
I
Saturday, July 1,1702, There were incloſed
in two glaffes of new, thermometers 2 unequal
maffes of air, one about double of the other, each
of them loaded with 14 inches, 4 lines of quick-
filver, and befides, with the weight of the atmo-
fphere, which was found to be 27 inches, 6 lines,
which made in all 41 inches, olines, of which
the third part 13 inches, 11 lines was the height
to which it was,eftimated that the quickfilver
ought to rife, on the air of the two glaffes being
heated by the heat of boiling water. Theſe mea-
fures were fo regulated, the glaffes dipping in the
$
water,
2
F
ROYAL ACADEMY of SCIENCES. 365
are.
water,cold as it was then; for by feveral experiments
made afterwards, it has been found that liquids
follow the temperature of the air in which they
The whole was afterwards fet on the fire,
which was raiſed till it made the water boil pretty.
brifkly for a confiderable time; and it was ob-
ferved, that when the quick filver was rifen in the
glafs with the biggeft ball to 13 inchies, line;
and only to 12 inches, 3 lines in the other, the
quickfilver ceafed entirely to rife in both: thus
the quickfilver rofe in the firft 10 lines lefs than
HM
was expected; and in the last 20 lines 4. As
thefe experiments were made in hafte, and without
preparation, the company defiring at firft only
to ſee theſe new thermometers loaded with quick-
filver, feveral circumſtances were neglected, which
cauſed theſe differences.
1. It was not obferved whether the ſtate of the
cold water, into which the glaffes were plunged
to regulate them, was that which we here call
temperate; for the experiments, which ferved as
a foundation to determine this augmentation of
the elaſticity of the air to about of its charge
were made in this circumftance, it being proba-
ble, that this augmentation is more than, when
the ſtate of the air incloſed in the balls is colder
than the temperate, and less than when it is
hotter. We had not alfo ufed the precaution to
have the tubes of Bignefs proportioned to the
capacity of their balls, becaufe we thought theſe
tubes ſmall enough not to caufe any confiderable
augmentations in the bulks of the air inclofed in
thefe balls.
J
J
1
Wedneſday, July 5, 1702. The 2 glaffes of the
preceding experiment were put again theo cold
water, but yet hotter than temperate, there was
added a fpirit of wine thermometer," and" an' dir
3
one
366 The HISTORY and MEMOIRS of the
}
one after the new manner, to know by their
means the ſtate of this cold water, and fo make
the correction neceffary to the height of the quick-
filver contained in the 2 firft glaffes, and it was
found:
1
1. That the ftate of the water held the ſpirit of
wine thermometer át 60 degrees, that is, 10 de-
grees above temperate, or the ftate of the air in
very deep places, as for inftance, the caves of
the obfervatory.
2. That the air thermometer fuftained 15 lines
of quickfilver more than the temperate, that is,
that the furface of the quickfilver in the tube was
27 inches, 3 lines above the ſurface of the quick-
filver in the ball.
3. That the furface of the quickfilver in the
two tubes of the glaffes of the preceding experi-
ment, was 14 inches, 8 lines above the furface of
that of their balls.
In the laft place, it was obferved on the baro-
meter, that the weight of the atmoſphere was
then equal to 27 inches, 5 lines of quickfilver;
fo that to this weight there was added that of 14
inches, 8 lines, which made 42 inches, 1 line,
of which the third part 14 inches, and of a
line, was the quantity which the quickfilver would
have rifen in theſe tubes above 14 inches, 8 lines,
if the ſtate of the cold water, in which thefe
balls plunged, had been that of temperate up-
on which it may be remarked, that tho' the
quickfilver of the air thermometer was 15 lines.
higher than temperate, yet there were taken but
12 lines from the height of the quickfilver of the
glaffes, becauſe the air of their balls not being
fo loaded as that of the ball of the thermome-
ter, it must not have increafed its fpring fo con-
fiderably fo that it was determined, that the
quick-
ROYAL ACADEMY of SCIENCES. 367
quickfilver in the two glaffes of the experiments
muſt have rifen only 13 inches, of a line, by
the heat of the boiling water.
1
3
As it was wanted only to know by experience,
whether unequal maffes of air, equally loaded,
increaſed the force of their fpring equally by the
fame degree of heat; but alfo to know, whether
this augmentation was fo much the greater, as
thefe maffes were the more loaded, and whether
it was always about of the loads of the air in
the ſtate of temperate: to be certain of this by
the fame experiment, it was determined alfo to
what height the quickfilver ought to rife in the
air thermometer, by the heat of the boiling wa-
ter; and as the height, at which it was then
found in the cold water, was 27 inches, 3 lines,
which being added to 27 inches, 5 lines, the
weight of the atmoſphere at the time of the expe-
riment, made in all 54 inches, 8 lines; of which
the third part 18 inches, 2 lines, was the quantity
which it ought to have rifen by the heat of the
boiling water: but as the cold water, tho' war-
mer than temperate, in which it was dipped,
kept it up 15 lines above temperate, it was deter-
mined that the quickfilver could not rife again
more than 16 inches, 11 lines, by the heat of the
boiling water.
71
>
3
After having thus determined on thefe three
glaffes the height to which the quickfilver ought
to rife, namely, in the 2 firft to 13 inches, of
a line, and in the laft to 16 inches, 11 lines
the whole was fet on the fire as before, till the wa
ter quite boiled and the quickfilver rofe to the
height that it ought in that of the two firft glaffes,
where the ball was biggeft, and where the dif-
ference was but lines in the preceding ex-
periment but in the fecond, there wanted, about
:
$
+
6
368 The HISTORY and MEMOIRS of the
6 lines; and in the thermometer, or third glafs,
there wanted 2 lines, which, without doubt,
proceeded from the bignefs of their tubes of three
glaffes, being confiderably difproportioned to
the bignefs of their balls, and from the bulks
of air not remaining conftantly the fame, but
altering as the quickfilver of the balls is
driven into the tubes, as was faid before; for
tho' it is proved by all theſe experiments, that
the air does not dilate in proportion to its bulk,
as fpirit of wine, and all other liquors do, and
that therefore it does not feem neceffary, that the
balls and their tubes fhould be fo proportioned to
each other, as to acquire equal degrees of elaſti-
city, the bulks of air muſt remain the fame, or
at leaſt increaſe proportionably from what they
were before the heat had acted upon them; and
tho' it is impoffible, let the tubes be ever fo
narrow, that the quickfilver driven in ſhould not
alter theſe bulks a little; yet it is neceffary, in
order to obtain a perfect uniformity in the motion
of the quick filver of theſe thermometers; that the
tubes ſhould be nearly proportioned to their balls;
for the little exactneſs is here of no confequence.
Saturday, July 8, 1702. A glaſs of the new
thermometer was charged with quickfilver, after
the fame manner, and with the machine defcribed
in the former part of this paper. The glafs was
afterwards put in water over the fire, which was
increaſed as ufual till it quite boiled. In this
ſtate we finiſhed the reducing of the height of the
quickfilver, which was rifen higher than the 45
inches above that of the ball exactly at thefe 45
inches as was faid before, except that there was no
regard had to the weight of the atmoſphere, which
was then 27 inches, 4 lines, that is, 8 lines lighter
than it ought to have been, and that confequently
there
ROYAL ACADEMY of SCIENCES. 369
there muſt have been 45 inches, 8 lines of furface
to the other to make the total charge be 73 in-
ches.
I have faid before, that the air which we call
temperate, ſuſtained 19 inches of quickfilver lefs
than the heat of boiling water. The day before
theſe experiments were made, I placed two of thefe
new thermometers in the caves of the obfervatory,
one fell to 18 inches, 10 or 11 lines, the other
only to 18 inches, 6 or 7 lines. From all thefe
experiments therefore we may conclude,
1. That when the bigness of the tubes is not
proportioned to the capacity of the balls, unequal
maffes of air increaſe almoft equally the force of
their ſpring by the fame degree of heat.
2. That the more thefe maffes of air are loaded,
the more they augment the force of their fpring
by the fame degree of heat.
That this augmentation would probably be a-
bout of the loads at the time of temperate, if
155
theſe maffes did not increaſe their bulks, by driv-
ing into the tubes a part of the quickfilver con-
tained in the balls.
4. And that laftly, it is probable alfo, that the
effects would be uniform in all thefe glaffes, of
what fizes foever the balls may be, if the capa-
cities of theſe balls were proportioned to the big-
neſs of their tubes, as I have really found by ex-
periment; upon which it may not be amifs to
obferve, that having broken the glaffes ufed in
the experiments of July 5, in which the quick-
filver ought to have rifen to 13 inches, of a
line by the heat of boiling water, tho' it did not
rife to this height, except in the first of the two
glaffes, and only to 12 inches, 6 lines in the
fecond; and that having exactly meaſured with
quickfilver the capacity both of the tubes and the
VOL, I. N. 10. Aaa
balls,
370 The HISTORY and MEMOIRS of the
1
67
balls, I found that on the length of 31 inches
the capacity, of the first tube was part of the
capacity of its ball, and that the capacity of the
tube wherein the quickfilver, rofe only to 12 in-
ches, 6 lines was part of the capacity of
its ball; whence we fee, that tho' this laft tube
was almoft twice as big as it ought to have been,
yet the difference was but 6 lines, that is, about
2 part of the height to which the quickfilver
rofe, whereas it should have been near half, that
is, about 6 inches, if the motion of the quickfilver
in thefe two glaffes had been made according to
the proportion of the tubes to the balls, as it would
have happened, if they had been full of fpirit of
wine, or any other fluid than air. We fee allo by
this experiment, that the fmaller the capacity of
the tubes is, in comparison of the balls, the more
the increafe of the fpring of the air, by the heat
of the boiling water above what it is in the tem-
perate ftate, approaches more truly to the third
part of the load which this air fupports: but as
thefe tubes were already fo fmall, that it is not
convenient to leffen them, it would be better to
increaſe the bignels of the balls, and to make
them 3 or 4 inches in diameter.
M. Mariotte's rule for the equilibrium of the air
by its spring.
1
When the height of the quickfilver with which
we propofe to load a.mals of air, preffed at firft
"only by the weight of the atmosphere, which he
fuppofes with me equal to 28 inches of quickfil-
ver, is given, and we would find the bulk to
which the ait would be reduced by this load,
M. Martoute confiders this mals of air as inclofed
in the branch EC, of the tube ABC of equal
bigness
Fig
ROYAL ACADEMY of SCIENCES. 371
ร
bigneſs in its whole length, open an A, bent
fquare at D and E, and clofed in C, the part B
is full of quickfilver to the prickt line DE, the
branch DA ſerving to contain the loads which
ferve to prefs the air at EC after this, M. Ma-
riotte makes the following analogy As the fum
of the weight of the atmoſphere and of the
height of the quickfilver, with which we propofe
to load the maſs of Wir EC is to 28 inches of the
atmoſphere, fo is the bulk of air EC to the bulk
to which this load reduces it:
+
1
Now to make application of this rule to our
experiments, let us fuppofe 3 tubes, as ABC,
in which the tubes EC are to one another in the
proportion of 1, 2, 3, and confequently the
maffes of air which they inclofe: let us fuppofe
alfo the load, with which thefe maffes of air are
to be preffed, equal to 45 inches in height of
quickfilver; then to have the bulk to which the
air will be reduced in the firſt glafs, it must be,
1. as 73 inches (the fum of the weight of the at-
mofphere 28 inches and of the load 45 inches) is
to 28 inches (the weight of the atmosphere) fo
is 1 (the bulk of air preffed only by the atmo-
ſphere) to the bulk of air loaded with 45 in-
ches in this first glafs. 2. To have the bulk to
which the quickfilver will be reduced in the fe-
cond glaſs, it muſt be as 73 inches to 28, fo 2 to
2
1
the bulk of air loaded with 45 inches in the
fecond glaſs. 3. In the laft place to have the
bulk to which the quickfilver will be reduced in
the third glaſs, it must be as 73 inches to: 28 in-
ches, fo 3 to the bulk of air loaded with 45 in-
ches in the third glafs. Now as thefe fractions (18
2 + are to one another as the numbers 1,2,3, thefe
unequal maffes of air by acquiring equal forces
of elafticity, have not changed the proportion
73
Aaa 2
fi
that
372 The HISTORY and MEMOIRS of the
i
S
{
}
that they had to each other, and confequently they
muft, continuing the fame, acquire equal force
of clafticity,g.feeing the caufe which produces
them is equal, ag the degree of heat is here fuppo-
fed to be.
400 }
Befides we can hardly have any other idea of
the parts of fire, than that they are in a continual
and very violent motion; nor can we conceive
how theſe parts can heat thofe of the moft folid
bodies, but by fuppofing that by the effort which
they make to penetrate them, they communicate
a part of their motion to them...
But as in the experiments which fhew that un-
equal maffes of air acquire equal forces of clafli-
city by the fame degree of heat, it is eafy to
judge by the preceding calculation, that all the
parts of air which compofe the three different
bulks of air, are neither more nor lefs cloſe the
one than the other, and that befides, the parts of
fire, which put them into motion, being in like
manner the fame, they cannot communicate more
to one than to another. It is true, that unequal
maffes of air cannot acquire unequal forces of e-
lafticity by the fame degree of heat, but on the
contrary, they muſt acquire equal ones, and this
is what is confirmed by experience.
1
As for the fame maffes acquiring fo much
greater forces of elafticity, by the fame degree of
heat, as they are more loaded, it is eafy to con-
ceive, that the more the maffes of air are loaded,
the more parts of air they contain in the fame
fpace, and confequently the parts of fire cannot
infinuate themſelves: between theſe parts of air,
with the violence, which we know they employ in
feparating the moſt immoveable parts of the moft
folid bodies, without separating theſe parts of air
from each other; whence it neceffarily follows,
Knott
3
that
ROYAL ACADEMY of SCIENCES. 373
that the more parts of air there are in the fame
fpace, the greater the augmentation of the bulk,
to which the heat reduces it, ought to be: but
as the caufe, which would augment the bulk of
an elaſtic body, fuch as the air is if it had liberty
to extend itſelf, would in like manner augment
the force of its fpring if it had not this liberty;
it neceffarily follows, that the more the maffes of
air are loaded, the more the fame degree of heat
muſt make them acquire a greater elaſtic force,
this is what really does happen,
As for the experiment fhewing that the elaftic
force, which the air acquires, when it is heated by
the warmth of boiling water, is about of what it
has been when temperate; we do not yet fufficiently
know whether this happens by a neceffary confe-
quence of fome principles, or whether it is a
mere effect of chance. In the mean time all that
we can do therein, is to affure ourſelves, by a
long ſeries of experiments, of the truth of the
fact.
III. A comparison of the ancient itinerary
measures with the modern, by M. Caffini *
1
As the deſcription of all the earth is made by
the dimenfions, that have been taken in diverfe
places and at diverfe times, as well in the heavens
as in the earth, and as the meaſure of the earth' is
determined variously by various people, and
changes with time; nothing is of more confe-
quence in geography, than to know the propor-
tion of the itinerary meaſures, which the metent
geographers uſed in the defeription of a country
to the modern meafures: Pem odi gnoutopl
The itinerary menfures are fometimes différent
Jan, 28, 1702. sale, so bus wor
*
<
i
from
374 The HISTORY and MEMOIRS of the
*
from thofe, which are ufed in commerce and in
architecture. We fall into great errors, when we
uſe them indifferently in geography.
}
The measure of the distance from, Narbonne to
Nifmesub
In the last journey that we made by the king's
order into feveral provinces of France, we have
compared the distances that we have found be-
between the ancient towns and 'thofe of the fame
towns, related by the ancient geographers. We
fhall here relate fome examples of them. The di-
ſtance from Narbonne to Nifmes, by our dimen-
fions, is 67500 Paris toiles in
Strabo places Narbonne 88 miles from Nifmes;
the road from one of thefe towns to the other is
pretty straight, and there is but little reduction
to make. Divide 67500 toifes by 88 miles, there
comes to each 767 22. We throw out this fmall
fraction, becaufe we cannot pretend to have ex-
actly the fame bounds of theſe two towns, which
were taken by the ancients. Each pace was 5
feet, and the mile 5000 feet, the foot is divided
into 12 inches. The toife is 6 Paris feet, there-
fore 767 toiles make 4602 feet. Rejecting two
feet in fo large a number, of which it is difficult
to be certain in the practice, in round numbers
4600 Paris feet will be equal to 5000 ancient.
geographical feet, which are as 46 to 50, or 23
to 25.
1
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2
}
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>
་
Thus the Paris foot of 12 inches will be equal
to à foot and an inch and of an inch of the
ancient meafire, and the ancient foot will be e-
qual to 11 inches and of the Paris foot. If
we fuppofe the ancient mile be 764 toifes it will
be ſmaller by 3 toifes than by this comparifon,
and the ancient geographical foot will be exactly
1
2 j
to
ROYAL ACADEMY of SOLENCES. 375
to the Paris foot, as II to 12. We must now
fee if the other ancient geographers agree with
Strabo in this meaſure.
sitio.
1
By the itinerary of Antoninus, they reckon one
time between Nimes and Narbonne 87 miles, ano-
ther time 91; the dimenfion of Strabo is between
the two. By the ancient table of Peutinger, they
reckon it 95. We fhall prefer the dimenfions of
Strabo, who lived in the time of Auguftus and
Tiberius, the meaſures of the great roads having
then been made with care. We have neverthelefs
examined which of theſe meaſures agree moft
with others, which have been taken in Italy, as
well at the time of the Romans, as in our time. :
}
{ ་
The meaſure of the distance from Bolonia to
Modena.
Antoninus's itinerary marks many times the
diſtance from Bolonia to Modena, and always
makes it 25 miles., The table of Peutinger makes
it alfo 25 miles,
*
Thefe two cities are croffed by the Emilian
way, which in this interval was ftraight. The
fort Urbano, which they have built upon it,
makes it at prefent turn a little. But we fhall
make ufe of the fame, which has been taken by
the means of triangles in a right line,
F. Riccioli and Grimaldi have carefully taken
the diſtance between the towers, which are in the
middle of theſe two cities of a great height. I
affifted at fome of the obfervations that, they made
at Bolonia, and I examined their ftations at Mar
dena. They found the diftance between these two
towers 19,666 paces of Bolonia, which are 5 feet
each. The Balanian foot drawn from the fame
original, from whence F. Riccioli took his, qom
pared to the Paris foot by us, is to the Paris
{
foot.
376 The HISTORY and MEMOIRS of the
foot, as 701 to 600. Thus 600 feet of Bolonia
are equal to 701 Paris feet. The pace of Bolo-
nia is 5 Bolonian feet; and the Paris toife is 6
Paris feet: divide 600 feet by 5, we fhall have
120; and multiply that by 6, and we ſhall have
720 paces of Bolonia, equal to 701 toifes of
Paris.
Now, as 720 is to 701, fo is 19,666 paces of
Bolonia to 19,147 toifes of Paris, which is the
diſtance from Bolonia to Modena, by the dimen-
fion of F. Riccioli and Grimaldi réduced into toifes.
But this diſtance, by the agreement of the ancient
itineraries, is 25 ancient miles: dividing then
19,147 toifes by 25 miles, we ſhall have 766
toiſes for a mile, within almoſt one toife of 767,
which we found before, by the compariſon of the
diſtance between Nifmes and Narbonne given by
Strabo, with thoſe which we have determined by
our obfervations.
An inquiry into the fituation of the temple of the
Pyrenean Venus.
We made ufe of this meaſure of the ancient
miles to find the place where the temple of the
Pyrenean Venus formerly was, which Strabo places
on the confine of the Narbonnefe Gaul with Spain,
63 miles diftant from Narbonne. This diſtance
at the rate of 767 toifes for a mile, following
the dimenfions drawn from that of Narbonne to
Nifmes, would be 48,321 toifes. Altho' the ety-
mology fhews, that Port-Vendre is the port of
Venus, as Vendredi is the day of Venus, yet this
diſtance does not agree at all with that of Port-
Vendre, which is near Colioure. Perhaps the
port of Venus was diftant from the temple of Ve-
nus, or there were two ports on that fide a little
diftant from one another, which had the fame.
name.
ROYAL ACADEMY of SCIENCES. 377
name.
There was another Port-Vendre, called
now l'Etang de Vendre near Narbonne. The
diſtance that is between Port Vendre, which is
near Colioure and Narbonne, according to our di-
menfions, is 41,000 toifes lefs than that which
we have juft found by 7,321 toifes.
At the diſtance of 48,300 toifes from Nar-
bonne is the Selve, where there is a port capable of
a good number of gallies, with a tower to defend
the road. It is larger than Port-Vendre near Co-
lioure, and is fituated on the N. fide of Cape Creux
which is the celebrated Aphroditic promontory,
which Strabo alfo calls the Pyrenean promontory.
