Natural History Museum Library

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PHILOSOPHICAL

TRANSACTIONS,

GIVING SOME

ACCOUNT

OF T FI E

Prefent Undertakings, Studies, and Labours,

O F T H E

INGENIOUS,

IN MANY

Confiderable Parts of the W O R L D.

VOL. LI. Part II. For the Year 1760.

L O N T> O N :

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

M.DCC.LXI.

>

NTS

CONTE

T O

Part II. V o l. LI.

XL. A Letter to the Honourable J. Th. Klein,
Secretary to the City of Dantzick, from
Mr. Peter Collinfon, F. R. S. concerning the
Migration of Swallows. p. 45-5?.

XLI. Obfervations on the Comet feen in January
1760^ by jaincs Short, M. A. F. R. S. In a
Letter to the Rev. Tho. Birch, H.H. Secretary
to the Royal Society. p. 46)-.

XLII. Obfervations on the fame Comet j by the Rev.
John Michell, M. A. Fellow of Queen’s Col-
lege in Cambridge. In a Letter to Mr. James
Short, F. R. S. p. 4 66.

XL1II. An Account of the fame Comet j by Nicholas
Munckley, 0/Tin coin’s- Inn, Efqi p. 467.

XL1V. An Account of the faid Comet ; by Mr.

Mark Day. p. 469,

XLV. Gf the vitriolic Waters a/’ Amlwch, in the
Ifle of Anglefey; with occaVnal Remarks on the
Hartfgll SpaWy defer ibed in the firft Volume of
the Edinburgh Efays and Obfervations phyfical
and literary , and in the ^th Volume of the CPhz-
lofophical TranfaclionSy and their Comparifon
with other Waters of the fame Clafs. By John
Rutty, M. CD. p. 470.

XLV I. An Account of that Fart of America, which
is near eft to the Land of Kamchatka ; extracted

from

CONTENTS.

from the Defcription of Kamtchatka by Trofef
for Krafhennicoff, printed at Pcterfburg, in two
Volumes, 410. in 1779; and tranfated and com-
municated by the Rev . D. Dumarcfque, D. D.
Chaplain to the Englifh Fablory at Pcterfburg.

P. 477.

XLVII. Remarks on the Mutations of the Stars j
by Tho. Barker, Efq\ of Lyndon, in Rutland:
Communicated by the Rev. W. Stukeley, M. D.
F. R. S. p. 498.

XLVIII. The Method of making Sal Ammoniac in
Egypr 5 as communicated by Dr. Linnaeus, from his
(Fupil Dr. Haflelquift, who had been lately in
thofe Tarts : By John Ellis, Efcjs F. R. S. p. 704.

XLIX. Mont him quor undam pr re alt or urn, magna
ligni fojfilis copia quafi infarblorum , brevis de-
fer ipt 10 Sam. Chrift. Hollmanni, Thilof ophite Tro-
feffor . Gocttingcnfis, et S. R. Sodalis. p. 50 6.

L. Experiments in ElcTiricity : In a Letter from
Father Beccaria, Trofejfor of Experimental CP ki-
lo fop by at Turin, to Benjamin Franklin, L.L.D.
F. R. S. p. 5-14.

Remarks on the preceding Taper , by Benjamin
Franklin, L.L.D. F.R.S. p. 727.

LI. An uncommon Cafe of an Hamoptyfs ; by Eraf-

mus Darwen, M.D. p. 52 6.

Lll. /In Account of the late Earthquakes in Syria :
In a Letter from Dr. Patrick Rull'cl, to his Bro-
ther, Alexander Ruffe!, M.D. F.R.S. p. 729.

LI1I. Remarks on the Bovey Coal : In a Letter to
the Right Honourable George Earl ^ Mac clef-
lie Id, T ref dent of the Royal Society. By Jere-
miah Milles, D. D. F. R. S. p. 734.

LIV. A new Method of computing the Sums of cer-
tain

CONTENTS.

tain Series ; by Mr. John Landcn : Communicated
by Mr, Thomas Simplon, F. R. S. p.

LV. Conjectures concerning the Caufe , and Ob-
fervations upon the Phenomena of Earthquakes >
particularly of that great Earthquake of the
Fir ft 0/ November 1755", which proved fo fatal
to the City of Lilbon, and whofe Effetls were
felt as far as Africa, and more or lefs throughout
almoft all Europe; by the Reverend John Michel],
M. J. Fellow of Queen's College , Cambridge.

p. 566,

LVI An Extract of a Letter from Abbe De la
Caille, F. R. S. and Member of the Royal Aca-
demy of Sciences at Paris, to Matthew Maty,
M. D. and F. R S. p . 63 y.

LVIE Extracts of fome Letters from Signor A la-
bate de Venuti, F. R. S. to J. Nixon, A.M. and
F. R. S. relating to fever al Antiquities in Italy.

P ■ S 1,6.

Rc marks on the pr ceding ExtraFls j in a Letter to
Charles Morton, M. "D. Secretary to the Royal
Society . By John Nixon, A. M. F. R. S. p. 63 p.

LVII.I. A Catalogue of the Fifty Plant sfrom C h e lie a
Garden, prefented to the Royal Society by the
Worftipful Company of Apothecaries , for the
7 ear 1 7 yp, purjuant to the Direction of Sir Bans
Sloane, Baronet , Med. Reg. & Soc. Reg. nuper
Preefes, by John Wiimer, M.D. clarijf. Socie-
tatis Pharmaceut. Load. Socius , FLort. Chelfean.
PrdfeClus & Prelector. Botanic. p. 6 44.

L1X. Some Account of the Animal fent from the-
E.ih Indies, by General Clive, to his Royal High -
nefs the Duke of Cumberland, which is now m
the Tower of London : In a Letter from fames.

f Par-

CONTENTS.

Parfons, M. D. F. R. S. to the Rev. Tho. Birch,
D. D. Secretary to the Royal Society. p.64.8.

LX. An Account of the Frogfijh of Surinam, ad-
dr effed to the Royal Society , by Mr. George Ed-
wards, F.R.S. p. 65-3.

LX I. An Account of a remarkable Operation on a
broken Arm ; by Mr. Charles White, Surgeon at
Manchefter, Communicated by George Lloyd, Efq ;
F. R . S. p. 657.

LX 1 1. An Account of a Bone fqjund in the 'Bel vis
of a Man at B rude Is ; by Terence Brady, M. D.

In a Letter to the Rev. Tho. Birch. D. D. Se-
cretary to the Royal Society. p. 660.

LX I II. An Account of an extraordinary Cafe of a
Lady , who fwallowed Euphorbium. By Dr.
Willis, of Lincoln: Communicated by Sir Fran-
cis Dafhwood, Bart. p. 662.

LX IV. An Account of artificial Cold produced at
Peterfburg: By F)r. Himfel. In a Litter to
‘Dr. Do Caftro, F. R. h1. Tranflated from the
French by james Parfons, M. D. F. R. S. p. 67 o.

LXV. An Account of a complete Luxation of the
Thigh Bone , in an adult Ferfon , by external Vio-
lence ; by Mr. Charles White, Surgeon , at Man-
chefter. Communicated by George Lloyd, Ejq\

F. R. S. p- 676.

LX VI. Conje Shires upon an in edited Parthian Coin.
By the Rev. John Sw inton, B. D. of Chrilt-
Church. Oxon, F. R. S. p. 680.

LXV 1 1. An Account of a Jlony Concretion taken
from the Colon of an Horfei by Mr. H. Baker,
F. R.S. p. 65? 4.

