Natural History Museum Library

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PHILOSOPHICAL

TRANSACTIONS,

GIVING SOME

ACCOUNT

OF THE

Prefent Undertakings, Studies, and Labours,

OF THE

INGENIOUS,

IN M A N V

Confiderable Parts of the WORLD.
VOL. LIII. For the Year 1763.
LONDON:

Printed for L. Davis and C. R e y m e r s,
Printers to the Royal Society,
againft Grays-Inn Gate , in Holbourn.

M.DCC.LXIV.

<

ADVERTISEMENT.

THE Committee appointed by the Royal Society
to diredt the publication of the Philojophical
4 TranfaSlions , take this opportunity to acquaint the
public, that it fully appears, as well from the council-
books and journals of the Society, as from repeated
declarations, which have been made in feveral for-
mer 4 Tranfafiions , that the printing of them was al-
ways, from time to time, the Single adt of the re-
fpedtive Secretaries, till the Forty-feventh Volume.
And this information was thought the more neceffary,
not only as it has been the common opinion, that they
were published by the authority, and under the di-
rection, of the Society itfelf ; but alfo, becaufe feveral
authors, both at home and abroad, have in their writ-
ings called them the PranJaSlions oj the Royal Society .
Whereas in truth the Society, as a body, never did
intereft themfelves any further in their publication,
than by occasionally recommending the revival of
them to fome of their fecretaries, when, from the par-
ticular circumstances of their affairs, the Pranfaftiom
had happened for any length of time to be intermitted.
And this feems principally to have been done with a
view to fatisfy the public, that their ufual meetings
were then continued for the improvement of know-
ledge, and benefit of mankind, the great ends of their
firSt institution by the Royal Charters, and which they
have ever Since Readily purfued.

But the Society being of late years greatly inlarged,
and their communications more numerous, it was
thought advifeable, that a Committee of their Mem-
bers Should be appointed to reconfider the papers read
before them, and feledt out of them fuch, as they

a 2 Should

ADVERTISEMENT.

fhould judge mod: proper for publication in the future
Tranfadlions ; which was accordingly done upon the
26th of March 1 752. And the grounds of their choice
are, and will continue to be, the importance or Angu-
larity of the fubjedts, or the advantageous manner of
treating them ; without pretending to anfwer for the
certainty of the fadts, or propriety of the reafonings,
contained in the feveral papers fo publifhed, which
mud: dill reft on the credit or judgment of their re-
Ipedtive authors.

It is likewife neceflary on this occafion to remark,
that it is an eftablidied rule of the Society, to which
they will always adhere, never to give their opinion,
as a body, upon any fubjedt, either of nature or art,
that comes before them. And therefore the thanks,
which are frequently propofed from the chair, to be
given to the authors of fuch papers, as are read at
their accuftomed meetings, or to the perfons, through
whofe hands they receive them, are to be confidered
in no other light, than as a matter of civility, in re-
turn for the refpedt fhewn to the Society by thofe
communications. The like alfo is to be faid with
regard to the feveral projedts, inventions, and curio-
fities of various kinds, which are often exhibited to
the Society j the authors whereof, or thofe who ex-
hibit them, frequently take the liberty to report, and
even to certify in the public news-papers, that they
have met with the highed: applaufe and approbation.
And therefore it is hoped, that no regard will here-
after be paid to fuch reports, and public notices ;
which in fome inftances have been too lightly cre-
dited, to the difhonour of the Society.

CON-

NTS

CONTE

T O

VOL. LI 1 1.

I. AN Account of the Sun’s Difance from the

Earth , deduced from Mr. Short’s Observations
relating to the horizontal Parallax oj the Sun : In
a Letter from Peter Daval, Efq ; V. P. of R. S. to
James Barrow, Efq j V. P. of R. S. page i

II. Obfervatio comet ce3 qui menfe Maio3 A. 1759

apparuit , fa ft a Hagce-Comit . a Petro Gabry,
I. V. D. Societatis Reg. Scientiar. Socio, et com -
mercio Literar. cum Academ. Scientiar. Parifenfi et
Reg. Societ. Gotting .junfto : Communicated by Mr.
Emanuel Mendez da Cofta, Librarian of the Roy-
al Society. p. 3

III. Obfervatio cujufdam Meteori igniti inflar Chap
matis, fafta Hagae-Comit. d. 21 Decemb. 1758.
Nov. St. d Petro Gabry, I. V. D. Socio Reg. Socle -
tat. Scientiar. Londin. et ccmmercio Liter arum cum
Acad. Reg. Scientiar. Parifenf. et Societ. Reg. Sclent .
Gottingenf. junfto. Communicated by Mr. Emanuel
Mendez da Cofta, Librarian of the R. S. p. 5

IV. An Account op " a remarkable decreafe of the River

Eden, in Cumberland : In a Letter to Charles Lord
Bijhop of Carlifle, F. R, S. from William Mil-
bourne, Efq ; p. 7

V. An

CONTENTS.

V. An Account of the Rain j alien in a Foot-fquare at

Norwich, by Mr. William Arderon, F.R.S. Com-
municated by H. Baker, F. R. S. p. 9.

VI. Obfervations upon the Ejf'efts of Electricity ap-

plied to a Tetanus, or Mufcular Rigidity, of four
Months Continuance. In a Letter to the Royal So-
ciety. By William Watfon, M. D. F. R. S.
Member of the Royal Colleges of Phyficians of
London and Madrid, and Phylician to the Found-
ling Hofpital. p. 10.

VII. An Account of the late mild Weather in Corn-

wall, of the Quantity of Rain fallen there in the
Tear 1762: In a Letter from the Rev. William
Borlafe, M. A. F. R. S. to Mr. Henry Baker,
F. R. S. p. 27.

VIII. A Delineation of the Tranft of Venus expelled
in,theTear 1769, by Air. James Fergufon. p. 30.

XI. An Account of an Appulfe of the Moon to the
Planet Jupiter, objerved at Chelfea, by Mr. Samuel
Dunn. p. 3 1.

X. A Catalogue of the Fifty Plants fro?n Chelfea Gar-

den, prefented to the Royal Society by the worfipf ul
Co?npany of Apothecaries, for the Tear 1-762, pur/u-
ant to the Direction of Sir Hans Sloahe, Baronet ,
Med. Reg. et Soc. Reg. nuper Prafes j by John
Wilmer, M. D. clariff. Societatis Pharmaceut .
Lond. Soc. Hort. Chelfean. P reef eft us ct Pr Ac Cl or
Botanic. p. 32.

XI. Obfervations made by Mr. John Bartram, at
Penfilvania, on the Tellowijh Wafp of that Country :
In a Letter to Mr. Peter Collinfon, F. R. S.

P* 37-

XII. An Account of the Plague at Aleppo : In a Let-
ter to the Rev. Charles Lyttelton, LL. D. Dean of

Exeter

CONTENTS.

Exeter, now Lord Bijhop e/’Carlifle, and F. R. S.
from the Reverend Mr. Thomas Dawes, Chaplain
to the FaSlory at Aleppo. p. 39.

XIII. Obfervations on Sand Iron: In a Letter from
Mr. Henry Horne, to Mr. John Ellicot, F. R. S.

p. 48.

XIV. Extrall of a Letter from Simon Peter Pallas,

M. D. of Berlin, to Mr. Emanuel Mendez da
Cofta, Librarian to the Royal Society , relating to
the State of the Cold there loft Winter , dated Feb.
12, 1763. p. 62.

XV. An Account of a remarkable Darknefs at Detroit,

in America : In a Letter from the Rev. Mr. James
Stirling, to Mr. John Duncan : communicated by
Samuel Mead, EJq ; F. R. S. p. 63.

XVI. An Account of a remarkable Marine Inf e SI : In
a Letter of Mr. Andrew Peter Du Pont, to Mr.
Emanuel Mendez da Cofta, Librarian to the R. S .

P-57-

XVII. A Letter from Monfieur Wargentin, Secretary

to the Royal Academy of Sciences in Sweden, to Mr.
John Ellicot, F. R. S. relating to the late Lranfit of
Venus. p. 59...

XVIII. Remarks on the Cenfure of Mercator’s Chart ,
in a pojlhumous Work of Mr. W eft, of Exeter : In ’
a Letter to Thomas Birch, D. D. Secretary '
to the Royal Society , from Mr * Samuel Dunn.

p. 66.

XIX. A Defence of Mercator’s Chart againft the Cen-
fure of the late Mr. Weft of Exeter : In a Letter to
Charles Morton, M. D. Secret . R. S. from Mr.
William Mountaine, F. R. S. p. 69. .

XXI. An Account of a Species of Ophris, fuppofed to
be the Plant , which is mentioned by Gronovius in the

, Florae

CONTENTS.

Flora Virginica, p. 185, under the Name of O-
phris Scapo undo foliis radicalibus ovato-oblongis , di-
midii Scapi longitudine : By George Dionyfius

Ehret, F R. S. p. 81.

XXXII. New Experiments in Electricity : In a Let-
ter from Mr. Ebenezer Kinneriley, to Benjamin
Franklin, LL. D. F. R. S. p. 84.

XXXIII. Obfervations in Ele tricity and on a Lhunder-
Jhrm : In a Letter from Mr. Torbern Bergman, to
Mr. Benjamin Wilfon, F.R. S. Acad. Reg. Upfal.
Soc. p. 97

XXIV. Remarks on Swallows on the Rhine : In a Let-

ter from Mr. Achard, in Privy-Garden, to Mr.
Peter Collinfon, F. R. S. p. 101.

XXV. Fhe Properties of the mechanic Powers demon-

jlrated , with feme Olfervations on the Methods that
have been commonly ufed for that Purpofe : in a Let-
ter from Hugh Hamilton, D. D. F. R. S. apd
Fellow of Trinity College, Dublin, to Matthew
Raper, Efq ; F.R.S. p. 103.

XXVI. An Account of feme fubterraneous Apartments ,

with Etrufcan Inferiptions and Paintings dijcovered
at Civita Turchino in Italy : Communicated from
Jofeph Wilcox, Efe}’3 F. S. A. by Charles Morton,
M . D. S. R. S. p. 127.

XXVII. An Account of a new Peruvian Plant , lately
introduced into the Englifh Gardens ; the feveral
Char after s of which differ from all the Genera hitherto
deferibed ; Prefented to the Royal Society by George
Dionyfius Ehret, F. R. S. p. 130.

XXVIII. Obfervations on two Antient Roman Infer ip -
tions difcovertd at Netherby in Cumberland : In a
Letter to the Right Rev. Charles Lord Bifloop of
Carlifle, F. R. S. from the Reverend John Taylor,

LL. D .

CONTENTS.

LL. D. Canon Rejidentiary of St. Paul’s, and
Chancellor of the Diocefe of Lincoln. p. 133.

XXIX. A Method of lejfening the Quantity of Friction
in Engines , by Keane Fitzgerald, EJq ; F. R. S.

P‘ *39-

XXIX. The Difference of Longitude between the Royal

Obfervaiories of Greenwich and Paris, determined
by the Obfrvations of the Tranfts of Mercury over
the Sun in the Fears 1723, 1736, 1743, and

1753 : By James Short, M. A . F. R , S.

P- i85-

XXX. An Account of a remarkable Fifh, taken in

King-Road, near Briftol : In a Letter from Mr.
James Fergufon, to Thomas Birch, D. D. Secret .
R. S. p. 170.

XXXI. Rules and Examples for limiting the Cafes in

which the Rays of refraCied Light may be reunited
into a colour lefs Pencil: In a Letter from P. Mur-
doch, M. A. and F. R . S. to Robert Symmer,
Efq ; F.R.S. Jan. 3, 1763. ^ p. 173.

XXXII. An Account of the Succefs of the Bark op the
Willow in the Cure op Agues. In a Letter to the
Right Honourable George Earl of Macclesfield,
P ref dent of R. S. from the Rev. Mr. Edmund
Stone, op' Chipping - Norton in Oxfordihire.

P; J95-

XXXUI. An Account of an Earthquake in Siberia : In
a Letter from Monf Weymarn to Dr. Mounfey,
Principal Phy/ician of the Emperor op' Ruffia,
F. R. S. Tranfated prom the French, Communi-
cated by Mr. Flenry Baker, F. R. S. p. 201.

XXXIV. Roman Infer iptions at Tunis in Africa,
copied about the Tear 1730, by Dr. Carilos, a Na-
tive of Madrid, then Phyfcian to the Bey op Tunis,

b commu-

CONTENTS.

communicated by John Locke, Efq j F. R. S.

p. 21 I.

XXXV. A Letter from Mr, George Edwards,
F. R. S. to Thomas Birch D. D. Secret. R. S.
concerning an Obfervation ?nade by him in Opticks.

p. 229.

XXXVI. fwo remarkable Cafes in Surgery , by Mr,.
Francis Geach, Surgeon in Plymouth. Com-
municated by John Huxham, M. D. F. R. S.

p. 231.

XXXVII. An Account of a new Die from the Berries
of a Weed in South Carolina : In a Letter from Mr.
Mofes Lindo, dated at Charles Town, September
2, 1763, to Mr. Emanuel Mendez da Cofta,
Librarian of the Royal Society. p. 238

XXXVIII. An Account of the Eclipfe of the Sun,
April 1, 1764: In a Letter to the Right Honour-
able George Earl of Macclesfield, Pref. R. S.from
Mr. James Fergufon, F. R. S. p. 240

XXXIX. An Account of an Earthquake at Chat-
tigaon : Franfated from the Perfian by Mr. Edward
Gulfton, in the Service of the Honourable Eaft India
Company , and communicated by him to the Reverend
Mr. Hirft. p. 251

XL. An Account of an Earthquake in the Eaft Indies,
of two Eclipfes of the Sun and Moon, olferved at
Calcutta : In a Letter to the Reverend Thomas Birch,
j D. D. Secret. R. S. from the Reverend William
Hirft, M. A. F. R. S. p. 256

XLI. Extrait of a Letter from Mr. Edward Gulfton,
at Chittigong, to Major John Carnac, at Calcutta.

p. 263

XLI I. An Account of the Earthquakes that have been
felt in the Province of Iflamabad, with the Damages

attending

CONTENTS.

attending them , from the 2d to the 1 gth of April,
1762 : Tranjlated from the Perhan, and commu-
nicated to Henry Vanlittart, Efq ; Prefident and Go-
vernor of Fort William in Bengal, by Mr. Verelft,
Chief of the Hon. Eafl: India Company's Affairs at
Iflamabad. p. 265

XJLIII. A Letter from the late Reverend Mr. Thomas
Bayes, F. R. S. to John Canton, M. A. and F. R. S.

p. 269

XLIV. An Account of the life Ft called the Vegetable
Fly, by William Watfon, M. D. F. R. S. p. 271
XLV. An Attempt to explain a Punic Infcription ,
lately difeovered in the If and of Malta. In a Let-
ter to the Reverend Thomas Birch, D. D. Secret.
R. S. from the Reverend John Swinton, B. D. of
ChriPc-Church, Oxon. F. R. S. and Member of
the Etrufcan Academy of Cortona in Tufcany.

" . P- 274

XL VI. Problems by Edward Waring, M. A. and

Lucafian Prof ef or of Mathematics in the Univerfty
of Cambridge, F. R. S. p. 294

XL VII. Second Paper concerning the Parallax of the
Sun determined from the Obfervations of the late
Fr unfit of Venus, in which this Subject is treated of
more at length , and the Quantity of the Parallax more
fully afeertained. By James Short, M. A. and
F. R. S. p. 300

XLVIII. An Account of a Cafe, in which Green Hem-
lock was applied: In a Letter to the Rt. Hon. Hugh
Lord Willoughby of Parham, V. P. of the R. S.
by Mr. Joftah Colebrook, F. R. S. p. 346

XL IX. An Account of a remarkable Meteor : In a
Letter to the Reverend Thomas Birch, D. D. Se-
cret. of R, S. from Mr. Samuel Dunn. p. 351

L...

CONTENTS.

L. An Account of a Blow upon the Heart , and of its
Effecls : By Mark Akenfide, M. D . F. R. S. and
Phyjician to Her Majefty. p. 353

LI. Ratio conficiendi Nitrnm in Pcdolia : Author e

Wolf, M. D. communicated by Mr. Henry Baker,
F. R. S. ' p. 356

LII. An Ffay towards folding a Problem in the DoBrine
of Chances. By the late Rev. Mr. Bayes, F. R. S.
communicated by Mr. Price, in a Letter to John
Canton, A. M. F. R. S. p. 370

LIU. An Account of the Sea Pen, or Pennatula
Phofphorea of Linnaeus ; likewife a Defcription of a
new Species 0/ Sea Pen, found on the Coaft of South-
Carolina, with Obfervations on Sea-Pens in general.
In a Letter to the Honourable Coote Mole! worth,
j Efq-, M. D. and F. R. S. frGm John Ellis, Efqy
F. R. S. and Member of the Royal Academy at Upfal.

P-419

LIV. A Letter from Mr. B. Wilfon, F. R. S. and

Member of the Royal Academy at Upfal, to Mr.
iEpinus, ProfeJJor of Natural Philofoply in the Im-
perial Academy of Sciences at St. Peterfburg, and
Member of the Academies oj Berlin, Stockholm, and
Erfurth. p. 436

LV. A Difcourfe on the Parallax of the Sun. By the
Rev. Thomas Hornfby, M. A. Savilian Profejjbr
of A/lronomy in the Univerfity of Oxford, andF.R. S.

p- 467

LA I. A Difcourfe on the Locus for three and four
Lines celebrated among the ancient Geometers , by H.
Pemberton, M. D. F.R. S. Lond. et R.A. Berol. S.
In a Letter to the Reverend Thomas Birch, D. D.
Secretary to the Royal Society. p. 498

PHIL O-

— m.

PHILOSOPHICAL

t

TRANSACTIONS.

-1 -J.J .J ' . " ; ..

I. An Account of the Sun’s Diflance from
the Earthy deduced from Mr . Short’s Ob-
fervatiom relating to the horizontal Paral-
lax of the Sun : In a Letter from Peter
Daval, Efq\ V \ P. of R . S . to James Bar-
row, Efq\ V \ P . of R . S.

Read Jan. 13, A CCORDING to Mr Short,
17 3 j \ the mean horizontal parallax of
the Sun is 8", 65.

Now this parallax is the angle, which the femidia-
meter of the earth fubtends, being feen from the
Sun.

Therefore as 8", 65, is to 360° (the whole peri-
phery of a circle) jfo is the femidiameter of the earth
to the periphery of the orbit of the earth round the
Vol. LIII. B Sun.

[ * 3

Sun. But 8", 65, is very nearly T-rJT_T,h part of
360°, as may be eafily proved by divilion.

According to the lateft obfervations, the mean fe-
midiameterof the earth is 3958 Englilh miles, which
being multiplied by 149,826 produces 493,011,308
miles for the circumference of the orbit of the
earth.

The diftance of the earth from the Sun is the fe-»
midiameter of this orbit : and the periphery of the
circle is to it’s femidiameter very nearly as 6,283,185
to one.

Therefore if we divide 593,01 1,308 by 6,283,185
the quotient, which is very nearly 94,380,685, will
give the mean diftance of the earth from the Sun in
Englifh miles.

N. B. As the orbit of the earth is an elliplis, not
a circle, the diftance of the earth from the Sun will
be greater in it’s aphelion, and lefs in it’s perihelion,
than here afligned.

Dear Sir,

I have from Mr. Short’s obfervations deduced, as
above, the mean diftance of the Sun from the earth,
and am pretty fure I have made no material miftake,

I am

Dec. 18, 1762*

Your’s entirely,

Peter Daval.

II. Oi-

II. Obfervatio cornet x , qui tnenfe Mato A.

1 759 apparuit , faSla Hagz-Comit. a
Fetro Gabry, 7. 7Z Z). Societatis Reg. Sci-
entiar. Socio^ et Commercio Literar. cum
Academ. Scientiar. Farifienfi et Reg. Societ.
Gotting. junSlo : Communicated by Mr.

Emanuel Mendez da Coftaj Librarian of
the Royal Society .

Head Jan. 1 3,
1763.

D

I E 2 Mali, vefperi bora 9, ccelo
fere.no, prima vice cometam vidi
exorientem, et in gradu 190 i2r 24", Virginis, cum
28° 4c/ 5" latitud. auftral. exiftere, obfervavi : cau-
da exiftente admodum exigua, et vergente verfus
ftellam W Doppelmajeri Atl.ccel.in conftellatione Hy-
dra?, vel fi Bayeri Uranometr. Tab. 42. et FI am ft ee-
dii Atl. coel. in conftellationibus Hydras, Corvi, & Cra-
teris, in bad Crateris auftralis. Ipfe vero cometes ei
ftellas, quae eft tertia et proxima ante Craterem V Dop-
pelmajeri, vel y Bayeri Tab. 44. in conftellatione
Hydrae, quad fubfidebat, paulo tamen ilia auftralior.

Secunda vice obfervavi eundem cometam afeenden-
tem fupra horizontem proxime fequenti die 3 Maii,
poft nonam et dimidiam vefp. horizonte noftro me-
ridiem verfus exhalationibus infra cometam obtedto.
inveni autem ejus longitudinem 170 1 1' 40'' ijp cum
latitud. 270 20/ 20" auftral. Idem turn auftralior
fadtus longius a Crateris baft receflerat, ita ut fere in
redtacum ft ad alam dexteram Corvi Bayeri Tab. 43,
et fpica linea exiftere videretur.

B 2

Tertia

C 4 ]

Tertia vice cometa mihi fuit confpe&us velperi die
6 ejufdem menfis pod: horam nonam cum dimidia.
Vidi tunc cometam multo occidentaliorem quam v et
fupra <p Bayeri Tab. 44, fa&um efle, et cum corde
Hydra? et ala finidra Corvi y Bayeri Tab. 43, efficere
triangulum obtufangulum,cujus angulus erat in cometa
obtuius ethorizonti viciniorj bafis five hypotenufa erat
reda jungens didas dellas, et verdis zenith vergebat.
Cometa longitudinem habebat 120 51' 7" 1^, et lati-
tud. audral. 220 37' 24".

Proxime fequenti die 7, pod nonam et dimidiam
(paullo ante 10) velpertinam, eum iterum contem-
platus dim, et cum prima trium ante craterem S Dop-
pelmajeri , vel p Bayeri Tab. 44. et proxima ante cra-
terem V Doppelmaj. vel v Bayeri , iterum fere con flare
triangulum obtufangulum ; non ut heflerno die, fed
in datu inverlb, et non tarn obtufo : cujus angulus ad
cometam obtufus erat, et zenith verfus vergebat, hypo-
tenufa feu bads jungens didtas dellas, refta, et hori-
zonti vicinior, et cometa fane fine cauda. Longitude
ejus ii° 59' 14" cum latitud. 210 1' 44" meri-
dional.

Casterum, diebus 1 5 et 16 ejufdem menfis come-
tam admodum debilem vidi, et fine magno labore tubo
contemplatus dim, ita ut nulla amplius obfervatio a
me fieri potuerit.

III. Obfc -

III.. Ohfervatio cujufdam Meteori igniti injlar
Chafmath) fa&a Hagae-Comit . d, 21 De-
cembr. 1758. Nov, St. d PetroGabry, /.
V. D. Socio Reg . S octet at . Scientiar. Lon-
din. et Commercio Liter arum cu?n Acad.

Reg. Scientiar. Parifienf. et Societ. Reg.
Scient . Gottingenf. jun&o. Communicated
by Mr. Emanuel Mendez da Cofta, Li -
brarian of the R. S.

Read Jan. 13, TT ORA odtava vefpertina, lumen in-
1?63' ft dgne, ^lve meteoron ignitum inftar
chafmatis, a me confpiciebatur in coeli plaga fere oc-
cidental!, quum coelum eo tempore eflet nebulofum,
perobfcurum et tranquillum, zephyro leniter fpirante.
Aer hoc tempore erat caloris fere temperati, nam
thermometrummercuriale fub dio denotabat grad. 47.
Interdum plaga coeli occidua ardere videbatur, et aer
una cum inferioribus nebulis in flammas fumofque
nautatus. Ipfo momento contigit etiam, ut ex ipfa
plaga effulgentes flammae aliquando ad zenith fere
ufque afce’nderent, et {peciem radiorum ejaculantium
•cftormarent ufque circa cceli verticem.

Paulo poll fulgor apparebat candens et fatis nota-
bilis, repraefentans ignem quad continuum inftar
maftae igneae : ftib initium fulgor tenuis debilifque erat,
mox vero audtus, a plaga aquilonari ad occidentalem
ultra extendebatur, haud abfimilis lumini in horizonte
comparenti proxime ante foils ortum. Paulo poft
4 fulgor

[ 6 ]

fulgor rutilum ducebat colorem, ita ut ego, et alii me-
cum, incendium in vicinia extra urbem coortum ar-
bitraromurj fed aliter edocebamur, cum fulgor fenfim
altius fupra horizontem eveheretur, tantum emittens
lumen, ut circumjedtas axles collufiraret.

Ex ipfa mafia ignea flammae tarn rapido emitteban-
tur motu, ut duorum triumve fecundorum fpatio ab
horizonte fenfibili ad zenith fere eveherentur, paulu-
lum autem ad feptentrionem vergentes. Didtam maf-
fam evanefcentem excipiebat altera, flammas itidem
ejaculans. Quaedam fiammae alcendere videbantur,
altius tamen quam in vulgaribus incendiis evolabant;
quippe quae fere ad zenith ul'que tendebant, aliae ab
horizonte fenfibili ortas rutuli erant coloris, ferri in-
ilar igniti.

Hujus meteori figura valde mutabilis erat,' ita ut
nec certam defcriptionem neque minus ejus delinea-
tionem dare pofiim j licet hoc fpedtaculum pariter
jucundum et quodam modo vifu horrendum efiet.

Hie notatu dignum mihi efle videbatur, quod e-
jufmodi meteoron, tempeftate regelata, nebulofa, et,
quod magis eft, pluviofa, tanta nitebat luce, ut non
Junae, fed illam potius imitaretur lucem, quae folem
tempore aeftivo orientem praecedere folet. Fiudtuum
quoque inflar marinorum aut fegetis fpicatae in agro
undulantis, vento acrius fpirante, agitabatur. Micatio
praeterea continua cernebatur, qualis interdum tem-
pore aeftivo vefperi vel nodtu e nubibus promicare
cernitur, et apud nos vulgo Zee-vlammen appellantur.

Hora autem odtava cum dimidia meteoron hoc eva-
nuerat, ita ut ne minimum ejus veftigium amplius a
me confpiceretur.

IV. An

C 7 ]

IV. An Account of a remarkable Decreafe of
the River Eden, in Cumberland : In a ,
Letter to Charles Lord Bijhop of Carlifle,
F.R.S. from William Milbourne, Efq\

My Lord,

Read Jan. 13,
1763.

A:

S I know your Lordfhip fometimes
condefcends to amufe yourfelf with
natural curiofities, I have taken the liberty to fend
you an account of a very fudden decreafe of the ri-
ver Eden at this place, attended with fome particular
circumftances, of the exadt truth of which I can
venture to allure your Lordfhip.

In the night between the twenty-eighth and twen-
ty-ninth of December laft, the river Eden, at Armath-
waite, fell at leaft two feet perpendicular. The de-
creafe of the water was fo hidden, that feveral trouts
and young lampreys had not time to fave themfelves,
but were found the next morning frozen to death.
Of the former, eye-witneffes can fpeak to fifteen, of
the latter, two hundred, all which were found in
the extent of no more than forty yards. And feveral
dozens of young lampreys were eafily taken up alive,
by the hand, in the lhallows. The fuddennefs of
the water’s decreafe, may be fo far afcertained, as
follows. The miller of Armathwaite-mill left off
grinding at twelve o’clock that night, there being
then fufficient water to work the mill. He went to
the mill the next morning at fix, and there was not
then wrater enough to turn the wheel round. It hath

not

[ 8.]

not been known, that the river Eden was ever fo low
at this place, by a foot, in the dry eft fummer. The
water continued in this ftate, till about eleven o’clock
of the morning of the 29th, and then gradually in*-
creafed (no rain or fnow falling) till about one in the
afternoon, by which time it had rifen about a foot
perpendicular.

N. B. The trouts in general were Email, the lam-
preys about ten inches or a foot long.

I fhall only obferve to your Lordfhip, that there
was a moft intenfe froft that night, and a ftrong wind
varying from the North-eaft to the South-eaft ; -'and
that the river runs here from South.weft to Notth-
caft,

I am,

my Lord,

your Lordlliip s

r .

moft obedient humble fervant.

Aimathwaite Caftle.,
Jan. 4, 1763.

William Milbourne*

] J. ’ ! * \

V. An

V. An Account of the Rain fallen in a Foot-fquare at
Norwich, by Mr. William Arderon, F. R. S. Com-
municated by H. Baker, F. R„ S.

Read the i^th of January, 176*.

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Vol. LIII. C VI. 0,5

[ 10 ]

VI. Obfervations upon the RffeSls of RleEtricity
applied to 0 Tetanus, or Mufcular Rigidity,
of four Months Continuajice . In a Letter
to the Royal Society. By William Wat-
fon, M. D. F, R. S. Me?nber of the
Royal Colleges of Phylicians of London
and Madrid, and Phyfician to the Found-
ling Hofpital.

To the Royal Society.

Gentlemen,

Read Feb. 10, | ' VER lince your eftablifhment, the
1763. communicating the hiftory of un-

common difeafes has feldom failed of a favourable
reception by you, and has been frequently thought to
merit a place in your journals and regifter-books.
This has emboldened me to lay before you the fol-
lowing hiftory.

Catherine Field, a girl in the Foundling Hof-
pital, aged about feven Years, and otherwife a healthy
child, having been difordered a few days with what
were confidered as complaints arifing from worms,
was obferved, on Thurfday, July 8, 1762, to open
her mouth with great difficulty. This particular cir-
cumftance increafed fo much, that by the Sunday
following, when I firft faw her, her teeth were fo
much confined, it was with difficulty that even li-
quids could be admitted into her mouth. She had
two days befpre parted with two worms, and had

feveral

[ ii ]

feveral very offenfive ftools. Her breath was now,
and had been for fome days, very fetid.

Though her jaw was locked very clofe, fhe was
without pain; even in the Temporal and Maffeter
mufcles, whofe office is to bring the under-jaw to
the upper ; and which, in this indance, were tenfe,
hard, and fpafmodically affeded. She was feveriffi,-
her pulfe was quick, and her fleffi hot ; and ffie had
had but very little deep.

On Monday, July 12, I vilited this poor girl in
confultation with my learned and ingenious friend
and collegue Dr. Morton. We found ffie had had a
redlefs night ; her fever was high, and it was infi-
nitely difficult to introduce any thing between her
teeth. As there had been no wound, no eruption
repelled, we were of opinion, from her offenfive
breath and other indications, that the fpafm of her
jaw was fymptomatic, either of worms or foul
bowels.

Whatever was admitted into her mouth was fwal-
lowed without difficulty ; neither in this date of the
difeafe was her breathing at all affeded. The regi-
men we put this patient under, for this formidable
complaint, will be mentioned hereafter.

For near three weeks the diforder confined itfelf to
the jaw, during which time ffie was condantly fever-
iffi. At times indeed her fever ran very -high* and
her pulfe beat 130 drakes in a minute. At other
times it beat only about iooj but never for t'hefe
three weeks was it dower than that number.

Notwithdanaing our bed endeavours, the difeafe
not only continued, but the rigidity communicated
itielf to the mufcles of her neck, fo that ffie could not

C 2 move

[ » ]

move her head in the leaft : And from pains ffioot-
ing down her back, we had reafon to apprehend,
and which indeed did foon after happen, that the
mufcles of her back would foon likewife be rigid.

After the back was affe&ed, the difeafe extended
itfelf very faft ; fo that by the end of September, al«
mold all the mufcles of her body were rigid and moti-
onlcfs. To be fomewhat more particular; the rigi-
dity from the Temporal and Mafleter mufcles had ex-
tended itfelf to the cheeks, to the neck, breaft, ab-
dominal mufcles, all thofe of the back, the right arm,
the hips, thighs, legs, and feet. Nor were they
by any force, that could be exerted with fafety, to be
extended. By the rigidity and contraction of the
large and long mufcles of the back, the Os Sacrum
and hips were pulled towards the flioulders; fothat
the fpine formed a very confidcrable arch. By the
fuperior ftrength of the Flexor mufcles of the thighs
to that of the Extenfors, the legs were pulled up al-
moft to the thighs.

Of all h«r limbs, the left arm only preferved
any motion. Of this the joint of the ffioulder was
rigid, that of the elbow extremely impaired ; but the
wrift, hand, and fingers, were reafonably pliant.
The various mufcles fubfervient to the motions of the
eyes, eyelids, lips, and tongue ; as well as thofe,
internal ones at leaft, which affift in performing the
offices of refpiration and deglutition, did not feem in
the leaft to partake of the rigidity.

From the end of September to the middle of
November, the difeafe, as though it had exerted all
its power, was at a ftand. The feveriffi heat had
left her, and her pulfe beat generally between eighty

and

[ *3 ] ~ .

and ninety ftrokes in a minute. But during this in-
terval the poor patient was feized many times, both
in the night and in the day, with violent convullions
in thofe mufcles of the eyes, face, and right arm,
which had any mobility left. Thefe were fo fevere,
that, in her weak and wretched (late, her attend-
ants imagined every attack would put an end to her
diftreffes.

In this ftate, partly from the feverity of the difeafe
and partly from the very fmall quantity of food which
could be given to her, and which was only through
a fmall opening made by extracting two of her teeth
and without which fhe mud; inevitably have been
ftarved, fhe was emaciated in a mod extraordinary
manner. Her belly was contracted, and pulled in-
wards towards the fpine. Her whole body, to the
touch, felt hard and dry, and much more like that
of a dead animal than a living one. This, added to
the very great diftortion of her back and lower limbs,
heightened the difagreeable fpeCtacle, and called to
my mind that admirable paftage of * Aretseus, who,
when treating of and contemplating this difeafe, calls
it “ inhumana calamitas, injucundus afpeCtus, trifte
“ intuenti fpeCtaculum, et malum infanabile.” And
hefubjoins, that “ their diftortions are fuch, that they
“ cannot be known by their moft intimate friends
which in the cafe before us was moft ftriCtly true.

During the continuance of this diforder, which
had lafted now more than four months, nothing had
been omitted that either Dr. Morton or myfelf

* Cap. vi. ’Ej'cpi/Qgcaros ri (ruppogr, XC*1 axrt£ 7riij (Am ovfjf,
c’af-jyu cri $£ ra opt'ofli 6erj, avrxsfov ft- to $uvqv>

could

[ i4 ]

could fuggeft for her relief. While worms or foul
bowels could be fufpeded to have occafioned this
illnefs, as her ftools were at firft very offenfive, and
fhe had voided two worms, vermifuges of the mod
celebrated kind, linfeed oil both by the mouth and
by clyfters, and fucli other medicines as tend both
to carry off or dedroy the worms, and cleanfe the
bowels, were adiduoufly adminidered. But no re-
lief arifing from thefe, bleeding with leaches at the
temples, when her fever ran high, bliders behind
the ears, round the neck, upon the head, and in
various parts of her body, were from time to time
applied, as the diforder feemed to indicate. Nor
during this time were antifpafmodic remedies of va-
rious kinds omitted, and that in very liberal dofes.
Among thefe, as in feveral cafes of locked jaws, re-
lated by authors of undoubted credit, opiates had been
found to have been attended with great fuccefs,
Tindura Thebaica was copioufly given. So that,
between the 12th of July and the end of the month,
more than nine hundred drops of that tindure were
taken: A large quantity for fo young a perfon ! This
we fometimes thought had a good effed, as the jaw
was at times fomewhat loofened ; but this advantage
was temporary, and the ftridure foon returned as
fevere as before.

Though this medicine, given in large dofes, did
not affed her head, but only gave her quiet nights,
yet it was occafionally obliged to be fufpended ; as her
pulfe was at times much funk, and her l'weats cold
and clammy. Volatile liniments were liberally ufed
to the rigid parts, and warm bathing was continued
for many weeks, with much fridion, while in the
warm water.

1

After

[ I5 ]

After warm bathing had been fo long tried with-
out fenlibly good effect, cold bathing, recommended
by Hippocrates * for the cure of this difeafe, was
directed ; and fhe was dipped feveral times, without
being apparently the better or worfe for it.

From the end of September, as what had been
done hitherto had not been able to prevent the rigi-
dity extending itfelf, we defifted from attempting to
relieve her by medicine, and determined to nourifh
and fupport her ; and wait to obferve, though it was
fcarce to be expedted, whether nature unaffifl-
ed would point out any crifis for her relief. This
attention was continued to the middle of November,
without any other alteration than that her convulfions
increafed in their force; and every day, by thofe
who were about her, was expelled to be the lad: 5
and which was an event, as the profpedt was fo un-
promidng, much to be wifhed for. Dreadful how-
ever as her fituation was, fhe was {fill alive: we were
dedrous therefore of omitting nothing, that in the
lead; might be expedted to relieve her.

I had heretofore many times obferved, that in para-
lytic limbs, the mufcles of which had for a confider-
able time ceafed to be fubfervient to the will of the
patient, I had been able, by the means of eledtricity,
to make any mufcle I thought proper contradt itfelf,
and adt as a mufcle, without the patient’s being able
to controul it. I had feen in one inftance the good
effedts of eledtricity, in reftoring to the hands and
arms of a paralytic almoft their accuftomed ftrength,
and voluntary motion; but thefe good effedts, the

greateft

* Ilfcl vov<rwv3 Lib. III.

[ 16 ]

greateft part of them at leaft, were only temporary,
and the patient relapfed. But I had never feen or
known the effects of electricity in the contrary affec-
tion, viz. rigidity of mufcles. I was very defirous
therefore of trying its effeCts in this inftance, and of
ihaking the rigid mufcles by eleCtricity; efpecially
as I could have it done with very little pain, and no
danger to the patient.

I juft now mentioned, that I was able in paralytic
perfons to make any particular mufcle at my will ex-
ert its aCtion. This was to be effected by Jimple
eleftrifing only ; but by modifying and altering the
apparatus of the charged vial, I was able to do much
more. It is now feventeen years fince, that I dis-
covered, and communicated it to you at that time,
that by means of the elcftric circuit 1 could caufe the
eleCtricity topervade any mufcle, any number of muf-
cles, or whatever part of the body I pleafed, without
affeCting the reft with that unpleafing fenfation. Ma-
ny experiments, relating to this matter, and which I
laid before you, were printed in the forty-fourth vo-
lume of the Philofophical TranfaCtions.*

But to return to our patient : We ordered her to
be eleCtrifed about the middle of November. This
was done every day, or every other day for about
twenty minutes, by j imply elcBrijing the mufcles fub-
fervient to the motion of the lower jaw, her neck, and
her arms. This at firft was very difficult to be at-
chieved 3 as fhe was not capable of being placed in a
chair to be eleCtrifed by herfelf, and as an affiftant
could fcarce hold her on account of her being greatly
diftortcd. It with difficulty, however, was done.

After

* Pag. 718, & fcq.

[ ‘7 ]

After about a fortnight, the convulfions left her,
and her ileeps were longer and more quiet; but the
rigidity continued the fame. After this, fuch parts
of her body, as were thought expedient, were made
part of the eleBric circuit , and were fhook by the
explofion of the charged vial. Thefe applications
were at firft more particularly made to the Temporal
and Malfeter mufcles (the parts firft affetfted) and to
the mufcles of the neck and arms; afterwards to
thofe of her back, hips, thighs, and legs. Care
was taken to moderate the lhocks in a manner, not
to be too levere ; andfhe was eledtrifed every fecond,
and fometimes every third day.

The fits, as I juft now mentioned, and which were
of the epileptic kind, left her in about a fortnight
from her being ele&rifed, and have never fince re-
turned, even in the flighted degree. In about a
fortnight more her jaw was loofer, and the mufcles
of her neck and arms had a large fhare of motion : and
it was very obfervable, that as her mufcles increafed
in their power of motion, they increafed in their fize,
and the patient in her ftrength. By the end of Ja-
nuary, not to be too tedious in my narration, by
continuing the ele&ricity, every mufcle in her body
was loofe, and fubfervient to her will ; and fhe could
not only hand upright, but walk, and can even run
like other children of her age. With her ffrength,
fhe has fo far recovered her flefh and colour, that her
prefent appearance is that of a reafonably healthy
child ; and her breath has quite loft its late offenftvc
fmell. The only parts of her body not quite fo loofe
as the reft, are the Temporal and Malfeter mufcles,
which were the parts firft affe&ed by the difeafe.
Vol. LIII. D This

[ i8 ]

This prevents her opening her mouth quite fo wide
as Ihe formerly could ; but this hindrance is fo little
as not at prefent to be taken notice of, unlefs hinted at
beforehand. She now goes to fchool, lives at large,
and goes out every day when the weather is feafon-
able; but the eleCtrifing is (till continued, tho’ not
fo conftantly and regularly as before. This I propofe
fhould be continued,, until the return of warm wea-
ther. In the laft week this child was prefented to
the committee of the Foundling Hofpital, where
leveral of the governors, who were apprifed of her
cafe, exprefied their amazement at her, fo unexpect-
ed, recovery.

It is here to be obferved, that, except the mufcles
fubfervient to the motion of her jaw, none fo long
continued their rigidity as thofe of the back, deno-
minated “ longiflimi dorfi” by anatomifts. Thefe,
when almoft all the other mufcles of the body were
loofe, remaining tenfe and hard and, by pulling
the loins up towards the fhoulders, continued the
arch of the fpine before mentioned. As the patient
was fo much emaciated, thefe mufcles might be
traced, on each fide of the fpine, from their origin
to their infertion ; and for a confiderable time after
Ihe was in other refpeCts recovering, thefe felt hard
like twifted cords. At length, however, by directing
the eledricity through them, and the parts near them,
in a very liberal quantity, thefe likewife gave way,
and are now as loofe as any other mufcles of her
body.

In proportion as a matter is extraordinary, the
proofs to fupport its reality fhould be extraordinary.
That excellent maxim, “ Nil temere credere,” fliould

never

4'

[ *9 3

never be loft fight of in our inquiries ; otherwife no-
velty and the love of the marvellous will be apt to
mifiead us. On the other hand, the indulgence of
an extravagant Pyrrhonifm may prove equally
detrimental in every endeavour to extend the bounds
offcience. It may prevent the giving due weight to
matters of real information, and hinder their being
made ufeful. For my own part, I fhould think it
an indignity offered to the Royal Society, to lay be-
fore you any extraordinary phaenomenon, which is
fupported only by a flight degree of evidence. On
the contrary, when a number of concurrent circum-
ftances tend to eftablifh a fad:, we ought not in a
certain degree to refufe our afifent to it, though fome-
what out of the common courfe. Thus in the cafe
before us ; when an unufual difeafe of feveral months
continuance, and when the patient was fuppofed to
be reduced to the laft extremity ; when medicines
and applications of every kind, celebrated by the
ableft writers and praditioners both antient and mo-
dern, had been tried with little or no effed, at leaft
with regard to the rigidity; when during a courfe
of eledrifing no medicines or applications of any kind
were made ufe of ; when likewife, during this
courfe, the patient voided no worms, had no purg-
ings, eruptions on the fkin, or kindly impoftuma-
tions, which might have been confidered as critical
difcharges, and to have brought about the cure;
when, I fay, none of thefe things happened, and
the patient under eledrifing only, and that at a very
fevere feafon of the year, has been reftored to perfed
health, I cannot refufe my aflent in believing it
effeded by the power of eledricity. That fo adive

D 2 a principle,

[ 2° ]

a principle, when properly dire&ed to the difeafed
parts, fhould have important effeCfs, no one can
doubt who has been in the Ieaft converfant with it.
Though at the fame time I confefs, well apprifed of
the falutary effects of warm weather in reftoring a
more perfect motion to torpid limbs, that had the
eledrifing been begun in March, and continued to
the end of May, though attended with the fame fuc-
cefs as in the prefent inftance, I could not have fup-
preffed my doubts of the warm weather greatly con-
tributing thersto. But as this was done during the
depth of winter, and that a feverely cold one, no fcru-
ples, in my mind at lead, can arife upon this head.
I take the liberty however to lay the whole evidence
before you, that every one may make from it fuch
deductions as he thinks proper.

Perhaps indeed fome may be of opinion, that even
the cold weather contributed to cure this diforder.
But it is well known, that warmth relaxes the ani-
mal fibres, and that cold conffi pates and braces them.
In the cafe before us, the mufcles, compofed of mi-
nute fibres, were as rigid and tenfe as they well
could be, even in a difeafed and obftruCted ftate. If
cold therefore contributed any thing, it was to make
this cafe worfe. And this is conformable to the opi-
nion of Aretaeus *, who, among the caufes of the
difeafe, reckons intenfe cold ; and fays, “ that for
<£ this reafon the winter of all the feafons is moftpro-
“ duClive of this difeafe.” He fubjoins, “ thatwomen
tc are more fujeCt thereto than men, on account of
“ the coldnefs of their conftitution.” Celfus -f* like—

* Aretaeus, Lib. I. Cap. vi.

| Celfus, Lib. II. Cap. i. Frigus modo nervorum diftcntioncm,
mcdorigoreminfert: illud5'?r«<r(uoi-, hccTmxyo? Graecenominafur.

wife

[ 21 3

wife exprefly afferts, that cold fometimes is the caufe
of it, and in another part of his excellent work fays,
“ that the greateft caution fhould be ufed to defend
“ the patient from cold j and that therefore the fire
“ in his room fhould be conftant.” He moreover
recommends warm bathing both in v/ater and oil, as
conducive to the cure of the difeafe. To thefe may
be added the fentiments ofCaelius^ Aurelianus, who
confiders that cold is frequently the caufe of this
difeafe. He recommends various kinds of warm
external applications ; fuch as warm bathing, rubbing
the affedted parts with warm oil, the application of
warm cataplafms, bags of heated bran, or linfeed.
With Celfus, this author recommends, that attention
be given to the warmth of the patient’s chamber.
How far therefore, for the reafons and authorities
before-mentioned, cold weather could probably af-
fift in the cure of the cafe before us, need not in my
opinion be infilled upon.

And now, Gentlemen, permit me to make a few
obfervations upon the difeafe itfelf, which, at lead: in
the degree of the cafe before you, is a very rare one
in temperate climates. In warmer countries, and
efpecially between the tropics, it is too often feen.
It was well known to the ancients. Hippocrates §
calls it T iravog, and fays, that thofe who have it fe-
verely, die on the fourth day ; if they furvive that day,
they recover. He makes farther mention of it in
other parts of his works more particularly in
his book N ovrw, where he deferibes both the

X De Morbis Acutis, Lib. III. Cap. vi. viii.

§ Aphorifm, Lib. V. Se£I. vi.

* Vide Lib. Ilfjd >cg»<r (pm — lief* ruv hlos 7 raQvv, & alibi.

Tetanos

f>2]

* Tetancs and Opijlhotonos. In this part of his work,
inftead of the fourth, he mentions once, and repeats
it, that if they live beyond the fourteenth day, they
recover. Left it fnould appear, that the father of
the medical art feems to contradict himfelf, it may
not be improper to remark, that when he fays, that
the Tetanos is mortal in a very few days, he moft
generally means thofe which are fymptomatic, and
are attendant upon wounds, luxations, and bruifes ;
fuch as the three inftances mentioned in his Epidemics.
Thofe affeCted with this difeafe, mentioned by Hip-
pocrates in his book rW/ K t/tri'pcw, are exprefly faid
to arife from wounds. Thei'e were foon mortal.
But where thefe difeafes took their rife from other
caufes ; they were lefs violent, continued longer, and
the expectation of recovery was greater. In his book
therefore, Tle^J r tvT&'sraOuv, when treating of the
Opijlhotonos , attendant upon a fever, inflammation of
the throat, or other internal diforders, he fays, that
if they live beyond the fortieth day, they recover.

Aretseus *, under the fame appellation with Hip-
pocrates, has given us an excellent hiftory and re-
marks upon this difeafe, as well as upon the Opijlho-
tonos , and Emproflhotonos , which are nearly related to
it ; or, to fpeak more properly, the fame difeafe affeCt-
ing different mufcles, and throwing the body into
different kinds of diftortion. Celfus -f- has mentioned
and defcribed this difeafe, to which no name was
affigned by his countrymen, and has called it “ Qui-
“ dam nervorum rigor.” Tho’ this excellent author
reckons it among the difeafes of the neck, the parts

* Morb. Acut. Lib. I. Cap. vi.

t Lib. IV. Cap. iii.

firft

*[ *3 ]

firft affedted by it are the mufcles fubfervient to the
motions of the lower jaw, from which it is ufually,
if the difeafe continues, propagated to thofe of the
neck. Caslius * Aurelianus has, as it is fuppofed
from Soranus, defcribed it, and handed down to us
luch methods of cure, as had been found in his
time mod; fuccefsful.

Pliny § mentions the Tetanus in many parts of his
Natural Hiffory. He forbids the ufe of wine to thofe
who labour either under this difeafe, or the Opiftho-
tonus. He recommends in different parts of his work,
as internal remedies, caffor, hellebore j[, the alhes of
the fig-tree, pediculi marini, and pepper. Pie ad-
vifes warm baths, with the nitre of the ancients dif-
folved in them ; and diredts the patient at other times
to be rubbed with the coagulum found in the fto-
mach of a calf, or with the juice of Peucedanum, or
hogs-fennel. This, it is to be prefumed, was the
moft general method of treating thefe difeafes, in the
age wherein this author wrote.

This difeafe is frequent in Greece, Italy, and in the
warmer parts of Europe, where its effedts are feverely
felt. •f'Bontius, who refided long in the Eaft Indies,
has briefly defcribed it ; which, though he fays it is

* Morb. Acut. Lib. III. Cap. vi.

§ Plinii Hift. Nat. Lib. XXVI. XXXI. XXXII.

|| Ibid. Lib. XXV. The hellebore made ufe of, was to be pre-
pared in (at that time) a newly difcovered manner, which was to
prevent the effects of its acrimony. This was, by putting the
hellebore between radifhes fplit, and then tied together, including
the hellebore; which, by being macerated in this manner for
about feven hours, was fuppofed to become more mild in its ope-
ration.

f Bontii Meth, Medendi, Cap. ii. De Spafino.

rare

[ 2+ 1

rare in Holland, may be reckoned endemic in India.
He feems not to have known what had been written
by his predecehors upon this fubjedt. He takes no-
tice, that fometimes men feized with it became ditto
citius rigid as flatues.

An admirable account of this difeafe was a few
years fince communicated to the public by Dr. Lionel
Chalmers-f* of South Carolina, where it is very fre-
'quent, efpecially among the negroes. And I am
informed by a learned gentleman of undoubted credit,
that in our military operations between the tropics in
America, great numbers of our people, particularly
of thofe who were wounded, died with locked
jaw’s.

In England we generally to this difeafe give the
name of the locked jaw, but that, let it arife from what
caufe it may, is only one fymptom of it. If it con-
tinues, as in the cafe before you, the occafion of this
paper, it propagates its rigidity to the neck, bread:,
and then to the other parts of the body.

It is feldom leen here that the Tetanus is an ori-
ginal difeafe. It is generally fymptomatic, and the
confequence of fome other diforder. It frequently
is fubfequent to wounds andbruifesof the nerves and
tendons. I have known it arife to a certain degree
from the fudden checking of an eruption upon the
fkin. I knew a temporary Opifthotonus occafioned
by the too fudden lofs of a large quantity of blood.
To thefe permit me to add, that the Tetanus of the
Temporal and Maffeter mufcles conhantly attended
thofe whom I have known to have been accidentally

poifoncd

t Medical Obfervations, Vol. I. ^ag. 87.

[ 25 ]

poi Toned by taking the Oemnthe aquatic a fucco virofo
crocante of Lobel ; and of which, two communica-
tions of mine occur in the Philofophical Tranf-
adtions.

I muft here remark, that in the true Tetanus,
the arms, when rigid, are straight, and extended
along the trunk; the legs and thighs are likewife
ftraight; but the cafe before you, in fome degree,
partook of the Opifthotonus, efpecially in the lower
parts ; as the fpine was remarkably curved, and as
the legs were pulled up towards the thighs.

The Tetanus I now lay before you, was an origi-
nal difeafe ; as there had been no wound, no eruption
fupprefied, nor other caufe, which, we imagined,
could occafion it. A cafe of a fimilar kind, as an
original difeafe, occurs in Dr. * Storck’s Biermium
Medicum. And the Emprofthotonus, mentioned by
the ingenious Dr. Macaulay, in the fecond volume
of the Medical Obfervations, lately publifhed, Teems
to have been likewife an original difeafe, and not a
fymptom of any other. As the cafe I now commu-
nicate is a very fingular one, at leaft in Great Bri-
tain, and the treatment of it not lefs fingular, though
attended with all pofiible fuccefs, I had reafon to hope
that you would not be difpleafed to have it laid be-
fore you, in a manner fomewhat circumftantial. I
am firmly of opinion, if the epilepfy had left this
patient, and life had continued, that the would have
remained a moft miferably helplefs objedt, and as
confirmed a cripple as can be imagined.

At prefent the patient is well ; but if, contrary to

* Part I. Pag. 6.

E

expectation.

[ 26 ]

expectation, fhe fhould relapfe, or any thing fhould
occur in her cafe worthy your notice, I fhall not
fail to acquaint you with it ; and am, with the
utmoft regard.

Gentlemen,

Your moft obedient humble Servant,

William Watfon.

Lincoln’s Inn Fields, 9 Feb. 1763.

P. S. The patient continues well, her jaw is as loofe
as ever. The eleCtrifing has been difcontinued
above a month ; and fire is in every refpeCt
perfectly recovered.

27 March 1763.

July 8, 1763.

The patient is perfectly well, and there remain not
the leaft indications of her having been difeafed.

w. w.

VII. An

[ 27 ]

VII. An Account of the late mild Weather
in Cornwall, of the Quantity of Ram fallen
there in the Year 1762: In a Letter from

the Rev. William Borlafe, M. A. F. R. S.
to Mr. Henry Baker, F. R. R.

Dear Sir,

Ludguan, Jan. 22, 1763.

Read Feb. ro,
.763.

AM very fony to hear of your diftrefs
at London, by the rigour of the feafon.
— Our winters in Cornwall are indeed generally more
mild than any where in this ifland, but I do not re-
member fo wide a difference as that of the prefent fea-
fon with you and us. — In November, on the 12.
13. 14. our froft began, moftly attended with hoar
frofty mornings : here and there a pool of hill water
had a film over it, fcarce Ifrong enough to bear an
egg, not a large pebble : and the froft: was always
over before noon. — Froft of the fame degree on the
1 8th, and 20th, — hoar froft only the 26th.— -Froft,
but of no greater degree, Dec. 5. 6. and 7th. — Hoar
only on the nth. — On the 14th and 15th, froft, but
of the above degree only: a little fleet on the 31ft
poll merid. — To this day no froft or fnow. On
thefe coldeft days the Thermometer was never
fo low as 38° but on three days only, viz. Dec. 14
and 15th, and Jan. 9th. — I muft not conceal from
you, however, that fome allowance muft be made
for the heighth of the Quickfilver, becaufe my Ther-
mometer is not with doors ; but yet it hands in a
little flair- cafe far from any fire, where the Sun in

E 2 the

[ 28 ]

the midft of fummer never reaches till 6 o’Clock
P. M. and in winter never: and the cafe in which
the tube of Quickfilver is fixed communicates with
the open air, by three holes lined with tin, pierced
through the munnion of the window to which it is
fixed ; fo that tho7 it is not in the open air, yet muft
the Quickfilver be expofed to every extremity of the
Atmofphere byconftant intercourfe.

You will judge that our cold was no ways ex-
ceffive, when I add, that the balm of Gilead, in
the natural open ground, has not differed : the myr-
tles are in perfect health : the mignonettes in flower :
the clufter rofe and white Violet in bloom at Chrift-
mas ; and at the fame time I had the fcarlet double
ranunculus full blown given me by a neighbour.
The double hyacinths have formed their bells, and
fome are now ready to unfold.

It has not (I believe) been remembered in the age
of man, that in the weft of Cornwall we have ever
had fuch a long continuance of eaflerly winds.

About the middle of Nov. for 14 days the wind
had its prevailing turn from the eaft. — It was eafl-
erly, with a variation now and then (a point or two)
to the north or fouth, every day of December, ex-
cepting the 2 1 ft, when it blew W. S. W. and S. S. W.
— and to this 2 2d day of January it has blown
everyday from the eaft, varying half a point or fb
to the S. or N.

Since I have entered into thefe latter difquifitions
on the feafon, give me leave to add the quantity of
water fallen here in the year 1762,

January

C 29 ]

Inches. Tenths. Parts of a Tenth.

January — —

4

—

3

—

0

February - —

2

—

1

—

0

March — —

2

—

8

—

0

April — —

1

—

0

—

1

"aT

May — —

1

—

0

—

0

June — —

0

—

2

—

0

July _ —

0

—

5

—

0

Auguft — —

3

—

5

—

0

September —

4

—

3

—

0

October — —

5

— —

6

—

0

November — —

3

—

2

—

K

“S'

December — —

1

—

4

—

0

In the whole

29

—

9

—

♦

s

If you, Sir, or any of your acquaintance keep
an ombrometer, and regifter of the rain at London,
I fhould be glad to know how much fell there, for
by fuch obfervations it might in time be known where
the quantity exceeds. I think round Paris they rec-
kon but at 1 9 inches, but in iflands, and near the Sea
coaft it mud: be more.

I remain, Sir,

your moft obedient fervant

William Borlafe.

IX. An

[ 30 ]

VIII. A Delineation of the \ Tranjit of Ve-
nus expeSled in the Tear 1769, by Mr .
James Fergufon.

To the Right Honourable the Earl of Macclesfield,
Prefident of the Royal Socie'y.

My Lord,

Read Feb. 10, y Beg leave to prefent to the Royal So-
1 ?63* y cjety a delineation of the tranfit of
Venus in the year 1769 [Tab. I.] which will be a much
better tranfit for difcovering the Sun’s parallax than
that in 176 1 was.

Although I have only mentioned Wardhuys in Nor-
wegian Lapland, and the Solomon ifies in the great
South Sea, as proper places for obferving that tranfit ;
yet I am feniible, that any other place near the north
cape will be juft as well for the northern obfervers;
and Tuberon’s Ifie, or St. Bernard’s, or the Fly
lilands, in the great South Sea, will anfwer as well
for the Southern.

Although it cannot beexpedfed, that any delineation
can be fo exact as calculation, yet I hope this projec- .
tion will be found to come very near the truth j and
am, with the higheft refpedt,

My Lord

your Lordfhip s

and the Royal Society’s

moft obliged humble fervant

James Fergufon.

Mortimer- Street,
Feb. 10, 1763.

IX. An

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An Orthographic al Projection of the Earth's
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J-W

iPtn/os fnitts Vo/ X.D/ TAB J p so .

The TRANSIT of VENUS oyer the
SUN, June ^1760, Delineated fames Terguson.

Scale of Minutes ami Seconds of a. Decree.

(1 S j) to C//

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Scale of 21 -3 1 equal to "Venus's
horizontalParallax from the Sun
and to die S emnli aine tei- of "y.
EartlisIXfc in dhs Projection.

toffiSLs.

The Elements from wlncli thefe Projections are deduced-

'•n/unthen of/ At ./un kid run. t font ’ ,•{ . lo . 1 1 . o iP-M- 11 . //AetJnna forty n/n/'ffWi//a,r . af joined /p ft 0.00. 8. ,5

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13. /J/eir di/feitnce .=lttiiu',i Aorifon/n/fuini/Ai.rfn’in /Aft Am /...o.no.'il 0

LJ.. *yie f/uno •Jernidiahie/et I..„ . . o . i£. 45 . 5

. '/ 'e n/io i> i/'emwiamt/er. o . 00 . 29 .5

16. ./.ah hide of •// n n/Au./Tjoi/A 71. 00. O

J7. 1 7/i . Xonyi/udr. dho/fivn^ . fom/on ftnilime g /10TM//..30.00 .0

18. Na/i/udf of ,/fondon i \01W1eJ. 51. ,30.0

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20. t'/ta Tonyihide://ut from londanlaiiffiojed /o A'f fin //nit if. jo'i.. .140. 00 . o

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,9 . //Au i/uit’a L/hr/i nation I'Adort/l ' . 2 2.2], 30

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5 . d/dtr tf tart nine ./iaithiJt it/ //uit hint , ( o'r/A iTefcendutn u) 22

6 iJ/te t/ny/t af/ur I’fd/i fa/At' iri//i //it dr/fiho '/ 8,-jo.io

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B 1 . J: j ' A. y/ ' J' . . j /. \ t . . .

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•7/er If /ante firm /dr dai/At ’■ J ^ ■iSHgG yatny 100000 faudfadt

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flint oft'/nyrtf .tin a ten from anpjiven yt/.tte . k'tMr/tnihv i At Ante ofdyrfi.
Ay /Ae n u'mlt r of • /A uu/rj /Aa/ hit Aaff-thuvit Tine ow/Ae t/unolAuc/f
u a/torier aa .teen from /At jtvtn f/nec /Ann aa otett front /At dlard/io tenter,
iv/ten /emu fnfJet/oa/voe /At ti/ana eenAr, aa itv/Av £7ranoft; tin i/ou/A-
env f,)ttni//a.v 'in _/ 'iah/ttde ncte/t ra/ea /At tiny ref, and rr/nrda /Aeo dyrt^ ,

. tot/ A reafieot hi /At time /Aeuaf aa aeen
front/ /At • do r/A'a center. Ay /At numAeroft /Aiuifro /hat /At Aafitfanait
litt on /At t/un td (■ 'on.fr aa aeen fronv/Ae yiren ft/are //tan a.t atom front
//it d’tir/A.i center • Aid /Atae differentia .ire Afjy meaaunriy i./fr
Coinfin/jtki in /At aAove iHyart-’ of i/ie t/una Aliae^’. from /Ae t d.rtj
of- ‘/ftnuaj OrAt/fr? to /At (Ire. Jtx h toAtrt ‘/frnua'j ctn/tr v at / Ate f
t no tan/ of total ilnortfa ; and to /At 1 ire c d n'AtrfS'Atr ten fro- ‘to
n’Atn Atr Ayffi Ilyina • 1 /ml /Ana, tAe Anita of total fnyrtfo . and- ’
A/tyimii ny'rfdyrfa aa attn from /At a loot- ntt title net/ yt/.teia, totir fomu^i*'
r.tfrfnf ert/ /At //al’dt of /At Mmea andHaeationa of tAe ATranaits .

1

♦

T/ulos. Trans. Vol. TM TAB H Ta. 31.

[ 3i ]

IX. An Account of a?i Appulfe of the Moon
to the Planet Jupiter, obferved at Chelfea,
by Mr . Samuel Dunn.

Read Feb. 17, rp H E alteration of the angles of po-
j763- j| fition made by the cufps of the
Moon, and a planet to which the Moon makes a near
appulfe, will always enable the aftronomically inclin-
ed to determine from obfervation, the longitudes of
places, by the naked eye and a clock or watch fet to
apparent or equal time. — Such an obfervation I made
at Chelfea 25th Dec. 1762 at 1 ih - o' - 30" appa-
rent time, the fatellites being as in the figure at the
lame time. — Jupiter’s difiance from the Moon half
a degree. Tab. II.

Lat. 510 29' 5", Long. 41" Weft of Greenwich.

X. A Cata-

[ 32 ]

X. A Catalogue of the Fifty Plants from
Chelfea Garden, prefented to the Royal
Society by the worjhipful Company of Apo-
thecaries , for the Tear 1762, purfuant to
the DireElion of Sir Hans Sloane, Baronet,
Med. Reg. et Soc . Reg. nuper P reef es \ by
John Wilmer, M. D. clariff. Societatis
Pharmaceut. Lond. Soc. Hort . Chelfean.
PrcefeSlus et PrceleElor Botanic.

Read Feb. 24, | 2001 A Maryllis fpatha uniflora, co-
I763' ^ rolla aequali piftillodeclinato.

Hort Cliff. 135.

Lilio-narciffus Virginienfis. Catefby Carolin. 3.
p. 12.

2002 Antirrhinum foliis lanceolatis acuminatis, pani-

cula virgata. Linn. Spec. 616.

Linaria geniftae folio glauco. Herm . Par. App. 9.

2003 Afclepias foliis ovatis rugofis nudis, caule iim-

plici umbellis fubfeffilibus, pedicellis tomen-
tofis. Linn. Sp. 215.

2004 Calamintha montana praealta, pulegii odore,

dentatis foliis, floribus dilute caeruleis, exlon-
go ramofo et brachiato pediculo prodeunti-
bus. Boccon. Mufaeum, p. 2, 45.

2005 Canna folis lanceolatis petiolatis enervibus.

Prod. Leyd. 11.

2006 Chenopodium foliis filiformibus acutiufculis,

caule eredto. Hort. Upfal. 55.

2

2007

[ 33 j

2007 Ciftus arborefcens, foliis cordatis lasvibus acu-

minatis petiolatis. Hort. Cliff. 205.

Ciftus Ledon foliis populi nigri major. C. B.
p. 474.

2008 Ciftus l'uffruticofus ftipulatus, foliis ovatolance-

olatis caulibus hirfutis decumbentibus.

2009 Clypeola perennis filiculis bilocularibus ovatis

difpermis. Sauv. Monfp. 71.

2010 Colutea foliolis ovatis, racemis latcralibus fecun-

dis filiculis compreflis.

2011 Crotolaria foliis ternatis ovatis acuminatis, ftipu-

lis nullis, leguminibus pedicellatis. FI. Leyd.
278.

Crotolaria Afiatica frutefcens floribus luteis am-
plis, trifoliata. Hort. Lugd. 196.

2012 Cytifus Lufitanicus foliis exiguis, magno flore,

filiquis latis et tomentofis. Tourn. Inft. 648,

2013 Datura foliis obcordatis villofis integris, floribus

oblongis erectis, pericarpiis fpinofis nutanti-
bus.

2014 Daucus vulgaris. Cluf. Hift. 198.

2015 Echinops floribus fafciculatis, calycibus multi-

floris. Hort. Cliff. 391.

Chameleon niger, umbellatus flore cseruleo
Hyacinthino. C. B. P. 380.

2016 Erica antheris bifidis inclufis, corollis cylindri-

cis longioribus aggregatis, foliis verticillatis,
dentato aculeatis. Lin. Spec. 355.

2017 Gaultheria. Kalm. Linn. gen. nov. 1080. Sp,

PI- 395-

2018 Hedyfarum foliis fimplicibus ovatis acuminatis,

fpicis longiflimis nudis terminalibus.

Vol. LIU.

F

.2019

I 34 ]

2019 Hypericum fioribus monogynis foliis lineari-

lanceolatis obtuiis caule fruticofo.

2020 Ipomaea foliis trilobis cordatis pedunculis tri-

floris. Linn. Sp. 151.

2021 Leonurus foliis tripartitis multifidis linearibus

obtufiufculis. Hort. Upfal. 170.

Ballote inodora foliis Coronopi. Amman.
Ruth. 48.

2022 Ligufticum Pyrenaicum foeniculi folio, luci-

dum. Tourn. Inft. 324.

20^3 Linnia caule eredto hirluto foliis ovato-lanceo-
latis feffilibus, floribus terminalibus.

2024 Martynia caule ramofo, foliis cordato-ovatis

pilofis. Miller’s Icons 286.

2025 Mefpilus inermis foliis ovato oblongis glabris

ferratis, caule inermi. Lin. Sp. 478.

'2026 Ocymum caryophyllatum maximum. C. B. P.
225.

2027 Ptconia foliis quinque lobatis lanceolatis ex

Tartaria.

2028 Peryclymenum capitulis ovatis imbricatis ter-

minalibus foliis fummis conato perfoliatis
fubtus glaucis.

2029 Pifum caule angulato procumbente foliolis in-

ferioribus lanceolatis acute dentatis, fum-
mis fagittatis. Di6t. Hort.

2030 Polium candidum tenellum tomentofum flore

purpureo, J. B. 3—300.

2031 Prenanthes flofculis plurimis fioribus nutantibns

fubumbellatis, foliis haftato angulatis. Hort.
,C|>4. 383.

2032 Ricinoides, ex qua paratur Turnfol. Gallorum.

Tourn. Inft. 655.

I 2033

[ 35 ]

2033 Ruellia foliis petiolatis, frudtu feffili confedto.

Hort. Cliff. 318.

Ruellia ftrepens capitulis comofis. Hort. Elt.
3°°.

2034 Ruta fylveflris minor. C. B. P. 336.

20.35 Scabiofa Africana frutefcens, folio rigido fplen-
dente ferrato, ftore albicante. H. Amff
2. 185.

2036 Sibthorpia foliis reniformi fubpeltatis crenatis.

Lin. Gen. nov. 1099,.

Cliryfofplenium Cornubienfc Petiver. Herb.
Tab. 6. Fig. 11.

2037 Sida tomentofa foliis cordatis ferratis. fubtus.

nervofis.

2038 Solanum caule aculeato, foliis pinnato-finuatis,

frudtu racemofo. Schiru Schuna Hort. Ma-
lab. Vol. 2. Tab. 36.

2039 Solanum caule aculeato herbaceo, foliis cor-

datis dnuatis calycibus aculeatis. Virid.
Cliff 16.

2040 Solidago caule paniculato racemis confertis,

foliis inferioribus lineari-lanceolatis petiolatis
caulinis feffilibus glabris. Didt. Hort.

2041 Spigelia Anthelmia. Lin. Sp. 149.

2042 Teucrium foliis fubcordatis inasqualiter ferratis

petiolatis, racemis lateralibus fecundis caule
eredto.

2043 Trianthema foliis ovatis petiolatis, floribus con-

fertis feffilibus, caule diffufo. •

2044 Trianthema foliis abovatis petiolatis, floribus

feffilibus eaulibus procumbentibus.
Trianthema. Sauv. Meth. 127. Linn. Sp. 223.

F 2 2045

C 36 ]

2045 Turritis minor. Botan. monfp.

2046 Vaccinium foliis integerrimis revolutis ovatis,

caulibus repentibus filiformibus nudis. Lin.
#Sp. 3 51.

Vitis Idaea paluflris. C. B. P. 471.

2047 Viburnum foliis ferrulatis ovatis acuminatis gta-

bris, petiolis glandulofis. Lin. Sp. 268.

2048 Urtica foliis alternis ovato cordatis ferratis ra-

cemis compofitis ere&is. Miller.

2049 Wachendorfia foliis lanceolatis quinquenerviis

canaliculato-fpicatis floribus in thyrfum col-
ledis. Burman. Fig.

2050 Walkeria, Gen. nov.

XI. Ob -

XI. Obfervations made by Mr, John Bar-
tram, at Penfil vania, on the Tellcrwifh Wafp
of that Country : In a Letter to Mr, Pe-
ter Collinfon, F, R. S,

Read Feb. 24. "T" Saw feveral of thefe wafps flying about
«763* aheap of Tandy loam: they fettled on

it, and very nimbly fcratched away the fand with
their fore feet, to And their nefts, whilft they held
a large fly under their wings with one of their other
feet : they crept with it into the hole, that lead to the'
neft, and ftaid there about three minutes, when they
came out. With their hind feet, they threw the fand
fo dexteroufly over the hole, as not to be difcovered :
then taking flight, foon returned with more flies,
fettled down, uncovered the hole, and entered in
with their prey.

This extraordinary operation raifed my curioflty to
try to find the entrance, but the fand fell in fo fad,
that I was prevented, until by repeated eflays I was fo
lucky as to find one. It was fix inches in the ground,
and at the farther end lay a large magot, near an inch
long, thick as afmallgoofe quill, with feveral flies near
it, and the remains of many more. Thefe flies are
provided for the magot to feed on, before it changes
into the nymph date : then it eats no more untill it
attains to a perfect wafp.

The order of providence is very remarkable, in
prefcribing the different ways and means for this
tribe of infe&s to perpetuate their feveral fpecies, no

doubt

[3*] . -

doubt for good ends and purpofes, with which we
may not be well acquainted, but mod; likely, for the
prey and food of other animals.

One kind of wafp fabricates an oblong neft of pa-
per-like compofition full of cells for the harbour of
its young, and hangs it on the branch of a tree.

Some build nefts of clay, and feed their young
with fpiders ; others fuftain them with large green
grafshoppers : then there are thofe, that build combs
on the ground (like ours in England) to nourifh a
numerous brood.

But this yellowifh wafp takes a different method,
with great pains digging a hole in the ground, lays its
egg, which foon turns to a magot, then catches flj.es
to lupport it, until it comes to maturity.

The wifdom of Providence is admirable, by giving
annually a check to this prolific brood pf noxious
infers, in permitting all the males to die, which are
the mod numerous of the family ; only referving
a few impregnated females of each fpecies, to conti-
nue their race to another year.

Whereas bees, whofe labours are fo beneficial to
mankind, always furvive the winter to raife new co-
lonies.

XII. An

[ 3 9 'J

XII. An Account of the Plague , at Aleppo :
In a Letter to the Rev. Charles Lyttelton,
LL . D. Dean of Exeter, now Lord Eifhop
of Carlifle, and F. R. S. from the Reverend
Mr. Thomas Dawes, Chaplain to the
FaElo?y at Aleppo.

Sir, Aleppo, October the 26th, 1762.

Read Feb. 24, rj*1HE unexpected continuance of the
I763' A plague in this city during the whole
pad: winter having prevented the Englifh fhips, that
brought me your favour of October 16th 1761, from
receiving any thing on board from hence, I have been
obliged thus long to defer paying my refpedfsto you,
and rendering my grateful acknowledgments for -
your generous concern and good withes for my./
fafety.

Tho’ I find by experience, that accounts given 1
in news papers of occurrences in this dilfant quarter
of the Globe feldom deferve much credit, yet I can-
not contradict the report you mention of the plague’s
raging herein the funimer of 1761. You probably
will have had it confirmed long fince, and alfo have
heard of the accumulated diftreffes we have lately
been labouring under : but as the particulars may not
have reached you, I will venture to communicate them,
tho’ it is a fubjedt neither pleafing to me to dwell on,
nor can be very agreeable to you to read. Would to
God ! I could even now allure you they are at an end.

On

[ 4° ]

On the mercy of his protecting Providence has been
our foie reliance ; nothing elle could have fupported
us under the many apprehenfions and dangers we have
been daily expofed to.

This unhappy country for fix years pafl has been
in a very terrible lituation, afflicted during the greateff
part of that time with many of the Almighty’s fe-
vered: fcourges. Its troubles were ufflered in by
a very (harp winter in 1754., which deftroyed almoft
all the fruits of the earth. The cold was fo very intenfe,
that the Mercury of Farenheit’s thermometer, ex-
pofed a few minutes to the open air, funk entirely
into the bail of the tube. Millions of olive-trees, that
had withftood the feverity of 50 winters, were blaft-
ed in this, and thoufands of fouls perifhed merely
thro’ cold. The failure of a crop the fucceeding
harveft occafioned an univerfal fcarcity, which in this
country of indolence and oppreffion (where provifion
is only made from hand to mouth, and where, liter-
ally fpeaking, no man is fecure of reaping what he
has fown) foon introduced a famine with all its at-
tendant miferies. The (hocking accounts related
to me on this fubjeCt would appear fabulous, were
they not confirmed by numberlefs eye-witneffes, both
Europeans and natives. In many places the inha-
bitants were driven to fuch extremities, that women
were known to eat their own children, as foon as they
expired in their arms, for want of nourifhment.— Num-
bers of perfons from the mountains and villages ad-
jacent came daily to Aleppo, to offer their wives and
children to fale for a few dollars, to procure a tem-
porary fubftfience for themfelves ; and hourly might
be feen in our ftreets dogs and human creatures

lcratching

[ 4* ]

Scratching together on the fame dunghill, and quarrel-
ling for a bone, or piece of carrion, to allay their hun-
ger. A pedilence followed clofe to the heels of
the famine, which laded the greated part of 1758,
and is fuppofed to have fwept away 50 or 60 thou-
sand fouls in this city and its environs. I blefs God,
I was not a fpe&ator of this complicated fcene of
mifery : the very defcription of it mud didrefs a com-
paffionate^difpodtion j the fight of it mud have made
an impredion on an heart of dint.

I have already acquainted you, in a former letter,
with our troubles by earthquakes, &c. of 1759 and
1760 and therefore fliall proceed from the date of my
lad letter. The latter end of March 1761, the plague,
which had lain dormant dnce the autumn, made its
appearance again in this city, and alarmed us con-
fiderably. Tho’ I confefs, it did not furprize me; fo
far from hot expe&ing its return, I ihould have looked
on it almod as a miracle, if we had efcaped, after the
little progrefs it had made among us the preceding
year. The infedion crept gently and gradually on,
confined chiedy to one particular quarter, till the begin-
ning of May, when it began to fpread vifibly and
univerfally. We diut up on the 27th, and our con-
finement laded 96 days. The fury indeed of the con-
tagion did not continue longer than the middle of July,
and many of our merchants went abroad with caution
early in Augud j but as our conful had no urgent
bufinefs to induce him to expofe himfelf to any rifle,
we remained in clofe quarters till we could vifit out-
friends with tolerable fecurity. As an addition to
the uneafinefs of our fituation, the earthquakes re-
Vol, L1II. G turned

[42 3

truned the latter end of April, tho’ with no great
violence, except the firft fhock, and that much lefs
terible than thofe of 1759. We felt 6 or 7 within
the week, and 4 more at long intervals during our
imprifonment ; but as they were all flight, ourappre-
henflons foon fubflded. At our releafe from con-
finement the laft day of Auguft, we flattered our-
felves with the hopes of a fpeedy releafe from danger;
but it pleafed God to order it other wife. In all
the plagues, with which Aleppo has been vifited in
this century, the contagion is laid to have regularly and
conftantly ceafed in Auguft or September, the hotteft
months in the year; and it is pretty certain, that it dif-
appeared about that time in 1742, 1743, 1744 and
1760 ; but unfortunately for us that now reflde here,
the year 1761 has proved an inftance of the fallacy of
general obfervations on this dreadful fubjedt; for, from
the end of March 1761 to the middle of Sept. 1762,
fcarce a day has pafled without fome deaths or frefh
attacks from the diftemper ; and tho’ the violence of
it ceafed in the autumn, yet I believe on an average
it was fatal to at leaft 30 perfons in every week, from
that time to the end of the winter. In February laft
we were pretty healthy : hearing but of few accidents,
and thofe in the fkirts of the city, we once more be-
gan to entertain fome faint hopes of a farther exemp-
tion, but they were of very ihort duration: in March
the infedtion fpread again, and in April increafed with
fuch rapidity, that we were obliged to retire to our
clofe quarters on the 26th of that month. I have
now the fatisfadlion of informing you that, by the
blefiing of Providence, we are once more fafe and at

liberty.

4

C 4-3 J

liberty, tho’ after a confinement more tedious, and
much more difmai than even that of the laft year;
we got abroad on the 1 8 th of Auguft, when the
burials were reduced to about 20 a day : the infection
gradually decreafed till the middle of September, fince
which time we have heard of no accident. May the
Almighty gracioufiy be pleafed to prevent the return
of adiftemper, whofe very name ftrikes terror when-
ever it is mentioned and is undoubtedly one of the
moft lamentable misfortunes, that mankind is liable
to.

I wifh I could with any precifion determine our
lofs in the two laft fummers ; but, in times of fuch
general horror and confufion, it is in a manner im-
pofiible to come at the exadt truth. If you enquire
of the natives, they fwell the account each year from
40 to 60 thoufand, and fome even higher; but, as
the eaftern dilpofition to exaggaration reigns at p re-
fen t almoft univerfally, little accuracy is to be ex-
pedted from them : this however is certain, that the
mortality of this year has been very confiderable, per-
haps not much inferior to any in this century. Some
of the Europeans have been at no fmall pains and
expence to procure a regular and daily lift of the
funerals during our confinement, and their account
amounts to about twenty thoufand, from the ift of
April to the 1 ft of September this year, and about one
third lefs the preceding fummer. This calculation
I am inclined to think is pretty right, tho’ there are
fome ftrong objedtions againft a probability of being
able to procure a juft one in fuch circumftances : for
the Turks keep no regifter of the dead, and have

G 2 7a

[ 44 ]

72 different public burial places in the 7 miles cir-
cumference of the city, befides many private ones
within the walls. The Chriftans and Jews, who are
fuppofed to be rather lefs than a feventh part of the
number of inhabitants, have regifters, and each na-
tion one burial place only : their lots this year is about
3500 in the five months.

I will not fhock your compafiionate difpofition by
a detail of the naileries I have been witnefs to, but
only mention, that during the months of June and
July, (in the greateft part of which the burials were
from 2 to 300 a day,) the noife of men finging before
the corps in the day, and the fhrieks of women for
the dead both day and night, were feldom out of our
ears. Cuftom foon rendered the firft familiar to me ;
but nothing could reconcile me to the laft; and as
the heat obliges us to deep on the terrace of our
houfes in the fummer, many of my nights reft was
difturbed by thefe alarms of death.

I blefs God, all my countrymen have been fo for-
tunate as to efcape any infection in their houfes, tho’
each year 4 or 5 Europeans have been carried off, and
each year the plague broke out in two houfes that join
to ours. In one of them this year died a Francifcan
Prieft, after two days illnefs, whofe bed was placed
about fix yards diftance from mine. I believe I was
in no great danger, as a wall 9 or 10 feet high fepa-
ratcd our terraces ; but had I known his fituation, I
lhould have moved farther off. The year before, I
was thrown into a very great agitation of mind for a
few days, by the death of my laundrefs’s lnafband ;
for the very day he died of the plague, my fervant
1 had

[ 45 3

had received my linen from his houfe, and I had
careleflly put on lome of it, even without airing. This
accident happened many weeks after we were open,
and his illnefs was induftrioufiy kept a fecret. The
laft month of my confinement this year pafied very
heavily with me indeed ; for I found my health much
difordered. Whether it proceeded from a cold I catch-
ed in my head by fleeping in the open air in fome
very windy nights ; from want of exercife ; or from
the uneafinefs of mind naturally attending our me-
lancholy fituation, I know not ; but my nerves
feemed all relaxed, my fpirits in a hate of d ejection
unknown to me before, and my head fo heavy and
confufed,that I could neither write nor read for an hour
together with application or pleafure. Since our
releafe, I have pafied a month at a garden about an
hour’s ride from the city, for the fake of exercife and
frefii air, and find myfelf much relieved by it, tho*
my head is far from being yet clear.

Among many particulars relating to the prefent
plague, that I have heard, the following anecdotes
feem fomewhat extraordinary; and yet, as they are
well attefted, I have no reafon to doubt of the truth
of them; viz. Lafi: year as well as this, there has.
been more than one inftance of a woman’s being de-
livered of an infedfed child, with the plague fores
on its body, tho’ the mother herfelf has been entirely
free from the difiemper.

A woman, that fuckled her own child of 5 months,
was feized with a moft fevere plague, and died after
a week’s illnefs ; but the child, tho’ it fucked her, and
lay in the fame bed with her during her whole dif-

order,

[ 46 ]

order, efcaped the infection, A woman upwards
of an hundred years of age was attacked with the
plague, and recovered: her two grandchildren of io
and 1 6 received the infection from her, and were
both carried oft by it.

While the plague was making terrible ravage in the
ifland of Cyprus, in the fpring of 1760, a woman
remarkably fanguine and corpulent, after lofing her
hufband and two children, who died of the plague in
her arms, made it her daily employment from a prin-
ciple of charity to attend all her fick neighbours, that
flood in need of her affidance, and yet efcaped the
infection. Alfo a Greek lad made it his bufinefs
for many months to wait on the fick, to wafh, drefs
and bury the dead, and yet he remained unhurt.
In that contagion ten men were faid to die to one
woman ; but the perfons, to whom it was almofl
univerfally fatal, were youths of both fexes. Many
places were left fo bare of inhabitants, as not to have
enough left, to gather in the fruits of the earth : it
ceafed entirely in July 60, and has not appeared in
the ifland fince.

The plague feems this year to have been in a man-
ner general over a great part of the Ottoman empire.
We have advice of the havoc it has made at Conflanti-
nople, Smyrna, Salonicha, Brufa, Adena, Antioch,
Antab, Killis, Ourfah, Diarbekir, Moufol, and
many other large towns and villages. Scanderoon,
for the firfl time I believe this century, has fuffered
confiderably : the other Frank fettlements on the fea-
coaft of Syria have been exempted, excepting a few
accidents at Tripoli, which drove the Englifh con-

C 47 3

ful, Mr. Abbott, into a clofe retirement for a week or
two ; but the ftorm Toon blew over.

I am, with the greatefl rcfpedt,

Sir,

Your mod obliged and mod
obedient humble fervant,

Thomas Dawes,

November 4th, 1762.

P. S. Praife be to the Almighty, we dill continue
free from any bad accident : the 40 days necef-
fary for a clean bill of health are expired; and
the Reward, Captain Saunders, is taking in her
loading for England.

XV. An

C 48 ]

XIII. Obfervations on Sand Iron : In a hot-
ter fro?n Mr . Henry Horne, to Mr . John
Ellicot, R R. S .

S I R,

Read March 3, /l S the affair of the rich American
1 \ Iron Ore, commonly known by
the name of the Virginia black fand, has of late not
only engaged the converfation of many of the Vir-
tuofi, but has been taken very particular notice of
by the Society for the encouragement of arts and
manufactures ; I thought myfelf obliged, for many
reafons, to lay before you whatever has come to my
knowledge relating to this difcovery, either from my
own experiments, or from the information of others.
And I engage in this fervice with the greater pleafure,
as I look upon it to be one of the moft intereffing
difcoveries, with regard to this ufeful metal, that has
come to our knowledge for fome ages, and, if right-
ly conduced, may prove of infinite fervice to us in
this part of the world, as well as to the inhabitants
of our colonies, where (as it has been fuppofed, though
without fufficient foundation) this difcovery was firft
made.

Without any farther preface or apology, permit
me to remind you, that, in a converfation which for-
merly paffed between us upon this fubjeCt, I acquaint-
ed you, that, about twenty years fince, I was engaged
in making a variety of experiments upon the nature
of Iron Ores, and Steel; and that I then made a

very

[ 49 ]

itrery particular enquiry into the nature of this black

fand, and, in the courfc of thefe experiments, feveral
very interefting phenomena difcovered themfelves,
which, as they might be of great fervice to the world
in general, and more efpecially to fuch as are concern-
ed in fmelting of the iron from the ore, I had thoughts
of communicating to the publick ; but, as my bufi-
nefs will not permit me to go through the whole at
prefent, I fhall confine myfelf to what relates to the
black fand.

I procured, from Mr. Adams the Virginia merchant,
a fufficient quantity of the fand, and, in order to efti-
mate its comparative weight with that of iron ore,
I procured fome of the richefl ore I could get, which
having reduced to powder, I filled an ordinary tea-
cup with it. I afterwards filled the fame cup with
fome of the fand, and upon comparing the weights
with each other, I found that the weight of the land
was to that of the ore as 3 to 2 ; and having taken
notice how readily the fand was attracted by the
magnet, I was convinced that the fand mult certainly
contain a very confiderable quantity of Iron, and
therefore determined to make trial of it. I was how-
ever, for fome time, interrupted in my defign, by in-
formation I received from a friend, that fuch an en-
quiry had been made many years before, by a mem-
ber of the Royal Society, and a .gentleman of efteem
as a chemift, but without fuccefs; and that the
experiments were publifhed in the 2d vol. of
Lowthorp’s Abridgment of the Philofophical Tranf-
adtions. As this account is very fhort as well as cu-
rious, I fhall take the liberty to give it you entire,
with fome few remarks upon it.

Vol. Llllf H

A black

[ 5° ]

” A black fliining fand from Virginia examined by
Dr. All. Moulen.

A (mail vial filled with ordinary white fand, and
containing only 3 i. gr.xi. being filled with the Vir-
ginia fand, was found to contain Jij, By. gr. i.

This fand did apply to the magnet both before and
after calcination j but the latter did apply bettei to it

than the former. ....

A parcel of this fand, mixed and calcined with pow-
dered charcoal, and kept in a melting furnace for a-
bout an hour, yielded no regulus: but applied more
vigoroufly to the Loadftone than either of the for-
I fluxed a parcel of this fand with fixed nitre, m
a melting furnace, for above an hour, but could ob-
tain no regulus; nor any fubftance that would apply
to the magnet, except a thin cruft that ftuck firmly
to a piece of charcoal that dropt into the crucible

when the matter was in fufion. .

I fluxed it alfo with falt-petre and powdered char-
coal, dropping pieces of charcoal afterwards into the
crucible It continued about half an hour in the
melting furnace in fufion, and that without produc-
ing a regulus, or a fubftance that would apply to the
magnet, excepting only what ftuck to the charcoal

as in the former experiment. ,

I fluxed another parcel of it with falt-petre and
flower of brimftone, without being able to procure

“1 pom'cd good fpirit of fait on a parcel of this fand,
but coulcTcbferve no Inflation thereby produced.

I poured fpirit of nitre, both ftrong and weakened

rtS1"]

-with water, on parcels of the fame fand, without
being able to difcover any conflict.

* I poured Angle aqua fortis upon another parcel of
it, without being able to perceive any ebullition worth
noting.

I uied alfo double aqua fortis upon another parcel of
it, which, for ought I could difcover, had no more
effect on it than the former.

Tpoured fome aqua regia on a parcel of it, without
difcovering any fen Able effed. I poured good oil of
vitriol upon. another parcel of this fand ; but feeing no
bubbles thereby produced, I weakened the oil with
water, but without any vifible efFed.

I repeated all the former experiments with the
menftruums upon this fand after calcination per le in
a crucible, but could fcarce obferve a bubble pro-
duced by any of them.

I poured fome of each of the liquors upon parcels
of the powder of this fand calcined, without any
fuccefs.

Note, that I made thefe experiments both in the
cold, and upon a fand furnace. So that to me there
feems to be but little wanting to difcover any metal
known to us, if it contained any fuch : for there is
•no metal nor ore that fome of thefe menftruums will
not work on,

I powdered a fragment of a toad'ftone, and poured
fome of thefe menftruums upon it, without being
able to And that they in the leaft preyed upon it, any
more than they did upon the fand.

I poured fome of the aforementioned menftruums
upon ordinary fand taken out of a fand furnace, where
it muft have fuffered fome calcination 3 but could

H 2

r 52 t

find no more bubbles produced thereby, than what
might rationally be fuppofed to be produced from
lime, and other dirt mixed with the fand.”

Having thoroughly confidered thefe experiments,
they appeared to me far from being decifive, and
that if the Do&or had placed more confidence in the
power of the magnet, and lels in his menftruums,
he would rather have concluded that there might be
fome forts of iron ore which his menftruums would not
touch in the moift way, nor any regulus be produced
from them in the dry, as he made ufe of them, which
yet might, under fome other hands, be fubdued, by
more apt and powerful methods than any which at
that time he was acquainted with.

However I apprehended I might fairly draw this
conclufion from his experiments, viz. that the fand
was not altogether and limply iron, but that it was
ftrongly united with a very ftubborn, fixed, and per-
manent earth, which could not be feparated from it
without fome extraordinary, as well as powerful
means j but I could not think this a fufficient objec-
tion to the profecution of an experiment, which, if
it fucceeded, might be attended with very happy
confequences. Proceeding therefore upon this fup-
pofiticn, I mixt up about 8 or 9 ounces of the fand,
with a proportional quantity of a ftrong corrofive flux,
which I put together into a crucible, and committed
it to a very ftrong fire in an excellent wind-furnace,
where 1 kept it for between two and three hours, hop-
ing by this means to have anfwered the intended pur-
pofe j but I confefs I was not a little furprifed, that,
after the crucible was taken from tl\e fire, 1 could not

find

. C 53 ]

find one fingle grain of metal in the remaining con*
tents.

This difappointment greatly puzzled me, till hav-
ing thoroughly examined into the unexpedted event,'
without being able to difcover any reafon fufficient
to incline me to recede from my former opinion, as-
to the component parts of the fand, I concluded that
the flux might poffibly be a very improper one; for
though it might have effedted the intended feparation,
yet it might at the fame time be fufficiently powerful
to divide the particles of the metal, when feparated,
fo very minutely, as to be capable of fubliming and
carrying them off imperceptibly : And finding the
contents greatly diminifhed, fo that the quantity re-
maining bore but a fmall proportion to that which
was firfb put into the crucible, I concluded that thi3
muft really have been the cafe, and that fo'me very
different method muft be purfued in order to produce
the defired effedts. I immediately determined to make
a fecond trial, in which I proceeded in the following
manner. I took the fame quantity of fand made
ufe of in the former experiment ; and firft I fpread it,
without any addition to it, upon an iron plate over a
flrong fire, where I gave it a very powerful torrifica-
tion (or roafling) to try if, by that means, I could not
relax, and loolen the component parts to fuch a degree,
as to make the feparation and redudtion of the me-
tal more eafy, when I fhould bring it into the furnace.
When I had fo done, I mixed it up with a flux of a
very peculiar, but gentle nature, which I had before
made ufe of for other purpofes with great fuccefs, and
committed it (as in the former experiment) to the fur-
nace, where I urged it by a very flrong fire for about
i three

C 54]-

three hours, and upon taking it out, I found the event
anfwerable to my moft fanguine expectations : for in
the bottom of the crucible I found, as near as I can
remember, rather more than half of the fand I put
into the crucible reduced to a very fine malleable
metal.

In this very agreeable experiment I met with a very
furprizing phenomenon, which, as I am not at prefent
able to determine whether it was only cafual, or

• what would always happen in the like experiments,
you will excufe my divulging at prefent, efpeciali.y
as you, Sir, by furnifhing me with a frefh parcel of the
fand, have enabled me to make fome farther trials ^
which I fiiall embrace the firft opportunity of doing;
and fhould I be fo happy as to confirm what I then
obferved, or to make any farther difcoveries deferving
your notice, I fhall not fail communicating them to

* y°u* r

Being fully convinced, by the experiment, that the
fand was a very rich iron ore, I acquainted fome of
my friends with it, who being largely engaged in
trade to thofe parts of our American colonies, where
I was informed this fand was to be eafily procured,
and in very large quantities, I was in great hopes an
account of this nature would have inclined fome of
the gentlemen in that part of the world, tohavepro-
fecuted fo ufeful a difcovery in a larger way ; and I
own I have often wondered, that an affair of fuch
confequence fhould have lain dormant for fo many
years.

However I was a few months fince pleafingly fur-
prifed, to find in the hands of my very ingenious
friend Mr. Peter Collinfon, not only a pamphlet, but
.. . likewise

C 55 J

likewife a letter upon the fubjeCt addrefTed to the So-
ciety for encouraging of arts and manufactures, by
one Mr. G. Elliott, who relates, that, though previous
to his attempt of making iron from this fand, he met
with nothing but what was difcouraging from the
mod: fkillful perfons to whom he propofed his defign,
yet that he had fuch a perfuafion in his own mind of
the practicability of the thing, that he could not red
till he had made a trial, and the event proved encou-
raging much beyond his expectations, infomuch
that he could fcarcely believe the trial had been fairly
made, till a fecond trial evinced with certainty, that
eighty three pounds of the fand would produce a barr
of excellent iron weighing fifty pounds : a prodigious,
yield indeed, and far beyond what I have ever heard
of from the riched common ores that are any where
to be found ; mod of the ores I have ever met with
or heard of, yield little more than half in pig metal,
and which will differ a wade of near 7 part to make
tolerable good barr iron, and much more if I am
rightly informed, when the iron is intended for
more valuable purpofes, fuch as being drawn into
wire, &c.

After I had feen his addrefs in his letter to the So-
ciety, and his pamphlet j by the aflidanceof my friend
Mr. Collinfon, I fent him over two or three hints,
which I judged might be of fome fervice to him 5
this produced the favour of a letter from him, of
which the following is an exaCt copy.

Mr,

[56] ~

Mr, Henry Horn,

Sir, -Killingworth, 0&. 4. 1*62,

T Underftand by Mr. Collirtfon, that you have Teen,
and greatly approve of, the fample of fand iron
which was fent j that you >are defirous to know how
it was made, and whether it can be made in large
barrs. The little barr you faw, was cut off from a
barr of 52 pounds and a half, the firft that was made
•at my Ton’s work, the firfl; that was ever made in
America, and probably the firft that was ever made in
the world, in that manner, and fo large a barr. I ne-
ver heard of any attempt made upon the iron fand,
till that of yours 20 years ago, of which Mr. Collin-
lon gave me an account in his letter.

As to the manner of making the iron, it is wrought
or fmelted in a common bloomary, in the fame man-
ner as other iron ore is fmelted ; excepting this dif-
ference, this iron fand is fo pure, fo clean walked,
that there is not a fufficient quantity of cinder or flagg
to promote and perform the fmelting, therefore wo
add either the flagg which iflues from other iron, or
elfe add fome bog mine ore, which abounds with cin-
der ; in this way it is as capable of being wrought as
rock ore or bog mine.

T *was in hopes that if this iron fand could be
wrought at » all, the particles being fo very fine, -it
would fmelt very quick ; but herein I found myfelf
miffaken, every particle has a will of its own, and
muff have its own particular fmelting, for inftead
©f its being performed in lefs time, it took more than

common

[ 57 ]

4v*

V * ' 4

common iron ore, but, upon farther experience, and
more acquaintance with this fand, the workman has
fhortened the operation from five hours down to three i
if by any means it might be reduced to the fame time
with pigg iron, it would be a moft ufeful improve*-
ment. If you can afford any directions to haften the
operation, I (hould be greatly obliged for any inftruc-
tions.

There is fo much of this fand in America, that I
am apt to think, that there is more iron ore in this
form of fand than in mines.

I have writen an effay upon the futjeCt, which I
hope Mr. Collinfon will let you fee, as I hope to fee
what you are about to publifh. My fon has a fteel
furnace, which was ereCted feveral years before the
aCtof parliament prohibiting them in the plantations :
he has converted fome of the fand iron into fteel, of
which I fend you a fample ; as alfb a fample of the
iron. As my fon had noinftruCtions for making fteel,
we were forced to hammer out the fkill by various
trials as we could; fo conclude that he is ftill imperfeCt,
and wants your help and direction to bring it to per-
fection, in which art I underftand that you are a per-
fect matter, and withall kind enough to offer your
affiftance; for which I am very thankful, and look
upon it as an aditional favour, if you will be pleafed
to indulge me with the benefit of your correfpondence,
for I live in a corner of the world where fuch infor-
mation as, I truft, you are able to furnifh, will be high-
ly beneficial. Previous to my attempt of making
iron from fand, I propofed my projeCt to thofe who
were the moft fkillful in thofe affairs, but met with
nothing but what was difcouraging ; yet after all,

Vol. LIII, I had

MW

H)

✓

[ 58 ]

had a perfuafion of the practicability of the thing to a
degree next to enthufiafm, fo that I could not reft
till I had made trial. I am glad that the iron has fuch
qualities as to meet with your approbation ; I knew
that the iron was good, but did not know that it was
fo good as your fuperior knowledge has found it. I
want to know what fuch iron will fell for in England,
whether it will be worth while to fend it. This black
fand is a treafure that has long lain hidden from the
world, and is what may render the colonies more valu-
able to Great Britain.

% *•

I am, Sir,

Yourmoft obliged humble fervant,

Jared Eliot.

P. S. The barrs of iron which have hitherto been
made of fand, are from fifty to fifty grofs, hope in
time to have them reach to feventy pounds weight
each ; experience muft determine that matter, we
can do better than at the time the eftay was written.
We have been vifited with a long and fore drought,
have done nothing for a long time for want of
water.

The fimples which accompanied this letter, were
two fmall barrs, weighing only a few ounces, one ot
the iron made from the fand, the other of fteel made
from the fame iron. Thefe barrs I have tried, and
found that the barr of fteel worked extreamly well
under the hammer, was very pure and clean, and

free

C 59 ]

free from flaws. On the contrary the barr of iron
turned out much otherwife, for, though it appeared to
bear the force of the hammer, as well as the flee),
yet it was not near fo pure, but broke out in flaws
and hollows, almoft through the whole of the barr,
and which a welding heat would by no means bring
into proper union ; this however engaged us to try a
different method, which was, when the barr was re-
duced into a proper fize for the purpofe, to double it
up three times, one part of the barr upon the other,
and to try if it would then bear welding and become
more confident, and by this means we found the end
perfe&ly well anfwered ; for it bore the force of the
fire and the hammer, and became in a manner per-
fectly found. This fevere trial proved, to a demon-
dration, that the iron pofled all that agreable tough-
nefs and dudtility, for which the Spanidi iron is fo de-
fervedly famous, without partaking of that vile red-
fhire quality, for which the latter is very remarkable,
and manifedly tends to prove the excellency of this
land iron, when reduced into barr iron under proper
care and circumlpe&ion.

You will obferve, Sir, from the letter, that this
fand is fo pure, and fo clean wafhed, that their firfl
method of reducing the fand to barr iron proved
too tedious, for want of fome of thofe adventitious
materials, to promote and perform the fmelting, and
which always accompanies the common ore, whether
it be of the rock or bog kind j which materials, mix-
ing with the matter, made ufe of by way of flux, and
uniting with the afhes of the fuel employed in melt-
ing down the ore, is ufually run into a thick opake

I 2 glafly

C 60 1

glaffy fubftance, forming, as it were, a covering over
the metal, which, by its gravity, naturally links to the
bottom; this the workmen call cinder. Now the
want of this matter rendering the operation too tedi-
ous, I find they had recourle either to this cinder
brought from other iron works, or to a quantity of
the bogmine, which, I doubt not, would abundantly
furnifh matter for cinder. If they had ufed only the
firff, and that properly chofen, it might very probably
have been of fome fervico, without doing any material
injury to the metal ; but if the bog mine is ufed,
though the fervice might be apparently more, yet
in all likelihood the injury would be infinitely great,
and I am inclined to believe that fomething of this
kind occafioned the difference obferved between the
two barrs above mentiond, viz. that the one might
have been reduced by the help of more pure materials,
and the other by the afiiftance of their bogmine,
whofe conftituent parts abounding with many impu-
rities, fome of which, by mixing with the metal,
may have occafioned the defeats above complained
of, and which required fo fev-ere an operation both of
the fire and hammer to feparate from it. I am there-
fore of opinion, that as the profecution of this ufeful
difcovery deferves the greateft encouragement, if the
Society of arts and manufactures fhould take it under
their patronage, the premium they may think proper
to propofe fhould rather be given to the perfon who
fhall produce the pureft metal, than to him who fhall
produce the greateft quantity* for otherwife, I am
afraid, we fhall be deprived of what I fhould efleem
the moft valuable part of this difcovery, 1 mean the

obtaining

[60

obtaining a more pure, and better kind kind of iron,
than any we have hitherto been pofleft of, and which
I am certain this fand, under proper management, is
capable of producing.

Feb. 5,

I

1763*

am,

Sir, with the greateft refpeft.
Your mod obedient
humble fervant.

Henry Horne*

XIV. Ex-

[ 62 ]

XIV. ExtraB of a Letter from Simon Pe-
ter Pallas, M D. of Eerlin, to Mr. Ema-
nuel Mendez da Coda, Librarian to the
Royal Society , relating to the State of the
State of the Cold there lafl Winter , dated
Feb. i 2, 1763.

