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PHILOSOPHICAL

TRANSACTIONS.

Giving Some

ACCOUNT

0 F T H E

^refent Undertakings^ Studies, and Labours

O F T H E

INGENIOUS.

1 N M A N Y -

Gonfiderable Parts of the WORLD.

VOL. XXXII. For the Years i/xx, i7i3»

L O NT> O N:

Printed for W. and J. I n n y s, Printers to the Royal
Society, at the Weft End of St. Taul's. 1714.

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Numb. 370.

Beginning the Thirty Second Volume,

PHILOSOPHICAL

TRANSACTIONS.

For the Months of January , February, and March, 17x1,

Ihe CONTENTS.

h. ^ i H R Longitude of Buenos Aires, determined from
Jl an Obfervaticn made there by Fere Feuillee. By
Edm. Halley, LL. D. Aftronomer Royaf and F. R.

JI; A Defeription of an Engine, to raife Water by ' the
help of ^ici (liver, invented by the late Mr, Jofliua ;
Haskins, and improved by John Theophilus Defagu-
liers, LL. D. R. S. S.

lU. Part of a Letter- from Mr, Peter Derante Chirur^
geon Waterford to Mr* John Douglas, Chirurgeon^
F. R. S. Concerning the coming off of the Scapula
and Head of the Os Humeri upon a Mortification.

IV. Hyd&tidum ingenti copia in Ahdomine repertarum F/if-
toria. Communicavit cum Societate Regia . Johannes
Thorpe, M. D. S.. R. Soc.

\*.An Account of feme Experiments, maae upon the
Bile of Per(ons Dead of the Plague, at Marfeiiles,
jr it h what appear'd upon the ViffePfion of their Bodies, .
As likewife Experiments made with the Bile of Per^
fons Dead of other Dfeafes. By the Learned and Cu-
rious Dr* Dcidier, Profeffor of f hyfick in the Faculty
of Montpellier. Communicated by John Woodward
M. D. Prof* Med* Grejt* & S. R. Soc,

VI. The ^

I

( Z )

VI. The wd'j of proceeding in the Small Pox InocuU*
ted in New England. Communicated hy Henry New-
man, Efy ; of the Middle Temple.

VII. A Letter from Dr. Nettleton, Thyfcian at Hali-
fax in Yorkihire, to Dr. Whitaker, concerning the
Inoculation of the Small Pox.

VIII. A Letter from the fame Learned and Ingenious
Gentleman, giving an Account of his farther Progrejs in
Inoculating the Small Pox: To Dr*^ Jurin, R. S, Seer.

L Longitude of Buenos Aires, determmd from
an ObferVation made there by Pere Feuillee. By
Edm, Halley LL. D. Aftronomer ^yal, and

F.R. S.

1HAVE as Occafion offered, made it my Buff-
nefs to colled fuch Celeftial Obfervations as might
be of Ufe to determine the Longitudes of Places' on
the Sea coafl of the World 5 in order to get as near
as poffible the Out-line, or true Figure of the Earth,
without which our Geography of the Inlands muff ne-
ceflarily be very infufficient. The Memoirs of the Roy-
al Academy of Paris, afford a good Number of Ob-
fervations of this Kind, and among the reft, there is
.one made at Buenos Aires on the River of Plate, in
the South America, by Pere Feuillee in his Voyage to
Perux who, in the Memoirs for the Year 1711, is
faid to have obferved at that Place on the 19'^ of
Augufl, 1708. the Immerilon of the Star in the
Southern Foot of f'irgo (marked by Bayer with ?\.)
behind the obfeure Limb of the Moon. Being de-
firous to lee what Longitude might be deduced from

this

( J )

this Obfervatioti, I foon found that there was a Fault
in the Day, and likewife in the Star; for that A of
Virgo was then nearly in 5 Degrees of Scorpio, and
the Moon would not be there till the next Day,
Monday the of Attgujl\ and the Latitude of A
being about half a Degree North, the Moon at that
Longitude would be about 3 Degrees more South-
erly than the Star, and conlequently far from Eclip-
fing it; for that at that time the defcending Node
was in the very Beginning of Libra. Hence I con-
cluded it mull be fome other Star, that Pere Fcuillee
obferved Eclipfed by the Moon: The Day was cer-
tainly the and not the 19'^ of Augufi, as was
evident by the Place of the Moon ; but as to the Star,
it was neither in the Tychonick Catalogue, nor yet
' in that more copious Britijh. Catalogue of Mr, Flam»
fietd ; but turning over thsh: of Hevelius, I found a
Star whofe Situation agreed well with the Obfervation,
and was undoubtedly the Star that was feen to im-
merge behind the Moon .* The Place Mr. Hevelius
gives it, allowing the Preceflion of the Equinox, was
then m 1° 56'^ with South Latitude 51 '4. ft re-
mained then for me to be allured of the Place of this
Star, and accordingly on the and 24*^ of Decem-
ber lad, I got fuch Obfervations by help of the cir-
cumjacent Scars, that I was aflured the Place of the
Star, (which is a fair Star, of the Magnitude) was
at that time, m 1® 58' 40" with South Latitude 2° 5*4' 4,
being above z' in Longitude, and 3' in Latitude,
more than Hevelius gives it. The Hour of this Oc-
culcation is fee down precifely 9^ 5' 38'' at Buenos
Aires, the Latitude of the Place being 34° 3 5' South.
Whence the Altitude of the Moon there was then 42°
48', and the Paralladick Angle 76° 38', and the
Parallax in Longitude 40' 11" to the fTr/ and in

A 2, Latitude

( 4 )

Latitude 9' to the North. So the Moon's ohfervcd
Place correded by Parallax was m 4" with South

Latitude j'2%. To this i lacejby ih^Calculus of ihofe
Numbers I have fitted to our Prefident^s Theory of the
Moon ("but which would be improper and too long to be
here recited) the Moon will be found to have arrived
Augullx\\t 10^ 57' 36" apparent London. But ,

at Buenos Aires it was then computed but 7^5' 38", -
whence the difference of Longitude refulting from this ^
Obfervation is 3 ** 52' or 58 Degrees, by how much Bue^ |
nos is more Wefterly than London* I have twice re-
peated the Calculation to be Pure to avoid error, and by
comparingmy Chartofthe Variation with the Longitude
thus found, it appears that in this Cafe a Ship at Seaufing-
thofe Tables and that Chart, would by an Obfervation
of this Occultation have fallen with greater cxac3^ne(s on
the Coaft of America^ than by any Reckoning can be pre-
tended to be done.

11. A

( 5 )

II. ADefcription of an Engine, to raife Water hy the

Help of Quickplver^ invented hy the late
Jofliaa Haskins, and improvd hy J. T. Defagu-
liers, LL. D. R. S S.

R. Hnskins finding that all Hydraulic Engines,

working wirh Pumps, lofe a great deal of

Water, falways giving Ids than the Number of Strokes
ought to give according to the Contents of the Bar-
rels;) and that when the Piftons are new leather’d to
prevent that Lofs, the Friction is much increas’d, and
the Engines are fubjed: to Jerks, which in great Works
do often diforder an Engine for a great while, by
breaking fome of the Parts ; contriv’d a new way of
raifing Water without any Fridion of Solids; making
ufe of Quickfilver inftead of Leather, to keep the
Air or Water from (lipping by the Tides of the Pi*
Rons in the Barrels where they work ; hoping there-
by to prevent all the abovefaid Inconveniences, and
alfo to have Water Engines lefs liable to be out
of Order than any yet made.

The firft Experiment he made with an Engine that
he fet up at my Houfe about two Years ago, which
1 repeated before the Royal Society in a Model ; and
tho’, by the ill Contrivance of the Parcs, it did not
raife near the Quantity of Water that the Invemioa
is capable of ; yet 1 (hall defcribe the Machine here,
becaufe it will fcrve for the better Underftanding of
our prefent Engine.

B

F I G*

1

( 6 )

Fig. I.

Jdiid reprefents a Lignum Vit^ Plug or Pifton (which
Mr. Haskins call’d a Plunger^ about 6 Foot long made
heavy enough with Lead at top to fink into Mercu-
ry which is beforehand pour’d into the Barrel D i
D 2 up to m m. The Chain E i E 2, joyn’d to the
Pifton and the Power that moves it, being let down
till the Pifton comes to D 2, the Mercury rifes to the
fame Height in the Barrel, and in the Receiver K,
(which it fills) namely to nn, as appears in the Fi-
gure. Then drawing up the Pifton till its Bottom
is come to mm^ the Mercurj coming out of the Re-
ceiver down to makes a Vacuum^ and the Weight
of the Atmofphere caufes the Water to rife up thro'
the Sucking Pipe A i A 2, and Valve V into the
Receiver where the Hercury was before. Upon let-
ting down the Pifton again, the Mercury rifes into
the Receiver, and drives up the Water thro’ the Elbow
B, the forcing Valve //, and fo up the forcing Pipe
4 2 4 1: But when once the forcing Pipe (which here
was ^6 Foot high) is full, before any Mercury can en-
ter into the Receiver, and force any Water out at the
top of the Pipe 4 i, the Mercury between the Piflon
and Barrel muft rife up to near 3 v Feet above the
Bottom of the Receiver, and as it continues to rife
up to pp, the Water is thrown out with a Velocity
proportionable to the Freight that the Mercury is rais’d
■above the i.:jtb part of the Height of the Water*
Now tho’ the Fridion of Solids is here avoided, it
is plain that the Mercury muft move from mm to qq
without raifing any Water, and that it can only force
in going from q q 10 pp, and only fuck in falling
• from 0 0 to mmi And unlefs the Pifton is flopp’d a

little.

( ? )

little while when at lowed:, the Water won’t have
time to run out.* So likewife the PiUon mud be
flopp’d when at highed;, that the Receiver may have
time to fill.

Mr. Haskim likewife propofed another Way, rep;c-
fented in fig, 2 ; where the fame Letters rcprefenc the
fame Parts, on!y here the Barrel is moveable by the
two Chains El E 2, and indead of a folid Pidon,
the hollow Cylinder C i rc is fix’d, and the ^ete try
moving up and down in the lower Part of it fucks
and forces the Water thro’ the Elbow. The Figure
reprefents the Engine fucking, by means of the
fury hanging from a 0 to mm^ !n order to force, be-
fore any Water can be driven out, the Mercury in the
inner Cylinder mud defeend from 0 0 to mm, and rile
up to pp between that Cylinder and the Barrel i fo
that here alfb a great deal of time is lod 5 befidcs
the great Quantity of Mercury us’d, which is very ex-
penfive ; becaufe as much Mercury is mov’d every Stroke
as the Water rais’d.

Thefe Difficulties very much puzzled Mr, Haskins,
and quite difcoiirag’d fome other Perfons that had
got the Secret of the Invention, and were fetting up
againd him. But when I had confider’d the Matter a
little, tho’ I had not time to contrive a Machine for
it, I told him, That a little Mercury might be made
to raife a great Quantity of Water, and there fiiould
not be fuch a lofs of time as in his Engines ; but
that I would have him find it out before I affided
him farther. In a little time he found out the Con-
trivance reprefented in 4; and afterwards that of
Fig. 3 ; W’hich lad Was what I had thought of. And
both thefe were alfo found out by the late Mr. William
Ureem, who was an excellent Mechanick,

B 2

F I G.

( 8 ;

Fig. lit. .

Here the Barrel is mov’d as in Fig, 2, but the Plug
ddd taking up a great deal of Space, there is Oc-
cafion for no more Mercury than what will make a
concave Cylinder or Shell up to pp between the Bar-
rel D i D2, and the hanging Cylinder Ci Cz cc,
when the Stroke is made for forcing ; and a concave
Cylinder between the Plug and C i Cz cc, when the
Sudion is made. I gave Mr. Haskins the Proportions
for an Engine this way, of which he made a Draught,
and fhew’d it to the Right Honourable the Lord Chan-
cellour about fix Months ago. This I mention here,
that no body may endeavour to get a Patent for this
Invention, to the Prejudice of Mr. Haskins's Alfignees ;
who, fince his Death, have defir’d me to affill: them in
perfe(5ting the Engine.

Fig; IV.

Here the Barrel with a third Cylinder dddd in-
Read of the Plug of Fig. 3, is 'lifted up and down
every Stroke, and the Water pailes thro’ dddd, the Mer-
cisry making a Shell, fometimes between the middle and
inner Cylinder, as in the Sudion ; and fometimes be-
tween the Barrel and the middle Cylinder, as in th.e
forcing Stroke.

Mr. Haskins had contriv’d fuch a Machine as is re-
prefented by -this 4th Figure, and befpoke the feveral
Parts before he dy’d ; and therefore when I was de-
fir’d by his AfTignees to diredt the fetting up the Ma-
chine, I was oblig’d to make ufe of the Pieces alrea-
dy made, in order to fave the Expence of a new
Engine: And now the whole put together with feme

Al-

( 9 )

Alterations, make the Engine reprefented by F/f.
as it is fet up at my Houfe in Weflmhller, and by
the Force ol one Man, raifes a Hogfhead of Water
in little more than a Minute and a half to the Height
of 17 Feet. Ail the Fault of the Machine of Fig,- ^
is, that the Pendulum Handle Ff is too long, and the
Bottom of the middle Cylinder C ought to be juft
in the middle of the Height to which the Water is
CO be rais’d, fuppofing three Copper Cylinders to be
as they are here : if like wife the Barrel D i Dr

work’d under the forcing Pipe, the Lift would be
eafier. Therefore I defcribe the Machine with the
fmali Alteration rep'^efented in Fig. 6.

The fucking and forcing Pipe and Valves are mark’d
with the fame Letters as in the other Figures ; and
the Chains E i Ei mufl: be fuppos'd to hang from
fuch Pullies, and to be mov'd by fuch a Pendulum as
is in Fig. The Barrel D i Dr (call’d othervvife
ihe outer Cylinder, and reprefented by the fame Let-
ters in Fig. 7,) has within it another Cylinder (call’d
the inner Cylinder or Plug, as Fig. j,) between
which two Cylinders a certain Quantity of Mercury
is pour’d in, and the hanging Cylinder C coming
down into the Mercury, a Stroke of 13 Inches may
be made by the Motion of the Barrel, which, in ga-

Iing down fucks by making a Vacuum in C, and in
going up forces the Water out of the top of the
forcing Pipe, performing the Office of a common Pi-
flon ; only that inftead of Leather to make it tight
to the Cylinder C, there is always a chin Shell of
ij Quickfilver cither between the middle Cylinder C and
1 the inner one, (dddd Fig. y.) as happens when the
Sudtion is made, or between the middle and outer
Cylinder, as happens in lifting up the Barrel to
Force; In the Sudion, the Mercury is higher in the

( «o )

inner Shell than in the outer Shell, by an Height c-
qual to a little more than Part of the Height of
the Barrel above the Water to be rais’d .* And in
forcing, it is higher in the outer Shell than in the inner
by a little more than -ri- of the Height of the Pillar of
Water to be forc’d. And therefore if the Water is
not required to be rais’d above 64 Feet, the Barrel
fhould move fb as to make the Middle of its Stroke
at the Height of 30 Feet, or at the middle of the
way from the Water to be rais’d, to the Delivery at
top.

The 7th Figure drawn by a larger Scale, reprefents
the three Cylinders, which are here made of Copper
in their juft Proportions: And for the fake of thofe
that would confider this matter fully, I have here gi-
ven their Lengths, Diameters within and without, and
Thicknefs. - ’ '

Outer Cylinder
or Barrel, Di D2.

Middle or hang-
ing Cylinder, in
which the Stroke
is made Cl C2 cc.

Inner Cylinder or
lug clofed at top
y a Cap, and mo-
ving up and down
with the Barrel to
which it is joyn’d
at bottom, dddd.

Length

Diameter

within.

Thicknefs

Diameter

without

>

>

Inches

-30

- ^,74

- 0,10

- 6,94

Inches Inches

—29,0 ■ — — 31,2

6,35

<5,03

0,13

6,51

6,29

Here B B reprefents part of the Elbow of Fig,
or of the forcing Pipe of Fig, 6. But as the Spaces
between the Cylinders are fo fmall, as not to be vi-
fible even in a large Draught made by a Scale; I
have here given three more Draughts of the three

Cy-

i

( '• )

Cylinders, where the Height is agreeable to the Scale*
of the 7th Figure, but the Diameters of the middle
and inner Cylinders are made Id's than they are in
the Engine, to make the Space between ('where the
Mercury rifes and falls) vifible ; and the Cylinders
themfdves are reprefented by Tingle Lines.

Ihe Quantity of Mercury us’d in this Engine is
36 i Pounds, which being pour’d in between the outer
and inner Cylinder, riles up to the Height of 16 Inches.

When the Barrel is pull'd up (as in Fig* 9,^ fo as to
have the middle Cylinder within an Inch of the Bot-
tom of the Barrel ; the Mercury on both Tides the mid-
dle Cylinder will rife up to the Height of 23,1
Inches, that is about two Inches below the Cup Di,
to the Line q q*

When the Barrel is going down to fill the Tucking-
Pipe and middle Cylinder C, the Mercury in the inner
Shell will be 25 Inches high, and only 13 in the outer
Shell, Fig. 9, where the Ibaded part reprefents the

At the End of the lucking Stroke the Mercury is
up to the top of the inner Cylinder, and Tcarce an^
Inch in the outer Shell. Fig* 8.

In raiTing the PiBon from forcing to Sucking, the
firll It Inch drives the Mercury out of the inner
Shell, and raiTes it in the outer Shell 13,28 Inches.

The Depth of an Inch of Water in the middle Cy-
linder above the inner one or Plug is equal to a Space
in the outer Shell of 13,18 Inches, and L of an Inch^
is equal to the Tame Height in the inner Shell.

Therefore when the Mercury is equally high in
both Shells, a Motion of t of an Inch of the Bar-
rel will charge for Sudion- That is, upon letting
down the Barrel only L of an Inch, the Pieflure
of the AtmoTphere in the outer Shell will raife the
Mercury in the inner one 13,28 Inches, at the Tame

time

( M )

time, that it puflies up the Water from the Well 13
Foot and a half high into the fucking Pipe. And
when all the Pipes are full, if the Mercury be equal-
ly high in both Shells, upon railing the Barrel one
Inch, the Mercurj will rife 13,18 Inches in the outer
Shelly which I call charging for forcing; becaufe in
contitiuing to raife the Barrel, the forcing Valve im-
mediately rifes, and the Water comes out at top
during the reft of the Stroke, which is 12 Inches,
and delivers f,6 Gallon of Water, Wine Meafure.

Fi^. 10. reprefents the forcing Stroke half way up;
with the 517 Inches in the outer Shell 4 Inches in
the inner, and the whole fpace at bottom under the
middle Cylinder 7 Inches.

From this it appears, that in the whole Stroke of
19 Inches in Length, there is only t of an Inch loft
to charge for SuS:ion, and in the next ftroke, which
is likewile of 13 Inches, there is only one Inch loft
to charge for forcings fo that in a Motion of ^6
Inches, there is but i t Inch, or about rl part inef-
fetftual. But this is owing to the too large fpace of
the outer Ihell, which contains 4 times more than the
inner one, becaufe the Cylinders were only hammer'd,
and not turn’d 5 for if the outer fpace had been no
bigger than the inner, then 4 of an Inch of the ftroke
would have charg’d for forcing; fo that only 4 an
Inch in 2 6, or -4 part of the whole ftroke would have
been ineffedlual 5 and in that Cafe, 4 of the Quanti-
ty of Mercury, or a little more than iz Pounds, would
have been fufticienr.

There may ft ill lefs Mercury be us’d, if the mid-
dle Cylinder be made of Plate Iron turn’d on the
outftde, and bor’d within, the outer Cylinder bor’d,
and the inner one turn’d ; fo that if the Work be
well perform’d, eight or ten Pounds of Mercury will

( 13 ) ^

be fufficienc in this Engine, tho’ the Bore of the
middle Cylinder, or Diameter of the Pillar of Wa-
ter which is rais’d, be of 6,35 Inches. If the Bore
of the laid Cylinder was but 3 Inches^ lefs than 3
Pounds of Mercury would fuflice, and lefs than fix
if there were two Barrels, in order to keep a condanc
dream thro’ a Pipe of almoft the fame Diameter.
This will very much leflen the Expcnce of Mercu-
ry, which would otherwife be an Objedion againft
this Engine; and by making the inner and outer Cylinder
of hard Wood, as Box^ or Lignum the Cod of

the Engine may dill be reduc’d. But if the Engine
be very large, Cad Iron bor’d will be proper for
the outer Cylinder, and Cad Iron turn’d on the out-
fide for the inner Cylinder or Plug, and hammer’d
Iron bor’d and turn’d for the middle Cylinder.

There is an Objedion, which leems at fird to take
off the intended Advantage of this Engine, which is
this, njtz.. That indead of the Fridion of the Leather
of a Pidon, when we lift up our Barrel to force, the
Reddance, that the Mercury finds to rife in the outer
Shellj is at lead as great as the Fridion that we avoid.
Now that Refidance is never greater than the Weight
of a concave Cylinder of Mercury^ whofe Height is
the greated to which the Mercury rifes in the Paid
Shell, and the Bafe is the Area of the Shell it felf.
This Weight in our Engine is equal to 57,5 Pounds,
and therefore one would think it greater than the Re-
fidance made by the Fridion of a Pidon. But if it
be confider’d, that in the Defcent of the Barrel for
fucking, the Mercury fhifts immediately into the inner
Shell, rifing to the fame Height, and dill keeping the
fame Bafe; the aforelaid Weight of 57,5 Pounds
helps down the Barrel, and facilitates the overcoming
of the Force of the Atmofphere, confequently the

C Weight

( «4 )

Weight of the Mercur'j being balanc’d, is no Hindrance,
whether you work with a Tingle or a double Barrel-
There remains only then the Hindrance by loTs of
time in the Beginning of any Stroke : But I have

Ihew’d that to be but tv part of the Broke. I have
found that the beft Engines now in ufe generally
lole near -f of the Water that they ought to give,
according to their Number of Strokes. And Mr.
Hent'j Beighton^ an ingenious Member of this Socie-
ty, having a great many times meafur’d the Water
that is rais’d by Engines in Mines, found that fome
Engines loft and none ever loft lefs than t of
what they ought to give according to the Number
of the Strokes in their Pumps, whatever auxiliary
Powers they were mov’d with.

There is indeed another Objedion, but fcarce worth
notice, which is, that fome Particles of Mercury will
mix with the W^ater that is rais’d, and make it un-
wholefbme; but no body that confiders Specifick
Gravity, will imagine any fuch thing. However, to
fatisfie thofe that might ftill apprehend it, it is to be
obferv’d, that none of the Water that is rais’d comes
near the Mercury; For in the Cylinder C, and part
of the Elbow B, (^Fig. 5.) there is always above the
Mercury a certain C^antity of Water that tifes and
falls with the Barrel, and never goes into the forcing
Pipe. The fame happens alfo in the Machine of
Fig. 6. for the Water having once run into the Cy-
linder C, all that is rais’d afterwards, comes thro’ the
forcing Valve without coming down to the Mer-
cury,

Provided Care be taken to make the Barrel with
its Plug tight, 1 don’t fee that this Machine will
want Repair in a long time, except fome of the aux-
iliary Powers be out of order, which do not relate to

this

( 15 )

this Invention The Numbers given will ferve to
examine the Truth of what I have averted concern-
ing the Motion of the Mercury : And fiom them
one may make Tables to ferve to proportion thefe
Engines for raifing any Quantity of Water to any
Height, according to the Power one has to apply.

in. ^art of CL Letter from A/r. Peter Derante,
Chirurgeon in Waterford, to Mr. John Douglas,
Chlrurgeon^ F. % ^ concerning the coming off of
the Scapula and Head of the Os Humeri, upon
a Mortification,

\

I/^^N the 5th of November, 1713, On^John Fletcher,
on board the Neptune of Leverpool, had the Mis-
i fortune to break the Radius and Ulna (of his left Arm^
r and their Ends burft thro’ the Skin. He was immedi-
I ately drefs’d by the Surgeon of the Ship with the com-
i mon Aftringents and Bandage ; about five or fix Days
I afterwards I was fent for to go down to Faffage to fee
1 this Man. When I came there, I found his Surgeon along
with him, who told me. That the Man would do very
n well, becaufe he was in no pain at all? however, I
b defir’d him to take off the DrefTings, and let me look
3 on’t. Which being done, I found it was black and
i infenfible from his Fingers to his Shoulder, and there-
^ fore advis’d the Extirpation of it immediately, but
his Surgeon oppos’d it ; however, I fcarified it in fe-
veral Places, and very deep, and then apply ’d a warm
DrclTing. Next Day the Shin put to Sea, and the poor

C X Creature

( )

Creature was fent to Waterford, and committed to my
Care. As fbon as I could get my Apparatus ready, f
cut off his Arm (in prefence of Dr. Renet^ and Mr. Carr
an Apothecary) as high as poffible ; then I cauterized
the Stump, which was perfedly mortified as high as
the Acronfion. Next Day I perceiv'd the Mortification
fpreading toward the lower Angle of the Scapula^ then
I rubb’d the Edges of the Mortification with arm-
ed Probes dipt in a Solution of Argentum Vivum in
Aq. Fort, which compleatly anfvver’d my Intention ;
for from that time the Mortification fpread no further ;
next DrefTing I fcarified and cauterized all the mortifi-
ed part, and drels’d it S, A, 1 continued this Method’
for feventeen or eighteen Days, and then the Sloughs,
began to leparate and caff off daily; fome time after-
wards the Scapula began to part from the Gs fhmerv
and CUvicula, and at length came out whole ; I was,
then put to it what to do about the ftump of the Os
Humeri, which ffill adhered to the TcBoralis and La»
tiffmus Dorfi\ but in a little time it alfo feparated
and came away, without any Hemorrhage fucceeding,
which I expected. I was afterwards obliged to cut
off part of the Clavicula, before I could cicatrize the
Wound, which was (bon afterwards accompJiffied.
I have the Scapula and Head of the Os Humeri ffill in
my Cuffody, and have ffiewn them to many Surgeons
and Phyficians. All Waterford is Witnefs of this Fatff,
and they called him ever afterwards Three garters,
$f a Man.

I am i (5?c.

lyiT.

Waterfordf Jan,

Pet, Derantc.

( «7 )

rum Htfioria, CommunlcaVtt cum Societate
Johannes Thorpe, M D. S. % S..

Hedarius Excell. S. D. Baronis de Penterrider,

aecatis 58 annorum, Tern pcramenti Tic didi Cho-
lerico } hlcgmarici, Sracurce quadratic, non obefus fed
robuBus, bene appecens, officio fuo bene fungens, nec
vino, nec liquoribus fpiriruofis immoderate utens, bono>
fatis Regimine vivens prxterito Augufti Menfe auxili*
um meum petiic, pro Abdomine fortiter tumence &
tenfo, Afcitico mitiirre abfimili, urina attamen bomr
notic <y. in quantitate fufficienre optime prodeuntc,
pedum nullo cedemate comparente, Refpiratione iibcr-
rime procedente, ventre autem in dies crefcente (qui?
Menfe Jlinio tumere incepit^ fanguine in vafis ha:mor-
rhoidalibus ftagnante, nodos ibidem magnos elevante
& inrerdum dolorifice furente, Appetitu ac Viribus,
nunquam proftracis.

Fateor Tnigma mihi fuifle an Tumor lit ficcus hu*
midufne? Ad fatisfaciendum vero Indicationibus, itif
fpecie h.3EmGrrhoidibus fuppreffis, medicanienta ciialy-
beata cum Purgantibus mixta exhibui, per quse flu-
xus haemorrhoid um mox. excitatus, dolores fedati, &•
magna Tordium quantitas cum aliquali levamine per
tubulum inteftinaiem fuit eliminata. Poftea ad exem-
plum Ecmulkri in hydrope ficco, Nitr. prxparar. quo-
tidie ad unc. IT item Mercurium vitae & omnis gene-
ris Diuretica mitiora, fortiora, &c. omnia incalTum dedi.

Abhinc Patiens Tub fanitatis recuperandae Ipe, pro^
more Vulgi auxilium Empiricorum imploravit, qui fta*

timi

( «8 )

‘tim Aureos ip(i montes promiferunt, multisque fagi-
natum Arcanis miferum in malis deferuerunt.

Abdomine igitur mole fua maxime urgence, ad Pa-
racentefin fine niori progrediendum erac ; quam die
1 4 Januar. Chirurgus Expertifs. D. AneU unanimi
noftro confenfu Patienci adminiftravit ; contenta ve-
ro confiftenciam gelaiinofam nada per anguftius
' CannuliE immifTx Tpacium exire non poterant. In-
cifio ergo cum Lancetca facienda erat; qua fada, mate-
ria gelatinofa coloris grifei & lutei, albumine ovorum
fpiffior, cum magna quantitate globulorum alborum
fphaericorum, triangularium, vermicularium, gemello-
rum, tefticuli- & ovarii - formium, &c. magnitudi-
nem nucis avellanae adiequantium primo die ad menfu-
ras fex evacuata erat, xgxo quantum ad vires optim^
(e habente. Poftero die, cum facile judicarelicebat, fa-
dam incifionem non Tatis efie amplam pro exitu majo-
ribus hujus nature globulis concedendo, Lancettd igi-
tur vulnus ampliabatur, per quod globuli ovum Co-
lumbinum magnicudine fuperantes magno numero cum
fex iterum gelatinx menfuris, & magno frufto maflae
cujuldam albae portionem omenti referentis, de novo
excreti erant. Cui Maffe plures didorum globulo-
rum filamentis fibrofis adh^refcebant-

In examinatione materiarum, gelatina fuper carbonum
igncm indurefcit & albefcit, pellicula defuper fe for-
mante.

SpirituVirrioli, Spir. Sal. Ammon, vol, 01. Tart, per
deliqu. Spir. Vin. redif. Aceto affufis, manifcfti nihil
viderur, quam levis induratio macerice ab uno quoque
iftorum liquorum, etfi natura inter fe invicem contra-
riorum*

Globuli coloris funt albiflimi, fenfui tadus refiften-
tes ; rupti liquorem album chylo fimilem fundunt, mem-
brana feu pclliculi manifefla cindi. -

Mafia

( 19 )

Mafia i(la albicans qu£E porcionem omenti referf,
etfi craflitie pollicem adaequer, (ubftantiam pure mcni'
branaceam habcc

Numerus globulorum majorum & minorum »d fep-
tem vel odo millia fe extendit.

Hodie qiii eft inclufive decimus fextus ab operatione
dies, arger quam opcime fe haber, venter eft mollis, pla-
nus, vulnus pulcherrimum, urina, pulfus, relpirado
bona, confequenter nulla febris, fomnus tranquillus..
Evacuatio marerise gelatinofas durantibus 15 diebus
fuit copiofa, inodora, nunc pure ferofa & parca, fed for-
tem odorem fpirans, immilTumque Catheterem argente-
um nigricans, quod corporibus heterogeneis corruptis
I magis quam vilceribus gangrasna prehenfis attribuimus,

I quoniam febris abeft. Hodie poll inje<ftionem Decocfti
I ex Enula Campan. Agrimon. &Mell. cum Tindur. AloeSo.
Myrrhs & Balfam. du- Commandeur, rupti pellicula
jglobuli fuit excreta, quern inftatufuo natural! ovum gab
llinaceum mole adnequ^fte, fortaffis fuperilTc, certum eft.

Appetitus & vires nunc funt quae nobis facefTunc,
IMedicamenta porrigo Traumatica, Alexiteria & Con-
Ifortantia invicem combinata juxta vicftum Analepticum..
*^aclyofjL€vov notatu dignum examini verfatiorum in arte
samice diTcutiendum traditur, & ut animi fui fcnfa no-
Ibifcum communicate baud graventur, obnixe rogatur..
IDabam Parifiis d. IV. Calend.Januar. MDCCXXli.

BarchoL Anhorn, ab Hartuifs.

c 10 )

V. An Account of jome Experiments 7nade with the
Bile of Terfons dead of the Blague at Marfeilles,
with what appear'd upon the DiJfeBion of the So-
dies 5 as likewife jonie Experiments 7?2ade with
the Bile of Terjons dead of other Difeafes. By
the Learned and Curious t)r, Deidier, Brofejfor
of Thyfick in the Faculty of Montpellier. Com~.
7nunicated by John Woodward, M D. Prof.
Med. GreCh. a^id R. S. S.

Experiments rthxdc upon the Bile of Perfons dead of

the Plague,

Experiment T.

The Human Bile, taken from the Gall-Bladder
of the Bodies of thofe that dy’d of the Plague
at Mar fellies^ has been always found to be of a black
and greeniih Colour. It has become conftantly of a
lading Grafs Green upon the mixing of Spirit of Vi-
triol with it 5 and always very yellow when we mixt
Oil of Tartar per deliquium, or the Alcalous fixe Salt
of the fame difiblv’d in a fufiicient Quantity of Wa-
ter, Thefe two Colours, green, and yellow, have con-
tinued for whole Months. The faid Bile has become
of a black Colour, like Ink, but foon fading, by the
Afiufion of Spirit of Nitr

Experiment II.

The Bile, taken from the Gall-Bladder of the Bo-
dies of thofe that dy’d of the Plague, having been

pour’d

( 21 )

poured into a Wound made on purpofe in different
Dogs, has render’d them thereupon melancholy, drew
zy, and without caring to eat- All thefe Animals dy’d
in three or four Days with the effential Marks of the
true I'lague, declared by Buboes, Carbuncles, and gan-
grenous Inflammations in the Fifcem, in the fame man-
ner as in the human Carcaffes from whence the Bile
was taken.

Experiment lU.

A Drachm of the faid peftiferous Bile having been
I mix’d with two Ounces ol Fountain Water made lukc-
I warm, and injeded into the Jugular Vein of feveral
j Dogs, has render’d them prefently drowzy, and has
I kill’d them in four Hours, with gangrenous Inflam-
i macions, the Heart Buffed full of black thick Blood,
I the Liver (well’d, and the Gall Bladder full of green
f bile.

Experiment IV.

The fame Quantity of Bile, inje<5led by the Crural
- ’Vein, has produc’d in the Dogs a Heavinefs in about
> I an Hour. They have had fuch a ffrong loathing of
« itlieir Food, that they would not eat or drink the lead
rmatter after the Inje<dion was made. They pils’d
(frequently, efpecially if they were ftirr’d. On the
rthird Day there appear’d conffderable Tumors under
tthe Axilla, and on their Thighs, about 3 Inches from
lithe Wound. The Wound turn’d to a Gangrene, and the
(Creature ufually dy’d on the fourth Day, with all the
Marks of the Plague.

D

( 11 )

Experiment V«

A Dog, of the Hofpital at the Mail, in Marfeilles^
who follow’d the Surgeons when they went to drefs
the Sick, ufed greedily to (wallow the corrupted
Glands, and the Dreflings charged with Pus that they
took off the Plague-Sores 5 he lick’d up the Blood
that he found Ipilc on the Ground in the Infirmary
and this he did for about three Months, and was al-
ways well, gay, brisk, full of Play, and familiar vVvirh
all Comers. We injeded into the right crural Vein
of this Dog about a Drachm of the peftiferous Bile,
mix’d with two Ounces of warm Water He dy’d
the fourth Day, as the others did, with a Bubo on
the wounded Thigh; on which likewife there were
two Carbuncles, and the Wound gangren’d What
we took particular Notice of in this Dog was, that af-
ter the Injedion, both when he was living, and after
he was open’d, when dead, he had a very (linking
Smell, which we did not obferve in any of the o-
thers. He had moreover a confiderable Hirmorrhage
from the Wound, the Night before he dy’d, having
llruggled hard to efcape out of his Confinement.

j • ■ , •

Experiment VI.

The 2d of May having injeded about a Drachm of
humane Bile, taken from Perfons dead of the Plague,
mix’d with two /Ounces of warm Water, into the
Crural Vein of a Dog, the Creature was prcfcntly
drovvzy, refus’d his Food, and dyed about the third
or fourth Day after the Injedion, with all the inward
and outw^ard Marks of the Plague that the others
had.

Expe*

\

( M )

Expeyimetit VIJ.

The fixth of the fame Month we colleded the Bile
of this Dog dead of the Plague, and injeded it by
the Crural Vein into the Blood of another Dog^, who,
prefently after the Injedion, had Convulfive. Motions
all over him, which were follow’d by a Lethargick
Heavinefs. On the fecond Day after the lnje(Slion,
there appear’d a Carbuncle upon the great Pedoral
Mufcle on the right fide The third Day there arofe
a confiderable Bubo on the Thigh; and the Dog dy’d
the fame Day. Upon opening the Body, we found the
fore part of the Bread: all gangren’d under the Tegu-
ments; and, in the inward parts, the Vilen a were full
of black clotted Blood ; as in all the red. The out-
ward Surface of the Lungs was all Purple; The Heart
was fwelled as big again as ufual, with the four Cavities
full of black clotted Blood. The Creature had liv’d
three Days from the Injedion without eating or drink*

iog-

The loth of /^/ay we injeded the Bile of this fe-
cond Dog into the Crural Vein of a third Dbg, who
was thereupon feiz’d with violent Convulfions, and
different convulfive Motions, for about half a quarter
of an Hour. When he was recover’d from thefe, he
appear’d dull, and fleepy ; he vomited with violent
Strainings. The Vomiting was followed with a Hick-
up. He eat a little boiled Meat, haying faded a
good while before the Injedion was made; but he vo-
mited it up two Hours after he had taken it. He
died the third Day with the fame Symptoms of the
Plague that the other Dogs had.

D z ' The

( *4 )

The State of the bodies of Ter/onsdead of the blague ^
from which we took^ the !Bile for the Experiments
he foremention d.

Th: frfl Bodf

ONE Beleflsur, a Soldier, of Years of Age,
of a (Irong robufl: Conilicution, having a flac-
tifh Bubo growing on the hollow of the right Groin,
dy’d delirous We found in his Carcafs the Heart
of an extraordinary Bignefs, fluffed with black clot-
ted Blood. His Lungs covered with a livid Purple,
and flicking a little to the Pleura. The Liver was
double the natural Bignefs, and fluffed with a thick
BIooL The Gall Bladder was full of a black and green-
ifli Bile. The Dt^ra and Pia Mater by their Blacknefs
feem’d to have been feized with a gangrenous In-
flammation The inward J^ubflance of the Pram was
fprinkled over with an infinite number of fmall livid
Spots.

The fecond Bod),

Mary Pifanne, aged 30 Years, of a fanguine Habit,
had a Buho under her right Arm-pit, with a Delirium
that was followed by a mortal Sleepinefs. in the
opening of her Body, we remark'd, that the Lungs
were in their natural State. The Heart was of a
prodigious bignefs, full of black coagulated Blood, with
the left Auricle livid and gangrenous. The Liver,
which was much enlarged, was all cover’d with Pur-

( 15 )

pie; and the Gall Bladder fill’d with a black and
greeniih Bile. The Head was not open’d.

T^e third Body,

Peter Mculard, of a tender, feeble Conftitution, a-
bout 14 Years of Age. had a Buho under the hollow
of the right Groin very deep, and that never came
well out. He became delirous with Convulfions, in.
which this Child dy’d. We found in his Body his
Heart of double the bignefs that it ought naturally
to be, containing a black thick Blood .* His Lungs
were befprinkled with livid Spots. The Gall Bladder
full of a black and greenifli Bile. The Head was not
open’d.

The fourth Body.

Jean Raynaud, Cook, aged about Z5" Years, of a.
melancholy Temperament, had the whole Habit of
his Body cover’d with a purple livid Colour, and a
Buho under his left Axilla ; he dy’d in a delirous
Phrenzy. We found in his Carcafs two AbfcelTes, one
between the Teguments and the left great pedoral
Mufcle, 2nd the other in the Bread between the Ster-
num and the Mediafiinwn, His Heart was very large,
fill'd with black thick Blood. The right Auricle was
of the Breadth of three Inches; the left was in its
natural State. His Lungs were cover’d with little li-
vid Spots, remaining foft and pliant, without any hard-
nefs in the Subftance of them. The Liver was lar-
ger and harder than ordinary, and was alfo fulf of
livid purple Spots; and the like were found in the
Subfiance of his Brain, of which all the Velfels were:
fill’d with black thick Blood.

( i6 )

* I *

The fifth Bodj*

Jaijues Audihert, aged about 35’, of a melancholy
Complexion, four Months after he had been cured
of the Plague, the Mark of which was a Bubo in the
fold of the right Groin, which came well to a Suppu-
ration, was attack’d afrefli with three Carbuncles ; one
in the middle of the Arm, and the other two in the
fore Arm. He had but little Fever, with fome fmall
Sicknefs at Stomach; but a Delirium coming of a
fudden, carried him off. Upon opening his Body, we
found his Heart of a prodigious Bignefs. The right
Auricle being of the breadth of five Inches ; and the
left of three. We found a little Impoftume upon the
Body of the Aoru. The Lungs were cover’d with li-
vid Spots, and the Liver appear’d gangrenous. The
Gall Bladder was of a very black Colour. The Duo*
denum the Ke6ium were inflam’d* We did not o-
.pen the Head.

The fixth Body. ^

P^enture Cajole, about 40 Years of Age, of a melan-
choly Temperament, dy’d without any outward Erup-
tion on the third Day, of a violent Fever, with a
Sleepinefs. We found in the Body the Meduiftimm
torn towards thjS upper part. The Pericardium was of
a livid Colour. The Heart larger than in its natural
State, by the fwelling of its Ventricles full of black
thick Blood, as in the other Carcafles. The Liver
alfo was ^ very large, and 'of a livid Colour, with a
Carbuncular Puflule on the fide of the, Gall Bladder ;
this was flll’d with very black f3ile

The

' ( i7 )

The feventh Bodp

Margueritte Bachaire, aged i8 Years, of a lively
vigorous Conflitution, having two Carbuncular Puftules
on the middle and infide of the Thigh, with a iharp
Pain in the Head, dy’d delirous. We found in her
Body the Coverings of the Brain of a blackiih red ,
The Cortical part of a livid Colour, and the Medul-
lary rprinkled with a few black Spots; The Heart
of a prodigious Size, full of a thick black Blood :
The Liver alfo very large, and the Gall Bladder very
full of a black and green Bile. There were feverali
livid Spots upon the Surface of the Inteftines.

The eighth Body,

’ , -1

Louife Bdingere^ 20 Years of Age, having a Bi4ho'^
in each fold of the Groin, died very fuddenly with-
out any dangerous Symptoms. We found in her-
Carcafs the Heart all cover’d with a livid Purple, muchi
larger than natural, fill’d with thick black Blood, ha--
ving a Polypus in each Ventricle. The Lungs were,
in their natural State. The Liver of a prodigious
Greatnefs ; and the Gall Bladder full of Bile, of ai
deep green Colour.

The ninth Body*

One nam’d Rampeau, a Peafanr, aged about lo Years,
of a (anguine robuft Conflitution, having had a Car-
buncular Parotide for the Space of eight Days, accom-.
pany’d with a burning Fever, was carried to the Hof-
pital the id o{ May, where he dy’d the uh. We found
the outward part of the left fide of the Lungs cover’d

widi

( )

with a livid Purple. The Heart was of double the
natural Bignefs, having fcarce any Blood in the Ven-
tricles, whofe Cavities were fill’d each with a large
Polypff!, that on the right fide having dilated the Au-
ricle to the breadth of four Inches. The Liver alfo
was larger than ordinary, and the Gall Bladder was
full of a black and green Bile.

The Experiments, and the opening of the Bodies
mentioned above, were made in the Hofpital at the
Mall, and in the Apothecary’s Shop of the Reverend
the Reformed Fathers of Marfetllei, during the Months
of Fdruary, March, dpril. May, in Company of MefT
Roberts and Riheaud^ Doctors of Phyfick.

7‘he following Experiments were made at Montpe-
lier, In the Hofpital of St. Eloy, during the
Months of September, Odlobcr, and Novem-
ber, in company with Monf Fizes, T>r, of
ficky ^ttd ^rofeffor of the Mathematic ksy and
Mejfieurs Duli and Morel, young Surgeons of
the faid Hofpital.

A Soldier, between the Age of lo and 15, of a
lively brisk Temper, being fick in the Hoipi-
tal of St. Eloy of an ordinary malignant Fever, died
about the 15th Day by a Defluxion upon his Breaft.
His Lungs were found very much blown up, fil-
ling all the Cavity of the Bread, and adhering to the
Pltura. Having remark’d that the Bile in the Gall-
Bladder was ot a bright Grafs green Colour, we ga-
ther’d it for the following Experiments.

This

( *9 )

This Bile, being mingled with four Ounces of warm
Water, was part injeded into the Jugular Vein of a
Dog, and a Comprefs foak’d in the reft of the Li-
quor was applied to the reft of the Wound. The
Creature thereupon appear’d heavy and lleepy, and
would neither eat nor drink ; the third Day he eat
and drank willingly. The Comprefs falling off the
fourth Day, the Wound was diminiflied one half, and
was healed by little and little, and 'the Dog grew per-
fectly well.

The eighth Experiment,

A Peafant of about yo or 6o Years old, of a me-
lancholy Temperament, had been near a Month in
1 the Hofpital with an ordinary malignant Fever, having
{alternatively a Delirium and a Sleepinefs. After his
1 Death, the Bile was found extreme thick, and black
/as Ink, and a great deal of it. We put about a
1 Drachm in a Wound made for that purpofe on the
(^outer part of the right Thigh of a Dog, thrufting
iin Pledgets dipt in the faid Bile diluted, into the
Wound. There did not appear any Change in the
IDog. We made him (wallow fome of the fame Bile,
^without lofing his Appetite; and feeing he was like
tto do well, we left the Wound to it felf, which heal’d
iin fifteen Days only by the Dog’s licking it.

The ninth Experiment,

Being willing to injeeft fome of the fame Bile into
tthe Crural Vein of another Dog, and the Syringe be-
iing ftopt by the too great Thicknefs of the (aid Bile,
ttbe Injedion could not be made ; wherefore we took
n Pledget foak’d in as much of this Bile diluted, as it

£ could

( ?o )

could take up, and apply’d it to a frefli Wound made
in the infide of the right Thigh. The Pledget was faf-
ten*d within the Skin by tome Needles. This Application
produced no confiderable Alteration in the Dog ; he nei-
ther appear’d fleepy nor ftomachlefs ; but lick’d his Sore
readily enough; and after the Pledget was fallen offj
the Wound heal’d as in the foregoing Experiment.

The tenth Experiment,

%

About a Drachm of the fame black Bile drawn
from the fame Carcafs, and mixed with warm Water,
was injedled into the Jugular Vein of another Dog.
The Creature was not incommoded thereby, but was
as brisk as before the fnjed:ion, only he appear’d ve-
ry thirfty and he drank with Greedinefs. The next Mor-
ning being willing to view the Wound, we found it
black and dry, and the Dog becoming furly, bit one
of the AfTiftants. The two Ligatures made for the
Injedtion were taken away without our feeing any
Blood to run out. We apply’d a DolTil, charged
with the ordinary Digeftive, and kept on by a Ban-
dage; and about four Hours after the Drelfing, we
found the Dog dead, having lived 23 Hours after the
Injedtion. Having opened him, we found that his
Heart beat Bill with Violence, and the beating cea-
fing, there was no Blood either in the Ventricles or
the Auricles. This Liquor crowded together in the
great Vellels, appear’d of a lively red, and very flu-
id, without any of thofe Concretions that we conftant*
ly, obferved in all the Bodies that dy*d of the Plague.
Here appeared neither internal nor external Marks of
the Plague...

- u.

Tht

I

I ( )

The eleventh Experiment,

An Inhabitant of Montpellier, aged about 30 or
very fat and robuft, of a fanguine Complexion, having
j had a Fall upon the Pavement, had received a fim-
F pie Wound on the upper part of his Forehead on the
right fide. This being negleded, brought on an E-
ryfipelas all over his Face, which was accompany’d
f with a Swelling of the left Parotide, This appear’d and
i difappear’d thrice from Morning till Night. The Erj^
fipelas came fuddenly on 5 he grew' delirous, and di-
ed after fifteen or twenty Days Illncfs, reckoning
from the Fall. In the opening of the Body, we found
I a quantity of Water between the Skull and the Du-
ra Mater, The Brain, which was firmer than ordina-
\ ry, was a little red, and part of the Pia Mater cov^
y ering the hinder part of that Fifcus, appeared in*
i flam’d There was about half a Septier. of Water of
a yellowifh Colour, Ibed in the Cavity of the Bread,
i The great right Lobe of the Lungs was a little hard
on the upper part. The Heart had a Polypofe Con*

‘ cretion in each Ventricle : We found likewife two
Pints of limpid Water got forth into the lower Belly.
All the Fat of bis Carcafs was yellow. The Liver
I appeared to us a little Cwell’d ; and the Gall Bladder
aimoft empty, not having above two Drachms of
yellow Bile in it. That Bile of this Carcafs, mixed
with two Ounces of warm Water, was injected into
the Crural Vein of a Dog. The Creature eat and
drank heartily after the Injedion, and did not appear
at all incommoded. The Wound bleeding much, w^e
were obliged to fill it with reftringent Powders, kept
in by a Pledget and a convenient Bandage. Twenty
four Hours after, the DreflTing was taken away, the

E 2 Wound

( )

Wound appeared black and dry. The Dog licking
if, it fuppurated the next Day, and afterwards be-
came red and well colour’d ; and the Wound was le(^
fen d one half in eight Days, during which time, the
Dog appeared in perfed Health.

The twelfth Experiment.

Eight Days after the foregoing Experiment, the
Dog, that was the Subject of it, was kill’d by about
half a Drachm of Powder of Hungarian P^itriof dif^
folvcd in a fpoonful of warm Water, which we in-
jeded into the Jugular Vein. The Creature dy’d on
the fpot, with univerfal Convulfions. His Heart was
found lull of grumous Blood reduced to a kind of
thick Pap, but without any Clods. The Bile of this
Dog was yellow and in little quantity. Not being able
to injed it into the Crural Vein of another Dog, be-
caufe the Vein was too (mall, we contented our
felves to dip two Compreflcs in this Bile, which we
apply’d and kept under his Skin, by two Wounds
made on purpofe in this fecond Dog: There arriv’d
no notable Change. We obferved in thefe two Dogs
no Marks either internal, or external, of the Plague.

Done Montpelier the ^th of December, 1721.

VI, the

( 3? )

, Vi. The way of proceeding in the Small Pox inocu-
lated in New England. Communicated by Hcn^
ry Newman, Efq 3 of the Middle Temple.

i make ufually a Couple Incifions in

V V Arms where wc make our IfftteSy but
I fomewhat larger than for them, fome times in one Arm,

I and one Leg,

z. Into thefc we put bits of Lsnt. (the patient at
^ the fame time turning his Face another way, and guar-
i ding his Noftrils) which have been dipt in Tome of
i the Variolous Matter taken in a Vial, from the Puf-?--
\ rules of one that has the Small Pox^ of the more lau-
I dable Sort, now turning upon him, and fo we cover
\ them with a Plainer of Diachylon.^

3. Yet we find the P'ariolous Matter fetched from-
I thofe, that have the inoculated Small Pox, altogether as

I agreeable and effedual as any. other. And fo we da *
f what is taken from them that liave the Confluent
k Sort, .

4. Within Four and Twenty Hours, we throw a-»
I way the Lint, and the Sores are drefled once or twice *
t every Four and Twenty Hours,, with . warmed Cabbage ^

Leaves.

y. The Patient continues to do all Things, as at
other times, only, he expofes not himfelf unto the In-
i juries of the Weather t if that be at all Tempef-
tuous.

6. About the Seventh Day the Patient feels the
V ufiial Symptoms of the Small Pox coming upon him.;

* and he is now managed as in an ordinary Putrid Fe-
\ ver. If he cannot hold up, he goes to Bed\ If his

Head 1

( H )

'Head Ach too much, we put the common Poultice
to his Feet/\f he be very Sick at the Stomachy
we give him a gentle Vomit^ yea, we commonly do
thefe Things almofl of Courfe, whether we find the Pa-
tient want them or no. And we reckon the fooner we
do thefe Things, the better. If the Fever be too high,
in fome Conftitutions, we Bleed a little : And finally,
to haflen the Eruption, we put on a Couple of Blifers*

7. On or about the Third Day from the Decumbi-
ture the Eruption begins. The Number of the Puf
tules is not alike in all, in fome they are a very few^
in others they amount to an Ehndred, yea, in many
they amount unto feveral Hundreds \ frequently unto
more than what the Accounts from the Levant fay
is ufual there.

8. The Eruptio'n being made, all Illnefs vanifhes;
except perhaps a little of the Vapours in tbofe that
are troubled with them 5 there is nothing more to do,
but to keep Warm, drink proper TeaV, eat Gruel,
Milk Pottage, Panada, Bread, Butter, and almoft any
thing equally Simple and Innocent.

9. Ordinarily the Patient fits up every Day, and
entertains his Friends, yea, ventures upon a Glafs of
Wine with them. If he be too Intent upon hard Read^
ing and Study, we take him off.

10. Sometimes, tho’ the Patient be on other Ac-

counts eafy enough, yet he cant Sleep for divers
Nights together. In this Cafe we do not give him
Anodynes or Opiates, becaufe we find. That they who
have taken thefe Things in the Small Pox are gene-
rally peflered with miferable Biles after their being
recovered. So we /<f/ them alone Sleep will come

of it felf, as their Strength is coming on.

IT. On the Seventh Day the Puflules ufually cOme
to their Maturity ; and [oon after this they go away,

as

( 35 )

as thofe of the Small Pox in the DiJlM Sort ufe
to do.

12. The Patient gets abroad quickly, and is mod
fenfibly Stronger^ and in better Health than he was
before. The Tranfplantation has been given to
men in Child-bed, Eight or Nine Days after their De-
livery; and they have got earlier out of their Child-
bed, and in better Circumdances, than ever in their
Lives. Thofe that have had ugly Ulcen long run-
ning upon them, have had them healed on, and by
this Tranfplantation. Some very feeble, crazy, Confump-
iive People, have upon this Tranfplantation^ grown
hearty and got rid of their former Maladies.

1 3. The Sores of the Incifton do feem to dry a little
in Three or Four Days of the Fcvcrifh Preparation for
Eruption, After this there is plentiful Difcharge af

j them. The difcharge may continue a little while af-

! ter the Patient is quite well on other Accounts ; But

I the Sores will foon enough dry up of themfelves ; -

I but the /4rfr, the better, as we think. If they happen to be

inflamed, or otherwife Troublefome, we prefently help *
them in the ways we do any Ordinary Sores,

'VII- A Letter from Dr, Nectlecon, Thyjician at:
Halifax in Yorkfliire, to T>r. 'Whitaker, concern-^
ing the Inoculation of the Small Pox.

SIR,

Having too often found with' no fmall Grief "
and Trouble, how little the AfTidance of Arc
cou’d avail in many Cafes of the Small Pox, I was in-
duced to try the Method of Infition or Inoculation,
which came fo well recommended by feverai Phyfi-

cians

( )

dans from Turkey^ and which had alfo been lately
pradifed in London* This I thought was fufficientto
juftify the Attempt, and what fiiccefs it has met with,
1 have here fent, according to your defire, a faithful
Account of, and of every Thing that has been done
or obferved here, relating to that Affair, which might
be worth your Notice

It was in December laft, That I firfl began to put
this Method in Ptadice, and finding it to lucceed be-
yond my Expedation in the firft inftance, I was en-
couraged to repeat it upon fome others, and after-
wards feveral, feeing with how much eafe thefe got
thro’ the Diflemper, were defirous to have the fame
done to themfelves or their Children ; fo that there
are mow upwards of Forty here, who have received
the Small Pox by Infition ; who are all got well thro’
the Diflemper, and are at this time thro’ Gods Blef-
fing in very good Health. Only one that was ino-
culated, did Die , of which 1 lhall give you a par-
ticular Relation hereafter, and refer it to your Impar-
tial Judgment, whether that ought to call any Ble-
mifh upon the Operation or no.

What was done by way of Preparation was chiefly
purging with Rhubarb for Children, and fometimes
Vomiting or Bleeding for grown Perfons ; and many
have had no Preparation at alL But I always found,
as far as I was able to judge, That thofe, whofe Bo-
dies were well prepared by fuch proper Methods as
their different Ages or Conflitutions did feem tore-
quire, had more favourable Symptoms than others in
like Orcumftances, where that was omitted. '

The Method, which I always took in the Opera-
tion, was to make two Incifions, one in the Arm and
-another in the oppofite Leg. It is not material as to
xailing the Diflemper, whether the Incifions be large

or

( 57 )

or (mail ; but I commonly found, that, when they
were made pretty large, the quantity of Matter dif-
charged afterwards at thofe Places was greater j and
the more plentiful that Difcharge, the more eafy the
reft of the Symptoms generally are, and they are
alfo by this means the beft fecured fromany inconveni-
ence, which might follow, after the Small Pox are
gone off.

Ac firft I colleded fbme of the Matter from the
Puftules of one, who had the Small Pox of the natu-
ral Sort, into a fliell or Vial, and infufed two or
three drops of it into the Wound; but finding it to
be very rroublefome and difficult to get any quanta
ly of the Matter, and obferving alfo, that the Icaft
imaginable will be fufficient for the Purpofe, I com-
monly take fmali Pledgets of Cotton, and ripping the
Puftules, when they are ripe, with the point of a Lan*
cet, roll the Pledgets over them, till they have im-
bibed fome of the Moifture. I put one of thefe up-
on each Wound, and cover it with any common Plaif-
fter till the next Day, when I commonly take away
both the Cotton and the Plaifter, leaving the Wound
to it felf, only covering it with a flight linnen Roller,
to defend it from the Air. I have fometimes rubb’d
the Pledget only once over the Wound, without
binding it on, which I found to anfwer the End as
well 5 and from fome other Obfervations I have made,
I have been furprized to fee the Small Pox produ-
ced this way, when I was very well aflured, the quan-
tity of Matter received into the Veflels, cou’d not
amount to the hundredth part of a Grain.

The Perfons inoculated have not been confin’d to
any Regimen, but only to be kept moderately warm;
and thole, w’ho were grown up, to live very tempe-
rate and regular, to keep their Minds eafy and com-

F pofed,

( 38 )

and to ufe proper means to drive away all Fear and
Concern. Some have been obliged from the time of
the Infition to abdain from Fieih and all ftrong Li-
quors ; but I found afterwards, that the Eruption did
nor proceed fo well, when they were obliged to live
too low. Perhaps in warmer Climates, where they
are not (b much accuftomed to live upon Fieih, fuch
Abftinence may be neceflary 5 but here I find it belt
to let them eat and drink as ufual, tho* fomething
more fparingly, till the Fever begins to rife 5 and then,
but nor before, we enjoin fuch a Regimen as is ufual
in like Cafes.

The fird Thing that occurr’d after the Infition, was
the Inflammation of the Wounds, which commonly hap-
pen’d about the fourth Day, when they began to ap-
pear very red round about, and to grow a little fore
and painful; in about two Days more they began to
diged and run. In feme they begin to run fooner,
and the quantity difebarged is much greater than in
others. 1 generally found, that in thofe who difehar-
ged mod this way, the Fever was more flight, and
the Small f’o.v fewer, tho’ I have known fome do very
well when thefe places have only appear’d very red,
bur have fcarcc run any thing at all, as ir ufually hap-
pens, when the Incifion is made, fo fuperncial as not to
cut thro’ the Skin.

About the feventh Day the Symptoms of the Fe-
ver begin ro come on, which are the very fame, that
we always cbferve in the Small Pox of the didind:
Kind, in the natural way. A quick Pulfe, great heat
and third, pain in the Head and Back ^ and about
the region of the Stomach, vomiting, dofednefs, Barr-
ings, and fometimes Convulfions. All were not fa-
zed with all thefe Symptoms, nor in the fame Degree
or Continuance} fome began on the feventh Day, and

continued

( ?9 )

continued ill without any Remiflion till after the ele-
venth ;many not till the eighth or ninth Day 5 and the Fe-
ver in ihele was mote moderate with great Intcrmiflions;
and feme have karce had any illnefs at all. During
all this time the Places of Incihon continued to be very
fore and fweli very much, fo as to appear very large
and deep, and to difeharge a great deal of Matter.

On the tenth Day the Small Pox moO: commonly
did appear, foroetimes cn the ninth, and fometimes
not till the ’ eleventh ; but I never found that any
difference of Age, Conftitution, or any other Caule
ever made them vary above one Day from the tenth.
The Number was very different, in fome not above
Ten or Twenty, moll frequently from Fifty to two
Hundred, and fome have had more than could well
be numbered ; but never of the confluent Sort. Their
Appearance was the fame with thofe of the diftinc^
Kind, they commonly came out very round and
florid, and many times rofe as large as any 1 have
obferved of the natural Sort, going off with a yel-
low Cruft or Scab as ufual ; tho’ it fometimes hap-
pens, efpccially when the Sores difeharge a very great
quantity of Matter, that they are both few in Num*
ber, and do not rife to any Bulk; but having made
their Appearance for Four or Five Days they waft
infenfibly away.

After the Small Pox come out, the Feverilh Symp*
toms gradually abate, and when the Eruption is com-
pleted, they ufually ceafe, without any fecond Fever,
or any farther trouble in any refpeeft.

While the Puftules were rifing, and for fome time
after they were gone, the Sores continued to fwel) and
to run very much, the longer they did fo the bet-
ter; but they never fail’d to heal up of themfeives
after a certain Time.

F 1

( 40 )

I very rarely faw Occafion for any Medicines in
the courfe of the Diftemper, only fbmetimes when
the Symptoms ran very high, 1 gave a gentle Ano-
dyne, to be repeated as Occafion ftiould require, and
once or twice I thought it neceflary to blifter, and
to ufe fuch Medicines as are found to be mod fervice-
able in the Small Pox of the natural fort. After the
Pudules are gone away, they have always been purged
twice or thrice, and fometimes let Blood, vvhich is
all that has been ufually done. But tho’ the] Pradice
may feem to be very eafy, yet it is an Affair of fuch
a Nature as to require the utmod Care, and I pre-
fume it will never be undertaken without the Advice
of Phyficians to dired a proper Method of Prepara-
tion before the Infition is made, as well as a jud Re-
gimen afterwards ; to watch every Symptom, and lend
Nature all proper affidance, when ever it fliall berequi-
fite. Where this is done, with Gods BlelTing, it will
feldom fail of being attended with happy fuccefs.

It has happen’d in one Indance or Two, That the
Symptoms in the Didemper have been worfe than u-
fual i and Tome few, jafter the Small Pox were gone
off, have been fubjed to other indifpofitions. Of all
which ■ I fhall give you a particular Account.

The fird that was Inoculated, a Boy about a Year
and half Old, began to be ill on the Eighth Day, and
had. a brisk Fever for two Days, then the Pudules
began to appear, which were but few in Number, and
rofe” very large. The Child was foon well, and con-
tinued To for about a Month, when being carryed out
and ' kept a long Time in the Cold, he fell into a
Feverifh diforder accompanied with a Cough, and
’ .. was

♦ ‘Thomas ‘Thorp* & Son of HaUifax.

( 41 )

was ill for Four or Five Days; after that time it
went off, and he has ever fince been in very good
Health.

The Second was a Girl two Years of Age, in a
Family where they had formerly Bury’d three Chil-
dren fuccelTively of the Small Pox, and this they fear'd
might undergo the fame Face. The Fever came on
about the feventh Day, and (lie continued very ill
till the tenth, on which Day about Noon flie had a
flrong convulfive Fir. In the Evening the Small Pox
appear’d, and tho’ flie had more in Number than u-
fual, yet llie grew well as foon as they were fully
come our, and has continued fo ever fince.

. f The Eighth and Ninth were in a Family where they
had four Children, none of whom had had the Small'
Pox. 1 was call’d to the Eldeft, who was feized in
the natural way with the mod malignant Sort I ever
law, attended with the word Symptoms that cou’d be,
infomuch that he died on the fourth Day, all full of
purple and livid fpors. The Parents were very de-
drous, that any means might be,^ ufed to preferve the
red; but here I was in great doubt and perplexity
what part to acd. I knew very well, That iff ihou'd
venture lo make the Indtion, whatever fliou’d happen
wou’d be charged upon that, and itrwas not impro-
bable, but fome of them might have already taken
the Infedion, in which Cafe it was uncertain what
the event might be. On the other Hand, if it was .

I omitted, I did very much fear they might all Dye,
Tuch .indances having been known, and the Contagion
'which w^as got amongd them, being of fuch a de-

drudive.

4^

*~^er. ^Turners Daughter, m
t Mr. John Symfon's Children*

(40

ftrudive Nature. Wherefore I was willing to run the
rifque of my Reputation, rather than that the Child-
ren fliou’d all periih. They were therefore all three
inoculated the Day before the elded died, af-
ter having told the Parents that I cou’d not anfvver
for the Succefs, in Cafe they had already cacch’d the
Infedion, which would be known if any of them
fell ill before the Seventh Day. According as we fear’d,
one of them began on the fecond Day, much after
the fame Manner with the Elded, and the Small Pox
appear’d on the third Day, or rather an univerfal
rednefs all over the Skin, interfperfed with many pur*
pie fpocs There were none of ihefe fpocs near the
Places of Inficion, which began to fwcli a little, as
uliial about the fourth Day, and the Small Pov did
rife a little more about thofe Places than elfewhere;
but Nature was too far opprefs’d with the violence
of the Didemper, and tho’ this Girl continued longer
than her Brother, and was not delirous as he was,
yet fhe died on the feventh Day. I did not reckon
this Child in the Number of thofe who received the
Didemper by Inoculation; for I thought there was
diffident Reafon to conclude, that die had taken the
Infedion before , but of this I mud leave you to
judge as you pleafe, I only give you a Relation of
Fads. The other two continued well till the eighth
Day, when they both fell ill together. The Small f^ox
came out on the tenth, of a very good Sort, tho’
more in Number than feme others had. and they
both got very eafily thro’ the Didemper without any
Tndirpofition fince. It was obfcrvable, that the Elder
of thefe Children, about the time cf the Eruption,
had many Spots appear’d on him of a deep red Co-
lour, very much like thofe of the ocher two Children,
which changed in them to Purples afterwards, which

the

( 41 )

the Mother was very much concern’d at, fearing they
wou’d prove the fame in this; but when the Small
Pox came out, thefe Spots grew gradually lefs, and at
laft quite difappear’d The other Child had been ve-
ry fubje(fi|to Convulfions for a long Time, whenve-
' ry young, and it was afflided with the fame very
much, from the Time that the Fever came on, till
the Small Fox appear’d.

The Twenty Seventh was a marry ’d Gentlewoman
aged about Twenty Six; who got very well thro’ the
Diftemper ; but about a Week after was feized with
a very great Coldnefs and Shivering, which were fol-
lowed by a burning Heat, with a great Pain and
Diforder in her Head, which continued for feveral
Hours. She had fome time ago an intermitting Fever,
which I took this to be a Paroxyfm of, and expected
its return ; bnt (he felt no more of it, and has ever
1 (ince continued in good Health.

Of her two Sons, who were both inoculated at the *
•fame’ Time, the Younger got thro’ the Diftemper with .
:a great deal of eafe, the Small Pox being few, and
I the Symptoms very flight; but the Elder a Boy about'
I five Years old, fared quite otherwife. The Symptoms <
before the Eruption were more than ufually fevere,
tefpecially the Vomiting; the Puftules appear’d at the ^
lufual Time, but more numerous than ordinary, and
'When the Eruption was finilli’d, the Fever did not •

1 ceafe, as it has done in every inflance but this : on
ithe fifth Day after he was feized, the fwelling of'
Ihis Face began, which was follow’d by a Pain and
ISwelling in his Throat, and a Salivation, which con-
rtinuing till the eleventh Day, were fucceedca by a

Swelling

^ Mrs. Breara of EJand»

( 44 )

Swelling in his Hands and Feet, the ufual Symptoms
of the diftin6t Sort when they ^ are very full ; and
tho’ there appear’d fomc little Signs of Malignicy, yet
with the Ufe of Bliffers and the milder Cordials and
Alcxipharmicks, the Puftules rqfe very large, and all
Things went on very well, ^fo that he got thro’ the
Didemper without any Danger, but with much more
Pain and Trouble than any of the refi: have endu-
red. After the Small Pox were gone ofT, we found a
hard Swelling upon his Shoulder, which difabled him
for fome time from moving his Arm ; but by the Ufe
oflbrne common Applications, that is entirely gone. In
this Family the only Child they had before thefe, died
of the Small Fox, of a very malignant fort, and this Boy
was of an ill habit, and has had many dangerous illneffes.

The Twenty Third, was a Girl about Nine
Months old ; in this Child, after flie was well of the
Small Pox, the Mother difcover’d that one of her
Thighs was a little fwell’d, which was painful to her
for fome time, and made her unwilling to move that
part ; there were alfo fome fmall Tumours in the
Groin; but thefe went ofF in a few Days, there only
remaining a hardnefs about the Knee, which alfo dif
appear’d in a fliort Time without coming to Suppu-
ration, and the Child is now in perfed: Health.

,fThe Thirty Seventh was a Girl fix Years of Age;
Ihc got very eafily thro’ the Diflemper ; hut before
the Small Fox were gone, we found a fmall Tumor
upon the Mufcles of the Loins, which ripen’d very
fpeedily, and was open’d and heal’d up in a very
Ihort time. Her Sifter, a young Woman about Eigh-
teen

** Mr. y/. Hanfon*s Daughter.

•1 Mr. John Haigh's Daughters.

1

( 45 )

teen had alfo a Swelling of the (ame Kind in her
Leg, but it lay fomething deepeti and gave her a great
deal of Pain for Three or Four Days 5 afterwards it
difcharged a great quantity of Matter, and was heal’d
without any farther Trouble.

All the reft, excepting chefe I have mentioned, got
very well thro’ the Diftemper without any manner of
Trouble, or Hazard, or any ill Confequence after-
ward. Whether thofe (light Indifpofitions, which Tome
have been fubjeeft to afterward, were owing to the In-
fition, I have not been able to judge; but I prefume
what they have endured in the Courfe of the Dif-
temper, and what has followed after, is not to be
put in the Ballance with what is undergone in the
common way, by thofe who are thought to come off
very well j and if this Method were more generally
pradfifed, *tis probable forae means wou’d be found
out, to prevent even chefe fubfequent diforders, which
are no more frequent, nor near fo bad, as thofe
which follow the natural Sort.

In two Inftances the Inoculation had no eftedb, the
Reafon of which, in one, * was becaufe the Child had
the Small Pox before, as the Parents did believe ; but the
Diftemper had been fo favourable, as to leave it doubt-
ful. t In the other, the Matter was taken, when the
Puftules were wither’d, and almoft gone, and that lit-
tle moifture which they contain’d, I fuppofe, had (oft
its Virtue; the Boy to whom it was made ufe of,
was no way affeded ; the Places of Incifion did not
at all inflame, or fw^ell as ufual, nor did any Puftules
appear ; but about a Month after, he was feized with

G the

Micb, Bland^s Daughter,
f William Clark's Son.

( 4<J )

the Diflemper in the ordinary way, and. did very
well.

Some of thole who have been inoculated, that are
grown up, have afterwards attended others in the Small
Pox, and it has often happen’d. that in Families where
feme Children have been inoculated, others have been
afterwards feized in the natural way, and they have
lain together in the fame bed all the Time; but we
have not yet found, that ever any had the Dillem'
per twice ; neither is there any Reafon to fuppofe it
polTible, there being no difference that can be obfer-
ved, betwixt the Natural and Artificial Sort, (if we
may be allow’d to call them lo) but only that in the
latter the Pullules are commonly fewer in Number,
and all the reft of the Symptoms are in the fame pro-
portion mote favourable. There is one Oblervatioa
which I have made, tho’ I wou’d not yet lay any great
ftrefs upon it, that in Families where any have been
inoculated, thole Who have been afterwards Icized, ne^
ver had an ill fort of Small PoXy but always recover-
ed very well.

Thus, Sir, I have given you a Ihort and plain Ac-
count of what has occurr’d to me concerning this Me-
thod of Inoculation: ’tis not any pains or care I have
taken in waiting this Letter, chat can recommend it,
for I have been folicitous about nothings but Truth,
my defjgn being only to give you- a Ihorc Hiftory of
the Diftemper raffed by Inoculation, fo far as 1 have
obferved it. The Number might perhaps have been
greater, if I wou’d have prefs’d it ; but I only took
fuch as defired it of themlelves, being cautious of
perfwading any Body to it, becaufe I had but little
Authority hereabouts to fupporc me ; tho’ I ought
to aciuiowJedge the kindnefs of- many- of my Friends,
who being convinced, that this Method would be

of

( 47 )

tieman, Dri Rkhardforiy did upon all OccaGonS vindi-
cate this Prad^ice. I know nor whether \ (hall haVe

feen fo much of it, that I ftiou’d never be afraid of
its fuccefs.

There is only one Thing more 1 am obliged to men-
tion, which I wou’d rather have pafs’d over in filence, and
that is the vigorous oppofition it has met with from
many honeft well meaning Perfons, who cou d not but
fancy, that it is an unlawful and unwarrantable Prac-
tice. They have gain’d a great Majority on their fide
here, at well as in other Places, where it has , been
pradifed. I only wifli, that, as they adl upon a prin-
ciple of Confcience, they wou’d have been lefs bufy
in raifing, or fpreading fal(e and groundlefs Reports,
whereby this Matter has been very much mifrepre-
fented, and many, entertaining a w^rong Notion of
it, have been detcrr’d - from making ufe of this Me-
thod for themfelves or their Children, who have fince
been unhappily taken off by the Small Pox^ But
when this Affair is fet in a true light, and found
to be always fafe and effedfual, I believe all the Ob-
jedions raifed againft it will fall of courfe. Itw^ou’d
ibe of the greateft: moment that the World fliou’d
I know what you think of it in Town, and how you
have found it to fucceed ; ’tis commonly objedcd
Ihere, that it is not approved of in London; but if
1 thole Gentlemen, who have julUy gain’d the greateft
IHonour and Reputation in our Profeffion, Ihou’d
Iby finding it fuccefsful fee caufe to declare publickly
I in its favour, that wou’d be the gieateft means to

an opportunity of doing much more this way at pfe-
fent, the Small* Pox beings rn a great meafure
from this Town and Countrey 5 but 1 have 'already

G X

forward

(48)

forward it in the Country, and to remove thofe un-
reaionable prejudices, which do generally prevail
againll a Method, which I believe has no where been
put in pradice with any other Aim,^ than to do Come
fervice to Mankind : for which Reafon I doubt not
but this ihort Narrative )vill be acceptable unto
you from, &c^

' ’ A

’ « r

4

Thomas Nettleton

Halifax, Apr. 3.
1711.

yiii. A

( 49 )

^VlII, ^ Letter from the fame Learned and Inge^
nious Gentleman^ concerning his farther ^rogrefs
in inoculating the Small Pox: To Dr. Jurin
R. S. Seer.

]N Anfwer to what you require frbfti me, as to
what has been farther done, I have only to add
tthat fince I writ to Dr. Whitaker, I have made the
Ifnfition upon about fifteen Perfons, who have all ‘ had
tthe Diftemper very favourably, and got thro* it with
aa great deal of eale. As nothing, uncommon or
eextraord inary did happen in any of, thefe Cafes,
iic will not be nccellary to trouble you with a par-
rricular Account of any of them : They were moft of
tthem at fomc diftance, the Small Pox being in a great
rmeafure gone from this Town and Neighbourhood.

lam very fenfible of the Favour done me by the
IRoyal Society, who were pleafed to take notice of
nmy Letter to Dr. Whitaker, which you had nothing to =
rmove you to befides a generous Dilpofition to encou-
[rage the fmalleft attempts towards any Thing, that m ly

I tend to publick. Ad vantage. I muft own that all the
information I had concerning this Affair, which I have
Happened to be engaged in, was entirely from the Phi^
liojofhical Tranfadtions. ’Tis now about fix Years, fince
tlhe Royal Society did communicate to the World fome
LLetters from two very confiderable Phyficians refi-
lling in Turkey, whofe good Senfe or integrity we had
no Reafon to call in queftion t thele Gentlemen did fo« .

folemnlyy

( 50 )

4emnly affure us, that the Method of Inoculation had
been for many Years pradtifed in thofe parts of the
World, with almoft con(!ant fuccefs. 1 had, as well
as all others who have been engaged in the Prad^ice,
with fufhcienc Sorrow and concern, been called to ma-
ny in the Small Pox, whofe Cafes were fo deplorablci
as to admit of no relief. And therefore I cou’d not
but be very thoughtful about this Method, which
promifed to carry Perfons thro’ that cruel Diftemper,
with fo much eafe and fafety. I was fo far from know-
ing that it was a Crime, that I always thought it
the Duty of our ProfelTion, to do whatever we could
to prelerve the Lives of thofe, who commit them-
felves to our Care; And f knew no Reafon, why
we ought nor, with all humble thankfulnefs to Al-
mighty God, to make ufe of any means, which his good
providence fliall bring to light conducing to that End.
This Matter, tho’ of fo great Importance, lying dor-
mant fo long after it was known, is, I prefume a fuffi-
cient proof, that none have been very forward to try
Experiments. But when we had the Account in the
Publick Papers, that it had by their Royal Highnefss
Command been done with fuccefs at London, I cou’d
not be fatisfied without trying it here. I was foont
convinced, that it would be of very great ufe; and the
more experience I have had of it fince, the more I
am confirm’d in the fame opinion. T believe all others,
who have feen any thing of this Prat^ice, are in the
fame fentiment, and there is no doubt, but in a few
Years the World will acknowledge the fervice, which
the Royal Society have done to Mankind, in firfi: re-
vealing to this part of Europe a Thing fo beneficial
as it will certainly proves for tho'fome few unfortunate
accidents may fometimes happen, yet thofe will be vt>
ry rare in comparifbn of the many fad and difaflrous

Events

r 51 )

Events, which this Diftemper has been, and ever will
be very fruitful of, while ic is left Co rage in its full
force and violence.

Sir, I doubt not buf when you have colleded a
fufficienc Number of Obfervations for it, you will
be able to demonftrace, That the Hazard in this Me-
thod is very inconfiderable, in proportion Co that in the
ordinary way by accidental Contagion, fo fmalb that
' it ought not to deter any Body from making ufe of ic.
In order to fatisfy my felf, what Proportion the Num- /
ber of thofc that die of the Small Pox, might bear to-
I the whole Number that is feized with the Diflem--
per, in the natural way, I have made fome enquiry
hereabouts, and I ihall take the freedom to tranfinic
the Accouirts to yotr, because t bdferc you may (te--

Ipend upon their being taken with fuflicient care and.
impartiality. In Hallifax, fincc the beginning of laft:
Winter, 276 have had the Small Pox, and out of that.
Number 43 have died. In Rochdale^ a fmall Neigh-
bouring Market Town, 177 have had the Diftemper,
and 38 have died. In Leeds 792. have had the Small'
Pox, and 189 have died,' It is to be noted, that in
I this Town, Small Pox have been more favourable

!*

1

3

I

i

I

4

/

>

1

I this Seafon t-han- utuaiy and in Leeds they have been 1
I more than ufually mortal; but upon a Medium in thcfe:
ithree Towns, there have died nearly 12 out of eve-
iry hundred, which, is above a fifth Part^ of all thac^
have been infeded in the natural way. I have in thefc '
^Accounts confined. my felf to the Limits of the Towns.
;The Numbers that have had the Small Pox in the Coun-
itry round about, is vaftly greater; but the Propor--
ition of thofe that die is much the fame. I have made .
:the enquiry in feveral Country Villages hereabouts,.

3n.i

( )

iri Tome 1 found the Proportion to be greater, in o-
thers lefs, but in the main it is nearly the fame.
I am, &c. ' ,

' r ' Thomas Nettleton,

i: ' ' : ' "

T * •

. ' flalffax ^ ’ • ■ v i ; , ^ :

June i6. 1722. * ' •

■»

F I K I S.

LO M D 0 I Printed for and jF. Irmp, Printers
to the Ropl Society, at the Prince s Arms in St. Paul's
Church Tar lyxx*

Kr*.

Philo SOPH. Tuans ACT.

C 53 ) Numb. J71.

PHIL

TRANSACTIONS.

t 4*0'

For the Months of Jprtland May, 1712.

II.

111.

, 7he CONTENTS.

\

A Table of ObferVations on the Variation of the
Compafsy in the Ethiopick Ocean, in the Tear
1721, and the begmnin^^ of the frefent Tearm
Sy Capt, Cornwall.

A Letter to Dr. Mead, Coll. Med. Lond. O*
Soc. Reg. Soc. concerning an Experiment^ where»
by it has been attempted to {hew the Faljity of the
common Opinion^ in relation to the Force of So-
dies in Motion, Ey Henry Pemberton, M, T>.
F. R. S.

[Hf. An Account of the Falls of the ^her Niagara
taken at Albany, 0<5lob. lo. i/it. from
Monjleur BoralTaw , a French Tiative of
Canada. the Flonourable Paul Dudley,
E/q-, F. R. S.

M IV. An

( 54 )

IV. A Letter front A^. Leeuwenhoek, F. % S,
concerning the Mufcular Fibres in federal Ani-
malsy and the Magnetic k. Quality acquired by
Irony upon ftanding for a long time in the fame
'f^ojture,

V. An Account of the manner of bending blanks in
His Majeftys lards at Deptford, by a
Sand-heat ^ Anyented by Captain Cumberland.
$jf Robert Cay, EJq:^

vr. A Letter from the ^yerend Mr, James Field,
S(eFlor of St. Johns in Antegoa, concerjiing
two Cafes of Wounds in the Stomachy to Mr. John
Dbuglas, Surgeon, F. R, S.

VII. A Letter from Mr, Atkinfon, Surgeon in
White-Chappel : Concerning an ImpoJlhumatL
on in the Stomach, To the fame.

VIII. Account of the Quantity of %efin in the Cor-
tex Eleutheriae. iBy Mr, John Brown, Chy^
tnijly F. R, S.

IX. An Account of a new Method of cutting for the
Stone, !8y John Douglas, Surgeon, F. R. S.

( 55 )

I. Ohferyations of th Variation on board the Royal
African ^acquety in 1721. ©/ Capt, Cornwall.

r

N. S. The Meridional Diftance is reckon’d
from SCr

Month

and

Year.

Latitudes

90 &' Sou

Auguft 24th
1721.

Ditto 26|ii° 12' S

Ditto 27 11° 34' S.

Ditto 28 12'^ 3?’

Ditfb 31! 1 5°

Septemb. 2d\i6’^ 26' S
Ditto 5th|i8° 4j' S
619° 47' s
I7[28o 43' S
22|3I° 33' s
27330 30'S
30*32° 40 S
October ij?, 132° 53' S
Ditto 3 32° ;o' S
Ditto 5 32° 28'
Ditto 6^31° 22'
Ditto 731° 11'

Sii'

Ditto

Ditto

Ditto

Ditto

Ditto

Meridian

Diftance.

Longifud. Variation.

9° 23' W

10° 46'
no 28'
o 31'
S IQO 53'
80 25-^
90 31/

9° 10'

10 7'
30

no
1 93
210
250
o=>

W

W

w

w

w
w

W io°

S3

S3

S32

41

29'

6'

18'

37.

W

E

1° 40

t

o 4

90 25' W

10° 50'

ii°4i'
no 43'

ir° 6'
8° 30'

90 39'

10

30

o

57'

i'

240 5;^'

30° o'
52'
37° 7'
]^37° 47'

£120

£120

E
E
E
E

W

W

W

w

w

E

E

E

E

E

E

E

E

E

20 13' E

W 40 30' E
W AO <70' E

E
E
E
E
E
E
E

0° ii' W
30 o'W
7041'

7" 47
8° 44

0° 77
no 20

40 30^
40 29'
40 27'
6° I o'
70 16'
6° 17'
8° 6'
r 53'

4° lo'

W
W

w
w
w j

Ohfer--

( 5^ )

Oh/eryations on the Coajl of Africa,

Mionth

and

Year.

O^ober

1721.

Ditto 19

Ditto 21

Ditto 25

November
Ditto 7

Ditto 29

Latitudes Longitud.j Variation.

26=» >i"f S.

19’

17"

13°

10'

8"

5=>

41' S

4' s
56' s

SI S
19' s
o' SI

35“’ 35'E4I® 4i'Ei4°3o'W

in Caben da-Bay.

120 22
14° 29'
14° 48'

13° 11'
150 14

14033'

Fr om Cabenda to London, Merid. Diftance from thence.

December $th.
Ditto 14
Ditto 20
January 1

1724-.

Ditto (

3^ 25' Sji I'" 3b' "W
3° 30' S,2io i8'W
00 30' 8,30° 41' w
103 50' N'39’ 8' W

21'

w

no 32' W

w

w

10

1° 1' E

w

w

1° 41' ’E

II. A

( 5T )

1] , A Letter to 2)r. Meadj ColLMeJ. Lond. ^ Soc,
^eg. S. concerning an Experhnentj whereby it
has been attempted to [hew the faljity of the
‘ cotmnon Opinion, in relation to the force of bo-
dies in Motion^ !By Henry Pemberton, M 2).
R. S. S.

4

■ If ' ■ ' 1 'i • ; ■

s / R, • ^

PErufing the Learned Polems's Trac^ de CaftelUs*
you were pleafed to fend me ; I have found in it
)ti feveral curious Experiments, among which I reckon that
:• of letting Globes of equal Magnitude, but of different
weights, fall upon a yielding Subftance, as Tallow,

’ Wax, Clay or the like, from heights reciprocally pro-
portional to the weights of the Globes. This Experi-
ment, engaged in particular my Attention, as it is
: brought with defign to overturn one of the firfl: Princi-

Iples eftablilh’d in Natural Philofophy. And the Know-
ledge I have of your great Efteem for that part of
Science, emboldens me to trouble you with my
Thoughts upon this Experiment; for ! cannot by any
means admit of the Dedud:ion that is drawn from
{ thence, that becaufe the Globes make in this Experi-
J ment equal Impreffions in the yielding Subffance, there-
: fore they ftrike upon it with equal force.* whereby it is

) i attempted to prove the Affertion of Mr. that

^ I the force of the fame Body in defcending is proportional
j I to the height from whence it falls; or, in all Motion,
proportional to the Square of the Velocity, and not
' proportional to the Velocity it felf, as is commonly
thought. On the contrary, 1 think this very Experi-

N ment

( 58 )

ment proves the great unreafonabienefs of Mr, Leibnitz s
Notion.

I am furpriz’d, that fo careful a Writer as PoUnus
appears to be, from the accuracy wherewith he deli-
vers his Experiments, ihould not rather fufpcd his rea*
ioningin an intricate Cafe, than thus contradi(5t a Prin-
ciple in Philofophy,v that has been diredly prov’d by a
multitude o.f Experiments, in particular by thofe
Sir l^aac Nervton recommends for that purpofe (a) ; and
that is moreover abundantly cftablilli'd by its exadt
Agreement with all Obfervations ; as being the Princi-
ple upon which all appearances, hitherto obferved in
the motion of Bodies, are accounted for by juft and
undeniable Arguments^ and w’e fliall find on Inquiry,
that the prefent Cafe comes alfb under the fame
Rule.

As the ufc of Experiments in Natural Philofophy is
to difcover the Caufes of Things, by exhibiting more
fimple Eftedfs of thofe Caufes, than occur in the ordi-
nary courfe of Nature; fo for this end it is necefl'a-
ry, that our Argumentation upon Experiments be per-
fedily juft, otherwife they may lead us into Errors.
The firft' thing neceftary for making right Dedudfions
from an Experiment, is to determine the proper u;e
thereof , which I think in this before us is not rightly
underftood. Certainly this Experiment of Poiems is
much more fit to inform us of the Law, by which thefe
yielding Subftances refift the motion of Bodies ftriking
upon them, than to Ihew the forces, with which Bodies
ftrike ; for whatever' thofe forces be, the Effedfs muft
be very different, according to the Difference there
may be in the Rule obferved by fuch refiftance.

(<i) Prinelp. Philol, Nat. />. jp.

Now

C 59 )

Now this Experiment Ihews, that if two Globes in
Motion bear againft equal Portions of the yielding
Subfiance, the Oppofition, that Subfiance .makes to
the Motion of the Globes, will be the fame in both,
i| however difFerenc the Velocities be, with which they
I move. This I fliall. demonflrate as follows.

Let A and B be two Globes, equal in Magnitude,
but of different Weights, which are equally immerfed
t into a yielding Subfiance, Suppofe the Velocities, with
r which they move in their prefent Situation, to be reci-

Iprocally in the Subduplicate rath of the Weights of
the Globes ; that is, let the ratio of the Weight of the
Globe A to the Weight of the Globe ,5, be Duplicate of

I the ratio of the Velocity of the Globe to the Velo-
city of the Globe A, Since therefore the ratio of the
quantity of Motion in the Globe A^ or of the force
with which it moves, to the quantity of Motion in the
Globe B, or to the force with which that Globe moves,
is compounded of the ratio of the Weight of the Globe
A^ to the Weight of the Globe and of the ratio of
the Velocity of the Globe A<^ to the Velocity of the

[other Globe B^ the force, with which the Globe A
moves, is to the force, with which the Globe B moves,
as the Velocity of this Globed, to the Velocity of the
other Globe A. 13ut if the fame Oppofition be made
i) to the' Motion of the Globes, when they bear upon
; equal Portions of the yielding Subfiance, the Effedf of
that Oppofition, while the Globes enter farther into the
Subfiance by equal Spaces, will be proportional to the
^ time, in which the Globes are moving thofe Spaces,
or in which the Oppofition is made, if we confider
thofe Spaces while nafcenc or in their firfl Origine;
the Effcd: therefore of this Oppofition will be recipro-
cally proportional to the Velocity of each Globe**

I -namely, the momentaneous lofs of force in the Globe
! . N z A

I

( )

A will be to- the momentaneous lofs of force in- the
Globe i5, as the 'Velocity of the Globe B, to the Velo-
city of the Globe A ; and the whole force of the Globe
A has been found to bear the fame ratio to the whole
force of the Globe B ; confequently thefe Globes,
while they penetrate equal Spaces into the Subftance,
lofe parts of their force, which bear the fame pro-
portion to the whole: and therefore, if their Velo-
cities beat any time reciprocally in the Subduplicate
ratio of their Weights, fb that the forces or degrees of
Motion, with which they move, be reciprocally pro-
portional to their Velocities, the forces, with which
they prefs into the yielding Subftance, at equal In-
dentures made in the Subftance, will continue in the
fame Proportion j and therefore upon the Theory of
Refiftance here fuppofed, when the whole Force and
Motion of both thefe Globes is entirely lofl, they
will be plunged into the Subfiance at equal Depths.

Now whereas in the Experiment of Polcrms, the
Globes, falling from Heights reciprocally proportional
to their Weights, flrike upon the yielding Subfiance
with Velocities reciprocally in the Subduplicate pro-
portion of their Weights, and the Effed is in all
Cafes found to be, what is here deduced from the
Theory of Refiftance, J have propofed ; it is a fuf-
ficient Confirmation of the Truth of this Theory.

Only here. Sir, I ought to obferve to you. That I have
fuppofed the Globes to beftopt by the whole Refiftance
of the Subfiance, they move againft ; although in ftrid-
nefs they are ftopt only by the excefs of that Refi-
ftance above the Atftion of Gravity upon them. But
I have negleded the Confideration of the Adion of
Gravity, that being but fmall in Proportion to the
Refiftance, as will appear from the Globes being
much more fpeedily ftopt by this Refiftance, than

( <5 i )

they would be by the Adion of Gravity, if its force
were applied upwards 5 for by that force alone, the
Globes woutd not be ftopt, till they had mea^fured
Spaces equal to the heights above thercfifting Subftance,
from whence they fell ; which heights bear a great Pro-
portion to the depths, the Globes in this Experiment
are immerfed into the yielding Subftance, as I have
found upon trial

Thus, if I miftake not, may be removed the Difficul-
ty attending this Experiment. But as Mr. Leihitzs
Opinion is deduced from it by Means of this Axiom,
that Effeds are proportional to their Caufes ; fo that
here the Effeds being thought the fame, the Caufes
are concluded to be lo likewife ; it will not be a-
mifs to mention in this place an Experiment, where
'this Axiom may be more jnftly applied, than it can be in
our prefent cafe, from which Experiment the received
Opinion may be proved. This Experiment is men-
1 tioned by Polenus from Merfenms^ though tried by him
fomewhat rudely; but has been often fince made in
I the following manner. To one end of the Beam of
.a Ballance is hung a Weight, and from a proper
1 height is let fall upon the other extremity of the
Beam another Weight, which by Briking thereon
ihall raife the end, to which the Weight is fufpended,
to fuch a height, as is juft fufficient to fet free a cer-
itain Spring, if then a different Weight be bung in
I the room of the former; the height, from whence the
' fallingWeight muft defcend,in order to raife the Extremi-
ity'of the Ballance, to which this otherWeight is fufpend-
>ed, to the fame height as before, that is, high enough
I to fet the forementioned Spring at liberty, is found to
Ibe fuch, that the Velocity, with which the falling
Weight ftrikes upon the Ballance, in this latter Cafe,
iwill be to its former Velocity, as the latter Weight

( 6z )

to the former, (a) except only that, agreeably to what
Merjenms himlelf remarked, when the Weight dei’cends
from great heights, an Altitude fomewhat greater than
this Rule implies is required to raife the other Weight
as much as is defired. But whether the bending of the
Arm cf the Ballancc, when aded upon with a great
force, or whether any increafe of Fridion in this Cafe,
occafion the Irregularity here mentioned, we need not
ftridly enquire ; for this Irregularity is yet lefs recon-
cileable with the new Opinion, than the regular
Effeds of the Experiment. Hence therefore we may
fee, that the very Method of reafbning, w'hich being
applied erroneoufly, is fuppofed to prove Mr. Leibnitz^
Sentiment concerning the force of Bodies in Motion,
will, when jufHy ufed, confirm the other Opinion in
relation to that Matter.

But as I havealTerted in the beginning of this Letter,
that the very Experiment of PoUms is not only recon-
cileable to the common Dodrine of Motion, as I have
now demonflraced ; but even that it does it felf make
manifefl the great unreafonablenefs, if not the abfolute
Abfurdity, of Mr. Leibnitz's Opinion ; it remains that
I briefly make proof of this.