LXVIII. An Explanation of the Modes or Tones
in the ancient Grecian Mafic-, by Sir Francis

Haskins

CONTENTS.

Hafkins Eyles Stiles, Bart. F R. S. p. (Spy.
LXIX. An Enquiry into the Meafure of the Roman
Foot ; by Matthew Raper, Efq » F. R. S. p .774,
LXX. A Hefcription of a metalline Thermometer ;
by Keene Fitzgerald, Efq-, F. R S. Communi-
cated by the Right Hon. George Earl of Mac«
clesfield, Prefident of the Royal Society, p. 823.
LXXI. An Account of a Bird fuppofed to be bred
between a \ Turkey and a Pheafant } by Mr. George
Edwards, F.R.S. p. 833.

LXX II. An Account of a late \ Difcovery of Af
bftos in France: In a Letter to the Rev. Tho.
Birch, H. D. Secretary to the Royal Society ,
from Mr. Turberville Needham, F.R.S. p. 837.
LXXIII. An Account of the hot Baths ofV inadio,
in the Province of Coni in Piedmont; with the
State of the Weather at Turin in the Tear 1759 :

In an Extract of a Letter from Hr. Jofcph
Bruni, F.R.S. to Mr. Henry Baker F. R. S. p, 839-
LXXIV. An Account of a Specimen of the Labour
of a Kind of Bees, which lay up their Toung in
Cafes of Leaves , which they bury in rotten
Wood: In a Letter to Daniel Wray, Efq-, F. R S.
from Sir Francis Eyles Styles, Bart. F. R. S. p. 844-
LXXV. An Account of a Cafe of a luxated Thigh
Bone reduced ; by Mr. Charles Yonge, Surgeon >
at Plymouth ; Communicated by John Huxham,
M. H. F. R. S. p. 846.

LX XVI. Some Obfervations upon a Samnite-Etrul-
can Coin, never before fully explained i In a Let-
ter from the Rev. John Swinton, B. D. ^/’Chrift-
Church, Oxon. F. R. S. to the Rev . Thomas*
Birdi, H. H. Secretary to the Royal Society.

P* 85T •
LXXV It..

CONTENTS.

LX XVII. De Proximo Veneris fub Sole Tranfitu.

p. 86).

L XXVIII. A Propofal for discovering the Annual
Parallax of Sirius ; by the Rev. Nevil Maske-
lync, A. M. Fellow of Trinity College , Cam-
bridge, and F. R. S. p. 889.

LXXIX. Farther Experiments in Electricity ; by
Air. Benjamin VVilfon, F. R. S. p. 896.

LXXX. A Letter to Air. Benjamin VVilfon, F.R.S.
concerning EleClricity , from Air. Thorbern Berg-
man, 0/Opfal. p. 907.

LX XX I. SomeConf derations on a late Treatife, in-
tituled, A new Set of Logarithmic Solar Tables,
ere. intended for a more commodious Method of
finding the Latitude at Sea , by Two Qbferva-
tions of the Sun ; by H. Pemberton, M. D. R. V.
Lond. et R. A. Bcrol. S. p.910.

LXXXII. An Account of the Plants Halcfia and
Gardenia: In a Letter from John Ellis, Efq-,
F. R. S. to Philip Carteret Webb, Ejf F.R.S.

p. 929.

LXXXII T. An Account of an Eel ip fe of the Moon ,
2 id November 1760, obferved in Surry-Sireet in
the Strand, London j by James Short, M. A.
F.R.S. p -936.

LXXX1V. An Account of the Cafe of a young Alan ,
who had loft the Ufe of his Hands by cleanfing
Bra/s Wire ; by Air. Samuel More, Apothecary
in Jcrmyn-Streer. Communicated by Ch. Morton,
Al. D. Secretary to the Roy al Society . ibid.

LXXXV. A further Account of feme Experiments
ynade on the Bovcy Coal. p.941.

LXXXVI. De Aberratione Luminis , in Superficiebus
et Lentibus Spharicis refraCtorum . p. 944.

PART

[ 459 ]

PART II.

For the Year 1760.

XL. A Letter to the Honourable J. Th. Klein,
Secretary to the City o/D^ntzic^frofn Mr.
Peter Collinfon, F. R. S. concerning the
Migration of Swallows .

Read1Mgrch 9,1T not know which to admire moft
175 * I in my dear friend Klein, his learning,
or his judgment, in compiling fo many
ingenious and inftrudlive books in natural hiftory.

But I muft beg leave to diffent from my learned
friend, in an article he takes great pains to eftablifh ;
which is, that fwallows are not birds of paffage; but,
at the time of their going away, retire under water,
and live therein, all the winter. This I cannot com-
prehend, being fo contrary to nature and reafon ; for as
they cannot live in that hate, without fome degree of
breathing, this requires the circulation of the blood,
however weak and languid. Now, as refpiration is
abfolutely neceflary for circulation, how is it poffible
to be carried on for fo many months under water,
without the rifque of fuffocation ?

Vol. LI. O 0 o

Befides,

[ 460 ]

Befides, if fo remarkable a change was intended,
the great wifdom of the Almighty Creator would,
undoubtedly, be feen in lome particular contrivance,
in the ftrudture of the organs of the heart of this
bird, to enable it to undergo fo very remarkable a
change of elements : and my learned friend has not
attempted to fhow any thing of this nature, in order
to confirm his fyftem.

An eafy experiment may throw fome light on this

doubtful affair At the time of their going away,

take a fwallow, and confine it in a tub under water :
if it remains there for a week or two alive, without
any remarkable inconvenience, then there may be
fome probability for its continuing fo many months
in that ftate.

The conclufions, that are drawn from fome of the
tribe of infedts fubfifting under water, are far from
being conclufive, to found an analogy upon ; as in-
fers differ from other animals in fo many particu-
lars, that very little or nothing can be concluded, or
inferred, of the one, from what we obferve in the
other.

Towards the end of September, the fwallows af-
femble on the reeds in the iflands in our river Thames,
and have, no doubt, fo done for ages paft • and vet
I never heard, or read, of any fifherman, or other
perfon, that has ever found in the winter months a
fwallow under water, in a torpid living ftate ; for if
fuch a marvelous thing had ever happened, it would
have been foon communicated to the public. Befides,
as thefe iflands of reeds and willows are annually cut
down, for feveral ufes, and yet not a fwallow has
been difcovered in his aquatic abode ; and, confider-

ing

r

[ 461 •]

ing the multitudes I have feen on thefe reeds and
willows in the autumn ; if they took their winter’s
refidence under water, it is molt reafonable to think,
in a river fo frequented, and in fo long a courfe of
years, fome would have been found in that lituation.
Another circumftance I muft add; in great towns
remote from water, where rivers and reeds are not
near, I have frequently obferved that, a little before the
fwallows depart, they, every morning early, gather
together on the roofs of large houfes, expofed to the
morning fun : this they daily do for fome time, to
colled; themfelves, before they take their flight.

Next, to confirm my opinion, that the migration
of fome fpecies of fwallows is certain, I think I have
fome undoubted proofs.

I have often heard Sir Charles Wager, firft lord of
the admiralty, relate that, in one of his voyages home,
in the fpring of the year, as he came into foundings
in our channel, a great flock of fwallows came and
, fettled on all his rigging : every rope was covered,
they hung on one another like a fwarm of bees ; the
decks and carvings were filled with them ; they
feemed almoft fpent and familhed, and were only
feathers and bones ; but, being recruited with a night’s
reft, they took their flight in the morning.