Read March 3, TT T E have had great frofls here,
VV as indeed all over Germany.
I have obferved myfelf, on the twenty-feventh of
December of lafl year, a little after feven o’clock
in the morning, the Cold to have been fo excef-
live, that the mercury in the thermometer of
Fahrenheit flood at four degrees under o, which
is fifteen degrees under o of Reaumur’s Scale,
than which the Cold in 1740 -was but very little
more intenfe. Mr. Euler, junior, obferved the fame
day the thermometer at the fame degree: about
eight and at nine of the clock of that day, the mer-
cury in the barometer flood at the height of 30" i"r
the like of which never had been obferved at Berlin
before. 1

XV. An

[ 63 ]

XV. An Account of a. remarkable Darknefs
^Detroit, in America: In a Letter from
the Rev . Mr. James Stirling, to Mr.
John Duncan : communicated by Samuel
Mead, Ffq\ F. R. S .

Detroit, 25th 061. 1762.

SI R,

5‘ i

«

Read March 3, A Man in bufinefs feldom troubles
l76!’ himfelf about news j yet the fol-

lowing is fo uncommon, I cannot negledt acquainting
you therewith. Tuefday laft, being the 19th inftant,
we had almoft total darknefs for the moft of the
day. I got up at day break : about 1 o minutes after
I obferved it got no lighter than before ; the fame
darknefs continued untill 9 o’clock, when it cleared
up a little. We then, for the fpace of about a quarter
of an hour, faw the body of the Sun, which appear-
ed as red as blood, and more than three times as
large as ufual. The air all this time, which was very
denfe, was of a dirty yellowifh green colour. I was
obliged to light candles to fee to dine, at one o’clock,
notwithftanding the table was placed clofe by two
large windows. About 3 the darknefs became more
horrible, which augmented untill half paft 3, when
the wind breezed up from the S. W. and brought
on fome drops of rain or rather fulphur, and dirt,
for it appeared more like the latter than the former,

both

C 6+ 1

both in fmell and quality. I took a lelf of clean

paper, and held it out in the rain, which rendered
it black whenever the drops fell upon it ; but, when
held near the fire, turned to a yellow colour, and when
burned, it fizzed on the paper like wet powder.
During this fhower, the air was almofl fufiocating
with a ftrong fulphurous fmell j it cleared up a little
after the rain. There were various conje&ures about
the caufe of this natural incident. The Indians, and
vulgar among the French, faid, that the Englifh,
which lately arrived from Niagara in the veflel, had
brought the plague with them: Others imagined it
might have been occafioned by the burning of the
woods : But I think it moft probable, that it might
have been occafioned by the eruption of fome vol-
cano, or fubterraneous fire, whereby the fulphurous
matter may have been emitted in the the ai-r, and
contained therein, until, meeting with fome watery
clouds, it has fallen down together with the

rain.

I am. Sir,

Your moft humble fervant;

XVI, An

C 57 ]

XVI. An Account of a remarkable Marine
InfeSi : In a Letter of Mr . Andrew Pe-
ter Du Pont, to Mr. Emanuel Mendez
da Cofta, Librarian to the R. S.

Dear Sir,

Read March io, /T Y friend Robert Long, Efq; of
i763- x Vjl Jamaica, favoured me with the

drawing and defcription of a marine infedt he took
up at fea. I believe it is a non-defcript, and as you
have often defired me to communicate to you any
obfervations worthy attention to prefent to the Royal
Society, I fend you this to communicate to that
learned body, if you deem it worthy their notice.
I fhall always think it a pleafure to tender my re-
fpedts in whatever I can to the Society, which pray
allure them of. I am,, with great efteem.

Dear Sir,

Your very obliged friend,

and humble fervant.

Chifwel -Street,
Jan. 17, 1763.

Andrew Peter Dupont,

Vol. LIII.

K

In

[ 58 ]

Auguft 13, 1762.

|N a calm on my voyage to England, on board
the Friendfhip, captain Thompfon, two per-
fons fwimming took up this moil Angular creature
floating on the furface. Its motions mufcular. Its
length a little more than one inch. Four fmall and
fhort horns, probably its eyes. It protruded them in
the water only j an orifice in the front part Teeming
its mouth. Two round fpots opaque, marked A,
poflibly refpiracula. The mid-line of the back part
apppeared through a common magnifier like a filver
leaf, and was in continual undulating motion, either
from the mufcles or circulation of juices. Two fide
lines extending the whole creature's length, and end-
ing in one in the tail of a deep blue. The fingers,
or tentacles, end in a deep blue ; a filvery caft inter-
mixed with the blue over the whole back, or upper
parts, where the blue is lighter. Vide Tab. III.

This figure is a magnified drawing by the com-
mon hand-microfcope. It can turn itl'elf on the
back by a mufcular contraction of the head part,
the tail and ramified arms inwards. The inferior
parts are white.

It died the third day, though the water was fhifted
once every day.

XVII. A

Tkilos. Trans. T rol . LI IT. TA B.BL. p. 58 •

t f .II ym/t Sr

j£)upC7lt

AS.

[ 59 1

XVII. A Letter from Monfeur Wargentin,
Secretary to the Royal Acade7ny of Sciences
m Sweden, to Mr. John Ellicott, F.R.S .
relating to the late Lranft of Venus.

Stockholm, December 24, 1762.

Read March 17,
1763

T

HE obfervations upon the lad
tranfit of Venus over the Sun
made at the Cape of Good Hope are excellent, and
feem to decide, that the horizontal parallax of the
Sun is 8" 1 or 8", 3 at mod. I had before found
it to be that quantity, from the obfervations made
in Europe compared together; but the oofervations
made at the Cape confirm it with the greated evi-

^ q 0

It is of importance to be affured of the longitude
of the places where the obfervations were made. I
have endeavoured to determine them the bed I was
able by obfervations of the eclipfes of Jupiter s fatel-
lites, made at the fame places. That you may the
better judge, I thought proper to fend you all the
obfervations of thefe fatellites made at different places
the lad year. I defire you would communicate them
to Mr. Mafon, and all thofe who intered themfelves
in the* refearch of the parallax. It is pity that mef-
fieurs L’Abbe Chappe, and Rumoffi, did not fuc-
ceed in obferving feveral eclipfes of the fatellites, at
Tobiedce and Selenginfk, the better to confirm the
Longitudes of thofe places. However it appears to
me, that the difference between the meridians of

K 2 Green-

%

[ 60 ]

Greenwich and Tobiefke is fcarcely more than
4h 32' 55 ' • That between the meridians of Green-
wich and Selenginfk, to judge from the three im-
merfions obferved there, fhould be but yh 6' o, but
from other confiderations, I think it mud: be 1 o or
15' more. If the longitude of thefe places fhould
be more exadly determined, I am perfuaded that we
fhould obtain the parallax of the Sun to nearly the
tenth of a fecond, fo exad the obfervations made at
Selenginfk and Tobiefke and the Cape appear to me.

I fee you did not communicate to the Royal So-
ciety all the obfervations made by Mr. Planman at
Cajaneberg, they however deferve to be preferved.
He obferved

h / //

The beginning of the entrance - - at 3 59 56M
Total immerfion of Venus or inte- ) g

Second interior contad or beginning \

of the exit - - - -J-'° 7 59

Total emerfion - - - - - — 10 26 22

Mr. Planman made ufe of a telefcope of 20 or 21
feet; the latitude of Cajanebourg is 64° 13' 30";
the difference of meridians between Greenwich and
Cajaneburg is fufficiently determined by obfervations
upon the eclipfe of the Moon the 18th May
1761, made at Stockholm and Cajaneburg.

I have the honour to be with the greateft efteem,

S I R,

Your very humble and obedient fervant,

P. Wargentin.

2

Eclipfes

[ 6i ]

Eclipfes primi- fatellitis Jovis, obfervatae Anno 1761 :
addito errore calculi pro quavis obfervatione, ut ap-
pareat, quse fint praeftantiores. In calculo autem
pofui differentiam meridianorum inter

h ' "

Obfervatorium Grenovic. et Parif. — o 910
Grenov. et Stockholm — 1 1 2 o

Grenov. et Upfalienfe — 1 10 20

Grenov. et Mail'll. — — o 21 19
Grenov. et Cap. B.Spei — 1 13 35

Grenov. et Inful. Rodrig.- 4 12 52
Grenov. et Selenginlk — 7 615

Grenov. et Cajaneburgh - 1 50 40

Jan. 7. Em.
June 13. Im.

20. —
July 22. —

29. —

3I# —

Aug. 7. —

14.

h /

5 4

H 37

17 22

12 45
12 3$
16 48

14 38
>4 5°

1 5 42

q IO
IO 51

12 4

//

1 I

12

1 3
H

*3

5

59

o

35 Stockholmiae -\-
47 Maffilias - - - —
26 Cap. Bonae Spei -\-
15 Paris — - - +

39 Grenov. -|-

55 Inf. Rodriga - -\-
35 Paris — - - +

28 Maffiiias — - 4"
44 Cap. B. Spei - -f-

29 Inf. Rodrig. - -j-
52 Grenovic. - - -}-
51 Stockholm. bona ~\~

49 Maffiliae

46 Cap. B. Spei -
39 Siockholm.certa.-j-

50 Cap. B. Sp. - -j-

/ //
o 27

o 21*

o 31

7

o

o

o.

33
9

0 33

o 49

o

0

1
o
o
o
o
o

49

56*

8*

9

30

49

10

34

Aug.

[62]

Aug. 21. Im.

*> / //

14 51 56 Pans - - -

_

' . *
~r 0

//

34

41 5 56 2 Cap. B. Spei

-

4“ 0

53

23‘ —

9

20 49 Pans - - -

-

-4- 0

40

^10

22 42 Upfalias —

-

— 0

3*

10

25 10 Cap. B. Spei

-

~\- 0

44

25- —

10

46 24 Selenginfk -

-

+ 1

6*

-28. —

16 48 41 Paris - - -

-

— 0

12*

3°* —

1 1

7 58 Grenovici -

-

+ 0

2 7

12

17 43 Upfaliae - -

-

+ I

2 *

12

21 32 Cap. B. Spei

-

4- 0

28

12

58 50 Cajaneburgi

-

+ 0

J5

.Sept,

1. —

9

49 40 Inf. Rodrig.

-

+ 0

40

8. —

7

55 37 Maffilke - -

-

— 0

17*

9

23 40 Cajaneburgi

-

+ 1

1*

j5* r*

9

39 55 Paris

■ + o

5

24. Em.

8

7 46 Grenovici -

-

+ 1

1

8

29 11 Maffiliae - -

-

+ 0

55

9

21 35 Cap. B. Spei

-

+ 0

47

oa.

1. —

10

13 56 Paris - - -

-

+ 0

59

10. —

6

49 8 Paris - - -

-

+ 0

45

17- —

8

36 38 Paris - - -

-

4- °

46

Nov*

9. —

8

51 19 Paris - - -

-

+ 1

48*

16. — -

10

46 26 Paris - - -

-

+ 1

6

18. —

5

27 40 Malfilke —

-

+ 0

32*

JDec.

2. —

10

5 4 Stockholmke

-

+ °

32*

4. —

4

33 8 Stockholmiae

-

+ °

39

11. —

6

25 44 Stockholmke

-

+ 0

43

Obfer-

[ 63 ]

Obfervationes fecundi fatellitis, eodem anno habitae.

June ii. Im.

18. —
July 13. —
20.

31* “
Aug. 7. — .

14. —

25. —
Sept. 1 .

8.

//

14 51 24 Cap. B. Spei -
1 7 27 11 Cap. B. Spei -
13 28 53 Paris — - -
5 1 Paris - - <- -

54 28 Grenovici - -
9 42 Caput B. Spei

57 17 Selenginfk

30 9 Grenovici - -

43 1 Stockh. optima

43 26 Cap. B. Spei -
21 37 Stockh. certa -
18 39 Paris — - -
1 5- 4 Selenginfk - -

1 6 Stockh. certa -

2 20 Cap. B. Spei -

16

JS

J7

H

10

11

1 1
H
13

12

9

9

8 59 19 Upfaliae —

10 37 59 Parifiis - -
10 29 30 Grenovici -

o

Hh 0
+ 0
+ 0

+ 1

o

+ 1

+ 0

—p o

4- I
4* o

+ o
- \ - o

— o

o

4- 1

-)- O

— o

//

14

4
9

35

58*

19
41

59
7

17

17

25
9

5

16

2*

26

*

*

10

50

40

Maffili® - - ■

- ——

0

6

ri

42

20

Cap. B. Spei.

- *4

0

3°

r5- —

*3

6

36

Grenovici -

- +

3

12*

oa.

28. Em.

8

9

51

Maffiliae - -

0

7

Nov.

11. —

12

43

Paris — - •

- _

0

2

22. —

5

18

12

Maffilia; — ■

• +

0

49

6

9

24

Stockh. dub.

- +

0

18*

Dec.

6. —

10

J5

59

Paris — - •

■ +

0

46

Eclipfes

C 64 3

Eclipfes tertii fateliitis Jovis, obfervatae anno 4*761.

h ^ ^

Maj. 11. Im. 15 19 3 Paris — - - — 3 30

Jun. 1:6. Em. 15 26 32 Cap. B. Spei — 2 21*

23. Im. 15 20 6 Paris - - - - — 5 20

15 32 20 Maffiliae - 5 25

15 10 24 Grenovici 4 48

Jol. 29. — 11 18 49 Paris 4 10*

12 23 23 Stockh, certa - • — 55 4

12 24 o Cap. B. Spei — 5 8

Em. 15 17 13 Cap. B. Spei -|- o 23

15 15 22 Stockh. certa - o 51

Aug. 5. Im. 15 34 51 Paris 6 18

Sept. 3. — 8 36 36 Cap. B. Spei 5 25

9 39 Cajaneburg 5 4

10. — 11 2 7 6 Grenovici 4 53

1 1 49 9 Maffiliae — 5 37

Nov. 21. Em. 6 41 9 Paris - o 15

6 52 44 Maffiliae — - -f- o 51

28. Im. 8 10 29 Paris 5 24

8 23 31 Maffiliae - - - - — 6 18

9 14 22 Stockh. optima — 6 28

Em, 10 40 57 Paris o 16

10 52 55 Maffiliae — o 6

, 11 44 34 Stockh. dub. - — 1 4*

Eclipfes

C 6S ]

Ewlipfes quarti fatellitis, obfervat® Anno 1761.

Aug. 10.

Im.

14

25

15 Parifiis

+

2

18

U

32

57 Cap. bon® Spei

—

0

59

27.

—

8

41

40 Grenovici - -

—

0

21

9

2

3 Maffili® — -

0

35

9

53

32 Cap. B. Spei -

+

1

22

9

5°

1 8 Upfali® - - *

+

1

21

10

16

23 Torn®

1

34

Em.

11

47

41 Paris — - -

4-

3

10

12

1

52 Maffili® - - -

Hr

1

8*

12

49

0 Cap. B. Spei. -

+

6

16

12

48

7 Upfali® - —

+

3

54

12

47

31 Stockh. certa -

+

6

IQ

13

15

13 Torn®

+

3

6

Nov. 2.

Im.1

10

5l

47 Maffili® - - -

+

5

5°

Em.

12

57

37 Maffili® - —

+

7

44

19.

Im.

6

6

34 Stockh. tub. max. —

8

5i

6

2

30 Ibid. tub. minore —

4

47

4

57

16 Paris

—

2

23

Em.

6

56

29 Paris —

+

6

32

Obfervationes afterifco * notat®, minus certas fufpt-
cor.Differenti® inter reliquas tribuend® videntur diffe-
rentiis telefcopiorum, majori minorive aeris ferenitati,
et fortaffis cuidam incertitudini circa differentias meri-
dianorum.

Obfervationes Stockholmenfes habit® funt telefcopio
novo Dollondiano 10 ped. objedta I20es fecundum di-
ametros amplificante.

Vol. LIII.

L

XVII. An

C 66 ]

XVIII. Remarks on the Cenfure of Mercator’s
Chart , in a pof humous Work of Mr. Wei},
of Exeter : In a Letter to Thomas Birch,
D. D. Secretary to the Royal Society , from
Mr. Samuel Dunn.

Rev. Sir,

Read Nov. n, *T Should not be fo ready to trouble you
‘76z* with the contents of this letter, had

I not the higheft opinion of your readinefs to aflift
the fcientific, in all matters wherein vou are able.

I requeft therefore your confideration, between this
time and the next when I have the pleafure to fee
you, if any paper has been printed in the Philofophi-
cal Tranfadtions, concerning a fphere being infcribed
in a hollow cylinder, and lwelling its furface to the
iides of the cylinder, to conftrudt thereby a more
true and accurate chart for the purpofes of navigation,
than that which was invented by Edward Wright,
and hath long gone under the name of Mercator.

The realon why I afk this is, becaufe there is late-
ly published, a pofihumous work of one Mr. Weft
of Exeter, revifed by J. Rowe, in which it is ftrongly
infifted on, that the graduation of Mercator’s chart is
erroneous, and that the fame, if rightly correfpon-
dent with the loxodromiques or rhumbs, fhould be
graduated as a line of natural tangents, from the
equinoctial to the poles.

Now this error might have paft the lefs obfcrved,
but the Critical Review of laft month fets it forth as a

mafterly

C 6 .7 ]

mafterly performance, and a thing of the greateft
merit and importance in navigation.

That there is a refpeCt due to Edward Wright for
his invention, that his principles are true, that Mr.
Weft or his editor, and both (if both of the fame
opinion) are falfe, is moft certain.

That the characters and abilities of Dr. Halley, Sir
Jonas JVfoore, Mr. William Jones, Mr. James Hodg-
fon, Mr. Hafelden, and many others, for they are
almoft numberlefs, both of higher and lower mathe-
maticians, who have wrote on the certainty and uti-
lity of Wrights chart, I fay, that the characters and
abilities of thefe able geometricians are attacked
by Mr. Weft and his editor, and by the Critical
Reviewers, is plain, and that this will have great
weight with many not over well acquainted with ge-
ometry is no lefs plain. And what will an honeft
feaman fay, who knows but juft to make his calcu-
lations, when he reads the account given in this book,
of Mercator’s chart ? And what muft thofe gentle-
men among the fubfcribers to Mr. Weft’s book fay
or think, who, not being quite mafters of geometry,
are at liberty to believe or difbelieve Dr. Halley and
many others, or Mr. Weft and his editor ? Thofe who
are mafters of geometry muft fee the error.

But there are other circumftances; Edward Wright
himfelf gives the very fame conftruCtion by his words,
as Mr. Weft doth, although his tables make out
quite another thing, that is, both Wright and Weft
fay exprefsly, the fphere being infcribed in the hollow
cylinder, and the equinodial remaining fixed with-
out fwelling whilft the other parts fwell towards the
poles, the chart will be formed. Butin this, Wright

L 2 hai

[ 68 ]

has badly exprefied his own thoughts, for his tables
make it that the equino&ial muft either fwell or
contract itfelf. And this is very excufable in Ed-
ward Wright, for at that time geometricians had no
notion of Fluxions, or the increafe of magnitude by
local motion.

Mr. Weft and his editor have therefore fallen into
this error ; they have taken the words but not the
fenfe of Edward Wright, and the Critical Reviewers
vindicate them, and make it as though this property
had been communicated to the Royal Society by Mr.
Weft, the particulars of which may be feen in the
Review juft now mentioned.

The propofeddemonft ration of this tangential proper-
ty at page 58 of Mr. Weft’s book, is no demonftration
at all, there is nothing more plain, than that, in order
to have the meridians at equal diftances, the degrees
of latitude muft be enlarged to the fame proportion in s
every part, as the circular meridians are nearer to- ..
wards the poles, which proportion is as the coline of
the latitude to the radius.

I am,.

Rev. Sir,

Chelfea, Sept. 4, 1762*

Your moft obedient fervant,

Samuel Dunru.

XIX. A -

[ 69 ]

XIX. A Defence of Mercator’s Chart againft
the Getifure of the late Mr. Weil : of Ex-
eter : In a Letter to Charles Morton,
M. D. Secret . R. S. from Mr. William
Mountaine, F. R. S .

Fo DoBor Morton, Secretory to the Royal Society. .
Dear Sir, ,

Read March 17, Received your favour with Mr. Sa-
I763' J[^ muel Dunn’s letter, touching Mr.

Weft’s method of conftruding a nautical planisphere,
referred to me by the Royal Society, which I now
beg leave to return with the following account.

As this ifland is fttuate by nature, not only for
coafting trade, but foreign commerce, fo every real
improvement in the art of navigation has always met
with the approbation and encouragement of the in-
genious and fenfible part of thefe kingdoms.

The greateft fingle advantage that this important
bufinefs ever received, was from the invention of the
mariner’s compafs ; and next to this, the projedion of
a true nautic practical chart claims place; — this laft
was performed by that great improver of navigation,
Mr. Edward Wright, as appears by his book intitled ;
“ certain errors in navigation deteded and correded”,
publilhed about the year 1599.

In chapter 2d, of faid book, he tells us, ts that
cc the errors in the plain chart had been complained;

CC Of ;

C 70 3

u of by divers, as namely by Martin Cortefe, Petrus
“ Nonius, and even Gerardus Mercator feemeth to
“ have corrected them, in his Univerfal Map of the
“ World ; yet none of them had taught any certain
“ way how to amend fuch grofs faults And, in
his. Preface, he declares, “ that, by occafion of Mer-
“ cator’s map, he firft thought of correffing l'o many
“ and great ablurdities in the common Sea Chart, but
“ the way how this was by him done, he neither
“. learnt of Mercator, nor of any man elfe.”

Wright’s method (erroneoufly called Mercator’s)
was at this time then adopted, has continued ever
lince in ufe, and has been improved by fome of the
.greateft mathematicians who have flourilhed lince
. that time, and although fometimes attacked, yet it has
been found impregnable.

The frit perfon (that I am aware of) who charged
Mr. Wright with errors in his tables of rhumbs, is
Simon Stevins, in his large volume of mathematical
remembrances, which Wright himfelf plainly con-
futes in a fubfequent edition of his book : now, Ste-
vins does not condemn the principles, but onlyalferts
that his tables have fome faults in them, and endeavours
to prove that the fourth rhumb at 78 deg. of longitude
ought to have 6id. 26™. of latitude, whereas Wright
makes it only 6id. i4m. Hence, the great difference
is no more than 12 minutes; and what inconvenience
can arife hereby to the mariner in fuch a run, was this
the fadt ? But it turns out otherwife, for this difference
is reduced to lefs than one minute (even according
to Stevins own way) as evidently appears from Wright’s
anfwer in page 214.

If

[ 71 ]

If every rhumb is then found to poffefs its true
latitude in this chart at every degree and minute of
longitude, without any fenfible or explicable error
(to make ufe of our author’s own words) it follows,
that the degrees of latitude are duly encreafed, or that
the table of meridional parts are true.

The great Dodor Halley has given us a curious
method of dividing the nautical meridian, and of
performing the problems in failing according to the
true chart, in Philofophical Tranfadions, N°. 219. by
a method different from Mr. Wright’s, but fo nearly
correfponding in pradice, that this alone is a fufficient
teffimony in favour of my author.

Our worthy brother Mr. John Robertfon, in his
excellent Elements of navigation, vol. II. page 358,
expreffes himfelf thus: “ Now although a table thus
« made (Wright’s table of meridional parts con-
“ ftruded to minutes) be abundantly fufficient for
« all nautical purpofes, yet had the fecants of fmaller
<c parts than minutes been taken, the table would
« have been more corred; and therefore Mr. Ought-
“ red, Sir Jonas Moore, Dodor Wallis, Dodor
<{ Halley, and others, have been induced to find me-
<c thods of conftruding thofe tables with more ac-
<c curacy than by the addition of fecants to every
<c minute.

“ But a table of meridional parts, conftruded by
“ the inoft accurate method, only (hews that Mr.
“ Wright’s tables do no where exceed the true me-
“ ridional parts by half a minute, and this only near
“ the pole; for in latitudes as far as navigation is
“ pradicable the difference is fcarce fenfible”. —

About

• t72h

About the year 1720, a curvilinear fea chart made
ks appearance, faid to be done by Henry Wilfon,
the publishers whereof reprefented Wright’s chart
as puzzling, difficult, and fade.

But thele groundlefs affertions were rationally an-
fwered by Mr. Thomas Hafelden, afterwards mailer
of the Royal Academy at Portfmouth, in a letter
and pamphlet addreffed to Dr. Halley about the year
1722.

In the year 1755 was published a book intitled,
<c The art of failing upon the Sea”, by W. E. which
initial letters are lufficient to point out the inge-
nious author. — In page 74 he laies, “ It is demon-
<c ftrable (by the method of fluxions) that the length
££ of the part of the meridian line in Mercator’s
££ chart, which reprefents the difference of latitude
££ of two places upon the globe, is equal to the dif-
tc ference of the log. tangents of half the compli-
££ ments of the two latitudes, multiplied into the
“ number 2,30258509, and that product into the
££ radius of the Sphere”.

And in Scholium to his Fundamental principles,
page 75. “ In the few foregoing proportions, I

<£ have demonstrated the truth of the chief methods
££ of failing nowin ufe; and deduced them from their
<c genuine principles, and fixt them upon their pro-
<£ per foundations : By which the reader will be en-
<{ abled to fee that this theory is not founded upon
<£ falfe principles ; but upon fuch as are folid and
*£ true; and consequently that all calculations built
££ hereon may be depended on as exadt”.

Notwithstanding thefe, Wright’s method is charged
with great imperfection by the late Mr. WeSt of
Exeter, in his pofthumous work, referred unto by
2 Mr.

[ 73 ]

Mr. Dunn. — Mr. Weft therein declares that cc the er-
“ rors of the plain chart are corrected, in a great mea-
“ fure, by Mercator’s or Wright’s chart; tho’ the lat-
* f ter is not a true projection of the fphere in any fhape;
“ nor indeed is it pretended to be fuch by Mr.
“ Wright, one of its inventors”. — The firft part
of this paragraph furely contains a contradiction ; for
how can the errors in the plain chart be in a great
meafure corrected by a projection that is not true in
any lhape ? And in anlwer to the latter part, — Mr.
Wright has no where made fuch conceflions that I
know of; — and further Mr. Welt blends Wright and
Mercator together, when at the fame time it does not
appear that the latter ever publifhed any principles
of this kind of projection to the world.

In the 20th article of the beforementioned book,
Mr. Welt has laid down a method of conltruCting a
nautical chart, which he alTerts to be “ the firft re-
“ prefentation of the terraqueous globe ever yet in-
“ vented, in which the meridians, parallels and
“ rhumbs, are jultly and truly projected in right
“ lines, for the latter cannot be fo projected in Mer-
“ cator.” — If they cannot be fo projected in Wright’s,
they cannot in his-, for in both, the meridians are laid
to be right lines and parallel, and therefore the rhumbs
mull be right lines alfo, or how can they interfeCt
the meridians fo fituate at equal angles?

He alfo faies in his fcholium, that “ It does not
“ appear that Mercator or Wright ever thought of
“ this projection ; for the meridian line here is mani-
“ feftly a line of tangents ; whereas in their projec-
“ tion, it is a collection of fecants.”

Vol. LIII. M

What

[ 74 ]

What Mercator’s thoughts were upon this matter
when he formed his univerfal map, I know not, as
he has left us no account thereof; but what Wright’s
were, he has very plainly told us in his aforefaid
book ; and whether his primary conceptions, and
preparative modulus, do not only take in the whole,
but alfo the very manner, of Mr. Weft’s conftruCtion,
will better appear upon a due companion of their
refpeCtive methods, which I fhall beg leave here to
introduce in their own words.

Mr. West’s Proposition.

“ If a rectangular piece of paper be turned into
the form of a right cylindrical tube, and a fphere
“ be infcribed therein, fo as that the axes of the
“ fphere and cylinder do coincide, or that the equa-
“ tor be the line of contact between the faid tube
“ and fphere, and all the points of the fpheriG fur-
<c face be projected or transferred to the concave fur-
<f face of the tube, by right lines proceeding from
“ the center of the fphere, and terminating in the
“ faid concave furface of the tube: And then, if
“ the paper be opened, and ftretched upon a plane,
<c it will prefent a chart, in which the meridians,
“ parallels of latitude, and rhumbs are all truly and
“ geometrically projected in right lines”.

In Wright’s Correction of errors, reprinted by Mox-
on in 1 6 57, not having the original edition by me,
in Chap. 2. we have the following account —
“ Whereas the fpaces betwixt the parallels fhould in-

“ creafe

[ 75 ]

“ creafe more and more as you go from the equinoc-
£c tial toward either of the poles, which Martin Cor-
££ tefe alfo noteth in his third book and fecond chap-
<c ter of the art of navigation; But he omitted that
£C wherein all the difficulty lyeth ; that is, how much,
“ or in what propcrtion thofe fpaces ffiould increafe :
£t Which that it may the better be perceived, I think
“ it not unmeet firlt to ffiew by what kind of pro-
££ jeCtion (or extenfion rather) the nautical planifphere
“ may not unfitly be conceived to be geometrically
££ made, after this manner.

Mr. Wright’s Method.

“ Suppofe a fpherical fuperficies, with meridians,
£C parallels, rhumbs, and the whole hydrographical
£t defcription drawn thereupon, to be infcribed into
££ a concave cylinder, their axes agreeing in one.”

£C Let this fpherical fuperficies fwell like a bladder
<c (whiles it is in blowing) equally always in every
cc part thereof (that is, as much in longitude as in
££ latitude) till it apply, and join itfelf (round about,
££ and all along alfo towards either pole) unto th»
££ concave fuperficies of the cylinder: each parallel upon
£C this fpherical fuperficies, increafing fucceffively from
£C the equinoctial towards either pole, until it come to
££ be of equal diameter with the cylinder, and con-
<£ fequently the meridians ffill widening themfelves,
££ till they come to be fo far diftant every where each
“ from the other, as they are at the equinoctial. Thus
<£ it may moft eafily be underftood, how a fpherical
<£ fuperficies may (by extenfion) be made a cylindri-
“ cal, and confequently a plane parallelogram fuper-

M 2 ficies ;

[ 76 ]

“ ficies; becaufe the fupeFficies of a cylinder is no-
“ thing elle but a plain parallelogram wound about
“ two equal equidiftant circles that have one com-
<c mon axtree perpendicular upon the centers of them
<{ both’' &c — “ So as the nautical planifphere may
*c be defined to be nothing elfe but a parallelogram
“ made of the fpherical fuperficies of an hydrogra-
<c phical globe infcribed into a concave cylinder, both
“ their axes concurring in one; and the lpherical fu-
<c perficies fwelling in every part equally in longitude
“ and latitude, till every one of the parallels there-
<c upon be infcribed into the cylinder (each parallel
<c growing as great as the equinoctial) or till the
“ whole fpherical fuperficies touch and apply itfelf
“ every where to the concavity of the cylinder”. —

“ In this nautical planifphere thus conceived to be
C{ made, all places muft needs be fituate in the fame
“ longitudes, latitudes, and directions or courfes, and
tc upon the fame meridians, parallels, and rhumbs, that
“ they were in the globe; becaufe, that at every point
“ between the equinoctial and the pole, we under-
“ ftand the fpherical fuperficies whereof this plani-
“ fphere is conceived to be made, to fwell equally as
“ much in longitude as in latitude (till it join itfelf
<c unto the concavity of the cylinder) fo as hereby no
<f part thereof is any way diflorted or difplaced out
<c of his true and natural fituation upon his meridian,
“ parallel or rhumb, but only dilated and enlarged :
«c the meridians alfo, parallels and rhumbs dilating
K and enlarging themfelves likewife, at every point
* of latitude in the fame proportion”.

By comparing thefe two modes of conftruCtion to-
gether I think it is not very difficult to difcover that Mr.
Weft’s derives its original from Wright’s; for right

lines

.. [ 77 ] . . ..

lines drawn from the center thro’ all the points in the
fpheric furface, and terminating in the concave fur-
face of the tube, are fecants, and the tube becomes a
tangent line to all tnofe refpeCtive fecants: And, does
not Wright’s uniform dilatation, by the fecond law of
motion, produce the fame?

Weft flops here, and gives us a chart at once ; Wright
calls thefehis geometrical lineaments only, by which
he obtains a rectilinear planifphere, and from whence
he demonftrates the principles upon which his table of
meridional parts are founded.

And that he does not efteem this as a chart corn-
pleated, but only his apparatus, and preparative work,
which requires yet to be applied and moulded into a
true nautical chart, is evident from the next paragraph,
sc Now then (faies he) let us diligently confider of the
<c geometrical lineaments, that is, the meridians, rhumbs,
tc and parallels of this imaginary nautical planifphere,
<c that we may in like manner exprefs the fame in
“ the mariner’s chart: For fo undoubtedly we (hall
“ have therein a true hydrographical defcription of
<c all places in their longitudes, latitudes, and directions,
“ or refpeCtive fituations each from other according
<{ to the points of the compafs in all things corref-
“ pondent to the globe, without either fenfible, or
“ explicable error”.

And hence he proceeds to the proof and applica-
tion of thefe his lineaments, to the conftruCtion of
his table of latitudes, as he calls it ; which is, in
this edition, computed to minutes of parallel-dif-
".ance, but with a little contrivance in the calculus to
educe the fame yet fomewhat nearer the truth.

Notwithftanding this care and nicety in computa-
lon, he is duly fenfible that his increments of latitude

calculated

[ 78 ]

calculated to minutes, altho’ without any fen lib’s
error, are yet not ablolutely true, becaufe they ought
to flow with an uniform, and uninterrupted motion;
He therefore cautioufly guards againff critical remarks
hereupon, in the following paragraph :

“ In this table it was thought fuffieient to ufe fuch
cc exaCtnefs, as that thereby (in drawing the lineaments
“ of the nautical planifphere) fenfible error mighq
££ be avoided. He that liffeth to be more precife
C£ may make the like table to decades, or tens of fe-
cc conds, out of Joachimus Rheticus his Canon Mag-
“ nus Triangulorum : notvvithftanding the geome-
“ trician that defireth exaCt truth, cannot be fo fatisfy-
“ ed neither; for whofe fake and further fitisfaCfion, I
££ thought good to adjoin alfo this geometrical conceit
££ of dividing a meridian of the nautical planifphere.’'
“ Let the equinoctial and a meridian be drawn
<£ upon a globe: Let the meiidian, divided into
<£ degrees, minutes, feconds, &c. r oul upon a (freight
££ line, beginning at the equinodial, the globe fwell-
££ ing in the mean time in fuch fort, that the femidi-
“ ameter thereof may be always equal to the fecant
“ of the angle, or arch contained between the equi-
<£ noCtial and femidiameter in lifting at right angles
“ upon the forefaid (freight line : The degrees, mi-
<£ nutes, feconds, &c. of the meridian, noted in
££ the (freight line, as they come to touch the fame,
<£ are the divifions of the meridian in the nautical
<£ planifphere : And this conceit of dividing the meri-
<£ dian of the nautical planifphere may fatisfy the curi-
<c ous exaCfnefs of the geometrician; but for mecha-
01 nical ufe, the table before mentioned may fulBce.”
More might be faid in favour of Wright’s chart,
but I think it is altogether unneceflary ; if his own

5 principles

[ 79 ]

principles and documents be duly confidered; if almoft
general practice and experience for a century and an
half part can have any weight; and, if the concur-
rent teftimony and authority of fo many eminent
mathematicians who have handled this fubjedt fince
his time, and fome of them in a quite different
method, can have any poife in the fcale of reafon.

I have carefully endeavoured not tomiftake the true
enfe and meaning of Mr. Weft’s proportion in any
part thereof; if I have not, I cannot pronounce what
kind of chart may be formed from his tangent line
being made the line of latitudes, or that meridian line
whereupon the tangents are to determine the fedions
or their iefpedtive parallels: I fhall only obferve, that,
ii the meridians be right lines, and parallel to each
other, the rhumbs muff be right lines alfo; but by this
tangential projection, tbefe will be defleded from their
true bearings, or make the angles of the courfes too
great unlefs fome expedient be devifed to accommo-
date this error; and if the rhumbs be not right lines
fuch chart will then be embarraffed with more diffi-
culties in pra&ice than Mr. Wright’s.

• &°wh£WL?!e.’ i( feems as if ,he editor> cohftdins

!" J s abilities, hath, without examination, pub-
llflled thls propofition (found amongft many other loofe
papers, none of winch were, perhaps, ever intended for
public inflection, as himfelf faies in his apology) iuft
as he found it; and that the Reviewers in good opi-
nion of both, and out of tendernefs to the widow and
family, the book being published for their benefit, have
not fo critically examined and compared it with what
lias been already done. — But, notwithftanding what is
ipoken in favour thereof, I fufpedt it will have little
weight with the mariners, who very well know the

value

C 80 ]

value of the Mercator’s chart (as they call it) nor are
they ever very eafily induced to adopt new notions
or inventions, and thole contrary to what they are
familiarized unto by conflant practice.

The Critical Reviewers do indeed hint as if this pa-
per had been heretofore communicated by Mr. Well
to the Royal Society, and that in the following terms:
— cc Mr. Well lays down the following very ingeni-
“ ous proportion, which, if we do not greatly
“ millake, we havefeen, with little variation, in the
“ Philofophical Tranla&ions, communicated pof-
“ fibly by the fame hand”. — In this, I believe, they
are miftaken, for I cannot find any thing like it in
the tranfadlions fince the date 1746, the year in which
it is faid to be wrote.

I am duly fenfible of the frequent monitions, and
fincere defire of the Royal Society, that its mem-
bers may avoid all poffible occafions of controverfy ;
and whether this account has not a tendency there-
unto, if it fliould, in other refpe&s, be thought
worthy of a place in the public Tranfa&ions, is fub-
mitted, with all due refpedl, to the determination of
the Committee of papers.

I have the honour to be, Sir,

With the greatefl efteem,

The Royal Society’s,

Gainsford - Street, and alfo
Southwark; Jan.

26th, 1763. your mofl obedient, and

faithful humble fervant,

William Mountaine.

XXI. An

— I

[ 8i ]

XXI. An Account of a Species of Ophris ,
fuppofed to be the Plants which is mentioned
by GronoviuszVz the Flora Virginica,^. 185,
under the Name of Ophris Scapo nudo foliis
radicahbus ovato-oblongis , dimidii Scapi lon-
gitudine: By George Dionyfius Ehret,

F. R. S.

Read Apnl 14, H E root of this plant, from

2' which many flefhy fibres branch,

is compofed of the foot fialks of the leaves, which
envelope each other in fuch a manner, that they form
a kind of bulbous root. From the faid bulb proceed
two oval- fhaped, nervous, fmooth leaves, having
membraneous convolute petioli or footftalks. Thefe
encompafs a triquetrous fcapus, or a fingle ftalk arif-
ing from the centre of this root, which produces
many flowers of a Angular conflrucfiion. Thefe
flowers are fupported by fmall pedunculi, or flower
fialks, of a bloody-red colour, which fwell into feed-
veilels, having at their bale an acute denticle.

^ This very Angular plant blew (for the firft time in
England) in the Year 1758, in the curious exotic
garden ot Mr. Peter Collinfon ; who received it from
Mr. Bertram of Philadelphia.

Mr. Clayton has deferibed a plant, in the Flora
Virginica page 185, under the name of <c Bifolium
Scapo e medio duorurn foliorum nudo, aphyllo, ad
exortum tenui, paulatim verfus apicem accrefcente, lex
V ol. LIU. J\ vel

C 82 ]

vel feptem capfulas fuftinente : radice fibrofa carnofa
viridi, foliis obvoluta, humi jacente; fibras paacas
emittente, cui radix anni luperioris contigua et integu-
mcntis marcidis evoluta pellucida adhaeret.”

This defcription feemingly correlponds with the
prefen t plant j but yet Mr. Clayton’s character of
the feveral parts of the flower is very different
from thofe, which I have obferved, and reprefen ted
in this drawing ; and although it may be thought to
come near to an epidendrum, yet it is neither an
epidendrum nor a bifolium, as the following defcrip-
tion of the characters will fufficiently indicate.

This plant, however, fhould be ranged amongffc
the fi'rft order of Dr. Linnasus’s clafs of guinandria
diandria, which confifts of feveral genera.

The defcription of the characters.

Tab. III. Fig. a, reprefents a front and fide view
of the flower, which has but one broad, flat, oval-
fhaped petal, or leaf, of a pale red colour, marked
with three veins. It has alfo a fmall point or denti-
cle projecting at the top of the limbus or margin.
Fig. b. At the bafe of this broad petal is fituated an
irregular unequal-divided triphyllus periantheum, con-
fifting of three narrow feparate leaves, of a pale-green
colour, and almoft of equal length with the petalum.
Two of thefe leaves are ereCt, and both gibbous at
their infertion as in Fig. c , and placed at the back of
this petal. It would feem as if thefe two leaves were
fupporters of the corolla: the third leaf is fixed at
the oppofite fide fronting the flower, opening and
bending downwards, fee Fig. d.

In

r % a

In the centre of this flower is fituated a leafy flyle*,
of a convex figure, projecting outwards, and facing
the corolla as in Fig. e , the top of which is a mem-
branous foliacious fligma, which refleds downwards
to proted the male fperm, and forms (as it were) a
caliptra or lap, under which are inferred two yellow
globular apices (containing the farina) without fila-
ments, which are the flamina of the flower.

Fig. f. explains a front and fide view of the flyle
by itfelf, (the petal and calyx are feparated from thefe
figures:) the bafe of it is a gibbous flefhy fubflance,
which fhews apparently two bodies of nedaria, of a
crimfon-red colour, fee Fig. g.

The magnified figure above Fig. hy reprefents the
infide, and defcribes the parts more diftindly j whofe
leafy fligma is laid open, to expofe to view the in-
fertion of the two apices : beneath thefe globules ap-
pears a crofs line, on which is placed, on each fide,
a imall pointed leaf. From the corners of this flefliy
nedarium thus magnified, come forth two threads,
Fig. /, hanging downwards: they are of equal length
with the peduncle, of a fkinny fubflance, and of a
bloody-red colour.

The germen, which is twifted like a fcrew, repre-
fents the footftalk, which fupports the flower. Fig. k :
this fwelis into an oblong, oval flriated unilocular
feedveflel, Fig. /, which contains an innumerable
number of dufl-like feeds, as the open longitudinal
fedion Fig. ;;;, reprefents.

N 2

XXI L New

[ &4 ]

XXII. New Experiments in EleElricity : In
a Letter from Mr . Ebenezer Kinnerfley,
to Benjamin Franklin, LL . D. F. R. S.

Read Nov. 18, 1762, March 24, and April 14, 1763.

SIR, Philadelphia, Mar. 12, 1761.

HAVING lately made the following experi-
ments, I very chearfully communicate them,
in hopes of giving you fome degree of pleafure, and
exciting you to further explore your favourite, but
not quite exhaufted, fubjedt, Electricity.

EXP. I.

I placed myfelf on an eledtric {land, and, being
well eledtrifed, threw my hat to an uneledtrifed per-
fon, at a confiderable difiance, on another Hand, and
found, that the hat carried fome of the electrici-
ty with it y for, upon going immediately to the per-
fon, who received it, and holding a flaxen thread near
him, I perceived he was eledtrifed fufficiently to at-
tradt the thread.

EXP. II.

I then fufpended, by filk, a broad plate of metal,
and eledtrifed fome boiling water under it, at about
four feet diftance, expedting that the vapour, which
afcended plentifully to the plate, would, upon the
principle of the foregoing experiment, carry up fome
of the eledtricity with it 3 but was at length fully con-
vinced, by feveral repeated trials, that it left all its

fliare

[ 85 ]

fhare thereof behind. This I know not how to ac-
count for ; but does it not feem to corroborate your
hypothecs, that the vapors, of which the clouds are
formed, leave their fhare of electricity behind in the
common flock, and afcend in a negative ftate ?

EXP. III.

I put boiling water into a coated Florence flafk,
and found that the heat fo enlarged the pores of the
glafs, that it could not be charged. The electricity
paffed thro’ as readily, to all appearance, as thro*
metal ; the charge of a three-pint bottle went freely
thro’ without injuring the flafk in the leaft. When
it became almofl: cold, I could charge it as ufual.
Would not this experiment convince the Abbe Nollet
of his egregious miftake ? For, while the electricity
went fairly thro’ the glafs, as he contends it always
docs, the glafs could not be charged at all.

EXP. IV.

I took a flender piece of cedar, about eighteen
inches long, fixed a brafs cap in the middle, thruft
a pin, horizontally and at right angles, thro’ each
end, (the points in contrary directions) and hung it,
nicely balanced like the needle of a compafs, on a
pin, about fix inches long, fixed in the center of an
eleCtric Hand. Then eleCtrifing the hand, I had the
pleafure of feeing what I expected 5 the wooden nee-
dle turned round, carrying the pins with their heads
foremoTt. I then eleCtrifed the hand negatively, ex-
pecting the needle to turn the contrary way; but
was extremely difappointed, for it went ftill the fame
way as before.

5

When

[ 86 ]

When the Hand was eledtrifed pofitively, I fup-
pole, that the natural quantity of eledtricity in the
air being increafed on one fide, by what iffiued from
the points, the needle was attradled by the leffer
quantity on the other fide. When eledtrifed nega-
tively, I fuppofe, that the natural quantity of eledtri-
city in the air was diminifhed near the points ; in
confequence whereof, the equilibrium being deftroyed,
the needle was attradted by the greater quantity on
the oppofite fide.

The dodtrine of repulfion in eledtrifed bodies, I
begin to be fomewhat doubtful of. I think all the
phenomena, on which it is founded, may be well
enough accounted for without it. Will not cork
balls, eledtrifed negatively, feparate as far as when
eledtrifed pofitively ? And may not their feparation,
in both cafes, be accounted for upon the fame prin-
ciple ; namely, the mutual attradtion of the natural
quantity in the air, and that which is denfer, or rarer
in the cork ball ? It being one of the effablifhed laws
of this fluid, that quantities of different denfities fhall
mutually attradt each other, in order to reflore the
equilibrium.

I can fee no reafon to conclude, that the air has not
its fhare of the common flock of eledtricity as well
as glafs, and, perhaps, all other eledtrics per fe. For
tho’ the air will admit bodies to be eledtrifed in it
either pofitively or negatively, and will not readily
carry off the redundancy in the one cafe, or fupply
the deficiency in the other j

EXP.

[ 8y ]

EXP. V.

Yet let a perfon in the negative date, out of doors
in the dark, when the air is dry, hold, with his arm
extended, a long fharp needle, pointing upwards;
and he will foon be convinced, that elediricity may be
drawn out of the air; not very plentifully, for, being
a bad conductor, it feems loth to part with it ; but
yet fome will evidently be collected. The air near
the perfon’s body, having lefs than its natural quan-
tity, will have none to fpare ; but, his arm being ex-
tended as above, fome will be collected from the re-
moter air, and will appear luminous as it converges
to the point of the needle.

Let a perfon eledtriled negatively prefent the point
of a needle, horizontally, to a cork ball fufpended
by filk, and the ball will be attradfed towards the
point, till it has parted with fo much of its natural
quantity of eledtricity as to be in the negative ftate,
in the lame degree with the perfon who holds the
needle : then it will recede from the point ; ' being,
as I luppofe, attradted the contrary way by the elec-
tricity of greater denfity in the air behind it. But,
as this opinion feems to deviate from eledtrical ortho-
doxy, I fhould be glad to fee thefe phenomena bet-
ter accounted for by your fuperior and more pene-
trating genius.

Whether the eledtricity in the air, in clear dry
weather, be of the fame denfity at the height of two
or three hundred yards, as near the furface of the
earth, may be latisfadlorily determined by your old
experiment of the kite.

E X P.

[ 88 ]

EXP. VI.

The twine fhould have, through-out, a very fmall
wire in it; and the ends of the wire, where the fe-
veral lengths are united, ought to be tied down with
a waxed thread to prevent their acting in the manner
of points. I have tried the experiment twice, when
the air was as dry as we ever have it, and fo clear
that not a cloud could be feen ; and found the twine
each time, in a fmall degree eledtrifed pofitively.
The kite had three metalline points fixed to it 3 one
on the top, and one on each fide. That the twine
was eledtrifed, appeared by the feparating of two
fmall cork balls fufpended on the twine by fine flaxen
threads, juft above where the fllk was tied to it, and
fheltered from the wind. That the twine was elec-
trifed pofitively, was proved by applying to it the
wire of a charged bottle; which caufed the balls to
feparate further, without firft coming nearer together.
This experiment fhewed, that the electricity in the air,
at thofe times, was denfer above than below. But
that cannot be always the cafe ; for you know we
have frequently found the thunder clouds in the ne-
gative hate, attracting electricity from the earth.
Which hate it is probable they are always in when
firfl; formed, and till they have received a fufficient
fupply. How they come afterwards, towards the
latter end of the guft, to be in the pofitive date,
which is fometimes the cafe, is a fubjedt for further
enquiry.

After the above experiments with the wooden
needle, I formed a crofs of two pieces of wood, of

equal

• (

C 89 ]

equal length, interfering each other at right angles
in the middle; hung it, horizontally, on a central
pin, and fet a light horfe, with his rider, upon each
extremity ; whereupon, the whole being nicely bal-
anced, and each courfer urged on by an ele&rifed
point, inftead of a pair of fpurs, I was entertained
with an electrical horfe-race.

I have contrived an eleCtrical air thermometer, and
made feveral experiments with it, that have afforded
me much fatisfaCtion and pleafure. • It is extremely
fenfible of any alteration in the date of the included
air, and fully determines that controverted point,
whether there be any heat in the eledtric fire. By the
Plate [Tab. IV.] and the following defcription, you
will readily apprehend the conftrudtion of it.

A. B. is a glafs tube about eleven inches long, and
one inch diameter in the bore. It has a brafs feril ce-
mented on each end, with a top and bottom part, C
and D to be ferewed on, air-tight, and taken off
at pleafure. In the center of the bottom part D, is
a male ferew, which goes into a brafs nut in the ma-
hogany pedeftal E. The wires F and G are for the
eleCtric fire to pafs through, darting from one to the
other. The wire G extends through the pedeflal to
H ; and may be raifed or lowered by means of a male
ferew on it. The wire F may be taken out, and the
hook I be ferewed into the place of it. K is a glafs
tube with a fmall bore, open at both ends, cemented
in the brafs tube L, which ferews into the top part
C. The lower end of the tube K is immerfed in wa-
ter, coloured with cocheneal, at the bottom of the
tube A B. (I ufed at firft coloured fpirits of wine ;
but, in one of the experiments I made, it took fire.)
Vol. LIII. O Oa

[ 90 ]

On the top of the tube K is cemented, for ornament,
a brafs feril, with a head fcrewed on it, which has a
fmall air hole thro’ its fide at a. The wire b is a frnall
round fpring, that embraces the tube K fo as to flay
wherever it is placed. The weight M is to keep
ftrait whatever may be fufpended in the tube A B.
on the hook I. Air muft be blown thro’ the tube
K into the tube A B, ’till enough is intruded to raife,
by its elaftic force, a column of the coloured water,
in the tube K up to c, or thereabouts ; and then,
the gage wire b being flipt down to the top of the
column, the thermometer is ready for ufe.

EXP. VII.

I fet the thermometer on an ele&iic ftand, with
the chain N fixed to the prime conductor, and kept
it well eleCtrifed a confiderable time ; but this produced
no fenfible efteCt. Which fliews, that the electric
fire, when in a ftate of reft, has no more heat than
the air and other matter wherein it refides.

EXP. VIII.

When the wires F and G are in contact, a large
charge of ele&ricity fent thro’ them, even that of
my cafe of five and thirty bottles, containing above
thirty fquare feet of coated glafs, will produce no
rarefaction of the air included in the tube A B. Which
fhews, that the wires are not heated by the fires pafling
thro’ them.

EXP. IX.

When the wires are about two inches apart, the
charge of a three pint bottle, darting from one to

the

[ 9i ]

the other, rarefies the air very evidently. Which
fhews, I think, that the eledric fire mud produce
heat in itfelf, as well as in the air, by its rapid mo-
tion.

The charge of one of my glafs jars, which will
contain about five gallons and a half, wine meafure,
darting from wire to wire, will, by the diflurbance
it gives the air in the explofion repelling it in all di-
rections, raife the column in the tube K up to d , or
thereabouts ; and the charge of the above-mentioned
cafe of bottles will raife it to the top of the tube.
Upon the air’s coalefcing, the column, by its gravity,
inflantly fubfides till it is in equilibrio with the rarefied
air ; it then gradually defcends, as the air cools, and
fettles where it flood before. By carefully obferving
at what height above the gage-wire b the defcending
column firfl flops, the degree of rarefadion is difco-
vered ; which, in great explofions, is very confiderable.

EXP. X.

I hung in the thermometer, upon the hook I,
fucceflively, a flrip of wet writing paper, a wet flax-
en and woolen thread, a blade of green grafs, a fila-^
ment of green wood, a fine filver thread, a very fmall
brafs wire, and a flrip of gilt paper; and found that
the charge of the glafs jar, pafling thro’ each of thefe,
efpecially the lafl, produced heat enough to rarify the
air very perceptibly. The charge of the cafe of bot-
tles fent thro’ the brafs wire confumed great part of
it into fmoke. The thermometer appeared quite
opaque with it.

O 2

EXP.

[ 92 J

EXP. XI.

I then fufpended, out of the thermometer, apiece
of brafs wire, not quite fo fmall as the former, about
twenty four inches long, with a pound weight at the
lower end ; and, by fending the charge of the cafe
of bottles thro’ it, difcovered a new method of wire-
drawing. The wire was red hot, the whole length
well anealed, and above an inch longer than before.
A fecond charge melted it ; it parted near the middle,
and meafured, when the ends were put together, four
inches longer than at firft. This experiment I re-
member you propofed to me, as worth trying, before
you left Philadelphia; in order to find, whether the
ele&ricity, in palling thro’ the wire, would fo relax
the cohefion of its conftituent particles, as that the
weight might produce a feparation; but neither of
us had the leaft fufpicion, that any heat would be
produced.

EXP. XII.

That I might have no doubt of the wire’s being hot
as well as red, I repeated the experiment on another
piece of the fame wire, encompaffed with a goofe-
quill filled with loofe grains of gun-powder ; which
took fire as readily, as if it had been touched with a
read hot poker. Alfo tinder, tied to another piece
of the wire, kindled by it. I tried a wire about
twice as big, but could produce no fuch effe&s with
that.

Hence it appears, that the eledric fire, tho’ it has
no fenfible heat when in a date of reft, will, by its

violent

[ 93 ]

violent motion, find the refinance it meets with, pro-
duce heat in other bodies, when paffing thro’ them,
provided they be fmall enough. A large quantity
will pafs thro’ a large wire without producing any
fenfible heat ; when the fame quantity paffing thro’
a very fmall one, being there confined to a narrower
paffage, the particles crowding clofer together, and
meeting with greater refiftance, will make it red hot,
and even melt it.

Hence lightning does not melt metal by a cold fu-
fion, as we formerly fuppofed. But when it paffies
thro’ the blade of a fword, if the quantity be not ve-
ry great, it may heat the point fo as to melt it, while
the broad eft and thickeft part may not be fenfibly
warmer than before.

And when trees or houfes are fet on fire by the
dreadful quantity, which a cloud, or the earth fome-
times difcharges, muft not the heat, by which the
wood is firft kindled, be generated by the lightning’s
violent motion thro’ the refilling combuftible mat-
ter ?

If lightning, by its rapid motion, produces heat
in itfelf as well as in other bodies, (and that it does,
I think, is evident from fome of the foregoing experi-
ments made with the thermometer) then its fometimes
fingeing the hair of animals killed by it may eafily be
accounted for. And the reafon of its not always do-
ing fo may, perhaps, be this : the quantity, tho’ fuf-
ficient to kill a large animal, may, fometimes, not
be great enough, or not have met with refiftance
enough, to become by its motion burning hot.

We find, that dwelling houfes, ftruck with lightn-
ing, are feldom fet on fire by it ; but when it paffies

thro3

4 ;

[ 94 ]

thro’ barns with hay or ftraw in them, or ftore-houfes
containing large quantities of hemp, or fuch like mat-
ter, they feldom, if ever, efcape a conflagration.
Which may, perhaps, be owing to fuch combuftibles
being apt to kindle with lefs degree of heat than is
neceffary to kindle wood.

We had four houfes in this city, and a veflfel at one
of the wharfs, ftruck, and damaged, by lightning
laft fummer. One of the houfes was ftruck twice
in the fame ftorm. But I have the pleafure to inform
you, that your method of preventing fuch terrible
difafters, has, by a facft, which had like to have ef-
caped our knowledge, given a very convincing proof
of its great utility, and is now in higher repute with
us than ever.

Hearing, a few days ago, that Mr. William Well,
merchant in this city, fufpedled, that the lightning, in
one of the thunder-ftorms laft fummer, had paffed
through the iron conductor, which he had provided
for the fecurity of his houfe, I waited on him, to en-
quire what ground he might have for fuch fufpicion.
Mr. Weft informed me, that his family and neigh-
bours were all ftunned writh a very terrible explolion,
and that the flafh and crack were feen and heard at
the fame inftant. Whence he concluded, that the
lightning muft have been very near ; and, as no houfe
in the neighbourhood had fuffered by it, that it muft
have paffed through his condu&or. Mr. White, his
clerk, told me, that he was fitting at the time by a
window, about two feet from the conductor, leaning
againft the brick wall, with which it was in contadf;
and that he felt a fmart fenfation, like an eledxic fhock,
m that part of his body, which touched the wall.

Mr.

C 95 ]

Mr. Weft further informed me, that a perfon of un-
doubted veracity allured him, that, being in the door
of an oppofite houfe on the other fide of Water-Street
(which you know is but narrow) he faw the lightning
diffufed over the pavement, which was then very wet
with rain, to the diftance of two or three yards from
the foot of the condu&or. And that another perfon
of very good credit told him, that he, being a few
doors off, on the other fide of the ftreet, faw the
lightning above, darting in fuch direction, that it ap-
peared to him to be directly over that pointed
rod.

Upon receiving this information, and being defirous
of further latisfadfion, there being no traces of the
lightning to be difeovered in the condu&or, as far as
we could examine it below, 1 propofed to Mr. Weft
our going to the top of the houfe to examine the
pointed rod; alluring him, that, if the lightning had
palTed thro’ it, the point muft have been melted ; and,
to our great fatisfaClion, we found it fo. This iron
rod extended in height about nine feet and a half
above a ftack of chimnies, to which it was fixed ; (but
I fuppofe, three or four feet would have been luffici-
ent). It was fomewhat more than half an inch dia-
meter, in the thickeft part, and tapering to the upper
end. The conductor, from the lower end of it to the
earth, confifted of fquare iron nail rods, not much
above a quarter of an inch thick, connected together
by interlinking joints. It extended down the cedar
roof to the eaves, and from thence down the wall of
the houfe, four ftory and a half, to the pavement in
Water-Street ; being faftened to the wall, in feveral
places, by fmall iron hooks. The lower end was

fixed.

[ 96 ]

fixed to a ring In the top of an Iron flake, that was driven
about four or five feet into the ground. The above
mentioned iron rod had a hole in the top of it, about
two inches deep, wherein was inferted a brafs wire,
about two lines thick, and, when firft put there,
about ten inches long, terminating in a very acute
point ; but now its whole length was no more than
leven inches and a half, and the top very blunt. Some
of the metal appears to be miffing; the flendereft
part of the wire being, as I fufpedt, confumed into
i'moke. But fome of it, where the wire was a little
thicker, being only melted by ffie lightning, funk
down, while in a fluid ftate, and formed a rough ir-
regular cap, lower on one fide than the other, round
the upper end of what remained, and became inti-
mately united therewith.

This was all the damage, that Mr. Weft fuftained
by a terrible ftroke of lightning. A moft convincing
proof of the great utility of this method of prevent-
ing its dreadful effects. Surely it will now be thought
as expedient to provide conductors for the lig
as for the rain.

Mr. Weft was fo good as to make me a prefent of
the melted wire ; which I keep as a great curiofity,
and long for the pleafure of (hewing it to you. In the
mean time, I beg your acceptance of the beft repre-
fentation I can give of it; which you will find by
the fide of the thermometer, drawn in its full dimen-
fions as it now appears. The dotted lines above are
intended to ffiew the form of the wire before the light-
ning melted it.

And now, Sir, I moft heartily congratulate you on
the pleafure you muft have in finding your great and

well

C 97 3

well-grounded expectations fo far fulfilled. May this
method of fecurity from the dedruftive violence of
one of the mod; awful powers of nature meet with
fuch further fuccefs, as to induce every good and grate-
ful heart to blefs God for the important difcovery.
May the benefit thereof be diffufed over the whole
globe. May it extend to the latefl pofterity of man-
kind; and make the name of Franklin, like that of
Newton, immortal..

F am. Sir, with fincere refpeCf,

your mod: obedient, and

molt humble fervant,

Ebenezer Kinnerfley.

— ■« — — —

XXIII. Observations in FleSiricity and on a
‘Thunder-Jlorm : In a Letter from Mr. Tor-
bern Bergman, to Mr. Benjamin Wilfon,
F. R. S. Acad. Reg. Upfal. Soc.

Ampliflime atque Celeberrime Domine,

Read April 14, TT ]SJ epiftolis recentifiimis, quibus me
X honoradi, experimenta domini Dela-
val circa eleClricitatem cryftalli Idandicee commemo-
ras. Pluries hascce tentamina iteravi, fed conftan-
ter eventu prorfus contrario. Scilicet in hunc finem
varia hujus cryflalli frufta frigori 12 graduum expofui,
Vol. LIII. P in

C 98 ]

in thermometro Suecano, mercurio vivo impleto,
frigus numero infra pundtum congeiationis aquae, quod
in nive colliquefcente determinatur. (Quivis gradus
eft pars centelima diftantke pundtorum congeiationis
et ebullitionis aquae). Fricui dein pod quarundam
horarum l'patium, fed nonnifi valde debilem eledtri-
citatem elicere potui. Haec itaque iterum repofui, non-
dum fatis frigefada putans, et mane fequenti, dum
interea mercurius in thermometro quofdam gradus
defcenderat, in camera non calefada tentavi, fed ad-
huc minori fucceflu. Unum igitur fruftulum calefeci
\ fperans hoc ipfo omnem vim eradicari; fed inopinato
non modo non deflrudam inveni difpofitionem elec-
tricam, fed valde audam. Idem mox repetii cum
reliquis omnibus, codemque Temper effedu prima ten-
tamina fada funt cum cryftallis objeda duplicantibus,
quae in Suecia erant colledae : fufpicio igitur mihi inci-
dit has inter et revera Iflandicas effentialem effe diffe-
rentiam ; itaque comparavi in Iilandia natas, fed eadem
monftrarunt phaenomena *.

Ex hifce tentaminibus cum domini Delaval colla-
tis fequi videtur, diverfas hujus cryftalli dari fpecies,
quae eo diligentius examinand#, cum hucufque mine-

ralogi non nifi unicam diftinguant.

• •

* Mr. Delaval had already obferved, in the letter here referred to
by Mr. Bergman, that the property, in Iceland Cryftal, of lofing
its ele&ricity by a moderate heat, was not common to all kinds
of it : and mentions in particular a piece of cryftal, one part
whereof, when heated gently, becomes non eledtric ; while the
other part, with the fame heat, (or even with a much greater one)
remains perfedlly an eledhic. Vide Vol. L1I. Part i. p. 355* ^
have feen the experiments leveral times which Mr. Delaval men-
tions, and they always fucceeded as he has related them.

B. Wiifon.

Memo-

[ 99 ]

Memorabilem fulminis idtum arcem regiam Upfa-
lenfem d. 24 Aug. 1760 ferientem, paucis defcribere
forte non diiplicebit. Hoc die coelum, praecedenti-
bus ferenum, nubibus atris obducebatur, e quibus
pluvia per nodtem decidebat. Poft mediam vero
nodtem tonitrua audiebantur, quae, duabus interjec-
tis horis, horrendis fulgurationibus et fragoribus ar-
cem adgrediebantur. Haec arx infignem et natura et
arte habet altitudinem, tedtumque e laminis ferreis.
Aire auftralis paries tranfverfus occidentalis et ipfius
arcis murus primarius occidentalis, in contignatione
praecipue infima, injuriis violentiftimi hujus meteori
perturbabantur, unone, an pluribus fulminibus fefe
brevi infequentibus, non dicam. Mums fex diverfis
locis externe laefus eft, et multis variifque intra arcem
cameris, atriis veftibulifque percurfis, per murum pri-
marium orientalem, urbem fpedtantem, fulmen exi-
vifte videtur, nam foramen magnum fecerat ibidem.
Jpfum ordinem hujus idtus nemo novit : effedtus igi-
tur praecipuos tantummodo colligam.

i° Ipfe murus foraminibus, rimis, calceque lapides
connedlente fradta vel diflipata, violatus eft. Lapides ,
magni caefi, et adhuc liberi jacentes, diffradti funt.

2° Ligna funt tofta, imprimis in confinio ferri,
fepe diffradla, ftepe quoque iilaefa haec fortis eledlricitas
tranlivit.

30 Sedecim quadrata vitrea unius feneftrae, abfque
ullo remanente veftigio vel fruftulo in confinio, eva-
nefcebant. Speculi magni anguli duo oppofiti lique-
fadti erant,foliumque ibidem turbatum, vitrum praeter-
ea illaefum, fed macula horizontalisduos pollices longa
prope jundturam vitrorum in fuperiore fpeculi parte,
omni folio carebat.

P 2 40 Clavi

[ 100 ]

4° Clavi liquefadti. Pidturarum et fpeculorum
margines inaurati quafi tofti. In pavimento inaura-
turas fruftula confpiciebantur. Cymbalum claufum,
quod fub una e pidturis laefis conftiterat, nullum laefi-
onis lignum externe monftrabat, nihilominus 1 5 fides
e calybe abfciflas erant, et circa terminos candefadtas
fuilfe ligna aderant ; in fundo chorda, tres lineas lon-
ga, inveniebatur, quam ignitam fuilfe lignum tan-
gens toftum indicabat.

50 Parietes imprimis laeli, adeoque diredtio idtus
plerumque obliqua fuit, fluxui quoque aeris obtempe-
rare vifa.

6° Odor graviffimus alliaceo-fulphureus omnia im-
plebat loca, fequentique die fupelledtilia et pavimenta
floribus fulphuris adlperfa inveniehantur.

70 Nullum animal laefum.

iEftate 1759 fulmen per caminum in parvam hujus
urbis domum intrans per quadratum vitreum feneftras
perforatum mox horrendo fragore exivit. Sed pras-
cipue memoratu dignum vires nonnullos, ab hoc loco
ultra 250 pedes diftantes, in terram decidilTe, gravem-
que concuffionem eledtricam fuiffe expertos, dum inter-
ea hifee circumftantes nullo modo adficiebantur. Hoc
eodem redit, ac dum interdum finguli in circulo ex-
plofionis conftituti valde insqualem concuffionis gra-
dual fentiunt. Permaneo

Celeberrimi nominis tui

Dabam Upfalse,
<J. xx Apr. 1762.

Cultor obfervantiffimus,

Torbern Bergman.

XXIV. Remarks

C *01 ]

XXIV. Remarks on Swallows on the Rhine:
In a Letter from Mr . Achard, in Privy-
Garden, to Mr . Peter Collinfon, F. R. S.

dam : a little below Bafil the fouth bank of the ri-
ver was very high and tteep, of a fandy foil, fixty or
eighty feet above the water.

I was furprized at feeing near the top of the clift
fome boys tied with ropes hanging down doing fome-
thing : the Angularity of thefe adventrous boys, and
the bufinefs they fo daringly attempted, made us ftop
our navigation to inquire into the meaning of it. The
watermen told us they were fearching the holes in
the clift for fwallows, or martins, which took refuge
in them, and lodged there all the winter, until warm
weather, and then they came abroad again.

The boys, being let down by their comrades to the
holes, put in a long rammer with a fcrew at the
end, as is ufed to unload guns, and, twitting it about,
drew out the birds. For a trifle I procured fome of
them. When I firft had them, they feemed ttiff and
lifelefs. I put one in my bofom, between my Ikin
and fhirt, and laid another on a board, the fun Alin-
ing full and warm upon it. One or two of my
companions did the like.

That in my bofom revived in about Jj. of an hour;
feeling it move, I took it out to look at it, and faw

SIR,

Read t

Sept. 7, 1762.

N the latter end of March I took my
paffaee down the Rhine to Rotter-

1

it

[ 102 ]

it flretch itfclf on my hand, but perceiving it not
fufficiently come to itfelf, I put it in again : in about
another quarter, feeling it flutter pretty brifkly, I took
it out and admired it. Being now perfe&ly recover-
ed, before I was aware, it took its flight, the cover-
ing of the boat prevented me from feeing where it
went : the bird on the board, though expofed to a full
fun, yet, I prefume from a chillynefs in the air, did not
revive to be able to fly.

Remarks by Mr. Collinfon.

What I colled from this gentleman’s relation is,'
that it was the practice of the boys, annually to take
thefe birds, by their apparatus and ready method of
doing it ; and the frequency of k was no remarkable
thing to the watermen. Next it confirmed my former
fentiments, that fome of this Swallow-tribe go away,
and fome flay behind in thefe dormitories all the win-
ter. If my friend had been particular as to the fpe-
cies, it would have fettled that pqint.

XXV. The

[ I03 J

XXV. "The Properties of the mechanic Pow-
ers demonjt rated , with fame Obfervations
on the Methods that have been commonly
ufed for that Purpofe : in a Letter from
Hugh Hamilton, D. D . F.R.S . and
Fellow of Trinity College, Dublin, to
Matthew Raper, Efq\ F. R. S.

SIR, Trinity College, Dublin, 13 July, 1762.

Read April 2i, X" Have here ventured to fend you fome
763^* A remarks on the methods that have been
commonly ufed in treating of thofe engines that are
called the mechanic powers : and alfo an account of
the principles on which, I think, we may bed; explain
their nature and manner of adting.

The many ufeful inftruments that have been fo
ingenioufly invented, and fo fuccesfully executed,
and the great perfection to which the mechanic arts
are now arrived, would naturally incline one to think
that the true principles on which the efficacy and ope-
rations of the feveral machines depend, mud long
fince have been accurately explained. But this is by
no means a neceffiary inference: for, however men
may differ in their opinions about the true method of
accounting for the effeCts of the feveral machines, yet
the pradtical principles of mechanics are fo perfectly
known by experience and obfervation, that the artift
is thereby enabled tocontrive and adjuftthe movements

of

[ I04 ]

of his engines with as much certainty and fuccefs as
he could do, was he thoroughly acquainted with
the laws of motion, from which thefe principles may
be ultimately derived. However, tho’ an enquiry into
the true method of deducing the practical principles
of mechanics from the laws of motion, fhould not
perhaps contribute much to promote the progrefs of
the mechanic arts, yet it is an enquiry in itfelf ufeful,
and in lome meafure neceffary : for, fince late authors
have ufed very different methods of treating this fub-
jedt, it may befuppofed that no one method has been
looked upon as fatisfadtory and unexceptionable. I
fhould therefore wifh to contribute towards having this
fubjedt treated with more accuracy than has been hi-
therto done.

The moft general and remarkable theorem in ma-
chanics certainly is this, “ That when two weights, by
“ means of a machine counterpoife each other, and
“ are then made to move together, their quantities of
u motion will be equal’*. Now an aequilibrium al-
ways accompanying this equality of motions, bears
fuch a refemblance to the cafe wherein two moving
bodies flop each other, when they meet together with
equal quantities of motion j that Dodtor Wallis, and
after him mod of the late writers, have thought the
caufe of an ^equilibrium in the feveral machines, might
be immediately adigned : by faying, That, fince one
body cannot produce in another a quantity of motion
equalto its own, without lofing its own at the fame time;
two heavy bodies, counteracting each other by means
of a machine mud continue at red, when they are fo
circumdanced that one cannot defcend, without cauf-
ing the other to afcend,at the fame time; and with the

fame

t 105 ]

fame quantity of motion j and therefore two heavy
bodies in fuch cafes mull; always counterbalance each
other. Now, this argument would be a juft one, if
it could properly be faid, that the motion of the af-
cending body was produced by that of the defending
one ; but, fince the bodies are fo connected that one
cannot poffibly begin to move before the other, I
apprehend, that, if the bodies are fuppofed to move, it
cannot be faid that the motion of one is produced by
that of the other: fince whatever force is fuppofed to
move one muft be the immediate caufe of motion in
the other alfoj that is, both their motions muft be
fimultaneous effects of the fame caufe, juft as if the two
bodies were really but one. And therefore if I was
to fuppofe, in this cafe, that the fuperior weight of
the heavier body (which may be in itfelf much more
than able to fuftain the lighter) fhould overcome the
weight of the lighter and produce equal motions in
both bodies ; I do not think that from thence I could
be reduced to the abfurdity of fuppofing, that one
body, by its motion, might produce in another, a mo-
tion equal to its own, and yet not lofe its own at the
fame time. But thofe who argue from the equality
of motions on this occafion fay further, that, fince
the two bodies muft have equal motions when they do
move, they muft have equal endeavours to move even
whilft they are at reft, and therefore thefe endeavours
to move, being equal and contrary, muft deftroy each
other, and the bodies muft continue at reft, and confe-
quently ballance each other. In anfwer to this I muft
obferve, that the abfolute force with which a heavy bo-
dy endeavours to defcend from a ftate of reft can only
be proportionable to its weight ; and therefore I think
Vol. LIII, CL k

[ 106 ]

it is neceffary that fome caufe fhould be affigned why
(for inhance) the endeavour of one pound to defcend
fhall be equal to that of four pounds ; and efpecially
as the fulcrum on which both weights a requires no
greater force to fupport it than that of five pounds.

From thefe considerations I infer, that the reafon
why very unequal weights may ballance each other,
fhould be afligned not from their having equal mo-
menta when made to move together, but by proving
a priori without considering their motions, that either
the rea&ion of the fixed parts of the machine, or fome
other caufe, fo far takes off from the weight of the
heavier body as to leave it only juft able to fupport the
lighter. However, as this equality of momenta which
always accompanies an c equilibrium , affords a very ele-
gant theorem, it ought to be taken notice of in every
treatife of mechanics, and may ferve as an index of
an c •equilibrium . But I would not have it applied to
a purpofe for which it is unfit; as it has been in ano-
ther inftance by Do&or Keil, who from thence gives
the reafon why water hands at the fame heighth in a
narrow tube and a wide veffel with which it commu-
nicates. And an argument of the fame kind is applied
hill more improperly by Dr. Rutherforth and otherSj
to fhew why a drop of water included in a fmall
conical tube will move towards the narrower end ;
and yet the true ways of accounting for both thefe
phenomena are extremely obvious and eafy.

The fimple mechanic powers are ufually reckoned
fix, the lever, axle and wheel, pully, wedge, inclin-
ed plane, and fcrew. The only method I have met
with of explaining the nature of thefe machines on
one principle, is that which I juh now examined; and,
as that appears to me unfatisfa&ory, I fhall confider

[ io7 ]

the nature of each machine feparately in the order I
have fet them down.

The lever is faid to be a right line, inflexible and void
of weight. Its fundamental property is this; when any
two forces adbagainft each other on the arms of a level,
they will continue in asquilibrio, if their quantities are
inverfely as the diftances between the points to which
they are applied and the point round which the level
turns, which point is called the fulcrum or prop.

Several methods havebeen ufed,by different authors,
to prove, that this property muft neceflarily belong to
the lever. We find, in the works of Archimedes, a
proof brought for this purpofe, which has fince been
made ufe of by feveral writers of mechanics ; who, I
find, have fomewhats altered the form of his aigu-
ment, the fubftance of which is generally exprelfed
as follows. — “ When a cylinder of any uniform
£{ matter is fupported at its middle point, it will con-

« tinue at reft; for all the parts on one fide muft ba-

££ lance thofe on the other, being exadly equal to
££ them both in weight and fituation, fo that the
£C whole weight of this cylinder may be looked up-
£{ on as adding on the middle point on which it is fuP"
£t ported.” From hence it is inferred, that the weight
of fuch a cylinder will add upon whatever fuppoits it,
in the fame manner as it would do if it was all con-
tracted into the middle point of its axis. If theie oie
we fuppofe the cylinder to be diftinguifhed into two
unequal cylinders or fegments, the diftances between
the middle points of thofe fegments and the middle ot
the whole cylinder will be inverfely as the lengt s o
the fegments; that is, inverfely as their weights , but,
as it was faid above, the weight of each cylinder
ads in the fame manner as it would do if contrat e

[ 108 ]

contracted into the middle point of its axis j and there-
fore, if the weights of thefe cylinders be contracted
into thefe points, they will continue to fupport each
as before. And thence it is concluded, that any two
weights, aCting againft each other on a line fuftained
at a fixed point, will counterpoife one another, when
they are inverfely as the diftances of the points on
which they aCt, from the point on which the line
reds. To this argument there feems to be a manifeft:
objection \ for, when the whole cylinder is diftinguifhed
into two fegments, part of the weight of the greater
fegment aCts on the fame fide of the fulcrum with the
leffer fegment j and therefore when the whole weight
of the greater fegment is contracted into its middle
point on one fide of the fulcrum, and aCts all of it
againft the leffer fegment, it requires at leaft fome
proof to fhew, that this contracted weight will be
ballanced by the weight of the leffer fegment. Mr.
Hugens,inhisMifcellaneous Obfervations on Mechanics
takes notice of this objection to Archimedes’s method,
which, he fays,feveral mathematicians had endeavoured
to remove,but without fuccefs. He therefore, inftead
of this method, propofed one of his own, which de-
pends on a poftu latum that he ufes in common with
Archimedes, that I think ought not to be granted on
this occafion ; it is this : “ When equal bodies are

“ placed on the arms of a lever, the one which is
“ furtheft from the fulcrum will prevail and raife the
“ other up”. Now this is taking it for granted, in
other words, that a fmall weight placed further from
the fulcrum will fupport or raife a greater one. The
caufe and reafon of which faCt muft be derived from the
demonftration that follows, and therefore this demon-

ftration

C io9 3

fixation ought not to be founded on the fuppofed felf-
evidence of what is partly the thing to be proved.
But perhaps it may be faid, that the poftulatum may
be granted merely on this account ; the center of
gravity of the two bodies (which in this cafe is the
middle point between them) is not fuftained ; and
therefore the body which is on the fame fide of the
fulcrum with the center of gravity will defcend.

In anfwer to this I muft obferve, that this property,
which the center of gravity has of defcending, when
not pi aced diredtiy above or below the point of fufpenfion,
cannot be proved to belong to it in any cafe, nor can
we even fhew that there is only one center of gravity
between two bodies joined by a right line, until it is
proved in general that the center of gravity of any two
bodies is a point fo placed between them that their
diftances from it are inverfely as their weights : but
this in efFedt includes the principal property of the
lever, which therefore cannot be proved from any pre-
vious fuppofition,that the center of gravity will defcend,
even when the bodies are equal, and we know it is
the middle point between them.

I muft now proceed to confider what Sir Ifaac New-
ton hath delivered on this fubjedt in his Principia, after
the 2d cor. to the 3 d law of motion which Dr. Clarke ( in
his notes on Rohault) and all the fubfequentwriters,have
quoted as an elegant proof of the property of the lever 5
and therefore what appears to me at prefent an ob-
jection to this proof I fhall mention with great dif-
fidence, and in hopes of being fet right if I am wrong.
Sir Ifaac fuppofes two weights, as A and P. Tab. IV.
Fig. 1. to hang by threads, from the points M and N,
in a wheel or circular plane perpendicular to the ho-
rizon*

[ ”0 ]

rizon and movable about its center O ; and then pro-
pofes to determine the forces which thefe weights have
to turn the wheel round its center. In order to do this,
he fuppofes that it is indifferent from what points in
the perpendicular lines M A and N P the weights
are hung, for that they will ifill have the fame power
to turn the wheel about its center. Plis words are :
<{ Quoniam nil refert utrum filorum pundta K, L, D,
<c affixa fint vel non affixa ad planum rotas ; pon-
“ dera idem valebunt ac fi fufpenderentur a pundtis
“ K et L, vel D et L”. Now whether the points
of the threads K, L, D, are fixed or not to the plane
of the wheel is certainly of importance, as it muff
make a difference in the points of fufpenfion of the
weights, and confequently in the degrees of obliquity
with which the weights adt ; for the loweff point of
the thread that is fixed to the plane muff be confidered
as the point from which the weight hangs ; as the
parts of the thread above that point are quite ufelefs
not being at all adted upon. And from thence I fhall
endeavour to fhew that to fuppofe the weight A will
have the fame power to turn the wheel from what-
ever point in the line M A it hangs, is in effedt pre-
fuppofing what is intended to be proved. For it ap-
pears, from what he fays immediately after, that, when
the weight A hangs from the point D, if its whole
force be exprefled by the line AD, and be relolved into
two forces, D C and A C, the former only will have
any effedt in turning the wheel, as it adts perpendi-
cularly on the radius O D, while the latter is loft, its
direction being parallel to O D. But it is evident, that,
when the fame weight hangs from the point K, as it

[ 111 ]

is exerted to turn the wheel, and none of it loft by ob-
lique adion. Therefore the force which the weight
A, exerts to oppofe the weight P, and turn the wheel
when it hangs from D, is, to the force it exerts when
it hangs from K, as the line DC to A D, or as O
K, to O D, (fim. triang. ADC, DOK) that is the
force exerted by the weight A, hanging from the
points D, and K, are inverfely as the radii O D, and
O K. And therefore to fuppofe, that thefe two forces
will have the fame effect in turning the wheel and
oppofing the weight P, is the fame as fuppofing that
two forces will have equal efteds in moving the arms
of a lever (on which they ad perpendicularly) when
they are inverfely as the lengths of thofe arms. —
But this is the very conclufion Sir Ifaac draws from
his premifes, for he fays : c£ Pondera igitur A & P,
“ quae font reciproce ut radii in diredum pofiti O K,
cc O L, idem pollebunt et ftc confiftent in aequili-
“ brio, quae eft proprietas notiflima librae vedis et
“ axis in peritrochio”. This property of the lever,
which is here exprefled in general terms, includes two
cafes. For the arms of the lever may be either per-
pendicular or oblique to the diredions of the weights.
The firft of thefe cafes is the ffmpleft, and fhould
be firft demonftrated : And I do not fee how there can
be any room for applying the refolution of forces in
demonftrating this cafe, in which no part of ei-
ther weight is loft by oblique adion. But when
this cafe is proved, we have from thence, by the
refolution of forces, an eafy way of fhewing, in
the fecond cafe, when the arms of the lever are
oblique to the diredions of the weights, that the
weights will counterballance each other, when they
are reciprocally as the perpendicular diftances of their

lines

[ 112 ]

lines of direction from the center of motion. -—From
either of thefe cafes, we may deduce an obvious reafon
why the weight A, fhould have the fame power to
turn the wheel, from whatever point it hangs in the
line M A ; the truth of which, I am perfuaded, can-
not be proved independent of thofe cafes, and there-
fore think it ought not to be ufed as a poftulatum in
demonftrating the general property of the lever.

Mr.Maclaurin,in his View of Newton’s Philofophy,
after giving us the methods which Archimedes and
Newton have ufed for proving the fundamental pro-
perty of the lever, propofes one of his own, which,
he fays, appears to be the moft natural one for this
purpofe. However as to his method I fhall only ob-
ferve, that from equal bodies fuftaining each other at
equal diftances from the fulcrum, he (hews us how
to infer that a body of one pound (for inftance) will
fuftain another of two pounds at half its diftancefrcm
the fulcrum, and. from thence that it will fuftain one
of three pounds at a third of its diftance from the
fulcrum : and thus he goes on deducing, by a kind
of induction, what the proportion is in general be-
tween two bodies that fuftain each other on the arms
of a lever. But this argument (which I do not think
by any means fatisfaCtory) he obferves cannot be
applied when the arms of the lever are incom-
menfurable.

Thefe are the methods of demonftrating the fun-
damental property of the lever, which are moft worth
taking notice of; and, fince they feem liable to ob-
jections, and the other methods I have met with are
ftill more exceptionable, I fhall propofe a new proof
of this property of the lever, which appears to me

a very

[ "3 ]

a very Ample one, and depends on a poftulatum that,

I believe, will be readily granted.

If a force be uniformly diffufed over a right line,
that is, if an equal part of the force ads upon every
point of the line, and if the whole force ads accord-
ing to one and the fame plane ; this force will be fuf-
tained, and the line kept in asquilibrio, by a Angle force
applied to the middle point of the line equal to
the diffufed force, and ading in a contrary direc-
tion.

In order to fhorten the following proof, I muft pre-
mise by way of Lemma, that, if a right line be
divided into two fegments, the diftances between the
middle of the whole line, and the middle points of
the fegments, will be inverfely as the fegments. This
is felf evident when the fegments are equal ; and,
when they are unequal, then, Ance half of the whole
line is equal to half of the greater and half of the leffer
fegment, it is plain that the dilfance between the mid-
dle of the whole line and the middle of one fegment
muft be equal to half of the other fegment, fo that
thefe diftances muft be to each other inverfely as the
fegments, all which appears evident from the infpec-
tion of Tab. VI. Fig. 2.

Let now the line G H, whofe middle point is D, *
be divided into the unequal fegments G L, and L H,
whofe middle points are C and F, and let two forces
or weights, A and B, which are to each other as the
fegments G L and L H, be applied to their middle
points C and F, and let them a£t perpendicularly on
the line G H. Then (by the Lemma) the weights
A and B will be to each other inverfely as C D, and
F D, (the diftances of the points C and F, to which

Vol. LIII. R they

[ ”4 ]

they are applied from the middle of the whole line)
if then a third force or weight E, equal to the fum
of the forces A and B, be applied to the point D, and
ads on the line in an oppofite direction j I fay thefe
three forces will fuftain each other, and keep the line
in aequilibrio. For let us fuppofe the force E to be
removed, and infteadof it another force, equal alfo to
the fum of A and B, to be uniformly diffufed over
the whole line G H, and to ad diredly againft the
forces A and B, then the part of this force which ads
on the fegment G L, will be equal to the force A,
and therefore will be fuftained by it (poftulatum); and
the other part, which is diffufed over the fegment LH,
will be equal to and fuftained by the force B, fo that
the forces A and B will fuftain this diffufed force
and keep the line in aequilibrio. — Let now two other
forces ad on this line in oppofite diredions, one of
them the force E ading on the point D, as it was
firft fuppofed to do, and the other an uniformly dif-
fufed force equal to E (and confequently equal to the
other diffufed force), then thefe two additional forces
will alfo ballance each other, and therefore the aequi-
librium will ft ill remain. So that the two forces A
andB, and a diffufed force ading on one fide of the
line fuftain the force E, and a diffufed force ading on
the other fide : but it is manifeft, that, in this asquili—
brium, the two diffufed forces ading on oppofite fides
are perfedly equivalent, and therefore, if they are taken
away from both fides, the aequilibrium muft ftill re-
main. Hence it appears that the three weights or forces
A, B and E, any two of which are (by the conflrudion)
to each other inverfely astheir diftances from the third,
will fuflain each other, and keep the line on which

they

[ ”5 ]

they ad in sequilibrio : which is the firft and moft

iimple cafe of the property of the lever ; for here the
directions of the weights are fuppofed to be perpen-
dicular to the line on which they ad, and it is evident
that, if one of the points C, D or F, be fixed or con-
fidered as a fulcrum, that the weights ading on the
other two points will continue to fupport each other.
I (hall not trouble you with proving the fecond cafe
of the property of the lever; it is moft eafily deduced
from the firft: for, when two weights ad on the arms
of a lever in oblique diredions, and are to each other
inverfely as the perpendicular diftances of their lines
of diredion from the center of motion, then, by the
refolution of forces, it is eafily proved, that the parts
of thofe forces which ad perpendicularly on the arms
of the lever, and which only are exerted to turn the
lever, are to each other inverfely as the lengths of
thofe arms ; and therefore by the firft cafe they muft
ballance each other.

I (hall now mention fome well known truths in
mechanics, which, I think, cannot be proved otherwife
than by deducing them from what hath been here
demonstrated.

C O R. I.

It appears from hence, that the powers with which
any two forces move or endeavour to move the arms
of a lever, are as the redangles, under lines propor-
tional to the forces, and the perpendicular diftances of
their lines of diredion from the fulcrum.-

[ n6 ]

COR. II.

When therefore two bodies adting on the arms of a
lever fuftain each other, if one of them be removed
farther from the fulcrum, it will preponderate ; but if
it be brought nearer to the fulcrum, the other weight
will prevail : becaufe the produdt to which its force is
proportional will be encreafed in the firft cafe, and.
diminished in the fecond„

COR. III.

We learn from hence, to find out the center of gra-
vity of any two bodies joined by an inflexible right
line; and to prove that its definition will agree to one
point only in the line. For if a point be taken in the
line fo that the distances of the bodies from it may
be inverfely as their weights, that point will be their
center of gravity, becaufe, when it is fuftained, the
bodies will be in aequilibrio. But if the line be fuf-
tainedatany other point, then is the fulcrum removed
farther from one body and brought nearer to the other
than it was when the bodies ballanced each other;
and therefore, by the preceding Cor. that body from
which it is removed, or which is on the fame fide with
the center of gravity, will defcend. Consequently
there is but one point in the line, which being fuf-
tained, the bodies will continue in aequilibrio, and
therefore but one' point only can be their center of
gravity. Hence alfo it appears, that the center of gra-
vity will always defcend, when it is not diredtly above
or below the point by which the body is fuf-
tained.

I (hall

[ ”7 ]

I {hall now endeavour to be as concife as pofiible
in what I have to fay of the other mechanic powers j
having, I fear, been too tedious in my account of the
lever, which however deferves to be particularly con-
lidered, fince to it may be reduced the ballance, the
axle and wheel, and (according to fome writers) the
pulley.

The ballance I do not confider as a diftindt machine,
becaufe it is evidently no other than a lever fitted to
the particular purpofe of comparing weights together,
and does not ferve for railing weights, or overcoming
refiftances, as the other machines do.

When a weight is to be raifed by means of an axle
and wheel it is fafiened to a chord that goes round the
axle, and the power which, is to raife it is hung to a
chord that goes round the wheel. If then the power
be to the weight as the radius of the axle to the ra-
dius of the wheel, it will juft fupport that weight ; as
will eafily appear from what was proved of the lever.
For the axle and wheel may be confidered as a lever,
whofe fulcrum is a line palling through the center of
the wheel and middle of the axle, and whofe long
and fhort arms are the radii of the wheel and axle
which are parallel to the horizon, and from whofe
extremities the chords hang perpendicularly. And
thus an axle and wheel may be looked upon as a kind
of perpetual lever, on whofe arms the power and
weight always a<ft perpendicularly, tho’ the lever turns
round its fulcrum. And in like manner when wheels
and axles move each other by means of teeth on their
peripheries, fuch a machine is, really, a perpetual com-
pound lever : and, by confidering it as fuch, we may
compute the proportion of any power to the weight

4

L 118 ]

it is able to iuftain by the help of fuch an engine. And
fince the radii of two contiguous wheels, whofe teeth
are applied to each other, are as the number of teeth
in each, or inverfely as the number of revolutions,
which they make in the fame time; we may, in the
computation, inftead of the ratio of thefe radii, put
the ratio of the number of teeth on each wheel ; or
the inverfe ratio of the number of revolutions they
make in the fame time.

Some writers have thought the nature and effects of
the pulley might be belt explained by confidering a
fixed pulley as a lever of the firft, and a moveable pulley
asone of the fecond kind. But tho’ the pulley may bear
being confidered in that light; yet, I think, the beft
and moll natural method of explaining its effects (that
is, of computing the proportion of any power to the
weight it can fuftain by means of any fyftem of pulleys)
is, by confidering that every moveable pulley hangs by
two ropes equally ftretched, which muft bear equal
parts of the weight : and therefore when one and the
fame rope goes round feveral fixed and moveable pullies,
fince all it parts on each fide of the pullies are equally
firetched, the whole weight mud be divided equally
amongft all the ropes by which the moveable pullies
hang. And confequently if the power which ads on
one rope be equal to the weight divided by the number
of ropes, or double the number of moveable pullies,
that power mufl fufiain the weight.

Upon this principle, the proportion of the power
to the weight it fuftains by means of any fyftem of
the pullies, may be computed in a manner fo eafy and
natural as muft be obvious to every common ca-
pacity.

The

C 1 r9 ]

The proportion, which any power bears to the re-
fitting force it is able to fuftain by means of a wedge,
has been laid down differently by different authors ;
fome of whom therefore mutt have been mittaken :
and none of them feem to have treated the matter fo
generally as they might have done. Without exa-
mining their feveral opinions, I (hall proceed to con-
fider what proportion a power ading on a wedge
muff have to the remittance it fuftains in three different
cafes, to whicji I think all thofe relating to the wedge
may be reduced.

Firjl , When the refitting bodies ad perpendicularly
on the fides of the wedge, and recede alfo in lines per-
pendicular to the fides.

Secondly, When the refitting bodies ad on the wedge
in oblique directions equally inclined to the fides, and
recede in lines perpendicular to the fides.

Thirdly, When the refitting bodies are confined, by
planes put under them, or otherwife, to recede in
particular directions oblique to the fides.

CASE I.

Let the aequicrural triangle A, B, C, [Tab. VI. Fig,
3,] reprefent a wedge on whofe fides the two equal
refitting forces E and F aCt perpendicularly with lines
of direction meeting at the point D, at which the
power P ads perpendicularly on the bafe A C. Then,
fince thefe three forces are fuppofed to 'fuftain each
other and keep the wedge in asquilibrio, they mutt be
to each other as the fides of a triangle to which their
directions are parallel, and therefore they will be to
each other as the fides of a triangle to which their

diredions

[ 120 ]

directions are perpendicular ; that is, the fum of
the forces E and F will be to the power P, which fuf«
tains them, as the fum of the (ides of the wedge to
the bale, or as one fide to half of the bafej that
is, as the radius to the fine of half the vertical angle
of the wedge. Hence, when in cleaving timber the
wedge fills the cleft, in which cafe the refinance of the
wood aCts perpendicularly on the fides of the wedge,
the power which drives the wedge muffc be to the
cohefive force of the timber in a proportion fomewhat
greater than that above mentioned, in order that it
may divide the timber, whofe parts will then recede in
lines perpendicular to the fides of the wedge.

CASE II.

Let now the refitting forces of E and F be fuppofed
to aCt obliquely on the Tides of the wedge in the direc-
tions E K and F Lj and let thefe forces be expretted
by the lines E K and F L, and let each of them be
refolved into two forces, expretted refpeCtively by the
lines EG, G H, and F H, H L, whereof the forces
G H and H L, by aCting parallel to the fides of the
wedge, are loft : while the other forces, E G and F H,
by aCting perpendicularly on the fides of the wedge,
keep the power P in asquilibrio; therefore by the firft
cafe thefe parts of the whole refitting force are to the
power P, as radius to the fine of half the vertical an-
gle of the wedge. But it is evident that the whole
refitting force is to its parts expretted by E G,
F H, as radius to the fine of the angle E KG, or
F L H; and therefore (compounding thefe ratios)
the whole refitting force will be to the power which

luftains'

[ la* 3

fuftains it, as thefquare of radius, to a rectangle under
the fine of the angle which the directions of the re-
Ming force make with the fides of the wedge, and the
line of half the vertical angle of the wedge. Now,
lince the force of the wedge is exerted in lines perpen-
dicular to the furface of its fides, thefe refilling bo-
dies will naturally recede in that direction; as we
fuppofe them, in this cafe, free to move in any direction,
whatever.

CASE III.

Let us fuppofe laftly, that the refilling bodies are
confined, by planes put under them, to recede in the
directions K E, L F, then the power which drives
the wedge and the refilling force will be in aequilibrio,
when the former is to the latter, as the fine of half
the vertical angle of the wedge, to the fine of the
angle E K G, F L H, that each fide of the wedge
makes with the direction in which the refilling force
is confined to recede. For in the firll cafe it was
proved that the power P, which drives the wedge,
is to the force with which It piuuudcs bodies in direc-
tions perpendicular to the fides, as the fine of half the
vertical angle of the wedge to radius. Let then
the line G E, which is perpendicular to the fide A B,
exprefs the force with which the power P protrudes
the refilling bodies in the directions G E, and H F,
and let this force be refolved into two forces, exprefied
by the lines G O, and O E, one perpendicular and
the other parallel to K E, the direction in which the
refilling bodies are confined to move; then the force
G O is loft, and only O E has effeCt in protruding the

Vol. LIII. S refilling

[ IZ2 ]

refifiing bodies in the dire&ions K E, and L F . This
force therefore being to the force exprefied by G E,
as the fine of the angle (E G O, or) E K G, to the
radius, and the Force G E being (as was faid before)
to the power P, as the radius to the fine of half the
vertical angle of the wedge; it follows, that the force
with which the refilling bodies are protruded in the
directions K E, and L F, is to the power P , as the fine
of the angle E K G, or F L H, which thefe direc-
tions make with the fides of the wedge, to the fine of
half the vertical angle of the wedge: and confequently,
if the refilling forces, which at on the wedge accord-
ing to thefe diretions, are to the power P in this pro-
portion, there will be an aequilibrium between them.

Hence we may obferve, that, if from D (the mid-
dle point in the back of the wedge) a line be drawn,
as D A, meeting one of the fides ; the refilling forces,
which mull recede in diretions parallel to D A; will
be to the power which fullains them, as D B, the
height of the wedge, to the line D A ; and this power,
if at all increafed, will remove thefe refilling bodies.
When therefore the retifVing bodies mull recede in
lines parallel to the back of the wedge, their refin-
ance will be to the power which fullains it, as the
height of the wedge, to half the breadth of it’s back.
This proportion of the power to the refinance in this
lart mentioned cafe, is confirmed by an experiment ufed
by Gravefande and others, to Ihew the nature of the
wedge. For, in this experiment, a wedge is drawn
down between two cylinders, which roll on rulers par-
allel to the back of the wedge, and are kept together
by weights. And probably it was from their attend-
ing to this experiment, without conlidering other cafes.

4

[ I23 ]

that they concluded the fame proportion between the
power and refiftance would obtain in general.

I have already mentioned the proportion which the
power that drives the wedge mult have to the refift-
ance in cleaving timber, when the wedge exactly fills
the cleft ; which cafe however feldom happens ; for
the wood generally fplits to fome di fiance before the
wedge. And then, in order that there may be an
aequilibrium between the power driving the wedge
and the refiftance of wood, the former muft be to
the latter, as the fine of half the vertical angle of
the wedge, to the cofine of the angle which the fide
of the cleft makes with the fide of the wedge. The
truth of which is eafily underftood from what was
proved in the third cafe of the wedge ; for the cofine
of the angle, contained between the fide of the cleft
and the fide of the wedge, is the fine of the angle
which the fide of the wedge contains with the direc-
tion in which the wood recedes j becaufe, as the cleft
opens, the wood mull recede in lines perpendicular to
the fides of the cleft ; and in the direction of thofe
lines doth the refiftance of the wood adt on the fides
of the wedge.

The inclined plane is reckoned by fome writers
among the mechanic powers; and I think with rea-
fon, as it may be ufed with advantage in raifing

weights. *

Let the Line A B [Tab. VI. Fig. 4.] reprefent the
length of an inclined plane, AD its height, and the line
BD we may call its bafe. Let the circular body GEF,
be fuppofed to reft on the inclined plane, and to be
kept from falling down it by a firing C S tyed to its
center C. Then the force with which this body

S 2 ilretchei

[ I24 ]

Wretches the firing will be to its whole weight, as the
fine of A B D, the angle of elevation, to the fine of the
angle which the firing contains with a line perpendicu-
lar to A B the length of the plane. For let the radius
C E be drawn perpendicular to the horizon, and C F
perpendicular to AB: and from E draw EO par-

allel to the firing and meeting C F in O. Then, as the
body continues at reft and is urged by three forces, to
wit, by its weight in the direction C E, by the reaction
of the plane in the direction F C, and by the reaction
of the firing in the direction E O ; the reaction of the
firing, or the force by which it is ftretched, is to the
weight of the body, as E O to C E : that is, as the
fine of (the angle C E F, which is equal to) A B D,
the angle of elevation, to the fine of the angle E O C,
equal to S C O, the angle which the firing contains
with the line C F perpendicular to A B, the length
of the plane.

When therefore the firing is parallel to the length
of the plane, the force with which it is ftretched, or
with which the body tends down the inclined plane, is
to its whole weight, as the fine of the angle of ele-
vation, to the radius, or as the height of the plane
to the length. And in the fame manner it may be
fhewn that, when the firing is parallel to B D, the
bafe of the plane, the force with which it is ftretched
is to the weight of the body, as A D to B D, that is,
as the height of plane to its bafe. If we fuppofe the
firing, which fupports the body G E F, to be faftened
at S, and that a force, by adting on the line A D, the
height of the plane, in a direction parallel to the bafe
B D, drives the inclined plane under the body, and by
that means makes it rife in a direction parallel to A I>.

[ 125 ]

Then, from what was proved in the third cafe of the
wedge, it will appear, that this force muft be to the
weight of the body, as A D to B D, or rather in a
proportion fomewhat greater : if it makes the plane
move on and the body rife.

From this laft obfervation we may clearly fhew the
nature and force of the fcrew ; a machine of great
efficacy in raffing weights or in preffing bodies clofely
together. For if the triangle AB D be turned round
a cylinder whofe periphery is equal to B D, then the
length of the inclined plane B A will rife round the
cylinder in a fpiral manner ; and form what is called
the thread of the fcrew : and we may fuppofe it con-
tinued in the fame manner round the cylinder from
one end to the other j and A D the height of the in-
clined plane will be every where the diftance between
two contiguous threads of this fcrew, which is called
a convex fcrew. And a concave fcrew may be formed
to fit this exactly, if an inclined plane every way
like the former be turned round the infideof a hollow
cylinder,, whofe periphery is fomewhat larger than that
of thenthpr.’ T et ns now fuppofe the concave fcrew
to be fixed, and the cuuvca uuc iu be fitted into it,
and a weight to be laid on the top of the convex fcrew :
Then, if a power be applied to the periphery of this
convex fcrew to turn it round, at every revolution
the weight will be raifed up thro’ a fpace equal to the
difiance between the two contiguous threads, that is to
the line A D the height of the inclined plane BA;
therefore fince this power, applied to the periphery,
adts in a direction parallel to B D, it muft be to the
weight it raifes as A D to B D, or as the diftance
between two contiguous threads, to the periphery of
the convex fcrew.

N. B.

[ 126 ]

N. B. The didance betwen two contiguous threads
is to be meafured by a line parallel to the axle ; if
we now fuppofe that a hand-fpike or handle is in-
ferted into the bottom of the convex fcrew, and
that the power which turns the fcrew is applyed to
the extremity of this handle, which is generally the
cafe ; then as the power is removed farther from
the axis of motion, its force will be fo much en-
creafed (vide what was faid of the lever, cor i.)
and therefore fo much may the power itfelf be
diminifhed. So that the power, which, adting on
the end of a handle, fudains a weight by means of
a fcrew, will be to that weight, as the didance be-
tween two contiguous threads of the fcrew, to the
periphery deferibed by the end of the handle. In
this cafe we may confider the machine as compofed
of a fcrew and a lever, or, as Sir Ifaac Newton ex-
preffeth it, Cuneus a ve£le impulfus.

I have now given you my fentiments, as to the prin-
ciples on which, I think, the efficacy of the mechanic
powers may be mod; properly explained ; and hope
that, where 1 have preiUmed to differ from others, you
will think I have fome appearance of reafon on my
fide. I find my paper has been drawn out much be-
yond what I atfirft expe&ed, and I fear much beyond
your patience j and therefore ffiall detain you no longer
than to affure you that I am, Sir,

with the fincereff regard, your
mod obedient humble fervant,

Hugh Hamilton.