If two Globes A and R, of equal Magnitude but
of different Weights, ftriking on a yielding Subflance
with equal force, in every Cafe lofe all their Moti-
on at equal Depths, it is neceflary that at all times,
during their Motion, they lofe equal Degrees of force,

• when they bear upon equal Portions of the Subflance,
in entring equal Spaces into the Subflance. This will
be eafily feen from what has before been faid. Now
W’hereas Mr. Leibnitz fuppofes the powder of Gravity to

{a) ’J Gravefande Phyfic. Mlem. Tom. I. p. 59.

give

( ^3 )

give to the fame falling Body Degrees of force pro-
portional to the height from whence it falls ; accord-
ing to his Opinion, by the power of Gravity, equal
Degrees of force are added in the defcenc of the
fame Body through equal Spaces , and in different
Bodies defcending through equal Spaces, the Degrees
of force added will be as the quantity of Matter, or as
the weight of each Body. Therefore while the Globes
A and B penetrate equal nafcent Spaces into the yield-
ing Subfiance, by the Adion of Gravity, were nor that
Adion overcome by the Refiflance of that Siibflance,
additional Degrees of force would be communicated
in fuch proportion, that the force added to the Globe
A^ would be to the force added to the Globe as
the weight of the Globe A, to the weight of the
Globe B, or in the Duplicate ratio of the Velocity
of the Globe B, to the Velocity of the’ Globe A.
But fince the Globes lofe the fame Degrees of force
in entring equal Nafcent Spaces into the yielding Sub-
fiance, the Efted: of the Oppofition made by this
Subfiance to the Motion of the Globes, during the
time of their paffing through fuch Nafcent Spaces, will
be both the taking from them that fame Degree
of force, and moreover the additional force, which
would otherwife have been given them by their
own Gravity. But farther, the Oppolitioni made to
the motion of the Globe to the Oppofition
made to the motion of the Globe B, will be in the
ratio compounded of the ratio of the Effed of the
Oppoftion, the Subfiance makes to the motion of
the Globe to the Effed of the Oppofition, the Sub-
fiance makes to the motion of the Globe B, and of
the ratio of the Time, in which the Oppofition is
made againfl the latter Globe, to the Time in which
it is made againfl the former ; which latter r<itio is the .

fame

( ^4 )

fame with the ratio of the Velocity of the Globe to
the Velocity of the Globe B. But fmceit is (hewn, that
the EfTecff of the Oppofition made by the yielding Sub*
(lance to chefe Globes is two-fold, and that one part
of the Effect: of the Oppofition made to the motion of
the Globe A, is equal to one part of the EfFedf of the
Oppofition made to the motion of the Globe B; and
that another part of the Effecii of the Oppofition
made to the motion of the Globe A^ to another pare
of the EfFedl of the Oppofition made to the motion
of the Globe B, is in the Duplicate - ratio of the Velo-
city of the Globe B^ to the Velocity of the Globe

A. One part of the Oppofition it felf made to the
^motion of the Globe A, will be to one part of the
Oppofition againfl the motion of the Globe B, as the
Velocity of the Globed, to the Velocity of the Globe

B, and another part of the Oppofition to the motion of
the Globe A, to another part of the Oppofition to the
motion of the Globe B, will be as the Velocity of the
Globe B, to the Velocity of the Globe A. So that
•when the Globes bear upon equal Portions of the yield-
ing Subffance, the Oppofition to their Motion will be
in part as the Velocity of the Globes, and in part
reciprocally as their Velocity. Hence, becaule the re-
fifling Subfiance is of an uniform Texture, the Oppo-
fition to the Motion of either of the Globes in its pre-
fent Situation, and when moving with its prefent Velo-
city, will be to the Oppofition it would meet wit h in
the fame Situation, if it moved with any other Veloci-
ty, partly as the prefent Velocity to that other Velo-
city, and partly as that other Velocity to the prefent.
Ikit by that part of the Oppofition made againfi the

■ motion of the Globe, vvhich is direifily as the Velcci-

■ ty, the Globe can never be' wholly fiopt ; for upon
the flopping of the Globe, that part of the Oppofi-
tion

( )

don to its Motion will likewife totally ceafe. and con-
fequently the Globe’s Weight will catry it further
down, unlefs the other part of the Opposition againil
its Motion prevent it. But T (ay again, neither can
this latter part of the Cppofition made to its Motion
be ever great enough to flop the Globe ; for the
Degree of this Oppofttion being reciprocally as the
Velocity of the Globe, when the motion of the
Globe is wholly taken away, it will become infinite-
ly greater, than at any time, while the Globe is in
Motion; fo that when the Globe fhould be ftopt by
this part of the Oppofition made to its Motion, the
Oppofition to the Globe’s Motion will become infinite-
ly great h infomuch, that no Degree of force whatever
could be able to impel the Globe further into the Sub-
(lance, but this can never come to pafs. Befides, it
is not neceffary to apply any fuch refined Argument
againft this part of the Refinance ; it would be alone
fufficient to confider, how unreafonable a Suppofition
it is, that a Refiflance Ibould increafe, when the Ve-
locity of the refifted Body decreafes.

Thus may this Experiment be made ufe of to inva-
lidate that very Opinion it is brought to fupport.
But another ufe may likewife be made thereof: For it
will ferve to illuflrate what the great Sir /fjtac Newton
has more than once hinted, that the Refiflance of
Fluids, which arifes from the Tenacity of their Parts,
decreafes in a lets Proportion than the Velocity of the
refifled Body decreafes (a); for as this Refiflance bears
a great Analogy to the Refiflance of the yielding Sub-
fiances we have been here treating of, fb we have
found, that the Refiflance of thef' Subflances does

{a) Vid, Philof. Nat. Princip. Math. Prop. 52. lib, 2. in Schol.
Opticks. Qu. 28. p. 33P, 340.

O not

( ^<5 )

not much depend upon the Velocity of the Body,
againft which the Refinance is applied.

And thus, Sir, we may fee how all Experience con-
fpires in confirming and fetting forth that flupendi-
ous force of realbning, which has enabled our great
Philofopher mod furprizingly to fearch out, and di*
ftinguifli the Springs of Natural Operations; a Work
infinitely more difficult to accomplifli than even the
great Improvements he has made in pure Mathematicks,
which were previoufly neceflary inorder to hisfucceeding
in his Searches after the Knowledge of Nature ; for in
this lad Purfuit he has given Proof, not only of a more
unbounded Invention, than is required in the fubriled
Geometrical Speculations ; but has alfo there difcpvered
the greated Difcernment, and mod confummate Judg-
ment 5 fince in his Philofophical Writings, he has
never been once impofed on by an Hypothefis, nor
by any other of the various Fallacies, which my Lord
Bacon in his Novum Organon^ has reckon’d up as the
Caufes, that had hindred the Improvement of the
true Philofophy.

But here I ffiall put an end to this Jong Letter ; for
the Freedom of which, I know, I need make no
Apology to you, Sir, of whole great Candour I have
for fome Years pad been a condant Witnefs ; and as
I have frequently admired, how amidd the vad Em-
ployments of your Profeffion, you Ihould find time to
purfue with fo great Succefs fuch various forts of
Learning ; fo I have as often been delighted to ob*
ferve with what Benignity you receive thofe, who have
made any the lead part of ufeful Knowledge their
Study.

/ anty Sir, 6fc.

( 67 )

POST-SCR IPX

A Bout a Week after I bad fent you the Letter*
containing my Obfervations on Poknus's Experi-
ment, I had the good Fortune to hear an excellent and
learned Friend of yours, to whom you had been
plealed to fliew my Letter, give a very curious and
weighty Argument to confirm Sir Ifaac Nemoris. Senti-
ment in relation to the Refinance of Fluids, which I
had deduced from the above mentioned Experiment ;
and as this very much pleafed me, 1 lliall here endea-
vour to fend you an Account of it in the following
manner .* -

Suppofe pieces of fine Silk, or the like thin Sub-
dance, extended in Parallel Planes, and fixt at fmall
Didances from each other. Suppofe then a Globe to
drike perpendicularly againd the middle of the outer-
mod of the Silks, and by breaking through them to
lofe part of its Motion. If the pieces of Silk be of
equal Strength, the fame Degree of force will be re^
quired to break each of them ; but the Time, in which
each piece of Silk refids, will be fo much fliorter as
the Globe is fwifter ; and the lofs of Motion in the
Globe confequent upon its breaking through each Silk,
and furmounting the Refidance thereof, will be pro-
portional to the Time, in which the Silk eppofes it-
felf to the Globe’s Motion ; infomuch that the Globe
by the Refidance of any one piece of Silk will lofe
fo much lefs of its Motion as it is fwifter. But on the
other Hand, by how much fwifter the Globe moves,

Ox fo

{ <58 )

fo many more of the Silks it will break through in a
given Space of Time*, whence the number of the
Silks, which oppofe themfelves to the Motion of the
Globe in a given Time, being reciprocally proportio-
nal to the Effedt of each Silk upon the Globe, the
Refinance made to the Globe by thefe Silks, or the
lofs of Motion, the Globe undergoes by them in a
given Time, will be always the fame.

Now if the Tenacity of the Parts of Fluids ob.'
ferves the fame Rule as the Cohefion of the Parts of
thefe Silks, namely. That a certain Degree of force
is required to feparatc and difunite the adhering
Particles, the Refinance arifing from the Tenacity of
Fluids mufl: obferve the fame Rule as the Refiftance of
the Silks, and therefore in a given Time the lofs of
Motion, a Body undergoes in a Fluid by the Tenacity
of its Parts, will in all Degrees of Velocity be the
fame ; or in fewer Words, that part of the Refiflance
of Fluids, which arifes from the Cohefion, of theic
Parts, will be Uniform.

HI. Jn

( h )

III. An Account of the Falls of the ^her Niagara,
taken at Albany, 0(5lob. lo. i/is. from
Monfieur Boralfaw , a French Flatiye of
Canada, ©y the Honourable Paul Dudley,
F. R. S>

The Falls of t^iagira are a mighty Ledge or Preci-
pice of folid Rock, that lies acrofs the whole
breadth of the River (a little before it empties it felf'
into, or forms the Lake Ontario) and very deep;

Monfieur Boraffaw never meafur’d the Falls himfelfi
though he has been there at feven different Times :
But what he fays is. That,

This laft Spring the Governour of Canada^ Mon-
fieur f^Audreil, ordered his own Son, with three other
Officers, vfz. Meflieurs Longue I[le, St. Fille^ and
Lauhineau to Survey Niagara, and take the exad:
height of the Catarac3', which they accordingly did
with a Stone of half an hundred Weight, and a large
Cod-line, and found it upon a Perpendicular no more
than twenty fix Fathom; his W'ords were Fingt ^
Six Bras.

This differs very much from the Account Fatlier
Tdemepin has given the World of that Catarad, for he^
makes it an hundred Fathom ; and our Modern Maps ,
from him, as I fuppofe, mark it at fix hundred Feet ; .
but I believe Hciamftn never meafured it, and there:
is no gueffing at fuch Things..

When?

( 70 )

When r ohjeded Hennepin\ Account of thofe Falls, to
Monfieur Borajfawy he replied ^ That accordingly every-
Body had depended upon it as right until the late
Survey. Upon further Difcourfe he acknowledged,
That below the Catarad for a great way, there were
numbers of (mall Ledges, or Stairs crofs the River,
that lower’d it flill more and more, till you come to a
Level ; fo that if all the Defeents be put together, he
does not know but the Difference of the Water above
the Falls, and the Level below, may come up to
Father Hennepin^ but the ftridt and proper Cataratft
upon a perpendicular, is no more than twenty fix Fa-
thom, or an hundred and fifty fix Foot, which yet
is a prodigious Thing, and what the World I fuppofe
cannot parallel, confidering the greatnefs of the River,
for it is near a Quarter of an BngU^ Mile broad, and
very deep Water.

Several other Things Monfieur Boraff iw fet me right
in, as to the Falls of Miagara. Particularly it has been
faid. That the Catarad: makes fuch a prodigious noife,
that People can’t hear one another fpeak, at fome
Miles difiance, whereas he affirms, you may converfe
together cloie by.

1 have alfo heard it pofitively aflerted, That the
Shoot of the River, when it comes to the Precipice,
was with fuch a mighty force, that Men and Horfe
might march under the Body of the River without
being wet. This alfo he utterly denies, and fays the
Water lalis in a manner right down.

Wdiat he obferv’d farther to me was,

That th:; Mifi or Shower fhis Word was La BrumO
which the fails make, is fo extraordinary, as to be

ieen

( 7« )

feen at five Leagues di fiance, and rifes as high
as the common Clouds. In this Brume or Cloud,
when the Sun fiiines, you have always a glorious Rain-
bow.

Of the River it felf, which is there called the River
Wagard, he tells me it is much narrower at the Falls,
than either above or below, and that from below
there is no coming nearer the Falls by Water, than
about fix EnglilJ) Miles, the Torrent is lb rapid, and
withal fuch terrible Whirl-pools.

He confirms Father Hennepin s and Mr. K dings Ac-
count of the large Trouts of thofe Lakes, and folemn-
ly affirmed there was one taken lately, that weighed
eighty fix Pounds; which 1 am the rather inclined to
believe upon, the general Rule that Fifii are according
to their Waters. To confirm which, a very worthy
Minifier, now alive in Idew England, affirmed to me;
That while he was a Prifoncr at Mon-real, in Canada
River, he faw a Pike brought up one Day from the
River to the Governours Houfe, and carried upon a
Pole between two Men, that meafured Five Foot, and
' Ten Inches long, and proportionably large.

I my felf this laft Summer, faw a Cataract, three
] Leagues above AUran), in the Province of I^evo Tork,
I upon. ScheneBada'^vitt called the Cohes, which they

I count much of there ; and yet that is not above 40 or 50
IFoot perpendicular. From thefe Fall? alfb there riles
:a mifiy Cloud, which dcfcends like fmali Rain, thar,
iwhen the Sun fhines, gives a handfome fmali Rain-
Ibow that moves as you move, according to the An-
^gle of Vifion. The River at the Cohoes is to 40 or
<50 Rods broad, but then it is> ery fl^ailow Water, for

II was fold thar in a dry Time, the whole River runs
iin a Channel of not more than fifteen Foot wide.

In

( r* )

In my Journey to Albany, zo Miles to the EaAward
of Hudfons River, near the middle of a long riling
Hill, I met with a brisk noify Brook fufficient to
ferve a Water-Mill, and having obferved nothing of it
at the beginning of the Hill, I turned about and fol-
lowed the Courfe of the Brook, till at length I found
it come to an End, being Abforb’d, and finking into the
Ground, either palTing through Subterraneous Paflages,
or foaked up with the Sand ; and tho’ it be common
in other Parts of the World for Brooks and even
Rivers thus to be loft ; yet this is the firft of the Sort,
1 have heard of, or met with in this Country.

T. Dudley.

IV. A Letter from Mr, Leeuwenhoeck, K % Si
concerning the Mufcular Fibres in feVeral Ani-
77ials, and the Magnetick, Quality acquired by
IroHy upon /landing for a long time in the fame

Tojlure, I

Delft, Apr. lift, 172a. f

ft

To the llluftrkus Royal Society. |

Honoured Sirs,

IN a Letter I receiv’d fometime ago from one of bi
your Secretaries, among many Expreffions of your 11
kind Acceptance of my Labours, lamrequefted by that I

Gentle* 8

I

( 71 )

Gentleman in the Name of the Roy^l Society^ to en-
deavour by repeated Obfervations to confirm (bme of
my late Difcoveries, and to fet them in To clear a Light,
as to (lop the Mouths of the mod incredulous Gain-
fayers.

With regard to this, I beg leave to obferve to you,
that I examine a great many different SubjetSls, of
which I commit no account to Paper, bccaufe the Re-
fult is the fame with what I have already deferibed;
and that whenever 1 make any Difeovery, which I ap-
prehend will not eafily meet with Credit, I fuffer the
Objetd to lie before the Microfeope X)ay after Day,
and fometimes for whole Years together, till it is eaten
up by Infeeds. This I do with defign to let it be feen
by as many different Perfons as poOible.

ft is not above eight Days ago, that 1 was viewing
a Portion of the Fldh of a fat Ox, as like wife the
Mufcular Fibres of a Cod - Fifii, and of a Pearch,
which Fibres being cut tranfverny, 1 could fee in them
very diftindiy the great number of fmall VefTels, that
ran along the length of each Fibre. And I have feea
the fame this Month of A^ril^ in the Mufcular Fibres
taken from the hinder Leg of a Moufe, and cut thro’
iranfvcrfly.

I have at this time (landing before a Microfeope,
fome of the Mufcular Fibres of a fat Ox, with thofe of
a Moufe lying befide them, in order to have as many
Eye-W’itnefTes as poflTible, of their being of the fame
fize in thefe two Animals, and 1 ufc the fame Method
in fuch other of my Obfervations, as are likely to ap-
pear incredible to other Perfons.

In fpeaking formerly of the fmall FihrtlU^ that help
to fufpend the TeQicles of a Ram, I forgot to men-
tion, that each of thefe confifls of exceeding fmall
VefTels, which run parallel to its length.

P

I have

( 74 )

Thave likewife at this time (landing before a Micro-
fcope, a (mall Portion of the Bone of an Ox» in which
may evidently be (een the VelTels, which proceed
from the Bone, and compofe what is called the Perio-'
fteum, as likewife the Openings of thefe Veflels; the
reafon of whofe appearing (b clearly is, as 1 imagine,
that they are filled with the Medullary Oil,

I take this Opportunity of informing you, that the
Iron Crofs, which is fuppofed to have flood upon the
Steeple of the Nevv-Church here about two hundred
Years, having been lately taken down to be repair’d,
1 was informed by a certain Foreign Gentleman, that a
piece of Iron, that has flood for a long time in one
Situation, would thereby acquire a Magnetick duality.
Upon which I defir’d a Workman to procure me a piece
of that Crofs, who accordingly brought me a bit of it,
of about a Span long, and a quarter of an Irch thick,
which I apply’d both to a working Needle, and the
Needle of the Compafs, but without any EfFe<5t upon
one or the other.

Some time after, the fame Workman brought me
Ibme other pieces, looking like rufly Iron, which he
had broken off from the bottom of the Crofs, where
it had been faflen’d by four crofs pieces bound
down with Iron, to an ered piece of Timber nine
Inches fquare, and cover’d with Lead in fuch a man-
ner, that no wet could get to it.

This feeming rufly Iron w^ould take up feveral
Needles hanging by one another, and appear’d to have
a flronger Magnetick Virtue than two Loadflones,

- which I had then in the Houfe j and was fo hard,
that no File would touch it. I gave one of the
greatefl pieces to a Knifcgrinder, to grind it for me,
who was a long time about it, and complain’d that it
was harder than Steel.

The

( 75 )

The Report of this made fo great a Noife in tlie
Town, that in a little time my pieces of Iron were all
begg’d away, except one little one, which I kept for my
felf.

I am, &c.

Antony van Leuwenhock.

V. Jn A count of the manner of lending J^lanks in
His Majejlys tards at Deptford, <!^src. by a
Sand-heat 3 indented by Captain Cumberland.
^y Robert Cay,

THe place, where the Planks lie to be fofened in
the Stove, is between two Brick- Walls 5 of fuch
a length, height and diftance from each other, as fuf-
fice to admit the larged, or to hold a good number
of the fmalJer Sort : the bottom is of thick Ton Plates,
fupported by ftrong Bars ; under the middle of which,
are two Fire-places, whofe Flews carry the Flame to-
wards the Ends.

The Planks are laid in Sand ; the lowed about fix
or eight Inches above the Iron-Plates, they arc well
cover’d with the Sand, and Boards laid over all, to
keep in the Heat. The Sand is moidned with warm
Water, ffor which purpofe they have a Cauldron ad-
joyning to the Stove) and if the Timber be large, and
intended to be very much bent, lb that it mud lie

P i long

( 7^ )

long in the Stove, they water the Sand again, once in
8 or 10 Hours. When ’tis judged to be foft enough, the
Sand is remov’d ; and the Workmen carry away their
refpedtive Planks, to the feveral Places, where they
are to be us’d ; and having firft nail'd a thin Board
upon the ouc-fide, to preferve the Plank from Bruifes,
they fix one part in its proper place, and bring to the
others, by any power they can moft conveniently ap-
ply. This Work Teems to be perform’d with won-
derful Eafe ; notwithflanding Tome we Taw were To
knotty, that the Builders allur’d us, they cou’d not
have brought them to that Curvature by the former
Methods. Thofe we faw put in between others, very
exadfly fitted the Spaces they had been cut for; and
the Workmen told us, they had made no Allowance
either for the fwelling, or Ihrinking of the W ood.

This Method excells that of burning the Planks over
an open Fire in feveral refpeds; particularly, that no
part of the Wood is deftroy'd, but remains of the fame
Dimenfions ; at leafl very nearly ; a Plank of the
breadth of i6 Inches being Paid not to alter above
part of an Inch. The Edges of the Plank are
preferv’d ; and confequently the Work muft be much
firmer, and the Calking laft longer. The extraordi-
nary foftnefs of the Wood, while *tis warm, makes it
eafily bend to any Figure necefiary in Ship-building,
which it holds very well, if they have occafion to
take it off again after it is cold ; whereas the Blank
bent by burning, would ftart when loofened ; and
could only be fixed to the Timbers by fuch a force, as
was able to overcome the Refiflance occafion’d by the
Spring of the Plank. It likewife adapts it felf very
readily to the Surface of the Timbers, if they happen
to be uneven.

They

( 77 )

Theyfliew’d us the Gun» Deck-Clamps in a Ship of
the Second Rate ^ which are very large Planks, bene
and twifted in fo peculiar a manner, that they never
could by any other Method, bend them into that
Form, but uled to cut them into Shape. The wl>ole
Operation is perform’d with much lefs trouble to the
Carpenters, as well as at Ids Expence; and they hope
the Wood will be more durable; as tis evident, from
the deep Tindure the Sand receives, that a confide-
rable quantity of Sap comes out of the Oak, while
its in the Stove: and a large Plank was obferv’d by
the Workmen or Officers of the. Yard, to weigh fome
Pounds lefs, when it was taken out.

■ A Plank five Inches thick requires five or fix Hours
to make it fit for bending; and the Time requifite
for others, Teems to be in a Duplicate Propottion to
their thicknefs.

Explanation of the Figures*

Fig. 1. Reprefents a Plank, in the Buttocks of a
Second Race Ship, whofe length from A, to C. is
three Feet, and thicknefs ( A F) qi: Inches, the end
C, of this Plank was bent ii or 13 Inches from the
ftreight Line AB

Fig. X. and 3. are Sedions of the Stove.

A A the Fire-places.

B, Bt the Afn-holes.

C C. the Flews under the Iron bottom.

A D. the two Chimneys.

E. the place for the Planks and Sand,

F. F* the two Brick. walls.

AG.

( 78 )

6. G> two inclin’d planes, for the Men to ftand on,
drf, when they put in, or take out Planks, or water the
Sand.

1 he bottom of the Stove, made of Iron.

/. /. The Grates to lay the Fewel on.

VL ^ Letter from the ^yerend Mr. James Field,
i^eFlor of St, Johns in Antegoa, concerning
two Cajes of Wounds in the Stomach, to A/r. John
Douglas, Surgeon, F. R, S.

SIR,

H E Accidents of which you defire me to
give you an account, were as follows.

A lufly young Negro man returning home about
Noon, went into his Houfe, where feeing (ome ripe
Plantains, he cat of them heartily ; his Father in Law,
about 6o Years of age, coming to 'the fame Houfe
foon after, enquired of the young Fellow,' who
had taken his Plantain^ Who anfwered. That he
being hungry, had eaten them. Ay, you Dog, fays
the old Fellow, have you ferved me fo, I kept them
for my own Dinner ; and without more ado, took
his Kni e, and gave the young Fellow a moll defperate
Vi'ound in the upper Region of the Belly, a vail: Gafii
being made in the 'Stomach, in fo much that the Plan-
taini which he had eaten, burft 'through the Wound,
which was made ftreight up and down.

The

{ 79 )

The old Man immediately fled for it, the young
Fellow's Companions hearing whac was done, purfljed
the old Man with Bills in their Hands; the old
Man, feeing them follow him in this manner, and get
ground of him, and fufpeding their Defign was to
kill him, pull’d out the fame Knife, with which he
had ftabb’d the other, and gave himfelf as defperate a
Wound, as he had given him, and in the upper Region
of the Belly, his Stomach being likewife leen, only
with this Difference, that this laft Wound was tranf-
verfe, or from left to fight, the firfl directly up and
down^ the old Fellow was carried home and laid in
the fame Houfe, where the other wounded Fellow
lay.

This Accident happen’d about Noon, and Mr. Fot^
reflf the Surgeon came not to drefs them till between
four and five ; he ditch’d up the Stomachs of them
both entirely, and their Bellies too, only leaving in
each a fmall hole for Suppuration ; a Fever feized each
of them, the old Man was in mod danger^ the Fever
held them about a Fortnight, the Wounds were brought
to a good Digedion, and in a Months time or there-
abouts, the young Fellow W’ent abroad, but the old
Man lay fomething longer. They were both perfed-
ly cured, and have been very well ever fince, tho’
its above fifteen Years fince this Accident happen’d.

Windfor,

Aug. 24. 1720,

I am, &C.

Jam. Field;

( 8o )

VI A Letter from A//% Atkinfon, Surgeon hi
White^Chappel : Concerning an ImfojlhumatU
on in the Stomach, To 4he fame,

SJ R, ’

^ H E Cafe you defire a particular account of,
£ was as follows. I had a Patient atout feven
Years ago, which had a large Tumour on the upper
part of her Belly, it was hard and painful, but did
not alter the natural colour of the Skin, and had been
three Months in coming. I applied a warm Gum
Plaifter to it, which in about a Fortnights time brought
it to a Suppuration. T then applied a Cauflick about
the bignefs of a Shilling; when the Efchar fell off] I
faw a (olid kind of Subftance appear in the Orifice, I
laid hold of it with my Forcefs, and pulled it gently
towards me- upon which there thrufl; forcibly out a
quantity 'of it, that near fill’d my Hand, fo I drefl:
it. Next drcffing, the fame Subffance appear’d again,
which on her Braining, fofced out near twice as much
as before. I was at a greac Jofs to determine what this
BufT w^as, but at laB concluded it was the Omentum it
felf, in which Opinion I was confirm’d by Tome other
Surgeons I fliew^’d it to. I was Bill in doubt, whether
the Stomach was concerned in this Cafe or not, till
the next Removal of the DreBings, at which there
fpurted out above half a Pint of Ale in a full Stream,
which was part of a Pint flie had drunk a little
while before. I now concluded the Cafe mortal, how-
ever, I ordered her to keep her Bed, to lie con-
Bantly upon her Back, and feed on things of cafie

DigeBion.

( 8i )

Digeftion. The greaiefl: part of what (lie cat or drank,
came through the Ulcer for eight or ten Days, fo that
1 had no hopes of ever curing it, yet contrary to my
Expedation in about fix Weeks Ihe was petfedly
cured, and is now living and in good Health.

VIII. Jn /Account of the quantity of ^ejtn in the

Cortex Eleiitheriac, !By Mr. John Brown, Chy»
7niflj F. R. S.

Douglas having lately deliver’d in a Paper to

be read before this Society, giving an account
(from the Hiftory of the Royal Academy at Paris) of
the Cortex EkutherU ; and among other things having
Paid of it, that Monfieur Boulduc had from one
Ounce of the Bark, by means of Spirit of Wine,
gotten 5 Drachms of Refinous Extrad, there re-
maining 3 Drachms of Faeces \ and that Gentleman’s
account of fome of the Properties of this Bark being
founded on the quantity of Refin fuppos’d to be
contain’d in it .* 1 propos’d to Dr. Douglas and fome
other Gentlemen of the Society, (who agreed with
mein believing, that fcarcely any part of any Plant
whatfoever would yield that quantity of Refinous
Extrad^ to try the Experiment,^ which was perform’d
after the following manner.

I took two Ounces of pick’d Bark, and digefled
it in redify’d Spirit of Wine, which was often de-
• canted and frefli Spirit put on, until the Bark would
yield no more Tindure. The impregnated Spirit
' being evaporated by a very gentle heat ; there was
left two Drachms of Refinous Extrad ; the remains of

Q.

the

f

( 8i )

the Bark dry’d, weigh’d one Ounce, two Drachms
and a half ; the lofs this way is three Drachms and an
half.

I boil'd thefe remains in feveral Waters, until they
would no longer tinge the Water, which being eva-
porated yielded one Drachm and an half of extracft; the
remains of this dry’d weigh’d one Ounce and half a
Drachm ^ the lofs by this Method is half a Drachm.

I, took two Ounces more of pick’d Bark, and boil’d
it in feveral Waters, ’till the Bark gave no more Co-
lour ; and then upon an Evaporation of the Water,
had two Drachms of Excrad. The remains being
dry’d weigh’d one Ounce fix Draclims ; here the loft
was not any thing, except (b much as might anfwer
in weight to the quantity of the Menjlrmm left in
the Extract, which Allowance mud likewifebe made in
the other Extrads.

f digefted the remains in redify’d Spirits of Wine,
uncill they no longer ting’d the Spirit, and by a very
gentle Evaporation, I found remaining one Drachm of
Refinous extrad. What was left, when dry’d, weigh’d
one Ounce, two Drachms, and an half; in this the
lofs was two Drachms and an half.

The Difference in the quantity of Extrad obtain’d
by thefe two different Methods, is but half a Drachm,
and the Medium between them, upon putting together
the feveral Extrads made with Spirit of Wine and Water,
is in the whole but three Drachms and a quarter. But
the Extrad made with Spirit of Wine alone, is no
more than two Drachms from two Ounces of the Cortex,
inftead of ten Drachms, which it ought to have
yielded according to Monfieur Boulduc,

IX. An

( 8^ )

JX, Jn Jccount of the new Method of Cutting
for the Stone, !By J. Douglas, Surgeon^

F. R. S.

EVer fince I was Anaromift and Surgeon enough,

/ to reafon upon the Caufes of the Tedioufnefs
and bad Succefs of the common Methods of Cutting
for the Stone, I concluded that they were principally
owing to the natural Strudure and Situation of the
Parts concern’d.

Therefore I began to confider, why that Operation
might not be perform’d the high way, fo frequently
mention’d by Authors, but never approv’d of by
any, except the mod fagacious of all Surgeons, Fr,
Roj[fetuSy who has certainly been very little read, or
cll'e very ill underftood, elfe this Operation had not
been fo long a Secret.

After making fome Experiments on dead Bodies, I
was convinced, that the Stone might be extraded that
way with a great deal of lefs trouble than commonly,
. and I was perfwaded that the Wound would heal
. again, by the great number of authentick Inftances
we have of accidental Wounds in the fame place being
fpeedily and firmly cured , and therefore 1 refolv’d to
make the Experiment on the firft Patient I could meet
with, which I could not procure till December ^7^9'
and then I proceeded as follows.

The Patient was plac’d flat on his Back, on a
Table, with a Pillow under his Head , then his Wrifls
and Ancles were faften’d together, with Straps Then

I ordered

( 84 )

1 ordered one Afliftant to his Head, another to each of
his Shoulders, two to the Penis, one of which was to
manage the Ligature, and the other the Prepuce, and one
to each Knee, to hold them as faft and firm as poiTible.

The Patient and Afliftants being thus plac’d, the
Operation confifts of three Parts.

i/?. In filling the Bladder, which is done thus.*

Firft, Pafs the Catheter, Fig. i. then draw out the
Stiller, Fig. ii. then order the Ligature Affifiant to
call the Ligature, with is a Skein of Silk, round the
Penis, above the Gians. Then fix the Key, Fig. iii.
to the head of the Catheter, Fig. iv.' to keep it fteady,
while you fcrew on the Syringe, Fig. v. then fcrew
the fecond part of the Sucking-Pipe, Fig. vi. to the
firft. Fig. vii. Then order the Penis Ligature to be
ftraiten’d, and the Prepuce Aftiftant to gather the Pre-
puce up about the Catheter^ and to hold it as clofc
as poffible. Then order the Water, being a little war-
mer than Milk, to be clapp’d under the Sucking- Pipe,
then draw up the Water into the Syringe, and thruft
it into the Bladder at leifure, and repeat it till
the Bladder is fo full, that you can perceive its Tu-
mour through the Abdomen, (at which time you will
alfo obferve the Penis above, and the Prepuce below
the Ligature, very much fwell’d, and the Patient
in a great deal of Pain^ which is a certain Sign that
there is enough injetfted ; then withdraw your Sy-
ringe and Catheter together, taking particular care
that your Penis Afliftants ftraicen their gripe, leaft
the Water fhould follow the Catheter, which would
undo all.

%dly^ In making the fncifion, which is done thus :
Order the Penis Afliftants to turn the Penis to^
wards the Anus, that fo their Hands may be the
more out of the way, then take the firft Knife, Fig. viii.
and cut at leifure, and with a fteady Hand, from

near

(h )

near the upper part of the Tumour of the Bladder, or
lower, according to the computed bignefs of the
Stone, down to the Os Pubis, and exactly in the
middle; when you are got a little more than half
way through the abdominal Mufcles, take the fecond
Knife, Fig. ix. clap its back on the middle of the
Os Vuhis, then run its point down towards the
Sphin^ier, until you get into the Cavity of the Blad-
der, which is difeovet’d by the ilTuing out of the
' Water, then run your Knife along very quickly to-
wards the Fund of the Bladder, as far as is neceflary.
^dlj, In extracting the Stone, which is done thus :
Before you withdraw your Knife, introduce the
fore and middle Fingers of your left hand , be*

1 tween the Knife and the Os Pubis, into the Bladder,

I then withdraw your Knife, and thruft the fore
and middle Fingers of your right hand into the Anus,
and raife the Stone up towards the Wound, and fo
; you will eafily catch hold of it, (though never fo
fmall^ with your Fingers which are in the Bladder,
then draw it out with the fmalleft end foremoft.
Then introduce your Fingers again, to fee if there
: are any more Stones, which are to be drawn out as
before.

Then take a Needle and Thread, and make one
. Stitch through the Skin, in the middle of the Wound,
and tie it pretty clofe, then undo the Straps and car*
ry the Patient to Bed.

The Patient being put to Bed, I laid a Pledget
arm’d with Balfam over the Wound, and a bit of
•flicking Plaifter over that. Then I embrocated all
the Abdomen, Scrotum and Penisy with w^arm OL Cha^
r/i£mcL ; then I applied over the drelTing and all the
Abdomen an Emollient Pultice, fpread almoft an Inch
thick on fofe Flannel ; then I turn’d a fwath a little
broader than the Patient’s Hand once round him,

and

( 8(5 )

md pinn’d it on the Pultice Cloath, juft tight enough
to keep it on.

As icon as he was drefs’d, I gave him an Opiate (for
nothing is fo proper as reftj fuch as this ^ Atj.Cinnam,
Herd. Laud. Liq, Gutt, xv. Syr* de Mccon. which
may be encreafed or diminifhed as the Cafe requires.

Next Evening I took off thePultice and dreffmg, and
cut the Stitch ; then fomented the Wound and all the
Abdomen with Stupes wrung out of Aq. Calc, and freOi
Urine, as warm as he could bear it; then drefs’d the
Wound as before. Then I rubb’d all the Scrotum^ Fenis^
and Groins with Ungutntum Album, to prevent their
being ffalded by the Urine, which flows from the
Wound.

The Wound mufl: bedrefs’d twice a Day at leaft, till
you have a plentiful Digeftion.

After every dreffmg, the Ointment and Oil was
ufed, as before directed.

There is little Variation in the dreffmg of the
Wound, except what is common in others.

The Urine flows always through the Wound, until
the Wound of the Bladder is cured, which is (boner
or later according to the Conflitution of the Patient.

When the Urine begins to come the right way,
it pains and (calds them much after the fame manner,
as when they had the Stone, (which is caufed by the
Contraction of the Urethra^ that has been fo long ufe-
- lefs,) but it never lafls above a Day or two, and
then they make Water with the fame Eafe and Free-
dom, as any ether Perfon.

They ought not to be forced to go to Stool under
fix or feven Days, unlefs there is fome particular
reafon for it, bccaufe (training to go to Stool injures
the Wound.

They

( 87 )

► / ♦

. They ought never to be taken up, except to get

their Beds made, until the Urine comes all the right
way, becaufe it makes them (ick and faint; 'and con-
fequendy hinders 'the Cure of the Wound.

Cold is to be" avoided as the PefI:, bccaufe it puts
them to a great deal of pain either to flifle it, or to
Cough our.

N, B, If a, flexible Catheter could be pafs’d, and
kept in the Paflage without pain, it would very
much haflen the Cure of the Wound.

I made this Operation the firfl: time on the 13d of
December 1719. upon a Boy between 16 and 17
Years of age, and in five Weeks time he was perfedly
I cured.

The Stone was of the Figure and Bignefs of Fig. x.
I made the fecond Operation on the nth of May
1720, on a Boy of Eight Years of age, and in fix
Weeks time he was perfedtly cur’d.

The Stone was of the Figure and Bignefs of Fig. xi.
Ihe third Patient was but three Years of age, and
was Cut in Augufl 172.0. but died of Convulfions
: about 15* Hours after the Operation.

Fig. xii. Shews the Form and Bignefs of this Stone.
The fourth Operation was made on the 23d of
arch 1720-21. upon a Boy about 14 Yeats of age,
and in four Weeks afterwards he was per feeSliy cured.
This Stone is reprefented Jn Fig. xiii.

In this Patient I made a finall Wound in the Pcritcn£~
um, through which I faw the Guts prefent, but I pulh’d
I them back with my Finger, and then Hitch’d the
JSkin, and we had no farther Inconveniency by it.
"Thefe three Patients have been already Ihew’d before
rthis Society. ' ’

This

( 88 ) ^ .

This Operation may be perform'd with equal Suc-
cefs on Females, when the Stone is large, but' if it is
but fmall, the common way of extrading them is
very good.

From all which I think I may fafely conclude in the
Words of the inimitable Roffetus*

Pofl fj£C nemini duhium effe dehet, novm hanc noflram
Cyflorof^d^^f vetere ilia tot dodiiJJimQrum Chirurgorum Cjfto^
tonlik Xtam' f^eri0losat ut earn aggredi vel ipfe Hippocrates
Chiyurgon Cfiki&§^ & Icniorem ^ tutionm

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PHILOSOPHICAL

TRANSACTIONS.

For the Months of June^ Jtdy, and Augufi. lyix.

The CONTENTS.

I. An Account of a Parhelion feen in Ireland.
In mo Letters from Arthur Dobbs, Efq*^ of
Caftle-Dobbs in the County of Antrim, to his
brother Mr. Richard Dobbs, o/Trinicy-Coll.
in Dublin 5 and by this laft communicated to the
Royal Society.

II. A Letter to the Royal Society concerning the
Particles of Fat, <By Mr. jLeeuwenhoek,
Tranflated from the Dutch John Chamber-
layne, Ejf,

III. 'Part of a Letter from Thomas Forfter, Eff,
F. R.S. to Mr. Machin, F^rof. Ajlron. Grefham,
Seer. F(. S, concerning a new Ifland lately raifed
eut of the Sea near Tercera,

R

IV. >

IV* A Letter from Mr, Ralph Thoresby, F. ^ 5.
to Sir Hans Sloane, Sart, Trefident of the Col-
lege of Fhyjtcians, and Vice-Fref, S, concern-
ing the Effeds of a violent Shower of (^in in
Yorkfhire.

V. Fart of a Letter from Monf Couzier, Fhy fi~
dan in the Infirmaries at Alais, to Dr. Deidicr,
Frofeffor of Chymiftry in the Univ.erfity ©/Mont-
pelier, concerning a new F^xperiment ??iade with
the Flood of a Ferfon dead of the Flague. Com-

. municatedto the Royal Society hy Dr, Wood-
wardj F. F{- S, Frof, Med, Grejh,

VI. ExtraSi of a Letter from Dr. Deidier, con-
cerning an Experiment made with the File ofFer-
fons dead of the Flague, Communicated hy Dr,
Woodward.

yii. Solutio Frohlematis de curVis inVeniendisy qu^e
quada?n ratione in fitu inVerfo dijpofitd fe inter-
jecare pojfunt in angulo dato.

VIII. Jn Account of a Fook^y intituledy Harmo-
nia Menfurarum, five Analyfis &c Synthefis
per Rationiim 5c Angulorum menfuras pro-
moix. : accedunt alia Opufcula Mathema-
tica : per Fpgerum Cotefium. Edidit 5c auxic
Fphertus S??iithy Coll. Trin, Cantab. 5c Reg.

Soc.

Soc. Socius 5 Aftronomias & Experimentalis
Philofoph. poll Cotejtum ProfelTor. CantahrigU
1721. in 4to. Proliant apud Bibliopolas
Londinenfes.

ERRATA.

PAG, III. lin.iZy-pro ^ leg. proportionalem;

Pag. 1 14. lin. 15, dele

Pag. 123. lin. 13, leg. 4 4 4- ^ -H

Pagy 127. lin. 5, dele br event lineanij qua fuper b ducitur*

Pag. I2p. lin. 15, leg. q ^ y.

/'<3^.i3o. //«. uk.pofl invenietur adde fi modo m fit numerus af-
firmativus 1 vel eciam fi « fit unitas, m numerus affirmati-
vus, & 2 numerus impar negativus numero m major.
Pag. 132. lin. 12, pojl requiritur adde cujus fegmenti centrum
aequaliter diftet a lineis A B, CD.

Pag. 138. lin. ip, leg. ITS.

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I. Jn Account of a Parhelion feen in Ireland. In
two Letters from Arthur Dobbs Efq-^ o/Caftle
Dobbs m the County 0/ Antrim, to his IBrotlyer
Mr, Richard Dobbs of Trinity-College in
Dublin 3 and by this lajl communicated to the (^yal
Society,

I Saw a pretty diftinguilliable Earhelion here on
Thurfday Evening, of which I fend you the Ac-
count below, as I minuted it down after I came Home,
having been in the Fields when I law it.

March zzd 17X5, about half an Hour after 5 in the
Afternoon nearly, I faw a diflinguifliable Ear he lion,
the Sun near W eft^ about an Hour high, the Wind and
Carry of the Clouds, about N. and by E. the Sky in
fcveral Places obfcured with light Clouds, and the Sun
entring into one fbmewhat more watery, yet fb as to
diftinguifli its Disk, At firfl; appeared below the Sun,
breaking out of the Cloud, flich Rays as are ulually
feen in an Evening, in a Sky interfperled with Clouds.
In a little Time appear’d at the fame Height with the
Sun, as near as I could guefs, having no Inftru-
ment, a luminous Spot, being about four Times the
largenefs of the Sun’s Disk, and about 30 D. di-
flant from the Sun to the Southward, which was
covered with the lively Shades of red and yellow
on the Side next the Sun, and encreafed in Splendor
(fo as fcarce to be born by the naked Eye) till it ex-
ceeded the Brightnefs of the Sun, which was then un-
der a thin Cloud, fo as eafily to perceive his Disk.
After this had appeared about 3 or 4 Minutes, I find-
ing it to be a real Earhelion^ began to look about for
the Halo they generally appear in 3 and as I obferved

fome

( )

fome 'Rays refembling a Glory to point upwards from
the Sun, I faw in thole Rays at the fame Diftance (be-
ing, as near as I could guels, about 30 D. perpendicu-
larly above the Sun) the Colours of the Halo appear-
ing as in the luminous Spot ; but inftead of finding it,
as I expeded, in a Circle fiirrounding the fun, it was
inverted, yet not circular, but making an obtule An-
gle, the point towards the Sun. I then looked to
the Northward of the Sun, and as the Cloud, which
was thicker on that fide, moved Southwardly, a lumi-
nous Spot began to appear at the fame Diftance from
the Sun as the. other, and in the fame Parallel of Alti-
tude, which had the fame Colours towards the Sun,
and increaled in Brightnels, but did not come up to the
Brightnefs of the other Spot, yet was as luminous as
the Sun then appear’d : this Spot was very little big-
ger than the Sun’s Disk. As the Cloud mov’d on, till
It came to about 60 D. to the Southward of the Sun,
and 30 D. from the Spot, at an equal Height there ap-
peared another Spot tinged with the Colours of the
Rainbow. The whole Appearance lafted a Quarter
of an Hour. The Reafon of my not feeing the Haloes,
which generally appear with them, was, that there
was a good deal of clear Sky above the Sun, and the
.Cloud was too thick below it.

Cajilt' T^obbs^
March the z^th iyz\.

Arthur "Hobbs.

(■ 9» )

I Have fent you, as you defired, the Scheme of the
T^arhelion^ with all the Notes that I cou’d take in
the fliort Time it continued, having been only out oc-
cafionally, without any Inflrument to compute the
Proportions, or take Angles ; fo that my Obfervation
cannot be exadt, but only approach the Truth.
However I can recoiled nothing material, that I have
omitted.

A. The Place of the Sun, being nearly Weft about
IX or 13 D. above the Horizon, being about an Hour
before Sun-fet.

B. The luminous Spot, being about 30 D. to the South-
ward of the Sun, as near as I cou’d compute, hav-
ing no Inftrument to take the Angle, and in the lame
Parallelof Altitude ; the Spot was not fo well defin’d
as in the Scheme, being more imperceptibly lhaded
off in the Cloud, the two lemicircular Lines next the
Sun were thole tinged with the Colours ; the near-
eft the Sun being of a deep Scarlet, the inner one a
deep yellow, both the Colours being Ibftned as
they fell off from the Sun, all the reft of the Spot
being an intenfe Light, lb as the naked Eye cou’d
fcarce bear it.

C. The other Spot to the Northward, which appear-
ed fometime after that marked B, being not quire lb
large, nor the Colours fo intenfe, but the fame way
dilpoled, thofe next the Sun being red, the next yel-
low, and the reft white.

D. A Spot in the Cloud, as it moved Southwardly, till
it came to about 60 D. Diftance from the Sun, which
had the Colours as in the other Spots, that next
the Sun being red, the next yellow, but much fainter
than in the Tarhelia.

The

( 9^ )

E. The Appearance of two Segments of Circles, at
about the lame Diftance from the Sun, as the
helia^ being perpendicularly above it, the Colours
being fainter than in the Tarhelia, but the fame Way
difpos’d, the lower Lines next the Sun expre/fing
the red, and the upper the yellow.

The Colours at D, and E, as they were not fo in-
tenle, neither were they quite fo broad as thofe at B
- and C ; the two Colours being added together were
about I of the Disk at B, and the Colours in the fame
Proportion at C ; the Diameter of the Tarhelion at
B, being about double the apparent Diameter of the
Sun, as near as I could compute, as in the Scheme is
exprefs’cf.

The Centres of the Segments of the Halo's mark’d
E, if not in the ^arhelia^ were very little below ’em.

Below the Sun and Parhelia the Cloud was too
thick to difcover any thing thro’ it ; and above them,

;; till near the Segments mark’d E, the Sky was ferene
and nothing obfcured; but at E, where the Rays,
which pointed upwards from the Sun, terminated, it
appear’d hazy, and fb thick as to refled: the Colours. '

CaJHe "Hobbs^
1711.

Arthur "Hobbs.

II. A

C 9i )

IL'JLetter to t/?e Royal Society concerning the Tar
ticks of Fat. (By Mr. Leeuwenhoek, F. (?(. S*.
Tranflated from the Dutch by John Chamber-
layne, EJq^

Delft, Alay iji, 1722;

I Take the Liberty to lay before you the following
Oblervations, which I made about two Y ears paft.
I have formerly laid, that the Matter which we call
Meal, or Flower, in Wheat, Rye, Barley, Oats, and in
all Ibrts of Beans, is lliut up as it were in little Cells or
Chambers, and that thole little Cells are leparated from
each other by thin Membranes, which are thinnell in
Wheat. And foralinuch as in the Enquiry into what
is called the Feriofteum of an Ox or Sheep, I have
often broke in Pieces the fat Particles thereof^ and as
often viewed thro’ a Microfeope the laid broken Par-
ticles, lb have I likewile placed a few of the fat Glo-
bules upon a clean Glafs Plate, and afterward held the
faid Glals Plate over a Coal Fire, or the Flame of a
Candle, fo long, till they were all melted and reduced
into a liquid Matter ; fo that not only the Fat, which
was lliut up in the Skin of the fat Globules, but like-
wife the Skin itfelf was reduced to a fluid Matter ; and
thereupon I immediately brought it before my Sight 5
and viewing it with Attention, perceived, when the
melted Fat was cold, that there were different Mat-
ters inclos’d in the laid fat Globules ; for as much as
there appear’d an inconceivable great Number of ex-
ceeding linall coagulated Particles, and the reft of the

S Parrs

( 94 )

Parts, of which the Fat was compofed, lay in one
linooth and even Subftance, as I have formerly laid ;
and 1 have been confidering whether there might not
be inclofed in liich a Globule of Fat, fo many little
Cells and Partitions as we fee in a little Grain or Seed,
but if it be lb, it will remain concealed from our Eyes.

But having now again carefully contemplated thefe
coagulated Globules of Fat, many of which go to the
making of one little Bubble, I did often fancy, that I faw,
that each of the faid fmall Particles was provided with
fuch a tranlparent Dent, as I have before laid, that the
Meal Globules of Wheat, ^c. are furnifhed with ; From
which Obfervation I faid to myfelf, lince we find, that
the great Creator of the Univerfe has made all his Crea-
tures almoft after the fame manner ; and that there
grows no Plant whatever, let the Seed be never fo
linall, but there are inclos’d in it the lame Ibrt of Par-
ticles as are found in bigger Seeds ; and that tho’^ they
differ in Magnitude, yet are they analogous one to
the other : this being lb, we may eafily imagine,
that a fat Globule has a Bark or Skin as well as any
Seed, as we have often feen, and that they are fur-
nilhed within with Particles analogous to thole of the
Seeds, which we call Wheat, Oats, and th^ like ^ and
altho’ we render the Fat fluid by the help of Fire, yet
will the Irnall Particles which are inclofed in the far
Globules, again relume their former Figure, as I have
formerly faid.

Yea I have fancied to myfelf, tho’ it did not appear
to my Sight, that each fat Particle is furnilhed with
little Cells within, like the Seeds or Fruits of Plants.

Since I have fet this down upon my Paper, I was
informed that my Butcher had killed a Sheep of an
uncommon Bignefs, and that it weighed 140 Pounds,
without the Fat that they took out of it, after it was

kill’d

( 95 )

kill’d, which weighed 51 Pounds, fb that the whole
Sheep weighed above 190 Pounds.

I cauled a Piece of the Fat, that grew about the Kid-
neys of the laid Sheep, to be brought to me, imagining
that its fat Particles would be of a coarfer Grain than
thole of ordinary Sheep ; for I have obferved feveral
times, that the bigger an Ox was, the larger were the
fat Particles thereof; and fince not one Man in a
thouland has any Knowledge of the Contexture of thelc
fat Particles, for we find that there are not any two
of one and the fame Figure, they being comprelled by
other Particles with which they are furrounded, as
I have frequently taken notice, I have cauled Ibme
few of thefe fat Particles to be drawn here, as may be
feem in Fig. i. between A, B, C, D.

Now when we meet with one of thefe little Bundles
of fat Particles, as has frequently occurr’d to us, in
which the fat Particles were four times thisThicknels ;

1 imagine, that liich fat Particles cannot be produced
out of one Tingle adipofe VelTel, but that out of liich a
VelTel leveral Imall Sprigs ilTue forth, and out of each
of thofe linall Sprigs proceed others Hill Imaller, and
that out of thele Particles one larger fat Particle is
formed like a Bunch of Grapes.

Now I cut ofF with a Razor the Fat in leveral Places
of a greater Piece, as thin as I could, laying the thin
Pieces upon feveral Glals Plates, and put them upon a
Coal-Fire, lb as to caufe them to melt ; and being
melted, immediately viewed them with a Magnifying-
Glafs, when I oblerved the Skins, or membranous
Coats, of the fat Globules lying among the melted
Particles, and in the faid melted Particles there was
nothing to be perceived but a limpid Matter furroun-
ded with Imall Air-Bubbles ; but when the Fat was con-
gealed, we could obferve but very little of the Mem-

S % branes,

C 9^ )

branes, becaufe they were covered with the Particles
of Fat, with which thele Membranes or Skins had be-
fore been filled.

I caufed a few of thefe Skins of the fat Globules
to be drawn, as may be leen here at Fig. x. between
E, F, G, H. During the faid Obfervation, I fix’d my
Eye with attention upon the fat Particles of the Sheep
which had been melted, and were again coagulated ;
and I could not but judge, that thefe fat Particles,
which were exceeding fmall, were analagous to that
internal Matter, wherewith fbme of the fmallefl little
Seeds are furnifhed, and in a great many of thefe ex-
ceeding fmall Particles, I could in clear Weather dif-
cover fbme Tranfparency.

Moreover, I cut as thin Slices as it was pofiible
of the Fat, yea fb thin, that five or fix of them did
not weigh a Grain, and put them into a little Water,
in order to try whether I could make any farther Difi
coveries thereby, with refped: to the fmall Particles
of Fat ; but it was in vain : only I faw floating upon
the Water very fmall Particles of Fat, which were co-
agulated in a Ipherical Figure, and the very biggeft of
thofe fat Particles was no bigger than a Grain of Sand.
I placed thefe Particles upon a Glafs Plate ; and view-
ing them with a Microfeope, I obferved the Figure,
which I mention’d above, as plain as before ; and other
fet Particles feemed to be of a different Figure. I put
one 'of thefe into the hands of my Painter, or Defigner,
bidding him to draw what he obferved, it being the
Figure of one of the faid fat Particles, which was co-
agulated On the Water, as it is reprelented here by
^ Fig. 3. ‘‘between I, K? L, M, which was not very con-
formable with die other melted fat Particles ; for in
the doing it, all the Particles did not melt, for the
far Particles are not all extrabtedby the Water, and co-
agulate

( )

agulate upon the Water in fmaller and greater globular
Particles ; and when we take out of it the Remainder
of the thin Slices of Fat, which float upon the Water,
and view them with aMicrofcope, we find that many
of the fat Particles appear intire to the Eye ; and
whereas they were before very finooth and even in
their Sides, they were now changed into rough and
uneven Particles ; fb that one Ihould be apt to think,
that there were two different forts of Particles in the
Fat, and that one fort melted more eafily than the
other.

Now in order to get thefe melted Particles of Fat
out of the Water, without altering them, I made ufe
of a round Glafs, and with it skimm’d the Superficies
of the Water ; by which means fbme of the coagu-
lated Particles fluck to the Glafs. Moreover, I did
again melt fome of the fat Particles, which had been
coagulated upon the Water, over a Coal Fire, a$ they
lay in the Water ; and when they were again coagu-
lated, viewing them with a Microfeope, I found the
fmall fat Particles to be yet fmaller than thole that
were melted out of the Water.

In this lafi: Obfervation I obferved, with aftonifh-
ment, the inconceivable Number of Veins and Mem-
branes, which were diffus’d through the Fat, and the
Multitude of feparated fat Particles, that were invol-
ved in their feveral Membranes.

After this, there was laid before me the Hind-Quar-
ter of a flicking Lamb, over which w"as fpread what
we call the Net, or Caul ^ and having cut off fome
Pieces of the faid Net, or Caul, upon which there Was
little or no Fat, with a Pair of Sciffars, and placing
them before a Microfeope, I obferv’d again, that the
fat Particles, where there were very few of them in-
cluded between the Membranes, were of a more

( p8 )

globular Figure than in other Parts, where a good
many lay together, and that in other Places they
were prefled or bruifed, which I fancy was occafion’d
by the Butcher’s Iqueezing the Caul in that place with
his Fingers ; and in another Place the fat Particles
had been fo torn in pieces, that I could fee nothing
remaining but the Skins of the fat Globules.

Moreover, I law that the fat Particles had fuch a
Pinch, or Dent, in them, as I have lliewn, that there
were in the Globules of Flower of Wheat; from which
Spedbacle, I am confirmed more than before in my
Opinion, that the fat Globules might be feparated
intirely, or in part, from the Skin with which they
..are furrounded, by opening the Dents, without break-
ing the^Skiii.

Then I took off the thin Membranes, which en-
compals’d the fat Particles, and viewing them with a
Microfcope, obferved, that the fat Particles had im-
printed a roundilh Figure on the Membranes, inclining
,to a hexangular Shape, that it was a Pleafiire to look on
’em ; but in other Parts they were of an oval Figure.

Moreover, I took a flat Filli,which we call T^laife^ and
took off the Fat which adher’d to the Vefiels, or Bones,
and viewed it with a Microfcope, and obferved, that
the 'Fat Particles were of feveral Sizes ; and fome were
fo fmall, that I judged that fifty of the leaft were no
bigger than one great fat Globule ; and moreover, I
faw that many of the fat Globules had fuch a Pinch
in them, as we find in the Meal, or Flower, of thofe lit-
tle white Beans, which we call French or Kidney^
Beans.

Afterwards my Servant brought to me the Fat of a
^erch, which was nine or ten Inches long, and ta-
king a little of it, I viewed it with a Microfcope, but
could not difeover any fmall Particles in it, nor any

i internal

(99)

internal Dent, as I had obierved in the Fat of a fmall
^laife.

After that the Fat of the Terch had lain an Hour or
two upon the Glafs, I viewed it again, and obierved
that the Particles' were leilened, or become imaller,
and that the Skin of the fat Particles, which as yet
was beiet with Ibme fat Particles, was, as it were,
Ihrunk, or wrinkled, and the Fat that was burfl out,
lay about the fat Particles, and was fb fluid and trail-
Iparenr, that we could not difcover any Parts in it.

From this Oblervation I began to think, whether
each of thele fat Particles was not provided with an
Orifice, or Hole, out of which the Fat might be pro-
truded at all times, as often as the Parts of the Fifli
flood in need of Nourifliment, without an entire lay-
ing open the Skin of the fat Globules ; for we con--
flantly find, that when the Eggs of the Perch, which
we call the Roe, increafe in Bignefs, its Fat decreales ;
yea in luch a manner, that when the laid Eggs, or Roe,
are arrived at their utmofl Bignels, there is leldom or
never any Fat to be leen upon the Inteftines of the
Fifli.

Thus far my Notes go about Fat ; and if my Health
will allow me, I lhall Ihortly tranfmit to you Ibme
more of the Obfervations which 1 have fet down in
writing.

III. Tart

( ‘®® )

•

III. Tart of a Letter from Thomas Forfter, Ef^li
F. R. S. to Mr. Machin, Trof. Jjlron. Grefhaniy
Seer. Tc S. concerning a new IJJand lately raifed
out of the Sea near Tercera.

London, Ma'y iz. 1722.

I Here fend you a Draught of the feveral Bearings,
and the Captain’s Account of an Ifland lately broke
out of the Sea, bearing S. E. from Tercera, Diflance
17 Leagues.

John Robinfon, being Mafler of afmall Pink-Snow,
called the Richard ana Elizabeth from Rifiataqua
in Kew- England, arrived at Tercera, T>ecemb. lo.
1720. near which Ifland he faw a Fire breakout of
the Sea. The Governor hired him to go with the
faid Veflel to view it, and feiit on Board fixteen Sailors,
and two Priefts. Oi\ Sunday, the iSthof^^^m^.
we got under Sail at ix o’clock at Night, and flood
from Angras, S. E. The next Day at two o’CJock in
the Afternoon, we made an Ifland all Fire andSmoak :
we continued our Courfe till the Afhes fell on our
Deck like Hail or Snow all Night. We bore from if,
the Fire and Smoak roared like Thunder, or great
Guns. At Break of Day we flood towards it again :
at IX o’clock we had a good Obfervation, two Leagues
South from it. We fail’d round it, and fo near, that
the Fire and Matter it threw out, had like to have done
us Damage : In which Conflernation we all betook
our felves to Prayers, being in danger of driving a-
flioar : then a fmall Gale, at S. E. fprung up, and car-
ried us clear to our great Joy. The Breeze was ac-
a companied

( 101 )

companied with a finall Shower of Rain, which caus’d
a great Duft to fall on our Deck ; with the faid Breeze
we Hood away for Tercera. The Governor inform’d
us that the Fire broke out the xoth of Nov. 1710. in
the Night, and that the prodigious Noife it made, caus’d
an Earthquake, which lhattered down many Houles
in the Town of Angra^ and Places adjacent, to the
great Terror of the Inhabitants. We took leveral
Draughts of the Ifland at feveral Bearings in our failing
round, of which the inclofed is a Copy. Prodi-
gious Qiiantities of Pumice* Stones and half-broil’d
Fifli were found floating on the Sea, for many Leagues
round the Ifland, and abundance of Sea-Birds hover-
ing about it. So far the Captain.

An Acquaintance of mine informed me, that in his
PafTagefrom Cadiz to London (the latter end oi April
was IX Months) he obferved the Sea from Cape
r^T,almofl to the Chops of the Channel, to be covered
with Pumice-Stones, fome of which he gave me.

IV. A Letter from Mr, RalphThoresby,F. 5.
to Sir Hans Sloane, !Bart, L^refident of the CoL
lege of Thyficians^ and Vice-TreJ, (2^ S. concerning
the EjfeSis of a 'Violent Shower of ^in in York-
{hire.

TH E Effedfs of a violent Shower of Rain at Ri-
ponden, near Halifax^ were fo furprizing, that
I wrote to a Gentleman in thofe Parts for an Account
that might be depended upon ; and particularly de-
fired to know, whether there was not an Eruption of

T Waters

( )

W aters out of theHills, as the late ingenious MxTownley
of Townley wrote me there was out of Tendle-Hill^ in
that at Star-bottom mentioned in the Thilof. Tranf.
N° X45'. but all the Account I can learn of this is, that
what they call theDalhingof two great ’watery Clouds
upon the Hills, occafioned the Inundation ; what
ever was the more immediate Caufe, the Efled:s were
dilinal, and lb fiidden, that tho' it was upon the Day-
time, the poor Creatures could not fave their Lives.
This Calamity happen’d the i8th o^May, ijxx. be-
twixt the Hours of 3 and 5, when by the modefteft
Account the Beck was rais’d two Yards at lead in per-
pendicular Height above what was ever known before ;
which may be eafily conceived by the Situation of the
Place implied in the Termination den^ which dgnides
a deep Valley between pretty deep Hills on each Side..
Fontes in convallibus^ is in the SaxonYQ,x£\ow rendered
jnllar on 5eniim Yy^ciij. x. and (as this
now) Yy?lxxxiij. b. &ene ceopa. Several Houles, four
Mills, (Ibme fay fix) nine Stone-Bridges, and ten or
eleven of Wood, are taken down, and the Wheels,
Dams, and Sluices, {Eboracentibus Goits, from the
verbal Noun geocan fundere') of mod of the Mills
that are left danding, broken and damaged ; and a
great deal of Cloth gone. Fifteen Perfons were drown’d, ,
of whom Jonas Longbothom and his Servant are not
yet found. Seven out of eight in one Houle were either
llaiii by the Fall of it, or drowned. A young Man
efcaped by help of a piece of Timber, was turned over
and over again, in pading two or three Dams, but at
lad taken out alive, tho’ didraeded for the prelent ; but
it’s hoped he may recover.

The Rapidncls of the Torrent was lb violent, that
it took down the North-dde of Rifponde7i Chapel, and
carried off mod of the Seats. A Man of "Deusbury

told

( 10? )

told me, that he faw four of them that Were driven to
that Town ; and the Redlor of who vifited

me the Day after, inform’d me, that many Goods were
carried down lb far, tho’ above zo Miles off. It tore
up the Dead out of their Graves ; at firft I was willing to
believe it only of an old Woman that had been buried
that Afternoon, and fo the Earth not fully fettled
again ; but am fince informed by a fiire hand, that two
corrupted Corpfes were driven upon one Gentleman’s
Land, and as many upon another’s. It fwept away
all the Corn-Land, as deep as the Plow had gone.
Some Perfons fav’d themfelves by forcing a Way out
of the Roofs of their Houles, and fitting upon the
Ridges till the Floods abated.

I was that Day feized by a fmart Thunder-Shower,
upon the Moor, as I was coming home.

Leeds^ June f.

1721.

. V. of a Letter from Monf. Couzier, .

dan in the Infirmaries at Alais, to Dr^ Deidier,
L^rofeffor of Chymiftry in the Uni'Verfity 0/ Mont-
pelier, concerning a new Experiment ??iade with
the (Blood of a Berjon dead of the Blague. Com-
mujiicated to the Bpyal Society by Br. Woodward,
F. R. S. Brof. Med. Grefi.

ON the Firfl of this Month I took an Opportunity
of beginning the Experiments you had recom-
mended to me, and of which I had promifed to give
you an Account.

T z

I took

( 104)'

I took a Quantity of Blood from the Body of a Pcr-
fon dead of the Plague, and mix’d it with warm Wa-
ter, which Mixture I attempted to inject into the Cru-
ral Vein of a Dog, but the End of the Syringe being
too large to enter the Vein, the Experiment did not
fucceed.

This made me refblve to try the other Method you
had propofed to me, which was to lay fome of the
fame infedled Blood upon the Wound. This I ac-
cordingly did, and cover’d it with a Drefling, which
the Dog got off in the Night. I found the next Morn-
ing that the Dog had lick’d his Wound, and that he
refufed his F ood. T owards Night he began to bemoan
himlelf, and gave Signs of an approaching Death. The
next Morning I found him dead, the Wound being con-
fiderably fwell’d and gangren’d, and the Edges round
the Swelling were likewile gangrened.

Upon opening the Body we found the Liver Ibme-
thing larger than ulual, with Spots of a livid Purple,
as in the Bodies of Perfbns dead of the Plague. In
the Stomach was found a Quantity of black coa-
gulated Blood, of the Size of a Hen’s Egg. This in
all Likelihood was what he had fwallow’d upon licking
the Wound. The Heart was very large, with a black
grumous Blood in the Ventricles, and the Auricles
were turn’d blackifli and gangrenous.

Alais^ April 3 .

1711.

VI.

( »05 )

VI* Extract of ci Letter from Dr. Deidier, co?z-
cerning an Experiment made with the &le of Der^
foils dead of the Diague. Communicated by Dr.
Woodward.

WE caufed two Dogs to fwallow a pretty large
Qiiantity of the Bile taken from the Bodies of
Perlbns dead of the Plague.

Upon this the Dogs appeared heavy and melan-
choly, reflifed their Food, and made Water very often,
elpecially when they were any ways diflurb’d. Their
Urine was thick and very fetid, and their grols Excre-
mejits were tinged with the black and grecnilli Bile,
which they had fwallow'd. But in a few Days thole
Accidents went off, and the Dogs recovered their per-
fect Health, though they were all the Time confin’d
in a Cellar belonging to the Dilpenfary, in company
with the other Dogs that we tried our Experiments
upon.

MontLelier^ April 28.'

yii. So.

( »o<5 )

VII. Soktlo ^rohlematis de curVis in'Veniendts, qudt
quada?n ratione in Jltu hiVerfo difpojitd fe interfe*
care pojfunt in anguh dato-

JAM primura ad manus pervenerunt ErudU
torum ad hunc menlem Auguflt^ ubi invenio a me
peti, ut ea aperiam, quse notis fidis celata in Su^-
;plementorum ad ABa Eruditorumy Tom. 8. Sed. i.
cdita funt. Explicentur autem ea tabula fequenti.

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In hac tabuli fex funt notamm ordines : lupremus
literas continet, quibus verba celata Icribi dcbent, re-
liqui literas numerofque continent, quae verarum lite-
rarum loco ulurpantur. Literas autem b, g, n, q, x, quae
e Iseva horum ordinum inferiorum collocantur, pro-
pter earum ufum indices appellare licet. Scripturse
pars celata ab horum indicum duobus incipit, quorum
pofterror oftendit notas ilium fequentes in eo or dine,
cui pr^figitur, quaeri oportere, ut verae literse cog-
nofcantur, quae fupra has notas in ordine literarum

prinio

( \ 07 )

primo femper habeiitur : Ex hoc autcm ordiiie notae
delumendse funt, donee alteri alicui indiciim oc-
currirur, quod cum fit, hoc novo indice utendum eft
uc priori. Et hac regula tota feriptura explicabirur,
nifi quod qnandocunque plures indices flint contigui,
omnes praccer ultimum negligi debent : item verborum
aperte Icriptorum interpoutio hunc indicum iifum non
turbat. EIoc modo feriptura occulta, ft pauci errorcs
typographici emendentur, verba fequentia compledh
invenietur.

Curvarum^ qua prohlemati convenhmt^ quaamque
fiimattir ordinata^ illius fluxio fecunda ab ejufdem
fluxione prtmd divifa {ut fermone arlthmetlcorum
iitar') eandem dat quotient e?nj fed contrario figno^ ac
fluxio fecunda a fltixione frimd divifa ordinata ex al-
ter d princif ii abfcijfa farte jacentis^ & ad eandem
ab eo princifio diflantiam* . Hujufmodi autem curva
inveniri ^ojfunt tribus reguUs.

‘Prima regula curvam^ qualem problema re'qui-
rit, ope fpatii hyperbolici d curvd quacunque dedu-
cit^ qua babe at ad a quale s diflantias a principio fua
abfcijfa ordinatas aquales, ^ ab eddem parte abfeif
fa pofitas. Eft enim ordinata curva quaflta^ ut
area alius curva ordinatam habentis a qualem fegmen-
to afmptoti hyperbola terminato a fpatio hyperbolico
aquali area curva primo affumpta.

Regula autem fecunda pendet a primd, & curvam
problemati fatisfacientem fine ope fpatii hyperbolici
ex curvis derivat, qua habeant ad aqualia interval-
la a principio fua abjcijfa ordinatas aquales^ fed a
contrariis partibus abfcijfa pofitas^

Scilicet, fi abfcilTa a fuo principio in oppofitas partes xqualibiis mo- ^
mentis fluit.

Et

( 'o8 )

E't Imc fecunda regttla theorema fequensprabet^ ni-
mirum, Jl aliqua curva Jumatur^ qua problema folvi
fo£it ^er reguLam frimam^ ^ Jl hujiis ordinata in^
Jijiunt abjcijfa ad ferpendiculum^ mvenietur curva
Jroblemati fatisfaciens^ fi ad eandem abfcijfam con-
fruatur alia linea curva^ ed lege^ ut illius ordinata
ex altera farte abfcijfa ubique aqualis fit aggregate
ajjumfta linece curva 13 ejufdem ordinata ; excefui
autem hujus curva Jr a ordinata fud aqualis fit una-
quaque curva conjiruenda ordinata^ qua ex alterd
farte abfeiffa jacet ; omnes enim curva hac ratione
conjlruffa froblemati conveniunt .

Hoc autem theorema demonjiratur Jropoftione fe-
quenti^ quod in omni triangulo redtangulo quadratum
ab alterutro latere angulo reblo adjacenti aquale eji
reEtangulo fub fummd alterius lateris angulo reito
adjacentis laterifque angulo ei fubtendentis^ & fub
differentid eorundem laterum.

"Denique tertia regula derivatur a fecundd, ofe
fro^oftionis nona librl de quadratiird curvarum
Neutoni.

SCHOLIUM.

Exemflum generale, quod axhibui, curva loga-
rithmica^ & cyclois ^lurimis modis invefigari ^of
flint his regulis.

Unus cafus curva logarithmic a commode invenitur
fer regulam f rim am^ajfumftd lined reEid loco curva
in illd reguld memorata.

Alter hujus linea cafus deducitur ex reguld fecun-
dd ofe ffeciei quinquagefma nona linearum tertii
ordinis^ qua omnium curvarum in illd reguld ut ilium
eft fere fmflicijfma Jrater farabolam cubicam 3 hy-
per bo lam conic am,

Cyclois

10? )

Cytloh vptme invenitur theoretnate^ quod a reguld
fecundd deduct d'tximus.

Exemplum ifiud generate facile inveniUir regulci
tertid^ aliis vero regulis non fine ambaglbus.

Regulis fecundd & tertld commodijfime inveniun'-
tur curva geometrlce rationales ; qua deducuntur
etiam a theoremate in regulam fee undam pendetite ;
quandocunque enlm curva ajfumpta tam longitudinem
quam ordinatam rationalem habet^ cujufmodi fmplu
cijjma eft parabola femicubica^ curva quoque invent-
enda ordinata rationalis erit.

^enique his regulis^ vel etiam conditione in prin-
cipio poftd facile eft invenire^ an curva aliqua propo-
fita problemati fatisfaciet^ ^ quibus poftionibus id
fiet : unde intelligi poteft, an eadem curva diverfs
modis problemati conveniat,

Horum brevem explicationem jam apponam, deferi-
bendo, ex amici charta, problematis fequentis Iblutio-
nem.

PROBLEM A.

Datis duabus lineis reeftis AB, CD (in Fig. i.) pa-
rallelis, ad abfciflam A B curva E F deferibenda eft,
quse talis fit, ut in fttu’^inverfb ad ablciftam C D deferi-
pta feipfam femper interfecet in angulo quolibet dato.

Ad abfeiftam C D deferibantur curvse G H, K L ftmiles
& sequales curvae E F, quarum altera huic curvae E F
occurrat in punefto quolibet I, altera vero per pundtumM
tranfeat, ut partes E M, K M curvarum E F, K L ftmiles
Tint & aequales ; & per puneftum M, quod partes curvae
EF dirimit,quae fe mutuo interfecare debent, ducantur
lineae N M (5, n M o, quae cum redtis A B, C D angu-
los lub N OB & fub C N O, item angulos ftib n o A, &
fub o n D conftituant ei aequales, in quo curva feipfam
fecare ponitur. Ducatur I P T S lineis AB, C D paral-

U lela ;

lek; itemhuic proxima & parailela j x p t S ; deindc
ducatur I v lineas N O parailela, & denique I w, S y
parallels lineae n o, ut angulus fub I w j aequalis fit
angulo lub I v x. Jam anguli fob I x w & fob I j v fo
mul fompti aequales erunt angulo fob x I M, ideoque 8c
angulo fob I w v aequales ; unde foigulus fob x I w se-
qualis erit ei fob I j v ; & eodem mode angulus fob j I v
ei fob I X \v aequalis invenietur ; adeo ut triangula I j v,
X I w font fimilia, & jv:Iv::Iw;wx. Porro pro
abfoiffis aequalibus M P, M T feribatur z, pro ordinate
P pro ordinati T S, pertinente ad curva;

K L arcum K M, qui arcui E M curvse E F refpondet.
Crefeentibus autem abfcilHs M P, M T, & flmul in-
crefoentibus ordinatis P I, T S, earum fluxiones primae
cadem habebunt figna cum fois ordinatis, fed utraeque
fluxiones focundae idem habebunt fignum ; nam fluxk>
lecunda unius ordinatae idem habebk fignum cum
foi ordinata, fod alterius ordinatae fluxio lecunda fig-
num habebit a figno foae ordinatae diverfom ; propte-
rea quod curvarum K M, M F alterius concavitas ver-
fos convexitatem alterius convertitur, ut manifeftum
eft. His autem cognitis invenietur j v ; I v (= P p)
:: jy I z, I w (— T t) : w x (— sy) : : z : — &

y : z i \ z I — Vy item — y v — z^, oC denique pofi-
ta z invariabili — yv — y v o, \d y v y v

y . »»

o, ideoque —iz: —— —7- , quando^ ad curvam

y

* ••

E F, fed v 8cv ad curvam K M pertinent. Idem vero
locum quoque haber, quando omnes hae fluxiones ad
curvam EF referiintur, fi abfeifia in oppoficas partes
a fuo principio fluere ftatuitur; nam fompta MO
~ M P, & M q = M p, dudtifque Q^R, q r ad A B,
C D parallelis, pund:a R, r in curva E F pundbis S, s in
curva K M relpondent. Ponendo igitur abfeifiam in

contra-

( )

contrarias partca a fuo principio sequalibus momentis
flnere, Curvarim^ qua froblematt canveniunt, qita-
cunque fumatnf ordinata^ illius Jluxio fecunda a flu-
xmie flrimd d'tvifa eandem dat quotienteniy 8cc. ct
fupra. Haec autem curvarum qusefitarum conditio eft,
unde deducuntur regulse fequentes ad problenaatis fb-
lutionem.

(I^egula Trirna.

CUM requiritur, ut M exiftente =: M P ftc

• • ••

quando abfciffa in oppofitas partes a pun-

jy ^

cfto M sequabiliter fluit, ita ut ejns fluxioni in partibusab-
fciflie, quse a contrariislateribuspun<fti M jacent, figna

V

diverfa tribuenda ftnt, ponere licet ^ — ;a dncftse in

y

qnantitatem quamcunque, quse eadem maneat, & lub
eodem figno, pro eadem magnitudine five ilia aftir-
mativa five negativa fit. Ddcribatur igitur (in Fig. x.)
ad abfcifiam N O cnrva qnxlibet K L, cujus ordinatas
angulum quemcunque datum cum ablcil^ conftituant,
& quas habeat eas ordinatas ^quales, & ab eodem la-
tere ablcifise N O pofitas, quas scqualiter diftant a pun-

_ ••

do M, ut ordinatae P W*, Q^X \ deinde fiat Z- ordina-

y .

••

tae P W X ^ proportionalis, & ^ ordinatae Q^X X z.

Jam (in Fig. 3 .) cxponatur hyperbola Y Z ad afym-
ptotos FA, r 0, angulum lub 0 F A angulo dato liib N
P W squalem comprehendentes, delcripta, & in ab
terutra alymptoto, ut FA, fumatur ad libitum pundum
A, &ducatur AH alteri afymptoto F0 parallela, &
parallelogrammum F H compleatur : deinde in curva
K L ad ablciflam N O, & ad pundum M ordinatim

U 2 applicetur

(■ 111 )

applicetur M n ; fumatur fpatium hyperbolicum A S -
T 2, redta S T afymptoto r © parallela abfciffum, se-
quale fpatio W P M n, & fiat inr.S, e^ue ratione
defcribatur curva ; dico PI curv^ quaefitse

ordinatam efTe ut fpatium M P ^ Hoc autem ma-
nifeftum eft ; fluxio enim Ipatii M FI W P aequalis
eft fluxioni Ipatii A S T 2, ideoque P .W x ^

= fluxioni linese T 2 du(ftae in 2 T vel in j

erit igitur P W x ;s ut fluxio linese r 2 five linese P ^

• •

. y

per ipfam P^> divifa ; fed P W ^ ^ eft ut unde e-
• •

rit P $ X ^ ut 8c neceflario five P I ut fpatium M P
$ qr. ^rima igitur regula curvam^ qualem problema
requirit, ofe J^atii hy^erboltct^ &c. ut fiipra.

In exemplum hujus regulas loco curvse K L (in Fig.
a.) fumatur linea recfta lineae N O parallela^ & erit li-
nea w n ea, quae logarithmica dicitur, cui N O a-
fymptotos eft ; ideoque & linea E F etiam logarith-
mica, per puncftum M rranfiens, & alymptoton ha-
bens lineae N O parallelam ; propterea quod area M P
3>'*Fhic erit utp$ — M {a). Si vero ordinatse
en^, /See y ducantur aequaliter diftantes a punefto M,
ordinatseque M '*P proximse, erunt s n, cc 13 aequales
quando priraum nafeuntur, quoniam fjpatia
y cc tunc aequalia flint ; ex oftenfis autem eft g n x cc^

M g q velM a q, unde syi=:Mi;SCeyjad

'l 1 jyj q,.

ut radius ad finum anguli fub N M Quoniam igi-
tur P I femper eft ut fpatium M P <F, erit P I ubique

^d — , ut radius ad finum anguli fub N M ; &
(a) Vid. Bavrgv. Leitign. Ceometr. p. 123.

denique

( « > ; J

denique limes ordinatarum negativamm ad fpatium to-
rum comprehcnfum a parte ^ w linex logarithmicx w
Cl ab ordinata M ab afymptotoM O ad ordinatam
M ^ applicatum ut radius ad fmum angul>rub N M "i" :
eft autem recftangulum Tub M & iub linex logarithmi-
cx w "i" n fubtangenre ad fpatium prxdi(ftum etiam ut
radius ad finura anguli fub N M : adeo ut limes ordi-
natarum negativarum linex curvx E F .xqualis eric
huic fubtangenti- ; unde fi 'ir M retro producatur ad
ut M huic fubtangenti fit xqualis, & ducatur 6 ^ a
linex N O parallela, erit ilia curvx E F 'afymptotos ;
erit autem curvx hujus E F fubtangens linex M ^ x-
qualis ; propterea quod Me— eftgxj. igitur

cay^^s curva logarithmic £ commode mvenituir fer re^
gulam frimam^ dec. ut fupra.

Hxc autem regula primum oftendit modum, quo
problema folvitur.

^gula^Secmda. >.n ..

Deferibatur curva quxcunque;c M fj(^ per pundum M
tranfiens in Fig. vel;c n c, m p jw, in Fig, 4. ubi cur-
va invenienda duobus cruribus e M F, E M f conftac ;
ut curvarum x M yct, & x n c, m'p fx ordinktx ut P v, Q^,
qux xqualiter a pun(fto M principio abfciflx diftant,
ftnt xquales, fed a' contrariis partibus abfciffx pofttx,
ita ut mutato abfciffx ftgno ordinatx lignum etiam mu-
tetur.

Exponatur potro (in Fig.^.) hyperbola xquilatera
a b cujus axis tranfverfus ag,conjugatus h q, centrum
d, afymptoti dr, d s ; fumatur d t = P y, & 'ducatur
t V w ad h q perpendicularis, junda d vv, fumatur quo-
que d X zz: M n, & ducatur x y item redx linex h q
perpendicularis, junda d y Jam fit curva K L (in
Fig. X,) vel K k L 1 (in Fig. 4.) talis ut fpatium

nMPW

( "4 )

nMP W seqnale fit fpatio adw, fi cum per
pundum M tranfit, aliter aequale fpatio d a w — d a y ;
me enim ratione curyse K L, & K k L 1 non definent
conditionem habere, quse in r^ula priori requiritur,
nempe ut ordinatje ad ^equales diftantias a ptindo M
fmt aequales, & ab eidem abfeiffae parte pontse. Nam
area hyperbolica adw affirmativa efl, quando d t vel
P y eft affirmativa, & eadem area negatiya eft, quando
d t vel Pj^ negativa eft, quia area rota hyperbolica ab
e^cm parte lineae h q jacet ; ideoque area corvarum
K L, K k L 1 ad ordinatam M n terminata fignum
foum mutabit, quando abfcifta M P, magnitudine fer-
vata, fignum mutat ; & curvse ordinara nee magnitu-
dinemnec fignum mutabit, mutatione figni abfeiffie.
Sit porrp * a d ^ = parallelogrammo T S in hyper-
bola priori : quo efficietur ut t w -f- 1 v fit ad ad ut
r 2 ad r A ; fi igitur TA fiat == a d, erit t w -f- 1 v
r 2 m P ?>. Porro ducantur ordinatse g xi a/2y
ordinatse M proximse ; deinde in Fig. x. ubi curva
'P n fimplex eft, cum gw fit ad a /S ut fpatium
M 'p ^ g ad fpatium M y a, erit g n — ; unde

& earum utraque =;M £ zz: M<x. Ideoque g« ad

. M 'P
PI ad

ut radius ad finum anguli fub NM P, & ubique

M^^»P

M'P

in eadem ratione.

In fgurd quart d

ubi curva a> ^ ’P H ex duobus cruribus compofita eft,
£ « eft ad c6 /3 ut fpatium P M g ^ ad fpatium <x y
five ut M ’P ad M , propterea quod M g ~ eft M ct.
Cum igitur necefie fit, ut gw / a/S zz: fit Mg^, fcili-
cet ut crura M F, M E in angulo propofito fe mutuo
interfecent, erit ratio g « ad M g liiDduplicata rationis
g « ad a /3 vel fiibduplicata rationis M P ad M :

- I

(4) Vid. philof. Tixnfaft. No. 338. prop. 4.

ideoque

( llj )

ideoque e « ad fpatium M ^ applicatum ad me-
diam proportionalem inter M ’F, M u£ radius ad
finum anguli ftib N M ^ ; dc generatim P I ad fpa-
tium M ^ P applicatum ad mediam proportionalem
inter M & M in eadem ratione. Eft autem M ^
i=yx + dx, &M%|^=:yx — dx, & ad me-
dia eft proportionalis inter yx+dx&yx —
d X. Unde utrobique dicftis a d, ; d t vel P y, R ;

P$

erit P^> — V^45 + RR-|-R; R=t<2K —

a

a

1^^ P

& P I ad - — ^ — ut radius ad ftnum anguli ftib NM

Regula igitur fecunda fendet a frimd, ^ curvam fro^
blematl Jatisfacientem fine ofe Jpatii hyferhoMci^^c,
ut lupra. Nam hie fine Ipatio hyperbolico curva in-
venitur, cujus quadratuia problema fblvitur.

Duae autem funt in hac regula formulae. Formula prior
nimirum P zz: V ^ ^ R R -f- R, curvarum geome-

trice rationalium, quae maxime hie requiruntur, inven-
tioni accommodatur ; facile enim eft ita lumere quan-
titatem indeterminatam R, ut eurva quadra-

turam admittat; ^ ^ ' .. i=r _"i

Ne calus magis compofiti meihorentur,' ^natur R

m . , f ^ ; ■

vel Py — , lit m Sen ^ umueri fint impaces vel

inter ie primi, vcl eorum alter pnitas : 'hac enim^ratio-
ne curva, cujus -or^nata eftPy, .CQuditionem habebit
in hac regula neceflariam, & erit P$ slaa-\- R R

2JM

-r-am

■4”-R c c z ^ -^c z” z^ }/cc-f~aaz *

79$

Si igitur ^ i ft vel numero ^ ^

n n

qualis, vel ejufdem multiplex, id eft, ft fumatur m =

( "0 )

" 1, 6c ;/ numci'o cuilibct impari aequalis ; pars or'?

■ ' m ^ — 2 ^

dinarse ;s” jcc a a z ~ c fub vinculo in-

clufa, idcoque & 'ordinata rota quadraturam admit-
tQZr(a')

Verbi causa, ponatur — 4, c =z i, & P

® f

. . ; • , i : i J J , *

z:z vT I ~i~ a a T. Unde erit area M

i~\~ aa z\
a a, ' ’ ^

+ , 6c P I —

aa

+ -j-

- — , curvaque quxfita hac sequatione comprehende-

' 2 4

r» T ■ ' * r>T ' * I 3 3 .2*'

tur ^ P I ^ ; 3 >< P I = — + J, ^ : _|L

i ^ ' i '

.s . In hac aequatione cum .2* lignum non mutabir,
mutatione figni abfcifTae z ; pro eadem ipfius magnitu-
dine tarn negativa quam affirmativa P I eandem babe-,
bit magnitudinem, & fub eodem figno ; unicuique au-
tem magnitudini abfcifise z relpondet Sc affirmativa
& negativa ordinata : adeo ut curva quasfita habebit
formam hie appofltam (in F/g. 6.); e tribus conflans
cruribus a:b e, id.e, d f pundtis b, d aequaliter a pundo

M diflantibus quippe eflMd — Mb = — : quan-
do enim eft 5S = o, erit = &PI=±: — .

V V - f «« ai

1 I •

(<t) Vid. in Traft. de quadr, ciUV. Newton, tab. cury, /Implicior. qua:
quadraii polTunt,

Hxc

( '>7 )

Haec autem regulae hujus formula prior fecundum
cxhibet curvas quasfitas inveniendi modum.

p<^ n

In formula pofteriori, cum R fit = [ x — — — ,

R vel P j/ ejufdem magnicudinis manebit, fed fignum
mutabir, quando abfcilTa magnitudinem Itiam figno
mutato retinetjfi P $ talis liimatur,ut mutando abfcifl^

ligaum — convertatur m — , & contra ut ■— conver-
^ a P^ P$

tatur in — . Et hsec formula poflerior tertium conti-

net problema folvendi modum.

Verbi caus^, fitP^> = x — ; — , quando z ell; af-

c + ;s

firmativa, 3c erit R vel P v eodem tempore — \a%

C--Z c + z . n r

^ — J ~~ 5 quando autem z negativa eft, net

c z

= ay. , & R vel Qp z=: lay

c — z c — z

C ^ 'L a c z o

— i — . Hinc autem R a^qualis erit -J- , &

c ~i~ z ^ cc — zz

R z z^ zacz = ccR; ideoque curva jcM linea
tertii ordinis, imo Ipecies earum quinquagefima nona ;
propterea quod sequationis ccRR-j-aacc — O ra-
dices flint impofTibiles (a). Linea autem curva hinc
invenienda, ft fiat (in F/g. 7.) N M vel M O = c, lo-
garithmica eft, cui recfta A B eft afymptotos. Cum

(a) Vid. Newton. Enumerat. linear, tert. ordin, ad Fig. 65.

X enim

( u8 ;

cnim P <[> fit X

c — z

7+^’

erit eadem ==

a c

a z

c Ar &

, . Si igitur (in Fig. 8.) in red! line^ quacunqiic

C ~j <2»

oL g fiimatur a x zz: O M =z r, & ei ad perpendiculum
erigantur ol jul quarum x. — & fi afympto-

tis ociycc^ per pundum defcribatur hyperbola ^n,Sc
liimpta X y ~MP ducatur y p afymptoto a |5

a c

parallela ; parti -j- — ordinatae P relpondet area,

quae erit ad aream xjut^pv ut flnus anguli flib N P I ad

a

radium, 3c alteri parti — j- — ejufdem ordinatae relpon-
det area, quae erit xv — ;c ^ ^ v in eidem ratio-

ne (a) . Unde P I, quae eft ad ^ radius ad fi-

num anguli fiib N M f", erit zz: — xv. Si igi-

tur fumatur 0^—0 M, 8c ducatur M ordinatae P I
retro produdae occurrens in ut fit P =:= P M — ;c vy

erit : ideoque linea M I logarithmica,

cui A B alymptotos eft, & M ordinatim applicata,
efliciens cum afymptoto A B angulum fub A 9- M ver-
fus contingentem aequalem dimidio anguli fiib AON.
Alter igimr htijus linea c a fits deducitur^ dec. ut fii-
pra.

Magis generatim, ft r ordinatam curvae alicujus de-
notat, quae inftar curvarum % M /x, & n c, m p ad
abfcifTam N O deferipta ordinatas habeat aequales, quae.

Vid. New ten. de quadr. curv, tab. ciU'V. fimpl. qua; cum circ. & hy-
compai-. pofTunt, form. pi%.

sequalitcr

( 119 }

icqualiter diftant a pundio M, fed a contrariis parti-
bus abfcifl* pofitas, poni potefl ordinata Pi=an

— ' - ' I r ^

l,:^cr-l-drr^er^-}-dcc xh ^kr-\-lr r^&ccf^

^z±fr“f- drr-:t er^ -f~&c x/t:gr-j~ SccJ^ x J^':tkr-j~/nr£:&^^ •

Ex priori hujus regul^ fecund^ formula deducitnr

quoque theorema, cujus fupra fit mentio, ad inveni-

endas ciirvas tarn rationales quam irrationales utile,

quod quartus erit modus problema folyendi.

•

Theorema.

Quoniam eflP^> — ay^^^rf-RR + R, & R— Py,

R P p

manifeflum eft, ft — vel — fit ut fluxioordinatae, quas

ablcift^e fuce ad perpendiculum inftftat, alicujus curvae,

^ + R R . ^ .

erit — , ut ejuldem curvae fluxio ; curv« an-

tem hujus ordinata aeqnalis erit areae curv^ />«. ad
applicatce, ft angulus fub M P y recftus ftt, & cum area
curvarum (in /7^, 2,, 4.) & Jt n c, mp yu, eodem

ftgno ajfftciatur, tarn quando abfciffa eft aftirmativa,
quam quando eft eadem negativa, quoniam areae ad di-
verfas abfciftae partes in illis diverfts caftbus jacent ; &
praeterea cum eifdem abfciffte magnitudinibus areas
aequales refpondeant, curvae, quales problema requirit,
inveniri pofTunt curvarum ope, quarum ordinatx ad
cafdem abfciftae magnitudines aequales ftnt, & ab ei-
dem abfcifTas parte pofttae, ft modo ordinate inftftunt
abfciftse ad perpendiculum.

Defcripta ftt ejufmodi curva n o, qux tangat abfcif-
fam in puncfto M (ut in Fig. 9,) ft evanefcat, quando
abfcifta eft = o, fluens quantitas fluxioni longitudinis
curvae n o refpondens ; aliter, quse habeat ordinatam
primam M ni (ut in Fig. 10.) a^qualem magnitudini

X 2 fluentis

( )

fluentis iftitis quantitatis, quando abfcifTa eft — o. Eri-
gantur ordinatas P p, Qjq ; deinde erit P I curvse quae-
fitae ordinata, quae ab altera parte pundti M jacet, vel
= Mp + P p, vel = M m p 4- P p I) ordinata autem
aR, quae ab altera parte pundti M cadit, vel = Mq
— C^q, vel = Mm q — ■' Q^q.

Obfervandum autem eft hoc theorema aliquando
partem duntaxat curvae quaefitae delcribere.

Ex ratione autem, qua hoc theorema inveftigatur,
manifeftum eft duo crura curvae hie deferiptx ejuldem
lineae efte partes : nimirum utriufque naturam eidem
aequatione definiri. Hanc autem curvam in fttu inver-
Ib difpofitam fe intcrfecare in angulo aequali angulo fiib
NOB inde manifeftum eft, quod recftangulum fub flu-
xione PI & fub fluxione Q^R, ordinatarum fcilicet ae-
qualiter a pundto M diftantium, aequale eft quadrate
fluxionis abfeiftae : ft enim curvae n o ordinatae w r,x t
applicentur ordinatis Q^q, P p proximae, & P x, Qw
ftnt aequales, dc ducantur r s, tv abfeiftae N O parallelae,
erunt triangula p t v, q r s redtangula ftmilia & aequalia :
m omnt autem trtangulo re^angulo quadratum ab al-
terutro latere angulo re^o adjacent i aquale eft reVlan-
gulo fub fUmmd alterius lateris angulo re^o adjacen-
tis laterifque angulo ei fubtendentis^ ^ fub differen-
tia eorundem later urn. Igitur tv' = Px" — pt-f-pv
X pt — pv — pt + p V X qr — q s : eft autem ultima
ratio P X ad p t + P V ea, quam fluxio abfcilTae habet
ad fluxionem ordinatae P I ; & ratio P x vel Q^w ad
q r — q s ea, quam ftuxio abfcilTae habet ad ordinatae
Q_R ftnxionem. Unde conftat propofttum; Regula
igitur fecunda theorema^ Sec. ut fupra.

Jam ft n o fit circuli circumferentia, linea E F cyclois
€rit, quando anguliisfub NOB vel fub N P I reeftus eft.
Porro ft curvae no longitude cum reefta conferri poteft,
quarum curvarum ftmpliciftima eft parabola femicubica,

curva

( 'it )

cnrva inventa rationalis erit. Speciatim parabola le-
micubica, fi rite difponatur, ejus curvse partem dimi-
diam exhibebit, quam in exemplum formulae prioris
legulx fecundae delineavinaus ; Icilicet (in Fig. 6.) crus
d e, partemque inferiorem b c cruris a b c. Reliquse
autem illius partes defcribi pofTunt, fi retro producatur
ordinata I P donee pars produdla sequalis fit M m p —
P p, & producatur R ab altero abfeifix latere, do-
nee pars prodiidta aequalis fit M m q + Q^q.

Nunc tranfeundum eft ad regulam tertiam, quae etiam
curvas geometrice rationales largitur.

^gula Tertia.

Regula haec tertia duos quoque compleditur pro-
blema folvendi modos a prioris regulae formulis propo-
fitione noni tradtatus de quadratura curvarum Newfoni
.derivatos.

Propofitione ifta ad formulam regulae pr^cedentis
priorem adhibita invenitur area curvae, cujus abfeifi
fa eft 8c ordinata J -f- RR + sequalis areae

curvae, cujus ablcilla eft R & ordinata ^^/^« + RR

Hinc autem quinto modo folvitur pro-

blema.

Verbi caus^, ut exemplum generale, quod antea (a)
exhibui, inveftigetur, pofitis M P — js, & P = R, ut

prius, fiat R” 'n d R% & erit .s R

{a) In A<a, Erud. Menf. April. 1721.

( )

•f/ tl

yf JL r A d R* ; fmt autem mScn numer i im^

m * m-\~'2< ft

pares vel inter fe primi vel eorum alter unitas ; ut fig-
na abfciffse z dc ordinatae R fimul mutentur, ficut in

tegula priori requiritur ; jam erit ordinata — s/^ R R

R

m

m — n
n

R nZ R
R

j< + ^R" ; area igitur curvse, cujus abfcifla eft &
ordinata si a a ~i~ R R + R, aequalis erit are^e curvae,

nt — n __________

cujus abfcifta eft R & ordinata R"^ x c + ^ R" H

s/^^+RR + R” X c-j~ d R % fi modo haec pofte-
rior ordinata cum ablcifs^lu-^ angulum contineat aequa-
lem angulo lub N M ^ ; unde hujus pofterioris curvas
quadratura linea exhibetur problemati fatisfaciens. E-
rit autem haec linea curva geometrice irrationalis, nift
w & « certos quoldam numeros defignant, vel certa
quaedam fit relatio inter coefiicientes c,d; hae autem
conditiones ratione fequenti inveniuntur. Erit (a)

m _

area curvae, cujus abfcifta R & ordinata R" H
„+R ”

K c d R* X si 'd a ”4~ R ^d R

n

c +

n

m ft fn ^ '^n

m ___________

«/R‘ + R" n a + R R]’

n

m aa

d —

w -f-' 3 n

\/ r*

A C

maa

m-

-xn
a a

R* ut ftnus an-

n

{a) Per prop, quint, quadr. ciivv. Newton.

guH

ma a

Et hie quidem ultimus cafus curvaiii exhibet,qu2e theo-
remate prascedenti a parabola femicubica invenitur.