Capt. Wright, a very honeft man, whom I could
depend on, told me, the like happened to him, in a
voyage from Philadelphia hither.

But a yet ftronger confirmation of the fwallows
being birds of paflage is the obfervation in Mr. Adan-
fon’s hiftory of Senegal, lately pubiifhed ; which is,
as near as may be literally tranflated, from the author’s
own words; viz. “ The fixth of the fame month,

O 0 o 2 “ (October)

C 462 ]

“ (October) at half an hour paft fix in the evening,
“ being about fifty leagues from the coaft, (between
f< the ifland of Gorea and Senegal) four fwallows
<e came to take up their night’s lodging on the fhip,
<£ and alighted on the fhrouds. I eafily caught all
<c four, and knew them to be the .true European
“ fwallows. This lucky accident confirmed me in
u the opinion I had formed, that thefe birds pafs the
<c feas, to get into the countries of the torrid zone, at
Cf the approach of winter in Europe ; and, to that
C( purpofe, I have fince remarked, that they do not
tc appear at Senegal but in that feafon. A circum-
<{ fiance no lefs worthy of note is, that at Senegal
<c the fwallows do not build nefls, as in Europe ; but
<c lie every night by pairs, or fingle, in the fand upon
<c the fea-fhore, where they rather chufe to fix their
<c habitation, than up in the country.” Hift, de
Senegal, f>. 67.

This obfervation (as it comes from a profeffed na-
tural i ft, and one, who went into thofe countries on
purpofe to collect what was curious in that way)
feems to put the matter out of doubt; and the hear-
fay ftories of ignorant peafants and credulous people
are by no means to be put in competition with it.

I have, for many years, been very watchful in
taking notice of the times when the fwallows leave
us, and have twice feen them undoubtedly taking
their flight. At two different years, on the 27th and
29th of September, walking in my garden at noon,
on very clear funfhiny days, and looking up into the
fky, at a very great height I diftindtly faw an innu-
merable number of fwallows, foaring round and
round, higher and higher, until my eyes were fo

pained .

[ 463 ]

pained with looking, that I could no longer difcern
them.

But, as my friend Klein feems to be fo pofitive,
that the hirundo riparia, or fand martin, at the ap-
proach of winter, retires into the holes, in which that
fpecies breed up their young, and made their fummer’s
refidence, and there pafs that cold feafon in a dor-
mant ftate, as fnakes, lizards, and fome other ani-
mals do, I have been the more follicitous to come at
the truth. But as thefe fandy precipices, in which
thefe martins build, are moftly inacceffible, fome
years have palled, before I could find a fituation
where the experiment could be fairly made, without
difficulty or danger. Such a fand-hill I found in the
pariffi of Byfleet in Surry. The clergyman being my
friend, and well qualified to make the experiment,
at my requeft, was fo obliging to undertake it. I
lhall give his letter to me, in his own words.

<(
<c
((
< c
sc
cc
cc
cc
((
cc
sc
sc

“ Dear Sir “ Byfleet’ oa°ber 22, 1757.

“ I took a fquare of about twelve feet, over that
part of the clift where the holes were thickeft,
which, in going down from the furface, I judged
would take in about forty holes. I fet to work,
and came to the holes; but found no martins,
nothing but old nefts in the furtheft end of the
holes, which were from a foot and half to two
feet and half deep from the entrance. We care-
fully fearched forty holes, but found no birds ;
but at lead thirty of them had nefts. The paffage
to them was very near in a ftraight horizontal line ;
the neft was funk about an inch and half below
the level of the paffage ; the materials next the

(( bottom,;

[ 4^4 ]

“ bottom were draws, then coarfe and fine grades ;
“ the whole flru&ure of no great elegance. The few
“ e&gs> t^at were left behind, were of a clear un-
tc ipotted white, the fize of a robbin-red-breaft’s.”

This fair trial being made by a gentleman of ve«
racity and ability is very conclufive ; for it certainly
proves, that the fand martins do not take up their
winter abode in their fummer dwellings. There-
fore, there is fufficient reafon to believe, from the
before-recited obfervations on the common /wallows,
and this fo recently made on the J, and ?nartins , that
they are all birds of palfage.

Additional Remark.

There are four diftindt fpecies of birds, that go
under the general name fwallow ; viz. the fwift or
black martin ; 2. the fwallow, that builds in chimneys;
3. the martin, that builds againfl houfes; 4. the
fand martin, that builds in fand-banks. 1 hope, that
I have clearly proved, that fome of thefe fpecies are
birds of pafiage. Bur fome of my friends affert, that
they pafs the winter in clifts or caverns of the earth,
in banks or precipices. What is much to be regretted
is, that the gentlemen were not curious enough to
difiinguifii the particular fpecies, which they found in
a torpid date. Monf. Adanfon, in his account of
Senegal, has omitted this. So that nothing certain
can yet be pronounced, which fpecies flays, or which
goes.

XLI. Obfer*

[ 465 ]

XLI. Ohfervations on the Comet feen in Ja-
nuary 1760 ; by James Short, M. A ',
F, R. S. I?i a Letter to the Rev, Tho.
Birch, D, D. Secretary to the Royal
Society,

Dear Sir,

Surry-Street, 10 Jan. 1760.

Read Jan. 10,
1760.

A

Comet has made its appearance near
the conftellation of Eridanus, a
little to the weftward of Orion. Laft night I took
its tran fit over the meridian, and likewife its declina-
tion. Its nucleus is fmail, fubtending an angle of
not more than 5 or 6 feconds, but very vifible thro’
a two feet reflector magnifying about 70 times. Its
motion is to the weftward, with a conftderable velo-
city, feemingly about 2 degrees in a day ; for, about
an hour and a half after I had taken its tranfit, I
judged it had advanced about 10 or 12 minutes;
which I find to be about the rate of the great comet,
when it firft was feen in the end of the year 1743.
This comet is very vifible to the naked eye, tho’ I
could perceive nothing of a tail ; and therefore I con-
clude it is going down to the fun.

Comet pafied the meridian 9th January 7

1760, at------ - -y 0 53

Its declination fouth - - -

15

Rigel Orionis pafted the meridian at - 911 47' 49
v I am, Dear Sir,

Your moil humble fervant,

Ja. Short,-

[ +66 ]

XLII. Obfervations on the fame Comet ; by
the Rev. John Michell, M. A. Fellow of
Queen’s College in Cambridge. I?i a
Letter to Mr. James Short, F. R. S.

Dear Sir,

Read Jan. io, t g A Hough in all probability you will
1760 J. have feen the comet, which is
now apparent ; yet, left you fhould not, I was not
willing to omit this opportunity of informing you of
it. I received a meftage laft night from Dr. Mafon,
who, as far as I find, was the firft here, that difco-
vered it. We did not fufped at firft, that its appa-
rent motion was fo great, as it appeared to be on
examination j or elfe fhould have taken more obfer-
vations. Very luckily, however, I took its diftance
from four principal ftars, between a quarter and half
an hour after nine, which was as foon as I faw it ;
and, about an hour and a quarter after, finding that
it had manifeftly moved, to the naked eye, I took
other obfervations of it, every quarter of an hour, or
twenty minutes, till very near two o’clock, when it
ceafed to be vifible, on account of its being too low
■in the mud.