Mela fays, that between the promontories
formed by the Pyreneans, there is the port of
of Venus, celebrated on account of the temple;
which might be underſtood as well of one as
the other port. Pliny places the temple of the
Pyrenean Venus XL miles diftant from the river
Tichis, now Ter, in Catalonia. This diftance is
without doubt too great, and almost double of
that which comes from the preceding comparifon.
M. de Marca, inſtead of XL, reads XI, fup-
pofing that the I has been changed into L, but
this diſtance is too fmall, and does not agree even
with the diſtance between the Tech and Port-
Vendre, near Colioure, which is but 5500 toiles,
a little above 7 miles. Probably, inſtead of XL
miles it fhould be read XX miles; and the laft X
has been changed to an L. Thus the port of
Venus will be the port of la Selva.
The measure of the ftadia in France.
Strabo places the diftance between the temple
of the Pyrenean Venus, and the outlet of the Var,
which he gives for the two bounds of France, at
277 miles. He fays, that to this diſtance is reckoned"
VOL. I. N°. 10.
Bbb
2600
378 The HISTORY and MEMOIRS of the
I
2600 ftadia and that others add alſo to it 200
Stadia, which would make in all 2800 ftadia.
We fee by this, how different the proportion
of the miles is to the ftadia. In dividing theſe
two numbers of ftadia by 277 miles, the first
number gives 9 ftadia, and a little more than
for a mile; and the fecond, to ftadia and above
for a mile. Altho' in other places, Strabo, and
the reft, commonly give but 8 ftadia to a mile;
this comparifón however fhews, that we cannot
here allow less than 9 ftadia to a mile, divide
765 toifes, which make an ancient mile, by 9,
we fhall have a stadium in France of 85 toifes,
which make 510 Paris feet. Herodotus makes
the ftadia 600 feet, the foot of Herodotus will then
be to the Paris foot, as 51 to 60, fuppofing the
Stadium of Herodotus equal to the stadium of
France.
*
}
}
The measure of the pyramids of Egypt in feet and
ftadia...
Herodotus makes the breadth of the baſe of the
greateſt pyramid of Egypt to be 800 feet, and
confequently one stadium and, and as 60 is to
51, fo 800 is to 680 Paris fect, for the breadth
of the baſe of the pyramid. At the rate of 9
ftadia for a mile, of which each has 510 feet, this
bafe would have a ftadium and, as by the di-
menfion of Herodotus. M. Chazelles has actu-
ally measured the bafe of this pyramid by a line,
and found it 690 feet, upon an unequal ground
raifed in the middle; from whence he fays, there
must be fomething taken away to have the juft
bafe. If we take away 10 feet, we fhall have
for the breadth of the bafe 680 Paris feet, as we
W
have before calculated..
བྷི॰, ཙ, སྱཱནཾ,,
建
​IQ
M.
ROYAL ACADEMY of SCIENCES. 379
هم
M. Gemelli, who lately went round the world,
relates the meaſure of this pyramid, which he
faw in 1693, as he had them from F. Fulgence of
Tours, a mathematical capucin, who found the
breadth of this pyramid on each fide to be 682
Paris feet, which agrees with the meaſure that we
have juſt found at the rate of 9 stadia for a mile.
The meaſures which he gives of it agree with
thofe that M. Jeangeon has had from M. de Noin-
tel, the king's ambaffador to the Porte, and
which he has communicated to the academy. It is
furprizing, that Mr. Greaves, an English mathe-
matician, in his Pyramidographia, has found the
baſe of this great pyramid meaſured, by triangles,
to be 683 English feet, which are to the Paris
feet, as 15 to 16. In this proportion, having
fuppofed the breadth of the pyramid: 680 Paris
feet, it muſt be 723 English feet, from whence
we may ſee the difference, that there is between
the meaſures of the fame magnitude, taken by
diverſe perfons, and reduced to the fame feet.
1
Strabo himſelf, whofe meaſures taken in France,
we have compared with our own, and who was
in Egypt with Ælius Gallus about the chriftian
epoch, makes the breadth of this pyramid one
Stadium. He therefore makes the ſtadium here
greater than Herodotust or the geographers, from
whom he has drawn the dimenfions of the fouthern
coafts of France.
1
1
Diodorus Siculus, who was in Egypt: 60 years
before the chriftian epoch, fays, that the greateſt
pyramid had on each fide of its lower part 7 ju-
gera; 6 jugera make a stadium according to He-
rodotus: therefore each fide of the base of the
pyramid was one stadium and . We have there-
fore three different dimenfions, of the pyramid in
Stadia; one of an exact ſtadium, one of a sta-
dium
Bbb 2
A
380 The HISTORY and MEMOIRS of the
dium and, and one of a ftadium. The mea-
fure of the ftadia was therefore as different and
as equivocal among the ancients, as the meaſure
of the miles and leagues are among the moderns.
The meaſure of miles was more uniform, as we
have found by the compariſon of the fame dit-
tances taken in France and Italy, by the ancients
and by the moderns. We have from this compari-
fon drawn a conclufion of no ſmall importance,
which is, that the modern Roman foot of a palm
and, is equal to the ancient foot uſed in the mea-
fure of the diftances of the towns of France, and
that both are to the Paris foot, as 11 to 12, hav-
ing neglected a. fmall fraction, which is infenfible
in the practice.
"
of
But the foot of Herodotus, with which he mea-
fured the pyramid, being to the Paris foot, as
51 as 60 is equal to 10 inches, 2 lines and
the Paris foot. It is the large foot of a man of
tall ſtature, and fuch must be the foot of Hercules,
with which he meaſured the ſtadia for the Olympic
games, allowing them 600 of his feet, which
made 100 paces according to Herodotus. This
author divides the pace into 6 feet, as we divide
the toife into 6 feet. It is probable, that Era-
tofthenes, who allowed 700 ftadia to a degree of
the circumference of the earth, having drawn it
from the distance between Alexandria and Syene,
made uſe of theſe ftadia of Herodotus. Thus a
degree, according to Eratofthenes, would be the
product of 85 toiles by 700, which makes 58,500
toifes. This meature of a degree is greater than
ours by about 44 part.
}
Pliny allows 883 feet to the length of each ſide
of the bafe of the largest pyramid. Theſe are
not the feet of the itinerary meaſure, that we have
found by many compariſons to be to the Paris
foot,
}
1
ROYAL ACADEMY of SCIENCES. 381
4
£2.
1
foot, as 11 to 12. For in this proportion the
bafe, which has been found to be 780 Paris feet,
ought to be 702 feet of the ancient itinerary mea-
fure, inftead of 883 that Pliny allows them.
There is then 1810 feet difference,' which makes
more than of 702. This meaſure is therefore
to the ancient itinerary foot, which we found be-
fore to be equal to the modern Roman foot, as
12 to 15, and a little more, and exceeds the mo-
dern Roman palm only, which is to the Roman
foot, as 12 to 16. It is therefore probable, that
Pliny's was a foot of architecture of different mea-
fure, from the Roman foot and palm.^ flokka
Z
3
J
There is alſo a more confiderable difference in
the meaſure of the fquare place, which remains
at the top of this pyramid. Pliny makes its breadth
25
feet; Gemell relates it to be 16 feet. In
proportion to the meaſure of the bafe, as 682,
the meaſure of Gemelli is to 883 the meaſure of
Pliny, fo 16 feet are to 21 feet, inftead of 25
that Pliny gives us. There is 3 feet difference,
we may attribute it to the deftroying of the
cruft of marble with which this pyramid muſt
have been covered, in the time of Pliny, as the
other pyramids, one of which remains at pre-
fent covered at the point, the reft having been de-
moliſhed. The thickness of this cruft muſt have
been a foot and of Pliny's meafure. This di-
minution of the bafe, which has happened fince
Pliny's time, does not fenfibly vary the proportion
of diverfe feet that we have examined, and does
not fettle the different dimenfions that are given.
靠
​If it is fo difficult to make the meatures of the
fame bafe agree, which fubfift always without
fenfible variation, and which we may meaſure
exactly without difficulty, we may judge how
difficult it is to be affured of the diftances of
រ
towns
382 The HISTORY and MEMOIRS of the
}
towns which have not actually been meaſured,
but have been determined by the grofs eftimate
of the time commonly spent in paffing from
one to the other. We must nevertheleſs have
the diftances from one place to two others, of
which the fituation is known to determine with re-
fpect to them the pofition of a third by triangles.
Inevitable errors multiply according to the mul-
titude of places, and there remains no better way
of correcting them, than by the obfervations of
ftars made in places very diftant from one another.
1. The measure used by pilots.
S
The pilots of the Mediterranean allow 75
miles to a degree: Thofe of the ocean allow only
60. The ancient Italian miles are to the modern
miles as 60 to 75 for the ancients make the di-
ftance from Bolonia to Modena 25 miles; and
the modern reckon only do miles from one of
thefe towns to the other. Therefore thofe of the
Mediterranean make use of the ancient miles,
which are to this day in ufe in feveral provinces
of Italy; and thofe of the ocean make ufe of the
modern miles, which are in ufe in other provinces.
The modern meafure has this convenience, that
it takes a minute for a mile whereas the ancient
¹allows' to 'each' minute a inile and a quarter. We
may accommodate ourſelves to the ufe of both.
If we give 5 feet to the ancient pace, as they do
In Italy a degree of 75000 paces will be 375000
feet and fuppofing a degree of the circumfe-
rence of the earth 343,000 Paris feet, as we
o
have found pretty near this ancient Italian
foot would be to the Paris foot, as 343 to 375,
órkasını təl hope and if we give to the mo-
dern Italian pade 6 feet, the degree of 60 miles
wil be 360 obo feet, the modern Italian mile of
Enthute, will be 6000 feet, which will be to the
SW
I
9
V
Paris
ROYAL ACADEMY of SCIENCES: 383.
Paris foot, as 344 to 360, or as 44 to 45. If there
are more or lefs Paris feet in a degree, the pro-
portion of the Paris foot to the Italian foot will
be a little different, unless there happens fome va-.
riation in the number of the ancient or modern,
Italian feet in a degree. For we obtain it, as
the feamen do from the divifion of the degree,
by the approximation of theſe meaſures to thofe
of fome country of Italy, from whence they have.
taken the name altho' the feet, which we call
modern, approach more to the common feet of
France, than to thofe which are in ufe in the
greateſt part of the towns of Italy. We allow 6
of them to a pace, as Herodotus has done, con-
trary to the ancient and modern cuftom of Italy,
by this means bringing it nearer to the Paris
foot, and imitating the divifion of the toife into
6 feet, having feen that the pace of Bolonia is
much nearer to the Paris toife, than the Paris foot
is to the Bolonian foot. By this means a minute
of a thouſand paces has 6000 feet; a fecond has
100 feet, as a degree of 60 minutes has 60,000
toiſes, which are very convenient numbers to ufe,
and eafy to be calculated;
+
1
Of the trigonometrical measure..
३
It muſt be obſerved, that in the trigonometrical
table, where the femi-diameter of the circle is
ſuppoſed to be divided into 10 millions of parts,
a minute as well as its fine and tangent, which
do not fenfibly differ in fo fmall an arch, is
marked with 2909 parts. Doubling the radius
and the arch, we ſhall have the femi-diameter of
20 million of parts, a minute of 5818 parts.
But a minute is 6000 geometrical feet, and 5818
is to 6000, as 32 10:33. We may then eſtabliſh
a trigonometrical foot, which fhall be to the geo-
metrical or modern Italian foot,las 33 to 32.
We
384 The HISTORY and MEMOIRS of the
t
We may find the proportion of this foot to
any other, when we have found how many other
feet make a minute of a great circle of the earth.
We may, in fine, eſtabliſh a fathom of 2 trigo-
nometrical feet, of which there will be 10 mil-
lions in the femi-diameter of the earth; thus all
the numbers of the table will be fo many trigono-
metrical fathoms of two feet, of which there are
2909 in a minute, and 48 in a ſecond, as we
fee without calculating at the head of the table.
The third part of the numbers of the table will
be fo many trigonometrical toifes, of which there.
are 970 in a minute, and 16 in a fecond.
Theſe meaſures of geometrical and trigono-
metrical feet and fathoms, are means between
different feet and fathoms, which are eſtabliſhed
by different nations. We may then take them for
univerfal invariable meafures. Thus, if it is
afked how many miles, feet, or toifes are in a
determinate arch of the circumference of the
earth, we need only take the number of minutes
contained in the arch propoſed for the number of
geometrical miles, multiply them by 1000 to
have the number of geometrical paces or toiles, or
by 60,000 to have the number of feet; thus a degree
of 60 minutes will be 60,000 toifes. The whole
circumference of the earth, which is 360 degrees
will therefore be 21,600 000 geometrical toiles,
or 21,600 Italian miles; and becauſe the cir
cumference is to the femi-diameter as 44 to 7,
or as 220 to 35, or 21,600 to $3,436, the
femi-diameter of the earth will be 3436 geome-
trical miles or modern Italian ones. The half
1718, will be the number of geometrical leagues
almoft equal to the fmall league of France, as
thofe which they reckon from Paris to Orleans.
We may take a third for the mean ones which
+
3
approach
ROYAL ACADEMY of SCIENCES. 385
1
approach to thoſe of Auvergne, and a quarter for
the greatest which approach to thofe of Languedoc.
As for the trigonometrical meaſures, the femi-
diameter of the earth being fuppofed of 10,000,000
trigonometrical fathom, the circumference will be
62,831,852 fathoms.
The third part of thefe numbers will give the
trigonometrical toifes. The femi-diameter of the
earth will then be 3,333,333 trigonometrical
toifes, and the circumferences will be 20,943,950
trigonometrical toifes. The ro。 part of thefe
two numbers will give the trigonometrical
miles.
I
1000
The femi-diameter of the earth will then be
3333 trigonometrical miles, and the circumfe-
rence 20,944 trigonometrical miles.
Of the borary meaſures.
I have tried feveral times in going to Fontain-
bleau, and back again a good pace in a coach,
that in the plain of Longboyau, which has been
meaſured exactly, one travels 5 minutes of the
circumference of the earth in an hour. A man
on foot would go this way in the fame time,
and a degree in 24 hours; and if he was to tra-
vel 12 hours in a day, in a like road, with the
fame quickneſs, he would go round the world in
two years.
IV. Reflections on the measure of the earth,
related by Snellius, in his book intitled, Era-
tofthenes Batavus, by M. Caffini the fon*.
Snellius † meaſured on a plain near Leyden, a
baſe of 326 Rhinland perches and 4 feet: (the
* March 1, 1702.
VOL. I. N°, 10.
+ Plate XVI. Fig. 6.
Ccc
perch
386 The HISTORY and MEMOIRS of the
perch contains 12 feet, and the proportion of the
Paris foot to the Rhinland foot is, according to
M. Picard, as 1440 to 1390) he took from the
extremities of this bafe, with a femi-circle of 3
feet, the angles with the towers of Leyden and
Soeterwoude, and he determined their diſtance to
be 1092 perches. By this diftance, he determi-
ned the fituation of the greatest part of the towns
in Holland, and of fome in Flanders by trigono-
metry. The two towns where he obferved, which
are moſt to the N. and Sare thofe of Alkmaer
and Bergen op Zoom. He transferred to Alkmaer
a meridian line, that he had drawn at Leyden, and
having found the angle that the line drawn from
Alkmaer to Bergen op Zoom made with the meri-
dian, he determined the part of the meridian in-
tercepted between the parallels of theſe towns to
be 34,018 perches.
T
1
He afterwards obferved with a quadrant of
5 feet radius, the height of the pole at both
thefe towns. He found that of Alkmaer to be 529
40′, and that of Bergen op Zoom 51° 29,
which is lefs than the preceding by 1° 11',
and having fubftracted 25 perches of the diftance
between Alkmaer and Bergen op Zoom, for the re-
duction of the places where he had made his ob-
fervations, he determined the magnitude of the
'degree" of "the "circumference of the earth to be
28,473 perches. Having alfo obferved the height
of the pole at Leyden, he determined by the arch
of the meridian intercepted between theſe two
towny, the magnitude of the degree to be 28,510
perches! Taking a mean between theſe two de-
tethinations, we have the magnitude of the de-
gree 2835 Rhinland perches, or 55,021 Paris
'toiles.
A
gnum ad to custom butte
A
Snellius's
adi
ROYAL ACADEMY of SCIENCES. 387
Snellius's method is the fame that we ufed in
the prolongation of the meridian. The bafe
which he actually meafured, appears however
very ſmall, which might have occafioned confi-
derable errors in the feries of his triangles; but as
he has verified his meaſures by a new bafe, pretty
near the fame magnitude, we ſhall fuppofe his
obfervations to be fuch as he relates, and we fhall
ſee hereafter what refults from them, being com-
pared with the heights of the pole, that I have
obſerved in fome towns in Holland, which are
contained in his triangles.
$1
C
-
During my stay in Holland, whither I had
carried an octant of 3 feet radius, which we
have fince uſed in our laft journey, I obferved,
the 10th of Nov. 1697, the meridian height of
the polar ftar to be 54° 16'5" at Rotterdam,
which is one of the moſt fouthern cities of this
province. Going afterward to Alkmaer, which
is the capital of North Holland, I obferved the
meridian height of the polar. ftar to be 54° 58'
10". The difference between thefe heights is
42' 5", which is the arch of the meridian inter-
cepted between the parallels of Alkmaer and Rot-
terdam, neglecting the difference of refraction,
which does not amount to 2". The bufinefs, is
then to know how many toifes this arch of the
meridian is, that we may afterwards determine in
toifes the magnitude of the degree of a great
circle of the circumference of the earth. We may
thus draw it from the obfervations of Snellius.
Snelluis determines the difference of the arch of
the meridian intercepted between the parallels of
- Alkmaer and Leyden to be 14,215 perches. From
Leyden he obferved, that the tower of Goude de
clines from the meridian 44° 49' towards the E.
And he determined in the feries of his triangles,
Ccc 2
the
388 The HISTORY and MEMOIRS of the
1
f
the angle between Goude and Rotterdam of 43°
36, by which Rotterdam is more to the W. The
tower of Rotterdam declines therefore from the
meridian. of Leyden 1° 13' toward the eaft, and
the diſtance between Leyden and Rotterdam be-
ing, according to Snellius, 6972 perches, we
fhall have the arch of the meridian between Ley-
den and Rotterdam 6970 perches, which being
added to the diſtance of Alkmeer and Leyden up-
on the meridian, of 14,215 perches, give the
diſtance between Alkmaer and Rotterdam of
21,185 Rhinland perches, which being reduced
to Paris feet, make 40,913 toifes. The place
where I obferved at Akmaer, drawn from the
plan of this town, is 20 or 30 toifes more to
the S. than the great church where Snellius ob-
ferved; and the place where I obferved at Rot-
terdam, is 30 or 40 toifes more to the N. than
the tower of the great church, which is probably
that where Snellius obferved, fince it is diftin-
guifhed from all the reft by its height, as I have
obferved in my journal.
}
#
1
The places where Snellius obferved being there-
fore one more northward, and the other more
fouthward than thofe of my obfervations, by ad-
ding their difference, we fhall have 60 toifes,
that must be retrenched from the distance between
Alkmaer and Rotterdam, and we fhall have in
the interval 42' 5", which have been obferved
between theſe two towns 40,833 Paris toifes, and
58,245 toiles for a degree. This meaſure ex-
ceeds that which we have determined by the ob-
fervations made in the laft journey, by more than
1000 toifes, pretty near agreeing to that which
Snellius determined by his obfervations.
This difference appeared fo confiderable to me,
that I thought my felf obliged to examine the me-
-thod
1
ROYAL ACADEMY of SCIENCES. 389
thod which Snellius ufed, and calculate his tri-
angles upon the obfervations that he has made,
and related in his book. I have been alfo led to
it by fome errors of the prefs, which immedi-
ately ſtrike the eye, and among others, lib. I.
p. 173. 1. 20 and 21. inftead of diftantia inter
Leydam & Rotterodamum, we should read inter
Goudam & Rotterodamum, I have therefore firſt
calculated upon his bafe actually meaſured the
diſtance between Leyden and Soeterwoude, which
agrees with what he has marked. Upon this di-
ftance, I have calculated that between the Hague
and Leyden, which I have found, as well asche,
to be 4103 perches, and in the triangle: AEF
made by the Hague, Leyden, and Rotterdam,
the diſtance AE, between the Hague and Leyden,
being already known, the angle AFE, which
Leyden and the Hague make with Rotterdam,
being obferved to be 39º 53", and the angle
AEF, that Rotterdam and the Hague make with
Leyden, being obſerved to be 53° 40', I found the
diſtance EF, between Leyden and Rotterdam,
6386 Rhinland perches, and the diftance AF from
the Hague to Rotterdam 5154. Snellius, lib.II.