+ . . . . +/R^, ubi { numerum quemeun^

Z n

que parem denotat ; unde fiat z. R» x ^ +

Tf%

Sc curvae n ordinata zizR» xr-f-^R*-f-^ R* •

* * • • ^ ^aa~l~RR-}-R. Hinc (a) fi » fit imi-

tas & m numerus negativus numero /-{- i major, cur-
va dabitur geometrice rationalis, vel fi certa quiedam
relatio fit inter coeffidentes r, 4 ^5 quae re-

latio facile invenitur ut antea.

Porro ad alteram regulae lecundic formulam adhi-
bendo propofitionem nonam memoratam libri de qua-
drature curvarum, lextus oritur problcma Iblvendi.
modus.

Litere r denotante ut ftipra, fieri poteft ordinata

abfeifia eft .s & ordinata sequalis erit are^ ciirvae,

f» — «

Magis generatim ponere licet ^ R » xr-p<^R‘

P$ “ X

area curvee, cujns

^ — cr-\- dr' r —

(4) Per prop, proxim. citat.

ciyus

( >^4 )

cujus abfdfTa eft r 3c ordinata a y.

^ h-^cr + drr+&c
^ — cr-\-drr — &c

* w — n —

Ponatur igitur — zzr ” + + + x

r -

^ — cr-{- d rr — x ^ ^ ^ ^ ^ ^ ^

X r -j- -f- ^<^^5 & curva, cujus ordinata eft r

conditionem hie neceflariam habebit. Erit enim z

= r ” x b b X b d — cc x r r d d * x

A+ r r -\- Q (^c, cujus leriei coefficientes A, Bj
C dantur per propoficionem quintam Tradatus de
Quadratura Curvarum. Manifeftum autem eft nec

terminos hujus feriei nec quantitatem bb-{-zbd — cc
X rr -^d dr‘^-{~ ^ ' figna fua mutare mutatione

figni quantitatisr ;'quantitas autem , ft m, n numeri ftnt
impares, ftgnum mutabit, quando ipla r ftgnum mutat ;
ideoque ordinata r 8c abfcifTa z ftgna ftmul mutabunt .

Ordinata autem a x

m — n

z b-\-cr-\-drr-\- ^ c
^ ^ b - — cr-\~drr —

erit

” xbb-{-xbd — ccx r r '

X b-\~cr-\-drr-\-^cY • Et hinc facile inveniri poft
lunt curvse rationales.

Pro exemplo ftmplici ponatur ^ — i — m — d.

— o ; unde erit — ~ b b — c err, z~ b b r

r

— ~ c c r\ Ordinata autem curvae metiendx ^
abb-{-xabcr-\~accrr‘, ejufdem igitur area eft
0l6. a h b r a b c r r L a c c r^ ut ftnus anguli fub
N M 'i^ ad radium ; ideoque erit V\^ibr-\-bcrr

X. >15 )

4- 1 r f r\ Hinc autcm invcnitiir parabolam femicu-
bicfim proHcmati fatisfacei-e, quaiii ita dcfcribere opor-
tet. Data (in Fig. ii.) linca rcda A B, & ineapiui-
<5lo C, iina cum liiiea red^ C D anguium fub .BCD
cum linea C B conftituente sequalem angnlo, in quo
CLirva fe incerfecare requiritur. Ducatur ad libitum
H G I ad CD parallela, lumaturque in G H =:
2 C G ; deinde dividatur angulus liib A C D in duas
partes sequales linea reda CE, & denique ad diamc-
triim H I & verticem H defcnbatur parabola femicu-
bica K H L, quse tranleat per pundum C, ita ut C E
ordinatim applicetur ad diametrum H I. Hxc para-
bola ad eandem lineam fimiliter applicata, fed fitu in-
verlb, fe interfecabit in angulo sequali angulo fiib BCD.

Si placet curvas hac regula inventas theoremate
prsecedente conflruere, ex iis, quse hie tradita funt, cur-
va huic negotio apta inveniri poteft ; erit enim curvse
illius ordinata sequalis areae curvx ;t ^ ad ^ applicatas,
quando angulus fub M P v redus ell. Verbi causa,
hujus areae fluxio, nimirum P j/ x i in exemplo fecun-

m — K

do prioris partis hujus regulae erit = R R x R «

xr+^R' + ^’R^ +/RA izi R R^ X r + ^ R^

-f- ^ R^. • • • +/R^i ; ideoque curvae hie requifitae or-

I n n

dinata erit — — R n x — i — c 4 i d R*

a w + ^ mF I

n

+ — L— • • • + —

^ m-\~ 5'^

In exemplo poflerioris partis hujus regulae erit R

(=^ax

a

'2.bcr-\~icdr^~\~

bb-\-zb d^cc Xrr-\-ddr‘^

Y ideoque

( \t6 )

. ‘ . !? *'

ideoque K z — r n xzbc-\~2.cdr^~{- &c x

bb-\-i^bd — 9 haec igitur
eft fluxio ordinatse curvse qusefitse.

Si fit m~ I — n — d, &c z=z o, erit Rxi —
X b c rry 3c ordinata curv^e quxfitx — b c rr; quo-
niam igitur z — erit b b r — } c c r\ erit curva quse-
fita in hoc cafu parabola divergens cum nodo, quse
definitur hac ^quatione 3 e ;s — 2, eyy -f-

e e y (a). Et hac curva deferibetur parabola femicu-
bica ftipra inventa.

Verbi causa, ad reeftam lineam (in Fig. 12.) A B du-
catur perpendicularis C D, & ad illam ut axim delcri-
batur ejufmodi parabola divergens F E C E G. Dein-
de ducatur ad libitum H I angulum quemeunque datum
cum redla A B conftituens, Sc ducatur H K L AI ad
C D parallela ; deinde lumatur H N =z H K + ^irc.
C K, H O = H L ~r arc. C K L, & ab altera parre
pundi H, HP = CEM — HM; Sc curva hac ra-
tione delcripta parabola femicubica erit.

Hinc apparet quomodo curvse, quarum inveftiga-
tioni reguia hsec tertia aptatur, theoremate prsecedenti
conftrui poftunt, poftquam earum formas cognolcun-
tur, fed hae curvarum formas, a quibus rationales deri-
ventur, reguia hac tertia optime inveniuntnr.

Has funt tres regulae, quarum fupra fit mentio. Ul»
tima lententia, quae fub notis fidis celata fuit, exempio
fequenti illuftrari poteft. Sit y \c[ — a -f- ^

J c d x ~\- e X vel — , , quae

d-\-cx ^

dnae

I

ip) Vid. £aiuncj:ar. luicar^ tert, ord. Fig. 73'*

)

dux xquatioiies omiies compleduntur fcdiones'co-

« •

Bicas. Inde vcro inveniemus 4^ vel

y

■^dd

e c

d-j~ e X
z, vel

-j-^jjc-f-zdx-i-exxxc-l-idx-j-exx

z c d d z a e e ^ z b d e
‘ - - . — z ; qux xqua-

d e X X b d — a e-\- z c d x-\- c e X X

tiones oftendunt in nulli fedione conicaj quomodo-

cunque dilponatur, quantitatem 4^ conditionem ha-

I ^

bere, quam hoc problema requirit ; ideoque nullam
ledionem conicam problemati latisfacere . Quod com-
probari etiam poteft examinando redangulum liib flu-
xionibus primis ordinatarum xqualiter ad diverfas par-
tes a principio abfciflx diftantium.

Hinc autem cognolcitur nullam lineam curvam geo-
metrice rationalem problema fblvere, qux parabola le-
micubica fit fimplicior.

Si vero ralis inter quantitates a, b^ c, d^ e relatio fta-
« •

y

tui potuifTet ut ^ conditfonem in hoc problemate ne«

celTariam obtineret, nernpe ut quantitas, qux in z du-
citiir, eadem elTe potuifiet, & fiib eodem hgno, pro
cadem magnitudine tarn negativa quam affirmativa ab-

fcilTx z, quo eveniret ut foret r- , fi abfcif-

y

fa in oppofitas partes a fuo principio,. xqualibufque
liiomentis fluere ponitur : turn profedo fedio conica
hinc dcterminanda vel problema folveret, vel fedionis

Y z proble-

( )

problemati fatisfacientis ordinata ad ordinatam hujiis
rationem haberet datam.

Jam vero his regulis alias aliquot, quas ab amico
accepi, ad problema folvendum adjungam.

Quartxi*

lifdcm polrris ac in regula prima, fit (in Fig. 13.)
N O ad A B, C D perpendicularis ; Tint P I, Q^R ordi-
nat2e ^equaliter a pund:o M diftantes, & fit curva G H
per pund:um I dud:a fimilis & ^qualis curvse f E F.
Ordinatis P I, Q^R parallelas & proximas ducantur
Tr j 1, ^ r, & linese reciae I k, R s linese N O parallelae.
Angulus liib s R r = eft angulo lub k 1 1 ; unde an-
guli fub j I k, s R r ftmul fumpti aequales llint angulo
dato fub j 1 1 ; & quantum angulus fub j I k dimidium
anguli ftib j 1 1 fuperat, tantum angulus fub s R r ab eo-
dem dimidio deficit. Siigitur {mFig. 14.) radio quoli-
bet m n circuli arcus n o defcribatur, & lumatur angulus
fub n m p dimidio anguli dati fiib j 1 1, angulus fub
n m q angulo fub j I k, & angulus fub n m t = ei
fub s R r, fe&ores q m p, p m t erunt sequales. Pofica
autem I k — R s — i, erit j k ut tangens anguli fub
j i k vel anguli fub n m q, & r s erit ut tangens anguli
fub s R r vel anguli fub n m t ; ideoque & fluxio or-
dinatoe P I erit ut tangens anguli fub n m q, nimirum
ut n V ; & fluxio ordinatas Q^R ut tangens anguli fub
n m t, nimarum ut n w ; curvse igitur $ H, cujus areae
ordinata P I proportionalis eft, ordinata P<I> poteft
efte aequalis tangenti n v, & ordinata ab alters
parte pundi M n w. Quoniam autem fedtores
p m q, p m t funt sequales, conftitui poteft fecftor pm q
^qualis areas MIlWP curvae cujufcunque KL condi-
rionem habentis in regula primi indicatam; Sc fedfor
p in r aequalis areas M n X Q, ejufdem curv£e. Dcni-

que

( ‘i? )

^ %

que fi ducatur- Hnea redla lineae parallela 8c
proxima ; cum angulus lub s M w =: fit dimidio anguli fub
j 1 1, vel angulo lub n m z, erunt triangula ^ M n m z
fimiiia, 8c prima ratio $ n ad g M eadem cum ratione

zn adnm; ideoque g« — — — , propterea quod

nm

gM zn eft

& = n z. Hie autem ha-

betur feptimus modus, quo problema Iblvi poteft.

Si loco curvae KL linea redta fumatur, quicunque
fit angulus fub n m z eadem deftribetur curva ; adeo
ut hac ratione invenitur una eademque curva, quae di-
verfis fitibus in angulo quocunque dato problema Ibl-
vit. Hsec autem curva a circuli & hyperbolae quadra-
tura dependet ; ft enim ducantur m t, n o- ad m n per-
pendicularcs, quarum n o- = fit m n, 8c afymptotis
m n, m <r hyperbola w o- defcribatur,& deinde q (p y,
p 6 ducantur lineis m r, n o- parallelae ; quando M P

m eft arcui circuli p q, erit ordinata P I zn ■ ^ ^

mn

m n — ftt X Mn (a),'

ft

^gula Quinta,

Delcribatur (in Fig, 13.) curva zMyw. ut in reguld
lecundi, & (in Fig. 1 5*.) radio m m n deferibatur fe-
micirculus ct /3 cuj us centrum S', fit autem cT/S dia-

metro a y perpendicularis. Sumatur S' g z= P r, duca-
tur g ^ ad S' /3 parallela, jungaturque S' Deinde fit
curva K L ejus naturae, ut area M n W P lemper aequa-
lis fit fedtori /SS'^. In circuli area {Fig. 14.) no du-

dtis

{a) Vid. BaiTOY. led. geometr. pag. no.

( no )

&is p », fmu arcus p q, & p 9 fmu arcus np, pr^ducatur
mpadz, ducaturque z? adpn parallela. 1 orro di-
ais mn = mp,<?; ni6,^; nz.,f; p«,R; nv,jy;
erit ut mp : P« : mz : z|, fedut m9 : mn (mp) : :
m 11 : ffl z ; ex lequo igitur ut m9 (^) • p«(R) • • mn
r:.Z I : : : z V (j - C) uude -

^c = KJaa+yy^ & deniquejy _ n v _ P 1> —
i?l/c-\~aKJaa — RR

Hinc autem modo o6l:avo iblvitur problema.

^gula Sexta.

Per propofitionem nonam Trad:atus de Quadratura
Curvarum area curvae, cujus abfciffa eft z 8c ordinata

i/>c + R jequalis eft arete curvte, cujus

— R R ^

abfcifTa eft R& ordinata A ,

R

^ ^ . R R

Unde habetur modus nonus problema folvendi.

Liter£E m Sc n eadem denotent, ac in regula ter-

m — n

Z .I..-,.-— — — V p

tia, & fiat R ” x bb — R^ , & ordinata

R

m — a

z, b b c a'R ^ a a — RR

g-X ^^_RR fict = ^^CR »

m

^^_RRf ' -f- 4 R~” X <5^ — Rg''’~'xv'rt«— RR.
Unde fi n unitatem denotet, & ^ numerum quemcun-
que integrum & affirmativum, curva geomevricc ratio-
aalis invenktur.

Regula

( )

^gula Septima.

Ducatur (in Fig. /S a femidrculum cc(ly con-
tingens in /3, & producatur ad duda^j^/^. Sic
autem curva (in Fig, 13.) K L ejus iiaturse, ut area
M n W P — fit fedori ^ ^v. Didis igitur m n, ; n z,
c ; & tangente arcus p q, R ; erit n v P $ =:

aa c F

“Sa — decimus problema folvendi
modus.

Quando anguJus interfedionis redus eft, 8c c=i
hsEc regula lub formula pofteriori regulte fecundse com*
. prehenditur.

Item ft loco }ils/l (jL linea reda fumatur, quicunque
fit interfedionis angulus, cafus ille curvse logarithmi-
C2e invenietur, quern in regula fecundi tradidimus,

^gula OBaVa..

Ut antea, eft area curv£e,.cujus abfcifta .s &ordinata‘
— , sequalis areas curvas, cujus abfcifTa eft

aac~{-

Hie autem eft unde^

R Sc ordinata — x ^

R aa — cR

cimus modus problema exequendi.

Literis m, n iifdem denotantibus, ut antea, fit

z

¥

m — n

Z, c$ U C ^ <!?'R

R « X a"' — cc RKl^ ; Sc ordinata -7 x

I ’ R aa — cR

m — n

ftet=;R » X ^ xR + ^^^’K.'R

X a

t Mi )

: qux formula curvas geometries
rationales facile prtebet,

Si fit m~i:=:zn ; eadem parabola femicubica
atqne ex regula terdi invenietur.

^gula nona.

Si (in Fig. i6.) NO ad lineasAB, CD perpendi-
cularis fit, Sc ducatur curva K L, cujus ordinata: P W,
Q^X, quas aequaliter a pimdfo M diilant, aequales fint,
Sc ab eadem abfeiflas parte pofitse ; radio ordinatae
P W acquali deferibatur circuli fegmentnm a b c,
quae angulum comprehendat angulo sequalem, in quo
curva fe ipiam fecare requiritur. Ducatur autem 8c
alia curva jcM jut, cujus ordinate Vv, Q^p ^qualiter a
pundlo M diftaiites fint sequales 8c a contrariis partibus
abfeiffae N O pofitae. Deinde fumpti M f P i/ du-
<5taque f h linese NO ad perpendiculum,jun(St^uec h,
manifeftum eft, ft curva quaeftta E F ejus fit naturae,
ut contingens in punefto I femper fit parallela lineae ch,
propoftto fatisfaciet. Nam cum fit W P = Q^X, idem
circuli fegmentum ordinatis P W, Q^X convenit ; adeo
ut ft lumatur M g = ducatur g k ad NO per-
pendicularis, 8c jungatur c k, linea redta contingens
curvam quaefttam E F in pundo R parallela erit lineae
c k. Quoniam igitur Q^p eft P y, ideoque M g zzr
M f in fttu hujus curvae E F inverlb, 8c quando pun-
<ftum R in pundtum I cadit, contingens in punefto R
lineae punefta a, h conjungenti parallela erit. Sc cum con-
tingente in pundto I angulum conftituet aequalem ei lub
a h c, nimirum angulo in fegmento ab c comprehenfo*

Invenitur igitur hujuftnodi curva, ft fiat utjy : : : f h

: f c. Quamobrern ft pro P W ponatur m ; pro a M

(' !33 )

— Me ponatur 7i ; pro intervallo inter pundtum M
Sc centrum fegmenti ponatur / ; Sc pro P M f,

^ ; habebimus y \ z, \ \ j mm — ^ i/ • ^

Dantur autem ratio-

n-Vq

nes inter ob datum fegmenti a b c angulum, Sc

invenieturjy vel P I metiendo curvam, cujus abfcifTa eft

z Sc ordinata ^ ^ Hie autem exhibe-

n-\- q

tur duodecimus modus problema traeftandi.

Si angulus fub a h c fit redtus, erit ^ — o,n — m\

Sc ordinata curvx metiendse J

m

Qiiam profe-

m-\~ q

dto ordinatam problemati fatisfacere, intelligi quoque
poteft ex pofteriofi regulse fecundse formula.

Si loco linearum curvarum K L, ;c M /a redtee fuman-
tur, quando angulus fiib a h c redfus eft, erit curva E F
cyclois ; quse facile determinatur form^ undecima ta-
bulae curvarum fimpliciorum, quae cum circulo & hy-
perbola comparari pofTunt in Tradtatu de Quadratura
Curvarum Newtoni.

(^egula Dedma,

Porro area curvte, cujus abfcifTa eft ^ & ordinata

Vmm — q q P •. n
^ . — , ^equalis eft turn arese curva:, cu-

n-\~q

jus abfcifla eft & ordinata x

mm — q q -f~ p

m n q

turn areae cur vac, cujus abfcifla eft ^ ordinata

z V mm — qqd^P

~ X —

n -f- q

Unde habentur duo alii mo-
Z di,

( >34 )

ili, quibus problema folvi poteft ; quorum pofteriori,
ratione fequenti, curv^ geometrice rationales inveniri-

numeri impares, n numerus par, & ponatur

_ iT — g

z= ^ 6 X item m-=. Unde

eric z — areae curvae, cujus abfeifla eft ^ & ordinata

V m m — q q -\-p

^ t X & ordinata — x 2

q n q

fiet = — n'^’^'^q-{-n''~'^q q-]r8cc — —

X \ — 'nqq±f-

His quatuordecim diverfis modis generalibus amicus
mens problematis fblutionem abfolvit. Demonftratio-
ncs autem illiuS ex compofttione ufus in hoc proble*
mate curvarum Geometris notarum fic fe habent.

poftunt

Sint

T>q Caju prhno Line arum logarithmic arum.

Sit (in Fig. 17.) AB linea logarithmica afympto-
ton habens C D ; eique ordinatim appliceriir E F,
qux fit fubrangenti logarithmicae sequalis. Ad lineam
reeftam E F & ad quodcunque in ea pun(ftum I con-
ftituatur alia linea logarithmica G H I priori fimilis 8c
jequalis, fed fitu inverlb difpolita. Deinde ft contin-
gentes H L, H M ducantur, dico angulum ftib L H M
angulo fub C E F eftc sequalem.

Ordinatim applicetur H N, fiat E O ^ E N, ordi-
natim applicetur O P, & ducatur contingens P Q.
Punefta P & H aequaliter diftant a redta E I, unde
pundum P in curva A B pundo H in curva G I
relpondet, dc angulus fub O P Q_— eft angulo ftib
N H M, propterea quod curvse AB, GI ftmiles funt
& sequales . Quoniam vero curva A B eft logarith-
mica

( '35 )

mica & E N, E O sequales, erit NH kOP=iEF^.
Eft autem E F nz N L = O Q, unde ut N H : E F
(NL) : : EF (O Q^) : OP. Cum igitur anguli fiib
H N L, (^O P Tint sequales, triangula H N L, QO P
liint ftmilia, & angulus fiib Q^P O, qui cequalis eft an>
gulo fub N H M, iequalis quoque erit angulo fub N L H.
Unde anguli fiib N H M & fiib N L H asquales erunt,
& angulus fiib L H M angulo fub C N H five angulo
fub CEF ssqualis. Q: E. D.

De Cafu altero Linear um Logarithmic arum,

Sint (in Fig. i8.) AB, CD dux linex redx paralle-
Ix, intra quas quxlibet alia linea recfta E F ducatur.
Ad alymptoton A B defcribatur linea logarithmica
G H, cujus fubtangens fit xqualis linex E F, & ordi-
natim applicatx comprehendant cum afymptoto angu-
los verfus contingentes xquales parti dimidix anguli
fiib A E F. Quibus pofitis, fi ad alymptoton C D
alia defcribatur linea logarithmica I L M priori fimilis
& xqualis, & ft ducantur contingentes L N, L O, dico
angulum fub O L N angulo fub B E F efte xqualem.

Ducatur N P, ut angulus fiib A N P angulo fub A E F
fit xqualis, & erit N P n: E F. Sumatur N linex
E F five fubtangenti linex logarithmicx xqualis, jun-
gaturque L. Quoniam igitur L pun6tum Q_
conjungit cum puncfto contadus L, Q^L ordinatim ad
afymptoton A B applicabitur, ideoque angulus fiib
L verfiis contingentem L N xqualis erit parti di-
midix anguli fub A E F vel anguli fiib A N P ; eft au-
tem N P = E F = N Q^, quoniam igitur N P, N Q^fiint
xquales, & angulus fiib L Q^N xqualis dimidio angu-
li liib A N P, red:a QL producfta tranfibit per P efti-
ciens triangulum P N ifofceles. Eadem ratione fi
ducatur O S, ut angulus fub COS xqualis fit angulo

Z X fiib

(

fiib A E F erit O S = E F ; fi vero fumatur O R ::z;

E F, ducaturque R L, ordinatim ea applicabitur ad
alymptoton C D, & produdta tranfibit per S, propte-
rea quod liiiea I M nmilis eft & aequalis linece G H.
Erit autem angulus fub - P R L (= angulo fub L S Q^)
:= angulo fub LQ^S= angulo fub NPQ. Unde
erit angulus fub L S Q^= angulo fub N P Q^, &
triangula S L Q^, P N fimilia funt, angulufque
fub S L = angulo fub P N = angulo fub
B E F. Eft autem & L S zn L Qj O S = N item
angulus flib O S L {— angulo fub O R S) = angulo
fubNQ^L. Triangula igitur OSL, NQ^L sequalia
flint, habentia bafes O L, N L sequales. Sc anguJos lub
N L Q^, O L S, etiam sequales : auferatur communis
angulus fub N L S, & relinquetur angulus fub O L N —
angulo fiib S L angulo fub B E F. Q- E. D.

De Cycloide.

' Sint (in Fig. 19.) AB, CD duserecftse linear paralle-
Ix, quas E F ad perpendiculum fecet. In diametrum
E F defcribatur femicirculus E G F, & eo femicirculo
dcfcribatur femicyclois F H. Jam ft alia femicyclois
ILQ^priori ftmilis & seqiialis fed fitu inverfo intra pa-
rallelas defcribatur, & ft contingentes L M, L N du-
cantur, dico angulum fub M L N reiftum effe.

Sit I O P femicirculus, quo defcribitur femicyclois
ejus diameter IP; ducatur LGO, lineis A B, -
C D parallela, Sc jungantur F G, G E, I O. Erit de-
inde contingens LM parallela red'a; F G, & contin-
gens L N parallela redse I O, quae parallela eft redae
EG. Angulus igitur fub MLN m eft angulo fub
FGE redo, idcoque annulus fub MLN redus eft.
Q: E. D.

( '37 )

De Tarabola SemiculicL

Si (in 20.) redtam lineam AB alia red:a linea
C D interfecat in pund:o D cum linea A B anguluni
quemcunque conflituens ; Sc fi fumatur D E — j D C-;
dcinde ducatur EF, ut D F fit D E ; & denique
diametro C F & vertice C delcribatur parabola femi-
cubica G C H, qu2e tranfeat per pundtum E, habeat-
que ordinatim applicatas ad diainetrum C F linese F E
parallelas : his pofitis, fi parabola h^c ad lineam A B
in fituinverlb delcripta Fit, ut eandem in fitu jam didto
defcriptam interfecet, & contingentes ad pundtum in-
teriedlionis ducantur, iJIae contingentes fe interfeca-
bunt in angulo ^equali angulo fub CDB.

Sumatur in parabola G C H pundtum quodvis I,
ducatur I L C, 8c lumpta E M zn E L ducatur M N C.
Deinde ordinatim applicentur 0 1 P, N Q^R, ducatur-
que C E V, item E X diametro C O parallela. His
pofitis erit VX : X E : : EF : FC, & XE : XP : :
D F : E F. Unde ex ^quo ut VX:XP::DF :FC,
dividendoque ut V X : V P : : D F : D C. Qiioniam
igitur efl: D F ziz D E =: i D C, eft etiam V X “ 5 VP.
Porro utIO^:EF^:: COf:CFr::VOr:EFr.
Quatuor igitur ratione continuata proportionalium eft
V O fecunda, quarum I O eft prima & E F ultima. Eft
autcm Sc lO : O V : : LF : EF. Ideoque funt lO,
O V, F L, F E quatuor ratione continuata proportiona-
les; unde ut VO : LF : : LF : E F : : V O — L F :
L E, componendoque ut L F + E F : E F : : V O —
EF (=zVX):LE. Demonftratum autem fuitVX
jequalem efte dimidio linex VP. Ut igiturxLF-j-
a EF : B F : ; VP ;LE : : 2 LF E + 2 E F^ : E F
jamverout IO:LF (::IV:LE) ::LF^(2LFE

L E ^ — E F : E F ^5 propterea quod Jinex I O,

VO

C ‘38 )

V O, L F, E F funt quatuor ratione continuat^ propor-
tionales ; quoniam igitur ut V P : L E : : x L F E +
xEF^:EF^, erit ut P I : L E : : 3 E F^ — L E^
: E F Eodem modo demonflratur ut N R : E M : ;
3EF^-— EM^ : EF^. Cum igitur E M zz: fit E L,
erit N R zzz P I, lunt autem parallels, ideoque punda N,I
sequaliter diftant a linea AB. Si igitur parabola femi-
cubica G C H in fitu inverfo ad lineam A B delcribatur,
pund:um N incidere poteft inpun6tum I. Parabolae huic
detur ille fitus inverfus h eg-) Sc ducantur contingentes
lrS,EW,ANT,n^; item line^ WLY, WZM.
Erit ex natura parabolae hujus OS = ! OCjFW —
^ FCj&C^Tzii^QC. Eftautem&FD — ;FC;
undeFD, DE, &DWfunt aequales, Sc angulus fiib
FEW red^us : Sc, cum E L fit izz’ E M» erunt Sc an-
guli lub E W L, E W M aequales. Quoniam autem
L M F lineis I O, N Q^parallela eft, Sc linese O C, F C
Q^C fimiliter dividuntur in pundtis S, W,T, erit WLY
contingenti I S F parallela, & W Z M contingent!
A N T. Eft igitur angulus fub W Y D z= angulo fub
I r & angulus fub W Z D — angulo fub N A D =
angulo fob I ^ F. Porro cum anguli fub E W L,
E W M ftnt 2equales, Sc anguli fob D E W, D W E
etiam ccquales propter linearum D W, D E aequalitatem,
erit angulus fub Y W D =:= angulo fub W Z D. Ideo-
que angulus fub C D B, qui sequalis eft fommae angulo-
rumfob WYD & fob YWD, squalls erit fummae
angulorum fob IT t, Sc fub I ^ F, nimirum angulo fub
F I aequalis. Q. E. D.

Lond.Aug,%j, 17x2.

VIII. An

( M9 )

VIII. An Account of a intituled^ Harmo-

nia Menfurarum, five Analyfis &c Synchefis
per Rationum 6c Angiilorum menfuras pro-
mot<e : accedunc alia Opufcula Mathema-
tica : per ^^erum Cotefum. Edidic 6c auxic
^hertus Sjnithy Coll. Trin. Cantab. 6c Reg.
Soc. Socius^ Aftronomi^e 6c Experimentalis
Philofoph. poft Cotefum Profeflor. CantahrigiiC
1711. in 4to. Proftant apud Bibliopolas
Londinenfes.

H E Book confifls of three Parts. In the firfl.

called Logometria, the Author’s chief Defign is
to lliew how that fort of Problems, which are ufually
reduced to the Quadrature of the Hyperbola and El-
lip fat may be reduced to the the Meafiires of Ratio’s
and Angles ; and afterwards be folved more readily
by the Canons of Logarithms and Sines and Tangents.
He defines the Mealures of Ratio’s to be quantities of
any kind, whofe Magnitudes are analogous to the
Magnitudes of the Ratio’s to be meafured. In this
Senfe any Canon of Logarithms is a Syftem of nume-
ral Meafiires of the Ratio’s of the ablblute Numbers to
an Unit : The Parts of the Afymptote of the Logifiic
Line, intercepted between its Ordinates, are a Syftem
of Linear Meafiires of the Ratio’s of thole Ordinates :
The Areas of an Hyperbolut intercepted between its
Ordinates to the Afymptote, are a Syftem of Plane
Meafiires of the Ratio’s of thofe Ordinates : And fince
there may be infinite Syftems of Meafiires according

as

( >4° )

as various kinds of Quantities are made life of, fiich as
Numbers, Time, Velocity, and the like ; or accord-
ing as the Meafures of any one Syftem may be all iii-
crcafcd or diminillied in any given proportion ; in fiich
Variety much Confufion may polfibly arife as to the
Kind and abfolute Magnitudes of particuiar Meafures,
which happen to fall under Confideration. Our Au-
thor very happily removes this Difficulty ; by ffievv-
ing that the Nature of the Subjed: points out th^Mea-
fiire of a certain immutable Ratio for a Modulus in all
Syftems, whereby to determine the Kind and abfolute
Magnitudes of all other Meafures in each Syftem.

The firfl; Propofition is to find the Meafure of any
propofed Ratio. This he confidersin a way fb fimple
and general, as naturally leads to the Notion and De-
finition of a Modulus -^ namely, that it is an invariable
Qiiantity in each Syflem, which bears the fame Pro-
portion to the Increment of the Meafiire of any pro-
pofed Ratio, as the increafing Term of the Ratio bears
to its own Increment. He then ffiews, that the Mca-
flire of any given Ratio is as the Modulus of the Sy-
ftem, from whence it is taken : and that the Moduhs
in every Syftem is always equal to the Meafiire of a
certain determinate and immutable Ratio, which he
therefore calls the Ratio Modular 'ts . He ffiews that
this Ratio is expreffed by thefe Numbers 2,7181818
^c. to I, or by i to 0,-3678794 So that in

Briggs'^s Canon the Logarithm of this Ratio is the
Modulus of that Syftem ; In the Logiftic Line the
given Subtangent is the Modulus of that Syftem : In
the Hyperbola the given Parallelogram, contained by
an Ordinate to the Afymptote and the Abfeifs from
the Center, is the Modulus of that Syftem : and in
other Syftems the Modulus is generally fbme remark-
able Quantity. In the fecond Propofition he gives a
2 concife

( ‘4* )

concife Lincammon Method for calculating Briggs's
Canon of Logarithms ; together with Rules for finding
intermediate Logarithms and Numbers, even beyond
the Limits of the Canon. In the* 3d Propofition he
conflrudis any Syftem of Meafiires by'a Canon of Lo-
garithms; not only when the Meafiire of fome one
Ratio is gijven, but alfo without that T>atum^ by feeking
the Modulus of the Syftem by the Rule abovemen-
tioned. In the 4th, 5th, and 6th Propofitions he
fquares the HyferboLa^ defcribes the Logiftic Line and
iEquiangular Spiral by a Canon of Logarithms, and
fiiews fome curious Ufes of thefe Propofitions in their
Scholia. Take an eafy Example of the Logometrical
Method, in the common Problem for finding the Den-
fity of the Atmoiphsere. Suppofing Gravity uniform,
every one knows, that if Altitudes are taken in any A-
rithmetical Progreftion, the Denfities of the Air in
thofe Altitudes will be in a Geometrical Progreftion ;
tiiat is, the Altitudes are the Me*afiires of the Ratio’s
of the Denfities below and in thole Altirudes,' and lb
the difterence of any two Altitudes is the'Mealure of
the Ratio of the Denfities in thofe Altitudes. Now
to determine the abfolute or real Magnitude of thefe
Mealiires, the Author lliews, a^riori^ that the Mo-
dulus of the Syftem is the Altitude of the Atmo-
IphserejWhen reduced every where to the fame Denfity ‘
as below. The Modulus is given (as bear-
ing the lame Proportion to the Altitude of the Mer-
cury in the Barometer, as the Ipecific Gravity of Mer-
cury does to the fpecifick Gravity of Air) and conle-
quently the whole Syftem is given. For fince in all
Syftems the Mealiires of the lame Ratio’s are analo-
gous among themfelves ; the Logarithm of the Ratio
of the Air’s Denfity in any two Altitudes will be to the
Modulus of the Canon, (that is, to the Logarithm of

A a the

( 14^ )

the Ratio Modularis defined above,) as the difierencc
of thofe Altitudes is to the aforefaid given Altitude of
the homogeneous Atmolphsere.

He concludes the Logometria with a General Scho-
lium^ containing great Variety of elegant Conftru-
d:ions both Logometrical and Trigonometrical ; fuch
as give the Length of Curves either Geometrical or
Alechanical ; their Area’s and Centers of Gravity ;
the Solids generated from them, and the Surfaces of
thefe Solids ; together with feveral curious Pro-
blems in Natural Philofophy, concerning the At-
tradlion of Bodies, the Denfity and Refiftance of
Fluids, and the Trajed:ories of Planets. Several of
thele Problems have two Cafes ; one conllru6ted by
the Meafure of a Ratio, and the other by the Meafure
of an Angle. The great Affinity and beautiful Har-
mony of the Meajures in thefe Cafes, has given occa-
fion to the Title of the Book. Tlie Meafures of
Angles arc defined (jufl as the Meafures of Ratio’s) to
be Quantities of any Kind, whole Magnitudes are
analogous to the Magnitudes of the Angles. Such may
be the Arcs or Sed:ors of any Circle, or any other
Quantities of Time, Velocity, or Refiftance, analo-
gous to the Magnitudes of the Angles. Every Sy-
ftem of thefe Meafures has likewife its Modulus homo-
geneous to the Meafures in that Syftem, aud may be
computed by the Trigonometrical Canon of Sines and
Tangents, jufl as the Meafures of Ratio’s by the Ca-
non of Logarithms ; for the given Modulus in each
Sy flem bears the fame Proportion to the Meafure of
any given Angle, as the Radius- Circle bears to an
Arc which fubtends that Angle, or the fame as this
conflant Number of Degrees 5'7,i95'7795'i 30 bears to
the Number of Degrees in the faid Angle. Upon the
whole our Author thus expreffeshimfelf, /• 35- “ Fx

“ addud:is

C '4? )

addu(5Hs hadenus exemplis, Geometris integrum crit
“ de methodo noftri judicare ; quam quidem, fi pro-
“ ba fuerit, ulterius excolere pergent Sc excolendo Ja-
“ tius promovebimt. Patet utique campus ampli/Ii-
“ mus in quo vires fiias experiri poterunt, prselertim
Logometri^ Trigonometriam infuper adjungant,
‘‘ quibiis miram quandam affinitatem in fc invicem
“ euntibus intercedere notabam. Hifce quidem prin-
“ cipiis baud facile crediderim generuliora dari pofTe ;

cum tota Mathefis vix quicquam in univerlb fuo am-
“ bitu compledatur prxter Angulorum & Rationum
“ Theoriam. Neque lane commodiora Iperabir, qui
animadverterit effedionis facilitatem per amplilfi-
“ mas illas, omnibufque Itiis numeris abfolutas, turn
“ Logarithmorum, turn Sinumn & Tangentium tabu-
^ las ; quas antecelTorum' noftrorum laudatilTimx
“ folertix debemus acceptas. Ut vero tanti beneficii
“ ubcrior nobis exlurgat frudus, id nunc exponendum
‘‘ reflar, quibus artibus ad iltius modi conclufiones re,-
^ diflima perveniatur. In hunc linem Theoremata
“ quxdam turn Logometrica turn Trigonometrka ad-
“ jecilTem, qux parata ad ufum alTervo ; ni conliil-
tius vilum ellet, quum abfque nimiis ambagibus ea
tradi non polTent, intada potius prxterire atque
“ aliis denuo inveftiganda relinquere.

Why the Author takes his Principles to be lb gene-
ral, will farther appear by an Inllance or two. In the
Problem already mentioned he mealiires the Ratio of
the Air’s Denfities in any Altitudes, by th^ Altitudes
themfelves, making life of the Altitude of an uniform
Atmofphxre for the Modulus. So likewife when he
confiders the Velocities acquired, and the Spaces de-
fer ibed in given Times, by a Body projeded upwards
or downwards in a refilling Medium with any given
Velocity ; he lliews, that the Times of Defcent, added

A a 1 to

( H4 )

to a given Time, are the Meafures of Ratio’s, to a
given Modulus of Time, whole Terms are the Sum
and Difference of the ultimate Velocity and ,
the prefent Velocities that are acquired : that

the Times of Afcent, taken from a given Time,
are the Mealiires of Angles, to a given Modu*
lus of Time, whofe Radius is to their Tangents in the
Ratio of the ultimate Velocity to the prefent Ve-
locities : and laftly, that the Spaces delcribed in De-
Icent or Afcent, are the Meafures of Ratio’s to a given
Modulus oi Space, whofe Terms are the ablblute ac-
celerating andretarding Forces arifmgfrom Gravity and
Refinance taken together at the Beginning and End of
thofe Spaces.

' This general Account may fuffice to illufirate what
I am going to fay ; that fince the Magnitudes of Ra-
tio’s (as well as their Terms) may be expounded by
Quantities of any Kind, the Mathematician is at Li-
berty upon all Occafions to chufe thofe which are fit-
tefl for his Purpofe ; and fiich are they without doubt,
that are put into his Hand by the Conditions of the
Problem. He may indeed reprelent thefe Qiiantiries
by an Hy^erbola^ or any other Logomerrical Syfiem,
were not his Purpole anfwer’d with greater Simplicity
by the very Syfiem itfelf, which occurs in each parti-
cular Problem. And the fame may befaid for the Sy-
Hems of Angular Meafures, inflead of recurring upon
all Occafions to Elliptical or Circular Area’s.

As to the Convenience of calculating from our Au-
thor’s Conftrud:ions, he fliews that the Meafiires of
any Ratio’s or Angles are always computed in the
lame uniform Way ; by taking from the Tables the
Logarithm of the Ratio, or the Number of Degrees in
the Angle, and then by finding a fourth Proportional
to three given Quantities ; for that will be the Meafure

required

( M5 )

required. The fimpleft Hyperbolic Area may indeed
be fquared by the fame Operation taught in the Au-
thor’s fourth Propofition ; but the fimpleft Elliptic A--
rea requires fomewhat more : Thole that are more
complex in both Kinds (which generally happens) re-
quire an additional Trouble to reduce them to the fim-
pleft : to Iquare them by infinite Series is ftill more
operofe, and does not anfwer the End of Geometry.
Upon the whole therefore it may deferve to be confi-
dered, for what Purpofes lliould Problems be always
conftru(fted by Conic Areas, unlefs it be to pleafe or
alTift the Imagination. The Defign of Theoretical
Geometry differs from Problematical ; the former con-
fifts in theDifcovery and Contemplation of the Pro-
perties and Relations of Figures for the fake of naked
Truth ; but the Defign of the latter is to do Ibmething ,
propofed,and is belt executed by the X^zf^Apparatusoi
the former.

The Logometria was firft publillied by the Author
himfelf, in the Thtlofoph. TranfaVt. of the Year 1714*.
No 338. But his Logometrical and Trigonometrical
Theorems abovementioned were not publilhed till after
his Deceafe. Thele Theorems make the lecond Part
of the Book, and are calculated to give the Fluents of
Fluxions (reduced to 18 Forms) by Mealures of Ratio’s
and Angles ; in fuch a manner, that any Perfon may
perfecftly comprehend their Conltriuftion and Ule, ^
though altogether unacquainted with Curvilinear
Figures, as exprelfed by ^Equations. And this Cir-
cumftance does allb render the Application of them ^
to the Analyjis and ConJfruBiou of ’Problems ex-
tremely ealy. Of this kind the Author has given a
great many choice Examples both in abftrad: and phy-
fical Problems ; which make up the third and laft Part
of the Book.

The

<c

u

(C

u

(C

u

( >4^ )

The Author, a little before hisDeceafe has informed
us (in a Letter of May 5*. wrote to his Friend Mr. Jones)
that Geometers had not yet promoted the inverle
Method of Fluxions, by Conic Areas, or by Mea-
“ fures of Ratio’s and Angles, lb far as it is capable of
being promoted by thofe Methods. There is an
infinite Field (fays he) flill referved, which it has
been my Fortune to find an Entrance into. Not to
keep you longer in Sulpenle, I have found out a ge-
“ neral and beautiful Method by Meafures of Ratio’s
“ and Angles for the Fluent of any Quantity which

d z ^

“ can come under this Form — , in

which d^e,f are any conflant Quantities, .2 the vari-
“ able,yi any Index, 0 any whole Number affirmative or

negative, ~ any Fradtion whatever. The Fluents of

this Form which have hitherto been confidered are
. 9 yi — I ,• +

d Z Z d Z Z

^ r— : Thele you remem-

e-^-fz*' e-^-Jz^

« ber are Sir Ifaac Newton's two firfl, and fi'om
thefe all his others are eafily deduced. And as - his
“ irrational Forms of the quadratick Kind are derived
from the rational, fo from my general rational
Form I deduce irrational ones of all Kinds. For in-

fiance, if — reprefent any affirmative or negative

« Fradion, the Fluent of any Qiiantity of this Form

cc

dz.

6/]— I

or of this dzz

9.

« ^ e-j~fz>^] A ^nd fo of fome others, depends upon
g-\~h z>>! the

( >47 )

^ theMeafures of Ratio’s and Angles. Mr. Leibnitz
^ in the Leipjlc A6is of 1702, /. xi8 and 219, has ve-
ry rallily undertaken to demonftrate, that the Fluent

" of — . ^ cannot be exprelTed by Mealiires of Ra-

“ tio’s and Angles ; and he Iwaggers upon the Occa-
“ fion (according to his ufual Vanity) as having by
“ this Demonftration determined a Queftion of the
‘‘ greatell Moment. Then he goes on thus ; as the

“ Fluent of — j — depends upon the Mealure of a'
x~\~a

X

“ Ratio, and the Fluent of upon theMeaflire

xx~f~aa

‘‘ of an Angle ; lb he had more than once exprelTed
his Wilhes, that the Progredion may be continued,

“ and it be determined to what Problem the Fluents of

" — — — , , ^r. may be referred. His De-

x^+a^\v'+a^ ^

‘‘ fire is anfwered in my general Solution, which >

contains an infinite Number of fiich Progredions.

“ I can go yet farther, and diew him how by Mea-

“ lures of Ratio’s and Angles, without any Exception ’

“ or Limitation, the Fluent of this general Quantity

• 0 J1 -f- — « • I . 1

« dzz ^ (jj. eygjj a zz

e f z^ -{■ g z^^ e

“ may be had ; where 0, as before, reprelents any Inte- ■

« ger, and the Denominator A of the Frad:ion — , re-

“ prefents any Number in this Series, x. 4. 8. 16. s^.&c.
any whole Number being denoted by its Numerator
In truth I am inclined to believe, that Mr.

‘‘ nitz's grand Queftion ought to be determined

“ the

1

( ‘48 )

the contrary .Way ; and that it will be found at laid,
“ that the Fluent of any rational Fluxion whatever,

does depend upon the Meafiires of Ratio’s and
“ Angles, excepting thole which may be had in finite
“ Terms even without introducing Meafures.

Dr. Tailor knowing by this Letter what the Au-
,thor had done, was pleafed to propofe the Invention
of the Fluents of the two lall Fluxions as a Problem
to the Mathematicians in foreign Parts. Mr. Ber-
mullt in the Le'tffic A6is of 17x9.^. X56, did lliew
accordingly how they are reducible to Conic
JVrea’s. The Editor has publillied the Author’s own
Solution by Meafures of Ratio’s and Angles ; and upon
this Foundation has condriKded new Tables of Logo-
metrical and Trigonometrical Theorems, for the F luents
of Fluxions reduced to 94 Forms, part rational and part
irrational. . He has likewife added general Notes upon
the chief Difficulties in the Book, together with a Me-
thod of compofing Synthetical Demonllrations of Lo-
gometrical and Trigonometrical Conltrucifions, illu-
Rrated by various Examples.

The firfi; Treatife in the Mifcellaneous Works is
concerning x}a^Eflimatton of Errors in Mixt Mathe-
matic ks. It confifhs of 2 8 Theorems, to determine the
Proportions among the leall contemporary Variations
of the Sides and Angles of Plane and Sphserical Tri-
angles, while any two of them remain invariable. An
Example will fliew their great Ufe in Altronomy. The
Time of the Day or Night is frequently to be deter-
mined by the Altitude of fome Star. Let it then be
propofed to find the Error, that may arife in the Time,
•from any given Error in taking the Altitude. By ap-
plying the 2id Theorem to the Triangle form’d by the
Complements of the Star’s Altitude and Decimation

and

C »49 )

and by the Complement of the Pole’s Elevation, the
Author lliews, that the Variation of the Angle at the
Pole, and confequently the Error in Time, will be as
the Error in the Altitude diredly, as the Sine Conv
plement of the Pole’s Elevation inverfely, and as the
Sine of the Star’s Azimuth from the Meridian in-
yerfely. Confequently, if the Error in the Altitude
be given, under a given Elevation of the Pole, the Er-
ror in Time will be reciprocally as the Sine of the-
Azimuth contained by the Meridian and the Vertical
which the Star is in. This Error therefore will be the
fame, whatever be the Altitude of the Star in the fame
Vertical; and will be lead when the Vertical is at
right Angles to the Meridian. But will be abfblutely
the lead in the fame Circumdance, if the Obferver be
under the ^Equator. In which Cafe, if the Error in
the Altitude be one Minute, the Error in the Time will
be four Seconds, If the Oblcrver recedes from the
.Equator towards either Pole, the Error will be in-
creafed in the Proportion of the Radius to the Sine
Complement of the Latitude : So that in the Latitude
of 45“ Degrees it will be 5* * Seconds, and in the Latitudes
of 50 and d will be6i and Seconds relpedfively.

If the Star be in any other vertical Oblique to the Me-
ridian, the Error will dill be increafed in the Proporti-
on of the Radius to the Sine of that oblique Angle.
Ladly, if the Error in the Altitude be either bigger or
iefs than one Minute, the Error in Time will be big-
ger or lels in the lame Proportion. Much after the
fame manner may the Limits of Errors be computed in
otha Cafes,which arife from the Inaccuracy of Obferva-
tions, and from hence the mod convenient Opportu-
nities for oblerving are alfo determined.

The Second Treatile is concerning \X\^T^ijferential
Method, The Author having wrote it, before he had

B b feen

( 150 )

feen Sir IJaac Newton's Treatife upon that Subjed:,
bas handled it after a manner fomewhat different.

The Title.of the Third Treatife is Canonotechnia,
or concerning the Conftrudion of Tables by Diffe--
rcnces. It confifts of ten Propofitions, moft admira-
bly contrived for expeditious Computation of inter-
mediate Terms in any given Series. The laft Propo-
fition, which contains a general Solution of the whole
Dcfign, is this ; "Datisferiei cujufcunque terminis a-
liqmt aquidijiantihus, quorum intervalla fee an da
fimt in a quale s quotlibetcunq\ fartes^^ro^ofitum ft
invenire terminos interferendos.

The Book concludes with three ftiiall Trads, con*
cerning the Defccnt of Bodies, the Motion of Pendu-
lums in the Cycloid, and the Motion of Projediles,
compofed in a very natural and eafy manner.

The Author has wrote feme other Pieces, yet un-
publillfd, which the Editor has given an Account of
in his Preface to the Book.

The Reader will find every Subjed treated with un-
common Elegance and Simplicity.

FINIS.

LONDON: Printed for W. and J. Innys,
Printers to the Royal Society, at the Prince’s
Arms the Weft End of St, Paul’/ Churchyard.

0

I

Numb, J73.

■ ViiCwi .'’(C. o' • ',\i 7

• ,;,T R' A'lsl S A;QT 1 0 N S;'^"

-- i- ' 1 ia O' c- V . ■

, '>
' f* •

c ■

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1 • J 1

imrn

For the Months of September, and Obiober. i7xx. ,

. • ./■ '"r ^ ls\ , 7

, 7t

I. > ''<^1 (5^: V !,i--

'0

^ • i ^

, The CONTENTS. "■

-i;J '-\ \ >lu"\h*.rT\\<\0 C‘'- i:'U;.:V i I *

I; Ohferyatms^npon Foetus, and the ^arts of Ge^
‘ neration of a Sheeps' . >In a Letter to the Royal
Society,' from Mr. Leeuwenhoek,; K (^ 5*.
Tranflated from the, Dutch hy /i?V.-.2>prcngell,

' ' ■ ■ , . I

II. Obferyations upon the Callus of the Hands. a7td
Feet, hy the fame curious Gentleman* Tranflated
• hy John Chamberlayne, Efq;^

III. De Fradiohibus Algebraicis Radicalirate
immunibus ad Fraftiones Simpliciores re-
ducendis, deque fummandis Tefminis qua-
rumdam Serierum aequali Intervallo a fe
diftantibus. Au6tore Ahrahamo de Mo/Ve,
S, R. Socio.

/

IV. De-

IV. DefenflO TflJJertatlonis de Motu J^^uarum fluen*

, tmniy^in ^Hif^itofoplicis;^ 35 mt-f

tra AntmdiWrJiom Petri Amonii Mi-t

cheldt^ ^AuEiorp}^oho Juria, Mr J)- CoU>
Mei, Loni. Soc.'hv Tffcntro Tnhfth Chlhrg.
Lond, Tr<jileEiore AnatamicOy Soc* Seer,

V* Accom?^of^^^^ In^

feEiion of the Small Tox, Sy T)r, Jurin, Soc,

VI, An Account of two Ob/eryations upon the Cata-
rath of ^^the^ '^Eye • contained m \ a, Letter^ frwn
Si^ior Antonio Benetoli/ irt

' ^^the HoJ0(A o/^Si-Maria. Nuova Florence,

'0mukdv\hi' Italian. A<*t, /Flo-
rence, this pre/ent Year, andcommwUcatedto the

' o‘iorjiiqrr'» ' otoi;.. ■»-

N^^37x. p. 146. I. z. read, ‘May ^tby tyi6, ^

I " ■- ■ i I t ! •

A

^ ' i --» » 4 J.J [i i.

. / }

I. Ob/eryations

r

( )

I. ObferVations upon a Foetus, and the Tarts of Ge-
- neratlon of a Sheep, In a Letter to the Royal
Society, froyn Mr, Leeuwenhoek, K 5^ S.
Tranflated from the Dutch by Dr, Sprengell,

A Certain Butcher kept, about a League from
this Town, leveral young Wethers at Grafs,
with one Ewe, which within two Years time had
twice lamb’d. This Ewe being very fat, he re-
fblv’d to kill ; and to this end he brought it to ano-
ther Paflure juft by the Town, where he had feveral
other young W ethers ; but it happen’d, that among
them there was one young Ram, which he judged to the
be about twenty Weeks old ; this young Ram cover’d
the Ewe in his prefence ; foon after which the Butcher
kill’d the Ram, but left the Sheep about five Days
longer in the Failure before he kill’d it ; out of which
Sheep’s Belly he faid that he cut x8 Pounds of Fat.
But obferving, upon opening the Ewe, that the Ute-
rus was four times bigger than ordinary, he brought
the Dternsy with the Ovaria, to me, afTuring me, that
it was not yet quite five Days fince the young Ram
had cover’d the Sheep, and that there was no other
Ram thereabouts.

This mterus I put in an earthen glaz’d Pan, and co-
ver’d it over, in order to difTe<ft it next Morning, it
being pretty late in the Evening when the Butcher
brought it me. I then began firft to try to penetrate
into the Womb from iht Vagina^ with the Point of a

C c fmall

( )

fmali Pair of ScifTars, but I found it fo clofe, that I
could not enter it, therefore I cut a piece off from the
Womb, out of which ran a clear Water, and within it
lay the Fcettis with all its Coverings. I fpread this
upon the backfide of a China Tea-Dilh, and finding
that it Hill contained more Water, I made a finall In-
cifion to drain it, and to let it dry, that I might ob-
lerve it the better. I could plainly fee the Vertebra
of the Neck and Back, as alio the Joints of its Ihort
Xail ; I thought likewife that I faw the Eyes. But
when it was quite dry, I could not obferve its Back«
bone fo well as before, when it was as yet moift, tho'
the Painter, who made the Draught, and had lliarper
and younger Eyes than mine, law the Bones of the
Back very diftindly. My Defign in drying it was to
cut it in fmali Slices, that then I might the better ob-
ferve the inner Parts, for it was fo extremely loft and
tender when mo ill, that with the leall Touch its Parts
would be dilbrder’d and confounded. Therefore I cut
this Foetus into fifteen Slices, and obferv’d them with
a Microfcope, but could not be very certain what I
law. I thought that I law the Intellines, as allb the
Bladder ; and coming to the Bread, I fancied that I
law the Heart ; but I law and obferv’d, with a great
deal of Plealure, that two Blood- Vellels lay near
together in the Brain, and how they were fpread into
Branches. I had this Foetus drawn as it lay- in its Te-
guments. See Fig. i. A B being the Foetus^ and
A C D E I K and A F G H L K, the Membranes
wherewith it was involved, in the manner as I had
fpread and dried them, wherein the Blood- VelTels, as
much as polTible, are delineated. Now fome Perlbns
might expedl, that I Ihould have look’d for the Extre-
raities of the Blood- VelTels : but no, the Blood- Vellels
have no end, as I have frequently fiid. Befidcs, they

become

( )

become gradually fo exquifitely fine, that the Blood,
which pafTes thro’ them, can exhibit no red Colour to
our Eyes ; fo that there is no tracing them when entring
into the VefTels that return the Bipod back to the
Heart, except in living Animals, where one may fee
the Blood enter into the returning VefTels. Before the
Butcher gave me this Uterus, he fqueez’d it betwixt
his Fingers, and told me that he could feel nothing in
it ; and this I believe he had done feveral times before,
by which means he tore off the VefTels by which the
Foetus was faflen’d to the Uterus ; which I fuppofe
was the occafion that, upon opening the ^te-
rus^ the Foetus with its Coverings came fb eafily
forth.

I alfb took a Draught of the Tuba Falloplana. See
Ftg. ^. M N O P. At P, is the imaginary Orifice,
which is thought to fiick the Egg from the Ovarium^
according to the old abfiird Notion at M is fliewn
where the Tuba increafes in Bignefs, and at Q_ R
the flefliy Subfiance, which I cut away from the T)te-
rus. I then had alfb cut off the fo call’d Ovarta^ and
the pretended Ova^ which latter were much too big to
think that they could pafs upon Conception thro’ the
Tuba Falloptana. I therefore took the length of the
Foetus with a Pair ofCompafTes, and meafur’d it upon
a divided Brafs Rule, and this I did alfo as to its
Breadth ; I then took the middle Number between
thefe, and multiplied it twice by itfelf, to bring it to a
Cube Number. I next took the Length of the Axis of
^xsOvum^ as it lay in the Ovarium inclos’d in its Mem-
branes, and taking the Cube of that length, and divi-
ding one Cube Number by the other, I found that fucli
an Ovum was about feven times bigger that the Foetus,
notwithflanding it had had near five Days Growth. I
fiie\v’d this Foetus, with its Covertures, to two Phyfi-

C c 2 cians

( »54 )

cians and one Surgeon, and I gave them the pretended
Ovaria in their Hands, and they agreed, that not one
Ovum was miffing out of the Ovaria. Then I ask'd
them what they thought ? how it was poffible that
liich an Ovum could pals thro* the Falloppian Tube ?
Whereupon the one laid, that the Ovarium was quite
out of doors, and that it was nothing but Ibme flelhy
Subllance. But the other faid, that notwithllanding
this, all Animals came from an Egg, and the lalt told
me, that he believed that Tube to be neither of a Sheep
nor a Lamb ; but I Ihew’d them that it was from an
Ewe which at leall had lamb’d twice, and yet that the
Tube was neither thicker nor wider than the Tube of
a Lamb. Here I could oblerve more than ever, how
hard it is to bring Mankind off from their Prejudices,
when once they have laid them down as Principles.

After having kept thefe Ovaria Ibme Days, by
which means they were pretty much llirunk in the dry-
ing, I order'd them to be drawn, that the Bignels of
the Eggs might be oblerv’d. See Fig. 3. A B C D E is
the Ovarium^ which was on that fide of the Uterus,
in which the Foetus had lain. You mull obferve that
the Uterus of a Sheep is divided by a Membrane,
lb that the young ones cannot touch one another.
D E A is the part where it was fallened. In this Ova-
rium you may obferve a round Protuberance, which
is belet with leveral others ; this great Protuberance is
what is called an This Ovarium not here

reprefented fo large, as it was, when I cut it off from
the Parts that it grew to. There was befides, at
one fide of that Ovarium, a large round Body, grown
to the Ovarium, which feem’d alfo to be an Ovum.
Tliis is delineated in Fig. 4. F G, on which there ap-
pear’d leveral other little round Bodies protuberant from
it. Now on the other fide of the Uterus, there was a

large

( )

large flefliy prominent Ovum (as it is call’d) which
might plainly be obferved without a Microfcope,
whofc Bignels is likewife drawn in Fig. 5". at H I, upon
which you may likewife oblerve a foialler round Body,
and out of that again other flill fmaller round Bodies
appear protuberant. After I had quite dried thele
Eggs, reprefented in Fig. 3, 4 and 5*, I ftill oblerv’d
more and more of the prominent round Bodies upon
them, inlbmuch that upon one of them, I told fixteen
round little Bodies, whereof fbme, by lofing all their
Moifture, were liink in and had a Dent in the middle.
Furthermore, I cut thefe Eggs, with a very fine fharp
.Knife, into thin Slices, and then obferving them with
a Microfcope, I faw Blood -Veflels in them, and alfb
other forts of Veflels, which I did not take for Blood-
VcfTels, and among the reft one fb big, that a Hair of
ones Head might enter it, befides abundance of others
exceeding frnall. After many Obfervations, I could
think no otherwife,but that the fb call’d Eggs confifted
of nothing but VefTels, and’ that the fuperfluous Moi-
fture, which was fent to thefe Eggs, did not circulate
(except only what was in the Blood- VefTels) and by
overcharging the VefTels did elevate them into thefe
• fmall Protuberances, and fbmetimes burfting them,
did thereby leave a Dent in the middle; which Dent
having been obferv’d by Tome' Perfbns, they firmly
believ’d, that that was the Place where the Ovum was
fuck’d out, from whence fprung the Foetus. I was
very forty that I did not get this Uterus without its
having been fqueez’d, for Ido not queftion, but that I
might otherwife have plainly difcover’d all the Mem-
bers of this Foetus., ftnce I could plainly obferve its
Backbones even with the naked Eye, and that in a Foe-
tus not of quite five Days Growth. I hope after this,
nobody will pretend to fay, that the Animal inVtero

at

( )

at the Beginning, is nothing but an unform’d Mafs,
Thefe Obfervations I made in the Month of Sepem*
ber^ 1718.

June 13.
iy%%.

it

< I

,1.

II. Objeryations upon the Callus of the Hands and
Feety by the fame curious Gentleman, » Tranflated
hy John Chamberlayne,

IN the Month of 1719. feeling an acute

Pain in one of my Feet, at the Joint between the
Foot and the little Toe, which I imagined to proceed
from the more than ufual Thickneft of the Callus
or hard Skin, upon that part ; I caufed my Servant,
partly with his Nails, and partly with a Penknife, to
take ofF that hard Skin, and let it fall upon a blue Pa-
per, that I had let my Foot upon.

This Callus^ or hard Skin, was compos’d of little
fcaly Shivers lying upon one another, and the whole
Piece was as large as a fmall Nail of a Man’s Hand.

I view’d the faid Shivers thro’ a Microfcope, but
cculd not latisfy my felf, becaule they lay lb irregularly
on each other.

Moreover, I took a little Bit of the aforefaid hard
Skin, laid it on a clean Glals-Plate, fteep’d it in pure
Rain-Water, and gently dividing it with a Piece of a
Quill, I was amazed to lee into what a vail Number
of Particles it feparated, and that with as much Rea-
dinels, as if they had never been join’d.

Afterwards

C )

Afterwards I took two or three of the faid Particle^
of which many were of the Figure of a Weaver’s
Shuttle, being broad in the middle and pointed
at each End, with a Line in the middle, like thofe up-
on the uppermoft or outfide Skin of Fruits, or of our
Bodies, but generally irregular ; they were very thick
in Proportion to their Bignefs. I took, I lay, two or
three of the faid Particles, and laid them on a clean
Glafs, and put to them a Drop of Water, as large as a
coarle Grain of Sand, and divided the lame as well as
I was able ; and viewing the divided Particles thro’ a
Microlcope, I was aftonillied at the prodigious num-
ber of exceeding Imall Particles that occurr’d to my
Sight, and which were of the lame Figure as before-
laid.

Moreover, I took Ibme of the thickeft Pieces of the
horny Skin, but not half fo thick as the Back of a
Imall Knife, and flit them into as thin Slices as I
could, and placed them upon a clean Glals, with the
Deflgn of dilcovering the exceeding thin Particles
lying upon one another ; and having moiften’d them,
they Ipread themlelves out further, and when they
became dry again, they leparated into feveral Parts ;
and I oblerv’d likewife that each of thele feparated
Parts were compofed of many thinner Particles lying
on each other. In order to have a clearer Notion
of the Contexture of thole Particles, by which the
Skin of the Hands and Feet of thole who are inured to
hard Labour, or walk much, increales in Thicknel^
and is lurrounded, I cauled a Imall Portion of the
aforelaid leparated Particles to be drawn, as appears by

6. A B C D, tho’ they were not all fo exad: and
complear, as they are reprefented in the laid Figure ;
and according to the bell of my Obfervation, they

had

( )

had all been feparate Pieces, and none of them united
to one another.

Again I placed feveral little Pieces of this hard Skin,
which I had cut off at' the thickeft Part of it, before a
Microfeope, and moiften’d them with fair Rain-Water
when I put them upon the Glals-Piate, by which
Means they acquired a great Extent ; and being dry’d,
they flirunk again, and thereby appear’d in feveral
long Particles, and each of them feem’d to confifl:
of other long Particles, as they are rep: dented
in Fig. 7. E F G H. So that EH or F G, was the
Thicknds of that Piece of thick Skin, which I had cut
through.

From this Oblervation, I confider’d with myfelf, whe-
ther one of thefe long ftripe-like Particles, liich as ap-
pear’d to the Eye at E F or H G, might not be the
Thicknefs which the horny Skin had acquir’d in the
Space of a Month ; and whether the very thin Particles,
which appear’d in fuch a littleStripe, were not the Accre-
tion which the hard Skin receiv’d in one Day. Thislaft
mention’d little Piece, reprefented by Fig. 7. was not
io large to the naked Eye as a common Grain of Sand.
And whereas I placed before a Microlcope another
very Imall Piece of Skin, that was fomething thinner
than the former, I could perceive the exceeding thin
Particles reprefented by Fig. 8. IKLM, which were
the Strata., or Beds, in which the horny Particles
of the Skin lay, and fo compofed the Thicknefs
thereof

For my further Satisfadion, I fent for a Mafbn’s
Servant, who was a laborious Workman, and cut out
of his Hand, where it was moft thick and brawny,
two Bits of the hard Skin ; and then I flit it into finall
Slices, and obferved eafily enough the thin Particles
lying upon each other, bur could not fep'arate the little

Scales

( ^59 )

Scales, of which each little Stratum of the hard Skin
confifted, becaufe, as I fancy’d, thro' the hard work-
ing of the Man, the Particles of the laid Skin were lb
prelTed upon one another, and lb clofely join’d, that
they could be no longer leparated.

Now foralmuch as the Hands of the Mafons or
Bricklayers are often cover’d with the lharp Salts of
the Chalk or Lime, which might prevent the Separa-
tion of the very fmall Parts of the hard Skin ; I fent
for a Mailer* Carpenter, who was likewife a diligent
Workman, and viewing his Hands, in order to pare
off Ibme of the Brawn thereof^ I found them as foft in
the Palms, as if he had never been ufed to Labour ;
upon which I faid to him, you walh your Hands very
often I believe : to which he reply’d, ten times a Day
at leall, for I hate to fee them foul. Then I fent for
a Ploughman, who was mollly a Tiller of Corn- Land ;
this Perlbn’s Hands were very hard ; however, I cut
two Pieces of horny Skin out of them, which after I
had done, I cut them in little Bits, but they were fo
hard, that a lliarp Kiiife, which I us’d, got feveral
Notches in doing it. And I obferv’d that the upper-
mod part of the Skin was full of little Rents, and all
the Strata prelTed fo clofely together, that I
could not make any Dilcoveries therein, fave only
that the little Beds lay on each other, and that the
Thicknels of the Skin confided thereof.

Furthermore I put the two Pieces of hard Skin into
warm Water, in order’ to Ibfcen them, and then to
feparate the Parts from each other, but could not do it,
becaufe they were fo drongly joyn’d together.

I have feveral times obferved, in walhing my Hands,
that when I rubb’d the Palms *bf my Hands drongly
againd one another, with very little Water between
them, fome Particles would be rubb’d off from the
Skin, and continue between my Hands.

D d

For

( '<5o )

For my farther Satisfaction in this Matter, I put one
of my Fingers into fair Rain-Water, and with that
vvaflied the Part of my Thumb which is join’d to my
Hand ; after which I rubb’d both Finger and Thumb
hard againft each other, then I gently fcraped with a
Pen-knife, the Matter, which I had loolen d from the
Skin by moiftening and rubbing it ; and taking off a
little of that which ftuck to the Knife, I put it upon a
clean Glafs-Plate, and Petting it before a Microfcope,
I faw with Aflonifhment the great number of Particles
of Skin, which lay Icatter’d upon the Glals, but were
more irregular than thole, which I feparated from the
brawny Skin of my Foot, and which were not very
clolely prelied together, becaufe I don’t walk much, it
being troublelbme to me at my great Age.

After this I moillen’d the back of my Hands, and
then rubb’d them ten or twelve times againft each
other, and having lb done, I fcraped oft^ with a Pen-
knife very gently, Ibme of the Matter which I had
loofen’d by rubbing ; and placing it on a clean Glals,
I view’d it with a Microfcope, after having leparated
the Particles of the laid Matter from each other with
a little Water, and dilcover’d abundance of little Scales
which come off our Hands.

Foralinuch as the Skin of my Hand is in no part
thicker than that, which is upon my Thumb next to
the Nail, having in my advanced Age chiefly uled my
Thumbs in the Examination of Microlcopical Objecfts,
} made one of my Thumbs a little moift, and rubb’d
the other againft it, and placed the rubb’d off Matter
before a Microfcope, thro’ which I obferv’d ftich a
prodigious Number of Particles, like thofe reprclented
by Fig. 6. A B C D, but all irregular, that no Man
can conceive it without having feen it.

Now

( )

Now a§ we find, that Inch a Quantity of Particles
is feparated from the Hands, and is daily renewed in a
well conftituted Body ; we muft conclude, that we
eat leveral of the laid rubb’d off Particles in oui'
Bread, and that they turn to Nourifliment ; and
I am of Opinion, that there is hardly any Food pre-
pared for us, elpecially liich as palles pretty much
thro’ the Hands, but that fome of the rubb’d off Par-
ticles are mix’d therewith, efpecially when they knead
Dough from Meal or Flower ; and Hill more, when the
Bakers knead with their Feet, as in making of Rye-
Bread.

Since thele Oblervations concerning the Fridiioii or
rubbing of my Hands, I take more notice thereof,
when I walh and dry them, than formerly ; and I Hand
amazed at the numerous Particles that daily leparate
themfelves from my Hands, and grow on them again ;
and at the particular Provifion, that is made for pro-
ducing thele Particles, in the Palms of our Hands and
Bottom of our Feet, whereas we do not by far meet
with fuch a Quantity of Particles conllantly prodnced
in otlier Parts of our Body ; for if we obferve thole,
who work much with the back of their Hands, we lhall
not meet with any of that hard Skin we have been
Ipeaking of, but only a kind of Tumor, .or rifing, as
the Dry-llieerers, or thofe who drefs Cloth, have upon
their left Hands.

In lliort, the Manner of the Produdion of thele
fmall Particles will be a Myftery to us, though our
Hands and Feet mull be fortified with fuch a Matter,
to enable them to fupport all that Force, and Prellure
which they are obliged to undergo.

fDelft, July 7.
1711.

D d z

III. Dc

( )

; ;„i

. I iJIli? »

III. De Fraftionibus Algebraicis Radicalifate
.immunibus ad Fradtiones Simpliciores re-
ducendis, deque fiimmandis Terminis qua-
rumdam Serierum aequali Intervallo a [fe
diftancibus. , Au6tore Abrahamo de MoiVrey
S. R. Socio.

Eruditiffimo Viro JO Hj^NNI MACH IN,
Societatis Regalis Secretario, A. de Moivre, S. P*. •

ITT O tibi excerpt a qua dam e Chart is meis co^
ram Re gait S octet ate f Man 17x0, exhibit is,
quibus eodem diemanum appofuerunt Secretarii. Tars
altera harum Chart arum jam per biennium apud CL
Trafidem repojita fuerat\ continebatautemlOemon-
firationes Tropojitionum quarumdam in Libro a me
Anglice emiffb qui infcriptus eji. The Doctrine
OF Chances. Tars altera continebat explanatio-
nem ub'eriorem T>emonftrationum quas prior levius
tetigerat. Jam cum fapius me injtigafti nt feleHas
Tropofitiones quafdam ex his Chartis defkmptas pub-
lic i juris facer em, utpote exiftimans in illis qua dam
reperiri qua ad res majoris momenti quam fit fpecu-
latio ludorum applicari poffint ; huic tuo dejiderio
tandem obtempero, idque eo libentius, quo mihi videor
jure aliquo a Te itidem impetrare pofife ut pulcherri-
ma tua inventa in Tublicum proferre diutius non re-
luLferis, Vale.

2 Auguft,

1722,

P R O-

^ t'

( 1(^3 )

PROPOSITIO I.

♦ . #

lO I fit FraEfio qualibet — I

^ I — ex-f-fxx — gx^ 8cc.

cujus Numerator fit data ^lantitas^ ^ T^enomina-

tor ft Multinomium utcunque compoftum ex datis,

€ g) &c. ^ indeterminata x, dko Fra6iionem fi-

fradmam ad Fra5f tones fmfliciores reductbilem fore.

Cafus Frimus.

Sit Fradio propoflta — > ^i^g^ Deho-

nominatorem i — e x -\-fx x~ (?, fintque — , — ra-

^ m f

dices iftius iEquationis, five fade x x — e x~Ff znOy

fint radices /Equationis novse, fac A = .

- m — f

V

atqueB zz: — — j&eritFradiopropofitasequalislum-

A , B

mas f .

I ^mx I — fx

Cafus Secundus.

Sit Fradio propofita

; fin-

I — e X f X X — g x^
gatur — e x x~\~fx — g~o^ fintque ra-

m m

dices iftius iEquationis, pone A — ■■■■ — ,

m — / X m — q

Bzr:

( »<54 )

B =

// _
f — m-Af — q

yC —

X q — ^

&

eric Fradio propofita aequalis. fummse —

-f ^ — -f — ^:

I — • i^qx

Cajus Tertlns, ■

Sit Fradio propofita

I — ex-^fxx — gx^ -\~hx''’
Fingatur e x^ fx x — g x ~i~ h ^ Oy fintque

niy /, q^ Sy Radius iftius Equation es, pone A —

, Bin ^ ^

m xm — q X m ^ s

xf — s

, c=

f — m X ^ — q

. D =

q — m X q-rrf X q s

eritque Fradio propofita

s — m X s p .xs q '

asqualis fummse — — f — f- ^ — 4-

^ I — mx ‘ I — fx' I'^qx ‘

D

s X

Cajus partus.

Sit Fradio propofita rr r 4 ~ /

A ^ i^ex-^fxx — gx^~\rhx — kx^

fingatur a;’ — ex^-{~fx^ — ^ a; a; + ^ ^

que mypy qy s, Radices iftius sequationis ; pone A =

=__ = =ir—

m*^p xm-^q xm^s xm^t / — m xp — q

X p — s

( )

X J? S xjp — t

D =

,c =

q — m X q — ^ X q — s x q — t

, Err

t — m

s — m xs — / xj* — x^ — ^

Eritque Fradtio propoflta

xt — ^ xt — q X t — s

oequalis liimmse, — ^ f 5 4 4L

I — m X ^ I — £ X ' 1 — qx ^

— 5 L — 5 — . Lex Redudionis ita uno intui*

I — s X ‘ I — s X

• ,

tu fe prodir, tamque facilis eft illius continuatio ut in-
utile forec ilJam verbis explanare.

Qorollarium I.

Si Radices omncs fint sequales, non poterit Fra(ftlo*
propoflta reduci ad fimpliciores.

Cor'ollarmm II.

Si Radices aliquae fint sequales, ali^e vero insequales,,
poterit reduci fracftio propofita ad fimpliciores ; fit-i;.^.

fraiftio propoflta tt-t: tj faiftoque-

^ ^ • I — ex-\~fxx — g x^ ^

ut prsefcriptum eft x^ — e x x -}-fx — g—o. Sint

Radices iftius sequationis quarum m 8cp fint

scquales : erunt fra(ftiones fimplices in quas refolvitun

mm

propoflta =-■

tP

xm — q x x — m x ' p — m

+

x/' — ^xi — J? X q — m xq — f xi — q x"*
addantur du^e priores in unam fummam, do erit fumma.

(divifis.

(, }

(divifis Numcratore 8c Denomiiiatorc per m — /)
mj’' — ^ X m ^ ^ .

five

^ — q X p — q -|-i — m X X I — p X
mm — 2. q X m ^

m — q

'P XI — m X

2

. qm

m-

— q^ X m x\

erunt

m

- - i

m — q X I — mx

; five.:

m

X I

m X

m

m — q\ XI _ — m x\

m

X

Corollarlum- III.

Si Frad:iones fimplices in quas refblvitur Fradtio
propofita involvant Quantitates imaginarias, tunc quic-
quid eft imaginarii femper deflruetur per additionem
duarnm vel plurium fradlionum numero pari . lum-
ptarum.

t

Coro liar him IV.

Ex combinatio-he Fradtionum rimpliciuin, & apta
limitatione Radicum, plurima fuborientur Theoremata
in quibus inerit conciiinitas quaedam minime afpernan-

da ,Ex.^.. fit fradtio propofita ^

fadloque ut antea x"^ - _ ^

Sint J-, Radices -ffie|uationis, fintquc Fradtio-

A . JB

JO X

• +

I — ex-\-fxx — gx^-^hx‘^^
e X’ -j~ f'x X — g X ~j~ /j — 0.

nes in quas refblvitur propofita,

( )

. C , D

4 f- . PonatUT a — atque

I — qx I — s X

' s— — / ; addantur flmul duae priores, itemque
duas pofteriores, & reducetur fra^tio propofita ad
-f-/ — mfx

'LXm +f XI — mx XI —

—zr-— -- — — fi vero ponatur f =z at»

X i-\-m X xi+./A?

que j = — & addantur duae priores, itemque duse

pofteriores, reducetur Fracftio propofita ad zznzzzn

mm — q q-

mm

X I — mm X X

qq — mm x i — qqx x

PROPOSITIO II.

St Jit Fra5ito qualtbet cujus Numerator Jit data
^antitasj ^ F>enommator Jit Trinomium vel ^ta~
drtnomium vel ^tnqtitnommm<t &c. radicalitate non
ajfe6fum & utcunque compofitum ex datis, i, e, f, g, h,
&c. ^ mdeterminata x atque dividator Numerator
fer F>enommatorem^ ut habeatur Series Injinita ;
dico fore ut, Ji Jumantur Termini quilibet ijiius fe-
riei aqualibus intervallis a fe invicem dif antibus,
feries injinit£ inde refultantes, Jummabiles futura
fint.

Exemflum L

Sit Fracftio propofita ; reducatur ilia

I X ■***■ X X

E e ad

I

( la )

%

ad feriem infinitam, nempe ad
-f ^ x"^-\- 8;v^+ 13 a;'’ + XI 34 a;* ^c. fumantur-
que termini omnes alterni, incipiendo a prime, itidem*
que lumantur Termini omnes alterni, incipiendo a fe-
cundo, hineque conficiantur feries binse.

Videlicet, i + x a;a;+ i3 x"~}-s^x^&c.
AT-j-3 a;* “r 8:v^4-xi a;’

Fingatur Denominator Fradionis propofitce, i — x
— XX ~o, jam cum indices poteftatum indeterminatae
y, in novis feriebus fe invicem fuperent communi dif-
ferentia X, pone XX — atque ope duarum aequa-
tionum i— a: — xx = 0, Scx x = z, extermine-
tur X ; fietque i — 3;s + ;sjs = ^?; jam nunc refti-
tuatur AT, & erit i — 3 a: a* + a?"^— ^ ; dividatur haec
aequatio per primam, quotiens erit i+at — xx;-
lumantur alternatim Termini quotientis, propter
Terminos alternatim fiimptos in ferie propofita,
hineque orientur fummae duae, i — xx, 8cx; confli*-
tuantur hae lumm^ Numeratores Fradionum duarum
quarum communis Denominator fit i — -i, x x x"^

eruntque ^ — . — • Sc 1 — % fummae re*-

I — ^xx-\-x* I —

fpedivae novarum Serierum.

Exemflum II.,

Si vero defiderentur fummae termmorum intervallis
binis a le diflantium, fiat ut prius i — x — xx — 0,
jam cum indices poteflatum in novis feriebus fe invi-
cem fuperunt communi differentia 3, ponatur x^

Sc fiet I — 4^ — Z2i—0j atque reftituto x, fiet
1 — 4 at’ — x^ —0 ; dividatur i — 4 a;’ — x^ per-
I — X — XX, quotiens erit l-\-x-{-^x x — x^-{-x'^,
Cijus termini ordinatim fumpti ad intervalla bina, tres

conficienc

( \6<) )

confident fummas, videlicet, i — x x^, ^ x Xy
quae figillatim fumptae, erunt illx Numeratores, trium
Fradionum, quibus fi apponatur communis Denomi-

I x^

nator i — 4 — x\ erunt tres Fradiones, ; —

^ I — ^x^ — x\

V —I— V*^ ^ V v*

I j r, = 5, lummae tres Termmo-

I — ^x^ — x^ I — 4 — X

rum omnium binis intervallis a fe diflantium, incipien-
do refpedive a primo, fecundo & tertio Termino ; at-
que eodem methodo colligere licet fiimmas termino-
rum ternis vel quaternis vel quinis intervallis a le di-
ftantibus, five denominator fit quadrinomium, vel
multinomium quodcunque ex terminis finitis compo-
fitum.

PROPOSITIO III.

Si dividatur ‘Anitas fer Trinomium utcunque com-
^ojitum ex datis i, e, f, g, &c. indeterminata x ;
dtco Terminum quemvts Seriei ex hac divtjione reful-
t antis y ajjignabilem fore.

Sit Trinomium i — ex -ff x x finge x x — e x~l~
f znOy fint m defy radices iEquationis ; fit / -f~ i lo-
cus termini defiderati, hoc eft exprimat / intervallum
inter primum Terminum & Terminum quad! turn, fac

fft p

A B — — . Et erit Terminus defide-

m — f f — m

tus Km!' X xK

Eodem modo fi dividatur Unitas per quadrinomium
I — e x-\- fx X — g x\ pone x^ — ex xf fx —
g ~ Oy fintque ntyfy qy radices ^quationis, fac A —

mm P P ^

— — B=

m^f X

m

f — m X f
E e 1

qq

( »7o )

Et erit Terminus defideratus

q — m X q — /

xx^ , & lex eadem obtinet pro mub
tinomiis quibuicunque.

PROBLEM A.

A B quorum T^exteritates fint in ratione data
videlicet tit a ad b, ea conditione ludant, ut quoties
A ludum tmum vicerit, B tradat ifji nummum unum :
quoties vero B vicerit, A tradat tfji nummum unum :
non frius ludo dejijtant, quam eorum alter nummos
omnes alterius lucratus f tier it ; quaritur quantum
frobabile futurum fit ut cert amen intra datum ludo-
rum numerum x, vel exfir ante illo numero^ finiatur.

Sit n numerus nummorum quos uterque Colluforum
habeat ; fit etiam n numerus par, ponaturque ^ ad ^
habere rationem sequalitatis.

Cafiis Primus.

H

B C

D

E F

Centro

( I7« )

Centro D, Inter vallo D A = i, defcribatur Semi-
circumferentia A M Z quae dividatur in tot partes ae-
quales quot funt unitates in tunc ex primo H, tertio
K, quinto M &c. & impari quoque divifionis termino,
demittantur ad diametrum perpendicula H B, K C,MD,

OE, Q^F 8cc. ponatur Q^;

HB

a: + I

AB

CK

AC

X ^ 1
X I

+

DM

Jf + I

AD

EO

AE

a; *-p I

+

AF

a: q- I
~x^i

8cc. donee

finus omnes exhauriantur : quo fado, erit probabilitas
certaminis finiendi intra ludos non plures quam x, ad

probabilitatem non finiendi, ut x “ ^ ad

accurate.

Cofollarium I.

H B ^ *

Si fumatur pro Terminus primus , ;r~

A B

negledis caeceris, habebitur approximatio fufficiens nifl
forte fit X numerus valde exiguus.

Exemplum,

Sit n numerus nummorum quos uterque CoHufbrum
habeat = lo. Sit etiam x 76. Si iumatur pro
primus terminus & negligantur caeteri, invenietur pro-
babilitas certaminis finiendi intra ludos non plures
quam 76 ad probabilitatem non finiendi ut y°747 ad
49237, fi vero fumatur pro termini duo priores ne-
gledtis caeteris, invenietur ratio probabilitatumut 70743
ad 492.47.

Coroll-

( ^7^ )

Corollarmm II.

Invenire quotenis ludis, probabilitates ccrtaminis
finiendi & non finiendi erunt aequales.

Solutio.

H B ^ ^

Penatur pro Q^Terminus unicus ? fiatque

x""" \ — 0^=:: Q. Et pofito maximo numero

invenietur, x — o.y$6 n n proxime, aliquanto major
quam \n n.

Cafus Secundus.

Sit n numerus impar, ponaturque ^ ad ^ habere ra-
tionem sequalitatis.

Centro G, intervallo G A defcribatur femicircumfe-
rentia A M Z quas dividatur in tot partes a^quales, quot

fusit

'7? )

iunt imitates in n ; ,tunc ex primo H, tertio K, quinto
M, & impari quoque divifionis termino, demittantur
ad diametrum perpendicula H B, KC, MD, O E, QF
^c. ex diametri extremitate A, primo fcilicet arcui
contermina, ducantur fubtenfe A H, A K, A M,
ad quas e Centro G ducantur perpendicula Ga,

G G cT, G g, &c. ponatur Q_= x G a,

AB

X-{~ f

_ CK\G/3 DM%Gy

a: I * .V -i- I

AC“

AD

EO xG^

X H- I

AE-ir

X

F O Cj

— ! &c. quo fadto, erit probabilitas certaminis
A

finiehdi intra ludos non plures quam x, ad probabilita-

y— 3

tern non finiendi, ut x ^ n — Q^ad Q_ accurate.

Qorollarium I.

Si fumatur pro (^terminus primus

HB^'xGcc

X -jr I

AB^T~

ne-

gledis cseteris, habebitur approximatio fufficiens.

Exem^lum..

Sit n numerus nummorum quos uterque Collufbrujn
habeat zz: 45*. Sit etiam x— 15*19. Sumatur pro
terminus primus negledis cseteris, & invenietur
probabilitas certaminis finiendi intra ludos non plures
quam 15*19 ad probabilitatem non finiendi ut 49959
50441, qu« p/oportio eft vero proxima,

Qor.oU-

( '74 )

Qorollarlum II.

Invenire quotenis ludis probabilitates ccrtaminis fi*
nicndi & non finiendi erunt aequales.

Solutio..

r. • HB^xGcc

Ponatur pro Terminus unicus - 5 nat..

AB i

fLUJ

que X ^ « — Q.— 0.5 ^ pofito ^ magno numero,

invenietur ~ o. 756 proximo aliquanto major
quam i contra quam fentiebat Clariflimus Mon-
mortius.

Ca//^s Tert'ms.

Pofitis cseteris ut in primo calu, fit ^ ad ^ ratio inae-
qualitatis {vid. Fig. i.) Pone^zriir^^ = L,

a

+^i”

= d.

ab

MD^

HBq

r, Fac, I, X r : : ^ m w

CKq

AD

j ^ •

OE^

AE

AB

.. Oil

AF

AC

5

T, ^ HB ix CK

Pone Q = — T-fn — > ^ —

^ xrAB + ^ 2rAC^d

MD

,x

jVj j[3 \ X

+ ^ A D ^ ^ ^ probabilitas
ludi finiendi intra ludos non plures quam x ad probabi-

litatem non finiendi ut nF — - x L Q^ad x L Q.

CoroL

( ;

Corollarium II.

H B

Si fumatur pro Terminus primus 3 ^

\x

m negledis cseteris, habebitur approximatio fuffa*
ciens.

Cajiis ^lartus.

Pofitis exteris ut’ iu fecundo cafu, fit ^ ad ^ ratio
inaequalitatis {ytd. Fig. x.)

Pone quantitates L, r, j, t, &c. iit in tertio

calli.

Pone

BH X Go.
xr AB + <^

CK X G/g
2 r KC -\-d

X — r DM X G-v ^ — I

/ = + ^rAD + d ^ ~ P‘’°’

babilitas ludi finiendi intra ludos non plures quam x ad

n — ^ ,

probabilitatem non finiendi ut nr~l — 4 L ad
4 L Q.

Corollarium.

Si fumatur pro Terminus unicus

m~~F~ negledlis cseteris habebitur approximatio fuf-
ciens.

^emadmodum in FrogreJJione Geometrical Ter-
minus quilibet ad fr oxime fracedentem habet ratio-
nem datam^ ita flint alia Frogrejfiones qua fie con-
Jiitui fiojfunt ut ajjumftis ad libitum Terminis
duobus firimis^ Terminus quilibet fiubfiequens ad
duos fir oxime firacedentes babe at rat tones datas^
efi fiubje^a Series,

Ff

A B

( ^76 )

A B C D E F

lyx^ -j- 41 Scc. in qua

C nz xBx + I Axx
D— xCx-j“iBxx
E — 2 Dx-j- I Cx X
F — 2Ex+iDxx Scc.

^lantitates autem Numerales 2 -f i fmul fimptas
ftibque proprtis fignis mmexas appellare licet Indi-
cem Relationis.

Eodemmodo conftitui poffunt feries alia in quibus
ajfumptis ad libitum Terminis tribus primis^ Termi-
nus quilibet fubjeqtmis ad tres proxime pracedentes
habeat rationes datas ; hujus generis efi fubjel^a Se-
ries.

A B C D E F

i~\~zx-{- 3xx-{~iox^-}- 34X^ ()j x^ Scc. in qua
D= 3Cx — 2Bxx+5'Ax’

E = 3 Dx — 2CXX+5BX*

F = 3Ex-^2Dxx + 5'Cx^ &c.

^Quantitates autem Numerales 3 — 2. ~f- 5' fmul
Jimpta Jkbque propriis fignis connexa.^ componunt
Indicem Relationis.

Sunt alia feries in quibus Relatio fit ad quatuor^
^el ad quinque^i ^el ad fex Terminos pracedentes.^
^c.

Series autem omnes hujus generis recurrentes appel-
lare licebit propter Relationem Terminorum perpetuo
recurrentem.

PROBLEMA II.

In feriehus recurrentibus., ex datis Terminis duo-
bus primis., fi relatio fiat ad duos pracedentes ; 'vel

datis

( >77 )

dath Termhih trihus ^rtmis^ Ji relatto fiat ad tres
fracedentes^ &c. dato etiam indice relatidnis^ inve^
nire fitmmam Terminorum quotlibet quorum numerus
datiis fit.

Problema folvitur in Tradtatu noftro qui inicribitur.
The Tdo^rinc of Chances.

PROBLEMA III.

Afpumj^tts ad libitum feriebus qmtcunque recur-
rentibus ; Terminifque^ iifdem intervallis a prmcifio
ferierum difiantibtis, in fie invicem multifilicatis^ in-
venire Jumrnam feriei ex hac multifilicatione refiuU
tafitis.

INVESTIGATIO.

r Proponantur feries dux, fitque m~Yn Index Re-
lationis in prima ferie, atque fi q Index Relationis

in fecunda, ex prime Indice m + n, formetur Aqua-
tic XX — mx — n — o, ex fecundo Indice / +
formetur iEquatio j/jy — fiy — q — o, pone xy —
Atq?:/e ope trium iftarum ^quationum, expungantur
xdey, & orietur -ffiquatio — mfisij — mmqz>:2^
— q z-finnqq^o. — nfi fi

^T.nq.

in qua delete primo termino mutatis lignis omni-
bus, atque pofito z—i, obtinebitur Index Relatio-
nis, quo obtento, feries relultans facile lummabitur ;
ir eodem modo procedere licet, j(i dentur feries tres
vel quatuor 6cc. recurrentes.

Ff X

T>um

( t>8')

^um Ju^erkres pagiha ^ralo fiibjiciebantur, inci-
di fortuito in A<Sl:a Leipf: annorum ijoz 1703,-
quibtis comperi Cla. Leibnitium eadem fere methodo
ante me ufum fuijfe qua hie utor in reducendis
Fra6Honibus Algebraicis ad Jimplieiores^ quod mo-
nit um velim ut a me avert am vel minimam fufpicio-
nem^ aliena mihimet arrogare voluijfe ; ‘Propojitio
autem qua id prajHtimus aque ac Tropofitio noftra
tertia^ amba deducuntur tanquam Corollaria ex al-
tera Tropojitione maxime generali quam exhibuimus
coram Regali Societatey Maii f 1720 ; Rropojitio fic
fe habet.

F)ata ferie. qudvis reeurrente . quarum Tet'mini
quotUbet primi ad Libitum fumantur ; dato etiam ln~
dice Relationis Terminorum fequefitium ad pr^ceden-
tesy invenire Terminum quemlibet ajfignatum in hac
feriey priufquam ftimma feriei fit cognita.

^pui autem rite perfpexerit Solutionem Rroble-
math hie adduBiy is utique percipiet itlam pendere'
a Rropoftione noflr a generally cujus demonflrationem .
fmulqtie modum invefligationis brevi Jpero publici
juris faciam.

IV. 2)^*

( i7p )

IV. Tiefenjio Dijfertationis de Motu Aquarum fluen-
tlunij in Jfiis Thilofophicisy N° 355. edit a ^ con^
tra Anhnadyerfiones Viri CL Petri Anton ii Mi-
chelotti. AuEiore Jacobo Jurin, M Coll.
Med. Lond. Soc. in Tfoeatro Publico Chirurg.
Lond. TrAeBore Anatomkoy ^ Soc. Seer,

IN pervolvendo Opere pererudito Viri ClarifTimi,
^etrl Antonit Michelottiy de feparatione fluido-
rum in corpore animali, qui Venetiis miper ad nos de-
latus eft, pluribus in locis DifTertationem meam de Mo-
tu aquarum fluentium, in ABis Thilofoph. N° 3 5'5'*
ante aliquot annos editam, non leviter notatam depre-
hendi. Cum autem alia ex iis, quse reprehendit Vir
DodtilTimus, ex minus perlpedlo Diflertationis mese in-
ftituto profedfa videantur ; alia vero ita demonftrari
pofTint, utipfum Virum Cl. ea mihi non difficulter con-
cefTurum putem : operse pretium erit, fi primo in loco
DifTertationis mese propofitum & confilium paulo lu-
culentius exponam ; quod cum fecero, ad reliqua de-
inceps breviter expendenda progrediar.

Principio igitur explicandum eft, quid in Diftertatione
ifta intelligendum velim, per Motum Aqua ex imi vajis
for amine defluentis. Eft enim alius Motus, five quan-
tit as MotuSj Aquse, quse ex vafe per foramen delabitur :
(\mMottis eft in ratione compofita,ex ratione quantitatis •
aquxdato quovis tempore eftluentis ex foramine,&ra-
tione velocitaris,quacum eftiuit. Alius vero eft Motiis
totins aquse, feu Cataraiftse aqiieos, quse intra vas verfus

foramen i

( '8c )

foramen defcendit,& mox effluxura cfl. Hie efl in ra-
- tione omnium fadtorum, ex fingulis aquas par-

ticulis, Cataradram conflituentibus, dudis in velocita-
tes earundem reipedivas. Quorum Motuum cum al-
terum ikpe pro altero accipi viderem, animus mihi erat
pofteriorem ilium in pr^dida DifTertatione illuflrare,
ad calculum revocare, & liquoribus in Animalium cor-
pore fluentibus applicare.

Hie ergo cum femper mihi intelligeretur Motum
jiqua dejluent 'ts^ five per Motum Aquarum fluent U
Atm^ quod ex omnibus mcis Propofitionibus luculem
ter apparet, jure meo dicere poteram Motum hunc a
nemine adhuc^ quod feirem^ fAjfe determinatum :
quippe quern nemo Mathemaiicornm, quos quidem
ego viderim, nec etiam verbo tenus attigerit. Qiiod
cum ita fit, miror profedo non animadvertiffe neque
acutilhmum Michelottum, nec etiam llibtiliflimi 8c
pcrlpicaciflimi Ingenii Virum, Johannem Bernoullium^
me in illius DifTertationis Prooemio, quod toties citar
& tantopere rqprehendit Cl. Michelottus.^ ne verbum
quidem Icripfifie de velocitatc,quacum aqua effluit ex
foramine, mulro minus de Bernoulliani determinari-
one illius velocitatis. Hoc fi perlpexiflet Vir Cl. no-
luilTet fane, pro fua humanitate, ram inclementer Sc
inique mecum agere, ut me Bernoullianam ^emon-
jiratlonem extenuare njerbis conari * diceret, & me-
ram efle cavillationem id., quod Bernoullio objiciam.
Quod vero fubjicir, verba ifla mea, fieri omnino
‘‘ non poffe, utMotus aliquiscum pondere quiefeente
conferatur,” ne umbram quidem habere rationis
contra Bernoullianam TDemonflrationem ^ugnantis.^
libens agnofeo, quippe qui, cum ifta feriberem, tan-

Pag, 13 T, 13a,

turn

r »8i )

turn de Cl. Bernoullio, quantum de Sinenfium Inipe- ■
ratore cogitabam. Aio aurem Ledborem quemvis non
iniquiim, neque pracjudiciis occupatum, ne tmbram
qiiidem verifimilitudinis .reperturum, quod ilia verba
ad Bernoullianam Demonftrationem quicquam perti-
ncant ; quibus fcilicec de re longe diversa agatur,
nempe de quantitate Motustotius aqu^e verfus foramen
contendentis. Quoniam vero ita penitus inledit ani-
mo Viri Dodiflimi ilJa Demonftratio, eandem in ilJius
gratiam, ubi prius meiplum ab reliquis ejus Animad-
verfionibus vindicavero, ad examen revocare decrevi.