The firft obfervations gave its diftance from K Ori-
onis, 30 25/ ; from Rigel, n° 46'; from Betelgeufe,

1 70 10'; and from Syrius, ia° y6'. All thefe ob-
fervations were made between a quarter and half an
hour paft nine, and, as well as I could recoiled:, in
the order I have fet them down* which, not ima-
gining

r 4^7 ]

gining it was material, I had not been careful to mark
to tingle minutes. At 1 h 22', its diftance from Rigel
was 70 6'; at ih 24', from Betelgeufe 1 53'; and

at in 36', its diftance from Sirius was 170 36'.

This will be fufficient for you to find its place by.
The obfer vat-ions, together with above twenty others,
were made with a little Hadley’s quadrant, and may
mod; of them, I believe, be depended on to about
two or three minutes j but fome perhaps may err
four or five minutes.

I am, Sir,

Your obedient fervant,

Cambridge, Jan. 9, 1760. J0hn Miclltll.

XLIII. An Account of the fame Comet ; by
Nicolas Munckley, of Lincoln's-Inn, £/y-

Read Jan, 17, "TAnuary 9, 1760, I obferved what ap-
170 J peared to me to be evidently a comet,
weft of the conftellation of Orion, or (to fpeak more
aftronomically and exactly) over the two ftars marked
p and v in the river Eridanus, but nearer the latter
than the former ; right afeenfton, about 66 deg. de-
clination, about 3 deg. S. It was fomething dimmer
and larger than either of thefe ftars ; and through a
telefcope, appeared magnified, and furrounded with
a broad, faint, ill-defined hazinefs, like the laft
comet, fuch as plainly diftinguifhed it from any
Vol. LI. P p p thing

[ 468 ]

thing eTfe in the heavens* It feemed, even between
the times I obferved it that evening, to have a fen-
fible motion towards the north- weft (/. e. nearer the
zenith, and contrary to the order of the figns) : for
though at fir ft I apprehend its place to be as above,,
on reviewing it, two or three hours afterwards, it
was more over the ftar vy and a little to the weft-
ward of it.

This phenomenon was feen the night before (viz.
the 8th, when I was in London), by two or three
perfons, who mentioned it to me : but though they
particularly took notice of it as different from other
ftars, they were not aftronomers enough to. give any
exa£t account, either of its place or appearance*

The evenings following the pth were cloudy, till
the 13th, which, though far from being very clear,,
allowed me however, at times,, to fee the conftella-
tion Orion, and weftward of it, as far as Cetus, &c.
I faw particularly the ftars ^ and vt. mentioned be-
fore, and the places above-referred to over them 5,
but I faw nothing any more of the comet.

Hampftead, Nicolas Munckley..

XLTV. J-t

[ 469 ]

XLIV. An Account of the fald Comet \ by
Mr . Mark Day.

SIR, Lowick, near Thrapfton, Northamptonfhire,

Read Jan. 17, Had the pleafure laft night, about five
176°. 0*ciock) t0 obferve a comet in the

fouthern hemifphere, near the northmoft extremity
of the river Eridanus, tending its courfe towards Pega-
fus, and, near as I can guefs, it will crofs the ecliptic
about 200 in Aries. It moves one degree in lefs than
one hour and half ; but feems too hafty to give the
aftronomers leave to make many obfervations upon
it, unlefs the weather prove favourable. If there has
been any accurate obfervation thereupon, I would
gladly know j but if it has not been taken notice of,
then I hope the above will be acceptable from,

S I R,

Your very humble fervant,
Jan. 10, 1760* Mark Day,

It palled the meridian about p,

P p p 2

XLV. 0/

[ 4- 7° ]

XLV. Of the vitriolic Waters of Amlwch*
in the IJle cf Angle fey ; with occafional
Remarks on the Hartfell Spawy defer ibed
in the firfl V olutne of the Edinburgh EJfays
and Ohjervations phyfical and literary \ ami
in the \tyh Volume of the Philojophical
TranfaElions , and their Comp ar if on with
other Waters of the. fame Clafs . By John.
Rutty, D.

Read Jan. 17, K jj VRE truly vitriolic waters, altho’ by

much the Ilrongelt of tlie clialy-
beates, are fo rare in companion of the ordinary cha-
lybeates, that we have fcarceany accounts of them in.
the memoirs of the learned, nor any particular hi-
Ifories of fuch waters, until of late ; and therefore, it
is prefumed, that an additional account of a certain
notable water of this clafs may not be deemed un-
worthy of being prefer ved.

Such a water is that of Amlwch, fituate on
Tralklwyn mountain, in the parifh of Amlwch, iir
the Ihe of Anglefey, which was fent me by Ambrofe
Lewis, of Beaumorris, having been bottled May 31,
1757, and arrived in Dublin June the 3d following.

It appears, by the hydrometer, to be as light as
diltilled water, notwithstanding its ftrong impregna-
tion.

It is of a fubacid talte, and very naufeoufly vitri-
olic ; a lafting impreflion of that fort continuing in
the throat giving fufpicion of copper, of which,

however*.

[ 47 1 ]

however, it exhibits no evidence, by any degree of
the hue of that metal imparted to polifhed knives-
immerfed in it, nor of fulphur, by dilcolouring fiU
ver. It retained the above-mentioned take, on being'
expofed feveral days in an open veflel ; quite other-
wile than happens to our ordinary chalybeates.

It curdled with foap : it alfo curdled equal parts of
milk, exhibiting a pretty clear whey.

With fpirit of hartfhorn,. fpirit of fal ammoniac,
and the folution of potafhes, it' exhibited ochreous
and green grumes, as the martial vitriol.

Its appearances: with gallsr and other auheres, were
very fingular, and worthy remark: for tormentil
roots gave it. only a dilute ink colour, loon fading ;
and green tea a dark dun colour, on handing. It"
had not blackened the corks, except perhaps one out
of fix, that hopped the bottles fent me; and when-
the water was hrh poured out, it hruck no more
than a hightly bluihi tinfture with galls; which5
tindture, on handing all night, became like a dilute
ink; but in a glafs expofed thirty-two hours, the
galls hruck the. dilute ink colour fooner : and in fome
of the water, which I left expofed four days, and in
fome of it, which I left in a phial corked, but only
three quarters full, three weeks, the effedt was very
different ; . for. to each portion of water fo expofed,
as I have juh now mentioned, the galls imparted a
raoh beautiful bright iky blue ; which blue tincture,
a little fpirit of vitriol inhantly dehroyed.

Hence we may fee the fallacy of trading’ to a few
appearances, and the danger of rafh conclufions,
without repetitions of experiments and obfervations ;
which, if they had been omitted, I had been led to

conclude-

C 472 ]

conclude this water to be but lllghtiy impregnated
with either a chalybeate or vitriolic principle ; with
which laft it is, however, afluredly ftrongly faturated,
altho’ the ordinary tafte with galls does not dilcover
it clearly by the blue tindture, until the difiblving
acid is partly exhaled.

The Analysis.

It depofits an ochre, which ferves for painting.

It alfo depofits in the bottles a fediment*' partly of
a red and yellowifh colour, and partly white and
raggy ; which fparkled, and fmelt Itrong, on the red
hot iron.

Two pounds eleven ounces yielded 16 grains (/. e.
a gallon 4.9 grains) of a light green fediment, of an
acid fmell, and of an highly acid, vitriolic, and nau-
feous tafte.

It ferments ftrongly, both with folution of pot-
afhes, and with fpirit of fal ammoniac; and feparates
a green and ochreous matter with the laft.

