I

If

PHILOSOPHICAL

TRANSACTIONS.

Giving Some

ACCOUNT

O F T H E

Trefent %)ndertahings^ Studies and Labours

OF THE

INGENIOUS.

In Many

Confiderable Parts of the WORLD

VOL; XXX. For the Years 1717. 1718. 1719.

L 6 T> 0 N:

Printed for W. and J. I n n y s, at the Trinces-Arms^
at the Weft Corner of St. P^z//’s Church -Yard.
MDGC XX.

To the Right Honourable

THOMAS
Lord PARKIER,

Baron of (jMacclesJield ;

Lord High Chancellor

Of Great-Britain :

By Inclination as well as O f f i c e,

Firft PATRON of Ufeful Arts and
Difcov cries.

This THIRTIETH Volume
OF THE

Philofophical Tranfadtions

(As a fmall Acknowledgment for
very Great Favours)

Is Humbly inferib’d by

His Lordp7tp"s mojl obliged SerVanty

( 545 ) Number 95?.

PHILOSOPHICAL

TRAN S A C T ION S.

For the Months o^Januar, Febr, s.nd March^ \7\J>

The C O N T E N T S, .

I. Chfervationes Stella in Geminis a corf ore Jovis-
cccultat£, Januarii iimo. St. vet. 1717. Tranfitus
arilijfimi Martis infra Borealem in fronte Scorpii Febr.
^into mane.

II. An accurate Account of a teflellated Pavement, Bath,
and other Roman Antiquities, latelj difcover d near Eaft"
Bourne in Suflex. Being fart of a Letter of January
26. 1717 from the learned Dr. John Tabor «/ Lewis, -
to Dr. John Thorpe, R. S. S. and hj him communicated to
the Royal Society. ^

III. A jhort Account of the Nature and Vertues of the Pyr- ■
mont Waters ; mth feme Obfervations ufon their Chal)--
heat fiualit). Communicated by Dr. Frederick Slare,
R, S. See.

IV. Remarks on the fecond Pafer in the Hifery of the Royal
Academy of ScienceSj for the Tear lyii. concerning the
Caufe of the Fariation of the Barometer : to Pew that the
Wa"j «f accounting for it in that P afer is irffufficient, and
that the E^feriment made ufe of to frove what is there
averted, dors no way frove it. By J. T; Delaguliers,
M. A. F. R S.

V. An Account of an extraordinary EffeB of Cholick :
communicated to Royal Society, by that curious Ana--
tomift Mr. St. Andre* and read March zi. 1717.

VI. An Account of two late Northern Aurora’j as they were
obfeived at the Vicarage of Sutton at Hone in Kent®
By the Reverend Edmund hdcciCWyP rebend of Rochefterv;

( )

L Ohfer^atlones StelU fixk in Geminis a corpore
Jovis Januarii xuno. St. Vet. 1717.

Tranjitus arStiJfml Martis infra, ^orealem in
fronte Scorpii Febr, j. mane,

Ante biennium in TranjaB, Fhilof. No. 344. pag.

294, rerum coeleftium {tudiofis indicavimus, Jo^
vem corpore fuo ftellam quandam fixam obcegerc debe-
re, eofque ad obfervationem Phsenomeni rari/Iimi, &
magno in Aftronomicis ufui futuri, invitavimus, fignan-
tes diem Januarii hujus anni decimum. Jove autem
pene Stationario, & paulo amplius in orientem quam
per Tabulas noftras provedo, non ante undecimum in-
cidit pr^edida Occultatio ; quam quidem Londini ob Nu-
bes non contigit ex voto obfervare

Nec tamen fruftra invigilarunt Aftronomi noftri. D.
Martinus Folkes Londiniy pnefentibus aliis nonnullis e
Societate Regia, Jan. undecirao %h. P, M. vidit Jovii
centrum una diametro corporis ejus Fixam fequi, quas
dido centro Borealior erat quafi dodrante femidiame*
tri Jovis. Poftea Nubes Jovem occuparunt, fed, habira
ratione motus Jovis paulo poft medium Nodisflellam
Jovt conjundam fuifle, & a Borea dilci ejus parte oc-
culcatam, conclufit.

Reverendus Dominus J. Theoph. Defagulkrs, R, S. S.
& Stephams Grey, Wefiwonaflertt, viderunc Fixam,
Hor^i Sexta vefpertina, integra Jovis diametro diftare a
limbo ejus. Corum verfus. Unde & ex fequentium di-
ctum Obfervationibus, circa medium nodis incidilTc
conjundionern evincitur

Reverendus quoque D J. Found, ipud iVanfied, in-
frafcriptas nadus ei^ ob(erva(iones, quas ucique accura-

tiiiimas

( 547 )

tiffimas, Tube fcil. pridongo <5c Micrometro captas, hue
tranferibere non pigebit.

Itaque Januarii Quinto 6'. T* jeq, Jovis centrum
diftabac a Fixa 31'. 49'''. quam 5^ 38'. fequeba*
tur 34^ ii" Afeenfionis redes: fimulque limbus Jovis
Auftrinus eandem habuic Declinationem cum ftella.

Die autem Nono fequeme 6\ 6'. Jovis centrum dift^
bat a ftella 10'. \ & poft odo minuta erac differen*

tia Afcenfionum redarum n'. 31"; & turn centrum
Planetx, tantiiJo, ita uc vix perciperetur, erac Stelll Aa-
ftralius.

Die Undecimo s’’. 30'. T. ssq, crat diftantia centro-
rum i'. 2.4'. fimulq; vifa eft ftella quaft quadrante
diametri Jovis Borcalior centro ejus. Diameter autem ■
minima Jovis inventa eft o' 43". Deinde Nubes.

Die vero Duodecimo 5^ 17'. erac diftantia centre-*
rum 3'. 7"; ac 5^ 50'. Jupiter ftellam prxeedebac 3V
' 30''. Afcen. Red. Eodemq; tempore limbus Jpvis Bo-
reus eandem habuic Declinationem quam Fixa accu?
rate.

Collatis autem his Obfervationibus manifeftum eft 4
Fixam banc Jovi conjundam, Januarii undecim-o i
circitcr, non nifi 17" veri8" centro ejiis Borealiorem i
fuifie, ac proinde occulratam.

Fixa hese, etiamfi nulli Catalogo hadenus aferipta,
Locum tunc habuic jr az®. 13'. cum Lac. Auft, 0°.
13'^; Comicemque habet 17 min. earn prxeedentem =
& 7 min.- Borealiorem, five in n 1 1°. 56' cum Lac.
Auft 0°. ewi Jupiter conjungi vifus eft Jan, i6. d**! '
30'. veCperi.

Sic fpatio minus bimeftri Jupiter corpocaliter eclipfa-
vir duas Fixas, cujus rei ne fingulare quidem exem**
plum ab invento Telefcopio extar: proinde base obfer- -
vara inter pretiofiftima Uraniae in ufum Po»

Rerotum, merito reponenda funt.

1

. f 548 )

Noftra autem ftellula anno 1634. Feh. 6. Jovi Stati-
onario conjunfta, tribus ejus diametris Audralior erac,
obfervante Gaffendo : unde conftabit, calculo rite infticu-
to, Jovis Nodos quoad fenfum immobiles hsEfiile, per
S3 annos ultimo elapfos, idque ad x® 8®. 35'. a

Ad alteram autem Obfervationem Tranlltus Marti s
prope Boream Fronth ScorpH non minus infignem, iidem
Aftronomi eadem cum cura invigilarunc omnes. Mars
autem, Februarii Quinto Mane, vel Quarto 16’’* vifus
eft adeovicinus ftellae didas, ut ea nudis oculisnon con-
fpiceretur ; fed per Telefcopium inventa eft (upra & ad
ortum, adeoque Mars nondum ei conjundus. Hora
10'. T. app. Mars erat in recfta cum Borea frontis
& Telefcopica qujs earn fequitur ad Boream, ad diftan-
tiam ocfto circiter minurorum. i6^ 35'. Mars interme-
dins erat in reda cum Borea & Medii Frontis; & poft
horse quadrantem, cum Auftrina Frontis, ita ut i6'‘.
54'. T. app. seftimabatur Conjundio ipfa quoad Longi-
tudinem, quo tempore Mars fat accurate duobus tan-
turn minutis auftralior erat ftella. Obfervavit etiam D.
Pound Conjundionem refpedu Afeenfionis Redae I7^
a 5'. T. app. cum diftantia centrorum a'. 07"" Jucun-
dum autem erat fpedaculum, Martem viderc ftellam
pedetentim aggredientem, motumque fuum, lentiftimum
licet, manifefte prodentem.

Conferatur cum hac Obfervatio Horroxii noftri anno
1638. Februarii Septimo mane, quam vide in Epiftolis
ejus pag. 3oq. Tunc enim Mars ad eandem ftellam
appulfus, etiam multo propius ad earn acceflir, fed ante
ortum ejus prseterierat Conjundio.

His adde Saturni obfervationem Januarii a 5” to. la^.
25'. T. aq. a D. Pound habitam. Cum Planeta difta-
bat a ftella 58va. Virginis Catal. Brit^ 13'. i6\ verfus
Auftrum, eamque fequebacur 2'. 30". Afc. Red, Stella
in e? I 9 21'. 5a". cum lat. Bor. a% 47". 25".

II. An

( 549 )

II. accurate Account of a teflellated Pavement,
Bath, and other Roman Antiquities^ lately dif~
coyer d near Eaft Bourne m Suffex. ^ein^ part
of a Letter of J^Lnu^ry i6, xyxy. from the
learned 2)r. John Tabor of Lewis, to 2)r. John
Thorpe, R. S. S. and by him communicated to the
Royal Society,

ADefcriptipn of the tefTerated Pavement at Eafi
Bourne, near Pevenfey, mufl: have been more im-
perfed than what is now *^iven, had it come to youc
hands much fooner. I thought an exadi Account could
not be taken, unlefs the Ground about it was open’d.-
and it being part in a Meadow, and part in
plough’d Ground, and under a Fence which parts two
Perfons Lands; by realbn alfo the one was fow’d; I
could not procure the Digging in both Places at the
fame time.

It was in Marcli laft when the Meadow was dug;
and the laft Weekfave one in November, befoae we had
leave to open the Ground in the Corn Field. The Mea-
dow in which the greateft part of the Pavement lyes, is
near a Mile and half South Eaft of Bourne ; it contains
about four Acres, and is of a triangular Form ; the
Southern Side is againft the Sea 5 only a few Filhers Cot-
tages, and a fmallpublick. Houle or two being between
that and the Sea. On the Northern Side of the Meadow
is a High-Way, which leads from Bourne to Pevenfey : the
Weft Side is by a Fence of Polls and Rails leparated from
a large Corn Field, in Common belonging to the Parilh.

Q^q q q About

( 530 )

-About the middle ef this Fence is the Pavement, diflant
from High-Water-Mark a Furlong ; In former times it
might have been fomewhat more, becaufe from this Point
to the Weftward, the Sea is always gaining from the
Land,

More than four Years (incc, viz,, in the Summer
1712,, when the Fence was repair’d ; the Workman fink-
ing a Hole ro fix a Poll in, was hinder’d by fomeching
Solid like a Rock ; but calling out the Earth clean, found
the Obftacle to be Artificial. Mr. Thomas Willard of
Bourne, Owner of the Meadow, being inform'd of the
Novelty, gave Order that it Ihouid be uncover’d ;
and lent alfo to Herflmonceux, for one Purceglove an in-
genious Ingineer (who formerly had been imploy’d in
the Mines in the Northern Counties^, who with his In-
llruments bored through th^Pavemenc; and in many pla-
ces of the Ground about it, which he found to be full of
Foundations.* but this his Difeovery of thofe Founda-
tions, was only a Confirmation of what the Inhabitants
there have always obferv’d, as well in Ploughing, as in
the Growth of their Corn and Grafs* for in the common
Corn Field, Weft to the Meadow, to the diftance of near
half a Mile, they often raife bits of Foundations with
their Ploughs ; and in dry Summers, by the different
Growth of the Corn, they can plainly perceive all that
Tracft of Ground to be full of Foundations.

The Pavement was little more than a Foot below the com-
mon Surface of the Ground ; what lay next it was a fmall
Sea Gravel 5 the Pofition of it is very near due Eaft and
Weft fabout two Foot of the Weft end of it reaching
into the Corn Field^ ; its length is feventeen Foot and
four Inches; its breadth eleven Foot. At firft it Teem’d
to have been bounded with a thin Brick Tet on Edge,
about an Inch above the Tejfer£, To exadly ftrait and
even, as if Shot with a Plane ; and To well Cemented,

as

( )

as if one entire Brick. But when the outfide of the
Pavement was broke up, we found, that inftead of
Bricks fet on Edge, as was imagin’d, it was bounded
with a Border of Bricks laid flat, and their ends next
the Tf(fer£ turn’d up. The Thickncfs of thefe Bricks was
an Inch and a Quarter ; the Breadth not under Eleven,
and not more than twelve Inches; the length full fif-
teen Inches ; which, before they were turn’d up at their
Ends, could not have been lefs than Seventeen. They were
very firm, and not in the leaft Warp’d or Cad in Burn-
ing ; when broke, their Subftance was fine and well
mixt, of as uniform and clean a Red Colour, as a piece
of fine Bole: Except at the ends wliere turn’d up, they
were all over cover’d with a Plafter (the fame which
Vitruvius calls the Nucleus, of which more afterwards),
half an Inch thick ; fb hard, entire, and even, that it
feem’d as one Stone, quite round the Pavement.

Next within the Bricks, there was a Lift or Bordet
of white TefjerA, thirteen Inches broad; within that, a
Lift of brown Teffera (fomewhat darker than a Whet-
Stone, and fomewhat lighter colour’d than the Touch-
Stone ) four Inches broad ; then a Lift of the White,
five Inches broad ; next within that, another Lift of the
Brown, four Inches broad : all the reft of the Pavement
was fet with white Teffera, without any Ornament or
Figure ; which though not Gay, lookt very Neat and
Clean.

When' this was firft view’d, none of the Curious
doubted, but that the Work was Roman, many were of
opinion, that it might have been the Floor of a Temple,
or place of Worftiip- Pli^y indeed (a) informs us, that
thefe fort of Pavements or Lithofirota^ began to be in
ufe in Italy, in the time of SylU ; who caus’d one of them

(«) Plin. Sec. Hilt. Nat. Lib. XXXVI. Cap, XXV.

q q I

to

{ >

fo be made in the Temple of Fortune ac Tr<.tnefte ; perhaps
the fame which not long fince was taken notice of by
the Honourable Mr. Addifon {b ).

\ was rather inclin’d to fuppofe, it had been that A-
partment belonging to the chief Officer where Jufticc
was adminifter’d ; and the more, becaufe Pilats final
Sentence on our Saviour was pronounced from a Throne
on the Lithofiroton (e); which Appellation was given
to thefe kinds of Pavements by Farro (d) not lefs
than fixty Years before; and by Plin) {e) not lefs than
forty Years after our Saviours Suffering. That the Ro-
man Generals caus’d fucb Pavements to be made ac
their Stations; we may have juft reafon to conclude,
from that paflage {f) in Suetonius cited for this pur-
pofe by Dr. ( f ) Plot,

When the Ground about the Pavement was dug, all
thefe Suppofitions were quafh’d ; for on the North Side
of the Pavement, we difeover’d an entire Bath, fixteen
Foot long, five Foot nine Inches broad, and two Foot
nine Inches deep (which the Draught fent with this
reprefents) : Fig- 1. It was fill’d with Rubbifh of Buildings,
which feem’d to have been burnt ; fc. hard Mortar
adhering to pieces of Roman Brick, fquar’d Stones, and
headed Flint, mingled with Afhes and Coals of Wood.
From the Northweft Corner of the Pavement, was the
Paflage into the Bath, three Foot three Inches wide;
ac which place, the Bricks that bounded the Pavement,
were not turn’d up ac their, ends, but lay even with the
Tejfera. At the diftance of fifteen Inches from the
Tefferdt, there was a Fall of two Inches, to the Land.ing-

( 6 ) Remarks on feveral places in ItalVy Fag. 377^ . ( c )

K. XIX. 19. ( dy Ter. Var. de Re LiB. 3.' ^

C «-> PUn. Hift. Nat. Lib. XXXVI. C.-XXV, (/) Jnl.C«f,Sca.4(J.
i g y Oxferdjhire Plots.-Nat...Hiftoj:y, Chap. X.-, , . . .

place

s

( 553 )

place out of the Bath ; the Landing place v^as allb three '
Foot three Inches long, and two FOot two Inches broad .* *
Thence by two Stairs, was the Defcent into the Bath ;
the length of the Stairs, the fame as of the Landing-
place; the breadth of each Stair was eleven Inches; the
height of each Step a little more than ten Inches; the
lowed Stair was twenty Inches from the farther Side
of the Bath. The whole Work was very cempadi, and
exatdly well made; not in the lead injur’d by Time,
nor the Violence it underwent when fill’d up ; truly an-
fwering the Precepts of Viiruvim\ which (^) ad vile,
that for all Buildings, refpedt Ihould be had to the
Strength, Gonveniency, and Beauty of the Work de-
fign’d ; and that in order thereto, a careful and judicious '
Frovifion fliouid be made of Materials, without Parfi- ■
mony.

Although the Author and Time of thefe Works , can-
not as yet be difeover’d ; yet ’tis evident the Artificer
near enough follow’d the diredlions Vitruvius (F^gave-
for framing iuch like Strudures.

( ) yi. tollio Vitruv. de Architeftur. Lib. II. Cap. III. Hasc autem

ita fieri debent, ut habeatur ratio firmitatis, iitilitatis, venuftatis. Fir-
mitatis erit habita ratio, cum fuerit fundamentorum ad folidnm depref-
fio, & ex quaque materia copiarum fine avaritia diligens. eleftio.

( r ) M. Vitruv. Fol. Lib. VII. Cap, I. Primumque incipiam de Rude-
ratione, quae principia tenet Expolitiomim, uti suriofius fummaque pro-
videntia folidationis ratio habeatur. Et fi. piano pede erit ruderandum,
quaeratur folum fi fit perpetuo folidum. — Si aut omnis aut ex parte con- -
geftitius locus fuerit, fiftucationibus cum magna cura folidetur. — Tunc
infuper ftatuminetur ne minore faxo quam quod poffit manum implere;
ftatuminibus induftis ruderetur. Rudus fi novum erit, ad tres partes una
cal cis milceatiTt, fi redivivum fuerit, quinque -ad duum mixtiones ha-
beant refponfum, Deinde Rudus inducatur, & veftibus ligneis Decuriis
indudis crebriter pinfatione folidetur ; & id non minus pojl pinfum abfolu- >
turn cra>ffitvjdinc fit dndrantis. Infuper exTeftaNucleus inducatur, rerixtio- •
ncm habens ad tres partes unam Calais ; uti ne minore fit craffitudine pa-
vimentnm digitorum fenum. Supra Nucleum, ad Regulam 8c Libellam
exa£ia Pavimenta fttuantur, five. Seftilibus, feu Tefleris.. Cura ca ex-*
tnulat^ fuerint, & faftigia extru£Hones habuerint, ita fricentur, uti, fi
ScSilu fiut, nulU gradus in feutulis, aut trigonis, aut quadratis, feu favis

Fkftj .

( 554 )

' Fiffl:. as to the Pavement, it was fecur*d on every
Side, and the Edges of it refted on a very firm and
neat built Wall, made of Roman Brick, fquar’d Stone
and headed Flint ; between five and fix Foot deep be-
low the Surface of the Pavement, and full twenty three
Inches thick; which we may fuppofe to have been two
foot by the Roman Meafure. The Bricks were not in
regular courfes, as they are to be feen in thole Roman
Buildings, which are in view above Ground ; but with-
out order difpers’d about in the Wall. The Top of the
Wail indeed was but fifteen Inches thick; and that
was cover’d with the Bricks firft mention’d, which
bounded the Pavement : but about fourteen Inches be-
low the Top, there was a Set-ofF (as our Mafons term
it) in the infide of the Wall, eight Inches broad. We
did not dig up the Foundation of the Pavement to the
Bottom, but opened it at one Corner only, that we
might difeover how it was Fram’d : for wdien it was
bor’d through, they obferv’d, next under the Tejfer£, a
Bed of very ftrong Mortar, more tlian a Foot thick ;
under the Mortar a Bed of Clay two Foot thick ; and
under the Clay a firm Foundation of Brick. We ob-
ferv’d the Clay (which the Ground thereabouts do not
afford) to be very fine and red, and alfb clofe; no
.doubt but carefully Ramm’d. The Surface of the
Clay was neatly pitch’d with finall Flint and Stones,
Pointed at their lower ends, and Headed at their up*
per ends. This Pitching or Paving is by Vitruvius
. call’d Stutumimtio \ and the Stones ’tis done with, he

extent. Sed coagmentorum compofitio planam habeat inter fe dircQio-
nem. Si Tefleris ftruftum erit, ut eae omnes angulos habeant seqxiales,
nullibiquc a fricatura extantes. Cum enim anguli non fucrint omnes
squalLter plani, non critexada ut oportet'fricatura.

calls

( 555 )

calls Statitmina. He diredJs them to be fee, when the
Underwork is made Sound and Firm, by well Ramming.
Becaufe the firfl: Chapter in his Seventh Book, treats
only of the Method of making thefe kinds of Pavements,
which in his rime, and as may be obferv’d from his words,
were had in no fmall efteem by the Grandees of Reme ;
I have tranferibed what may fliew the accurate Me-
thods which that great People had in Framing them.

But to return, this pitch’d Work was exadUy even
with the Sct*ofF in the infide of the Wall; on it was
laid a Bed of coarfe Mortar of about nine Inches thick ;
the Skirts of this Mortar (which by Vitruvius is call’d
the Rudus) refled on the Set-ofF above-mention’d ; it
was compos’d of Lime, a (harp courfe Sand, fmall Peb-
bles, and bits of Brick. Upon this Rudus was a finer
Compofition, made, as near as I could guefs, with
Lime, a fine lharp Sand, fome kind of Afties, and
(which was the greater part) flampt Brick and Poc-fiicrds,
in grains not larger than Cabbage»Seed, and the Flower
or fine Powder feparated from it. This Bed w’as about
half a Foot thick ; and is what Vitruvius calls the Nucleus,
Whether we may call it Terrace, I mufl leave it to thofe
who are better skill’d than my felf, in giving proper Ap-
pellations to the feveral parts of Mafonry. Both this
Nucleus and the Rudus under it, very near equall’d the
TortUrtd>SionQ in hardnels and compadnefs. Upon this
Nucleus or Terrace were the Teffera fet : they were fet an
end ; but fb exadi was the Workman in Petting them, that
he us’d two forts of Cement to fix them withal ; their
lower ends flood in a Cement of Lyme only, well
work’d ; their upper halves were cemented with a fine
gray Mortar, confiding of fine Sand (and as it feem’d)
Afties and Lyme. This gray Cement every where fill’d
the Intervals at their Heads ; and was much harder than
the Teffeya themfelves. ^

’Twas,

( 55<5 )

' *Twas before intimated, that the Tejfera were but of
i two Colours, White, and of a dark Brown; they were
harder than a glaz'd and well burnt Tobacco*Pipe, and
of a Grit fomewhat finer ; the Brown feem’d to be of
^ the fame Subftance wich the White, but colour’d by Art,
{as Pliny informs us the workers in Clay of old bad
a Method to do) : they Teem’d to have been form’d in a
Mould, and afterwards Burnt. Hence I am inclin’d to
take the meaning of Vitruvius), where he makes fo plain
V a diftin<llion between the Tefferte and i\\Q&Silia; that,
the one was according to the import of the name,
form’d by Inflruments out of Stone, Brick, and Tyle;
the other lliaped in a Mould and Burnt. They were not
of an equal Size, none exceeding an Inch in length; the
fliorteft; were of an Inch: moll of them were equally
made their whole length ; but of fomc the lower ends ter-
minated almofl: as fliarpas a Wedge, on purpofe, as may
be fuppos’d, to be driven where any Interftices were left :
At their Heads likewife they were not all equal and
alike. Tome exa6Hy Square, Tome oblong Square, Tome
Semidunar, but none I'riangular; the Diameter of thofe
that were Square was about ~ of an Inch 5 the longed
Side of thofe that were oblong at the Head little exceed-
ed half an Inch. It may be obferv’d, that the prepa-
rations for fixing this Pavement here, go beyond thofe
W'hich Vitruvius preferibes (in the firm Wall near fix
Foot below the Surface, in the Bed of Clay within it
two Foot thick, and in tire Foundation of Brick under
the Clay). Bur when we confider the Scituation of
the Ground here is low, not many Feet higher than the
Sea might be elevated at Spring Tides; and that it
might as well be annoy’d by Land-Springs after great
Rains, as by Water owzing through the Earth from the

( jfe ,) Plin. Sccun. Hift. Mund. Lib. XXXVII. Cap. XII.

Sea

i

( 557 )

Sea fo near; from which the Work in time might receive
damage; we muft allow the abovemention’d Additions
to be the refult of a very judicious Forefighc.

The Bach alfo was form’d and lecur’d by a very com-
padi Wall, of the fame breadth and depth with that on
which the Pavement reded: the Wall, which fudain’d
the North Side of the Pavement, made the South Side
of the Bath. On the South Side of the Bath, from
the Ead end, to the ends of the Stairs, there was a fo-
lid Seat ; twelve Foot nine Inches long, very near ten
Inches broad, and fourteen Inches high. The Bottom
or Floor of the Bath, was made after the lame manner
as the Pavement was made, excepting the Tejfer^, and
the thick Bed of Clay : for under all, there was Brick ;
then a Bed of the Budus or coarfe Mortar fomewhac
more than a Foot thick ; above that the J^ucUiu or Ter-
race only, half a Foot chick. The Sides of the Bath,
the Seat, and the Stairs, were plader’d over with this
Terrace about half an Inch thick ; all which were
throughout fo Hard, Compad:, and Smooth, that when
fird open’d, the whole feem’d as if it had been hew’d
out of one incite Rock, and polilh’d. At the middle
of the Ead end, at the Bottom, there was a Sink-hole, a
little more than three Inches long, and above two Inches
deep : about four Inches above it, there was another
padage through the Wall of the fame fize ; the fird we
may fuppofe to let out the Water which had been us’d ;
the ocher to let in frefh. The Stairs and Seat were
chiefly made of Roman Brick, between fifteen and feven-
reen Inches long, between eleven and twelve broad, and
near one and a half thick. Ac the North Side of the
Bath the Ground was not open’d ; but at the Ead end
of the Bath and Pavement, at the South Side of the
Pavement, and at the Wed end of both, there feem’d
to have been feveral Vaults or Cellars; for there were

R r r r very

( 558 )

Very firm 23 Inch Walls contiriued every wav (ro the
fatcher eflds of which we did not irace), whofe Founda-
tions were as low as that which iupported rhe Pave-
ment; To that to the depth of fix Foot the Ground W’as
fill’d w’iih fuch Rubbilh as was taken out ot the Bath.
The Bricks in this Rubbtfli, which W’ere all broke, had
fcveral degrees of thicknds, from three Inches to a little
more than one Inch : fome had one of their Sides
wav’d as in Fig.x\ fome Fretw'ife as in F'tg. 3 others
had Roles on them well imitated ; we found ailb two
forts of channel’d Bricks ; the one like a Trough, the
Channel three Inches broad, and as many deep, the
Brick it felf an Inch and a half thick : The otl er fort,
had a Cylindrical Channel ; fo that when two were ciape
together, they form’d a hollow Cylinder of three Inches
l^iameter.. Thefechannell’d Bneks being all broken, their
Length when whole is uncertain, as is the Die they
ferv’d to ; whether for Paflages to conveigh Water ; or
whether they were placed in the Walls to dillribute
Heat throughout the Building, as was ufoal in the an-
cient Strudures at Rome,

’Tis farther obfervable, when the Ground was open'd
thefecond time; that off from the Soudt-Wefi corner of
the Pavement, which the Letter G Ihews ; five Foot low-
er than the Surface of the Pavement, there was dil’co-
ver’d a large Space (to the end of which we did not
fearchT paved witli Brick, eleven Inches broad, almofl:
one and a half thick, and fifteen long ; fubitand lly
was it pav’d ; for it had two Coutfes of this Brick.
There was half a Foot of Mortar under the lower Courfe;
and about an Inch of Mortar between the two Courfes ;
thefe Bricks alfo w'ere perfecftly well made,* but on
the under Side of each, were two Knobs, about rhe
fize of half a Wallnuc ; fix’d on them as may be guefs’d,

to

( 559 )

to keep them (Icddy, till the Mortar they were fet in
might dry. This pav’d Place was fearcht 6 or 8 Foot
every way ; it was all cover’d with a Coat about two
Inches thick, of Allies and large Coals of Wood : on
that lay confufedly large pieces of the Rudus or coarfc
Mortar aboveniention’d, and lamps of the in all

refpeds like thofe on the Pavement, and cemented as
They were. There were moreover mingled with the Allies
many large Iron Nails, bigger, but not quire fb long, as
thofe we call double Tenns ; fome Hooks for Doors to
(wing on ; feveral fmall pieces of earthen Ware; fome
like bits of Urns ; fome of a fine yellow Clay ; fome
red, thin, neatly wrought and adorn’d with Flowers;
and laftly part of a Human Skull, and pieces of Bones
near it; which Bones were not inclos’d in any Vellel, but
lay loofe; they were difcolour’d like thofe I have feen in
Urns ; fo that the Body they belong’d to, might perifli
by the fame Flames, that thefe Buildings were deftroy’d
by. There was no Infcripnon found either on Stone or
Brick ; no Statue, or other Figure, fave thofe on the
Bricks mention’d 5 neither were there any Coins met
with there. But fomeching more than a Furlong North-
Weft of theft Works, near three Years fince, there was
a Malt Houft, and near two Y'ears fince a Dwelling-
Houft eretfted ; in digging the Foundations for the firft,
there was a Coin of Pojihumus ; and in the Ground dug
for the laft, a piece of Cofiflamines founcT ; both which
1 fend with this, that the inferiptions and Reverfes may
be incerced if neceflary.

From the nearnefs of the Bath, it may reafonably be
concluded that the Pavement was neither a part of a
Temple, nor for a place of Juliice: the continuation of
the Foundations every way to be traced from it, and
what was Jaft diftover’d, are rather ^n Argument it was
an Apartment of a magnificent Palace.

R r r r 2 PUny

( 5<^° >

fUn) ruppofed that thefe Lithoftrota (i ) or tefFerated
Pavements had their original in Greece ; but perhaps the
Grecians borrow’d their Patterns from Afia : for from the
Book of Efther ( w / we learn, there was a mod Royal
Banquet at Suza^ on a Lithoflroton (io tire Septuagint has
ic^ of cohly Stones, four Hundred Years before the
time of S-jlU, who brought them firft into Italy. Jofe~
phiu afSrms (»), that the Grecian Laws, Learning and
Arts were fetch’d from Afia ; and indeed when we reflecd
on the Antiquity of the Law , the Pyramids of

Egypt ‘-f the Temple of Sdmbn; the Walls and Palaces
oY Babylon; and the fumptuous remains of i'almyra and
Ferfepol/s; We have no reaibn to eflccm the Grecians Au-
thors, but as good imitators of thofe early Examples of
Learning and Arts th:y had to follow.

When ^in^us Cicero was here with C^fir, the fecond
lime he invaded Britain ; his Brother the incompaiable
Tfli/y, had the overfight of fome Buildings he had ap-
pointed to be made in the f^illa dar/l/ana atArcano . and
in a Letter fent into 77/i/y informs ^inU u, that

he was well pleas’d with the Seat, and the more, be-
caufe the Pavimented Piazza was Magnificent : that

the Pavement feem’d {o) to be exadtly well made ^
that he had direded fome Chambers to be alter d bccaufe
he did not approve of them.* that in the Bathing Apart-
ment, he had remov’d the Sweating Room into another
corner of the Apodyterium. And afterwards in the
fame. Letter makes mention of fuch another Work which
was in band for him in the City alfo. Again, about
the time ^inclus return’d out of Britain, and was fixt
with the Legion he prefided over, in Winter Quarters

1_

( / y Plin. Sea. Hift. Lib. XXXVI. Cap. XXV.

( ZB ) Efth. Chap. I V. ^ ( » ) jofeph againji Appion. Book II.

{a ) Tull. Cic. ad Qviinft. Frat. ^ib. III. Ep. I.

among

( 5^1 )

among; the l^ervH ('of which Cafar in his Commentaries
makes mention^ ; TuUy (p) takes notice of a Pavement
that was making for himidf alfo .• Expolitiones utriufqus
nojirum, f'int in manihus \ fed uta pcene ad ttcluni jr-n per-
duda res e(l rufiica. Arcani Laterii. ’Tis hinted by Far-
ro that a Litho[troton was one of the Members of a coni-
pleat ViUj. (qj: Farro vvas eighty Years old when his
Books de Re ruft ca were compoled : Tully was fomerhing
more than fifty when the above cited Epifiles were
W’rote; Lafar when a General, made the Te(ferr { r ) and
Sedilia for Pavements, to be part of his Baggage ; and
Fifruviiis, Coremporary with thefe three, calls the Litho-
firotay : rincipia Expolitionum (/) ; which make it evi-
dent theie Floors were held in efteem, by as great Men
as the World has afforded, even in their riper ^ Years.
From ail this, we may obferve, that fometime before,
and in the firfl Age of riie Empire, the humour of thefe
kinds of Floorings much prevail’d among the Romans %
wherefore ’tis no wonder they are found in fb many
places of this Ifland. Bur, as unprofitable Inventions
and Culloms in time grow Stale, and are laid afide,
fo fared it with that of Pavements : For in the time of
Eliny they began to be out of ufe on the Ground;
but then he relis us, they were made above Stairs ( r ),
or in his own Words in Chambers. Whether the Li-
thofirota in Chambers were ufual in Fitruvius'^ days,
we have no Warrant to fuppofe, from any hint in his
Writings ; notwiihftanding he gives Rules for making
them, piano pede^on the Ground ; and fab (h) dio, (which

( ^ ) Ibid. Ep. ri. ( ^ ) Ter. Varro de Re ruft’e. Lib.-III.

(r) Suet. Tranq. Jul Caf. Cap. 4^. (r) M.Viiruv. Pol.

Lib VII Cap, I. (t) Plin. Hift. Lib. XXXVI. Cap. XXV,

Pulfa deinde ex hiimo Pavimenta in cameras tranfiere e vitro: novitium
& hoe inventum. ( « ) M. Vitruv. Lib. Vll. Cap. I, Sob dio vero

maxime idonea faciunda funt pavimenta,

from

( )

from the Method by him prefcrib’d muft be) aloft : be-
caufe for fuftaining thofe f«h dio, he oidcrs the work un-
derneath to be well fecur'd, with two lays of Plank that
(hould crofs (rr) each other, and be nail’d down ; then
the Statumtmtio or Pirching, the Mortar^ Terrace and
Tepr^, as before on the Ground, but bccaulc by fuh
dio Vitruvius could not defign Chambers ; and although
Flitiy informs us the Grxeiam us‘d ( x ) lo cover or flat-
roof their Houfes with thefe Pavements; yet fmee nei-
ther Vitruvius nor Plir.) mention any luch Mode prevail-
ing in their times at Rcme\ it remains, that we may
imagine Suh dio, or the Subdi^Iia of P'itruviiu, to mean
Pavements mounted on Pillars or Arches, which might
afford delightful Terraces out of the upper Rooms, and
lhady Piazzas underneath: and in this Senlc perhaps
may be underllood the Porticos Pavim>:ntata of 7«//y
above-mention’d. By the many Apartments, the Found-
ations about thefe Works point out, there feems to
have been nothing wherein the Buildings that once flood
there, might come fhorc of the magnificent Strudlures,
wherewith the Romans delighted to gratify their Luxury.
The ufes each were dcfign’d for, is not to be deter-
min’d: whether there was a Piazza cover’d with a Li-
thofrotott, cannot be affirm’d. But be that as it will;
*tis next to Demonflration, there was fomc upper Floor
fuflain’d by Wood, and pav'd with the Tejfer£, after
the fame manner as Pltravius directs ; and, on the
Brick Pavement (lafl difeover’d), the Coat of Afhes and
Wood Coals with Nails, cover’d with large pieces of
the Rudus, and great lumps of the Tcffer^ well cemented

( w) Ibid, itaqne fi neceffitas coegerit, ut minime vitiofa fiant fic erit
faciundum: cum coaxatum fuerit, fuper altera coaxatio tranfverfa fter-
rvatnr, clavifque fixa, SPr.-- »-Statuminatione fafta rudus inducatur, &c,

C ;r ) Plin, Hift. Lib. XXXV. Cap. XXV. Subdialia Grsci invencre tali-
fcoj domuscontegentes.

together

( 5^; )

together, and the Nuchuf adhering to them • {hew there
was an upper Pavement broke by its fail, when Fire had
confum d its lupport.

I have been thus prolix, in giving you the mofl: exa<S
account I could of this piece of Anerquity ; becaufe we
cannot have a lefs Senfe of the admirable Rules and Me-
thods, the Roman People made ufe of, in framing their
Buildings, and ordering other Conveniences for Enjoy-
ment and Magnificence 5 than of the incomparable Ma-
nagement they had in their Military Preparations and
Dil'cipline; which are To to the Life reprefented by (j)
JoJfphus, and fo pundually deferibed by ( z.) Vegetius.

As to the Roman Architedlure, it may not be amifs
here to note* that when they defign’d a Building, they
could not immediately begin it : their Preparations re-
quirdtime: By their well fliap’d durable Bricks, and
by their Stone-like Mortar, we may plainly perceive,
they built not with fuch hady Materials as are now
us’d. Fitruvius (a) and Flin) both diredf, that Brick --
fhould be form’d in the Spring, and be two Years dry-
ing And where Pliny fpeaks of their Mortar, he lays,
’twas ordain'd by the old Laws f ^ ) of Rome, that no
Undertaker fliould Build a Houfe with Mortar which had
not been made three Years before. We find indeed,
their Walls Icem to bid fair for Eternity 5 whereas ours,
from Parcimony and ill Management, are fcarce able to
endure one Age.

The refl of this learned Difeourfe, hy ithich *tis made
more than prohalle that here once flood ih? Roman City An-
deridee, deflroyed Ly the taxons ahoui the Tear 500 ; though
ver) curious, yet i,eing chiefly Hi (lor; cal, fee ms hot Jo pro-
perly the Sul\eB of the f' Trunjacl ions.

(^) Jofephus’% Wars of the J-e-ws Book III. Chap. III.

{X.) Vef^et. de Re Wilitari. (a J M. Vitruv, tot. Lib. II. Cap, IH.
Plin Hift. Lib. XXXV. Cap. XIV. ) Plin. Hift.

Lib. XXXVI. Cap. XXIII.

m. A

( ^<54 )

i!L A fhort account of the Nature and Vertues of
the Pyrmont Waters 3 with fome Ohjeryations
ul>on their Chalyheat Quality. Communicated by
Vr, Frederick Slare, R. S. Soc.

HAving procur’d about a dozen Quarts of P<jrmont
Waters this laft Summer, I made fome Tryals
with them. I found by the Tafte that they contain’d
a rich Chalybeat Vertue, and alfo made a very brisk
and lively impreflion on the Palate, more grateful and
fpirituous, than the bed: Sfarr Waters 1 ever tailed The
Waters are look’d upon as mod excellent, if they
Sparkle a little in theGlafs; but thefe in Summertime,
when pour’d into the Glafs, nay fbmetimes even in
the Bottle, as Toon as the Cork was open’d and the
Air was admitted, would make a notable Ebullition,
fomewhat like bottled Cyder, tho’ this was foonover;
but they did yet continue their fmart and brisk Tafte, and
high Chalybeat Relifli to the lad Drop, tho’ we were
fome Hours in Drinking them off. In the Winter time,
thefe Waters do not Sparkle, nor Ferment, at lead mine
did not; but they were not carefully preferv’d, being
expos’d in cold Cellars, where our Beer or Wine dood in
the Winter; and yet notwithdanding, they iod not the
Chalybeat Tafle, and alfo retain’d a very pleafant brisk
Gud. Thefe Waters have been reckon’d in the Number of
the German ’BjHUltlfn or AcihU, and fome of my

'Friends to whom 1 gave a Glafs of the Water, have af*
crib’d to it a (harp i ade. and have been ready to run
away with a podefs’d Opinion of its being Sour: but
when I requir'd them to call back that hady Afler-
tion, and to confider it better, whether that Tade was

really

( 565 )

Sour or Acid, they have been forc’d to recant and con-
feft, that the fmart and brisk Tafte mifled them to call
it Acid or truly Sour. Thus Cyder and fofc Ale when
Bottl’d, will give fuch an acute Affedion to the Palate,
when it is far from being Sour ; And even Volatile Alka-
lies of Sal Armoniac or of Hartshorn, may be made to
give the like pungency to the Tongue.

In order to a more nice Enquiry, whether any Acidity
weredifcoverable in thcfe Pjrmont Waters, we dropt in
confiderable Quantities both of Spirit of Hart' horn, and
of Spirit 6f Sal Armoniac, both juflly prepar’d ; but could
not di (cover the lead Ludation or Motion to appear upon
this Conjuntdion, as it ufually does with an Acid.

I made a yet more nice and certain Examen of thefe
Waters, by mixing Milk with them, fometiraes in equal,
(ometimes in double proportion; and in various degrees
o‘ Warmth, both in Lukewarm degrees, and alfo with ,
a boyling Heat but I could not perceive any Curdling.
But rather on the contrary, the Water preferv’d the
Milk from Coagulation, for four or (ive Days, even
in September, it being hot Weather.

Take a very little Gall in Powder, about half a Grain
to a Glafs of a quarter of a Pint; this does in a Mo-
ment render it turbid, and make a dark Purple, efpe-
cia'lly if you flir it : but if you drop the Powder on the
Surface of the fame Water, it then caufes a fine blew
Tindure If you will make a very fine Tindure plea-
fant to the Spedator, Take five Leaves of ftrong Green
Tea, put them into the bottom of a Glafs holding a
quarter of a Pint, and you will fee thofe Leaves unfold
themfelves, and in a quarter of an Hour, tinge the Wa-
ter with fuch aCerulous azure Blue, chat few Vegeta-
bles do afford the like. We obferve, that the longer
thefe Leaves, or any other Stipticks, (which are the

S f f f Preci-

( 5 66 )

Precipitators) do flay together, the more they degenc*
pate into a deep Purple, <x even to air Atramentarious
Colour.

Id reference to the internal Ufe of thefe Waters, I
drank about a Quart at a time, after this rr/anner. I
firft began with ihQ Spiirv Waters, which \ r?rocurd very
good, and drank them fora Week, and they agreed very
well- 8 then drank thePymm Warers for three or four
Days, and continu’d the ufe of thefe Waters alternately,
until I had drank about twenty Days. By the refult of my
Experiment it feem’d to me very plain, that the Pjrmont
Water was more agreeable, gave more Strength and
Spirit, and was as much or more preferable for its internal
Vertue, as for its excelling the other in a brisker and
more fprightly Tafte.

There is another Excellency in thefe Waters whicli
will make them more ufeful to us, than any Foreigir
ChdlyhfAt Waters we yet l^ow, becaufe thele will keep
better ; they are not fo foon fpoil’d by any accidental
Infinuations of Air, as tbeSpan> are fubjedt to be. The
Chalybedt Mineral is here throughly diflblved and well
united, and mix’d in this Water, fo that it does not
eafily precipit^er. for which Reafon it may alfo the
better pafs the vafa U5iea^ and even enter into the Mafs
of Blood it felf, and work the more confiderable Effeds.
That this is not a bare Hypothefis may be prov’d by
this Experinaent.

Having fufferd the Spdw Water co be expofed in a
Bottle which was half full, and unftopc iz Hours,.!
examin’d it, and found it taft juft like common Wa-
ter; but the Pyrmom Waters that were open’d to the
Air after the fame Manner, tafted ftrong of the Mine-
ral, and gave their Tindure as at firft; nay, they coii'
tinued thus for full two Days, and perhaps might have
done longer, buE.,1 thought chat TimefUffied.

There

( >

There remain (cver^l. other Ej^pcriments to he made,
jn order to a further Search! ^to, the. Excellencies, of
this noble Water, bvjt’ this I cannot do at prelent for
want of a Quantity, which I hope to obtain the next
Sunsmers for they can with more Eafe be brought into
EngUnd than the S^arv, 1 may allb fairly conclude,
that lince the has been very beneficial to our
Patients in Chronical Dileafes, thefe Waters of a
much fuperior Virtue will lurpafs them in conquering
many of our obllinate Dillempers.

Sorm Additions to the aforefatd Account of the
Pyrmont Waters .

Having had lately fome Dilcourfe about a
Purging Quality contained in thefe Waters, I
am now inquiring into the Truth of this Quellion,
whether they in Reality do contain any Purging In»
gredients or Properties.

I evaporated about a Quart of this Water ad ficcita-
im\ I then poured on the reliquU fome Rain-Water,
•enough to dilTolve and take up the Salts, and exhal’d
that Water, and had a Grane or two of the Salts, that
tailed murhtic, fuch as moll River and Pump Waters
give. It is well known that the Purging Waters have
a very bitter Talle, and by the moll learned Dodor
Qrm fU MemorU, and an illullrious Fellow of this
Society, that Salt was called Sal Catharticum amarum,
which dillinguilh’d it from all other Species of natu-
ral Salts: that of the Pyrmont Water abovementioned
has no Relation to this, but to the Sea- Salt, not being
in the kaR bitter.

Sfff a R

L

( 5-58 )

It is alfo Well known,, that u;ilefs,0Dt; Waters be im-
pregnated witb a confidfei^ble^'Qba^Vnfy^ 'bfrter

Sale, it will fiQt purge at, all; jTwo pV three’ Gianes
fignifie nothing,, nor have the Cathartic Power,
For Example, Put two Drains of the purging S^lts.rOa'
Quart of common Water; and this t^^Atltj^Vull '^iv'e^
but a Stool or two to orre :Wh6 is hAtar,aliy ’^'tj eafle’
to work upon, f have exarhM’d feweral/blheY' Chd)^'^at
Waters, and found much the like ingredients, and ne-
ver any that I could (ufpedf to carry any purging Pro-
perties.

I think, we -cAo Vnuch better, dtiflorcflcjtte riiar ihe
Chaljheat Waters do contain Stipric and ReQringent Vir*
tues, becaufe they owe their Birth to the Iron Mineral,
and mpre particuj.9rly to die wjiicli .Dodor

X//f<rrfuggefli», (dbtfwithdut ie ReArdn/ id be ’the Pa-
rent? eVen'of as i^ is doubtlefs’the Caule of

all Waters: Thu.s I have often examined the

Solution of the Pjrites by' the Rain Water at Oekforel,
and at other Places vvbere Copperas i$ made, and found-
it a Very'ftrong Chlyheat Water. It is from this Minera
we have our flrong Stiptic and conflringent Medicines,
for external and internal ufe ; we have our Powders
and Salts of Steel, or Fitriol of Mars, from hence ; nay,
even thofe obflinate and inveterate Diarrheas which
have bafHed the Force of all Medicines, have, by a
judicious Ule of Tunbridge and other Iron Waters, re-
ceived a Cure. ,

• But notwithftanding all we can fay, it will be retor-
ted, that there is Matter df Fad and Experience againR
us, that the Waters really do purge at Pymonr, where
they are drank. '

This we do allow to be true, that Tmlridge Waters
do not only purge but fometimes vomit, when drank
haftily and in great Quantity 3 but our Phyficians have

cor-

( 5^9 ) ,

,corre(Sled this Irregularity, and we hear of no fuch“
Complaints, where they cbferve a jud : And we
do all agree, that thofe Waters are, in their own Nature,
binding, . and do oft require fome opening Medicine.
The' (^a.nticies, of Water drank at FjrmQM: 2liq very
large, .often two or three Enflijli Quarts. It is. no
Wonder that, their Weight forces them thorow the Bow-
els; for any common Water, drank haftily, and infucli
Quantity, will do the fame. Whereas, if you take
this Method, and will drink Pjrmom^ or any other
CBaifheAt Waters leifurely, a Pint-Glals in an Hour,
or rather two Half-Pint GlalTes, you may drink three,
Pints in fo n>any Hours without Danger of lofing them
by Dejedion, But if any, one will be careful, and cake
^h^s■Cautibn'‘^^hth him, he will fcarce fail of Succefs ;
that is, let him be very quiet and {fill, both in Body
and Mind; the lefs he ftirs or walks, the better he
will pa(s off his Waters by Urine, And tho’ this will
appear a Paradox, efpcciaUy to thofe Phyficians who
pradife abroad, .and commend to their Patients' much
Adion in walking, yet I know I have both Reafon and
Experience on my Side. To avoid Prolixity I {lull not
declare them at this Time, and {liall only ask leave to
mention one Obfervation 1 have made, that none of,
our Ertglifh Steel Waters do ftrike fuch a Purple as
the Foreign celebrated Chaljheat Waters do: for ours do
give a more turbid and dark Colour, and the worfe
the Waters are, the blacker Sediment- they make.-
Thofe of Jflington abound with a coarfe Oksr, the Mi-
neral is not well dillolved, but gives an atramentarions
Colour ; but the Pyrmont Waters excell all i have hap-
pened to examine, in its bright Luftre.

N. B. Moft of the Experiments alledg'd- hy Dr. Slare, in
the foregoing Difcottrfe, vrere likerrife by him [bervn before the

C 570 )

^oyal Society, Feb. 28. lafi: and. it was found that thr
Pyrmont Waters gave a much brighter TitdSure with Gatls
and Tea, and had a much more exalted Cbalybeac Tafle
than the Spaw; and a [mail ^antity of each being kept for
fome time in Bottles, to compare them, the Pyrmont was •
found to have retained its Virtues much better than the
Spaw. The Vrefident^ and feveral of the Members prejent,
'having drunk a Glafs of it, found it of a very agreeable Re-
difh, and to fit eafie on the Stomachs

rV. ^emarkg on the fecond Taper in the fdiflory of the
^oyal Academy of Sciences ^ for the Tear 171 u
concerning the Caufe of the Variation of the Taro»
meter ; to fhew that the Way of accounting for it
in that Taper is injufficient^ and that the Experiment
made u/e of to prove mhat is there ajferted, does
no way prove it, TyJ, T. Defaguliers, M A,
F, % S,

The Paper is as fo Hows,

* T T appears by the Barometer, that when it rains,

* or a little before Rain, the Air commonly be-
‘ comes lighter.

‘ That it mull rain when the Air becomes lighter it

* is eafie to imagine ; for the imperceivable Particles of
‘ Water, that fwim about in the Air in prodigious

Quantity, not being fiiificiently fuftain’d when tlie

* Air has loft a pertain Degree of its Weight, begin to
‘ fall, and feveral of them joining together in the Fall,

* make Props of Rain.« when about half of tlie
^ Air is drawn out of the Recipient of the Air-Pump,

: (and

C 57' )

* Cand confeqiiently the remaitiiag Air is as weak again

* as at fomeching like a fmall Rain falls. But
‘ why Ihou’d the Air become lighter? One might ima-

* gine that in the Place where it rains, it may have loft
‘ feme of its Weight and Bulk, by means of the Winds

* carrying away fome Part of it; but Monfieur Leibnitz,

‘ in a Letter to the Abbot Bignon, gives a more inge'

* nious and more new Reafon for it.

‘ He pretends that a Body, which is in a Liquid,

* weighs with that Liquid, and makes up part of its
‘ whole Weight, fo long as it is fuftained in it; but if
‘ it ceafes to be fullain’d, and confequencly falls, its
‘ Weight no longer makes a Part of the Weight of the

Liquid, which thereby comes to weigh lefs. This

* may naturally be applied to the abovementioned Par-

* tides of Water; they encreafe the Weight of the Air
‘ when it fuftains them, which is diminiftied when it lets

* them fall : and as it may often happen that the Parti*
cles of Water that are higheft, fall a confiderable time

* before they join with thofe that are low, the Gravity
‘ of the Air diminilhes before it rains, and the Barome*

‘ ter Ihews it.

‘ This new Principle of Monfieur Leibnitz^ is furpri*

‘ zing. For muft not a Grange Body, whether ruftain*^

‘ ed in a Liquid or not, always weigh? Can it gravi-

* rate upon any other bottom than that which fuftains
‘ the whole Liquor.^ Does that Bottom ceafe to car-

‘ ry a ftrange Body, becaufe it falls? And is not that..

* body all the while it is falling, part of the laid Li-
‘ quid as to the Weight .> ALthat race, whilft a Chy#

‘ mical Precipitation is made, the whole Matter ought

* to weigh left, which has never been obferved, andt
‘ fcarce appears credible,

* Notwithftanding thefe Objections the Principle'
^ holds goodi when more clofely examin’d. What fu-

‘ ftaitis.

C )

(lains a heavy Body is prefs’d by ic. A Table, for
Example, which fuftains a Pound Weight of Iron, is
prefled by ic, and is To only becaufe it fuftains the
whole Adion and Effed of the Caufe of Gravity,
(whatever it be) to pufli that Lump of Iron lower.
If the Table (hou’d yield to the Adion of that Caufe
of the Weight (or Gravity) it would not be prefs’d,
and therefore would carry nothing. After the fame
manner the Bottom of a Veflcl, which contains a
Liquid, oppofes it fclf to all the Adion of the Caufe of
Gravity againfl the faid Liquid : IfaflrangeBody fwims
in it, the bottom oppofes it felf alfo to the faid Adion
againfl that Body, which, being in yEquilihrio with the
Liquid, ii' in that refped really a Part of it. Thus the
Bottom is prels’d both by the Liquid and the Orange
Body, and luflains them both. But if the Body falls,
it yields to the Adion of Gravity, and confequently
the Bottom does no longer fuflam it ; neither will ic
fuflain it, till the faid Body is come down to the
Bottom There.fore during the whole Time of the
fall, the Bottom is eafed of the Weight of that Bo-
dy, which is no longer fuflain’d by any thing, but
puili d down by the Caufe of Gravity, to which no*
thing binders'it from yielding.

‘ Monfieur Leihitz, to confirm his Notion, propofed
an Experiment, tie fays, that two Bodies mufl be
tied to the tw*o Ends of a Thread, the one heavier,
and the other lighter than. Water, yet fuch as both
together may fwim in Water : Put them into a Tube
full of Water, the Tube being tied to one End of
the Beam of a Bailance whofe other End has a con-
frepoiiing Weight: Then if we cut the Thread which
ties the Bodies together (that are of unequal Weight)
fo that the heavieft may prefently defeend. He fays, that
in filch a Cafe the Tube would be no longer in
hrio, but its counterpoifing Weight wou’d preponde-

‘ race

C 573 )

' rate, becaufe the Bottom of the Tube wou’d be lefs

* prefs’d. It is plain, that the Tube mufi; be fufhciently
‘ long, that the falling Body may not reach the bot-

* tom before the Tube has time to rife. !n Chymical

* Precipitations, the Veflels are either too fliort, or

* what is precipitated falls fometimes too faft and
‘ fometimes too flow^ for then the little Bodies are
‘ always (as to Senfe) ift /Equilibrio with the Liquor

* that contains them.

‘ Monfieur Rantazzini, the famous ProfelTor at Padua,

* to whom Monfieur Leibnitz had propoled his Expe-
‘ riment, has made it with Succefs, after fome fruitlefs
‘ Trials. Monfieur Reaumur (to whom the Academy
‘ had recommended itj has alfo made it with Succefs.*

‘ This is a new View in Natural Philofophy, which,

‘ tho’ it depends upon a well known Principle, is very
‘ fubtie and far-fetch’d 5 and gives us juft Reafbn to fear
‘ that in Subjeds that Teem to be exhaufted, feveral

things may yet efcape us.

^mnr/{S upon Monfieur Leibnitz’^
principle.

Figure 4.

Let a B be the Bottom of a Veftet full ©f any
Fluid, whole Top is either wider than the Bot-
tom as GH, narrower as EF, or equal to \t as CD.
The Preflure of the Fluid upon the Bafe AB will be
equal to the Weight of CB, or of a Cylinder or Prifm of
the fame Fluid, made up of the Area of the Bafe multi*
plied into the perpendicular Height above it.

Jf the Fluid be equally dcnfe every way as Water,
or of a Denftty uniformly diminifh’d as you go upwards*
this Propofition (call’d by Mr. Boyle the Hydroftatical

T t t c Pa-

( 574 )

Paradox^ will hold good. This is demonftrated by aU:
Bydroftaticai Writers.

s

Figure 5“.

Let EF reprefent part of the Surface of the Earth;
and GEFH a Pillar of the At:7iofphere, whole
Height is GE the whole Height of the Air. Let us
imagine the Vapours rifing out of the Earth to form
themfelves into two Clouds A and B, and to fettle in
that Place where the Air is of the fame fpecifick Gravity
with themfelves. It is evident that they will caufe the
Air to rife fo much higher as their Bulk amounts to,
and will therefore make the Surface which was at GHto
rife up to IK, fo that the bottom EF which was
pfefs’d by a Pillar of Air as GEFH, is now prefs’d
by an higher Pillar as lEFK. Now if the Clouds
A, By by any Caufe Ibever, change their Place, fo as to
come downwards, ffor Exemple to E, D) the Height of
the Pillar I EF K will remain the fame as it was, and
therefore the Bottom E P will be prefs’d as before .- by th&
foregoing Propofition,

Corollary L

If the Clouds A, B defeend, and in their Delcent
keep the fame Bulk as they had before, the Surface IK
will remain the fame, and therefore EF will be prefs’d.
as before.

CoroUar'j II.

Whether a Body be fpecifically lighter or fpecifically
heavier than a Fluid ; fo long as it is detain’d in it, it
will add to the Fluid as much Weight as the Weight
of an equal Bulk of that Fluid: wherefore a Body does
not. iofe all that Weight which it added to the whole

Weiglit

f 575 )

Weight 6f the Fluid, when it ceafes to be fudain’d in
the faid Fluid : contrary to Monfieur Ldhnitz's Princi-
ple.

Scholium.

If a Cloud (by any Caufe whatfoever) becomes fpe-
cifically heavier chan that Parc of the Air in which ic
fwims, the Excels of its Gravity above an equal Bulk
■of Air will make it delcend, and accelerate its Motion
downwards; and then indeed ic will lofe of its Weight
by the Refiftance of the Medium, till it comes to an
uniform (or lenfibly uniform) Motion : but all the
Weight that ic will lole will only be the Excefs of its
Gravity above that of the Air ; for with the reft of its
Weight it will ftill make up part of the Weight of the Air.

E>efeYiment I. Figure 6.

Having with a Weight in the Scale C of the Balance

B counterpois’d the long Glafs of Water E /, with
a Horfe-Hair I let down the leaden Weight fV into
the Water, which from F6 arofe up to EH; and
therefore the V'/ater became heavier by the Weight of
a Bulk of Water equal to ^he Lead. Having with ano-
ther Weight in C made up the Counterpoife to the
whole, with fine Sciftars I cut the T hread of the Plum-
met ; and all the while the Plummet was falling, the
Water defcended rather than rofe ; and when the Lead
was at the bottom the Water overpois’d, becaufe it had
then added to it all the Excefs of Weight of the Lead
above an equal Bulk of Water, which by Experiment
is about n of its Weight. Had Meftieurs Reaumur
and Ramazzini trfd the bxperiment thus, the Succefs
had been the fame ; but Mr. Ramazzini (as I under flood
from a Gentleman who was prefent) tried it in the fol-
lowing Manner, as I have fince done.

T 1 1 t L

C 57<^ >

Experiment II. Figure 7,.

Making ufe of the abovemention’d Machine, after I
had balanc’d the Water and Lead in it, I fix’d to the
End of the Beam B the Thread of the Plummet, which
in tbe former Experiment I held in my Hj»nd. This
added to the Weight hanging at B, and oblig’d me to
put into the other Scale a Weight equal to n of the Lead,
to recover the Mquilihrium. Then cutting the Thread
or Hair, the Scale with the Weights overpois’d whilfl: the
Lead was falling ; but the Equilibrium was reftor’d when
it came to the Bottom. So that the Lead even then
mull have loft only its Excefs of Weight above Water,

Experiment III. Figure 8.

I tried the Way propofed by Monfieur Leibnitz in
the following Manner.

I took a Cork C weighing an Ounce, and fomething
more than four times lighter than an equal Bulk of
Water, and a Ball of Antimony fV about four times fpe-
cifically heavier than Water, and of four Ounces Weiglit.
The Cork laid upon the Water in the Veftel EAB D
rais’d the Water from SS'^to 6G, and added an
Ounce to the Weight of the whole Water: then fufpen-
ding the Bali of Antimony by a String, and letting it
hang in the Water at N, it rais’d the Water from 6 6
to HHy and fo added another Ounce to the Weight
of the Water. Then tying the Antimony to the Cork
fSee the Figure of the Veftel mark’d with little' Letters)
the Cork had added to it three Quarters of the Weight
of the Antimony which the Hand before had fuftain’d,
and made it fink fo as to be almoft cover’d, and raf-
fed the Water to ik, adding three Ounces to its Weight.
Hanging this Veftel of Water upon the Balance, and a

Coun-

( 577 )

Counterpoife at the other End, upon cutting the Strings
the Veflei of Water was rais’d up, and the ^quilihrium.
was not reftor’d tiil the Antimony came to the Bottom.

By obferving that as the Cork (being freed from the
Weight of the Antimony^ arofe, and that during the Fall
of the Body, the Water funk to hh^ it appears that
tills is, in efTed:, the fame Experiment as the former,
and concludes no more. As to the real Caufe of the Va-
riation of the Barometer, namely, the Accumulation of
the Air by Winds over the Place where the Barometer
rifes ; and part of the Air being blown away where the
Mercury in the Barometer finks, fee Dodor Hallefe>
Account of it in the Thil. Tranla6ihns. Numb. l8i, -

TO s

I N making the firfl Experiment before the R. Society,
of a Piece of Lead liifpended by a Thread, whilft^
it was wholly cover’d with Water in the large Tube
in which it hung (whofe Length was 4 Feet) it was
obfervable, not only that the End oTthe Balance (to *
which the Tube of Water with the Lead in it w^as
fixed) did not rife when the Thread was cut, (to •
Jet the Lead fall from the Top to the Bottom of the
Tube) as it muft have done according to Mt. Leibnitzs
Principle; but that the Paid End of the Balance began '
to defcend from the Time that the Lea'd began to fall.
Therefore to be fure that it was not the Plummets
rubbing againft the Sides of the Tube in its Fall, which
caufed that fhtznomenony I hung to the Balance a
long Giafs of three Inches diameter inftead of the Tube;
and making the Experiment as before, it fucceeded in

( 578 )

fame mannec ; the End of the Balance which carried
the Veflel of Water funk as Toon as the Thread of the
Plummet was cut ; tho’ this Glafs was not above half
To long as the Tube

When by holding the String I drew the Lead upwards
and downwards in the Water, there was no fenfible
Alteration of the y^quilihrmnt. Neither was it alter’d by
cutting the String cf a Stone- Plummet, becaufe of the
Shortnefs of the Glafs, and the little Excefs of fpecifick
Gravity in the Stone ; for the greater the Difference is
betwixt the Body made ufe of in this Experiment and
Water, as well as the bigger the Body it felf is, the
better the Experiment will fucceed.

Hence it appears, that when a Body, fpecifically hea-
vier than a Fluid, is (by what caufe foever) detain’d iti
any Place of the faid Fluid, it adds as much to the
Weight of the whole Fluid as an equal Bulk of the faid
Eluid amounts to: And when the laid Body, by the
Adion of its Excefs of fpecifick Gravity above the
Fluid, defcends with an accelerated Motion; fo long as
that Motion is accelerated, the Refiflance of the Fluid
C which is as- the Square of the Velocity^ takes off
Tomething of the whole Weight of the Body ; but as
much as the Body lofes, fo much the Water gains, over
and above what was given it by its rifing on Account
of the immers’d Body.

A Body therefore that falls in a Fluid is fo far from
making the Fluid lighter as it falls, that it makes it
prefs more upon the Bottom that fuflains it, when it is
falling, than when it was at reft in the Fluid.

If the Veflel of Water be long enough for the falling
Body to come to an uniform Motion before it reaches
the bottom, the Force impref ’d on, the Water under
the Body will make it prefs the Bottom, as much as if the
Body were adually at bottom ; the Body in that Cafe lo-

fing

I

{ 579 )

fing all its Excefs of Gravity above that of the VVater^
and the Water gaining it.

Hence it follows, that a falling Oloud, when it
comes to an uniform Morion, will not only add to the
Weight of the Air as much as the Weight of an equal
Bulk of Air; but even as much as its whole Weight
amounts to, tho’ it be fpecifically heavier than the Air
about it.

All the Diminution of Weight that can be allow’d in
this Cafe is this. If we imagine the Air to have a
fmooth, regular Surface, as we have at firft flippos’d, for
if that be not allow’d, we may take any imaginary Sur-
face of it above the Clouds) when a falling Cloud is
diminilh’d in Bulk, (as when ic is chang’d into Rain j
the Surface of the Air will fubfide in proportion to that
diminution, and therefore will weigh lefs, by lb much
as is the Weight of a Quantity of Air equal to the Bulk-
that Cloud has loft: But when the Drops of Rain after*
their Acceleration (occafion’d by their Excefs of Gra-
vity above that of the Air^ are come to an uniform^
Motion by the Refiftance of the Air, they reftore ro the
Air the Weight that it had loft. Now this uniforns'
Motion being acquir’d in about two Seconds of Time,
and the Diminution of Gravity in the Air being infen-
fible, when compared to near three Inches of Mercury
ffor fuch is the Variation of the Barometer with us) can ^
no way be the Occafion of thofefofenfible Alterations iiii
it, which happeaforae time before Rain or Fair Weather.

Add to this that the vphole ^antitj of Rain that falls in
England and Vtuncc, in the Space of one Tear, [cares
ever equals tm Inches yf Mercury s And in moji t laces^-
between the Tropicks, the Rains fall, at certain Seafons,.
in very great ^anilties, and yet the jhervs -

there very little or no Alteration^

( 5^0 )

•

V. Account of an extraordinary EjfeB of the
Cholick : communicated to the Royal Society,
. hy that curious Anatomifl Mr, St. Andre, and
^read March 21. 1717.

TH E Peri/fall ick Motion of the Tnteftins is by all
Anatomifts fuppos’d the proper Motion of thofe
Cylindrical Tubes.

The ufe of this Motion is to propel the Chyle into
the vafa la^ea, and to accelerate the grofler Parts of the
Aliment downwards, in order to expel them, when all
their nutritive Contents arc extraded.

This Motion thus eflablilli’d, it naturally (eems to
' follow that an Inverfion of it (call’d for that Realbn an
JfitiperiAaltick Motion) fliou’d force the Aliments, Bile,
pnncreatick jmee, and laftly the F-£ces to alcend cowards
the Mouth.

The Caufe of this imaginary Antivermkular Motion,
•is affigned to a Stoppage of the Inteftin, or to a great
length of it being ingaged in the fame manner as the
Fingers of a Glove are choak’d by inverting the
Glove in drawing it off : Or like as a Silk-Stocking, which
when ’tis not gartered, falls upon the Foot, and is in
a manner ffrangled, fo that Tome Force is required to
bring it up again.

This fuppos’d, the Antiperifialtick H'jpcthejis ieems
at firft Sight very natural, and anfwers moft Difficulties.
For if the P'ermicuUr Motion accelerates the Contents
of the Inteffins downwards ; the Antwermiedhr, by the
Law of Contraries, Ihould force them upwards cowards
.the Mouth.

Was

f )

Was this Suppofuion as certain as 'tis generally re*
ceiv’d, I Ihou’d not prefume to advance chat there is
no fuch thing as an Antipertftaltick Motion of the In-
teftins; nor that the Miferere mti is ofrner a violent
Contradlion of the Abdominal Mufcles, than a Stoppage
or Inverfion of the Inteftins, as 'tis fuppos’d.

So laying afide all Prevention, let it be granted that
this Difeafe is a violent Contradion of the Abdominal
Mufcles, as I have already fuppos’d it, caus’d by the
Redundancy of the Inceftins or tlieir Contents. Then
comparing the Symptoms of this Difeafe, with thofe
of the different Kinds of Hernias, vve (hall find by the
Analogy of the Parts, Reafon and repeated Experience,
that the Chordapfas, fo call’d by Cdfns, is a Difeafe in
which the Inteftins and Omentum \ at other Times the
Pancreas or Spleen ; nay, even the Mcfentery it felf arc
forc’d through the Diaphragma into the Thorax.

All thefe tender Parcs being flrongly comprefs’d, by
the continual Motion of this Mufcle, muff by confe-
quence caufe the fame Accidents as in the Buhonocele
or com pleat Hernia, there being no difference in thefe
two Cafes ; but that the firft is a ffrangling of the In*
teflin by the Diaphragm, and the latter a choaking of
the Intefiins by the Abdominal Mufcles.

One Example of the many of the like Nature, that
I can produce, will much confirm this Affertion, and
may ferve to convince any Perfbn that is impartial.

The Cafe is this: A Gentleman that came to Town
yefterday was Sevennight in good Health, meeting with
fome Friends, drank a great deal of new bottled Oat-
Ale, after fome Pints of Wine. Thefe Liquors fer-
mented fo violently in his Stomach and Inteftins ; that
he was taken with a violent Cholick the fame Night.

In the morning an Apothecary was fent for, who
adminiftred a Clyfter, and took fome Ounces of Blood

U u u u' to

(5^1 )

rte reKevc the Patient, who complain’d <i( a great Pain
in his left Side.

The Clyflers being repeated the Night following, as
alfo the next Morning, and the Patient growing worfe ;
the Apothecary, without Order of any Phyfician, gave
him a violent Vomit; which operated Eight or Nine
Times: This added Fewel to the Fire; and the Patient
having from that Time been in a defperate Condition,
two eminent Phyficians were call’d, who order’d that
the Clyfters fliou’d be repeated: But they not prevail-
ing, I was lent for about fix Hours before the Patient
died : I found him complaining of a violent Pain in all
the Region of the Abdomen \ a frequent Inclination to
vomit ; having a great Difficulty of breaching, together
with a very Bow Pulfe ; his Belly being as hard as a
Stone, tho’ not fwell’d.

This lad Indication made me conclude, that the
DiCcafe was a violent Contrailion of the Abdominal
Mufcles, which had overcome the Diaphragm, and that
probably the Inteflim might be forc’d into the Thorax,

I was the more confirm’d in this Opinion from the
Examples of the like Cafe, which I ftiall fliortly lay be-
fore the Society ; upon w'hich 1 order’d a Fomentation
=of hot Milk, adding to every Quart a Drachmtjf Liquid
Laudanum, which in thefe Maladies gives great Relief.*
But before it cou’d be got ready, the Patient expir’d in
a violent Convulfion.

My Opinion having been highly cenfur’d by the
tvyo Phyficians; I open’d thisr Gentleman, to juftifie
ray felf, or to own my Fault openly, if I had been mi-
ilaken : But as the thing happen’d as I conje<3ured,
thofe Gentlemen will forgive me for taking the Liberty
of juftifying my felf. ^

In opening this Body, I found the Abdominal Muf-
cles fo much contradled, that it was almoft impoflible
to penetrate them with a very fharp Scalpel. Upon

( T9? )

Upon Examination, 1 found the Stomach empty, and
feme Parts of the Duodenum, but the fejunum and Ilium
io much diftended with the fermented Oat- Ale, that the
Ilium had four Inches of Diameter, and the Colon above
eight.

The Ilium was alfo pretty much inflam’d in its infe-
rior Part; and all the Valves of the Colon were oblite-
rated, by the great Diftention of that Inteflin,

But the greateft Difafter was, the Dilatation made in
Diaphragm, as I fuppos’d ; made jufl: upon the Chink
which remits the intercoftal Nerve to the l^i[cera of the
Abdomen, through which a Portion of the Colon was
forc’d, and the greateft Part of the Omentum and Pan-
creas.

Thefe tender Parts being choak’d, foon inflamed, a
Mortification of them following ; and a Rupture of the
Pancreatick Vein caus’d an internal Hemorrhage, which fill’d
all the left Cavity of the Thorax, infomuch that the
who’e left lobe of the Lungs was comprefs’d almoft un-
der the Muf cuius Scalenus.

The Quantity of extravas’d Blood was very great,
and it was not in the leaft coagulated.

I have brought the difeas’d Parts with me, to fiiew
the Society the Certainty of this Account, and I fliou’d
have been more particular in proving the Impoffibilicy
of the Antiperi^altick Motion ; if Dodlor Hagumot had
not prevented me by his Memoir.

This Gentleman is not far from Truth, and what he
fays is certain : but I am furpriz’d that the like Cafe
has not occurfd in his Prat^ice*

Vf. An

( m )

VI. Account of Tm late Northern Aurora's, as
they were ohferVd at the Vicarage of Sutton at
Hone in Kent. % the ^Verend Edmund Bar-
.rell, Trehend of Rochefter.

ON February the 5th 171^. at Eight at Night, an
Aurora Borealis appeared. Ft occupied at lead or
near ~ of the Horizon ; it was low, and fliot out bright
Rays, and, I believe, would have appeared very light,
had it not been that the Moon flione at the fame time,
being about Five Days old, and chat the Aurora dilap-
pear’d before the Moon fet^

Again, on the )oth of March following, there was
another Aurora Borealis 1 faw it not till paft Nine :
’was dim then, and its highell Part cover’d the lowed
Star in Cajftopea’s Chair. It did not feem due lAorth but
one Point to the iFejl. About Ten it Ihoc out very
bright 'Rays, high, and tending fomewhat towards one
another. Near Eleven a Clock, there was (befides the
northern firightnefs) a long Streak, not very broad,
extended Eafi and JVc/l' : Which beginning in the
fenV s^Headf near Hercules-Club, and covering Ar6furus,
proceeded max. Berenices Hair, and lb went ovtcCorLeonis,
and thence to the Canicula, and ended a little beyond
that Star. It flione very bright at fird, but faded away in
about Eight or Nine Minutes. If it had Motion (which
I am not lure of) it was Southward. I waited for the
next Fit of Brightnefs of the Aurora; and in about Se*
ven Minutes, the Eajlern Kart of the Streak, viz. from the
Serpent* S‘Head to near Berenices Hairy became vifible again
tho’dim, and was quite effaced in Four or Five Minutes
more : And I did not yet perceive any Change of its Place.
Finis.

Errata. Page 5’5’6. in the Note, lege Lib.xxxv. pag. j'6;.
line antepenult, lege AnderUa.

LO NDOJAf Printed for W. Innys, at the Princes Arms in
Sc. Paul s-Churcb-Tard, 1 7 17.

I , "'J,'

I ^ : ■

^Kan/cict: ^ J^'2.

I

%

(5^5 ) Number 352.

PHILOSOPHICAL

TRANSACTIONS,

For the Months of Jpr'dj May^ and June, 1717.

I. Jn Account of the Aurora Borealis, feen at Lon-
don, on the 30th of March laft, as it teas cu^
riouflj ohferVd by Martin Folkes, R. S. Soc.

II. Guilhelmi Mufgrave ^gide Societatis Socii^ de
Britannia quondam Toene-^hifula, T> I S S B ^
T At 10.

III. Extracls from Mr. Gafeoigne’^ and Mr. Crabtrie’i
Letters, proving Mr. Gafeoigne to haye been the
ln\entor of the Telefcopick Sights of Mathematical
InflrumentSy and not the French. !Bjy W. Derham,
Prebend of Windfor, and R. Soc. Soc.

IV. An Attempt towards the improyement of the Me~
thod of approximating., in the ExtraBion of the
^oots of Equations in Numbers. (By Brook Tay-
lor, Secretary to the Royal Society.

V. Broprietates qu^dam fimplices Sed:ionum Conica-
rum ex natura Focorum deduB^e 5 cum Theoremate
generali de Virtbus Centripetis 5 quorum ope Lex Virium
Centripetarum ad Focos SeFtionum tendentium, Velocita-
tes CoYporum in illisreyByentium^ gs* Deferiptio Orbtum
faciliime deter minantur. Ter Abr, de Moivre. R.S.Soc.

X X X X L An

( 5^6 )

L M Account of tk Aurora Borealis, at Lon-
don, on the 3 oth of March lafl, as it was cu^,
rioufly OhferVd by Mart^in Folkes, Efc['^ R. S. Soc.

BEing in the Street, between 8 and 9 a Clock on Sa-
turday lad,- (30 Martii) I perceiv’d a Lighp over the
Houles to the Northwards, Htrle inferiour to that the Full
Moon gives when (he firfl: rifes, Upon. this, fufpeding lome
fuch Meteor as we fawthe lafl; Year, 1 made all the halt
I could into the Fields, where I immediately found my
Conjedure. verified,; and was for fome time agreeably en-
tertain’d with the fight of an Aurora Borealis^ attended
with, moft of the Phenomena that have been delcribd ia
that very remarkable one of the 6th of March, 1 7 1 5-6.

The whole Northern Part of the Horizon was in the
fame manner cover’d with fomewhat refembling a very
confiderable Light, whole lower part was pretty well de-
fin’d by the common Edge of the Cloud, but the upper
dy’d away more gradually. This upper Limb of rhe Light
refembling the Arch of a Circle, whofe highefl Point be*
tween 9 and 10 of the Clock (when the Meteor was moft
confiderable) was elevated about Degrees, and bore, as
I imagin’d, about zo deg; Weft ward of the due North.
It touch’d the Horizon in the Weft at the difiance of about
65 or 70 Degrees from the North, whence the whole inter-
cepted Arc of the Horizon would have been of near
100 Deg. had not fome few Degrees in the Eaft been hid
by Clouds which lay between us and the Meteor.

The feeming black Cloud, when I firft (aw it, ran near-
ly parallel to the Horizon, and at the diftance of 6 or 7
Degreear but in about half an Hour it changed its Figure

very

( 5Sr )

very much, finking down in the North to about half
its height, and rifing in the Wed near as much. What
J principally took notice of this for, was that the Light
iduing from behind it did not change with it, but re-
main’d of the fame Figure, hovvever the Cloud ap-
proached or receded from differing Parts of its Limb.

There arofe at firft fome Streams in the N.N.fV, but
of no confiderable Length, few of them paffing j De-,
grees above the Arch ; but beginning from behind the
Teeming Cloud, To as to be about ix Degrees high in alL
They were Pointed at the Ends, and nearly vertical
to the Horizon. Between times there Was nothing but
the Arch to be feen, and that only refembling a com-
mon Aurora ; and again in an inftant, by a fort of tremu •
ious Motion, feveral Parts of it would appear convertcd
into a vad number of parallel Streams, for the mod part
very little higher than the Arclv it felf About xo Mi'
nuces before Ten, afmall part of the Arch, almod due
North, grew remarkably lighter than the red, and con-,
tinned to encreafe for about half a Minute ; when there
fuddenly broke out fome very tall Streams of at lead 6o
Degrees high, as I found by one in particular which arofe,
full North, and pading over the Pole .Star itfelf, reach’d
fome Degrees beyond it. This was the mod remarka-,
ble time of the Appearance, fome fuch Lances, though
not fo high, immediately fhooting out of the Place that
firdof all radiated, as did fome more a good way to,
the Ead. They were all nearly Perpendicular to the
Horizon, and mod of them did arife quire from the
black Subdanc*^ at bottom, tho* i faw fome few that did,
not reach fo low, appearing as if their lower Parts had
been broken off. Some of them were full as bright as
any 1 Taw the lad Year, the Axes fif 1 may fo call
them) of fome of, the called Streams coming up very

( 588 )

near to the Colour of that pale Fite we fee in feme
forts of Lightning.

About this time the Ground Weftward was all co-
ver’d with an odd fort of Mill:, the fame from which I
remember lad Year a great many People faid there
came an ill fmell, which I did not at all perceive ; how-
ever as I remember it to be the very fame Appearance, I
thought it might not be improper juft to take notice of it.

About 10 the Phenomenon very much decreas’d,
and fo continued till after 1 1 , only fending up now and
then 2. or 3 Streams. At half an Hour after ii it was
again pretty much encreas’d, and I faw it^^again fend
out fome Streams almoft as confiderable .as any I had
before feen this Evening ; the Arch yet continued, but
not fo entire ; and from wdiat I could judge, its mid-
dle was fome Degrees nearer the North than when I
firft took notice of it. Till a quarterof an Hour before
iz the light continually abated, .and then I left it; but '
a Watchman, 1 order’d. to bring* me an Account of it
next Morning, tells me it continued till towards Day-
break, but never ftream’d . remarkably after I w’enc a-
way.

Tho’ I could. not this time fee any Stars through
vthe black Matter at Bottom, l am fenfible it was not a
Cloud, tho’ tit bore the refemblance of one; for when
a real Cloud (as fevcral fmall ones didj came over
any part of it, their difference was very confpicuous.

I have ftnee receiv’d two Letters, one from Wislkh
in the Mle of El'^^ the other from within iq Miles of
the ' both which take notice of it, tho’ with no
further Particulars, than that on Saturday Night, they
had feen the fame Light, tho’ not fo confiderable, as in
fethe beginning of March the iaft Year,

II. Guil-

( 5 8? )

II. Guilhelmi Mufgrave Soaetatis Sodi^ de
Britannia quondam pome Infula^ D IS S

U M Belgmm noftrum a Britunnico adluitur 0»

ceano, illo latere Infulse hajus triquetrse, quod eft
ex adverfo GallU ; vifum mihi fuit, pnufquam id de-
fcribere conarer, antiquam & diuagitatam movere quse-
flionem, .de Britannia cum GaUu conjundioue, &, an
revera unquam eflet, exquirere.

' PR/IMUM igitur, pofita Cherfonefo Britanmca^
urrum exedi potueric i Deinde, utrum exefa fueric, ediG-
feram.

* D E priori propterea dicendum, quod a dodd &
magni nominis Viro, Vojftorum altero, ftrenue negatum
fit, unquam, ubi hodie Fretum eft, fuifle Cheribnefum:
& quidem ideo negatum, quoniam, illo fentiente, nihil
oi deterendae dividendaeque par inveniatur. Uc Tapro*
banam (Infulam Ct)lon'^ a vicina continente non avelli
probet Vir ClarifE [Otio (a), inquit, abundant, qui ifttuf-
wedi fahelUs:, jam mi flies froduBis, totiefq; reco~

Bis, aurem commodant. ^am conflans © tenoris fui eh-
fervans Jit rerum natura, patet e Bojporis^ omnihufque omni-
um terrarum Fretis. lis cum pracipue Mariam & ipjius
Oceani vis femper incuhutrit, eadem tamen uhique a tot an-
fjoram millibus & ah ipfo, ut verifmile efi, rerum exordio,
■fervaret intervalla. Currant licet, ac recurrant JJnd/R, al-
latrent undequaque FluBus, fortius ejl Elementum quod re-

-fa) In Notis ad Mclam., i

7 AT 10.

Y y y y

JiJIit

JifUtf qaam quod oppuguat. Exeji Scopuli, ac vafla marit
'atitrd, fafil ubique ojhndunt, quantum Oceani impetus lapfu
feculorum pojfit efficerex vzrum h£c ipfa qucque, quid non
fojjtt efficere Ocemus, multercUrius ofiendunt.]

Haec Ifaacus.

UT' difputationem ea de^re ingrediar, Vir hie Cla-
riff Naturse, ncc qua agit ilia nec qua paticur, flatum
ac conditionem, ex omni parte, fic, ut eft revera, ani-
mo fatis advertifle videtur. Cum nen de Taprohan£ fo-
lum FretQ commentatur, fed de Fretis in univerfum, &
quidem Argumento a conjlante tenoris fui ohjervante
reram natura accepto, videamus quam hsec cum Ocea-
nis & Freto noftris convenianc, & in iis quam conftan-
ter agat Natura.

OCEANI Britannici^ prout nunc dierum eft, cum
latitudo turn profunditas inveftiganda, ut ex iis de
prifeo feu Freto, five Sinu, poflimus fententiam ferre.
Ut autem eas comperiamus, adeunda eft Tabula Hal-
leiana, fui generis omnium accuratilTima, ex juftii Regis
Guilhelmi ejus nominis Tertii conftrudJa. Ea docemur,
in Oeeano Britannko, ubi Terrarum hiatus, hac iliac
ampliflimus eft, a veterum OcrinoiLizard-Point) ad Infu-
1am ei oppofitam ZJfhant, unum efie gradumeum femifle,
id eft Leucas quafi triginta, five milliaria fo. Hinc
Oceanus fe in oriente parum adducit, at multo magis
ubi Promontori um in eum procurrit Normannkum : ibi
enim eft dimidio addudiorj cum inter Feverel-Point,
& Cap. de Hague e regione ftta, Leucarum Anglkarum quafi
i6 diftantia fit. Tunc fe iterum effundit, ubi Sequa-
nam recipit; at brevi in ardlum agitur, inter Beachf-
Head & Qape St. P'allery. Dein paulatim anguftior, fa-
ftigiat fe molliter, ufque dum in Fretum contrahitur^
inter Nefs Angiorumt & Gallorum Blacknefs, non ampli**
us o(fto Leucis, id eft: 24 milliaribus patens. Terrs

tunc

/ -

( 5P* )

tunc aperiuntur longe lateque vaftilTimc, & fpatium
Mari faciunc GtrmAntco.

func Oceani Fretique^Sr/w^^/V/ Jiverfe lacitu-
dines; quibus apparef, eas, fi non coritinuo, tamen adeo
rara tamque exigua cum ampliatione minui, ut argii-
mento noftro nihil inde queac derogari. Tta cnim O'
ceanus contrahitufj ut qui initio, feu Facicibus ejus -5;'/-
tanniciSi Leucas triginta, five Milljaria prsterpropter
nonaginta latus fit, poft Leucas 153. circiter, five
Milliaria 460, (quae hujus Oceani longitudo eft) ad ^4
milliaria contrahatur; id eft ad prim^e latitudinis par-
tem quafu quartam.

PROFUNDA hujus Oceani altero jam loco funt
Cxpifcanda, & quidem optime beneficio ejufdem Tabu-
la. In ea dividitur Oceanus Bntannicus una cum Fre-
to, in Columellas numero decern, oblongas. Harum
fingulae latera funt ex circulis Meridianis accepta ; qu£C
cum in piano duda finr, yidentur efte ^reita. Colu-
ipelhe terminantur adverfis GMU ;

hoc eft, Lineis hue illuc curvatis in litorum morem. "

INCIPIAMUS a prima in occidente, quae &
iongiflima Columella eft : & (prsemiftb, quod Hibernia
Am & Galliam inter, Oceanus orgyias alt us fit in locis
compluribus o(ftoginta; iiti paulo ulteiius in a perto
Mari, 100, 12,0, 140) notandae funt in prima CdlumeTIa
frofunditates omnium akiftimae ; quse decies exploratJe fe
habent, ut 58, 66, 63, 6 58, 65, 68, 60,. 60, 60., quae
profupditatum Summae faciunt 6zy orgyias, Lae per de-
cern, i* e. pofunditatum numerurh, divifae, mediam ea-
rum profunditAtem oftendunt efte 62.

IN Columella altera, decem altiflimarum media fro'
funditaSi fimili modo inveftigata, eft orgyise 51. In
tertia 51. In quarta 40. In quinta 43. Infexta 40.
In feptima 36. In oeftava 37. In nona ^ ^. Poft no-
nam Columellam, cum Oceanus in laevam fleeftitur, &

Y y y y 1 * obli-

( 59* )

obliquas iii Ftetum defmit, accipiam illud ut Terris in-
terjacet, in Britannia lo^is appellatis $outh-ForeUnd &t
Haftings, in Gallia, St, Valery & Bftaples inclufum. Hie
frofurjditatum dQczm media eft 30, In Freto anguftiffi-
mo 16 : quae ad profunditacem mediam in prima Colu-
mella, eft, uc 16 ad 62; id eft, ut i ad 4 fere; & ad
altiftimam profundicatem Galliam inter Hjherniamque, uc
16 ad 80, i. e._ i^t i ad 5 .* ad alciftimam in aperto
Mari, uc 16 ad' 140 ; i. e. ut i ad 9 fere.

QU A proportione minuitur altitude Maris, ea crefeic
Terrae Mari fubjedtae acclivitas; & eft illi inratione in»
verfa; quae udque propofitio, .ft non exomni parte ve-
ra, ('propter orbis figuram rninim^ rotundam) tamen
adeo vera: proxima eft, ut argumentatiohi noftrae fuffi-
ciat. Eft ergo Terra, in Freto noftro anguftilfimo un-
dis fubjeda, quam in Oceani Britannici faucibus, or-
gyias 46, id eft pedes z 76 aftior ; & quam Terra, Gal^
Ham Hihernidmque inter, Oceano fubjeda, orgyias <^4,
five pedes 384 altior s & quam Terra, aperto Mari fub-
jeda, iz4 orgyias, five pedes 744 altior. Vide quanta
fit Terrce ab alto Mari ad Fretum accliviras; eaque uc
ex cakulo prkdido patet, fere continua, Hxc eft O-
ceani Britannici,, tarn in illius Laticiidine, quam Pro*
funditate contradio,

AGE, nunc tendamiES ultra, velis expanfts, in Oce-
anum Germanicum: Hie Mare fubito patentius. ftc, uc
etiam ■'profund ius/ qUpd ititer Promontoria l^orth-fore*
iandy Orfordnefst Oppida Cai/^/»w & interfluic de^

cem maxirrias habet menfuras. quarum media z4 Qrgyi-
as cum f continec : quod inter /rfirdrjefsf & Tarraouthi
Texdlam & Oflenddm eft, maximas decern men I’uras ha-
ber, quarum media 2 y Orgyias cum, 7. Quicquid ul-
tra eft, Terris,' --hinc ad oeddentem illmc ad orientem,
fe retrahentibuS', vaftilTimus eft Oceanus, .in quo mem
furae func ab orgyi'is 4*5 ad 5'6''numef6 quaniplutite.

H^C

( 593 )

H /E C a Freto Britarmko tarn in orience, quam oc*
cidente Terrs declivicas (qus a Maris alticudine utro-
biquc auda patefit) omnino probatT in iffo Freto jugum
e(fe Terra exeelfumy. acutum ; quod cum hodie non mul-
tum infra Maris fuperficiem die reperiatur, olim fc emei'
gere, hoc eft Cherronefum olim fiic fui^e, monflrat.

ALIA funt duo, qus cum in hac re momenti fine
immenfi, tenore rum minus cerco, & nacura minus funt
conftanci; quandoquidem a Maris motu & ventis ac-
cepca. In refluxu Maris Aqus nunc quiefeentes incu-
bant areas ; nunc earn mollicer prsterlabuntur. In
situ miciori, Litus & ima Rupium blandidime lam-
bunt, tenerrime ofculantur. Fervente vero situ, res
omnino alia eft: Aquarum Fremitus auditur, Fludtus
cernunrur, & fe non parum attollunt. Nihilominus fine
multa ftrage, terrifve aliquot annorum millibus exefis,
hsc omnia pofle fieri, cum yojjio, cogitandum eft.

S I N sftuanti Mari, quod alcero loco dicendum eft,
Ventus fuperveniat (F/4? autera Ventus fie, ut vdt, Sz
quis ei tempos fiatueric, aut modum impofueric?) pa-
ps ! quoti, quantique Fludus advolvuntur ! Alpes exifti-
mare licet Cryftallinos, nifi quod, cito diifluant. Mon-
tem enim Mons invadit, detrudit, difeutit ; tantifper
ejus fpoliis adau6tus, dum in coelum altiffimus exurgic_
Aqus Mons. Tanta vis Aquarum ex Oceano Occident
tali in Britannicum immittetur, & tanto impetu, quan-
tus in univerfo Terrarum orbe rams inveniatur; imo
quantus ab ipfo rerum initio rarifiime. Oceani Britan-
niei turn brevia, turn anguftis, continue poene (quod
ofienfum eft) creicentes, faciunt, ut Aqus fic impulfs
iuirum in modum elevencur,. & in Ifthmum fquem
argument! gratia fuifle damus) arietenr, ita ut ab iis
Ifthmum exundari, deteri, ablui ; ficque Infulam . fieri.
Brhanniam non videatur dS'uvd'rm verum e contra-
rio fadu probabile, Quants Ventorum, at prscipue

Zs'

( 594 )

Zeplryri Cauriq; virtutes fine, in cogendo impellendoq;
hoc Oceano Brttamko, paucis expendam, a DodiiiTimo
viro Rad. Bohun, (Novi olim Colkgii Socio, qui de Men-
tis omnium erudiciflime fcripfiO hac in re adjutus.

E T I A M S I Zephyrus a Poetis vitam rehus ferre di-
cacur.

<*r, ejufyue tefentihus auris

Laxent Arva Sims\ — —
interdum ita fit, ut

— — Euriq'-i 2,efhyriq\ tenet domus ; & ut
— — !Zefhyo multa turhentur arenae.

Adeo fevus, horribilis, iracundus faepe Zephyrus, Vires
in Oceano, qui Europdm & Americam vaftus interjacet,
acquirens, & in ampliffimo hocce campo recenfens, vix
concipi poceft, quanto BritannU Galliaique oras impetu
invadac. Exploratidimum enim eft, in hafee oras eum
communirer anni plus dimidio flare, (quod jam olim a
Julio Cafare notatum) & flacu eas fteviftime verberaie.*
maxime autumno, a quo fumunt originem Tempeftates
Idiomate noftro dicftiE [Michaelmafs-S terms'] eumq; adeo
interdum fevire, ut ft cum reftu fervente jungi Ventus
hie acciderit, tarn Oceanus Britannieus, quam Frerum
Sahrtnianum immane quantum augeantur. Sahrina va-
ftiflime turget. UzelU longe lateque Somerfettenfem
Agrum exundat; Mirum ab hifce Cataclyfmis quantum
mea patria perpefta eft. Continuatur reftus ad ufque
Tevpkeshry, id eft milliaria magis ducenta. Apud Chef-
fiovp Aqua pedes interdum odoginta aflhrgit. Idem
fere dicendum de Oceano Britannico, Venti ejufdem
viribus elato: nifi quod hie, Cherfonefo ^am effrada,
liberius Aquse moveantur, non adeo ftftantur, non
tantum eleventur; qqse utique Aquarum libertas ante
Cherfonefum abrupcam, nequaquam adeo magna efle
potuit.

HAC

( 595 )

H A C igitur de caufa [Zefhyro nempe, Cauro, five
alio Ventorum aliquo, Maris seftui fuperveniente] Oce-
ani Britannki Undam in Ifthmum validiffime impingi,
& ab illis primum ejus fuperficiemf quae ex Silice &
Cake Cprout hodie Terrae e regione oppoficte^ confta-
banr, ablui ; deinde Iflhmi quod rcliquum erac, fpatio
bis mille annorum & eo ampiius. Aquae fluxu refluxuq;
ad 1 6 orgyias, quce hodierna Freti hujus Fquod dixi-
mus^ alticudo eft, atteri credibile, verifimile eft,

T A N T U M abeft, ut Vejfio^ Fretorum perpetuita-
tem a naturae in operjbus fuis conflantia tenoreque eodem
arguenti, fidem habeamus, ut e contrario Fretum hocce
noftrum illius i/JC6»fia»tU deberi, lubens agnofcerem^
Vir ille c!a.riftimus, naturae ufitatum agendi modum
unice rerptciens, extraoydharium fratermifit ; qui tamen,
in raris huju(modi effedis, potifTime videtur rerpicien-
dus. In Freto Siculo confiderando, ejufque diducendi
modo inveftigando, quis Ignis fubterranei fupra mo-
dum erumpent^’s, tamquam Caufe hac in re probabilis,
non meminerit? nifi iftam Catanenfium d'ro'mctv con-
fecutus, qui (tradente Alphonfo f Boreh) poft Eruptio-
nem diu intermifTam, Ignem ejus immodicum ne^
femel quid&m unquam fuifle, latis infulfe putavcre. Ut
Vento nihil inconftantius, fic ad Fretum hoc apcrien-
dum (pofito caufarum apparatu c^tero) nihil conducibi-
lius: & cum CO res deduda eft, fortiui dementum ejfe
quod oppugmt, quam quod refiflitf Calicer quam Fojfws
ftatuit) omnino probabile mihi videtur Salmajjum ille,
Virum & candidum & dodum convellic, quod de
Navibus ablque Coftis & Interamentis, ita fcripfic, ac
fi in HurgundU manfiftet, nec quid rei Navis aur Mare
forct, intellexiflet. Nequeo Tatis Ifaacum mirari, quod de
Mari & Ventis fcriptor luculentus, horum vires in Marit

-j- In Libro de Irtcendiis Mtn<» p. 1I7>

tUft

( 596 )

tiirbando agitandoque, in terris obrucndis abrnmpendi(q;
prorfus omicteret; atque adeoquod BatAvus : ea

fcil. Regione oriundus, qux Mari & Venro tarn obnoxia,
NON alienum eric hie Inundarionum aliquot ex-
cmpla, uti revera fuere, in medium proferrei quibus
abunde patet, Terrse faciem frequenter obrui, & ab iis
non parum mutari, Hie autem nihil necefle eft, uc
fielken ^ Burin ^ Jc hai ^ Urhes adeamus: de quibus
tamquam magnarum Inundationujn argumencis, (i^
OvidiuSj & diu ante ilium Arifioteles. Graviftimas
fuifle Oceani noftri, tarn Germnnici quam Britannici,
(atis oftendunc Hiftorici Geographique.

IN Zeelandid (3) Infulx undecem, & in iis Oppida
Pagi fquorum hodie fummitaces aliquae, refluxu Maris
in conlpedum veniunr) numero ter centum (^) obrue-
bantur.

ANNO 1014. [fl^are Lit us egreditur III. Cal, Odoh.
^ in Anglia VtlUs quamplurimas innunterabilemffue fofuH
multitudimm fummer/it.] (q) Simeonis Dunelmenjis Hiftoria
<^de Geftis Regum Anglorum De hac, ut opinor, Inunda-
tione videatur etiam Chronicon Job. Brompton (6),
ANNO 1099. [Tertio Non. Novemh. mare Litus egre-
ditur ^ villas & homines cpuamplures, Boves Oves in-

numeras demerfit\.Sim. Dundmenfis (7) Hiftoria.

A D. 1176 [Mare extra fines in Anglia erumpens muU
tos in Hollandia homines d? pccora abforhuit, df quap

/i) Invenies fub Aquis, 8c adhuc oftendcre nauta
^Inclinata folent cum mcenibus oppida verfis.

1 Metam. Lib. 15.

(i-) Ta Apdreyev ffviiA'Ati 7«T0it tv ydg,

yip^Ai apA^a^n/xATA v»r.\AKii, KvyLATaip verS

tAiV eLv'l^rpAKO'TrlA ’JTOjl <A' •ffg/i'O’/Jf f/OvLoU, cS isSfUTAI OTei 'E-

r<iKLuu re ^ Anji.de Mundo, (3) Heylin's Geogr. L. 2, In Belgio.

Deicriptione Belgii, pag. 124. (5) Apud Hiftoria Anglican^
Sci iptores X. pag. 1 71. iT6j Apud cofdcm, pag. 8p2. p^’Fag. 224. '

fofi

597 )

■fe(l hiduum furore fedato in [emet ipfum red/if.] Chroni-
con Johannis Brompton, (8) <

1 N S OL I T A M maris inflationem & commotionem
Anno D. 1x50. fadJam, cradic Matth^eus (9^ PArifienfis.
^nde Mare pert urhatum finei /elites pertranfiens, tarn herri-
hiltm mugitum cum fremitu tdidit, ut per remota Teir£
./pittAf non fine jlupore audientium, r el caret. Vi/utn e/i
etiam fuh opaca nocie ip/um Fretum quafi accenfum ardcre,
^ Flu^us FluPHhus conglomerates dimteare. Apud Win"
chelefe plufquam 300 domus cum quihu/dam Ecclefis per
Maris violentum a/cen/um funt fuhmerfe.]

A NN O 1151.. inquic idem (lo) Matthaus [In Frigia
Frifeiandia appellatur) Aqua Diluvium fecit particu-

■ lare, occupans Terra illius fpatium itineris circiter feptem
dierum. Pojl 40 dies Hie damnofus FluHus in locum juum

■ remeavit ]

ANNO ii86. [Tngruente fortijftmo Vento, fiante de
part Hus Orientis, qui & Eurus dicitur, flux u Maris
fuper provinciam Hollandix terrihiliter iuvalefcente, prdva-
luerunt Aqua Maris, adeo ut Foffata, qua Terr am ip/am
Mare dijlerminant, inopinatifts quam credi poterat, tranfgrc'
derentur; pofuitque Terram fruHiferam in falfuginem tarn
repentinus Maris impetus 5 qui per indigenas nullatenus po^
ter at obviari .* ^ maxima pars S. Botolfi (uhmerfa, homi-
numque ^ pecudum ina/limahilis periit multitudol] Ita
Chronicon Tho. (11} Wikesi,

FIellandi<e Inundatione fic Hadrianus Junius (sij
in Batavia Hiftoria ^fiPuadringentis abhinc annis inaudit a
ilia Inundatione qua univerfam Hollandix faciem longe
latcque eperuit, ob/lruHo fluminis (Rheni) curfu, fleriles
arenarum colles Litus occuparunt^ Mare, Terras, ipfamque
Litoris oram attrivit\

<8) pag. 1-117. (-9) Pag. 53 j. Ed. WatRana,

Cl i) Pag. 114. (iz)Pag. 156,

Z z z z

(lo; Pag. 549.

ANNO

( 59^ )

ANNO 1404. quo beatinTimus nofter Wiccdmus
obiit, [Tanta repe/ite ruptis limitibus irrupit Aquarum in-
fiuintia in Cant io, quanta nunquakj fu:rat illtc ante vifa,
qua [uhmsrfa funt ammalia numtro ^ pretio excfjjive: nec
Jolummodo d flevit Anglia damna talia, fed ut fertur, Se-
iandia) Flandria ^ Hoilandia, per Undarum excrementa,
innumerabilia ftnjit di'^pendia eo'anno] Hypodigmate
ftria Tho. Wdlfingham,

[R EG N ANTE Edwardo I. cum Oceanus ventorttm
•violentia exafperatus, hunc ("Cantii) traBum speruijfet, lafeq;
hominum^p corum adificiorumque firagem dedijfet, (jr Brom-
hill viculo frtquente peffundato; etiam Rother, ^ hic prius
fe in Oceanum exoneravit^ alvee emovit^ oftiumque ohfiruxit,
novo in Mare aditu compendii per Rhiam aperto ] Camdenus
in Britannia Cantia.

Q^U I D quod Tungros^ oppidulum Leodicnfe, a Mari
pene centum milliarta jam remocum, Mare quondam
adluere opinaci funt Viri dodiflimi, argumento non uno
perfuafi ( £4).

N EC^U E noftra xcas caruic hujufmodi Exundacio-
nibus : Narrant Novellx Feh, 27. 1719. \n£{fexia, plura
Terras jugerum millia, per milliaria aliquot, inter Bark-
ing & Purfleet, everfis obftaculis, Maris influxu obrui.

C dc Occani Germanici exundationibus .* Britan-
mci noftri, & Sahrin<ie, neque pauciores, ncque minores
funt. Enimvero vidimus setace noftra Iflhmum, uno
eodemque Pedredi fluxu & refluxu (Terras fupecficie
prius ab Agricolis (emota) dilui, fluviumque veteri
curfu relido novum acquirere: hoc, inquam, unico fluvii
jflius aeftu fadum vidimus, nullo auxilium prsebentc
vcl Undas adigente Vento.

(15) Pag. 564 F-d Francofurt. MDCIII. (14) Antiqoi-

tie?, pag. 102. Bay s Phyfico-Theological Difcourl'es,.]^^. pag. 16^.

S A-

( 599 )

S A B R I N fluminis impulfu fieri probabils eft
Exundationem illam, qua in Agrp MonumetenJj, Paroe-
ciae N®. 26. A. D. 1607. Januario Aqui obrueren-
tur: Cujus eodem Anno publicata fuit (15) Hiftoriola.

J O H A N N E rerum AvgUcurum potito [Subita ^
improvifa Acfuarjtnt hundatio plurilus in Iccis per Angliam
fa£fa eft, unde pl'ures fjominei fubmer/j funt, ^ domus everfd,
waxime apud Exceftre dr San^um Ivonem ] Imagines Hi-
ftoriarum Autore 0 6) Fiidulfo de Diceto, [Poftdiucinam
malaciam, mare Vergivinm, adeo per totam hy^emem,
regnance tunc Henrico (ecundo, tempeftatibus agitaba-
tur, ut toco illo temporis fpatio, Navicula nuHa ad
iTiherniam 2id'p\\\{^y de reliquo terrarum orbe nihil apud
earn inauditum. Terror hinc univerfus, tamquam malo
impendence quodam gravi, de ca:Jis mific. Arenarum ag-
gere?,in Auftrali<T4wi’/M, quafi Cacaclyfmo, abluebantur,
Litora fubvertebantur] Giraldi Camlrenfis (17) HihernU
expugnata

AT 6 quam terribilis ilia tempeftas, qua. Maris
Undam in Oceanum Britannicum impellente AfricOy ica
ille turgebat, uc Pharos ilia celeberrima, Eddiftone ap-
pellaia, qurs fuit e regione Tlimutha, tamquam in con-
teraptum ^oli Neptuni^^ue fabricata, quafi ludibrio habita
fimul cum tEdificatorc dirueretur. Cujus utique tem-
peftatis in hoc noflro Oceano fi non eadem vis &
potefias eile videacur, arque illarum in preedidis Oceani
Germanici Exundationibus, propter majorem ab hifce
ftragem & damnum in Hollandh !ZeelAnd}aq'-i fadam;
Litoribus hoc noftris rupibus munitis, quae & duriores
& altiores quam apud Batavos Tunc, deberi judico.

TEMPESTATES fut argumentum hoc confi-
ciam^ qute'in Oceanis Germanico & BritanntcOy noftra

(15) Lamentable News from Monmouthfhirc. (i<J) Pa^. 710.
(17) Capo XXXV.

Z Z Z Z 2

&

( 6oo )

& patrum memoria faeviere, & de quibus omnino con-
flat, adeo fuere turbulentae, ut fi earum aliquae in
Cherfonefum, ad hofce dies ufque manentem, redla fu-
iflent collineacx, nullus (ut opinor) eflet dubicandi locus,
quin a tanta vi auferretur Ifthmus: & tot annorum
feculis, quoc illico dicentur, revera hoc accidifle^ ne-.
quaquam improbabile videtur.

S I N ex America turbo maris aeftui fuperveniat, mare,
ctelum, omnia mifcens, omnia confandens, ac fi nature
inflaret diflblurio, ( pofle veto hxc concurrcre nemo
fanx mentis ibit inficias) En caufam huic negorio parem !

ALTER UM hujus Diflertationis m-mbrum jam
aggrediamur, & fpcciatim inquiramus, utrum exefa
fuerit revera hxc Clierfonefus ; annon. Si de ejus di-
videndx modo, qui fieri poflet, conveniat, magna inde
lux emanabit, unde argumenta, qux a Viris dodlis
paffim afleruntur, ad divifionis hujus probabilitarem
arguendam, egregie confirmabuntur; pramillb nempc
(quod haolenus fuit defideratum) Vento, ejufque in
elidendo hoc Ifthmo virtute omnium caufarum maxima,
tantoque negotio (cum cxteris) pari Horum ego ar-
gumentorum ncnnulla perfequar; fed levicer tangam,
utpote ab aliis fufius antehac tradata.

PRIMO, Terrx jugum illud notabile, quod Freto
fubjicitur, & de quo fupra ; quid a'iud fibi vult, quam
quod CO loci Terra olim multo altior eflet ; at Maris
per aliquot annorum millia reciprocatiombus, ad eum
in quo nunc eft flatum abluta & detrita? Prxeipue, fl
advertamus Regulam hanc conflantem & perpetux ve-
ritatis efle, Maris Icil. imum, quo magis Oceano prdterla^
hente tritum, (quantum patitur ejus durities') eo magis
planum ^ aquale reddK

QUID deinde Rupes in Freti Litoribus oppofitis,
five Montes prxrupti, aibi, ex cadem materia, Calce
nimirum ^ filice compofiti, ad fex uirobique milliaria,

flbi

( 6ot )

fibi invicem, tamquam Tefler^e refponderttes ,♦ quid, i/i-
quam, volunt, nifi olim intsrfringi fe, & ablucione
Terras interpofit^E difrumpi?

TERTiUM, apprime convenit cum ifthac Cher-
fonefi Britannic^ opinions, tradus illius, qui hodie
Ruinnty Mdrfh appellatur, ratio & ingenium. Durance
enim Iflhmo, cum Occani fluxus eo tamquam obice
fifteretur, icftuare cum necefle erat, atque adco Terram
illam Rumneiinfem^ uipots plaram & humilem, in pro-
pinquo exundare Hoc otlendunc Oceani Britannki
Fluxus. bodiequs hac planicie alcior.es, aggere fohifli-
mo & magnis lumtibus afpulii .• Dentes item oQendunc,
atque Olla, five Hi|^popotami five alius cujufdam
marini animalis («8^, anno 1668, Chart hami,' 2\x\i\xd\nQ
pedum 17, diim puteus aperiretur, eruta : at luce clarius
oftendit -^nchora non ita pridem ex alto loca hac
circiter effoda. Pcrrupto autem Iftlimo obicequejam
remoco, OCeani unda fubfidic, a Terra ilia recelTit, in
alveum* fe contraxic ; unde'quae olim ^duarium, hodie
Planities, longa viginti milliaria, lata odfo, eaque fer-'
tililTima bobus faginandis aptiflima reperitur.

N O V I S S i M E, fac Cherfonelum olim fuilTe, Lu-'
pos, aliaque animalia, generi humano inimica, pode
hue migrate, conceptu facillimum eft: at ft ilia non'
fuic, navigiis ea tamquam ad tuendas & conlervandas ■
eorum .species, advehi, ftulte cogitabimus ^

NbC^E me moratur, quod nulla fwQ Latinorum^'
(\WQ Gr£corum<i five' alius cjjufvis populi Hiftoria Chcr-
fonefi hujus abrupcic mentioncm feciftTe perhibeatur,
Cquamvis hoc nequaquam ex omni parte verum:) Die
(odes, Hiftorix quam brevis ftc secas, ft ad cetacem
mundi comparetur. A rerum initio ad primam, quas

(18) Vide Clirifll Diatribam Chart}>am-Ne'WS appcllatum ;

Aftorr.m Rhilofoph. No. 272. Et Clarifr'^^////?i de hac Cherfonefo Dif=
fertationera. Ad, Phil, No. 275.

nunc

( <5oz )

' nunc exftat (i. e- Herodoti) Hiftoriam, .3500 circiter
anni funt; & a Ifoa Diluvio, 1800. At cam immenfo
temporis fpatio Cquod fupra innuimus) qua? Caufarutn
accidere poflint cv^vylcu ; qu^eque ex iis in orbe noftro
fieri mutationes, nemo cam cito ftatuere debebic.

D I X I hoc mqtiaquAm ex mni parte veram : quid
enim planius illo VirgHii^

— Tenitus toto divifos orhe Britannos.

futatis, (inquic eruditifljmus & Anciquiratum
Pifit Annie AY um fcierttifilmus (19) Joh, Twinui) vocahulum
[divilos] hAhere earn vim ut fignificAt AhfciJJionem alicujus
ah Aliquot Et Angler em mire gnarum Jigni^cationis fuijfe,
& rerum antiquArum maxime peritum, ^ bene memorem
fait Ad h£C verba Servius [^ia olim junlla fuit Orbi
'Britannia.] Nihil clarius efie poteft ad demonftrandum
ifihmi hujus divifionem veteribus fuifie notam. Uc
omnino fruftra efie P'ojJiuSy & nimio plus VTo^ea-st cTou-
. ?vei>eiv exiftimetur, cum in Fabellis jeEgyptiacis (quo
nempe fuse opinioni habcatur honos^ earn poni voiu-
erit

CONCLUpIMUS ergo e praedidis fimul acce
pcis, Britanniam non jam inde ab initio fuifje Infulam ,
fed ex Pane-fnfula fa6tam: idque ut videtur^ a Vento e
fdviorihus aliquo, cum Maris afiu concurrente ^ Jfthmum
perrumpente.

^ij>) De rebus AWionicUy pag. 22.

ExtraSfs

( <5o3 )

III. ExtraSis from Mr. GafcoigneV and Mr. Crab-
trie x Letters, proVing Mr. Gafcoignc to haye
. been the Inventor of the Telefcopick Sights of
Mathematical hiftruments^ and not the French.
!By W. Deiham, Trehend of Windfor, and
R* Soc. Soc.

IN Monfieur de U Hire's firfl Part of his T alula A>
(Iron, publifhed in 1687. I find an Invention,
which was undoubtedly our Countryman Mr. Ga[~
coignes, afcribed to Monfieur Picard, and that is, the
.application of Telefcopick Sights to Aflronomir.al Infiru»
ments. Mr. de la Hires Words are, Paucis ahhinc an-
nis D. Picard infignis Aflronomus, afcjue in eadem Acade-
mia ^ Regia Scientiarurn\ Socius, Dioptrarum crenas ah in-
firumentis fujlulit, eorumque loco fuhfiituit Telefcopia ;
res Predytis Myopikus,8iC. In which Words it is not
indeed exprefly (aid that Mr. Picard was the Inventor
of this way, but only that he applied Telefcopes. But
by reafon it implies that it was that curious and in-
genious Gentleman Mr. Picards Invention, and it is in
effecfl: claimed as luch, in Monfieur Auzout's Account
of the Telefcopick Micrometer^ in the Philof Tranf. No. xi.
therefore I think my felf in Duty bound, to do that
young but ingenious Gentleman, Mr. Gafcoigne. the
Juftice, to aflert his Invention to him ; by reafon all
his Papers, that by the late ingenious Mr. Torvnelefs
Diligence could be picked up, are now ^together with
Mu Towneleys own Papers^ in my Hands.

As for the Invention of the Micrometer, which Mr.

, A uz>out claims as his and Monfieur Picards, I fliall fay
little to it, Mr. TortneUj having fufficiently prov’d it to
be Mr. Gafeoignes, in the Philof. Jranfa^' No. And
the OeCcriptions and Draughts of that, and Come other
Jndruments of that kind, are now by me, in Mr. Gaf-
ceigne's own Hand, to confirm Mr. Torvnekjs Account,
if occafion were.

(And, as Mr. Gafcoigne.'^2LS x\\Q, .firft that meafured the
Diameters of the Planets, ^c, by a Micrometer r fb I
fhall prove that he was the firft that applied Telefcopick
Sights fo Aftronomical Inftruments. In a long Letter
to his fagacious Friend Mr Crahtrie, of Jan. 164V
C wherein he deferibes his Micrometer, and ihews his
way of finding the Refradtions, the Moon’s Parallax,
and how he meafured the Diameters of the Planets)
Mn Gafeoigne tells him how the meafuring Glajfes, which
he had been (peaking of, might be applied to a
Quadrant. If, faith he, here (that is in the Diftindi-
Bafe) place the Scale that meafures — , cr if here an
Hair he fet, that it appear per f elf If through the 6lafs—r.,
you may ufe it in a ^adrant\ for the finding of the Alti*
fude of the leaf Star vifihle hf the Perfpeliive wherein it
is. If the Night be (0 dark, that the Hair or the Point-
ers . of the Scale he not to he feen, I place a Candle in n
Lam horn, fo as it cafi Light fuficient into the Glafs^^
which I find very helpful when the Moon appear eth not, or
it is not othenvije light enough.

In another Letter, dated on Chriftmas Eve 1641.
fwlierein he deferibes the Wheel Work of his Micro-
meter, and Ihews how he could apply it to the taking
of three Points ; and fpecifies his ()bfervations of the
Diameters of the Sun and Moon; and mentions a Theory
he had contriv'd of the Sun ; &c. and faith what pains
he had taken in the Anatomy of the Eye) he tells Mr.

Crab-

( <5o5 )

Crahtrie how he had applied his Telefcopick Sights to
a Sextant. Saith he, Mr. Horrox hh Theory of the Moon
J (hall be fhortly furntihed to try. for I am fitting my Sex^
tant for all manner of Obfervations, by trro Perfpicills mth
Threads. And alfo I am confulting my Workman about
the making of Wheels like (i. of f Diagr. 3, to uje

trro Glajfes like a Seilor. If I once have my Tools in rea-
dinefs to my Defire,! fhallufe them every Night. I have fitted
my Sextant by the Help of the Cane, two Glaffes in it, and a
Thread, fo as to be a pleafant Infirument, could Wood and
a Country-Joiner or Workman pleafe me.

In another Letter (the Dare of which is worn our,
but is, in Mr. Crabtrus Hand, called his icth Letter
to him) he faith, I have given order for an Iron filua-
drant of Five Foot, which will give me the 1000th Part
of One Degree, which (hall be furnifhed like my fir ft Scale ;
only my Workman is fo * throng for my Father, that / fear
it will not he finifhed before the Eclipfe. I have caufed
a very firong Huler to be exalily made, and intend to fit it
with Curfors of Iron, with Glajfes in them and a Thread,
for my Sextant.

To thefe I could have added many other PafTages
•of the like Nature: but thefe may be fufficienr,to fliew
that Mr. Gafeoigne, as early as 1640, made ufe of Te-
lefcopes cn Quadrants and Sextants, as well as in his
Invention of the Micrometer.

What Commendations thefe Contrivances got him,
and what Expedations they railed in fome of the A-
flronomers of that Time, particularly in two of the mofi:
acute of that Age, Mr. Horrox, and Mr. Crabtrie, may
be feen in the fame Mr. Crahtrie s Letters to Mr. Gaf
coigne, which are alfo in my Hands. Some PafTages of
which I (hall recite, and at the fame time give the Society
a Tafte of what thofe curious Letters do contain.

This Diagram is wanting in the Letter. * A Tor.kjhire Fhrafe

for fully employed.

A a a a a

!n

C 606 )

Tti Mr. Crahtrits fecond Letter, which is of Oiibher
30. 1640; after a very clear Demonftration that the-
Solar Spots are not Planets at a Diftance from the Sun^
but fomething adhering to, or very near the Sun’s Bo-
dy ; and alfo after a no lefs clear Demonftration of the
Errors of Lansherges Hipparchian Diagram, his Lunar
Farallax, his Dod:rine of Edipfes, and indeed bis whole
Lunar Afironomy, together with divers other curious
Matters, too many to be fpecified : after this, I fay. Mr.
Crabtrie faith thus, Something I am fare you rrere telling
me concernin'T a way of obferving the F laces of the Planets
ly your Glajfes. But 1 have not a little lamented that my
Time cut me fo fhort, when 1 was with you, that I could not
more fully ruminate and digeft thofe flrange Inventions
which you Jhewed me, and told me of. My Laffitude after an
unexpeded and unacquainted Journey ; my unpreparedncfs for
thofe Cogitations {not intending that Journey the Day le-
fore) and the Multiplicity and Variety of the Novelties you
jhewed me, fo wholly difiraded my Thoughts into Admiration,
that I cannot now give my Meditations any reafonabie Ac-
count of what I favp r but mufl intreat you, in a few LineSy .
to rub up my Memory, and tell me again what you fhewed me,
and the Extent of thofe your Inventions^ Which I dcftre^
that I might confidcr, and rejoice to conftder^ how much
and wherein Urania’/ Strudure will grow to Perfedion by
your Ajiflancei and that {what in me lies) I may help you
to remember when and wherein your Inventions and Obferva- .
tions vcilL be of mofl ufe. I Jhould alfo defire you to inform
me what Bignefs of a Quadrant you . conceive, to he large
enough for Obfervation with your Devices. For I ant e’re
long going to Wigan, iz Miles from hence^ where much
Brafs is cafl 5 and then / could fee whether I could procure
fuch an one cafl. Toutold me as I remember) you doubted
not in time to be. able to make Obfervations to Seconds. J can-
not but admire it and yet, by what 1 faw^ believe it i hut long

( ^07 )

to have [ome farther Hints of four Conceit for that Tur^
fofe. One Means, I think, you told me voas, hy a ftngle
Glafs in a Cane, ufon the Index of your Sextant, hy vphich
f^as / remember) you find, the exati Point of the Sun's Rays*

But the may how, I have quite forgotttn, and much defire:
Tour Device for the exaSi Divifion of a ^adrant, hy divi-
ding i I Degrees into i o Parts, I did then under f and, hut
do not now fully remember. If it might not be too much
Trouble to you, I Jhould intreat you to give me fuch a Paper-
Demonfration thereof as you fhevred me, and two or three
Lines plainly of the Z)fe thereof, how to find thofe [mall
Parts. I loft the little Paper, wherein I noted the Moons r
Diameter, which we ohferved when I was with you i I pray
you fend it me, if.^ 8ic.

I cannot conceal how much I am tranfported beyond my
felf with the Remembrance fof that little I do remember) of
thofe admirable Inventions which you [hewed me when I was
with you. I fhould not have believed the World could have
afforded fuch exquifite Rarities, and I know not how to flint
my longing Deftres, without fome further Tafte of thefe fe-
lelled Dainties. Happier had I been, had I never known
there had been fuch Secrets, than to know no more, hut only
that there Are fuch. Of all Defires the Defire of Knowledge
is mo ft vehement, moft impatient : and of all kinds of Know-
ledge, this of the Mathematicks affelis the Mind with mofl
imenfe Agitations. I doubt not hut you can experimentally
witnefs the Truth hereof, and one time or other have been no
Stranger to fuch Thoughts as mine. And therefore although
Modefty would forbid me to requeft any thing [until you
give me leave) hut what you pleafe voluntarily to impart,
yet the V chemence of my Deftre forceth me to let you know
how much I defire, and how highly I fhould prize any thing
that you fhould be p leafed to communicate to me in thofe
Optick PraHices. Could 1 purchafe it with Travel, or procure
it for Gold, / would not long be without ^ Telefcope for eh-

A a a a a z fervinr

c (5oS )

fervhg (mail /Angles in the Heavens ; nor want the Ufe of
your other Device of a.Glafs in a Cane upon the movealle
Kuler of pur Sextant (as I rememher) for helping to the
ex&6t Point of the Suns Rays. But feeing Urania //, ike.

Thus was the mofl: ingenious Mr. Crabtrie tranfpoit-
ed with Mr. Gafeoigne’s Devices, although at that rime
far iefs perfed than they were in a ftrort Time after.
And no lefs affeded was the incomparable Horrox, as
Mr. Crabtrie fets forth, in his third long Letter of Dec.
a8, 1640. which hath thefe iVords, My Friend Mr.Yioc-
rox prfejjeth, that little Touch which I gave him of your
Inventions, hath ravijhed his Mind ejuite from it felf, and
left him in an Extafie between Admiration and Amazement,
1 befeech you, Sir, flack not your Intentions for the perfelf ing
of your begun Wonders* We travel with Defire till rre hear
of your full Delivery. Tou have our Votes, our Hearts, and
our Hands fhonld not be wanting, if we could further you.
And then after many curious Matters f which would
take up too much of the Societies time to relate^ he
thus proceeds, Diagrams for Perfpe6Hves 1 have view-
ed again and again, and cannot fufjciently admire your inde-
fatigable induflry, and profoursd Ingenuity therein. I arr»
much afelied with the Symbolical Exprefftons of your De-
monflrations* I never ufed them before (but I will do) yet
I underfiand them all at the firfi Sight, and fee well the
Truth of your Demonf rations.

To thefe I fliall only add one Paflage more, and this
becaufe it fhews feme ocher of Mr. Oafeoigne’^s exqui-
iite Contrivances, or at lead the Accuracy of what are
mentioned ; and chat is in Mr. Crabtrie’s Letter of Dec:
6. 1641. arthe Beginning of which he faith. That which
you give me a full FrojeBion of was above my Hope :
and if the Screws keep an exalt Equality of Motion forward
in each Revolve, it is a mofl admirable Invention’, and
with the ether Accommodations, I had almoft [aid without

Com-

(, 6ogi )

Compare. But that the Divifiom of a Circle fhould he mea~ -
fired to Seconds, without the Limh of an Infirument, or*
that Diflances, Altitudes, Inclinations, and Azimuths Jhould
he taken all at one Moment, without the Limb of an
flrument likewife, and each to any required Humhir of Parts \
or -that the Diameter of Jupiter fiould he projelied in Juch
prodigious Me afire s as you [peak of. Sec. were enough to a-*
mufe and amaze all the Mathematicians in Europe, and-
may indeed be rather a Suhjdl of Admiration than Belief to
any that hath not known your former Inventions to exceed
Vulgar {Ijhad almofi [aid Humane) Ahiliiies- And. for my
Part, I mujf confejs Modefly fi checks my amhithus Defires,
that 1 dare [carce hope fich Miracles (hould ever he produced
in real PraPtke to fich ExaUntfs. Then (to give the
Society a further Tafte of thofe Letters^ follows an -
Account of the Agreement of Mr. Horrox's Theory ,
of the Moon with Mr. Gafcoigne’s Obfervations ; and
alfb very curious Ratiocinations, and a Difquifitiori
about finding the Parallax of the Sun and Moon, and
their Diftance from the Earth. In which he. cenfures
Morinus% Braggs, ^c. and then faith, that no Man that
hath written of the Diagram [of Hipparchus] underflood
it fully,- or 'defer ibed it rightly, but only Kepler and our Hor-
rox5 for whofe immature Death [|which was fuddenly* and
about the Age of 25.] there is yet fcarce a Day - which /
pafs without feme Pang of Sorrow.