Ad Motum prxdidum definiendum non alio nobis
opus erat, quam Theorcmatc noftro generali, quod
tertio loco pofiiimns : led cum Curvae Hyperbolicae
Newtonian^e proprietatem, qua Cataradam aquae de-
feendentis format, non indignam cenferemus contem-
plationc Geometrarum, voluimus obiter quaedam de
Catarada ilia praemittere. Hanc auteni ex Viri In-
comparabilis, 36. Lib. 2.. Lrincip. deliimptam
proponebam, non ut ex Trifode editam^ fed evidentia
Mathematica, omnibus oraculis certiorc, munitam.

Qiiod enim Catarada talis formari debeat ex aqua
libere defeendente, & accelerata in modum corporuin
omnium gravium, quam nulla alia aqua circumcinga-
tur, aperta res eft ; ut patet Newtoni Propofitionem
attente perlegenti. Si etiam Catarada glacie concava,
figurse Cataradae aqueae adamuffim congruente, Sc
propter ftimmam polituram nullam refiftentiam adfe-
rente ambiatur ; ea glaciem ne minim'l quideni vi pre-
met, fed tanget foliim liberrime cadendo, unde nihil
mutabitur non modo in figura, led nec etiam in vclo-
citate Cataradae defeendentis. At ft dreumpoftta
Glades in aquam refolvatur, neutiquam jam opus eft
ranto Machinarum Sc Arietum validijjimorum appa-

ratu,

( )

yatu, quos magno moliminc ij: adduxcrunt turn ipfe Vir
Cl. turn etiam Geometra Eximius, Johannes Bernoul-
Ihts, 2idfragilem noftram QataraEiam confringendam

commtnuendam ; quippe quam ipfe prius Newt onus
hifce verbis, * Liquefcat jafn glacles in vafe ; ^c.
difTolverit penitus ac diffipaverit. Nullo igitur aiit
Genio nobis opus eft, aut Erjthrai Marts Miraculo,
ad Cataradlam iftam five indicandam, five confervan-
dam, quippe qui non adeo ufque ftolidi aut inftilft fi-
mus, lit confervatum iri earn fpereinus ab omni aquie
circumpofitce communione puram & illibatam. Ig-
nofeat autem nobis, pro sequitate Ilia, Cl. Michelot-
tusy quod, quse Providentiftimus Newtonus de glacie
ambiente, & eadem poftea in aquam refbluta fufius
tradiderit, ea nofinet Ledtorein ex iplb potius Cl.
Audtore petere voluerimus, quam ingrata &: minime
nobis neceftaria repetitione detineri.

Non diftitemur fane paulum diferiminis, ut id obiter
notemus, inter callim a Newtono pofitum & noftrum
interefte. Qiiem enim fingit ille Cylindrum glaciei,
velocitate data uniformi defcendentein, ac liquefcen-
tem & in aquam converfum, quam primum ftiperficiem
attingit aqua; vale contents, in eiim Iciiicet f nem, ut
vas lemper.asque plenum confervetur ; hunc nos omi-
fimus, & ejus loco fuperficiem aqua; iiifinitam pofui-
inus, ut ea ratione integrum Solidum, five Cataraeftam
Hyperbolicam reprsefentaremus. At hsec pofitio ni-
hil mutat neque in velocitate, nee in Motu aqua; de-
currentis.

Quod autem f ait Vir. Cl. me fimere., quod
eft m contentione., 8c paulo infra, cejfare igitur
quaftionem.y cE' tot am E>emonJirationem abire in Hy-
^othejin., non mehercule intelligo, quid fibi velit.

^ Paj. 129, 130. Pindp. Pag, 304. ^‘^7-

aut

( >8? )

Mihi eniin, in loco citato, nulla movebatur quxftio
de velocitate aquse effluentis, nec demonflrationem
ullam de ea velocitate adferebam, led id unum ageba-
tur, ut ex pofita ilia velocitate iEquationem Curvx
Hyperbolicse Newtonianse deducerem. Velocitatem
nempe aquae effluentis jam antea determiuaverain, vel
etiam, fi placet, lumpleram, pofitis fcilicet iis, quse a
Newtono pofita fiierant, aquam nempe gravitatis vi li-
bere cadere, & inter cadendum accelerari. Hoc autem
qui fieri poflet, prius tradiderat Newtonus^ ponendo
aquam per glaciem politiffimam ambientem, vel etiam
pereandem in aquam folutam, ledquietem adhuc fer-
vantem, tanquam per infundibulum, fine ulla refiftentia
tranlire ; quod in eum finem ponebatur, ut fimplicior
& magis Mathematica redderetur Problematis folutio.

Liber hie loci, propter argumenti affinitatem, er-
roris meminifle, cujus Newtonuniy Hugenium^ Keil-
lium temere nimis, uti nobis videtur, ex Bernoullianse
demonllrationis fiducia * inculat Cl. Micheluttus ;
quod fcilicet vim, qua totus aquse exilientis Motus ge-
nerari potell, aequalem llatuerint ponderi Cylindricae
columnse aquae, cujus balls eft foramen, cujulque alti-
tude dupla eft altitudinis aquae vale contentae. Hanc
paucis admodum verbis, nec tamen idcirco minus per-
fpicue, demonftravit Newtonus in Corollario fecundo
Propofitionis fupradieftae. Potuiftet alia quoque dediici
demonftratio ex contemplatione Cataraeftae integrae Hy-
perbolicae, quae huic Cylindro aequalis eft, cujufque pon-
dus totum in aqu^ delcenfum impenditur : fed hac mi-
nime opus eft, cum idem ex ipsa Propofitione Bernoul-
liana, quam toties laudat, ac tarn vehementer defendit
Cl. Mkhelottus, apertiftime lequatur. Id nullo negotio

* Pag. iiZj 1 1 3.

Gg

animad-

( i84 )

animadvertet Vir T)o5HI[imus^ fi fepofita pammper
Columnar foramini incumbentis confideratione, calculo
inftituto, ex mole aquae dato quovis tempore ex foramine
effluentis, & ex velocitate, quicum aquam effluere ftatuit
Cl. Bernoulliusj ejus aqu^ Motum determinare voluerit^
& delude pondus iiivenire, quod eodem dato tempo-
ris Ipatio, libere cadendo gravitatis vi, eandem Motus
quantitatem generare pofTit. Hoc autem pondus repe-
riet ponder! duplae Columnae aquae foramini infiftentis
aequale, prorfus uti definivit Newtonus in Corollario ■
prsedid:o. Idem vero pondus, alter! Librae Radio ap-
penfum, ab impetu aquae, cum primum ex foramine
effluit, continuato rivo in alterum Librae aequalem Ra-
dium impingentis, atqne ftatirn poll impulliim dela-
bentis, in qiiiete fuflinebitur ; quod pofito calculo fa-
cile patebit.

Videor mihi non malam gratiam a ^o£UJ}imo Mi^
chelottOj pro candore fuo, initurus, fi altero inliiper |
pr^judicio, quo & alios plures teneri video, ipfum li-
beravero. Newtonus., Brof. 37. Lib.r.
ma editioms, aquam demonflravit ex foramine in fun-
do vafis ea cum velocitate erumpere, qua afllirgere
pofiit ad dimidiam altitudinem aquae in vafe exiilentis.
Demonftrandi rationem nemo refellit : conclufionem
plures redarguLint. Experientia, inquiunt, contradicit,
qua deprehenditur aqua exiliens ad totam altitudinem
alTurgere : quin etiam Newtonus ipfe in Problematis
ejufdem Iblutione, Brof. 36. lib. z. editionis fecund^,
earn tribuit aqu^ velocitatem, qua ad totam altitudi-
nem profilire polTit ; adeoque ipfe fibi contradicere
videtur. Atqui fi res ilia accuraitius & cum judicio
* perpendatur, reperietur primae Iblutioni Newtonians

8c

I

t Pag. 11?.

( i8y )

8c cum fecundi, & cum experientia ipsa, optime con-
venire. Nam in fecunda folutione, aquas venam exili-
entem, ad parvam a foramine diftantiam, contrad:io-
rem diametro ilatuit Terjpicacijfimus, quam in
ipib foramine, in ratione xi ad xy. Ed: itaque fed:io
vense in ea diftantia, ad foramen ipfiim, ut xi x xi, ad
X5* X X5, h. e. ut I ad V 2. proxime. Cumque eadem *
aquse quantitas, five per foraminis, five per venae con-
tracd:ae ied:ionem, dato tempore perfluat, & proinde
velocitates aquae in iis fedfionibus dnt in ratione ipfa-
rum fedfionum reciproca ; erit velocitas in foramine ad
velocitatem venae contradfae, ut i, ad ^ x : proinde, d
ea fit velocitas venae contradfae, qua aqua profiliat ad
integram altitudinem aquae in vale, non major erit
aquae velocitas in iplb foramine, quam qua ad di-
midiam altitudinem deferatur. Confentiunt itaque
inter fe duae folutiones ; & experientia porro cum
iifdem confcntire deprehendimr. Nam fi per alter-
utram earum folutionum, ex definita velocitate, qua
aqua, five per foramen, five per venam contradfam,
tranfire ftatuitur, calculo indituto inveniatur quantitas
aquae elfluxurae ; reperietur eadem cum quantitate
aquae, quae per experimenta effluere deprehenditur,
proxime convenire. Certe experimentum ab ipfo //-
luflrijfimo Newtono lumptum, adhibito foramine, cu-
jus diameter erat quinque odfavarum digiti partiura,
huic calculo relpondit ; ut etiamalia plura experimenta
minoribus diametris Londini facda, quibus iple cum
pluribus Regiae Societatis Sodalibus, ante aliquot annos
operam dedi. Abludunt quidem aliquantum
tijjimi * Toleni experimenta, fed tamen minorem aquae
quantitatem exhibent, quam fecundum hunc calculum,
nunquam majorem, forte quod angulliora fuerint vafa
pro ratione amplitudinis foraminum.

^ Polcn. de Caftellis.

Gg 2.

Supereft

(■ i8(5 )

Supereft adhuc nobis confideranda * Animadverfio
iina, five potius Scrupulus Viri CL ex eo natus, quod
in Cor oil. 17. Theorem. 3. DifTertationis pr^didse ma-
jorem ftatuimus Motum^ five Imfettm, fanguinis in
Arteriis omnibus capilJaribus fimul fiimptis, quam in
ipsa Aorta. Hoc ut explicet VirT)oBi(fmusy nefcio
quam Hypothefin nobis affingit, de majore fanguinis
denfitate in capillaribus ArteriiSjquamin Aorta. Nos
vero nullam ejufmodi conditionem pofuimus, fed Co-
rollarium deduximus ex Thcoremate prsecedente, in quo
agitur de Motu aquse per Canalem plenum quemcunq;
fluentis : unde patet fanguinem non aliter confiderari
in noflris Corollariis, quam quatenus fluidus efi: &
aquamaemulatur. Sed patet inde proyenire Scrupulum
Viri Cl. quod per fanguinis intelligat, quant i-

tatem Mot us ejus effeLfam ex mult ip lie at tone velocita-
tis per majfam dato tempore tranfluentem. Atqui hie
longe alius efl ac nofler fanguinis Motus.^ five Impetus.^
quippe qui in iflo Theoremate aqualis ikzimKwx Motui
molts aqu£.i qua dato quovis tempore effiuit ex Canali,
cujufque ea fit volocitas., qua percurratur eodem dato
tempore fpatium a quale longitudini Can alts. Facile
autemex hoc Theoremate fluitCorollariumpr^edicSl’um,
quippe cum dato tempore transfluat eadem fanguinis
moles per Aortam & per Arterias capillares, major au-
tem fit Canalis longitudo ex Aorta & Arteriis capilla-
ribus compofiti, quam Aortas folius. Hoc eo libentius
notavi, quod videam non folum T)o6iiJ]imum Miche-
lottum.^ fed alios etiam feriptores Mathematicos, pluri-
bus in locis, ubi agitur de potentiis, qua^ liquorem per
Canales eodem plenos aut in motum impellunt, aut ef-
fluentem fiftunt, nihil aliud confiderare pr^eter molem

7 Pag- loi, 102,

& ve.

( iB/ )

& velodtateiii fliiidi efflueiitis ; quum debuiflet ctiam
longitudinis ipforum Canalium ratio haberi. Nam cx-
teris paribus, eo difficilius vel cxpeliitur fluidum ex
pleno Canali, vcl in effluxu fiftitur, quo Canalis lon-
gior fuerit; quippe quum tota moJes fluidi Canale con-
tenti in motum concitandus fit, priufquam ulla pars
ejufdem effluere poffit ex orificio ; ficuti etiam
tota eadem moles neceffario fiftenda eft, ft exitum par-
ti jamjameftluxuras prohibere volueris.

Accedo jam ad expendendam Viri Celeberrirai, Jo-
hannis BernouUii^ Demonftrationem de velocitate aquae
ex foramine vafts pleni effluentis. In quern finem legi
diligenter ac relegi, turn quae protulit ‘t>o6HjJimus Mi-
cbelottus de j: principiis illius Demonftrationis, turn
ipfam Demonftrationem a CL Hermanno communica-
tam in ABis Ltfjienfibus^ Anni 1716. Quae quam-
vis nulla ex parte mihi fatisfaciat, tamen cum imbecil-
litatis meae confcius longe facilius accidere pofte fen-
tiam, ut ipfe a vero aberrem, quam ut Virumnobilifti-
mis inventis clarum, & acerrimo, ft quis alius inge-
nio pollentem, erroris alicujus redarguam ; cuncftanter
idcirco & dubitantius proponam, quid in ilia Demon-
ftratione minus firmum mihi videatur.

“ Fundamentum Demonftrationis {fir tbit Vir CL')
“ in hoc conftftit, ut conftderetur guttula liquoris in-
‘‘ fima, & foramini vafts immediate incumbens, tan-
“ quam prefTa, vel (ut ego voco) animata a gravitate

quadam acceleratrice quse le habet ad gravitatem na-
‘‘ turalem ut altitudo aquse vel liquoris totius foramini
“ vafts incumbentis ad altitudinem guttula, fcilicet ut
“ pondus abfolutum columnse aqux foramini infiftentis

« ad

4: Pag. 1 3 1.

( i88 )

ad pondus abfolutum guttulse ; Sic qiiippe nihil aliud
reftar, quam ut qiiseratur quantam velocitatemacqui-
“ rere polFit guttula animata ab ilia gravitate majori
quando cadit per lineolam fuas altitudini aequalem,
“ hoc ell, pollquam tota exierit per foramen ; tarn din
“ enim premitur a tota columiia aquea adeoque anima-
tur a gravitate majore qiiamdiii aliquid de guttula
(quam ut columellam Iblidam concipio) fupra foramen
exillit.”

Pofito hoc fundamento pergit Cl. ad Demon-
flrationem Hiam condnnandam : nobis vero lulpedfa
ell ipfius fundament! firmitudo. Ut id quo jure fiat,
videatur, ita, fi placet, procedamus.

Quoniam nulla alia re utitur Cl. Bernoullms, ad
animandam, ut vocat, guttulam infimam gravitate pr^e-
didla acceleratrice, nili fol^ preflionc, five pondere,
columnte aque^ foramini infillentis ; congelari pona--
tur omnis aqua columnam illam ambiens, & columna
aquea per politilUmam glaciem fmeomni refiflenti^ labi
concipiatur. His pofitis, quamdiu foramen clauliim
tenetur, urg'ebitur lane guttula foramini proxima toto
pondere columnse aque^e incumbentis, prorfus uti Ita-
tuit Cl. Bernoullms.

Referetur jam foramen, 8c permittatur liber exitus
aquae effluxurae. Quid deinde futurum cenfes ? Niun
urgebitur, vel animahitur guttula hifima gravitate
acceleratrice^ qua fe hahet ad gravitatem naturalem^
lit altitude aqua totius foramini incumbentis.^ ad al~
titudinem guttula. Minime vero ; fed urgebitur Ibla
gravitate liii acceleratrice namrali. Nam quam pri-
mum guttula infima moveri deorliim incipit, etiam ve-
locitate, fi placet, infinite parva, non amplius utique
urgebitur a pondere Columnx aqueae infiHentis. Fieri
enim non poteft, ut Columna aquea guttulam fub-
je(ilam premat, nifi ab ilia guttula impediatur in defcen-

( *89 )

fu. Non aiitem impeditur, quia non conatur velocius
defcendere, quam infima guttula gravitate fua deorfiun
fertur ; fed columna & gutta pari paiTu defcendunt,.
adeo ut gutta neque columnam deiertura fit, nec ab
eadem uliam vim aut preflionem fit paiTura.

Cedit itaqu€,ni fallor,& fatifcit Bernoulliana Demon-
flrationisFundamentiim : fed circumfpicientimihi,quid-
nam potiflimum tanto Viro occafionem dederit a vero
aberrandi, id prxcipue occurrit, quod fcilicet minus
animum intenderit Vijc Acutijjlmus ad difcrimen, quod
eft inter corpus preftiim a pondere incumbente, qusm
pondus iftiid non nifi a naturali Gravitatis vi accelera-
trice urgetur, & corpus impulfum, five animatum
(quoniam ifto verbo uti voluit Vir Cl.) a Gravitatis
vi acceleratrice prxter naturam audta. In cafu pofte-
riore defcendet corpus majore velocitate, quam qu^e
ex Gravitate naturali proficifci queat , prorfiis ex
lententia T)o5HJJimi Bernoullit : at in priore, utut
corpus prellum, dum quiefcit, urgeatur a pondere in-
cumbente, tamen ubi primum defcendere incipiet, ea-
dem prorfus velocitate defcendet, ac ft prius nullp-
pondere incumbente preftiim fuiftet.

Nefcio an operx pretium fit, rem per fe fatis claram
exemplo illuftrare.

Quiefcere ponatur in mensa columna lolida ejc cen-
tum Aureis ftbi invicem impofttis confeifta, & urgeatur,
ut fit. Aureus infimus pondere Aureorum incumbenti-
um. Si fiat jam foramen in mensa fubter Aureos, ut
labi ftnatur Aureus infimus : quamprimum ifte Aureus
defcendere incipiet, liberabitur ftatim ab Aureorum
incumbentium pondere, & eadem velocitate defcendet
turn Aureus infimus, turn reliqui omnes, ac ft folus illc
Aureus in mensa conftitutus fuiftet.

Mitto dicere, quod, ft quis ex velocitate, quacuiiT
aqua fecundum Ql. Berimilln placita ex foramine e-

greditur,.

C ipo )

gredimr, d>c ex determinata per earn velocifatem mole
aquiE dato quovis tempore elfiuentis, Motum ejufdem,
lit fupra monui, definite voluerir, eundem duplo majo-
rem reperturus fir, quam qui ex pondere Columnse a-
queas foramini infiftentis, eodem tempore, Gravitatis
vi generari quear. Profed:o videntur ifia mihi tantam
veri fpeciem prae fe ferre, ut miiltum debiturus fim
five Cl. Michelotto^ five ipfi Demonftrationis Audori
Celeberrimo, fi me aliquid redtius docere dignabitur.

Liceat interim ipfis, pace tantorum Virorum, fequen-
tia duo Experimenta, ad controverfiam iflam certius
dijudicandam, vel de novo inflituenda, vel faltem dili-
genter expendenda commendare. Akerum Newtonia-
num^ pag. 305'. Trincl^. fecund. Ed. ut

inveniatur, ex mole aquas dato temporis fpatio effluen-
tis, velocitas, quacum tranfit per iplum foramen : al-
terum Cl. Mariotti^ Libro E)u Mouvement des Eaux^
Eart.z. E)ifc. 3. Regl. i. quod tubo Cylindrico, u-
trinque aperto, parte inferiore fiirfum reflexo, & aqua
pleno lumptum eft ; unde facile asflimari pofiit, utrum
guttulae primx aquae effluentis ad tantam altitudinem
profiliant, quantam requirit BernotiUiana Demonftra-
tio.

V. An

( >9^ )

y« Jn Account of a remarkable Inftance of the In->
fe^ion of the Small ¥ ox, ©j 2)r. Jurin, Soc.

Secret.

A Young Gentleman ill of the Small Pox, of that
fort which is call’d the coherent, or the middle
between the diflindt and the confluent Kind, on PF ed-
nefdayOn^. 3d 17x2, being the fixth Day from the Eru-
ption, grew delirious in the Night, and got out of bed
in fpite of the Oppofition of twaNurfes that attended
him ; and feizing one of his Nurles by the Neck with
his bare Arms, he prefTed her Forehead againfl; his
naked Breaft, then cover’d with the Small Pox in the
State of Maturation, and held her for fome time in
jtjat Pofture. She was heated by ftriving with him,
and in ftruggling to get loofe, flie was fennble that flie
bruis’d and broke fome of the Puftules with her Fore-
head. The Woman was about 40 Years of Age, of a
clear, florid, languine Complexion ; flie told me Ihe
had had the fmall Pox, when flie was about feven or
eight Years of Age, and had been pretty fall of them,
but I favv no Marks upon her Face. On Friday
Morning the Small Pox began to appear upon her
Forehead, and increas’d by Degrees to between 5:0
and 6c ; Ihe had likewife a fmall Number of Puftules
upon the back part and Tides of her Neck, where the
Gentleman had grafp’d her with his naked Arms ; but
had none, as flie told me, upon any other Part of her
Body. The lower Part of her Face was perfectly clear,
and thofe upon her Forehead were chiefly confin’d to

H h the

( )

the middle and mod prominent Part of it, which had
been prefs’d againft the Gentleman’s Bread. They rofe
gradually, and came to Maturity, in the fame manner
as the Small Pox of the milder cohasrent Kind ulc to
do, with a great Inflammation and Swelling of her
jForehead, and the adjoining Part of her Face, efpeci-
ally between the Eye-brows, where a finall Cluder of
the Pudules were feated, infomuch that owT^e/daythc.
9th of October^ her right Eye was quite clos’d up, and
.the leftalmod in the fame Condition ; but all this Time
Hie had no Fever, Sicknefs, or other Symptom of the
Small Pox, befide this Eruption, and the Inflammation,
and Pain that attended it. That Night die caus’d a Blider
Xo be applied to her Neck, upon which die recover’d
the Sight of her Eye the next Day, being the dxth
from the Eruption, when the Pudules were turning,
.and beginning to fcab. The Scabs agreed with thole
.of the milder coherent Small Pox in their Appearance
and Duration. I faw her hitherto every day, as like-
wife at feveral times after this, and particularly on
Monday Obf. xzd, which was the eighteenth Day
from the Eruption of the Pudules, when die had dill
fome dnall Part of the Scabs remaining upon her Fore-
head.

In this Indance it is worthy of Remark : id. That this
Woman, tho’ die had had the Small Pox before, was yet
infecded again by the immediate and dole Application of
the variolous Matter to her Skin, when her Body was
heated with Exercife. Which feems to prove, that liich
an Application is more effedual to give the Infedtion
.than the bare morbid Ejfluviay arifing from the Body
of the Tick Perfbn, and received into the found one by
Infpi ration ; for that die receiv’d no Infection by In-
Jpiration is plain, from the appearing of the Small Pox
, upon thofe Parts only where there had been fuch an

Applica-

( »pr)

Application and Contact. From which it appears very
probable, that a Perfon who has already had the Small
Pox, as the Man inoculated by Mr. Tanner in St. Tho*
mas's Hofpital, may poffibly receive it again in fome
flight Degree by Inoculation ; that being flill a more
dole and immediate application of the Variolous Mat-
ter to the Blood and Juices of the found Perlbn, than
when it is applied only by Contad: to the. Skin whole
and unvvounded.

adly. That the Infedion communicated to rhis Wo-
man not being univerfal,as appears from her having no
Fever, or Sicknefs, or general Eruption of the Pultules
all over her Body, but only on the Parts infeded by
immediate Contad, no Argument can be drawn from
hence, for a Perfon’s being liable to undergo the Small
Pox a fecond time, fo as to have the ufual Symptoms
of that Dileafe, and a general Eruption of the Puftules ;
but rather the contrary.

Sdly, That the Time in which this Infedion fhew’d
itfelf, by the appearance of the Puftules, is very diffe-
rent from that obferved upon Inoculation ; the firft
appearing in about a Day and an half ; whereas in the
latter Cafe, the Eruption generally fliews itfelf on the
tenth Day, or not above a Day fooner or later, as ap-
pears from the accurate and curious Oblervations of
Dr. Nettleton. Which difference is what ought in rea-
fon to be expeded, fince in one Cafe the Infedion
went no further than the Parts affeded by immediate
Contad ; whereas in the other it muft be propagated
thro’ the Mafs of Blood to all Parts of the Body.

H h 2

VI. An

( '94 )

VI- An Account of two OhferVations upon the Cata- "
raEl of the Eye 5 contained in a Letter from
Signor Antonio Benevoli, MaJler^Surgeon in
the Hofpital of S- Maria Nuova in Florence,

. to Valfalva 5 printed in Italian at Flo-
rence, this prefent lear^ and conununicated to the
Royal Society, at the Deftre of the Author ^ hy
Sir Thomas Dereham, F. S'.

IN this Letter the learned Author informs Signor F'al-
falva^ that, on the 13th of July in the Year 1710,
he had couch’d a German Soldier of Cataracts in both
his Eyes, who immediately after the Operation reco-
ver’d the Sight of both Eyes, and continued to lee till
his Death, which happen’d of an Acute Illnels on the
6th of April in this prelent Year. Upon this. Signor
' Benevoli took the Eyes out of their Orbits, in order
to examine whether the Cataradts, which this Soldier
had been couch’d ol^ confifted of a membranous Pel-
licle, as Ibme W riters maintain ; or, as others pretend,
of a preternatural Opacity in the Cryftalline Humour.
•Proceeding immediately to the DilTedtion of the left
Eye, upon a careful and very exadt Examination of all
the Contents of it, he could not find any fuch thing as
a Pellicle within it, but difcover’d a fmall yellowilh
Body at the bottom of the Bulb of the Eye, of a lenti-
.cular Shape, without Adhellon to any of the other

Parts

( >95 )

Parts of the Eye, which, upon taking it out, appear’d
to be the Cryftalline Humour grown opake,and fome-
thing left than its natural Size, having two or three
linallDents, or Impreflions, made in its Circumfe-
rence, which it had received from the Needle during
the Operation of couching.

The next Day he examin’d the right Eye in the lame
manner, in the Prefence of feveral eminent Phyltcians
and Surgeons, and other curious Perfons, whom he had
invited to the Demonftration, and found in it the Cry-
ftalline grown opake and deprefted in the fame manner .
as the former, to the bottom of theEy e, ftill carrying the
Marks of the Needle evidently upon it, but found no Pel-
licle within the Eye, notwithftanding the moft diligent
Search he could make for it. Signor Benevoli farther
relates, that having formerly made fome Experiments
upon the Eyes of dead Subjects, at Bologna^ in company
with Dr. Valfalva^ he had introduced the Needle into
the Eye in the fame Place, and in the lame Manner, as
is commonly praeftiled in the Operation of couching,

' and having afterwards difteefted the lame Eyes, he had
always found, that the Needle had pafs’d into the Eye on
the backfide of the Cryftalline Humour, fo that it had
been impoftible to bring the Needle forward from
thence into that Part of the aqueous Humour, which
is feated between the 'Vvea and the Cryftalline Hu-
mour, in order to deprefs a Pellicle feated there, ac-
cording to the common Opinion, unlefs he would have
pafs’d his Needle thro’ the Body of the Cryftalline.

This curious Author likewife oblerves, that the
aforelaid Space, between the ^vea and the Cryftalline
Humour, is lb very narrow, that tho’ he finds it not
impolTible to introduce a Needle into that Space, yet
there is by no means room enough to turn the Needle
up and down in all Dire<ftions, with that Freedom,

that

( )

that is ufed in couching Cataradts, without wounding
either the Vvea, or the Cryftalline.

Laflly, Signor Benevolt obferves, that in his Pra-
d:ice of couching Catarad:s for many Years, having
generally couched about twelve or fourteen in a
Year, he had always found, that he work’d upon a
hard and refilling Subftance, which being tenderly
touch’d by the Needle, would vibrate and fludluate
backwards and forwards, and would fometimes return
againft the Needle with a fenfible Imfetusy which by
no means agrees with the common Notion of the Ca-
tarad’s confifting in a Pellicle or membranous Sub-
ftance.

FINIS:

LONDON: Trlnted for W. and J. Innys,
Printers to the Royal Society, at the Prince’s
Arms the Weft End of St. Paul’j Churchyard.

I

Numb.

374.

PHILOSOPHICAL

TRANSACTIONS.

For the Months oi November and December,

The CONTENTS.

I. Ohferyatio Edipjts Solaris^ ah Edmundo Hal-

leio, LL-T>. ^S.S. Jjlron. Geom»

Trof. SayiLOxon. Novem. 27^ 1722, p,
Grenovici.

II. The fame Eclipfe oljeryed in Fleetftreet, Lon-
don. Mr. George Graham,, F.

III. T)e Tartkulis StruSlurd Adamantum. Epi*
Jlola Domini Antonii Leeuwenhoek, (?^. S. Soc.
ad Jacobum Jurin, M. D. (2^. S. Secret.

IV. An Account of an Optical Experiment made be-
fore the Royal Society, on Thurfday, Dec.
6th, and repeated on the 13 th, 1722. Dy the
(^Vermd J. T. Defaguliers, L L. D. F. S.

li

V. Tart

V. JPart of a Letter from Dr. Netdeton, Dhyjt^
cian at Halifax, to Brjurin, S. Seer, con-
cerning the Inoculation of the Small Pox,
and the Mortality of that Dijlemper in the natu->
rat Way,

Vh A Letter to the Learned Dr. Caleb Cotef-
worth, F. ^ S. of the College of Dhyfeians^
London, and Fhyftcian to St. Tliomas^i Ho-
fpital 5 containing a Comp ar if on between the Dan-
ger of the Natural Small Pox, a)id of that given
by Inoculation, ©j/ James Jurin, M.D.dLS.
Secret.

VII. ■ De SeBione JngiiU, Jutore A. de Moivre,

R. S. S.

VIIL An Account of a new fort o/Molofles made of
Apples 5 and of the degenerating of Smelts. Dy the

. Honourable Paul Dudley, F. 5^. 5.

; S

E R R AT V M,

Pag. 104. liii. penult, read, i'n icone 7.

( >97 )

I. Ohferyatio EcUpfis Solaris^ ah Edmundo Hal-
leio, LL.D. ^S.S. Jjlron. ^ Geofu,
Trof, SaVtLOxon. Novem. 27'' 1722. p. nu
Grenovici.

h I ft

I X9 16 T] Clipfin jam inceptam vidi.

I 31 6 Diftantia Cufpidum 7 ' 4'^, unde pars

deficiens of 47 ft ac initium verum
I ^ z8 ^ tt

I 34 18 Diftantia Culpidum iQt ^ott
I 4x x8 Repet, 16 1 zo ft
I 43 x6 Inclinatio Cuipidum ad dextras 44® 30 '
z 32 37 Partes Lucidse rellduae 17
z 40 16 Repet. in med. Edipfts proxime. 17/9''

3 18 45" Inclinatio ad finiftras 19°

3 31 45' Diftantia Culpidum 15' 'zi''

3 37 Repet. 10 ' 5'o

3 43 Z5' Finis Eclipieos dubius, ob limbum Solis
alperum & undulantem nec lat bene de^
finitum.

3 43 45* Certe defierat Edipfts.

Codum toto tempore ferenum & tranquillum.

K

II. m

( )

II. The fame Eclipfe obferVed in Fleetftreec, Lon-
don. 'Ey Mr. George Graham, F. S.
h I n

P. M. I 38 Beginning. Apparent Time.

2 19 34 By Eftimation the Cufpes Parallel to

3 43 22 The End. (the Horizon.

2 14 44 The Duration.

Quantity eclipfed 5 Dig. 716

1000

I Had very corred: Obfervations both of the Sun and
Stars, the 26, 27, and 28th, for determining the
exad Time by my Clock.

For fome Minutes before the Eclipfe began, I ob-
ferv’d the Sun with a Telefcope of 12 Foot, furni-
Ihed with a Micrometer ; keeping that Part of the
Limb in the middle of the Glals, where I expeded the
Moon firfl to touch, and in lefs than four Seconds of
Time, from the Moment I judged the Eclipfe begun,
it was fo confiderably advanc’d, that I cannot doubt
of having the Beginning to Icfs than three Seconds. I
believe the exad Time of ending was within the fame
Limit, notwithftanding that the Undulation of the Limb
was then much greater than at the Beginning. The Parts
eclipfed, meafured with the Micrometer, at the Time
of the greateft Obfcuration, were 927 luch Parts as the
Sun’s Vertical Diameter contained 1946 ; which was
taken a little before the Beginning of the Eclipfe.

The Sky was clear, and free from Clouds, till near
the End, when a narrow one obfcured fbme part of
the Sun’s Disk, but that part of the Limb where the
Eclipfe ended, continued clear till after it was over.

By

( >99 )

By this Obfervation the Beginning differed not x ^
and the End not | a Minute from Dr. Halkys Com-
putation, which he lent me the Day before. And if his
Computation, which was made for Greenwich^ had
been reduced to the Meridian of London-^ the Diffe-
rence would have been Hill lels.

The fame Ecliffe was obferv" d by Mr. Hawkins at
Wakefield, in Yorklliire, to begin at ih. xim. p. m.
and to eud at m. ^ 'f. The Sun' sTyiameter was

obfcured fomewhat more than 5* T)igits,

III. De Tarticulis ^ StruBura Jdamantum. Epi^
ftola Domini Antonii Leeuwenhoek, <2^. S.Soc.
ad Jacobum Jurin, Mi D. ^ S. Secret,

POftquam invelligando compereram Metalla quse-
dam, & iplas etiam Arenas ex perexiguis ejuf-
dem materise particulis compofitas effe, meditatio-
nem meam converti ad Adamantem ; fcilicet niim ille
etiam ex iftiufmodi conllet particulis, quse quidem ope
microlcopii conlpici poffint.

Igitur exiguum quendam Adamantem per microlco-
pium contemplatus, in ea Adamantis parte quae polita
non erat, & Iplendore carebat, complures particulas
ociilis oblervavi ; & Adamantem ex parvis particulis
compofftum effe comperi. Verum cum haec nondum
mihi latisfacerent ; Adamantem in fmffa confringere
decreVi, ut ilium in fragments fuis confiderarem.

Ergo Adamantem, malleo impofitum, alio nialleo
lemel iterumque percuffi, qui fic percuffus in quatuor
aut quinque frufta diffiliebat. Quod cum nondum
mihi fatisfacerer, & Adamantem in exiguiffimas micu-
las comminuere vellem ; fruffum, quod caeteris majus

K k X erat,

( 200 )

erat, duplici chartii circumvolvi, ne quae Adamantis
miculae difliliendo perirent.

Hie ego duritiem Adamantis admiratus fum : qui
multa vi aliquoties id:us, in quatiior tantum aut quin-
que frufta fine ullis miculis di/Iiliebat —

Pofteriora ifta Adamantis fruftula microlcopio etiam
admovi : quae cum peripecularer, pene omnia ex minu-
tiflimis particulis compofita effe comperi. Cum autem
fruftula ilia radiis.folaribus objicerem: quandam quafi
flammulam ex iis emicare videbam, & quidem majo-
rem, quam unquam vidillem.

Fruftulum unum oculis notabam, quod locum fra-
<51:urx fuse, planae quidem ac quadratae, fbli dired:e
oppofitum habebat : qui locus, quantum vilu dijudica-
bam, tribus aut quatuor pilis menti virilis latitudine
refpondebat.

Ex hoc Adamantis fruftulo tanta afeendebat copia
ardefeentium flammularum, ut plures effe numero
quam quadringentas judicarem. Flammularum ifta-
rum nonnullse, fed numero paucse, fibi erant vicinius
jundtae, 8c reliquis majores : unde concludebam, ipfas
Adamantis particulas illic etiam aliis particulis majores
effe, vel ordinatius effe difpofitas.

Exinde oculos conrerti ad aliud Adamantis fruftu-
lum, paris circiter magnitudinis cum priori, quod ra-
dios fblares itidem diredte excipiebat; 8c baud paucio-
ribus exiguiflimic molis particulis conftare comperie-
bam. Ex una fruftuli illius parte eaque circiter dimi-
diata, fpecies illse ardefeentium flammularum etiam
exoriebantur, fed mole minores : in altera medietate
flammula quxdam cernebatur, aflidue fe mobilitans,
cum continua quadam corufeatione, qu^ fpeciem habe-
bat debilioris fulgetri.

Cseterum, poflquam ifla Adamantis fruftula radiis
folaribus fubduxeram, adhuc multiformes rerum fpe-
cies

( iOl )

cies ocuiis meis objiciebantur. Inter alia, ex fingulis
Adamantis particulis flammula quaedam in altum emi-
care videbatur.

Porro, novem prseterea Adamantis fruftula micro-
Icopio applicata habebam : & in eorum leptem parti-
culas illas agnovi, quas Ipeciem flammularum ejacula-
ri dixi. In duobus aliis etiam particulas illas agnofce-
re poteram, ex qiiibus Adamantem comporitum elle
ftatui ; fed illse planitiem luam ita foli obverfam habe-
bant, ut plures eodem tempore particulas digno-
fcerem.

Mihi autem peramsenum erat lpe<fl:aculum, tot in-
tueri imagines flammularum, qu^ omnes colorem pr^e-
ferebant corufcum, Sc plerasque viridantem, Iflud au-
tem infolens mihi viliim eft, quod ad flammularum qua-
rundam extremitatem talis perciperetur in acre motus
ac vibratio ; tamquam ft flammula adeo illic debilitata
foret, ut confpicua effe deftneret. Pr^ cseteris autem
admirabar, quod ex tali Adamantis particula circumqua-
que ignis exiret, debiliter rutilans, ftcuti cum fulmen e
longinquo corufcare videmus. Quod quidem tarn ere-
bro intuente me accidebat, ut oculos avertere non
polTem, nift jam fatigatos.

Verum tarn jucundo fpecftaculo faspius fi*ui decrevi,&
fruftulumiftud Adamantis, donee fponte a vitro decidat,
microfeopio applicatum relinquere. Neque enim ope
glutinofae alicujus materise aflixum eft vitro : nift quod
vitrpm, antequam illi ftuftum Adamantis aftigerem,
humore anhelitus mei irroraflem.

Cum tam grato Ipecftaculo folus frui non vellem ;
quae modo relata funt, legenda tradidi cuidam N. cui
& microlcopium in manus tradidi. Cumque poft
aliquantum morae requirerem ; nonne omnia delcri-
ptioni meae convenire comperiret ; ille prorlus con-
venire refpondit, & admirationem fuum fuper Ipedta-
culi infolentii confeftus eft.

Porro,

( *01 )

PorrOjCum fruftulum quoddam Adamantis adhuc mi-
crofcopio applicatum eflet, cujus particulas, Jamellarum
modo fibi incumbentes, vifu dignolcere poteram ; baud
abs re me fadurum putavi, fi lamellas iftas delineari
curarem, quse hie inicone i denotantur per ABC.

Deinde Sc aliud Adamantis fragmentum microfeopio
applicaveram, cujus lamelliE, invicem fuperflratse, lefe
oculis meis diftincftiilime ofFerebant ; qu2e hie in icone
X defignantur per D E F G H I K L M. In hac autem
figura particulae illae five lamellse, qu^ per F G, F H,
F I, F K, & L denotatse funr, reliquis aliquanto craffi-
ores elTe videntur : verum ifl^e particulse ex pluribus
lamellis, invicem fuperflratis, funt compofitse. In ilia
vero fragmenti parte, quam inter D E F M exprimendam
curavi, diflindtilTime apparent tenuilTimse lameJlse, ex
quarum congerie totum Adamantem concretum efie
pro certo habendum eft.

Priufquam fecundam iconem in charta exprimendam
curaveram ; forte Celebris Gemmarius, AT. Verbrugge^
sedes meas praeteribat, quern ego ad convifendum A-
damantis fragmen, ficut microfeopio applicatum erat,
invitavi. Ille fragmen iftud non fine admiratione con-
templatus, quafdam fe Adamantum glebulas, quae fibi
inutiles elTent, mi hi milRirum recepit.

Nec multo poll bina mihi mittit Adamantum frag-
menta : item exiguura Adamantem, ex arte quidem
politum, fed fordidum, uti vocant, feu vitiolum.

Cum fingula fingulis microfeopiis applicalTem, primo
fragmentum iftud, quod in Fig. 5 . per NOP Q^R de-
notatum ell, delineandum curavi. Lineolse, quae per
totum hoc fragmentum excurrunt, revera non lunt nill
lamellae, ex quibus Adamantes conftare modo dixi ;
& apertius conlpiciendas le praebent ad P Q.

Ceterum

( ^0] )

Caetcrumut eorum, quae de hac Adamantis glebula,
five fruftulo, jam dixi, clarior atque diftincStior fit
pcrceptio ; fruftulum iftiid eadem prorfus magnitudine
exprimi jufTi, quam nudo delineatoris oculo, fine mi-
crofcopii ope, offerebat : quae vera fruftuli magnitudo,
in icone 4, exhibetur inter S T. Iftud autem tantii-
lum fruftulum ex tarn multis tamque exiguis particulis
compofitiim eft ; ut qui non viderir, capere baud
poftir.

In altero Adamantis fragmento, quod ejulHem pro-
pemodum magnitudinis erat, lamellae dignofci pote-
rant : & pars illius circiter quinta conftabat quinquan-
gulo tarn polito, tamquam fi ex arte laevigatum fuiffet,
nifi quod illi aftixus efiet perexiguus Adamas, qui cir-
citer quartam quinquanguli partem obtegebat ; & uti
dare vifii agnoftebam, etiam ex lamellis, five particu-
lis lamellarum formam habentibus, concretus erat.

Quantum ad perexiguum iftum Adamantem ; ilium
quidem ex arte politum, fed fordidnm feu vitiolum efi'e
dixi ; fordidos enim vocamus, dum vel fubfiavi lunt,
vel rimis aut lineolis deformes : quamvis nonnullae hu-
jus Adamantis rimae atque lineolse nudis oculis confpi-
ci non pofient ; imo, adhibito etiam microfcopio, vi-
fum pene eftugerenr.

Exiguus hie Adamas erat quadrangulus : prope unum
iftorum angulorum, intra iplum Adamantem, varias
vidi particulas ab invicem fejundas ; nifi quod aliquan-
tulum lele attingere viderentur, quod initio infolens
mihi vifum eft. Particularum iftarum maxima coloris
erat llibflavi, 8c altero circiter latior quam craftior :
neclplendore cedebat vitro, Reliquis particulis varise
erant figurae ; nonnullis etiam par fplendor ac primae :
nec pauciores efie judicabam quam viginti j licet deli-
neator tantum numerum non exprefierit.

Ifte

( )

Ifte conlpedus hanc* mihi perluafionem iiiduxit;
■quo tempore materia, Adamantum produdtrix, vaga-
batur in acre ; exiguas illas particulas, quae itidem A-
damantes erant, priori quern dixi Adamanti adjacuifle :
materiam autem adamantinam, quamdiu talis materia
aeri infedit, iftam Adamantum congeriem paulatim
circumveftiifle, Sc minores Adamantes inclufifTe ma-
jori.

Qua occafione recordor complures me habuifTe Cry-
ftallos montanas figure fexangulae ; in quarum non-
nullis quafi incluf^ jacebant jfigurse qusedam perexiguas
Sc oblongae, coloris fubcoerulei ; fed tarn exiles ut,
adhibito etiam optimae notie microfcopio, vix agnofci
polfent.

Porro iftius Adamantis, quern vitiolum appellavi, ve-
ram magnitudinem delineari curavi : quam in icone 5
expreflam babes inter V Sc W.

Deinde& perexiguos iftosAdamantes, qui in majorem
Adamantem inclufi exhibentur in icone 5", feorfum deli-
neandos curavi ; quos in icone 6 defignatos vides per
X Y Z A B C. Ubi per X Y Z denotatur exterius Ada-
mantis latus, quod licet ex arte politnm, ope tamen mi-
crofcopii confpecStum, colorem tarn fufcum prseferebat.

PerZABCDE ifti dcnotantur exilidimi Adaman-
tes ; quos in majufculo Adamante yelut inclufbs latu-
ilTe prsemonui.

Cum poflea latus Adamantis in icone f exprelTi, cui
longe minores Adamantes inclufos fuiffe mox dicebam,
ad micro fcopium admoviffem, Adamantem ilium variis
foraminibus pertufum elTe comperi ; quoe ego foramina
tunc fadla elfe cenllii, quando latus illnd poliebatur.
Ita nimirum ut exiguiffimi, quos dixi, Adamantes loca
ilia prius infederint, fed poliendo delapfi foramina ilia
five puteolos produxerint, qu^ foramina in icone 5- con-
ipicua flint inter F G H.

Porro

( io5 )

Porrro exlguum ilium Adamantem, inter V W"
in iconc $ expreflum, in latus liium verteram ; & ubi
crafliufculus erat, novaculum illi aptaveram, ut Ada-
mantem ipfum id:u mallei diffinderem : quod tamen,
licet iterate tentanti, non fuccelTit.

Quare Adamantem charts munda circumvolutum,
imponebam malleo ; & alio malleo, crebrius tamen
feriendo, diflregi. Poftquam omnes diffi'ad:i Ada-
mantis glebulas diverfis microfeopiis applicaveram ;
unam, quse plures qam reliquae lamellas oculis exhibere
videbatur, delineatori effingendam tradidi,qu2e in icone
8 denotatur perlKLM. Hand tamen pollibile de-
lineatori fiiit e^dem perfed:ione glebulam iliam expri-
mere, qua lefe oculis confpiciendam oflerebat.

Cum autem microlcopium, cui fruflulum iilud iconis

8 applicatum erat, diverlum efTet ab iis microfeopiis,
quorum ope alia Adamantis frufta delineari curaveram;
Delineator poftremum hoc fruftulum ea magnitudinc
ejmreflit, quam fine microfeopio conlpedlum oculis
offerebat : quae vero fruftuli illius magnitudo in icone

9 exhibetur inter N O.

Quaedam ex his Adamentum fragmentis, ope mi-
crofeopii confiderata, jucundos praebebant conlpedus ;
quos etiam nonnullis, talium rerum ftudiofis, exhibui.
Illis autem jucundilhmum erat, in uno Adamantis fru-
flulo tarn multiplices agnofeere partes ; imprimis etiam
quod lamellae, ex quibus Adamantes concreti limt, in
duobus Adamantum fruflulis valde diftindte pollent
internolci ; nempe dum lamellae iftae juxta dudtum lon-
gitudinis oculis objiciebantur.

Exinde fludium meum converti ad examen Cryftalli
cujufdam montanae, fex lateribus praeditae, cujus longi-
tude circiter relpondebat latitudini duorura digitorum,
crallitudo vero minori digito.

LI

Cryftallum

( io6 )

Cryftallum iftaai in complura frufta confregi, 8c
frufta microfcopiis applicavi ; difquirere volens num
8c ilia ex liiperftratis fibi lamellis compofita efTent :
qua ratione Adamantes magnitudinem mam adeptos
efle dixi. Sed, tametfi perquifitionem iftam faepius
iteraverini, ne tantillam quidem lamellam in iis depre-
hendi. Iflud autem in Cryftallis, quas quidem prae
manibus habebain, plerumque animadverti, in omni-
bus earum lateribus, qu^ numero fena erant, tranf-
verfas protendi lineolas, alias aliis fitu aliquantulum fu-
periores ; tamquam fi illic, increfcentibus Cryftallis,
ortae producftaeque fuiftent : qua ftiper re, quantum-
cumque Cryftallorum numerum ante conftderaverim,
atque confregeriin, numquam iple mihi fatisfacere potui.

^elphls in Hollandidy
Nov. xo. I71X.

IV. An Account of an Optical Experiment made he-,
fore the Royal Society, on Thurfday, Dec.
6th, and repeated on the 13 th, 1722. Ey the
<I(eVerend J. T. Defaguliers, L L. 2). K S.

SI R Ifaac Newton., in his Optics, {B. i. Brop. i.

Exp. X.) relates an Experiment made with a Card,
or Paper, painted red on one half and blue on the
other, which being enlighten’d by a Candle, the I-
mage, by the Interpofition of a Lens, is fb projecfted
on a white Paper, held on the other fide of the Lens,
that the Place where the blue half appears diftind:, (or
as the Opticians term it, the diftind Safe of the Image
of the blue half) is much nearer to the Lens than the
Place, of the Image of the red half. And this is made

apparent

( 2^7 )

apparent, by feeing On one of thefe Images the Reprc-
fentation of the black Threads, that are wrapp’d round
the Card, whilft they are not vifible on the other.
This is fully defcribed in the Place abovemention’d ;
but yet a * Gentleman abroad has call’d the Experiment
in queftion,and denied the matter of Fadi, faying, that
he could nor make it liicceed, but propofes an Expe-
riment ofhis own to difprove the different Rcffangibi-
lity of the Rays.

Upon this I was defir’d to make the Experiment
over again, before the Royal Society, which fucceeded
well. But becaufe there muft be care taken in the
making it, I fhall mention all the Particulars obferved in
the Performance ; which, if duly put in pradiice, will
make the Experiment always fiicceed.

I painted one half of the Card RB, {Fig, X.) as B,
with Ultramarine^ made deeper with a fhaall Mixture
of Indigo^ and the other half R, I painted over with
Cinnabar heighten’d with a little Carmine^ fb that the
Line, that feparated the red from the blue, was per-
pendicular to the long fides of the Cord.

Then I wrapp’d a black Silk four times together,
over the middle of each painted part of the Card, as in
Fig. XL

Upon a fquare Trencher, Fig. XII. painted black,,
and liifpended vertically againfl a Wall, I fix'd my co-
lour’d Card with a Pin, and the Room being made very
dark, I enlighten’d the Card with a ftrong Light thrown
upon it from a dark Lanthorn, that had two Convex
Glafles in it ; then letting up the Lens L L, (repre-
lented by Fig. XIII.) in fuch manner, that its Axis
pafs’d perpendicularly thro’ the Image of the Card, at

* A£t. Erudit. Lipf. Supplem. tom. 8. 3. p. 130. 13 1.

L I X

the

( 208 )

the diftance of nine Feet from the Card, the Image of
the Card being receiv'd upon a white Paper, at the
diftance of nine Feet on the other fide of the Lens^ at
B, the blue half appear’d diftind, with the Image of
the black Silk going vertically along its Plain, whilft
no Appearance of the black Silk was perceivable on
the red half. Then removing the Paper about two
Inches, to R, the red half of the Image had a black
Line very plain upon it, whilft it was invifible on the
blue half. This was more evident, when a ftrong I-
mage of the Candle was fucceftively thrown on that
half of the Card, whole Image was under Examination.
When the Paper was held in the middle between R
and B, the black Line upon each Colour was vifiblc,
but indiftind.

N. B. Care muft be taken that the Colours be deep,
becaufe having accidentally rubb’d off fome
of the blue, the Whitenels of the Card under
it, made its Image fly out farther, almoft as
far as that of the red.

V. ^urt

( iop )

V. of a Letter from Dr, Nettleton, ^hyji^
dan at Halifax, to X)r.Jurin, (1^. S. Seer, con^
cernin^ the Inoculation of the Small Pox,
and the Mortality of that Diftemper in the ?iatu»
ral Way,

HERE are two Propofitions advanced by the Fa-

vourers of the Pradiice of Inoculation, concern-
ing which the Publick feems to require more full Satif-
fa&ion. That the Dijiemper rais'd by Inoculation is
really the Small Tox ; and, That it is much more
mild and favourable^ and far lefs mortal than the
natural fort.

The former of thele is not fb much dilputed now,
as it was at firft, when this Method was introduced,
nor can it be made a doubt of by any one, who
has feen thole that have been inoculated, and has allb
been much converlant in the natural Small Pox.
There is ullially no manner of diflerence to be obler-
ved betwixt the one fort and the other, when the
Number of Pullules is nearly the fame ; but in both
there are almoll infinite Degrees of the Diftemper, ac-
cording ta the difference of that Number. All the
Variation that can be perceived of the Ingrafted Small
Pox from the Natural, is, that in the former the Pu-r
llules are commonly fewer in Number, and all the red
of the Symptoms are in the fame Proportion, more fa-
vourable. They exactly refemble, what we call the Di-
Hindi Sort : the Symptoms before the Eruption are the
very lame, and when the Pullules begin to rile, their
Appearance is the fame, as well as their Periods of
Maturation and Declenfion ; they are at firll of the
fame florid, rofy Colour, and when fully ripe, of as
2 fair

( 2tO )

fair a yellow. They commonly rife as round and as
large as the other, and when they are very numerous,
the Inflammation and fwelling of the Face comes on
at the ufual Time, and is followed by the fwelling of
the Hands and Feet, and only once I oblerved a Sali-
vation, tho’ the Puftules were diftindt. In the Natu-
ral Small Pox, when the Puftules are very few, we
fometimes oblerve, they do not rife to fo great a Bulk,
neither do they ripen fb fully, nor continue fo long
as ufiial ; and it is the fame in the way of Inoculation.
In ihort, as this Diftemper is raifed by an Ingraftment
from the Small Pox, as it has the very lame Appear-
ance, and as it is capable of producing the fame by In-
fedtion, there feems to be no room to doubt of its
being the true and genuine Small Pox. And if that
be allowed, it will follow from thence, as a Corolla-
ry, that Thofe^ who have been inoculated^ are in no
more danger of receiving the Tliftemfer again, than
Thofe who have had it in the ordinary Way. And
this is alfb thus far confirmed by Experience. We are
very ready to own, that the Operation may fometimes
fail : thofe Gentlemen, who firft communicated to the
Royal Society fbme Account of this Pradfice from
Turkey, did both of them intimate lb much ; tho' I be-
lieve that will but rarely happen. In one * In-
ftance here, I obferved no Eruption at all, nei-
ther did the Wounds inflame and fxvell any more
than would have follow’d from a common Incifion,
which made me conclude, that what was apply’d had
not taken Effedt, and indeed the Reafbn of it was very
well known to me. In three others, tho’ the Wounds
did inflame, and fwell, and difcharge confiderably, yet
the Eruptions were fb imperfedt, as to leave me a little

william Clark’s Son. See Philofopli, Tranfad. No. 370, p. 45.

in

Cm)

in doubt : but two of thefe have fmce been fufficiently
try’d, by being conftantly with thofe who had the Small
Pox, without receiving any Infedion ; which make«»
me inclined to believe they will always be fecure from
any danger of it. As to all the reft, neither I nor any
body elfe, who faw them, did in the leaft queftion,.
but that they had the true Small Pox.

As to the latter Propofition, That the Ingrafted
Small I^ox is far lefs dangerous than the Natural:
the Truth of this, I fuppofe, can only be found by
making a Comparifon, fo far as our Experience will
extend. In order to this, I have taken an Account in*
this Town, and Ibme Part of the Country, and have-
procured the fame from- feveral other Towns here-
abouts, where the Small Pox has been Epidemical thiS’
laft Year, with as much Exadtnefs as was poftible,
how many have had the Small Pox, and how many
out of that Number have died. Some of thele I did
fend you the laft Summer, but I will beg leave to re-
peat them amongft the reft, that they may be all under,
one view.

Have had the
Small Pox. Died..

In Halifax — — — — — — ijS 45

In a Part of the Parifii of Halifax^ flretch- ?

ing towards Bradford — ■ — — f

In another Part of the fame Parifii — 268 28

In Bradford — — — — — I2p 35

In Leeds — — — — — — — 792 — — 189

In Wakefield — — — — — — 418' 57

In Rochdale ■ — — • — — — 177 38

In AJhton under Line, a fmall Market- 1

Town in Lancafiirey including two? 279

neighbouring Villages — — — N

Macclesfield — — — — — — 302 — — 37-

In Stockport — — — — — ' — 287 73

\xi Hatherfield — — — — — — 180 — — 20

Total 3405 6-3^6

( )

1 am very fcnfible you will require a great number
of Obfervations, before you can draw any certain
Conclufions. I would only crave leave to remark,
that it appears from thefe Accounts, that this laft Year,
in this Part of the Kingdom, almofl nineteen out of
every hundred, or near one fith of thofe^ who have
had the natural Small Tox^ have died ; whereas out of
Jixty one which have been inoculated hereabouts^ not
one has died ; for as to the Cafe of Mr. John Symfon's
Daughter, which would have made the fixty fecond, I
leave it out of my Account, and I will refer it to any
impartial Judgment, whether I may not juflly do fo
The Fadfs are open to every one's Enquiry, and who-
ever will give himfelf the Trouble, may be latisficd as
to the Truth of them.

t

Halifax, T>ec. i6.

^ See Philofoph. Tranfadl. No. 370. p. 41, 42.

VI. J

X 213 )

. VI* A Letter to the Learned Dr, Caleb Cotef-
worth, F, ^ S* of the College of Dhyficians^
London, and Thyflcian to St, Thomas'’^
fpital 3 containing a Comp ar if on hettveen the Dan-
ger of the Natural Small Pox, and of that given
by Inoculation, % James Jurin, Mi J). S.
Secret,

S I

TH E fincere and difinterefled Regard for the Good
of Mankind, which you have always manifefted,
as well in your extenfive private Practice, as in that
publick Poll, which you have lb long and fo ulefully
fill’d, muft afied: you, 1 am lure, with a great and fen-
fible Concern for the Dellrudtion made among us by
that terrible Calamity the Small Pox. We have leen,
for Ibme confiderable Time paft, above loo Perfbns
J^er Week in this City and Suburbs, taking one Week
with another, to be carry’d off by this Difeale ; a Con-
fideration certainly that ought to dilpofe us to enter
into any Mealures, by which we may reafonably hope
to put Ibme Stop to the Progrefs of fo cruel a Di-
ftemper.

To this Purpofe, Sir, the Method of Inoculation,
which has lately been introduced among us, is ftrongly
recommended on the one hand, and has been oppofed
with a great deal of W armth and Zeal on the other.

M m

I have

( ^‘4 )

I have no Inclination to enter into this Contro-
verfy ; it is in better and abler Hands : but, as the
Point in Dilpute is of the utmoll Importance to Man-
kind, I heartily wilh, that, without Paffion, Preju-
dice, or private Views, it may be fairly and maturely
examin’d. In order to which, if the following Ex-
trad:s and Computations, concerning the comparative
Danger of the Inoculated and Natural Small Pox, may
be of any Ule to your felf, or to other impartial and
difinterelled Judges, I fliall think my Labour well be-
llowed.

The Number of Perlbns, who have had the Small
Pox by Inoculation here in England^ is, by the bell
Information I have been able to colled:, as follows.

Inoculated by

'Dr. Nett let on - - - - - - - - 6i
Claudius Amyand^ Efq; Serjeant Surgeon - 17

Mr. Maitland^ Surgeon 5*7

Dr. T^O'ver -

Ml. Weymijh^ Surgeon 3

The Reverend Mr. yohnjbn . - , . 3

Dr. Brady at Bot^tfinouth - - - - 4

Mr. Smithy Surgeon, and Mr. E>ymer^'2^
Apothecary, 2.rChichejier - - - 5

Islr. IVallet\ K^othtc^iry 2.1 GoJ^ort - - 3'

A Woman at Leicefter 8

Dr. Williams at Haverford Weft - - - (5

Two other Perfons near the lame Place - - x

Dr. French^ at Briftol - i

In all — i8x

Out of this Number the Oppolers of Inoculation
affirm, that two Perfons died of the Inoculated Small
Pox ; the Favourers of this Pradice maintain, that their
Death was occafioned by other Caufes. If, to avoid

dilpute,

( ilj )

clifpute, thele two be allow’d to have died of Inocula-
tion, we muft eftimate the hazard of dying of the In-
oculated Small Pox, as far as can be collected from
our own Experience, to be that of x out of 182, or
one out of 91.

The Reverend Mr. Mather^ in a Letter dated March
10. 1721. from Bofton in New England^ gives an Ac-
count, That of near 300 inoculated there^ ^ or 6 died
upon tt or after it^ but from other E>ifeafes and Ac-
cidents^ chiefly from having taken the Infection in the
common way by Injpir at ion^ before it could be given'
them in this way ofTranfplantation.

If, as we have done before, to avoid all occafion of
difpute, we allow 5' out of thefe 300 to have died of
the Small Pox by Inoculation, notwithftanding what
Mr. Mather has faid of their dying by other Acci-
dents or Difeafes ; the hazard of Inoculation will
thence be determin’d to be that of i in about 60. But
here it muft be oblerv’d, that by all the Accounts
from New England, the Operators there appear not
to have been fo cautious in the choice of their Subjeds,
as here in England. For Mr. Mather tells us, that
the Perfbns inoculated were young and old, from i
Tear to 70, weak and flrong ; and by other relations
we are inform’d, that kF omen with Child, and others
even in Childbed, underwent the Operation. Appa-
rently the Greatnefs of the Danger they were in, from
the Infedion in the natural Way, which then raged
among them with the utmoft Fury, made them the
more adventurous.

VTe come now. Sir, to the fccond Part of our De-
fign, which is to form an Eftimate’ of the Hazard,
which all Mankind, one with another, are under of
dying of the namral Small Pox, that, by comparing
this with the Hazard of Inoculation, the Publick may

Mm2 be

( )

be enabled to form a Judgment, whether or no the
Pradice of Inoculation tends to the Prefervadon of
Mankind, by leflening the Danger to which they are
otherwife liable.

With this View I have confulted the Yearly Bills of
Mortality, as far back as the Year 1667, being the
Year after the Plague and the Fire of London^ com-
prehending to the prefent Time the Space of 5-6
Years, from 42 of which I have given Extrads in the
two following Tables.

The firft ofthefe takes in the hrB xo Years, diftin-
gliihiing for every Year the total Number of Burials,
and likewife the Number that died of the Small Pox, in
two feparate Columns. The third Column Ihews, how
many died of the Small Pox out of every Thoufand that
were buried ; and the fourth Column reprelents the
Proportion between thole that died of the Small Pox,
and the whole Number of Burials, by the nearell Vul-
gar Fradion, having always i for the Numerator.

The lecond Table gives the lafl Years, after the
fame manner, and at the bottom of each Table is given
tbe Total Number for each Series of Years, and like-
wile the Number that died each Y ear, taken at a Me-
dium, one Year with another : by which it appears,
that the Proportion between the Number of thofe that
die of the Small Pox, and the whole Number of Bu-
rials, is very nearly the lame, upon an Average for
each Series of Years.

The 14 intermediate Years between 1686 and 1701
are left out, becaule in the Bills for thole Years, the
Accounts of the Small Pox and Mealies are not di-
llinguillied, as in the preceding and following Years,
but are join’d together in one Article, lb that from them
no certain Account can be drawn of the Number of
Perfons, that died of the Small Pox.

TABLE

( ii7 )

TABLE I.

Total N“' Died of the Small

Tears

a ^

of Burials

In all.

I ih lOoo

In Proportion

166-]

15842

1196

75

X

TT

166^

17278

1987

115

9'

X

1669

i5>432

951

49

2 0

t

16JQ

201^8

1465

73

j?

i6']i

15729

696

44

1(572

18230

1116

61

T3-

1573

17504

853

49

'a'l

1(574

21201

2507

118

1575

17244

997

58

T7

i6']6

18732

359

19

sT

190^7

1^78

88

X-

Tr

1(578

20(578

1798

. 87

7

\6j9

21730

1967

91

T

iT-

i58o

2105J

689

33

r

IT

1681

23P7I

2982

125

<

£

1(582

■20C?y i

1^0 9

X
X f

1583

20587

2096

102

lo*

1684

23202

156

7

X

T4v

1685

23222

249(5

107

X

9*

16U

22(5o9

10(52

47

20 Years

398200

28459

7x1

z

r+

Each Year at 7
a Medium $

I99I0

1423

.

-

/X *

X

( ii8 )

table II,

Total N°

Died of the Small Pox.

, Years

or Burials

In all.

In 1000

In Proportion.

170I

20471

1095

53 .

X

19

1702

19481

31I

16

X

1703

20720

898

43

r

1704

22684

1501

66

X

* i

1705

22097

1095

50

X

To

1706

19847

721

36

t

Ts

1707

21600

1078

50

X

*2 0

1708

2129I

1687

79

X

1 ?

1709

21800

1024

47

X

Tr

1710

24620

3138

127

X

1711

19833

915

46

X

Tz

1712

21198

1943

92

X

i IT

1713

21057

1614

77

t

X f

1714

26569

2810

106

X

1715

22232

1057

48

X

zT

1716

24436

2427

99

t

To

1717

23446

22 11

94

X

TT

171S

26523

I8»4

71

t

1719

28347

3229

1 14

X

9

1720

25454

1440

57

X

z T

1721

26142

2375

91

X

TT

1722

25750

2167

84

X

X 2

2 2 Years

505598

36620

72

T

14

-Each Year at 7
a Medium, _S

22982

1665

72

X

\4

42 Years

90379S

65079

72

X

Each Year

4z at a Me- >
dnim. 3

21519

15.50

72

X

I +

( il? )

By thefe Tables it appears, that upwards of feven
per Cent, or fomewhat more than a fourteenth ^art of
Mankind^ die of the Small Tox ; and confequently the
hazard of dying of that Diftemper, to every individual
born into the World, is at lead that of one in four-
teen. And that this Hazard encreafes after the Birth,
as the Child advances in Age, will appear from what
follows.

From this Eftimate it is demonftrable, that, in the
Cafe of Perfbns actually having the Small Pox, the
Hazard that they run, one with another, of dying of
that Diflemper, is greater than that of one in fourteen ;
or, which is the fame thing, there muf be fewer than
thirteen^ that recover^ for one that dies of the Small
Tox. For fince one fourteenth part of Mankind die
of the Small Pox, and the other thirteen parts die of
other Difeafes ; if thefe thirteen have all had the Small
Pox, and recover’d from it, before they fell ill of thole
other Difeafes of which they died, then juft thirteen
will have recover’d from the Small Pox, for one that
dies of that Diftemper : but, as it is notorious, that
great Numbers, elpecially of young Children, die of
other Difeafes, without ever having the Small Pox, it
is plain, that fewer than thirteen muft recover from
this Diftemper, for one that dies of it.

To determine exadly how many of thefe thirteen
Parts of Mankind, die without having the Small Pox,
is a very difficult Task: but it is eafy to fee, that a
confiderable Deduction is to be made from them.

In the firft place, the two Articles of Stilborn and
Abortive Children-^ which are put into the yearly Bills,
as part of the Number of Burials, are unqueftionably
to be deducted.

With

• ( no )

With thde two, Sir, you will not I believe, think it
unreafonable to join the following Heads, which, by
the bell; Information I can procure, comprehend only
very young Children, or at moft not above one or two
Y ears of Age. Overlaid^ Cbryfoms and Infants^ Con-
vuljions^ Hor/ejhoehead, Headmoldfhot, Teeth, Wa-
ter in the Head, Worms, Rickets, Liver grown, Chin-
Cough, and Hooping-Cough, which Articles in the
Yearly Bills for Years laft pafl:, amount at a Medi-
um to 386 in each 1000, of the whole Number of
Burials.

It is true indeed, that, in all Probability, fome
fmall part of thele mult have gone thro’ the Small Pox,
and therefore ought not to be dcdudred out of the Ac-
count ; but then, on the otha- hand, as it is certain,

that of the remaining of Mankind, that are above

1000

one or two Years of Age, there are great Numbers,
that never have the Small Pox, it will T prelume be
judged to be no unequal Suppofition, if I fuppofe all
that are contain’d under the Heads abovemention’d, to
have mifsM that Diflemper, when by way of Com-
penfation, I allow all the remainder of Mankind to
undergo it ; which ConcelTion is fo large, that it will
/ abundantly make up for what I alTume too much in the
former Suppofition.

Allowing therefore, that out of every 1000 Chil-
dren that are born, 386 die under one or two Years
of Age, without having the Small Pox, and yz do
fbme time or other die of that Diflemper ; it follows,
that the Hazard of dying of it, to the remainder of
Mankind, above one or two Years of Age, who are
all fuppoled to undergo that Difeafe fooner or later, is
that of 71 out of 6x4, or nearly z out of 17 : lo that

no

( 111 )

no more^ than between 7 and 8, can recover from that
*T>tftem^er^ for one that dies of it. And if any confi-
rable part of the aforefaid remainder of Mankind,
more than is allow'd for above, do efcape having the
Small Pox, then the Proportion of thofe that recover
from it, will be flill linaller.

This Confideration Ihews the Fallacy of one plan-
fible Argument, that has been often made ufe of on
occafion of the prefent Difputes about Inoculation :
Which is, that whatever be the Danger of dying of the
Small Pox, to thofe that actually have that Difeale, yet,
as great Numbers of Perfons never have the Small Pox
at all, this Danger is what any particular Perfon may
never be in ; and therefore it will be Madnefs to under-
go the hazard of Inoculation, be it great or fmall, in
order to prevent a Difeafe, which pollibly may never
befal one.

For if two parts in leventeen of all Mankind, that
are above one or two Years of Age, mull: fooner or
later die of the Small Pox, it is plain, that how many
parts foever of thefe feventeen are luppofed to efcape
that Diflemper, the Mortality among the remainder,
who undergo it, mufl: in proportion be fo much the
greater. As for inftance, if 7 parts efcape having the
Small Pox, and 10 undergo it, then x out of 10, or i
out of that have the Small Pox, mud die of that
Difeafe.

- And as it can never be known, whether or no any
particular Perfon be one of thofe, that are to have the
Small Pox ; his Hazard of dying of that Diflemper,
being made up of the Hazard of having it, and the Ha-
zard of dying of it, if he has it, will be exadlly the
fame, namely, that of x in 17, or i in 8 or 9, whether
the proportion of Mankind, that efcape having the
Small Pox, be great or fmall.

Nn

But

( 111 )

But as what has been faid concerning the Hazard of
the natural Small Pox, is taken from an Account of
Years; whereas the Hazard of Inoculation is eftimated
only from what has happen'd in the fpace of about i8
Months, fince which time it had its hrft Rife among
us ; it will perhaps be asked by fbme Perfbns, why
we do not likewile make the Eftimate of the hazard of
the natural Small Pox, from the lafl two Years alone,
without running back into fo great a number of Years,
before Inoculation was begun ?

To which we anfwer, that the Proportion of thole
that die of the Small Pox, varies fo much in different
Years, as appears from the Tables above, that it was
impoffible to come at any Certainty in this point, from
the confideration of the two fall Years alone : and if
any one fulped:s us of Partiality in proceeding after the
manner we have done, he need only call his Eyes upon
the fecond Table, where he will find, that the Morta-
lity of the natural Small Pox, for the two lall Years,
has conliderably exceeded the Medium we have de-
termin’d, from taking in two and fourty Years.

There is another Method, which, if it were put in
pradlice in leveral large Towns, or Parillies, and for a
lufficient Number of Y ears, would enable us to come
at a nearer and Hill more certain Computation of the
Proportion between thofe that recover, and thofe that
die of the Small Pox : which is, to fend a carefiil Per-
fon once a Year, from houfe to houfe, to enquire
what Perfons have had the Small Pox, and how many
have died of it, in the preceding Year. This has been
done by Dr. Nettleton the lad Year, at leveral Towns
in Torkjhire^dcc. and the fame was done at Chichefter
for the fame Year, to the 15th oiO[ioberhS!i^ by a
Perlbn of Credit, whole Account was communicated to
me by my learned and ingenious Friend, Dr.

Sucli

( )

Snch another Account has bcentranfiiiitted tome from
Haverford W in South JV^les^ by the Learned
Dr. ‘Terrot Williams, Phyfician in that Place. The
Sum of thefe Accounts is as follows.

m

Sick of the Small Pox. DIecK

Sevei'al Towns in • ■5405' — 636

Chichejier — — — — — — k58

Haverford Wefl — — — , — 1x7 — 5'^

Total 46x6 —

From which it appears, that, upon a Medium be-
tween thele Accounts, there died of the SmallTox al~
mofl 19 fer Cent, or nearly one m five, of Perfons of
all Ages, that underwent that Diftemper. Which is
the more to be remarked, for that out of%t Perfons,
that had the Small Pox by Inoculation, the fame Year,
and in the Neighbourhood of the fame Places, not one
mifearrfid.

Mr. Mather obferves, in his Letter mention’d above,
that out of more than ^000 Perfons that had the Small
*Pox at Bofion in Nevu England, within little more
than half a Tear, near 900 died, which is more than
one in fix ; and this Account added to thofe from
Torkjhire, Chichejier^ and Wales, reduces the Propor-
tion of thofe that die of the Small Pox to fomCwhat
more than 18 fer Cent, fb that the Hazard of dying
of that Diflemper, to thofe who are taken ill of it, is
that of one in between five and fix, or fomething
above two in eleven.

The Refult therefore. Sir, of thefe Computations is,
that, if the fame Proportions fhould ftill continue, as
have hitherto been determin’d by ObfervatioU, we
muft exped,

N n 1

That

( Z24 )

That of all the Children that are born, there will,
Ibme time or other, die of the Small Pox, one in
fourteen.

That of Perfons of all Ages taken ill of the natural
Small Pox, there will die of that Diftemper, one in five
or fix^ or two in eleven.

That of Perfons of all Ages inoculated, without
regard to the Healthinefs or Unhealthinefs of the Sub-
jed:, as was pradifed in New England^ there will die
one in fi,xty.

That of Perfons inoculated with the fame Caution
in the choice of the Subjects, as has been ufed by the
feveral Operators one with another, here in England^
(if we allow in the two difputed Cafes abovemention’d,
that the Perfons died of the inoculated Small Pox)
there will die one in ninety one.

But if thole two Perfons be allowed to have died of
other Accidents or Difeafes, then we diall have reafon
to think, as far as any Judgement can be made from
our own Experience here in England-^ that none at alt
will die of Inoculation, provided that proper Caution
be ufed ; as we are inform’d, on all hands, is the Cafe
in Turkey : where out of many thoufands^ that, in the
fpace of about fourty Years paft, have been inoculated
in and about Confiantinofle^ by one Greek Woman,
who ftill continues that Practice, notwithflanding her
extreme old Age, not fo much as one Terfon has mif
carried, as I am affured by the ingenious Dr. le T)uc,
a Native of Confiantinofle, who was himfelf inocula-
ted there under the Care of his Father, an eminent
Phyfician in that City.

I am, &c.

James Jurin.

( 12? )

' .

fp 0 STS C<llIfT.

SrNC E this Paper was drawn up and communicated
to the Royal Society, the following Account of
the Succefs of Inoculation in and about Bofton^ in New
England^ was procured at my Defire, by my Inge-
nious Friend Dr. Nesbitt^ from Capt. John Osborne^
who refided in that Town and Neighbourhood during
the whole time of that Pradfice. I thinR proper to
infert it, here, as it confirms the Extradf given above
from Mr. Mather's Relation, and is a more particular
Account of the Matter of Fadf, than any that I have
yet feen.

In May, the Small Pox was, by the Provi-
dence of God, brought into the Town Bo ft on ; in

June it began to fpread pretty much, and in the
Month of Jtily it was got into mofi: parts of the Town,,
and a confiderable Number of People died of it. At
this time Inoculation was firft put in pradlice by
Dr. Boylefton, who then perform’d it upon his own
Child and a Negro-Servant, who both did well; not-
withfianding which, this Attempt gave great Uneafinels
to the Neighbours.. However the Practice went on,
to the Number of about 40 Perfons, one of which was
a Woman of about 40 or 45" Years of Age, who got
well over the Small Pox, as her Husband publickly
declared, but had been before, troubled with Hyfle-
rick Fits, of which file died fome little time after.
When about 70 Perfons had pafied under the Opera-
tion, myfelf and Wife, who had hitherto been at a
Place called Roxbury, a Mile from. Bofton, went into

^ Mrs, nLxwdl,

Town

( ii6 )

Town and received the Small Pox by Inoculation. We
had it with all the Gentlenefs and Moderation that
was poflible, neither of us having an hundred Pu-
(lulcs, or being lenfible of any Fever worth mention-
ing ; lb that we did not find it necefiary to keep our
Beds for it.

In Augufi the Small Pox in the natural Way proved
more mortal, and Inoculation made a greater Progrefs,
the People continuing to come into the Pradlice of it.
A fecond Perfon that died after Inoculation, was an
Apothecary’s Houfekeeper, that was out of Town,
till an Indian Maid got the Diftemper in the lame
Houle, and remov’d, and died. Upon which this Wo-
man coming to Town, her Mailer undertook to per-
form the Operation upon her, which by the Way was
the firll and lall that he ever perform’d ; and on the
third Day after the Inoculation, the Small Pox came
out upon her very full ; from which it was plain, that
file had taken the Infe<Slion before^ in the common
way.

The third Perfon that died after being inoculated,
was a f Gentleman, that lodged in the fame Houle
with my Wife and lelf at Roxbury^ who was under
great and extreme Infirmity of Body, as mylelf was
Witnefs, that we fear’d he would have lived but a
Ihort time under it. His Friends much perfuaded him
to make ufe of Inoculation, believing that it would
have carry’d olFhis Illnefs ; but when he made the Ex-
periment, he had not Strength to go thro’ with it. He
was about 45* Years of Age, and by the way was a
Gentleman of great Worth and Piety.

His Siller :j: was the fourth Perfon that died upon
this Operation. She was about fourty Years of Age^

f John White, Efc^i :j: Mrs. Wells.

Of

f

{ M7 )

of great Indilpo/ition of Body, and weak, as was her
Brother.

The hfth, that died upon Inoculation, was a Wo-
man Servant in a Houfe, where the whole Family, to
the number of eight, were inoculated at the lame time.
She lay in a cold upper Room during her Illnefs, and
was much negledted, the whole Family being down
together, lb that llie died merely for want of a little
Attendance. This was in the Town of Roxbury^
where oblerve, that 13 Men, Mailers of Families, got
the Small Pox, and all died ; which inclined the People
to make ufe of Inoculation, having before been much
againlt it, and there were 43 Men inoculated there,
who all did well. The * Miniller of the Town was
the firll, that put it in Pradlice there, much againll the
Mind of his People at firll,' though afterwards they
were very well pleasM with it, feeing with what great
Succefs it was attended ; and then whole Families came
into it, and underwent the Operation. There were
in all at leall a 80 Perlons inoculated, chat I knew of^
and I fuppole there might be "about ac or 30 more, but
of thofe I can give no certain Account.

.1 . ' i - - - - - - John Osborne,

"* The 'Reverend Mr, Walter.

VII. De

( 22 8

1 1 I

VII. T)e Se^ione Angiili, Jutore A. de Moivre/
R.S. S. .

^ ij

I

Neunte Anno 1707, incidi in Methodum qua, iE-
quatione data hujus formse.

ny-Y

X X 3

&c. =

Vel iftius,

2/jy-f

A +

nn — 9

^ 4x5

+

*\ t ’ ~ ^ \

nn — ^s
6x7

C y^

■ nn

Aj' f

2x3 ' 4X5- “ 6x7

&c. =: a ; ubi quantitates A, B, C, 8cc. reprsefentant
Coefficientes Terminorumprxcedentium, Radices de«
terminavi ad hunc modmn.

Pofito n.y ^ ^ a-\-^ — • -z; in primo calu.

a a a — i — v in fecundo.

I

Erit^ zn ^ ^ in primo cafii.

— V iu fecundo.

2- V

Solutiones autem iftse inferta^ fuerunt in Philofophicis
Tranfadionibus, Num. 309, pro menfibus Jan. Feb.
Mart, ejufdem anni.

Jam quibus perfpedum erit quo artificio Formula
iftae inventse fuerint, his procul dubio patebit aditus ad
demonftratioaem fequentis Theorcmatis.

Sic

( ii? )

Sit X Sinus Verfus Arcus cujuflibet.
t Sinus Verllis Arcus. alt erius.

I Radius Circuli.

Sitque Arcus prior ad pofteriorum ut i ad Tunc,
a/Tumptis binis .®quationibus quas cognatas appellarc
licet,

H IH » .

I Z JZ z — — zzx.

Expundloque orietur iEquatio qua Relatio inter
X dc t determinatur.

CORO LLJRIV M I.

Si Arcus poflerior fit Semicircumferentia, iEquatio*
lies erunt.

+ ** -
z z=z o

I — zz-f-zz= — zzx.

e quibus fi expungatur z, orietur iEquatio qua deter-
minantur Sinus Vcrfi Arciium qui fint ad Semicircum-
ferentiam, femcl, ter, quin<iui®c, Szc. flimptam, ut x
ad

CO RROLLy^RIVM IL

Si Arcus poflerior fit Circumferentia, iEquationes
erunt

I — z — o

I — 2 Z~i~ zz = — zzx.

e quibus fi expungatur z, orietur Aquatic qua deter-
minantur Sinus Verfi Arcuumqui lint ad Circumferen-
tiam, femel, bis, ter, quater. Sec. fumptam, ut i ad n.

CO RALLARIV M III.

Si Arcus poflerior fit 6o Graduum, .ffiquationes
erunt

O 0

t

C i30 )

• 'x: 0 , •

nmZn

I — + ~ i^a;.

. -tf; -r .

c quibus fi expungatur orietur iEquatio qua deter-
minantur Sinus Verfi Arcuum qm*flht ad Arcum 6o
Graduum.

ill Irl Ul z9&C'}““‘«plicatum

utiad».

I

Si Arcus poflerior fit no Graduum, iEquationes
erunt

2»

o

.1 + ^" + ^;

‘I — ZZ~ — zzx.

e quibus fi expungaair Zy orietur Aquatic qua deter-
minantur Sinus Verfi Arcuum -qui fint ad Arcum no
.Graduum. : lo

Z* &c. 1 multiplicatum

i : , r lx, tt, 14 , > ^

Utiad^;

Novemh, 15,

•) - T

' ’yrii. An

C i3' )

VIII. An Account of a new fort o/Moloflfes made of
Apples-^ and of the dege?ierati?ig of Smelts, (By-
the Honourable Paul Dudley, F. ^ S.

TH E Apple, that produces the Molojfes^ is a Sum-
mer-Sweeting, of a middling Size,plealant to the
Tafle, and full of Juice, fo that feven Bulliels will
make a Barrel of Cyder. The manner of making it is
thus ; you grind and prels the Apples, and then take
the Juice and boil it in a Copper till three Quarters of
it is wafted, which will be done in about fix Hours
gentle boiling ; and by that Time it comes to be of
the Sweetnels and Confiftency of Molojfes.

Some of our People feum the Cyder as it boils, -
others do not, and yet there feems to be no great dif*
ference in the Goodnels.

This new Moloffes anfwers all the Ends of that
made of the fweet Cane imported from beyond Sea.
It ferves not only for Food and brewing, but is of great
Ule allb in prefer ving of Cyder ; two ^larts of it put
into a Barrel of rack’d Cyder, will both preferve and ^
give it a very agreeable Colour.

The Apple Molojfes was difeovered a few Years
fmee, by a * Gentleman of my Acquaintance, 2XJVood-
ftock^ in this Province, a Town remote from the Sea,
and where the TV eji India Molo ffes is dear and Icarce ;
he ingenuoufty confeftes the Difeovery was purely ac-
cidental; but ever ftnee he has fupplied his Family
with Molojfes out of his Orchard, and his Neigbours
alfb now do the like to their great Advantage.

^ J. Chaiidleij iyjj

Gur

( ^ ^ X

Our Country Farmers run much upon planting Or-
chards of thefe Sweetings, for fatting their Swine, and
afTure me it makes the beft fort of Pork. And I know
the Cyder made of them to be better than that of
other Fruit for Tafle, Colour, and keeping.

Two fliort Miles from my Houfe we have a fine
Pond, of half a Mile over, little or no Communica-
tion with the Sea. An ingenious man, fome three-
fcore Years ago, for an Experiment, took a Pail of
large Smelts from the River and put them into this
Pond, where they have increafed abundantly, but
are degenerated to a very fmall fort ; for our River-
Smelts I fuppofe are iiill as 4rge* as thole of the
Thamesy fomc of them I knovV,'* Yhll weigh two
Ounces and an hflf, whereas rhefe Imall ones will
not weigh five Penny- Weight. We reckon the Pond-
Smelt eats much better than the other, and then they
are very tranlparent, and of a beautiful fliining Pearl-
Colour.

Roxburyy New England^
October lyiz.

j .

Taul T>ndley,

FINIS.

»

LONDON: Erinted for W. and J. Innys,
Printers to r/j^^Royal Society, at the Prince’s
Arms the Paul’r Churchyard.

)

i

>

r. .

i

B.

%

¥

#

4

Numb,

PHILOSOPHICAL

TRANSACTIONS.

For the Months January and February. 17x3.

The CONTENTS.

I. Ohferyations on the Ecllpfe of the Moo?ty June 18,
1722. and the Longitude o/Porc Royal m Ja-
maica. Dr. Halley, Ajlronomer ^Hpyal^

' >

IL The Longitude of Carthagena in America.

Dy the fa77ie.

«>

nil. Cometce Berolini, anno 1718. Vtft OhferVatio>'
nes a i 8 Januarii, Stylo noyo^ ad j Febr. ex
piftold * Viri Cl. Chriftfridi Kirchij, <l(eg. Sod
Sclent. Berolin. Aflron. ad Edm. Hallejum,
LL. 2). 3^- 5. S. defu7npt(e.

IIV. ExtraBs of feVeral Letters to the ^^ublijher,
fmi the (^yerend Dr. Lang with, (J(eBor of Pet-
worth in Suflex, concerning the Appearance of
' feyeral Arches of Colours contiguous to the inner
Edge of the common ^inbow.

P P Y. A

y* A Letter to ©rjurin. Coll Med. Lond. Soc.
^ Seer. S. concerning the abovementioned Jp^
pearance in the (^inboWy with fome other (Lefle^
Ctions on^the fame SubjeB. !By Henry Pem-
berton, M.D. ^S.S*

yi. ^art of two Letters concerning a Method of
' procuring the Small <Pox, ufed in South Wales.
From Perrot Williams, M. D. Thyjlcian at
Haverford Weft, to Dr. Samuel Brady,
fician to the Garrifon at Portfmouth.

VII. ^art of a Letter from the fame Learned and
Ingenious Gentlemany upon the fame Subjeliy to
£)r. Jurin, ^S. Secret. Q:>

/ o

VIII. A Letter on the fame f^n Mr. Ri-

chard Wright, Surgeon at Haverford Weft, to
Mr. Sylvanus Bevan, Apothecary in London.

IX. An Account of fome Experiments* made to pro^Cy
that the Force of Moving Dodies is proportionable
to their Velocities: {or rather that the Momen-
tum of Moving Dodies is to he found by muU
tiplying the Maffes into the Velocities) In Anfwer
to fuch who have fometime ago affirrndy that that
Force is proportionable to the Square of the Velo»
cityy and to thofe who flUl defend the fame Opinion.
Dy the (Kmrew^/John Theophilus Defaguliers,

LL.D.F.%S.

I. Obfervations

( m )

I. Obferyations on the Eclipfe of the Moon^ June 1 8 , 1721*
and the Longitude o/Port Royal m Jamaica determined
thereby, !By Dr, Halley, Ajlronomer ^yal^ F.(2^5.

TH E Eclipfe of the Moon which happened in June
lafl, 17x2, was fb far hid by the cloudy Sky, that
neither myfelf, nor any ofourAflronomical Friends,
in or about London, could furnilh an Obfervation thereof
worthy to be laid before the Society. But the fame having
been well obferved at Jamaica, by the late curious Capt.
Candler, Commander of his Majeflies Ship Launcefton,
(whofe Example it were to be wifhed, others in the like Poft
would imitate) and at Berlin, by Mr. Chriji fried Kirck,
Aftronomer of the Royal Academy of Sciences there. I
thought it notamifs to prefix to their Accounts that little I
was able to note concerning it.

Sunday, June \%, mane. Having perfecSbly redlified my
Clock fb as to iliew the Apparent Time, neither the tranfit
of the Moon over the Meridian, nor the beginning of the
Eclipfe which foon followed, could be feen thro’ the very
thick Cloud. At 13 ix/ !T. aff, a fmall Particle of the
Moons Body was feen through a very little hiatus in the
Cloud, by which glimpfe I could only be affured that the
Eclipfe was not yet Total. At 13 h. 29' by fuch another
view. I was fatisfied that it was now become Total ; but
in a Moment, it again difappeared, till 14 h. 49^ ro^/, when
the Cloud beginning to break, I got time to meafure with
the Micrometer, the Tartes Lucida now recovered in the
Moon’s Diameter, which I found 14'. 00", though this not
fo well as I could wifli,by reafbn of a thinner Sort of Cloud
which perpetually intercurr’d, and render’d the Edge of the
Shadow fomewhat dubious.

At 1 5^ 1 5 ' the Moon was pretty well got out of the thick

Cloud, but being very low, and the Daylight become flrong,
Ihe fhone very fointly, and the Shadow became worfe and
worfe defined.

From

( )

From IS h. i6f to 15 Z?. ^7^ T. app, I doubted of the End,
and am confident it did not exceed the 17th Minute. It
ended overagainft the North Part of the Talus Maotis of
Mr. Hevelius^ much about the middle of theW eflern or Right-
hand Limb of the Moon, flie being then very near fetting.

Capt. Barth, Candler, being then at Tort Royal, in Ja-
mate a, had much better Fortune, and a ferene Sky from
the Beginning to the End ; who having ufed due care to be
affured of his Times, by Altitudes taken with an Inftrument
of three Foot Radius, was pleafed to fend us the Refult of
his Obfervation as follows.

h. / /'

The Eclipfe began 6 79 10
Immerfion 8 7 50

Emerfion 9 11 o

The End 10 19 40

Whence the Middle 8 39 27

And fiippofing the Eclipfe to have ended at Greenwich,
at \sh. ~ the Difference of Longitude between Tort
Royal and Greenwich, will be sh. so^', or 5* 6' from

London, that is, 76 37^ L

Mr. Kirck being in a more Eafterly Meridian, could fee
nothing of the Emerfion, but has carefully noted the Time
of the Beginning and Immerfion, as he obferved them at
Berlin, viz. the Beginning of the Eclipfe at \%h. s<)^ $5^^
..and the Immerfion at 14 8^ 8/^ Now by comparing feve-

ral Obfervations made at both Places, we have formerly
concluded Berlin to be 54 Min. of Time, or \ \\ grad, of
Longitude more Eafterly than London ; wherefore at Lon-
don it began at ix h, s’ SS” ^i^d immerged at 13 Z>. 14/ 8^'
that is, the beginning was later here than at Jamaica s h.
6!4fS’\ and the Immerfion later s h. 6' i8^^, punctually agree-
ing with what refulted from my own Obfervation of the End
as abovefaid ; and fufticiently with what I had long ftnee
determined from Obfervations fent me from Jamaica by my
old Aftronomical Friend Mr. Charles Boucher,

II. The

( )

II. T$e Longitude o/.Carthagena in America.

/J: ri, ;

- -'’^■

HAving lately, by the Favour of Sir Hans Sloane^
received a Packet of Obfervations from Carta-
gene in America^ made by Colonel T>on Juan de Her-
rera^ Chief Engineer of that City, I find among them
one Imraerfion of the firft Satellite of Jupiter into his
Shadow, obferved there by a Telefcope of 17 -1 Feet,
on April 9. Stilo vet. 1722. at 15^. 58 ^ 44 appa-
rent Time *, and two Emerfions of tlte fame^, viz. Ju-
ly %.\\ 25 ' 41 and July 21. 9 42 ' 17 Stil.

vet» all which tally with Obfervations made at Wan-
fted^ by the Reverend Dr. ^oimd and Mr. Bradley who
obferved there the very next Kclipfes to all the three ^
that is to fay, the Imraerfion by a fifteen Foot Tube,
on April 1 1. 1 5 28 / 40" Temp, aqu. or 15 30 '

25 // Temp. app. And the firft Emerfion, July y, 10 h.
59 f 2^ f! Temp. aq. by the Refiedler, and ti after,
or 10 h. 59 f 46 " by the 15 foot Glafs, that is, 10 h.
54 ' 12 // apparent Time. The other was obferved at
Wanjled. July ^3. 9 /;. 19 ' Temp. aq. both by
the Refledter and 1 5 foot Glafs •, that is to fay, at
^ h. 13 ' 35* apparent Time. Subflrad: from each of
thefe one Period of this Satellite, or i 18 28 ^ 36

and April i). 1$ A 58 ^ 44 ft at Cartagene will be
21 I ' 49 of the fame Day at JVanfled^ and the
difference of Meridians 5 Z?. 3 / 5 Likewife by the
firft Emerfion, July 5. ii h, X3' 41// diCartagene was
at Wanted 16 h. 25/ 3 6 // of that Day, whence the Dif-
ference of Meridians 5 A i ' 55 ". But by the laft E-

a merfion,

( 2J8 )

inerfion, 21. 9^.41/17^' at Qartagene was
14/^. 44 ' 59 Wanfied'^ whence Wanjled is

5 X ^ 4x more eafterly than Cartagene : and taking
the Medium of all three, 5 /a x ^ 34" or 7$ ® 38 ' may
be taken for the true difference of Longitude,' that is,

75 T from London^ which compared \Yith .Capt,

/er’s Obfervation of the late Lunar Eclipfe, fhews
Cartagene to be about 20 Leagues; to the Eafl wards of
^ort Royal in Jamaica.

* - 1 j >

' '' \ \ ‘

■— ■■ I tty ‘j 1'- ' ■*

' ‘ * ' * f

III. Corned Berolini/ ^?2wo xyxZ. VtJlObfer^Jutio^i^
ms ' a i 8 Januarii, Stylo no^o^ ad 5 Febr. exEpi^
Jlold Viri CL Chriftfridi Kirchij, Soc»

Sctent. Berolin. Jjlron. ad Edm. Hallejurrij
LL.'D^%S*S,^defumptde. ' ^ .

MOnere hie debeo obfervationes Cometas a me invent!,
inNovis Literariis LipJienf.x\ow elTe accuratas j
primo quidem, cum eas tantum amico cuidam fefti-
nanter tranfmiferim, ut etiam ille Cometam qusereret •
deinde, cum etiam vitium typographicum irrepferit*
nam die 23 Januarii mane, Cometa cum 0 6c 9 CafTio-
pese (non vero ^ 6c cp) conftruebat triangulum sequi-
crurum 3 <5c vefperi (p Perfei, Cometa 6c 6 .Cafliopece ^
ad fenfum erant in linea_ reda.y Pleniorem Comet^e
hiftoriam jam paratam.habeo, ex-^qua hsc breviter at-
tingam. Obfervavi eum a die 1 8 Jan. ad 5 Februarii,
Loca ejus ex obfervationibus ad horam i o vefpertinain
cujufque diei, quo Cometa pbfervari potuit, reduda,
hasc Tabella exhibet. • , •. V ! ^ .