Galls added to its dilutum in diftilled water turned
it of a deep blue ; the charadteriftic of martial vitriol,
to which it alfo agrees in the experiments of the laft
paragraph.

It produced fome degree of coagulation with albu-
men ovi ; and fome flight opacity, and fmall grumes,
with faliva.

It turned of a brown greenfth colour with fyrup
of violets.

It was not attracted by the magnet, until roafted
in the crucible; and then it was ftrongly attradted,
and turned as red as minium.

F rom

C 473 ]

From the above experiments, it appears, that
Amlwch water is ftrongly impregnated with an acid
martial vitriol.

It kills all the fifh in its paffage.

It has fometimes been drunk ; but cannot be borne
in a greater dole than half a pint, unlefs diluted with
common water, being otherwife vomited up.

It cures the mange in horfes, and the itch in men,
by bathing.

From the above account of the Amlwch water, it
appears evidently to agree to that of the Hartfell,
above-mentioned, and defcribed ’ in the Edinburgh
Effays, and in the Philofophical TranfaCtions, even
in certain diftinguifhing characters common to both,
and in which they differ from our ordinary chalybeate
waters > viz.

1. In the acid and vitriolic tafte, which, more-
over, they retain, when long kept, and at a diftance
from their fountains ; and even upon boiling, yield-
ing an acid vitriolic fait, on exhaling to drynefs, which
the common chalybeates never do, but lofe their
ftrength by a fmall degree of heat.

2. In the blue tinCture, which they give with galls
another diftinguifhing character of Englifh vitriol, of
which a weaker folution, like the common chaly-
beates, gives only the purple colour with galls..

3. In exhibiting green clouds, or grumes*, with oil?
of tartar, like the martial vitriol..

The fame, or like appearances, are exhibited by
the Shadwell water y by another at Swanzey in Wales
and, upon a late diligent fearch into the waters of this
kingdom, by thofe of Kilbrew, in the county of
Meath ^ of Ballymurtogh, in the county of Wick.-

[ 474 ]

low; and of Crofs and Cofhmnore, in the county of
Waterford, and fome others : and, to conclude, as
cryftals of martial vitriol have been demonftrated in
feveral of them, I fhall not hefitate to pronounce them
acid vitriolic waters ; which waters, as they are new
in practice, and different in operation and effedts from
the common chaiybeates, I apprehend it will be worth
while to endeavour to place them in a more confpi-
cuous point of view, which the hiftories lately given
or the Britifh waters of this clafs above-mentioned,
compared to our own, will enable us, in fome mea-
fure, to do.

There are, indeed, in thefe waters different de-
grees of acrimony ; for tho’ mod; of them are fo acid
as to curdle milk, yet this is not altogether univerfal ;
and tho’ in many of them the acid is fo far developed
•in their folid contents, as to ferment with alcali’s, this
appearance is not always confpicuous ; from whence
one would imagine, that the milder fort might be
ufed with more freedom, or lefs danger : .and yet it
is certain, that one of the fharpeft of them all, viz.
ours at Kilbrew, in the county of Meath, hath been
taken inwardly, with amazing fuccefs, in fome very
ftubborn cafes.

Yet, on the other hand, it hath been obferved,
that even the German fpaw fometimes hath proved
too irritating in fome tender conftitutions, where our
ordinary milder chaiybeates have fucceeded well ; and
we are otherwife informed, by an accurate obferver,
that, in fome tabid cafes, particularly that called the
galloping confumption, the mildeft and lighted of our
own chaiybeates, and even altho’ blended with milk,

have

[ 475 J

*

have been found to increafe the heddic heats and
tendon of the pulfe.

Nov/, this obfervation feems not eafily reconcile-
able to another of Dr. Horfeburgh, in the place
above-mentioned, on the Hartfeli fpaw (a much
Wronger and hardier chalybeate than either the Ger-
man fpaw, or any of our ordinary ch^Iybeates), viz.
that it hath actually been given, with notable fuccefs,
from half a pint to a pint a day, in confumptions of
the lungs, far advanced, even attended with hebtic
heats and night fweats.

So memorable a fact, in the cure of a deplorable
difeafe, deferves attention ; and the Scotch phyficians
in that neighbourhood are called upon to corroborate
it by further obfervations ; as how long thofe cures
dood, and how far they may have been confirmed by
the like fuccefs in fimilar cafes ; whether ufed with or
without milk j and ladly, whether, as an acid audere
medicine, they may cool, correct, and give a better
confidence, in a colliquative date of the blood ; feems
well to deferve further inquiry, and that the refill t
fhould be communicated for the public utility.

There had indeed formerly obtained a general
prejudice againd the ufe of the ordinary chalybeates
in difeafes of the lungs ; but, at length, experience
hath convinced us, not only of their fafety, but ufe-
fulnefs, and good effects, efpecially when tempered
with milk, in many of thofe cafes. And moreover,
it is but doing judice to our acid vitriolic waters, to
acknowlege, that the empirical trials made on them
by the giddy vulgar have been frequently fuch, as
demondrate, not only their fafety, but even powers
ful effects in other rebellious diforders 5 as, particu-
Vol. LI. larly,

[ 476 ]

larly, our Kilbrew water (one of the fharpeft and
moft ftrongly faturated with martial vitriol of all
thefe waters yet difcovered), in the notable cure of
an afcites, complicated with a jaundice, which I
have elfewhere related; and I lee no reafon why
phyficians fhould not, in this as well as other cafes,
avail themfelves of the happy fuccefs of fuch cafual
experiments.

In order, therefore, to promote a view of this
kind ; and, furthermore, as thefe vitriolic waters are
better adapted for ufe than the ordinary chalybeates,
as bearing carriage to remote places, and may be
kept fit for ufe at all feafons of the year, and are to
be preferred in medical intentions, whenever the
fixongefi: of the chalybeates are required, and can be
borne ; I fhall here, from fadts and obfervations made
on the feveral waters of this fort, which have fallen
under my notice, give a fhort fketch of their general
operation and good effedts, as a foundation for fur-
ther improvements.

Thefe waters, then, generally operate as an emetic
or cathartic, or both ; and have recommended them-
felves, in external and internal ufe, as a powerful de-
tergent, repelling, bracing, ftyptic, cicatrizing, anti-
fcorbutic, and deobftruent medicine, as hath ap-
peared by the notable cures they have effedled, not
only by external ufe in inveterate ulcers, the itch,
mange, fcab, tetterous eruptions, fcald head, and
fore eyes ; but alfo by internal ufe in hot tetterous
eruptions, dyfenteries, internal haemorrhages, in
gleets, the fiuor albus, and diarrhaca, in the worms,
agues, dropfies, and jaundice.

Such

[ 477 ]

Such hath been the fuccefs, that has not unfre-
quently crowned the empirical ufe of tbele waters ;
which, though, in fome of thefe cafes, it might un-
doubtedly have been better conducted in the hands of
the prudent phyfician, may, however, fuffice to con-
vince us, that the vitriolic waters are a branch of the
materia medica, not to be defpifed nor overlooked,
in the cure of many ftubborn chronical difeafes.

Dublin, 15 February, 1750.

XL VI. An Account of that Part of America,
which is neqrefl to the Land of Kamt-
chatka 3 extraEied from the Defcription
of Kamtchatka by Profejfor Kraflienni-
coff, printed at Peterfburg, in two Fo~
lumes , 4to. in 1759; and tranflated and
communicated by the Rev. D. Dumarefque,
D. D. Chaplain to the Englifih FaElory at
Peterfburg.