Thus, among many, I have related fome of the Paf-
fages of Mi. Gafeoigne’s and Mr. Crahtrie's Letters rela-
ting to Telefcopick Sights. From whence it is very ma-
nifeft, that long before tht French Gentleman’s Claims,,
our Countryman Mr. Gafeoigne had made ufe of thofe^
Sights in his Aftronomical Inftruments; particularly in
two or more Sorts of Micrometers (as I plainly find)
and in his ffiadrant and Sextant. And had it pleafed
God to have given him a longer Life, we might have ex-<

( ^*0 )

' peded greater things from his pregnant and fagacious
Wit. For he was fcarce xo Years of Age when beheld
thefe Correfpondencies with Mr. Crabtrie And at the
Age of z3. he was killed at Marflori’H^oor-Eattle, on
July X. 1644 fighting for King Chnrles]. His Father
was Henry Gtfeoigne Efq; of Middleton, between Leeds
and Wakefield.

IV. An Attempt towards the Improyement of the Me^
thod of approximating, in the ExtraStion of the
^ots of Equations in Numbers. IBy Brook
lor. Secretary to the %oyal Society.

IN Phil, Tran No. xro. Dr. Halley, now Secretary of
the Royal Society, has publifli’d a very compendious
and ufeful Method of extrading the Roots of afleded
Equations of the common Form, in Numbers. This
Method proceeds by affuming the Root defired nearly
true to one or two Flaces in Decimals f which is done
by a Geometrical Conftrudion, or by fome other con-
venient way) and correding the Aflumption by com-
paring the Difference between the true Root and the
affumed, by means of a new Equation whofe Root is
that Difference, and which he (hews how to form from
the Equation propofed, by Subflitution of the Value
of the Root fought, partly in known and partly in un-
known Terms,

In doing this he makes ufe of a Table of Produds
(which he calls Speculum Analyticum,) by which he com-
putes the Coefficients in the new Equation for finding
the Difference mentioned. This Table, I obferved,
was formed in the fame Manner from the Equation

pro-

( I )

propos’d, as the Fluxions are, taking the Root fought
for the only flowing Quantity, its Fluxion for Unity,
and after every Operation dividing the Produd fuccef^
fively by the Numbers i, z, 3, 4, Hence I fooii
found that this Method might eaflly and naturally be
drawn from CVr. 2. Prop.y. of, my Methodus Incrmento-
rum^ and that it was capable of a further degree of Ge-
nerality; it being Applicable, not only to Equations- of
the common Form, {yi%, fuch as confifl; of Terms where-
in the Powers of the Root fought are pofitive and inte-
gral, without any Radical Sign) but alfo to all Expref-
lions in general, wherein any thing is propoled as given
which by any known Method might be computed; if
vice versa, the Root were confider’d as given : fuch as are
all Radical Expreflions of Binomials, Trinomials, or of
any other Nomial, which may be computed by the Root
given, at lead by Logarithms, whatever be the Index -:
of the Power of that Nomial ; as likewile Expreflions of
Logarithms, of Arches by the Sines or Tangents, of
Areas of Curves by the Ahfciffds or any other Fluents,
or Roots of FlUxional Equations, d‘c.

For the i^kc of this great Generality, it may not be
improper to fhew how this Method is derived from the
forefaid Corollary. Therefore jss and a: being two flowing •
Quantities ( vvhofe Relation to one another may be ex-
preft by any Equation whatfoever) by this Corollary,
while z. by flowing uniformly becomes z-\-Vj x will

OC OC' X

become x -| r v —7- v ^ — -- -|- drc. •

"L . z X. i«2«3^'

XV 'xV^ .

or ^ A 1 J- for ^ putting i.

I I Xz I .z.j

Hence if y be the Root of any ExprcfTion formed of •
y Jind -known Quantities, and fuppofed equal to nothing,

and ,

( <5ti )

' and zhc ^ part of j, and x be formed of z and tlie
‘known Quantities, in the fame manner as the Expreffion
made equal to nothing is formed of y ; and let jf'be equal
'toz~^V‘. the dilFerence v will be found by Extrat^ing

xv X

"the Root of this exprelEon -1- \

I I .X I . X . 3

‘ -]- ^c. r= G. For in this Gale z being become z-\-v =j,

xv^

AT, which is now become x xv -\ (jrc.

z

' muft become equal to nothing.

xvxv^'ic

The Root V in the Equation x-\ 1

I I . X 1 . X . 9

^ (^c. = o, is to be found upon the Suppofition of its
being very fmall with refped: to z, fas it muft be, if
z be taken tolerably exadl} by which means the Terms

jf X

■. \- may be negleded, upon ac-

1.1.3 i.x.3.4

count of their fmallnels with refped to the other Terms,

^ xv xv"^

fo as to leave the Equation x -\ -P- =o, for

I 1 .X

finding the firft approximation of v,

- By extracting the Root of this Equation, we have

x“ ZX X

That is,

X X

^ je“ IX

X .

X V

Firft, ~ —

-rr, \i X xV

• = o.

^ X X

X

X

X* 2 X

X .

xv^

Sec. *r- ^ r —

if — X XV

— O.

x"; X

X

2i

Thirdly

I

I

t ^

4* — — V— -] if — X — itv -\ , &c. •=. o.

XXX 2,

This approximation gives v exad to twice as many
places as there are true Figures in 2;, and therefore tre-
bles the number of true Figures in the Expreflion of y by
z -\-v, which may be taken for a new Value of for
computing a fecond v, feeking other Values of at, x, x,
(jrc, Tho’ when z, is tolerably exadl (which it may be
efteem’d when it contains two or three or more true
Figures in the Value of y, according to the Number of
Figures the Root is propofed to be computed to,) the
Calculation may be reftofd without fo much trouble,

'z

X

2> X

only by taking V ~ — —

X

^ X 2, X

2-. 3a; I, ^ . ^j.x

inftead

- X

of — r

x“

X

taking every time for v

its Value lad computed.

SC X

From the fame Equation x -\- xv -] -f-

% I .z. 3

= o, may be gather’d alfo a rational Form, viz.

3

&c.

V

For negleding the Terms

X X 1. 2.. 3

Z X

X

X

we have v = r which is nearly —

. , * X

« -} V

There-

forejn the Divifor inftead of v writing r we have

B b b b b

more

more exafUy v

X

( ^14)

X X
2. X

that is

I.

2.

— X

X V

X

X X
X X

when X it v~\

2

o.

X

X V

.XX
X *~T
2 X

X

when — X x v 4 &c, — o.

X •

X X
2 X

X

xx

X -| :

2 X

• . X V

when X — ic -y -| &c. = o.

2

when — X — i -v + - — &c. = o.

This Formula, will alfo triplicate the number of true
Figures in s. And the Calculation may be repeated, af-

^ter every Operation, taking for a Divilor +

2

ic , X X

— ~\ 1- ^jrc. inftead of at -]

1.2.3 ^*^‘3 *4 ^ ^

Dr. HalUf has fully explain’d the manner of ufingboth
thele Formulas in -Equations of the common Form;
wherefore I fliall be the Ihorter in explaining two or
three Examples of another fort.

Ex. I. Let it be propofed to find the Root of this E-
quation — 16 — 0. In this Cafe, for

y writing 2, and for o writing x, we have -\- i\^''

( )

i6=:x. Whence by taking the Fluxions,
we have i, and i =

2 v' ^ X 8 — 4 ^ X i\'^ ^ For finding

the firft Figures of the Root y, for v' z take f , and we

have the Equation ih-j-y — 16 = 05 which being
expanded gives y^ y^ z %z y — 255 = o.

By this Equation I find that for the firft Tuppofition
we may take z — %. Therefore in order to find v, let
us now make 2 = (which is nearer than before)

and we have x — i\^ z, 16 — 2^ 4. 14

— 5^ — 14= — 4,48 ; x=z 10, 66; it =4,72. Whence

by the fecond rational Form v = =

io^66 + 4j-7Jl.><-4>-1L,
2 X 10, 66

= o, 38 ; which mufl be too big, becaufe \<s/ z, and
therefore will require a larger Value of y to exhauft the
Equation, than where V 2 is exadt. For the fecond fup-
pofition therefore, let us take z—'i, 3, and make V 2
= 1, 4142136, and by help of the Logarithms we fhali

have z^ 1 1 = 13,47294, whence x = — ^0,22706;
;cn=; 14, 93429, and x= 5, >84/9. Hence by the zd.

irrational Formula v ■=. V ^4>934i9 j __

5,18419" ‘ 5,^8419

^5* i^!~9 “ oiyi6, which gives y =: z v

2,31516, which is true to fix Places. If you defire
it more exadt than to the extent of the Tables of
Logarithms, taking z. = 2, 31516 for the next fuppo»
fition, the Calculation muft be repeated by computing of

zz-\- to a fufficienc number of Places; which, mufl
be done by the Binomial Series, or by making a Loga-

B b b b b 2 rithm

( 6j6 )

rithtn on purpofej true to as many places as are necef-
fary.

Ex. II. For another Example, let it be required to find
the Number whofe Logarithm is o, z9> Tuppofing we had
no other Table of Logarithms but Mr. of 200 Lo-
garithms to a great many places. This amounts to the
refolving this Equation / 3/ =: o, 29, or ly — o, 29 = o.

Hence therefoifc we have x —lx — o, 29, » = — ( a.

T.

being the Modulus belonging to the Table we ufe, vrz,

^ „ — a .. 2 .. — 6 a

0.4342-944819) X = x=— , •; = —

&c. In this Cafe becaufe x has a negative Sign, changing
the Signs of all the Coefficients, the Canon for v will
be found in the fourth Cafe, which in the irrational Form

. ^ Z X ZX

gives — ^ .

X X Z . 3 * 2 . 3 ■ 4>r

zlz — 0,58 zv^ zv"^

'^C. z=z‘Z. -f- ————— — '

^ 3^ ' 4^.

2

+ — : &c. In this Cafe to avoid often dividing by z,. ic

5 -2^ .

will be mofl convenient to compute ~ , which is got

from this Equation = i — -v/ J +

zl z — o, 58

2D-

3 2^

2 D'l

4 z^

2 D

+ , &c. The neareft Logarithm, in

5

the Tables propofed, to the propofed Logarithm o, 29
is o, 2900346114, its Number being i, 95. Therefore
for the firfl fuppofition taking = r, 95, we have x
{=: I Z — O, 29 = O, 2900346114 — O, 29 ) =

O, 0000

o>ooco34^i^4>3nd

C'diz)

1 I z — o, ^8 o, 0000692,2 2^8

434^944^19

. , ^ / z O, 50

oooi5'939i 39, and i + =1,000159-

59139. Whence for the fir ft approximation we have

ly —

— = I — v' I, 00C15939139 = — o, 00007969247,
z

and V = — o, 000 15 54003 and y = z -}- v ~
1,94984459968. Which fs true to eleven places, and

may eafily be -correded by the . Terms — ;■ which I

3

leave to the Readers curiofity.

Being upon the Subjed of Approximations, it may
not be amifs to fet down here-two Approximations I have
formerly hit upon. The one is a Series of Terms for
exprefting the Root of any Qoadratick Equation: and
the other is a particular Method of Approximating in the
invention of Logarithms, which has no occafion for any
of the Tranfcendental Methods, and is expeditious e-
nough for making the Tables without much trouble.

gensrd Series for expeffing the Root of any ^adrM'ick

Equation.

Any Quadratick Equation being reduced to this Form
XX — mqx-]-my=.o, the Root a; will ^ be «xpreft by
this Series of Terms. ^

X = — -f A X — 1 B X C X TT~

q ‘ mq^ ‘ h" — %

0,5^

+ D X

&c. Which muft be thus interpreted.

c — 2,

I. The Capital Letters A, B, C, (jrc. ftand for the
whole Terms with their Signs, preceding thofe where-

I

( 6i8 )

-in they are found, as B = A x — , — •

~~y, “

2, The little Letters a, h, c, ^c. in the Divifbrs, are
equal to the whole Divifors of the Fradion in the Terms
immediately preceding ; thus b — a^ — 2.

For an Example of this, let it be required to find
V2. Putting V 2 = X i, we have 2x — 1 =
o, which being compared with the general gives
— — 2, and m f — — i : therefore for m taking
-—I, wx have ^=2, and y = i, which Values fubfti-

tuted in the Series give at ^ y

^ ^ 2x6 2x6x34

I I

2 x6x34Xiij4 xx6x34Xii54Xi?3*7i4*

^c. The Fradions here wrote down giving the Root
true to twenty three Places.

A new Method of confuting Logarithms.

This Method is founded upon thefe Confiderarions.

1. That the Sum of the Logarithms of any two Num-
bers is the Logarithm of the Produd of thofe two Num-
bers Multiplied together.

2. That the Logarithm of Unite is nothing, and
confequently that the nearer any Number is to Unite,
the nearer will its Logarithm be to o. 3^/y. That the Pro-
dud by Multiplication of two Numbers, whereof one
is bigger, and the other lefs than Unite, is nearer to U-
nite than that of the two Numbers which is on the fame
fide of Unite with its fdf ; for Example the two Num-
bers being f and the Produd ^ is left than Unite,
but nearer to it than which is alfo lefs than Unite.
Upon thsTe Confiderations, I found the prefent Ap-
proximation ;

( 6ip )

proximation ; which will be bed explain’d by an Ex-
ample. Let it therefore be propcfed to find the Re-
lation of the Logarithms of 2 and of lOa la order

tothis, ItaketwoFradions^— and — , viz, and if

100 10 lor 10;',

whofe Numerators are Powers of and their Denomi-
nators Powers of 10; one of them being bigger, and
the other lefs than i . Having fee thefe down in Deci-
mal Fraedions in the firft Column of the Table annexe,
againfl them in the fecond Column I fet A and B for
their Logarithms, expreffing by an Equation the manner
how they are Compounded of the Logarithms of z and
10, for which I write / 2 and 1 10. Then Multiplying
the two Numbers in the firft Column together, I have
a third Number 1,024, againft which I write C for its
Logarithm, exprefling like wife by an Equation in what
manner C is formed of the foregoing Logarithms A and B.
And in the fame manner the Calculation is continued ;
only obferving this Com^endium^ that before I Multiply
the two lafl Numbers already got in the Table, I confl-
der what Power of one of them muft be ufed to bring ,
the Produdi the nearefl: to Unite that can be. This is
found, after we have gone a little way in the Table> only
by Dividing the Differences of the Numbers from Unite
one by the other, and caking the Quotient with the near-
eft, for the Index of the Power wanted. Thus the two
laft Numbers in the Table being o, 8 and i, 014, their
Diflerences from Unit are 0, 2co and o, 024; therefore

gives 9 for the Index; wherefore Multiplying the

ninth Power of 1,024 by o,8, I have the next Number
99035^03 -9, whofe Logarithm is D = 9C-]-B<,

In feeking the Index in this manner by Divifion of the
Diflerences, the Quotient ought generally to be taken

with

( 6zx) )

'a^ich the lead : but in the pre(ent cafe it happens to be the
mod, becaufe inftead of the Difference between o, 8 and
I, we ought flridly to have taken the difference between
the reciprocal i , and i, which would have given the In-
dex 10? and that would be too big, becaufe the Product
by that means would have been bigger than i, as 1^014
IS. Whereas this Approximation requires that the Numbers
in the'firfl Column be alternately greater and lefs than
I, as may be feen in the Table.

When I have in this manner continued the Calcula-
tion? till I have got the Numbers fmall enough, I fup-
pofe the laft Logarithm to be equal to nothing. Which
, gives me an Equation, from which having got away the
Letters by means of the foregoing Equations, I have
the relation of the Logarithms propofed. fn this man-
ner if 1 fuppofe G =0, lhave 2136/ 2 — 643 / io = a
Which gives the Logarithm of 1 true in feven Figures, and
too big in the Eighth ; which happens becaufe the
Number correfponding with G is bigger than Unite.

There is. another Expedient Which renders this Cal-
. dilation ftill fhorter. It is founded upon this Confidera-

tion, that when x is very fmall i -|-xl'’is very nearly
I Hence if i and i — are the two laft

Numbers already got in the firft Column of the Table,

and their Powers i -j-^rl^and i — are fuch as will
make the Produtft i x i ^1” very near to Unite,
w and » may be found thus : i -f- i -\-7nx, and

I — z\" =.1 — ff Zj and confcquently* 1 xl”* x i ~ z\’*
i -^-f»ix — itz, — X, orfnegleding 2; at) 1 -f-
mx'—n/c- Make this equal to i, and we have
zixi'.li — z: / I W hence a:/i — z-\- zl i -j-AT
= 0. To give an Example of the Application of this,
let 1,024 o»99035'2. be the laft Numbers in the

Table, their Logarithms being C and D. Then we have

1, 0x4

Qo.^

O' H, O

( 6ii )

O k-

o o «

s ^

’ so

-> -• \o

«JO

” SW C\ OS o

Q-n ^ -fi. ws>
I '*-» O' — ^

OO

' s*J --O 1-1 -f*

N

o

o

o

o

o

N)

OJ

s-s

Usj

if

N<

V*s»

O

w

'-o

CO

'•'1

oo

K»

*-0

►h

CO

OS

VD

M

''J

a:.

o

o

so

k-»

SO o
so O
VD O
'O O

<-i — ^

*'v) -fs
OS ts' -fs
" O *-i
O CO (V
4- •-.

CS O

V

o

«>■>

o

l-l

o

N>

SO

VO

VO

Os

OS

SM

SO

QO

*vj

so o VO
so O VO
VO O ■'X
VO I-. VC

V»J CV'-^

CV hj VO
h> 03-^
OOVO a-»
*- -fv Os
oo -1 >-
OS O
-p' -n ^

O SC' O

O 'O M

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O M

w u

CO N
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v» o

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M

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1^. !>3 7"a;

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SO 63

^ oa^i

++■^++■^++1
II II II II II II II II II II I

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VO

O

w-/

vis

t®

S- 3 II

vj- rf 11

CS)

rT

p

PP

C

3

g*

>f

V)

>-><

(A

S®S I t®

o lo

O I»-|

p

3

CP

n

O

3

7?

|X5

C

r»

3

r-r

H

O

V*

O

t®

p

3

Cu

V

N

( ^6ii )

rbave computed this Table fo far, that the 'Reader
viuay fee in what matmer this Method Approximates ;
this whole Work, as it appears, coding a little more than
three Hours time.

Y. Troprietates Jtmj)Uces Sedionum Coni-

-carum ex natura Focorum deduSliC ; cutn Tl^eore-'
mate gener alt de Vtnhus Centrij>etis 5 quorum ope Lex
"Virlum Centri pet arum ad Focos Setiionum tenden-
tium, yelocitate.s Corporum in illis reyolventiuniy
Vejcriptio Orhium facdlime deter?ninantur. Ter
Abr. de Moivre, R. S. Soc.

Sit D £ Axis Tranfverfus Ellipfeos, AO Axis*alter,
& C centrum Sedionis. Sic F pundum quodvis
in circumferentia ejus ; P ^ Tangens curvsc ad P, oc-
currens Axi Tranfverfo ad punda S, F Foci ; C P,
C K femidiametri Conjugata: ; P H Semilatus redum
ad diametrum FC; ? G normalis adTangenrem, cui oc-
currac HG, perpendicularis ipfi F C in punda G, ut
fiat FG radius Curvaturac Ellipfeos in pundo P,* fint
etiam S F, CP, FF perpendiculares in Tangentem
F ^dcmidae : Jungatur S'O, & demittatur in Axem
normalis P L. His pofitis. Died quod,

I. Re6iangulum [ub cP (I ant Us ab utroque Ellipfeos Focc,
■five S P xU F <equaie ejl -qua Jr at 0 Semfdiametri C K»

Demonjlratio.

f S q~P Cq CS q — ^CS L per

P Fqz=t P Cq CS q -F vC S x C L per iz. \\. Elem,

Unde PSq‘\-PFq — zPCq-\-zCSq.

Jam P S -]- P F —D E —zzC D\ ac propterea
T S a -\~ P F q z P S x P Fz=: ^CPq. Quare

- _ ( )

Quare tran^onendo, xP S xP F~ ^CDq ^%PCq
’-^zCSq.

Ac Dimidiando P S xP F — 2 C Dq — PCq — CS q.

Eft autem CS quad. — CD quad. — CO quad, acque adeo

PSxPF=ztDqAr<^Oq --PCq.

S&dCD q C 0 q—PC q CK q.fem.YW.Coff/c.
/ipollonii.

Quarc P S x P F ~C K q. ^E.Dl

n. Diflantia h Foco SP eft ad perpendicular em in Tan^ -
gentem demi([am, ut Semidiameter Conjugata C K ad
axem minorem C O.

Demonftrath.

Ob fimiJia Triangula S P T, FP erit P S : PF n
St\FV', ac componcndo P S P F eiit 2dST-\- FF^
& earundem dimidia C D ad C R, \xt P S ad ST. Unde
C D xC X eric ad C R x C X ut P S ad ST. Sed
CR X CX ^equale eft redangulo fub Semiaxibus C Din -
C 0, per ^ 1 . VII. Conic. >. Proinde P .S' eft ad iS TutC D in
C A' ad C D X CO, five ut C A' ad CO. Ac pari argu-
mento demonftfabitur P F efle ad FV in eadem ratio*-
ne. ^ E. D'.

III. In. eadem etiam eft ratione Semiaxis Tranfv'erfuc CD
ad normalem e centre C ad Tangent em demiff am, five ad C R.

Etcnim cum -reiftangulum CR x C.^asquale fit red-
angulo C D X C 0, uti jam didium eft, erit dvd^oyov
CDadCR ut CX ad CO. ^E.D.

IV. Semidiameter qu£vis P C eft ad diftantiam puniii
P a foco Sfive ad S P, ut diflantia ah altero Foco FP ad di-
midium lateris refti ad Verticem P pertinentis, five ad P H.

Hoc autem manifeftum eft ob Propr. I. cum nempe
quadratum ex CA' aequale fit redangulo Pu\) S P xP F.

V. ReUanguhm Semiaxhm C D xCO eft 'ad quadratum
femidiametri conjugata CX, ut C X ad Radium Curvaturx
w-punPio P, five . Ad P G. .

Smt

t ^

Sant enim Triangula PC R, PG H inter fe fimilia,
unde C R efl; ad /’C, ut femilatus redum F H ad P G:

C D X CO

hoc e(l, per pr^Emiflam Propriecatemllf,

CK

C R eft ad F C ut

F//ad

c/r*

CDxCO —

proinde dvdhoyov C D xC 0 :C : \ C K : PG. ^E.D.

THEOREMA GENERALE J.

P'is cefftrifita ad idem fun^^um S undetis, in Curvis

S P

emnihus, efl femper proportionalis ^antitati -p-Q ^ 0 ^3

Hoc Tbeorcma ante plures annos a me inveftigatum
& cum amicis communicatum, propriis demonftrationi •
bus firmavere Geometric Clariflimi D. J. Bernoullius in
Liplt£ ; 'D. J. .Keiilius- in harum Tranfa£i. N. 3 1 7. &
D. Jac. Hermanrms iwPJooronomik fua pag. 70. quos vide.

S P

Scribenda autem C pto PG, per Propr.Y; &

C K

juxta Propr> II, pro S T ; (ob datas fciJicec Q D, CO) eric

Vis centripeta tendens ad focum Ellipfeos S, fcmper ut

SPxCK’ ,^SP,i . s

CfO"x S^' hoc eft ut vel — „ nempe reciproce ut

quadratum ex SP. Unde patet quod fi Sedio fuerit Ellip-
lis UK«:u corporis defcriptaj erit Vis Centripeta ut quadra-
tu'mdiftantiica centro Virium reciproce. Ex his Proprieta-
cibusconrequunturCorollarianonnulla notatunonindigna.

Coroll i« Velocitas Corporis in Ellipfi r evolvent is, ad
panShtm cfuodlihet P, efl ad Velocitatem revolventis in circula
ad eandem diflantiam S P a centro Viritm^ in fuhdupU ra-
tione difiantia ah alter 9 foco PF, ad Semiaxem tranfverfum
Sedlionis, five ut media proportionalis inter P F dr C D
ad CD.

Eft enim velocitas revolventis in Ellipft ad diftantiam
F, ad Velocitatem revolventis in Circulo vel Ellipfi ad

• • dift-

C ) '

diflantiam Semiaxis C D vc\ S 0, uc C 0 ad 5 7* ; hoc eft
per Propr, II. ut V P F ad a/S P. Velocitas aarem re-
volvencis inCirculo ad diftantiam C D eft ad velocira-
tem revolvencis in Circulo ad diftantiam S P, ut v'SP
ad VCD. Ex ^quo igitur, Velocitas revolventis in El-
iipfi ad diftantiam S P, eft ad Velocitatem revolventis in
Circulo ad eandem diftantiam \\x.VPF ad V C />.

CoroU, 2. Ex datis Velocitute in EWpfi, p o fit tone Tange n-
tis, ^ centre Firium feu Foco^ facile efi determinare Focum
nlterum. n

Sit enim Velocitas Data R ; ea autem Velocitas qua
deferiberetur Circulus ad datam a centre diftantiam S F fit
ac per priccedens, R eft ad ^utV F Fad vC D,
adeoque ^^eft ad R R ut C D ad P ^ — R R

erit ad ut S P adP F : Datur autem S P ; data eft i-
gitur P F magnitudine. Datur etiam pofitionc, ob angu-
lum angulo S F /"xqualem. Datur igitur pundlum
F alter Focorum ; Quo invento pronum eft Sediionem
defcribere.

Si vero ~RR majus fuerit quadrate ex 2 — RR

fit quantitas Negativa, & loco Ellipfeos Trajedoria de-
feribenda in Hy perbolam tranfit. Eritque RR — .2 ad
RR ut S P ad P F diftantiam alterius Foci, ad alterum
Tangentis latus ponendam, uc babeatur Focus F. Pro-
prietates autem omnes quas in Ellipfi demonftravimus;
mutatis mutandis etiam Hyperbolse competunr. Fig. II,

Quod ft acciderit ^2„:rquale efte dimidio quadrati
cx R ; evaneftente quantitate 2^^ — RR — o, quarta
proportionalis P F fit infinita: proinde Trajedoria de-
cribenda Parabolica eft, Foco fcilicet akero in infinitum
abeunte. Axis autem Trajedorice pofitione datur; eft e-
nim ipfi P F parallelus, exiftente fcilicet angulo F P V
angulo dato S PT asquali.

Coroll. 3. Velocitas revolventis in data SePiione Conic a
ad diftantiam S P e(l ad Veiocitatemejufdem ad diftantiam alP
am S JF, ut media proportionalis inter F P ^ S Jl adme-
diafn proportionalcm infer S P ^ F JC. Velo*'

( )

F P

Vclocitas cnim in P eft ut v' ('per pr^pr, II.; & per

F

candem, Velocitas in ut v' ^^-^.Undemanifeftaeft
propofitio.

Coroll. Ratio etiam Velocitatum duorum Corporum in eo‘
dem S)fiemate,fed in datis Clnife^ionibus diverfis, revolven*
tmmy datis utriufqu: a communi Orb turn Foco di ft ant its, ope
Coroltarii fiatim obtinebitur*

Cum enim Velocicas corporis in P fit ad Velocitatem
inCirculoadeandemdiftantiam^' /', ut v'f F ad i/C D. ;
& in alia fuppofita Conifedione, cujus Semiaxis cd
& FociS, f, ad diftantiamS^ Velocitares illse Tint utV pf
ad V c d'.- Velocicas autem revolventis in circulo ad di-
ftantiam SF fit ad Velocitatem in Circulo ad diftantiam
S pntV Sp2idiV S P Compofitis rarionibus, ericVeloci"
tas. in P ad Velocitatem in p,\xx.^^ 1 1 x c d x S p ad
V pf X C DxS P. Quod fi Sedio ilia altera fueric Pa-'
rabola, erunt cd, pf infinitae, fed in ratione i ad 2;
proinde ratio Velocitatum erjt ut VPFxSp ad
V.zCDxisP^

Coroll. Quod ft in Hyperbola punBum P aheat in infir

nitum, ex pr^cedentihus manifefium eft, Velocitatem ultimam
ac minimam, qua cum corpus in sternum afeenderet, aqualem
ejfe ei qua, ad diftantiam CD Semiaxi tranfverfo £qualem,
Circulum deferiberet.

Coroll, 6. Ex data difiantia a Foco, datur quoque Pofitio
Tangentis, five angnlus R FT, fub diftantia S P (jr. Tangent e
F T contentus.

- Eft enim fper propr. II.) P 5 ad S ^ ut C ad C 0 five
nt VSP xP ^ ad CO, atque ita Radiusad Sinum anguli
CPT. At in Ellipfibus Circulis aflinibus pr^ftaret angulum
^ S 7*,ejurdem complementum ad quadrantem,inquirere :
Hujus autem Sinuseft ad Radium \xW ;s F xP F.^CO q
^dk\/SFxFF,r -

Cftrefl,.

( 6^7 )

X^oroU. 7. Atcfue him confequuntur f^elocitates ^uihufcum
difiAHtU S P srefcunt vel decrefcunt.

Nam cum, ex Corollario pr^cedente, ^ S P xP F fic
2d d S P xPF — C 0 ^ uc Radius ad finum anguli PST,
ac in eadem fit ratione Velocitas Corporis in P ad Ve-
locicatem momenti ipfius S P ; Velocitas autem ilia in

P F

P fit (per frofr. II.) ut V cl*fis rupcrfluis, erit

^ Velocitati, quacrefcit vel dccrefcit

difiantia S P, Temper proportionalis.

THEOREMA GENERALE \l

In omni TrAjeSforia CurvilineA Telocitates anguUres circa
antrum Tirium funt reciproc'e proportionales quadrat is difian-^
tiarum a centra.

Nam ob Sedorum minimorum Areas aequales, arcus
angulis minimis Tubccnfi five Safes, funt reciproce ut Ra-
dii; Anguli autem minimi quibus Bales xquales fubten-
duntur funt etiam reciproce ut Radii. Proinde anguli Sec-
torum minimorum Area jEqualium, funt inter fe reciproce
in dupla rationeRadiorum, five ut quadrata diftantiarum.

Coroll. 8. Hinc Telocitates angular es revolventium in di-
ver/js Elltpfibus datis comp ar ant ur inter fe.

Velocitatescnim angulares quibufcum ad difiantias Se»
miaxibus Tranfverfis aequales circuli defcribereatur, funt

reciproce in ratione felquialtera Axium, five ut

Velocitates autem angulares has medias habent Corpora
revolventia, cum quadrata diftantiarum sequanturredan-
gulis Tub femiaxibusEllipfeon. Ideo Cpcr Theor. W.y ^iit

quidem Quantitas eft ut Velocitas anguli ad centrum S,
mptu redse S P, tempore quam minimo dato, defcripti.

Coroll. 9. Velocitas angular is qua circumgyratur Tangens
P 7, five re^ a in Tangentem perpendicuhris S'T, eft ad

locitatem

( 6it )

kcifAtem angular m rc3a S P, ut SemUxis tra^fverfus C D
4,(1 dijlantim ab altero Foco F F,

Demonprutid,

In Fig* III. Sint punda F,p, quamproxima inter fe;
dudiCque S P . S g, fine PT, pt dux Tangentes, adquas
demittantur normales ST, St; iifque parallela! ducantur
radii Curvacurje PG, />G coeunces in 6: ac deferibatur,
centre S & radio S P, arcus minimus P E occurrens ipft
Sp 'm E. Manifeftum eft angulum P 6p aqualem efte
. anguIoT'5/, five angulari Velocitati norma'is 5 71 Eft
autem angulus angularis velocitas redx S P ; quare
angulus P G p eft ad angulum P Sp ut angularis VeJoci-
tas ipfius S 7 ad angularem velocitatem redlx S P ; hoc

eft, ut^ad.^. SsdPp.PExxS.P .Sr-.-.CK:CO

r\j r o

C K CO

(per propr. II). Hx jgitur Velocitaces funt ut ad
Pro P G r«ribe ^

CDxCO CDxCO

Hinc

CDxCO

• j CO
crit ad t:-

—^ FSxPF PSxP f P
five, deletis fuperfluis, C Dad P F, ut angulus TSt ad
angulum PSp^ five Velocitas angularis Tangencis ad an-
gularem Velocitatem diftantise S P : proinde Velocitas
qua circumgyratur Tangca«, Temper proportionalis eft

. .COxVCD
quantitati — jttt •

^ P F X S P q

^leraque horum CoroUarlorurn ex aliis Conkarum
SePiionum ^roprietatibus deduPia^ Vel facile deducen**
da, inVeniet LePlor in Seifl III. Lib, I. Princip.
Nat. Philofophiae.

FINIS.

LO ND G Nf Printed.-for W. Innys^ at the Princes Arms ifl

( 6t^ ) Number jyjv

PHILOSOPHICAL

TRANSACTIONS.

For the Months of Jtdy^ Augufi, and Sef, 1717.

I* A N Account of a ^iffeSlion of a ChiUy €om^
municated in ec Letter to Dr, Brook.
Taylor, % S» Sec^ Dy 2)r.. Patrick Blair, % S.

11. De Seriehus infinith TraBatus, ^ars ^rtmak
AuBore Petro Remundo de Monmorc. R.S.S.
Und cum Appendice Additamento per D, Brook
Taylor, % S*Sec,

-jodrmiM ( )

JADIH'TO^O'JJH'T

A

r .>'

A - t nr

iOi--

^l.'.

' !-N *>

VrJ i, ly

1

A ■■

JooiU

Vi

\>"nA R

l(\

■ J~y

,'Vj'

(. ’ ■■’ ' ' ■

• . . ''

. ^ . . A 9 ^ .

*-

\ r-> ■

i » ; «

*Aft • •

•tsw^riQ

li

• iZ 'A- .11

.2 .j-i

c::i-jcjioM v\i cb/L'jfT?>i o'n’AJ

s'ic'ijift.

o'

i'^KV.V.V. , w

f »v

* < > ^ i -

i

-,^v> ?

ljl/..l'

\L:

n I.

h

0

4

I. Jn Jccomit of the DiJfeEllon of a Child, Com^
municated in a Letter to Dr, Brook Taylor,
S. Seer, Dr, Patrick Blair, fi. 5.

AS nothing is more apt to lead us to the Know-
ledge of the feveral Diftempers which affedl the
Human Body, and to acquaint us with the juft Prog-
nofticks of the like Cafes, than the opening of dift*
*. cmper*d Perfons. I hop’d it would not be an unaccepta-
ble inftance of my Zeal and Readineft to ferve the
Moft Honourable the Royal Society upon all occafions,

: CO defire you to prefent them with the following ac'

; count of the Diftedion 1 lately made of a Child.

This Child was five Months old, and was fo craa-
: dated, that he appear’d rather to have decreafed, than
CO have encreafed in Bulk, from the time of his
Birth; his whole Body not weighing above five Pounds.

1 The Skin and Muftles of the Abdomen were vefy
i thin, but the Peritoneum was preternaturally thick.

’ Tbe Ventriculus was more like to dn Inteftin than to
a Stomach, its length being five Inches, and its breadth
but one Inch. The Coats of it were thick and flelhy,
and the Cavity very inconfiderable. The Pylorus, and
almoft half of the Duodenum were Cartilaginous, and
fomething inclin’d to an Oftification, lb that no Nou-
rilhment could have pafted into the Inteftins, tho’the
Stomach had been capable of containing it, which
makes it no Wonder that the Body was fo emaciated.
There were fcarce any foot-fteps of the Omentum to
be'feen, even at the Bottom of the Stomach, to which
it ufually adheres.

The

'( )

The right Lobe of the Lungs adhered firmly to the
Ribs SSd h'a^ fhr€e ExuleefiflSfiS, WhRh c6titain*id pu-
rulent Matter. It was fb very thin and compad, thaa
it Ihem’d as if that Lobe had never been of life id
Reipiration. The left Lobe was of a more florid Red^
fpongy, and free from any Adhefioft.

Upon enquiring after the Symptoms this Child had
been aflet^ed with, his Mother told me, he feem’d tO'
be healthy till he was about a Month old, when he
Was feized with a vidlerit Vomiting, and a Stoppage
of Urine and Stool. Sothe time after« both thele
became more regular, blit , the Vomiting ftill continued*
^e (eeni’d to have a great Appetite, taking, what Sutk,^
Drink, or dtlier ^dod was oner’d him, with a kind of
eagerneis ; but he immediately threw it all up again* He
bad all along breathed freely, and had no Cough,
notwithfianding the Exulceracions above mention'd*
"This confirm'd me in the Opinion that he had never,
breath'd, by the right Lobe of the Lungs. ,

There could be nothing more emaciated than this
Child was; ^d it ^ems to be worth confidering,
ti^hether his lUhers might not be owing in a great
nieafure to the want of the Omentum,, (for he ieem'd
never to have had any) ; as alio, whence it is that
cliis Part is generally confum'd in an Atrophy, and
ip moft Hydropical Cafes, except where it feif is more.
dTpeciaily concerned*

I

!

%

!

I

II. Vz Seriehus infinitls TraFhtus. Tars Trimal
JuFlore Pecro Remundo de Monmorc. R. S. S.

I

Trop. 1. Troh,

Nvenire fummam terminorum quot libuerit Seriei
hujus axa-^n xa -\-xnx &c. xa-^ p — i »

4“ r}xa-\-^nxa -{-'^nx&c-xa pn

a-\-% nxa-\--^nXa-\-^nx &c. xa-^p in
4 4" 3 nx&c, Ubi eft n differentia data, ram inter
Fadores continues, 4, 4 -j- 4 -{- *■ »» &c ejufdem cu“

jufvis termini, quam inter Fadores homologos termino*
rum diverforuni in Serie continuata ; atque defignat p nu-
merum fadorum hujufmodiin quovistermino.

&ol»tio. Fer x defignetur primus Fadorum in ultimo ter-
minorum quorum fummarequiritur, atque fumma ilia eric

xy.x~\~ n-<^c.xx-\rpn — 4 — ;; X X

p in

Proponatur

^EJ.

Ex. I. Proponatur Series numerorum naturalium
I ^ 4“ 3 4 -|- Sc invenienda fit fumma toe

terniinorum quot funt unirates in numero z, qui in hoc
cafii eft etiam ultimus terminorum quorum fumma requiri-
tur. In hoc itaque cafu funt 4 — i , n= i, p — i,6t
x~z. Unde Fitxxx-\-nx&c. xx ~\-p n'=:z,xz-\- i„

1 n

ox I, atque />4~^^

zyz,'\- i

a — nx AX &c. xa -\- p

■=zzxi; adeoque fumma qusefita eft

Ex- X. Invenienda fit fumma tot terminorum, quoc
funt unitates in numero z, Seriei t -|- 3 6 -|- 10 -1- &c.

Numerorum Triangularium. Numsri 1,3, <5, in hac

E e c e e ' Serig

( )

Serieficfctibipoflunt^^, &(■

Hoc pado, fepofito diviforc dato i, Series revocatur ad
foimam Propofitionis, exiftentibus a—i, n—\, &
x — z> Unde fumma Seriei duplicata eft

X X x-l-i XX 4- 2, -—ox t XX _ X X X -1- « X X -i- ^ ^

3 ■” 3 ’

adeoqucliabit^ ratione diviforis 2, Summa Seriei ipfius efl

i X 3 2- X 3

exiftente x eodem ac z. Ad eundem modum inveniun-
turfummae cseterorum numerorum figuratorum, quosum
ormulaejam vulgo innotefcunc.

Ex. 3. Sine = I, » = X, p = 3. ut (It Series pro-

pofita 1 X 3 X 5 -j- ? X 5 X 7 5 X 7 X 9 -1- In hoc

itaque cafu formula fummae fir
ATXX-l-XXX-l-4x.V-|-^ — 1 2^1x3.

4x X

XXX

2 X

x-1-4^x-|-6+i5

8

Verbi gratia, fi quae-

ratur fumma decern terminorum, fit x = 19 (nempe ter-
minus decimus in Serie Arithmetice proporcionalium,

i» 3» 7» adeoque fumma eft ^ M _L£

= x868o. Propofitio vero fie demonftratur.

Demonfir.atia. Sit Series quantitatum A, 5, C, D,
quarum differentiae conftituant Seriem 4, h, c, d,
(nemp uc fine 4 — 5 — A, b:=zC — B, c :z=: D — C, )
Hinc ftatim colligitur elle a -\-b-==.C — A,a-\-b-^ c —
D — A, a^b-\-e-\-d~E — A: & in genere aggre-
gatum quGtlibet terminorum Seriei 4, t, c, d, C'^c. sequale
eft termino proxime infequenci Seriei A, B, C, D, Ey ^c.
muldato termino primo A. Vio A^ B., C, fume terminos

a — n

a

( <^35 )

ft y. a 'x. &c. y/i-\-p — i « a y a pn
p-\- If} p -f- I »

•y a'i- in y &c- x 4 -I- p 4- i n , . n i

, crc. hoc eft, valoo

r ^ . r xy X -\-f}y ^c. x x -j- p

res iuccemvos iplius ^

; & eo-

p-\-i n

rum differencia:, pro a, I, c, <&c. fumendse, crunt
4 X /t - - n X &c. ^~a4p — * 4 »x 4 -f z » x ^f.x a~rpff,

^c. qui fume ipfiflimi termini Seriei propofitae. Sed
comparando has Series, fi terminus aliguis Seriei pofte-

rioris fit x Y^^-r-ny ^c. x x •+ p — i cohftac termi-
num uno ulceriorem in Serie priori fore

— 'ffT Summa itaque Serici pofte-

tioris ufque terminum x x xJ^ny&c,^ x q- p i ^ m-

clufive eft

xyx-\>nx^c.yx4pf} — 4-*-»X4X^g.x gJ^p-^jn
pHr i»

^E. D.

Scholium I. In hie propofitione continetur particula
qusedam Methodi incrementorum, de qui ante biennium
librum edidit-D. Brook Taylor Soc, Reg. Lond. Seer, mihi
amicitia conjundiflimus. Librum ipftjm adeat qui de
ea methodo plura feire velit •• ad inftitutumnoftrum ftiffi-
cit obiervare quanta interfit afSnitas inter Method um hanc
& Methodum Fluxionum feu differentialem Nam ut in
Methodo differentiali, ad inveniendum difterentiale ip-
fius X dignitatis x”, unum latus x convertendum eft in
differentiam <a?x; & ortum ducendum eft in dignitatis
I ndicem m, ui {it m dx x”* - ^ difterentiale qusfitum ; ftc
in Methodo Incrementorum Ad inveniendum Incrementum
fa6H hujufmodi xxx-|-»xxq'z^, (ythi f Adores x +

( 6i6 )

funt in frogrejflone Ari hmetica^ cnjus differ
Communis eft i^fius x Incrmentum datum n.) pjclorum mini-
mus X convertendus eft in Increment um, ^ ortum^ducendinn
‘Cfi in numerum Fdtiorum, ut ftt ^ n v. xl\ n n. x n In*
crementum quxfftum^ numero Faclorum in cafu expojito ex-
dftenu 3.. . Sic etiam ipfius » x a; -f ^ Incrementura fit
X n X n,

' 2. Incrementa etiam Recipirocorum hujufmodi FacfJo
rum inveniuntur per eandem regulam ; hoc nempe obr
fervaco, quod cum fit Divifio contrarium Mulciplicatio-
nis, viee;ai)lationis minimi Eadorum, fit jam addendus
^lius fadlor. adhTTC uno Incremenco major ; item quod
Fadiorum numerus . fit fcribeiidus cUm figno negacivoi

Hoc pado ipfius —Incrementum fit

^ » xxx-^n

Jncternemum fit

— 2 X »•

& fic

“a'x a; '’'•.r*****. xAr n ^ ^ *

do_aliis hujufmodi. Hoe facile probacur fumendo difie-
rentias inter Integralium' valores duos continuos.

3. Infiftendo vefiighs Methodi diredas, hinc colli-
guijitur pr^cepta jV^ethodi- inverfie, quil^us inveniuntur
Infjsgralia Incrementorum. oblatOfum App licet ur enim
Jncfsementum oblatum ad later is Incrementum, datum \ adda-
fur Faltor adhuc uno Increment 0 minor y ^ applicetur ortum ad
numerum FaH or umftc au^oium. Sic e» g. oblato ’ncre-
mento » x x y. x ^ n x x -{r % n.^ Ht primo x x x n
xx-{-zn~; deinde — »xxXA;-E»x«q-2;?, addito Fa-

dore X — n; denique ^ quod

eft Tntegrale quaefitum* Hoc quidem ubi Fadores func
Mulciplicantes ^ Ubi vero Faitores occupant locum diyi-
foris, mutacis mutandis, rcgiila' haec eft, Jpplice-tur In’^re-
metttum- oMamm ad Uteris inc remeftt urn f -datum rejiciatur

Falforum

( <>57.)

faBorum maximus, & applicetur ortum ad nmnerum TaBo^
rum reliBornm cum figno negative. Exempli grati^

©blato Incremento — ■■■ — : ; , fit primo

X -K X n X 2 »

— ==zz, deinde — =L=- , denique

x\x-\-ny.x-^2n ■ xxx ft

— ==, feu quod eft Integra:^

— . z '< X X ft z X % X ft

qu^iitum.

4. In cafu hoc noviftimo Intcgrale invemum, cum
figno contrario, xquale eft fumm^ omnium Incremento*

rum in Serie in infinitum continuata<; v. g-, eft — —

2 x: X X -j- »

xy.x-]-ftxx-\-zft x-\- ft X X -\~ 1 ft X X ^ ft
+ r---' -T'-T — .= — ■ . -}- Nam in hoc ca-

X Z ft -a X ^ ft X X ft

I

fu, fadox' tandem infinite, evanefeit ==^j hoc

Z X XX -[- ft

eft, ultimus terminorum B, C, ^c. fit nihil ; & ob
contrariecatem fignorum Integralis & Incrementi, vice
— A exprimitur aggregatum per A.

Lefftma i.

Per X defignetur terminus quilibet in Serie quivis
numerorum M, N, O, P-; ; per x defignetur locus

termini iftius X in Serie ilia {y,g. utfit i, quando
defignat X terminum primum M, fit x: — 2, quando
defignat X terminum fecundum N, & fic de c^eteris) &
fint terminorum N, O, P prima differentiarum pri-
marum h, c prima differentiarum fecundarum, d pdma
tertiarum, e prima quartarum, & fic porro. Turn eric

F f f f f X=^M

4*^X

( 6)^ )

X T X — 1

X

X — i

X X — , X — f X’ X X 2

X — -\- e X- X X X

X 3 i X 3

X — — 4. '

1- Sequitur hoc ex tabula- a^quationum pag.

4 ^

66. tra(^atua noUri Effay d'^Analyfe, 6‘c-.

Lemma x.

lifdem po(itis,per 2. dcfignecur terminus quilibet in Se-
rie Arithmetic^ proportionalium a, a a^z», &

fit jam A zx 2.Ar ft D z x z -j- rt
Xz-\- ^ yt E zx"!^ nxz> -\-2.nx^

Turn ipforum Af BrC, D, B, &c. valores erunt.

A=.M-\-h X — --\-cx — -X — i —
n n . zn

. . — a — a — n — a —

4“ « X X

+

X n

n

2 n

3^

+

, — a — a — n — a — zn — a — \n , , ,

4- f X K ^x- X ■:

B

n

x^ 4-^ X

n zn
— a — n

-1-^

n n

A — n — A~^zn — a —

zn

— X

<? — x-^ X c -A-

n 'o-n

n 2n

-a-zn

n

■4 f X

6‘c*

-a~zn -A-2,n

X J_ .

n x»

1 I

— X

n

X dA-ey^

2n 3 » ‘

I

n

£ 1_ X — X X e 4 &Q»

n zn- ■ 3^" 4»

Ordo

( )

Ordo formandi coefficienres ipforum h,_c, e, ^c.
in his valoribuSj per fe eil fatis tnanifeftus.

Demonftratio. Quoniam per x ^ z, defignantur termini
correfpondentes progrefTionum Arithmericarum i, x, 3,4,
^c. tk a, a-\- a ~\~ zn, a ^n, (^c. indicabit — i
numerum differentiarum qui in ^ cominetur, uc fic

Z — A

z~ aA- X — in. Hinc fit x — i = ■, — 2, r=:

' n

z *'■— n ■ A Zt — — X n — A c* A • j •

— — , X — 3 = , vse. Subuituendo ica-

n ^ n

que hos valores x — i, — x, x — 3, ^c. in Serie
Lemmatis prsecedentis, & terminis in ordinem redadtis,
prodeunt ipforum A, B, C, valores exhibici.

Cor, Vhi d=z n, prodeunt A, B, C, D, ^c, per for*
mulas fimpltciores, nempe

M

— h-Yc —

d A- e ^c.

Bz=

1

n

X ■“ X c

3 — 4 ^ ^c.

C =

I

X — X f -

^ id ~Y 6 e &c.

n

X n

I

I I

X d -Y

Dz=z

X X —

n

xn 3 z?

Lemma 5.

Symbolis X &C. x eodem modo interpretatis^c in '^Lem-'
mate p imo, Tint r, s, t, u, (Al'c. generatores Triangu-
]i 'Arithrnetici cujus Imeam tranCverfam, occupat Series
Al, in ordine nempeinverlb, utfit^frri: M)

gencrato uicimus, r penultimus, / antepenukimus, &
fic porro. Tumeric

^ , AT — I , X — I x‘, X — I X jr-pr

X—q-\-rx \-sx ^X— r^X- x— x— 1—

^ I X 1x3

-1- &c.

Conkac

'(■ 640 )

Cotiftat J0X contemplatione ipfius Trianguli Ariihmeti-
i^ci, quam exhibuimus pa^. 63 tradatus^/rf> d'Anuljfe, &e,
, ubi idem fufius explicatur.

Ltmmd 4.

'lifdem pofitis, & Symbolb eodcm modo interpretato

'ac in Lem. z, Ci fit = A B z -\- C z, x z> ff
.ut m Lem. erunt coefficiendum A, B, C, D, valo-
res.

I - — d I — — d — ^ 4 —1— fi

.A — q r X — ^ + X

n zn
J~n

n

X

B — —Xr-\-s

I

zn

a

— a — 4 — a n

n

a

a

X

z n

D

— X — X j -1- ^ X 1- &€.

n In n '

— X X — X t + &c.
n zn

Ordo coeffidentium in his valoribus eft manifeftusj
-& demonftratur Lemma ad modum Lemmatis z.

Cor, I. Ubi 4 — coefficientes, A^ B, C, D, d^c. pro-
deunt per formulas fimplidores, nempc

A=^q^r, Cz^— ^ — xi— ]f

n zn j

VC*

j5 = — \ r — Si D
n

— X X — t

n zn 3 »

Cor, z. Unde ft generatorum q, r; s, f, tt, d'c* aliquot
iint inter fe ^quales, exhibebitur X per formulam
ftmpliciorem , evanefcentibus aliquot coe/Edemium
A, B, C, Dy &c, ®

Sic

( <54* )

Sic exempli gratia, propofita Seric numerorum
4» 6% J30, 2676, 10350, qui conftituunt lineam
decimam cranfverfam in Triangulo Arithmetico cujus ge-
ncratores tres priores func 54, — 18, 5-, & feptem pofte-
riores (unt sequales 4; exiftentc 4=1 =z», Terminus
exhibetur per formulam quatuor tantum terminorum.

_ ± Z^ z±i ^ ^

I r 3 7 ^ ^ I z

z-\-6 z

-7Xy

,&c.

Z’\"\ j z-^ 7 . z z~\~i

J I J 8

z -4- 8

evaneicentibus coefficientibus fex primis B, C,

^ 9

Z), f-

Invenire

fummam

M

Trop. II. ^rok

quotlibec

+

terminorum

M

Seriei

a -x a -{- &c. a-\-»x &c» ^ a -\-pn

4- ' ■ — ■■ ■ + &c, ubi numeratores

d -\-z &c. X 4 -f- p 4- I »

Af, M, 0, &c. conftituunt Seriem quamlibet termino-
rum, quorum difterentije, vel primae, vel fecundse, vel
aliae quaedam dantur ; vel quod perinde eft, qui confti-
tuunt lineam quamvis tranCverfam in dato quovis trian-
gulo Arithmetico ; Denominatores autem conftituunt
Seriem in Prop. I. exhibitam.

Solutio, per X defignetur primus fadorum 4, 4 -j- xi,
4 -{- 2 ^c. in denominatore ejufdem termini, uc fine

X 8iZ iidem ac in Lemm: praemiftis, adeoq iie deftgnetur

X

terminus quilibet Seriei per — -.-j

zxz-^n^ &c. — n

Per Lm,Zf vel per 4. Cprout magis commoduna

G g g g g videatur

( ^41 )

videatur vel difTerentias,vel generatorestriangulr Arithme*
tid adhibere,) refolvatur^ in Multinomiuno A^-\~

C z xz ^ z>-\- ^ 'i- ^ -|- Hoc
pado (terminis multinomii ad denominatorem ^ ^ & 4“ ^
&C:. -X. z p — n, afpplicatis) terminus quilibec Seriei

revocabitur ad.formulam

B

X -]- » X z. p — I «

— .

z-T»'>^&c,xz.-\-p — I » ai.-{-z«x

Unde Cper Scholium 4 Prop. T.j aggregatum totius
Seriei, a termino ===■ inclufi-^

2, y. X » X ^£, xz. 4- p — I ^

ve in infinitum continuarse, eft'

A

p — I ZJ4 n X z -\-p — ^n^

p — z4~ ft X ^c. p — -2, n

■' ' ' ; ' — “H

3 X X z, 4- X X X z. p — i »
re- ft demacur hoc aggregatum ab ejufdem aggregatii
valore quando zr—a, refiduum erit fumma omnium

terminorum ante terminum ^ , hoc eft, tot ter-?

minoEum quot funt unitates in ~ — Q^E. I.

Sit primum exemplumiaSerie ^ p u i ^

41

( <^43 )

41

5-7-9-II -13 If

+

liL

7 . 9 . 1 1

IS . 17

473

9. II. 13. 15^. 17. 19 ' 11.13.15.17.59 x1

^r. Sunt hie 4 r= 3, n f — 6, 7Jf — 5, & ca-
piendo differemias numeratorum inveniuntut h = 36',
c ==: 54, dz=iQ — e — ^c. Hinc in L^mmate fecun=

X

i£-

4"

?-CQ

4

do flint — 5 -|- 34 X — ^ -j- 54 X
5 = X 36 + 54 X— —

X7 •

:= — , D—.o-=.E-=:^c, Summa itaque totius Seriei
4

C = — X — >*54

2. 4

109

eft

•*4XfXiX3.5.7'9»Ai

+ :- ' -

+

99

^ X4 XX x5 -7 »9-i^
183

atque

4 X3XxX7»9«^i 80 x3 • 5 • 7 -9 •

fumma terminorum numero C= ")

x8?

X09

24 X 2i-|-4 . 2:, 4-6 .

^ -3

X -

80 X3* 5 . 7- 9 • 40 X ^ & "h 2- . Z-\- Z-\- 6 .

I 99 27

1 6 y; z~\-z x 2i-H4 • ^ ^ ^

Quajrantur v. g. odto termini ; turn exiftente

8 fit 23—19, quo valore in formula ad hibito, prodic

funama.— ’ ,

2. 3 .3 . 3. 3 . 5 . 5 . 5 . 7 . II . 19 .23

lidem Numeratores occupant lineam tertiam tranfver-.'

in Triangulo Arithmetico

54 . 54 . 54 . 54 . 5.4 • 54 ‘

— 1 8 . 3 6 . 90 . 1 44 . 1 98 .

5 -41 . 131 . 275 .

’( <^44 )

Unde in formula Lm. 4. funt generatores ^ = f ,
~ 18 ; i = 54, t = o = & piodeunc qoeffi-

^cientes^ = 5 — i8 y ^ + 54 x ^ x

— 18 + 54 X ^ C=r= —

4 ' a 2, X X

X — X ^ 4 = — » D =?: o = B = iidem ac fupra»
4 4

i-

£;c’. 2. Sic Series

ii'X*.^ <4*5*^ •7*8«9*^o« II
M ^9 _ . , no , . ,

~ X . 3 . d'c. 1 X ^ 3 . 4 • M 4 . 5 • 14 ”

+ d'?* Ubi font 4 = 1, » := I, /) = ir.

f . 6 . d'^^. 1 5

atqueNumeratores coflftituant Seriem in Coni. xo. Lem. 4.
exhibicam. Applicando itaque valorem ^ in Ctfr»/. illo

ad denominatorem 4 xd<^. x^+io, fk Serici

propoficas Terminus

— ,I

i.x.3.4.5.6xs:,-|-6.z,4‘7’^4"^*^-}"9‘^+*o

+

I.2,3.4.5.6.7X;c + 7*^+8.;c + 9.x-)-iq

7^

iix.3.4. 5'^ *7* 8’t?i4-8,si4-^.x.4-io

il

Adeoque

.]

f-i‘2,3 »4*^*^*7*8*5^^'& ”j~ ^ ^ x> ~j * 1 o

per hanc Prop fumma Serici a termino ilia in infinitum
concinuatx eO:

— I

4^^»a*3»4*J' 6 » Si 7 • ^ 8 • si -j“ 9

I

+

( <^45 )

+

3X1 .^•3 *4 •5' •6.7X«-|-7

7^

2Xi.2*3»4\5‘^*7*8^-2i4“2
54

I XI .2. 3-4-5*6^ 7- 8 . 9 x*i + 9‘

Itaque pro ^ fumpto i, fit fumma totius Seriei

305

iz XI. 2. 3. 4. 5. 6. 7. 8. 9. 10
ai — I

. £c in genere fumma

terminorum numero

^cft

[2><I .2.5,4. 5- . 6 .7. 8.9. lO

+

+

4x1.2. 3 ,4*5*^ 6 . Si -|— 7 • ^ "H 8 » ^ 9

3Xi»2.3 .4.5 .6.7Xai-}-7.s-|-8.2i-|-9

72

zxi.2.3.4.5.6»7.8xs4-8x2i4'9

54-

ixi.2.,3.4. 5.6.7.8.9x=^ + 9

Scholium i. In computandis fummis hujufmodi Seric-
rum, calculus plerumque levior eft adhibitis generacori-
bus crianguli Arichmetici, quam fi adhibeantur difteren*
tiae. Libet itaque hac occafione oftendere quomodo ex
datis difterenciis inveniri pofiunc geneiatores Trianguli
Arichmetici.

Sunto itaque w primus Seriei terminus, 4 difl'erencia
ultima data, h prima difterenciaruni pehuftimarum, e
prima antepenultimarum, & fic porro d, e, ^c. atque
fine f, », )f, &c generatores quafiti Trianguli Arith-

metici, cujus lineam tranfverfam ordine occupet Series

H h h h h pro-

/

( f 4^ y

pro^o^ka* Turn (qmod^ex . coHtempktione Jriangiirl?'
Aricbmectci facile con{lat) fik«J • • r < ♦

<tr=fr

I <

P — I . P — I f — ^-r

cr.z=:^ +

— I 2 ' I '

;r— F fr-^% 3. 1 — 1

a — ^ X x* *^ — - — t + - — — X ^ u

' - 5< l- 2r-

r-

V I

+

Z:zJ^

Undecolliguotur geaeratoruni'ValoreS'.?.

/tzi; 4i-

Ufrz=zh^

r-

p'1^% ^ p-^2''

X>z= g ^ X ^ ^

1 a'*

i >■»

-■ • I ir ,j _■ ■.•!■■ . . ..

Ukimus; aucem>:genesa«)i[ squalls refl Seriei termino
pfimo * - .

de -^nfvury -'Ahhs Orlactnfi^ mihi amidfli-
muSj ruri yicinuSj poftquaiai’T&um eo hsc communf* '
caveram/ aliam invenk liujus Preblematis" Solutionem,
cujus formulam ob ejus nnram fimplidcatem hie referre
Juvac* Jtaque in Serienumeratorum fint <« terminus pri-
mus, ^ pritna'differentiarum primarum, g prima fecunda-
rum, d prima tertiarum^ & fic port 6 ; argue (it termini

pipiiDenominatpri&xx-l-;? x^g.xai+f ^ j »; Turn

fumma ^

ftfmma totius Seriei in infinitum contitiuat^ cxhibebitur
pQt fotmulani

+

n •< p — - &c. xz,-\- p — 2 »

+

— I >c f — 2 ^ » X *- + p —

ti^\ p—^i X ^ p — 3’ X 2i -f- 1 ^ &c. X z~\" p — • 2

-f- drc\

4^

Sit exempiiim in Serie .

3'.5.Csr. *3 ‘ S.7.&c.i$

V -U

d-

131-

■+

^7$

. 1 > ■ &c. cuius fum-

7.9.e;-r. 17 9. ii.,v2r.i9 ^ ^

mam jam cxhibuimusj In hoc ^aiu func w — ,, .b,^. ^ 6^1
c = 54, d — or=: ez=^c\ Unde per forraulam/jfumma

Seriei ihfegts fit" j^r-p ^

+

d-

_1 £

4’. 5 . 4 X 5- .... I j

- i8U . u^ra-fcr-^

z<»^ X3 •

o =^-^r = y ^ ■ ut pbr for-

8.5 . 4. 3x7. ..II 80x3. 5... ii» ,

. ' ;/ '<•• ^ -■ \ \\ s i 4 ■••

mulam noftram exhibetur. Si quseratur fumma ejuf-
dem Seriei incipientis a termino decimo — in

*■ - - . r,*'3;=*’ . f-c

eo cafu 6) = 22,73, ^ = 522, ^^54» & fumma eilet
- X ——111— _| - ^4' .

x*5x 21 . ..39 ^4,5 .4XXJ ...29~|~8.5.4.3 X2^....i9

Hsec fortbula bft'comraodifiima, & fummam exhibet
nullo fer^' negotio, quoties quarritur fumrna Seriei inte-
grsc, & difFerentice non funt nimis mults.' Sed ubi plu-
res funt differentire, & quceritur non Series integra, fe4 _
termini tamfim initiales aliquammulti, formula: noftrs
" comihodiores. . ...

3. Quando

( ^4« )

-3. Quando Serierum termini formantur tantum per
' Multiplicationem, nec afficiuntur diviforibus variabili-
* bus, fummx Temper exhiberi poffunc per Methodum in
Trop. I. traditam, fine ' licet formulae quantumlibec
compofitae. Nam poflunc Temper revocari ad terminos
in forma quam poftulat Propofitio ilia. Sic fi differentiae
l ipforum*. Si xCintw & n, ^defignetur terminus Seriei
per z x; hie terminus revocabitur ad formam a — »z-\-

~ t xsj w; cujus Integrale datur per Prep, I ; nempe

- quoniam dx—n, .& d x, — m, eft ~ ; unde

' regrediendo ad integralia x — a (adje^o in-

variabili a, ut habeatur ratio relationis inter ai & x in

Seriei termino primo,^ quod fic feribi poteft 4 —

X Si ut deinde in si dudJum induat formam re-
quifitam. Et ad eundem modum- procedere licet .in
aliis cafibus ejufmodi. Sed ubi formulae oblatae divi-
foribus afficiuntur, eaedem ac in Calculo integrali, ut vo-
cant, difhcultates occurrunt, eadem induftri^ Tuperan-
dx, Nec tamen Temper Tuperari polTunt. Nam prxter-
quam quod vix certo Tciri poflit q\jx debeat relatio in*
fercedere inter Numeratorem fradionis & Denominato-
rem, ut formula oblata ad Integrale revocari poftit ;
fsepe etiam difficillimum eft explorare an adiit jam tails «
relatio in formuli ift^, aut ft deftt, an introduci polftt.'
Quicquid ego in hac materia potiflimum inveni, coii-
tinetur in tribus Tequentibus propofttionibu£»

Prop, III. Proh

Crefeentibus, z, u, y, x, &c, per differentias da-
tas n, /, 0, dre, invenire valorem numeratoris in-

tegri

( <J4P ) __

tegri Af, ut exi^lente Denominatore z.z,-^ff .&c.Z‘\-pH
xu^u-\-m,drc.»-\-^f»^y> y-^l ,&c.y ^ rlxx,x ~{- o
&c. j 0 . ^c. Fradio ad Integrale revocari pofllc.
Solutio. Fiat N=z-\-pn Xu -\- q m xy rl x ;c j
&c. — zuyx &c. atquc Integrale erit frac^io, cujus

Denominator g. . -j- » . &c» ^ -\-p — \n %u . u-\- m.

€^c. t4 q — I m y . y I , ^c. y — x — \ l^-x o ,
^c. X ^ s — 10^ &c. exiftente i Numeratore.

Differentia enim hujus fradionis eft fradio cujus nu-
merator eft ipfius N valor exhibitus, & denominator
idem eft ac denominator propofitus, ut fieri debuit.
Ex, 1. Sit denominator propofitus

In hoc cafu funt n — 'i^ m=zS> P=^f t;

adeoqueeft N = -}- 2 x»-|-3 6,

& per — ^ reprefencatur terminus Seriei
z,z xy. u . u-\- ^

fummabilis, cujus nempe in infinitum continuat^ Turn*

tna exhibetur per

Z H

Sint verbi gratis, ipforum

primus valor communis i, atque Series fummabilis erit

I r

2.3

+

35

&Ci quip-

mini cujufvis in h4c Seric, erit p

1. 3x1. 4 ' 3-5x4. 7 ’ 5.7x710

pe cujus totius fumma eft i. Per p defignetur ordo ter-

% — r-f-2 u — 1 4-^

2 i *

adeoque z=^p — i, 8i u — }p — i; quibus valori-
bus pro z & u icriptis, defignabitur terminus per for-

mulam itp — t — ===-=. Summa

2/) — I xzp ^ xSp — ^ X3P -r *
autem lerminorum omnium ante terminum ilium, hoc

eft terminorum initialium numero =:p — i, eft

I i i i i I — >

( <550 )

^ ^

'' zu* zu

re pro ^ fcripto p-]-U crir

turn tot terminorum inicialiura quoc furrt unkates in f.

Ex, r Tifdem manentibus js, u, n, m, fit denomina-
tor 4" 2. • ^ ^ per formulam

numerator eric z. -|-q x« -f- 3 — 3 z, -}-

& fumma Seriei exhibebitur per formulam — — / , — ,

Sit ipforum a & » primus valor communis i, & hinc eii- i

cietur Series j- ~ ^

‘•S-5’^^-4 V^-7^4-7 5-7-9’^7.io

+ = i- . , ; i

Scholium. In Seriebus jam expoiitis eadem itbique eft j
differentia inter fadores continuos ejuldem cujuivis ter- j
mini, ac inter fadores homologos terminorum conti- !
nuoraniv In fequentibus exempla qusedam liint Serie- {

rum, quarum lummse in terminis numero finitis exhi-
beri pofliint, quamvis ea regula non obfervetur.

Crefccnte z per differentias datas ^1?, invenire nu.^ 1
meratorem integrum N, ut ad Integral e rcvocari poflic I
ftadio, cujus Denominator fit ex certo numero /> ter- f
minorum ai, z-\-z», Arithmetice propor-

tionalium in invicem dudorum. Debet autem efle q
numerus integer minor quam fadorgm numerus p. ^

Solmio. Erie N=: z-\-p^my.zJ^ p — % n\^c. '

x x ^c. x i Iiv

z, Z-\~Z-Att

Prop, IV. Proh,

tegraJe

< <^5 * )

tegrale exiftcnte — De-

X X (^c. / — in

mondratur ad modum propoficionis prascedentis.

Sumptis ad libitum p, q, & prime valore hinc
oriuncur infinicae Series fummabiles, cujufmodi funt Se-
ries tres fequentes.

tc

<(

13 . i4 . 15 . I6 . 17

Has Series jampridem communicavi cum primariK
quibuldam Geometris, a quibus minime contemni vi-
dentur. Sic ad me fcribic periciffimus Geomecra D N/cs-
Uus Bernoulli in epiftola dati if Julii 1716. “ Vous
“ me ferez un extreme plaifir^ Monfieur, de me com-
** muniquer la Solution de voftre probleme, donn^
une fuitte des Fra^Hons dont ks Numerateurs foient dts
nombres figures quelconque, ^ dont les Denominateurs
** f&ient formes du produit d'un mmhre egd de Fd^eurs
“ qui foient en ProgreJJion Arithmetique, trouver U fom-
*•' & principalement comment vous avez trouv6

“ ces deux fbrmules ■, ,

a4X4/>+i i2X3/’+‘X3?T-i

Hae formulae fpedlant ad Series C & B, defignante p
numerum terminorum, quorum fumma requiritur- Sic
eciam ad me (cribit D. Taylor in epiftola data Augo
1716. “ Uc 6c qui ratione incidifti in fummationcni

“ Serieium : a te exhibitaruna, pratfertim 4oquos> de

Sene

( )

“ Serie ,-~tT~s + 4.5-^7"8 + 7. 8 '.9’ *0“'.. +

quas videtur efle altioris indaginis.

Sed ut ad exempla jam redeamus. In Serie func
p = 4, ^ = <1 primo valore exiftentc i. Eft

itaque z. 3 y.z,-\-% — i ==:xxi-z;-|-3 for*

mula, unde frejedo dato numero derivantur nume-
ratores 5, 9, 13, 17, Formula etiam furamx eft

Quare habita ratione numeri 2, quern ex

numeratoribus rejecimus, fumma totius Seriei, a termino
in quo eft z, in infinitum concinuatie, exhibecur per

formulam ; adeoque fumma Seriei integras eft

I 1

3, X t xt 4

In Serie B funt » = i, /> — 5", ^ = 3, ptimo valore
z exiftente i . Eft itaque z-\~%

— X2i-|-2 = 6>t^:4" Ipflus autemsi-|-2

valores continui funt 3, 6, 9, &c. qui quoniam om-
nes funt divifibiles per 3, ponendo 21 + 2 = 3;^, fit
N = 6 ^ 3 = 6 X 9 r=: 54x% ipfius x valoribus

continuis exiftentibus i, 2, 3, (jre. Rejedo itaque nu-
mero dato 54, hinc prodeunt numeratores i, 2^ drc.
hoc eft t, 4, 9* &c. Formula etiam Integralis eft

~^-q— ; quare habiti ratioas numeri 54 quern ex nu-
meratoribus rejecimus, fumma Seriei a termino in quo
eft 8k in infinitum continuatae eft Unde fui»-

54 ? r *

ma Seriei Integra eft

108

In Serie denique C funt = r, /> = 5, ^ = 4, &
primus valor z, — i .Unde dtN=z + 4 x % -|~'3 x ^+"2
XS-|-I — ^X^-r|-lX2;-]-2XSk^-3 ■— 4 ^ -|- I

X

( )

z.-\- ^ x5^-f- 3* Valoresautem Nper hancformulam pro*

deuntes femper pofTunc dividi per 4^ ix 3x4 — 5^5.
Ergo hoc divifore rejedo prodeunc numeratores i, 14,
S5,i^o, &c. Ec formula Summse, habita ratione nu-

meri 96, eft Adeoque SummaSeriei Integra eft^.-

i

t

I

I

Scholium I. Per Propofitiones has duas noviftimas
nullo negotio inveniri poftunc Series quot iibuerit
fummabiles. Et viciflim oblata Serie hujus fpeciei, fi
fummari poteft, ejus fumma plerumque revocatur ad
alterutram ex his Propofitionibus. In examine tamen
folertia eft opus. Optime autem procedit fi termini
Seriei oblata revocentur ad formulam Prop- HI. Sice.gr,

Serie 2 .4. LI 1_

3 . J . 7 .9 . II 7 . 9 . II . 13 . 15

propofita

LJ J_ Denominatores fic fcribi pof-

11 . 13 . 15 • «7 • ‘9

funt 3. 7. 11x5’. 9, 7. II. 15x9. 13, II. ij. 19

X 1 3 . 1 7 •

Unde Juxta Prop. IH. fitT^^q, m — ^, ^ —

primus valor 2s— 3, primus valor 5. Hinc formula Nu-

meratoris invenitur 4^z,-|-x»-l-8,Eft autem -f- 2, » -j- 8
femper divifibile per 3 ; quare rejedis diviforibus da-,
tis 4 & 3, per hanc formulam prodeunc Numeratores
7, ii, iidem ac Numeratores in Serie propofi-

ta, qu£E proinde fummabitur per illam propofitionem.

2. Cum Series illas B, C, communicaveram cum
D. Taylor, refcripfit fe earum fummas invenifte primam
quidem ^ & tertiam C, eas revocando ad cafus fim-
plices Method! Incrementorum, tertiam C, e g. revoca-

vit ad hanc formam ^ - d — ■ — h — 4- — ^

24 1 . 5 5.9 9 . 13 * 13 . 17

ut habeatur fumma per praccepra tradita in SMio Prop, i-

Kk k k k In

( <5j4 )

In Serie autcm fecundi cum hoc non (squo fucce/lit,
fequenti ufus eft Analyfi, quam, ipfius venia jam im-
petrata, ob ejus eximiam elegantiam hue transferre
non piget. Seriei iftius terminus [in Stylo ejus] ex-

hibetur per formulam =4= j pro

1 Xi[X;t+ I
» /

} in denominatorc feripto z, quoniam eft 2; = 3.

"B B

“ Pone acquale efle Integrali quaefito, hoc eft

X I 1 X ^ ♦

^ efle Integrale ipfius — == * -■ ■■—» fepolito divi-

fore dato 27. Ipfius autem incrementum eft

" Debet ergo idem eflo ac

^ cc ^ cc

t •'

I x;?.;?+l‘

‘ #1

Comparando' denominatores inveni-

“ tur C = » X I. Hinc itaque fumendo incremenr
** ta fit C= z zz, z (=zz zz ^Zi quoniam

“ eft a — 3,^ His vaioribus in locum C & C fubftitu-
" tis prodit B C — Be — zz-]- zy- B — % z>xz-\- z Bt
** quod debet efle idem 2iC z-]^z x z, SiiB—a-\-*v,
exiftente a ipfius B parte invariabili, & parte va-
“ riabtii. Turn fumendo incrementa fit B z=. 'o. Unde
‘‘ ad invenienda a (k v habetur aequatio zz-\-^"^
“ — 2!&-x2i-h2X4-j-'z;:?=2i-H2xfc,. quae fic feribi
poteflz-ai + ai •o — % z%z-\- zv— X i+2-4>

** vei etiam C 'zf — C<i/ — Pone

‘‘ I o (unde fit 4 — Cv=o;

“ uhi

♦I

( <^55

ubi fieri poteft vr=:o, (quoniam srquationis termini
fmguli affiduncur vel ab v, vel ab 'v) Plinc ergo fit B ^

I ____ I

4 = —, adeoque -F = — 7=^. Unde habita ra-

^ ■* ^ X:?X;^q-£'

“ tione divifbrrs 27, Integrale qu.^fitum fit- L=:r

54X;(X;? + i

“ Sed & comparando sequationem C

^ ^ B C

formula general! • — o, inde etiam condude-

9 T

** re licet elIe-^= quantitaci datse, ('qaoniam ipfius

“ incrementum eft o.) Unde pro n fumpto quovis
** numero dato, fit v — n C, atque B = ^ c.

Quo pado Integrale qusfirum fit

“ 4" Sluod ab-Tntegrali prius iavcnto diftert quan-
“ titate data Hoc inde fit, quod, ut in quadracura
Curvarura Area inventa angeri poteft vel minui arei
“ data, fic in Methodo inerementorum Integrale inven-
“ turn augeri poteft vel minui quantitate data. Per
“ Integrale autem primum, ubi deeft », exhibetur
I* fumma Seriei in infinitum continuatie.

Prop. V l- ,

Crefcente 2. per unitates, & exiftentibus-^*,
numeris datis integris, quorum nullse inter (e aequantur; -

invenire Integrale ipfius — === — — •=— — rr-.

Solufio. Ducendo tarn numeratorem quam denomi= -
natorem- fradionis in terminos ^ 2,,

z-\-a -\- 1^ z-\- a -\- z<i ^c. z-r\-h-\-T^f z-\-b .

z -\-c-\- I, z~\-e-\-^, ^c. in denominatore deficien-
tes, . revpcetur Denominator ad forraulam

XX

I

( <5j<5)

■Xsi + l X^c. denominatoris in Prep.]. SchoL
Deinde revocetur Numerator ad formam /i B z, -^Cz
X z-\- i Dz>^ z -]-i Xz-\-z Turn appli-
cando terminos ad Denominatorem novum z>^z-\- i
xz, -\-x y. c^c. revocetur fradio ad hanc formam

^ — -4- : JL- h=

^ X ^ -f- * (3c. K~[' ^ ^ K "h i K (3c.

+ X (3c Unde denique quseratur Inte-

grale per &chel. Prop. I. 3.

Ratio Solutionis per le facis eft manifefta.

Scholium r. Hujus Solutionis tota difficultas latet in
revocatione numeratoris ad formam requifitam, quod
tamen quomodo fit faciendum uno exemplo patebit.
Proponatur icaque fadlum ?X^ + 7» quod

ad formam propofitam fit revocandum. Terminos ita-
que evolve gradatim ut fequitur. Faeftorem primum
z-\-z fie feribo cujus terminum primum z

duco in 3 unde fit 6j^\~zz>: Terminum fecundum z
duco in z z. 1 f = z -j- 5) unde fit z ^ i.

Dein fada in unam fummam colligendo, fit z -{-%

x*^-l-3 =^ + ^+ * X '■+ ‘ = '5+4s + «ix

Supereft ut hoc ducatur in & 7* Ttaqnc
terminum primum 6 duco in .7 z. (= z. 4~ 7) unde
fit qz 6 z; terminum fecundum 4 z, duco in 6 % 'j- i

i~ z. -|- 7) unde fit 24 i?i 4 zx z i ; terminum
tertium z. x z-f- 1 duco in 5 -f- z-^ z ("— 2^-4- 7,) un-
de fit ^ zx i z-j-z. Fadis iraque

in unum colledis ut prius, fitz.4-zxx z-'r^

rzr:4X-|-30Z.-|-92:,’«2i-|-I-|-Z.X!&-|-iX!&_^2. Ec
ad eundem modum procedere licet in aliis cafibus.

z, Sic

( )

z. Sit autem exemplum Propofitionis in fra(3rone
Reftituendo faflores ^ + i, si + 3,

z-j-4 in Denominatore deGcientss, fradlio fie

l±_L21ljhiJLL±4 r> ,

:^x^i-ixK-h2x:( +1211.+ 4illi ^ ' ^^^afidus ita*

que eft Numerator ?i-}-ix2i-j-3X«'-f4 ad formam
requifitam. Itaque per mechodum jam tradiram fit

primo z-\-i xz -[-3 — i x }-\-z -\- zxZ-\- -|-i

~ 3 -|- ^ -j- ^ ^ z, I — 3 -|- 3 ^ -j- g g I.

Deinde z-^ i x^-j-3Xg + 4=z3 % z

X 3 -\-z -]-l-|-2,xz,_|-i — ix-j-jg-j-qg

-]-3!&X!5,-[-I ^ % Z X Z I -}- 2i X g. I Xg
rzr: I 1 — j— Ix Z — 1~ ^ Z> "><■ z I —j" Z x z — I X g ~1“ ^ •
Applicando hoc fadum ad Denominatorem x z. i x
&c. ^ z-\- 5 fradio tandem revocatur ad hanc for-

mam

II

+

^X^+iX^-hiX;i-f3X^+4X;?-f-5

4-

^ ^+»X^ + iX^4-3X;?-l-4X^-t-5

’ +

^ + 2,x;?+ 3 X;? + 4X^4-5

Cujus denique Integrale eft

+

^ -4- 3X3] Hr 4 ^ 'f~ '

— 1^

— 12

4.3' + iX3:4-2*‘;{+3 ^^4*4

— I

5;^X;^4-ix;?4'^X;?4-3X3;4-4

H-

3.;^4-2x^4'3''^^H-4

2.;?4~3^^H-4

3. Quando duo tantum lunt fadores a & g +

I I

exhibebitur etiam Integrale per formulam—

. d’c.

-4x2

1 — /jx2 — 4x3 — a

33[x;^4-i>^^4«2 45 ^^4“I>^^4-s. >«;?4-3

Seriem nempe continuando donee abrumpacur per eva-

L I 1 1 1 neicentianai

e 658 )

ncfcentiam tctminorum. Si Fadiores duo Tint — #
cxhibebicur Inregrale per formulam

— &c. Poteft idem Integrale

— I -f> J ^ — r a

3 • ‘ • 3: — 3

exprimi ucroque modo, prout fradionis oblatai fador
vel minor vel major fumatur pro 2:.

4. Si primus valor g. fit a -\~ t, migrabit formula

pofterior in hanc ^X-7 ^ ^ ^ ufque

inclufivc, qu^, cum figno contrario, cxhibctur fumma

Seriei „ -4- ■ ,■ -1- , ^

' 2X2“T4 3X3“T*«

nitum continuarse. Sit r. g-/*, 4= 1, atque Scries eric
+ r^3 + F^4+^‘'- = T’'T = *-S'‘' = »>e-

1^3 2,x4 3><^5 * » g 4

Si «=3, Series erit ,-^+ril +T^ +

+ &c. in infi-

J X 2

rit Series

3 1 ^ 3 18

+ ■

<. Ex eadem Serie — === . ^

■* lXI-t-4 2’^2-f~<* 3>^3“r<*

'4 &c. pro diverft) valore a oriuntur Series plures
forml fatis elegantes, quarum nonnullas Ledori ob
oculos fiftere, credo, ingratum non erit.

Si pro a fumantur fucceflive numeri pares, ^, 4, 6, 8,
&c. Series erunt

Si<*:=2)

4)

6)

8)

+

■f

ixi-^-2 2X2-p.2 3^3-t-» 4><4-i-2

L^4- — L=r--J. L=- 4-

I X I 4-4 * 2 X 2 -r4 3 X 3 Hh 4 4x44-4

I , I j i I

Wil im— _ ■■ L,— ■■■■—— ~j ■" ~ ■

I X I 4“ 2x2 4“ ^ 3^3 "i" 6 4^4 4“ 6

I » I . 1 J , I

T'f'

3+

i X 4* 8. * 2 ^ 8*3X34“8 4X44-8

+ ^c:.

Vel

( <^5? )

JIT, +?~. + +

5^7 +:^, + pr

— I L ^ _r _Jl L — L- 4- (^c.

l6 — 9 ‘ 25 — 9 ^ ^ 49 — 9

v5-4

I

3^—9 I 49—9

___i — f ? — 4_ r -I ! s- r^c.

25-16 ‘36 — i6~49— 16 ‘ 64 — 16

* 4" £^c.

Vel — ^ -f* — ^ + -^— +

4 — I 9 — I 16 — I 25 — I

.-1. ,

44-1 94- 3~ 164-5

+

+

— ^ f * t I

44-3-94-7~‘ 164-11^254-15

C^c.

254-7

* 4" G?c.'

4 4_ y 4“^^ J , 4~ J54_iy 4" 254-23
Si pro a fumantur fuccelTive numeri impares i, 3 > 5“» 7»
&c. Series erunt

a = i)

3)

■r+.

4- h- +

IX14-1 ‘2x24-1 ^3 ^3”t“i 4x44-1

“ ' f— =+ '

I X I 4-3~^2 X24-3^3 X 34-3^4^44-3

5)

7)

i ^i4-y*^ax24-5~^3x34- 5^4 x 4 4“ 5

4~;

■+■

I .

i x j 24-7^3 X3 4“7^4^44-7

Vel— X

4-

4- -- 4- -

‘6 ^10

-fx -i_ . ^ , _1_

2- 3 — I* 6 — I 10 — I ^ I 5 —

X ^ — L — L_ ^ 4_ L_

2 6 — 3 I 10 — 3 ‘ IJ — 3 *^21 —

— X L.

2 JO — ly — 6

3 • I?

' + 2-7^. '

Vel — X '

— -X --L

2 14-0*

t

21—6
I

28 — 6

I

r I

— X — —

2 j-f.

I I

4- * _L __i-_

‘ 6 4- ° ‘ 1 ® 4" °

3 -J- o

T+ f+T + A — !■» o + ‘

6 -i- 3 10 4- 4

II I j

» ^ I Hh 2 3~4-1^ ^ 64-6

1 I

— X -
Z I

I o — 3

j 1 _i ^ y I

4" 3 3 ri" 6 4- ^ _j_ ^ 4- ^ J2.

-i“ ^c.
4"

4-0'c,
4-
4-

4“ C^c-

4"

4-

4-(^cr,-

4"

4

6 Ante

6, Ante aliquot annos D. Jac. Bernoulli Geometra

infignis invenit rummam Seriei cujuflibet, cujus Name- ,
ratores conftitaunt Seriem aequalium, Denominatores i
vero conftiruunt, vel Seriem quadratorum dato aliquo .
quadrate 2jnioutorum, vel Seriem Triangulorum, dato '
aliquo Triangulo T minutorum. Haec invenit ille ob-
fervando quod hujufmodi Series oriantur ex ablatione '

Seriei Harmoniee proportionalium truncatas ab e^dem ■

Serie Integra ; nempe ita ut numerus terminorum defi- !

cientium in Serie truncata, fit, vel du plus lateris dati 1

quadrati vel duplus unitate audus lateris dati Tri- •

anguli T. Idem etiam obfervavit fruftra quaeri fum-
mam Seriei reciprocal Quadratorum. Hoc idem etiam
verum eft de reciprocis Cuborum, vel aliarum quarum*

Ubet dignicatum numerorum in progreftione Arithmeti-

ca. Ratio eft, quod nulla intercedit differentia inter J

fadores denominatorum, quod ad hujufmodi fumma- {

tiones femper requiri conllac ex Methodo fumendi >

differentias in SchoUo Prop. jam explicata. Nam fi -j

per formulam aliquam exhiberi poflet fumma quicfita, '

differentia iftius formula exhiberec terminos Seriei
propofitae.* fed in tali differentia denominator femper ^
afficitur per fadores ab invicem diverfos, quod quo-
niam in Seriebus pr.xdidis non obtinet, fumma: Serie- j

rum hujufmodi in terminis finitis haberi nequeunt. Ad *

eundem fere modum, argumcnco petito a Prop, HI. &

IV. demonftrari poteft fummas Serierum exhiberi non
pofle in terminis numero finitis, quarum Numeratores .J
conftituunt Seriem a’qualium. Denominatores vero con- ;
ftant ex certo numero terminorum in progreftione A- ;
rlthmetica, maximo fadore cujufvis termini minore ex- . |
iftente quam fador minimus in termino proximo in- |

fequenti, cujufmodi eft Series

7. _Jam liceret regulas nonnullas tradere quas pro j
cafibus quibufdam fingularibus concinnavij fed hare

nos I

( 66 1 )

nos longius abducerent. Sufficiat itaque quas ; genera-
liora ;funt explicafle, & fimul monuifle, ad nov^ hu
jufce Serierum infinitaruni dodrinse provedionem ni"
iiii magis facere, quam fi excogitentur formulse ge-
neraliores fummarum, ex quarum diff^endis, .per re»
gulas fupra traditas computatis, deinde conficiantur Ca-
nones quantitacum fummabilium ; ica fere -uc jam fa-
dum eft in Calculo Integral!, h. e> in Stylo Newtoniam^
in Methodo Fluxionum. _

'8. Reftituendo fadores in Denominatore deficient
tes potuillet prsefens Problema revbcari ad Fropalftio~
mmW, Sed & in terminis generalioribus proponi po-
teft, nempe pro Numeratore fumpti quavis For-
mula, cujus differentia aliqua datur. Sub ea ramen
conditione ut dimenfiones Denominator is ad minimum
binario fuperent Dimenfiones Numeratoris ; alias enim
fumma Seriei in terminis numero finitis haberi ncquit.

Sit hujus rci cxemplum in Serie 777777^ + T. 4^6. 8

37177^+ ^70777 4- “b* I^utoeratores funt

numerorum naturalium quadrata. Applicaiido turn Nu-
meratores turn Denominatores ad numeros naturales,

I 2/

Series revocatur ad forraam fimplkiorem ^ ^
5T7~9'^6.8.'jo + ^^» Per P defignatis numeris na-
luralibus i, 2, 3, 4, &c. terminus Seriei defignabi-
tur per formulam — ; 7—^ — =f^ ; vel per formu-

pro/> -f i fcripto z. Quo-

niam progrediendo de termino iii terminum augetur
z. per unitates, reftituendi funt fadores in denomina*
tore dcficientes ^ pado revoca*

tur terminus Seriei ad formulam — ^ j_=r-

Per methodum in h^c Propofitione jam explicatam re-

M m m m m vocatur

( )

7ocacur numerator ad formam — 5 — — zxz-\- i*

-|-xxz-+iX^4‘^’ Unde habitai rationr denomi--

natoris Terminus revocatur ad ibrmam .

, - r

* » X l + X X t.4- 8 X ^ + 4 ■ ^+2.X ^4" 3 X 4.

4- ===r-^-^«==. Adeoqufc Cumendo^ Imegrale fit.

6'

3.x? +i X?4-»X? + 35

— »== 4- J-r-r ; , quo, . Tub figno contra-
rio, exhibetur. fumma. Seriei in’ infinkum continuaca?^
incip;ieatis . a . termino > ^ ^ itaque :

Seriei integrae. incipientis a termino ~ eft‘

Si i per Pr»p, \h proeedere eflet animus, ex formula t
z — i x.zi -\t 1 x 3^ colledii numeratoribus primis-
a4, 70, i44i x52,.fiimendo eorum difierentias babe-
rencur 46=^, 28 =r, 6=d, e=:o=i&c» exiftente
M=z 24 ; unde perXfw. 2. prodiret formula — 6 — 6 z 1
— z X &-f" * X z- + qud defignatur Tet'

minu&, eadem ac fupra ; acque pergendo per Prof. U.i
baberecur fumma^

Frof. VI. Prohl

Invenire fommam quotlibet terminorum Seriei Fra-»

' Sionum^ quarum Numeratores & Denominatores epn-
fiituunt lineas duas quafvis tranCverfas in Triangulo>
Arithmecico Pafchalir; nempe cujus generatores funt
unitates.

-Svlutio* Per*;? defignetur Ordo Seriei Numeratorum.
in Triangulo Arithmecico, & fit f differentia inter
ordtnem Numeratorum & Denominatorum, & per.^
defignetUcT numerus terminorum quorum fumma re-

quirkur

( d6j )

qairicur. Turn (1 Deaominatores fmc plurium
fionum quam funt Numeratores, Summa exhib^bitar
per formulam primam' {equcntem j Ci dimenfiones-
Numeratorum plureS/ fint quam dimenfioncs Deno
minator um, . Summa. exhibebitur per formulam fecundam.

Formula:. I.

n 'T^p — I w ■ »-t~j .«>4- 2 « €^c. w «4~ P — »

f — ^ ”” p — I ^

Formula IL

n — f — I . \ — 1 ,^c.q~\-n — p — i

P + * — i.« — — p

Ex, I. Inveniendum fit aggregatum fex primorum?

terminorum Seriei — + -i'4- ^ -f - ^ H ^ "F ^

ubi Numeratores conftituunt lineam quartam, Deno*
minacores condituunc lineam feptimam in Triangulo
Arithmetico. Sunt itaque. » = 4, f — y*
quoniam dimcnfiones Denominatorum fuperanc dimeu-
iiones< Numeratorum, dabttur fumma per Formulam <

primami nempe — ; — T“ — ; dve

^ 3 — i 3,— I X 4 + 6X4 + 7

Ex, z: Quseratur fumma (ex primorum terminorum >

Seriei +— -1“ ^ 4“ cuius ^

termini funt terminorum Seriei prioris reciproci. Sunt
itaque » = 7, f = 3» adeoque per formulam ?

fecundam fiimma fit — ^\‘xl \ ~

Scholium 1, Formulas in->hac propofitione exhibitas^
ante biennium communicavi cum Viris celeberrimis
Molvreo & BermullHs, Facile autem derivarr polTuntr
ex prxeeptis in Pro^, I. traditis. Sit exemplum in Se-

rie priori "7 4"-^ + ^ + ? defignato loeoi*

Tet?‘

( <J<i4 )

"JermK)> rri‘Se46,^jic» exhibetuf Terminus per formulam

• • .^_y ^ ' 11^0

Unde regtediendo ad Inregtale,

4- 5 .<$

fumma Ssriei incipiencis a cermino illo exhibetur : per
formulam — -r^ ’4===» ; a4eoquepro/>fumpto f, Se-

^desr integra fit 'atque fumma primorum

fex terminorum fit g ij-Lii- omnino ut per for-

- X . IQ. . 14 .

mulam jam. exbibetuf. , ^ ^ <

2. In formula prima fumma Seriei in infinitum con-

tinuatse eft.” ? ~.d./ evanefcente jam parte altera for-
mulae. Sed jn cafu formula: fecundae fumma bsec eft
infinitum quid, , cujus fpecies, refpedfu numeri infiniti
q, exhibetur per formula: partem alteram, qii£ in hoc

p ~i~ I

cafu fit -=~ — =

^ p-\- \ y.n—^ I ,n — X. (^c. n — p ^

V De hujufinodi Scrkbus in_ epiftolfi data 'menfc
Mato 1716, fic ad me fcrrpfrjVir. lil. D. Le^mtius,
quern magno Scientiarum damno nobis nuper ereprum
lugemus. ‘‘ 11 me femble qu’autrefois jay aufii fomme

quelqu'es Series ou- foktes coriilnr'~4''-^ + ^ + ^

«

C(

^ -r ^ Lc ' termd de cette Tuitte exprime

Analytiquement eft

X . R

X . a; I , X- 4- 2. X r • -i . 7
^ On demande done

■tt

<(

x4-i-x-±x

la Torn me d’une fuitte donned, dont un terme (bit

XX ^ fignifie les nombres naturales ^

*' I, 2,, 3, 4, & / fignifie rUnite, ou la difterence

y des X Suppofons que le terme de la fuitte fom-

matrice

( 66y)

** matrice demand^e foie

fx

mx n I

O

Or DifT.2

2

® J. o_Li® = : fed o ^f>lx;

}) D -j- Da J) ^ ^

Sid D —mdx

nftl

m /; done la Dil?erence de — eft

mmxx-\-imnlx n nil'
-j- mmlx'\-mnll

nfll

Maintenanc il fauc faire

mfl I .

mm X X ^ i mm I x-\-z mm 1 1

m m X X -{- 1 m yi I x-\-n nil
-j- m ml jf =-J-w3 nil

“ e’eft a dire, il fauc identifier ces deux formules, ou la
**'donnee eft Multipliee per done egalant les

m m

termes refpedifs, puifque les .vat conviennent, on
“ aura par les x, z -f- w — 3 w, e’eft adire il y aura
“ m — n.Si par les abfolus on aura nn -\-m n—'i.mra,
ce <^ui donne encore w — »; done i’idencification
“ reuftit, & nous pouvons faire n — m — 6c

f— i (car / demeure arbitrairej & le terme de la

“ fuitte fommacrice fera — — , car diff. — — donne

X V .r I

donne la fomme des

X

O '

Jf + I

3> 4’

—5 — j 5>— , Series Jummatrix, emus ter^
2 J 7 ^

■ 6 X

X.X-\-I.X-\-ZXt.{.7

1 1 ^ 1 4 -1

CU‘

“ 4- X ^ . s tries fummsnda,

i«s lermlms ^ ^ ^ Ec pout

f’en fetvir aux fommations, les 5 termes, Ex. de
N n n n n la'

'( 6^6 )

" la fuitte donnee feront y — 3 —

ment la fomme des termes jufqu’a quelque terme

X - X

** — ^ — : excluilvemenc, fera — ; —

X .x-\-^.x-\-^Xr^r.T .

“ — 3 : Et pour la (bmme de la fuitte cnticre a 1 infi-

“ nie, devient infini, & — 6 ; done la fomme

“ de route la fuitte eft 6 — 3 = 3» comme vous
“ I’avez trouve.

“ Cette methode eft le calcul des differences ap-
plique aux Nombres; & il faut vous avouer qu’a-
vane que de I’appliquer aux Figures, & mcme avanc
“ que d’avoir ete Geometre, Je le prattiquai en quel-
que fa^on dans les nombres ; ayant trouve encore
jeune gar^on que les fuiites dont les Numeratcurs
fuflent des Unites, & dont les Denominateurs fuffenc
‘‘ les Nombres figures, comme Triangulaires Pyrami-
daux C^c. etoient les differences 3^®“^ (^c-

‘‘ multipliees par les conftantes de la fuitte 7'”hy*l~Y

-j- y & par confequent fommables, Mais

quand je devins un peu Geometre & Analyfte, Je
“ vis qu’il y avoir moycn de venir a bout de telles
‘V fommations par une Methode gegeralle, autant qu’il
etoit poffible ; & que le calcul des differences elloic
“ encore plus commode dans la Geometric quq dans
“ jes Nombres, puis qu’il y a plus d’evanouiffements,
“ & que les differences repondent aux Tangentes, les
fommes aux Quadratures. Cette methode generalle
“ de chercher la fuitte fommatrice de la fuitte donnee,
“ quand elle eft poffible, reufffit toujours, quand le terme
de la fuitte donnee exprime Analytiquement n’a
“ point la quantite variable enveloppe dans une racine,
ny entrant dans I’expofant; & aiors, on peut tou-

“ jours

V

( 667 )

^ jours determiner la fuicte fommatrice, cu prcuver
qu il eft impoftible d*en trouver. £c la chofe reullic
meme bien louvent, iors meme que la variable en*
tr§ dans TExpofanr. Mais comme il y a quelque-
“ fois des Quadratures particulieres de quelques por-
tions d’une Figure, done ou ne ftauroic donner Ja
“ Quadrature generalle ou la Figure quadratrice ; de
“ meme on peue trouver quelquefois la fomme de
** route la fuitte, ou d’un certaine partie, quoy qu on
ne puifte pas trouver la fomme de cliaque partie ; &
alors il faut avoir recours a des Methodes particulieres,
“ dont on n’eft pas toujours le maiftre, noftre Analyfe
n’eftaat pas encore port6e a fa perfedion.

ProJ>. VII. Proh-

Tnvenire fummam Seriei cujus Numeratores conftf
tuunt lineam quamlibec eredam in Triangulo Arith-
metico Pafeialii, Denominatores vero conftituunt li-
neam quamlibet tranfverfam

Soltitto. Delignetur ordo linea? erediE per />, ordo
linese tranfverfe per q, &fit w aggregatuni tot fermino-
rum primorum in linea ereda ordinis — > t quot

(unt unicates in q — i , arque fumma quxfita eric

1 • 2 . 3 . (^C. q — t

m X

p rp -f- 1 . GJc. /) -f ^ — 2 '

Ex. I . Proponatur Series T '1' X + if + ^ +

56

Ubi Numeratores conftituunt lineam fextam eredam,
Denominatores occupant lineam quartam tranfverfam.
In hoc itaque cafu funt p — 6, ^ — 4, p — J ~ 9,
q — I = adecque m—\ -p 8 --j- — 37 i e. tribus

terminis primis lineae nohse eredx. Unde fit fumma

quKfita — 37x5-^^=^-

Ex. X. Conftituant Numeratores lineam cenrefimam
eredam, & fint Denominatores Numeri Trigonales, qui
occupant lineam tertiam tranfverfam. * Turn erunc

P

( 66^ )

tft= loz. atque adco fumma quaefita fit

X‘°‘ — 101 X — —

lOO . i©x

f

Cor. Si'^rzzi, formula fit qua exhibetur ag-

gregacum primi termini; una cum femifie lecundi,
triente tertii, quadrante quarti, & fie porro, linex cu-
jufvis eredf^e ordinis Trianguli Arithmetici Fajchdii,

Sic r. . eft -1 A + X

lO

• Trop. VIII. Troh.

Invenire. fummamejufdetivSeriei, quando te^inorum- ,
figna funt alcernatim -\- & —

Solutio. Summa quxfita exhibetur per formulam fim-

plicifiimam - .

? +“Z — ^

Ex, Invenienda fit fumma Seriei y — ^ ~ 1^5
— -4- -f— 1— , ubi Numeratores confiituunt li-

“495 I2&7 * 3003’

neam feptimam eredam, Denominatores confiituunt
nonam tranlverfam. In fornaula itaque pro p Si ^ ferip*.

g

tis 7 & 9, fit fumma — .

Manente eadem Serie Numeratorum fnempe linea fep-
tima ereda), fi pro Serie Denomipatorum fumantur
fucedfive linex tranfverfx 1^*% 3"% 4*% &c, Summas •

erunt , (jrc. quae fic pofiunc feribi,

— > d“^- ubi tarn Numeratores, qu am

Denominatores excerpuntur ex line^ tranfvers^ ordinis
feptimi. Idem eveniret fi loco feptimx, Numeratores--
conftituifient aliam quamlibet lineam eredam ordinis />;
Summae quippe orirentur ex applicatione terminorum

linex- ■

( <5^9 )

linese tranfvcrfe ejufclem ordinis p ad terminos proxi-
me iequentes in eadern linea.

Propoficiones hse dua: noviflim^ potius elegances funt
quam utiles 5 quare Formularuna noftrarum demon-
ftracionem LetSoris folercia inveftigandam relinquimus,
ad Propofitionem ultimam jam properantes, quae ter-
tiam continec Serierum fpeciem, ob ufum mukipliccm
fads infignem.

Lemma, 5:.-

&c. cujus termino-

e- c • . M N 0 P

Sic Series quxvis j,,

rum Denominatores conftituunt progrelTionem quam-
iibec Geomecricam &c. Sint etiam Nu-

meratorum primus A prima difJerentiarum pri-

marum B, prima fecundarum C, prima tertiarum D,

quartarum & fic porro ; Si fine

refpedive, aggregata, Unius, Duorum, Trium, Qua-

M N 0 j

I’ h^’

tuor, vel plurium terminorum Seriei

que fint Numeratorum primus a {— a) prima diffe-
rentiarnm primarum h, prima fecundarum c,, prima
tertiarum d, & fic porro ; & fit ^ — iz==.q. Turn ip«
forum a, c, d, (^c valores erunc.

a— A—a—M
b— h A B
c T=.q h A -\- h B -\~ C
d = qH A 4- q b B h C D
& fic porro.

Demon^ratio» '

Satis conftac efie a — a,— A~M.

^ . . M M 0 P , ,, .9. r»1

Termini Numeratoribus 0, P^

O 0 O O G ^

( 670 )

6‘c. express pet A, B, C, D, dc, transformantut in
A A jB a -|— 1 B C A -|— 3 ^ “]"■ 3 ^ ^

I’ “T" *

terminos

(^e. Unde colligendo fummas terminorum, inveniuntur
Numeratores /3, y, <f, ^c. nempe

ct 3H: A

|8 zrr h -|- I A -|— B

y ■=: h 1 A h 7. B

t'=zP fr -\- h-\“ I A 7. h B h C D

&c.

Unde fumendo differentias fiunc
h z=: * h A -}- B

c =: q h A'\- h B C
d — q qh A -y q h B -\- hC-\- D
& fic porro, uc in Propofitione exhibentur.

Cor. I. Si Numeratomm N, 0, P, &c. differen-
tia vel prima, vel fecunda, vel alia quaedam detur,
terminis omnibus poft primes aliquot in Serie A, B, C,
D, drc. evanefeentibus, Differentiae h, c, d, &c. tandem
incurrent in Progreffionem Geometricam in ratione 1
ad q. Exempli gratia, fi detur Numeratorum M, N,
0, P d’c differentia prima B, erunt c, d, drc. in ra*
tione conrinui Geometrica i ad ^ ; ut conftat per ip-
forum valorcs q h A h B, qqhA-^qhB, &c. ex-
iffentibus C ==: o == D =

Cor. z. Ordo autem primx differentiarum B, C, D,
C^c- qu£E hoc mode evanefeunt, idem eft ac ordo
differentiae vel h, vel c, (^e. unde incipit Progreffio ilia
Geometrica. Sic B =zo —C =: erunt c, d,

in Progreffione Geometric^ ; fiC=o=:Dr=:^^-. erunt
€y d, &c. in Progrefffone <aeometrica. Et (ic porro.

LemmA 6.

lifdem pofitis fit r terminus unde incipit Progreffio
Geometrica in Serie differentiarum h, c, d, &c. & per

t+i

( <^7i )

»4-i defignetur ordo Termini in Serie f-,

^ h h

<^c. Turn Terminus il!e defignabitur per fradionem
cujus Denominatore exiftente ^ Numerator eft

a -\-c Ar ^ p

xh^ — I — qp —

2 23

nempe per ft defignato ordine differentiae evanefcentis
in Seiie ff, C, £), drc. ut & Numero cerminorum
a A-^pi item terminorum — i — (p p, ^c.

Dmonflratio. Lemma 1. Termini iftius Numera-
tor exhibetur per formuiam

aA-hpA-cp- A-^PX (/'+!

fubeunte vices x in Lemmace ifto^

Ergo fi ilt, ex.gr. nz=z, per Lemm. 5. Cor. 2. erunt
r, d, in ratione continua i ad q. Numerator ita-
que in hoc cafu eft

aAr^P -\-cpX— — -A- cq^ f

yp— x^-^ Sed fi termini c p x^-^

X^-^ X^-~ + ducantur in'^, & produ-

<ftui addantur termini ^ -{-qp, prodibit Series qua ex,
primitur binomii 1 A~ q dignitas i A~ — h^. Ergo
produdum illud sequale eft — i — qp; adeoqus ter-
mini + &c. — —

X^'’ — I — q p. Quo pado Numerator fit aA~Pp

exiftentibus duobus terminis aA~^p,

ut & duobus — i — q p, juxta fenfum Propofitionis,
quoniam n~z. Atque eadem eft demonftratio in aliis
cafibus. De Denominatore voro per fe fatis conftac.

Prop.

( (>T>- )

Prep. IX. Prth.

Invenire fummam quotlibec terminorum Seriei cu-

julvis cujus terminorum Denomina-

tores confticuunc progreflfionem quamlibec Geometri-
cam h, h^, &c, Numeracores autem func quan-

titates difFerentil aliqua conftanti gaudentes.

Solutio. Sunto Numeratorum /W, N 0, P, ^c. pri-
mus A, prima difFerenciarum primarum 5* prima I’e-
oundarum C, prima tertiarum D, & fic porro; & fit
ipforum A, B, C, D, &c. numerus «, arque h — i — q.
Turn fiat 4 (— M), h —h A -\- B, c =.q h A -\-h B

-|- C, d'— h A q h B h C D, &c. ut fint
tot termini 4, h, c, d, quot (unrunitares in
Terminorum iftorum ultimus dicatur r, atque per /> -j- i

1 r • M N O F ,

defignetur numerus terminorum ‘juo-

rum fumma requiriturj Dico fummam illam exhiberi
per fradionem, cujus Denominatore exiftente ^ ^ %
Numerator eft

a-\-hp -y ^

' — P ^ ~ ^

Demonjlratio. Nam (per 6.) per banc formulam

leprsefeniatur terminus ordine P 4- i Seriei -y. ^,77,

h h IF

^3- &C'. qui terminus (*per conftrueftionem Lemmatis 5’.)
a^qualis eft aggregate terminorum numero p + i Seriei
EiopoCtse j, ^ E. D.

Ex* !•

( <^75 )

Ex. I. InvenienJa fit fumma novem terminorum Se-
riei — , — , -f, 4* hoc cafu h=:z. a

2 ^ o lo ^

( = ^ — l) ~I, p-\-l =:^, p=zS, A=J, Bz=t,
C=:o, — P=&ct adeoque» = i, (quoniam funtduo
•^yB,) Hinc fit a (r= A) — \,b (= h a\- B — ^

= 3, c {^ffh A h B ^C— o)
= 4 = r, Adeoque per formulam fit fumma qusfica

l+3X8-f i« — I — I x8

2’ fiz’

Ex. Quaeratur fumma fex terminorum Serici i x J
+ 3 X3^ 4- 6 X 3H" X X3^-l-2-i X3^+c^r.

In hoc cafu funt ^ = y, q~ zi|, p -\- i z=:6, p = s,
Az=i, B—z, C=r, D ~o = E=&c. adeoque
» = 3, atque4=i, i=‘ +x = i. f==i+-|-|-

1=:—, d—-^ Unde fumma qux-

9 ^7 9 ‘ 3 27

fitai fit = 19956. five

2+f XS-f fx5X^+-

II i 4 4

X^-^+ jX5-yX?X ^

8

3 ' ^

Cor. I. Ejufdem Seriei, a termino primo y in infini-
tum continuatse, fumma exhibetur per formulam fim*
plicifTimam + ==^ -f ==3 -1*

h — i h — i| b — ij h — l|

Com, Si =: X , Seriei totius in infinitum continua-
tae fumma habetur fbl^ additions terminorum A, B,
C, D, ^c. Et base fumma eadem eft ac fumma line£e
eredtas refpondentis termino primo A, in Triangulo
Arithmetico, cujus lineam tranfverfam occupant Nume-

P p p p p latoros

( 674 >

rarores M, N~, 0, P, &c. (^od facile confl:at cx con-
tcmplatione Trianguli. Si itaque fuerinc M, N, 0, (jrc.

M

Numeri figurati cujufVis ordinis n, fumma Seriei —

M 0 P ^

-I L — 4-— -\- &c. a^qualis eric Numeri binari-

' 4 0 16 •* 1

dignicati z\"~ \ Sic Series -7 + ^ -K =

2 * " * = I, ut vulgQ notum ; Series — J- — 4. A

-’p =: 1 ” ^ 1 ; Series*^ +‘^ + y "V ~

2 ’ “ ^ = 4, & fic porro.

Scholium. Celeb. D, Jac. Bermnlli, iti TracSlatu fuo de
Seriebus infinitis, folvic illud Problema. ‘‘ Invenire
“ iummam Seriei infiniras: Fradionum quarum Denomi-
“ natores crefcunc in Progreflione quacunque Geome-
“ trica, Numeratores veto progrediuntur vel juxca Nu-
meros naturales, i, 2, 3, 4, vel Trigonales i,
** 3, 6, ro, d'c. vel Pyramidales t, 4, lo, 20,
aut jaxta-Quadratos i, 9, 16, ^c. aut Cubes r,
“* 8, 27, 64, ^c» eorumve mulriplices.” Ipfius folu-
tionem confula^ Ledor. Aliam vero, & quidem mub
to generaliorem invenic D. N/V. ^illius Nepos,

eamque ( poftquam ei hsec miferam, fed fine demon-
ftrarione) mecum communiGare dignatus eft, in epiftola
data i8° Septemhris 1715’, miris quidem invencis refer*
tiflima, quaiibus me crebro dignatur vir Dodiftimus.
De hoc vero Problemace fic fcribic. Pour la fbmme
“ d’un nombre determine « de termes de la fuitte de
“ voftre Theoreme 7. [ Ccrcllmum primum eft hujus

Propoiltionis] j’ay trouve cette formule x

m —

m — I

i_j_ d

4_ 0^ Jes X-fiCtres B, <jre. marquenc

ies

( <^7f )

“ les Coefficients des termes immediatement prece-
‘‘ dents. Et en mettant dans cetce formule p i
“ pour n> If' pour m, h en raultiplianc tout encore
par on a la iolucion de voftre Proh.

“ IX'”'”. Ec me monuit Vir peririffimus hanc fuam
formulam generalem in noftram pardcularem {Cor. i.
hujus propofmonis) migrate quando » — oo ; quippe

turn evanefcunc i, n • n . ^ ref-

i 2 3

peduipforum m". A, B, C, ^c. adeo ut Series in eo .
JpTi “ + fzTi ^ ^ 0“- "

b c

nino coincidit cum noflra —^-4- =.4-==, -1-

ni — 1 ' m — 1 1 m — i { ‘

^C.

Ad hue aliam hujus Probicmstis folutionem, & qiiidem -
ab hifee admodum diverfara, inVenit D. TA’^lor ope
Method! fuce incrementorum. Viri dodiffimi rogatu,
ad eum miferam formulam meam fecundam pro folu»
tione Problematis item formulas alias fpectantes ad
Propoficiones tertiam, quartam & quintam^ fed fine de» *
monflrationibus : quippe non dubitabam quin Vir acu-
tiffimus, atque ipfe Method! iftius Incrementorum In-
ventor, hifce, yel fakem paribus inveniendis par effiet,
Refcripfit fe harum foluciones invenifle, .& fimul alia
qusedam communicavic ad hujus method! profeduni '
multum facientia, quae jam noftro horcatu indinihis hif
cQ fubjungere dignatur.

( (>?(> )

APPENDIX

Qtia methodo diversd eadem materia traBatur :
AuBore Brook Taylor, LL» T>» S, Seer. '

HOrtatu Viri ClarifT, cui nos innumeris ofEciis da-
vindtiflimos elle libenter'facemur, fequentes jam
Propofitiones exhibemus, quasquidem in aliam occafio'
ncm refervandas efle decreviflemus, ni xquum vifum
fuifict parendum efle imperio amici qui, dum Propofleio-
nes quafdam prjecedentes fuas olim nobis inveftigan-
das propofuir, earum inveniendarum occafionem dedic.

Definitiones.

I. Quantitatis cujufvis variabilis valorem prxfencem
. deflgno litera fimpliciter feripta, ut ^ j valores prece-
dences diflinguo lineolis • eidem licere ex parte fupe-
- riori pofitis, (equentes lineolis ex parte inferiori fcrip» ,

u /

tis. Utvi hujus Definitionis lint x, x, x, x, e, ejuf-

* t If

dem variabilis valores quinqiie continui, exiftente va-

lore prxfenti, x proximo prxterito, x fecundo practeri-
to ; X proximcj atque x fecundo futuro. Et fic de aiiis.

I II

Ad eundem modum (unt interpretandee lineole qu* »i

II t ^

•incrementis apponuntur. Sic funt x, x, x, x, x, ip-

Xius X valores quinque continui ; ut fit ^ incrementum

lecun-

( ^77 )

it i

fecandum iplius Tit x incrementum fecundum ipfius

f

•4

X, Et fic de aliis. ’ ’

Cor» Vi hujus Definitionis, x -\-x=:x, x-\~x — x,

• • /

3

X -\-x=z X. Et lie de aliis hujufmodi.

Quando ufu venit ut varjabilis quantitas, puta x^
fpedanda fit tanquam Incrementum, ejus Integrale de-
figno litera inter uncos [ ] inclusa, llb'us etiam Inte-
gralis [a;] Integrale ('vel ipfius a: Integrale fecundum,)
defigno numero binario uncorum priori fuperimpofito,
z

ut Iftitis etiam Incegralis Integrale Cvel ipfius at

Integrale tertium,) ad eundem modum defigno numero

3

ternario, uc[a;]. Et fic deinceps. Unde vi hujus

3 ^

Definitionis conflituunt [a:], [at], [^], x Seriem
terminorum, quorum quilibet eft ipCum immediate ‘

^ 3

praecedentis incrementum primum, ut fit [^] = [a;], •

z

[jf ] = [x], x = [x], . :

Lemma,

Facfti a: 'z;ex Multiplicatione duorum variabiiium a" &

V. incrementum x v xv, .

Nam aueftis variabiiibus per propria incrementa, fit novum '
produeftum x ^ x xv ~\~ five xv ^ v x x
hoc eft X X V X V (pro gs: + x fcripco * Def. i^.)

Unde dempto priori produ'^o xt/'/ieftat increm^ntiVm

X V X V.

[ ■ Q.<iqqq - ••

( <5/8 )

Frop* 1. Theor,

Ejufdem Fa6H xv Incrementum, vel primum, vel fe-
cundum, vel tertium, vel aliud quodvis, cujus ordo de-
fignatur per fymbolum exhibetur per formulam hanc
generalem

xv-\-n X V n

n — I , n — I n — ^

X X

» — I

X V &c.

'n— 3

In bac formula haec func obfervanda, i®“ Termino-
rum numeri coefficient es i, »x-— * x^^

X J

©f. iidem funt ac in binomii dignitate n. Numeri
n — r, n — x, n — 3, f^c. ipfis x infrafcripti de-
iignanc numeros pundlorum quibus definiuniur Incre-
menta. 3“'’ Lineolse ^ ipfis x infrafcriptai,
interpretandsE (unc per Def. i. 4”* In quovis Termino
numerus pundorum ipfis x fimul infrafcriptorum,
eft ». Sic <1;.^. » — 4: turn per formulam, ipfius;cv
incrementum quartum prodit x v 4 x v 4- 6 x y

^ 4 X V X V.

* ///. •• till •• ‘ *“

Theorema hoc generale demonftrari poteft per In-
dudionem, incremencis continue fumpeis juxta formam
in Lemmate prsecedenci cradicam. Sed & colled^i
forma Seriei ex hujufmodi calculo, Theorema eciam
demonftrari poteft per Method um Incrementorum, ad
eutn modum cujus fpecinien mox dabimus in demon-
ftratione Propofitionis terti^e.

Prop. If; Theori,

Ipfius XV Integrale primum [xv'\ exhibetur per Se-
1 '3 4

riem [x]i/ — +

Series autem ita terminatur, utfit[«v]=:

( ^79 )

^ I” a

j — ['^] Y [^[^] =

Nam fumendo incrementa refltituicur propofitum a: 'y.
Cor. I. Datis duobus ex iftis [x- ], [xv], ^[•^]'V][»

i

Z

datur tertium. Item datis tribus ex iftis [x"], [-^],
(xx'], *1/ J,-datur quartum, Et fic potto.

Cor. 3. Si V o, datur [ ^ ] ex dato [ x ]. Si

X

•:^r=o datur [xv] ex datis duobus [^]» & [^]» Si

•«

2 3

V =. Of datur [ « ex datis tribus [ x], [ ^^ ], [ ^ 1*

• •

Et fic porro.

Ex* i . Sit exemplum hujus formula in inventione In-
tegralis ipfius — ^ , dato nempe z,. atque exiftenta

zzzz,

/ II trt

'v — Ot qui cafus eft fpecialis Propofitionis fecundas
Tradtatus praecedentis D"‘ Monmort. Fadlo itaque x ==

I II Ilf *1/1 j ..in

atque [x] = y

— I

Unde per formulam

fit

lxv]f hoc eft f— —

*- ■” zzzz I zz z z

^ / II lll'-^ •- t II

V

V

z zy.7 z zz

• I II

IZX% zx^^^

. . . It

Ex*

( 6^0 )

Ex. Sit aliud exemplum in inventione Tnte-
gralis ipfius ubi eft z=i, atque dacur a,

Turn pro fumpro 4% & pro v fumpto ft, fit x~g^
hoc eft a: =4x, leu x = ax, adeoquc x 4 — 1 x.

X

atque X — Regrediendo itaque ad- Integralia fit
[*] = -£-; item [x]=^E^=j=,, item[*]

X ^

; & fic porro. Adeoque (quoniam x — ax,) funt
[ » J = f ] - 7=i’ J =f=x,» Unde

per formulam prodit [ » 4 ^ ] r= ^ - - ” _l *1-

In hoc exemplo concinetur Solutio Froblematis, de
quo agit de Monm^^' in Prppofitionc nona. Goin-
cidit autem formula cum ea quam exhibit ille in
Corollario primo«ejufdem Propofitionis.

Scholium. Pofiunc eciam ex liac formula alii deriva-
li valores Integralis quxfiti, pro yario modo quo in-
terpretantur It)crementi propofiti facftore?. Sic in ex-
emplo fecundo integrale ipfius na^ exhiberi poteft per

* ' a 3

iofmulam a^[»] — a — ^ — *1" <**■[«]

f n

^ ^c. pra X nempe fumpto n, & pro v fumpto
Sed de his fortafie alia occafione fufius dicemus.

Prop. III. Theor*

Ejufdera jc <y Integrale, vel primuhi, vel fecundum,^
vel tertium, , vel aliud quodvis cujus ordo defignarur
fymbolo », exhibetur per Seriem in hac forma gene-

n - n~ n-^-u

rail prodeuntem- [x ^:\ ^ fx ] ^ — y [atJ

X

( ^8i )

+ 2.

Jf ] v —

X

« -}- 1
3

« + 3

[ X ] V -\- ^C*

Colleda forma Seriei ex Propofitione prsecedenti,
CoefScientes i, — — n-x. x

2i 2t 5

fic inveniuncur per Methodum Incrementorum* Potve

« 71 n-\-l M-fz

' ■ ; • // •• I// V

Turn audio » incremento fuo » — i, atque ipfis A,

C, D, &c. incrementis fuis comemporaneis A, B, C, D,
d^c. ut jam evadant A, B, C, D, (^c. fiet novum

W M-f- I

integrale fquod Integrale eft ipfius [xv],)[xv] —

n-}-i «-pi w~f~4

A[x ]v-\-B [x]v -|-C’[ &c. Hujus

itaque Incrementum primum coincidere debec cumln-
tegrali prius pofito. Sumptis ergo incrementis, fit
« « ”+• -j- C«4~3

[ X v] x] x' ' '[.vj-y '[xj-y-j-

+ 5 : ’ + c ;; "+D :: '•*

/ / ' /

idem ac Integrale prius pofitum. Itaque terminos lio-
mologos inter fe comparando fit i^°Az=J. Unde eft

I

A datum quid. Sed ubi = o, cik A — i\ ergo
A ~ i. B — B-\~ Af hoc eft ^ = S -{- I, leu

II

B — — I = — n. Ergo regrediendo ad Integralia, fit
B— — n\ A. Sed ubi n~o, eft i? = o. Ergo a—o,
atque B——n. 3'*“. C = C + hoc e(i C — n. Regre-

ii

K r r r r ‘ diendo

\

( <S8i )

n n

diendo itaque ad Integralia fit C — — + Sed ubi

n n

n = Oy eft C = o Ergo h —o, atque C~ — , hoc eft,
4*'’. Ad eundem modum invenitur D — -.n
^Liz_' Ec fic pergendo invcniuntur cxtcri

^ 3

Coefficicnces.

Scholium. I. In hac Propofitione comparata cum
Propofitione prima, cernitur fingularis quadam relatio
Incrementa inter & Integralia- Uc enim in Arichme-
tica vulgari, Multiplicatio & Divifio funt invicem ita
contrariae ut ft Multiplicatio deftgnetur per Indicem
affirmativum, Divifto defignabitur per Indicem cum
figno negative; ftc etiam in Methodo Incrementorum,
ft Incrementum deftgnetur per Indicem affirmativum.
Index negativus Integrale ftftet Sic in Propofitione
prim^, ft pro n fumatur Numerus binarius », per for-
mulam exbibebitur ipfius xv incrementum fecundum,
nempe xv-\-xxvA-xv\ Sed ft pro n fumatur nume-

rus negativus — x, ut jam quarratur ipfius v incre-
mentum (ita loqui liceat) negative fecundum, ('quod
idem eft ac Integrale fecundum) prodeunt coefficien-
tes iidem ac ft fumatur n affirmative in Propofitione
praefenti : atque interpretatis infuper ipfts->i', x, x, (jrc.
X, 3 4 — i '—3"— 4

p:r [ AT ], [ If ], [x],^c. Series fit omnino eadera ac

per Propofitionem praefentem prodit, ubi quxritur In-
tegrale fecundum.

z. Ex his autem formulis quaft fua fponte proce-
dunc formula Propoiicionum undecimae aiq-ie duode-
dmas i-ibri de Methodo incrementorum. Nam pro

incre •

( <585 )

incrementis (cribe Fluxiones, atque evanefcentibus in-
crementis fiant jam oranes x, r., inter fe ;e-

quales, atqae migrabit ftatim h;sc Propofitio fecunda
in ibam undecimam, acque pr.irens tertia in liiarnduo-
decimam. Quod quidem exemplum iatis infigne eft
Methodi l^errtonhn^, qua colligit ille rariones Fiuxio-
num ex rationibus ultimis incrementorum evanefcen-
tium, vel ex primis nafcencium.

Rsecedentium impreffioni intentus dum Typoche-

tarum erroribus corrigendis do operam, arque ed
occafione in animo ilia fepius revolve, fubiic Artibcium
illud quo jam olim ufus elt D Jac. Bernoulli in inven-
tione quarundam Serierum, ope Progreftionis Harmo-
nicse cujus meminicD de iMonmcrt in Scholia 6. Prof. V,
prxcedente commode etiam appHcari pofle ad inven-
tionem ipfius /^lonmort i i PropoCitionum 3**^, 4'®, 5-

atque id genus aliarum aliquanco fortafte generalic--
rum. Hoc in fequentibus paucis oftendifte, credebam
Ledtori non fore ingratum.

Sit Progrcftio Aritlimecicaf, p n, p 2, n, ^c. cu-
jus termini finguli fucccflivc dcfigneniur per x, &
funto by Cy d, C'-c. quivis mukiplices ditTerentia; datts
n terminorum Progrellionis iftius Arithmetica:. Sint
B, C D, (^c. Numeri quillbet dati, <k conftituantur

a: fucceffive fcriptis valonbus fuis p, p f ~'r

Theorems,

* A

fradtiones quocvis — ,

ex

( <584 )

cx harum firadionum quilibec, oritur Series Harmoni-
ce proportionalium Sic v g> ex fradione prima

oritur Series — . -4—, —4 — • Dico quod agere-

f ' p n p-]~2n ^

gatum quotlibet hujufmodi Serierura in infinitum con-
tinuatarum in terminis numero finitis exhiberi poceft,
fi modo fueric numeratorum A, B, C, D, aggrega-
tum sequale nihilo. Duobus exemplis hoc fiec mani-
feflum.

^ ^

Ex. Sint dux tantum fradiones — , atque ^ ,

exiftente h z=. Scribantur Series harmonicx ex his
formulis ortx, eo ordine, ut termini, in quibus func
denominarores xqualcs, fibi invicem refpondeant, & col-
led:is fummis terminorum homoiogorum, prodibit ag-
gregatum Serieruilti in terminis numero finitis, ut in
calculo appofito videre eft.