Via

A •

( 139 )

\ Longitiido.
0 '

Latitude.
0 f

18 Jan,
21 Jan.

27 26 Oq

16 25t^

69 1 8 S.
^2 s.

23 Jan,
26 Jan.

9 28 i ^5
5 25-*^

39 45 S.

32 55 S.

27 Jan.

28 Jan.

4 4^^ ^
4 4

31 24 s.

30 13 s.

30 Jan.

31 Jan.

3 40

^ 43

28 234^8.

27 40 s.

1 Febr.

2 Febr,
5 Febr,

2 25 D

2 10 ^

i 3P ^

27 I S-
26 22 S.

24 S3 s.

Via ejus tranfiit fupra tergum Urfe minoris, prope
Polarem, per crura 6c genua Cepliei, Caffiopeas 6c An-
droinedcB. Nodus cjus dcfcendens fuit in 2iigradu
•Arietis, cum aliqua mutationc : Angulus orbit^e come-
ticae 6c Eclipticas 69 \ grad, circiter, etiam cum aliqua
variatipne. Via Cometas 2 fere gr. a Polo mundi tranf-
iit, 6c A^quatorem fecavit in 20 1 gr. a pundo ^quino-
diali. Peri^um Comets fuit in 6 ^ 6 f vji, cum latitu-
dine feptentrionali 62^^*, Cometa in Perigso fuit, Z>.
18 Jan. hor. 5. min. 9. mane. Motus Comets diiirnusin
orbita propria, in Perigso (12 fcilicet horis ante, 6c 12
poll Perigsum) 22^8'- ultimis veto diebus apparitionis
3x '. Suppofita Terra quiefcente, 6c Cometa in reda
linea trajiciente, motus Comets fuit 391 partium, qua-
lium diftantia minima Comets a Terra 1000. De Pa-
rallaxi Comets nihil certi affirmare poiTum, nili quod
niultum fupra Lunam fuerit elevatus Cometa. Proba-
biliter vero conjicio, ilium intra Planetarum orbesexfti-
tide, iino in Perigso multo propiorem nobis fuiffe

Q. 2 Maitis

( 240 )

Martis Splisra. Sit enim femidiameter orbitag Terras
I oooo partiura, erit ita motus diurnus Martis 1 5 9 vel
140. Si vero Cometam in orbita Martis exftitilTe fuppo-
no, cum latitudine 62^ 7' 6c inotu diurno 22° 8', ejus
velocitas diet 2847 partium, fi fcilicetfimul fuiffet in op-
pofitione Solis , cum autem differentia Longitudinis So-
lis &c Cometae in Periga;o tantum fuerit 1 4 1 ^ 40 ino-
tus diurnus Cometae evadit 3200 part. 6c proportio mo-
tus CometcB ad raotum Martis ut 23 ad i. Q_uare colli-
go Cometam intra fphasram Martis exflitiffe. Si vero
quis Cometam ad Saturni orbitam evehere vellet, debe-
ret ipfi velocitatem tribuere, qu^e dfet ad velocitatein
Saturni ut 60c ad i ^ <5c quod uno die inajus fpatium
percurriflet, qua m Terra dimidio anno abfolvere foleat.
Ne dicam de dia metro Comete, qux non multo minor
exiftere debuiifd tribus diametris Solis.

Comparationem inftitui hujus Cometae cum aliis, 5c
invenio Cometam, quern Regiomontanus anno 1472 vel
1475. menfe Jan. Febr. obfervavit, viara tenuiile
non multo diverfam a via noftri Comets , tranbit enim
per Urfam minorem 6c.Cephei femora, per pedus vel
collum Calliopes 6c cingulum Andromeds j ac velocitas
ejus maxima uno die fuit 40 grad. Anno 15 5^, alius
Cometaeft obfervatus, cujus Nodos Camerariusm ii®
dcw 6c Y ponit, 6c qui prope pedes Urfs minoris, per
Cepheum, fupra CafTiopeam, 6c per partes fuperiores
Andromeds tranliit, motu valde veloci in Perigso.
Quod fi Regiomontanus Cometam anno 1475 obfervavit,
(de quo tamen Aftronomi valde dubitant) admirabilis
eifet convenientia inter hofce tres Cometas : intervallum
enim prioris a medio elTet 81 annorum, 6c a medio
Cometa ad ultimum 162 ann. ut ita revolutio Comets
podet elTet 81 annorum nec etiam Hiftoria alioruin
Cometarum hifce male refponderet.

IV.

< ^4' >

IV. ExtraSis of feVeral Letters to the TuhliJherj
from the (^Verend Dr, Langwith, (I(eBor of Pet-
worth in Suflex, concerning the Appearance of
federal Arches of Colours contiguous to the inner^
Edge of the common ^inhow,

t

WHEN the Primary Rainbow has been very vi-
vid, I have obferv’d in it, more than once,
a fecond Series of Colours within, contiguous to the
firft, but far weaker, and foinetimes a faint Ap-
pearance even of a thiri Thefe increafe the Rainbow
to a Breadth much exceeding what has hitherto been
determin’d by Calculation. I remember, I had once an
Opportunity of making an ingenious t fiend take no-
tice of this Appearance, who was much furpriz’d at it,
as thinking it not to be reconciled with the Theory.

Tetworth.Jan.iz, .

Since my laft I have obferv’d fomething of the fame
Nature, though not in the fame Degree of Perfe-
dion, with what I fent you an Account of before. On
Saturday lafl, a little before fix in the Evening, Wind
at N. W. by W. we had here a lively, diflind, primary
Rainbow, the inner and purple Colour of which had a
far greater Mixture of red in it, than I could ever ob-

ferve

( ^4^ )

ferve in Sir Ifaac Newton*^ oblong SpeBrum, - Un'
der this was a fpace, of a Breadth confiderably lefs than
that of the Limbus of the Rainbow, in which I could
not diftinguiih any Colours : Still lower was a faint in-
V terrupted Arch of red, inclining to purple, which ap-
pear’d and yanilh’d feveral times, while I was intent
upon obferving it. ^ -

My Sufpicion about this Pha^nomenon is, that the
extraordinary Rednefs in the purple of the firft Rain-
bow, is owing to the Mixture of the red Rays of a^ fe-
cond Series of Colours, with the purple Rays of the
firft j that the colourlefs Space confifted of Rays which
are too weak to affedthe Sight with diflincl Colours y
and that the innermoft broken Arch was the ending
of afecond and beginning of a third Iris.

» • ■

L*. S. I forgot to tell you, that as in the Account I
fend you here, I faw the purple of the fecond Iris
without the other Colours, To I have feen the other Co-
lours, but not very diftind, without the purple ; as al-
fo, that I could never fee more than one Series of Co-
lours near the Horizon.

t • .

\ . I

*Fetworth, March ix. ‘ .

YEflerday in the Evening, about a quarter before
Six, Wind S. W. we had one of the fineft Rain-
that ever I beheld.

The ‘firft Series of Colours was as ufual, only the
Purple had a far greater Mixture of red in it, than I
have ever feen in the prifmatick Purple: Under this
was a colour’d Arch, in which the green was fo pre-
dominant,

I

( H} )

dominant, that I could not diftinguifli either the yellow
or the blue : Still lower was -an Arch of purple, like
the former, highly faturate with red, under which I
cou’d not diflinguifli any more Colours.

^ I bad the Pleafure of viewing this delightful Objed
for a conliderable time, without that vaniihing. and re-
turning of Colours which 1 defcrib’d in my laft.

The Order of the Colours irrthis compounded Rain-
bow was, you fee, red, yellow, green, blue, a Mix-
ture of purple and red, green, (or rather a Mixture of
yellow, green, and blue) a Mixture of purple and red.

I begin now to imagine, that the Rainbow feldom ap-
pears very lively without fomething of this Nature,
and that the fuppos’d exad Agreement between the Co-
lours of the Rainbow and thofe of the Prifm, is the rea-
fon that it has been fo little obferv’d.

Tetworth^ March x"],

ly'L'L.

I Am afraid I (hall tire you with the Hiftory of this
Phaenomenon ^ but I have feen it in fuch Perfedion
lince the writing my laft, that I cannot help being,
particular in my Account of it.

j^uguji 21% about half an hour pad 5 in the-
Evening, Weather temperate. Wind at N. E. the Ap-
pearance was as follows j viz.

The Colours of the Primary Rainbow were as ufual,
only the purple very much inclining to red, and well
defin’d : Under this was an Arch of green, the upper part
of which inclin’d to a bright yellow, the lower to a more*
dulky green : Under this were alternately two Arches of
reddilh purple and two of green: Under all a faint Ap-
pearance of another Arch of purple, which vaniih’d

( H4 )

and return’d feveral times fo quick, that we cou’d not
fteadily fix our Eyes upon it. Thus the Order of the
Colours was

I. Red, Orange Colour, Yellow, Green, Light Blue,

Deep Blue, Purple, ,

/

II. Light Green, Dark Green, Purple,-

III. Green, Purple, -

IV. Green, faint vanilhing Purple, ^

You fee we had here four Orders of Colours, and
perhaps the beginning of a fifth, for I make no quefHon
but that what I call the Purple, is a Mixture of the
Purple of each of the upper Series with the Red of the
next below it, and the Green a Mixture of the inter-
mediate Colours. I fend you not this Account barely
upon the Credit of my own Eyes ^ for there was a
Clergyman and four other Gentlemen in Company,
whom I defir’d to view the Colours attentively, who
all agreed, that they appear’d in the manner that I have
now defcrib’d.

There are two things, which well defer ve to be ta-
ken notice of, as they may perhaps dired us in fome
meafure to the Solution of this curious Phsenomenon.
The ift is.

That the Breadth of the firfl Series fo far exceeded
that of any of the' reft, that as near as I could judge, it
was equal to them all taken together.

The 2d is.

That I have never obferv’d thefe inner Orders of Co-
lours in the lower Parts of the Rainbow, tho’they
have often been incomparably more vivid than the

upper

( 14J )

tipper Parts, under which the Colours have appear’d. I
have taken notice of this fo very often, that I can hard-
ly look upon it to be accidental, and if it Ihould prove
true in general, it will bring the difquifition into a nar-
row compals ; for it will Ihew that this Effed: depends
upon fome Property, which the Drops retain, whilfl:
they are in the upper part of the Air, but lofe as they
come lower, and are more mix’d with one another.

Tetworthy 1 3 .

lyxx.

V. A Letter to Dr.Jurin, Coll, Med, Lond. Soc.
<2^ Seer, ^ S, concerning the ahoVementioned Ap^
pearance in the (p(ainboWj with fome other (^fle-
Elions on the fame SubjeEl* !By Henry Pem-
berton, Mil>»

SIR,

UPON your communicating to me the curious
Oblervations, your Friend Dr. Langwith had
made on the Rainbow, I inform’d you thofe Appear-
ances might, I thought, be explain’d by the Dilco-
veries, the Great Sir Ifaac Newton had made in
the Subject of Light and Colours, in his wonderful
Treadle of Optics. As you leerned not dilplealed
with what I mentioned to you in relation to this Mat-
ter by word of mouth, you defired that I would let
down in writing my Thoughts thereupon, which 1
have here accordingly done in the following manner.

R

Let

( )

Let AB rcprefent a Drop of Rain, B the Point from
whence the Rays of any determinate Species being
refled:ed to C, and afterwards emerging in the Line
CD, do proceed to the Eye, and caufe the Appearance
of that Colour in the Rainbow, which appertains to
this Species. It is oblerved by Sir Jfaac Newton %
that in the ReflecStion of Light, beiides what is re-
flected regularly, fome finall part of it is irregularly
fcattered every way. So that from the Point B, be-
frdes the Rays that are regularly reflected fromB to C,
Ibme fcattered Rays will return in other Lines, as in
B E, B F, B G, B H, on each Side the Line B C. Fur-
ther it mufl;. be noted from Sir Ifaac Newton that
the Rays of Light in their Paflage from one Superficies
of a refracting Medium to the other undergo alternate

* Optics, Book II. Part 4. ^ Ibid. Part III. Prop. xi/.

Fits

( H7 )

Fits of eafy Tranfmifrion and Refledion, fuccecding
each other at equal Intervals ; infomuch that if they
reach the further Superficies in one fort of thole Fits,
they lhall be tranfmitted ; if in the other kind of
them, they lhall rather be refle(!^ed back. Whence
the Rays that proceed from B to C, and emerge in the
Line CD, being in a Fit of eafy Tranfmifiion, the feat-
tered Rays that fall at a Imall Dillance without thele
on either fide, (fuppole the Rays, that pafs in the
Lines B E? B G) lliall fall on the Surface in a Fit of ealy
Refledfion, and lhall not emerge ; but the fcattered
Rays, that pafs at fome Dillance without thefe lall, lliall
arrive at the Surface of the Drop in a fit of eafy Tranfi
million, and break through that Surface Suppole
thele Rays to pafs in the Lines B F, B FI ; the former
of which Rays lliall have had one Fit more of eafy
Tranfmillion, and the latter one Fit lels, than the
Rays that pals from B to C. Now both thele Rays,
when they go out of the Drop, will proceed by the
Refradlion of the Water in the Lines FI, FiK, that
will be inclined almoll equally to the Rays incident
on the Drop, that come from the Sun, but the Angles
of their Inclination will be lefs than the Angle, in
which the Rays emerging in the Line CD are inclined
to thofe incident Rays. And after the fame manner
Rays fcattered from the Point B, at a certain Dillance
without thefe, will emerge out of the Drop, while the
intermediate Rays are intercepted ; and thele emergent
Rays will be inclined to the Rays incident on the'
Drop in Angles Hill lels than the Angles, in which the
Rays F I and H K are inclined to them ; and without
thefe Rays will emerge other Rays, that fliall be in-
clined to the incident Rays in Angles yet lels. - Now
by this means will be formed of every kind of Rays,
befides the principal Arch which goes to the Forma-

R i tion

( i4S )

tion of the Rainbow, other Arches, within every one
of the principal, of the fame Colour, though much
more faint : and this for divers Succedions, as long as
thele weak Lights, which in every Arch grow more
and more oblcure, fhall continue vifible. Now as the
Arches produced by each Colour will be varioufly
mixed together, the diverfity of Colours obferved by
Dr. Langwith may well arife from them.

The precife Diftances between the principal Arch of
each relpedlive Colour and thele fainter correfpondent
Arches depend on the Magnitude of the Drops of Rain.
In particular, the Imalleft Drops will make the fecon-
dary Arches of each Species at the greatell Dillance
from their refpedtive principal, and from each other.
Whence, as the Drops of Rain increale in falling,
thefe Arches near the Horizon by their great Nearnels
to their relpecfiive principal Arches become invifible.

AND now. Sir, we are upon the Rainbow, I lliall
here take the Freedom of letting down two Propoli-
tions, which I have formerly conlldered, relating to
this Subjedl. For the greater Brevity I lhall deliver
them under the Form of Porilms ; as, in my Opinion,
the Ancients called all Propolitions treated by Ana-
lyfis only.

PROPOSITION I.

a given refraUting Circle, whofe refraciing
bovver is given, the Ray is given in Rojition, which
pajjing parallel to a given *T>iameter of the Circle />
refried by that Circle to a Roint given in the Cir-
cumference of it.

Let

( HP y-

Let A BCD be the given Circle, the given Diameter
A C, and given Point G ; and let the Ray E F, parallel
to A C, be refracSted to G. I fay E F is given in Po-
fition.

B

Produce E F to H, and draw the Diameter F I, draw-
ing likewife I K H, I G. Then is Fi F I the Angle of
Incidence, and G F I the refracted Angle ; fo that I H
being perpendicular to F H and I G perpendicular
to F G, I H is to I G as the Sine of the Angle of
Incidence to the Sine of the refradFed Angle, and
the Ratio of I H to I G is given, as likewife the
Ratio of I K to I G. Therefore I K being perpen-
dicular to A C the Point I is in a Conic Sec^tion given
in Pofirion, whole Axis is perpendicular to A C,.
and one of its Foci is the Point G Confequently
the Points I and F are given, and laflly the Ray E F
given in Pofition.

r

* See Papp.,1. 7. prop. 238. Milnes Conic, part. 4. prop. 9.

‘DETEE-

( ijo )

'D ET ERM I NATION. -

I T is evident, that this conic Sedion, may either
cut the Circle in two Points, touch it in one Point,
or fall wholly without it. Therefore let the Se-
ction touch the Circle in the Point I, and let I L touch
both the Sedion and the Circle in the lame point I.
Then GL being joined, the Angle under IGL on ac-

count of the conic Sedion is a right one ^ lb that
F G L is one continued right Line, and IF is to I L as
FGtoGI; as likewife, M being the Center of the
Circle, M I to I L, or F H to H I, as F G to twice
G I, becaule M I is to I F as G I to twice G I. Hence
by Permutation F H is to F G as H I to twice G I ; that
is, as the Sine of the Angle of Incidence to twice the
Sine of the rehaded Angle.

* De la Hire Conic, lib. 8, prop. 23.

Moreover

( lyi )

Moreover F H being to H I as F G to twice G I, the
Square of F H will be to the Square of H F, as the
Square of F G to four times the Square of G I. There-
fore, by Compofition, as the Square of F H to the
Square of F I or of AC, lb is the Square of F G to the
Square of F I together with three times the Square of
G I, and fo likewife is the Excefs of the Square of F G
above the Square of F H, which equals the Excefs of
the Square of I H above the Square of I G, to three
times the Square of G I ; for as one Antecedent to one
Conlequent, fo is the dilFerence of the Antecedents to
the difference of the Confequents. Hence in the laff:
place, the Square of half F H will be to the Square of
A M, as the Excels of the Square of I H above the
Square of I G to three times the Square of I G, or as
the Excels of the Square of the Sine of Incidence above
the Square of the Sine of Refra(5tion, to three times
the Square of the Sine of Refradrion,

Another

( 2J1 )

Another ‘DETERMIRATION.

Draw the Diameter GO and the Tangent OP,
meeting G F produced in Q_: then the Angle under
I F G is equal to the Angle under O G F, the Angle

under F I L equal to that under G O Q^, both being
right, and F I is equal to G O ; whence the Triangles
G O Qj, F I L are fimilar and equal ; fo that G is
equal to F L, and the Point F in an Hyperbola paffing
through G, whofe Afymptotes are A C and O P

« Apoll. Conic. 1, z, pi'op. 8.

p R o p o-

( M3 )

. ■/ . ' 'A rx) i

«

. • r . . f.

PROPOSITION II.

1.

. - - - - * ■ ■ >

refraBtng Circle and its refraBing ^ower he^

ing given, the Ray is given in Rojition, which, faf-
fing parallel to a given RDiameter of the Circle, after
its RefraBion, is fo refleBed from the farther Sur-
face of the Circle, as to be inclined to its incident
Courfe in a given Angle.

Let A B C D be the given Circle ; let A C be the
given Diameter, E F the incident Ray parallel to it,
which being refracited into the Line F G lhall lb be re-
fled:ed from the Point G in the Line G H, that E F
and FI G being produced, till they meet in I, the
Angle under E I FI fhall be given.

Let K be the Center of the Circle, and K F, K G be
joined ; let the Semidiameter L K be parallel to the

S reb:a(%ed

( 254 )

refraded Ray F G, and M K being taken to the Semi-
diameter of the Circle in the Ratio of the Sine of In-
cidence to the Sine of Refra^Stion ; let L M be joined,
and laftly make the Angle under K M N equal to half
the given Angle under E I H. This being done,
if F G be produced to O, F O fhall be to K O as
the Sine of the Angle of Incidence to the Sine of
the refrad:ed Angle, that is as M K to K L ; in fb
much that -K L being parallel to F O, and the Angle
under M K L equal to that under F O K, the Angle
under ML K iliall be equal to that under FK O, and
the Angle under *K M L equal to that under K F O e-
quat to that under FGK or half that under F GH,
whence the Angle under KM'N being equal to half
Ae Angle under F I H, the refiduary Angle under
N'M L will be equal to half the Angle under I F G or
to half that under M K L. Therefore L C being drawn,
the Angle under L M N will be equal to that under
M C L ; and in the laft place, if M C be divided into
two equal Parts in P, and P Q^R be drawn parallel to
CL, the Angle under Q^M R will be equal to that
under R P M, and the Triangles QM R, M P R flmi-
lar, fo that the Redtangle under P R ihall be equal
to the Square of M R. Whence R L being equal to
M R, the Point L Ihall be in an equilateral Hyperbola,
touching the Line M N in the Point M, and having
the Point P for its Center But this Hyperbola is gi-
ven in Portion, and confequently the Point L, the
Angle under M L K, and the equal Angle under C K F
will be given, and therefore the Ray E F is given in
Pofition.

» Apoll. Conic, lib. i. prop. 37. compared with lib. 7. prop. 23.

r

( )

TtETERMINATIOK

\ f

Let the Hyperbola touch the Circle in the Point L,
and let their common Tangent be L S ; draw LT pa-
rallel to M N, fo as to be ordinately applied in the
per bo la to the Diameter C M. Whence L S touching
the Hyperbola in L, P T will be to T L as T L to
T S % and the Angle under T S L equal to that un-
der T L P, but as the Angle under S C L is equal to
that under N M L, the fame is equal to the Angle un-
der T L M ; therefore the Angle under S L C is equal
to the Angle under M L P. Farther, M L being pro-
duced to V and V C joined, the Angle under L V C is

equal to that under S L C, by reafon that L S touches
the Circle in L ; hence the Angles under L V C and
under M L P are equal, L P, V C are parallel, and

Apoll. Conic, lib. i. prop. 37. compared with lib. 7. prop. 23.

s X M P

( 15<5 )

M P being equal to P C, M L is equal to L V ; and
K W being let fall perpendicular to LV, M W is equal
to three times L W. But now if the incident Ray E F
be produced to X, the Angle under M L K being equal
to that under C K F, or to that under E F K, F X fliall
be equal to LV, equal to twice. L W ; and the Angle
under KM L being-equal to that under K F G ; fince
K W is perpendicular to MW, F G lliall be to twice
M W as M K to K F, or as the Sine of Incidence to
the Sine of Refradlion : whence M W being equal to
three times L W, F X fliall be to F G as the Sine of
Incidence to three times the Sine of Refradlion.

Moreover, M W being equal to three times L W,
the Square of M W wilF be equal to nine times the
Square of L W^ and the Redlangle under V M L, or
the Redlangle under C M A, that is, the Excels of the
Square of K M above the Square of K A, will be equal
to eight times the Square of LW ; therefore the Square
of L W or the Square of half F X will be to the Square
of K L, or of KA, as the Excefs of the Square of K M
above the Square of K A to eight times the Square of
K A, that is, as the Excefs of the Square of the Sine
of Incidence, above the Sine of Refradlion to eight
times the Square of the Sine of Refradlion.

)

'»■

-Another

1

Afiother 7)ETERMINATI0N.

Draw A Y parallel to M N, and A Z parallel to
MV : then is the Angle under YAZ, equal to that
under L M N, which is equal to that under L C A ;
whence the Arches A L, Y ^ are equal ; but the

Arches A L, V Z are likewife equal, becaufe LV, AZ
are parallel, therefore Y V being joined, and L r drawn
perpendicular to A C, the Chord V Y ihall be the
double of L r ; but V A being likewife let fall per-
pendicular to AC, becaufe M V is the double of M L,
V A iliall be the double of L r ; and therefore V A
and V Y fliall be equal ; whence the point V lhall be
in a Parabola, whole Focus is the Point Y, its Axis
perpendicular to A C, and the Latus re6fum^ belong-
ing to that Axis, equal to twice the perpendicular let
fail from Y upon A C But if K V be joined, the

; Vide de la Hire Sed. Conic. lib. 8. prop. 1,3.

Angle

( )

Angle under L K V is equal to twice the Complement
to a right Angle of the Angle under KX V, which is
equal to the Angle of Incidence, and exceeds the re*
framed Angle by the Angle under A K L.

’ The Determinations of thefe two Propofitions,
have relation to the lirft and lecond Rainbow ; thole
of the firlt Propofition relpe(Sling the interior, and thole
of the fecond the exterior. The firll Determinations
of thefe two Propofitions alTign the Angles, under
which each Rainbow will appear in any given refrad:-
ing Power of the tranlparent Subltance, by which they
are produced ; the latter Determinations of thele Pro-
pofitions teach how to find the refrading Power of the
Subfiance, from the Angles under which the Rain-
bows appear ; the Angle under C M G, in the Deter-
minations of the firft Propofition, being half the Angle
which mealures the Diftance of the interior Bow from
the Point oppofite to the Sun ; and in the Determi-
nations of the fecond Propofition, the Angle under
CMN is half the Complement to aright Angle of
half the Angle that mealures the Diftance of the exterior
Bow, from the Point oppofite to the Sun. But where-
as thefe latter Determinations require Iblid Geometry,
it may not be amifs here to lliew how they may be
reduced to Calculation, feeing the Oblervation of thele
Angles, as the learned T>t. Halley has already re-
mark’d % afibrds no inconvenient Method of find-
ing the refrading Power of any Fluid, or indeed of any
tranlparent Subftance, if it be formed into a Iphericd

» J^hilofoph, Tranfa£l. No. 267. 722,

or

( )

or cylindrical Figure. For this purpofe therefore I

have found, that in the latter Determination of the
iirft Propofition, if the Sine of the Angle under CMG
be denoted by a, the Tangent of the Complement of
this Angle to a right one be denoted by and the Se-
cant of this Complement by c ; the Root of this E-
quation 2;’ — — ^aa){^c — a will exceed

the Sine of the Angle under F M A, that is the Sine
of the Angle of Incidence, by the Sine of the Angle
under CMG; and the Sine of the Angle under FMO,
which is double the refradled Angle, will be the Root
of this Equation aa xin ; this Angle

being acute, when the Tangent of the Angle under
C M G is lefs than half the Radius^ or when the
Angle itfelf is lefs than 1.6 degr. 33/. and

when this Tangent.is more .than half the Radius, the
Angle'undcr 6 M.F is obtuie.

■ r 7

The

( ,i6o y

TbeUoots of thefe cubic Equations ate found by
feeking the firft of two mean Proportionals, between
each of the verfed Sines appertaining to the Arches
C G, A G, and the Sine of thofe Arches, counting
from the verled Sines ; for the Sum of thele two mean
Proportionals is the Root of the former Equation, and
the difference between them the Root of the latter ;
as may be colledfed from Cardan's Rules.

And hence likewife if the fird: and laft of the five
mean Proportionals, between the Sine and Cofine of
half the Angle under C M G be found, twice the Sum
of the Squares of thefe mean Proportionals applied to
the Radius exceeds the Sine of the Angle of In-
cidence by the Sine of the Angle under C M G ; and
twice the difference of the Squar es of the fame mean
Proportionals applied to the Radius is equal to the
Sine of double the refracSIed Angle. Moreover this
double of the refraded Angle exceeds the Angle of
Incidence by the Angle under CM G.

In the latter Determination of the fecond Propofi-
tion draw K Y, and A Y being parallel to M N, the
Angle under CKY will be equal to twice the Angle

under

( )

itnder CMN, that is equal to the Complement of half
the Diftance of the exterior Rainbow from the Point
oppofite to the Sun. Then putting a for the Radius
A K, and b for the Sine of the Angle under C K Y,
the Sine of the Angle under A K V will be the Root
of this Equation ^ by^ — %aaby-\-^aabb — o.

But the Angle of Incidence and Refraction may alfb
be found as follows. '

Let two mean Proportionals between the Radius
and the Sine of the Angle under C K Y be found, then
take the Angle, whofe Cofine is the firfl: of thele mean
Proportionals, counting from the Radius ; and alfo the
Angle, whofe Sine together with the lecond mean
Proportional fhall be to the Radius as the Cofine of
the Angle under C K Y to the Sine of the Angle before
found. The Sum of thefe three Angles is double the
Complement to a right one of the Angle under A KL,
the Angle under K M L, or the refradted Angle, being
equal to half the Sum of this Angle under A K L and
the Angle under C K Y ; as in the lad Place the Angle
under K LV, that is the Angle of Incidence, equal to
the Sum of the Angles under K M L and under M KL.

I need not obferve, that the geometrical Methods of
deducing thefe Angles of Incidence and Refraction
from the Angle meafiiring the Didance of each Rain-
bow from the Point oppofite to the Sun, adbrd very
expeditious mechanical Condrud'ions.

T

7art

( )

VI. of two Letters concerning a Method of

procuring the Small (Pox, ufed in South Wales.
From Perrot Williams, Af. 2). Fhyfician at
Haverford Weft, to Dr. Samuel Brady, (P/^-
fician to the Garrifon at Portfmouth.

However new the Method of communicating the
Small Pox may appear in this Kingdom ; yet I
am to acquaint you, that it has been commonly pra-
(flifed by the Inhabitants of this Part of ales {Lem-
hroke/lAreytlmt out of mind, though by another Name,
that of buying the Difcafc,, as I have been long
ago acquainted by leveral, who procured the Diflem-
per by that means. There is a married Woman in the
Neighbourhood of this Place, who prad:ifed it on her
Daughter, about a Year and a half ago, by which
Means flie had the Small Pox favourably, and is now
in perfect: Health, notwithftanding flie has ever fince,
without Referve, converfed with liich as have had that
Diftemper this lad Summer.

In order to procure the Didemper to themlelves,
they either rub the Matter taken from the Pudules when
ripe, on feveral Parrs of the Skin of the Arms, or
prick thofe Parts with Pins, or the like, fird infeeded
with the fame Matter. And notwithdanding they omit
the necedary Evacuations, loch as Purging, yet,,
as I am inform’d, they generally come off well enough ;
and what’s remarkable, I - cannot hear of one Indance
of their having the Small Pox a fecond time.

% A Learned'

( )

A Learned and very Ingenious Gentleman of this
Country told me not long fmce, that ^ above twenty
Years ago, when at School, he- and leveral off his
Schoolfellows, (how many I don’t exactly remember)
infedled themfelves at the lame time;' frorn_ the fame
Perfon, and that not one of them milcarry’d, though
he had more of the Small Pox than he defign’d. I am
latisfy’d he will readily give a more particular Rela-
tion of this Aflair, if defired. , I am forry he happens
at prefent to be at a confiderable Dillance from- this
Town, otherwife I would have been more exad: in
this Account.

Haverford JVefiy
Se^t. i8. I71X.

‘Ter rot JViUiams.

I Should not have lb long omitted the Return of my
Thanks, for the Favour of yours of 06i, 15'. but
that I hitherto waited an Opportunity to Ipeak with
the Gentleman, whom I mention’d in my lafl. His
Name is George Owen^ a Counlellor at Law, elded
Son to Dr. Owegi, formerly Archdeacon in the Dio-
cele of St. ‘David’s. He Iblemnly declares, that ha-
ving, when at School, as I formerly faid, rubb’d the
Skin off his Left Hand, where the Scar is now very
vifible, with the back Edge of his Penknife, till the
Blood began to appear, he apply’d the variolous Mat-

T 2 ter

( 2^4 )

ter to that part ; which by Degrees growing inflam’d,
about a Week afterwards he fell into the Small Pox ;
and that he has fi|iee fi^quentlyconverfed with fuch as
were flckofthat Diflemper. He fays alfb five or fix
more at leaft of his Schoolfellows made the like Expc*
riment on themfelves, at the fame time, with the like
Succefs.

I have flnce talk’d with feveral more, who made
the like Experiments on themfelves, fame twenty,
fbme fixteen, Years ago : who all pofitively af-
firm, they never had the Small Pox a fecond time. '

Haver ford Wefty

Nov. 23. 1722. ' ^

. T ,u. ‘

^errot Wtlltams,

VII. ^art of a Letter from the fame Learned and
Ingenious Gentleman^ upon the fame SuhjeBy to
Dr, Jurin, 5^ S'. Secret,

TH E Bufiuefs of my ProfciTion obliging me to
go into the Country, as fbon as I had the Fa»
vour of yours of Ja». 22. prevented my re-
turning an Anfwer fooner to the Queries you arc
pleas’d to propofe.

I have little to add to what I have already men-
tion’d to Dr. Brady y concerning the manner of com-
municating the Small Pox, more than that Mr. Owen
was about fifteen Years of Age, when he made the
Experiment on himfelf, and that he queftionlefs had
the genuine Small Pox ; the Signs of ’em on his Face,
2 and

( )

. and the Mark on his Hand, where he ^ipply’d the
1 Matter, being ftill fo very vifible, as to put that mat-
iter beyond Dilpute. The Phyfician, who then at-
led him, is dead. Tho’ I can’t pretend to remem*
how many inform’d me of their procuring the Di-
aper in this manner ; yet I can aver, that within
compafs of twenty Y ears laft pail, I have been
)ften afTured of the Truth of it, not by Children,
grown Perfbns of undoubted Credit, that I am en*
ly latisfied it has been an immemorial Cuftom in
Te Parts ; and not only pradifed by Boys when at
ool, but alfo by many others of both Sexes more
anced in Years, and conlequently capable of di-
^uifhing the Small Pox from other Diftempers.
^e are now living, in this Town and Neighbour*

d, five or fix Perfons, who undoubtedly bad that
:emper after taking the forefaid Method to infedt
nfelves; one of whom, a young Woman aged

I me (fince I received your Letter) that, about 8 or
cars ago, in order to infecft herfelf, file held twenty
ky Scabs (taken from one towards the latter end
he Diftemper) in the hollow of her Hand, a confi-
ible time ; that about ten or twelve Days after-
ds Ihe ficken’d, and had upwards of thirty large Pa-
ss in her Face, and other Parts ; and that llie has
:e freely converfed with fiich as have had the Small
[ on them.

To make it appear that Inoculation is a lufficichr
fervative againft receiving the Small Pox a fecond

e, about fix Weeks ago, I caufed my two Boys,
D had been inoculated this laft Summer, not only
ee, but even to handle a Child, dying of a moft
ignant fort of Small Pox ; who notwithftanding, I
ak God, continue in perfecft Health.

Upon

( i66 )

Upon a v.ery exad Inquiry I find, that out of
•^vlio have had the Small Pox in the natural way, in
this Town and a neighbouring Parilli, fince the Begin-
ning of Jmw lafl, have died.

Haver ford Wefi^

Feb. z. i72|.

Ferrot Williams,
T O S T S C R I F T.

Jufl as I was concluding my Letter, being lent for
by a Gentleman about fix Miles off, (where I faw two
very melancholy Inftances of the Severity of the con-
fluent Small Pox) he took an occafion to inform me,
that a near Neighbour of his caus’d his Son, about ten
Years of Age, near three Weeks ago, to buy (as he
term’d it) the Small Pox, after the manner I defcribed
in my firft Letter to Dr. Brady. Carefully viewing
the Boy, I found him recovering from thediftind: Kind
of that Diftemper, having not had, as I could perceive,
above 40 pretty large Puftules, which were then dry-
ing off. Had I not been fcanted in Time, I queftion
not but I fliould have been able to have given a great
many Inftances of the like Nature ; but the hurry I
have been continually in, ever fince I receiv’d yours,
muft be my Apology, for that Deficiency, as well as
the Uncorrednefs of this Letter.

/

IX. ^

( ^^7 )

Vni. J Letter on the fame Suhjed^^ from Mr. Ri-
chard Wright, Surgeon at Haverford Weft, to
Mr. Sylvanus Bevan, Apothecary in London.

I Received yours the 9th inllant, and, in Anfwer to
it, will readily give you all the Satisfadlion I can,
in relation to a very antient Cuftom in this Country ;
commonly called buying the Small which, upon
a ftrid: Inquiry, fmce I had your Letter, I find to be
a common Practice, and of very long Handing ; being
afTured by Perfbns of unqueflionable Veracity, and
of advanced Age, that they have had the Small Pox
communicated to themfelves this way, when about
fixteen or feventeen Yeai'S of Age, they then being
very capable of diftinguifliing that Diftemper from any
other; and that they have parted with, the Matter
contain’d in the Puflules to others, producing the fame
Effed:s. There are two large Villages in this County
near the Harbour of Milford., more famous for this
Cuftom than any other, namely, St. IJhmael's and
Marloes. The old Inhabitants of thofe Villages, (with
which they abound, being in a healthful Situation)
lay, that it has been a common Practice with them
time out of mind ; and what was more remarkable,
one William Allen ^ of St. Ijhmael\ ninety Y ears of
Age, (who died about fix Months ago or thereabouts)
declared to fome Perfans of good Senfe and Integrity,
that this Pracftice was ufed all his Time ; that he very
well remember’d his Mother’s telling him, that it was
a common Pradice all her Time, and that fhe got the
Small Pox that way, Thefe, together with the many

othcj&;

( )

Other Informations, I have met with from almofi: all
parts of the County, confirm me in the Belief of its
being a very antient and frequent Practice, among the
common People ; and to prove that this Method is flill
continued among us, I will give you the relation of an
elderly Woman, a Midwife, who accidentally came
into Company, when your Letter was reading, whole
Name is Joan Jones^ aged feventy Y ears, of good Cre-
dit, and perfedl: Memory. She folemnly declares, that
about fifty four Years ago, having then the Small Pox,
one Margaret Brown (to the bed of her Remem-
brance then about twelve or thirteen Years of Age)
bought the Small Pox of her ; that the laid Margaret
Brovjn was feized with the Small Pox a few Days af-
terwards ; that the laid Mar gar et Brown had not had
the Small Pox a lecond time, a twelve-Month ago,
and Ihe verily believes, that Ihe has not had them fince.
She farther fays, that llie has known this way of pro-
curing the Small Pox pradtiled from time to time, above
fifty Years ; that it has been lately ufed in her Neigh-
bourhood, and that Ihe knows of but one dying of
the laid Diftemper, when communicated after the Me-
thod afbrelaid, which Accident happened withinthefe
two Years lalt pad ; the Perlbn who milcarried (a
young Woman about twenty Years of Age) having
procured the Didemper from a Man then dying of a
very malignant Small Pox. The above Relation I
heard the old Woman declare two Days ago, and llie
was willing to take her Oath of it before Dr. JVUliams^
who is a Magidratc. As to what you mention con-
cerning the manner of communicating the infeedious
Matter to the Blood, by feraping the Skin thin with a
Penknife, and fo rubbing in the Matter, that was only
the Cafe of one particular Gentleman, Mr. Owen, a
Counfellor at Law, whom I heard fcveral times pofi-

tively

( )

tively affirm, that he bought the Small Pox when at
School, and of Inch a Lady, now living, and gave her
three Pence for the Matter contained in ix Puftules.
That hundreds in this Country have had the Small
Pox this way is certain ; and it cannot produce one
fingle Inftance of their ever having them a lecond
time.

Haver ford Wef^

Feb. 15*. 171^.

(^chard Wright,

IX. An Account of fome Experiments made to prove y
that the Force of Moving ^Bodies is proportionable
to their Velocities: {or rather that the Momen-
tum of' Moving Bodies is to he found by muU
tiplying the Majfes into the Velocities) In Anfwer
to Juch ioho have Jometime ago affirm dy that that
Force is proportionable to the Sepiare of the Velo-
city ^ and to thofe who Jiill defend the fame Opimon.
By the BeVerend]ohn Theophilus Defaguliers,
LL,V,F,^S,

AS far as I can learn, Monfieur Leibnitz was the
firft that oppos’d the receiv’d Opinion, con-
cerning the Quantity of the Force of moving Bodies ;
by faying, that it was to be eflimated by multiplying
the Mafs of the Bodies, not by their Velocity, but by
the Square of it. But, infteadof Ihewing any Para-
logifm, in the mathematical Demonftrations, which

U arc

C i70 )

are made ufe of to prove the Pfoporidoii, or
any Miftakes in the Reafonings from the Experi-
ments made to confirm it, he ufhs other Mediums
to prove his AfTertions ^ ; and without any Regard to
what others had faid on that Subjedt, brings new Argu-
ments, which the Reverend and Learned Dr. Clark
has fully anfwered in his fifth Letter to him. Mef-
fieurs John BernoulliyW olfius^ Her m annus ^2x16. others,
have follow’d and defended Monfieur Leibnitz's Opi-
nion, and in the fame manner, fo that what is an An-
fwer to him, is fo to them.

Boknns (Profefibr at Badua) has adfed after the
fame manner in the experimental Way, making fbme
Experiments to defend Monfieur Leibnitz's Opinion,,
without having Ihewn thofe to be falfe. which are made
ufe of to prove the contrary ^ ; and now lately, an in^-
genious Profeffor abroad (who was of the Opinion
commonly receiv’d, and in his Writings had demonflra-
ted it in the ufual way confirming it with the commom
’Experiments made in that Cafe) happening to make
fome Experiments like thofe of Bolenus, has drawn-
Conclufions from them to fliew the Force of moving
Bodies to be proportionable to the Square of their Ve-
locity ; and being wholly come over to that Opinion,,
endeavours to deduce it from Phyfical Principles.

As there can hardly be faid any thing new, or bet-
ter than has been faid, to fhew the Force abovemeh-
tion’d to be proportionable to the Mafs multiplied in-
to the Velocity ; I only repeat here the Subflancc
of what others have laid, and make fome old Experi-
ments over, again ; but then I confider fome Circum-

». Afta Emdit. ad ann. 1686. p. 162. ^ Polenus de Caftellis, p. 56,.

57j &,c. ' Gvavcfande Imroduitio, Vol. I. No. 132,

ftances.

{ i7i )

fiances, that perhaps have been overlook’d, and at lafl,
by a new Experiment, endeavour to fhew, what has
led into an Error fome of thole, who defend the new
Opinion.

If a Man with a certain Force can move a Weight
of fifty Pounds, through a Space of four Feet, in a de-
terminate time ; it is certain he raufl employ twice
that Force to move one hundred Pounds Weight,
through the lame Space in the lame time. But if he
ules but the fame Force, he will move the one hundred
Pounds Weight but two Feet in the fame time. For
as the one hundred Pounds Weight contains two fifty
Pound Weights, if each of them has two Degrees of
Velocity given to it, it will exadlly require the lame
Force that would give one of them four Degrees of Ve-
locity ; hence it appears, that the Force is propor-
tionable to the Mafs multiply ’d into the Velocity.

EXPERIMENT L

Fig. I. Let the Balance A B, whole Fulchrum, or
Center of Motion, is at C, be fo divided, that the Bra-
chium A C be but the fourth Part of the Brachtum
CB ; it is known to all Mechanicians, that a Weight
of one hundred Pounds at A, will keep in .^quiltbrio
a Weight of twenty five Pounds hanging at B, where
it will have a Velocity four times greater than that of
the Weight at A. For, not only when the Balance is
horizontal, there will be ^inAiquilibrium^ but when the
Balance is put in Motion, it will return to JEquili-
brium in an horizontal Pofition ; the equal and con-
trary Forces applied at each, dellroying one ano-
ther. Whereas, if the Forces were as the Mafs multi-
ply’d into the Square of the Velocity, the twenty five
Pound Weight fiiould have been fulpended at D, only

U 2 twice

( 270

twice as far from C, as the Weight at A ; and in gene-
ral, let the make of the Engine be what it will, let the
mechanical Powers be combined in any manner, when
two heavy Bodies, by means of a Machine, ad: upon
one another in different dired:ions, if their Velocities
are reciprocally as their Maffes, they will deltroy each
others Forces and come to reft.

As this is true in relped: of mechanical Powers, lb
it is in relped: to the Shock or Blow given by falling
Bodies. An heavy Body, falling with an accelerated
Motion, goes through a Ipace of one Foot in a quarter
of a Second, and acquires a Velocity, which would *
carry it two Foot in the fame Time with an uniform
Motion ; the fame Body falls through a Ipace of four
Foot in half a Second, and acquires a Velocity, that
w^ould with an uniform Motion carry it eight Foot in
half a Second. Therefore, as the Time of the fall
through a Ipace of four Foot is twice the Time of a
fall through one Foot, the Velocity in the' latter Cale
is double that of the firft, and conlequently the Blow,
that the Body will give, will be double.

EXPERIMENT II.

Fig. II. Let the Weight P of one Pound, be placed
m the Scale fulpended at the end A, of the Ballance A B,
which bears upon the Gnomon^ot Iron Supporter, khi.
Then if the Weight C be let fall from D, or one Foot,
it will by its Stroke on the end of the Beam B, raife
up the oppofite end A with the Weight P,fb high, that
the Springy ^ will fly from the Button /, which kept
it ftreight and upright before the Shock. If the Weight
P be of two Pbunds, it cannot be railed by the fall of
C from any height lefs than F or four Foot ; whereas, if
the force of the Shock was proportionable to the Space,

X without

( 175 y

without any regard to the time, as Monfieur Leibnitz,^
and his followers have affirmed, P ought to be raifed,
when C falls only from E, or two Foot, which never
happens ; or, if the Stroke was proportionable to the
Mafs multiplied into the fquare of the Velocity, when
C falls from F, then P might weigh four Pound, where-
as the Experiment will never lucceed under thofe Cir-
cumftances.

I know it is objedted, that the Blow cannot be al-
ways diredf, and that the String that goes through the
hole in the falling Weiglit, to guide it in its Fall, caules
a fenfible Fridrion, and therefore that fomething of the
Force is thereby loft. But we are to obferve, that if
that vras all, there would be no need of railing up C
in the fecond Cafe quire up to F, inftead of E, whereas
in Fad:, it muft always be raifed beyond F, to allow
for the Fridtion, that hinders it from producing a dou-
ble Eftedt in failing from F. For if the Experiment
be repeated an hundred times, the Weight, P when of
two Pounds, will never be raifed by letting Cfall ftom
any place between E and F.

EXPERIMENT III.

If (in order to avoid Fridlion) inftead of a Blow
ftruck upon the end B, by the falling Body, the laid .
Body C be faftned to a pretty long String tied to the
button as at r, and ftrft lifted up one Foot, and
then let fall ; fo that in falling oneFoof^ it may pull
down B, and lift up' A with the Weight P of one
Pound ; whenever P is two Pounds, C muft fall from a
height greater than f or four Foot, otherwile it will
not raim the Sraehium A, elpecially if it be let fall
between e and f.

EXPE-

( V4 )

EXPERIMENT IV.

■i

I took the Weight C of feventeen Ounces Troy,
which was a round ball of Lead with a hole through the
middle of it, and having palTed the String N-X through
it, before it was faftened to the Hook X, I placed the
whole Machine in fuch manner, that the String being
flretchcd by the Weight N, went through the hole of
the Weight C, and likewile through the hole of the
Brachium B, upon yhich C lay, without touching
the Tides of the hole either in the Weight or Ballance ;
then having put fiich a Weight P in the oppofite Scale,
as C falling from the height of one Inch, was able to
raife high enough, to let loofr the Spring g h from the
Button : I added to P another Weight equal to it,
and then letting fall C along the String that guided it,
from an heighth of two Inches, then of three, and then
exacfrly of four, it would not raife the double Weight
P to the former height, but falling from five Inches,
or a little higher, it raifed it up. ^ ,

EXPERIMENT V.

\

Leaving every thing as it was before,. I changed the
Weight C for another leaden Ball of twice the Weight,
which falling from one Inch, raifed the double Weight
P to the ulual height ; then changing the Weight B
in any Proportion, whatever height was requir’d for
the heavieft Ball C (or C z) to fall from, in order to
raife the Weight at P ; more than four times the height
was required for the firft Ball C, to raife the fame
Weight fb high, as to let loofe the Spring.

EXPE-

( ^75 )

i;/ .. '

EXP E R I M E N T VI.

I tried the Experiment with the Weight C hanging .
at the String m c (^as in Experiment III.) and a Fall from
an height of five, or near five Inches, was required to
raife double the Weight in the oppofite Scale, that a
fall from one Inch would raife ; only here the heighth
above four Inches was not fb great as in the former
Experiment, the Frid:ion being lomething lefs. Then
I fufpended the great Ball C (or C x) by the String m r,
and when by falling one Inch it raifed the Weight P,
the little Weight C could not produce the fame Effedf,
without falling from a greater height than four Inches.

It , is here to be obferved, that which way foever
thefe Experiments are tried, the Objed:ions rifing from
the Frid:ion do no way ferve to confirm the new Opi-
nion, becaufe they fliew that (upon account of the
Frid:ion) the Heights muft be fomething more than in
a duplicate Proportion of the Velocities, but never lef^
to give a Blow with the fame Body in Proportion to
the Velocity.

That the Momentum of Bodies is in Proportion to the
Mafs multiplied into the Velocity, is alfo moft evidently
Ihewn from the Congrefs of elaflic Bodies, as has been
demonflrated by Sir Ifaac Newton in his ^rincifidy
in the Corollaries to his Laws of Motion, ' I had often
tried the Experiments there mentioned with Balls of
Ivory and Balls of Glafs, and fbme of them with two
Balls of Steel, of two Ounces each, and found every
thing anfwer, allowing for the want of perfedf Elafti-
city in the Bodies. But now upon this Occafion,. as
the Objedfions to the receiv’d Opinion were re-
newed, I was willing to repeat the Experiments with
the utmoft Accuracy and therefore, as Ivory Balls

are

( )

are not equally denfe in all their Parts, and Glafs Balls
break after two or three ftrokes ; I caufed Balls to be
nicely turned of Steel, and made as hard (as the Work-
men call it) that is, as elaftick as polTible, and the
Weights of ithem were precifely as .follows : Two
Balls of twelve Ounces Troy each, one of fix Oun^
ces, one of three, one of two, and one of Eight-pen-
ny-weight. Then making Pendulums of thele Balls,
and hanging them upon the Machine contrived by
Mariotte for the Congrefs of Bodies, and lately im-
proved by Dr. Grave fande % I meafured 5'y \ Inches
between the Center of Sufpenfion and the Center of
Gravity of the Balls, and then every Degree of the Cir-
cle they defcribed in their Ofcillation was one Inch,
and the Degrees being marked upon a line of Chords
on a Brafs Ruler above the Balls, by their Strings iuc-
celTively covering the crofs Lines of DiviBon, the
Degrees that the Balls fell from, and thole to which
they rofe, were very difcernable to an Eye placed at a
convenient Diftance.

EXPERIMENT VII.

I took the two Balls it, and removing each from
the lowed: Point of their equal and refpecStive Circles,
up to 4 Inches, or 4 Degrees, I let them fall lb that
they met at bottom, and were both relle(d:ed again to
4j the Place from whence they fell.

EXPERIMENT VIII.

Every thing elfe being as before, inllead of one of
the Balls it, I took the Ball 6, then letting 6 go from

» Introd. No. 170. Vol.' i.

8 Degrees,

( i77 )

8 Degrees, and 12 from 4, after Reflexion it was
driven up again to 4, as before.

. EXPERIMENT IX.

The Ball 5 falling from fixteen Degrees met the
Ball iz that fell dill from 4, and after Reflection iz
went up again to 4.

EXPERIMENT X.

The Ball z falling from 6^ and iz from i®, iz was
reflected to i, and when z fell from iz Degrees, and
the Ball iz from 2, the 12 was reflected to 2.

EXPERIMENT XI.

The Ball of eight Penny Weight (which weigh’d
but 3 4 of the Ball 12) falling from fifteen Inches or De-
grees, rais’d up 12 (that fell from half a Degree) to the
lame Place again.

In all thele Experiments the Error, or want of per-
fect Reflection, was greater in the little Balls than in
the great ones, on account of their going thro’ a grea-
ter ^rc of a Circle, whereby they deviated more
from a Cycloid than the great ones ; as likewiie on
Account of the Refiftance of the Air, which muO:
be greater becaufe of the little Balls going through a
greater moving with more Velocity, being llif
pended by a String as thick as that of the great ones,
and having more Surface in Proportion to their Weight.
But all the Errors do not bring the ^hanomena any
thing near what they ought to be,iftheForce ofthe Bo-
dies was as the Square of their Velocities multiply’d in-
to their MalTes, for then the Ball 12 would have been
driven to Heights very different from what it rofe up to.

X X In

( 178 )

In the eighth Experiment, the Ball ii ihould have
fifen to near five Inches and three quarters, for the
Ball 6 falling with the Velocity, 8 muft have had its
Force =18x8x6 — 384; and then, that the Ball iz
might have the fame Force or Quantity of Motion, it
mnfi: rife near to 5, 7 becaufe 5,7 x 5',/x ix = 389,88.

'In the ninth, iz fhould have rifen to 8; for the
Ball 3 muft have had its Force zz 16x16x5 — 768,
and if 12 receiv'd its whole Force it muft have rifen to
8 becaufc 8x8x12 = 768.

In the fecond Part of the tenth Experiment, 12
fiiould have rifen to near 5',becaufe 12 x 12 x2 =: 288,
and 5* X 5 K 12 is but 300.

In the eleventh, the Ball 12 (thirty times heavier
than the little one) muft have gone to 2 | Inches, be-
caufe the Momentum of the little Ball being = 1 5* k i y
X I =: 22y, that of the Ball 12 muft be =: 2,75” x 2,7y
X .12 — 226 &c.

It may be here alledg’d, that one ought to fubtradl

Momentum^ with which the great Ball comes upon
the little one ; but that won’t mend the Matter much,
tho’ indeed the Dificrence will be lefs. For,

In the eighth Experiment, if we fubtrad: 4X 4 x 12

192 from 389,88 there will remain 197,88, and the
Ball 12 will go but to 4 ; but then in Experiment 9, if
we fiibtrad: the fame N° 192 from 768, we fliall have
576, which would carry 12 to near feven Degrees, be-
caufe 7 xyx 12 — 5-88.

In the tenth Experiment, there is only 48 to be fub-
rraded ; and in the eleventh only ly ; and therefore
the Velocity of 12 will very much fall fhort of what is
agreeable to the new Opinion.

After the Experiments made, and what has been laid,
till thefe Confequences are overthrown, no notice
ought to be taken of any Objedions, or new Experi-
ments.

( )

ments. But to give the ObjedorS all polTible Satisfa-
d:ion, I Ih.all, in another Paper, endeavour to Ihew
the Fallacies of the Arguments, and Iblve the ^hoeno*
mena of the Experiments made ; Ihewing, both by
Realbn and Experiment, that the Fadts ought to be as
they are, in confequence of the receiv’d Opinion and
Laws of Refiftance,

FINIS.

E R R AT V M.

pA G. zjo. Ill the Note for, de la Hire, &c. read Millies^ ibid*’

LONDON: Trtnted for W. md J. Innys,
Printers tv the Royal Society, at the Prince’s
Anns the Weft End of St. Paul’j Churchyard.

V

I

\

‘***d;V‘

Fig.I

I

fcuip.

Numb.

PHILOSOPHICAL

TRANSACTIONS. '

For the Months of and April. 17x3.

*) f / ■ >-3 ^ i

The CONTENTS.

I. A Catalogue of fifty Plants lately prefented to the
'‘ /Royal Society, by the Company o/Apotheca-
' ries of London 3 purfuant to the Direction' of
- Sir Hans Sloane, Dart, Drejident of the Col-
lege of Phyficians, and Vice-Dreftdent of the
Royal Society.

l ^ ^ ' ' '' tv. i

A

f • • j ■ ^

II. Jnmiadverjtons upon fame Experiments^ relating
' ' to the Force of 7noVmg Dodies 3 with two new

per merits on the fame SubjeCi. Dy the
rend Dr, Defaguliers, F. (Z(. S.

I r-

III. An Account of an Experiment ^ made to afcer^
C tain ■ the ' proportion of the Expanjion of the Li-
quor in the Ihermometerj with Regard to the De-
grees of Heat, Dy Brook Taylor, LL,D.

Yy

IV. An

p»

IV. Jn Account of the ^ttkfnake. the Ho^
nourabk Paul Dudley, F. 5^ S,

y. Some ObferVations upon Vipers 5 on occafion of
the foregoing (Relation. !By C. J. Sprengell,
M.V. F.% S.

.VI* Ohferyations on the Figures of Snow, ©^ the
^Verend Benj. Langwich, ©. D, (F^Eior of
Pec worth in Sufiex. In a Letter to Dr, Jurin,
(2^ S'. Seer.

* V

yil. Ob/erVationes Aurora Dorealis per qiiadrienni^
urn faEi^y Lennae Regis in Korlolcia. Ex
epifiola doEtiffimi Objeryatoris ad Marcinum
Folkes, Arm. F^g, Soc, Vice -Dr

VIII. An Account of a Catadioptrick^ Telefcope, made
John Hadley, Ejq;^ F, S. . M^ith the ©e-

. feription of a Machine contriVd by hhn for the
applying it to ufe. ^

IX. Anatomia fenis decrepiti, annorum 1 op. faEia
Tiguri, die z. Feb. 1723. Jjoh. Jacobo
Scheuchzero, TgurinOy Med. DoEl, Mathefeos,
Dref (^gU Societatis Socio,

\ 1. A

( ^79 y

... • — T '-■'

I. A Catalogue of fifty plants lately frejented to the
Royal Society, by the Company of Apotheca-
ries of London 5 purfuant to the DlreSiion of
Sir Hans Sloan e, (Bart. Trefident of the Col-
lege of Phyficians, and Vice-^rejident of the
Royal Society.

1

The Apothecaries Qi{ London^ having,

in the Year 1673, eflabliftied a Phyfick-Garden,
which they have fince furnifh’d with a great Variety
of Plants, for the Improvement of their Members in
the Knowledge of Botany j Sir Jians Bart.' in

order to encourage and promote an Undertaking fo fer-
viceable to the Publick, has generoufly granted to the
Company the Inheritance of the ^faid Garden, being
part of his Eflate and Manor of Chelfea^ on condition
that it be for ever kept up and maintain’d by the Com-
pany as a Phylick-Garden ^ and as an Evidence of its being
fo maintain’d, he has direded and obliged the Compa-
ny, in Confideration of the faid Grant, to prefent year-
ly for ever to the Royal Society, at one of their weekly
Meetings, fifty Specimens of Plants, that have grown
in the faid Garden the preceding Year, which are all to
be fpecifically diftind from each other, until the Num-
ber of 2000 Plants be completed.

Accordingly the Company ^ did lately prefent to the
Royal Society, by the Hands of Mr. Rand, and Mr.
Meres, the following fifty Specimens of Plants, for the

Y Y ^ laft

( )

laft Year 1722. which Specimens, together with thofe
that are to follow them in fubfequent Years, will, by
order of the Rojal Society^ be carefully preferv’d for
the Satisfaction of fuch curious Perfons, as may delire
to have recourfe to tliem..

The V Catalogue, by Mr. Jfaac Rand,
Apothecary, F. R. S.

I. A Nemone Virginiana^ tertU Matthioli JtmiliSj

flore paryoy Par. Bat. i 8.

II. Sellis Jfrlcana^ capitulo aphyllo luteo, Corompi

folio j caullhiis procumhentibws- H. L. Bat.

III. ^upleurum an^uftifolium. Dod. 633.

IV. Calamintha^ fnagno flore ^ ^ C. B. 2 2p.

V. Cardum capite rotundo tormentofb, C. B. 382.

VI. Chryfanthemum perenne, minus ^ Salicis folio gla-

hro. H. Ox. p. 3.21.

VII. Cirfum altiffimum, alhis maculis notatmn^ fe^

mine Vifcofo. Cardum albis Jiiaculis notatm^ ca^
pitulis- Cirfij. Schol. Bot. 2 1 5.

VIII. Clematitis coerulea ereCtui C. B. 30a.

IX. CkmatiWy f 'Flammula furreSia alba, J. B. 2..

127.

X. Cnicus

(

X. Cnicm feremis coerulem^ Tingitanm, H. L.
. Bat. i6z*

IX. Cony^^ ^Africandy Senecipnis florCy retufis foliis,

H. L. Bat.

XII. Corona Solis altijjlmay alato caule. T. Infl,

4po.

XIII. Cor onilla maritlma glauco folio. T.Inft. ^5^0,

XIV. Cucubalus Tlinij. Lugd. 1429.

XV. T>auctis F(£niculi foliis tenuiffimis, C. Bwi5o.

XVI. ‘Dapicus maritinm lucidus. T. Infi. 307.

XVII. Dens Leonisy foliis Eryfiyjii vulgaris. T..
Cor. 2 5.

^ I

XVIII. Geranium columhinum diffeEtis foliis y pedi*
culis florum longijfmis. Raij Syn. 2 1 8.

XIX. Geranium columhinum perenne Dyrenaicum 77ia^

ximunu T. Inft. 268.

XX. Geranimn pufllum maritimum fupinmny Jlthiece.
aut Detonicie fotioy yiojlras. Raij Syn. 21 6.

XXI. Gnaphalodes Lufitanica, T. Inft. 439...

'XXII. Horminum Syheftre latifolmn. Verticillatunu

C. B. 238.

XXIII. Hypericum perfoliatum ^ perforatum,. T-
Inft. 25 j.

XXIV..

( )

XXIV. Jacea altiffima, folio dijfelio, capite (harit

nudo. D. Vaillant.

XXV. Jacea Lufitanka, femper yirens. H. Reg.
Par.

XXVI. Jacohaea perennis Afplenii folio. D. Vaillant.

XXVII. Lotus pentaphyllos minor hirfutus, ftU^ua
angufiijfmL C. B. 352.

XXVIII. Lunaria yajculo Juhlongo intorto, Raij
Syn. 164.

XXIX. Lychnis Imtfolia torojis ^ laxioribus capitulis.

Bar. Obf. 64.

XXX. Majorana Creticay Ortgani foliisy ViUofay
Satureite odorCy corymhis majoribus albis. T. Cor,
13. Origanum Smyrnaum Whcclcn,

XXXI. Marrubium Hi/panicum fupinuniy foliis

• Jericets argenteis. T: Inft.

XXXII. Tentaphylloides palujlre rubrum. T. Inft.
298.

1

XXXIII. Tentaphylloides fruticoja, Raij Syn.
142.

XXXIV. Thlomis fruticofay Sahice folio latiore ^
rotundiore, T. Inft. 177.

XXXV.

( 3*! )

XXXV. fhlomis fruticoja; SalvU folio lonpore <st'
angujliore, ' T. Inft.

XXX Vi. Thlomis^orientatis lutea^ aiigujltfolia cj-
viis futvejcentihus, D. -Sherard.

XXXVII. ^hlomis Sarnia herhaceay Lmaria foliis,

T. Cor. ^ o.

\

XXXVIII. ^tarmica orientalis pinnulis criftatis,
T. Cor. Jhjinthium Santonicum /Sgyptiacum,
C. B. 319. . '

XXXIX. Quinquefolium album majus alterum. C. B.
3M-

XL. ^ta ChalepenJtSy latifoliay florum petalis y tilts
fcatentibus. H. L. Bat. 431.

XLI. ^bus odoratus, Cornuc. 150.

XLII. Sdarea orientalis y !Betonkie folio acutijjimo,
coma pur pur afcente, T. Cor. 10.

XLIII. Securidaca lutea major* C. B. 348.

XLIV. Thlajj>i Halimi folio y femper Virens. H.
L. Bat. Jlyjfon, T. 217.

XLV. Trtfolium pekatum Creticum, C. B. Prod.
142.

XLVI. Veronica f^icata hirfuta^ folio fubrotundo
jerrato.

XLVII.

(' iS\ "•

■ XLVII* Veronica, multicaulis <Pannonica. T. Inft, i

« 45 • y

. • . . '1
XLVIII. Fir^a aurea floribus fijlulojlsy Seneclonis

injlar^ foliis angujlioribus non ferratis. H, Ox.

p. 3. 1 ly.

XLIX. Virgd aurea angujiifolia, panicula jpeciofay
Canadenjls, H. Reg. Par.

L. Firga aurea altijjimdy ferotina, panicula Jpeciofky
patuld,

f' V - •

V ••

f ; i \

II. Jnimadverfions

•V

( iSf )

/

II. Animadverjions upon fome Experiments reletting
to the Force of 7noVmg Oodles 5 with two new Ex-
permients on the fame SubjeSi, (By the F(eve-
rend Dr, Defaguliers, F. S.

IN a former Paper I demonflrated, by Reafon and
Experiments, that the Momentum^ or Force of mo-
ving Bodies, is always proportionable to their Mafs
multiplied into their Velocity ^ as it is the Opinion of
the greateft Part of the Mathematicians and Philofo-
phers. Now I come to conlider the Experiments, that
have led fome ingenious Men into an Error, in relation
to this Propolition. Polenus in his Book f gives an
Account of his Experiments relating to this Matter,
in thefe Words : “ I took a VelTel, that had in it con-
“ geal’d Tallow fix Inches deep, and fix’d it to a
“ level Floor, in fuch manner, that the Surface of
“ the Tallow, which was flat, fhould every where be
“ equally diflant from the Floor. I had caufed to be
“ made two Balls of equal Bignefs, the one of Lead,
the other of Brafs, the lafl: of which was a little
“ hollow in the middle, that it might weigh but one
“ Pound, whilfl: the other weigh’d two. Sufpending
“ ihefe Balls from the Ceiling by Threads, in fuch
“ manner, that the lighter Ball hung over the Surface
“ of the Tallow, from twice the Height that the hea-
“ vier Ball did I cut the Threads, and the Balls fal-
“ ling perpendicularly upon the Tallow, by their

* Philofoph. Tranf, 3SIo. 375. f Caftellis, pag. 56. No. 118.

Zz “Fall

( lU )

“ Fall made Pits in the Tallow, that were precifely
“ equal : the Ball of one Pound, from the Beginning
“ of its Fall, till it came to reft, going through a Space
exprefs’d by the Number two, produc’d an Effed:
“ equal to that, which the two Pound Ball did pro-
duee, in falling thro’ a Space exprefs’d by the Num-
“ ber one. It follows therefore, that we may look
“ upon it as a fettled Truth, That the adive Forces
“ (vires vivas') of falling Bodies are then equal, when'
“ their proper Weights are in a reciprocal Ratio of
“ the Spaces, which the faid Bodies defcribe by their
“ Fall. And becaufe thefe Spaces are in the fame Ra-
tio^ as the Squares of the Numbers exprefling tlie Ve-
” locities *, it appears by the Experiment, that the
adive Force (vim vivam) of the falling Body, is
“ that which is made up of the Body itfelf, multiplied
“ into the Space defcribed in the Fall, or into the
Squareof the Number, that exprelfes the Velocity of
the Body, at the end of the Motion. This Experi-
“ ment I did not only make once, but feveral rimes,
“ changing the Balls, the Diftances, and the Body on
^ which they fell ^ as for example, making ufe of Clay,
“ or of foft Wax : and notwithftanding thefe various
“ ways of trying the Experiments, the Effeds were
** conftantly the fame j which made me eahly con-
“ elude, that there was always the fame Reafon in Na-
ture for this Phenomenon.

Thus far Rolenus^ whofe Miftake lies in this j that
he eftimates the Force of the Stroke of the falling Balls,
by the Deptlv of the Impreflion made in* the Tallow,
Clay, Wax, or any yielding Subftance. Bur we muft
confider, that when two Bodies move with-equal Farces,
but different Velocities, that, which moves the fwifteft,
muft make the deepeft Impreflion, whilft the floweft

( )

Body communicates its Motion to the Clay round abouti
and therefore does not ftrike in fo deep as the fwifcer
Body, which puts in Motion few Parts of the Clay, be-
fides thofe that are before it, and which Parts have fo
much lefs Time to oppofe this Body’s Motion, as its
Velocity is greater than the other’s. To make this
plainer. Let us fuppofe a Door half open, and moving
very freely on its Hinges ^ if aPiftol be fir’d againfi it,
the Ball will go thro* the Door without moving it out
of its Place*, but if we take a large Weight of Lead,
and throw it againft the fame Door, with the fame
Force as the Pifiol Bullet mov’d, the Door will be re-
mov’d from its Pofition, and carried out of the Place
on its Hinges by the Stroke •, becaufc in the firft Cafe,
the Motion of the Ball is communicated but to a few
Parts of the Door, and in the laft it is diffus’d all
over it. Nay, the Door will be mov’d by the Stroke,
even tho’ there flaould be a prominent Part in the Lead,
that fiiould be no bigger than a Piftol- Bullet, in order
to ftrike the Door upon no more of its Surface, than
the Bullet had done.

For illujirating this farther I contriv'd the following

Experiment,

I caus’d a Machine to be made, as reprefented inP/.I.
Fig, I. confifting of a Bafe of Wood AB, which could
be fet horizontal by means of three Screws, fuch as
SS : Upon this Board, or Bafe, there ftood upright two
parallel Boards, about four Inches wide, and four In-
ches afunder, with the Elbow-piece E F Aiding behind
one of them, fo as to raife its upper End F to any
Height defired. Between thefe Boards, fquare Frames
of Wood GG &c, with Paper extended upon them,
could Aide in, to the Number of Six, in an horizontal
! Z z 2 Pofition,

( 288 ) .

Pofition. Thefe Paper Diaphragms being thus plac’d,
I fufpended an Ivory Ball of about one Inch and an half
Diameter, weighing fomething more than an Ounce
and an half, by a fhort Thread, under F, fo that its
Center of Gravity hung four foot over the firft Dia-
phragm^ then cutting the Thread, the Ball fell upon the
Paper, and by its perpendicular Stroke broke thro’ that
Diaphragm, and the three next under it. Then put-
ting fo much Lead into the Ball abovemention’d, (which
was made hollow for that Purpofe) as to make it weigh
twice as much as it did before ^ and bringing down F,
to let it fall but from one foot, it broke thro’ only two
Diaphragms by its Fall. Making the Experiment fe-
veral times with different Heights, but flill keeping the
Proportion in Height of four to one, when the Balls
were as one and two, the heavy and floweft Ball broke
thro’ but half the Number of Papers. It happen’d
indeed fometimes, that there was fome little difference,
when the Papers were not equally flrong, or equally
flretch’d, but the fwiftefl: Ball always broke through
more Papers than the flow one.

Now tho’ this Experiment does at firft feem to con-
firm Potenus'^ Theory , yet, when duly weigh’d, it
proves no fuch thing. For the lighter Ball does not
break thro’ more Papers, becaufe it has more Force, or
a greater Qu^antity of Motion, but becaufe each Dia-
phragm has but half the time to refill the Ball, that
falls with a double Velocity, and therefore their Refi-
nance being as the time, as many more of them muft
be broken by the fwift Ball, as by the flow one.

P. S. To all the Objeftors, that allow the Force of
moving Bodies, and their Cluantity of Motion to be the
fame, what has been faid in this and my former Pa-
per, feems to be a full Anfwer^ but as there are now
fome Philofophers, who diftinguiflithat Force from the

Qiiantity

( iSp )

Quantity of Motion, I am oblig’d to fay foinething
more for the clearing up of that foint.

If! underftand them right, they call vis viva a Force,
whofe Effed is fenfible, as the Force of Gravity, when it
accelerates Bodies in their Fall j-and vis mortua a Force,
which being deftroy’d, product no fenfible Effed, as
the. Force of Gravity ading upon a Weight in one Scale
of a Balance, when the Weight cannot defcend by rea-
fon of a Counter poife in the other Scale. But certain-
ly no Man, that confiders the thing attentively, would
make that Difiindion. However, lince Polenns allows,
that the Quantity of Motion in Bodies is as the Mafs
multiplied into the Velocity (or MV)^ but fays, that
the Force, with which they ad, which he diftinguiflies
by the Name of vis viva^ is as the Mafs multiplied 'in-
to the Square of the Velocity, or M V V : I have made
the following Experiment to fhew his Notion to be in-
confiftent , tho all the Fbosnomena of unequal Weights
applied to a Statera, fo as to make' an ^Equilibrium,
might ferve for that Purpofe, if it had not been obje-
ded, that the particular Conftrudion of the Machine
hinder’d it from agreeing with the fuppos’d Theorem,
that the Force is as the Matter multiply ’d into the
Square of the Velocity.

EXP ER I MEl^T..

Let two Bails, A and B, (P/.I. Fig, 2.) be joyn’d by a
String, which going thro’ the fmooth Hole C of an even
Table, and under the Pulley P, fufpends a Weight W,
It is plain, that upon letting go the Balls A and B, from
the Places A and B, they will move towards C with
the fame Force, becaufe each of them will be drawn
towards C by half the Force of the Weight W, whe-
ther the Balls be equal, or unequal.

I. The

( 2P0 )

1, The Balls being of two Ounces each (of Ivory),
were, at the fame injftant of Time, let loofe from A and
B, each diftant twelve Inches from C, and both came
to C at the fame Time. Here the equal Forces will
agree with the Produd of the Maifes into the Veloci-
ties, or into the Squares of the Velocities ^ becaufc
AkI2:::z:Bxi2, as well as Ax 144 is equal to
Bx 144,

2. If A be taken of four Ounces Weight, and let go
from D, or fix Inches, whilfl: B, frill equal to two,
moves from 1 2 Inches , both Bodies will again meet at
C : therefore here the equal Forces muft be exprefs’d by
theMafies into the Velocities, and not into their Squares *
for tho’ A X 6 be equal to B x 1 2 (4 x 6 zr: 2 x 1 2),
A X 6 X 6, or 144 is but half of Bx 12 x 12, or 288.
Whereas if the Forces had been as Folenus affirms, B
fliouid have been let loofe only from 8,4 Inches.

5. When A is fix Ounces, it is let loofe only from
E, or 4 Inches, to meet at C with B let loofe from 12^
for then Ax4~ B^xi2, whilft AX4X4, or 96, is
three times lefs than Bx 1 2 x 1 2, or 288. So that ac-
cording to Folenus, B raufr have been let loofe from 7 ,
but in that Cafe it comes fooner to C than A.

"N. B, The Weight W muft be greater than the
Weight of both Balls, leaft the Fridion of the Table
fhould fpoil the Experiment.

c

III. An

( ipi )

III. Account of an Experiment^ made to afcer--
tain the proportion of the Expansion of the Li-
quor in the Thermometer^ with Regard to the De-
grees of Heat, Dy Brook Taylor, LL.D,
T(,S.S.

IT has, I believe, been generally fuppofed, tho’ not
proved, that the Expanfion of the Liquor in the
Thermometer, is proportional to the Increafe of Heat,
To determine this Matter with Certainty, I made the
following Experiment.

I provided a good Linfeed Oil Thermometer, which
I marked with fmall Divihons, not equal in Length,
but equal according to the Capacity of the Tube in the
feveral Parts of it, as all Thermometers ought to be
graduated, f likewife provided two VelTels of thim
Tin, of the fame Shape, and equal in Capacity, contain-
ing each about a Gallon. Then (obferving in every
Trial, that tile Veifels' were cold, before the Water was
put in them, as alfo that the VefTell meafured the hot
Water with, was well heated with it) I fucceflively
fill’d the Vefiels with one, two, three, &c. Parts of
hot boiling Water, and the reft cold ^ and at laft with
all the Water boiling hot^ and in every Cafe I iminer-
fed the Thermometer into the Water, and' obferved^to
what Mark it rofe, making each Trial* in both' VelTels
for the greater Accuracy. And having; firft obferved
where the Thermometer ftood in cold Water, I found
that its rifing from that Mark, or the Expanfiomof the
Oil,, was accurately proportional to theCiiiantity ofhot
Water in the Mixture, tliat is, to the Degree of Heat.

I IV, An

IV. Ayi Account of the (^ttlefnake, . , (By the Ho->
nourahle Paul Dudley/ ^^3 F.B^S* , ■ v

The Rattlefnake is reckoned by xhe Al^-orr^ines,
to be the moft terrible of all Snakes, and the
Mailer of the Serpent-kind 3 that which caufes their
Terror, without doubt, is their mortal Venom, and the
Enfign of it is their Rattle 3 and it is moll certain, that
both Men and Bealls are more afraid of them, than of
other Snakes 3 and while the common Snake avoids a
Man, this will never turn out of the Way.

There are three Sorts, or Kinds, of this Snake, and
dillinguilhed by their Colour, viz, a yellowilh Green,
a deep Alh Colour, and a black Sattin.

The Eye of this Creature has fomething fo lingular
and terrible, that there is no looking lledfallly on him 3
one is apt, almoll, to think they are polfell by fome
Demon.

A Rattlefnake creeps with his Head clofe to the
Ground, and is very flow in moving, fo that a Man
may eafily get out of his Way: This ought to be re-
marked as an Inllance of the Goodnefs of God, who
preferves Man and Beall. His leaping and jumping to
do Mifchief, is no more than extending, or uncoiling
himfelf 3 for they don’t remove their whole Body,
as other Creatures do, when they leap 3 fo that a Man
is in no Danger of them, if his Dillance be more than
their Length 3 neither can they do any Harm when
they are in their ordinary Motion, until they firll coil

and

{m )

and then extend, or uncoil themfelves, but they both
are done in a Moment’s Time.

When a Rattlefnake refts, or lleeps, he is coiled, and
they are obferved to be exceeding fleepy.

Our People at firft took the Noife this Creature
makes, to be owing to fome little Bones, or hard loofe
Kernels lodged in their Tails ^ butfoon difcovered their
Miftake, and found the Tail to be compos’d of Joints,
that lap over one another, fomewhat like a Lobfter’s
Tail *, and the ftriking them one upon another, forms
that Noife, which is fo terrible to Man and Bead. The
fierceft Noife is obferv’d to be in clear fair Weather,
for when ’tis rainy, they make none at all ^ for which
Reafon, the Indians don’t care to travel in the Woods,
in a Time of Rain, for fear of being among thefe Snakes
before they are aware. One other Circuraftance of their
rattling has been obferv’d, to wit, that if a (ingle Snake
be furprized and rattles, and there happen to be others
near him, they all take the Alarm, and rattle in like
manner.

I dare not anfwer for the Truth of every Story I
have heard, of their charming, or Power of Fafcination ^
but yet I am abundantly fatisfied from many WitrtelTes,
both Englijh and Indian^ that a Rattlefnake will charm
both Squirrels and Birds from a Tree into his Mouth.
A Man of undoubted Probity fometime (ince told me,
that as he was in the Woods, he obferv’d a Squirrel in
great Diftrefs, dancing from one Bough to another, and
making a lamentable Noife, till at lad he came down
the Tree, and ran behind a Log : The Perfon going to
fee what was become of him, fpied a great Snake, that
had fwallow’d him.

And I am the rather confirmed in this Relation, be-
caufe my own Brother, being in the Woods, opened one
of thefe Snakes, and found two drip’d Squirrels in

A a a his

( )

his Belly, and both of them Head foremofl'. When
they charm, they make a hoarfe Noife with their
IVlouths, and a loft Rattle with their Tails, the Eye at
the fame time fixed on the Prey.

Their general Food confifts of Toads, Frogs, Cric-
kets, Grafshoppers, and other Infeds, but principally
of Ground Mice , and the Rattlefnake again ferves for
Food to Bears, and even our Hogs will eat them with-
out Harm.

They are viviparous, and bring forth generally about
twelve, and in the Month of June, A Friend of mine
in the Country, being defirous to difcover the Nature
and Manner of the Generation of the Rattlefnake, gave
me the following Account, vi^. About the middle of
Maj, the Time when the Rattlefnakes firfi: come a-
broad, he took and opened one of them, and in the
Matrix found twelve fmall Globes, as big as a common
Marble, in Colour like the Yolk ofanEgg^ in three
or four Days more, he took and opened another, and
then plainly perceived a white Speck in the Centre of
the yellow Globe ^ in three or four Days more, he dif-
feded a third, and difcovered the Head of a Snake ^ and
in a few Days after that, three Quarters of a Snake was
formed, and lying round in a Coil. In the latter End
of June, he kill’d an old one, and took out perfed live
Snakes of fix Inches long. In September, when the
old ones take their Young in, and carry them to their
Dens, they are not quite a Foot long. They couple
in Aiigufl, and are then mofi: dangerous.

I cannot fay, what other Serpents, or poyfonous Crea-
tures, may do, but I am fatisfied the Rattlefnake does
not trajed his Poyfon j and that unlefs the Skin be firfi:
broke, or an Incifion made with his Teeth, his Venom
can dp no Harm ; for my Friend alfured me, that he
had made an Elxperiment of it in this manner: He took

f *95 )

the Breech of his Gun, and fet it upon four or five of
them, and after they had bit it, and left feveral Drops,
of their Poyfon, he with his Hand wiped it off with-
out any Harm.

Our People have feveral Remedies for the Sting of a
Rattlefnake ^ among others, that which is much made
ufe of, is a Root they call Blood-root, I fuppofe fo na-
med, from the Colour of the Root, and the Juice, which
is red like Blood. It grows in great Abundance in our
Woods 5 they bruife the Root, and bind it above the
Place that is bit, to prevent the Poifon’s going farther,
at the fame Time fcarifying the Place affected ^ fome
of the Root is alfo boiled, and the Perfon poifoned drinks
the Water.

They are generally from three to five Feet long, and
do not commonly exceed twenty Rattles ^ and yet I have
it attefted by a Man of Credit, that he killed a Rattle-
fnake, fome Years fince, that had between feventy and
eighty Rattles, with a fprinkling of grey Hairs, like
Bridles, over his Body ^ he was full five Foot and an
half long, and as big as the Calf of a Man’s Leg.

They fhed, or throw off their Skins every Year,
fometime in the Month of June, and turn it infide out
when they throw it off. It has alfo been obferved, that
the Skin covers not only the Body, but the Head and
Eyes.

They generally den among the Rocks in great Num-
bers together •, the Time of their retiring is about the ^
middle of September, and they don’t come abroad till
the middle of May, when our Hunters watch them, as
they come out a funning, and kill them by hundreds.

%

Roxhury, New-England,

O6iob.2$> 1722.

A a a 2

Raul Dudley,
V. Some

( 19^ )

y» Some Ob/erVations ufon Vipers 5 on occajton of
the foregoing (Illation. C. J. Sprengell,

M. D. F. ^ S*.

At Milan I found a Viper-Catcher, who feldom was
without 60, or more. Vipers alive, kept together
in a back Room open at the Top he had them from all •
Parts of Italy, and fold them dead or alive, according
to the Ufes they were defigned for. He having got one
day a female Viper big, with young, gave me notice
to fee her manage her Prey, whereupon we catch’d
fome Mice, and throwing them in one at a Time,
amongft all that Number of Vipers, (which were ra-
ther above 60) there was none of them, that in the
leaft concern’d himfelf about the Moufe, tilh the laft
mention’d pregnant female Viper and the Moufe inter- -
changed Eyes ^ whereupon the Moufe flartled, but the
Viper rais’d her Head, and turn’d her Neck into a per--
fed Bow, the Mouth open, the Tongue playing, the
Eyes all on. Fire, and the Tail ered. The Moufe
feem’d foon recover’d of his Fright, would' take a.
Turn, or two, and fometimes more, pretty brifldy,
round the Viper, and giving now and then a Squeak,
would run with a great deal of Swiftnefs into the Chops
of the Viper, where it gradually funk down the Gullet.
All this while the Viper never flirr’d out of its Place,^
but lay in a Ring.

It is to be obferv’d, that no Viper will feed, when,
confin’d, except a female Viper impregnated.

The

( i?7 )

The fame I faw at BruJJels^ where a Soldier had
catch’d a large Viper big with young. The Houfe, where
I and fomeof my Companions lodged, was near theFilh- •
Market, where my Landlord had a Sow, and five fmall
Pigs of nine or ten Days old. We got one of the Pigs,
which we caus’d to be bit by the Viper in the Tail,
and in four Minutes time chopp’d off the Tall, the Pig
appearing to be lick and dizzy, and the remaining part
of the Tail being fwell’d , but I believe the bleeding ,
fav’d it, for the next Morning it was well again. The •
fame happen’d to another Pig, which we had got bk im
the fore Foot, and flaying feven Minutes after the Bite,
cut off his Leg about two Inches above the Bite. Af- -
ter thefe two, we took the other three, and had them
bit in feveral Places, whereof two died that Night,
and the third recover’d, we having given it, about*
five or fix Minutes afterwards, ten Grains of Emetic
Tartar.

This I try’d afterwards upon Dogs bit by Vipers,
and I found that they all recover’d ‘upon the Emetic-..
Tartar...

V

VI. Ohfer^

( )

A

VI. ObferVations on the Figures of Snow, the
(I(e'rerend Benj. Langwith, T>. T>, ^Hor of
Petworch in Suffex. In a Letter to Sr. Jurin,
5^. S. Seer.

ON the 30th of January laft, fomething paft Nine
in the Morning, Weather cold, Wind South-
wefterly, but not very high, Barometer above thirty
Inches, I faw that pretty Phenomenon of the Star-like
Snow, and tho’, upon comparing my Obfervations af-
terwards with thofe of Defcarter, Dr. Grew^ and
Mr. Morton^ I find I have but little to add upon the
Subjed ^ yet, as I obferv’d the Progrefs of Nature in
this fort of Cryflallization, with a great deal of Plea-
fure, I hope it will not be difagreeable to you to re-
ceive an Account of it.

I fhall begin with the moft fimple Figures A and B,
(VI. I. Fig. 3.) of which the former is a roundifh Pellet
of Ice 5 thefecond, a fmall oblong Body, with parallel
Sides, which is often as fine as a Hair. Of this latter
kind the Flakes of Snow chiefly confift, and tho* they
look white to the Eye, yet when view’d with a fmall
Magnifier of a Microfeope, they appear like fo many
tranfparent Needles of Ice thrown together, without any
Manner of Order.

The next Figure is C, in which the Pellet has fiiot
out fix of thofe final! Bodies of equal Length, and fet
at equal Angles : Of this kind I faw a confiderable
Number,

The

( m .

The next Step in the Cryflallizatlon is D, in which
thofe Bodies are lengthen’d, and have fliot out a great
many more from their Sides, at equal Angles, but une-
qual Lengths, as growing continually Ihorter and fhor-
ter, till they terminate in a Point : I meafur’d fome of
thefe, and found them to be about one quarter of an Inch
in Breadth. I faw but very few of them in Perfedion,
for the collateral Shoots were fo exquifitely fine, as to
be liable to be broken in their Fall, or confounded to-
gether by the leaf: Degree of Heat.

Of the next kind, E, I faw a very great number,
which being examin’d by the Microfcope, plainly ap-
pear’d to be nothing but the former in Diforder. The
Edges of thefe were in general very irregular, but fome
of them happened to be fo indented, as to look like the
jagged Leaves of Plants.

The next Kind, F, had twelve points regularly difpo-
fed, and probably might confifi: of two of the former
fo join’d together, as to cut their Angles equally.

Perhaps alfo thofe Mr. Morton defcribes, as confiding
of Raciiii which, inftead of terminating in a Point, grow
bigger, as they advance from the Centre, might be for-
med from-two of the Kind, C, fo join’d at the Centre, as
to cut each other’s Angles unequally *, for in the Pro-
grefs of the Cryftallization, thefe Radii would quickly
unite.

Laftly, that Sort, which Defeartes compares to Rofes,
and of which he has given a Figure in his Treatife of
Meteors, may be nothing but the Kind E, when the
Points are rounded off, by being gently thaw’d.

I propofe thefe things only by way of Conjedure^
becaufe, as the final I Drops of Water may be impreg-
nated with very different Particles in the Air, it is not
eafy to determine, whether thefe Figures may not be the

Refult

I

( J®0 )

Fefult of a Cryllallizaticn quite different from the
former.

i had almoft forgot to tell you, that I faw but very
few Figures of twelve Points, andthofe moftly iinper-
fed in one refped or other.

Petmrth^ Feb,i^^

urn faB^e, Lennae Regis in NorfoJcia* Ex
epijlola Obferyatoris ad Marcinum

Folkes, Arm. Soc, Vtce-F^rdf.

ON ingratum fore arbitror, Vir Dodillime, obfer-

vationes quafdam de Aurora Boreali, apud Len-
nam Regis in Norfolcia, quatuor fuperioribus annis a
me habitas tibi impertire. Miruin illud Ph^enomenon
fexto Martii 171I. non iicuit mihi infcicnti videre, quod
infortunium baud exiguum in me peperit ftudium
fubfequentibus Phaenomenis invigilandi, Priorem ob-
- fervationem, quam hie fubjeci, fumma cura delinea-
vi, ftatim atque vidi, ideoque, ni fallor, a vero parum
diicrepat. Reliquas etiam deferiptiones pro certo
habeas accuratas elfe. Qusnam fit caufa harum coru-
fcationum, nondum, ut opinor, fatis exploratum efl.

Die Veneris Sept. 5. 1718. circa hor. x. Phasnome-
non hoc, delineatum PI, I. Fig, 4. obfervatum fuit Len-
n^e Regis, in pundo boreali.

Die

^ )

Die Saturni Sept. 6. circa horas viii 5C x. perplures
Luminis coluranai, fimiles fupradefcriptis ( a a) obfer-
vabantur, non asqiie lucid* ac pyramides node praece-
dente obfervatas, qu* ferebantur verfus orientem, h*
vero ad occidentem.

Die Jovis Sept. ii. perplures iftiufmodi column*
iterum confpiciuntur cum motu occidentali.

Die Saturni Sept. 13. circa horam xi. Aurora Bo-
realis lucidior ac altior fuit, longioribufque pyramiJibus
adornata, quam adhuc obfervata fuerat. Adeo lucebat
hac node, ut charaderes. in libro legerentur.

Die Saturni vero Odob. 1 1. circa horas x -6c xi. Au-
rora Borealis lucidior quam unquam fuit, ac corufcatio- .
nibus pyramidalibus interfperfis, haud multum abli-
milis Phsenomenopriusobfervato, Sept. 5! Lumine ite-
rum ita fplendente, ut legere liceret.

Die Veneris Dec. 19. circa horas vin Sc ix. Hie
node vili funt cum Aurora Boreali perplures lucis radii,
e nube veluti nigra exorientes revera autein non fuilfe
nubem exinde patet, quia dell* per illara dare videban-
tur. Quid vero aliud fuerit,haud facile eft dldu. Sed
quod pr*cipue notavimus, fuit motus horum lurainuin
fane mirabilis. Hos radios obfervavimus inftatu femper
mobili, politiones fuas, feu loca, perpetuo mutantes j cur-
fum fuum modo hac, modo iliac, rurfum, prorfum diri-
gebant, dc interdum alii ex aliis eadein via lingulatim
progrelli funt, dC aliquandiu fibi invieem collihone mu-
tua impingebant cum tremulo ac vibrante motu, 3c ce-
leritate fereincredibili. Radii quidam obfervati funt uf-
que ad Zenith fe porrigentes. Vifa eft f*pe lux fe in a-
cervum collegilTe, atque ita mirum exhibuilfe fulgorem
coloribus Iridis tindum, 6c iterum vifa eft fe dilaiiife.
Luna hie node lucide fplendebat.

Die Jovis Martii 1 2. 1 77I. circa horas x 6c xi. Au-
rora Borealis rurfus obfervabatur. .

B b b Die

( )

Die Veneris Martii 27. iterain vifa eft Aurora Bore-
alis cum radiationibus variis obliquis, fcundum hanc
Figuram. PI, I. Fig, 5.

Die LunseOdob. 26. 171^. hie node etiam vifa eft
circa horas vii 6c viii.

Item die Lunse Nov. 9. 1719.

Die Domin. Jan. ult, 17M. Hie node, ab hori fepti-
mi ufque ad decimam, Aurora Borealis vifa eft altior,
quam iinquam antehac obfervata fait, per dimidiumcoe-
li ab oriente ufque ad occidentem, fere obduda corufea-
tionibus variis interfperfis, adeoque lucebat, ut charade-
res in libro perquam diftinde videri polfent.

Die Saturni Sept. 17. 1720.

Die Lunas Jan. 6, 17*“. circa horas vii 6c viii. vifa
eft iterum Aurora Borealis cum corufeationibus pyra-
inidalibus, undique a Zenith, veluti centro, obdudis,
imaginem exhibentibus paene inftar Umbell^e.

Die Domin. Jan. ix. 172^.

Die Luns Sept. 1 1. 1721.’ circa hor. ix.

Die MercuriiSept. 5. 1722. ab hori decimi ad fefqui-
decimam.

Die Mercurii Odob. 5. circa hor.ix.

Die Jovis Odob. 4. circa hor. x.

Die Domin. Dec. 23. 1722. circa hor. viii.

VIII. Jn

( }0} )

yiii. Jn Account of a Catadioptrick^ TelefcopCy made
by John Hadley, F. 5^. S. With the 2)e-
fcription of a Machine contriv'd by him for the
applying it to ufe.

The Inftrument confifts of a metalline Speculum,
about fix Inches in Diameter. The RaJius of
the Sphere, on which its cone ive Surface was ground,
is ten Feet, five Inches and one quarter, and confequent-
ly its focal Length is 62 i Inches. The Back has a
hollow Screw made at its Centre, to receive the End of
a Handle, which is ferew’d on, whenever the Metal is
to be moved, in order' to avoid fullying its polilh’d Sur-
face by handling.

This Objed-Metal A, PL WFig, i. is placed in one
End of an odangular Tube, B B, about fix Feet long, and
fomething wider than what is fufficient to receive the
Metal, dyed black on the Infide. About fix or feven ^
Inches in -Length of the three uppermofl Sides of the
Tube C, (toward thatEnd, at which the Metal is plac’d)
are feparated from the reft, and open with two Hinges,
to make room for the Metal to be put in and taken out.
The End of the Tube is clofed by an odangular Piece
of Board D, which has an opening d, about 1 of an Inch
broad, from the Top down to a little bel )w the Centre,
to giv^e room for the beforemention’d Handle, when
the Objed-Metal is lifted into or out of the Tubc^ at
Other times it is clofed with a Aiding Shutter. The

B b b 2 Metal

( 3°4 )

Metal is placed fo, as to have its Axis coincide with that
of the Tube, by the means of three fmall Buttons fix’d
to the Infide of the Tube, having their hinder Ends all
in the fame Plane, to which this Axis is perpendicu-
lar. Two of thefe appear at a a, the third being at the
middle of the Bottom of the Tube, is not feen. The
forefide of the Metal refts againft thefe Buttons in three
Points of its Circumference, nearly equidiftant from
each other, and is held to them by three Screws, (one
of which appears at which run through the odaii-
gular Board at the End of the Tube, and bear againft
the Back of the Metal, (in three Points, whicli diredly
anfwer thofe three on the forefide) with juft fo much
Force, as is requifite to keep it fteady in its Place. They
muft not be fcrew’d harder againft the Metal for Fear
of bending it, which (tho’ it is half an Inch in Thick-
nefs) a very little Force is fufficientto do. When the
Inftrument is not ufed, thefe Screws are loofen’d, and
the Objed-Metal is taken out and laid by, to prevent
its tarnilhing.