CHAPTER X.

Of America.

Read Jan. 24, & Lthough we have no exadl and cir-

y \ cumftantial accounts of America,
which lies eaft of Kamtchatka, for which reafon,
the defcription of that country might be deferred to
the time, that the voyage to America, at the Kamt-
chatka expedition, will be published $ neverthelefs,

Q^q q 2 for

[ 47§

for the fake of regularity, and that the reader may
ftill have fome notion of all the countries, that are in
the neighbourhood of Kamtchatka, we are going to
communicate here, what is collected in the memoirs
of Mr. Steller, in different places.

The continent of America, which now is known
from 52 to 6o° of north latitude, extends from the
fouth-weft to the north-eaft, every-where almoft
at an equal diftance from the Kamtchadalian fhores,
viz. about 370 longitude: for the Kamtchadalian
fhore, alfo, from the Kurilian Lopatka [the fhovel *J
to cape Tchukotfki, in a ftrait line (except where
there are bays and capes), lies in the very fame di-
rection. So that one has grounds to infer [from
thence], that thofe two lands were once joined, efpe-
cially in thofe parts, where lies cape Tchukotfki : for,
between that and the coafl, that projects, which is
found at the eaft, direCtly over-againft it, the di-
ftance does not exceed two degrees and a half.

Steller brings four arguments to prove this :

1 . The ftate of the fhores, which, both at Kamt-
chatka and in America, are ragged [broken, cragged].

2. The many capes, which advance into the fea,
from 30 to 60 verftes.

3. The many iflands in the fea, which feparate
Kamtchatka from America.

4. The fituation of thofe iflands, and the incon-
fiderable breadth of that fea.

As to the reft, we leave this to the confideration
[or judgment] of more fkilful perfons : fufftcient it

* The words included between the [ ] are added by way of
illuftration, or elfe are, for the moft part, the literal tranflation of
the Rufs,

i

will

[ 479 ]

will be for us, barely to relate what was obferved
round about thofe parts.

The fea, which divides Kamtchatka from Ame-
rica, is full of iflands, which [lying] over-againft
the fouth-weft end of America, extend [as far asj to-
wards the ftreights of Anian, in fuch an uninterrupted
feries | row, order], as the Kurilian iflands do [as far
as] towards Japan. That row of iflands is found be-
tween 5 1 and 54° latitude, and lies diredtly eaft ;
and it begins not farther than 5 degrees from the
Kamtchadalian fhore.

Steller thinks, that Company’s-land is to be found
between the Kurilian and the American iflands (which
many doubt of), if one [fetting out] from the fouth-
weft extremity of America, advances fouth-weft :
for, in his opinion, Company’s-land muft be the bale
of a triangle [which it forms] with the Kurilian and
the American iflands ; which feems not to be defti-
tute of foundation, if Company’s-land be rightly laid
down on the maps.

The American land is in a much better ftate, with
regard to the climate, than the farthermoft eaftern
part of Alia, though it lies near the fea, and has,
every-where, high mountains, fome of which are
covered with perpetual fnows; for that [country],
when its qualities are compared to thofe of Alia,
has, by far, the advantage. The mountains of [that
part of] Afia are, every-where, ruinous and cleft
[broken] ; from whence they have, long, flnce, loft
their confiftency, they have loft their inward warmth;
upon which account, they have no good metal [of
any kind] ; no wood, nor herbs, grow there, except
in the vallies, where is feen fmall j brufh-] wood and.

ftifft

[ 4^o ]

did* herbs. On the contrary, the mountains of Ame-
rica are firm, and covered, on the furface, not with
mofs, but with fruitful earth [or mould] ; and there-
fore, from the foot to the very top [of them], they
are decked with thick and very fine trees. At the
foot of them grow herbs proper to dry places, and
not to marfhy ones ; befides that, for the mod; part,
thofe [plants] are of the fame largenefs and appear-
ance, both on the lower grounds, and on the very tops
of the mountains; by reafon, that there is every-where
the fame inward heat and moidure. But in Afia,
there is fo great a difference between them, that, of
one kind of plants growing [there], one would [be
apt to] make leveral kinds, if one did not obferve
a rule, which holds generally, with regard to thofe
places [war.], that in lower grounds herbs grow twice
as large as thofe on the mountains.

In America, even the fea-fhores, at 6o° latitude,
are woody; but in Kamtchatka, at 510 latitude, no
place fet with fmall willows and alder-trees is found
nearer than 20 verdes from the fea: plantations [or
woods] of birch- trees, are, for the mod part, at [the
didance of] 30 verdes; and, with regard to pitch-
trees, on the river Kamtchatka, they are at the di-
dance of fo verdes, or more, from its mouth. At
62°, there is no wood at Kamtchatka.

In Steller’s opinion, from the afore-mentioned la-
titude of America, the land extends as far as 70°,
and farther; and the chief caufe of the above-faid
growth of woods in that country is the cover and
fhelter it has from the wed. On the other hand,
the want of this [of wood] on the Kamtchadalian
fhores, efpecially on the fhore of the Penfhinian fea,
5 doubt-

[ 48i ]

doubtlefs, comes from a (harp north wind, to which
it is much expofed. That tliofe parts, which lie from
the Lopatka, farther to the north, are more woody
and fruitful, is owing to cape Tchukotfki, and the land
that has been obferved over-againft it, by which thofe
[parts] are (heltered from the (harp winds.

For this reafon, alfo, fifh comes up the rivers of
America earlier than thofe of Kamtchatka. The
2cth of July, there has been oblerved a great plenty
of fi(h in thofe rivers ; whilft at Kamtchatka, it is
then but the beginning of an abundant fifhery.

Of berries, they law there an unknown kind of
rafberries, which bore berries of an extraordinary big-
nefs and tafte. As to the red, there grow in that
country black-berries [with feveral other kinds of
berries, called in Rufs, jimaloft , golubitfa , brufnitfa ,
and JhikJha ], in as great plenty as at Kamtchatka.

There are creatures enough, good for the fupport
of the inhabitants of thofe parts j particularly feals,
fea-dogs, fea-beavers, whales, * canis carcharias ,
marmot tes [rnarmotta mine r], and red and black
foxes, which are not fo wild as in other places, pof-
fibly becaufe they are not much chaced [hunted].

Of known birds, they faw there magpies, rayens,
fea-mews [■f* urili], fea-ravens, lwan-s, wild ducks,
jackdaws, woodcocks, J Greenland pigeons, and

* In Rufs, ah/!, or mokoia ; in bignefs, it is inferior to the
whale; and it is like it in this, that it caffs no fpawn, but brings
forth young ; upon which account, feme reckon it a fpecies of
whale. Lefcript. p. 308. ift vol.

f Uril, corvus aquaticus rnaximus, criftaceus, periophthalmiis
cinnabarinis, poftea candidis.

% Coluraba Groenlandica, Batavorum, faiwer, vel kaiour.

* tniteba ~

[ 4§2 ]

* mitchagatkl , otherwife called northern ducks.
But, of unknown birds, they obferved more than
ten forts, which it was not difficult to diftinguilh
from European birds, by the livelinefs of their co-
lours.

With regard to the inhabitants of thofe parts, they
are fuch a wild people, as the Koriaki and Tchuktchi.
As to their perfons, they are well fet, broad and
ftrong fhouldered. The hair of their head is black,
and drait, and they wear it loofe. Their face is
tawny [brown], and fat as a plate; their nofe is
fat, but not very broad ; their eyes are as black as
jet ; their lips thick ; their beard fmall ; and their
neck Ihort.