T‘+ — r~ H i -hn rn h (5c. = Scnei ortae ex —

, -A . -A

p -f- ? « ‘

— = Seriei ex —

+

p ' p ~j~ n^p -[-in

Ex, 1, Sint tres fradiones — ,

-f &c.= Aggreg. Serieru.
B C

, exift-

X x + iw’ X 3 a

2.n, c — ^n, atque ^ -}-B-|-C=:o. In

entibus b

hoc cafu Calculus fic f'e habet.

^ hy. _L oT +■ • • • — Seriei or:* ex —

A A
■+

f ~^p + n~p -f - 2 w ' + 3 «

/ ^ 4 ~ "h • • • • ~t~ — Seriei ex — ^ —

' p f-2« .* p-\rin x-f-zn

-f — 1- . . . i . -f- C^c. rrSeriei ex — —

‘ p-h'i» x-f-3„

A , A-[-B , A [~B [~C = o , ^ I

7+7^ St-

rierum.

Ubi

( )

Ubi etiam. prodit apregaram Serierum in termini’s

numero finitis, nempe'4.4- — ^ ob Nume-

P P ~r ^ . P~r i ”

tatorum A, B, C, aggregacum acquale nihilo. Et ad
eundem modum demonftratur Theorema in aliis cafi-
bus quibufvis.

Cor, I. Ex his principiis derivari poflunt innumerae
Series in infinitum continuatce, in terminis tamen nu-
mcro finitis fummabiles. ‘

Caf, I. Sint — & formulae duarum Serierum

' X X P

harmonicarum quarum aggregatum prodit in terminis
numero finitis per fuperius demonftrata. Turn, formulis

iflis in unam fummam coIlecStis, fit == formula

' xX X \-b

Seriei fummabilis. Sint v.^r. A=r, /'=i»
atquc b z= '^n — 6. Turn formulae Serierum harmoni-
carum erunt formula Seriei compofitae

X ^ ■f~ ^

Serie ilia exifiente

1 X 7

fummabilis efit

-L— i— 4--I \-&c. atque fumma Seriei, pec

'3X9'5Xix*7xi3 - -

calculum inpraemifiis demonftratum, erit -7^

Sint tres formulae Serierum harmonicarum

. ' j i.. fexiftente A B uc fit Se-

rierum a'ggfegatufo_ finitum'per^^p^^^ Turn for-

"^6x5

A B

mulis in unam fummam cgliedis fit

A y( X b X c -V Bx X x X -4- c -f“ C X x X x 4— b,

X X X 4" b y^x ^\-c

, feu (ter-

minis^ revocatis ad _formam fadlorum A-,

j:

A cb .q* /^c'4~g — bBXx-^A-^-B-^-CXxXx b

XXx4-6xx4~c

S f f f f Co

( )

for-

(•pb ^ + B + g = ^ ^

' jf X X 4-f Xx’+c

miila Seriei fiimmabilis. Si (JuatuoE fine Frai^lioncs

B

D

, 'exiftente^ -j- 4^ C -}-£>= o)

i’ j: -f- c’ Jf -j~

ad eundem modum invenietur formula Seriei fummabilis

Abcd-\-Acd-^'^Xo~b X d—h\ x x -YAd^Bxd~b-\^Qx4 — -C; "K x >iC xvj-^
X X X b X X~^c X X d .

Et fic pergere licet ad formulas ad hue magis compo*
fitas.

Ca(, i. Et fi plures Tint formula Serierum hujufrao-
di rumm^bilium,. qparum denominatorum fa<^ores ex*
cerpantur p:x diverfis .prpgreirionibus Aritlimecjcis, ex
ifiarum foirmularum quptvis in unam fummam addi*
tione, conficiecur formula hova Seriei fummabilis.

Sint e. gr, formulas dux Serierum fummabilium

& . excerptis a:; ex Progreffipne AricbmeticAj^;,

a.» 3, 4. &c* ex ProgrefTione Aricnmetica i, 3,
Turn ex his formulis in unam fummam colledis

■V X X -j- 3

fiet formula, nova j

vel, (expofi^

x>tx 4- 3 X?

to z per X St numerosdfttdS^}'^^ — — — ; —

^ 'xxx-\~ix%x IX2X-|-I

Cor. %* Hinc omnis Series in infinitum cominuata

I. X z^sx-4- » jf:A? ><•■* -17 3

fummabilis eft, cujus termini defignantur per Fiadfio-
nem, cujus, denominatoHY faeftores exeerpuntur ex da-
ti-qualibet Progreflione Arithmetic^, numerator .autera
eft multinomium, cujus <(im^i)fip;ie^.fu^^"^d minimum
binario pauciores. quam funt dimenftones E>e^mina-
tpris. omnis hujufinodf fra^io rcfplvi poreft in

tot fradiones fimplices, quot funt dimenfion,es, {ho^
eft, quot funt faiiftores) Denorfiihatoris, qualriim nume-
ratorum aggregatum, eft nihil. S^it^exempli gratis,
, V ^ ' ^ .formula

f

( 6^7 )

formula oblata Pons hancfor-

X XJC-J-’^X-J»+CX .<71" ^

mulam arquan aggregate fradionum ~ q- -~y +

f — ^. Turn fradionibus iflisinunamfummamcoiledis

fiet Ah € d -\- A s d B c — b V, d — h y. X
^ ^ 5 X cL — b -\^C-=i ^ ~ c X XX X -f- ^

-j-^-|-^-[-C’-'rDxx^x-|-/>xx4-r applicatum ad

— — , — i — — — ; — , a.-^^x-\-yx>ix-\-h

c ^x-\-d^ — ' j!L= — =f=/

xX x-^bxx~\~c>(.x-\-d

Unde per comparacionem terminorum homologorum

Ah c 4^=: cc, A c d B xc — .bxd — h z=: A d -\- B

X d — h — 1~ C "x d — c =: A — 1~ B — |— C — D — o»

j yt ^ jj /3 A c d

sdCOC^UC ^ • — ' ■; f ?' B —

hed'

c — bxd — b

c=^

— Ad xd — b

d — c

, D— — A — B — C, Quo pado

a,

formula oblata refolvitur in fradiones fimplices

t/ 1/ £/» ^

^ ' B — A c d , y — A d — B X d — b

*-p« ~ ~ . . — .nr: ■ ■■ — "