XXVI. An

_

'

i

■

•f

%

l^bifos Trans . Vol.LflT.TAB. JTL. 127.

Ill 1 JZ

r

Til/o-i. Trans Vol .TM. TAB.JDC. p. 127.

i/iMyiuk Je.

C I27 ]

XXVI. An Account of fome fubterraneous
Apartments , with Etrufcan Inf cript ions and
Paintings , di/covered at Civita Turchino
77Z Italy [Tab. VII. VIII. IX.] : Commu -
nicated from Jofeph Wilcox, £/y; F. S. A .
Charles Morron, M. Z). £. R, S .

Read March 17, Ivita Turchino, about three miles
!763* to the north of Corneto, is an hill

of an oblong form, the fummit of which is almoft
one continued plain. From the quantities of medals,
intaglio’s, fragments of infcriptions, &c. that are oc-
cafionally found here, this is believed to be the very
fpot, where the powerful and mofl ancient city of
Tarquinii once flood : tho’ at prefent it is only one con-
tinued field of corn. On the fouth-eafl fide of it runs
the ridge of an hill, which unites it to Corneto. This
ridge is at leafl three or four miles in length, and al-
mofl entirely covered by feveral hundreds of artifici-
al hillocks, which are called, by the inhabitants,
Monti Roffi. About twelve of thefe hillocks have
at different times been opened ; and in every one of
them have been found feveral fubterranean apartments
cut out of the folid rock. Thefe apartments are of
various forms and dimenfions : fome confifl of a large
outer room, and a fmall one within j others of a fmall
room at the firfl entrance, and a larger one within :
others are fupported by a column of the folid rock,
left in the centre, with openings on every part, from
twenty to thirty feet. The entrance to them all is
by a door of about five feet in height, by two feet

f 128 ]

and an half in breadth. Some of thefe have no
other light but from the door, while others feem to
have had a fmall light from above, through an hole
of a pyramidical form. Many of thefe apartments
have an elevated part that runs all round the wall,
being a part of the rock left for that purpofe. The
moveables found in thefe apartments confift chiefly
in Etrufcan vafes of various forms ; in fome indeed
have been found fome plain farcophagi of ftone with
bones in them. The whole of thefe apartments are
flucco’d, and ornamented in various manners : fome
indeed are plain j but others, particularly three, are
richly adorned ; having a double row of Etrufcan
infcriptions running round the upper parts of the
walls, and under it a kind of freize of figures in
painting : fome have an ornament under the figures,
that feem to fupply the place of an architrave. There
have been no relievos in ftucco hitherto difcovered.
The paintings feem to be in frefco, and are in gene-
ral in the fame ftile as thofe which are ufually feen
on the Etrufcan vafes : though fome of them are
much fuperior perhaps to any thing as yet feen of the
Etrufcan art in painting. The paintings, though in
general flight, are well conceived, and prove that the
artifl: was capable of producing things more fiudied
and more finifhed : though in fuch a fubterranean
fituation, almofl void of light, where the delicacy
of a finifhed work would have been in a great mea-
fure thrown away ; thefe artifts (as the Romans did
in their beft ages, when employed in fuch fepulchral
works) have in general contented themfelves with
flightly exprefling their thoughts. But among the
immenfe number of thofe fubterranean apartments

which

[ I29 ]

which are yet unopened, it is to all appearance very
probable that many and many paintings and infcrip-
tions may be difcovered, fufficient to form a very en-
tertaining, and perhaps a very ufeful, work : a work
which would doubtlefs intereft all the learned and
curious world, not only as it may bring to light (if
fuccefs attends this undertaking) many works of art,
in times of luch early and remote antiquity, but as
perhaps it may alfo be the occafion of making fome
confiderable difcoveries in the hiftory of a nation, in
itfelf very great, though, to the regret of all the learn-
ed world, at prefent almoft unknown. This great
fcene of antiquities is almoft entirely unknown even
in Rome. Mr. Jenkins, now relident at Rome, is
the firft and only Englilhman who ever vifited it.

Vol. LIII,

T

XXVII. An

[ *3° ]

\J\j O' Gft/Vv^V*,

XXVII. An Account of a new Peruvian
Plant , lately introduced into the Englifh
Gardens ; the fever al CharaSlers of which
differ from all the Genera hitherto defer ibed ;
Prefe?ited to the Royal Society by George
Dionyfius Ehret, F. R. S.

Read May 1 2, r b ^HIS plant blowed in the Phyfick
I/63* Garden at Chelfea, and flourilhed

there in great perfe&ion in the year 1761. It pro-
duced abundance of branches, which fpread them-
felves on the furface of the ground : thefe branches
were greatly multiplied by fide ones, which grow
alternately; and are fmooth towards the ground, and
ftreaked towards the top, as the figure [Tab. X.] ex-
preffes. Each joint isfurnifhed with many ovate- fhaped
leaves, having membraneous ciliated footftalks.

This plant was alfo richly ornamented with abun-
dance of buds and flowers : the flowers being of a
fky-blew, with a dark embroidered purple bottom,
made a beautiful appearance.

Thefe flowers are monopetalous, or tube-flhaped,
having five obtufe laciniae, which expand themfelves
exadly like unto the Alkekengi Indicum glabrum che-
nopodii folio, Dill. Hort. Elth. The difference in
both thefe flowers is only in the infertion and fituation
of their filaments: the filaments of the alkekengi
adhere at the bafe of the tube, but in this flower they
are inferted in faux corolla at the fwelling of the
tube: in both of them the filaments are alfo hairy at
their bafe, and their antherae are diftant from each
a. other,

[ J3i ]

other, whereas in the reft of the Akekengi their an-
therae incline to each other. The moft remarkable
character in this plant is, the pofition of the five fi-
milar feeds, (each of thefe has its peculiar receptacu-
lum) which lay in fuch a manner in the center of the
calyx, that, at firft fight, it appeared as if it belong-
ed to that clafis of plants called Herbae verticillatae.;
but, on a clofer infpe&ion, it appeared, that each of
thefe fimilar feeds were feparate feed veflels (or a.
trifpermous fruit) and contained three feeds.

The ingenious and learned Dr. Albert Schl offer, of
Amfterdam F. R. S. prefented me with many curi-
ous dried fpecimensof plants, which he had collected
in the Botanic Garden at Paris in the year 1755 ;
amongft which was this plant, under the name of
Belladona Peruviana minor. Jufiieu. Hort. Reg..
Paris.

.Mr. Philip Miller propofed to honour this plant
with the name of Walkeria, in gratitude to-
Richard Walker, D. D. Vice-mafter of Trinity
College in Cambridge and Cafuiftical Profeflor, who, by
his indefatigable pains, and at a large expence of his
own, has lately founded a Phyfic Garden in thatUni-
verfity, to incite and extend the ftudy of Botany in that
famous feat of the Mufes,.

Defcription of the Chara&er, Tab. X.

Fig. a. Reprefen ts a fide view of the calyx, whofe
leaves are open, and cover the tube of
the flower : when thefe flowers drop off,
the calyx clofes inftantly again (to pro-
tect the Embryo) and forms a pentagonal
conical figure, fee Fig. h,

T 2 Fig:

*»•

[ *3* ]

Fig, c. Is a fide view of the corolla, feparated from
the periantheum : it has a fmall tube which
fwells into an open (monopetalous) bell-
(haped figure : the limbus of the corolla,
Fig, dy having fimall fifiures, divides it into
fo many obtufie laciniae.

Fig. e. The infide of the corolla laid open, to ex-
pofe to view the five (lamina, whofe fila-
ments are inferted at the lwelling of the
tube: they are hairy at their bale, and of
equal length, and their apices are difperfed
in the middle of the flower.

Fig. f. This figure reprefents the calyx laid open :
it is monophyllous, divided into five laciniae :
it alfo (hews the fituation of the five ger-
mina, which are furrounded with a yellow-
i(h nedtariferous flefhy fubftance. From
the center of thefe germina or embryos
comes forth the fiyle, which is of equal
length with the (lamina, having a globu-
lar or capitated ftigma.

Fig. g. Five capfulae or feed- veflels, which are clofely
connected to each other, adhere together,
and yet may each of them be feparated,
independent of its companion : they are
pundtated, rough, of a hard woody fub-
ftance: each capfula contains three fmall
ovate feeds : fee the tranfverfe fedtion

fig. h.

Fig. z. Reprefents the calyx and receptacle: the
nedtariferous part divides the receptacle into
five femicircles: each of thefe velligia had an

oval-fliaped round capfula, fig. k.

XXVIII. Ob -

2

C 133 ]

XXVIII. Obfervatiom on two Antient Roman.
Infcriptions difcovered at Netherby in Cum-
berland: In a Letter to the Right Rev .
Charles Lord Bijhop of Carlifle, F. R. S.
from the Reverend John Taylor, LL. D:
Canon Refidentiary of St. Paul’s, and Chan-
cellor of the Diocefe of Lincoln.

Lo the Right Rev. the Lord Bifop of Carlifle.

Read May 12, f H A H E following obfervations I beg
1763. ieave iq prefent to your Lordlhip,

who was pleafed to communicate thofe remains of
antiquity, that gave birth to them. The Society of
Antiquaries cannot but be greatly delighted to fee your
Lordlhip advanced to an Epifcopacy, in a country
Antiquitatum Romanarum feraciffima j and fucceed-
ing, at a diftance, a very confummate Antiquary, to
whom this kingdom {lands greatly indebted, the great
bifliop Nicholfon.

Your Lordfhip’s former fituation in another remote
part of England contributed greatly to the cultivation
of this kind of letters, and brought us acquainted
with what might otherwife have lain unknown or
negledled. We begin already to experience the be-
nefit of your Lorfhip’s removal to this.

I am,

my Lord,

etc. etc.

John Taylor.

Amen-Corner,
April 28th,
1763.

[ i34 ]

TH E infcriptions [Tab. XT.] marked N°.I. N°. U.

were difcovered at Netherby in Cumberland, the
former in the year 1762, the other early in the prefent
century: they both make mention of Marcus Aurelius
Sal vius, Tribune of theCohors Prima AiliaHifpanorum
Milliaria Equitata. The former moreover points out
the particular emperor M. Aurelius Severus Alexander,
in whofe reign it was engraved: and almoft directs us
to the very year alfo: which mu ft have been either
the CCXXVIth or CCXXIXth of the Chriftian sera,,
for in thole two years was that emperor conful : and
one of thofe confulates this done alludes to, in the
laft words of it ; which I read thus:.

IMPERATORE DOMINO NOSTRO-
SEVERO ALEXANDRO, PIO,

FELICE, AVGVSTO, CONSVLE..

And here I take occadon to obferve, that this apei-
iation Dominvs Noster was given to our emperor
in the infcription before us, notwithdanding what
is recorded of him by his hidorian, Lampridius,
T)ominum fe appellari vetuit. And be it obferved, that,
whatever inclination Alexander Severus might have
towards Chridianity, as has been imagined, his forces
in Britain, as appears from that pagan and frequent
compliment, which occurs in the fourth line of this
infcription, were not in the fecret :

DEVOTA NVMINI MAIESTATIQVE EIVS.

And

t

TfAot /?//0}',>o/r*s ' //Sru&np
a/ G. Jvtmrpt/ 'faeatV fe/ere /At,
AQutAAny woo /a/csn o/> t — ^

A A A A {////ar.f iJyiuz/n& C< Ay/e' one/ a/en/e' a-noi/ter nnA^A el- /sit/e Ceon^eoit/ /e/oneewi-. BB. >_heon/y t ////aM o^/^Ae. Jam* ^m//. —

C . C . f //wa 4u6s or r //r^j/$/r-eO.^ B.P.D. * J/ree Ao/Zotv S /y/eo or //yeoj/ow /Au’ /ia// . ^

EE. ' ’ ^&u/r AAH//aoV t/o/z/ t/sone , 3 A. o^~ w t^ao'e' eoner/A ?o/// i//eyyo /roneort. T. laA //la/Ao t//oeoi>e-> r/ <» /yj i

G. t ///e^/A/soor nnV/v an t /n^oryi/ion/. yion tA^orene/ t/i. A/te- Oao??e '^£w/\'H.H. //it// o^ //y/e/ Zo//f- /ro/Zonr fc^l/iutt •

^^ore</n*d«, m/I del '///yy./rUm 6>an*r*, nartt /£<■< fourth ^ A/on,. ^

t A'. P/?). e //i oomo were

J.Ml/nJzfc.

Tkifos. Tronj. Vol.zm. TAB. JC1.V. 134

fauy/iP //?ai/e a£ <w //<> Wtfto/i

*U6/>

A^mSy //Aonz/o^ « f/ry./^yj.

*y%e e /ovation o^J6 //*//&*&
^ /ounA rA/aiu/my et~ E IE .

t

*

i

[ r35 ]

And farther ftill, a Cumberland infcription, marked
LI. in Horfeley, carries the pagan compliment to the
fame emperor fomething higher *:

DEABVS MATRIBVS T R A MARINIS
ET NVMINI IMPERATORIS ALEXAN-
D R I A V G^f S T I E T IVLIAE MAMMAEAE
MATRI AVGVSTI NOSTRI ET CASTRO-
RVM TOTIQ. DOM VI DIVINAE
AETERNAEQ. VEXILLATIO Pofuit.

The pafiages, which feem to favour the opinion I
mentioned, of this emperor’s tendency to Chriftiani-
ty, are thefe of Lampridius, fcil.

Judaeis privilegia refervavit : Chriftianos efle pa£
fus eft.

Matutinis horis, in larario fuo (in quo et divos
principes, fed optimos et elecftos, et animas fan&iores,
in queis & Apollonium, et, quantum fcriptor fuorum
temporum dicit, Chriftum, Abraham, et Orpheum,
et hujufcemodi Deos habebat, ac majorum effigies)
rem divinam faciebat.

Chrifto templum facere voluit, eumque inter Deos
recipere.

Quum Chriftiani quendam locum, qui publicus fu-
erat, occupaflent, contra Popinarii dicerent, fibi eum
deberi, refcripfit, Melius efle, ut quomodocunque il-
lic Deus colatur, quam Popinariis dedatur.

Clamabatque ftepius, quod a quibufdam five Ju-
daeis five Chriftianis audierat, et tenebat : idque per
praeconem, quum aliquem emendaret, dici jubebat,
QVOD TIBI FIERI NON VIS ID ALTERI NE FECERIS.

* This, as far as we know for certain, is the only infcription
in Britain made under this emperor, except that we are now dif-
courling of.

Quam

[ 136 ]

Qnam fententiam ufque adeo dilexit, ut et in palatio
et in publicis operibus prsefcribi juberet.

I mention this the rather, becaufe I believe, that
one of thofe infcriptions mentioned by Lampridius
is come down to our times, but fomewhat mutilated.
It is to be found on the Via Appia, not far from the
Tres ‘Taberiu and is marked N° III. in the paper
before you.

Netherby, whether the Caftra Exploratorum of
Antonine, with Horfley and Wefieling, or the JECic a
of Ravennas, with Camden and Gale, is the place,
where the infcriptions marked N° I. and N° II.
were lately difcovered. N° I. ferved as a cover to a
drain, which did not feem of any conliderable age :
the table part of which is five feet feven inches, by
two feet four inches and a half: the margent two
inches more. N° II. was found in a room or apart-
ment belonging to a large building, lately difcovered,
but now pulled to pieces for the fake of the materials.
My L. of Carlifle has a draught of it, where there
appears to have have been an hypocauft, and poflibly
thereabouts was the Bafilica alio, mentioned in our
firfl infcription.

A Durham infcription, marked XI. in many in-
flances explains ours, and is proper to be compared
with it. It runs thus :

IMP. CAESAR M. ANT. GORDIA

N V S P. F. A V G. B A L N E V M C V M

BASILICA A SOLO INSTRVXIT

PER GN. LVCILIANVM LEG. A V G.

PR PR CVRANTE M. A V R.

QVIRINO PRAE. COH. I. LEG. GO R.

The

[ >37 ]

The purport of the Infcription now under confi-
deration is this, viz.

In the reign of Severus Alexander, Pius, Felix, &c.
the Cohors Prima iElia Hifpanorum Milliaria Equi-
tata put the finilhing hand to a building, termed
here Bafilica Equeftris Exercitatoria, the foundations
of which had been laid fome time before. This
was conducted under the care and direction of Vale-
rianus, the emperor’s lieutenant and pro-prastor, at
the inflance of M. Aurel. Salvius, tribune of the
aforefaid company.

Line 3. The Cohors I. Hifpanorum is mentioned
in many inferiptions found hereabouts, but in none
of them called Ailia, as here in thefe two inferi-
ptions. coh. 1. aelia dacorvm is very frequent.
And in the Notitia we meet with Cohors prima JElia
Clajfica.

Line 4. I read hispanorvm milliaria eqvi-
tata; the Monogram {landing for m. or milliaria,
and ec^ for eqvitata, not eqvestris. For the
auxiliaries ferved on foot, fome of the regiments be-
ing lined, or flanked, with horfe, and called there-
fore Equitatas : for that is the meaning of the word,
not promoted from the joot fervice to the horfe , which is
the opinion of fome, as Mr. Horfley, for inflance,
&c. I have fpoken to this point more fully in my ob-
fervations upon the Rutchefter Infcription, which are
printed in the Philofophical Tranfadtions *.

Line 5. Bafilica is a word of large extent, and
commonly fignifies what is built for public life , or by
public authority. It is therefore frequently applied to
a burfe or exchange. The public roads are termed

* A.D. i747. N° 482. III.

Vol. LIII. U

Bafilicse :

[ *3® ]

Bafilicae : and the Christian writers took this word for
their churches.

Though this be the common ufe of the word, it is
not the primary. It fignifies, I fay, originally and
principally, as it does in this infcription, a portico or
colonnade, which being very large and confiderable
in places built for courts of juftice, for public audi-
tories and meetings of merchants, it came to pafs,
that the name of the principal was funk in the ad -
jun£i ; and all thefe places called alike hafilicre , from
the colonnade, which attended, and perhaps fome-
times encom palled them:

Bafilicarum loca, adjunSla foris, quam calidifiimis
partibus oportet conftitui, ut per hyemem fine mo-
leftia tempeftatum fe conferre in eas negociatores pof-
fent. Vitruv. V. i.

In the law-books I find them fometimes diftin-
guilhed :

Sacram vel religiofam rem vel ufibus publicis in
perpetuum reli&am, ut forum , aut bafilicam , aut ho-
minem liberum, inutiliter fiipulor. L. 83. § 3. D.

dc V. O.

And fo likewife Afconius upon Cic. Orat. pro Mi-
lone :

Quo igne & ipfa quoque curia flagravit, & item
Porcia bajilica , quae erat eijundla, atnbufta eft.

In Capitolinus I meet with bafilica centenaria , ba -
plica pedum quingentorum . And in the lame light we
muft certainly view the words of Vopifcus in the
life of Aurelian :

Miliarenlem deniqueporticum in hortis Salluftiis or-
tiavit, in qua quotidie et equos et fe fatigabat.

Which paflage will explain the words of Juvenal,
Sat. IV. init*. Quid

1

[ J39 ]

Quid refert igitur, quantis jumenta fatiect

Porticibus

And both together, the ufe and detonation of the
building, which is. the fubjed of our Infcription,
basilica (i.e. porticus) eqvestris exercitato-

BIA.

As the Roman affairs in Britain are little known
under this emperor ; one only Infcription befides, as
I ohferved, either bearing his name, or referring to
his age, thefe notices may poffibly be more wel-
come. And what makes the firif Infcription more
fo, is the mention of a new Legate, or lieutenant and
pro-prastor, Valerianus, in this province, never taken
notice of before. A copper Infcription lately difco-
vered in the eftate of the D. of Norfolk in Yorkfhire,
und now in his Grace s poffeflion, affords us another,
and that a very remarkable perfonage, under the em-
peror Hadrian, and one much known in the Roman
hiflory.

What was the pranomen of this Legate, 1. 9. is
a matter of farther enquiry.

XXIX. A Method of lejfening the Quantity
of FriSiionin Engines , by Keane Fitzgerald,
Efr, R R. S. •

ReadMayi2, *|i /TECH A NICS, or that branch of
3 lyl mathematics which confiders mo-
tions and moving powers, their nature and laws, is
properly ditongufhed into rational, and practical.

U 2 A know-

[ H° ]

A knowledge in rational mechanics, which com-
prehends the whole theory of motion, upon which
natural philofophy fo greatly depends, is chiefly con-
fined to the learned; and the proper conftrudtion of
engines and machines, which is the principal objedt
of pradlical mechanics, altho’ fo very neceffary to carry
on the feveral branches of hufbandry, manufadture,
and commerce, upon which, the riches and power
of a nation depend in a great meafure, is feldom at-
tended to, but by the meet handicraftfman ; who is
little acquainted with the principles he works on, and
from whom no great improvements can well be ex-
pedited ; yet it has happened fometimes, that excellent
contrivances have been invented, for railing heavy
weights and overcoming their refinances, by perfons
who never took the trouble of examining into the
caufe of gravity. .

As this branch is certainly molt ufeful to mankind;
and a knowledge in it, generally deemed one of the
marks by which a civilized nation is diftinguifhcd from
barbarians, one would imagine, it fhould have in-
duced a greater attention to improvements in it, than
has been generally found : But it often happens that
mechanical powers, feemingly demonftrable in theory,
are found very deficient in operation, from unexpedfed
obftrudions ; which, with the expence and trouble
that generally attend the reducing fpeculations of this
nature into pradiice, have probably been the greateft

obftacles to improvements in it.

One of the greateft obftrudtions to the mechanical
powers of engines proceeds from the fiidlion, or
refiftance of the parts rubbing on each other;

which in general, is greater, or lefs, as the rubbing
D ° ' parts

[ m J

parts bear the greater, or Jefs preflu re * and yet this
obdru&ion is but little attended to. The theorid
makes no allowance on account of friction ; and the
practical mechanician, who feels the effeds, yet, as
if unavoidable, feldom takes the trouble of fcarching
for a remedy.

Amongd the few who have endeavoured to afcer-
tain the quantity of fridtion proceeding from weight,
fome have deemed it equal to q, others to 4, and
others more, or lefs, according to their different me-
thods, or accuracy in making experiments. Dodtor
Defaguillers gives an account of fome experiments,
which (hew the quantity of fridfion in a cylinder, to-
be equal to 1. of the power required to move it,
when the furface of the cylinder moves as fad as
the power.

In order to examine the quantities of fridfion pro-
ceeding from different weights, I had an exadt bal-
ance made, which weighed 27 ounces; the pevets
of the axis were 4. inch diameter, and turned in brafs
fock'ets, fixed in a frame for the purpofe.

Seven pound fufpended on each arm, at 18 inches
diftance from the center, required 1 I ounce, 2 penny
weight, to be applied to either end, to overcome the
refiffance from fri&ron in the flighted degree; and 3
ounces to carry it down 2 inches.

Fourteen pound, applied in the fame manner, re-
quired 3 1 ounces to move the balance; and 6± ounces
to fink either end 2 inches.

Twenty one pound required 41 ounces to give it the
lead motion, and 7*. ounces to fink it about 2 inches.

Seven pound, fufpended on each arm at 9 inches
diftance from the center, required 3 ounces and _L to
move cither end in the lead degree.

Fourteen

[ *42 ]

Fourteen pound required 64 ounces ; and 2 1 pound
required 9 4 ounces.

I placed another axis in the fame ballance, the pevets
of which were 1 inch diameter, and lufpended 7 pound
on each arm at 18 inches diftance from the center,
which required 3 A ounces to be applied to either
end, to overcome therefiftance from fridtion 5 and then
that end funk near 2 inches.

Fourteen pound, applied in the fame manner, re-
quired 74. ounces, which carried that end down fome-
what more than 2 inches.

Twenty one pound required 1 1 1 ounces, and funk
either end 24 inches.

Seven pound, fufpended on each arm at nine inches
diftance from the center, required 74 ounces to move
cither end. — Fourteen pound required jounces, and
21 pound required 20 4 ounces.

On repeating thefe experiments, there was little or
no variation ; and altho the feverai powers, required to
overcome the refinance from fridtion, do not cor-
refpond exadtly in proportion to the feverai weights
and diftances; yet it appears, that the lead: power
required, was equal to 4 the weight on the pevets ; and
that it required a power nearly equal to the whole
weight, to overcome the refiftance from fridtion, with
but a fmall degree of velocity. But it does not fol-
low, that the extraordinary power, feemingly required
to overcome the fridtion with this degree of velocity,
is to be attributed entirely to that caufe, as part of it
is neceffary to raife the oppofite weight with the fame
degree of velocity, tho’ fome part of it certainly is.
For when there is little or no obftrudtion from Iridt ion,

a power

C r+3 ]

a power of one ounce, more than what is juft ne-
ceftary to counterbalance a weight of y pound, will
raiie it with as great a degree of velocity, as 2 ounces
over and above what is juft neceftary to overcome the
refiftance from fridtion. So that it muft require an ad-
ditional power in proportion, to overcome the refiftance
from fridtion, with the fame degree of velocity, that
it may be neceftary to raife the weight.

It is not imagined that thefe experiments ftiould
determine the exadt quantity of fridtion proceeding
generally from weight, or preffure ; which probably
can never be afcertained by any experiments, however
accurate ; for even in engines of equal dimensions, and
loaded with equal weights, the quantities of fridtion
may be very unequal, from circumftances differing, .
which arefometimes imperceptible; fuch as the firm-
nefs, elaft icity, roundnefs and fmoothnefs of the parts
rubbing on each other; particularly the roundnefs, and
fmoothnefsof the gudgeons, orpevets, which, in large
engines, are feldom turned true, or polifhed. But it ap-
pears from thefe experiments, that the quantity of fric-
tion in large engines may reafonably be eftimated at 4.
the weight, or preffure, on the rubbing parts ; al-
though in fuch as are ffnall, and finifhed with exadt-
nefs, the quantity may probably be about 4.

It is evident that the quantity of fridtion in any
engine, is equal in its oppofition to a certain portion
of weight, or preffure on the parts rubbing on a
dead furface. And, altho’ gravity is an adtive
principle always tending to a center, and fridtion,
a kind of vis inertiae in oppofition to motion, yet it
may be confidered mechanically as fo much weight
which requires a power to overcome its refiftance, in

a ratio-

[ i44 ]

a ratio of the velocity of the power, to the velocity
of the part rubbing on a dead furface ; as in the axis
in peritrochio, Tab. XII. Fig. i. If the wheel A be 20
feet diameter, the axis B 1 foot diameter, the pevets
f of the axis B 4 inches diameter, and the weight C
to be raifed by the axis B, 12 tons or 24,000
pounds

The power D, in the wheel A, with refpedt to the
weight C to be raifed on the axis B, is required in a ratio
of the femidiameter of the wheel A to the femidiame-
ter of the axis B, which is 40 ; therefore the power D—
1200 pound is fufficient to counterbalance the weight
C, and the lead: additional power would raifeit, if there
were noobftrudlion. But the quantity of friction in the
pevets y, l'uppofed equal to 4 the weight or preifure
on that part, requires an additional power in the wheel
A to overcome its refinance, in a ratio of the femidia-
meter of the wheel A, to the femidiameter of the pevets
j\ or of the velocity of t he power in the wheel A, to
the velocity of the part rubbing on a dead furface in
the pevets f which are 6°. And as the weight of
the wheel A, fuppofed 1500 pound, alfo the power D
1200 pound, required to counterbalance the weight
C 24,000 pound, in all 26,700 pound; center in the
pevets f the quantity of fridtion in the pevets j\
being equal to 4 the weight, or 13,350 pound hang-
ing on them, will require a power in the wheel A
fomewhat more than 220 4 pound to overcome its
refiftance. And as this additional power E 220 4
pounds caufes an additional fridtionr=i 10 - 4 pounds,
it alfo requires a further power K = 1 4 pounds to
overcome its refinance; but the quantity of fridtion
proceeding from thence, need not be ellimated in a
.calculation of this nature.

As

P/>iZos . 2ranj . IGl. U/T.^TAJ3 . XU. f?. J44--

[ r55 ]

As the power E, in the wheel A, with refped to
friction in the pevets f is in a ratio of the femidia-
meter of the wheel A to the femidiameter of the pe-
vetf it is evident, that, by enlarging the diameter of
the wheel A, or reducing the diameter of the pevets
the power over fridion will be increafed in pro-
portion; but whatever power is gained by enlarging
the diameter of the wheel A, will be loft equally
in time, or velocity, with refped to the weight C to
be railed; and altho there will be no lofs in time, or
velocity, by reducing the diameter of the pevets f;
yet tnis cannot be done beyond the proper degree of
ftrength required to fuftain the weight C &c.

. ^ alfo appears that the power E with refped to

fridion in the pevets f is in a ratio of its velocity
to the velocity of the pevet f rubbing on a dead fur-
face, it follows, that if the velocity of the part rub-
bing on a dead furface can be decreafcd, whilft the
velocity of the power D continues in the fame ratio,
with refped to the weight C to be raifed on the axis
B; the power E over fridion, will be increafed in
proportion, without any lofs in time or velocity, as to
the weight C to be raifed ; which may be effeded in
the following manner, and the quantity of fridion re-
duced to any degree that may be required.

Fig. 2. Let the pevets / of the wheel A, turn on the
peripheries or the wheels G. G. 3 feet diameter, whole
pevets g, g, are 1 inch diameter, and the whole fric-
tion will be transferred from the pevets f to the
pevets g, which will then be the only parts rubbing on
a dead furface, by which means the velocity of the
power in the wheel A, to the velocity of the pevets gy
will be in a ratio of 1 *„6 °. For as the pevets 4
Vol. LI1I. X . inches

[>56]

Inches diameter, turn on the peripheries of the wheels
G, 3 feet diameter, 9 revolutions of the pevets f>
are equal to 1 revolution of the wheels G ; and the
circumference of the pevets /, being 4 times the
circumference of the pevets g , the fpace the pevets J,
would have rubbed on a dead furface in one revolution,
is equal to the fpace the pevets g rub on a dead fur-
face in 36 revolutions of the pevets therefore the
velocity of the pevets y, being \.6 to velocity of the
pevets g, and the velocity of the power D in the
wheel A being 6_° to the velocity of the pevets fy
the velocity of the power D, to the volocity of the
pevets g, is x V = * V S° ^at
13250 pound, which was the weight equal to the
quantity of fridtion in the pevets J or a power
fomewhat more than 6 pound 2 ounces in the wheel
A, will be fufficient to overcome the refinance from
fridtion in the pevets g.

To reduce this quantity of fridtion to a lefs degree,
let each of the pevets g, be placed on the peripheries
of the wheels H, 2 feet diameter, vvhofe pevets h
are 1. inch diameter j and the whole fridtion will then
be transferred from the pevets g, to the pevets h ; by
which the velocity of the power in the wheel A, to
the velocity of the part rubbing on a dead furface, in
the pevets f, will be in a ratio of 2 0 713 6 °. bor the
circumference of the pevet g, being of the cir-
cumference of the wheel H, on which it turns, makes
24 revolutions, for 1 of the pevet h. And the cir-
cumference of the pevet g, being 4 times the cir-
cumference of the pevet ht the fpace the pevet g
would have rubbed on a dead furface in 1 revolution,
is equal to the fpace the pevet h rubs in 96 revolutions j

therefore

C r57 ]

therefore the velocity of the pevet g, to the velocity
of the pevet h, is And as it appears that the
velocity of the power in the wheel A, is in a ratio of
* V ° to the velocity of the pevet g ; confequently its
velocity to that of the pevet h, is 1 / ° x 9—=:z ° 7_3 6 ° .
So that T?T‘T^ of 13,250 pound the quantity of
weight deemed equal to the friction originally in the
pevets / or a power E fomewhat more than 2 ounces,
will be lufficient to overcome the fridion in the
pevets h.

Thus it is evident, that, by the application of addi-
tional wheels, or by enlarging the diameters of
thefe, the refiftance from fridion may be reduced
to lefs than the refiftance of the medium the wheel
paffes through.

The whole weight which centers in the axis of the
wheel A, being equally divided on the pevets f and
further fubdivided on 32 pevets h3 the weight on
each of thefe pevets, being but _V of the weight on
each of the pevets/, does not require more than of
its ftrength. And as the quantity of fridion in each
of the pevets h is in proportion to the weight or pref-
iure it bears, tne fum of the feveral quantities of fric-
tion in the 32 pevets h3 is equal to the quantity of
fridion that was originally in the 2 pevets f in pro-
portion to their velocities.

1 here is alio lome additional fridion in the pevets h3
on account of the weight of the wheels G and H; but,
with refped to the power in the wheel A, it is not of
confequence'to require a calculation.

There is no engine for railing heavy weights, that
lias lefs fridion than the axis in peritrochio. If the
fame weight were to be raifed by 2 wheels, one mul-

X 2 tiplying

f

L !58 ]

tiplying the other ; the power in the fir ft wheel, being
in a ratio of *■ to the weight to be raifed, and -f- to
the fridlion in its pevets j and the power of the fe-
cond wheel in a ratio of ± to the weight, and t to
the fridlion in its pevets j which powers are the lame
as in the wheel A, viz. 2_° with refpedt to the weight,
and with refpedt to the fridlion ; although the
powers required to counterballance the weight on the
axis, are equal in each ; yet it would require a power
above 733 pound to overcome the rehftance from
fridlion in this engine, which is nearly treble the
power required to overcome the fridlion in the wheel
A, on account of four pevets rubbing on a dead
furface in one, and hut two pevets in the other.

By reducing the fridlion in the pevets of this en-
gine, in the fame manner as in the pevets of the
wheel A, the power 733 pound, which is required
meerly on account of fridlion, may be applied to
raife an additional weight of 14,650 pound, without
any diminution in point of time, or velocity, with
refpedl to the weight to be raifed 5 which at firfl view
may feem contrary to the general principle, that
whatever power is gained mechanically over weight,
is loft equally in point of time, and velocity ; and is
fo in reality, with refpedt to pradtical mechanifm ;
For the faving a power, otherwife, hitherto, found
neceffary to overcome the refinance from fridlion,
and applying it to the ufeful purpofe of railing a
greater quantity of weight, in equal time, is, in ef-
fedt, equal to an acquifition of fo much power.

If thefe wheels are made with tolerable exadtnefs,
and placed, as in the drawing, on a line oppofite to the
point of preffure of the pevets they lupport, the

preffure

[ r59 ]

preffure will be equal on each wheel ; and the greater
the preffure, the more fecurely they are kept in their
proper places. I have a double fet of brafs wheels,
8 inches diameter, with which I have made feveral
experiments, and find the pradice anfwer as near as
poffible to the theory. But as the expence of brafs
wheels, to large engines, would be very confiderable,
had wheels made of wood, which I find to anfwer
tne purpofe as well, if not better ; as they are much
lighter , and may be made ffrong enough to fupport
a great weight, at a moderate expence.

The wooden wheels are fixed on an arbour, whofe
pevets have been turned true, and the edge of the
wheel turned after it is fixed on the arbour. Thefe
v/heels are placed in a wooden frame, with a fmall
plate of brafs fixed properly in the frame, for the
pevets to turn in. They may be made with fpokes,
and fellies, capable of fuftaining a confiderable weight;
and there is no danger of their wearing, as the pevet
only rolls on the edge. I had wheels made of white
deal, with feveral lamina glewed together, eroding
each other in different diredions of the grain of the
wood, which hinders them from warping, or crack-
ing ; and which I found, upon trial, anfwered ex-
tremely well. By eroding the grain of the wood,
the oppofition to the preffure on the periphery is pret-
ty equal in all parts; and the edge of the wheel, in a
little time, becomes as fmooth, and almoff as hard as
brafs.

Thefe wheels cannot be applied to wheel carriages,
unlefs they were to move on very even ground, as
fudden jerks, and turnings, would foon diforder
them. But they may certainly be employed to ad-

1 vantage

&>

[ !5° ]

vantage in all fixed engines, that are loaded with
heavy weights ; efpecially when the power that ope-
rates is expensive, as men, horles, fire, &c. And in
finer kind of engines, where it may be neceflary
to avoid any obdrudion from fridion as much as pol-
fibie, the double, or treble wheels, where there is fuf-
ficient room, will reduce the quantity to any degree
that can well be required.

Another advantage alfo arifes from the application
of thefe kind of wheels, that, if the motion is requir-
ed to be extremely fwift, though the pevets be as
imall as the weight they fuftain can allow of, yet
they fcarce ever wear the holes they turn in ; for the
lad pevets in a treble fet of wheels, which are the
only ones that rub on a dead furface, will hardly
make one revolution in two days.

There are feveral engines to which thefe wheels
might be applied to advantage, even where the aid-
ing power coifs nothing ; as watermills, where water
is not always to be had plenty, which, by this means,
would grind with much lefs water. Windmills, par-
ticularly, muff receive great benefit from them ; the
fhaft being fo large, the quantity of fridion, which
is in proportion to the part rubbing on a dead furface,
mud be greater in this, than mod other engines ; be-
fides, the rubbing part being wood, mud did in-
creafe the quantity: I Ihould therefore imagine, that,
if the draft were placed on wheels 5, or 6 feet dia-
meter, it would not require above half the drength
of wind, necelfary at prefent. The frame in which
thefe wheels might be placed, could eafily be made
in luch a manner, as to be lowered, or railed ; fo
that if any inconvenience were found from too great

velocity

[ r5* ]

velocity, when the wind increafed, the fhaft mio-ht
then be let to turn in the ufual manner. But there
would be no danger of the fhaft taking fire by any
degree of velocity, whilft it turned on thefe wheels,
as it would not then rub at all.

There have been many ingenious attempts, and
fome confiderable improvements made, with refpedt
to the having of fuel necefiary to work a fire engine,
which is an article of great expence : but I do not
find the diminution of fridlion has been confidered
as any ways material in this point, although it muff
necellarily 1 educe the quantity of fuel in proportion.

The power of a fire engine is eftimated by the di-
ameter of the cylinder and pifton ; on which the at-
mofphere prefies, when there is a vacuum made by
the condenfation of the fleam with which the cylin-
der has been filled. This power, or preffure, is
deemed equal to 15 pound per inch fquare on ame-
oium : but I fhould imagine, that the fleam, with
which the cylinder is filled, being water expanded
into 4000 times its bulk by the adlion of fire, when
reduced to its original ftate by a flrong injedlion of
cold water dafhing againft the bottom of the pifton,
and mixing with it, muft occupy fuch a fpace in the
cylinder, as to hinder a perfedt vacuum, which ap-
pears, in fome meafure, from the effedts ; for the
power of the atmofphere on a fire-engine is feldom
found to raife 7 pound per inch, and it can hardly
require 8 pound per inch to overcome the fridlion of
the feveral parts of the engine, and alfo to give a
proper degree of velocity to the leaver.

The fridlion of the piflon moving up and down in
the cylinder, and of the forcers or working rods, is

in

[ i62 ]

in proportion to the diameter of the cylinders they
work in. That of the plug frame, which is a piece
of timber moved by the leaver through a wooden
groove, by which the fleam valve, and injection cock
are opened and fhut alternately, is pretty considera-
ble; but the quantity proceeding from the feveral
parts cannot be eftimated with any tolerable degree
of precifion.

The whole weight to be raifed, as alfo the fuperi-
or power by which it is raifed, center in the pevets
of the axis of the great leaver, and the quantity of
fri&ion in the pevets, may be deemed equal to half
fo much weight hanging on them.

In order to form fome eflimate of the quantity of
weight with which the axis of the leaver of a fire-
engine is loaded, I took the dimenfions of the feve-
ral parts of that at the York-Buildings water-works j
the leaver of which is 27 feet long, 2 feet 6 inches
by 2 feet 2 inches in the middle, and 2 feet by 22
inches at the ends. The weight of which, with the
archeads, chain, rods, and working frame hanging
at one end, and the pifton and chain at the other,
may be computed at 6 tons, or 12,000 pound. The
cylinder is' 45 inches diameter, about 1591 fquare
inches ; which, at 15 pound per inch prefiure of the
atmofphere, is 22,274 pound. The pillar of water
to be raifed is 10,060 pound, which is not 6 4 pound
per inch ; fo that the remainder of the power is em-
ployed in overcoming the refiftance from fridhon in
,the feveral parts of the engine, and giving the leaver
a degree of velocity equal to 120 feet per minute,
•which it moved in common work.

The

[ I53 ]

The weight of the power, or predure, of the at-
mofphere taken at 14 pound per inch fquare,
,22,274 pound, with the pillar of water 10,060
v pound, and alfo of the leaver, See. 12,000 pound;
amounting in the whole to about 22 tons, center in
the axis of the leaver. The quantity of friction re-
fulting from this weight, fuppofed equal to half, or
1 1 tons, hanging on the pevets 6 inches diameter,
the leaver being 27 feet long, requires a power at ei-
ther end — 425 pound to overcome its refinance in
the leaf! degree, and muft dill require a further
power to overcome the fridion of the other parts of
the engine, and give the leaver a degree of velocity
= 120 feet per minute.

Before I give an account of the method I took to
reduce the quantity of fridion in the pevets, it may
be proper to mention a general error in the manner
of placing the axis of the leaver under the beam.
A ballance, having its center of motion underneath,
and equal weights at each end, being placed horizon-
tally, will remain in that pofition ; as both weights
are equidiftant from the center of gravity, which is
perpendicular to the center of motion ; but when it
is made to incline to either fide, it will continue to
move on that fide, untill it becomes parallel to the
horizon, with the center of motion above the bal-
lance : for when either end is depreffed in the lead
degree, as in fig. 3, it becomes more didant from
the center of gravity; and the oppofite end which is
raifed in proportion, is brought nearer to it, although
both ends dill continue equididant from the center
of motion.

Y Fig.

Vol. LIII.

' [ *54 J

Fig. 3. The lever A of this engine is 2 feet 9
inches from the upper part of the beam, to the cen-
ter ot it's axis B placed underneath; and weighs,
with it’s arch- heads, about 5 tons. When it was placed
in a horizontal pofition, it required but 93 4 pound-
to overcome the refiftance from fridtion in the pevets;-
but when either end was deprefled 4 feet below the
level, at which diftance the fprings are fixed, it re-
quired 534 pound to be applied to the oppofite end
to bring it back again : fo that a power =440.1 was
required, on account of the center of gravity being*

10 much changed by the pofition of the axis under-
neath.

Fig. 4. To avoid this general error, I had the axis
B placed on the upper fide of the leaver, and fixed
by proper bolts and fcrews to a bar of iron equally
ftrong, placed underneath : and, in order to reduce
the quantity of fridtion, which is in proportion to the-
fpace rubbing on a dead furface in equal time, I had
them made in the form b B, fig. 4, by which they
are equally ftrong, though the rubbing part b , is but

1 1 diameter ; fo that by changing only the form of

the pevets, the fridtion is reduced to 4 of it’s origi-
nal quantity. I applied two quadrants, D D, to each
of thefe pevets, whofe radii are 2 feet 6 inches, by
which the whole fridtion of the pevets b of the axis
of the leaver, are transferred to the pevets d of the
quadrants, which are 14 inch diameter. Thefe qua-
drants are equal in effedt to wheels 5 feet diameter;
the radius of which is 4 0 to the femidiameter of its pe-
vet, and reduce the fridtion in the pevets of the qua-
drants to _^-’h part of w'hat it was in the pevets b of the
axis; which x by 4 the reduction made by changing
the form of the pevets by which means the

fridtion

[ >55 ]

fridtion that was in the pevets B, fig. 3. of the great
axis, which was — 425 pound, is reduced to
or fomewhat lefs than 2 4 pound.

Upon trial, the leaver, that before required a power
of 95 pound to overcome the leaf! refiftance from
fridtion, was as eafily effected by the application of
4 pound ; and the refiftance from fridtion occafioned
by a weight of 6 tons is of fo little confequence,
that the leaver may he fwung with a flight thread,
and will continue in a ftate of vibration for feveral mi-
nutes after.

The original quantity of fridtion in the pevets B
of the leaver A, fig, 3. which, when loaded with it’s
full weight 22 tons, required a power = 425 pound
to overcome it’s refiftance, is by this method reduced
to 2 pound 10 ounces j and, if there were any need
of reducing it further, it might be done by applying
two fmall quadrants to each pevet of the larger,
which would reduce it to one ounce or lefs.

It is not eafy to determine the quantity of friction
that was in the plug frame, but that has alfo been
reduced to by the application of feveral rollers 5
inches diameter, whofe pevets are 4 inch diameter,
on which it now moves. But it is evident that a
power 440 4 has been faved by changing the
pofition of the axis of the leaver ; and a power of
42 1 pound 6 ounces by reducing the quantity of
fridtion in the pevets.

The vifible effedt, with refpedt to the working of
the engine, according to the moft exadt obferva-
tions by different perfons, both before, and after
thefe feveral alterations were made, is, that it
now makes 1 3 ftrokes at 8 feet per ftroke, for 1 5

Y 2 that

that it ever made, with the fame, or rather a fmaller
quantity of fuel; and muff therefore difcharge 4
more water in equal time ; which confequently faves
4 of the fuel. But the effedt is found ftill greater,
as to fupplying the tenants with water ; for the en-
gine performs the fame fervice better now in 5 hours,
than ever it did before in fix : which can only be
accounted for, by the extraordinary regularity of its
ffroke, which does not abate of it’s full length fud-
denly, as it ufed to do, when the ftrength of the
fire abated : this I take to be occafioned in a great
meafure, from placing the axis above the leaver, by
which the center of gravity becomes reverfed to
what it was before ; fo that it requires the fame
power to keep the end of the leaver depreffed as low
as the fprings, that it required before to bring it back,
when fo much depreffed ; which is a particular be-
nefit ; for the ffop, or fett, generally in large engines,
when the ends of the leaver come to the fprings, is
a defedt that has been endeavoured to be remedied
in fome degree, by the help of the fprings. But
when the axis is placed above the leaver, and the
fridtion reduced, as in fig. 4, if one end is brought
down to the fprings, and let to return, it carries the
other end down to the fprings without any affiftance,
and will continue to do fo feveral times, abating
fomewhat of the length of the ffroke, each time.

This engine, from feveral improvements that have
been made in the boyler, confumes but 4 bufhels of
coals in an hour; which is deemed 4 lefs than others
of equal bignefs ; and it performs the fame work
now in 20 hours, that it did before in 24 hours, it
is a faving, in effedt, of 16 bufhels in 24 hours, a-
4 mounting

[ i57 3

mounting to 162 chaldrons in a year’s conftant work;
which is a very confiderable article, even where coals
are to be had at a cheap price.

It may be proper to obferve that the archeads C
of the leaver, muft be drawn from the center of the
fmall part b of the pevet, which turns on the qua-
drants. The quadrants and frame muft be made
fufficiently ftrong, which I had made of caft iron.
The pevets of the quadrants are made of tempered
fteel, and turned true. There are four pillars G in
the back plate of the frame, with fhoulders, and
ftrong fcrews, which pafs through the fore plate, and
are fcrewed tight by a nut z, when the quadrants are
placed in the frame.

The back plate E (fig. 4.) of the frame, is longer
than the fore plate F, in order to admit the iron bolts
G at each end ; by which the frame is fcrewed to a
wooden block. The edges of the frame reft on a
broad plate of iron, laid on a level board; upon
which the blocks and frames are placed, and bolted
down in the ufual manner. The holes that the pe-
vets of the quadrants turn in, are made in fquare
pieces of brafs e, riveted for the purpofe into the frame
plates.

The round part b , of the axis B, fig. 4, is made
of hardened fteel, and the edges g of the quadrants
are alfo of the fame metal ; otherwife the very great
weight they fuftain, would make a deep impreftion
in that part. There are two fprings, h h> to each qua-
drant, which keep them in their proper places, and
yield eafily to the motion of the quadrants.

There was great care taken to make the frame
fquare, and place the quadrants upright and level ;

and

[ ^ ]

and alfo to place the leaver exa&ly in the center. By
-which means there has been no alteration required
fince they were firfi: fixed j and the engine continues
to work as even, and true as it is pofiible.

I have applied wheels for reducing fridtion to fome
other engines with great advantage, which I fhall
take the liberty of laying before the Royal Society
fome other time ; and fear I have trefpafied too much
on their patience already by this long detail.

XXIX. The Difference of Longitude between
the Royal Obfervatories of Greenwich and
Paris, determined by the Obfervatio?is of
the Tr unfits of Mercury over the Sun in the
Tears 1723, 1736, 1743, and 1753 : By
James Short, M. A. F. R. S.

Read June 2, y T will, no doubt, appear furprizing,
1763- y that [ fhould attempt to determine the
difference cf longitude between two of the moil ce-
lebrated obfervatories in Europe ; and in which fome
of the greateft aftronomers, that ever lived, have,
for above eighty years, been conftantly obferving
the motions of the heavenly bodies : yet it is moil:
certain, that, to this day, we are ignorant of the Paid
difference of longitude : the Englifh aftronomers
reckoning it to be = t)r 2o//, and the French let-
ting it down at y' io//, which, they tell us, wras

found

C !59 ]

found by M. Caflini, by obfervations of the eclipfes
of Jupiter’s firft fatellite made by him, whilft in Lon-
don in the year 1698 : we are no where told, that
I know of, by what obfervations the Englifh aftro-
nomers have fixed this difference at g' 20" .

In the Memoirs of the Royal Academy of Sciences
at Paris, for the year 1734, there is an account given
of thirty-three correfponding obfervations of the
eclipfes of the firft fatellite of Jupiter, made at
Greenwich and Paris, from the year 1 677, to the
year 1701 : The mean of thefe thirty-three obfer-
vations gives the difference of longitude between Pa-
ris and Greenwich = g' 2g" .

I had lately the honor to deliver to this Society, a
paper concerning the parallax of the Sun, determin-
ed by the obfervations of the late tranfit of Venus :
Jn that paper I took notice that obfervations of the
tranfits of Venus and Mercury over the Sun, have al-
ways been looked upon by aftronomers, as very pro-
per for determining the differences of longitudes be-
tween the places where fuch obfervations have been
made. I have calculated, and it may be demonftrat-
ed, that, if we compare the obfervations of the late
tranfit of Venus made at Greenwich, and by M. de^
la Lande at Paris, and fuppofe that the difference of
longitude between thefe two places is — g' 25' , it
will follow that the Sun and Venus are at an infinite
diftance, which is abfurd. Again, if we fuppofe the
difference to be greater, it will follow, that the Sun
and Venus are more than infinitely diftant, which is
likewife abfurd. We are therefore certain, if thefe
obfervations are to be depended on, that the differ-
ence of longitude between Greenwich and Paris is

lefs

[ i6o ]

lefs than 9' 25". If we compare the obfervations
made at Savile-houfe with the fame obfervation by
M. de la Lande at Paris, and reafon in the fame
manner, we fhall find that the difference of longi-
tude between Greenwich and Paris muff be lefs than
9/33/- Thus far, therefore, a limit, oneway, is
fixed for the difference of longitude between thefe
two places.

The late tranfit of Venus was the only one which
had ever been obferved at Greenwich and Paris, and
by comparing the obfervation at Greenwich, with
that made by M. de la Lande at Paris, the difference
of longitude comes out — g' and if we compare
the obfervations at Savile-houfe (3c/7 of time weft of
Greenwich) with that of M. de la Lande *, the faid
difference of longitude comes out = 9' 16". Since,
therefore, we have only this one tranfit of Venus,
by which we can determine this difference of lon-
gitude, we mu ft have recourfe to the tranfits of Mer-
cury, of which there have been four fince the year
1723, obferved at London, at Greenwich and at

* M. de la Lande faw the internal contact

nus with the Sun’s limb

Pere Clouet

M. Meffier »

M. Ferner — —

M. de la Caille

M. Maraldi -

Since, therefore, the obfervations of meflieurs Maraldi and de

la Caille differ fo much from the obfervations of the firft four
gentlemen (who agree very nearly together) it is plain that they
ought to be rejected ; and indeed M. de la Caille fays, in a letter
to Dr. Bevis, that the telefcope he obferved with was a bad
one, and confequently his obfervation not to be depended on :
M. de la Lande fays the lame in a letter to Mr. Mafkelyne, read
at the Royal Society.

Paris.

[ i6i ]

Paris. I have, therefore, extracted from the Philo*
fophical Tranfadions, and the Memoirs of the Roy-
al Academy at Paris, the feveral obfervations of the
four tranfits of Mercury over the Sun in the years

J723> j736> 743» and 1 753 -

The obfervations in the year 1723, were made by
Dr. Halley at Greenwich, by Dr. Bradley at Wan-
ted, and by Mr. George Graham at London, by
meffieurs Caffini, Maraldi, and De L’ifle at Paris.
Thofe in the year 1736, were made by Dr. Bevis at
Greenwich, and by meffieurs Caffini and Maraldi at
Paris. Thofe in the year 1743, were made by mef*
lieurs Caffini, Maraldi, Le Monnier and de la Caille
at Paris, and by Dr. Bevis and myfelf at Mr. Gra-
ham’s houfe in Fleet-ftreet, London. Thofe in the
year 1753 were made by meffieurs Caffini, Bouguer,
de L ille, Merville, Libour, le Gentil, and de la
Lande at Paris, and by Dr. Bevis and myfelf in Sur-
ry-ftreet, London.

By means of thefe obfervations, I have got no lefs
than 63 determinations of the difference of longitude
between the royal obfervatories of Greenwich and
I aris, and having corrected them by parallax, they
are as follows.

Vol. Lin.

z

1723 By

[ *2 ]

*723-

By the internal contadl at ingrefs obferved by Dr.

Halley.

/ //

. Caffini

= 9 23

de L’ifle

—914

de L’ifle

= 9 14

Maraldi

— 9 23

Dr. Bradley.

de L’ifle

= 9 12

Caffini

= 9 21

Maraldi

de L’ifle

— 912

Mr. Graham.

de L’ifle

— 8 56

_____ n r

Maraldi

— 9 3

de L’ifle

— 8 56

12

IIO 22

9

/>

12

I736:

By the external contact at egrefs obferved by Dr.
BCTis. , „

M. Maraldi — — — — 9 37

Caffini, jun. ■ ■ = 9 44

Caffini, fen, — — — — 9 14

31 28 35

/ //
9 3f

1743. By ■

[ i63 ]

i743-

By the internal contad at egrefs obferved by Dr.
Bevis.

M. de la Caille — :

Maraldi -

Le Monnier
Caffini, fen.
Caffini, jun.

/ n

— 94,
= 9 l8>
= 8 53>

— 9 33»
= 9 2 7,

5

5

5

S

5

46 17. 5

/ //

9

1743.

By the external contad at egrefs obferved by Dr.
Bevis.

M. de la Caille — — 916,

Maraldi — 9 36,

Le Monnier — ~ 9 23,

Caffini, len. = 9 20,

Caffini, jun. — = 9 42,

5

5

5

5

5

5147 *9. 519 27, 9

. J743*

By the internal contad at egrefs obferved by my
felf. /

M. de la Caille — 8 57, 5

Maraldi . — 9 11, 5

Le Monnier = 8 46, 5

Caffini, fen. = 9 26, 5

Caffini, jun. — = 9 20, 5

51 45 42> 5

£

Z 2

2743. By

I743*

By the external contadt at egrefs obferved by my
felf.

M. de la Caille

IVlaraldi ■

//

Le Monnier
Caffini, fen.
Caffini, jun.

= 9 1 8, 5

= 9 38> 5
= 9 2J. 5
= 9 22, 5

= 9 44. 5

47 29, 519 29. 9

//

1 7 5 3 1

By the internal contadt at egrefs obferved by Dr.
Bevis.

M. Caffini — —— — — -

Bouguer —
de L’ille —

Merville

Libour

Le Gentil -
de la Lande

/

9

9

9

9

9

9

9

//

25>

6,

5>

1,

o,

9>

3>

5

5

5

5

5

5

5

71 63 52» 5

//

7>

r753<

By the external contadt at egrefs obferved by Dra.
Bevis.

M. Caffini =

Bouguer.
de Lille -
Merville
Libour -

26,

Le Gentil -
de la Lande

/

9

8 57>
7>
*9>

3°>

26,

25>

9

9

9

9

9

5

5

5

5

5

5

5

C 165 ]

*753-

By the internal contact at egrefs obferved by my
felf.

M. Caffini = 9 18,

Bouguer = 8 59,

de L’ifle 8 58,

Merville — ■ — 8 54,

Libour = 8 53,

Le Gentil = 9 2,

de la Lande — 8 56,

5

5

5

5

5

5

5

71 63 3> 5

//

T753-

By the external contadt at egrefs obferved by my
felf.

M. Caffini » — — - ... 9 22,

Bouguer — ...... — 8 53,

de L’ifle ■ ■ ■■■.»■■ — 9 3,

Merville — - ■ . — 9

Libour — — . 9

Le Gentil ■— — ... ■ = 9

de la Lande

*5»

26,

22,

= 9 21.

5

5

5

5

5

5

5

64 45> J

/ //

9 1

The mean of the above 10 means is -
The mean of the above 63 refults of'
the difference of longitude between r

Greenwich and Paris is — .

v -

= 9 15

7

The

[ 166 ]

The mean of 43 refults which differ
not more than 1 5" from the mean
of the whole is

The mean of 19 refults which differ
lefs than 1 5 ', and more than S' *
from the mean of the whole, is — .

The mean of 24 refults which differ 1
lefs than 8" from the mean of the >
whole is — J

/ //
9 16

= 9 r4>

= 9 r7> 5

The mean of the above 5 means is = 9 15,8

And even the mean of thofe 20 refults which dif-
fer more than 1 5" from the mean of the whole,
and which are rejected, gives the faid difference
— 9' 1 2//-i, which differing only from the 43
refults, is a proof of the great accuracy in the deter-
mination of the differences of longitudes by obferva-
tions of the tranfit of Mercury over the Sun.

Let us now examine the limit of the errors in thefe
10 feveral fets of determinations, and we (hall find
that the limit of the errors in the year

1723 is = 27 by the internal contadt at ingrefs.

1736 is — 30 by the external contact at egrefs.

1743 is — 40 * by the internal contact at egrefs.

1743 is — 26 by the external contact at egrefs.

I753 isr=z25by the internal contadt at egrefs.

1753 is = 33 by the external contadt at egrefs.

* If we reje<ft the obfervations of M. le Monnier, in which
there feems to be fome miftake, becaufe it differs confiderably
from the reft, the limit of the error will be rz 29", agreeing
nearly with the other limits.

From

[ l67 ]

From hence we may fafely conclude that the dif-
ference of longitude between any two places may be
determined by one fingle obfervation of the contact
of Mercury with the Sun’s limb, made at each place,
i'o that the error in the determination will not exceed
30" of time from the truth: whereas in the above
33 obfervations of the eclipfes of the firft fatellite of
Jupiter we find the limit between the errors to a-
mount to 3' 44" of time. If we take a mean of the
faid obfervations of the firft fatellite, the difference of
longitude between Greenwich and Paris is — g' 2g" ,
and if we rejebt thofe which differ the moft from the
reft, the mean of the remaining 25 obfervations gives
the faid difference — g' 40'', and the mean of thofe
8 obfervations, which are reje&ed, gives the faid dif-
ference = 8' 53", both which laft determinations can
be proved to be very far from the truth by the obfer-
vations of the late tranfit of Venus ; for by the faid
obfervations of Venus it appears that the difference
of longitude between Greenwich and Paris cannot
exceed g' 33", as I faid before; and if the faid dif-
ference is — 8/53//, then the parallax of the Sun,
by the Savile-houle obfervation compared with that
of M. de la Lande at Paris, would amount to 20 "
which we are fure it cannot be.

Upon the whole therefore we may cnnclude, that
the difference of longitude between the royal obfer-
vatories of Greenwich and Paris (as determined by
63 obfervations of the contaft of Mercury with the
Sun’s limb made at each place) is— g’ i6//-. This de-
termination would have been perhaps more decifive,
if I could have had recourfe to the books containing
the obfervations of the late aftronomer royal, Dr.

Bradley,.

[ ,68 ]

Bradley. Obfervations ! made by one of the greated
adronomers, and by the bed; and mod: accurate ob-
ferver, abided by the bed and mod accurate indru-
ments, which are in any obfervatory : But alas ! the
public are hitherto deprived of the ufe of thefe mod
excellent obfervations*.

In a former paper which I had the honor to give
into the Royal Society, concerning the parallax of
the Sun, I therein aliumed the difference of longi-
tude between Greenwich and Paris to be ~g' 10" ;
and as the determination of this difference is now
more certain by the trandts of Mercury above men-
tioned, being found — g' 16" ; and as this difference
of longitude will make fome fmall difference in the
refult of the faid parallax from the obfervations made
at all thofe places -f-, which are to the ead of Green-
wich, where the late trandt of Venus was obferved:
I have therefore computed them again, and they are
as in the following fynoptic table.

* On Thurfday following, being the 9th of June, a motion
•was made, at the meeting of the Royal Society, by the Rev.
Nevil Mafkelyne, F. R. S. and unanimoufly agreed to, recom-
mending it to their Council, as vifitors of the Royal Obfervatory,
to take proper meafures for obtaining and fecuring the aftrono-
mical obfervations, that have been made there in times paft, for
the benefit of the publick : It was alfo agreed on to publifh them,
when obtained, at the expence of the Society ; and for the fu-
ture, to publifh the obfervations made at the Royal Obfervatory
annually, in the Philofophical Tranfadlions.

f Becaufe the longitudes of all thofe places were taken from
the Connoijfance des Temps ^ and the' Swedtjb in which then-
differences of longitude from Paris are marked down.

4

The

[ i6g ]

The time of the internal contafl of Venus with
the bun s limb obferved at the Cape of Good Hope
compared with that at r

Sun’s Parallax.

Greenwich

8,

Shirburn-Caftle — = 8,

= 8,
= 8,
= 8,
= 8,
— 8,
== 8,
= 8,
= 8,
= 8,
= 8,
= 8,
= 8,
= 8,

Savile-Houfe
Leskeard

Paris

Bologna -
Rome
Drontheim
Upfal
Stockolm
Hernofand
Calmar —

Abo

Tornea —

Cajaneburg

42

I5

57

69

54

54

74

33

60

59

78

97

68

°9

43

By the mean of thefe 1 4 refults, the Sun’s i

parallax on the day of the tranfit 1

And if we rejed: the 2d, nth, 12th,
and 14th, which differ the mod: from
the red, the mean of the remaining

eleven gives the Sun’s parallax

Therefore the mean horizontal parallax 1
of the Sun is ... - - , j

3

4

5

6

7

8

9

10

1 1

12

13

14

*5

= 8, 54

8, 56

8, 69

A a

Vol. LIII.

XXX. An

C I7° ]

XXX. An Account of a remarkable Fifh,
taken in King- Road, near Briftol : In a
Letter from Mr. James Fergufon, to
Thomas Birch, D. D. Secret. R. S.

Reverend Sir, Bdllol, May 5th .763.

Read June 2d, T Herewith take the liberty of fending
*763* you a drawing of a very uncommon

kind of fifh [Tab. XIII.] which was lately caught
in King -Road, a few miles from this city ; and is
now fhewn at the Hot- Wells. It fought violently
a^ainfi: the fiffier-man’s boat, after they got it in then-
net, and was killed with very great difficulty. No
body here can tell what fiffi it is, only fome fay it is
a Sea Lion j but, to the beft of my remembrance,
it anfwers not to the defeription or figure of the
Sea Lion, that is given in Lord Anion’s voyage. I
took the drawing on the fpot, and do wifh I had had
my Indian Ink and Pencils, by which it might have
been much better {haded j but I hope you’ll excule
the rough nefs of the draught, as it is the fir ft I evei
made with a pen.

The length of the fiffi is four feet nine inches, and
the thicknefa in proportion as in the figure. The
mouth is a foot in width, and of a fquariffi form :
it has three rows of ffiarpfmall teeth, very irregularly
let, and at fome diltance from each other: it has no
tongue, nor narrow gullet, but is all the way down,
as far as one can fee, like a great hollow tube : in the
back of the mouth within, there are two openings

a

S.^{<ffuUJc,

[ *7‘ ]

like nodrils ; and about nine inches below the jaw,
and under thefe openings, are two large knobs, from
which proceed feveral fhort teeth ; a little below
which, on the bread fide, is another knob with fuch
teeth. — On each fide within, and about a foot be-
low the jaws, there are three crofs ribs, fomewhat
refembling the draightbars of a chimney-grate, about
an inch didant from each other ; through which we
fee into a great cavity within the fkin, towards the
bread; and under the fkin, thefe cavities are kept
didended by longitudinal ribs, plain to the touch on
the* outdde. I put my arm down through the
mouth, quite to my fhoulder, but could feel nothing
in the way ; fo that its heart, domach, and bowels
mud lie in a very little compafs near its tail, the
body thereabout being very fmall.

From the neck proceed two long horns, hard and
very eladic, not jointed by rings as in lobders : and
on each fide of the back there are two confiderable
fharp edged rifings, of a black and long fubdance.
Between each eye and the bread, there is a cavity
fomewhat like the infide of a human ear; but it doth
not penetrate to the infide. From each fhoulder
proceeds a drong mufcular dn, clofe by which, to-
wards the bread, is an opening, through which one
may thrud his hand and arm quite up through the
mouth: and between thefe fins proceed from the
bread two fhort paws, fomewhat like the fore half
of a human foot, with five toes joined together,
having the appearance of nails. Near the tail are
two large fins, one on the back, the other under the
belly. The fkin is of a dark brown colour, but
darker fpotted in feveral places, and entirely with-
out fcales.

A a 2

If

C 172 ]

If you think this any way deferves the notice of
the Royal Society, I fhall be very glad of your com-
municating it and am, with the greatefl efteem,

Reverend Sir,

Your mod: obliged humble Servant,

James Fergufon.

The fhh was kept in the pofition it is drawn, by
two cords one of which was hooked into its
upper jaw, and the other tied round it near the
tail : the other ends of the cords being tied to a
flick above.

XXXI. Rules

S'

, /«. Uftdtjc.

V ^

[ *73 ]

XXXI. Rules and Examples for limiting the
Cafes in which the Rays of refraSted Eight
may be reunited into a colourlefs Pencil : In
a Eetter from P. Murdoch, M. A. and
F.R.S. to Robert Symmer, Efq\ ERA.
Jan. 3, 1763.

Read June 2, j i. T ET SO, a fmall pencil of the
I763‘ J j folar light, pafs through the re-

fracting medium ABCD [Tab. XIV. Fig. J.] whofe
oppolite furfaces, reprefented by AB, CD, are paral-
lel planes : then the violet rays OV, will, in the
fecond refraCtion into the air, emerge parallel to the
red ; for both will be parallel to the incident ray S O,
and confequently to each other: that is, Vnu will be
parallel to R r, as is plain from the common prin-
ciples of Optics.

2. If the light after its emergence is received on a
fcreen placed any where beyond RV, it will be tinged
with violet on the fide V*u, and with red towards Rr:
and if the incident pencil SO is exceeding fmall, all
the intermediate colours will be feen in the fame or-
der as when light is refradted by a prifm.

But if the incident pencil is not very fmall j or if
the luminous body from which the rays are tranf-
mitted through a fmall opening at O, has a confide-
rable breadth, like that of the Sun’s difk; then lo
many rays of every kind will mix towards the mid-
dle of the fpedrum as to produce a pure white ; but
at the extremities V v and R r, it will ftill be ting

C 174 ]

cd with violet and red : for a violet ray from the up-
permost point ot the Sun’s difk will be more refract-
ed than the other can be ; and a red ray from the
lowed; part of his difk, will be lefs refraCted than any
other.

; If BC, the diftance of the refra&ing furfaces,
is increaled or diminished ; R V, the diftance of the
extreme rays, will be increafed or diminished in the
fame proportion: and if RV approaches very near
to the aperture O, the colours will become imper-
ceptible.

4. To reunite thefe rays, we may place another
medium of the fame refractive power, and of the
fame thickneSs {be — BC) as in the figure ; fo as the
rays V v, Rr, &c. may enter its Surface c d at the
fame angle as they emerged at from CD, or as SO
entered A B ; and after refraCtion at the point 0 ot
the furface ab, to which they converge, they will be
reunited into os the continuation of SO, in a pencil
every way like the incident pencil SO, excepting that
the lieht will have been fomewhat weakened in its
paftage through the media.

5. Other things remaining, let the thicknefs ot
the fecond medium be cp> lets than cb or CB, the
furface parallel to cd being pe-, and the emergent rays
utr will be indeed parallel to the incident as formerly,
but the fpedtrum will fall below the place of the
lcrcen where SO or os would fall. It will like wife
be coloured, as the rays were not yet united at the
point 0. If the thicknefs be greater than cb^ the
ipeCtrum will fall above the line SO os , and the violet
and red, after their interfeClion in 0 , will have chang-
ed Sides.

6 Other

[ *75 ]

6. Other things remaining, fuppofe the refractive
power of the medium ac to be increafed, making
the extreme rays to interfeCt before they reach the
furface ab ; in that cafe, let the medium be turned
round upon an axis perpendicular to the plane of re-
fraction (reprefented by the plane of the figure) in
the order of the letters a> b , c , fo that the angle of
incidence of the rays V v, Rr, the line vr, and the
angle v or may be continually decreafing till the in-
terleClion o falls into the fide ab ; and the rays will
emerge colourlefs and parallel to the incident pencil
SO ; above, or below, or in the line SO or, accord-
ing to the afiumed place of the axis of revolution.

If, on the contrary, the refraCtive power of the
medium ac be diminished, and, with it, the angle of
convergence of the extreme rays ; the point where
they would interfeCt falling beyond the furface ab-,
the medium muft then revolve the contrary way, in
the order c, b, a ; to bring the point of interfeCtion
to the furface ab. But if the refraCtive power be fo
finall that even when cd becomes almoft coincident
with V v, the point of interfeCtion falls ftill beyond
ba , in that cafe the rays cannot be made to emerge
colourlefs, otherwife than by encreafing the depth of
the medium till its furface pafifes through the point of
interfeCtion. And in like manner, when the refrac-
tive power of the fecond medium ac is greater than
that of A C, making the rays to meet within the me-
dium, as at q a point in the lin ope> we may, in-
ftead of turning the medium round on an axis, cut
off the part pat leaving the furface pe parallel to cd-,
and the emergent light will be colourlefs.

From

[ !76 ]

From thefe few principles we may determine the
phenomena of light tranfmitted through parallelepi-
pids that are contiguous to the air, their pofition and
refractive powers being given. Or we may difpofe
them fo that the emergent light fhall, or fhall not, be
tinged with colours.

And we already fee (what (hall be more diftin&ly
explained below) that if light be tranfmitted through
whatever number of media (A, B, C, &c.) all the re-
fractions may be corrected by the equal and contrary
refraCtions of the fame number of the fame media
7,) fimilar and limilarly lituated to the former;
provided there is a medium Z interpofed between
the two feries, thus; A, B, C, Z, c,h,a ; and that
the rays in their palfage through Z, are parallel to
one another.

7. But to give the rays this parallelifm in their paf-
fage through Z, and to explain the feveral phenome-
na of refraCted light, we fhall need the following

LEMMA, a Problem.

Given (in Fig. 2.) DCB the difference of two an-
gles A CD, ACB, and the ratio of DI the fine of
the greater to B H the line of the lelfer being like-
wile given, to find the angles.

For DF, the line of the given difference, write s ,
and for its coline C F write c ; for the lelfer line B H,
the letter z, and let the given ratio of D I to B H, be
that of m to », the radius C B being unity.

Then, having drawn F G perpendicular to DI;

from the fimilar triangles in this figure, we (hall have

C B

4

[ 1 77 ]

C B : C H :: D F : D G, or i :\J i — -z% :: s : DG =

5 1 — ; and C B : BH :: CF : GI, or i : z :: c :

GI = cz. But (by Hypoth.) DI:BH :: m : n ;

that is D G d- G I, or 5 \J i—z" -V* cz i z :: m \n\
which gives \j i — zz : z, or CH : BH, or i : tang.

n s

ACB :: m — nc : ns\ that is, tang. ACB~- .

In words — multiply the fine of the given difference
by the lead term of the given ratio for a dividend :
from the greater term fubtradt the product of the co-
line of the difference and the leffer term for a divifor ;
and the quotient fhall be the tangent of the leffer an-
gle ACB.

Or, if you prefer a geometrical conftrudlion ; In
the femidiameter C B produced take CM to C B as
D I to BH; and in the tangent to the circle at B,
make BL to BC, as DF to FM, and BCL fhall
be the leffer angle fought.

Or you need only join D M and draw the femidia-
meter C A parallel to it.

8. But before we apply this folution, it may be
proper to give a table of the refra&ive powers of glafs,
water and fpirit of wine, whether contiguous to the
air, or perhaps the fluids contiguous to glafs : thefe
being the fubffances in which experiments may be
moft conveniently made : and it is alfo neceffary to
know the limitations that arife from thofe feveral
powers.

Vol. LIII.

Bb

I. When

[ 178 ]

I.

When light paffes from air into glafs, and the an-
gle of incidence is next to 90°, whofe fine is unity >

The fine of the refradion of the red \ 0 ' " ,

rays = 4° is .6493508 = fin. - -|4 2<? 33,0

And of the violet 44 = . 64 1 0256 = fin. 39 52 6

Whofe difference o 37 27, 6

is the greatefl angle at which the violet and red rays
can diverge in the refradion from air into glafs, want-
ing very little of 37/ir.

And when an unrefraded pencil paffes from glafs
into air, as foon as the angle of incidence exceeds
390 52' 6", the violet rays will begin to be refleded;
and when the incidence exceeds 40° 29' 33", 6 the
rays will be totally refleded.

II.

From Air into Water.

The fine of refradion of the red is I* g ' "

•75I79°5=M 4

Of the violet .7454080 = s. 48 11 39

And the greateft divergence 0 33 5

the angle of beginning refledion from water into air
being 48° 1 1' 39".

III. From

[ *79 ]

III.

From Water into Glafs,
Sin. incid. : s. refr. of the red :: i : j

o / //

59 44 204.

0,863739

Of the violet :: 1 : 0,859966 59 45

The difference of which
is the greateft divergence.

IV.

o 25 354*

From Air into Spirit of Wine

Sin. incid. : s. refr. of the red :: 1 : 1

>1 = s.\

o / //

47 10 20, 2

0,7334001 == S.) '

Of the violet :: 1 : 0,7266366 = s. 46 36 18,6

The difference of which
is the greateft divergence.

o 34 1,6

V.

From Spirit of Wine into Glafs.

Sin. incid. : s. refr. of the red :: 1 : j6°2 /g ^ x

0,8853964 = s. j

Of the violet :: 1 : 0,8821802 = s. 61 54 24

And their difference — — — — 0 23 3^

is the greateft divergence.

B b 2

Thefe

[ i8° ]

Thefe numbers are partly tranfcribed from Sir Ifaac
Newton, and partly computed by a rule of Mr. Eu-
ler in the Philafophical Tranfadtions.

They are indeed carried on to more decimal places
than the experiments hitherto made can well bear:
but it is hoped that hereafter methods may be devif-
ed to meafure the refractions of light to a very great
degree of preciiion.

9. When a {lender pencil SO, is refraCted by the
furface of a denfer medium OT (Fig. 3.) the
extreme rays being OV, the violet, and OR the red;
we have feen that the furface RVT, at which the
rays pafs again into the rarer medium, being parallel
to the fir ft furface OT, the extreme, and all the in-
termediate, rays will emerge parallel to each other,
and to the pencil SO.

But if the laft furface RVT cuts the former in a
line perpendicular to the plane of refradtion at the
point T, on the fide of the radiant point S, then the
extreme rays being refraCted at the points V, R, will
converge to fome point F in the rarer medium : and
if the light be received on a fcreen at F, it will be
colourlefsj if nearer to the refra&ing medium, or
farther from it, it will be tinged, but on different
fides.

Thus if the denfer medium is water, and the fur-
rounding medium is air; the angle of incidence LOS
being 20°, the angle of divergence V O R will be
7' 46". And O VP the angle of incidence at the
fecond refradtion for the violet rays being taken of
30°, the angle of convergence RFY will be 14' 26".

On the contrary, if the plane VR/, (Fig. 4.) which
terminates the denfer medium cuts the firit refradting

plane

[ 181 ]

plane on the other fide of the perpendicular OL, the
rays will diverge from fome point f on the other fide
of the fecond furface : the violet ray O V being more
refraCted from the perpendicular VP, than the red
is from the perpendicular R p.

And it is evident, that if the diftance (OT or Ot)
of the point of incidence from the edge of a prifm,
the angle of incidence LOS, and the angle of the
prifm (OTV or OfV) are given, together with the
refractive powers of the media, the lines OV, OR,
will be given in magnitude and pofition. And thence
the diftance VR being given, with the angles of re-
fraction at the fecond furface, the points, F or /, to
which the rays converge, or from which they diverge,
will be given. And their locus, or the Curve in
which all thefe points are found, may be affigned ;
whether the angle of the prifm is conftant, and the
angle of incidence is variable, or the contrary ; and
whether the rays are refraCted, or, at a certain obli-
quity, come to be reflected by the fecond plane.

io. If it is further required that the extreme, and
all the intermediate, rays which meet at F (in Fig. 3.)
fhould thenceforth remain united in a colourlefs pen-
cil : through the point of convergence F draw (by
the lemma) the line ZX, making the angles ZFR,
ZFV, fuch that their difference RFV being the
given angle of convergence, their fines may be as the
lines of refraCtion of the red and violet rays, when
they pafs from a given denfer medium GKH into the
air, at a common angle of incidence : and H F G
perpendicular to ZX will be the line in which the
furface of that medium mud cut the plane of refrac-
tion, when the rays RF, VF, are refraCted into the

fame

[ 182 3

fame line FN. And if the medium be terminated
on the other fide by any plane KN to which FN is
perpendicular, the pencil N Y, continued in the air,
will remain colourlefs.

For inftance, if the medium GK is glafs, and the
angle RF V is 14' 26", ZFR the angle of incidence
of the red rays will be found of 170 54' 14"; and
the angle of refradtion XFN, common to all the
rays, will be 12° 6' 34'

But if the plane HG, to which ZX is perpendi-
cular, paffes not thro’ the point of reunion F, but on
this or the other lide of it ; the rays in their paffage
thro’ the medium, though parallel to each other,
will be laterally feparated.

11. Let a ray SOL (Fig. 5.) of a mean degree
of refrangibility be refradted by AB the fide of a
glafs prifm ABC, fo that the refradted ray O M may
be perpendicular to the fide of the prifm AC; it is
required to apply to this another prifm of a differently
refradting fubftance, as of water, fo that the ray Mo
being refradted at 0, by the fide DC, the refradted
ray so may be parallel to OS.

The angle of incidence SOP, and the refradtive
power of the glafs being given, the angle SOM,
and its fupplement LOM, are given produce Mo to n\
and becaufe os is to be parallel to LO take for the
difference of the angles in the lemma, the given
angle jios (=LOM), and through the point 0 draw
ropy fo that the fine o i p on may be the fine of posy
as the fine of incidence to that of refradtion, when
a meanly-refrangible ray paffes from water into air y
and D 0 C, perpendicular to rp} will be the pofition
of the fide required.

1

We

C i83 ]

We have here fuppofed the ray SO to be homo-”
geneous, of a mean refrangibility ; but if it is a ray
from the Sun the image at j will be very much tinged.
The colours will have been feparated at O ; a fmall
matter more at M, but they will diverge very confi-
derably at o ; for fetting afide the refractions at O
and M ; that is, fuppofing a pencil Mo to pafs unre-
fraded in water till it falls upon a furface of air at
an angle of incidence of about 47° 32/-i) the diver-
gence of the extreme rays will be about 2° 51 'L.: a
fmall difference of fines anfwering to a confiderable
difference of the angles when they approach to 90°:
the ultimate difference to which they converge, being
(from water into air) 70 26 'JL.

12. Let a pencil of the lolar light SO (Fig. 6.)
fall upon the furface of water B C, the extreme rays
being refraded into OV, OR; it is required to af-
fign the glafs prifm PN« (whofe fedion PN7Z is an
ifofceles triangle) fuch, that the bafe N;z being paral-
lel to SO, and the furface of the water AC being
inclined to the bafe N n in the fame angle as the fur-
face BC; the extreme rays, in their paflage through
the glafs prifm, fhall be parallel ; and all the rays
fhall emerge colourlefs in the line SO os-, that is, in
the incident ray produced thro’ both the media.

The angle SOB, and the refradions from air into
water, being given, the angles VON, RON, and
their difference VOR, are given. Draw therefore,
by the lemma, the line OG, making the fine of ROG
to that of VOG, as the fine of refradion of a red ray,
in paffing from glafs into water, is to the fine of refradion
of a violet ray, their angles of incidence being equal,
and PN perpendicular to OG will be the interfedion

[ j84 ]

of the plane of refraction with the fide of the prifm
that is required.

Thus the angle SOB being 30°, VOR will be
18' 12% VOG=5o° 3 8' 4% ROG==5o° 19' s*”i-
whofe hnes are as the fines of refraction of the violet
and the red, in palling from glafs into water at a
common angle of incidence. And therefore, the an-
gles of the emergence of the rays OV, OR, in pair-
ing from water into glafs will be equal, that is Vv
will in its paflage through the glafs prifm, be parallel
to Rr, and the rays meeting with equal and contra-
ry refractions at the points v, r, 0 , as they fuffered
at V, R, O, will emerge colourlefs at 0.

Yet we muft not be furprized if the pencil os is
not abfolutely pure light (even fuppofmg, the mat-
ter, the figure, and the dilpofition, of the media to
be faultlefs) becaufe (i°) perhaps the refraCtive powers
have not been determined with fufficient exaCtnefs
(20). If the glafs plate which contains the water
be not very thin, the light will have received a flight
tinCture in pafling through it at O : This however
may be remedied by confining the water between two
glafs prifms. And (30) it its fcarce poffible to make
experiments of this kind with a pencil of light fo
flender as the theory prefcribes (fee § 2.)

But proper allowances being made on thefe ac-
counts, and the refraCting planes adjufted as the lem-
ma directs, the light will emerge fufficiently pure to
juftify the theory. And the refractions of either me-
dium being given, it will appear from the experi-
ments whether thofe of the other medium have been
determined with fufficient accuracy.

Obfervc

[ l85 3

Obferve likewife, that as, in practice, we mud fit
the water to the glafs, not the glafs to the water, we
are to begin by aflliming VR of a convenient mag-
nitude; and fuppofing the rays V v, Rr, &c. to be
parallel within the glafs, find the point O to which
they converge in the water, through which a plane
may be drawn which fhall fend them, out into the air,
in a colourlefs pencil OS.

REMARKS.

I.

The 8 th experiment in Sir Ifaac Newton’s optics
(Book I. Part 2.) feems to have been made under
the conditions which are limited by the foregoing
problem ; though he does not Ipecify thefe conditions.
For, it is to be prefumed, he did not combine his prifm
and water at random, but adjufted them fo as to pro-
duce the expected effeCt. It is obferved likewife,
that he does not give us a defcription of his experi-
ment fo particular as, in mod: inftances, he was wont
to do. He thought perhaps that the confequences he
deduces from it might fufficiently explain his mean-
ing; efpecially as he had, in the foregoing propofiti-
ons, fully eftablifhed the principles of his theory.

However this be, feveral perfons of fkill and addrefs
in optical matters, have produced experiments in con-
tradiction to that of Sir Ifaac, and have affixed mean-
ings to his conclufions which he never could intend,
without being grofsly inconfiftent with himfelf: an

Vol. LIII. C c imputation

[ 186 ]

imputation from which common candor and decency
ought to have protected fo great a name *.

For inftance, when he fays that “ light as often
as by contrary refractions it is fo corrected that it e-
mergeth in lines parallel to thofe in which it was in-
cident, continues ever after to be white”; can this
affertion poffibly bear the meaning they would ob-
trude upon us ? Flad Sir Ifaac fo entirely forgot his
own doCtrine as not to know, That if the glafs pritm
PN», in the laft fcheme, is, any where above V v,
terminated by a plane to which the pencil SO is per-
pendicular, the rays V v, Rr, &c. though emerging
parallel to SO, will exhibit their feveral colours?
The fenfe therefore which the experiments affix to
Sir Ifaac Newton’s words being fo abfurd, had not
they done better to look out for one that was con-
fident with his theory ? and fuch a one they would
have found by only drawing a figure like the fore-
going; where the rays of the pencil, reunited in os,
as well as when feparated within the glafs prifm, are
parallel to each other and to the incident pencil. But,
if the water is terminated by a plane different from
AC, paffing through the point o, and making the
rays (no longer parallel to SO) to diverge, then the
light will, by degrees, in paffing on from o, become
coloured : which is Sir Ifaac’s other pofition.

To this meaning his own words ought to have led
the objeCtors. It was light, not feparate rays, which

* The reader ought to be told, that it is not here intended to
detract from the merit of the late Mr. Dollond’s improvement of
refradting telefcopes ; but only to corredt a miftake of his con-
cerning that difference of difperlion of rays, which he has fo
happily applied to ufc.

emerged

[ i87 ]

emerged in his experiment ; and which (being paral-
lel to the incident light) continued to be colourlefs.

He adds farther, “ the permanent whitenefs ar-
gues, that in like incidence of the rays, there is no
reparation of the emerging rays”: as much as to fay,
that in his experiment (as in our 6th Figure) the pen-
cil, in palling or repaffing, is fuppoled to meet with
furfaces of equal refractive powers, fimilarly lituated.

The other cafes in which refraded light may re-
cover its whitenefs, although it emerges not parallel
to the incident, or may be tinged though parallel to
it, Sir Ifaac does not treat of: the experiment he had
made, being fufficient for the purpofes to which he
applies it. But he allures his readers, that if they
will argue truely upon his theory, trying all things
with good inftruments, and fufficient. circumfpedion,
the expedled event will not be wanting. And the
fad is, that in all the experiments which have been
made, if none of the necellary data are wanting,
the appearance of the emerging light may be certain-
ly prodided.

II.

When a (lender pencil of light is refolded at the
furface of any medium, the extreme rays, the violet
and red, and the leveral intermediate rays, each of
its particular degree of refrangibility, will all diverge
from, or converge to, the fame phyfical point: or
when that point, by altering the pofition of the plane,
is thrown to an infinite distance, will all Oi them be-
come parallel. And it appears from the roiegoing
folution, that fuch parallelism may always be efreded,

C c 2 whatever

C *88 J

whatever be the refracting power of the medium
PN», provided that, in a given medium, the quan-
tities m, n, &c. of the lemma, which reprefent the
fines of refraction of the feveral forts of rays, to a
common fine of incidence, continue to be in con-

flan t ratios to one another.

Converfely, if, from experiments fuch as that
which Sir Ifaac Newton made, it follows that, what-
ever be the refractive powers of the media, and the an-
gle of incidence of the light, the pencils SO, so, may
be made to reciprocate with each other, while all
the forts of rays, in paffing or repaffing through the
prifm P N n, become parallel 5 if, I fay, this is con-
firmed by experiments, it is a proof that, for any
given medium, the ratios of thofe quantities m, n , &c.
are invariable.

III.

And hence Sir Ifaac deduces the two theorems fub-
joined to his 8th experiment ; by the firft of which
he contrives to make the ratios of the fines of refrac-
tion belonging to the feveral forts of rays, to a com-
mon fine of incidence, when they pafs from glals in-
to air, to ferve for finding the like ratios for the rays
patting from water into air, without the trouble of
new experiments.

His firft theorem may be deduced in this manner :

Let all the forts of rays, whether united in a pen-
cil of light, or leparated parallelwife by refraction,
have the fame angle of incidence whofe fine is I,
when they pafs from a denfer into a rarer medium ;

and let V and R Hand for the fines of refraction of

„ the

C i89 ]

the extreme (or any two forts of) rays. Then feeing
by the experiments, the ratio of V to I is given, as
alfo that of R to I ; the ratio of V — I to I, as alfo
(invert.) that of I to R — I, and (ex^quo) that of
V — I to R — I, are given : for this laft write the ratio
of i to p.

In like manner, let the refractive power of the
medium from which the rays emerge into the fame
medium as before, be increafed or diminifhed, as alfo
the common angle of incidence ; and we need only
write other marks <v and r for the fines, and i for
the common fine of incidence j for we fhall have as
before v — i to r — i in a given ratio ; which call
that of i to q. And, from thefe two, we have

V— I R-

-I q
- x

p

But p is always nearly equal to y;

in the refractions from glafs, and from water into air,
their difference is lefs than part of either ; we

V I

may therefore put the ratio -• equal

is the firfi: theorem.

And thence, if one difference R--I becomes equal
to r— /, the other differences V— I, &c. will be re-
fpeftively equal to v— i, See. and the fame fet of dif-
ferences may be made to ferve for feveral media, pro-
vided the fines of incidence are taken in their due
proportion.

Thus when red rays pafs from glafs into the air,
we have I : R :: 50 : 77 and R— I : I :: 27 : 50, and.
when they pafs from water into air i : r~i :: 3 : i,
and therefore, as we are to make R— I every where
equal to r— /, we get, ex aequo, / : I :: 8 1 : 50, as
Sir Ifaac Newton finds it.

IV. But

[ l9° ]

VI.

But to explain this matter a little farther, and ob-
viate fome difficulties concerning it, I ffiall add the
following

EXAMPLES.

The refraCtive powers being as marked above, let
red rays fall from glafs into air at the angle of inci-
dence 20°, the angle of refraction will be 31° 47'.

Again, let them fall from water into air at an
angle of 340 1 ', making their angle of refraction
48° 5'.

And the difference of the fines of 310 47', and 20°
will be precifely equal to the difference of the lines
of 48° 5', and 340 1'.

At the fame angles of incidence 20° and 34° L,
let the violet rays fall from glafs and water into air ;
and the angle of refraCtion from the glafs, will be
32° 14T. nearly, and that from the water will be 48°
38' nearly, And the difference of the fines of 3 2°
14C1 and 200 will equal the difference of the fines of
48° 38' and 340 i', within .000488, or lefs than
~o-Wh part.

We fee like wife that the red and violet rays diverg-
ed from the glafs medium at an angle of 27'J-; but
from the water at an angle of 33' j making the diffe-
rence of divergence in this example 5T; that is .1
of the whole divergence of the red and violet rays
when retraCted from glafs into air, at incid. 20°.

Whence

[ 19i ]

Whence it appears, that although the differences of
fines above fpecified, or the exceffes in Sir Ifaac’s the-
orem, may, in refra&ions from different media into
the fame rarer medium, be made equal, it does by
no means follow, that the divergences of the feveral
forts of rays (or if you chufe to call it their difper-
fion) will be the fame in the two refractions; for Sir
Ifaac’s exceffes 27, 2 74., &c. are the exceffes of fines;
not of angles, as fome opticians feem to have mil-
apprehended.

Again, let an unrefracted pencil of light fill from
common glafs into the air (Fig. 7.) at the incidence
39°, and the angles of refraction will be,

° / //

Of the violet - - - - 79 2- 2
Of the red 75 43 55

And their difference - 3 iH 7 is the diver-

gence of the extreme rays.

And the angle of refraction of the mean ray is
770 16 ' 19". — By mean ray is underftood the ray
whofe fine of refraction is a geometrical mean be-
tween the fines of refraction of the extreme rays,
the common radius being unity.

Let now the fame rays be refracted the contrary
way by a furface of water WT, then, to make the
mean emergent ray parallel to the incident pencil, its
angle of incidence mull be 86' ^ \ ex~

treme rays will now converge at an angle of 2oi.
minutes, nearly.

Through the point of convergence <?, draw (by the
Lemma) a plane to terminate the water, and
unite all the rays into a colourlefs pencil os : and this

emergent

[ 192 ]

emergent pencil will be found to make with a per-
pendicular to the terminating furface an angle of
49° 6'4-j and will be inclined to the firft incident
pencil in an angle of 14 degrees, 28 minutes, 20 fe-
conds. Nor is there any other plane belides this
which will thus unite the rays. If planes parallel
to it cut the rays any where but in their point of con-
vergence, they will be parallel to each other, but ex-
hibiting their feveral colours. And planes not pa-
rallel to it, will every where give a coloured image,
excepting only when they pafs through the point of
convergence; but then the rays having crofs’d at
at thatpoint, will thenceforth diverge from one an-
other, and give a coloured lpedrum.

From all which it appears that light refraded thro’
different media may emerge colourlefs, although its
firft direction be confiderably altered. And that its
mean diredion may remain the fame, though its.ex-
tremities be fenfibly tinged with colours. Pofitions
which, I know not by what mifhap, have been deem-
ed paradoxes in Sir Ifaac Newton’s theory of light ,
but which are really the neceffary confequences of it.

Of Telef copied Objett-GlaJJes giving an Image free
from Colours . Fig. 8 and 9.

If the extreme rays, the red and violet, after one
or more refradions, diverge from points D and d ,
the diftance of the point of divergence of the leaft
refrangible from the lens, being greater than that of
the moft refrangible, fuch a femidiameter of the laft
fpherical furface, from which they are to pafs into

C r93 3

the air, may be afiigned, as fhall unite the extreme,
and all the intermediate, rays in the fame focus F ;
neglecting the aberration from the figure.

The RULE is this i

For the diflances of the points of divergence from
the lens, write D the greater, and d the leaft ; the
femidiameter of any of the given furfaces being af-

fumed for unity: And — , — exprefiing the ratios of

the fines of incidence and refraCtion of the violet and
red rays out of air into the laft medium whofe fur-
face is required : the femidiameter of that furface

wiU be 7? as may be ea% demonftrated

from a theorem of Dr. Smith, in the remarks fubjoin-
ed to his Optics.

Thus if the laft medium is glafs, the femidiame-
ter of the furface from which the rays pafs into the

air, muft be -gD_77^» it being, in this cafe, — =t^»

m

Example I.

Let M/> CN cM (Fig. 8.) be a double convex
lens of water confined between the plano-concave
MTLN and the menifcus MKNcM, both of glafs,
and having the radii of their furfaces contiguous to
the water, equal to each other, or to unity . an 1
a ray S p, parallel to the common axis of the lenies,
after being refrafted by the aqueous lens, have its
Vol. LIII. Dd extreme

C *94 ]

extreme rays, the red and violet, divergent from the
points D and d ; the diftance of F, the focus where
all the rays can meet, will be 8.898 : and when this
happens, the exterior furface oi the menifeus, that
is, the furface reprel'ented by MPKN, will have its
radius to that of the inner iuriace McN, as 139
to 154.

Example II.

4

When a double concave of glafs (the radii of whole
furfaces are unity) is inclofed in water, as in Fig. 9, the
water being confined on one fide by a thin glafs plate
TL, and on the other by a concentrick lpherical fhell
MPKN i the femidiameter of this fhell muff; be to
unity as 47 1 to 547 : and the focal diftance CF, at
which the colourlefs image is formed, will be 4.774.
In thefe examples the thicknefs of the lenfes is neg-
lected ; but it may eafily be taken into the account, if
it is thought neceffary.

The fame thing may be effected by means of any
media of different refraCtive powers : for the femidi-
ameter of the laft refraCting furface being determined
according to the foregoing rule, the nearer diftance of
the points of divergence ( d ) of the more refrangible
rays will be fo compenfated by their greater refrangibi-
lity, that all the rays will converge to the fame focus F.
And this without introducing any new principle into
the fcience of optics, or any difperfion of light diffe-
rent from the refractions difeovered by Sir Ilaac New-
ton near a hundred years ago.

XXXII. An

C 195 ]

XXXII. An Account of the Succefs of the
Bark of the Willow in the Cure of Agues .
In a Better to the Right Honourable George
Earl of Macclesfield, P ref dent of R. S.
from the Rev. Mr. Edmund Stone, of
Chipping-Norton in Oxfordfhire.

My Lord,

Read June 2d, A Mong the many ufeful difcoveries,

which this age hath made, there
are very few which, better deferve the attention of the
public than what I am going to lay before your
Lordfhip,

There is a bark of an Englifh tree, which I have
found by experience to be a powerful aftringent, and
very efficacious in curing aguiffi and intermitting
diforders.

About fix years ago, I accidentally tailed it, and was
furprifed at its extraordinary bitternefs ) which im-
mediately railed me a fufpicion of its having the
properties of the Peruvian bark. As this tree delights
in a moift or wet foil, where agues chiefly abound,
the general maxim, that many natural maladies car-
ry their cures along with them, or that their remedies
lie not far from their caufes, was fo very appoflte to
this particular cafe, that I could not help applying it j
and that this might be the intention of Providence here,
I muff own had fome little weight with me.

The exceffive plenty of this bark furnilhed
me, in my fpeculative difquifitions upon it, with an

D d 2 argument

C >96 ]

argument both for and againft thefe imaginary qua-
lities of it ; for, on one hand, as intermittents are
very common, it was reafonable to fuppofe, that what
was defigned for their cure, fhould be as common and
as eafy to be procured. But then, on the other hand,
it feemed probable, that, if there was any considerable
virtue in this bark, it muff have been discovered from
its plenty. My curiofity prompted me to look into
into the difpenfatories and books of botany, and ex-
amine what they faid concerning it; but there it ex-
ited only by name. I could not find, that it hath, or
ever had, any place in pharmacy, or any fuch qualities,
as I fufpe&ed afcribed to it by the botanifts.

However, I determined to make fome experiments
with it ; and, for this purpofe, I gathered that fummer
near a pound*weight of it, which I dryed in a bag,,
upon theoutfide of a baker’s oven, for more than three
months, at which time it was to be reduced to a
powder, by pounding and fifting after the manner
that other barks are pulverized.

It was not long before I had an opportunity of
making a trial of it ; but, being an entire ftranger to its
nature, I gave it in very fmall quantities, I think it
was about twenty grains of the powder at a dofe, and
repeated it every four hours between the fits ; but with
great caution and the ftrideft attention to its effedtst
the fits were confiderably abated, but did not entirely
ceafe. Not perceiving the lead: ill confequences, I grew
bolder with it, and in a few days encreafed the dofe
to two fcruples, and the ague was foon removed.

It was then given to feveral others with the fame
fuccefs; but I found it better anfwered the intention,
when a dram of it was taken every four hours in the
intervals of the paroxifms.

I have

[ >97 1

I have continued to ufe it as a remedy for agues'
and intermitting diforders for five years fuccefiively
and fuccefsfully. It hath been given 1 believe to fifty
perfons, and never failed in the cure, except in a few
autumual and quartan agues, with which the patients
had been long and feverely afflicted ; thefe it reduced
in a great degree, but did not wholly take them off;
the patient, at the ufual time for the return of his fit,
felt fome fmattering of his ditlemper, which the in-
ceflant repetition of thefe powders could not conquer .
it teemed as if their power could reacn thus far
and no farther, and I did fuppofe that it would not
have long continued to reach to far, and that the dis-
temper would have foon returned with its piifiine
violence j but I did not ftay to fee the iffue . I added
one fifth part of the Peruvian bark to it, and with
this final l auxiliary it totally routed its adverfary.
It was found necefiary likewife, in one or two obfti-
nate cafes, at other times of the year, to mix the fame
quantity of that bark with it j but thefe were cafes
where the patient went abroad imprudently, and
caught cold, as a poft-chaife boy did, who, being
almoft recovered from an inveterate tertian ague,
would follow his bufinefs, by which means he not
only negleded his powders, but, meeting with bad
weather, renewed his diftemper.

One fifth part was the largeft and indeed the only
proportion of the quinquina made ufe of in this
compofition, and this only upon extraordinary occa-
fions: the patient was never prepared, either by vo-
miting, bleeding, purging, or any medicines of a
fimilar intention, for the reception of this baik, but

he entered upon it abruptly and immediately, and it

was

[ 1

was always given in powders, with any common ve-
hicle, as water, tea, Tmall beer and fuch like. This
was ■ done purely to afcertain its effects ; and that I
might be allured the changes wrought in the patient
could not be attributed to any other thing : though,
had there been a due preparation, the moft obftinate
intermittents would probably have yielded to this bark
without any foreign affiftance : And, by all I can

judge from five years experience of it upon a number
of perfons, it appears to be a powerful abforbent,
aftringent, and febrifuge in intermitting cafes, of the
fame nature and kind with the Peruvian bark, and to
have all its properties, though perhaps not always in
in the fame degree. It leems likewife to have this ad-
ditional quality, viz. to be a fafe medicine ; for I never
could perceive the lead: ill effect from it, though it
had been always given without any preparation of
the patient.

The tree, from which this bark is taken, is fliled
by Ray, in his Synopfis, Salix, alba, vulgaris, the
common white Willow. Hasc omnium nobis cognita-
rum maxima eft, et in fatis craflam et proceram Ar-
borem adolefcit.

It is called in thefe parts, by the common people,
the willow, and fometimes the Dutch willow ; but,
if it be of a foreign extraction, it hath been lo long
naturalized to this climate, that it thrives as well
in it as if it was in its original foil. It is eafily diftin-
gui died by the notable bitternefs and the free running
of its bark, which may be readily feparated from it
all the fummer months whilft the fap is up. I took
it from the (hoots of three or four years growth, that
fprung from Pollard trees, the diameters of which

(hoots,

/ 0\

[ lS.9 ]

fhoots, at their biggeft end, were from one to four or
five inches: it is poffible, and indeed not improbable,
that this cortex, taken from larger or older fhoots, or
from the trunk of the tree itfelf, may be ftronger ;
but I have not had time nor opportunities to make
the experiments, which ought to be made upon it.
The bark, I had, was gathered in the northern parts
of Oxfordfhire, which are chiefly of dry and gravelly
nature, affording few moift or moory places for this
tree to grow in ; and therefore, I fufpeCf that its bark
is not fo good here as in fome other parts of the king-
dom. Few vegetables are equal in every place ; all
have their peculiar foils, where they arrive to a greater
perfection than in any other place : the beft and
ftrongeft Muftard-feed is gathered in the county of
Durham 3 the fineft Saffron-Flowers are produced
in fome particular fpots of Eflex and Cambridgefhire;
the belt Cyder- apples grow in Herefordfhire, De-
vonfhire and the adjacent counties; the roots of
Valerian are efteemed moff medicinal, which are
dug up in Oxfordfhire and Glocefterfhire : And there-
fore why may not the Cortex Salignus, or Cortex
Anglicanus, have its favourite foil, where it may flo-
rifh moff, and attain to its highefl perfection ? It is very
probable that it hath ; and perhaps it may be in the
fens of Lincolnfhire, Cambridgeflflre, Eflex, Kent, or
fome fuch like fituations; and, though the bark, which
grew in the county of Oxford, may feem in fome
particular cafes to be a little inferior to the quinquina,
yet, in other places, it may equal, if not exceed it.

The powders made from this bark are at flrfl: of a
light brown, tinged with a dufky yellow, and the
longer they are kept, the more they incline to a

cinnamon

[ 200 J

cinnamon or lateritious colour, which 1 believe is the
cale with the Peruvian bark and powders.

I have no other motives for publifhing this valua-
ble fpecific, than that it may have a fair and full trial
in all its variety of circumftances and fituations, and
that the world may reap the benefits accruing from
it. For thefe purpofes I have given this long and
minute account of it, and which I would not have
troubled your Lordfhip with, was I not fully perluaded
of the wonderful efficacy of this Cortex Salignus
in agues and intermitting cafes, and did I not think,
that this perfuafion was fufficiently fupported by the
manifold experience, which I have had of it.

I am, my Lord,

with the profoundeft fubmiffion and refpe£t,

your Lordfhip’s inoft obedient
humble Servant

Edward Stone.

Chipping-Norton,
Oxfordfhire,
April 25, 1763.