They wear ffiirts with lleeves, which reach lower
than the knee ; and they tye them up, with thongs
of leather, below the belly. Their breeches and
boots [which are made] of the fkins of feals, and
dyed with alder, much refemble the Kamtchadalian.
They carry, at their girdles, iron knives, with
handles, fuch as [are thofe] of our boors. Their
hats are platted [matted] of herbs, as with the Kamt-
chadalians, without a [riling] top, in the ffiape of
an umbrella; they are dyed in green, and in black,
with falcon’s feathers, in the fore-part, or with [fome]
herb, combed, as if it were a plume of feathers, fuch
as the Americans ufe about Bralil. They live upon fiffi,
fea animals, and the fweet-herb, which they prepare
after the Kamtchatka manner. Befides this, it has
been obferved, that they have alio the bark of poplar,

* Mitchagatka , alca monachroa fulcis tribus, circo duplici utrin-
que dependence. Anas ar&ica cirrata.

or

[ 48.3 ]

or of the pine-tree, dried, which, in cafe of neceffity,
is made life of as food, not only at Kamfchatka, but
likewife throughout all Siberia, and even in Ruffia
itfelf, as far as Viatka; alfo fea weeds made up into
bundles, which, in look and in ftrength, are like
thongs of raw leather. They are unacquainted with
fpirituous liquors and tobacco ; a fure proof, that,
hitherto, they have had no communication with the
Europeans.

They reckon it an extraordinary ornament, to
bore, in feveral places, the lower parts of the cheeks,
near the mouth ; and in [the holes] they let fome
ftones and bones. Some wear, at their nodrils, (late
pencils, about four inches long; fome wear a bone
of that bignefs, under the lower lip ; and others a
like bone on the forehead.

The nation, that lives in the illands round about
cape Tchukotlki, and frequents the Tchutchi, is,
certainly, of the fame origin with thofe people : for
with them alfo it is thought an ornament [thus] to
inlay [ingraft] bones.

Major Paulutlkoi, deceafed, after a battle, which
he once fought againft the Tchutchi, found, among
the dead bodies of the Tchutchi, two men of that
nation, each of whom had two teeth of afea-horfeunder
the nofe, let in holes made on purpofe : for which rea-
fon, the inhabitants of that country call them Zubatai
[toothed]. As the prifoners reported, thefe [men]
did not come to the abidance of the Tchutchi, but
to fee how they [ufed to] fight with the Ruffians.

From this, it may be inferred, that the Tchutchi
converfe with them, either in the fame language, or,
at lead, in languages of fo great affinity, that they

V o l. LI. R r r can

7

[ 484 ]

can underffand one another, without an interpreter $
confequently, their language has no fmall refem-
blance with that of the Koriaki : for the Tchukot-
chian comes from the Koriatfkian [^language], and
differs from it only in the dialed; : neverthelefs, the
Koriatfkian interpreters can fpeak with them, with-
out any fort of difficulty. With regard to what Mr.
Steller writes, that not one of our interpreters could
underffand the American language, poffibly, that
comes from the great difference in the dialed, or
from a difference of pronounciation ; which is ob-
ferved, not only among the wild inhabitants of Kamt-
chatka, but alfo among the European nations, in
different provinces. In Kamtchatka, there is hardly
any fmall * ojlrog, but what the fpeech there differs
[fomewhat] from that of another that lies neareft.
As for thofe fmall ojirogs , which are at fome hun-
dreds of verffes from one another, thofe can no
longer underffand each other, without [fome]
trouble.

The following remarkable refemblances between
the American and the Kamtchadalian nations, have
been obferved :

1 . That the Americans reiemble the Kamtchadales
in the face.

2. That they eat the fweet-herb, after the fame
manner as the Kamtchadales j [a thing] which never
was obferved any-where elfe.

* OJlrojka, a fmall ojirogs is a place fenced and fortified with a
pallifade, made of trees, fixed perpendicularly in the ground, and
cut (harp at the top : fomctimes they are beams laid over each
other. OJlruiy in Rufs, fignifies (harp.

3. That

C +8s ]

3. That they make ufe of a * wooden machine
[inftead of a tinder-box], to light fire with.

4. That, from many tokens, it is conjectured,
that they ufe axes made of ftones, or of bones : and
it is not without foundation, Mr. Steller thinks, that
the Americans had once a communication with the
people of Kamtchatka.

y. That their cloaths and their hats do not differ
from the Kamtchadalian.

6. That they dye the fkins with alder, after the
Kamtchatka manner.

Which marks fhew it to be very poffible, that
they came from the fame race. This very thing, he
rightly judges-, may help alfo to folve that queftion,
“ Whence came the inhabitants of America ? ” For
though we fhould fuppofe, that America and Alia
were never joined ; neverthelefs, confidering the near-
nefs of thofe two parts of the world at the north,
no one can fay, that it was impracticable for people
from Afia to go over to fettle in America ; efpecially,
as there are iflands enough, and at fo fmall a diftance,
which might facilitate not a little fuch a paffage [in
order to fettle].

Their armour for war is a bow and arrows.
What kind of a bow it is, we cannot fay, as it did
not happen [to our people] to fee any ; but their
arrows are much longer than the Kamtchadalian,
and greatly refemble the Tungufian and Tartarian
[arrows], Thofe, which came in the way of our
people, were dyed black, and planed fo fmooth, that

* See Description of Kamtchatka.

R r r 2

they

[ 486 ]

they left no room to doubt of [the Americans] having
alfo iron tools.

The Americans fail upon the fea in canoes made
of fkins, in the fame manner as the Koriaki and the
Tchutchi. * Their canoes are about two fathoms
[14 feet] long, and about two feet high. The fore-
part of them is (harp ; and tney are flat-bottomed.
Their inward frame conflfts of flicks, which are
linked together at both ends, and in the middle are
prefled outwards, in a rounding [a belly], with crofs-
flicks [which keep the Tides at a proper diftance].
The fkins, which they are covered with, all around,
feem to be thofe of fea-dogs, dyed of a cherry colour/
The place where the Americans fit is round, about
two arfhines [4 feet 8 inches] from the poop; there
is fowed upon it the ftomach [of lome gieat fifh],
which one may gather and loofen as a purfe, with
the help of thongs of leather, pafled through fmall
holes at the edge. An American, fitting in that
place, ftretches his legs, and gathers round him the
flomach [above-mentioned], that water may not fall
into the canoe. With one oar, fome fathoms long,
they row on both Tides alternately, with fuch a pro-
grefiive force, that contrary winds are but a fmall
hindrance to them ; and with lo much lafety, that
they arc not afraid to go upon the water, even whilft
the fea rifes in terrible furges. On the contrary, they
look with fome terror upon our larger veflels, when
they are tolled, and advife thole, who fail in them,
to beware, left their veflels fhould be ovcifet. This

* See the two figures, in ill vol. of the Description of Kamt-
•hatka, over againft page 128.

happened

C 487 ]

happened to the boat Gabriel, which, fome years
fi'nce, was going to cape Tchukotfki. As to the
reft, their canoes are fo light, that they carry them,
with one hand.