P. 173. 1. 12. in the fame triangle, where he re-
lates the angles obferved which I ufed, gives the
diſtance AF between the Hague and Rotterdam of
5616, and the diftance EF from Leyden to Rot-
terdam 6972, greater than that which refults
from the calculation by 586 Rhinland perches,
which make more than 1100 toifes.,
"
i
33
Suppofing the diſtance A-E between the Hague
and Leyden 41030, He afterwards determines in
the triangle AES made by the Hague, Lorden,
and Goude, the diftance ES from Leyto
Goude 5898 perches and having dbferved from
the two extremities of this baſe, the angles at
Rotterdam,
?
390 The HISTORY and MEMOIRS of the
Rotterdam, he determines in another triangle
EFS made by Leyden, Goude, and Rotterdam,
the diſtance EF between Leyden and Rotterdam to
be 4883. In calculating this triangle upon his
obfervations, I found the diſtance from Leyden to
Rotterdam 6972, the fame as he had marked in
the preceding problem mifplaced, and the dif
tance between Goude and Rotterdam 4883, which
fhewed me, that inſtead of Leyden, it muſt be
read Goude, and that it is only an error of the
prefs. But I know not how to reconcile theſe two
determinations of the diftance EF from Leyden
to Rotterdam, which refult from two different
triangles, one of 6386, the other 6972. The
firſt determination is the most immediate; but
the fecond is that, upon which he has eſtabliſhed
his meaſure, and is verified by other triangles;
but there is no angle obferved at Rotterdam. We
may therefore conclude, either that the obfervations.
of the angle of the first triangle AEF are faulty, or
that he has miſtaken another place for Rotterdam;
and then there would be no error in his meaſure.
This would be at leaſt a fact that would de-
ferve to be proved, and this might be eaſily ex-
ecuted by a perſon, who fhould be upon the ſpot,
by making a ftation upon the top of the tower of
Rotterdam, and obferving from thence the an-
gles between the Hague and Leyden, Goude,
Dort and Willemstadt.
Let us now examine the reſult of the diſtance
from Leyden to Rotterdam determined by the
first triangles. I have already faid, that the tower
of Rotterdam declines from the meridian of Ley-
den 1 13" toward the eaſt, and fuppofing the
diſtance EF, from Leyden to Rotterdam 6386
perches, as we have juft found by the triangle AEF,
we fhall have the arch the meridian between
3
Leyden,
ROYAL ACADEMY of SCIENCES. 391
Leyden and Rotterdam 6384, which being ad-
ded to the arch of the meridian between Leyden
and Alkmaer of 14215, gives the diftance be-
tween the parallel of Alkmaer and that of Rotter-
dam of 20,599 Rhinland perches, or 39,767
Paris toifes; and retrenching 60 toifes, for the
difference between the places where I obferved and
thofe of Snellius, we fhall have 39,707 toifes
for 42′ 5″, and for a degree 56,612 toiſes.
This meaſure differs very much from that
which we found at firft; it exceeds that of Snel-
lius by 1600 toifes, and is lefs by above 400 toifes
than that which M. Picard has determined be-
tween the parallels of Sourdon and Malvoifine.
f
}
ふ
​But, to leave nothing that may ferve to clear
this fubject, I fhall here examine what refults
from the obfervations made at Alkmaer and the
Hague. I have not obferved in the laft town the
height of the polar ftar; but I have feveral times
taken the meridian height of the fun, by which I
have determined the height of the pole to be 52"
4 13". The height of the pole at Alkmaer
drawn from the obfervations of the polar ftar, is
52° 38′ 34″, the difference between the parallels
of this town and of the Hague, is therefore 34
21". Snellius has obferved from Leyden, that the
tower of the Hague declined 52° 22 from the me-
ridian. The diſtance from Leyden to the Hague
being therefore allowed to be 4103 perches, we
fhall have the difference between the parallels of
theſe two towns 2505, which being added to
14,215, the distance from Leyden to kmaer up-
on the meridian, gives for the difference between
Alkmaer and the Hague 16, 720, perches, which
agree with 34 21" of latitude, Neglecting the
difference between the ftations of Snellius, and
thoſe where I obferved because they are hardly
Tenfible
392
The HISTORY and MEMOIRS of the
fenfible; we ſhall have the magnitude of the de-
gree 29205 Rhinland perches, or 56,382 toiſes;
which gives a ftill lefs determination than that
which reſults from the laft comparifon, wherein
we fuppofed the diſtance from Leyden to Rotter-
dam 6386 perches, the fame as we have found by
the calculations from the rules which he relates.
V. Remarks on the different manner of ma-
naging the common oars, and turning
oars, lately propofed by the Sieur du Guet,
by M. Chazelles * Tranflated by Mr.
Chambers.
To judge of the effect of common oars, and
the velocity they are capable of giving; we are
to confider them in a galley, a veffel to which
in all ages men have endeavoured to give all the
advantages poffible.
Now a common galley has 26 oars, on each
fide; each oar being 36 feet long: whereof 24
feet are out of the galley, and 12 within; but
the part within is proportionably bigger, and be-
fides is fortified with wood in order to balance
the part without the fulcrum or point of fup-
port, being on the edge of the galley. The end
of the oar which enters the water, called the blade
thereof, is half a foot broad, and about 5 feet
long; fo that each oar ſticks on a furface of water
2 feet, and the 26 oars on 65 feet, and that there
are 5 men to each oar. We may therefore con-
fider that 26 oars as all connected, acting at
the ſame time, and impelling 65 fquare feet of
water with the ſtrength of 130 men.
The rowers exert unequal forces. He at the
end of the oar works hard, as moving at each
#March 1, 1702.
ftroke
ROYAL ACADEMY of SCIENCES. 393
ſtroke or ſtretch of the oar, the ſpace of 6 fect,
but the others lefs in proportion, and the next
the fulcrum ſcarce ſtirs; fo that when they are to
continue rowing any time, they are obliged to
relieve and fucceed each other, which makes a
little hindrance.
The ſtroke may be confidered, as confifting of
3 parts in the firft, the men recover and raiſe
themſelves; in the fecond, they carry the oar
forwards; the foreman advancing a ſtep, and
ftretching his body before the ftern; in the third,
they recline or throw themfelves backwards, with
the arms upwards, in order to plunge the blade
in the water: which laft motion alone tends to
make the galley advance. It muſt be obſerved,
that at the fame time the fall of the whole crew
of 260 men, makes another impulſe or impreffion
on the galley, tending to fink it deeper, which
of conſequence muft retard its velocity; fo that
the motion is performed in jirks, or fhakes.
We have obferved, that a galley rowed with
all the ſtrength it can maintain for a continuance
of time, in a ſtanding water, does not give a-
bove 24 ftrokes in a minute and that the firſt
oar falls into the fame part of the water, as the
ſeventh ſo that at each ftroke the galley ad-
vances the ſpace of 6 banks, which is 3
*fa-
thoms; and confequently 72 fathoms in a mi-
nute, and 4320 fathoms in an hour, which makes
5 good miles or 1 league in an hour. This calculus
I have compared with feveral experiments and
obfervations, from all which I am confirmed,
that a galley in a full calm, cannot go 2 leagues.
an hour, for a continuance: fuch is the rate at
which the common oars will carry us.
*It is toifes in the original.
VOL. I. Nº. 10.
Ddd
Now
394 The HISTORY and MEMOIRS of the
Now fuppofing the turning oars to be 12 feet
from the centre of their motion, to the tip of the
blade, making them dip 6 feet in water; and
placing the point of fupport 5 or 6 feet above
The water line; the blade may be 3 feet broad,
if required, or even more, which will impel 18
fquare feet of water continually, and without in-
terruption, with a force greater or lefs, according
to the number of perfons applied to the handles,
who all exert an equal force, and only move 3
feet, which they may continue to do much lon-
ger than the foreman of the common galley, who
moving at double this rate, is foon thrown into a
fweat, and obliged to work naked.
The velocity of the galley in this cafe of turn-
ing oars, is eaſily eftimated, if they only make
one turn or revolution in 10 feconds, the velocity
will equal that of the common galley, by reafon
the turn. is equal to 12 fathoms: fuppofing, as
we have done for the common oars, that the
water does not give way in the leaft. But for a
greater juftnefs in the eftimate, we fhould find by
repeated experiments in known diſtances, how
much the water yields or gives way in propor-
tion to the velocity of the turns, and we fhall
have the greater accuracy the more of the turn of
thefe oars exceeds the fpace advanced at a ftroke
with the common ones.
There is no doubt but the ftrength, for inftance,
of 100 men, acting contiru Hy on a bulk of wa-
ter of 18 fquare feet on a fide, will foon put the
largeſt veffel in motion; fince a common cha-
loop makes itfelf felt, notwithſtanding the incon-
veniences of fuch towage.
I am perſuaded therefore, that fuch oars would
be of great advantage to large veffels, and even
more than to fmall ones, by reaſon befides the
{
great
ROYAL ACADEMY of SCIENCES. 395
great number of hands they have in readiness to
work them, there is more room for the flights of
the handles, to make them move without any
embarraſs, which cannot eafily be done in a fmall
veffel, where the fpace between the two decks is
but low, and uſually much encumbered.
VI. An obfervation on a column of light feen
at the obfervatory, May 11, 1702, in
the morning, by M. de la Hire*
I obferved a great luminous ray perpendicular
to the horizon, and equal to the diameter of the
fun, in its whole height, which was about 9 or
10 degrees. This light appeared fome time be-
fore the rifing of the fun, and we faw it again
after it rofe. The heavens were overcaft with
little clouds, lying along the horizon, which did
not hinder the fun from being feen very plainly;
they only made little black bands and jaggs to
ward the edges but the vertical diameter of the
fun at its rifing, appeared to me at leaft equal to
the horizontal.
In the memoirs of the academy for the year.
1692, there is related an obfervation of M. Caf
fini's, of a light almoft like this. M. Caffini
fays, that this phenomenon is very rare, and that
he never faw but one like it, which was in 1672.
But both theſe obfervations having been made af-
ter fun-fet, he could not fee the proportion of the
fun with this light.
We may explain the light that I have ob
ſerved in this manner. It is certain, that all the
parbelia, and thefe appearances of light, never
appear when the air is very ferene, and that we
fee them generally toward the horizon, when it
+ Plate XVII. Fig. 1.
Ddd 2
May 17, 1702.
is
396 The HISTORY and MEMOIRS of the
is full of little, long, thready clouds. Befides,'
it is manifeft, that there happens to the rays of
the fun, which met thefe clouds, the fame thing,
as that which we perceive when we look at the
light of a candle through a glafs that is a little.
greafy; and when we rub it a certain way with
the hand; for it then makes an infinite number
of little furrows, of which the elevated part re-
turns the light toward the eye, and we ſee theſe
rays extended according to the perpendicular in
the direction of the furrows. The ray of light
muft appear pretty near equal to the diameter of
the luminous body; for only thoſe which meet
the direction of the furrows perpendicularly, can
be reflected toward the eye, the others which are
oblique turning away from it, as we may try up-
on a thread of glafs, by looking at a candle
through it.
The fame thing muft happen to the little threads
of the clouds, or to the little long parts lying
this way, of which they are compofed, as to the
little furrows juft mentioned.
VII. Obfervations made by means of the
burning-glass, by M. Homberg.
The great burning mirrours, which we have
ufed till now, have been concave, which reunite
exactly the rays of the fun, and make a very
burning focus: but as this focus is made from re-
flected rays, which are united upwards, we are
obliged to hold the fubftance in the air which
we would expofe to it, without being able to fup-
port it in any veffel. As foon as this fubftance is
affected by the heat of the focus it begins to melt;
1
when it is melted, not being fupported by any
thing,
ROYAL ACADEMY of SCIENCES. 397
thing, it runs and quits the focus, and conſequently
receives no more impreffion from it, fo that we
cannot make any continued experiment by thefe
fort of burning mirrours. Thus they have only
ſerved for a curiofity without any ufe; this has
made us wifh for great glafs lens's, thro' which
the rays of the fun paffing, would make a focus
downwards, to which we might expofe the ſub-
ſtance ſupported in convenient veffels, as long as
we pleaſe which would not only give an op-
portunity of making continued obfervations, but
alfo experiments, which are abfolutely impoffible
with the concave mirrours.
1
The duke of Orleans having fix months ago
brought one of thefe glafs lens's, of 3 feet diame-
ter, made by M. Tſchirnhauſen, one of our affo-
ciates, ordered me to make ufe of it for examining
all fort of ſubſtances, which I do as often as the
fun permits me. I relate here fome of the moſt
extraordinary obfervations that this glafs has fur-
nifhed us with; by which we fhall fee that gold
and filver are volatile metals in the fire of the fun,
as other metals are in the fire of our furnaces.
t
اد
Gold eaſily melts with the burning-glafs; and
it diſappears at length three ways, which differ
from one another according to the degree of heat
to which they are expofed.
Fine gold reduced to a calx by fpirit of falt
melted with the fun, fumes at firft very much,
and changes a part of it quickly into a glass of a
very deep violet colour.
2
}
Fine gold, reduced to a calm by quickfilver,
melted with the fun fumes at firft very much,
and quickly changes a part of it into a tran-
fparent cryftalline glafs without colour; but if
we hold this glafs for fome time in fufion with
the gold, it lofes its tranfparence, and becomes
opake
3
398 The HISTORY and MEMOIRS of the
opake by degrees, at firft the colour of opal, then
white as milk, afterwards it grows brown at the
fummit of the drop, and at laft the drop of glaſs
becomes of a deep brown, inclining to a green.
This glaſs ſwims upon melted gold, fometimes
whirling about all ways, fometimes running over
it in a right line, and waving, changing place
with a very great velocity, without fixing to the
veffel which contains the gold, unleſs the veffel
itſelf begins to vitrify. Then the glaſs of the
gold, and that of the veffel mix together, and
fix themſelves to the veffel.
When the fine gold, that we would melt with
the fun, is not in a calx, but in a mafs, there does
not at firſt appear any glaſs upon it, but it is
formed by degrees; as thus:
The gold which I fuppofe to be pure, when
firft it is melted, appears in a drop, fair and clean
like a looking glafs, but foon after its furface be-
comes as if we had thrown duft upon it: this
duft very quickly gathers into a little drop of whi-
tish glaſs, upon the middle of the melted gold,
leaving the whole furface of the gold for a mo-
ment very clean and clear, as it was in the begin-
ning of its fufion; after which the furface of the
gold appears again dufty: this powder at firſt co-
vers the whole furface of the gold, like a general
fpot, which diminishes its breadth by degrees,
but pretty quickly, till it terminates upon the
middle of the mafs of gold, and enlarges a little
the first drop of glafs that was formed by the
firſt duft. It does this fucceffively, during the
whole time that we hold the gold in fufion to the
fun.
When the little drop of glafs is come to the
fize of a very ſmall pea, its weight makes it run
towards the edges of the melted gold, and then
the
ROYAL ACADEMY of SCIENCES. 399
the duſty ſpots make a new little drop of glafs,
which becoming a little bigger, runs alfo towards
the edges of the melted gold; this joins to the
firft and makes it bigger, and then the third little
drop of glaſs begins to form itſelf.
The whole mafs of gold will change this way
into glass; but to the end that this may happen,
it muſt be obſerved not to hold the melted gold
exactly to the focus of the two burning-glaffes; it
is well to prefent it to it from time to time to
ſtrengthen the fufion, and then to take it away a
little; for the true focus of our two glaffes is too
violent to hold long in fufion any metal what-
foever.
For the metals which are hard to melt, there
are three ways of placing them to the focus,
which produce three different effects. The firft
is to the exact point of the focus. The gold be-
ing held in this place a little while, begins to
crackle and throw out little drops of its fubftance,
to 6, 7, and 8 inches diſtance, the furface of the
melted gold becoming very fenfibly prickly,
like the green fhell of a chefnut.
All the fubftance of the gold lofes itſelf this way,
without fuffering any alteration; for if you fpread
a fheet of paper under the veffel which contains
this gold that crackles in fufion, we fhall gather
upon this paper a gold powder, of which the little
grains being viewed through a microfcope, ap-
pear to be little round balls of gold, which may
be again melted into a maſs.
The fecond way to place the gold in fufion, is
to draw it a little from the true focus, till you
fee that the gold does not appear any longer
prickly nor fparkles. In this place the gold vitri
fies, as we have just mentioned, which is a true
changing of the fubftance of a heavy, malleable,
and
400 The HISTORY and MEMOIRS of the
and ductile metal, into a light, brittle, and ob
fcurely tranſparent glaſs.
The third way to place the gold in fufion, is
to draw it ſtill a little farther from the true focus,
than it is in the vitrifying place, and here it only
fumes; its lofs there is very flow, and we are
obliged now and then to bring it nearer to the
focus, to prevent it from fixing.
Theſe are the 3 different changes that fine gold
fuffers at the burning-glafs; namely, to evapo-
rate in fume, to change into glafs, and to fly into
the air by little grains.
It is pretty near the fame with fine filver, but
with thefe differences, that filver fumes much more
than gold, that it goes away incomparably fafter
in fume, that it fparkles at the leaft heat, and
that it does not vitrify entirely in the fame man-
ner as the gold.
Silver refined with lead fumes confiderably,
and the furface becomes dufty, as we have ob-
ferved in that of the gold; but the powder which
it makes does not melt into glafs, as it does with
the gold, for it is white and light as flower, it
gathers in fo great a quantity, that there is the
thickneſs of more than a line over all the furface
of the filver, when we hold it about a quarter of
an hour together to the fun, and during this time
a dram of filver has loft 26 grains, that is, more
than of its weight.
438
Silver refined with antimony fumes yet more
than that which is refined with lead, and the
pow-
der that it makes upon its furface, melts into
glafs as does that of gold; but this glass does not
keep in a drop upon this filver, as the glass of
gold does; on the contrary, it fpreads over the
whole furface, as if it was a yellow varnish. This
glafs is volatile, and evaporates in fume, with
the
ROYAL ACADEMY of SCIENCES. 401
the mafs of its filver, in which it differs from
the glaſs of gold, which does not go off in fume,
and differs alfo from the powder gathered upon
the filver refined with lead; for this powder in-
creaſes more and more upon the filver expoſed
to the fun, but this varnifh does not feem to in-
creaſe by expofing it a great while to the fun
upon the filver.
When fine gold and filver have been for fome
time melted with the fun, they are with difficulty
melted with the common fire, and their diffol-
vents do not diffolve them fo faft, nor with fo
much ebullition as they did before, which is ob-
ſerved more fenfibly in gold than in filver.
It would be well here to give the reaſon why a
glafs is formed upon gold and filver refined by
antimony, and why upon filver, refined with lead,
it only makes a powder which does not vitrify at
all? Why thefe glaffes and this powder have not
the fame weight as the metals, which have pro-
duced them? Why gold melted for fome time in
the fun, melts with difficulty with the common
fire? And why fpirit of falt diffolves it almoft
with out ebullition ?
To give the reaſon of all thefe facts, I find
myſelf obliged to fay before hand, 1. What the
fire of our furnaces appears to be. 2. In what
manner it acts. And, 3. the difference I believe
there is between the common fire, and the fire of
the fun.
I fay therefore, that the fire, which we com-
monly uſe, or flame, is nothing but a liquid com-
pofed of the matter of light and of the oil of the
wood or coal; this fluid, or flame, is much
lighter than the air that furrounds it, and being
preffed on all fides but unequally by the air, it is
driven by it continually to the tide where it is
VOL. I. No. II.
Eee
leaft
402 The HISTORY and MEMOIRS of the
MINH
leaft preffed, which is ufually upwards with re-
gard to us, or from the earth.
The particles of the flame are very fmall, and
capable of paffing into the
folid bodies," beings of the moſt
driven violently against thefe
bodies by the air, of which the preffure is more
or lefs violent, according as this air is more or
leſs condenfed by the cold, by the wind, or by
an artificial blowing, fuch as bellows, reeds, &c.
The violent paffage of the flame acroſs the
bodies, which are penetrated by it, diforders and
difunites the parts of thefe bodies this difunion
produces in fome an entire diffolution of their
parts, as it happens to all bodies reduced to afhes;
in the others, it only produces a fimple fufion,
as it happens in metals and bodies, that vitrify,
of which the particles reunite and become again
a folid body, as foon as the violence of the flame
begins to ceafe: but as the interftices of thefe fu-
fible bodies preferve the traces of the flame which
has penetrated them, thefe interftices remain
greater or leffer in the coagulation of thefe bo-
dies, according as the flame has been more or lefs
great, and as there remain more or lefs parts in its
interftices. Thus much for the common fire.