XXXIII. An

[ 201 ]

XXXIII. An Account of an Earthquake in
Siberia: In a Eetter fro7n Monf Wey-
marn to Dr. Moun fey, Principal Phy-
fician of the Emperor of Ruffia, F. R. S.
Iranjlated from the French. Communi-
cated by Mr. Henry Baker, F. R. S.

ReadJu6ne l6» y Cannot exprefs the excefs of joy and

i

compleat fatisfadion, with which I
heard, by our friend Dr. Erafmus, and the Reverend
Mr. Minau, and foon after by the Peterfbourgh Gazette,
the pleafing and long expected news, that his Im-
perial Majefty, our mod gracious Sovereign and Ma-
tter, has been pleafed to confer on your Excellency
the Office of Archiater, and Supreme Head of the
Medical Faculty, throughout the whole Empire, with
the rank and dignity of a Privy Counfellor.

As I fuppofe your Excellency has received my laft
letter, as alfo the Ikin of a monftrous lamb ; and not
doubting but you will be glad to colled: other curb*
ofities of this country, I fhall not fail to fend you,
by the firft opportunity, feveral pieces, with proper
remarks, on different fubjeds relating to the natural
hittory and geography of thefe regions. In the mean,
time, I have the honour to fend you inclofed, an
account of an earthquake we felt, on our frontier
lines, in the month of November laft year; and,
tho’ thefe accidents are no uncommon thing here,
yet I think it deferves our attention, confidering the
circumftances it has been attended with, which has

Vol. LIII. E e induced

your important avocations will allow you time.

It is a great concern to me, that the immenfe
labours of my very burdenfome and fatiguing poll
will not allow me to follow my inclination for the itu-
dy of nature, and for curious and ufeful enquiries into
the phyiical fciences, which would enable me to
fatisfy the defire I know your Excellency has to ac-
quire a particular knowledge of the properties and
produce of this country, which well deferve the atten-
tion of the learned, and would require an abler hand
and more leifure than I am mailer of.

The more I examine this country, the more I find
it worthy of the clofeil attention. The air and moil
of the waters are excellent, the foil is fruitful, and
produces all that can be imagined. With a little
more application and induilry, and if the inhabitants
would diveil themfelvesof their old prejudices, it might
eaiily be made a moil delightful and wealthy country.

Your Excellency’s time is too well employed to be
wailed in reading voluminous epiilles, wherefore
1 ihall put an end to this letter, that has already
taken up too many of your moments ; but cannot
conclude without renewing the proteilations of the
iincere and inviolable reipedl and attachment, with
which I have the honour to fubfcribe myfelf.

From Fort Omfk,
March 26th,
1762.

Sir, Your Excellency’s

ilk. Moil obedient humble Servant*

W. W. Weymarn.

The

[ 203 ] .

THE weekly papers are filled with all the remark-
able events, which happen in all the known and
inhabited parts of our globe, altho’ they are neither
extraordinary nor uncommon, either with regard to
the productions and effects of nature, or the places
where they happen. Thefe laudable endeavouis to
impart whatever may be unknown, or but little known
as yet, to the generality of the world, are ufeful
helps towards getting an infight into the various works
of nature, and the promoting of arts and fciencc in
general, as they put ingenious and learned men,
and lovers of fciences, upon fearching into the caufes
and effects of natural events : in order to improve
fuch as may prove beneficial to mankind, and like-
wife to find out the means of preventing or removing
fuch as may be hurtful : And fhould thofe commu-
nications be productive of neither of thefe advantages,
they would at lead; ferve to make us more acquainted
with the countries and places where thofe things
happen. Hitherto it does not appear that any thing
of this kind has been publifhed relating to Siberia,
a vaft and rich traCt, abounding in all kinds of na-
tural productions, and well worthy the notice of the
learned and curious. But this fcarcity of news front
Siberia feems to be rather owing to the inattention of
the inhabitants than the negleCt of the news writers.
The times of indolence and inattention feem how-
ever to be now at an end even in Siberia, from whence
we have the following account of an Earthquake,
which was felt there on the 28th of November
laft (old ftile) in the evening, towards the frontier
lines on the fide of Zengoria. The fhocks were felt

E e 2 at

• [ 204 ]

at the fame inftant to the extent of above a thoufand
verfts *. The inaccuracy of this account, and the
omiffion of minute circumftances, muft be imputed
to thefe people’s being unaccuftomed to make or
defcribe any obfervations. However we fhall relate
it fuch as it is.

From Fortin Nowikowfki, the laft but one on
the line of Kufnetfk, to the Eaftward. 0£t.
24, 1761.

The day before yefterday, Oft. 2 2d, at one in
the afternoon, a noife was heard under ground, which,
tho’ of a fhort duration, was pretty diftindtly obferved
by the whole garrifon, and particularly by thofe
whofe houfes ftand without the walls of the Fort.
This fubterranean noife, whilft it lafted, was attend-
ed with a trembling of the earth, which only fhook
the timber-houfes. The next day, at four /in the
morning, it lightned as in fummer, but this did not
laft long.

Fort of the Mines of Koliwan, fituated on the
Line of the fame name, adjoining to that of
Kufnetfk, Nov. 30, 1761.

The 28th inftant, between 7 and 8 in the even-
ing, we felt an Earthquake, which begun by a fub-
terranean noife. Its courfe was from Eaft to Weft.
The fhocks were not fo violent as to do any damage,

* N. B. A Ruffian Verft is 11664 Englifh yards.

and

C 205 ] ■

and but flightly (hook the houfes. This Earthquake
laftejd but three minutes. On the fame day, at the fame
hour, and with the fame circumflances, this Earth-
quake was felt at Fort Czagirfk, and at the Redoubt
of Inefk, both on the Line of Koliwan, but with
this difference, that not only the houfes, but alfo the
baflions, and even the timber tower at Czagirfk,
were fhaken, but no damage enfued.

Fort Ufl Kamenogorfki, fituated at the Southern
extremity of the Line of Irtifch, and on the
Eaflern bank of that river. Nov. 30. 1761.

The day before yeflerday, between 7 and 8 in the
evening, was heard a fubterranean roaring noife, like
that of a very violent ftorm : and foon after were felt
fuch violent fhocks of an Earthquake, for the fpace
of about 20 minutes, that feveral wooden houfes
were removed from their places : and the green turfs,
that the roofs are covered with, were cracked and
dropped off. Water, that flood in pails and other
wooden veffels, was fpilt on the ground. The rum-
bling noife was diflindlly obferved to come from the
Eafl, and to extend toward the North. The fame
thing was likewife obferved in all the fortines and
redoubts dependent on Fort Ufl Kamenogorfki, fitu-
ated lower down the banks of the Irtifch.

From;

[ 206 ]

From Fortin Sclioulbinfk, fituated on the banks
of the Irtifch, 125 verbs from Ub Kameno-
goriki, Nov. 30. 1761*

It was the day before yeberday, between 7 and 8
in the evening, that, without hearing any noife under
ground, we felt the Earthquake here, which labed
but about two or three minutes, and did no other
mifchief than fhaking the houfes a little. Its direc-
tion feemed to be from South to North.

Fort Sempalat, near the Trtifch, 206 verbs from
Ub Kamenogorfki, Dec. 1. 1761.

On Wednefday lab, Nov. 28, fome officers hav-
ing met at my houfe to fpend the evening, between
7 and 8 we felt the bench on which we were fitting
fhake feveral times pretty violently ; and, thinking
at firb that fome of the company did it in fport, we
began to chide one another ; but, being at length con-
vinced that the motion proceeded from an Earthquake
that ffiook the whole houfe, and made the beams
and doors crack, every one habed to the door, to
efcape the danger they apprehended from the falling
of the houfe. We were fcarce got out, but we heard
the centry, who was upon duty on the top of
the timber tower, call out, that the whole tower was
fhaking, as well as all the other works of the for-
tification. However, we were foon delivered from

our

[ 2°7 ]

our fears, t He Earthquake having lafted but about
i 2 minutes, without doing any other damage than
throwing down and breaking fome earthen ware here
and there. Upon my return home, I found my books
tumbled off the fhelf and lying on the ground,
as did likewife my ink-bottle that flood upon the
table. As the fhaking of the houfes was oblerved
to be from Eaft to Weft, it is to be conjectured that
the direction of the Earthquake, or rather the kind-
ling of the lubterranean combuftible matter, was from
South to North, as fome pretend to have exprefly
obferved. Juft as the poft is going out, we have an
account that this Earthquake was felt at Fortin
Glouchowfkoi, as alfo at the Redoubt of Pj a nojar Ik,.,
with the fame circumftances, and at the fame time,,
as here.

Fort Jamifcheff, on the banks of the Irtifch, 460
verfts from Uft Kamenogorfki, Dec. 3. 1761.

The Poft from Sempolat, and other places higher
up the Irtifch, as likewife that which is come in at the
fame time from the Line of Koliwan, having brought
us an account of a violent Earthquake that was felt
on the 28 th of laft month, not only on the line of Irtifch
from Uft Kamenogorfki, but likewife on thofe of
Kufnets’k and Koliwan, we muft credit the obfer-
vations made Here, by numbers of people, of an
Earthquake on the 28th of November between 7
and 8 in the Evening, which, tho’ it Lifted near 1 2
minutes, was fo flight as not to occaflon the lead;
damage, but only a gentle motion hardly to be
felt.

ExtraCk

[ 208 ]

Extract of a Letter from the Foundery at Bar-
naoul, Feb. 9. 1762.

I here fend you an account of the Earthquake,
which was felt here on the 28th of November laft
year. At above half an hour after 7 that evening,
the air being denfe, calm and quite hill, an undu-
lating motion was felt, like that of large and high
waves, which continued for fome minutes, and was
immediately fucceeded by the Earthquake, with fuch
violent fhocks, that the beds, chairs, tables, and other
houlhould goods, were removed from their places and
thrown about the rooms. The lhaking of the houfes
was very ftrong. Its dire&ion was from South-Weft
to North-Eaft. Some perfons palling, at that inftant,
over the great dyke, before which are the melting
furnaces, have reported that they heard a loud noife,
like that of the great hammers when they are all
employed in the works.

I beg leave to add, to thefe feveral accounts, fome
reflexions, relating to the origin, progrefs, and effects
of this common and well known phenomenon,
which all parts of the world are liable to.

1. The ridge of mountains, called Altaiikoi
Chrebet, or Chain of Altai, from Lake Telet-
fkoi to the Eaftern bank of the lrtifch, covers
all that part of the frontiers of Siberia towards
the South, which lies between the laid Lake and the
river lrtifch, and extends from Eaft to Weft, and
4 ' fo

[ 209 ]

fo goes on beyond the Irtifch, in the fame direction,
thro’ the country of Zengoria.

2. Thefe mountains abound with all forts of mi-
nerals ; particularly that part which borders on the
river Dgelo, which runs from the Weft into the river
Katunja, is all full of a kind of Saltpetre, which is
found in form of a cement, in great plenty, in the
clefts and between the beds of rock ; with this the
Tartars and Kalmucks make very ftrong and good

■Gunpowder, by an induftrious, fimple and expe-
ditious method.

3. This place is fituated almoft Eaftward of Fort
Uft Kamenogorfki, from whence they feem to have
given the moft exadt account of the Earthquake.
The inhabitants, being accuftomed to thefe events,
which happen there almoft every year, muft be better
able to trace its origin, progrefs, and effedts than thofe
of other places.

4. If . the combuftible matter took fire at firft in
the places mentioned in the fecond article, and if it
may be conjedtured that in this ridge of mountains,
infinitely more combuftible matter may be contained
than in the flat country, without any interruption;
the diredtion of the Earthquake muft undoubtedly
have followed the courfe of the ridge of mountains,
that is to fay, from Eaft to Weft, till it was interrupted
by invincible obftacles.

3. According to advices juft received from the
Kirgifs Kaifacks, who inhabit the parts beyond the
Irtifch, they have had no Earthquake, neither on the
28th of November, nor for a long while before or
after; and, as it came in a diredt line from the Eaft
Vol. LIII. F f to

C 210 3

to Uft Kamenogorfki, and did not purfue its firft
dire&ion from Eaft to Weft, but turned off to the
North, as appears from the accounts from the Forts
Schoulbinfk and Semipalatnaja and others, its courfe
muft have been interrupted in its way, by fome unfur-
mountable obftacle, towards Uft Kamenogorfki. This
obftable fee ms to have been no other than the river
irtifch, which runs from South to North, whence
it follows too, that the inflamed matter did not lie
fo deep as the bottom of the river, as it would other-
wife have followed the direction of the ridge of
mountains that extends towards the Wed.

6. The account from Barnaoul feems to confirm
this opinion, and fhews that the deviation of the
Earthquake happened near Fort Ufl: Kamenogorfki,
which lies directly to the South Weft of Bar-
naoul.

XXXIV.

JPbilos I runs. Vol. lid TiAB ■ AE.

C2WD

Jioman Jnscr^tion-a at Tunis in- Africa , copied ahout tie Year 273 o . Tty
DT Carflos, a native- of Madrid, then Fhysician to tie Bey of Tunis ,
communicated Ty JolniLotike ,Esy. UK. S.

Menterue- Anfiquetntu-m qua ire Tire
Tcnednet Keqno Jnyesiiusitur.
lutteda ho die- been repterit/nhtr

Jit siucdnci co/nmneo; qua? in tube in a Kura- Mamet
a Tu-rav, a dhoietuznie retv icZotmevrdi vodtaUvr
/uec metnona- aidtzaru ImyertiCori/ reyeaitu/r

IMP. CAE S AR-
ID I VI MRVE NEPOS
D1VI TRAIANI PARTHICI. F.
TRAIANVS HADRIAN VS
AVG. P ONT . MAX.TRIB .

POT. YU. cos. m.

VI AM A CARTiAGINE
THEVESTEM STRAVIT.

PER LEG JI. AYG.

P.METILIO SECVNDO
PEG. AVG. PR. PR.

J A f -iitii. 1 c.

PAtbsJhmsyoL LM. TAllJVI.

Tri, Jaei/xj 2) owuoi 2) et au& yurrftci/rud

Su/>jtant, /uxc <4eyi{//c/ira/ici, eyiitnyi/Ua/

, £eyiwitwr.

2

D. M. S.
AN ARIA

V c

D. M. S.

FRVTA

APRON I A

CONIVX

VICTORIA PIA

CARISSIMA

VIXIT ANN IS XL11X

PIAVIXIT

ANN IS XXXI

ESTO BOTI.

—

£

IMP. CAE S. C. VIBIVS
TREB OXTANVS G A LEVS
PIVS FELIX AVGPONT.
MAX TRIB. POTEST.
COS. II JE SIC. P.P.

ET IMP CAES. C.

AFFNTVS

VO LV S IAN V S -

PIVS FELIX. AVG
PONTIF. MAX. TRIE .
POTEST. II COS
DESIC.

PP. PRO CONS
RE STITVERVNT.

XX.

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Tri'/z/jafiJ mt/ariam yrn\(fot /?? marmena r<2unn?<i
fizJu {/>i2em dyierfuta.

J. Aft/nde Ss-

[ 2I3 ]

In antiquae Thuggae minis adhuc haec perftant, hodie
ab Arabibus corrupte Tucca.

D. M. S.

D. M. S.

C. MATTIVS

TIRINIVS FORTV

MAODIVS

PVLIAIENVS

NATVS VIR ARM1S

VENIATERIA

BELLICVS P.

INGENIO ETANIMO

NI FILIVS

V. A. L V.

MAXIMO QVI CVM

P. V. M XX

H. S. E.

. . . NIS ET GRAECIS
. . .TIMIS H. I. T. P.
VIXITQVE IAETOS DVOS
ZOZIMOS IOVIS P.V.XXXI1II

H. S. E.

In Marmoreo fepulchro hoc carmen legitur,

Detrahe ferta comis et amorum apta tuorum, ,
Triftis inops pulla vefte, Thalia, veni.

Non manus id alia improba virga,

Nec fiat ante tuos lucida palla pedes.

Iulius hoc feci mellitus qui vocor olim,

Cupito Patri, Matri venufte meae.

Me pofui conjugem meam mihi Iuncia rogatam,
Ut fit in aetemum condita fama loci.

Viximus ad fatiam, pietatem implevimus ambo,
Praeftitimus fobolem faemineam duplicem.

Vos quoque qui legitis verfus, et fadta probatis,

Difcite fic veflros merito fancire parentes.

Vi te Gafriane, excolerem, titulofque relinquam
Vivos, vi hoc facerem, fata dedere mihi.

Iulius hoc peto nunc a te, Dominator Averni,

Cum moriar manibus jaceant foffa quieta mihi.

i SufFetula *

[ 2I4 ]

Suffetula.

In quodam templo.

In quodam lapide.

DIVI MARCI SACRVM

IMP CAES AVG

In lapide vero.

M.C.L1NARIO PROCONS
REIPVBLI C AE..ROM AE OB
PIET'ATEM ET DBEDIENTIAM
D D. P P.

SVFFETVLENTIVM HANC--
-» - AEDIFICAVERVNT.
ET DD. PP.

In Civitate Sicca Veneria, hodie Chef.

HERCVLI SACRVM M. TITACIVS PROCVLVS PROCV-
RATOR AVGVSTI SVA PECVNIA FECIT.

In lapide haec infcriptio. In alio lapide.

V 1CTORI

10VI OPT. MAX.

CENTVRIONI

CONSECRAVIT VI

LEGIONARIO

EX EQVITE

SANT ISSIMO

ROMANO

PRINCIPI CAES.

OB MVNIFI

In alio lapide.

CENTIAM ORDO

SEXTO IVLIO GIMNAS

SICCENSIVM

TRIARCHO EIS VB -

- - CIVI ET

PROFICII MESV1 - -

ET CONDECVRIONI

OPVLENTI AE ETME

DD. P P.

LIVIO ORICVLONI. -

In Civitate Mufta,qua3 hodie Praedium Mufti vocitatur.

INVICTISSIMO FELIC1SSIM0QVE IMPERATORE IVLIO
AVGVSTO CAESAR1 ORBIS PACATORI MVSTICENSIVM Ul>.

DIIS

4

t 2i5 ]

DIIS MANIB. SAC.

D. M. S.

D. M. S.

ANONIVS FELIX PRON.
ANIONIS ET PIVS VIXIT.
ANNIS XXIIII H. S. EST.
OT. EQ^ II. L. S.

PATVLCIVS
PRIMVS
PIVS VIXIT
ANNIS LXXX
VHS 10TI

C. MEMMIVS
FELIX VIXIT
ANNIS

LXXXII MENSIBUS
QVINQVE DIEEVS SEPTEM
H. S. E.

D. M. S.

LURANAR - -

D. M. S.

MAR CVS POTITIVS AV
RELIANVS PIVS VIXIT
ANNIS LXXXV

©. T. B.

H. S. E.

CLODIVS VXOR1
DVECISSIMAE

D. M. S.

TVRIVS GEME
L 1 VS VXOR FILIO
PIISSIMO FECIT.

D. M. S.
NVPTIALIS
VIXIT ANNIS XXT
H. S.B.Q^T.BOTI SIT.

Inlapide rotundo

D. M. S.

COC. T. N.
IVS SOROR
EX P. VA.

In magnis lapidibus haec fragmenta infcriptionunx
leguntur in diverlis locis.

patraeei CIVIVM svorvm

ATVIS MARMOREIS N. SEX SETO

ET OMMEMIO RVFO FORT

RVNDATORVM REMVM -

TRI EORVM ET CAECII FAE. - -

MERCVRIO

IRM SARMITI DIVI COMMODI FR
ET ADNJPOTIS M AVRELII ANTONINI
SEPTIMIVM.

I DIVI MAR. ANTONINI PII
THICI ET DIVI NERVAE..

IMP C.S.T.S. M AVRELIO
PONT MAX TRIB POT. XXIIII. M

In

[ 216 ]

In Civitate municipali Thiburfica, hodie corrupt©
nomine Taberzoc, hsec reperiuntur monumenta.

In lapide in arcis antiquae collabentibus muris afifixo
exterius hasc infcriptio vilitur.

SALVIS DOMINIS NOSTRIS CHRISTI ANISSIMTS ET
INVICTISSIMIS I MPE RAT OR IB VS IVSTINO ET SOFIA
AVGVSTIS HANC MVNITIONEM THOMAS EXCELEN
TISSIMVS PREFECTVS FELICITER AEDIFICAVIT.

In interioris lateris arcis lapide fic.

VRBI ROMAE ETERNAE AVG - -
RESP MVNICIPI SEVERIANI ANTO
NINIANI LIBERI THIBVRSICENSIVM
BVRE.

In quodam fonte alibi.

NEPTVNO AVG. SAC. PRO SALVTE IMP. CAESARVM
L. SHTIMIS.

In quodam muro.

AEDEM NOVAM L. PALACIVS HONORATVS ET BONI
TATE AE. VXORIS SVAE -S-S- XX
MIL. N. EX.

MVLTIPLICATA PECVNIA EXCOLVIT ET OMNI RE
PERFECIT.

Alibi.

QVAM IN HOC TEMPLO OB

VAP SVA PECVNIA RESTITVIT OPERI « - -
TAVET.

In

r 2,7 ]

In alio laplde hoc fragmentum legitur.

ACILIO C PAPIER

INONIAE AVGG. L. NN
SICENSIVM PROCON
RES THE ATRI PONR
IB. C. ADVOCATO CODICI
ADMINISTRATION IS HEREDI
IN ME ET COHERENTIVM CV
LAVRENTIVM VICO AVGVSTINORVM
SACERDOTEM LAVRENTIVM

CAC APIVM RESP

MVNICIPI SEVERIAN I

ANTONI NIANI LIB. THIB. BVRE

PAT RON O

In loco qui dicitur
Bervic.
d. m. s.

POMPON I VS
ROGATVS
FRVGALISSIMVS
VIXIT ANNIS LXXV
CERFICIA SIGGES3
MARITO

DVLCISSIMO S.P. F.

In loco Telel
vocato.

PETRONIA
DONATA PIA
VIXIT ANNIS
LXXXV. M. I.
PRO MERITIS
El VS MEMORIAE
BENIGNISSIMAE
OP PI A CELSINA
FILIA FECIT.

Inlocoquiappel-
latur Bujobfa.
IMP. CAESAR
M. AVRELIVS
ANTONINVS
AVG. PON. MAX.
TRIBVNICIA POTES.
XIIII COSIIII PP

restitvti

LVIII.

Vol. LIII

Gg

In

[ 218 ]

In praedio ab Arabibus vocato Manfu, quod antiqua
Maramana efle videtur.

d. m. s.

ANTONINVS
DOM IT 1 VS
VIXITIN PACE
ANNIS LVII.

L. 1. S.

D. M. S.

CAR I ROMANI ET AVG
PARENT VM MEMORIA

D. M. S.

M. ANTONIVS
DONATIANVS
NEPOS PIVS
V. ANNIS XXII
M. VI.

S. P.

D. M. S.
CAMILIVS
DONATIANVS
VIXIT ANNIS

D. M. S.

M. ANTONIVS
DONATIANVS
NEPOS PIVS
V. ANNIS XXII
M.VI.

S. P.

In Sufacivitate hodie hujus regni praecipua.

MARCELI ALFONDI EPISCOPI.

In pago hodie Augen.

IVLIVS SA
BINIVS V.
ANNIS LVI
PM. ME
H. S. E-

In

[ 2I9 ]

In turre Manaera didla.

AVRELIO

1

C. SVELLIO

QVARTO

1

PONTIANO

PATRI --

PATRVELI

CLAVDIA

t

L. AEMILIO

CASTA - -

AFRICANO

XEI

AVVNCVLO

In vico ab Arabibus hodie Taztor

In unius column® fcapo.

fortissimo

IMP. ET.

P AC AT OR I
ORBIS M. CLA
VDIO TACI
TO PIO FEL
A VG.

In alia

appellatur.

In alterius fcapo.

DD. NN FLAVII F.
VALENTI N I ANO ET
VALENTI PII FELICES VIC
SEMPER AVGG.

MVNI MIZADO
TERENI

columna.

IMP. CAES. C.
VALERIVS
DIOCLETIANVS
PIVS FELIX
AVG

In

[ 220 ]

In lapide quadrato..

D. N. IMP. VALERIO LICINIA
NO LICINIO AVG MAX.

SARMATICO MAX. GERMA

NICO MAX. TRIBVN 1CIA POTES

TATE X CONS V IMP. X PATER PATRIAE PRO

CONS. COL, BISICA LVCANA DEVOTA NVMINIBVS

MAIESTATIQVE EIVS.

In alio fimili lapide.

POLLENTES IN FINE IMPERIO

DD. NN. HONORII ET THEODOSII PPS IMP. AVG.
ADMINISTRANTE FELICE INNODIO.

In alio lapide, qui Bovis caput infculptum habet, haec
fuperfcriptio notatur.

SATVRNO AVG.

SAC.

MAFRINIVS FE
LIX SAC.

V. S. L. A.

In alio lapide.

ANTONIVS VICTOR
V. S, L, A.

In

[ ]

In lapidibus quadratis haec epitaphia Chriftianorum

fepulchralia funt.

SANCTAE TRES

ENATIANVS ....

MAXIMA

DIACONVS IN PAC

ET DONATILLA

IT ANNO LXIII

SECVNDA

SIKTO PRIDIE KA

BONA PVELLA.

LEND AVG.

IGNICIA D. VICIS VOLVSINA

IN PACE. CAST VLA PIA

VIXIT ANNIS L
H.S.P.O.T.P.Q^ TIIS.

Hxc vero epitaphia in lapidibus cubicis Gentilium
Romanorum funt.

d. m. s.

M. HORTENSIVS
FAVSTINVS ER. V
CARISSIMVS
PIVS VIXIT
ANNIS LX.

H. S. E.

S. T . E. O.

T. T. I. S.

D. M. S.

L. VALERIVS
VICTOR
L VC AN I AN VS
VIXIT ANNIS
XXIII M. III.
D.XXV.

d. m. s.

Q^SENTIVS
MARTI ANVS
PIVS VIXIT ANNIS
XLVIIII. MEN. II II
H.S. B. Q^T.B.Q.

Quinque

/

[ 222 ]

Quinque leucis a Tunete pagus eft, qui ab Arabibus
appellatur Taborba ; amphitheatri veftigia proftant
adhuc, quod Mahamet Bey omnino diruit, in
epiftylio autem portae fie legitur.

/

PRONEP. T. AELIO HADRIAN

r V M GENTI QVE MVNICIPIVM AELIVM AVIT.
PROCOS ET Q^EGRILIO PLARIANO LEG. PR.

In lapide quadrilatero.

SEXT CAEL FILIO. F.

QV ESS CRECEN -

VOL VSI A NO PRAEFEC - - -
FABIO SACERD CVRION - -
SACRIS FACIEND. ADVO
CATO FISCI ROMAE PROC
X HER AB EPI ST VI
VIC ANTONINI AB EP
ISTVI AVGVSTORVM PA
TRONO MVNICIPII DD. PP.

In lapide marmoreo cominus in loco, qui ab Arabibus
nuncupatur Sidi Tabet, a memoria illis cujufdam
landti veneranda, ftc legitur.

MEMORIAE SANTISSI
MAE FEMINAE
DONATAE QVAE VIXIT ANNI.S
XLI. MENSIBVS VIIII.

It)

[ 223 ]

Inter veftigia Civitatis Thugse, hodie Arabum mapa-
lia, ab aliifque nomine corrupto Tucca appellate,
templi ruinae viiuntur, in cujus porticu legitur.

L MARCIVS SIMPLEX ET L MAR
CEL VS SIMPLEX REGILIANVS S. P. F.

In hujus templi latere fie.

CLAVDIO CAESARI AVG.

MAXIMO TRIBVNICIA POT.

R. CRASSVS AEDIL ORNAM. T.R.M.

TI VIR AVGVR IIVIR QVINQVE
C. FAR PERPET V VS SACERI
VS PAGI THVGGENSIS NOM
ET PERPET VI ARCV,

In alio lapide abhinc feparato-.

IMP CAES DIVI
NERVAE NEPOTI
TRAIANI DACICI
P ARTHICI FIL. L TRA
1ANO HADRIANO AVG.

PONTIF MAX. TRIEVN
POTEST COS II PP.

CIVITAS THVGGAE DD. PP.

In alio lapide quadrato.

IMP CAES DIVI ANTONINI MAC -

MARCO AVRELIO SEVERO ALEXANDRO
P0NT1FICI MAXIMO TRIBVNICIA POTES.

ET CASTRORVM ET SENATVS ET PA
LI VM LIBERVM THVGGA.

4

In

[ 224 ]

In praedio Caferim appellato proftant adhuc duo mag-

nifica monumenta.

In Turri.

SIBI ET CLAVDIAE LEG III AVG LEG XVI LEG IIII LEG.

Ill APOLLINARIS I.EG II ADIVTRICIS CONSECVTVS OB
VIRTVTEM IN EXPEDITIONEM PARTHICAM CORO
nam mvralem vallarem torqves et phaleras

AGIT IN DIEM OPERIS PERFECTI ANNOS LXXX.

Ex oppofito ejufdam Turris.

SIBI ET CLAVDIAE MARTIAE CAPITOLINAE CONIVGI CA
RISSIMAE QVAE AGIT IN DIEM OPERIS PERFECTI ANNOS
LXIV. ET MARCO PETRONIO FORTVNATO FILIO MILIT A
VI r ANNOS VI LEG XVIII. PRIMOGENITO LEG II AVG
VIXIT ANNOS XXXV CVI FORTVNATVS ET MAR
TIA PARENIES CARISSIMO MEMORIAM FECERVNT.
________ COLONIA SIMPLICIBVS QVONIAM FELIX

CIVIBVS SPARTAM DIRIPVERE ROMANORVM HAEC
POSSESSA FVERE.

In alia Turri.

FLAVIVS SECVNDVS FILIVS EPAMINONDAS FLAVIAE
VXORI REGINAE SPARTAE SORORI EMILIANI FILIAE
P05VIT HIC PRIMO FLAMINI PR AESIDENTIS IVSSV
RECONDI F AE K.ALEND. — — — — — — IDVS IX

MENSE AVGVSTO. FLAVIVS FLAVIVS EPAMINONDAE
SECVNDVS IVRISCONSVLTVS AD PERPETVAM REI MEMO
RIAM ANNO- LX. REGINA VERIA BIENNIO XXXV.
AGESILAO SECVNDO COLOCATA FVIT IN MATRIMONIO
ABSOLVTE LIBERAM POSVIT HIC TER STATV AM
VXOR PI A. VIXIT ANNOS XL. M. V. D. Ill MAXIMIANO
II ET HEREDIBVS HIC FVERE.

Poftea

[ 225 ]

Poftea Diftichis vitae fragilitatem et miferiam de-
ploratj ut conftat ex his fragmentis!1 j

~ I

CVIVS SI MEMBRIS VOCEM NATVRA DEDISSET
COGERAT HI C OMNES SVRGERE MANE DEOS

OPTO SECVNDE GERAS MVLTOS FELICITER ANNOS
ET QVAE ELEGISTI HAEC MONVMENTA LEGAS.

Omnia carmina exfcripilt Dnus Herneftus Aberftreit,
quae hie deficiunt: primum Diftichon alludit ad
lapideum Galium, qui in cacumine turris erat.

Inter Civitatis Tignicae veftigia, hodie T’anica , haec

reperiuntur.

C. MEMMIO FELICI
FLAMINI AVG PERP
VTRIVSQVE PARTIS
CIVITATIS TIGNICEN

In Magnae Porticus fragmentis.

ALTISSIMO SAECVLO DDDNNN - -
ORI HOLITORI INDVLTA PAC - -
CIPII THIGNICENSIS PROCON

SIS C MEMMIVS

In alio vicino.

FORTVNATVS FLAM

AVG PERP VTRIVS

CONST AN TIN I MAXIMI V. - - -

QVE PARTIS CIVI
TATIS THIGNICENSIS

NIA A FVNDAMENTIS ET S

VLATV DO. DOMITICENO FILIO -

PROPTER EXIMIAM
PIET ATEM ETAFECTIO

Alibi in alio fragm.
ANTONINI PII

NEM FRATERNAM QVAM

CASTRORVM

C. CAES ET TIBERIO I

THIGNICA DF.VOTVM,

X HIBIT. POSVIT.

H h

Vol. LIII

In

[ 226 ]

\

In Fornlcibus et domibus cpitaphia fepulchralia

•#

reperiuntur.

D. M. S.

D. M. s.

D. M. S.

FABIVS FAVS

ABIDIVS

F. MELLVS

TVS PIVS

FAVSTVS

AVSVMELLVS

VIXIT ANNIS

LVCILI ANVS

PIVS VIXIT

LXXVI.

PIVS VIXIT.

ANNIS LV.

H. S. E.

H. S. E.

H. S. E.

D. M. S.

D. M. S.

D. M. S.

C. HERCVLEIVS

T. VRANIA

MARCVS HER

IANVAR1VS

IANVARIA

CVLEIVS IANVA

P. VIXIT

P. V. A.

RIVS

ANNIS LXV

•

LXV.

P. V. A. LV.

H. S. E.

H. S. E. •

D. M. S.

D. M. S.

D. M. S.

C. HERCVLEIVS

IIERCVLEI A

C. HERCVLEIVS

ABIBI AN VS

MARCIANA

VICTOR

P. V. A. XII.

PI A

PIVS V. A

H. S. E.

V. A. XII.

XIII.

H. S. E.

In minis Civitatis Beifoi, hodie pagus Beiffones vocatur.
In Arcis dirutas frontifpicio legitur.

MAGNIS ET INVICTISSIMIS DDDD. NNNN
DIOCLETIANO MAXIMIANO PERPETVIS
AVGG. ET CONSTANTINO MAXIMIANO NOBB CAESARIBVS
RESPVBLIC A ------- BEINSIVM DEDICAVIT.

' MARCO IVLIO PROCONS PA. MAIESTATI QV E EORVM DICATO.

Supra

4

[ 227 ]

Supra Arcis feneftram.

DIOCLETI ANI ET MAXIMIANI ET

In alia.

PRO SALVTE IMP ANTONINI AVG PII ET
LIBEROR VM SVORVM.

CINCIVS ET VICTOR AD LAVDANDAM

D. M. S.

D. M. S.

D. M. S.

MAGNIA

CECILIA

ANIANVS

NVS IVLIVS

FORTVNATA

P. V. A. L.

P. V. A. XII.

PIA V.A.LXXXII

H. S. E.

H. S. E.

H. S. E.

VXOR MAR ITO

AMANTISSIMO

In templi veftigiis.

D. M. S.

D. M. S.

AVG. SACRVM

CK MORASSINA

VII A VICTORIA

SI ST EMPLVM

FELICIA P.

V. A. LXXXII 1 1

CVM SVA PECVNIA

V. A XXX

H. S. E.

DICAVIT.

BAIS'AM.

In fragmento.

MARTI AE CHAR. N VICTORIAE PIAE VXORI
ET MARCITILIO VALERIANO NEPOTI
IB VS SVIS FECIT.

In

[ 228 ]

In Seluquia.

Tn columns.

IMP. CAESAR
MARCO AVRELIO
PROBO
PIO

FELICE

AVG.

IN FRAGMENTO.

PRO S ALVT E IMP.C.
Q^MARTIVS FELIX
DEI LIBERI PAT R 15

Iti L ap ide.

T. FLVAN
CONSTAN
NOBILIB

CAESARIB. NVMI
NI FORVM
VC ATISSIM A
SVA PECVNIA
MVNICIPI CHIDIBB

In Templi ruinis.

H.DIANAE AVG. SAC.

IMP CAES DIV1 M . . .
ANTONINI PII GE . .
NEP. DIVI HADRIANI
PRONEPOTI DIVI
TRAIANI PAR. AB
NEPOTIS DIVI NERVAE
SEPTIMIO SEVERO
PERTINACI AVG. ARA
N.PP.PONT MAX TRIB.
POTEST. IMP.VII.COS.II
HIDIBELENSIS.

In Tempi o.

IIOVI OPTIMO
VIAXIMO AVG. SAC

D. M. S.
MEMMIVS
I ANVARIVS
PIVS VJXIT
ANNIS XXXV
H,. S. E.

In Column a.

SOLI INVICTO

CAES. M. AVRELII PROBI PII

DOM V S E I VS MVNICIPIVM dill.

— - - .

In fragmento.

PRO SALVTE IMP. CAES
M.NVM1SIVS DONATVS FLPP CONTIC.

Epitaphia*

LVRIA C. F

D. M. S.

POSILLA

3ATVRNI N VS FELICIVS

VICTORTS P I A

SISENNE FIL. PIVS

V. AN. XX. H. S. E

/IXIT ANNIS LXXIII.

XXXV. A

[ 229 ]

XXXV. A Letter from Mr. George Ed-
wards, F. R. S. to Thomas Birch D. D .

Secret . R. S. concerning An Obfervation
7nade by him in Op ticks.

Sir,

Readj Jgne l6, X Having lately accidentally difcovered,.

X that the fhadows of things floating
in water, a little below its furface, are reflected from
the air above the water more ftrongly (to my appre-
henfion) than objeds above the furface of the water
are reflected from the water j and confequently, that
fillies playing beneath the furface of a ftill water,
may fee their images diftindly playing in the air, with
this advantage over men, who view their faces in the
water ; for things in air, that are reflected from the
water, muft have, when placed over the water, have
their dark or fhadowed fides reflected from it,, which
renders the images obfcure. On the contrary, the in-
habitants of the waters have almofl: a hemifphere of
light falling on their upper fides, which are the fldes,
that are reflected from the air, which confequently ren-
ders fuch images lighter, and more ftriking to the eye,
than refledions of obfcured things in air, when refled-
ed from the water.. As I have never heard of, or
read, any account of this difcovery, I imagine it may
be new : but you, Sir, in far more extenfive reading,
may be acquainted with fuch a difcovery. If fo, I ac-
knowledge my ignorance of it 5 and aik pardon for

giving.

C 230 ] ;

giving you this trouble, and deiire it may be Iayed
afide j but, if it be thought worthy communicating
to the Royal Society, I will be ready, in a very
fimple and eafy manner, to demonftrate the truth of
the above difcovery. I do not fee any ufe of this dif-
covery at prefent, more than an amufing fpeculation;
tho’ perhaps, when it is reconfidered by perfons fu-
perior to me in penetrating into the fecrets of op-
tics, fome real ufe may be made of it.

I am Sir, with great

June 15, 1763.

refpedl, your very
humble fervant

George Edwards.

XXXVI. An

[ 23r ]

XXXVT. Two remarkable Cafes in Surgery ,
by Mr. Francis Geach, Surgeon in Ply-
mouth. Communicated by TohnHuxham
M. D. F . A S.

Fxtradl of a Letter from John Huxham, M. D.
F. R. S. to W. Watfon, M. D. F. R. S. dated at
Plymouth, the 10th oj May, 1763.

I Have herewith fent you two extraordinary cafes,
which Mr. Francis Geach, one of our furgeons!
put into my hands fome time ago. I think there
are fome things remarkable in them. I have fent
alfo three of the concretions found in the gall-blad-
der of the itteric perfon. The three others I referve
for making fome experiments on them. They are
all nearly of the fame fhape and fize.

The perfon, wounded in the eye, is now confi-
derably ffronger and better. The obfervation, that
wounds of the brain often caufe a paralyfis on the
oppofite fide of the body, is as old as Hippocrates,
and is taken notice of alfo by Aretasus.

I am very well allured that the fads are exadly
related ; and I choofe to fend them in the words,
nay even in the hand writing of Mr. Geach.

[From

[ 23 2 ]

CASE I.

S I R,

Read June 23, yl Man aged forty-two years, not
1763. much addicted to fpirituous li-

quors, nor too rigidly abftemious, feven months ago
received a violent blow on the right hypochondri-
um: foon after he was feized with the colic, and
had a yellow fuffufion over his fkin : himfelf dated
the aera of his misfortune from the blow. At firft
he had a diarrhoea, but at laft became fo coftive as to
have no regular inteflinal difcharge, but by the help
of lenitives. He was much emaciated towards the
end of life, his fkin was aftonilhingly yellow, and
dry as parchment, or leather fhrivelled by the fire.
Many medical proceffes were employed ineffectually.
He had no confiderable pain any where. A week be-
fore his death the left arm turned quite black. He
had frequent haemorrhages from his nofe. On difleCtion,
the liver was found confiderably enlarged, external-
ly of a pale lead colour, harder and more folid than
in a found date, but not fchirrous j internally, more
porous and fpungy. The inner fubftance not deviat-
ing from its natural colour, feemed to be made up
of diftinCt fibres interfe&ing one another, with va-
cuities between them equal in fize to the fmall cells
of honeycombs. The duCtus cyfticus, and hepaticus,
as well as the pori bilarii were perfectly ligamentous.
The gall-bladder had changed its pyriform figure,
and affeCted that of a cylinder, the fibres of which

were

t

C 233 ]

were hard, white, and compa&ed. The pylorus,
and the duodenum were in a fimilar ftate. The cir-
cular fibres of the pylorus were rigid beyond conjec-
ture. The concretions, fix in number, each weigh-
ing half a drachm, and fpecifically heavier than wa-
ter, a circumftance unufual, were all ranged in a par-
allel line, and tallying pretty exa&ly with one ano-
ther, fo completely filled up the tube (for it might
be callled with more propriety fo than bladder) as to
allow but little intermediate fpace. The paflage into
the duodenum was almoft clofed up. Scarce any
fincere gall ifi'ued forth on incifion; but a fmall quan-
tity of a turbid, faponaceous fluid, not unlike choco-
late in colour, came out, or rather was exprefled out,
gradually. — The bile, not finding a ready exit through
the dudtus choledocus, ftagnated probably in its re-
pofitory, became difeafed, and, acquiring the confid-
ence of l'oapy dregs, proved the conftituents of thofe
concretions, which on experiment are found com-
buflible as wax, and as no fermentation arifes from
pouring acids upon them, it may be concluded the
bile is no alkali. The omentum was almoft deftroy-
ed, the little that remained of it, was hard and black,
and afforded no ill emblem of fea weed, when dried.
The glands of the mefentery were in fome parts
fchirrous ; in others, they reprefented fmall and dif-
tindt fteatomas. It may be needlefs to obferve what
is common to other dead bodies, that the diftenfion
of the ftomach and inteftines was in the greateft ex-
tremity.

v ol * Lin.

ii

CASE

I

[ 234 ]

CASE II.

Read June 23, Tl yTR, James L d, midlhipman

17 3’ ▼ JL of his majefty’s fhip Liverpool,

in a riot, December 10, 1762, was wounded in the
left eye : a fmall fword entered in at the external an-
gle, and palling quite through the eye, towards the
balls, ftruck againft the inner part of the orbit. He
fell down inftantaneoully fenfelels, with lofs of fpeech,
and an hemiplegia of the oppofite lide : blood was im-
mediately drawn, the texture of which was not lirong-
ly cohering : the next morning he was found lying
upon his back, with the right eye widely opened,
and the pupil (though in a light room) confiderably
dilated. This eye was incapable of difcerning ob-
jects, never winking at the waving of the hand, or
the clofe application of the finger j though fometimes
it was convulfed. The left eye was extruded from its
orbit, and enlarged to the lize of a pullet’s egg, though
deftitute of all its humours : his pulfe beat at long in-
tervals, with a lazy motion, and Hopped upon gentle
preffure : the body was not feverilh, but preferved a na-
tural heat, the paralytic lide, arm, and thigh excepted,
which were livid, cold, and rigid ; the lancet was
employed without exciting any fenfation, and blitters
lay on feveral days without railing any vefications ;
thefe benumbed parts were conftantly bedewed with
clammy fweat. He was devoid of anxiety, or in-
quietude, the powers of nature feemed to be almoft
fufpended, and life to be carried on, only through
the large organs and velfels. The functions of the
c lower

C 235 ]

lower belly were debilitated, lenient and ftrong purg-
atives producing no irritation in the ftomach and in-
teftines ; and clyfters, though repeatedly injected, were
never repelled. The urine was emitted by drops
only, and fometimes it would run off fuddenly in a
deluge : his hearing, though not quite loft, was con-
fiderably impaired ; he lay lethargic and dead almoft
to every thing, though by pulling the arms and fhak-
ing the body, by loud and frequent calling, by de-
ftring him to extend his tongue, he would gape wide-
ly ; and forgetting feemingly what had been faid to
him, keep his mouth wide open, when the tongue
might be feen quivering and retraced . Five weeks
elapfed in this ftate of infenfibility, every thing he
took was with voracity, but without relifh and with-
out diftin&ion. About this time a new and dreadful
iymptom began to threaten, the jaw feemed to be
moved with difficulty, and liquids only could be pour-
ed down ; the hypocondria were hard and diftended,
and every effort to procure an inteftinal difcharge
proved ineffectual, when very large eruptions of the
miliary kind were fuddenly diffufed over the found
parts. From that critical moment he perfpired freely,
and had an eafy motion of the jaw ; his urine was
rendered in a due quantity, and purgatives of the
lenient kind eafily operated, the hypochondria were
foft, and equal ; the difcharge from the eye, which
hitherto had been acrid, was now copious and laud-
able, the found eye had its motion, he could fee dif-
tinftly, and feemed in other refpedts lenfible, when
roufed from his ftupefa&ion : foon after he could bear
to be moved from the bed to a chair without fatigue,

I i 2 the

/

[ 236 ]

the paralytic parts were rubbed with vinegar and
muftard, and he took the following medicines.

Pulv valerian 9fs

— Caff. Ruf. gr. 4.

Spec. Diambrae gr. iij.

Syrup. Croci q. f. m. f. Bolus ter die fumend.
ex hauftu feri finapini.

A cataplafm of bread and milk had been daily
applied to affwage the inflammation and fwelling
of the eye, and a decoction of thyme and muf-
tard was employed as a gargarifm to help the
fuppreffion of voice. Soon as he began vifibly
to mend, he had fometimes loud and fudden burSts
of laughter, and fometimes only a long conti-
nued filent fimpering, a fpecies of convulsion not un-
like that called by the Greek phyficians Kvvmcs ma<r-
fxogt fave only that this was not attended with a fever.
When he attempted to walk, he had fuch geflures as
accompany the St. Vitus’s dance ; and feemed a per-
fect idiot, throwing eagerly forward one leg, and
dragging the other trembling after. His appetite is
now naturally moderate, his lleep found and refresh-
ing, his hearing acute, he fpeaks, but drawls out his
words rather indiffin&ly than articulately, the para-
lytic arm and thigh ale again animated, and recover
but Slowly their flexibility and extenfion. He tells
me that he remembred nothing from the moment he
received the injury, to the time he recovered and fat
up; there was a temporary privation of the intellec-
tual faculties. It may be worth while to oblerve,
that though feveral large Sloughs were thrown off

from

[ 237 ]

from the Eye, though the fuppuration was in a large
quantity; yet the bulk of the parts did not diminish,
nor the inflammation leffen, till an aftringent fotus of
red rofe-leaves and port wine was applied, which fo
effectually braced up the relaxed parts, that the lids
now cover the deformity. Though it may be diffi-
cult to account fatisfaCtorily for the paralyfis of the
oppofite fide, yet monfieur de la Faye * has fomething
pertinent to the matter ; the paffage is not long, and
may be worth tranlcribing.

La Moelle Allongee n’eft que le prolongement de
la fubftance medullaire du cerveau, & du cervelet. Les
fibres qui la compofent, fe croifent, de forte que celles
du cote gauche paffent au cote droit, & cedes du cote
droit au cote gauche ; c’eft de cette Moelle Allongee
que partent immediatement les dixpaires de nerfs qui
fortent du crane. Comme les fibres de la fubftance
medullaire fe croifent, les nerfs fe croifent auffi, c’eft
a dire, que ceux qui viennent du cote droit, paffent au
cote gauche, & que ceux qui viennent du cote gauche,
paffent au cote droit. Dela vient, a ce qu’ on pretend
que la paralyfie, lorfqu’elle eft la fuite de la compref-
fion de quelque endroit du cerveau, fe trouve pour l’or-
dinaire au cote oppofe a celui de l’endroit comprime.

* Principes de Chirurgie, premiere partie.

Francis Geach.

XXXVII. An

C 238 ]

XXXVII. An Account of a now Die from
the Berries of a Weed in South Carolina :
In a Letter from Mr. Mofes Lindo, dat-
ed at Charles Town, September 2, 1763,
to Mr. Emanuel Mendez da Cofta, Li-
brarian of the Royal Society.

Read Nov. 10, TT N Auguft 1 757, I obferved the
17 63 * mocking bird fond of a berry, which

grows on a weed called Pouck, reprefented to me as of
a poifonous quality j the juice of this berry being a
blooming crimfon. I was feveral times inclined to
try, if I could extrad a die from it ; yet the very
thoughts of its quality prevented me from proceed-
ing, till obferving thefe birds to void their excrement
of the fame colour as the berry, on the Chinefe rails
in my garden, convinced me it was not" of the quality
reprefented. I therefore made a tryal in the following
manner.

1 ft. I ordered one of my negroes to gather me a
a pint of thofe berries, from which I extra&ed almoft
three quarters of a pint of juice, and boiled it with a
pint of Briftol water, one quarter of an hour.

idly. I then took two pieces of flannel and num-
bered them 1 and 2, boiled them in a feparate tin
pot with alum a quarter of an hour, and rinced
them in cold water.

3dly. I then dipped the piece of flannel N° 1. into
the pot, where the juice was, and left it to funnier

five

[ 239 ]

five minutes, then took it out, and rinced it in Cold
water j when, to my furprize, I found a fuperior
crimfon dye fixed on the flannel than the juice of the
berry.

4thly. I then dipped the piece of flannel N° z. in
the fame juice, and being defirous to clean my hands
from the ftain, which N° i. had caufed, I ordered
fome lime water to be brought me, fuch as we ufe
to fettle our indico, and found the colour of the ftain
change to a bright yellow. This unexpe&ed change
urged me to throw a wine glafs-full of lime water
into the pot, where the piece of flannel N° 2. was
fimmering ; on which, all the juice, as well as the
flannel, became of a bright yellow, by which I find
alum fixed the crimfon, and lime the yellow.

5thly. Having then put a quart of frefh juice in
two pint decanters, in one of which I put a fmall
quantity of powdered arum, I laid them up : about
lix weeks after, I then examined them, and found the
juice in the decanter, which had no alum, was turned
black, and the other retained its colour.

XXXVIII,

[ 240 ]

XXXVIII. An Account of the Eclipfe of the
Sun, April i, 1764: In a Letter to the
Right Honourable George Earl of Mac-
clesfield, Pref. R. S. ft '077i Mr, James
Fergufon, F. R . S.

My Lord,

Read Nov. 17, tt Beg leave to prefent to the Royal So-
ciety a projection of the eclipfe of the
Sun, which will be on the 1 ft of April 1764. The
diagram fhews the time ar.d phaies of that eclipfe,
for the Royal Obfervatory at Greenwich, and the cal-
culation is from Meyer’s Tables.

According to Flamdeed’s Tables, and Dr. Hal-
ley’s, and M. De la Caille’s, the eclipfe fhould be an-
nular at London ; and De la Cable, in a map in his
Ephemerides, makes it a! mod Central. But, ac-
cording to Meyer’s Tables, the appearance will be
very different ; for the fouthern limb of the Moon
will be about the 20th part of a digit over the fou-
thern limb of the Sun ; and Meyer makes the begin-
ning, greated obfcuration, and ending, to be at lead
a quarter of an hour fooner than Flamdeed, Halley,
and M. De la Caille do.

As the padage of the dradow will be north-ead-
ward over Europe, and all thefe authors make it’s
center to pafs more or lefs eadward of London and
Greenwich; and fince there is fuch a great differ-
ence in Meyer’s time from that of all the others, and in

the

t »+* ]

the phafis at the greateft obfcuration ; a clear fky is
much to be wifhed for : and it might be proper to
have obfervers placed about ten or twelve miles from
one another, all the way between Greenwich and
Deal, that the truth may be found by obfervation.
For, if Meyer’s tables are right, all the others muft
want much correction.

About five years ago, I delineated the path of the
Moon’s fhadow over all the parts of the earth, where
it will pafs in this eclipfe, from fun-rifing till fun-
fetting, according to mean or equal time. I con-
ftrudted the map much upon the fame principle with
that of Manfredi and De la Caille, and took moft of
the lunar elements from Meyer’s tables.

According to this projection, the center of the pen-
umbra will firft touch the earth at fun-rife, in the
Atlantic Ocean, between theCaribbee Iflands and thofe
of Cape Verd ; in 47 degrees weft longitude from
Greenwich, and 18 degrees north latitude; from
which it will go on, almoft parallel to the equator,
for about 20 degrees eaftward : then it will bend
north- eaft ward, and pafs over the fouth of Portugal,
near Cape St. Vincent : from thence, in its progrefs,
it will go over Valadolid, crofs the Bay of Bifcay a
little weft of Bayonne, pafs over Rochelle, then mid-
way between Rouen and Paris, go over Holland a
little weft of Amfterdam, crofs the German Sea a-
bout 40 miles weft of the mouth of the river Elbe,
enter Denmark, crofs the Baltic by Gottenburg, tra-
vel over Sweden weft of Stockholm, pafs clofe by
the weft fide of the Gulph of Bothnia, go a little weft
of Torneo, enter the Frozen Sea at Wardhuys, crofs
over to Nova Zembla, and a little to the eaft thereof
Vol. LI1I. Kk it

[ 242 ]

it will end in the North Sea with the fetting Sun, in
105 degrees eaft longitude, and 72 degrees north lati-
tude.

If the motions of the Sun and Moon were equa-
ble, any given eclipfe would always return in a courfe
of 223 lunations, which would conlift of 18 years
1 1 days 7 hours 43 minutes 20 feconds (as wasobferv-
ed by the antients) for 1388 years; and would for
ever do fo, if, at the end of each period, the Sun and
Moon fhould be in conjunction either in the fame
node, or at the fame diftance from it as before. But
that is not the cafe : for, if the Sun and Moon are
once in conjunction at 18 degrees diftance from the
node, which is the greateft diftance at which the
Moon’s fhadow can touch the earth, at the next pe-
riod of 1 8 years 1 1 days, &c. the Sun and Moon
will be 28 minutes 12 feconds of a degree nearer the
fame node than they were at the period laft before.
And fo by falling gradually nearer and nearer the
fame node every time, the Moon’s fhadow will pafs
over the center of the earth’s enlightened difc, at the
end of the 38th periodical return of the eclipfe from
the time of its firft coming in at either of the earth’s
poles ; becaufe the conjunction falls in the node at the
end of the 38th period.

In each fucceeding period, the conjunctions of the
Sun and Moon will be gradually farther and farther
from the node, by the quantity of 28 minutes 12 fe-
conds of a degree; which will caufe the Moon’s fha-
dow to pafs over the difc of the earth, farther and
farther on the oppofite fide from its centre, till it
quite leaves the earth, and travels in expanfion for
about 12,492 years, before it can come upon the
earth again at the fame pole as before.

The

[ 243 ]

The reafon of this will be plain, when we confider,
that 1 8 degrees from either of the nodes of the
Moon’s orbit is the greateft diftance, at which her
Shadow can touch the earth at either of its poles.
And as there are 18 degrees on each fide of the
node, within the limits of a lolar eclipfe > and twice
1 8 make 36, thefe are all of the 360 degrees of the
Moon’s orbit about either of the nodes, within which
there can be an eclipfe of the Sun : and as thefe eclipfes
fhift through 28 minutes 12 feconds of thefe 36 de-
grees, in every Chaldean or Plinian period, they will
fhift through the whole limit in 77 periods, which
include 1388 years and 3 months. And then, the
periods have the remaining 324 degrees of the Moon’s
orbit to fhift through, at the rate of only 28 minutes
1 2 feconds of a degree in each period, before they
can be near enough to the fame node again, for the
Moon’s fhadow to touch the earth ; and this cannot
be gone through in lefs than 12,492 years: for, as
36 is to 1,388, fo is 324 to 12,492.

The eclipfe, April iff, 1764, fell in the open fpace,'
quite clear of the earth at each return, ever fince the
creation till A. D. 1295, June 1 3th old ftile, at i2h
52' 59" p. m. when it firft touched the earth at the
north pole, according to the mean (or fuppofed e-
quable) motions of the Sun and Moon j their con-
junction being then 17° 48' 27" from the moon’s a-
feending node, in the northern part of her orbit.
In each period fince that time, the conjunction of the
Sun and Moon has been 28' 12" nearer and nearer
the fame node, and the Moon’s fhadow has therefore
gone more and more foutherly over the earth. In the
year 1962, July 1 8th, old ftile, at ioh 36' 21 " p.m.

K k 2 the

[ ^44 J

the fame eclipfe will have returned 38 times j and as
the conjunction will then be only 24/ 45' ' from the
node, the center of the Moon’s diadow will fall but
a little northward of the center of the earth’s en-
lightened difc. At the end of the next following
period, the conjunction of the Sun and Moon will
have receded back 3' 2 7" from the Moon’s amend-
ing node, into the fouthern part of her orbit; which
will caufe the center of her fhadow to pafs a very
fmall matter fouth of the center of the earth’s difc.
After which, in every following period, the conjunc-
tion of the Sun and Moon will fall 28' 12" farther
and farther back from the node, and the Moon’s
fhadow will go dill further and further fouthward on
the earth, until A. D. 2665, September 12, old
ftile, at 2311 46' 22" p.m, when the eclipfe will have
finidied its 77th period, and will finally leave the
earth at the fouth pole ; and cannot begin the fame
courfe over the earth again in lefs than 12,492 years,
as above mentioned.

And thus, if the motions of the Sun and Moon
were equable, the fame eclipfe would always return
in 18 Julian years 1 1 days 7 hours 43 minutes 20 fe-
conds, when the lad day of February in leap years
is four times included in the period : but when it is
five times included, the period is one day lefs ; or 1 8
years 10 days 7 hours 43 minutes 20 feconds.

But, on account of the various anomalies of the
Sun and Moon, arifing from their moving in ecliptic
orbs, and the effeCts of the Sun’s different attractions
of the Moon in diderent parts of her orbit, the con-
junctions of the Sun and Moon never fucceed one
5 another

[ 245 ]

another at equal intervals of time ; but differ fome-
times by no lefs than 14, 15, or 16 hours j and there-
fore, in order to know the true times of the returns
of any eclipfe, recourfe muft be had to long and te-
dious calculations.

In order to fhew both the mean and true times of
the above mentioned eclipfe, through all its periods,
whilft it is vifible on this earth, together with the
mean anomalies of the Sun and Moon, the true dis-
tance of each conjunction from the afcending node,
with the true latitude of the Moon at the time of each
of her true conjunctions with the Sun, according to
the old Stile, I have calculated the four following ta-
bles, of which I beg the Royal Society’s acceptance.

According to the mean (or fuppofed equable) mo-
tions of the Sun, Moon, and nodes, the moon’s iha-
dow in this eclipfe would have firffc touched the earth
at the north pole, on the 13th of June, A.D. 1295;
and would quite leave the earth at the fouth pole, on
the 12th of September, A.D. 2665, at the com-
pletion of its 77th period ; as fhewn in the firffc and
fcond tables.

But, on account of the true (or unequable) motions
of the Sun, Moon, and nodes, the true lines of con-
junctions of the Sun and Moon, and the Sun’s true
diftance from the Moon’s alcending node, are as fet
down in the third and fourth tables : and the Moon’s
true latitude is too great at the end of the firft mean
period, to allow her fhadow to touch the earth. So
that the firft time of the coming-in of this eclipfe
was at the end of its fecond mean period ; and the
true time was on the 24th of June, A.D. 1313,

at

C 246 ]

at 3h 57' 3" pall noon at London: and it will final-
ly leave the earth on the 31ft of July, A. D. 2 5 93’
at ioh 2^' 31" paft noon, at the completion o! its
y2d period. So that, the true motions do not only
alter the true times from the mean, but they alfo cut
off five periods from thofe of the mean returns of
this.eclipfe.

In this, and all other eclipfes of the Sun, which
happen about the afcending node of the Moon’s or-
bit, the Moon’s fhadow firft touches the earth at, or
about, the north pole; and goes more and more
ioutherly over the earth in each return, till it quite
leaves the earth at, or near, the South pole. But
when eclipfes happen about the defcending node, (as
that of July 14th, A. D. 1748 did) the Moons
fhadow firft touches the earth at, or near, the louth
pole ; and goes gradually more and more northward
in each periodical return, till it finally leaves the
earth at the north pole. And as the obliquity of the
Moon s orbit to the ecliptic is the fame about both
the nodes, there mull be the fame number of eclipfes
about the one as about the other.

But I beg pardon, for mentioning things to your
Lordfhip, and the Royal Society, which muft be
much better known to you all, than they can be to
me who am, with the highefl degree of refpedt,

My Lord,

Your Lordfhip’s
moft obliged, and

Mortimer-Street, mofl obedient humble fervant,

Nov. 16, 1763.

James Fergufon.

TABLE

[ 2+7 ]

TABLE I.

The mean time of new Moon, with the mean anomalies of the
Sun and Moon, and the Sun’s mean diftance from the Moon’s
afcending node, at the mean time of each periodical return
of the Sun’s eel ipfe, March 21ft, 1764, from the time of it’s
firft coming upon the earth fince the creation, till it falls right
againft the earth’s center, according to the old ftile.

w

-0

<4-. .

Mean time of new
Moon.

Sun’s mean
Anomaly.

Moon’s mean
Anomaly.

Sun’s mean
Diftance from
the node.

H

O

a,

5.3

M.

D.

H.

/

f!

S.

O

/

it

S.

0

/

//

S.

0 1,7

O

3277

June

2

5

9

39

I i

37

57

41

I

26

3*

42

O

18 16 40

I

1295

June 13

12

52

5«

ir

28

27

38

I

23

40

39

O

37 48 27

2,

1313

June

23

20

36

39

O

8

57

35

1

20

4*

56

O

17 20 15

3

*33*

July

5

4

39

39

0

39

27

32

I

37

57

33

O

36 52 2

4

1 349

July

3 5

32

2

59

0

29

57

29

I

35

6

IO

O

16 23 £0

5

1367

July

26

39

46

39

I

IO

27

26

I

32

34

47

O

3 5 55 37

6

1385

Augi

6

3

29

39

1

20

57

23

I

9

23

24

O

1 5 27 25

7

1403

Aug.

37

II

12

59

2

I

27

20

1

6

32

I

O

34 59 32.

8

1421

Aug.

27

38

56

39

2

11

57

37

I

3

40

38

O

1431 0

9

H39

Sept.

8

2

39

39

• 2

22

27

14

I

0

49

35

O

34 2 47

30

3457

Sept.

38

IO

2

59

3

2

57

I I

O

27

57

52

O

3 3 34 35

1 I

1475

Sept.

29

38

6

39

3

33

27

8

O

25

6

29

O

13 632

12

1493

o».

,30

I

49

39

3

23

57

5

O

22

35

6

O

12 38 10

13

3511

oa.

21

9

32

59

4

4

27

2

O

39

23

43

O

12 9 57

14

3529

0£t.

31

3 7

36

39

4

14

56

59

O

16

32

20

O

11 41 45

15

'547

Nov.

12

O

59

40

4

25

26

56

O

33

40

57

O

11 13 32

16

356;

Nov.

22

8

43

O

5

5

5 6

53

O

10

49

34-

O

10 45 20

*7

*583

3601

Dec.

3

l6

26

20

5

l6

26

5°

O

7

5«

9

O

10 17 7

38

Dec.

34

O

9

40

5

26

56

47

O

5

6

48

O

9 48 55

J9

1 619

Dec.

25

7

53

O

6

7

26

44

O

2

35

25

O

9 20 4x

zo

3638

Jan.

4

35

36

20

6

17

5 6

41

II

29

24

2

O

8 52 30

21

1656

Jan.

3?

23

39

40

6

2&

26

38

I I

26

32

39

0

8 24 17

22

3674

rjan.

26

7

3

O

7

8

S6

35

I I

23

43

34

O

7 56 5

a3

3692

Feb.

6

34

46

20

7

39

26

32

1 z

20

49

53

O

7 27 52

24

3710

Feb.

l6

22

29

40

7

29

56

29

II

1 7

58

3°

O

6 59 40

25

3728

Feb.

28

6

33

0

8

IO

2b

2(r

II

1 5

: 7

7

O

6 31 27

26

1746

Mar.

30

33

56

20

8

20

56

53

II

32

35

44

O

6 3 35

27

3764

Mar.

20

21

39

40

9

I

26

20

1 1

9

24

21

O

5 35 2

28

3782

April

I

5

23

0

9

II

56

37

II

6

32

58

O

5 6 50

29

3g00

April

1 I

3 3

6

20

9

22

26

J4

1 1

3

43

35

O

4 S8 37

3°

3818

April

22

20

49

40

10

2

56

I I

* II

O

5°

12

O

4 1© 25

31

1836

May

3

4

33

O

10

13

2.6

8

30

27

58

49

O

3 42 32

32

1854

May

34

12

16

20

10

23

5<5

5

IO

25

7

26

O

3 14 O

33

3872

May

24

f9

59

40

11

4

26

2

IO

22

l6

3

O

2 45 47

34

1890

June

5

3

43

O

II

34

55

59

IO

39

24

40

O

2 37 35

35

3908

June

35

I I

26

20

1 1

25

25

56

10

16

33

37

O

1 49 22

36

3926

June

26

39

9

40

0

5

55

53

IO

3 3

41

54

O

I 21 70

37

1944

July

7

2

53

O

0

l6

25

5°

IO

10

5°

3*

O

0 52 57

*8

3962

Ju,y

18

30

36

21

0

26

55

47

10

7

5?

8

0 0 24 45

TABLE

[ *4» ]

table II.

The mean time of new Moon, with the mean anomalies of the
oun and Moon, and the Sun’s mean dillance from the Moon’s
amending Nede, at the mean time of each periodical return
o the Sun s eclipfe, March 2 iff, 1764, from the time of it’s
falling right againft the earth’s center, till it finally leaves the
earth ; according to the old ftile.

Vm

Jt

.1

n .t;

Js *-

CJ r—

(4

V

6.

>5

39

1980

40

1998

2016

42

2034

43

2052

44

2070

45

2088

46

2106

47

2124

48

2142

49

2160

5°

2178

2196

52

2214

53

2232

54

2251

55

2269

56

2287

57

2305

58

2323

59

2341

60

a359

61

2377

62

2 3 9 5

63

24i3

64

2431

65

2449

66

2467

67

2485

68

2503

69

2521

70

2539

7i

2557

72

2575

73

2593

7+

2611

75

2629

76

2647

77

2665

0

2683

Mean Time of new
Moon.

M. D. H. ,

July 28 18 19 41
Aug. 9231
Aug. 19 9 46 21

Aug. 30 17 29 41
Sept. 10 1 1 3 i

Sept. 21 8 56 21

oa. 1 16 39 41
Oct, 13 o 23 1

Od. 23 8 6 21

Nov. 3 i5 49 4,
Nov. 13 23 31 1

Nov. 25 7 16 21

Dec. 5 ,4 59 4 1
Dec. 16 22 43 1

Dec. 27 6 26 21

Jan. 7 14. 9 4i

Jan. 17 21 53 1

Jan. 29 5 36 21

Feb. 8 13 19 41
Feb. 19 21 ^ 1

Mar. 2 4 46 21
Mar. 13 J2 29 42
Mar. 23 20 13 2

April 4 3 56 22

April 14 ix 39 42
April 25 i9 23 2

May 6 3 6 22

May 1 7 10 49 42
May 27 18 33 2

June 8 2 16 22

June 18 9 59 42

June 29 17 43 2

July 10 1 26 22

July 21 9 9 42

July 31 16 53 2

Aug. 12 o 36 22
Aug. 22 8 19 42

Sept. 2 16 3 2

Sept. 12 23 46 22
Sept. 24 7 29 42

Sun’s mean
Anomaly.

Moon’s mean
Anomaly.

Sun’s mean
diftance from
the node.

0 / »/

S.

0

/

//

S.

0

/

/>

1

7

25

44

10

5

7

45

IT

29

56

33

I

17

55

41

IO

2

l6

22

1 1

29

8

20

I

28

25

38

9

29

24

59

j r

29

O

8

2

8

55

36

9

26

33

36

I I

28

3*

55

2

J9

25

33

9

23

42

13

II

28

3

43

2

29

55

30

9

20

50

5°

I I

27

35

30

3

IO

25

27

9

>7

59

27

I I

27

7

18

3

20

55

24

9

15

8

4

I I

26

39

5

4

I

25

21

9

12

l6

4i

1 1

26

10

53

4

11

55

l8

9

9

2S

18

I I

25

42

40

4

22

25

15

9

6

33

56

1 1

25

14

2?

5

2

55

12

9

3

42

33

I I

24 46

IS

5

*3

25

9

9

0

5i

IO

II

24

18

3

5

23

55

7

8

27

59

47

I I

23

49

5°

6

4

25

4

8

25

8

24

I I

23

21

38

6

»4

55

I

8

22

27

I

I I

22

53

25

6

25

24

58

8

29

25

38

I I

22

15

23

7

5

54

55

8

16

3i

J5

II

21

57

O

7

16

24

52

8

*3

42

52

11

21

28

48

z

26

54 49

8

10

5i

29

1 1

21

O

35

8

7

24

46

8

8

O

6

1 1

20

32

23

8

17

54

43

8

5

8

43

II

20

4

IO

8

28

24

40

8

2

17

20

II

19

35

58

9

O

54

37

7

29

25

57

II

19

7

45

9

J9

24

34

7

26

34

34

I I

18

39

33

9

29

54

3 1

7

23

43

I I

I I

18

I I

20

10

10

24

28

7

20

51

48

1 1

17

43

8

IO

20

54

25

7

18

O

25

I I

17

14

54

I I

I

24

22

7

*5

9

2

I I

l6

4*

43

I I

I I

54

*9

7

12

1 7

39

1 1

l6

18

3 1

I I

22

24

J7

7

9

26

l6

1 1

>5

5°

18

O

2

54

H

7

6

34

53

1 1

>5

22

6

O

*3

24

I I

7

3

43

30

11

14

53

34

O

23

54

8

7

0

52

7

I I

J4

25

4i

I

4

24

5

6

28

0

44

I I

13

57

28

I

14

54

2

6

25

9

21

I I

23

29

16

I

25

23

59

6

22

17

58

1 I

23

1

7

2

5

53

56

6

19

26

35

II

12

32

\ I

2

l6

23

53

6

16

35

12

I I

12

4

38

2

26

53

5°

6

*3

43

39

11

2 I

36

26

TABL1

[ 249 ]

TABLE III.

The true time of new Moon, with the Sun’s true diftancc from
the Moon’s afcending node, and the Moon’s true latitude, at
the true time of each periodical return of the Sun’s eclipfe,
March 21ft, 1764, old ftile, from the time of it’s firft coming
upon the earth fmce the creation, till it falls right againft the
earth’s center.

Periods.

Years of
Chrift.

True time of new
Moon.

Sun’s true
Diftance from
the node.

S. 0 In

Moon’s true lati-
tude.

M.

D.

H.

/ //

O

/

t)

North.

O

1277

June

2.

15

9 36

O

19

5

40

I

37

5°

N. A.

I

1295

June

>3

21

54 32

O

18

40

54

I

3 3 45

N. A.

1313

June 24

3'

57 3

O

17

20

22

I

29

34

N. A.

3

1 3 3 1

July

5

10

42 8

0

16

29

35

I

25

20

N. A.

4

1 349

July

15 17

14 15

O

15

34

l8

1

20

45

N. A.

5

1367

July

20

23

49 24

O

14 46

8

1

l6

39

N. A.

6

1385

Augi

6

b

41 17

O

13

59

43

I

12

43

N. A.

7

1403

Aug.

17

13

32 19

Q

13

l6

44

I

9

0

3

N. A.

8

1421

Aug.

27

20

30 17

O

12

37

4

I

5 42

N. A.

9

H39

Sept.

8

3

51 46

O

12

I

54

I

2

41

N. A.

10

M57

Sept.

18

IO

23 1 1

O

I I

30 271

O

58 53

N. A.

1 1

'475

Sept.

29

17

57 7

O

1 1

3 56

O

57 43

N. A.

34

J493

oa.

IO

I

44 3

O

IO

4i

55

O

55 49

N. A.

*3

J5 1 1

oa.

21

9

29 53

O

10

2S

I I

O

54

28

N. A.

14

X529

oa.

3*

17

9 18

O

IO

II

27

O

53

12

N. A.

15

’547

Nov.

12

O

51 25

O

10

I

IO

O

52

*9

N. A.

l6

1565

Nov.

22

8

54 56

O

9

52 49

O

51 4»

N. A.

17

1583

Dec.

3

l6 48 17

O

9 4s

4

O

51

I I

N. A.

IS

1601

Dec.

>4

O

5i 5

O

9 43

42

O

50 49

N. A.

19

1619

Dec.

25

8

54 59

O

9 4°

23

O

5°

3i

N. A.

20

163S

iJan.

4

l6

56 1

O

9

34

57

•O

5°

3

N. A.

2.1

1656

Jan.

15

O

54 4i

O

9 29

24

O

49

57

N. A.

22

1674

Jan.

26

8 48 24

O

9

19

44

O

48

44

N. A.

23

1692

Feb.

6

16

36 28

0

9

8

58

O

47

49

N. A.

24

1710

Feb.

*7

8

8 37

O

8

54 20

O

45

43

N. A.

25

1728

Feb.

28

7 43 4o

O

8

34

53

0 44

52

N. A.

26

1746

Mar.

10

«5

H 33

O

8

IO

38

O

42

46

N. A-.

27

1764

Mar.

20

22

30 26

O

7

42

14

O

40

18

N. A.

28

1782

April

I

5

37 4’

O

7

9

27

O

37

28

N. A.

29

1800

April

I I

12

36 38

O

6

35

3°

O

34

3 1

N. A.

3°

1818

April

22

19

27 34

■o

5

51 48

O

3°

43

N. A.

31

1836

May

3

2

12 7

O

5

5

5

O

26

40

N. A.

32

1854

May

h

8

50 40

O

4

19 45

O

22

42

N. A.

33

1872

May

24 15

28 15

O

3

26

3

O

18

1

N. A.

34

1890

June

4

22

8 0

O

2

35

5

0

>3

34

N.

35

190S

June

1 5

4 38 J3

O

I

4i

43

O

8

54

N. A;

36

1926

June

26

II

13 5

O

O

47

38

O

4

IO

N. A.

37

1944

July

6

17

5° 35

11

29

55

28

O

O

24

S. A.

38

1962

July

18

O

31 38

11

29

z

35

O

5

2

S. A.

By the true motions of the Sun, Moon, and nodes, the Moon’s fhadow falls even witk
the earth’s center two periods fooner than by their mean motions.

Vol. LIII. LI TABLE

[ 25° ]

TABLE IV.

The true time of new Moon, with the Sun’s true diftance from
the Moon’s afcending Node, and the Moon’s true latitude, at
the true time of each periodical return of the Sun’s eclipfe,
March 2lft, 1764, old ftile, from the time of it’s foiling right
againft the earth’s center, till it finally leaves the earth for up-
wards of 12,492 years.

to

U-. .

0 ctS
co rn

True

Time of
Moon.

new

Sun’s true
diftance from
the node.

Moon’s true lati*
tude.

0

*c

V

a,

C3 r*

£0

M.

D.

H.

/

//

S.

O

/ //

0

/ //

South.

39

1980

July

28

7

18

53

I T

28

11 32

0

9 29

S. A.

40

299 8

Aug.

8

24

12

32

I I

27

26 41

0

23 2 5

S. A.

41

2016

Aug.

18

21

*4

53

I I

26

42 16

0

17 18

S. A-

4*

2034

Aug.

30

4 25

45

II

26

2 O

0

20 48

S. A.

43

2C52

Sept.

9

11

45

27'

II

25

26 46

0

23 53

S. A.

44

2070

Sept.

2C

J9

17

26

I I

24

55 4

0

26 39

Si A.

43

2088

0£h

I

2

57

8

I I

24 27 43

0

28 58

S. A.

46

2106

Oft.

12

10

47

39

I I

24

4 38

0

31 2

S. A.

47

2124

Oft.

22

18

37

39

I I

23

48 28

0

32 26

S. A.

48

2142

Nov.

3

2

56

29

I I

23

35 12

0

33 53

S. A.

49

2 r 60

Nov.

13

11

I I

20 •

I I

23

22 22

0

34 42

S. A..

5°

2178

Nov.

24

J9

36

24

I I

23

18 57

0

35 0

S. A.

5*

2196

Dec.

5

4

4

9

I I

23

14 40

0

35 22

S. A.

S2

2214

Dec.

l6

12

35 48 f

I I

23

10 43

0

35 43

S. A. .

53

2232

Dec.

26

20

29

9

I I

23

6 47

0

36 1

S. A.

54

22 I

Jan.

7

5

42

9

I I

23

4 27

0

36 16

S. A.

53

2269

>n-

17

J4

14

8<

II

23

O 41

0

36 35

S. A.

56

2287

Jan.

28

22

43

34

I I

22

53 58

0

37 10

S. A.

57

2305

Feb.

8

7

8

30

II

22

44 44

0

37 59

S. A. .

58

2323

Feb.

29

25

7

IO

II

22

3 1 1

0

39 8

S. A.

59

2341

Mar.

2,

O

6

5

II

22

17 46

0

40 28

S. A.

60

2 3 59

Mar.

*3

7

59

17

I I

21

55 29

042 9

S. A.

6l

2377

Mar.

23

75

5 1

59

II

21

39 40

O

43 4i

S. A.

62

2395

April

3

23

45

7

I I

21

0 53

O

46 58

S. A.

63

2413

April

14

7

32

40

1 I

20

26 22

O

49 48

S. A. .

64

2431

April 25

12

57

I I

29 47 34

O

53 27

S. A.

63

2449

May

5

22

45

J4

1 1

19

6 22

O

56 5°

S. A.

66

2A67

May

!7

6

27

3°

II

18

21 16

I

0 40

S. A.

67

2485

May

27

13 46 30

1 I

07

34 20

I

4 42

S. A.

68

25°3

June

7

21

10

3 1

1 1

l6

43 27

I

9 3

S. A«

69

2521

June 18

4

24 42

1 1

15 5* 4»

I

13 26

S. A.

70

2539

June 2q

1 1

58 46

II

J5

1 12

I

27 43

St A«

7*

2557

Ju)y

9

29

24

7

II

14

9 23

I

22 6

S. A.

72

2 575

Juiy

21

2

52

34

II

13

19 22

I

26 16

S. A.

7?

2 59 3

July

31

IO

23

32

I I

12

i3 43

1

31 44

S« At

74

2611

Aug.

I I

17 c8

39

I I

I I

45 13

I

36 23

St A.

75

2629

Aug.

22

I

42

37

I I

I I

2 49

I

39 5°

St Ak.

76

2647

Sept.

2

9

29

37

I I

10

22 59

I

42 0

S. A.

77

2665

Sept.

12

*7

25

23

I I

9

46 48

1

45 45

S. A.

O

2683

Sept.

24

I

29

1

1 1

9

25 49

1

47 58

S. A.

The true motions carry oft the eclipfe four periods fooner than the mean.

XXXIX. An

[ 25r ]

XXXIX. An Account of an Earthquake at
Chattigaon : Tranflated from the Perfian
hy Mr . Edward Guidon, in the Service
of the Honourable Ead India Company ,
and communicated by him to the Reverend
Mr . Hird.

To the Reverend Mr. Hirst.

Reverend Sir,

Read Nov. 17, f g ^HE following was written by a
17 5' 1 Perfian writer, purfuant to an or-

der of Harry Verelft Efquire, chief of the honor-
able Eaft India company’s province Chattgaon, in the
kingdom of Bengal, and fent to Calcutta, for the
information of meffieurs Vanfittart, Haftings, and
others, acquainted with that language. As it is of
indifputable authority, I have taken the pains to copy
and tranflate it for your fatisfadion, being,

Reverend Sir,

Your moft obedient humble fervant,

Calcutta, Nov, 1,

1762.

Edward Guidon.

ACCOUNT

[ 252 ]

ACCOUNT of an earthquake, which happened
in the region of Iflamabad on the 2 2d of the
month Chytt 1168 Bengal aera, anfwering to the 2d

of April 1762, on Friday about 5 o’clock in the
afternoon, which, according to the beft advices, I
have written, and now fend yon.

Particulars are as follow ;

The land of Mohamd Affad Chowdhrv of the

J

Pargannah Deeang, at a place called Bareeah, is laid
open by the fhock from 10 to 12 cubits in width,
and become, as it it were, a deep creek ; the water
riling upfo, that the ground of the farmers inhabiting
the place is 8 cubits overflowed.

And at Deep in the chowdhraij of Mohamd A-
thijar the like hath come to pafs.

And Moktaram Fowtahdar, dwelling at Goyparah,
has written, that to the north and eaft his houfe was
cracked, and water there fpouted up like a fountain,
and the ground alfo finks every day by little and
little.

And by letter from Satoo Mefter Daroogah of the
falt-works at Banflbarceah, it fo fell out, that, to the
weftward, Akl’poorah, an illand of the falt-works, was
levelled with the water on its eaft fide, and on the
north and fouth the ground opened from 5 to 7 cu-
bits in width, and funk like a pit to the depth of 10
cubits, the water fpouting up ; nor is there the leaft
appearance of it’s fubfiding : we know not what will
come of it.

And from the reports of the people there we hear,
that thefe places were never before overflowed by the

water.

5

[ 253 ]

water: we cannot at prefent tell what misfortune has
happened. However all the government’s fait was
before this laid up in ftorehoufes. Moreover, a mud-
building of your fervant’s (the writer of this account)
was almoft deftroyed by the fhock, but it flill ftands
upright.

And at Haldah about 12 doan of land belonging
to Sacheeram Cannoongoeij is entirely funk into the
water.

In like manner in Takaleeah, about 5 doan of
ground, the property of Barjallaal Chowdhry has

fallen fomething below its primitive level.

And at Do Hazary, Harry Singh’s houfe, and a
orick d building of Sheer Zaman CHan’s came down,
and the CHan was hurt by the fall of his 5 and there
opened a cavity like a ditch of 200 cubits in length,
which filled with water.

At Howla, the houfe of Shiam Ram taxgatherer,
broke down, and his whole inclofure was torn up,
and in mofl places his houfe and fifh-ponds were fill-
ed with fand- banks: even now the whole fpot is two
cubits under water.

And, at Dahrampoor, the houfe of Santeeram,
the Cannoon-Goeys writer, intirely fell down.

The Kutwall, of Iflamabad, alfo informed us with
his own mouth, that, in a place called Baramcharah,

the water was up to a man’s waift, and the people
there have betaken themfelves to flight, through fear
of perifhing ; no living creature but the cattle now
remaining.

And in the houfe of Santeeram Cannoon-Goey of
Iflamabad, a bricked room was ruined, and one of

his

[ 25+ ]

his brethren, named Rajah Ram, killed by the fall
of the bricks.

And the houfe of Nandaram coming down in
the fame manner, a fon of his was knocked of the
head.

And to the eaftward of Kadr Katcheeah a large

hill, called Kaddaleah, very near Karn Phooly, was
rent, and it flopped up the paffage for boats in and
out that river.

And at Bajaleeah, Sangotty and Do Hazary creeks
were clofed up by banks of fand riling from their
bottom.

And at Gandarab Jowar, about 3 doan of ground
belonging to Mohamd Aly Chowdhry, rent and was
fwallowed up, and the paffage dn and out to his houfe
alfo cleaving afunder; the water rofe up and has flow-
ed all round the houfe.

Moreover (the factory houfe) a flrong building in
the fort of Illamabad cracked from top to bottom
and tumbled down, and an apartment newly built
was alfo rent.

And to the eaftward a large pond of Bilah CHan
became a deep gulph ; and to the eaft alfo of Aghy
G*nge, belonging to the city of Illamabad, the
ground in different places clave afunder , water rifing
up as from fo many fprings.

And at Chehpaijttlee about 12 katy of land be-
longing to Shah Sagier Chowdry was overflowed and
rendered unfit for tillage.

And, by letter from Chehtarnaraijn furveyor of
the lands, we learn, that the north fide of the Chach-

iah Sowabeel, juft by Haldah river, broke down and

is

f 255 ]

is fwallowed up by the river, and alfo four people
were overwhelmed in it’s ruins.

And Mr. Griffith's bricked houfe (in Mama bad)
has been ciacked, alfo the houfe and walls of Tuan
de Baris, a Portuguefe, here.

And from Nahar Charah there is news, that the
greater part of the ground of that Aland clave afun-
der, and is fwallowed up by the waters, and a num-
ber of people periled with it. Befides this, the
hate of that ifland will be known to you from a
Bengal account.

From the Jooms, whofe country is about 4 days
oil. from Iflamabad, we learn, that Reang Hill
fplit in two and funk 40 cubits ; alfo that Kachalang

Hill is even with the ground.

And Bahngoo Changee, a Joom hill,, rent in twain,

and.is funk 30 cubits, and the houfes of moft of
the inhabitants in thofe parts thrown down.

And a Joom hill Chahter Pattuah fplit by little and
little, till it is almofl: level with the plain : and becaufe
of the opening of the hills, and deftrudlion of the
trees on them, the way by which the Jooms nfed to
pafs is hoped up.

And Bajaleeah, another Joom hill upon the river,
opened 30 cubits, and linking water rofe up ; and Pa*
lang, a Joom hill, fplit and funk 25 cubits.

The defign of this is to lay before you the won-
derful diforders, that have. come to pafs in thefe regi-
ons, and which continue to happen, infomuch that
from the time of Adam untill now, in this place,
no one has heard of the like.

If

[ 256 ]

If I fhould defcribe them with a thoufand inftances
and relations, and make mention of fo many parti-
culars, hill there would not be a part in ten that
I could bring within the compafs of writing. But
thefe few particulars I fend for your excellency’s in-
formation.

XL. An Account of an "Earthquake in the
Eaft Indies, of two Eclipfes of the Sun and
Moon, ohferved at Calcutta: In a Letter
to the Reverend Thomas Birch, D . D.
Secret. R. S. from the Reverend William
Hirft, M. A. F. R. S.

To the Reverend Thomas Birch, D. D. Secretary t»

the Royal Society.

Reverend Sir, Calcutta, Nov. 3d 1762.

Read Nov. 17, rpO theinclofed accounts of the tranfit
j763- I 0f Venus, I have fubjoined others
of an extraordinary earthquake felt in this part of the
world, which, I flatter myfelf, will not be unaccepta-
ble to the Royal Society. This earthquake happen-
ed the fecond day of April laft, was very violent in
the kingdoms of Bengal, Aracan, and I egu, but
particularly at the metropolis of Aracan, where, ac-
cording to the accounts of an Englifh merchant re-
ading there, the effects have been as fatal as at Lit-

C 257 ]

bon, and where it is thought the chief force of the
earthquake vented itfelf.

At Dacca, in this kingdom of Bengal, the confe-
rences have been terrible : the rife of the waters

_ if 1 j r*Ver WaS ver^ ^uc^en an(^ violent, that fome
hundreds of large country boats were driven afhore,
or loft, and great numbers of lives loft in them.

No.lefs deplorable are the accounts from Chatti-
ly011 in this lame kingdom: three of thefe accounts
I herewith inclofe, one of them wrote by Mr. Ed-

W*F a y°unS gentleman in the fervice of

our Eaft India Company, and two others, trandations
from a Perlian original, made out by order of Mr.
Verelft, chief of our Eaft India Company’s affairs in
that province; in confequence of which account the
Company s lands there, have not been fo highly af-
fefled as before this calamity. Both thele accounts are
trandated from the fame original ; but that, which I
received from governor Vanfittart, being thought ex-
aggerated foi interefted reafons, I begged of Mr.
Gulfton to give me a litteral trandatfon from the
Pei dan, in which language he has made an uncom-
mon piogrefs, as much to his prefent honour, as I
hope it will be to his future advantage. This favour
he obligingly granted me, and I fend it to you, Sir,
not only to compare it with the other trandation, but
to give you fome diftant idea of the idiom and o-reat
dmplicity of this eaftern language.

The fame earthquake was alfo very alarmino- at
Ghirotty, where colonel Coote with His Majefty’s
troops are in cantonment about 18 miles up the river
from this place. The waters in the river and tanks
there were violently agitated, and, in many places,
Vol. LIII. Mm rnfe

[ 258 ]

role to more than fix feet perpendicular height, of
which I had ocular convidtion myfelf on my return
from Chandernagore, a fettlement lately belonging to
the French, about three miles north from Ghirotty,
and in latitude 220 54/ N. where it was felt, but not
in a great degree ; for I myfelf knew nothing of it,
till it was foon after told me by certain French gen-
tlemen there.

Nearly at the fame time was this earthquake felt
at Calcutta, where, as I am informed, the agitation of
the waters in the tanks rofe upwards of fix feet, and
was in the direction north and fouth. The height of
the thermometer on Farenheit’s fcale was then at Cal-
cutta at 950 30' much higher than it had been obferv-
ed to be during the whole month, the lowed defcent of
the mercury being 89 degrees. In this month was
much thunder and lightening, and there were frelh
gales of wind at S.E. the weather in general being
clofe and fultry.

A fubfequent earthquake was felt at Calcutta the
13th of July following at half pad; two in the af-
ternoon. The thermometer was then at 87° 4/ at a
medium, the wind S.W. and the weather fair: to
this I was a witnefs myfelf, being then at dinner with
captain Eifer, of his majefty’s 84th regiment. The
motion of the earth caufed a very fenfible vibration
of the wine in our glades, and the fhock was re-
peated twice at the interval of a few feconds.

I conclude. Sir, with communicating to you the
obfervations I made in thefe parts, of two remark-
able eclipfes of the Sun and Moon. The fil’d was
of the Sun, which I obferved at Ghirotty on the

banks of the Ganges, Oftober 17th ult. where I
r was

[ 259 ]

was then on a vifit to colonel Coote. This indeed was
a Hying obfervation, or taken, as the French would
fay, en paffant, being unprovided with a neceflary
apparatus. I had luckily adjulted (very carefully) my
watch to apparent time, by the meridian line of a
large fundial, on the noon immediately preceding the
eclipfe : my watch in general keeps time very well,
but it not having a hand to fhew feconds, I deter-
mined the feconds as near as I could by the minute
hand. Though I had fet my watch to the apparent
time, I defpaired of making any obfervation of this
eclipfe for want of a telefcope, for which, happen-
ing to exprefs fome concern, not above half an hour
before the eclipfe was to come on, captain Eifer re-
collected he had a refleCtor, with which he immedi-
ately obliged me : it was about 1 6 inches long, and
in very tolerable condition, fo that I may venture to
fay this obfervation, though not perfeCt, may be de-
pended on to be very near the truth.

I had not time nor conveniency to throw the Sun’s
image on a fcreen in a darkened room 5 fo was oblig-
ed to lay it down as near as I could by my eye.
The following fcheme fhews the folar maculaa, as
they then appeared : the appulfe of the Moon’s limb
to, and it’s recefs from them, being refpeCtively noted
by the literal references.

N. B. I examined my watch by the meridian line
the fucceeding noon of the eclipfe, without being a-
ble to afcertain any fenlible error, owing doubtlefs to
the want of a better method of making the obfer-
vations.

Mm2

Obfer-

[ 26o ]

Obfervations of a To-
lar eclipfe made at Ghy-
rotty about the latitude E
22° i north, the watch
adj ufted to apparent time.

H M S

Beginning of the lunar immerfion 2 49 30

Appulfe of the Moon’s eaftern limb to the 1 o

lpot A - - --------- - -J 3 354

Appulfe of the fame to the fpot B - -- -341 42
Appulfe of the fame to the fpot C - - - 3 49 43
Appulfe of the fame to the fpot D - - - 3 53 o
Greateft vifible obfcurity near 11 degitsl o

eclipfed -- - — — — - - - - [ ? $

The Moon’s weftern limb receding from 1 ,

the fpot A - - } * 46 5°

The fame receding from the fpot B — - 4 50 20
The fame receding from the fpot C - — 5 o 8
The fame receding from the fpot D- — 5 335

End of the eclipfe — — 5 12 20

Total duration — - -- 2 22 50

The next obfervation was of the eclipfe of the
Moon, which I made yefterday in Conjunction with
Mr. Hancock, at his houfe in Calcutta, to whom I
am greatly obliged for fupplying me with fome ex-
cellent agronomical instruments, particularly, with a
large land quadrant of two feet radius, made by
Cole in Fleet* Erect, with which I took the corrcf-
4 pondent

[ 26i ]

pondent altitudes of the Sun to adjuft his watch
(which was furnifhed with a hand to diftinguifh fe-
conds) to the apparent time, Mr. Hancock himfelf
marking the Times while I obferved. The telefcope
I ufed was a refledtor made by Dollond, in perfect
order, being fent out of England by the laft fhips,
and in length about 22 inches.

Our firffc obfervation was on November the firft,
the day preceding the eclipfe, the Sun’s upper limb
being at the horizontal wire of the quadrant’s mov-
able telefcope, on the eaftern fide of the By the watch

meridian when the watch marked - — -

Nov. 1.

O Altitude,
47° 8'

Sun’s upper limb at the fame on the

weftern fide -------j *4 2 4 31

Dividing the Sum by - - - - -2/24 15 1

H M s

9 SO 3°

Sun’s center on the merid. by the watch
Equation of the day - - - - -

Watch fafler than equated folar time -

12 7 30

11 43 49

o 23 41

Nov. 2,

O Altitude,
5l° 26'.

Sun’s upper limb at the horizontal wire 1

on the eaftern fide - - - - _ j 10 24 33
The fame at the fame on the weft fide - I 13 59 50

Dividing the Sun by ----- 2 ^24 24 23

Sun’s center on the merid. by the watch
Equation of the day - - - - -

Watch falter than equated folar time -
Watch fafler yefterday - - -

Gain of the watch thefe 24 hours - -

12 12 11
11 43 48

o 28 23
o 23 4r

o 4 42

Obfervations

[ 262 ]

Obfervation of a lunar eclipfe November 2, 1762,
made at Calcutta in the. kingdom of Bengal, latitude
22° 30' N.

Immerfions.

-The beginning of the eclipfe at
Mare Humorum immersing -
Tycho immerging ------

The fliadow at the middle of Copernicus

By the

watch.

Apparent

time.

H M S

H M S

i 15 IC

I 7 40

I 24 54

I 17 24

I 36 3c

i 29 0

2 9 33

2 2 3

Emerfions.

Middle of Copernicus emerging
Total emerfion of Tycho - -

. End of the eclipfe - - -

Total duration - - - - -

2 50 2;

3 44 3C

4 3 2
2 47 52

2 +2 57

3 37 O doubtful

3 55 32
2 40 22

Near eight digits eclipfed by ocular eftimation.

By the preceding obfervations the' watch gained
4 minutes 42 feconds thefe 24 hours.

I have the honour to be,

S I R,

Your obliged and very humble fervant.

William Hirft.

XLI. Ext raft

[ 2°3 ]

XLI. ExtraEl of a Letter from Mr. Edward
Guidon, at Chittigong, to Major John
Carnac, at Calcutta.

Dear Sir,

Read Nov. 17, f n \ H E reafon principally of this ad-^
JL drefs is to give you a particular ac-
count of the fhocks of a violent earthquake, which
were felt here on the 2d inftant at 5 in the afternoon
lafting the fpace of four minutes. The factory, a
brick building, is totally fpoiled, fo as not to be fafe-
ly habitable ; for thereabouts, and in many other
places, the earth opened, and- the waters gufhed out
prodigioully ; and in the chaife-road, efpecially to-
wards the north quarter,, there are great chafms two
feet wide and upwards, fo ftrange, that the morning
after, riding that way, the horfe ftarted and went
round another way, not willing to go over them.

At the time of the frit fhake, great explofions
were heard like the noife of cannons, of which Mr.
Plaifted and others counted . 15.

All the tanks overflowed their banks, fifh were call;
up, and the river rufhed upon the fhore like the furf
of the fea. It was the mofl: extraordinary event I
was ever witnefs to : by the enclofed paper you will
difcern how many alarms we had, however nothing
equal to the firff, in which the whole force of the
earthquake feems to be exerted. At prefent, the af-
ternoon of the 4th of April, all our heads feem to be
quiet and ftill, and confequently the earth at reft ; but

really

[ 264 ]

really yefterday, from the repeated tremours of the
ground, every one appeared giddy and alarmed, fan-
cying the earth to be in perpetual vibration, which
however an experiment of a glafs of water upon the
floor by no means admitted of. I would not that
fuch a fhock as the firft fhould happen at Calcutta for
all I am worth, flnce of neceflity the terrafled houfes
muft fall to ruin, and I pleafe myfelf with the thoughts,
that we have had the worfl: of it.

Chittigong, April 4, 1762. I am, &C.”

Copy of the Paper mentioned in the foregoing letter.

Chittigong, April 2, 1762.

a * ' C P. M. a fevere fhock of an earth-

April 2 at 5 quake lafted + minutes_

512a fecond lafted one minute.

530 a third.

7 o a fourth,
o a fifth.

o in the morning of the 3d, a fixth.
o a feventh.
o an eighth,
o a ninth.

10 25 a tenth.

10 30 an eleventh.

Between 6 and 7 in the evening I felt a twelfth
{hock j alfo others upon Marriet’s hill, at a diftance
from mount Pleafant, which every one thought in
continual motion.

10

1

2

3
5

XLII. An

[ 265 ]

XLII. An Account of the Earthquakes that
have been felt in the Province of Islamabad,
with the Damages attending them^ from the
2d to the ltyh of April, 1762 : 7 'ranfat-
ed from the Perfian, and communicated to
Henry Vanfittart, Efq\ Prefident and Go-
vernor of Fort William in Bengal, by Mr.
Verelft, Chief of the Hon. Eaft India Com-
pany s Affairs at Iflamabad.

Read Nov. 17, r|“A HE weather being very clofe and
/ JL warm for fome days preceeding,

on the 2d of April, about 5 in the afternoon, we
were alarmed by an earthquake j which beginning
with a gentle emotion, increaled to fo violent a de-
gree, for about two minutes, that the trees, hills,
and houfes fhook fo feverely, that it was with difficul-
ty many could keep their feet, and fome of the black
people were thrown on the ground ; whofe fears ope-
rated fo powerfully, that they died on the fpotj others
again were fo greatly aftefted, that they have not re-
covered themfelves fince.

On the plains, by the rivers, and near the fea, it
was chiefly felt with great feverity.

Our bungaloes proved very convenient on fo me-
lancholy an occalion ; for had we been in brick houfes,
they mufl: inevitably have been fluttered or levelled
with the ground ; as there is not a brick wall or
houie but is either greatly damaged or fallen.

N n

Our

[ 2^6 ]

Oar new room in the fort, though as ftrong as
bricks and chunam could make it, is Shivered on all
fides from bottom to top ; and the old building equal-
ly cracked is in great part tumbled down.

The ground opened in feveral places in the town,
throwing up water of a very fulphurous fmell; and
feveral ditches and tanks were filled up, which are
now level dry land.

The emotions were fo complicated, that we could
not well determine their direction ; being fometimes
from weft to eaft, and again from eaft to weft ; and
the tanks in fome places overflowed north and fouth.

In Purgunnah Deang, Burfea Gong, the ground
in feveral places opened ten and twelve cubits wide ;
and in fome parts So deep, that they could not fathom
its bottom j the water immediately overflowing the
whole town, which is funk about feven cubits.

Deep Gong, a village near the other, is alfo funk,
and now lies feven cubits under water.

From Patter Gottah to Howlah, about 8 cefs dis-
tance, the ground opened, and a great quantity of
water was immediately thrown out, and in feveral
places the ground entirely funk.

At Bans Burreah, Akul Poor, near the fea, the
earth opened in feven places, like wells, throwing
up the water ten cubits high : the great Cutcherry
there, with brick walls, is cracked and Shivered to

piece8. _ . i r

At Hulda Creek, near Sancharam Conguy s houle,

twelve don of ground is entirely funk.

In the Purgunnah Do Hazarree, Hurry Sing Ha-
zard's brick houfe was entirely thrown down : the

hall of Seer Jumma Cawn’s brick houfe alfo fell, and
r himfelf

[ 267 ]

himfelf was greatly hurt by the bricks : near which the
ground opened 200 cubits, and immediately filled
with water, which is now unfathomable.

In Howla Purgunnah, Sam Roy Gaflildar’s houfe
broke down, and his compound was filled with water
of two cubits deep for two days.

In Berrum Cherra, the ground overflowed about
two cubits deep.

The hall of Santaram Conguy’s brick houfe fell
down, and killed one of his relations.

Near Cutcha Gaut, Kurrolea hill opened, and a
great part of it fell into the river.

Bazally Creek, and Do Hazarry Creek, are both
flopped up.

At Gunderub Juwar, three don of ground is en-
tirely funk.

Ali Chowdry’s compound opened, and the water,
that immediately flowed out, filled a deep ditch, that
furrounded his houfe.

From Sawabill Purgunnah to Mooradabad, three
Taluckdar’s grounds are entirely funk, and four peo-
ple killed.

At Bar Chara, near the fea, five or fix cefs of
ground immediately funk, and out of four or five
hundred people, above two hundred were loft, with
all their cattle ; and the greateft part of the remain-
ing inhabitants, who ran into the woods, have not
yet been heard of.

Nulla Nundaram’s brick houfe was broken down;
and his fon, who was then in it, was fo much bruiz-
ed, that he died in three days afterwards.

At Lafettee Silcope Chuckla the ground in fome
places opened, and threw up great quantities of fait

N n 2 water,

[ ]

water, and in others entirely funk : the channels of
feveral creeks and little vallics between the hills
were filled up with great quantities of find: in fome
parts the water ftill continues twenty cubits deep,
and in others unfathomable.

Silluk creak, and lffamuttee river are both flop-
ped up ; feveral boats laden with goods then coming
down are not now able to get out of them : the
country around there opened greatly in fome places,
and in others entirely funk ; and a great many tanks
filled with land.

Bur Coller hill opened about forty cubits wide.

Cefs Lung Joom hill, one of the Mug mountains,
is entirely funk.

Chunggee hill opened between twenty and thirty
cubits.

Puddooah creek, at that time without water, open-
ed, and threw up two hills of fand ; and all the houfes
in thefe parts were broke down.

Joom Chater Pedea hill, is funk fo low, that its top
is now’ on a level with the plains.

Rigerree hill, which was very large, opened thirty
cubits wide.

Joom Palang hill opened twenty-five cubits.

By the accounts already come in, there are 120
* Dons of ground loft in different parts of the pro-
vince; but thefe I am afraid will not be one eighth part
of the whole damages, as we have further relations
coming in every hour.

* One fye don of ground is 1920 cubits long, and 1600
cubits broad.

As

[ 269 ]

As we are informed, that there are two vulcanoes
opened, I am in great hopes thefe will prove a fuf-
ficient vent to difcharge all the remaining fulphurous
matter in the bowels of thefe countries, and put a
flop to any further earthquakes here; at lead for
many years to come.

XLIII. A Letter from the late Reverend Mr,

Thomas Bayes, F. R. S. to John Canton,
M. A, and F. R. S.

S I R,

Read Nov. 24, 'T' F the following obfervations do not
17 3‘ X feem t0 you to be too minute, I fhould
efteem it as a favour, if you would pleafe to commu-
nicate them to the Royal Society.