c- — hxd-^hxx-\-b d — cxx-\-(^

~~~~' ~x'^~d — qiiibus ortarum Serierum ag»
gregatum, hoc eft, fumma Seriei ortx ex formula ob-

, ^ tt 4" r}- ^ AT X at -t- ^ 1-

lata ~~7 — r per jam dida prodic

■ X-^'4-r-xA: -}-f^ ■

in terminisiv numero finitis. Quod veto dimenfiones
numeratorlv. in -formula oblat^, debeant ellc binario ad
minimum pauciores, quam func dimenfiones Denomi='
natoris, hinc conftac, quod in redudione fradionum

j^^.Viiibec numerator C, D,

' ducitur

( 6S8 )

ducicur in omnes denominacores excepto unoj nempe
fuo ; unde prodeunc Numeratoris Dimenfiones unicace
pauciores quam func dimenfiones Denominatoris. Sed
per jequationera = perit altiilima

dimenfio in numeratore ; Unde fuperfunt Numeratoris
Dimenfiones ad minimum binario pauciores quam func

• dimenfiones Denominatoris. Ad hoc veio Corollarium

revocari pofliint D. de Monmort Propofitiones 5"

Cor. 3. Item oblati formula juxta Ca[, z. Cor. r.
adhuc magis compofita, ex iidem principiis perfpici
poteft an fit Series fummSbilis. Sint progrcfliones
du2E Arichmeticse i, 3, s* x, 4, 6, quarum
termini homologi defignentur per <* & zi, & fit formu-

* la Seriei oblata — , ^ ^ ^ ^ yel ( pro a

X X~1~z ^ Z, Z. ^

fcripto AT -j- I, & fa(5toribus Denominatoris in ordi-

_ A- X (Sx A-.y nr

nem coaais) === — —-■•=-— — ==. Pone fdrmu-

X* >< X "h * X ^ + X X a: + 3

lam hanc arquari aggregate formularum •

« X * +

^ Serierum per fuperiUs di(3a fummabi-

X + 1 x^T 3

lium, ut Cformulis his noviflimis in unam fummam

colleau) x.x + v

X X 3e 4- I ^ X -f- 2 X X -f" 3

3 P -1- 4 ^ “h 2 /3 y 4* ■

x_|_ ’ xx 4" ^’X<« 3 x-x:-|-i X J^4x.Xx~1“3*

Hinc comparando terminos homologos oriuncur arqua-
tiones3P— a, F + Unde

eliminatis P &i ^ per debitas operationes, Analyticas,
prodit ^quatio 2 a. -r- 3 ^ y — o, . qua idefinitur >re-
latio quae inter coefBcientes oi. (B, y intercedere debet,

a f3 w - -I- y

Ut Series orta ex formula oblat^

xxx-|-ixx_|-2,xx-|-3

fit

( 6%9 )

f\t fummabilis. Ad eundem modum fi formulae obIat2e
Denominatcris faClores excerpantur ex tnbus Progre*
iJionibus Arithmedcis, invenientur duse ^equationes
quibus definiancur relationes coefficientium Numerato-
ris, ut fit Series fummabilis. Si quatuor (int ProgrefJio-
nes Ariihmecicse, Coefficiendum relado definiecur per
tres seqiiadones. Ec fic porro. Ec in hujufmodi for-
iTiuIis uc fine Series fummabiles, hxc infuper obfer-
vanda funt, Frimo ut Numeratorum dimenfiones Tint
ad minimum binario pauciores quam funt dimenfio-
nes Denominatorum, Deinde ut ex fingulis Progreffio-
nibus Aridimedds excerpantur ad minimum duo fa(5lo-
res Denominatoris. Denique, quod fi Tint duo vel plures
fadlores Denominatoris inter (e sequales, ponendum Tie
tot etiam Progrefiiones Arithmecicas, ex quibus excer-
puntur, effe inter fe tequales. Pr^emiilis attentius per-
penfis, hsec obvia erunt. Ad hoc veto Corollarium
facile revocantur D. de Monmort Propofitiones 4^*,

'B 1 K 1 S.

)

ERRATUM in N°. 3^2.

PAge 586, after the end of line if, add llact
Clotidf from behind which there ijfued a,

L 0 M D 0 N:

^Printed by W. and J. I n n y s, Printers to the Royal'
Society ^ 2Xt\\Q l^rinces^Arms in St. Church- Yard..

1717- > ’ ' " ” '

'Rp!. »

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' ■ : , ,ni ni 1 1 U T A 2 .1 3 ’

* ' V I f ^ • f • ,

V.Y M I ;C I onn r

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•.M 0 G Vi 0 ,a

/ '

Vv/\ i)i\i OT .7^'=' '■* ’ .( brc .V7 V"*

.l;.oY-it:,:;fiO c\r*\ ' v:.v\^.*v,‘i-Av i oni :.: ,t'

1

■/rjn/.u/u'n /K' jj4-

IMPr^ARMANT«N¥S

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QVIRIN0-IP-6HH.QCE

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( 6^1 ) - Number 3 54.'

PHItpSOPHICAL

TRANSACTIONS.

H'.JI— ■■T™^ —

For the Months of QBob. ]SloV. and Decemh, 1 7 1 7.

-ta/V’ Tfhc^ O N T E N T- S. ’

I. An Advertifentent fo 'Aftronomers, <>7 Advantages that Tn<*y

accrue from the Ohfervation of the hA,o6n s fre<^ttent A’ppuljes to
Hyades, during the-threemekt infumgTears.-

II. Solatia Prohlematis d Dom. G. G. Leibnitio Geometris Anglis
nuper propafiti. ; Per Brook Taylor, LL. £). ^ R. S, Seer.

III. ! ExiraSlof a Lettet of Dr. Q.hf. Hunter, M.D. to £)r. J.VVood*
ward, M.D. & K, S. S.from Durham, giving an Account of a,

/ Rojnan infeription, lately dug up in. the North (^England;

, with fime Hifianicahand Chrondogical Retnarks thereon. ; -f

IVi. A Genus 0/ P L A N T S, call’d Araliaftrum, of
which the famous Ntn-ztn or Ginfeng of the Chinefes, is a
•Species. Communicated by A/r. Vaillant Prademoti/lrat'or at
. the Royal Garden at Paris, to the Learned Dr. Will. Sherrard,

• LL. D. late Conful Smynia,! and by him to the Royal
-Society. i c i, i

V. ExtraPi of a o/" A/r. Ed w. Berkley /rew Naples, giv-
ing Jeveral curious Objervationt and Remarks on the Eruptions of
Fire and Smoak from Mount V E S U V I O. Communicated
by. Dr, John Arbuthnoc, M. D. and R. S. S,

VI. An Account of an extraordinary Tumour or Wen lately cut
off the Cheek of a Perfon in Scotland. Communicated to the
Royal Society by Dr. Thomas Bower, M.D. and F. R. S.

VII. An Account of an Experiment to prove an interfpers’d Va-
cuum,* or to jhew that all Places are not equally full. By the
Reverend J.Theoph. Defaguliers, M, A. and R. S. S.

T 1 1 1 1 VUE An

CONTENTS.

VIII An Account of a fm'ill Telefcopical Comet feen at
London on the lotb of June *717^ ^7. £dm. UaUey, LL. D,
R. Soc, Seer.

IX. An Account of Bocks i I.'Joannls Poleni in Gymnafio
Paravino Phil Ord. Prof. & bcienr. Societatum Re^alium,
qu3c Londini & Berolini font, Sodalis, De Mutu
rnixto, Libri duo, 4‘®. Patavii 1717. J. Apollonii
Pergjei Conicorum Libri O£to Sereni AntifTenfis At SeBhno
Cjlindri Coni Libri duo. Fal. Reg, E Tbtatro Oxoti. 1710.

I. Jn Jdvertifement to Aftronomcrt, of the JJvajf
tages that may accrue from the ObJerVation of the
Moon’5 frequent Appulfes to the Hyades, during
the Ihree next enfuing lears,

OF all the Methods hitherto propofed for finding
the Longitudes of Places for Geographical Ufes,
none Teems more adapted to the purpofe, than that
bv the Oeeultations of the fixe Stars by the Moon obferved in
dillant Parcs: For thofe Immerfions of the Stars which
happen on the dark Semicircle of the Moon, and their £«
meriions from the fame, are perfe^ly momenianeous, with-
out that Ambiguity, to which the Obfervacions of the Eclip-
fes of the Moon and thofe of Jupiter s Satellites are fubje^.
Befides, whilB the Moon is horned, and her weaker Light
lefs daziing, an ordinary ftiort Teiefcope, fuch as bv Ex-
perience is found to be manageable on Ship board, fuibces
to obferve thofe vloments, even in the Occulta ions of ve-
ry minute Stars: On which account, this way feems to bid
fairelt for the defired Solution of the grand Problem of find-
ing the Longitude at Sea. Bur fince it would be needlefs
to enquire exa<5Hy what Longitude a Ship is in, when that
of tlie Port to which fhe is bound is dill unknown it were
to be wiflit that the P inces of the Earth would caule fuch
Obiervations CO be made, in the ; ons and on the princu
p4i Head-Lands of their Dominions, each for his own, as
. might

( ^9} )

might once for all fettle truly the Limits of the Land and
Sea. This Work however being likely to be left to the Care
andCurioficy of private Perfons, it may not.be amifs hereby
to give notice of the prefent Opportunity of performing
itj in this our Northern Heroilphere, by help of the fiequent
Appulfes of the Moon to the mure Southerly of the Hy^des^
many of which fhe eciiples in each monthly Revolution,
and will continue fo to do, during the Years- 1718, 1719,
and 1720.

Thefe Stars are but Three or Four in all former Cata-
logues, but the Britijh of Mr FhmfieeJ encreafes them to
Sixteen ; to them we have added Three others fomewhae
fmaller, 'viz. c, i, and n in the Figure of the Hyadet here-
to annext. In it the principal Stars are markt with Bayer*s
Marks, and the reft with the Letters of the Italick Alpha*
bet ; their Longitudes are fitted to the beginning of the
Year *718, and being truly laid down, may ferve to in-
ftrud the curious Obferver, when and where to look for
them, when the Moon is among them.

It appears by this Scheme that the Diftance between a
and « or Palilicium, is about Nine Hours Motion of the
Moon, in which time fuppofing her to pafs from one to the
other, (he muft eclipfe y and e, and Four or Five of thofe
about 9, and muft apply very clofe, with her Southern
Limb, to all thofe which have about Six Degrees . South-
Latitude i which would be a very entertaining Sight for
the Lovers of thefe Arcs. But if the Times of-the Occul-
tations of any One of thefe Stars, or even of anv Two of
tliem in the fame Night, be accuratel obferved under di-
ftant Meridians, the difference of thofe Meridians may be
truly obtain’d thereby ; efpecially fince the Mooni Parallax,
and all orner parts of her Theory thereto required, are at
prefent fufficiently ftared and known.

For the fake of fuch as are willing to make ufc of this
Method, we have added the Places ot all the Hyaiet fitted to
the prefent Time, and chiefly i.aken from the Britifh Cata-
logue, which being faulty in the Scars wc call k and/, we
have here rectified them-

Catahgns

( 6^1 )

^ * i*.' - » ' *

f

Xatalogui ^Hy adum, immte Amo 1718.

Steilarum NiOMIN^.
1

Long

31

■ Lat. Au(V.

Ma.

I ,

pr£fedit y Tauri

a

51

3

,'5

50

*4

7

nartbus Tauri, Bayerc

y

ri

50

54

46

XX

3

fuh':*y :• — . ti frr , —

b.

'I

56

31

6

19

57

7

ijft (J^igwe~Na/i TauVt —■ — : — •

c

IX

54

25

,4

47

5

7

^ Inter mtti ^ ociilum Tsuri 7

54

47

1 Eortnrn. — ‘ ^ J

S'

1

4

0

34

3

\l^uic (ontfgun, 4d^

d

3'

10

33

4

9

4

6

\l:r<tcedenti»m 6 Borealis — —

e

3

17

1 •

5

41

50

8

Earttm Auftralis c Ur tor, - —

f

5

2-5

33

6

X

44

Y^quitur^ — s- ^

g

a

35

2

3

43

27

5

Conxiguarurn intfr pares (St\

'e

3

59

45

5_

47

16

4

^Earundtrn Auflralior — —

6

4

0

11

5

51*

55'

4

Duarum fttpra 6 Bore a

h

4

X

52

5

= ^3,

43

7 ,

Ejcrundem Aujlrdlior j ,■ ■

• i

4

7

44

5

3<5

40

8

sib % trhm in reif^ prncedens

k

4

^7

6

9

45

. A

Ea'rum media —

1

4

i6

55

6

7

J1

7

tJ'*”' fl fequen^ium Borea — ^ .

m

4

30

i6

5

37

49

7

Ocuhs Boreus Tauri »■■■'

£

4

30

3‘

X

35

58

. 3 .

Seqaentium Qi Auftralis,

n

4

32-

35

5

4*

00

8

Trium Jub ^ fequens —

0

4

45

55

6

0

35

7

Paltlictum Bayero

tt

s

50

lO

5

X9

50

I

^a hanc feqnitur fn oxime —

P

17

35

6

3

xp

7

Contig* fequenttHm Auflralis —

q

6

30

34

(5

19

19

6

Borea ® clarior —

a

6

33

11

6

IX

35

7

II. Solutio

i

( (95 )

II. Solutio Trohlematis a G. G. Leibnitio,
Geometris Anglis nuper propojiti. (Per Brook
Taylor, LL. T>. (Or R. S, Seen

GU M Dom. G. G. Leilnitius nuper defun(5ius, in
concroverfia jampridem orta circa Inyentionem
Mechodi Jluxionum, ( quam is DifFerentiaiem
vocarc maluic, fibique pertinacicer appropriari nifus
eft,) nihil omnino refponfi dederit argumentis, qui-
bus inclyci iftius Inventi gloria Neutono vendi-

catur ; cn tandem, hortante Dom”® Job. Bernoulli, Pro-
blema Geomecris folvendum propofuic ; quo fei-

licec vires eorum in Methodo ifta experiretur; quad
Problemacis iftius Solutioni fi cocteri iftius Nationis de-
prehendantur impares, rede concludatur, nec ipfum
t^eutonum, qui, fatente etiam Leibnitio, ab hujuimodi
contemplationibus jam jure immunis efte debet, olim
fuifle parem inventioni iftius Methodi. Sive Problema
folvatur, five infolutum maneac, nihil exinde confeque-
tur quod Neutonum afficiac ; nec iftis certe Leihnttii Fau-
tonbus, qui I’roblematis folucioncm eriamnum conti-
nenter efflagirant, jus ullum eft nos ad certanien ingenio-
rum tanta cum licentia provocandi; adeoque Problema
corum jure merito negligi poflet. Verum ne aliquando
exinde occafionem triumphandi arripianc, fi hoc Pro-
blema maneac ab Anglis omnino intadum, ipfe, Gco-
metra longe non fummi inter noftrates fubfellii, inducor,
uc folucionem edam qualern qualem Problemacis, nec
ufu, nec difficultate adeo infignis. -

Problema a Leibnitio primo proponcum, ita fuit in-
telledum quafi nihil aliud reqaifitum fuiflet, quam uC
fecarentur ad angulos redos Hyperbolce Conicse iifdem
Centro & Vercicibus defciiptse Verum cum illi nuncia-

V V v V ti m

■7

folutum, refcripfit, non (olutionem casus particularis, fed
generalem requiri. Quo fadum eft uc folutiones iftre
particularcs non editse fuerincs vcrum in Tranfadione
Philofbphica N° 347.fubinde prodiic Solutio maximegc-
neralis Sed nec ilia content! fuerunt Leibnititts & Fau-
tores ejus, quin illam derifui habuere, quafi qui illam
excogitaverat non potuiftec earn ad cafum (pecialem ap- ' '
plicate. Si nondum viderint quomodo ex illi icqua-
tiones fine deducendsc, id profedd illorum iraperitiae
tiibucndum erit. Paulo ante Luhnitn obitum prodiic
tandem Problema (equens; quod quidem diverfimodc
fbivi poteft, premendo veftigia Solutionis gsneralis mo*
d6,citac£e, fed quod in pra^fentia folvimus uc fequitur*

Su^tr re St a AG tanquam sxet ex funSio A educere in-
CurvaSt qualis eft A B D, ejus naturee, ut radii
Ojculif in Jingulis fun St is B ^ uhique ducti^ B O fecentur
ab axe AG in C, in data ratione^ ut nemfe fit BO ad
BC I ad n.

Deinde conftruenda funt Tra^eStarl£ EBF primas Cur^

Problema.

VAS A B D nor malt ter (ec antes*

Solutionis

£

A H C\ Q

\

O

( <^P7 )

Solutionis Pars prinaa 5

Hempi Inventh Curvarum fccandarum A B D.

I. ordinata axem AG normali, fine,

Abfciila A H—z, Ordinata H B=x, Curva

A Bz=.v. Turn per Methodum Fiuxionum diredam e-

• * ♦ '

tit B C=^x, & fluente oniformiter B 0=^* Unde
K , , K

per conditionem Problematis fit £0 (■f) ; JSC

; I I adeoqus;c;f — ft 'zx=:0^

z. Collat,4 hac xquatione cum formula Fiuxionum fe-
cund^* in cake Prop. 6. Methodi Increnientorum^ inve-

nitur z x~^ =.v cc.'~'^ /; exiftente «- linea data, per cujus
valorem poteft Curva ABD accommodari condiciohi a-

licui Problemati annexse.

3. Pro v fcripto ipfius valors migrat ^qua-

-«

in banc z=

X X

Unde dacur

tio zx-”ziz^>ya>

z ex datd x, per quadraturam Curvae cujus abkifsa exi»

- •X”

flente x efl ordinata

4. Sint o- & '1- numeri int;^egri, yel affirmativi vel ne-
gativi, tales ut fit Curvarum ifto modo provenientium

fimpliciffimai ea cujus eft Abfcifsayj'St Ordinata')' z»

' ‘ 4: : -

^ „

* ; turn erit ea ojcnnium- Curvarum fimplicifE-
ma, per quarum Quadraturam datur Abfcifla z, ex dat^
Ordina.ri x.

5. Eft Curva ABD Gepmetrica, qupties pro » fu-
mitur reciprocum numeri cujufvis imparis>

V V V V V ^

6> In

( )

6. In prscdicSlis Curvam A B D confideravimus uc ver-
fus axem A G concavam, quo in cafu maxima ordinara
X xqualis eft lines dans a, quam Parametrunr Curvs
commode vocare licet. Et in hoc cafu Curva adlu oc-

currct Axi. Unde flucnte ipfius -r=^^= debite fum*

pd, hoc eft, ita uc ftmul evanefcant z ^ x, tranfibit
Curva per piindtum- datum .^4, fieut poftulac Prpblcma.

7. Sed ft qusracur Curva A B D, qus fit versus axcm
convexa, ad eundem modum pervenietur ad sq^jado-

• rt’ X

nem z--;==i.

Vjf *'»_**'»

; qus eiiam ex squatione priori de-

rivari poteft mutando ftgnum ipftus n, Et in hoc cafu
eft curva ABD Geometrica, quories pro» fiimitur reci*-
procum cujufvis numeri paris. In hoc veto cafu Ordi*
nata omnium minima x aqualis eft Parametro a.; adeo-
que Curva. nufquam occurric Axi. C^are limitatur
Problema ad caiiim priorem.

8. Ex prsmiftis facile colligitur Curvas omneS/^^D
efle inter fe ftmiles, & circa pundum datum A fimili-
ter pofttas,. lateribus earum homplogis exiftencibu^ pro*
portionalibus Paramctris

Solutionis Pars altera 3.

Nempe Invent io Curvx fecantis.

9. Ex $ i^ikv : z z'ycc." : x”. Sed BC : B H :: v \ z,
Unde fit 5 C : 5// : : a’ : X". Ex conditione veto Pro-
blematis eft B C tangens Curvs qusefits E B F. Qpare
ft jam fumantur A H { z) 8^ B f/ ( x ) pro coordina-
tis Curvs EBFy Curva ipsa EB exiftente r, eric, per
Meth.Flux.diretft, r t — x '.'.^BC: BfF\\)oi":x^. Un-

^e fit -

■X-

J f:

10. In

( )

10. In Curva A B D finge aequationem z =

' ^A*a_ AT*

transformari in aequationena fignis radicalibus non affe-
<aam ^ — Turn rcgredrendo

ad Fluentes fiet z—^^A~ —

coefficience novi introduda nulla, quoniam per condi-
tionem Problematis debenc fimul nafd z ^ x, Hinc

vice ^ fubftituto ipfius valore ^ in.^ 9 invento> fie

tK f

fiuxionalis eft primi gradus ad Curvam qu^fitam EBF.
Revocacur autem ad formulam ftniplicioreni in terminis
numero finitis, modo fequenti.

II. Fluac uniformicer r, & exiftentC4 quantitate non

fluente, fit Subftituto hoc valore ipfius ^

in xquatione noviflime invent^, atque duda iequatione

in -7, transformatiir'ea in hanc^;

X oillL J- ejc. Unde capiendo Fluxioncs fit
--aV-~ -}-g Quod ultimum conftat ex

Analogia Serierum Ax^—-\-

pro s 8c s fubftitutis eorum valoribus ex eequatione
— — colledis, elicitur xquacio nx^i^z — xxzz,^-

-X

r

«••• .... . ^ -I

> Quas ad Fluxiones primas. revo-
catur modo Cequenrit .u *; ■ '"q ; ^’ ’.f

V. X .V . fit

f

( 700 )

. Tij Tn u^ipD. -7- vice 4: a: fcripto ip-

frus valofc sec^uacione dcinde applicaca ad i,

fit n z.-Lt x 'x x irdo.* Quai xquatio in

duda eft Fluxio scquationis — x x~*' z.-\- x^~'‘ z,
= 4‘“”r; cxiftcntibus a ^ r non fluentibus. Eft ergo
— !&x — ;s x- X ^=rx x'' ,
scquatio fluxionalis primi gradui ad Curvam quarfitam
EBF.

13. In ifl^ autem xquatione eft a valor Ordinara; B H,
quando- incidit puncftam // in pumftum A.

14. Haud proclivc eft a?quationem %x zxy.d'-'^

— rx“, manente n in tcrminis gcneralibus, revocare
ad sEquationem Fluentcs tancum involventem, vel ad
quadraturam Curvarum. Sed puncfta curvae EBF po(^
I'unt commode inveniri pef defcriptionem Cufv:e A B £>,
& ciiii}i^dam GeomeCric»E; Per Geometricam hie
intelligo Curvam, cujus acquationem non ingrediuntur
Fruxioii^s, nec fluentcs in Indkibus digniratum. Scce-
tur enim Curva 4 B D, cujus Parameter fit ct, in B, a
Cyirva, geometric^ cujus sequatio eft aoB^x^ — —

x*-'; Qtque eric pundum illud interfedionis B
ad upiana ex Xrajedoriis quseficis, nempe qua! rranfic per
piindum C, cxrftente AF-=.a & nOrmali* ipft AG.

15. Hinc ft ABD fit Curva Geometrica, erit etiam
‘B F F gebmerrica.

^choUum, Poreft & alio tnodo inveniri xquatio
xx—zx 'x^”'^’=^^''r qu^dam AHalyft quam

nunc edare ftacup, invem xquationem —=—JLL . Qyj

tKi-

X X

comparatS cum xquation,e ~=-4 C § P P eiiminando

Si ct, tandem pervenitur ad prsedidam* xquatiPnem
•j X— >z K X x” . Exmflum.

( 701 )

Exemplum. Ad demonftrationem Solutionis noflrie fuf-
fecerit exemplum (impliciffimum. Sic itaque »— i ; quo
in Cafu eft A B'D femicirculus diametro AG defcripcus,
acque E B F item (emicirculus defcriptus diametro

A E. Eft aucem in hoc Cafu .. Unde

in ^ 3. fit adeoque z=a. — quas

a^quatio eft ad Circulum diametro Gz=a defcriptum,
ut fieri debuic. Item pro-» (cripto sequatio — z.x-

( § II. ) migrac in hanc 2.^ — zx — rx,.
Unde extecminandOjr ope s^uationia f 2, fit

— — = —X ; adeoque regredicndo ad Fluentes

K K

^ a, qucE sequatio eft ad Circulum diametro
AE^a deftriptum, ut etiam fieri debuic.

III. ExtraSl of a Letter of Dr. Ghi*. Hunter, M.D. .
to Dr. J. Woodward, (Z5; 5. 5. from Durham, gt-
Vmg an Account of a Roman InfcriptioUi lately
dug up in the North of England 3 with fome Hi-
Jlorical and Chronological ^marks thereon».

T he Infcription which comes herewith, {Ftg. II.)
was dug up, two Years agOj in the Roman
C AST RU M, LancheHer : The Infcription ^

is very legible, and gives me reafon to hope, a Search .
after the firft Fortifying this Place will not be unnecef-
fary ; eipecially, being able to fix the Time of Gordian s

R-epair-"'

( 701 )

Repairing this Fortrcfs, to the i45d Year of Chrifl-.
We may reafonably aferibe the Foundation to the pru-
dent Adminiftration of Julius AgricoU,. in the Reign of
Fl, Fefpafian, about 169 Years before. M Conlirmajion
of this, I find the following Particulars very material,
and think it not unbecoming to begin my Enquiry with
Fefpafians firft Appearance upon the Theatre of Fame
in Britain.

fn the ^cond Year of the Emperor CL AXJD IV
jAfin. Lorr. 44, the Romans invaded Britain^ under the
Command of Aulus Plautias, in which Expedition Pe-
Jf afian *, then Legate of the Second Legion, made a glo-
rious Figure ; having been engaged in no left than thirty
Battels, and reduced two powerful Provinces, above
I twenty Towns, and the Ifle of Wight. All thefe Suc-
cefles, tho’ continued with good Improvements in fomc
of the following Years and Governments , could not
frighten the Natives into an entire Submiflion ; efpe-
cially, no Ad varree being made into the Country of the
Bri^ntfs^ till the Advancement of Vffpajtan to the Im-
peril'Th7on*e,‘‘libTur“i‘?r Years after, Ann. Dorn. 70.
Then the w’hole Empire was deliver’d from the Miferies
‘ of Nero's, and the fhort but lamentable Devaftations
of the three fucceeding Reigns : Fefpajian then refblv’d
to pulh on his begun Conquefts in Britain-, dioice
Armies, commanded by experienced Generals, arc lent
over; and the XX Legion, having in the preceding
Troubles adfed feditiouny, ( nor without Difficulty
, vyas reduced to fubmit to P'efpaftan ( mofi: of the Offi-
^ cers as well as Soldiers having been advanced by Pi-
Julius' A'grioola \s conftituted Legate, who, under
the Govttnom'P etilius Cerealis, bore a confiderable Share

* Suetonius f Cap, 4.

in

f 7°5 )

in the Succeffcs againfl: the Sed primo

Cer^alfs modo labores & diicrimina; mox & gloriam
communicabat: Ssepe parti Exercicus in experimen-
turn, aliquando majoribus copiis ex evencu prjcfecir.
Tacitus afterwards in a few Words Turns up the Whole
of Cerealis his Acqiiifitions, f “ Terrorem ftatim incu-
“-iit Petilius Cerealis y Erigantum Civitatem, quae nu-
“ merofiffima Provinciae totius perhibetur, aggrellus ;
VjPiulra praelia, & aliquando. non. incruenta'; magnam*
** a^^\Brtgamum partem aut vidloria amplexus;<^ auC
*[ be)lo. Not withlianding thefe Advantages, I dare'not
fuppofe Romans to have then penetrated* fo far into
this Province as our Longovicumy which is i Tifuate fo
near the Northern Bounds of the^Sr/^4;>/«, that at prdd
l^nt it’s not diftlanc above'twelve Miles from
the Roman the chief Town of the adjoining Peo*
pie th^p/4<!//>i. I now advance* to my principal Mo-
tive, ( I hope its Length may d eferve Patdon, being un-
der no Obligation to account for the Government of
Jul. Frontinus Succeflbr to Cerealis ) to fix upon the fe-
cond Year of Julius Agricolas Government for this Work,
which Tacitus thus defcribes, || “ Sed ubi y^ftas adve-
“ nit contrado Exercitu — loca Caftris ipfe capere,
** scftuaria ac fylvas ipfe prxtentare ; & nihil interim
** apud Holies quietum pati| quo minus fubitis Excur-
fibus popularetur 4 ^que ubi latis terruerat, parcen-
“ do rurfus irritamenta Pacis ollentarc. Quibus rebus
“ multse Civitates quas in ilium diem ex sequo egeranc,
datis Obfidibus iram pofuere, & Praefidiis Callcllil^
que circumdatac, tanta ratione cur^ue, ut nulla an-
“ te Britannise nova pars illaceflita tranfierit. This ex-
cellent Condud Tacitus further confirms from the Ob-

* Tacit, Ftt, Agrit, 8* t Cap. I7. Q Gap. 20.

X X X X X fervatioft

f 704 y

n^adon of Others. Adnotabanc pcriti, non aliunt,

Ducem Opportunitates locorum fapientius legiflc,
“ nullum ab AgricoU pofitum Caftellum aut vi Ho
'* ftium expugnatum, auc padione aut fug^ dcicrtum.

Agricohy this Summer, having c^uieted to large a;
Trad, and hnithed fo many Fortreffes, it cannot be ex-
peded- all Ihould be built with the mod cxquifite Arc,
fufficienc to perpetuate them. I proceed to GotdUns
Repairs 9 whofe Bidorian Julius Cafitoliniu having ne«
vcr once named Britain, yet giving fo many Hints of
the excellent Oeconomy of his Government, under the
prudent Adminidration of his Father in-Law Mifithttu,
I dare not fixvthis Work till the Third Year of his Reign^
He having before been under the Direction of the Eu-
nuchs and Officers of the Court, whom Capitelinus
repretencs, in Mifitheus his Letter to Gordian, to have
j^odituted all Employments to their own Covecoufne^
and mercenary Creatures. .

JSurham, Julj.5.^

' ■

m L

'■rfnMi ' w. I .ij Ilf

A

IV. A new Genus of PLANTS, caWd Ara-
liaftrum, of which the famous Nin-zin or Gin*
feng of the Chincfcs, is a ^ecies. Communi-
cated by Mr. Vaillant Trademonfirator at the
H{pyal Garden at Paris, to the Learned Dr. Will.
Sherrard, LL. D. late Conful at Smyrna, and
by him to the Royal Society.

ARaliaflrum is a Genus of Plants, whofe iFlqvper A *
is complete t» regular, polypecalous, and her-
maphrodite, (landing t>n the Ovarj B. The
Ovar-j, which is crown’d by a Calyx cut into feveral
Parts, becomes a Berry D, in which are, for the moft
part, two flat Seeds, like a Semicircle, which both to-
gether reprefent a fort of a Heart. Add to this the
Stalk, which is finglc, ending in an Umbel of which
each Ray bears but one Flower. Above the Middle of
the Stalk come out feveral Pedicles, ( as on that of the
Anemone ) on the Extremities of which grow feveral
Leaves like Rays, or like an open Hand.

Tbe Species of this Genus are,

I. Araliaflrum ^luinquefolii folio, majus, Nin-zin vocet^
turn D. Sarrazin. 6in-feng. Des lettres edifiantes
& curieufes, Tom. X- fag. lyi.

2. Araliaflrum ^inquefoUi folio, minus, D. Sarrazin.
Plantula Marilandica, foliis in fummo caule ttrnis,
quorum unumquodque quinquefariam dividitur, circa,
marlines (err at is. N° 36. Raii Hift. IH. 658.

* W, A R A 1 I A Inji. rei htrb. Tab. 154.
t Coinplece, th»t it ta f*j, that bat 0 Calyx.

X X X X X 2 3. AralU*

w

( To6 )

3. Araliaflrum Fragrarix foliot Vailknt^^-

flurthmlifirUmm Anemones Jjlvaticx Joltts, enned^
fhjllon, fiorihus exiguis. Pluk. Manciff. .135# Tab.
45J-' Fig- 7- ■' ,

’ I * , • - ■ ' ’

To fli€W wherein Arnliaflrupt differs from Anlia,
( from whence it takes its Name ^ 'tis co/ivenknc to
give, aifo the Charader of this laft Gextu, fucb as
Mr. yaillavt eftablifh’d it; in his Demonftrations of the
Year 1^17.

Aralia * is altogether like the AralUfirum^ as to the
Strudfure and Situation of its Flower ; but its Berry
confifts. of^ Five $eeds plac’d round an Axis. Moreo-
ver, itsi-eavesare branched ^ almoff like thofe An^
gdka\ and its Stalks ( which in fbme Sfecies arc na-
ked, and In othets have Leaves fet alternately ) bear
each Several Uipbeis at their top, in the Form of a
Bunch of Grapes.

The Species of Aralia, are

I. Aralia caule aph^llo, radice repente. D. Sarrazin.
Chriftophoriana , Virginiana 2.arza radicihus furculo~
Jis ^ fungofiSf Sarfaparilla mjlratibus diCla. Pluk.
Almag. 98. Tab. 238. Fig. ZarfaparilU yir-
ghienfibus nojlratibus di£fa^ lobatis nmbelltferx foliiSy
Americana, Ejufd. Almag. 39^

a.- Aralia caule folio fo Uviy~ D. Sarazzin. Aralia Ca-
nadenfis. Inft. rei E5erb 300.1

3. Aralia caule folio fo & hijpido D. Sarazzin.

Aralia arhrefcens fpinoja, ‘ D. Vaillant. Angelica
arborefcensy fpinofa, feu Arbor IndicUy Fraxini folio,
con ice fpinofo Raii Hid. II. 1798. Chriftophoriana
arbor aculeata Virginienfts Plukv Almag. 98. Tabio.

* vid. Injl, rti Herb, jco. Tab. 134.*

All

( 7°7 )

All the Sfecie-s of thefe two Genera, except the lail: of
each of them, are common in Canada, whence Mr. Sar-
razi», Counfeilor jn. the upper Council, Phyfician to
bis Majefty, and Correfpondent of the Royal Academy
of Sciences, lent them to the Royal Garden firil in i'?oo.

The Inhabitants of^ that Col ;n/, and thofe of Vir^
giiiia, call the firft Species of iiralla by the JS^ame of Sar-
faparilla, becaufe its Roots have almoft the fame Figure
and Vertues

Mr. Sarrazin vvrites, that he had a Patient who had
been cured of an Anafarca^ about two Years before^, by
the ufe of a Drink made of thefe floors. Thac>able
Phyfician aflures us alfb, that the Roots of the fecohd
Species, well boyPd and apply ’d by way of Cataplapne',
are very excellent for the curing of' old Ulcers;' as al*
fo the Decoction of them, with which they bath ahd fy-
ringe the Wounds. He does not at all doubt, but the
Virtues of the third Species ( which i (hall briefly de-
fcribe ) are the fame with thofe of the fecond.

Its Roots creep, and' fend forth Stalks, ■ which rife
commonly to the Height- of a Foot and half, and fomc-
times to two Foot ; the bo:tom part of them is rough,
with reddifh, ftiff and prickling Hairs Thefe Stalks
are fet from the Bottom to almoft the Top ( which are
divided fucceflTively into feveral naked Branches tharg’d
with Umbels ) with branch’d alternate Leaves, almoft
like thofe of Podagraria hhfuta Angelicat folh ^ odore
D. Vaillanti which Plant is grav’d in the fecond Tome
of Boccones Mufaum^ by the Name of Cerefolium ru^ofo
Angdkx folio, Aromaticum. Tab. 19. 'and in Rivini by
that of Myrrhis folto Podagrarid

See the Account of the Chinefe Gin-feng, in Phil.
Tranfa(ft. Anni 1713. p*237,

V. ExtraB

'( 70^ )

V. ExtraB of a Letter of Mr. Edw. Berkeley from
Naples, federal curious Ohjer^ations and

^marks on the Eruptions of Fire and Smoakjfrom
Mount V E S'U V I O. Communicated by
Dr. John Arbuchnot, M. D, and R. S. S.

April 17. 17 » 7. with much Difficulty I reach’d
the top of Mount Pefuvius, m which 1 faw a
vaft Aperture full of ^moak. which hinder’d
the feeing its Depth and Figure. 1 heard within that
horrid QuU certain odd Sounds, which feem’d to pro-
ceed from the Belly of the Mountain ; a fort of Mur-
muring, Sighing, Throbbing, Churning, DaOiing ( as
ic were) of Waves, and between whiles a Noife like
that of Thunder or Cannon, which was conftantly at-
tended with a Clattering, like that of Tiles falling from
the Tops of Houles on the Streets. Sometimes, as the
Wind changed, the Smoak grew thinner, difeovering a
very ruddy Hame, and the Jaws of the Pan or Crater,
freak’d with Bed, and feveral Shades of Yellow. After
an HouiV day. the Smoak, being moved by the Wind,
gave us fhort and partial Profpeds of the great Hollow,
in the flat Bottom of which i could dilcern two Fur-
naces almofl contiguous ; that on the Left, Teeming a-
bout three Yards in Diameter, glow’d with red Flame,
and tlirew up red-hot Stones with a hideous Noife,
which, as they fell back, caus’d the fore mentioned
Clattering. May S. in the Morning, 1 afeeoded
to the Top of Fefuvius a (ecood time, and found a dif-
ferent face of things. The Smoak afeending upright,

gave

( )

gave a full ProfpeA of the Crater, which, as I could
judge, is about a Mile in Circumference, and an Hun-
dred Yards deep. A conical Mount, had been formed
fince my laft Vifit, in the middle of the Bottom. This
Mount I could fee was made of . the Stones thrown up
and fallen back again into the Crater- In this new Hill
remained the two Mouths or Furnaces already mention’d ;
that on oar Left Hand was in the Vertex of the Hill,
which it had formed round it, and raged more vio-
lently than before, throwing up every three or four
Minutes, with a dreadful Bellowing, a vaft Number of
red-hot Stones^ fometimes in appearance above a r hou»
fand, and at lead 300 Foot higher than my Head as
1 ftood upon the Brink. But there being little or no
Wind, they fell back perpendicularly into the Crater ,
incrcafing the conical Hill. The other Mouth to the '
Right was lower in the fide of the fame new formed
Hill. I cou’d difeern it to be Hlfd with red hoc li.«
quid Matter, like that in the Furnace of a Glafs-Houfe,
which raged and wrought as the Waves of the Sea^.
caufing a (hort abrupt Noife like what may be ima-
gin’d to proceed from a Sea of Quickfilver dafhing a-
mong uneven Rocks This Stuff wou’d fometimes fpew .
over and run down the convex fide of the conical Hill,
and appearing at hrft red-hoc, it changed Colour4 and
harden’d as it cool’d, fhewing the firft Rudiments of an
Eruption, or, if I may fo fay, an Eruption in Minia-
ture. Had the Wind driven in our Faces, we had been
in no fmall Danger of flifling by the fulphurous Smoak or
being knocked on the Head by Lumps of molten Minerals,
which we faw had fometimes fallen on the Brink of the
Crater^ upon chofe Shots from the Gulf at Bottom. But
as the Wind was favourable, I had an. opportunity to
fuKvey this odd Scene for above an Hour and a h ill

together;

C 710 )

together ; during which it- ^as very obfervable, that all
tli^^JiTolleys, of^^moak, Flame, and ^qrning Scones,
c|Lii^,only oji^cipr the Hole to our LeS, while the li-
quid- Stuff in the other Mouth wrought and overflow’d
as hath been already defcribed. June .5, After a

horrid Noile, the Mountain was. at t^aple^ to fp^w
a little out of Crater, jThe fame condnu’d the^
^th. The 7th, niching vyas obierv’d till within two
Hours of Night,, when it began a hideous bellowing,
which continued all ,tl)ac N)gh;t; gfd the ne^^, Day till;
Noon, caufing the Windows, aq4^^ , tho;
very Boufes m fJapl^Xo (hake ; From that time it fpewldi
vaft Quantities of molten Stuff to the ISouth, which^
flream’d down the fide of the Mountain, like a great
Pot boyliijg over. This Evening I return’d from., a
Voyage thro* ApulU. iix\d wasjfurptifed, pafling by the
North fide of the Mountain, 'to fee a, great Quantity;
of ruddy Smoak lie along a huge Tcadt of Sky over,
the River of molten Stuff which was, it delf out of,
fight. The 9th, Vefuv'iuj raged lefs vjplendy ; that
Night we faw from Napla a Column of fire, (hoot,
between whiles out of its Summit. Thq loth, wl^n we,
thought all wou’d have been over, the Mountain grevy!
very outragious again, roaring and groaning mofl dreadr^
fully. You cannot form a jufler Idea qf this Noifc: in
the mofl violent Fits of it, than by imagining a mix’d
Sound made up of the raging of a Tempeft, the Mur-
mur of a troubled Sea, and the Roaring of Thunder
and Artillery, confufed all together. It was very ter-
rible as we heard it in the further End of Naples y at
the Diflance of above twelve Miles. This moved my
Curiofity to approach the Mountain. Three or four
of us got into a Boat, and were fet afhoar at Torre del
Gw, a Town fi,cuate at the Foo; of Fejuvius to .the

South-

( 7'« )

South-Weft, whence we rode four or five Miles before
we came to the burning River, which was about Mid-
Night. The Roaring of the VolcAno grew exceeding
loud and horrible as we approach’d. I obferved a Mix-
ture of Colours in the Cloud over the Crater^ green,
yellow, red and blue; there was likewife a ruddy dif-
mal Light in the Air over that Trad of Land where
the burning River flowed ; Allies continually Ihower’d
on us all the way from the Sea-Coaft. All which Cir-
cumftances, fet oT and augmented by the Horror and Si-
lence of the Night, made a Scene the moft uncommon
and aftonilhing I ever law; which grew ftill more ex-
traordinary as we came nearer the Stream. Imagine
a vaft Torrent of liquid Fire rolling from the Top down
the Side of the Mountain, and with irrefiftible Fury
bearing down and confuming Vines, Olives, Fig-trees,
Houles, in a word, every thing that ftood in its way.
This mighty Flood divided into different Channels, ac-
cording to the Inequalities of the Mountain. The lar-
geft Scream feem’d half a Mile broad at leaft, and five
Miles long. The Nature and Confiftence of thefe burn-
ing Torrents hath been deferibed, with fo much Exadt-
nels and Trudi, by BorelluSg in his Latin Treatife of
Aloiifit Mim. that 1 need fay nothing of it. I walked
fo far before my Companions, up the Mountain along
tbs fide of the River of Fire, that I was oblig’d to re-
tire in great hafte, the fulphureous Steam having lur-
priz'd me and almoft taken away my Breath. Du-
ring our -Return, which was about Three-a-Clock in the
Morning, we conftantly heard the Murmur and Groan-
ing of the Mountain, which between whiles would
burft out into iouder Peals, throwing up huge Spouts
of Fire and burning Scones, which failing down again
refembled the Stars in our Rockets. Sometimes 1 ob-

Y y y y y ferv’d

( 711 )

ftrv’d two, at others three Columns of Flame,

and fometimes one vafl; one that Teem’d to fill the whole
Crater. Thefe burning Columns, and the fiery Stones
leem’d to be (hot a icqo Foot perpendicular above the
Summit of thQ^olcano. The nth at Night, 1 obferv’d
it, from a Terrafs in Naples^ to throw up incefl'antly ^
taft Body of Fire and great Stones to a furprifing Height.
Thexith in the Morning, it darken’d the Sun with Alhes
and Smoak, caufmg a Tort of EclipTe. Horrid Bellow-
ings this and the foregoing Day were heard at t^aples,
whither part of the Afties alTo reached. At Night I
obTerved it throw up Flame, as on the nth. On the
i3th> the Wind changing, we Taw a Pillar of black
Smoak (hot upright to a prodigious Height. At Night
I obTerved the Mount caft up Fire as before, tho’ not To
4iftindly becauTe of the Smoak. The 14th, A thick
black Cloud hid the Mountain from Naples. The 15th,
in the Morning, the Court and Walls of our HouTe in Na-
fles were cover’d with Allies. In the Evening, Flame ap*
pear’d on the Mountain thro’ the Cloud. The i6th, the
Smoak was drivenby a Wefterly Wind from the Town to
the oppofite fide of the Mountain. The i7th, the Smoak
appear’d much diminifli’d, fat and greaTy. The 18th,
the whole Appearance ended, the Mountain remaining
perfe(3iy quiet without any vifible Smoak or Flame. A
Gentleman, of my Acquaintance, whole Window^ look’d
toward Fefyvius, aflur’d me, that he obferv'd this Night
Teveral Flafhes, as it were of Lightening, ifliie out of
the Mouth of the Volcano. It is not wmrth while to
trouble you with the Conjedfures I have formed con-?
cerning the CauTe of thcTe Phsenomena, from what I
obTerved in the Lacm AmjanBi^ the Solfatara, ^c. as
well as in Mount Vefuvius. One thing I may venture
to Tay,. that, I, Taw the fluid. Matter- rife out of the Centre
' of

( 71 3 )

of the Bottom of the Crater^ out of the very middle
of the Mountain, contrary to what BoreUm imagines*
whofe Method of explaining the Eruption of a Folcana
by an indexed Syphon, and the Rules of H^drofiaticks^
is likewife inconfiftent with the Torrent’s flowing down
from the very Vertex of the Mountain. I have not
feen the Crater fince tlie Eruption, but defign to vifit
it again before I leave Naples. I doubt there is no-
thing in this worth Ibevving the Society 5 as to that,
you will ufe your Difcretion.

E. Berkeley

yi. An Account of an extraordinary TUMOUR.'
or WEN lately cut off the Cheek, of a ^erfon in
Scotland. Communicated to the ^yal Society by
T>r, Thomas Bower^ M. D, and F.

IT is generally acknowledg’d, that the exacSb Obler-
vation of internal Difeafes, and the faithful Ac-
counts of external Tumours, and extraordinary
Cafes in Chirurgery, have contributed very much to
the Advancement of Medicine. Hippocrates and Galen,
and other ancient Fathers of Medicine, have fet us fait
Copies of this ; and the Moderns, happily following
their Footfteps, have illuftrated this Matter by many
curious Obfervations and Reflections. The Royal So-
cieties and Colleges of Firtuofi, that are now over all
Europe, have taken much pains in this Affair, and have
given us many Inftances and Examples of Extraordi-
nary Cafes in Medicine, which are of great ufe to all
the Pradifers of Phyfick and Chirurgery. Accordi^^g
to thefe laudable Examples I fhall, for the Satisfadion

Y y y y y 2 of

( 714 ) I

of the Curious and Ingenious, give a true and faith- j
ful Account of an extraordinary Excreicence cut off
from the Cheek of a Man, which weighed Nineteen
Pounds, and the Patient entirely recover’d in few
Weeks time. I never before faw the like, nor never
read of it in any Author, tho’ I have confulted ma-
ny on the Head. This Excrefcence is preferved a- I
mong the Rarities of the College of Phyficians at £•
dinhurgh. The Phyfician concern’d in this Affair, was
Dr. Alexander Rujfel of Elgine, a learned and ingenious
Man, and the Operator was the ingenious Mr. George
Cordon of Keithf from whom 1 had the following Infer. !
mation. I i

Alexander Palmer, of the Parifli of Keith, in’ the '

County of Bamf, in the North of Scotland, now about |

Fifty Four Years of Age, obferved, when about Twenty
Seven, a little hard Swelling in the Mufcle of the lower
Jaw on the Left Side, without any Hurt or mam'fefl:
Occafion, which at firfl: went on flowly, but afterwards
it proceeded more quickly, and the older it grew, it
{till came on the fafter; until it increafed to a prodi-
gious Bulk and Weight : From the fir ft Appearance of
this Tumour to the total Excifion of it, there were a-
bout Twenty Seven Years. He had exceflive Fains
and Uneafinefs in it, and at laft it mightily extenua-
ted and emaciated him, who was otherwife a flrong
and robuft Man.

This Excrefcence was of the natural Colour of the
Skin, and feem’d to be an Atheroma being a glandulous
Subftance with feveral big Blood-VefTels in it. and had j
Hair growing on it, as on the other i arts of the !'
Body, as may yet be feen. It was almoft round and ■
very hard, and was as fenfible as any other Parc of the j

Body ; for, when the poor Man was working in the i

Fields, I (

I-

r )

Fields, feme fix or feven Years ago, he accidentally
made a great Gafh or Wound in it with a fliarp Iron,
which was very painful, but was cured by a burgeon,
after the manner of an ordinary Wound ; the Cicatrice
is flill to be fecn in it.

This Excrcfcence having grown fo big, was attach’d
to the Mufcle under the Left Eye, call’d Obliqtms minor
or inferior^ to the Ear and its Mufcles, and to the
Mufcle of the low’er Jaw, named De^rimens. By rea-^
fon of its great Bulk and Weight, it could not hang
down freely without fome Support, therefore it refled
on the top of the Shoulder, which made a confidera-
ble Dimple in it, that is yet very obfervable; befides,
it was holden up by the Man’s Hand in the Day-
time, and laid on a Pillow in the Night* feafon. '

Some three or four Days before the total Excifion
was made, the Patient obferved this Tumour begin to
mortify at the lower end, which made him fo unea-.
fy, that he took a Knife and cut off a good part of
it. This occafion’d a great Haemorrhage; fo that he
reckon’d there was loft a Scots Pint or four Pounds of
Blood, before it could be ftopt. The Patient, after
fb great Trouble and Pain, at laft applied himfelf to
Mr- Gordon, Surgeon of the Place, who made a total
Extirpation of it, on the 1 9th of Jnnmr% 1717.

He made a clofe Ligature, taking in the Bafis of
the Excrefcence, and all the loofe Skin, and contradf*
ing it as much as poftible, he cut it entirely off with
a (harp Pvafour. There gufhd out of the Excre-
fcence, after it was cut off, and was lying on the
Ground, as near as could be guefs’d, two Pounds of
Blood; for it was nourifh’d by feveral large Biood-
Veflels, perhaps by fome. Branches of the Carotide Ar-
tery much iniarged, and other Blood- Veflels coming

from

( 7\(> )

from tbc Ear, and the Mufcles of the Eye and lower
Jaw abovementioned. When Mr. Gordon brought it to
us, which was full three Months after it was cut off,
we cut off with a Knife about a quarter of an Inch
broad of the Bafis of it ; and in that fmall Space wc
obferved four big Blood Vellels. The Bafts, as it now
appears, is five Inches Diameter, which feems too large
for the whole fide of the Face : So that after the Ex-
fedion, I think the loofc Skin has turn’d backwards,
which may make the Bafis now appear fo big.

After all this Blood was loft, the Excrefcence was
weighed, and was full Nineteen Pound Weight ; fb
that before bis own Incifion and this Operation, it
behoved to be feveral Founds heavier, which is a
moft prodigious Weight to be depending on fuch a
place. This Tumour was of a Spheroidical Figure,
and when meafured, was Thirty four Inches about by
the longeft way, and Twenty eight by the broadeft.

The Haemorrhage, which was great, was flopped by
the Vitriolic Powders and other Aftringents, and the
ordinary Drefling w^as ufed. So this great Cure was
completed in fix Weeks time, and the Patient entirely
recover’d, and goes about his Bufinefs, to the great
Admiration and Aftonilhment of every body. The Lid
of his Left Eye continues ftill downwards a little, as
does that fame fide of the Mouth, which was occa-
fiond by the great Weight depending on that fide of
the Face ; but it may be expeded they may come a-
gain to their right Pofture ; for the Head, at firft af-
rer cutting, enclined much to the Right fide, by rea-
fbn of the great Weight on the Left Cheek having
been removed ; but it now begins to ftand upright,
•finee he is perfedly recovered. Tho’ the Skin, and e-
ven a deal of the mulculous part of the Cheek and

lower

(. 717 )

lower Jaw was cut away, yet, according to the Infor-
mation I have from Mr. Gordon the Operator, it is
grown up again, and is of the ordinary Colour of the
5kia, and like the other fide of the Face ; fo that
there grows Hair on that fide of the Face as well as
on the other, which he ordinarily fliaves; and this is
as furprizing as any thing in the whole Affair.

I have given a true and plain Account of this ex-
traordinary Cafe from certain Information; I have con-
tented my felf to relate only Matters of Fadf, without
making any Obfervations or Reflexions on it; for I
leave it to the Philofbphers and Virtuofi 'to make their
own Reafonings and Refinements as Teems beft to them-
feives.

yil. An Account of an Experiment to pro);e an incer-
fpers’d Vacuum 5 or to Jhew that all Tlaces are.
not ec[ualy full,

This Experiment was made before the KING, and-^
HER Royal Highnefs the Princefs of Wales, at
Hampton-Court, in the Month of September 17 17.
afterwards before the R o Y A l-S o c i E T Y , on Thurfday,
December^. 1717. and fince that, in Channel-Rowe, ,
Weflminfter, before [ome Members of the Royal-Society,
by I. T. Defaguliers, M, A, F,R^S. as follows;

Having had the Honour to make fome Experiments
laft Year before his Majefiy and their Royal Highmfes
the Prince and Princefs of Wales ; among others, ' lliew’d
that of a Guinea and a Piece of fine Paper ; then oi a
Guinea and a Feather dropt together ftom the top of
an exhaufted Glafs Receiver about zo inches high ; both

which

( 7«S )

wliich fell to the Bottom at the fame InBant of Time :
Now fince the chief Refifiance of a Medium ( and in-
deed almoft all of it ) depends upon the f Quantity
. of its Matter 5 therefore this Diminution of Refiftance,
whereby the Feather fell as Toon as the Guinea, fliew’d
a Diminution of the Quantity of Matter, and conle-
quently prov’d an interfpers’d Vacuum. Some time
after this, I was inform’d that fome here in

England objeded againft the i hormefs of the Glafs-Re-
-ceiver; as if the Difference of Time in the Fall of the
two Bodies, which they affirm’d to be real, could not
be perceiv d in fuch a Glafs ; and that lome Philofb-
phers from abroad affirm’d that in a Glafs Receiver 7 or
8 Foot long, there would be fuch a manifeft Difference
in the Time of the Fall of the faid Bodies, as to fhew
this Experiment no Proof of a ^ ncuum ; though at the
fame time, Tome of the Objedors well knew that there
- could be no Receivers of half that Length made at
the Glafs Houfe, and therefore thought the Experiment
impradicable. To obviate this, I contriv’d a Machine
for the purpofe, which confifted of a flrong wooden
-Frame 15 Foot high, that held the Air-Pump and four
Cylindric Glafs-Receivers of about two Foot long each,
and fix Inches Diameter Of thefe, having fet the firft
upon the Air-Pump Plate, I laid on the Top of it a
Brafs-Plate of feven Inches Diameter, that had an oil’d
Leather fix’d to it above and below, with an Hole
through the middle, of between four and five Inches
Diameter; then on that Plate I fet the next Receiver,
with a like Plate at top; and after the fame manner
fix’d the other two with Plates between them : The
upper Receiver being a little narrower at the Neck,

t See Sir //i Brinci^ia, Book II- Prop. 4o.

went

( 71? )

went into the Hole of a Board, whereby it was ferew’d
down pretty hard on the ocher Glaffes, and fix’d, to
the whole Machinei On the top'of .this upper Receiv-'
er I laid the Brafs Plate, wet Leather, and Brafs Springs
which contain’d the Bodies to be dropt ' ;; i

Having acquainted His Majefty with what I had pre-
par’d, he order d me to fhew him the Experiment wnth
this long compounded Receiver, and

when 1 made- it before him and her Royal Highnefs,: he
was pleas’d f by pulling down a String fix’d to a Lea-
ver at the top of the Machine ) to let loofe the Bodies
himfelf, to fee that the Experiment was fair.

:W-hen the Receiver .was^fuU of common Aimbefore
Pumping, the Guinea, came <to 'the Bottom, jiift. as the
PapetiWas about the Middle of the fecond.Giafs ; buc
when the Receiver^was .exhaiihed, the .Guinea and Pa-
per came to the Bottom precifely in the fame InRanjt of
Time., -'C io 'htiat dl .ja

Upon: my giving ait, aacoum^of rthc Succefsj^f ;this
Ex perimenc to the S' :they order’d-me tp; r^eac
it before them on the 5th Day ,of £>w«?^^n 71 7^: being
the Thur[day next after the Yearly Meeting focchoofing
Officers on St, .Andrew's Day? x)n which Day an {an-
nual Experiment is appointed to , be-maidd, in .Confor-
mity to the. Will jof theiri late wenthy, Nleinber arid, Be?
nefadlor Sir Coj^lej. . jUTiUL; , .. d

I made the Experiment firft with two of the Rccei*
vers:;, then iwitiKali the four ; : dropping afiGuinea.and a.
fmall Piece of Paper together ; and the Succefs anfwer’d
Expedation : But not being willing to try with a Down-
Feather, becaufe I fear’d the Air might infinuate between
fbme of the Glaile8,-by reafon the Number of Perfons
prefent lhak’d the Room , the Society order’d me to
make the Experiment at home before one or more of
their Members.

Z z z 2 z

Martin

7

( 7io )

J^arth Fffulkes, Efq; a very ingenious Member of th«
Society, did me the favour to be prefenc when I made
the Experiment at my Houfe ; where w'e made four
Tryals in the following manner.

The whole Machine being fix’d, as above mention’d,
we firft let fall a Guinea and two Papers ; the one placed
over, and the ocher under it, (before any Air was pump’d
" out) and the Guinea came to the Bottom when the Pa-
pers were only in the Middle of the fecond Glafs from
the Topi Then having laid a Feather on the Brafs*-
Springs clofe by the Guinea, we kc them loofe both
together ; and the Feather was fallen only down to the
4th part of the Length of the firfl Glafs or ^ of the
whole DKlance, when the Guinea was got down to the
Bottom of the Receiver. We then laid two Papers
and two Feathers, one of each under, and the other
over the Guinea between the Springs ; and having drawn
out (b much of the Air as to bring up the Mercury in
tht Gage-Tube within a quarter of an Inch of the great*
cR Height to which it could be then rais’d by the Prel^
Eire of the external Air, we caus’d the Bodies to fall
all at once : And tho’ the Papers came down to the Bot-
tom at the fame time as the Guinea, yet the Feathers,
being much lighter, wanted about three Inches- But
at lad, having laid the Papers, Feathers, and Guinea^
as before, we pampd out all the Air, and then the
Feathers, as well as the Papers, came to the Bottom of
the Receiver at the fame indant of time as the Guinea.

yilf. Jn

( 711 )

VIII. An Account of a /mail Telercopical Comec
feen at London on the loth of June 1717.
by Edm. Halley, LL. D. R. Soc. Seer.

«

That the Number of Comets traverfing our So*
lar Syftem is much greater than feme, on ac-
count of the late rareneis of their Appearance,
have fuppofed it, may be collected from feveral fmall
ones which have within few Years been deferibed in the
Memoirs of the fretfcb Royal Academy of Sciences.;;
thofe diligent Obfervers alTuring us that they difeover’d
one in Sept. 1698. another in Fehr. 1699. a third in
^prtl 1702: and again a fourth in Novemh. 1707. none
of which, as far as I can learn, were ever (een ’m,E»Sr
Und\ all of them having been very obfeure and with-
out Tails, by means whereof Comets ufually firft Ihew
themfelves. And bcfides thefe, two other Comets with
remarkably long Tails> the one in Movemb, 1689. the o-
ther in Febr. 1701. pad by unobfervable in thefe our
Northern Climats, they having great South Latitude,
and their Motions dire(ded toward that Pole. Hence
we may juftly conclude that the Returns of Comets arc
much more frequent than is vulgarly reckoned, and
chat it is only contingent that for thefe ; 5 Yeats no one
of them has been feen and obferved by our Adronomers.

But there may be dill a much greater Number of
thefe Bodies, which by reafon of their Smallnefs and
Didance are wholly invifible to the naked Eye ; fo that
unlefs Chance do dire(d the Telcfcope of a proper Ob-
ferver, almod to the very Points where they are (againft
which there are immenfe Odds^ it will not be poffible

Zzzzz % for

( )

for them to be difcovcred : And that this is not barely
a Conjedure, take the following Inftancc.

On Mcnddjy June lo in the Evening, the Sky being
very ferene and calm, I was dcfirous to take a View of
the Disk of Mates ( then very near the Earth, and ap-
pearing very glorious ,) to fee if I could diftinguifli in
my 24 Foot Telefcope, the Spots faid to be (een on him.
Direding my Tube for that purpofe, I accidentally fell
trpon a fmall whitilh Appearance near the Planet, refem-
bling in all refpeds fuch a Nebula as 1 lately deferibed
in Philof. Tranja^. N° 347. but fmaller. It leemed to
emit from its upper part a very lliort kind of Radia-
tion difeded towards the Eaft, but Northerly withal ';
^jj^hich, confidering its Situation, was nearly towards the
Point oppofite to the Sun. The great Light of the
Moon, then very near it and alfo near the Full, hin-
der’d this Phenomenon {torn being more diflindly feen ;
bue its Place in the Heavens was fufficiently afeertained
frbm the Neighbourhood of Mars, from whom it was
but about half a Degree diftant towards the SouthwelV,
the difference of* Latitude being fomewhat more than
tbat bf Longitude and Mars being at that time in t
30'^ with 5°. 48^ South Latitude, I concluded the
place thereof in .17®. 12' with 4°; Lat, South,
or thereabouts ; the which may yet be more fecurely de-
termined by help of two fmall fixt Stars I found near it,
the more northerly of which I judged to have the“fame
Latitude with it, and ito follow it at about the Diflance
'of>ft5C'Mihttires;' tKo^other Star was ilbouc- four Minutes
more foutlierly chan. rhe former, and about one Minute
ili-:conrequence rhereof ; the Angle at the Northern Star
whsta httld ohtufe,, as of about lOp Degrees, and thie
f)iftanpe pf'-okr Nebulaitxom iX 'fefquiaber to tliO Diff-anefe
ibf?the)cwoi Stark; or rather a little more. “ The Re^er^id

Mt, Alban Thomas, and my- ‘4 If,
;;l concern-

( )

contemplated this Appearance for above sn Hour, v/z.
from lO:'' to near twelve, and we could not be deceiv’d
as to its Reality ; but the Slownels of its Motion made
us at that time conclude that it had none, and that it
was rather a Neh'ula than a Comet,

However, fufpedling that it might have fome Motion,
I attended the next Night, June i ith, at the lame Hours
and in the fame Company, when with fome Difficulty by
realbn of the Thicknefs of the Air, we found the two
little Stars, but the NehuLt could not at that time be feen,
which we then imputed to the want of a clearer Sky.
But on Saturda), June i$. the Moon being abfent, and-
the Air perfedlly clear, we had again a diHind: View
of the two Stars, with an entire Evidence that there re-
mained no Footftep or Sign of it, in the place where we
had firfl; leen this Phanomenon, which we therefore now
found to be a Comet, and that being far without rhe
Orb of the. Earth, and in it felf a very fniall Body, it
appeared only like a little Speck of a Cloud, fuch as,
would fcarce have been difcerned in an ordinary Tele-
fcope, much lefs by the naked Eye.

IX. An Account of ^ooks, I. Joannis Poleni in
Gymnafio Patavino Phil. Ord. Prof. Sc Scienr.
Socictatum Rcgalium, qux Londini& Bero-
lini fuilt, Sodaiis, Ve Motu A^u^e mlxto^ Libri
duo, ere. 4^®. PataVii 1/17.

The Sub}ed;;herfi treated, of not having hitherto
•fajleii under the Cpnfideration of Mathematical
Writers, the Learned;iAuchor is obliged to make
ufe of feverai XermSi which are either wholly new, or at
r ' ' Isaft

( 7i4 )

lead are applyM in a fenfe fomewbat different from their
common Acceptation; for which rea on he begins his
Work with a Sett of Definitions.

^^tta mortua, or a dead Water is that whofe Surface
being every where equally diflant from the
viuWf no part of it can defeend any lower, without for-
cing fome other upward, and confeqw-iitly the Whole
is without Motion.

viva, or a running Water is that which is put
into motion by the Prefiure of the Incimibcnt Water,
and whofe Motion is oppofed by no other Water lying
in its way.

The motion of a running Water is call’d Motus fim*
flex, or the fimple Motion.

If a running Water m )Vtng over the Surface of a
dead Water, do, by its Prefiure, communicate part of
its Motion to the dead Water ; the compound Motion
with which the whole Body of the Water flows, is
called Motus mixtus, or the mixt Motion.

If a Water at different Depths from the Surface run
with different Velocities, thewr^w is that, which

being the fame at all Depths, will difeharge the fame
Quantity of Water.

Next follows a ftiort Hiftory of the Original, and
Progrefs of the Dodrine of running W'aters, the Inven-
tion of which our Author juftly afierts to the Learned
Cafiellus, and defends him againft Fabretti, who has
maintain’d that Cajlelluss fundamental Propoficion of
the Quantity difeharged being cateris faribm in pro-
portion to the Velocity, was known, and publickly
taken notice of before him by Frontinus,

The Author allows CafleUus to have been miflaken
in determining the Velocity of Water running out at
the bottom of a Veflel, he having aflerted that Velo-
city to be as tlie Depth of ihe Water.

Three

1

( 7*5 )

Three Years after Cafiellus*s Book came ouri this
Miftake was correded by the famous Torrkdlius, who
was the firft that maintain’d, that the Velocity of the
Water running out was in a fubduplicate Ratio of the
Depth, but gave no Demonftration of it.

This Propofition, fays our Author, .was confirm’d by
the Experiments of Maggiotti, Mariotu^ and GugUdmini,
and has fince been demonflrated by Mr. Varignoriy by
Herman in his Phoronomia, and John Bernoutti, as re-
ported by Herman in the Ada Lifftenfia.

Here it may not be improper to take notice^ chat
the Demonftrations of thofe three Learned Perfons are
all grounded upon this Suppofition, that the Water
running out from the Hole is preft upon by the Co-
lumn of Water incumbent upon it, which may eafily .
be demonflrated to be a Miftake. Likewife, if their
Demonflracions be juft, it will follow, that the ftrft
Drops of Water, which iflue out from the Hole, muft
run with the fame Velocity, as after the Water has
been running Tome time; the Contrary of which ap-
pears to be true in Fad by the Experiments of the fa-
mous Mr. Mariotte.

The Author might have found a jufter Account of ^
this matter in the Writings of a Great Man, whom he -
cites on another Occafion; the fccond Edition of whofe
Book was come out fome time before Herman pub-
lifh’d either of thofe Demonft rations, and had been feeu .
by him, as appears by his quoting it frequently, and
mentioning the Difference in this very Particular be- -
tween the firft and fecond Edition.

Our Author goes on to confider the fimple Motion
of Water running out by a Sedion perpendicular to the
Horizon, in the fide of a Receptacle, which is always
entertain’d at the fame Height. He (hews, that the
Velocities, with which the Water iflues out at different

Depths,

• ( )

Depths, being as the Roots of thofe refpet^iive Depths,
may be rcprefented by the Ordinate- of a Faraho.n,
whole Axis repteleiUj the entire Depth. of the Water.
ConCet^ueiitly, fince. the C^ua;K,iiies of ^Vater, running
bur at different Depths, are as thofe Velocities, th^
likew:j(e may be. reprefented by the fame Ordinates, and
the C^anrity of .Water difeharg’d from the whole Sc-
dibn, will be repceiented .by the Rsrabolick Space; and
the! mean Velocity by that fame Spaep divided by the
Abfciffe.

The Times, being as the Qiiantities of Water dif-
charged , may be reprefented in the fame manner as
thofe Quantities.

Hence he derives hi^ general Theorem, That the Qjaan-
titics of Water difebaiged, are in a ratio compounded
of the fe(quip!icate of the Depths of the Water, the
ratio of the Breadths of the Section,, and of that of the
times of the Efffux.

The Author proceeds now to the mixt Motion of
Water; in order to' ^ifeover the Nature of wliich he
has made fbme curious Experiments, after the folloiving
manner :

- A large cylindrical Veflel, with a perpendicular Se-
dion through the fide, of it, was placed upright in a
dead Water ; fb that the bottom of the Veffel was a con*
fiderable Depth below the Stirface of the Water; and
the' Veflel was kept immovable in this fituation.

Above this was Ext another Veflel, full of Watery
whbfe Bottom was pierced >yith >6 Holes, exadly round,
and of the fame Bore, and fb order’d,, as- to be open’d,
or flppt at pleafure. The Water in this Veflel was al-
ways kept at the fame Height, by means pf a third
Veflel, Which fiipply’d the Wace^, . as fafl: as it.ran out
at the round Holes, in the Bottom ; and a large Aper-
ture^ in the fide, of the fecond, WefTel near' the Top.

' . ' ' ’ pre vented

( 717 )

prevented the Water in it from exceeding the due
Height. To break the 'Force of the Water running in-
to the two lowermoft Vcflels, they were each of them
- divided by a Board , placed perpendicujar , but nor
reaching the Bottom, which feparated the Part where
the Water came in, from that where it went out. '

The j^pparatus being thus fixt, three of the round
Holes in the Bottom of the (econd Veilel were un-
ftopr, to let the Water run into the lower Veflel. Where
not running out at the Sedion in the fide, fo faft as it
came in from above, it rofe to a confiderable Height
above the Surface of the dead Water ; after which, the
Efflux of the Water becoming equal to the Influx, it
rofe no higher.

In other Tryals the Water being fuffer’d to run fiom 6,
from 9, li, and 15 of the round Holes, the Water rofe
fuccefflvefy to greater Heights, before the Sedion dif*
charged it as fall, as it came in.

The Experiment being repeated with opening other
Numbers of the round Holes, with Sedions of diffe-
rent Breadths, and at different Depths of the dead Wa-
ter, rhe icveral Heights, to which the Water rofe in the
Veffel, w'ere carefully obferv’d and fet down.

Other Experiments were made by placing the lower
Veffel on dry Ground, and the feveral Heights to which
the Water rofe in the Veffel, according as different Quan-
tities were fuffer’d to run in, were likcwife obferv’d,
and found agreeable to the Heights deduced by Calcu-
lation from the general Theorem above-mention d, con-
cerning the fimple Motion of Water.

The Learned Author comes now to apply thefe Ex*
periments, in order to difeover the Theory of mixe
motion, to which end he lays down thefe two Hy-
pothefes.

A a a I a a

Firfl,

( )

Firft, he fuppofb, that the Velocity of the running
Water is every where in a fubduplicate rafU of the
Depth, and conrequencly the Quantities difcharged may
be reprefented by the Parabolick Spaces, juft as in the
cafe of the firtaple Motion of Water

Secondly, that the Velocity of the dead Water, is the
fame at all Depths, and equal to the greateft Velocity
of the running Water. Wherefore the Quantity of dead
Water difcharged may be reprefented by a Redangle,
whofe Height reprefents the Depth of the ftagnant Wa-
ter, and whofe Bafe is the greateft Ordinate of the 1 a-
rabolick Space abovementioned.

Having thus contrived a way of reprefenting the
Quantities of Water difcharged by the mixt Motion,
as had been done before for the fimpJe Motion of Wa-
ter, our Author obfervcs that the Velocities of the Wa-
ter iftuing out at different Depths, and confequently
the Parabolick Spaces reprefenting the Quantities of W^a-
cer expended, muft be lefs in the mixt, than in the
fimple Motion.

In order therefore to find a general Rule for deter-
mining the Proportion between the Parabolick Spaces,
which reprefent the Quantities difcharged by the mixt
and fimple Motion, or between the Parameters of ihofe
Patah/as, he draws fome Obiervations from the foregoing
Experiments, by the help of which he hopes fuch a
Rule may be found out.

Firfly he obferves that, if the Depth of the running
Water continue unchanged, a greater Depth of dead
Water requires a lefs Parameter.

Secondly y Thar this Parameter does not decreafe in
fd great a Proportion, as the Depth of the Water in-
cteafes-

Thirdlyy That, if the Depth of the dead Water de-
creafe, or the Depth of the running Water increafe in

fuch

( 719 )

fuch manner, that the latter becomes infinitely gr^t in
proportion to the former, then the Parameter of the
mixt Motion muft become equal to that of the fimplc
Motion.

Fetirthly, That, if the Depth of the dead Water be-
come infinitely great in comparifon of the Oepth of the
running Water, the Parameter of the mixt Motion va-
nifhes, or becomes equal to nothing.

The Rule, therefore, which is to be found, ought
to agree with all thefe Obfervations, and befides mufl:
produce the fame Quantities of Water by Calculation,
as were found by Experiment to anfwer to‘ the feveral
Depths of running and dead Water, in the above mc*n-
tion’d Tryals.

Upon this Foundation the Learned Author proceeds,
in a tentative Method, to find his Rule, and having
difeover’d it, he fhews by Calculation, that it anfwers
all the Conditions before requir’d.

This Rule is expreft in a pretty high Equation, which,
befides other Operations, requires the extracting the
Root of the fixth Power

From this Equation is derived another, ferving to
find either the C^antity of Water difeharg’d, the Depth
of the running, or that of the dead Water, the other
two of them being given ; as likewife a third Equation,
to find the mean Velocity.

Our Author goes on to fliew the Ufefulnefs and Ne»
ceffity of confidering the Doctrine of mixt Motion, in
all Queftions relating to the Courfe of Rivers, the Quan-
tities of Water which they difeharge, the enlarging or
narrowing their Outlets, the fcouring and deepening
their Channels, and ^ the Motion of the Tides in Har-
bours. Thefe he illuftrates by feveral Deductions from
the Equations above mention’d; to render which of grea-
ter Evidence, it were to be wifiit, that thofe Equations

A a a a a a z were

( 7?o )

were built upon a more folid Foundation than a ten- '
tative Calculus and that Allowance had been made for
the Velocity impreft upon the preceding Water in Ri-
vers, by the imf>etus of that which follows, which is
omitted by the Author in his Theory, both of mixt
and fimple Motion.

In the Second Book, this Learned Writer propofes
the State of the Laguna of Venict^ as a proper Exam-
ple, to demonftrate the Ufefulnefs of his new' Theory.
He confiders very minutely the feveral Caufcs of choak-
ing up the Laguna, examins the Methods propofcd by
various Authors for fcouring and keeping it clear, fome
of which he rejcds as impradficable on account of the
Expence, others as ufelefs, or prejudicial; and laftly de-
livers his own Opinion.

The principal Caufes, which he afTigns, of filling up
the Laguna, are the Rivers running into it, and the Sea.

The Rivers, which enter it, arifing out of the Alp,
and running down with great Rapidity, carry with them,
efpecially after Rains, great Quantities of Soil, which is
eafily fufpended in the Water, fodong as that Swnftnefs
of Motion continues. But w'hen they come into the
Laguna, the Water, upon extending it felf over that vaft
Surface, loofes almoft all its Velocity, and confcquenC'.
ly the SoiLand Filth, which before it carry ‘d with it,
fubfides in great Qiiantities to the Bottom.

The Remedy our Author propoles for this Incon-
venience, is either wholly to divert the Courfe of the
Rivers and carry them, by another W'ay, diredfly in*
to the Sea; or at lead, to fecure their Outlets with
Sluices, (o as to fufTer them to pafs into the Laguna,
when their Waters are clear ; but after great Rains, when
they run foul and turbid, to flop* their PalTage that
way, and let them out by the other Channel into the
Sea.

The

( 71 i

The Tecond principal Caufe of choaking up the Ld-
gftna, is the Sea Concerning which our Author ob-
ferves, that the Tide of Flood iets into the Laguna from
along the Coad of I(lria and Friuli, where it is per-
petually walhing away the Land in great Quantities^
with which, and the Sand which it raifes upon high
Winds in the Shallows near the Shore, it enters the
Laguna excedingly turbid and foul ; efpecially, when
the Wind blows hard at South- Ead, at which times
the Tide of Flood is feveral Hours longer than the
Ebb. This occafions very high Tides in the Laguna,
and a great part of the Water, which enters by the Flood,
not being carry ’d out by the fubfequent Ebb, has the
more time to difeharge its Soil and Sand in the Laguna.

This IS an Enemy very hard to deal with, however
our Author propofes fome Works of flrong Piles, and
large Stones thrown in between them, to be carried
diredly forward into the Sea, in order to break th»
Violence of the Waves, and prevent their ’wafhing and
carrying away the Land.

Fde feems likewife to favour a Propofal made by the
late famous Guglidmini, and fome others, to let the Tide
enter the Lai^una by more PafTages than it is to go out
at, in order to make it run out with a greater Velocity,
and thereby fcour and deepen the Channels. Bur he
thinks this Contrivance will fcarcely perform all that
is expeded from it; befides that, it will be attended
with great Difficulties in making Works, and Flood-
gates of a fufficienc Strength, to refifl: the Violence of
the Waters.

He occahonally combats the Opinion of Guglidmini,
and moft other Mathematicians who have thought up-
on the Subjedlf', that in order ro give a greater Velo-
city to the Water of a River, thereby to fcour and
cleanfe the Channel, it is proper to make the Outlet

narrower.

( rji )

narrower. This our Author maintains to be ofcnec
falfe, than true, and endeavours to (hew from his
Theorem above-mention’d , that making the Outlet
narrower, will frequently caule the rman f^elocitf of the
Waters to become left than it was before. But whe-
ther a Propofition of fuch Confequence, and fecraingly
fo well rupported by Reafon and Experience, ought
to be condemn’d upon the Authority of a Theorem
founded only upon a tentative Calculation, mud be
left to the Judgment of the Learned.

II. Apollonii Pcrgaci Conicorum tihri OSio, Se-
reni AncilTenlis de SeEitone Cylindn ^ Coni Libri
duo. FoL B Theatro Oxon. 1 7 1 o.

The worthy Curators of the Orfard PVefs having
obliged the Publick with a very elegant Edition of
the Works of Euclid^ Graeco- Latine, were pleas’d fur-
ther to proceed in the laudable Intention of giving the reft
of the ancient Greek Mathematicians in the fame beautiful
Form; In this Delign they were chiefly animated by the
late learned and beneficent Dean of Lhrifi Churchy Dr. Henry
Aldridge, who pitching upon Apollonius, as moft proper to
fucceed Euclid, engaged the two SavtUan PrefeHTors to take
upon them the Care and Pains of the Edition ; Dr. David
Gregory promtfing his Affiftance as to the fiift Four Books,
which are fti’l extant in Greek ; and Dr. Edm. Halley under-
taking to franfiate the Fifth, Sixth, and Seventh Books out
of Arabick ( in which Language they were only to be
found ) and to endeavour to reftore the Eighth, long fince
wholly lort. But T>:. Gregory foon after dying, the Care
of the Whole devolved on Dr. Halley, who hath fpared no
Pains to render the Work complete.

He in his Preface tells us what Helps he had to perfed
the Text, That he had the ufe of two Greek MSS. of the
ftrft Four Books, one of which was Sir Henry Savil's, and
is in the Suvilkn Study at Oxford, the other is now in the

Roy.al

( 7li )

Royal Society’s Mufeum, having been lately prefented them
by that skilful Mathematician Mr. William Jones, F. R, S.
That he had only one Manufcript of Commen-

tary, out of the Bodley Library ; and two Greek Copies, from
the Savilian Study, of Pappus’s Colledions, out of whofo
7ch Book he took the Lemmata, which ferve as a Comment
on the more difficult Places of his Author ,• and that he was
forced to revife and correct the Miftakes and Improprieties
of the Latin Tranflation of Commandine.

As to the latter Books, which were only in Arahick, he
informs us, that he made ufe of the Boddey Txanfcript of
a Manufcript that is at Leyden, which it felf is a late Co-
py of that ancient Arahick Book of the Conickt, heretofore
Gclius's, but fince purchafed by that great Patron of Uni-
verfal Learning, NarciJJus late Primate of Ireland, who was
pleafed to favour him fo far as to fend over into England
this Original Book, whereby he not only amended feveral
Faults committed by the Copyifts in a double Tranfcrip-
tion, but was alfo affured that this Arahick Book was a ver-
bal Tranflation from the Greek; the fame Schemes markc
with the fame Letters, and the whole Context being the
fame in the firft four Books of it, as in the Greek Apollo-
nius This valuable Manufcript, with about 800 others,
Oriental and Greek, has fince, by the Donation of that moft
venerable Prelate, made a noble Acceffion to the Bodley Li-
brary, wherein it is now depofited. It appears by an Epi-
grapbe at the end, to have been written in the Year of
Chrift 150;. and to have been a Copy of a Tranflation of
the Conicks, made fome Ages before by Thehit Ben Corah,
but ther) newly revifed by that famous Perfian Mathemati-
cian Nafir-eddin, who flourifh’d about the middle of our
thirteenth Century.

Behdes this , the Editor tells us, that on occafion he
confulted another Arahick Manufcript ( heretofore Ravim’s )
of great Antiquity, being an Epitome of the fame Books by
Ahdolntelec of Schiraz, every where agreeing in the Order
and Argument with the former, but abridg’d. So that ha-
ving had thefe Helps, he is in hopes that he has fo far re-
trieved thofe Three Books of Apollonius, that the Lofs of the
Greek Text may henceforth be lefs lamented.

The

( 7H )

The Eighth Book of theie Gonicks, was wanting in the
Gruk Copies even before the Tradudion of them into Ata--
. bick lhebit: rf>wt it having been obferv’d that there
was a very near relation between the Arguments of the
Vllth and Vlllth Books, for that the fame Lemmata of
Pappus were common to them both, which are different to
all the reft, it feemed that the Tbmemata Diariflica of the
Vllth Book were defigned to determine the Limits of the
Yrobkmata Diorijmena of the Vlllth; and therefore fuppo-
fing whac thofe. Problems might have been, and their Order
from that ^of the faid Theorems, Dfj has.in XXXlil
Propofitions given the Analyfes Synthefes of. them, after
the Method of the Ancients, every where, following the
Steps of Apollonius to be found in his Vllth Book. This he
t calls Qonicorum Liber OBavus rejlitutus^ and may ferve the
turn, till fuch time as the Original Eighth Book come to
light ; if that be not now to be defpair’d of.

Becaufe of the Affinity of the Subjed, he hath fubjoin’d
the two Books of Serenus AntiJJ'en/ts, the Greek Text of
which was never befoie in print. This was procured by
the abovefaid Reverend Dean of Chriftchurcb, Dr. Aldrich^
in a collated Copy of three Manufcripts, extant in the
King’s Library at Paris, and by him, according to his wont-
ed Goodnefs and Generofity, freely communicated for the
ufe of the Publick. To this alfo is added the Latin
Tranflation of Commandine, which in many Cafes needed
Caftigation.

As to the Authors themfelves little needs be faid, they
having flood the Teft of fo many Ages, and been highly
valued by the Learned in all Times, efpecially the Conicks,
juftly efteemed a Mafterpiece in the Geometry of the An-
cients : So that it may feem ftrange, that a Book fo ex-
celling in its kind, (hould not till now have been printed
in its native a Tongue fo peculiarly adapted to Mathe-
matical Purpofes. But this preient Edition may make am-
ple Amends, the Paper and the Elegance and Corre<ftnefs of
the Print being remarkable. The Book is now to be had of
Mr. Chrifiopher Bateman in Pater-nofier Roiv, London,

Printed for and J, Innys, at the Princess Arms
in St. Paul's Church-yard. 1718.

X TE7U1IVIJ

f r>..»C

( ^55 ) Number 35^5*

PHILOSOPHICAL

TRANSACTIONS.

For the Months of Jan. Feb. March and Jpr. 1718.

The CONTENTS.

/""^Onfiderations on the Change of the Latitude
j of fome of the principal fixt Stars. 'Ey
Edmund Halley, R.S Sec.

II. Jn /Account of fome Experiments fhown before
the Royal Society , with an Enquiry into the
caufe of the Ajcent and ^Sufpenfion of Water in
Capillary Tubes. Ey James Jurin, M.D. and
R. Soc. S.

III. De Motu Jquarum fluentium. Authore eodeni
T>. Jacobo Jurin, M. D.

IV. An Account of the Sinking of three Oaks htto
the Ground^ Manington in the County of
folk. Communicated by Peter Le Neve, Efq‘j
Norroy £\jng at Arms, and Fellow of the Roy-
al Society.

V. A ^eBifcation of the Motions of the five Satel-
lites of Saturn j with fome accurate ObferVations
of theWy made and Communicated by the E^Verend

A/r. James Pound, R. S. Soc.

Aa a aa a

I. Conf^

/ ^ ^ X \
V /

L Conflderations on the Change of the Latitudes
of tome of the principal fixt Stars. ^By Edmund
Halley, R. S. Sec.

HAving of late had occafion to examine the quan-
tity of the Prcceflion of the Equinodial Points,
I cook the pains to compare the Declinations of the fixe
Stars delivered by Ptolomy, in the 3^;^ Chapter of the yth
Book of his Almag, as obferved by Timocharis and Ari-
fljUus near 300 Years before Chrift, and by Hipparchus
about I/O Years after them, that is about 130 Years
before Chriji, with what we now find : and by the re-
fult of very many Calculations, I concluded that the
fixt Stars in 1800 Years were advanced fomevvhat more
than degrees in Longitude, or that the Preceflion is
fomewhat more than j>er arm But that with To much
uncertainty, by reafon of the imperfect Obfervations of
the Ancients, that I have chofen in my Tables to adhere
to the even proportion of five Minutes in fix Years,
which from other Principles we are aflured is very near
the Truth. But while I was upon this Enquiry, I was
furprized to find the Latitudes of three of the principal
Scars in Heaven directly to contradid the fuppoied great-
er Obliquity of the Ediptick, which feenis confirmed by
the Latitudes of moft of the reft; they being fet down
in the old Catalogue, as if the Plain of the Earths Orb
had chang’d its Situation, among the f«xt Stars, about
20' fince the time of Hipparchus. Particularly all the
Stars in are put down, thofe to the

the Eclipttek, with fo much lefs Latitude rhan we fmd,
and thofe to the Souihvrard With fo much more Southerly

Lati-

Latitude. Yet the three Stars TaUUcium or the Bulls
Eye, Sirius and ArEfurus do contradid this Rule di-
rc(9:ly: for by it, ? alilicium hting in the days of Hip‘
parchus in about lo gr. of Taurus ought to be about
Min. more Southerly than at prefent, and Sirius being
then in about of Gemini ought to be xo Min. more
Southerly than now ; yet e contra Ftolomy places the fird
^o Min. and the other xx more Northerly in Latitude
than we now find them. Nor are thefe errors of Tran*
fcription, but arc proved to be right by the dedinarions
of them fet down by Ptolemy, as obferved by Timocharis,
Hipparchus and himfeh, which (hew that thofe Latitudes
are the fame as thoie Authors intended. As to ArEiurus,
he is too near the Equinodial Colure, to argue from
him concerning the change of the Obliquity of the
Ecliptick, h\xi ^Ptolomy gives him 33' rooit North Lati-
tude than he now^ has ; and that greater Latitude is like-
Wife confirmed by the Declination^ delivered by the a-
bovefaid Obfervers. So then all thefe three Stars are
found to be above half a degree more Southerly at this
time than the Antients reckoned them. When on the
contrary at the fame time the bright Shoulder of Orion
has in Ptolemy almoft a degree more Southerly Latitude
than at prelent. What fliall vve fay then? ftisfcarce
• credible chat the Antients could be deceived info plain
a matter, three OblCrvers confirming each other. Again
thefe Stars being the mofl confpicuous in Heaven, are in
all probability the neareff to the Earth, and if they have
any particular Morion of their owmi, it is mofl likely
to be perceived in them, which in fo long a time as s 800
Years may fliew it felf by the alteration of their places,
though it be utterly imperceptible in thefpace of a fin*
gle emuvy of Years. Yet as to Sirius it may be obfer-
ved that Tycho Brahe makes him x Min more Northerly
than we now find him, whereas he ought to be above as

much

( )

much more Southtrl'^ from his Ecliptick, (whofs Ohliqui-
ty he makes 2 ' greater than we elleem it at prefent) di-
ffering in the whole 4 f Min Cn . half of this difference
may perhaps beexcufed, if refraflion were not allowed
in this ( ale by T)cho\ yet two Minutes, in fuch a Star
as Sirius^ is fomewhat too much for him to be mifta-
ken

But a further and more evident proof of this change
is d.rawn from the Oblcrvation of the application of
the Moon to ^ahlichsm Anno Chrijli 509 Mart, ii®,
when in the beginning of the Night the Moon was
feen to follow that Star v ry near, and femed to have
Eclipfed it, lml2<x?^e ja'js 0 ^rLu S^^ofjuxr

fjtJpei iiofl/ii '’n^cpsfleiOis ■rgfw fMput. /. c Stdl/i

appoju.t erat parti pir iju.im h/J cabatur tim ,ts Lnnx illumi’
natus, as BuuiaUus, to whom we are beholden for this
Anticnt Oblcrvation has tranflatcd it. Now from the
undoubted principles of Aflronomy, it was iirpofliblc
for this to be true at -^th ns, or near ir, unlefs the
Latitude of Palilicium were much lefs than we at this
time find it. Vide BnllUldi f hilolaicd, pjg I^z.

This Argument Teems not unworthy of the Boya/ So-
fifty's Confideration, to whom I humt'l) offer the plain
Fa^ as I find it, and would be glad to have their Opi-
nion.

fiut whether it were really true, that the Obliquity of
the Ecliptick was, in the time of Hipparchus and Ptole-
my, really 2z Min. greater than now. may well be que-
flioned ; (mao. Pappus Alexandrinus, who lived but about
200 Years after Ptolemy, makes it the very fame that
Wc do. Fide Pappi Cclk^> Lth, VI. Prop. 35".

II. An

( )

II. An Account of form Experiments [hown before
the Royal Society 3 with an enc^uiry into the
canfe of the Afcent and Sulpenfon of Water in
Capillary Tubes, James Jurin, M.D, and
fs,, Soc. S.

SOme Days ago a Method was propofed to me by
an ingenious Friend, for making a perpetual Mo*
tion, which feem’d To plaufible, and indeed fo eafily
demonftrablcfrom an Obfervation of the late Mr. Hdrvks^
hee, faid to be grounded upon Experiment, that, tho*
1 am far from having any Opinion of attempts of this
Nature, yet, I confeft, I could not fee why it (hould
not fucceed. Upon tryal indeed I found my (elf difap-
pointed. But as fearches after things impoflTible in
themfelves are frequently obferv’d to produce other
difcoveries. unexpeded by the Inventer; fo this Pro*
pofal has given occafion not only to redify fome mi-
(lakes into which we had been led, by that ingenious
and ufeful Member of the Royal Society above named,
but likewife to dcted the real Principle, by which
Water is rais’d and fufpended in Capillary Tubes,
above the Level.

Friend* s Propofal was as follows*

Fig i. Leti4^Cbea capillary Siphon, compos’d
of two Legs A B C, unequal both in length and
Diameter, whofe longer and narrower Leg AB ha-
ving its orifice A immerft in Water, the Water will
rife above the Level, till it fills the whole Tube A B,
and will then continue (ufpended. If the wider and
Ihorter Leg B C, be in like manner immerft, the Water

Bbbbbb will

]

( 74® ) I

will only rife to Tome height as FC, lefs than the entire
height of the Tube B C. I

This Siphon being fill’d with Water, and the Orifice !

A funk below the Surface of the Water DE, my Friend i

reafons thus.

Since the two Columns of Water AB and FC, by
the Supppfitiori, will be fufpended by (bme Power adling
within the Tubes they are contain’d in, they cannot de-
termine the Water to move one way, or the other. #3uc j
the Column B F, having nothing to fupport it, mult j
defcend, and caufe the Water to run out at C. Then
the prefTure of the Atraofphere driving the Water up-
ward through the Orifice A, to fupply the Vacuity,
which would otherwife be left in the upper part of the
Tube B C, this muft neceflarily produce a perpetual
Morion, fince the Water runs into the fame Veflel,
out of which it rifes. But the Fallacy of this reafoning
appears upon making the Experiment. i

Exp.i^ For the Water, inftead of running out at |i

the Orifice C, rifes upward towards /^, and running all f

out of the Leg B C, remains fufpended in the other ||

Leg to the height A B.

Exp. 2. The fame thing fucceeds upon taking the
Siphon out of the Water, into which its lower Orifice
A had been immerft, the Water then falling in drops
out of the Orifice A, and (landing at lad at the height
AB, But in making thefe two Experiments it is ne-
cefiary that A G the difference of the Legs exceed FC, [

otherwife the. Water will not run either way. !

Exp. Upon inverting the Siphon full of Water, it
continues without Motion either way. i

The reafon of all which will plainly appear, when 1
we come to difeover the Principle, by which the Water
is fufpended in Capillary Tubes.

Mr.

f 74' )

Mr. Havphslce's Obfervation is as follows.
z. Let A B F C he a capillary Siphon, into
the which the Water will rife above the Level to the
height CF, and let B A \>q the depth of the Orifice
of its longer Leg below the Surface of the Water D E.
Then the Siphon being fill’d with Water, if B A be not
greater than C F, the Water will not run out at A, but
will remain fufpended. **

This feems indeed very plaufible at fiirfi: fight. For
fince the Column of Water FC will be rufpended by
fome power within the Tube, why fliould not the Co-
lumn B A, being equal to, or lefs than the former,
continue fufpended by the fame Power ?

Exp. 4. In fad, if the orifice C be lifted up out of
the Water D E, the Water in the Tube will continue
fufpended, unlefs 5 ^ exceed FC.

Exp, 5". But when C is never fo little immerft in the
Water, immediately the Water in the Tube runs out in
drops at the Orifice Ay tho’ the length A B ho confide-
rably lefs than the height C F.

Mr. Hair kshee in his Book of Experiments has advan-
ced another Obfervation, namely, that the fhorter Leg
of a Capillary Siphon, asABFCy muH be immerft in
the Water to the depth /^C, which is equal to the height
of the Column*, that would be fufpended in it, before
the Water will run out at the longer Leg.

Exp, 6. From what miftake this has proceeded, f
cannot imagine ; for the Water runs out at the longer
1-cg, as foon as the Orifice of the Ihorter leg comes
to touch the Surface of the ftagnant Water, without
being at all immerft therein.

Having proceeded thus far in obedience tothe com-
mands of this llluftrious Society, I beg leave to go a
little farther, and to enquire into the caufe of the aicent
and fufpenfion of Water in capillary Tubes.

B b b b b b 2

That

( 74» )

That this Phafnomenon is no way owing to the
prefllire of the Atmofphere, has been, I think iufficient-
Jy prov’d by Mr. Havksbees Experiments*

And that the caufe aflign'd by the fame ingenious
and inquifitive Perfon, namely the attradion of the
concave Surface, in which the fufpended Liquor is con-
tain’d, is likewife infufficienc for producing this effed,
I thus demonftrate. •

Since in every capillary Tube the height, to which
the Water will fpontaneoufly afeend, is reciprocally as
the Diameter of the Tube, it follows, that the Surface
containing the fufpended Water in every Tube is al-
ways a given Quantity : but the Column of Water fuf
pended is, as the Diameter of the Tube. Therefore,
if the attradion of the containing Surface be the caufe
of the Waters fufpenfion j it will follow, that equal
caufes produce unequal effeds, w hich is abfurd.

To this it may perhaps be objeded, that, in tW’O
Tubes of unequal Diameters, the circumftances are di-
fferent, and therefore the two Caufes, tho* they be equal
in themfelves, may produce effeds that are unequal.
For the lefler Tube has not only a greater Curvature,
but thofe parts of the Water, which lie in the middle of
the Tube, are nearer to the attrading Surface, than in
the wider. But from this if any thing follows, it muft
be, that the narrower Tube will fufpend the greater
quantity of Water, which is contrary tb Experiment.
For the Columns fufpended are as the Diameters of
the Tubes.

But as Experiments are generally more fatisfadory
in things of this nature, than Mathematical reafonings,
it may not be amife to make ufe of the following,
which appear to me to contain an Expirmemum Cru-
(is.

Tig,

( 743 )

Fig. The Tube CD is compofed of two Parts, ifi
the wider of which the Water will rife fpontaneoufly
to the height B but the narrower Part, if it were of
a fufficient length, would raife the Water to a height
equal to C D

Exp. 7. This Tube being fill’d with Water, and the
wider end C immerft in the fiagnant Water d B, the
whole continues fufpended.

E^p. 8. Fig. 4. The narrower end being immerfl,
the Water immediately fubfides, and ftands at lafl at
the height D G equal to B F.

From which it is manifeft, that -the fufpenfion of the
Water in the former of thefe Experiments is not owing-
to the attradion of the containing Surface .* fince, if
that were true, this Surface being the fame, when the
Tube is inverted, would fufpend the Water at the fame-
height.

Having fhown the infufficiency of this Hypothefis,

I come now to the real caufe of that Pha:nomcnon,^
which is the attradion of the Periphery, or Sedion of
the Surface of the Tube, to which the upper Surface of
the Water is contiguous and coheres. -

For this is the only part of the Tube, from which thC’
Water muft recede upon its fubfiding, and confequently'
the only one, which by the force, of its cohefion, or at-
tradion, oppofes the defeent of the Water.

This likewife is a caufe proportional to the efTed,
which it produces ; fince that Periphery, and the Co-
lumn fufpended, are both in the fame proportion as the
Diameter of the Tube.

Tho’ from either of thefe particulars it were cafy to
draw a juft Demonftration, yet to put the matter out of
all doubt, it may be proper to confirm this afiertion>
as we have done the former, by adual Experiment.

( 744 )

FJg. S'. Let therefore EDC be a Tube, fikc
that made ufe of in the 7th and 8th Experiments, ex-
cept that the narrower Parc is of a greater length ; and
let AF and BG he the heights, to which the Water
would fpontaneoufly rife in the two Tubes E D and D C.

Exp. 9. If this Tube have its wider Orifice C im-
merft: into the Water A and be fill’d to any height
lefs than the length of the wider Part, the Water will
immediately fubfideto a Level with the point G\ but if
the Surface of the contain’d Water enter never (b little
within the fmaller Tube E D, the whole Column D C
will be fufpended, provided the length of that Column
do not exceed the height AF.

In this Experiment it is plain, that there is nothing
to fuflain the Water at fo great a height, except the
contadl of the Periphery of the Icfi'cr Tube, to which
the upper Surface of the Water is contiguous. For the
Tube D C, by the Suppofttion, is not able to fupport the
Water at a greater height chan B G.

Exp. 10 Fig. 6. When the fame Tube is inverted,
and the Water is rais’d into the lower- extremity of the
wider Tube CD, it immediately finks, if the length of
the fafpended Column D N he greater thanO 5; where-
as in the Tube D E k would be fufpended to the height
A F. Erom which it manifeflly appears, that the fuf-
penfion of the Column DH does not depend upon the
actradion of the Tube D E, but upon the Periphery of
the wider Tube, with which its upper Surface is in
contad,

For the fake of thofe. who are pleas’d with feeing the
fame thing fucceed in dii^rent manners, we fubjoin the
two following Experiments, which are in fubhance the
fame with the 9th and loth.

Fig. 7. ABC h z Siphon,: in whofe narrower, and
fborter Leg ^ if it were of a fufficient length, might

be

( 745 )

be fafpended a Columaof Water of the height E F; but
the longer and wider Leg B C wilLfufpend no more
than a Column of the length G H.

Exf. II. This Siphon being fill’d with Water, and
held in the fame Pofition as in the Figure, the Water
will not run out at C the Orifice of the longer Leg, un-
lefsD C, the difference of the Legs A B and B C, exceed
the length E F.

• Fig. 8. Exf. 12. If the narrower Leg £Cbe long-
er than AB, the Water will run out at C, if DC the
difference of the Legs exceed EF\ otherwife it will
remain fufpended.

In thefe two Experimentsit is plain, that the Columns
D C are fufpended by the attradfion of the Peripheries at
A, fince their lengths are equal to E F,or to the length of
the Column, which by the fuppofition thofe Peripheries
are able to fupport; whereas the Tubes F C will fuflain
Columns, whole lengths are equal to G H.

Tho’ thefe Experiments feem to be conclufive, yec
it may not be improper to prevent an Objediion, which
naturally prefents it felf, and which at firll view may
be thought fufficient to overturn our Theory.

Fig. 5*. For fince a Periphery of the Tube E D is
able to fullain no j more than a Column of the
length A F, contain’d in the fame Tube ; how comes
it to (uffaina Column of the fame length in the wider
Tube £)C, which is as much greater than the former,
as the Sedion of the wider Tube exceeds that of the
narrower ?

Again, if a Periphery of the wider Tube
DC be able to fuftain a Column of Water in the fame
Tube, of the length BG\ why will it fupport no more
than a Column of the fame length in the narrower
Tube ED}

Which

( 74<S )

’ Which Queries may likcwife be made with regard
to the rich and lath Experiments.

The anfwer is eafy, for the Moments of thofc two
Columns of Water arc precifely the fame, as if the fu-
ftaining Tubes £ D and C D, were continued down to
the Surface of the ftagnant Water A B ; fmee the velo-
citiesof the Water, where thofe Column grow wider, or
narrower, are to the velocities at the attrading Periphe-
ries, reciprocally as the different Sedions of the Co*
iumns.

Fig. 9. Exp. 13. From which conflderation arifes
this remarkable Paradox, That a VefTei being given of
whatfoever Form, as A BC^ and containing any afligna-
ble quantity of Water, how great foever ; that whole
quantity of Water may be fufpended above the Level,
if the upper part of the Veffel C be drawn out into a
capillary Tube of a fuflicienc finenefs.

But whether this Experiment will fucceed, when the
height of the Vcflel is greater than that, to which
Water will be rais’d by the preffure of the Atmofphere,
and how far it will be alter’d by a yactium, I may
perhaps have the honour of giving an account to the
Society fome ocher time, not being perfedly fatisfy’d
with thofe Try als which I: have hitherto had the oppor-
tunity of making.

Having difeover’d the caufe of the furpenfion of Wa-
ter in capillary Tubes , it will not be difficult to
account for the feemingly fpontaneous afeent of it. For,
fincQ the Water, that enters a capillary Tube as foon
as it’s Orifice is dipt therein, has it’s gravity taken off*
by the atrradion of the Periphery with w’hich it s up-
per Surface is in contad, it muft neceffarily rife high-
er, partly by the preffure of the ftagnant Warer, and
partly by the attradion of the Periphery immediately
above that, which is already contiguous to it.

It

( 74? )

It might now be fliown, how naturally the various,
and -feemingly contrary appearances of the above
mention’d Experiments are deducible from this Theory^
but this- is (6 ealy, .that it is needlefs to infifl; upon it ;
and our difcourfe upon this minute Subjed: has been
already lb tedious, that we could fcarce hope for Pardon,
unlefs it were direded to thofe, who are fenfible to
how many of the greater, and more iconfiderabie, Phte*
nomena of Nature this 'Dodrine is applicable.

■ ‘ e ■

P 5. When this i Paper was* reading "before. the So-
ciety, I found that our incomparable PreTident. was
already acquainted with the above-mentioned Prindplo,
and 1^ have fmcemet with feveral PalTages in the..} i(t
Query fubjoin’d to the late'* Edition of his Opticks
wh^h plainly Ihevv/ that he was Mailer of it, when
they were written. ‘ * - •• .

1 mud do the fame Judice to that excellent Mathema-
tician Mr. ^ohn Maihinf Profeflbt of Adronomy in
6 refham College. i j >

To thefe two worthy Perfons l am obliged for the
following Obfervatioii,'’ That, what 1 call a Periphery,
or Sedion of the concave fur^ce of the Tube, is really
a fmall Surface, whole Bale. is chat Periphery, and
whofe height is the didance, to which the aettadive
power of the Glafs is extended. r

IIL Tk

• •

C c c c< c

i 748 )

* ' C I .

III. De Motu Aquarum fluentiim, Authore fodetn.
’ 2). J^cobo Jurin, M. 2).

O; vl'M’i 1 cri. ;.)ti ; ■ ,> ' ,

.•iA. Qu3Ci Motum 3£x imi yafis fora^'n^ de8ycutis/(k-
pa v'idcmua, tftiov iii, ipfa re HydraUjic^ . turn in
ejus Principiisad Oeconomiam Animalem applicandis, a-
Iris ctt'm .CQ»Jpaiajci»i: r<2qjus Mot us quantita-

tem cani)In^snus neino, qjiipdrficiatn^ re^^ie deter

foienr 'Cjijts^rloQO'iferiptares Hydtaulict
CojuoimajaqusaE pondijs^/oraijiioi itroimbentis ..Quod
qui f^iBhb/lid fane ti^utiquatnlanimuln adVercuQii fieri
ondningcindo poJilc; • ujiMotrisiaiiqqi^^univpwd^re flui^
efcente conferatur. Poteric autem Aqu^djefluentis Mot
cu$fak:Hr4)pct^i!d:dbm ntcHfum. ■

i j fi^;. x(Q.i'Sk S H AHt^-^quae ruperficies infinita, C C
foramen circulare in fundo fadum, AJ^ r^da perpen-
d icM Itttls bpw I fiaranfltti lis eedt^Um,- .djuda, < ^ C C <5 ^ Co-
lomdaj rosier, Catjamdai AqiiePiTpqijdwamfiBff C G decur-
lentiSjt 5 GiljCuiii'a.-cujasieomiflQeici/ca ^x^m A B ge*
ncratuc SiQljdiunh, zH/it rCaJafidasu Q C, QS. Aqua e>
nith CDiOElibarQi'iiSd nnotu .aeceleiarorirdie^endai: :^d nor<>
mam corporum omniunj. ;grayiumi;inqce(&rid. in mino-
rem amplitudinem contrahitur, prout majorem velocita-
tem acquirit inter cadendum. Sc profluic ex foramine
CC ea cum velocitatc, qux cadendo ab altirudine^^
comparatur.

, V^qcitas autem corporis gravis cadendo genica, ex
demonftratis, ratiemeni obtinet fubduplicatam
altitudinis unde cecidic. Quare, fi ducacur ad Curvam
S6C Ordinaca qusevis D E, atque ipfa D E vocecur j,
^ AD ;v, exponetur velockas Aqux in fedione EE

per

( 749 )

peryj^/fi?^Fadlwii tx -ea ?n feq-i

tionem perVxx/. rr;:; r wpl: it: ^.yf i>ijji::.

Quod Factum eft., u t . l»ol$Sj 4i^%%4^Co ^ qe^j^qris
fpatio per earn fedtionem iranfeufltjs^i q^mque .e^denr*
;Aquae molea date iempjo^e;pqr|finiulao';p^^ia:^%(^^
nes tranfeac, proinde Factum iftud perpetuo fibi^pqn-
ftabir, eritque Vxx y^-z-z: i , .

Quie eft ^.^qyatio Curvsc S\GC, part^fp^- mtra
datum vas comprehenfam, delinea^^^.^jufclgpique^^/^k-
^uacionem non obfeurg .ci^gnps ,

Frop,^6i .Lfh.ii Prhf.ip. qui primi^%5iqr5inj^rr»p>XSj-ara
Aquae* efftuenris velocitatem, ex\gepuinis Prirf^ipuf^de-
du(ftam, Orbi Literate expofuifi : - j ; ^ ,,

•. Eft aucem ipfa Curva F3ypbrbolofiid§s quarci OrdP
-ois^ cujus altera Afymptotos eft' re^a >4>S- ad-FJorizod*-
tern parallela, altera ^.B eidem perpendiculafris.

. Hujus Poteftas eft Quadrato-Cubus OrdinacGE ./^C7,
dujSbs.ad pundum G, ubi reda^G, bifecan§ ;angulum
ab Afympcotis comprehenfum, Curvx qccurrit*

Spatium S A D BS, inter Curvam SQ E, Ordinat^m
X)fi & Alymptotos A D,AS inclufum, ffquale eft qua-
cuor panibus tertiis Redan^guli //£>* fubAbfeifla A P 8c
Ordinata DE content!. Eftque proinde-Spatium •S’/Z.E
-pars tertia ejufdem Redlanguli. , j

Solfdum SG E EGS, convolutionei fpacii S A DBS,
circa Axem A D, generatum, duplum eft Cylindri in-
cumbentis fedioni E E, Unde Solidum cayum, quod
gignit converfro fpatii S H EG S, circa eundem Axem,
Cylindro incumbenti aequale eft. Quae omnia facili cal«
culo inveniuntur per Methodum Fluxionum inyerfam.

Theorem A L

Aqui ex vafe amplitudinis infinicae, per foramen cir-
culate in fundo fadum, decurrente, Motus totius Ca-
taradae aqueae Horizontem verfus sequalis eft Motui Cy-
C c c c c c a iindri

( 75® )

imdrt aquei* fiib ip(b foramine 6c alcicudine Aqux,
cujus velocitas sequec velocicacem Aqu^ per foramen
effluentis ; vel^qualis eft Motui' molis Aquae, qux dato
quovis tempore effluit, cujus ea f»c velocitas, qua per-
curratuf eodem dato tempore fpacium xcquale altitudini
Aquie, , .

Demonfiratio frim^e partis.

Ducatuf ad Curvarn SGC alia Ordinata priori
B E quam proxima.

Gurva circa. Axem A B converse, generabunt Ordina^
ixD’E, dty Circulos duos, quibus incercipitur Solidum
naicens EEee* Id folidum arquale eft Fa<fto ex*akito-
dine D d du(3a in fe<3:ionem EEy & Motus ejus »-
quatur^ Faefto ex ipfo (blido duefto in vdocicatem
dem, fiveFado ex altitudine Dd\ fediene EE^ &vo>
locicate Aquae in^ ea Seft^ione. Cumque fupra oftenfum
fit, Fadum ex quavis Sedione Cataradae & velodtate
Aquae in ea Sedione, quantitatem eftc conftantem, erk
proinde Motus totius Cataradae aequalis Fada ex quai»>
titate illa conftante dudaJn Summam omnium alcitddi-
num Ddt fiVe in ipCam A B, hoc eft, Motui Cylindri fiib
ipfb foramine & altitudine Aquae, cujus velocitas aequet
velocicatem Aquse per foramen effluentis. ^E^ D.

Corel. 1. Data altitudine Aquae, erit Motus. Cata-
radae in ratione foraminis.

X. Dato foramine, erit Motus Cataradae in ratione
fefcuplicata alritudinis,- five in ratione triplicata veioci-
catis, qua Aqua per foramen exit;

3. Dato Motu Cataradae, erit foramen reciproce in
ratione fercuplicata altitudinis, vel reciproce in ratione
velocitatis triplicata.

Depionflratio fecund^e partis.

Moles Aquae dato tempore effluentis eft ad Cylin*
drum^ Tub iplo foramine & altitudine Aqus, ut longi-
tude quam Aqua effluens arquabili velocitate dato. ifto

ccmporcL

( 75* y

t^ibpore p^urfura fit, ad altitudinem Aquae. Cumquc
velocitas, quae tribuitur moli Aquae cfHuentis, fit ad
velocitatem Cylindri reciproce in eadem ratione, erunt<
Moruum quantitates utrinque a?qWales. E. D.

Data aicieudine Aquae &. mole effluentc,*
Mio^us Cararad^ae ell in ratione inverfa temporis quo>
tfta tnoles efHuit.

Data altitudine & tempore, Motus Cataradac
itr moles Aquae tempore iQo edloentis.

0^3 i parosr rempore & mole Aqux efHuentis, erit Mo-^
tusCatara^^ in ratione altitudinis.

4- Dato Motu Catarat^x &>altitudine, moles efiluens
e(l in ratione temporisV

S» Daco Catarada: Motu & mole- Aquae cfflucntis/
altitude e(l ut tempus.

6.: Dato tempore & Motu Cararac^ae, erk Aquae -
cfHuentis moles reciproce ut altitude^

, . TheoremA IT. .

Figi II.' Si capiatur B A, quae fit ad B D, ut D 6^ ad< -
D6+— AC+; Aqua decurrente ex dato vale Cylin^
drico femper pleno G GEE, per foramen circulare C C
in fund© medio fadum, Motus Cataradae aquese Ho*
rizontem verfus rrqualis erit Motui Cylindri Tub fora*'
mine & altitudine AB^ cujus velocitas aequet veloci^i
tatem Aquae per foramen exeuntis; vel erit aequalis
Motui molis Aquae quae dato quovis tempore effluir,
cujufque ea fit velocitas, qua percurratur eodem dato
tempore fpatium aequale altitudini A B.

Demonfiratio prima partis. '

Ducatur AS ipfi D G patallela, & Afymptotis AS^, .
ABf per punda G, C delcripca coiKipiatur Curva New^
toniana SG C,

Ut conftet Aquae altitude, fupplendus eft exeuntis >
locus Cylindro aqueoj-^GG, defeendeme cum ea ve/*

locitate .

( )

leckate uniformi, qu2 acquiricui cadcndo ad D,
qucmadmodum docec Vir iiicompatabiiis PcopoOcione
pc£edid:a. • .

Motui bujus Cylindri a^quacur, per Theorcma fupe*
i;ius, ^otus Catacadse S GGi Ergo Mocus Aqux def-
oendencis.^ cuin.rit^coniporitus ex Mom Cylindri a<|Mei
& Motu Cataradx GGCC, xqualis eft Moon

, A. B% ctt)U3' Telo^itas.asqealis ftc veiocitaci Aq«z pec fo*
ramcn dccurrentis. ^E*D» '

Pars lecunda iequitur cxpriorc.

Carol. I. Oriuntur hinc omnia Pibpofitionis pracceden-
(is Cordllaua* ftihlUcueado alcitudinem AM, pco Aqux
akicudine.

^ 2, ‘ $i vas alia figura ffueric^ atque Cytindika ; auc
fornminis ligura pro circulari fiieric quadraca, triaagu*
Jaris, vel quaiilcunque ; auc ipfum foramen non fit in
medio fundo fitum, vel'etiam in latere vafis fa(ftum;
iidcmerit Motus.Cacart<9x^ fcit&ci acqualis Motui Pdf-
macis aquei lub foramine altiiudinc A cujus ve-
locitas par Ac velocitati Aqirx eiHuentis. Nam eadem
Aqux moles, cum eadetn velocicace atque in priori Hy«
pctheft,.ruTi per ipfum fdramcn, tutn pec finguias Ca-*

; taradse fediones traLufibit.' ■ *

' Si vafis Diameter permagnam rationem obtineat ad
Diametrum foraminis, negligi poterk altitude A D, dc
vafis .ipfuts akrrudo. pro altitudinc Cylindri, vcl Prif-
. matis aquei, ufurpariai. .f-'

Hadenus cafum ilium particularem, quo Aqua, Gra-
Vitatis vi, ex i^afe deftuit, leorfim conlideravimus. Id
eo fecimiis lubentrius, turn ^ quod ilium fere fplum adhi>
. bere foleant Mathematici, quoties agitur de Fluidorum
impetuy turn quod Gurva: Hyperbolioeiupra exporuam
; prpprietacemp,qua Cataradam Aqux defeendentis for'

mat,

( 7f1 )

mac, non indignam ccnfeamus contcmplationc Gcome-
cxarum Aiioqui pocuilTet ifte caHis nullo negocio de-
duci ex Thcoremarrc general!, quod proximo loco pro-
penemus.

Theorem A Ilf.

Fig, rr. Aqua fiuente per Canalem plenum qucn>
cunque ABC D iecundum iineam E F, cui-fic perpendi-
culare utrumque Canalis ofificium AS Sc C D, Motus
Aqux verfus Orificium C ,Q, five Motus impedimenti,
quod in ipfo orificio oppofiuim fiflat Motum tocius A-
qux, xqualis eft Morui Prifmacis aquei fub qualibec
6edtionc Canalis C H Sa linea dirediionis, five longicu-
dine Canalis E F, quod moveatur eadem cum Teloci-
tate, qua Aqua fluit per iftam Seeftionem: five xqualis
Mbtui molis Aqux, qux date quovis tempore effluic
ex Canali, cujulque ca Tie velociras, qua percurracur
eodem daro tempore fpatium xquale longirudini Cana*
iis. '

Caf. I. Sit linea dirediionis reifta quxvis E F,

Facile demonftracur pars prima eodem modo, quo
Theorema primum. Eft enim Fadlum ex quavis fedlio*
ne Canalis C H, h Aqux vclocitate in ea Sedionei
quantitas conftans. . > 1

Pars fecunda fequitur ex prima.

-! linea diredionis ABCDE, ex

pluribus redis /f F, .FC, C E F, ad fefe invicem in-
clinatis fit compofita, idem eric Aqux Moms. Nani
Motus Aqux in toco Canali compofito A B C D E, con*
ftcitur ex Motibus Aqux in partibus Canalis A B, E C,
C D, D E‘ additis fibi invicem Stacuimus autem A*
quam fluentem fecundum redam F, mutaw dba di*
redione in aliam, qua feratur fecundum redam »F C,
nihil ex Motu deperdere- Leges enim ilia?, qux in mo' '
tu. corporum folidorum obfervantur, quoties coruudem^

diredio

< 754 )

'xHrcdio mutatur, flu id a non fequuntur. Alioqui flui-
■dum, mutaca diredtione in aliam priori perpLndicula‘>
rem, penitus fiftcrecut, quod Experimencis neuriquam
depreh^nditur. Aqua porro ex Vafis foramine exiiiens,
, five deorfum, five lecundum Horizontis planum, five
reda furfum feratur, eandem obrince vclocitacem. Quod
•fi aliquando vei raciocinio (ubtiliori/ ve4 Experimemis
'innoteicet, aliquam Morus imminutionem ex mutaca di-
<redione proficiici, eric ejufdem ratio habenda.

, Si Curva fueric linea diredionis AB^ referctur ad
•buQc Cafutn, quippe quae ex pluribus reduiis con*
feda Goncipi queat. Fig. rq. '

Caf. 3. Fig, 15. Si divifus fuerit Canalis AB m plu-
ses ramosfiC, B D, B Ey longicudine aequales, eadem
racione invenictur AquiE Mocus, ufurpando pro linea
diredionis longicudinem A B D, compofitam ex lon-
gicudine Canalis principis A B, & longicudine cujufvis
fami B D. Perindeautem eft, five Aqua a Canali prin*
cipc verfus ramos, five a ramis fluxeiic verfus princi-
pem Canalem. Quod fi rami fuerinc inarquales, inve-
niendus eft; Mocus Aquae in fingulis ramis, adhibendo
pro linea diredionis longicudinem confedam ex longi-
tudine cujufque rami, & longicudine principis Canalis.

Nullo negotio deducitur ex Cafu fecundo.

Caf q. Fig. 1 6- Si rami aequales, in quos diftribucus
eft Canalis AB, iterum in Canalem unicum FG colli-
gantur, ad Morum Aquae inveniendum adhibenda eft
pro linea diredionis longitudo Integra A B D FG, con-
feda ex longicudine principis CanaUs A By rami cujuP
vis B D Fy & Canalis recompofiti PG. Si Rami fine in-
aequales, inveniendus eft in fingulis Aquae ‘Mocus, &
corum Motuum Summa Motui Aqux in Canali recom-
pofico addendus- Sequicur ex Cafu i, & 3.

Cora/, I. Data longicudine Canalis, & qualibec Sec-
tione ejufdem, eric Mocus Aquae in ratione velocitatis,

qua

( 755 )

qua Aqua fluit ptt iftam Se(3ionem.\

z. Data quavis Sediione, & velocitate Aquse Sedio*
nem iftam praeterfluentis, eric Mows Aqu^ uc longitu-
de Canalis.

3. Data Canalis longitudine, & velocitate Aqua's in
quavis Sedione, eric Aqus Motus in ratione iliius
bedionis.

4. Dato Mow Aquie, & aliqua Sedione, eric longi-
tude Canalis in ratione inverfa velocitatis.

5* Dato Aqux Moru, & longitudine Canalis, eric
Sedio quGEvis reciproce uc velocitas.

6. Data velocitate in qualibec Sedione, Mow
Aquee, eric ifla Sedio in ratione reciproca longitudi-
nis.

- 7. Data longitudine Canalis, & mole Aqu^ cerco

quovis tempore efiluentis, eric Aqux Motus reciproce
uc iflud tempus.

•8. Data Canalis longitudine, & tempore, eric Aqua:
Mows uc moles effluens.

9. Dato tempore, & mole Aqux effluentis, ericAqutE
Motus uc longitudo Canalis.

10 Dato Mow Aqux, & longitudine Canalis, moles
effluens eft in ratione temporis.

11. Dato Aqua: Mow, & mole effluence, eric tem-
pus uc longitudo Canalis.

12. Dato tempore, &MotuAqiur, eric moles effluens
reciproce ut longitudo Canalis.

I Si binae moles Aquae mow contrario in diredum
occurranc, & pares fine utrinque turn fupcrficies quibus
in I’e invicem impingant, turn velccitates quibus iftae
fuperficies I'n adveriiirn moveantur, fucric autem altera
moles Aqu^ guttulae uni aequalis, altera Aqua omnis
Oceano contenta, vel eciam quantitas Aquae infinita;
fieri poceft, uc una ifta guccula Aquam omnem Ocearii,
vel quantitatem Aquae infinitam, non folum iuftineat, ted

D d d d d d po ft

( 75<^ )

pofl: occurfum, eacJemac prius velo itate, ip<*ain plaj^am
eandem moveri pergar, eadem illarft in partes conua-
' rias repeilac. Quod eft miraVilc taraiJoxon in re Hy-
draulica.

14. Si certa moles Aquae, per canalem ex tubis duo-
bus cylindricis, Diametro inaequalibus, compofitum, a
tubo ampliore verfus anguftiorem fluat, & motus A-
quae neque minuatur inter fluendum neque augeatur, fj-
mul ac prima pars Aquae tubi minoris initium ingrefla
fuerir, ftatim rardius fluere incipiec, & continuaco efflu-
xu ex tubo laciorein anguUiorem, gradanm magis rcrar-
dabitur Aqua in tubo anguftiofe, uique dum tota in
eum tubum perveneric. Contrario modo res evenier,
fluente Aqua a tubo minore verfus ampliorem. Quod
eft alterum f'aradoxon in re Hydraulica. Ponitur au-
tem Aqua ubiq-ue fibi cohacrere ^

Oriuntur bina ifta Corollariaex Cafu i.

1 5 Ex C afu fecundo datur Mechodusaeftimandi Mocum
Sanguinis in qualibet Arceria.

1,6. Uatis quibufcunque Arteriis binis, acqualem San»
guinis moiein tranfmiuentibus, major eft impetus ban»
guinis in Arceria a Corde remotiore quam in propiore.
Quod eft Paradoxon notatu dignum in Oeconomia A»
nimali.

17. Ex Cafu tertio oritur alterum Paradoxon in Ge-
conomia Animali, nempe majorem efte Sanguinis mo-
turn five impetum, in Arteriis omnibus Capillaribus fi-
mul fumptis, quam in ipla Aorta. I|;em, major eft in
Capillaribus Venis, quam Arteriis.

»8 Ex Cafu quarto deducitur Methodus definic-
mocum Sanguinis in quavis Vena.

19. Ex eodem deaucicur fertium in Oeconomia Ani-
mali Paradoxon, nempe majorem efte ‘an^uinis impe-
tuni in Vena quavis, quam in Arceria eiVen e refpon-

der-:ej

t 757 )

dcftte, & proinde majorem eiTe in Vena Cava^ quam in
Aorta*

Prohlema I.

Tnvenire motum Aeris ex Pulmone effluentis*

Mc / ~ Longicudo totius du<3:us aerei, ab Ore & Na«
ribiis ad extremes ramos Trachisae.

if =■- Quantitas Aeris mediocri exfpiratione ex Pul-
mone emilTa.

f^eris copia validiilima exfpiratione expulfi.
t =: Tempus mediocris exfpirationis.

T — Tempus exTpirationis fortiffim^e.

Inde, per Theorema 3, Caf. 3, Mocus Aeris ex Pul-
mone efHuentis, in exfpiratione mediocri =

h

fortiflima

r*

Hoc eft, Motus Aeris ex Pulmone exeuntis a^qualis eft
motui molis Aeris, qu3E unica exfpiratione emittitur,
cujus ea fit velocitas, qua percurratur tempore exfpi-
rationis longitudo totius Canalis Aerei. ^ E. /.

Aeris quantitatem exfpiratione mediocri emiftam Vic
Cjariffimus, /^l^honfus Borelltis, fadio Experimento 18
circiter, vel lo unciis cubicis definic. Eft autem diver-
fa, non folum in diverfis Hominibus, fed etiam tempori-
bus diverfis, in Homine eodem. Ipfe Experimentum in
hunc modum infticui.

Veficse madefaeftae a parte inferiore pondus appende-
bam, & aptato eidem fuperius tubo vitreo Diametro
circiter unciali, naribus obturatis Aerem veficae leniter
infpirabam, per fpatium trium minuforum fecun-
dorum, pondere interim in menfa quiefeente. Poftea
Veficam cum Aere inclufo & pondere appenfo, fub A-
quam in vafe Cylindrico contentam, demergebam, no-
tata diligenter akitudine, ad quam Aqua attollebatur.

D d d d d d X Deinde

3

/

( 758 )

Deinde, Aere cx vefica expreffo, iterum candem- cum
pondere in Aquam immitcebam. Quod cum efl’et fadum,
facile invenkbatur Aquae moles, quae vafi infufa altiiudi*
nem priys notatam conficerer. Experimento decies repe-
tito, & additis fibi invicem quamicatibus fingulis inven-
tis, earum decima, five media moles Aquae vafi infufa,
reperiebatur 3 j ujiciis cubicis :^qualis. Quae moles eft
Aeris vefica contentae ;*& adjeda circiter parte duodcci*
maj feu 9 unciis cubicis, ob Aeris condenfationem a
frigore Aquae fadam, cum tempeftas fuerit hyemalis,
efficiuntur 38 unciae cubicac. I raeterca addendum eft
tantillum, turn propter Aquae preflionem in veficam,
turn ob Vaporem qui cum halitu emittitur in humorem
coadum ; quod fiat necefle eft ex frigore Aquae, &ye-
fic^ madidae contadu. AEftimavi igitur Aeris copiam,
leni exfpiratione emiftam tempore trium niinutorum fe-
cundorum, numero rotundo 40 unciarum cubicarum. *

In exfpiratione validifTima exfpirabam uncias cubicas
izf, tempore minuti fecundi unius.

Hujufmodi autem exfpiratione, cum vehementi Pul-
monis contentione ad ftrangulatum fere continuata,
220 uncias cubicas ex Pedore eraictebam. Unde pa-
ter, ut id obiter moneam, multo plus Aeris in Pedore
ftjperefife, quam unica exfpiratione mediocri emitti.

6'i ergo ponatur 1-= ^ pedes

^ = 40 unciae cubicae
^=125 unciae cubic;S'

^~3"

Aeris Gravitas Specifica ad Gravicatem Aquae, ut i
ad 1 00c.

Pes Aquae cubicUS = 1000 unc. Avoir

Erit Motus mediocris Aeris Pulmone cxeuncis acqua-
lis motui pondcris Scrupulorum 4 & Granorum 9,
quod percurtat unciam^ unais minuto fecund© 4 . vcl

motui .

( 759 )

motui ponderis Gram i f, quod eodem tempore confi*
ciac longitudinera $ pedum & 7 unciarum. Q,use eft
velodtas Aeris per Laryngem effluentis, pofita Laryn-
gis Sedione = unci^e quadratce.

Motus maximus Aeris Pedore expulii xquatur mo-
tui ponderis unci:^ i f circiter, percurrentis unciam
nam minuto (ecundo ; five motui ponderis grani r
currentis eodem tempore 52, pedes. Qjjse eft veioci-
tas Aeris in fortiftima exfpiratione per Laryngem erum-
pentis,

Corel, r. Data Aeris copia & iongitudine Canalis
aerei, motus Aeris eft in ratione inveria temporis exfpi-
randi.

2,. Data mole Aeris & tempore, erit motus in ra^
tione direda longitudinis.

3. Data iongitudine & tempore, motus eft ut Ac-
ris copia.

4. Dato motu & Aeris copia, erit longitudo in ra-
tione direda temporis.

5. Dato motu & Iongitudine, erit Aeris moles di-
rede uc tempus.

6. Dato motu.& tempore, erit Aeris moles recipro-
ce ut longitudo Canalis Aerei.

7. Motus Aeris eft in ratione compofita ex ratione
quadruplicata Diamerri cujufvis homologae ipftus Ani-
malis, & ratione inverfa temporis exfpirandi ; vel in ra-
tione compofita ex ratione ponderis totius Animalis,
ratione cjuCiem ponderis fubcriplicata, & ratione tem-
poris reciproca.

Nam pondus Animalis, Diametri cujufvis homologx
Cubus moles Aeris expulfi func in eadem ratione. Po-
nitur autem Corpora Animalium Machinas elTe fimili-
ter fadas.

Scholium. Longitudinem hie ufurparam, vel ipfam
efle :3ncipjies Canalis aerei longitudinem, ft R-ami omnes

Tra-

( '76q )

Trachsese longitudine se<iu4les potiancut ; vel mediam
inter longicudinei diverfas, fi Rami fmt inaequales.

Pr^hlema II.

Determinare impetum, five impreflTionem quam exci-
pit interna Pulmonum fupcrficies ab Acre exfpirando.

Cum a(5tioni sequaUs & contraria fit readlio 5 nc-
^ cefl'e eft, ut, quanto motu urgeturab'inrerna Pulmonum
fupsjficie Aer exfpirandus, tanto viciftim ab Acre re-
pellatur fuperricies 1 ulmonum.

Unde, per Problema fupetius, impetus diftus in cx-

IJ

t

fortiftima — O^E.I.

Hinc pofitis iifdem qur in fuperiore ponuntur, im-
petus mediocris Aeris in Pulmones aquales tft n^orui
ponderis drachmae circiter I 7, quod minuti fecundi pa-
tio percurrat unciam unam : vel motui ponderis ly H-
brarum, co ficientis eodem tempore uhciac. qu.reft
velocitas Aeris in contaflu fupcrf.ciei Pulmorjjs mt rrfc.
Ponimus autem cum Viro Dotftiflimo "^acoho KJlio iu-
perficieni Pulmonis internam 21900 circiter uncii.vqua-
dratis aequalem.

Impetus vero xnaximus Aeris in Pulmones arquatur
motui ponderis unciae circiter i ~ moti unciam unam
minuto fecunda; vel motui ponderis 19 librarum, quod
partem 7^ unciae conficiat eodem tempore. Quae eft
Aeris velocitas ad fuperficiem PuJmonis in exfpiracione
vehememi.

Corol I. Sequuntuc ex hac Propofitione Corollaria
pra-’cedenti fubjunda.

2. Impetus mediocris incumbens in partem fuperfi-
ciei Pulmonis, quae fit ipfi Laryngis Sedioni sequalis, eft

imotus

fpiratione mediocri =;

f( 7<5i )

i- '»i<? p^io’.?r!S gnni, con.icientis unda: rpatiuin mi-
r\ ' ; ''uiiuo vel motus grani i ~ quod eodem tem-
ple .currac uncix panem Irrpecus aucem maxi-
niu ill pnrem (upcrficiCTi eft motus ponderis — partiS-
grani quod unciam uuam; vci m.otus ponderis grani
1 ‘ quod 777 uneix fingulis minutis (ecundis confidst.

5. impetus Aeris in mediocri exTpiratione in Fulmo-
ncs imprelJus, xquarur motui Columns aquex percur-
rentis unciam unam minuto fecundo, cujus Columnse
ba6s eft ipfa Pulmonum fiiperficies interna altitude au-
tern eft rhi uncis. Eftqiie Columns akitudo pars ~ un-
dse, in exfpiratione omnium vehementiffima.

4, impetus incumbens in fuperficiem parem circalo
madmo Globuli Sanguinei, in leni exfpiratione, eft pars
ponderis Gbbuli Sanguinei ; in exfpiratione vehemenii
\ ejuidem ponderi?, moti unciam unam rninuco fecundo.
Qua autem ratione Diametros Globulorum Sanguinis
dimenfus ftm cum ufui efte queac ad aliorum Objedo-
rum minimorum magnicudines dePiniendas, Jibec obiter
exponere- Capillum tenuem, & fatis longum, aciculss
piuries circumvoJvi, ut omnes convolutiones fefe invi-
cem accurate contingerent, quod admotum fubinde Mi-
crofeopium luculenter oftcndebac. Deinde cum inter-
capedinem inter exrremas utrinque circumvolutiones Cir^
cino cepiftem, eandem ^calse, quam vocant, Diagonals
applicabam, Tpatiutnque in Scala repertnm per convolu-
tionum numerum dividcbam Unde invenca eft unius
convolutionis latitude, five ipfa Capilli Diameter. Po-
ftea Capillum eundem, in Segmenca minutula divifum,
piano Microfcopii, cui ' angumis parum ita erac ilHtum
ut Globuli conlpiccrentur diftin<fti, fupennfpergcbam.
Ea cum Microicopio contuerer, reperiebam aliquibus in
locis C apilft Segmenta ii a commode ditpoftca. ut nume*
rare iiceret, quot Gicjbuli Diamecro Segmenti oppone-
rentur. Eranc autem Segmenta Diametro inaequalia.

C z6i )

quod CapilluS tcnuior verlus extremum fuerir, quatn
propius a Radice, ac'do 'iit jam 7, vrl 8, jam ii, i ^vc
Globuli rranfverfae SeOboni Capjll- r 'lpenderenr^ Ucro-
quc autem Expcrimento (sepia ato, ajfiimavi tan-
dem mediam Capilii Diameu'un> j 1 c ~ uncia:, Dia-
metrum Globuli ^^anguinei parte tic.-ima-Uiametn Ca-
pilii, five parte ~ unci«

5. Impetus, quern patitur inrcrr !'uImonum fuperfi.
cies ab i^erc exfpirando, m nor ci‘ iOtu lemliimi loris
c Csdo decidentis.

Scholium. NeglccJa e(l in folucicnc Problematum
d-uorum prarcedentium impcdimcnti confidt ratio, qu d
/^eri ex Pulmone egredienti objkuur cx affndlu lareium
ArreriteTrachxsc, cjufque ramorum 3 cum id perparvum
iit, nequeiillo experimtnro fatis accurate aftiman pode
Videarur. Ncc fuimus admodum follici i dc rationibus
r.umerorum cxquifire fervandis, cum id unum nobis pro-
ponium tueric, uc mcchodum exponeremus azRimandi,
aliquanro certius quam vidctur antehac fadum, vires
xas, quibus agit Aer inter cxfpirandum in vaia langui-
nea fupernxicm Pulmonis internarn perrcpcanria. Unde
dignolci porefl-, utrum pares fine bar vires effedis iflis
producendi', qusciirdcm a Dodilfimis qujbufdam Scrip-
torihus Medicis tribuuntur. Quod liberum eQo Ledoris
Scieiitia Mecbanica &Anatomica inftrud:i Judicium.

Trohlema 1 1 1.

Dcunire impetum Sanguinis in Vena C^ava prope
dextram Auriculam Cordis ; five motum Sanguinis per
omnes Artcrias & Venas fluentis, prtster i ulmona*
res.

’Sit q — Quancitas vSanguinis una Cordis Syftolc in Aor-
tam projedi.

I — Longiiudo media dudus integri ArteriO'Venofi,
tacioiie habita ramouim longiorum& breviorum

t ~

t = Tcmporis fpatium inter binos PulCus intercept
turn.

Inde, per Theorema 3. CaC 4. impetus quacfitus

— li

■ •

t

Hoc eft. Impetus Sanguinis in Vena Cava aiquatur
motui molis Sanguinex, qux una Syftole in Aortam pro-
jicitur, cujus ea fit velocitas, qua percurri cjueat Inte-
gra Arteriarum & Venarum longitude, temporis fpa-
tio inter binos Pulfus intercepto. ^ E. /.

Si in Corpore Humano ponamur
^ ~ X uneix Avoird*

I ~ 6 pedes

4

Erit impetus Sanguinis in Vena Cava xqualis mo-
tui ponderis ix librarum, quod uneix unius longitu-
dinem conficiat fingulis minutis fecundis ; feu motui
ponderis x librarum, quod pari temporis fpatio percur-
rat pedem f. Qux eft fere Sanguinis velocitas in Ca-
va fluentis. Ponimus autem, ex dimenfione Viri Doefti-
ftimi fupra diefti, Cavx Sedionem dodrantem efle un-
eix quadratx.

Corel, Oriuntur ex hoc Problemate mutatis mutandis
omnia Problematis primi Corollaria.

ProhUma IV.

Determinare motum abfolutum Sanguinis in Vena
Cava; five motum Sanguinis, per omnes ^rcerias &
Venas fluentis rd xter Pulmonales, fublata Vaforum
reftftentia.

Sit velocitas Sanguinis Naturalis, ad earn velocitatem
qua Sanguis flueret, dempta omni refiftentia, ut 1 ad x,
Cumque per CoroL fuperioris Problematis, & Corol r„

Eeceee PtohL

«

Pi oW f/ Mctus 'm U- m ratibne* ■ vclocifatis,

ciit . in4e mot us quxliCu^ t=r ^ E, I. , , .

Quod fi propottio per Exp-rimcntum a Viro CIoj-
riffimo fijpra iaudaro inliuutuni inventa, ut verte pro-
pinqiia, admictatiir, erit a; = i . 5.

Unde, pofitis ii(dem qute in fuperiore ponuntur,
morus abrolutus Sanguinis in Vena Cava tcquatur mo-
tui pcnderis 30 librarum, quod minuio iecundo lon-
gitudinem uncialem percurrat ; five motui ponderis z
librarum percurrentis eodem tempore pedem i Qua
fere velocitate Sanguis, omni refiftemia liber, per Ca-
vam deferretur.

Prohlema V.

Motumi Sanguinis- invenire in Vena Pulmonali pro*
pe finiftram Cordis Auriculam ; five motum totius
Sanguinis per Pulmonem fluentis.

Prseter notulas in Probl. 3. ufurpatas, fit AzrzCanalis
ArteriO'Venofi Pulmortici media longitude.

Unde, per Theor. 3. O/. q. invenitur motus quiEfi

Hoc'ed:, motus Sanguinis per Pulmonem fluentis se-
qualis eft motui molis Sanguineje, quae una Syftole in
Arteriam Pulmonalem projicicur, obcinentis earn veloci-
tatem, . qua percurratur longitude Arteriarum ac Ve-
naruni Pulmonalium, tempore inter duos Fullus inter-
cepto. Q, E. /.

Si ponatur in Corpore Humane A =: i ^ pes.

Erit motus Sanguinis in Pulmcne sequalis motui pon-
deris 3' librarum, percurrentis uneiale lj3atium minute
fecundo.

Prohhmd

( 7^f )

■ FroUema VL

Definite momentum Sanguinis abrolutum in Vena
Pulmonali.

Eodem argumento, quod in Frohl. 4. ufurpatum eft,
invenitur motus quarfitus = a . j x ^ E, /.

t

Pofitis veto iifdem quas fupra ponunrur, motus ab-
fblutus Sanguinis Pulmonem prasterfluentis xquacur mo-
tui ponderis 7 7 librarum, quod fingulis minuds fecundis
uncix unius fpadum percurrac.

Scholium. Experimento Keilimo definita eft proper-
tio, quam obtinet Sanguinis per Aortam ejurque -ramos
fluencis velocitas namralis, ad earn velocitatem qua
Sanguis per eofdem flueret, fublata refiftentia Arteria-
rum & Sanguinis prxeedenti?. Earn nos propoftionem
ad Sanguinem per Arteriam Pulmonalem fluentem tran-
ftulimus. Quia vel fublata vel imminuta fecund um
quamvis rationem refiftentia, qu2s Sanguini per utram-
que Arteriam fiuenti objicitur, neceflario Sanguis piri*
ter acceleratur in urraque Arteria. Id enim nifi fiat,
bini Cordis Ventriculi aut eodem tempore non contra*
hentur, aut eandem Sanguinis quantitatem non ejicienr.
Quorum utrumvis, abfque fumma totius Machinae per*
turbatione & diferimine, fieri omnino non poteft.

Ccrol. Ad tria Problemaca praecedenda.

Sequuntur hinc Corollaria Problemati quinto fab-
junefta, mutatis mutandis.

Scholium ad quatuor Problemata fuperiora.

Notandum Sanguinis velocitatem, turn per Pulmo'.
nem, turn per reliquum Corpus fluentis, cum reipfa se-
quabilis non fit, hie tamen talem fingi, uc motus San-
guinis medius inveniatur.

E e e e 6 e r Scholium

< 766 )

Stholmm gentrde.

Si cui numeri minus accuraci videantur, qui rparfim
Chara(3eribus fpeciofis apponuntur, poterit illc facili o-
pera, inventis per experimenta numeris qui propius ad
verum accedanr, mocuum exempla fupra pofica, vel Pro-
pofitionum ipfarum vel Corollariorum ope, corrigere.
Ignofcat aucem nobis Ledor ingenuus, fi per viam ince-
dentibus nullis prsecedentium veftigiis triram, adeoquc
Erroribus in omnes partes opportunam, Human! all-
quid forte acciderit.

Damus h*nc venum^ p^timufqut vkiffim.

IV. An Account of the Shilling of three Oaks inta.
the Groundy at Manington in the County 0/ Nor-
folk, Communicated by Peter Le Neve,
Norroy ^ng at Arms^ and. Fellow Roy-
al Society,

ON Taefday July the 2,3/i of the laft Year, 1717, iir
the Grounds, and near the Seat of Sir Charier
FottSf Baronet, in the County of Morfolk, and Parilh
of Man'mgtony (which lies about mid- way between the
Market . Towns of Holt zwd Ayljham, and about (even
Miles from theCoaft nczr Cromer daytime, to

the great allonifliment of thole that were prefent ; firfl:^
one fingle Oak, WMch the Roots and Ground about it,
was feen to fubfide and fink into the Earth, and not
long after, at about 40 Yards diftance, two other Oaks
that were contiguous, funk after the fame manner, into
a much larger Pit ; being about 3 3 Foot Diameter,
whereas the former is not fully 18. Theft, as they
funk, fell a-crofs, fo that obftruding each other, only

th«

( ?(>7 )

the Roots of one^of them reaches the Bottom> whereas?
the firft {lands Perpendicular.

When the firft Tree funk, it was obferved, that the
Water boyfd up in the Hole; but upon the finking of
the greater Pit, that Water drain’d off into it, from the
former, which now continues dry. The depth thereof
to the firm Bottom is nine Foot three Inches ; and the
Tree that Bands upright in it, is 5 Foot 8 Inches in
Girt, and its Trunk about 18 Foot long, half of which
is now within the Pit. In the Bottom of the greater
Pit, there is a Pool of Water about 8 Foot Diameter ;
whofe Surface is ii Foot 3 Inches below the Ground,
and the Trees that are in this Pir, are much of the (ame
length with the other, but fomevvhat fmaller, the one
being in Girt 3 Foot j Inches, the other but two Foot
9 Inches

The Soil on which thefe Trees grew, is Gravelly;
bat the Bottom is a Quick fand over a Clay, upon
which there are Springs, which feed large Ponds ad-
joyning ioSkCharUs Potts’s Houle, at about a quarter of
a Mile from thefe Holes. ,

The Nature of the Soilfeems to afford us a reafonable
conjedure at the Caufe of this odd accident, which
Tome perhaps may be apt to reckon as a Prodigy. The
Springs running over the Clay at the bottom of a
Bed of very minute Sand, fuch as your Quickfands
ufually are, may reafonably be fuppofed in many Ages
to have walht away the Sand, and to have thereby ex-
cavated a kind of Subterraneous Lake, over which
thefe Trees grew: And the force of the Winds, on their
Leaves and Branches, agitating their Roots, may well
have loofened the Sand under them, and occafioned it
to fall in, more frequently than elfewhere ; whereby in
length of time the thin Bed of Gravel being only lefc>
it might become unable to fupport its own w'eight and

that

(.76%)

tint of the Trees it bore. That this is not a bare con-
jediure, may appear from the boyling up of the Water
at firll: in the lefler Hole, and its ftanding in the bigger
and lower. And if it fiiail be found that it was a
very windy day whereon this accident happen’d, it
Will much add to the probability of this Solution I

An accident not unlike this lately happened in 1
FUet’flreet^ London^ by the defcd: of the arched Roof of /

a very deep Common-Sewer. The Earth gradually
falling into the Sew-er, was carried away by it, fo as J
not to obllrud the Water 3 and the continual tremour
of the Ground, occafioned by the conftant palTing of ^
Carts and Coaches, by degrees (hook down the rarth,
fo as CO leave a very great C vern, the Top wherqof
at length grew fo very thin, that one day a weighty
Cart having juft paft it, a great fpace of the favemenc ^
funk in, in the middle of the Street, not without hazard
to a Coach then driving by. ]

V. A ^eBification of the Motions of the five Satellites ^
of Saturn 5 with Jome accurate ObferVations of
them, made and Communicated by the *^everend
James Pound. R.S. Soc.

IT is now above thirty Years fince that great Aftro-
nomer Mr.CaJJini communicated to the World his
difeovery of two new Satellites of Saturn, W’hich made
their number Five ; and the account he gave of them to
the Ropl Society, (of which he was a Member) is to be
4een in N°. 187, of thefe Tranfadions. Much about
the fame time the excellent M. ChrifHan Huygens'ot !Zu-
iichm, made the Society a prefent of the Glaftes of a

XelefcopG

( 7h )

Telefcope of 115 Foot length, with the Apparatus for
ufingthem without a Tube; by help whereof we might
have fatisfied our fdves of the reality of rhefe Difco- .
veries. But thofe here that firft tried to make ufe of
this Glafs, finding, for want of Pradice, feme difficul-
ties in the Management thereof, were the cccafion of its
being laid afide for fome time. Afterwards it was dc- -
figned for making perpendicular Obfervations of the fixt
Stars paffing by our Zenith, to try if the Parallax of
the Earths annual Orb might not be made fenfible in
fo great a Radius, according to what Dr. Hook had
long fince propofed : but in this we mifearried alfo, for
want of a place of fufficient height and firmnefs, where-
on to fix the Objedt Glafs, fo that it lay by negleded
for many Years.

In the mean time we could not but remark a great re-
(erve in x.\\q French Aftronomers, in relation to thefe Sa-
tellites, of which they have given us in their Yearly
Memoirs no Obfervations till very lately, nor have they
feetned willing to ihew them in their GlafTes to fuch as
fequefied it: fo that rdimight poffibly occafion in fome
Perfons a fufpicionof the reality of this Difeovery : And
the Reverend Mr. William Derham having borrowed of
the ‘■-ociety their long Glafs, could not thereby aflure -
himfelf that the fmall Stars he fomecimes found about
Saturn, were really his Satellites, their ficuatipn not a-
greeing with their places derived from the Tables of
their Motions exhibited in N°. 187. of fhil, Tranfa3.
befides that he wanted a fufficient height to raife the Ob-
jedf Glafs, fo as to v {c:\st Saturn to advantage, above the
Vapour- of the Horizon But Memoirs for £714,
publifhed bur about a Vtar fince M.CaJieni, the worthy
SuccelTor ot his great Father, has given us fomeCbler-
vations which clear up the i oinc, and by (licwing the er-
rors of thole iirit Tables, has enabled us to be affured,

that

( 770 ) !

that we have feen the whole SatdUtiam of Saturn out-
felves.

'The Subftaiice of thefe Obfervations is as follows.

Anno 1714 Matt 6. St N about Mid-nighc, Saturn
being tlienStafionary in ’t? 4°; zy', the Fifth and ouccrmoft
Satellite was in its fuperiour Conjunift on with the
Planet, and at the fame time, the harth was nearly in
the Plain of this Satcilic’s Orbit, lo that it appeared to
pals very near the Center of Saturn : From hence and
from fome other preceeding Obfervations. Mr CaJJini
Concludes that the Nodes of this batellit s Orb are in
4 degrees of ’f? and X, and that its Inclination to the
Ecliptick is not much more than half that of the other
Satellites. Fience it fliould follow that the Elliples ic
defcribes by its apparent motion about Saturn, when in '
It and t are much flatter and nearer to his body, than
thofe of the other four, which he allows to move* in
the plain of the and to have their Node^ in it*” |
of and X, with an Inclination to the Ecliptick of
31 degrees To confirm this dificovery, he produces a-
nother Obfervation of his Fathers, near Thirty Years
before, viz. that. Anno i68y, Maii St. fT. about
Noon, the fame Satellite was obferved in fuperiour con-
junction with Saturn, with lefs than one Diameter of the
Ring North Latitude, Saturn being then^in np 11° 48'.

So that the Satellite wanted but 7°. ii' of compleating
134 Revolutions, in the Interval of time between them. i,

From thefe Data it was eafy to fettle the Theory •

of this Satellite. i

As to the Fourth or the Hugenian Satellite; in the •
Memoirs for but juft now come to hand, we find

a very curious Obfervation of it, and the firft of its kindi