The fire of the fun is only the fimple matter of
the light, which is difperfed in the air, without
the mixture of any oily fubftance of wood, or
the like, driven by the fun.
This matter being reunited by a burning-glafs,
and driven in a pretty large quantity against any
fubftance whatſoever, penetrates it, croffes it, and
difunites the parts almoft in the fame manner, as
we fee the common fire to act.
The firft fenfible difference of thefe two fires,
confifts in this, that one, which is the fun, is a
fimple matter, whofe parts are infinitely fmaller
*
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than
TAIN
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ROYAL ACADEMY of SCIENCES. 403
1
hidw betivo
than thoſe of the common fire, which confifts, as
we juſt ſaid, in a grofs mixture of the oil of the
wood with the matter of the light p
The fecond fenfible difference of theſe two
fires is, that the air, which is heavier than the
flame, drives the flame according to the laws of
the equilibrum of fluids, without which the flame
would have no motion; whereas the fire of the
fun is driven by the fun, without the air contribu-
ting any way to its action, which is plainly proved,
becauſe the flame cannot fubfift nor act in a place
void of air, and becauſe the rays of the fun act
with as much violence in a vacuum, as in the
open air.
Knowing therefore the principal differences of
the nature of thefe two fires, we must examine
alfo their different effects.
We have obferved before, that the pores or in-
terſtices of fufible bodies, preferve after their fu
fion, the traces as well of the common fire, as of
that of the fun, which is plainly feen by the in-
duration and boiling of the metals.,
We have alfo obferved that the flame, accord-
ing as it is more or lefs thick, leaves in the pores
of the body which it penetrates, a part of its fub-
ftance, which is proved alfo, as well by the
weight that certain bodies acquire in their calci-
nation, as becauſe certain metals which are foft
under the hammer, become brittle if we melt
them, or if we make them red hot in a coal
fire.
$
This being fuppofed, we muft imagine that a me
tal, for example, gold, having been melted with the
fun, muft have its pores or interfaces more, clofe,
than if it had been melted by the common firs,
fince the fubftances, which have pafled through
the pores of thefe two different maffes of gold,
Eee2
ID
are
404 The HISTORY and MEMOIRS of the
ป
ན
are very different in thickneſs. And as thefe
pores do not remain void, the matter which is
introduced into thofe of gold melted by the com-
mon fire, which are large, muſt be in a greater
abundance than they are in the pores of gold
melted by the fun, which are fmall.
4
We muſt alfo confider, that the points of the
fpirit of falt, which are diffolvents of gold, muſt
drive out its foreign matter which poffeffes them,
and that a greater quantity of this matter muft go
out of the pores which contain much of it, 'than
there muft out of thofe which contain but a little.
And as it is only this foreign matter, which is
introduced into the pores of a metal, that makes
the bubbles which appear in the diffolution of a me-
tal, there muſt be much more ebullition in the dif
folution of gold that has been melted by the common
fire, than in that which has been melted by the fire
of the fun. Befides, we fee that in the diffolution of
this firft, there are many more of theſe bubbles
very fenfible, and that in the other, there are fo
few, that thofe who have been prefent at this ex-
periment have hardly feen any.
-
We have allo obferved, that gold which has
been melted with the fun, melts with much more
difficulty at the common fire, than it did before
it had been melted with the fun. It is eafy to
underſtand the reafon of it, if we fuppofe, as we
have done, that the pores of gold melted by the
fun are more clofe than thofe of gold melted by
the common fire, and that the parts of the flame,
or of the commion fire, are groffer than thofe of
the fire of the fun."
It must follow from hence, that the cloſe pores
of gold melted by the fun, give a more diffi-
cult paffage to the grofs parts of the flame, than
do the larger pores of gold melted by the common
fire
ROYAL ACADEMY of SCIENCES. 405
fire; or which is the fame thing, the common
fire with greater difficulty puts in fufion the gold
which has been melted by the fun, than that
which has not.
TA
We have alfo obferved, that the glafs of gold
is lighter than a like bulk of gold is. To
underſtand the reafon of it, we muſt imagine that
the parts which a perfect metal is compofed of
are of quickfilver, of a metallic fulphur, and fome
terreftrial matter, that the quickfilver is always
volatile, and that the metallic fulphur and the
terreſtrial matter are fixed.
We may alſo imagine, that the parts of the
matter of light, or of the rays of the fun are fmall
enough to be introduced even into the compo-
fition of the metal, to difunite the principles, a-
mong which the quickfilver being naturally vola-
tile, finding itſelf difengaged from the metallic
fulphur which held it, is carried away in fume
by the violence of thefe rays: but that the me-
tallic fulphur being thus fixed, and remaining
with the earth of the metal, they melt together
and appear afterwards in the form of glafs; fo
that in this glafs of gold, there is only found the
earthy fubftance of the gold, melted or vitrified
by its fulphur, and as the heavy part of a metal
is its quickfilver, which does not make any part
of the glafs of the gold, this glafs muſt be lighter
than the gold itſelf which contains all its quick-
filver.
We have alfo obferved, that the earth of filver
does not vitrify as does that of gold, which pro-
ceeds probably from this, that filver has much
lefs fulphur than the gold; that the fulphur muft
ferve for a flux to its earth, and that there is not
enough found in the filver to put the earth in fu-
fion, and to vitrify it.
1
This
406 The HISTORY and MEMOIRS of the
This is confirmed by filver that has been re-
fined by antimony, the earth of which vitrifies as
does that of gold, becauſe there remains in this
filver a part of the fulphur of the antimony,
which ferves for a flux to this earth: but the ful-
phur of antimony not being fixed as that of gold
is, the glafs which is made with the earth of filver
is raiſed in fume with its quickfilver.
We fee by theſe obſervations, that the idea
which we had formed in chymiftry of the invin-
cible fixedneſs of gold and filver does not fubfift
any longer.
VIII. A defcription of the labyrinth of Can-
dia with fome obfervations on the growth
and generation of stones, by M. Tourne-
fort. Tranflated by Mr. Chambers.
4
The labyrinth of Candia is a fubterraneous paf-
fage, in manner of a ftreet, which, by a 1000
turns and meanders on every hand, without the
leaſt regularity, traverses the whole inſide of a
hillock, fituate at the foot of mount Ida, 3 miles
from the ancient city of Gortina. The entrance
of this labyrinth is by an aperture 7 or 8 paces
wide, but fo low, that a man of moderate fize
can hardly paſs without ftooping; the bottom of
the entrance is very uneven, but the top quite
flat, and naturally terminated by feveral beds or
Strata of ftones, placed horizontally over each
other. The firft thing we meet withal, is a kind
of ruftic cavern, the defcent whereof is very gen-
tle: but upon advancing further, the place ap-
pears perfectly furprizing. Among the multitude
of turnings, there is one alley, much lefs intricate
than the reft, which by a path about 1200 paces
long,
ROYAL ACADEMY of SCIENCES. 407
long, whofe extremity divides into two, leads to
a large beautiful hall at the farther end of the la-
byrinth: to find this alley, we are to turn en the
left, about 30 paces from the entrance, if any
other paffage be taken in lieu of it, after travel-
ling a good way, we find ourfelves engaged in a
multitude of nooks and blindholes, which we have
much ado to recover ourſelves from.
In half an hour's time we advanced 1160 paces
in the principal alley, without turning either to
the right or left; it is or 8 feet high, and roofed
with a horizontal Atratum of rocks, tho' in fome
places one is obliged to ftoop a little, and par-
ticularly in a place about the middle to walk on
all fours, it is commonly broad enough for two
perfons to walk in front, and the floor very even,
without any confiderable rife or fall; the walls
are cut perpendicularly, or formed of ftones which
had obftructed the paffage, and have fince been
ranged very neatly, as in walls where no mortar
is ufed; but there are fome partings to encounter
withal, that a perfon would be inevitably loft,
without the neceffary precautions. As we had a
great defire to come back again, we, firft, pofted
one of our guides at the entrance of the cavern,
with order to fetch people from the neighbouring
town to come to our deliverance, in cafe we did.
not return before night. Secondly, each of us
carried a large flambeau in his hand. Thirdly,
we fattened papers, marked in all the paffages
on the right, which appeared difficult to be hit
again. Fourthly, one of our Greeks left little
bundles of thorns provided for the purpofe on the
left, and another took care to ftrew chaff along.
the road, of which he carried a bag, full under his
arm.
1
.
Tyoll
de docq 5
day!
1
al gaiara|| D
By
it
duta da adi ofer
408 The HISTORY and MEMOIRS of the
1
"
By this means we made a happy journey, but
after having well examined the place, we were all
agreed, that there was no appearance of its be-
ing an ancient quarry from whence ftones have
been dug to build the cities of Gortina and Gnof
fus, as Bellonius and fome modern authors have
imagined, what probability is there, that they
would feek for ftones in the recefs of a narrow
alley above a mile long, and interfecting by fuch
a multitude of other roads, which run through a
whole mountain, that a perfon is in danger every
moment of being loft? They would much ra
ther have opened the quarry in the uſual manner,
as we find practifed in the famous quarries of
Paros and Scio, how would they get the ftones
along in a place only paffable upon the hands and
feet, and which yet is upwards of 100 paces long,
and is certainly all natural? Add that the moun-
tain is fo rough and fharp, that we had much a.
do to mount it on horfeback; we looked but in
vain for the ruts of the waggons, which Bello-
nius affures us he had obferved therein; fuch ruts
however could only fhew, that they had made
uſe of waggons to clear the alleys of the laby-
rinth, not that they had dug in it for ftones for
building; it may even be obferved, that the ftone
of this labyrinth is neither hard nor beautiful, be-
ing of a dirty coloured white, like that in the
mountain, at whole foot the city Gortina ſtands »
and as to the city Gnofus, it was a great diftance
off.
'Tis much mone probable therefore, that the
Labyrinth is only a natural paffage, which fome
wealthy people had amefyd themiclves many ages
ago with ming paflable, by opening moft of
the places which had been too narrow to raife the
roof, they had only to pull down fome beds of
I
1
itone
ROYAL ACADEMY of SCIENCES. 409.
ſtone, which naturally lie in horizontal ftrata,
through the whole thickneſs of the mountain;
and they were at the pains of cutting the walls
perpendicularly in fome places, and to range
moft of the ftones which obftructed the paffage
of the low place, where we are to creep on all
fours, they might poffibly leave untouched, as a
document to pofterity, what all the reft had na-
turally been; for beyond this place the alley is as
beautiful and commodious as on this fide. As the
ancient Greeks were ftruck with every thing which
had the appearance of grandeur, eſpecially in
matters of building, 'tis probable they undertook.
to perfect what they found nature had only fketched
out.
Some fhepherds perhaps firft difcovered
theſe fubterraneous paffages, and gave room for
the great men of thofe times to enlarge them;
and thus to make that wonderful labyrinth, which
now only ferves as a retreat to bats, though it
may anciently have afforded ſhelter to feveral fa-
milies during the civil wars, or under the reigns
of tyrants; for the place is quite dry, and void
both of drains and congelations. It may be added
to this conjecture, that there are two or three o-
ther very deep natural paffages in the hills, near
the labyrinth, which might be formed into the
like wonders, if it were found worth while. Ca-
verns are very frequent through the whole ifle of
Candia; and moft of the rocks, efpecially thoſe
of mount Ida, are pierced with holes, into which
one may thrust the head, and through them we
frequently difcern deep perpendicular caves; nor
can any reafon be alledged why there may not be
horizontal paffages between them, eſpecially in
places where the banks of ftones are laid horizon-
tally over each other. 'Tis probably, that they
who dug the amphitheatre of Douvai in France,
VOL. I. N°. II. Fff
were
410 The HISTORY and MEMOIRS of the
were invited thereto by fome cavern, whofe aper-
ture might be like that of our wells, and the
beauty, or perhaps the oddneſs of the place, én-
gaged them to enlarge it, and give it the form of
an amphitheatre, which ftill poffeffes the cavity
of a large mountain, all the outfides whereof are
covered with earth; nor is this lefs wonderful
than the labyrinth of Candia.
Be this as it
will, 'tis certain the labyrinth, which is now feen
in that ifland, is not the famous labyrinth men-
tioned by the ancients. This latter was built by
Dedalus, upon the model of the labyrinth of
Egypt, which was one of the moſt celebrated
buildings in the world, being adorned at its en-
trance with a vaft number of columns, and 100
times bigger every way than that of Candia, as
we are affured by Pliny, who adds, that there
was no remains of this latter extant in his time.
I cannot quit the labyrinth without mentioning
a very remarkable obfervation, which I had long
been feeking for to confirm a ſyſtem, which I
have formerly advanced concerning the vegita-
tion of ftones. Thofe of this labyrinth do fenfi-
bly grow, and
and augment
augment without
without any room for
fufpecting any foreign matter employed externally
to them; they who engraved their names on the
walls of this place, which are all of living rock,
and are hewn perpendicularly, little imagined,
that the ftrokes of their chizels would gradually
fill up, and in procefs of time, they fhould be-
come raiſed or prominent 2 or 3 lines above the
naked of the ftone; fo that the characters, which
at first were indented, are now fo many baffo
relievos, the matter thereof is whitifh, tho' the
ftone they arife from be greyish; and I can no
"'otherwife conceive them, than as a kind of cal-
lus formed by the natural juice of the flone,
心
​which
ROYAL ACADEMY of SCIENCES. 411
*..
which had gradually oozed or extravafated into
the wound, cut in their fubftance much like the
callus formed between the fibres of fractured
bones, tho' as the fubftance of thefe prominences
is all rough, and as it were grained, it might
likewiſe be compared to young flesh, which every
body knows rifes much in this manner. Some-
thing of this kind is alfo obfervable in the bark
of trees, whereon names have been graven by the
point of a knife; the poet had reafon to fay,
that the characters grew as the tree grew.
Crefcent illa crefcetis amoris.
Before my departure I fhewed the academy an
eagle's ftone, wherein there were callus's of the
like kind. Upon breaking this ftone to ob-
ferve its inward ftructure, I found it covered in
certain places with feveral ancient callus's, which
had cloſed the parts which had been broken at the
ſame time when it was growing. Thefe callus's
were only the nutritious juice of the fame ftone,
which, after uniting the parts, had thruſt about
half a line thick beyond the fame, and were at
length hardened into a kind of folder. The fame
thing had befallen one of thofe ftones brought
from the Indies, wherein we frequently find chry-
ftals, and fometimes little diamonds. This ftone
having been cloven by fome accident into feveral
pieces, they had been knitted together again by
a natural callus.
OL NA
Theſe three obfervations evidently hew, that
there are ſtones which grow in the quarries, and
which confèquently are nourished, and that the
fame juice which nourishes them, ferves to rejoin
their parts, when they happen to be broken, Af
ter the like manner, as is obferved of the bones
of animals, or the branches of trees, where care
Fff2
}
ས བ ད་
is
412 The HISTORY and MEMOIRS of the
་
is taken to cloſe them with a bandage, this
being fo, we can hardly make any doubt, but
that there are ſtones which are organized, for their
nutritious juice can only be drawn from the
earth; and this juice muft have been filtrated
thro' their ſurface, which we may here confider
as a kind of bark, and conveyed thence into all
the other parts. 'Tis more than probable, that
the juice, which filled up the cavities of the cha-
racters graven in the labyrinth of Candia, had
been conveyed to the furface of this rock from
the bottom of its roots; nor is there any more
difficulty in conceiving this, than in conceiving
how the fap paffes from the roots of the largeſt
oaks and pines to the tips of their higheft branches.
The heart of theſe trees, 'tis certain, is extremely
hard; and that of ebony guaicum, and the
lignum ferri much harder. Coral is as hard in
the fea, as out of it; and what we call fea-mufh-
rooms, whoſe ſtructure is fo much admired, and
which have the confent of all mankind for their
growth, are really ftone, and fo like the common
ftone, that they are uſed in America to make
" lime of. No body, I fuppofe, will deny but
that fhells likewife grow, by means of a nutri-
tious juice yet this juice, as well as that, where-
by the other hard bodies above-mentioned are fed,
is convey'd into the tubes of fuch bodies how nar-
row foever they be, as easily as into thoſe of
plants, which are much fofer.
{
It cannot be denied therefore, but that fome
ftones feed themfolves like plants; and there is
even room to fufpect, that they are likewife pro-
pagated after the fame manner, at leaft we have
a multitude of ftones, whofe generation can hardly
be conceived, without fuppofing that they arite
drumasikind of feed, it may uſe the term,
#
that
ROYAL ACADEMY of SCIENCES. 413
}
that is, from a germ, wherein the organical parts
of thofe ftones are contained in miniature, as
thofe of the largeſt plants are in the embryos of
their feeds.
The ftones called cornu ammonis, lapis judai-
cus, toadſtone, aftroites, ferpent's eyes, with the
Bolonian and Florentine ftones, the feveral fpecies
of pyrites, fea-muſhrooms, chryftals of the rock,
and an infinity of other ftones, fuppofe their fe-
veral feeds as much as common muſhrooms, truf-
fles, and feveral fpecies of moffes, whofe feeds
have not yet been diſcovered; how ſhould the
cornu ammonis come to be conftantly in the figure
of a ſcroll or volute, unleſs we fuppofe a feed
wherein the fame ftructure was contained in little?
Who was it that moulded it fo accurately? Where
are the moulds? So far from this, that thefe
ftones are found in the ground like common peb-
bles, notwithſtanding all the enquiry I have been
able to make in Provence, Poitou, and Norman-
dy, where theſe ftones are common enough, I
have found none of their moulds, nor any thing
like them. The ftructure of the metallic cornu
ammonis is ftill more remarkable than that of the
ftony ones; the former are likewife fpiral; but
there are fome ſpecies of them, where each fpire
confifts of feveral pieces, articulated together by
fuitures, like thofe of the fkull, as is eafily per-
ceived upon breaking them. we wor
!
1
i
The lapis judaicus is in the figure of an olive,
but flatted on the outfide, and roughened with
little grains; in breaking it always dleaves oblique-
ly, and glitters like talc to the genus whereof it
muſt be referred; fince by calcination, it becomes
plaiſtered, like the fpecies of talo, taalled lapis
Selenites: now the jews ftones, are not cortainly
moulded thus, and confequently recourfe muſt be
had to their feed.
The
414 The HISTORY and MEMOIRS of the
The toad-ftone, and thofe called ferpent's eyes,
which are naturally of a beautiful poliſh are alfo
formed by their peculiar feeds, faftened upon
rocks, which furniſh a juice proper to dilate them.
The feveral fpecies of eagle-ftones, which are
commonly in figure of an egg, and have a chore
in their cavity, like the ball of a little bell, can-
not be produced without a feed; and the fame
may be faid of the belemites, otherwife called
lapis lynfis, wherein we find radii iffuing from
the fame centre, and terminating in the circum-
ference and a baſe, ufually hollowed in form of a
cone. Such a ftructure fuppofes either feeds, or
moulds; but no moulds are found; or if they
were, who was there to break them, in order
to difengage the ftones? If we fometimes find
thefe kinds of ftones in rocks, tis by reafon the
rock happened to involve them in its growth; as
likewife befalls thofe, called fhell-rocks, whofe
genefis may be explained from the inftance of thofe
ftones, which are fometimes found in the trunks of
large trees.
The aftroites is called by Gefner lapis aftereas,
by reafon its figure always confifts of fix radii.
Thofe ftarry ftones, which are radiated like a
fifh's bones, are commonly found ſeveral of them
faftened together, in horizontal ftrata. The ftones
called entrochi, are alfo in ftrata, but their cir-
cumference is round. Some of them are jointed
together, as it were, with mortices and tenons.
The fpecies of pyrites, both oval, fpherical and
cylindrical, whofe furfaces are either polifhed, or
cut like diamonds, are penetrated by radii, which
terminate in a fpecies of axis, which pafs thro'
their centre, traverfes, them from pole to pole.
Thele pyrites, I lay, were not certainly caft in a
mould, any more than the ftones of Bologne or
Florence,
ROYAL ACADEMY of SCIENCES. 415
Florence, which commonly reprefent the fame
landſcapes, or the fame ruins of towns; and it is
not more probable, that thofe fpecies of agates,
which, from their reprefenting little thrubs, or
foliages, dendroides, arife from their peculiar
feeds. Theſe ftones are found in the earth fepa-
rate from each other.