It has been afferted by fome eminent mathemati-
cians, that the fum of the logarithms of the num-
bers 1.2. 3.4. &c. to z, is equal to 4. log. c-\-z-\-l. x

log. 2; leffened by the feries -4-k- 1 — 1

J J j I2Z~36o Z3 I26oz5^

-rr — 7 ^ c denote the circumference of

a circle whofe radius is unity. And it is true that this
expreffion will very nearly approach to the value of
that fum when z is large, and you take in only a
proper number of the firft terms of the foregoing
feries : but the whole feries can never properly ex-

prefs

[ 27° ]

prefs any quantity at all ; becaufe after the 5th term
the coefficients begin to increafe, and they afterwards
increal'e at a greater rate than what can be compcn-
fated by the increafe of the powers of z, though z
reprefent a number ever fo large; as will be evident
by confidering the following manner in which the
coefficients of that feries may be formed. Take
a — T-j ^b=d', ycz=zzbay gd~z ca-\-b\ lie —
zdaAr2cby 2 ea-\- 2 db\-c*y 1 5 g — 2 y'rf q-

ze b-\-zdc, and fo on ; then take A —a, B— 2 b, Cz=z
2 x 3 X 4Cy D— 2 x 3 X 4 X 5 X 6d, E—z x 3 X 4 X 5
X 6 x 7 X 8 e and fo on, and A, B, C, D, K, b , 6cc.
will be the coefficients of the foregoing feries : from
whence it eafily follows, that if any term in the feries
after the 3 firft be called y, and its diftance from the
firft term n> the next term immediately following

will be greater than Whereforeatlength

the fubfequent terms of this feries are greater than
the preceding ones, and increafe in infinitum, and
therefore the whole feries can have no ultimate value
whatfoever.

Much lefs can that feries have any ultimate value,
which is deduced from it by taking z= 1, and is
fuppofed to be equal to the logarithm of the fquare
root of the periphery of a circle whofe radius is
unity ; and what is faid concerning the foregoing fe-
ries is true, and appears to be fo, much in the lame
manner, concerning the feries for finding out the fum
of the logarithms of the odd numbers 3. 5.7. &c....z,
and thofe that are given for finding out the fum of
the infinite progreihons, in which the leveral terms
have the fame numerator whilft their denominators

are

[ 27I ] .

are any certain power of numbers increafing in arith-
metical proportion. But it is needlefs particularly to
inlift upon thefe, becaufe one inftance is fufficient to
fhew that thofe methods are not to be depended
upon, from which a conclufion follows that is not
exadl.

XLIV. An Account of the InfeSl called the
Vegetable Fly : by William Watfon
F. R. S.

To the Royal Society.

Gentlemen,

Read Nov. 24, / ■ ^HE beginning of laft month, I re-
>763- ceived a letter from our learned and

ingenious mem ber Dr. Huxham of Plymouth in which
among other things he informed me, that he lately had,
by permiflionof commiffioner Rogers, obtained a fight
of what is called the vegetable fly, with the following
defcription of it ; both which he had from Mr. New-
man, an officer of general Duroure’s regiment, who
came from the ifiand Dominica. As this delcription
feemed to the dodtor exceedingly curious, he has fent
it me, exa&ly tranfcribed from Mr. Newman’s ac-
count, and is as follows.

“ The vegetable fly is found in the ifland Dominica,
“ and (excepting that it has no wings) refembles the
“ drone both in fize and colour more than any other
tc Englilh infedt. In the month of May it buries itfelf

“ in

[272]

in the earth, and begins to vegetate. By the latter
“ end of July the tree is arrived at it's full growth,
“ and refembles a coral branch; and is about three
<c inches high, and bears leveral little pods, which
<c dropping off become worms, and from thence
“ flies, like the Englifh caterpillar.” An account of
this extraordinary production, fimilar to the above,
was given to Dr. Huxham by captain Gafcoign, who
lately commanded the Dublin man of war, which
hath been at Dominica. The doCtor fubjoins, that
poflibly I may have heard of this fly; or feen it in
the collections of the Britifh Mufeum, or Royal So-
ciety ; but, if it is in neither, he believes he can pro-
cure it to be fent to the Royal Society.

Though the doCtor can by no means think the
above relation true in all it’s circumffances, yet he
is perfuaded there is fomething of reality in it ; which
perhaps further accounts and obfervations may fet
in a full and true light : though at prefent, as repre-
fented, it feems quite repugnant to the ufual order of
nature.

As I had never feen this production myfelf, but
had been informed that doCtor Hill had had the ex-
amination of fome of them, I wrote to that gen-
tleman to deflre to be informed of the refult of his
enquiries. To which he very obligingly fent me the
following anfwer.

<c When colonel Melvil brought thefe flies from
tc Guadalupe, lord Bute fent me the box of them to
“ examine. The refult was this. There is in Mar-
“ tinique a fungus of the Clavaria kind, different
“ in fpecies from thofe hitherto known. It produces
“ foboles from its fides. I called it therefore Cla-

“ varia

[ 273 ]

ee varia Sobolifera. It grows on putrid animal bodies,
“ as our fungus ex pede equino from the dead horfes
hoof.

\\ The Cicada is common in Martinique, and in
cc it s nympha ftate, in which the old authors call it
<c Tettigometra, it buries itfelf under dead leaves to
<c wah it s change ; and when the feafon is unfavour-
“ able, many perifh. The feeds of the Clavaria find a
“ proper bed on this dead infeCt, and grow.

“ The Tettigometra is among the Cicada? in the
iC Britifh Mufeum : the Clavaria is juft now known.

“ This you may be aftured is the fad, and all the
cc fadt ; though the untaught inhabitants fuppofe a
“ fly to vegetate i and though there exifts a Spanifti
drawing of the plant’s growing into a tri-foliate tree;
<c and it has been figured with the creature flying
“ with this tree upon its back.

“ So wild are the imaginations of Man j fo chafte
and uniform is Nature !”

Commiflioner Rogers, at Dr. Huxham’s defire,
has prefented this extraordinary production to the
Royal Society, and it now lies before you.

A careful examination of it feems to confirm, to
me at leaft, Dr. Hill’s opinion of the manner of this
phasnomenon’s being produced.

The ingenious Mr. * Edwards has taken notice of
this extraordinary production, in his Gleanings of Na-
tural Hijlory , and has given us a figure of it in that
elegant work.

There is in the Britifh Mufeum among the Ci-
cadas one, nearly refembling the animal part of the

* Vol. III. page 262, plate 335,

Vol. LIII. O o

pro-

[ 27+ ]

production before you ; but it came from the Eaft'
Indies. 1 here is likewile from the Weft Indies, in
its perfedt or winged ftate, the infeeft, of which this-
production is believed to be the nympha. [Vid. Tab.
XXIII.J

I am with all poflible regard.

Gentlemen,

Your moft obedient humble fervant,

Lincoln’s-Inn Fields,

Nov. 15, 1763.

William Watfon.

XLV. An Attempt to explain a Punic In-
fer ipt ion , lately difeovered in the IJland of
Malta. In a Letter to the Reverend Thomas.
Birch, I). D. Secret. R. S. from the Reve-
rend John Swinton, B. D . of Chrift-
Church, Oxon. F. R. S. a?id Member of the
Etrufcan Academy of Cortona in Tufcany.

Good Sir,

Read Nov. 24, "T Received fome months lince from the
l/ A Honourable Mr. Lyttelton of Chrift-
Church, fon to the Right Honourable the Lord Lyt-
telton, a copy of a Punic infefiption, lately difeovered
in the illand of Malta, fent me from Rome by Sig.
Abate Venuti, antiquary to the Pope, and a gentle-
man of profound erudition. This copy was inclofed
in a letter to the Right Reverend the Lord Bilhop of

Carlille,

[ s75 ]

Carlifl e, who was fo good as to trail fm it it to me at
Oxford. The infcription has been mentioned, but not
explained, by M. l’Abbe Barthelemy in the Journal
des S$avans , who has deduced a new Phoenician al-
phabet from it ; though he feems to doubt whether
any of the tranfcripts that had appeared, at leaft any
of thofe he had feen, agreed perfectly in all particu-
lars with the autograph itfelf. However, from the
known accuracy of Sig. Abate Venuti, I think we
may venture to fuppofe the copy now fent you to be
in the main fufficiently exadh I fhall therefore, at the
requeft of feveral friends, fubmit to the confideration
of the Royal Society a few curfory remarks upon this
curious monument of antiquity ; efpecially, as it has
not yet in a proper manner been communicated to
the learned world.

L

The three firft letters undoubtedly form the He-
brew word Tin, PENETRALE, CONCLAVE, INTI-
mvs R ecessvs, &c. for a farther account of which,
recourfe may be had to the 2 Hebrew lexicographers.

The next two elements feem to be Beth and Thau ,
of which is compofed the Phoenician word n3, pro-
bably the fame with the Plebrew domvs • as
the Phoenicians not feldom omitted, or fuppreffed, the
letter Jod. This moil evidently appears from CDTf,
pv, onv, &c. for pn% mm, cm, &c. ex-

1 Journal des Sfavans, Suite de Decembre 1761. p. 82, 8?,
84. A Amfterdam, 1761.

Val. Schind. Jo. Buxtorf. Chriftian. Stock. Jo. Leonhard.
Reckenberg. aliique plur. lexicograph. Hebr.

O 0 2 hibited

[ 276 ]

hibited by the Tyrian and Sidonian coins. The
form of the Thau here feems to indicate the infcrip-'
tion to be of a later date. This character bears lome
retemblance to the figure of Tzade , preferved on certain
medals of Tyre and Sidon ; though thefe two, what-
ever may have been infinuated to the contrary by a
writer of confiderable note, are fufficiently diftin-
guifhable from each other.

The three following letters prefent to our view the
Hebrew word oSy, secvlvm, ^ternitas, per-
PETVITAS, DVRATIO HOMINIBVS ABSCONDITA,
&c. Not the leaft difficulty occurs here.

The three preceding letters are fucceeded by Koph ,
Beth, and Refch, forming the noun ^Dp, sepvl-
chrvm; which, with the introduction juft explained,
fufficiently points out to us the nature of the infcrip-
tion I am now upon.

The four next Phoenician elements anfwer to the
Hebrew deposit vs. The true fignification

of the term, as ufed here, is preferved in the 3 4 Sy-
riac.

With regard to the following word npj, clarvs,
innocens, 1 vst vs, &c. I fhall only beg leave to ob-
ferve, that it cannot well be mifunderftood. It will
be almoft fuperfluous to remark, that both this and
the preceding word alfume the nature of fubftantives
here; the term vir, by a moft common ellip-
fis, being fuppreffed.

The four following characters combined produce
the Hebrew consvmmationibvs, omnino,

pen it vs, &c. The reality of this word, from what

3 Buxtorf. Lex. Chaldaic . & Syriac, p. 97. Bafilcae, 1622.

4 has

[ 277 ]

has been laid down by the Hebrew 4 lexicographers;
may be moft clearly evinced.

The letters He , Zain, He , feem to conftitute the
participle run, dormiens, decvmbens, &c. M.
l’Abbe Barthelemy, unlefs I am deceived, takes
the fecond of thefe elements for Jod. But this will
neither be admitted by the form itfelf, nor the tenor
of the infcription. The fmall ffroke, or fcratch, above
this character, feems to be only an accidental blemifh,
occafioned by the injuries of time.

The participle Dm, vehementer amans, or
intime diligens, probably begins a new fentence.
Some doubts may perhaps arife about the power of
the fii ft character. However, after the clofeft exami-
nation of the infcription, it appears to me to be cer-
tainly Refcb.

The verb fp, tremvit, or commotvs est, im-
mediately follows. This Chaldee word may likewife
be rendered magno cvm affectv motvs est, and
deduced from the Arabic, according to 5 Maius.

The fubftantive DK, popvlvs, which immediate-
ly follows, comes in appofitely enough here. The
Carthaginians fometimes ufed the word p in the
fame, or at leaf; an extremely fimilar, fenfe. This
appears from fome of the medals 6 of Menas, now
called Meneo, an ancient town of Sicily, fubjedt to
the Carthaginians ; on which we find n^riD DJL po-

f

4 Val. Schind. Lex. Pentaglot. p.866. Hanoviae, 1612. Chrift.
Stock. Clav. Ling. Santt. Vet. Tejl. p. 528, 529. Jenze, 1727.
Jo. Leonhard. Reckenberg. Lib. Radio, five. Lex. Hebraic, p-
777. Jenae, 1749.

5 Maius, apud. Jo. Leonhard. Reckenberg. ubi fup. p. 1386.

6 Numifm. Antiqu. &c. a Thom. Pembr. et Mont. Gomer.
Com. Collett. P. 2. T. 87.

PVLVS

[ 278 ]

TVLVS MENARVM, or POPVLVS MENENIVS, to Omit
others that might with equal facility be produced, as I
have many years fince obferved. For a farther ac-
count of CDSt I mud beg leave to refer the cu-
rious to the Hebrew lexicographers, and particu-
larly to Maius 7. r

The next word in ponendo, or* rather

QVVM PONERETVR, (i. e. 'm®'?, Or IN SE-

pvlchro, or IN terra) occurs in the very fame
fenfe, Psal. xlix. 15. which pad'age throws confidera-
blc light upon this part of the inlcription. That the
Punic diaiedt of the Phoenician, the language of our
infcription, was not without luch ellipfes as that men-
tioned here, mud: be allowed probable enough, if
* Bochart’s Latin verfion of the Punic words in Plau-
tus may be confidered as not very remote from truth.

The three lad words of the infcription are appa-
lently “pOID p hannibal filivs barme-

LEC, BARMILC, BORMILC, Or BARMELECI. As the
letter r in the converfion of Oriental words into
Greek is fometimes lod, the Carthaginian name
barmelec, or bormilc, might have been pro-
nounced bomilc (and perhaps bomilcar) both by
tlie Greeks and the Romans. For that the ge-
nuine Carthaginian names, when either written or
pronounced by the individuals of thofe nations, were
not a little corrupted and depraved, I think we have
no manner of reafon to doubt.

7 Maius, apud Jo. Leonh. Reckenberg. ubi fup. p. 51.

* Vld- St°ck. et Reckenberg. in vocib. /W et fintP.

Boch. Chan. Lib. II. c. vi.

9 Id, ibid. c. vii, viii, xi.

II. From

[ 279 ]

II.

From the foregoing obfervations it moft evidently
appears, that the following arrangement of the words
forming this infcription may be confidered as not ve-
ry remote from truth..

"op ob ro rrn
~m ntn rfrro npj
on fp o-
*$0*0 p by-

The Latin and English verfions of which words
may, as I conceive, be appofitely enough drawn up in
the following terms.

PENETRALE DOMVS SECVLI (five DOMVS PERPE-

TVJE) SEPVLCHRVM DEPOSITI (hlc) CLARI (viri)

CONSVMMATIONIBVS (i.e. OMNINO, PLANE, Vel ARC-

TISSIME) DORMIENTIS INTIME DILIGENS (eum)

COMMOTVS (eft) POPVLVS QVVM PONERETVR (foil.
IN TERRA i.e. SEPELIRETVR) HANNIBAL BARME-
LEC (BARMILC BORMILC vel BARMELECl) FIL1VS.

THE INTERIOR PART OF THE HOUSE OF LONG DU-
RATION (or LONG HOME i. e. THE GRAVE) THE

SEPULCHRE OF AN UPRIGHT MAN DEPOSITED (here)

IN A MOST SOUND (or DEAD) SLEEP THE PEOPLE

HAVING A GREAT AFFECTION FOR HIM WERE
VASTLY CONCERNED WHEN HANNIBAL THE SON
OF BARMELEC (BARMILC Or BORMILC) WAS PUT

into the earth, or interred.

It

[ 2 8o ]

It ought to be here remarked, that the word tum
terminates the fecond line, and begins the third; as
alfo that the proper name hannibal, by a

fimilar kind of bifTeCtion, belongs both to the third
and fourth lines. But this is by no means to be won-
dered at. The Greeks obferved the fame method
of writing in their infcriptions *°, both of an earlier
and a later date.

III.

That the words above explained form a fepulchral
infcription, will admit of nodifpute. The three firft
of them in particular, which feem to be a fort of
preface or introduction to the proper infcription, render
this inconteftable ; and the others, either in conjunc-
tion with or exclulive of them, amount to an afler-
tion of this in direCt terms, and confequently prove
it to demonftration. ^ That the term the fecond
word of the infcription, is equivalent to the Hebrew
/Y3, notwithflanding the omiffion of Jod, is evident
beyond contradiction, not only from the reafon above
aligned, but likewife becaufe the expreflion oSy
denotes the house of long duration, a man’s
long HOME, or the grave, the very fenfe it is
ufed in here, Eccles. xii. 5. Nor can the Jod well be
looked upon as an effential part of the noun, fince
the plural of fiO in the Hebrew is QTD, and the
Ethiopic term for a houfe is agreeing in all re-
fpeCts with the fecond word here. M. l’Abbe Bar-

,0 Chifh. Antiquitat. Ajiatic. pafl*. Vid. ctiam Tho, Reinef. Syn -
tagm. Infcript. Antiqu. palf. Lipfix*, 1682.

thelemy

t 28i ]

thelemy 11 takes the third letter of the third line
for Vaiiy and affigns it the place of that element in

” Journal des Sfavans, ubi fup. M. PAbbe Barthelemy * take*
a very fimilar character for Vau , in the infcription of Carpentras;
which probably induced him to affign this figure the power of
that element, though the infcription of Carpentras does not ap-
pear to me to have been firft difcovered in the ifland of Malta.
The letters forming the Maltefe-Phcenician infcription, which
the French Abbe has attempted to explain, are very different from
thofe of the infcription I have been confidering, and the two cha-
racters in particular imagined to reprefent Vau in thefe monuments
bear fc rce any refemblance to each other. Hence it fhould feem
to follow, according to M. 1’Abbe who b attributes the diverfity
of charadter in the Phoenician or Punic infcriptions rather to diffe-
rence of place than diftance of time, that the letter in qucfti-
on ought by no means to be looked upon as Vau. I {hall not
however pretend to avail myfelf of a notion, how hard foever it
may bear upon him, that I confider at leaft as arbitrary and pre-
carious, if net plainly falfe ; but {hall fufpend any farther obfer-
▼ations I may have to make on this head, ’till tne publication of
M. i’Abbe’s famous memoir on the Phoenician letters, upon the
fuperior merit of which he has himfelf with fo much complacency
cbeen pleafed to dilate, and which fome of his d admirers have placed
in fo glorious a light. In the mean time I muff beg leave to re-
mark, that the character before me does not only referable one
of the Cnaldee forms of Pe, but likewife the e antient Samari-
tan and Greek forms of the fame element ; and that the word
formed of Refch and Pe, ^"1, is confonant enough to the tenor
of the infcription. This, I conceive, fufficiently authorizes me
at prefent to aferibe to the fuppofed Vau the power of Pe. If
in this point I fhould happen to be wrong, M. l’Abbe will moft
certainly r redtify my miftake. I fhall ever lye open to convic-
tion, being determined in my refearches and inquiries to facri-
fice all inferior confiderations to the love of truth.

a M. de Guignes, De I'Orig. des Chin. p. 54. A Paris,' 1760. Recueil d'
Antiquit. &c. de Comte de Caylus, Tom. I. p. 73, 74. pi. XXVI. A Pa-
ris, 1752.

b Journal des S fa-vans, ubi fup.

« Journal des Sfavans, Aout 1 760. p.277.

<* M. de Guign. ubi. l’up. p. 60. Journal des S fa-vans, Decembre 1760.
P- 348.

e Joan. Baptift. Biancon. De Antiqu. Litter. Hebraor. et Greecor. p. 31,
32. Bononise, 1748.

f Recueil des Medailles de Peuples et de Villes, £sY. Tom. III. p. 140. A
Paris, 1763.

V 0 l. L11I. P P his

C 282 ]

his alphabet. But the form of this character is total-
ly different from that of the Phoenician Vau, efpeci--
aily as it is exhibited by the other Maltefe infcription,
of which he pretends to have given us fo accurate a
copy. Nor will the fenfe of that part of the in-
fcription in which this letter appears afford the lead
countenance to fuch a fuppofition. On the con-
trary, the figure of this element well enough corref-
ponds with that of the final fquare or Chaldee Pc,
and the verb formed of Rcfch and Pe leems confo-
nant enough to the tenor of the infcription. To what
has been obferved of the letter Zain, in the fecond
line, we may add, that this character fufficiently re-
fembles the Hebrew and Palmyrene Zain and that
the word HiH, dormientis, very naturally con-
cludes the fentencc, of which it is a conlfituent part.
All which if we admit, and allow Sig. Abate Venuti’s
copy to be in the main exadt, as I cannot help think-
ing it is ; the following alphabet, plainly deducible
from that copy, will be found to contain feventeen
of the Punic literary characters ufed in Malta, when
our infcription firft appeared.

The Maltefe-Punic alphabet.

Aleph
Beth -
Ghimel
Daleth
He - -
Vau -
Zain -
Heth -
Teth -
Jod -
Caph -

£

- - 'J

- - 4
- 'Ti

- )

©T3

Lamed
Mem -
Nun -
Samech
Ajin -
Pe - -
Tzade ■
Koph -
Refch .
Schin -
Thau -

AA

yy

rr

uu

0

il
- S*

rn

%

C 283 ]

Hence ’tis obvious at firft fight, tint the forms of
feme of thefe letters differ from thofe of the corref-
pondent elements in M. l’Abbe Barthelemy’s alpha-
bet ; and that the characters he takes for Vau and
yod, which has indeed been already remarked, I
fuppofe to be Pe and Zain. Which of us is in
the right, after a more accurate copy of the inferip-
tion can be procured, perhaps the learned may be
able to decide.

IV.

Who Hannibal the fon of Barmelec, Barmelc,
or Bormilc, was, or when he lived, for want of fuf-
ficient light from ancient hiftory, I cannot take upon
me precifely to determine. We may however, I
think, reft allured, that he died a confiderable time
(perhaps feveral centuries) after the Citiean inferip-
tions, or at lead the earlieft of them, firft appeared.
The forms of feveral of the letters, particularly of

P p 2 the

2

C 284 ]

the Aleph , Ghimel , He, Heth , Caph , Koph, Schin,
and Thau, io confiderably differing from thofe of the
fame elements in the earlier Phoenician times, feem to
render this inconteftably clear. I know, indeed, that
M. l’Abbe Barthelemy would be thought to infinuate,
if he does not dire&ly affert this, that fuch variations
are 12 always to be attributed to difference of place,

11 Journ. des Sfav. Suite de Decembre 1761. p. 83. The cha-
racter reprefenting Koph in our infcription was not the original,
nor even the earlier, form of that element. One fomewhat refem-
bling it was however ufed by the Carthaginians in Sicily, before
they were difpofleffed of that ifland by the Romans. This plainly
enough appears from the Punic coin in Tab. XVII. now in my
fmall cabinet, and never before publifhed. This piece feems to
exhibit the word tnmp, Carthada, the very Punic name
of Carthage, according to a Solinus, in Punic characters ; the
fxrft of which bears fome refemblance to the later figure of Koph ,
as preferved on the monument under confideration. The letters
on the reverfe are not fo legible. They neverthelefs appear to
me to form the names of two Carthaginian cities in Sicily. The
firft of thefe was perhaps KAtD, mot a, or rather motya ; the
Vau and Jod having been not unfrequeptly omitted in Phoenici-
an, and therefore probably in Punic, words. The name of the
other towrn, as originally impreft on the medal, being in a great
meafurc defaced ; I fhall not venture at a communication of it
to the learned world, but leave it to be cleared up by fome other
coin or infcription that may pofiibly hereafter occur.

That the names of two Sicilian cities in Punic chara&ers were
fometimes impreft upon the reverfe of one coin, may be fairly
inferred from a Carthaginian medal now in my pofieflion ; of
which I may probably, in a future paper, give a particular ac-
count. A form of Koph pretty fimilar to that vifible on the mo-
nument I am confidering likewife appears on a coin of achola,
acholla, or achvll A, as the medal prefents the word to our
view, ftruck in the Auguftan age. b rom what has been here
obferved, as well as from the refemblance both thefe figures of
Koph bear to the fquare or Chaldee form of the fame element, we
may collect the remains of antiquity that exhibit them not to
have been the produce of the earlier Phoenician times,

* J. Solin. Tolybijt. cap. xxvii. Trajcft, ad Rhen. 1689.

rather

[ 2S9 ]

rather than didance of time. But befides that fuch a
notion runs counter to what he had before 13 advanced,
this by no means feems agreeable to truth, or the na-
tural courfe of things. For the Punic and Phoenici-
an alphabets were originally the very fame, and con-
tinued fo, or nearly fo, I make not the lead doubt,
long after the foundation of Carthage. And this is
rendered highly probable by the letters preferved on
many Carthaginian coins. To what then can we fo
properly afcribe the aforefaid variations as to didance
of time, fince the letters fo varied in the Carthagini-
an territories had undoubtedly the fame forms with
thofe of the correfpondent elements in the more an-
tient Phoenician alphabet, (ufed both there and at
Tyre, Sidon, Citium, &c.) feveral ages before? In
fine, the fame characters at fird prevailed both at
Carthage and in Phoenicia ; though thefe, or at lead
feveral of them, in after ages, affumed pretty different
forms. So that the more any Punic or Phoenician
literary characters, in whatever country found, re-
cede from thofe that formed the Samaritan or earlied
Phoenician alphabet, the later they ought undoubted-
ly to be deemed, as I have elfewhere obferved. Nor
will M. l’Abbe, I flatter myfelf, notwithflanding the
infinuation hinted at here, be dilpleafed with me, if
on this occafion I fhould adopt another I+ of his opi-
nions.

After the Carthaginian provinces had been fubdued
by the Romans, the people dill retained the ufe of
their antient proper names, and fpoke the Punic

i

f

13 De I'Orig.des Chin. par M. d*e Guignes, p. 39’ A Paris, 1700.

14 M. de Guign. ubi fup. p. 39.

tongue.

[ 2<?0 ]

tongue. The former of thefe points is abundantly
cicai from corns and inlcriptions, pubiifhed by the
15 authors here referred to; and the latter of them is
no Ids clear horn writers, of the beft and moll un-
doubted authority. Nay, we have good reafon to be-
lieve, that the Phoenician or Pun c language was
fpoken and underitood in fome of thole provinces
even to the days of St. 16 Auftin.

With regard to the ifland of Malta in particular,
which was ib long fubject to the Carthaginians, it
may not be improper to remark, that the intire re-
duction oi it items lcarce to have been effected be-
fore the time of Julius Caefar by the Romans. For
although the people of that ifland were obliged to
fubmit to the Roman power, after the deftrudtion of
Carthage; yet they found means afterwards to affert
their independency, and (hake off the Roman yoke.
But notwirhfLndmg they had been rendered a formi-
dable maritime power, by the extenfive commerce
which they enjoyed, they were finally 17 fubjugated
by Ctdar, though with no imall difficulty, about
lbrty-live years before the birth of Christ. It may
juffly therefore be queffioned whether the Latin
tongue was ever much uled in Maita beiore the
death of that conqueror, or rather before the com-
mencement of the Chriftian asra, which was but lit-
tle pofferior to it. Be that however as it will, that

15 Jo. Goth. Richter. Nov. Num in Colon. Karthag. African.
Percus. See. p. 8. Lipfiae, 1742. Numiftn. Antiqu. l'hom. Pem-
broch. et Montis Gomeric. Com. P. 2. 1 . 89. Sam. Bochart.
Chan. Lib. II. c. xxiv. Tho. Reinef. ubi flip. p. 487, 488.

16 Chiiftoph. Hendreich, in Carthag. p. 8, 9. Francofurti ad
Oderam, 1664.

17 Appian. Alexandria, apud Burchard. Niderfted. in Malta
Vet. et Nov. lib. II. c. vi. p. 69. Heimelladii, 1660.

the

[ 29 1 ]

the life of the Punic language and the Punic proper
names was retained in Malta, as an antient part of
the Carthaginian territories, at lead; three or four cen-
turies after the lad; mentioned period, if not much
longer, from what has been here advanced, is abun-
dantly clear. Nay, that the Punic tongue is even at
this day the vernacular language of the lower part of
the Maltefe, though deformed by many corruptions,
and difguifed by the accedion of various foreign
words, after perufing what has been communicated
on that head to the learned world by ,s Canonico
Agius, I am dxongly inclined to believe.

Since therefore the duds of feveral of the letters
indicate this infcription to be of a later date, we can-
not but fuppole it to have been many years (perhaps
feveral centuries) pofterior to the conclufion of the
fil'd: Punic war. And fince Hannibal Ben Barmelec,
or Bormilc, is mentioned therein as a perfon of con-
fideration, whofe death was greatly lamented by the
peoplej perhaps he was either a popular fenator of
Malta, or one of the fuffetes there, (the Punic form of
government not improbably prevailing in that idand,
even when dependent on the Romans, as it did in
other 19 places that had been fubjed to the Carthaginian
ftate) a century at lead; after Julius Casfar had given
the finidiing firoke to the liberties of the Maltefe.
T his, I fay, appears to me by no means improbable}
but that he ready fuftained either of the charaders
here mentioned, or lived at the time here fuppofed, I
mud: not prefume pofitively to affirm. The forms
of fome of the letters will not permit us however, 1

13 Gio. Pietro Francefco i^gius de Soldanis, Delia Lingua P u. -
nica prefentamente ufata da Maltefi, kc. In Roma, 1750.

19 Hendreich, ubi fup. p. 316. Reinef. ubi fup.

think,

[ 2Q2 ]

think, to affign this infcription a higher age. They
rather announce a later than an earlier dace.

V.

The words forming this infcription are for the mod
part either Hebrew or Punic. Of the former fort are

p, nvi, ok, am, nrn, “Dp, cSp, *nn ; of the
latter nSoD, npb rO> befides the proper names
lb that only and fp feem to

bear any relation to the Chaldee and Syriac. Hence
we may plainly fee, as well as from what I have for-
merly obferved, that neither the Punic nor Phoenici-
an was almod intirely Syriac; and confequently, that
the oppofite notion, advanced by M. l’Abbe Barthe-
lemy 20 and M. de Guignes, together with the fuper-
drutdure they have ere&ed upon it, mud; necefiarily
fall to the ground.

’Tis worthy obfervation here, that we have not met
with the proper name of a Carthaginian in Punic cha-
racters, on any of the remains of antiquity, before the
monument whofe infcription I have been confidering
occurred ; and it likewife ought to be remarked, that
the word Hannibal is formed of the very fame
Punic letters in this infcription that it has been fup-
pol'ed to have antiently confided of by the 21 learned.

With regard to the elliples pointed out to us in
the Latin and Englilh verfions of this infcription,
they are fuch as have ever been common in the eadern
world ; and fimilar ones will prelent themlelves to

10 M. de Guign. ubi Tup. p. 6o. Journal da Sfav. Deccmbre
1760. p. 348.

11 Boch. Chan. Lib. II. c. xii. Hcndr. ubi fup. p. 149. Ad.
Littlct. Ling. Latin. Ditt.

our

[ 293 ]

our view in paflages of fcripture, too numerous, as
well as too obvious, to be cited here **.

The length of the infcription, as it feems to have
only a fingle perfon for it’s objedt, as well as the forms
of it’s letters, will undoubtedly evince it to be the pro-
duce of a later age ; though the precife time of it’s fird
appearance, for want of fufficient light from antient
hidory, I cannot take upon me to alcertain. Nor
fhall I be fo vain as to pronounce the explication now
fubmitted to the judgment of the Royal Society in ail
points true, as I have not yet met with a copy of the
infcription abfolutely to be depended upon. However,
I hope it will not be found very remote from truth.
If hereafter, by means of a more accurate tranfcript,
I fhould difcover any errours in what has been here
advanced, I fhall mod readily retradt them, and ever
with great pleafure liden to better information. AH
farther remarks on this curious monument of antiqui-
ty, fo highly meriting the attention of the learned,
1 mud at prefent fuperfede ; having now only time to
beg you would believe me to be, with the mod per-
fedt confideration and regard,

S I R,

Your much obliged,

and mod obedient fervant,

Chrift-Church, Oxon<

May 20th, 1763. SwilltOll.

Vid. Johan. Buxtorf. Thefaur. Grammat. Ling . SanSi. Heir.
& Chriftian, Nold. Concordant. Particular. Ehraco Chaldaic. pafl*.
Vid.etiam Boch. Chan, Lib. I. c. xxxv. p. 705, Franccfurti
ad Moenum, 1681.

Q.q

Vol. LIII.

XLV". Some

[ 29+ ]

XLVI. Problems by Edward Waring, M. A.
and Lucafian ProfeJTor of Mathematics in
the Univerfity of Cambridge, F. R. S,

PRO.

Nvenire, quot radices impoffibiles
habet data biquadratica aequatio

a:4 4- qxz — rx 4- s— o .

lmo Sit 256 s 3 — 128 q* P 4- 144 rz q-\- 16 q 4 X * —
27 r4 — 4 r1 q2 negativa quantitas, & duas & non
plures impoffibiles radices habet data aequatio.

2do Sit affirmativa quantitas, & vel — q vel q — 4 s
negativa quantitas, & datae aequationis quatuor radices
erunt impoffibiles.

3tio. Sit nihilo aequalis, & vel — q vel qz — 4 s
negativa quantitas, & datae aequationis duae inasquales
radicis erunt impoffibiles.

2. I nvenire, quot radices impoffibiles habet data
aequatio x3-\-q x3 — r x1 -\-sx — tz=. o.

imo Si figna terminorum aequationis w'°4- 10 q w9

4- 3Q q1 4- 10 5 X w84-8o ^4-50 ^^4-25 r X W 4-

gs V -^r 124 95 **4-92 + 200 r; X ‘w6 4-

66 q;- — 360 q s-y 196 q< s-\- 1 iti g~ r 4-260^54-625
?4-4oo y71xws4- 25/ 4-40 P— 53r4+52?3r— ‘
522 ^ / 4- 194 <?4 54-708 4-, 240 qz r t 4- 1750

y r — 5 r t X ‘t#4 4~ 4 Q 4- iq6 -S’ — k° ? J 3°^

j* — ■ 02 y r4 — 7 y4 ra4- 370 r4 5*4-612 q~ r~ s 4-700
r1/ — /a j 4, 2500 Py'4- 80 r t q3 — 2150 qrst

Xw34-400 s' — 360 q 5’-— -i 5 5,+ 5 4* 24 ^ ^ ;

— 45

Read April 21, 1

i763- J

I.

[ 295 ]

—45 qz r* — lyotr* s\- 140 r2 5 ^4-960 rz s'1 q-\- 1 875
t r" 4- 1 000 t r s'" — 5000 f q s 4- 1 750 f a1 4- 40 t r <?4
4- Ooo t r3 q — 1650 trscqy wr 4- 36 r— 224 q' sL

4-320 q i4 4- 4 r4 4-27 r6 — 40 r2 4- 434 r2 qr s’ — >
24 r~ s q 4 — 198 q s 4- 5000 /2 s' — 450 t r' s- — 6250

V ^4-675 f qA — 3750 f qx s 4- 3000 f r2 q-\-bo tr3 qz
4- 200 t r sz q — 3^0 t r q3 syw 4-3125 f — 375° qr ?
4-2000 s" q 4-2250 r?\y — 900 jt ^ 5 4- 8 2 5 r2^''4- 108 q 5
X f — 1 600 j3 r — 560 r q 2 / — 16 r3 ^4-630 r3 q s-{-

72 r — 108 r5 x^4"25^ ^ — J2% <1 ^4- 144 r2 q s3
4- 16 ^4 f — 27 r4r — 4 r2^3 j2— o. continuo muten-
tur de 4- in — j & — in 4- j nulias impoffibiles ra-
dices habet data aequatio.

2d0. Si figna terminorum aequationis haud conti-
nuo mutentur de 4- in — & — in 4- ; duae vel
quatuor datae aequationis radices erunt impoffibiles,
prout ultimus ejus terminus fit negativa vel affirmati-
va quantitas.

3d0. Si ultimus ejus terminus nihilo fit aequalis, &
figna terminorum aequationis haud continuo mutentur
de 4- in — & — in 4- ; turn vel quatuor vel duae ra-
dices datae aequationis erunt impoffibiles, prout duo
& non plures ultimi datae aequationis termini nihilo
fint asquales, necne.

PRO.

Sint x, y, v3 abfcifia, ordinata & area datae curvae,

& fit y" y y +c+dx+exx yy + j 4- g x

~+h~~9f+k x 3 x y*~+ o* invenire, utrum area

(•u) quadrari poteft, necne.

Supponamus aequationem ad aream efie vr‘ 4-

A-^Bx^Cxzv~+ D 4- E*4-F <+jGx34-H^x

[ 296 ]

v + I -f K x 4- L 4. M a;3 4- N x4 4- O * 5 4- P *6

r. — 3 _ n—\ -

X v 4- &c. = o. & confequenter crit nyv +n — 1
A 4- hx-\- Cx'yv + n~ 2 x Dx Ex 4- Ex 1 4- GxJ 4- Hx+
B4-2CX v + E4-2 t x + 3 G x1, -^Hx3

n — 3

X y v + &c.

X V + 6cc.

Ex quibus aequationibus, 11 tnethodis notis extermi-
netur (v), habebimus aequationem, quae exprimit re-
lationem inter (x) Sc (jy). Hujus autem aequationis
ccefficientes aequari debent coefficientibus datae aequa-

tionisjy -\-a-\-b x y + c d x + e xz ~\-y -f See.

— o j & fi quantitates A, B, C, & c. exinde determi-

nari poftunt, curva quadratur, eft enim v -|- A -[-Bat

n — 1

-\-Cxz xv + D + Ex -f- + Gx3 +H/

X v ” + See. = o j aliter autem quadrari non poteft.

Ex. Sit data aequatio y1 x* — 1 = o, Sc fuppona-

mus aequationem ad aream vz D 4" E x ~\~ F x7 +
G a;3 -\- H x*z= o ; Sc erit 2 vy -j- E -\- 2 F x 4 ■ 3 G
xz -)- 4 H xs = o, ita reducantur hae duae aequationes
in unam, ut exterminatur (y), Sc refultat aequatio yz-
16 H1 A6 + 24 HG Xs + 16 HF 4- q G~ .y4 + b h H + 12 F G

4 x H^+-4Gxi+Jt,x24-t^ + D

^6gTTTTfV + 4FEx ±e; = o. debet autem

fradlio

i6H^6 + 24HG^+i6HF + QG^4 + 8EH-f 12FG

4 x H*+ + G*3 + F x' +
*M- 6 G E -f 4 F* x* + 4 F E * + E*

E x 4- U
fequenter

5

efte x* — 1 5 6c con-

4 h

[ 297 ]

4 H — 16 Hz
4 G = 24 HG
4F--4H- 16HF4-9 G4
4 E — 4G— 8 HE-]- 12FG
4D-— 4 F = 6GE + 4F2

— 4 E = 4FE

— 4 D — E’

led e methodo communes divilbres inveniendi con-
Hat has asquationes inter fe contradibtorias efte, &
confequenter curvam haud generaliter efte quadra-
biiem.

T H E O.

Sint x,y, v, abfcifla & ordinatss curvarum A BCD
EFGHI&C.&A § ejkc. & fit y— p x\ & “Urr:

JLpa^x'^n pan-^x^nx~1^

2-3

X n-

X

30 X 2 x 3

42 X 2 X 3

— .‘lilful h a n — -5 S 77 x 77 — 1 x n — 2 x n — 3 x 4 x n~5

x x 5 "30x2x3 x 4 x 5 x 6 x 7

X 72 6 , 72 7 7

pa ' x1 4

572 X 77 1 X 72 2 X 72 3 X 72 4 X 72—5

X 72 6 X 77 7 x 72

~

X 72 4 X 72-

X7 x8 X9 xio xii

66 x 2 x 3 x 4 x 5 x 6x7 x 8

2^0 69J x 72 x 72 1 x 72—2 X 77— —3

r ' 2730 X 2 X 3 X 4 X 5 x6

5 X 72 6 X 72 7 X 72 8 X 72 Q X 72 10 72-11

pa

x" + &c. cujus ultimus terminus debet efte x 1 vel

71 2

x , prout (;z) eft par vel impar numerus.

Sit AP = a, bifecetur A P in T in duas
asquales partes, & ducatur linea E T <5, & ft AE,
EAI, AM, jungantur; erit triangulum AEM =
TP e A T areas.

Deinde,,

[ 298 ]

Deinde, bifecentur TP, AT in R and V, &

ducantur R G, CV^; & jnngantnr AC, CE, EG,
GM; & erunt duo triangula ACE-J-EGM =
VT V ares.

Eodem modo, fi partes A V, V T, TR, R P ite—
rum bifecentur in W, U, S, Q, Sc ducantur lines
BW/3, UD, SF, QH; & jungantur A B, B C,
CD, DE, EF, F G, GH, HM; erunt quatuor
triangula ABC + CDE + EFG + GHM =
W V y @ W ares ; Sc fic deinceps.

Cor. i. Si curva A B C Sc M lit conica parabola,
( c,e)y—pixz , erit v = 4 p a x ; Sc A See. erit
reefta lineaj Sc propofitio eadem eft cum notiftima
propofttione Archimedis de quadratura parabols.

Cor. 2. Si y—px\ erit v = a 1 x, Sc

See. iterum re<fta linea.

Cor. 3. Data curva, cujus squatio eft y =/> a: 1 ",
inveniri poteft altera curva, < cujus dimenftones Funt
(2 tz-i), in qua fumms triangulorum ad lingulas bi-
feftiones erunt refpeStive squales fummis triangulo-
rum dats curvs.

His adjici poteft, quod ft loco bife<ftionis abfcifta
A P alia quavis ratione in squales partes dividatur,
fumms triangulorum curvs A B C D See. ad iingu-
las diviftones squales erunt fegmentis curvs A/3y J

See.

IM

C 300 ]

1

XL VII. Second Paper concerning the Paral-
lax of the Sun determined from the Obfer-
vations of the late Tranfit of Venus, in
' which this SubjeSl is treated of more at
length , and the Quantity of the Parallax
more fully afcertained . By James Short,

M,A. and F. R. S .

Read Dec. 8, TT N the lad: volume of the Memoirs of
1 "63* the Royal Academy at Paris for the

year 1761, there is a Memoir by M. Pingre, who
went to the ifland of Rodrigues, and oblerved the
tranfit of Venus there ; in this memoir M. Pingre
endeavours to determine the parallax of the Sun, by
the obfervation of the late tranlit of Venus, to be
— 10". both by the obferved durations, the lead: dif-
tance of the centers, and by the internal contact at
the eorefs ; and feeems to think that there mud; be
fome miftake in the obfervation of Mr. Mafon at the
Cape of Good Hope, particularly with regard to the
difference of longitude between Mr. Malon’s obfer-
vatory and Paris, becaufe by comparing the obfer-
vation of Mr. Mafon at the Cape with the European
obfervations, he finds the parallax of the Sun, from
thence refulting, to be between 8" and 9", confe-
quently differing from the determination by the ob-
fervation at Rodrigues when compared with the lame
places. I (hall therefore, in this paper, endeavour
to prove, beyond all doubt, by a companion of the

obfervations

Thilcs. Tra-ns. Vol.znr. TAB XV JIT p. 3 00

[ 301 ]

observations on this fide of the Equinodfial Line alone,
that the Sun’s parallax is between 8 7 and 9", and that
this determination is the fame or very nearly the fame,
as when the obfervation at the Cape is compared with
the fame places. I fhall all'o endeavour to prove,
that there is a miftake of one minute in time in writ-
ing down the time of the internal contact at the egrefs
at Rodrigues, and that this being corrected, the re-
fults of the Sun’s parallax, by a comparifon of the
obfervation at Rodrigues with the observations at the
feveral places on this fide of the Line , is the fame with
that which refults from all the reft ; and this a^ree-
ment is alfo an argument that there muft have been
fuch a miftake in fetting down the time of the inter-
nal contadt at the egrefs at Rodrigues. I Shall alfo
Shew that the parallax of the Sun, determined from
the obferved durations, and from the leaft diftance
of the centers is very nearly the fame as that which
is determined from the internal contact at the egrefs,
though thefe laft determinations cannot be fo much
depended on becaufe of the minute elements from
which they are drawn.

I Shall therefore proceed to compare the obfervati-
ons of the internal contadt made on this fide of the
Line only, and from thence determine the Sun’s par-
allax. In order to do this it is neceffary that the dif-
ferences of longitude between the places of obferva-
tion, compared together, be well ascertained : and in
the doing of this, in all places where the ingrefs was
obferved, I have been much obliged to a very inge-
nious method, propofed by M. Pingre in his aforelaid
Memoir, to which I refer ; and for the longitudes of
other places I have confulted the Philofophical Tranf-
Vol. LIII. R r adtions

C 3°2 ]

actions and the Connoiffance des Temps. Thefe diffe-
rences of longitude are as follow.

Tobolfk and Abo — 3 \ $7 Weft.

Bologna = 3 47 46 W.

Calcutta — 1 20 38 Eaft.

Cajaneburg =2 42 12 W.

Calmar — 3 27 32 W.

Cape of G. Hope — 3 19 32 W.

Florence — 3 49 3W.

Gottingen - - - — 3 53 35 W.
Grand Mount — — o 46 26 E.

Greenwich — - — 1 33 7 W.

Hernofand - — — 3 21 55 W.

Lefkeard = 4 n on W.

Madrafs — o 47 1 1 E.

Paris — ----== 4 23 51 W.
Rodrigues - - - == o 20 25 W.

Rome = 3 43 14 W.

* Savile-houfe,Lond.= 4 33 37 W.
Stokolm - - - - rrr 3 20 41 W.

Tornea — 2 56 7 W.

Tranquebar — o 46 9 E.

Upfal — = 3 22 40 W.

I have deviated from the above mentioned method
of M. Pingre in fettling the longitude of Stokolm, by

* latitude of Savile-houfe, London, is ~ 510 30' 50" N.
The latitude of Florence is = 430 46' 30'' N. and that of Got-
tingen =r 51° 31' 54" N. The latitudes of the reft of the places
are fet down in my former paper on this fubjedt, only that of
Tranquebar fliould be = n° 30' o'',

the

C 3°3 ]

the ingrefs, becaufe it appears clear to me that there
muft have been a miftake in the obfervation of the in-
ternal contadl at the ingrefs at Stokolm, owing, as I
mentioned in my former paper, to the fmall altitude
of the Sun at the time of the ingrefs : for by com-
paring the times of ingrefs and egrefs obferved at
Stokolm and Upfal, we find that the difference of
longitude between thefe two places is i' 39", and
T 59^, and as we are fure that the obfervation at the
egrefs, gives the difference of longitude the moff cer-
tain in this cafe, therefore it follows that the error was
at the ingrefs, and it is eafy to prove that the error is
in the obfervation at Stokolm.

To avoid all uncertainty, and to be as clear and
diftindt as poffible, I fhall fet down, in the following
table, the obfervation at the egrefs at each place com-
pared, the difference of longitude between each place
compared, the effedt of the parallaxes refulting from
the comparifon, and alfo the effect of the parallaxes
computed on a fuppofition that the Sun’s parallax is
= 8" 5, in order, that if there is any miffake, it may,
the more eafily, be difeovered.

I compare Cajaneburg with 18 places, Bologna
with 17 places, and Tobolfk with 18 places, and they
are as follow.

h r ff

in

10 7 59 Cajan. 2 59 C.
o 38 29 = D. M. 2 18 S.

h

/ U / //

10 7 59 Cajan. 2 59 C.

o 40 28 D. M. 2 21 U.

9 29 30 4T

9 30 11 Stokolm.

9 27 3r 3s

928 9 Upfal.

//

Par, := 8. 50

R r 2

Par. =: 8. 50
10 7

41

38

[ 3©4 ]

k

b

1° 7 59 Cajan. 2 59 C.
0 22 25 = D. M. 2 30 A.

k

10 7 59 Cajan. 2 59 C.

0 45 20 =: D. M. 1 59 C.

9 45 34 29

9 45 59 Abo.

25

par. = 7. 33

9 22 39 10

9 23 40 Calmar.

011

Par. = 8 64

h

in 1,1

1° 7 59 Cajan. 2 59 C.

0 39 43 = D. M. 2 26 H.

h

1 H / Jl

10 7 59 Cajan. 2 59 C~

2 42 12 =r D. M. 3 44 T.

9 28 16 33

9 28 52 Hernofand.

12 50 11 45

12 49 23 Tobolfk.

0 0 36

Par. = 9 27

0 0 48

Par. = 9. q6

h

10 7 59 Cajan. 2 59 C.

1 11 23 = D. M. 1 18 G.

h / /

H U

10 7 59 Cajan. 2 59 C.

1 50 55 = D. M. 1 12 G.

8 56 36 1 41

8 58 26 Gottingen.

0 1 5°

Par. = 9. 25

8 17 4 1 47

8 19 0 Greenwich.

° 1 S6

Par. = 9. 09

h

• " . / //

10 7 59 Cajan. 2 59 C.

1 51 25 r=D. M. 1 11 S.H.

8 16 34 1 48

8 18 22 Savile-houfe..

0

' n # / //

10 7 59 Cajan. 2 59 C.

2 9 27 = D. M. 1 4 L.

7 58 32 1 55

8 0 21 Lefkeard.

0 j 48

Par. r: 8. 50

0 • 49

Par. = 8. 06

10 7

[ J°5 ]

•

/ /# ^ , lit

10 7 59 Cajan. 2 59 C.

1 41 39 = D. M. 0 53 P.

h

10 7 59 Cajan. 2 59 C.

1 5 34 = D. M. 0 29 B.

9 26 20 2 6

9 28 25 Paris.

9 2 25 2 30

9 4 54 Bologna.

02c

_ //

Par. 8. 43

0 2 2Q

7 T* 7/

Par. = 8. 44

h

10 7 59 Cajan. 2 59 C.
1 1 2 = D. M. 0 13 R.

h

10 7 59 Cajan. 2 59 C.

1 6 51 -D. M. 0 24 F.

9 6 57 2 46

9 9 36 Rome.

9 1 8 2 35

9 328 Florence.

0 2 39

Par. = 8. 14

0 2 2a

Par. 7. 68

h

10 7 59 Cajan. 2 59 C.
4 2 50 = D. M. 2 22 C.

14 10 49 0 37

14 11 34 Calcutta.

0 0 45

• •* n

Par. = 10. 34

h

10 7 59 Cajan. 2 59 C.

3 28 38=D.M. 1 oG.M.

r3 36 37 1 59

x3 38 3° G. Mount.

0 1 S3

J //

Par. =: 8. 07

h

7 77 _ . / //

10 7 59 Cajan. 2 59 C.
3 28 21 =: D. M. 0 52 T.

h

10 7 59 Cajan. 2 59 C.
3 29 23 = B>. M. 1 0 M.

x3 36 20 27

*3 3^ 25 Trancuebar.

*3 37 22 1 59

13 39 38 Madrafs,

0 2 C

«■* ^ n

0216

Par, rr 8. 36

Par. = 9. 71

10 7

1

C 3°6 ]

h

/ // / //

9 4 54 Bologna o 29 B.

0 27 5 — D. M. 2 18 S.

h

in 1 >i

9 4 54 Bologna 0 29 B.

025 5 z D. M. 221 Up.

9 31 59 1 49

9 30 8 Stokolm.

9 29 59 1 52

9 28 9 Upfal.

0 1 5i

Par. = 8. 65

0 1 50

Par. rz 8. 35

h

III / u •

9 4 54 Bologna 0 29 B.

0 43 9 rz D. M. 2 30 A.

h

in in

9 4 54 Bologna 0 29 B.
0 20 14 z: D. M. 1 59 C.

9 48 ~ 3 21

9 45 59 Abo.

9 25 8 1 30

9 23 40 Calmar.

0 ^ * 4

Par = 8.71

0 1 28 „

Par. z: 8. 31

h

/ // / //

9 4 56 Bologna 0 29 B.

0 25 51 == D. M. 2 26 H.

h

9 4 54 Bologna 0 29 B.

3 47 46 = D. M. 3 44 T,

2 3° 4 7 1 57

9 28 52 Hernofand.

►

12 52 40 3 15

12 49 23Tobolik.

0 1 55

Par. zz 8. 36

0 3 17

Par. == 8. 58

h

111 in

950 Bologna 0 29 B.
0 5 49 =: D. M. i 18 G.

h

/ // / //
950 Bologna 0 29 B.

0 45 21 = D. M. 1 12 G.

8 59 11 0 49

8 58 26 Gottingen.

8 19 39 0 43

819 0 Greenwich.

» *

® 0 45

Par. = 7. 80

0 0 39

Par. =7.71

h

[ 307 ]

h

in in

9 4 54 Bologna 0 29 B.

0 45 51 rr D. M. 1 11 S.H.

h

* n ill

9 4 54 Bologna 0 29 B.

1 3 53 = D. M. 1 4 L.

8 19 3 0 42

8 18 22 Savile-Houfe.

8 1 1 0 35

8 0 21 Leafkeard.

° ° 4i

Par. = 8. 30

0 0 40

Par. == 9. 71

h

! >> / //

9 4 54 Bologna 0 29 B.

0 36 5 = D. M. 0 53 P.

1 h

in in

950 Bologna 0 29 B.
5 8 24 = D. M. 2 22 C.

8 28 49 0 24

8 28 25 Paris,

! 14 13 24 1 53

14 11 34 Calcutta.

o 0 24

Par. = 8. 50

0 1 50

Par. = 8. 28

h

in i //

9 4 54 Bologna 0 29 B.

4 34 i2 = D. M. 1 oG.M.

h

i 7/ ti , III

9 4 54 Bologna 0 29 B.

4 33 55 = D. M. 0 52 T.

1 3 39 6 031

^ 38 30 G. Mount.

0 0 36

Par. r= 9. 87

J3 38 49 0 23

13 38 25 Tranquebar.

0 0 24

Par. =: 8. 86

h

' H / //

950 Bologna 0 29 B.

4 34 59 = D. M. 1 0 M.

J3 39 59 0 31

13 39 38 Madrafs.

h

• II 1 II

950 Bologna 0 29 B.

051 39 r= D. M. 3 5 T,

9 56 39 2 36

9 54 8 Tornea.

0 p 21

Par. — 5. 76

0 2 3!

Par. =: 8. 23

12 49

I

*

[ 3c8 ]

h

12 49 23 Tobolfk 3 44 T.
3 20 41 = D. M. 2 18 S.

h

in in

12 49 23 Tobolfk 3 44 T.
3 22 40 rr D. M. 2 2i U.

9 28 42 ^ 1 26

9 30 8 Stokolm.

9 26 43 123

9 28 9 Upfal.

0 1 26

Par. ~ 8. 50

0 1 26

Par. rr 8. 80

h

/ // / //

12 49 23 Tobolfk 3 44 T.

3 4 37 rr D.M. 2 30 A.

h

1 n 1 n

12 49 23 Tobolfk 3 44 T.
3 27 32 = D. M. i 59 C.

9 44 46 1 14

9 45 59 Abo.

9 21 51 1 45

9 23 40 Calmar.

0 1 13

Par. = 8. 40

0 1 49

Par. = 8. 82

h

/ n j n

12 49 23 Tobolfk 3 44 T.

3 21 55 = D. M. 2 26 H.

h

/ // / n

12 40 23 Tobolfk 3 44 T.

3 53 35 = D* 1 18 G*

9 27 28 1 18

9 28 52 Hernofand.

8 55 48 2 26

8 58 26 Gottingen.

0 1 24

Par. rr 9. 02

0 2 38

Par. rr 10. 57

9

i 44 i 4!

12 49 23 Tobolfk 3 44 T.

4 33 7 r= D. M. 1 12 G.

h

/ 44 4 44

12 49 23 Tobolfk 3 44 T.

4 33 37 =D.M. 1 iiS.HT.

8 16 16 2 32

8 19 0 Greenwich,

8 15 46 2 33

8 18 22 Savile-Houfe.

0 2 44

Par. st 9. 1 1

0 2 36

Par, rr 8. 66

12 49

[ 309 ]

*

III in 1 11

12 49 23 Tobolfk 3 44 T.
4 51 39 = D-M* 1 4 L,

h

12 49 23 Tobolfk 3 44 Ti
4 23 51 =D. M. 0 53 P.

7 57 44 2 40

8 0 21 Lefkeard.

8 25 32 2 51

8 28 25 Paris.

0 2 37

Par. = 8. 34

0 2 53

Par. == 8. 60

h

• " _ , , ! H

12 49 23 Tobolfk 3 44 T.
3 49 3 rrD. M. 0 24 F.

9 0 20 3 20

9 3 28 Florence.

h

12 49 23 Tobollk 3 44 T.
3 4314 r= D. M. 0 13 R.

9 6 9 3 31

9 9 36 Rome.

038

Par. = 7. 99

0 3 27

Par. = 8. 34

h

in / //

12 49 23 Tobolfk 3 44 T.

1 20 38 = D. M. 2 22 C.

14 10 1 i 22

14 11 34 Calcutta.

h

ill ill

12 49 23 Tobolfk 3 44 T.

0 46 26r:D.M. 1 oG.M*

U 35 49 2 44

13 38 30 G. Mount.

0 1 33

Par. = 9. 64

0 2 41

Par. = 8. 34

h

/ // / //

12 49 23 Tobolfk 3 44 T.

0 46 9 == D. M. 0 52 Tr.

h

in ill

12 49 23 Tobolfk 3 44 T.
0 47 11 = D.M. 1 0 Mi

13 35 32 2 52 •

^ 38 25'rranquebar

13 36 34 2 44

12 39 38 Madrafs.

0 2 53

Par. =8. 55

0 3 4

Par = 9. 54

S s

Vol. LIII.

I have

C 310 ]

I have explained the manner of this table in a for-
mer paper on this fubjedt to which I refer. I (hall
now fet down the refult from each comparifon in the
following order, that they may be the more eafily
feen.

Sun's Parallax.i Sun’s Parallax.

Sun’s Parallax.

_ // |

Cajan. and Stokolm = 8. 50
Upfal - - r= 8. 50

Abo - - = 7- 33
Calmar - — 8, 64
Hernofand - r= g. 27
Tobollk - — g. 06
Gottingen - 3- 9. 25
Greenwich - — 9, 09
Savile-Houfe = 8. 50
Lelkeard - =8.06
Paris - - = 8. 43,

, Bologna - 2=8-44
Rome - — 8. 14
Florence - = 7. 68
Calcutta - r= 10. 34
G. Mount = 8. 07
Tranquebar = 8. 36
Madrafs - — 9. 7 1

Bolog. and Stokolm — 8. 65
Upfal - — = 8. 35
Abo - - - — 8.71
Calmar - = 8. 31
Hernofand = "8. 36
Tobollk - — 8. <;8
Gottingen = 7. 80
Greenwich x= 7. 71
Savile-Houfe=8. 30
Lelkeard - 2=9. 71
Paris - - — 8. 50
Calcutta - = 8. 28
G. Mount = 9. 87
Tranquebar=r 8. 86
Madrafs - — 5. 76
Cajaneburg x= 8. 44
Tornea - = 8. 23

Tobollk and Stokolm — 8r 50
Upfal - - = 8. 80
Abo - - — 8. 40
Calmar - = 8. 82
Hernofand - =s 9. 02
Gottingen = 10. 57
Greenwich =* 9. 1 1
Savile-Houfe = 8. 66
Lelkeard - — 8. 34
Paris - - =s 8. 60
Florence - = 7, 99
Bologna - = 8. 58
Rome - = 8- 34

Calcutta . — 9- 6+
G. Mount - = 8. 34
Tranquebar =8.55
Madrala - — 9. 54
Cajaneburg — 9, 07

The mean of thefe 53 comparifons gives the Sun’s
Parallax = 8", 61.

Rejecting all thofe refults which differ more than
one fecond from the mean of the whole, the mean
of die remaining 45 refults gives the Sun’s parallax

Rejecting all thofe refults which differ more than
half a fecond from the mean of the whole, the mean
of the remaining 37 refults gives the Sun’s parallax
= 8" 57.

The mean of thefe three means gives the Sun’s
parallax = 8", 58.

I fhall next compare the obfervations of the inter-
nal contadt at the egrefs made at Paris, Greenwich,
Savile-Houfe, Bologna, Madrafs, Grand Mount, and
Tranquebar, with thofe made at Stokolm, Upfal,
1 Tornea,

C 311 ]

Tornea, Cajaneburg, Tobollk, Abo, Calmar, Her-
nofand and Calcutta. They are as in the following
table.

h

in in

9 28 52 Hernofand 2 26 H.
4 8 4 = D. M. 0 51 T.

ll

/ // / //

14 II 34 Calcutta 2 22 C.

0 34 29 r= D. M. 0 si T.

*3 36 56 1 35

13 38 25 Tranquebar.

0 1 29 „

Par. r= 7. 96 |

*3 37 5 1 31

J3 38 25 Tranquebar.

0 ! 2°

Par. = 7. 47

h

8 28 27 Paris 0 53 P.
1 3 10 = D. M. 2 18 S.

h

! // _ / //

8 28 27 Paris 0 53 P.

1 1 11 = D. M. 2 21 U.

9 31 37 1 25

9 30 io Stokolm.

9 29 38 1 28

9 28 9 Upfal.

° 1 27

Par. = 8. 70

o 1 29

Par. =: 8. 60

h

/ // / //

8 28 27 Paris 0 53 P.

I 27 44 = D. M. 3 5 T*

9 56 11 2 12

9 54 8 Tornea.

h

in in

8 28 27 Paris 0 53 P.

1 19 14 = D. M. 2 29 A.

9 47 41 1 36

9 45 59 Abo.

023

Par. rr 7. 92

0 1 42

Par. r= 9. 03

h

8 28 27 Paris 0 53 P.
O 56 19 r: D. M. 1 58 C.

9 24 46 15

9 23 40 Calmar.

016

Par. = 8. 63

h

_ / // / //

8 28 27 Paris 0 53 P.

1 1 56 = D. M. 2 26 H.

9 3° 23 i 33

9 28 52 Hernofand.

0 * 3i

Par. 8. 42

S s 2 82?

[ 312 ]

* - -

in _ i n n

8 28 27 Paris 0 53 P.
5 44 29 = D. M. 2 22 C.

h

/ n in

9 30 1 1 Stokolm 2 18 S.
1 12 26 = D. M. 1 12 G.

14 12 56 1 29

14 11 34 Calcutta.

8 17 45 16

8 19 0 Greenwich.

0 1 22 //

Par. 7. 83

0 1 15

Par. = 9. 66

h

in i n

9 28 9 Upfal 2 21 U.

1 10 27 = D. M. 1 12 G.

h

/ // / //

9 54 8 Tornea 3 5 T.

1 37 0 = D. M. 1 12 G.

8 17 42 1 9

819 0 Greenwich.

8 17 8 1 53

819 0 Greenwich.

0 1 18 „

Par. =: 9. 61

0 1 52 //

Par. = 8. 42

/ // • n

9 45 59 Abo 2 29 A.
1 28 30 — D. M. 1 12 G.

h

in in

9 23 40 Calmar 1 58 C.
1 5 35 =D.M. 1 12 G.

8 17 29 1 17

819 0 Greenwich.

8 18 5 0 46

8 19 0 Greenwich.

O I 31 ,,

Par. 10. 04

0 0 55 „

Par. = 10. 16

h

in in

9 28 52 Hernofand 2 26 H.
1 11 12 r D. M. 1 12 G.

h

in in

14 ii 34 Calcutta 2 22 C.
5 53 45 =: D. M. 1 12 G.

8 17 40 1 14

8 19 0 Greenwich.

8 17 49 1 10

8 19 0 Greenwich.

© 1 20 ,,

Par, = 9. 20

O J II yy

Par. =: 8. 62

9 3°

[ 3*3 ]

h f

/ // 7 //

9 30 11 Stokolm 2 18 S.

1 12 56 = D. M. 1 11S.H.

8 17 r5 17

8 18 22 Savile-Houfe,

h

9 28 9 Upfal 2 21 U.

1 10 57 = D.M. 111 S.H.

8 17 12 1 10

8 18 22 Savile-Houfe.

017

Par. = 8. 50

0 1 10

Par. — 8. 50

h

111 / //

9 54 8 Tornea 3 5 T.

1 37 30 = D.M. i 11S.H.

h

III III

9 45 59 Abo 2 29 A.

1 29 o = D.M. 1 1 1 S.H.

8 16 38 1 54

8 18 22 Savilc-Houfe.

8 16 59 1 18

8 18 22 Savile-Houfe.

0 ^44

Par. “ 7. 75

0 1 23 /,

Par. = 9. 04

h

III 1 11'

9 23 40 Calmar 1 58 C.

1 6 5 = D.M. 1 1 1 S.H.

h

in in

9 28 52Hernofand2 26 H.

1 11 42 = D. M. 1 1 1 S.H.

8 17 35 0 47

8 18 22 Savile-Houfe.

8 17 10 1 15

8 18 22 Savile-Houfe.

0 0 47

Par. = 8. 50

0 1 12 ,,

Par. = 8. 16

h

7 /✓ J U

14 11 34 Calcutta 2 22 C.
5 54 15 = D. M. 1 11 S.H.

h

in in

9 30 10 Stokolm 2 18 S.'
4 7 52 = D. M. 0 59 M.

8 17 19 1 11

8 18 22 Savile-houfe.

13 38 2 1 19

*3 39 38 Madrafs.

0 13 »

Par, =: 7. 54

0 I 36

Par. = 10. 33

9 28

[ 31+ ]

h

9 28 9 Upfal 2 21 U.

4 9 51 = D. M. 0 59 M.

n

/ // / //

9 54 8 Tornea 3 5 T.

3 43 18 =D. M. 0 59 M.

13 3^ 0 T 22

13 39 38 Madrafs.

0 1 38

Par. = 10. 15

13 37 26 „ 26

x3 39 38 Madrafs.

0 212

//

Par. = 8. 90

h

9 45 59 Abo 2 29 A.

3 5 1 48 = D. M, 0 59 M,

*3 37 47 1 30

13 39 38 Madrafs.

0 1 51

J U

Par. =r ro. 48

h

9 23 40 Calmar 1 58 C.
4 14 43 = D.M. 0 59 M.

*3 38 23 0 59

13 39 38 Madrafs.

0 1 *S

Far. = 10.80

k

9 28 52Hernofand2 26 H.
4 9 6 = D. M. 0 59 M.

J3 37 58 1 27

13 39 38 Madrafs.

° 1 4°

Par. = 9. 77

h

14 ii 34 Calcutta 2 22 C.
0 33 27 = D. M. 0 59 M.

13 38 7 1 23

13 39 38 Madrafs.

0 1 3'

Par. = 9. 32

h

9 30 8 Stolcolm 2 18 S.

4 7 7 = D.M. 0 59G.M.

b

9 28 9 Upfal 2 21 U.

4 9 6r:D.M. 0 59 G.M.

37 J5 1 19

13 38 30 G. Mount.

0 1 15

Par. = 8. 07

*3 37 15 * 22

13 38 30 G. Mount.

0 1 15

Par. = 7. 77
9 54

r 3

‘ _ y y/

9 54 8 T ornea 3 5 T.

3 42 33 =D.M. 0 59 G.M.

13 36 4i 26

13 38 30 G. Mount.

0 x 4q

' J //

Par. = 7. 35

TS ]

h

^ ^ / //

9 45 59 -Abo 2 29 A.

3 5i 3 — D.M. 0 59 G.M.

'337 2 1 3o

*3 38 3° G. Mount.

° * 1 * 28

Par. = 8 31

h

9 23 40 Calmar 1 58 C.

4 13 58=D.M. 0 59 G.M.

h

9 28 52 Hernof. 2 26 H.

1 4 8 2 1 ~D.M, 0 59 G.M,

*3 37 38 0 59.

*3 38 3° G. Mount.

0 0 52

J //

Par. = 7. 50

*3 37 13 1 27

J3 38 3° G. Mount.

0 I 17

' n

Par. = 7. 52

h

ill in

14 n 34 Calcutta 2 22 C.

0 34 i2=D.M. 0 59 G.M.

h

9 30 8 Stokolm 2 18 S.
4 6 50 = D. M. 051 T.

13 37 2* r 23

1 3 38 30 G. Mount.

° 1 8

Par. = 6. 96

13 36 58 r 27

13 38 25 Tranquebar.

0 x 27

' _ u

Par. = 8. 50

h

h

//

9 28 9 Upfal a 21 U.

4 8 49 rD. M. o 51 T.

12 36 58 1 30

1 3 38 25 Tranquebar.

1 27

Par, == 8. 23

/ //

/ //

9 54 8 Tornea 3 5 T.
3 42 16 = D.M.-o 51 T.

*3 36 24 2 14

*3 38 25 Tranquebar.

0 2 J

Par. =; 7. 68

9 45

C 316 ]

9 45 59 Abo 2 29 A.
3 50 46 rr D. M. o 51 T.

13 36 45 1 38

r3 38 25 Tranquebar.

1 40

Par. 8. 67

9 23 40 Calmar 1 58 C.
4 13 41 =D.M. o 51 T.

13 37 21 17

13 38 25 Tranquebar.

Par. = 8. 12

The refults are fet down in the following table.

©’ s Par.

Stole.

Upfal.

Torn.

Cajan.

Tobo.

Abo.

Calm.

Herr.

Calcu.

Mean,

Paris.

8. 70

8. 60

n

7.9a

8.43

8. 60

//

9.03

8. 63

8.4*

ft

7. 83

8. 46

Greenwich.

VO

ON

ON

9. 61

8.4a

9. 09

g. 11

10. 04

10. 16

9. 20

8. 62

9.32

Savile-Houfe.

8. 50

8. 50

7-75

8. 50

8.66

9.04

8. 5c

8. 16

7' 54

8. 36

Bologna.

OO

On

<-/i

8.35

CO
1 UJ

8. 44

8. 58

8. 71

8. 31

8. 36

8.28

8.43

Madrafs.

10. 33

IO. I5

8. 90

g.71

9-54

IO. qS

10. 80

9-77

9. 32

9. 89

Grand Mount.

8. 07

7-77

7- 35

8. 07

to

CO

S.JI

7-50

7- 52

6. 96

7. 76

Tranquebar.

8. 50

3. 23

1 ^
ON
1 OO

8- 36

8.55

8.67

8. 12

7-9

7- 47

8.17

Sun'sPar.mean.

8. 91

8.7s

8. 03

8.66

1 8.77

9. 18

8.86

8.48

8. 00

8. 63

1

The mean of thefe 63 refults gives the Sun’s pa-
rallax =r 8", 63; and if we rejedt all thofe which dif-
fer more than one fecond from the mean of the whole
the mean of the remaining 49 refults gives th^ Sun s
parallax = 8", 50.

And if we rejedt all thofe which differ more than
half a fecond from the mean of the whole, the mean
of the remaining 3 7 refults gives the Sun s parallax
— 8", 535 ; the mean therefore of thefe three means
gives the Sun’s parallax = 8//, 55.

Thus

[ 3^7 ]

Thus by the mean of 53 comparifons the Sun’s
parallax is determined to be r= 8' , 58, and by the
mean of 63 comparifons the Sun’s parallax is deter-
mined to be — 8", 55. The mean of thefe two
means gives 8 ", 565 for the parallax of the Sun on
the day of the tranlit.

It may be objected, that this determination cannot
be depended on to a very great precilion, becaufe the
greateft difference of the effedt of the parallaxes in any
of thefe comparifons does not exceed 3' 31" : confe-
quently that this is too fmall a bale, from which we
can expedt any great exadtnefs in the determination of
the Sun’s parallax : But if we confider the great num-
ber of comparifons (no lefs than 116), the certainty
of the differences of longitude of moft of the places
of obfervation, and the fmall differences in the refults
themfelves, I cannot help thinking that the force of
this objection is in fome meafure removed ; and that
this determination of the Sun’s parallax, by the ob-
fervations at places on this fide of the Line only,
muft be very near the truth.

In order, therefore, to remove the force of this
objedtion entirely, let us next confider the obfervati-
on at the Cape of Good Hope, by which we fhall
have a bafe very near three times greater than the
former, and alfo the obfervation at Rodrigues, by
which the bafe is nearly double of the former. But
before I proceed I muff take notice, that, in the Me-
moir, by M. Pingre, before mentioned, the time of
the internal contadt at the egrefs at Rodrigues is fet
down at oh 36' 49//. But in the fame volume there
is an account of M. Pingre s obfervation fent to the
R. Academy before his arrival in Europe, and the
V o l. LIII. T t time

[ 3i8 ]

time of the internal contact is therein fet down at
ch 34' 47 '. Alfo in a letter from him to the R. So-
ciety, on his arrival in Europe at Lifbon, and dated
the 6th or March 1762, and which letter is printed
in the Phil. Tranfa&ions, vol. LII. part I. the time
of the internal contact is therein fet down at oh 34'
47' true time. In another letter from him at Lifbon
to the Royal Society, dated the 14th of March 1762,
the time of the internal contadt is again fet down at
oh 34' 47" true time, and he ends this letter in thefe
words, “ Notez que l’attouchement interne des Bords
s’efi faite a oh 34' 47 Je fais cette remarque, par-
ceque, vu la proximite de prononciation, qui dans no-
tre langue eft entre 30 and 40, celle attouchement fe
trouvoit marque 10" plutot qu’il ne devoit letre, dans
une copie que j’ai faite pour mon ufage ; cette erreur
aura pent etre pafle dans quelque autre copie. Mais,
felon l’original, il faut abfolument lire oh 34' 47//.
M. Pingre has no where, that I can find, in the faid
memoir given any reafon for this alteration of the
time of the contact. If the internal contact at the
egrefs at Rodrigues happened at oh 34' 47", and if
this is compared with the fame obfervation at Tobolfk
the parallax of the Sun comes out = 7", 36. If the
time of the contadl at Rodrigues was at oh 3 5' 47",
and if this is compared with the fame obfervation at
Tobolfk, then the parallax of the Sun is found =2
8", 62. Again if the time of the contact at Rod-
rigues was at oh 36' 49", and if this is compared
with the obfervation at Tobolfk, the parallax of the
Sun will be found 9", 93. But to return.

M. Pingre, in his letter to the Royal Society dated
at Lifbon the 14th of March 1762, fets down the
time of the internal contact at the egrefs at oh 34' 47"
5 true

[ 319 ]

true time, and with regard to the time of the exter-
nal contadl exprefles himfelf thus “ a oh 53' 18" le
foleil a paru pendant 3 ou 4 fecondes. Je n’ai pas
vu le difque du foleil bien ferme, il me paroiffoit un
peu altere au lieu de la fortie de Venus. M. Thu-
illier ne voyoit rien avec la Lunette de 9 peids. J’ai
de la peine a me perfuader que Venus foit fortie
plutot.” It is plain from thefe words that M. Pingre
believed that the external contadl did not happen be-
fore oh 53' 1 S''. This being allowed, let us com-
pute the duration of the egrefs at Rodrigues, which
we fhall find — 17' 55//. It follows, therefore, that
the internal contact happened at oh 35' 23". But
this fuppofes that the obferver could fee the very laft
contact of Venus with the Sun’s limb, the contrary
of which I have fhewn in a former paper on this
fubjedt We are therefore certain that the externa!
contadt happened later than oh 53' 18", by feveral
feconds, confequently the internal contadt happened
later than oh 35' 23" by feveral feconds. Upon the
whole, therefore, we may fafely conclude that there
is a miftake of one minute in fetting down the time
of the internal contadt at the egrefs at Rodrigues, and
that, inftead of oh 34' 47", it fliould be oh 35' 47".
This fort of miftake has happened feveral times in the
obfervations of this tranftt, but they are eafily difco-
vered.

I fhall now proceed to compare the obfervation oi
the internal contadt at the Cape, with the obfervation
of the fame contadl at Rodrigues and at 20 places to
the north of the Line, and alfo the obfervation at
Rodrigues with the fame 20 places, and they are as
follow.

9 39

T t 2

[ 32° ]

k

III / //

9 39 5° Cape 6 8 C.
2 59 yrD. M. 2 59 R.

b

in tu

9 39 5° Cape 6 8 C.
1 4 19 = D. M. 0 53 P.

12 38 57 39

12 35 47 Rodrigues.

8 35 31 7 1

8 28 27 Paris.

0 3 10

Par. rr 8. 54

0 7 4

Par. r= 8. 56

h

ill / n

6 39 50 Cape 6 8 C.

0 28 14 =: D. M. 0 29 B.

h

ill in

9 39 5° Cape 6 8 C.

0 23 42 =D. M. 0 13 R.

9 11 36 6 37

9 4 57 Bologna.

9 16 8 b 21

9 9 36 Rome.

0 6 39

Par. r= 8. 54

0 6 32 „

Par. = 8. 74

•> / // tu

9 39 50 Cape 6 8 C.

0 29 31 =: D.M. 0 24 F.

h t n 111

9 39 5° Cape 6 8 C.

0 34 3 =D.M. 1 18 G.

9 10 19 6 32

9 3 28 Florence.

9 5 47 . 7 26

8 58 26 Gottingen.

0 6 51

Par. — 8. 91

0 7 21 „

Par. ~ 8. 40

^ 1 II III

9 39 5° Cape 6 8 C.

1 13 35 =D. M. 1 12 G.

9 "?9 5° l^ape 0 0

1 14 5 - D.M. 1 11S.H.

8 26 15 7 20

819 0 Greenwich.

8 25 45 7 I9

8 18 22 Savile-Houfe.

#7 J5

Par. = 8. 40

0 7 23 ,,

Par, — 8. 57

9 39

[ 3'

k / a in

0 39 50 Cape 6 8 C.

1 32 7 rr D. M. 1 4 L.

» ]

h / / / n

9 39 5° Cape 6 8 C.

0 8 0 = D. M. 1 59 C.

8 7 43 7 12

8 0 21 Lefkeard.

9 3* 5° 8 7

9 23 40 Calmar.

0 7 22 ,,

Par. = 8. 69

0 8 10 n

Par. = 8. 55

Si in in

9 39 5° Cape 6 8 C.

0 2 23 =: D. M. 2 26 H.

h in 111

9 39 50 Cape 6 8 C.

0 3 8 r D.M.2 21 U.

9 37 27 8 34

0 28 52 Hernofand.

9 36 42 8 29

9 28 9 Upfal.

0 8 35

Par. = 8. 51

0 8 33

Par. == 8. 57

b / // III

9 39 5° Cape 6 8. C.

0 1 9 = D.M. 2 18 S.

hill ! u

9 39 5° Cape 6 8 C.
0 14 55 = D.M. 2 30 A.

9 38 41 8 26

9 30 10 Stokolm.

9 54 45 8 38

9 45 59 Abo.

0 8 31

Par 8 . 58

0 8 46

Par. = 8. 63

h i n in

9 39 50 Cape 6 8 C.

o 37 20 = D.M. 2 59 C.

10 17 10 97

10 7 59 Cajaneburg.

Par. = 8. 56

9 39 50 Cape 6 8 C.

o' 23 25 = D.M. 3 5 T.

10 3J5 9 J3

9 54 8 Tornea.

//

Par. =: 8. 41

9 39

o 9 11

097

[ 322 ]

fc ' '/ _ / //

9 39 50 Cape 6 8 C.
3 19 32 = D.M.3 44 T.

h / // 11.

9 39 5° Cape 6 8 C.
4 40 10 = D. M. 2 22 C.

12 59 22 9 52

j 2 49 23 Tobol fk.

14 20 0 8 30

14 ir 34 Calcutta.

0 9 59

Par. = 8. 64

0 8 26 n

Par. = 8. 43

h • n / //

9 39 5° Cape 6 8 C.

4 6 43 = D. M. 0 59 M.

*3 46 33 77

13 39 38 Madrafs.

h / u in

9 39 50 Cape 6 8 C.

4 5 58 =D.M. 0 59G.M.

13 45 48 77

1 3 38 3° Grand Mount.

0 6 55

Par. = 8. 28

0 7 18

Par. r= 8. 70

/ // _ / //

9 39 5° Cape 6 8 C.
4 5 4i = D.M. 0 51 M.

*3 45 31 6 59

13 38 25 Tranquebar.

076

Par. = 8. 60

Rodrigues and the following
places compared together.

• tt _ , in

12 35 47 Rodr. 2 59 R.
4 3 26 = D. M. 0 53 P.

*> tu in

12 35 47 Rodr. 2 59 R.
3 27 21 = D. M. 0 29 B.

8 32 21 3 52

8 28 27 Paris.

9 8 26 3 28

9 4 57 Bologna.

•

* 3 54

Par. ss 8. 58

0 3 29

Par. r= 8. 54

13

C 323 ]

fa / // ill

12 35 47 Rodr. 2 59 R.

3 22 49 =D. M. 0 13 R.

h ' U / II

12 35 47 Rodr. 2 59 R.
3 28 38 == D. M. 0 24 F.

9 12 58 3 12

9 9 36 Rome.

979 3 23

9 3 28 Florence.

0 3 22

Par. = 8. 94

0 3 4i

Par. = 9. 24

t / // in

12 35 47 Rodr. 2 59 R.

3 33 10 = D. M. 1 18 G.

fa / // / a

12 35 47 Rodr. 2 59 R.
4 12 42 = D. M. 1 12 G.

9 2 37 4 17

8 58 26 Gottingen.

8 23 5 4 11

819 0 Greenwich.

0 4 11

Par. — 8. 30

0 4 5

Par. = 8. 33

fa / n ill

12 35 47 Rodr. 2 59 R.
4 13 12 — 0. M, 1 11S.H.

fa / a i a

12 35 47 Rodr. 2 59 R.
4 31 14 = D. M. 1 4 L.

8 22 35 4 10

8 18 22 Savile-Houfe.

8 4 33 v „ 4 3

8 ; 0 21 Leikeard.

0 4 13

Par. = 8. <q

0 4 12 ,,

Par. = 8. 81

h / 11 III

12 35 47 Rodr. 2 59 R.
3 7 7 = D. M. 1 59 C.

fa ! II III

12 35 47 Rodr. 2 59 R.

3 1 30 = D. M. 2 26 Hv

9 28 40 4 58

9 23 40 Calmar.

9 34 17 5 25

9 28 52 Hernofand.

0 5 0

Par. = 8. 56

0 5 25

Par. = 8. 50

12

[ 32+ J

kill III

12 35 47 Rodr. 2 SQ R.
3 .2 15 ^D,M. 2 21 U.

h / // / //"''■
12 35 47 Rodr. 2 59 R.

3 0 16 r D. M. 2 18 S.

9 33 3* 5 29

9 28 9 Upfal,

9 35 31 5 1 7

9 jO 11 Stokolm.

0 5 23

Par. == 8. 58

0 5 20

Par. = 8. 58

* / // / //

12 35 47 Rodr. 2 59 R.

2 44 12 = D. M. 2 30 A.

*> / // / //

12 35 47 Rodr. 2 59 R.

2 21 47 — D. M. 2 59 C.

9 5i 35 5 29

9 45 59 Abo.

jo 14 0 5 58

10 7 59 Cajaneburg.

0 5 36

Par. = 8. 68

061 „

Par. ~ 8. 57

h / // / n

12 35 47 Rodr. a 59 R.
2 35 42 = D. M. 3 5 T.

kin 1 u

12 35 47 Rodr, 2 59 R.
0 20 25 = D. M. 3 44 T.

10 0 5 64

9 54 8 Tornea.

12 56 1 2 6 43

12 49 23 Toboltk.

° 5 57 T, "

Par. =833

0 6 49 ,,

Par, 2= 8. 62

fc / 1/ ' /J n

12 35 47 Rodr. 2 59 K.
1 41 3 = D. M. 2 22 C.

bin 1 n

12 35 47 Rodr. 2 59 R.
i 7 36 = D. M. 0 59 M.

14 16 50 5 21

14 11 34 Calcutta.

'3 43 23 3 5«

1 3 39 38 Madrafs,

0 5 16 „

Par. = 8. 37

0 3 45

Par. = 8. 03

>2 35

[ 325 ]

*> / // ' " T>

12 35 47 Rodr. 2 59 R.

1 6 51 mD.M. o 59G.M.

h t a t n

12 35 47 Rodr. 2 59 R.

1 6 34 = D.M.o 51 T.

13 42 38 3 58

13 38 30 Grand Mount.

13 42 21 3 50

13 38 25 Tranquebar.

048

Par. “ 8. 85

o 3 56

74

The refults of the Sun’s parallax from thefe feve-
ral comparifons are as follow.

Sun’s Parallax,

Sun’s Parallax,

//

Cape of G, Hope and Rodrigues = 8. 54

//

Rodrigues and Cape of G.Hope= 8. 54

Paris - - = 8. 56

Paris - - = 8. 58

Bologna - = 8. 54

Bologna - = 8. 54

Rome - = 8. 74

Rome - = 8. 94 r.

Florence - = 8. 91 r.

Florence - sss 9. 24 r.

Gottingen - = 8. 40

Gottingen - — 8. 30 r.

Greenwich - ss 8. 40

Greenwich =8. 33

Savile-Houfe = 8. 57

Savile-Houfe ss 8. 59

Lelkeard - =8. 69

Lelkeard - =s= 8. 81 r*

Calmar - rr 8. 55

Calmar - = 8. 56

Hernofand - = 8. 51

Hernofand - ss 8, 50

Upfal - - — 8. 57

Upfal - - = 8. 58

Stokolm - =8.58

Stokolm - - =8. 58

Abo - - = 8. 63

Abo - - m: 8, 68

Cajaneburg - = 8. 5#

Cajaneburg =8.57

Tornea - - =8.41

Tornea - - = 8. 33 r«

Tobollk - = 8. 64

Tobollk - == 8. 6a

Calcutta - 8. 43

Calcutta - = 8. 37

Madrafs - = 8.2.8r.

Madrafs - — 8. 03

G. Mount es 8. 70

G. Mount *r=8. 85 r.

Tranquebar 8. 60

Tranquebar = 8. 74

The mean of the 21 comparifons with the obfer-
vation at the Cape, gives the Sun’s parallax = 8r/, 56.
There are only two of thefe 2 1 comparifons, marked
with the letter r, which differ more than JL. of a fe-
cond from the mean of the whole j let thefe be reject-
ed, and the mean of the remaining 19 refults gives the
Sun’s parallax =; 8", c6.

Vol. LIU. U u If

[ 326 ]

If we fele<ft out of thefe 21 comparifons thofc
places whofe difference of longitude may be fuppof-
ed to be the bell determined, the mean of thefe may
be regarded as the moft exaft determination, viz.
Paris, Bologna, Greenwich, Savile-Houfe, Upfal,
Stokolm, Cajaneburg and Tobolfk; the mean of
thefe gives the Sun’s parallax rrr 8", 55, and if we
leave out the refults of Greenwich and Tobolfk,
which differ the mod from the reft, the mean of the
remaining 6 refults gives it — 8", 56 the fame as
before.

The mean of the 21 comparifons with the obfer-
vation at Rodrigues gives the Sun’s parallax — 8", 57,
and if we rejedt 8 of them, which are marked with
the letter r, and which differ more than Vr of a fe-
cond from the mean of the whole, the mean of the
remaining 13 refults gives the Sun’s parallax 8", 57,
differing only one hundredth part of a fecond from
that which was determined from the obfervation at
the Cape, and agreeing in a moft furprizing manner
with what was formerly determined by the compan-
ions of the the obfervations at places on this fide of
the Line only, where the bafe was fo fmall, as I faid
before; a moft convincing proof of the great precifi-
on with which the parallax of the Sun is determined
by the late tranfit of Venus.

We fhall now enquire into the limits of the error
that may attend the determination of the parallax by
the obfervation of the internal contact. An error of
V iov of time in the obfervation at Tobolfk when
compared with the obfervation at the Cape, will pro-
duce an error of 1" in the Sun’s parallax : and
if we fuppofe an error of 3 5" of time in the obfer-

vation

[ 3a7 ] '

vation at Tobolfk, and an error of the fame quanti-
ty in the obfervation at the Cape, and both in con-
trary directions, this alfo will produce an error of
only in the Sun’s parallax. If therefore no greater
error could be committed in the obferyations at To-
bollk and the Cape, we are certain that the compa-
rifon of Tobolfk and the Cape gives the Sun’s paral-
lax fo exaCt, that the error does not exceed one fe-
cond from the true parallax. But this is too great an
error to be fuppofed in the obfervations, becaufe I
have fhewn, in my former paper, that an error of
only 6" in time was committed in the obfervation of
the contaCt by perfons obferving even in the fame
place ; therefore, if we fuppofe an error of 6" of
time in the obfervation at Tobollk, and an error
of the fame quantity in the obfervation at the Cape,
and both in contrary directions, the error produced
in the parallax by thofe 1 2", will amount only to 4.
of a fecond, even though we had only thefe two ob-
fervations to determine the Sun’s parallax : But fince
we have a great number of very good obfervations,
made at other places, it follows that the mean of
all thefe, muft give the Sun’s parallax to a lefs error
than 4. of a fecond, and confequently very near the
truth.

In all places where the internal contaCt at the egrels
was obferved, and where there were more obfervers
than one, we find a difference in the time of each
obferver ; the obfervation at Greenwich is an excep-
tion to this, as the three obfervers all agree to the
fame fecond, in the obfervation of the contaCt of
Venus with the Sun’s limb ; which is the more fur-
prizing as they ufed telefcopes of different conftruc-

U u 2 tions

[ 328 ]

tions and of different magnifying powers. This co-
incidence not only furprized me, but alfo the reve-
rend Mr. Hornfby, now Savilian profeffor of Agrono-
my at Oxford. Mr. Hornfby went to Greenwich in
the beginning of the year 1762, and on his return
told me, that his furprize was at an end, for he had
been informed at Greenwich, that Mr. Green, the
afliftant obferver there, as foon as he judged that the
internal contadt was formed, called out now. This
muff certainly have caufed fome difturbance to the
other obfervers, and might pofiibly influence their
judgment : and the fadt (as I am informed) was that
each obferver had a fecond watch in his hand, and
they inflantly ftoped their watches, each having his
hand at his watch ready to flop. This problem,
therefore, is eafily folved, and the furprize at the co-
incidence entirely vanifhes; fo that this obfervation
can be looked on as no more than the obfervation of
one perfon, and he too not much pradtifed in ob-
ferving. Moreover it is proper I fhould obferve
that another perfon was prefent at this obfervation,
who confirmed the above account.

The very near coincidence of the three obfervers at
Greenwich, in the time of the external contadt re-
mains now to be accounted for. Mr. Green did not
call out at this time, becaufe he was forbid by Dr.
Bradley, who was prefent, though not in a condition
to obferve becaufe of his bad flate of health. This
problem therefore may be folved in the following
manner. The obfervation of the external contadt
was undoubtedly more uncertain than the former,
and yet we find two of the obfervers agreeing to the
fame fecond, and the third differing only one fecond
from them. If we attend to the following circum-

r fiances.

[ 329 ]

ftances, we fhall be immediately fatisfied by them.
Each obferver had a fecond- watch in his hand ; the
three obfervers were at the fame window of the fame
room, one of them on the leads immediately with-
out the window, and the other two within the win-
dow 5 therefore each obferver was within hearing and
feeing of each other j confequently the inftant one of
the obfervers flopped his watch, may it not be pre-
fumed that the noife of the nicking of it might be
heard by the reft ? efpecially as there was a profound
filence during the time of the obfervation.

I have thought proper to take notice of thefe fads,
becaufe feveral perfons both at home and abroad have
exprefled their furprize at this coincidence, and that
fuch an exadnefs may not be eftablifhed as a prece-
dent in thefe fort of obfervations ; and becaufe I think
it eftentially neceftary, in all forts of obfervations,
efpecially in one of fo much importance in aftronomy
as this, that every the minuteft circumftance fhould
be particularly related.

We are now to find the limits of the error arifing
from the difference of longitude between Tobolfk
and the Cape. I find that an error of i' 10" in time
in the difference of longitude between thefe two
places will caufe an error of 1" in the Sun’s parallax.
But as we are certain that this error in longitude
does not take place ; therefore we are certain that
the error in the parallax is within one fecond of the
truth. The difference of longitude between the
Cape of Good Hope and Paris is determined, both
by the obfervations of M. de la Caille and Mr. Ma-
fon ; the difference of longitude between Paris and
Upfal in Sweden is fettled by the obfervations of Ju-
piter’s

[ 33° ]

piter’s frit fatellite, and the difference of longitude
between Upfal and Tobollk is fettled, by the obfer-
vations of the contact at the ingrefs at both places,
by the method of M. Pingre above mentioned.
Therefore the difference of longitude between the
Cape and Tobollk is very exadtly fettled, fo exa&ly,
that I am perfwaded that the error does not amount
to 5 or 6 feconds. Therefore the error in the paral-
lax arifing from the error of the difference of longi-
tude is extremely fmall, fcarcely amounting to — L.
part of a fecond. Therefore we are certain that the
error in the fun’s parallax arifing both from the error
of obfervation and the error of longitude does not
exceed ^ of a fecond in the comparifon of the ob-
servations of the internal contact at Tobollk and at
the Cape, even though we had no more obfervations
to determine the Sun’s parallax ; but the mean of a
great many more mull bring it very near the truth.

I now proceed to determine the parallax of the
Sun from the total durations obferved at different
places. If therefore we compare the durations ob-
ferved at Tobollk, Cajaneburg, Abo, and Tornea,
with the durations obferved at Madrafs, Grand Mount
and Tranquebar, which give the greatelf differences,
the refults of the Sun’s parallax will be as follow.

Tobollk

[ 33i ]

Sun’s Par, Difference of duration, ■

Tobolfk and Madrafs - - = 9. 61 2 50

G. Mount = 8. 33 2 27

Tranquebar = 8. 52 2 40

Cajaneburg and Madrafs — 10. 09 r. 1 49
G. Mount == 8. 00 1 26

Tranquebar — 8. 33 1 39

Abo and Madrafs - -- = 10. 66 r. 134
G. Mount =8.33 1 11

Tranquebar = 8. 60 1 24

Tornea and Madrafs - - — 9. 20 1 34

G. Mount - — 7. 00 r. 1 11

Tranquebar = . 7. 50 r. 1 24

The mean of thefe 12 refults gives the Sun’s pa-
rallax — 8/V 68, and if we rejedt four of them,
which are marked with the letter r, and which differ
the moll from the reft, the mean of the remaining 8
gives the Sun’s parallax 8", 61.

This determination of the Sun’s parallax cannot
be depended on to any great precifion, becaufe of
the fmall differences between the durations compared,
the greatefl of which amounts only to 2' 5 o'7, and
alfo becaufe of the fmall number of comparifons. It
ferves only to fhew nearly what is the quantity of the
Sun’s parallax.

We are now to determine the limits of the error
in the determination of the Sun’s parallax by the du-
rations obferved at two different places. The greatefl
difference of duration is between Tobolfk and Ma-
drafs, which amounts only to 2' 50". If therefore
1 ana

[ 332 ]

an error of 2on in time is committed in the obfer-
vations of the ingrefs and egrefs at both the places
compared, this error of 20" in time will caule an
error of 1" in the refult of the Sun’s parallax, and
in the comparifons of thofe places where the differ-
ence of duration is lefs, will occafion a greater error,
and therefore the determination of the parallax, by
this method, cannot be depended on to any great ex-
adlnefs, becaufe of the fmall differences of the dura-
tions compared. In this method, however, we are
free from the uncertainty arifing from the difference
of longitude not being exactly known.

I now proceed to the determination of the Sun s
parallax by the lead diftance of the centers. There
are come to my hands only two meafurements of the
greateft diftance of the limbs of the Sun and Venus,
one at Tobolfk and the other at Rodrigues. I fhall
only confider the meafurement at Rodrigues, becaufe
there feems to me to be fome miftake in the meafure-
ment at Tobolfk. If we fuppofe the Sun s parallax
~ 8", 5, then the apparent middle of the tranfit hap-
pened at Rodrigues at 9’* 37' 30 '. There is a mea-
furement by M. Pingre of the greateft diftance of the
limbs at 9h 38' i3//, which is fo near the middle of
the tranfit that we may fafely take this quantity, viz.
5' 54", 6 *, for the greateft diftance of the limbs of
the Sun and Venus, and efpecially as it is marked an
exadt obfervation. This meafurement, therefore,
gives the apparent leaft diftance of the centers of the

* I all along confider the obfervation of M. Pingre at Rod-
rigues as it is printed, from his own letter, in the Philofophical
Tranfa&ions.

Sun

C 333 ]

Sun and Venus at Rodrigues =: g' 2i7, 4. Suppo-
sing then this meafurement to be exadt, here follows
an irrefragable argument, independent of all other
methods, to prove that the parallax of the Sun is
very nearly — 8", 5. Let us fuppofe the Sun’s pa-
rallax — ioy/, and let us compute, by the following
method, the apparent lead; diftance of the centers at
Tobolfkj from thence we fhall find that the geo-
centric lead didance of the centers at Toboldc is
56 j ,4^6, and by the oblervation at Rodrigues the
geocentric lead didance of the centers is = 572", 6-12,
io that, on this fuppofition, we have two different
geocentric lead didances of the centers, which be-
ing ablurd, it follows that the Sun’s parallax is not
io . Again let us fuppofe that the Sun’s parallax
is — 7", we fhall find that the geocentric lead dif-
tance of the centers by the obfervation at Tobolfk
— 57 5" > 35^> and by the obfervation at Rod-
ligues it is 56 g", 248. Thus then, again, we
have two different geocentric lead didances of the
centers, which being abfurd, it follows that the pa-
rallax of the Sun is not '• Again if we fuppofe
the Sun’s parallax = 8" or 9", we fhall find that
the fame abfurdity will follow, but in thefe two lad
fuppofitions we fir all find that the differences of the
geocentric lead didances of the centers are not fo great
as on the fuppofitions of 10" and 7", it therefore
follows that the parallax of the Sun is lefs than 9"
and more than 8, and if we continue to reafon in the
fame manner we fhall find, that on the fuppofition
that the Sun’s parallax is — 8", 5, the geocentric lead
didances of the centers feverally found by the obfer-
\ol. LlII. Xx vation

[ 334 ]

vation at Tobolfk and at Rodrigues is very nearly the
fame, confequently that the Sun’s parallax is very nearly
— 8", 5. If we purfue this fubjedt to a greater preci-
fion, and fuppofe that the meafurement of the greatefl
diftance of the limbs of the Sun and Venus, taken
by M. Pingre, to be perfe&ly cxadt, and compute
on true * principles the apparent lead: diftances of
the centers from the durations obferved at the differ-
ent places in the north (the method of which I fhall
afterwards give) the parallax of the Sun will come
out as follows, when they are compared with that
meafured at Rodrigues :

| Cajan. I Calm. 1 Tobol.
Rodrigue* 1 8”, 60 1 8", 58 J 8", 65

Torn. | Upfal. | Stoko. | Abo. ] Herno. J
8", 48 1 8", 60 j 8", 4o 1 8", 63 1 8", sj |

The mean of thefe eight comparifons gives the
Sun’s parallax = 8", 56 being the very fame, as that
which we found before by the comparifons of the
internal contacts.

Again let us reduce the obferved durations, at the
following feveral places, to the center, on the fup-
pofition that the Sun’s parallax is =- 8", 56 as in the
following table.

Tobolfk.

j*

5 48 53— Obf.Du.
o 9 6=Parallax.

5 58 59=Cent.D.

Cajaneburg.

b

5 49 54=Obf.Du.
o 8 8=Parallax.

5 58 2=Cent. D.

Tornea.

h

5 50 9nObf. Du,
o 8 3=:Parallax.

5 58 i2=Cent. D.

* I fay on true principles, becaufe I have realon to think that
there is a miftake in the method given by M, Pingre in the a-
forefaid Memoir.

1- Upfal.

[ 335 ]

Upfal.

k

5 50 26=Obf.Du.
O 7 36 = Parallax.

Stokolm.

h

/ //

5 50 42 = Obf. Du.
0 7 37 :i:Parallax.

Abo.

H

/ // _ w

5 50 9=Obf. Du.
0 7 49 = Parallax.

5 58 2=r.Cent. D.

5 58 i9rrCent. D.

5 57 58 =Cent. D.

Hernofand.

h

Calmar.

h

Calcutta.

h

5 50 26:= Obf. Du.

5 5° 39=Obf. Du.

5 50 36 — Obf. Du.

0 7 39 m Parallax.

0 7 24 = Parallax.

0 7 35— Parallax.

5 58 5 = Cent. D.

5 58 3=:Cent. D.

55811 = Cent. D.

Madrafs.

h

Grand Mount.

Abo.

h

5 51 43 = Obf. Du.

5 51 20~ Obf.Du.

5 33 = Obf. Du.

O 6 35 — Parallax.

0 6 35 = Parallax.

0 6 26=Parallax.

5 58 i8 = Cent. D.

5 57 55=Cent-D-

5 57 59=Cent> D*

The mean of thefe 12 central durations gives the
mean central duration — 5h 58' 5" ; from this cen-
tral duration, we fhall find that the geocentric leaft
diftance of the centers is — 57 1", or 9' 31". Let
us compare the above apparent leaft diftance of the
centers meafured at Rodrigues with this geocentric
leaft diftance of the centers, and we fhall find that
the parallax of the Sun from thence refulting is =
8 ", 56 the fame as before. Thefe refults of the pa-
rallax, arifing from the companions of the apparent
leaft diftances of the centers, agreeing with the for-
mer determinations of the parallax by the internal
contacts, are a proof of the accuracy of this mea-
furement of the created: diftance of the limbs made

O

by M. Pingre at Rodrigues.

There

[ 33^ ]

There are 12 places at which the total duration was
obferved, three of thefe had a northern parallax of lati-
tude at the middle of the tranfit, the other nine had a
fouthern parallax of latitude ; let the apparent lead:
didance of the centers at each place of obfervation be
found, by the following method, let thefe be com-
pared together, and we fhall have the parallax of the
Sun refulting from them. For this purpofe I have
computed the apparent lead didance of the centers at
the 8 following places, and have compared them with
the apparent lead didance of the centers at the four
following places, and from each comparifon I have
computed the parallax of the Sun, and they are as
in the following table.

4

Cajan.

Calm.

Tobol.

Torne.

LJpfal.

Stoko

Abo.

Herno.

n

//

11

1/

/

'!

11

//

Tranqucbar

8.48

8.45

8.54

8.31

8.48

8.

2C

8.52

8.

42

Madrafs - -

8. 79

8. 76

8- 93

8. 6j

3. 79

8.

5C

8. 82

8.

73

G. Mount -

8. 42

8. 38

8.45

8. 24

8. 42

8.

12

8.45

8.

35

Calcutta - -

8. 69

8. 65

8. 8i

8- 43

8. 68

8.

35

8- 73

8.

61

0 ’sP.mcan.

,8. 59

8. 56

8.68

8. 4c

8. 59

8.

29

8.63

8.

53

0’s Par,
mean.

11

8. 42
8. 74

8* 35
8. 62

The mean of thefe 32 comparifons gives the Sun’s
parallax — 8", 53.' This very near agreement with
the former determinations is fomewhat furprizing,
when we confider the fmallnefs of the bale from
which they are computed, the greated fcarcely ex-
ceeding 20" of an angle ; but we are alio to cond-
der, that the apparent lead didance of the centers
may be found, from the duration obferved, to a very
great exadtnefs, and nothing affecds the accuracy of
it, but the errors in the obfervation. Let us fuppofe
then that an error, of 6" in time, happened in each

of

C 337 ]

of the obfervations of the ingrefs and egrefs, both in
contrary directions ; the fum of the errors, therefore,
in each comparifon, will amount to 24" of time ;
this will produce an error of 1" of fpace in the ap-
parent leaft diftance of the centers by computation,
but this error of 1' cannot produce an error of fo
much as half a fecond in the determination of the
Sun’s parallax. It therefore follows, on the above
fuppofition of an error of 24' of time in the obfer-
vation, that though we had no other obfervations of
the tranlit of Venus than two of the above total du-
rations, (luppofe that of Cajaneburg and Madrafs)
yet we fhouid have been abfolutely certain of the pa-
rallax of the Sun within lefs than an error of half a
fecond, and therefore of courfe it follows, that the
mean of fo great a number of refults muft be very
near the truth.