viz- i\\2iZ Mart. z$°.S. N. about F. M, this fourth Sa-
tellite, then in Afogeo, did immerge behind the Body of

Saturn

i

( 771 )

tu'n. Widvthts Fmendation the place of this Satellfte
may for the fiirurc be computed witli a fufudent exat^-
nefs.

The Third Satellite by an original miftake in the
Letters in N®, 187, is ail wrong* its dayly Morion
being there printed 2\ 18°. 41'. ^o" inflead of z'.

41'. 50"; as may be perceived by the Period thereof
being determined, in the_ aforefaid PArmoirs of 1714. to
be 4''. \z’’* 25'. iz". that is, that it makes 400 Revolu-
tions in 1807 days. This Satellite was obferved by
Mr.CafJlnr, Apll 4”. St. N. lok P.M. to have newly pad
its inferior conjundion with Saturn, and a perpendicu-
lar from it fell on the extremity of the weftern Anfe^ fo
that at about 5''. P. M. it was with the center of the Pla-
net then in ’tP. j”. 23'. and confequently in X 5°. 23'. But
ineunte anno Gregoriano 1686, Epochs thereof was
n?9° 39'. So that from the Noon of the lad of De-
cember 1685’, to April 4°. 6'’, 18'. anno 1714, that is, in
10320 Days 6'’. 18', there have been made 22847 Re-
volutions of this Satellite to the Equinodial; from
which Data, the Tables of its Motion are readily deriva-
ble

The Radix of the penintime or fecond Satellite, ac-
cording to theaforefaid Letter, ineunte anno Greg. i685.
was in 9°. I o'. But by the Oblervarions of Mr* Cajftni
made the Nights before and after, this Satellite was in
its iuperior COnjundion anno 1714 April 1 1' 7. St.
that is, in 5°. 21', where Saturn then was: So that
April 22''. 12', an entire Number of Revolutions were
performed fince the Epochs of 1686, that is, in 10320
Days zz'". I2 : which Number can be no other than 371,
according to the Period thereof given Memoire,

viz. 2^ 17^41' 22".

Ladly the innermod or fird Satellite, at the fame
time, vizt 1714, April 30'. iSr. N. was in jcs

Ffffff feiiuur

( 771 )

fcriour conjun(3ion fr oxime , and confequcntly in
X But th^Efoche thereof for 1686, is >y 24®. 50!.

which place the Satellite had paft 40^'. 31' at the time
of the Obfervation. Tliis Arcbit movesin 5*. 6': Where-
fore from the time of the Epoche to ^^pril 4*^. 16". 24^*
1*714, or in. 10320 Days 16'’. 24'. the Satellite has per-
formed 5467 Revolutions, its Period being determined
to be I Day, 2 1 hours, 1 8'. 27", in this Memoir e.

Having by the help of thefe. late Obfervations cori*
re<9^ed the motions of the Satellites, which it was not
pofTible for their firft Difcoverer. to fettle truly, in the
fhort interval before 1687 ; and having fixed their Epo-
ches for the prefent *Year. we were enabled to know
where to exped them with more certainty, and to di-,
flinguifh them one from another, and from the fmall
fixt Stars appearing with them- And the Reverend
Mr. James Pounds (whofe indefatigable induftry is no
way inferiour to his incomparable Skill in Aftronomical
matters/, having, by means of his Steeple of Wan(ted,
provided a Gnomon hig\i enough for the purpofe, and
having fitted a very commodious Apparatus for ufmg
the Society’s aforefaid long Telefcope, foon dilcovered,
by it all thefe five*, Satellites ; and, lately communicated
to them,. the following very curious Obiervations.

1718. April 21*'. id'’. 40'. The. third and, fourth Sate!*
lies of Saturn were in Apog£o^2. little, pafi their Conjundtioa
Vfiih’Saturn: A perpendicular from the fipurth to the
Tranfverfe Axis of the Ring for Lioe of the Anf<e)
fell a little without the Eallern Anfa 3 and a Line
through the fourth and third touched the Eaftern ,Limb.
of. Sat urn. Fig. 1 7.

The firft; was Northward of the Line of the Anf4.
fand therefore in the Apogaon Semicircle allo> diflanc.
from the faid Line about as far as the end of the Con-
jugate Axis . of the Ring was from the Center of 'hyviz,^

nearly

( 771 )

nearly \ of Saturns Semidiameter h and it was about a
Semiciia meter of the Ring from the Weftern Arifa.

The fecond was a very little Southward of the Line,
of the (and therefore in the Ptrig^cn Sen>kLc!e),
above a Semidiameter of the Ring ("or about the ‘''emi-
diameter of the Ring the Semidiam. of from, the

Weftern /infa. And the Third, Firfl and Second were
in a flrait Line.

At lo^ 50'. A Perpendicular from the to the Line,
of the Ar*[<e fell almofl on the middle of the bright part,
ofthe Eafterii but fomewhat nearer the Center,

than the faid middle.

Af>ril 5'. The four innermofl: Sarellits were,

all Eaffward of T?. The zd and in the Afog^on,
and the ift and in the Ferig<zon Scm\c\xc\Q. A Line,
through the zd and ^th touched the South Ea[l Limb
of Tj. A Line palTing through the T,d and the end o£
the Conjugate Axis of the Ring, was parallel to the
Line of the Anf£.

At ii'*. ro'. A Perpendicular from the firft to the Line
ofthe Anfa fell on the Eaftern Extremity of the Ring.
Fig. r8.

Thefe Dillances and DiretTions were taken only by
Eftimation, and not by any adual Meafuremenc

The fifth (or outermoft) Satellite being at this time .■
near itsgreateft Elongation Eafi; ward, among feveral ve^
ry fmail Telelcopick Stars, he could not determine its >
Pofition. But by obferving the Motion of this fbme o-
ther Nights, before, he was now fully farisfied, from the.
Motions rediified as above, that there are five Satellits
of Saturn, as Mr. Cajfini had long fince afTerted.

In the bright part of each Anfa was a darkifh Ellipfe
nearer to the.out fide than the in-fide of the Ring, as i£y
it w'as compofed oE^two Rings near to one another. ■

©n

'( 774 ) •

Oti i^e Bd'Jy of r? ,1yende the Ring on the fide,
there appear^cl^on the f/tfr/Mfide a Zone not fo far frcm
the Ccncer as the Ring, and not much unlike the fmall-
efl: of Jupiter's Belts. Thefe appearances were firll taken
notice of by as may be fsen in Phil. Trarf. -1

N°. Iz8 pag 690 Fide Fir. ir. t

We fhall in our next give the Publick Tables of thefe
Motions, corredcd from the atcrefaid Obfervations , j
ioftead of thofe in N®. 187. 13ut it is not to be expc(5t-
cd that thefe Satellites, exceedingly minute in them-
felves, and fb faintly illuminated, flimild appear when
the Air is but ordinarily Serene, they requiring not only
the Medium to be fummo modo defecate and limpid but
withal in perfedl Darknefs. For which reafons it may ,

well be underftood why the Gentlemen of the Varifian 1

Obfervatory may have fometimes made a difficulty to i
undertake to flicw them upon demand. |

F 1 N I S.

Printed for W. and J. Innys, Printers to the Ro^al
Society, at the Princes-Arms in St. Pauls Church- Yard,
Ludgate-flreet, 1718.

( 775 ) Number 55 <5.

PHILOSOPHICAL

TRANSACTIONS,

For the Months of and Jme^ 1718.

The CONTENTS.

I. TahuU Motuum quin^ue Satellitum Saturni, ad
fidem nuperarum OhferVat'mum cornB'ie, Cosloque
conformes reddiu,

II. T^he refl of the Treatlfe of that Learned Anti-
quary iDr.John Tabor 0/^ Lewes (whereof the
Firjl Tart h puhltjh’ d in N° 351. of thefe Tranf^
actions ) concerning the Site of the ancient City of
Anderida, and other ^(emains of Antiquity in the
County of Suflex.

HI. TraSlatus de Curvarum ConflruBione ^ Men-
fura ; uhi plurimde feries Curyarum Infinitee Vel
reSlis menfurantur vel ad fimpliciores Cary as redu->
cuntur. Autore Colin Maclaurin, in Collegia
noyo Abredonenii Mathefeos Trofeffore.

i'V* Tpmarky on a Fragment of an old Roman In-
jeription lately found in the Morth of England,
and tranferibed by the Curious and Learned

Dr, James Jurin, M, D. and Reg. ^oc. S.

Gggggg iTaMa

T —T*'

( rr<5 )

Li TahuU Motmm quinque Satellitum Saturni ad
fidem nuperarnm. Ohferyatmum coneSidy Caloque
conformes reddiu,

e'^frca finem Aiirti 1686. D.Jo, Dom. Ca^nl, Reg.
Soc. Sodalis, & in Aftronomicisnemini fecund us>
cum Societate noftri inventa fua de motibus
quinque Satellitum Saturni communicavit, Epochafque
fingulorum ad annum ineuntem i685. eorumque motus
diuenos in Epiftola N°i87. harum Tranfa^. edita ex-
hibuit.* E quibus dads motuum Tabulas concinnavimus,
dida?que EpiRolae fubjundas una edidimus. Cum veto
deinde per triginta fere annos nullas omnino Oferva-
tiones eorum tradiderint, qui foli poteranr, ARronomi
Galll ; cumque aliunde, ob intervallum temporis nimis
breve, non nifi laxe periodos Satellitum, praefertim in-
reriorum, definite potuerit praeclariflimus Inventor, non
prius dicSarum.Tabularum defedus corrigere datum eR,
qqam in nu peris Adis Academise Regise Pariftenjis Phy-
ficis & Mathematicis, obfervata ea, quae fub finem prse-
c^dentis Tranfa6}, N° 355., protulimus, prodiere.

Horum veto ope fada aliquali Motuum caftigatione,
rum demum Telefcopio Hugtniano omne Saturni Satelli-
tium ipfi agnovimus ; adhibitifque accuratis Rev. D.Jac*
obfervationibus, Tabulas fubfequentes caelo fatis
CQnfonas obtinuimus. Addendo fc mocui annuo Imerio-
ris, ^ 9 ' ; Fenintimi vero 3°. retentis Epochis D.

•Caffmi ad Annumi686. Augendo etiam motum annuum
Exiimi 9 min. fublatis vero 1 6 grad, ab Efocha, quae in
Epiftola dida 187. perperam feribitur x 16°. 19', pro
X p®. 16“. Hugenianum 6' annuatim tardiorem invemmus.
Tettii 2L\Mtm Tabellas, ob motum diurnum falsd in tpi-
ftpla ilia rraditum, de^integro recud, ere necefie habuimus,

reijenta^ialtem. Tduh

( f?7 )

Tabula Alediorum Adotuum htimi SateUitis

Saturni a Caffmo deteBi Anno 1^86.

Aiinis

Epoch iS

Mot. Med.

5

A4o#,

Mot.Med

Motus

Chrifii

d

Sti. 0 ,

I

Medi.

ineunt

S 0 1

g 0 •

s ® '

0 «

?■

0

§

1681

8 48

I

4 4 4?

1

6 10 42

1

0 7'S7

31

4

■ -'6

1686

^ 4

2

8 9 2J

2

0 21 24

2

0 ly 55

32

4

14

1701

n? 6 54

;

0 14 8

3

'726

3

0 23 50

33

4

22

1714

9 5-7

4

lo 29 5;

4

I 12 47

4

051 47

34

4

30

17IJ

14 59'

y

3 4 16

5

7 23 29

J

0 59 44I

3S

4

38

1716

31 19 21

6

7 8 J9

6

2 411

6

047 40

36

JL

46

1717

^ 4 47

7

II 15 42

7

8 14 55

7

OSS 37

37

4

S4

1718

nX 9 JO

8

9 29 6

8

3S

8

I 3 34

38

s

2

1719

y? 14 I?

5

2 ; 49

9

9 6 17

9

I II 31

39

s

10

V 18

10

6 8^2

10

3 S9

xo

1 19 28

40

r

18

Menf

Met, Med.

II

10 ij ij

1 1

9 27 41

II

I 27 24

41

s

26

Anni .

12

8 28 40

12

4 8 22

12

I 3521

42

s

34

I?

I 3 2J

10 19 4

'3

I 43 18

43

s

42

Jan.

000

14

S 8 5

14

429 46

14

I 51 15

44

s

Febr.

f I 58

IS

9 12 48

I)'

11 10 28

IS

I f9n

4S

s

S8

Mat.

; I 10

16

7 28 15

16

5 21 10

16

278

46

6

S

April

8 248

17

025-6

17

0 1 52

17

2 15 s

47

6

13

Mail

62544

18

4 7?9

18

6 12 54

i8

2 23 I

48

6

21

Junti

II 2^ 22

19

81221

19

0 25 16

19

2 30 58

49

6

29

Julii

xo 16 19

20

6 27 46

20

7 3 57

20

2 38 55

SO

6

37

Aug.

; '7 51

40

I 25 52

21

I 14 39

21

2 46 52

S»

6

4S

Sept.,

8 19 55

60

8 25 19

22

725 21

22

^ S4 49

S2

6

S3

ohcb

7 io 51

80

; 21 5

^3

263

23

3 245

S3

7

I

Nov.

012 9

100

10 18 yi

24

8 16 45

»4

5 10 42

S4

7

9

Dec.

II 5 s

120

S IS 37

2S

2 27 27

2S

3 18 39

55

7

17

26

989

26

3 3S

S6

7

25

In Anno Biffextili pofi Fe-

27

3 18 50

^7

3 3432

S7

7

33

bruarium adde unitis diei^°

9 29 3^

28

3 42 28

S8

7

41

motum.

29

4 10 14

29

3 S© 2S

S9

7

49

t.

JO

10 20 56

30

5 58 22

60

7

S7

Psgggg i.

( 77^ )

Tahuta Mectiorum MotuumSatellius Saturnr

J^enlntimiy a Cafliao deteBi Jnno 1686.

Arnii

Epochit

Mot.

p

Med. Mot.

\4ot,Med

\t(TtUS

Jtil.

h

V.x 0 «

Medi.

inemt

s

0

i

«*

s

0

# •

I:

s

0

1

M

0 #

0

«

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3

2;

1

4

10

2

1

4

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32

i

0 y 29

3J

2

y^

1686

2y

■ 2

8

20

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2

8

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4

2

0 10 j8

32

2

y6

1701

X

22

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r

o-

6

3

I

4

3

0 16 26

33

3

I

1714

7

y

4

9

21

40

M

y

16

8

4

021 ss

34

\

/

J715

17

7

y

2

1

42

y

9

27 40

y

0 27 24

3y

3

12

1716

n0

27

9

6

6

1 1

44

6

2

9

12

6

332 y3

3

>7

1717

n

18

43

7

10

21

46

7

6

20

44

r-

/

258 22

37

3

23

1718

sa

28-

4y

8

7

13

20

8

ri

2

16

8

343 yj

38

4

28

171S

X

8

47

C

✓

1 1

23

22

9

3

13

49

9

049 19

39

3

34

172®

s

18

49

lo

4

3

24

10

7

2y

21

io

3y4 48

40

%

40

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1 i

8

1;

26

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0

6

n

( ]

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4

3

4y

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12

5

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c

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25

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r 946

4^

3

yi

Mi.

—A—

f

0

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13

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ly

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8

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13

r II 15

43

3

y6

'jan.

JX

0

0

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ly

4

H

"I

1 1

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14

r 1644

44

4

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Pebr.

■1

^7

34

M

6

y

6

'y

y

23

I

»y

( 22 i;

iS

4

7

Mar.

6

20

3^

If

2

26

4^

i6

10

4

33

i6

I 27 42

4^

4

12

Afr.

iO

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6

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2

16

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17

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io

4

7

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ri

16

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1-

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26

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9

1 1

9

9

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4

2b

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I

17

43

20

0

18

2C

iO

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20

41

2C

‘ 49 37

yo

4

34

Aug.

s

iy

17

40

I

6

4c

i j

8

2

13

21

I SS 6

y

4

39

Sept.

9

12

yi

60

I

2y

c

12

0

«3

4y

22

I 0 55

y^

4

4y

Qbt.

8

28.

y3

So

2

13

20

^3

•4

■»7

23

z 6 t\

y;

4

y

Nov.

0

26

27

ibo

3

j

4

9

6

■49

24

ill 32

y4

4

y6

Dee^.

0

12

28

120

3

20

0

I

18

22

2y

i 17 1

yy

)

1

26

y

29

y4

26

2 22 30

y6

y

7

In ,A^o

EiJTextfli Vofi FehruA'

^7

lO

II

20

.427 99

y?

y

12

rintp aide miui, did

r/totutn.

28

2

22

y8

28

2 33 27

y8

y

18

29

7

4

3c

2 38 ff.

)'9

y

23

Li

30

i6

'2

3^

244 2J

5b

y

29

( 779 )

Tahula Mediorum Motuum SatMtit

Sacurni Medii^ ^Caflino deteEli Anno \6j\.

Anyiis''

Efocha

Mea

5

Motu

H

M

Alo/

Med.

Julia.'

ineunt

0

$

•>'

s

0

f

«-»

s

0

• '

iCX.o

» *

#

/ 1

M

Met.

i /#

l68l

12

16

1

9

17

2

1

2

19

4'

1

D

IS

31

1

43

1 686

nt

27

6

2

1

4

?

2

f

9

2?

2

0

6

38

32

c

46

iJOl

•rw

I

17

5

4

21

f

3

7

29

4

3

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9

f8

33

1

49

1714

II

4?

4

4

27

48

4

10

18

46

4

0

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34

f

f3

I7I J

©

28

4f

f

2,

14

fo

f

r

8

27

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0

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36

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t

f6

1716

V-

1

47

6

0

I

f2

6

3

28

9

6

0

19

ff

V

2

0

,717

22

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9

i8

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7

6

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fo

7

0

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37

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3

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X

9

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8

9

2f

8

9

7

31

8

0

26

34

38

i

6

1719

26

H

9

7

12

38

9

II

27

13

9

0

29

f3

39

2

10

1720

uTU

3f

10

'4

29

40

£C

.2

16

f4

1 0

0

33

12

2

13

Menf.

Med. Mol us

II

2

16

42

1 1

f

6

36

ii

0

36

31

-M

16

dnni

Com.

s

0

12

2

0

2?

10

2f

26

(2

13

7
; 0

26

If

17

fS

12

13

0

0

39

43

f '
10

P

43

2

2

19

23

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•0

0

0

4

9

27

28

‘4

I

f

40

14

3

46

29

44

2

1\

26I

Pebr.

ta

10

24

If

7

14

;o

3

2f

2 1

15

0

49

48

If

2

29

Mar.

0

21

44

16

7

2 I

13

16

6

If

3

[6

0

f3

8

46

2

33

Afr.

i i

2

9

17

f

8

If

17

9

4 44

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0

56

27

47

2

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6

22

fi

18

2

2f

16

18

11

24

26

18

0

f9

46

48

2

39

lun.

5

?

1 6

IS

0

12

18

‘9

2

14

7

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3

f

49

2

43

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0

f8

20

0

19

1

20

f

3

49

20

r

6

24

)'°

2

46

A'Ug.

n

4

1

2?

40

1

8

2

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23

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21

r

9

44

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2

49

Stft.

9

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47

6c

I

27

4

22

to

13

1 1

22

1

13

3

•f2

2

f3

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S

50

8-

2

16

5

23

I

2

f3

t

1 6

22

f3

1

f6

Nov

?

If

54'ioo

?

f

6

3

22

34

24

t

19

4‘

f4

2

fS

Dec.

i r

6

?7

120

14

7

Af

6

12

IC

M

1

25

1

ff

3

3

In- Anno

BiJJextili fofi

Februa’

i6

^7

9

11

I

21

f7

39

26

27

t

I

26

29

20

39

f6

f7

3

2

i

C

num adds

umus Viei

ni-otum.

v8

2

1 1

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28

i

32

f8

f8

3

13

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f

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3

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■> '

7

20

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f

39

36

60

3

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( 78o )

Tahla Mediorum Motmm ^etiextimi Sa-

tellitis Saturni ah Hugenio inventi Anno i<555.

Annis

3uL

ineunt

Epocbx
s ; ,

Amis

Mea

s

0 #

0

Mea

s

. Mol.
0 •

a

M

Vio.Mo.

» «

f /I

5'

Motus

Medi.

t H

1641

^ 2 48

1

10

20

;5

I

0

22 3f

I

0 f6

31

29 10

i66i

K i; 2;

2

9

II

10

2

I

ly 9

2

I y3

32

30 6

1681

r 27 y8

;

8

I

4y

3

2

7 44

3

2 49

33

31 3

«686

in 3 28

4

7

14

yy

4

3

0, 18

4

3 46

34

31 59

1701

n 12

s

6

y

30

y

3

22 f3

y

4 42

3y

32 yi

171^

6

4

26

y

6

4

ly 28

6

y 39

36

33 52

1715

SJ5 828

7

;

16

40

7

y

8 2

7

6 3y

37

34 48

1716

t 29 ;

8

2

29

yo

8

6

0 37

8

7 3*

38

3y 47

1717

? 12 i;

9

I

20

2y

9

6

23 12

9

8 28

39

36 41

1718

m 2 48

10

0

1 1

0

10

7

ly 46

^o

9 24

40

37 38

1719

25 23

II

1 1

1

55

1 1

8

8 21

1 1

10 2i!4*

38 34

■ I72«.

-Tb 13 5-8

12

10

14 4?

12

9

0 yy

12

II 1742

39 3»

1721

S 27 8

1;

9

y

20

^3

9

23 30

«3

12 1443

40 27

. Men).

Med. Mot,

14

7

2f

yy

14

10

16 j

«4

13 10,44

4' 24

An'Co

S 0 ,

ij

6

16

30

ly

IX

8 39

*y

H 74y

42 20

Jan.

000

f 29 40

i6

0

1 14

16

^y 3 [46

43 17

Peer.

II 9 H

17

4

20

ly

17

0

23 48

17

16 0

47

44 13

Mar.

i 8 12 2

18

?

10

yo

i8

i

16 13

18

16 5"6

48

4y 10

/ipr.

7 21

19

2

I

25

19

2

8 f8

«9

i7 f2

49

46 6

, Mail

6 9 14

20

I

14

;y

20

3

I 32

20

18 49

yo

47 3

Junii

y 7

40

2

29

10

21

3

24 7

21

i9 4y

y^

47 59

Julii

4 ^ 26

60

4 I?

4y

22

4

16 42

22

20 42

y2

48 f6

■Aug.

3 16 18

80

28

20

^3

y

9 16

23

21 38

y;

49 y2

: Sept.

2 26 12

100

7

12

yy

2^

6

* yi

24

22 3f

54

yo 49

on.

I I? 30

120

8

27

3'

^y

6

24 2J

2y

23 31

yy

yi 45

r Nov.

0 23 24

140

10

12

y

26

7

17 0

26

24 27

y6

52 42

Dec.

II 10 42

i6o

II

26

40

27

8

9 3y

27

2y 24

y7

53 38

In Anno Bijfextili fofi Fehrua-
rium adde unius diet motum.

28

29

30

929

9 24 44
10 17 18

28

29

30

16 20

27 17

28 13

y8

y9

6c

54 35

yy 3'

f6 27

(>8i )

Tahnla Mediorum MotmmSapMtis Saturni

Extimi) a Cafliao deteSi Anm 1671,

Annii

Julia.

ivfunt\

1681

f686

1701

1714

171^

Men/,

Anni

Com,.

1716

1717

1718

1720

yon.

Febr.

Mar.

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Jun.

Julii

Sept.

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In Anno BiJJextili pojl Fehrua
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( 781 )

Motibus mediis Sacellitum ad hunc modum cortftita-
Tis, proveniunt Revoluciones eorum jam veris proximx,
fcilicet

- -- -

D

h

>

u

Primt fivs Tnt 'mi

I.

11.

x8.

^6

Scemdi Penintimi

17.

41-

10

Tertii five Medii

4-

11^

15.

10

^arti Hugeniani

If-

11.

41.

^inti five Extimi

79-

7-

46.

00

Pofito autem, juxta regulam Naturae C faltem in hoe
noftro Syftemate) univeilalem quaequetam injovialiutn
ac Lun« motibus, quim Plaaecarum Primariorum circa
Solem, obcinet, Vires centrum Saturni petcntes eile in
duplicata ratione diftantiarum reciproce, f>roinde Cu-
bos diftantiarum a centre efle ut quadrata Temporum
periodicorum ; ex data diftantia & periodo HugtniAnU
hunt reliquorum diftantiae ut fequitur.

Sernidiam, Semidiam,

/int/uli Globi

Dtfl. Primi 1.9189 4,3400

Stcundl 14708 5»5593

Tertii 5.4508 7*7643

Sludrtl 8.CO00 18 ocoo

^inti 23.3145 51,^573

Qtioe quidem diftantix cum D. Cajfini obfervatis fatis qua-
drant. Quatuor autem interiores Satellites juxta planum
Annuli Saturni orbitas fuas deferibunt proxime ; in pia-
no, fc. ^quatoris noflri piano quoad fenfum parallelo,
quicquid in contrarium proferant nonnulli. Quintum ve-
to orbem fitu paulo diverfum a caeteris deferiberej nuper
deprehendit D Jac.CajJims prioris filius &virtutum hseres,
m videre eft in Aeftis Academise ScientiarUrtl Parifiends
Anni 1714. Sed hsec autem omnia propriis oculis con-
templari. atque penicius introfpicere jam ipfi accingimur.

H. Tk

C 78? )

II. The refl of the Treatife of that Learned JntU
quary T)r, John Tabor 0/ Lewes (whereof the
Firjl Fart is puhltJJ^d m 3 5 1 . of thefe Tranf-
adlions ) concerning the Site of the ancient City of
Anderida, and other ^mains of /Antiquity in the
County of SufTex,

TJFIB former Part of this curious Treatife having
found a jttji Efleem among feveral vrorthy Members
of the Royal Society, vfho are Lovers of Antiquity^
At Their inftance we have adventured to infert here the Re-
mainder thereof; entreating our Pholofo^hical and Mathema-
tical Reader, to indulge the Liberty we now take, of break-
ing in upon the ufual SubjeLl of thefe Papers.

Where 7rfc////j fpeaks of Britain and its Affairs, his De-
Icriptionsarefo lively deliver’d, chat one would think him-
felf had been here, with his Wife’s Father ; and

where he mentions the Irijh ^ Prince, the ExprefTion by
him us’d feems to give Strength tofuch a Suppofition.

The gaining the Southern part of this Ifland, was the
greateft, if not the only Acquifidon, made to the Ro-
man Empire, from the Death of Tiberius to the Sixth
Year of Claudius ; which we may well fuppofe was not
pafs’d over in filence by chat excellent Hiftorian Tacit m :
but his Four Books of Annals, which contain’d the
Tranfadions of thofe Nine Years, we have reafon
nough to fear, are irretrievably loft. From the mention
Suetonius makes of Claudius his Expedition hither; *ds

H h h h h h commonly

’Tac, Agric. cap, XXIV.

( 784 )

commonly infinuated his Conquefl: here * coft no Blood.

' Our Countryman Bedcy we may fee, was of that opi-

nion ; becaufe, in the Account given by him of CUudim^
the Words of Suetonius ^ are copied- But Dio Cajfius^
from whom we have the moll particular Information of
that War, gives a quite different Relation of the Mat-
ter: He takes notice of at lead Four Battels, fought
with the Britons ( before Claudius came over ) by Aulus
Tlautitts\ who had Flavius P^efpaJjanus, Flavius Sahinus,
and Hcjidius G^ta, that commanded under him.* In the
firft Conflidf, Cataratacus was defeated ; in the fecond,
Togodumnus, and, as may be infcrr’d from his Words
afterwards, (lain. From the manner of his delivering
the Story, all thofe Battels feem to have been fought,
South of the River Thames^ and North of the Sjlva
Anderida, except the lafl ; and that in the fir ft Cam-
pagne the Conquefts of Flautius could not have exten-
ded beyond Kent and Surry : For it s likely ^ that the
Two firft Atftions happen’d about the Skirts of the
Sjlva Anderida, Eaftward of rise River Medrray; and the
Third, which held Two Days, on the Banks of that
River ; becaufe, from the River, where they were rout-
ed Two Days fucceffively, the Britons retiring, afiem*
bled f their Strength again before their Fourth Over-
throw,

* Suet. Claud, cap. 17. Ac fine uUo prxlio aut fanguine, intva paucijfi-
mos dies parte infula in deditionefn recepla, fiexto qnam profeRus erat men-
f* Romam rediit 3 Beda Ecclef. Hi!l. Gent. Angl. Lib. I. cap. 2.

+ Dionis Caffii Hift. Rom. Lib. LX. Claud. V. p 768. A. Oj ^ Bfer-
TfUo} fjti anrii <fi' Smp Iwuu.SttVov'Je i

td'ts <wmi baSoj', e? 7? m if jdf Zhat ng.TitiU~

jPK, y omg Fin n heuaHgpj ft ’IhaIis tyi’

yim, dlttKAt-wi (oJtkj 'O turn OXcuitj©

ff^ify iTti Q iSgi vmi (mV iTtfjct, To-

jp/s/tMfoji cTBUc/k{ c,niKtmy-—fvyl/]ay ^ hieivay crg/ssi uf

mi i}4perlo. ’ Pag. 678. D. J'’

^ liy TaiAevt S if Tin/ dyudnir liyQiRcHf

( 785 )

throw, in that part of Kent which borders on
not far from its entrance into the Sea ; and having
pafs’d it, were follow’d by Plautius his Germinns, and
on the other (ide put to flight ; which was the Fourth
Adion mention’d by Dh. Claudius having been fent for,
comes the Second Year with powerful Succours to the
AlTiftance of Plautius\ who with his Forces waited his
Arrival near the Thames , not unlikely flill where he
quarter’d in the Winter ; which perhaps was in that
large flrong Camp, as yet to be fecn t not far from
Eroml’^ in Kent^ on the River Ravenshottrn- The E npe-
rour joining him ^ immediately crols’d the Thames %
overthrew the Britons polled on the other fide to refifl:
him; advanced to Cynobelin's chief Refidence Camalodu-
num^ and took it .* Then receiving Homage of feme
States, return’d to Rome*

Confidering therefore that Claudius (laid but Sixteen
Days ® in this Ifland, we muft conclude his Difpatch
was great ; and that his Progrefs could not have been
through more Parts than Kent, Ejfex, Hertfordshire^
Mtddlefex, and Sitrrf. As to what elfe relates to the
Britilh War in the time of Claudius, fave that Three
Years after Titus refeued his Father Fcfpafian when in
great danger, we have no Account from Dio. But
where Suetonius ^ treats of Eefpafan sLikj we are told,
when that Emperour commanded in Britain for Claudius ;
that he fought Thirty Battels, fubdu’d Two of the

H h h h h h x rnofl

^ Camden Brit, Edit. 1695' Col. 215. c. ^ Dion. Caffii, Hifl:,

Rorn. Lib. LX. pag. 679. B. Ktf -m tw ^ tib*,

mxfd 78 W ’SluifM0¥ {iftiUla, if liiu PfST-

•nuimi, n7( r£^]omJhn tz/S T ttuXetu dvtttjSpmv miiy

(T^Af, l«.etvov Tc ^ raif t{w 'ifaJhv amv smti-

if 6XSb)|/, 78 ** Dion. Lib LX. pa?.

680. B. 78 it liw ‘PeiuUu 0 I; ubjicts ^PufMtTUf (. itp’ ^

^ T? imnn- ) I Swet. Ycfpalian, cap.,*.

( tU)

moft powerful Nations, won Twenty Towns, and.
brought the !fle of Wight under the Roman Obedience.
Of which Adions, befides what might have been faid
in the ioft Books of Annals •, Tacitus, in other Pieces,
of his, largely ‘ hints, that when Claudius rul’d, Vef-
pafians Behaviour and Succefs in this IBand, fliew’d to
the World his Condud and Courage in the Affairs of
War.* The fame is alfb taken notice of ^ by Dio:
From his Conqueft of the Ifle of Wight, it may be,
imply ’d, the Stage of his Ad ions here, was in thofe
Countries which border on the South Channel rather
than in the North ; Since therefore the Clime, the Soil,
and the more ready Conveniencies for foreign Trade
and Correfpondence, might entitle this Part of the Land,
to fuflain as numerous, as flout, and as experienc’d a
People as any other ( becaufe Cafar * takes notice they
not only lent Aids to the yeneti in their Revolt, but
were wont to affifl: the Gauls in moft of their Wars a-
gainfl ^ the Romans : ) And whereas no Hiflorian af-
terwards mentions any Difturbance given to the Rod-
mans from the Southern Parts ; we may conclude, Fe-
fpajian entirely fubdu d them ; and that before he left
the Ifland, the Methods he eflablilh’d for fecuting
Peace, were no way inferior to thofe he- had fliewn in
making War.

The

* Tacit. Agricol. cap. xiii. Divus Claudius auSor operis tranfveflis le-
gtonibus aux'tliifque^, Qp ajfumpto in partem return Vefpajiano ; quod initium
‘Ventura max fortuna fuit, domita gentes, capti Reges, & nionjlratus fatis
Ve/pafianus, Tacit. Hift. Lib. III. cap. xliv. Et Britanniam inclytus erga
Vefpafianum favor^ quod illic fecunda Legioni a Claudio prapojitus, & beU
Jo clarus egerat, non fine motu adjunxit caterarum. * Dion Caff.

Hiff. Rom. Lib. LXV. p. 756. C. iv^uTmv ivvoitv Lw

Vffi aum — 3IS ^ Bgtijeutat )i]ri Ik. n m mKtpus

5 De Bello Gal. Lib. 111. Soctos fihi ad id Bellum Ofifmios, Lexohios,
&>c, auxilia ex Britannia, qua contra eas Regiones pofita ejl, accerfunt.
Idem Lib. I-V. CEamen in Britanniam profieijei contendit, quoj, omnir
kioffte Qallifis Belli sfiojlibus-nojiris inde fubminijlrata auxilia irHelligeb.at„.

( 78/ )

.'The Romans well knew, that thofe who were Scran-'
gers to Civility, could not without great Difficulty be,
kept in Obedience: As foon therefore as the Coun-
tries they had conquer’d, were reduced to fome degree,
of Quiet ; they endeavour’d to make the People in love,
with their Government, by introducing their Arcs and.
CuUoms among them : From that inconfiderable Inftance,
recorded ^ by Plin), we may fee, how ready the Rc-^
mans were, to oblige the People under their Power,,
with any Curiofuy that might entertain their Sences,,
in order to endear them to the Authority they had o-
ver them. ( He tells us. Cherries were not known in^
Ital'jy till the dSoth Year of Rome^ when L, Lticiillus-
firft brou^TC them thither from Pontus ; and that in
Hundred and Twenty Years, they were fo increas’d,
that not only many other Countries, but Britain alfb^
was fupply’d with them; which mufl: have been about.
Three Years after Claudius himfelfhad been here. The
ufual Landing kom.Rome being then in the County
of Kent ; that Fruit without queftion was there firfb
planted ; and the Soil well agreeing with it, may, be the
reafon that the bed and greated Quantity of it is.
yet there to be had.^

Agricola, ir^the Second Year of his Lieutenancy hercK
when in Winter-Quarters, purfu’d the fame Maxims^

( which Tacitus terms Sal uberrima Confilia ; and, as.
it may be inferr’d from an Expreffion of® Cafar
ducive to the fame End ) to gain the Britons, by ma-
king them acquainted with the Roman Manners : He
not only in private perfuaded, but publickly help’d.

and

5 Plin. Lib. XV. cap ^ De BelL Gallic. Lib. I. Hcrnm

*mmum fortijfimi funt Belga : Propterea cjttod a cuHti atcjue humanitai-9
ProvittcU longijfime abfnnt, mlnimeque ad eos Jidercafores fape commewt^
atc^ui ea fi^4. ad effeminandgs animos pertinent, iniperSant.-

( 788 )

and incourag’d them to build Temples, Places for com-
mon AlTemblies, and private Houfes after the Roman
Mode : He took care to have the principal Youth in-
ftruc^^ed in the Liberal Arcs; He ailur’d them to aflecfl
the Habit of the Romans : And lafl of all, to engage
them the more firmly, help’d them to a Taft of the
Roman Luxury and Goodfdlovvftiip, by introducing the
Ufe of lhady Piazzas and Barhs \ an J their way of 8an-
queting. But here, Tacitus may be underftood to {peak
of what was done in order to civilize the Northern
Parts of this Nation, where A^r kolas Prefence was re-
quired : The Southern was, we may fuppofe, fofcned
and quieted by the fame Methods near Forty Years
.before, when reduced by T'efpafian. *-

From hence it may be infcrr’d ; that fliould never
any other Tokens of the Antiquity of thefe Works be
found; yet would the Bath denote the Age of the
Pavement, and fet it near as high as the moft early
Time, that the Romans had any real Authority in this
Ifland.

As by the Lofs of Lome of the Annals of Tacitus ^
■\ve may have been depriv’d of the moft early Hiftory
of this County ; fo likewife, for want of ancient Re-
ligious Houfes; there has been little or.no Accounts
left of its Circumftances, in the Times next after the
Roman Authority expired here. Malmshury ^ fays, that
in his Time, there were here only the Abbies of Bat-
tcll and Le^xes, and thofe not long erecfted. The ear-
lieft Mention made of it, is by ^ Bede, who informs
us, that Bifiiop Wilfrid, in the Year 6; 8. being thruft
cut of his Province of Northumbria by King Ecgfrid,
reeled at Selfey in 68o. and ftaid Five Years, labouring

in

’ Tacit. Agricol. cap.xxi. * Gul. Malmsb. dc geftis Pontific.

An£^l. Lib. Jl. » Bed* Hift. Ecclef. Lib. IV. cap. xiii.

( 7h )

in the Converfion of the neighbouring Parts ; but of
what elfe relates to the County, fave the miferable Ig»
norance of the Inhabitants, and the Number of Fami-
lies, he has left no Account. Bede (pent mofl of his
Time in the Monaderies of Wiremcuth and Jarrow,
and travel’d little ; fo, that confidering the Didance
from thence to this County, and the different Govern-
ments and Intereffs that lay between, he may well be.
excus’d for the few Particulars he has left us of it.

The next Records we have to view are thofe of £-
theherdt the Chronicon Saxonicum, and Henrj Arch-
deacon of Huntingdon, But that you may the more
clearly apprehend the antient State of this County ;
look int(T the beft Map of it you can get. At the
Weft End, you will find iVefi-Harting and Stanfted, di-
ftant from each other Six or Seven Miles; imagin ai
ftreight Line to be drawn from Harting to Bourne near
Fevenfef, and another to be drawn from a Point which '
muft he little South of Stanfiead to Brighthetmfiom \ .
What lies North of thefe Lines is the Weald or Low-
lands, formerly the S^jlva Andcrida'^ that which is com--
prehended between thefe Lines, and bounded by the'
Sea, from Brighthelmflone to Bourne, is the Downs, fo*
famous for their pleafant Situation and Fruitfulnefs.
The Part South of thefe Lines, is a flat champaifii
Ground, ending like a Wedge at Brighthelmftom. Thefe
two laft Parts were thofe only that were inhabited
Bede's Time; they contain not more than Two Fifths-
of the whole County ; which muft be the reafon why--
Bede (aid,: Su[fex. ‘ confifted not of more than 7000 ;■
Families or Farms ; whereas in another place he com-
putes to have 1 5000, Families.

1 04

I Be^dx Hift. Ecclsf, Lib. IV. cap, xiU,

( 790 )

In the three Accounts ‘ above-mention’J ’tis agreed,
--that in the Year 477. ElU^ with his Three Sons Cj~
me)7, Wlencing^ and Cijfa^ landed his Forces at Cjmenes-
Ora ( which from a Charter of King Cedmllas to the
Church of Stlfe-^ the learned ^ Catr.bdetJ proves to be
-about Witterir;^^ near S£lfejj) not far from which he
routed the Britons y and drove them into the Weald
- ( 3nt);eDfnetee ) : Their farther Progrefs is moft di-
flindly and naturally deliver’d by the Archdeacon of
Ziuntingdon y in thele Words; Saxones autem occuparunt
littora Maris in aucrtjt, magis magifque fthi regionis
fpatia capejfentes, ufque ad nonum annum advent us eorum.
Tunc vero cum audacius regiomm in longinquum capeffe^
rent ; convenerunt Reges & Tyanni Brittonumjpud
■XCft)f|3bUtnC) & pugnaverunt contra File ^ filios fuos, ^
,fere duhia fuit viZloria. Uterque enim Exercitus valde
Ufus ^ minoratuSy alterius congrfjfum devovens, ad pro-
^pria remearunt. Mi fit igitur Elle ad compatriotas fuos au~

X Hi urn fag! tans.

This County having been invaded in the moft Wc-
ilern part of it by the Saxons ; if what they did after-
wards, was to poftefs themfelves of it ; their Progrefs
mu ft have been from Weft to Eaft. And fo much
Henr. Huntingdon^ Words plainly imply. He fays
farther, they were Eight Years about it; which, if
we coufider the Circumftances of the Country, ’twill
-be no great wonder it fliould take up fo much Time ;
unlefs their Forces had been very great, which we have
-no warrant from any Hiftory to fuppofe : For the Weald
then uncultivated, muft have been moft difficult to pafs,
even in the drieft Summers. The Downs y like a Wall
X with a Terras-Walk on the top) have a very fteep

Defeenc

'■f Ethel ward Hilt. Lib.I. Cap. 5.
Hen. Hunt, Hift, Lib. IT.

Chronic. Saxon. Ann. CCCCLXXVII ,
* Camden Brit. Suflex.

( 791 )

Dcfcent into it, their whole Length 5 excepting! that
every Ten Miles, or thereabouts, they have deep Chan-
nels through them to afford Pallage for the Rivers into
the Sea : Therefore, what was then habitable, being
thus canton’d out into fo many Parcels by the Rivers ;
nothing could be more difficult to gain, than thofo
Cantonments ; were there any Forces to defend the
Pafles that ffiould have been attempted ; the Rivers be-
ing deep and muddy, and the Moralles on each fide
broad and boggy .* Hence we may conceive, ’twas' no
very difficult Task for the Britons to defend, nor an
eafy one, for the Saxons to gain the Country. And in-
deed, the many old Camps, Rill to be feen on the
Dovrns, are an Evidence that fcarce any part effaped
being a Scene of War. Mr. Camden mentions but two,
Cifshury and Chenkhury. In the new Edition of his Works
"Dr.Harris has added Three more ; 2l Roman Camp at the
Brile near Chicheder, St. Rooks-hill, and Gons-hill near the
Weft Limits of the County. It may not be improper
here to infert an Account of the reft ; in which, I (hall
firft take notice of thofe that are on the North Edge of
the Downs, and overlook the Weald.

Firft, Chenkhury, mention’d by Mr. Camhdcn, Two
Miles Weft; of Steyning, and about Three Miles North
of Cifshury ; ’tis circular 5 its Circumference about two
Furlongs. From Chenkhury Eight Miles Eaft, over Foy^
ntngSy is a very large one, an Oval, not lefs than a
Mile round s acceffible at one narrow Neck only, and
that fortify’d, with a deep broad Ditch, and a very
high Bank: 1 could never learn any other Name it
has gone by, than Poor- Mans Wall; perhaps from its ha-
ving been a Security to the diftrefled Britons. About
Three Miles Eaft from thence, is Wolfenbury, on a Hill,
projeefted beyond the reft of the Downs, like a Baftion ;
it comes near a Circle in ftiape ; its Diameter a little

liiiii mote

( 79» ) 1

more than a Furloiigi Near Three Miles Eaft of WoU
finhurj, on the higheft pare of the Donns in that Quar*
ter, is a Camp, near fquare, about 6o Rods long, and
50 broad ; much like a Romnn Camp ; the fide next
the North is fecur’d by the Precipice of the Hill, which
is both very deep and deep ; the other Three Sides
have each their Porta after the Roman manner dill ve-
ry vifible 7 the Ditch feems to have been not lefs than
Eleven Foot broad ;but the Ground having been plough’d,
the Bank, is but low : This is call’d Ditchltng^ as is the
old Town under it. Near Seven Miles farther Ead,
and a Mile and half Ead of Lewes, is the lad on the
North Edge of the Downs , it goes by the Name of
Cahurn ; which perhaps is but a Corruption of the Bri~ |
'ttjh VVbr<^ Cadir ; the Parilh below it dill retains its j|
^itiP) Naifie Glynd: This is a round Catnp, fcarce !
Three Furlongs in Circuit ; its Ditch very broad and i

deep, and ,the Rampart within very high ; the Places ?
where the Tertts were pitch’d are yet vifitle ; which,
from the, Strength of the Out-Works, intimates that
thofe wfthin held it no fmall time. Near a Quarter of
a Mile Wed of it, there is a drong Work much larger,
but pot fo perfed ; yet epough to flievv, it was made •
to'lecure a Power, that might lie there to bridle thofe
in the drong Carhp, and prevent their making Excur-
dons towards Lewes.

The Camps, on the Southern Limits of the Downs'^
me St. Rookfmzi Chichefter. High- Down, a fmall Square,
Four Miles Ead of Arandeil, and in the Parilh of Goring:
Cifshury, Four Miles South-Wed of Sieyning. Holling*
lurj is the only one in the middle of i\\q Dow»s, Two
Miles North of Brighthelmp one, and Three Miles South j|
of Ditchiing ; ’tis a Square; the Porta dill remaining; !;|
it contains about Five Acres. A Mile Ead of Bright- If
helmftone da the top of a Hill, half a Mile from the. Ij :

Sea,

( 79 ? )

Seai is a Campi which has a triple Ditch and Bank 5
this alto is a Square, only the Corners are bounding ;
the outmoft Trench meafures about three Quarters of a.
Mile. In the Parith of Telfcomh, about Five Miles Eafl:
of the laft, are two^ but both imperfedb ; the. Cliff is a
South-Fence to One; the Other is' a Mile diftaht from
it; their Weft Sides are both finrfh’d with very able
Works ; they were defign’d for Squares, and to contain
1 2 or 1 5" Acres. At Meeching or NewhAvcn, on the
Point of the Hill, which overlooks the Harbour’s Mouth
from the Weft, is a Fortification which they call ths
Cafiley its Banks are very high, the Shape near half o*
val, containing about Six Acres ; formerly it might be
much more, becaufe the Cliff, which forms the Diame-
ter, every Year more or lefs moulders away, and falls
into the Sea. Near a Mile Eaft of Seaford is another
call’d alfo the Caflle, bounded by the Cliff on the South ;
its Figure almoft femicircular, the Trench and Ramparc
large, inclofing Twelve Acres. Three Miles Eaft of
Cukmere Haven is the laft, near a narrow Pafs coming
up.frbm the Sea call’d Burlmg-gap ; it inclofeth a Hill
nam’d Belli »ut of a half oval Shape ; the Works have
the fame Figure, and meafure about three Quarters of
a Mile? the Cliff here alfo makes the Diameter.

Though neither Hiftory nor Tradition, has banded
to us any Relation, when either of thefo Works were
made or by whom us’d ( except Cifshury by Ciffa ) yec
from this View we may conceive, the Calamity of
War once rag’d in all thefe Parts .* that the Ground
was difputed inch by inch : that in the Attack) a§ well
as Defence of it, the Pick* Axe and Spade, Were as much
made ufe of, as the Sword ; and laftly, that, unlefs the
Aggreflbrs were very numerous, eight Years was no
long time taken up, in difpofleffmg the Inhabitants of
this faft Country.

/ I i i i i i ' ^015®

{ 7P4 )

Some may imagine, many of thefc Camps were made
by the Dams ; but by what may be ob(ery’<i from the
Hiftory of thofe Times, that People feem’d not to l^e
fo. formal an Enemy, as to prolong Wac by Encamp?
ments; Their Refuge was in their Fleets that always
attended them ; fo. that, when likely to be vigorouny
oppos’d, they betook themfelves to their Ships, and;
fuddenly invaded, another Part where was lefs Oppofi-
tion and what they could not carry with them, con-^
{lim’d; with Fire and Sword. Thus continually haralTing
the Nation by their hafty and rapacious Vifits, they
exhaufted it of its Riches, and Strength, and as it werc;
imitating the Quality of the Faulcon their Enfign, they
ffcw the Prey to a iitand, and then feiz’d it.

The Archdeacon of Huntingdon, in the Prologue or
Dedication of his Annals, to Alexander Bifliop of Lin-
coin, aflures his Diocefan, that he compil’d his.Hiftory
from Chronicles referv’d in ancient Libraries ; no qua*
(lion therefore, when fpeaking of tire Saxons \\qiq, lie:
had good Author|ry to lay (as above cited ), magii
magifaue fibi Regionis fpatia capeffentes-; and that no o-
ther lyleaning could belong to it ; than that they car-^
ri$d‘ their Conqueft from Weft to Eaft, in longinquum.
lengthways. Flad they entirely raadethemrelvesMa--
fters ordie Country, ’tWQuld have been too late: But,
before they had. wholly gaind it, the allembleci-

againft,them; the Saxon Chronicle fays tUdlJj i. e* prope ;
Etheherd, juxta ; oXy ZS Hantingdon h^ it, apud^tttXt^
tlf^Dunits where a Battle was fo hard fought, that
each Side had enough on’t, and retir’d. The Saxons
were fo diminilh’d,, that was oblig’d ta fend for
more Forces. This A<ftion, was in the Ninth . Year af-.
terf^/Z/s firft footing ^here,. Three Years, before Hen-
Deaths. Ann. Dom. 48^ y. It- fa, weaken’d Ella,., that
Ws; hear; noi more, of him. till he, receiv’d his.Snpplies .

from'.

( 791 )

/torn Germdfjy ; which came not, according to j^un'
tingdon, til], the firll Year of the Emperour Anaftafins^.
Three Years a&er Hengifi.'s Death, and Six Years af'
ter the hard Battel, viz.. An.

Bein^ thus ftrengthned, Ella mov’d again, befieg’di
Andtrida f in Words, Urhtm mtmitijfima>7i )
at lad forced the Place ; and by. reafon of the flout.
Befiftance the Defendants made. Savage like, left not.
a Soul alive, and raz’d the City, which, in Huntingdoti^,
Time remain’d delolate.

As to the Field where the Battel was fought; the.
Saxtons extending their Power Eaflward, the Check-
that was given them, in all probability muft have beem
where they pulh!d on. their Victories; and it being-
near ^CtCtC5f)3bunt> this Bourne near Pevenfey may
b.e the Place meant, fince it founds like the iattet
part of that Name ( for there not being a Weft Bourne
that it relates to, the Name of it may rather be Es-
hourne than ^z^-Bouine and likewHe that Anderida,,
the Britons laft Stake and Support, was not far from?
it. ’Tis probable therefore the Battel was fought on the.
Dorvnst between the Camp laft mention’d at Burling^-
Cap and Bourne ; for there are no where on. the;
Dojrns, that I have fecn ( and there are few Parts of.
them that I have not often view’d J, Marks of a grear
ter Battel than there 3 becaufe, from the top of that:
very, high ClifF, by the Inhabitants, call’d T/je Three'
Charles. (. and by Mariners Bcachy-Head') to Willingr-
ton Hill, which is four Miles, die Ground is 'full of?
large. Tumuli or Places of Burial ; . and in many parts^,
within that Tratft, where the Pofition of the Ground,
feems to offer, there are deep Trendies and ^nks^^^,
which one would irriagin were Breaft-VVorks made to de->
fend the Front of an Army ; and the on eacfeTidei

ofthemdeem to ffiew, there was no fmalU Struggle, im
forcing as wdl as defending’ thcOT Tte

( 79*5 )

The Learned and Judicious Mr.’ Somntr * diflikcs,
that the Sira Andiridx fhould be fix’d at Newertde»,
and is inclin’d to aflign fbme Place in Sajfex for it :
But from a modeft Deference to the Opinions of the
Learned Camden and Selden, he drops the matBcr.

But let us fee, what our more elder Hiftorians fay
of it ; Hern*) of Hmtindon^ Words are, Et quia tot
ihi detmna toleraverant Extranet, ha Urbem dejlruxe-
runt, quod nurquam puflea readifcata e(t. Locus tantum,
quaji nohilijfima urlisy tranfeuntibus ofienditur dejolatus,
Matherv of Wefiminfier fays. Locus autem Civitatis ufque
hodie tranfeuntibus oflenditur dejolatus. Manfit ergo ibidem
Ella cum tribus Filiis fuis, Kegionem illam, qu£ u[-
que hodie Anglice Lathe autemRegio Aujlralium

Saxonum dkitur, colere ccepit. From the ExprefTions
above*cited, it may be ftippos’d the Ground where
that City flood was not quite forgot, in either of thofe
Hiflorian’s Days. Henrj of Huntindon being the elder
by zoo Years f had Nervenden been the Place liis
Words might have been true, in faying it was defb-
lare : But ’tis very improbable Mathew of Wefimin(ler
Ihould have faid fo likewife; or at leafl, not taken
notice of the Ad of Piety and Charity of Sir Thomas
Alhuger, who, in his Time, had newly ereded a Mo-
naflery at Mewenden ^ for the Carmelites who came
from Ralefline : But let that pafs ; what Authority Mr.
Camden had for faying ^ Hengift fent for Ella out of
Germany, to help him reduce Anderida^ is not to be
found. From the Accounts above flated, and others
-that might be produced, it is clear, that Hengifl was
dead Three Years before the Siege was laid to Ande^
rida. In the Time of Hengifi*s Life, we find, for Eight

Years

* Somner’j Roman Forts and Forts in Kent, p, zo6, 2

Kent ^it, i5p5. Cot, zii.

( 797 )

Years ElU had enough to do in Suffex ; and the Blow
he had given him the Ninth Year at
oblig’d him to be quiet the other two Years of Hen-
gift^ and till his Succours { as above*mention’d ) came
to him from German'^, Befides, we have not the lead;
Hint from any of our Hiftorians, that Andtrida, was an
Eye- fore, either to Hengift or his Son Esk after him ;
or that Ella affided the Kcntijh Saxons, or the Kentijh
Saxons E^lla in reducing it : Therefore this mufl: be a
Suppofition only of Mr. Camden, in order to give Strength
to the Notion of Anderidds being at Nervenden. Ta-
king no notice therefore of that Suppofition, we may
confider Nesvenden is on the Kent fide of the Limen
( for fo is the River Rather call’d ^ in the Saxon An-
nals, and by Mathevp Weftminfler ; and the Mouth of it
nam’d Partus Lmeneut, and CinUttE hy Ethelrverd and
/denr. HuntindonO and that Kent having been fubdued
by Hengif; and his Saxonr, near Forty Years before i
the Town at the Mouth of the L'men, and the reft,
if any, up the Stream on the fide of Kent, weiQ aUb >
part of their Conqueft.

Furthermore, after it had coft Ella fo much Time,
and no doubt Pains too, in reducing the plain Ground
of Su(fex, ’tis not likely he fhould call more Forces out
of Germany, that he might lead them Thirty Miles,
through the Difficulties of the great Wood ( which he
muft have done if Netvenden were the Place, ) to be°
fiege a City, fo far from his own, and within the Ken-
tijh-Saxon Limits, efpecially if there’s any heed to be
given to the Words of Math. V/ejlminjier before cited 5
who, after relating the fad Fate of the Inhabitants and

City

’ Chron. Sax. A. Dom DCCCXCIII. Mat. Wcftm. Fl. Hift. A. Dom,
DCCCXCII. ^ Ethelwerd. Lib. HI. cap. iii. A. D. DCCCXCIIL.:,

Hen. Hunt. Hift. Lib, V, Alfr. Reg, an. 19,

( 79» )

City of Anderidd, immediately fubjoinSi Mdnjit ergo^i^t,
Ella And his Sons refided there C that part of

Su^ex where Anderida was ), and began to cidthate and

improve the Country,

In the laft place, from the Ufe made of Anderida by
the Romans^ ’tis not likely ( as Mr. Somner ^ judici-
oufly hints ) its Place was at Nervenden ; for being one
of the Stations, under the Prafe6tus littoris Saxonici,
where Forces were quarter’d, to have a watchful
Eye on the Sea, when ever the Saxon Pyrats came

to infeft the Coaft ; We may fuppole it, like the reft

of the Garifons under that Officer, conveniently fitua-
ted for the fame purpofe ; as were Branodunum ^ Bran-
cafler at the North Point of l^orthfolk ; Gariannenum,
'^on\\'Tarmouth^ or very near it ; Othona Ithanchefter
in Dengy Hundred, in Ejfex, ibme Ages fince fwallowed
up by the Sea ; Regulbium, Reculver in Rent 5 Rutupis,
Richbororv ; Duhris Dover ; ^'Lemannis (which from the
Saxon Chronicle ^ we muft look for. Four Miles Eaft
of Apple dor e ) probably New Romney, all fituate near
the Sea, on Ground which had a full Profpeeft of the
Sea : whereas t^emnden lies low, at leaft Eight Miles
within Appledore, on a turning of the River, where
the Land Eaft ward muft have cut off any Profpedt of
the Sea. To all this may be added, that the Romans
having a Numerns, Cohort, or Battalion of the Tur-
nacenfes, in Garifon at the Portus Lemanis on the Mouth
of the Haven, we may fuppofe they knew how to
husband their Strength to better purpofe, than to place

another

* Somner Rom. Ports and Forts, pag. 105. * Not. Imperii a Pan-

cirol. cap. Ixxiii. pag. 162. 7 Chron. Sax. A. Dom. DCCCXCIII.

‘Turn appulerunt ( fc. Dani ) in JLimenioJHum , cum CCL. Navibus. Su-
per eum Fluviiim traxerunt fuas Naves uf(fue ad fylvam, quatuer mtUariit
ah exteriore parte afiuarii ; ibique expugnarunt quoddam mun'mentum
( fc. Apuidre. )

( 799 ).

another Garifon to watch the Motions of the Saxon
Rovers, Twelve Miles up the little River, quite out
of fight of the Sea, where they could be of no Service*
Thofe who would have the Seat of Anderida to have
been at Hayings ; let them look on thele Words of
Hem. Huntindon ^ (Haraldus rex Anglorum, eadsrn die re*'
verfus ad COUlttOlC cum fumma Utitia, dum pranderet,
audivit nunthm dicentem fihi., Willielmus dux i^ormanntx.
Uttora Ati fir alia oceupavit^ ^ caftellum conflruxit apud
and they will conclude Hafiings was not a
defolate place, in the Ages of the Hiftorians, who af-
firm Anderida was : If at Pevenfey j that Place was fo
far from being raz’d by Ella, that even after the Nor-
man Conqueit it remain’d a ftrong Caftle, where Odo,
Bilhop of Bay on and his Forces fullain’d a Six Weeks
Siege ; and for want of Provifion were oblig’d to lur-
render to K. William II. At this time there is I’o much
of Pevenfey Handing, that perhaps 'tis the greated and
moft entire Remain of Roman Building, any where to>
be feen in Great Britain.

From the Arguments on the foregoing Authorities,
Anderida mull; have been fomewhere in Suffex, not in
the Wed but Fall part of it, and not far from the Eaft
End of the Downs, near the Sea. From the Bath, Pave-
ment, Coins, and Bricks, ’tis fure the Romans had once
an Abode, and not a lliort one, at this Place near Eaji-
bourne : From the large Extent of Foundations about
the Place where thefe were difeover’d ; that there was
a large Town or City there 4 From the common Height
thofe Foundations bare under the Surface of the Ground;
that the Buildings they fufiain’d were effedua'ly levell’d
or raz’d : And from the Coals dug up amongfl the Rub-
bilh, ’tis evident that Part was burnt ; all which Cir-

K k k k k k cumdances

i Mtnr. Huntindon, Hift. Lib. VI. #

( 8oo )

cumftances well enough agree with the Account given
us of Anderida,

The Situation likewifc of a Town here, gives reafon
enough to fuppofe, it was a Place of Importance, and
whence it had its Name 5 no Part hereabouts being any
way fo convenient, for a f'ecure Settlement ; or for fuch
a ufe as the Romans might have occafion to make of it.
We are inform’d by Cafar, that the Maritime Parts of
Britain (fpeaking of what he faw, which was the South-
Eaft ) were inhabited by People from Belgium ; and '
that they call’d their Settlements by the Name of the
Places from whence they came. It was the Opinion of
Tacitus alfo, that ^ thofe who inhabited next to Gaule,
came from Gaule. And Bede fays, the Tradition in his
Time was, that the Southern Part of the Ifle was peo-
pled * from Bretaign. In the Third and Seventh Books
of Cafar’s Commentaries, mention is made of the Andes,
a City and a People belonging to it among the Celta, in-
habiting on the Sea-Coaft. Time varying the Names of
Things, near Two Hundred Years after Cafar, Ftolomj
calls the City Anderidum : And near 250 Years after him,
when the Notitia Imperii, now extant, was in ufe, the
Clajfis Anderetianorum '* is regifter d ; and the Refidence
of their Admiral fix’d at Paris. From whence ’tis to be
inferr’d, that tho’ the Capital of the Andes might have
been Angers near the Loyre, yet their Country had on the
North the Britifh Channel ; and on the Eaft the Seine for
its Bounds. The Britijh Coaft about Eafi Bourne is the
neareft of any to the Mouth of the Seine ; Therefore,

according

* De Bell. Gal. Lib. V. omnes, fere its nominibus civitatum appel..

lantur, quibus orti ex civitatibHS eo pervenerunt. ’ Tac. Agric. cap. xi.
la univerfum tamen xftinianti^ Gallos vicinum folum occupaffe credibile efi.

5 Bedoe Hift. Ecclef. Gent Angl. Lib. I. cap. I. In primis hac Infula
^ritones folum^ d quibus nomen accepit, incolaj habuit ; qui de traHu Armo..
vicano ( ut fertur ) Britanniam adveBi Aujlrales flbi partes illius vindi^
0UTUH4. J Pancirol, Comm, ia Notit. Imp. Cap. XC. pag. i yp, i8o.

( 8oi )

according to the Ufage before C^efars Time, the Name
of Anderida there, is readily accounted for. Moreo-
ver, this Place feems moft naturally featcd, for giving an
Appellation to the great Wood, to which it adjoin’d :
For, as it felf is on the Shoar, fo alfo the Sylva Ande>
rida here, came very near the Shore ; and a large part
of it might be (een from the Sea before it : Indeed, on
the Sea off of Ronuuy, it might be difcover’d ; but then
the Diftance w’as great : At all ether parts of the Coaft,
the Sight of it from Sea, is hinder’d by Hills, or high
CliSs.

Setting afide the want of a navigable River, the Spot
of Ground where this old Town flood, yields to none
in the County for Importance and Fleafure : For here,
like a Wedge, ends the firm Soil of the Downs j Nature
* has fhap’d it like an Equilateral Triangle, having each
fide half a Mile in Length : Towards the Sea, on the
Southern fide, ’tis fenc’d by a low Cliff, of 12, i^, and
in fome Places zo Foot high ( in which Cliff is now to
be feen a ftrong Foundation, that has acute Angles,
which fhews it to have been for a Fort rather than a
Dwelling-Houfe ^ On the Northern fide is a Morafs,
with a large Rivulet of very good Water. Between
the Weft fide and the Downs lies a fmall VaWey, by
which Advantage, there was formerly a Harbour, ca-
pable of a fmall Fleet ; the Banks on each fide of it arc
an Evidence it was funk by Induftry; but by Weeds
and Gravel from the Sea, and by Mould annually added,
as is obfervable ’ in Valleys, it is now fo rais’d, that
*tis never flow’d but at high Spring-Tydes, when a ftrong
Wind forceth the Waves into it. This Harbour muft
have been a good Security to part of the Weft fide ;
what other Works might have been to guard it, from
K k k k k k a the

‘ Philof. TranfaCl. An. 1701. N® S74. Pag. $i6.

( 8oi )

the end of the Harbour to the Morals, cannot be faid .;
by reafon the Ground between has for many Ages been
ijn Tillage. It is eafy to imagin of what importance
a Town fortified at this i lace mud have been in ihofe
Ages, when the only Pafs by Land from the Wed to
the tad End of the County was through it ; for other
there could not be, in many Miles North ; unlefs the
Lands, in that Tratd, which are dill very owzy and ten-
der, had been well drain’d.

As the Situation deferib’d, render’d this Place drong;
it is very pleafant withal ; for the Ground is high enough
for a good Frofpetd of the Low Lands adjoining, and
the Country towards Battell ; befides, it has a comman-
ding View over that Bay,- which is between Beachy f/ead
and Haftings, If the Ufe made of it by the Romans,
was to guard the Coad, there was this Advantage be-
longing to it ; that a Centjnel on the top of Bcachj, not
Two- Miles from it, in a cleat Day, without turning
his Body, might fee the J(le of Wight, the Hills in France
near Bologn, and the Nir/r in Kent , fo that from the Nefs
to. Selfey it muft have been a (mall Sail that could efcape
his Eye. It was my purpofe to have added a Defeription
of feven/ey-CMe ; together with an Account of Tome
Rjcmains of Antiquity, difeover’d lad Summer towards
the Wed End of the County : But having been too te-
dious already, mud defer that for the prelent, and fub-
dribe my feif

Toftr moft humble Servant^

John Tabor.

Tiewes, Jan, 26.

x6

1 7..1.

Ill, Trci^dtus

( 8oj )

III. T/'aSlatus de Carvarum Confl niH lone ^ yen-
fura ; ubi plurimit feries CurVarurn hifinttd Vel
reSlis menfurantur vel ad fimpUciores Cur^^as redu’*
cuntur. Jutore Colin Maclaurin, in CoUegio
noyo Abredonenfi Mathefeos Trofejfore.

Ximise Mathefeos Theori^?, ob infinitam Propofiti-
jW num Univerfaiitatem, .secernam ac necen'ariain
■* Veritacem, Evidentiam omni dubitatione majo
rem, Idearum claritacem luculencifllmam, Demonftratio-
num cleganciam, Theorcmacum nexus & mutual depea-
denrias, pulclierrimis certe ac fummis humarii intdicdtus
tepertis Tunt annumerandae ; inter eas vero eminent futn-
morum hujus fxculi Philofophorum de Curvarum Loa-
gitudinibus & arcis menfurandis ardua Theoremata^
Ad hos diffufos cognitionis campos diu alte latentes tanr
dcm cruendos infinite fcienti^e portiunculam mutuari, vix
libi temperare poilet quin pronuntiaret, qui ArithmeticJC
Infinitorum vires in immenfb elegantiflimarum Verita-
turn abyfTo eruendo, & bumani intelledus Horizontem
infinite fere extendendo, paucis practeritis annoriim de-
cadibus, ample fatis comprobatas, animo perpenderit ;
Hujus vero methodi ( ficut nunc auda & exculta efl )
ope, incidi in rationem menfurandi' infinitas Curvarum
feries, quam paucilTimis explicabo.

Cum in omni linea curva fit aliqua curvarurx regula-
ritas licet force implicata, fecundum quam figura detex-
minatur; ideo Geometrce varias Curvarum charaderes ex
if,quationc Ordinatarum relationem ad abfcifTas axis ali-
cujus exprimente definiriinr. Cum vero idem fieri pofBt
ex confideraiions Curvarum refpedu unius dati centri,

iUIQ.!!

( 8o4 )

imo fimplicinTmia Nature uniformitas in ejus indagine id
fieri fepe poflulet, ideo hanc Curvas confiderandi Me-
thod um impra^fentiarum ufurpabimus, & imprimis often-
demus qua facillima ratione ( fecundum hanc Mecho-
dum Curvas detcrminandi ) ex fimpiicibus complexiores
conftrui pofTmc.

§ I. Sint L & / punda quamproxima in Cutva B / L ;
fit / 0 arcus centre S defcriprus perpend icularis in S L ;
& erit L/ ut momentum Curvse & L c momentum Radii
SL.* Ac fi detur ratio L / ad L o, vcl ad / o in diftan-
tia S L, dabitur aquacio Curvx ad centrum S. ,Sint L P,
/ p Tangences Curvae in pundis L & /, in quas ex S de-
miitantur normales S P S p iis occurrences in pundis P
'Sc pi fimiliter in omnes Curvx Tangentes dem^ttantur
perpendiculares ex dato pundo S, & conftruecur Car-
va tranfiens per omnes Tangentium & perpendiculorum
interfedioncs. Hujus triangulum elementare P p fi-
mile erit tiiangulo L <? /, qua proinde dabitur ex data
• Curva B I L. Quippe ob aquales S/?/>, P L, & redos
S S P L aquiangula erunt triangula Sp n, P » L, &

ta ratione L/ ad lo, Sc reda S L, dari rationem P/> ad
p jiSi redam S P, adeoque Curvam DP p. Eadem ratio-
ne ex D P conRrui poteft Tertia, & ex ea dein Quarta,
& progrediendo prodibit feries Curvarum infinita, qu^E
• omnes ex uno dato innotefeunt. Quod fi erigantur L N

proinde P : pn :: L n:
S» :: L <7 : I o, adeoq;
ob angulos P » />, S « L,
hoi sequales, erunt tri-
angula P»p, S;?L, Lei
fimilia. Cum igitur ea-
dem fit ratio hi ad
qu£E P/>ad pn,ScSh ad
S P, manifeftum eft, da-

( 8oj )

^ 1 3^ perpend iculares in radios S L, S /, fibi mutuo oc-
currences in » ; & per omnia fimiliter definita perpendi-
cularium concurfuum pun6la defcribatur Curva E N: ca ?
ipfa eric Curva ex qua deduci pocell B L, eadem ratio-
ne qua conftruximus D P ex B L. Ex E N fimiliter
conftrui poteft alia Curva, atque ex hac quoque parce
Series infinita Curvarum conftrui poteric.

^ II. Curvarum vcro hac racione confidcratarum fimr
pliciftimsE lime quarum L / eft ad L t? in rarione pore» ~
ftatis alicujus Radii, ita uc, ft a fjc data quanticas, r de-
nocet Radium Curv^e, » numerum queracunque, fit L/ '
ad / (j ut 4” ad r” aequatio earum gencralis. Omnes ve-
ro hx Apfidem habenc cum rz^zaj quoniam in eo cafu ;
L /— / 0. Ut inveftigem aequacionem Curves D P, cum in 4

B L eft ut L / ad I o a" ad r”, ita r ad S Pr= — , ita ?.

X S P^+T ad S P, ita ad S P"+q ita P /» ad ,

Proinde ft s reprefentet momentum Curvae, ^ ar-
Gum circularem radio deferiptum a cencro S, 8c r radium >
correfpondentem, qusecunque fit Curva cujus ^Equacio »
inveftigatur, erit i^quatio Curvas B L, s y :: 4” : r”;

Aquatic vero Curv:e DP, / : : 4»TT ’ Angulus ^

autem P S /> eric ad Angulum L S / ut || ad five

ut ^ ad vel ( ft S Pdicatur a: & S L, ^ ) ut ad C ^ ,

hoc eft, ( ob ) ut ^ ad C,fiveut »-|-£ ad r, ,

Hinc ( vid. Fig. II. ) B S P eft ad B S L uc n-\-i ad i ; ,
unde facilius abfque Tangentium ope duci poteft Cur-
va B P. Si fumacur angulus BSP ad BS L in rations •
»~\~i ad I, & in S P demittatur perpendicularis ex Lt
eric occurfus perpendiculi cum S P, in Curva B P prius >
Tangentium ope deferipta.

^ ill. Oftea^^.^.

( 80(5 )

^ ni. Oflendimus quo pado ex una feries Curvarum
infinita deducicur; quo vero padto f'ngularum longitu-
dines ex illius & unius altetius longitudimbus datis in-
notefcant pergo demonftrare. Cum angulus S P S L /,

atque L $/ fit ad P S/> ut i ad »+i, erit L / ad P/» uc
S L ad n-\-i S P, (ive ^ ob S L : S l: LI : I o) ut L/
ad »-\-l 1 0, ac proinde P p=n-\-i / o : ted / g— / n — o n

= / n — L N4"N n ; ergo P 1 x / n — L N-}-N »,

Sed I n — L N eft momenrum re<ft2e L N normalis in S L,
P p momentum CurviE BP, & N » momentum Curv;2
B N : Cumque BP, BN, B L fimul evanetcanc in B, e-
runt in ratione momentorum, adeoque BP— k-|-ix
B N-|-vel — L N. Unde Curva B P eft ad fummam vel
differentiam Curvse penultimae in Serie ejufque Tangen*
tis ab intermedia interceptx, ut »-|-i ad i ; five, fiwfic

Index xquationis Curvx 6 P ( quoniam ^ ut i

ad I— .7».

Hinc I’”" in ferie Curvarum infinite fupra defcript^, ft
dentur Longitudines duarum proximarum, dabuntur
longitudines omnium ; quippe menfiira cujufvis pendet a
fnenfura penultimx femper in (erie, & proinde imum

par

( 867 )

' par oinnibus menfurandis fufficiec : Si uria CurVa
dis commenfurabilis vel incommenfurabilis, erit integras
feriei pars dimidia redis commenfurabilis vel incommen-
furabilis. Hinc 1''*. Licet CurvsE'B P & B N eflent recSlis
incommenfurabiles, differentia tamen Curvse B P ab
»-f~* CurvscBN effet sequalis affignabili redse, 3’’. Si
Gurva tranfit per S, reciia LN evanefcente in^, eric

BPS:

BNS

I — w»

^ IV. Curvarum de quibus egimus, quarum nimi-
rum j : y : ; a” : r”, raaxime infignis eft Circulus, exi-
ftente S in circumferentia, cujus sequatio eft i ; : : a': r,

uc ex fimilitudine triangulorum Lol, B L S ( Fig, HI. )

manifeftum eft, adeoque ; 8c proinde

« • I I . ^

.& asquatio Curvae B P crit s : y ii t r", quae ipfa eft:
aequatio Eficycloidis revolutione Circuli fuper baftm fibi
! aequalem revolventis defcripti, ad pundum ubi puniftum
i iefcribens tangit bafrni, quae D"° Pafchl dicitur la tz-
! Llllll

t

( 8o8 ;

mASoyi de M> Roherval, quatnque De la Hirt confiderat ^
ut Comhoidm Bafis Circularis, in Adlis Academism Pa-
rifienfis Anni 1708. Perpendicularcs omnesLN, In
concurrunt in pundo B, adeoque BNr=o: unde B P=

tB L : Hinc Cutva tota B P S=^ B S, ac Ion-

I — m ^

g\t\xdo Epcycloidis femperdupla eft chords arcus in cir- .
culo correfpondentis. ‘Ex Eftqcloide defcribacuc

Curva BnS, eadem ratione qua Epicjcloidm ex Cir-

culo defcripfimus : In hoccafu>?=r» &

4-f*

_ • • * f

z=z\, ac proinde squatio Curvs BnS eric s : y :: a^:r^

BL-fLP

Longitude Curvs eric — rBL-|-LP=^BL-|-LG,

& proinde Bn eft fefquiplus fumms Arcus circularis ejuf-
que Sinus redi. Quod ft fumatur C D^B D, & radio
S D centre S deferibatur Circulus occurrens reds S P in
H, & ftt H K perpendicularis in B S; quoniam D H=
jBL, eric B n=D H-j-H K. Hinc arcus Bn neque
lunt redis neque arcubus circularibus commenfurabi-
les, differentia tamen arcuum Bn & DH eft reda
H K. In pundo S evanelcit LG, adeoque Bn S=tB L S,
unde tota Curva eft fefcupla femicirculi. Nulla vero
pars hujus Curvs alBgnabilis commenfurari poceft toti,
nee Integra Curva in data quavis ratione fccabilis eft,
ita ut portiones rationem affignabilem habeant ad fe mu-
tuo aut ad totam. Si hsc curva in data aliqua ratione
Geomecfice fecari poffec, conftarec Quadratura Circuli,
nam fi e.gr. eflet B n ad B n S ut i ad w, & BL ad B L S

ut I ad », eflet Bn=--=— = = HT+lg „

unde eflet H & B L S=:^. L G j"' Ex BnS

ft — M

conftruatuj: explicata. methodo Curva B R, & quoniam

( Sop )

"i -

i?~erit atque ^quatio Curv^ BR etk

Yl ^1

» • 'L * -

s : j i: afi : , Hinc longitude Curvae fiet |xBL-|-Pn,

totalis veto Longitude Curvs BRS=:^ diametri SB.
Si harum Curvafum Conftrudiones continuentur, prodi-
bit, hujufmodi feries ^^quationum quse facile produd-
tur ad libitum.

« •

iLquatio Circuli i. s : y : : a > r

• * r I •

Epicycle id is 2. s : y : : : r

• • r r

Secundi 3. s : j : : a’-' i

• • J I

Tercii q. s : y :

• • It

Cujufvis n. Sly : : i r ^

Cbfervare licet in genere, omnes quarumTndicum deno»
minatores funt Numeri pares, perfedse redilicationis elie
capaces ; cumque qujsvis fit ad penultimam ut i ad i —
perpendenti nianifellum erit Curvse cujiifvis longicudi-

nem fore

: — m

X

I — 2»I 1— 4»»

-6m

l — 3»J ^ I— 5»i ^ I — 7»2-

&c* X SB

continuando feriem donee ad nihilum reducatur Fradio.
Quod fi Indicis denominator fit Numerus impar, Curvae
erunt perfedte rediiicationis incapaces, & earum arcus
quicunque erunt fibi mutuo, ipfis totis, redis quibufyis
& arcubus Circularibus incommenfurabiles : exprimi veto
polTunt omnes arcubus circularibus & redis : At Cur-
vac cujufvis totalis Longitude erit ad Semicirculum ut

* X X ad unitatem. Denique fi Areo-

I — m

-3»j

la a Corpore in harum quavis revolvente fumatur con-
dans, hoc ed fi ry=.i, fubtenfa anguli contadus, cui
femper ( ob datum data area tempus ) proportionalis ed
FisCentripeta tendens ad S, eric reciproce ut potedas di-
dantiae cujus Index ed % m-\-^ ; atque hoc ed non con-
L 11 111 X temnenduni

(^8iO; ) '

t^mnendum harum Curvarum privilegiujm, quod in iis .
omnibus Vis centripeta tendons ad S fit uc aliqua reci-
proca diftantise dignitas, quse^fimpliciflima eft, & utiliC- .
iima in Naturse indagine, Virium Centripetarum lex.

• • n H

iT.,V. Curvarum quarum i : y .a : r proxime con*
fiderandajcnic ( qqse Curva quidem improprie dicitur)
ip(a Linea recfta, exiftence S extra redam. > In hac li-
Jifa,, obrfimilia crianguia P /» », PBS erit C H B Srz= a &
S^^r) / : y :.vr : 4. Ex linea reda mechodo diredi a

nihil nifi pundum B conftrui poteft, Mechodo veto in- v
versi>' perpendicularium nimirum P L,r pi concurfu. con-
ftfui 4>Qceft .Cutva, cujus Index .( fi m fit Index Curvae

B-P ) sequalis erit — ^ ; nam fi Index Curvse B L fit #,
eric ac proinde Unde in hoc cafu,

cum «i£= — I erit & ;^quacio Curvse B L eric

. ^ . i , i ■

5 : r‘ : 4*, quse xquatio eft Parabolse ad Focum. Ex
hac <onftrue aliam, conftituendo anguJum- L S N=2;L S B

6 erigendo ,L N normalem in S L occurrentem ipfi SN

inN..Quoniam vero«w=~ erit & sequatio Cur-

• • * I RN I

& B =iBN — LN, ergo

I

t 8ii >

P^-L N ; proinde hnsc Curva eft recftificabilis.. •
Si Series cojicinuetur, prodibunt uc prius xquationes in -
hoc ordine.

^quatio Re<ftae

s : y : ; r t a

Parabolae

• • It

Sly : r F :

Secundae

• • Z 7

Sly 11 F 1 0}

Tdti^

Sly : : F i a*

Cujufvis

• • II

Sly : r^i^'

In’ hac Serie primas funt Reda & Parabola,' unde pa-> ■
' tet dimidiam hujus fimilicer ac prioris Seriei efle recftis -
menfurabilem *. alia vero dimidia pars in recftis & arcu-‘

1 bus Parabolicis exhiberi poteft. In his omnibus Vis cen-
: tripeta ad S eft redproce uc poteft as diftantiae cujus In-^

I dex 3 — zw, ac proinde femper inter duplicatam & tripli-.

I catam racionem diftanciae reciproce.

^ VI. i£quatio- Hyperbolae aequilater^E ad centrum «

eft J : jr : : r ; ex qua deducitur methodo dire<fta Se- -
ries hujufmodi, .

• > • 2 2

I. : y : : ^ ' a-

. . * 2

z, s : f .* : ^ • r

. i. *

3. j :y :: /i’ '•

• •

4. i : ^ : 4 5 ifT

• ’ 2 2

S* S' y : :

Ex bis Curvae, quarumbridicum denominatores funt in j
progre/Tione— I, 3, 7, itt&c. exhiberi poflurir in redis ’
& arcubus Hyperbolicis ; reliquae vero in rediis & arcubus
Curvae, cujus aequatio ad axem S B (fix fit abfcifta, f
vero Ordinata ) eft x-]-yy quaeque con*

ftiuitur . ( vid. Fig, Ml ) bilecando angulum B S L

fumendo

( 8ii )

fumendo SN mediam proportionalem inter SB & SL.'
Curv^ qux ex Hyperbola methodo inverfa conftrui
, pofTunc progrediuntur in hac Serie,

■ : ■ . ' -2 2
Hyperbola i. s : y :: r : a

• • . . * i

a. s : j ::

• • 2 a

. 5. s : y : : ri :

' Ubi CtirvK quarum Jndicum denominatores funt in pro-
.greffione i, 5, 9, 13, (^^c. exprimi polTunc in reiJtis &
arcubns Hypeibolicis; reliqua; vero in redis & arcubus
Curv^e modo explfcacx.

Si ali;2 Curvae defiderentur quce alias exhiberent Se-
ries, id facillime fieri potefl ope vel Circuli vel Redsc :

h n

ex eamm aliqua omnes, in quibus s : y'l a : r,
conftrui poflunr, fumendo, fi o-
pe Circuli Problema fit folven-
dum, BSR ad BSL uc i ad

»— r 1

&SNinipraSR=^ ” xSL”;
quippe Curvae pet omnia pun-

• • n n

^ua N dudiE ^quatio eric s : y : : a : r . Similiter ope

• . n n

Redse conftrui poflunt quarum icquatio s : y :: r : a-.

Duas exhibuimus Series infinitas Curvarum redis
commenfurabilium ; aliam arcubus circularibus, aliam
Parabolicis, .aliam Hyperbolicis una cum redis menfu-
rabiles demonftravimus : ex vero ad redarum menfu-
ram arte fola infinica reduci pofTe videntur, ficut X-
-^quatione fola infinica in redis exprimuntur.

Cl. Author hrevitati fiudms paucis tradit, tlltm
'tern fknius rem pro dignitate ejus iUuflraturum fperamus,

IV. ^mar^s

( )

IV. ^marks on a Fragment of an old Roman In*
fcription lately found in the Morth of England,
and tranfcribed hy the Curious and Learned I
James Jurin, M D. and Reg. Soc. S.

^UR worthy Member, Dr. Jttrin, having refi-
ded for Tome time at Neircafile upon Twe, had
the Curiofity to travel the Country between
that and Carlijle, in order to obferve what might oc-
cur worth notice in the Remains of the Ruins of the
famous Ti^isWally built by the Romans to fecure them-
felves, againfl; the Incurfions of the Natives of that
part of Britain they cared not to conquer, fn this
Perambulation, befides many other valuable Obferva-
tions which in- time he may be prevail’d with to bellow
on the Publick, Dr. lurin faw and tranfcrib’d no lefe
than Twenty Roman Infcriptions, fome of which we had
formerly receiv’d from others, but many of them whol-
ly new; among them the following, which, tho’ broken
and in great part illegible, fuffices to fix the Name of
one of the Ancient Nations of Britain, that has hithei-
to been greatly mifcaird, ’Tis thus.

CIVITATE CAT
VV I L L A V A'
ORVM- L- OC 6-
C D / 0 '

and is to be feen on the Wall, about two Miles Wefl
from Lenercrofs-Abhy, near the Confines of our two Nor-
thermoft Counties. ,. ,;

Here,

( 8i4 )

' Here ’tis obfervable, that the laft A of the fecond |
.' Line has a Mark that follows it, not unlike to the laft
Stroak of an M ; and if inftead of we put N, we ^

dhall read it CIVITATE CATVVI LLAVNORVM, }
which we cannot doubt to have been the true Name of
that People which Dion. Cajjius, Lib. LX» calls Ka7«eA- *
. AaroJ, and Ptolom% in his Geography, Lth.W. cap. |

more falfly, Kccfveux^^ctyoi ; the firft A by producing the 3

tranfverle Stroak having been miftaken for This Na-
rion appears by Dion to have been more potent than their ;
Neighbours the Dohuni (whom he calls Boduni) and had,
according to Ftolomy, f^erolamium for their Capital, which
’tis moft probable, was the Caj[fivelUuni oppidum of ^ ]

far. So that it Ihould leem Cafftvellaunus King of thefe
Catuvillauni when C<e[ar invaded Britain^ cither gave i
his Name to his People, or took theirs. But he was no
doubt the moft potent Prince at that time in Britain^
fince by common Confent of the reft, he was made Gc-
:neral of their united Forces, in defence of their Coun-
itry’s Caufe againft the Romam.-

Printed for W. and J. Inny s, Printers to the Royal
Society^ at the Princes-Arms at the Weft-End o{Si.Pa»l'^
Church Yard* 1718.

1 K 1 S.

ERRATUM,

Page 770, lin. 2 x. for Maii ^ i , lege Marti! jr.

( 8ip ) Number 357*

PHILOSOPHICAL

TRANSACTIONS,

For the Months July ^ Jugujl^ and Septemh, 1718.

J 9 , I IM I ■■ ■ I I ■■■■ . —

The CONTENTS.

I. Conteta Berolini m^er vifi ohfervatioms^ ut & Eclipfeos
Solaris Feb. 1 9. vuney Noribergas ^ Berolini habita,

j r Novis Litterariis Berolinenfibus, hoc anno primitm
1 edi coeptis, dtfumpt£.

II. A Difeourfe occafiond by an Infcription found, about
Three Tears ago, at Langchefter in the Bifhoprick of
Durham, and communicated to 'the^oyA Society from
Dr. Hunter by Dr. Woodward, as it is printed in the
Thilojophical TranfaUions, N° 345;. By Roger Gale,
Efquire, R. S. S,

III. A Letter of that curious Naturalif Mr. Hen. Barham,
R, S. S, to the Publifjer, giving a Relation of a fiery
Meteor feen- by him, in Jamaica, to flrike into the
Earth 3 with Remarks on the Weather, Earthquakes,

of that JJland.

IV. An Attempt to prove the Antiquity of the Venereal
Difeafe, long before the Difeovery of the Weft'lndies;
in a Letter from William Beckett, Surgeon, to
Dr, James Dowglas, M, D. and R. Soc.Soc, and by
him communicated to the Royal Society.

V. Accuratarum Ohfervationum Agronomic arum, anno fu-
periore df currente cum Reg* Societate commimicata~
rum, Sylloge.

Mmmmmm 1. Cometa

I. Comet dt nuper Vtji obferyatlones^ ut

Edipfeos Solaris Feb. 1 9''° mane^ Noribergae
Berolini hahit^e, e Novis Litterariis Beio-
linenfibus, hoc a?ino primum edi captis, defumptie,

L. Chriftfridus Kirchiuss motus Corporum ccelc-

Aiuni) ut luunere fibi ^ Societate Scientiarum

Regia ( Berolini ) demandato red:e fungeretur,
fedul6 obfervans, a. d: XV. Kal. Febr. (Jm 1% fi.n.)
anni prsefentis, vefperi dimidid Septim^, verfus Septen-
triones fortuito Comecam confpexit. Vicinus crat ad
dexcram (ftellarum) y ^ ^ Bayeri inUrfa minore, nudo-
que oculo longe diftindius apparebat, quam /3 Urfa mi-
noris , licet ea infignis fit Stella fecundae magnitudinis,
cum longe pallidjot quidem majore tamcn diametro,
atque fatis data luce maxime circa centrum, confpice-
retur. Fer Tubum vifus lucidam rotundamque refere-
bat nubeculam ; Caudae autem nullum obfervari potuit
veftigium, neque Nucleus dignofci Motu celerrimo
ab bora VII. ad XI. proceflit, gradufque quatuor cum
dimidio abfolvit, ut ex obfervatiombus colligitur.

Die 19"° & 10'”° Januarii coelum nubibus fuit obdu-
dum. Die vero Cometa longe receflerat k loco'
fuo nupero, atque in Caffiopea deprehcndebaiur, ubi
cum ftellis g & cT triangulum conficiebat (an d^uicrure ? )
fcil. Hora 5'' 45' in 17° 34' v, fub latitudine Boreali
49° 54' bserebat: Deinde 9^ 15*, in 16° 38' ^ fub
Lac- Bor, 49° x' confpiciebatur. Cseterum multum de-
cieverat) atque a celeritate fua remiferat ; pricterquam
enim quod pallidior quam ante apparebat, Rellas etiam
quartan, dignitatis magnitudine baud fupeiare nudo ocu-

lo

( 8ii )

lo confpedus videbatur. inque crbita fua, quataor cum
dimidia horis, non ultra 'idqjigradiini :

Tubi autem beneficio diameter ejus 7 min. invenie-

batur.

jfav. a9 bora IV. mat Cometa cum >$( (p
triangulum squicrurum efficiebac, cum ab utraque
41 1 abefict Hoc mane duarum hcrarum fpatio vix
dimidium gradum abfolvit; bora decima' vcfpertina
cum Cajiepe^ & 9, Ferfei in iinea reda cernebatur,
atque a priori 3° 38', a poftcriori 3° 9' dillabat. Dia-
meter ejus erat $ min. nudoque oculo confpedus ftel- >
lam quintse magnitudinis referebat.

Die Z4'° Jdff. bora VI. mat nondum attigerat (p.Per-
fei^ fed cum o ejufdem Afterifmi triangulum asqui--
crurum fiftebat, & ab utraque non plane 3r grad, ab--
erat. Plura ex obfervationibus docebit Aftrophilos Vic.
accuratiflimus, in pleniori quam parat hujus Comette.
Hidoria.

H»5ienus Nova Litteraria pag- 43, qq. uhi defi^-
derantur Ohfervatknes Dki 18''"', cum Cometa velocijfime
mot us terr^ froxiims erat, unde ccrtius de Via ejus tarn,
vera quam apparente judicium ferre poffemus. Mamfe^-<
flum autem e(l eum Polo ^quatoris Boreo vicinijjtmum die ■
Januarii 19"° tranjtijfe, ^od ft cm liheat has Obferva*-
tiones ad examen revocare-, calculoque accurate fubjicere 5 in
illim gr at i am, loca Stellarum fix arum, quarum hie fit men^
tie, ex Catalogo Britannico excerpt a, fubne^untur : Unde -
etiam patebit nonnulla in hac motm Cometa de/criptione baud I
rite fe habere % qua tamen a Cl. Kirchio corrigi, in pU^:-
niori ejus quam promifit hifioria, fpes tfi.

Stellarum i

( Six )

SteOarum fxarum Loc4 inemte ^nm 1 71 8.

BAYERO

'Long. 1 Lac. Bor.

0 ' "(o'."

Ur [a minor i^ ^

1 y

fT. 9 18 072 58 1 0

17 3^ 13 15

C S'

Qaffiope£ ■< g

C <p

y 14 00

y 20 50 8(47 31 50
>r II ^6 354f 4 5

c ^

Perfei J q>

c ?

b- 8 32 035 23 45

V 10 41 35 35 49 iq
^ iz 15 2c(35 18 37

£x iifdem Novis etiam ohinuimus dttplicem ohfervati(h
nem Eclipfeos exiguA Solaris ^ currcntis a»/>i Feb. 19'“ ft. ver.
wane celeb rat A '-i alteram Noribergce a CL £). W urtzelbau,
alteram a prafato D. Kirchio Berolini hahitam,

' Noribergce autem Sol ortus efl aliquantulum deficiens in
limbo fupcrioref qui quidem defeLtus ad tres flene digi-
tos accrevit j Defiit Eelipjis 8'’ 8' 48'' circa 60 grad, d
Vertice Solis ad Stniflras. Berolini veto Sol Jlatim ah or~
tu ccepit dtficere^ Hora ftil. 6 49^ '^il r» Circa me~
dium Eclipfeos, nempe 7^ erant Partes lucidA in Sole
refiduA 24' 40", unde digiti ohfcurati 50'. Finis
' autem incidit S'* 28' id‘. ^ui pluta de his cupit, adeat
Nova ipfa Berolini edita.

II. A

( 8ij )

IT, A D/fcourfe occajtond Ij an Infer ipticn found, about Throe
Tears ago, at Langchefler in the Bijhoprick of Durham,
and communicated to the Royal Sociecy from Dr. Hunter
hf Dr. Woodward, as it is printed in the Philofophical
Tranfaliions, N'’ 354. By Roger Gale, Efq\ R. S. S,

Dr. Hunter, who communicated this infeription,'
having only given us his Conjedlutes as to the
firft fortifying the Place where it was found,
and the Time of its Repair after it had been deftroy’d,
but faid nothing relating to the Explanation of the In-
feription itfelf, tho* extremely curious ; it will not, 1
hope, be taken amifs, if I offer fome Thoughts that oc-
curr’d to me at firft fight of it, and afterwards indu-
ced me to put together what follows upon that Sub-
jedl. I fhall not in the lead difpute or call in queftion
the Time of its Foundation, as fix’d by the Dodor,
but begin with the Place where it was difeover’d, name-
ly Langchefier or Lancafter, in the Bilhoprick of Dur^
ham, which I am, ‘ with him, fully perfuaded was the
Longovicus, where the Notitia Imperii places the Hume-*
rus Longovicariorum.

This place is feated upon a great Military Way, a-
bout I % Miles diftance from Blnchejler, and 7 from Eb*
chefter, the one the Vinovta, and the other the Findome-
ra of Antoninus, as the Correfpondence of the Numbers
may evince; Binchefter being 19 Roman from Bb~
chefler, as that is 9 from Corhridge, the exadl Numbers
the Itinerary gives us between Vinovia, Findomora, and
Corjlopitum. What is very ftrange is, that the Itinerary,
which mufl: go upon the great Road dircdly thro’ this
t Nnnnnn Town

’ Wilofepb, Travf, N® 2^5. p. ^57. * Not, Imp. fol. 17^.

( 8*4 )

Town of hongovicus betwixt Vindomon and VinovU,
takes not the lead Notice of it, but meaiuresche Way
at the whole Length and Number of Miles, fiom the
firft to the latter of thofc Stations. If Lo>'<gcvtcu- was
founded, as Or. Hunter fuppofes fo early as the
Time of Julius Agricola^ and if that Itiner*rj was com-
pofed by any of the Emperors that bore the Name of
Antoninus, this Station might have been deftroy’d or
deferred during the Wars wirh the Britains. and not bc-
ing repair’d till the Reign of Gordian I if. was pa(s*d over
by the Author of the itinerary, as a Camp not then in be-
ing, or of no ufe to the Armies ; and this would

be no weak Argument for tlie Antiquity of that Work i
And perhaps feme Parts of it may have been defcribed
as early as the Reigns of thole Emperors, or earlier, and
fuch Names of more modern Places as are found in it.
may have been afterwards added as Occafion requir'd.
As a farther Confirmation of this Conjedfure, I beg leave
to obferve, that this Place, after it was repair d by Gor-
dian, fubfifted even to the Roine of the B$mjn Empire in
Britain, as is evident by the Mention of it in the NotitU
Imperii', fo that had this '' Journey which carries us from
Vindomora to Vinovia been compos’d after ihe Reign of
Gordian, it would be very hard to account for the Omi&
fion of this remarkable Station and Towm, a'< if appears
to have been from this, and many otlier Inicriptiona
found there

Having this Opportunity of doing it f am unwillmg to
iet it flip without redif) ing a Miftake in the t jjjy towards
the Beeevery of the Roman Highways Rritam, printed
in the Volume of Mr. Hearnc’i Itinerary of L eland
which having brought the Erming/lreet ( not the
iingflreet, as Or Hunter and the Country call it) alirtle
beyond Cattarkk in Torkjhire, divides k there into two

Branches.

N° 354. p.701. t P.111,114,

c 8zj )

Branclies, tradng one of them to TlnmtmtJfj and tfie otlicr
to iafiifle, but omits the maiiiStemmof ic, tiiat runs al-
fnoft dtrediy Northward to Piercehrt^gf, (o to Denton,
liou^htcn, binche(ier, Lan^ch'0er, Ehchifter, Corhridge^
and through the Heart of Northumberland into Scotland,
about a Mile and a half to the Weft of Berwick, ft is in
fevcral places very intire and fair, efpedally between Cor-
bridge and Binch^fler, the Ridge of it there being for the
tnoft part two Yards in Height above the Level of the
Soil, no lefsthan Eight Yards broad, and all pav’d with
Stones, that are as even as if new laid : as I am inform’d
by the ingenious Mr. Warhurton, who has often view’d
it, and to whom we are obliged for the moft accurate
and ufeful Map of the County of Northumberland that
was ever yet publifh’d. This Digrefllon, if it may be fo
call’d, I hope will be excus’d, lince it not only fets light
an Error, but acquaints you with a noble Roman Way^
fcarcely yet known or obferv’d by any body.

Having fix’d the Seat of this Long vicus, where the
Infcription was found, let us conlider next what fort of
a Place it was; and upon due Enquiry it will appear to
have been one of the mod ancient and eminent stations*
the Romans were poftels’d of in thefe Parts. As to its
Antiquity, Dr. Hunter has made it probable, that we
ought to look for it as high as ']ultus ^^r/V^/a’s command-
ing under Domitian, in this I Hand : As to its Emincncy,
the Infcription that came laft from him to the Society as
well as feveral others found there, is an undeniable Evi-
dence-of its being a Place of great Confideratioti ; but
nothing can put that more out of Di fpute than the firft
which was iome Years ago tranfmitted by the fame
Hand ^ which therefore I beg leave to infert here with
that which came laft from him, and the rather becaufe
little or nothing has ever been (aid upon it, and that they
will give great Light one to the other.

Nnnnnnx I^P

i Fhil. TCturf. N<* 266.

IM* C^M NT G-EDI A

N«-PmGM2&M0M

B'S*GAfclNTRVXT

PRENfcOJl^NM LB AG

TRPRGRIITMAVTl

OYTRINCffRECoHILGR

IT.

MPCASAR M ANT-N AS
G«RDI ANAS P F AVG
PELNCIPIAFTARMAFER
TARI A CONBPSARBTT

ITEERMEPEVMIVSeMIEG

AVGPRPRGRANTEMAVR
' QVIRINO PR OH IT GOR

( 827 )

The Stone whereon the firfl: is cut has been broke
in two, whereby feme of the Letters are defaced, how-
ever, it may be very well read as follows ; the Letters
PRE in the fourth Line I take to be a Miftake of the
Workman, having feeri feveral Copies, where they are
fo tranferibed; that they lliould be PER is evident
from the fifth Line of the fecond Infciiption.

I. ImperAtor Cafar Marcus Antonm Gordianus
fzus Felix Augujlus Balneum cum
Eafilica a folo inftruxit ^

Ter Qneium Luciliamm Legatum Augaflalem
Propratorem Cur ante Marco Aur,elio
Huirino PrzefeSio cohort is prim£ Longovicariorum] or
rather, Legionis Cordiana,

The (econd can be read only after the following
manner.

IF. Jmperator Csfar Marcus Antonius
Gordianus Pius Felix Augufttis
Principia Armamentaria ^

Conlapfa rejlituit

Per Mdcllium Fufeum Legatum

Augujlalem Propratorem curante Marco AuriUo-

^irino PrrefeSto Qohortis prima Legionis Gordianee.

From thefe Two Infcriptions compar’d together, it
will be apparent that they were not only eroded un-'
der the fame Emperor, but by the Care of the very
fame Petibn Aurelluc ^uirinus, tho’ not in the fame
Year^ The Emperor can be no other than Gordianus
the youngeft, or third of that Name ; the two former
having been flain fb very fbon after they had afliimed
the Purple, that it is improbable they Ihould have gi-
ven*

( 8i8 )

vcn any Orders or Commands for the crewing of new,
and repairing of antienc Buildings, in (b remote a Pro-
vince as Britain was from Africa ^ where they w’erc
murder d after a fliorc joint Reign of fcarce (even Weeks.

‘ Dr„ Hunter ceils us, that that which was firft dil-
cover’d ( and which I (hall therefore always diOinguifh
by the Name of the firft ) was dug up about a Hundred
Yards Eaft from a great Square, which had been forcihed
with a thick, ftrong Wall, faced with he wen Stone,
within which, and without, efpecially towards the Eaft,
are nothing but ruinous Heaps of Stone, and thinks the
Lodging of the Garifon only to have been included with-
in ihofe Walls. His Conjedurc is very much confirm-
ed by the * Account he gives us of the finding the laft
Infcription within that fquare Inclofure ; fo that there
feems to have been at this Longovicus a large Town, and
• one of thofe Camps call’d Cafira ftativa, where the Lc-
, gions lay in Quarters during the time of Peace and
Quiet.

The firft Infcription tells us, that the Emperor Gordian
' built the Balneum and Bafilica from the Ground, a Solo;
whereas, ^by the fecond he appears to have been only
' the Repairer of the Princifiia and Armamentaria. Per-
haps therefore here might be no Town, till the Romans
thought fit to repair their old deferred Camp at this
Place, ^nd then the Emperor might alfo build the Bath
and Palace for the Refidence of the Preprator, when in
chefe Parts of Britain ; the Word Bafilita importing both
a Palace, and an Edifice for hearing of Cau fes, and
cranfaefting ail publick Affairs. As this eminent Buil-
ding was ereefted by the Emperor's Command, it is
.an undeniable Argument of the Splendor of this Town,
: as are the great Heaps of Rubbifh, and RuineSj where

this

2 thh, TranJ. N* p. 658.

I tbii. Trsn/. N® 354.

( 8i? )

this ^nfcription was found, of its Largenefs and Ex-
tenc-

1 he fecond equally puts the being of the Cafirum fid*
tivum out of difpute, when it acquaints us with the Re-
building of the Armamentaria ^nd Prtneipia there, that fS^
the Arcenali and Quarters either of the Legionary Soldi-
ers, that were call’d the Principe^, or the place where
the Fagles and other military Enfigns were kept. It is ^
probable they did not belong to one particular Legion,
but to leveral, as they had occafion to be employ’d here ;

‘ tho the Legio fexta ViSirix Teems to have the bed ^
Title to them, as being conQantly quarter’d in the
North 3 whereas, the ^ Legio Secunda, and * Ficefimd
were generally garrifon’d, the firft at Caerleon in VVales
and Richhurrovp in Kent^ and the other at and about Che-
fier\ To that the ^ Monuments they have left in the
North were ereded by them, when the Wars, and other ,
Works, as particularly the Walls carry’d crofs the Ifland,
calld them thither; which being finilh’d, they returned
home to their more Southern Quarters, and continu d .
in them till commanded Abroad upon new Services. I
will not pretend to determin when thefe Armamentaria
and I rincipia fird fell to ruin ; perhaps it might be
when Hadrian, Lollius Urbicus and Severus had car**
ried their Conquefts farther into the Enemy’s Country,
and having built thofe famous WalL^ the Relicks of
which we ftill fee in the Shire of Sterling in Scotland, and ^
in tforfh^mherland and Cum’^e^land in En^i^land, that this
Camp might be thought ufelefs, the Roman Forces be--
ing drawn nea-er to, and quarter’d upon the Frontiers;
and lo this Fortrefs abandoned and tulferd to fall into >
decay, as the Word conlapfa implie : and not that it ^

was -

• PtA. Leg. VI. Niceph . Eb»r heat, ® Anton, [tin. Not Imp. -

p. i6i. J jintop. bin. IL ^ Camd. p. S35, ^io. thU, %rapj> N®

( 8jo )

was deftroy’d by any Fire, War, or other Enemy than
Age and Neglect.

Tho’ the Word conlapfa is wrote here with an iST, there
can be no doubt but the Pronunciation of it was as we
ufually find it fpelt, collapfa ; a certain Argument of the
Letter N’s being filent in the middle of a W ord, before
two Confonants, efpecially NS, and NT, when the T
was pronounced like an S. To omit what ' ^intitian
fays to this purpol’e, it is confirm’d by the Abfence of
that Letter in numberlefs Infcriptions in Gruter^ Reine-
Jius, ^c. and no wonder, fince the Workmen in thofc
Days, as well as ours, ufually wrote as they fpoke their
Words. 1 fliall nor trouble you with Quotations of any
of them to this end, but as a Proof of what f fay, on-
ly affure you from ocular Infpedion and a moft accu-
rate Examination . that there is no trarifyerfe Line over
the Letters tS belonging to the Word FABRIQESIS in
the inferiprion of IVL. VITALI at Bath, whatever
has been affirm’d to the contrary, but that the Letter
N is totaly omitted there. Yon will alfo pardon my
Endeavours, before I leave this Subject, to explain a
ihort fnfeription belonging to fome of our Countrymen,
tho* found at Amerhach in Germany \ fince it will be a
new Proof of the foregoing Afiertion.

III.

NYMPHIS'^
N 9 BRITTON
TRIPVTIEN
SVB CVRA 9
VLPI
MALCHU
!>LEG XXII

Nymfbis.

l^umerus Brittonum
Triputienjis, or —

Sub cur a
Marci Ulpii
Malchi

CenturionU Leg. 22.
Trmigenia, Via, Felicis.

PR<j.P<?F<f

There

! Ipjfit, Li|>. I. c. 7;

* Cruter. p, xclil.

{ )

There is no Difficulty butrin the Word TRIPVTIEN,
and that will prefently vanifh if you infert the Letter N.
and read it TRIPVNT, /. e. Trifontienus or Trifontienjis,
the Mutation of the O and V being fo frequent, that
no body is ignorant of it. This will bring you to TVi-
fontium ‘ or Dorvhridge in Morthamptonjhire-^ tho’ that ex-
cellent Antiquary Dr. Battdy % in his Amicjuitates Ru-
tQfin£, would read it RiPVTiEN, and fix’d the Place
whence this Numerus took its Appellation at RichhurroTP
in Kent.

But to return where we left the Camp at Longovicus,
it will be as difficult to affign a Reafon for its being
repaired, as it was for its being deferred ; unlefs that
the Frcpr^tors might judge it advifable about the Time
of Gordian III. to fix their Refidence there, and confe-
quently refortify the old Camp for their State and Se-
curity. And that it was not refortify ’d upon any fud-
den Emergency, but for Time and Duration, is evi-
dent both from the Rrong Stone-Works that encompafs’d
it, and a Body of Forces lying here, even at the Expira-
tion of the Roman Empire and Authority in this Ifland,
which from its Continuance in the fame Station, had
got the Name of the Longcvicarii

The Ferfon that under the Emperor gave Diredfion
for thefe Repairs, was M^cilius Fufcus : As M^cilius is a
Diminutive of M^cius, it is not unlikely that he was
the Son of Maicim Fufcus, who was Conful with Turft-
lius Dexter, A. D. 225 in the Reign of Alexander Seve»
rus : By this Infcriptien it appears that this Meecilius
was the Emperor Gordian's Lieutenant here and Prcpraitor 3
For tho’ in Phil. TranfaP^. N° 354, by the lnadver<>
tency of the Engraver, we read only PR. infiead ef
PR. PR ; it is right in the Original, and in the Tran-

O o o o o o . feript

* Antonin, hin. VI, ^ p. 21. \ Notit. Imp. fol. r~6. b,

(

fcript fent up by Dr. Hunter ^ and accordingly in pag,
Sx6. the Fault is amended. And as the Name of
cus (lands in the fame Place in the fecond as that of
LucHianus does in the firft, and with the fame Ad-
junds both before and after, we may fairly conclude
he was either his I’redecedbr or Succeflbr, but which,
it is impodible to determin.

And here, perhaps, it may not be amUs to re-
mark5 w’e never meet with a Legatus Auguflalis in any
Infcription in this llland, without the joint Title of
Prepr^tor'-i and ’ Tacitus himfdf either makes them the
fame Odice, or at lead unites them in the fame Perfon,
when he tells us. In Britannia P. Ofiotium Propraio-
rem turhida res excepere ; and having prefently after
related the manner of the Fight with the keni, fliles
him Legatiis, £lua pugna flius Legati^ P4. Oflorius, f:r-
vati civis dtcus meruit ^ ; and a little after he gives both
the fame Titles to A. Didius the SuccefTor of Oftorius.

We are indebted therefore to thefe two Monuments,
not only for the Account they have preferved of the
Roman Arms and Magnificence at Longovicus, but for
the indifputable Records of the Names of tw^'o Legates
and Proprafors of Britain, that would otherwife have
been buried in Oblivion, viz. Cneius LucHianus and Ma»
cilius fufeus: For from Firius Lupus (who was Propra-
tor and Legate here about the Year io8, under Seve~
rus, and juft before that Emperor’s coming into this
Iftand repaired a Bath burnt down at Lavatroe, or
Bovees ^ in Torkjhire) we have no where extant the
Name of one of thofe Officers, till we come to Non-'
nius Philippus, whom I take to have fucceeded the la ft
of thefe ; the Stone which was found at Old Carlijte

in

’ Tac.Lih. Ann. XII. c. 32. * Ibid. c. 39. I Camd. p 762*

Edit. < C*md. An'Mw.'p. 830^

!

' ( 853 )

in Cumkrldfj^, and has preferv’d his Memory, fetting
forth that he*was Legate and Proprdtor when Attkus
and PrdtextatMs were Confuls, which was A. D. 241.
the very Year that our Gordian went upon his Perfian
Expedition, from which he never return’d. And as that
Emperor left Nonnius Philippus in that Poft, when he
march’d into the Eaft, where he was murder’d about
two Years after, it is highly probable that he was the
lafl; Prcprdtor of his appointing, and confequently, that
Mdcilius Fujcus was his Predeceflbr, and the Repairs be-
gun at Longovkus before the Year 243 b I would not
have troubled you with this Infcription, but that it is
faultily tranfcribed in Camden^ and that I lhall have oc-
€afion by- and* by to refer to it again, upon a material
Point, which therefore I hope will plead my Pardon.

IV. I. O. M.

PRO. SALVTE. IMPERATORIS
M. ANTONI. GORDIANI. P. F.

INVICTI. AVG. ET. SABINAE. FvR
IE. TRANQVILE. CONIVGI. EIVS. TO
TAQVE. DOMV. DIVIN. EORVM. A
LA. AVG. GORDI A. OB VIRTVTEM
APPELLAT. POSVIT. CVl. PRAEEST
AIMILIVS. CRISPINVS. PREF
EQa.N ATVS. IN. PRO. AFRICA DE
TVSDRO. SVB. CVR. NONNII. PHI
LIPPI. LEG. AVG. PROPRETO.
ATTICO. ET. PRETEXTATQ COSS.

O 000 00 % The

‘ Phijof, Tranfdji, N° 554. p. 752.

{ 8U )

ThePerfon who had the Care of thefe Repairs both
in Town and Camp, was Marcus Aurelius Quirinus, Pra-
fePi or Commander of a Company of Foot ; another Ar»
gumenc for the Propixtors Lucilianus and Fufcns fuccced«
ing immediately one the other, he ferving in the fame
Poft under both. I mud obferve however, that altho’
the two fird inferiptiens have been cut very near the
fame time, and by the fame Hand, as appears by the
Form of the Letters, and Manner of the Abbreviations
in each of them, yet the Office that this Quirinus bore
is fomething differently exprefs’d in the fird from what r
it is in the fccond, if they have been accurately tran-
feribed ; the Fird fliewing, after Qj^IR I NO the Letters
PRE.GH. I. LG. R, which, before I had feen the Latter,

1 was induced to read Prdfe^fo Coherlis .friwA Longovica-
riorum, the ' Notitia Imperii placing the Prerfeltus nume-
ri Longovicariorum Longovico. That Numerus and Cu*
hors WQTQ the fame thing, " Pancirollus^ in his Notes
upon that Book, quotes St. Chr)fo(lome to prove, and
fome other?, Cohors erat qui vocatur Numerus ; but I ra-
ther take it to be an indefinite Number of Men, which
might comprize feveral Companies, independent of a-
ny Legion. ^ Negetius, fpeaking of the Legati Impera^
toris, fays, in quorum locum nunc illufires viros confiat Ma-
gi(lros Militum jubjlitutos, a qaibus non t ant urn bina Legio-
nes, fed plures Nwmeri gubernantur\ by which it is plain,
the Numeri were no Legionary Cohorts. Neither was the
Name fo modern as from the Notitia Imperii and Chr^-
foflome it might appear to be 5 for we meet with a Nu-
meras Britonum upon an Altar found in Tranfylvania, de-
dicated to the Nymphs, when the Emperor Cemmodus and '
Glabrio vatiQ Confuls, A.D. 186. And ^ another Nume- ‘
rus upon an Altar ereded to Hercules for the Profperity !

of j

b *fol,i6i,b 5 Lib, IIr.c.9. < Gf«^r, p.94. 4. ’id .46.9. j

( «55 )'

ef Septimlus Scv;rns, when Laterams and Rufimts were'
Confuls, A. D^ !Q7. Eui: after 1 had review’d ihe LeC'
lers ac the end of the fecond Infcripcion, which are plain-
jy tranftribed PR. CoH. i. L. GOR- I could read them
no otherw ife than Trxficfo Cohorth pr'mu L^gionh Gordid-
7i£. Gordian III. was fo beloved of the Soldiery, that fevc-
ral Legions complimented him by honouring themfelves
with his Name, as the ^ Legio tertia linlica, w'hich took
the Addition of Gordiana ; and the ^ Legio decima ge-
mina, and ^ Decima terliA gemina^\<\ both give themfelves
the fame Appellation. But which of the Legions quar-
tered in this Ifland ib filled itfelf is not determin’d by
this Infcription or any other that I know of. Howe-'
ver, - as the Legio fexta ViBrix was all along quarter’d
in the Northern parts of this Kingdom (" as i obfer-
ved before) where thefe Infcriprions were ereefted, I
make no doubt but it was that which call’d it felf Got-
diana^ tho’ the numeral Diftineftion of Vi is omitted,
only perhaps for want of Room on the Stone. We find
by feveral inferiptions in Carnkn, that there was an Ah
in thofe Parts which prided it felf upon its Valourj and'
was therefore call’d ihQAla.Augujta; of the many Me-
morials it has left us of its Title, I lhall only mention
^ one round ac Old Carlijle, and which is the ancientefl
of them all, by any certainty of Date.

I. O. M.

AL. AVG. 03
: ; . RTVT. APPEL. CVI
PRAEEST. TIB. CL. TIB. F. P.

LING --N IVSTINVS.

PRAEF. FVSCIANO.

II. SILANO. I!. COS.

that "

• VeJf. Monum, Augufi& Vindd, p.431. » p._ 80. GrHtfTd’^^

p. 433..1. ^

( 8r<; )

that is,

Jovi Optimo Mdxtmo^ Ala Augufla oh Virtue
urn apptliata, cut pr£ejl Tihtritis Claudius\Tiberii
frovincid Lingoncnfi^ Ju(linus prafedus^
Fufciano fecund\ SiUno fecundo Confulihus.

This Altar was dedicated when Fufeianus and SiU-
Kus were the fecond time Confuls, that is, in the Year
188. under the Reign of Commodus, and Fifty Years
before our Gordian came to the Empire. At the fame
place was alfo difeoverd the Fourth infeription by me
quoted, where we find this fame Ala Augujla filling
itfelf alfo Gordiana'-, from whence I think it is not a
little probable that the Legion to which this Wing ap-
pertain’d was xhtLegio Gordiana mention’d in the Infcrip-
tions found at Langchefler ; and that Legion to have
been thQ^Legio [ext a FiSlrix, from the long Continu-
ation of this Ala Augufla in thefe Northern parts of
the Nation, the conftant Quarters of that Legion.

if Ay 10.
1718.

Ill, A

( )

III. A Letter of that curious Naturalifl A/r.Henry
Barham, % S. S, to the ^uhlijJnr^ a %e~

latlon of a fiery Meteor feen hy him, in Jamaica,
to ftrike into the Earth 5 with ^marks on the
Weather, Earthquakes, See, of that Ifland.

SIR,

According to your Requeft I have colleded what
I can remember, relating to a Meteor I law in
Jamaica about the Year 1700, as I was riding
one Morning from my Habitation fituaced about Three
Miles North- Weft from St.Jago de la Vega: I faw a Ball
of Fire, appearing to me of the Bignefs of a Bomb,
fwiftly falling down with a great Blaze. As 1 thought
it fell into the Town ; but when I came within a quar-
ter of a Mile of the Town, I faw many People gather’d
together a little to the Southward in the Savanna, to
whom I rode up, where they were admiring at the
Ground’s being ftrangely broke and plough'd in by a
Ball of Fire, which, as they faid, fell down there. I
obferved there were many Holes in the Ground, one in
the middle of the Bignefs of a Man’s Skull, and five or
fix fmaller Holes round about it, of the Bignefs of a
Man’s Fift, and fo deep ( efpecially the biggeft ) as
not to be fathom’d by what long Switches or Sticks
they had at hand^ I did not hear that any was fo cu-
rious as to make any farther Search : It was obferv’d,
that the green Grafs was perfedly burnt near the Holes,
and a ftrong Smell of Sulphur remain’d thereabouts for
a good while after.

Note that we had a terrible rainy Night before, with
much Lightning and great Thunder-Claps, which we

havp

c 858 ) I

liave very frequently in JamaicA, often killing Cattle in |
the Fields. Mr. Henr) Lord, who lives at Dry-Riv:r, i
had two Sons (big Boys) ftruck dead with Lightning, 1
in 1716, without any Wounds or /Appearance of Hurt J
found about them. And as thefe Claps are much louder ”1
and Wronger than any I ever heard in Europe, fo are our 1
Showers of Rain, pouring down in a moR violent man- I
ner. We have Lightning all the Year round, but oar I

great Rains are in the Months of May, ^u^u/l, and 0c~ |j

tokr. I knew May for two or three Years without Rain, 3
which was lookt upon as a great TVonder; and we paid
dear for it in our Indigo; for a Catcerpillar appear’d and ^
wove a fine Silk about the Indigo-Flant, and deftroy’d it ®
all, hurting nothing elle. May-Rzins us’d to deftroy
thefe Worms. Auguft and OUohernQSQx: go out without a ^
Flood, we having then univerfal Rains, all over the Ifiand, jE
coming from the Sea : For we have often Rains in the
Mountains from the Clouds lodging there, when we have jl
none in the Lowlands. ™

Our Ifiand is full of Mines, and, if fearch’d into, I j' '
queflion not but very rich. We are very fubjed to Earth- '
quakes, feveral happening every Year, efpecially after
great Rains, which fill up all our great Cracks in theSur. ^
face of the Earth : For in a very dry Time, we have them 4
fo very large, deep, and gaping fo open and wide, that 4
it is dangerous to ride over Tome Parts of the Savannaes,
for fear a Horfe Ihould get his legs into them. Our
Earthquakes make a Nolle or Rumbling in the Earth, %:
before we feel the Shake ; and feem to run fwiftly to
the Wellward. This is all I can inform you of this kind
at prefent, relating to the Ifiand of Jamaica, being ever • {
ready to fliew how much I am, &c.

Bmy 'BarhawJ:

Decemb. 1 9.
1 7 17-

( 8^9 )

IV. An Attempt to pro^e the Antiquity of the Vene-
real Difeafe, long before the Vifco'Very of the
Weft- Indies ; in a Letter from Mr. William
Beckett, to 2)r. James Douglafs, M.T>,
and R. Soc. Soc. and by him communicated to the
Royal Society.

SIR,

TH E Undertaking I am at prefent engaged in,
has unavoidably obliged me to confult, among
others, a great Number of ancient Phyfical and
Chyrurgical Books, written by my own Countrymen .•
From thefe I cook the Hint, that the Vsnsrsal Difeafe
was known among us, much earlier than the ^ra^
which has been generally alTign’d for its Rife by mo-
dern Authors ; for it’s believed it was not known, at
lead in Europe., till about the Year *494. Not with-

Handing which, I determin, in the following Papers,
to make it evident, it was frequent among us fome
Hundreds of Years before that Date. ! could men-
tion feveral Phyficians and Surgeons of Eminence, who
have been of the fame Sentiments with me, particular-
ly, the Learned Dr. Charles Fatin, who has written a
curious DifTertation to prove the Antiquity of this Dif-
eafe, which is fufficient to excufe me from the Impu-
tation of having ftarted a Novelty, or being at the
trouble of quoting ancient Authorities before taken
notice of, from the mod ancient Writers of Medicine;
as the Great Hiffocrates, Galeri, Avicen, Cdfus,^c* and
even the Holy Scriptures. I fiall in thefe and Ibme fol-
lowing Papers, lay afide all thofe foreign Aids and Af-

I^PPP.PP fiftances,

( 840 )

fiftances, and trace out the Sj^mptoms of the Difeafe,
as they naturally ar ife, from the firft Infedion to the
laft deftrudive Period, and (hew that, by learching in-
to our own Antiquities, we may be furnilhed with In-
ftances of the Frequency of the Diftemper among us,
in all its refpedive Stages, before ever our Modern Au-
thors dream it had its Appearance in Europe.

I (hall begin with the firft Degree of this Difeafe,
and prove from authentick Evidences, it was anciently
call’d the 05?Cnmng or 'Burning *, and that this
Word has been fucceffively continu’d for many Hun-
dreds of Years, to fignify the fame Difeafe we now
call a Qla^ 5 and that it was not difeontinu’d till that
Appellation firft began to have its Rife. The moft like-
ly Method to accomplilh my Defign, will be firft to
examine thofe Records that relate to the Stevos^ which
were by Authority allowed to be kept on the BAnk^Sid'
in Southwark, under the furifdicftion of the Bp. of Win-
chejler, and which were fupprefied the of //r» VIH.
For it’s impoffible but, if there were any fuch Diftem-
per in being at that Time, it muft be pretty common
among thofe lewd Women who had a Licence for en-
tertaining their Paramours, notwithftanding any Rules
or Orders which might be eftablifii’d to prevent its In-
creafe : But if we (liall find that there were Orders e-
ftablidi’d to prevent the Spreading of fuch a Difeafe,
that Perfons might be fecure from any contagious Ma-
lady after their Entertainment at thofe Houfes f which
were anciently Eighteen in Number, but in the F^eign
of VII. reduced to Tw’elve^ we may then fecurely
depend upon it, that it was the Frequency of the Dif-
eafe that put thofe that had the Authority, under a
necefiity of making fuch Rules and Orders. For the
fame Powers that granted a Liberty for keeping open
fuch: lewd Houfes,^ muft find it their Incereft to fecure,

aS:

( 841 )

as much as poflible, all Perfons from receiving any In-
jury there; left the Frequency of fuch Misfortunes
fiiould deter others from frequenting them, and fo the
original Defign of their Inftitution ceafe ; from the en-
tire finking of the Revenues. Now I find that, as ear-
ly as the Year ii6z, divers Conftitutions relating to
the Lordlhip of Winchefler, f being alfo confirmed by
the King were to be kept for ever, according to the
old Cuftoms that had been time out of mind. Among
which thefe were fome, v:z. No Stew-holder to take
more fora Woman’s Chamber in the Week than ir^d.
Not to keep open his Doors upon Holy Days. No Tin-
gle Woman to be kept againfl: her Will, that would
leave her Sin. No Tingle Woman to take Money to
lie with any Man, except Ihe lie with him all Night
till the Morning. No Stew holder to keep any Wo*
man that hath the perilous Infirmity of 'BUtninQi.
Thefe and many more Orders were to be ftridly ob-
ferved, or the Offenders to be (everely punifhed. Now
we are affured there is no other Difeafe that can be
communicated by carnal Converfation with Women,
but that which is Venereal, by reafon that only is con-
tagious ; and it’s evident the 05Utnin3 'vas certainly
fo : For, had it been nothing elfe but lome Timple Ul-
ceration, Heat, or Inflammation, there would have
been no Contagion ; and that affeding only the Wo-
man, could not be communicated by any Venereal Con-
grefs, and lo not inferr a Neceffity of her being com-
prehended under the reftraining Article. Thefe Orders
likewife prove the Difeafe was much more ancient than
the Date above-mentioned ; becaufe they were only a
Renewal of fuch as had been before eflablifiied time out
of mind.

But to confirm this farther, I find that in the Cu-
ftody of the Bifiiop of Winchefler, whofe Palace was

P p p p p p z fituated

( 842 )

fituated on the Bayik ftde, near the Steves, was a Book
written upon Vellum, the Title of which runs thus j

mu begrnne fte O;itiuiance0, Eulcg, ant) cu=
Oimug, as toell fo? tlje ^altiatton of pannes
itf, as fo;i to afctetoe ma;tp ^pfchicfs ano 3in=
conbniieius tljat Oaplep be lik tbece fo.2 to fall
otote, to be risbtfuUp liept,.anD owe Ctccution of
them to be ooit unto any laerCoiiue toptbin tbe

fame* One of the Articles begins thus ; De his qui
cu^odiunt Mulieres h.ihentes Nfphandam infirmitattm. It

goes on, Item, Cbat no Steto=boloci: keep noo
man toptbin pis e;ous.tbat peUp anp S)pckneire
of BRENNiNG. but tpit (pe 6e putte out upon
tpe pepne of makeit a fpne unto tpe lo?t) of a

pUnO^ell 0pplpn9S. This i« taktn from the Origi-
nal Manuferipe which was preferv’cK in the Bifliop’s
Court, fuppos’d to be written about the Year 1430.
From thefe Orders we may obferve the Frequency of
the DiQemper at that Time ; which, with other In-
conveniencies, was oaplep lik tpere fo? to fall otDte^
and the Greatnefs of the Penalty, as the Value of Mo-
ney then was, that is laid on it, proves it was no tri-
fling or infignificanc thing.

But the bare Proof of there having been anciently
fuch a Difeafe as was called the 'BUCniUS? may be
thought to be infuflicient, unlefs we were perfedtly
aflured what it was, and how it was in thofe Times
deferibed : I fhall therefore do it from an unqueflionai-
ble Authority, which is that of 'john Arden, Efq; who
was one of the Surgeons to our King Richard \\. and
likewife to King Henry IV. In a curious Manuferipe
of his upon Vellum, he defines it to be, a certain in-
ward Heat and Excoriation of the Urethra-, which Dc-
feription gives us a perfect Idea of what we now call
^Qlaf \ for frequeat Dif]e.(5fions of thofe that laboured

undei^

( 843 )

under that Difea(e, have made it evident, that their
Urethra is excoriated by the Virulency of the Matter
they receive from the infed:ed Woman ; and this Ex-
coriation or Ulceration is nor confined co the OJHoU
or Mouths of the GlanduU Mu[co[£, as has been late-
ly thought, but may equally alike attack any part of
the Urethra not beyond the reach of the impelled ma«
lignant Matter. The Heat before deferibeJ, which
thefe Perfons are fenfible of, as well now as formerly,
is a Confequenc of the excoriated Urethra ; for the
Saks contained in the Urine mud neceflarily prick and
irritate the nervous FiJ?rillx, and excite a Heat in thofe
Parts of the Urethra which are diveded of its natural
Membrane ; which Heat will always be obferved to be
more or lefs, as the Salts are diluted with a greater
or lefs Quantity of Urine ; a thing I have often ob*
ferved in Perfons that have laboured under this Infir-
mity in hot Weather, when the perfpirable Matter be-
ing thrown od in greater Quantities, the Salts bear a
greater Proportion to the Quantity of Urine, and there
by make its Difcharge at that Time fo much the more
painful and troublefom.

Thus we fee this very early and plain Defeription
of this Difeafe among us, to be entirely conformable
to the latcd and mod exacd Anatomical Difeoveries. ,
Here is no Tone of the Tefiiclcs depraved, according
ioTrajanus ?etromus\ no Exulceration of the Faraflatx,
according to Ror^dtUtius ; no Ulceration of the SemR
?ul Fejfels, according co P Uterus \ no Seat of the Dif-
cafe in the Feficulx Seminales or ProfiateS, according to
Bartholin-, not in thofe Parts and the Tedicles at the
fame Time, according to our Countryman Wharton and
others, who have falfly fixed the Seat of this Difeafe,.
and whole Notions, in this refpedl:, are now judly ex*
ploded ; but a fing|e and true Defeription of it, and-

( 844 )

Its Situation, about an Hundred and Fifty Years be-
fore any of thofe Gentlemen obliged the World with
their learned Labours.

Having, I hope, fufficiently made it appear, the
*BUtninS was a Difeafe very early among us, and
given the Defeription of it, I lhall proceed to fay fome-
thing of the ancient Method that was made ule of to
cure it. We are not to expecS: the Meafures our Pre-
deceflbrs, in thofe early Times, made ufe of, fliould
be calculated for the removing any Malignity in the
Mafs of Blood, or other Juices, according to the Pra-
<5lice in Venerial Cafes at this Time; becaufe they
looked upon the Dileafe to be entirely local, and the
Whole of the Cure to depend upon the Removal of
the Symptoms .* Hence ’twas they recommended fuch
Remedies as were accommodated to the taking off the
inward Heat of the Part, and cure the Excoriations or
Ulcerations of the Urethra. The Procefs for the ac-
complilhing of this, I lhall fet down from the before-
mentioned John Arden, who wrote about the Year
1380. his Words are as follow. Contra Incendium. Item
contra incendium Virga Fir tits inter ius ex calore ^ exco-
riatione, fiat talis Syringa (" i. e. inje^io ) ienitiva, Ac-
cipe Lac mulkris mafculum nutrientisy & parum zucariim.
Oleum viola © ptifana, quibus commix t is per Syr ingam
infundatur, ^ fi pradiHis admifeueris lac Amigdalarum me^
lior erit medicina. There is no doubt but this Remedy,
being ufed to our Patients at this Time, would infal-
libly take off the inward Heat of the Part, and cure
the Excoriations or Ulcerations of the Urethra, by which
means what illued from thence would be entirely ftopt;
and this was all they expedfed from their Medicines,
forafmuch as they were entirely unacquainted with the
Nature of the Dillemper ; and did not in the lead ima-
gine, but if the Symptoms that firft attack'd the Parc
were removed, the Patient was entirely cured. I

( 84J )

I (hall now, as a farther Confirmation of what I have
advanced, proceed to prove, that by this or

'BUntinS meant the Venereal Difeafe, by demon-
ftrating that fucceeding Hiftorians, Phyfical and Chi-
rurgical Writers, and others, have all along with us in
England ufed the very fame Word to fignify the Vene-
real Malady. In an old Manufcript i have by me,
written about the Year >390. is a Receipt for

ning of t^c pyntpl, pt men clepe ve apegalle 5

0alle being an old Englilh Word for a running Sore.
They who know the Et'jmologk of the Word Afron^
cannot be ignorant of this. And in another Manufcript,
written about 50 Years after, is a Receipt for *BUCn=
ing in that Part by a Woman. Simon Fijh, a zealous
Promoter of the Reformation in the Reign of Hen.VUL
in his Supplication of Beggars, prefented to the King
in 1530, fays as follows, Thefe he they ( fpeaking of the
Romijh Priejls ) that corrupt the whole Generation of Man-
hind in your Realm^ that catch the Pocket of one Woman
and hear them to another 5 that he 'BUtnt tvith one Worn n
and hare it to another ; that catch the Lepry of one Wo-
man and hare it unto another. But to make this Matter
fUll more evident, 1 am to obferve, that Andrew Boordf
a Dodor in Phyfick, and Romifh Pried, in the Reign
of Henry VIII. in a Book he wrote , entitul’d Ihe
Breviary of Health, printed in 1546. fpeaks very par-
ticularly of this fort of Burning ; one of his Chapters
beginneth thus, 19th CtepUCC Cbcti) Of

Burning of nn l^atlottc *, where lus Notion of com-
municating the Burning is very particular. The fame
Author adds, that if a Man be 'BUtUt with an Har-
lot, and do meddle with another Woman within a Day,
he fliall OBUlCn the Woman that he lhall meddle with-
al ; and as an immediate P^.cmedy againft the 'BlltU-
ing; he recommends the vvafiiing the Pudenda two or:

three

( 84-5 )

K"*

three times with White Wine, or elfe with Sack and
Water ; but if the matter have continued long, to go
to an expert Chirurgeon to have Help. In his 8id
Chapter, he (peaks of two forts of Burning, the One
by Fire, and the Other by a Woman through carnal
Copulation, and referrs the ^Perfbn that is 05Unit of ^
a Harlot to another Chapter of his for Advice, what ^
to do, pf set a €>o?|[fr o? ttoo, fo called from
its Protuberancy or bunching out : For I find about that
Time the Word EuUco was moftly made ufe of, to fig- '
nify that fort of Swelling W’hich ulually happens in pe«
flilential Difeafes. ■ ; ,

From hence it appears, the Burning,, by its Confe-
quents, y^2LSveneria(, fince every Day’s Experience makes a*-
it evident, that the ill Treatment of the firft Symptoms ii-
of the Difeafe, either by aftringent Medicines, or the
removing them by cooling and healing the excoriated
Parts, will generally be attended with fuch Sw’ellings in f
the Groin, which w’e rarely obferve to happen from a-
ny other Caufe wiiatfoever.

1 fliall give a few more Inflances of this Difeafe be-
ing call’d the Burning, and conclude. In a Manulcript «■

I have of the Vocation of Jckn Bale to the Bifhoprick
of OJfory in Ireland, written by himfelf, he fpeaks of
Dr. Hugh Weficn (who W’as Dean of Windjor in *

but deprived by Cardinal Pole for Adultery ) as fol-
lows, “ At this Day is lecherous Weflon, who is more
pra£Hfed in the Art of 05UtninS than all ‘

the Whores of the Stews. And again, fpeaking of the
fame Perfon, he fays, He not long ago bilCllt ^Beg-
* gar in St Botelfh s Parifli. The fame Author fays of
him elfewhere, “ He had been fore Bitten with a Win’.

cheJierjGocfe, and was not yet healed thereof ; which \.-
W’as a common Phrafe for the Pox at that Time , be-
caufe the Stews were under the Jurifdidion of the Bifiiop

of 1

( 847 ')

of Winchefler. Mich. Wood, in his Efiflle before 5tqh.
Gardiner's Oration de vera Ohedientia, printed at Rhoan,
i5’53* gives another Evidence of the ^Burning. And
William Bullsin, a Phyfician in the Reign of C^een Eliz,,
in a Book he poblifh’d, call’d The Buhark of Defence,
d^c. printed in 1562. bringing in Sicknffs demanding
of Health what he fliould do with a Dileafe call’d the
French Pockes, Health anfwers, “ He would not that a-
“ ny ihould fiflie for this Oifea'e, or to be bold when
“ he is bitten to thynke thereby 10 be helped, but ra-
“ ther to efehewe the Caufe of thys hifyrmity, and
f filthy rotten BUnUnQl Harlots.

I believe, by this time, I have fufficiently prov’d
what I propofed, that the firfl: Degree of the Venereal
Difeafe was very anciently known among us, under
the Title of BUtning ; and that you may lofe no
more Time at preient upon this Subjed, I fhall referve
my Colledions, which (hew that the Difeafe, when it
came to be confirmed, was no Novelty here dn thofe
early Times, for a further Opportunity, and detain you
no longer than to exprefs my Pieafure in profelling
my felf, Tottrs, &c.

London, Feb. 4.
I7I7-1S«

Will. Beckett,

V. Jeeuratarum Ohferyationum Jflronomicarumj a\u
no fuperiore zs* currente^ cum Societate com^
municatarum Sylloge.

INterefl fane Sciential ne pereant Obfervata Aflrono-
mica, debita curd hdifque Inftrumentis ab Artifi-
cibus idoneis cielitus deprompea : Hoc enira fblo
fundamento nicicur Urania pradica. Itaque in hisTranf

4449 (^^lonihus,

( 848 )

0mihus, per plufquam quinquaginta annorum curri-
culum, paflim {parguntur hujus generis Noras. Aufini
tamen fpondere vix ullas unquam reperiri pofle Obfer*
vationes quas certitudine cas quas nunc damus vincanr,
ne dicam quae pares Tint, ucpote Tubis pradongis ac
Micrornetris praeter folitum affabre fadis menluratas.
Cape igitur primo.

Tlanetarum Ohfervationes.

Anno 1717. A^rilis 15°. 9'' 49" T. ccq. obfervavit
D. P otitid Wanfled, Jovem jam reverium ad ftellam
illam, quam Novemh.zz°. 1716. mane corpore fuo te-
xerat, de qua vide N° 350. P^il. Tran{aPt. pag. 508,
Jovis aucem centrum rum temporis diftabat ab ea Stella
( quae tcrtia eft Geminorum in Catalogo Britannico )
13' xi" boream verfus ; fimulque ab alia vicina, qux
quarta eft Geminorum in dido Catalogo, 37' n''. at-
que huic fere conjundus erat planeta.

Jprilis 25'° fequentc, eodem obfervatore ac loco,
10’’ 3' T. xq. Jftpiter apud quatuor Fixas exiguas vi-
fuseft, eas omnes praecedens, & in ipfo quafi principio
Cancri. Centrum autem planetse diftabat ab e 12' 00",
ab h 13' 50", ab / 19' 5-3", & a ^ 9' x;".

Poftridie veto Apr. 16°. 9'’ f Jovis centrum difta-
bat ab e 8' 35", ab/ 9' 00", a ^ 4' 5", & ab ^ 13' 50".
Jamque prceterierat omnes praeter / ad quam tendebar,
quamque parum admodum die craftino infra fe relin*
quere debuir.

Eodem fere momento, bora fcil. nona, Londini vila
eft ftella g in vertice Trianguli Ifofcelis ac fere Ifopleu-
rt cum Jovis centro ac tertio Satellite, turn fex Jovis
diametris ad occafum diftante, nifi quod parum admo-
dum bafe longjora crane crura; ac intra quadrantem

hora:.

C 849 )

horx, angulus ad Jovis centrum, qui prius major erat
angulo ad Satellitem, fadus eft eo fenfibiiiter minor.

Tres autem StelJas h, g, e, funt ii'“% & 12'^V
Geminorum in Catdl. EritAn. juxra quern turn temporis
fttum habuere, h 'm s- 0° 55", cum Latic. Borea

o^iirs". Et^ in s- 28' 25". Lat. Bor. 0° 3' 40'' ;
e veto in s o° 29' cum Lar. Auft. 0° 8' oj". Di-
ftat autem quarta / a Stella g ii' 40", ab 5 i% 50",
ac denique ab b 20' 36", unde conftabic locus ejus.
Ex his manifeftuoi eft Jovem Latitudinem habuifte par**
vam admodum Borealem, nec femiminuto majorem,
faltem ft didis ftellarum locis habenda fides. Hxc
pofteris ufiii efle polTunc definiendo Nodorum Jovh
motu, ft quern habeant-

Ejufdem anni Junii i8'’° 10'^ Londini^ in xdibus So- ’
cietatis Regiae, vifus eft SAturnas Stell^e fixse Telefcopi-
cx admodum propinquus, a qua vix diftabat ad Au-
ftrum una Annuli diametro, & normalis in lineam An-
farum a Stella demifta incidebat in medium Anfas ori-
entalis. Fixa hsec parvula nullique Catalogo adfcripta
tunc habuit 12° 58' r cum Lac. Bor. 2° 33' proxi-
me,; comitemque habet ftbi adjundam ac luce sequalem,
quatuor minutis ad orcum diftancem, ac paulo auftra-
liorem, unde facile dignofci poterir, loculque ejus fi
cui libeac veriftcari.

Eadem node lo’^ yJ Mats vifus eft prope Stellam
quns prsecedic 35'. Scorpil, a qua diftabat Tubo 24 pe-
dum menfurata 7' 1 6" ; idque in reda per claram in
pede Ophiuchi G & didam Stellam produda. Hsec
autem Stella prtecedit 35-. Scorpii 30' 27" Afc- Red. ea-
queAuftralior eft 2' 28 ', unde fit locus ejus turn tern-
iporis SAgitt. 15° 24' 20" Lar. Auft. 3* 59' .25". Sed
6 Ophiuchi tunc habuit 17° 28', & Lac. Auft.

4° 47' 38". MArs itaque Stellam prcEcedebat Longi-
tudine 4' 58”, auftralior ea 5' 30".

Q.S1 S ft ^ ^ 2, Deinde

( 850' ) I

Deinde Sept. 13® S’’ 5'. T. seq. Mars vifus eft a Dom;

Fcu/3^ prscedere claram in humero Sagittarii o- 11' 54"

Afc. Redt. fimulque borealior erat Steilliz' 56"* Hora ^ i
8’’ z^' erat diftantia Planetx a Stella 25' co" accurate.* * |
Decemb. iS** 30'. T. xq, confenfu fxpius repetita- £
rum oblervationum, invenitD. Pound Saturnum prxcedere- I

Telefcopicam claram fibi vicinani xj 19" Ale. Red:. f
Stellaque auftraliorem efte i' 59". S\mu\ Sat urnus^tx- r

cedebat x in Syrmate 1° ^5* x\'\ eaque au- T
ftralior erat 4' 05". Hinc Saturni locus Libra 19°. „

16' zi'\ Lat. Bor. 1° 21". Telefcopica autem tune ^

habuit Libr. 29° 40' 5'6". Lat. Bor. 2° 33' 43". j|

Anno 1718. Jan.y, 5'’ 30'. T. xq. apud duas X
Stellas in Catal Britan, omiftas obfervata eft. Erat au^ m
tern Planeta utraque Fixa Borealior, diftans a prxcc- jj
dente 32' 30", a lequente 17' 30". Stella prxeedens «
tunc habuit / ifc. 14^42' 20", cum Lat. Auft. 0° 40' 10"; 1

altera \ero fequens Fife. 15° 21' 55", Lat. Auftral. 0° 3

‘ 5"> prout ex obfervationibus D. FUmflidii collige- *
ff2 licet..

Jan.i^. 8' 00', T. xq. Jupiter prxeedebat r\ in pe-i .ji
dore Cancri 3° 30' 50" Afc. Red, fixaque Auftralior
erat 14' 15". Hinc provenit locus 28" 20'
cum Latitudine Borea 0° 36' 45'".

MartJi II. 10^ 36', T. xq Saturnu' prxeedebat jc in
Syrmacc. iS' 51", eaque Fixa auftralior erat

5' 23. Hinc fit Locus Saturni Scorp^ o i8' 34'^ cum
Lat. Bor. 2. 44' 8 Poftto fcilicet, juxta CataL Britan,
jc Virgtnis occupare m o. 34'' 10'', cum Lati2. 55' 40".
Eadem node i,'’ 00' PVejlwonaflerti obfervarunt DD.
F>i[aguliers & Cray Saturnum prxeedere Stellam oo^j
cum dedinatione majore in Auftrum 4' 45".

^pril 8,>iL 30' Londini \ Xus ci\ Saturnus nupet A- '
ccon^chus parum admodum occidentalior Telefcopica .
clara, eademque 5 minutis borealior. Unde Fixx locus

Lihr rs .

( 8ji )

hilrdi%%. 1 8' 30^' Lat. Bor. 2.. 41'. Circulus autem
magnus per banc Stellam <5c Saturnum dudtus dirigi
videbatur ad Stellam 5^* magnitudinis in Catal. Brit»
omiflam, fed qu2C Htvdio efl: in cufpide AU Bore/e Vtr-
ginis, cuique locum affignat Lihr. %6. 10', cum Lat. 14.
43' Bor.

Eadem node 13^ 10', apud Wanfied, perpendiculum
a dida Stella Telefcopica in lineam Anfarum Saturni
demiflum prtccedebac centrum planetoc quafi fefquial-
tera diamecro annuli ; aberat autem Stella ad Auftrum
ab Anfarum axe 4' 30". Simul Anfe orientalis extre-
mitas deprehenfa eft in linea reda inter banc Stellam
& aliam eidem quafi longitudine conjundam^ quse
tunc a Saturno diftabat 14' 48" verfus Boream. Locus-
autem prioris Stella tunc fuic Lihr. i8. i8' 30" cum
Lat. Bor. x, 41' proxime*

Sept, 7. circa meridiem incidit conjundio “Jov-h & Vc--
mris ardiftima, cujus quidem fpedaculum Aftronomis.
noftris inviderunt Nubes. Die autem (exto prtccedsn-
te mane, vel 5"^ ix*' 57' 30" T. arq. apud IVanficd, Ve-
mi occidentalior diftabat a Jove i. 3' x8". Die autem
7. 21', Venus jam fada orientalior a Jove aberat

43' 18"; ac 17^34', auftralior erac 'jove difle-

rentia declinationum 14 Et 17'’ 39.' capca eft di-

ftantia Planerarum 44' 4". Hinc calculo accuraciftimi
Obfervatoris conjundi funt Sept, 7. 9' T. xq. Vc-

neris cenrro turn Jovis auftraliore non nifi i' 4x".

Denique Sept. 18. mane, apud Wanfled, Jupiter vifus
eft prope - or Ler>nis, quocum die praecedence conjun-
dus fuerat. Sept, 17. 16'’ 51' 1l .xq. Jovis CQnimm ab»
erat a Corde Leon, 24' 2.2"; & 17'’ 6' io"erat diff. DecJin.;
12' 43". Dein poll Horam, nempe 17'’ 54', fada eft
diftantia 24 44"; ac 18*^7' differentia Declinationum >
inventa eft 12' 35". Hinc fupputance Dom^ i ound^ fit
Sept I/. 18 go' T. teq« Jpvh locus 2.6 ii' 7" cumv=
Lac, Bor. 45' 39''- Objerv at tones j

( 851 )

Obfervationes Lm<e &• EcUpjium-,1

Anno I7i7» WtflmonAfterti Dorn.

Stephanus Gray^Lunx appulfum ad quatuor Stellas con-
tiguas fub cornu Auftrino apud quas obfervata

eft Luna Anno 1683. Mart. 23. ft. v. ab Hevelto &
FUmftedio. Itaque 9^ T. app. Luna gibba vifa eft
quafi conjunefta cum Stella h quatuor pricedente, quae
icft Tauri 107. Catal. Brit, quaeque tunc Auftralior erac
Lunse limbo Auft. fefquialcero minuto. ii*' 29' altera,
qux’ minor eft, & ideo in Catalogo omifta, occultaba-
tur paulo infra- medium cbfeuri limbi. Ad 12*’ 24^
Tertia & clarior ( no. Tauri) in ipfa fere conjundtio-
ne fex minutis diftabat a limbo boreo. Denique 1 2’’ 54'
fequens c quatuor f in. Tauri ) limbo Boreo fuperior
trat 3' 30". Locus autem praecedentis, five 107. Tauri,
ex»di(fto Catalogo tunc erat Gemini 18. 12. Lat. Auft.
5. 18'; Tauri autem ilohabuit Gem* 19, i6'~ cum Lat.
Auft. 4. 44': Sequsns vero, five in Tauri, erat in Gem,
19.45'. Lat. Auft. 4. 48' r* Secunda parvula, ut ex
aliis obfervationibus conftat, Locum tunc habuit Gem,
19, if, Lat. 5. 5' fere.

Eodem anno Mart, 16, mane, erat Eclipfis Lunce par-
tialis, apud nos ob coelum nubilum inconfpicua. Ac
apud Cambridg Mov-Anglorum, Dom. Robie Aftronomise
;peritiftimus vidit Eclipleos initium circa horam nonam.
Finera vero, juxta Paludem M.utida, ad 1 1*^42' 30" fat
accurate. Eft autem Canthridg fub aititudine Poli 42.
25', Londino 71 grad, five 4^44' occidentalior, ut ex
pluribus antea obfervatis conftat.

Dein Sept, 9. vefperi, in .^dibus Societatis Regia;
JLondini, obfervarunt nonnulli e Sociis finem Eclipleos
iunaris 7^ 26^ Luna autem orta eft juxta medium

EeJipfeos,

{ 855 )

Eclipfeos, nec nifi paulo ante finem e nubibus horizon-'
tern obfidentibus fe(e cxtricaverat.

Sept, !4- Vefperi, hac prima vice poft longum inter-
valium rediic Luna ad occultanduin Pdtlichm, Favic
autem admodum ccelum Londirn prxter (olitum piirum,
ira ut Luna & Stella exoricntes in ipfo quafi Horizon*
re fimul confpicerentur. Inddit Irnmcrfio Steiia: 9^
6' zo", Luna nondum 3° aha, in ipfo quan medio Lim*
bi orientaliSj e regione fciiicet Boreas partis macul.'e il-
lius exigu^ quam Hevelius Scagnum Mteridis vocat,
quamque Ricchlus fui ipfius nomine infignivit. Emer-
fit autem paulo infra medium limbi obfcuri ad 9’"
58' zo", in idu oculi tota lua claricate effulgens; un-
de etiam in tarn illuBri Stella quafi nullitas diametri de-
monftratur.

Septemhris vefperi, incidit Eclipfis Solis vix ullibi
in Europa confpicua. Ex America autem noflra dupli.
cem obtinuimus ejus obfervationem ; alteram ex literis
illuftris Viri D. Keith Provincise Perifylvaniat Pix^Q^i dig-
nifTimi, qui Philadelphia, Tub altitudine Poll 40° 00' fere,
vidit Edipfm jam cceptam (fed. quae ante minutum,
temporis nondum inceperat ) ad 1 1" Circa medium.
DigiM erant quafi decern. Finis autem vifiis eft accurate.,
ad z'’ 46' 35"..

Altera autem hujus obfervatio habira eft ad Camhridg
Nov£ /4ngli£ Academiam, a Dorn. Rohie, de quo fupra:
Initium Eclipfeos ibi obfer varum eft z3' co" poft meri-

diem. Ad 47' defccere IX Digiti. Ad 3'^ 5' ro" defiit
Eclipfis, Sole integro per Tubum Z4 pedum confpedo.,,
Hoec ex literis accurati Obfervatoris communicavit cum
Reg. Societate Reverend us Vir D. GuiL Derham, R.S.^o,.
Ecclefioe apud Wind[or Canonicus, &c.

Dec»<^c Luna paulo fupra Palilicium invedfa eft: Tran-
fitum autem lads ardurn pbfervavit D. Jac» Bradley,
eruditus JuveniS; qui fimul ingenio induftria pollens

his."

( 8J4 )

his ftudiis promovendis aptiffimus natus eft, idemquc
Reverend i D'‘' Pound ex forore nepos. Hie, cum Luna
j arn propemodum plena eflec, Stellam contulic cum in-
fjgni ilia Macula quam Ricciolus Tychongm, Hevelius Sinam
appellac, & ex pluribus xqualibus diftantiis Microme-
tre ante & poft captis, Stellam dieftx maculx centre pro*
ximam apparuifle conclufic ad ii*' 15' 8" T. xq. apud
Wanfied. Ad 1 1'" 15' diftabat Palilicium a limbo
Lunx proximo & Auftrino 5' 5 j". Macula autem Tycho
.ab eodem limbo aberac 4 16'. Ad ii*' 18' qx" Stella
erat in lined reda cum maculis Tychonh & Copernici,
five Sina & /^tn£ 5 & 1 x5' 27" T. xq. erat in re*
(fta cum Tjehone & Kepkro. Inter hxc oblervata eft Lu-
nx diameter 3x' 45".

Anno 1718. Jan. 29. vefperi, DD. Defagulhrs&iGraj^
\We(intona(lerii alteram Palilicii Occultationem prxfto-
labant ^ ied nubium interventu impediti, viderunt fal-
tem quod $2 nondum immerferat Stella; attenua-
tis autem poftea nubibus conclufa eft Emerfio ad
7*^ xo', e regione Promontorii Sarmatia AJjaticx Htvdii,

Feb. 19. mane, lidem obfervatores ibidem varie cum
nubibus colludiati Eclipfm Solis xgre confpexerunt :
.Hora tamen 6. 59' vifi I'unt deficere duo Digiti, dt poft
unum temporis minutum chorda inter Culpides vifa eft
•xquajis femidiametro Solis.

Apud Wanfted autem D. Pound notavit ad 6^ jq' y"
T. app. chordam inter Cufpides 1 8' 30". Ad 7^ 17' 00"
erat lo' i8"* Ad 7^ 19' 30" eadem inventa eft 8' 05".
Defiit autem Eclipfis ad 7^ X3' 20".

Feb. X5’, velperi, 6^ 44' T. app, WefimonAfierii.i Stella
4>rima Hyadum in Naribus Tauri ( y Bayero ) vifa eft in
re£l^ per cufpides Lunx, adeoque propemodum con-
junda; diftabat autem a limbo Lunx Auftr. 5' 51".
LJiameter Lunx 3 1' .4 j" meniuraca Micrometro.

n

•1

V

r

'4

>•

ij

( ) .

Feh» 2S. ;6'T. app. etiam Weflmnaflertlt vifa eft

Immerfio Stellse in Poplice Vollucis ( a Geminorum
Bayero ) fub limbi Lund obfcuri ea parte, quse paulo
Borealior erat macula quara Hevelius Cretam vocat.
Emerfio ipfa ob ccelum minus purum non confpe(^a eft .*