Chryſtals of the rock may likewife probably
be produced from feeds. Thefe chryſtals are na-
turally cut in flat fides, and their figure is confe-
quently the fame in all the fame fpecies; that is,
all the pieces of the fame block of chryſtal con-
fift of 3, 4, 5, 6, or 7 faces; yet there is no room.
to fufpect either their being moulded, or formed
by any coagulation like chymical falts: for, be-
fides that we evidently fee thefe chryftals come
out of the rock, where they are faſtened variouſly
againſt the fides of caverns, with their points
turned upwards, downwards, or fide-ways. It
cannot be alledged, that the juice, which produ
ced thefe ftones, had been caft in the caverns like
diffolutions of nitre, for inftance, evaporated in
earthern pans, that of the chryſtals muſt have ne-
ceffarily paffed thro' the rock; and we cannot
fuppofe that it paffed all at once, and fixed there-
on by little and little, efpecially if we confider,
that there are pieces of chryftal, which weigh
upwards of 60 pounds, as is obferved by Hottin-
ger, in the country Valais; thofe brought from
Madagaſcar are very maffive. Father Kircher
affures us, he had met with fome which weighed
above 100 pounds; and Pliny relates, that Livia,
the wife of Auguftus, carried fome to the capitol,
which weighed above 50 pounds. If fo large a
quantity of liquor was fhed all at once, out of
the pores of rocks, 'tis evident, it would run
down every way, and form a lump of ice, in
lieu
416 The HISTORY and MEMOIRS of the
1
9
lieu of a cylindrical body, regularly hewn in
flat fides. 'Tis certain therefore, that the juice,
which contributes to the growth of the chryftal,
tranſpires by little and little through the rock
and this being fo, how can we conceive it to rife
ip tall columns, from an inch to upwards of a
foot high, without fuppofing feeds, which gra-
dually fwelling by the nutritious juice they re-
ceive from the rock, unfold and difplay the regu-
lar ſtructure which they included, perhaps, under
the furface of a point. There feems to be a good
deal of relation between the genesis of theſe chryf-
tal columns, and that of teeth; each feed, as it
fwells, may perhaps form a kind of hexagonal
trunk, whoſe infide only hardens by little and
little. This ftructure might be treated as imagi-
nary, were it not known that diamonds them-
ſelves cut more eaſily one way than another; that
marbles have their veins; and that rock-chryſtal
has its pores open enough, to imbibe the colours
which are given it; but after ſeveral enquiries
upon the figure affected by chryftals, concludes
it as natural to thofe ftones, as that of the leaves.
and flowers of plants; and he attributes both the
one and the other to an architectonical fpirit, and
a plaſtic power, how much eafier is it to fuppofe
a kind of eggs, fince every body agrees, that the
feeds of plants are as much eggs, as the parts of
birds or fishes, which, in all ages, have bore that
name? And what is an egg, if it be not the bird,
fifh, plant, or perhaps ftone in miniature? We
may therefore fuppofe, that chryſtals vegitate,
like feveral other tones; that is, begin with a
feed, or germen, and that the fame juice, which
is communicated to them by the rock, from
whence they arife, hatches and makes them grow
3
as
ROYAL ACADEMY of SCIENCES. 417
as far as their folid texture is capable of ftretch-
ing; and what can we think of thoſe found
near Allenfon and Medoc, the former whereof are
hexagonal and pyramidal, at the two ends having
a colour withal much like diamonds, and found
in fprings, while the latter are almoft oval, of
a darker colour, and found in the ground; do
not both of them fuppofe real-feeds, as much
as thoſe naturally found in the lentil form, or
which, with their lenticular figure, have a ridge
like an afs's back?
*
→
We are not to conclude that rock chrystals
are form'd as large as we find them, from there
being piles of hay, hogs briſtles, and the like matters
fometimes found in them, for befides that what
we call hogs briftles, &, may only be defects of
matter found in the feeds, 'tis poffible that thefe
feeds in the courſe of their growth, may have fallen
upon fuch bodies, and gradually inclofed them.
Ificles begin by a round hollow tubercle,
which in thofe fufpended from above downwards,
lengthens as a tube, and grows or fwells by rinds,
like the ftems of young trees; fuch as begin
from below upwards, grow likewife by rinds,
but their cavity neceffarily fills up, on account
of the fituation; the congelations themſelves be-
gin with a kind of germ or femen, and 'tis pro-
bable the generality of thefe germs remain
hollow ever after.
What we call fluores lapidum may perhaps
be referr❜d to the fame caufe, efpecially fuch
as are form'd in thofe oval or roundifh pebbles
found in the Levant, feparate from each other,
their outer furface is fmooth, and as hard as Aint,
but the infide is hollow and lin'd with chrystals
or other matters, whofe figure and colours are
wonderfully beautiful; does it not appear that
VOL. I. No. 11.
Ggg
thei
418 The HISTORY and MEMOIRS of the
+
1
their germs had been dilated by little and little,
and their parts open'd and difplay'd from each
other, by means of a juice imbib'd from the
earth.
11
..
را
4
7
That immenfe quantity of common pebbles
which covers the Craudarles, feems to confefs
the fame principal; that tract of ground, which
is upwards of feven leagues around, is fo full of
roundifh pebbles, that we find them in plenty
wherefoever we dig. M. de Peiresc, who firft
ftarted this notion of the feeds of ftones, tho'
he fhewed that term in a different ſenſe from
ours, alledges this plain as a proof of his opinion,
for how fhall we fuppofe all theſe pebbles were
form'd; it must not be pretended that they are as
old as the world, unless we maintain, that all the
ftones upon the earth were produced at the fame
time, whereas the obfervations already deliver'd
upon the vegetation of ftones, afford a proof
that there are new ones produced every day;
and the fame M. de Peireft, while he was yet
very young, made a notable remark to the
fame purpoſe; bathing one day in the Rhone,
-near the city Avignon, he perceived that the
bottom of the river was become all uneven, and
cover'd with little foftifh pebbles like hard eggs,
ftripped of their fhells; but he was ftill farther
furpriz'd, when he found fome days after, that not
only thoſe which he carried home with him, but
thofe which had remained in the Rhone, were
become as hard and folid as any other pebbles
on the edge of the river; he fuppofed that thefe
germs or young ftones had been turn'd up by an
earthquake, which was felt fome days before,
and had thrown them out of the bowels of the
earth.
!
t
}
!
To
ROYAL ACADEMY of SCIENCES. 419
To thefe
邵
​which we obfervations may be added another
}
}
*
→
4
which we made in an ifland of the Arabipelago,
called Antiparos, becaufe fituate overagainst the
famous inland Paros. From the bottom of one
of the fineſt grottos imaginable, lined all over
with beautiful congelations, arife feveral marble
pillars, the higheft whereof is upwards of fix
feet, and one foot in diameter, being pretty cy-
lindrical, and equally thick everywhere; there
are other little ones all about it like fo many
young horns, and shot far off there is half a
one remaining, which had been broke off, and
now repreſents the trunk of a felled tree; the
middle, which is a fpan broad, bonfifts of a
brownish marble, and reprefents the woody part
of the tree; this is furrounded with a blea and
bark, and even with old bleas of different co-
lours, which are diftinguiſhed by fix concen-
trical circles, two or three lines thick, whofe
fibres proceed from the centre to the circum-
ference; theſe marble trunks feem to have ve-
gitated, and perhaps ftill continue to vegitate;
for befides that there fall no drops of water
in this place, 'tis inconceivable that any fuch
drops falling 25 or 30. fathoms high, fhould
have been able to form regular cylinders, termi-
nated uniformly domewife. In the fame grotto
to the left hand we find a pyramid more fur-
prifing than any thing, it is 24 feet high in-
fulated, and made like a tiara, being adorn'd
with feveral capitals in relievo, which are fluted
lengthwife, and fuftain'd on their pedeſtals. This
pyramid, whofe bafe is 12 or 15 feet broad,
is all full of enrichments, the tops whereof are
bigger than the bottoms; and it may be obſerved
that their branches, like thofe of cabbage flowers,
ſhoot from below upwards, and terminate in
Ggg 2
large
1.
{
}
{
420 The HISTORY and MEMOIRS of the
large cluſters; 'tis next to impoffible all this
fhould be perform'd by the drop of falls of wa-
ter, where the laft would always cover the work
of the firft.
What has been faid concerning the generation
of ftones, may be extended to metals; 'tis
very probable theſe bodies are likewife propa-
gated by their feveral germs; nor will this con-
jecture be thought too daring by fuch as will ob-
ferve this natural vegetation of pure gold, which
has fhot, in manner of foliages, thro' a hard,
as it were, chryftallized ftone; there likewife
prefents you a piece of filver, which fpringing
of it felf thro' a piece of chryftal, fubdivides
into feveral threads, all of which catch upon
pieces of the fame chryftallization. Another piece
which I offer you, feems ftill more furpriſing,
being little germs of filver inclos'd in a lump
of marble; thefe germs are fhap'd like flat plates,
about the third of a line thick, radiated like
fiſhes bones. A little piece of copper which I
likewife lay before you, has fhot into branches
in the ground, as here you find it; 'tis fcarce
poffible to explain all theſe productions, by veins
of metals running in the vifcera of the earth;
nor can it be objected that theſe foliages have
no determinate figure, and are only imperfect
vegetations; let, their name be what it will, our
bufinefs here is to account for their generation,
fuppofing there were fluid metals in the ground,
they could not pafs thro' pores of chryſtallized
rocks, and thus fhoot into foliages.
1
The arbor Diana, or thofe icy branches found
on the glafs in a fudden fit of froft fucceeding a
fog, will give no affiftance towards explaining
thefe phenomena; every body knows that 'tis
with fogs much as with diftill'd waters: if a
piece
ROYAL ACADEMY of SCIENCES. 421
•
#
piece of linnen dipt in cold water be applied
on the capital of a glafs alembic, the fpiri-
Euous parts of the diftilled matters having more
motion than the reft, will be. reflected back
again, and paſs thro' them in different ways,
fo as to form tolerable ramifications; but what
imports all this to rock chryſtals, for instance,
which line the fides of a cavern as well as
the top, and are always fhaped in one uniform
manner; the inftances above do indeed fhew,
that all things which are naturally figur'd, do
not ariſe from any peculiar feeds, but this is
what we have not alledged, and how fhould
the inftance of branches on glafs be applied to
account for metallic vegetations, will any one
ſay they are form'd of vapours rifing in ca
verns? vapours would make a metallic cruft or
ftratum, inftead of leaves of gold or filver, which
have feveral inches projecture, and whoſe roots
penetrate the rock. As to the arbor Diane, all
naturalifts are agreed that it arifes either from
chryftalifations of particles of nitre, to which
metallic particles precipitated on account of the
weakness of their diffolvent faften themſelves,
or from the effects of mercury, which by the
heat it is agitated with, carries off the particles
of the metals it is amalgumated withal; our
fubject is of a quite different nature, the foli-
ages I juſt prefented to you being perfectly
folid, they are pure gold, fpringing from a
hard rock, where nothing like what paffes in the
arbor Diane can be fufpected.
1
Among the feeds of ftones and metals, there
are fome which not only foften by the juice
of the earth, but become quite liquid, and if
in this ftate they penetrate the pores of certain
bodies, they harden and petrify therein, as has
befallen
422 The HISTORY and MEMOIRS of the
1
A
1
befallen the piece of fern here prefented, as
well as thefe lobſters, which are turn'd to meer
ftones by this accident. If the ftony feeds be
lodged in the cavities of certain bodies, they
harden and affume the figure or moulding there-
of; thus what we call pectinites, conchites, mytu-
lites, oftracites, nautilites, echinites, are
are real
ftones, whofe liquid feeds had been received
into the cavities of the fhells, called pecca, con-
ca, mytulus, oftrea, nautilus, echinus, &c. whofe
figure they still bear in thefe cochlites; we fee
a piece of a fnail, and there are multitudes around
Paris, where the fhell feems as if it had been
infenfibly turn'd to duft; when the feeds of
different ftones happen to be mingled together,
they always retain their proper characters; thus
the feed of chryftal produces chryftal, and what
was intended to form ftone produces ftone, as
we may fee in this cornu ammonis, and this con-
chites, whofe cavities are all chryſtallized.
·
C
On the contrary, if thefe liquid feeds be fhed
on pebble fhells or fand, they incloſe thoſe bo-
dies by degrees, and infinuating between them,
form a kind of cement, which continues grow-
ing, notwithſtanding its hardness, like other liv-
ing ftones. 'Tis probable that thefe rocks, which
are only cluſters of pebbles cemented together,
were originally form'd by a multitude of fuch
liquid feeds like the quarries, which are full of
fhells, unless we fuppofe that the rocks had in-
clofed theſe bodies in the courfe of their growth.
音
​We also find the feeds. of real stones in the
ſpawn of certain fhell fishes, together with that
hard folid matter intended to make the covers
of thofe animals. All the fishes inclofed in fhells
either fpawn or lay eggs, but there are few of
this latter kind, and I know of none but the buc-
$
cinum,
· ROYAL ACADEMY of SCIENCES. 423
$
cinum, which is reputed oviparous; be this as it
will, the feeds both of the one and the other muft
contain the matter of the fhell, how hard and
thick foever it may afterwards become, as much
as the feed of an elephant includes all the folid
maffive bones thereof. There is a kind of fhell
called pholas, never found but in the cavities of
pebbles, which cavities are of the fize proper to
receive them; yet it is hardly conceivable that
thefe fishes fhould have come and dug their cells,
we rather fuppofe that the ftones they are inclo-
fed in were once foft, and that the kind of jelly
they began withal was found in the ſpawn, as the
matter which afterwards becomes the egg-fhell,
is found in the firft feed thereof; and certainly
the fhell of an oftrich's egg is incomparably
harder than the rocks we are fpeaking of.
After all the obfervations hitherto rehears'd,
we may fuppofe the feed of ftones and metals
to be a kind of duft, which perhaps feparates
from the ſtones and metals while they are yet
alive, that is, while they grow, as we have found
that fome of them do really grow. This feminal
duft of ftones may be compar'd to the feeds of
feveral plants, for inftance, thofe of ferns, ca-
pillaries, moffes, truffles, and the like, whofe feeds
were never yet difcoverable by a microfcope;
yet theſe feeds propagate as well as the largeft,
and pebbles may perhaps be among ftones, what
truffles are among plants. This notion is not quite
new; Pliny affures us, that Mutionus and Theo-
phrastus believ'd that stones produced other
ftones; and Gregory Nazianzen affures, that
there were ſome authors who held that flones
made love.
How many fishes are there, whofe fpawns
are at leaft as inall as grains of fand? yet
the
424 The HISTORY and MEMOIRS of the
the naturalifts allow that whole fishes are couch'd
in miniature, in the germs of theſe grains of
fand; the bufinefs here therefore is only as to
more and lefs, and who doubts but that the
author of nature, who has inclos'd the huge
fifh narwel, called the fea unicorn, which is up-
wards of 20 feet long, in the germ of an egg
a of a line big, may not have inclos'd a bank
of ftone, in a germ no bigger than a grain of
fand. Nothing fhews the grandeur of the deity
more, than this fimplicity and uniformity found
in the production of all bodies; what can be
more glorious than to fee men, fiſhes, birds,
quadrupeds, reptils, plants, ftones, and metals,
all fpring from infenfible molecules? And as
there are ftones which evidently grow by an
inward principal, depending intirely on their
particular organization, which receives and diftri-
butes the juice, furnish'd them by the common
mother of all creatures, why may we not
admit the fame principal in the other foffils?
not that we are to conceive the largeſt moun-
tains as only confifting of a fingle piece; thofe
huge maffes of rocks are ufually compofed of
a multitude of feparate blocks, which were pro-
duced by ſo many germs, or perhaps by feveral
germs, which had blended together as they grew.
Banks of ftone are commonly horizontal, and
thoſe which are vertical or oblique, 'tis probable
are only render'd fuch by fome extraordinary
fhock; we may fuppofe that it is the preffure
of she atmoſphere, which bearing equally on the
Laid of the earth, makes the growing feeds
wys fpread horizontally.
IX.
ROYAL ACADEMY of SCIENCES. 425
IX. An estimate of the power neceffary to
move boats, both in ftagnant and running
waters; either by a rope, or by oars, or
any other machine; by M. de la Hire *
Tranflated by Mr. Chambers.
The power neceffary to tow a boat in ftagnant
water by a rope faftened thereto, and pulled by
a perſon on the ſhore, is the fame as is required
merely to hold or fuftain the boat in a running
water, whofe velocity is the fame, as that where-
with the boat is towed in the ftagnant one.
This propofition is felf-evident; by reaſon the
impulfe or reſiſtance of the water againſt the boat,
is the fame in both caſes.
But it is likewiſe the fame, either to tow a boat
in a dormant, or to hold it in a current water, tho'
the power be placed in the boat itſelf, and act by
a rope faſtened to fome fixed point, fuppofing
the velocity of the water impinging on the boat,
to be equal in both cafes.
To determine the power neceffary to this ef
fect, we muſt know the furface of the boat,
which is prefented to the direction of the motion
of the water; and the velocity wherewith either
the boat is pulled, or the water runs.
What is known of the nature of water and of
motion, we here fuppofe as principles to build on :
as,
1. That heavy bodies in falling any given
height, acquire thereby a velocity, which uni-
formly continued, would carry them double the
fpace in the fame time that their accelerated
velocity has carried them.
*Nov. 22, 1702.
VOL. I. No. II.
Hhh
2.
426 The HISTORY and MEMOIRS of the
!
2. That theſe velocities are in a fubduplicate
ratio, that is, are to each other, as the fquares of
the spaces they paffed thro' in falling.
ནྡྷུ རྩ
3. Thatthe fame laws of motion obtain in fluid
bodies, as in folid ones. the root w
ť
4. That a heavy body falling with an accelera-
ted velocity, moves 14 feet in a fecond of time.
Hence we learn, that water, after falling 14
foot high, will have acquired a 'velocity thereby,
which would carry it 28 feet in a fecond of time;
and confequently that water, iffuing from the a-
perture of a tube 14 feet below the level of the
water of a reſervoir, has a velocity which will
carry it with an uniform motion, the ſpace of 28
foot in a fecond of time. Which property of wa-
ter is confirmed by all experiments.
701
}
From an experiment made in the middle of
the river Seine, and the molt rapid part thereof,
M. Mariofte found, that it ran 3 feet in a fe-
44
cond of time. From a fecond experiment, made
in the fame place, to learn the force of the wa-
ter in that velocity; by making it ftrike or puſh
againſt a thin plate 36 inches in furface, he
found the fame equivalent to a weight of 3
pound and
FORE
7
From thefe experiments together with the
principles above laid down, may feveral confe-
quences be reduced. —— For fince a heavy body
falling 14 foot in a fecond of time, acquired a
velocity thereby capable of carrying it in the fame
time, with a uniform motion, the space of 28
feet: fuppofe A D the height of a refervoir 14
feet, the water muft fpring out in D, with a ve-
locity, which uniformly continued, would carry
it 28 feet in a fecond of time. And fuppofe it were
WOSA AT THIS.
Plate XVII. Fig. 2.
enquired,
ROYAL ACADEMY of SCIENCES. 427
>
4
enquired, what height the refervoir A B muft
have, that the water in B may fuftain 3 pounds
under a furface of 36 inches, or of a foot? It
will be found, that taking 17 pounds for the
weight of a cubit foot of water, AB need only be
the height of 31 lines, or 2 inches 7 lines nearly.
The fame lines AD, and AB, being fuppofed
together with the velocity in D, fuch as above
determined; Ifay
}
rep
at live
A
1. Rule for finding the velocity of water from the
height of the refervoir
That the root of AD, is to the root of AB, as
the velocity in D to the velocity in B
or which
is the fame thing, AD is to AB, as the fquare of
the velocity in D to the fquare in the velocity in
B.
TO DHODS/
And in our inftance, we fhall have
we fhall have 14 feet, or
2016 lines, a conſtant number; or elfe 18 to 31
lines as 784, which is the fquare of 28 feet,
that the water in D is to run in a fecond, and
which will be alfo a conftant number, or even
to 12, and fomewhat more, which will alfo be
the fquare of the fpace, which the water is to
move in a ſecond in its fall from A to B.
90 A
But the fquare root of 12, is fomewhat lefs
than 31, which therefore is the way in feet that
water moving uniformly will pafs in a fecond of
time, under the given depth of AB below the le-
vel of the refervoir.
Jor
Hence we advance, that water running in wa-
ter itſelf, has the fame velocity, as if iffuing at
an aperture at a certain depth below the furface of
a refervoir, which is determinable by the ftroke
or impulfe of the water againft an oppofing body:
which is a piece of knowledge of great confe-
quence, for afcertaining the motion and impulfe
Hhh2
of
428 The HISTORY and MEMOIRS of the
of waters, which run at large, and unconfined by
any obftacle. By means hereof we may learn
the different efforts or impulfes of the water againſt
floating muſcles, and of confequence the ftrength
required to hold, e. gr. a boat in running water,
or make it proceed either in ftanding or running
water; the velocity of the water againſt the boat in
the feveral cafes being given, fuch power being
reducible to that required to fuftain a load of wa-
ter at a certain depth below a refervoir, deter-
minable by the velocity propofed.