This determination of the Sun’s parallax, by the
leaft diftance of the centers, is alfo a convincing proof
that there is no miltake in the obfervation of Mr. Ma-
fon at the Cape, as alledged by M. Pingre, and that
there muft be a miftake of 1' in fetting down the
time of the internal contact at the egrels at Rodrigues,
notwithftanding M. Pingre, in the aforelaid memoir,
prefers his obfervation to that of Mr. Malon, be-
caufe, as he fays, that after a ftridt examination of
ail the circumftances attending his obfervation, he
could not find any miflake in it , but alfo becaufe he has
proved that no miflake could pojjibly be committed. In
this. determination of the parallax by the apparent
leaft diftance ot the centers, we are not embarrafted
with an exadf knowledge oi the difference of longi-
tude between the places compared, which therefore

in •

[ 33« ]

in Tome meafure compenfates for the fmalnefs of the
bafe.

The fame irrefragable argument, made ufe of in
the apparent lead; diftance of the centers, meafured
at Rodrigues, to prove that the parallax of the Sun
is very nearly = 8 ', 5, may like wife be deduced from
the apparent lead diftance of the centers, computed
from the total durations dbferved at thefe 1 2 places,
but with more certainty ; becaule the determination
of the apparent lead: diftances of the centers from
the obferved total durations may be depended on to
a very great precifion, but the fame cannot be faid
with regard to the apparent lead; diftance of the cen-
ters meafured at Rodrigues : For M. Pingre tells us
that he ufed a very good micrometer fitted to a re-
fracting telefcope of nine feet focus, the objeCt-giafs
of which was but an indifferent one ; and we are
very certain, that in meafuring, with a micrometer
of this fort, dark objeCts on a white field or ground,
if the image is any way indiftindt, the angle meafur-
ed will be lefs than the true angle, and 'vice vcrfa
when a bright objedt is meafured on a dark ground j
as a proof of this remark, we find that M. Pingre
meafured and found the diameter of Venus, when
on the Sun, — 54", 7, whereas we are certain
that it was above 58", and therefore we may prefume
that the meafurements of the greateft diftance of the
limbs might be greater than the true diftance, and as
a further proof of the uncertainty of the meafure-
ments made with this inftrument we find that M.
Pingre makes the diftance of the limbs greateft, fe-
deral minutes after it was paft the greateft.

I fhalt

C 339 ]

I (liall now produce, at one view, the means of
the feveral determinations of the Sun’s parallax, by
the before-mentioned three feveral methods, which
will contain the fubftance of this whole paper.

im0. The mean of 1 16 comparifons of
the internal contacts obferved at places to
the north of the Line only, gives the f

Sun’s parallax — -J

2do. The mean of 2 1 comparifons of
the internal contacts, with that at the
Cape, gives the Sun’s parallax - - — -
3ti0. The mean of 21 comparifons of
the internal contadls with that at Rod-
rigues, gives the Sun’s parallax - - — _
4t0. The mean of the comparifons of
the total durations gives the Sun’s parallax
5t0. The mean of the apparent leaft dis-
tances of the centers compared with that
meafured at Rodrigues, gives the Sun’s
parallax - - — __________

6t0. The mean of the apparent leaf! dis-
tances of the centers by computation from
the total durations compared together,

gives the Sun’s parallax - .

The mean of thefe 6 means gives the
Sun’s parallax - - — - - — _ — _
And if we rejedt the mean arifing from
the comparifons of the total durations,
which is the leaft certain, the mean of
the other 5 means gives the Sun’s parallax.

= 3. 565

= 8. 56

= 8.57
— 8. 61

= 8. 56
= 8. 53

} =

8. 566

8-557

Thus

[ 34° ] ’

Thus is the Sun’s parallax, on the day of the tran-
fir, concluded to be = 8r/, 56, and that from three
different modes of comparing together a great num-
ber of observations varioufly combined; the feveral
results fo nearly coinciding that to me it ieeir.s im-
potlible, that the mean of them all can err _L. of a
fecond, and that probably the error does not exceed
^4-er part of the whole quantity, as the great Dr.
Halley had, many years fince, confidently prefaged*,
and thereupon I cannot but congratulate cur age and
nation, particularly this fociety on being enabled,
through the roval munificence, to fend fit obfervers
to the Cape of Good Hope, whole pofition affords
the largeft bafe, and confequently the laieft founda-
tion for the truth.

P. S. M. Pingre, in his aforefaid memoir, feems
to think that there muff be fome miftake in Mr. Ma-
fon’s obfervation at the Cape, becaufe by comparing
the obfervations of Jupiter’s fatellites made by Mr.
Mafon at the Cape, with thofe made by M. Meffier
at Paris, he finds the difference of longitude between
thefe two places lefs by 1' of time, than between
Paris and the obfervatory of M. de la Caiile at the
Cape, and therefore imagines that Mr. Mafon’s ob-
fervatory was to the weft of M. de la Cai lie’s. If
M. Pingre had looked into the map of the Cape by
M de la Caiile, be would have l'een, that, if Mr.
Mafon’s obfervatory had been 1' of time to the weft

* Ut junioribus noftris aftronomis, quibus forfan hrec obfer-
vare, ob minorem aetatem, obtingere potdb, viam praemonftrem,
qua immenfam fobs diftantiam, intra quingentefimam iui partem,
rite dimetiri poterint. Ph. Tr. N. cccxlviii. p. 454.

of

[ 3+i ]

of M. de la Caille’s, it muft have been in the ocean.

I am not at all furprized to lee a difference or error
of i' of time in deducing the difference of longitude
between Paris and the cape, by comparing Mr. Ma-
fon’s obfervations with thole of M. Meffier ; for I
find, in the laft volume of the Memoirs for 1761,
a difference of 1' 5" between M. de la Lande and M.
Meffier in an immerlion of the firff fatellite of Ju-
piter, both of thefe gentlemen obferving at Paris,
owing I fuppofe to the different goodnefs of the tele-
fcopes ufed on this occafion, for M. dela Lande fays
that he ufed an 18 foot refrader, the objed-glafs of
which was tolerably good, and that M. Meffier made
ufe of a very good refleder of 30 inches. If M.
Pingre will take the trouble of looking into the Phi-
lofophical Tranfadions, vol. LII. part I. he will
there find obfervations made at the Cape, and in Sur-
rey- ftreet, London, of the immerlions of the firff and
fecond fatellites of Jupiter with refleding telefcopes,
of equal goodnefs, of two feet focal length, where
the difference of determination of the longitude of
thefe two places, does not exceed one fecond in thofe
of the firff fatellite, and not above 16" in thofe of
the fecond fatellite. Mr. Mafon’s obfervatory at the
Cape was about half a mile to the fouth of M. de la
Caille’s, and about 10 or 12 yards to the weft of the
meridian of the fame.

M. Pingre alfo feems to think that the time fhewn
by Mr. Mafon’s clock was taken from a falfe meridi-
an. When M. Pingre fhall read the account given
by Mr. Mafon of his obfervations at the Cape, which
lie fays in his Memoir he has not feen, I am per-
fwaded he will be fully fatisfied, from the many e-

Vol. LIII. Y y qual-

[ 3*2 ]

iqual-altitudes taken by Mr. Mafon, that there can be
no doubt of the times of his obfervations being found
from a true meridian.

I cannot leave this fubjedt without taking notice of
a remarkable expreflion in the hi dory of the Me-
moirs of the R. Academy at Paris page 96, for the
year 1757. It is there faid that the Englidi intend-
ed to fend an adronomer to North America to ob-
ferve the tranfit of Venus (according to the plan laid
down by Dr. Halley) before they faw the map of the
tranfit by M. de L’llle, and the authority produced
for this affertion, are the Englifh news papers, which,
if they had underdood the nature of thefe papers,
can be no authority at all. I mud therefore, on the
bed authority, inform the gentlemen, who are the
compilers of the hidory of thefe memoirs, that the
R. Society never once thought of fending an obfer-
ver to North America, even before they faw the map
of the tranfit by M. de L’ide.

N. B. In this paper I have employed the fame ele-
ments as in my former paper on this fubjedt, except
that in reducing time to fpace I have made ufe of
4' o" 03 for the horary motion of Venus in her path.

A method

[ 343 ]

A method of determining the apparent lead: didance
of the centers of the Sun and Venus from the ob-
fervation of the total duration of the tranfit ob-
lerved any one place, and alfo the geocentric lead
didance of the centers.

JET BC PL [Tab. XVII. Fig. i.] reprefent the
difk of the Sun, LSP the ecliptic, OR the
geocentric path of Venus over the Sun, AD the ap-
parent path at any place, to the north of the plane
of Venus’s orbit, SM the geocentric lead didance of
the centers, A K the parallax of latitude at the in-
ternal contact at the ingrefs, ND the parallax of la-
titude at the internal contadt at the egrefs, Ab the
parallax of longitude at the ingrefs, and rD the
parallax of longitude at the egrefs. It is required
to find S F, which is a perpendicular let fall from
the center of the Sun on the apparent path, and from
thence to find S M the geocentric lead didance of the
centers of the Sun and Venus.

If the parallax of longitude at the ingrefs retards,
and the parallax of longitude at the egrefs accelerates,
the total duration will be diortned by the fum of
thefe two parallaxes of longitude, viz. by Ab and
c D, and if we make no allowance for thefe paral-
laxes, the apparent path will appear to have been
B C, confequcntly a perpendicular from the center of
the Sun on BC will be SE, longer than the perpen-
dicular on the true apparent path by F E. But fince
it is certain that the parallaxes of longitude do not
deprefs or elevate the planet, and only alter the po-

Y v 2 fition

[ 3+4 ]

lition of the planet in a direction perpendicular to the
axis of the orbit of the planet, therefore the paral-
laxes of longitude, in time, are, in this cafe, to be
addea to the obferved time of the total duration ; in
confequence of which the obferved time of total du-
ration, be »h A b -f cD are = to the chord deferibed
by the planet in its paffage over the Sun 3 and if the
femidiameters of the Sun and Venus are known,
their dinerence is known, which is m: to the line
AS 3 AF, from what has been laid is alfo known,
therefore S i" may be found. But this S F is not the
apparent lead: didance of the centers, for if we com-
pute the parallax of latitude for the apparent middle
of the tran fit, we fhall find it greater than MF,
which MF is only a mean between the parallaxes of
latitude at the ingrefs and egrefs. Let therefore the
difference between MF and the parallax of lati-
tude computed for the middle of the tranfit be add-
ed to S F, and the fum will be = to the apparent
lead: didance of the centers nearly 3 and if from this
fum we fubtradt the parallax of latitude, computed
for the middle of the tranfit, the remainder will be
the geocentric lead diftance of the centers nearly.

A true and more ready method to find the geocentric
lead: diflance of the centers, confequently the ap-
parent lead: difiance of the centers at any place,
where the total duration has been obferved.

Reduce the total duration obferved to the center,
reduce the central femi-duration, in time, into fpacej
then in the right-angled triangle SMA [Fig. 2.] or
S M a, we have the two ddes S A or S<rr, and A M

or

[ 345 ]

or a M given, therefore the third fide S M may be
found, therefore S M the geocentric leaft diftance of
the centers is found ; and if to S M, we add or fub-
tradt the parallax of latitude for the apparent middle
of the tranfit, the fum or difference will be the ap-
parent leaft diftance of the centers.

EXAMPLE.

To find the apparent lead diftance of the centers

at Tobolfk.

The total duration obferved at Tobolfk was
5h 4^ 537/ a^d 9' z" (— to t^e effedl of the paral-
laxes of longitude and latitude both for the ingrefs
and egrefs, on the fuppofition that the Sun’s parallax
is — 8", 5) to this total duration, the fum 511 57' $6"
is — to the central duration, confequently 2h ^8/ ^8//
is — the central femi-duration : reduce this time in-
to fpace, and it will be found — to 71 5", 956 —
AM or ^ M, and S A or S a (— difference of the
femi-diameters of the Sun and Venus) — 9 r6//, there-
fore S M will be found — : 571", 37 — the geocen-
tric leaf: difiance of the centers of the Sun and Ve-
nus. The parallax of latitude, computed on the
above fuppofition of the Sun’s parallax, for the appa-
rent middle of the tranfit at Tobolfk, will be found —
i47/> 13* which being added to the geocentric leafi
difiance of the centers above found, the Sum 585 v, 50
will be the apparent leaft diftance of the centers at
Tobolfk.

XLVIII; An

[ 346 ]

XL VII I. An Account of a Cafe , in which

Green Hemlock was applied : In a Letter
to the Rt. Hon . Hugh Lord Willoughby of
Parham, V. P. of the R.S. by Mr. Joiiaii
Colebrook, F. R. S.

My Lord,

Read Dec. 15, "T Take the liberty, from the friend-
l?6i' lhip you are pleafed to honour me

with, to addrefs the enclofed caie to your Lordfhip,
and hope you will think it worth communicating
to the Royal Society. It is a bare relation of mat-
ters of fa6t, mod of them within my own know-
ledge, the others attefted by perfons whole veracity
I can depend on. As the hemlock taken in this
manner gave great relief to this poor woman, la-
bouring under the mod dreadful dileafe human na-
ture is liable to •> it may be attended with the fame
fuccefs to other perfons, in the fame circum-
ftances.

I am well allured your Lordfhip rejoices at every
opportunity of doing good to mankind, by com-
municating any beneficial difcoveries of your own,
or your friends ; among whom you will excufe my
vanity in placing myfelf, who am,

with the greateft refpedt,
your Lordfhip s

moll humble Servant,

J. Colebrook.

ANN

C 347 ]

ANN James of the parifh of Boughton Mon-
^ chelfey in Kent, aged 55 years, a married wo-
man, had for fome years complained of a pain,
and hard lump in each bread:. In September 1762
die afked my advice about them : upon examining
them I found a very hard fchirrus in each bread :
that in the left bread, had the mamillary glands
indurated and knobbed like ramifications toward
the axilla, a little adhelion to the pedtoral rnufcle ;
was as big as a turkey’s egg, and fhe was under
daily apprchenfions, that it would break. That in
the right bread was not near lo large, or had
ramifications nor adhered like the other. She com-
plained of mod excruciating dabbing pains in both
breads, which prevented her having any red in the
night, and made her fo very miferable all day, whe-
ther fhe lay down, dood, fat, or walked, that fhe
was unable, not only to go out to work, but even
to do any thing for her family at home, not even to
make her own bed and fhe had totally lod her ap-
petite : her ufual employ was fpinning, wadnng,
brewing, and what we in London call the bufinefs
of a chairwoman. The breads were but little dis-
coloured, but the pains fhe defcribed, and the ra-
mifications attending the fchirrus, in the left bread,
induced me to pronounce it a cancer.

I advifed her to take the green hemlock, viz.
cicuta major vulgaris caule maculofo ; mince it with
parfly (to difguife the tade) and eat it with bread
and butter twice or three times in a day, the third
part of a leaf, or one of the three dividons, which
are in each leaf, at a time 5 that her condant drink
5 diould

[ 3+8 ]

fhould be lime water and milk; that fhe fhould take
as many millepedes every day, as her ftomach would
bear, or (lie could get, that her body fhould be kept
open by Rhubarb, or Magneda, as occadon required ;
that Ihe fhould have an blue in her arm, and lofe
fix or eight ounces of blood once in fix or eight weeks,
if her pains continued.

A good lady in the neighbourhood, whofe huma-
nity is only to be equalled by her good fenfe, gene-
roudy promifed to fee,- that fhe purlued this regimen,
and from time to time give me an account of the
fuccefs.

I delired a leaf might be weighed, that I might
afcertain the quantity of each dole, and found fhe
took fifteen grains of the green plant three times in
a day ; finding it agree with her ftomach, and that it
eafed her pains, though it caufed a tingling to her
fingers ends : fine encreafed the quantity. In the be-
ginning of November fhe had a very large menltrual
difcharge, which had not happened to her for many
years before; the fchirrus was much lefTened, and her
pains were confiderably abated.

About the end of November fhe found her bread:
more dwelled, and the pain more acute than it had
been for fix weeks before, had a reftlefTnefs, giddi-
nefs in her head, and weight over her eyes; the dif-
charge of the ifTue flopped, and a violent humour
came all round the orifice. As I had dedred a little
blood might be taken away, if occaiion required it,
fhe was bled about the lad: day of November, on
which fhe fainted away, and afterwards had fainting
fits two or three times in a day, great ficknefs at her
domach, and fometimes bled at the node. On thele

fymptoms

[ 349 ]

fymptoms coming on, notwithdanding die had
t?ken fomewhat purgative twice in a week, from
from her firft beginning to take the hemlock, it
was thought proper to fufpend the taking the hem-
lock for fome days.

I then ordered her an infufion of the cortex Pe-
ruvianus an ounce, in powder, to a quart of fpring
water, to let it Hand three or four days, Shaking it
every day; and thfen that (lie diould take three
fpoonfuls, twice in a day ; that die fhould repeat
the hemlock in the lame quantity die took at the
fird ; that fhe fhould not again exceed that quan -
tity on any account ; and that die diould continue
the lime-water and the millepedes.

About the latter end of December fhe had a re-
gular appearance of her menfes, but very moderate;
her pains were very much abated, and the fchirrus
much lefs, though die often complained of a fwim-
niing in her head, and a redlednefs in the night.
From this time, viz. the end of December, die
continued mending in all refpedts fo much, that
I heard nothing of her ’till March 1763; when
Mrs. Savage (the lady under whofe infpedtion die
took the hemlock) came to London, and told me,
that Ann James was furprizingly recovered ; that
her cancer was much ledened, that die could
ufe her arms, work for herfelf and family, and that
her pains were fo much abated, that fhe was quite
happy.

In September lad I was at Boughton, faw her,
and examined her breads : the fchirrus in her left
bread was not half fo big as when I faw it before.;
the ramifications were all gone, and it did not at

V o l. LIII. Z z all

C 350 ]

all adhere to the peCtoral mufcle ; her appetite was
good, and {he was able to do her bufinefs as ufual,
and had that day I faw her been brewing : {he {aid
{he fometimes felt fome of thofe {tabbing pains
{he before complained of, but they were not fre-
quent nor very fevere.

The beginning of this November I had a farther
account of her from Sir Thomas Ryder, who lives
in that neighbourhood, and whom I defired to be
fo kind as to inform me of her prefent hate of
health : he with his ufual benevolence (than whom
no man hath more) fent for the woman, and had
the following account from herfelf ;

That the lump in her bread:, which die expect-
ed would break, is not half fo big as it was, and
continued decreadng ; that the hath great fpirits ;
and, from being one of the molt miferable of the
human fpecies, lhe now enjoys eafe and happinefs,
and can, without any great pain, do all her ufual
bufinefs, as wafhing, brewing, baking, and nee-
dle-work, except fpinning, that motion {till giving
her great pain : {he continues to take half a drachm
of dry hemlock twice in a day, but takes the green,
when lhe can get it, in larger quantities. Sir Tho-
mas adds, that lhe looks very well for a woman of
her age.

. From the happy fuccefs of the hemlock in this
inftance, it were to be wilhed it might be tried in
fome other fimilar cafe, and that the weight of the
plant taken in one day (whether green or dry)
might be particularly afeertained, which was too
often in this cafe taken by guefsj and as the ex*-

traeft

[ 351 ]

ira6t recommended by Dr. Stork in his ingenious
treatife hath not, upon trial in England, been at-
tended with the fame fuccefs it had at Vienna,
I Should prefer the herb itfelf to any preparation
of it.

XL IX. An Account of a remarkable Mete-

or : In a Letter to the Reverend Tho-
mas Birch, D. D. Secret . of R. S. from
Mr . Samuel Dunn.

»

Reverend Sir, Chelfea, Dec. 9th, 1763.

Read Dec. 15, T" N the Months of September and
17 3’ x October laft, on many different days,
but always in the afternoon, when the Sun was
nearly of the fame height above the horizon, I
was amufed with the appearance of a kind of me-
teor, which I do not know that it hath been before
taken notice of by others. As it appeared under
nearly ‘the fame circumftances at other times* and
therefore may contribute towards the better un-
derftanding the theory of a parhelion, I fhall give
the defcription of this meteor, as it appeared the
6th of October laft, at five o’clock afternoon. A
kind of mock Sun appeared of equal altitude with
the real Sun about 22~ foutherly therefrom. A

littls

[ 352 ]

little above the mock Sun the Sky was clear, but
the phasnomenon was in the midft of clouds that
were not very denfe. The diameter of this
phenomenon was nearly like that of the real
Sun, and a remarkable red ftream of light pointed
therefrom as at all other times towards the real Sun,
which fhined clearly at the fame time. As there
was no defcending rain, nor any other colour of
the rain-bow, I take this to have been a meteor
not yet regiftered amongft meteorological obferva-
tions,

I am>.

Reverend Sir,

Your moft obedient fervant,

Samuel Dunn:

L. An

[ 353 ]

L. An Account of a Blow upon the Hearty
and of its EffeSis : By Mark Akenfide,
M. Z). F. R. S, and Phyfcia n to Bier
Majefy.

teen years of age, was brought to a confultation of
the phyficians and furgeons of St. Thomas’s Hof-
pital. His diforder was a palpitation of the heart;
fo very violent to the touch, that we all concluded
it to be an aneuryfm, and without remedy. He
had a frequent cough. His pulfe was quick, weak,
and uneven; but not properly intermitting. It was
apparent that nothing could be done, farther than
by letting blood in fmall quantities, and by the ufe
of emollient pedtoral medicines, to leffen now and
then, however inconliderably, the extreme danger
to which he was continually fubjedt. He was taken
into the hofpital that fame day, being Saturday;
and treated according to what had been agreed up-
on. But on the Tuefday morning following, he
died, without any previous alarm or alteration.

The origin of his complaint was a blow, which
he had received fix months before, from the mailer
whom he ferved, as waiter in a public houfe. The
mafter had owned that he had pulhed him flightly
on the left fide with his hand. The boy informed
us that he himfelf was then carrying a plate under
his arm; and that the blow or pufh, from his maf-

N the nth of September, 1762,
Richard Bennet, a lad about four-

ter,

t 354 ]

ter, drove the edge of the plate forcibly between
two of his ribs. He was immediately very ill from
the hurt j fick, and in great pain. His mother
alfo informed us, that fhe thought the palpitation
was more violent about a. fortnight after the acci-
dent, than when we examined him. The day af-
ter the blow, they took eight ounces of blood from
his arm : about three weeks after that, they again
opened a vein, but got not much from it : and
three weeks from thence, they let him blood the
laft time, to the amount of eight ounces. He be-
gan to have a cough foon after the hurt, with fre-
quent fpittings of blood in very large quantities ;
and had nodturnal fweats almoft the whole fix
months, during which he furvived the blow. A-
bout four months after it, there came, over the
umbilical region of the abdomen, a livid appear-
ance like a mortification : but it went off gradual-
ly, and at length vanifhed. He had nothing par-
ticular in his habit of body or ffate of health ; fave
that, about a year before this accident, he had been
crippled with the rheumatifm. He was, when we
law him, a good deal reduced ; but had not a hec-
tic nor confumptive look.

On the day of his death, Mr. Cowell opened
him ; when, to our great furprize, we found no
aneuryfm, nor the leaft extravafation of blood
either from the cavities of the heart or the large
veffels. But on the left ventricle of the heart, near
it’s apex, there was a livid fpot, almoft as large as
a half-crown piece, bruifed and jelly like ; the part
underneath being mortified quite to the cavity of
the ventricle. From thence upward, toward the

auricle.

C 355 ]

auricle, there went feveral livid fpecks and traces
of inflammation, tending in like manner to gan-
grene. The heart did alfo, throughout its whole
furface, adhere very clofely to the pericardium ;
and the whole outer furface of the pericardium, as
clofely, to the lungs. The other vifcera were
- quite found.

So that the mifchief here was properly a contu-
fion of the heart ; the edge of the plate having
(truck it, probably at the inflant of its greateit di-
aftole. This produced an inflammation on its fur-
face, followed by a gangrene, and terminating in
that double adhefion : by which the whole heart
was fad tied up j till on this account, as well as
by reafon of the mortification, it was no longer
able to circulate the blood.

* ) .

LL Rat to

C 356 ]

LI. Ratio conjiciendi Nitrum in Podolia : Au -

■ thore Wolf, M. D. communicated by

Mr, Henry Baker, F, R. S.

Read Dec.
1763.

22,

N1.

T R U M, quod in Europa con-
fumitur, longe maxima parte ex
India Orientali adfertur : ceterum fere omne ex
Ucrainia, tarn Polonica, quam Ruftica, vel adja-
centibus provinciis venit. Obtinetur elixivatione
ex humo et cineribus. Humus quidem fola eft ve-
getabilis et animalis ; fed prasterea etiam opus eft,
ut diu fit immota, inculta, deferta. Talis in U-
' crainia et Podolia eft valde frequens. Nam incul-
ta jacet hsec regio quad a tertio asraa chriftianse fe-
culo, quo Getac, antiqui pofleffores, a Bulgaris ex-
trudebantur, quorum pofteri pecorum magis quam
agrorum, urbiumque culturas incubuerunt. Max-
ime vero ob bella luperioris feculi. Turcica, Cofa-
cica et Tartarica, ab incolis deferta atque reliefta
eft ; noftra tamen vita, confluentibus colonis ob
prascellentem fertilitatem foli, jam fatis colitur.

Ampliftima hsc planities, quantum videre licuit,
tegitur humo nigra vel fubrubra, ad paucorum pol-
licum, vel pedis profunditatem, fub qua jacet ter-
ra plus minus alba, cretacea, calcaria, margacea, (vel
faxum ex his induratum) conchyliis marinis pluri-
um generum referta, multis in locis adeo copiofe,
ut tota non videatur, quam iis folis, conftare. Ar-
gilla et fabulum minus frequenter occurrunt. Ifta
humus vero eft adeo levis, et in aqua adeo folubilis

ut

C 357 ]

ut a paqca pluvia ftatim diffluat, atque a levi vento,
vel a iole citiftime ficcefcat, et in pulverem nigrum
fubtilcm, viatorum veftimenta, ad cutem ufque pe-
netrantem et denigrantem, attollatur.

Indicia terrae, nitro prasgnantis, talia habent co-
loni: fi bene nigra, tadu lasvis, non fabulofa, in
farinam fubtilem friabilis : fi fimofa, pinguis : fi
faporis frigidi nitrofi : fi din videatur relida, immota:
maxime vero dives aeftimatur fi efflorefcentia nitrofa,
inftar lanuginis albas, obteda fit : hinc, ubicunque fuf-
picio eft, oppidum quondam fuifte, vel pagum, vel
ftabulum, vel ccemeterium. Prasfertim tamen colles
appetunt, in his locis valde frequentes, quos Mogily
appellant. Horutn figura conica arte fados efte fa-
cile prodit: de plurimis etiam certo fcimus, in memo-
riam prceliorum, ibi editorum, congeftos efte; de
reliquis vero ob fimilitudinem idem arbitramur. Ex
his unus, ob inftgqem magnitudinem, Szeroka Mo-
gila, feu magnus collis, didus, prope Granoviam fitus,
perantiquus, forte per ioo annos jam nitro confici-
ondo infervit. Hujus diameter 300 circiter eft paf-
i-ium, et, quantum ex reftduo fegmento hyperbolico
aeftimatur, 300 pedes facile altus erat. Fabula nar-
rat, Reginam quandam, accepto nuncio, de rege ab
inimicis profligato, cum novo exercitu approperafte,
et errore inimici, proprium maritum in hoc loco op-
preflifte. an ofta occiforum fub fundo lateant, ulte-
rior effoftio docebit.

Pro fabricatione nitri, locum eligunt vicinum illi,
ubi terra nitri ferax fatis copiofa, ut faltem per aefta-
tem unam operi continuando fufticiat : rationem ta-
men etiam habent aquae et ligni, quonempe commodi-
us atque minori pretio convehi poftint. Utenfilia hue
Vol. LIII. Aaa pertinentia

[ 35§ ]

pertinentia uno vocabulo appellant Maydan, et confif-
tunt fequentibus.

1. Ahenum aeneum magnum, continens dolia 15,
feu amphoras 60, quarum quaelibet capit congius 6
(gallons) feu libras 54 aquas.

2. Dolia lignea 100 fuperius aperta, et prope fun-
dum pertufa foramine, pro lubitu claudendo : capaci-
tas horum eft talis, ut contineant terras carrum unum,
quod redit ad amphoras 4 vel quinque.

3. Cadi duo permagni, amphorarum circiter centum.

4. Alvei 3 2, feu excipula lignea lata,amphoram unam
vel paulo plus continentia, quae criftallifationi inferviunt.

5. Praeterea amphorae aliquot pro apportanda aqua.

Furnus ex terra effoditur, in quo ahenum ope late-

rum firmatur, in eadem cum horizonte linea. In
peripheria aheni adhuc circulum ex afferibus parvis
conftruunt, ad odto circiter pollicum altitudinem, at-
que luto fuperinducunt, ne lixivium, forte nimis ebul-
liens, marginem aheni tranfcendat et effundatur.
Proximo loco ad ahenum ponunt cados illos duos
magnos, cetera circumftant. Pro transfundendo lix-
ivio vel aqua, utuntur canali ligneo portabili.

Jam terram nitrofam effolfam ad furnum vehunt,
vel, fi is propinquus, earn ftatim in loco effoflionis
probe comminuunt fpatulis ferreis, lapides et fimilia
auferunt, atque in acervos congerunt, ita, ut laxe fibi
invicem incumbat. Si hasc terra nitro valde dives,
(quod ex pinguitudine et efHorefcentia lanuginofa nof-
cunt) admifcent ei aliam minus divitem, asquali copia,
bene tamen nigram, diu reliftam : nimirum, termi-
no chymico, terras animali admifcent pure vegetabi-
lem. Tandem addunt cinerum partem quintam cir-
citer, vel minus, prout experientia docuerit, et fimi-
liter bene fubigunt. Alii turn demum cineres addunt,

dum

[ 359 ]

dum terrain in dolia immittunt. Cineres funt ex frax-
ino utpote communion arbore. Si urina ad manus,
vel matrix nitri fuperabundans, has etiam adfundunt.
Calcem vivam vero, quantum audivi, non addunt. Sic
copiam terrae praeparant, incipiente aeftate, et per totam
aeftatem ft mil iter continuant, ne Tub continua codtione
deficiat. Alii terram, quae aeftate fequenti elixivari de-
bet, per antecedentem aeftatem convehunt et praeparant.
Communis tamen praxis eft, terram effoftam et prae-
paratam, ftatim in ipfo loco effbfllonis elutriare j quod
ita peragitur.

In quodlibet doliorum ioo fupra N°. 2. memora-
torum, immittunt terrae praeparatae nitrofse carrum
unum, nempe amphoras 4 circiter. Aquam frigidam
(alii fervidam) fuperaffundunt ad repletionem dolii :
cineres, ft nondurn additi, addunt : et baculo bene
circumagitant. Sic relinquunt per 24 horas, nift quod
agitatio cum baculo interdum repetatur. Hoc tem-
pore elapfo, lixivium fic enatum, per foramen, prope
fundum doliorum, emittunt, et in cados duos magnos
N°. 3. memoratos, transfundunt. Terram ftc elutri-
atam ex doliis ejiciunt, novam immittunt, et ftmiliter
operantur. Ita quotidie fit, quoufque nitri codlio
durat.

Pro nitri excodtione opus habent matrice nitri,' quse
eft lixivium fpiftum, poft nitri cryftallifationem relic-
turn, jam ulterius in cryftallos non cogendum : quare
hoc lixivium follicite ex anno noviffimo in fubfequen-
tem fervant. Hoc enim deficiente, per odto faepe
dies, fub continua ebullitione, lixivium recens nitro-
fum coqui et infpiftari debet, antequam ad cryftalli-
fationem idoneum evadat. Cujus phaenomeni ratio
in eo fita videtur, quod lixivium recens iftum caloris

A a a 2 gradum

[ 36o ]

gradurn non aflumat, qui pro abigendis partibus pin-
guibus et alcalinis volatilibus requiritur, quas denfi-
tas requifita ipfi conciliatur per matricem nitri, copi-
ofam terram calcariam in acido falis et nitri folutam,
continentem. Hoc lixivio vero femel obtento, ex-
codio citius perficitur.

Nimirum hujus matricis nitri dolium unum vel al-
terum in ahenum infundunt, et lixivium recens ni-
trofum in cadis magnis colledum addunt, ad reple-
tionem aheni, ignem fubdunt, et fub continua ebulii-
tione coquunt, fere per 24 horas. Tunc fignis cryf-
tallifationis in fuperficie apparentibus, lixivium hoc
excodum, fpilfum, ex aheno, in alveos illos pianos
32 fub N°. 4. memoratos transfundunt : ibique ite-
rum per 24 horas relinquunt. Sic cryftallifatione fac-
ta, matrix nitri, ab hac cryftallifatione relidua, ex al-
veis decantatur, et in ahenum reaffunditur. Cryftalli
nitri eximuntur, et exftccantur, quas impuriores funt,
et pro depuratione, in aqua pura iterum folvuntur, per
lanam filtrantur, in aheno minori infpiftantur, et fe-
cunda vice cryftallifantur in nitrum purius vendibile.
Matrici nitri in ahenum reinfufae addunt fimiliter no-
vum lixivium recens nitrofum ex cadis illis duobus
magnis, coquunt per 24 horas et cryftallifant. Hac
ratione opus per totam asftatem continuat : hieme a
gelu impeditur.

Produdum diei unius dicunt doba, et ad minimum
computatur ponderis unius (kamien, five i4oko) quod
redit ad libras communes 42. Sub depuratione oko
unum vel 3 libras ab hoc quanto decedunt. Pondus
unum nitri venditur hodie in loco confedionis rublis
4(17 (hillings). Verum tempore pads multo vilius.

Quod

[ 361 ]

Quod li carrum unum, feu amphoras 4 terra ni-
trofa praparata cum cineribus, laxe cohasrentis, fu-
mamus pro pedibus cubicis quatuor j patet, ex 400
pedibus cubicis hujufmodi terra obtineri libras 40 cir-
citer nitri, adeoque libra una nitri in 10 pedibus cu-
bicis terra praparata, vel in 7 aut 8 pedibus cubicis
terra compadtionis effofla haret, licet hoc adeo exadte
computari non poffit.

Terrain iftam, ex qua nitrum didta ratione extrac-
tum, ex doliis ejedtam, in aggeres quatuor circiter
pedes altos congerunt, et fic relinquunt per annos
leptem, quo tempore elapfo, maydan in eodem loco
collocant, et ex eadem terra, fimili opere aqualem
fere nitri copiam elutriant. Sed tertia vice poll fep-
tem alios annos, non quidem omni nitro caret, fed
jam opera pretium non folvit.

Nullus dubito, hunc nitri parandi modum ex ori-
entalioribus regionibus hue perveniffe, et in India at-
que China non abfimili modo fieri. Qua ratione vero
in Europa fiat, autores bene multi deferibunt. Om-
nes htimum et cineres requirunt, alii etiam urinam,
alii etiam ealeem vivam. Hanc mifcelam omnes aeri
exponunt, vel libere, vel fub tedto, vel muris ex luto
conftrudlis fuperinducunt, vel in aggeres altos con-
gerunt, vel in fofias profundas laxe conjiciunt. Om-
nes etiam, quocunque modo hoc fiat, nitrum obti-
nent : copia tamen valde diverfa, quas, ut facile vide-
tur, non tarn ab operofa et fumptuofa expofitione,
quam ab ipfa pinguedine humi pendet.

Nitrum puritate multum differt. Naturale primae
cryftallifationis nunquam caret fale communi. Non
femper efi: prifmaticum, fed etiam invenitur cubicum,
asque bonum ac illud, fi balls alcalina fit mineralis, ex

fale

[ 362 ]

fale communi, vel aliunde. Figura enim Temper ab
alcali non ab acido pendet, licet Linnaeus bonam par-
tem fyftematis foffilium huic errori fuperftruxerit. Si
mu 1 turn terrae calcariae, et non Tatis cinerum. Tub coc-
tione nitri adhibitum fuerit, cryftalli erunt minus fir-
ms, et Tolutae per alcali praecipitantur, quod bono ni-
tro non accidit. Si cineres Tuerint ex durion ligno,
nitrum erit magis firmum, et in cryftallis bene mag-
nis, quale eft Indicum. Si in humo adhibita, terra
metallica, uti martialis delitefcit, Temper ejus aliqua
pars, Taltem tindtura in nitro relinquitur. Sic Indi-
cum eft rubellum, et aquam fortem dat multo magis
fumis rubris refertum, quam Polonicum. Ex hoc
enim cum vitriolo Anglico defiillata aqua Tortis eft vi-
ridis, quae fi a mercurio abftrahitur, relinquit praecipi-
tatum flavum, et per cohobationem, album, bona-
que pars mercurii in aqua forti abftradta latet. . Piae-
fertur vero nitrum Polonicum a chemicis omni alio,
utpote fincerrimum.

Ut plurimum, nitrum ab Anglis, Hollandis, ro-
lonis et Ruffis, multo minori pretio emi, quam domi
fieri poteft. Ratio facile patet quod in his regiombus
ligna et cineres quafi gratis habeantur, vedtura quoque
et opera manualia a colonis Tervis fiant. In regis Bo-
ruffiae dominiis forte plus nitri conficitur, quam in
omni reliqua Europa, et tamen vix credo, millefimam
partem domefticam fuifle ejus, quod in praefenti bello
abfumtum. Nempe magis neceflana, magifque pro-
ficua nobis eft terra, nitro et fale volatili praegnans,
pro foecundandis agris, atque conficiendo pane, quam
ut nitrum deftrudtivum inde elixivetur, vel parum
utilis fill ammoniacus inde fublimetur. Talia dcieitis
incultisque terris relinquenda lunt.

Cogitationes

[ 363 ]

Cogitationes quaedam circa originem Nitri.

VTITRUM commune ex alcali fixo vegetabili
et acido nitrofo componitur. De origine prioris
non difputatur, cum cineres ad nitri confedionem fu-
mantur, neque fine his bonum nitrum in copia fieri
poftit. Cum tamen etiam fine additis cineribus pau-
cum nitrum ex humo elutriari poflit, valde probabile
eft, in humo adhuc aliquid alcali fixi, per putrefac-
tionem nondum deftrudi, latere. Vel etiam per coc-
tionem alcali fixum eadem ratione hie generatur, qua
oritur dum Tartarus cum calce viva, vel creta coqui-
tur. Hoc experimento Kunkel, et poft ilium alii,
demonftrarunt alcali fixum vegetabile fine igne geni-
tum. In humo vero, et terra calcaria, et acidum,
tartari acido fimile, per calcinationem et deftillatio-
nem demonftratur.

Sed de acido nitri, res multa difficultate laborat.
Omnes chemici hoc acidum ex aere derivant, ibique
genitum dicunt ex acido univerfali vitriolico, atque in-
de per partes humi alcalinas attrahi. Ne dicam : aci-
di vitriolici univerfalitatem per omnem atmofphasram,
precario afiumi j et nitrum in omni humo generari,
licet in tali loco, ubi longe lateque de minera vitrioli—
ca nihil videtur : item, in fale alcalico fixo, puro,
fincero, per annos in aere relido, repetitis experi-
mentis, vix micarn falis medii, multo minus vitrioli-
ci, obfervari, modo hoc non fiat in laboratorio, vel
alibi, in vicinia vaporum acidorum. Sed pulcras Marg-
grafii deftillationes aquas pluvialis et nivalis lucem huic
rei affundunt : obtinuit nempe ex libris 225 harum
aquarum lentifiime infpifTatarum, per additionem falis

tartari

C 364 ]

tartari purl, pauca grana nitri et falis communis, qua?
quantitas inaffignabilis minor certe erat fcrupulo uno:
adeoque in ilia pluvias quantitate, quas fere eft pedum
cubicorum 34 vix tanturn acidi nitrofi continetur, ac
in fcrupulo uno nitri. Jam obiervationes mcteoricas,
docent, omnem aquam per annum unum de coelo
delabentem raro ad duorum pedum altitudinem afeen-
dere. Dixi vero in deferiptione confedionis nitri po-
dolici, ex pedibus cubicis 10 terras nitrofae prasparata?,
ad minimum libram unam nitri elixivari, atque banc
terram femel elutriatam in aggeres congeftam, poft
feptem annos, fimile nitri quantum largiri. Ponamus,
10 pedes cubicos hujus terra?, contingere aerem in
fuperficie 10 pedum quadratorum, et omne humidum,
in hanc fuperficiem delabens, acidum fuum omne
nitrofum hie figere, nihil vero nec in auras iterum
afeendere, nec per aquas defluentes abripi. Cadunt
vero in hanc fuperficiem per 7 annos, aquas coeleftis
pedes cubici 140 qua? per Margrafium deftillata, da-
ret, cum fale tartari, fcrupulos 40 nitri, quod lon-
ge abeft a libra una. Cum vero rationi magis fit con-
fonum, ex aere non plus nec minus in humum de-
feendere, quam ex humo in aerem afeenderat: at-
tradio etiam acidi per alcali valde fit precaria, cum
exinde fequeretur, montes calcarios et cretaceos, ab
omni humo denudatos, hoc acido tandem faturari de-
bere, faltem nitro abundare, quod omnino falfum ;
patet, hanc chemicorum hypothefin flare non pofi'e.

Verum ex omni humo plus minus nitri elixivatur;
ex ceteris terris nullum, nifi humo permixtas fint :
omnes qui nitrum conficiunt, humum adhibent, ne-
que experimentum feitur, ubi fine humo fieri poffit,
atque omne nitrum non nifi in fuperficie terras ad

parvam

[ 3 6S ]

parvam profunditatem invenitur, ubi nempe humus
eft j cum ergo humus non fit, nift vegetabilia et ani-
malia per putrefadtionem deftrudta, vix dubitare licet,
acidum nitri ex regno vegetabili et animali originem
ducere, et quidem per deftrudtionem horum compo-
ni, cum in recentibus non inveniatur. Salia enim
eftentialia, nitrofa didta, Borraginis, Portulaccas, Pa-
rietarias, Millepedum, Lumbricorum terreftrium, etc.
etc. non nift per fimilitudinem quandam ftc dicun-
tur. Ex faecibus humanis elixivatis, quidem, nitrum
obtinuit Hombergius, fed fasces jam ad humum per-
tinent.

Vegetabilia et animalia recentia, deftillatione, dant
fpiritum plus minus acidum oleofum foetentem, ad
fpiritum tartari accedentem, cum oleo fcetido; priora.
quidem plus acidi ; pofteriora plus olei : ex carbone
vero reftduo utroque paucum fal commune elixivari,
atque poft ulteriorem calcinationem etiam alcali fixum
elutriari poteft, relidla tandem terra calcaria : et qui-
dem vegetabilia plus largiuntur alcali fixi, animalia
vero plus falis communis, et plus terras calcarias. Hu-
mus contra vegetabilis et animalis largiuntur deftillati-
one ftmiles fpiritus acidos, ftmilique oleum prioribus,
fed longe minori quantitate : prasterea vero alcali vo-
latile, quod in recentibus non aderat ; et quidem ex
vegetabili plus acidi, ex animali vero plus alcali volati-
le: refiduus carbo utriufque, prater fal commune,
etiam nitrum, elixivatione prasbet, quod in recentibus
non aderat ; atque poft ulteriorem calcinationem, al-
cali fixi nihil fuppeditat, quod tamen in recentibus ad-
erat ; fuperftite tandem, ut prius, terra calcaria.
Vegetabilis tamen humus plus nitri, animalis vero plus
falis communis, continet. Omnis ergo mutatio,
Vol. LIII. Bbb quae

[ 366 ]

quae vegetabilibus et animalibus per putrefadtionem
accidit, videtur confiftere, in diminutione acidi et
olei, in deftrudtione alcali fixi, et in generatione
alcali volatilis et acidi nitroii. Idem fere efficiunt
chymici, qui norunt, omne alcali fixum ab addito
pauco oleo et acido, repetita delfillatione, in alcali
volatile mutari. Acidum vero nitri hac ratione ars
chemica nondum produxit, licet, ut infra dicetur,
ex combinatione acidi falis cum acido vegetabili
vel animali, et parte alcali volatilis, omnino fimil-
limum quid obtineatur.

Videretur alcali volatile ad nitri confedtionem
parum conferre, cum, fub codtione, omne in au-
ras difpellatur %y tamen, fine hoc, nitrum vel nul-
lum vel pauciffimum obtinetur. Hinc nitri coc-
tores urinam valde expetunt, et humum animalem,
divitiorem alcali volatili, folicite conquirunt, talem-
qiie praeferunt, quae diu immota jacuit, cum in fas-
pius mota, hujus alcali volatilis multum per aerem
et per pluviam abripiatur. Ob hanc rationem etiam
calcem vivam, vel aliam terram calcariam humo
admifcent. Haec emm putrefadtionem, et obinde
alcali volatilis generationem valde accelerant, uti
conftat ex pulcris celeb, Pringlii circa feptica ex-
perimentis, et ex deflillatione quorumcumque ani-
malium vel vegetabilium cum calce viva. Ex qui-
bus etiam vera ratio foecundationis agrorum per
terras calcarias patet, ut ad vanatn attradtionem aci-
di nitroii ex aere non opus fit recurrere. Obinde
etiam humum praeparatam aeri exponunt, qui pu-
trefadtionem fimiliter promovet. Lanugo alba,
tempore nodturno, terram nitrofam obducens,

nitrum fapit, et per microfcopium cryftallos

nitri

[ 3^7 ]

nitri oftendit, fed a foie oriente cito diflipatur :
ut profedo vix dubium relinquatur efle hanc lanu-
ginem nitrnm volatile, ex alcali volatili et nitri a-
cido conftans, quod acidum fub codione neceftario
cum alcali fuo volatili in auras difpelleretur, nifi ab
additis cineribus vel etiam calce viva retineretur.
Videtur ergo acidum nitri in origine fua cum alcali
volatili conjundum efte, et verofimiliter inde etiam
phlogifton l'uum fpecificum, in detonationem adeo
pronum habet. Nam aurum ex aqua regis per al-
cali prsecipitatum, non fulminar, nifi alcali volatile
vel in confedione aquae regis, vel in praecipitatione
adhibitum fuerit.

Artificialem acidi nitrofi compofitionem chymici
faepius tentarunt, de qua re fequentia proferre li-
cebit. Multi acidum vitriolicum mutari dicunt in
nitrofum per additum phlogifton : fed fpiritus vi-
trioli fulfureus Stahlii, ex vitriolo per retortam frac-
turalam deftillatus, non eft fpiritus nitri : neque
ille, qui ex oleo vitrioli per retortam tubulatam,
injedis fenftm carbonibus candentibus, deftillatur :
neque ille, qui ex oleo vitrioli glaciali leni igne def-
tillatur : neque ille, qui ex arcano duplicate per
additum alumen uftum vel fabulum deftillatur : li-
cet multo fint volatiliores ipfo nitri fpiritu.

Alii acidum vitriolicum cum alcali volatili com-
binant, et obtinent falem ammoniacum fecretum
Glauber i, cum fpiritu fulfureo, qui non eft nitri.
Si fal tartar! extemporaneum bene calcinatum in
duplo fpiritus urin® folvatur, et cum parte una et
dimidia vitrioli Salifburgenfis calcinati mifceatur,
et deftilletur j rcftduum vero in aqua folutum a ter-
ra me tallica ftltrctur, evaporetur et in fpiritu uri-

B b b 2 nx

[ 368 ]

naa iterum folvatur, obtinentur fub lenta infpiflati-
one cryftalli nitrofas, qua? fal commune fapiunt,
metalla omnia volatilia reddunt, et fuiione in oc-
clufo folvunt : minime vero nitrum conftituunt.
Pietfchius ex fpiritu vitrioli, urina putrefadta et
calce viva, verum nitrum produxifle dicitur, quod
tamen a vero, ball ialtem alcalina vegetabili, om-
nino difterre debet.

Alii acidum vitriolicum combinantcum acido ve-
getabili vel animali. Sed oleum vitrioli cum tar-
taro deftillatum, dat ipiritum tartari fulfureum,
nitri nihil : neque ex fpiritu theriacali et fpiritu
tartari, cum fpiritu vitrioli et alcali fixo mixtis et
deftillatis : neque ex fpiritu cornu cervi et tindtura
antimonii acri, verum nitrum obtinetur, licet fi-
mile quid.

Sal commune totum quantum in nitrum muta-
tum multi fruftra gloriantur. Alii magni nominis,
inter quos Pottius, volunt : fpiritum lalis purum
per phlogifton purum, in fpiritum nitri mutari.
Sed lpiritus lalis volatilis per retortam tubulatam
injedlione fuccefliva carbonum candentium deftilla-
tus, non eft tabs : neque ille, qui ex iale commu-
ni pulvere carbonum (vel fuligine) atque fabulo
(vel alumine ufto) mixtis, ignitis, tandem per ad-
ditum oleum vitrioli deftillatur. Stahlius vult, a-
cidum falis purum lola folutione ferri in acidum
nitri verum mutari : fed repetitum experimentum
forte non femper fuccedit. Obtinetur quidem fpi-
ritus cum vaporibus rubris, fed hi non femper ni-
tri praefentiam arguunt : aliter plurimas aqua: gra-
datoriaj ex ferro, auro, zinco, partim etiam cupro,
paratae, omniaque menftrua, mercurium rubro co-
lore fablirnantia prascipitantia hue pertinerent :

[ 369 ]

qualis, exempli gratia, ex folutione ferri in fpiritu falls
fumante (ex fale ammoniaco et oleo vitrioli fadto)
cum o&uplo butyri antimonii martialis deftillatur: vel
etiam ft folutiones metallorum rubrorum cum addito
fale ammoniaco fecreto deftillantur. Licet enim fpi-
ritus nitri coficentratus futnis rubris ut plurimum vi-
deatur, tamen hoc ita proprium ei non eft ut abeftfe
non poftit. Nam, ft talis fpiritus abftrahatur mode-
ration igne, vel a nitro crudo, vel ab arfenico,' vel
mercurio, vel alio quocunque metallo, praefertim al-
bo ; tindturam banc fuam rubram, licet volatiliftimam
fui partem, in abftradto corpore relinquit, et fubviri-
dis, licet debilior, tamen fincerus fpiritus nitri tranfit.
Aurum fugax, quod hac ratione abftradtus in argento
vel alio metallo relinquit, naturam metallicam horum
fumorum, bene demonftrat. Neque chemici aliud
quidpiam in via humida quaerunt, quam ut hanc tinc-
turam rubram ex metallis imperfedtioribus ope men-
ftruorum extrahant, et in aurum figant.

Propius ad verum accedunt, qui acidum falis cum
vegetabili combinant. Nullibi enim nitrum genera-
tor, ubi non iniimul fal commune occurrat. Sic fo-
lutiones vitrioli cyprini et falis ammoniaci ftxi, con-
fufa?, a precipitato filtrate, infpiftatae ad ftccitatem,
tunc cum aceto concentrato folutae, iterum infpiftatae,
tandem deftillatae, dant fpiritum fumantem omni fere
nota, nitrofum ; fimile quid obtinetur, ft fcoriae re-
guli martialis chalybeati, fortiter reverberate, in aceto
deftillato fepius alternatim folvantur et infpiftbntur,
tandem cum fale ammoniaco fixo et vitriolo calcinato
deftillentur.

Facile vero videtur, non fumos rubros, non figu-
ram prifmaticam, non detonationem cum inflamma-
bilibus, non folutiones metallorum fpecificas unum-

quodque

[ 37° ]

quodque folum, certa nitri figna pra?bere, fed plura
concurrere debere, ut de vero nitro produdto dubium
non relinquatur.

LI I. An FJfay towards folving a Problem in
the Doclrine of Chances. By the late Rev.
Mr. Bayes, F. R. S. communicated by Mr.
Price, in a Letter to John Canton, A. M.

F. R. S.

\

Dear Sir,

Read Dec. 23, x- Now fend you an effay which I have
1763 JL f°un^ among the papers of our de-
ceafed friend Mr. Bayes, and which, in my opinion,
has great merit, and well deferves to be preierved.
Experimental philofophy, you will find, is nearly in-
terefled in the fubjedt of it; and on this account there
feems to be particular reafon for thinking that a com-
munication of it to the Royal Society cannot be im-
proper.

He had, you know, the honour of being a mem-
ber of that illuftrious Society, and was much efteem-
ed by many in it as a very able mathematician. In an
introduction which he has writ to this Effay, he lays,
that his delign at firft in thinking on the fubject of it
was, to find out a method by which we might judge
concerning the probability that an event has to hap-
pen, in given circumftances, upon fuppofition that we

know nothing concerning it but that, under the lame

ci rcutn-

[ 371 ]

circumftances, it has happened a certain number of
times, and failed a certain other number of times.
He adds, that he foon perceived that it would not be
very difficult to do this, provided fome rule could be
found according to which we ought to eftimate the
chance that the probability for the happening of an
event perfectly unknown, fhould lie between any two
named degrees of probability, antecedently to any ex-
periments made about it ; and that it appeared to him
that the rule muff be to fuppofe the chance the fame
that it fhould lie between any two equidifferent.de-
grees ; which, if it were allowed, all the reft might
be eafily calculated in the common method of pro-
ceeding in the dodtrine of chances. Accordingly, I
find among his papers a very ingenious folution of this
problem in this way. But he afterwards confidered,
that the populate on which he had argued might not
perhaps be looked upon by all as reafonable j and
therefore he chofe to lay down in another form the
propofition in which he thought the folution of the
problem is contained, and in a Jcholiwn to fubjoin the
reafons why he thought fo, rather than to take into
his mathematical reafoning any thing that might ad-
mit difpute. This, you will obferve, is the method
which he has purfued in this effay.

Every judicious perfon will be fenfible that the
problem now mentioned is by no means merely a
curious {peculation in the dodtrine of chances, but ne-
ceffary to be folved in order to a fure foundation foi all
our reafonings concerning paft fadts, and what is likely
to be hereafter. Common fenfe is indeed lufficient
to fhew us that, from the oblervation of what has in
former inftances been the confequence of a certain
c ‘ caufe

[ 372 ]

caufe or a&icn, one may make a judgment what Is
likely to be the confequence of it another time, and
that the larger number of experiments we have to
lupport a conclufion, fo much the more reafon we
have to take it for granted. But it is certain that we
cannot determine, . at lead not to any nicety, in what
degree repeated experiments confirm a conclufion,
without the particular difeuffion of the beforementi-
oned problem ; which, therefore, is neceflary to be con-
lidered by any one who would give a clear account ot
the ftrength of analogical or indaSUve reafoning ; con-
cerning, which at prefent, we feem to know little more
than that it does fometirrtes in find convince us, and
at other times not ; and that, as it is the means ot
cquainting us with many truths, of which otherwife
we muft have been ignorant ; fo it is, in all proba-
bility, the fource of many errors, which perhaps
might in fome meafure be avoided, if the force that
this fort of reafoning ought to have with us were more
diftindtly and clearly underftood.

Thefe obfervations prove that the problem enquired
after in this etfay is no lefs important than it is curi-
ous. It may be fafely added, I fancy, that it is alfo
a problem that has never before been folved. Mr.
De Moivre, indeed, the great improver of this part
of mathematics, has in his Laws of chance *, after Ber-
noulli, and to a greater degree of exadtnefs, given
rules to find the probability there is, that if a very
great number of trials be made concerning any event,

* See Mr. De Moivre’s Doftrinc of Chances , p. 243, &c. He
has omitted the demonftrations of his rules, but thefe have been
fince fupplied by Mr. Simpfon at the conclufion of his treatife
on The Nature and Laws of Chance .

the

[ 373 ]

the proportion of the number of times it will hap-
pen, to the number of times it will fail in thofe tri-
als, fhould differ lefs than by fmall aligned limits
from the proportion of the probability of its happen-
ing to the probability of its failing in one fingle trial.
But I know of no perfon who has fhewn how to de-
duce the folution of the converfe problem to this ;
namely, “ the number of times an unknown event
“ has happened and failed being given, to find the
“ chance that the probability of its happening fhould
« lie fomewhere between any two named degrees of
« probability.” What Mr. De Moivre has done
therefore cannot be thought fufficient to make the
confideration of this point unneceffary : efpecially, as
the rules he has given are not pretended to be rigo-
roufly exadt, except on fuppofition that the number
of trials made are infinite ; from whence it is not ob-
vious how large the number of trials muff be in or-
der to make them exadt enough to be depended on
in pradtice.

Mr. De Moivre calls the problem he has thus folv-
ed, the hardeft that can be propofed on the fubjedt
of chance. His folution he has applied to a very
important purpofe, and thereby fhewn that thofe
a remuch miftaken who have infinuated that the Doc-
trine of Chances in mathematics is of trivial confe-
quence, and cannot have a place in any ferious enqui-
ry *. The purpofe I mean is, to fhew what reafon
we have for believing that there are in the conftitution
of things fixt laws according to which events happen,
and that, therefore, the frame of the world muft be

* See his Doctrine of Chances, p. 252, &c.

Vol. LIII. Ccc

the

[ 374 ]

the effedt of the wifdom and power of an intelligent
caufe; and thus to confirm the argument taken from
final caufes for the exigence of the Deity. It will be
eafy to fee that the converfe problem folved in this
efiay is more diredtly applicable to this purpofe ; for
it fhews us, with diftindtnefs and precifion, in every
cafe of any particular order or recurrency of events,
what reafon there is to think that fuch recurrency or
order is derived from liable caufes or regulations inna-
ture, and not from any of the irregularities of chance.

The two laft rules in this efiay are given without
the deductions of them. I have chofen to do this
becaufe thefe deductions, taking up a good deal of
room, would fwell the efiay too much ; and alfo be-
caufe thefe rules, though of confiderable ufe, do not
anfwer the purpofe for which they are given as per-
fectly as could be wifhed. They are however
ready to be produced, if a communication of them
Ihould be thought proper. I have in fome places
writ fhort notes, and to the whole I have added an
application of the rules in the efiay to fome particu-
lar cafes, in order to convey a clearer idea of the na-
ture of the problem, and to fhew how far the folu-
tion of it has been carried.

1 am fenfible that your time is fo much taken up
that I cannot reafonably expect that you fhould mi-
nutely examine every part of what I now fend you.
Some of the calculations, particularly in the Appen-
dix, no one can make without a good deal of labour.

I have taken fo much care about them, that I believe
there can be no material error in any of them ; but
fiiould there be any fuch errors, I am the only per-
fon who ought to be confidered as anfwerable for
them.

Mr.

C 375 3

Mr. Bayes has thought fit to begin his work with
a brief demonftration of the general laws of chance.
His reafon for doing this, as he fays in his introduc-
tion, was not merely that his reader might not have
the trouble of fearching elfewhere for the principles
on which he has argued, but becaufe he did not know
whither to refer him for a clear demonflration or
them. He has alfo made an apology for the peculiar
definition he has given of the word chance or proba-
bility. His defign herein was to cut off all difpute
about the meaning of the word, which in common
language is ufed in different fenfes by perfons of dif-
ferent opinions, and according as it is applied to pajl
or future faCts. But whatever different fenfes it may
have, all (he obferves) will allow that an expectation
depending on the truth of any pajl faCt, or the hap-
pening of any future event, ought to be eflimated fo
much the more valuable as the fa Ct is more likely to
be true, or the event more likely to happen. Inflead
therefore, of the proper fenfe of the word probabi-
lity,, he has given that which all will allow to be its
proper meafure in every cafe where the word is ufed.
But it is time to conclude this letter. Experimental
philofophy is indebted to you for feveral difcoveries
and improvements ; and, therefore, I cannot help
thinking that there is a peculiar propriety in direct-
ing to you the following effay and appendix. That
your enquiries may be rewarded with many further
fucceffes, and that you may enjoy every every valuable
bleffing, is the fincere wifh of, Sir,

your very humble fervant,

Richard Price.

N ewington- G reen ,
Nov. xo, 1763.

C C c 2

SEC-

[ 376 ]

PROBLEM.

Given the number of times in which an unknown
event has happened and failed : Required the chance
that the probability of its happening in a fingle trial
lies fomewhere between any two degrees of pro-
bability that can be named.

SECTION I.

F) EFINITION i. Several events are in-
confident) when if one of them happens, none
of the reft can.

2. Two events are contrary when one, or other of
them muft ; and both together cannot happen.

3. An event is faid to jail , when it cannot hap-
pen i or, which comes to the fame thing, when its con-
trary has happened.

4. An event is faid to be determined when it has
either happened or failed.

5. The probability oj any event is the ratio between
the value at which an expe&ation depending on the
happening of the event ought to be computed, and
the value of the thing expected upon it’s happening.

6. By chance I mean the fame as probability.

7. Events are independent when the happening of
any one of them does neither increafe nor abate the
probability of the reft.

When; federal events are inconfiftent the probabili-
ty of the happening of one or other of them is the
fum of the probabilities of each of them.

Suppofe

[ 377 ]

Suppofe there be three fuch events, and whichever
of them happens I am to receive N, and that the pro-
bability of the i ft, 2d, and 3d are refpeCtively ^
1, 1. Then (by the definition of probability) the va-
lue of my expectation from the ift will be a , from
the 2d b , and from the 3d c. Wherefore the value
of my expectations from all three will b e a-\~ b c.
But the fum of my expectations from all three is in
this cafe an expectation of receiving N upon the hap-
pening of one or other of them. Wherefore (by de-
finition 3) the probability of one or other of them is

or A 4- A _U -L. The fum of the proba-

N N 1 N 1 N A

bilities of each of them.

Corollary. If it be certain that one or other
of the three events muft happen, then a -j- b -f- c
— N. For in this cafe all the expectations to-
gether amounting to a certain expectation of re-
ceiving N, their values together muft be equal
to N. And from hence it is plain that the proba-
bility of an event added to the probability of its fai-
lure (or of its contrary) is the ratio of equality. For
thefe are two inconftftent events, one of which ne-
ceftarily happens. Wherefore if the probability of

P N — P

an event is — that of it's failure will be xt-»

P R O P. 2.

If a perfon has an expectation depending on the
happening of an event, the probability of tire event
is to the probability of its failure as his lofs if it fails to
his gain if it happens.

Suppofe a perfon has an expectation oi receiving
N, depending on an event the probability oi which

is

[ 378 ]

p

i* N • Then (by definition 5) the value of his ex-
pedition is P, and therefore if the event fail, he lofes
that which in value is P ; and if it happens he re-
ceives N, hut his expedition ceafes. His gain there-
fore is N — P. Likewife fince the probability of the
P

event is — , that of its failure (by corollary prop. 1)

. N p ^ p XT p

1S ~N~' ^Llt N *S t0 ”n~ aS ^ *S t0 ^ u e*
the probability of the event is to the probability of it’s
failure, as his lofs if it fails to his gain if it happens.

PROP. 3.

The probability that two fubfequent events will
both happen is a ratio compounded of the probabi-
lity of the 1 ft, and the probability of the 2d on fup-
pofttion the ift happens.

Suppofe that, if both events happen, I am to receive

p

N, that the probability both will happen is ^ , that

the 1 ft will is — (and confequently that the ift will

N a w

not is — — ) and that the 2d will happen upon fup-

pofttion the 1 ft does is jq-. Then (by definition 5) P

will be the value of my expedation, which will be-
come b if the ift happens. Confequently if the ift
happens, my gain by it is b — P, and if it fails my lofs

is P. Wherefore, by the foregoing propofition, — is to
i. e. a is to N — a as P is to b — P. Where-

fore (componendo inverfe) a is to N as P is to b.
But the ratio of P to N is compounded of the ratio
of P to b , and that of b to N. Wherefore the
c fame

C 379 ]

fame ratio of P to N is compounded of the ratio of
a to N and that of b to N, i. e. the probability that
the two fubfequent events will both happen is com-
pounded of the probability of the ift and the proba-
bility of the 2d on fuppofition the ift happens.
Corollary. Hence if of two fubfequent events the

probability of the ift be and the probability of

P ^

both together be — , then the probability of the 2d

N # p

on fuppofition the 1 ft happens is -.

PROP. 4.

If there be two fubfequent events to be determined
every day, and each day the probability of the 2d is

^ and the probability of both ^ , and I am to re-
ceive N if both the events happen the ift day on
which the 2d does; I fay, according to thefe con-

p

ditions, the probability of my obtaining N is For

if not, let the probability of my obtaining N be ~

and let be to x as N — b to N. Then fince — is the

probability of my obtaining N (by definition 1) x is
the value of my expectation. And again, becaufe ac-
cording to the foregoing conditions the ift day I have
an expectation of obtaining N depending on the hap-
pening of both the events together, the probability of

which is — , the value of this expectation is P. Like-

wife, if this coincident fliould not happen I have an
expectation of being reinflated in my former circum-
ftances, i, e. of receiving that which in value is x de-
pending

[ 3^0 j

pending on the failure of the 2d event the probability
of which (by cor. prop. 1) is ' or -, becaufe y is
to x as N — b to N. Wherefore fince x is the thing

expeCted and - the probability of obtaining it, the

value of this expectation is^y. But thefe two lad; ex-
pectations together are evidently the fame with my
original expectation, the value of which is x, and
therefore P -\-y — at. But y is to x as N — b is to N.

Wherefore x is to P as N is to b, and — (the

. P 1

probability of my obtaining N) is -•

Cor. Suppofe after the expectation given me in the
foregoing propofition, and before it is at all known
whether the ift event has happened or not, I fhould
find that the 2d event has happened ; from hence I
can only infer that the event is determined on which
my expectation depended, and have no reafon to
efteem the value of my expectation either greater or
lefs than it was before. For if I have reafon to think
it lefs, it would be reafonable for me to give fomething
to be reinftated in my former circumftances, and
this over and over again as often as I fhould be in-
formed that the 2d event had happened, which is evi-
dently abfurd. And the like abfurdity plainly follows
if you fay I ought to fet a greater value on my expec-
tation than before, for then it would be reafonable for
me to refufe fomething if offered me upon condition
I would relinquifh it, and be reinftated in my former
circumftances and this likewife over and over again
as often as (nothing being known concerning the ift
event) it fhould appear that the 2d had happened.
Notwithftanding therefore this difcovery that the 2d

event

[ 381 ]

event has happened, my expectation ought to be
efteemed the fame in value as before, i. e. xy
and confequently the probability of my obtaining

N is (by definition 5) ftill ^ or j*. But after this

difcovery the probability of my obtaining N is the pro-
bability that the ift of two fubfequent events has hap-
pened upon thefuppofition that the 2d has, whofe pro-
babilities were as before fpecified. But the probability
that an event has happened is the fame as the proba-
bility I have to guefs right if I guefs it has happened.
Wherefore the following proportion is evident.

P R O P. 5.

If there be two fubfequent events, the probability

of the 2d — and the probability of both together

and it being 1 ft difcovered that the 2d event has hap-
pened, from hence I guefs that the ift event has al-

fo happened, the probability I am in the right is

PROP.

* What is here faid may perhaps be a little illuftrated by con-
fid ering that all that can be loft by the happening of the 2d event
is the chance I fhould have had of being reinftated in my former
circumftances, if the event on which my expe&ation depended had
been determined in the manner expreffed in the propofition. But
this chance is always as much againji me as it is for me. If the
1 ft event happens, it is againji me, and equal to the chance for
the 2d event’s failing. If. the ift event does not happen, it is
for me, and equal alfo to the chance for the 2d event s failing.
The lofs of it, therefore, can be no difadvantage.

t What is proved by Mr. Bayes in this and the preceding pro-
pofition is the fame with the anfwer to the following queftion.
Vvrhat is the probability that a certain event, when it happens, will
Vol. LIII. Ddd be

[ 382 ]

PROP. 6.

The probability that feveral independent events
lhall all happen is a ratio compounded of the proba-
bilities of each.

For from the nature of independent events, the
probability that any one happens is not altered by the
happening or failing of any of the reft, and confe-
quently the probability that the 2d event happens on
iuppofttion the ift does is the fame with its original
probability ; but the probability that any two events
happen is a ratio compounded of the probability of the
1 ft event, and the probability of the 2d on fuppofition
the 1 ft happens by prop. 3. Wherefore the probability
that any two independent events both happen is a ra-
tio compounded of the probability of the ift and the
probability of the 2d. And in like manner confidering
the ift and 2d event together as one event ; the proba-
bility that three independent events all happen is a ratio
compounded of the probability that the two ift both
happen and the probability of the 3d. And thus you

be accompanied with another to be determined at the fame time ?
In this cafe, as one of the events is given, nothing can be due
for the expectation of it ; and, confequently, the value of an ex-
pectation depending on the happening of both events muff be the
fame with the value of an expectation depending on the happen-
ing of one of them. In other words ; the probability that, when
one of two events happens, the other will, is the fame with the
probability of this other. Call x then the probability of this

h • P

other, and if - be the probability of the given event, and —

the probability of both, becaufe ~ ^ x x zz ^ zz the pro-

bability mentioned in thefe proportions.

may

[ 383 ]

may proceed if there be ever fo many fuch events j
from whence the proportion is manifeft.

Cor. 1. If there be feveral independent events, the
probability that the 1 ft happens the 2d fails, the 3d
fails and the 4th happens, &c. is a ratio compound-
ed of the probability of the ift, and the probability
of the failure of the 2d, and the probability of the
failure of the 3d, and the probability of the 4th, &c.
For the failure of an event may always be confidered
as the happening of its contrary.

Cor. 2. If there be feveral independent events, and
the probability of each one be a , and that of its fail-
ing be by the probability that the ift happens and the
2d fails, and the 3d fails and the 4th happens, &c.
will be abbdy &c. For, according to the algebraic
way of notation, if a denote any ratio and b another,
abba denotes the ratio compounded of the ratios
at by by a. This corollary therefore is only a particular
cafe of the foregoing.

Definition. If in confequence of certain data
there arifes a probability that a certain event fhould
happen, its happening or failing, in confequence
of thefe data, I call it’s happening or failing in
the ift trial. And if the fame data be again re-
repeated, the happening or failing of the event in
confequence of them I call its happening or failing
in the 2d trial , and fo on as often as the fame data
are repeated. And hence it is manifeft that the hap-
pening or failing of the fame event in fo many diffe-
trials, is in reality the happening or failing of fo
many diftindt independent events exadtly fimilar to
each other.

Ddd 2

PROP*

[ 384 ]

PROP. 7.

If the probability of an event be a , and that of its
failure be b in each fingle trial, the probability of its
happening p times, and failing y times m p-\-q trials
is E d b* if E be the coefficient of the term in which

occurs d b ’ when the binomial a b\ b^rq is ex-
panded.

For the happening or failing of an event in differ-
ent trials are fo many independent events. Where-
fore (by cor. 2. prop. 6.) the probability that the event
happens the iff trial, fails the 2d and 3d, and hap-
pens the 4th, fails the 5th, &c. (thus happening and
failing till the number of times it happens be p and
the number it fails be q) is abb ab &c. till the
number of as be p and the number of b's be y, that
is; ’tis d b\ In like manner if you confider the event
as happening p times and failing q times in any other
particular order, the probability for it is d b 1 ; but
the number of different orders according to which an
event may happen or fail, fo as in all to happen p
times and fail y, i \\p \ q trials is equal to the num-
ber of permutations that aaaa bbb admit of when
the number of as is p, and the number of b’s is y.
And this number is equal to E, the coefficient of the
term in which occurs ap bq when a -\-b\ pJtq is ex-
panded. The event therefore may happen p times
and fail y in p -j- y trials E different ways and no
more, and its happening and failing thefe feveral dif-
ferent ways are fo many inconfiftent events, the pro-
bability for each of which is ap bq> and therefore by

prop.

[ 385 ]

prop. I. the probability that fome way or other it
happens p times and fails q times in p -|- q trials i
E a* b*.

SECTION II.

is

Populate, i. I Suppofe the fquare table or plane
A B C D to be fo made and levelled, that if either
of the balls o or W be thrown upon it, there fhali
be the fame probability that it relfs upon any one
equal part of the plane as another, and that it mud
necelTarily red fome where upon it.

2. I luppofe that the ball W fhali be id thrown,
and through the point where it reds a line os diall be
drawn parallel to A D, and meeting C D and A B in
s and o and that afterwards the ball O fhali be
thrown p 4. q or n times, and that its reding between
AD and os after a dngle throw be called the hap-
pening of the event M in a dngle trial. Thefe things
fuppofed,

Lem. 1. The proba-Q
bility that the point 0
will fall between any
two points in the line
A B is the ratio of the
didance between the
two points to the whole
line AB.

Let any two points
be named, as f and b
in the line A B, and B
through them parallel
to A D draw fF, b L
meeting CD in F and
L. Then if the rect-
angles CfFb,LA are

com-

[ 3§6 ]

commenfurable to each other, they may each be di-
vided into the fame equal parts, which being done,
and the ball W thrown, the probability it will reft
fomewhere upon any number of thefe equal parts
will be the fum of the probabilities it has to reft upon
each one of them, becaufe its refting upon any differ-
ent parts of the plane AC are fo many inconfiftent
events ; and this fum, becaufe the probability it fhould
reft upon any one equal part as another is the fame, is
the probability it fhould reft upon any one equal part
multiplied by the number of parts. Confequently, the
probability there is that the ball W fhould reft fome-
where upon is the probability it has to reft upon one
equal part multiplied by the number of equal parts in F b;
and the probability it refts fomewhere upon Cy'or LA,
i.e. that it dont reft upon Fb (becaule it muft reft fome-
where upon A C) is the probability it refts upon one
equal part multiplied by the number of equal parts in
C/, LA taken together. Wherefore, the probability
it refts upon F b is to the probability it dont as the
number of equal parts in F b is to the number of
equal parts in Cf LA together, or as F b to CJ]
LA together, or as/£ to B f A b together. Where-
fore the probability it reft upon F b is to the proba-
bility it dont as f b to B f, A b together. And ( coni-
ponendo inverfe ) the probability it refts upon F b is to
the probability it refts upon F b added to the proba-
bility it dont, as fb to AB, or as the ratio of fb to
A B to the ratio of A B to A B. But the probabi-
lity of any event added to the probability of its failure
is the ratio of equality ; wherefore, the probability it
reft upon F b is to the ratio of equality as the ratio of
jb to AB to the ratio of AB to AB, or the ratio
of equality i and therefore the probability it reft upon

[ 3§7 ]

¥b is the ratio of fb to AB. But ex hypothefi ac-
cording as the ball W falls upon F b or not the
point o will lie between f and b or not, and there-
fore the probability the point o will lie between f and
b is the ratio of f b to A B.

Again j if the rectangles Cf F b, LA are not
commenfurable, yet the laft mentioned probability
can be neither greater nor lefs than the ratio of j b to
A B 3 for, if it be lefs, let it be the ratio of fc to AB,
and upon the line fb take the points p and t, fo
that p t fhall be greater than f c, and the three lines
Bp, pt , t A commenfurable (which it is evident may
be always done by dividing A B into equal parts lefs
than half cb , and taking p and t the neareft points
of divilion to /'and c that lie upon fb). Then
becaufe Bp, pt, t A are commenfurable, fo are the
rectangles C p, D t, and that upon pt compleating
the fquare AB. Wherefore, by what has been faid,
the probability that the point o will lie between p and
t is the ratio of p t to A B. But if it lies between p
and t it muft lie between f and b. Wherefore, the
probability it fhould lie between f and b cannot be
lefs than the ratio of pt to A B, and therefore mufl
be greater than the ratio of /r to AB (fince pt is
greater than fc). And after the fame manner you
may prove that the forementioned probability cannot
be greater than the ratio of fb to AB, it mufl there-
fore be the fame.

Lem. 2. The ball W having been thrown, and
the line o s drawn, the probability of the event M
in a fingle trial is the ratio of A o to A B.

For, in the fame manner as in the foregoing lem-
ma, the probability that the ball o being thrown fhall

reft

[ 388 ]

reft fomewhere upon D o or between A D and so is
is the ratio of A o to A B. But the refting of the
ball o between A D and r o after a fingle throw is
the happening of the event M in a fingle trial.
Wherefore the lemma is manifeft.

PROP. 8.

If upon BA you erefl the figure Bg hi k m A
whofe property is this, that (the bale B A being di-
vided into any two parts, as Ab, and bb and at the
point of divifion b a perpendicular being erected and
terminated by the figure in m ; and y, x, r repre-
fenting refpedtively the ratio of bm> A b, and bb to
AB, and E being the the coefficient of the term in
which occurs a p bq when the binomial a-\-b\J is
expanded) y = E xp rq. I fay that before the ball W
is thrown, the probability the point o lhould fall be-
tween j and by any two points named in the line
A B, and withall that the event M fliould happen p
times and fail q in p q trials, is the ratio of
f g hi km by the part of the figure bghi k m A in-
tercepted between the perpendiculars J g, bm raifed
upon the line AB, to C A the fquare upon AB.

DEMONSTRATION.

For if not; ift let it be the ratio of D a figure
greater than fghikmb to C A, and through the
points e,d>c draw perpendiculars to jb meeting the
curve A tn i g B in hy i, k ; the point d being io
placed that di fhall be the longeft of the perpendi-
r culars

[ 3§9 ]

ctilars terminated by the line Jb, and the curve
A in i g B \ and the points e} d, c being fo many and
fo placed that the redangles, b k, c /, £> /, fh taken
together fhall differ lefs from Jghikm'b than D
does ; all which may be eafily done by the help of the
equation of the curve, and the difference between D
and the figure fghikmb given. Then fince di is
the longed: of the perpendicular ordinates that infid:
upon j b, the red; will gradually decreafe as they are
farther and farther from it on each fide, as appears
from the conftrudion of the figure, and confequently
eh Is greater than gf or any other ordinate that in-
fills upon e f

Now if Ao were equal to Ae , then by lem. 2.
the probability of the event M in a fingle trial would
be tne ratio of A e to A B, and confequently by cor.
Prop. 1. the probability of it’s failure would be the
ratio of Be to A B. Wherefore, if x and r be the
two forementioned ratios refpedively, by Prop. 7. the
probability of the event M happening p times and
failing q in p -j- q trials would be rq . But a:
and r being refpedively the ratios of Ae to A B
and Be to AB, if y is the ratio of eh to A B, then,
by conftrudion of the figure A i B, y — Ex* rq\
Wherefore, if A 0 were equal to Ar the probability
of the event M happening p times and failing q in
p \-q trials would be y , or the ratio of eh to A B.
And if A 0 were equal to A f or were any mean be-
tween Ae and Af, the lad mentioned probability
for the fame reafons would be the ratio of fg or fome
other of the ordinates inditing upon ef to AB. But
e £ is the greated: of all the ordinates that infid: upon
ef. Wherefore, upon fuppofition the point ffould lie

Vol. LIII. Eee

[ 39° ]

any where between f and f, the probability that the
event M happens p times and fails q in p-fq tri-
als can’t be greater than the ratio of eh to A B.
There then being thefe two fubfequent events, the
iff that the point o will lie between e and f the
2d that the event M will happen p times and fail q
in p q trials, and the probability of the iff (by
lemma i ft ) is the ratio cf ef to AB, and upon fup-
pofition the iff happens, by what has been now
proved, the probability of the 2d cannot be greater
than the ratio of eh to A B, it evidently follows (from
Prop. 3.) that the probability both together will hap-
pen cannot be greater than the ratio compounded of
that of ef to A B and that of eh to A B, which
compound ratio is the ratio of fh to C A. Where-
fore, the probability that the point 0 will lie between
f and <?, and the event M happen p times and fail
y, is not greater than the ratio of J h to C A. And
in like, manner the probability the point 0 will lie be-
tween e and d, and the event M happen and fail as
before, cannot be greater than the ratio of e i to C A.
And again, the probability the point 0 will lie between
d and c, and the event M happen and fail as before,
cannot be greater than the ratio of c i to C A. And
laftly, the probability that the point 0 will lie between
c * nd b, and the event M happen and fail as before,
cannot be greater than the ratio of b k to C A. Add
now all thefe feveral probabilities together, and their
fum (by Prop. 1. ) will be the probability that the point
will lie lomewhere between f and b, and the event
M happen p times and fail q in p -j- q trials. Add
likewise the correfpondent ratios together, and their
fum will be the ratio of the fum of the antecedents

to

>

[ 39i ]

to their common confequent, i. e. the ratio of fb%
e /, c i, bk together to CA; which ratio is lefs
than that of D to C A, becaufe D is greater
than fb, ei, ci, bk together. And therefore, the
probability that the point o will lie between f and
and withal that the event M will happen p times
and fail q in p -p q trials, is lefs than the ratio of
D to CA; but it was fuppofed the fame which is
abfurd. And in like manner, by infcribing redangles
within the figure, as eg , dh , dk , cm , you may prove
that the laft mentioned probability is greater than the
ratio of any figure lefs than fg h ik m b to CA.

Wherefore, that probability mud be the ratio of
fg h i km b to C A.

Cor. Before the ball W is thrown the probability
that the point o will lie fomewhere between A and B,
or fomewhere upon the line A B, and withal that the
event M will happen p times, and fail q in p -j- q
trials is the ratio of the whole figure A z B to C A.
But it is certain that the point o will lie fomewhere
upon A B. Wherefore, before the ball W is thrown
the probability the event M will happen p times and
fail q in p q trials is the ratio of At B to C A.

PROP. 9.

If before any thing is difcovered concerning the
place of the point#, it fhould appear that the event
M had happened p times and failed q in p -f- q trials,
and from hence I guefs that the point 0 lies bet ween
any two points in the line A B, as jfand b , and con-
lequently that the probability of the event M in a lin-
gle trial was fomewhere between the ratio of A b to
A B and that of A f to A B : the probability I am in

E c e 2 the

[ 392 ]

the right is the ratio of that part of the figure A / B
de fcri bed as before which is intercepted between
perpendiculars erected upon A B at the points f
and b, to the whole figure A i B.

For, there being thefe two fubfequent events,
the firfi that the point o will lie between f and b ;
the fecond that the event M fhould happen p times
and fail q in p q trials ; and (by cor. prop. 8.) the
original probability of the fecond is the ratio of
A i B to C A, and (by prop. 8.) the probability of
both is the ratio of j'g h im b to C A; wherefore
(by prop. it being firfi difeovered that the fecond
has happened, and from hence I guefs that the
firff has happened alfo, the probability I am in
the right is the ratio of fghimb to A/B, the
point which was to be proved.

Cor. The fame things fuppofed, if I guefs that
the probability of the event M lies fomewhere be-
tween o and the ratio of A b to A B, my chance
to be in the right is the ratio of A b m to A / B.

Scholium.

From the preceding propofition it is plain, that
in the cafe of fuch an event as I there call M, from
the number of times it happens and fails in a cer-
tain number of trials, without knowing any thing
more concerning it, one may give a guefs where-
abouts it’s probability is, and, by the ufual methods
computing the magnitudes of the areas there menti-
oned, fee the chance that the guefs is right. And that
the fame rule is the proper one to be ufed in the cafe
of an event concerning the probability of which

we

[ 393 ]

we abfolutely know nothing antecedently to any
trials made concerning it, feems to appear from the
following confideration ; viz. that concerning fuch
an event I have no reafon to think that, in a certain
number of trials, it fhould rather happen any one
poffible number of times than another. For, on
this account, I may juffly reafon concerning it as if
its probability had been at firft unfixed, and then
determined in fuch a manner as to give me no reafon
to think that, in a certain number of trials, it fhould
rather happen any one pofifible number of times
than another. But this is exactly the cafe of the
event M- For before the ball W is thrown, which
determines it’s probability in a Angle trial, (by cor.
prop. 8.) the probability it has to happen p times
and fail q in p -j- q or n trials is the ratio of A i B to
C A, which ratio is the fame when p -j- q or n is
given, whatever number p is ; as will appear by
computing the magnitude of A i B by the method
* of fluxions. And confequently before the place
of the point o is difcovered or the number of times
the event M has happened in n trials, I can have no
reafon to think it fhould rather happen one pof-
fible number of times than another.

In what follows therefore I (hall take for granted
that the rule given concerning the event M in
prop. 9. is alfo the rule to be ufed in relation to any
event concerning the probability of which nothing

* It will be proved prefently in art. 4. by computing in the
method here mentioned that A / B contracted in the ratio of E

to 1 is to C A as 1 to n + 1 X E : from whence it plainly follows
that, antecedently to this contraction, A i B muft be to C A in
the ratio of 1 to n + 1, which is a conftant ratio when n is given,
whatever p is.

at

[ 39+ ]

at all 19 known antecedently to any trials made or ob-
served concerning it. And fuch an event I fhall call
an unknown event.

Cor. Hence, by fuppofing the ordinates in the fi-
gure A i B to be contracted in the ratio of E to one,
which makes no alteration in the proportion of the
parts of the figure intercepted between them, and
applying what is faid of the event M to an unknown
event, we have the following proportion, which gives
the rules for finding the probability of an event from
the number of times it actually happens and fails.

PROP. io.

If a figure be deferibed upon any bafe A H (Vid.
Fig.) having for it’s equation y — xpr?-, where y,
x , r are refpedtively the ratios of an ordinate of the
figure inlifting on the bafe at right angles, of the
fegment of the bafe intercepted between the ordinate
and A the beginning of the bafe, and of the other
fegment of the bafe lying between the ordinate and
the point H, to the bafe as their common confequent.
I fay then that if an unknown event has happened
p times and failed q in p -|- q trials, and in the bafe
AH taking any two points as f and t you eredl the
ordinates f c, t F at right angles with it, the chance
that the probability of the event lies fomewhere be-
tween the ratio of A f to AH and that of A t to
AH, is the ratio of t¥ C f that part of the before-
deferibed figure which is intercepted between the two
ordinates, to ACFH the whole figure infilling on
the bafe A H.

This is evident from prop. 9. and the remarks made
in the foregoing fcholium and corollary.

c Now

o

.. . , [ 395 ]

Now, in order to
reduce the forego-
ing rule to practice,
we muff find the
value of the area
of the figure de-
fcribed and the fe-
veral parts of it fe-
parated, by ordi-
nates perpendicu-
lar to its bafe. For

which purpofe, fuppofe A H — i and H O the
fquare upon AH likewifecrr i, and Cf will be— yt
and Af~ x , and Hfy=z r, becaufe y, x and r denote
the ratios of C f A f and Ilf refpedively to A H.
And by the equation of the curve y — xp rq and (be-
caufe Aff-J H — AH) r x — i. Wherefore

y — xp x i-x\q ~ xp — qx -\-qX q— 1 X x — q
X q-f X g—2 x x + Sec. Now the abfcifTe being

* 3 P ' /.q-i

x and the ordinate x the correfpondent area is x

(by prop. io. caf. i. Quadrat. Newt.) * and the ordi-
P+-* # /> + 2

nate being qx the area is qx ; and in likeman-

~P + 2

* *HS very evident here, without having recourfe to Sir Ifaac
Newton, that the fluxion of the area AC f being yx—xfx —
P + i p+2

1 x * + ? * x x &c. the fluent or area itfelf is x ^>^~I

x*

x X? + 3 &C.

p+

P + 2

P + 3

ner

[ 396 1

ner of the reft. Wherefore, the abfcifte being x and

P p + 1

the ordinate v or x — qx -|- &c. the correfpondent

P + i p + 2 P+3

area is a; -qxx ~V q X q- i X*

/»+ i /> + 2 2 /> + 3 2

^ + 4

y-2 x a? 4“ &c* Wherefore, if x ~ A f — A f,

3 P+ 4 AH

\

p+ i

and y — C f = C /, then A Cjf = A C/ — a:

AH H O />-fi

/>+ 3

— y X at 4" q^q- 1 X a: — &c.

/> + 2 . 2 ^+3

From which equation, if q be a fmall number, it is
eafy to find the value of the ratio of A C f to H O.
and in like manner as that was found out, it will ap-

q + i

pear that the ratio of HC f to HO is r — p x

q+ 1

q + i. q + 3 q+ 4

r — pxp-ixp-ixr_ &c.

q+ 2 2 q+3 2 3 q+ \

which feries will confift of few terms and therefore
is to be ufed when p is fmall.

2. The fame things fuppofed as before, the ratio of

p+i p + 2

A C/ to H O is a rq q X x rq -f- q X

p+l~ p+l p+ 2 P+ I

P+3 A+4

y-i X x 2 -f f X ?-i X q-2 X * rq 4~

Z + 2’ ~ /> + 3 /)+! p + 2 p + 3 /> + 4

&c.

[ 397 3

» + t

&c. Jp x X g X y-i x &c. XI where n =

7/ -f I /> + I + 2 T

/>+ I

p -j~ y. For this feries is the Tame with # — q x

2 />+ I

* &c. fetdown in Art. ift. as the value of the

P + 2

ratio of A Cy to HO; as will eafily be feen by put-
ting in the former inftead of r its value i-x, and
expanding the terms and ordering them according to
the powers of x. Or, more readily, by comparing the
fluxions of the two feries, and in the former inltead
of f fubftituting - x *.

p q p -f- r I

* The fluxion of the firft feries is at r- x + q x i -P Xr-f

P + 'q- 1

/> + i

lq~ I P~b^q—z P+^-q—2.

qx r x -f q x q— I X x r r + q X q- 1 X x r* .

" — X

p 4- 1

H”1 p+-:

P'h1 p+z

p -f- 3 .

+ g X g-i x q-q 3 X .v 7-^ “3 Sec. or, fubftituting - x for r ,

P+ 1 P+7- />-H

p q p+i p + i

x r x — q x 1x + qx 1 x — q X q — I X

P + 1 /’ft*1 /’ft*1

P+2q— 2 P+2i 7-2

* ^ * + q x q~ 1 x .v * &c. which, as all the

/> + 2 /> + ! 1 /> + 2
terms after the firft deftroy one another, is equal to x* r? x —
X? X I — *1 q x = x? x X I — qx+qXq — I xz &C. — X? x —

P+i p-bz 2

qx x + q x q- 1 .v x See. — the fluxion of the latter feries
p-bi _T~ p + 2

or of x — q x x See. The two feries therefore are

p-b 1 p + 2

the fame.

Vol. LIII.

3. In

Fff

[ 398 ]

3- In like manner, the ratio of HC/ to HO is

? + 1 * ? + 2^ q + 3

£ r xr 1 +_/ x p-i X r 4-

?+I ?+I £+2 ^+1 £ + 2 q + 3

occ.

4* If E be the coefficient of that term of the bi-
nomical a + b\P + 9 expanded in which occurs aP b
the ratio of the whole figure A C F H to HO is

TTTi x £■> n being —p + For, when A/— AH

^ — 1 5 r — o. Wherefore, all the terms of the fe-
ries fet down in Art. 2. as expreffing the ratio of
A C f to H O will vanifh except the laft, and that

becomes ,7; X ^ x ^ X &c. x But E

being the coefficient of that term in the binomial

a -\- b\ expanded in which occurs ap bq is equal to

X ~y x &c. x 1. And, becaufe Af is fup-

pofed to become — AH, AC/=ACH. From
whence this article is plain.

5. The ratio of AC f to the whole figure ACFH

is (by Art. 1. and 4.) « 4. 1 x E x /+X — q X
p+2 P+Z , ?+'

* T^Xf-i X a: &c. and if, as x exprefies

P + 2 . ~ 7+3~

the ratio of Af to AH, X ffiould exprefs the ratio
of At to AH; the ratio of AF? to ACFH

- p + I p ~h 2

would be n 1 X E x X — qX

P+Z p+ l p+2 2

X X — &c. and confequently the ratio of tFCf

P+'i . ,/

to ACFH is » 4 1 X E x into the difference

between

[ 399 ]

between the two feries. Compare this with prop. 10.
and we fhall have the following practical rule.

RULE i.

If nothing is known concerning an event but that
it has happened p times and failed q in p-\-q or n trials,
and from hence I guefs that the probability of its
happening in a fingie trial lies fome where between
any two degrees of probability as X and x, the
chance I am in the right in my guefs is H-f i

X E x'4 into the difference between the feries X^ + I

P+2 p+3

— q x + q x g- 1 x x

P + 2

p+i
feries x

p+i

&c. and the

2 p+$

p+2 p+3

qx + qxq-+_xx_ ~ &c. E

P+I p + 2 2 p + 3

being the coefficient of ap bq when a\-\-b\n is expanded.

This is the proper rule to be ufed when q is a fmall
number ; but if q is large and p fmall, change every
where in the feries here fet down p into q and ^q into p
and ^ into r or and X into R — i-Xj which
will not make any alteration in the difference between
the two feriefes.

Thus far Mr. Bayes’s effay.

With refpett to the rule here given, it is further
to be obferved, that when both p and q are very large
numbers, it will not be poffible to apply it to practice
on account of the multitude of terms which the fe-
riefes in it will contain. Mr. Bayes, therefore, by

F f f 2 an

[ 4-00 ]

an inveftigation which it would be too tedious to give
here, has deduced from this rule another, which is as
follows.

RULE 2.

If nothing is known concerning an event but that
it has happened p times and failed q in p -j- q or n
trials, and from hence I guefs that the probability of

its happening in a fingle trial lies between - +2 and

- — % i if —— a — b — f, E the coefficient
n p q n n

of the term in which occurs af b* when a -|- /£)"■- is
expanded, and ^ X x E J bq x

n V n

np z 3

by the feries mz —

3 * 1 * * * 2«

, m7 z7 . n-2 n-A. n- 6 m9 z9

+ TTX-X — x —

. n—2 ^ nf z5 * »— 2 X n— 4

1 o» 5

2 n X yi

See.

my chance to be in the right is greater than

2 v

i + 2 E af b? -|- 2 E af b? * and lefs than

2JB n

1-2 E apbi — 2 E af b*. And i i p q my chance

n

is 2 £ exa&ly.

* In Mr. Bayes’s manufeript this chance is made to be gieater

2X 2S

than — ; — — 7-— and lefs than — — jr— . The third term

1 + 2 aP bl 1 — 2 h af b*

in the two divifors, as I have given them, being omitted. But

this being evidently owing to a fmall overfight in the dedu&ioN

of this rule, which I have reafon to think Mr. Bayes had himfelf

difeovered, I have ventured to correct his copy, and to give the

rule as 1 am fatisfied it ought to be given,

In

[ 40i ]

In order to render this rule fit for ufe in all cafes
it is only neceflary to know how to find within fuffi-
cient nearnefs the value of E a? b* and alfo of the

feries mz — &c*. With refpedt to the former

Mr. Bayes has proved that, fuppofing K to fignify the
ratio of the quadrantal arc to it’s radius, E a? bi will

be equal to

v/ n

2 a/K/>

by the ratio whofe hyperbo-

lic logarithm is — v - — -

° 12 n p

I

rr

+ 7

260

n

1

<1

I

1680

I I 1

— X — — 77
360 n p

~i ~

^ n1 p1

~T + 7700 X -4 — ~ — 4" &c* where the nume-

q I loo n pJ q y

ral coefficients may be found in the following man-
ner. Call them A, B, C, D, E, &c. Then A —

2. 2. 3
10 B + A

3 4* ^ 2. 4. 5

2. 6. 7

.D —

35 C +21 B + A £ I

5 2. 8. 9

1 26 C + 84 D 4- 36 B 4- A

7

F

2. 10 .11

2. 12. 13

* A very few terms of this feries will generally give the hyper-
bolic logarithm to a fufficient degree of exadtnefs. A fimilar fe-
ries has been given by Mr. 2De Moivre, Mr. Simpfon and other
eminent mathematicians in an exprefiion for the fum of the lo-
garithms of the numbers 1, 2, 3, 4, 5 to a-, which fum they

have afferted to be equal to l log. c + x + i x log. a- — x +
ttx — tFo*3 + t-zVct#5 &c. c denoting the circumference of a
circle whofe radius is unity. But Mr. Bayes, in a preceding pa-
per in this volume, has demonftrated that, though this exprefficn
will very nearly approach to the value of this fum when only a
proper number of the firft terms is taken, the whole feries' cannot
exprefs any quantity at all, becaufe, let .*• be what it will, there
will be always a part of the feries where it will begin to diverge.
This obfervation, though it does not much affect the ufe of this
‘ries, feems well worth the noticeof mathematicians. 462

[ 402 ]

l!LP„±«0C J^6j*+isB + A &c where the co -

efficients of B, C, D, E, F, &c. in the values of
O, E, F, Sec. are the 2, 3, 4, &c. higheft coeffici-
ents in a -(- b\7 , a -|- b\\ a 4- ^1", Sec. expanded;
affixing in every particular value the leaft of thefe
coefficents to B, the next in magnitude to the fur-
theft letter from B, the next to C, the next to the
furtheft but one, the next to D, the next to the fur-
theft but two, and fo on *.

With refpeCt to the value of the feries ^2 —

Sec. he has obferved that it may be

tn 3 z 3 . «— 2

3 ‘ ~

X

m z

calculated direCtly when mz is lefs than 1, or even
not greater than \/y: but when mz is much larger
it becomes impracticable to do this ; in which cafe he
fhews a way of eafily finding two values of it very
nearly equal between which it’s true value muft lie.

The theorem he gives for this purpofe is as fol-
lows.

Let K, as before, ftand for the ratio of the qua-
drantal arc to its radius, and H for the ratio whofe

hyperbolic logarithm is - — - — - — 4- ^—r~i — ■
yr & 2 n 0O0 »3 1 1 loon5

2 — 1
1680 n1

See. Then the feries m z

mi is

Sec, will be

2

greater or lefs than the feries — r— x

0 »-j-i V2 ” + 2

n

1 — 2 tn

? + 1

2 mz

+

2 'i

2 m z

n

? + 2

n+ 2

n + 4 X 4 mz z3

X

+:

* Thi9 method of finding thefe coefficients I have deduced
from the demonftration of the third lemma at the end of Mr.
Simpfon’s Treatife on the Nature and Laws of Chance.

a 3*

[ 403 ]

?+3

I 2.mx z 1 % -j- 4

n

3*5

n

n + 2 » + 4x* + 6x8^z5 « + 2 a«+4x«+ 6x^+8xi6zW

- &c. continued to any number of terms, accord-

ing as the laft term has a poiitive or a negative fign
before it. °

From fubftituting thefe values of E a f b i and m z

z3 n — 2 ms z5

— ^ r X — j- &c. in the 2d rule arifes a

3d rule, which is the rule to be ufed when mz is of
fome confiderable magnitude.

RULE 3.

If nothing is known of an event but that it has
happened p times and failed q in p q or n trials,
and from hence I judge that the probability of it’s

happening in a fingle trial lies between - z and ■

p

“ — % my chance to be right is greater than
V K /> y X & v o TT Vrw »4- I w I

multiplied by the 3 terms 2 H — x

Vk

Vk »-J- 2 :

m\ K, b

and H ftand for the quantities already explained.

An

[ 404 ]

An APPENDIX.

CONTAINING

An Application of the foregoing Rules to fome parti-
cular Cafes.

H E firft rule gives a dired and perfed folution
in all cafes ; and the two following rules are
only particular methods of approximating to the fo-
lution given in the firft rule, when the labour of ap-
plying it becomes too great.

The firft rule may be uled in all cafes where either
p or q are nothing or not large. The fecond rule
may be ufed in all cafes where mz is lefs than Vy;
and the 3d in all cafes where iti z is greater than

1 and lefs than ^ , if n is an even number and very

large. If n is not large this laft rule cannot be much
wanted, becaufe, m decreafing continually as n is
diminifhed, the value of z may in this cafe be taken
large, (and therefore a confiderable interval had be-
tween — —z and 4- z,) and yet the operation be

n n

carried on by the 2d rule; or mz not exceed \/y.

But in order to fhew diftindly and fully the nature
of the prefent problem, and how far Mr. Bayes has
carried the folution of it ; I fhalJ give the refult of
this folution in a few cafes, beginning with the loweft
and moft fimple.

Let

C 405 ]

Let us then firft fuppofe, of fuch an event as that
called M in the effay, or an event about the proba-
bility of which, antecedently to trials, we know no-
thing, that it has happened once, and that it is en-
quired what conclufion we may draw from hence
with lefpedt to the probability of it’s happening on a
fecond trial.

The anfwer is that there would be an odds of three
to one for fomewhat more than an even chance that
it would happen on a fecond trial.

For in this cafe, and in all others where q is

nothing, the expreffion n -\- 1 x f 1 x^^1

/>+i p-\~i P+ 1 P + ~l

or A — x gives the folution, as will appear

fiom confidering the f rft rule. Put therefore in this
expi efiion p + x ~ 2, X = 1 and x = JL and it will be
1 01* -I y which fhews the chance there is that

the probability of an event that has happened once
lies fomewhere between 1 and i.; or (which is the
fame) ^the odds that it is fomewhat more than an
even cnance that it will happen on a fecond trial

In the fame manner it will appear that if the event
has happened twice, the odds now mentioned will be
feven to one 5 if thrice, fifteen to one 5 and in gene-
ral, if the event has happened p times, there will be
an odds of 2^ + 1 — 1 to one, for more than an equal
chance that it will happen on further trials.

Again, fuppofe all I know of an event to be that
it has happened ten times without failing, and the

, . There can *' fuppofe, be no reafon for obferving that on
tms fubjedt unity is always made to ftand for certainty, and ~
for an even chance,

Voi. LIII. G g g enquiry

[ 406 ]

enquiry to be what reafon we fhall have to think we
are right if we guefs that the probability of it’s hap-
pening in a fingle trial lies fomewhere between -I®.
and A, or that the ratio of the caufes of it’s happen-
ing to thofe of it’s failure is fome ratio between that
of fixteen to one and two to one.

Here p + i = 1 1 , X — II and * = £ and X

— — 't'11 = .5013 See. The anfwer

therefore is, that we fhall have very nearly an equal
chance for being right.

In this manner we may determine in any cafe what
conclufion we ought to draw from a given number
of experiments which are unoppofed by contrary
experiments. Every one fees in general that there is
reafon to expedt an event with more or lefs confidence
according to the greater or lefs number of times in
which, under given circumftances, it has happened
without failing ; but we here fee exactly what this
reafon is, on what principles it is founded, and how
we ought to regulate our expeditions.

But it will be proper to dwell longer on this
head.

Suppofe a folid or die of whofe number of fides
and conftitution we know nothing ; and that we are
to judge of thefe from experiments made in
throwing it.