The oval Plane is compos’d of a Plate of the fame
Metal with the great Speculum, about rf or of an
Inch in Thicknefs, folder’d on the Back to another
ofBrafs. Its Breadth is fomething lefs than half an
• Inch, and is in Proportion to its Length as i to v' 2. At
one End of the Oval, the Brafs Plate projeds a little be-
yond the other, and has a Screw cut through it in that
Part, as likewife another diredly againft the Centre of
the forefide. The other End is cypher’d away on the
Backfide, that it may intercept as few of the Rays, in
their PalTage towards the Objed-Metal, as is poflible.
The two Screw-holes in the Back ferve to fix this Oval
A, fig, 2. to a Brafs Arm, B, which is faftened at
the other End into a Slider EE. Bg* i. and 2. This

Slider

( )

Slider is of an equal Thicknefs with the- Side of the
Tube, and has a Groove, G G, F/^. i. cut for it in that
Side, parallel to the /^xis, and long enough to give
room for its Motion, to fet the two Specula at the diffe-
rent Dilfances, which the feveral Eye-Glafles require.
It. refts on the Infide againft two thin Ledges, faftened
within the Tube along the Sides of the Groove. On
the Outfide it is kept in its Place by a Aiding Shutter,
not expreffed in the Figure. In the Middle it has a
Cyliiidrick Cavity, D; Fig. 2. whofe Axis is exadly
perpendicular to its inner and outer Surfaces. Each of
the Boxes, in which the Eye-GlalTes are contained, is
fitted to this Cavity. The beformention’d Brafs Arm
is fix’d into the Infide of this Slider, towards the End
fartheft from the Objed-Metal ; it rifes perpendicular
for about two Inches, and is made flat, fo as to turn one
Edge to the Rays, which come from the Objed. About
it is bent forwards and flatted the other Way, fo
that when the Back of the oval Plane is held flat to it;
by the two Screws c c, the Axis of the Cyliiidrick
Cavity may fall on the Centre of its forefide, inclin’d
to its Surface in an Angle of fomething lefs than fourty
five Degrees. This Angle is brought to be exad by
two very final! Screws, / i, whofe Threads take hold
in the flatted End of the Brafs Arm, and their Points
bearing againft the Back of the Oval, raife one End of it-
a little from the flat of the Arm. ‘ The Specula are fet
at their due Diftance, by turning of a long Screw, C C, .
for which there is a Nut lodged in the Slider at^ *, the,
Screw is- kept from moving backward or forward, when
’tis turned, by a Brafs Plate,- F, which is to be fix’d to
the flat End of the Side of the Tube, and.taken off at
Pleafure. Each of the Eye-Glafs Boxes^ H, has a
Screw on the outward End, to faften to it a . Bowl, or

Difh

( ^o6)

Difli, I, to receive the Ball of the Eye, and guard it
from external Light,

On the Top of the Tube is fix’d, on two final! Pede-
ftals, a common Dioptrick Telefcope, H, Fig, i, about
cighteeen Inches long, its Axis parallel to that of the
Tube ^ and having two Hairs plac’d in the common
Focus of its Objed and Eye-GlalTes, crofling one an-
other in its Axis,

There are three convex Eye-Glafies belonging to the
Inflrument, The firft, or fhalloweft, has its focal Di-
ftance of about j of an Inch , the fecond, of -A •, and
the deepeft, of or fomething lefs. When the firft
of thefe is ufed with the Inftrument, it magnifies about
1 88, or 190 times, in Diameter ^ with the fecond, about
208 ; and with the third, 228 or 230. Each of thefe
GlalTes has placed, in that Focus neareft the Oval, a
Circle to determine the Part of the Objed feen at one
View^ and in the other Focus toward the Eye, a Brafe
Plate with a little Hole in the middle, to let no Light
pafs to the Eye from the Infide of the Tube, but what
comes from the Oval. Befides thefe three convex, there
are two concave E}^e-Glaires, with which it magnifies
about 200 and 220 times ^ and alfo a Sett of three
. Convex, which turn it into a Day Telefcope, magni-
fying about JL25 times. The Aperture is limited by a
Circle of Card, or Paftboard, placed before the Ob-
jed-Metal in the Tube. To vary the Aperture there
are three of thefe Circles, and the Apertures allowed
by them are five Inches and an half, five Inches, and
four and an half, tho’ for fome Objeds the whole Me-
tal may be left open.

The Engine made ufe of to dired the Tube to any
Objed, confifts of a ftrong Plank, FF, Fig, i.and^.
about fourteen Inches wide, and two Feet and an half,
or three Feet long, which ferves as a Foundation for

the

( 107 )

the whole. Near one End of this Plank is placed an
upright fourfided Box, III, Fig, i. and 5. about two
Feet high, narrower at the Back next the End of the
Plank than before : Its two Sides are mortifed both in-
to the Plank below, a a, Fig,^, and into the Top of
the Box above, dd'^ the back and fore Part are faften’d
to the Edges of the Sides with Wood-Screws. The
Top has a circular Hole cut in it, fomething above
three Inches in Diameter, whofe Centre is about three
Inches diftant from the outhde of the Back, and at an
equal Diftance from the two Sides. This Hole gives
PafTage to a turhing Pillar B, in the Bottom of which
there is fix’d an Iron Pivot to turn* in a thick Brafs
Plate lodged in the Plank, b. The upper End of the
Pillar rifes about an Inch and an half above the Top of
the Box, and is mortifed into a ftrong Head, K, Fig, i..
and 3. about eight Inches in Length, and four or five in
Breadth and Thicknefs. This Head carries two Cheeks,
L L, about thirteen or fourteen Inches in Height, their
hinder Edges, towards the lower End, extending five In-
ches beyond the Axis of the Pillar backward. ufVlong
the Back of thefe Cheeks, at equal Diftances above one
another, there are Notches, tending obliquely down- •
wards, and anfwering one another in each Cheek, to >
receive the Pivots of a crooked Iron Axis, C, Fig. 3.
on which the Tube is plac’d. The Notches are made
at different Heights, to keep the Eye-Glafs at a proper '
Height for the Eye, in different Elevations of theOb-
jed above the Horizon. The Figure of the Axis an- •
fwers that of the three under Sides of the Tube. The
of the Tube lies about two Inches and an half
higher than the Axis of the Motion upon thefe Pivots,
and the Centre of Gravity, when the Cbjed-Metal is in,
is about three Inches backwarjer. To keep the Tube
from flipping back, when its fore End is raifed, it has

( jo8 )

two Buttons fixed to it, which reft againft the fore Part
of the Axis.

To keep the Pillar from touching any of the Sides
of the round Hole, in which it turns, a Cylindrick
Sedor, containing about 65° or 70°, and about an Inch
in Height, is cut out on the back Part of the Pillar, near
the upper End D. In the fquare Angle of this Cavity
is fix’d a thin Steel Plate 00, bent crofs the middle to
the fame Angle. The internal angular Edge, between
the two Parts of this Plate, lies in the Axis of the Pil-
lar, and turns upon the harden’d Edge of a Wedgelike
Iron, f\ whofe Bafe, or Board Part, is faften’d with
two ftrong Screws on the Top of the Box, diredly
behind the round Hole beforemention’d.

The upper Parts of the Cheexs are ftrengthened by
two Brackets, GG, leaving Room between them for
the Bottom of the- Tube to touch the upper Edge of
the fore Part of the Head. The hinder Part of the
’Head is alfo hollow’d, in the Manner reprefented in the
third Figure.

The Head on its fore Part carries a flat Arm, M,
Fig. I. about twenty feven Inches long, a little taper
• towards the farther End, where it is four Inches broad.
This is ftrengthened by a narrow Slip, glew’d edge-
wife a longthe middle underneath, O, and aUb by a Brace
or Stay, N, reaching from the turning Pillar to within
nine Inches of the End of the Arm. The Stay paffes
through a tranfverfe opening cut in the fore Part of the
Box, P, which is long enough to allow room for a fuf-
ficient Motion of the Pillar round its Axis.

On the other End of the Bottom Plank, tranfverfely
to its Length, is erefted a Board about twelve Inches
wide, and twenty fix or twenty feven high, Q_, the
Top of it reaching within an Inch and an half of the
under Side of the Arm. -This Board is held firm in its
I Polition

( 30? )

Portion by a Spur, R, part of its upper End on the
outlide is pared off toward the Edges, to form it into
the Segment of a Cylinder, whofc Axis coincides with
that of the Pillar. Its Ufe is to fupport a Reft, S3, on
which the End of the fiat Arm moves backward and
forward. This Reft being apply’d trarifverfely to the
outer Part of the upright Board, where it is made Cy-
iindrick, is bent into the fame Figure, by the means
of four Screw-Pins, two of which pafling through each
End of this, and of another Piece of the fame Length, T,
(but fomethiiig narrower) placed over agaihft it on the
infide of the Board, by their Nuts, draw them together,
fo as to grafp the End of the upright Board between
them the upper Edge of the Reft being firft (hot with
a Plane very ftrait and fmooth. To render the Mo-
tion of the Arm along the Reft fmooth and eafy, it
has two Rollers lodged in a Box fix’d near to the End,
on its underfide, V, to roll upon the Edge of the Reft,
when the End of the Arm is moved along it. One of
the Rollers is placed near each Edge of the Arm, and
their Axes lye in Lines paffing through the Axis of the
turning Pillar. The Reft is kept up to them, with a
proper Degree of Force, by two Screws, W W, which
run in two Plugs, XX, faftened on the Sides of the up-
right Board, and bear againft the under Sides of two Pieces
hx’d on the Infide of the Reft.

The Motion of the Tube is governed by two Brafs
Pegs, Y and Z. The firft of thefe, Y, is plac’d about
10 or II Inches from the End of the Arm, and has a
Line wound round it, which pafling under a fmall Pul-
ley, f, fix’d in a vertical Pofition near the End of the
Arm, is faftened to a Staple on the under fide of the
Tube g. This Line, by the turning of the Peg, brings
the fore End of the Tube to its due Elevation, being
aded againft: by the Excefs of Weight in the hinder End

C c c of

( ?’0 )

of the Tube, when the Metal is in it, which is equivalent
to about two Pound at where the Line is faflened*
In great Elevations of the Objed above the Horizon, the
Line is not carried fo far as the Pointy, but is faften’d
a little above the Pulley, to a light fquare Stick,
having at one End a Hook, by which it takes hold of
the Staple g. This is done, that the Springynefs of the
Line may not continue a vibrating Motion in the Tube,
(when any thing happens to fhake the Inftrument) and
make the Objeft appear to tremble. The lower Part
of the Stick refts againft the end of the Arm, and by
its flight Fridion contributes to the fameEffed.

The other Peg, ss, is fo plac’d, that it may be con-
veniently reached by one Hand of the Obferver, while
the other is employed about the Peg Y : It regulates the
Horizontal Motion of the Tube, by means of a Line,
which being wound about the Peg at one End, paffes
by another fmall Pulley placed clofe by the Side of the
aforementioned one in an Horizontal Pofture (not to be
feen in the Figure) and is hung on a Pin driven into
the little HeadK. It is aded againft by two Springs, m
andw Fig, 5. placed in the Box, III, one on each Side
of the turning Pillar ^ that on the right Hand, w, draws
the right Side of the Pillar forward, by a very ftrong
Line, which being faftened to the Head of the Spring,
palTes round the back Part of the Pillar to a Pin, at P,
by which it is drain’d to its due Strength, The Spring
on the Left Hand », draws the Left Side of the Pillar
backwards in the fame manner. Thefe Pins are plac’d
on the Pillar a little higher than the Tops of the Springs,
that being drawn a little downwards, as well as turn’d
round its Axis^ the Pivot in its Bottom may not be
raifed out of the Hole in the Brafs Plate, when the Reft
bears hard againft the Rollers at the End of the Arm.
&ich of thefe Springs draws with a Force equal to about
■ 18

( 3»> )

1 8 or xo Pounds Weight, when the End of the Ann
is carried clofe to the fmall Head^, Fig. i. and confe-
quently (the Semidiameter of the Pillar being an Inch
and Half, and the Diftance of that Head from the Axis
about 28 or 29 Inches) the End of the Arm will be car-
ried by the united Forces of both the Springs, towards
the other End of the Reft, with a Force equivalent to the
Weight of about two Pounds. Each of the Pegs, Y and Z,
turns in a Hole made in a Piece of Wood /, faftned to
the under Side of the Arm ^ and the Pieces being flit with
a Saw from one End through the Hole, and about half
an Inch beyond it, the feparated Parts are drawn to-
gether by a Skrevv w, till the End of the Peg is griped
between them, with a due Degree of Force. By thefe
Pegs, with the help of the Telefcope H, the Tube is
eafily direfted to any Objed, and made to accompany
a Celeftial one in its Diurnal Motion, while the End of
the Arm moves the whole Length of the reft.

If it be deflred, that when the Objed is found, the
turning of one Peg fliould carry the Tube along with
the Motion of the Heavens, fo as to keep the Objed al-
ways in fight 5 this may eafily be effeded in various
Manners.

The concave Surface of the Objed-Metal has many
little Spots in it, which could not be brought to take
a Polifh. In one, or two Places, the Metal itfelf
feems to have fome fmall Parts, fomething harder or
fofter than the reft, occafioning an irregularity in the
Figure of the Metal about them. But thefe Parts being
fmall, in Proportion to the whole, do not feem confi-
derably to affed the Diftindnefs of the Appearance.

The open Air has commonly an undulating Motion
in* its Parts, efpecially in the daytime, which occafions
the Rays of Light to defied a little from theftrait Lines,
in which they ought to move, in order to render the

C c c 2 Species

'( Jtl )

Species perfedly diftind. The EfiFed of this, though
infenhble to the naked Eye, or even through a final I
Telefcope, becomes confderable, when the Objed is
very much magnified. The Inftrument, when try’d at
an Objed enclofed, fo as to fecure it from this Inconve-
nience, feems to bear an Aperture of five Inches and an
half, with the deepefl oftheforementioned Eye-Glalfes,
as well as the common Telefcopes do the ufual Charge
and Aperture given to them, except that in thefe the
Objeds appear a little brighter.

Fig, 1. Reprefents the Infirument placed on the Ma-
chine, in order to be apply ’d to Ufe.

Fig, 2, Reprefents the Infide of the Slider, with the reft
of the Apparatus belonging to the oval Plane and
Eye-Glafs.

Fig, Reprefents the hinder Part of the Machine, the
Back, and one fide of the Box, being taken away,
to ftiew the turning Pillar and Springs on the Infide.
Fig,^, Reprefents as it appear’d in^ww^, 1720^
by this Telefcope.

3X* Anatomia

( )

IX. Jnatomia Jenis decrepitiy annorum i op. faSict
Tiguri, die i. Feb. 1723. A Joh. Jacobo
Scheuchzero, TtgurinOy Med, DoB, Mathefeos
Trof. ^gict Societatis Socio.

SUOS habent charadercs varii astatis gradus. A
fiuiditate afcendithomo fenfim per foliditatis varias
mutationes, donee cum rigiditate dc fibrarum veluti
immobilitate amittat vitain. Nec contemnendi eft usds
base in medicini confideratio.

; Accidit ante menfes aliquot, ut ob decrepitam fuam
cBtatem 6crarara, in Nofocomium fuerit receptusy^?^^«-
77 es Leonbardus Vopper^ Rhoetus, Sharanienlis ex coetu
Glantino Feederis fuperioris. Is juxta tenorem teftimo-
niorum lucem primum vidit, 1, Maij 1614. A. 1634.
Metalli foftbr in vena fepultus, per boras 55. fub terri
jacuit : Mortuo, quam vivo, fimilior inde protradus,
propter Abdominis validara, quam paftus eft, preftio-
nem, inde ab illo tempore incontinentia urin^ kbora-
verat. A. 1637. iter fecerat per Hungariam^ Turciam^
Terr am SanBam, reverfus Venetias, Poll: A. 1639.
inilitem egit fup Capitaneo Cafparo de Monte, in fervi-
tiis Caroli Ducis LotharingiA, in ftatu Mediolanefifi,

A. 166^, in Lufitanih, fub Colonello F. Planta, A. i68x.
interfuit obfidioni Viennenfi, 5c in ultimo bello oblidio-
ni Landavidi 6c Cladi Hockjlettenfi, Ita vitam, per va^*
rios cafus 6c mille rerum diferimina, protraxit fejnex
nofter ad annos 109. menfes 3.

In cadavere obfervavimus, curforie veluti, (non equi-
dem licuitper temporis anguftiam fedionidiu immorari),
lequentiai

Ifi'

( JH )

In abdominis cavo erat, parvi quidem copia, ferum
fanguinolentum extravafatuyn.

Inteftina tcnuia faere omnia inflammata, rubro colo-
re tinda, Duodenum prse primis integrum admodum *
dilatatum, interna fui parte fracidum prorfus 6c gangrs-
nofum ; Omentum prorfus emaciatum, ut vix agnofci
pottierit : Pancreas contradum ; Hepar fanum : Ve(i-
cula fellis bile repleta : Dudus Choledochi eadem tur-
gidi, 6c tota vicinia Inteftinorum 6c Mefenterii viro-
re infeda, ut alicubi extravafata videretur bilis, cujus
egreflum in Duodenum invenire baud potuimus. Prope
Pylorum, in Ventriculi fuperiore parte, aderat expanfio
veluti flatulenta, nuce juglande major. Renes fani, ut
6c Lien, cujus exterior inembrana, jucundo admodum
fpedaculo, obfeffa erat hiric inde maculis nivei can-
doris, magis minufque latis, qua3 priino intuitu refe-
‘rebant puftulas Variolarum maturas, fed cartilagi-
nese prorfus erant duritiei, 6c ultra fuperficiem reli-
qua? membranae aliquantum elevat^e. Obfervo heic,
anteqUam progrediar ulterius, non duntaxatrigefcere li-
bras, 5c contrahi fuprema aetate, fed tantum non infen-
(iles fieri, nemo quippe juvenilis vel confifientis ^etatis
pateretur inflammationem Inteftinorum, qualis base fuit,
abfque acutiflirao dolore,*de quo tamen sger poll: fenile
delirium, quod aliquamdiu eft perpelTus, ad fe ultimis
vit^ diebus rediens, nibil eft conqueftus. Cartilaginea
ilia Lienis crufta manifefto eft indicio, polfe ita rigefeere
membranas, ut tandem indurentur.

Tboracis apertio non parum facelfebat laboris. Fue-
runt quippe non folum Stern i 111$ coftofie prominentia,
alias cartilagine$, beic plane olTe$, fed 6c cum ipfis Co-
ftis tantum non continue, indicio manifefto, Cartilagines
fieri fucceftu temporis olfeas, quemadmodum membra-
ne 6c arterie fiunt cartilaginee, 6c ex cartilagineis non
femel olfeas narrant Hiftorie. Pulmones viridantibus

paflim

)

paflim maculis obfefG, in utroque Thoracis latere, po-
ftici fui parte affixi erant Coftis : Pericardium amplum
^ multo fero refertum, cujus 6c aliqua portio in cavo
fiuitabat Thorace. Cor ipfum vidimus fatis amplum,
imprimis Auriculas dilatatas prseter modum, 6c turn
hafce, turn Ventriculos fanguine concrete refertos, unde
patet fubftitilTe tandem fanguinis motum, propter defe-
dum contradionis elafticae in tubulis-arteriolis, 6c Cor-
dis machinam fanguini ad concretionem*difpolito expel-
lendo non amplius fuilTe fufHcientem, imo propter nimiam
reliftentiam obrutam. Prsftabat Tendinem ilium, quo
Cordi inferuntur arteri^, vel odeum plane, velcartilagi-
neuinfaltem: Olfeusfane, quod novimus, fit in Cervis
adultioribus, unde Os de-Corde Cervi. Et fane aliquid
tale ofFendimus, mimirum^Valvulas femilunares, praspri-
inis Aortae, cartiiagineas peiie, prascipue media fui par-
te. Aortam ipfam ‘defeendentem^ obfervavimus valde
amplam, diametri duplo majoris, quam eft Gula, Ta-
rifini circiter pollicis. Gulx inftratse pafliin erant Glan-
dulae lentiformes indurate. Amplitudo ilia Aortte indi-
cat tardiorem ultimis forte vit^e annis progrefllvum mo-
tum fanguinis, unde :art^i^, * quas propiores funt Cordi,
fuere fenfira diktats, ficuti fspe obfervamus dilatari
adeo, ubi nimia eft molis refiftentia, ut in Aneurifma
abeat egrediens e Corde Arteria magna.

Pergimus ad Caput, ubi prsdura Cranii fubftantia
rurfum fqlito majorem pofeebat laborem : Suturs, im-
primis Sagittalis 6c Lambdoidea, erant ferine obliterats,
nec prorfus penetrabant utramque Tabulam,ut nulla fu-
erit per illas e cavitate ilia magna Capitis perfpiratio, 6c
fuccus ille Ofiium nutritius, inter filfuras Suturarum ex-
travafatus, faftus quoque fuerit ofteus. Foramina qui-
dem tria quatuorve fatis; ampla, infupremp vertic^, ad la-
tas utrumque Sinus, Sagittalis, poUicis ferme diftaotk ab'
invicem vifuntur,internan>Lawinama^d.externam ufque

* penetrantia.

/ y\^ ))

abfque quod ulluin illorura utramque perforet Tabuhm*
Dura Meninx triple fere craflior fuit,quam eft ordinarie,
coriacea pene : Pia feparabatar facile, ' nimib utpbte ir-
yigata fero, a Cerebri fubftaritii : Ventriculi omnesfefo
erant referti, 'quod -fat magni copii quoque fluitabat in
Cerebri baft, imprimis ad Spinalis Medulla egreffum.
Plexus Choroides Glandulis pifalibus, lymphs coagulata
xefertis, erat obfeftus : Septum pellucidum egregie pote-
rat confpici : Cseterum Cerebri ipfa fubftantia, imprimis
interioris, flaccidior folito. ' ,

Innotuit mihi, inde ex quo obiit .decrepitus nofter,
retulilTeeum perfonis fide dignis,' quod-p.uer ejus,' fecu-
lum jam fupergreirus; tres genuerit liberos, <3c ex majo-
ribus pauci infra feculi astatem obierint. Hoc certain
eft, noftro natain filiam Mariam Magdalenam ex uxore
TJrful^ Hirzeli^ de Naniken pagi qui£ S, Bap-

tifmatis charaftere fignata fait Diejpinhov^, 1 8 Aug.

1707- ^ \ ^ ^

, F I N I S.

'I

LONDON: Printed for and 5^. Printers
to the Royal Society , at the Prince*s-Arms^ the Weft
End of Su Paul* s Church-Yard.

, I

%

b

. - 9

f

' \

►

f

\

Y. An

Numb. 377.

PHILOSOPHICAL

TRANSACTIONS.

For the Months of May and June. 17x3.

The CONTENTS.

I. A Letter from Dr. George Mackenzie, to
Sir Hans Slbane, ^ Coll. Med. Lond. DrdeJ.
concerning the Coa'ti Monidi o/BrafiL '

•Ml. . . ' »

II. Iniher Calculorum inter aquarum Pyrmontana-
rum ufum in Viro, nunquam antehac calculum

* expertOy ac alias perfeCte fanOy fuhjequente pojlea
miflu cruentOy tandemque "Veficai ulcere. Comrnu^

• nicanteViro Clarijjimo AbrahamoVatero, M D.

Anat. O* Dot an. Dr of. Wictemb. D(. S. S.

\

Ohferyations upon diffeCting the Dody of a Der*
Jon troubled with the Stone. Dy Dr. Perroc
Williams, Dhyfician at Haverford^Weft in
South-Wales.

‘IV. Hijloria SeSiionis Viri ex D(enum Calculo de^
funCli. Ex Epiftold Viri DoEiiJJhni P. Hardif-
- *^way, M. D. ad Gulielmum Stukeley, M. D.
Coll. Med, Lond. (^g. Soc. Soc.

Dd d

V. An

’V. An A'ccount of the Depth of ^In fallen from
April I, 1722, fo April i, 1723. OhferVed
at Widdrington in Northumberland, a?id
communicated to the Dublijher by the (J^eVerenT
Mr, Horsley.

VI. Pappi Alexandrini Dropofitiones duce genera*
leSy quibus plura ex Euclid is Dorifmatis complex*
us ejlj reftitut^ a Viro Do^ijfnno Rob. Simfon,
Math. ^rof. Glafc. ,

VII. De Globulorum Sanguineorum 7nagnitudhie^
<src. ex Epijtola D. Anronii a Leuwenhock
ad Jacobum Jurin, M, D, Seer.

yiii. So7ne Amendments and Additions to the Ac*
count of TInngs found under Ground in Lincoln-
fhire, hi the Tranfa6tions a/ May and June,
An. Dorn. 1702, Numb. 279. Se6t. 4, 5.
(By Mr, Ralph Thoresby, K 5.

IX, An Account of a ^nonftrous double (Birth in Lor-

• rain. Communicated to the Bubli flyer by Mr, Co-
lin Mac Laurin, ipro/. Math, Aoredon. 5. S.

X. ObferVatiom and Experiments on the Sal Cathar-
ticum Amarum, commonly called the Epfom
Sale. By Mr, John Brown, Chymiftj F, (Z^ S'.

(517)

r

I. A Letter from Dr. George Mackenzie, to
Sir Hans Sloane, Dar. Coll Med. Lond.
concerning the Goad Mondi o/Brafil.

SIR/

YO U know that the Coati Mondi of Brafil is fel-
dom or never brought alive into Europe ^ yet
there were two of them found in Capt.Gr^^w’s Ship,
who was fome Years ago try*d and condemn’d here for
Piracy, one of which being given in Compliment to
my Lady Seafortb^ dy’d in my Cuftody of a Wound it
had received in the Thigh, which I caufed to be dif-
feded, and have fent you the Account of it, compared
with that which the Parifian Academifts publifli’d of
one of them j and which differs from theirs in feveral
Particulars, moft of which, as I believe, may proceed
from the Difference of Sex, theirs being a Male, and
ours a Female.

Theirs was fix Inches and an half from the end of
the Snout to the hinder part of the Head, ours was
only four j theirs was fixteen Inches from the Occiput
to the Beginning of the Tail, ours was ten ^ theirs from
the Infertion of the Tail to the End was thirteen Inches,
ours twelve j theirs from the Top of the Back to the
Extremity of the fore Feet was ten Inches, ours was
fevcn^ theirs from the Top of the Back to the Extre-
mity of the hinder feet was twelve Inches, ours eight;
the Snout of theirs was very long and moveable, like

E e e that

( ?>8 )

that of a Hog, but freighter and longer in Proportion,
but ours was only two Inches , the four Paws had
each five Toes, the Claws of which were black, long-
and hollow, like thofe of the Caflor ^ the Toes of the
Fore-paws were a little longer than tliofe. pf the Hind-*
paws • the Soles without Hair ^ the Palms and Soles
of thefe Fore- paws were covered with a foft and ten-
der Skin 5 the Sole of the hinder Paw was long, hav-
ing a Heel, at the Extremity of which there were fe-
veral Scales a Line broad, and five or fix long, in all
which they perfectly agreed.

The Ears were round, like thofe of Rats, and co-
vered at the Top with very fliort Hairs, and' in this
they likewife both agreed, as they did in the Eyes,
which were extreamly fmall and beautiful, but there
was fome Difference in the Hair , for theirs was fhort,
rough and knotty, blackifh on the Back and Head*,
and the reft of the Body mixt with black and red ^
but in ours the Hair was long^ in Proportion to the
Animal, efpecially on the Tail, and the whole was
beautified with white and black Circles, which made
it have a moft lovely Afped ; But from the Snout
down all the Throat and Belly to the top of the Tail
and the infide of the Legs, was of a reddifh ‘Colour.
The Tongue of both theirs and ours was chopt with
feveral Fiifures or Strokes, which made it rough to
the Touch. The Incifores were fix in each Jaw ; The
Cantni were very large, efpecially thofe of the lower
Jaw-, but they did not turn up like Tufks as theirs
did ^ their Figure was not round, blunt, or white, like
thofe of a Dog, Wolf, or Lyon, but fharp, by the
means of three Angles, which at the Extremity form’d
a Point fharp like an Awl; As to their Colour, they
were greyifh and fomewhat tranfparent ; The Gula

was

( 3'9 ')

was large, and cleft like a Hog’s ; and the lower Jaw,
as in a‘ Hog, very much fhorter than the upper.

We (hall now proceed to the internal Parts. By the
DilTedion we found in ours, as the Parifian Academifts
did in theirs, that under the Skin, and between the
Mufcles, there was a great deal of Fat, white and hard,
like Tallow. Theirs being a Male had a Penis pro-
vided with a Bone, whofe Length did in proportion
exceedingly furpafs that of the Bones which are found
in the Penis of other Animals , fo we in ours, being
a Female, observed, that it had an exceeding large Ma-
trix, and that the Infertion of the Urethra was upon
the right Side of the Vagina, The Epiploon in ours,
as in theirs, was very fraall j it had little Fat, and
was a Complication of Fibres and Fillets, rather than
a Membrane j it was not laid upon the Inteftines, but
touched upon the Ventricle. In theirs they obferved a
very large Spleen, but in ours we could difcern none.
We did not obferve more than they any VelTels in the
external Membrane of the Ventricle, but the Coronaria
Stomachka, which appear’d as in theirs towards the
upper Orifice, and foon difappear’d, (hooting forth a
few Branches. The Liver in ours, like theirs, was
fomewhat blackifli, and of a Sabftance very homoge-
neous, without any Appearance of Glands : It had fe-
ven Lobes, two great ones on the left Side^ and five
other fmall ones on the right Side. The Pancreas in
ours, as in theirs, was faftened along the Duodenum,
inclining more towards the right Kidney than the left *
but whereas it was very fmall in theirs, it was very
large in ours. The Mefentery in ours, as in theirs,
was filled with a very hard Fat, which inclofed and
almoft concealed all its Velfels. The hitejlines 'mt'aelx?,
were feven Foot long, and all of one Thick nefs, having

E e e 2 nothing-

( po )

nothing to diftinguifti them , but in ours they were
only 42 Inches and a half. Theirs had no CAcum, but
we found it in ours at the upper end of the ReSIum,
The Bladder was very large ^ the right Kidney in ours,
as in theirs, was a great deal higher than the left, and
covered with the Lobes of the Liver.. The Lungs in
theirs had live Lobes, two on the right Side and two
on the left, and the fifth in the MediaJHnum, which
was as thin as a Spider’s Web j but in ours there was
feven Lobes, three on the right and three on the left,
and the feventh in die Middle. The Heart in ours,,
as in theirs, refeinbled that of a Dog, having the right
Auricle extreamly great,, and as they found a great
deal of fiimy Matter hardened in the right Ventricle,
fo we found in ours a Polypus, The Mufculus Croto^
phites palling under the Zygoma was in ours, as in-
theirs, faftened there, being extraordinary fiefhy even-
to its Infertion, made by a very large Tendon, which
was inclofed between two Pieces of Flefh, much thick-
er than thofe which are generally found in this Place,
and which are thought to be put there to defend and
ftrengthen. the Tendon of the Mufcle of the Tem-
ples.

The Tendons in the Articulations of the fore Feet
were very big and- ftrong.. In ours we obferved- two>
Glands on each Side of die Anus^ with a Pailage to*
each of them, full of a greyifh foetid- Matter. The Or--
hita in ours, like theirs, was not bony throughout, but
it was fupply’d in the upper Part by a cartilaginous
Ligament, which joined the Apophyfis of the Qs Fron-
tis to that of the firfl: Bone in the upper Jaw. The
Bone, which feparates the Cerebrum fxom the Cerebel-
lum^ was as in Dogs. The Dura Mater \n ours did not
adhere to. the Cranium^ as in theirs. The Sinus's of

the.

( )

the Oj Frontis in ours, as in theirs,' were full of Mat-
ter, like a friable Fat. The Mammillares Procejf/tts, in -
curs, as in theirs, were very large. In the Eye both of
them agreed exadly, the Globe not exceeding four
Lines and a half in Diameter, the Aperture of the-
Lids being much larger, and the Pupilla being, as large
as the whole Globe of the Eye ^ the Cryftalline con^
tained three Lines in- Breadth, and two and an half im
Thicknefs, and was more convex inwards than out-
wards*, this Thicknefs of the Cryftalline made the
two other Humours to be lefs in Quantity. The Ch‘a-
roides was all over of the fame Colour, viz, of a very
brown red, without any Tapetum, which is hardly ever
wanting in the Eyes of other Animals.

Thefe are all the remarkable I>ifFerences, that we
could difcover,. Ipetwixt ours and that of the Parijidn
Academifts ^ only I muft inform you of fome Things,
as t0‘ the Maimer of its Living and Diet, which they
had- not the Occahon to obferve in theirs..

I believe they are mifinform’d in faying, that they
carry their Tails ere.fted, at leaft the Tail of this was
always trailing on. the Ground * neither can I be
induced to believe that they eat their Tails, for there
was no Part of her that fhe could endure lefs to be
handled than her Tail, the leaft touching of which
would- mak-e her cry, or rather hifs like a Snake 5, fhe
could endure no manner of Cold 5 for in the Intervals
betwixt the Times of eating, fhe was either beneathr
the Bed-cloathSi or on a Cufhion before a Fire, with-
thc Heat of which, ftie feemed to be extreamly well'
pleafed.

Her ordinary Meat was butter’d- Eggs, Milk and^
Bread, all manner of roafted Flefh, but no Fifh: L
once, try ’d her with a new kill’d Partridge, which fhe.*

cat-

( >

eat of moft voracioufly, and, for feveral Days after, flie
was very wild' and ungovernable, which- made me ne-
ver afterwards try her with raw Flefh* I am apt iike-
wife to believe, their ordinary Dens or Habitations are
under Ground in fandy Banks, like our Rabbits^ for
when file was brought to the Fields, (he would dig up
the Sands with lier Paws, with an incredible Swift-
nefs, fo that had fhe not been chain’d, tlaere had been
no Pofiibility of recovering her.

( • , . r - : -

r . .1 ' . - '' . •

i • , V ^

George Mackenzie.

= V , .

¥ A V ‘I »

II. Imber Calculorum inter aquarum Pyrmoncana-
rum ufumy in VirOy nunquam antehac calculum
expertOy ac alias perfeEie fano^ fubfequente pojlea
miBu cruentOy tandemque "VeftCce ulcere. Commu^
nicante Viro Clarijjimo Abrahamo Vatero, M. D,
Jnat, <ts^ ^otan. Trof. Wittemb. 5'. 5.

t

NObilis Pomeranus, fanus ac vegetus, uti ipfe de
fe refert, nulliufque mali fibi confeius, ante hos
tres annos, fuafu amici, converfationis caufa, focium fe
ip(i adjunxit, in bibendis aquis medicatis Fyrmontanis,
Facliim autem eft, ut, cum potando aliquot dies trinfe-
giftet, calculos quofdam minores, abfque ullo qu-idem
dolore, excludi inter mingendum fentiret. Effeduin
hunc criticum eife fibi perfuadens nofter, ac[uas iftas
aufta doh bibere incipit, quo fado, quatuor vel quin-

que

( 3^? )

que dienim fpatio', ultra qiiadragiiita calculi, rurfus
tamen fine luolcftia, exierunt*. Hoc vifo, firenue '5c a-
lacriter potare continuat, optimum hujus curs effedl-
um fibi promittens. Afiumpta vero ita nimia aqus
quantitate, udna fupprimitur, >adeo, 'ut ne minittiain
ejus portionem per tres dies emittere potucrit, ufque
dum catheteris ope via aperiretur. G^mmonefatlius ita-
que a Medicis, ab ufu aquarum ulterior! abftinuit, rem-
■ita ’ peradam elfie credens. ’ Non ita multo poll, vir
ifte iter faciens, continuo' mingendi coriatu laceflitur,
ac item in iterumque ex rlieda defcendere dbgitur, tan-
demque inter graviffimos dolores fanguinem purum ef*
fundit. Dufavit mi(3:us cruentus dC dolorofus, quam*
dib aeger in itinere conftitutufe fuk, ‘poUquam irero hie,
domum reverfus, quieti fiud’uit, ftatim celfavit, nee
quicquam doloris remanfit. Qppties vero ab iiio tem-
pore five rheda, five equo' velietetur hofler, red i it do-
lor, 6c fanguis cum urina feceflit^ fed quiete reftkuta,
iterum evanuit, Hullo' plane dolore fuperfiite. Contigit
quidem interdum, ut calculus unus v^l alter prodiret,
rarius tamen hoc factum eft, nec ullum ex eo dolorein
percepit sger, quoniam hi loQge minores, quam quos
inter aquarum ufum reddidit, fuerunt. Symptomat6 hoc
admodum molefto per duos integros annos veXatur s-
ger, tandem ufu mcdicamentorum liberatus eft. Cef-
lante itaque penitus mifta cruento, nil inagis timuir,
fed integrs fanitati reftitutus fibi vifus, medicameritis
valedixir. At, quid fit ? Aiigetur poft illud tempos in-
dies Stranguria, virque eontinuo dienofteque ad urinam
reddendam ftimulatur, quo malo ipfe ad hunc ufque
diem atfligitur. Urina, qus parciflima quantitate, fum-
moque cum dolOre emittitur, crafta exit, ob pkuithn
vifeidam admiftam, qus fundum ftatim petit, glutini
ex farina confefto firnilis, tants tenacitatis, ut in fila

quafi

(?H);

quafi trahi qaeat* ‘ ^ger interea appetitu bono gaudet»
& fomno quoque fufficienti utitur, nee ullibi prasterea
in corpore dolorem fentit,

Conjideratio Cafus^ ejt4fque circumjl antiarum Jingularum.

»

Si quis hiftoriam morbi, quoad omnes ejus conditio-
nes, accurate perpendat, mecum confitebitur, eandein
vix parein inter obfervationes Medicas agnofeere. No-
tatu dignifliinum imprimis eft, potu aquarum iftarum
raineralium, calculos fat infignes, in tanta copia, atque
intra tarn breve remporis fpatium exclufos efte, a viro,
uti ipfe de fe refert, ante aquarum ufum perfefte fano,
nec ullum calculi indicium unquam fentiente. Non le-
vem hoc in animo excitare poteft fufpicionem, calcu-
los non tarn ab aquis propulfos, quam ex croco mine-
rali, qualem aquas tales medicate in finu gerunt, ge-
nerates potius in hoc segro fuifte. Parum quidem huic
fententte favere videtur tempus admoduni breve tot
calculorum concretioni vix idoneum, quoniam hi, pau-
cos poft dies ab inchoato aquarum potu, excluh funt.
Non tamen exiftimo, quenquam facile definire pofte,
quantum tempbris fpatium ad calculi in corpore gene-
rationem requiratur ^ poterit hoc forte efte exiguum.
Longe enim minus veritati confentaneum videtur, cal-
culos iftos jam turn in viis urinariis latitafte, quoniam
vir ille nunquam antehac urincB difficultatem, aut ali-
ud calculi lignum percepir. Confirmant e contrario
omnes hujus cafus circuinftantte, concretionem iftam
fubho faEiam effe. Calculi enim ipli nullatenus afperi
atque anguloii, quales alias velics calculi efte folent,
ob fucceftivam fpiculorum falinorum cohasQonem, fed
piforum ma jorum minorumqiie inftar, rotundi, glabri,
politi obfervantur, quod coagulationem eorum fu-
2 bitaneam

C jij )

bitaneam docere videtur. Color eorutn luteus conve-
nit exade cum fedimento iilo, coftione ex aquis Pjr-
montanis extrado, cujus minimam portionem ex qua-
tuor unciis aquae hujus paratam addere volui, ut tan-
to melius convenientia ifta patefcat. Fradi calculi
ftrata ejufmodi variegata interius monflrant, qualia in
tophis tliermarum Carolinarum deprehenduntur, quo-
rum pariter particulam exiguam adjcci, Addidi prop-
terea quoque calculos duos, cum aliquot fruftulis con-
tritorum, pauciflimos enim tantum obtinui. Ultinjo
tandem loco attend! quoque meretur lingularis ifta cir-
cumftantia, quod maxima horum calculorura pars in*
ter ipfom aquarum ufum exclufa fit, poft illud tein-
pus vero rariflime tales, iique longe minores prodie-
rint. Non tamen ideo culpa hujus rei in aquas iftas
medicatas conjicienda erit, quafi hse ad calculi genera-
tionem difponant, cum potius debilitati vifcerum, ac
pravas digeftioni adfcribi debeat efFedas ille extraordi-
narius. Nolo etiam levifiimas has meditationes atquc
conjeduras pro veritate indubitata venditare, rem to-
tam potius llluftrifiimae Societati Regali decidendam,
ea, qua erga ipfam fum, pietate ac obfervantia trado.

Dab am Wittemberg^s Saxonum,
d, vi. Jan. MDCCxxiiif

, F f f

III. Ohfefvations

( )

1 » »

- I - -- h. -■ — i

III. Ohfer’Vations upon diJfeSiing the (Body of a Ber->
Jon troubled with the Stone, , By Dr, Perroc
_ . Williams, Bhyfician at Haverford-Weft in
South-Wales.

• f

Mr. William Bowen of the Town and County of
Haverford-Weji, aged between 40 and 50, hav-
ing been, for about the Space of feven Years, feverely
afilided with the ufual Symptoms of the Stone in the
Kidneys and Bladder, viz. Bloody Urine after Exer-
cife. Strangury, c^c, Dy’d in May 1722. His Body
being opened, there were found in the Bladder fix
fmooth oval Stones, exadly of the fame Figure, and
nearly of the fame Magnitude : There were alfo three
Cells in each Kidney, the Figure of each fuitable to
that of the Stones : The Ureters were fo preternatu-
rally extended, as very ealily to admit the largeft of
the Stones to pafs from the Kidney to the Bladder.
The Vifcera, appear’d in their natural State.

IV. Hifiorta

( )

lY. Hijloria SeSlionis Viri ex (^mm Calcuk de*
fmiEli Ex Eptjlold Vtrl DoBlffimi P. Hardif-
way, M. D. ad Gulielmum Stukeley, M T>.
Coll Med. Lond. Soc. Soc.

HOmo feptuaginta circiter annosnatus,ventris dolore
horrendo correptus eft die Odlobris 19° An. 17x2.
Accelferunt Voinitas 6c Urinse difficultas, prse doloris
atrocia fefe crigere non poterat, fed mifere incurvatus,
dies nodefque prope focum jacebat ejulans. Sexto morbi
die,urina prorfus fapprefs^, de dolorosi circa Hypochon-
dria ftridura, perinde ac a funibus circumjeftis, quere-
batur, poftea de pondere quodam in velici molefto, quad
Rapi majoris, (he aiebat) inibi hofpitantis. Omnibus in
pejus ruentibus, die morbi duodecimo ad plures abiit.
Oadavere aperto vehcam fecuimus, quam ab ullis vel
minimis calculi veftigiis immunem invenimus^ in utro-
^ue autem rene (multi aqua refertis) repertus eft calcu-
lus, (Fig, I, 2.) inhgnis, fcaber 6c multiplici ramo per
parenchyma fe difpergens, quern integrum extrahere
nulla arte potuiftes, nih toti prius fruftulatim decerpta
came. Ramorum maximus in ureteris caput fe inhnu-
ans, perbelle adeo id occupaverat, ut ampulla obtu-
ramento fuo arftius occludi vix poffet. Ulterius feru-
tari nobis non licuit, ideo unum tantum addam, nempe,
quod Omentum inftar fafeias anguftioris fub hepate
retradum delitefcebat. Pauper erat 6c corpore athle-
tico, femper fanus, nih quod a paucis annis, aliquando
fabulofa per urinas excerneret.

Fff 2

V. Ah

( 3^8 ); •

V. Jn Account of, the Depth of ^in fallen from
April 1, 1711, fo April 1, 1723. ObferVed
at Widdrington in Northumberland, and
communicated to the Dubltfher by the (J(eVerend
Mr: Horsley.

I Have kept an exad Account of what Rain has fal-
len the laft Year in this Place, which I have here
lent you. The weighing the VYater and reducing it
from Weight to Depth feem’d pretty troublefome, even
when done in the eafieft Method: To remedy this In-^
convenience (befides a Funnel and proper Receptacle
for the Rain) I ufe a cylindrical Meafure and Gage.
The Funnel is go Inches diameter, and the cylindrical
Meafure exadly , the Depth of the Meafure is 10
Inches, and the Gage of the fame Length, with each
Inch divided into 10 equal Parts ^ or, inftead of a
Gage, the Inches and Divihons may be mark’d on the'
Side of the cylindrical Meafure, The Apparatus is
(imple and plain, and it is eafy to apprehend the De-
lign and Reafon of the Contrivance for the Diameter

of the cylindrical Meafure being juft ~ of that of the

Funnel, and the Meafure exadly 10 Inches deep, ’tis
plain that 10 Meafures of Ram make an Inch in

Depth 1 one Meafure, —1 one Inch on the Gage,

10 ° 100

and — of an Inch on the Gage, — By this

Means the Depth of any particular Quantity which
falls, may be let down with Eale and Exaftnefs, and

the

( )

tlie whole at the End of each Month, or every Year,
may be furam’d* up without any Trouble. "

By the following Account you’ll fee, that fome of the
Summer Month^ particularly Majf and Jufy, were very
wet^ .and fame of the Winter ones very dry , fo that,
one with another, this Year’s Rain, as far as can well be
conjedur’d, may be look’d upon as a Medium,. And
if fo, it differs not above two or three Inches, from
the mean Quantity of Rain which falls at Upminfierj
and being lefs than at Lijle^ and more
than at the other two Places.,

An Account of the Depth of Rain fallen from April

1712, to April I,

1723.

Inch.

In April -----

- . 1,01 y

I n May -----

- - 3,532

In June -----

- - 3,570’

In July -----

- - 4,3 fcx

In Auguji - - - -

- - X,I32

In September - - -

- - 1.IS5

In OBoher - - - -

- - ,600

In November - - -

- - 2,205

' In December - -

- - 1, 780.

In January - - - -

- - I»22S

In February - - - -

- - ,48s

In March - - - - -

- - .195

In the whole Year - -

■ - 21,244;

VI. Pappi

( J )

^ s '

VI. Pappi Alexandrini Tropofitiories dta genera-
Jesy'^quibus :plura ex EudidisTon^^^

^’us ejly (^ejlitutii a Plro VoBiJflmo K.oh, Simfon,
Math'Trof, Glafc. Fid. Pappi ’ pr^fationem ad
Lib- 7. ‘ Coll. Math. Apollonii de SeClione ra-^
tioniFlibrh Ambus a Clariff. \\2d\F\0 pr<tmiffa7n'

pag: vin. XXXIV.

-Ec^ifV7r1iHt^’oiTocpV7rliHri'STccj3oc,?\^^iiydfC,

t ' V '

- "■ ■■ ..X ■ - '* ?

Textus Pappi^^qui in hac d>^ fequente Propofitlone inju-
ria temporis truncatus e[l^ hoc mo do PLefiituendus vi-
detur.

■■[SI

it

Cl

cc

it

cc

du^E refe lines in daas redas lineas fibi mu-
tuo occurrentes vel inter fe paralleks ducantur,]
Sc dentur in una earum tria ^ punda [vel duo, fi re-
da in quai»funt, parallela fuerit alicui ex tribus re-
liquis] : cstera vero punda prster unum ^ tangant re-
dam pofitibne datara, etiam hoc quoque tanget re-
dam pofitione datam. ” Hoc auteiii de quatuor tan-
tum redis dicitur, quaruiu non plures quam dus per
idem pundum tranfeunt. In quolibet vero propofito
redarum numero ignoratur, quainvis vera lit, hujuf-
modi Propolitio. “ Si quotcunque reds occurrant in-
ter fe, nec plures quam dus per idem pundum ^ data
vero fint punda omnia in earum una, unumquodque

autem

tt

ti

» Tria punila'] interfeftioniim fc. ^ Tangant re^am] i. c. unum pun-
num tangat unam aliquam redani pofitione daiam, 6c aliiui tangac ali-
am pofitione datam, 6cc.

^ autem pundum in alia tangat redam pofltione da-

tarn ^ ” vel generalius lie. Si quotcunque redae cKcar-
rant inter fe, neque fint plures qaam dua; per idem
pundum, omnia vero punda in earum una data finf *,
■reliquorum numerus erit numerus triangularis^ cujus
latus exhibet numerum pundorum redam pofitione
datam tangentium , quarum interfedionum fi nullsetres
exiftant ad angulos triaiiguli fpatii, [nullas quatuor* ad
angulos quadrilateri, null^e quinque, 6cc. i. e. univer-
fim, fi nullae harum interfedionum in orbem redeant]
unaquaeque interfedio reliqua tanget pofitione datam.
Propofitio prima in decern dividitur cafus, monente
ipfo Pappo, quorum ejus, in quo nulls ex quatuor re-
dis funt inter fe parallels, neque reds pofitione dats
per data punda tranfeunt, demonftrationem hie appo-
nemus5hic enira Cafus inter omnes maxime eft generalis,
ejufque demonftratio fecunds propofttionis demonftra*
tioni omnino eft neceftaria. 3. 4.) Sint igi-

tur quatuor reds AB, AD, BE, C-E. Et data lint
tria punda interfedionum A, B, C in earum qualibet,
reliquarum vero interfedionum D, E, F, una D tangat
redam G K pofitione datam, alia E tangat redam H K
pofitione datam , tanget etiam reliqua F redam^pofitione
datam. Ducatur per F reda MF parallela ad AB,,
qus occurrat ipfis H K, K G, C E, in M, N, O.^-CLuo**
niam igitur data eft ratio H B ad B C dabitur ei-
dem squalis ratio M F ad F O, quoniam datur ra-
tio AC ad A G, dabitur eidem squalis ratio F O ad
F N quare datur ratio M F ad F igitur fi junga-
tur F K, qus occurrat ipfi A B in L, dabitur ratio H L
ad L G 5 6c datur H G pofitione 6cmagnitudine *, qua-
re pundum L datur, 6c. datum eft pundum K, igitur
K L pofitione datur.

Sit igitur H Lad' LG in ratione compofita ex ra-
tionibus HBadBC6cACadAG, 6c jungatur K L,

erit

erlt ha3C reda quam tangit putidum F, hoc efl, (i du-
catur/quaevis C E, pofitione datis occurrens in D, E, 6C
^ungantur A D, B E fibi mutuo occurrentes in F ^ re-
da erit linea quse per K, F, L tranfit. Nam per F du-
catur M F paralleia ipfi A B, & quoniam ratio M F
ad F N compolita eft ex rationibus M F ad F O &
F O ad F N, hoc eft, ex rationibus H B ad B C 6c
A C ad A G, ex quibus etiam componitur ratio H L
ad LG', erit H L ad L G ut M F ad F N, igitur
H G ad M N, hoc eft, H K ad ,M K ut H L ad M F:
Qiiare reda eft linea quas per K, F^ L tranftt, per
14. 1 aut 32. 6 Elem«

Explicatio Secmda fropofitionis,

Obfervandum hie eft, Numerum interfedionum, qua;
in una reda reperiuntur in qu^cunque propofita mul-
titudine redarum, quarum non plures quam duae per
idem pundum tranfeunt, 6c quarum nulls funt inter
fe parallels, unitate minorem efle ipfo numero reda-
rum: Nam dus in unico pundo fe invicem fecant,
tertia vero duda priores in duobus, quarta priores in
tribus pundis fecat, 6cc. Et igitur nuinerus interfedio-
num in tribus redis eft unitas binario auda, i, e. ter-
narius numerus eorundem in quatuor redis eft ter-
narius ternario audus ^ in quinque veto redis eft^ ul-
timus prscedens feu fenarius quaternario audus, 6cc.
in infinitum Qui numeri, ut manifeftum eft, trian-
gulares funt, quorum cujufque latus eft numerus in-
terfedionum, qus inveniuntur in una qualibet reda,
i, e. numerus qui unitate minor eft numero omnium
redarum. Igitur ft ex hoc numero omnium interfedio-
num dematur numerus omnium pundorum datorum,
qui idem- eft cum numero interfedionum in una qua-
vis reda^ reliquus erit adhuc triangularis, cujus la-
X tus

. . . ^ .

tus fc. unitate, deficit; a latere priorji^ quod

laerum omaium. pundlorum, & proinde binirio*ia^i4^
eft numero reftarum proppfitarun?. ,Et liic eft nuiaqr.us
interfedionum quas tangere redam pofitione datam
Fappus in hac Propofitione requirit, quarumque ft nul-
las tres Tint, ad angul^ jrkngu|i * [nulls .quatuor ad
angulos ^ quadrilateri & ita deinceps unainquamque
interfedionem reliquam tangere redam pofitione datam
aflii'mat.. Qus auteinmncis inclufa funt, textui necefli-
tate coadi adjecimus, nam fine ikpropofitio yera'noa
eftet extra cafum quinque redarum.

Commode vero in duos cafus dividitur propofitio ;
quos etiam aperte fatis indicat Fappus^ qui Hypothefiri
cafus facilioris propofitioni hujus generis univerfalif-
fims fiinul 6c elegantiffims prsmittit.

CASUS PRIMUS. .

r

Si quotcunque reds occurrant inter fe nec plures
quam dus per idem pundum ^ data vero fint punda
omnia in earum una, unumquodcunque autem pundum
in alia tangat redam pofitione datam unaqusque in-
terfedio reliqua tanget redain pofitione datam. . Sint e-
nira quotcunque reds, (Fig» 5.) ex, gr. (ex A F, B G,
C H, D K, E L', E A 5 6c data fint omnia punda in
earura una, fc. A, B, C, D, E ^ omnia vero punda in
alia fc. F, L, M, N, tangant redam pofitione datam :
unaqusque reliqua interfedio tanget'pofitione datam.

Sumatur enim qusvis ex reliquis ex,gr, O, dC quo-
niam quatuor funt reds O L, O N, A N, A B, 6c da-
ta funt tria punda in una earum fc. A, B, E, reliqua
- G B §

c Intelliguntur etiam hie figura: quarilW lateia fe mutUO decu^ant Pia-
gonaiium iitftar, aeque ac caetcia;.

( m )

vero praeter unum O, viz. ipfa L, N tangunt reflam po-
fitione datam, tanget etiam O pofitione datam per
Vrop. I. Eodem modo idem de omnibus reliquis often-
detur.

CASUS SECUNDUS.

Casteris manentibus jam non fint omnia punfla re-
flam pofitione datam tangentia (quorumque numerus
binario minor eft numero reflarum propofitarum) in
eadem refla, fed nulla eorum in orbem redeant *, often-
dendum eft reliqua omnia tangere reflam pofitione
datam.

LEMMA I.

Si quotcunque reflae inter fe occurrant neque plu-
tes quam dux per idem punflum, fumantur quasvis
reflarum, fit vero numerus interfeflionum, qui confi-
citur fumendo duo punfla in unaqu^que reflarum fum-
ptarumaequalis numero harum reflarum • punfla hxc in
orbem redibunt. Nam quoniam funtduo punfla in una-
qu^que refla, erunt ad minimum tria in duabus reflis.
Sc quatuor in tribus dc ita deinceps , Temper fc. erit
numerus punflorum ad minimum mnitate major nume-
ro reflarum nifi refla ultima tranfeat per punflum pri-
mum 3 i. e. nifi reflse in orbem redeant, in quo folo
cafu ^qualis erit numerus punflorum numero reflarum.

LEMMA II.

Si quotcunque reflse inter fe occurrant neque plures
quam duae per idem punflum, fumantur vero qua^libet
iplarum interfefliones, quarum numerus numero omni-
um

um redlarum asqualis vel interfedliones oinnes,
vcl earuin aliquse, in orbem redibunt, feu invenientur
ad angulos polygoni vel ^ trianguli.

Nam tres interfedliones trium redarum funt ad an-
gulos trianguli, fi vero lint quatuor reto, <5cfuman-
tur quatuor punda, una harum necelfario invenietur
in uniquaque reda j quod li in un^ aliqua ex quatuor
redis unum tantum inveniatur pundum, tria reliqua e-
runt in tribus reliquis redis, Sc igitur ad angulos tri-
anguli : Si vero nulla fuerit reda, in qua unum dun-
taxat pundum invenitur, erunt duo in unaquaque ex
quatuor redis, dc funt quatuor punda, ergo per i,
funt ad angulos quadrilateri. Et manifeftum eft ft fue-
rint quatuor redas, dC fumantur plura quam quatuor
punda, multo magis aliqua eorum in orbem redire*

Sint jam quinque redae, 6c fumantur quinque interfe-
dionum punda, 6c, ft fuerit aliqua ex redis in qua
nullum invenitur pundum ex hifce quinque, erunt
omnia quinque in quatuor reliquis redis • Si vero fue-
rit aliqua reda in qua unum duntaxat invenitur pun-
dum, erunt reliqua quatuor punda in reliquis quatuor
redis ^ igitur in utroque cafu punda aliqua erunt ad
angulos trianguli, vel quadrilateri, per prsecedentem ca-
fum : Si autem nulla fuerit reda in qua vel nullum vel
unicum invenitur pundum, erunt duo in uniquaque
ex quinque redis, 6c funt quinque punda, ergo per
L<?w. I. lunt ad -angulos quinquelateri. Eodem prorfus
ratiocinio oftendetur in fex redis 6c ita in infinitum.

In FJg* 6. funt odo reda?, 6c odo fumuntur punda,
quorum quatuor in orbem redeunt.

Hifce praemiflis propofitio hoc modo demonftratur. Pri-
mo (int quinque red^e (Fig. 7.) A D, A E, B F, C G, D H,
6c demptis pundis datis in una reftarum, viz. A, B, C, D,

G g g 2 reliqua

reliqua erunt fcx pun<5ta E, F, G, H, K, L/ in qua-
tuor redtis, <5c tria liorum (nam latus numeri triangu-
laris 6 eft g) quas non funt ad angulos trianguli, a tri-
bus fc. redtarum propofitarum contenti, ex, gr, E, F, G,
tangant re<ftarn pofitione datam , oftendendum eft reli-
qua tria K, H, L etiam tangere recftam politione datam.

Quoniam igitur funt quatuor redas A E, B F, C G,
DF, tria interfedionum pun<da in iplis fumantur,
viz. E, F, G erit una aliqua harum redfarum in qua ne-
ceftario invenietur unum tantuiil exhifce tribus pundlisj
nam fecus erit vel aliqua iti‘ qua nullum eft puncftum,
6c proinde erunt tria puncfta in tribus reliquis redtis,
i. e. ad angulos trianguli contra Hypothefin ^ vel e-
runt ad minimum duo pundfa in undquaque quatuor
redfarum, 6c igitur quatuor eifent ad minimum pundfa ^
fed funt tantum tria , quare neceffe eft elTe aliquam re-
dtam in qua unum tantum invenitur pundlum : Sit base
re<da A E, 'in' qua fc. eft pundtum E, ergo reliqua duo

F, G, funt in reliquis trrbus redi^is BF, C G, DF^
igitur, quoniam dantur tria pundfca B, C, D, reliquum
'pundtum L in iftis tribus reeftis, tangit redlam pofitione
datam per primam Propofitionem : Sumatur nunc G E,
redta fc. ex hifee tribus qute tranfit perpuneftum E in
quartd redta, (3c omnia pundta in hac redia G E tangent
pofitione datam. Quare, per cafum primum hujus pro-
pofitionis, reliqua pundta K, H tangunt redlam pofi-
tione datam.

Sint jam fex redl« (Fig, 8.) A E, A F, B G, C H, D K,
E L 5 6c demptis quinque datis pundlis A,B, C, D, E, qua;
funt in una rcdlarum, reliqua erunt decern pundta F,

G, H, K, L, M, N, O, P, in quinque rcdlis , 6c ex
Hypothefi quatuor horum, quas non in orbem redeunt,
tangunt redlam pofitione datam *, (int h^, F, G^ H, K ;

^ 6c oftendendum eft Teliqifa fex L, M, N, O, P, d
tangere redlam pofitione datam,.

Quoniam

Quoniain igitur fumiantur quatuor purd?. interfedtio-’
num F, G, H, K, in quinque redtis A F, B G, C H,
D K, E L 5 erit una aliqua redta in qua iinum tantuin
ex hifce pundtis reperitur-, nam fecus erit vel aliqua in
qua nullum eft pundtum, 6c proinde quatuor pundla e-
runt in quatuor reliquis redtis, 6c igitur aliqua eorum
in orbem redibunt per hem, 2. contra hypothefin : vel
erunt duo ad minimum pundta in unaquaque quinque re-
dlarum, <5c ita elTent quinque ad* minimum pundta , fed
funt tantum quatuor, quare necefte eft efte aliquam re-
dam in qua unum tantum invenitur pundum*, fitli^c
A F in qua fc. eft pundum F ^ ergo reliqua tria G, H,
K funt in reliquis quatuor redis B G, C H, D K, E L,
dantur punda B, C, D, E , ergo per primam partem
hujus demonftrationis reliqua tria punda in his qua-
tuor redis, fc. L, P, (i, tangunt redam pohtione datam.
Sumatur nunc B F, reda fc.exhifce quatuor, qu^ tranfit
per pundum F in quiqta reda *, 6c omnia punda in hac
reda B F tangent redam pofitione datam : Quare per
Cafum primum hujus Propofitionis reiiqua punda M,
N, O tangunt redam pofitione datam. Eodem prorfus
m©do demonftrabitur Propofitio in feptem, odo,
redis in infinitum, ut pater.

Quod autem conditio uncis inclufa in hac propofitio-
ne omnino fit neceffaria, patet in his duobus exemplis,
idem vero univerfaliter pr^cedentium ope demonftrari
poteft.

His adjecit ClarlJJimus Frofeffor Ponfmata duo fequentia
pritni Lihri Porifmatum Euclidis a fe qiwque reflituta,
Porifma primum, Lib: i. Porifmatum Euclidis^ quod
fervavit Pappus Alexandrinus in prrefatione ad Lib, 7.
Math. Coll. Vid, pag, xxxv. Ejufd, Pr^f.

Si a duobus pundis datis infiedantur duse reda? ad
redam pofitione datam, abfcindat autem earuin una a

3 reda

( )

rcda. pofitione data fegmentum dato in pun6lo adja-
cens, auferet etiam altera ab alia red;a fegmentum da-
tarn habeas rationem.

Sint enim duo punda data D, C, (Fig, 9.) a quibus ad
pofitione datain A B infiedantur D B, C B , quarum una
D B abfeindat a pofitione data E F fegmentum K M adja-
cens dato pundo M : Oftendendum eft alteram C B au-
ferre ab alii quadam reda fegmentum datain Iiabens
rationem ad ipfuin K M.

Junda C D occurrat pofitione datis A B, E F in A,
F pundis, quae proinde data erunt. A pundo K, in quo
infiexa B D occurrit ipfi E F, ducatur K H parallela ad
A D, & occurrens alteri inflexs B C in H, ipfi vero B A
in N. Qiioniam igitur dantur punda A, D, C, dabitur
ratio A D ad D C, 5c igitur ratio N K ad K H ^ quare
fi jungatur E H occurrens ipfi A D in G, dabitur ratio
A F ad F G fed datur A F, quare 6c F G datur, 6c
pundum G j 6c datum eft E, quare E G pofitione 6c
magnitudine datur *, 6c datur E F, quare ratio E F ad
E G datur , 6c duda M O per datum pundum M pa-
rallela ipfi A D, 6c occurrens EG in O, dabitur M O
pofitione, 6c ideo pundum 0 , 6c propter parallelas M O,
FG,KHeft MKadOH, ut E F ad E G, qus funt
in data ratione. Igitur reda B C aufert a reda E G
pofitione data, fegmentum O H dato pundo O adjacens,
in data ratione ad fegmentum MK. Q. E, D,

Componetur vero ita, fiat A F ad F G ut A D ad
D C, 6c junda E G, per M ducatur M O parallela ad
A D ^ oftendendum eft, fi a pundis D, C infledantur
ad A B quaevis D B, G B abfeindentes ex ipfis E F,
E G, fegmenta M K, O H pundis M, O adjacentia,
fore ipfa in data ratione E F ad EG, feu, quod idem
eft, elTe jundam H K parallelam ipfi A D j hoc vero
v^detur omifium fuilfe ab Euclid^, utpote quod tribus

verbis

3

( )

verbis indirede demonftrari poflit j Fappus autem in
Lem. 1°. ad Porifmata, duas direftas ejufdem demonftra-
tiones affert, quarura fecundam, quse paululutn eft cor-
rupta apud Commandinum^ hie fubjungemus integritati
fuse reftitutam.

Vid. Pap. h\b. J.fol, pag. prior.

"Per Compofitam vero proportionem hoc paBo.

Quoniam eft ut A F ad F G ita A D ad D C (Fid.
jig. Papp. fo\. 2^^.pag. poji. vel jig. nofir. 9.) con-
vertendo erit ut G F ad F A ita C D ad D A, 6c com-
ponendo, permutandoque 6c convertendo ut A D ad DF
ita AC ad C G* Sed proportio A D ad D F compofita eft
ex proportione A B ad BE, [6c E K ad K F, 6c propor-
tio AC ad CG compofita eft ex proportione AB ad
B E3 6c proportione E H ad H G. Proportio igitur com-
pofita ex AB adBE6cEKad KF eadem eft, quse
componitur ex A B ad BE 6c E H ad H G. communis
auferatur ratio A B ad B E, reliqua igitur E K ad K F
eadem eft quse E H ad H G , quare H K ipfi A G paral-
lel a eft.

Porifma Secundum. Quod pundum ill ad tangit re-
dam pofitione datam. Secundum Porifma videtur fe-
quenti modo explicandum efie.

Si a duobus pundis datis C, G (Pig. i o.) ducantur duse
redsE C B, G D occurrentes duabus redis pofitione datis
A B, E D, fitque reda D B punda interfedionum jungens
parallela ipfi C G, quse per datum pundum ducirur, in-
terfedio K dudarum tanget redam pofitione datam.

Occurrant enim pofitione datx fibi mutuo in H, 6c
junda K H occurrat C G in F 6c B D in M. Igitur
propter parallelas eft A E ad E F (ut B D ad D M hoc
eft) ut C G ad G F *, 6c igitur A E ad C G ut E F ad
G F, datur itaque ratio E F ad G F,6c datur E G, quare

pun-

‘( 340') ^

.punftum F,' '5c datur pundum-H, qua'fe HFpofitio-
ne.'lnSit itaque ut A E ad E F ita^C G ad G F^''6tqiitl-
da HF erit ^ reda ^ quam tangit piindmn K ^ hoc eft
duda quagvis G D, occurrens'hpfi F M in K, erit r^da
iinea qu^e per C KBtranfit, nam eft D B ad DM-ut AC
.ad-£ F,^ 'hqc eft' k%. cohftrudione ut C G ad G F, quare
D B ad C G ut (D M ad GF hoc eft ut) DK ad K G,

igltur eft C K B feda linea.

Pappus idem aliter demonftrat in Lemmate, quod

hoc ( ihodo debet legii'fc. Ddcatur per G, (Vid, ¥'ig»
Pap. foL 2^^,^pag\ poft^ vel Fig. «<^^-i6.)^reda linea
G L parallela D E, ek; junda H K ad L producatur.
Qupniam igitur eft ut A E ad E F ita C G ad G F,
6c permutando [^A E ad G G ut E F ad G'F] , ut auteiii
A E ad C G ita eft E H ad G L» ^ quod dux duabus
funt parallelse. Ut igitur E F ad F G ita E H ad G L,
atque eft E H parallela ipft G L, ergo reda linea eft
quag per H K L F tranftt. • ^ .

^od du£ duabus funt paralieU, fc. A E ad D B, 5c G L ad D E, unde
eft A E ad D B ut E H ad D Hj 6c eft D B ad C G (ut D K ad K G, i. e.) ut
D H ad L G 5 ergo per zx, 5. eft A E ad C G ut E H ad G L.

1 ’

' i F . . . '

X k ^ ‘

1 ■

VII. De

( 34' )

YII. De Globulormn Sanguineorum magnitudinCj
ex Epijiola T>, Antonii a Leu wen hock
ad Jacobum Jurin, M, D, S, Seer.

Del PHIS, 19 MarEi, 1723.

EX tuis litteris intellexi inventam tibi rationem efle,
qua diametros globulorum fanguineorum, aliarum-
que minutifTimarum rerum, certo cognofeere poflis, a-
deo quidem ut deprehenderis diametrum globuli fan-

guinei cum parte ~~ Lti pollicis magnitudine con-

venire.

Hoc ego inventum cum legerem, fumma voluptate
affedus liim ; ftatimque fic mecum ratiocinabar : fi
1940 globulorum fanguineorum diametri lato pollici
longitudine refpondent ; adhsec fl corpora inftar globi
rotunda earn ad invicem proportionem habent, quam
habet numerus cubicus ad fuum axem, ficut a Geome-
' tris traditur ; fequitur corpus, quod ex 7301384000
globulorum conjundtione componitur, baud majus efle
corpore globofo, cujus axis latum pollicem longitu-
dine adsequet.

Et quia de examinando denuo fanguine me rogave-
ras ; meum ipfius 8c duarnm prseterea perfonarum fan-
guinem vifii exploravi : planeque comperi 4 diametros
globulorum fanguineorum, uti fcripfifti, convenire cum
diametro fili argentei, quod mihi mittere dignatus es.
Id folum dicere habeo, quod globulos quofdam fan-

H h h guineos.

» Huius fill argentei diametri 48 5 pollicem, five duodecimam pedis Loudinen-
fis partem, conficiebant 5 c^uod compertum fiuerat per Methodum in A^lis Philo-
kfioph. expofitam. No. 3 55-P^g-

( )

guineos, fed perpaucos, vifu perceperim ; quorum qua-
ternse diametri diametrum fili argentei longitudine ali-
quatenus excedebant. Verum conjiciebam globulos
illas, quos ex pollice per acus pundionem eduxeram.
Sc adhuc calentes vitro imponebam, a rotunditate fi-
gmx nonnihil defciviffc ad figuram plaiiam.

Hoc etiam addere habeo, prseterquam quod gravis
mea fenedlus vifui non incommodare non poflit, o-
culum dextrum, inagno incommodo meo, aliquantum
mihi caligare. Id vero bine accidere puto, quod plu-
res globuli fanguinci, in humore cryftallino innatan-
tes, ante vifum meum vagentur : quorum alii nullo vel
confufo ordine inter le conjiind:i, alii feorfim fluitan-
tes, imaginem quandam mibeculae in oculo meo ef-
fingunt. Cum autem plerumque utar oculo dextro,
^inifl:rum enim inter fpeculandum facile claudo, hinc
obtufior mihi vifus eft quam efte folebat.

Hand ira pridem, fcilicet Januario nuper elapfb,
circa magnum illud 6c neceftarium organum, quod
diaphragma vocitamus, vehementi fum motu correp-
rus ; adeo quidem ut adftantes non parum turbarentur.
Cum rnotus remitteret, Sc morbi illius nomen exqui-
rerem, Mcdicus, qui aderat, cordis e/Ie palpicationem
refpondit. Ego verb Medicum falli cenfebam ; licet
enim, durante motu, pulfum arteri^ faepius manu ex-
plorarem, nullam pulfiis accelerationem percepi. Ve-
hemens ille rnotus, per intervalla recrudefeens, tres
circiter dies duravit ; quo tempore ftomachus mihi
Sc inteftina in officio motuque ceftabant ; mortemque
pro foribus efte certiffime credebam.

Ego vero obftrueftionem in diaphragmate haerere
judicabam, non minorem nummo imperiali.

Addis in epiftola tua, prsenobilis Domine, quod o-
varium exterminare ftudeam ; ad quod falva

pace re-
Ipoiidcoj

( 34? )'

fpondeo, iftum meum conatum non efle nuperum vel
no vellum, fed me ante xf, & amplius annos in illo e-
vertendo laboralTe ; eo quod opinio, quse geiieratio-
nem ab ovario arcellir, mihi prorfus infulfa videatur,
. Ego a permukis modo annis turn aliorum animalium,
turn avium atque pifcium, mafculina femina exarainare
foleo: quod potiilimum lub iftud tempus quotannis
facio, cum pifces ova fua emittunt : Plerumque autem
comperi lemen mafculinum innumerabili fcatere co-
pia exiguillimorum animalculorum ; ex iilque potiili-
mum componi. Quare pro certo ftatui, minutiflima
ilia animalcula in iftius generis animalia, unde exorra
funt, crefcendo evadere. Anguillas tamen, Iquillas,
pifces conchatos, 8c varias mulcas excipio ; quse om>
lies funt femellse, 8c fru6tus edunt, hac in parte con-
venicntes cum frudiibus arboreis : quorum in lemini-
bus Plantulas delitefcere comperimus ; quae vice maf>
culinorum feminum frudtus iterum proferent, frudbibus
illis congeneres, ex quibus lemina jam didta exorta
fuerunt.

H h h 2

VIII. Somie

( 344 )

VIII. Some Amendments and Additions to the Ac-
count of Things found under Ground in Lincoln-
{hire, in the Tranfadions o/May and June,
An. Dom. 1702, Numb. 279. Sed. 4, 5.
Mr. Ralph Thoresby, F. ^ S.

WHEREAS in the Paper aforefaid, pag» 1157.

lin. 55. and pag, 1158. lin. 15, 16. there
is feme Difference betwixt the Accounts of the Depth
of the Things found ^ that in the Letter, SeB. 5, ac-
counting it to be about 8 or 10 Foot, and that in the
Letter, SeB. 4. to be ix or 14 Foot deep *, the Reader
may pleafe to underftand, that the Depth was not
meafur'd, but conjeffur’d, and accounted for according
to the Relator’s bell: Remembrance. That which makes
the Depth the greater being that of SeB. 4. (tirll: pla-
ced, but laft wrote) was wrote upon Information (but
by Conjeffure alfo) of another that lived near the Place,
and view’d it often. But the Difference may ealily be
accommodated or falved, by fuppoling (which will not
be far from Truth) that when the Labourers or Di-
kers firft difeovered and encountred the Jetties and o-
ther Things there found, it might be about the Depth
of 8 or 10 Foot', but the Bottom of them, when they
came to be all taken up, might be at the Depth of a-
bout IX or 14 Foot, as in the other Relation.

Take notice alfo, concerning what is faid pag. 1159.
I'm. 14. that fome, and thofe very judicious Perfons,
fay, that the Stones which the Spedators faw at the
Bot&oin of Hammon Beckj were Rich as the Dikers had

firff

( 345 )

firft thrown out, (when they were taking up the old
Goat) and were fallen in again. But that it was a hard
and firm Soil is certain , and probably that on which
the famous Steeple of Bojion Hands. See the Record of
the Foundation of the faid Steeple in the Philofophical
TranfaEiionSy Uumb, 22^,pag, 243,

The Form of the Shoe Soles found at Spalding was
after this Manner, Fig. 1 1.) each Foot had its pro-
per Shoe : This was for the right Foot.

Now, by fome PalTages in Hiftory, it may proba-
bly be conjedured, when thofe Shoe Soles were left
there, and how long it may be fince that Atterration,
that makes the prefent Country, began. Take an In-
flance or two.

In 5r^7£;’s Chronicle, ad An. 1465. we read of a Pro-
clamation againft the Beaks or Pikes ofShoone, or Boots,
that they (hould not pafs two Inches upon Penalties
there mentioned. And by other PalTages in Hiftory
it appears, that thofe Pikes of Shoes were before that
time exceeding long, and held up by Chains, that they
might not hinder the Wearers going , which Chains or
Ligaments were fometimes of Silver, if not of Gold,
that they might be rich, as well as ornamental. The
other Inltance is this.

In Melchior Adamus^s Life of Conrad Pellican; at the
Bottom of Page 263, in the Edition, there is

this Pahage. Illo ipfo tempore (viz, A?i. 1484.) milites
ex Flandria reverfi multa nova introduxerunt^ nempe
V arte gat as caligas^ ohufos calc e os ^ qui ante a acuti ge-
flabaiitur a viris mulieribns ^ fimul quoque novum fan--
daliorum genus obtujiim^ quod vocabant q^d^-

bus fuos etiam parentes uti conjpexit.^ omijjis paulatim
calopodiis |>0l2rcf)Ul) ditlis : qu^ quidem novitates inte^
rim immenfum creverunt,.

No'vv;

( 34<5 )

Now by this Account it appears, that it is not much
above 200 Years fince thofe Shoes, before defcribcd.
were worn , and confcquently it cannot be much lon-
ger, fince the Earth hath been raifed there to the Thick-
nefs before mentioned, of 10 or 12 Foot 5, and
fince Bicker Haven grew up to be (as now it is) higher
Land than the Country on each Side of it. By which
may be conjedured, what a Change a Century or two
more may make in the Out-falls of the Rivers of JVi-
thatn, Welland, Njne and Oufe'^ and confcquently the
Neceflity of taking fome other Method for preventing
the impending Mifchiefs, which threaten the Naviga-
tion of the faid Rivers, and thofe who have Efiates
and Interefts in the great' Level of the Fens, and are
concerned about the Draining of them.

IX, An Account of a monjlrous double &rth in Lor-
rain. Communicated to the Tublijher by Mr, Co-
lin Mac hzunn/Prof Math. Abredon. 5^. vS. S.

I The Under written, Surgeon in Ordinary to his Royal
Highnefs the Duke of Lorrain, certify, that on the
lafl of December, 1722, I went by his Orders to Domp
Remy la Pucelle, to lee there SebaJUana Camus, aged 44
Years, delivered on the z4th of the faid Month, being
Chrtjlmas Eve, about eight o’Clock in the Evening, of
two Children, or Twins, joined together in the Man-
ner as appears by the Draughts, (Fig* i, 2.) viz.
There is one Head, one Neck, one Breaft, one Abdo-
men, and two Hands on one Side , and there are as
many Parts on the other • the whole being well pro-
portioned and plump, joining together by the Belly,
which is common to both, fo that one of the Heads is

3 in

( 347 )

in the Place where the other’s Feet fliould be, and the o-
ther Head is in its natural Place they have but two Legs
for both of them, which feem to arife from the tranfverfe
Apophyfes of the Vertebrdi of the Loins on one Side ^ and
from the oppofite Region of the Loins, comes out a Leg
ending with a Joint which bends forwards, and at the
the Extremity forms a fmall Stump, like a Finger, arti-
culated by Ginglymus, There is but one Fundament for
both, by which they void their Excrements- they
have but one Navel-ftring, and the Parts proper to the
Female Sex are alfo (ingle : They eat and drink with
their Mouths feverally, and while the Breafl is given
to one, the other cries for it ; They deep and are a-
wake, fometimes both at the fime time, fometimes fe-
parately. Each of thefe Children has been baptized :
one of them is fomewhat plumper than the other,
which is more puny, and not fo frefh-colour’d. The
Head of the one, which is a little bigger than that of
the other, came firft to the Birth, the two Arms ly-
ing on the Bread: followed next the Legs lay on the
Sides of the Bread of the Second^ the oppofite Leg,
which is (ingle, was extricated afterwards , lad of all,
the Arms of the fecond Child, being ranged on the
Side of its Head, made it eafy for the red to come /
out. The Bodies of both thefe Children make no more
in Bulk than that of one ordinarily does.

It is obfervable, that the Mother can affign nothing
that had had any relation to this Event, during the
Time of her Pregnancy.

I am jud now informed, that both thefe Children
are equally well in Health.

Nancy, the 2 iji of January,

1723. Ah S.

F E V R r.
By

( H8 )

By another Account communicated to the Royal So-
ciety, we are infonnd^ that thefe Children lived two
Months after the Birth.

Fig. I. Reprefents the fore View of the Twins.

2. Their Back-part.

3, 4. The Skeleton.

5. The Breafts and Abdominal Mufcles, after

the external Teguments were removed.

6. Part of the Vifcera of the Abdomen.

7. The Urinary and Genital Parts.

The two firjl Figures were drawn in their Life-tbne^
and the five following were taken after their Death, by
Order of his Royal Highnefs the Duke Lor rain.

X. OhJerVations and Experiments on tin Sal Ca-
tharcicum Amarum, conwionly called the Ep-
fom Salt. Sy Mr. John Brown, Chymtfij
F.%S.

That the Salt, of late Years diftinguiihed by the
Title of Sal Catharticum, is made from what, at
the Salt Works, is called Bittern, is pretty commonly
known ^ but the particular Manner how this Bittern
is produced, and from it, thefe Salts, has not yet, as
I know of, been communicated to the World, in fuch
a Manner, as to become intelligible. And the Oppro-
brium unjahly call upon the Salt, of its being a coun-
terfeit’or fomcthing made in imitation of
it, or common Salt dilfolved and recryflalized, has

3 . very

( H9 )

very much funk its Efteein among the Learned in
Phyfick.

By the Account M. Bolduc gives no longer ago, than
in the Hiflory of the Royal Academy of Farls^ for the
Year 1718, 1 find he did not fucceed according to his
Wifii in the Experiments he try’d, to find out what
this Salt was made from, juftly grounding his Reafons
for its not being all made from thej^y^fwWaters, or other
Springs that afiPord bitter purging Waters, becaufe of
the large Quantities confum’d, and the Cheapnefs of its
Price. After all his curious Endeavours, it ftill re-
main’d a Secret, until the Information he received from
hence by Dr. Mendez^ whofe Account is as follows,
though very imperfed. It comes, fays he, from Le-
tnington and Fortfea, both in Hampjbire, where from
Heaps of folTile Salt, there runs a faltifli, bitter, fharp,
and pungent Liquor, One would judge by itsBrackilh-
nefs and Bitternefs, that it contained two Kinds of Salt,
the one a Sea Salt, the other a bitter Salt. To feparate
thefe Salts, they caufe this Liquor to run through hol-
low Drains on the Ground \ there it gets together, and
condenfes into Salt , this they put into a large Veifel,
with a great Qiaantity of common Water, and boil it
as long as is fufficient to dilTolve it, then they let it
cool and fettle for feveral Days. The Water, im-
pregnated with the Sea Salt, which is the heavieft,
links to the Bottom of the Veifel with the earthy Parts,
and the Water impregnated with the bitter Salt, which
is the lighted, fwims at Top. They take off this up-
per Liquor, as long as it retains its bitter Tafte, without
any Pungency *, afterwards they boil it in one or two
Waters, then evaporate it, and it yields white and tranf-
parent Crydals, which are the counterfeit Epfom Salt.

lii

What

( 55° )

What Experiments M. Bolduc made with the Bit-
terfiy fent him by that Gentleman, I do not remember
to have met with, in any of the fucceeding Memoirs.

Dr. Seipp, in his Defcription of the Fyrmont Waters,
?age 127, fays, that the common Englijb purging Salt,
which is fold in great (Quantities in Germany, under
the Name of Epfom Salt, is not prepared from the Ep-
fom Waters, but is made in London from common Sea
Salt, and Oil of Vitriol.

In the fame Fage he fays, that the Salt obtain’d from
the Pyrmont Waters will part with its own acid Spirit,
upon pouring on the 0/. PltrioL which the Sal Mirahile
and the Englijh purging Salt will not. By this Means
he diftinguifhes the firft Salt from the two la ft.

Dr. Quincey, in his PraleBiones Pharmaceutics, pub-
lifh’d fince his Death, fays, there hath lately been con-
triv’d a Salt from the Mineral Purging Waters, made
by Evaporation, Filtration, and Cryftalization. It
was firft entitled Sal Mirahile, or Sal Cathartieum Ama-
rum ^ but it is now fo fcandaloufly counterfeited, that
it is little elfe than common Salt dififolv’d and recry-
ftalized.

Before I enter into the Account how this Salt is
made, it may not be amifs, firft, to fay fomething of the
genuine Salt that has been made from the bitter purging
Waters, of which the learned Dr. Grew was the firft
who attempted the making it at Epfom, Some Years af-
ter, feveral other bitter purging Springs were found in
different Counties, and Salts in fmall (Quantities were
boyl’d up from them, but from no Place, nor all the Pla-
ces put together, in fuch large (Qaantities, as from the
Springs on one fide of Shooters-Hill in about theYear

1700, which were then in the Poffeffion of thofe two
ingenious Chy mifts, Mr. George and Mr. Francis Moult ^

( 35» )

and where they made fuch large Apparatus for ei'a-
porating the VYater, that they have fuinetimes boyFd
down 200 Barrels in a Week, from which, in a dry
Seafon, and when the Land Waters did not get into
their Drains, they have obtain’d 224 Pound of Salt.

- After theie Works had gone on fome time. Dr. Hoy
found out a more expeditious Way of making a purg-
ing Salt fo nearly refembling that from the purging
Springs, in all its Properties, that it foon pafs’d on the
World for the other, and continued fo to do.

The great Confumption of thefe Salts (which then
went only by the Name of Epfom Salts) as well at
Home as Abroad, engaged fome of our Phyficians, (ma-
ny Years before M. Bolduc took Notice of it) to fu-
fped, that even what was made at Shooters-Hill was
fpurious, and received an Addition of fomething to en-
creafe the Quantity. But thefe Sufpicions, I dare po-
fitively affirm, were entirely groundlefs, as to the Salts
made there, and readily believe the fame of any other
Place, where the Spring Waters were boyled down for
S lit. But upon a Confideration, that there were greater
Qjaantities of this Salt confumed than all the Places
where the Waters were boyl’d could produce, which
was the real Fad at that Time of Day, there was
fufficient Room to fufped, that fome of them were not
genuine, as appear’d to be true fometime after.

For the Secret, which was then in a few Hands, of
making thefe Salts cheap, gave thofe, who had it, an
Opportunity of underselling thofe who made it from
the Waters, and, in a Year or two, render’d them in-
capable of making it to any Advantage, confidering the
Price it was fold for by the others: So that the Work
on Shooters-Hill was thrown up, and I believe there has
not been 100 Pound of Salt made from the Waters
fince that Time, in any Part of the Kingdom.

I i i z

Some

c )

Some time before this Work at Shooter s-Kill was
broke up, fome Pains was taken to difcover the Secret
thofe had, who fold the Salt fo cheap • and upon exa-
mining the feveral Salts, that were fold about Town,
thofe difpos’d of by Mr. George and Mr. Fraiicis Moult,
were certainly genuine, and were therefore a proper Stan-
dard to judge of the reft by. But from all the Experiments
then made, there could no material Difference be found
between the Salt made from the Waters, and that made
by them who were in the Secret. There was indeed
Salt fold by fome, which, in the Courfe of thofe Try-
als, was found to be a Sal Mirabile, made from the
0/. Vitrioli and common Salt, but fhot into fuch fmall
Cryftals, as not at firft Sight to be diftinguifhed from
the other.

NecelTity being the Mother of Invention, it was not
long before it was difcovered, and the Experiment was
try’d at the Lady Carringtons, Salt-Works near Portf-
mouth ^ where it was found the fame Thing could be
done, as at another Work, not far from it, and in which
Dr. Hoy had been concerned.

It was fome Years after this Salt had been made at
Portfmouth, before the Saitmakers at Lemington attemp-
ted, or indeed knew the Method of making it- who are
now the greateft Traders in it, and have fent feveral
Ton in a Year to London, beftdes what has been diredly
exported from thence.

I remember it to have been the Opinion of the Pro-
prietors of the Salterns near Portfmouch, that this pur-
ging Salt could not be made at any other. Salt-Works
except theirs, and that the bitter Tafte in the Salt
was coinmunicated from the Earth to the Sea Water,
whilft it flood expofed in their Sun Pans. But Time

has

. / 353 )

has prov’d this Opinion falfe , for befides what has
been faid of its being made at hcmington^ it was about
4 or 5 Years ago begun to be made near tlewcaflle^
where it is ftill continued to be made and doubrlefs
may be made at any other Salt-Works, where the com-
mon Salt is made from Sea Water by Evaporation.
Whether any Thing of this Kind has been attempted at
any of our Inland Salt Springs, either in CheJJnre^ or
Worcejlerfiire^ I am not yet fatisfied.

There is fome Difference in the making the com-
mon Salt in Hampjhire, from that about t^ewcajile : At
the firft of thefe Places, in the Beginning of the Sum-
mer, at Spring Tides, or at New and Full Moon, the
Sea Water is let into their feeding Ponds, which are
their Refervoirs for their Summer’s Working, and from
hence is conveyed into fmall fquarePans, and again, after
fome time, from thefe it is convey’d into larger Pans, or
Beds, which they call Brine, or Sun Pans \ all which are
made of Sea Mud and Earth. In thefe laft Pans, or Beds,
it lies expos’d to tlie Sun and Wind, in order to exhale
the weakeft Waters ^ and it is in thefe Beds, if the Wea-
ther prove very favourable, that they can make as good
Bay Salt as any we have from France, and at fuch a
time they never bring their Brine to the Boilers. But if
the Weather is not hot enough for that Purpofe, their
Brine is expos’d fo long in thefe Pans, till it becomes
of fuch a Strength as to fupport their Eggs, .made of
Glafs or Wax, to a certain Height above the Surface
of the Brine, which from thence is convey’d into large
Store Cifterns, and then into Boiling Pans made of
Iron, where it is boyl’d down (after having been fre-
quently fcumm’d) to a Sea Salt. ’Tis obfervable, that
whilft the Brine is boy ling, there precipitates a hard
crufty Matter, which is partly taken out by Velfels

placed

( 3 54 )

placed in proper Parts of the Pan for that Purpofe, and
Part of it fixes, on the Bottom of the Iron Pan fo hard,
as to be afterwards dug off •, and this the Workmen- call
Scratchy and is what Dr. Collins,^ in a former Tranfa-
dioii cdncerning the Sea Water boyl’d at Shei/Js, calls
a Stone Powder. When the Operation for the Sea Salt
is finilh’d, it is taken out hot, and. put into, wooden
Troughs with Holes at the Bottom, through which
runs the fuperfluous Liquor : Under thefe Troughs are
fet other Vefiels (with Sticks fixed in them in a perpen-
dicular Poflure) to receive what runs through. In thefe
Veffels the Liquor is fuffer’d to continue fome time,
and according to the Quantity of Sea Salt ftill left in
it, will cryftalize to the Sticks, fomething like Sugar-
candy, but in much larger Shoots j and this they call
Cat-Salt^ or Salt-Cats, 'and it holds fome (hare of the
bitter Salt. When this Salt is broke fmall, or rather
powder’d, it is fo white, that fome Gentlemen choofe
it for their Tables-, but the greateft Confumption of
it is among the Cake Soap-Boylers. The Liquor that
will not Ihoot to thefe Sticks, is what at thefe Works,
they call the Bittern, fit for making the Sal Catharticum^

The Remainder of this curious Paper flail be commu-
nicated in our next, .

LONDON: Printed for TT, and J, ZnwjJ, Printers
to the Royal Society * at the Princess- Arms, the Weft
End of St. Paul's Church-Yard.

«

\ '

. \

'•V *■

\

&

%

■ •

I

VA'

* •

•V

N

t

X

Numb. 378.

PHILOSOPHICAL

«

TRANSACTIONS.

For the Months of July and Augufl, 1713.

The CONTENTS. ,

I. Florum Geometricorum Manipulus Societa^
ti exhihitus a D. Guidone Grandi Jhhate Ca-
maldulenfi, Pifani Lyc^iet Mathematico, ^S.S.

II. The remammg ^art of the Ohjeryations and Ex^
periments on the Sal Catharcicum Amariim,
commonly called the Epfom Sale, ^y Mr. John
Brown, Chymift. F. (?(. S.

III. J Letter frojn the Mr. James Pound,
<S^Eior of Wanftead, F. ^ S. to Dr. Jurin,
Seer. (J(. S. concerning Ohferyations made tPith
Mr. HadleyV ^fleBlng Telefcope.

Kkk

IV. Ohfer^^

IV. OhJer'Vations on the Satellites of Jupiter and
Saturn, 7nade with tJ>e fame Telefcope, % John
Hadley, E/fy F. 5. ExtraSied from the
Minutes of the Royal Society, Apr. 6* 1721.

V* An Account of an ExtraAlterine Foetus^ taken
out of a Woman after Deaths that had continued
five Years and an half in the 'Body, By Robert
Houftoun, M i)*

A

I. Florum

( )

I. Florum Geometricorum Manipulus Societa-
ti exhihitus a D. Guidon e Grandi Jbbate Ca-
malduknfi, Pifani Lycai MathematicOy

A ^ - ■

Sues Geometria hortos habet, in quibus aimula
(an potius magiftra ?) naturae lukre folet, fua ipfius
manu fiores elegantiflimos ferens, irrigans, enutriens,
quorum contemplatione cultores fuos quandoque recre-
at, ac fumma voluptate perfundit. Hos inter bonis a-
vibus Sc ipfe quondam admifTus, nonnullos decerpfi flo-
res, vario frondium numero coronatos, quandoque Sc
infoiitis foliis fibi per innumeros gyros circumpofitis e-
legantiflime compados, quorum exiguum hunc faltem
inanipulum vobis, Viri Ciarifliau, ofFere ftatui, ut me-
um vobis obfequium aliquo argumento teftatum face-
rem. An nature induftria fimili fortaffe artificio flo-
rum, fruticum, arborum folia conftruere fatagat,* tali
proportione fucci nutritii motum temperans, ac diri-
gens, ut eadem frondium figura dimanet, quales in va*
riis ejufmodi florum geometricorum foliis, juxta varias
leges, quibus deferibuntur. obfervare licet, Philofophis
difeutiendum, ac decidendum relinquo, praecipue ver6
folertiflimis naturse indagatoribus, qui magni Nentoni
exemplo naturales leges 'ex profundioris Geometric
principiis repetendas fibi merito perfuadent, quibus u-
tique illuftrillimus caetus vefter, prae aliis maxiine a-
bundat. Valete.

L 1 1

DE-

( )

DEFINITIONES.

I. Flores Geometricos generatim appello quaflibet fi-
guras curvi quadam per aliquot foiiorum, fefe ab uno
centro expandentium, perimetrum^ recurrente eireum-
fcriptas, quales exhibent Figurse i, 2, 3,4, 5 j quos
quidein flores, pro numero foiiorum, bifolios, -trifolios^
tetrafolios, pentafolios, exafolios, die, licebit nuncupare,

IT. Cura porro innumeris raodis ejufmodi flores ge-
nerari poflint, earn genefim hie fpeciatiin conflderamus,
quae per raraos a centro floris prodeuntes, aequales ve-
rb finubus angulbrum, iis angulis, quos cura data po-
' fitione Tinea rami comprehendunt, in data aliqua ra-
tione proportionallum, procedit : cujufmodi curvas Rho--
doneas dudum appellavimus , eamque proportionem
Rhodone^ cuilibet propriam dicimus,

III. Rhodoneam Jimplicetn appellamus, quae una circu-
Tatione perficitur, duplicem quae duplici, triplicem quse
triplici, fic deinceps pro nuraero circulationum.

Itaque ad Rhodonearum deferiptionem aflumpto quo-
libet'circulo, cujus centrum C(Vid, Fig, 7.) 6c du-
db ubilibet radio C D ad radium pofltione datum C A
utcunque inclinato, fit angulus A CD ad angulum
A CG (five arcus AD ad arcum A G) in data ratione
a ad dudoque finu G H, fiat C 1 aequalis G H ^ erit
pundum I ad Rhodoneam fupra definitam.

Ejufmodi Rhodonearum proprietates praecipuas entN
cleabimus, nec non fpatia, 6c perimetros breviter di-
metiemur fequentibus propofitionibus.

PRO-

( 357 )

r •

PROPOSITIO L

Si fgerit arcus E A ad quadrantem A F (live angu-
lus EGA ad reftum) ut a ad erit E C unus e
maximis ramis Rhodoneae, five erit E apex unius ex ejus
foliis, (Vid. Fig, 6, 7.)

Nam ex delcriptione patet, ponendum elfe ramum
C E jequalem F C finui quadrantis A F, qui omnium
finuum eft maximus.

PROPOSITIO II.

$

Quodlibet folium Rhodone^ circa axem CE hinc
inde asquali, uqiformi, fimili expanfione fpargitur.

Fadis enim hinc inde sequalibus angulis ECM,
E C D, ob arcus aequales interceptos E M, E D, fi fue-
rit arcus AM ad AN, ut AE ad AF, utAD ad
A G, nempe in data ratione a ad etiam refidua E M,
F N, itemque ED, F G in eadem ratione erunt, adeo-
que cum antecedentia EM, ED sequalia lint, etiam
confequentia F N, F G invicem aequabuntur, uti 6C
refidua ad quadrantes N K, G A, quorum finubus cum
«quari debeant rami Rhodones C L, C I, ipfi aequa-
les erunt ^ quare ab.axe CEdiinc inde squali, 6c uni-
formi expanfione fpargitur quodlibet folium Rhodone^.
Quod erat, <5cc.

C 0»R O L L,A R I A,

I. Ob aequales arcus E Mi E D fit A E inedius A-
rithmeticus inter A M, A D, qui intercipiunt sequales
rainos Rhodone^e ^ ideoque horum fumraa illius dupluin
adsquat, five asquatur toti AE P arcui fedoris cir-
cumfcribentis unym Rhodoneas folium.

Lll 2

II. Hinc

( )

II. Hinc etiam arcus M P ^quatur A D.

III. Et eorundem arcuum AM, AD fumma ad fe-
luiperipheriam A N K eft in data rationed ad b, quam
habet A E ad quadrantem' A F.