But in examining the refiftance of the water a-
gainst a boat; in lieu of a boat we fuppofe a
plain furface perpendicular to the ftream or cur-
rent of water; which will amount to much the
fame as that irregular furface, which the boat
prefents thereto.
Suppoſe then, a furface immerged vertically
in a running water, the current whereof ſtrikes
directly against the fame, and that in the middle
thereof, a cord is faftened, whofe other extreme is
hung on a fixed point G*. Here it is evident,
the force wherewith the water impels or ftrikes
againſt the ſurface B, is the fame as that where-
with the fixed point G is pulled or drawn: by
reafon the whole refiftance of the furface B, to
the current of water is derived originally from this
fixed point, without which there would be no
refiftance at all.
To find what this power is, the furface B, as
alfo the velocity of the water, or the way it
makes in a fecond of time being given, we muſt
ule,
+ Fig. 3.
2.
ROYAL ACADEMY of SCIENCES. 429
2. Rule for finding the force of water from its
velocity.
Take the fquare of the number of feet the wa-
ter moves in a fecond of time, and divide it by
56, which is a conftant number, and obtains in
all cafes; the quotient will be the number of feet,
which the water muſt be fuppofed above the given
furface, to find the effort or impulfe thereof. For
multiplying this height by the given fürface, the
product is the cubie or folid bulk, which will be
fuftained thereby, which is the force required.
Now for every cubic foot we are to take 17
pounds; and for every cubic inch 5 drams,23%,
tho' in ordinary computations, it may fuffice to
take 5 drams, which amounts to nearly 17
pounds the foot, which number we fhall keep to
in what follows.
If the velocity be given in inches, and the ſquare
thereof be divided by 56, the quotient will be the
number of lines which the water is to be above
the propofed furface.
To demonftrate the rule, it has been already
noted, that the velocity of water iffuing at an a-
perture 14 feet below the furface of a refervoir,
is fuch as carries it 28 feet in a fecond of time,
and confequently the fquare of the velocity of 28
feet, is to the fquare of the number of feet, which
will be moved in a fecond, with the propofed ve-
locity; as the height of the refervoir, 14 feet, is
to the height required: or thus; the fquare of the
velocity of 28 feet is to the height of 14 feet,
(which is a conftant ratio in all cafes, and is
the fame as 56 to 1) as the fquare of the feet
moved with the propofed velocity, to the re-
quired height of the water, in feet. But if in
lieu of feet, you take the given velocity in inches,
the
430 The HISTORY and MEMOIRS of the
the number muſt then be divided by 56, multiplied.
by 12, to have the inches dividing only by 56,
the quotient will be but twelfths of inches, i.e. lines.
I
4
Suppoſe, for an example, a velocity of water
propofed to be fuch as carries it 6 feet in a fe-
cond of time. The fquare of 6 is 36, which di-
vided by 56, gives or ofica foot; amount-
ing to 92 lines, or 7 inches, 8 lines, for the
height of water above the propofed furface. And
the fame arifes upon fuppofing 72 inches velocity
in lieu of 6 feet.
1
'
Now, if the propofed furface be 36 inches
fquare, that number must be multiplied by the
height found, which will give a folid bulk of 277
inches, and a weight of 480 drams, or II
pound, 9 ounces of water: the quantity of the
effort or impulfe of the water againſt the furface
propoſed. 1. nowa &**
It follows hence, that if the furface, which a
boat prefents to the current of water, be one fa-
thom or 36 feet, which is 144 times more than
that of the foregoing inftance, and the velocity of
the water the fame, i, e. moves 6 feet in a fe-
cond; there be a power required 144 times
greater than the above power of 11 pound, 9
ounces, which will amount to 1665 pounds. Such
power therefore of 1665 pounds, will be required
to hold or retain a boat of the magnitude here
fuppofed, in a water that runs at the rate of 6
feet in a fecond.
If the water only make 4 feet in a ſecond,
(which may be the velocity of the Rhone, there
being no ordinary river that runs fo faft as 6 feet
in a fecond) and the boat be fuppofed to run a-
gainst the ftream at the rate of 2 feet in the fame
time; it follows, that the water will ftrike againſt
the boat with a velocity of 6 feet in a fecond; fo
that
ROYAL ACADEMY of SCIENCES. 431
that on this fuppofition a power of 1665 pounds
will be required!
conte ed the
An estimate of the strength of horses employed in
towing or drawing barges, boats, and other
bodies, either in running or standing waters.
A large barge on the river Seine, prefents about
three fathoms, or ro8 feet furface to the ftream
of water, which, taking it about the middle of
the river, may be computed to move at the rate
of 2 feet in a fecond of time; 12 horfes yoaked
플
​to fuch a veffel tow it againſt the ſtream at the
rate of 1 foot in a fecond; which amounts to
900 fathom in an hour, and 9000 fathom, or 4
leagues in to hours; the fpace of time the horſes
are able to work per day, that
1
'
Now on a fuppofition, that the ftream of water
runs 2 feet in a fecond, and that the barge rifes
플
​againſt it at the rate of 1 foot in the fame time,
the velocity of the water impinging, or ſtriking
on the barge, may be raiſed at 4 feet in a fecond;
agreeably now to the foregoing rule, the fquare of
4 feet, or 48 inches, being 23045 this divided by
56, yields 41, the height of the water in lines
amounting to 3 inches, 5 lines This height,
therefore, multiplied by the furface of the barge
108 feet, yields 26 cubic feet of water very
nearly. So that fuppofing the cubic foot of wa
ter to weigh 72 pounds, we fhall have 1896
pounds for the quantity offered, required to tow
the barge in the prefent cafe; confequently each
horſe muſt fuftain an effort of p58 pounds, on
the fuppofition of its walking one foot in a fee
Soqqot w
I bas (book) & ai
What is here fhewn of a running water will hold
equally of a ftanding water; fuppofing the barge
to be towed therein at the rate of sulfeet ind fea
cond.
-
17
2
6
Gond,
432 The HISTORY and MEMOIRS of the
cond, the velocity of the water ftriking againſt
the barge, being the fame in both cafes.
And further it will be the fame ftill, if you ſup-
poſe ſome fixed point, either in a running or
ftanding water; and that the barge being faftened
thereto by a rope, is pulled towards the fame by
a power placed in the barge itſelf. For the bufi-
nefs here, is only to overcome the refiftance of
the water ſtriking against the barge with a certain
velocity, which determines the quantity of the
power.
But of all the various ways of applying a power
to a machine, in order to pull a body by a rope,
'tis certain, there is none whereby any thing can
be gained. For if the power be finall, it will
pull the body faftened to the rope the more flow-
ly; if great, the more fwiftly, and fuppofing the
ſame power to be employed, the motion will al-
ways be in proportion to the time.
We now proceed to the motion of boats, and
other veffels rowed with oars: but by the way, it
may not be amifs to note, that all firength arifes
from fome refiftance, as may be feen in levers :
for if you pull one end of a lever kept faft by the
other end, the efort you make on the middle
parts of the lever, is derived wholly from
the refiftance of the part where the lever is fixed.
It being evident, that if this end was not fixed,
you could make no effort on the middle of the
lever, by any power applied to the other end.
In like manner, if you pull a rope, in order to
move a weight faftened thereto, you will not ftir
it in the leaſt, whatever power you employ, o-
therwife than by an effect arifing from the fixed
points were you ftand; and you exert an equal
hat fixed point towards the body,
newly towards the fixed point.
powe
as to
}
is
ppoſe
ROYAL ACADEMY of SCIENCES. 433
Suppoſe now two boats in a ſtanding water,
and let one of them have a rope faftened to
it by one of its ends, the other end being pulled
by a power placed in the other boat. Here
the power pulling the rope makes an equal
effort to puth from it the boat wherein it is,
as to pull toward it the other, to which the
rope is faſtened; fuppofing the direction of the
power to be the fame as that of the rope: In
confequence whereof, the two boats muft approach
equally to each other; and if the effort of the
power be given, as alfo the furface of the boats
immerged in water, the velocity of their appulfe
may be determined. But in regard the fame
effort is made on both boats, to pull the one and
puſh the other, the quantity of water which de-
termines or meafures fuch effort, would be the
fame for the motion of each, and confquently
the heights of water, as in the cafe of reler-
voirs, which would produce this cdot, would
be to each other, in the reciprocal ratio of the
furfaces of the boats, prefented to the motion;
but the roots of thele heights give the velocity,
and therefore the velocity of the boats would be
to each other in the reciprocal ratio of the roots
of the furfaces of the boars.
After the like manner, if the velocity of the
boats, together with the furfaces, were given, the
effort of the power that would move them might
be determined; one inftance or two will make
this propofition clear.
Suppofe two boats in a tanding water, and
let the furface of one of them be 16 feet, ard
that of the other 64: I mean only the furfaces
preſented to the motion, or which are directly
oppofite one to the other. If the boat of 16
feet furface, either puſhed or pulled, with a force
VOL. I. No. 11.
Iii
equal
A
434 The HISTORY and MEMOIRS !
of the
IN
equal to that which pufhes or pulls the other of
64 feet, the powers which pufh thofe furfaces may
be confidered as 2 folid parallel epipeds of water,
equal to each other, confequently their heights
will be reciprocally as their furfaces, whatever
the quantity of thefe folids may be. But we
have demonſtrated, that the velocities of the boats
will always be as the roots of the heights of the
folids of water, and confequently the velocity of
that of 16 feet furface, will be 8, the root of
64, and the velocity of that of 64 feet furface,
will be 4, the root of 16
Thus let what powers foever be employed to
move the boats, the velocity of the boat of 64
feet furface, being exprefs'd by 8, the other of
16 feet furface, will advance with a velocity
exprefs'd by 4, which is the ratio of 2 to 1-
Hence,
I
ned
If the boat of 64 feet furface move with a
velocity which would carry it two feet in a ſe-
cond, that of 16 feet furface will move with the
velocity of 4 feet in a ſecond.
But thefe velocities being given, the effort ne-
ceffary to make the two boats move towards a
fixed point, placed between them in the line
of their motion, may be determined by the rule
above laid down. For fuppofe the boat of 16
feet to have a velocity of 2 feet, or 24 inches in
a fecond, its fquare will be 576, which divided
by 56, gives 10, the height of the water above
the furtage of the boat in lines, which gives the
effort required for taking 72 pounds for a foot
of water, we have 82 pound very nearly for
the power required to move this boat 2 feet in
a fecond, as was fuppofed, w
"
?
But fince the velocity of this boat of 16 feet
furface, is to be to the velocity of the other boat,
as
ROYAL ACADEMY of SCIENCES. 435
} m
BIH
as two to one; the fame calculus must be made
for the other, by dividing the fquare' of one foot,
or 12 inches, by 56, and multiplying the
quo-
tient, which is the height of water in lines, by
the furface of the boat, the product gives the
fame 82 pounds, for the power required to move
this boat the space of 1 foot in a fecond. The
two boats therefore will be each moved with the
fame force of 82 pounds, by one fingle power,
and will approach each other 3 feet in a fe
cond, one of them moving 2 feet, and the other
I foot.
16/13
Ada
}
But as in the prefent example, we have only
one power of 82 pounds, which being placed
in a boat, pulls a rope to which another boat
is faftened, it follows, that this power will ga.
ther three feet of rope in a fecond, whereas with
the fame power, one of the boats being fuppos'd
immoveable, we fhould only gather the quantity
of rope answering to the motion of the other
for it is not the quantity of rope we
gather, that determines the effort to motion, as
is eafy to be obſerved; for that if there was
nothing faften'd to the rope, we fhould gather
it as fast as we pleas'd, without making any
effort at all; fuppofing the rope void of weight,
as is here done.
boat;
If any doubt remain, as to what we have faid
of the greater or leffer quantity of rope gather'd,
not having any effect towards diminiſhing or
augmenting the effort, you need only attend to
what befalls the weights * A, B, and F, two of
which A and B, are falten'd to the two ends of
a rope, which paffes over two pullies C and D,
and fuftains a third pully E, to which is hung
the weight F; for whether you raife or lower the
*
Y
Fig. 416 14 20
4-
e vipi zelo ad or 2 weight
436 The HISTORY and MEMOIRS of the
1
weight A, the weight F will have the fame effect
on the weight B, tho' F rifes or falls.
1
ตัว
!
Perhaps a clearer idea of what we have faid,
in relation to the effort of a power pulling a
-boat, may be formed by confidering it in a
machine. Imagine therefore two furfaces
* A
and B, immerged perpendicularly in a standing
water, and conceive a little pully D faften'd in
the middle of the furface B, with its plane per-
pendicular to the plane of the furface B; the axis
of the pully being laid horizontally on the fame
furface B; if now a rope be faſtened to the
middle of the furface A, and pafs horizontally
over the pully D, and afterwards fuftain a weight
E, 'tis evident this weight E will make two
efforts at the fame time, each equal to the whole
weight, one to pull the furface A, and the
other to puſh the furface B; and further, theſe
efforts will be the fame, whether one of the fur-
faces be moveable or both; with this difference,
that in the cafe of only one moveable furface,
the weight will defcend a space equal to the mo-
tion of fuch furface; whereas, if both be move-
sable, it will defcend a ſpace equal to the mo-
tion of both together-For we here overlook
that little acceleration the weight will have at
the beginning of its defcent; fince it can only
odefcend fo far as the furfaces moves along the
whter. Befides, in the prefent compariſon of a
weight to a power, the acceleration of the weight
bras not concern'd, by reaſon the power to which
the weight is compar'd, has no acceleration; and
for the like reafons we difregard the friction of
to the pully on its axis, and the refiftance arifing
from the fliffness of the rope.
r
*
Fig. 5.
1
Hence
X
ROYAL ACADEMY of SCIENCES. 437
Hence we learn that whatever yelocity a fall-
ing weight may have action depending on its
weight, will have the fame effect on both fur-
faces, and either puth or puſh them alike fince
it cannot act on one of them to pull without act-
ing at the fame time on the other to puſh it.
Y
And the cafe would be the fame, if a power
ſupported on any fultrum, or fixed body, were
to lift perpendicularly a weight faftened thereto,
for whether the power only fuflained the weight,
or whether it raided fowly or quickly the ful-
crum would have the load of this weight, befides
that of the powerbSuppofing the medium, where-
in the weight is ruifed, makes no refiftance.
1
{
}
This fort of niechanifm is quite different from
that of bedies faftened to the arm of a lever,
where the weight of the body and the space it is
able to paſs thro',, being multiplied by each other,
yield a quantity of motion to be confidered in
order to find the reciprocal effort of thofe bodies,
and deduce the balance thereof. But here we are
confidering bodies in an uniform and continued
motion, without any effort of percuffion.
There are alfo different kinds of motions to be
confidered in bodies immerged in water: as if a
furface* A be immerged perpendicularly in wa-
ter, and to the middle thereof Ba rope be faftened,
which paffing over the pully P, is turned back to
D, where a power is applied. Here it is evident,
that the power pulling the rope in D, and in fo
doing pufhing the furface A, exerts the fame
force to push the furface towards P, as to pull it
towards P, and confequently the furface A is im-
pelled towards P, with a force double to that of
the power.
Fig. 6.
L
2
1
1
Note
438 The HISTORY and MEMOIRS of the
A24 36
Note alfo, that in this difpofition of machines
a weight might be applied in lieu of a power, by
fitting a little pulley in the furface A, and paffing a
rope over the fame to which a weight is faſtened.
?
Hence appears the great advantage of this me-
thod of application, fince in virtue hereof one and
the fame power placed in the boat has an effect
double of what it would have in walking on the
ground, and thus pulling the boat or even of
what it would have, tho placed in the 'boat, but
fo as to pull a rope faftened to axed point, in
order to make the veffel advance thereto.
་་སྙ
Indeed this power, which is only of the other,
muſt move double the fpace of that other in the
fame time: but fuch excefs of the ſpace of the
power is not to be confidered as an augmentation
of force, as has been already obferved.
iL
We fee alfo, that this way of applying a power,
by a returning pully, amounts to the fame, as the
2, boats made to approach one another; tho' in
that cafe, the power is applied to 2 furfaces, and
in this only to one; for which reafon, if the fingle
furface be lefs than the 2 others together, either a
lefs power will fuffice to give the fame velocity, or
the fame power will fuffice to give a greater velocity.
The following experiments confirm what we
have advanced concerning the augmentation of
the power, by means of returning the pully; feat-
ing myſelf on a fort of fledge, in a place paved
with ſmooth ſtones, I fixed a rope on a wall 5 or
6 fathoms from me, and about the fame height
with myfelf, fo that the rope was horizontal; in
this difpofition I pulled the end of the rope to
draw myſelf, towards the fixed point; but all my
ftrength was Tcarce able to make me advance.
Upon this a pullly was fixed in the place of the
fixed point, over which I paffed the rope, then
faften
1
ROYAL ACADEMY of SCIENCES. 439
faftening one of its ends to the fledge, and pull-
ing by the other, I found no difficulty in draw-
ing myſelf, along -- for it is evident, from what
has already been faid, that only half the force im-
ployed in the former cafe, was required here.
}
But the great friction of the fledge upon the
pavement, induced me to make another more
fimple experiment, to the fame purpoſe.—Faſten-
ing a rope to a high place, I endeavoured to
clamber up the fame by ftrength of arms: but
finding myfelf too weak thus to raife my whole
body on one arm, by holding with one hand,
and taking higher hold of the rope with the o-
ther, I faftened, a pully in the place, where the
rope was faftened before; andpafling the rope over
this pully, made a fort of ring with one end thereof,
where putting my foot, and pulling the other end
of the rope, I drew myfelf on high with a deak
of eafe.
いい
​سیدیم
Here it is obvious, that in fuftaining the body
by fuch rope and pully, the arms only make half
the effort which they muft to fuftain the body by
a rope only. For the pully in fuch cafe, has the
effect of the fulcrum of a balance, at the extremes
of whofe arms the whole weight of the body is
fuftained, but fo as to be diftributed equally on
bath fides, in which ſtate of equilibrium the ef
fort of the arms need only be half the weight of
the body; fo that the finalleft effort more, e.gr. a
pound, will discharge, the other half of fo much,
upon which the arms will furmount the weight
of the body by two pounds, fo that gathering
the rope at the fame time, the body will enfily
be hoisted up the pulley. Hereto we overlook
the friction of the axis of the pully, and the
ther difficulties, which may arife on the part of
the rope.
IT
e-
As
440 The HISTORY and MEMOIRS of the
As the velocity wherewith the body is raifed,
it depends on that of the arms in gathering the
rope; nor need there any augmentation of power
on that account, fince the refiftance of the medium
is not increaſed thereby. Indeed if the experi-
ment be made in the water, and the power be
placed for inftance in a boat, where it pulls a
rope; which paffing over a pulley, has its other
end faftened to another boat. Here, fuppofing
the two boats equal, the power muſt be twice as
great, as would be required, if the rope was faf-
tened to the fame boat where the power is; by
reafon the refiftance of the water againſt the two
boats is double of what is againſt one, which does
not hold in air, the refiftance whereof to any mo-
derately flow motion is too inconfiderable to be
regarded. Befides, that this fame refiftance of
the water requires an effort proportional to the
velocity of the motion.
But theſe two motions may be diverfified, and
confidered in other manners. Suppofe a boat
in a ſtanding water pulled by two oppofite powers,
applied to two ropes in the fame right line, 'tis
evident, that if the powers be equal, the boats
will remain immovable. If one exceed the other,
the boat will approach towards the fame, and
fuppofing the two powers given, the way or ſpace
it will pass over may be determined. For feek-
ing by the above rule, that two velocities belong-
ing to the 2 powers, the difference thereof will be
the velocity wherewith the boat approaches the
greater power, and confequently gives the quan-
tity of rope this power gathers, and the other
lofes.
What has been faid of boats drawn by ropes,
holds equally of boats, if the fame be pushed, or
**
fhoved
ROYAL ACADEMY of SCIENCES. 441
fhoved directly by oppofite powers, whether
they be equal or unequal.