In this cafe, it fhould be obferved, that it would
be in the highefl degree improbable that the folid
fhould, in the fir ft trial, turn anyone fide which could
be affigned before hand ; becaufe it would be known
that fome fide it mud turn, and that there was an in-
finity of other fides, or fides otherwife marked, which
it was equally likely that it fhould turn. The fit ft
4 throw

[ 4°7 ]

throw only fhews that it has the fide then thrown,
without giving any reafon to think that it has it ana.
one number of times rather than any other. It will
appear, therefore, that after the firft throw and not
before, we fhould be in the circumftances required
by the conditions of the prefent problem, and that
the. whole effedft of this throw would be to bring
us into thefe circumftances. That is: the turning
the fide firft thrown in any fubfequent fingle trial
would be an event about the probability or improba-
bility of which we could form no judgment, and
of which we fhould know no more than that it
lay fomewhere between nothing and certainty. With
the fecond trial then our calculations muft begin ;
and if in that trial the fuppofed folid turns again the
fame fide, there will arife the probability of three
to one that it has more of that fort of fides than of
all others; or (which comes to the fame) that there
is fomewhat in its conftitution difpofing it to turn that
lide ofteneft : And this probability will increafe, in
the manner already explained, with the number of
times in which that fide has been thrown without
failing. It fhould not, however, be imagined that any
number of fuch experiments can give fufHcient reafon
for thinking that it would never turn any other fide.
For, fuppofe it has turned the fame fide in every
trial a million of times. In thefe circumftances there
would be an improbability that it had lefs than

1.400.000 more of thefe fides than all others; but
there would alfo be an improbability that it had above

1.600.000 times more. The chance for the latter is

exprelTed by raifed to the millioneth power

fubftra&ed from unity, which is equal 10.4647 6cc.and

G g g 2 the

[ 408 ]

the chance for the former is equal to 44°°°.°.? raifed
to the fame power, or to .48955 which, being both lefs
than an equal chance, proves what I have faid. But
though it would be thus improbable that it had above

1.600.000 times more or lejs than 1.400,000 times
more of thefe fides than of all others, it by no means
follows that we have any reafon for judging that the
true proportion in this cafe lies fomewhere between
that of 1. 600, coo to one and 1.400,000 to one.
For he that will take the pains to make the calcula-
tion will find that there is nearly the probability ex-
prefted by .52 7, or but little more than an equal
chance, that it lies fomewhere between that of

600.000 to one and three millions to one. It may
deferve to be added, that it is more probable that this
proportion lies fomewhere between that of 900,000
to 1 and 1.900,000 to 1 than between any other
two proportions whofe antecedents are to one another
as 900,000 to 1.900,000, and confequents unity.

I have made thefe obfervations chiefly becaufe they
are all ftridtly applicable to the events and appear-
ances of nature. Antecedently to all experience, it
would be improbable as infinite to one, that any par-
ticular event, before-hand imagined, fhould follow
the application of any one natural objedt to another 5
becaufe there would be an equal chance for anv one of
a-n infinity of other events. But if we had once feen
any particular effects, as the burning of wood on
putting it into fire, or the falling of a done on de-
taching it from all contiguous objedts, then the con-
clufions to be drawn from any number of fubfequent
events of the fame kind would be to be determined
in the fame manner with the conclufions jufl: men-
tioned relating to the conftitution of the folid I have

fuppofed

[ 409 ]

fuppofed. — In other words. The firft experi-

ment fuppofed to be ever made on any natural objedt
would only inform us of one event that may follow a
particular change in the circumftances of thofe objedts ;
but it would not fugged; to us any ideas of uniformity
in nature, or give us the lead: reafon to apprehend
that it was, in that inftance or in any other, regular ra-
ther than irregular in its operations. But if the fame
event has followed without interruption in any one
or more fublequent experiments, then fome degree
of uniformity will be obferved ; reafon will be given
to expedt the fame fuccefs in further experiments, and
the calculations directed by the folution of this pro-
blem may be made.

One example here it will not be amifs to give.

Let us imagine to ourfelves the cafe of aperfonjufl
brought forth into this, world and left to colledt from
his obfervation of the order and courfe of events what
powers and caufes take place in it. The Sun would,
probably, bethefird: objedt that would engage his atten-
tion; but after lodng it the fird: night he would be en-
tirely ignorant whether he fhould ever fee it again. He
would therefore be in the condtion of aperfon making a
hrb experiment about an event entirely unknown to
him. But let him fee a fecond appearance or one
return of the Sun, and an expedtation would be raifed
in him of a fecond return, and he might know that
there was an odds of 3 to i lovfome probability of this.
This odds would increafe, as before reprefented, with
the number of returns to which he was witnefs.
But no finite number of returns would be fufiicient
to produce abfolute or phyfieal certainty. For let it
be fuppofed that he has feen it return at regular and
ftated intervals a million of times. The conclufions
5 this

[ 4io ]

this would warrant would be fuch as follow

There would be the odds of the millioneth power
of 2, to one, that it was likely that it would return again
at the end of the uiual interval. There would be the
probability expreffed by -5352, that the odds for this
was not greater than 1.600,000 to 1 ; And the pro-
bability expreffed by .5105, that it was not lefs than
1 .400,000 to i .

It fhould be carefully remembered that thefe de-
ductions luppofe a previous total ignorance of nature.
Alter having obferved for fome time the courfe of
events it would be found that the operations of nature
are in general regular, and that the powers and laws
which prevail in it are liable and parmanent. The
confideration of this will caufe one or a few experi-
ments often to produce a much ffronger expectation of
fuccefs in further experiments than would other wife
have been reafonable; juff as the frequent obfervation
that things of a fort are difpofed together in any place
would lead us to conclude, upon difcovering there
any objeCt of a particular fort, that there are laid up
with it many others of the fame fort. It is obvious
that this, fo far from contradicting the foregoing de-
ductions, is only one particular cafe to which they are
to be applied.

What has been faid feems fufficient to fhew us
what conclufions to draw from uniform experience.
It demonflrates, particularly, that inftead of proving
that events will always happen agreeably to it, there
will be always reafon aguinft this conclufion. In other
words, where the. courfe of nature has been the molt
conftant, we can have only reafon to reckon upon a
recurrency of events proportioned to the degree of

this

[ 4” ]

this constancy; but we can have no reafon for thin Ic-
ing that there are no caufes in nature which will ever
inrerfere with the operations of the caufes from which
this confiancy is derived, or no circumftances of the
world in which it will fail. And if this is true, fup-
pofing our only data derived from experience, we fhall
find additional reafon for thinking thus if we ap-
ply other principles, or have recourfe to fuch confi-
derations as reafon, independently of experience, can
fuggeft.

-But I have gone further than I intended here ; and
it is time to turn our thoughts to another branch of
this fubjeft: I mean, to cafes where an experiment
has fometimes lucceeded and fometimes failed.

Here, again, in order to be as plain and explicit
as pofiible, it will be proper to put the following-
cafe, which is the eafieft and fimpleft I can think
of.

Let us then imagine a perlon prefent at the drawing
of a lottery, who knows nothing of its fcheme or of
the proportion of Blanks to Prizes in it. Let it further
be fuppofed, that he is obliged to infer this from the
number of blanks he hears drawn compared with the
number of prizes j and that it is enquired what con-
clufions in thefe circumftances he may reafonably
make.

Let him firft hear ten blanks drawn and one prize,
and let it be enquired what chance he will have for be-
ing right if he gueftes that the proportion of blanks to
prizes in the lottery lies fomewhere between the pro-
portions of 9 to i and n to i.

Here taking X = x=zT%,p=io, q — 7, »=n,
E = 1 1, the required chance, according to the firfi:

rule^

C 412 ]

rule,

IS n + 1 X

E

into

the

difference

between

P+i

P+2

P+i

p+2

X

-qX

and

X

—

q x —

12 x 11

p+i

P+2

p+

r

p + 2

"77”

r Triii

~

«. 1

TT

X 12

■ — 12I

—

10

—

10 1 =

.07699

1 1

12

1 1

1 2

&c. There would therefore be an odds of about 923
1076, or nearly 12 to 1 agctin/l his being right. Had
he gueffed only in general that there were lefs than
9 blanks to a prize, there would have been a proba-
bility of his being right equal to .6589, or the odds
of 65 to 34.

Again, iuppofe that he has heard 20 blanks drawn
and 2 prizes ; what chance will he have for being
right if he makes the fame guefs ?

Here X and x being the fame, we have n = 22,
p — 20, q — 2, E — 23 1 , and the required chance

~P +7 J+2 V+3

equal to « + 1 x E x X -yX-j-yxy-ixX

p + i p + 2 2 p + 3

P+l p + 2 P + 3

- — * — qx -|-yxy-iXtf =.10843800.

p + i ’p + 2 2 p + 3

He will, therefore, have a better chance for being
right than in the former inftance, the odds againft
him now being 892 to 108 or about 9 to 1. But
fhould he only guefs in general, as before, that there
were lefs than 9 blanks to a prize, his chance for be-
ing right will be worfe j for inftead of .6589 or an
odds of near two to one, it will be .584, or an odds
of 584 to 415.

Suppofe,

C 413 ]

Suppofe, further, that he has heard 40 blanks
drawn and 4 prizes j what will the before-mention-
ed chances be ?

The anfwer here is .1525, for the former of thefe
chances j and .527, for the latter. There will, there-
fore, now be an odds of only 54. to 1 againft the
proportion of blanks to prizes lying between 9 to 1
and 11 to 1 ; and but little more than an equal chance
that it is lefs than 9 to 1.

Once more. Suppofe he has heard 100 blanks
drawn and 10 prizes.

The anfwer here may ftill be found by the firffc
rule ; and the chance for a proportion of blanks to
prizes lefs than 9 to 1 will be .44109, and for a pro-
portion greater than n to 1 .3082. It would there-
fore be likely that there were not fewer than 9 or
more than 1 1 blanks to a prize. But at the fame time
it will remain unlikely * that the true proportion
fhould lie between 9 to 1 and 11 to 1, the chance
for this being .2506 &c. There will therefore be
ftill an odds of near 3 to 1 againft this.

From thefe calculations it appears that, in the cir-
cumftances I have fuppofed, the chance for being
right in guefting the proportion of blanks to prizes to
be nearly the fame with that of the number of blanks

* I fuppofe no attentive perfon will find any difficulty in this.
It is only faying that, fuppofing the interval between nothing
and certainty divided into a hundred equal chances, there will be
44 of them for a lefs proportion of blanks to prizes than 9 to r,
31 for a greater than 1 1 to 1, and 25 for fome proportion be-
tween 9 to 1 and 11 to ij in which it is obvious that, though
one of thefe fuppofitions muft be true, yet, having each of them
more chances againft them than for them, they are all feparately
unlikely.

Vol. LIJI. Hhh drawn

[ 4*4 ]

drawn in a given time to the number of prizes drawn,
is continually increafing as thefe numbers increafe ;
and that therefore, when they are confiderably large,
this conclulion may be looked upon as morally cer-
tain, By parity of reafon, it follows univerfally, with
refpedt to every event about which a great number
of experiments has been made, that the caufes of its
happening bear the fame proportion to the caules of
its failing, with the number of happenings to the
number of failures ; and that, if an event whole
caufes are fuppofed to be known, happens oftener or
feldomer than is agreeable to this conclulion, there
will be reafon to believe that there are fome unknown
caufes which difturb the operations of the known
ones. With refpeCt, therefore, particularly to the
courfe of events in nature, it appears, that there is
demonftrative evidence to prove that they are derived
from permanent caufes, or laws originally eftablifhed
in the conftitution of nature in order to produce that
order of events which we obferve, and not from any
of the powers of chance*. This is juft as evident
as it would be, in the cafe I have infifted on, that the
reafon of drawing io times more blanks than prizes
in millions of trials, was, that there were in the wheel
about fo many more blanks than prizes .

But to proceed a little further in the demonftration
of this point.

We have feen that fuppoling a perfon, ignorant of
the whole fcheme of a lottery, fhould be led to con-
jecture, from hearing ioo blanks s&d io prizes drawn,

* Sec Mr. De Moivre’s Doddne of Chances, png. 250.

that

C 4i5 ]

that the proportion of blanks to prizes in the lottery
was fomewhere between 9 to 1 and 11 to i, the
chance for his being right would be .2506 &c. Let
now enquire what this chance would be in fome
higher cates.

Let it be fuppofed that blanks have been drawm

1000 times, and prizes 100 times in 1100 trials.

In this cafe the powers of X and x rife fo high,

, P 1

and the number of terms in the two feriefes X

— qX

p + i

6cc, and x

P+ 1

x

p+ 2

p + i
&c. become

p + 2 p + 1 p-\- 2

fo numerous that it would require immenfe labour
to obtain the anfwer by the firft rule. ’Tis neceifary,
therefore, to have recourfe to the fecond rule. But
in order to make ufe of it, the interval between X
and x muft be a little altered. 44. - _9_. is _i._, and
therefore the interval berween 44 — _ *o and 44
-}- --fo- will be nearly the fame with the interval be-
tween _9_ and 44., only fome what larger. If then
we make the question to be j what chance there
would be (luppoling no more known than that blanks
have been drawn 1000 times and prizes 100 times
in 1100 trials) that the probability of drawing a
blank in a lingle trial would lie fomewhere between
-14 - -4-0 an^ -44- + -4-5- we 4hall have a queftion
of the fame kind with the preceding queftions, and
deviate but little from the limits affigned in them.

The anfwer, according to the fecond rule, is that

2 s

this chance is greater than 1 - 2 Ea? bi 2 E at b*

and

Hhh 2

n

[ 4i6 ]

2 Y

and lefs than 1-2 E at bi - 2 E «/’ bq, E being «+• 1

n

n

ipq

P A

xE^ p xmz-

m z

, ??-2 m

+ X —

2 n 5

2;

&C.

V n ' 3

By making here 1000 =/> ioorrr:^ noo = ?z

,-U = s, ct=— ’= i.o483o8.E<A? = _ x £T. h

pj 2 %/ K y

being the ratio whofe hyperbolic logarithm is T'T X

1 1 1 1 1

— - - X -

n P q 360 rp

I I
— 7- X —
x 260 «1 * 3 * 5

1 --&C.

*>* ?S

and K the ratio of the quadrantal arc to radius; the
former of thefe expreffions will be found to be .7953,
and the latter .9405 &c. The chance enquired after,
therefore, is greater than .7953, and lefs than .9405.
That is; there will be an odds lor being right in gueff-
ing that the proportion of blanks to prizes lies nearly
between 9 to 1 and 1 1 to 1, (or exactly between 9 to
1 and 1 11 1 to 99) which is greater than 4 to 1,
and lefs than 16 to 1.

Suppofe, again, that no more is known than that
blanks have been drawn 10,000 times and prizes 1000
times in 11000 trials; what will the chance now
mentioned be?

Here the fecond gs well as the firft rule becomes
ufelefs, the value of m z being fo great as to render

it fcarcely poffible to calculate diredtly the feries ;nz -
4 -t—1 x ?,LJL - &c. The third rule, therefore,

3 2 \n 5

mull; be -aTed ; and the information it gives us is, that

the required chajice is greater than .97421, or more
than an odds of 40 to 1.

[ 417 ]

By calculations fimilar to thefe may be determined
univerfally, what expectations are warranted by any
experiments, according to the different number of
times in which they have fucceeded and failed; or
what fhould be thought of the probability that any
particular caufe in nature, with which we have any
acquaintance, will or will not, in any fingle trial,
produce an effeCt that has been conjoined with it.

Molt perfons, probably, might expeCt that the
chances in the fpecimen I have given would have been
greater than I have found them. But this only fhews
how liable we are to error when we judge on this
fubjeCt independently of calculation. One thing,
however, fhould be remembered here; and that
is, the narrownefs of the interval between and
™ or between i-° 4. ^ and -L° — ° Had

this interval been taken a little larger, there would
have been a confiderable difference in the refults of
the calculations. Thus had it been taken double, or
z — -5-t> it would have been found in the fourth in-
flance that inflead of odds againft there were odds
, for being right in judging that the probability of draw-
ing a blank in a fingle trial lies between 4 4. -j- and

10 1

nr r TT*

The foregoing calculations further fhew us the
ufes and defeCts of the rules laid down in the effay.
’Tis evident that the two laft rules do not give us
the required chances within fuch narrow limits as
could be wifhed. But here again it fhould be confi-
dered, that thefe limits become narrower and narrow-
er as q is taken larger in refpeCt of p ; and when p
and q are equal, the exaCt folution is given in all cafes
by the fecond rule. Thefe two rules therefore afford

a direction

1

. [ 418 ]

a direction to our judgment that may be of confider-
uble ufe till fome peri'on Shall difcover a better ap-
proximation to the value of the two Series's in the
£rft rule -J-.

But what moft of all recommends the folution in
this Effay is, that it is compleat in thole cafes where
information is moft wanted, and where Mr. De
Moivre’s folution of the inverfe problem can give
little or no direction ; I mean, in all cafes where ei-
ther p or q are of no considerable magnitude. In
other cafes, or when both p and q are very confider-
able, it is not difficult to perceive the truth of what
has been here demonstrated, or that there is reafon to
believe in general that the chances for the happening
of an event are to the chances for its failure in the
fame ratio with that of p to q. But we Shall be greatly
deceived if we judge in this manner when either p or
q are fmall. And tho’ in fuch cafes the Data are not
Sufficient to difcover the exadf probability of an event,
yet it is very agreeable to be able to find the limits be-
tween which it is reafonable to think it muft lie, and
alfo to be able to determine the precife degree of affent
which is due to any conclufions or alTertions relating
to them.

f Since this was written I have found out a method of confi-
derably improving the approximation in the 2d and 3d rules by

2 s

demonftrating that the expreffion 1 + 2 E a? $ + 2 Ea? Incomes

n

almoft as near to the true value wanted as there is reafon to defire,
only always fomewhat lefs. It feems neceflary to hint this herej
though the proof of it cannot be given.

LIII. An

C 419 ]

LI 1 1. An Account of the Sea Pen, or Penna-
tula Phofphorea of Linnaeus ; likewife a
Defcription of a new Specks of Sea Pen,
found on the Coafl of South-Carolina, with
Obfervations on Sea-Pens in general. In a
Letter to the Honourable Coote Molef-
worth, hfq\ M D. and F. R. S. from
John Ellis, Efq ; F. R. S. and Member of
the Royal Academy at Upfal.

Dear Sir,

Read Dec. 22,

j76 3-

I Should make fome apology for de-
ferring fo long the account I pro-
mifed you of the Animal you were fo kind to lend
me in February 1762, which was taken in a trawl
in 72 fathoms water near the harbour of Bred in
France; but a new fpecies coming to my hand
occalioned this delay. This curious fea-produc-
tion, I find, by your letter, you took for a new
kind of coralline, and not without reafon, when up-
on examining it (as it was not long taken out of the
fea) there were dill remaining feveral of the fuckers
like heads of Polypes difpofed along its fickle-fhaped
Pinnulae. But when you hear of more of its proper-
ties, you will agree with me, that it belongs to ano-
ther clafs of Animals ; I fhall mention only oneatpre-
fent, till I come to defcribe it more particularly, and
that is, that it floats or fwims about freely in the
fea; whereas Corals, Corallines, Alcyonia, and
2 all

[ 420 ]

all that order of beings, adhere firmly by their
bafes to fubmarine fubftances.

This Animal was well known to the ancients
by the name of the Sea-Pen ; many of the old
authors took it for a Fucus or Sea-Plant.

This fpecies of yours has been found in the Ocean
from the coaft of Norway to the moft remote parts
of the Mediterranean Sea, and not only dragged up
in trawls from great depths of the fea, but often
found floating near the furface.

Dr. Shaw, in his Hifliory of Algiers, remarks that
they afford fogreat alight in the night to the fifhermen,
that they can plainly difcover the fifh fwimming
about in various depths of the fea. From this ex-
traordinary property Dodtor Linnaeus calls this fpe-
cies of Sea-Pen, Pennatula Pbofphorea , and re-
marks, after giving the fynony ms of other authors.
Habitat in Oceano fundam illuminans.

In order to attempt a defcription of it ; the out-
ward appearance of this Animal is not unlike one
of the quill feathers of a- bird’s wing, but they are
found of different fizes from 4 to 8 inches in length;
this of yours is about 4 inches long; the lower
half of it, is naked round and white, not unlike
the quill part of a writing pen ; the upper part
reprefents that of the feathered part of the pen,
and is of a reddifh colour, but faded by foaking
it often in water in order to examine it more
minutely. This upper half (which arifes from the
quill and is feathered on both fides) is a little com-
prefled and becomes fmaller and fmaller till it ends
in a point at the top ; along the back of this, in
the fame manner as in the inner fide of a common
writing pen, there is a groove in the middle from

the

[ 421 ]

the quill to the extremity : from each fide of this
upper part of the ftem proceed little parallel fea-
ther-like fins; thefe begin at the top of the quill
part, very fmall on each fide at firft, but lengthen
as they advance towards the middle; from hence
they fhorten gradually on each fide, till they end at
a point at the top ; their terminations preferving
on each fide the figure of the fegment of a circlet
I come now to confidermore minutely thofe Pinnulse,
or feather-like fins, that projedt on each fide and
form the upper part of this animal. Thefe are
evidently defigned by nature to move the animal
backward or forward in the fea, confequently to do
tne office of fins, while at the fame time, by the
appearance of the fuckers or mouths furnifhed with
filaments or claws, they were certainly intended to
pi ovide food for its fupport ; for notwithstanding
what Dr. Linnaeus has faid in regard to its mouth
in his fyftem of nature, viz. Os bafeos commune ro~
tnndum , I could not, with the help of the befl
glaffies, difcover that the point of the bafe was pene-
tiated in the lead, fo that I am. clearly of opinion,
that this animal, like the Hydra Ardtica or Green-
land Polype, which I have defcribed in my Effiay on
Corallines, nouriffies and fupports itfelf by thefe
fuckers or Polype-like figures; that by thefe, both,
kinds taKe in their food, and have no other vifible
means of difcharging the exuviae of the animals
they feed upon, than by the fame way which they
take them in ; and that, from attentively confiderino-
the ftrudlure and manner of living of both thefe'
animals, I ffiall make no doubt in claffing them in
the fame genus of Pennatula, though they vary

C 422 ]

very much in their exterior form and dze, and con-
fequentlyare of very different fpecies.

The Idem of the fuckers of this animal is of a
cylindrical form ; from the upper part proceed 8
fine white filaments or claws to catch their food :
when they retreat on the alarm of danger they
draw themfelves into their cafes, which are formed
like the denticles of the Corallines ; but here each
denticle is furnifhed with fpiculas, which clofe toge-
ther round the entrance of the denticle, and protect
this tender part from external injuries.

Some time after I had made my remarks on this
very extraordinary animal, the Royal Society did
me the honour to recommend to me, for my opinion,
fome very curious obfervations lately publifhed
by Dr. Bohadfch of Prague, a book of great
merit, which fhews that the author has taken a good
deal of pains, in examining very minutely into thoTe
animals called by the old authors Zoophytes: but as
many of them have not the lead refemblance to vege-
tables, I fhall beg leave to pafs over fuch, and only
confine myfelf to this clals of the Penna marina,
which he feems to have been happy in obferving; and
therefore fhall take the liberty to add fuch of his ob-
fervations, as the opportunity of his feeing this
animal alive in fea-water afforded him, without
which it would have been impoflible for me to
have had the oleafure of gratifying you, and
the reft of the Royal Society, fo fully on the
fubjedt.

Some of the mod curious remarks of Dodtor Bo-
hadfch on the anatomy of this animal, as alfo on
the appearance of it while alive in lea-water, are
as follows.

4

« When

[ 423 ]

" When the trunk is opened lengthways, a fait-
“ ifh liquor flows out of it, fo vifcid as to hang
“ down an inch ; the whole trunk of the flem is
** hollow, its outward coriaceous membrane is more
** than a line thick, and forms a ftrong covering
“ to it: between this and another thinner membrane
“ of the pinnated part of the trunk are innumerable
“ little yellowifh eggs, floating in a whitifh liquor,
“ about the flze of a white poppy feed ; thefe are
** befl: feen, when the trunk is cut acrofs : This
“ thin membrane lines the whole inflde of the
“ trunk, in which we obferve nothing but a
“ kind of yellowifh bone, which takes up three
“ parts of the cavity.

<f This bone in fome of thefe animals is above
“ 2JL inches long and about half a line thick j in

the middle part of it, it is four fquare or quad-
<( rangular ; towards each end of it, it grows round
tc and very taper r that end is fmalleft, which is
“ neareft the top of the pinnated trunk. The
<c whole bone is covered with a yellowifh clear
“ fkin, which at each end changes into a liga—
(e ment; one of which is inferted in the top of
“ the pinnated trunk, the other in the top of the
“ naked trunk ; by the help of this upper liga-
“ ment, the end of this little bone is either con-
(C trailed into a very narrow arch, or dif-
<f poled into a flraight line, according to the
“ motion of the trunk.

“ The fins likewife are compofed of two fkins ;
lt the outward one ftrong and leathery and covered
“ over with an infinite number of crimfon ftreaks,
u the inner fkin is thin and clear; The cylindrical

Iii 2 “ part

£ 424 3

part of the fuckers are in the fame manner, only
with this difference, their outward fkins may be
fofter.

<( Both the fins and fuckers are hollow, fo that
the cavity of the fuckers may communicate with
the fins, as their cavity does with the trunk.

<( We now come to the appearance which this
animal makes when alive in fea-water.

(t The trunk then was contracted circularly at
the bottom of the naked part of the ftem, and
by this contraction formed a zone of the mod;
intenfe purple, which moved upwards and
downwards luccefiively : When it moved up-
wards through the length of the pinnated trunk,
it there became paler, and at length terminated
at the top : the motion being fcarce finifhed, a
like zone appeared at the end of the naked trunk,
which finifhed its motion in the fame manner
as the former.

“ When this zone becomes very much con-
ftriCted on every fide, the trunk above it fwells
and acquires the form of an onion; and then
it appears, as if a comprefifed globe moved along
through the whole fpace of the trunk; thiscon-
ilriCtion of the trunk gives that fine red colour
to the zone ; for when the fkin of the trunk
is outwardly full of purple papillae, the interme-
diate fpaces are of a whitifh colour. In this
conftriCtion then of the fkin the intermediate
fpaces are obliterated and the papillae are
brought nearer together; confequently only the
purple colour prefents itfelf to the eyes and ap-
pears more bright.

<( More

[ 425 ]

“ Moreover the end or apex of the naked trunk
“ is fometimes curved like a hook, and fometimes
“ extended in a right line; both thefe motions
“ then muft be directed by the little bone in the
“ infide, and from this motion of this little in-
“ ternal bone, that finus or cavity at the lower end
“ of the trunk (thought by authors heretofore to
“ be the mouth) feems plainly to be formed ; for
“ fometimes it is deeper, fometimes Shallower;
“ it is deeper while the moveable globe appears
“ in the middle of the pinnated part of the trunk,
“ and fhallovver when it is in the bottom of the
“ naked trunk, at which time the bone is moil
“ extended.

“ Tbefinsorpinnulae have four different motions;
“ they are moved both towards the naked flem>
“ and towards the pinnated hem; fometimes they
“ are drawn in very much to the belly, a little af-
“ ter they are inclined to the back ; further, the
“ fiefhy filaments or claws move in all directions,
“ and the cylindrical part with the filaments is
“ either extended out or drawn in and hid in
“ the fins. DoCtor Bohadfch concludes this
chapter by obferving, that there are fome varieties
to be met with in thefe red Sea-Pens: fome, he fays,
are paler and inclining to arofe colour, others of an
intenfe deep red : in the firfi: kind be remarks that
there are fewer denticles or tentacula (from whence
the fuckers proceed) in the fins, and that thefe are
placed in one row within half a line of one another;
but in the latter, he fays, the tentacula are placed in
a double row and as near as they can be together :
this is the Pennatula of winch I have juft now given
you his account, and which he faw alive in fea-

water.

[ 426 J

water. The other feems to be the fame with yours,
and is, no doubt on it, Linnsus’s Pennatula Phof-
phorea , fo that heconcludes them to be two diftindfc
fpecies, and calls them by the following names, viz.

Penna f Rubra J pinnis falciformibus , tentaculis in
pinnarum facie concava denfiffime difpojitis.

Penna ( Rofea ) pinnis falciformibus , tentaculis in
pinnarum facie concava laxe difpoftis.

In the three following chapters Dr. Bo-
hadfch defcribes three other kinds of Sea-Pens.
One he calls Penna Grifea or the Grey Sea-Pen
with crenated fins ; this is figured and defcribed
from a dry fpecimen in Seba’s Mufeum, Tom. III.

The next is a very lingular one without fins,
having a fquare bony ftem 2 feet 10 inches long,
covered with a fkin, and furnifhed on 3 fides with
tentacula or fuckers : but this was unfortunately
broken off at the bottom before he received it : he
fays, the fifhermen call it Penna del Pefche de Pa -
vone , or the Feather of the Peacock- fifh. To thefe
he has added the Alcyoniurn called, Manus marina ;
he calls it Penna ramofa pi tints carens , tentaculis
in ramis poftisy and in another place, Penna Exos.
In order to give you and the reft of the Royal
Society fome idea of thefe extraordinary Animals,
I have copied his figures, and alfo the 'figures of the
three laft fpecies of Linnasus’s Pennatula, viz. his
Pennatula fFilofdj Pennatula (Sagitta) and Pen-
natula f Mirabilis J from the authors which he refers
us to, and have added an exadt delineation of our
Alcyoniurn ( Manus marina J or Dead mans hand, with
fome microfcopial drawings of different fedtions of
it, to fhew that although the fubffance of it is
flefhy, yet that it approaches much nearer to the

Madre*

[ 427 ]

Madiepora Corals, than to any known fpecies of"
the genus of Animals called Pennatula. At the
fame time I allow his remark to be very juft, where
he obferves that the Hydra Arttica or Great Green-
land Polype, which I have defcribed in the Philofo-
phical 1 ranfadtions, and in my Effay on Corallines,
is certainly a fpecies of Pennatula ; but he will
find, from both the drawing and defcription, which
I have given of it, that it is not ftxt by its bafe, but
floats freely about in the fea ; whereas this Alcy-
onium as well as his (which differs in colour from
ours) are always found fixt by their bafe to fome
folid fubmarine body, and confequently cannot be
admitted among the Pennatula?.

I muft now conclude this letter with a fhort ac-
countof a new difcovered fpeciesof Pennatula, which
my ingenious friend John Greg Eiq; of Charles
Town in South -Carolina, difcovered on that coaft
andprefented to me fome time ago. This beautiful
purple animal is of a compreffed kidney fhape.
The body is about an inch long, and half an inch
acrofs the narroweft part, it has a fmall roundifti
tail of an inch long proceeding from the middle of
the body, its tail is full of rings from one end to the
other like an Earth-Worm, and along the middle
of the upper and under part of it there is a fmall
groove which runs from one end to the other.

I examined carefully the point of the tail and
could find no perforation in it, which is agree-
able to what I have obferved in the reft of this
genus.

The upper part of the body is convex and near a
quarter of an inch thick ; the whole furface of it is
covered over with minute yellow ftarry openings,

through

. [428]

through which are protruded little fuckers like po-
lypes each furnifhed with 6 tentacles or filaments,
like what we obferve on fome of the Corals, and
feem to be the proper mouths of the animal. The
under part of the body is quite flat, this furface is
fall of the ramifications of flefhy fibres, which,
proceeding from the infertion of the tail, as their
common center, branch themfelves out, fo as to
communicate with the fiarry openings on the exte-
rior edge and upper furface of this uncommon ani-
mal : for a clearer idea I mull refer you to the fi-
gure of this, as well as that of your own Penna-
tula, and am.

Dear Sir,

T , ~ , Your much obliged

London, Dec. 15, 1763. 0

Humble Servant,

John Ellis*

N

8 on d C). cTf3otA *J /r/co of' f/tv r JrrT/r)

fOttfjtoit of?/Ac toAjre of /Ac t/frfz**’/ •Jf/ifnoe A//jA/y f/imj/i

o/ A/iO' f*c//i . e /

jyo/is/V a?//*)

*or't>Lt,

o?u

Oreti co// 1 (tty

[ 429 ]

P. S. Juft when the two plates XIX and XX of
the Pennatula were finifhed, and fent to the
Printer, I received three kinds of Sea-Pens,
finely preferved in fpirits, from my learned friend
Thomas Pennant Efq; of Bychton in Flintfhire,
which he informs me were fent him from the
Mediterranean-Sea. One of them is Entirely
new to me, and, I believe, not yet defcribed ;
the other two, which are the Red and the Gray
Sea-Pens of Dr. Bohadfch, are fo very indiffe-
rently defigned by the Do&or’s painter, and
which I have copied in Plate XX, that I thought
a better drawing would give you a clearer idea
of thefe ftrange animals, and be more agreeable
to the Royal Society in general.

An Explanation of the Plates.

Plate XIX.

FIG. i. The back part of the Red-Sea-Pen, or
Pennatula Phofphorea of Linnaeus. This was
found on the coaft of France, they are fre-
quently met with on the coafts of Norway and

* Sweden.

2. The front of the fame.

3. and 4. Both fides of the fame magnified.

5. One of the fins more highly magnified, to fhew
the Polype-like fuckers by which it takes in its
nourifhment.

6. The kidney-fhap’d purple Sea-Pen from South-
Carolina in its natural fizej this upper part is full

Kkk

of

C 43° 1

of ftarry openings, which fend out fmall fuckers
like polypes by which it feeds.

7. The under part of the fame, with its ramifying
fibres, that lead from the infertion of the item
as from a center to the circumference, and cor-
refpond with all the ftarry openings on the edge
and back of it.

8 and 9. Both fides of this animal magnified.

10. A part of the exterior edge higher magnified,
to fhew the form of the ftarry openings and fuc-
kers, which confift of 6 rays and claws.

Plate XX.

The four following Sea-Pens were found by Dr.

Bohadfch, in the Sea, near Naples.

Fig. 1. Reprefents the forepart of the Red-Sea-
Pen with many rows of fuckers on its fins.

2. The back part, the middle of which is covered
with the appearance of fmall papillae.

3. One of the fins magnified.

4. One of the fuckers feparated.

5. The bone taken from the internal part of the pin-
nated trunk j this is fattened to ligaments at both
ends which are likewife inferted in both ends of
the animal. When the ligament at the bafe is
contracted, it forms that finus at a a , that has been
taken for a mouth by molt authors.

6. The Grey-Sea-Pen.

7. One of its crenated fins. N. B. There is a figure
of this Sea-Pen taken from a dried fpecimen in the
third tome of Seba’s Mufeum.

8. The

a tr ,r//is /&//i)nf or * /tnttO on
.to/,*r,a/o</. J). r/7io //one /o/.

i'Mfr ti&Mn. cn/M //r ‘ft,,
tt< / /*/ r f/t/ l>!f Lj),, >/3o//rt/,H’/t Ci

foott .

^TS! SUt/t//<> * .

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itt'/t// tr/t’ti

' of Wt f/t/t it* rt
frfiooo/ * (‘lO /

rnntt ( *ro*i

»

[43i ]

8. The Sea-Pen called by the Italian Filhermen
Penna del pefche Pavone , or the Pen of Peacock
Fifh ; this appears to be broken off, and is def-
cribed to be yet 2 feet ten inches long, the fquare
bony part of this is not fo hard as that in the
Red-Sea-Pen.

9. This lafl of Dr. Bohadfch’s four Sea-Pens is
the Alcyonium called by authors Manus marina ,
or vulgarly Dead-man’s Hand : he calls it Pen-
na Exos and the branched Sea-Pen without fins
having fuckers placed on its branches : but it
by no means belongs to this clafs of animals,
which float freely about in the fea ; whereas
this adheres to Rocks, Shells, or other marine
fubftances. I have introduced our Alcyonium
Manus marina or Dead-man’s Hand, which is
found in great plenty all round the coafts of
the Britifh Iflands, to fhew its internal ftrudture,
and how near it comes to the Madrepora Coral,
which appears by itgrowth and form to be produced
by animals of the fame fhape.

10. A piece of the Alcyonium Manus marina ,
cut perpendiculary through the middle, to fhew
that it is formed of tubes, which branch out
into others, each ending on the furface in a ftarry
opening of 8 rays ; in each of thefe openings is
a polype-like figure or fucker with eight claws,
faflened to the infide of the tube at it’s lower
part by 8 fine tender filaments, by which it can
raife or fink itfelf at pleafure in its tube : all thefe
tubes that compofe this Alcyonium are connected
together by minute reticulated fibres ; thefe in-
clofe a kind of ftiff gelatinous fubftance, which

teems

[ 432 ]

feems to be the flefh of this compound animal,
and thefe fibres with their inclofed contents to be
the mufcles ; for by the exertion of thefe it
affifis in opening or clofing the ftars on the fur-
face, while the fuckers or polype-like figures are
pufhing themfelves out in fearch of food, or
when they are retreating to fecure themfelves
from danger.

11. Is the magnified part of an upright fedtion of
this Alcyonium reprefented in its natural fize at.
b. Here the polype like fuckers appear in different
attitudes ; one has extended itfelf through the
ftarry opening, and is fending forth it’s fpawn
or eggs ; at the bafe of the next fucker you may
obferve fome of the tender filaments by which
it is fixt to the bottom of the tube; the fucker
next to this is contracted and its ftarry opening
is clofed over it ; the cell or ftar next to this is
cut in half to fhew the manner that the fucker is
placed in it.

12. Reprefents one of thefe fuckers taken out of
its cell.

13. Is a crofs or horizontal fedtion of a piece of
this Alcyonium, the natural fize is expreffcd

at c *.

14. The Madrepora coral is introduced here to
fhew how near it approaches to this Alcyonium
in its external appearance and in the ramification
of its tubes.

The

* The reticulated flefhy part of this Alcyonium approaches
very near to the nature of fponges ; for fponges, when firft taken
out of the fea, are filled with a gelatinous or mucous matter of a
1 ftrong

C 433 ]

The other 3 figures in this plate are introduced to
(hew the form of the Pennatula referred to by
Dr. Linnaeus, in his Syft. Nat. 10 Ed.
p. 819.

15. Is the Pennatula Ftlofa , and is figured in
Boccone’s Recherches, pi. 287, pag. 287. This
animal infefls the Xiphias or Sword-fifh in the
Mediterranean-Sea by fucking their blood, and is
called by Boccone, Hirudo cauda utrincpue pen-
nata .

16. Is the Pennatula Sagitta ; it is defcribed in
Linnaei Amcenit’s Vol. v. Chin. Lagerftr. p.
14. f. 3. and faid to infefi: the Lophius Hijlrio
or Sea-Bat, in the Chinefe Sea.

17. Is the Pennatula Mirabilis. This is called
the Polypus Mirabilis , and is defcribed in the
Mufeum of Adolphus Frederick King of Sweden,
p. 96. t 19. f. 4.

ftrong fifhy fmell : Yet I much doubt whether Sponges have fiich
polype-iike fuckers a3 the Corals, Alcyonia, and Pennatulae,
or are even produced by Worms, as the late ingenious Dr. Pey-
fonel informs us j for in the title to the fecond part of his ma-
nufcript on this fubjeit, which he dedicates to the Royal Society,
he fays, that Sponges, as well as Corals, Madreporas, &c. are
produced by animals that are of a particular fpecies of Urtica
marina or Purpura ; but I am inclined to believe he took this for
granted from the fimilitude they bear to Corals, Alcyonia, &c.
rather than from adlual experiment. I rather take thofe holes,
which I have obferved in them, to be fo many mouths upon the
furface of the animal ; and I am the more inclined to believe it,
from a remark I made with Dr. Solander at the Sea-Coaft of
SulTex in the fummer 1762, on the Spongia Medullam Panis re -
ferens , while it was in a glafs veflel of Sea-Water ; where we
obferved, that the Mamillas that were on the furface opened and
fhut, but that no fucker or animal-like figure appeared to come
out.

Plate

[ 434 3

Explanation of Plate XXI.

Fig. i. Reprefents the front of the Red-Sea-Pen a
little larger than life, as are the figures of the two
following Sea-Pens.

а . One of the fins fhewing, the alternate order in
which the denticles incline like the teeth in a
faw.

2. The back of the Red-Sea-Pen, with the rachis
or middle part between the fins covered over
with a rough fkin like fhaggreen.

3. The finger- fhaped Sea-Pen, or Cynomorion ,
called fo from its likenefs to the fliape of the
Fungus Melitenjis .

The upper part of this animal is covered over with
circular cells, one of which is reprefented at
Fig. 4, from whence proceed Polype-like fuck-
ers, having eight pennated arms or claws, one of
which fuckers is figured at 5.

The Rugae or Furrows in the fwelling part at b ,
fhew that this animal can extend and contract
this part, perhaps to raife or fall itfelf in the
fea.

б. The front of the thorny Sea-Pen, called by Dr.
Bohadfch Penna grifea .

7. The back part of it.

8. Shews the front of one of the fuckers mag-
nified.

9. the back view of the fame.

10. One of the lower fins a little magnified,
which fhews the pofition of the fuckers, and

the

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re tier

'/i or

tttor/torr on.

</rotP, //t/tf //to * {//t t t 'tn/t /
'ere/ //ft./ !j/oe/ .

4i/irne

ft ppree/r ./

r>t/t/ftt/A

//o //•//ro’y tt oz/tie/

' tie Ot

‘or tt/zt/itt/fre/x

■ i ft rt/t/ // ,i

'to tt '//■

[ 435 ]

the infertion of the fpines 5 Thefe fpines arc
combined of many fine fpiculae, which unite
and form one fpine. When thefe fpines open
at top, each forms a ftar of fmall fpicula?,
which nature feems to have pointed out as a
protection for the mouths or fuckers under-
neath, which have no other covering to defend
them, whereas in the Red-Sea-Pen there is a
circle of fpiculas to each fucker, .

LIV. a:

[ +36 3

LIV. A Letter fro?n Mr. B. Wilfon, F. R. S.

and Member of the Royal Academy at
Upfal, to Mr. iEpinus, Profejfor of Na-
tural Philofophy in the Imperial Academy
of Sciences at St. Peterfburg, and Member
of the Academies of Berlin, Stockholm,
and Erfurth.

Read Dec. 23, 1763, jqave not had the favour of hear-
March.764. X mg from you li nee I fent you
fome experiments upon Gems fimilar to thofe pro-
duced by the Pourmalin, which induced me to con-
clude, that the elehlnc current moves always along
the grain thereof. It was the more agreable to
communicate thefe new experiments to you, be-
caufe from the lead hints the greated difeoveries
have been made ; and what may we not expedt
from that curious obferver of nature, who firft dif-
covered thefe extraordinary qualities in the Pour -
mat-in, which have fince excited the attention of fo
many Philofophers.

Your treatife upon this done, publidied in 1762,
feems to be the fame you formerly mentioned in a
letter to me. The remarks at the end of that work
intered me in a particular manner, as they contain
objections to feveral parts of the letter to Dr. He-
herden. I am obliged therefore to lay fomething
in the defence of my own experiments and deduc-
tions, which I hope will merit your attention, and
remove your difficulties.

In

2

C 437 ]

In repeating fuch of the experiments with the
’Tourmalin as were moft proper to anfwer your ob-
jections, I accidentally obferved an appearance which
has given rife to-fome new experiments, very fimple,
and of great confequence in eleCtric refearches.
Thefe dilcoveries you fhall be acquainted with,
before I conclude this letter, that I may have the
pleafure of hearing your fentiments concerning them,
the fooner.

I am glad to find we * agree in admitting what are
called the two fpecies of eleCiricity, one whereof con-
fifts in the augmentation of the eledtric fluid, and the
other in it s diminution. But ftill, notwithftanding the
experiment made with the bent tube in order to deter-
mine that interefting queftion, you feem to doubt which
of thefe is the plus , and which the minus electricity.

1 ou fay •'j'* 1 have proved the oppofition of the two
fpecies, by the knobs of light appearing at the up-
per

* Mi . Wilfon reconnoit de meme que moi, l’exiftence de deux
cfpeces d eledtricite, dont l’une confifte dans ^augmentation, et
1 autre dans la diminution, de la quantite naturelle du fluide elect-
nque. ^ C eft une queftion qui doit interefler chaque phyficien,
de demeler, quelle de deux eleCtricites, ou la vitree, ou la refineufe
de Mr. du Fay, eft la pofi-ive, et quelle en eft la negative ?
Cguant a moi j’ai declare, il y a long terns, dans raon Sermo de
Jimilitudine electriatatis et magnetifmi , que je ne connois aucune
experience, propre a decider cette queftion. Je fuis maintenant
encoie du meme fentiment, car la belle experience de mylord
Charles Cavendifti, rapportee ici et perfecHonee par Mr. Wilfon,
me femble laifler pareillement la chofe indecife.

. + Quant a l’oppofttion des deux efpeces d’elearicite, je con-
viens qu’elle eft fort clairement prouvee par l’experience de Mr.
Wilfon, et par ce phenomene, que la lumiere elearique eft beu-
coup plus vive qu’ailleurs dans le vuide, aux furfaces fuperieures
es colomnes du mercure, (jufqu’a y former commedes boutons
Vol.LIII. L 11

[ 43§ ]

per furface of the quickfilver, when one electrifies
with glafs and at the under furface , when one elec-
trifies with wax, or fulphur j but that, in your
opinion, is all which can be concluded from it. You
then declare, that was you difpofed to argue againft
me, it would be in this manner. “ It is eafy to

de lumiere) quand on elearife avec un tuyeau de verre ; et que
ces boutons fe trouvent au contraire aux furfaces inferieures du vif
argent quand on fe fert d’un baton de cire d Eipagne ou de tout-
fre. Mais felon moi e’eft tout ce qu’on en peut conclure. Voila
comme je raifonnerois, fi j’avois envie de difputer contre Mr.
Wilfon. II eft facile de concevoir, que, quand un fluide (et fur
tout un fluide elaftique, ou dont les parties fe repouflent rnutu-
ellement) fort d’un corps, le fluide, dis-je, doit etre plus denie
proche de la furface d’ou il fort, que la, ou il trouve plus de li-
berte de fe repandre. La furface done, proche de la quelle la
lumiere electrique eft la plus vive, doit etre celle, de la quelle fort
le fluide, qui caufe ces apparences lumineufes.

Ces raifonneinens, n’ont ils pas autant de probabilite, que
ceux de Mr. Wilfon ? Mais ne prouvent-ils pas direaement le
contraire de ce que Mr. Wilfon a avance ? Nc prouvent-ils pas,
dis-je, que l’elearicite reiineufe eft la meme que la pofltive, et
la vitree la meme que la negative ?

Pour dire le vrai, le raifonnement dont je me fuis fervi, me
femble prefque avoir plus de vraifemblance, que celui de Mi.
Wilfon. Il eft inconteftable, que la matiere elearique entretres
librement, et fans eprouver une refiftance confiderable dans les
metaux et autres corps non eleariques, comme je le prouve-
rai clairement tout a l’heure. Le raifonnement de Mr. ilfon
femble, par confequent, etre fonde fur une hypothefe gratuit-e-
inent admife, favoir, que la matiere elearique s’accumule a la
furface du vif argent, parce qu'elle n’y peut entrer librement.

Je ne pretends pourtant pas prouver par tout cela, qu elieaivc-
ment l’elearicite refineufe foit la meme que la poiitivc, et la vi-
tree au contraire la meme que la negative. Mon unique but eli-
de faire comprendre, que cette hypothefe eft au moms aufli pro,
bable, que celle, pour laquelle Mr. Wilfon s eft declare.

4

“ conceive

[ 439 ]

“ conceive that when an elaflic fluid iflues from a
“ body (as from the quickfilver in the bent tube) it
“ willbedenfer at the furface from whence it iflues,
“ than it is where it finds more liberty to expand
“ itlelf. And therefore the furface near which
“ the electric light is the brightefl, fhouldbe that
“ fr°m whence the fluid iflues, which caufes thofe
“ luminous appearances.”

This reafoning appears intirely new to me, and
I am at a lofs to comprehend why an elaflic fluid
confined witnin a tube, whofe fides are fuppofed
parallel, will be denfer at the furface of a body from
whence it iflues, than in any other part; fince its
expanfive force muft in that cafe be limitted by the
fides thereof. As you have not given any particular
experiment to prove what you afl'ert in this cafe,
you will therefore give me leave to differ from you
in opinion. If, as you fay, there is really more
liberty^ for an elaflic fluid to expand in any other
part or the exhaufted tube, than at the furface it-
felf, you muft produce fome evidence in favour of
that opinion, before it can be admitted. On the
othei hand, I fhould have thought, if all rejijlance is
fuppofed to be removed from within the tube, the
liberty, for the fluid to expand itfelf, will be equal
m every part; reckoning from the furface of one
column of quickfilver through the whole void,
to the furface of the other column of quick-
filver.

A.s I am for fupporting this opinion, let us exa-
mine it more particularly, and attend only to the
appearances which glafs affords in certain circum-
ftances : becaufe when the direction of the fluid,

fr 1 1 2 caufed

5

[ 44° ]

can fed by glafs, is once traced, that which is cauled
by wax, amber, or refin, follows of courfe. The
eieCtric fluid, when it is emitted from any fmooth
lurfaceof metal without edges, cr angles, appears,
in certain circumflances, to ilfue from all parts of that
lurface equally. This fact, I apprehend, is fo well
eifablilhed that it needs no further proof

Now the column of quickfilver being confined
.by the fides of the glafs, which are fuppofed par-
allel, the top of the quickfilver will anfwer to
the fmooth lurface defcribed. The eleCtric fluid
therefore that is to pals from it, into the void fpace,
which is of the fame diameter with the column of
quickfilver, will move forward within the hollow
of the tube to the next, column of quickfilver.
And lince no refiflance is fuppofed to be within any
part of the vacuum, there can be no caufe for any
accumulation : confequently when the fluid is fuf-
fered to pals along the tube, the appearance ought
to be the fame at the furfaces, that it is in every
part of the void fpace. But by my experiment
there is a greater quantity of light feen at the le~
cond lurface of the quickfilver, than in any other
part, (when polifhed glafs electrifies the firfl: co-
lumn) and that this light which appears fo denfe,
extends itfelf about one tenth of an inch from the
furface. Whereas the light extending all along the
intermediate hollow of the tube, appears to be
much thinner, and rarer, and of an uniform
denfity. I conclude therefore that this luminous
accumulation at the fecond furface is caufed by a
rejijlance exerted at, or near, the furface ol the
quickfilver ; when the eledtric fluid, ifluing from

[ 44i ]

the glafs that eledrifies it, is pufliing forward to
enter the fecond column of quickfilver.

At the time I related this experiment with the
bent tube in the letter to Dr. Heberden , I omitted
certain phenomena, which attended the experi-
ment, greatly favouring the dodrine here advanced.
If when glafs is eledrified, and applyed to the firft
column, we buffer the eledric fluid to pafs along
the tube in fmall quantities only, and at fhort in-
tervals, little luminous dreams will be feen to
move from the firft to the 2d column of quick-
filver, and confequently from the glafs. The like
appearances happen, but in a contrary diredion,
when refin or amber is made ufe of, and applyed to
the fame column. Glafs therefore eledrifies plus ;
or fills bodies with more of this fluid than belongs to
them naturally: and refin, &c. vice verfa.

When you fay, your reafoning appears to have as
much probability as mine, I believe you do not in-
clude your obfervation, that the eledric fluid enters
with great freedom, and without any confiderable re-
finance , into metals and other non-eledric bodies. Be-
caufe the words any conjider able refinance, imply jotne
rejijlance, which is all that is contended for: and
a very fmall rejijlance willoccafion very extraordinary
appearances, as I fhall be able to fhew by and by.
There is no occafion to trouble you. with any further
arguments to prove this rejijlance • of which your-
felf feem to entertain no doubt ; and the accumulation
caufed by the rejijlance is evident.

In

[ 442 J

In yourfecond remark, refpe&ing the impermeability
ofglafs, you fay you agree with Mr. Franklin * as to

the

* Je me tourne vers un autre objet, fur leque], il me femble,
que Mr. Wilfon a eu envie de favoir mon fentiment. C’eft la
queftion de 1’impermeabilite du verre. On peut bien favoir par
mon livre: Tentamen Theoriae Eleftricitatis et Magnetifmi , ce que
j’en penfe, et que bien que je tombe d’accord avec Mr. Franck-
iin, de l’exiftence de cette impermeabilite, je differe pourtant
beaucoup de lui, par rapport a plufieurs autres points. II ne fe-
roit done pas a la verite neceffaire, d’expofer ici de nouveau mon
fentiment, neanmoins je me charge de ce travail, pour ne laifTer
rien a defirer a ceux qui liront ce recueil.

Qu’on fufpende un fil de fer ou d’archal, quelque Jong qu’il
foit, a des fils de fo ye, et qu’on en eledrife un bout par le moy
en d’un tuyeau de verre, ou d’un baton de cire d’efpagne. Dans
moins d’un clein d’oeil non feulement le bout qu’on eledrife,
devient eledrique, mais aufii le fil entier le fera d’un bout a l’au-
tre, et le fera partout egalement. Qu’on touche apres 1’un des
bouts, et l’eledricite fera detruite dans tout le fil, d’un bout a
1’autre, avec la meme viteffe, qu’elle avoit ete produite.

Qu’on fufpende au contraire de la meme fa<pon un tube de ver-
re bien fee, ou un cilindre de cire d’efpagne ou de fouffre, et
qu’on le traite de la meme maniere. Le fucces en fera tout a fait
different. Ce n’eft pas le cilindre entier, qui devient alors elec-
trique dans un inftant, mais feulement une partie de la longueur
de quelques pouces, ou d’un pied tout au plus, acquiert cette
force, et il faut travailler fort long terns, fi on veut amener les
chofes, au point d’en rendre eledrique une partie d’une lon-
gueur un peu confiderable. Qu’on touche apres la partie eled-
rifee du tuyeau, et l’eledricite ne fera detruite, ni dans un in-
ftant, ni dans le tuyeau entier, comme dans l’experience prece-
dente. Au contraire, encore que l’endroit touche perde fon
eledricite, il n’en fera de meme, des parties tout proches, qui
conferveront plutot leur eledricite pendant fort long terns.

J’en tire la conclufion : que la matiere eleftrique , traverfe les
metauxou d' autres corps non eleftriques et fe dijlribue en eux fort fa~
Ailement et fort rapidiment , ?nais qu’au contraire elle pajje par le
verre , la are d’efpagne , et d’ autres corps eleflriques par eux mernes
haucoup plus dijficilement et plus lentement . Cette regie ne doit

pas

[ 443 ]

the exigence of this impermeability, though you
differ from him in many other points : and refer to
your Eflay upon the Theory of magnetifm and electri-
city. ^ ou then relate two experiments, one with a
wire, and the other with a glafs tube, or cylinder of
wax: and obferve that the firfl may be eafily elect-
rified, and the latter alfo, though with great diffi-
culty, to any confiderable length. You then draw
this conclulion from the two experiments, that the
eleCtric matter pervades metals and other non-eleCt-
ric bodies, and expands itfelf in them with the great-
eft eafe and rapidity. But that on the contrary it
pafes through glafs, wax, and other eleCtric bodies,
more fowly and with much greater difficulty.

This conclufion, inftead of eflablifhing the im-
permeability of glafs, moft evidently affirms the con-
trary : for though, according to your obfervation,
the fluid pafles more fowly and with much greater
difficulty through glafs than iron ; your admitting
that it does pafs at all through the glafs , ends the
difpute, as to the point of permeability : and at the
fame time efablijhes my doCtrine of reffance ; at lead
in glafs, and reflnous fubflances.

In regard to my experiments upon the Tourmalin,
you fay * that the firfl; and fecond correfpond with your

difccverics.

pas etre prife pour une hypothefe. C’eft une loi, prife immediate-
ment et d une maniere inconteftable, de l’expericnce.

Cette propriete des corps eledtriques par eux memes, eft felon
yroi lameme que celle, queFrancklin a appellee d’un autre nom,
impermeability. Au rnoins, je ne fais confifter Fimpermeabiliie
en rien autre chofe, qu’en cela.

* Je viens aux experiences de Mr. Wilfon. La premiere et
la feconde s’accordent tout a fait avec mes decouvertes. 11 n’en

L 1 1 4 cii

C 444 1

difcoveries; but that thofe from the 3d to the 8th
do not agree with your notions and experience : and

then

eft pas de meme, de celles qui fuivent, depuis la troifieme
jufqu’a la huitieme, qui demandent d’etre difcutees avec plusde
loin.

J’ai etabli comme une loi conftante, de l’ele&ricite de la
Tourmaline : £{ue cette pierre ejl toujour s dans /’ etat contraire {c'ef d
dire , que fon cote pofitif, \ ejl negativement elettrique , et le cote negatif
V eft poftivement) quand un de fes cotes, quel qu it foi,, ef plus chaud
que l' autre ; et quelle no ret our ne dans fon etat naturel, qu'apres que la
chaleur s’ eft diftribuee uniformement en elle. Par les experiences de
Mr. Wilfon au contraire, il fautetablir une regie tout a fait diffe-
rente, favoir : j -due la Toarma!iner quand elle chaujfee inegalement,
des deux cotes , a l' ef pec e d' eleftricite qui ejl naturelle au cote le plus
chaud ( c'ejl d dire , que la Tourmaline ejl pofitivement eleflrique des deux
cote's, quand c'ejl le cote pofitif , qui ef le plus chaud ; et qu' elle l'e/1
negativement , quand c'ejl le cote negatif, qui ef le plus chaud ) mais
qu' elle retourne dans fon etat nature l, quand la chaleur s' ejl repandue
uniformement. Cette regie ne s’accorde en aucune fa^on avec celle
que j’avois avancee.

Encore que je fuffe tout a fait convaincu de la jufteffe de mes
affertions,et de leur parfaite conformite avec l’experience,je ne pou-
vois pourtant que fort difficilement me refoudre, a douter de Pex-
actitude des experiences faites par un aufli habile Obfervateur, que
Mr. Wilfon. J’ai done mieux aime fuppofer, qu’l y avoit, dans
la maniere, dont Mr. Wilfon et moi avions procede dans ces ex-
periences, quelque difference, qui put etre la caufe de la difference
qui fe trouve dans nos refultats. Je croyois a la verite de trouver
facilement une circonftance fur la quelle on put fonder quelque
foupcon. C’cft que moi j’avois toujours pofe la Tourmaline , ou
fur un charbon ardent, ou fur une plaque de metal ou de verre
echauffee, de fa^on, que l’un des cotes de la pierre, avoit toujours
touche a quelque corps. Mr. Wilfon au contraire, en echauf-
fant la Tourmaline , y a precede tellement que la pierre n’a jamais
touche a quelque corps. Voilaune circonftance, qui icmble affez
importante, pour avoir pu caufer une difference, fenfible. C etoit
a Pexperience d’en decider.

Celt

L 445 ]

tnen declare that you have eftablifhed this, as acon-
ibnt law, namely, that the Tour malm is always in
an inver ted flats ; that is, its plus Jide is elefirifed mi-
nus and the minus Jids plus , whenever either op the tides
p hotter than the other .* and that it does not return to
its natural Hate, until the heat is diftributed uniformly
therein. My experiments on the contrary, you ob-
its ve, lead one to lay down a rule intirely different,
viz. That the Tourmalin, when its Jides are une-
qually heated, exhibits the Jpecies of elefiricity which is
natural to the hotter fide, that is, the Tourmalin is
plus on bothfdes , when the plus fide is the hotter 3 and
tmnus on both Jides , when the minus jide is fo: but that
it returns to its natural Hate aifo, when the heat is uni-
formly diftributed. To account for thefe different opi-
nions, you think it more agreeable to fuppofe fome dif-
ference in our methods of making the experiments, than
to queftion the fads I have declared. Accordingly you
obfeive one cucumfiance which would naturally rive
rife to fuch a fufpicion. And then tell us, that you
always placed the Tourmalin upon burning coals, or
upon a plate of metal, or heated glafs: fo that one
fide of xhzjlone was always in contact with fome (non
define) body. That I, on the contrary, in heating

C’eft die qui me force et m’autorife a declarer, que la reele
que j ai avancee, eftla feule, qui lui foit conforme. J’ai echaufte
la Tourmaline de la meme inaniere que Mr. Wilfon, et j’ai pris
garde, qu elle ne touchat a rien, mais pour le refultat, je l’ai,
non obftant cela, toujours trouve conforme a ma regie, et tas une
fade fois a celle de Mr. Wilfon. P

Je le repete encore ; il m’eft extremement difficile, de fuppofer,
que Mr. Wilfon foit tombe ici dans une meprife, neanmoins je
uus convaincu, que de ma part, il n’y a allurement, aucunefaute.
Ainlije ne fais qu’en juger.

Vol. LIU.

M mm

the

[ 446 ]

the Tourmalin , never differed it to be in contact with

any ( non elebtric ) body.

Here, fay you, is a circumffancethat feems ofcon-
iequence enough to caufe a fenfible difference; and then
you appeal to the experiment which is to decide it:
adding at the fame time, it is experiment that obliges
and authorizes you to declare , that the rule advanced
by you , is the only one that agrees therewith. Now
your experiment tells us no more, than that you
heated the Tourmalin in my manner, taking care
(as you exprefs it) that it was in contadt with nothing.
But notwithffanding this, that you have always found
the event agreeable to your rule , and not one Jingle time
to mine.

From your defcription of this experiment, your
exadt method of making it does not appear. I am
inclined tobelieve fome material circumffance has been
omitted in the method ; or thatour apparatus’s are effen-
tially different; (though you feem to have had a regard
to fome of the neceffary requifftes for making the
experiment properly:) otherwife, I cannot appre-
hend why you were not able to fucceed : becaufe
the experiment always anfwers with me. Perhaps
the difference in the fize of our Tourmalins may
have contributed towards caufing the different effedts.
The Tourmalins I employed in the experiments with
the fame , are above Jive times larger than yours : and
muff therefore require a longer time in heating. Now
the degree of heat given to my large Tourmalins ,
was much below that of boiling water; and there-
fore I fupedt, that the fmall Tourmalins , you em-
ployed, were made hotter ; whereas they ought to

have

[ 447 ]

have been at the moft, but about blood warm. For
jlnce a difference of heat , between the two Jides , is ab~
folutely neceffary , it is of importance that this difference
be incrcajed as much, and as feuddenly , as the nature
of the circumjlances will admit.

Jf you follow this rule, I apprehend you will be
more likely to fucceed : but that you may be the bet-
ter enabled to make my experiments aofwer, it may
not be amifs to relate them again in the manner they
were lately repeated, and frequently, with two different
‘Tourmalins , before feveral members of the Royal-
Society of London , who are well acquainted with en-
quiries of this kind.

EXPERIMENT.

After the convex fide of the Tourmalin ( b , fig. r.
Tab. XXII.) has been held for a fhort time, about
one tenth of an inch, from the flame of a candle,
both fides thereof are elettrified plus: and con-
tinue fo for half a minute or more. And in a
fhort time after, the fame Tourmalin , without being
heated a frefh, or difturbed by any other caufe than
that of the air furrounding, returns to its natural Rate ;
as you have called it; that is, th z plain fide changes to
minus, and the convex fide remains plus. Thefe appear-
ances continue whilffc the Tourmalin is cooling.

Upon heating the Tourmalin again, as before, ex-
cepting that the plain fide was now next the flame,
both fides thereof were ele&rified minus : and conti-
nued fo, for half a minute or more ; and in a fhort

Mmm 2 time

C 44$ ]

time after, the fame Tourmalin , without being heated
afrefh, or didurbed by any other caufe but that of
the air furrounding, returned to its natural date again;
that is, the convex fide changed to plus , and the plain
Jide remained minus.

One of the Tourmalins that were employed in thefe
experiments, ( marked b ) belongs to Dr. Heberden , and
is the fame I formerly made ufe of: but the larged of them
was put into my poffeffion by the favour of Dr. Morton
Secretary to the Royal-Society, of London , who re-
ceived it, with feverai others, from Mr. Loton F. R. S.
late governor of the Illand of Cylon. This done
weighed about one hundred and eighty grains: but
the form thereof not being the mod favourable for
experiments, I had permifiion to fafhion it into fuch
fnape as would anfwer the purpofe bed. For this end,
alterations were made therein ; and at, one time, the
eledtric poles (if they may be fo called) were pretty
near in the longed direction of the done, and at
another time, in the fhorted. Thefe trials terminated
in the form and fize, nearly, as reprefented by the
letter fig. 2 : and the direction of the poles is now
in the fhorted line that can be drawn between any of
the oppolite fides.

I have to obferve, that when this Tourmalin is held
between the eye and the light, and viewed in the
diredfion though which the eledtrie fluid is found to
pafs, irappears ot a darker colour confiderably, than
when it is viewed at right angles to the former direc-
tion. This appearance obtains in many other Tour-
malins , efpecially if they happen to be as conveniently
fhaped.

In

d

1

y

>•

= - ll

[ 449 3

In regard to the other experiments with th cheated
iron, and Tourmalin, which you have only hinted at,
it is enough to recommend the utmoft care, to avoid
the leaft degree of fridtion ; and the iron itfelf mull
be fo managed, that there may be as eafy an elefiric
communication with the air, from it, as the fame of
a candle is found to have.

Give me leave, in this place, to make fome obferva-
tions on the apparatus you have made ufe of in thefe
experiments, as it does not in my opinion, feem the
bell calculated for fuch nice purpofes ; at leaft in our
climate, which is certainly more moift than yours.

The inftrument firft defcribed, * confifts of a bal-
lance 12 inches long, fixed upon a fmall ftand ; from
one arm of which, that moves upon a hinge, is fuf-
pended,, by a filk. ftring, a fmall cork ball : but there is.

* Le premier de ces inftrumens eft reprefente par la Fig, I.
Sur un pied quarre A B. je fis drefter un baton C D. environ
d’un pied de hauteur. Ce baton avoit au haut une charniere
pres de D. au moien de laquelle le levier a bras egaux F G. .
etoit un peu mobile. Chaque bras de ce levier F D. et D G.
avoit la longueur de 7. pouces a peu pres. J’employai cet in-
ftrument pour pouvoir fufpendre. commodement le pendule HI..
Le levier F G. etoit un peu mobile, afin de pouvoir au befoiiVi
haufler, ou baifler un peu le pendule.. Pour faire le pendule H I.,
je pris un fil de foie crue, j’y attachai par le bas un petit morceau,
de liege arrondi de la grofleur a peu pres d'unelintille. La long-
ueur du fil FI I. etoit de 5 a 6. pouces environ, et j’attdchai le
pendule avec de de la cire a' m des bras du levier F G. Sur un,
autre petit pied quarre MN, qui eft reprefente dans la Fig. II.
je mis dans le milieu un tub ; mince de verre O P, a peu pres de
6. pouces de longueur, don. le haut fe terminoit dans un hemif-
phere O R, de deuxlignes environ. II eft tres-facile de faire ce
tube en foufflant une petite boule de verre, comme on fait en
faifant un Thermometre, et en brifantenfuite cette boule jusque’a
la moitie. Je me fers /ans les experiences de cet inftrument
pour y pofer la Tiurme.me, afin qu’elle puifle agir librement.

no »

[ 45° ]

no mention of what the ftand or ballance is made ;
though a difference in the materials will, I apprehend,
make fome difference in the experiment. And if
the cork is, as you fay, theflze of a pea , it will be a
confiderable objection with me : and the more fo, if it is
to be moiftened with water. For the force employed
to move it, in fome of my experiments, is too incon-
fiderable. And I fhould imagine the ballance itfelf
could not be very nicely adjufled ; becaufe fuch an in-
creafe in the weight of the cork, by moiftening it (as
you fay) from time to time, ought to make it not
only preponderate, but unfteady ; as an evaporation
of the moifture is conftantly making fome alteration
in the weight. My apparatus contrived for the fame
purpofes, hath already been defcribed, except that
part of it which refpeds the lize. of the pith balls,
and each of thefeare about the thirtieth part of a pea .
This fmallnefs, neverthelefs, does not require any moif-
ture to retain the eledric fluid, as the balls communicate
with the fineft flaxen threads, and the threads with a
flender piece of wood, about one inch long, and the
greater part one tenth of an inch thick; with the angles
rounded off, and polifhed. This is fixed upon the end
of a cylinder of amber, properly fupported. But that
there may be no miftake in the conftrudion thereof,
I have given a drawing and defcription of the one
I ufe at prefent, fee fig. 2. When I at any time want
to examine the ftate of the Tourmalin , it is brought
flowly towards the eledrified balls in an horizontal
diredion.

Your glafs ftand feems liable to an objedion, unlefs
the air be extreamly dry : becaufe the mere breath-
ing, if not properly guarded againft, in very delicate

experi-

C 451 ]

experiments, is fufficient to caufe an unfavourable
alteration j by the moifture condenfing upon it.

We are not told of what materials your pincers *
were made, but I fuppofeof fomeeledric fubftance;
otherwifein removing the Tourmalin from time to
time, they may interrupt the experiment, by conduc-
ing away the fluid. And even fuppofing them made
of an eledtric fubftance, the unavoidable fridion may
poflibly difturb the experiment. I have therefore
always preferred a different method, which will ap-
pear prefently.

I fhall now comply with the promife I made in
the beginning of this letter, to acquaint you with
fome Ample and interefting experiments upon the
Tourmalin: moft of them were made during the
froA in Nov. laft, in confequence of an appearance
which I then obferved accidentally.

With me it has been always found moft conveni-
ent to flx the Tourmalin at the end oj a long flick ofl
the hardefl kind of Sealing-Wax , and when I am not
ufing it, to put the other end into the top of a can-
dleftick, or other fuitable ft and ; that the [tone may
be the lefs expofed to any kind of fridion (See fig I.)
And it is a rule with me never to take hold of the
Sealing-wax, or even to touch it, but by ihat end
(d ) the fartheft from the Tourmalin. One day on

* J’emploie encore de petites pincettes ABC, pour ne pas
toucher la Tourmaline avec les doigts, er je la prens toujours par
les cotes, comme il eft indique dans la Fig. III. afinque la pierre
foit touchee le moins qu’il eft poffible par des corps non eledri-
ques. II faut encore avoir un Tube de verre et un baton de cire
d’Efpagne tout prets, pour qu’on puifle examiner de la maniere
que nous decrivons plus bas l’elpece d’Eledtricite produite par la
Tourmaline ,

removing

C 452 ]

removing the 'Tourmalin into another room, to repeat
the experiments we have here been treating of, I
obferved it was electrified, j though no caufe for its
being fo then appeared : the friction arifing from the
air, in fuch circumftances, being not fufficient to pro-
duce that effedt. And I muff here take notice, that
many months before this fadt was afcertained, I fre-
quently fufpedted the like appearance : but it happened
at thole times that the effedts were fo uncertain, and
appeared fo accidental, that I did not think they de-
lerved attention -j-.

In tracing out the caufe of this appearance, it feem-
ed molt necelfary to obferve the changes in the air
with refpedt to warmth : for, it is well known, thofe
changes caufe manifeft alterations in the expanfion and
contraction of bodies.

EXPERIMENT I.

In a room with a fouth afpedt, and where no fire
had been for fometime, Farh. Therm, flood at 42.
The Tourmalin was in the fame room, and had con-
tinued there fome hours, undiflurbed, without fhew-
ing any figns of eledlricity. On removing the Tour-
malin into a warm room carefully, and the Therm.
along with it, in lefs than 3 minutes (the Therm.
having rifen to 47) the convex fide of the (lone fhewed

f N. B. The experiments upon the Tourmalin , by Mr. Epi-
nus, which refpedt the heating and cooling of its Tides equally ,
when occafioned by violent and artificial means , are, it is apprehend-
ed, very different from the ten following experiments ; tho’ they
alfo refpedt an equal heating and cooling of the {tone ; becaufe
the degree of heat employed, is not only cxtreamly different, but
the means of obtaining it, is fo likewife. The one being natural
and the other artificial

a minus

[ 453 ]

a minus , and the plain fide a plus , electricity. Thefe
figns increafed for a time, and then decreafed, till they
entirely difappeared. When this happened, the 'Tour-
malin appeared to be of the fame temper, in refpeCt
to warmth, with the room; and the Therm, was
raifed to 58.

The fame degree of warmth, or nearly fo, was
continued in the room for thirty minutes and more,
without caufing any alteration; for the Tourmalin
afforded no ele&ric appearance whatfoever.

EXPERIMENT II.

I then removed the Tourmalin with the Therm .
into the cold room and with equal care *. The fione ,

fome little time after, fhewed figns of electricity again :
but then, thofe figns were contrary to what had been
obferved before. For, in this cafe, the convex fide was
plus , and th t plain fide minus, in nearly the fame time ;
and thefe figns encreafed alfo for a time, and then
decreafed, till they entirely vanifhed. When that
happened, the j tone appeared alfo of the fame temper,
in refpeCt to coldnefs, with the room. And the
Therm, was fallen to about 420. During half an
hour, or more, after that time, the Tourmalin fhew-
ed no eleCtric figns whatfoever, nor did the Therm .
fall any lower.

* It is indifferent which fide of the Tourmalin is moved
foremoft, provided it be done Jlowly.

Vol. LIII,

Nnn

EX PE-

[ 454 ]

EXPERIMENT III.

Not content with this laft difcovery, I removed the
Tourmalin and Therm, into the open air. In about
three minutes, the Therm, having fallen from 42 to 3 9,
the Tourmalin was eledrified again, in the fame man-
ner as in the lad experiment. But when the eledric
figns difappeared, the Tourmalin and the air were
in this cafe alio of an equal temper: at which time
the Therm, had fallen to 34. The (lone was con-
tinued in the open air for half an hour or more, but
no further eledric figns appeared.

0

EXPERIMENT IV.

On returning into the room where the firft experiment
was made, the eledric figns were Wronger than in any
of the preceding trials, and contrary to the two laft }
for the convex fide was minus , and the plain fide plust
which agrees with the appearances in the firft ex-
periment.

EXPERIMENT V.

When the Therm, fhewed the ftate of the out-
ward air to be confiderably lefs warm, than what an-
fwers to the degree at which water is fixed, the fame
changes happened, by carrying the Tourmalin from
it, into a room, where the Quickfilver ftood at 34:
and afterwards, from thence, back again into'the open
air.

Sir

[ 455 ]

Sir Ifaac Newton carried two Thermometers , pro-
perly prepared, out of a cold place into a warm one,
in order to fhew that the warmth was conveyed
through the vacuum , by the vibrations of a much
fubtiler medium than the air : and had thefe laft ex-
periments upon the Tourmalin at that time been
known to him, he mull have been agreeably furprifed
to find them tending fo ftrongly to efiablifh the ex-
i fiance of that fubtile medium This dodrine re-
ceives a further confirmation from the experiments
that follow.

EXPERIMENT VI.

About the middle of this month, December, the
wind being full fouth, and the air loaded with a thick
fogg, which you know is the worft of weather for
eledric experiments, thd Tourmalin afforded the fame
appearances as before, by removing it from one room to
another j and even into the open vapourous air j not-
withftanding the unfavourable feafon : but then, the
appearances were weaker.

EXPERIMENT VII.

In the mofi wet feafon, and during frequent heavy
fhowers of rain, I repeated the firft, fecond, third, and
fourth experiments. And though the eledric power
was not very firong, yet they always fucceeded fo well
as to afcertain the fads.

* See Newton, Opt. page, 323.

EX-

Nnn 2

C 456 ]

EXPERIMENT VIII.

After being acquainted with the preceding expe-
riments, you will not wonder that the Tourmalin
afforded the fame appearances on removing it, in the
open dry air, from the fun-fhme into the {hade ;
and again, from the (hade into the fun-fhine.

If thefe fmall differences, in the degrees of warmth,
are capable of caufing fuch appearances ; well may
the greater differences; and flich more particularly as
Mr .Brawn and yourfelf have experienced in freezing
of Quick- filver : and therefore I cannot now agree with
you in calling that the natural Jlate of the Tourmalin ,
which arij'es from the heat given it by boiling water .

EXPERIMENT IX.

It appears by the preceding experiments, that when
the Tourmalin was of the fame temper with the air
in the different rooms, there were no electric figns to
beobferved. From which we may underftand, if
the heat of the air fhould be increased, even beyond
that of boiling water, a Tourmalin expofed therein
for a time, would afford no eledtric figns ; that is,
whilft the flone continues of the fame temper with
the air. I have lately caufed the heat of the air to be
increafed, in a convenient room, beyond the degree of
vital heat, even to 108 : and then placed two Tour-
malins, in the fame room, very near the Thermometer ,
without being able to obferve any eledtric effedts ; that
is, after they had remained therein a {hort time.

E X-

C 45 7 ]

EXPERIMENT X.

Upon a very nice examination, and during Tome fa-
vourable opportunities, I have obferved the Tourmalin
to be feebly electrified r, when the Therm, varied , up or
down only one degree.

The fmallnefs of the force here required to caufe
thofe manifeft effects, and even them by natural means
only, is a new difeovery, and, perhaps, deferves the
attention of philofophers.

In my firft and fecond letters upon the Tourmalin ,
there are experiments that give us affurances of a
flux and reflux of the eledric fluid, or aether > at different
times, even without artificial means to occafion it. And
I did not fcruple to advance that dodrine, as appears
from a paflage in the opticks which I quoted in the
fecond letter, fomewhat favouring the fame opinion.
This you fee has happened to be a right conjedure ; for
thefe laft experiments, are I apprehend, fo clear and
fatisfadory, that there is no room left for a doubt about
it. And I do hope they will lead to fome ufefui
difeoveries. For thefe forces, however fmall they may
appear, are probably fufficient to anfwer very great
purpofes in nature.

Upon confidering the effeds which heat and cold
occafion in the Tourmalin , it may not be improper
here to obferve, that all bodies we are acquainted with,
are dilated by heat, and contracted by cold : and when
they acquire the fame temper with the air, whether
it be hot or cold, the fame flate of dilatation, or con-
tradion, continues unaltered.

The

[ 45'5 ]

The 1 1 ourmaltn we find, when uniformly aiffurb-
ed on ail Tides, by changing the temperature of the
air ; is not only electrified, but Thews two oppofite
and contrary effeCts. That is, in pafiing from a great,
to a lefs, degree of warmth, it is ele&rified in one
manner ; and in pafiing from a lefs to a greater de-
gree of warmth, it is electrified in another manner;
which evidently (hews, that there is lome power , be-
longing to the (lone, which is differently affeCted by
fuch contraction and dilatation. The fame thing appears
from other different effeCts it affords, when its two fides
are equally warm. But the ‘ Tourmalin , affording no
eleCtric appearance whatever, when the whole mafs
is of the fame temper with the air, agrees with the
obfervation that all bodies ceafe in that l late , to con-
tract or dilate : and is a manifeft indication, that the
fluid , which caules thefe eleCtirc appearances, is in fuch
circumftances, in equilibria ; and muff ever remain
fo, unlefs difturbed by violence.

The importance of this laff obfervation befpeaks
your attention, as it greatly tends to throw more light
upon this curious fubjedt.

From the experiment with the bent tube, menti-
oned in the former part of this letter, it was proved,
that there is a refljlance exerted at, or near, the furface
of the Quickfilver where the light is accumulated.
This refljlance , which I apprehend is effential to all
bodies, merits a further illuftration ; becaufe the elec-
tric phenomena in general greatly depend upon it.

When a bladder is well blown up, and fecured
properly, it will yeild or give way, and change its
form, in that part againff which any given preffure is

exci ted .

[ 459 ]

exerted. And upon removing the preflure, the bladder
will immediately recover its firft form.

This yielding or giving way of the form, and then
aftei wai ds i ecovering it, proves an elaftic fubftance ex-
ifting within the bladder, and between the two lides
where the preflure is employed.

In like manner when two glafs prifms, or the ob-
jedt glaffes of two long Tellelcopes prefs upon each
othei with their own weight only, philofophers know,
by the phenomena of light, that they do not touch :
and that there mu ft be Something between the glafles
lo keep them at a diftance. T. hey alfo know, by the
like phenomena, that more prefting is required to
bring them nearer to a contad 3 and that when the
preflure is removed, they immediately recover their
firft diftance.

Now this yeilding or giving way, and the recovery
of the diftance between the glafles, proves the ex-
istence or fome elajlic fubftance between them ref-
pedively. Since we find the effeds of applying, and

removing, the preflure, exadly fimilar to the cafe with
the bladder.

Hence it is evident that the fame elaftic fubftance
or medium caufes prifms, and convex glafles, when
prefled againft each other, to exhibit feveral rings
of different colours 3 by having its denfity vari-
ed : and that it occafions all bodies to ad upon
light at a diftance, by refleding, refrading, and
infleding it 3 and light [to ad upon bodies, at a
diftance, by caufing a motion of their parts, and
heating them.

This is the medium then which gives rife to the reftft -
ance found inelefflric experiments.

For

[ 460 ]

For when a quantity of the eleCtric fluid is forced into
the apparatus , which fupports the two balls, we fhould
from its elaftic principle, expeCt it to pafs out again
immediately: whereas the faCt is, that it paffesoutby
flow degrees ; and takes a confiderable time in eva-
cuating the apparatus effectually. Some power there-
fore muft hinder the fluid, at leaft, in fome meafure,
from efcaping : and that power mull be exerted at, or
near, the furface of the body.

To fay it is detained by an attraction of the body,
will not anfwer the purpofe : for the power which is
fuppofed to draw the fluid into it, muft certainly be
fufficient to hinder it from pafling out. Now by the
experiment, the fluid does pafs out, though flowly :
this power therefore, which reflfts its pafling out, can
be no other than what arifes from the medium we have
proved to be fpread upon the furfaces of bodies.

The evidence in favour of this doCtrine is greatly
flrengthened by the following experiments, the three
firft of which, are well known to eleCtric en-
quirers.

When glafs is properly electrified, and held over
the wooden part of the apparatus (c) at the diftance
of fix or eight inches, and there continued for a time,
the balls are feparated to a confiderable diftance.

But upon taking away the glafs, the feparation is
at an end, and there are no eleCtric figns remaining
in the balls.

Thefe appearances therefore argue, that no part of
the eleCtric fluid, appertaining to the excited glafs,
pafled from it into the wood. And that the caufe,
which ohftruCted its paflage, is a refinance , exerted at
or near, the furface of the wood : becaufe we know,
from a variety of experiments, that the repujfive power

5 of

[46i]

of this fluid ads at great diftances, and in grofs bo-
dies particularly ; without the fluid being able to en-
ter them. There can then be no doubt that the re-
paration of the balls, in the prefent circumftances,
entirely depends upon this repulfwe power ; which
drives the natural quantity of the fluid belonging to
the wood, or part of it at leaft, towards the balls.
And though the repulfive power is fuflicient to force
the fluid from the wood into the balls, and there oc-
caflon the effeds of a plus eledricity, (as is found
upon tryal j) * yet the experiment fhews, it is not fuf-
ficient, in the fame circumftances, to force it out of

them, as they ceafe to be eledrified on removing the
power. °

. lf this ^ not the cafe, and the fluid from the glafs
is fuppofed to enter to the wood j I would afk, why
the balls do not retain the fluid, or at ieaft fome part
of it, and continue feparated when the glafs is taken
away ? It would be unphilofophical to fay, the glafs
adually fuffered a quantity of the eledric fluid to pafs
from it, into the wood and balls j and then, on re-
moving the glafs, that it took it away again j or at-
traded it back : becaufe when the fame glafs is
brought near enough to the wood, the balls will be
eledrified, and feparated fo effedually, as to continue
in that ftate of fepaiation, after the glafs is removed i
which pi oves clearly, that the repulfive power is not
only great enough to overcome the refinance of the
balls ; but even to force out fome part of the fluid
contained therein : therefore in this cafe the balls are
eledrified minus. And this minus may be increafed,

* For the proof of this, fee the Eflay by Dr. Hoadly and my-
felf, page 13. J

VOL. LIU.

O 0 o

by

[ 4^2 ]

by bringing the power gradually nearer, and then re-
moving it quickly.

We may then veryjuflly conclude, that this repara-
tion of the balls, is occafioned by the expanfive power
of the electric fluid, or ather> crowding from without ,
and through the air, to enter the bails, and reflore the
equilibrium . And in like manner that the plus electri-
city caufes a reparation of the balls in confequence
of the fame electric fluid, or cether , crowding from
within to get out of the balls, and palling through
a like quantity of air, in order to reflore the equili-
brium ; for the fame medium which appertains to the fur-
faces of bodies , mufi reff the exit and entrance equally :
and therefore the one cafe will be always the converfe
of the other.

We have feen that on bringing the electrified glafs
near enough to the wood, the balls are electrified mi-
nus. If now the circumflances are changed, by
bringing the fame glafs conjiderably nearer to the wood,
and much quicker, the balls are electrified plus and
continue fo for a confiderable time after the glafs is
removed : which is the ftrongeft confirmation that
this effect entirely depends upon the ref fiance of the
wood being overcome, and the electric fluid entering
the apparatus, by the nearer approach of the glafs.

There are then two different methods of caufing
a plus appearance in the balls. The one, we find, de-
pends upon an actual enterance of the fluid, from the
glafs, into the wood, 6tc. And the other upon a quan-
tity of the fluid, originally in the wood, being forced

* The glafs in this experiment mull not only be brought
quickly towards the wood, but it mull likewife be removed from

it as fuddenly.

2

from

[ 463 ]

from it into the balls, by the repulfive power of the
fluid appertaining to the excited glafs.

In thefe experiments we alfo learn, that when the
glafs is held neater to the wood, than in the minus t
and farther from it than in the plus appearance of the
firfl experiment, it does not produce any eledric figns
whatever in the balls. Which fliews a kind of ba-
lance fubfifting between the power of the glafs, and
the ref fiance of the wood, &c. For, if we deviate the
leaf! on either fide from this intermediate diflance,
eledric effeds, of the one kind or other, immediately
take place.

I fhall produce another experiment in favour of
thefe forces, and of the ballance obtaining between
them, in certain circumflances. In the experiment I
am about to mention, it is neceffary, firfl to eledrify
the wood and balls; by properly rubbing that end
of the fealing-wax, amber, or glafs, to which they
are affixed.

You know then, that, if we touch the balls with
the hand, we immediatly uneledrify them, and the
wood; but not the amber : and that thefe balls with
the wood, will continue uneledrified. But if I blow
ever fo gently again/ t that part of the amber which is
eleCt rifedy the balls will be feparated to a conjiderable
dijiance , and continue in that date. On the other
hand, if the amber has not been rubbed , no electricity
can be produced by the fame force of blowings or even
by a blafl fix or eight times greater : but if the blaflis
confiderably increafed, the amber will be eledrified*.
By which it appears that in the firfl cafe, the eledric
power in the amber receives fuch an additional force from

* See the letter to Dr. Heberdcn, page 332,

O 0 0 2

the

C 464 ]

the flight fri Elion of the breath , as enables it to de-
Aroy the ballance and overcome the ref fiance at the
Jurface of the wood, in that part, where it is joined to
the amber.

Th t Leyden experiment depends alio upon a certain
ballance , which obtains between the mediums at the
oppoiite furfaces of the glafs, by the power of re-
pulfion * : but this enquiry, being of a very exten-
flve nature, would lead me too far for the bulinefs
of a letter ; I mud therefore refer you to the works
quoted laA. In feleddng the experiments above re-
lated to prove ref fiance, I have purpofely confined

myfelf to a few, and thofe fucli as appeared to be the
mod Ample and mod worthy of attention. You
will therefore do me the honor to examine, and
confider carefully thefe experiments and obfervations,
as I think they have fufficiently eflablijhed a ref (lance
appertaining to bodies, independent of the grofs
matter they contain : and that it arifes from the fame
elajhc medium which we before proved to exift
between the convex glafies.

London Dec. 20, 1763. I am, &c.

B. Wilfon.

* The confideration of this experiment was particularly at-
tended to, in a former work, by Dr. Hoadly and myfelf. Sec
alfo the Phil. Tranf. Vol. LI. Part II. and Pages 898, 899.

Expla-

[ 465 ]

Explanation of Fig. 1. Tab. XXII.

a, b , Two ’Tourmalins fixed upon
c. c. Sticks of the hardefi kind of fealing-wax.
d > dy Two handles of wood, in which the other
ends of the fealing-wax are fecured.

J, f A hand of wood, with holes to reft the han-
dles therein, when the Tourmalins are unem-
ployed.

Explanation of Fig. 2. Tab.XXIIL

a> a> Two very fmall balls of the pith of Elder,
fufpended by

by by The finefi flaxen threads about fix inches long-
The balls and threads together weigh about the
fiftieth part of a grain.

Thele threads are neatly faflened in a fmall
hole on the under fide of the thin end, and fo as
to touch the wood

Cy Which is mahogany. Every part of this
fmall piece of wood is well polifhed, and neatly
joined to *-

dy the cylinder of amber; which is about four
inches long, and near half an inch thick. It is
finely polifhed alfo, and the other end Hides
into

<?, which is part of the arm : e is joined to f by a
fcrew ; and the other end of
f Hides into the upper part of the Hand g. One
end of the upright h fcrews on to g, and the
other end, into the crofs pieces/, /, and kk ;
which are let into each other by a mortafs, and

thus

[ 466 ]

thus fecured. The whole apparatus takes to
pieces eafily, for the conveniency of packing up
in a cafe fix inches and half long.

The ftand is made of Cocoa-tree, without
angles, or edges, and well polifhed.

The fize of my apparatus is about twice as
large as the drawing before you.

LV. A

[ 467 ]

LV. A Dtfcourfe on the Parallax of the
Sun. . By the Rev. Thomas Hornfby, M. A.
Savilian Profeffor of AJlronomy in the Uni-
verfty of Oxford, and F. R. S.

— — - ***Yv/A vuiiw i-'vjiii ivJ LliC

theory and Prac^ica^ Part °f aftronomy, that every
method of determining it hath been employed by the
aftronomers of every age. Mr. Flamfleed informs
us, in the 9 2d and 96th numbers of the Philofophi-
cal Tranfadhons, that from fome obfervations made
upon the planet Mars, he had found the Sun’s paral-
lax not to exceed 10 feconds ; and Dr. Halley, in a
memoir written exprefsly with a view to afcertain the
exadt quantity of it, , fuppofes it not to be greater than .

12 a"?

When we confider the imperfedt date of'aftrono-
my at the Ume when Mr. Horrox lived, we cannot
iumciently admire the wonderful genius of that youn?
gentleman, who at the age of 24 could colledt from
his own obfervations, that the parallax of the Sun
did not exceed 14 feconds; while many celebrated
aftronomers, whole tables were then in the greateft
repute, had afhgned a parallax of more than two
minutes to the Sun, which Kepler had fuppofed could
not be lefs than 59 feconds, and which Hevelius, who ’
pubhfhed the admirable treatife of Mr. Horrox, in—
titled, Venus in Sole vifa, fixed at 4 1 feconds.

HE quantity of the Sun’s parallax
is of fuch importance both to the

[ 4^3 ]

In the year 1719, Dr. Pound and his nephew,
that illuStrious aitronomer, Mr. Bradley, did, when
Mars was in opposition to the Sun, demonstrate (to
uie the words of Dr. Halley, Phil. Tranf. N°. 366,
p. 1 14.) the extreme minutenefs of the Sun’s paral-
lax, and that it was not more than 1 2", nor lefs than
9", upon many repeated trials. At the fame time and
by the fame kind of obfervations Mr. Maraldi deter-
mined this parallax to be 10 the refult of his ob-
fervations agreeing exactly with thofe deduced from
the correspondent obfervations by Mr. Richer at Cay-
enne and by Mr. Caffini at Paris in the year 1672.

The voyage which the Abbe de la Caille undertook,
to perfect a catalogue of Some of the principal fixt
Stars, furnished the aflronomers with the means of
determining the Sun’s parallax by corresponding alti-
tudes of the planets Mars and Venus, to be oblerved
on each fide of the equator, with all the accuracy of
which that method is capable. The aflronomers
here in Europe were invited to determine the distances
of the planets from particular Stars on Stated days,
while the Abbe himfelf propofed to make the corres-
ponding obfervations on the fouthernmoSt part ot
Africa at the Cape of Good Hope. By the differences
of the altitudes of the northern limb of Mars and
of fuch Stars as were nearly in the fame parallel ob-
ferved on the fame day at the Cape with a lextant of
6 f. radius ; at Greenwich by Dr. Bradley with a
mural quadrant of 8 f. ; at Bologna in Italy by M.
Zanotti with a fimilar instrument of 5k; at the Royal
Obfervatory at Paris by Meflieurs Cafhni de Thury
and Gentil with a moveable quadrant of 6 f. *, and in
Sweden by Meffieurs Wargentiri, Stronmer and

Schem-

[ 469 ]

Schemmark, with telefcopes of 7 and 8f. armed with
micrometers, it was found, when every reduction is
made, that, according to each obfervation, the dates
of which are given below, the horizontal parallax of
the Sun, when at its mean diftance from the earth,
was as is reprefented in the following table.

Greenu

ich.

Bologna.

1

Pa

ris.

Stockholm.

Up

"al.

Herno

fand.

1 75 1 *

//

1751.

//

1751.

//

1 75 1 *

//

1 75 r •

//

1751.

//

Aug. - - 30
Sept. - - 13

14

oa. . . 3

4

‘+9

9. 677
9- 3M
9> 096

10, i6j
10, 504

9. SM
10, 961

Aug. 31
Sept. 1

*3

14

0£t4- 7

9> 753
9> 89S
9. 97i
10, 238
11,075

Sept. 13
+ 24

oa. 8

9> *34
9. 7*5
11, 912

9> 895

Sept. 1
25

Oa.4.3

5

6

10, 466
10, 504
12, 864
10, 085
9> 735

Sept. 2

+ 24

25

oa. 6

9»438

12,255

9> 7 r5
9. 134

Sept. 25
27

9. 933

10, 61S

M can of all
Mean rej. -j-

9> 89!
9, 712

10, 186
9,964

10, 164
9, 5S1

10, 734
10, 202

10, 135
9,421

I0> *75

By taking a mean of all the obfervations, it follows
that the Sun’s mean horizontal parallax is 1 o", 2 ;
and if we rejedt the obfervations which differ moft in
excefs from the reft, the mean will give 9,842 for
the Sun’s mean horizontal parallax.

Befides thefe 27 determinations, the Abbe de la
Caille compared 41 obfervations, the mean of which
is given in the following table.

N°of

Obf.

7

6

3

6

12

7

Obfervations.

The late M. Cafiini and M. Maraldi
Mr. Delifle — at the Hotel de Glugny
Father Beraud

M. M. Garipuy and d’Arquier
M. Sabatelli and Father Carcani
M. Bofe

Mean of all obferv. according to A. Caille
Mean of Refults (rejetting the 2d)

Vol. UII.

Inftruments.

| Places.

0 Par.

Quadrant 2 f, rad.

jThury

8, 9^2.

Mur. circle 2 f.

'Paris •f

II, 5 3*

Refr, tel. 7 f.

Lyons

9, 020

Ditto.

Touloufe

8, 944

Quad. 4f. diag. div.

Naples

9- 933

Tel. of 6 and 8 f.

Wittemberg

ro. 9Q9
IO, 210

9> 575

Few

Ppp

[ 47° ]

Few obfervations of Venus near the inferior con-
junction with the Sun on OCr. 31. 1751 were made,
on account of the unfavourable weather here in Eu-
rope. By an obfervation made at Greenwich on OCt.
25, the mean horizontal parallax was 9", 8 ; but
according to the obfervation made at Paris on the fame
day at the Royal Obfervatory, that parallax was
1 1 ",4. On OCt. 27, by an obfervation made at
Paris, the © ’s mean horizontal parallax was 9^,8 5 ;
but by an obfervation at Bologna on the fame day it

was found to be By the obfervation at

Paris on Nov. 17, the Sun’s mean parallax was 10", 5.
By a mean of all the obfervations of Venus, the
Sun’s mean parallax is 10^,38 ; and if we rejeCt
the Paris oblervation on OCt. 25, that parallax is

io'v,i3*.

We fee then that,according to thefe obfervations, the
Sun’s mean horizontal parallax is not lefs than 8", 94.
If we take a mean of the whole, that quantity is
10,09: But if we rejeCt the obfervations that differ
moff in excefs, the Sun’s mean horizontal parallax will
be found to be 9^,92 a determination in which every
affronomer might readily acquiefce, when he con-
fiders the accuracy of the obfervers and the nice
agreement of almoft all the obfervations.

And fuch was the ftateof the Sun’s parallax as de-
duced from the lateft and beff obfervations, when
the approaching tranfit of Venus in 1761 engaged
the attention of the curious of all nations. Dr. Hal-
ley, in Philofophical TranfaCtions, N°. 348, had pro-
pofed a method of determining the Sun’s parallax

* See the Abbe de la Caille’s Introduction to- his Ephemerides
Celeftes from 1765 to 1774.

by

C 471 ]

by procuring obfervations to be made upon this tranf-
it in fuch places where the difference or time between,
the ingrefs and egreis would be the greateft poffible;
namely near the mouth of the Ganges, where the Sun
would be vertical at the middle of the tranfit, and
at Port-Nelfon in Hudfon’s-Bay, where the planet
would enter upon the Sun’s difk about the time of Sun-
let, and leave itfoon after Sun-riling; for in the former
place, fays Dr. Halley, the planet would be equally
diftant from noon both at ingrefs and egreis, and the
apparent motion of Venus upon the Sun would be ac-
celerated by almoft double the quantity of the horizon-
tal paiallax of Venus from the Sun : becaufe Venus is
at that time retrograde, and moves in a direction con-
trary to that of the eye of an obferver upon the earth’s
fu trace. Whereas in Hudfon’s-Bay, under an oppolite
meridian, the eye of an obferver will be carried, while
the Sun feems to move under the pole from fetting to
rifing, in a diredion contrary to the motion of the ob-
ferver s eye at the Ganges ; that is, in the direction of
the planet s retrograde motion from eaft to weft . — From
thefe conftderations, and fuppofingwithDr. Halley the
axis of the planet’s path to be inclined to the axis of the
equator in an angle of 20. 1 8' only, the interval between
the two contacts would have been 15'. 10" longer in
Hud foil’s Bay than at the mouth of the Ganges.

But upon examination the cafe is found to be fome-
what different. T. he axis of the equator on the 6th
of June 1761 rrtade an angle of 6° io' with the axis
of the ecliptic on one fide, and the axis of the planet’s
path an angle of 8°. 30'. 10" on the other; the
axis of the planet’s path therefore made an angle with
the equator of 140. 40'. 10", — The planet’s latitude
was 5 4. minutes greater both from obfervation and

i"PP 2 the

[ +72 ]

the Do&or’s own tables, than he had fuppofed in his cal-
culation made from the Rodolphine tables corrected :
and therefore the planet’s egrefs could not have been
obferved at Port Nelfon. Having made a computa-
tion for a place in North America fituated $h. 3 o' to
the weft of Greenwich, and in the 60th degree of
latitude -} and alfo for a place to the eaft of Ganges,
and 6h. 30' to the eaft of Greenwich in the latitude
of 220. 42' north, that the places might be nearly
lituated in the fame circumftances with the mouth of
the Ganges and Port Nelfon, I find that the interval
between the two contacts would be but 4.'. 56"
longer in America than in the Eaft Indies, fuppoling
the Sun’s parallax 12A5, and the inclination of
Venus’s path 14°. 40' to the equator.

And here perhaps it may not be altogether unnecef-
fary to enquire how far the miftake which Dr. Hal-
ley committed, by ufing the difference of the two an-
gles inftead of their fum, would influence the times
of the tranfit as feen at Ganges and Port Nelfon.
For this purpofe I made ufe of the fame elements
which Dr. Halley has given in his paper, and calcu-
lated the angle of the vertical with the orbit of Venus
at the two internal contacts at both places, fuppoling
the orbit to be inclined firft only 2°. 1 8' to the equa-
tor, agreably to Dr. Halley’s fuppofition, and alfo
1 40. 40'. and I found that the duration would be
15'. 13" longer at Hudfon’s-Bay than at the Ganges
upon the firft fuppofition ; and 14'. 44", if the circles
be duly inclined to each other ; the difference being
only 29 feconds. It has already been found by cal-
culation, fuppoling the latitude of Venus to be about
9 4 minutes, that the difference of duration at the
two places would have been only 4'. 56" t It may

[ 473 ]

fairly therefore be concluded that the tranfpofition of
the circles contributed very little towards giving fo
different a refult, the reafon of which need not here
be mentioned; and Dr. Halley feems to have been
led into the miftake entirely from fuppofing the lati-
tude of Venus to be about 4'. o" according to the
tables, which he then ufed, conftruCted upon the
principle that the nodes of that planet were fixed.—
Having determined that the difference of duration
at the two places above mentioned would be 1 . 10"

(differing only 3" from the method I ufed which is
independent of projection) the DoCtor proceeds to
fhew, that if Venus had no latitude at the time of
the middle of the tranfit, the difference would be
1 S'. 40"; and if the planet fliould pafs 4/.o// to the
north of the Sun’s center, that difference would be
21'. 40", and would become If ill greater, if the
planet s north latitude fhoukl be farther increafed.
And fuch would have been the event, had the mo-
tion of the nodes been progreffive. But, agreably to
the principles of univerfal attraction, their motion is
really retrograde, and this Dr. Halley fays he himfelf
fufpeCted, lit ob nuperas quafdam obfervationes fujpicio
eft. And therefore it is fomewhat furprifing that he
did not determine by calculation what would have
been the difference in the whole duration between
the two places, if Venus fhould pafs more to the
fouthwardof the Sun’s center, then he had fuppofed.
He would then immediately have perceived that the
two ftations were not fo advantageoufly placed, as the
folution of the problem required;

Obfervers were therefore to be fentto other places,
in order to determine the Sun’s parallax agreeably to
the method propofed by Dr. Halley. The city of

Tobolfki

. f 474 j

1 obolird in Siberia is fo fituated, that the interval be-
tween tne two contacts was perhaps as fliort as could
poffibly be obferved on any part of the earth’s fur-
face; to this place was fent the Abbe Chappe d’Au-
teroches, one ot the French aftronomers. Near Hud-
Ion s Bay and in '6oJ ot latitude the duration would
have been 5 minutes longer, fuppofing the Sun’s par-
allax — 9". xAt Eencoolen, where it was firft propofed
to fend Mels. Malon and Dixon, the difference
would have been about 4 4 minutes. At the ifland
of Rodrigues, where Mr. Pingre could onlyobferve
the lad internal contact, the difference would have
been about 7 4 minutes. On the fouthern coafl of
New-Holland, it would have been fomewhat more
than 10 minutes. And in the great Indian Ocean,
under 1154 of abfolute longitude from the I lie of
Ferro and in 57° of fouth latitude, where the begin-
ing of the tranfit would happen foon after Sun-rif-
ing, and the end juft before Sun-fet, the difference
would amount to 13 4 minutes. The greateft differ-
ence between the interval of the two internal contacts,
as determined by actual obfervation on the 6th of
June, was 2h 49", 75, a quantity hardly fufficient to
determine the Sun’s parallax agreeably to the method
propofed by Dr. Halley.

I have however made the neceffary calculations,
and compared the duration of the tranfit obferved at
feveral places with the duration as obferved at To-
bolfki. The parallax refulting from each obfervation
is contained in the following table, in which the 3d
column contains the obferved duration, the 4th the
difference of each obferved duration; the next con-
tains that difference as deduced by computation upon
a fuppofition that the Sun’s parallax is 9". In the

laft

[ 475 ]

Iaft column is given the horizontal parallax on the day

° j e tranfit, refulting from a comparifon of the Ath
and 5th columns.

PI

aces.

Tobol flu
Cajaneburg
Tornea0
T ornea°
Upfal
Upfal
Upfal
Hernofand
Abo

Stockholm

Stockholm

Calcutta

Madrafs

Obfervers.

Abbe Chappe
Mr.Planmann
Hellant
Lagerborn
Bergman
Mallet
Stromer
Giller
Juftander
Wargentin

Obferved

duration.

Klingenfiiern 5
Magee
Hirft

48 53^5

49 54

50 c9

50 2 1
50 26
50 o7
50 02
50 26
50 09
50 45
50 42

50 3i

51 43

Difference offDifferenceby iSun’s Paral-
obferv’ddur. calculation. lax.

//

00, 75
*5,75
27, 75
32,75

r3» 75
08, 75

32.75
J5, 75

51.75
48, 75

37.75

49.75

00, 88
05, 27

05, 27

33, 78
33, 78

33, 78
25, 76

20, 68

34, 21
34,2i
37, 02
39, 50

Mean of the whole -

Meanp ejeding 2 obfervations at Upfal and 1 at Tornea-

8, 980
10, 444
fl2, C98

8, 901
t 7,077
t G 597

9, 733

8, 450

ro, 675
10, 389

9, 067

9, 577

9, 332
9,579

The duration at Cajaneburg was the fhorteft ex-
cept at Tobolfkij with which if we compare the du-
ration obferved at Madrafs the parallax is 9", 948 :
and by taking a mean of the parallax deduced from
a comparifon of the obfervation at Madrafs with

thofe of Tobollki and Cajaneburg, the parallax
is 9 ,762. r

The obfervations at the above places agree as well
together as can be expeded from fuch lmall differ-
ences in the duration, which mud: in fome meafure
be influenced by the neceffary and unavoidable errors
in obfervation.