fed ad 9'' 51' cgrefla erat Stella e limbo lucido, a quo
diftabat 3 rain, drciter, e regione Boreae partis Infulac
Majoris Ca/pii.

Aug. 8. Luna orta eft paulo infra Tdiltcium, cum
quo tamen ob nubes conferri non potuic. Apud W^n*
jied autem 13” x' 00" T. app. vifa eft Prarcedens conti-
guarura ad o- Tauri Bayero, ( five Penultima in noftro
Hyadunt Cz^2\ogo, in Num° 35"4. TrunfaB, litera (\ no-
taca ) in linea re<fta per cufpides Lundt diftans ab Au-
ftrino 4 36". Ad 13*' 7' ij'' Stella p cjufdem Cata-
log! emerfit paulo infra medium obfcuri limbi. Ad
IS*' 19' emerfit Sequens contiguarum didarum, tan-
turn diftans a Cornu Auftrino quantum contiguaj iilae
inter fe, hoc eft 7 min.

Aug. 19. Vefperi, Luna fere Apogxa pafla eft deli-
quium totalem ac fere centralem : orta autem eft Eclip-
fi jam coepta. Hujus obfervationes maxime luculentas
Regise Soc. exhibuit toties laudatus Rev. D. rounds co
ordine quo notatae funt, nempc

o

^2

Temfus

apparem

2

3

4

5

J3 38
53
56 31

37 4
39 J8

Eclipfis Lunse chfervdta apud Wan*
fted, 29. Augufti, 1718.

Chorda inter Cufpides Micrometro
Eadem repetita ( menfurata

Repetita - —

9 (terum
Denuo

22

37
14
19 St
18 28
IS 00

Rrrrrr

7. i

( 85 d )

-0

T. appar.

EcUpfis Jug. 29. 17184

*

h ,

• «*

6

1 1 41

ImmerfiG Totalis in Umbram

7

8 36 13

Stella data in Catalogis omifla oc-
cultata eft a Luna, Faludem

Mareotida Hevelti -

lO 2

8

8 48 18

Luna ccepit emergere ex Umbra —

9

s^ 13

Terminus Umbrs per. med. Mareo-
tidis j fimul Chorda inter Cufpides

5 c

iC

II
I »

5*3 7

H

54 59

Chorda inter Cufpides —

Eadem repetita

Iterum

18 28
9 51
21 14

8 18

Denuo —

37

I

9 0 48

^orphyrites emerfit ex umbra.

*5

8 3

Mons Sind incepit emergere.

t f)

9 17

Umbra per medium Sin(£.

17

IO (

Jam totus Sind extra Umbram.

.8

I I 2C

Umbra per medium JEina*

•9

17 25

’er medium Corficx.

iO

zO C

Per medium Lacus Nigri majerif*

1 1

27 5^

er medium Bcshici.

2-)

28 4)

Emerfit Stella prsdida.

32 34

Byzantium & Horminius fimul emcrgunr^

24

^5

z6

33 58

43 18
47 1

■itella eandem habuit Declinationem cum
Cufpide Auft. fclipfeos.

Chorda inter Cufpides— —1 8' 28''-
^adem repetita 15 00

^7‘9 Si c

□efiifte videbatur Defedus.

lO^ 30', Gapta eQ Lun;^ diameter 29 45". Colla*
tis aucem inter fe Obfervation bus, ubi Chords partis
deficientis squales deprehenfs funt, provenic Eclipfeos
medium.

Ex- Obfenv

r 857 )

Medium.

Fx Obferv. prim? & decima tertia

Ex fecunda & duoc^ev’ma

Ex tertia & undecima —

Ex quarta & dechna

Ex quinta & nona
Ex fexta & odtava

Quorum omnium Medium fit

7

-7

■7

“/

'7

■7

■7

54 58

55 3
55 ^4

55 i8

55 25’
5S 2,9

55 i8

Non minore cum cura eandem Eclipfin, Londini in
Vico Fleet fireet ^ inftrumentis & Telefcopio optimo
Y>. Geo. Graham Automatoposi pr^eftanfis, obfervavic
D. Martinus Folkes Armig. cum aliis quibuidam Regte
Societatis Sodaiibus, uc lequitur.

<538 o Luna per fumum Urbis & Vapores ^gre vifa^

6 54 I 3 Chorda inter Cufpides utcunque, xj"
y X o Immerfio Totalis in umbram.

7 qx 1 5 Stella fixa fatis clara diftabat in limbo Lunae

orientali 19' 21".

8 3 5" 18 Eadem fixa occultata eft, 10' circiter minu-

tis centro Lunse Auftralior.

8 '45 50 vel, ut quibufdam vifum eft, uno minuto
tardius Luna coepit emergere.

8 49 38 Palus Mareotis primo margine emerfir.

8 50 14 Integra Palus extra Umbram.
o 5 Montis Fcrphyritidis medium emerfir.

7 39 - Er^us margo emerfir.

9 8 Mons Sinai totus extra umbram.

10 35 Umbra per medium yFtn<g.

IX o Totus mons ^Etna extra umbram*

18 51 Umbra per medium Lacm Ni^ri majoris.

9 27 35' kifuia Befbicus tota emerfit.

9 42-

2 X

’ { 858 )

9 4^ Chorda inter Cufpides 19' 9".

9 xj Finis Eclipfeos uf quibuidam vifum eft.

9 4J Finis ex pr.'ccedcntc diftancia Cufpidum

conclufa.

9 5-6 Lunx diameter 29' 45", iterumque 29' 48^.

\

Erat autem Umbra admodum diluta, unde orta e(l
difficultas in dijudicandisEmerfionis & Finis momcntis! j
Atque Maculx etiam obfcuriores dare confpedx funt» I
pluribus minucis antequam Umbrx marginem attingc* j
rent. Stella vero qux durante Eclipfi occultata eft, lo- j
cutu tunc habuit x *7! 16',- cum Lat. Auft. i® 6' 30" j
proxime. '

Recepimus etiam Obfervationes hujus Edjpfcos a Rev. j
D’’® Derham^ apud Upminfter in agro tffexunft habitas ; ^ \

D"® Wright apud Crew in agro Celtrienfi ; & a O’" Hawkins j
apud Wakefield la Ehracenfi, cum prxmiflTis ubique fere I
conlentientes, ft adhibcantur meridiaaorum differentix .* 1
pofico fcil quod Upminfier fit 1 min. Landino orienta* i
liuSj Crew vero i o min. & Wakefield 5 min. occidentaliora. '
Denique Coronidis loco obfervacionem adjiciamus, e- j
ximiam quidem, fuique generis, quod feimus, ab inven- <
to T elclcopio primam ; quamque mdefeflx D. Jac. Bradley ,
debemus diligentkr. Quinto enira Sepembris mane. Sole ^
jam fere 30 gr* alto, vidit apud Wanfted ardiflimum Lu-
nx infra Paltluium tranfttum, cujus diftantiam a lin)bo
proximo, ad 59' 00" T.xq. Micrometro invenit 5^38".
Ad S'* 17' 5" diftabat a limbo i' 25''. Stella autem ad
8'' 33' I f" erat in linea reefta per Lunx Cufpides turn ob*
tuftufculaSj nec nifi o' 1 3" diftabat a Bore^. S'* 41' od'
jam Cufpidem illam reliquerat 3' 42". Et S'* 45' 37" ab
cadem diftabat 5' 36". Lunx diameter ad S'* 58'capta

eft 31' 7"-

f

Printed for W. and J. Innys, Printers to the Reyat
Society, at the Prhjces-Arms at the Well-End of
St. Church^Yard* 171S.

7J

■n .

m

I ^59 ) Numb. 358.

PHILOSOPHICAL

TRANSACTIONS,

For the Months of OBoL KoV, and Dec, 1718.

The CONTENTS.

I. InvtnHo Curva qi4Am Corfus defcendens hreviJlim»
tempore defcriberet ; urgente Vi Centripeta ad datum
punSium tendente, c[t4<e crefcat vel decrefcat juxta quam-
vis Potentiam di(iantU a centro ; date nempe imo Curva
pun5io ^ altitudine in principio Cafus, Per Johan«
Machin, Aftron. Profefl' Grefti. & Reg. Soc. Secret.

II. De Potent ia Cordis. Differtatio Authore Jac. Jurin,
M. D, Reg. Soc. Soc.

III. A Brief Account of the Contagious Difeafe vphich ra*
ged among the Milch Cows near London, in the Tear
1714. And of the Methods that were taken for [up
prefjtng it. Communicated to the Royal Society hj
Thomas Bates Efqh Surgeon to His Majejlies Houfioldi
and R. S. S.

IV. A Defer ipt ion of the Organ of Hearing in the Ele-
phant, with the Figures and Situation of the OHicIes,
Labyrinth and Cochlea in the Ear of that large Animal.
Communicated to the Royal Society, hy Dr, Patrick
Blair, R» S. S.

Sfffff I.

L InVentlo Cury^e quam Corpus defcendens hrtViJJi^ |.
mo tempore defcriberet 3 ur^ente Vi Centripeta ad |
datum pmiSlum tendentej quae crefcat Vel decref- '>
cat juxta quamyis Totentiam diflantid d Centro ; i
data nempe imo Cury<^i punSlo <Cr altttudine in |
principio Cajus, ^er Joh. Machin, Aftron*
Profefs. Grefli. ^ Reg. Soc. Secret.

Sit centrumVirium C,(Fig. i. i^,quo centre ad diftan* [ i

tiam CB j^qualem altitudini undeCorpuscafurum eft, |
defcril5atur Circulus B E G, & fiat angulus BCG redlus.- f
Ponatur A putt(Slum Curvse infimum, ubi axi C B occurrit >
ad datam diftantiam C A. Oportet invenire pun<ftum {
ubi Curva celewimi defeensfts E Q^A occurrit circu* •=
lo Q^F, ad datam aliam diftantiam CF. Problema
hoc duos habet Cafus, quorum alter pendet ab Hyper?- I
hola & Circulo, alter ab Ellipfi & Circulo. ^

Caf. r. Sifuerit Vis centripeta reciproce ut diftantia a .
Centro. Sit KLM (Fig. i.) Hyperbola quoevis reeftan- /
gula centre C & Afymptoto C B deferipta, quse oc-
currat normalibus BK, A M fuper ipfam B C ad pun--
tfta B, A eredis, in K & M ; ordinatx veto cuilibet inter-? « |
medias F L ad pundtum F ereds, in L. Fiat C D ad
G G ut v' A F L M ad A B K M, & fit D H normalis. :

fuper CG; dein capiatur Sedor RC B ad Aream HDCB
ut data Area Hyperbolica A BKM ad datum Re<ftanr
gulum CA xAM. Turn reda RCoccurret circulo
EQ^iii pundo Q^, quod quidem eft ad Curvam ce- "
Idrimi defeenfus E

( 8^1 )

Habebitar autem pundum E, a quo indperet Corpo-
ris cafus, capieudo Sedorem B G E aci Aream Qua-
drarvtis BCG, in eadem raclone Arese Hyperboiicae
A BK M ad rcdangulum Tub C A & A M coruentum.

CorolL Hinc fi reda R C, drca centrum C revoluta, fa-
cial Sedores RGB proporcionales Areis H D C B, in
quibus quadrata Bafium C D fumuntur in progreflione
Aiithmetica : turn redse C R interfecabunt Curvam E QA
ad diftantias a centro CQ, quce decrefcant in progref-
fione Geomecrica

Caf. z. Si vero Vis centripeta fueric reciproce ut
lia qu:Evis Poteftas diftanti^e a centro ; fit n-\-i In-
dex iftius Poteflatis ( ubi n potefl: efle Numerus quili-
bec integer vel fradus, affirmativus vel negativus ) fit-
que H=rCB altitudo maxima Curv^e quafitoe E
h — C k altitudo minima ejufdem, & A = CF altitu-
do alia qusevis intermedia. Fig, z.

In reda C G capiatur CD ad C B ut V ad V A? %
atque etiam C H ad C D ut V A" — ad V H" — h'".
Centro C, femiaxibus CD, C B, delcribatur Ellipfis
B L D, cui occurrat ordinatim applicata H L in pundo^
L; & ducatur reda LK, quas Ellipfm tangat in L, & ;
Axi minori CD produdo conveniat in K : dein Tan-
genti KL parallela ducatur NM, circulum B E MG '
tangens in M & ipH CD occurrens in N. Denique
capiatur Sedor RGB, qui fit ad Aream NMBLKN^
inter Circulum & Ellipfm & utriufque Tangentcs rec-
tamque N K comprehenfam, in ratione Numeri binarii »
ad Numerum n. Turn reda R C inter fecabit Circulum t
F Q^in pundo Q., quod erit ad Curvam celerrimi De(^
cenfus E Q^A.

Quod fi fiat Sedor BCE ad aream BDG, inter El»i ,
lipfeos & Circuli Quadrantes interceptam, in rations .'
dida Binarii ad Numerum », coeuntibus fcilicet pundis
L, D & M, G j (ob A” = H*") erit pundum E wnde in-.

( 86i )

cTioarctut Cafus Corporis brevifljmo tempore defceti-
dentis ad A, defcenfuque fuo Curvam E Q^A defcri-
bentis, quam cangic reda C E in E^ quamque ad angu-
los red^os fecac C 6 in A.

Harum Conftrudlionum Demondrationfis e Celeber-
rimi D. Newtojti ^adraturh, ejuidemque Philof.Mat. Pri»-
cipiis (Pi op. XXXIX. & fequentibus aliquibus) petitse,
ali^ data occafione odendentur- Problema aucem ed
alcerius generis, Defcribere Curvas per quas Corpora,
de puncdo fummo E, feu principio cafus, demida, ce-
ierrimo defcenfu ad inferiora data punda d, urgente
<iualibet Vi centripeta, ferrentur; cujus quidem folu'
tio in potcdate ed. In pr^feniia fufliciat generalem
hujufniodi Curvarum tradidide Ideam, earumque ad
Circuli & Hyperbolae Quadraturas relationes indicadc,
abfque quibus eafdem Geometrice.condruere baud a-
deo proclivc ed.

II. De

II. De Potentia Cordu,

Diflertatio Authore Jac. Jurin, M.D.

Soc. Sodale,

Viro Eruditiffimo

R I c H A R D o Mead, M.D.
s. <P- D.

Jacobus Jurin.

Dirquifitionem iftam, VirCIariffime, ututrudem &
imperfed:am, acri tamen ac perfpicaci tuo Judi-
cio mukis nominibus non illibenrer permitto. Quern
enim mihi potero auc Judicem aequiorem praeopcare,
auc Cognitoreni deligere magis idoneum, quam cujus
Viri candorem animi fingularem, morumque liumani-
tacem, non minus atque Mentis dotes priceiientes illas,
& optimo quoque Literarum genere perpolitas, omnes
fufpicimus; cujufque turn acumine Ingenii, turn Judicii
fubtilitate, Thcoriam Medicam videmus clarilTima luce
perfufam & illuO:ratam,Ufum veto medendi confirmatum
pariter tenemus & expeditum.-^ Nec fane quifquam efl;
Mortalium, cujus calculocogitata ifia nokra comproba-
ri magis kudeamus, aut cujus audoritate, fi tibi forte
fortuna minus diiplicuerint, ea contra Hominum quo-
rundam perverfbrum iniquitatem tutiora Tint furura. Ex
quibus alii praejudicio dudi 6f fama magnorum Nomi.

T 1 1 1 1 c num,

( 8<^4 )

nunij quorum fententias in lequemibus paffim redargui.
mus, naftra forfuan ne examine quidem aut perle(3u dig-
na cenfuri func. Alii vcro, ut five labore difcendi, five
imperiti^e pudore fe expediant, omnia fciliceo, quae-
cunque ipfi non inrelligunt, videri volunt ako fuperci-
lio conremnere. Quibus uri non gravate concedimus
doftos Vires & olini exllicille, & hodie reperiri non
paucos, qui nulla in[tru6li difciplina Mathematic^ me-
dendi Artcm tamen felicitcr & cum laude exerceanc ; ita
viciiTim ipfos fatcri xquum eft earn doiftrinam in Praxi
expedienda non inutilem, ad naturam vero & caufas
Morborum explorandas plane efte ncceftariam. Corpo-
ra enim Animalium, quod tu profeifto, fi quis alius,
©prime incelligis, cum partim folidis canalibus parcim
fiuido conftent per cofdem jugiter propulfo, Machinas
efie patet, ac proinde opus efte, ad eorum Fabricam, Vi-
rC'S, Adiones, & agendi Impedimenta five Morbos rite
per fpiciend os, rei Mechanica: pentiam.

De quibus tamen'multa traduntur etiam a Mathema-
ticis Scriptoribus adeo parum accurata, fecumque invi-
cem & cum rations pugnantia, ut nobiliftimae Icientiiis.
non modo commendacionem non addant & dignitatem,
fed etiam contemptui & hominum indedorum ludibriis
eandem objiciant. Quis emin, non ipft dodrina Ma-
thematica imbutus, cum videat, Exempli gratia, Cordis
Humani vires jam ponderi 3, ooo librarum pares, jam
180,000 pondo fuperantes, jam vcro ad iincias f vel 8-
dedudas; Aerem qaoque ex fiilmone inter exfpiran-
dum propulfum modo 100, mci o jo oco librarum vi ;
Quis inquam, qui iilas conciufiones Icgerit eiferimine
tarn immani a le invicera remoras & tamen omnes de-
monftrationibus fuis munitas, fi ^orce fe a rilu remperer,
non ranien inucilem plane & ineptam pronunciaverit ad
explorandas Corporis faculratcs feu ntlnm Mechanicam?
SedjiieminerJuc oportet a;qui rsrum judices neuriquam

mirandum.

( 8(5j )

mirandum eHe, fi quandoque in difiicili Problemate vel
fumma ingenia aliucinentur, neque errores, fiqui forte
inciderint, Arti ipfi, fed Artiiici imputandos. Quod
ut Exemplo manifeftius declarecur, libet celeberrimi Pro-
blematis de Cordis viribus indagandis folutionemnovam
proponere. Utque facilius mibi temeritatis opinionem
detraham, qui ejufmodi inceptum pofl: Alphonfum Bo-
rellum aggredi aufim, utque viam fimul Ledori expe-
diam ad :rquam certamque fententiam in tanta ictipto-
rum diflenfione ferendam, ptimo loco oftenfurus fum,
quas in Borelli demonftratione reprehendi debeant,dcinde
Virorum Dodliffimorum, MorUndi, & Keilii folutiones,
cum eadem philofophandi libertate ad examen revocabo.

Primum nobis, & quidem longe prcecipuum videcur
Borelliafia fo-lutionis vitium, quod Cordis Potcntiam per
pondus iners & quiefcens expofueric. Corenim cum &
ipfum inter contrahendum movetur, & corpora oppofita,
Sanguinem nempe Arteriarum tunicas, in motum im-
pellic, pacer ejus Potenciam non alia ratione fciri polle
quanta fit, quam uc motus hujus quantitatem cognitam
teneamus. Motus autem quilibec cum pondere quief-
cencecomparari non magis potefi:, quam Linea cum Rec-
tangulo.

Secundum, quod in ipfo Experimento a Circulatore
in(lituto,neutiquam conftec pondus illud furpenfum fuifle
a fold Mulculorum vi contradlrice ; quuni etiam vis ilia,
qua turn Mufculi adhibici, turn gena: quoque, & ipla
forfitan ligamcsita divulfioni fui ipforum Stfibrarum rup-
tioni obiliterint, qu^ue Mufculi etiam ex cadavere ex-
fcdi pondera latis magna fuftinent, venire in fubfidium
potuerit.

3. Quod vires Mufculorum pondere sequalium a Bo-
rello pares ftatuancur : quod profedo dubium admodum
videtur, prsefertim ubi Mufculi func figura dilTimiles.

T t c 1 1 1 2 4 Quod

{ 8^<5 )

Quod integram Cordis Potentiam, quanta maxi-
ma exeri potefl; cum fumm^ fibrarum contentione &
molimine, ad fingulas Sy doles ad hiberi pofuerir, Quum
ipfe Circulator, fi pondus fufpenfum vcl continentcr, vel
alternis vicibus brevifTim^ quiete interpofid, fublevarc
contenderer, non ita longo tempore plane fuccubiturus
labori fuiflet,

5. Quod Sanguinis & Arteriarum refiftentiam fexage-
cuplam ftatueric tetius Potentix Cordis, loco ejus Poien-
das, qucE ad fydolem peragendam a Corde impenditur,.
qua?que forte totius Potential minima pars eft.

6. Quod in ea ratione fexagecupU definiend^ errorem
infignem admiferit. Nam in Prep. 60, loco rationis, .
quam obtinet Summa Potentiarum F ad Summam
R 8c S, adhibuit rationem, qux eft inter Redangulum
ex Potetitiis P, ^ confeeftum, & Redangu!um ex R, S.
Quod errati ft per Propofttiones fubfequentes corrigatur,
habebitur in Prop 7}, reftftentia longe major quam abip-
fo Bordlo definita eft, nempe pondus iibrarum 1,076,000,
loco Iibrarum 1 80,000, idque fecundum pofttiones ab.
ipfo Viro Clariftimo ufurpatas-

7. Denique quod pondus illud Iibrarum 1 80, cco,

quum a Cordis Potentia libris 3,000 ccquali fuperetur,
miraculi cujufdam aut monftri loco lecftoribus obtrudat ;
& Vim Percuftionis, quaft quendam &eov am in

auxilium advocet. Reipsa enim nibilo plus hie ineft pro-
digii, quam ubi pondus 3,000 Iibrarum pondus aliud
180,000 Iibrarum, ad fubfexagecuplam diftantiam a cen-
tro Librie inaequalium radiorum appenfum, in aequili-
brio fuftiner. -

Minora aliquot Sphalmata, & Hypocliefes plurestum
prorfus arbitrarias, turn alias aliis contrarias, non illi-
benter omittimus. Et quidcm delida fupra reprehenfa,
autfaltem majorem eorundem partem, non tarn ipfi Vi-

( 8^7 )

ro Docfliffimo impucandam cenfemus, quam Operi F oft-
hurno condonandam.

Froximus requicur Vir DoflilTimus Jofephas Morlan-
ius, qui in Dilquincionibus de Cordis vi Sermone An-
glicano ediris, Methodum peringeniofam expofuit Poten*
tiam Cordis ad Experimentum revocandi. Hie aiuem,
prseter delidum fupra m Bor ello reprehenfum, quod
Gordis vires cum pondere quiefeente contuleric, nobis
videtur eo quoque nomine norandus, quod integram
Gordis adionem in tunicas Arteriarum diilendendas
impendi pofuerit. Cor enim non folum Arterias tendir,
fed Sanguinem quoque certa velocitate per totum Arte
riarum & Venarum cradum propellir.

Sapereft, utViri AcutiiTimi Jacobi Keilii folutionem,.
in Tentaminibus Medico-Pbyficis ad Oeconomiam Ani-
malem percinentibu?, non ita pridemeum Publico com-
municatam, expendamus. Qui primus omnium aufus eft
PotenTiam Cordis a Borello definitam, ae magno Scrip-
torum confenfu exceptam &> laudatam, non folum rejice-
re, fed aliam eidem infinite prope diferimine minorem
numeris difertis exprelf'm fubftituere.

Hunc autem cenfemus, prteterquam quod primum il-
lud Boreli/anx [biin'wnls vitium imicatus fir, in fequenti-
bus etiam a vero aberrafic.

Qiiod Corollarium Newtoniamm, quo utitur ad Cor-
dis vires definiendas, auc male incellexerit, auc cerce nod
fatis apte ufurpaverir. Pond us enim illud ab Archtmc’
de Britanmeo decerminarum, quo Motus aquas ex vafe
eftluentis generari potefl, ncquaquam gencrat Motum a-
quse ; quippe quio gravuacis vi cadendo ipfa Motum '
fuum acquirac. Sed h c pondus per datum tempus ca*
denuo, Viotum concipic Motui aquse eodem daco tempo-'
re effluenris ctquaiem.

Prastcrea ponit Vir Clariffimus velocitatem Sanguinis >
ex Cord e effluencis pprpetuo sequalem per totamSyfto»*

isS-J

( S68 \

Ics durationcm, quam nos infigniter inaequalem fieri in
fequcntibus oftendemus.

In Mechedoilla fimpliciore, quam poftca adhibet Vir
Dodiflimus, prxcer dclidta hadtenus reprehenfa alia e-
tiam bina admittir.

Adfumic enim Vires Cordis in -diverfis Animalibus ^
earn inter fe rationcm obtincre, quae efl: inter pondera '
corundem ; quod infra falfum efle demonftrabimus. Turn ;
ponic velocitatem Sanguinis ex feda Iliaci Arterii pro-
fluentis, eandem efle qua ex Corde in Aortam emittitur. i
Arqui cum omnis fere languis ex Corde expulfus per Ilia- j
cam alteram refedam emittitur, patet ejus velocitatem
tanto efle majorem in lliaca quam in Aorta, quanto fee-
tio Iliacae circularis a fedione Aortje fuperatur. Praeter- »
quam quod velocitas aequabilis, qua Sanguis per Aortam
fluic, longe diftet ab e4 veJocitatc, quicum exit ex ipfo |
Corde. f

Similiter fere redargui poteft & ilia Methodus, qu^ u- t
fus eft Vii Cl. ad rationem definiendam inter velocitates f
diverfas Sanguinis, refiftentia nunc oppofica, nuncfubla- f
la, per Aortam profluentis. Sed cum ifto Experimento ?!
non altera folum, fed utraque velocitas major sequo re- ?
periatur, unde ratio, quse eft inter ipfas, non magnope-
re pcrcurbetur, poteric Tatis tuto proportio ab ipfb ex-
pofita, tanquam verae propinqua, ufurpari,

Curfu hadenus expedite, fcopulifque decedis, in quos
impegerunc Viri egregii fupra laudati, erit modo nobis
ipfis, uc in via difticili & erroribus plen^, fumm^adhi- ^
biia cautione progrediendum. Et primo quidem loco .Jt'
ad ambiguitatem prsecidendam necefte eft, ut id, quod I
quaeritur, quale fit, accuratius paulo declaretur. v

Cordis Virium, five Potentitc, nomine fignificamus
vel ipfum Cordis Motum, dum in contradionem agitur, ••
vel Motum ponderis cujusliber, quod Sanguini cbjedum

‘ ex

( S6p )

ex Corde proruenti & velocitate idonca delatum in par-
tes concrarias, Sanguinis efHuxum, adeoque ip'ati Cor-
dis contradiioncm, squali vi librare valet & fiftere.

Potentiam idam, cum a priori vix fperandum fit ut
dennire poflimu’3, quod neque fabricam Cordis interiO'
rem, neque caufre contrahentis nacuram, auc vires fatis
I habeamus exploraras, relinquicur, ut eandem per eiieda,
five a poderiori, a’dimsmus.

Cordis adio in Ventriculorum ruonim contradione
omnis conddit. Ventriculi autcm inter contrahendum
in fang.uinem impingunt, eique Moius lui partem com-
muiiicandoj eundem magna vi, qua datur porta, urgent,
& expellunt- Sanguis hoc modo in Artcrias, Aortam
& Pulmonalcm, protrudis, impetu in omnes partes fado,
partira in tunicas Arteriarum ex Sydole fua pragrefia
coJlapfas & fiaccidas, partim inSanguinem priorcm tar-
dius fluentem impingit. Unde gradatim cxurorfum tru-
duntur Arteriarum tunica, ^ Sanguis antccedens curdi
celeratur. Quod fi animo concipiantur Arteri^ fedio-
nibus tranfvcrlis minimis didindx, prima San'iuinis por-
tiuncul^ ex Corde in primam fedionem irruente, partim
didenditur ida (cdio, partim Sanguis eadcm ancca con=
tencus in fedionem proxlmani detruditur, earnque did-
cr.dit, arquc idaadio per (iiccedentes Arteriarum' fedio-
nes continuatur. Deinde fccunda, & tertia d>nguinis
portiuncula, & ccetera! deincens, in primam Aiterire fe-
dionem incidunt, earnque paulo niagis dilatant, & fan-
guinern eadem contentum in proximas fediones fuccef
i?ve propellunc ; idque fieri pergir, donee omnis fangiiis
ex Ventriculis fuerit ejedus, Ca^terum id auique ebdr- ■
vandum ed Arcerias, quo magis contradre flaccida:
fuerinc, eo minus dilatatiom obfidere, quanto autem
magis fuerint diiatatte, tanto fortius ulteriori didradio-
2u reniti ; arquc idcirco Vim Sanguinis ex Corde pro-
lumpcntis primo m?g!S impendi ii didendonem Arte-

z riatym,..

( 870 )

riarum, quam in Sanguinis prsecedentis protrufionem’
* Tub finem vero magis propclli Sanguinem antecedentem
quam diliendi Arterias, quippe qux jam rigidsc h&x
majorem dilatationem vix admictanc.

Sanguis autem ex Corde profiliens, cumj uti didlum
eft, Motus fui partem Arteriarum tunicis, partem San-
guini pracedenti communicat, ipfe neceflario de prifti-
na celeritate remittit; adeoquedum Ventriculorum con-
tract jonemmoratur, novum abiis impulfum excipit, ejuf-
que partem, eadem ratione atque antea, tunicis Arteriarum
& prascedenti Sanguini impendir, unde iterum retarda-
tur, & alium Ventriculorum irftum fufcipit, & fic dein-
ceps, donee omnis ex Ventriculis fuerit expulfus.

Prater caufam (upra expofitam, fupereft alia, qua
Sanguis ex Corde effluens gradatim retardatur, adeo-
que novos fucceftive impetus excipit ex Ventriculis fefc
contrahentibus. Nam Sanguis in Arteriam Aortam
infiuens, etiamft nulli omnino reftftentice occurrere
ponatur, adeoque nullam pati Motus fui imminutio-
nem, tamen, cum ex lato in anguftum fertur. Ion-
gitudine perpetim crefeit, donee totus in Aortam perve-
nerit; cumque fedtio Aoftse non minuatur, neceftario
rainuitur Sanguinis velocitas. Motus enim Sanguinis eft
in ratione compofita, ex ratione SeCtionis Aorcse, velo-
cicate in eadem, & longitudine Columme Sanguinese,
per Theorema noftrum 111. De Motu Aquarum fluentium.
Cum vero ea Sanguinis portio, qu^e jam pervencrit in
Aortam, gradatim retardetur, retardabitur inde San-
. guis ifle qui adhuc Ventriculo conrinetur, & hinc re-
tardabitur ipfius Ventriculi contradio. Unde Ventri-
culi perpetuo aliam atque aliam Motus fui partem
Sanguini contiguo, his de caufts perpetim retardato,
communicabunt. Patet vero ifthinc, ut id obiter note-
mus, aiium efte Motum Sanguinis ex Corde erumpentis,
ahum ejufdem jam ex Corde expulfi, & intra Arterias

ftuentis.

( 8/i )

fiuentis. Item idum. five impulfum Ventriculofum in
Sanguinem imprefTum, qui alioqui unicus eflet futurus,
& pundo temporis tranfigeretur, tamen caufariim (u-
pra didarum vi, quibus Sanguis perpecim retardatur,
per cotam Cordis Syftolen continuari.

Ventriculum itaque alterucrum Cordis Sanguinem
impellentem licebit fpedare, ut datum corpus cum
data celeritate impingens in aliud corpus quiefcens,
cui Motus fui parte commiinicata ambo corpora com-
muni velocitate deferuntur. ^quatur autem Potentia
ejufdem, vel Fac^o ex pondere Ventriculi Sc velocitate
ejus initiali , priufquam in Sanguinem impingat; vel
Sumniac Motuum ipfius Ventriculi ac Sanguinis ex eo-
dem profluentis, & Moms qui tunicis Arteriarum &
Sanguini prsecedenti communicatus eft; vel etiam, ft
abcfte ponatur omnis Arteriarum & Sanguinis prjeceden-
tis refiftentia, Summce Motuum ipftus Ventriculi &
Sanguinis efHuentis.

Theorema I.

Motus, Machina cava inaqualiter contra^ His in
contraSiionem agitur^ <equalis eft Summon Fa^orum ex ftn*
gulis Machine farticulis duHis in velocitates re[pe.5fivas»

Patet ex Mechanica.

Corel, r. Machinse Motus minor eft Faefto ex ponde-
re Machine dutfto in’ velocicatem earum Machin^e par-
tium, quse omnium celerrime moventur inter contra-
hendum.

z. Motus Machine cequatur Fado ex pondere ejul^
dem, dudo in velocitatemaliquam mediam inter veloci-
tates earum Machinx partium qux omnium celerrime,
& earum qux omnium tardiftime, moventur.

3. Si Machinx plures ftmiles fimiliter fefe contra-
hanc, velocitate medi^, vel xquabili vel inxquabili, ft-
militer tamen aud^ vel imminud in omnibus Machi-

U u u u u u nis ;

( 8/1 )

nis; Motus, quo Machina qusque in contradionem ^
gicur, racionem obciner compofitam ex racione quadro-
piicata Diamecri homologns ipiius Machinae, & ratio ne
inversa temporis, quo Machinae concradio perficitur;
vel rationem comporitam ex ratione ponderisMachinae,
racione ejufdem ponderis fubcriplicat^, & ratione tem-
poris inversa. Thcoremata rcli^ua hue fpe^antia in Trani-
aiSione proxime tdenda exhibebuntur*

III. A !Brief Account of the Contagious Vifeafe which
raged among the Milch Cowes near London, in
the Year 1714. And of the Methods that were
taken for fupprejftng it. Communicated to the
Royal Society hy Thomas Bates Efq^ Sur»
geon to His Majeflies Houjholdj and R. S. S.

Bout the middle of July the Diftemper appeared

at /(lington, and thereupon their Excellencies the

Lords Juftices having notice of it, were pleafed to Com-
mand chat I ihould examine into the truth of the Report
of its being Contagious ; and order’d the Lord Hur court,
then Lord High Chancellar, to grant fuch Authority as
wou’d be proper to make the Difeovery. Accordingly
Mr. Milner, Mr. Offley, Mr. Richardfon, and Mr. Ward,
four Juftices of the PeSce for the County of Middlejex,
were appointed to make the neceflary Examinations.

Purfuant to thofe Orders we went to Iflington, where
Mr. Ratcliff had loft no out of 200 ; Mr. Hufford Sz
out of 72; and Mr. Pullen 38 out of 87. They were
very unwilling to own it, becaufe lo foon as it Ihould
be known, none wou’d buy their Milk ; but Mr Ratcliff,
a Man of good Judgment in Cattle, after much per-
fwafion, gave us the following account, viz. That they

*

firft

( sn )

firft refufed their Food ; the next Day had Huskilh
Coughs, and voided Excrements like Clay ; their Heads
fwelled, and fometimes their Bodies. In a Day or two
more there was a great difcharge of a Mucous Matter
by the Nofe, and their Breaths fmelled offenfively*
Laftly, a fevere Purging (fometimes Bloody^ which ter-
minated in Death. That fome died in three Days, and
others in five or fix, but the Bulls lived eight or ten.
That during their whole illnefs, they refufed all man-
ner of Food, and were very hot.

We then advifed with feveral of the Cow-leeches, or
Dodtors, who all agreed that it was a Murrain, or ra-
ther a Plague ; and that the Methods they had tryed
for a Cure, had proved unfuccefsful. This Difeafc was
fo furprifing, that fome of thofe Men who ufed to look
after them, were afraid to go near them.

We then ordered fome of the fick Cows to be Houfed,
and feveral forts of Cattle to be kept with them, to fee
whether the Contagion would affed: any other Species*

The next Day I made a Verbal Report to their Ex-
cellencies, of all the feveral Opinions and Difcouries
which I have had about it, and left them debating what
Method to take ; at laft I was called in, and Ordered
to confider of it again the next Day, and to deliver to
them in Writing what would be proper to be done. Ac-
cordingly I drew up, and gave them the following
Propolals*

1. That all fuch Cows as are now in the pofieflion of
Mr. Ratcliff, Rufford, and Pullen, be Bought, Kill’d, and
Burnt : or, at lead, that the Sick be Burnt ; and the
Well kept and fecured on the Grounds where they
now are, that (uch of them as Sicken or Dye of this
Diftemper may be Burnt.

U u u u u u 1 n. That

( 8/4 >

II. That the Houfes in which thoie Sick Cows have
flood be Waflied very clean, and then fmoaked by the
burning of Pitch, Tarr. and Wormwood, and be kept
three Months at leaft before any other Cows are put
therein.

III. That the Fields where thofe Sick Cows have
Grazed, be kept Two Months before any other Cows
are FufTered to (land or Graze thereon.

IV. That the Perfons looking after fuch as are III,
fliou’d have no Communication with thofe that arc
well.

V. That the fame Methods be Obicrved if any o-
ther of the Cow-keepers fhou’d get this Diftemper a-
mongthem; and that they be all Summoned and told,
that as foon as they perceive any of their Cows to re-
fufe their Meat, or have any other Symptoms of this
Diflemper, that they immediately feparate them from
their others, and give notice to fuch Perlons as your
Excellencies Ihall appoint, that they may be Burnt ;
and the places where they have flood or Grazed to be
ordered as before*

VI. That the Cow- keepers be required to divide
their Cows into fmall Parcels, not more than ten or
twelve in a Field together; and that they be allowed
fuch fatisfadion for complying with thefe Propofals, as
your Excellencies fliall think fit ; all which is moft
humbly fubmitted,

The next day their Excellencies confulted the four
Gentlemen before-named, and gave them Orders to com-
ply with the preceeding Propofals, and to allow Forty Shil-
lings for every Sick Cow which they Burnt, that be-
longed to Vit. Ratcliff, Rufford, Pullen \ but the free
intercourfe which both Maflers and Servants had had
with each others Cows (before we were appointed^
^ 2 had

(^75^

had fpread the Contagion , and the Difeafe began foon
to appear in feveral other Neighbouring places.

The Gentlemen then fummoned all the Cow- keepers
in the County, and acquainted them with the above-
named Propofals (to mofl: of which they readily Com-
plyed, as being vifibly their interefl:) and offered them
Forty Shillings for every Cow which they Burnt, that
had not been Sick above twenty. four Hours ; but for
fuch as had been longer 111, or were Dead, they wou’d
allow them only the value of their Skins and Horns.

Some of the Cow-keepers appeared not content with
this Regulation, and believing that the Difeafe wou’d
become general, defign’d to have fold their Cows at
fome diftant Market; which the Gentlemen having no-
tice off, appointed feveral Butchers to Watch near their
Grounds, and count their Numbers every Morningj,
with Orders to follow fuch as they fent to any Market,
and prevent their being fold, by telling the people what
they were.

Another great Obflacle at the firfl was the Cow-
keepers not owning the Difeafe, till they had loft fe*
veral of their Cows; for fo foon as it was known that:
any Man had but one Sick, none wou’d buy his Milk ;
and to thofe who kept many Cows, that lofs was
eonfiderable.

Nor was there ever wanting one or other who gave
them hopes of a Cure.

To obviate thefe three difficulties, the Gentlemen
encouraged them to hope for a Brief, but aflured them
that fuch only as complyed with thefe Oiredions, fliou’d
have any benefit by it- Accordingly they ordered a
daily account to be taken of the Condud of each Cow-
keeper, and allowed or difallowed their pretenfions to
this Brief, as well as to, the. Forty Shillings per Cow, as
they complyed qr difregarded thefe Ditedioiis:

This..

( 8/(5 )

This had a pretty good effcd ; but here in England^
where every Man is at liberty to difpofe of his Cattle
as he plcafes , nothing but making them fenfible that it
was each Mans particular intereft to comply with thele
Methods cou*d do ; this, tho’ true in fa<S, yet the Rea-
der will readily judge to be very difficult among fuch a
Number ; but the Gentlemen fpared no labour to ac-
complilh it; for that purpofe they fummoned them once
or twice every Week, urged all that cou’d be faid to in-
duce their Complyance, and omitted no warrantable
means to fruftrate their Folly.

1 had Orders from the beginning to aflift thofe Gen-
tlemen with my Advice, which I did at mod of their
Meetings ; as alfo to make a ftrider enquiry into the
Difeafe by Difledions, &c.

Accordingly I difcourfed the Corv-leeches about the
'Cuftoms and Difeafes that Cows were fubjed to, and
confulted fuch Books as treated of them ; but concern-
ing this Diieafe, I cou’d gain but fmall adidance from
either.

I then made Didedions of fixteen Cows, in diffe-
rent degrees of Infedion ; and found the Putrefadlon
of their Fifcera to encreafc, in proportion to the time
of their Illneft.

The fird five that I opened, had bearded with thofe that
were 111, and the Symptoms of thisDidemper werejud
become vifible ; in thefe, the Gall-bladders were larger
than ufual, and filled with Bile of a natural Tade and
Smell, but of a greener Colour. Their Pancreas's were
ihrivelled, (bme of the Glands obdrutded and tumi-
fied. Many of the Glands in their Mefenterys were twice
or thrice their natural bignefs. Their Lungs were a
little inflamed, and their Fleih felt hot. All other parts
of their Fifcera appeared as in a healthful State.

The

( *77 )

The next (ix that I opened, had been ill about two
Days ; in them the Livers were blacker than ufual, and
ill two of them, there was ieveral Gyfts filled with a
Petrified Subftance like Chalk, about the bignefs of a
Pea. Their Gall-bladders were twice their ufual big-
nefs, and filled with Bile of a natural Tafte and Smell,
but of a greener Colour than the fird. Their Pancreas's
were ftirivelled, fome of their Glands very large and
hard, and of a blackifli Colour. The Glands in their
/klefenterys were many of them five times their natural
Bignefs, and of a blackifii Colour. Their Lungs were
inflamed, with Ieveral fmall Cyfts forming Their In- •
teftins were full of red and black Spots . Their Flelh i
was very hot, tho’ not altered in Colour. .

The five lafl: that I opened, were very near dying ; ;
in them I found the Liver to be Blackilh, much Shri-
velled and Contra^ed, and in three of them, there was i
feveral Cyfts as big as Nuts or Nutmegs, filled with a =
Petrified Subfiance like Chalk. Their Gall-bladders
were about three times their ufual bignefs, and filled .
with Bile of a naturaLTafie and Smell, but of a deep >
Green Colour., Their Pancreas's were Shrivelled and
Contratfied, many of their Glands very large and hard,
and of a black Colour, The Glands in their Mefenterys .
were niany of them..diftended to eight or ten times ..
their natural bigneis, were very Black, and in the Pelvis
^ of moft of thofe Glands in two Cows, there was a {
yellow Pctrefa<fiion, of the confifience of a fandy Stone,
Their Intefiines were the Colour of a Snake, their in-,
ner Coat excoriated by Purging. . Their Lungs were -
much Inflamed, with feveral Cyfis containing a yellow 7
Purulent Matter, many of them as big as a Nutmeg,
Their Flefti was extream hoc, tho* . very little altered
in Colour.

I have. .

( 87? )

I have here only given you a general account of my
Difledions, in the three different Stages of cheDifeafe;
for as the difference was but fmall, and the Difeafe i
incurable, it could neither be ufeful nor pleafant to the j
Reader, to have each particular Difledion at large, tho* j
! have now the Minutes by me. But the following j
Cafes being very extraordinary, I coud not omit the
mention of them, viz. In one of them the Bile was Pe-
trified in its Veffels, and refembled a Tree of Corral,
but of a dark yellow Colour, and brittle Subftance.

In another there were feveral Inflammations on the Li-
ver, fbme as large as a half Crown, cracked round the
Edges, and appeared feparating from the found parr#
like a Peffilential Carbuncle.

In a Third, the Liquor contained in the Perieardium ;
(for Lubricating the Heart in its Motion^ appeared like \
the fubfidings of Calcis ; and had excoriated, and
given as yellow a Colour to the whole Surface of the
'Heart and Pericardium, as Aqua Calcis cou’d pofTibly i"
have done. S

In giving my Opinion of this Diftemper, I muff beg
leave to premife, that all Cows have naturally a Pur-
gation by the A^us for five or fix Weeks in the Spring,
from (as the Cow-keepers term it) the frimnefs of the f
Grafs ; during which time they are brisk and lively, their
Milk becomes thinner, and of a blewifli Colour,
fweeterto the Tafte ; and in greater Plenty; but the
Spring preceeding this Diftemper, v.'as all over Europe
fo dry, that the like has not been known in the Me-
mory of any one living ; the confequence of which was
little Grafs, and that lo dry and void of that frimnefs
which it has in other Years, that I could not hear of
one Cow keeper, who had obferved his Cows to have
that Purgation in the fame degree as ufual ; and very
l^w who had obferved any at all. They all agreed

{ S/p )

I that their Cows had not given above half To much
Milk that Summer as they did in others; that fome of
I them were almofl; dry; that the Milk they did give
( was much thicker, and yellower than in other Years.
It was obferved by the whole Town, that very little
of the Milk then fold wou’d Boyl without turning ;
and it is a known Truth, that the weakeft of the com-
mon Purges you can give a Cow entirely takes away
I her Milk ; from all which Circumftances, I think it e-
vident, that the want of that natural Purgation was
the foie caufe of this Difeafe ; by producing thofe Ob'
ftrudfions, which terminated in a Putrifadion and
made this Didemper Contagious.

During my daily Converfation at that time with Cow-
keepers, &c. there occurred many other Circumftan-
ces of iefs Moment, to confirm me in this Opinion :
but as there was no one reafon to give me the lead
notion of any other Caufe, I (hall not trouble the Rea-
der with a ulelefs detail of them.

Cows are like wife fubjed to a Purgation ftho’ in
a lefs degree) from the fame quality in the Graft, about
the latter end of Seftemher ; which is called the latter
Spring; and which I believe contributed not a little,
to the preventing the encreafe of this Difiemper; for
this Purgation coming fo foon after the Difeafe appear-
ed, it is not unrealbnable to fuppofe, that it freed
fuch Cows as were not much injured, from the ill ef-
'feds of thofe Obftrudions, occafioned by the want of
their Vernal Evacuations.

Several Phyfitians attempted the Cure, and made
many Edays for that purpofe; but the Difiedions con-
vinced me of the improbability of their fucceeding,
with which I acquainted their Excellencies. However
they having received the following Recipe and Dire-
dions from fome in Holland, faid to have been uled

X x; X X X X there

( 88o )

there with good fuccefs, gave me Orders to make tryal
of it : But the effedt was anfwerable to my expectation,
for in very many Inftanccs, I was not fenfible of the.
leaft Benefit.

Herh. Ariftoloch, Rotunda,

Veronica^ a~a M.viij
Palmonaria,

Scordfjf (Ta M. 4

Rad. Gentian^f
Angelica,

Petafitidis,

TcmemilU,

Carlina, a~a ft fs.

Bacc» Laurif

Juniperi, ^a fxi). Mifce fiat Tulv,

See Phil. TranfaPl. N°. 338. in fine.

This Powder is to be given in Water, one Ounce
at a time, three or four Mornings fuccefiively ; then
reft four Days, and if the Difeafe continues, repeat the
Powders in warm Water, as before.

I think there is no one Method in Practice, but what
was tryed on this Occafion, tho’ I cannot fay that any
of them was attended with an appearance of Succefs ;
except that of Bleeding plentifully, and giving great
quantities of Cooling and Diluting Liquids. But by
this Method,' the inftances of Succefs were fo few, that
they do not deferve any further mention.

Their Excellencies being informed that the feeding
Cows with Diftillcrs Grains was a new Cuftom, and
was the caule of this Difeale, gave me Orders to exa-
mine into theTruthof it3 but upon enquiry 1 found it
to have been the Practice of feveral ot die ' ow kecpcis
above twenty Years,, without the leaft- appearance of

2a any

( 88i )

any inconvenience; and that fome of thofe Perfons who
bad fuffered moft, had never given any. Nor is there
I any difl’crence between thofe of Brewers and Diftiiiers,

I only that the latter are the dryer.

It was likewife faid, that the want of Water was
the caufe of this Difeafe, for that the Springs and pla-
ces where People ufed to Water their Cowes, were
almoft every where dry ; and that many were obliged
to fend them feveral Miles for Water. This might pro-
duce fome Difeafes, but fuch only as they got by the
fatigue of being driven fo farj for Mr. Ratcliff, Mr. Ruf-‘
ford and Mr. Pullen, the three Perfons where this Di-
feaie firfl appeared, had the New River Water running
thro’ the very Grounds where their Cows conftantly
Grazed, and cou’d drink at their Plealure, and fo had
mod of the Cow* keepers at Iflington.

There were at that time feveral other reports of the
caufe of this Difeafe, but none that had a fliew of
Reafon.

About the latter end of September, the Difeafe in-
creafed, and the Numbers brought to be burnt were
fb great, that it cou’d not be well executed ; therefore
it was judged proper only to bury them fifteen or twen-
ty Foot deep: but firfl to make large fneifions in their
mofl Flefliy parts, and to cover them with quicklime.

At the fame time, having notice that it was a Cuflom
with the Cow-keepers, to fend their Calves when a
Week old to Rumjord, to be Sold; and apprehend-
ing by this means that the Contagion might be carried
into the Country, 1 required all fuch as had Sick Cows,
to bring their Calves to be buried ; to which they rea-
dily confented, and were allowed from Five to Ten Shtl-
lings per Calf.

In the beginning of OBoher, being informed that fome
of the Cows in Norfolk, Suffolk, and Hcrtfordjhtre, had
Xxxxxx z got

( 882 )

got this Dileafe, and apprehending that it wou’d be-
come general ; I gave in the following Report to a Com?-
mittee of Council.

The Diflemper among the Cattle encreafing, and be-
ginning to appear in feveral other Counties, I thought
it my Duty to acquaint your Lordfhips, with the ha-^
zard that may attend their not being duely buried. It
is the Opinion of all Authors in Phyfick that treat of
Contagious Difeafes, as well as of feveral of the Phyfi-
tians in Town, that a Putrifadion of fo many Cows
as there is reafon to fear will dye of this Diflemper,
may produce fome Contagious Difeafc among Men ;
unlefs they are buried fo deep that the Infectious £/-
fluvU cannot injure the Air, which I am certain has
very feldom been complyed with, except in the Coun-
ties of Middlefex, EJfex, 2ind. Surry, the Gentlemen em-
ployed being capable of aCling in thofe Counties on-
ly. It is affirmed by feveral now living, that there
was a Mortality among the Cattle, a little before the
laft great Plague in the Year 1665, which was imputed
to the want of a due Care in burying them. And your
Lordffiips may know of what importance it was judg-
ed by the King of Prujjia, x\\q States of Holland, and fe-
veral other Princes and States, by the Care they took
to publilh Decrees and Placarts, commanding them to
be buried upon pain of Death, or other fevere penal-
ties; and I humbly conceive it wou’d be neceflary, not
only to bury thofe which (hall Dye, but that fuch as are
already Dead may have the fame Care; as alfo that they
be buried nine or ten Foot deep at leaft. All which is
mofl humbly fubmitted,

Their Lordffiips thought fit to defer all proceeding
upon this Report, till the Diflemper becoming more
general ffiou’d make it Neceflary;, but I thank God
that Neceffity never happened, for within three Weeks

( 885 )

or a Month after the giving in of that Report, the fol-
lowing particulars concurred to put an end to the Di-
feafe.

The Cows began their latter Purging, which con-
tributed much to prevent the Difeale from appearing
in frefli Places ; and the Cow-keepers were convinced
that the Difeafe was incurable.

The knowledge of the Difeafe was {pread all over
Englandy fo that none wou’d buy a Cow in the Coun-
try ; and the Gentlemen prevented their being kill’d
in TowHj by having, the Markets examined daily ; and '
fuch Meat condemned as appeared Sufpicious.

They now divided their Cows into fmall Parcels,-
by which they loft only that in which the Difeafe hap-'
pened ; whereas before that Method, when one Cow
got this Difeafe, if fhe had herded with One, Two, or.
Three Hundred (the Contagion was fuch) ftarce one
did efcape.

Thofe who had no Sick Cows avoided all Com-^
municarion with fuch as had.

They likewife found that the keeping their Cows
fb long when 111, had been the chief Caufe of their Lofs;
they therefore now brought them to be Buried on the
firft appearance of the Difeafe, before the Contagion ^
cou’d poflibly have got to any great heighr.

Thefe were the eftecfts of the Cow-keepers dear^
bought Experience ; but it was the indefatigable Care -
and Diligence of thofe four Gentlemen, who gave a dai-
ly Attendance, both early and late, that fecured Gw#
Britain from that terrible Ravage, which was made '
by this Diftemper in feveral parts of Europo

The ftverity of this Difeafe in England did not Jaft
above three Months ; tho it was not entirely fupprefted ^
till about Chriftmas ; But in feveral other Countries it
continued ! two or three Years 5 and I am credibly af-

fured,, ,

( 884 ) I

^ured, that in Holland it now rages with as much vio- J

lence as ever; and that they have loft in Cows, I

Oxen and Bulls, above Three Hundred Thoufand.

The Providence of God has fo dilpofed the matter
of Animal Bodies, as to render Contagious Difeafes ve-
ry feldom infecftious to different Species; but Expe-
rience demonftrates, that Contagions may be commu-
nicated to the fame Species, by touching the Woolen,
Linnen, to which the Infedious Effluvia of the
Difeafed had adhered, tho’ the two Bodies Ihould be at
a very great diftance ; and I verily believe that more
•Hundreds died from the Infedion, which was carried
by the Intercourfe that the Cow keepers had with each
other, than Tingle ones by the original Putrifa6lion.

The Nature of Contagious Difeafes are but little j
underftood, and it would neither be agreeable to my j
Defign, nor ufeful to the Publick, to' fay more of this 1
than what was evident : But 1 have been particularly J
careful, not to omit any thing Materia), either for j
defcribing the Difeafe, or manitefting the Methods that ]
were taken for fiipprefting it; becaufe it is more than ^
probable that the fame Care wou’d be equally fuccefs- j
ful in any other Species of Cattle. j

The number of Bulls and Cows loft by this Difeafe, 1
in the Counties of Middlesex, £(fex and Surry, were |
Five Thoufand Four Hundred and Eighteen ; and of |
Calves, Four Hundred and Thirty Nine ; and the Mo- i
ney iftiied for them, at Forty or Ton Shillings fer Cow, |
was the Royal Bounty of his Majefty, from his 1
own Civil Lift : and tho’ neither the four Gentlemen, |
nor I, made any demand for a Reward, or for Expences, j
yet it amounted to 6774/. i /. \ d* But the entire lofs I
to the Cow-keepers, as delivered in upon Oath, was |
24500/. (exclufive of the 6774/. ^ tho‘ com- 1

puted but at Six Pounds fer Cow ; which at a Medium, I

was 1

t

( 885 )

was not more than their Prime Coftj the dearnefs of
keeping them near London neccffitating the Cow keep-
ers to buy the very beft.

His Majefty was further plcafed, on the Sollicitarion
of the four Gentlemen, to grant a Brief fot the 24500/.
but the many lalfe Reports that were then induflriouG-
Jy propagated, to leflen the value of thofe poor Mens
Ioffes, fo fruftrated that Charity, that the entire Sum
Collcded (the charges of Colleding being firft paid)
was but 6278 /. 2 6 d, which on a Dividend, amount-

ed to Five Shillings and Three Half Pence in the Pound,
computing their Lofs as above, at Six Pounds per Cow ;
tho’ if we confider their Contrads with Brewers for
Grains, their Rent of Grounds which lay ufelefs. Ser-
vants wages, (0c. their real Lofs may (by a modeft Com-
putation) be allowed to be Ten Pounds for every Cow
that died*

IV. A Vefcription of the Organ of Hearing in the
Elephant, whh the Figures and Situation of the
OfTicles, Labyrinth and Cochlea in the Ear
of that large Animal. Communicated to the Roy-
al Society, by Dr. Patrick Blair, 5. S.

IN the Defcription I formerly wrote to the Honour’d
Sir Hans Sloanc.^ Barr, of thQ f l.fhant \ Difleefed in
Dundee^ Anno 1706. which he was pleafed to Commu-
nicate ro the Roj dSociety^ as you have it in Philo f Tr mf,
N°. 226 227. I treated of the Bony part of the Far
of tf at prodigious Animal a little too (uperhcially ;
bccaufe ) unwilling at that time to break up the
Qs Petrofum of the right Far, which- had accidemaliy.

Beeni

( U6 )

been feparared on dividing of the Scull, by which the
account I then gave of the Stmilunares, or Laby-
rinth and Cochlea was but Lame. But I have chofen fince
rather CO dedroy that Bone (however feldom fuch Bones
are to be met with) than that the Publick iliouJd be
depiiv*d of an exacfi Defcription of that curioujOrgane,
and thit I may give a clear Idea of all its Bony parts, I
fhall repeat what 1 formerly advanc’d upon that Sub-
jed:, and add what Improvements 1 have made upon
it fince.

Before I proceed, ’tis fit I obferve that the /4uris Ex-
terms of this big Creature lyes fiat, and not Protube-
rent as in other C^uadrupeds, whofe Cartilaginous Sub-
fiance is capable of divers Motions perform’d by fe-
vcral Muxles, whereby the inner Ear is preferv'd
from the great violence of the External Air, which up-
on fbme occafions might perhaps injure or break the
thin and delicate Membrane of the T^mpamm. It is
aJfo for this reafon that the Meatus is further guarded,
by the Contorfions and oblique Pofition of the Carti-
lage at the Orifice of the Meatus^ which only admits
of a determinate quantity of Air, fufficient for the vi
bration of the Membrana Tympni, by which a diflind
found is convey’d to the Senforium commune \ whereas
did the Air admitted exceed its due proportion, no-
thing but the confus’d Idea of a Sound would follow,
fuch as refemble the rulhing of Waters, or that
noife often obferv’d when, by a fupervenient Cold or
the like, obflrudions are generated within the Ear it
felf; And in Man, becaufe the Anris externus is alfo
flat, not only are thefe turnings and windings obfer-
vable in the Cartilage at the entry, but the Meatus it
felf is likewife obliquely Situated, to prevent the afore-
faid Inconveniencies. But there is no need for fuch
a contrivance in the Elefhanty whole external Orifice of
2 the

( 887 )

the Meatus patulent, open (fcarfe being guarded by the
Cartilage) and ftreight, w hofe length (it reaching from
the external to the internal Table of the Scull) ia fuffi-
dent to prevent the accelTion of too ^reat a quantity of
Air to the Tympafiuw, for in its progrefs moft of the Ctf-
lumna Aeris beat againft one or other of the fides of the
Meatus, in fomuch that their force is inhibited, and on-
ly fo many as fulEce to convey the Sound, can' reach
the Tympanum it felf.

The Meatus Auditorius then is a long
ftreight Tube or Canute fituated Horizontal-
ly, and reaching from the outer to the in-
ner Table of the Scull, in Figure not unlike the Barrel
of a Piflol, but fomevvhat Oval, the fides of whofe Ca-
vity are hard and folid, about the thicknefs of a Half-
penny, from whofe outer Part feveral of the Lamina be-
twixt the two Tables of the Scull do arife, (Fig, T.) hs
Cavity is an Inch or ^ of an Inch Diameter, and length
9 f Inches ; being fomewhat enlarg’d as it arrives at the
Crena for the Memhrana Tympani, (Fig, II.)

This Crena is two Inches in Circumfe-
rence, within which is the Cavitas Tym^
pans, confifting of two different Surfaces ;
the one much deeper and Cellulous, the other more
fuperficial and Smooth. The firfl runs perpendicular-
ly down ~ Inch from the Crena Tympani, Its bottom is
varioufly divided into feveral Celluls, not unlike a
Hony Comb, but irregularly difpos’d. Its Bony Lami-
rj£, by which thefe Cellules are diftinguifh’d from each
other, are thicker at the Top than at the Bottom, they
being one Line, two Lines, or i - Line diftant from each
other, and about \ Inch deep. Could I have got it fo
well cleans’d as I wifli’d for, doubtlefs I might have
obferv’d their Communication with each other, by means
of certain Orifices which ferve to convey what fuper-

Y y y y y y fluous

s

( 888 )

fluous Moifture is contain’d in them for we may reafona*
bly fuppofe, as in all other Cavities of the Body, there are
certain Glands for feparating proper Liquors convenient
for the ufes dehgn’d ; fo here there feems to be a ne-
cefTity for feparating a certain quantity of Moifture,
fit to lubrifie the Mufcles of the OfTicles, and facilitate
their Motion; as alfo to preferve the Memhrana Tjm
fmi from becoming too dry. This drynefs of the
Memhrana Tympani, and the thicknefs of the Liquor
feparated by thefe Glands, is often the caufe of a Deaf-
neis in Human Subjedls ; efpecially thofe that are ad-
vanc’d in Age. This cellulous Strudure of the Cavitas
Tympmiy (eems to be very proper for receiving of the
fuperfluous Humidity ; and thefe Communications are
requifite for conveying it from one Cellule to another, till
it is emptyed into the ReceptacuJum Commune the Aque-
duct, whereof hereafter.

This firft or cellulous Cavity is two Inches broad, and
reaches from the Crena Tympani to the foramen Ovale^
or entry into the Fefttbulumy which is (hut by the
Stapes, The fecond Part of this Cavity is more fuper-
ficial (Fig^ II. fr), in form not unlike a Pear, from a
narrow beginning becoming broader and more fuperfi-
cial, terminating Semicircularly, fmooth in the Bottom,
and having feveral incurvated Lines running acrofs it ;
it reaches much farther than the Veflibulum, being one
Inch five Lines from before to behind, and one Inch
tranfverfiy where broadefi:. What fuperfluous Moi-
flure it contains is difeharg’d into the fore«named A-
quedu6l.

Befide the above-mentioned ufes for thefe two Ca-
vities, viz» to receive and dilcharge the fuperfluous
Moifture; they are alfo moft beneficial and afiifiing
to the Hearing ; for, no fooner is the external Air mo-
dulated, and thc^ Memh^m Tympani mov’d thereby,

than

( 88p )

than the Sound is conveyed by the Ojftcles to the J^er^
vus AuMtoriuSy and the Undulation continued, firfl; by
the Anfra^iuofities of the firft Cavity, and then by the
Gyres and incurvated Lines of the fecond, fo that we
may eafily account for the acute Senfation of Hearing,
wherewith Elephants are faid to be endow’d : For as the
Tame ones are moft exad in obeying their Maflers
commands ; fo the wild Ones are foon aware of what
Traps or Snares are laid to catch them, by the tremu-
lous Motion convey’d to their Ear from the Cavous
parts of the Earth, where the Pit into which it is expeded
they fhould fall, is digg’d. It is eafy therefore to ex-
plain whence the acucenefs of the Senfation of rhis A-
nimal may proceed ; for as the Nervus OlfaPiorius has
a large Space and Bounds wherein to be difpers’d,
the two Cavities of the Prohofcis, which are both long
and large, fo that fcarce any Columna aeris can enter
them, but feme one or another of the Filaments of
the Nervus OlfaPiorm difpers’d in thefe Cavities muft
be toucht, whereby the Idea of fmelling mufl: be con-
veyed to the Senforium commune in a more intenfe De-
gree, and the Animal foon become fenfible of what-
ever approaches that is noxious or naufeous to it, and
thereby is taught hew to avoid it ; fo this Strudure,
for a quick conveyance and long continuance of the
Sound, is a great means both to make the Elephant
foon receive the Sound and have a deep imprefTion
of it.

The^^«f<s?«^isa flatTubeorPipe,whofe _

Orifice is fo fituated betwixt the two fore- ^
mentioned Cavities, that if there be any
fuperfluous Humidity contain’d in them, it mufl needs
be difeharg’d (at lead in this Animal) into the Mouth;
for as it is fituated where the firft Cavity terminates,
fo the fecond, from a broader and more fuperficial be-
Y y y y y y x ginning,

( 8?o )

ginning muft needs difcharge its Moiflure by its more
narrow and deeper termina ion, into rhis receptacle; alfo
it defcends diredly towards the Mouth, paflTmg through
the Scull below the hole for the Ju-
ofteegraphia Eie- gular Vein {mm) bctwixt the hole for
rZijak. No. 327! the Carotid Artery, (ff) and that for
Tab. 3. Fig. 3* the ArterU dura, matris {q q) whence
deicending {nn) it is joynd with its
Flefliy part, which difeharges it felf into the Mouth on
each fide, behind the back part of the inner Teeth of
the Upper Jaw. This fituation of the Aquedud makes
it* plainly appear, that its Ufe is to receive the fuper-
fluous Moifture from the Cavitas Tjmpani ; for befide
the Glands above-mentioned, 6t for feparating fuch a
quantity of Humidity as may lubrifie the Muicles, and
facilitate both their Motion and that of the Oftcles ;
the very Vapours that arife in fuch a Cavity as that
of the Tqmpanum in this Animal, muft at laft be com
verted into a Liquor, and that muft either again be re-
ceiv’d into the Blood Veflels, or otherwife difeharg’d
by fuch a Receptacle as this. Further if there be a
neceflity for Glands in the Meatus Anditorius without
the Tympanum, to feparate a certain Liquor, by which
the acrimonious Particles of the Air are obtunded, and
hindred from being offenfive to the Nervous Membrane
of the Tympanum, ( which muft be of a moft acute
Senfation) and for moiftning it, by which it the more
eafily receives the Vibration of the Air ; fb fuch Glands
as thefe feem to be moft requifite in the Cavitas Tym-
pani for the Ufes above nam’d. And fince what fuper-
abounds of this Moifture, cannot be dftcharg’d out*
wardly as that of the Meatus, this Aquedueft ieems to
be moft convenient for that purpofe. Some are of
opinion that this Aquedurft is alfo aftifting to the Hear*
mg, efpecially in Men j becaufe it is generally oblerv’d

( hi )

that they who are Deaf, open their Mouths wide, when
they are defirous to hear more diftindly : But I fee not
how that can be, for tho’ the Cavity of the Bony part
of the Aquedudl, in mod of Animals, is proportional-
ly large enough ; yet its carnous or flelhy Part lyes
for the mod part fo flat, and its two fides are (b collapsed
together, that fcarce any Air can be admitted, at lead
fo far as to be fubfervient to the Hearing,

. The Ojficles in this as in other Animals
are three or rather four in number; for
though I did not procure the Os qaaf/ra»-
guUre of Du F^ermy, yet I have good reafon to believe'
it was there ; becaufe there is a confpicuous Sims in the
extremity both of the Incus and Stapes, where they are
articulated, fo big as to contain the Head of an ordi-
nary Pin; and when I confider the Angle which mufl
have been form’d by the articulation of thefe two Bones,,
I look upon this fmall Bone to ferve for the fame pur*
poles as the Patella in the Knee, and Sefamotde Bones
in the Fingers and Toes.

The Malleolus is an irregular Bone, and
doubtlefs has been endow’d with pretty ’

large Mufcles, becaufe of the rugofities,
protuberances and Sinus% obfervable in it. • It has
a protuberant Head IV. ( i ) four Lines broad,
next to that a Qrena or femicircular Sinus , (2-^
after which the Bone is rais’d , affording a protu-
berant Margin to an oblong Sinus ( 3 ) for receiving
the head of the Incus, four Lines broad. The oppofite
part of this Sinus, or back part of the Bone, is con-
vex or an unequal rugous Surface, with a great many
protuberances and depreffions, for the Origins and in-
fertions of the Mufcles, for the fpace of five Lines 1
where it forms an Angle, from whence it becomes Flat
and Smooth, being three Lines broad and reaching four.

( 8pi )

Lines to another Angle, ('5.) where the Manuhrium
Malleoli begins, and where it becomes more round ;
from whence it gradually Tapers to the Point, being
fix Lines in length.

The head of the Incus is four Lines broad, {Fig. Vi
( i. ) below which is the Neck or an oblique Sinus; (i)
next to that are two /ipophyfes^, one on each fide. Thefe
defcending obliquely outwards, and becoming flat,
meet in a Point, (Fig.VU. (5.) whence afcending ob-
liquely inward, this Produdion is join’d to another
fmall round one, like the Manubrium Malleoli 41 Lines
long ( 6. ) This has the fore- mentioned fmall excava-
tion or half round Sinus-i ( 7. ) which with the extremity
of the Stapes, I fuppofe to have contain’d the Os qua^
dr angular Cy or rather Orbicular e, according to the Figure
of the Sinus.

The Stapes differs much in Figure from the Ffuman
one. from its Concave extremity ’tis enlarg’d on each
fide by two fmall (lender Productions, not unlike the .
ProcefTes of the Vertebrae of fome Filbes ( Fig* VI. (x z)
to which is join’d the Bajts, ( }.) Co thin almoft as the
Scale of a Fifh. This was accidentally feparated from
its two Sides, and remain’d in the Foramen Ovale, from
whence I pull’d it, with a Pin ; ’Tis Concave towards the
Stapes, and Convex toward the Vefiihulum.

The Foramen Ovale lyes fo hid and obliquely in the
fide of the Cavitas Tympani, that it could not be deli-
‘neated in its true Dimenfions. Near to it is another
hole Oblong and Sharp at both ends, both which give
an entry into the Veftibulum,

The Vefiihulum is of an irregular Figure, {Fig. X.(a)

’tis for the mod part three Lines from the one fide
to the other, and perforated by eight Orifices, viz.
five for the Canals of the Labyrinth, {Fig IX. X- (”4 )

one

( m )

one for the Cochlea, ( Fig, X. ( h) and two for the
FemflreB ( b,c.)

The Cochlea is a long Cavity confiding of three 6'^res
or Meanders ; f Fig. XI. {de f) Its Orifice where it pro-
ceeds from the Vefiihtlum is but fma!] ; but it afterwards
widens, fo that the firft courfe of this Cavity is a third
part larger than the fecond ( e), and proportionally
the third is lefs than the odier two {f), till it termi-
nates in an Orifice ( g ) fituated in the Top, for receiv-
I ing a branch of the loft portion of the Nervus Audi-
tortus, which accompanies and pafles along all its G)res.

The hardnefs and folidity of the Bone (for which
I it may be juflJy called Os Petrofnm in this Subjeff^ was
I fuch that 1 could not fo exadly trace the three Ca-
I nals or Duds of the La^rinth, fo as to give a true I-
I dea of the manner of their feveral Turnings. But Fal-
falva’s Figures of the Humane Ear direded me fo ex-'
adly, that I eafily found out the feveral Orifices, and
opened them fo far as to find out their fituation and
true Dimenfions, by introducing a Hogs bridle, then
cutting it off and ftretching it out to the Scale. Thus
after laying open the two Foramina which gave an inlet to
the Vefiihulum, I foon perceiv’d the feveral Orifices
which in fo large a Subjed were pretty confpicuous.
I firft turn’d to the one hand and difeovered the Du6l
of the Cochlea ; this I purfued all along the Protube-
rance, {Fig.Wl, ( d) \n doing of which 1 laid wholly
open the Leffer Du6l of the Lal'jrinth ( Fig. IX. {d )
Then turning up the other fide of the Bone, I trac’d
the (oft Portion of the Nervus Auditorius divided into
two Branches, one whereof was diftributed into the
Cochlea, and the other to the Lal'irinth. Tn filing the
Bone a little further, I opened a fmall part of the Mid-
dle DuH, and in a^fiiorc time I difeovered

Major-' °t.

( )

Major ; after which I meafured their (everal lengths as
is faid.

j , . The Lahyrinth then confifts of three Linea
ayrint. incurvatcd Duffs, whereof

the Major lyes in that part of the Procejfus Petrofus
which regards the feat of the Brain {b ) This is
twenty Lines or one Inch eight Lines long. The Medius
Duff us, onQ part whereof regards the Oririce of the Cochlea,
and the other is common with the Major for the
fpace of three Lines ; ( ^ ) this is fifteen Lines or one Inch
three Lines long : And the Minor which regards the Ca^
vitas Tjmpani, has one Orifice which is near to the
Medius, were it approaches the ; and the other

near to the Orifice of the Major. This is one Inch long.

The feventh pair of Nerves called in general the Nrr-
vus Auditorius, enters the Procejfus Petrofus, and is
divided into the hard and foft Portions,
ojicog. EUph. ag other Animals. In this Subjed I
Fig. IV. find one Lanule entring the Bone from

the Tides of the Orifice for the Carotids
Artery, about three Lines diameter/ e)( h) from thence
running forward for the fpace of one Inch four Lines,
then bending downwards one Inch, till it meets with
the Orifice at the Sides of the Meatus Auditorius, by
which it pierces the Scull, and pafies outward. This
Canule, after it is entred the Proceffus Petrofus for the
fpace of eight Lines, communicates with the 'Orifice
which ufually enters the forefaid Procefs from the
Bafe of the Scull ; and both thefe Orifices, after they
have accompany’d one another about five Lines, are
feparated, and the foft Portion penetrates the Bone at
two places, as is faid.

I have now endeavoured to give fuch a Defeription
•of the Offeous or Bony part of the Ear of this ftupen-
dious Animal, as I am in hopes may be ufeful for the

* clearing

( 8pj )

clearing up of fome Th^nomtna. in lefler Subjeds. Ac
i leaft we may hereby obferve, what a variety of Mecha-
i nifm the great Author of Nature has thought fit to em-
j ploy, in the feveral parts of different Spcies of Animals.
, Thus both the external Ear of Man, and of the Ek'‘
I fhunt lye flat, as being moft convenient: for if they
I had been Protuberant as in moft Quadrupeds, how un-
I fuitable would it have been in Man, who is the moft
I perfed of all Creatures, not upon the account of his
I Reafon alone, but aUo as he is a Pattern for Beauty
! and the Symmetry of his Parts; and how unfeemly
■ would it have been in th^Ele^hd^t, if his external Ear
I had ftuck out, and been proportional to his other Parts ;

I confidering wlwt an extraordinary afped he makes al-
j ready by his Trunk and Tusks? But the Ears in thefe
I two Subjeds differ by the tortuofity of the Cartilage,
and oblique Meatus, to prevent the injury of the Air,
by its immediate accefs into the inner Ear in Man :
whereas in the Elephant the external Orifice is fully ex-
pos’d to the Air ; but then the length of the Meatus
hinders any more Air than is convenient from arriving
at the Tympanum. We likewife fee in the Seal and Otter,
that thofe two Amphibious Quadrupeds have no exter-
nal Ear further protuberant than the other Parts of their
Head ; for had it been otherwife, their fwimming and
diving would have been much hindred : But its two
fides are fo collaps’d, that no Water can enter in
when in the Deep, though it can receive fufficienc Air
when alhoar. The cellulous Cavity of the Tympanum
in the Elephant, may well be compar’d to the Apophyfis
Maftoides in Man ; and the fecond Cavity of a plain
Surface Teems to be Analogous to the Cavous Maftoides
in Sheep, Cats, Dogs, So that we Tec that whereas
other Animals have but one Cavity for affiffing
the Vibration of the Air, and continuation of the

Zzzzzz Soujii

( 8?<5 )

Soimd in the Tympanum ; this Animal has two, or a
large one with two diSerenc Surfaces. The AqueducS:
both by its Figure and Pofition in this Animal doth
plainly fliew us the Ufe of it in other Animals, which
is to receive the fuperfluous Humours in the Tympanum,
and convey them to be difcharg’d in the Mouth.

Explication of the FIGURES.

Figure h

REprefents the Bony part
of the Meatus Audi*
tori us of the Right Ear 9
a The eoeternal Orifice of the
Meatus Auditorius.
b 7 he Prcceflus Petrofus.
c The Orifice where the Ner*
vus Auditorius enters.
d The Meatus Auditorius.
e A part of the Laminic
which proceed from it on
each fide, hy which the
Cellules betwixt the two
Tables of the Scull are
form’d ; thofe Jit uated above
the Meatus being remov’d.
3 Part of the inner Table
of the Scull,

Fig, II.

Reprefents part of the
^.atus. (Auditorius o-

pened, with other parts of
the inner Ear.

a The ragged part of the
Bone from whence the Os
Petrofum was feparated.
b The ProceiTus Petrofus o»
pened.

c The Crena for the Mem-
brana Tympani.

d The Hony comb Cavity of
the Tympanum.

e It 's inner Cavity o f a Jmooth
Surface,

f Its Semicircular or undu'
hted Lines.

g The Ottfice of the Aque-
duct.

h The Orifice of the hard
Portion of the Nerve.

Fig. III.

Reprefents the lower Surface

of

( 807 )

ef the Os Petrofum, as
it was feparated from above
the Tympanum and other
farts of the inner Ear.
a a The ragged Margine of
the Bone.

bb The upper part of the
Caviras Tympani.
c The Foramen Ov'ale.
d The Frotuberance in which
the Labyrinth and Coch-
lea are lodg'd.

e The Orifice of the hard
portion of ?^^NervusAu-
ditorius.

Fig. IV.

Reprefents the Malleolus a
lone in its true dmenfions.
I The Protuberant Head.
z The Semicircular Sinus he<.

iwixt it and the Margin
^ The Sinus which receives
the head of the Incus.

4 The angle below the Sinus
for the head of the Incus,
y The angle where the Ma-
nub ium Malleoli begins.
6 The Manubrium Malleoli.

Fig.V.

Reprefents the Incus.

I The head of the Incus.

X The Sinus or neck of the
Incus*.

3 Two Apophyfes.

4 A long protuberance with
the Sinus for the Os qua-
drangulare at its extre-
mity.

Fig. VI.

Reprefents the Stapes.

I The fmall part of the
Scapes, where it is articn^
lated with the Incus, with
a Sinus at its extremity,
being the other half of the
Cavity for the Os qua*
drangulare.

1 z Two fmall portions of
the Stapes, where it is ar-
ticulated with the Bafis. ,

} The Bafis of the Scapes
feparated.

4 The whole S'^^L'gQS.
Fig.VW.

The Malleolus and Incus,
joind together, with their,,
lower. fide turdd. up.

i The Malleolus.

X Its articulation with the.
Incus.

3 The Incus.

4 7/^^ Manubrium Malleolr..

y A point of the Incus,^

• fram’d hy the- other two^
froduFtknu.

6. The

( 898 )

6 the long frctuherance of
the Incus.

7 The Sinus in the extreme
ty of its long Produ^ien,

Fig. VIII;

The Malleolus, Incus and
Stapes articulated toge-
ther.

1 The Incus.

^ The Malleolus.

3 The Stapes rrhere it [huts
the Foramen Ovale.

Fig. IX.

Reprefents the upper part of
the Linese Semilunares, or
that fide which is towards
the paffage of the NetVUS
Auditorius.

a The five ex tremi ties cut off.

b The Linea Semilunaris
Major.

The Semilunaris Media

d The Minor.

e The common Camle bet ween
the Major and Media.

Fig. X.

Reprefents the Cochlea and
Labyrinth together.
a The Veftibulum.
b The Foramen Ovale,
c The Foramen Oblongum.
d The Linea Semilunaris
Minor, which is towards
the CavitasTympani.
e The common Canule to the
Major and Media,
f The Major,
g The Media
h The Cochlea-

Fig. XI.

Reprefents the Cochlea,
a The Veftibulum.
b The third Gyre or turn-
ing.

c The Orifice-

d The firfl Gyre or turning
opened.

e The Jccond turning.
g The Orifice at the' top of
the Cochlea.

FINIS.

ERRATA. N°. 3 57, Pag. 847. lin. 22. lege ab h n'. 32". pag.
885. lin, 17. lege N*. 3z6. 327.

LONDON:

Printed for W. and J. I n n y s, Printers to the Royal
Society, at the Princes-Arms at the Wefi-End of
bt. Pauls Church-Yard. 1719.

( 8pp ) Numb.

PHILOSOPHICAL

TRANSACTIONS,

For the Months of Janmry a.nd February, i/ip*

The CONTENTS.

I. ^^Urious Ohfervittions of the Tranjit of the Body And

Shade of Jupiter’/ fourth Satellite over the Dijque
of the Planet. Communicated hy the Reverend Mr. James
round, R. S. S.

II. A Difeourfe tending to (hew the Situation of the an-
cient Carteia, and fome other Roman Towns near it.
By John Conduicc, Fellow of the Royal Society.

III. A Letter of M T Abbe Conti, R. S. S. to the late
M. Leibnitz, concerning the difpute about the Inven-
tion of the Method of Fluxions, or Differential Me-
thod ; with M Leibnitz his Anfrver thereto.

IV. Parsreliqua Differtationis De Potentia Cordis. Authore
Jacobo Jurin, M. D. ^ R. Societatis Soc.

V. tTova Methodns univerfalis Curvas Omnes cujufeun-
que Ordinis Mechanice deferihendi, Jola datorum Angu-
lorum dr Reel arum ope. Per D. Colin Maclaurin in
Collegia Novo Abredonenfi Mathefeos Profeffore.

VI. Extraci of a Letter of the Reverend Mr. William Rice,
ReEior ^/Caeileon upon Usk, to Charles Williams Efq-^
giving an account of an ancient Roman infeription late-
ly found there. With fbme Con) enures thereon, by the
Reverend Dr. John Harris, S, S»

Aa a a aa a

I. Curiom

L Cumus Oh/erVations of the Tranpt of the !Body and
Shade of JupkcTS Fourth Satellite o^er the Dif^ue
of the Tlanet. Communicated by the ^yerend
'Mr. James Pound, R, S, S.

fnding by the Tables of Jupiter’s Satellites that the

Fourth Satellite was to pafs over the Difque of
Jupiter the 1 5//^ of this prefent February, at Night; we
were very defirous to obferve the fame with the
Hugeman Telefcope, having never before, fince I have
had the Ufe of it, been able, by reafon of the foul-
nefs and inconftancy of the Weather, tamake any to-
lerable Obfervation of this kind,

Ac thro’ a fliorc Tube, we faw all the 4 Sa-
tellites, the 3 outermoft on the Eafi fide of Jupiter,
and the innermoft near the Weflern Limb approaching
to an Eclipfe. The Fourth at that time was about
half a Semidiameter of Jupiter from the Edfiern Limb.-
Then it proved Cloudy till about 8\ at which time
01110’ the long Glafs) we could fee only the fecond
and. third Satellites, the hrft being behind Jupiter in
the Shadow, and the fourth entred upon the Difque.
We faw at this time a dark Spot, a little Morthward
of the great Northern Zone, and near the Eajlertr
Limb, where the Satellite was to enter on the Difque ;
which Spot we took for the Shade of the Satellite.
The Clouds then again intercepted our View, till
8^ 53'. JEe^.T. at which time the firfl Satellite was
lately emerged out of the Shadow, and the Spot ad-
vanced fo far, that we perceived it would arrive at ‘
the middle of Jupiter, near two Hours fooner than

the

. { po' )

the Shade ought to have done by our Computation ;
but not imagining that this dark Spot could be any
thing die but the Shade, we concluded there had
been feme Error in the Calculation, which we thought
to re examine afterwards. On this prefumption we
left off obferving till 9’’. 35'. at which time we were
furprized to fee a Notch in the Limb of Jupiter, near
the place where the former Spot entred. This laft ap-
pearance agreeing well with the time that the Shade
of the Satellite ought to have entred the Difque,
foon made us alter our former Opinion, and conje-
dure that this and not the other Spot was the faid.
Shade. At 9^. 39^7 T, the Notch vanilhing, a
round black Spot appeared within the Limb, but in
conrad with it. At 9^ 4^'. we judged the firft Spot,
and at ii^ 45’. the fecond, to be in the middle of Jupi-
ter.

At ii\ 50'. the firft Spot touched the Limb, being
within the Difque ; foon after which the Limb in that
place Teem’d a little protuberant- At iz*". 5'. appear-
ed the fourth Satellite juft come out of the Diique,
and touching the Limb in the place where the Fro-
tuberancy was. At lx’"- 7', we could perceive the
Satellite feparated from the Limb. At 13'’. 56'. the
fecond black Spoti ftill within the Difque, juft touched*
the Wejhrn Limb ; foon after which there appeared a
Notch in this part of the Limb, as it did on the o-
ther at the coming on of this Spot, At I4^ 6'. the
Spot was all gone off, and the Limb appeared clear
and entire.. The firft Spot, when in the middle of
piter, was almoft as black, as the fecond when near.,
the Limb, but fomewhat lefs and a little more Nor-
therly.

Atithe time that the firft: Spot was in the middle
of the Difque, the three inneimoft Satellites appeared

( pOl )

to the Eafl of Jupiter \ the firfl: ( as flfoteraidi ) having
lately emerged out of the Shadow ; the fecond being
almod at its greacell didance; and the third having
pafled the Axis of the Shade about twelve Hours be-
fore, and appearing at this time about three Diame-
ters of Jupiter from his Limb. The times that thefe
Spots arrived at the middle of the Difque are agreeable
to the times found by Calculation , in which the
fourth Satellite and its Shade ought to have appear*
ed there. From all which ’tis very plain, that the
fird of thefe Spots was the fourth Satellite itfelf, and
the fecond its Shadow#

We have feen the fird and fecond Satellites ap-
pearing not as dark Spots but as bright ones Cfomewhac
different from the light of Jupiter') for fome little
time after they entred his Dilque, but as they ap-
proached nearer the Middle we lod fight of them.
And we have frequently obferved that the fame Sa-
tellites appear brighter at fbme times than at others;
and that when one of them hath diined with its ut-
mod Splendour, the Light of another hath been con-
fiderably diminifhed. From whence ’tis very probable
at lead, not only that the Satellites revolve upon their
proper Axes, but alfo that fome parts of their Sur*
ftces do very faintly ( if at all ) refletd the Solar
Rays to us.

All which hath for fome time fince been obferved
and taken notice of by MefT. CaJJini and MiraleH, as
may be feen in the Metnom of the Academie Bojale,
for the Years 1707 and 1714.

( 9°i )

II. A Vifcour/e tending to P?ew the Situation of the
ancient Carteia, and fome other Roman Towns
near it. By John Conduitc Efq‘^ Fellow
of the Royal Society.

A Bout four En^lijh Miles N. IV. from Gihraltar., at
the end of the Bay, there are confiderable Ruins.
The place is called at prefent Rocadillo, and confiBs of
a few Huts, and a Modern Square Tower, which ap-
pears to have been raifed on the Foundation of a much
greater Pile. The Walls of the old City are very eafy
to be traced. They feem to have been about two
Englilh Miles in Circumference, and were built upon
the Brow of a rifing Ground. The fpace within is co-
vered with Ruins, among which are a great many pie-
ces of very fins Marble well wrought ; and innumera<-
ble fragments of Vellels of that kind of red Earth'en
Ware, which Amlrojio Morales in the firfl Chapter of
his Difcurfo de las antiguedades de las chtdades de Ef>
fanna, lays down for a certain mark of a Roman City,
and takes to have been a Compoficion of the Clay of
Sagitntum, often mentioned among the Romans*

Fi^a Saguntino pcuU malo luto. Mar. Lib. Vllk Ep. 6.

Sume Saguntino pcula fi^a luto. Lib. XlV.Ep.io8.

There are remains of a rude Semicircular Building,
raifed on Arches, which defcends gradually into an
Area, and Teems to have been a kind of Theatre. I
brought away with me a Marble Pedeftal of a Statue,
dug up near to the Square Tower. The Marks where

Bbbbbbb th«

( ^04 )

the Feet and the extremities of the Drapery were fatt-
ened to it, are ftill to be feen, and the following Let*
ters finely cut V A R I A M A R C E. It was given
me by the owner of the Ground, who faid he had read
upon it formerly three other Letters L L A fince bro-
ken off There are other Infcriptions, but fo Defaced
and ill Cur, that they do not deferve a particular
mention. I have a confiderable number of Medals,
that were found among thefe Ruins ; moft of them
have a Caput turritum with C A RT E lA in very le-
gible Charaders. The Reverfe is generally a Fijh, a
Neptune^ or a Rud/^er, Towards the Weft there is an
eafy Defcent to the River Guadarranque, which takes its
Source at Caftdkr, about four Leagues in the Coun^
try, and is very deep at Rocadillo. There is a Bar
where the River falls into the Bay; but it does not
hinder the entrance of Veffels of 1 5 Tun, to load
Charcoal and other necefTarie^, that are Shipt off from
thence for Ceuta. Along the fide of the River there
is ftill a great deal of Stone Work and vifible remains
of an Ancient Key. At a fmall diftance to the Eaft,
upon an Eminence, there are confiderable ruins of a
Square Caftle, which appears to have been an ancient
Building of very great Strength The Country People
now call it Cajitllon^ but the Corrigidor of that Diftrid
told me he remember’d it called Torre Cartagena. The
Situation agrees exadly with the Tower of that Name,
mentioned in the and -^i6th Chapters of the

Chronicle of Alphonfo XI of Ca(li[et A Book of great
Authority among the Spaniards, who are generally of
Opinion that it was formed upon the Memoirs of
Fernando Nunnez de P'alladolid, a Favourite and Mini-
fter of that King, tho’ it goes under the name of a-
nother Perfon.

All

( 9°5 )

All the 3p4fihrds who live about the Ruins I have
been defcribing, fay they are the remains of a City of
the Gentiles called Cartago. The corruption of CarteU
into a name fo much more talked of, might eafily hap-
pen in an Oral Tradition of fo many Years ; and I
cannot help thinking that, where other Circumftances
concur, an account deliver’d down from Father to Son
is an evidence not to be flighted, in matters of fo
much obfcurity.

Frequent mention is made of C^rteia by the Ancient
Geographers and Hiflorians. I build fo much on two
Pafl^ges of Livy, that I am obliged to infert them at
length. The firfl is Lib. XXVlll. C. 30. ( Livy does
not mention from what Port Letlius failed for Carteia,
but by what goes before, it feems to have been from
Cartagena, at that time Scipio's Head Quarters) Lidius
interim, freto in Oceanum eveoius, ad Carteiam cU^e ac»
cejfit, (Urhs ea in ora Oceani fit a eft, uhi primfem e fauci-
hit anguflis panditur mare ) Gades fine certamine prodi^
tione recipiendi (ultro, qui earn rem pcllicerentur, in cafira
Romana pervenientilus) fpes, Jicut ante a dititim eft, fue-
rat. Sed patefa^a immatura proditio eft, comprehenfcfque
omnes Mago Adherbali Carthaginem devehend&s

iradit. Ad herbal, Conjuratis in quinqueremem impofttis,
pr^miffaqne ea, quia tardior quam triremis erat, ipfe cum
oBo triremihus medico intervallo fequitur. Jam /return
intrahat quinqueremis, cum Ledius ipfe in quinquere-
mi, e portu Carteiae, fequentihus f/ptem triremibuSy eve^
Bus, in Adherbalcm triremes invehitur; quinqueremem
fatis credens deprekenfam rapido in freto, in adverjum reftum
recifrocari non poffe: Pcenus, in re fuhita parumper in-

certus^ trepidavit utrum quinqueremem [equeretur, an in
hoftes roftra converteret, Ipfa cunBatfo facultatem detre-
Bandre ptigna ademit: jam enim fuh iBu teli erant, ^
undique inftabant hoftes, ^Lflus quoque arhitrium moderan-

Bbbbbbb 2, M

( 9°o )

M nnvzs admerat\ mque erat navali fugna ftmiliSi quippe
ubi nihil vcluntarium, nihil artis aut confilii e(f(t. IJns
natura freti aflujquc totius ccrtaminis potens, fuis^ alienis
navibus, nequicquam remigio in contrarium tendentes inve->
hebat ; ut fagientem videres retro vortice intortam vi^ri*
clbus illatam, [equentem, fi in contrarium traBum inci-
dijfet maris, fugienth modo Jefe avertentem. Jam in ipsa
fugna h£c, cum infefto ro/lro peteret ho(lium navtm, ohli*
qua ip[a Hium alterius roflri accipiebat: ilia, cum tranfver^
fa objiceretur hofli, repente into.rta in proram circumage-
batur.

The other Pailage is Lib. XLIII. C. 3. Et alia novi
generis hominum legatio ex Hifpania vsnit : Ex militibus
Romanis ^ ex Hifpanis mulieribus, cum quibus connu-
hium non effet, natos fe memorantes, [upra quatuor millia
hominum, orabant ut fibi oppidum in quo habitarent dare-
titr. Senatus decrevit, uti mmina fua apud L» Canuleium
frofiterentur, eorumque fiqaos manumifffet^ eos Carteiam
ad Oceanum deduct placere ^i Carteienfium domi ma-
nere vellent, pot eft at em fore uti numero coionorum cffent,
agro ajjignato. Latinam earn coloniam fuijfe, Libert ino-
rumque appellari.

The bed Spanifh Authors, and Ortelius and Cellarius
trufting to them, take this Carteia of Liv^ to be diffe-
rent from that which was the next to Calpe^ and place
it generally about ConiL Rodrigo Caro in his Qonvento
Juridico de Sevilla C. 2^. applies the Carteia in the XLIII
Book of Liv) to Rocadillo , and in Cap. to Car^
taia near Lefe. It is furprizing he takes no notice of
the Paflage in the XXVIII Book, For the particular
mention of ad Oceamm, and Urbs ea in ora Oceantfita eft,
implies they both relate to the fame place ; perhaps it
was becaufe he could not reconcile it with his CartaU
near Lepe. Cellarius makes Bsjippo this Carteia of Livy,
c. Ba/ippOf qu£ videtur Carteia Livii eft'e, extra

(return.

( 9^7 )

fretunf columnas fofitA. Aliam pro Livio Carteiam non
invcnh 5 tho’ in all the ancient Geographers B^fippo is
mentioned by it felf as a diftant Town f am To far
from feeing any necefficy of ereding a oe ’ Cartcix
in the Ocean for theie Faflages in Livy^ that I take
that in Lib. XXVIll. to be rather a proof that the City
there mentioned, flood diiRccitdillo. m, certainly agrees
much better with that Situation, than with Conti or
Cartaia near Lepe. It is not to be reconciled with the
latter, b caufe that lies North Wefi of Cadiz, from
whence Aclh^rhal fet out for Carthage, and is a good
way up the Country, on the fide of a River, and not
in ora Qceani. Neither can Conti be faid properly to be
Situated Uhi primtim e faucilus angttflis pandit f/r mare ^ for
the Sea widens confiderabiy before it reaches the Capes
Spartel and Trafalgar, and becomes an Ocean where
that Town (lands It is obfervable that Mela applies
words of the fame import with thofe of Livy to the
Sea between Calpe and AhiU. BarhefuT, Aperzt deinsU
anguftijftmum pelagus* There is no Harbour at Conil,
or any other place between Cape Trafalgar 'awA Cadiz,
If th<^ Carthaginian ^iinejtteremls had only been going
into ( intrahat ) the Mouth of the Streights between
Capes Spartel and Trafalgar, L^elitis could not have be-
lieved it fatis deprehenfam rapido in fteto, in adverfum
flum reciprocari non pejfe, for there is no fuch flrong
Current there; and the adion between him and Ad?
herb ah Triremes, which were at fome diflance behind
the ^inqueremis, mud have happened fVeflward of thofe
Capes ; which is inconhflent with the defeription Liv/^
gives of it ; bccaufc in that part of the Ocean there
are none of thofe Eddies, that appear to have had Co
particular an effed on both the Fleets, during the Eri’
gagement, and are peculiar to the Middle of the Gut,

( ?o8 )

This general miftake feems to have been occafioned
by giving too eafily into the opinion, that Liv^ un-
derllood by the FrcUtm all the Sea between the Gapes
Spartd and Trafalgar, and the Rock of Gihrdtar and
Apts-Hill\ when it is more probable that he termed
flridly fo only the narrowed Fart, which was general-
ly reckoned to be between the two latter : Mda.l’roximt
Africa & Europe littora monies efficiunt Calpe AhiU.
Plin) takes MellarU to be neared to A/rick, and there-
fore places there the Eretum ex AtUnttco mart Lih. 3,
which is an argument his Freium was not the fame
with our Sttcights, and that he carried the Atlantick
Ocean much farther Eafi th^a the Capes Spartd and Tre-
falprar.

Other Authors feem to make the Pillars of Hercules
the Boundary of the Mediterranean and the Ocean.
Marcianus Heracieotes. <7re^« rvs BcuIck^s

la-'TPxvloc.s TO TO TO-frl)(^y •srccp \)s^Ti^i <Ta5 ^Actcr-

'TECS nno)- TOv Tvy^^vliQiS, tiw ts

»(9l6’ <£ T^v e^co, tvt tgi Toy O,yjf0.y'oy. Hic finem

habet Hiffani^e pars condngens utraqut maria, qua

circa freium Herculeum, tarn mare noftrum quam mare ex~
terius^ h.e^ Oceanum, TUs jjay Bculcxvs to 7rA«jDv 'tofO
Tris jc^tu^ 'Hg^xAawi' eyTOs

Awt', m TOy SuU>i^v Slyaoivoy. Baiica qui-

ekm pars maxima pratenditur nofro^ mart, Herculeas intra
cdumnas, pars vero qu£dam occidentali Oceano.

Polybius L. III. KaA«TO^ ^ to yav Try r facts
7rapVJ(fiy eoos Hg^jtAawj' ?jjAwj/, to H TVy e^ca

^ faeyd?\./iv 'zxrQpaity>p€uofatv>u> if^ivTiv fx)y oyojxccoixy vie
TtT^a-ipciTws i{^TV7rTiveSzif porrigifur

Jecundum mare mil rum port to ad column as ufque Herculis
Iberia nominatur ; qu£ (eenndum mare externum quod ^
magnum appdlatur, communem appellationem nondum tnve-
Mzi, quia non diu efi cum fuit fxplorata.

Appian

( pop )

AfpUn //. ’E/t4(pyA- tos sr^as 'ms 'Hg^tjtAaas

TdV s'Tri^y. TrajeBo ad Columnar Hercalis

Oceano.

florus Lib. IV. C ^ Jn ipfo oftio Oceani Varus Didiuf’
que legAti conflixere ; [ed acrius fuit cum ipfo mart, quam
inter fe navihus helium : Siquidem vdut furorem civium
cafligaret Oceanus ^ utramque claffem naufragio ceeidit.
Qttin&m tile horror, cum eodem tempore fiudus, procell£,
viri naves, armament a confligerent ? Adde }vus ipfius for-
mtdinem, vergentia in unum hinc Hifpani:2 inde Mauri-
tani:E littera; Mare dr inleflinum externum, imminen*
tefque Herculis [peculas ; cum omnia undique ftmul pratllo
tempeftate J^virent, Here the Pillars of Hercules are
made the very Mouth of the Ocean. If you underftand
the Fret urn of Livj in this Senfe, and reckon it to fig-
nify only the Sea between Calpe and Ahila, and the
Ocean to begin from thence 'Weflvrard, the Paflage in
the %%th Book is an accurate defcription of Rocadillo.
LseUus Interim freto inOceanum eve6im ad Carteiam claffe
accejjit. Urbs ea in ora Oceani ftta e(l, ahi prirntm c fait-
cihus angufiis panditur mare* And allowing Lalius to fet
out againft Adherhal from thence, every circumflance
mentioned by Livy is fo eafy to be accounted for, that
it is needlels to make Application. A Paflage in V/o^
Cajfius Lib. XLHI, induces me to believe the Veflels an-
chored in the Guadarranque, and that that River, and
not the Bay, was properly PortusCartei£ ''OuotpQ* Si \zod
S’ 'c%/? KQ^r>lca,y evccuasscrri^, ^ fad)

(pvytiv es Tvii' ywi', ay^vj^jis es ro S ?\.ifjidv©^ aMas

aums 01

(r(p(xs, ua-'TnjSj} i^'nrixeiQ.v, omv oiv ro

yecvky(}v amAcoAexei.. Varus vero d Didio apud Crantiam
navali fralio juperatus in terram evafit, conjedifque in
introitum portiis anchoris, ltd ut una ah alia, teneretur, cum
ad cas, tanquam ad feptum - qmddam, prints infeqmntium -

naves i

( pio )

tJAnjes offendiffentt pericalum totius clajfts amittenda declina-
v'lt. 1 his cannot be underftood of the Bay, becaufe
that is three Leagues over at the narroweft part, and
much too deep for a work of fuch a Nature which
might eafily have been efFeded upon the Bar of the Ri-
ver Guadarranque.

There is no room to doubt of the emendation Luts
Names, in his HifpnnicA, has made here of KapTnU for
Kepivno.; for no ancient Author mentions any other
Town or Harbour thereabouts of a name like that ;
and Cartcia was the place which held out the longeft
for the younger Pompey, and wl>ere he kept his Fleets.

Floras in the Paflage I have already quoted, relating
the fame Affion between Didias and Varus, reprefents
in very lively Colours, the very Scene near Rocadillo.
Adde fitus ipfius formidimm^ vergenth in anum hinc Hif’
par,t£ inde ManritanidS littora ; mare inteftinam ^ exter-
nam, imminent efqae Herculis fpeculas <SvC.

Hirtius, in the latter part of his Book de hello Hif-
panico, fays Cn. Pompeius ad navale pr£jidium parte altera
contendit Carteiam, qaod Oppidum aheji' a Corduba miUta
pajfaam CLXX. which diftance, as well as the circum*
fiance of navale praftdium, agrees with the Situation of
Rccadillo The ancient Geographers place Carteia next
to Calps Weftivard. Pomponius Mela, after having given
us a perfefl: Fixture of Calpe, and deferibed thofe la-
fling Marks, in which fo many Centuries have made
no alteration, fays — Sinus ultra efl, in eoque Carteia.
Strabo L Ilf* ’Ey>mvja. ^ g<rt <7^ in KecAmi,

&c. ^ ccuTO K-xAtzm oriAiS ey TSTTa£p&>tp>'7rc. ?a(hoif,

cc^ioAoyt^ ^ vecugx.'^^i croTi yivo/Mvn

’'Evioi fs 'H^xAeye x.lio'fJia, Afyniaiv ccvrr.y ^ d)y tc^i <t
Tifj^Ssvns. os (pn<at ^ H^x-Aoiay oro|«,a^g^ to 'uzcAaciOy,
S^&jtvuSziu <n {Myoiv ^ vsvQiTcys, thi mans HiP

panorum eft Calpe, &c. ^ ad XL inde Stadia Urbs Calpe

vetufla

\

( 9“ )

vetufla & mmorahilis^ dim Stutio ffavibus Hifpanorum*
Havc ab Hercule quidam conditnm aiuntj inter quos efi
Timofthenes, qui earn antiqdtus HcraclQum fuijfe appella-
tarn refert, ofiendique adhuc magnum murorum circuitum

Navalia. Cafaubon, in his Notes on this Paflage is of
Opinion it fliould be KapTu/a. miXis. Legendnm cenjeo
Kap'ir'ioc 'TToAiSy ttam earn urbem hie intelligi res ipfa docet ;

ex eo colligi potefb, qttod toties earn infra nominans
nihil tamen de ejus (itu alibi dix/Jfe reperitur. At Calpen
Urbem nemini V Herum ne nominatam quidem reperio.

Marcianus Heracleotes makes Carteia 50 Stadia from
Calpe» Either of thefe Diftances agrees vikhRocadilloy
according to the part of the Rock from which they rec-
kon; for it is above fix Miles from Europa Point to
Rocadillo,

Bochart in his Geographia Sacra Lib. I. Cap. 34i
ftrengthens Cafaubons Opinion Nee frufira Heraclea
Carteise fuife vet us nomen ^ tanquam ab Hercule conditore,
Herculem enim fuum Phtenices MeAscap<Snr appellabant.
Philo Biblius ex Sanchoniathone apud Eufebium L. T.
Fraparat. owJ'g Ajjpca.paj-'n yivSTU)Me^x,ccf>Qo£ 0 ^

Ex Demarunte autem natus e(i Melcarthus qui & Her-
cules. MgAxapr^Ds autem eft Melech Kartha.

Rex Urbis, i. e. Tyri. Idem Gnccis Melicertes five Pa-
l.'cmon Maris Deus, quern Cad mi nepotem e([e fingunt.
H'tnc Hefyehius rurfus MaA/>ca rov *Afjt.x%v<not.

Omnino igitur ex Melcartho, vel Hmp TbO Melech
Kartha. Urbs quam, ad Calpen condidit Hercules Phoeni*
cius, primo Melcartheia vocata eft , Melech Karthiia,
quafi dixeris ; deinde per Apharefin Cartheia vel

Carteia. Apud Hebroeos frequens eft heec Aph<erefis in
nominibus locorum compofitis. Tale Sittim pro Abel- Sit-
tim, Salem pro Jerufaiem, &c.

I have fome Medals that were dug up at Rocadillo,
with the Head and Club of Hercules upon them ;

Ccccccc which

( 9‘* )

which feetn in fome meafure, to fupport chat great
Mans Aflertion. Upon the Reverfe are Tunny Fifties,
which according to Strabo and Flinj abounded former-
ly> near Carteia, and are ftiU taken in great quantities
near the Shoar of the Eaft Sea, a {mall diftance
from Roeadillo.

Bernardo Aldrete an Author of fuch Weight, that
Bochart does not difdain to copy him on feveral ocea-
fions, in the fecond Book and fecond Chapter of his
Antiguedades de Efpanna, accounts for the Addition of
eia to Cartha; which in the Sjriack and Chaldean fignifies
Tulcher, Fermofus, and was affixed to the Name of this
City to diftinguilh it from the Cartha in Syria, men-
tioned in the zi/? Chapter and 34?^ Verfe oijo/hua*^

By all accounts, the Fheenicians founded moft of
the Cities on this Coaff, and probably Carteia was
one of their earlieff; Settlements j for it lies very near
Africk, in a mod inviting Situation, having on one
fide a Bay, and on the other a. River, which waters
a rich Country. Its height gave, it ftrength and a very
beautiful ProTpedl ; circumffances which, (eem to juft ifte
Aldretes interpretation of the latter part of it’s name.

In the Itinerary of Antoninus, it is Calpe - Carteiam,
not tanquam dm urhes diverfa, 2.S Cafaubon intimates in,
his Notes on the third Book of Strabo, for then it
would be Calpen Carteiam', nor, according to Suritds
Comment on that part of the Itinerary, ut JigniJicet non
re£ha iUr ex Suel Carteiam deduct , fed paultdum ad Calr
^tndejteSiiy becaufe (lands at the end of a nat'
row neck of Land,, which projetds to the Southward a
great way from.. the reft of the Continent; and confe-
quently is qnite. out of the Road from Suel to any o-
thet place Wefiward o( it ; probably Calpe -Carteia is
Carteia, ad Calpen, to diftinguilh it from die other
Cmeia itSk CeltiherMy mentioned in. the.z.1 Jt Book and

^th

( )

^th Chapter of Livy : for, as Caro obferves, there is no
neceffity for the alteration Sigonius has made in that
paflage of Althaa for Carteia, from the Text of Polj-
lius\ becauie Livy never mentions the other Carteia
without adding Oceanum, l/rhs ea in ora Oceani Jita efli
which diftintJ^ion were needlefs, hacf there been only one
City of that Name. Strabo in his thiid Book mentions
a City called KccprnbxUs, and places it near Saguntam,
which is agreable to«the Situation given this Carteia
by Livy,

I am very much furprized that Mariana, and feveral
others, fliould take the prefent Gibraltar to have been the
ancient HeracUa ; when neither Fliny, who reiided fd
long in thofe Parts, Mela who was born there, nor any
ancient Geographer or Hiftorian that I have met with,
makes the lead mention of fuch a City thereabouts, ex-
cept Strabo ; and he places it 40 Stadia from Calpe^ at
the Foot of which Gibraltar is fituated. The Spanijh
Hiftorians give good ground to believe there was no
Town upon that Mountain till the Moors invaded Spain
under Tariff, who gave it the name it has retained ever
fince. I ftiall not enter into the detail of the reafons
of thofe Authors who place Carteia at Tarifa or Alge-
zeira : the true one (eems to have been their not know-
ing any other place which agreed better with the old
accounts of Carteia, or where tlie ruins of a City,
which made fo great a Figure, could be buried ;
the common praSice of Authors who deicribe pla-
ces they have not feen. This appears to have been
the cafe of mod of thofe, efpecially Mariam ; who,
had he been in thefe Parts, would not have been
guilty of the overfight he has committed Lib. XVI. C. 9.
where he places two Bays in the Streights, one at Gi-
braltar* and the other at Tarifa ; which error he Was'
probably led into (as it often happens) by another.

Ccccccc % For,

( 9'4 )

For, giving into the Opinion that Tarifa was the an-
litmCarteia, and finding that City placed in a Bay by
MeUf he concluded there muft be one at Tartfa^ which
is an open Road, and fo much expofed, that in the
leaft bad Weather, the fmallefi: Veflels muft be haul’d
afliore. Which Circumftance alone is a fufficient proof
of its not being Cart eh, by all accounts, a famous
Harbour.

Tho* there are very great Ruins at Algezeira, they
are not fuch as give any room to believe they are the
remains of a Roman City. For neither pieces of Marble,
nor Infcriptions are found there, nor any Roman Coins.
The Circumftance of f^arus his fhutting up the Mouth-
of the Harbour of Carteia, and the diflance ef 40 or
50 Stadia from Calpe, are not applicable, either to Ta-
rifa or Algezeira , and if one of thofe Towns was Car-
teia, to what City belong thofe Ruins I have been de-
fcribing? fince all the ancient Geographers make Car-
tel a not only the neared Town to Calpe, but the only
one in that Bay. There is better ground to believe
Tarifa dands on the Ruins of an other Town, as 1 fliall
endeavour to fliew prefently.

But before I proceed to a Defeription of the Coad,
it may not be improper to mention fome Ruins I law
at Ximena; an inland Town, about five Leagues
from Gibraltar, fituated on a Rocky Hill, at the bot-
tom of which to the Eafirrard is a very plentiful Coun-
try, waflied by the Jofgarganta, a fmall Branch of the
River Guadiaro. On the top of the Hill is the old
Town, which by the Arches and Vaults, appears
to have been built by the Moors. On the right-hand
Corner of the fecond Gate of it, there is a courfe Stone
with Mouldings on the Edges, which has tlie follow-
ing Infcription^

L. HE-

( P»5 )

L. H E R E N N f O RE
R E N N I A N O
L. CORNELIVS HEREN;

NI VS R VST I C V S
NEPOS EX TESTA
MENTO POSVIT
NONIS MARTIIS
SEX. QVINTILlOtCON:
DIANO SEX. QVIN
TILIO MAXIMO GOSS..

Rodrigo Caro in his Convento Juridico de Sevilla C. 13=.^
fays he faw the beginning of this Infcription in E^fer
de la mkl\ but when I was in that Town, I was inform-
€d by a very intelligent Perfon, that there is no Ro<^^
Infcription in any part of it. The Author Ca~ .
diz el Emporio del Orhe, when he inferts this infcrip-,
tion, makes itSEXOViNTILIO CONDIMIO; ;
But the Dafti of the CL is very plain, and the other
word Teems rather C O N D I A N O. The Latin Fafi ,
in A. U. C. 903. place Confuls-

SEX. QUINTILIUS GORDIANVS.

SEX. (QUINTILIUS MAXIMUS,

But the very learned Dr. has obferved to me ■
that i\\Q Greek Fafti and Dio call him which .

reading is confirmed by this Infcription.

I have brought with me from this Town a piece of
Marble with the following Words upon it,^

AVCTIN VS CLEMEN
TIS SI-BI

ET SVIS BRITTLE
MATER AN LX
H.S.E, SIT T.T.LE VIS;

I fe,'V

( 9»6 )

I (aw another on the Wall of the great Church
which (eems to have been the Bale of a Statue ; the
Jnfcription is as follows.

RESP VBLICA OBEN'
SISE..LO DATO
DEDI...VIT CVR AT
LIBE..OR H..REN
NIO RVSTICO H.M.

SINILO RESTITVTO
II VIR.

'The manner in which the Moors have placed thefe
Infcriptions plainly Ihews the little value they let upon
them, and there is fo great a plenty of Scone on the
Rock where Bands, that it is not to be thought

they would fetch them for fuch an ufe, from any di-
Rant place ; which induces me to believe a Roman
Town formerly Hood there called O B A.

I do not find any Town of that name in tlie ancient
Authors. Strabo L. 111. mentions McuVoiSa ^

cT^&iss, which may polTibly comprehend Oba. The6V^>«
grafhia Nubienjis, in the fourth Climay makes a Town
called Rothan^ the firlt Station from Algezeira to Seville,
which perhaps may have been this Oba ; for it is about
a Daysj journey from AlgezeJra, zod in the diredRoad
fronii thence, to Seville.

Mariana places Lib.ni, C. z. the Cave vthetQ Craffus
hid himfelf, near JCmena ; the Marks of it, given by
Plutarch, are common to moll others. I went three
Leagues in fearch of it ; but the Country People having
a notion that there is a Treafure in it, and not being
to be perfuaded that I would take fo much Pains out
of pure Curiofity, would not (hew me the Way, tho’
^they acknowledger! there were feveral fuch Caves
thereabouts. I cannot help taking notice of one very

( )

odd tho’ trifling circumflance. The name of the^
Perfon who owns the Land where thofe Caves are, is
Pachmo, which is very near the fame with that of the '
Spaniard, who is faid by Plutarch to have entertained
C rajf us Co courteoudy, Ua,->uctt(ps. . f/irtius in t\\Q begin-
ning of his Book de hello Hifpanico mentions a Spaniard
of Note, in provincia B£tiea, called Patiecus. ^ibus
frafecit hominem ejus provincU notum ^ non parum
fcientem, L. Julium Patlecum, which was probably the
Roman Name ; and therefore .1 am furprized the Latin
Tranflator of Plutarch makes it Pacianus.

Moft of the antient Geographers defcribe the Caad
Weftward of Carteia in the following manner. JulU
Traducia, Mdlaria^ Balo fiuvius ^ oppidum^ Portus Bajippo^ ,
Tromontorium Junonis, &c. The Itinerary of Antoninus, .
makes no mention of Julia Tradu5ia, and Pliny places iton ;
the African Coaft, which Hardouin endeavours to account
for Pag. 227. in his Nummi Uluftrati.i Straho c^\h it Ju- -
Ham Jozam, which as obferves Lib. I. C. 24. fig- *

nifies the fame in the Phanici an Language as TraduPtam
in the Latin.: Ptolomj calls it LranfduBao He places s
Barhejula between that and Carteia. But all the other
old Geographers put both the Town and River of
that Name Eaftward of Calpe. I faw fomd Ruins on
the Eaji fide of the River Guadiaro, four Leagues
oi Gibraltar which I take to be the remains of the
ancient Barhefula. For I find in the Cadiz Emporio del
Orbe, mention made of two pieces of Marble, brought .
from thence to Gibraltar on one of which was M M '
BARBESVLANI. I was credibly informed they '
were ufed for the Fountain on the Parade. The Letters -
probably were either fa wed off, or turned inwards; for r
they do not appear. This Barhefula is probably ^ the^
placed' in the Itinerary X. P* Bafciiom \

Carteia,,

1

(pi8)

"Pmpomus Mtla, who was born in thofe Parts, and
therefore is moft to be depended on» gives the follow-
ing account of the Coaft, according to the Edition of
'^ronovius. Sinus ultra efi, in eoque Carteia, ut quidam
putant, aliquando Tartcflus, ^ quam tranfve^li ex Africi
‘ PhxnicQS /jahitani ; atque unde nos fumus^ Tingentera.
Turn Mellaria & Bcelo, & Bacfippo ufque ad Junonis pro-
‘fnontotium or am freti occapat. The Text of MeU in
this place has occafioned great dil'putes among the
Learned. Cafauhon in his Notes upon Straho, fays,
lego autem — atque unde nos funsus Tingi contraria Mellaria^
aut Tingi e tegione jita Mellaria. Nam Tingis fa6iam hie
d Mela mentionem mihi efi perfuafijfmum ; primiim quidem
veterem UBionem fpeBanti, qu£ efi^ ut dixi^ Cingentera-
tum ; aut etiam ut in Juts libris doBijfimus Elias Vine-
tus reperit Tingentera ; ut jam de eo dubitari non pojfit.
Deinde autem 'video morem Mel:e hur\c effe^ ut locorum in
altera ora oppofitorum mentionem facial. Sic alibi; Ma-
jorem Sabcei tenent partem, oftio proximam, & Car-
mariis contrariam Mac^c. Nec moveri quifquam debet
quod alii Tingin Bedoni non Mellariae faciunt contrariam.
Nam Bcelo & Mellaria it a funt vicina, ut mirari hoc ne-
mo debeat, Saknafius, whofe opinion is approved by Bo-
charts makes it Tingis altera, turn Mellaria, &c. and
takes the preceding tranfvecli to denote Julia Tradu-
Ba. Cafaubon feems to have been once of the fame
Opinion. Sed a Strabone fiare Ptolemseus videtur, qui
in hac HifpanieS ora oppidum quoddam memorat cui nomen
Tranfduda, in quod jcilicet collocati fuerint ifii, de quh
bus nunc loquitur Strabo ; & de quibus dubitavi aliquando,
an hac Melx verba effent accipienda. In eoque Carteia,
ut quidam putanr, aliquando Tarteflus, & quam tranf-
vedii ex Africa Phsenices habitant. Nam videbatur fatis
aperie Tranfdudlam Ptolomsci a^(pfci^€iv. Nunc iis afi
fentior qui ad Carteiam ea referunt. The -opinion of

* Salma*

' ( 9*9 )

Salmajjui feems to be the moft probable ; for B<£lo and
not Julia Tradu^a is faid to be over againft Tingis,
Marciams Heracleotes makes the two former about
zfo Stadia diflant from one another, and Mellaria is
generally placed between them ; therefore they could
not be fo near one another as Cajauhon infinuates.
Tho’ Carteia was originally founded by the PhcenicianSf
it had been eredied into a Roman Colony long before
Mdas time, and therefore he could not very properly
fay Carteia, quam Phaenices habitant ; and had be intend-
ed to take notice of the Founders of that City, it is
probable that one whofe Stile is fo pure and accurate,
would have made ufe of another word, or at lead
another Tenfe. Befides, if Julia TraduPia, according
to Cajauhon, is not meant by that paflage, it muft have
been entirely omitted by Mela ; which is very unlikely,
confidering he was Born in or near it ; and that it is
mentioned by Strabo, who lived before him, and Pto-
lorn) and feveral others who were after him ; and ap-
pears to have been remaining at the time the f^andals
were in poflefTion of Spain ; for Greg. Turcn, Lib. If. fays
Profequentibus Alamannis ufque ad Tradudfam, tranfito
mart, Vandali per totam African! ac Mauritaniam funt
difperf. The Letters of Tingi altera come nearer the
Tingentera of Elias Vinetus, and the Tinge Hiera of
Cronovius, than Cafaubons Tingi contraria or Tingi e re»
gione fita. The © and the atque, by making the flop
at Tarte(fus inftead of Habitant., may very well relate
to the fame place; and it is not improbable that Mela
was defirous to illuftrate the obfcure place of his Birth
by a PeriphrafiS, and a name of fome Eclat ; tho’ k
has happened, the method he took to do Honour to it,
has been the occafion, that we are in doubt even of
its Name.

D d d d d d d

I

( 5>20 )

I met with two Medals of Julia TrarluCia among the
Brafs Spanijh Coins; but as I cannot alcertain where
they were found, I will not pretend to form from thence
any judgment of the fituation of the Town to which
they belong. But I prefume in matters fo dark, a con.
jetfure n?ay be offered. It does not ieem very im-
probable, that Julia Trada6la flood where Tarifa is at
prefent. The Spanifh Authors reckon that Town to
have been built by Tarif at his fecond coming to Spain.

I cannot fee what could invite him to fettle on a Spot
which has neither the convenience of a River, nor a
Harbour, and is commanded by a rifing Ground ; un-
lefs he found fome Tenements (landing, or Ruins to
ferve for Materials to Build. I have feveral Roman
Coins that were found there after great Rains, in the
Common Sewer ; which is fome flight inducement to
believe it was formerly a Rowan Town.

About a League and half to the Weft of Tarifa^ is
a place which goes now by the name of Fal de Vaca,
The Country People have a Tradition among them,
that it was once a confiderable Town, fince fwallowed.
up by the Sea. There is a fmall Brook called el Ar-
roffo de Juan Francifeo, which ferves to turn fome Mills,
that a Pried of that Name was encouraged to build
there, by finding an antient Stone Channel for the
Water. I faw fome other fmall Ruins, and was credi-
bly aflured there are vifible remains of an old Town
a good way under Water. There is a Shoal almod
off this place, that runs pretty far in the Sea, on
which a Hamburgher was loft fome Years ago. Per-
haps Mellaria flood hereabouts.

Wherever it was, the Ruins of it muft be a confide-
rable way in the Sea, if credit is to be given to Rliny,
who upon the Teftimony of one Born there, reckons
only five Miles from thence to Afric. Lib. III.

whereas

' ( )

whereas it is at preftnc five Leagues over at the nar-
row Parc. Cnjauhon is miftaken in that Note on Strabo
L. H. where he fays. At Maris Mediterranei cftium vix
LXX Stadia latum e(l y

I cannot help oblerving that the beft Hony in all
Spain is made in thefe Parts, and that the fame caufe
to which the ancient Mdlaria ow’d its Name, dill
fubfifts, and has given a modern Appellation to feve-
ral places hereabouts, as Playa de Orimd, Rid de la Midt
Bejer de la Miel. The latter of thefe is generally rec-
koned by the Spaniards to be the old Mellaria, for no
other realbn, that I can fee, but the Name. For it is
at lead two Leagues from the Coaft of the Streights,
and, by what I could judge when I was on the Spot, as
near the Ocean, and therefore may as well be aferibed
to the one as che other. Whereas Mdlaria, according
to all the old Geographers, wasfituated on the Sea fide
in the Streights, and is reckoned by Vliny the nearefl
Town to A^ric , a plain proof that it was not what is
now Bejer de la Mid.

About a League and half further Wefl, in a fmall
Bay, there are very great Ruins, which appear evi-
dently to be the remains of a Roman Town. A League
Eaftvpard from that place, upon an Eminence, are to
be feen the Quarries from which the Stone was fetch-
ed for building it; and all the way from thence are
large remains of an Aquedudf, of which in fome pla-
ces there are entire Arches dill danding. Among the
Ruins of the old Town, I faw the Body of a Roman
Statue of fine Alabader, fomething bigger than the
Life. Our Guide faid his Father had feen it entire ;
but as it was an Idol of the Gentiles, they, like good
Catholicks, had broken ic to pieces. He likewife
cold us that Urns of old Coins had been found there ;

Ddddddd x but

C pii )

but not being Current in Spah^ they had thrown
them away. The place is called Balonh. ft is over
againft: Tangier^ and frequently infefted by the Moors
from thence; on which account it is uninhabited. A
fmall River, called Alpariate, runs by it : all which
circumftances correfpond with the ancient accounts of
Bdlo, I have a Medal that was given me at Tarifa^
with the following Letters upon it B A I L O, which
probably belonged to this City, called by Ftolowij
BfluAwv Martianus CapdU i^ib. VI. mentions it under the
name of Velomnfis B^ticaCivitas- The Itenerary of
Aniomnus places VKM. P, Wefi Mellaria, which
is about the diftance of thefe Ruins from Val de Faca*

About five Leagues farther is the Cape of Trafalgar i i
the fight of which immediately brought to my mind ^
Melas delcription of it. Idud jam in Occtdentem (jr ft
Oceanum ohliquo jugo excurrens, atque f/, quod Ampelnjium t

effe dixeramus, adverfam, &c. Near the Capes Point are ^

the Ruins often mentioned by the SpaniJJ) Authors, un- ^
der the name of Aguas de Mecca, I was not there, but
was afiured at Bejer de la Mid, that there were fiill
fome Ruins on the Shore, and more in the Sea, that
run all along under the Cape ; particularly remains of
a Mole, which muft have made it a tolerable Harbour.
Thele Ruins feem to be the remains of old B<sfippo,

Flin» L. III. Portus Bcefippo. Mela Bafippo ufque ad Jtt-
mnis promontorium, cram freti occupat.

The placing of Watch-Towers along the Coaft of
Spain to Alarm the Country, upon any Defcent, feems
to have been a practice of a long (landing. Livy ,
Lib. XXII. C. 19. Mult as dt* locis alt is pojitas turres Hif-
pania hahet^ quihus & fpeculis (jr propugnaculis contra la*
trones utuntur : inde primo, confpedis hojiium navihus, da* \ \
turn figmm A.^^t\xh2t\.iejl, See,

m. A

( pi? )

m. A Letter of M. T Abbe Conti, R. S. S. to the
late M. Leibnitz, concerning the di/pute about
the Indention of the Method of Fluxions, or
Differential Method 5 with M, Leibnitz his
Jnfwer,

J’Ai diflere jufqu’ a cette heure de repondre a vo-
tre Lertre, parce que j’ai voulu accompagner ma
Reponfe de celle que Nervton {a) vient de fair a?
TApoftille que vous y avez ajoutee. Je n’ entrerai
dans aucun detail a I’egard de la difpute que vous
avez avec M. Keillf ou plutoc avec M. l^cwton. Je ne
puis dire qu’ hiftoriquemenc ce que j’ai vu, & ce que
j’ai lu, & ce qu’il me manque encore de voire & de
lire, pour en juger comme il faut.

J’ai lu avec beaucoup d’ attention, & fans la moin-
dre prevention, le Commercium EpiftoUcum, & le petit
Livre (b) qui en contient /’ Extrait. J’ai vu a la So~
ciete Royale les Papiers Originaux des Letters du Cotn^
mercium; une petite (c) Lettre ecrite de votre main
a M. l^eivton; & 1’ ancien Manulcript ( d) que M. Nerp-
ton envoya au Dodeur Barrow^ & que M. Jones a i
public depuis peu.

( ) In his Letter dated Feb. %6. 1715-16. fi- vet. and Printed at the
end of I^ph/on's Hiftory of Fluxions,

( b ) Printed in the Phihf. Tranf. N. 34^. and in Tome VII. du
journal Literaire.

( c ) Dated 17 March, 1693. and Printed at the end of Saphfm’s
Hiftory of Fluxions.

( d j Eutituled Analyfis per Series numero terminorum infinitiis.

( p^4 )

De tout cela j’en infere, que fi on ote a la difpute
toutes les digreflions etrangeres, il ne s’agic que de
chercher fi M. Mewton avoit Is Calcul des Fluxions ou
infinitdfimal, avant vous, ou fi vous i avcz cu avanc
lui Vous I’avez piiblie le premier, il eft vrai; mais
vous avez avoue aufti que M Neirton en avoit laiffe
entrevoir beaucoup dans les Letters' qu’il a ecrites a
Mr. Oldenhourg & aux auttes On prouve cela fort a
long dans le Commerchm^ & dans fon ^xtrait. Quel-
les Ton VOS Reponfes ? Voila ce qui manque encore au
Public, pour juger exadlcment de I’aftaire.

Vos amis attendent votre reponCe avec beaucoup
d’impatience, & il leur femble que vous ne fauriez
vous dilpenfer de r^pondre, ft non a M. Keill, du moins
a M. NervtonlxximkmCf qui vous fak un deffi entermes
expres, comme vous verrez dans (a Letrre.

Je voudrois vous vok en bonne intelligence* Le
public ne piofite guere des difputes, & il perd fans
reftburce, pour bien de ftecles, toutes les lumieres que
ces memes difputes lui derobenc.

Sa Majefte a voulu qiie je rinforraafte de tout ce
qui seft pafle entre M Nervton vous. Je I’ai fait de
mon mieux, & je voudrois que ce fut avec fucces pour
I’un & pour I’autre.

Votre Probleme a ete refblu fort aisemcnt en peu
de terns. Plufieurs Geometres a Londres & a Oxford
en ont donne la Solution. Elle eft generale, car elle
s’ecend a routes forces de Courbes, (bit Geometriques,
foit Mechaniques. Le Probleme eft un peu equivoque;-
ment propofe : mais je croi que M. dt Moivre ne fe
trompe pas, en difant, qu’il faudroic fixer i’idee d’une
(bite de Courbes. Par exemple fuppofef qu’elles ayent
la meme Soutangeante pour la meme Abfcifle ; ce qui
conviendra non feulement aux Sections Coniques,
mais a une infini-ce d’autres taut Geometriques que

* Me-

( 9»5 )

Mechaniques. On pourroit encoce fairs d’autres fuppofi-
tions pour fixer cecte idee.

Je vous parlerai une autre fois de ia Philofbpie de
M. Nervtofi. II fauc convenir auparavanc de la Methode
de Philofopher, & diftinguer avec beaucoup de foin la
Philofophie de M. Newton, des confequences que plu-
fieurs en tirent fort mal a propos. On attribue a ce '
grand homme bien de chofes qu’il n admet pas ; com- •
me il I’a fait voir a ces MefTieurs Francois qui vinrent
a Londres, a I’occafion de la grand Eclipfe.

Je fuis avec tout le refpe<5l pofTible
h Londres \q Monfieur, votce

de Mars iyi6>

N. B. Mr. I’Abbe Conti /pent fome Hours alfo in ,
looking over the old Letters and Letter Books kept in the
Archives of the Royal Society, to fee if he could find "
anj thing which made either for Mr* Leibnitz, or again/}
Mr, Newton, and had been omitted in the Comiaercium i
Epiftolicum Coliinii & aliorum ; hut could find nothing
of that kind.

A Letter of M, Leibnitz to M.U Abbe Conti, ,
in An/wer to the former.

Monftear, Hanover ce 14. /x\vril, 1716.

POur ne vous faire attendre, je vous dirai par advance :
que j’ai repondu d’abord a I’honneur de votre ,
Lettre, & en meme terns a celle que Mr. Newton vous
a ecritej & j’ai envoys le tout a bAt. Remond ^ Paris^ ,
qui ne manquera pas de vous le faire tenir. Je me
fuis fervi de cette voie, pour avoir des temoins neu-
tres & intelligens de notre Difpute : & M. Remand era ;
fera encore part a d’autres. Je lui ai envoye en meme j

terns, i

( 91i5 )

terns une copie de votre Letrre & celle de Mr. Nevpton,
Apres cela vous pourrez juger, fi la mauvaife chicane
de quelques uns de vos nouveaux Amis m’embarraflc
beaucoup.

Quant au Probleme dont quelqaes-uns parmi eux ont
voulu refoudre des, cas parciculiers, pour en fixer,
difent-ils, les idees; il y a de I’apparence qu ils (e feront
.jettez fur des cas faciles : car il y en a dans les Cour-
^bes Tranlcendantes, aufii- bien que dans les ordinaires ;
mais il s’agit d’une folution generale. Ce Probleme
n’eft point nouveau. M. Jem BermuilU fa deja pro*
pofe dans le mois de May des Adies de Leipfic 1697,
p.%i\, Et comme M. Fatio meprifoit ce que nous
avions fait ; on en repeta la propofition pour lui &
pour fes femblables, dans les Ades de May i-joo.p.

11 peut fervir encore aujourd’hui a fair connoitre a
quelques- uns, s’ils font allez aulTi avant que nous en
Methodes ; & en attendant qu’ils trouvent le moyen
de parvenir a la folution generale, ils pourront efiayer
ce qu’jls p^uvent, en fixant les idees fur un cas parti-
culier, qu’on leur propofe dans le papier cy joinr. Sa
folution vient encore du meme M. Bernoulli. Ainfi vous
aurez la bonce de ne pas vous rendre crop tor aux in-
finuations de ceux qui nous font contraires ; comme
lorfqu’ils vous font a croire que notre Probleme leur etoit
aifd. Je fuis avec zele, Monfieur Votre

Prohlema continens cafum fpecialem Prohlematis genera-
Its de invenienda Serie Curvarum, quarum qualibet fit ad
aUam Seriem Curvarum perpendicularis.

( 9^7 )

Suptt rtciA A G tAn"
quAm AXCy ex fun^o A con-
ftrucris Curvis quotcm^ttc
qualis ejl A B D , ejiis
nature ut rAdtus cfculi ex
fingulis (ingularum CurvArum
punHis B edu6lus B O ^ece-
tur ah axe A G in Q in Da-
ta fefnper confianti rat tone :
ut ncmpe fit ^ Q ad ^ C nt
M ad N. Conflruendx jam
fttfjt Traje^ortA qualis ejl ENF, priores Curvas ABD
fecantes ad angulos reBot,

Thus far this Letter. Mr. Leihnitz firfl; propofed the
general Probleme to M, I'Ahhe Conti in ihefe words;
Trouver une ligne B C \y,qui
coupe a angles droits toutes
ies courhes d' une juite de-
termine d'nne rneme gcndre\
par excmplcy. toutes Us H)-
perholes A B, A C, A D, qul
ent le meme fommet & le
neme centre; ^ celapar une
<voje generale. And in the ABa Eruditorum for OBo>
her, i6>i8. />. 4/0, 471. he calls the Curves in this
determinate Series, Curvas ordinatim datas, & pofttione
datas, & pofitione ordinatim datas. And by all this,
the Series of Curves to be cut is given, and nothing
more is to be found, than the other Series which is
to cut it at right Angles. But Mr. Leihnitz being
told that his Probleme was folved, he changed it into
a new one, of finding both the Series to be cut and
the other Series which is to cur it. And the.particu-
Eeeeeee lar

( ?i8 ) 1

lar Probleme propofed in this Letter is a fpecial Cafe, |

not of the general Probleme firft propofed, as it ought I

to have been, but of this new double Probleme. And I

the firft part of this double Probleme (viz. by any I

given property of a Series of Curves to find the Curves) I

is a Probleme harder than the former, and of which a I

general Solution is not yet given. Mr. Leibnitz in a /

Letter to Mr. John Bernoulli, dated i6 December, 1694. f

and publiflied in the A^a Eruditorum for October 1698. ^

/>. 471, letdown his Solution of the Probleme, when j

the given Series of Curves is defined by a finite Equa- |

tion, exprefting the relation between the Abfcifs and 7

Ordinate. The fame Solution holds when the Equa-
tion is a converging Series, or when the property of the
Curve to be cut can be reduced to fuch an Equation,
by the And)(is per Series numero terminorum infinitas.

But Mr. Leibnitz was for folving the Probleme without,
converging Series.

IV. ^ars

( 9^9 )

IV. reli^ua 'Dijfertatlonis De Potentia Cordis.
Authore Jacobo Jurin, 6c R. Socie-

tatis Soc.

ThiormA II,

SI ex Mdchina cAvk inaquAliter contrAlHUt A B C D,
aquA per MAchina contrAlliomm expriwAtur, Motus a-
qua ex orificto A profilkntis aquAtur Summ<s pAliorum ex

SeBionihus qutbufvis trAnfverfis omnium aqua fiUmentorum
A B, AC, A D 3 fingulis duIHs in longitudines vela-
citAtes refpeliivAs.

Demonjlratio, Loco filameotorum aquse, concipiatur
Machina tubis minimis, insequaliter amplis, A B, A G,
A D, in orificium A definentibus, tota conftare.

Eft aquGe Motus in quovis tubo sequalis (edioni
cuivis ipfius tubi, dudse in velocitatem aquae per fe*
dtionem iftam fluentis, & longitudinem tuki, ^QiTheor. 3.

Eeeeeeex' De

C 950 )

De Mo\it A(j»Ar. fluent. Proinde Summa Motuum a-
quse in omnibus tubis fimul fumptis, five Motus aqux
ex Machin:E orificio prorumpentts, sequalis eft Summae
Fadorum cx omnium tuborum five filamencorum aquae
fedionibus, dudtis in longitudines, & velocitates, reG
pedtivas. ^ E. D.

Cor&l. i. Motus aquae effluentis minor eft Faefto ex
orificio A, yelocitate aquae exeuntis, & longitudine fi-
lamenti aquae omnium longiftimi. Eft enim Faftum ex
orificio & velocitate aquae effluentis, aequale Summae
Faeftorum ex fedionibus filamentorum fingulis dueftis
in velocitates refpeftivas,* & Summa horum Fadcrum,
duda in longitudinem filamenti omnium longiftimi,
major eft quam Summa eorundem dudorum cujufque in
fuam longitudinem.

X. Motus Aquae aequatur Fado ex orificio A &
velocitate aquae exeuntis, dudo in longitudinem ali-
quam mediam inter longitudines filamentorum longifti-
morum & breviftimorum : v.el xquatur Fado ex quan-
titate aqux dato tempore effluentis, & longitudine mo-
di^ praedida, applicato ad tempus illud datum.

3. Si Machinae plures fimiles aqua plenae fimiliter
contrahantur, five aequabili velocitate medi3, five inx-
quabili, fimiliter tamen in omnibus Machinis auda, vel
.imminut^ ; Motus, quo aqua ex Machinx cujufque o-
rificio prorumpit, rationem habet compofitam ex ra-
tione quadruplicate Diametri cujufvis homologx ipfius
Machinx, & reciproca temporis ratione, quo peragitur
Machinx contradio : vel rationem compofitam, ex ra-
tione ponderis Machinx, vel molis aqux, five Machine
contentx, five ex eedem expulfx, ratione ejufdem pon-
deris, vel molis, fubtriplicac^, & ratione temporis reci-
proce.

ProUema

( 9?* )

<p <!{ O S L E M J.

InVenire Totentw?i Cordis.

Sicp = Pondus Vencriculi finin:ri, five quantitas
Sanguinis cidem ponderi aequaUs.

S — Superficies interna ejttfdem,

/ = Longitude media filamentorum' Sanguinis ex
eodem prodeuncium.

s ==. Sedio Aortic.

^ — Quantitas Sanguinis Ventriculo finitlro con-
tend.

t — Tempu?, quo Sanguis ex Corde expellere-
tur, fublata Arteriarum & Sanguinis pruce-
dentis refiftenria.

= Velocitas variabilis, qua Sanguis ex Corde
profiliens per Aortam flueret, fublata refi-
ftentil

X — Longitude variabilis Aortas a Sanguine ex
Corde effluente percurfa.

z = Tempus, quo longitudo x percurritur.

Inde velocitas media variabilis Sanguinis Ventriculo

contigui, five media velocitas ipfius Ventriculi =

Motus Ventriculi (per T^eor. r. £or %.) ■= p x^.

Motus Sanguinis effluemis (ipQtT^eor, z. Cor. z^ — sv

X X.

Horum Summa^ five Potentia Ventrkuli :=. s vx

Y -\~ i 4' autem v — —. Unde p^r Methodum

_ K

Newtonianam inverfam, elicicur Potentia Ventriculi =

Y X y- Sed cum z> = f, Qtiisx — q.

Hinc Potentia Ventriculi xy~]-~

( 951 )

Simili ratione itivenitur Pocentia dextri Vcntriculi

# S ' '

Literis autem Grsecis eadem fignificantur in dextro
Vencriculo, quse Latinis in finiftro.

Hinc tora Cordis Potentia

Si ponatur

p = S unc. Avoird = 13.118 unc. cub.

7T=4 =6. J64

S = 10 unc. quadrat.

S = 10
/ = ^ unc.

A =17.

^=1 unc. Avoird. = 5.181 unc. cub.
j = o . 41 8 f unc. quadrat. 1 Ex Kdllianis Experi-
0- = 0 . 583 ^ mentis.

? = o . 1"

Erit Potentia Ventriculorum srqualis motui ponde-
rum fubfcriptorum, nempe, lib. unc.

Ventriculi fmiftri ^ 9 • i

Ventriculi dextri — — ^ ^

Cordis totius *5” • 4

Quorum ponderum ea eft velocitas, qua percurratur
longicudo uncialis fingulis minutis fecundis.

Cor. I. Quoties Pulfus fit celerior ; aut minuitur
refiftentia, aut Potentia Cordis augetur, aut minor foli-
to Sanguinis copia fingulis contradtionibus ex Corde
expellitur.

1. Si Pulfus folito tardior fiat necefie eft, vel auge-
atur refiftentia, vel Cordis Potentia minuatur, vel ma-
jor Sanguinis moles ex Corde ejiciatur*

3. Au(fta

( 955 )

5. Auda refiftentia, neceflario vel Pulfus retarda-
bitur, vel augebitur Cordis Potentia, vel Sanguinis
quantitas folko minor ex Corde exprimetur.

4. Imminuta refiftenci^, vel Pulfus acceleratur, vel
major Sanguinis copia quaque Syftole ejicitur, vel Cor-
dis vires minuuntur.

5. Audtis Cordis viribus, neceflario vel augebitur re-
fiftencia, vel Pulfus accelerabitur, vel plus Sanguinis ex
Corde ejicictur.

6. Viribus Cordis imminutis, vel minuatur necefle
cfl: refiftentia, vel Pulfus tardier fiat, vel minus San-
guinis ex Corde exprimatur.

7. Cum minor Sanguinis moles ex Corde projicitur ;
vel acceleratur Pulfus, vel Cordis vires minuuntur,
vel augetur refiftentia.

8. Gum plus Sanguinis ex Corde exprimitur; vel
Pulfus tardior fiet> vel augebitur Cordis Potentia, vel
refiftentia minuetur.

SchoL r. Ventriculorum fuperficies internas, cum
fadilu difficillimum videatur, ut accurate determinen-
tur, aut etiam ratio habeatur imminutionis, quam in-
ter contrahendum patiuntur, contenti fuimus pra:ter-
propter ceftimare : cum five eafdem ix, five 8 unciis
quadratis fingulas rcquales ftatueris, perparva repe«
riatur Potentiarum fada mutatio. Quod etiam obfer-
vari poterit de longitudine media filamentorum Sangui-
nis. Prasterea difterentias, qua Arterice ambx, earum-
que rami proximi a Corde progredientes, feeftione au-
gentur, ut xftimatu perdifficiles & pene infenfiles,
negligimus. Alioqui eftet Cordis Potentia tantillo
minor ftatuenda, quam qux fupra definita eft.

X. Determinavic Vir Celeberrimus, Jaeohus Kdllius,
velocitatem Sanguinis, refiftentia fubmota, ex Corde cf-
fluentis, eam'circitcr, quS percurrantur pedes 6~ fingu-
bs minuds fecundis. Ponic veto illc celedtatem San-
guinis

( ?54 )

guinis per totam Syftolem a:quabilem, quam nos infig-
niter inxqualem fieri, & perpecim a Syftoles initio re-
tardari fupra oftendimus^ Hanc fi cui definite libue-
ric, fubftituenda eft, in quartd i^quatione iupra pofita,
Potentia Ventriculi proxime inventa, & ipfi x valor
quivis tribuendus, ut eliciacur v, five velocitas eidem
refpondens. Ita, cum initio Syftoles fit x = o, fub

finem vcro x = ^, determinarur inde ea Sanguinis ve-
locitas initio Syftoles, qu3 pedes 14^ ; in fine autem
qua 4 minuti fecund i (patio percurrantur. Pariter in
dextro Ventriculo : velocitas Sanguinis initialis pedes
circiter 1 o ultima veto 3 pedes eodem temporis
fpatio conficiet

Adhibuimus hacftenus earn Hypothefin, qua Mufculi
Cordis Veniriculos conftituentes Motum omnem, quo
adjguntur in contradionem, Momento temporis conci-
piunc Quod fi ponamus Motum iis communicari non
unico quidem Momento, fed tantillo tamcn temporis
fpatio, quod cum tota Syftoles duratione comparatum
rationem obtineac admodum exiguam 5 erit Cordis Po-
tenria paululo major ftaiuenda, quam qux fupra deter-
minata eft. Si veto ftatuatur ifte Motus, procedentc
Syftole, in ratione temporis augeri; erit totus Motus
in fine Syftoles acquifitus duplo major quam fupra
pofu mus, ubi nulla rcfiftentia Sanguini ex Corde pro-
fluenci objicitur: Ubi autem folita adeft refiftemia, e-
rit idem quintuple major ; quod inftituto calculo facile
patebit* Pari ratione potent calculus nofier ad aliam
quamlibet Hypothefin, qua Ventriculorum Motus in
duplicata vel fuperiori quivis ratione temporis augea*
tur, accommodari. Potentia veijo in fine acquifita fu-
prapofira elicietur longe major, nempe ex ratione du-
plicata Potentia tripla, tx triplicata quadrupla, ex qua-
druplicata quintupla, & fic in infinitum.

Nobis

( )

Nobis autem videtur fecunda Hypothefis, qu^ Vett=
triculi parvo admodum temporis fpatio Motum om-
nem concipiunt, cseteris longe verifimilior. C^uum ne-
cefle fit, ut aliqiiid temporis impendatur ad Motum
quemlibet generandum ; nequs videatur adeo tarde in-
crefcere Ventriculorum Motus, ut non celerius augea-
tur, quam fecundum temporis rationem. Motus enim
Mufculorum impetu folo Fluidorum quorumcumque,
qus ex Sanguine proveniunt, perfici nequic ; quumBra-
chio alterutro Motum exerere poffimus Motu Sangui-
nis per vala Corporis univerfa profluentis longe majo-
rem. Relinquitur ergo, ut MufculorUm fibrce Ventri-
culos Cordis conftituentium, rarefcentia qu^am liquo-
rum in eafdem influentium, in Motum impellantur.
H^ec autem, quoties vim magnam concipit, plerumque
fubita eft, & fere inftantanea. Adde quod Ventricu*-
Jorum Motus fecundum hanc Hypothefm longe minor
efficitur, quam in tertia. Non folet autem iapientifli-
mus Artifex, Rerum Conditor, in operibus fuis plus
Virium adhibere, quam quantum fufficit ad finem pro-
pofitum confequendum.

Caeterum five admittatur ifta Hypothefis, five alia
qu^cunque ex fupra didlis verior cenfeatur, poterunc
omnia Corollaria noftra eodem jure ex Problemate de-
duci. Quae utrum aliquid adjumenti afferanc ad Mor-
borum Hiftoriam explicandam Medico fagaci confide-
randum permittimus. Facile autem ex Morbi cujufque
Nacura fciri poterit, utrum autfta fit vel imminuta re-
fiftentia. Augeri vero credibile eft vel imminui Cor-
dis vires audis vel imminutis Mufculorum reliquo-
rum viribus; quamvis aliter ftatuifte video VirumCc'
kberrimum, Laurentium Bdlimm,

F f f f f f f Thcmmti

Theorem A III.

Totus Motus refiJlentU, ofua Sanguini ex Corde erum-
fenti duranpe Syftole obpeitur, five totus Motus, eyul San-
gutni .'pracedenti ^ /4rtersarum tunkis eommunicatur, toti
Cordis PetentU quamproxime aqualis e(i,

Dem. PeradlS Cordis Syftole, quae pars Aortae &
Arceriae Pulmonalis Cordi psoxima eft, perftat plena
Sanguine per cotam Syftolem Arteriatum. Nec enim
patitur carum fabrica & nexus, quo Cordi conjuneftre
func, ut cunicis in fefe penicus collabencibus totae oc-
cludancur, neque poteft earum cavum Sanguine vacare.
Alioqui enim, contrahentibus fefe reliquis Arteriarum
partibus. Sanguis iildem concentus retro in vacuum im-
pellerecur motu, & inutili & motui Sanguinis naturali
contrario. Turn etiam Valvulx Semilunares non ten-
derentur verftis Ventriculos, adeoque Sanguis ex Auri^
culis in Ventriculos expreflus, etiam in Diaftole Cordis,
in Arterias protruderetur.

Hinc patet Sanguinem proximo ex Corde expulfum
Syftole perad^ immotum in Arieriis perfiftere, adeo-
que turn omnem Ventriculorum Motum excepifte, turn
eundem rotum parcim Sanguini antecedenti, partim tu-
Bicis Arteriarum communicafte. ^ E. D,

Theorema IV.

Motm, qui in Syftole Cordis communicatur Sanguini
pracedenti^ eft ad Motum tunkis Arteriarum communka-
turn, ut iempus Syftoles Cordis ad tempus Diaftoles quam
proximo.

Dem. Quum Sanguis per vafa Corporis univerfa,
fi partes Arteriarum. Cordi propiores exceperis, a^qua-
bili curfu deferatur ; necefle eft, ut cum Motus affntJu
Sanguinis ad valorum latera deperditus, turn Motus
Sanguini redditus a Syilole five Cordis five Arteria-

rura

( 957 )

rumi sequalibus temporibus ^qpalis fit, Qui autem
Motus a Syftole Arteriarum Sanguioi communicatur,
idem eft prsecife, qui prius a Cordis Syftole Arteria-
rum tunicis fuerac irapreflus, cum Arteriie eodem im-
petu quo diftrate fuerint eciam reftituantur. Et
Syftole Arteriarum cum Cordis Diaftole duratione coa-
venit. Unde patet Propoficum. E. D.

Cor. Si ponamus cum Viro Dotftiftimo Jacoho Keillh^
Syftolen^ Cordis peragi tertia parte temporis inter Pul-
fus binos intercept! ; erit Motus Sanguini prsecedenti
communicatus totius Potentise Cordis pars tertia : Mo-
I tus vero Arteriis communicatus prioris duplus, fiv,e
du£ partes tertian totius Cordis Potential.

Theorema V.

In diver fis Animalihus Votenth Cordis rationem ohtinet
I compofitanty ex ratione qmdruplicata Diametri cujujvis ho-
mology AnirndiSy ^ ratione inversa temporisy quo Cor