IV. Et feftor A P C Rhodonese circumfcriptus, eft
ad femicirculuin ineadem data ratione a ad quam ha-
bet arcus A P, five fumma duorum AM, AD ad fe-
miperiplieriam A N K.

PROPOSITIO III.

Nume'rus foliorum, quibus Integra Rhodonea fim-
plex compingitur, eft ad unitatem, ut x ^ ad a.

Tot enim folia emergunt ex hac defcriptione, quot
fedores unicuique folio circumfcripti, intra circulum
difponi polfunt , fed quilibet fedor eft ad femicirculuin,
ex Coroll. 3. pr diced, ut a ad adeoque ad circulum
ut ^ ad 2 b, quare numerus foliorum in una circulatione
eft ad unitatem ut 2 ^ ad a. Quod erat, 6cc.

’ COR'OLLARIA.

^ I. Hinc Rhodoneam fimplicem defer ibere poffumus,
quas datum foliorum numerum w, puta fex, compleda-

fft

tur, fi nempe pro ratione a 2id.b affumatur ratio i ad -

(in cafu propofito i ad 3) quomodo erit x ^ ad ut
m ad I (in propofito ut 6 ad i) adeoque prodibit da-
tus foliorum numerus m.

II. Sed Rhodoneam duplicem, triplicem, quadru-
plicem, 6cc. eadem arte componemus, dato foliorum
numero in fe recurrente)n, fi nimirum pro Rhodonea

duplici

( 3 59 )

ftl •

duplici fumatur ratio i ad exiftente dato numero

m impari, alias prodiret Rhodonea (iinplex fubdaplo
foliorum numero, qua; in fecunda circulatione (ibiinet
fuperponeretur, per eadem foliorum vefligia recurrens.

tn

Pro Rhodonea triplici ratio i ad— dummodo numerus

m non fit per 3 divifibilis, alias iterum fimplex Rhodo-
nea prodiret fubtriplo foliorum numero contenta. Simi-

liter pro quadruplici Rhodonea ratio i ad g- inferviet,

dumodo numerus m fit impar, alias Rhodonea fimplex,
aut duplex, ut antea oriretiir ^ oportet enim in prim a
circulatione refpedu Rhodonese duplicis haberi inte-
grum aliquem foliorum numerum cum \ alterius folii,
refpedu triplicis cum i, vel | folii, refpedu quadrupli-
cis cum vel i alterius folii atque ita pariformiter in
aliis.

PROPOSITIO IV.

Si ratio ^ ad ^ non fit numeris effabilis,fed arcus D A,
G A fint incommenfurabiles, innumera folia fibimet
per infinitas circulationes advoluta circumponentur.

Qjaslibet enim circulatio, prseter certum foliorum
integrorum numerum, partem folii fuo toti incommen-
furabilem comprehendet, nec unquam ad idem pun-
dum defcriptio revertetur, adeo ut ^equatio ejufmodi
curvx infinitorum fit graduum. (Vid, Fig, 5.)

PROPOSITIO V.

At fi ratio ^ ad ^ fuerit dupla, prodibit Rhodonea
unifolia*

Nam

( }

Nam ex Prop, 4. multitudo foliorum efl ad unita-
lein ut 2 If ad /? *, 'fed in hoc cafu ^ eft 2, 6c ^ eft i,
quare multitudo foliorum eft ad unitatem ut 2 ad 2, five
ut I ad I ;,'”adeoque humerus foliorum eft unitas, Et
fane arcus E*A, 'qui fit’ ad quadrantem A F ut ^ ad'^,
nempe "m ratione dupla, eft femiperipheria, adeoque fe-
micirculus eft fe,ctor AFE circumfcriptus femifolio,
cujus axis EC'ex Prop, prim'a, ideoque integro folio
circulus integer circumfcribitur.

COROLLARIA.

I •

I. Facilis eft hujufinodi Rhodoneje unifoli® defcri-
ptio, fi fuper radio EC defcribatur femicirculus,
duda chorda E S D, in radio C D ponatur C I sequalis
intervallo C S ^ nam cum C S fit finus anguli C E S ad
radium CE computatus, ejufque anguli duplus fit A CD,
erit ramus C I adRhodoneam rationis duplse, juxta ge-
nefim pr^emiftam.

II. Unde etiam, fi centro C, quolibet intervallo C S, in
dido femicirculo arcus P S defcribatur, 6c tantundem ex-
tendatur in I, ut fint.arcus P S, S.I squales, erit pundum
I ad Rhodbneain, quippe C’ S perpendicularis chordas
ED.bifariam fecat in pr^cedenti defcriptione angulum^
E C D;, cumque fit CM asqualis CS, pundum I eft. in
arcu circulari, centro C per I, 6c S tranfeunte, qui.
continuatus in P remanet bifariam fedus in S.

III. Et hinc patet, hanc Rhodoneam duplam efle
circuli fuper diametro E C defcripti, ob quollibet ar-
cus ISP duplos ipformn S P, indeque dimidiam cir-
cumfcripti circuli, cujus diameter E A ^ id, quod con-
fonat infra generaliter demonftrandis P/op. oEtava.

P R O-

( 3<5> )

PROPOSifiO VI.

Ubi ratio /zad ^ eft asqualitatis, efficiturRhodonea bi-
folia, quae nihil aliud eft, quam' duplex circulus fub-
duplGe diametri ad diainetruin circul'i, qui Rhodonese
circumfcribitu-r. (Vid, fig. 9.)

Nam ratio 2 b ad erit ratio dupla, ergo ex Prop,
quarta multitudo foliorum' dttpla erit unitatis ; 6c fane
deferipto circa radium F G; velut diametrum, femicir-
Culo, quoniam rairius Rhbdonei C I debet in hoc cafu'
sequari (inui iphufifiet arcus AD,' utique puntfum f
ad peripheri'am diftf femircircuii peftmget, adeoque du-
plex circulus', cirta^ radios F C,- C‘ V, velut di’ametros,'
defcriptus, erit locus talium ramorum, id eft, Rhodo-
neam ipfam bifoliain conftituet.

COROLL ARIUM.

Etiain hie conftat Rhodoneam bifoliain dimidiam
efle circuli circumferipti, atque adeo aequalein unifoliae
Rhodonese prsecedentis pfopofitionis.

PRO POSIT 10 VII.

Quodlibet folium Rhodoneae eft ad qiiadfantein cir-
cularein ut a ad b,

Dudis enim radiis infinite proximisCID, C i d^
<5c dudis finubus G H, ^ ^ correfpondentibus, nempe
ajquantibus (Vid. Fig. 10, 1 1.) famos interceptos C 1,

C i; deferiptoque concentrico arcu I R, patetfore elemen-
tum C I i femifolii Rhodoneae ad elementum GH hg
quadrantis, ut 4 arcus I K ad H F, eo' quod- bafes C;,
g h trianguli elementaris C H, 6c redanguli elementa-
ris^ ^ H G aequentur j ergo duplum ipfius CTi ad G H

(3^^ )

hg efl: ut integra RI ad H nempe in ratione compo-
lira ex R I ad D d, D ^ ad G^, 6c G ^ ad H led
quia Gg ad (ex theoria intinite parvorum) eft ut
radius ad finuin g nempe ut C D ad C I, vel
D ad R 1, ratio G^ ad H h elidit ^qualem fibi reci-
procam R I ad D ^ quare fupereft, ut ratio R I ad
H ^ eadem fit, qus Y)d ad G^;, led hxc eadem ell
quae a ad cum in tali ratione lint, tarn A D ad A G,
quam A ad A^, adeoque 6c relidua eandem rationem
fervent ergo R I ad H live duplum elementare fpa-
tium C I i ad elementum quadrantis G¥Lhg^ ell in
dida ratione ^ ad 6c hoc Temper ^ igitur duplum fe-
mifolii C 1 E, nempe integrum folium P.hodonece, efl
ad quadrantem, ut ^ ad ^ , Quod erat,

COROLLARI A.

I. Hinc femifoliuin C I E ad quadrantem ell ut »
ad b, (live ut a ad i b.

Item fegmentum Rhodonese C I i ad femifegmentum
circuli A ^ ^ ell in eadem ratione ^ ad 2 A

PROPOSITIO VIII.

%

Quodlibet folium Rhodones medietas ell fedoris
circularis libi circumfcripti, 6c integra Rliodonea lim-
plex medietas circuli, duplex duorum, triplex trium cir-
culorum, 6Cc.

Nam Q^prAcedente quodlibet folium ell ad quadran-
tein ut a ad b, ideoque ad femicirculum ut ^ ad 2
fed ex CorolL 4. Prop, 2. femicirculus ad fedorem folio
circumfcriptum ell ut ^ ad ^ ergo ex sequo perturbate
quodlibet folium ell ad circumfcriptum fedorem, ut b
ad a fcilicet in ratione ^ubdupla, quare 6c omnia

folia

folia Rhodoneae ad omnes circumfcrlptos fe(^l:bres, id eft
Rhodonea (implex ad circulum, duplex ad duos circu-
los, triplex ad tres, 6cc. in eadem fubdupla ratione.
erit.

Aliter, Numerus foliorum ex ?rop, 5, eft ad unita-
tein, ideoque Rhodonea ipfa ad unum^ folium ((i eft
(implex) ut x ^ ad a-^ fed folium eft ad quadrantem
circuli, ex prac, ut a ad ergo Rhodonea (implex eft ad
quadrantem circuli ut 2 ^ ad^, fcilicet in ratione dupla ^
quare (implex Rhodonea sequatur femicirculo. Similis
difcurfus Rhodoneis duplicibus, 6c triplicibus applicari
poteft 5 nam in illis numerus foliorum eft ad unitatem
ut 4 3 ad in his verb ut 6 ^ ad 6cc.

COROLL ARIA.

I. Quselibet Rhodonea (implex cuilibet (implici Rho-
dones eidem circulo infcriptse agqualis eft, quocunque
foliorum numero conftet, femper enim asqualis eft fpa-
tio ejufdem femicirculi.

II. Item qu^libet Rhodonea duplex cuilibet duplici, 6c
quaslibet triplex cuivis triplici aequalis eft, ob eandem
rationem , quippe ilia fpecies eft femper circulo agqualis,
base felquicirculo ^ 6c (ic de aliis. Oportet autem in
duplici, aut triplici Rhodonea^ computare fpatia folio-
rum, quae (ibi fuperponuntur, tanquam diftinfta elfent.

PROPOSITIO IX.

Bifariam fefto angulo EGA, quern axis folii Rho-
doneae cum tangente C A continet, per reftam C D, 6c
ramo Cl deferipto arcu circular! 1ST, erit lunula
T E I quadrabilis, nempe ad quadratum radii, ut a ad
4 b, (Fid, Fig. ii.)

M in m

Cum

( 3^4 )

C^m fit enim quadrans FAadAE, utAGad AD»
qui eft ipfius A E femiflis, erit A G medietas quadran-
tis, ergo quadratum radii CG, vel C D, duplum eft
quadrati finus G H, five rami Cl*, ideoque feftor SCI
ad feftorem E C D fimilem, ut i ad 2 ^ fedor vero
E C D ad F C G eft ut ad ^ ^ haec enim eft ratio ar-
cuum ED, G F, ut eadem eft integrorum E A, F A,
ablatorum A D, A G *, ergo ex sequo fedor S C I ad
fedorem F C G erit ut a ad 2 nempe ut femifolium
C 1 E ad quadrantem F G A C,vel ut fegmentum Rhodo-
neag C I ad fegmentum A G H, vel ut refiduuin CEI C
ad refiduum F G H C, quare etiam reliquum femifolii
S E I eft ad reliquum triangulum C H G, aut tota lu-
nula ad quadratum C H G P,in eadem ratione ad 2
6c ad quadratum radii CG, quod prsedidi quadrati eft
duplum, erit ut ^ ad 4 (^od erat, 6cc,

COROLLARIA.

I. Cum numerus foliorum Rhodonese fimplicis fit ad
unitatem, adeoque etiam fumma omnium lunularum,
quas integra peripheria radio CT defcripta abfcindit,
ad unam lunulam T E I, ut 2 ^ ad ^ j ipfa vero lunu-
la ad quadratum radii ut ad 4 patet efie fummam
didarum lunularum- ad quadratum radii ut 2 ^ ad 4
nempe fubduplam ^ hoc eft fummam talium lunularum
aequare quadratum ipfum G H C P quadrant! infcrip-
tum.

II. Unde fumma lunularum, ex una Rliodonea per
didam peripheriam abfciffarum, sequatur fummae lunu-
larum ex qualibet alia Rhodonea, quotcunque folio-
rum fuerit, eidem circulo infcripta fimiliter determi-
natarum.

IIL Cum

C )

III. Cum ejufdem fedoris EGA medietas fit tarn fe-
inifolium E I C, quam fedor ECD, vel EDA, nec
non fedor CSV, fiunt fegmentum C I jequale trilineo
E I D, 6c femiiunula ESI trilineo C IV squalis, quod
propterea erit pariter quadrabile, utpote ad triangulum
G G H in data ratione ^ ad x

IV. Et fumma Iiorum trilineorum in qualibet Rho-
donea pariter ejufdem erit quantitatis, utpote fummae-
lunularum ejufdem, vel cujufcunque alterius Rhodo-
ne^'fii'n^^licis eidein circulo infcriptae femper asqualis.

V. Adeoque fi ilia triangularia foliorum Rhodonese
interftitia pro/oliis computentur, flos inde totidem fo*
Iiorum perfede quadrabilis exurget, ut in Ftg, 13.

PROPOSITIO X.

Ad quodlibet Rhodoneae pundum I tangentem du-
cere.

Fadum jam fit *, dudaque ramo I C (Vtg, 14, 15.)
perpendicularis C M, conveniat cum tangente I M in
M 5 radio C I arcus I R infinite parvus defcriba-
tur ufque ad alium ramum C i infinite proximum,
fintque ramis Cl, Ci sequales finus GH^ gh, 6c cir-
culi tangens G L occurrat diametro in L. Erit ergo
I C ad C M ut i R ad R I, nempe in ratione compofita
ex i R, feu ^ O, ad O G (hoc eft g h, vel i C, ad
h\S) 6c O G, five H ad R I (quas ex Prop, 7. eft
eadem ration! b ad a) quare i C ad CM erit in ra-
tione compofita ex 2 G ad ^ L, 6c ex ^ ad 5 fed eadem
ratio i C ad C M componitur qUoque ex i C ad L,
6c ^ L ad C M 5 ergo oportet rationem h L, five H L,
ad C M efie datam, fcilicet earn, qua3 ^ ad a, ideoque
fi fiat, ut ^ ad a, ita fubtangens circuli HL ad

M mm2 G M

( )

C M ramo C I perpendicalarem, jundla M I erit tan-
gens Rhodonese in pundo.I j Qjiod erat faciendum.

COROLLARIA.

I. Si fiat ut a ad ita C H ad C N ramo perpen-
dicularem, junda N I erit curvas Rhodoneas normalis
nam quia H L ad C M eft ut ^ ad C H ad C N
ut a ad erit H L ad C M ut reciproce C N ad C H ,
6c ideo redangulum MCN xquabitur redangulo
LHC, id eft, quadrato GH, vel quadrato rami CI^
ergo junda N I eft tangenti M I, feu curvae Rhodoneas
in pundo I, perpendicularis,

II. Patet, tangentes angulorum CI M^^ 6c LGH,
vel G C A femper effe in data ratione a ad b.

PROPOSITIO XL

Si fiat ut b ad ita radius A C ad CCl, 6c femi-
axibus F C, C CLdefcribatur quadrans ellipfis F V CL?
erit ejus perimetur sequalis perimetro femifolii Rhodo-
ne% E C I, 6c partes partibus correfpondentibus. (Fid^

Erit enim ubique etiam G P ad V P, vel gp ad up
in eadein ratione, quae eft AC ad CCL id eft, ^ ad
quare 6c refidua G O, V X in eadem ratione erunt.
Quod fi infinite proximse fint F G,pg , GH, g h, 6i
correfpondentes C 1, C i cum arcu infinite parvo I R,
quoniam I R ad H vel GO ex Prop. 7. eft ut a ad
b^ in qua etiam ratione erit V X ad eandeixi G O, patet
ipfas 1 R, V X aequales fore ^ cum ergo 6c fint sequales
Ri, VX (ob ^equalitatem quarumvisCI, G H, vel
T V, nec non C i, g t u) patet fubtenfas quoque I
V u aequales faturas. Singula igitur elementa, turn cur-

( )

vx Rhodoneas E I C, turn ellipticas F V Q, invicem se-
quantur-, quare & perimeter femifolii Rliodonese erit
quadrant! curvse ellipticas ^equalis, 6c duo quselibet
folia perimetrum habebunt integrae curvas eliipfeos x-
•qualem'. Quod erat, <5cc.

COROLL ARIA.

I. Patet, Rhodoneain effe ellipfim quandam contra-
dam nam (i confiuentibus in centrum C pundis T, f,
ordinatag elliptici quadrantis V T, w in ramos abeant
a centro C didudos, quadrans ellipfis in femifolium
Rhodoneae contrahetur, eadein curvae longitudine ma-
nente.

II. Hinc iterum patet, Rliodoneam elTe medietatem
fedoris circularis circumfcripti ^ eft enim femifolium
E I C medietas quadrantis elliptici F V Q,C, in quern
expanderetur, ft rami ab eorum centro diffoluti fierent
paralleli, 6c redae C Q,perpendicuiares ^ cumque qua-
drans ellipfis fit ad quadrantem circularera, ut bafis
Q^C ad bafim C A, nempe ut a ad in qua etiam ra-
tione eft fedor E G A ad eundem quadrantem, ex Prop,
primay patet, ejufmodi fedorem squari quadranti ellip-
tico, ideoque duplum efie infcripti folii Rhodonese.

III. Infuper colligitur, asquales efie foliorum perime-
tros in Rhodoneis^, quaruin ratio fit reciproca, & radii
fuorum circulorum in eadem reciproca ratione fibi re-
fpondeant, nam fi radius CF, vel EC Figur^i 17. 2d-
quaretur bafi ellipfis CQ^Figur^ 16, <5c viciflim radius
C F iftius sequaret bafim C Q, ellipfis alterius F/gnr^^
patet, eandem ellipfim F V utrobique refultare debere,
quippe iifdem femiaxibus defcriptam, eamque fore u-
trivis folio ifoperimetram, exiftente ibi ratione ad

hie

( ja )

hie rcciproce ^ ad a. Exempli caufa, fi ratio a ad h fit?
fubdupla, ut juxta ^rop. 5. hinc proveniat Rhodonea
tetrafolia, radio autein fubduplo (adeoque aequali bafi
quadrantis elliplis ifoperimetras) viciffiin fiat Rhodonea
juxta rationcm dupiam, qu^ ex Vrop» 5*. unifolia eva-
det, erit hsec ifoperimetra uni folio illius ^ nam bafis
quadrantis elliptici huic refpondens bafim habebit illius
radio aequalem, adeoque eadem curva elliptica utrivis
folio cequalis oftenditur.

IV. Si verb in eodem circulo duae Rhodonea deferi-
bantur, altera juxta rationem ^ ad altera juxta reci-
procam h ad perimetros fuarum foliorum habebunt
ipfis rationum antecedentibus bi b proportionales ^
nam fi prirn^ Rhodone* tertia qusedam Rhodonea fimi-
iis deferiberetur in circulo, ad cujus radium prioris ra-
dius effet ut a ad elfet perimetur prim^ ad perime-
trum tertiae fibi fimilis in ipfa ratione radioruin a ad b,
Verum perimeter hujus tertiae, ex CorolU praced, asqua-
retur perimetro fecundae, utpote reciproca ratione, <5c
juxta reciprocos radios deferiptae, ergo perimeter primae
ad perimetrum fecund^ ell in eadem ratione a ad b»

PROPOSITIO xir.

Rhodoneam datas rationis ^ ad ^ minoris inaequalita-
tis ex conica fuperficie fecare.

Fiat ut a ad b^ ita radius bafis NB ad latus NC
coni redi N C K, cujus bafis diametro N K fit perpen-
dicularis radius BF, (Fid. Fig. 18.) qui fit ad BR ut
^ ad be circa diametros B R, B F deferibantur femi-
circuli BLR, B S F, quos fecet quilibet radius B G
in pundis L, S, fitque G H diametro N K perpendi-
cu laris. Si fuper circulo BLR ereda fuperficies cylin-
drica intelligatur fecare conicam in communi fedione

I CIE,

( 3*^9 )

CIE, erit hsec (in planum explicata) ipfamet Rhodonea
propofitse rationis, Nam communes fediones cylindri-
cae illius fuperficiei cum planis triangulorum C B G,
CBF per axem coni C B tranfeuntium, erunt rete L I,
R E ip(i axi parallels, ideoque tarn C 1, ad B L, quam
C E ad B R erunt ut latus coni ad radium balls, fcili-
cet ut ^ ad ^ cmflruBione^ live ut F B ad B R, live
S B ad B L adeoque CE squatur B F, Cl squa-
tur B S, live linui G H. Explicata autem fupcrticie
conica in planum fedorem circularem ipli squalem,
radio C N defcriptum, ejus angulus planus N C G fub-
tendetur eodem arcu N G, fubtendente in ball coni an--
gulum N B G adeoque ut B N ad N C, live ut a ad

ita erit angulus N C G ad ipfum N B G, cujus linui
GH, ut vidimus, squatur ramus C I folii CIE, cu-
jus maximus ramus GE asquat radium BF circuli hi*
fis 5 quare folium ipfum ad Rhodoneam pertinet in da-
ta ratione ad ^ defcriptam , Qjiod erat, 6cc.

COROLLARIA.

I. Cum lit etiam C E ad E 0,uf C F ad F B, ut b ad ^ , ut
F B ad B R lintque C E, F B squales,itidem squales erunt
B R,E 0,6c femicirculusB LR quarta pars erit femicirculi
A E P duplum diametrum habentis, live erit medietas
quadrantis A E O j eft ver6 fex noftra Appendice de
Fornicibus conicis, quam Vivianets fubjunximus jam
inde ab anno 1698) fuperficies conica A DEC ad fu-
am balim A D E O, ut fuperficies femifolii CIE ad
fuam ichnographiam BLR, nempe in eadem ratione
lateris coni ad radium balis ^ ergo cum A D E O du-
pla lit B L R, 5c fuperficies A D E C iplius femifolii
CIE dupla erit, ut aliunde fupra demonftravimus fe-
dorem folio circumfcriptura ijlius duplum efle.

H. Cum

C 570 )

II. Cum oflenfdm fit die angulum ACladNBG,
uti 6c ACE adNBF, in data ratione ad patet
etiam in eadem ratione efie angulum reliquum ICE
ad reliquum S B F, exiftente (ut probavimus) ramo Cl
^quali ipfi B S ^ (Vid, Fig. 1 9.) unde fi femicirculi
C S E, in arcus concentricos, centro C defcriptos, re-
foluti, arcus quilibet P S, ^ j dividantur ad punda I, i,
ut fit fern per P I ad P S, i ad ps in data ilia ratione
a ad erunt punda I, i fic inventa ad curvam Rho-
doneam.

III. Imo etfi ratio <2 ad ^ majoris fit insequalitatis, ad*
hue Rhodoneas ope femicirculi deferibere licebit ge-
neralius quam in Coroll. 2. Prop. 5. fi arcus PS, p^
producantur ad punda I, ut fint PI ad P S, /? i ad

in data ratione a ad b. Fado enim arcu EAR ad
quadrantem EA in eadem ratione, dudoque radio CR,
tiet angulus R C E ad A C E, ut angulus I C E ad an-
gulum S C E. adeoque <5c reliquus i C R ad reliquum
j.C A, cujus finus aequatur C j, five C /, in eadem ra-
tione erit ad ideoque punda I, i funt ad Rhodo-
neam dat^e rationis.

IV. Et fi arcus illi P S, j in femicirculo deferi-
pti, turn dividantur in ratione a ad turn augeantur
in reciproca ratione h ad curvaj interioris longitudo
ad longitudinem exterioris erit ut a ad per Coroll, 4.
Prop, prAcedentis,

S C H O L I O N.

Verum haec,pro inftituto noflro, circa hujufmodi cur-
vas delibafie fufficiat : quanquam alia etiam Rhodonea-
rum fymptomata enucleate in promptu efiet, uti alias
florum fpecies divers^ genefi efformatas exhibere facile
2 foret,

( ?7i )

foret, quorum etiam folia (ut poftrema propofitione
■folia Rhodonearum circa conicam fuperficiem advoluta
dedimus) circa aliquam conoidalem fuperficiem convo-
luta defcribere pofemus, dC quandam foliorum in ca-
lice floris latentium imaginem adumbrare, nifi jam
taedio Ledorum parcendum efiet. Unum hoc admone-
re non prastermittam, quod ex ultimo propofita gene-
rali foliorum Rhodoriem defcriptione fimpliciflima ex
circulo derivata, fufpicari quis non immerito pofiet
etiam prima natufalium foliorum ftamina, qum in flo-
ris, aut fruticis femine latent, non neceflario fimilia
efie folds ipfis confpicuis, 6c jam germinantibus, five
adultis ^ ficut enim fi florum, & fruticum folia noftras
Rhodoneas reipfa imitarentur, pofiet quis concipere,
illorum prima ftamina feminibus cujullibet fpeciei in-
clufa fimpliciflima circular! figure infinite parvi cir-
cumfcribi, fed mox peculiar! vi cujullibet fingularis
fpeciei, dum germinant, ita determinari fuccum nutri-
tium, ut dum in longum eorum axis extenditur, per
quafdam undas, five gyros, ipfi origin! fui pedunculi,
velut centro, circumpofitos, expandatur, eofque femper
in determ inata ratione, vel ardiores, vel ampliores,
quam fi circularis priinorum ftaminum figura retinenda
elTet : quo pofito talis fpecies foliorum Rhodonem, ac
talis nuraerus, 6c forma exurgeret, qualem ratio ilia
determinaret. Ita etiamfi alia lege florum, 6c fruticum
frondes natura inoliatur, non necefie eft earum figuram,
ufque ad ipfa prima earundem ftamina, ex quibus ger-
ininant, obfervari^ fed ilia in ouibuflibet unius certm,
ac determinate figure efie poUet, que tantum pro di-
verfa vi, determinante in ipfis expanfionem fucci nu-
tritii, in fingulis fpeciebus varianda foret, juxta di-
verfain rationem, que per ipforum ftaminum fibras di-
rigeretur. Sed ne extra chorum fa Item us, hec Philofo-
phis innuilfe fufficiar.

N n n

II. The

( 371 )

II. The remaining ^art of the OhferVations and £x-
periments on the Sal Cathardcum Amarum,
commonly called the Epfom Salt. Sy Mr. John
Brown, Chymifl. F. ^ S.

Near 'NewcaJHe^ their Method is, to receive the
Sea Water into their Refervoirs High-Water, at
any fimeof the Moon, if there be no Frefli in the River,
occafioned by Rain in the higher Country ^ and from
thefe Refervoirsy without expofing of it in Beds, as at
Lemingtofiy they pump it into their boyling Pans,
where, evaporating it almoft to a Pellicle, they fill it
up again 8 or 9 Times, and then wafte it with a gen-
tle Heat for the common or Sea Salt. The Liquor, that
runs from this Salt, when taken out, and put into pro-
per VelTels, is what they call the Bittern ^ which if it
Rands feme time in thofe VelTels, a Salt will (hoot and
cryftalize to the Sides, in Tafte pretty much like Sea
Salt, but with a fhare of Bitternefs, and feems to an-
fwer to the Cat’Salt of the hemington Works, and very
probably would Ihoot after the Tame Manner, if they
made ufe of the fame Apparatus*

I could not but mention this general and loofe Ac-
count of making the common Salt, as necelTary to in-
troduce the Liquor Bittern^ which, before Dr.
Hoy found out an Ufe for it, was always flung away 5
being To different in its Properties from the Brine made
Ufe of to produce the Sea Salt, that it would not
boil up into a Sea Salt again, and required the nicefl:
Skill and Attendance of the Operator, to determine
the Time when to take out the Sea Salt from the Pans,

before

before the Bittern incorporated with it, which would
otherwife fpoil the whole Making.

The Bittern at Lemington (as obferv'd before) not
Oiooting to the Sticks, is carry ’d by Channels into Pits
made tight with Clay, where it hands for fome Months,
and there will (hoot again : What Liquor remains is
boyl’d down, till fuch Time as it is obferved to be in
a Difpolition to cryftalize, and then is convey’d into
wooden Coolers lined with Lead : The Liquor, which
will not (hoot there, is boyl’d down after the fame
Manner, in order for another Cryflalization. By this
Time the Liquor feems to have alter’d its Property,
and becomes of a very pungent biting Tafte, and, if
boyl’d down, will no longer (hoot into Cryftals as be-
fore, but precipitates, during the Boiling, a fmali
grain’d Salt^, and if you, for Lxperiment-fake,^lhould
continue to boil down the Liquor, feparated from this
Salt, each Quantity of Salt thus produced, will hill
be more pungent than the other. If you boil down
the whole Quantity of this Liquor, it will produce a
Salt, which if expos’d to the Air, will r\in,per deliquium.
But as this Salt is not the Bufinefs of our prefent En-
quiry, it may probably be the Subjed of another Pa-
per. The Liquor, that produces this Salt, is always
flung away, wherever the Sal Cathartuim is made.

This is what, at prefent, I can give no other Name
to, than a third Salt produc’d from the Sea Water,
differing, in fome refpeds, as much from the otlier
two, as they differ from one another.

To return to tlie feveral Cryftalizations, fuch as
mention’d to be fhot from the Bittern ^ thefe will be
of different Sizes, as to their Figures, and hold fome
fhare of the third Salt but now taken Notice of, which
makes them apt to give and dilTolve j nor is their Tafte
come yet to that fimple Bitter of the pure Salt* Thefe
therefore are either feparately, or altogether, to be flung

N n n 2 into

( 174 )

into a Copper, with as much common Water as is fuf"
ficient to diffolve them, and allow of a gentle Evapo-
ration, till fuch Time as they are again ready to be
pour’d into the Coolers in order for Cryftalization.
This generally proves to be the pure Sal Catharticum,
throughly freed (as far as the Experiments I have try’d
can be convincive) from either a Sea Salt, or the third
Salt. The Liquor decanted from this Shooting, may
be. boil’d down again ’in order for a fecond Shooting,
and after that a third *, but as the Liquors from thefe
Shootings are boyl’d away more or lefs, fo you will
fooner or later meet again with the pungent Liquor,
which contains the third Salt, as you did in the former
Shootings ' froiti ( the Bittern, which the pure Sal Ca-
tharticum is as hecelfarily- required to be freed from,
as froip the common Salt, a Proof of which cannot
be better determined than by one of the Experiments
to be taken Notice of hereafter (viss.) that with the 01.
Vitriol, which will certainly ferment with this Salt, if
the Sea Salt has not been well feparated from it, or if it
Hill holds fome of the third Salt. And when any of
the Cryftalizations will not hand the Teft of this Ex-
periment, they ought to be dilfolv’d and fhot again-, as
before, by which means the pure Salt is to be obtain’d.
I do not mention this as a Tryal made ufe of at the
Salt-Works, but what I have by Experience found to
be true. And the fame Experiment will ferve to diftin-
guilh a Sal Mirabile made at thefe Works, from that
made with 01. VitrioU and common Salt. The Account
they give of it is this.. They take any Qiaantity of
coarfer grain’d Cryftals boyl’d from the Bittern, which
when dilfolv’d and evaporated, more than they would
otherwife do for making the Sal Catharticum, they
throw into a wooden Bowl, with forne Oil of Vitriol,
where it hands for ten Days, and Ihoots into large

Cryftals,

( 575 )

Cryftals.j tranfparent, and like the S^jI Mirahile: But
as this Salt, by this Method, is not fufficiently fatiated
with the 01, VitrioL(if they ufe any) fo it is eahly dif-
covered by the 01. Vitriol, which will readily ferment
with it whereas it has no ElFed on the other Sal Mi-
rahile made as above.

By the AlTiftance of my ingenious Friend, Robert Cay.,
Efq^ at Newcajile., I have received the feveral Shoot-
ings of Salts from their Bittern, as alfofome of the Bit-
^ tern it felf ^ from >each of which I have obtain’d a pure
Sal Catharticum, as * alfo the like kind of third Salt,
as mention’d from the Lemington Bittern, The Method
I took in doing it is agreeable to that I have already
mention’d, and many Years ago try’d at the Salt-Works
near Portfmoutb, It is by Mr. Cay that I am inform’d,
they fometimes boyl their Bittern without letting it
Hand any time to (hoot of itfelf. The Difference is not
very material.

If this Account be intelligible, what the Sal Ca-
tharticum is will no longer be a Myftery. And the
next Thing worth the enquiring into will be, whether
this Salt deferves the Refiedions, that have difeouraged
the Prefer ip don of it } And why it may not pafs for a
Salt as excellent in its Kind, and be of the fame Na-
ture, and have the fame Properties, as that produc’d
from the Epfom, or any other bitter purging Springs.

And in order to prove it to be fo, I lhall give a very
Ihort Abftrad of what Dr. Grew fays of his Salt, and
then pbferve how nearly the two Accounts agree.

The Dodor in hisTreatife de Natura SalisCathartici
Amari, Chap, 2. fays, that in the Evaporation of any
of the bitter Purging Waters, they yield a Cremor at
Top, as alfo a Sediment, both together weighing 6, 8,
or about lo Drams,, from a Gallon of Watery and
that the lefler Part of this Sediment is, in Subftance,

the

(370

tlie fame \vlui rliis Creinor ^ the red: is all Salt, buf:
condfts of two forts, one a muriatick Salt, the other
which is proper or peculiar to thefe Waters.

In the Epfom W atcr, the muriatick Sait is about a
20th Part of the faiine Mixture , in the Dulwich it is in
a greater Proportion, and the fame in feveral others it is, ‘
both in its acrimonious Tafte and Figure of its Cry-
ftals, not unlike to common Salt. The other Salt is
that which he fays is particular or proper to the purg-
ing Waters, and is [made by Evaporation and Cryft.a-
lization. In this Preparation, firft the earthy or plai-
ftery Part is to be feparated, next the muriatick Salt,
and, laltly, a brown and dark Liquor from the proper
Salt of the Waters.

And in the 4th Chapter of tlie fame Part, having
fliewii the Difference of the Figure betwixt the Cry-
Ifals of this Salt and thofe of Alum, he goes on. Nei-
ther is there any better Ground to account the purging
Salt a Species or common Salt, from which" being per-
fedly freed, it differs as much in Tafle as from Alum.
And in the fame Chapter, he fays it will appear, the
bitter purging Salt, although it hath fome Qualities in
common with other Salts, yet is truly, or fpecifically
different from them all. Thus far Dr. Grew.

Now I cannot fee any Thing in this Account, but
what will, confideratis confiderandis^ very well agree
with the purging Salt from the Sea Water.

For firft, there is an earthy or plaiffery Part contain’d
in thefe Waters^ and this muft be feparated. The very
fame is in the Sea Water, and is precipitated in the
Boiling them down, as has been obferv’d, and by the
Operators is called Scratch.

Next there is a muriatick Salt allow’d to be in
thefe Waters- in fome more, in lome lefs, and this is •

likewife

( ?77 )

likewi^b to be feparated : The very fame is done from
the Sea Water, though in a vaftly larger Proportion.

i\nd, laflly, there is a black and dark Liquor to be
feparated tho’ this is but a dark Way which the Doctor
makes ufe of to exprefs himfelf, it cannot be better
explain’d, than by what has been found to be Fad in
boiling down the Waters at That after

feveral Sliootings of Salts by repeating the Boilings of
the Waters, there would, at laft, remain a Liquor of a
deep brown Colour, which would no longer yield a
cryftaliz’d Salt ; but if boil’d up dry, would afford a
Salt of the fame Kind with the third Salt already men-
tion’d: And this explaining Dr* Grew's black and dark
Liquor, helps at the fame time to prove, in this Ar-
ticle too, that the Sea Water affords the fame kind of
third Salt*

I have try’d feveral of the Experiments mention’d by
the Dodor, by which hediftinguiflies his Sait from other
Salts. Such as not aflFeding the Colour of Syrup of
Violets*, curdling of Milk, when boil’d , in jthe Figure
of its Cryftals j in its eafy Dilfolution in the famie
Quantity of Water j in its coagulating with tlie OL
Tartar, per D, L* in its Calcination, and in the Bitter-
nefs of its Tafte, as well before as after Calcination,
and find this Salt, thus feparated from the Sea
Water, anfwer to all the Tryals. Some few Experi-
ments, that the Dodor has not taken Notice of, I (hall
here fubjoin, and then leave the Whole to the Opini-
on of better Judges j Whether there be any fpecifical
Difference between thefe two Salts >

In order to have a Standard for thefe Experiments*
I purpofely got my Friend, Mr. Hyet^ Apothecary at
Epfam (whofe Fidelity 1 could depend on) to boil me
down fome of their Waters, which he did from the

Well

( )

Well in the Town, and fent me a fufficient Quantity
of the Salts, to anfwer the'Purpofel wanted them for.

I procured likewife fome of the hrft Salts from the
Lemington Bittern: Thefe do not hold fo much of
(what I have already diflinguiflied by the Name of)
tlie third Salt, as I find the Neweajile Salts do. This
Lemington Salt, for Diftindion’ fake, call the firfi
Lemington Salt,

Part of this I diifolv’d, and fhot into pure Sal Ca-
'tharticum^ being freed, as well from the Sea Salt, as
the 'third Salt y and this I QdXl t\\t fecond Lemington
Salt.

I procured likewife from NemaJUe the firft Salts
fhot from their Bittern^ which- 1 call the firjl Newcajile
Sait.

Part of thefe I likewife dilfolv’d and fhot, and ob-
tain’d a pure Sal Catharticum, and this is what I call
the fecond NemaJUe

I am obliged to inake Ufe of the Sal Mirabile, made
from the 01, Fiiriol, ^Lud' common Salt, that having been
taken for the Sal Cathakicum, '

As alfo common Salt, that having been reprefented
as the principal Subftance of the Sal Cathanicum,

i took half an Ounce of each of thefe Saits, and dif-
folv’d them in about ‘two Ounces of Water to each
half Ounce of Salt.

A fmall Quantity of each DiiTolLition I pour’d into
as many Glalfes, and dropt into them all fome Butyr,
Antimo?tii, ‘The Precipitation that follow’d, feem’d to
be alike in them all * and Upon dropping a little 01,
Vitriol, into each, what was precipitated being more po-
werfully attraded by-th'e Oil, the feveral Liquors be-
came Clear. Thefe are ‘ the two only Experiments, in
which 1 found the Confequences fd much^- alike in
them all.

In

0

( )

In the following Experiments, the Sal Mirabile is
fuihciently diflinguifh’d from all the refl.

Slices of Gall cut into thefe feveral Solutions have
no manner of Effecl upon any, except that of the Sal
Mirabile^ which is foon ting’d of the Colour of Sack,
or rather deeper.

Sp. Sal Arm, c. Tart, dropt into the feveral Solutions
turns them all milky, except that of the Sal Mirabiley
which keeps its Tranfparency.

The Sp, Salts Armon, c, cake, the 01, Tart, p,
deliq,i\\Q TinHura Coccinell in Sp, Vin.faEi. do every
one, ufed aftet- the fame Manner, fufticiently diftin-
guilh the Sal MirabiU from all the reh:.

In the following Experiments, the Epfom Salt, the
fecond Lemington Salt, and fecond Nezveajile Salt, agree
together, and differ from the common Salt, the firjl
Lemington Salt, and firfl ILeivcaJile Salt,

In the feveral Solutions I dropt a Solution of Silver
in Aq. Forth, from which follow’d thefe Confequences.
The Solution of the Epfom Salt, fecond Lemington Salt,
and fecond FJewcaJile Salt, became equally milky, be-
fore the Precipitation. The Solution of the Sea
Salt, and firjl Flewcafile Salt, let the Precipitation pafs
without receiving any milky Tinge. The firfi Leming-
ton Salt, as holding lefs of the third Salt, than the firjl
Llewcafile Sdli took a little milky Tinge. The Pre-
pitation fell nimbly thorough the Solution of the Sal
Mirabile, leaving it milky.

In the Condition thefe were in, I pour’d fome 01,
Tartar, per deliq, to each of them, on which, after
fome time, a biueiH). Scum arofe on the Surfaces of
the Epfom Salt, fecond Lemington Salt, and fecond New-
cafile Salt : There likewife appear’d a little on the firfi
Lemington Salt, but not any on the reft.

O o o

A So-

( 3^0 )

A Solution of corrofive Sublimate was made inWater,
ten Drops of which, mixed with the feveral Solutions,
produced little or no Alteration but upon dropping in
the 0/. Tartari per deliq, the following Appearances
were produc’d : In the Solution of the Epfom Salt, fe-
cond hemington Salt, and fecond 'NewcaJUe Salt, the
Precipitations were red ^ in the Solution of the com-
mon Salt, and firft NewcaJHe Salt, the Precipitations
were white 5 in the Solution of the firft Lemington^'Ax.^
the Particles precipitated approach’d pretty near the
Colour of the three hrft.

I took fome of thefe feveral Salts in Subftance, and
to each of them pour’d a little 0/. VttrioL which is one
of the Experiments Dr. Grew try’d upon his Salt, and
which he fays caufes a moderate Ebullition, whereby
it appears to partake of an alkaline Principle ; But
without looking for this alkaline Principle from its fer-
menting with an Acid, (Terms juftly exploded by the
learned Dr. Freind in his PraleSriones 1 am

inclin’d to believe, that the Salt he try’d the Experi-
ment on, had not, according to his own Diredions,
been thoroughly feparated from his muriatick Salt,
For this Oil pour’d on the Epfom Salt, fecond Leming-
ton Salt, and fecond Nevpcajile Salt, produc’d no fenh-
ble Fermentation. On the Sea Salt it ads with Vio-
lence, forcing off its acid Spirit with an infufferable
Qas, The fame Elfed in proportion it had on the firji
hemington Salt, and firfl NewcaJUe Salt ^ none at all
on the Sal Mirabile, as being a Sea Salt already fatia-
ted with the Oil.

What I have all along call’d the third Salt, anfwers in
mod of thefe Experiments to the Sea Salt, and yet has
fome Properties exceedingly different from it ^ to thofe I
have mention’d thefe may be added j k will not de-
crepitate

I

( ;8i )

crepitate like Sea Salt ^ it readily melts, when put in a
Crucible in the Fire and when calcin’d till red-hot,
affords a Calx equal to, if not flronger than a Lime-
flone, and ferments violently, as well with Water as
with 01. Vitriol. This Calx^when expos’d to a moift Air,
will Part of it run per deliq. but not fo foon as before
Calcination. All thefe Properties differ in every Re-
fped from the common Salt, and leave me flill in doubt
what to call it, as alfo how far Experiments of this
Kind may be deem’d conclulive.

O 0 0 2

III* A.

( ?8i )

%

HI. A Letter from the d^eV. Mr. James Pound,
(^flor of Wanftead, F. ^ S. to Vr. Jurin,
Seer. S. concerning ObferVations made with
Mr. Had ley V fie Bing Telefcope.

IT were to be wifh’d, that with the particular De-
feription given in a late Tranfadion (Numb, 376.)
of the curious Mechanifm of that Catadioptrick Tele-
fcope, which was made by Mr, Hadley^ and by him
prefented to the Royal Society ^ that inoft ingenious
Gentleman would have communicated alfo a full Ac-
count of what Obfervations he had made with it,
whereby the Publick might at length have been ap-
prized of the Ufefulnefs of an Invention, (worthy of
its great Author, Sir Ifaac Newton^ which, perhaps
from the vain Attempts made by fome of putting 'it in'
Pradice, hath lain negleded thefe 50 Years ; for it is
fo long, (ince it was firft publifhed in the Philofophical
TranfaBionSf Numb. 81.

Mr. Hadley hath fufhciently convinced us, that this
noble Invention doth not confift in bare Theory and
it is to be hoped, that he, or fome other fuch curious
and worthy Perfons, (who fcruple not at a little Pains
and Coll:) will in a fhort Time find out a Method, ei-
ther of preferving the concave Metal from tarnifhing,
or of clearing it ealily when tarniihed, or elfe of ma-
king a good concave Speculum of Glafs quicklilver’d on
the Back- part. When a Method for either of thefe

Ihall

( 3^? )

fliall be difcovered, ’tis not to be doubted, but that
the old Dioptrkk Telefcope will be for the moft Part
laid by, and this Catoptrick one will be chiefly in ufe
among the pradical Aftronomers , inafmuch as feveral
Inconveniencies and Difficulties, which are unavoida-
ble in the Management of the former, efpeciaily when
long, are in this latter wholly avoided.

It is no fmall Convenience, that by means of one
of thefe reflefting Telefcopes, whofe Length' exceeds
not five Feet, (and which may be managed at a Win-
dow within the Houfe) Cceleftial Objeds appear as
much magnified, and as diftind, as they do through
the common Telefcope, of more than loo Feet in
Length.

Mr. Bradley^ the Savilian Profelfor of Aflronomy,
and myfelf, have compared Mr. Hadlefs Telefcope (in
which the focal Length of the Objed Metal is not
quite 5 Feet and i) with the Hugenian Telefcope, the
focal Length of whofe Objed Glafs is 123 Feet; And
we find, that the former will bear fuch a Charge, as
to make it magnify the Cbjed as many Times as the
latter with its due Charge^ and that it repreieiits Objeds
as diftind, though not altogether fo clear and bright
which may be occafioned partly- from -the Difference
of their iVpertures (that of the Hugenian being fome-
what the larger) and partly from feveral little Spots in
the concave Surface of the Objed Metal, which did
not admit of a good Polifti.

Notwithftanding this Difference in the Brightnefs
of the Objeds, we were able, with this refieding Te-
Jefcope, to fee whatever we have hitherto difcovered by
the Hitgenian-^ particularly the Tranfits of Jupiter's
Satellites, and their Shades, over the Dilk of Jupiter \
the black Lift in Saturn s Ring , and the Edge of the

Shade

(?84)

Shade of Saturn caft on his Ring, as reprefented by
Fig. 4. plate 2. of the foremention’d Tranfa&, Numb,

We have alfo feen with it feveral Times the 5 Satel-
lites of Saturn *, in viewing of which this Telefcope
had the Advantage of the Hugenian, at that Time
when we compared them ; for it being in Summer,
and the Hugenian Telefcope being managed without a
Tube, the Twilight prevented us from feeing in this
fom6 of thofe fmall Objects, which at. the fame Time
we could difcern with the refleding Telefcope.

I am^ dec,

Ja. Pound.

"If

IV. 0^

( 385

\

IV. ObferVations on the Satellites of Jupiter and
Saturn, made with the fame Telejcope. (By John
Hadley, Eff^ F. 5^. S. ExtraEied from the
Minutes of the Royal Society, Apr. 6* 1711.

Mr. Hadley gave the Society a Relation of fome of

the moft remarkable Obfervations, which he

had made with his Refiedling Telefcope, before he

prefented it to the Society,

In obferving Jupiter^s Satellites he has feen diflind-

ly the Shadows of the firft and third Satellites caft

upon the Body of the Planet , Mr. Folkes and Dr. Ju-

rin, being prefent, affirmed, that Mr. Hadley had like-

wife fhewn them the Shadow of the third Satellite

\

through the fame Telefcope.

In obferving Saturn the laft Spring, at a Time when
that Planet was about 1 5 Days pad the Oppofition, he
faw the Shade of the Planet cafi: upon the Ring, and
plainly difcerned the Ring to be diftinguiffied into
two Parts, by a dark Line, concentric to the Circum-
ference of the Ring. The outer or upper Part of the
Ring feemed to be narrower than the lower or inner
Part, next the Body, and the dark Line, which fepa-
rated them, was -ftronger next the Body, and fainter on
the outer Part towards the upper Edge of the Ring.
Within the Ring he difcerned two Belts, one of which
crofs’d Saturn clofe to its inner Edge, and feemed like
the Shade of the Ring upon the Body of Saturn ^ but
when he conhdered the Situation of the Sun, in refped

to

(^$6 )

to the Ring and Saturn^ he found that Beit could not
' axife from fuch a Caule,

He fays, that at Times he has feen with this Tele-
fcope three ditferent Satellites of Saturn^ but could
never have the Fortune to fee all five.

Aug. 1723. Mr. Hadley 2lMs^ that he has feveral
Times feen the Shadow of the firh, fecond, and third
Satellites of Jupiter pafs over the Body of that Planet,
and that he has feen the firfl: and fecond appear, as a
bright Spot upon the Body of Jupiter., and has been
i able to keep Sight of them there for about a Qjaarter

of an Hour, from the Time of their entring on his

Limb.

Jupiter's, Satellites have of late Ye irs been fo fitua-
ted, with regard to the Earth and Jupiter., that he has
not had fufficient Opportunity of obferving the Tranfit
of the fourth Satellite, or of its Shadow.

The dark Line on the Ring of Saturn, parallel to
its Circumference, is chieiiy vifible on the Anfji., or
Extremities of the Elliptick Figure, in which the Ring
appears •, but he has feveral Times been able to trace
it very near, if not quite round , particularly in May.,
1712, he could difcern it without the Northern Limb
of Saturn, in that Part of the Ring, that appeared be-
yond the Globe of the Planet. The Globe of Saturn
(at leaft towards its Limb) refleds lefs Light than the
inner Part of the Ring, and he has fometimes diflin-
guifh’d it from the Ring by the Difference of Colour.

The dufky Line, which in 1720 he obferved to ac-
company the inner Edge of the Ring crofs the Dilk,
continues clofe to the fame, though the Breadth of the
Ellipfe is corifiderably encreas’d fince that Time.

V. An

( )

V. An Account of an Extra-Uterine Foetus y taken
out of a Woman after Deathj that had continued
five Fears and an half in the !Body. !By Robert
* Houftoun, M.

I Was fent for m Auguji 1717^ to a Woman near
FJewport- Market^ who had been married eighteen
Years to a Native of the Eaji Indies^ by whom ftie
had eight Children, befides two Mifcarriages. At my
viliting her, now, (he was with Child in a fecond Mar-
riage, and her Husband a vigorous young Man.

She was near her full Time, and had felt Pains for
feveral Days, which, returning by Intervals, (he con-
cluded, would, as ufual, bring on her Delivery. Her
Mother and her Midwife, apprehending no Difhcuity,
alTured thofe about her, that only Time was wanting.

But I found, on Examination, that her Womb was
of no Bulk to contain a Child near its Time*, and that
its Neck, of an uncommon Hardnefs, was alfo clos’d fo
ftraitly, as to* refufe the lead Admidion, even of a
fmail Probe or knitting Needle.

I declared upon this, that her Delivery was impol^
(ible 5 becaufe the Child was not within the Womb,
but between the Womb and the Guts : That it might
be remov’d by a Paffage to be made for it, without
any great Pain, and with Safety to the Mother. I of-
fer’d to undertake it, and alTur’d them, that this was
the only Opportunity ^ and that if (he negleded it, it

P p p would

{ in )•■

woul.1 hereafter be out of the Power of Art to giv«
her the Relief, (he 0111(1 languifli for till Deathj unlefs
favour’d by fome unlikely and extraordinary Accident.

However conlidently I affirm’d it, they liRened with
a Mixture of Disbelief and Amazement, and rejeded
my Affidance. At that Time, in Probability, it would
have been fuccefsful for (lie was a (lender welJ-(hap’d
Woman, in good Habit of Body, and of a fprightly
Difpolition.

It was a Year after this, when Mrs. Hexel, a noted
Midv/ife in St. y^/w^Ys Pariffi, defir’d me again to vi-
lit her. I found her much diforder’d by a growing Im-
polthumation in her Belly : I order’d her fome cordial
Stomachicks, Cajjia, and fuch gentle Lenitives ^ and
they met a Succefs beyond my Expedlation : So that,
by aid of a regular Diet, and the watchful Exadnefs
of a very tender Mother (a Nurfe of above thirty Years
Experience about this City) I reftor’d her to fuch
Strength, that (he- went chearfully Abroad, and re-ap-
ply’d herfelf to Bufinefs. I told her (he might frankly
benefit herfelf by my Advice, or my Medicines : And-
(he call’d as (he found Occalion.

But about fifteen Months from the Time when I
vifited her firft, her Mother came from her to entreat
my Affiftance: She complain’d of great Pain in the
lower Part of her Abdomen'^ and I found a Tumour of
a conick Form, projeding about an Inch beneath the
Umbilicus : Its Inflammation, with Tenlion, and a Fe-
veriffinefs attending it, fo plainly indicated Suppura-
tives, that I was not furpriz’d to hear, in a few Days,
that it had broke, as I wiffi’d.

I propofed to lay it open, both to give a free Emif-
fion, and prevent its becoming fiftulous, but (he was
apprehenflve, that I would, as (he call’d it, cut open

her

( ;89 )

her Belly ; So that not being able to prevail with her/
1 order’d a Pot of Unguent, and fome Plaifters.

The Ulcer foon grew fiftulous, and fo continued
till (he dy’d, which was on the 23d of March laft, in
the 41ft Year of her Age.

For above five Months before her Death, fhe voided
her Excrements by this Vent, and all the foft Parts of
the Foetus, with fome fmall Bones of its Fingers. But
the reft of the Skelet on' revmimng entire, I took it out
of her Body, together with the Vagina, Uterus, Re-
Bum, &c, wherein it had involv’d itfelf, as may be
feen more particularly in the Figure annexed.

Explication of the Figures,

Fig, 21.

A The Clitoris,.

' B'B The N^mph^.

C The Rima, or Entry into the Vagina,

D The Bladder, - '

E E The Ureters cut off.

F The Uterus found and entire.

G The Left Ovarium,

H H The Tubes,

I Part of the Colon cut off.

K Part of the Feritonmm,

L Part of the Ileum cut off.

M Part of the C^cum,

O Part of the Cranium that plainly appears.

P The Ulcer, through which the Excrements pafs’d,
with fome fmall Bones.

O^CLCLQ,The Bulky Mafs, wherein the Skeleton is
contain’d, between the Uterus, part of the Vagina,
and Re&um,

R R Part of the Cutis,

p p p 2

She

( 39® )

She was full nine Months gone in Au^uft 1717,
and dy’d the 23d of March 1723, on which Day I
took it out.

Fig, 22. A Lateral Viera,

A Orificium Vagina,

B Anus.

C Inteflinum Re&um,

DDD The Mafs, wherein the Skeleton is contain’d.

E The CoJIa plainly appearing.

F The Bladder laid afide.

G The Ureter cut off.

H The Uterus,

I The Ovary.

K The Tube. ^

L Part of the Colon,

M The Ulcer ^ through which the^Excrements pafs’d,
about one Inch beneath the Navel.

N Bones in the Orifice of the Ulcer.

F ' r N' I S.

ERRATUM,

\

Nnmh 3 7<r. Tag, 308. /. 7. del. fquare.

LONDON: Printed for and 7. Printers
to the Royal Society , at the Prince's- Arms ^ the Weft
End of St. Paul's Church-Yard.

I

AT)VE RTl S E M ENT.

H E Pra^Ece of inoculating the Small Pox being now
extended into many Parts of the Kingdom, and it being
highly requifite that the Publick fhould be faithfully in-
form’d of the Succefs of that Method, whether Good

or Bad ; It is defir’d, that all Physicians, Surgeons,
Apothecaries, and others therein concern’d, will be pleas’d
to tranfmit to Dr. Secretary to the Royal Society,

a particular Account, fpecifying the Name and Age of every Per-
fon by them inoculated, the Place where it was done, the Manner
of the Operation, whether it took Effect or no, what Sort ofDif-
temper it produced, on what Day from Inoculation the Eruption
appear’d j and, laftly, whether the Patient died or recover’d. They
are delired to comprehend in their Accounts all Perfbns inoculated
by them, from the Beginning of this Practice among us to the End
of the prefent Year, and to fend them fome Time in January or
February next.

I N cafe this be comply’d with, the Advertiser promifes
to give the Publick an exa(5l Account of the whole Number of Per-
fbns inoculated in Great ‘Britain., diflinguifhing them into Clafles
according to their feveral Ages ; as likewife of thofe that it has
had no Effeft upon, and of thofe that have died of it.

And he farther promifes to preferve the Original Accounts,
that fhall be fent him, and to give a Sight of them to any Gentle-
man who fhall defire it, that in cafe any of thofe, who have been
inoculated, fhall afterwards have the Small Po x in the natural
Way, it may be known, whether fuch Perfon had before received
the Small Pox by Inoculation, or not.

N. S. The Names of the Perfons inoculated fhall not be
printed without Leave of the Parties concern’d.

J)ec, nth. 1723.

James Jurin.

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{ -

TRANSACTIONS.

: ■' ,r'1; iT 'v> , v.-,.u»r)\

)

For the Months o{ September smA Off ober] 17x3.

‘ .1 '■) - . ■ i - J:

■ )

■\ r V

.Vo) y, . ' ,\iM .".-1 I ./•

The CONTENvT-S.'J

I. An Account ofU Komin In/cnptmny.found at
Chichefter,' ©j/ Roger GAle,c ^pK <^ S.

-'V?- \

II. De StruBura Diaphragmatis. Epijlola ^Domini
Antonii van Leeuwenhoek 3^. S. S. ad So*
cietatcm RegiamV'- v - Ap isvncjjK .ft

:;'0 - rvf o:.-frrr-i.

Ill; ^arttum Genitalium in^MuUere^StyuBura pr<z*
ternaturalis. - Ex Bpijlola- Vtri
hannis Huxham, M. ®. ad Jacobum Jurin,
(2^. S. Seer.

w. -MAieris ejufdem Hijloriay ex Epiftola Medici
DoBiJfmiy Gulielmi Oliver, ad Richardum
Mead, M. D. ^ S. ColL Med. Lond. Soc.

V. Fluxus

' V. Fluxus Jcmguinis per fPmern pilrahills. . Ex Epi^
.fiola Viri DoEliffimi Domini Howman, Af. 2).
ad Dominum Hans Sloane, Damiettum, ColL
Med. Lond. S. Vice FraJ.

yi- An Account of the Tits for Fullers-Earth in
Bedfordiliire 5 in a Letter from the (^Vercfid
. Mr. B. Holloway, F. 3^. S. to 2)r. "Wood-
ward, Tr. Med, Grefli. S. Coll, Med.

Lood. Soc* ^ /' /

; ■‘■i

V »

VII. InVttatio ad OhferVationes Meteorologkas xgm^
- muni conjilio injiituendas. A Jacobo Jurin,
M. D. Soc. Teg. Seer. Colleg. Med. Lond.
Socio. • ,'C

\';U I iu 0 L .i I

. ./, ur.'r iiKf!i.;A.

VIII. Account of a Dooh^ Adverfariorurn

Anatomico - Medico - Chirurgicorum Decas
t^xti2L. , AuBore Frederico Ruyfeh, M. D.
Anatom: O* Dot an, Trof: Arpftel. (^. S. Soc.

r

- i

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1

I. An

( )

*

X Jn Account of d Roman InJcriptioHy found at
Chichefter. iBj; Roger Gale, F. ^ S-

This Infcription, Fig, i. as curious as any that
has yet been difcovered in Britain^ was found
the Beginning of laft April at Chichefter^ in digging a
< Cellar under the Corner-houfe of St. MartinsAane, on
the North Side as it comes into Florthftreet. It lay a-
bout four Foot under Ground, with the Face upwards,
by which it had the Misfortune to receive a great deal
of Damage from the Picks of the Labourers as they
endeavoured to raife it *, for befides the defacing of fe-
veral Letters, what was here disinterred of the Stone
' was broke into four Pieces : The other Part of it, ft ill
wanting, is, in all Probability, bury’d under the next
Houfe, and will not be brought to light till that hap-
pens to be rebuilt. The Infcription is cut upon a grey
Suftex Marble, the Length of which was fix Roman
Feet, as may be conjeftured by meafuring it from the
Middle of the Word TEMPLUM to that End of
it which is entire, and is not altogether three Foot
Bnglijb^ from the Point mentioned. The Breadth of
it is two and | of the fame Feet, the Letters beauti-
fully and exadly drawn, thofe in the two firft Lines
three Inches long, and the reft 2

Being at Chichefter in September laft with Dr. Stuke-
ly^ we took an accurate View of this Marble, which
is now fixed in the Wall under a Window within the
Houfe where it was found, and that we might be as
. fure of the true Reading as poflible, wherever the Let-

dft q ters

( )

ters were defaced, we impreffed a Paper with a wet
Sponge into them, and by that Means found thofe in
the fifth Line to have been as we have exprefs’d them
above, and not as in other Copies that have been hand-
ed about of this Infcription.

The only Letter wanting in the firff Line is an N
before E P T V N O, and fo no Difficulty in reading
that.. As to the fecond, though it was more ufual in
Infcriptions of this Nature to exprefs the Donation by
the Word S A C R V M only, referring to the Temple
or Altar dedicated ^ yet we have fo many Inftances in
Gruter's Corpus Infcriptionum of TEMPLVM and
A R M alfo cut on the Stones, that there is not the
leaft Occafion to fay any Thing farther upon that
Poinu

* The third Line can be no other Way fill’d up, than
as I have done it by the prick’d Letters ; I mufl: own,
however, that I have had fome Scruple about the Phrafe
of DO MVS DIVINA, the fame Thing as D O-
M VS AVG VS T A, the Imperial Family, which
I cannot fay occurs, with any Certainty of the Time
it was ufed in, before the Reign of Antoninm Pius^
from whom, down to Conjlantine the Great, it is very
frequently met with in Infcriptions. This kept me
fome Time in Sufpenfe, whether this found at Chiche-
(ier could be of fo early a Date as the Time of Clau-
dius : But as we find feveral Infcriptions in Gruter ■
with thofe Words in them, or L HrD. D. In honor em
Domus Divina, which is much the fame Thing, with-
out any Mark of the Time when they were cur, they
may have been before the Reign of Antoninus Pius, and
then only came into more general Ufe ^ and as the Time
that Cogidunus lived in, will not let this be of a la-
ter Handing, I think we may offer it as an Authority

' fbfi?

. ( m )

for the ufe of this Piece of Flattery to the Emperors
long before that excellent Prince came to the Purple.

The third Line, as 1 believe, was EX AVC ^0-
R I T A TE. T I B. C L A V D. and the fourth CO-
G I D V B N I. R. L E G. 6Cc. that is. Ex Au^orita-
te Tiberii Claudit Cogidubni Regis, Legati Auguftt in
Britannia for the following Reafons : We are inform-
ed by Tacitus in Vita AgricoU That after Britain
had been reduced to a Roman Province by the fuccefs-
ful Arms of Aulus Plautius, and OJioriits Scapula, un-
der the Emperor Claudins, Qu^dam Civitates Cogidu-
Tio Regi erant donate, is ad nojiram ufqus memoriam fi~
diffimus remanjit, vet ere ac jam pridem recepta Populi
Romani confuetudine ut haberet inflrumenta fervitutis
Reges. This Cogidunus feems to be the fame Per-
fon as Cogidubnus in our Infcription, the Letter B in
the third Syllable making little or no Difference in the
Word, efpecially if pronounced foft, as it ought to be,
like a V confonanr.

It is fo well known to have been the Cuflom of the
Roman Liberti and Client es^ to take the Names of their
Patrons and Benefadors, that it would be wafting of
Time to prove the conftant Ufage of that Pradice.
Now as this Cogidubnus, who, in all Probability, was
a petty Prince of that Part of the Dobuni which had
fubmitted to Claudim, and one that continued many
Years faithful to him and the Romans ^ , had given him
the Government of fome Part of the Hand by that Em-
peror, nothing could be more grateful in regard to
Claudius, nor more honourable to himfelf, after he
was Romani fed, than to take the Names of a Benefa-

CLq q 2 dor

* Cap, i4«

V. Tacit, ut fupra.

1

»

( m )

dor to whom he was indebted for his Kingdom, and
focallhimfelfTIBERl VS CLAVDIVS GO-
GIDVBN VS.

I fuppofe him to have been a Regulus of the Dobu-
ni ^ becaufe we are told by Dion Caffim , that Aulm
Plautius having put to flight Cataratacus and Togo-
dumnus^ Sons of Cunobelin^ part of the Eoduni (the
fame People as the Dohunt) who were fubjed to the Ca-
tuellani^ fubmitted to the Romans ^ and the Name Cogi-
dubnus^ or Cogiduvnus, COC 0 ©Ubtt, or 2)Uhlt hg-
nifying exprefly in the Britifh Language P R I N-
CEPS DOBVNORVM, feems to put the Mat-
ter out of all doubt.

How far his Territories extended, it is irnpoffible to
define. Bifiiop Stillingfleet ® fuppofes them to have
lain in Surrey and SujJex *, Suffex certainly was Part
ofthem, fince the Temple mentioned in this Infcrip-
tion was ereded in it by his Authority , and it is
not unlikely, that befides the Rogni, who were the
People of thofe two Counties, he might have that Part
of the which had fubmitted to the Romans, and

feems to have been his own Principality, together with
the Ancalites, Bibroci, and Segontiaci, whofe Countries
lay between the Dobuni and the Regni, bellowed Upon
him ^ the Words Civitntes qu^dam in Tacitm, not im-
porting no more than {ome few Towns, but fever al Peo-
ple, the Word Civitas always fignifying a People m that
Hiftorian.

Before I proceed any farther, it will not be amifs to
obferve, that Togodumnus and Cogiduhnus, tho’ tlieir
Names are fo much alike, were two dildincl Perfons :
The firfl was Son of Cunobelin, King of the Trinoban-

tesy

c In lib. LX, V. Eaxtei-i Gloflar. in verbis Cogidvmnv% &

T)o B V N I. 5 Orig, Britan, p, 63.

I

( ?95 )

tes^ vanquiflied and killed in Battle by Aldus Plautius.
The fecond a Prince that fubmitted to OJiorius Sca^
pula, and continued in his Fidelity to the Romans ^ in
nopram ufque memoriam, fays Tacitus^ who was born
at the latter End of Claudius*^ Reign ; fo that Togo-
dumnits was probably dead before Cogidubnus had his
Government conferred upon hiiri.

1 call it his Government, for tho’ by the Letter *R*
{landing in the Infcription with a Point both before
and after it, by which it plainly denotes an entire
Word of itfelf, it may feem that it was intended for
COGIDVBNI REGIS, and I believe was fo
in refped of his quondam Dignity, yet it is evident, that
he had condefcended to take the Title of L E G A-
TVS AVGVSTI IN BRITANNIA from
Claudius and that too muft have been only over thofe
People that he had given him the Government of,
Aulus Plautius, OJiorius Scapula^ Didius Gallusy Avi-
tus Veranius^ and Suetonius Paullinus, having the fu-
preme Command fucceflively about this Time in this
liland, the fecond and lafl of which are called exprefs-
ly Legati by Tacitus K Tlie Legati Cdijaris or Ait-
gujii were thofe, qui Cafaribus fubditas regebant Pro-
vincias.

The fixth Line has loft at the Beginning the Letters
COLL E, but fo much remains of the Word as makes
it to have been indubitably, when entire, COLLE-
G I V M, and the following Letters are an Abbrevia-
tion of fabrorvm/

Thefe Colleges of Artificers were very ancient at
Rome, as ancient as their fecond King Numa Pompilius,

if

f Lib. xii. Ann. cap. 32, 5c Agric. cap 15.

( )

if we may believe Plutarch \ who tells us, that the
People were divided by him into what we at this Day
call Companies ofTradefmen, and mentions the T(^ove<;
or Fahi among them, tho* ^Florus fays, that Populus
Romanus a Servio Tullio relatus fuit in Cenfuniy digef-
tus in Claffes^ Curiis atque Collegiis dijiributus. But as
the Power of the Romans extended itfelf, it carry’d the
Arts of that great People along with it, and improv’d the
Nations that it fubdued,by civilizing, and teaching them
the Ufe of whatever was necelfary or advantageous' a-
mong their Conquerors, from which mofl wife and
generous Difpolition, among other beneficial Inflitu-
tions, we find thefe Collegia to have been eflablifiied
in every Part of the Empire, from the frequent men-
tion of them in the Infcriptions colleded by Gruter^
Spon, and other x'intiquaries.

Several Sorts of Workmen were included under the
Name of Fabri^ particularly all thofe that were con-
cern’d in any kind of Building, whence we meet with
the Fdbri Ferrarii^ Lignarii, Tignarii^ Materiarii, Na-
vales, and others ^ the laft named may have been the
Authors of dedicating this Temple to Neptune, having
fo near a Relation to the Sea, from which the City of
Chichejler is at fo fmall a Diftance, that perhaps that
Arm of it which ftill comes up within two Miles of its
Walls, might formerly have wafla’d them. The reft of
the Fraternity might very well pay the fame Devotion
to Minerva, the Goddefs of all Arts and Sciences, and
Patronefs of the Dxdalian Profeflion.

As no lefs than five Letters are wanting at the Be-
ginning of the fixth Line, there cannot be fewer loft
at the Beginning of the feventh, where the Stone is

more

*• la vit. Niinwe.

h Lib, I. fiip. 6.

( 197 )

more broke away than above , fo that probably there
were fix when it was perfed. What we have left of
them is only the Top of an S ^ I will not therefore
take upon me to affirm any Thing as to the reading
of them, which is fo entirely defaced , perhaps it was
A. SAGR. S. a facris funt'^ perhaps it was HO-
NOR. S. Honorati funt : As to the former, we find
thefe Collegia had their Sacerdotes, therefore Qui a
facris funt, which iS' found in Infcriptions * , would
be no improper Term to exprefs them ^ or it might
have been SAGER. S, facer dotes funt, fince we find;
fuch mentioned in the following Infcriptions ^ .

MAVORTI SAGRVM
HOC SIGNVM

RESTIT

COLL. FABR. ART
CINORVM ANTIQ^VISS.

VETVST ATE
DILAPSVM ET
REFECER. CVR. L. LVGILIVS>
LATINVS PROC. R.P. ARIC.

ET T. SEXTIVSMAGGIVS
SACER. COLL. EIVSD.

Mavorti facrum hoc Signum rejlituit Collegium Fa--
brorum Aricinorum Antiqui[fimum, vetujiate dilapfum^
et refecerunt, Curabant Lucius Lucilius Latinus, Pro«
curator Reipuhlicdi Aricinorum, et Titus Sextius Mag-
gius Sacerdos CoUegii ejufdem.

i V. Gl ut. Corp. XXIX. 8. cxxi* i. BCXXXII. 1, .
k Spon.- Mifcell. Eiud. Antiquir. p. 58, .

'( J?8 )

1 L. TERTENI AMANTi
SACER. COLL. LOTORVM
IIVIR. C. S ARTIVS C. F.
ITERINVS ET L. ALLIVS
PETELINVS D. D.

hiictus Terteniiis Amanthis Sacerdos CoUegii Lotorum,
Dnimviri Cains Sartius^ Caii Filius^ Iterinus^ et Lu^
0116 Allins Fetelinm Dedicaverunt,

As to the latter, thofe Members of the College that
had paired through the chief Offices of it, as that of
FvdifeBus, or Magijler quinquennalis^ had the Title of
H O N O R A T I conferred upon them : You have fe-
veral of thefe HONORATI mentioned in Gruter^
particularly a long Catalogue of them in Collegia Fa~
brorumTignariorum, p. ccLxviii. i. and in Reinefius's
Syntagma there is an Infcription.

EPAGATHOTVRANNO
HONORATO COLLEGI
FABRVM TIGNARIORVM
ROMANENSIVM &c.

So that the Vacuity in our Infcription may very
well have been filled up with one or other of thefe
Words, and the three next Letters that follow them
D. S. D de fuo dedicaverunt^ will agree with either of
them, and what precedes them.

The

• Ibid. p. 64.

f P^g. 605.

C ?99 )

The lad Line has been PVDENT-E PVDEN-
TlNl FILio^ but there mull: have been a Letter
or two of the Vrainomen at the Beginning of it, unlefs
it was fhorter than the reft at that, as well as at the
latter End of it^ and from what 1 have faid, the whole
may be read as follows.

"Neptuno ^ MinervA Templum pro Salute Domus Df- ’
vina^ ex AuBoritate Tiberit Claudii Cogidubni Regis^
Legati Augujli in Brittannid^ Collegium Fabrorum^

Qui in eo a Sacris [^or] Honorati funt^ De fuo Dedica*
verunt^ Donante aream Fudente Fudentini Filio,

Chichejler^ by this Infcription found at it, muft have
been a Tov/n of Eminence very foon after the Romans^
had fettled here, and in Procefs of Time feemsto have
been much frequented, by the Roman Roads, ftill vi-
lible, that terminate here from Fortfmouth^ Midhurft^
and Arundel^ tho’, what is very ftrange, we have no
Roman Name now known for it. I once thought it
might have put in its Claim for Anderida, which our
Antiquaries have not yet. agreed to fix any where, be-
ing fituated, very near, both to the Sjilva Anderida^ and
the Southern Coajl of the hland, the two Properties of
tha,t City ^ : But Henry of Huntingdon^ who lived in
the Time of Henry II. telling us, that the Saxons fo
deftroyed Andredecefler^ that Nunquam pojiea readifi-
cata fmt^ & locus tantum quaji nobiliJfimA urbis tran~
feuntibus oflenditur defolatus ° , it could not be Chi-
chejier , for that was not only rebuilt before his Time,
but was a Place of fuch Note, that when the Bilhops,
foon after the Conqueft p , removed their Churches

R r r from

“ V. Camb. Brit, and Sonner’i Roman Ports and Torts.
o Pag. 312. V. Dr, TaborV Difcourfe of Anderida. Philof. Trairf. N. 356.
£ A, D. 1076.

( 4°o )

from fmall decay’s Towns, where feveral of them were
then feated, itr Urhes Celebriores^ Stigand then Bi-
fhop of Seljey fettled his Epifeopal Chair at that Place.

I lhall conclude with obferving, that when this In-
fcription was dug up, there were alfo two Walls of
Stone difcovered clofe by it, three Foot thick each, one
running North, the other Eaft, and joining in an An-
gle, as the J^orth-JIreet and St, Martins-lane now turn,
which, in all Probability, were Part of the Founda-
tions of the Temple mentioned on the Marble,

OBob, 31. 1723.

II. T>e StruSiura Viaphragmatis, Epifiola Domini
Antonii van Leeuwenhoek, S, 5. ad So-
cietatem Regiam.

*DelfhtSy 31 Mali 1713.

IN epiftola ilia, quam ad Dominum yurln nuper per*
fcripfi, paucis aperueram opinionem meam de morbo,
qui nuperrima hyeme me invaferat. Statuebam enira ma-
lam affedionem Diaphragmatis originem morbo prse-
builfe.

Ut autem de hac Diaphragmatis afPedione omnein
mihi dubitationem -eximerem, Diaphragma ovis anni-
eulag ad me deferendum curavi ^ partem illius Diaphragm
matis in minuta fruftula confedam, ope microfcopii,
qua potui diligentia conlideravi •, comperique Diaphrag-
ma ex parte compofitura eife ex tenuiflimis fibrillis ;
quas fine microfcopio confpedse latum eiiciter capillum-
inter fe diftant,.

Cum

('40' )

Cum deinde dlverfa Diaphragmatis frufta diverfis '
microfcopiis applicaiHem, 6c vi(u diligenter examinaf-
fem ^ pro certo ftatui fibrillas illas ex partibas exoriri
carnods, qux Diaphragmati circa coftas intexuntur.
Eafdein fibrillas Diaphragmati vice tendinam infervire
judicabam. Tendines ifti, fic mihi di(d:i, non funt per
totuin Diapliragraa seque fibi vicini : Quin alii aliis,
quamvis fibi vicinis, funt aiiquanto crafliores.

Cum autem & fibrillas modo didas, <5c membranam
inter fibrillas exporredam, rite confiderafiem ^ animad-
verti Diaphragma, quantum ad maximam fui partem,
ex fibrillis iftis, & membrana fibrillis interjeda, com-
pofitum efie : Si tamen vaforum fanguineorum &C co-
piofi adipis, quse Diaphragmati magna copia infident,
rationem modo non habeamus.

Membrana vero, inter tendines (ita mihi didos)
interjeda, tot rugulis exiguifve plicis fcatebat, ut pene
obftupefcerem : iflas autem rugas five plicas ad hunc
ufum naturaliter deflinatas elfe credebam, ut Diaphrag-
ma per aeris infpirationem extenfum rurfus contrahe-
rent ^ eaque ratione opem fuam conferrent ad aerem,
qui Pulmones per infpirationem impleverat, inde expei-
lenduim

Ut Diaphragmatis contexturam oculis fpedandum
exponerem *, exiguam Diaphragmatis ovilli modo didi
portionem delineari, ^ in icone 2. per ABCDEFGH
defignari curavi. Ubi B G, C F ^ 6c D E, tres funt
tendines, ea magnitudine exprefii, quam microfcopiuin
oculis cxhibebat : qui tendines, ut jam ante mcxiui,
magnitudine non parum inter fe differ unt. Inter illos
vero tendines membranam interjedam videmus , exqui-
bus tendinibus, Sc interjeda membrana, Diaphragma
maximam partem compofituin effe modo dicebam,

Ut autem de vera iconis 2 magnitudine judicare pof-
fitis, delincatorem, ut veram fruftuli delineati magnitu-

R r r 2 dinein

( 4°i )

dinein digito indicarcr, rogavi ^ qui mox fpatium inter
Y Z in icone 5. coinmonftravit.

Adhaic membranam inodo diclam permultis iifque
exiguiiTimis foraininibus pcrtufain eiTe obfervavi : quas
exiguiflima foramina ab abdomine patebant in pedus,
& a pedorc viciiTim in abdomen. Cum autem fieri non
poffe hadenus judicaverim, ut humor quifpiain ex pe^-
dore delabatur in abdomen, vel ex abdomine fubve^
hatur in pedus ^ nunc fatius mihi videtur, indicium
fuper ea re meuin fufpendere. Qjain fic mecura differo j
forte etiain pulmonibus noflris vafcula infunt incom-
prehenfibilis exilitatis. Quippe fi cogifemus, quantum
humoris ex pulmonibus noflris per exfpirationem edu-
cator in aerem, pr« exigua humoris copia quam infpi-
rando ex acre inferimus in pulmones , facile in fenten-
tiam illam propendebimus.

Sed & hoc non femel obfervavi, quod fibrillas illas,
quas tendines appello, vafai qusedam perrepant itinere
tranfverfo.

In alio ejufdem Diaphragmatis fruflulo, quod mi-
crofcopio applicatum fervabam , dare intueri licebat
flruduram exortumque membranularum ^ quas inter
fibrillas, five tendines fic mihi didos, interjacere dixi.
Membranulas illas permagno plicarum numero, ut e-
tiam prjcmonui, inflrudas videmus : quse omnia in ico-
ne 3, exhibentur ad LK. Fibrills vero, five exigui
tendines, de quibus modo diflerebam, in eadem icone
defignantur per L M N O P Q. Verum fibrillse ifl^
funt hie majores, quam ufpiam mihi occurrerint.

Prseterea membranam illam, ex qua Diaphragma
maximam partem conflare dixi, quamvis tarn tenuem,
a fe divelli, 6c exiguain avulfae partis portionem ope mi-
crofeopii in icone 4 exprimendam curavi. Quod eo con-
filio feci, ut laceros tendines atque membranulas, quan-
tum

f

(405) . ..

turn ars imitari naturam poterat, oculis fubjicerem.
Ergo hie per R S T V particula indicatur tendinis ex-
tend : ubi & exiliflimse exhibentur fibrillse, ex qnibus
prsedida tendinis portio contexta efi. In eadem icone
per V T 6c W X portio delignatur tendinis quiefeentis.

Kind vero neque explicari, neque fatis comprehendi
poteft, quam incredibilis librillaruin, vafculormn, 6c
particularum numerus hie inter fe eonglomeretur , 6c
ad tenuiflimae membrane, Diaphragmatis inquam, for-
mationem coneurrat. Sie autein ftatuo, quoties validi-
us infpiramus, omnes illas plieas five finuofas eorruga-
tiones in Diaphragmate evanefeere atque coraplanari :
quoties autem exfpiramus, Diaphragma rurfus in plieas
rugafve eontrahi, quod 6C fuperius notavL

Dum igitur tantam adipis copiam in Diaphragmate
gigni, 6c eongregari videmus^ prsetereaque cogitamus
fubftantiain Diaphragmatis per adipem ilium lie utrim-
que poiTe erallefeere, ut in tumorem extuberet j faeile
intelligemus Diaphragmatis expanfionem atque eontra-
dionem ea ratione poffe impediri atque pigrefeere, at-
que hine fpirandi diffieultatem confequi : ob quam ra-
tionem homines obefos prae aliis anhelos effe judiea-
mus. Modieo autem adipe Diaphragma perfundi obli-
nique neeefTarium ftatuimus : cum enim Diaphragma^
lingulis horis nongenties expand! 6c nongenties contra-
hi neceffe fit ^ motus illos per adipem magnopere adju-
vari cenfemus.

Ceterum frequentiori indagatione explorare cona-
tusfum, qua ratione carneae Diaphragmatis partes, quas
coflis vicinas effe dixi, tranfiifTent in membranam^,
live. qua ratione membrana Diaphragmatis ex iiiis efTet.
exorta.. Verum licet indagationem illam crebro fre-
quentarem, ipfe mihi fatisfacere non potuL

lam

f 4®4

Jam 5c ilia dubitatio me fubierat, an non tendines,
quos ego quidem fic voco, vafculis (int inftrudi : Et
licet microfcopio meo vix tantum tribuere auderem ;
tamen tertio poft die indagationem iteravi, 6c tendines
tranfverfe diffecui : quando 6c iliuc indagationem me-
am dirigebam, nt etiara in membrana Diaphragmatis,
quam rugofain effe dixi, fanguinea vafa requirerem.
Tandem igitur fucceflit, ut languinea vafa fecunduin
longitudinem tendinum protendi, imo o6lonos de-
nofque invicem adjacere viderem. Inde ad membra-
nam, quae tendines quafi circumveftit, oculos converti ;
in eaque tam ingentem obfervavi numeram exiliffimo-
rum vafculorum, ut admiratione defixus hsrerem. Com-
plura iflorum vafculorum velut areolis inclufa jace»
bant^ quas tendinum tranfverfe perfedorum vafcula
elfe cenfebam. Ut autem eorum omnium, quse modo
narravi, teftem haberem ocularem \ microfcopium iftud,
cui didas Diaphragmatis particulas applicaveram, Chi-
rurgo meo tradidi j qui dida mea cum iis qu^e vide-
bat, examuflim convenire refpondit.

Hac tamen obfervatione non contentus, comparavi
Diaphragma bovillum , ex quo circa partes illius car-
neas, quas coftis adjacere dixi, fruftum circiter palma-
riuin excidi : comperique Diapliragma bovillum circi-
ter quadruple craffius eife ovillo , 6c hanc craflitudi-
nem maxima ex parte illius adipi acceptam elfe refe-
rendam.

Exinde ex ilia Diaphragmatis portione lamellam
quam potui tenuiffimam abfeidi , quoties enim paulo
crafliorem exfeindebam, perfecabam adipem, qui verfus
medium Diaphragmatis protenditur* puta, ubi Dia-
phragma fatis eft cralTum, neque adipis expers. Dia-
phragma vero utrimque, id eft, fuperius atque inferi-
us, quatuor diftindis conftat meinbranis, earumque

tendinibus •

C 405 )

tendinibus;, qui tendines membranis veluti inelufide-
litefcunt.

Iftorum autem tendinum ingens multitudo non po-
terat mihi non admirationem parere ; neque fatis cre-
dibile videbatar in corpore, cujus firuclura fandionef-
que tain parum funt cognitae, in Diaphraginate inquam,
tales tamque multipiices partes includi.

Ut Diaphraginatis bovilli ftruduram oculis expo-'
nerein, partem illius in icone 6 ad A BCD expri-
mendam curavi, ubi primo quataor exhibentur partes
diftindorum tendinum, qui magno numero invicem ad-
jacent, fupra in Diaphragmate ovillo etiam funt
exhibiti. Verum per integrum bovis Diaphragma ifti-
ufmodi diffunduntur exiguiiTimi tendines, quos ego
quidem (ic appeilo. Et hos quidem tendines, una cum
membranis, necelTe eft in rite conftituto corpore line
ulla interm’iftione alternatim extendi atque contralii j
qucB omnia in icone 6 fatis accurate delineator expreflit*

Tenuiflimas illas fibrillas, uti 6c membranarum ru-
gulas plipafve, per crebram indagationem etiam ex vo-
to meo deprehendi in Diaphragmate ovillo ^ nec ipfe
tantum fepius cum voluptate conftderavi, fed 6c aliis
confiderandas exliibui. Ceterum tendines illos, ita mi-
hi didos, 6c tenuiffnnas particulas tranfverfe perfecui j
inquirere volens num forte lint perviae, 6c cavitatibus
prasditae. Quando incredibilis exilitatis vafcula tanto
numero in oculos meos incurrerunt , ut, qui ipfe non
viderit, vix mihi fit habiturus fidem* Turn 6c ingen-
tem percepi numerum exiguiflimorum vafculorum, qu^
tranfverfo Diaphragma itinerepermeabant, 6c quantum
ego quidem fentiebam, ad hoc officium a natura defti-
nantur, ut adipem per omnes Diaphraginatis partes cir-
cumferant, 6c ipli Diaphagmati continuum alimentuin
fubminiftrent*

% Super ius

( )

Superius modo dixi adipem in Diaphragmate inclu-
fum latere 5 dc utrimque fuper adipem quatuor expor-
rigi membranas, inter fe omnino diftindas. Addo mem-
branas iftas tam arde libi conjundas eire,ut (implex effe
membrana videatur. -

Jam vero alter! microfcopio, quodpaulo minus quam
microfcopia modo dida magnitudinem objedorum au-
gebat, fruftum Diaphragm atis mediocris craffitudinis
admoveram. Qiiod eo fpedabat^ ut demondrarem, qua
ratione membrane partes Diaphragmatis adipofas, five
ipfum Diaphragmatis adipem, utrimque circumdentj "
adeo ut adeps in membranis iliis includi videatur. Id
autem in icone 7 indicatur per E F G H I K L M, ubi
per E F G H, item per I KL M, duse idas quadruplices
defignantur membran?e ^ in G H vero, 6c I K, adeps
Fepe jam didus inciuditur.

Cum deinde tenuiflimam Diaphragmatis portionem,
quae pr« manibus erat, in orbes confcindere conarer,
Diaphragma in duas partes five lamellas feceflit 5 unde
fufpicatus fum Diaphragma fic a natura comparatum
ede, ut adeps eo facilius per Diaphragmatis fubdanti-
ain didribuatur.

In icone 7, ubi membrance tranfverfe fed^e exhiben-
tur, quasdara exiguae apparent corrugationes, quas in
iis plerumque percepi. Podea comperi inembranulas,
in quibus adeps coeundo producitur, exiliflimis vafcu-
lis annexas effe , quae tamen vafcula per contiguarum
partiuin exficcationem in Diaphragmate jam dido e-
rant difrupta. Hanc ego membranularum vafculo-
rum connexionem ex eo capite necefiariam exidimo j
ne Diaphragma, quoties extenditur, omnino complane-
tur, fed in cavitatem pene globofam fefe expandat*

Forte complures Diaphragma fentient elfe membra-
nam apprime crallam , cum tamen fit membrana per-

exilir.

( 407 )

exilis. Ut igitur hunc illis errorem eximam ^ fruftu-
lum Diaphragmatis bovilli, ficut fe nudis oculis ofFert,
delineandum curavi: Iftud tamen verum eft, Diaphrag-
ma pro tenuitate fua efTe oppido robuftum, quod mul-
titudini exiliflimorum tendinum, de quibus faspius egi,
tribuendum effe ftatuo.

Igitur per NOP CL, in icone 8, fruftulum defigna-
tur Diaphragmatis bovilli : ubi per fibriilam N O unum
latus, five dimidia cralTitudo, Diaphragmatis bovilli in-
dicatur j per P CL altera craflitudinis illius medietas ex-
prim itur. Reliquum Diaphragmatis, nempe quidquid
inter O P 5c N CL interclufum eft, adipe five partibus
adipofis eft obfitum : nifi quod inter N CLnqnnihil car-
ols interjaceat, pertinens ad carnem coftis adjacentem,

Igitur quo morbum antedidum, qui nupera hyeme
me corripuit, 5c quem ego Diaphragraati maxima ex
parte imputabain, fiepius in memoriam revoco j eo e-
tiam fiepius Medicos errare cogito, dum palpitationem,
quam in pedoris regione quandoque percipimus, cor-
dis palpitationem appellant. , Certe ego tales palpita-
tiones ex mala Diaphragmatis afFedione oriri cenfeo j
five afFedionem illam producat alimenti defedus, five
vaforum quorundam efficiat obftipatio, quse Diaphrag-
ma magno numero pervagantur. Talis enim obftipa-
tio in ante-didis tendinibus facile convuifivos motus
excitare poteft • 5c hanc morbi mei ipfifiimam fuilTe
caufam exiftimo.

Sff

III. Partium

( 4o8 )

III. Tartium Genitalium in Muliere StruSiura
ternaturalis. Ex Epijiola Ftri DoEiijJJmi Jo-
hannis Huxham, M. T>* ad Jacobum Jurin, ,
3^. S. Seer.

I ■

Tl'mutho^y^ Kalend.OBob.

' ^ D De parochia Lanteglafs in Comit. Cornu
Jl% mJ • prope Fowye oppidum, annos nata-

XXIII nupta fuit cuidam Naut^e robuflo, tandemque-
praegnans, fibi parti um male conformatarum confeia, ,
opem imploravit chirurgicam. Sibi accerfitum efle vo-
luit Dominum Bonnett de Fowye oppido, Sc artis
chirurgicae, 6c obftetriciae peritillimum. Ille vero per-
lpe(5to denudato eorpore fequentia oblervavit.

Loco umbilici, in medio abdomine, paululum vero
inferius, • prominet malTa quaedam Ipongiofa, carnis
quail ofJam pras fe ferens, abdomini traniverfe incum-
bens, magnitudinis fere ovi gallinacei, longa autem
tres digitos : ex hac duo erumpunt meatus urinarii
exiles, qui urinam perpetim exftillant, quam neque
vel retinere vel ejaculare potefl: ; hinc veficam, (fi
quae adiit) Iphindlere caruiife concludendum. Spon-
giofa haec mollilque mafia, uriii^ acrimonia corrofa,,
tad:um fere refugit molliflimum, adeo ut incurvata
obambulare coadta fit, ad dolorem a vefiibus impref-
fum evitandum, eamque tenuiflimis linteis involvere.
Hanc quidem maffam funem fuifie umbilicalem male
a partu abfeiflum, male dein curatum, exifiimo ; ne
vei minima enim umbilici, uifi hie, apparent veftigia;
quid quod Sc urina per urachum pervium, 6c in duos:

ibrCui

( 40? )

forfan tubulos divifum, vel faltem per canales duos
proprios, effluit. Priori potius credo opinioni ; quia
daiitur Hiftorias urinam per umbilicum in adultis eti-
am excretam fuifTe atteftantes. Vid. Hift. de VAca^
demie Roy ale des Sciences^ Ann. 1701.

Hanc infra ofJam fubintrat Vaginae foramen, ab of-
fa diftans breviflimo fpatio ; ex hoc effluxere Catame-
nia, per hoc etiam gravida fa6ta fuic mulier, baud
magnam vero tempore coitus percepit voluptatem;
fumma etiam Penis glans in hoc orificium vix fuit in-
tromifla, multo minus ipfa virga. In hoc foramen
digitum aegre introduxit Chirurgus, eo fcilicet animo,
ut iplum uteri collum explorarer, quod tamen ne vei
tad:u percepit, plane autem deprehendit membranatn
craflam hocce orificium ab altero inferiore, jam de-
fcribendo, feparantem.

Eo fere iplb loco, fiiperius vero paululum, ubi in
mulieribus rite conformatis adeft fofia magna, inven-
tum fuit foramen alterum oblongum, ne vel minirm
digiti apicem altius admittens, redto inteftino, uti poll
partum obfervatum fuit, pervium (quod a fedtione
fortaffe accidit) : nullus autem hie occurrit Sphincter :
inferius vero redlum inteftinum, more folito, cum
Sphindtere circundato terminatur.

Orificium hoc oblongum ab orificio vaginae, abdo-
mine maxime tumente, duos faltem digitos tranverfos
dillitit, inter quae membrana delcripta intervenic ab
interiore parte, hujufee vero FiiTur^ oblongae quafi
labiorum coalitio exterius e fiiperiore foraminis parte.

Nulla hie Clitoris, hie nulla ofiium Pubis adfuerc
veftigia, nifi, quafi Apophyfes breviores ex utriufquc
ofiis Ilii parte infeiiore protuberantes, ofiium Pubis
ludimenta dixifies. Hie fuit ante partum rcrum ftatus-

Sff ^

Die

( 4'o ) ,

Die i8 Julii 1712, hora nodis advocatus efl
Bonnett Chimrgus, uc parturienti opem ferret. Per-
penfis omnibus, Foetum invenic Vaginse orificium in-
fra dilapfum, quern muliere decumbente liiperiora ver-
llis propellere fruftra adiiixus efl, ob fortiflimos Foetus
moms graviflimos Matris dolores, cui etiam jam
fupervenere Convulfiones, Syncope, &c. Vaginae au-
tem orificium vix ac ne vix quidem dilatatum, ita ut
illi jam jam moriendum efle flierit omnium expeda-
tio.

In hoc miferrimo rernm ftatu, mifericordia & hu-
inanitate addudfus Chimrgus, poflhabuit omnino,
quid vel ignarum vulgus, vel invidus hie garriret auc
hie : anceps experiendum efle remedium porius. quam
nullum apud fe flatuic, morte aliter citifiimo ingruente
pede.

Parentibus periculofi/limum rerum flatum enarra-
vir, nil nifi a fedtione expedFandum, ancipitem prae*
dixit eventum. Annuentibus hujus miferrimae ma-
tre, & aftantibus, in orificium oblongum inferius
fcalpellum chirurgicum introduxir, 6c uno idFu coali-
tionem labiorum hujufee orificii & membranam fepa-
rantem divifit : hinc in unum coivere & orificium Va-
ginae & oblongum inferius. Jam digitis facilis introi-
tus, orificium Uteri internum attredavit ; dilatavit
paululnm, caput inde fenfit infantis : quid plura ? Foe*
rus ori intrufo digito, Puellulam vivam, probe format
tam, mirantibus maxime aftantibus, demum extraxit,
quae & adhuc & viget & valet ; uti etiam & ipfa Ma-
ter, quanquam poft puerperium febre graviter collu-
data eft.

Jam a partu prolapfu ipftus Uteri divexatur, quo
prolabente nec per horas 8, 10^^ redudo, earn dein ft
ibrtius intrudas, exiliunt e raeatibus urinariis deferip-

tis

( 4' I )

tis rivuli diio ad pedis falrem diftantiam ; argumcii-
tum fane Cyftidis cujufdam urinam excipientis : aliter
revera lulpicafTem meatus iftos duos urinarios ipfb-
rum ureterum fuifTe orificia, hie terminantia.

Quaerat fortafTe curiofior aliquiS) quo forte modo
gravida fadfa fuit muliercula noftra. llli refponderem,
Penis intrufionem ad prolem concipiendam baud ab-
Iblute efTe iiecefTariam, feminis autem intra vaginam
ejaculationem quam maxime. Vid. Hiji. de VAcad.
Roy ale des Sciences^ i7ix. Videatttr etiam Mau^
riceau.