If

C 476 ]

If the quantity of the fun’s diameter, and the lead
didance of the centers were very exadtiy known,
tha Sun’s parallax might fafely be determined by
comparing the duration of the tranfit as obferved at
different places with the duration as fuppcfed to be
ieen from the earth’s center. According to this me-
thod, fuppofmg the lead didance of the centers to be
9'. 29" 4-, which is a mean between the Greenwich
Shirburn and Paris obfervations, and the difference of
the femidiameters of the Sun and Venus— 9 1 6", 4,
the duration as obferved at Tobolfki was more than
10 minutes fhorter than if feen without parallax; at
Tornea0, at Stockholm, at Cajanehurg, at Adracan,
and indeed in almod every part of Europe and Alia,
the duration was conliderably Shortened ; and if a
number of good obfervations made in feveral of thofe
parts were procured, the Quantity of the Sun’s,
parallax might be well enough afcertained, as the
difference in duration for a difference of one fecond
in the Sun’s parallax will be found very confi-
derable.

Tho’ this method fhould not be pradtifed, unlefs
the neceffary requifites for the computation be known
with fome degree of precifion, I have ventured to
compare the durations obferved chiefly in the north-
ern parts of Europe, and fome in Ada, with the du-
ration, as feen from the earth’s center, — 5h. 59'. 1 9", 1 o
mean time, or 5 h. 59'. 1 6", 64 apparent time, and cal-
culated from the elements above mentioned.

Places

Places,

1

Obferved durati-
ons.

Ml ]

Duration withou
parallax.

Difference 0
durations.

Differ,
for i"o]
parallax.

Sun's par-
allax.

Tobolfki - -
Cajaneburg -
Tornea0 - -

Tornea0 - -
Abo - - -

Upfal - *.
Upfal .. - -

Upfal - - -

Hernofand -
Stockholm -
Stockholm -
Calcutta - -
.Madrafs - -

h

5 48 53 25

5 49 54
5 50 09
5 50 21
5 50 09
5 50 26
5 5° 07
5 50 02

5 50 26
5 5° 42
5 50 45
5 50 36
S 5i 43

h

5 59 *6, 64

/ //

10 23,39

9 22, 64

9 *7, 6 4

8 55,64

9 07, 64

8 50, 64

9 °9, 64
9 15,64
8 50, 64
8 34, 64
8 31,64
8 40, 64
7 33,64

//

64, 09
57, 32

5<A 83
56, 83

55> 12

53,67
53,67
53,67
53, 65
53, 62
53, 62

53,3i
f6, 36I

9, 726

9,815

9,636
9,425
9,935
9,888
10, 241
10, 352
9, 890
9,579
9,523
9, 769
9,785

N. B. The 4th column contains the difference be-
tween the obferved and calculated duration ; in the
5th is given the difference in the duration for a dif-
ference of 1" in the o ’s parallax, and the 6th column
is obtained by dividing the 4th by the 5th.

The mean of all the refults is 9", 8 12: and if
we rejed two of the obfervations at Upfal, which dif-
fer rnoft in excefs, the Sun’s parallax is 9^,724,
agreeing very nearly with the quantity refulting from
a companion of Ibrne of the obferved durations with
the fhorteft obferved at Tobolfki and Cajaneburg.

We may alfo proceed to find the Sun’s parallax by
means of the lead diftance of the centers as obferved
in two or more places where the effed of parallax
was contrary ; or if the leaft diftance of the centers
was only determined at one place, it may be found
by calculation at any other place, where the total du-
ration was obferved. But in this and the laft cafe the
elements of calculation are required with fo rigorous
Vol. LIII. Q q q an

[ 47§ ]

exadlnefs, that perhaps thefe methods are only to be
called in to illuftrate and confirm the others.

Mr. Pingre confined himfelf principally to the de-
termination of the lead: diftance of the centers. At
2 i h.43'. 1 1" he found the diftance between the neareft
limbs of Venus and the Sun to be the greateft
— $7" ,2. or 5' .57" ,4 when corre&ed by refrac-

tion. This diftance being fubtrafted from 15'. 19'', 5
the difference of the Semidiameters, leaves 9'. 22", 1
for the leaft apparent diftance of the centers. But as
that obfervation was made rather too late, when the
diftance of the centers was greater than it ought to
be, he found by calculation that it fhould be dimi-
niftied by o",22. The true apparent leaft diftance
of the centers by actual obfervation was therefore
9'. 21", 88. In order to be more fecure of this re-
fult, Mr. Pingre compared a large number of ob-
ferved diftances, both at the beginning and towards
the middle of the tranfit, with the diftance deter-
mined by internal contadt, and after excluding every
doubtful obfervation, he found the leaft apparent
diftance of the centers to be 9'. 2 1", 69. By com-
paring this diftance with the diftance deduced from
the total duration as obferved at any place (the me-
thod of finding which he has given at large in his
memoir inferted in the Memoirs of the academy
of fciences for 1761) and by knowing from cal-
culation what influence a parallax of 10" for inftance
would have upon thofe diftances, he found the Sun s
parallax as in the following table.

Places

[ 479 ]

Places.

Obferved dura-
tions.

L.diflance ofl
centers from
the durati-
ons.

L>. diftance

deducedfrom

calculation.

Sun’s pa-
rallax.

h

/ //

/ //

/ //

//

Tobol fki - - - - -

<s\

OC

Ln

IaJ

N>

Lri

9 5U53

9 52, 24

10, 125

Stockholm - - -

5 50 43> 5

9 54,85

9 55, 83

10,03

Upfal ------

5 50 26

9 55, 62

9 55,95

10,23

Cajaneburg - - - -

5 49 54

9 55, 61

9 55, 61

10, 00

Tornea0 - - - - -

5 50 09

9 55, 28

9 5b, 08

0

0

0

— <

By taking a mean of thefe determinations, we find
the Sun’s parallax to be io",i. In the above calcu-
lations the Sun’s femi-diameter was fuppofed =
i5/.48//,5, and that of Venus 29''. Obfervers,
fays Mr. Pingre, have found the former to be about
2" lefs, and the latter on the contrary half a fecond
larger. By calculating upon the l'uppofition of a
difference of 2" in the difference of the femidiameters
of the Sun and Venus, the lead: diftance of the cen-
ters at Tobolfki, Stockholm, Upfal, Tornea0, and Caja-
neburg, ought to be 3", 12 lefs, and at Rodrigues
2", 56 or 2//,6o, and the Sun’s horizontal parallax
ought alfo to be o'\iy lefs. If then this correction
be admitted, which is warranted by the beft obfer-
vations, the Sun’s horizontal parallax will be
9//,92.

There is ffill another method by which we are
enabled to determine the Sun’s parallax, by compar-
ing the obfervations made in different places where
the effedt of parallax upon the planet is confiderable
at the times of the two contadts. It was more con-
venient to make ufe of the 2d internal contadt for
this purpofe, and the obfervers were very advantage-
oufiy ftationed at St. Helena and the Cape of Good

q 2 Hope :

[ 48o ]

Hope : for by comparing the obfervations made there
with thofe at Tornea0, Tobolfki, and in fome of the
Eaftern parts of Alia, the difference of the times of
the contacts when reduced to the fame meridian will
be found to be very confiderable, amounting to more
than 9 ^minutes at the two firft places above mention-
ed, and being greater, as the places are farther litu-
ated to the North-Eaff But if this method be uled,
it is abfolutely neceffary that the longitudes of the
places Ihould be determined with the utmoft accuracy,
iince an error of a few feconds would have a confi-
derable influence upon the refult, and would increafe
or diminifh the quantity of the Sun’s parallax, in pro-
portion. The unfavourable flate of the heavens at
the time of the internal contadt prevented the Rev.
Mr. Mafkelyne from making an obfervation at the
Iile of St. Helena ; which is the more to be lamented
as his obfervation would have confirmed or corredted
the obfervation at the Cape, if neceffary ; fince the
effedt of parallax at both places would have been
very nearly the fame. The obfervers at the Cape
were more fortunate, and differed only 4/' in their
obfervation of the internal contadf . — But before we
proceed to deduce the quantity of the Sun’s parallax,
by comparing as well the obfervation made at Green-
wich as thofe at other places, with the obfervation at
the Cape, it will be neceffary to lay before the reader
the authorities upon which the longitude of each
place has been determined.

The longitude of the Cape of Good-Hope was
not even nearly known till the Abbe de la Caille
went thither in the year 1751. By a companion of
9 eclipfes of Jupiter’s fatellites as well immer lions as
emerlions obferved at the Cape with the correfpond-

ing

C 481 ]

ing obfervations made at Paris, the Cape was found
by the Abbe de la Caille himfelf to be to

the E aft of Paris, or ih.i 3 '.3 1" to the Eaft of Green-
wich. Mafon and Dixon obferved many

eclipfes of Jupiter’s Satellites at the Cape, but the
weather was not fo favourable here in England.
However by comparing four obfervations made in Sur-
ry-Street and one at Greenwich with thofe made at
the Cape, the difference of longitude at a mean is
found to be ih.i3'.2 8' , which I have ufed in the fol-
lowing computations.

The internal contact, as reduced from fiderial to
appaient time by Mr. Mafon, happened at
2lh-3 9'-52"- — But upon examination it will be
found to have happened later : for whether we make
ufe of the Sun’s mean R. afcenfion from the bed: folar
tables extant* or the Sun’s apparent R. afcenfion
reduced to the meridian of the place as determined
by adtual obfervation on the day of the tranfit, the
true apparent time of the contaft will be found to have

happened at 2ih2g'.^4. or at 2 \L if the

time by the Ear Antare.s be ufed, wbofe fituation was
more favourable to an oblerver in 340. of South lati-
tude. I fhall therefore fuppofe the internal contact to
have happened at 2iI\39/.52// by taking a mean of
the two obfervations

The Royal Obfervatory at Paris was fuppofed by
Sir Ifaac Newton, in his Principia, to be g'.2o" to
the Eaft of Greenwich. And the editor of Dr. Hal-

* Mr. Mafon, before heleftEngland, acknowledged, inalettcr
to me, that he had committed a miftake in his calculation, by
iorgetting to apply to the Sun’s place the equation of pneceffion,
which on the clay of the tranfit amounted to 15A6.

1 ley’s

[ 482 ]

lev’s tables has followed that determination, which
has alfo been generally ufed by the Englith Aftrono-
mers. — The French Aftronomers have till very lately
imagined the difference of meridians to be 9'. i° •
as deduced from a fingle obfervation of an eclipie o
Jupiter’ s firft fatellite made by Mr. Caffini when m
London, with a telefcope of fimilar fize and con-
ftru&ion with that ufed at Paris when the lame eclipie
was obferved. — In the year 1734 Mr. Maraldi pub-
lilhed a comparifon of 33 eclipfes obferved at Green-
wich by Mr. Flamfteed, and at Paris by the French
Aftronomers, 19 of which are immerfions, and the
reft emerfions. The longitudes refulting from each
correlpondent obfervation differ widely from each
other, the two obfervatories being n'.2j" diftantby
an immerfton of the 2d fatellite, and only 7 43 bY
an emerfion of the firft. But if we take a mean of

the whole, the difference of longitude will be 9 .24 ;

and if we exclude the obfervation of the 2d fatellite
above mentioned, which muft be very faulty, the dif-
ference of meridians will be g'. 22", arefult which in
all probability is but a very few feconds from the truth.

• It may be obferved that the immerfions all give the
difference of longitude too great, and almoft all the
emerfions too little j a circumftance owing either to
the badnefs of the air here in England, or to an in-
equality in the goodnefs of the telefcopes, or per-
haps to both ; for whatever was the advantage in ob-
ferving the immerfions, was ballanced by the emer-
iions : for which reafon whenever the eclipfes ot Ju-
piter’s fateliites are ufed, the longitude Ihouid, it potii-
ble be deduced both from immerfions and emerfions.

As the obfervations of tranfits of Mercury may be
very ufeful in fettling the longitudes of places which

[ 483 ]

are not far diflan t, I have examined the feveral obfer-
vations that I can meet with made at Paris, and either
immediately at Greenwich or in fuch parts of London
whofe longitude from Greenwich is known within one
fecond of time. And the refult of fuch companions
is as follows.

On the 29th of Odlober 1723 Dr. Halley obferved
thefirft interior contact of the limbs of Mercury and
the Sun at 2h. 42/.26// apparent time at Greenwich.
The Rev. Mr. Profeffor Bradley obferved the fame
at 2h.42/.38//, at Wanfled in Effex (io" to theEaft of
Greenwich) or at 2h.42/.28// when reduced to the
meridian of Greenwich. Mr. Graham in Fleetflreet
obferved the fame at 2h.42/.i9//, or at 2h>42/.44//,
when reduced to Greenwich. The mean of thefe
is 2h.42/. 32", 7. In the obfervatory at Paris Mr.
Maraldi obferved the fame at 2h.5i/>48// apparent
time j and Mr. Delifle at 2h.5i/.37'/, but fufpedts it
might have been fome few feconds later. I will
fuppofe it to have happened at 2h. 51'. 43", 5.
The difference of meridians therefore is 9'. 10", 8.
If we take a mean of Dr. Halley’s and Mr. Bradley’s
obfervations only, the difference of meridians is
9'- 1 b'^-

Inthe year 1736 Dr. Bevis obferved the laft con-
tacts of the limbs of Mercury and the Sun at
oh 8/-33// at Greenwich. The fame was obferved
at Paris by M. Maraldi and M. Cafftni de Thury, and
at Thury by Mr. Caflini, at oh. 18' 05", 5 by a mean
of the three obfervations. The difference of longi-
tude therefore is 9/.32//,5.

In the year 1743 the laft internal contadl of the
limbs was obferved by Mr. Graham in Fleetflreet at
ih.o/.42//, and by Dr. Bevis at Beaufort-Buildings in

the

[ 4«4 ]

the Strand at ih.o/>33// : or by a mean of both when
reduced to the meridian of Greenwich at ih. l'.o^/f —
The fame was obferved by the Abbe de la Caille, by
Meff. Maraldi, Monnier, and Caffini the fon, at Paris,
and by Mr. Caffini at Thury : which obfervations,
whenreduced to the meridian of the Royal Obier-
vatory, give ih.io".i 5", 5 for the time of the internal
contad: the difference of meridians is therefore

9'. 12". 5. By a mean of the obfervations of Mr.

Graham and Dr. Bevis when reduced to Greenwich,
the laft external contact on the lame day happened
at \h.2f .4.2" . and by a mean of the obfervations in
France the fame happened there at 1 h. 1 2'. 1 o". The
difference of longitude therefore is g'.zS". N B. No
obfervations were made of this traniit at the Royal
Obfervatory at Greenwich, on account of clouds.

In the year 1753 was another tranfit of Mercury,
when the unfavourable date of the heavens a few fe-
conds before the time of the internal contact prevented
any obfervations from being made at Greenwich, as
appears from a paper communicated to me by the ex-
ecutors of the late Dr. Bradley. Both contacts however
were luckily very well obferved, by Mr.Short, Dr. Bevis
and Mr. Bird; by a mean of whofe obfervations reduced
to the meridian of Greenwich the internal contact
happened at ioh. 9'. 27"^>5‘ The fame contad was
obferved by 13 obfervers at Paris, and was found not
to happen fooner than ioh.i 8'. 36", nor later than
ioh.i9/.o3//. But by a mean of all at ioh.i B/-45/'.
The difference of meridians therefore is 9'. 07", 5.
By a mean of the obfervations of Mr. Short, Dr.
Bevis, Mr. Bird, Mr. Canton, and Mr. Silfon, all re-
duced to the meridian of Greenwich, the external

con tad

[ 485 ]

contact happened at iob.i2'. 17", 5. and at the Royal
Obfervatory, by a mean of all the obfervations at Paris,
at ioh.2i'.33'/. The difference of longitude therefore
is 9k 15", 5. And if we take a mean of thefe 7 re-
fults, the Royal Obfervatory at Paris will be found to
be 9'. 1 7" 4. to the Eaft of the Royal Obfervatory at
Greenwich, a determination very nearly agreeing with
that mentioned by Sir Ifaac Newton, and which, I
believe, was deduced from a companion of Dr. Hal-
ley’s and Mr. Caffini’s obfervations.

The Abbe de la Caille, in his memoire on the par-
allax of the Moon, fuppofes the difference of meri-
dians to be g'.iy" tho’ he has not mentioned from
what authority he drew that conclufion. I fhalL
therefore fuppofe the difference of meridians to be
9 /-17 /- — The laft internal contadt was oblerved at
Paris by Mr. de la Lande at 20h.28/ 25" or 26" ; at
2oh.28/.26// by Father Clouet, and by Mr. Maraldi
and Mr. Barros feparatelyat 2oh.28/.42 Mr. Pin-
gre, in a very curious memoire on the Sun’s parallax
already referred to, fuppofes the internal contacft to
have happened at Paris at 2oh.28'.38//. 1 fhall

therefore make ufe of the Abbe de la Caille’s obferva-
tion at 2oh. 28k 37" 4.

The difference of meridians between Paris and
Stockholm, fays Mr. Wargentin, is i*».2'.5i"or 52" at
moff. Mr. de la Lande from a comparifon of 17
obfervations of the firft fatellite of Jupiter made from
1750 to 1759 and communicated to him by Mr.
Wargentin, determines the difference of longitude
to be ih.3'.ro". And the Abbe de la Caille, in his
memoire on the Moon’s parallax, fuppofes it to be
ih.3'.i3". As thefe two laft determinations agree fo
pearly together, I fhall fuppofe Stockholm to be

R r r

[ 486 ]

ih.3/.io''/ to the Eaft of Paris, and ih. to the
E aft of Greenwich; and the laft internal contact to
have happened at 2 ih.3o/.o9//,5, which is a mean
between the obfervations of Meff. Wargentin and
Klingenftiern.

The City of Cajaneburg in Sweden is 38'. 40" to
the Eaft of Stockholm, according to very late obferva-
tions 5 and therefore Cajaneburg is ih.5i'.o7" to the
Eaft of Greenwich. The 2d internal contad hap-
pened at 22h-7/.59//, when the error in writing down
the minutes is corrected according to the inftrudion
given in Philofophical Tranladions, for 1761, p. 23 1.
Indeed (fuppofing the longitude of Cajaneburg as
above fet down to be exad) it is very eafy to prove
that the error of one minute was made at the egrefs
rather than at the ingrefs.

The City of Tobolfki in Siberia (according to the
obfervation of the end of the folar eclipfe on June 3d
by Mr. Chappe and Mr. Planmann at Cajaneburg and
calculated by Mr. Pingre) is 2h.42/.i 1 " to the Eaft of
Cajaneburg; and this determination is alfo confirmed
by Mr. Wargentin’s obfervation of the fame phafe.
Tobolfki therefore is 4h.33/.i8// to the Eaft of Green-
wich : and I fuppofe Mr. Chappe to have obferved
the laft internal contad at oh-49/.23// 4., without
making any allowance for the luminous ring which
appeared round Venus in his telefcope.

The Obfervatory at Upfal (according to Mr. War-
gentin in the Philofophical Tranfadions) is iW.io"
to the Eaft of Paris, and is therefore ih.io'.27'' to
the Eaft of Greenwich. By taking a mean of the
three obfervations made there, the internal contad
happened at 2lh.28/.o6//.

Tornea”

[ 487 ]

Tornea0 has been generally fuppofed to be
ih*27'3o" to the Eaft of Paris; but with this differ-
ence of meridians, the obfervations at Tornea0, tho’
made by Mr. Hellant, a very excellent obferver, will
give a parallax of the Sun much lefs than the other
obfervations made in high Northern latitudes. In
order to fettle the longitude of this place, I am of
opinion that we may have recourfe with fafety, and
without incurring the charge of reafoning in a circle,
to the oblervation of the tranfit itfelf; I mean the
obfervation of the internal contact at the ingrefs.
Whether we fuppofe the Sun’s parallax to be 8" or
lo", the firff internal contact would have happened
foonerat Tornea0 than at Stockholm 19" or 24'''. As
the Sun’s parallax will readilly be allowed to be more
than 8V, I fhall fuppofe the firff internal contact to
have happened 2 \" fooner. Tornea0 is therefore
24/ 55" to the Eaft of Stockholm, and confequently
ih*37/,22// to the Eaft of Greenwich. I fhall make
ufe of Mr. Hellant’ s obfervation of the internal con-
tad; at 2ih.54/.o8// in preference to that of Mr. La-
gerbom.

Abo, the capital of Finland, where Mr. Juftander
obferved the laft internal contadat 2ih<45/.i9// (when
a correction is made in the minutes) is ih. 1 1/.29// to
the Eaft of Paris, and ih.23/.34// to the Eaft of
Greenwich.

At Hernofand, which is ih.i T.29" to the Eaft of
Greenwich, I fhall fuppofe the 2d internal contad
was obferved at 2ih.2b/.52//, as publifhed in the Phi-
lofophical Tranfadions by Mr. Short from the Swed-
ifh ads.

1 find the Ifland of Rodrigues by comparing three
obfervations of eclipfes of Jupiter’s latellites with

R r r 2 others

[ 488 ]

others made in England and at the Cape, to be
4h. 1 2'. 38" to the Eaft of Greenwich : and this deter-
mination is exadlly confirmed by Mr. Pringre’s com-
parifon of the fame eclipfes. The obfervation of the
occultation of a fixt Ear gives the longitude 6" or 7"
greater. In the Philofophical Tranladtions, and even
in the former part of the volume of the Memoirs of
the Academy of Sciences for 1761, we find the inter-
nal contadl was oblerved at Rodrigues at oh.34/-47
And yet in the memoire on the Sun’s parallax it is laid
to have happened at 0^.36' .4.9" . Upon comparing
this latter with the time by the clock, it fhould leem
that Mr. Pingre had committed a miftake in fubtradl-
ing the error of his clock inflead of adding it. But he
has no where mentioned any reafon for this difference.

Gottingen, where the celebrated Mr. Mayer ob-
ferved the firft internal contadl at 20h.58/.26//
to the Eaft of Paris is 30' 16" or 3*/ 33^ to the Eaft
of Greenwich.

The Abbe de la Caille has placed Bologna
to the Eaft of Paris : By comparing the obfervations
of the tranfit of Mercury, I find, by a mean of three
refults agreeing very nearly together, that Bologna is
45'. 1 5" to the Eaft of Greenwich. Mr. Zanotti ob-
ferved there the 2d internal contadl at 2ih.o4/.34//.
But as he ufed a refradling telefcope of 2 4 feet, and
as two other obfervers with telefcopes of 10 and 22
feet faw the contadl 24" later, I fhall fuppofe it to have

happened at 2ih 4' 58//.

At Florence, the internal contadl was obferved
with a refledlor of more than 4 feet at 2ih*4 •2S/ by
Father Ximenes. The longitude of this place is
34' 48" to the Eaft of Paris, according to the table in

theConnoiftance des Mouvemens Celeftes, or 35'. 58"

according

[ 489 ]

according to the table in the Elemens d'Aftronomie
by Mr. Caffini. By taking a mean of both, Florence
is 44/<4o// to the Eaft of Greenwich.

The longitude of St. Peters at Rome is 49/-54//
according to the French Aftronomers. The internal
contact was obferved to happen at 2ih.09'.36/'. But
as it is not faid where this obfervation was made, the
longitude given above will be found to be fomewhat
inaccurate.

Oblervations were alfo made at Madrid and Lifbon;
at the former, the internal contad happened at
2oh.6/.$6" apparent time : and at Lilbon at

i9h.44/.26//. The longitude of Madrid, as given in
the Philofophical Tranfadions, is certainly erroneous ;
being more than a minute and a half too little, if the
obfervation of [the tranfit can be depended upon.
At Lifbon, the longitude of the place was not
determined by Mr. Ciera, who obferved the tranfit,
when Mr. Pingre, from whom I have taken the ob-
fervation, left it in his way from Rodrigues. From
the belt accounts that I can colled, particularly
from the 385th number of the Philofophical Tranff
adions, and from an account of fome obfervations
by Mr. Short, Lifbon is about 36'. 2 6" to the Weft
of Greenwich.

Now in order to deduce the Sun’s parallax from
the obfervations related above, 1 proceeded in the fol-
lowing manner. Having fubtraded the difference
of longitude between Greenwich and the Cape
=ih.i3/.28// from 2ih.39/.52// the mean of the ob-
ferved times at the Cape, and compared the remainder
with the obferved time at Greenwich, I find that the
internal contad was obferved 24" later at the Cape
1 than

[ 49° -J

than at Greenwich, on account of parallax. I then
calculated what would be the effect of parallax at each
place, fuppoling the Sun’s parallax to be 9 leconds ;
and found that the time of the internal contadf would
be accelerated i'.i 6", 63 at Greenwich, and retarded
W 31', 09 at the Cape: the whole effedt of parallax

therefore is .But the difference in time’

as found by obfervation, is only 7' •24// • and there-
fore the difference by calculation is to the differ-
ence by obfervation, as the affumed parallax is to the
true parallax on the day of the tranfit, which by this
obfervation is 8//,543. The parallax refulting hom
each obfervation will be found in the following table,
which will be fufficiently explained by the foregoing

example.

Places.

Difference of cal-
culated times.

Difference of
obferved tims

Sun’s par*
all ax.

Greenwich
Paris - -
Stockholm
Upfal - -
Cajaneburg
Tobolfki -
Tornea0 -
Abo - —
Hernofand
Rodrigues
Gottingen
Bologna -
Florence -
Rome - -

/

7

7

8

9

9

10

9

9

9

3

7

7

6

6

/

7

47 j 7 2

28, 40

53’ l2,

01. 03

42> 3°

29, 06

48>9 5
1 1, 16

21, 1 7
i9>72
54. 36
°3* 3J,6
57.79 6

45> l6,6

7

8

8

9

10

9

8

9

2

7

//

24

°3>

4!>

45

32

18,

38

59

01

*3
3 1
41
36
4i

//

8, 543
8, 494
8,712

8, 7?7
8, 841
8, 848
8, 832
8, 801
8, 676

5’ 993
3. 55s
8> 525

8. 536

4 9 °7

Such

[ 49i ]

Such is the refult of a comparifon of the beft ob-
iervations made in places whofe longitudes are as ac-
curately ascertained as the prefent ftate of Aftronomy
w,U permit : by a mean of the whole, rejefling only

,h! , bru Jat'on at Rodrigues, the Sun's parallax on

the day of the tranfit is 8 ',692 1 have excluded

- companion of the obfervation at Rodrigues, be-
caufe the parallax refulting from it differs fo confider-

t I tIle rcft' we fuppofe the internal con-

thm 1, haVe.flr“lly happened one minute fooner,

the nfh|f miftake, m 'vnt'ng down the obfervation,
the parallax will then be 8 \6gy.

This obfervation made at Rodrigues, fuppofino; it
exadt, will furmfli another term wherewith to com-
pare the feveral observations made in Europe. The
un s parallax refulting from each obfervation may be
feen m the following table. 7

Places.

Difference
of calculated
times.

Greenwich - - -

Paris -
Stockholm
Upfal - - _ _

Cajanebtirg
Tobolfki - - -

Tornea0 - - _

Abo - - _ _

Hernofand
Gottingen
Bologna - -

Florence -
Cape of Good Hope

28, cc

8,98

39, 00
42, 11

22.58

°9, 34
29> 23

51,46

or, 45
34,64

43.59
38, 07
19, 72

Difference
>f observ’d
times.

//

1 1

50.5

28.5

32
19
°5» 5

25

47
49
18

33

23

J3

Sun’

s par-

allax.

//

(O, 444
IO, 500
10, 314
10, 3 I 2
10,327
ID, 177
10, 289
10, 422
10, 183
10, 421
10, 787
10,854

5, 993!

Difference
ofobferved
times.

//

I I

50,5

Sun’s

parallax.

8, 429
8, 332
28,5 8, 72
32

19

8,734
8, 915
7 °5- 5 8, 919

' 25
5 47
49
18

33

23

*3

8, 902
8, 88 6
8, 690
8, 454

8,372
8,449
8, 697

The

[ 492 ]

The mean of the whole, rejecting the companion
of the Cape, is fuppofing the internal con-

tact to have happened at oh.36'.49/r. But if a mis-
take of one minute was really committed, the 3d
column will receive a confiderable alteration and the
parallax refulting from each oblervation will be re-
prefented in the laft column, the mean of which is
654, agreeing as nearly as poffible with the paral-
lax relulting from all the beft obfervations compared
with the Cape.

Mr. Pingre finding the parallax refulting from his
own obfervation to differ fo widely from that deduced
from the Cape, and that both obfervations might be
made to agree by fuppofing an error of one minute
in the obfervation at Rodrigues, has examined every
fource of error that might be committed ; and upon
the whole fees reafon to prefer his own obfervation to
that of Mr. Mafon , not becaufe he could find no mijlake
in his own , but becaufe he has proved that no miftake
could poffibly be committed. His obfervation indeed is
in fome meafure confirmed by comparing all the ob-
servations with that at Lifbon : from which compa-
rifon if the longitude above laid down may be de-
pended upon, the Sun’s parallax is fomewhat more
than 10 feconds.

The feveral obfervations, that have been compared
with the obfervations both of the Cape and Rodri-
gues, may alfo be compared together; and by com-
bining fome of them, we may obtain different re-
fults, upon which we may more or lefs depend, as
the differences between the obferved times are greater
or lefs.

Places

C +93 ]

Places compared.

Difference
of calculated
times.

Difference

ofobferv’d

times.

Tobolfki and Greenwich

/

2

4 1 j 34

/

2

//

54. 5

Tobolfki and Paris - -

3

0, 36

1

*5

Tobolfki and Gottingen

-

-

-

2

34» 7°

2

47.5

Toboliki and Stockholm

-

-

-

1

3°. 34

1

37.o

Tobolfki and Upfal

-

-

-

1

27.23

1

33. 5

Tobolfki and Bologna -

-

-

-

3

25. 75

3

37.5

Tobolfki and Florence -

-

-

-

3

3*. 2;

3

42, 5

Stockholm and Greenwich

-

-

-

1

II, c

i

*7. 5

Stockholm and Paris - -

-

-

1

30,02

1

38, c

Stockholm and Bologna

-

-

-

1

55.41

2

co, 5

Stockholm and Florence

-

-

-

2

o.93

2

05. 5

Tornea0 and Gottingen

-

-

1

54. 59

2

07

Tornea0 and Paris - - -

2

20, 25

2

34.5

Tornea0 and Greenwich

-

•

-

2

u 23

2

14

Cajaneburg and Greenwich

-

-

-

r

54.58

2

08

Cajaneburg and Paris - -

-

-

-

2

13,6c

2

28, 5

Cajaneburg and Gottingen

-

-

-

r

47’ 94

2

01

Cajaneburg and Florence -

-

-

-

2

44. 5'

2

56

Cajaneburg and Bologna

-

-

-

2

38.99

2

51

Upfal and Paris -

-

-

-

1

33. *3

I

4i. 5

Upfal and Greenwich - -

-

-

r

14, 1 1

I

21

Hcrnofand and Paris - -

-

-

-

1

52.47

I

57. 5

Hernofand and Greenwich

-

—

-

1

33» 45

I

37

Herr.ofand and Bologna

—

-

-

2

17. 86

2

20

Hernofand and Florence

•

-

-

2

23. 38

2

25

Abo and Paris - - - -

1

42,46

I

55. 5

Abo and Greenwich

-

-

r-

1

23> 44

I

33

Abo and Bologna - -

2

07,85

2

18

Abo and Florence - - -

-

-

-

2

1 3’ 37

2

23

Tornea0 and Bologna

-

-

-

2

45. 64

2

57

Tornea0 and Florence -

-

-

2

51, 16

02

Greenwich and Paris

-

-

-

0

19,02

0

20, 5

The mean of the whole is 9", 695.

Sun’s par-
allax.

9’ 734
9. 736
9? 744
9? 663
9,646

9.5*3
9.525
9, 824

9j 797
9» 396
9. 340
9.974
9. 9*4
9, 948

10,054
10, 003
10, 088
9, 628

9’ 679

9, 808

9. 836
9, 402
9. 342
9. 139
9, ior
ro, 145
10,031
9, 714
9, 649
9,617

9.5^9

9, 700

Vol. LIU

sa

it

C 494 3

It has been (hewn that the parallax reflat-
ing from the total durations is

— from a comparifon of the obfervation at
- Madrafs with thofe of Tobolfki and Ca- j* 9,763

janeburg is — — — J

— • from a comparifon of the obferved, with!

a calculated, duration without parallax, isj ^24

— from the lead diftance of the centers — 9, 920

— from the obfervations combined together is 9, 6 95

} 9.579

It can hardly be fuppofedthat as fuch different me-
thods give a parallax of the Sun on the day if the
tranfit equal to 9^,736, that this parallax fhould yet
be only 8,692 as deduced from a comparifon of the
obfervations with the Cape, while the fame obferva-
tions compared with thofe of Rodrigues and Lifbon
fhew that the parallax exceeds 10 feconds. Let us
therefore fuppofe that the obfervers at the Cape have
let down their obfervation one minute too foon, tho’
it muft be confelfed that the time of the duration at
the egrefs cannot warrant fuch a corre&ion, and that
the time of the internal contact fhould have been ob-
ferved at 2ih.40/.52/' j the parallax, by taking a mean,
will then be 9^,732, exa&ly agreeing with a mean
of all the other determinations. And in this Quan-
tity of the Sun’s parallax we muft either acquiefce, or
remain as ignorant of the true quantity of it as wc
we were before, till we can have recourfe to the next
tranlit on June 3d 1769, when the planet Venus will
again pafs over the Sun’s difk, having fomething

more

[ 495 ]

more than io minutes of North latitude ; and will
be fo favourably circumftanced, that, if the errors
in obferving each contact do not exceed 4" or 5",
the quantity of the Sun’s parallax may be deter-
mined within lefs than part of the whole :

as the total duration, or the interval between the two
internal contacts, will be found to be about 18 mi-
nutes longer at Tornea0 than at Mexico. But the
feveral circumftances of that tranfit mull: be the fub-
je£t of a future paper. Let it fuffice at prefent to ob-
ferve that it will in part be vilible to the inhabitants
of this ifland, as Venus will be feen wholly entered
upon the Sun’s difk more than half an hour before
the time of fun-fet at Greenwich.

SI! 2

LVI. J

[ 496 ]

LVI. A Difcourfe on the Locus for three and
four Lines celebrated among the ancient
Geometers , by H. Pemberton, M. D. R. S.
Lond. et R. A. Berol. S . In a Letter
to the Reverend Thomas Birch, D. D. Se-
cretary to the Royal Society .

S I R,

Dec. 15. 1763.

Read at R

15 Dec. 1

of the

thought

tion of

nuation

mention

matical

s; TV /T Y worthy friend, and affociatc
in my early Rudies, the collector
late Mr. Robins’s mathematical tra&s,
it conducive to a more compleat vindica-
tive memory of his friend againft an infi-
prejudicial to his candour, to make fome
of the courfe, I took in my early mathe-
purfuits, and how foon I became attached

to the ancient manner of treating geometrical fub-
jefts. This gave occafion to my looking into fome
of my old papers, amongft which I found a difcuf-
fion of the problem relating to the locus ad tres £?
quatuor tineas celebrated among the ancients, which
I then communicated to a friend or two, whofe
fentiments of thofe ancient fages were the fame
with mine. What I had drawn up on this fub-
jedfc is contained in the papers, I herewith put
into your hands, which if you fhall think worthy
of being laid before our honourable fociety, they
are intirely at your difpofal.

I am your mod obedient fervant,

PI. Pemberton.

T PI E

4.

c

Philos. Trans. Vol. IHL. TAB. XXIV. p. 4yy .

A

H B q MK /

\\v- /

\ xoA

D. \T PY \

I

22.

/ Z'" D

\ H

/a I

4e

i -A.fr-

- / \

(h^» IP\ -

B

[ 497 ]

HT H E defcribing a conic fedtion through the
angles of a quadrilateral with two parallel fides
is fo ready a means of affigning loci for the folution
of folid problems, that it cannot be doubted, but
this gave rife to the general problem concerning
three and four lines mentioned by Apollonius, and
defcribed by Pappus ; and it may be learnt from
Sirlfaac Newton, who has confidered the problem,
how ealily the mod: extenfive form of it is reducible
to the cafe, which I have fuppofed to give rife to
it.

Sir Ifaac Newton refers the general problem to
this : Any quadrilateral A B C D being propofea,
to find the locus of the point P, whereby PRQJaeing
drawn parallel to A C and S P T parallel to A B,
the ratio of the redtangle contained un-
der QP, PR to that under S P, PT pi.,,
fhall be given ; and this by purfuing
the fteps, whereby he proves, that the point P will
in every quadrilateral be in a conic fediion, may be
readily reduced to the cafe of a quadrilateral with
two fides parallel, after this manner. Draw B t
and DN parallel to AC, then find the point M
in N D, that the redtangle under M D N be to
that under ANB in the ratio given, and draw C r
M d.

Here Rr will be to A Q, or SP, as M D to
AN, and B /, or QJ*, to T/ as ND to NB
whence the redtangle under R r , QJP will be to
that under SP, T t as that under MDN to that
under ANB, that is, in the ratio given of the rec-
tangle under R P Q to that under S P T. Therefore,
by taking the fum of the antecedents and of the

confequents.

[ 498 ]

confequents, the redangle under r P Q^will be to
that under S P t, that is, to the redangle under
A Q B, in the quadrilateral ABC d, whofe two
lides AC, B d, are parallel, in the given ratio.

In like manner, if three of the given lines palfed
through one point, as the lines C A, C B, C D, and
the redangle under QJP R be to that under S P T
Fi<r. 2 *n a S*ven ratio> this cafe is with the fame fa-
cility reduced to the like quadrilateral thus.

Draw B E parallel to A C, that (hall cut S T
produced in t, and let the point F be taken, that
the redangle under C A , E F be to the fquare of
A B in the ratio given ; then CrF being drawn,
B t, or Q P, will be to T t as A C to A B, and
R r to A Q, or S P, as E F to AB; whence the
rectangle under QJP, R r will be to that under
T t, S P, as that under AC, E F to the fquare of
A B, that is, in the given ratio of the redangle
under QJ3 R to that under S P T, and the rec-
tangle under QJP r will be to that under S V t or
A QJB in the quadrilateral A B C F, whofe two
fides A C, B F are parallel, in the fame given
ratio.

Now let A B C D be a quadrilateral having the
two fides A C, B D parallel, with any conic fec-
tion palling through the four points A, B, C, D ;

. alfo, the point E being taken in the fedion,
and E F G being drawn parallel to A C
or B D, let the ratio of the redangle under AG B
to the redangle under F E G be given : then the
conic fedion will he given.

Let the fides A B, C D meet in M, and draw
M I bifeding A C and B D in K and L. Then the
4 ' diameter

[ 499 ]

diameter of the ffedtion, to which AC and BD
are lines ordinately applied, will he in the line
M I ; and if NP, QS are tangents to the p.
fedtion, and parallel to A C and BD, the " lt;’
points O, R, in which they interfect M I, will be
the points of their contadi, and the vertexes of that
diameter. But the fquare of N O is to the rectangle
under A N B, and the fquare of Q^R to the rect-
angle under A QJ3, as the rectangle under E G H
or F E G to that under AGB, therefore in a given
ratio ; but the ratio of N M to NO, the fame as
that of QJVI to QJG is alfo given ; whence the
ratio of the fquare of N M to the rediangle under
A N B, or of the fquare of O M to the redtangle
under K O L, is given, as likewife the ratio of the
fquare of R M to the redtangle under K R L.

Now in the ellipfis the fquare of M O, the di-
ffance of the remoter vertex of the diame-
ter O R from M, is greater than the redt- =’ J
angle under KOL; that is, the ratio given of the
rectangle under FEG to that under AGB muft be
greater than the ratio of the fquare of half the differ-
ence between A C and B D to the fquare of A B=,
But in the hyperbola the fquare of M O is lefs than
the rediangle under KOL ; whereby the ratio of
the redtangle under FEG to that under p .
AGB fhall be lefs than that of the fquare
of half the difference between A C and B D to the
fquare of A B [«]. In

[a] As the fquare of O M fhall be greater or lefs than the rect-
angle under KOL, the fquare of NM will be refpedtively greater
or lefs than the redtangle under ANB ; therefore the ratio of the
fquare of N O to the redtangle under ANB, that is, of the
redtangle under FEG to that under AGB, will be accordingly

greater

E 5°° ]

In both cafes, if the point T be fuch, that the
redangle under MOT be equal to that under
Fig. 3,4. LOK, whereby MO fhall be to OT in
the given ratio of the fquare of M O to the
rectangle under L O IC, the given redangle under
KML will be to the redangle under L T K (by
Prop. 35. L. 7. Papp. [b] ) in this given ratio, and
therefore given ; confequently the points T and O
will be given.

In like manner, if the redangle under MRV be
equal to that under L R K, fo that M R be to R V
in the given ratio of the fquare of R M to the rec-
tangle under L R K, the given redangle under
K M L (by Prop. 22. L. 7. Papp.) will be to the
redangle under L V K in the fame given propor-
tion, whence the points V and R will be given.

Thus in both cafes the points T and V will be
found by applying to the given line K L a rectangle
exceeding by a fquare, to which the given redangle
under KML fhall be in the given ratio of the
fquare of M O to the rectangle under K O L, or
of the fquare of M R to the rectangle under
KRLj MO being to O T, and MR to RV, in
that given ratio.

But in the laft place, if this given ratio be that
Fir ^ of equality, fo that the fquare of RM be equal
to the rectangle under K R L, by adding to
both the redangle under MRL, that under RML
will be equal to that under KM, LR, and MR to RL
as KM to M L, and the vertex R of the diameter

greater or lefs than the ratio of the fquare of N O to the fquare
of N M, which is the fame with that of the fquare of the differ-
ence between A K, B L to the fquare of A B.

[i] See pag. 51 1.

R I

L 5° 1 J _

R I will lie given, the conic ledtion being here u
parabola, tills diameter having thus but one ver-
tex.

Hitherto the point E, when the line E F G falls
between A C and B D, is without the quadrilw
teral', and within the lines A B, CD, when E F G
is without the quadrilateral.

But when E is within the lines AC, B D in the
hr ft cafe, and without in the lecond, the locus or
the point E will be oppolite fedtions, each palling
through two angles of the quadrilateral.

When one fedtion paftes through A and C, and
the other through B and D ; then if the diameter
M I be drawn, as before, and to K L be applied a
redtangle deficient by a fquare, to which ^
the given redtangle under KML (hall be in 1&'
the given ratio of the fquare of M O to the redtan-
gle under K O L, or of the fquare of M R to the
redtangle under K R L, the points T and V, con-
fti tuting the redtangles under KT L andunder K VL,
being thus found, M O will be to O T, and M R
to R V, in this given ratio (by prop* 30. L.7. Papp.)
O and T being the vertexes of the diameter M I.

But the redtangles under K T L, K V L cannot
be aftigned, as here required, unlefs the ratio given
for that of the fquare of O M to the redtangle under
KO L, or that of the fquare of R M to the rec-
tangle under K R L, be not lefs than that of the
redtangle under K M L to the fquare of half K L ;
that is, when the ratio of the fquare of O N to the
redtangle under ANB, and that of the fquare of
R Q_to the redtangle under A Q B, or that of the
given ratio of the redtangle under F E G to that
under A G B is not lefs than that of the redtangle

Vol. LIII. Ttt under

[ 5°2 ]

under AK, BL to the fquare of half AB, or of the
redangle under AC, B D to the fquare of AB.

But if one of the oppofite fedions pafs through
A and B, and the other through C and D, the ra-
tio of the redangle under F E G to that under
A G B will be lefs than that of the redangle under
Fig 7 AC, BD to the fquare of A B. For CL
y' being drawn parallel to A B, and A D joined
and continued to M, the line D M falls wholly
within the fedion palling through C and D : there-
fore K M is lefs than K L, and the ratio of K D
to K L lefs than that of K D to KM, that is,
of B D to A B i whence B K being equal to A C,
and C K to A B, the ratio of the redangle under
B K D to that under C K L, being the ratio of the
redangle under E G H, or F E G, to that under
A G B, will be lefs than the ratio of the redangle
under AC, B D to the fquare of A B.

And here the point L is given ; for the given
redangle under B K D is to that under CKL in
the given ratio of the redangle under H G E, or
that under F E G, to the redangle under AGB;
hence C K, equal to A B, being given, K L is
given, and confequently the point L.

Again, B L being joined, and N E O P drawn
parallel to A B, alfo G EF continued to Q, as A G,
equal to C Q, to F Q_ fo will C K be to D K, and
O P to E G, equal to O B, as K L to B K, con-
fequently the redangle under O P, A G will be to
that under E G, F Q_ as that under K L, C K to
that under K B, D K, that is, as the redangle un-
der A G B to thrtt under FEG; and by combining
the antecedents and confequents the redangle
under PEN will be to that under Q^E G in the
fame given ratio. More-

[S® 3 ]

Moreover D K being to A C as K M to C M, the
ratio of D K to A C, that is, the ratio of the rec-
tangle under JBKD to the fquare of AC, will belefs
than the ratio of KL to C L, or the ratio of
the redangle under C K L to that under A B, CL;
therefore, by permutation and inverdon, the ratio
of the redangle under C K L to the redangle under
B K D, that is, the given ratio of the redangle
under N E P to that under A N C, equal to that
under G E is greater than the ratio of that un-
der A B, CL to the fquare of A C. And hence
the oppoiite fedions pading through the angles of
the quadrilateral A B C L, whofe fides A B, C L
are parallel, will be given as before.

When the given ratio of the fquare of O M to
the redangle under L O K {hall be that of ^
the redangle under K ML to the fquare
of half K L, whereby the given ratio of the
redangle under FEG to that under A G B {hall be
that of the redangle under AC, BD to the fquare
of A B, the points T and V {hall unite in one, bi-
feding K L, and the points O and R fhall alfo
unite in one, dividing the line KLM harmonical-
ly ; and then the Incus of the point E will be each
of the diagonals of the quadrilateral.

In the laft place, if the diagonals AD, B C of
the quadrilateral were drawn, cutting G E pifr g
in I and K, and the ratio of the redtangle
under K E I to that under AID were given, and
not that of the redangle under G E F to that un-
der A G B ; then the interfedion of thefe diago-
nals, as L, will be in the line drawn from M bi-
feding A C, and B D, and the point L will fall
within the quadrilateral, whereby the locus, when an

T 1 1 2 ellipds

[ 5°4 ]

elliplis or lingle hyperbola, will be aiTigned by the
36th proportion of the forelaid book of Pappus :
and when oppolite fe&ions, by the 30th proportion,
or be reduced to the preceding cafes thus.

Since K G will be to G B as C A to A B, and
I G to G A as B D to A B, the rectangle under
K. G I will be to that under A G B, in the given
ratio of the reftangle under AC, B D to the fq uare
of A B. Therefore when the ratio of the redtan-
gle under K E I to that under A I D is given, the
redlangle under AID alfo bearing a given ratio to
that under A G B, the ratio of the redtangle under
K E I to that under A G B will be given, and in
the lad; place the ratio of the redangle^under G E F
to that under A G B will be given, this redtangle
under G E F being the excefs of that under KGI
above that under K E I [c]. And thereby the fedli-
ons will be determined, as before.

AND thus may the locus of the point fought be
afiigned in all the cafes of this ancient problem,
which Sir llaac Newton has diftindtly explained.
T he other cafes, he has alluded to, may be treated,
as follows.

When three of the given lines fhall be parallel,
as A C, B D, and H I, the fourth line being A B,
FjV an^ K E L M being parallel to A B, the
0 9 ratio of the redtangle under K E L to the
redfangle under E G and E M fhall be givenj;
that is, three points A, B, and H being given in
the line AB, with the line GE infilling on AB in
a given angle, that the redtangle under AGB fhall be
to that under G H and G E in a given ratio : then

p] By Prop. 193, Lib. 7. Papp.

take

C 505 ]

take A N equal to B H, and draw N O paral-
lel to AC, BD, and H I.

Then if N P be drawn, that P O be to ON in
the given ratio, N P will be given in pofition, and
P O will be to O N, that is, E G, as the rectangle
under KEL to that under EM, E G ; fo that the
rectangle under KEL will be equal to that under
PO, EM. But the redangle under O K M is equal
to the excefs of that under OEM above that under
KEL [d 1 ; therefore the redangle under O K M,
or that under N A H, or under NBH, is equal to
that under E M and the excefs of OE above O P,
that is, to the redangle under PEM; the point E
therefore is in an hyperbola defcribed to the given
alymptotes PN, MH, and paffing through A and B.

Again if two of the given lines only are parallel,
but the redangles otherwife related to them, than
as above. Suppofe the ratio of the redangle under
A G, E F to that under B G, GE is given. Let
C D meet A B in L, and let H E I, M F N be
drawn parallel to A B, and L K parallel to A C and
B D. Then the parallelogram E M will
be to the parallelogram EB in the given I0*
ratio. Take AO to OB in that ratio, and draw
OP parallel to A C and BD. Here the point O
will be given, and the parallelogram P A will be in
the given ratio to the parallelogram P B ; whence
A B will be to B O as the parallelogram B H to the
parallelogram B P, and as the difference between
the parallelograms E M and E B to the parallelo-
gram E B,confequently as the parallelogram G M to
the parallelogram P G ; therefore the ratio of the
redangle under A G, F G to the redangle under
[d~] By Prop. 194. Lib. 7. Papp.

[ 5°6 ]

E G, E P or O G will be given ; and in the laft
place the ratio of F G to GL being given, the
ratio of the reCtangle under A G and G L to that
under E G, O G will be given. And thus three
points A, L, O, will be given with G E infilling
on A B in a given angle, as in the preceding
cafe.

Moreover, AC and BD being parallel, AB and CD
may be alio parallel. And then, when the ratio of
^ the rectangle under AGB tothatunderGEF
A J°’ 1 * is given, the determination of the locus is fo
obvious as not to have required a diftinCt explanation.
But when the reCtangle under AG, EF bears a given
ratio to that under B G, G E ; let the diagonals
A D, B C be drawn, and H E L K drawn parallel
to A D. Then the rectangle under H E L will be
to that under K E I in the fame given ratio ;
and if C M be taken to M B in the fame ratio, the
lines MNP, MOQ_ drawn, the firft parallel to
A C, B D, and the other parallel to A B, C D, will
be given in pofition, and the diagonal B M will
bifeCt both IK, NO, and H L ; therefore the
reCtangle under H E L being to that under K E I
as M C to M B, that is, as NH to N K, here by
divifion the reCtangle under H E L will be to that
under I H K [ e~\ as NH to HK; therefore equal to
that under N H and I H or K L. But the rect-
angle under N E O is equal to the fum of the red-
angles under H N L and under FI E L \ f\i there-
fore the redangle under N E O is equal to that
under N H, N K, equal to that under A P D,
that is, equal to that under P A or that under
P D Q, the diagonal B M bifeCtingboth P Q^and

[c] By the prop, of Papp. before cited, [/] By the fame.

A D.

[ 507 ]

A D. But thus the point E is in an hyperbola de-
ferred to the afymptotes MN, MO, and paffin^
through A and D. °

THE determination of this locus for three lines is
folved almoft explicitly by Apollonius in the three lalt
propofitions of his third book of Conics. For if the
three lines propofed were A B, AC, B C, and the
point fought D, that the ratio of the redtangle under
EDF (the line EF being drawn parallel
to B C) fhould be in a given ratio to the fquare Fl§-12»
of a line drawn from D to B C in a given I3, 14*
angle, the iquare of which line will be in a given
ratio to the redtangle under BE, C F ; then if B H,
Cl are drawn parallel to AC and A B refpedively,
alfo BDL, CDK drawn through D, the fquare
of B C will be to the redtangle under B K, CL as
the redtangle under D F, DE, to that under C F,
B E.

Hence if the ratio of the redtangle under D F,
D E to the fquare of a line drawn from D on B C
in a given angle, is given; the fquare of this line
being in a given ratio to the redtangle under C F,
BE, the ratio of the redtangle under BK, CL to
the fquare of B C will be given ; whence a conic
fedtion palling through D will in all cafes be given.

In the frit place let the point D be within the
angle B A C. Tl hen if B C be bifedted by the line
A M, this will be a diameter to the conic
fedtion, which fhall touch BA, AC in the FlS- I2*
points B, C, and B C will be ordinately applied to
that diameter; the vertex of this diameter being N,
the given ratio of the redtangle under BK, CL to
2 the

[ 5°8 ]

the iquare of B C will be compounded or the ratio-
of the Iquare of MN to the l'quare of NA, and of
the ratio of the redtangle under B A C to the fourth
part of the fquare of BC; and thus the line A M
will be divided in N in a given ratio, and the point
N, one vertex of the diameter, to which B C is or-
dinately applied, will be given.

If A N be equal to N M, the point N will be
tlie only vertex of this diameter, and the fedtion will
be a parabola.

Otherwile by taking the point O in A M extend-
ed, fo that the ratio of A O to O M be the fame
with that of AN to N M, the point O will be the
other vertex of the diameter.

And here if the ratio of A N to NM be that of
a greater to a lefs, the point O will fall beyond M
from A within the angle B AC, the conic fedtion
being an ellipfis.

But if the ratio of AN to NM be that of a
lefs to a greater, the point O will fall on the other
fide of A, and the fedtion will be an hyperbola.

F. And in this cafe if the oppofite fedtion be

drawn, that alfo will be the locus of the
point D within the angle vertical to the angle
B AC.

In the laft place, if D be in either of the collate-
ral angles, A M drawn as before will contain a Se-
condary diameter in oppofite fedtions, one of which
fhall touch BA in B, and the other C A in
g'I4‘ C. Then if one of thefe fedions pafs thro’
D, the fedtions will be given. For here P A (^be-
ing drawn through A parallel to B C, the given ra-
tio of the redtangle under CL, B K to the fquare

of

[ 5°9 3

of B C will be the fame with that of the given red-
angle under BAC to the fquare of AP: therefore
AP is given, and thence the fedions. For let Pv S
be the fecondary diameter, to which BC is ordi-
nately applied, and T the center of the oppofite
fedions. Then the fquare of BM will be to the red-
angle under AMT as the fquare of the tranfverfe di-
ameter conjugate to the fecondary diameter R S to the
fquare of this fecondary diameter ; and if a line were
drawn from M to P, this would touch the hyper-
bola BP in P Qg*], and the fquare of AP will be
to the redangle under MAT in the fame ratio ;
therefore the given ratio of the fquare of M B to the
fquare of A P will be that of the redangle under
AMT to the redangle under M A T, or the ratio
of M T to AT; confequently the ratio of M T
to A T is given, and thence the point T. But alfo
the diameter R S is given in magnitude, the fquare
of R T or of S T being equal to the redangle un-
der M T A ; whence in the laffc place the tranfverfe
diameter conjugate to this is alfo given ; for the fquare
of this diameter is to the fquare of RT as the given
fquare of B M to the redangle under AMT now
alfo given.

But a more fimple cafe may alfo be propofed in
three lines, when the ratio of the redangle Fiff>154
under EDF fhould be equal to the redan-
gle under a given line, and that drawn from D to
B C in a given angle.

This line will bear, both to B E and F C, a given
ratio, and the redangle under EDF will be in a given

jjr] Apoll. conic. L. II. prop. 40.

Vol. LIII. Uuu

ratio

[ 5*0 ]

ratio to the redangle under the given line and E B
or CF.

Let the line given be H, and take M B and N C,
that the redangle under M B C, and that under
B C N be to that under B A and H in the given ra-
tio of the rectangle under E D F to that under B E
and H, B M and C N being equal. Then draw from
M and N lines parallel to B A, C A, which fhall in-
terfed E F in K and L, whereby, MK cutting
C A in I, the redangle under MBC will be to that
under B A and H as the redangle under BMC to
that under M I and H, and alfo as the redangle un-
der E K F to that under K I and H, that is, as the
redangle under E D F to that under H and B E or
M K, whence by adding the antecedents and confe-
quents the redangle under K D L will be to the red-
tangle under H and M I in the fame given ratio,
which is alfo that of the redangle under BMC to
the fame redangle under H and MI: the point D
therefore, is in an hyperbola paffing through B and C
having for afymptotes the lines M K and N L given in
pofition, the redangle under KDL being equal to
that under BMC, or that under M B N.

If the two lines AB and A C are parallel, the
locus may be known to be a parabola by the laft'
propofition of the fourth book of Pappus.

But if B C were parallel to one of the other, the
locus will be an hyperbola, as the preceding, but
affigned by a fhorter procefs.

Suppofe the given lines to be A E, A F,
and BC parallel to A F. And let the
redangle under E D F be equal to that under D G,
and the given line H, the line E G making given
angles with A E, A F. Here take E I equal to H,
i and

[ 5« ]

and dedud from both the redangles that under E I
or H, and DF, whereby will be left the redangle
under IDF equal to that under H and FG, both
whofe fides are given. Draw therefore I K parallel
to A E, and the redangle under IDF will be equal
to this given redangle, the given lines KI, AF being
the afymptotes to the hyperbola pafling through D.

Coroll. If L M be drawn through B parallel to
E F, L B fhall be equal to F G, and B M equal to
E I or H, whereby the hyperbola oppofite to that
pafting through D will pafs through B.

SCHOLIUM.

The proportions of Pappus, which have been refer-
red to in pag. 500, 501, 504, 1. 2. are given by him,
among others, for Lemmas fubfervient to the loft
treatife of Apollonius De J'ediione determinata , and the
four here cited refped and comprehend all the cafes
of the problem, where three points are given in any
line, and a fourth is required fuch, that the redangle
under the fegments of the propofed line intercepted
between the point fought, and two of the given
points, fhall bear a given ratio to the fquare of the
fegment terminated by the third point.

The cafes indeed of the problem, from the diver-
fity of fituation in the points given to the point fought
and to one another, are in number fix. The given
extreme of the fegment to conftitute the fquare may
either be without the other two given points, or be-
tween them. And when it is without, the point
fought may be required to be taken without them all,
either on the fide oppolite to the given extreme of the
fegment to conftitute the fquare, which will be one
cale,or it may be required to fall on the fame fide,

U u u 2 which

[ 512 ]

which will be a fecond cafe. If it be required to fall
between this point and the other two, this will be a
third cafe. A fourth cafe will be, when the point
fought fhall be required to fall between the other two
points. Alfo when the given extreme of the feg-
ment to conftitute the fquare lies between the other
two given points, the point fought may be required to
fall, either there alfo, or without, compofing the 5th,
and 6th cafes.

The propofitions in Pappus referring to thefe cafes,
though but four in number, fuffice for them all, each
proportion being applicable to the problem two ways.
For inftance the thirty-fifth proposition, as exprefted
by Pappus, is this, being the firft above cited. Three
points C, D, E being taken in the line A B, fo that

the redangle under ABE be equal .

to that under C BD, AB is to B E q ^ £ jj
as the rectangle under D A C to
that under C E D. Now A B is to B E, both as
the fquare of ABto the redangle under ABE, and
as the redangle under ABE to the fquare of B E.
Therefore if the ratio of A B to BE be given,
the ratio of the fquare of AB to the rectangle under
C B D will be given, which is the firft of the cafes
above defcribed, and alfo the ratio of the rectangle
under C B D to the fquare of B E given, which is
the fecond cafe. In both cafes the redangle under
DAC will be to that under CED in the given
ratio of A B to BE. But in the firft the red-
angle under DAC will be given, and the point E
in the redangle under CED to be found by ap-
plying a redangle, which fhall bear a given ratio to
the given redangle under D A C to the given line C D
exceeding by a fquare ; and in the fecond cafe the

redangle

[ 5i3 ]

rectangle under CE D is given, and A in the red-
angle under D A C to be found by applying to the
given line C D a redangle exceeding by a fquare,
which fhall bear a given ratio to the redangle under
C E D now given ; whence by the ratio of A B to
B E given the point B will be found in both cafes.

The 2 2d propolition either way applied refers to
the 3d cafe only, the 30th relates both to the 4th
and 5th, and the 36th propolition to the remain-
ing 6th.

The 45th, and other following propolitions, are
accommodated to the lolution of Apollonius’s prob-
lem, when four points are given, and a fifth requir-
ed, which with the given points fhall form four feg-
rnents fuch, that the redangle under two fhall bear
a given proportion to the redangle under the other
two. The various cafes of this problem appear to
have been the fubjed of the fecond book of the
mentioned treatife of Apollonius 5 and, according to
the charader given by Pappus of thofe proportions,
thefe lemmas ferve to reduce them to problems in the
firfl book, not thofe above mentioned, but thofe,
where three points being given, the redangle under
the fegments included by two, and a fourth point
fhall bear a given proportion to the redangle under the
fegment formed by the third point and a given line.

For inflance the 46th propofition is this ; in the

line A B four points , , ,

A,C,E,Bbeinggiven; ac D If B

and the point F album- | j

ed between E and B; G

alfo D taken, according to the 41ft propofition, that the
redangle under ADC be equal to that under BDE;
if G be equal to the fum of A E, C B, the redan-

[ 5*4 ]

gle under AFC together with that under EFB
will be equal to the redangle under G and D F.

Here if it were propofed to find the point F, that the
ratio of the redangle under AFC to that under EFB
fhould be given.the ratio of the rectangle under AFC
to that under DF and the given line G would be given.

But this analyfis may be carried on to a compleat
folution of the problem thus. If C N be taken to
G in the given ratio of the redangle under AFC to

that under DF and G, | j__j j |

the point N will be given, a C D E F B N

and the redangle under j \

A F, C N will be to G

that under A F, G in this ratio of CN to G ; confe-
quently the excefs of the redangle under A F, C N
above that under AFC, that is, the redangle under
A F N, will be to the excefs of the redangle under
A F and G above that under D F and G, or the given
redangle under A D, G, in the fame given ratio, and
in the lad: place the redangle under AFN will equal
the given redangle under A D and C N.

Here I have chofen this proportion in particular,
becaufe the cafe of the problem, to which it is fubfer-
vient, is fubjed to a determination, when F N fhall
be equal to A F. And then the redangle under
AFN being equal to that under AD and CN, as CN to
FN fo is AF to AD, and by divifion as CF to FN fo DF
to AD; therefore when AF is equal to FN, CF will
be to A F as FD to A D : confequently CD to F D
as FD to AD, and the fquare of DF equal to the
redangle under ADC, when the problem admits of
a fingle folution only, wherein the rectangle under

AFC

C 515 ]

AFC will bear to that under E F B a lefs ratio than in
any other fituation of the point F between E and B.

Moreover CN is to G as the reCtangle under
AFC to the fum of the reCtangles under AFC and
EFBj therefore FN being equal to A F, when the
problem is limited to this fingle folution, the rectangle
under AFC fhall be to the rectangles under AFC
and E F B together as the fum of AF and F C to
Gj which is equal to the fum of A E and C B ;
whence by diviiion the ratio of the reCtangle under
AFC to that under E F B, when the problem is
limited to this fingle folution, will be that of the
fum of AF and C F to the excefs of F B above E F.

Thus direCtly do thefe lemmas correfpond with A-
pollonius’s firft mode of folution, and lead to the ge-
neral principle of applying to a given line a reCtangle
exceeding or deficient by a fquare, which ./hall be equal
to a fpace given. This being a fimple cafe of the 28th
and 29th proportions of the 6th book of Euclid's ele-
ments, admits of a compendious folution. Such a one
is exhibited by Snellius in his treatife on thefe problems
(in Apollon. Batav.) and Des Cartes has exhibited
another more contracted in it’s terms, but not there-
fore more ufeful. It may alio be performed thus.
If upon a given line A B any triangle A C B be
ereCted at pleafure j then if the legs CA, CB,
whether equal or unequal, be continued to Fig. 1 7.
D and E, that the reCtangles under CAD
and C B E be each equal to the given fpace,
and a circle be defcribed through C, D, E cut-
ting A B extended in F and G, the reCtangle un-
der B F A and B G A will each be equal to F. 0
the fpace given. Alfb if in the legs CA, 'IS,I°’
CB the reCtangles under CAD and CBE be each

taken

[5*6]

taken equal to the fpace given, and a circle in
like manner be defcribed through C, D, E, cutting
A B in F and G, the redangles under A F B and
AGB will each be equal to the given fpace.
Here it is evident, that the fpace given muft not
exceed the fquare of half A B, when equal, the cir-
cle will touch A B in it’s middle point.

POSTSCRIPT.

A S this application to a given line of a redangle ex-
ceeding or deficient by a fquare, or the more
general problem treated of in the fixth book of the
elements, of applying a fpace to a line fo as to exceed
or be deficient by a parallelogram given in fpecies,
is the mod obvious refult, to which the analyfis of
plane problems, not too fimple to require this con-
ifrudion, leads ; fo the defcriptions of the conic fec-
tions here treated of, ftand in the like head in regard
to the higher order of problems ftyled folid from the
ufe of the conic fedions deemed necefiary for their
genuine folution. And thefe are the only modes of
folution, the modern algebra, which grounds its ope-
rations on one or two elementary propofitions only,
naturally leads to. But as the form of analyfis a-
mongft the antients, by expatiating through a larger
field, often was found to arrive at conclufions much
more concife and elegant, than could offer themfelves
in a more confined track ; the antient fages in geome-
try, that the folid order of problems might not want
this advantage, fought out that copious and judicious
colledion of properties attending the conic fedions,

which

[ 5i7 ]

which, with fome ufeful additions from later writers,
have been handed down to us.

And as the advantages of this ancient fyftem of
analyfis cannot be too much inculcated in an age,
wherein it has been fo little known, and almoft to-
tally negledted, permit me, Sir, to clofe this addrefs
to you with an example in each fpecies of problems.

Were it propofed to draw a triangle given in fpe-
cies, that two of its angles might touch each a right
line given in pofition, and the third angle a given
point. It is obvious, how difficult it would be to
adopt a commodious algebraic calculation to this prob-
lem notwithftanding it admits of more than one
very concife folution, as follows.

Let the lines given in pofition be AB, Fjo.

A C and the given point D, the triangle 2o,' 2
given in fpecies being E D F.

In the firft place fuppofe a circle to pafs thr ,
the three points A, E, D, which fhall inter- Fja 1
fed AC in G. Then E G, D G being a‘ 9'
joined, the angle DEG will be equal to the given
angle DAC, both infilling on the fame arch DG;
alfo the angle E D G is the complement to two right
of the given angle B A C : thefe angles therefore
are given, and the whole figure EFGD given in
fpecies. Confequently the angle E G F, and its equal
ADE will be given together with the fide D E of
the triangle in pofition.

Again, fuppofe a circle to pafs through the three
points A, E, F, cutting AD in H, and
EH, F H joined. Here the angle E F H 'g'
will be equal to the given angle E A H, and the an-

Vol. LIH. Xxx gle

c 518 ]

gle FEH equal to the given angle F A H. There-
fore the whole figure E H F D is given in fpecies,
and confequently the angle A D E, as before.

In the laft place fuppofe a circle to circumfcribe
r-. the triangle, and interfedt one of the lines,

^ 2I’ as AC, in I. Here DI being drawn,
tlie angle DIF will be equal to the given angle
D E F in the triangle ; confequently D I is inclined
to AC in a given angle, and is given in pofition,
as alfo the point I given ; whence I E being drawn,
the angle FIE will be the complement of the angle
E D F in the triangle to two right. Therefore I E
is given in pofition, and by its interfedtion with the
line A B gives the point E, with the pofition of
DE, and thence the whole triangle, as before.

Here it may be obferved, that the angle D of
the triangle EDF given in fpecies touching a given
point D, and another of its angles touching AC, the
line I E here found is the locus of the third an-

gle E.

Again, in the agronomical lectures of Dr. Keil, it
is propofed to find the place of the earth in the eclip-
tic, whence a planet in any given point of its orbit
{hall appear flationary in longitude, and a folution
is given from the late eminent aflronomer, Dr. Hal-
ley, upon the affumption, that the orbit of the earth
be confidered as a circle concentric to the Sun.

But for a compleat folution of this problem let the
following lemma be premifed.

The velocity of a planet in longitude bears to the
velocity of the earth the ratio, which is compounded
of the fubduplicate ratio of the latus re Slum of the
greater axis of the planet’s orbit to the latus reflum

of

[ 5^9 ]

of the greater axis of the earth’s orbit, of the ratio
of the cofine of the angle, which the orbit of the
planet makes with the plane of the ecliptic, to the
radius, and of the ratio of a line drawn in any angle
from the center of the fun to the tangent of the or-
bit of the earth at the point, wherein the earth is, to
a line drawn in the fame angle from the fun to the
tangent of the orbit of the planet projected upon the
plane of the ecliptic at the place of the planet in the
ecliptic.

Let A be the fun, B C the orbit of any planet,
D E the fame projected on the plane of the ecliptic,
F G being the line of the nodes, B the place of the
planet in its orbit, D its projected place : then the
plane through B and D, which fhall be perpendi-
cular to both the planes B C and D E, interfe&ing
thofe planes in BH, DH, the lines BH, DH will
be both perpendicular to the line of the nodes, and
the angle BHD the inclination of the orbit to the
plane of the ecliptic. But tangents drawn to B C
and DE at the points B and D refpedtively will
meet the line of the nodes, and each other in the
fame point I, and the velocity of the planet in lon-
gitude will be to its velocity in the orbit B C, as D I
to BI.

Now from the point A let A K fall perpendicular
on B I, and A L be perpendicular to D I : then
the ratio of D I to IB will be compounded of the
ratio of D I to D H, or of A I to A L, of the ratio
of DH to BH, and of that of BH to B I, that is,
of AK to A I. But DH is to BH as the cofine
of the inclination of the orbit to the radius, and the
two ratios, that of A I to AL, and that of AK to
A I, compound the ratio of AK to A L : therefore

X x x 2 the

[ 520 ]

the velocity of the planet in longitude is to the ve-
locity in its orbit in the ratio compounded of that of
tire coline or the inclination of the planet’s orbit to
the radius, and that of AK to AL.

Moreover the ratio of the velocity of the planet in
B to the velocity of the earth in any point of its or-
bit is compounded of the fubduplicate of the ratio
of the laius re Slum of the greater axis of the planet’s
01 bit to the latus reffium of the greater axis of the
taiths orbit, and of the ratio of the perpendicular
le t fall from the lun on the tangent of the earth’s or-
bit at the earth to AK, the perpendicular let fall on
the tangent of the planet’s orbit at B. Therefore
the velocity of the planet in longitude, when in B,
to the velocity of the earth in any point of it’s orbit
is compounded of the fubduplicate ratio of the latus
rechim of the greater axis of the planet’s orbit, to the
uiius re Hum of the greater axis of the earth’s orbit, of
the ratio of the co-line of the inclination of the pla-
net s orbit to the radius, and of the ratio of the lore-
laid perpendicular on the tangent of the earth’s orbit
to A L, the perpendicular on D I : thefe perpendi-
culars being in the fame ratio with any lines drawn
in equal angles to the refpedfive tangents.

This being premifed, the place of a planet in the
ecliptic being given, the place of the earth, whence
the planet would appear hationary in longitude, may
be aihgned thus.

A denoting the fun, let B be a given place of any pla-
net in it s orbit projected orthographically on the plane
T>. 23. the ecliptic, CB the tangent to the pla-
net’s projected orbit at the point B, which
will therefore be given in pofition. All'o let DE be

the

L 521 ]

the orbit of the earth, and the point D the place of
the earth, whence the planet would appear ftationary
in longitude at B.

Join AB, and draw a tangent to the earth’s orbit
at the point D, which may meet CB in F, and
the line AB in G5 draw alfo AH making with
DF the angle AHD equal to that under ABC.
Then the point D being the place, whence the pla-
net appears ftationary in longitude, as F B to F D fo
will the velocity of the planet in longitude in B be
to the velocity of the earth in D, this velocity ot
the planet in B being al('o to the velocity of the eartn
in D in the ratio compounded of the fubduplicate of
the ratio of the l atm re Bum of the greater axis of
the planet’s orbit, to the latus rcSiuni of the greater
axis of the orbit of the earth, of the ratio of the
co-line of the inclination of the planet’s orbit to the
plane of the ecliptic to the radius, and of the ratio ot
AH to AB : therefore the ratio of FB to FD will
be compounded of the fame ratios ; and it I be taken,
that the ratio of A B to I be compounded of the
two firft of thefe, I wiil be given in magnitude, and
the ratio of F B to F D will be compounded of the
ratio of A B to I, and of All to AB. Whence
FB will be to FD as AH to I; and the angles
CB A, or FBG, and A H G being equal, where-
by F G will be to FB as AG to A II, by equa-
lity F G will be to F D as AG to I, and D H
being drawn parallel to FB, BG will be .to BK as
FG to FD, and therefore as AG to I.

But now, as this problem may be diftributed into vari-
ous cafes, in the firft place conlider the eartn as mov-
ing in a circle concentric to the iun, and likewife C I*,
the tangent to the planet’s orbit, perpendicular to AB.

But

[ 522 ]

But here DK alfo will be perpendicular to AB,
and A B meeting the earth’s orbit in L and M, the
2 redangle under K AG will be equal to the

fquare of A M. But B G being to B K as

A G to I, if B N be taken equal to I, B G will be to

B K as A G to B N, and A B to KN alfo as A G to

B N, and the redangle under NK, AG equal to
that under A B and I : therefore the redangle under
K A G being equal to the fquare of A M, N K will
be to K A as the redangle under A B, I to the fquare
of A M, that is, in a given ratio, and K D with the
point D will be given in polition.

Again, when C B is not perpendicular to L M,
let D O be perpendicular to L M. Then the
redangle under OAG will be equal to the fquare
pio. 2„ of AM. But BN being taken equal
to I, as before, the redangle under N K,
A G will be equal to that under AB, I; whence
N K will be to AO in the given ratio of the
redangle under AB, I to the fquare of AM, There-
fore N P being taken to P A in that ratio, the point
P will be given, and K P, the excefs of N P above
N K, will be to P O, the excefs of A P above
A O, in the fame ratio. Hence, as D K is parallel to
C B and D O perpendicular to LM, the triangle K O D
is given in fpecies, and if P D be drawn, the angle
O P D will be given ; for the co-tangent of the angle
O K D will be to the co-tangent of the angle O P D,
as KO to OP, that is, as the redangle under A B, I
together with the fquare of A M to the fquare of A M,
and hence the point D is given by the line P D drawn
from a given point P in a given angle APDj and if
A D be drawn, A D will be to A P as the line of the
angle A P D to the line of the angle PDA; this angle

therefore

[ 523 ]

therefore is given, and the angles A P D, P D A be-
ing given, the angle P A D is given.

Coroll. Here, where the orbit of the earth is fup-
pofed a circle, the ratio of 1 to A B, that is, of the
rectangle under A B, I to the fquare of A B, will be
compounded of the lubduplicate ratio of AM, the
femidiameter of the earth’s orbit, to half the latus rec-
tum to the greater axis of the planet’s orbit, and of the
ratio of radius to the co-line of the inclination of the
planet’s orbit to the plane of the ecliptic ; and adding
on both fides the ratio of the fquare of A B to the
fquare of A M, the ratio of the redangle under A B,
I to the fquare of AM will be compounded of the
ratio of the fquare of A B to the rectangle under A M^
and the mean proportional between A M and the half
of this latus reffium of the planet’s orbit, and of the ratio
of the radius to the co-line of the inclination of the
net’s orbit.

In the next place, though the earth’s orbit is not a
circle concentric to the fun ; yet if the projection of
the planet falls on the line perpendicular to the axis
of the earth’s orbit, the point A will Hill bifed L M.

In this cafe draw to the points L and M tangents
to the elliplis meeting in P, from whence through
D drawP D meeting the elliplis again in Q^and in-
terfering L M in O. Here if a tangent be drawn to
the elliplis in it will meet the tangent at Fig<

D on the line L M in the point G.

Now L G will be to G JV1 as L O to O M, and
the point A bifeding L M, the redangle under GAO
will be equal to the fquare of A M. But B G is to
B K as A G to I. Therefore B N being taken
equal to I, A B will be to K N as A G to I, and
the redangle under AB, I equal to that undei AG,

[ 524 ]

KN: whence AO being to K N as the redangle
under GAO to that under AG and KN, AO will
be to K N as the given fquare of A M to the red-
angle under AB and I, alfo given.

Draw R P parallel to C B, and take PS to A P,
alio N T to A R in this given ratio inverted. Then
will the points T and S be both given, alfo A O will
be to K N, and R O to K T, as A R to N T, that
is, as A P to P S. Therefore if T V be drawn par-
allel to C B, that is, to K D, and V S parallel to
LM, thefe lines will be both given in pofition ; and
WDXY being alfo drawn parallel to LM, WD will
be equal to KT, and RO being to KT, as
AP to PS, DY will be to WD as XP to PS, and by
compofition YW to WD as XS to PS, and the given
redangle under YW, or SV, and PS equal to that un-
der W D, and XS. Whence SV being parallel to LM,
the point D will be in an hyperbola paffing thro’ P, and
having for afymptotes the lines VS, VTgiven in pofition.

But if the projedion of the planet fall on the axis
of the earth’s orbit, or the fame continued, A B ex-
tended to the earth’s orbit in L and M will be the
axis of that orbit.

If alfoC B fhould be perpendicular to AB, K D
Fj _ would be ordinately applied toLM; and
lg‘ 2"‘ the point R being taken, that Q^being the
center of the orbit, the redangle under A QJl be
equal to the fquare of Q_ M, the fame will be equal
alfo to the redangle under G Q^K ; whence as G Q
to A QJo R Q^to Q^K, and A G to A as K R
to QJC. But, as above, B G being to B K as A G to I,
and B N taken equal to I, B G will be to B K as
A G to B N, and A B to K N alfo as A G to B N or I.
1 herefore if N S be taken to A B as 1 to A Q, by

equality

[ 525 ]

equality N S will be to N K as A G to A Q, that is,
as K R to Q^K ; and in the lad place N S to K S as
K R to QJl, that is, the rectangle under S K R equal
to the given redangle under N S, QJl • whence the
point K, the pofition of K D, and thence the point
D will be given.

But it D K be not ordinately applied to L M, let
D O be oidinately applied to L M. Then here the
rectangle under A QJl, equal to the fquare of QM,
will be equal to that under O QG, and
G t0 A Q_as QJl to O Q^whence by 2^*
compofition AG to AQjis OR to OQ^ But BN be- “
ing now alio taken equal to I, and N S to A B as
I to A Q, A B will be here in like manner to
K N as AG to I, and NS to K N as A G to A Qj
therefore NS will be to KN as OR to OQ, and'
by converfion NS to K S as OR to Q^R. But
N S and QJl being both given in magnitude, if S P
be taken to N S as QR to P R, the point P will be
given, and alfo by equality S P will be to K S as O R
to PR; whence if R V be drawn parallel to D O,
and S T to K D, both R V and ST will be given
in pofition, one pafiing through the given point R,
parallel <o the ordinates applied to the axis LM, and
the other through the point S alfo given, and parallel
to K D or C B : alfo DTV being drawn parallel to
M L, D T will be equal to K S and D V equal to
O R, therefore as S P to D T fo D V to P R, and the
redfangle under SPR equal to that under TDV,
confequently the point D in an hyperbola paffing thro’

P, and having for afymptotes the lines ST, RV given
in pofition.

Yyy

In

[ 526 ]

In the laft place when the line LM drawn through
t’ne fun in A, and the proje&ed place of the planet
in B, is neither the axis of the earth’s orbit, nor bi-
feded in A, the tangents to the points L,M
29* being drawn to meet in P, let LM be bifed-
ed in Q, and the point R taken, that the redangle under
A Q R be equal to the fquare of Q M, whereby
P D O being drawn, the redangle under A QR (hall
be equal to that under O QG, and QG to A Q as
QJl to QjO, or by compofition A G to A Qjis O R
to QO. Therefore if N B be here alfo taken equal
to I, and N S to A B as I to A Q, A B being as
before, to N K as A G to I j by equality N S will be
to NK as A Gto AQ^thatis, as OR to CfO. Whence
by converfion N S will be to K S as O R to (VR ;
and if P T be drawn parallel to C B and S V be here
taken to N S as QJL to T R, by equality S V will
be to K S as O R to T R and alfo by converfion S V
to K V as O R to O T. Moreover S V will be given
in magnitude, and the point V given; therefore VW
drawn parallel to C B, or K D, will here be
given in polition. But WDXY being alfo drawn
parallel to R V, S V will be to K V, or D W, as
Y D toXD, and Y Z being taken equal to the given
line S V, Y Z will be to D W as Z D to X W, equal
to T V, and the given redangle under Y Z, T V
equal that under W D Z. Therefore r Z being
drawn parallel to R P, R T, and its equal Y Z, be-
ing given, the line r Zis given in pofition, and the
point D in an hyperbola having for afymptotes V W,
F Z, and palling through P.

4

Thus

C 527 ]

Thus is this problem in all cafes folved either by a
right line, or an hyperbola given in portion, which
fhall interfe6l the projected orbit in the point fought.
For though in each cafe the proje&ion of the planet
has here been confidercd as within the orbit of the
earth, the form of argumentation will be altoge-
ther fimilar, were the projection of the planet without.
And this is agreeable to the method, I have pur-
fued throughout this difcourfe, where I have al-
ways accommodated the expreffion to one fituation
only of the terms given and fought in each article ;
the variation neceffary for the other cafes, when one
has been duely explained, being fufficiently obvious.

In the 5th volume of the Commentaries of the
Royal Academy at Peterfbourg is given an algebrai-
cal computation for a general folution of this problem
in the orbits of any two planets projected on the
plane of the ecliptic ; but with this overfight of ap-
plying to the projected orbits a propolition from Dr.
Keil’s Agronomical Lectures, which relates to the
real orbits (<3).

However from the geometrical folution now given
a calculation for affigning the point D may be formed
without difficulty. L D M being the orbit of the
earth, A is the focus, and R P perpendicular to the

(tf) The demonftration of Dr. Keil’s proportion proceeds on
the known property in the planets of having their periodic times
in the fefquiplicate ratio of the axes of their orbits, which con-
fines the propofition to the real orbits; for in each planet the pe-
riodic time through the projected orbit is the fame, as through the
real, though the axis in one be not equal to the axis of the
other.

Yyy 2

axis..

C 528 ]

axis. Let this axis be ab meeting R P in c, rZ in
d, P T in * and W V in f Then the angle a AM
is given, being the didance between the heliocentric
place ot the planet in the ecliptic from the earth’s
aphelion. Alfo PT being parallel to C B, the angle
AT e, and confequently the angle A e T, will in
like manner be given, whence the points r, R, T, V
being given, as in the folution above, the points d,
c, e , and / will be given, the triangles A II c, A T e,
being given in fpecies, and fimilar refpedtively to the
triangles A r d , and A V f Alfo the redtangle under
W D Z being equal to that under R r, V T, if D K
be continued to the axis in^, and D/6 be drawn par-
allel to PR, the redtangle under f g> hd is equal to
that under j c, d c, and both being deducted from
the rectangle under f h d the excefs of the re&angle
under/’ h d above that under/ e, dc will be equal to
that under g h d, fo that this difference will be a mean
proportional between the fquare of h d and the fquare
of bg, which is in a given ratio to the fquare of h D,
and therefore in a given ratio to the recftangle under
abb , D b being ordinately applied to the axis
a b.

Thus a biquadratic equation may be formed, where-
by the point b fhall be found, and thence the point D,
whofe diftance from A is to h e as the excentricity of
the earth’s orbit to half its axis.

Therefore I fhall only obferve farther, that here
occurs an obvious queftion, what, in fo extended a
fearch for principles leading to the folution of any
problem, as the ancient analyfis admits of, can con-
duct to the mod; genuine upon each feveral occafion.

But

[ 5*9 ]

But for this end, where commodious principles do
not readily offer themfelves, the moff general means
is to confider firft fimple cafes of the problem in
queffion, and from thence to proceed gradually to
the more complex, as has been here done in the pre-
fent problem, where the feveral preceding cafes lead
one after another to the points and lines required for
the laft cafe, wherein the problem is ffated in its moff
extenfive form.

<

INDEX.

'

-

*

X

X

I N D E

TO THE

Fifty-Third VOLUME

OF THE

Phllofophical 'Tranfa&ions .

For the Year 1763.

A.

Cademy Royal at Paris, animadverfion on a paffage in
the hiftory of it’s memoirs, p. 342.

Achard , Mr. his remarks on fwallows along the Rhine, p„

A

ioi.

Atpinus, Mr. his account of his eleflrical experiments, p.
437. — Note, p. 442, 449.

AElia, an epithet given to feveral cohorts, p. 137.

Akenfide , Dr. MaVk, his account of a blow upon the heart
and it’s effefts, p. 353.

Aleppo , account of the plague there and other calamities,

p. 39 Intenfe cold there, p. 40 — Extraordinary a-

necdotes relating to the plague, p. 40.

Alexander ,

index.

Alexander Severus, ftyled Dominus, p. i34. The opinion of
hls tendeney to chriftianity, on what founded, p. 11c.

Alphabet, Maltefe-Punic, p. 282— The Punic and Phce-
nician originally the fame, p, 2 89.

Antiquities , great fcene of, p. 127.

Apartments , Subterraneous, difcovered at Civita Turchi-
no in Italy, p. 127.

Appendix to the problems on chances, p. 404.

Archimedes , a mechanical affertion of his obieCted to p
107. 5

Arderon , Mr. William, his account of rain fallen in afoot
iquare at Norwich, p. 9.

Agronomical oblervations, p. 241 Tables, p. 247,

B,

Bark of willow, a remedy for agues, p. 95.

Lartram , Mr. John, his obfervations made at Penfilvania,
on the yellowifh wafp of that country, p. 37.

Bafilica , it’s various fenfes, p. 137.

Bayes , Rev. Mi. Thomas, his letter on a logarithmetical

miftake of fome eminent mathematicians, p. 269 His

elTay towards folving a problem in the doctrine of
chances, p. 370.

Bergman , Mr. Torbern, his obfervations on electricity and
a thunder ftorm, p. 97.

Berlin , intenfe cold there, p. 62.

Bohadfch , Dr. his remarks on the Sea-pen, p. 422.

Borlafe , Rev. Mr. William, his account of the late mild
weather in Cornwall and quantity of rain fallen there in
the year 1762, p. 27.

C.

Camhridgejhire produces fine faffron, p. 198. — The bcft
Cortex Anglicanus , ibid.

Cafe of a perfon, juft brought forth into this world, con-
cerning events, p. 409. — Of a perfon feeing a lottery
drawn, p. 41 1.

Chalmers ^

INDEX.

Chalmers , Dr. his account of the difeafe called Tetanus,
p. 24.

Chances, doctrine of, problem in it folved, p. 370.

Cold, extreme at Aleppo, p. 40. — At Berlin, p 62.

Colebrook , Mr. Jofeph, his account of a cafe in which
green hemlock was ufed fuccefsfully, p. 346.

Conductor, iron, inftance of it’s great utility, p. 94.

Comet of 1759, obiervations on it, p. 3.

Cornwall, winter there milder than in any other part of
this idand, p. 27 — Quantity of rain fallen there in the
year 1762, ibid.

Cyder-apples , where bed, p. 198.

D.

Darknefs , remarkable, p. 63.

Daval , Peter, Efqv his letter fhewing the Sun’s diftance
from the earth, from Mr. Short’s obfervations relating
to the horizontal parallax of the Sun, p. 1.

Dawes, the Rev. Mr. Thomas, chaplain to the fadtory at
Aleppo, his account of the plague there, p. 39.

Die, new, from the berries of a weed in South-Carolina,
p. 238.

DoEirine of chances, eflfay towards folving a problem in
it, p. 370.

Dominus , a title given to Severus Alexander, tho’ Lan>
pridius fays he refufed it, p. 134.

Dunn, Mr. Samuel, his account of the appulfe of the
Moon to the planet Jupiter, obferved at Chelfea, p. 31.
His remarks on a cenfure of Mercator’s chart, p. 66.
His account of a remarkable meteor, p. 351.

Du Pont, Mr. Andrew Peter, his account of a remarka-’
ble marine infedl, p. 57.

Durham, county of, Roman infeription there, p. 136..*.
Yields the belt muftard feed, p. 198.

Earth ,

Vql. LIII.

Z zz

INDEX.

E.

Earth , it’s mean diameter 3958 miles, p. 2.

Earthquake , in Siberia, large account of, p. 201. — Re-
flexions on it, p. 218. — At Chattigaon, 252.— .In the
Eaft Indies, p. 256, 263, 265.

Earths , calcareous, their fecundating qualities explained,
p. 366.

Eclipfe of the Sun, April 1, 1764, projection of it,
p. 240. — Of the Sun and Moon obferved at Calcutta,
p. 256.

Eden, river, in Cumberland, a remarkable decreafe of.

p. 7.

Edwards , Mr. George,

obfervation made by him in op

tics, p. 229.

Ehret , Mr. Geo. Dionyfius, his account of a fpecies of
Ophris, p. 81. — Of a new Peruvian Plant lately intro-
duced into the Englifli gardens, p. 130.

EJaJiic fubftance, p. 459.

Electricity, it’s effects on a tetanus, or mufcular rigidity,
p. 10. — New experiments in it, p. 84. — Electrical
horfe-race, p. 89.— Further experiments, p. 43^*

Eliot , Mr. his letter on the Virginian fand iron, p. 56.

Ellis , John, Efq; his account of the Sea-pen, or Penna-
tula Phofphorea of Linnaeus, with obfervations on Sea-
pens in general, p. 419.

Emprejihotonus , account of this diforder, p.22,25.

Engines, method of leflfening the quantity of friction in

. them, p. 1 39. ■ ; ■

Equitata, the meaning of the word, in diftinction to
eqtiefiris, p. 137.

Ejfex, the fineft Saffron-flowers produced there, p. 1 89 —
alfo the beft cortex fait gnus, ibid.

Etrufcan inicriptions and paintings, p. 12 7.

Events, mathematical problems concerning their degrees of

probability, p. 376. #

Experiments ,

INDEX.

Experiments on fand-iron, p. 48 — New, on electricity, p.

84, 436. — On the tourmalin, p. 447, 451;
Extraordinary anecdotes relating to the plague at Aleppo,

P- 45*

F.

Fergufon , Mr. James, his delineation oF the tranfit of Ve-
nus expected in the year 1769, p. 30 — His account of
a remarkable fifh taken in King’s- Road near Briftol, p.
170. — His projection of the eclipfe of the Sun on
April 1, 1764, p. 240.

Fire, electric, whether any heat in it, p. 89, 92.

Fijh, remarkable, taken in King’s-Road, p. 170.

Fitzgerald , Keane, Efq; his method of leffening the quan-
tity of friction in engines, p. 139.

Fly , vegetable, account of the infect fo called, p. 271.

G.

Gabry , Mr. Peter, his obfervations, at the Hague, of the
comet which appeared in the month of May 1759? P* 3*
— His obfervationc at the fame place of a fiery meteor
like a chafm, p. 5.

Geach , Mr. Surgeon at Plymouth, his account of two re-
markable cafes in furgery, p. 231.

Geometers , ancient, a diicourfe on the locus for three or
four fines celebrated among them, p. 496.

Glafs , it’s refractive power, p. '177.

Gloucefterjhire , beft Valerian-roots grow there, p. 198.

Guidon , Mr. Edward, his tranflation from the Perfian of
an account of an earthquake at Chattigaon, p. 251. —
His own account of the fame, p. 263.

Gunpowder , Tartars and Kalmucks make it very expedi-
tioufiy, p. 209.

Zzz 2

Hamilton ,

I N D E X.

H.

Hamilton , Hugh, D. D. his letter, demonftrating the
properties of the mechanic powers, with obfervati-
ons on the methods commonly ufed for that pur-
pofe, p. 1 03.

Hazardous way of taking fwallows, p. 10 1,

Heart , account of a blow upon it, p. 353.

Heat , whether any in eledtric fire, p. 89.

Hemlock , green, account of a cafe, when it was happily
tried, p. 346. .

Hirjly Rev. Mr. an account of an earthquake at Chatti-
gaon, communicated by him, p. 251. — His account of
an earthquake in theEaft Indies, and of two eclipfes of
the Sun and Moon, obferved at Calcutta, p. 256.

Horne> Mr. Henry, his obfervations on fand-iron, p. 48,

Horfe-race , eledtrical, p. 89.

Horfeley , Mr. miftaken in the meaning of the word equi-
tata, p. 137.

Hornfby , Rev. Mr. his obfervations on the parallax of the
Sun, p. 467.

Huxham , Dr. his letter on two remarkable cafes in fur-
gery, p. 231.

L

Infcriptions , Etrufcan, p. 127.— .Roman, at Durham, p.

j 26. Very curious, at Tunis, p, an.* Punic*

p. 274.

InfeH, remarkable marine, p. 57.

Iron , made from the Virginian black fand, p. 48. — And
the excellence of fuch iron, p. 58.

Iron-conduttor , inftance of it*s great utility in thunder-
ftorms, p. 94,

Keih

INDEX,

K.

Keily Dr. charged with a miftake, p. to6.

Kent, the Cortex Anglicanus, or willow-bark, there con-
jedtured to be the beft, p. 198.

King's-road , remarkable fifh taken there, p. 170.
Kinnerjley, Mr. Ebenezer, his accounts of new experiments
in electricity, p. 84.

L.

Lever , Sir Ifaac Newton’s proof of it’s property, p. 109.

New proof of it’s property, p. 112.

Light , refra&ed, rules and examples concerning it, p. 73.
Lightening , it’s fetting things on fire difcuffed, p. 93.— Sin-
gular effedt of it, p. 100.

Lincolnjhire, fuppofed to produce the beft Cortex Salignus,

p. 198. _

Lindoy Mr. Mofes, his account of a new die from the

berries of a weed in South Carolina, p. 238.

Linnaus, account of his Pennatula Phofphorea, p. 419.

Logarithms , letter on, p. 269 . .

Longitude , diflcicncc of, between Greenwich and Pans,

" obfervatories determined by Mr. Short, p. 158.

M

Marine-infefty P-57-. . - „ ,

Mechanic powers, their properties demonluated, p. 103.
Mercator' s chart , remarks on a cenfure of it, p. 66.— -De-
fended, p 69. #

Meteor , hey* obfervations on it, p. 5.— account of a re-
markable one, 341.

Melbourne, William, Efqs his account of a remarkable
decreafe of the river Eden in Cumberland, p. 7.

Megilp

INDEX.

Mogily, or barrows-, account of a remarkable one, p. 357.
— Abound in nitre, ibid;

Monti RoJJi , account of them, p. 127.

Moon , account of it’s appulfe to the planet Jupiter, ob-
ferved at Chelfea, p. 31.— Eclipfe of it obferved at Cal-
cutta, p. 25.6.

Mount ame, Mr. William, his defence of Mercator’s chart
ao-ainli the cert fare of the late Mr. Weft of Exeter,

o

p. 69.

Murdock , Mr. P. his rules and examples for limiting the
cafes in which the rays of. refraCted light may be reunit-
ed in a colourlefs pencil, p. 173.

Mufcular rigidity , effects of electricity on it, p. 10.

N.

Netberby, it’s name under the Romans, p. 136.

Newton , Sir Ifaac, his proof of the property of the lever,
p. 109.

Nitre , method of making it in Podolia, p. 356.— Signs of
it in a foil, p. 357.— Thoughts on it’s origin, p. 363.— -
More of it made in the PrufTian dominions than in all
Europe befides, p. 362.— Chemical proceffes concern-
ing it, p. 3d/.

Obfervatories at Greenwich and Paris, theii difference of
Longitude determined by Mr. Short, p. 158.

Opbris , fpecies of, p. 8ii

Opiftbonos , account of this difeafe, p. 22.

Opticks , obfervations in, p. 229. . .

Oxfordjhire , it’s Valerian-roots the moft medicinal, p. 19S.

P.

Paintings , Etrufcan, 127.

Pallas, Dr. Simon, of Berlin, his ftate
in the winter of 1762.

2

of the cold there
p. 62
Parallax

I N D E x;

Parallax of the Sun, horizontal, obfervations on it, p. i —
Treated of more at length, p. 300. — Means of the fe-

veral determinations of it, p. 339 Mr. Hornfby’s

obfervations on it, p. 467.

Pemberton , Dr. his difcourfe on the locus for three or
four lines celebrated among the antient geometers,
p. 496.

Plague and other calamities at Aleppo, p 39.

Plants , catalogue of fifty from Chellea Garden, prefented
to the Royal Society for the year 1762, purfuant to the
direction of Sir Hans Sloane, p. 32. — Singular, p. 81.
— A new Peruvian one lately introduced into the Eng-
lifh gardens, p. 1 30.

Podolia , manner of making nitre there, p. 356.

Powers , mechanic, properties of them demonftrated, p.

io3-

Pringle , Dr. utility of his experiments, p. 366.

Problems , by profeiTor Waring, p. 294.

Punic, infcription, p. 274.

Punic tongue, ftill the vernacular language of the com-
mon people at Malta, p. 291.

R.

Rain fallen in a foot fquare at Norwich, account of, p. 9.
— Quantity fallen in Cornwall in the year 1761, p. 2 7.
— Mean quantity of it in a year, p. 364.

Refinance in eledtrical experiments illuftrated, p. 458.
Rigidity , mufcular, effedts of eledtricity on ir, p. io.— .
Cold a caufe of it, p. 20.

Roman infcriptions at Netherby in Cumberland, p. 133.—;
At Tunis in Africa, p. 211.

Rutherforth , Dr. an argument faid to be improperly appli-
ed by him, p. 106,

i 1 C i ■ t ^ 2 1

INDEX.

S.

Saffron, where the ftneft, p. 198.

Salt-petre , mountains of it in Siberia, p. 209.

Sand-iron , experiments on, p. 48.

Sea-pen, or Pennatula Phofphorea of Linnaeus, account
of, with obfervations on Sea pens in general, by John
Ellis, Efq-, p. 419.— Dr. Bohadfch’s remarks on it, p.

422 Variety of them, p.426, 430.

Short , Mr. James, his obfervations on the Sun’s horizon-
tal parallax, p. 1. — His determination of the differences
of longitude between the royal obfervatories of Green-
wich and Paris, by obfervations of the tranfit of Mer-
cury over the Sun in the years r 723, 1736, 1743^ anc^
1753, p. 158.— His fecond paper concerning the paral-
lax of the Sun, p. 300.— His animadverfion on a paffage
in the hiftory of the Memoirs of the Royal Academy at
Paris, p. 342.— His method of determining the appa-
rent leak diftance of the centers of the Sun and Venus,

P* 343* _ . . r

Siberia , earthquake there, p. 201 — Worthy the notice or

the curious, p. 203. — Reflexions on the faid earth-
quake, p. ao8. . ,

South -Carolina, new fpecies of Sea-pen found on it s coaft,

p. 426* _ . , ,

Sterling , Rev. Mr. James, his account of a remarkable

darknefs at Detroit in America, p. 63.

Stone , Rev. Mr. his account of the fuccefs of the bark of
the willow in the cure of agues, p. 195.

Sun's mean horizontal parallax, p. 1,59. — Its diftance
from the earth proved from it, p. 2. — Account of it s
eclipfe, April 1, 1764, p. 140. — It’s parallax farther
determined, and the quantity thereof more fully aicer-
tained, p. 300. — The apparent leaft diftance of it s cen-
ter and that of Venus determined, p. 34 3> 344'

Surgery , two remarkable cafes in, p. 231.

Swallows ,

INDEX.

Swallows, remarks on them, p. ioi.

Swini on, Rev. Mr. his attempt to explain a Punic infcrip-
tion, lately difcovered in the ifle of Malta, p. 274.

T.

Tables, adronomical, by Mr. Fergufon, p. 247.

Taylor, the Rev. John, LL. D. his obfervations on two
antient Roman infcriptions difcovered at Netherby in
Cumberland, p. 133.

Tetanus, account of this difeafe, p. 21;

Thoughts on the origin of nitre, p. 363.

Thunder-Jlorm , obfervations on, p. 97.

Tourmalin , experiments on it, p. 436.

Tranfit , fee Venus, p. 447, 451.

Tunis , remarkable Roman infcription there, p. 211.

y.

Valerian Roots, where the mod medicinal, p.198.
Vegetables, that they have their peculiar foils, exemplified,

p. 1 98.

Venus, it’s expe&ed tranfit, p. 30 It’s late tranfit, p.59.

lead di dance of it’s center and that of the Sun, p. 343.
Verelfi , his tranflation of the Perfian account of the earth-
quakes that have been felt in the province of Iflamabad
from the 2d to the 19th of April 1762, p. 265.

W.

1

Wargentin, M. his letter on the late tranfit of Venus, p. 59,’
Waring, profeffor, his problems, p. 294,

Wafp, yellowilh one of Penfilvania, p. 37.

Water , it’s refradive power, p. 177.

4 A Watfon >

INDEX.

Watfon , Dr. William, his obfervations on the effedls of
eledbicity applied to a Tetanus, or mufcular rigidity of

four months continuance, p. His account of the

infedt called the vegetable fly, p. 271.

Weft, remarks on a cenlure of Mercator’s Chart in a pofl>
humous work of his, p. 66.

Weymarn , Monf. his account of an earthquake in Siberia,
p. 201.

Wilcox , Jofeph, Efq; his account of fome fubterraneous
apartments, with Etrufcan infcriptions and paintings, dif-
covered at Civita Turchino in Italy, p. 127.

Willow-bark , a remedy for agues, p. 195 — It’s favou-
rite foil, p. 198.

Wilmar , Dr. John, his catalogue of the fifty plants from
Chelfea Gardens, prefented to the Royal Society by the
worfhipful company of Apothecaries for the year 1762,
purfuant to the direction of Sir Hans Sloane, Baronet,
p. 32.

Wilfon , Mr. B. his letter on electricity, and the tourmalin,
p. 436.

Wine, fpirit of, it’s refradtive power, p. 177. .

Wolf, Dr. his account of the method of making nitre in
Podolia, p. 356.

The End of Vol. LIIL

ERRATA.

VOL. LI. Part II. for the Year 1760.

Page 688. line 21, he. for Viftoriam in averfa parte Gradientem
prae fe ferentes, denarios tamen, in perpetuam rei memoriam,
lignari ]\ifihX..—infert— Denarios tamen, Vidtoriam in averfa parte
Gradientem prae fe ferentes, in perpetuam rei memoriam, fignari
juffit.

VOL. LIII.

Pag. 136 line 21 dele have.

375 2 from the bottom, dele every.

397 firft line in the note, for rP~l read r1~l .

4c 1 erafe the afterifk in the 4th line from the top,

and place it in the iothline.

405 6 and 10, for on read in

415 4 from the bottom, for 1-2 E read 1 + 2 E

416 1 for E read £ : and in the fecond line draw a

ftroke over z3, he.

418 3d and 4th lines in the note, for comes almoft as
near read, comes, in moft cafes, almoft as near
446 31 for fupedt r. fufpedl

448 22 for fig. 2. r. fig. 1.

446 1 7 /or fig. 1. r. fig. 3.

30 for fig. 2. r. fig. 4.

29 f°r % 3* % 5-

12 for equally r. unequally
9 for Tab. XXIII. r. Tab. XXII.

45i

458

465