! (ontrahitar: vel rationem compofitamy ex ratione fonderis
I vel ipfius Cordis vel integri AnimaliSy ratione ponderis^
ejufdem fuhtriplicata, d>* ratione temporis reciproca,

Facile demonftratur vel ex Corel, j. Theor. i & z-
vel ex Potentia Cordis Problemate prxeedente definita,

Cor. 1. Si ponatur Cordis Potentiam rationem obtinere
ponderis vel ipfius Cordis, vel integri Animalis, vel Sam-
I guinis copiae in toto Animali ; erit. Animalis longitado
in ratione temporis, quo Cordis Syftole perficitur, five
in ratione inversa frequenti^ Pulfuum.

! z. Si ratio longitudinis integri Animalis major fuerit
ratione inversa frequentias Pulfuum , neceffe eft ma-
jor fit ratio Potentise Cordis ratione ponderis ejuldem,
, Schol. Quum conftet Experimentis Puerorum Pulfus
non elTe tanco frequentiores Pulfibus Virorum, quanto
Pueri Virorum longitudine fuperantur, concludendum

Fffffffz eft.

{ 9j8 )

eft, vi fecundi Corollarii, Potentiam CorcKs Virilis ma*
jorem obtinere radonem ad Pocenciam Cordis Pueri»
quam eft ratio ponderum. Et par eft ratio in cazeeris
Mufculis. Nam fi Corporis robur rationem ponderis
iequeretur, poflent Pucri sequalia icinerum fpacia eodem
tempore cum Viris conficere.

Simili ratione ac Motum Sanguinis cx VentricuKs
Cordis erumpentis ope fecundi Theorematis determina-
vimus, poterit quoque Urinse Motus ex Urethri pro-
fluentis deternfinari. Nempe ft ponacur Urethra & Vc^
ftcaz iongitudo i £ unciis xqualis, & bin£ uneix Urioae
minuti fecundi fpati& emtccantur. erit Motus Urinae
effluentis sequalis Motui ponderis librae i f , quod ua*
cialem longitudinem ftngulis minutis fecundis percur*
rat Quoniam veto Urina non folis Veftes LJrinarise
viribus contradivis^ led etiam Diaphragmatis & Muftu.
lorum abdominalium ope in (ubftdium vocati, expelli-
tur, nequit Veficse Potentia ex Mocu Urinae profluentis
aeftimari.

Haec tu, VirDodiflime, squi boniqueconfulas rogo:
ipfe autem uc diutiftime valeas» utque exiftimationem
tuam, & iplam Artis ^fculapiae dignitatem uique uc
badenus fecifti, inftgnirer tueri pergas, ac magis in-
dies magifque extendere, idcirco ex animo voveo, quia,
publicam ad falutem peccinere arbitror*,

Galendis fanuaril^
tyih

V*.

( 9i9 )

V. Nova Methodus Unherfalts CurVas Omnes cu- -
ju/cunque Ordinis Mechanic ce defcrihendi fola dd-
torum Angulorum <sr ^Elarum Ope. Go-
lin Maclaurin in Collegio KoVo Abredonenfii
Mathefeos Trofejfore.

INter innumera fiiWimiaque Magni Nemoni ihventa,^
quibus Geometria ampliffime ditata in . immcnt
fam excreyit luculentiffimse Cognitionis molem,- Con^“
ftrudionem exhibuit Curvarum Mechanicam, poU Enur
merationem Linearum Tertii Ordinis, ad dnenv Optf-
c& edkam, arduo funami Viri ingenio dignam ; qua*'
fimpliciorem & fimul adeo Univerfalena aiiam exhibuit
Nemo, Methodum vero fuam ad Curvas Terdi Or-
dinis pundo duplice carentes, aut eas akiores Ordinis
pundo mukiplice deftitutas, non extendic ; earumque
defcriptionem Problematibus Geometria: difficilioribus
annumerandam pronuntiat. Atque hinc in fpem venio -
Methodum fequentem, qua Curvse Geometrical cuju(>
cunque Ordinis, licet pundo. duplice aut multiplice.
quoyis deftitutae, conftruuntur, non fore Geometris in»
gratam.

I. Linese primi Ordinis ipfae funt Redae ; qtjae in ^
uno (bio pundo fibi mutuo occurrere pofl’unt. Lineae :
fecundi Ordinis funt Sediones Conicae,* quae in pluribus r
pundis quam duobus a reda quavis fecari non polTunc.

vero omnes lecundum Lemma zi. Lib. I. Princif^r
D,. Mevptoni fic ,conftrui pofFunt, Circa data duo punda

( P40 )

C & S moveantur AngtiH daci
MCR,LSN; icaucCrurum
CM S’ L concorfus femper
ducacur per red^am indefini-
cara poficione dacam A £; tunc
crurum aliorum CR & SN
concurfus in P defcribet Li-‘
neam (ecundi Ordinis (eu Se-
d^ionem Conicam.

IT. Moveatur ut prius Angulus MCR (v-Fig.z.)
circa datum punc^um C; Angulus vero datus L N
Temper percurrat Angulari fuo pundTo N redTam datam

A E, ita ut crusN QJem-
per tranfeat per datum
pundum S. I. Si con-
curfus crurum C R & S N,
turn pundum Q^ducatur
perr^am infiniram A B,
concurfus crurum CM
N L deicribet Curvam
lineam Tertii Ordinis
pundum duplex haben*
tern in C. z. Reliquis
manentibus, fi crurum
C M & N L concurfus
{vide Fig. I’) ducatur per
redam indefinicam A B:
S concurfus crurum G R
& SN in P defcribet
Curvam Tertii Ordinis
t^undum duplex habentem in S.

TH

( P4» )

B

£

Exemplum Cafus i. Sine
anguli M C R. L N S re6li,

(vide Fig, 4)&AE, DB, CS
parallelse ; fine quoque S A &

5 D normales relpedive in re-
<5las A E & DB;fitque SD =

2 8 A. Hifce pofids, fi SD fit
minor redla CS, Curvafecun-
dum regulam Cafus primi deicripta, erit Parabola No-
data cum Ovali, Speciei 6Zva Curvarum D. Meuteni;
Quod fi S D = C S, Ovalis evanefcic & nodus evadic
Cufpis, atqoe Curva deferipta erit Parabola Meiliam feu
femicubica ; Si vero fit S D major quam CS, erit Cur-
va Parabola pundata Campaniformis Speciei 6^na*

III. Moveantur Anguli da-,
ti R M T, K N L, ita ut pun-
da M & N percurrant redas
indefinitas B M, D N refpedi-
ve ; & crura R M, K N Temper ^
tranfeant per data punda C

6 S. Si primo Crurum M T
& NL concurfus Q^ducatur
per redam indefinitam AQ^;
tunc concurfus crurum M R -
& N R in P deferibet

lineam Quarri Or*
dinis punda duo du-
plicia habentem, alte-
rum in C alterum ^
vero in S. Sed fe-
cundo fi crurum MR
& N K (vide Fig. <S.)
concurfus ducacur ..
per redam indefini*

( 94» )

tarn A Q^; tunc concurfus crurum M T & NL defcri-
bet Lineam Quarti Ordinis pundto duplice caren-
tem.

. IV. Quod fi in primo cafu hujus Conftru(5tionis (v.
Tig, 5 .) redx C M R, S N K, una coincidant cum CS;
tunc pun<3a C & S evadunc fimplicia 6c Curva cm
Tertii Ordinis abique pund:o duplice. Exemplum. Sine

rete B M, A D N, fibi
mutuo parallels atque om-
nes perpendiculares in C S.
Sint quoque Anguli RMT,
K N L redi, & fi fecund um
regulam primi Cafus def«
cribatur Curva , Crura
CMR, SNK una coin-
cident cum C S ; & hac
conftrudionc deferibi poG
funt CutV2E D. Nevrtoni
10, II, xo.ai, 40, fecundum varias pofitiones pun-
dorum C & S refpedu trium redarum BM, A Q^,
DN, Omnes veto hae Species pundo duplice carent.

V. Lineae vero Quarti Ordinis quae pundum triplex
babent fic conftrui polfunt. Sint tres redae A Q, B N,
D M pofitione datae ; fine etiam Anguli Q. C T, SN M

& NML dati & invariabi-
les; percurrant punda N &
M redas B N & D M, ita
ut crus N femper tran-
feat per datum pundum
S: Revolvatur QjC T circa
C ita ut concurfus crurum
C K, S N percurrat tertiam
ledam A Q^; tunc concur-
■ . fus

{ P4? )

fus crurum C T, M L delcribet Lineam Quarti ordinis
pundum triplex habencem in C.

VI. Oflendi quo pado Lines Quarti Ordinis def-
cribi poflunr, qus pundum triplex babent auc duo
duplicia; Alis qus unicum habent pundum duplex
fic commode delcribuntur.

Sint tres reds ut prius po-
(itione dats, AQ, BN,

DM, dentur etiam Angu-
li SNK, SML, RCT;
fint punda N, M & S Tem-
per in eadem reda linea ;

Moveantur punda N & M
ut prius per redasB N, D M ;

Si concurfus crurum C R,

N K ducatur per redam indefinitam A Q_, tunc con-
curTus crurum C T, M L deicribet Lineam Quarti Ordinis
habentem pundum duplex unicum in C. Hs vero dus
ultims Propofitiones novas Methodus fuppedicanc lineas
Tertii Ordinis defcribendi, turn qus punda duplicia
habent, turn qus iis deftituuntur ; Es vero in brevi
hoc Methodus Noftrs fpecimine funt omktends.

VII. Maneant Anguli at-
que reds ut in Prop, III.

Concurfus vero nunc rec-
tarum MT, NK ducatur
per indefinitam redam AQji
& Concurfus crurum MR
& N L defcribec Lineam
Quinti Ordinis pundum

-quadruplex habentem in S.

•Habeo etiam alias Me-
thodus curvas defcribendi

Quinti Ordinis, qus pundum habent triplex, duplex,
aut duo duplicia, vel nulla nifi punda fimplicia ; fed
Ggggggg hsc

( 944 )

h^c (ufficiant ad rimplicitatem & univerfalitatem Me*<
thodus demondrandam. Nocandum vero in fpecialibus
fimplicioribus Angulorum & re<darum circumdanciis,
Lineam aliquando migrare in curvam ordinis inferioris
quam in Prop, explicacur ; Imo fingulx Propofitiooes
Mechodus dippedicant particulates, curvas aliquas or-
dinis cujufcunque inferioris defcribendi.

VIII. Propofitio Gemralis. Sumanrur ad libitum Reds
in eodem piano ubicunque pofitae, quarum fit numcrus
(»^ut BN, ER, FT. Sumantur eciam ad libitum
alias redas ut D M, GL, & H quarum fitnumerus

(/»). Sint Anguli CNR, NRT, atque,

anguli S M L, M L K, L K Q &C4 invariati, dum pun-
da angularia N, R, T, M, L, K, percurrant rcdas •
indefinitas BN, E-R, FT, DM, GL, HK; Ducatur
concurfus crurum XQ & K Q. per redam indefinitam
Invenire ordinem curvse quam concurfus cruris <
SM cum aliqua redarum C N, NR, RT,
cum R T, perpetuo tanget.

In Serie redarum CN, NR, RT, TQ deno^
tet i numerum redas R T, cujus concurfu cum S M
Curva ed delcribenda, a C N inclufive ; qui in hoc cadii
ed ternaiius: erit Curva ordinis quern exprimit nume*

rusv

( P45 )

rus w » -f- 1 : unde in cafu quern figura defig*

nar, cum j — w* — a? — 3 erit Curva ordinis 1 6'".

in his defcriptionibus RecSas folummodo atque An-
gulos dari poftulavimus; fed facilius fepe fimpliciorum
Curvarum ope complexiores defcribuntur ; atque Pro-
pofitiones his non minus Univerfales hue pertinences in»
veftigavi : Eas vero cum harum demonftrationibus uc-
pote prolixis impr^fentiarum omitto, Eafdem poftea-
publici juris faiturus, fi luce non videantur hxc Geo-
metris indignar

VI. ExtraSi of a Vetter of' the Reverend Mr. W illiam Rice,,
p/ Caerleon upn Usk, to Charles Williams Efqy
giving an account of an ancient Roman Infcription late*
ly found there. With fome Conjectures thereon^ hy the
Reverend Dr. John Harris, S. T, P. and R, S. S.

Sir,

APerfon laft Week being at Plow in a Clofe near
the Bank of the River Usk, which the Ancients
called Jfca, (which glides by us about a quarter of a
Mile off, and in fight of this Town^ came thwart a
Stone, and finding Letters thereon, took it up whole ;
*tis about a Yard in length, and about three Quar-
ters broad I went to the place, and took a true
Copy thereof, which 1 here make bold to fend you. ^
There was underneath it fome feeming Oblong Square
Sepulcher of Stones, rude in order. A little further
in that Glofe, where that River wears out the Land,
there was, fome time before, a large Earthen Pot taken
out of the Bank by the River- fide, which had therein
the Scull and Bones of fome Perfon, by fome thought
to ber%kCbild , Murther’d j But I rather conjecture it a 4
Roman iJrn.

Caerleon, March 21. . four humUe Servant ,

J 717. William Rice.

D...-

D M I

G. VALERI VS. G.F f
GALERIA. VICTOR *

LVGDVNI . SIG LEG . II AVG
STIP.XVII.ANNORXLV GV

R A. AG I NT. AMNIO. PER PIT VO. B

Sir,

This ancient and fair Infcription confirms what others i
have found hereabouts 5 and what Camhden and other
Hiflorians flievv us, viz. That the fecond RomAn Legion t
called Au^ujia^ brought into Britain by Claudius C^far un- ^
o'er the Co^du(^i of yefpafian, was placed here at Ifca
or Caer Legion, by Julius Frontinus, in order to awe the /
Silures\ And that General obtained feveral Vidories over
them and their Neighbours in feveral places hereabouts.

There feems to be nothing of Moment or of difficulty
in this Infcription ; but Vi^or Lugduni : Which as I think,
we have no ground from Hiftory to refer to Lyons in
France, lb 1 guefs that ExprelTion may be thus accounted
for. The River lugg is famous in the Neighbouring
Parts ; and as Dynas or D^n hath been faid to fignifie a
Town in the Ancient Britijl) Language ; and that Dun
doth alfo ferve to exprefs a Hill or Dorvn as we ftill call
it ; {'which 1 think is derived from the Britijls allb) proba-
bly Lugduni here may exprefs fome Town or Hid near the
River Lugg ; and fincc there is a Place called to this Day <
Luckten, on the fide of ihtRAWttLuggm HerefordP)ire^
perhaps that may bid fair to be the very place wh^e Fa~ f
ierius obtained the Vidtory perpetuated by this Tnfcnption.

FINIS.

M

( P47 ) Numb. 3 (Jo.'

PHILOSOPHICAL

TRANSACTIONS,

For the Months of March^ Jpril and May 17 ip#

The CONTENTS.

I. Maximis & Minimis qu£ in motihus Corpo^
y rum Ccelefiium occurrunt.

II. Apologia D. Brook Taylor, n D. R,S, Soc^ con-
tra y, C. J. Bornoullium Math. Prof. Bafilise.

III. An Account of the Imprejfion of the almofi Entire
Scelcton of a large Animal in a verj hard Stone ^ late*
ly prefented the Royal Society, from Nottinghamfliire.
By Dr. William Stukely, M* D. and R. S. Soc,

IV. A curious Defeription of the Strata olfervd in the
Coal* Mines of Mendip in Somerfetfliire ; being a Let*
ter of John Strachey Efqh to Dr. Robert Welftcd, M.D,
and R. S. Soc. and communicated hy him to the Society*

y. Some Inftances of the verj great and fpeedy Vegeta*
tion of TURNIPS. Communicated hy the Rev,
Dr, J. Theoph. Defaguliers, R. S. $•
yi. An Account of fome Experiments tried with Monf,
VilletteV Burning Concave, in June 1718. By the
Rev. Dr, J, Harris, and Dr. J.T. Defaguliers, Reg. Soc. SS.
yil. An Account of the Extraordinary METEOR feen
all over England, on the i^th of March 171^. ^ith
\ a Demonf ration of the uncommon Height thereof. By
£dm. Halley, LL,D. and Secretary to the Royal Society.

7 H ' 1. DC

( >

I. De Maximis Minimis in motihus Cor*
forum Calefiium occmrmit.

NTE Keplerum Aflronomi aniverfi, per tot re-

tro fecula, rianetarutn motum circularem non

aufi funt in dubium^ocare, ex prceconcepr^, ut
videtur, in figura Circuli nefcio qua perfcdionis Ide3.
Keplero autem Inventori debetur ea qua nunc utimur
Theoria, nempe quod Corpora cceleftia Solem ambiunt
incommuni orbium Ellipticorum Foco fitum, ea lege uc
Arese Temporibus proportionales radiis ad Solem du-
.^iis defcribantur. Sublimiorem vero poftulat Geome-
tfiam, ad ollendendum quam ob caufam hoc ica fe ha-
beat, quodque aliter efle non poflTit. Hoc in fempiter-
nam celeberrirai D. Nevotoni Prscfidis noftri gloriam re-
fervatum eft.

Hujus veftigiis infiftens, CoroIIaria quasdam exhi-
buit eximius Mathematicus'D. Ahr. de Moivre R. S. S.
in PhiUf.Tranfa^, N° edita; Thcoremata fcil pa-
rata, quibus determinantur Velocitatcs five Momenta
Motus tarn veri quam apparentis circa Solem, ficut e-
tiam accefsus vel recefsus a Sole, in dato quovis datq-
;um Orbium pun(fto. Deinde ut I'heoriam lyftematis
Pla'netici pehitius excoleret, ope eorundem Theorema-
tum, duftorum Momentorum Momenta perfcruiatus eft,
ofteqdirque quibus in orbium puneftis fiant Mdx'mA
harum Velocitatum mUtat^nes, idque Soludoriibus
.ci|tcWe,&!c6ncinnitate.pr^ ^

'Si^ AdP Orbis Pldfiftce ElhptfCuSj AP Axis Tranf^
yerrus,' C B Jemiaxis ccbjuga'tu^,"; S Sol^ Q_ Focus alter

. V I y y/ V 1 i-i I'd jvio w V* I j ^ ^ ^ ® ^ ^ ^ ^ j a w V i4 ^ oaa V *

ElJi|>reos. Per S dUcacuF S'M ^pfi C B p^r^llela : &
;^n^ pan«ftura M iA 4^p tftm-

( 95‘i )

fcit veldecrefcrc didanda a Sole, & S M±=:AC^~

. AC®

oi vero capiatur SL media proportionalis inter S®-
miaxes AC, CB, erit pundlum L in quo Maxima fie. so
quatio Centri, uc vocanc ; five ubi motus anguiaris fit
xqualis medio Motui : Quod fi Eccentricitas non ma*>
jor fit quam in plerifque Planet is. BL—BM quam
proxime ; • Eft vero S L=\/v^ A C"— A C*S C% '

Si quxratur pundum N, in quo fit Maxima mutacio
Velocitaris motus realis in Curva, Problema Solidum
eft. Eft enim ^ N S=:4 A C — z N ad ^ N Qj— A C
uc AC^ — CS^zrzCB^ ad NQ^; adeoque ft, ponatur
AO— a, CB— &NQp=y, habebitur squatio — .
ia'j’j~\-\cq—\acc—o. Qua refoluta eric y five NQ,
diftantia pundi quaefiti N ab alcero Ellipfeos foco. In
Orbibus autem parum Eccentricis, quales funt Planeca-
rum, fi fiat CD^rSQ,, & jundas AD sequalis ponatur
A K, eric reliqua pars Axis K P— N S diftanticC pundi N
a Sole quamproxime. Si veto Orbis fuerit Parabo’ica
eric SN ad SP uc 5 ad 4, angulufque NSP eric
53®. 8' fere, cujus Sinus eft \ Radii.

At Pundum O, in quo motus apparentis five angu-
iaris acceleratio Planecas defcendencis, vei rerardatio

* afeenden*

( P54 )

afcendentis Maximifii, hoc modo ohtinebicur. In AC
capiatur CGr=?AC, ac fiat angulus CSF 30 du-
dicque SF squalis ponatur CE, ipfique GE fit GH
aequalis. Dico, fi diftantia SO fiat sequalis ipfi P
quod in pundo O proveniet Maxima muratio motus an-
gularis Planetas in Orbe Elliptico A BOP gyrancis;
eo fcilicet in Orbis loco fecundx ditferencise scquatio-
num centri Planctae repericntur Maxima, Eft autem
S 0=rr A C— Vi A S Q*« Quod fi Orbis Parabo-

lica fuerit. ut in Cona^cts, fiet SO ad SP ut 8 ad 7,
angulufque OSP fiet 41°. 2,4'r, five cujus Sinus fit
ad Radium ut ^ V7 ad i.

Denique Minima cum Veiocitate mutatur diredio
Tangentis Orbits in pundo R, fi fiat SR xqualis dua-
bus tertiis Axis majoris A B. Quod fi Eccentricitas SC
minor fuerit quam fPC, Minimum hoc non locum ha-
bet, led decrefck fempet hsec Velocitas quacum revol- *
vftur Tangens, ufque m ipfum Aphelion , quemadmo*
duni leies hahet in omnium Planetarummotibusi Ne-
que eciam in orbe Parabolko obtinet, ob Axem e)us
in infinitum protenlum.

Haec omnia demonftrantur, juxta praecepta Dodri-
nse de Maximis & Minimis^ ex Theorematis prjedidis
in N° 35X exhibitis, quas quidem hac oc^fione revi-
fere Ledorem rariolum non pi^ebit.

IL JfologU

( 955 )

II. Jpologta T>, Brook Taylor, J V T>. 8c %S.Soc.
contra C J. BernouUium, Math. frof. Bafilea:.

[uam odiofas contehtioties obi-

ic uitiitciiuu. verum cum patientia noftra pro
ignavia habetur, filentium pro confefljone criminis, 8c
nuperam calumniam jam nova fequicur concumelia, om-
nino refpondendum eft, ne npbis ipfis deefte videa-
mur. In Epifiola pro emin:me Mathemattco D. J Berno-
ullio, A(fris Lipfienfibus An. iyi6- inferta, plagii reus
ftftor fequentibus verbis : “ Hoc nihil novi eft in qui-
“ bufdam Anglis, qui fibi folis licere putant, aliorum
‘‘ inventa tanquam fua impune afurpare; quando ipfi Ho-
minefque Deofque invocant, ubi vident, vel laltem
** videre arbitranrur, Excraneos in fixorum Inventa ma-
nus inferre. Exempla funt quorundam, uc Chey-
** nxi, Des Hayes, Taylori, aliorumque, qur pa(Jtm in-
“ ventis Bernoullti funt ufi alienifque, vel nulla prorfus
fa8l a mentione Autoris, vel — Palam eft abipfo Ber-
noullio promanafte hanc accufationem. Nam in Acftis
Lipfienfibus An- 1718. ‘ per filium fuum fatctur le res
ipfas tn ilia epiflola contentas quoad maximam partem ami-
CO alicni perfcripfiffe. Invidiam equidem praediift^ ca-
lumnia! a fe amovere follidte ftudet, atque transferre
in vicarium ilium fuum, cum ipfe profitetur, Je non ap-
frohare qu£ in alios durius di^ta cenferi pojfunt \ Sed
admodum imperfecfta eft hxc purgatio. Nam calum-
ni£E funt qure durius dida vocat. Ait le di^a ilia non
approbare : Sed improbafte necefte fuit. Teftimonium

1 Pag. i6i.

ftudiofb fatius eftet injurias

I i i i i i i

i Pag. 262.

denique

( 95^ )

denique eft pro fe teftantis : Autorem ilium anonymutn
citafle opoctebat, ux cum ipfo agere liceret.* Sed is ad-
huc laticac. Quam vere autem & ex animo fe durius
S^a. non approhare yid&zzwTt couftace quodammodo po-
teft ex fequentibus, qux de me ipfe proferr, proprio
fuo nomine, nulla ulus peribna ; “ Taylorus Geomerra
“ inftgnis & acutus, qui ad profundiora mftra felicicer
penerravic, tefte ipfius libro de Methodo incremen-
“ torum, probe fenciens impeditam nimis Analyfeos
“ fraterniE prolixitatem, eamque in compendium contra-
“ here, ac limul generaliorem nonnibiL reddere volens^
tancam. rei affudic obfcuriratem ( qua in aliis quoque
“ brevicatem afiecftans impense deletftari videcur) uc du*
bitem quenquam fore etiam inter perfpicaciores, qui
“ ubique & hie imprimis mentem viri affequatur, imo
etiamfi aliunde rem cognitam habeat. tJr jam nihil
dicam de ipfo calculo, pro more- ejus, concifo qui-
“ dem & contrado, fatis tamen adhuc longo & intri-
*'* cato, ft quis fingula ejus capita minutim perfequr
** velir ; praeterquam quod cum Fratre meo ad certias
“ quoque fluxiones excurrat ” ^ ' Sit fane liber rile
meus nonnihil obfeurus : Difficile eft in re fere nova,
& ab ufu communi aliquantulum remota, non efie ob-
feurum, Sed maxime obfeurum oportet efle librum, in
quern ilia omnia vere dicantur- Et ft vere dicantur,
tamen fine ullS. omnino causa talia dixifte, ab inge-
nuis moribus prorfus alienum eft, & mera contumelia.

Sed audio Bernoullium de exordio conquerentem quo
nuper ufiis fum, in folutione problematis Leibniciani in
Tranladionibus Philofophicis editi. Stylum acriorem
reprehendit quam virum bene moratum deceat, item
iilmium contcraptum Extraneorum. Quse liberius ef-
fttus fum, h£EC funt : Si nondum viderint [ fautores

3 Aa. Leipf. An. M. Jan. p.-iS-

Leibnitii \

( 957 )

Leibnicii ] quomodo ex ilia ’’ [ ex anteriori nempe fe*
lutione general!] ^equationes fine deducendiE, id pro*
“ fe£to illorum imperitice tribuendum eric ” Hxc
fateor paulo durius fonant ; fed fi ad caulam attendas
conturaelia vacant. Faurores Leibnicii ( non omnes in-
telligo, fed Bernoullium tantum, & Socios ejus anony-
mos nobis infenibs, ^ univerfos Anglos indigne trada-
runt. Solutionem illam generalem cum non intcllige-
rent, derifui habebant : In injuriofos & deiifores me
liberius explicui; contumelia non eft. Sed ubi ille
contemptus Extraneorum ? Neminem ego nominatim
citavi: De Faucoribus Leibnicii fum fo)um locutus. Sed
abfic ut omnes defignatione ilia omnino intelligerem
quocunque modo caufe Leibnicii favences ; canquam
ipfe caufe Neuconianse eftem tarn percinacicer addidus,
ut alios omnes odio habeam. Sed concroverfia ifta
Neutonum inter & Leibnitium nihil ad me. Solos in-
tellexi Faucores illos qui in Anglos eftenc infenfi, qui
me nominatim calumnia provocarunt j Bernoullium ice-
rum dico quem Frincipem agnovi caufx iftius, foci-
ofque ejus anonymos vel veros vel fidos. H^ec a-
percius dico, ne alii de noftra in alios contumelia im-
merico querantur. In immerentes injuria eftet, in Ber-
noullium non eft. Sed ad fuperiora ilia redeo.

Plagii accu(br,tanquam inventa Bernoullii, aliorum, u-
furpaflem ut mea. Exempla proferat, dabitur refponfum.
Plura fane tradavi cum aliis communia; fed inventis
alienis fum minime ufus ut meis. Propria ubique fum
ufus Analyfi, ( fi Ifoperimetrum excipias, de quo po-
ftca dicetur ; ) ut nullo modo dici poftic me alios frau.
dafte. At Autores nominafle oportebac, unde artem
hauferam. Tanta me quidem tenet reverent ia illu
ftrium nominum, Hugenii, Hofpicalii, Varignonii, Leib

A Tnnf. Phi). N° 354.

I i i i i i i z nitii.

C )

nitii, aliorum, ut nerciam an ex hac parte non p€cca->
verim, cum mihi ipfi deelTe videar, cui tamos viros
citafle (emper fuiflec ornamento. Nimia fortafle igna-
via erat, quod de rebus cum eflem maxime follicicus,
hiftorias rerum penicus neglexerim. Sperabam tamen
me in tantse fraudis fulpicionem incidere non potuifle,
cum illuftriflTima tantorum virorum opera earn faci!c
detegerent. cum Bernoullio communiter trada*

vi problemata, funt, de Funicularia, de Centro Ofcil-
lationis, & de Ifoperimetris. In duobus primis fum
propria omnino ufus anal)Ti; in Ifoperimetro ufus fum
analyfi Autoris Jacobi Bernoullii, Viri k rebus Mathe-
maticis optimc meriti, cui debitos nunc perfolvo ho-
norcs. Solutio noftra problematis de Centro Ofcilla-
tionis, cum amicis meis communicata eft ufque ab ini-
tio Anni 1712. ut teftes pofliim citare epiftolas auto-
graphas Keillii noftri; Liber item nofter erat penes So-
cietatem Regiam, & cum omnibus fere noftris Mathe-
maticis communicatus, ulque a menfe Aprilis Anni 1 7 14.
quod hie monicu neceflarium duxi, ne Solurionem
iilam fibi vindicec Bernoullius ; cujus Solutiones ^ dux
extant eodem Anno editx ; quarura pofterior cum no-
ftra, quoad principia, tarn mire conftntit, ut jurares
ab eodem homine efle ucrafque inventas. Materia de
Ifoperimetris excogirata primum eft a Jacobo Berno-
ullib, ficiit jam innuimus. tjus extac Solutio cum Ana-
lyfi, in Adtis Lipfienfibus Anni 1701. Extat Analy*
fis fratris in Conimentariis Regix Scientiarum Acade-
mix Anni 1706. Extat & Solutio in Lihro noftro.
De eadem materia Commentarium nuper edidir Ber-
noullius in Atftis Lipfienfibus Anni 1718, proxitni

5 Altera m Aft. Lipf. M.Jun. In Comm. Reg. Sc Acad. MAugjkeia.
^ P. 16. & Has igitur afiafque ob rationes, aftum a'gere miaime vi-
debor, «c. p. iS, '

Ibi,

( 959 )

Ihi, tje aiSum agere videatur, non meis folummodo,
\^rum edam fraternis folucionibus malevolus derrahere
aggrediturj fratri prolixitatem \ mibi obiiuritatem ^
objiciens. De novis iliis inceptis nihii non magnum ^
poIHcecur ; & ofe cujufdam princif^iiy ah miformitatis le-
ge, qu^nt nems hucttfque ohfervavlt, pet it i, rem totam
pene fine calculo, nullo labore abfolvet. Sed nefcio
quo faco fit, ut in hac materia de Ifoperimctris, 6er-
noullius Deos omnes Temper offendac iratos, Nam pri»
mo, prifiina ilia Analyfis ejus a capite ad calcem quafi
imum aliquod vicium maximum conftituic : Secundo,
quod tamum jacliicat Principium, a lege uniformitatis,
quam nemo hucufque obfervavic ( fic enim ftrenuus af-
firmac) peticum, a me olim obfervacum eft: Denique
quam hie tanquam novam cxhibec Analyfin, cota me-
ra fraterna eft. Analyfin enim conftituunc Prsccepta,
juxta quas deinde inftituitur calculus; qui non Analy-

7, Nullos hie ofFendet 'LtSlor jeopuks, quos^bjicit operofa Fratris anaiy-
fis-, atque difFtfrentiarum tertiarum tncas ac fpinas, quibus undique oi/Jip-
ibi fentit viam, in noftra methodo nullas percipier.— — Nec fratris
calculi prolixitatemi nec Taylori obfeuritarem aeque ingiatam ac moleftam

fibi metuendam habeat, />. 18 quam Frarer per operop.JJim^m fuam analy-

fiu eliciii% p- 23.— —non tanrum ea, quae a fratre meo quondam propo-
fita magna pempa, nec minor i cmatu & l»bore foluca fuere, ego ex fola lege
Uniformita is folvi citra calculum analyticum, &c.

S Fide Not. prated- item ejua ex p. 18. j/tm funt deferipta.

9 -publictim ei gratinm h»bitu'f»'7i, quod occafio mi“

hi extucrir, taiia nunc divulgandi, quae forte cum mulris aliis in fehedis
m«is psrpetuo manfiflent fepulta, quamvis recondita Geomciria fines non pa-
rum prolatura, p i7. quod ibi ex incuria prrerervifum reparabo hie «eie
folvndi modo„ qui fingulari facilirare expedic problemaC', non tantum omnia
qUE de-Ifo-pctimetris propolUcrat Frater, fed & innumera alia iliis affinia,

tb. ope cujufdam principii ab unifor nitatis lege, qua7n nemo hucuf/jne eb-

fervavif, penri, ex ibU Figurae inTpsttiore, ac line ullo pene calculo lequa*
tfones pro cufvis quailitis fponce veluc fe off:rentes I'.arim eliciam , &c. uc
in Not, 7. aftum agere minime videbor, fi in hoc arguinenro per fe difficili
viam monftfsm & rationem brevem, platiam, elaram, & facilem, qua qui(-
que medio. ri quoque inge- io prtedicus ad veritates I'las ablfiuliores ( non
^dealiorum, fed) propriis oculis fpe£tandas per venue poUitj ita nempe,
uc, &c, ut in Not. 7.

( )

fis eft, (ed inftrumentum Analyfeos. Praeceptis ftmel
pofitis, quivis facile calculum inftituit, more quifque
fuo, hie prolixius, ille magis concinne, prout unicui-
que faveric Minerva. Negandum non eft, Bernoul-
lium calculum tandem concinnafl’e, & reddidifte clegan-
tiorem 5 (ed tamen in Analyfi fraterna fecit, non liia :
Nec dubicandum quin frarer, adhuc ft vixiftet, rem red-
didiftet non minus illuftrem Analyftn diximus in prae-
ceptis contineri ; praecepra verb lunt omnia fraterna.
Nam quod curvac quasfttx arculum minimum, tanquam
ex tribus lineolis elcmentaribus compoftcum contempla-
tur, vel ipfb fatentc a fratre eft ; quod ex data Ion-
gitudine arculi iftius minimi quxrit rationem differen*
tiarum Ordinatarum in Lemmatis fuis, a fratre eft :
quod rationem eandem denuo quaerit, faciendo ut fit
areola nafeens, ex FuniHonibus ( ut vocat ) compoft-
ta, vel maxima vel minima, a fratre eft : quod deni-
que ex duplici ilia expreftione ejufdem iftius rationis
arquationem colligit qua curvae quaefitae natura definia-
tur, a fratre eft. S'ed hxc Solutionem conftituunt. Er-
go vSolurio mera fraterna eft. Dixi me olim ufum efie
Principio illo, quod tanta cum oftentatione ftbi arro-
gat Bernoullius *. Ex eadem una pagina, en duo exem-

w m

pla. In pagina 113, Libri mci haec funt — =^..Sed

m *

“ eft — novus valor ipftus unde eft ^ quantitas
“ data Luce clarius eft me hoc loci ex obfervata

lo Ltar pro hoc, ut ipfe fecit in fua Analyfi, contemplatione arculi
minimi, &c. ?• iS.

uniformi-

f p6i )

tn

uniformitate inter formulas, — , — , conclufifle quod

A. ‘A

t

fit ^ quantitas data. Idem feci in fequentibus. ‘‘Pone

V

mn m^n m nn

hoc eft &c ubi ut unifor-

^ >

m nn mn n
// y /

micas appareret inter formulas -y, scquationem

transformavi' Videtis, credo, quam feliciter penetra-
verim ad profundiora Bernoullii. x\n hrec obfcura dicet ?

Ad primam jam pattern promifti pervenio, uc o-
ftendam priftinam illam Analyfin Bernoullii efle omni-
no corruptiftimam.- Primo per fubftiturionem fatis rir-
diculam, ex profundiorihus juts nefcio quibus petitam,
sequationem FJ \ A BO=(pco x Apw transformat in hanc
FO X F—(pu) X i quod in cafu particulari ( nem-
pe quando funcftiones Tunc ut quadrata ordinatarum )
hue redir, ut Tint fimul /^O x A 0— Xfw & FOx
P F-(poaX'n-(p h unde confit P F : RO :: 7r(p : pea Sed
hoc impoftibile eft, quoniam eft vel P F-i Pk0~^p(>}-
’^7T(p, vel P Fc-ROzrpatC-^tp'^ quorum neutrum cum
analogia expofita conciliar! poteft. Nam ft P F~:^R0
-ypca^it<p, pet Analogiam etiam erit ’jr(p~:^pM ( propter
p F~:^R O ) contra hypotheftn *, vel ft P FcrR 0 Cpuc-rrf,
per Analogiam etiam eric Trtp tTfw, contra hypotheftn-
Secundo parum feienter ftngit curvaturam in F c{Tq ad
curvaturam in <p ftcuc eft 9O ad FO ; cum nihil in hac
tota Analyft fit q^jcd privilegium illud vindicec pundo
0 potius, quam alio cuilibec pundo w in arculO'mini=»
mo FOoxp ubivis fumpto. Nee /ane Curvedo tarn ri-
dicule

( )

dicule vuk sefiimari. Tertio nimis imperite facie

mn~d^x^ nl—ddy, & cum (\m mn=.\ddxi

d^Jdy

jjlz=z'-ddy, & nd — ^' Denique quod omnium pef-

fimum eft, vitiofiftimis hifee principiis perfecftiftimam
alligavic condufionem. in probkmate primo dico ;
nam in feco eft talium parenrum magis digna pro-
les- Errorti bernouiln \eteres & exclcios me expo-
fuifte pucacis. Non ita eft; ip(e cnim hic habec J
“ Omnid dudum j j/opla accurtue rurfus extutiendo A-d fe-
“ ve/i' exAm'inis ttutinam revocjvi ‘‘ Notandum au-
tern Solucionon piwi problematis in fehediaf^mate
‘‘ meo Commentariis Acad./>.x;5 inleito. rc^ijfioefe
habere ” Errores ergo fuos jam denuo adopta-
vic. Unde fortafte nunc qucrrec aliquis. Quo jure hie
primas fibi in fublimiori ilia Analyft ram obftinata am-
birione arroget ? Uc nemo fit qui in ilia aliquid profe-
ceric. quin continuo acculetur ad frofundiora Bernoullii
per/etf'rffe Unde conftec verum efte, quod quidam
nuper afErmavic, regulas extantes in libro de Analyft
infinite parvarum a Bernoullio emanafte Quod lau-
des Excellentiflimi Marchionis Holpitalii ftnt fuo Pr^-
ceptori cribuendae ? An hie fit idoneus qui alios do-
cuerit regulas differentiandi differentias ? Cum multis
aliis qu.T ftgillatim enumerare non eft opus. Sed iftis
refpondeat qui volet : nos in hifee diutius non moramur.

II Pag l6. 12 Pag I7» 13 Pag. 18. vid^ ttiam €p. pro Em»

Math. ^ feripta ipfins BirnoHlhi p»Jj[im,

14 Concedit Dn. Mafchionem de I’Hopital cakulum iftum intellexiflej
nec ignoiat, il!uftri(fimum hunc virum eundem a Cel. Bernoullio didicifTe:
trque n.inime ipfom fugit, regulas in di&o libro [ de ^nmlyfi infintte peerva^
rum ] extantes a Cl- Bernoullio ptomanafle- aB. Lipf An. 1718. p. 4^4-

15 Dum irrerea conjici poteft, ilium enm Dn, Newtono ab initio in
ifto eirore baelifle, donee tandem liberati fuillent ufu calculi differcntialis, ^
regulas differentiandi different ias d Cel. Bernoullio edeUi ejfeut. ib. p. 465*

*

Res

'( 9^1 )

Res ipfas expofui. peroratione non utor • fiarum e-
nim tceder. Nec fi quidquam regellerit Bernouliius,
ukerius refpondere neceflo habebo. A contumeliis nos
femel vindicate & jus & ratio poftulat ; ulterius non
expedic.

III. An Account of the ImpreJJion of the almofl En-
tire Sceleton of a Urge Animal in a Very hard
Stoney lately prefented the Royal Society, fro7u
Nottinghamfliire. By Dr, William Scukely,
M D. and R. S. Soc.

Having an Account from my Friend, Rohert
Darwin^ E(q; of Lincoln’s-Itm, a Perfon of
Curiofity, of an human Sceleton ( as it was
then thought ) imprefs’d in Stone found lately at the
Rev. Mr. John South's^ Re(3or of Elfton near Nejvarkt
Nottinghamjhire, I was defirous of a Delcription of it,
for the Entertainment of the R o y a l Society, and
have at length procured the Stone it (elf for their Re-
pofitory, where fuch remarkable Appearances are befl:
preferv d, and delervedly valued. It cannot but be mat-
ter of Regret, that fo confiderablc a Rarity, the like
whereof has not been obferv’d before in this llland fco
my knowledge ) (hould be maim’d and imperfedi, yet
we may content our (elves if enough be (lill vifible to
favour a Conjedure of what it has been. The Stone
it felf is a blue Clay Stone, the fame as ( and un-
doubtedly came from ) the neighbouring Quarries of
Fulheckf or thereabouts, upon the Weftern Cliff of the
long Trad of Hills extending quite through the ad-
jacent County of Lincoln, k lay, time out of mind,

Kkkkkkk ac

at the Tide of a Well near the aforefaid Mr. Scuta's
Farfonage- Houle, where it had ferv’d for a Landing*
place to chofe that drew Water ; but upon removal,
the Under fide exhibited this unufual Form, and was
accordingly taken notice of by that worthy Gentleman,
and laid up in his Garden for Curiofity-lake Where
the remaining part of the Stone, which contain’d the
Upper-part and Continuation of the Sceletoft, or that
which was the other fide, and tally’d with it, may be,
is now utterly unknown : but upon view, I am per-
fuaded, it cannot be reckon’d Human, - but Teems to
be a Crocodile or Forpoife. There arc Sixteen rerte-
ht‘£ of the Back and Loyns very plain and diftind:,
with their Procefles and intermediate Cartilages, Nine
whole or partial Ribs of the Left-Tide, the Os Sacrum^
JUum in Jitu, and two Thigh-Bones difplac’d a little,
the Beginnings of the Tibia and Fibula of the Right-
Leg ; on one Corner there feem to be the yefli^ia of
a Foot with four of the five Toes, and a little way
off an entire Tod> now left perfed in the Stone: there
are no lefs than Eleven Joints of the Tail, and the
Cartilages between them of a White Colour diftin-
guifhable from the reft We fhould impofe upon our
Senles, to quefiion, whether thefe be the real Reliques
of an Animal ; for the very Bones themfclves are now
to be feen as plainly, as if prelerv’d in an Egyptian
Mu,mmy ; a .very little while ago, the Society had a
Draught of a Crocodile, tho’ a fmall one, found af-
ter the like manner inclos’d in Scone, from a Quarry
in the Mountains of upper Germanj. I fuppofe the fame
Reafbn accounts for both and all the reft of thefe
kind of Fofiils, and 1 pleafe my felf in an ocular E*
vidcnce, and fb great a Confirmation of what f had
the Honour to prefenc to the lio^al Society, in a late
Difeoutfe, where I hinted ac_a Solution of fome ob-
vious

( 9<55 5

vious and remarkable Pbxtiomena, in the externa! Face
cf the Globe, confequenc to its Formation, as fee forth
in the Mo fuc Account; and of fome Changes it fuf-
fer’d at the univerfal Catacljfm, and Proofs of chat
great Cata/irepbe of the animal and vegetable World in
Plants, Shells, and Parts of living Creatures found in
Rocks and Qiiarries.

Its remarkable, that all the Stone Pits about the
Country whence this came, abound with prodigious
Quantities of Shells, and the like, and the greaceO:
part of the Subfiance of the Scone is a Compofition
of them. There are many Account'' of them in the
Tranfa^ions, and this Stone has many Shells of dif-
ferent kinds in it. S'r Hans Sloan has a Fidi-Sceleton,
amongfl his immenfe Treafure of Curiofities, found
near this Place, given by the Duke of Rutl-n-^ If
we look upon a Map of the Coun.ry, and obferve
the Lincolnfhire Alfos which 1 fpoke of before, how
they run 50 Miles North and ^outh, and on the Well
fide are fleep and rocky, we may fee the Reafdn why
thefe Quarries (liould be fo fluft with them ; for it
is juft to conceive, that upon retiring of the^ Waters
of the Deluge from the Superficies of this Country,
into the Eaftern Seas, tliele heavy Bodies met a full
flop, and were intercepted by thisCiifF, which has re-
tain’d fuch vaft Quantities of them ever fince: whflft
thofe which fell upon common Mold are moftiy rotten,
and now loft.

Sir I^aac t^evoton^ DocSlrine of the Attraction of tne
Particles of Matter, according to the Quantity of its
Solidity, Proximity, and Surface, efpecially that it is irs-
finitely greater in the point of Contaft, upon which
depends its Cohefioii and all- the Varieties of Phyficat
Adiod, will eafily direct us to a Notion of PetrifJ
(tion. We karn how a proper Degree o-f Heat or Cold,
Kkkkkkk 2, Moifturs,

( )

Moidurc, Motion, Reft; and Time, promote tlii? Prin-
ciple, from the common Experiments of Chryftalliza-
tion and Freezing even before the Fire, and in many
Chymical Mixtures. Whence we cannot be ignorant
of tone growing in the Quarries gradually, not by
any fancied Vegetation, tho’ there is fomething like it
in Corals, but generally by Appofition of Farts to
Parts, as is notorious in the Fluors of fubterraneous
Grotts and Caverns. So that we have no reafon to
doubt but what was Clay, Sand, or Earth 5000 Years
ago, may now be Stone or Marble, according to the
Proportion of Concurrence of fuch mentioned Caufes.
This will perfuade us that the now barren and rocky
Plains of the Countries of Syri/t, India, and Arabia,
are owing to Natural Caufes, as well as an immediate
Curfe of God for the Difobedience of irs ancient Pof*
feflbrs his peculiar People, becaufe the fame is obfer-
vable of the famous Countries of Gretce and Africa,
warm Regions fo renowned for Fertility in antient Au-
thors. Wherefore there may be fome likely hood in
the Opinion of thofe who think that in many Ages the
whole Face of the Globe may become one great Rock.
Dr. Plott, in his Natural Hiflory of Oxfordfldre, gives
an Account of a Tumulus, now a perfedl Mount of Stone:
and upon St. VincenPs Rock near Briftol are Fortifica-
tions now become Folid Cliff I remember, about fix
Years ago, Vix.. Ralph Widdrington, Brother to the Earl
of that Name, Ihew’d me many human Bones taken
from whole Sceletons, with Brittifh Beads, Chains, I-
ron Rings, Brafs Bitts of Bridles, and the like, which
were dug up in a Quarry, near the Seat of the Fami-
ly, at Blanknej, Lincolnfhire ; which very probably was
plain Mold when thefe old Corpfes of the Britons
were interr d ; and fince then I faw many human Bones
and Armour, with Roman Coins, Fibula^ dre, found in

a Stone-

( 9^7 )

a Srone pit in the Park at Norfolk ; belongs

ing to Sir Nicolas V Eflrange, in whofe Ciiflody they
no'.v arc, which were conjediircd to have been buried
in Earth after a Battle- From whence we may judge
it a vulgar Miflake- when in the Ruins of old CaBles
and Walls, wc admire theTenacity of the Mortar, and
arc apt to praife our Ancefiiors, .for an Art which we
fuppofe now loft; when doubtlefs the otrength of the
Cement isowing to the Length of Time : and in future
Ages our Modern Buildings may obtain the fame Judg-
ment.

From all which IniJances, I only defire to infer the
antient Bate of thefe ClifTs, where thisSceleton was, and
Shells are daily found, intimately mixt in the Subfiance
of the Stone, to have^been formerly of a fofter Con-
fiflence, capable of admitting them into its Bowels, and
to have immur’d them as part of it felf; and that Earth
which is now manageable by the Plough, may pofTibly
in time afTume the fame Denfity, at lead: very little
below!' the Surface ; for in this very Cliff the upper
Strata are yet Clay, growing harder as deeper. VVhac
Creature this has been, for w^ant of a Natural Hiflory
of Sceletons, W’dl worthy the Endeavours of this So-
ciety, we cannot pofitively determine; but generally
find the like to be amphibious or marine Animals.
Why fuch rather than many others, fliould chance to
be thus entomb’d, may be thought, becaufe they Were
able much longer than Terreflrial Animals to live in
that World of Waters, even till they began to abate
and fall away into their deflin’d Receptacles; fo that
while the Bodies of the reflToon perifhing, were cor-
rupted, and their Bones feparated and difpers’d much
earlier; thisSceleton, with others of its like, fell entire
into the Fiflures of this Bed of Clay, which has fince
turn’d into Stone, and made this noble Monument and

■ pregnanE

( 9^8 )

pregnane Teken of that general rmiudation, durable
as the vain glorious Monarchs I'yramids ar

Mmpkis; to be perpetuated in the lading Records of
this Society. See the Figure of this ImprejUion, in Tab, T,

IV. J curious De/crlftion of the Strata ohferVd
in the Coal-Mines of Mendip in Somerfet-
(hire, being n Letter o/John Scrachey Efq-^ to
Dr, Robert Welded, M.D. and R. S. Soc. and
by him communicated to the Society,

I Now fend you the Obfervations which f fome-
time fince promifed you, relating to the different
ttrata of Earths and Minerals found principally in
the Coal-Mines in my Neighbourhood. For the bet-
ter Illudration whereof, 1 have inclofed a Draught,
wdiich you mull fuppofe the Setdion of a Coal-Coun-
try, and to take in about Four Mile from the North-
Wed ro Soutl>Ead, and may be applied to the Veins
of Coal as they lye at Faringdon-Gourny, and likewife
at Bifiop-Sutton, W'hich lad Place is near Stowy, but in
the Pariili of Cherv Magna in this County of Somerfet.
For Difeovery of Coal, they fird fearch for the Crop,
which is really Coal, tho’ very friable and weak, and
fometimes appears to the Day, as they term it. ; or
elfe for the Cliff, which is dark or blackilli Rock, and
always keeps its regular Courfc as the Coal does, ly»>
ing oblicjueiy over it. For all Coal lies flieiving like
the Tyie of a Houfe, not perpendicular nor horizontak
unlefs it be broken by a Ridge, which is a parting of
Clay, Stone, or Rubble; as if the Veins by fome vio-
lent Shock were disjointed and broken, lo as to let

in

in Rubble, between them. The Obliquity or
Pitch, as they term it, in all the Works hereabout, is
about Inches in a Fathom; and when it rifeth to
the Land is called iXxQCrop, but in the North Baffsthg,
In the Works near Stowy, and likevyife at Fartngdon it
rileth to the North Weft, and pitcheth to the South
Eaft ; but the farther they w'ork to the South Weft,
the Pitch enclines to the South ; and e centra, when
they work towards the North Eaft. So likewife they
obfervC: as they work to the South Weft, when they
meet with a Ridg it caufetli the Coal to trap up, that
is, being cut off by the Ridg, they find it over their
heads, when they are thro’ xhtRidg: but on the con-
trary, when they W’ork thro’ a ridg to the North Fajl,
they fay it traps down, that is, they find it under their
feet.

Coal is generally dug in Valleys or low Groundso
The Surface in thefe parts is moftly a red Soyl, which
under the firft or fecond Spitt degenerates into Malm
ot Loom, and often.yields a Rock of Reddifli Fireftone,
till you come to four, five, and many times to twelve
or fourteen Fathom depth, when by degrees it changeth
to a Gray, then to a Dark or Blackifti Rock, which
they call the Coal. Clives. Thefe always lye ftielving
and regular as the Coal doth But in thefe parts they
never meet with Fire ft one over the Coal, as at Nmcaflle
and in Stajfordjhire. Thefe CZ/Wj- vary much in Hard-
nefs, in fome places being little harder than Malm ot
Loom, in others fo hard as that they are forced to fplic
them with Gunpowder So likewife in Colour, die
top inclining to red or grey, but the nearer to Coal
the blacker they gi%!b; and wherefoever they meef:'
with them they are fure to find Coal under thenio.
But to their difappointment ’tis not always worth the
the digging. The firfl or uppermoft Vein at ^Sutton

( P70 )

is called the Stinktr^g Vein» It iS hard Coal fie for Me*
chanick ules, but of a fulphurous 6mell. About five
Fathom and half, fddom more than feven Fathom un-
der this, lyes another Vein which from certain Lumps
of Scone mixt with it like a Qafux monnum not Infla*>
mable, called Cats-head, they ca l the Cathead Vein.
About the fame Depth under this again lyes ihtThree
Coal Vein, fo called becaule it's aivided into three dif-
ferent Coals ; Between the firfl and fecond Coal is a
Stone of a foot, in fome places two feet thick ; but the
middle and third Coal feem placed loofe on each other,
without any feparation of a different viarter. Thefe
three Veins before- mentioned arc fomeiimes work’d in
the fame Pit: But the next Vein which 1 am going to
mention is generally wrought in a feparate Pit ; for tho’
it lyes the like depth under the other the C7/j^ between
them is hard and fubjed: to Water; whe' fore i have
reprefented a Pic funk thro’ the three Upper Veins at
A. and another funk upon x\-\tjhree od i^eins only acB.
and fo if they fink on any of the lower Veins they go
more to the North Weft. See Fig Tah II.

Next under the three Coal Veins is the Peaxv Vein, fo
denominated becaufe the Coal is figured with Eyes re-
fembling a Peacock’s Tayl, gilt with Gold, which Bird
in this Country Dialed is called a Fea'x. The CUjf
alfo over this Vein is variegated with Cockle-jh -lls and
Fern Branches, and this is always an Indication of this
Vein, which, as I before hinted, is always fearched
for about 1 5 Fathom to the North Weft of the former.

Under this again between five and fix Fathom lies
the SmitVs Coal Fein, about a >%rd thick; And near
the fame depth under that again«the Shelly Vein: And.
under that a Vein of 10 Inchd^ thick, w'- ich being
little valued, has not been wrought to any purpofe

Some fay there is alfo another under the lafl, but

that

Taht-JT: ^7o .

( 97* )

that has not been proved within Man’s Memory^ At
Faringdon they have the fame Veins, which, as I am
informed, agree in all Parts With thofe of Bi(l36p-Sutton
before-mention’d. But as Faringdon lies four Miles
South-Eaft {tomBijhop-Sutton, fo, in the regular Courfe,
they would lye a Mile and deeper than thofe at Sm^
ton. But as in faift they are dug near the fame Depth,
it follows there mull be a Trap, or feverai Traps down,
which in all mud amount to that Depth between, the
faid Works;

Between Faringdon and High-Littleton tht fame Veins
feem to retain their regular Courfe ; but at Littleton
their undermoft and deeped Vein is the bed Coal,
which at Faringdon proves fmall.

On the other hand, in the Parilh of Stanton^Drew,
to the North* Ead of the Coal- Works at Sutton afore-
faid, about a Mile didant, and in the true Courfe
with thofe at Sutton, the fame Veins are found again.
But here they wind a little, and their Courfe or Drift
runs almod North, and they dip to the Ead ; which
Winding is attributed to Ridges, which the Workmen
have met with on both Sides, and have occafion’d them
to difeontinue the Work that way. At Stanton they
have little of the Red Earth or Malm on the Surface,
but come immediately to an Iron-Gritt or grey Tile-
Stone, which is a Fore-runner of the CoaUClives ; in all
other Matters they agree with the Works near Stowy:

In the fame Parilh of Stanton- Drew, a little to the
Eadward, they have another Coahwork, but the Veins
are in all refpe<ds different from the former. Their
Drift or Courfe is to the Eleven a-Clock Sun, as they
term it, they Titch to the Five a Clock Morning, and
rife to land ; confequently to the Five a- Clock Evening-
Sun. They have feverai Veins, but as yet only three are
thought worth working. The uppermod about three

L 1 1 1 1 1 1 Feec

/

( )

Feet thick fmall Lime Coal. The next is about three
Fathom under it, about two Feet and an half thick,
fit for culinary Ufes: the undermoft is about the like
Depth under the former, only lo Inches thick, but
good hard Coal.

At Glutton, about two Mile from thefe latter, in the
fame Drift, viz., almoft to the South Eaft and by South,
thefe laft Veins appear again. The Surface here is red,
and fo continues to ten, and fometimes to fourteen
Fathom, and in other refpeiis agree with the laft-men-?
tion’d Works at Stanton’ Drerr,

At Burnet, ^jteen-Charlton, and Briflston, they have
Four Veins which Pitch to the North nearly, and
confequently the Drift lies almoft Fall and Weft. The
Surface is red land generally to the Depth of four or
five Fathom. The uppermoft is from three to fix Feet- ■
thick at Brijleton, but lefs at Charlton and Burnet. The i
next, call’d Fot-Fein, is fix Fathom under the former,
eighteen Inches thick, all hard Coal. Thirdly, The
Trench-Fein, y Fathom under the other, which is from
two Feet and half to three Feet thick, all folid Coal.
Fourthly, Rock-Vein, always diftinguifli’d by a Rock of
Paving-Stone, call’d Tenant, lying over it, which Rock-
is fometime twenty Feet thick, or more, and therefore
this Vein is never wrought in the fame Pit with the
former Vein, but about 200 Yards more to the South,
or to Land, as they term it. It’s computed feveii Fa-
thom under the former.

This is all 1 can fay in relation to the different Veins ]
of Coal and Ea ch in the Coal* works in thefe Parts ; j

wherein all agree in the Oblique Situation of the 1

Veins ; and every Vein hath its Chff or Clives lying, ]

over it, in the faTne oblique manner. All of them |

Pitch or Rife about Twenty two Inches in a Fathom, 1
and almoft all have the fame Strata of Earth, Malm,

and

{ P75 )

and Rock over them, but differ in refped to their
Courfe or Drift, as alfo in Thicknefs, Goodnefs, and
Ufe.

Now as Coal is here generally dug in Valleys, fo
the Hills, which interfere between the feveral Works
before mentioned, (eem alfb to obferve a regular Courfe
in the Strata of Stone and Earth found in their Bowels:
For in thefe Hills (I mean thofe only that aredifpers’d
between the Coal-Works above mention’d) we find on
the Summits a ftony Arable mixt with a fpungy yel-
lowifli Earth and Clay ; under which are C^arries of
lyas, in feveral Beds, to about eight or ten Feet deep,
and fix Feet under that thro’ yellowilh Loem, you have
a blue Clay enclinable to Marie, which is about a Yard
thick : Under this is another Yard of whitifli Loom,
and then a deep blue Marie fofr, far, and foapy, fix
Feet thick; only at about two Feet thick, it is parted
by a Marchafite about fix Inches thick. But as this
fwells beyond the Bounds of a Letter, I mud defer the
farther Defcription of thefe and fome Lead-Mines to
another Opportunity ; only ’tis to be noted, that the(e
Beds of Stom and Marie, different from Coal, lie all
Horizontal.

Tour humhle Servant,

John Strachey.

VL Sme

Llllllll 2

( 974 )

V. Some Infiances of the Very great and fpeedy Vege-
tation o/TUR NIPS- Communicated by the
^ey. Dr. J. Theoph. Defaguliers, (2^. S’. S'.

At Sutton Coldfield mWarmcklhire, a peaty Ground
near a Pool ( of which ic was formerly a part)
was fown with Turnip-Seed on the zd Day of
Julf 1701. In lefs than Three Days Time the Turnips
were feen above Ground. At Three Weeks end the
Roots were in Bignefs equal to Walnuts. Within lefs
than Five Weeks after the Sowing, the Gardener drew
great Quantities of Turnips to fell, they then being
as big as large Apples. At the end of Six Weeks, viz>,
on the ixth Day of ^ugufl, a large Turnip was plucked
up ( though probably not fo big as feveral others then
growing upon the fame Ground ) which, together with
its Top and long defcending part of the Root, weigh-
ed above Two Pounds and Fourteen Ounces. At the
fame time alfo was weighed an Ounce of the fame fort
of Turnip'Seed, that the Gardener had fown his Ground
with ; and afterwards a Thoufand of the Grains were
counted fmgly out of the Ounce fo weighed ; and the
reft of the Ounce was divided into Heaps, as near as
could be guefled, equal to the 1000 Seeds firft fevered
and laid together : And it was found that the whole
Ounce contain’d above 14600 fingle Grains ; which
Number multiplied by 46 ( viz. the Number of Oun-
ces that the Turnip Weighed ) produceth 6yi,6oo,viz„
the Number of fingle Grains of Seed required to equal
the Weight of the Turnip. From whence may be ga-
thered, that ( upon fuppoGtion, that the Increafe of
the Turnip was ail along uniform ^nd equal, from the

Time

Time ic was {own till it was pluck'd up ) the Grain
of Seed which it fprung from, weighing when ic was
fown but ,7^, of an Ounce, was increafed in Weight ac-
cording to the following Proportions, vlz^^

In Six Weeks time ^ '

Some time after, another Ounce of the fame fort of
Seed was exadly weighed, and the Grains were found
, to be in Number 14673.

Another Turnip of the fame Crop was plucked up
on the 21/? Day of O^oher; and being put into a Scale,
j: was found to weigh above Ten Pounds and an half 5
which unufual and truly wonderful Bulk it acquired
i ( it being fuppofed, as above, that the Growth was
all along alike ) by increafing the Weight of the Seed
it was raifed from, ly times in every Minute of an
Hour from the Sowing to the Drawing of it.

The Gardener negleded to thin his Turnips in due
Time, elfe probably their Growth had been more con-
fiderable.

At anotherTime, in two other forts of Turnip-Seed,
it was found by counting, that an Ounce of one fort
contained i47oz Grains-^ and an Ounce of the other
fort no fewer chan E490J Grains.

It’s credibly reported, chat of late Years, Turnips
have been prcrry frequently found growing in feverai
Counties of this kingdom that have v/eighed above
twice as much , one of v, hich was fsen at Birmingham
about the Year 1710.

Every < Hour

JMinute of
C an Hour

Week

Day

times its own
Weight.

VL An

VI. Mcount of fome Experiments tried with
Mo7if.Y'i\\cttes'Burnin^Con£aVe^ mjune 1718.
(By the ^ev. Dr. J. Harris and Dr. J.T. Defa-

HIS Miroir is a Concave 47 Inches wide, and

ground to a Sphere of 76 Inches Radius ; fo

that its Focus is about 38 Inches diftant from
the Vertex of the Glafs. Ihe Metal of which it is
made is a Mixture of Copper, Tin and Tin-Glals,
whofc Reflexion has fomething of a yellow Caft. The
Concavc«Surface has Icarce any Flaws, and thofe very
fmallj but the Convex fide, which isalfo polifli’d, has
fome Holes in it.

Having held feveral Bodies in the Focus of this Mi-
roir, we obferv’d what happen’d to them whilft expos’d
to this great Heat ; and with an half Iccond Pendulum
took notice of the Time in which any material Change
happen’d to them.

The Experiments were as follow, and made from
Nine till Twelve in the Morning.

I . A red piece of a Roman Patera^ which began to
melt in 3 Seconds, was ready to drop in lOo.

X. Another black Piece melted at 4, and was
ready to drop at 64 Seconds.

3. Chalk taken out of an Echinus Spatagus fill’d

with Chalk only, fled away in 13 Seconds,

4. A FoITil e-Shell calcin’d in 7 Seconds, and did

no more in 64.

5. A piece of Pompeys Pillar at Alexandria, was

vitrified in the Black Part in 50 Seconds,
and in the White part in 54. 6. Cop-

guliers, %eg, Soc. SS.

r

( 977 )

6. Gopp^r-Oar, that had no Metal in it vifiblc,

vitrified in 8 Seconds.

7. Slag, or Cinder of the ancient Iron-work

faid to have been wrought by tliQ Saxons,
ready to run in 29 Seconds and an half.
the Glafs grovsing hot, burn d wit h much lefs Force.

8. Iron-Oar Bed at firft, but melted in 24 Se-

cond:.

9. Talk began to calcine at 40 Seconds> and

held in the Focus 64.

ic. Calculus humanus in 2 Seconds was calcin’d,
and only dropp’d off in 60.

]j. An anonymous Fifh’s Tooth melted in 32
Seconds and an half.

12. - The Ashejlos feem’d condens’d a little in

28 Seconds; but it was now fomething
cloudy : MonC Vilktte fays that the Glafs
ufually calcines ic.

13. -A Golden Marchafite broke to pieces, and

began to melt in about jo Seconds.

14. A Silver Sixpence melted in 7 Seconds and,

an half.

15. A King rT/7/;^««s Copper Halfpeny melted in

20 Seconds, and ran with an Hole in it in 3 1.
1 5. A KmgGeorge*s Halfpenny melted in 16 Se-.

conds, and ran in 34.

17. Tin melted in 3 Secondsi

18 Cafl: Iron in 16 Seconds.

j 9. Slate melted in 3 Seconds, had an Hole in 6i

20. Thin Tile melted in 4 Seconds, had a Hole

and was vitrifi’d thro’ in 80.

21. Bone calcin’d in 4 Seconds, and vitrifi’d in 33.
An Emerald was melted into a Subftance;

like a Turquois Stone.

A Diamond weighing 4 Grains loft .i.
its Weight. yik

( 978 )

VII. Account of the Extraordinary METEOR
feen alt oW England, on the i ^th of March
17 if. With a Demonflration of the uncommon
Height thereof, Edm. Halley, LL, D. and
Secretary to the Royal Society.

HIS wonderful luminous Meteor which was feen

in the Heavens on the 19th of March lafl:, as

it was matter of Surprize and Aftonilbment to
the Vulgar Spedlator, fo it afforded no lefs SubjeeJt of
Enquiry and Entertainment to the fpeculativc and cu-
rious in Phyfical things : Some of its Phanowerfa being
exceeding hard to account for, according to the No-
tions hitherto received by our Naturalifls ; fuch are
the very great Height thereof above the Earth ; the
vaft Quantity of- the Matter thereof; the extravagant
Velocity wherewith it moved ; and the prodigious £x-
plofions thereof heard at fo great a Diffance, whole
Sound, attended with a very ienfible Tremour of the
fubje6t Air, was certainly propagated through a Me-
dium incredibly rare and next to a Vacuum.

In Num* 341. of thele TranfaBions, I have colle(3ed
what I could find of fuch-like Meteors, and fince, turn-
ing over the Ephemerides of Kepler, I accidentally hit
upon another, prior to all thofe there deferibed, and
which was feen all over German'^. Of this the Words
of Kepler are.* Die ~ Nov. 1623. Meteorwm ignitum,
Clohus ardens ah occaju in. ortum volans tota pajlfim Ger-
mania fuit cortfpeefus. In Auflria etiam fragorem exau-
ditum affirmarunt epuafi a fulmine ; ^uod vanum tamen puto :
nihil enim talc confamant defer iptienes epum extanu Yet

neither

( 979 )

neither this, nor any of the other hitherto defcrihed,
feem to come up in any Circumftance to this late Ap-
pearance; of which I am in hopes to give a fatisfa*
^ory Account, being enabled by the very many Re-
lations thereof communicated to the Royal Society, from
moft parrs of the Kingdom ; tho’ it was not my good
Fortune to fee it my felf ; and tho’ very few of our
Countrymen who befl; know the Stars, had better luck.
Some of the moft perfed Defcriptions we have receiv’d
are the following :

/v>/, Our very worthy Vice-Prefident S\x Hans Sloans
Baronet, being abroad at that time, happen'd to have
his Eyes turned towards it, in its very firft hruption j
and the next Day he was pleafed to give me in Writing
what he had with great Exadnefs noted about it, in
the Terms following : “ On Thurfr/ay, March 19. i7[|,

“ pafting along Eaftward by the N E. Corner of Sou-
“ thamfton-jireet in Bloowshury-Square, London, at about
“ a Quarter after Eight at Night, I was furpriz’d to
“ fee a fudden great Light, much beyond that of the
“ Moon, which flione then very bright. 1 turn’d to
the Weftward where the Light was ; which I appre-
bended at firft to be artificial Fire-works or Rockets,
The firft place I obferv’d it in, was about the Pld-
** ades Northerly, whence it moved after the manner,

“ but more flowly than a falling Star, in a Teeming
“ dired Line, delcending a little beyond, and withal
“below, the Stars in Orions Belt then in the S, W.

“ The long Scream appear’d to me to be branched about
“ the middle, and the Meteor in its way turn’d Pe^r-
fafhion’d or tapering upwards. At the lower end it
“ came at laft to be bigger and Spherical, tho’ it was
“ not To big as the Full Moon. The Colour of it was
“ whitifh, with an eye of Blue, of a moft vivid daz-
“ ling Luftre, which Teem’d in Brightnefs very nearly
, 7 M to

{ p8o )

ro refemble, if not furpafs that of the Body of the
Sun in a clear Day, beheld by the naked Eye. This
Brighcnefs obliged me to turn my Eyes ( which had
“ their Pupils adapted to the Light of the Moon ) fronr
“ it feveral times, as well when it was a Stream, as
“ when it was PearTafliion’d and a Globe; tho’ I had
“ a great Curioficy to obferve it with Attention, ft
“ feem’d to move in about half a Minute or lefs, about
“ the Length of and to go out, as I guefs’d, about
“ as much above the Horizon. There was left behind
it, where it had pals’d, a Track of a cloudy or faint
“ reddifli Yellow Colour, fuch as red-hot Iron or glow-
“ ing Goals have, which remained more than a Minute,
“ feem’d to fparkle, and kept its Place without falling.
“ This Track was interrupted, or had a Chafm towards
its upper end, at about two Thirds of its Length. I
“ did not hear any Noife it made, but the place where
“ the Globe of Light had been, remain’d after it was
extind^, of the fame reddiOi Yellow Colour with the
“ Scream for fom^ time, and at firft fome Sparks feem’d
“ to iffue from it, fuch as come from red-hot Iron bea-
“ ten on an Anvil. The Surprize, Brighcnefs of the
“ Light, and Noife of the People upon the Variations
“ of the Appearance, calling to one another to obferve
“ what they never had obferv‘d in* their Days, and
thought to be prodigious, hinder’d me from taking
“ notice or remembring any thing farther about it.

• It were to be wiiht that Sir had more efpedal-
ly regarded the Situation of the Track of this Meteor
among the fixt Stars, and let us know how much it
part above the Pleiades, and how much under the Belt
of Orion, that fo we might with more Certainty have
determin’d its Pofition in refjped: of the Horizon of
London \ for which purpofe the whole Number of Spe-
dacors there has not furniihed us with one fuiHcicnt

Obferva-

( 5>8i' )

Obfervation. But all the Relations, however otherwile

differing, agree in this, that the Splendour was little

inferior to that of the Sun; that within doors the

Candles gave no manner of Light, and in the Streets nor

only all the Stars difappear’d, but the Moon then Nine

Days old, and high near the Meridian, the Sky being

very clear, was fo far effaced as to be fcarce leen, at

leaft not to caff a Shade, even where the Beams of

the Meteor were intercepted by the Houfes : fo that for

Tome few Seconds of Time, in all refpeds it refembled >

perfedt Day,

The Time when this happen’d was generally rec-
koned at a quarter paft Eight; but by the more ac’
curate Account of the Rev. Mr. Pound ( who only law
the Light J agreeing with what has been lent us from
the Pariftan Obfervatory, it appears to have been at
8*^ 8' apparent Time at London. And the Sun being
then in 9r gr. of ArkSt the R^ht Alcenfion of the
Mid-Heaven was gr. qy', whereby the Pofition of
the Sphere of fixt Stars is given. Hence the Lucida
Pleiadum will be found at that time to have been
gr. high, in an Azimuth 6 gr. to the Northward
of the Weft, and confequently the Arch the Meteor
moved in, was inclined to the Horizon with an An-
gle of about z7 gr, having its Node or Interfedion
therewith, nearly South South Wefl ; as will be more evi-
dent by what follows.

At Oxford five Minutes earlier, Mr. John Whitefidel
R. S. Soc. Keeper of the Ajhmole Mufeum, and very
skilful in both Mathematical and Phyfical Matters,
immediately alter the Extindion of the Meteor, made
hafte out to fee what it might be, and well confider’d
the Situation of the Track it had left in the Sky :

He found it to have paft about i r Degree above the
preceding Shoulder of Orion, and about 3 r above

7 M X the

{ p8i )

the middle of his BelPy where there appear’d a lumi-
nous Nubecula of a rcddifh Lighr, being a Dilatation
of the Track, feemiog to have been occafion’d by
fbme Explofion there; and by'what he could learn from
thofe that faw it, it was thereabout that it broke out,
and 6rft began to efface the Scars. Hence it proceed-
ed as to fenfe in an Arch of a great Circle, and pal^
fing in the middle between the Tail of Lepus ( 6 Baj*
ero ) and /3 in the Fore-Foot of Cauis major, it termi-
nated about § in the Breaft of the fame, nearly in
gr. of Right-Afcenfion, with gr. South Declina-
tion: and at the place of its Extindlion there remained
a large whitilh Nebula, much broader and of a Wronger
Light than the reft of the Track, which he took for
a certain Indication of a very great Explofion made
there. By Computation it will be found that the An-
gle this Track made with the Horizon of Oxford was
neareft r\ogr. and its Interfedtion due SSPV; and
that the place of its Extinffion was about 9 gr. above
the Horizon, in the Azimuth of ^^gr. to the

At Worcejler Mr. Nicola! Fatio, a Perfon greatly
skill’d in Aftronomical Affairs, faw this Meteor defcend
obliquely towards the South, making an Angle with
the Horizon of about 65°, and interfe^ling it about
S SJV ~ S, as may be colleded from a Scheme thereof
Pent up by him, and communicated to the Royal So-
defy, Teeming to be defign’d with fufficient Exadncfs.
By this the Track left all Orior! and Caais major to the
Wcftward, and divided the Diftance between Sirius
and Procyon, To as to be almoft twice as far from Pro-
tyon as Sirius. The Time here was one Minute before
Eight, this City being about 9' of Time to the Weft
, of London, and confequently the Right-Afcenfion of the
Mid-Heaven 118 T gr*

Now

' (9^)

Now the Situation of the three Cities London^ Oy-
ford, and IVorcefter being nearly on the
Point, whereon the Track of die Meteor had its grea*
reft Altitude above the Horizon, equal to the Angle
of its vifible Way; if we fuppofe it at London to have
been 17 ^i*gh, and at the fame time at Worcefter
to be 611 gr. high, in the Plane of the Vertical Circle
palling through London and IVorcefier ; fuppofing like-
wile the Dillance between them to be 90 Geographi-
cal Miles, or one Degree and half of an Arch of a great
Circle of the Earthy we lhall by a Trigonometrical
Calculus, too obvious to be here inferred, find the per-
pendicular Height to have been 64 fuch Miles ; and
the Point over which it was then perpendicular to have
been 30 fuch Miles W.N.W. from Worcefter. And the
Geographical Mile to the EngUjh Statute Mile being as
^3 to 20, this Height will be no lefs than 73 En^lilh
Miles. The place alfo direoUy under it, will be found
to be about Preftain on the Confines of Hereford and
Radnor^hhkti. Nor can we be much out in this De-
termination, the Oxford Obfervation concurring nearly
in the fame Conclufion.

This Altitude being added to the Semidiameter of
the Earth as Radius, becomes the Secant of Eleven De-
grees, fo that the Meteor might be feen above the Ho-
rizon in all Places not more than 120 Leagues diflanc
from it. Whence it will not be flrange that it fhould
be feen over all Parts of the Iflands of Great Britain
and Ireland, over all Holland and the hither Parts of
German'^, France and Spain, at one and the lame inllant
of Time.

This fuggefts a very great ufe that might be made at
thele momencaneous Vheenomena, to determine the Geogr^t^
fhtca' Longitudes of Maces. For if in any two Places two
Obfervers, by help, of Pendulum Clocks duly coircfted

by

( 984 ') \

by Coeleftial Obfervation, do cxadly note at what i
Hour, Minute and Second fuch a Meteor as thii blows
^ up and is extinguilht, the Difference of thofe Times
Will be the Difference of Longitude of the two Places,
as is well known. Nor does it require To much as the
Ufe of a Telefcope, as in the Methods hitherto put in
practice for that purpofe : fo that if thefe Appearances
could be predidted, and Notice given of their coming,
that we might know when to exped them, I lliould
make no Difficulty to prefer this way of fettling the
Geography of a Country before all others.

Having thus fixt one Point in the Line of its
Mention, let us now confider what courle the Meteor
took from thence. And firft at th^ Town of Kirkhy- \
Stephens y on the Borders of Torkjhire and WeflmoreUnd,
in a Meridian very little to the Weflward of fVorce/her,
but about z r more to the North, it was obferved
to break out as from a dusky Cloud, diredly under .

the Moon, and from thence to defeend, nearly in a Per- !

pendicular, almoft to the Horizon. Now the Moon, be-
ing at that time in the third Degree of Leo, was about ■
half an hour pad the Meridian, and confequently much
about a point to the Weft, ot S bW : and the Situation
of Preftain from Kirhy-Stevens being fufficiently near
upon the fame Point, it follows that the Diredion of
the Track of the Meteor was according to the Great
Circle paffing over thofe two Places.

And this is further confirm’d by the Obfervation of ;
Sam. Cruup, Efq; Reg. Soc. Soc. who at Tiverton.^ about
twelve Geographical Miles nearly due North from Exe^ i
ter, obferved the firft Explofion of this Meteor exad* 1
ly in his .Zenith, as he was aflured by applying his
Eye to the fide of his' Door, which he took to be per-
pendicular, and looking upwards.* And from thence he i

law it defeend to the Southwards diredly in the fame :

^ Azi-

I

( 9^1 )

Azimuth, without declining either to the Right or Left:
Hence it is plain, that the Track likewife pafs’d over
this place, which by our beO: Maps is found to lie in
a Line with Frejiain and Kirbj-Stevem with Tufficienc
Exatlnefs ; fo that we fhall take it for granted that
this was the very Courfe it held.

On this Suppofition, that the firfi: Explofion, at-
tended with the reddilh Nuhecnla, was diredly over
Tiverton^ we have the Oxford Obfervation to compare
with it, in order to determine more nicely the per-
pendicular Altitude there At Oxford this Nubecula
W’as found to be 3 gr, above the middle Star of 0-
rio»s Girdle^ at 8*^3', and was therefore gr, a-
bove the Horizon ; and the Diftance between Oxford
and Tiverton, being i°. or 115 Geographical Miles,
it will be as the Sine of 61°. 35' to the Sine of 63° 30'
So the Semidiameter of the Earth being 3437 r fuch
Miles, to 3498 Miles the Diftance of the Meteor from
the Center of the Earth ; from W'hich deduding the
Semidiameter, there remains 60* Geographical Miles
for the Height of the Meteor above Tiverton : And that
this was fo is confirmed by the Obfervation of the
Revc Mr. Will. Derham^ who at Windfor faw the afore-
faid Nubecula about two Degrees above the moll Sou-
therly of the Seven Stars in the Shield of Orion \ that
is { the Time being 8*^6'^ in the Altitude of 13 \ gr*
whence, the Diftance between Tiverton and Windfor
being 150 meafured Miles, or 130 Geographical, by a
like Proportion we fhall find the fame Height of the
Meteor 60 fuch Miles wanting only one Quarter. So
tliat in a round Number we may conclude it to have
been juft 60 Geographic or 69 Statute Miles above
the Earth’s Surface. Nor is it poftible to come at a
precife Determination of this matter, by reafon of the
Coarfenefs and Inaccuracy of our Data, which were

(9^6) I

only the Notes of Perfons under the Surprize of the I
fuddennefs of the Light, ►and no ways pretending to I
Exadnefs; how^ever, fuch as they are, they abun- |
dantly evince the Height thereof to have exceeded 6c i

Englifh Miles, not to fay 38 or 40, as fome would *

fain have it.

I was unwilling to leave off, till I had pitcht upon
fome Hypothefis that might fubjedi the Motion of ;
this Meteor to a Calculus, that the Curious might be >
uble to compute the vifible way thereof, either in re-
fpedl of the Horizon, or among the fixt Stars: This
I found might be done with tolerable Exadinefs, fup- f
pofing that it mov’d in the Arch of a Circle concen-
trick with the Earth, but 60 Geogr. Miles without it; j-
and that the Point of the firfl Explofion was over the i

Lar. of 50° 40' and 3® 40' to the Weft of London', and 5

that of the laft Extinction over Lat. 47°. 40' with
4°. 5'o' Longitude: The Time being iixt to 8 ?

Minutes paft Eight at London, Hence it will be eafy, ;
by a Trigonometrical Procefs, to obtain the vifible Al- ^
titude and Azimuth of the Meteor at either of its Ex-
plefions, as feen from any Place whofe Longitude and •
Latitude is know^n ; and from the Time given, the
Points in the Sphere of Stars anfwering to thofe Azi-
muths and Altitudes are readily deduced. Let thofe !
that contend for a much lefs Height of this Meteor try ;
if they can on fuch their Suppofition reconcile the feveral i
Phanowena before recited with one another, and with
' the Obfervation of the Rev. Mr. William Ella, Redior |

of Famfton in Nottingha'mlliire, between Gainsborough |

and Bedford, which for its Exatftnels I muft not omit. j

Here at 8'^ f the Meteor W’as feen to pals precifely in |

the middle between Sirius and the Fore* Foot of Canis j

major, moving obliquely to the Southward, in a Line !

whofe Direction feem’d to be from the middle between ]

the ,|

I

( 9^7 )

the two Shoulders of Orioff, The Latitude of the
place being nearly %o', and Longitude fTr/? from
London o°. 45'. Let them try how they can account
for its being (een five Degrees high at Aberdeen in Scot-
land, and near as much at Peterhead half a Degree more
Northerly : and then they will be better able to judge
whether it did not exceed the reputed Limits of our
Atmofphere. Laflly, if the apparent Altitude of the
Meteor at Parts was not 5r but ii gr, on the If'
Point, when it muft have been in its greatefl: Luftre,
there will be no pretence to bring it lower than 1 have
made it, efpecially if it be allowed to have follow’d
the Track I have allign’d it, over Prejlaln, Cardijf,
Minhead, Tiverton, and Breji in Bretan'j.

Allowing this to have been the Path it mov’d in, it
would be eafy to aflign the real Magnitude and Velo-
city of this Meteor, if the feveral Accounts of its ap-
parent Diameter, and of the Time of its Paflage from
one of its Explofions to the other, were confident with
themfelves. But fome of them making its vifible Ap-
pearance nearly equal to the Sun’s, w'hich in the Opi-
nion of many it far exceeded, we may fuppofe with
the lead that, at the time when it fird broke out o-
^*er Tiverton, its Diameter was half a Degree, And its
Horizontal Didance being * yo Geogr. Miles from Lon-
con, and its Altitude 60, the Hypothenufal or real Di-
dance from the Eye will be more than 160 fuch Miles;
to which Radius the Subtenfe of half a Degree will
be above an Englilh Mile and half, being about 2800
Yards quamproxime: After the fame manner it is dif-
ficult to aflign its due. Velocity, whild forae make tc
half, others lefs than a quarter, of a Minute, in paf^
dng from its fird Explofion to its lad Extindion:
But the Didance it moved in that time being about
3 gt, or 1 80 Geogr. Miles, we may modedly compute

.7 N it

‘ ( J>88 ) j

it to haVe run above ^oo fuch Miles in 2 Minute;
which is a Swiftnefs wholly incredible, and fuch, that
if a heavy Body were projeded horizontally with the
fame, it would not defcend by its Gravity to the Earth,
but would rather fly off, and move round its Center in
a perpetual Orb, relembling that of the Moon.

Of feveral Accidents that were reported to have at-
tended its Paflage, many were the effed: of pure Fan-
cy ; fuch as the hearing it hils as it went along, as if
it had been very near at hand : others imagined they
felt the Warmth of its Beams ; and fome there were
that thought, at lead wrote, that they were fcalded by
it« But what is certain, and no way to be difputed, is
the wonderful Noife that follow’d its Explofion. All
Accounts from Devon and Cornrval and the neighbour-
ing Counties are unanimous, that there was heard
there, as it were the Report of a very great Can-
non, or rather of a Broad fide, at fome diftancc, which
was foon follow’d by a rattling Noife, as if many fmall-
Arms had been promifcuoufly difcharged. What was
peculiar to this Sound was, that it was attended with
an Uncommon Tremour of the Air, and every where
in cliofe Counties, very fenfibly Ihook the Glal^Win-
dows and Doors in the Houfes, and according to fome,
evert the Houfes themfelves, beyond the ufual Effed of
Cannon, though near ; and Mr. Cruvpjs at Tiverton^ on
this occafion, lofl a Looking-Glafs, that being loofe
in its Frame, fell out on the fliock, and was broken.
N&rvjdo We yet know the Extent of this prodigious
Sound, which was heard, ^gainft the then Eafterly Wind,
id th^fe Neighbourhood of London^ as I am inform a ; and
by the Learned Dr. who difliodly heard it be-,

yond Lems< in .Sujfex : So that I cannot help thinking,
a Meteor.as jthis might hav.e oecafion’d that
: F arcus Pfcrum cnUor, &c

* — ■ "Nam^ut

I

( 9^9 )

' ' Namcfue DiefpHer
Igne corufco nuhiU dividtns
TUrumqne^ per purum to»antes

Egit equos volucremque currum^

^0 hrula tellus, (jrc. Concutitur.

But whether the Report heard near Lervis were of that
Explofion right over Devonjhire, or rather of that latter
and much greater at the Extinction over Br/tany, I (hall
not undertake to determine, till we have fome further
Accounts from France, whence hitherto we have only
had, that at Paris the Time of the Appearance was at
17 Minutes pad Eight.

It remains to attempt fomething towards a Solution
of the uncommon P/j^nowena of this Meteor; and by
comparing them with things more familiar to us, to fliew
at lead how they might podibly be efFe(ded. And firft
the unufual and continu’d Heats of the lad Summer in
thefe Parts of the WorkJ, may well be fuppos’d to have
excited an extraordinary Quantity of Vapour of all forts;
of which the aqueous and mod others, foon condens’d
by Cold, and wanting a certain Degree of Specifick Gra-
vity in the Air to buoy them up, aicend but to a fmall
Height, and are quickly returned in Rain, Dews,
whereas the inflammable fulphureous Vapours, by an in-
nate Levity, have a fort of f^is centrifuga, and not only
have no need of the Air to fupport them, but being agi-
tated by Heat, will afeend in Facuo BoHeano, and fublime
to the top of the Receiver, when mod other Fumes fall
indantly down, and lie like Water at the bottom ; the
Experiment whereof was flrd fliewn me by the Reverend
Mr. Whitefide ^x.Oxford, and was very lately made before
thz Royal Society. By this we may comprehend how the
matter of the Meteor might have been raifed from a large
Tra(d of the Earth’s Surface, and afeend far above the re-
puted Limits of the Atmofvhere being difengaged

from all other Particles, by that principle of Nature that
congregates Homogenia vifible in fo many Indances, its

Atoms

( 9P<^ )

Atoms might in length of time coalefce and tiih * firtuU
toujlj together, as we fee Saks fiicor in Water; and gradu-
-ally concrading thcmfelves into a narrower compafs, might
lie like a Train of Gunpowder in the Ether, till catching
fire by feme internal Ferment, as we find the Damps in
Mines frequently do, the Flame w’ould be communica*
ted to its continued parts, and To run on like a Train fir’d.

This may explain how it came to move with fo uncon-
ceivable a Velocity; for if a continu’d Train of Powder
were no bigger than a Barrel, it is not eafy to fay how
very faft the fire would fly alongft it, much lefs can wc
imagin the Rapidity of the Accenfion of thefe more in*
flammable Vapours, lying in a Train of fo vaft a Thick-
nels. If this were the C ale, as it is highly probable, it was
not a Globe of Fire that ran along, but a fuccelfive kin-
dling of new: Matter : and as fome parts of the Earth might
emit thefo Vapours more copioufly than others, this Train
might in fome parts thereof, be much denfer and bigger
than in others, w'hich might occafion feveral fmaller Ex-
plofions, as the Fire ran along it^ befides the great ones
-which were like the blowing up of Magazines. Thus we
may account for the rattling Noife like fmall- Arms, heard
after the great Bounce on the Explofion over Tiverton ;
the Continuance of which for fome time, argues that the
Sound thereof came from Diflances that encreafed.

What may be faid to the Propagation of the Sound thro*
Vi Medium, according to the receiv’d Theory of the Air
above 300000 times rarer than what we breath, and as I
faid before, next to a Vacuum, I mufl confefs 1 know not.
Hitherto we have concluded the Air to be the Vehicle of
Sound ; and in our artificial Vacuum we find it greatly
diminifh’d t but we have this only Inftance of theefletS
of an Explofion of a Mile or two diameter, theimmenfi-
ty of which may perhaps compenfate the extream Finc-
nefs of the Medium,

F I N 7 S.

* Dele fjrtuitoujt/.

/

f 99* ) Kumb.

PHILOSOPHICAL

TRANSACTIONS.

For the Months of June, '^uly and Auguft, 1719*

The CONTENTS

I. \ N Ohjcrvation of the End of the Total Lunar
Jf\ EcUfje on the ^th of March 1 718. ohfrved
■near the Cape of Good Hope, fervtng to determine the
Longitude thereof. With Remarks thereon By E. Halley,
R. S, Seer.

II. D. Jacobi Keill, Medicina. nuper DoLloris eruditiffmu
De V iribus Cordis Epiflola.

HI. An rtccount of fome Experiments relating to the Specifick
Gravity of Human Blood, By James Turin, M. D.
Fellovp of the College Phyficians, and^. R. S.

IV. Bn account of the Sunk Lfland in Humber, fome Tears
fince recover'd from the Sea., Being an Extract of a
Letter Communicated to the Royal Society by John
Chamberlayne, Efep^ R. S. S.

V. A Way for Myopes to ufe Telelcopes Eye^Glaf-

fes, an OhjeLL^Glajs alone becoming as ufeful to them^ and
jometimes more, than a LLombination of GUffes. Commu’»
micated to the Royal Society, by the Reverend J. T. DeC-
aguiiers, LL. D. and F. R. S.

VI tdlerc and accurate Tables for the ready Computing of the
EcUpfes of the of Jupiter hy Addition only.

By the Reverend Mr.]^mQS Pound, R S. S.

9 o

I. An

( 99* )

I. An Ohfer^^atlon of the end of the 'Total Lunar
Eclipfe on the ^th of March 1718. ohJcrVed
near the Cape of Good Hope, JerVmg to deter^
ynine the Longitude thereof. With ^markj thereon,
E. Halley, ^ S, Seer.

I S no A^ better than thirty Years fince 1 had a
.1 Difpuce with fome of the French Geographers about
the Longitude of the Cape of Good FJope, faid to have
been obferv’d by the Religious Mifllonaries fent to China
in the Year 1685, By an Emerfion of the firft Satellite
of Jupiter, they determined that Cape to be 11' or
I?! grad, more Eafterly than Paris, i\\^i is xograd. from
London ; Which for the reafons I then gave, \ concluded
could not be more than i"] grad, ^ See Phil, Tranfa^.

185. Very lately I have fallen upon an Obfervation
which I believe will determine the Controverfy in my
favour: for I had accidentally a Journal of an O dicer of
the Ship Emperor put into my Hand^, who in his re*
turn from India, on the fifth of March 1718. obferv’d
the End of a Lunar Eclipfe, when the vifible altitude of
the Moons Centre was i}°. x5', he being then in the
Latitude of 34°. 23' South, and as they found afterwards,
juft 1 80 Leagues to the Eaft wards of Cape Bonne Efperance.
By Calculation J find that in that Latitude the Moon
had that height at yh, iy'~ P. M, and by comparing
this Eclipfe with that we obferv’d with great exatftnefs on
Fehr. i\°. i68z. (which agrees perfedly well without
.Numbers^ I conclude the middle of this to have been
ijt London at 3^ 48' P,M. To which adding I*’. 46' for

f 99} )

the Semiduration (this being very certain from the ob-
fcrv’d Continuance of the Edipfe of l6Sz.) the End
will be found to have been at London at 34'- The
Ship was therefore in a Meridian to the Eaftwards
of London : But (he was at that time i8o Leagues to
the Eaftwards of the which diftance in that La-
titude gives eleven Degrees of Longitude ; this there-
fore being deduced from the Longitude of the Ship,
leaves juft or one Elour, for the difference of

Meridians between London and the Cafe. So that by
this account the Cafe is yet nearer our Meridian than I
had formerly made it, and nea fix Degrees nearer than
M. De la Hire places it in his Talks.

This Edipfe was attended with all the Circumftances
requifite to make the Conclufion as certain as the na-
ture of the thing will admit of: For the Moon was near-
ly in Ferigdo and the Edipfe almoft central ; for which
reafbns (he emerged out of the Shadow as fwiftly as
poffible ; The Sea was very fmooth, there having been
little Wind for above 30 Hours before; and the Moon
was not too high to be well obferved with a ForeftafI'
.Nor were they long at Sea before they made the Land,
for in lefs than five Days, on the tenth of March at
Noon, they had paft d' Agulhas the moft Southerly
Promontory of Africa, which then bore from them
l^orth Eafl, about feven Leagues diftant. The End of
this Eclipse, though not vifible here, might have been
feen in Germany, both at Narenhurg, Leiffick and Berlin,
but we cannot learn that it was any where obferved
there ; however our Numbers in this Cafe may be fecurs-
Jy relied on.

On this occafion it may not be amifs to infert an Ob-
fervation or two I procured to be made at ih^Cape.^ by
Mr, Alexander Brovpn a Scotch Gentleman, who went to
refide in on our Cornpanks sccoimL He carried

with

{ 994 )

with him a very good Brafs ^adrant of above tvib
Foot Radius, and at the Dutch Settlement at Table Bay,
Pendulum-Clock by correfpondent Al-
titudes, on the 4th of Augufl 59' the
diftance of the bright Limb of the Moon from the right
Shoulder of Orion was obferv’d tobez5° 3'. And the
next Morning Aug< 5. at 5I1. rT. 1 1", the fame Limb
was diQant from Prccyon 25’. 57', and at 48''

from the Lucida Atiais 29'.

It were much to be wilht that the Moon had, either of \
thefe Mornings, been accurately obferv’d at Greenvrich ‘
or Paris, or at fome Place in Europe, W'hofe Longitude ^
from them is well known. But that failing us, 1 had re- ■
courfe to the Period of the Lunar Motions, which is
perform’d in 18 Years and ten or eleven Days, after
which the Eirors of our Lunar Computations return
very nearly the fame ; and I found among my own old
Obfervations, one that tallyed well with that of the 4th
of Augu(l. Viz^ Anno 1676. 23°. 13’'. ii'. 35".

at Oxford, I obferv’d the Moon to apply to the Star in
medio Collo Tauri, by Bajer markt A. The Star at that
time was diflant from the Southern and neared Cufp of
the Moon by the Micrometer zo'. 32". and at I3^ 17'.

15''. when it Teem’d to immerge upon the bright Limb
of the Moon, it was diftant from the Northern Cufp
2?'. 20"; but this lefs certain by reafbn of the hazey
Air. The Star at that time was in ^ 28°. y6^ with
^1°. if .xd\ North Lar. whereby I found that our Lunar
Tables, founded on Sir cor retd Theory of 1

her Motion, gave her place at that time only two Mi- 1

nutes too flow; which Error being allowed on the 4th I

of Augujl 1694. the refult was, that 5\ 59'. at Cape Bonne f
Efperance was London 53'. whence the difference of
Longitude i6f degrees, fu&iently near what we had
before determin’d. i

( 995 )

; II. JACOBI KEILL, M,‘D,
De Viribm Cordis EpiJIola.

R I C H A R D O M E A D, M Z).
S. <f. D.

Piftolam D. Jurin^ Tibi, Vir Clariffime, infcriptam.

in Adis Philoibphicis nuper publicatam legi ; in
qua, ea quse a me traduntur de viribus Cordis, infir-
mare conacur vir Dodi/Timus. Cum aeftimatio virium,
quibus Cor Sanguinem expellit, a BoreUio fada, fere
omnibus valde incredibilis videljatur, non me temera-
rium, non Eorelli nomini injuriofum, non orbi literato
ingratum fadurum exifiimavi, fi ad verum propius
accedere tentarem. in quo Tentamine, non accuratam
virium Cordis definidonem mihi propofitum erat dare,
fed potius methodum, qu3 hse vires forte inveniri pot
Pent, indicare ; & Geometrise peritiores ad Problemads
valdc defiderati inveftigationem incitare. Quo ani-
mo tentamen illud primum fufcepi, codem ea, qu:K in
€0 reprehendit vir DodifTimus, nunc defendam. Ne-

Viro Celeberrimo

quaquam

quaquam enim mihi honorem qu^rro (utcunque par*
va mea exiftimatio fit, eft certe debito major) fed
Genti Medicse lueem undecunque illacam gaudeo. Id-
circo non uc Decreta mea fultineam, fed uc vir huic
iiegotio plufquam par, fuas demonftrationes fecum re*
putare, & Reipublicx LiceraricC corrediores denuo red-
dere dignetur, hancTi-bi fcripfi literam. Quern enim
Adverfarius Patronum fibi ambivic, ego Te judicem
ComroverfitE inteiligentem & aequilTimum mehercule
exopto.

Prsecipuum quod Bordlto, D. MoreUndt mihi objicit
vitium eft, quod in Potencia Cordis teftimanda, quam
rationem ad pondus iners, vel corporis gravitatem ob-
tineat, determinare fufcepimus. “ Sed Cor, inquic,
“ cum & ipfum inter conirahendum movetur, & coipora
** oppofita, Sanguinem nempe & arteriarum tunicas
“ in motum impellit, patec ejus Potentiam non ali^
“ ratione fciri pofle quanta fit, quam ut motus hujus

quantitatem cognitam teneamus. Motus autem qui-
“ libct cum pondere quiefcente comparari non magis
“ poteft, quam linea cum redangulo. * Ac a nemine
certe noftrum, quod fcio, eft Motus Cordis cum pon-
dere quiefcente comparatus. Potentiam autem Cordis,
feu vim Cordis motricem & Sanguinem impellcntem
cum pondere conferre, quid prohibec non video. Quam-
quam enim inter Pondus & Motum corporis folidi nulla
fit relatio, vis tamen mocrix, fi in fluid urn agic, ad
vim gravitatis quandam certe rationem haber. Et re-
vera vis corporis motrix, certam in fluido motus
quantitatem in daco tempore efSciens^ sequalis eft pon^
deri, quod vi gravitatis cadendo, in eodem tempore,
eandem motus quantitatem fibi acquiric. Hinc vis,qui
cx-orificio aliquo aqua exprimitur, certo ponderi icqua-
lis efle diciturs quia pondus datum, & vis aquam ex-
primens ^quales motus in temporite ^qualibus ge-

neranc.

'( ppr )

nerant. Hie genuinus Corollarii NeiftonUnl fenfuS ini-
hi videtur efle, nec ab hoc fenfu diferepanr, quse de
Cordis vitibus explicui. Verba Nerrtoni funt, qua
totus aqua cxilkntis tnotus generari foteji, aqudis eft fon-
der i quK non fatis atcendifle videtur Jurinius^

cum dicic Vondus autem illud quo motus aqud& ex vafe
effluentis generari pteftt &c.

Sed fi hac re a nobis peccatumeft, cum fummis
certe hujus feculi Geometris Hugenio & J^evptono pec-
cavimus, quorum uterque vim fluidorum per vim gra-
vitatis exponit. Nec in Orp/. preedidtoid folummodo
facie Nevptonus, fed in aliis etiam locis oilendit Metho-
dum, qua ratio rcfiftentia: Medii, id eft, adionis fiuidi
in corpus folidum, ad vim Gravicatis vel centripetam
inveniri poteft, ut videri licet in Prop, & pa Libri
fecundi, eorumque Ccrollariis. Alia profedo eft adio
fluidorum in folidum, & alia folidorum in fe invicem.
FJuidum data velocitate motum, datum pondus fufti-
nere poteft, cum fluidi partes fibi mutuo continud
fuccedentes in pondus impingunt, adeoque vis fluidi eft:
revera ponderi aequalis ; fed cum Solidorum non par eft
ratio, eorum Vis cum Gravitate comparari nequic.

Me infuper reprehendit Vir ingeniofifTimus, quod ve-
locitatem Sanginis e corde detrufi, per totam fyftolem
sequalem pofui, quam ille valde inaqualem efie de*
monftravit. Verum a me nufquam Sanguini aequalis
data eft velocitas, fed pro fumma omnium velocitatum
mediam pofui. Sed utrum sequalis vel inasqualis eft
Sanguinis e Corde ejedi celericas, nondum fatis mihi
conftat; certe quae pro tequali velocitate flat ratio, ea
mihi in prsefens firmior videtur.

Sic emaculatis vitiis quae in primi noftra methodo
reprehendit vir Cl; quid in alteri quae fubjunda eft,
illi difplicet, videamus. Et eft certe affumptio ilia
quae a EmlliO) aliisque viris dodis f^pius ufurpata efl,

5 P a

( p<?8 )

nempe, quod fimilium mufculorum vires funt in ratio*
ne ponderum. Aliam virium racionem in Theoremate
po flabilire conatur Jurinius : fed cum ex communi
omnium fuorum Theorematum Principio oritur demon-
llratio, CO in muni etiam eorum fato involvetur ; Si e*
nim principium illud fallax eft, (ut mihi videtur^ nec
ad cafus ad quos adhibetur, congruit ; corruunt certc
omnia, quae hac bafi innituntur. Supponit Vir Clar :
Vaforum tunicas in Sanguinem intus contentum im-
petu irruere, 8c motus fui partem Sanguini itftu com-
municare : & hic in motu Cordis, vulc Ventriculum
tanquam folidum Corpus, data vclocitate motum, in
Sanguinem impingere, & idu motus fui partem illi
impercire: qux fuppofitio nec Sanguinis nec Cordis,
nec Aeris e Pulmone exprefli motui competit, nec ulla
minimorum iduum reiteratione, horum motibus ita
accommodari poteft, quin quae inde deducentur coni-
clufiones pro incertis & omnino falfis haberi debeant.

Cum inter Sanguinem & Cordis intimum nullum
intercedit fpatium, fed eft alter alteri contiguus, non
idu Itoc in ilium, fed preflu agic: nec ullam in initio,
fuse contradionis celeritatem ventriculi habent, fed (e.
contrahendo velocitatem tempore acquirunt, tanquam
gravia cadendo, vel ut fluida rarelcendo, ex quo forte
omnis vis Cordis oritur. Adeoque non acquabilis eft
motus contradionis, ut vult Vir Dodiflimus, fed eft
motus inftar cadentis acceleratus. Idem igitur eft dif
crimen inter idum quo Cor Sanguinem ferire vult3^«-
rinius, & prefluram qua Cor revera in Sanguinem agit,
quod eft inter adionem corporis foiidi moti & vim
gravitatis: fedipfofatente.hxccomparari nequeunt, adeo-
^ue preflura feu adio cordis in Sanguinem per idum nec
a Viro laudato expofita eft, nec unquamexponi poteft.
Hanc fentenciam confirmat ipfa Cordis potentia a Viro
Cb inventa*. Si, enim pondus dat^ veiocicate motum,

cordis

( 999 )

cordis potenti^e sequale eflet, tunc Sanguis omni vi
Cordis in pondus iliud dire£le impulfus motum ponde-
ris temporis momento deftrueret (ed quocunque mag-
no impecu ponderi occurrat Sanguis, nunquam illi
omnem motum in inflanti eripiet, adeoque eft hoc pon-
dere potentia Cordis minor, nec rede per motum pon-
deris vires Cordis exponuntur.

FJuidorum vires in corpora folida, ubique eodem
prorfus modo quoTolidorum vires in fe invicem, Juri-
mus aeftimat & perpendic, cum tamen maxima interfit
differentia; & ab hoc capice fluit quicquid eft in il-
lius Propofttionibus erroris. Ubi enim corpus folidum,
cujus partes firmiter inter fe coherent, in aliud impin-
g't, unaquxque corporis particula fimul & femel fuam
alceri vim impertit ; at res alicer fe habec in fluid i«“, in
queis nulla eft partium cohserentia, nulla fluidi pars,^
nifi in ipfo tadu, in corpus fibi oppofitum agit; idcir*
CO cum columna aquae adverfus corpus loliduni fur-
fum vercitur, parccs columnae a corpore remotiores
nullam illi vim imprimunr. Corpus etiam folidum
unicum folummodo ictum akeri communicat; at co-
lumna fluidi in corpus fibi oppofitum continue agit,
& minima columnar pars minimo temporis momento,
idum infinite parvum illi imprimit, eodem prorfus
mode quo gravia cadendo agunt, quibus igitur fluido- ^
rum motus rede comparatur. Porro omnis motus
corporis fdidi in alrerum direde impingentis in
temporis momento deftrui poteft : fed moms folidi vim
fluido imprimentiSi non nifi gradatim imminuitur, &
in dato tempore evanefeit, pari ratione, qua Gravitas in
corpus furfum miffum vim fuam exerit. Ex quibus
fatis abunde conftat, inter vim fluidi in motum adi,
& vim gravitatis magnam efle afRniratem, & unam per
alteram rede exponi pofle 3 vim au tern corporis folidi ad^
vim gravitatis. referri non polle. Cumque banc diff'e--,

rentiam

( tooo

rentiam non Tatis attendiHe videtur Dod^iffimus Jurlfilus]
a vero multum aberrafle mihi videtur. Si igitur fepo-,
fid fua, de Vaforum idu, hypothec, & vi preflurae,
qu^ Natura utitur, pro Principio adhibit^, alia Theo-
remara de Cordis & Sanguinis motu & viribus, elegan-
te fu^ demonftrationis methodo, conftruere dignabitur,
fefe dignum, mihi cerre grarum, nec eruditis inutile
praeftiterit. Tu, qui Rci Medico principatum tenes, Vir
Ampliffime, dilfentientium difputationes tua prudentia
ita moderari digneris, ne IndotHs ludibrio, fed ut Do-
(Stis emolumento efl'e pofTint. Dabam NorthamptonU
^3. die Junii 1719.

III. An account of feme Experime?its relating to the
Specific k Gravity of Human Hood, <By James
Juriiij M. D. and F. R. S,

IT is well known from the Obfervations of Mr<
Leeujvenhoek and others, that Human Blood confifts
of red globular Particles, fwimming in a pellucid Lym-
pha, or Serum. Which two different Subftances, tho*
of unequal Specifick Gravities, yet fo long as they con-
tinue to circulate in the Veins and Arteries, are pre-
vented from feparating by their Motion and Warmth,’
But when the Blood comes to ftagnate and cool in a
Porringer, the globular Particles uniting together by
their attractive Power, 'and finking by their Weight,
which is greater than that of the Serum^ form the
Coagulum, or Craffamentum, at the bottom of the Por-
ringer, the Serum fwimming above it.

Ihings always happen in this manner, when the
Craffamentum is at liberty to fubfide : but it often falls
out, that, either by its adhefion to the fides of the
yeflel, or by the bubbles of Air, which the Blood

. ^ gathers

)

( !00l )

gathers upon falling into the Porringer, and which
ftick to it s Surface, the CrA^Amentum is kept from fink-
ing, and Teems to float upon the top of the Serum,

Thefe Accidents Teem to have given tiie firft occa-
fion to that Opinion, which, I think, has been gene-
rally entertain'd by thole who have writ upon this
Subjed:, namely, that the globular part of the Blood
is fpecifically lighter than the Seram, in which it
fwims.

But that which has fo fully eflablillit this perfua-
fion, is the Authotity of the late excellent Mr. Boyle,
who, among the many valuable and curious Experi-
ments he has given us in his Natural Hiftory of Human
Blood, has left the following ones upon this Subjed.

The fpecifick Gravity of Serum of Human Blood
was found by weighing a piece of Sealing Wax firll in
Serum, and afterwards in Water, to be to the fpecifick
Gravity of Water, as 10x4 to 1000.

In a fecoiid Experiment, which for grpter accuracy
was made with an Inflrument contriv’d* on purpofe,
the fpecifick Gravity of Serum was found to be to that of
Water, as 1194, to 1000.

In a third Experiment made by the fame Inflru-
ment, and with Serum from the Blood of another Per-
fbn, it’s fpecifick Gravity appear’d to be 1186.

The Medium between thefe two lalt Experiments is
1190, which has fince been univerfally receiv’d for the
fpecifick Gravity of Serum of Human Blood, the firfl
Experiment being declar’d by Mr. Boyle himfelf to be
lefs exadly made than the other.

The fpecifick Gravity of Human Blood was found
by Mr. [Boyle, to be to that of Water, as 1040 to 1000 ;
though on account of difficulties by him mention’d,
he was far from being fatisfy’d with this Experiment,
and recommended the thing to farther tryal5.

Thefe

( 1002 )

Thefe Experiments however having hitherto pad
uncontroverted, and it appearing from them, chat the
fpecifick Gravity ot Serum was greater than that of
Blood in the proportion of 1190 to 104O or of 8
to 7 nearly ; it was a necdfary confequence of rhis,
that the Blood Globules were fpecificaliy lighter than
the Serum, and that in a very great degree, confide-
ring the fmall proportion, that the bulk of the Craffa-
mentum was found to bear to that of the Strum, {tova
other Experiments.

From this it was not improbably conjedured, that
thefe Globules were thin Veficles fill’d with an Aereal
fubftance : and this Opinion feem’d to receive a great
confirmation, upon it’s being obferv’d, in viewing the
Circulation by a Microfeope, that a Blood Globule, in
pafiing through a very narrow Vefiel, would change
its fhape from a Globular to an Oval Form, and would
recover it’s former Figure, as Toon as it was got thro’
the narrow Paflbge; which appearance feem’d to be na-
turally accounted for from the Elafticity of the included
Aura.,

Upon this conjedure have been built a great many
Solutions of the Fhxnomena oblcrvable in the Animal
Oeconomy, and the dilbrders of it ; particularly a late
ingenious account of Mufcular Motion, It it net my
bufinefs at prefent to examine any of thefe, nor is it
my defign to cad any refledfion upon their Authors,
who were led into this miftake by the natural confe-
quence of a matter of Fad, for the truth of which they
had To great an Authority, as that of the excellent Per-
fbn above-mentioned. But I hope, I lhall eafily be
pardon’d for enquiring into the found nefs of the
Foundation, when the Superftrudure ereded thereupon
is fo confiderable ; and the following Experiments,
however trivial in themfelyes, will not appear unworthy

the

( lOOJ )

tlie confideracion of the Royal Society, if it be found,
that they may prevent us from running into Errors of
the greateft ccnfequence.

Exp- 1. 1 have feveral times cut off a fmall pare

of t\\Q Crajfamefitum, when by its adhefion to the Tides
of the Porringer it has Teem’d to fwim upon the Sur-
face of the Seruw, and have put it into another Vef^
fel fill’d with S'rum : upon which it has immediately
funk to the Bottom.

Exp. II- When the Coagulum has been buoyd up in
the Serum by the bubbles of Air adhering to its Sur-
face, I have Teparated a fmall part of it, where thofe
Bubbles have been thickeft, and put it into a Glafs of
Serum> in which it has fwom, as before. Then letting
the Glafs upon the Air-Pump, thofe Bubbles burfi; af«|
ter one another, as the Receiver was exhaufling, and
the Air being again let into the Receiver, the lump
of Cra([amer)tum funk to the bottom of the Glafs.

Exp. Ill I have often placed a drop of Serum upon
a clean Glafs before a Microfeope, in which I had
diflblv’d a very fmall quantity of Blood, and obferv’d,
that when the Glafs was held in a perpendicular Po-
fture, the Blood-Globules fubfided to the bottom of
the Drop ; and inverting the Glafs, the Globules again
defeended thro’ the Serum to the Bottom. I had the
^fame fuccefs with a fmall quantity of Serum and
Blood in a Capillary Tube, And the fame thing has
been long fince obferv’d by the famous Mr. Leeumn-
hoek.

Thefe Experiments undeniably demonflrate, that the
Cra([amentum, or globular part of the Blood, is fpecifi-
cally heavier than the Serum; and confequently it is
by no means probable, that the Blood Globules are
Veficles fill’d with Air, or any other Fluid lighter than
Serum. And that they are not fill’d with any fort of

9 0^

f 1004 )

Elaftick Fluid, will appear from the following Experi-
ment.

Exp.W. In a fmall quantity of Serum o{ Human
Blood, I dillblv’d fo much Blood, as that the Globules
might not lye too thick together, to hinder their being
feen diftin(^Iy. Then having lodged a fmall drop of
this Liquor on the infide of a thin Glafs Tube, I fitted
the Tube on to the Air-Pump, and placed a MicroB
cope by it, fo that I could fee the Blood>Globules
through the Tube. This being done, I caus’d the
Tube to be exhaufled, keeping my Eye upon the Glo-
bules all the time, in order to obferve whether they
dilated themfelves, as the Air was withdrawn ; but
could not perceive the lead alteration, they appearing
exadly of the fame bignefs in the Facuum^ as they
had done before. Whereas if they had been fill’d with
an Elaftick Fluid, they would either have burft, or
have been dilated to at lead 70 or 80 times their
former Magnitude. The Stop- cock being afterwards
turn’d, and fuffer’d to re-enter the Tube, the

Blood-Globulesdillretain’d the fame bignefs, as in Facuo,

To this it will perhaps be objedled, that a learned
Member of this Society, in a Book lately pubiifh’d, has
aflerted the diredi contrary to what I here affirm, and
has afiur’d us, that the Blood’Globules in an exhauded
Receiver, indantly fwell, and dilate themfelves fo, as
to become incredibly large. But as that Gentleman
does not tell us, upon what Experiment this affertion
is grounded, it may not be unreafonable to fuppofe,
that he was milled by the common Hypothefis, which
he there maintains, of the Blooa-Globules being fill’d
with Air, and by what he has heard or feen of the
bubbles of Air, which arife from Blood in the Air Pump in
the fame manner as from other Liquors, and which not
cafily breaking out from fq a Fluid; cccafion

( 7ooj )

the appearance he mentions. Howevir this may be*
to prevent any difpute, and avoid the coming to
Utri creditis, Omrites > I fhall offer a Teftimony, that
every body will be fatisfy’d with, namely that of the
learned and ingenious Mr. Machin, Profenor of Afiro^
mm'j in Grcjham CoUedge^ and one of our Secretaries,
who having honour’d me with his Company at a re-
petition of this Experiment, in order to be witnefs to
the Event, was fully fatisfied upon repeated tryals,
that there v/as no perceivable difference between the
Magnitude of the Blood Globules in the Air, and in
Vacuo. Upon this occafion the two firfl: Experiments
were likewife repeated in his prefence, with the fame
Succefs, as above related.

Though what has been already faid is a fufficienc
proof of the Opinion above- mention’d, yet however
to prevent the Objedbions, which may arife for want
of Experiments made in the fame manner with Mr.
Boyle% as well as for the fatisfadion of the Curious,
who may be defirous to know the true Specifick Gra-
vities of Serum and Blood, I lhall proceed to demon-
ff rate^ the fame thing by Hydroftatical Experiments.

Exp. V. Novemh. 13. 17 13. Having fuffer’d a quan-
tity of my own Blood to Hand about 24 Hours in
the Porringer, and then drawing off the Serum carefully
with a fmall Siphon into a convenient Glafs, 1 found
by the Hydroftatical Balance it’s Specifick Gravity to
be to that of Water, as 1029,8 to 1000^

Exp, Vf* Feh, a 1. 1716-7. I examin’d the Serum
from the Blood of another Perfon in the fame manner
and found it’s Specifick Gravity to be 1028,6.

Exp.Vll. VIII. and IX. April 8th, 1717* I obtain’d
three feveral quantities of Serum ftom the Blood of
different Perfons. The firfl: of thefe wasj of a deep

9 0^2 colour.

( Too^ )

Colour, inclining fomething to red, and a little Turbid.
It’s Specifick Gravity was 1019, 7.

The fecond was likewife a little Turbid, and of a
pale whitifli Colour. The Specifick Gravity of this
was 1030, 2.

The third quantity of Seram was perfedly clear, and
of the colour of Canary. It’s Specifick Gravity was
found to be 1050.

Though thefe five feveral Experiments were all care-
fully made, and with a Balance whofe accuracy I. was
well afiur’d of, yet for farther Evidence, I thought it
proper to make that which iollows, after another man-
ner.

Fxp. X. lyth. 1718-9. I drew off* all the
Serum from five or fix feveral Porringers', containing the
Blood of different Perfons. This I found to be a lit-
tle tinged with Blood, which was occafion’d by my
being oblig*d to draw it off pretty near to the bottom
of the Porringers, in order to obtain a quantity (uffi-
cient for my purpofe. For this reafon I fuffer’d it to
Band about two Days, in which time the Globular
part of the Blood was entirely precipitated to the Bot-
tom, and the Seram was become perfeBrly fine and
tranfparent. I then drew it off with a Siphon into a
Glafs Vial with a narrow Neck, which 1 fill’d to a
certain mark made in the Neck for that purpofe.
This done, I plac’d my Vial in a nice pair of Scales,,
in which I had a counterpoife for the \yeight of the
Vial, and found that quantity of Serum to weigh
Grains.

^ Then pouring out the Serum, I fill’d the Vial with
common Water to the fame mark, and found the
weight of the Water to be Grains.

From which it follows, that the Specifick Gravity
of this was 8029,4.

%

( 1007,)

Exp, XI. July 14. 1 71 9. I procur’d a quantity
of Blood taken from the temporal Artery, from which
I drew off the Serum the next Day, 'and weighing it
in the fame manner found it’s Specifick Gravity to be
I0i8, 8.

Thefe Experiments agree fo nearly together, that
the little difference between them may very well be
attributed to that which is between the Serum of dif-
ferent Perfons; or to the variations occafion’d by heat
and cold in the feveral Seafons of the Year, in which
they were made. So that from them we may fafely
determine the Specifick Gravity of Serum of Human
Blood at a Medium to be 1019, or in a round num^'
ber lojo. From which the greatefi: Variation in any
of thefe Experiments is little more than one in 10005
whereas the difference between Mr. Boyle's Experiments
and mine amounts to 160 in 1000.

Exp, XI k ^pril 6. 1717. In order to find the
Specifick Gravity of Human Blood, which, by reafon
of it s tenacity, and fudden alterations upon {landing,
cannot be determin’d by the Hydroftatical Balance ; I
took a narrow* neck’d Vial , and fill’d it to a Mark,,
with Blood pour’d immediately out of the Porringer,
as foon as the Perfon was blooded. This 1 weigh’d,
as I had done the Serum before, and found it’s Speci-
fick Gravity to be 105'r.

Exp. XIII. Aug, 5th. 1717. Having fill’d the fame
Vial with the Blood of another Perfon, running im-
mediately out of the Vein through a Funnel, it’s Spe-
cifick Gravity was determin’d at 1053.

Suffering this to (land till it was cold, I found the
Blood was funk a fmall matter below the Mark in the
neck of the Vial. This being fill’d up with the Wa-
ter, w’hich in fb fmall a quantity could make ao fenfi-

ble.

{. ioo8 )

tie difference from Blood, I found the Specifick Gra-
vity of cold Blood to be

Exp, XIV. /iug. 6th. 1718. The laft Experiment
being repeated in the fame manner as the Year be-
fore, the Specifick Gravity of cold Blood was again
found to 1055'.

£x/>. XV. 14th. 17*9. The Arterial Blood,
from w'hich the Serum w^as afterwards drawn off for the
iith Experiment, being w^eighd in the fame manner,
it’s Specifick Gravity was 1051,

As this Arterial Blood and it’s Serum, differ no more
in Specifick Gravity from Venal Blood and Serum,
than the feveral Portions ot thefe do from one ano-
ther, it’s plain, that the difference in this refped be-
tween Arterial and Venal Blood is wholly inconfide- '

rable. The Animal Oeconomy indeed teaches u% v

that the Serous Liquor is perpetually drawing off .
from the Arterial Blood by the ieveral Secretions, but
as the quantity feparated in one Circulation is very ♦
fraall, the Blood muft arrive in the Veins nearly of
the fame denfity, as when it runs through the Arte-
ries.

In the 15th Experiment we obferv’d, that the Blood
altered it’s Specifick Gravity upon cooling from icyf3 ^
to 1055; ^t:otn which we may infer, that if the Blood '
made ufe of in the nth Experiment had beenfuffered
to Band till ir was cold, it’s Specifick Gravity would
have been 1053 5 wherefore, taking a Medium be-
tween the four laft Experiments, w'e may allow the
Specifick Gravity of cold Human Blood to be 1054.

The difference of 14 Parts in a 1000, between this
and the Specifick Gravity determined by Mr, Boyle, is
eafily accounted for, if we confider, that that Gentle-
man did not make ufe of a Veflel with a narrow
Neck, as plainly appears from the circumflances men* .

tioned

it

( loop )

tioned in his Experiment; and confequenriy a fmall
error in the height of the Liquor would make a confi-
derable alteration in the Specifick Gravity.

Since therefore the Specifick Gravity of Human Blood
is lo^q, and that of its Seruw 1030, it is plain, that
Blood is heavier than Serum by about one part in 43.
From which it manifedly follows, that the Globular
part of the Blood is fpscifically heavier than the Serum,
fince the Globular part being feparated from the Blood
leaves the remainder, or the Serum) fpecifically lighter
than the intire Mafs.

But in order to determine the exadt Specifick Gra-
vity of the Blood Globules, it is firft necefiary to know
the Proportion, which the whole quantity of the Craf.
famentum contained in Blood bears to the Serum. To
this end Mr. Bo^le has given us two feveral Obferva-
tions of the weights of the Crajfamentum and Serum, af-
ter they have feparated one from another in the Por-
ringer. But befides the difficulty of making this Ex-
periment with any tolerable exadfnefs, it is to be con-
fider’d, that there is a great deal of Serum contain’d in
the interftices of the Globules, that compofe the Crajfa-
mentum.

This difficulty however is in fome meafure anfwer’d
by two other Experiments, which Mr. Boyle made for
this purpofe, after the following manner. He put a
quantity of the Craij'amerrtum, already feparated from
the Seram, into an Alembick, and diftill’d off the re-
maining Serum to drynefs, but without drawing off the
Oil, or Volatile Salt ; after which he weigh’d the di-
ftill’d Liquor, and the dry Mafs left behind.

By comparing, thefe Experiments with the two for-
mer, it will be found that the entire weight of Serum
contain’d in Blood is nearly If of the whole, and con-

fequently

1010 ;

confequently the weight of the dry’d is

only two fifteenths of the Blocd*

But for farther fatisfadion, an Analyfis was made
at ,my defire with a large quantity of Blood, amount-
inn to four Pounds fcuitcen Ounces, by that ingeni-
ous and skilfull C hymiit, Mr. John Brown.

From tills was obtain’d, with a very gentle heat, two
Pounds, fourteen Ounces , and fix Drachms of a
Phlegmatick Liquor, that had fcarce any thing of the
fetid Scent, which is ufual in the difiilJation of Ani-
mal Subftances; and its Specifick Gravity was nearly
the fame with that of common Water, being but
I oo, 8. This being mixt with a (trong folution of
Alum, fcarce a.Torc’cd zny Coagultim but exhibited a
confiderable one upon mixture with a folution of Ro»
man Vitriol.

The difiillation being continued with the fame
Hear, we had feven Ounces more of Phlegm confide-
rably impregnated with Volatile Salt, as was manifefl:
from the Smell. The Specifick Gravity of this was
1007, and having mix’d it. with Tindiura Martis opi-
ma. Solution of Alum, and of Roman ViinoX,' a large
Coagulum was precipitated. In diflilling thefe there
was loft by Evaporation, two Ounces and two Drachms.

The third portion of Liquor, being rais’d with a
ftronger Fire, amounted to feven Ounces fix Drachms.
This was reddifti, and turbid, and to ftrongly charg’d
with Volatile Saits, that it might very well defer ve
the name of Spifir. Its Specifick Gravity was »o8o, i.

Befides thefe we had feven Drachms of Volatile
Salt, an ounce of Oil, and eight Ounces four Drachms
of Cafut Mortuum, which ftill retain’d fome fraall re-
mainder of the Oil, as was manifefl: from its taking
Fire at the flame of a Candle. In this latter part of
the Operation was loft three Ounces, feven Drachms.

! Upon

( 'Oil )

Upon making due allowance for the diflerence be-
tween the Specifick Gravities of the three firft Portions
of Liquor and that of Seruw^ as likewife for what
was loft in the two feveral parts of the Operation,
which we may reafonably conclude to have been of a
Specifick Gravity nearly the fame with that of the Li-
quor drawn off, it will be found, that the quantity
of Serum contain’d in this Mafs of Blood was about ^
of the whole VVcighc, and confequently that the quan-
tity of Craffmentum was .7 of the fame Weight.

If we calculate therefore upon this Suppofition, that
the weight of the Globular part of the Blood is ~ of
the whole, we fhall find the Specifick Gravity of a-
Blood Globule to be to that of Water as 1177 to rooo.

If we follow the proportion of ,7, which refults from
Mr. Bo)le*s Experiments, the Specifick Gravity of a.
Blood Globule will be 1241.

But this computation is in all appearance a great’
deal too large ; for we cannot be affur’d, that our
whole quantity of aqueous Liquor was rais’d from the
Serum of the Blood. On the contrary it is more than
probable, that a confiderable part of it was afforded
by the Blood Globules themfelves, efpecially in the'
latter part of the Operation, when their texture muft of
neceffity have been broken and diffolv’d by the ftrong'
Fire that was made ufe of. To prove this, we need
only confider the condition of the dtyd^Craffamentum,
after the Fhlegm is drawn off, chat being now a hard
and brittle Subftance : whereas the Globules in their
natural State are fofe and yielding. For which reafbns'-
ic may perhaps be more facisfadory , if we at-
tempt to find the quantity of the Globular part of the
Blood after another manner.

k appears therefore from Mr Boyle's Obfervations,'
that the quantity of Serum, w’hich may be pour’d off

^ R from V

( 1012 )

5from the Craffamtntum^ is about one half of the whole
Mafs. The remaining Crajfamentum confifis of the
Blood Globules, and a quantity of Serum filling up the
Interftices between them ; which, if the Globules keep
their Spherical Form, may eafily be found by the prin-
ciples of common Geometry, to be nearly one half of
the bulk of the Craffamentum: but if the Globules by
their prefTure againfl one another change their Figure,
the quantity of Serum will be fomething lefs.

If this quantity of Serum lying between the Blood
Globules be added to that pour’d off. it appears, that
the Serum contain’d in Blood is about *- of the whole
bulk, and confequently that the Blood Globules make
about ~ of the whole. From which we ftiall find the
Specifick Gravity of the Blood Globules to be to that of
Water as iix6 to looo.

If we fuppofe the Blood Globules to make f,
or I of the whole bulk, their Specifick Gravity will be
refpe<3ively 1174, 1150, noz, or 1078. So that
upon any of thefe Suppofitions, the Specifick Gravity
of the Blood Globules will be confiderably greater than
that of the Serum, and confequently they cannot be
fuppos'd to be Veficles fill’d with an Aereal Subftance.

It will therefore perhaps be>askt, What do they re-
ally confifl of ?

In order to come to a Solution of this Quedion, it
may be proper to take notice.

That Blood is compos’d of Phlegm, Oil, Volatile
and fixt Salts, and Earth. For as to the Spirit, we
look upon it with Mr. Boyle, to confift of the Phlegm
and Volatile Salt united together.

That the Serum, upon a Chymical Analyfis, exhibits
a great deal of the firft of thefe, and the others in a
Tery fmall quantity.

That

( lot^ )

That on the contrary the Crajfame^taf?t yields muchi
iefs Phlegm, bat the other Principles muchi more co-
pioufly than the Serum.

From which Data^ I think, we may fafdy conclude,,
that the Craffamentum, or Globular part of the Blood,
confifts of fome Phlegm united with the Oil and
Salts, and a fmall quantity of Earth

But what is the exaifi proportion of thefe feveral
Principles to one another ; what alterations are produ--
ced in the Body by a change of this proportion ; how,
and in what part thefe Globules are form’d ; by what
means they preferve their Figure, without difiblving in
the Serum, or uniting with oiie another ; what varia-
tions are made in their Specifick Gravities by Heat and
Cold ; and what are the efFeds of thofe Variations,
are Queftions not very eafy to be folv’d, and yet of
lb much importance to the Animal Oeconomy, that
it were greatly to be wiflit, we had a number of Dafa
fulEcient to determine them.

F. S. Since this F^per was lent to the Prefs, I made
the following Experiments, which ferving to confirm^
the Method lad made ufe of, for finding the Specifick..
Gravity of the Blood Globules, it may not be impro^
per to relate them.

Augufl 6 1719. I took a lump of the Craffamen^
ium, and walk’d it gently in fair Water, to free it
from the loofe Globules, which precipitating out of
the Scrum, after the Coagulum is form’d, do not unite ■
into one Body with it. This done, I laid it on
fpungy brown Paper, in order to drain off the fuper-
fluous Moifture. After which, weighing it firft: ins
Air, and then in Water, I found its Specifick Gravity
to be

9^ R z

Anothetr

( 1014 )

Another lump of the lame Craffamentutn being weigh’d
in the fame manner, its Specifick Gravity was Ic8^.9.

Sept, 1 8. 1719. I found the Spec fick Gravity of
another piece of Cra(famentum to be loSx.i.

A fecond piece from the Blood of a different Per-
fon gave me 1086,1.

A third from the fame Perfon gave 1086,6.

From this it follows that the Specifick Gravity of
the Blood Globules is at lead 1084, whicli is the
Medium between thefe five Experiments.

But if we allow one half of the bulk of the Crajfa-
mentum to confifl: of Serum^ filling up the Spaces be-
tween the Blood Globules, we fhall find their Spe-
cifick Gravity to be 1138.

From this we mud make a fmall abatement, becaufe
fome part of the Serum mud have been (quees’d out
from between the Globules, by their yielding to one
anothers Preffure, when the lump of (Cra(famertum lay
upon the Paper : and this will reduce their Specifick
Gravity fufficiently near to ^I^6, as we had before
determin’d it.

IV. Jn Accomt of the Sunk Ifland in Humber,
fome Tears fince recover’d from the Sea, (Being
an ExtraH of a Letter Communicated to the
Royal Society hy John Chamberlayne,

R. S. S.

THis Idand goes by the name of the Sunk

fo called 1 luppofe from the finking Marlh Ground
about it. As for its Original, one may make pretty
dire Conjecdures of that I believe, becaufc ’tis yet with-
in

( *015 )

in the memory of Man, fince it began to raife its Head
above the Ocean, there being ieveral old People here
alive, who can remember when there appeared nothing
of it but a waft and barren Sand; and that only at
Low-Water too, when for the fpace of a few Hours it
(hewed its Head, and then was buried again till the
next Tides Retreat : thus fucceflively it liv’d and died
until the Year 1666, when it began to maintain its
ground againft the infult of the Waves ; about which
time it began to be refcued wholly from future dan-
ger, by the Care and Induftry of Colonel who

having, as 1 am imform’d, a Leafe or Gift of it from
the Crown, did raiie Banks about the rifing Grounds
of it, and fo defending it from the Encroachments of
the Water, it became Firm and Solid 5 and in a Ihort time
afforded good Pafturage for Sheep and other Cartel.
The Expences at firft to improve it to what it is,
muft needs have been very confiderable ; it being en-
compar’d with high Banks, and deep Canals for re-
ceiving and difcharging the Liquid Element, which
every now and then nocwithftanding threatens to re*pof*
fefs it felf of its ancient Hereditament, but hitherto in
vain; for I now acquaint you of its prefent Safety.

This Ifland is now about 9 Miles in Circumference,
within the Banks, which Teem to render it impregna-
ble againft all future attacks of the Sea, and is of a
very fat and fertile Soil, affords good Graft, Corn and
Hay, and is repleniihed with numerous flocks of Sheep,
which are of a larger Size and finer Wool than thofe
in Holdernefsi from which it is divided by about two
Miles in Water ; and from Lincolnjhire by about four, k
is ftor’d with vaft numbers of Rabits, that feem innu-
merable, they appearing through all Parts in prodigious
Swarms; their Skins are counted the fincrt in England,
of a dark Moufe Colour, Shagg’d, and foft as iilk.

1 here

( 1016 )

There are alfb Cows and Horfes feeding con-
dandy in the Place, with great plenty of Wild Foul.

The Inhabitants are not fo numerous, there being
only three Families that live conftantly upon the Place;
however they are never too folitary,there being abundance
of Workmen and Labourers that continually refort thi.
ther, fometimes I am told to the number of a Hun-
dred and upwards, for the repairing of the Banks,

The Yearly Income of the Proprietor Mr. G/%, a-
mounts to about 800/. and pays the King’s Taxes to thofe
who Colletd for the EaH»Riding^ and is ufually uplifted
by thofe of the Liberty and Townlhip of Ottringhum,
from the Marlhes of which there is a Paflage over the
Sands to the Sunk at Low-water. But this Cuftom of
paying the King’s Cefs to them, proceeds only from
the conveniency, not NecelTity 5 for it never belong’d
to that or any other Parifh, fo that I cannot refolve
you in what Diocefe this (Band lyes, unlefs it had
been united to feme neighbouring Parifh, or converted
to one of it felfj which if effeded, the Tyth of Lambs,
Wool and Habits, &c. would make up a handfbme
BeneHce. It lyes nearer indeed to the Diocefe of
Torkt by at lead two Miles, than to that of Lincoln,
being two Miles South of Holdernefs, in the River
Humbtr, and four Miles North of Lincoln(hire,

Wehick, April 14.

1717*

V. A

I

( 1017 )

V. A IVay for Myopes to ufe Telefcopes mth»
out Eye^GlaJfes, an ObjeEi-GlaJs alone becoming
as ujeful to them, and fometimes more than a
Combination of Glides. Com?nunicated to the
Royal-Society, by J, T. Defagu-

liers, LL. D. and F. R. S.

Lemma i:

WHat is requir’d of a Telefcope is to give large,"
and diftind Vifion ; that is, to make the Ob*

; ]eGc (as in GaliUds Telefcope) or its Image (as in the
Telelcopes made up of Convex Lentes) appear under
a great Angle, and to have all the Rays of thofe Pen-
cils that enter the Eye, meet in a point upon the /ir-
tina of the Eye, on their refpedive Axes.

The firft Figure reprefents the Combination of two
Convex Lentes for the Aftronomical or inverting Te*
lefcope; where the above-mentioned Requifites are ob-
tain’d. A B is the Objedl fuppos’d at a vaft diftance
from the Oje<iiive Lens LL, fo that Rays coming
from the extremity A of the ObjecSt, will fall upon the
Lens L L, in the fame manner as if they were paral-
lel to their Axis AX; and after palling the Glafs u-
nitd at a, where they projed the Image of the Point
A ; from whence diverging, they fall on the Eye-
Glafs //, and having pafs’d through it, go on parallel
to each other, and enter the Cornea, of a common Eye E,
which unites thofe parallel Rays upon its Retina R R R
at a, where the Image of a is projedcd : The fame
may be faid of the Rays that come from B, and after

their '

V

( ioi8 )

their feveral refradions through the two GlafTes and
the Coats and Humours of the Eye, meet upon the
Rttlnx at /3, where they projed the diftin<3 Image of
the Point h. The Rays that come from all the Points
of the ObjeQ: A B being afFedled after the fame man-
ner, give a diftindt Image of thole Points upon the
Retina, and therefore the Objedf does appear diftin(5.

The Objedt will alfo appear magnified in the fame
proportion as the Angle IQI=. lo blA a ( under which
its Image is feen J is greater than the Angle A C B un-
der which the Objedl AB would be feen by the naked
Eye ; as is more at large deraonflrated by Dioptrical
Writers.

Lemma i.

If parallel Rays fall upon the Cornea of a My ops, or
fhort-fighted Perfbn, they will unite in the Eye, before
they come to the Retina, the farther from it the more
Convex the Eye is ; but if the Rays which fall upon
the Cornea diverge in proportion to the too great Convc«"
xity of the Eye, as from D, fuch Rays will be fo refra-
dled by the Coats and Humours of the Eye as to meet
in one point upon the Retina RR, (cc Fig. z and 3.
Where I have in the Scheme negledfed the Refradfion
of the Rays paflTing out of the Cryftalline 1C into the
treous Humour V, as 1 do in the other Cafes-

This Lemma is alfo demonftrated by Dioptrical
Writers.

Lemma 3.

If two Pencils of Rays ( in each whereof all the
Rays are parallel to the Axis, as a C) fall upon diffe-
rent Parts of the Cornea, at the greateft difianre from
one another that can be allow’d for thofe Rays to en-
ter the Pupil PP, their Axes will, after encring the.

Aqueous

( » 0I<> )

A<\»ms Humour, converge, and .meet cither in the
Vitreous, or Cryftallihe Humour, according to the
Convexity of rhe CornzA thro’ which they pafs^d, and
diverge again before they come to the Rttim ; the
Rays of each Pencil converging upon their refpedive
Axes, to the place where the faid Axes crofs one ano-
ther, Fig,

Dmonjlration,

The Axes aQa, aCa, falling obliquely upon the
(Cornea at C,C, and entring from Air into the Aqueous
Humour, will be refraded towards the Perpendicular
to K : v/here ftriking more diredfly upon the Cry-
flalline , they will go on to a, a, upon the Retim
R R R R, decuflating at V within the Vitreous Humour,
The other Rays r, r ; js, after their Refradion in the
Aqueous Humour, fall more obliquely on the Cr^jlalline^
and therefore are refraded again fo as to meet at V,
where the Axes alfo meet, and thence go on to the Re-
iina R R R R, Fig. 4.

Lemma 4,

But if the Axes of the above-mention’d Pencils are
Parallel, the Rays that accompany them diverging
from a Point fo near the Eye, that the divergence may
be proportionable to the too great Convexity of the Eye ;
then only the Axes will meet in the Eye before they
come to the Retina (by Lemma j.) but the other Rays
will not unite upon their refpedive Axes^ till they
come to the Retina ^ (by Lemma 1.)

Fropo/ftion,

I fuppofe the Eye of the Myops fo Convex that he
can fee no farther than a common Eye, with the Eye-
Glafs of a Tekfeope before it ; then the Eye of the

p S Myops

( 10 zo )

Mpfs being in the place of the Eye*Glafs, will receive
the Rays diverging from the feyeral points of the Image
f projected by the Obje<^-Glais in yx^ Fof^s,) in fucb
manner, that they will after their fevcral refra(9ions
meet in refpedive Points on the Retina^ and the Axes
of the Pencils which come from the extremities of the.
ObjetS, will, in the Eye, make the Angle B V A =: to
h ca, under which the Image ah feen, by Lemma 4.
The Cornea and (pilous Humour here fupply the
place of the Eye-Glals, and the Cryflallwe and Fitreous
Humours that of a common Eye, See the 5th Fig,
wherein R is the Retina^ V th? Fitreoua Humour, and
KK the Crjfialline Humour; and the Image ha isfup--
pos’d to be brought down from the Jfrfi Fig. which re-
prefents the Ajlronamick Tele/egpe: the too great Con-
vexity of the Eye here being in the place of an Eye—
Glafs.

An Objeeflion may be made to^ this, viz. that P P ‘
the Pupil of the Eye being fmall, will take in but a ve-
ry little Image, or a fmall part of the Objed : - But
then if the Eye be mov’d fuccelTively, to all the parts
of the Space where the Eye-Glafs was, it can take
any part of theObjed; and if the Ob jed- Glafs be
large, which may more eafily be made than a large
Ey€*GlaIs, and the Tube a Foot wide or wider, as
much may fucceflively be taken in, as if an Eye-Glafs
might be had of a Foot Diameter. A little ptadice
may make any /kljops fo ready, to k^ep an Objed:
when once found, though: the placo - where- he fland^
be (haken. . It would not be amils. to hold a in
one’s Hand (for an Eye-Glafs) to find the Objed at .
firft, tillcuftomhas madeitcafy without it : \^hen once
the Object is foundi it ma^'he. eafily kf^c^ , • ;

An- Eye mote thort-figbied than );;}ha\e.ifuppos’d, ■
will perform 'thei Office., oE a Ey^> Glafs,

being

C loii )

being brought nearer to the diftin^t Bafe of the Ob-
ject Glafs ; and an Eye lefs Convex, the office of a
lefs Convex Eye-Glafs : but with this difference, that
the more Convex the Eye is, the eafier may any part
of the Objed be found, and the larger and more
lucid it will appear.

I have feen Sattirns Ring very plain with an Ob-
jcd*GIals of little more thart fix Foot Radius^ without
an Eye-Glafs.

I have alfo found out a way for the Prefb'jtx to
make ufe of an Objed-Glafs, by placing their Eye
nearer the Lem than its Focus^ by fb much as their Eye
is flatter than a common Eye, fo as to make ( as it
were) the Telefcope of GaliUo ; the fiat Eye ferving
as a common Eye arm’d with a Concave Lem. I have
fo fixed the Telefcope, as to make a Prefbjta read at a
great diftance a fmall Print. The truth of this may
be eafily demonfirated, if it be requir’d.

If this Experiment be made at bea with a very large
Tube, big enough to put in the Head and move it
about, and the ObjedGia.fs be alfo large, it may not
perhaps be difficult to obferve the Eclipfes of the
Satellites of Jufiter^ which I would recommend to the
Confideration of thofe that would try for the Longi*
rude by fuch like Obfervations.

VI. “Hew and accurate Tables for the ready Compu^
ting of the Eclipfes of the firft Satellite of Ju-
piter , by Addition only. <By the Reverend
Mr James Pound, R. S. S.

IN ISumb. 2iq. of thefe TranJaSfions, for the Months
of tLovem and Decern. 1694. exhibited an Epi-
tomy of Mt.Caffims curious Tables then newly pub-

9 S ^ liflied.

( J022 )

lilhed. for computing the Eclipfes of the Jirfi Satellite
oi Jnpiter, without the heip of any other Numbers.
The eafe of this Calculus gave great fatisfadion to thofe
that delight in Telefcope obfervations ; and has been
of good uie to encourage Aftronomers to afcertain the
Geographical'Longicudes of many places, by help of
thefe Eclipfes; whofe frequency feeras to afford us thc.
propereff means for that purpofb.

But it being now Years fince thofe Tables were
publifhed, length of Time has difcovered that this Sa-
tellites motion is a fmall matter fwifter than M. Cajftni
had fuppofed it; and the Reverend Mr. Pound being
provided with all the Qualifications requifite for fuch
a Work, has of late apply ’d himfelf to reif ify by fre-
quent Obfervacion what he found amifs in the afore*
laid Calculus ; and withal has put it into another Form
yet much more eafy and compendious, by bringing
what M. Caffini had given us in odd Numbers, to the
Millefimals of a Circle, both as to Numb. 1.. which he
calls Numb, A. being the mean Anomalie of Jupiter in
fuch parts; as aUb to Numb. IE or our Numb. B. which
is the diftance of the mean place of Jupiter, frqm the
true place of the Sun, and which with the addition of
the Equation of Numb. B. gives the true angle of
Commutation in the fame Millefimals of a Circle. And
having dedudfed from the Epoches the greateff Equa-
tions both of Numb- A. and B. he reffores them by ad*-
ding as much to the Equations themfelves, by which
means they all become Affirmative, fo that the whole
computation, is performed by Addition only.

The Reader is fuppofed to be acquainted witb the
Method of M. CajhnPs Calculus, which is at large ex-
plain’d in theaforefaid Tranfaciion, Num, 214. For which
reafon this ffioner Defeription may fuffice at prefenc.

E P 0 C H M

( 1013 )

Epochit ConjunBmum ’Primi Satellitis Cum JoVe.

An.Jal

Cnrr

D.

conjunct,

H

,,

Num.

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Num.

B.

An. Jul.
Curr.

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Revelu,

( T014 •)

•f^^evolutiones Tritni Satellitis JoVis in menjibusl

'fanuarii.

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Nu.

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23P

( jojy ) -

^yolutiones J^rlm Satettitis ^oVis M men/lius,

N.

Nu.

Maii.

N.

Nu.r

D. h. , ,,

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I OSiobris*

\

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( i027 )

(^Volutiones frimi Satelihis JoVis in menjlhus.

OBobris.

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Nu.

D. h. , „

A.

B.

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63