It remains to fhew the application of this doc-
trine to the operation of rowing, i. e. the motion
of boats, &c. by means of oars.-'Tis not eafy to
frame a fimple machine, which fhall fhew the
furface a boat prefents to the motion of the water,
and fit oars therein, whofe fulcrum, or point of fup-
port, called by mariners the filling, fhall be in the
middle of this furface: but it is more difficult ftill,
to apply the moving power to the end of fuch
oars, and contrive that this fame power, i. e. the
rowers, fhall be fuftained precifely on the mid-
dle of this furface. However, as the length of
the boat only bears a fmall proportion to the fur-
face it oppoſes to the motion of the water; it
will make no great difference, tho' the oars be
refted on the edge of the boat, inſtead of the mid-
dle of the furface, which is the true point of fup-
port, or even tho' the power, which pulls the end
of the oars, do not act in a direction perpendicular
to the oar, and to the furface at the fame time.
For as to the direction of the power, there can
only arife hence a fmall diminution of the force
that acts on the one and the other, fince it is to be
confidered withal that thefe directions are conti-
nually changing.
To bring the matter to an eafy calculus, with-
out entering into a long and intricate difcuffion;
fuppofe* A the furface, which the boat prefents
to the motion, whofe length we have no regard to,
in as much as this makes no effort againſt the
motion of the water. To the middle of this fur-
face is faftened perpendicularly a fulcrum, or fill-
ing A B, upon whofe extreme B, the oar DC
Fig. 7.
Vol. I. No. 12.
K kk
bears,
442 The HISTORY and MEMOIRS of the
**
bears, whoſe broad end or blade, is reprefented
by the furface C. Lafiy the power is fuppofed
in D, pulling perpendicularly that end of the
fbank of the oar, and bearing alfo perpendicularly
against the power A of the furface A. Here then
it is evident, that the power pulling the end D of
the oar towards G, and bearing against the fur-
face in A, will bring the blade C towards F. But
the abfolute power wherewith this is done, muft
Be, reduced to a relative one, according to the
Tength of the arms BD, BC, of the oar confidered
as a lever for BC will always be to BD, as the
abfolute power to the relative power applied in C,
to push towards F. But the fulcrum itſelf B, or
the furface A, is alfo impelled towards G, with a
force, which is the fum of the abfolute and rela-
tive powers added together: and, on the con-
trary, the fame furface A, being puſhed by the
abfolute power towards B or F, the equal and op-
pofite efforts deftroying each other, nothing re-
mains of the effort wherewith the furface A is im-
pelled towards G, but that of the relative power,
which is the fame as that wherewith the furface C
is impelled towards F; fo that theſe two efforts
will be equal in all cafes.
象
​*>
Now to determine the velocity of the motion.
of thofe furfaces, the power being given, or elfe
the velocities and the way being given to deter-
mine the power: we fhall make a calculus ac-
cording to the preceding rules.
}
Suppofe, for example, the furface A be 80
feet, and the power be 1oco pounds; i. e. able
to futain a weight of 1000 pounds, dividing
1000 by 80, the quotient 12 will be the weight
belonging to each foot of the furface and fuppofe
72 pounds, the weight of a foot high of water
15000
under
ROYAL ACADEMY of SCIENCES. 443
PIL
+
110
201
YLO
under a foot furface, i. e. a cubic foot of water,
as 72 lb. are to 12 lb. fo is I foot, or 144
lines height of water under a foot furface to 2.5
lines height of water, under the fame furface. I
fay therefore by the firft rule, as 2016 lines, a
conftant or given number in all cafes (or elfe as
18 lines) to 25 fines height of water; ſo is 784
a conſtant number for elſe 7) to 94, whoſe ſquare
root is fomewhat above 3 feet, the velocity ar
way the boat will make in a fecond of time. But
now if the furface C be triple the furface A, 2. e.
be 240 feet; we fhall find, fuppofing the fame
power of 1000 lb. acting against the fame fur-
face a quantity of water 416.
Therefore as 72 lb. are to 46 lb.
height of water, under a furface
8 lines and fomewhat more height of water;
which is a third part of the height found for the
other furface. For the power being the fame,
the heights of water muft be reciprocally as the
furfaces; and this furface is fuppofed triple of the
other.
for each foot.
foare
fo are 144 lines
of one foot, to
Now by the rule, as 2016 lines a conftant num-
ber (or even 18) is to 8 lines, fo are 784 a
conftant number (or even 7) to 3 nearly; whofe
fquare root is 1 foot nearly, which is the ve-
locity or way the oar C will make in a fecond,
by the effect of the power.
But we have found, that the fame power which
is always the relative, with regard to the abfolute
power, impells both the boat and oar, and throws
them both off with regard to a fixed point, found
betweeen the two; viz. the boat at the rate of 3
feet in a fecond of time, and the oar i foot in the
fame time. It follows therefore, that the boat
and oar will recede from each other the face of
K kk 2
3
4
444 The HISTORY and MEMOIRS of the
+
F
;
4 feet in a fecond of time, being the fum of the
ways of the boat and oar: but if the velocity or
way of the boat, a determinate in time, be given
with regard to a fixed point, the power required
thereto, will be found by the fecond rule: fup-
pofe, e. gr. the way to be go fathoms in a minute,
and that the furface of the boat, which it prefents
to the motion, be 4 feet, the boat then will go 3
feet in a fecond; fo that by the fecond rule, the
ſquare of 3 feet or 36 inches, which is 1296,
being divided by 56, a given number, gives 234,
the lines in the height of water to be fuppofed
over the furface of 4 feet. But an inch high of
water upon a furface of one foot, weighs at the
rate of 72 lb. the cubic foot; the 23 lines there-
fore will yield 11 lb. 15 ounces nearly, which
multiplied by 4, the feet in the furface of the
boat yield 47 lb. for the effort of the power,
which would make the boat advance, as if it fuf-
tained fuch weight.
;
1
But it mulb be obſerved, that this effort is only
that of the relative power; and that the abfolute
power may be greater or lefs, according to the
different lengths of the arm of the oar; fo that
the relative power must be reduced to the abfo-
lute one, by faying, as the length of the arm of
the oar, from the point of fupport to the hand, is
to the length of the other arm, from the fame
point of ſupport to the middle of that part of the
blade of the oar which enters the water; fo is the
power found by the calculus to the abfolute power.
An application of the above rules to the motion of
in boats crolling the Seine, and other rivers.
Here we have no regard to the current of wa-
ter, but confine ourſelves to the confideration of
the
4
ROYAL ACADEMY of SCIENCES. 445
the way the boat makes directly a-crofs, tho' it
be all the while driven downwards by, the ftream.
And we fuppofe withal, that no part of the ef-
fort made by the rowers, is employed againſt the
current of water. Now a waterman will row a
boat about 20 fathoms or 120 feet in a minute of
time, the furface fuch boat prefents to the mo-
tion of the water is about 3 feet; and the furface
of the 2 oars immerged in the water, may be a-
bout 7 feet. Laftly, the diſtance from the point
of fupport to the rower's hand, is nearly the fame
as that from the middle of the oar immerged in
the water, to the fame point of fupport fo that
in this caſe the relative power is equal to the ab-
folute one.
{
By the velocity of the boat here fuppofed, we
have 2 feet or 24 inches for each fecond of time;
and by the rule, the fquare of thefe 24 inches is
576, which divided by 56, a ftanding number,
gives 10 lines for the height of water over the
furface propoſed an effort not very confiderable,
fince a man, by means of a fimple pully, will
eafily raiſe 15 or 16 lb. weight the ſpace of 2 feet
1
in a ſecond of time. As to the motion of the
hand, it muſt be twice as much with the fame
power, viz. 4 feet in a fecond, for that the blade
of the oar recedes from the fixed point, as far as
the boat itſelf, but ina contrary direction.
'
We have no regard here to the interruptions in
the motion of the rewer; for if he only works
half the time, he will be enabled to make double
the effort in that half, by refting the other; ef-
pecially in the prefent fituation, for remaining in
the fame place,is arm only makes half the ef-
fort that would be required, were he to tow a boat.
on the edge of the water; befide the further fa-
tigue
446 The HISTORY and MEMOIRS of the
1
tigue of walking, and fupporting of the weight
of his body.
V
OX
Another application to the motion of gallies.
£
F
{
The furface a galley prefents to the motion of
the water, is 80 feet, and it has 26 oars on each
fide, or 52 in all; each oar being 36 feet long,
and the blade 9 inches broad. There is ufually
4 feet and in the water, and the diftance from the
fulcrum of the oar to the hand, is only a third of
that from the fulcrum to the middle of the part of
the blade which dips in the water: fo that the
furface of that part of the oar, which in the wa-
ter is 3 feet, and this furface in all the oars
together 175 feet. Now a galley with 3 men
to each oar, ufually makes 2800 fathoms in an
hour, and confequently 46 fathom, 4 feet, or 280
feet, in a minute: or laftly, 4 feet, 8 inches, or
56 inches, in a fecond.
Now it is required
to find the power which the rowers exert in order
hereto.
}
By the fecond rule, we take the fquare of 56
inches, viz. 3136, which divided by 56, a
ſtanding number, gives 56 lines for the height of
water over the 80 feet furface propofed, confe-
quently multiplying 56 by 80, we have 4480
lines height of water on a foot furface, which di
vided by 144 lines for a foot height, give 31 feet,
1 inch, 4 lines, for the whole load or refiftance,
which being reduced to weight, at the rate of
72 pound the cubic foot, yields 2240 lb. for the
effort of the relative power of the rowers, which
acts equally on the blade of the oars, and the
ledge of the galley. Now dividing this weight
among 156 rowers, there only will be 14 lb.
1
for
ROYAL ACADEMY of SCIENCES. 447
for the relative power of each, reducing therefore
the relative power, by faying as 1 is to 2, which is
the ratio of that part of the oar between the fulcrum
and the hand, to the part from the fame fulcrum
to the middle of that part plunged in the water;
fo is the relative power 14. to the abfolute
28 16.2/
3
3
Ocenia
1
Farther, each rower making fuch effort. of
28 lb. in a fecond, needed only pufh the extre-
mity of the oar with his hand the ſpace of 2 feet,
4 inches, provided the fhank of the oar reſted on
a fixed point, by reafon the way of the oar is to
the way of the hand, as the diftances of the ful-
crum, which are 2 to 1. But in regard the oar
does likewife recede from the fame fixed point,
between the galley and the oar, with regard to
which the way of the hand has been found to be
2 feet, 4 inches, we muft alfo determine, what way.
the fhank of the oar makes in a fecond. It has been
already found, that the power acting againſt the
furface of a galley of 80 feet, is 2240 lb. and 'tis
this fame power which acts againſt all the oars,
which are 175 feet in furface. The height of
water therefore
theſe oars,
upon
will be reciprocal
of that on the furface on the galley, which we
have found to be 56 lines. Confequently we may
fay, as 175 feet is to 80 feet, fo are 56 lines
플
​to 25 lines nearly, which muſt be the height of
플
​water on the furface of all the oars, or each there-
of; wherefore by the firſt rule, as 2016 lines, a
given number, are to 25 lines height of water;
fo are 784, agiven number, to 10 nearly, whofe
fquare root is 3 feet, or 38 inches, which the
oars must make in a fecond, at the fame time
that the body of the galley advances 56 inches
But
448 The HISTORY and MEMOIRS of the
3
But on account of the different lengths of the arms
of the oar," which are as 2 to 1, the hand need only
make 1 inches, or 1 foot, 7 inches in a fecond,
with regard to, the motion of the oar, and, con-
fequently the rower's hand, which makes 2 feet,
4 inches in a fecond, with regard to the motion
of the galley, will make in all 3 feet, 1 inches in
each fecond of time, with the fame force of
28.16.3.
}
This effort and motion have nothing in them
extraordinary; and as in the common practice of
oars, the labour is interrupted, it will be eafy
to make up for the time loftshereby by pulling,
when the ftroke returns with fo much the more
vigour.
Twill now be eafy to determine the power re-
quired to row a veffel up a river, and what will
be the velocity thereof with any power affigned
for, if both the power and the time be given, there
needs only to find, as already taught, the way it
muſt make in a ſtanding water, and deduct from
this the way or drift of the ftream, the remainder
will be the way the boat makes up the river in the
given time; provided the motion of the boat
confidered as in a ftanding water, be greater than
that of the water; for if it be lefs, is evident the
boat will drive notwithstanding the rowers.
4
If the way be given which a veffel is to be
rowed in a given timesup a river, whoſe motion
or velocity is alfa given, thofe two motions muft
be joined togethers; and it made found by the
preceding rates, wash-powers.is that will fuf-
tain thein, actie on the surface of the boat pre-
fested to the notion ofthe water, which fame
power aftings alle against the oars, must be rec-
koned for in theinction of the arm or hand of
the
?
ROYAL ACADEMY of SCIENCES. 449
the rower, as was before done in gallies. For an in-
ſtance, if a river runs 3 feet in a fecond of time,
and you would have the veffel likewiſe afcend 4
feet in the fame time againſt the ftream, here will
be a velocity given of 7 feet in a fecond, which
muſt be confidered, in order to make the calculus
as in ftanding water.
As to any machines that may be uſed to this
end, we know in the general, that they are of no
other advantage but to take the benefit of natural
powers, as the motion of water and wind by
ufing fails, &c. and that by their means we can
fave time by uſing a greater power, or improve
a little power, fo as to produce a great effect.
But in the motion of boats and gallies, by means
of oars, it is eaſy to fee, that no great motion
can ever be produced by a weak power; for if
the machine increaſe the effort, it will take up
the more time, fuppofing the time and the way
to be always in the fame ratio. But the cafe is
otherwife in animals, which pull or thrust in
walking or moving; for it is an hypotheſis of
fome mechanicks, whereby they would prove,
that a man, who can lift 100 lb. 10 feet high in a
minute, might lift a weight of 1 lb. 1000 feet
high in the fame time; tho' this be really impoffi-
ble, fince a man can only move a certain fpace in
a given time, even without any additional weight
at all.
From the whole, we may learn what is to be
expected from the generality of engineers, who can
undertake to bring boats up any very rapid rivers,
by the uſe of fome machine, whofe effects they are
not always over well acquainted withal, imagining
the force of their genius, without ftudy, fufficient
to enable them to determine the effort neceffary to
VOL. I. No. 12.
L11
furmount
450 The HISTORY and MEMOIRS of the
furmount their refiftance of fluid bodies, either in
a state of reſt, or moved by fome machine, which
is a mechaniſm of a higher kind, and a more dif-
ficult confideration than that of folids, where the
equilibrium is all that is ufually to be confi-
dered!
#
ROYAL ACADEMY of SCIENCES. 451
esrbod biuß to concilier mol
An EXPLANATION of the TERMS
of ART fed in this Volume.
H
on vilay an id lin
**
AVING fet down the weights and mea-
fures among the terms of art, with the pro-
portion of them to thofe ufed in England, I fhall
take this opportunity of informing the reader,
that all the weights and meafures, which are
mentioned in this tranflation, are to be underſtood
of thoſe uſed at Paris. I did not think it con-
venient to reduce them, in the body of the work,
to the English ftandard; becauſe it would have
continually occafioned the ufe of a great number
of fractions, which would have made the reading
troubleſome. Thofe, who have curiofity enough
to defire an exactneſs in theſe particulars, may
eafily reduce them by the proportions here fet
down. In papers, where no very great exactneſs
was required, I have tranflated pinte a quart, and
chopine a pint ; but where exactneſs was required,
I have preſerved the French words, pinte and
chopine.
A
Adjutage, of a fountain, is a tube fitted to the
mouth of the veffel, through which the water is
to be played, and determined to any figure.
Aorta, the great artery, from which all the
reft rife.
Apex of the heart, the lower point which is
turned a little toward the left fide.
Apophyfis, an eminence or protuberance.
Arbor the principal part of a machine, which
ferves to fuftain the reft; alfo a fpindle or axis
upon which a machine turns.
Afpera arteria, the wind pipe.
L112
Au-
452 The HISTORY and MEMOIRS of the
Auricles, the two appendages of the heart.
Axillary veins and arteries are thofe which paſs
under the arm-pits.
B
20 Basis of the heart, the upper and broader point
of it. Sys flowers didwadin sul
the broad thin part, with
Blade of an oar is
which they ſtrike the water.
Bronchial the little tubes, into which the tra-
chea is branched. -
and end
Cook d
Carotids, two arteries, one on each fide of the
neck, which convey the blood from the aorta to
the brain. un 10
7
-Chopine, half a Paris pinte SAL
* Chryfalis, called alfo aurelia and nympha, is
that ſtate of an infect between a worm and a fly,
in which it lies incloſed in a hufk, as if it was
dead toda
to 31sed s
Celiac artery, the firft artery, which is fent
from the defcending trunk of the aorta into the
abdomen. The caliac vein is that which runs
through the inteftinum rectum.
A
Coronary. The coronary veffels are the arteries
and veins, which furround the heart, to nouriſh
and fupply it with blood. The coronary arte-
ries carry the blood into the furface of the heart.
The coronary vein returns the blood into the vena
'tava.
voleno 30
1...ndion
31
cent Culmpel have hade ufe of this word, to ex-
Cranium the ſkull
prefs the fall of any
called in Latin culmus.
fort of corn or grafs it is
D
426 & 20%
It con-
Dram, the 8th part of a Paris ounce.
tains 72 of their grains,, or 59 grains troy.
The
ROYAL ACADEMY of SCIENCES. 453
The dram is divided into
into 24 grains
deniers; the denier
the grain into 24 carats.
E
Eye-glafs of a telescope is the glafs placed at
that end of the tube, which is neareft the eye.
F
Foot, a meaſure containing 12 inches, or 144
lines. The Paris foot, or pied de roy, is longer
than the English foot, which contains but 11 in-
ches, 4 lines The Rhinland, Rhonife, or
Leyden foot is to the Paris foot, as 1390 to 1440.
The ancient geographical foot and the modern
Roman foot, are to the Paris foot, as 110, 12.
The Bolonian foot is to the Paris foot, as por to
600.
a haarmul d” sim na to steff wi
Foramen ovale, an oval aperture, or pallage.
through the heart of a fetus, which cloſes up
fometime after the birth.
In ad
Fulcrum, the prop or point of support hoftia
lever.
Ginglymus is that
3
771
7
n
wilea sďT ramcádo
das Gangifsing sdi dzwords
kind of articulation, where
each bone mutually receives therathem There
are three forts of it: When the bones receive
each other reciprocally, after the rhanner of a
hinge, as at the elbow. 2. When one bone re-
ceives another at one of its extremities, and is re-
ceived into another at the other extremity, as the
vertebræ do. 3. When one bone is received into
another, after the manner of a wheel, or axle of a
wheel in a box ; as the fecond vertebra of the neck
in the firſt.
£2
3
Is suta
G
Inch, the twelfth part of a footio It contains
1 parts of an English foot, and therefore is
3
454 The HISTORY and MEMOIRS of the
a little more than 6 fuch parts longer than the
English inch.
1
L
Lamella, a little thin lamina, or plate, fuch as
a fcale of a fifh; it is often ufed for a fubdivi-
fion of laminaan patag des ad
Lamina, a thin plate. 201L19
Line, the twelfth part of an inch,
Lunule, little crefcents, or half-moons.
h
M
Maxilla, the jaws, cow d
Mediastinum, a double membrane, which di-
vides the thorax and lungs into two parts.
Mefenteric; the arteries are fo called, which
arife from the aorta, and proceed to the mefen-
tery; and the veins, which proceed from the me-
fentery.
Q
Object-glass of a teleſcope, is the glafs placed at
that end of the tube, which is neareft to the ob-
ject.
J
1
Ounce, the fixteenth part of a pound. It con-
tains 576 Peris grains, or 476 grains troy. It
is equal to 19 penny-weight, and 20 grains troy.
Р
Pericardium, the membrane, which inclofes
the heart.
{
Peritoneum, a thin foft membrane, which co-
vers and contains all the bowels in the lower belly.
Pinte, the Paris pinte contains two of their
pounds of water, that is, 15,232 grains troy,
or 2 pounds, 2 ounces, and 13 grains aver-
dupois therefore the Paris pinte is larger
than our quart, which is fuppofed to contain 2
pounds averdupois of water.
Piſton
ROYAL ACADEMY of SCIENCES, 455
Pifton the fucker of a pump; fyringe, or fuch
like machine.
Pivot, a foot of metal, whereby a body intend-
ed to turn round bears upon another which is
fixed.
ol butu ah..
Pound; the Paris pound contains 16 of their
ounces, or 9216 grains. It is equal to 15 ounces,
17 penny weight and 8 grains troy.
R
Retina, the innermoft coat of the eye, ſo cal-
led becauſe it is woven like a net.
Rundle, that part of a pulley, which is like a
wheel.
S
f
Sigmoidal valves, fo called from their refem-
bling the Greek letter figma, which was anciently
written like our C.
T
Thorax, the capacity of the breaft, or cheft,
containing the heart and lungs.ht
h
I
Toife, a meaſure containing 6 Paris feet, or
6 English feet, and to parts. Mr. Chambers
tranflates it fatkom, which is a meaſure of 6 Eng-
lifh feet.