Hujus rei narrationem tibi citins tranfmififfem, ni
diu, fruftra autem hadenus, mulieris alteram gravidi-
tatem exped:afTemus, quum per fat longum tempus a
puerperio cum marito cohabitaverit..

Figura p reprejentat mulkrem graVidam,

A A Spongiofam aflimulat quafi carnis maflam,
quam partem fuifTe chordee umbilicalis autumo, mag-
tudinis fere ovi gallinacei, tres vero digitos longam.
Ex hac duo erumpunt Fiftulse urinariae ^ quae uri-
nam perpetim exflillant, nec ex ullo alio orificio red?-
ditur urina.

c Orificium Vagina, cloaca galli gallinacei quam
flmillimum, fpifTo quafi fepto circumdatum : per hoc
efRuxere IfjLfjdwcL^ per hoc etiam gravida fadFa fiiit
mulier. Hoc orificium, dum perpena fuit mulier gra-
vifTimos partus dolores, nullo fere modo dilatatum*
fuit, quanquam anus ipfe, ob vehementiflimos mufeu-
lorum abdominis, &c. contradiones, maxime hiaret.

d Locum indicat, ubi inventum fuit foramen oblon-
gum, minimi digiti apicem vix admittens. In hoc, tem-
pore puerperii,Chirurgus introduxit fcalpellum chirurgi-

cum

( 41 i )

‘ cum, idque ab hoc • in orificium luperius acJegit : ita
ut jam a paitu dehifcat monltrofum horrendum in-
- forme ingens foramen.

Orificiiim fuperius tranfverfum ab inferiore oblon-
go (appropinquante partu) 2 fere digitos diftitit. Ex
hoc magno hiatu iphus uteri prolapiiim f^epiffime
nunc patitur. Ex loco etiam, ubi adfuit olim orifi-
' cium inferius, jam a puerperio , partim excrerse
funt Foeces alvinae : hoc vero ante partum minime
obfervatum fuit, ita ut a fecStione forte acciderit.

Orificium hoc oblongum paulo altius quam par eft,
in Figura defignatur.

e Anum reprsdentat paulo magis antrorfum quam
in aliis pofitum : per hunc maxima foecum pars egeri-
>tur. Pudendum hoc, quale quale, eft non denle cri*
nitum.

■ ' • ^ : V' IV. MuUcris

■I ' • - -i

i

IV. Mulieris ejufdem Htjloriay ex Eptjlola Medici
DoEUjJimiy Gulielmi Oliver, ad Richardurn
Mead, M. T>» 3^. S. ^ ColL Med, Londr Soc^

Vir cekberrime,

IBI omnium animalium natoras 5c formationes
JL optime callenti, acerrimo judicio quocidie per- -
Icrutanti, hiftoriam inufitatse, ac plane mirandae cu-
jufdam ftmdiurae p^tium ingratam non fore, nullus
dubito. '

Mulierem, Comitatus Cormhia incolam, in hunc-;
modum, quern jam fiim delcripturus, a cunabulis for^
matam fuifle, matronae vicin^e, & non paucis res &
nota & examinata fuir, uno ore confentiunt. Subftan-
tia quaedam carnola, fpongiola, floride rubefcens, le-
vi/Iimum tacSlum, ob atrociffimum dolorem inde oriun-
dum, fugiens umbilici, v. Fig. lo. quae non ex Auto-
pda fed ex Chirurgi narratione delineata eft, naturalem
locum ufurpabat, & e cavitate, quae plerumque ibi eft,
quad pullulabat. Ex hac excrefcentia, quae nec au-
geri, nec minui, per multos annos fentiebatur, conti-
nuo deftillabat urina, cui nec alia patuit e corpora
via, neque hac potiiit vel violentiftimis nixibus cum
impetu expelli, vel per faltiim excerni, ,ade<> ut
paulatim exfudans veftes interdiu, fubftiagulaque no-
d:e madefaceret, inquinaret. Paulo infhi, ad diftantiam
paene palmi minoris,. orificiuin quoddam, longitudinc
unciam unam> latitudinc digitumtranfverrum aequans,

■CaCfx

( 4H )

fefe oftendebat, ut indicem admitteret, Sc tamen per-
flringeret, fatis amplum. Hac via eftluebant a pubertate
menilrua, unde ad Vaginam 6C Uterum hunc eflb adi-
tum facile patebat. Ad eandem fere diftantiam, qua
orificium hoc Vaginae ab excrefcentia ilia diftabat,
patuit Sc orificium alterum, fuperiore minus, digitum
minimum vix capiens. Huic autem prificio cum in-
teftino re^tocom municationem dari, tenuifiimae faecum
partes, ex eo frequenter protrufe, fatis demonfirabant.
Ab hoc autem Pfeudo-Ano Anus verus, per quern ex-
crementa duriora dejiciuntur, unciis quinque vel fex
oxtitit. Sc naturalem fere pudendorum fitum obtinuit.
Pili quidem aderant, fed rari, nec margines alicujus
orificii magis quam reliquorum ornantes, fed duas
lineas delcribentes, quae a medio fpatio inter excre-
fcentiam illam & commifiuras femorum cum abdomi-
ne incipiebant. Sc fibi mutuo appropinquantcs angu-
lum, in cujus vertice pofitus eft verus Anus, confide-
bant. Hunc in modum conformata, valetudine fatis
bona fruebatur virgo, 8c aeterna virginitate ex necefii-
te Jaboraturam concluferant omnes, quibus res inno-
tuerat. Advenit tandem Nauta quidam, cui xs triplex
circa petftus erat : Illam vidit, amavit, duxit, Sc non
multo poft impraegnavit. Geftationis tempore opti-
me fe habuit mulier, quo propemodum finite, de dif-
ficultate pariendi, non fine ratione, aderat gravis fuf-
picio. Orificium Vaginae a viri congrefiu non omnino
dilatabatur, adeo ut de modo impraegnationis multae
inter mulierculas ortae fint dilputationes ; Sc afleruere
aliquae non fine dedignatione Sc horrore, maritum aut
viri nomine non efie dignum, aut per aliam introivifie
viam, quod bonus Deus vetet ! Immifiionem autem
Penis in Vaginam ad impraegnationem non effe abfolu-
te necefiariam, non eft quod tibi, Vir clariflime, cui

t

( 4»5 )

haec omnia optime nota, narrarem. Exemplis tur-
gent libri Medici. Mulier tamen de Jfua vita anxia
Chirurgos aliquos adivit, confilium petiit, opem preca-
ta eft. Unus tandem apud Foj/^ oppidum non procul
a mulieris noftras habitaculo, cafu audito, reperferata-
ta, ad promovendum partum, ft opus fuerit, operam
fuam navare promifit. Geftationis tempore perfede ft-
nito, dolores aliaque fymptomate partum prognofti-
cantia illam tentaverunt. Chirurgus advocatus aderat.
Refert ille infantem conatus fuos ad regionem pubis,
ilia ipfa autem ad orificium Vaginae fecifte dicit. Quid
eft agendum ? Dixit ille incifione exitum infant! effe
aperiendum *, ex crudeli mifericordia renuunt adftan-
tes, ingravefeunt dolores, fuperveniunt convulliones,
vita defperabatur. Tandem cum mortem prae foribus
efte omnes judicaverunt, illam psne expirantem in ma-
nus 5c poteftatem Chirurgi tradiderunt. Ille ftatim dif-
fedionem iftius Ifthmi, qui inter orificium Vaginas dc
Pfeudo-Anum erat, baud improprie Perineum pof-
fit vocari, inftituit. Integumentis exterioribus difiedis,
membrana quasdam valida crafia, tranfverfe locata,
fefe in confpedum dedit, qus Vaginam a canaliculo
illo inferiore dividebat. Hac dilTeda iter ad Uterum
fatis amplum patuit, manum introduxit, os Uteri digi-
tis dilatavit, infantem capite prehenfo in lucem tuto
eduxit, matrem ad vitam revocavit. Hanc mihi ipfe hi-
ftoriam retulit, ilia ipfa confirmavit. Rei enim novi-
tare perculTus Fojf adivi, utrum verum elTet necne feiendi
gratia. Chirurgum de ftrudura partium original!, 6c o-
peratione fua tantum non Caefarea, folicite interroga-
vi. Omnia, ut fupra narravi, graphice defer ipfit. Foe-
minam autem ipfam videndi maxima mihi fuit cupido.
Amicum quendam meum, honore femper colendum,
ut fub prjetextu alicujus negotii mulierem ad domum

T 1 1 fuam

( 4*<5 )

fuam accerferet, rogavi. Accerfita venit. Defiderium
iTieum aperui. Ilia ab ullo examine, tanquam re om-
nibus modeftiaj 6c virtutis regulis contraria, religiofe
abhorrebat. Me Medicum profelfus, rem tarn ab om«
ni immodeftia alienam elie probavi, quod cum in ufuin
publicum cederet, cafum fuum communicare ejus elTe
officium demonftravi. Hac ratiocinandi methodo, 6c
argumenti alterius aurei ope, votum obtinui. Muliere
igitur ad examen commode locata, excrefcentiam illam
umbilici cavitatem ufurpantem fuperiori defcriptioni
ad amuffim refpondentem inveni. Illam cum fummo
digit! leviffime tetigerim, mifella, non aliter ac fi gla-
dio perfolTa fuilTet, difcruciata ejulavit. Mirum lane
mihi videtur hanc mulierem cum marito fuo pofTe con-
gredi ex fitu enim partium nihil aliud cogitare poflis,
quin vir rei Venerese incumbens, excrefcentiam illam,'
aliter prorfus intadilem , abdomine fuo duriter perfri-
caret. Rogata quomodo hxc perficiebantur, refpon-
dit fe omnia ob amorem, quo maritum fuum profeque-
batur, poffe pad. Sic amor omnia vincit, Sed ad
Rem.

Hasc excrefcentia ex multis lobulis, propriis mem-
branis obduftis, a fe mutuo diflin(ftis, conflari vi-
detur. In interftitiis horum lobulorum poruli, per
quos ftillabat urina, ofcula fua ad fuperficiem ape-
riebant. Paulo infra hiatus, magnus, ex unione
chirurgica duorum orificiorum ad partum facilitan-
dum confedus, fefe oftendebat. Procidentia Uteri tunc
temporis laborabat, qui extra labia, fi eircumferentia
ilia mereatur nomen, propendens, longitudinem fex
unciarum, magnitudinem ovi anferini sequabat. Tali
procidentia fe femper a partu ufque laboralTe narravit,
6c quidem mirum effet fi aliter accidiifet^ tanta eft
enim ad orificiura Vaginae apertura, ut nihil poflit ab

extra

( 4»7 )

extra Uteri prolapfui obftare, 5c Uteri corpus multo
magis, quam in ftatu vulgari, a vefica premitur. Veri-
fimile enim eft urinam ad excrefeentiain illam per u-
rachum afeendere, per ilium ab initio fluxifTe, quia
per meatum urinarium nullum natura prsbuit exitum j
impoflibile tamen eft, ut urina per urachum ad umbili-
cum afeenderet, ufque dum vefica fit turgide repleta ;
ex ilia vero plenitudine necefie eft, ut femper in Ute-
rum non parvo pondere gravaretur, 5c ilium foras ex-
truderet. Ut conform atio partium melius appareret, re-
clinata in ledum Muliere, repofitionem Uteri tentavi.
Non citius ilium introducere caepi, quin urina a pref-
fione in veficam repletam fada, per poros excrefeentiaj
umbilicalis, multis rivulis, pilum crafliorem magnitu-
dine non fuperantibus, cum impetu ad plures pedes
profiliebat, fontem artificialem non mjucunde aemulans.
Exinanita vefica, Vaginam inverfam in naturalem fitum
facile reftitui , reftitutis Vagina, <3c Utero dehifeebat
chafma magnum, ex pofitione corporis circulare, cujus
diametrum tres pollices tranverfos metiri credo, cujus
fimbrias, potius quam labia, multis farcomatis ins-
qualiter horrebant. In fuperiore ejus margine interno
meatum urinarium fruftra qusfivi, in inferiore Pfeudo-
Anuin facile inveni, per quern digitum fub pubem,
quae ad cartilagineam mollitiem accedere videtur, ad
inteftinum redum immifi, necnon contentis ejus turpi-
ter infedum eduxi, unde credo redum, ad tres pollices
fupra fphinderem Ani, elfe perforatum. Paulo fubtus pu-
bem, fitum, quo aliarum finus ipfe pudoris gaudet,
verus Anus hujus feemin^e obtinet, non confueta cali-
gine 5c profunditate occultus, utpote non intra dunes
pofitus.

T 1 1 X

Figura-

1

( 4»8 )

Figurcirum to ii Ex[flicatm»

Fig, 10,

a Excrefccntia umbilicalis^
b Orificium Vaginse,
c Pfeudo-Anus.
d Anus.
e e Pill.

Fig, II.

a Excrefcentia umbilicalis.
b Os Uteri.
c Anus.

G. Oliver.. [

y, Fluxus Janguinis per Tenem mirabilis. Ex Epi^
Jlola Firi T)oBiffimi Domini Howman, M, D.
ad Dominmi Hans Sloane, Daronettum, ColL
Med, Lond; Tr^f. S. Fice Draef,

Q:

|Uadragenarius quidain civis Norvicenfis pancra-
tice valens, profiuvio fanguinis finceri per cana-
lenftrethrcB correptus eft, 30 die Junii, 171^. Idem
rediit phaenomenon, 31 Julii. Adhibitis quibufdam
medicamentis, 6c celebrata venaefedione in Brachio,
cohibitus eft fluxus fanguinis prasdidus, ufque ad oda-
vum diem Septeinbris, ac deinceps penitus evanuit.
Notatu tamen eft dignum haemorragias fupra memo-
ratas abfque omni prasvio dolore, feu poftea fpirituum
dejedione contigiffe.

. VI. An

. ( 4 '.9 )

VI. An Account of the ^its for Fullers-Earth in
Bedfordfliire 5 in a Letter from the (Reverend
Mr, B. Holloway, F. S, to Dr, Wood-
ward, Dr, Med. Grefli. S. 5^. ^ ColL Med,
Lond. Soc,

Bedford, SJuly^ 1725.

I Went a few Days ago to the Fuller $.Larth Pits at
Wavendon near Woburn^ where there are feveral
Pits now open •, but, as Men were then at work only
in one, and 1 underftood the Earth was difpofed in
much the fame Manner in all, I did not trouble my
felf tO'go down into more than that wherein they were
then dkging^ in which I found Things difpos’d thus.

Frwii the Surface, for about fix Yards Depth, there
are feveral Layers of Sands, all reddifli, but fome
lighter colour’d than oti^^r^, under which there is a
thin Stratum of red SaniSft^^, which they break
through j and then for the Depth' b'f about feven or
eight Yards more, you have Sand again, and after
that come to the Lul/ers-Earth ^ the upper Layer of
which, being about a Foot deep, they call the Cledge\
and this is by the Diggers thrown by as ufelefs, by
reafon of its top great Mixture with the neighbouring
Sand, which covers, and has infinuated itfelf among
it : After which they dig up Earth for Ufe, to the
Depth of about eight Feet more, the Matter whereof
is diftinguifli’d into feveral Layers, there being com-
monly about a Foot and an half between one horizon-
tal

( 4io )

tal Fiffure and another. Of thefe Layers of Fullers-
Earthy the upper Half, where the Earth breaks itfelf,
is ting’d red, as it feems by the running of Water from
the fandy Strata above , and this Part they call the
Crop 5 betwixt which and the Cledge above-mention’d,
is a thin Layer of Matter not an Inch in Depth, in
Tafte, Colour, and Conliflency, not unlike to Terra
Japontca, The lower half of the Layers of Fullers-
Earthy they call the Wall-Earth j this is unting’d with
that red above-mention’d, and feems to be the more pure
and fitter for Fulling *, and underneath all is a Stra-
tum of white rough Stone, of about two Foot thick,
which, if they dig through, as they very feldom do,
they find Sand again, and then is an End of their
Works.

One Thing is obfervable in the Site of this Earth,
which is, that it feems to have every where a pretty
equal horizontal Level , becaufe they fay, that when
the Sand-Ridges at the Surface are higher, the Fullers-
Earth lies proportionably deeper.

In thefe Works they feldom undermine the'tltound,
but as they dig away the Earth below, others are em-
,ploy’d to dig and carry off the Surface^ otherwife, the
Matter above, being of light and flitting a Nature,
would fall in and endanger the Workmen : For, as
was obferv’d before, that Stratum of Sand-Stone, which
occurs before they come to the Fullers- Earthy does not
lie, as in Coal-Pits, immediately over the Matter they
dig for, like a Cieling, but even in the midfl: of the
fuperjacent Strata of Sand, and therefore can be no
Security to them if they undermine. •

The perpendicular Fiflures are frequent, and the
Eardi in the Strata^ befldes its- apparent Diflindion
into Layers, like all other Kinds of Matter, by.reafon

2 of

( 4ii )

of its peculiar Unduoufnefs, or the running of the
adjacent Sand imperceptibly among it, breaks itlelf
into Pieces of all Angles and Sizes.

For the Geographical Situation of thefe Pits, they
are digg’d in that Ridge of Sand-Hills by Woburn j
which near Oxford is call’d Shotover • on which lies
Hewmarket'Heath by Cambridge^ and which extends
itfelf from Eaft to Weft, every where, at about the
Diftance of eight or ten Miles from the Chiltern Hills,
which in Cambridgefiire are called Gog-Alagog ^ in
Bucksy and Oxon, the Chiltern Hills, from the chalky
Matter, of which they chiefly confift: which two
Ridges you always pafs, in going from London into
the North, North-Eaft, or North-Weft Counties in the
Manner I before-mention’d : After which you come into
that vaft Vale, which makes the greater Part of the
Midland Counties of Cambridge^ Bedford, Bucks, 'North-
ampton, Oxford, and Gloucefter, and in which are th»
Rivers Cam, Oufe, Nen, Avon, Ifis, and others , which
I take Notice of, becaufe it confirms what you fay of
the regular Difpofition of the Earth into like Strata,
or Layers of Matter, commonly through vaft Trails,
and from whence I make a Queftion, whether Fullers-
Earth may not probably be found in other Parts
of the fame Ridge of Sand-Hills, among other like
Matter.

VII. Invi-

( 4‘i )

VII. InVitatio ad ObferVationes Meteorologicas com-
muni conjilio injlituendas» A Jacobo Jurin,
M. ®. Soc, Seer, Colleg, Med, Lond.
Socio,

CELI 6c Aeris, quern fpiritu ducimus, conditio-

nes varias, frigoris, puta, 6c caloris, fudi, vel hu-
midi commutationes 6c viciflitudines, magnas praifer-
tim atque fubitaneas, ad Human! Generis valetudinem
pertinere merito cenfetur. Operam itaque 6c laborein
in iisdem obfervandis minime contemnendum pofuerunt
non Medici foluin, fed 6c alii quoque ab omni sewo
Naturae rerum contemplandae ftudiofi. Superiorc tan-
dem fasculolnflrumenta etiam 6c Machinse Philofopho-
rum ingenio 6c diligenti^ repertae funt, quibus ponde-
ris, caloris, humiditatis, 6c elateris aerii momenta 6c
mutationes fimul oculis repraefentantur, fimul ad men-
furam ac trutinam, 6c quidem fubtiiem admodum il-
1am atque accuratam, exiguntur.

Ncc hie etiam fubliftendum judicarunt Eximii illi
Viri, fed ftudio 6c feiendi amore incitati ad caufas ha-
rum mutationum, qua licuit, iiidagandas contenderunt.
Quern in finem Obfervationes Inftrumentorum recens
inventorum ope fadtas de pondere, humiditate, 6c ca-
lore ambientis diligenter in Diariis notabant •, iifque
multa alia adjiciebant ad Tempeftatem ac Coeli faciem,
Ventos, 6c Pluvise copiam pertinentia, quod in Adis
Philofophicis 6c alibi fparfim videre eft.

Methodo

( 41? ) .

Methodo 6c obfervandi ratione mdiorem facile
non reperias. Quod fi fuiffent Obfervatores &c numero
idoneo, & commodis locis per magna terrarura fpatia
difpofiti 5 ac tandem unus aliquis omnium Diaria, quid
inter fe convenirent aut difcreparent, contuliiTet ^ pro-
- fedlo jam a multis annis earn haberemus Aeris Hiftori-
am, qualem hoc temporis vix animo &c votis fas eft
concipere.

Id etenim compertum habemus, ut quod maxime,
fubitas Tempeftatum commutationes Ventis prascipue
acceptas effe referendas ^ quumque fcire liceret per ta-
iem obfervandi rationem, qualem fupra expofuimus,
quibus in locis orti, quem curfum, quo tempore, 6c
per quanta terrarum fpatia Venti tenerentj his cognitis,
forfan ad Originem etiam 6c Caufas Ventorum alTe-
quendas via patuilTet. Unum hoc fdtem, quod ipfum
non leve momentum ad has difquifitiones attuliffet,quod.-
que jam-, ut plurimum, pro Conjefturi verifimili habe-
tur, potuilTemus certiffimis obfervationibus live veri,
five fahi arguere. Opinionein dico fagaciffimi Viri,
Edmondi qui Hydrargyrum ideo cenfet in

Barometro afcendere, quod Venti ex contrariis regioni-
bus utrinque eodem fpirantes Aerem cogant 6c quafi
in cumulum attollant ^ ut contra Hydrargyri defcen-
fum Ventis, ex eodem loco verfus oppofitas partes Ae-
rem deferentibus, 6c quafi exhaurientibus, attribuit.

Rogantur itaque Eruditi, qui ad excolendam hanc
partem Hiftoriae Naturalis operam fuam conferre vo-
luerint, ut quotidie femel minimum, vel utcunque fe-
pius libuerit, notare dignentur in Diario Barometri 6c
Thermometri altitudinem, Venti Plagam cum aliqua vi-
rium aeftimatione, Coeli faciem, 6c Pluvise vel Nivis

U u u quantita-

* V. Philof. Traufd^l. N. i8i.

C 4^4 ) .

quantitatem, quas tempore poft obfervationem fuperio^
rem elapfo deciderit. Quod fi quis Obferyationes Hy-
grofcopii cujuflibet, five Acus Magneticae ope fadas ad^
jicere voluerit, non erit ingratum.

Quoties ingruerit Procella vebementior, utile fuerit
ortum ejufdem, incrementum, fummam violentiam, re- .
jniflionem 6c exitum notatis temporibus accuratius de-
fignare, uti dc altitudines Barometri, qu^e didis tempo'
ribus refpondeant.

Monendum cenfemus, ut qui Barometri replendi dc
conficiendi modum callent, Barometro vulgari, five a-
perto, quod vocant, utaritur^ Sit autem Tubus quar-
tam, ut minimum, vel etiam tertiam digiti partem la-
tus *, quum in Tubis anguftioribus Hydrargyrus infra
Juftam altitudinem fubfidere deprehendatur f . Cifternas
vero, five Vafi Hydrargyrum excipienti tribuetur dia-
meter odonis faltem, vel decern partibus major Tubi
diametro, idque eum in finem, ut afcendente, vel fubfi-
dente Hydrargyro in Tubo, altitudo Hydrargyri in
Cifterna invariata permaneat, aut certe quam paululuin
immutata..

Qui vero Barometro claufo, five portatili uti malunt,,
ejufmodi Barometra magna diligentia fabricata compa-
rare poterunt apud Laudatum Artificem Francifeum
Haukjbejum^ in Area vulgo did^ Crane-Court^ Londi^
ni degentem j qui Thermoinetra etiam fubrniniftrabit
ad earn Scalam, five graduum notationem exada, quse
jam per multos annos, exquifitis ejus Thermoraetris in-
iculpta, iniiotuit Eruditis,.

Qui Thermometro utuntur alii quicunque ratione
conftrudo, rogitos volumus, ut in Diario Thermometri
fitum, fabricam, difpofitionem graduum in Seal i, no-

men

} V, Pbilof. Tranfaft. N. 363,

-( 4^5 )

inen etiam Opificis, ex cujus Officini prodiit, apponere
Jie graventur, Situm Thermometro commodiffimum cen-
femus in conclavi ad Septentriones obverfo, ubi focus
aut nunquam accenditur, aut faltem quam rariflime.

Quo fecilius inter fe conferri poflint Diaria, commo-
.dum fuerit omnia in hujufmodi formam difponere.

Columna prima indicet diem dc horam obfervatio-
nis^ ftylo autem ut omnes Juliano, five Vetere, in
Diariis utantur, Ob ferva tores rogamus.

Secunda altitudinem exhibeat, ad quara attollitur
Hydrargyrus in Tubo Barometri fupra fuperficiem Hy-
drargyri in Vafe, per digitos, five partes duodecimas
Pedis hondinenjis y per partes decimales eorundein
digitorum notatam. Habet autem Pes Londinenjis ad
Farifienfent earn rationem, quse eft inter 15' <3c 16
proxime.

Columna tertia gradum monftret, & partes gradus
decimales, quas Spiritus in Thermometro attingit.

Quarta Venti Plagam 6c fpirandi vires reprasfentet ^
qus vires Temper denotari poterunt per aliquem ex nu-
meris fequentibus, i, 2,3,4: ex quibus i fignificet
lenifiimum Aeris motum vix arborum folia agitantem,
4 vero fuinmam Venti violentiam^ numeris 2 6c 3 in-
termedias inter hafce Ventorum vires exponentibus, 6c
denotante cyphri, five o, perfedam Malaciam.

Quintam occupet Coeli facies, 6c fuccinda Tempe-
ftatis hiftoria.

' Sexta 6c ultima altitudinem pluvis, vel nivis in a-
.quam refolutas, quas poft fuperiorem obfervationem de-
ciderit, per digitos Lo7idinenfes 6c eorum partes decima-
les metiatur.

Haec facile ^ftimari poterit ope Infundibuli duos
circiter, vel tres pedes ampli, Vafis alterius aquam ex
Infundibulo defluentem excipientis, 6c Menfurai Cylin-
dvkx cum Reguld in digitos 6c partes decimales divis^.

U Li u 2 Infundi-

( 4^6 )

Infundibulum ita fitum fit, ut, quicunque ventus fla^
verit, nulla tainen pluvial pars five sediticii interventu,
five quocunque alio impedimento intercipi queat. Sit
autein vas aquam continens undique probe claufum, ne
quid in vapores attollatur, angufto folum fbramine,
ad aquam defuper ex Infundibulo excipiendam, relido.
Menfiirae porro Cylindricse Diameter decern partibus
minor Diametro Infundibuli tribuetur : quo fiet, ut
aqua digitum unum alta in menfura ad aititudinem
eentefimse partis digiti in Infundibulum, atque adeo in
reliquam terrain, cecidifie intelligatur j dc fimiliter pro
partibus digiti decimalibus.

Ad finem vero Menfis dC Anni cujufque apponatur
media altitude lUenflrua, vel annua, Barometri 6c
Thermometri, uti etiam fumina omnium altitudinum
Pluvis, qu2B Menfe, vel Anno integro deciderit. Ha-
bebitur autem dida media altitudo, redigendo in unain
fummam, omnes Barometri altitudinum obfervationes
mane fadas, Thermoiiietri vero five matutinas, five
totius diei maximas, (qua nempe circa horam tertiam,
vel quartam pomeridianam contingunt) dC fummam
iftam per numeruin dierum dividendo.

Omnes rogamus, qui fuprafcriptas Obfervationes, vel
univerfas, vel aliqud ex parte volent inftituere, ut Dia-
riorum Exempla, ad finem anni cujufque continuata,
ad Secretaries Regiae Societatis tranfmittere dignentur ^
uti cum Diario, quod Londini juifu Societatis Regise
conficitur, conferri poflint. Confilium vero eft, ut quic-
quid ex Diariorum iftorum collatione colligi poterit,
fingulis annis in Adis Philofophieis cum Publico coiu-
municetur.

Diarli

( 4^7 )-

Diarii Forma,

Dies&Hora
•.lyas*

Nov. St. V.

I. 8 aim.

4 m.

i. 7

5. ^ ?;?.

5

4. 7 m.

10

. i ^

3 f. m.
5
7
9

5; 7 a. m.

£arom.j

Therm

‘Vent.

alt.

alt.

dig.dec

gr. dec.

■ N •, ( '

2P.75

49 . 6

S.W. i'

2p.5<J

47 . 3,

S.W. 2

( ■

29.24

29.95

48. 5
49 • 7

s. . 1

N.-^'i

30. 4

49 • i

N. I

^9, 9

47 .iO

S. W. I

29. 7

4<^ • 2

S.W.

29. 4

45 • 0

S. '3

28. 8

4<5 . 0

S. 4

28. 6

47 • ^

S.W. 4

28. 9

48 . 0

S.W. 2

28. 9

48 . 2

1

0

29. 7

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N.E.:i

•* T

•i

.Tcmpeftas.

Coelum nubibusobdudl.
Imbres interrupt!.

Sol pervices inter-
currcns

Pluvia fprc perpetual
Co&lum fudum-
Ccelum fudum
Nubes fparCe
Imbres intercurrentes
Coelum nubibus un-
dique fere teftum
Nubes fparfae
Eadem Goeli facjes
Pluit ,

Pluvia fere perpetua
Sudum. G^u.

uvia.

(Jip.dec

0.035

0.043

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o.ood"*

0.000

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0.050'

olooo

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0.250

■IJfi

'■/

VIII. An

C 41^ )

yill* Account of a ©oo^ Adverfariorum

Anatomico- Medico -Chirurgicorum Decas
j tertia. AuBore Frederico'^ Ruyfch, M 2).
AnaWn. ^oUn* Trof Amftel. ^S.'Sdc-

§ I. H E learned Author, who has fo long improv’d
JL the World by his curious Searches into the
niceft Secrets of the Animal-Machine, ‘and illiiftrated
them by his admirable’ Preparatioiiis, gives an Ac-
count of preternatural Things found in 'Tumors, of that
Sort which we call ordinarily a Cyjl filled

with a thick Matter ^ike Pult, fuch are- Bones, Flefh,
Hair, TeetH, and other Things very furprizing and
unaccountable. ' He tells us, he firft found out the Fa-
brick of the cortical Part of the' Brairi j ' that ’tis made
of fmall pulpy Canals from the Ends of the Arteries :
That many Years ago he drew, by (imple Diflillation,
from crude Vegetables, a perfed volatile Salt^ and
that ’tis ealily done from frefh Seeds of the hot antifcor-
butic Herbs, fuch as Muftard, Rocket, Onions,

§ II. He diffeds a Pear, which he fays is entirely
compos’d of the Pipes in the Stalk, dilated into a fofc
and moift Pulp, like what they antiently call’d the
Parenchjima, that compofes the Liver and Spleen, which
he affirms to be pure VeiTelSjhot Glands diftinguiffi’d
by being invelop’d with one proper Membrane.
You may, if you pleafe, call the Pear, the Liver and
the Spleen, taken in the whole, a Gland • but he de-
nies any particular Glands in their Compolition.

§ III. He tells a remarkable Story of a Girl, who
had frequent Eruptions of Blood from the Skin of her
Head, Ears, Mouth, Navel, and the Nipples of her

Bread :

( 41? )

Bread : For fourteen Weeks the eat no Meat, nor had
any Excretion by Siege or Urine , and many other
odd Symptoms. ^

S IV. He gives us a pretty Obfervation of the Ci-
catricula, as commonly call’d, in the Ovaria of Fe-
males, whence the impregnated Elgg is dropt into the
Falloppian Tubes. He fhews, that in reality it is a Ca-
hx, or natural Aperture, which enlarges itfelf for that
Purpofe by Degrees, and after Excluhon clofes again,
as the Os Uteri afterwards fo that the Egg truly drops
from it, as an Acorn wlien ripe from its Cup ^ and^the
Trace of it foon becomes imperceptible. He fays far-
ther, he has frequently feen the thick Part of the
Male Sperm carry’d up even into the Falloppian Tubes
upon Impregnation.

§ V. He fpeaks of an Obifrudion, that has fome-
times happen’d in the Inteftines of new-born Infants, fo
that they have had no Manner of Paifage by Stools,
and that gentle Lenitives have not been able to relieve
them : In this cafe, he advifea ftrong Purgers, adapted
to their tender Age.

§ VI. The Author informs us of wonderful Appear-
ances within the very Center of human. Bones *, for in
eight feverai Preparations he has, of Leg and Thigh
Bones, and others, of Men and Infants, he has ob-
ferved plain Chryfalis*s of Infeds, and very perfed, of
different Sorts, lodged in the Cavities of the Marrow :
How they come there, he can no more account for, than
for whole Bundles of Worms twilled together, which
he has found in the great Artery juft by the Heart ^
or for fix fat, thick Eruca in a Sheep’s Brain \ and ma-
ny of the like Nature, that have happened in the Way
of his Obfervation, which are in the Czar’s Repofitory.

In 5 VII. he fays, very often, upon Diffedionvof
the Bodies of old Women, he has found the mefenteric

Glands,,

( 4?o }

Glands, that mlnifterto the Conveyance of the Cliyle,
perfeftly wafted away , fo that he judges it not im-
probable, that, in fuch Cafes, the mefaralc Veffels ab-
ibrb the Chyle from the Guts, and carry it into the
Blood, at leaft in part, according to the Notion of the
Antients, who knew not the la&eal Veffels: This he
thinks not a little confirm’d by the like wafting of the
glandular Part of the Breafts in old Women, which
though formerly very large, ftiall have nothing but
the Nipples left.

§ VIII. He treats of the Epidermis, or Scarf-Skin,
with a good Method of feparating it for publick De-
inonftrations : He takes off a Piece of the whole Skin,
and nails it upon a Board with the Outfide uppermoft,
and then puts it into boiling Water, which raifes it fo,
that with a blunt Knife it is eafily feparable, which is
a much better Way, than that of burning or bliftering.
He fays, the different Colours of the Skin are owing to
the Corpus Reticulare, which in Blackmoors is per-
feftly black, in Moors of a tawny Colour, in white
People perfectly white. The Epidermis is ever found
abfolutely void of Blood-Velfels : upon which occa-
fion the Author offers to lay Two Guineas with
Mr. St, Andre, who, he fays, falfly alferts he has
Preparations fhewing thefe Veffels, and has pretended
to ftiow them to fome of his Countrymen the Dutch,
He adds, that he gueffes the’Occafion of his Miftake
to te thus : The Skin of new-born Infants, in fome cer-
tain Places, if it be carefully feparated from all Fat,
is fo fine and thin, that it becomes like the Epidermis
in Adults. This no doubt is extremely full of Veffels,
and is what he has imagined to impofe upon Mr.
St, Andre,

S IX. He tre'ats of 'human Bones, in which Search
he has long laboured ; He obferves the Epiph^fes up-

2 on

( 4?' )

on the Ends of the Bones are chiefly faftened to them
by the Periojieum ^ which being taken off, they eafi-
ly fall afunder, ’Tis a Miftake, that we vulgarly think
this is done by means of an intermediate Cartilage :
The Truth is, both the Epipbjifes and Ends of the
Bones, at firft, are cartilaginous but in Time become
bony, and then are only joined by the Periofteutn*
The Offification always begins in the middle of Bones.
Sometimes he has found human Bones fo void of Ca-
vities, that he has made Knife-Handles of them: It
has been thought that cartilaginous Parts were cxfan-
guious ^ but falfly, as he demonftrates by feveral Pre-
parations thereof.

§ X. He confiders the PaptlU of the nervofe Tu-
nic in the Infide of the Stomach, and finds that the
Figure of them is round i(h, in that Part of the Sto-
mach over which the Spleen is fixt *, but longifli in
other Parts thereof, and in the Infide of the Jejunum,
He takes Notice, that the Fabrick of the Womb is
made of much the fame Sort of thick mufcular Fibres
as the Bladder, both to facilitate their proper Exclu-
fion 5 particularly thefe Fibres are more remarkable
upon the Fundus Uteri, to which Part the Placenta
moff generally faftens its felf, and mofi: evidently for
this Reafon.

FINIS.

E R R AT V M.
P, 402. /. p. pro indicium /. judicium.

LONDON: Printed for W. and J, Innjs, Printers
to the Royal Society ^ at the Prince's- Arms, the Weft
End of St. Paul's Church-Yard.

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Numb. 3 So.

PHILOSOPHICAL

TRANSACTIONS.

For the Months of November and December. 1713.

The C ONTENTS.

I. A Letter from Mr. David Marcineau Surgeon
in Norwich, to Sir Hans Sloane, ^art. Coil,
Med, ' Lond. (Pr. 5. K Tr, Concerning
Stoms Voided {>er Anum.

n. Epijlola Viri T>o&iJJlmi Johannis Hoogvlietii
ad Jacobum Jurin, M. ®. (^. 5. Seer, Ve £-
pijlolis duabus Tojlhumis Viri Celeberrimi Anto-
nij a Leeuwenhoek, S. 5.

III. De Globtdis in Sanguine in Vini Foecibus^
Epifiola pofthuma 'Domini Anconij a Leeuw-
enhoek, Societatis <I(egi^je Londinenfis^ dum

-.-^.Veret, S.odalis dignijfmlj^ ad Jacobum Jurin,
5^. S. Seer,

IV. Ejufdem Viri ClariJJimi ad eundem Epijfola pojl^
huma, De Generatione Anmaliuniy de ^atpi^

.. tat tone Diaphragmath*

V. A

botanical Defcn^tlon of th Flomr andSeed^
Vejjel of the Tlant^ called Crocus Autumnalis
•Sativus, that produces the true Englifli Saffron
of the Shops : IFuh a Figure, Sy Dr. James
Douglas, Honorojy Fdlow of the College 0/
Phyficians, and Fellow of the Koy^il Society.

VI. Some Accoujit of Mr, Leeuwenhoeks curious
Microfcopes, lately prefented to the Royal So-
ciety. ©jv Martin f olkes, Eff^ Vtce-Trefident
of the Royal Society.

VII. 71’e ©i//s of Mortality,, See. of federal confide-^
rahle Towns in Europe, beginning with the
Tear 1 7 1 7, i. e. from Chrillmas 1716, to
Chriftmas 1717. ExtraSied from the A6la
Breflavienfia. ©y Conr. Joach. Sprengell,
M. D, 3^. S. vS. Coll, Med, Lond, Lie,

I. A Letter from Mr. David Martineau Surgeon
in Norwich, to Sir Hans Sloane, ^art. Coll.
Med. Lond. Pr. S. R. V. Pr. Concerninz

^ . i . Ofc

Stones Voided per Anum.

Nonvich, OB.

These Srones (Vid. Fig. I, 2, 3,4,5.) were
voided by a poor Woman, per Anum, on 'the
26, 27, and 28th of March lafl: paft, who was tiien
pregnant about the ii, or 12th Week, according to
‘Computation. I was call’d in the Night to this poor
Woman on the 23d, who in x'Vppearance was in the^
Extremity of a Con vulfioh Fit, attended with violent^
Vomitings, which when over, fhe complain’d of great
Pain in her Back, from her Reins downward to the A-
nus, upon which 1 blooded her, order’d fome Anti-Erne-
ticks, and left her : She continued with much Pain the
whole Day* on the 24th, in the Night, lief Fits re-
turn’d again with double Force, her Pains alfo increa-
fing like unto Labour- Pains, put me upon further In-
quiry, but nothing appear’d more thanordinary j the Ex-
tremity of Pain drove me to the Ufe of Glyfters, which
was attempted, but none could be thrown up, although
repeated by one and another of the moft experienced
Nurfes, upon which 1 g'ave her a gentle Draught, which
fhe obferved increas’d her Pain with a ftrong Tenefmus,
that continued near three Hours before the largeh Stone
appear’d, which flopp’d at the upper Part A, D, Fig. i.
but was quickly remov’d by prefling the lower Protube-
rance C, upon which, with a plentiful Difcharge, fhe had

X X X Eafe,

c 434 y

Eafe, flept fome Hours, waking with a Defire to ftool,
and voided with it the ad and 3d , and the next Day, at
four Hours-Diftance, the other two. She recovered per-
fectly, and was deliver’d of a very fine living Girl, on the
24th o(Auguft paft.» Upon Inquiry, itfeemSiftie had been
frequently troubled, for fourteen Years -pad, with Pains
in her Side and Stomach without Vomitings which
is all (he remembers. * '

The Largenefs of the Stones, their Seat- and Subdance,
is what to me feems worthy Speculation , their.being all
alike in Colour and Weight, according to their Dimen-
fions, is the Reafon 1 broke but one.

Wt. of the Stones.

ez. dwts. gr.

Their Dimenfions in Circumference.

Inch:

Fig. I.

2 1612-

A. B. C. D.

8 A. D. the top of
the Stone oval.

Inch,.
^ r

Fig. 2.

8 12

E.F.G.H.

5 ; E.a

4- V

F’g- 3-

7 5

I. K. L. M.

5 I. L.

Fig. 4.

7 12

N.O.P.Q,

4 4, N.P.^

3.T

Fig. 5.

5

R.S.T.U.

4, ^ R.T.

4-r.

I* A Shell taken of the Stone at the End 2^ The Stone
and Shell being like a Chefrmt foft and like Wool^ ,
cutting into the Stone at 5, I found it hard..

f

h

IT Epijkla

( 4iy )

II. Bpijiola Viri Johannis Hoogvlietii

ad Jacobum Jurin, M t>, ^ S- Seer. ,,

^pijlolis duabus^fpojlhumis Vtri Cekberrimi Anto-
nij a Leeuwenhoek, ^ S. 5. ‘

SEnex nofter venerandus Leeuwenhoekius^ jam in a-
• gone Mortis Verfans, ac nihilominus art is fuas me-
mor, me ad fe vocari juflit, attollenfque oculos jam
gravatos morte, verbis femiabruptis me rogabat, vellem-
ne hafee binas literas ex vernaculo in Latimim Sermo-*.
nem vertere, tibique, Vir Ampliflime, mittere. Ut er-
go hifee tanti viri, quo abhinc jam aliquot annos ufus
fueram familiariflime, parerem prseeeptis, non poflurn?
quin tibi, Vir eruditiflime, hoc extremum, Viri mihi
amiciflimi morientis, munus mittam, fperans fore ut,
h^c ultima ejus conamina tibi grata fint futura.

$

Delphis in Batavis^
pridie Nonas Sept.

172^.

X X X 2

*•

III.

(

III. De Qlohulis hi Sanguine <sr in Vini Foecihus,
Epifiola pofthuma pomini Antohr] Leeuw-
en hoek , Societatis' Loiidinhtjts^ dum Vi*
Veretj Sodalis digniJ/irnij ' ad Jzcobum Jurin,
5^. S'. Seer,

' ■ li;;f ' >' ‘ D Delphis in Batavis,
i ^ ' '' i- *!i '

EX proximis tuis literis Septimo Kalendas Jultt da-
ds^. innotuit inihi,. nobiliflimos D. D. Regias
Societatis,. meas tres ultimas epiftolas perlibenter acce-
pilTe, quod raihi gratifliinura erat intelledu , Tibique,
Vir dodillitne, placuilTe, tuas obfervationes de glo-
buloruin languineoruni magnitudine', meis obfervatio-
nibus congruere. Pgrro, dicis, Vir dodiffime, non credo
hanc explorationera fore indilFerentem, feu inutilem,quo-
niam non impoflibile eft, quin ilia obfervatio de globu-
iorum fanguineorum magnitudine in variis animalibus,
una cum fuis parvulis vafeulis, dudura fit nos aliquan-
do ad detedionem ubi, 6c quibus mediis hi globuli
formentur, 6c inde determinatam craflitudinem in eodein
animali confervent.

Deinde dicis, mi dodiflime, hoc ampliori tua explo-
ratione bene dignum eft.

Ad hsc mihi affumo tibi, Vir eruditifiime, objicere,
me ad imaginationera earn adduci, nos nunquam ad ex-
plorationein illam perventuros, quomodo fcilicet hi
globuli ex materia fluida ad ma^nitudinis determinat^e
globules fint coagulaturi.

Multis

( 437 )

Multis abhinc annis ad me afportari juffi vinura fer-
mentans, quia hoc Vinum globulos producit fere fan-
guiiieis ?equales, quos vini foeces vocamus : <5c quam-
vis tale vinum microfcopio apponerem, tamen nil aliud
videbam, quam innumerabilem multitudinem parvif-
(imorum globulorum aereorum, furfum ad -fuperficiem
vini adfcendentium, dc fecum illos* globulos, quos vini
foeces nominamus, ducentium. Cum jam in fuperfici-
em vini venerant, feparabantur vini foeces a globulis
aeris, 5c fundumrepetebanr, mihi non apparente, quo-
modo globuli, quos dicimus vini foeces, formabantur :
6c fimulac, ni fallit meinoria, globuli illi inferius de-
fcendilTent, exibat ex globulo quoquc iterum globulus
aereus, 6c ita denuo ad fuperficiem Vini devehebatur.

Imaginor mihi, coagulationem illam, ac determina-
tara globulorum fanguineorum magnitudinem a rerum
primordiis elfe creatas ^ nam fi unus globulus altero ma-
jor erat, fufpicamur exinde inordinatam circulationein
fore fecuturam, quoniam fanguinem per varia vafcula
fanguinea rapide transfluentem vidi, quae adeo exilia
erant, ut fimplex faltem globulus tranfire potuerit.

» » ■' ■

f

IV. Ejufhm

C 433 )

IV. Ejufdem Viri ClarijJmii ad euudariEpiJlola pojl^
l:aima. De Generatione Animaltum^ deE^alf l-'

tatione Diaphragmatls.

' Delphi s in Bat avis,

INTER alia ex tuis proximis literis, feptimo Ka-
lendas Julii datis, inteiiexi, Sentcntiam meam de
generatione tibi videri firnaifliinain omnium, liadenus
in lucem editaruin *, & quod mihi non incognitum erat,
quofdam Anatomicos fupra mea fundamenta novum
ftruere Syftema aiifos efle, aftinnantes ovum elTe pro-
prium nidum, in quo animalculum feminis mafculi-
ni hofpitatur, 6c quod idem ovum ex eo impraegnatum,
poftea per tubam Fallopiandm deducitur ab ovario ad
uterum.

Multos expe^lavi contradicente?, & dodiifimus qui-
dam dominus dicebat, poftquam meum Syflema de ge-
neratione legilTet, rede putas, fed vita tua convincendis
omnibus non fufficiet • alius dicebat, me mendacia de
animalculis memoris prodere.

Paulo ante obitum Domini Leibnitz, fcribebat ille
Dominus mihi Hannonia, fe meam fententiam de gene-
ratione amplexilTe, feque in libro quodam, a fe edito,
idem demonftralTe, fed quendam dominum in Italia elTe,
qui contra meum Syftema de generatione aliquid effet
editurus^ atque in Germania dominum eiTe, qui cum
iilo communicaverat totum ovarium in tuba Fallopiana
repertum elFe j ProfelTorefque in Germania inveniri,
qui animalcula feminis mafculini elfe negabant. Ve-
rum enimvero, quamvis contradiftiones quamplurimas

( )

palTus (iin, 6c adhuc patiar, permanebo in Syftemate
ineo, quoniain animalcula in omnigenis feminibus in-
vcni, (i faltem animalia rite tradare polTein, ne exceptis
quidem variis avium ac pifcium fpeciebus.

Porro comperimus in omnibus arborum 6c plantarum
feminibus, etiamfi parvifTimis, fi modo tradari poflinr,
plantam efFe formatam, quam plantain antea comparavi
cum animalculis feminis mafcuiini. Et farinofa mate-
ria in feminibus plantarum plantis nutrimento effe debet
ramdiu, quam pl mta fuos ejecerit radices, 6c ex terra
all pofllt.

Dodiflime Vir, concede mihi libertatem dicendi, me‘
percipere non poife, quomodo politiones adeo vanas fta-
tuere, eafque in lucem edere audeant, quod animalcula
feminis mafcuiini in utero vei’ tuba Fallopiana effuli,
poftea per tubam Fallopianam deducerentur ab ovario
ad irterum, Hae politiones funt adeo omni fundamento
carentes, ut ulteriori contradidione indigns lint.

Ulterius dicis, eruditiflime Vir, ineain pridinse fani-
tati reftitutionem tibi gratam fuilfe, pro qua benignitate
erga me gratias ago maxiinas, 6c tibi dicere cogor, me
multis ab hinc annis pro certo habuilfe, quod diaphrag-
ina inftruinentum fit adeo magnum, ut totum abdomen
continue moveat, quo motu cibi in ventriculo 6c inte-
llinis adeo conteruntur, ut in materiam tain fluidam re-
digantur, quag apta eft, ut intret parvula ilia v^fcula
fanguinea, qu^ multa in inteftinorum caviratibus fita
funt; non autem per ofcula iiiorum vafculorum, ut
quidain hominibus perfuadere conati funt, fed inejudi-
ce per tenues tunicas iiiorum parvifllinorura vafculorum-
fanguineorum.

Si jam ponamus arteriam in corpore bene conftitu-
to, intra hor^e unius fpatium ter miliies 6c fexcenties-
pulfare, quatuorque pulfus tier! in una rerpiratione,,
computabiinus nongentas refpirationes fpatio unius ho-

( 44® )

r?e, ac toties fiet preilio ventriculi dc inteftinorum,
quam voco fubadionem in vcntriculo dc inteftinis con-
tentorum.

Sit mihi quoque venia tibi, dodiiTimeVir, dicendi,
quod duos abhinc inenfes varias lentas paipitationes per
diaphragma fenferim : quare cogitabam de tuba quadam
vitrea, a me inventa, ad fpiritum cujufdain liquoris in
pedus ducendum, ut experimentum facerem, num info-
litus ille diaphragmatis motus, quein cordis palpitatio-
nem vocant, fedari pofiet.

Implevi ergo meam tubam ad altitudinem triuin
tranrverforum digitorum fpiritu vini, in quo jam diu
hsec aromata fuerant infufa, nempe nuccs mofchat^e, ma-
cis, <3c parum garyophilloruin, fed cinnamomi inultum,
ut 6c croci, & infpiravi aerera tranfeuntem per hunc fpi-
ritum vini, 6c quidem non modefte, fed fortiter aerein
in pulmonem impuli, quo diaphragma, quod fortis
membrana eft, valde extendebam, experiendi gratia,
num palpitationem, vel inordinatum diaphragmatis
motum,hoc fado componere poftem, quod illo tempore
bene fucceflit : Sed poftea quidem cvenit, ut experi-
mentum hoc, quam vis aerera tam fortiter in pedus in-
ducerem, ut prelTus aer cum tufli ex guttere erumperet,
expedationem meam eiuferit.

Sententia tua mihi longe vifu erat gratiflima, nempe
quod diaphragmatis palpitatio validiori niteretur fiin-
damento, quam ilia cordis.

1

V. A

( 44» )

V. A botanical Defcription of the Flower and Seed^
Veffel of the F^lant, called Crocus Autumnalis
Sacivus, that produces the true Englifh Saffron
of the Shops : With a Figure, !By Dr. James
, Douglas, Honorary Fellow of the College of
Phyficians, and Fellow of the Royal Society.

TH E Flower of this curious Plant is of the Lil-
ly Kind, monopetalous, infundibuliformis, with-
’ out any Calyx or ferianthtum^ its long fiftulous Be-
ginning being afterwards expanded into fix beautiful
oblong Segments. Vid, Lit. A. A. Fig, 6,

It confifls of the following Parts, the Fetalum^
the Stamina^ the Apices^ the Ovarium^ and the Stylus •
with its Capillamenta Tubtformia^ of all which in Or-
der.

T ETA LON.

The Petalum is diflinguifhed into a long, hollow, or
fiftulous Part, which lies inclofed within the common
and proper Involucra of the Plant, arifing from the
Top of the Ovarium, or Seed-VeffeL and fix Segments.
Vid. Lit. a, a.

While this narrow, tubulous Part runs between the
Leaves and Integuments that furround them, it is of a
white Colour^ but, alfoon as it is difengaged from
thefe, it infenfibly acquires a Purple Colour, which, a
little before its Divifion, as it begins to be enlarged,
and grow more open, inclines to a Red.

y y y This

( 44i )

This^ narrow fiftulous Part of the Flower, about i
or 7 Inches above the Theca Communis^ forms fix folir
aceous Segments, or divides into fo many oblong
P urple- coloured Vid, Lit, b,c.

Three of thefe Flower-Leaves are larger than the
other three, but, in all other Refpeds, are much alike.
Vid, Lit, c,c, c.

The Length of the larged is from i |/to z Inches ^
the Breadth feldom above ~ Inch : The fhorter Leaves
are from i, to i i Inch in Length, their Breadth be-
ing fomething lefs in Proportion.

, The Infide of each Fetalum is of a Violet Purple-
Colour, vein’d with a few fmall Lines of a deeper Dye,
running length'Ways, intermixed with White, or the
whole is beautifully checquered with Blue and White
Colours.

The Outfide is of a whiter Blue, with feveral whi-
tifh Rifings or Ridges, and jud at the Bottom of the Leaf
it is of a deeper Blue^ the three fmall Leaves (Vid.
Lit, h, h, b, ) are much of the fame Colour, only the
Purple feems to be fomething deeper.

The Number of the Petala is, for the mod Part, 6 j
yet, in fome Flowers we may obferve 7, or 8 j but
then they are not fo large as when they are fewer.

STAMINA.

In every Flower there are three Stamina^ or Chives,
( Vid, Lit, d, d. d. ) properly fo called, aridng from
the inner Surface of the tubular Part of the Flower, jud
before its Dividon into the Petala, where they make,^
for fome Space, an apparent Ridge, and then they dand

3

( 44^)■

Upright, oppofite to the three large Leaves *, they are
of a whitilh Colour, inclining to a light Purple, being
but little above \ of an Inch in Length.

In thofe Plants that have 7 or more Petala, the Num-
ber of the Stamina is likewife encreafed to 5, or more.

JUICES.

Each of thefe Stamina has its proper Apexy ( Vid.
Lit. e. e, e, ) which is a peculiar longilh Subftance,
Handing upright, oppofitc to the larger Flower-Leaves,
of a Yellow Colour, forked, not unlike the Tongue of
afmallBird, at the lower End, where it is fixed to the
Stamen , here likewife it is broadeft, but as it afcends
it becomes narrower, and its upper Extremity is a little
crooked, or turned to one Side : It feldom exceeds
Inch in Length.

It appears as if it was double, with a longitudinal
Furrow in the middle, in which Hollow the Stamen
feems to be faintly continued for fome Space.

When the Plant is full grown, they are all loaded
with that Kind of fmall Duft called Farina f oecundans,

0 V A (^1 U M. -

Called likewife the Vafculum Seminale^ and Piftillum
by fome. Vid. Lit» f.f.

It is a particular Body, which arifes from the Top of
the PedunculuSy ( Fid, Lit, g,) about i of an Inch
long, or a little more, of a deep White Colour, three
cornered, and divided into three Loculamentay or Cap-
fuUy in which the Seeds (which however feldom come

Y y y X to

( 444 * ^

to Perfe£lion with us) are formed, growing bigger and
bigger after the Flower falls off ^ nay, even in this
blooming State, if you cut this VelTelacrofs the middle,
you may perceive the whitiih Rudiments of the Seeds.

STYLUS,

From the upper Part, or Jpex, of the Ovarium,
arifes the Stylus ^ (Vid, Lit, b.) which is a long flen-
derTube, that lies enclofed within the tubulous or fiftu-
lar Portion of the Flower, being there of a whitifli
Colour, but changing into a Yellow before its Divifion.

This Stylet ordinarily fplits into 9 Parts, juft oppo-
fite to the Top of the Stamina, where the Apices take
their Rife, (Fid, Lit, i, i, i,J and thus far it ftands up-
right in the Middle of the Stamina'^ for the fake of
.which only, this Plant is cultivated, and being prepared,
(as (hall hereafter be defcribed) makes the true Saffron
of the Shops, which we fo frequently ufe in Phyfick.

I call thefe Parts of the Stylus, from their Figure and
Shape, Capillamenta Tubiformia, or. Appendices Styli
Salpingoeides, in as much as they very exadly repre-
fent a Trumpet, and are not unlike the Falloppian Tube
in Women, being narrow at their Origin, and grow-
ing gradually larger towards their other Extremity,
which, like the common Trumpet, is open and expand-
ed^ and, Tubdi Fdlloppii, is jagged, or fringed

at the Edge. Vid, Lit, k, k, k.

It may alfo be very fitly named Crocus officinarum^
becaufe that is the Part only that is ufed in the Shops.

They are of a Yellow Colour, juft at their Begin-
ning, continued from the upper Part of the Stylue, but

af-

C 445 )

afterwards they are all of ,a deep Red Colour, only
their jagged Extremities are tipt with a White inclining
to a Yellow.

Thefe Tub£, or Capillamenta, are from i, to i 4
Inch in Length.

The Stylus^ while undivided, is ftrong enough to
fupport itfelf, being enclofed within the tubular Part
of the Flower-, but the Capillamenta being very weak
and (lender at their Beginning, this occafions them to
hang down between the Petala.

F 1 G U 6.

Reprefents a Root of the Saffron- Plant, that has two
Stalks enclofed in one common Vagina, the whole
Flower with the Stamina and Apices in one, and the
Stylus only in the other with the Leaves, peduncuU, '
and Ovarium in both, being fairly delineated from the
Life.

Ji A, The Flotper expanded into Jix beautiful Segments.

a a. The Fijiulous Part of the Flower.

b. c. The fix Petala.

c. c, c. The three larger Petala.

b. b. b. The three frnaller ones.

d. d. The three Stamina, or Chives.

e. e, e. The three Apices.

ff. The Vafculum Seminale.

g. g. The Pedunculi.

h. h. The Stylus.*

i. i, i. The three Capillainenta Tubifbrmia.

k. k.k. The jagged Extremity of the Oipillainenta.

B. B. The Root.

C. C. The Graffy Leaves.

VI. Som

( 44^ )

VI. So??je Account of Mr. Leeuwenhoek’^
Microfcopes, lately prefented to the Royal So-
ciety. Bj Martin Folkes, Vtce-f^refident
of the Royal Society.

IT is now* above $o Years, fince the late Mr, Leeuwen-
hoek hrfl began his Carrefpondence with the Royal
Society^ when he was recommended by Dr. Regnerus
de Graaf, as a Perfon already Gohhderable by his Mi-
crofcopical Difcoveries, made with GlalTes contrived by
himfelf, and excelling even thofe of the famous Eujla-
chio Divini^ fo much talk’d of in the learned World:
And as he has ever fince that Time apply’d himfelf,
with the greateft Diligence and Succefs, to the fame
Sort of Obfervatioris, no Doubt can be made of the
Excellency of thofe Inftruments he fo long us’d, fo
much improv’d, and .upon the fullelt Experience fo
often commended in his Letters ^ great Part of which,
at his Deceafe, he thought fit to bequeath to this Socie-
ty, for whom he ever exprels’d the greateft Efteem and
Refpeft.

He had, indeed, intimated this Defign in feyeral of
his Letters, and in his laft Will and Teftament gave
Orders, that the Glalfes ftiould be delivered as'foon as
conveniently might be after his Deceafe which was
accordingly done, by the Direftions of his furviving
Daughter, Mrs. Maria Van Leeuwenhoek^ to whofe
great Care we are oblig’d, for the fafe and fpeedy De-
livery of this very curious and valuable Prefent.

- ' . The

( 447 )

The Legacy confifts of a fmall Indian Cabinet, . in
the Drawers of which are 1 5 little Boxes or Cafes, each
containing two Microfcopes, handfomely fitted up in
Silver, all which, not only the Glafies, but alfo the
Apparatus for managing of them, were made with the
late Mr, Leeuwenhoek^s own Hands : Befides which,
they feem to have been put in Order 4n the Cabinet by
himfelf, as he defign’d them to be prefented to the Roy-
al Society, each Microfcope having had an Objed pla-
ced before it, and the Whole being accompany’d with a
Reglfter of the fame, in his own Hand- Writing, as be-
ing defirous the Gentlemen of the Society fhould, with-
out Trouble, be enabled to examine many ofthofeOb-
jeds, on which he had made the moit confiderable Dif-
coveries.

Several of thefe Objects yet remain before the Mi-
crofcopes, tho’ the greater Number are broken off,
which was probably done by the fhaking of the Boxes
in the Carriage. I have, neverthelefe, added a Tran-
flation of the Regifter, as it may ferve to give a jufier
Idea of what Mr, Leeuwenhoek defign’d by this Legacy,,
and alfo be of Ufe, by putting any curious Obferver
in Mind of a Number of Minute Subjeds, that may
in a particular Manner deferve his Attention.

The 13 Cafes abovemention’d are numbered from ly
to 27 inclufively, correfponding to which is the Regi-
Iter of the Objeds, Two to every Cafe, as follows.

No. 15- Globules of Blood, from which its Red*
nefs proceeds.

A thin Slice of Wood of the Lime-Tree, where
the Vellels conveying the Sap are cut tranf-
verfely.. ' N°. 16..

N”. I <5.

( 448 )

The Eye of a Gnat.

17. A crooked Hair, to which adheres a
Ring-Worm, with a Piece of the Cuticle.

A fmail Hair from the Hand, by which it ap-
pears thofe Hairs are not round.

N°. 18. Flelh of the Codfilh (Cabeljaeuw ) (hew-
ing how the Fibres lie oblique to the Mem-
branes.

An Embrio of Cochineal, taken from the Egg,
in which the Limbs and Horns are confpi-
cuous.

N°. 19. Small Pipes, which compofe the Ele-
phant’s Tooth.

Part of the Cryftalline Humour, from the Eye
of a Whale.

20. A Thread of Sheeps-Wool, which is
broken, and appears to confift of many lelTer
Threads.

The Inftrument, whence a Spider fpins the
Threads, that compofe his Web.

N°. 21. A Granade, or Spark made in flriking
Fire.

The VeiTels in a Leaf of Tea.

N°. The Animalcula in Setnine Mafculino, of
a Lamb taken from the Tefticle, JuL 34.
1702.

A Piece of the Tongue of a Hog, full of (harp
Points.

N°. 25. A Fibre of Codfi(h, confifting of long
(lender Particles.

Another of the fame.

24. A

( 449 )

24. A Fikment, conveying Nourlfliment to
the Nutmeg, cut tranfverfly.

Another Piece of the fame, in which the Figure’
of the VelTe Is may be feen.

N°. 25. Partof the Bone or TootKabovementioiH
ed, conhfting of hollow Pipes.

An exceeding thin Menftbrane, being that which
cover’d a very fmall Mufcle.

N°. 26. Velfels by which Membrames receive'
Nourilhment andincreafe.

A Bunch of Hair from the Infed call’d a Hair*
Worm.

N°. 27. The double Silk, fpun by the Worm^
The Organ of Sight of a Flie.

It were endlefs to enter into any Particulars, of what
is to be obferved in any of thefe Objeds, or indeed to
give any Account of Mr, Leeuwenhoek's Difcoveries j
they are fo numerous as to make up a confiderable Part
of the Fhilofophical TranfaSions^ and when colleded
together, to fill four pretty large Volumes in Quarto,
which have been publifh’d by him at feveral Times :
And of fuch Confequence, as to have opened entirely
new Scenes in fome Parts of Natural Philofophjf, as we
are all fenfible, in that famous Difcovery of the Animal-
cula in Semine Mafculino^ which has given a perfedly
new Turn to the Theory of Generation, in almoft all
the Authors that have fince wrote upon thatSubjed.

For the Conftrudion of thefe Inftruments, it is the
fame in them all, and the Apparatus is very fimple and
convenient : They are all fingle Microfcopes, confift-
ing each of a very fmall double Convex-Glafs, let into

Zzz a

( |4?o )

a Socket, between two Silver Plates rivetted together,
and pierc’d with a finall Hole : The Objed is placed
on a Silver Point, or Needle, which, by Means of
Screws of the fame Metal, provided for that Parpofe,
may be turn’d about, rais’d, or deprefs’d, and brought
nearer, or put farther from the Glafs, as the Eye of
the Obferver, the Nature of the Objed, and the conve-
nient Examination of its feveral Parts may require.

Mr. Leeuwenhoek fix’d his Objeds, if they were folid,
to this Silver Point, with Glew^ and when they were
Fluid, or of fuch a Nature as not to be commodioufly
view’d unlefs fpread upon Glafs, he firft fitted them on
a little Plate of Talk, or exceflively thin-blown Glafs,
which he afterwards glewed to the Needle, in the fame
Manner as his other Objeds.

The Obfervation, indeed, of the Circulation of the
Blood, and fome others, require a fomewhat different
Apparatus^ and fuch a one he had, to which he occa-
fionally fix’d thefe fame Microfcopes, but as it makes
no Part of this Cabinet, I lhall omit giving any farther
Account of it, only taking Notice that it may be feen in
a Letter to the Royal Society, of the 1 2th of January,
1689. and printed in his Arcana Naturdi DeteBa,
2V°. 69. But I was willing to mention juft fo much, as it
may ferve to fhew the univerfal Ufe of thefe Micro-
fcopes, and as it induces me (among other Things) to
believe, thefe were the Kind of Microfcopes generally,
if not folely,, us’d by this curious Gentleman in all his
Obfervations, and to which we are obliged for his inoft
furprizirig Difcoveries.

Another Particular, to the fame Purpofe, I would
not omit, and that,% That upon th«. late Qpeen Mary's

» doing

( 45*' )

doing Mr. heeuwenhoek the Honour of a Vifit at T>elft^
and viewing his Curiofities with great Satisfadion^ he
prefented her with a Couple of his Microfcopes, which,
as I have been inform’d by one who had them a confi-
derable Time in his Hands, were of the fame Sort as
thefe, and did not any ways differ from one of the 15
Cafes contain’d in the Drawers of this Cabinet.

The Glaifes are all exceedingly clear, and ihew the
Objed very bright and diftind, which muft be owing
to the great Care this Gentleman took, in the Choice of
his Glafs, his Exadnefs in giving it the true Figure ^
and afterwards, amongft many, referving fuch only for
his Ufe, as he, upon Tryal, found to be mod excel-
lent. Their Powers of magnifying are different, as
different Sorts of Objeds may require^ and, as on the
one Hand, being all ground Glalles, none of them are
fo fmall, and confequently magnify to fo great a De-
gree, as fome of thole Drops, frequently us’d in other
Microfcopes^ yet, on the other, the Diftindnefs of
thefe very much exceeds what I have met with in the
Glaffesof that Sort ^ and this was what MxXeeuwenhoek
ever principally propos’d to himfelf, rejeding all thofe
Degrees of magnifying in which he could not fo well
obtain that End 5 for he informs us in one of his Let-
ters, where he is fpeaking of the exceflive Praife fome
give to their Glaffes on this Account, that although he
had above Forty Years had Glaifes by him of an extra-
ordinary Smallnefs, he had made but very little Ufe
of them 5 as having found, in a longCourfe of Experi-
ence, that the mod confiderable Difcoveries were to be
made with fuch Glaifes as, magnifying but moderately,
exhibited the Objed with the mod perfed Brightnefs
and Didindion.

Z z z 2

But

( 45* )

But however excellent thefe GlafTes may be judg’d,
Mr. Leeuwenhoek's Difcoveries are not entirely to be
imputed to their Goodnefs only : His own great Judg-
ment, and Experience in the Manner of ufing them,
together with the continual Application he gave to that
Bufinefs, and the indefatigable Induftry with which he
contemplated often and long upon the fame Subjed:,
viewing it under many and different Circum fiances,
cannot but have enabled him to form better Judgments
of the Nature of his Objefts, and fee farther into their
Conflitution, than it can be imagined any other Perfon
can do, that neither has the Experience, nor has taken
the Pains this curious Author had fo long done.

Nor ought we to forget a Piece of Skill, in which he
very particularly excelPd, which was that of preparing
his Objeds in the befl Manner, to be view’d by the
Microfcopej and of this I am perf waded, any one will
be fatisfied, who (hall apply himfelf to the Examina-
tion of fome of the fame Objeds as do yet remain be-
fore thefe GlalTes at lead, I have my felf found fo
much Difficulty in this Particular, as to obferve a ve-
ry fenfible Difference between the Appearances of the
fame Objed, when apply ’d by my felf, and when pre-
pared by Mr. Leeuwenhoek, tho’ view’d with Glaffes
of the very fame Goodnefs.

I have the rather infifted upon this, as it may be a
Caution to us, that we do not rafhly condemn any of
this Gentleman’s Obfervations, tho’ even with his own
Glaffies, we ffiould not immediately be able to verify
them our felves. We are under very great Difadvantages
for want of the Experience he had, and he has himfelf
put us in Mind, more than once, that thofe who are

( 4H )'

thebeft skiird in the Ufe of Magnifying- GlalTes, may
be mifled, if they give too fudden a Judgment upon'
what they fee, or ’till they have been allured from re-
peated Experiments. But we have feen fo many, and
liiofe of his moft furprizing Difcoveries, fo perfedly
confirm’d, by great Numbers of the moft curious and
judicious Obfervers, that there can furely be no Reafon
to diftruft his Accuracy in thofe others, which have
not yet been fo frequently or carefully examin’d.

Upon the whole, it is to be hoped, fome of the So-
ciety will purfue thofe Enquiries, the late Polfelfor of
thele Microfcopes was fo defervedly famous for ^ and
that as we have loft in Mr. Leeuwenhoek moft worthy
Member, and a moft valuable Correfpondent, this laft
Piece of his Refped to the Royal Society will not only,
enrich our Repofitory, but both encourage and enable
fome other diligent Obferver to profecute the fame cu-
rious and ufeful Difcoveries.

VII. m*

r 9

( 454 )

•f

yil. Ti!>e %\\s of Mortality^ See. of federal confide--
Table Towns in Europe, beginning with the
Tear 1717, i. e. from Chriftmas 1716, to
Chriftmas 1 7 1 7. ExtraSied from the A(5ta
Breflavienfia. !Bj; Conr. Joach. Sprengell,
jVf. 2). (2^. S. S. ^ Coll. Med. Lond. Lie.

The Ufefulnefs of this Sort of Regifters is now
fo well known to the Learned World, from the
Labours of many curious and inquifitive Perfons in Po-
liticalArithmetick, that we conceive the following will

need no Recommendation

the Publick.

Breflaw,

Buried.
In January,

91

February,

113

March

136

April

108

- May

127

June

144

July

144

Auguft

io8

September

128

Odober

96

November

113

. December, only till

^ the 24th,

77

to render them acceptable to

Silefia.

Chrijlened.

Males 5" 84

Females 5-76

1160

Among the Buried were
Married Men 226

Married Women 144
Widows 6c Widowers 157
Bachelors 60

Maidens 57

Boys JunderTen4i9
and Girls7 Years old, 397

148s

i5«4

B. Here

C, 455' >

N. B. Here, in the Sum Total, are 29 more than in
the Number of the Buried above, by Reafon of feveral
Stillborn Children which had no regular Burial, and
fo were not reckon’d,

s ‘ ' r -> ‘

In the Imperial Town Vienna, there diedy

Young People—-

3179

Old

- 2026

* Total —

- 520s

Among which were.

Of9oYearsold a

Of 99

z

91 I

ICO

I

92 3

lOX

2

93 *

103

I

94 3 ■

104

. I

9S. 2.

II5

X

' 96 3 ■ ^

-

- Born and Chriftened ■—

— 4.030

Children.

1

In Drefdeny Saxony^ died

/

- 1908^ '

Chriften’d

■ 1443

In Dantzkk died 1605:

, Chriftened 1 V , ^Io^> i

in Efperies^ or Eperies^ alias Epperies^ a Town in

\] met Hungary^ diedu-'-^- ■ ■■■ 132

Chriften’d 1^7

, Moft of thefe died of the Small-Pox;

The

( 45«5 )

77>e Bills of Mortality of the Year 1718. i. c.
/low Chriftmas 1717, to Chrillmas 1718.

B R E S L A W.

Buried.

From the x5'thofDec.

. to die 31ft,

XI

January

1x9

February

IIX

March

108

April

98

May

88

June

97

July

86

Auguft

118

September

98

Odober

119

November

ICO

December, till the

X4th,

81

' Total —

-IXff

Chriftened,

Males 5*9 8

Females— —TT— 5’5'4

IlfX

Among the Bead were.

Married Men x38

——Women 141

Widows 6c Widowers ixx
Bachelors 60

Virgins 60

Children to ten J Boys x8x
Years of Age,2Girls x8o

Mlbo,. g

In Vienna died— -Men — 14^^ — Women —1119

Boys — 1844— Girls — lyoy

Inall— — 6110.

-

. Amongft

r 457 ;

Amongfl: which were froze
to Death in the Street x

Murder’d ^

Kill’d by a Waggon x

By Falls from Houfes,

6cc. ^ II

Kill’d with Swords, ' ^
Knives and Sabres, 9

By taking wrong Phy-
fick I

Trod to Death by Hor
fes ^

Drowned
Beat to Death
Smother’d in a Houfe
of Office
Cut their Throats
Kill’d by the Fall of
Houfes $

Among the Dead were founds
8 Perfons of 90 Years old.

7

92

X

93

5

94 .

3

9S

I

96

X

97

X

98

2

99

I

loy

‘ Chrljlened,

Males —1185'

Females xo$y

Total-— 4X4X

Amohgft which were
48 Pair of Twins, and once
Tergeminu

In Ratishon died of the Lutherans, 235’ Perfons;
amongft which were 117 Children,. 13 young Men,
and II young Women.

A a a a

»-* Vi 4v

( 458 )

The following Lift gives an Account of feveral Cities
w S A X O N Y. ■

Chrlflene d

Bajiards.

Buried.

Pair

Married.

Commu-

nicants.

In Drefden

lyyS

99

1412.

SOI

788;?-

Wittemberg

zU

16

317

61

Leipzick

86i

68

9S^

303

Torgau

i'^6

9

148

5*4

79^7

Freyberg

340

13

373

104

24098

Stollberg

88

I IX

27

7314

Pulfnitz

73

75*

39

4381

Konigsbruck

67

95

16

3351

Elftra

63

45

1 1

3021

Bautzen

Z07

S

135

55

14520

Annaberg

146

19

IIX

37

8426"

Chemnitz

173

4

166

38

10690.

Ofchatz

103

3

8x

20

5169

. Altenburg

141

248

57

I290I

Euleiiberg

96

S

86

. 41

6194

Pirna

138

133

43

9164

Marienberg

91

194

18

5903.

Georgenftad

i8x

191

36

3580

Harta, near
Waldheim

40

3

*

29

20

3291

This

( 45? )

'This prefehts you it>ith ^ L r s T for u whole Century^
of the tJumbers of People Married^ Cbrtjiened, Buried^
and Communicants^ viz. from the Tear 1617, to
. lyij inclujive^ in the EleB oral City of Freyber^,""^!
• famous and pleafant Town^ near the Banks of the
Molde iw Saxony. Lat, yi. Long, about 8

^ Miles S. W. Drefden.

N'* Tears.

Pair Mar-

Chr'ijlened,

Bajlards,

Buried.

Communi-

ried.

cants

1617

89

539

4

430

105*30

18

122

423

10

384

9631

19

124

495'

13

371

9789

20

97

428

10

451

10093

21

ic6

4^0

6 ■

507

9676

22

no

380

7

517

95’3<5

2^3

100

357

8

989

9206

■ ^4

96

383

4

417

9509

2'5'

98

375'

7

454

1005*8

z6

78

381

6

J49

11642

'27

108

372

• ' 7

331

I 1027

28

82

371

4

318

10749

29

• S7

412

19

936

II53I

'30

80

330

7

III4

. III80

1631

13^

353

4

284

105*24

'32^

88

425

5

, 1343

I 1326

33

174

163

4

879

9131

34

170

375

I

175

7447

3y

87

285*

9

231

7323

3^

61

299

II

I81

7990

37

68

386

3

383

7723

38

53

262

9

I5I

7682

A a a a 2

»<>39

t

I

( 4<?o )

Tears,

1639

40

ried.

- 4S
6y

Chrijlened,

291

368

Baffards.

4

6

Buried,

354

173

Communu

(ants,

9609

7S94

1641

61

^26

2

163

7562

42

48

309

4

193

8128

43

60

383

7

340

' 7770

44

6?

231

7

156

7699

45

62

196

5

163

7050

- 46

57

230

6

187

7263

47’-

59

2©I

2

136

7173

48

59

• 197

i

182

7698

49

44

2s22

5

201

7739

50 '

6j

199

I

162

7639

1651

65

232

I

1^8

8148

52

50

190

2

202

7948

53

62

208

X

21$

8342

' 54

62

234

3

21 1

8645

55

73

202

194

6351

56

60

.237

5

I5I

8493

57

58

23a

174

8730

58

61

.198

4

184

8561

59

57

251

3

177

8431'

60

66

Q3O

_ ™ -

240

88y6

\66i

47

225

3

217

8962

62

53

203

2

206

9423

63,

47

2q6

2

247

92.64.

64

48

219

V 2

179

9279

6s

6t

213

207

9406

66

65

xi8

'4

216

9979

67

' 79

223

306

9448

1668

( 4<^» )

N® Tears.

166^

6^

70

/>47V Al<rr-
ried.

.

55

70

Chrljiened.

2i8
x3 2
xi8

Bajiards.

' 5

: - 4

Buried,

232

204

20(5

V

Communlrn

cants,

9588

957X

, 95154

\6y\

'6s

X37

291

10080

' 7^ '

<54

‘Loy

^ 2

285

9221

73

'69

2«34

I

215

9912

74^

xx8

1

‘‘ I

204

9678

'7S-

. ■'60

X39

2^-46

10093

' 7^

- y8

2,26

'277

9955

77'^

" 80

240

" • -3

295

104^2

, ■

; 70

^5.6

^■4 1

•jox

10422

■ '79

' 91

''225

■^‘ 4 '

■i:S4

10356

- go-

292

267

II349

168 £

87

285

5

218

1 1043

8x

69

282

-7

■ 2.53

10894

83

77

’315

8

V

333

11054-

84 ‘

' 78

'334

‘ 6

314

10625

85^

73

249

4

251

1 1070.

8(j

73

282

5

243

11488

87

, ^ 80

3^7

6

292

1 1 542

88

88

^08

II

- .?:34.

u^L?30q

89

-5 9 t

276

4

501

11593

90

72-

2,90

5

3IO

11580

1691 •

72^

269

6

289

1172-4

9X

58

284

7 -

29.6

12679,

93

\ 72^

‘ 51(5

la ,

: 253 -

11597-

94

65

256

7 •'-1

355

l2•553^

95

57

239

6

339

1319^

96

85,-

.1 277

%

10 *.

' 290

■ ii49C3>o
169.7

( )

N° Tea'rSt

Pair ^iar-

ChriJlenJd.

Bajlards.

Buried,

j— ■ 'i'-7 ,

Commmi-

Tied.

cants.

1697

76

.216

4

180

, 15619

98

. 73

• 274

£ 7

^218

15677

99

,64

264

0. 5

^2"5 8

16155

1700

74

-251

7

310

18569

1701

81

283

r 10

ii88

, 19282

2

88

272

«2

239

20383

. 3

-95'

271

; 6

241

20494

4

88

319

II

273

20837

' ^ 5

7'^

295*

12

35*7

2^0743

85

332

- 10

21813

7

82

310

• 18

378

21367

8

83

310

17

288

21838

9

71

‘302

lO

30s

21708

10

83

313

15

■ x83

21699

1711

81

327

8

22334

12

82

310

9

325*

00

...*3 .

:^7

308

9

340

23627

14

; 70

349

6

237

2^3 470

17

82

313

8

-283

23275

i6

105

317

14

361

23371

17

79

. 373

^ 13

32^5'

23904

Total — 7546—

1

00

00

M

1

1

00

.1

30295

I2ii7>6i

.g*... . -V-. J *-

Here is to be obferved, That in the Years 16x5, 26,
^•7, 32, and 33, the Plague raged very much ; as alfo,
that in the Year 1630, there died of the Plague ineerly,
7^4. and in 1680, -103. Behdes that, amongft the
Chriftened in 1713, a Girl was baptized, which* was
born and bred in Turkej^, but from Chrijiian Parents.

( 4<^3 )

But, in general, it may be obferved. That this Place
was more populous before the War than it is at pre-
fent j tho* in this Century it cannot but very much re-
cover and increafe.

. > The following LIST we have receiv’d from
lin, confifting of all that were Born, Married and Buri-
~ed in Pruffia, in Four Years.

In the Kingdom
of PruJJia,—

Year.

Born.

Pair

married.

Buried,

171s

19606 —

- 4571 —

- 12000

16

.^0669 —

- 45'30—

-I2I55'

17

•2.1443 —

- 4743 —

— I230I

18

• 20994 —

- 4^87—

-IIO47

Sum —

82712

- 18331-

— 47f03

The next LI S T contains the Numbers of all that
were Born, Married and Buried, in the reft of the King
of Dominions in Germany, &cc, for Four Years.

In the Eledorate
of Brandenburgs

Year.

Born.

Pair

married.

Buried.

1715

■ 14820 —

- 4368—

~ 11663

16

■ 15'75'8—

4995'—

-13149

M —

‘ 16636

- 45*39—

— 10805

18-^

I73I9

4677—

— 12891

Sum—*

^45'33—

-i8yj9-

—48508

i = f . '

In the

march, —

( 4<^4 >

Tear, Barft.

171V — 7487-

16 49;j-

17 7072--

. l8; 6684—

»

, 'ntarried.

— 1683—

— loio —

— i85'o —

— 1881-^

Buried.

'• •' r '

- 47J7

- 47°i

- 4673

- 5-069

-- ! •• ‘ *■ ^
^ . • • ‘

Sum

—14196

— 7iif—

-I9OOI

In the Dutchy of

1715-

16-
- 17-

i8-

— 7tSy-

— 7ii7-

— 8746-

— 83x5'-

— 1064 —

— 1186 —

— 1^06 —

— 1934—

- 4981

- 5'60i

- 6191

- 5744

... - - r

Sum

—31481 -

— 6490—

—11619

The Dutchy of
Ckvd,

I7if-

16-

17-

18-

— 6771—

7313-

— 7y8^-

— 7J4i-

— 1964—

— 1001 —

— io5'i —

— 1891 —

- 5'o66

- 6iii

- 6055-

- S^6s

Sum

— 19109 -

— 7907—

-13207

*■ 5

The Dutchy of
‘ Tojnerania^^

1715'-

16-

17-

18-

}

— 7H3-

— 7386-

8196-

7896—

— 1190—

— 2407—

— 1108 —

— 1138 —

- f373

- f7

- yoio

- 6131

Sum

—30711 -

— 8843—

-21181

The

Buried,

The Principali-
ty of Kalber^
ftacl.

The County, of.
Hohenfisin^^

The Principali-
XyofMinden, .

The City of
Meurs. ^ .

'( 4<5J )

Tear, Born, Pair

•

married.

171^-

— 2371^

710

■ 1834

16-

— 2567 —

• 759 —

■ 2,^41

17-

— ^7S9—

■ 764 —

■ 1961

18-r

■rr. 2527

• 715

XOIX

Sum

—101x4 ~

1948

1

00

V>2

NO

16—

17—

»

528 —
639—
644—
6ix —

- 164

- 155—

- 148—

- 158-

- 406

444

" * 449

- 416

Sum

r.2-383 —

- 625

- i7ijT

1715' — :

I7IX

- 579_

- 1618

.16—

1788—

- 564 —

- 1819

17

1991—

- 54^

- *4»9

18 :

1831

- ys-i—

- i48<>

Sum,—

731Xr—

- 2.137—

- <5351

1714—-

406

i^i—

- 386

16 ,

439 —

■ 161 —

- 331

17

45-4—

166—

181

i8

't -

470 —

• 170 —

- 368

. ' N "

Sum —

1769 —

648 —

* 1366

Bbbb In

'( 4<5<5')

In Geldern,

Year*

iyiS —

i6 —

Sorn,

. Pair
married.

Buried,

17 —

18—

■ 1990 —
■losi —

- 497 —

- 489 —

- 1066

- 1064

j

Sum*—

4043

- ij86 —

- 213a

X ^ ‘ \ r

* ! •

The County of
Ravenjberg,

171s —

16 —

17—

■ 18—

- xi88—

- 24 10 —

- X3IX —

- X344—

679 —

- 716

672

- 641

• *987

• i349
■ 1817
- 1951

Sum—

■ * 92'5’4—

- 2708^— 8104

The County of
’ Teckhnherg,

1715-^

‘16^

"18—

- 342'—

- SS3—

- SOS—

- 5:07—

- 15*3—

- "‘163 —

- 186 —

- i3y—

-

“ 5'43

- 370

- 387

Sum—

.--1907—

- 637 —

- 1815

The County of
Lingen,

1715—

16—

17—

18—

- 6^8—

- 699—

- <?97
706—

- 213 —

- 154—

— 248 —

— 221 —

- 484

- 638

- 449

- 840

*.

Sum— a730—

- 836—

- 2411

Iti Lauenburg
atid Butow,

In the French
Colonies,

V. - ^

(4<^7 )

Ytars,

Born.

Pair mar»

Buried.

T

riid.

171s

• 5.8y—

• 144 —

S6z

16

j87—

- 169—

410

17-

—

- I18

366

18

-

.

Sum—

2^312,. —

- 584 —

1469

1715:

.

. - .

i6._.

.

17

607 —

- 181

y«4 ■

18

603 —

- 136—

639-

Sum— .

mo —

- 317

1X03-

The Sum Total of all that were Born?
in'4 Years **3

- - - - of all that were married 8i88i Fair.

- - - of all that were Buried 217943
More Born than Buried, in Number, 88064

Here is alfo to be obferv’d, that in the Yeari7i8. -

there died 84 Perfons .above 91 Years old, and 32 •

.above 100 •, and, i died in the ii6th Year of his

Age,. Befides in that very Year are reckoned 1088

^Baftards.

*

Xf

Here

f

Bbbb 2

( 4<58 )

Here follows a particular Lift of fever al Borough Towns
irh the Kingdom ^/Pruflia,' received from the Chan-
cery f^/Koningiberg, of all that died in the Tear 1718,

In the Borough of
Brandenburg
— : Schackeri

— Fifhaufen

— Taxiuin
-r-Balga.. ^

— ^ Preufs.Eylau

— Bartenftein

— Birthen

— Ofterode and Ho-

henftcin - - - -

— Seheften

— Neudenburg and
. Saldau - - -

— Lyck 1 ' *'

— Oletzko .

— Angerburg
— Rhein

— wOrfelfbiirg
— i-Johannifburg ' ! ’

— Lotzen

— Neuhaufen

— Labiau

-j8l:

346

3IX

39^

319

16 J
i8s

^77

\S9

330

141

188

i8x

107

zzo

I4I

‘137

In the Borough of
Raftenburg

— Preufs Holland

— Marungen and

Liebftadt
Marienwerder and
Riefenburg - _ .

— Preufs Marck
^Tilfit

— Ragnit

— Infterburg

— Georgenburg
— ^ Salau"

— Mummel

— Schonberg ‘ '

— Gerdauen and Nor-

Died.

264

206

393

312

5-29

381

808

iz6

denburg - - - -
— Gilgenburg
Teutfch Eylau
— NeuhalF

- ^ , In the three Cities of
148 I Koninglberg - - - 17^5

249 [

Sum 11047

269

109

41

in all thefe foremention’d Places were Chriftened 20994

Pair Married 4287
3

In

( 4<>? )

In T>antz>uk in
the Year 1718. i$y^
In Ep penes 113

Chrijiemd.

1470

173

, Married.

446 Pair.

In the Royal Hofpital at Lijbon out of ixfi Found-
lings maintained by the King, without knowing their
Parents, there died 469, remained 781.

N. B. The Remainder of thefe Lijis will be communica-
ted at another Opportunity,

A N.

* ■' T

JL _ f

r

V. V ' '
ft ft

r'

. CTJi.1

)

J. rM.

rl h\::xVM-.^k rl

.€r~l

-hnuo'I i>j:i lo :^c If.'/-, ?! iByr orl: x:I

uLsiiJ jri,;oA. ! jiJo-^-jbf/ ;r:' vc! o^iii jiuBrr: rtiMi

• • ,rly LzjI (lji ?..? ozi:li i

Avr isvi'i tVx?::; vvg,5\-> *t? i ^dT , '*.?/[

vU'wVu U 'VwuiCiuVi ::il,'.:;

4 i i V

4 '■

M y.

/

-

i

I

A N

i

•'J"

i

1

%

1

■

<

■

E

1

N

E

TO THE

Thirty Second Volume of the Vhilo-
fophical Tranf anions.

A.

A^mrum fluemium motus, 373* P- ^19-

Aurora borealis obferved zxLynn-Regisy n.^yS. p. 300. ,

B.

Births and Burials, &c. Accounts of them, n. 380./), 454.'
Booksy Accounts of them ; I. Harmonia menfuraru?n, five Ana^
lyfis & Synthefis per Rationum & Angulorum menfuras promo-
la : accedum alia opufcula mathematka Rogeri Cotefii. Edidit
& auxit Robertas Smithy Coll. Trin. Cantabr* & R. S. Soc. &c.
w. 372. p> I S9- II. Adverfariorum Anatomko-Medico-
Chirurgkorum, Decas tertia, AuElore Frederko Ruyfchy M. D.
Anat. & Botan. ProJ. Amflel. R. S. S. n, 37^. p. 428.

C.

CataraEl of the Eye ; two Obfervations upon it, «. 373^
p. 194.

Comety one obferv’d at Berlin, n. 375.^. 238.

Cortex Eleutheria, Quantity of Refin irr it. n. 371. />. 81.

D.

DijD'ecikn of Bodies dead of the Plague, n. 370. p. 24. Of a
Man of 109 Years of Age, n. 375. p.313. Of the Coati
Mondi of Brafily n. 3 77. p. 3 1 7- Of a Perfon troubled with
the Sxone, «. 3 77. />. 3 2 5, ibid. p.^iy,

,C c c

Earth

INDEX.

E.

Eanh raifed in Lincolnjhire^ n, ^^6,

Engine to raifc water by the Help of Qiiickfilver, «. 370.
p. 5»

Experiments on the Bile of Perfons dead of the Plague, n. 37®,
p. 20. n: 372. p. 103. ibid. p. loj. On the Bile of Perfons
dead of other Difeafes, n. 370. 28. An Optical Expe-
riment on the different Refrangibihty of red and blue
Light, n. 374. p. 206. On the Expanfion of the Liquor
in the Thermometer with different Degrees of Heat,
n. i']6.p. 291. On the Force of Bodies in Motion, «. 37J.
p. 269. n. zi^'P* ^^5- On the Salt, «. 377. />. 348.
«. 5 78.^.372.

F.

Ecetus extra Uterum. One continuing five Years and an half in
the Body, ». 378. />. 387.

Force ofBodies in Motion confider'd, n. 371. p. 57. n. 375'.
p. 2<?p. n. 375. p. 285.

Fuller s Earth ; the Pits for it defcrib’d, 379. p. 419.

H.

Hydatides in great Number in the Abdomen, n. 370. p. 17.

X*

Inoculation of the Small Pox in Nevi England, n~ 370. />• 33»
In Torkjhire, «. 370 p. 35. ibid.p. 49. n. 374. p. 209.

Infcription Roman at Chichefler, n. 379. p. 391.

Inundation in Torkjhire, 372. /». loi.

7/7W lately raifed out of the Sea near Fercera, n. 372. p. 100.

L.

Longitude of Buenos Ayres, n. 3 70. p. 2. Of Port Royal in Ja-
maica, «. 375. 2 3(5. Of Carthagena in America ibib.p. 237.

M.

Magnetkal Quality acquired by Iron continuing long in the
fame Poflure, n.iyi.p. 74.

Mathematicks. Florum Geometrkorum Manipulus, n. 378. />.3 5 5*
De jraBionibus Algebraicis Radicalitate immunibus ad fraBiones
Jimplkiores reducendis, &c. n. 373. p. 162. Solutio Problema-
tis de Curvis inveniendis, qua quadem ratione in Jitu inverfo

difpojitafe interfecare pojfunt in Angulo dato, n. 372. p. 106.

[De

INDEX.

De SeSlione Anguli, n. 374. p. 228. Pappi Alexandrini Pro-
pofitiones du a generates refiituta. n. 377. p, 330.

Meteorology : A Method tor Obfervations propofed, «. 379.
p. 422.

Microfcopes. Thofe of Mr.I.^’fwu'^w^o^^defcribed, ». 380. p-^^6.

' Microfcopical Obfervations on the Mufcular Fibres, n. 371.
p. 72. On theParticles of Fat, n. 372. p, 93. On a Foetus,
and the Parts of Generation in a Sheep, b, 373. />. 1 5 1. On
the Callus of the Hands and V^Qt,ibid.p. i$6. Upon the
Strudlure of Diamonds, n. 374. p. 19^. On the Size of
the Blood Globules, n. 377. />. 341. On the Strudure
of the Diaphragm, n. 379. p. 400. On the Blood Glo-
bules, and the Globules in the of Wine, b. 38a.
p. 435. On the generation of Animals, and the Palpita-
tion of the Midriff, p. 438.

Mohjfes made from Apples, n 374. p. 231.

Monfirous Twins in Lorrain, n. 3 77. p. 34(5.

Moon. Eclipfe o’f it obferv’d, «• 375. p. 235*

Mortality i Bills of it from feveral Parts of B.380.P.4J4.

Mortification caufing the Lofs of the Scapula, and Os Humeri,
n. 370. p. 15.

N.

Niagara River, its Falls, b. lyi.p- 69.

P.

Parhelion feen in Ireland, n. 372. p. 89.

Planks, the Manner of bending them by a Sand-Heat, n 371*

75-

Plants prefented to the Royal Society, n. 375. p. 279.

Probkmatis de Curvis inveniendis, qua quadam ratione in jitu in-
•verfo difpofita fe interfecare pojfunt in angulo dato, Solutio,
n. ‘il'i^p

Pudendorum firuBura praternaturalis in muliere, n. p. 408,

R.

Rain meafured in Northumberland, n. 377. p.

Rainbow, a Series of Colours within it not commonly obferved,
»*375* P' 24D 242, 243. This Appearance explain^,
31^‘P' ^45*

Rattlefnakes, an Account of them, n. 37<^. p. 292.

Refin. Quantity of it in the Cortex Ekutheria, b. 371, p. 8r.

Saffi'on.

I N D' E X.

. •_ _ .r : S,. • ■

Saffron.' k Pefcn*j>tiori of^its Flower, n 380. />. 441. *

Sal C^thanicuntt op Epfom Salt, an Account of it, n, 377. p.

3^. 378. 372. . •

Sanguinis fluxus per penem, ». 379 />. 418.

Satellites oi Jupiter. Eclipfes of the firft obfervM, «. 375. /’•237*
Small Pox, a remarkable Inftance of their infedious Nature,
n 373-A <9^* Mortality of them^»». 37/ 21 r. ACom-

. parifofi between the Danger of them whem taken natural-
ly, and when given by Inoculation, n. 374. />. 213. A Me-
thod of procuring them, ufed in South Wales, 375. p. 262,

2^3, 2^4, i6j.

Smelts degenerating in a Pond, n. 374. p. 232.

Smvj, the Figures of it obferv’d, n. '^'j6.p. 298.

Stomach, Wounds in it cured, «.37i. p.'j^. Impoflhumation
in it cured, ibid. p. 80.

Stone, new Method, of cutting for it, «. 371. />. 83. A re-
markable Cafe of one troubled with it3 n. 377. p. 322.
Stonei voided per Anum, «.38o. p-433-
Sun. An Eclipfe of it obferv’d at Greenwich, n. 374. p. 197.
The 4ame obferv’d at London, ibid. p.i^S. In Torkfiire,
ibid. p. 199.

T.

lelefcope, a Catadioptric one deferibed, n. 375. p. 303. Ob-
fervations made with it, n. 378. /». 382. ibid.p. 38

•

Variation of the Needle in the Ethiopick Ocean, n, 3 71. p. 55.
Vipers, Obfervations upon them, n. ^']6, p. 295.

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