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Nu.

D. h. , „

A.

B>

16 8 i6 29

74

799

i8 2 45 5

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21

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21 IJ 42 16

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0 12 J 16

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( 1028 )

prhfite ^quationes ConjmiBionmn Prmi Satellite

cum Jove,.

Xquat.

!®9

A-quat.

XEq

/Equal.

iEq

/Equal,

/Eq

Num.

Conjun.

Nu.

Num.

Conjun.

Nu.

Num«

Ccnjun.

Nu.

Nuir.

Conjun.

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A.

Addc,

B

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Ths

( J03* )

The life of the foregoing TABLES.

' H E Eclipfes of the firft Satellite of Jupiter j as
Jl^ has been already faid, afford the beft means of
determining the Longitude of places on the Land,
where Telefcopes of a convenient length may be ufed ;
thirteen of thefe Eclipfes happening every x3 Days;
but it is requifite that the Obferver know near the
matter when thefe opportunities offer themfelves,
leaft on the one hand he let them flip, or elfe grow
weary by a too long attendance on them.

Thofe therefore who are curious to obferve them,
may readily compute the times of the Immerfions
or Emetfions of this Satellite, and that with great
exadnefs, by the following very fliort Precepts, which
admit of no Exception or Caution, viz.

Out of the firft Table take the Epoche for the Year,
with its correfponding tJumb. A and Numh B ; and to
them add, out of the Tables of Months, the Day,
Hour, Minute and Second, neared lefs than the time
of the Eclipfe you Peek for, together with its Nam,
A and B: the Sum of the times is the mean time of
the middle of the Eclipfe. a. With Nam, A thus coL
lefled take out the fird ^Equation of the Conjun-
tdions ; as alfb the iEquaxion of Num. B. always to be
added to Num. B. before found, j. With Num. B. fb
equated, take out the fecond /Equation of the Con-
lundions ; and in the lad Table, the third /Equation,
as alfb the Semi-duration of the Eclipfe anfwering to
Num. A. 4. To the mean time of the middle of the
Eclipfe, add all thofe three /Equations ; the Sum fhall
be the true equated time of the middle of the Eclipfe
fought. 5. If Num. B. equated be lefs than 500^ fubdradl

^ ^

i 1035 )

the Semiduration, and you will have the time of the fm-
merfion, or if it be more than 500, adding the fame,
it will give the time of the Emerfion.

But Note, the times thus found are equal time, ftill
to be reduced to the Apparent : and that in the B/(fex-
tile Year, after February ^ one Day is to be dedu<fled
from the Day of the Month.

The lefs skilful may perhaps be pleas’d with an
Example or two, which may ferve them to imitate.
Let it be required to find the time of the immerfion
of this Satellite into Jupiter s fliadow, November the
^th 1719. in the Morning. The Work (lands thus.

D. h. ' "

Nu. A.

Nu.B.

1719. I. 6.11.13

872

396

Novembi 7 . 1 1 . 53 . 29

72-

yj6

Conj. Med. 8 . 1 8 . 4.42

944

iEquat. 1. 51 *55

10 AEq. B.

^quat* ll> 10.26

^quat.IIT. 3*^^

182 B. .^quat.

8.19.10.27

1 . 6.33 Semidur^ Subfi,

Novemb, 8*i8* 3*^4

So that by this Catcuks^ on the ninth of Novemb*.
at 4 Minutes after 6 in the Morning, equal Time,
may be feen the Immerfion of thb Satellite into Jupk
ters fliadow.

Another Example (hall be of the Emerfion on tha
fifth of April 17x0* viz^

t

{ t034 )

1710.

D. h. ' '' Nu.A.

o. 20. X2. . 40 95^

4 . 13. /}4 . 22 Bifs. 22

Conj. Me^. 5 . 10 • 07 . Oi 97^
^quac. f. 44 • ^ J

j'T.quat II.. O' 45"

j^quat. Hf. 3 • '9‘

1 . 5 . 40 SemUar. Add*

April 5. 12. 01. 09

Na.B.

yiQ

244

1 ? JEq B.
567 B. Aiquar.

Hence it appears that at one Minute after Mid-
night following the fifth of ril, equal l ime, will
happen the Emerfion rcquiied Nor do we doubt
but that the Event will very nearly anfwer.

LaBly, it may not be amif^ here to inform the R^aS-
der, that we have learnt, by the experience of many
Years Obfervation, that the iecorid inequality of this
Satellite proceeds from the progrelTive Propagation of
Light, and is common to all the fed of the Satellites:
Light being foUnd to proceed in about feven Minutes
of time as far as from the Sun to thu Earth, whether
with an equable motion or ocher Wife iS ftlH a'^efli'on*
For this reafon we have added a Third j/^qitation,
whereby to account for the greater diflance of Jnpiter
from the Earth in /iphetio dhan in faAhxtro^ as the
Second ^Equation anfwerS to the greater diftance of the
Planet when near the Conjundlion of the Sail, than
when near his Oppofition-

F / N I

JLondoni Printed by W. and J. Innys, Printers to the
Ro)al Society, at the Princes-Arms at the Wed Corner
of St. Qiurch-Yard. 1719.

•i i

f / N /

JLondom Printed by W. and J. I n n y s. Printers to the
Royal-Society, at the Princes^Arms at the Weft Corner
of 5’t. Paul[^ Church- Vard. 171^.

( 1035 ) Num^ 3<^2.’

PHILOSOPHICAL

TRANSACTIONS,

For the Months of September and OBober 17 sp.

The CONTENTS

h A Letter of the curious Mr. Henry Barham, R. S. Soc.
to Sir Hans Sloan, Bart. Vice-Prefident of the Royal
Society, giving fever al Experiments and Ohfervations
on the production of Silk- Worms and their Silk in
England, as made hy himfclf lafl Summer,

II. Epifiola Jacobi Jurin, M. D. e^R. S. Socii, qua.
dodrinam fuam De Potentia Cordis, contra nuperas Ob~
jediones Viri Clarifs* D. Jacobi Kcillii, M. D. in Num.
361. Philof. Tranfad:. editas^ defendit,

III. Meihodus Differentialis Newtoniana illuflrata, At>
thore Jacobo Stirling, 'e Coll. BallioU Oxon.

I

*

IV. An Account of feme Experiments made on the ^yth
Drfytf/ April, and onthexyth of July 1719* find how
much the Refi (lance of the Air retards falling Bodies ^ by
J. T. Dcfaguliers, L. L. D. and F. R. S.

9X

I. A

{ «oj<5 )

I. A Letter cf the curious Mr, Henry Barham, R. S. Soc.
to Sir Hans Sloan, Bart, Vice-Prefident of the Royal
Society; ghing feveral Experiments and Ohfervations
cn the production of Silk-Worms, and of their Silk in
^England, as made hy him lajt Summer,

Worthy Sir^

AS you are the Patron of Induftry and encourager of
Natural Experiments, I think you juftly claim the
firft View of thefe fmall ones, I made upon Silk
Wormsy the laft Summer.

And altho’ they may have been done before by others in
fome other parts of the World ; yet in all the Authors I
have Read I do not find they make ufe of the fame Me-
thod ; and I dare be bold to fay, that thefe following Ob-
fervations and Experiments were never made in England
with that Nicety, as 1 have done, and, fhall do if 1 live.

It being the firft Attempt of this kind, it may come fhort
of that compleat Methodical Manner it may be brought to
hereafter ; the which I hope you’ll excufe.

. After you ha»'e pecufed it ^'our felf, if you fee any thing
in it worthy the Communicating to the Rojal Society (\z
being defigtfd for the Publickj you may do me the Honour.
J3ut I wholly fubmit to your Judgment and Opinion in this,
as I do in all other things whatloever. 1 am,

.• Tour bumble Servant

Henry Barham.

Experiments made in Chel/ea Park, in the Months of May
June and July 1719.

l receiv’d a fmall parcel of Eggs from.

Languedoc.

May 6. Early in the Morning I found them. Hatcht of
themfelves, the Wind fhifting in the Night from Nor- ^
therly to the Wefi .South erly\ changing the^ Air of.9:.fudd,enho
Warm, two Days before the change of the Moon.

Aftejc Feeding and Managing them according to Art,
through the whole Courfe of their four Sickneffes, they
were come to their State of Perfedion, being then as
thick as a Man’s little Finger, and from 4 to f Inches long, of
a yellowifix Colour,, and when held againft the Light, they -

might

( ‘0J7 )

mtght be feen through as you may an Egg, being of the fame
Colour andConfiftence ('fill’d with the matter th^at makes the
Silk) This is a certain Sign that they will begin to Spin in-
24 Hours or lefs. They then forfake their Food ('being very
Voracious beforej and hunt about for a convenient Place to
fix their firft Hold-fafts, for fupporting the Balls or Cones
that they arc to make, which they do in a molt wonderful
Mathematical Manner, with a Mixture of a Gummy Sub-
llance that tyes all together^ and vs^hen the loofe furzy Sub-
ftance is taken off, and forae of the Silk is wound olF, the
remainder is fo Smooth and Compadt, (hining like
that they are made ufe of for Artificial Flowers,and efteemed
the bed of any thing yet known for that purpofe, for which
(only) they are generally kept in Boarding Schools. I weighed
many hundreds ofthefe Silk-Balls or Cones, which I found
to weigh from 5 j to 40 Grains, with their Aurelias or Chryfa-
Us within them.

June 27. They begun to Spin, having been Hatcht 7
Weeks and ; Days^ and in 4 or 5 Days finifhed their labo-
rious and curious Work : but their Balls were not fit to be
removed until 8 or 10 Days.

July 7. Monf. Lacbivre began to wind off their Silk- Balls
with a Machine that made great difpatch, winding much
fine Silk in a Day: I found that an Ounce of Silk-Balls
would make about a Dram of fine Silk ; but to be more cer-
tain, I weighed out to the Winder 12 Pounds of Silk Balls
at 4 times, and told the Balls ii^ every 3 Pound as follow-
etb, 'viz,.

The firft 5 Pound contained 8j2 Balls
The fecond 5 Pound contained 842
The third 3 Pound contained 797
The fourth ■; Pound contained 868
So that the whole 12 Weight contained 3319 Balls.

Which when wound off, was found to yield and make one
Pound and one Ounce, or 17 Ounces of fine Silk, and about
7 Ounces of coarfe Refufe unwound, in all a Pound and
hdXi oi Averdupois Weight, or 2 Pounds Trc/ ; which is as
great or greater making or yielding as in any part of the
World, and the Silk as fine, f (hewed it to a noted Silk Bro-
ker, who faid it was Italian Silk, (not knowing it was made
in England) and worth about 30 Shilling} per Pound, .if I had;
never (o many Bales of it, &c.

Now;

( ioj8 )

Kowupon this Experiment finding that ;;i9 Silk-Balls
would make one Pound and one Ounce of fine Silk. I was
<3efirous to know what quantity of Silk might be expe(fted
from the Worms Hatched from one Ounce of Eggs.

Of which to obtain the Knowledge^ I made ufe of the
following Method; by often weighing and telling 1 found
that one hundred Eggs weighed b^ut one Grain, fo that if
one Grain contains loo, a Scruple mutt contain 2000, and
a Dram 6ooo, and an Ounce at 8 Drams to the Ounce, mutt
contain 48000 Eggs. Now if every Egg hatch a Worm,
and every Worm makes a Silk-Ball, there mutt be from one
Ounce 48000 Silk-Balls,- and if Balls will make one
Pound and one Ounce of fine Silk, ( v;hich by Experience
I found they did) then 48C00 Silk-Balls will make 15-
Pounds and 6 Ounces of Avtrdupois Weight in fine Silk, or
i8 Pounds and eight Ounces of Troy Weight, which is
very confiderable. And in the fame Proportion one Pound
of Silk Worms Eggs, will produce Worms fuflicient to make
above 180 Pounds of Silk. But allowing for Cafualties, and
fuppofing but 12 Pound of fineSilk made from theWorms and
their Silk-Balls produced from an Ounce of Silk Worms Eggs ;
it will be found much to exceed molt Countries, according
to Augufiino Gallo's Computation ; For he fayeth, that in the
Southern parts of France, viz. Languedsic and Trovettce, they
make but 7 or 8 Pound of Silk from Silk Worms hatched
from an Ounce of b'ggs ; and inBrefcia in Italy, but 8, 9,
or 10 Pound of Silk from an Ounce; only in Calabria, where
the Silk Worms and their Eggs are larger, they make 11 or
12 Pounds of Silk from an Ounce of Eggs ,- which ftill doth
not exceed, nay hardly comes up to, what we make in Eng.,
land.

As to the Charge and Expences of making the aforefaid
quantity of Silk in England, different from that of other
Places, I fliall be able to give you a more particular Ac-
count in my next Experimental Obfervations.

1 have only this to add, that Experience hath taught me
how to hatch Silk Worms twice in a Year, fo as to have two
good Crops of Silk in one Year. And that the Mulberry
Trees will have Leaves in England twice in a Year, without
prejudice to either Tree or Fruit, is'moft certainly true.
But more in my next.

II. V IRC

Viro Celeberrimo,

Richardo Mead,

Collegii Medicorum Londinmfium & Socio
tatis Regime Socio. S, T. D,

facobm fmn, M. D- Reg. Soc* S;

Pologiam Prseftantiffimi Viri, Jacohi KeilH, qui

acetbi nuper & immaturi morce praereptus mag-

num fui defiderium Eruditis reliquit, ftudiofe pervolvi-
mus. Quam inter legendum fingularem fimul candi-
diiTimi Ingenii humanitatem, qu^ nofmet, utut a placi-
tis fuis dilTentientes, excipere dignatus eft, fimul Ani-
mi magnicudinem, & ftudium in Rempublicam Litera-
riam canto Viro dignum, magn^ admiratione profe-
quebamur. Huic enim ills non fblum per omnem vi-
tx curfum diligentem & ftrenuam operam navavit, (ed
etiam pulcherrimo Exempio, confedlus jam atroci mor-
bo & fe perire fentiens, eruditam illam Epiftolam tan-
quam fupremi amoris pignus, eidem legavit. Cui ta-
men neceflario nobis refpondendum eft, non (ane quod
acerrimo tuo Judicio diffidamus, (ed ne aliis Le^ori*
bus minus idoneis impedimento efte poflit, ad re(ftam
fententiam ferendam, Viri illius Do(ftiflimi Au(3:oritas.
Accipe igirur, Vir Clariftime, quse in ejus defenfione
minus rede tradita cenfemus, & tuum fimul Arbi-
crium efto, utrum concentionis abrepti ftudio iniquiores

fimus

{ 1040 )

iimus ipflus Manibus, an ita difputemus, ut qui de Ve-
ritate potius quam de Vic3otii fimus folliciti.

Queritur primo Vir Clariflimus, quod fefe una cum
Dodtiffimis Viris Borello, & Morlando, tanquam Cordis
Motum cum pondere inert! conferentem, injufte per-
ftrinxerfm^ Ego cerce, cum prius notaflem Motum
quendam Sanguinis & Artcriarum ex Cordis Vi or iri,
dixi tandem iciri non pofle Cordis Potentiam quanta
fit, nhi Motus hujufce quantitatem cognitam tenea-
mus: Motum vero quemlibet cum pondere quiefcente
comparari non magis pofic, quam Lineam cum Re-
dtanguloi. Quibus verbis id fignificare volui, DodiiTi-
raos Viros non quidem diferte Motum Cordis cum
pondere quiefcente comparare, fed ipfos, cum Cordis
Potentiam per pondus cxponerent, nullam oftendifle
rationem, qud Motus quantitas ex Cordis Potentia ori-
undi pofjet seftimari. Ex hSc Objedione, fi rede afle-
quor mentem Viri Clariffimi, ita fefe expedite conatur.
Cordis Potentia in preffione confiftit, eamque ajquabi-
litcr in Sanguinem impendit, eodem prorfus mode,
quo Gravitatis vis deorf'um pondus impellir, & adione
perpetua in motum accelerat. Proinde, cum Cordis
Potentia ponderi per Corollarium Newtoniamm definiro
arqualis eft, ea Motum eundem durante SyftoJe in
Sanguinem imprimet, quern pondus iftud eodem tem-
pore cadendo per Gravitatis Vim comparabir. Ita
vero cum menrern fuam exponic Vir Cl. fubla-
tum iri penitus Objedionem iftam Uoftram confi-
remur ; ft nimirum Cordis Potentia prardido ponderi
^qualis ftt, eademque conftftat in trquabili preftione
per totam Syftolen continual. Atqui'ex duabus iftis
Propofttionibus p6fteriorem neiftiquam pr.obare cona-
tur Vir Dodiillmus , fed Hyp’Othefeo>s ';Joco ponit ;
quamvis nos rationibus quiburdam addudis contrariam
Smtenn^m conati fumus veriftmiliorem redd ere ; nem-
pe, quod Cordis Potentia nequaquam ^equabilicer agat

ifi;

( 1041 )

in Sanguinem per totam Syftolcn, fed cum totas vires
exigua temporis particula collegerir, inde uno impetu
in Sanguinem irruat, eumque ex Vencriculis expcllac,
eo modo quern in Diflercatione noftra Epiftolari fufius
expofuimus. Priorem vero Propofitionem, cciam cbn-
cefla Viro Cl. Hypothefi, falfam efle mox demon-
ftrabimus.

Corollarii Newtomani fenfum quod attinec, nolumus
Ledori moleftiam niraiam facelTere, cum neque puce*
mus ejus interefle ucer Newtoni mentem redius acce-
peric ; neque ita perfpicue fenterttiam fuam expofueric
DodilTimus AdverfariuSj quin periculum fit, nealiquem
ei fenfum affingamus, quern ipfe forfican, fi poilet ad-
huc fe defendere, forec repud iaturus. Id vero adno-
taffe operce pretium eric, quod cum loquatur KcHUus
de Vi qui ex Orificio aliquo aqua exprimitur, Mewto-
ms nullum omnino verbum in illo Corollario pofueri-^
quo Aqua per Vim aliquam exprimi fignificetur ; fed
pond us folum determinaverit cequale ifli Vi, qua to-
rus Aquse effluentis Mocus generari poteft, five quod
Gravitatis Vi cadendo Motum comparare poteft Mo-
tui aquse eodem tempore effluentis rsqualem.

Quod aucem Corollarium illud, fi non male intel-
lexerit Vir Cl. certe non fatis apte ufurp^rit, facile
perfpiciet Ledor Erudifus, qui animum adverteric,
quid incerfic difcriminis inter elHuxum aquce ex fora-
mine in fundo vafis femper pleni, quomodo a Newtono
confideratur in eo Corollario, &: elfiuxum Sanguinis ex
Cordein Aortam. in cafu enim priori aqua jam to-
tam velocitatem comparavic, & per datum temporis
fpatium aequabiliter effluit ex foramine. At Cordis Vis
per Hypothefin Kdllimam, applicatur Sanguini in Ven-
triculo quielcenti, & eum primo temporis momento
velocitate infinite par\4 verfus Aortam propellit ; con-
tifiuat.^ vero a:quabili preffione taiideni ei finitam ve=

9 Y z locitatem

( 1042 )

locitatem imprimit, camque perpetiiti auger, donee
omnem Sanguinem ex Ventriculo expulerit.

Rurfum in cafu Newtoniano confideratur Motus noa
quidem toCius aqu2 Cataradd contentae, quae omnis in
mom conftituta eft, & diverfa velocitate verfus exitum
tendit, fed aquae folum in ipfo foramine pofitas & jam
exilientis. Vis autem Cordis tori Sanguinis moli Ven-
txicuio contencae Momm imprimit, tocamque Aorcam
verfus propellit.

Denique negamus pondus quinque undarum, 5 Viro
Cl. decerminacum, pofte earn Motus quanticacem duran-
te Cordis Syftole per Gravitatis Vim comparare, quam
Cordis Potentia producic, concefta etiam ei Hypothefi
iftd, quod Cordis Potentia in srquabili preflione con-
Cftat. Per hanc enim Hypothefm' erit Motus a Ven-
triculi finiftri Potentia produdus, ex Calculo noftro-
[TrafsJ. Numb. 359. p. 932., 934.] aequalis Motui Pon-
deris Ododecim librarum cirdter, quod fingulis mimi-
tis fecundis longitudinem undalem percurrat. Motus
autem, quern pondus quinque undarum durante Cor-
dis Syftole, ft tollatur omnis Arteriarum & Sangui-
nis praecedentis refiftentia, ftve dedmi parte minuti fe-
cundi. per Gravitatis Vim comparabit, aequabitur fere
Motui Ponderis duodedm librarum, quod fuprapoftr
ta velocitate moveatur. Quod ii cui libuerit adfump-
ta hac Hypotheft verum pondus definite, quod Cordis
^otentiae aequale eft, is pofito Calculo eliciet pondus
unciarum circiter (eptem cum ^mifte. Hoc enim du-
rante Syftole Cordis eundem fere Motum cadendo .
comparabit, quern producic ipla Cordis Potentia.

Sed inquiet forfitan aliquis diferimen modo expofttum
inter Motum pondere acquifitum, & Motum

ex Potentia Cordis oriundum inde proficifti potuifle,
quod forte minus accuratae fuerint pofttiones illx, quibus
Cfiaratoes Algebraicos in Calculo noftro ad numeros

leva-

.

( *045 >

revocavimus. Cuidubio ut occurramus, & oftendamus
fimul nos longe majus difcrimcn invencuros fuifle, ni(i
contigidec ut pofitiones iUss Keillio faverent; operse
pretium erit cafum aliquem fimpliciorem adfumere,
quo data moles aqux, per datum oridcium> dato tem-
pore, per vim aliquam five predionem asquabilem ex-
primatur, qus funt conditiones ab Adverfario pofitae
ad Potentiam Cordis dedniendam.

In eo autem cafu demonftrabimus neque Motum
aquae efHuentis, neque Motum toti tandem moli aquse
per Vim illam impredum, Motui aquiE in Corollario
Nnvtomano ; neque Vim earn five predionem, ponderi-
per iftud Corollarium definito, sequari. Quod d prae-
ftare licuerit, corruat funditus necede eft tota demon**
ftratio KdJUana,

Adfumemus igitur Cylindrum aquae datum, tubo ^
Gylindrico infinite longitudiniscontentum ; eritque pro
oridcio ifta fetftio tubi ad quam pertingic utralibec
aquae fuperdcies, alteri autem iuperdciei Vis applicabi-
tur ope Emboli eadem Diametro cunt ipCo tubo. Per-
fluat jam dato tempore data quaevis aquae quantitas per
didam (eiftionem tubi ; cum alia quantitas aequalis per
foramen pari Diametro faftum in fundo vafis, quod
more Newtomam ufque plenum confervatur : & primo •
loco difpiciamus, urrum pares futuri fint in utroque
calu Motus aquae edluencis.

* Exponatur tempus edluxus aquae per re<ftam A C,
velocitas autem aequabilis, qua aqua edluic ex fora-
mine in fundo vafis per re^am A B. Unde moles aquae
edluentis ex foramine, cum fit in ratione temporis & .
velocitatis conjunftim , exponetur per Redangulum i
ABCD ; & Motus ejufdem exponetur per folidum Pa- -
rallelepipedon, ex eodem Redangulo dudo in altitu-
dinem A B, quippe qui fit in ratione compofita ex ra* -
tionibus molis & velocitatis.

( 1044 )

In cafu altero, ubi aqua per tuburti Cylindricum
fiuic, tempus, uc prius, cxponetur per eandem recStam
A C ; velocitas aurern aquas eric in ratione temporis,
quippe cum vis adhibita, ex Hypothefi, in dacam a^
quae molem sequabiUter agar, & proinde repraefencabi-
tur per redJam mutabilem F G, reto A F, five tempo-
ri ab initio effluxus, proportionalem* Molecula au-
tem aqu£E, parciculS temporis F H praedidam Sedionem
pricterfluens, exponerur per Redangulum ex ipfa F H
duda in exponentem velocitatis FGj vel fi evanefcere
intelligatur redula FF5, per Trapezium F G I H, & mo-
les aquae toto tempore AC praeterfluens fignificabitur
per Triangulum redangulum ACE* Et quoniam ex
Hypothefi moles ifta moli aquae in cafu priore effluen-
ti arqualis eft, erit Triangulum ACE aequale Redan-
gulo ABDGj unde C E, five velocitas acquifica in
fine temporis AC, dupla eric velocitatis CD five AB,
qu^ aqua ex foramine in fundo vafis eiHuebat. Mo-
tus autem aquae particuli temporis F H practerlaben*
tis, cum fit in ratione molis & velocitatis conjundim,
exponetur per Prifma evanefcens, quod fit ex Trape-
zio FGI H dudo in velocitatem FG: Unde totusMotus
aquae toto tempore A C prsetcrfluentis exponetur per
Pyramidem, cujus bafis eft Quadratum redae C E, cu-
jufijue altitudo perpendicularis eft ipfa AC. Quse Py-
ramis cum fit ad Parailelepipedon cafu priore defini-
tum, ut 4 ad 3, erunt quoque Mocus aquse effluentis
in utroque cafu in eadem ratione, & proinde insequa-
les, quod primo loco demonftrandum lulceperamus.

Proxinium elS, uc oftendamus Motum tandem ira-
preflum toti aquee tubo concentae non efie aequalem
Motui in exempio primo determinaco. Hie autem,
cum toca ifta moles aqux per pofitiones fupra feriptas
neuciquam definita fit, adfiimemus earn arqualem mo-
li expofit£e per Redangulum A BCD, qu£E in cafu

Vide Fig. II.

primo

( «o4J )

primo effluic ex foramine, qusque in (ecundo fedionem
didam prseterfluit. Unde cum totus Motus ei tandem
imprefTus fit in ratione molis & velocitatis in fine ac-
quifitjs, idem exponetur per Parallelepipedon ex Re-
dangulo A B D C dudo in redam C E. Hoc autem
eft ad Parallelepipedon, primo ca(u definitum, ex eo-
dem Redangulo & reda C D, ut akitudo C E ad al-
titudinem CD, five in ratione dupll Porro, cummo-
lem aqu:s tubo contentas per quodvis aliud Redangu-
lum, loco Redanguli A B G D, exponere licuiflet, pater
inde Motiim hunc pofie quamlibet rationem ad Motum
primo cafu definitum obtinere, & idcirco nequaquam
eidem efle rrqualem. Quod erat fecundo loco demon-
ftrandum.

Supereft, ut oftendamus Vim in hoc cafu adhibitam
ponderi per Corollarium Newtoniamm definito non efle
cequalem. Hasc autem Vis & vis Gravitatis agens in
iftud pondus, cum ambx fint sequabiles, erunt in ra-
tione Motuum ex iifdem date tempore produdorum.
Quos cum inscquales eflemodo demonftratum fit, erunt
iWx Vires itidem insequales. Quod erat deraonftrandum
-poftremo.

Pergit Vir Cl. ad alterum illud vitium, quod ego
in ejus folutione reprehenderam, nempe quod velocita-
tem Sanguinis ex Corde effluentis aequabilem pofuerit*
quam infigniter inaequalem fieri a me demonftratum
eft. Negat autem fe sequabilem velocitatem Sanguini
tribuifle, fed pro fummi diverfarum omnium velocita-
tum velocitatem mediam ufurpafle. Prseterea nondum
fatis fibi conftare dicir, utrum tequalis vel insqualis fit
Sanguinis ejedi velocitas, fed quse pro a:qnali veloci-
tare ftat ratio, earn fibi firmiorem vidcri. Utrum ve »
ro, qui velocitatem Sanguinis inventurus molem San-
guinis expulfi ad orificium Aort^e applicat, nulil fada
mentions neque diverfarum velocicatuna, neque veloci'

ta£is>

104^

«tatis mediae, velocitatem Sanguinis aequabilem ponat,
penes aequum Ledorem fit Judicium. Idem quoque
facile arftimabit, utrum Vis aliqua five preflio fluido
in vafe quiefcenti applicata, quae eft Hypothefis Viri
Dodifiimi, id fluidum prime temporis momenco, e^dem
velocicate qu<1 in fine, propulfura fit.

Pofiquam ita fatisfadum putac Vir Cl. iis Objedio
nibus, quas contra priorem fuam Methodum attule-
ram, jam ad alteram illam faciliorem vindicandam ac-
cedit. In hac Ego animadverteram Virum Cl. adfu-
mere iftam Propofitionem, quod Vires Cordis in diver-
fis An'malibus fint in ratione ponderum, item ponere
velocitatem Sanguinis ex (edd lliaca Arteria profluen-
tis aequalem ei, qua Sanguis ex Corde in Aorcam emit-
^itur ; quas ambas pofitiones falfas efife nobis demon-
ftratum eft. Vitium pofterius non defendic Vir Cl,
prius vero tuetur BorelU & aliorum Dodorum Viro-
fum audoritate, qui afilimptioncm iftam fkpius ufur-
parunt. Ita quidem, & nos ejurmodi afiumptionem
in Bordlo reprehend imus, neque valet cujufquam au-
doritas contra legitimam demonftrationem. Supereft
ergo ViroCl. ad examen revocanda noftra demonftra-
tio. Hanc autem fallaci quodam Principio inniti pu-
tat, quo cum omnia Theoremata noftra fuperftruda
fine, communi ruin4 omnia involvit. Air enim me
ponere, quod Ventriculi Cordis, tanquaro folidum cor-
pus dat^ velocicate motum, in Sanguinem impingunt,
^oque idu Motus fui partem eidem communicant*
<^am Hypothefin. Motui neque Sanguinis , neque
Cordis, neque xAeris ex Pulmone expreffi, competere
cenfet Vir Clarillimus.

Quod Pulmonem attinet, quoniam hoc obiter attin-
gere voluit Vir D.agnofco me confiderafte Pulmonem inter
concrahendum tanquam data velocicate impingentem in
Aerem contentum, idque confulto fecife proficeor.

Quum

( 1047 )

^Qyum'enrm turn BelUnus, turn alii multi Viri Dod^i-,
flimi, quos inter cminet Cl. Adverfarius, multa protu-
lerint de Vi illd, ^ua Aer inter exfpirandum in Sangui-
tiem Pulmones praeterfluentem agit, ejufque moleculas
dillblvit; quam folucionem ipfo exrpirationis initio
cenlent accidere ; mihi propoiitum erat hanc ipforum
fententiam ad trutinam revocare, Videbam autem,
quod, fi aerem per Vim arquabilem five preflionem ex-
pelli ftatuerem, Motus aeri a Pulmone impreflus initio
exfpirandi, five readio aeris in Pulmonem, adeoque in
Sanguinem praeterfluentem, pro quantitate infinite par-
vi habenda erat, adeoque nihil omnino eorum efied-
uum, quse ipfi adfcribebantur, pr^sfiare poterat. Ita
vero fi fcciflem, jure quefturos putabam Bellini (equa-
ces, quod inique fecum ageretur ; quippe cum rejicere-
tur ipforum fenrentia propter demonftrationem ex Hy-
pothefi arbicraria & eadem omnium adverfifiTima de-
dudam. Malui igitur ex ilI4 Hypothefi demonftratio-
nem deducere, qua: omnium maxime ipfis faveret,
maximamque Motus quantitatem exfpirandi initio aeri
tribueret. Ha:c autem erat, qua ponebatur Pulmo ini-
tio exfpirationis data velocitate in Aerem impingere.

C^terum in Potenti4 Cordis definiendi ifiam quidem
Hypochefin, qu4 ipfius Ventriculi, omni impetu mo-
menco temporis concepto, tanquam (blidum corpus da-
ti velocitate prsdirum, in Sanguinem irruunt, primo
loco propono, tanquam omnium fimplicilfimam, ex ea-
que folutionem deduco. Atqui deinde confidero turn
earn Hypothefin, qu4 Ventriculi Cordis Motum omnem
fuum particul4 temporis admodum parva concipiunt^
quseque mihi veri fimillima videtur, turn ipfam Hypo-
thefin Keillianam, atque alias infinitas, iifque omnibus
iblutionem meam accommodo. Adeo ut, five ifiud
Principium uiceicum & fallaxi five verum & fiabile

9 Z repe-.

( to48 )

raperiatar, nihil exitide folucionis noftrse certitudini de-
traliatur.

Non tamen videmus aliquid argument! allacum, quo
minus iftam pofitionem nobis adhibere, pari jure at-
que Viro Cl. contrariam illam de Vi five preffionc
ufd'rparo licuerit. Nihil fane fpatii inter parietes Ven-
friculorum & Sanguinem intercedere non difficemur, Sc
tamen quare res i(^u peragi nequeat nondum liquet.
Certe, fi Cubo Globum contingenti idius imprimatur,
Cubus partem Motus fibi impreffi Globo communica-
bit pari facilitate, ac fi fpatium inter eos interceflerit.

At haee funt corpora folida, & ubi de fluidorum
Motu agitur, longe alia res eft. Difcrimen fane inter
i(ftus corporum folidorum, & adtionem five folidi in
fluidum, five fluidi in foiidum, fufius exponit Vir Cl.
quod difcrimen cum me minus advertifle cenfeac, ex
eo fonte fluere pronunciac quicquid Erroris in meis
Propofitionibus cominetur. Ego vero differentiam
iftam uc redte traditam a Viro Cl. lubens admitto, &
aio me communCm illam dodrinam neutiquam igno-
rafle, cum nihil frequendus in Mechanicis fcriptoribus
occurrat, fed cafus quofdam novos expofuifle, quibus
ea dodrina cum adhiberi nequiret, alia erat ineunda
ratio atque hadenus fuerat ufurpata. Ea tribus verbis
abfolvi poteft. Nam, ut exemplo facillimo utamur,
quiefcere pqnatur Cylindrus aquae datse longitudinis in
datp tubo, *& moyeatur per iftum tubum Gylindrus
alius rolidus p^i diamctro, ac dat^ velocitate in Cylin-
drum aqueum impmgat. (^id inde futurum eft? Nem-
pe totus Cylindrus aquae eo iiftu in motum ciebitur,
pa^; ratione, ac ft fuiftet & ipfe ‘ folid'us Cylm^^ al-
^er Motus fui ^arj:^ mpmento temporis
deperdet, amfeo Cyhhdri^cbftjtnUnt vclocitat^ pe^
tubum deferehtur. ^Simili modo res eveniet, fi Cy-
lindrus aqueus per tubuna’fluens Cylindro folido quief-

centi

( '049 )

centi impegerit. Quod fi Cylindru^ aqueus data velo-
citate per tubum feratur, eique occurrac Cylindrus fo-
lidus alia velocitate, ica ut quantitates Motuum Cy-
lindri aquei & folidi utrinque pares fint, jam mometi-
to temporis deftruetur utriufque Cylindri Motus,. pari-
ter ac fi duo folida corpora :squali Motu prsedita fibi
mutuo occurrant. Cafus magis compofitos quofcunque
ex diflertatione noftra de Motu Aquarum fluentium
facile eruet Le<5lor Eruditus, idemque fimtil videbit,
quomodo id fieri polfit, quod Adverlarium Cl. prxci-
pue torfifle videtur, nempe, quod Sanguiqem toto impe-
tu ex Ventriculo ruentem fifti pofie docuerim, occur-
rente in contrarium corpore folido dad Motus quan-
titate prsedito.

Quod autem nos amice admodum hortatur Vir
Candidifiimus, ut (epofid noftra de Vaforum idu Hy-
pothefi, & Vi preflurse, qua Naturam uti cenfet, pro
Principio adhibita, Theoremata alia conftruamus; id
profedo, nifi gravi morbo impeditus perfundorie
prorfus evolviflet noftram Diftcrtationem, dudum a nobis
prxftitum animadvertere potuifter. Quum enim poni-
mus Motum Cordis in ratione temporis augeri, eadem
utique Hypothefi utimur, ac ft Vim preflionis adhibea-
mus. Hoc autem pofito, Motum ex Cordis Potentid
oriundum determinavimus, duplo fcilicet majorem
quam ubi Ventriculorum idu res peragitur. Galculum
vero ipfum, ut fatis facilem & priori noftro ftmilem,
Ledori reliquimus inftituendum. Quas autem fequun-
tur Theoremata & in iis Theorema quintum, quod reji-
ciendum ftatuit Vir Cl. tanquam ex Hypothefi de Ven-
triculoriim idu dedudum, neutiquam pendent ex ifti
Hypothefi, fed ex ipfa Hypothefi DodilTimi Adverfar
rii pari facilitate demonftrantur.

Nequaquam dubitamus, quin ipfe Vir Cl. quid ifta
vcri habeant, ft in vivis adhuc ageret, pro (ua (agaci-

9 Z X rate

(■ lo^o )

rate facile petfpe^mus foreci; jam veroj quoniam ei
gregium illud Rei Medic^e Lumen amifimus, eadem
aliis Eiudicis perpcndenda fimul proponimus jk dijudi-
canda. Tibi praefertimj Vir Dod:iffime, cujas audori^
cacem & ille plurimi fecit, & nos praecipuam habemus,
Judici fimub incegerrimo & maxime idoneo, cotam
iRam diTpucationem lubentiilime fubjicimus.*

IIL Methodus Differ entialis Newtoniana llluflrata,

Juthore Jacobo Stirling, e Coll, DallioL Oxon,

f A Rithmeticse pars prascipua confiftic in invenienda
,Xx in numeris quantitate quacunque determinate ;
cum veto quantitatum & numerorum natura non pa-
tiatur ut omnes quantitates exhibeantur in numeris ao
curate, necefle habemus ad Approximationes confugere.
Hoc efl, ubi quantitatum valores maihematice accura-
ti neqeunt obtineri, qusrendi funt ii qui ab accuratis
diftant minus date quevis diflerentie.

Quicquid hec de re a Veteribus ad nos pervenit,
vel eft particulare, ut Methodus eorum reducendi JE-
quaciones Quadraticas ; vel faltem ufibus generalibus
male deftinatum, ut Methodus Exhauftionum. Het4
quidem primus erac qpi aliquid generals in hac arte
aftequutus eft.* quippe invenit methodum reducendi
iEquationes Rationales, quaz fol^e tunc in ufu erant.
In hec acquievere omnes Geomecrse ex ejus tempori?
bus ufque ad ea Newtoni. Hie ex Intetpolationibus
primo pervenit ad Series : quas poftea ad redudionem
iEquationum omnium< omnino generum univerGiliter
applicuic. Hsc autera methodus procedit per quan«
citatum naftrentium & evanefeentium rationes primas
It ultimas^ feu ft ita loqui liceat, per quantitatum coin>

cidencium

( «05« )

dxkntium dif!eretitias infinite parvas* Sed- & ulcerius^
promovic Nervtonus hanc mechodum; docuitque qua
ratione approximandum fit ad quantitates quss deter-
minantur per regularem feriem terminorum, non pet
j^quationem ut vulgo fif. Atque fic pofuit fundamcn-
ta calculi hujus Differentials, qui procedit per quanti-
tatum differencias cujufcun^ue magnitudinis .* ideoque
eft methodo Serierum univerfalior. Per hafee artes
Mevetcniaius univerfa docftrina Approximationum redu-
citur ad folutionem Probiematis, Invemre Lmam Geo-
metricam qua per data quotcunqm pun6la tranftbtt.
Ex hujus inquam folutione inveniuntur radices ySqua-
tionum quarumcunque, & etiam quantitates quarum
relationes ad alias datas per nullas iEquationes hadc-
nus notas poffdnt exprimi. Exiffimo \^\\.\xx. i^evetonum
perduxiffe methodum Approximandi ad fumnium per-
I'ecftionis faftigium ; dum ex unico fimpliciffimo prin-
cipio totam hanc dodrinam' longe lateque patentem *
deducit. Quapropter credendum eft animum J^evptoni
non fatis perfpedum fuifle iis, qui ejus methodos ap-
pellant particulates, & alias tanquam fuas & folas ge-
nuinas atque generales venditant? quse aliis non eranc
quam Corollaria facillima a Newtontanis.

Author nofter, in Epiftola ad OUenhurgum^ 05toh. iq;
1^76. data, mentionem fecit de methodo expedite du-
cendi Lineam Parabolicam per data quotcunque pun-
<3a ; qua dixit fe ufum fuifle ubi Series fimplices non 1
func I'atis tradabiles. Et hanc methodum primo pub-
licavit in Lemmate quinto Libti tertu Principiorum,
Atque in Leflionibus publicis, circa idem tempus quo •
dida Epiftola fcripta eft, Cantahrigia habitis, expofuic
modum generalem determinandi Curvas cujufcunque “
generis qu£ tranfibunc pec totidem data punda quot
earum natura patitur. Hse Lediones fub tiiulo Arith^
meticA Unmr{a\h anno 1707. publicatas funt, ubi ha»

betas r

( To5» ^

'betur methodus exemplis illuftrata in fe<3ionibus Coni-
cis. Anno vero 171*. tandem prodiit, inter alios ejuf-
^ dem Authoris tradatus, ipfa Methodus DifFerentialis
plenius quam ante expofica, cum fundamento ejus de-
imonftrato*

Archimedes in methodo Exhauftionum, Cavallerius
in methodo Indivifibilium, & Wallifim nofter in A-
rithmecica Inhnicorum, pofuerunc fundamenca dodrinse
de determinanda quantitate quccfiti per locum quern
obtinet inter terminos in data Serie : at qua ratione
approximandum eflet ad valores quantitatum fic deter-
minatarum. horum nemo docuit ; Hoc primus & (blus
perfecit Idemonus: atque exinde baud parum ampliata
eft univerfa Analyfis. Nam ficut ante hoc inventum,
ea Problemata Arithmetica Cola pro fplutis habebantur,
'Ubi relatio quantitatis qusefitse ad alias datas definie-
■batur iEquatione, jam pro folutis habenda funt non
minus ea, in quibus quantitas qusefita locum datum
forticur inter terminos datas Seriei ; fiquidem numeri
defiderati non minus accurate obtinentur perMetho-
dum DifFerentialem, quam per extradionem Radicum:
hifce vero habitis, parum intereft quomodo ad cos de-
ventum eft. Et experientia multiplex docuit, quod
plurima Problemata ad ^quationes asgre deducuntur,
dum ad methodum DifFerentialem facillime. Qpalis
eft ex mulcis aliis tories decantata Circuli Quadratura ;
quam tarn perfedam, mea opinione, Wallifius in Arith*
imetica Infinitorum exhibuit quam Archimedes illam
Parabok.

PropoJjtio

( iofj

^rofoptiol

lAvtnln LhsAm TaraholicAm qu£ trAnfihif . fer txtn*-
mA OrdinAtornm quoteunqus aquidifianthm, .

C Cz C3 C4 Cq C6 C7

D Di DS D$ D6.

E Ez E^ ^4 Eq^,^

F Fz F^ F^ ,

G Gz Gi

H Hz

1. I

Cajus Trimusl

Dengneiit A, Az, Aq, A 6, A j] A S,' A ,

Ordinatas sequidiftantes infiftentes Abfciffe iti^
dato angulo. Collige earum differentias B, Bz, B ,
B^,Bq,B6, By^ C^c, harumqus differentias C, ,
CZi C C4, C 5, C6, C7, &c, harumque differentias ^
£), Dz, D3, r>4i Dq, D6, &c* harumque differentias
E, Ez, £3, E^, Eq, &c. harumque Fy Fz, F3, F4, ^
Et fic porrq. Differentiae autem cqlligi debent au-.

" “ ' ----- - ferendo^

( I0J4 )

-ferendo priores fempcr de pofterioribuS. Hoc eft po-
nendo B=.Az — A, Bir=:A^—mAz, Bi~A<i^ — ^3,
=zA$ •— A^, B$=: A6 — A$, &c. Turn C=Bz —5,
Cz =zB^ BZi C^z=B4 — 53, C^4=5j — B4,
deinde Dz=:Cz — C, D2=C} — Ci, X>j=C4 — C3, CS'f.
£t ftmilicer (unc omnes difterentiac fequentes colligeud.'e.
;Vel fint a,/3, squales A, Az, A^,

A^, A6, Ay,^c» Eritque A = oc,, B = B — «, C — y
' 2, /3 “1“ a, £) rrz — Jy-|— 3/2 — 0-, e — 4^”4~^^
— 4^ + 06., — je + ioj^ — icy 5/3 — a, G—

« — 6^ + 156— 20<^ -f- 1 5y — 6/3 -j- a, In hilce
yaloribus numerales Coefficiences ipforum a, /3, y, JVfs&c.
gcnerantuf ut in dignitatibus integtis Binomii 1 — a[®,
I— *1*, 1 — I— &c, Scribendo numeros

*» 2,, 3, 4, la Sene i X y x — X — x — X

X &c. iucceflive pro n. Sit jam P ^quaelibet Or-

dinata reliquis intermedia, 6>c A P ejus diftaniia ab Or-
-dinata prima A appelletur a, turn crit

B X -4-
■ *

Cx4xS=^4-

* X *

Vt.. ‘

dideoque

( 1055 )

Ackoque fignum ipfius mutandum eft, quatido ? ^
cadic ad alteras partes Ordinatse primse, nt

Cafus Secundus,

Sit jam A q Ordinata in medio omnium ; pone

H -}- drc. 6>c a C4, £3, ^ d= /, &c.

id eft, fifmt A6z=a, Aq=::/3, J8 = y, Ap==/^,

= 3t> ^3 = A, Az ■=.fA, A — V, cjrc. Pone ^=ra— .jc,
/3 — 2a-|-2}t — A, 4/3-f

-f 1 4/3 — 1 4a *f 1 4»t — 1 4A -1- 6//^ ^ y,

+ ^ = /3 — 4a-}- 6/45 —

/3— 56 «-}-70/45— 56>c4-i8A^8At-fy, ^c.
Ec dicatur A qP, z, turn eric

PX=A; + ^l^ +

+ 5;5_r

f

3*4*

3£i+5? _

I . 2

X

+

3.4 y -6

+ I 4 9

I *2

X

I .2

X

3 .4

X

X

7i8

+

5,6 7 , 8 ^ , 10

Cafus Tertius.-

Sint jam Aq, Ordinatse duas in medio omnium:

A4 -f- -45 _

Pone A

g = gj±l^, C=:^2+/\ D

z z

10 A

G+6z

( ioj<5 )

&c. a = B4, i = Vj, c = Fz', d = H, &c.

Vel fine As=za,, A6 — {^t Aj~y, A^z=S^, &c.
A4 = x. As = h, Az=.fA, Az=, p, &c. Deinde erunc

zA =: (X, -\- X., zB z=: ^ a, — X zC y — g/3

4- xa -V" — 3^ + zD=S^ — Sy-^9^—5‘^ —

9^ — Sf^ Et<t = a — X, h z=z^ — 3‘*’~h

356 — A, f == y — 5|3-|- lOa — IOJC-I-5A — fAi, dz=i
^ — 7-y + X I|8 — 3 ^cc -i- 3 5jt — II A + 7/A &C.

Et fit 0 pundlum medium inter ^4, -^5, atque appel-
letur OP, zi eritquc Ordinaca

“7“ ^177 '

5C-4-c^ 4^^— I ■

4* > • 3 4 • 5 '

7Q 4^^— I ^KK—9 ^ AKK—^S t

4’ 6.7"^

9E+3^ ^ 4H=9 X ,< ^S=*2 + &C.

4+ 2.3 4-5 6.7 8.9 '

In hifee duobus etiam cafibus z eft negativa, quando
Ordinata P ^ cadit ad alceras partes inicii Abfcifc
Ec in omnibus tribus cafibus diftantia communis Or-
dinatarum ponituc unitas,

Omnes tres cafus demonftrantur facillime per calcu-
lum. In cafu primo pro F^feribo fucceflive a, /3, q<-,
g, &c. & pro z interea p, i, x, 3, 4, &c. quse funt
longitudines Abftiffie ordine fequentes ; & provenient
sequationes

€ zz:. A -]f 4^ H“ 4^ "1“

/3 — a

( 1 ojr )

^ — ^ — 5/ n: B iC -|-
e — eT = B + 3G4-3D-p£', &c.
y T!Z 2/3 -j- cc zzz C, <r — “f“ Df € ■“ 2^ -]- y

= C-1-2D + £, &c.
fT — 3?^ “h 3/^ 2 — 3«^

e — 4c5^ -1- 63/ — 4/3 + a = B, &c.

Hx ^quationes, capiendo earum dif?erentias, nullo
labore refolvuntur, uti videre eft. Et dant eofdem
ipforum A, B, C, D, &c- valores, qui antea pofiti func
in foludone. Et ad eundem modum demoiiftrantur
cafiis duo reliqui.

Harum trium ferierum unaquseque converget ad va-
lorem OrdinatSE P ubi Ordinatarum datarum dif- ^
ferentise funt juftse magnitudinis. At ubi non conver-
gunt, alisE artes adhibendsE funt. Sed impraEientiarum
de hujus Propofitionis ufu pauca adjiciamus.

Defignent a, /3, y, (T, e, 6, k, A, &c. terminos
quofcunque sEquidiftantes, quorum differentise funt
perexigusE; & relationes quas inter fe obtinent de*
finientur quamproxime per ^quationes fequentes, quse
oriuntur capiendo difterentias & difterentias differentia-
rum continue, & ponendo eas a:qual&s nihilo.

a — /3 = O
ec — - 2/3'-f~ >■ =: O
a — 3/3+ — ^=0

a, — 4/3 + 63/ — 4J^ + €r=:0

a. •— 5/3+ lOy -.-IO<i^+ 5g— .^=:0

ex, — - 6/3 + I aoJ' + 1 5s “*r 6^ + ft o

a — 7/3 + 213' — 35^<J' + 35g — 2iC + 7M— 6 = 0

cc — 8/8 + 283/ — $6S^-\~yQe — 56^ + 28)} — 89 +5C—0

«^9/3-[-363/-“84«J^4'I i6g— I i654-84>? — 3 69+9J&— A=o.

&C. HfEC

I

( ioj8 )

H*c Tabula in ufum teiervanda «(V, ut contiilatut
quoties opus fit. Quod autem ha: i^quationes vel ob-
tinent accurate, vel ad verum approximant, ubi diffe-
ssentisc terminorum funt parvar, patet ex d^onftratio-
ne cafus primi Propofitionis.

Affumatur quaslibet Series- &c.

Et quaeratur terminus qui flat proximus ante : patet
quod ille eft ; vidcamus ergo qualem hsc methodus
exhibebit eundem. Repraefentet ct terminum quasfitum,
eritque

,-7, = /S— 0099,0099,0099,0,
0098,0392,1 568,7,
~r:r;'^oo97, 0873,7864, 1,
a— 0096,1 538,461 5.4,
i^=C=°°9S*i38o,9523.8,
-^n^M.;=oo94, 3 396,2264,2.

1*" ima'

T

ro®99, 0099,0099,0,'

1 2da

■

0099,9805,8629,3;

1 Jtia

* dat It <

0099,9994,3455,0,

4ta

0099,9999,7824,8,

5taJ

0099,9999,9895,8,

6ta

L J

_Qo99,9999,9993,i.

Patet ergo quod h^c methodus continue approxi-
mac. Si terminorum differentiae fuiftent minores, va-
lores acceffiftent citius ad verum, & contra tardius
quando differentiae funt majores* Hinc fi in Tabuiis
numericis defit terminus, poteft is per. hanc methodum
inferi.

Hocmodo etiam prodeunt ipfiflima: Series Speciofte, quae
per alias method os prod ire foie nt. Proponatur
OrdinataCurvae quadrandae; Ea eft prima in ferie regU'

lari. &C.

Ordinatarum, quae omncs praeter primam dant fuas
areas z-\-~z\ z-\-jz^ -f \z\ z
&c.. conftituentes novam feriem cujus primus terminus
erit Area quaefita : quae ideo invenietut ponendo pro
& pro reliquis in fuo Oirdine /3, 3/, g, &c.* Pri-
mal .Aiquatio dat <z-=.Zy fecunda a = a tertia

4* ? quarta

/

( 1059 )

8ic. Eft ergo univerfim area quseHta z ~ ~ z^,

jz"^ — hz^^ &c. Eftque hsec Series arcus ad

Tangencem r, in circulo radium habente unitati ccqualem.^
Earn invenic Jacohus Gregorius nofter, & cum Qollinio
communicavic initio anni i67£. a quo, mediante 0/-
^ denhurgo ad Leibnitium delata eft*

Sic jam &c, e, d, c, h, 4, P, e, &C; Series

utrinque excurrens in infinitum, ubi dantur omnes ter-
mini prseter P in medio omnium. Sit A — cb-\- a;
B ^ hj C zzzy Ct ^ ~ df E i c, &c*
atque eric

6

4

60

, 7A — i4B-f-9C— 20

— [-

140

42/^— ^6B-p8iC— 3aD-f-5£ ,

1260 '

66^— i65B-f-i65C— 88D-f 2<;£— 3P ,

277Z '

429^^ — H44B4-1287C — 832D-4-325B — 72F--f-7G , ^

— — h CXC.

24024

Tnveftigatur h^ec Series ex ^Equationibus, excerpendo->
ulcernas in quibus numerus terminorum eft impac*
Nam earum differentiae relinquent cerminos in hac Se*
rie ; quae itague ad libitum produci poteft.

Sit Ordinata Hyperbolae, & quaeratur Area

^us qux jacet fupra Abrciffam z, quando ea evadic
unicas. Haec Ordiaata eft media in Serie Ordinata-

rum^

rum, &c. 14-4"^} ^4~^l %

i-\-z\\ i+z-f, &c. sequidiftantium,

hinc inde excurrente in infinitum- Adeoquc Arex ab
hifce Ofdinatis genitas conftituent feriem confimilem,
cujus medius terminus eric Area quaefica; quse proinde
obtinebitur per Seriem modo expofitam. Quando z eft
unitas, ut in cafu prsefente, arex curvarum evadunt
&c. a. K f, & I, r, h r. Hinc eft i +

* i n — 5 1? — 15 rmL_L2.r=” D — ’J I »5 — i?s

r==r» ^r“r“r« — ^ *> ^ 4~r«4 «4»

&c. Hifce in Serie fubftitutis, prod it P, id eft, area
Hyperboix, | + <Sic. id eft, —

4^ 4^ 5^ o ¥ Tl- - • A

— &c. Ubi jam A

4-3 4-5 4-7 4-9 4-”

JB, C D, &c. more Mewtoniano, defignant terminos in (uo
ordine ab initio. Calculum appono.

AffirmatWi

7 yoo,oooo,oooo, 0000,0
61,5:000,0000,0000,0
7440,47^^j9047>^
97.5'58<^,9I30»8
3 90.4086,1
i88,774S'.5
2,7085,0

393j4

5.7

Negathi.

o6i5<oooo,oooo, 0000,0
6,6964,2857,1428,5
845,5086,5800,8
11.3818,4731,9
^585,7062,8
22,5708,7
3260,2

47.5

7

’+7563>^539»3930,7494‘I — 0631,7821,3370,8041,1

Summam negacivam fubducens ab aftirmativ^, babeo
pro Arei, id eft, pro Logarichmo Hyperbolico Binarii,
numerum 6931,4718,0559,9453,

Pro

_ ( lo^l )

Pro conftrudiione Tabularum quarumvis numerica-
rum percommoda eft Series quce fequitur. Defignent
&c. f, c, h, a, a, y, cT, g, &c. terminos alternos in
Serie utrinque ferpente in infinitum ; Pone Az=a -J- a,
Q C rrr: ‘y -\- D n:; ^ dt E — S &C»

Ec terminus inter a & <* eric

^ *

rx— +

1^3 2 A — jB-f-C ,

X +

1 . z
1.3.5

X

5/4— 9B-f-5C— D

I . z . 3

1 . 3 . S • 7

14. A — zSB-l-ZoC — 7D-f--E

1 • z . 3 • 4 ^

I . 3 . 5 , 7 . 9 41/4— 90B4-75C— ^‘>0+9^ — F ,

1" Z .3.4.5 ^ z'“ ‘

il3i?.7.9‘ir l^^A—l97B-h^7 5^ — 154D4-54^ — TlF-p*^ t

i.Z.3.4.5.6 ^ 2'^ ‘‘

8ic.

Hsec Series fequitur ex cafu tertio Propofitionis,
ponendo z=^o. Coefificientes numerales literarum fie
producuntur ; exempli gratia, in quarto termino coe-
fficiens literal penukimae C eft 5 ; pone 5 -f- i = », &
numeri qui proveniunt ex multiplicatione terminorum

I ^ Y “1“ ^ ^ ^ ~5~ ^ erunt i, 6, 1 5:, 20,

&c. Horum differentiae 5’, 9, funt numeri quaefiti,
Atque adeo Series ad libitum produci poteft.

Datis Logarithmis numerorum q6, 48, 50, $%, jq,
56, 58 & 60 ; invenire Logarithmiim numeri 53, qui
confiftic in medio omnium. Pone /, 5”2 -j-;/, ^4 = ^4 =
344S3>97*o>34> $o+h ^6 = B ;=a, 4471, 5803,1 Y

( lo6l )

/, 48+/, 58 — Crrr 3,4446,6913.08, /, 46 + /, 60 =
D =: 3,4409,0908,19. Hifce valoribus in Serie fcrip-
tis, primi quacuor termini dabunc I,7^42,^586,96 pro
Logarithmo numeri Ec eadem ratione invenire licet
quemvis alium intermedium.

In Conftrudione ergo Tabularum fufficit primo quae-
rere aliquos terminos in debitis didantiis, nam reli-
qui poiliint hoc modo interCeri. Etenim continuo
lunt intercalandi termini primo inventi, ufque dum
perventum fuerit ad ultimos qui defiderantur. Hoc
modo habebitur tota Tabula ex datis paucis terminis
Tub iniiio pro fundamento operationis. Sed non con-
venit ut termini quos primo quxrimus, fint omnes per
totam Tabulam aequidillantes ; nam fi omittimus al-
ternos ubi eorum differentia efl maxima, poflumus ali-
bi per faltum omitterc duos, tres, viginti aut forte
plures terminos. Numerus autem terminorum inter
duos datos confiflentium, qui omittuntur, debec Tem-
per efie aliquis fequentium i> 3, 7, if, 31, 63, &c.'
dummodo volumus inferere eos per hanc b'eriem ; hoc
veto neutiquam incommodabit opus.

PofTunc autem pro Praxi lernrini in unam fummam
colligi. ut fadum vides in hac Tabella. Prima expreffio
eft primus terminus ; fecunda eft fumma primi & fecun-
di $ teitia eft fumma primi, Tecundi Sc tercii : Sc Tic porro.

4

I

8

10

z

^A—B

ia2 5/j-.243B-f~49C-.-5D
2048

3969o-»^— 882GB+2268C>-3o;D-f-3sg

6J536

Sic

{ I0(5j )

Sic daCiS' aiiquibus terminiSrf altern^i^ intefTn^tfii
confeftim dabuntur pec hafce expreflTiones, nulll ra-
tione habit^ naturae Tabulae particularis. Nam hae fe-
gulae funt eaedem in omnibus. Areas curvarum funt
proxime squales areis Parabolicae iigurae quae, tranfic
per extrema Ordinatarum fuarum. ’Sed quoniam labd-
riofum nimis eflet Temper recurrere ad Parabolam.
computavi Tabulam fequentem, qua Areje dire^e exhi-
bentur ex dacis Ordinatis* ' ‘

I

3

5

7

9

II

-R

I

R

90

41 A-\-2, {6B“f-27C-f-27lD

840

R

’li D

989/^+58882 — 9z8C-f-ro496D — 454oE^

28350

i6o67y#4-f 06300B — 4852504.2714000; — 26o5-5oE4-4^73^8F

598752

-/?.

St ,

Hie numerus Ordinatarum eft impar, A eft fumma
primae & ultimse, B fecundae & penultimae, C tectias &
antepenulcimae ; & Tic porro> ufque dum deventum fit
ad earn ,in medio omnium, quse per ultimam literam
in quiq'ue expreffione reprsefehtatur.^ eft bafis feu
pars Abfciilae inter primam & ultimam Ordinatam in-
terceptse- Expreffiones funt Areas contentae inter Cur-
vam, bafin & Ordinatas hinc inde extremas. Tabulam
pro pare numero Ordinatarum non appofui, quoniam
Area cseteris paribus ex impare earum numero accura-
tius definitur. •“ ' '

(^^ratur area quae generatur ab Ordinad i
6? jacet fupra Ablciflam z qdando ea evadic unitas. In

^ ^ 10 B i zz>

< i'o<54 >

X “J— 2 2I ^ pro Sj fcnbc ,"3» i'o» , io> is> » « &

prodibunt undecim Ordinate i , S, H*

;-n,^ Hinceft A=I + i = f, B — If: +

ez=:i4.:i=^,i?==:f:+Tr,r=iis,

F = f . Hifce vaEoribus fubftitiitis in, w^ti/Pa ^xpreffipae,
& unitate pro./?, invenies areamj eiTe ; 7^5398187;
Juftus eft hie numerus in feptim^ figura; in odav^ ve-
rum fuperans Binario.

Si undecim Ordinatas non dent aream fatis exaeftam,
crige plures; & concipe aream divifam efle in plures
partes, quarum quamque feorfum qusrens habebis pro
lubicu juftam.

^Valor ipfius i + exprimi poteft per quameunque
trium ferierum fequentium.

I+^1”= i-f

ex 4 -If:

"

n n — I n — % ,

£, ,t; ‘ ■- ^ ■^T?f 1JT ^ ■ 3 ■ ’

n ^ «— 3

Ji f!I>.

jj:' zC

^ '*'8

nr r;.. ' . .. m'J. ■ v.

Veli+^'’'=i+ ■

. iJx '

i -!Jv -I.. . . I ir- ; n

. ,n? ' X j Ui .'i. - it ' j.

■q

Lii .L.:. o

^uur 'ij ■ nsq i.o )r

^ Jil

T

, A Z’ tjp
t j -I

H u: yy>i
\

Htx

j

«■

I z

pofito fcilick R

1 +^1'’= ^

i— f-W-f-I VS

^Vd'

X X

4

-f- 8iCr

X'^

1 . 1

■ I ^

4+«+ax6>. ,

— , I — x^’x —

»4-gj; ^ i.

*+2^1* ^ i.i 3,4

« «« — . I ,

X 4-

3-4

««•

5.6

H-

1

J+21

-S,

» w«— I M»_4 nn~^Q .

X ^ ^ 9_|^

I. a 3.4 5.6 '' 7 .8

io4-«+«;yQ.

-I- &c.

» ^ww — 4^^w»~9 ««— ig.

3 -4

- , X- —

5.0 7 . a

9,10

PrimsE dusE Series demonftrantur per Cafiim primum
Propofitionis Nam i -{- ^|°, i -j-^|‘, r^jT^ja

I I defignenc Ordinatas totidem
cequidiftantes in ParaboKca figura, erit
dem Ordinata, cujas diftaiitia Ec lie

prod it Series pHma. At Ciiti alia Parabola *-1-.^°,

&c. fmt

if^uidiOantes Qrdiftar^^- dit '1 4*7^'* 'Ordinata iii-'eaL
dem.cujus diftantii a i d&'—ji; ^fic proveiiiet
Series lecund^^ ^tjam in rertia Parabola &c. i +^|r‘*i

7+^1°, r+^iC

• + » + ^P, I + ^P, &c. Series Ordinatarum

lo B X £Equi-

( io66.)

ssquidi{lantium hinc inde progrediens in iniinitumf
eritque in eadem i + ^1“ Ordinata, diftantii » a ter-
mino medio i ^1° remota. Ec fic provenit Series
tertia per Cafum Secunduni Propofitionis. Prima ab*
rumpit quando eft » integer & affirmativus, fecunda
quando eft » integer & negativus, & tertia in cafu utro-
que abrumpit. Per harum quamque radices numera-
les commode evolvuntur in Series. Tertia reliquis mul*
to citius convergit: ejus terminus fecundus adhiberi
poteft pro correSione, ubi fit extratftio per repetitio-
nem calculi.

Halleius in fua methodo conftruendi Logarithmos,
ex prima harum ferierum demonftrat Seriem Mercato-
rls pro Quadratura Hyperbola. Sit ejus Ordinata

I -|- veil 2,l”~’,exiftente»numero infinite parvo;
unde per methodos (^adrandi, area quse jacet fupra
Abfciflam id eft, Logarithmus numeri i -j- jc, eric

aaeoque

1 'i z '.I 2 3

in cafu prsefente, ubi eft n infinite parvus, eft i zY

= I -U — zi z^-\- — z' — —z'^ (S-c. quo fubftitu-

I 13 4

to in valore arese, ea prodic z — \ 4*

\z^ — &c.~ quse eft Series Mercatoris,

Similiter per Seriem fecundam prodic ha:c regula ;

Sic datus numerus i + ^ eritque ejus

Logarithmus /J + ^ 4‘ T "V 5 4"

Per Seriem tertiam provenit fequens regula. Sic

p j ia

quilibet numerus /?, pone z eritque ejus Lo-

garithmus

( >0(57 J

garithmus — ^ Bz—’-Cz~ fDz — f.Es'

— &c. Ubi A, B, C, DfEf &c, more Nerctemano defig-
nant terminos Seriei ficuc ab initio. Hxc Series, uc ea
ex qua deducitur, reliquis duabus multis vicibus cele-
rius approximac: eftque eadem generalius exprefia
quam, ex fundamento baud abfimili, pro invencione
Logarithmi Binarii prius dedimus.

Methodus inVeniendi yalores Seriertm Arithmetical
rum utcunque tarde conyergentium.

In aliquibus Seriebus fumma terminorum haberi ne-
quit nil! ad pauciffima figurarum loca, dummodo prse-
ter fimplicem eorum additionem alise artes non adhi-
beantur.' Proponatur jam Series quaelibec cujus termi-
ni omnes iifdem fignis afficiuntur, & quorum proximi
continue tendunt efie inter (e tequ’ales; quales funt fe»

quentes + '+? + ? +

Collige fummam aliquot terminorum fub
initio, ii proxime addendi fint a, |8, y, g, &c. In

numeris proximis fit r ■=

«i3 — 2M.y-f-/3y*

8c quantitatum

+ tJ' + + differentiae

fint a, l>, c, Cy &c. Deinde in numeris proximis fit

ac — bb o • /- a , . b~i-sc . .

<x iplorum 4X — 4 -{-» >« -r — ,

« 4—4^ n /*

ab^zac-\~bc
c-^sd

d’^se

+ f X ar\-h-{-c -\-dx , &c. differentiae fint

AC — BB

Ay By C, D, «{C. & fit / =

cede

( t0^8 )

cede quoad libuerit. Turn erit «

, a-\-sh , j ^ A-^tB

f o 1 a-Tst? ,

+ &C. + &c.

at-

que ultra duos pritnos tetminos hujus novse Seriei ra-
re opus erit progredt. ‘ ’

Ut fi defideretur valor Seriei — + — h

1.2 ' 3.4 5.6 ' 7.8

&c. collige primos zi terminos, quorum fummam
reperio fore68i3, 8410, 1885. Termini proximo ad-

dendifiint a=, 0005, /3 =,0x304,8309,1 787,
^ =,0004,43 i6,x4i I, ^=,0004,0816,3265, &c. Hinc

fit r = i proxime, & =»ou 7*6449, 6182,

a = — ,0000,0017,5096, ^= — ,0000,0014,7410,'

^ = — ,0000,0012,4986, &c. Unde ^ = i prope, &

.4X^-i^ = — ,0000,0141,8111, quern propter fignum
negativum fubduco ab a x— &remanet, 0117,6307,

A [5

8171: hie additus fummse primo invents 6813,8410,
1885, dat pro fumma totius Seriei numerum 6931,
4718,0056, qui juftus eft in nona decimali ; at ante
duas hafee corrediones fumma erat jufta in prima fi-
gura foli. Si animus fit propius fcOpum attingere,
pergendum eric ad approximationes fequentes. Si^er-
mini Seriei diverfa habeartt figna, conjuOgendi funt, ut
omnes eadem tandem habeant, ut in Serie i — f + f

“-l- i — &o conjun(ftis terminis ea evadit

h &c. Sed hie notandum eft

quod difterentis a, h, c, e, &c. ut & A, B,C,D, c8rc.
colligi debent fubducendo quantitates antecedences dc
fubfequentibus. Et in omnibus hujufmodi Seriebus fi
pi 4, r, reprsfentOttt tres terminos' ofcdifie ft^emes; p pri-

mum.

( lO^p )

mum, f fecundum, »■ tertium, & reflangulum ttT x «

non fic majus />r, valor Seriei erit infinite magnus: at
inagnifudinis femper finirse ubi accidie contrarium.
Poteft hxc regula nonunquam failere, ubi termini p, q,
r parum diftant ab initio Seriei, at fi confiftant inter
eos ab initio aliquantum remotos, evadec regula cer-
rilTima.

Ad alia Serierum genera debent alije regulae adhibe-
ri. Sit Series regulaiium Polygonorum Circulo Incrip-
prum, exiilente Kadi^Vwnitate. ' —

H~ z,oooo,cooojOOOo,coo 1 4
G ~ 1,8x84,17 IX, 4746, 1 90] 8
=3 3,0614,6745,8910,718!

A == 3 J 1 1 j 4,4 5 1 58,051-1 \%

jD = 3,1365, 4849,0545*93:^ I64

^ ~ 1 1 5,6954,751] 1 18

5=: 3, t4ii,77i5, 093^,772.125^

^ = 3,1415,1380,1144,2991512.

Dicatur jam ultimuili Polygonum penultimum B,
.:antepeiiukiniuin O, & reliqua . iu fuo ordine retrorfum

^ g

'p, £, F, 6:c. atque area Circuli quaefita eric A

+

4. 5 ® 4~ , 64^ ‘ ’ 84 n ^ T~ 1^

3 i 1 f

»409i?^ — S4.40B-4' 1418C

3 .15 -63
— "4~ E-

•5.i?v63 .a55

Ubi fi pro A,

B, CyDf Ef &'c. feribantur proprii valores, primi q.uatuor
termini dabunt 3,1415,9265,3589,790 pro area circuli.
H^cc autem Series eft generalis, ex natura Circuli neu*
Iriqiiam dependens: applicabilis eft quociefeunque nu-
'merorum approxirnaatium differentiae priores ftinc po-
fteriorum quaff quadruplae. Fadores in Oenominato-
. ribus Punt dignitaces' integrse numeri 4 unicatibus mi-

f nUttKo

( to7o )

iiutse; quibuS datis, coefficientes literarum in diverfis
terminis formantur ex multiplicatione continua nume-

rorum i, — . &c. Ubi pro n Tub-

fticuendus eft ultimus Fadorum in Denominatore.
Ultima quantitacum x — 1, zljx — 2, ^ijx — 4,
— 8, 16, &c. sequalis eft Logarichmo

numeri x. Pro x fcribe 2. & per repetitam excradio-
nem radicis quadratse exibunt numeri

JM= 1, 0000, 0000,0000,0000.

/.=; 8284,2712,4746,1901.

/=r 7968,2864,0010,8843.

7240,6186,1322,0613.

6 = 7083,8091,8838,6214.

= 7007,087^,693 1,73 3 7.

£= 6969,1430,7308,8294.

V = 6950,2734,2438,7611.

C =: 6940,8641,2891,8363.

B =: 69^6,1698,4799,4014.
6933,8182,9699,9493.

Dicatur ultimus numerorum penultimus B, & Tic
retro, atque Logarithmus quxfitus erit ^ -| 1-

lA — ^B-+C t^A — .I4B-4-7C— D ,6^A — ■tzoB-4-7oC — rfO+H
1.3 1.3.7 * . 3 • 7 - 15

4-&C. Prirai quinque termini dant 6931,4718,0999,
9497 pro Logarithm© Hyperbolico Binarii. Et quo-
modo hsEc Series procedit in infinitum facile colligiturex
eo quod de priore diximus: eftque etiam univerfalis, '
proprietates Hyperbola minime relpiciens.

Extenditur quoque Methodus h^cce Difierentialis ad
Refolutionem .^£quationum & alia quamplurima quorum
hie non fit mentio- Continetque fundamenta Serierum ge-
neraiiftima; ut inRedueftione ^quationumlrrationalium
& Fluxionalium brevi forfan mohftrabo.

ly.

C 10/i )

IV. Jn account of fome Experiments jnade on the
27th day of April, i7ip. to find how much the
^efifiance of the Air retards falling Eodies, By
J. T. Defaguliers, LLt D. O' F. R. S.

ITook iz Balls ('fix of which were folid Leaden
Globes of about z Inches Diameter ; three hollow
Glals Balls of about 5 Inches Diameter; and three
light Paftboard hollow Globes of abou: the fame Dia-
meter) and having carried them to the upper Gallery in
the Lanthorn, on the Dome of St. Paul's Church, I
caufed them to fall down by two at a time, in the
following manner;

Firfi, a Leaden Ball and a Glafs Ball.

Secondly, a Leaden Ball and a Glafs Ball.

Thirdly, a Leaden Ball and a Glafs Bali.

Then I let fall in the fame manner the three other
Leaden Balls, each with a Paflboard Ball.

After that, having the Leaden and Paftboard Balls
brought up again, i repeated the Experiment twice
more with a Leaden and Paftboard Ball ; then I made
the Experiment twice more with a Paftboard Bali
alone, to fee how long it would be in falling.

Upon the whole it appeared that the Leaden Balls
were a very little longer than 4 ~ Seconds in falling ;
the two largeft of the Glafs Balls 6 Seconds, and the
Paftboard Balls 6 7 Seconds.

The height of the Gallery, from whence the Bodies
fell, was zjz Foot above the Pavement of the Church
(then cover’d with Boards) upon which they fell.

The times of the Falls were taken two ways above,
viz* with a Wheel- Chronometer, which meafures a

to C fmali

( 1072 )

fmall part of Time accurately, nearer than to a quarter
of a Second ( made and contriv’d by Mr. George Graham,
an ingenious Clock-maker) and with an r Second Pen-
dulum: And the differences of Time between the fall of
the Leaden Balls and the other Balls were taken below, by
the Prefident, Martin Folkes E(q; F. R. S. and another
Perfbn,whoall agreed in their Obfervations of the Time,
which they made each with an half Second Pendulum*.

The following Table gives the Marks, V, ^eights,
and Diameters of the feveral Balls, in three
Columns.

Leaden Balls

Troy iVtight,

Diameters in In:hes

L oz. d.

and Decimals,

1 c

1 : I : f

1 , I

1C

I : 11 : 4

* » 99

3^

I : 1 1 : 11

1 , 0

AC

I : 1 1 : 1 1

1 , 0

sc

I : 1 1 : 11

1 , 0

6c

I : 10 : 0

I ,98

Pafthoard Balls.

>

A

0 .* 3:6

S , S

B

0 .* 1 .* 14

5 , I

C

0 .* 1*17

S * *

Glafs Balls,

D

0 .- 3- 13 1

3 > 9

E

0 .• 3-:

5 »42-

F

0 .* 6: 0,-

5 ,SS

N,B, The Polar and Equatorial Diameters of the
Glafs Balls being different, I have fet down a Mean
Diameter for each of them ; the true Diameters are thus,
of D 4 ^ 3)8. of E 5-, 6 and ^,2.5. of F f,7 & 5,4 Inches.

the

( «07J )

the particular Experiments are as folio ms.

Experiment I. Fall of ic and D.
c fell by the Pendulum in 4^".

The Fall of D was fo near it, that the Difference was
not taken either above or below.

Experiments II. Fall of ic and E.

%c fell by the Chronometer in 5", by the Pendulum in 47".
Time of the fall of E not taken above.

The Difference taken below xf'.

Experiment III. Fall of ‘^c and F.

3<r fell by Chronometer in 47", by Pendulum in 47'^

F fell in Six Seconds.

Difference taken below was I7".

Experiment IV. Fall of 4c and A.

4c fell by Chronometer in 47, by Pendulum in 4I.

A fell in 67 Seconds.

Difference taken below =: z".

Experiment V. Fall of $c and B.

We made no Obfervation above nor below.

Experiment VI. Fall of 6c and C.

6c fell by Chronometer in 4|"» by Pendulum in 4*''.

C not taken above.

Difference below = z j-".

Experiment VII. Fall i c and B.
z f fell by Chronometer in 4I", by Pendulum in
B not taken above.

Difference taken below z| "

10 Cz

Experx-

( 1074 )

Experiment VIII. Fall of $c and A.
fell by Pendulum in 47".

A fell foul and fo was not obfeiv’d at alL
Difference taken below

Experiment IX. Fall of B alone,
by the Chronometer in 6r", by the Pendulum in 6\"\

Experiment X. Fall of C alone
by the Chronometer in 6j" by tlie Pendulum in

By Galileos Theory the Lead, which was 4'r" in fal-
ling, muff fall 4 Foot the firft or 16 Feet the firfl:
Second, which amounts to 314 Feet in 4r". But as
the Sound of the Ball (as it Ilruck the Bottom) by which
we reckon’d our Time, had xyx Feet to move, we muff
abate a ‘ of a Second nearly, fruppofing Sound ta
move one Mile in ^\") which will take away 35 Feet,
that the Body muft have fallen in the latk ~ of a Se-
cond, and reduce the number of Feet to aSp : fo that
the Lead will have only fallen 17 Feet Ihort of the
Theory, which muff be attributed to the Refiftance of
the Air.

The large Glafs Ball in the 6 Seconds of its Fall, wou’d
ina i^4r»»wgo thro’ 576 Feet.* but taking away the laft
- of a Second or 47 Feet, for motion of Sound, it muff
only fall 5x9 Feet in Facuo. Now fince it fell but
27 there have been 2^7 Feet taken off* from the Fall,
by the Air’s Refiftance.

Likewife the Paff board Ball in 6\ Seconds muff
have fallen 676 Feet: but deducting the laft quarter
of a Second or 51 Feet for the motion of the Sound, theie
remains only 625 Feet for its fall in Vacuo. But as
k fell only 27a Feet, we muft allow a Retardment of
3^3 Feet for the Refiftance of the Airv

( «07J )

At a mean we may call the weight of the Glaft
Ball 5 oz. Troy, and its Diameter $ Inches and - ; and the
weight of the Paftboard Ball ^ Ounces Troy, and a lit-
tle more than f Inches Diameter.

The Lead Balls all fell within near a Foot of one an-
other, and made an impreffion in the Boards of about
of their Depth.

The Barometer flood at 30, i Inches, and the Mer-
cury was very Convex, and therefore inclined to rife
ftill.

A further Account of Experiments made for the fame
purpofe^ upon the i^th Day of July laft. Dy the.
fame.-

HAving found by our former Experiments, that thin.

Glaft Balls, and even Balls of pafted Paper^,
were too heavy to make fo confiderable a Difference
between the time of their Fall and the fall of Leaden.
Balls, that it might be eafily Obferv’d ; I contrived a
way to make dryed Hogs Bladders perfeflly round,,
by blowing them (when moifl) within a ftrong Sphe-
rical Box of Lignum Vita, and letting them dry in the
faid Box before I took them out ; which 1 did by
opening the Box that fcrew’d in the middle, and had.
a hole in the Pole of one of its Hemifpheres to let
the Bladder pafs thro’, in order to tye it after blowing ;
and feme few fhiall holes all over the Box, that in,
blowing no Air might be confin’d between the infide
of the Box and the Bladder, lo as to hinder it from
putting on a Spherical Figure. Befides I took off the:
finds of the Ureters, the Fat and a great deal of the:

uppest

( 10/6 )

-upper Coats of the Bladders, before 1 blowed them in
the Box, to render rliem dill lighter.

The Bladders I ufed were feme of the thinned I
cou’d find ready blown at a Druggifls, which I moift-
ned in Water, taking care to leave none in the infide.
I chofe thole rather than Green ones, which in drying
wou’d have duck fo fad to the infide of the Box, that
it wou’d fcarce have been poflible to have got them out
without tearing.

Having prepared five Bladders in the manner afore-
faid, (which 1 have deferibed the more fully to direct
any body elfe that fhou’d be willing to try the like
Experiments) 1 took them up to the upper Gallery in
the Lantern on the Top of the Cupola in Sc. Pauls
Church; and there by a Contrivance, which I (ball
jud now deferibe, I let them fall by one at a time,
together with a Leaden Ball of about x Inches Dia-
meter, and weighing x /. Troj : and I took notice of the
time of the Fall of each Bladder, knowing by former
Experiments that the Balls are about 4 Seconds, or a
little longer time, in faling the fame Height, which is
^27x Feet.

The following Table, confiding of five Columns,
gives in the fird, the Marks of the Bladders ; in the
next their Diameters ; in the third their Weights in
Grains Troy, in the fourth the times of their Fall in
Second Minutes of time ; and in the fifth, the difference
of Time between the Falls of the Leads and of each
Bladder , taken below by the Prefident, Dr. Halley,
Dr. Jurin, Martin Folkes Efq; and Mr. George Graham
the Clock-maker. The Time was taken above with
Mr. Graham's Chronometer, (formerly deferibed) ; and
below with the fame Indrument, and three half Second
PendulumS) all which agreed very well together.

The

( 1077 )

The Experiments having been made twice over, the ’
Table is twice fet down ; and thofe Experiments in
which the Bladders fell ftreight down, and the moft
regularly, have this Mark before them ("^ ).

Marks.

Diameters
in Inches

Weight in
Grains Tro)

lime of tht
vphole Fall

Diff. between the
Lead and Bladder.

A

128

19 f'

14, Seconds.

f'B

5.^93

156

I7b

C

^.33

137*.

>8:

*4r

D

97r

22i

5)02,

21 F

17

* A

19"

i4r

B

i8|

Hr

* C

i8|

H

D

24

i9r

E

2-li

The Diameters and Weights may be reLyed upon,
being taken the Day that the Experiments were made,
and the Day after ; but the Diameters and Weights
taken i o Days before, not agreeing with thele, I have
left them out. For the Bladders by drying had loft
of their Weight, and altered their Diameters.

As the Necks of the Bladders in drying (brink, fo
as to open a little, they muft be blown before each
Experiment. And for the manner of letting them fall
exadly in the fame Inftant of time, it is defcribed by
Figure If, in which

A, A, A A, is the Hole through which the Bodies
fell; I, 2, is a Board laid over the Hole. G, D, D is
another Board fixt to the firft Board by the two Wood-
Screws D, D, with a Pulley G at the other end of it,
over the Hole. W is a two Pound Ball of Lead

faftned

( 1078 )

fdftned to a {Irong Thread, which going over the Pulley
is (Iretched horizontally from G to the Nails F; to
which it is faftned, fo as to be about a quarter of an
Inch above the Board.

B is one of the Bladders, hanging with the Neck gr hea-
vieft part downwards, by means of a Loop of fine Thread
as E H, which goes over the Horizontal Thread G E F.
Now when with a pair of Sciflars the Thread of the Lead
( which in all is but one Foot long) is cut juft at E, before
the Loop of the Bladder, the Lead pulling away the String
the Loop of the Bladder flips off the remaining Thread
F E, and begins to fall exadly in the fame Inftant as the
Lead : But if the Thread fhould be cut between E and
F, as the Lead falls its Thread might give the Bladder
an oblique Oiredion.

He that obferves the time either with a Pendulum or
Chronometer may take it very exa(ftly, by feeing the
motion of the Sciflars as they cut the Thread.

tJ. B. As the Diameters of thq Bladders were taken
by wrapping a Thread twice round them, and fomething
muft be allowed for the thicknefsof the Thread; i have
here under fee down the Diameters of the Bladders, as
eorreded by that Allowance. Fiz. A y.aS Inches;
B 5,19 ; C 5,30 ; D 5” and E juft y Inches in Dia-
meter.

The Bladder E was rough, with feveral Wrinkles and in-
equalities, which made it be longer in falling than it ought
to have been, according to its Diameter and Weight.

A Pail of Water thrown down met with fuch a Refi-
ftance in falling ^7^ Foot thro’ the Air, that it was all
turn’d into Drops like Rain.

F I M r s.

Errata. Phll. Itrarf. N°. 357. Page 848. 1, aa.lege ab ii' 32"
N°. 359. p. 932. 1. 1 7- lege t rr o",i. p. 957. 1. 5, 6. lege reftitui^
tur. Et Syftole Arteriaram cum Cordis DiaRole duratione convenit.
p. looj, I. i(S. read, pooj of the f^ipy of the Opvion.

■’T" ■

\

,^•’1

J^Aclc/rjp/i. ^ran/ac^ •

Numb. 3(^5; ( 1079 )

PHILOSOPHICAL

TRANSACTIONS.

* , ^

For the Months of NoVemk and Decemb. 1719-

• The CONTENTS.

I. A Letter of Air. Jofeph Williamfon Jf^atcJnnaker^ to the
Pithlifer., wherein he ajferts his right to the curious and
life fill Invention of snaking Clocks to keep Time with the
Suns Apparent Alotion.

II. An Account of fome new Experiments.^ relating to the
ABion of Glafs Tubes upon Water and ^uickflver. By
James Jurin, M. D. Reg. Soc.& Coll. Med. Lond. Soc.,

III. Part of a Letter from Dr. Rich. Richardfon, to Dr. Will.
Sherard, R.S.S. giving a relation of a wonderful Fall of
Water from a Spout, upon the Alores in Lancaihire.

IV. An Account of the Phenomena of a very extraordina-^
ry Aurora Borealis, feen'at London on November to.
1719. both Adorning and Evening, By Dr. Edmond Hal-
ley. R. S. Seer.

V. A Relation of the fame Appearance, feen at Cruwys
Morchard in Devonfhire. Being part of a Letter to
Sam. Cruwys, Efq-, R. S. S. and by him Communicated to
the Royal Society.

VI. A further relation of the fame Appearance as feen at
Dublin, communicated to the Publifer by an unknown
Hand.

VII. An Account of another very confiderable Aurora Bo-
realis objerved at Streatham in Surry, by Air. Thomas
Hearne ^ and Communicated by Coll. Francis Nicholfon,

R. S. S.

VIII. Nupera Obfervationes AfrroiiomicA cum Regia Socie~
tate communicate.

10 D

T. A

( io8o )

I. A Letter o/A/r.Jofeph Williamfon Watchmaker,
to the Tuhlijher, wherein he ajferts his ^ight to the
' curious and ufeful Indention of making Clocks to
keep Time with the Suns Apparent Motion,

HAving been inform’d of a French Book lateiy pub-
lifhed, wherein the Author fpeaks of making
Clocks to agree with the Sun’s apparent Motion 5 and fup-
poleth that it was a thing never thought of by any before
himfelf.- I was therefore willing by the advice of (bme
of my Friends, to write this fliort Account of what I
have performed in that matter my felf.
r And in the firfl place I mull take notice of the Copy
of a "Letter in this Book, wrote by one Krefa a JeJuit,
to one Mr Williamfon, Clockmaker to his Imperial Ma'
j^Jly; of a Clock found in the late King Charles the
Second of Spains Cabinet, about the Year 1 699 or 1 700.-
which llieweth both equal and apparent Time according
to the Tables of Equation; and which went 400 Days
without winding up. This I am well fatisfied is a
Clock of my own making; for about fix Years before
that time, I made one for Mr. Daniel ^uare, for whom
I then wrought moftly, which agrees with the Delcrip-
tion he gives of it, and went 400 Days as he faith.
This Clock Mr. Daniel Square fold, foon after it was
made, to go to the faid King Charles the Second of
Spain: and it was made fo that if the Pendulum was ad-
julled to the Suns mean Motion, the Hands would
Ihew Equal Time on two fixed Circles, on one the
Hour, and on the other the Minute. But there were
other two moveable Circles of the fame kind, that

moved

( loSi )

moved forwards and backwards, as 'the time of the
year required; on which the fame Hands fhewed Ap-
parent Time like wife, according to the Equation Tables.
This Method the Author owns he knew of. and appiyed
the fame Motion to Pocket Watches iz or 14 Years
ago, which I confefs I never did ; being well fatisfied
that Watches with Springs and Ballances are very unfit
to Ihew the minute difference, as it iucreafeth and de-
creafeth, between equal and apparent Time.

Soon after this Clock was fent to Spain, I made o-
thers for Mr. ^lare which Ibewed Apparent Time by
lengthning and fhortning the Pendulum, in lifting it up
and letting it down again, by a Rowler fomew^hat in
the form of an Ellipfis, through a flit in a piece of
Brafs, which the Spring at the Top of the Pendulum
went through* By this means every vibration of the
Pendulum would agree to a Second of Time of the
Suns apparent Motion ^ that Rowler which lifted up
the Pendulum, and let it down again, being continually
moving about all the Year ; fo that it may feem very
ftrange that this Author never heard of it, fo many
Years after they were made ; For one of thofe, and
not the firft, made with the rifing and fetting of the
Sun, Mr. Quare fold to the late King William, and it
was fet up at Hampton-Court in his Life time, where it
hath been ever fince. This contrivance of lengthning and
fhortning the Pendulum, I thought of feveral Years before
I made any of them. Since then 1 have made others for
Mr. ^are likewife, which (hewed the difference between
equal and apparent l ime according to the Equation Ta-
bles, by a Hand moving both ways from the top of a
Circle; on one fide fhewing how much a Clock keeping
equal Time ought to be fafler than the Sun, on the
other fide how much flower.

But

( loSi ) I

But thefe Clocks that I then made to agree with the 1
Sun’sApparent Time,were done according tothe Equation ■

Tables, which I found nor to agree very exactly with the t
Sun’s apparent Motion : neither can any other be made
to keep equal Time that will gain and lofe all the Year a-
greeable to the faid Tables: for though the Tables them-
(elvesmay be true, yet fome difference in Motion does
proceed, in both forts of Clocks, from Cold and Heat al-
tering the length of their Pendulums* This difference by
fome Obfervations I have made, I fuppofe to be about
the 77, part of an Inch in the length of a Pendulum vibra-
ting Seconds, which will alter the Motion of the Clock
about 1 1 Seconds in xq Hours. Hut to make my Clocks
made for keeping Apparent Time to go as exad as poffi-
blc, I made a Table my felf by Obfervation ; For obferv-
ing the Sun, as often as it was to be feen, when it came on
the Meridian, for feveral Years together, always fetiing
down the Difference between its coming to the Meridian
and the Time by a Clock I had adjufted as well as I could
to equal Time, and always taking notice how much my
Equal-Time Clock gain’d or loft at the end of every Year,

1 compleated my Table in the Year lyti. Since then I
have made a confiderable many of thefe Clocks, feveral
of which I fold to Perfons of great Note and Ingenuity;
and in particular one I made about five or fix Years fince
for the Right Honourable the Lord Parker, at prefent
Lord High Chancellor of Great Britain ; and all of them
have given good content to thofe that bought them So
that I think I may juftly claim the greateft right to this
contrivance of making Clocks to go with Apparent Time ;
and I have never yet heard of any fuch Clock fold in
England^ but what was of my own making, though I
have made of them fo long.

Ik An

( 1085 )

ir. An Account of fome new Ex[)enments, relating
to the AEiion of Glafs Tubes upon Water and
Quick^/Uver, By James Jurin, M. D. Reg.’
Soc. Coll. Med. Lond. Soc.

IN a Difcourfe formerly prefented to the Royal Socie-
ty, T maintain’d, that the SufpenfTon of ^/ater in a
Capillary Tube was owing to the Attradion of a (mail
annular furface on the infide of the Tube, which
touch’d the upper part of the Water. Among the feveral
Experiments made ufe of to prove this AfTertion, was
that of a Glafs Funnel of feveral Inches Diameter, hav-
ing its fmall end drawn out into a very fine Tube,
which Funnel being inverted and fill’d with Water,
the whole quantity of Water therein contain’d was fli-
fiain’d above the Level by the Attradion of that nar-
row Annulus of Glafs, with which the upper furface
of the Water was in contad.

Soon after that Difcourle was printed, came out a
Book publilh’d by a very Learned and Ingenious Mem-
ber of this Society, in which that Experiment was ac-
counted for in the following Manner.

If there be a Funnel, as ABC, Fig, r. full of IVater^
and rrhoje rride end fiands in a F'effel of Water as B C ;
and the Top of the Funnel A ends in a Capillary Tube
open at A, the rohole Water will he [uflaind: the Pillar
'a a by the Attrallion of the Circle of Glafs within the
Tule immediately above it ; and all the rejl of the Pillars
of Water, as F f D d, Ee, G g, <jrc. in fome meafure by
the AttraClion of the parts of the Glafs above them, as F,

* mUf. TranfaH. N“. 355.

10 E

Dt E, Gy

( 1084 ) •

D, B,G A/td that tin fimil Pillars tf Threads of Water
Dd, and Ee^ do not Jl' Je dorrn to F f, and G c, and fo go
(^uite do!vn, feem to he owing to their Qohe^on with the
Pillar A 4, which is fufiainA hy the Capillarji Tu^e A:
, For if you break off the (aid Tube at D the whole Water
will prefently fink donn.

As this Solucttm was very different from what I had
before given, and the Reputation of that Gentleman,
whole great Knowledge in Experimental Pliilofophy is
generally known, was fufficient to give weight to any
of his Opinions, 1 thought my felf under an Obliga-
tion to examine his account of the Experiment, in or-
der either to demonffrate its infufficiency, or to retradJ
my own Solution. Accordingly at the next meeting
of tltc Society, I produced the foflowing Experiment.

The Funnel, AFGBC, Fig whole lower part
B C F G, was Cylindrical to a confiderablc height, and
W’hofe top was drawn out into a fine Tube at A,
being fill’d with Water to the height BF, fo that the
furface of the Water F G, did not reach to the arch-
ed part of the Funnel, I touch’d the end A with a wet-
ted Finger, whereby a fmall quantity of Water being
infinuated into the Capillary Tube at A, the Water
contain’d in the Funnel W’as fufpended above the Le-
vel of the Water in the Cillcrn D E, as in the fornier
Experiment.

In this Experiment it is manifeft, that the little
Columns, into which we may luppofe the Cylinder of
W^ater, FGBC, to be divided, are no way fuffaiii’d
by the Attra6lion of the arched part of the Glafs above
ibem, fince they have no contadi with it. Nor is
there any fuch middle PiUar of Water, which, by its
contad the Tube at top. is both fuftain’d it lelf,
and helps to fupport the Pillars about it. Upon the

t' ( io8y )

fappofition of which two Particulars that Geutlemaiv*s
Solution was founded.

This Expaiment may be thus accounted for. The
Cylinder of Water F G B C, by its weight balances a
part of the prefTurc of the Atmofphere, which is in-
cumbent on the Water in the Ciftern, and endeavours
to force that Cylinder upwards. The reft of that
preflure is balanced by the Spring of the Air, A F G,
which is included between the Cylinder of Water
F G B C, and the little Column of Water in the Ca-
pillary A. But, as this Air by its Spring preffes e-
qually every way, it muft balance as much of the
preflure of the Atmofphere upon the little Column of
Water at A, as it does of that upon the Water in the
Ciftern. The remainder of the prefture of the Atmo-
fphere upon the Column of Water at A is fuftain’d by
the force with which that Column adheres to the
Capillary Tube, which therefore does exadly balance
the weight of the Cylinder of Water F G B C, and
is the real, though not the immediate, caufe of its Suf*
peniion.

- The experiment fuccecds in, the fame manner when
a Column of Quickfilver is railed into the Funnel, in-
ftead of the Column of Water F G B C, the top of the
Tube being touch’d with a wet Finger as before. But
then the height of the Quickfilver in the Funnel muft
be as much lefs than that of the Water, as irs Spect-
fick Gravity is greater.

1 proceed now to acquit my felf of a Promife I
made in the Difeourfe abovemention’d, of examining
whether the Experiments therein contain’d would fuc-
ceed in Vacuo \ and whether Water could be fufpend-
ed in a wide Tube by means of a Capillary at Top,
at a greater height, than what it can be rais’d to by
the Prefture of the Atmofphere.

10 E 1

In

( io8(^ )

Tn order to this, I toil’d Tome Water, and after-
wards purged it of its Air by means of the Air-pump ;
which being done, thofe Experiments all lucceeded in «
the exhaufled Receiver, in the fame manner as in the •
open Air.

The i^th Experiment in particular was made with a .
Tube of about 35 Inches in length, and a quarter of
an Inch Diameter, the top of it being drawn out into
a fine Capilla y. Which being fill’d with Water pur-
ged of its Air, as before mention’d, the whole quan-
tity continued fufpended in the exhaufled Receiver.

This plainly fliews, that the fuccefs of that Experi-
ment does not depend upon the PrefTure of the Air,
fince the fmall quantity of Air left in the Receiver was
b.y no means capable of fuflaining the Water at fo
great a height, and confequently that the height, at
which Water may be fufpended in this manner, is
not limited by that PrefTure.

But here I mufl not omit taking notice of a confi-
rable Difficulty, which prefents it lelf to thofe who at-
tentively confider this Experiment. In order to make
which the better appear', it will be proper to obferve
wha: happens, when a fimple Capillary Tube is fill'd
wifh Water purged of A|ir, and inclos’d in the exhaufl-
ed Receiver.

In this cafe the whole Column of Water contained
in the Tube A C B, Fig, ^d, is fufpended by the At-
tradlion of the Anmlus ar tlae top of the Tube, A. And
r’hough that does not immediately upon,

any part of the Water, except what is either cpnt'iguous
to it, or fo near as to be within the Sphere of its At-
rradion, which extends but to very fmall difiance;
yet it is inipofTiblc,. that .any, other part of the Wearer,
as for mflance that at'C, flioiild part from the Water
above it and fink down, becaufe its defeent is oppos’d

I io8r )

by the attradion of the contiguous Annulus at C. For
rhis, being equal to the upper Annulus at A, is capa-
ble of llifiaining a Colamn of Water of the length A B,
and confequently is more than fufficient for fupporting
the Column of Water below it, CB From which it is
plain, that no part of the Water contain’d in the Tube
can poiTibly defcend, unlefs the upper part, aflifled by
the weight of the Water below it, be fufficient to over-
come the Attra(5fion of the Annuhis of Giafs at A.

But in fuch a compound Tube as that made ufe of
in our Experiment, Fig- ^th A CB, the cafe is very dif-
ferent, and it does not eafily appear, why in a Facu-
urn any part of the Water in the wider part of the Tube,
as for Example at C, ffiould not leave that which is
above it, and defcend ; fince the Annulus at C is by
much too wide to fuflain a Column of Water of fo great
a length as C B,

The bed anfwer I can give to this difficulty is, that
the Cohefion between the Water contain’d in the Ca-
pillary and that below it, is fufficient to balance the
weight of the Column fufpended. But how far this
Cohefion may depend upon the PrefTure of a Medium
fubtile enough to penetrate the Receiver, is worthy of
Confideracion. For though fuch a Medium will pervade
the Pores of the Water, as well as thofe of the GlaCs,
yet it will adt with its intire PreiTure upon all the (olid
Particles, if I may fo call chemi, of the futface of the
Water in the Ciflern ; whereas fb many of the folid Par-
ticles of the Water in the Tube, which happen to lie
diredlly under rhe folid Particlesof the Water above them,
will thereby be fecur’cl from this Preflure; and confe-
quently there will be a lefs PrefTure of this Medium up-
on any furface of the Water in the Tube below dig
Capillary, than upon an equal furface of the Water in
the Ciflern. So that the Column cf Water uvfpended

( io88 )

in the Tube may be fuftain d by the difterence between
thofe two Preflures. This Explication Teems to be fa*
vour’d by the following Experiments, which may all be
accounted for in the fame manner, though I fliall anon
mention another Caufe, which contiibutes to the Suc-
eeXs-of the firft and (econd.

The lirft I (hall mention, is the famous Experiment
of the fulpenfion of Mercury purged of Air, to the
height of 70 or 75 Inches, in the Tcrrktllian Tube, in
the open Air. To which we may add the fuftaining
of Mercury likewife purged of Air within the exhauft-
ed Receiver, as related by that Learned and Succefsful
Promoter of. Natural Knowledge, Moof. Papin, in his
Continuation du Digefteur. 1 forbear to mention the
furpenfion of Water purged of Air, in the Vacuum,
which he deferibes in the fame Book 5 becaufe there is
little difference between that Experiment and oar own
abevementioned, the very tf p of the arched part of his
Tube, which top we may fuppofe as fmall as W’e pleafe,
(applying the place of the fine Capillary at the top of
our Tube. ' But we mufl: not mnit the Experiments
made by the famous Monf Huygens^ and defenbed by
him in Phil. Tranfaci. No 8^. of the cohering of po-
lifh’d Plates with a confiderable force in the exhaufled
Receiver; as likewife of the running of Water and Mer-
cury, when purged of Air, through a Siphon of une-
qual Legs in the Vacuum : All which he accounts for
from the fame Principle, and much in the fame manner,
as we have ufed for explaining the Experiment above.

• As to the Exiflence of fuch a Medium, ! lhall con-
tent my felf to refer to what has been (aid by our //-
l'4^ricus Preftdent in the Queries at the latter end of
the laft Edition of his Opticks : and as 1 have lately
had the Honour to entertain the Society with fome Ex-
periments upon Quickfilver, which were exadly the

reverfe

( io8p )

rcverfe of thofe made by Dr. Tayion the late Mr. Havpks^
hte and my felf, upon Water ; by which I am now en-
abled to throw this tt’hole affair into a little Syffem
by it felf, I (hall beg leave to lay it down in the follow*
ing Propoficicns, the Proof of which is contain’d in the
Experiments annext

PROPOSITION I.

Particles of Water attract one another.

This. I think, is now univerfally acknowledged, and
therefore needs no Demonftration ; the Sphericity of the
drops of Rain, and the running of two drops of Water
into one another upon their contadf, manifeftly proving
it.

PROPOSITION II.

The Particles of fluickjtlver attraH one another*

This is likewife manifed from the Spherical Figure,
into which a drop of Mercury forms it felf upon a
Table; and from two of them immediately running to*
gether, as foon as they come to touch.

PROPOSITION III.

Water is attra6ied hy Glafs.

This plainly appears from all the Experiments, that
we have (hewn upon this Subject.

PROPOSITION IV.

^ickflver is attraBed hj Glafs,

Experiment I. If a fmall Globule of Qukkfilvec
be laid upon a clean Paper, and be touched with a
piece of clean Glafs; upon drawing the Glafs gently

away.

( lopo )

away, the. Quickfilver will adhere to it, and be drawn
away with it. And if the Glafs be lifted up from the
Paper, the Quickfilver will be taken up by it, in the
fame mariner as a piece of Iron is drawn up by the
Loadftone, and will ftick to the Glafs by a plain Sur-
face of a confiderable breadth, in proportion to the
bulk of the drop, as manifeftly appears by an ordina-
ry Microfcope. Then if the Glafs be held a little ob-
liquely, the drop of Mercury will roll (lowly upon its
Axis along the under fide of the Glafs, till it comes to
the end, where it will be fufpended as before.

B.xf, ^d. If a pretty large drop of Mercury be laid
upon a Paper, and two pieces of Glafs be made to
touch it, one on each fide ; upon drawing the Glafies
gently from each other, the drop of Mercury will ad>-
here to them both, and will be vifibly drawn out
from a globular to an oval Shape; the longer Axis
palfing through the middle of thole Surfaces, in which
the drop touches the Glafies.

PROPOSITION V.

s 1 ^ '

The Particles of Water are more ftronglj attrafied hy
Glafs, than ly one another.

This manifeftly appears from the rifing of Water in
fmall Tubes above the Level For when the Water
begins to rife into a Capillary Tube, all the Particles of
Water, which touch the fmall Anrmlm at the bottom
of the T«be, muft have quitted the contacft: of the
other Water, and have rifcn contrary to their Gravity,
to come into conta<ft vvith the Glals. After the fame
manner the other Experiments of Dr. Ta-jlor, Mr. Haroks-
he and my felf, upon this Subjeift, are ea'fily explica-
ble. For upon a careful Examination, it will be found

• in

( jopi )

in them all, that (bme parts of the Water quit the con-
tael of the other Water, and join themfelves to the
Glafs.

PROPOSITION VI.

The Particles of Mluickfilvtr are more frongl'j attraPied
hf one another, than ly 6(afs.

Exp I. Fig. 5'.^ If a fmall Tube as A B, open at
both ends, be dipt into a Glaft Vcflel fill’d with Mer-
cury, and be held clofe to the fide of the Vefiel, that
the rife of the Mercury within it may appear ; the Mer-
cury will partly enter into the Tube, but will fiand
within it at feme depth, as CE, below the Surface of
the Qjjickfilver in the Vefiel, CD; and this depth will
always be reciprocally as the Diameter of the Tube

In this Experiment a Column of Quickfilver of the
height C E endeavours to force the Mercury higher in-
to the Tube ; and as Glafs has been already prov d to
attract Quickfilver, the AttradHon of the annular Sur
face on the infide of the Tube, which is contiguous to
the upper part of the Mercury, will likewife confpire to
farther its afeenr. What oppofes the afeent of the
Quickfilvet, is the Power, by which that part of it,
which endeavours to rife into the Glafs, is drawn back
by the Atrra(9:ion of the other Mercury, with which it
is in contad laterally, and this does not only balance the
Atcradion of the Glafs, but likewife the weight of the
Column of Mercury of the height C E, and conle-
qucntly this Attradion is confiderably ftronger than
the Attradion of the Glals.

The caufe therefore that fufpsnds the weight of the
Column of Mercury CE, being the difference between
the Attradion of the annular Surface of the Tube at E,
and that of an equal Surface of the Quickfilver in the
Ciftero, from which the Mercury, that endeavours to

10 F rife

( lopi )

rife into tlu Tube, raufl: recede, iaorder to unite it fclf
to fuch an Annulus of the Glafs, will always be pro-
portional to that annular Surface, or to the Diameter
of the Tube. And fince the Column fuftain’d mud be
proportional totbeCaufe that fufpends it, that Column
mufl; likewife be as the Diameter of the Tube. But
the Column fufpended is as the Square of the Diame-
ter of the Tube and the height C E conjointly ; from
which it follows that the height C E muft be as the
Diameter of the Tube reciprocally, as it is found to be
by Experiment.

The Experiment of the Afcent of Water above the
Level in a Capillary Tube, is juft the Reverfe of this.

Exf. II. fig. 6. Quickfilver being poured into the
inverted Siphon AGB, one of whofe Legs AC is nar-
rower than the other C B ; the height C E, at which the
Mercury ftands in the wider Leg CB, is greater than
the height C D, at which it ftands in the narrower Leg
C A,

On the contrary, Water ftands higher in the narrow-
er Leg, than in the wider.

Exp. in. Fig. 7. xA B C D leprefents a retftangulao
plane of Glafs, which makes one fide of a w’ooden
Box. On the infide of this is another Glals plane of
the fame fize, which at the end A C is preft clofe to
the former, and opens to a fmall Angle at die oppofite
end B D. When Mercury is pour’d into this Box to
any height as C E, it infinuates it felf between the
two Glafs planes, and rifing to different heights be-
tween the Glaffes where the opening is greater or lels,
it forms the common Hyperbola C G F; one of whofe
Afympeotes E F is the line on which the Surface of the
Mercury in the Box touches the inner Glafs; rise other
is the line A C, in which tlie Planes are join’d., < This
Hypetbola being carefully examined by Mr. Hankshee

( »op? )

and my felf, the Redangle E H G, wherefbever taken,
proved always equal to it felF, to as great an accuracy as
could be expeded, when the Planes were opened to any
confiderable Angle : But when the opening was very
fmall, the inequalities of the Planes, though the bed f
could procure, bearing a greater proportion than be-
fore to the diftance between them, occafion’d a fenfi-
bie variation. Which, by the way, 1 take to be the
reafon, why the Ordinates found by the late Mr Huivks’
ke, in examining the Curve produced in a contrary (i*
tuation, upon dipping two Glafs Planes fo join'd into
5p)rit of Wine, do not anfwer to thofe of the Hyper-
bola.

Exp. IV. Fig> 8. A B is a perpendicular Sedion
through two Glafs Planes join’d at A, and open’d to a
fmall Angle at B. C reprefents a pretty large drop
of Mercury, the larger the better, which being made
to defcend as far as C, by holding the Planes in an e-
red pofture, with the end A downwards, retires from
the contad of the Planes to D, upon inclining the Planes
towards an horizontal Situation ^ and the diflance C D
becomes greater or lefs, as the Planes are more or lefs
inclin’d towards the Horizon.

A drop of any Oily or Watery Liquor moves the
contrary way, as has been fliewa by the late Mtr Hawks-
hee.

Exp. V. Fig. 9. A B is a Tube open at both ends,
and a Foot or two in length, whofe lower part is
drawn out into a fine Capillary at Bi This Tube being
fill’d with Mercury, the whole Column of Quickfilver
will be fufiain’d in it, provided the Capillary Tube
at B be fufficiently fmall. But if the Mercury in the
end B be fuffer’d to touch any other Mercury, it runs
all out of the Tube if, without letting it touch any
other Mercury, a fmall part of the end B be broken off,

I o F X the

( *094 )

the Mercury will run out, till it comes to fomc Icller
height as B C, at which it will again flop, the height
B C being nearly in a recipr -cal proportion to tire Dia-
meter of the (mall end of the Tube.

The Seventh Experiment in Phil. Tranf. N®. 35J i^
the Reverfe of this.

Exp. VI. Fig. lO. Is the fame in fubflance with the
former, but made with a large Glafs Funnel A B,
inftead of a Tube.

The Reverfe of this in Water is the thirteenth Expe-
riment in the fame Eranfadfion.

In all thefe Experiments it is eafily feen, that the Ef-
fect is owing to the difference between the two Artra-
dions, by which Mercury tends to Glafs and to its
own body ; they being always oppofed to one another,
fo that a particular Explication is no way neceflary.
But perha^ it may fave fome little trouble to the Rea-
der, to remove the following Objediion, which wHl
readily occur to him.

In the Experiments brought to demonflrate the
fourth Propofition, the Globule of Mercury adheres to
the Glafs in a plane Surface, w’hich cannot be done
without encreafing the Surface of the Globule, and con-
iequently removing fome of its Particles from the con-
cad of one another. If therefore they tend more flrong-
ly to one another than to the Glafs, |yhy do they nor
recede from the Glafs, and alTunie a figure perfedly
Spherical, that they may all have the greateft poffible
contadt with each other I

To this we may anfwer, that the Power, by w hich
Mercury is atttaded either by Glafs, or by other Mer-
cury, is proportional to the attrading Surface; and
therefore, though, cotter is parihus, the tendency of Mer-
cury to Glafs is not fo ftrong as its tendency to other
Mercury, yet in this cafe a much greater number of

Met-.

( 1095 )

Mercurial Particles coming fnto contact with the Glafs,
than what recede from the contadt of one another, it
is no Wonder, that the Attraction of tlie Glafs prevails,
and cautes the Globule to adhere to it For the num-
ber of Mercurial Particles which lofe their contaCl with
the other Mercury, is no more than what makes up
the difference of Surface, which arifes from changing
the figure of the Drop: whereas the Particles, W’hich
by this means come to adhere to the Glafs, are all
thofe that conftitute the plane Surface, in which the
Globule touches it.

Which Confideration ought likewife to be apply’d
to the Sufpenfion of Quickfilver in Glafs Tubes, cither
at extraordinary heights in the open Air, or at lefTer
heights in a f^aerntm, as above mention'd. For the top
of the Tube being Spherical, or nearly fo, it will be
found, that the contaCf of the Mercury with the extre-
mity of the Tube, is to the contad with other Mercu-
ry, which would be gain’d by its leaving the Top of
the Tube and defeending a very fmall fpace, in zRath
infinitely great ; and confequently that the contaCl of
the Mercury with the top- of the Tube is one caufc
of its Sufpenfion.

Coroll ifi. From this Propofition it appears, that in a
Barometer made with a narrow Tube, the Quickfilver
will never (land at fb great a height as in a wider.
Which accounts for the I hxnomenon fo often mention’d
in the Yearly Hiftory of the Royal Academy of Scien-
ces at ?Arh^ by Monf. De Ia Hhc \ that in the Barome-
ter, which he confiantly made ule of for his annual Ob-
i'ervations, the Quickfilver did nor rife lo high, as in
another he kept by him, by about three Lines and a
half, which is near a third of an Inch our Mealure :
For he tells us, that the Tube of his Barometer is very
fmall*^ So that there is no need to have recourfe to any

pc.CllS

( '®9<^ )

peculiar'fty either in the Quickfilver or the Glafs of
which that Tube was made; or to an unperceived remnant
of Air left in the Tube, from fome of which caufes that
EfFedl and fome others of the fame kind were imagined
to proceed.

Cor. xd. In a Barometer made with a fmall Tube,
the Mercury will rife and fall irregu'arly. For, as the
height of the Mercury depends partly upon the Dia-
meter of that part of the Tube that touches the up-
per Surface of the Mercury, it is plain, that the unavoi-
dable inequalities in the Diameter of the lube will be
more conflderable, in refpedi to the whole Diameter ;
and confequently will afTc<^ the height of the Mercury
more in a fmall Tube than in a wider. And this I
take to be the reafon, why it is fo very difficult, noc
to fay impoffible, to make two barometers, which ffiall
exaiSfly agree in the height of the Quickfilver in all
conftirutions of the Air, efpecially if the Tubes be ve:
ry narrow. This irregularity is flill more conflderable
in the Pendent Barometer in which the Quickfilver
moves through a large fpace, in order to make a fmall
alteration in the length of the Column fufpendedJ The
fame confideration is eafily extended to ihofe Levels,
that depend upon the rifing of Mercury to the fame
height in the oppofite Legs of a bent Tube ; an loftru-
ment of which kind has been lately offer’d for the
fervice of the Publick. And as the effedi is juft con-
trary in Levels made with Water or Spirit of Wine,
due regard ought to be had to this Property in the
conftrudlion of thofe Inftruments, by making the Tubes
fufficiently wide, in order to diminilh the Error as much
as poffible.

III. Fart

( '0J»7 )

III. Tart of a Letter from Dr, Rich. Richard-
foiij to Will. Sherard, LL. D. R. S. S. giVtng
a relation of a wonderful Fall of Water from
a Spoutj upon the Mores in Lancafhire.

JHad an opportunity when in Larjcafhire of vifidng a
fecond time a vaft breach in the Ground, which
was made by a Spout, which fell upon Emott-more.
The account I took of it when I firft faw it, I put into
Writing ; and upon a fecond Infpedion, finding it to be
pretty exadit, I thought a Tranfcript of it, would not
be ungraceful to you, which you may communicate to
your Friends, and make what ufe of it you pleafc.
You may depend on it as true.

Tho’ our printed Voyages of feveral parts of the
World furnifli us with frequent accounts of damage
done at Sea by Spouts of Water, yet fuch rarely hap-
pening at Land, induc’d me to take the following Rela^
tion of a remarkable one, which fell on EmotUmorCj nigh-
Coin in Lancapire, on Tusjday the 3<^of 1718. about

ten in the Morning: when feveral Perfbns who were im-
ploy’d in digging Peat nigh the place where this Acci-
dent happen’d, upon a fudden were fo terrify ’d with an^
unufual noife in the Air, that they left their Work and
ran Home, which was about a Mile from the Place : But
to cheirgreat fu^ prife they were intercepted by Water ; for
afmall brook in the Way was rifen above Six Foot Per-
pendicular in a few Minutes time, and had overflown,
the Bridge.

It is to be obferv’J, that there was no Rain at that
time on Emott-mors, ojily a Mill, which is very frc-*..

quent

( lojiS )

quenc upon thofe high Mountains in Summer time-
There was a great Darknefs in the Place where the Wa*
ter fell, without either Thunder or Lightning, ('as I had
my Information from an Eye Witnefs^ The Meadows
at Wicolae were fo much floated that the like had not
been feen in feveral Years before, tho' there it was a
very bright Day.

Upon this account, I went to view the Place where
the Water fell; tho’ 1 believ’d this Inundation might
proceed from an eruption of Water out of the fide
of the Mountain ; fuch being not unfrequent, where
Lead or Coal have been Dug, but neither have
ever been fought fOr here. Upon approaching the Piacc,,
I was ftruck with unfpeakable Horror, the Ground was
torn up to the very Rock, where the Water fell, which
was above Seven Foot deep, and a deep Gulf made for
above half a Mile, and vaft heaps of Earth call up on each
fide of it, fome pieces remaining yet above twenty Foot
over, and fix or feven Foot thick. About ten Acres of
Ground were deftroy’d by this Flood. The firft Breach
where the Water fell is about fixty Foot over, and no
appearance of any Eruption, the Ground being firm a-
bout it, and no Cavity appearing. 1 muft not forget
to mention, that the Ground on each fide the Gulf was
fo fhaken, that HxgQChajmes appear’d at above 30 Foot
diftance, which a few Days after I obferv’d the Shep-
herds were filling up, leaft their Sheep ihould fall into
them.

IV, An

{ lop? )

IV. An Account of the Phaenomena of a very
extraordinary Aurora Borealis, feen at London
on November lo. 1719* hoth Morning and
Evening, Dr. Edmond Halley. R.S.Secr,

UPON Tuefdaj^ November 10. 1719. in the Morn-
ing, Jnpiter applying to the Second in the Wing
of N/rgo, I got up about $ of the Clock to obferve him,
and having had the Satisfadion to fee my Calculus per-
fedly well anl’wer the Heavens, I found certain white
Streaks in the Sky, feeming nearly Perpendicular ; which
whilft I confidered them feemed inftantly to vanifli, and
foon after others came as inftantaneoufly in their room, f
began to imagine that this was likely to be (bme part of
the Phenomena of the Aurora Borealis. But there appearing
nothing like that luminous Arch which we haveof late fo
often feen in the Norths knew not what to think; till look-
ing up towards the Zemth, 1 perceived an entire Canopy
ot (uch kind of white Stride, feeming to defcend from a
white Circle ol faint Clouds, about 7 or 8 degrees in
Diameter, which Circle fometimes would vanilh on a
fudden, and as fuddenly be renewed. I obferved that
the Center of th s place of Concourie was not precifely
in the Zenith, but rather 14 degrees to the Southwards
thereof ; which I was well enabled to eftimate by a Star,
which on each return thereof fliewed its felf about the
Center of the Circle. This Star is the iph Star of the
Great Bear in r-yf^o’s Catalogue, whole diftance from the
Pole at this time is 5i Ydegrees, and which about half an
hour paft Five that Morning pad the Meridian, fo that
thofe Rays centred very nearly on the Meridian it felf It

i o G was

( I lOO )

a very entertaining Sight, till fuch time as the Day-break
began to oWcuri thcfe Lights, whrdi were but faint,
though fufliciently diftinguilhable. They came none of
them low'er than to about 30 or 40 degrees of Altitude,
and (eem’d not to have afcended from the Horizon. The
Sky was perfectly Serene and Calm, which fccms to be
one of the concomitant Circumftances attending the Au-
rora Borealis, of which this was certainly a Species. For
the Night following a Neighbour gave me notice of a
flrange ftreaming of Lights feen in the Air, wJiich there*
.Upon I attended from the Hours of 97 to 11, when a
Fog came fo thick as to put an end to my Pr fpeiL. but
during thk whole ttme there afcended out of the E.
and N. E. a continued fuccellion of whitifli Striae, ari-
fing from below ; and after changing as it wc'^e into a
fort of luminous Smoke, pad over head with an incre-
dible fwifenefs, not inferiour to that of Lightning; and
as it pad, in Tome part of its Padage, feemed as it w’ere
guilded, or rather as if the fmokc had been drongly illu-
minated by ablaze of Fire below. Some of the StH£
would begin high in the Air, and a wdiole let of them
lubordinatc to one another, like Organ Pipes, would
prefent themfelves with more rapidity than if a Curtain
had been drawn from before them ; fome of which would
die away where they fird appeared, and others change into
a luminous Smoke, and pals on to the Wedvvards with
an immenfe Swiftnefs And I am of opinion that had
it not been for the Moon, then ten Days, old and ve-
ry bright, this for the time would have been reckoned
as confiderable an Appearance as that of the, 6th of
March, 17^6.

V. A

( 1 1 0 1 )

V. ^ Relation of the fame appearance, Jeen at
Cruwys Morchard in Devonfhire. ^eing part
of a Letter to Sam, Cruwys, Efq-, R. S S. and
hy him Communicated to the Royal Society.

yO U have doubtlefs been furprized again afrefli by
the wonderful Lights which have been feen feve-
ral times of late like thofe defcribed in the Philofofhicd'
TranfaPHons ; feen on P/Iarch 6. 1716.

Monda) the 26 of OPioher, between 7 and 8 in the
Evening, 1 faw Come fmall appearance of it, •viz. 3 or 4
large Corulcations in form of Pyramids, of reddilh Co-
lour inclining to Yellow, which rofe about 50 degrees
above the Horizon, and continued but few Minutes. But
the North part of the Hemifphere was very bright and
red all the Evening both before and after, till Ten, if
not longer.

Tuefday, Movemh. 10. Thefe Lights were feen again a*
bout 4 in the Morning, of which fome fay (to ule their
own Exprelfions^ that the Element opened fometime
at one place; then at other ; from whence came great
lliining Lights that continued a while and then went a>
way by degrees, and the Holes clofed up again. This
continued till Day break.

The Evening following coming from Tyvertm 2h''uz
half an hour after Eight, I faw* the North part of the
Horizon, very light and reddilh fnotwithftanding the
Moon being about 10 Days old, was then in or pad
the Meridian, and ihone very bright) in a fhort time
the ftrearaing luminous Rays began to appear very
plain, fome in one Ihape, Tome anothef; many of them

10 G 2 like

( 1101 )

like Cones or Pyramids, but mod of them badly ter-
minated ; feme of which mounted very highf almoft to
the Zenith, to which place, or near, they all or mod,
feemed to point. Shortly after there appeared a long
Streak of about 30 Degrees, parallel to the Horizon and
about 1 5 or z6 didanc from it, and about i or ; broad,
but badly terminated and of a fiery red Colour: which Cent
out Tome of the fame dreaming Beams towards the Ze-
nith. About 6 or 7 Minutes after there appeared (fome-
W'hat fudden) a Circular Figure like an IriS; but twice as
broad, of a pale Colour* The Fad part w’as termina-
ted by the Horizon at full Had, if not fomething to the
South, and the Wed End about North Wed; the up-
per part of its Arch being 50 or 60 Degrees high,
great numbers of luminous Rays darted from it up-
ward and downwards, (or elfe pading crofs it from the
Horizon) at oblique Angles pointing to the .Zenith, ef
pecially from the North Ead parr. This continued, as
near as I can guefs Cby the didance I rode) about 8
or Q Minutes, when it divided and difappeared. After
an Interval of 3 or 4 Minutes, another Iris-like Figure
appeared, (of a Colour (as it feemed) paler than any of
the dreaming Lights had been) whofe Diameter w as lefs
than that of the former, and (hewed more than its Se-
micircle above the Horizon, tl>e upper part of its Arch
approaching near the Zenith. I could not obferve any
Rays to pafs from, (or a- crofs) this as from the others
The Centre of this lad was much more to the Wed than*
that of the fird- After the continuance of a Minute cr
o, it began to break in the upper part of its Arch and
fliining Particles being fent out from both its broken
Ends towards the Zenith, (to which they w’ere near be-
fore) or rather a little beyond it to the South or >5outh
W^ed, they there formed a fort of Corona, curving and
bending fomewhat like Flames reverberated, on tl3e Arch

of

{ 1105 )

of an Oven : tho’ this exprefleth it but badly, yet I
know not how to defcribe it better. It Teemed to me
and others to be finely tinged with various Colours,
Red-Yellow and Blueilb, and Tent out every way
from it (except South and South- weft) long flame-co-
loured Rays, After this had continued about two Mi-
nutes, its ftiining Light abated, and it left behind it
for Tome Minutes, fomething like a whitiQi Cloud (like
in Colour to what the Light on the of M^nch laft;
left behind it, after the fiery Particles were extinguiftied,
but thinner).

M. B. All this while the Moon (hone very bright,
from which this Corona was not very far diftant, per-
haps not twenty Degrees, to the North Eaft. After this
there continued to be fent up many fiery Coloured cr
Yellowifli dreaming Lights, fometimes more, fome-
times lefs, now here, now there, all along the North
part of the Hemifphere, but moftly from the North
North Eaft All this while fomething like fmall whitifli
Clouds f which to me Teemed to move towards the Ze-
nith, or to point a little more Southward, but difap-
peard as they approached the Moon) were carried ve-
ry fwiftly, and at very Ihort Intervals, moftly coming
from the Eaft and North Eaft, bur many alfo from
North and North Weft. We took but little notice of
this at firft, fuppofing it had been nothing but the re-
fledion of the other Lights, or the fhadows of the
Clouds ( whereof the North parts were pretty full)
as the ftreams of Light paft behind them: But af laft
we obfervcd that, when the Lights at any time abated,
thefe kind of Clouds continued to fly as fwift and
frequent as ever. This \ faw till Twelve or One next
Morning : many others faw it next Morning till al-
moft break of Day, when it appeared much more red
and fiery than it was in the Evening ; the Moon perhaps.

bcingj;

( ‘104 )

being then fet. Some People obferved tall Cones ro
arife in the Eaft, and to be carryed to the Weft pretty
fwiftly in an ered Pofition, but I faw them not. It has
been reprefented here in all forts of Appearances, Ar-
mies, Battles, dv and has put abundance of People
in difmal Frights : But I had not an Imagination ftrong
enough for it,

1 6. IVill, Maffndfr.

\l. J further relation of the fatne- Jfpearance as
feeji at Dublin, communicated to the Tuhlip?er
by an unlqiown Hand.

IT is with pleafure that I now give you the trouble
of reading the enfuing Account of the furprizing
Lights which on Tuefday the tenth of November
we faw in the Northern Semicircle of our Horizon,
The Afternoon was very Calm and Serene; about
fix in the Evening the Sky was ting’d with a ftrange
kind of Light, and fomc Streams began to projed from
the North and North Eaft. One of them arofe about
N by E- and was nearly a Subtenfe of an Arc between
that and S. W. by Weft ; it was a little curvated toward
the Sun, and what I faw of it (for the North part of
the Horizon conceal’d by Houfes) very much re-
fembied the tail of a Comet : About the fame time
there was one or two which arofe in the Eaft, afeend-
ing obliquely fo as to leave she Zenith feveral Degrees
to the Northward,

Thefe Strid continu’d to appear and difappear alternate-
ly till toward Eight in the Evening ; they were Pyramidal,
and their Vertices frequently projeded feveral Degrees
to the South of our Zenith.

Between

I

( )

Between nine and ten I was agreeably furpriz’d with
a kind of Corufeation, or Flalliing, that fliew’d it felf
between twenty and fixty Degrees from the Ze/iith, iii
the South or South by Weft 5 and which from four or
five, fometimes from more places at once, darted with
a Velocity not much inferior to that of Lightning ; and
by interfering with each other produc’d a beautiful Tre-
mour or Undulation in that ['ubiWo. which I can-

not better illuflrate, than by comparing it to the Beams
of the Sun, refletfted on a Ceiling from the Surfaces of
two or three Bafons of Water ; Thefe Waves of Light
were only vifble at the inftant of Corufeation, and
were of a pale whicifli Colour, fomewhat refembling the
flaflies produced by the violent agitation of Quickfiver
in an Exhiufted Receiver; but fo ftrong that a Gentle-
man who about that time w^as in a Room by himfelf,
without a Candle, afTur d me he took it for common
Lightning : Thus it continued inceftantly for more

chan an Hour, during which time feveral lucid Areas^
like little Clouds, difeover’d themfdves in the pure
Sky, and after they had continu’d about fve or fix
fecond Minutes, as near as 1 could guefs, would in-
ftantaneoufly difappear ,• moft of them pretty much.re-
fembl’d a very thin white Smoke or Vapour illumina-
ted by the Full Moon.

About three quarters paft Ten, this Vapour was al-
moft fpent, or by a brisk Gale at South by Weft difpers’d
and driven to the Northward; at which time, be-
tween the Weft and North, a vaft body of it, like a
very bright Flame-colour’d Crcfufculum, feem’d to be
fix’d : From this Bafts feveral Beams or StrU of {hmmg
matter were at uncertain intervals, emitted ; and tho’ it
was not fo feniibie to tbe Eaftward of the North, yes;
feveral mighty Pillars wefe alio cjjtfted from thence;
One, which if 1 rmftake not, arofs dired^Iy under

( 1 1 o6 )

the Pole, was, above all others that had preceded
it, both as to its Magnitude and Denfity fo furprizing,
that I’m perfuaded the fmalleft Print might have been
read by the Light thereof, had not that of the Moon,
which (hone very bright, pretty much effac’d it: ’twas
ting’d with a kind of Yellow and Violet Colour. In
about two or three Minutes it died away, and was fuc-
ceeded by others of an inferior Order: It was now about
a quarter part Eleven of the Clock, and nothing but
repeated Fhafes of the fame Spesflacle offering them-
felves to View; the Vibrating Motion had cealed j-thc
Vapour fliewed it felf no longer in lucid Areas ; the
dreams of Light were not fo frequent, and thofe more
langtiid than before ; and the bright Aurora having fet-
led nearer the Horizon^ I concluded iht Scene was at an
End, and accordingly gave over the queft of new Ph£-
nomena^ with only oblerving that about N. E there ap
pear’d feme Clouds that refleded an unufual kind of
reddifh fight. Others, who thro’ a Principle of Feat
fat up longer than I did, reprefent the End with very
luf prizing Circumflances ; but as it, efcap’d the Eyes of
thofe who were bell qualified to oblige the World
with an Hiftory of it^, fo I defpair of adding any
thing that may be fatisfadory : and there were no doubt
many Circumflances of Weight that I did notobferve;
for the wonderful Variety x.\\\s Fi'Anomenon and

the frequency and fuddennefs of its Alterations, made
it impoihble for the Eye of any Tingle Perfon to trace

It.

On Tuefd&y the iqr/; of Novemher we had the fame
Thdtnomena repeated, tho’ not with the lame Variety:
About a quarter pafl ten at Night, a vafl Body of
fiiining matter was colleded between N. W. by Wefl,
and N. by E. in the form of the Segment of a Circle,
whofe Center was about 25 or 30 Degress below the

Horizon ;

( 1107 )

Horizon ; from its Periphery a few fhort Pyramidal Streams,
of the fa^ne luminous Vapour, afcended by a flow and
nearly uniform Motion, and were exceeding rare fo as
not to efface the fmallefl of the fix’d Stars ; and in a Mi-
nute or two vanifh'd : It was very remarkable that the
Light which that Colletiiion of Vapour emitted was fo
great, that in the otherwife very dark Night, I cou’d
thereby ('at three quarters pafl: Ten) read the Title of the
laft Philo f. Tranfa^. which then happen’d to lye on my
Desk ; and at four or five Yards diflancefee the fmal-
left Books in my Study.

VII. Jn Account of another Very confiderable Au-
rora Borealis obferVed at Streatham in Surrey,
by Mr, Thomas Hearne j and Communicated
by Coll. Francis Nicholfon, R, S. S,

Aving feen Dr. Halleys Account of the Coruf-

cations in the Morning and Evening of Movemh.
lOth. (and the Letter annexed to it from Devonfhire) I
had the Pleafure to find the Obfervations made upon
that Appearance very agreeable to what 1 had my
felf obferved the Evening of that Day ; and to what i
did not at that time obferve, but had an opportunity
of obferving in the Night of Dec, ii. I believe much
more plainly than Dr. Halley had in the Night of No-
vember lO.

Dec. nth. About one a Clock at Night (or rather
in the Morning of Dec. itth) I was called to obferve
Corufeations which appeared of a much different Co-
lour, and in a very different manner from any I had
before feen.

10 H

The

( 1 1 0 .8 )

The dreams of Light that darted upwards from the
Horizon Teemed to be at confiderably a greater diftance,
but not at all in Icfs quantity than thole of Mov.ioth,
But their meeting in a Point near the Zenith, and there
forming a kind of Can<>j>j, was what was particularly
remarkable in the Manner of the Corufeations now di^
ferent from thole of t^ov. i o.

The dreams of Light role from the Horizon only
towards the North, and on each hand towards N. Ead
and N. Wed : But near the Zenith a Canopy was formed
of dreams of Light meeting in a Point, not only from
thofe Quarters, but allb from the South, &C. Only
to thofe Points they extended downwards from the
Zenith but a little Way, and were neither in To great
quantity nor quite To bright as thofe Northwards. At
fird I thought the Point in which the Streams met was
cxadly the Zenith, but upon obferving it fomething
longer, I found it was not To, but a few Degrees to
the South of the Zenith. The dreams of Light near
the Zenith, which formed this Canopy, were of a pret-
ty bright Colour, and in great Quantity, and darted
very Iwifily.

On each fide of the N. towards E. and W. but not
exactly in the N. it felf fat lead when I faw it) from
about 10 or 15° to 40 or 50° above the Horizon, the
Streams were of a glowing red Colour, whereas all that I
had ever feen before vv^ere very pale. The rednefs
was like that of a burnt Brick, and neared of any
thing I have feen to the Colour, which remained for a
few Minutes, like that iradt through which the Meteor
paded in the Spring.

The Streams appeared of this fierce Colour when
I fird faw the Corufeations, and continued fo for
fome time, till the rednefs by degrees wearing off, in
about ^ of an Hour they appeared of the ufual Palenefs,

when

( no? )

when I left them ftill forming a Canopy neat the
Zenit hf as is above defer ibed.

The Air was very Calm and Serene, not a breath
of Wind ftirring ; as I remember it was alto Nov. lotk
The Moon was now a Day or two older than it was
on Nov. loth. and a good deal further to the W. than
when I faw the Corufcacions that Night being then
near full South. She had now round her what is
commonly called a Burr larger than ordinary, and fe'
veral very lucid Clouds at a little diftance.

VIII. Nuperce Obferyationes Jjlrommicd cum ^egta
Societate communicate.

CU M in Num. harum Tran[a6iionum 357“°. Obfer-
fervationes nonnullas Planetarum ac Luncs con-
fervari digniflfimas in unum congellimus, ac probante
Societate noftra edidimus; liceat paucuia folia hujufmo*
di colledionibus in fequentibus quotannis confignari.
Nuper^e autem quas habemus Obfervationes has funt.

1718. OSioher 10°. mane, applicabatur Jupiter 2id Fi*
xas Telefcopicas, quarum loca, occafione primee appa-
ritionis Cometse anni 1680, fde qua vide Phil. Tran].,
N'^. 341^ ledulo inquifivit Rev. D. Pounds ac nuper ve-
rificata nobifeum communicavit, una cum accurata ob-
fervatione tranfitus Jovis juxta eas hac vice, ac deinde
alters Fehr. 1 1°. Batim ab oppofirione Solis & Jovis.
Ineunte autem Januario 1719. loca fteilaruro ficfe habuere.

Long.

^ A 2.9°- 59' -43"
^ jt? o . 6.13
C It? o . 3.13

Lat. Bor.

Long.

I- 7-50

4n? o°.xy'. 41"

I . 10. 18

xmo , y .43

0

•

0

10 ti

Lat. Bor.
i°.x8'54"
o . yi .56

Ubi

t mo )

Ubi notindum ftellas d & e eandem precise hoc ft*
culo fortiri declinationem, ,v vero exiguam cfTe (Idlulam
in priore defcriptione ob parvitatcm oniiflam.

Jam O^ob. 9°. 17^ 50' T. sq. Jovis limbus orientalis.
atcigic lineam ftellas e h c jungentem, fimul centrum
ejus diftabat ab^ zi' . zq" & a c U> . ftatimque a-
berat k d 19' . 35". Parvula a; Jovi proxima latuic, luce
ejus obumbrata.

Decemb. 1 1°. i8K 30. T. a:q. Saturni centrum diftabat
a /X Libra Bayero, zS' . 3.1", & Fixa Borealius erat 4' • 3 1".
Hinc conclufic D. Pound Obfervator Saturni locum jt?
10°. 41' . 10 ", cum Lau Boreal. . 16'. 43".

1719 Feb. 11°. 6^ 561 T. s:q. Jovis retrogradi cen*

trum diftabat a ftella d fuperius defcripta Io'.4^"

6. 58^ Idem centrum diftabat ab ^ 6. 7

9. 377 Iterum diftantia capta a d — - ■ • lo. 9

9 . 437 Icerum ab ^ 6. n

9 . 497 Jovis centrum diftabat ab a — 15 . a i-

9.587 Idem centrum a parvula x — ^ -q-jS

Circa Horam feptimam Jovis limbus orientalis attigit
lineam per at & ^ produdam; Jupiter itaque tunc ha-
buit np o°.(5 cum Latitudine Boreal. 1°. 16'. 30"'.
Deinde,

Feb. 13°. 8’’. o'. T.xq. Declinatio centri Jovis, Ml-
crometro menfurata, Borealior erat ea ftellje urriufque d
II ' . 37", & 8^. 20' eadem differentia inventa eft 1 1'.
36". Hord vero 8^ 48' centrum Jovis diftabat ab e
1-7'. 40'''.

Apr. 22°. ^o^ 45'. T. aq. Saturni centrum fequeba-
rur fA, Libra 4"iTemp. five i'. 8" Afc. Red^. Micro-
metro autem Borealior inventus eft Fixa 3 5'. zs". Stella
autem in Catahgo Britannko tunc habuit, m 8'V

Iu.3t. Bor.. 2°. 3.'. 54^.

Math

( 1 1 1 1 )

1 6°. 8\ oo' T.seq. .r fcqucbatur Cor Leo^is i°. 34'^
Afcenfionis redce ; Borealior auremerat (lelia ilia o'. 41 "j-.
Temporis, licc eft, 10'. 7" Arcus cceleftis.

Fadem node, 15*', 18' T. app. Obfervavit D. Ste->^
fhanus Gre-j Murtem, ratione Afcenfionis redt^, fequi
ftellam in Cauda Cafricorni Ofiencalem 16'. 15"; ftmul
non nifi o'. 1 1''. auftralior erat quam Fixa.

'^mii 7°. io\ 15'. T. app. Jufitcr diredus keriini !£■*
verfus eft ad ftellas Telefcopicas pr^^didas, & turn (e-
quebatur ftellam d. o'. 35" Afcenfionis reda?, &^o^ 30'
diftabac ftxa a limbo Jovis proximo 4'. 1 8".

Poftridie Junii 8*^. lo^. lo', Jupiter fequebatur ftel^
lam alteram e \'. 30'’ Afcenfionis red^e, ac ftatim di-
ftantia limbi Jovis proximi a ftella capca eft Microme-
tro 7'. 30".

JulH 5. 8^ 26’. T. app, Conjungebantur arde J^^pt-
ter & Fenu^, quce turn Borealior prxcedebat Jovem fe-
cund um Afcenfionem redam 1'. 20": Centrorum autem
diftantia ex decies repetitis media, capta eft 13'. 36".
H£Ec tria Londini obfervata communicavit harum Scien-
tiarum eximius Cukor D. Martinus Folkes, R. S. Soc.

3. I2^ 20' T, xq. Mars pene Acronychus fe-
quebatur ftellam t Aquarii Bajero I o'. 58" 'Temporis,
five 2°. 44'. 57" Afcenfionis Redae*^ Erat autem fixS
Mars Borealior o'. 36" tanium ; unde concefTo loco ftel-
\x Eritannico fit locus Martis obfervatus x 1°' 10'. 10"
cum latitudine Auftrali 6°. 38'. 10".

Aug. 10°. 50. T. xq Mars fequebatur fixam

minorem qux prxcedit t Aquarii 1°. 39'. 30" rations'
Afcenfionis redx ; Auftralior veroquam fixa lo'. 42".

Augi 16°. 7^ 18'. T*xq. SpicA firginis prxcedebat
Veneris centrum 5 "" fecundis temporis, five i'. 20" Afcert-
flbnis redx, auftralior Planeta i8”~ temp, five 4’, 35'^-

Aug. 17^ Mar’s pridie Acronychus ac Terris proxi-
mus obfervatus eft ad duas fteliulas contiguas, Parallaxis^

( »'•» )

cjus invefligandi gratis, juxta method um ^ D. Cajfinot
in libro de Cometa anni 1680, exhibitam, Unde
tis Parallaxin etuere in Tranfail. proximi conabimur,
Harum vero ftellularum borea turn temporis locum
habuit X 5^- ' cuni Lacitudine aullrali 6®. 6'^ *

altera vero Auftralior habuit x 3° 5 • 30”* cuni Lar,
Auft. 6°. lo'jproxime. Hor^ vero 10'’. 40'. T. seq. Au-
Hralem (equebatur Mars 41' min. 40" Afcenfionis redlse,
€aque adhuc Auftralior erat 7'. 50*'.

Sept. 18. 9^ zQ*. T. aeq. Mars vifus eft praecedere
ftellam in Catakgo Britannko Aquarii 53*®"’. 5*. 45*'
Temporis, five 56'. 24". xAfcen. Recftx ; fimulque Stella
Borealior erat limbo Martis boreo, non nifi una Pla*
netae diametro. Locus ftellae tzi 19'. 57 7 Lac. Auft.
4-487. ^ ,

O^cb, 30. Vefperi 5\ 45. T. app. Mars proximus
ftellis duabus contiguis ad ^ Bayero^ quae funt 73*®
& 74'^ CataL Brit. Practerierat reeftam per eafdem du-
<3am, eratque angulus ad Martis centrum ad fenfum
redus .* Borea vero ftellarum eandem habuit declinatio-
nem cum limbo Planetac auftrino. 53' diftantia ftel-
lae a centro Martis 30". 5^ 56' centrum difta*

bat a tertii & Auftraliore ad b, five 75'® Aquarii, 17'.
04". 6\ s8' diftantia centri a Bore^ five 73'* erat 3'. 5".
Hinc concludere licet Martem, hora 3^ 30' proximo,
ftellae Boreae conjundum fuifte, eamque uno tantum mi-
nuco ad Boream reliquifte. Fixac autem locus eCatalo*
go'Britarmico tunc erat x 00" cum Lat. Auft.

1°. 40'*. 74*^ vero habuit x 10° 29'. $o cum Lat.
Auft. 1°. 44 7.

Novemh. 16°. l9^ 18', T. xq. Venus praecedebat Lan-
•eern Lihr^ Aufirinam 3’. 13" Temp, five 48'. 23" Af-
cen. Red. fimulque fixa borealius erat centrum Veneris
7'. 45". Venus quafi Stationaria apud Nodum ejus Af-
cendentem.

Decemk

I

( in? )

Decemh. 5®. T 9^ T. seq. Saturnus prsececlebat certiam ad
I ^Lihr<Xf (\vQ Lihr£ Cat. Brit. d. 46 ' Temp, five i T.
jz” Afc. Rect. Erat autem fixd Auftialior 15'. 19". dif-
ferentia per Micrometrum captl Unde Sacurni Jocus
tn.^0.25* cum Lac- Bor. s'". 5'^,

Ohferyationes Lun^e ^ EcUppum.

In dida Tranfa^^N^. 35'7. par. 8^z. Obfervationem
dedimus Eclipfeos Lunaris anno 1717 Martii P.M^
St. vet* apud Cambridg Nov-Anglerum habitam ; apud
nos vero ob Nubes inconfpicuam Defiic autem Eclip-
fis ibidem 4»’ r, neque alia ejustum temporis fup-
petebat obfervatio. Poftea veto arte Nautica &indu-
ftria inter primes infignis Dom. Candler Navarcha Re-
gius, ex America attulic & nobiicum communicavit ejuG-
dem Eclipfeos phafes Lim£ Peruvia a Dom. Petro Pe^
ralta^ Mathematico Regio multis titulis claro, obfer-
vatas, Typifque ibidem impreflas. Initium autem E-
clipfis ponic Lima 8’’. 41'. 8". Finem vero ii’'. 19'. 55",
Simul laudatus D. Candler propriam obfervationem, ^ad
Infulam quam Virgine Gorda vocant captam, concedir,
Ibi deflic Eclipfis i2^ 13'. P. M, Fine per ccelum fudum
diftindle vifo. Poftremo inter A6ta Regi^ Scientiarum
Academiae Parifienfis iftius anni, comperimus duas &
quidem fatis conformes hujus Eclipfeos obfervationes,
alteram a D* CafJinoj alteram a D. de la Hire in Obfer-
vatorio Regio captas : Hie Initium aeftimavic I3^f4'*.
Finem vero certius id’’. 38'. 10". Ac lllelnitium 1 3’’.

Finem 16’’. 3 8'. 15". Maxima obfcuracio huic 7j- Dig. illi
7rDig.

Hinc ex Fine, in fngulis locis ut videtur accuratius
fumpto, proveniunt Longicudinum differentia inter Pa-
r'lfios ^ Limam 5’’. 18'. ao", Inter Parijtos & Camhridg

4"' J 5 -

( tn4 )

4^ 55'. 50''. Inter Tarifios & Infulam Virgtne GtrdA
20". E quibus fi 9'. 40* fubduxeris, provenienc
Longitudines ad occafum Londirti t Lma 77°. 10*.

Cambridge Nov Anglorum 71°', ac denique Infulae Virgi-
ne Gorda 6^°. 55' i unde Iiifularum adjacentium fitus
Geographici certo corrigi poterinr.

Altera Lunae Eclipfis ejufdem anni Septemlris nono
Verperi, ab iifdem obfervatoribus & D. Maraldo Patifiis
confpeda eft. Finem Londini obfervavimus in jedibus
SocieCatis Regiac 7^ 26'. Parifiis vero D. Cafjino Finis
7^34'. 5’o", D. Maraldo 7^ 35*. 50", & D“° U Hire
yK 34', 15;". Simul D, fVurtzelhaur NoribergA eundem
Finem vidic 8^ id. 45" Fiinc confirmantur Meridia-
norum differentiae Londinum inter & Par'tfios, pratfertim
ex obfervatione D. Maraldii nempe 9'. 30"; uti & in-'
ter Londtmnt & Noribergam 44'. 45", quantam fxpius
olim expert! fumus. Porro quinto die poll Eclipfin,
Septemhris vefperi, Luna occultavit Palilicium Pa»
rifiis, obicrvantibus figillatim DD. Maraldo^ Delifle]\x^
niore. Evanuit autem ftclla c regione Maculx Grimal-
di five Paludis Mareotidis, Hora 9^ ii'. 35". Emerfit
autem e limbo Lunx obicuro 10*’. 3*. f 5”. HujusOc-
cubationis obfervatio Londini habetur Phih

Tranfaid.

Obfervafiones illaf, in quihus Temp. xq. adhibetur.
Rev. D " Pound accept as debemus* Tubo autem qutndecim-
pcdali capta pro ccrtifimis hahenda funt.

A N

-^A N

■;r'.N .D E X::

To. the TJnrtieth Yolumc of ,t\iQ ^hilojophkal

TranJaBions, • ' *

- . 1 w. r J i _ . ' - ^

A.

ALgelra. An Attempt to improve the Method of
Approxirhating in extradling the Roots of Equa-
tions* in Numbers, n.yi^z, f. 6io, A Difcourfe of In-
finite Series’s. ». 3^3.

Antie[Hities m Suffex. f* 5’49» 55^- /^. 7S3.

ArchiteBure Romans Obfervations on it. 361. /?. 561.
Aftronowi'cal Obfervations. ,n. ^§7. p. 847. n. 363. />* ii09»
Aurora Bore ales in Kent. n. 35'i-’ p. 58^. OnQ in London.
n.‘^$^.‘p. 585. Another n.%6‘^,p. 1099, 1101, 1104*
At StreathaWf ihid. p. iioy.

. . - B. ■ '

Barometer, The Caufe of its Variation, align’d in the
Hi/l. Acad. Rojale, confides 35 i , 570.

Blood, Of its Motion, n. 355, p. 7^6. Of its Specifick
Gravity, 361, />. 100

Books, Accounts of them. I. Polenus de Motu Aqu^n rnixto.

^•3 J4 P-T^}‘ l\. Apollonius Fergaus de CorAcisJkQ.Ah.pj
Britain, Whether once aPeninfuIa, p $p, .Spme

Account of its Affairs under the Roman Government,
».356.^783. * ■ “ ‘

Burning Loncave, Experiments made with it, n. 360, p. 97^.

- • » • -‘-C. ■ .ii ■ ‘ , ,

Cape of Good Hope, Its Longitudev ^*..3^1. /». ypr.
CatuviiUuniJ A People formerly in the South of England,
n. 356, /^. 8i4.

10 I

Chsik,

INDEX.

Cheekt Ad extraordinary Wen cut out of it,

Colick, An extraordinary EfTedt of it, n, 351, p» 58c.

Comets, A Telefcopical one, 3J4> 7^^• One Ber-

lin, n» 357, f, 820.

Conick Seilions, Some fimple Properties of them,

Cows, Of the contagious Difeafe among them, ^.358,
872.

Curves, Of the Condrudlion and Meafure of them, 3 56,
803. An univerfal Method of delcribing them only
by the help of Angles and Right Lines, n, 359. p, 939.
Of the Curve defcrib’d by a Body defcending in the
lead Time,with a given Law of Attra<3ion, »«3 58.^.860.

Clocks, made to agree with apparent Time, f.ioyy.

D.

Viffe6Hon, of an emaciated Child, 631I

E.

Earth, An unufiial Falling in of it, 355. p» 768.

Eclipfe, Of the Sun, ». 357, ^.822. Of the Moon,
n, 361, />. 991. Another, «. is?*?- ^55*

Elephant, Its Organ of Hearing defcrib’d, n. 358, ^.885*

Experiments, To prove an interfpers*d Vacuum, ». 354,
p*Til* Of the Refidance of the Air to falling Bodies,
n* 361, p, loyii Of theCaufeof theAfcent andSuC-
penfion of Water in Capillary Tubes, 355, />.' 739.’
On the Adion of Glafs Tubes upon Water and Quick-
filver, n, 363, p> ?o83.

G.

Gafcoigne, fMr.) his excellent Inventions, and great A-
bilities, ». 351, 606.

Gibraltar, The Situation of feme Roman Towns about it,
359, f.903.

H. Heart,

INDEX.

H.

f/eart^ Of ics Force, 95^. p» S6^, 35^9, /«• pip.

p»99S» 361, f. 1039.

J»

Jamaica f Some Remarks on it, ». 357. P» 838.
Infcriptions, A Roman one in the North oi England, /?. 3 5"^.
p, 701. n* 3 J7, p* 8x5. Another n» 3 jt. /. 813. Ano-
others. 359, 94

Jupiter, The Occultation of a Fixt Star by him, n, 3jr,
^46. Tranfit of xhe 4^^ Satellite over its Disk. 359-
p. 900. Tables of the Eclipfes of the firft Satellite,
n»}6i» p» loii.

Lanchefier, Of the Roman Caftrum there, K»\$^,p*

M.

Mars, His Tranfit near a Fixt Star, n* 3^1, p, 54 8.
Maxmazwdi Minima in the Celeftial Motions; ^.960 /'.948
Meteors, One in Jamaica, n. 3^7, f. 837, One feen all
over England, n» 360. p» 978.

Method of Fluxions, Two Letters concerning it, n. 35*9,
An Illuftration of it, n, 362, p, 1050.

Moon, Of its Appulfes to the Blades, n, 354, p. 6^1,

O.

Oaks, Of Three which funk into the Ground, ft»}SSfP*7^^

P.

Plants, A new Genus call’d Araliafrum, n: 3 J4, p. yoy
Problem, Propos’d by Mr. Leibnitz, folv’d, ». 3^4, p 69 y
Pyrmont Waters, Their nature and quality, 3 y i. 7, 564

S.

Saturn, An Obfervation of him, 3 y i , p. yqS. His Sa-
tellites Motions redified, 35y, p» 768. ». 3y6,f. jy6
Sceleton, The Imprcflion of one in a very hard Scone,
». 360, 963

Sea, Several Irruptions of it, n, 352. p, yp7
Silk. Worms, Experiments of them and of their Silk iii
England, n»l6%,p* 1036. SpouU,

I N D E- x:

Scouts, The ftrange Effedsof one in Lancajhirey fJ»

V Y* 1097 • * ^ ‘ .

Stars, On the Change of Ldcitudo of fome of them,

^ 73^

Strata in a Coal' Mine defcnb’d, r* 360, f» 968 .

6‘a;?/^ Ifland in Hamher^ 1014 '

• • T\ •

Taylor, (Dr.) his Defence againft Mr. BernoHlU, tf»^6o,
P-955

Telefoopes, A way for Myopes to ufe them without Eye
Glafles, rj» 36r, p* »Gi7 • , .

Tdefcopick Sights, Who firfl: invented the Application
them to Mathematical Inftruments, ^. 3 52, p* 603

Tubes Capillary, Of the Afcent and bufpenlion of Water
in them, /?. 35'^, p»7l9

Turneps, Their great and fpeedy Vegetation, W. 9^^

‘ f.974« ' ^

• V.

b^enereal Difeafe, Of its Antiquity,

Ari Eruption of it, 35/j, />, 708 >

. W. . . . ' .

Water, An Enquiry ir.to the Caufe of its Afcent and
Sufpenfion in Capillary Tubes, 35'5', f. 739. Of
the Morion of tiinnihg W’aters> 74^ ^

Williamlon (Mr.) alTerts his'lnvcntion of making Clocks
to agree with apparent Time,^/?. 9^3* f* *079 '

Wine-y £hQ Danger of drinking cold Liquors after a
•large Quantity of it, m 351, f» 58k v ■

' 'r- . ’

ERR A T.UM;' P.ii*ic. /. ii, pro m /. uv. .

.

I

■

*4

I^mV t
.V -Ov