Trachea, the wind-pipe.
V
t.
Vene cave, the veins which carry the blood
into the heart.
Vena porta, the vein which carries the blood
into the liver.
Ventricles of the heart, the two great cavities.
of it; the tortoife is faid to have three.
Vertebra, the bones of the hinder part of the
neck, and of the back, commonly called the
ſpine or chine.
Z
456 The HISTORY and MEMOIRS, &c.
:
Z
Zymoftmeter, an inftrument propoſed by Swam-
merdam, to meaſure the degree of fermentation
cauſed by the mixture of fubftances, and what
heat they acquire by fermentation, and the degree
of heat or temperament of the blood of ani-
mals.
"
{
}
A
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Triangulum AES, Leida, Haga, Gouda
AE 4103.8
AES, 979 11 ASE, 32? 25! FAS, 50° 23
Triangulum ESR Leida Gouda Dordracum
RES 25 49
ES 5897.8.
ERS 25,49'
Triangulum EAR, Leida Haga Dordracim
AE 4103 3
FAR 85" 51 AFR 71.31.
AR,1002. 7 ER 10634.7
AE 4103 3
Triangulum AEF Haga Leida Roterodamum
Ex observatis angulus EAF 39°53′
et angulus AEF
Unde reliquus AFE
AF
et FE
53 40
8627
5616 8
6972 3
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Fig.5.
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SEF 43936
ESF 8090'
FF 4883
Fig. 2.
F
H
A
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B
B
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曰​:
1000
20
30
A Scale of 7200 Rhiland perches
Alemaer
Fig.6.
p. 392.
Haerlem
Amfterdam
Leyden
the Hague
Goude
Rotterdam
1000 20 30 40
100 110 120 130
A Scale of 13000 Toises
50
Go
70
Willemstadt
T
R
Utrecht
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Dort
Breda
1
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IS
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}
A
GENERAL INDEX
A
A
OF THE
CONTENTS
OF THE
FIRST VOLUM E.
A
Dder-bolts, obfervations on them
pag:
A Æther, the proportion of its weight to that of the
atmosphere
38
Air, the rarefaction of it by the heat of boiling water 69
the effects of its elafticity in gunpowder and thunder
313
--the means of knowing the temperature of it in all the
climates of the carth
-- a rule for its equilibrium
353
370
Alkmaer, the distance of it from
Bergen op Zoom
386
Leyden
380
Rotterdam
the Hague
Allum, how made
Amber, yellow
1
Amphitheatre at Douvay
Ants in Surinam
Aphroditic promontory
Apulia, tarantulas common in that country
VOL. I. Nº. 12.
M in in
391
ibid.
326
186
409
35%
377
377
Arbor
IN DEX.
ག་
Arbor Dianæ, how formed
Armenia, the pofition of fome towns in it
Aftroites defcribed
Suppoſed to fpring from faed
Auderville, a body of fire feen there
5
૧૩એ
B
་ ཏྭཱ
pag.
421
21, 25
414
413
185
Barometer obferved
how rendered luminous
k
Belemnites fuppofed to fpring from feed
11, 204, 272, 351
208, 262, 272
Bergen op Zoom, the distance of it from Alkmaer
Birth of four children at once
Bite of the tarantula, its fymptoms and cure
Bladder of a mare, a fione found in it
Blood, the circulation of it in fuch fishes as have gills
414
386
325
321
187
294
Boats, the power neceffary to move them
425
Bolonia, the distance between it and Modena
375
Bolonian ſtones, ſuppoſed to ſpring from fecd
413
Bombs, a general method of throwing them
237
Brazil, a strange fort of ferpent there
Breft, the tides there
Bretagne, the tides there-
Burning-glaffes of 3 or 4 feet in diameter
how to be placed.
their effects
235
325
ibid.
25
ibid.
26, 396
$
}
C
( 、,
Candy, a deſcription of the labyrinth there
Cannon, why it recoils
Canton, its pofition
}
Cap Creux, the aphroditic promontory
Cats, why they fall upon their feet
Centres of converfion
Chamois found on the inacceffible mountain
Chanfeaux (le) famous for finkings of the earth
Cherbourg, a body of fire feen there \\
Cheefe-mite microſcopically obferved,
China, the pofition of fame of its towns
406
315
23
377
200
191
181
15
328
186
21, 22
China,
INDEXI
China, the tygers in that country
Circulation of the blood in fuch fifbes as
Civita Vecchia, allum made there
Clocks, remarks on the construction
pag.
teland.cl20
have gills 294
Retrolul cone 326
of their pendulums
thun 5,,alia19221
Cobra de los cabeças, a ſerpent in Brazil
Colours, reflections on them
Column of light obferved
235
32
395
Conoids, a method of turning them
96336
Coral, a real ftone
412
Cords, their ftiffness confidered
121
Cornu ammonis, fuppofed to spring from feed
10 197413
Corfica, tarantulas found there
321
Cryſtals of the rock defcribed
Cows, obfervations on their ovaries
1
fuppofed to fpring from feed
Cylinders hollow and folid, their resistance
287
10415
413, 415
344
عاكم
D.
r
4
Damps in a well, the fatal effects of them
253
Dauphiny, the natural hiſtory of it
14, 181
Declination of the needle obferved
·207, 272, 352
at Lisbon
232
at Paraiba
233
a general theory of it.
245
Delta, or lower Egypt, the map of it corrected
330
Dendroides, fuppofed to Spring from feed
415
Dialling, an improvement in that art
}
Douvay in France, the amphitheatre there
Dragon-flies, obfervations on them
254
409
94
E.
"
Eagle-ftone
deſcribed
+
411
414
fuppofed to fpring from feed
Echinites, how formed
Egypt, the map of that country, rectified
the miafure of the pyramids
ibid.
422
330
tabloy al
378
Mmm 2
Ela-
INDE X.
pag.
Elafticity of the air, its effects in gunpowder and thunder
313
Entrochi, fuppofed to ſpring from feed
414
Eruan, its pofition
25
Erzeron, its pofition
ibid.
J
F.:
Fall of bodies, a machine to prove the proportion of it
Feathers of birds
Fire common, what it is
of the fun, what it is
the generation of it.
its ufe in moving machines
the engine defcribed
a body of fire feen in Normandy.
Fishes, the structure of their heart
the circulation of the blood in them
30, 347
17
401
402
43
69
82
185
150
294
Flanders, the fituation of ſome of the towns of that coun-
386
try
47
413
417
قم
14
Flood-gate, a new fort
Florentine-ftones, fuppofed to ſpring from feed
Fluores lapidum, how formed
Fountain burning
France, obfervations on the fingularities of the natural hi-
the distances between the ancient towns
Story of that country
Friction in machines confider'd
Frog, the structure of its heart
the trembling of its nerves after death
G.
S. Germain des Vaux, a body of fire feen there
Gills of fishes, the use of them
•
their structure
to
1
14, 181
374
112, 193
145
187
185
152, 295
152
52
Glaffes, fome Angular effects, which happen to them
hyperbolical, the manner of cutting moulds for
them
teleſcope-glaffes
333
91, 188
Gold
INDEX.
Gold render'd volatile by the burning-glafs
Goude, the diſtance of it from Leyden
Rotterdam
Grenoble, a burning fountain near it
a remarkable grotto near it
2
Grotto, a remarkable one near Grenoble
another at Antiparos.
pag.
397
389
100 390
2 14
181
ibid.
419
Gunpowder, the effects of the elasticity of the air in it
... 313
H.
Hague, the distance of it from Leyden
389
Rotterdam
ibid.
Alkmaer
391
frog
viper
fifbes
7
La Hague, a body of fire feen there
Heart of the tortoise
Holland, the fituation of most of the towns of that coun-
try
Horary meaſures
386
385
Hyperbolical Glaffes, the manner of cutting moulds for
185
137
145
148
150
them
333
I.
Iceicles, how formed
Infects, particularly worthy of our attention
Inacceffible mountain
are the only animals that are of both ſexes
Iſlands floating
Italy, a fort of black fand found there
tale found there
¡
417
181
15
16
183
251
252
comparison of the ancient and modern meaſures there
Itch, produced by touching a ferpent in Brazil
375
236
Itinerary measures of the ancients compared with the mo-
dern
1
373
Κ.
INDEX.
K. Assic
Kám-cheu-fu, its pofition
-24bold 1 X D
Kiam-cheur, its positions ads to vis
pag.
23
22
ते
OPT
Labyrinth of Candy
Egypt
Lapis Judaicus defcribed
NL.
JNE
ぶら
​406
410
413
ibid.
414
*
235
16
83
189
fuppofed to fpring from feed
Lyricis, fuppofed to fpring from feed
Latitude of Lisbon
Leaches are hermaphrodites
Lével defcribed
1
Leveret, a monftrous double one
Liampo, its pofition
Light, reflections on it
a column of light obſerved
Lightning, how produced
what falls at Paris
1
Leyden, the diſtance of it from Soeterwoude 386, 389
Rotterdam 388, 389, 390
the Hague
Goude
→
*
1
389
ibid.
22
32
tranfmits itself 600,000 times fafter than found
38
395
318
Lille, the quantity of rain that falls there compared with
Liquids, on the bodies which ſwim in them
' હું
13
197
Lisbon, the longitude of it
230
the latitude of it
231
the declination of the needle there
232
the difference of the length of the pendulum there
from what it should be at Paris
233
Loadſtone, one of great value
324
230
Longitude of Lisbon
·
1
M.
4 1
Machines, the reſiſtance caufed in them confider'd
S. Malo, the tides there
112
325
Ma-
INDEX
Manihot, a plant of Brazil
Mare, a ftone found in its bladder
Meaſure of the earth
pag.
236
187
THE 385
Od
Meaſures itinerary of the ancients compar'd with the mo
dern
373
Mediterranean, an ancient communication of it with the
Red-fea
Microſcopical obfervations on a cheeſe-mite
Miles, the proportion of the ancient Italian ones to the mo
dern
Monſters, double, how formed
a double leveret A
two kittens joined together
Montagne de l'Arguille
Moon, the apparent largeness of it near the horizon
Motion, the continuation of it.
of animals reduced to the laws of mechanicks
exterior, its effect on bodies
330
328
382
329
188
329
181
183
249
336
186
perpetual, the impoffibility of it demonftrated 203
Mountain, inacceffible
181
Mountains finking
15
Muſhrooms of the ſea, real stones
$
412
Suppoſed to fpring from feed
413
Mufick, cures the bite of the tarantula
32X
Mytulites, how formed
3
422
N
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Nam-cham-fu d
Nan-ghan-fu
Nan-kim, its pofition
'
23
ibid.
22
Narbonne, the distance between it and Nifmes meaſured
Natural history of France
Nautilites how formed
374
14, 181
422
Needle magnetical, its declination obferved 207, 272, 352
Needle mountain
a general theory of it
Nerves of a frog trembling after death
Ning-po its pofition
245
181
187
22
Nif
INDEX.
pag.
Nifmes, the distance between it and Narbonne meaſured
Normandy, a body of fire ſeen there
the tides on the coast of it.
374
185
325
O
Oars, the different manner of managing them
Omer (S.) floating islands near it
Origni, a body of fire feen near it
Oftracites, how formed.
Ovaries of cows and ſheep, obfervations on them
Paraiba, the latitude of it
P
the declination of the needle there
392
183
186
422
287
233
ibid.
the difference of the length of the pendulum there
and at Paris
Serpents there
ibid.
235, 236
Parmaraibo, an extraordinary fort of ants there 251
Paris, the difference of the weather there from what it is at
Upminfter
II
the difference of the length of the pendulum there and
at Lisbon
Pectinites, boy formed.
Pekim, its pofitirm
Paris
232
at Paraiba 233
422
22
Pendulum, the difference of length of it at Lisbon and at
232
at Paraiba and at Paris 233
Pendulum clocks, remarks on the construction
of them
Pernambuc, an extraordinary large ferpent there
Perpetual motion, the impoffibility of it demonfirated
Pefaro, a curious fort of fand found there
Petards, how to augment the effect of them
Pholas, how formed
Phoſphorus of quickſilver
Pilots, the measures ufed by them
221
236
203
253
317
423
208, 262, 272
382
Port
INDEX.
Port-Vendre
V
Provence, yellow amber found there
Pyramids of Egypt, the measure of them
Pyrenean promontory
Pyrenean Venus, the fituation of her temple
Pyrites, defcribed
fuppofed to fpring from feed
е
Quickfilver turned to a black powder by motion only
-rendered luminous
1
376
186
378
377
376
414
413
187
208, 262,272
1
R
Rain, the quantity of it obferved
13, 204, 270, 349
Rarefaction of the air by the heat of boiling water 69
Red-fea, an ancient communication of it with the Mediter-
330
319
Rennes, the fatal effects of the damps in a well there 253
ranean
Refraction, the cauſe of it
Refiftance of hollow and folid cylinders
Refpiration of fishes
Roch allum, what it is
Rockets, the cauſe of their afcending
Rome, a black tale found there
344
294
327
315
252
Rotterdam the distance of it from Leyden 388, 289, 390
Alkmaer
the Hague
Goude
Rudder of a ſhip, what angle it ought to make
keel
388, 39E
389
390
with the
260
S
Salt, a pyramid of it formed in a ery@allifotion
Sand, a black fort found in Italy
Selve, a port there fuppofed to be the port of Venus
Serpents in Brazil
324
255
377
235
Serpent's eyes, a fort of stone fappoſed to ſpring from feed
Vol. I. No. 12:
Nan
413, 414
Sheep
INDEX.
Sheep, obférvations on their ovaries
Silver rendered volatile by the burning-glafs
Sing-ghan-fu, its pofition
Sluice, fee flood gate.
Smyrna, its pofition
Snails are hermaphrodites
287
397
23
25
16
386, 389
327
35
38
224
377
1
Soeterwoude, the distance of it from Leyden
Solfatara, allum and fulphur made there
Sound, how it is heard.
travels about 180 toifes in a fecond
Springsof clocks and watches
Stadia in France, the measure of them
Stiffness of cords confidered
Stone found in the bladder of a mare
Stones, the vegetation of them"
Strength of man confidered
121
187
410
Su-cheu-fu, its pofition
Sulphur made of Solfatara
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100
23
327
Surinam, an extraordinary fort of ants in that country 251
T
Ꭲ .
Tarantula defcribed, and the cure of its bite by muſick 321
Tarentum gives name to the tarantula
Tartary, the tigers in that country
Tchaotcheou, its pofition
Teleſcope glaffes, a method of centering them
ibid.
21
24
91
Temple of the Pyrenean Venus, the fituation of it 376
Thermometer observed
of air
206, 271, 350
355
356
357,359
-the imperfections of the old ones
conftruction of the new ones
Thunder, the effects of the elasticity of the air in it 313
Tides, a method for obferving them
on the coaf of Bretagne and Normandy
Toad-ftone fuppoſed to ſpring from feed
Tigers in China
Tortoife its heart defcribed
Trebifonde, its pofition
the uſe of its heart
Trigonometrical measure
Turky, the pofition of fome of its towns
Turkeys, an obfervation on their feathers
247
325
20
413, 414
137
156
25
383
21, 25
19
U
INDEX.
*
prus Spar-qur me kujutu
it is at Paris
Upminster, the difference of the weather there from what
1}}}} as
„kougomrad ar aligne
How to mopy to youth distrowie200
V
Pada skaists vade
Valognes, a body of fire feen near it
Vegetation of ftones
taa
335
Venus Pyrenean, the fituation of her temple
sbuowis
Ja mulle 26756lo?
oi si to wood bogy
zunde de reti
zkiola tuzga
410
370
Vibrations of preffure explained
33
Vinegar made by motion only
187
Viper, the structure of its heart
OF
148
fotosu ut
W.
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Water, remarks on the measure and weight of it
Weather observed
Wheels to draw water
Windmill, the pofition of its axis
Wine turned to vinegar by motion
Worms are hermaphrodites
their manner of copulation
Xambay, its pofition
Xoacheu
285
II
110
258
187
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INDE X
OF
AUTHORS NAMES.
A.
Amontons, 69, 112, 195, 353.
M. Antoninus, 375.
Archimedes, 204.
S. Auguftin, 14.
B.
Bellonius, 408.
M. Bernoulli, 208, 262, 273:
F. de Beze, 25.
M. de Billettes, 47, 110.
M. Blondel, 240.
M. Borelli, 198, 340, 341:
M. Boulduc, 286.
M. Boutier, 330.
F; Bouvet, 24.
C.
M. Carré, 319, 324, 325, 326.
M. Caffini, 208, 246, 373, 385, 395.
M. Chazelles, 378, 392.
M.
An INDEX of AUTHORS NAMES,
M. Colbert, 357.
F. le Comte, 24.
F. Coronelli, 22, 25.
M. Couplet, 83, 230.
D.
**
M. Delifle, 330, 331, 333..
Dr. Derham, II.
M. Deſcartes, 32, 35, 40, 43, 44, 46, 184, 211,
249, 266, 319, 334, 335.
M. Dieulamant, 14, 15, 182, 183.
Diodorus, 331, 332, 379-.
Elmacin, 333.
Eratofthenes, 380.
M. Fermat, 319.
F. de Fontenay, 24.
M. Forger, 328.
F. Fulgence, 379.
E.
F.
G..
Galileo, 30, 345, 346, 347.
Gaffendi, 184.
M. Gemelli, 379, 381.
M. Geoffroy, 251, 252, 321, 323, 326, 327, 328.
F. Gerbillon, 24.
F. Gouye, 21, 24, 25, 184, 185, 247, 323.
Mr. Greaves, 379.
Gregory Nazianzen, 423.
F. Grimaldi, 375, 376.
Sieur de Guet, 392.
Dr. Halley, 245, 246.
M. du Hamel, 208.
H.
Hero-
A
An INDEX of AUTHORS NAMES.
Herodotus, 331, 332, 378, 379, 380, 383, a
M. de la Hire, 13, 14, 52, 91, 100, 204, 221, 237,
247, 250, 255, 270, 285, 313 314 317, 318, 349,
395, 425.
M. Homberg, 15, 17, 94, 181, 251, 324, 396.
M. Hottinger, 415.
M. Huygens, 38.
I.
+
M. Jeaugeon, 379.
F. Kircher, 415
K.
L.
M. Lemery, 187, 188, 325.
F. Louvard, 253.
115
M.
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F. Mallebranche, 32.
Malpighi, 308.
M. Maraldi, II.
M. de Marca, 377..
M. Mariotte, 70, 80, 346, 370, 371, 426.
Mela, 377.
M. Mery, 329.
M. Mollard, 328.
Mutianus, 423-
M. de Nointel, 379.
N.
P.
*
M. Parent, 191, 193, 194, 195, 196, 18, 20c, 201,
202, 203, 250, 255, 257, 258, 26 1, 335, 336,
340, 342, 343, 345, 346.
M. de Peirefc, 418:
Peu
An INDEX of AUTHORS NAMES.
DATA to s
Peutinger, 375.
M. Picard, 208, 218, 255, 285; 286, 386, 391obl
Pliny, 377, 380, 381, 410, 415, 423.1 97HA ob ha
Count de Pontchartrain, 2475 330.25 YRS
Lord Portland, 263.
M. Poupart, 16, 1772018140
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M. Renau, 260.
Riccioli, 25, 375, 376.
Rouanez, (duke of) 47.
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Sanctorius, 272.
Sanfon, 230, 231.
M. Sauveur, 203, 328.
F. Sebaſtien, 30, 347, 348.
M. de Seneffey, 186.
Snellius, 385, 387, 388, 389, 391.
Strabo, 332, 374, 375, 376, 377, 378, 379.
1
T.
Theophraftus, 423.
M. Tournefort, 186, 405.
M. Tſchirnhaus, 25, 188, 189, 1905 19143951 h g
V.
SASTOM I
M. Varignon, 253, 346, 347, 348. Br. baking
M. de Vauban, 13.
M. de Vauleſard, 257.
M. du Verney, 137, 187, 287, 294.
M. de Villeroy, 263, 264, 265.
F. Vifdelou, 24.
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FINI SO James
This Day is published, Price 3s: few³d;
Price~35.
THE DOCTRINE of ANNUITIES and REVERSIONS, des
duced from general and evident Principles: With ufeful
Tables, fhewing the Values of fingle and joint Lives, &c. at
different Rates of Intereft. Likewife the value that ought to
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A Method of inveftigating the Value of Annuities by Approxi-
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In a plain and fimple Manner, and illuftrated by a great Va-
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*
Printed for 7. Nourfe, at the Lamb without Temple-Bar.
Where may be bad, lately publif'd, by the fame. Author, in
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A
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