When the Americans fee [upon their coafts]
people, whom they do not know, they row towards
them, and then make a long fpeech : but it is not
certain, whether this is by way of a fpell [or charm],
or fome [particular] ceremony ufed at the reception
of ftrangers : for both the one and the other are in
ufe among the Kurilians. But before they draw near,
they paint their cheeks with black lead, and ftuft
their noftrils with [fome] herb.

When they have guefts, they appear friendly ; they
like to converfe with them, and that in an amicable
manner, without taking off their eyes from them :
they treat them with great fubmiftion, and prefent
them with the fat of whales, and with black lead,
with which they ufed to befmear their cheeks, as
was before obferved ; doubtlefs from a notion, that
fuch things are as agreeable to others, as they are to
themfelves.

With regard to the navigation about thofe parts,
it is fafe [enough] in fpring and in fummerj but in
autumn it is fo dangerous, that hardly a day paftes,
but one has reafon to fear being fhipwrecked : for
they [the Ruffians fent upon the fea expedition] ex-
perienced fuch a violence of winds and ftorms, that
even perfons, who had ferved forty years at fea, af-
fured, with an oath, that they never faw fuch in their
lives.

The marks, by which they obferve there [in that
fea] that land is near, are, particularly, the following

confider-

[ 4S8 ]

confiderable ones: i. When there appears a great
quantity of different kinds of the [fo called] fea-
cabbage, fwimming upon the water. 2. When one
fees the herb, of which, at Kamtchatka, they platt
cloaks, matts, and bagsj for it grows only on the
fea-fhores. 3 . When there begin to appear, at fea,
flights of fea-mews, as well as droves of fea animals,
fuch as fea-dogs, and the like : for though fea-dogs
have a hole open at the heart, which is called fora-
men ovale, and a dudt called duBus arteriofus Botalli ,
and, upon that account, may remain long under
water, and, confequently, go to fome diftance from
the fhore, without danger, inafmuch as they can, at
a gi eater depth, find food proper for them: never-
thelefs, it has been obferved, that they feldom go
farther than ten [German] miles from the fhore.

The fureft fgn, that land is near, is, when there
are leen Kamtchatka beavers, which live only upon
crabs, and, from the make of their heart, cannot be
under water above two minutes [at a time] ; confe-
quently, they cannot get food at the depth of ico fa-
thoms, or indeed at a much leffer depth j upon which
account, they alfo breed always near the fhore.

It remains ft ill to fpeak of fome iflands neareft to
Kamtchatka, which are not found in a ftrait line
with the above-mentioned, but north of them ; efpe-
cially of Berings illand, which now is fo well known
to the inhabitants of Kamtchatka, that many of them
go. thither, to catch fea-beavers, and the like fea
animals.

That ifland extends from the fouth-eaft to the
north-weft, between jy and 6o°. Its north-eaft end,
which lies almoft diredtly over-againft the mouth of

the

[ ]

the river Kamtchatka, is at about two degrees di-
ftance from the eaftern fhore of Kamtchatka : and
its fouth-eaft end is about three degrees from cape
Kronotlki. This illand is 165 verftes long; but its
breadth is unequal. From the fouth-eaft end to a
rock, which hangs perpendicularly over the fea, and is
at 14 verftes diftance from that end, the breadth of
the illand is from 3 to 4 verftes : from that fteep
rock to Suiputchei bay, it is 5 verftes : from Suiput-
chei bay to Beaver’s fteep rock, it is 6 verftes : at
Whale’s-ftream, it is y verftes ; but from thence
farther on, it grows gradually broader. Its greateft
breadth [wx?.], 23 verftes, is over-againft the north
cape, which lies 1 15 verftes from the above-men-
tioned end.

In general, it may be faid, that the length of that
illand is fo difproportioned to its breadth, that our
author doubts, whether there can be, in other parts
of the world, any illands of fuch a lhape ; at leaft, he
never heard nor read of any fuch : and he adds, that
the illands, which they faw about America, and all
the rows of them, lying to the eaft, have the like
proportion.

This illand conlifts of a ridge of rocks, which is
divided by many vallies, that ftretch to the north
and to the fouth. Its mountains are fo high, that,
in clear weather, one may fee them from about half
the diftance between the illand and Kamtchatka.
The inhabitants of Kamtchatka, of old times, thought,
that there muft be ffome] land over-againft the mouth
of the river Kamtchatka, by reafon that [the Iky] ap-
peared there always cloudy* though it were never fo
clear every-where elfe about the horizon.

The

[ 49° ]

The higheft mountains [of the ifland] do not
mealure above 2 verfles in a perpendicular.

[Here follows a defcription of this barren rocky
ifland, of which the following four pages are not to
our prefent purpofe. Then, at page 13 6, the account
proceeds thus :]

The fouth-weft fide of the ifland is of a quite dif-
ferent nature [from the other, as to accefs] : for tho’
the fhore [there] is more rocky and craggy, yet there
are two places, by which, in flat-bottomed boats,
fuch as are the * tfcherbotui , one may not only land
on the fhore, but even advance as far as a lake, by
the ftreams [that flow from it]. The firfl of thefe
places is at 50 verftes, and the other at 1 1 y, from
the fouth-eaft end of the ifland.

This laft place is very remarkable from the fea ;
for the land there goes rounding from the north to
the weft ; and, at the very promontory, there runs a
lfream, which is the largefl of any in that ifland ;
and, when the water is high, its depth is not lefs
than 7 feet. It runs from a great lake, which lies
a verfle and a half from its mouth : and becaufe that
ftream grows deeper, the farther it is from the fea,
therefore one may conveniently go upon it in boats
as far as the lake : and upon the lake there is a fafe
Hation ; for it is furrounded with rocky mountains,
as with a wall, and fheltered from all winds. The
chief mark, by which one may know this flream
from the fea, is an ifland, which is about 7 verfles
in circumference, and lies to the fouth at 7 verfles
diftance from the mouth of the flream. The fhore

* Large canoes, or boats, fomewhat refcmbling ferry-boats.

from

C 491 3

from thence towards the weft, is fandy and low
for 5 verftes. Round the fhores, there are no rocks
under water; which one may know from thence,
becaufe there are no * eddies [breakers].

From the higheft rocks of that ifland, one fees
the following lands : at the fouth, two iflands, one
of which meafures about 7 verftes in circumference,
as was oblerved before ; but the other is over-againft
the very end of Berings ifland, at the fouth -weft: it
conflfts of two high and cleft rocks, of about three
verftes in circumference, and is at 14 verftes diftance
from Berings ifland.

From the north-eaft end of Berings ifland, in clear
weather, one may fee, to the north-eaft, very high
mountains, covered with fnow, and their diftance
may be computed at 100 or 140 verftes. Thofe
mountains our author thought, with better grounds,
to be a cape of the continent of America, than an
ifland: 1. Becaufe thofe mountains fallowing for]
confidering their diftance, were higher than the
mountains on the [neighbouring] iflands. 2. Becaufe
that, at a like diftance towards the eaft, one obferves
plainly, from the ifland, fuch like white mountains,
from the height and extent of which all judged that
it was the continent.

From the fouth-eaft end of Berings ifland, they
faw, to the fouth-eaft alfo, another ifland, but not
very clearly : it feemed to lie between Berings ifland
and [fome] low part of the continent.

From the weft and the fouth-weft Aides, it was
obferved, that, even in clear weather, there is a per-

* In German, brtnnung.

S S S

petual

[ 492 ]

petual fog above [higher up than] the mouth of the
river Kamtchatka ; and from thence, in fome mea-
fure, they came to know the inconfiderable diftance
of the land of Kamtchatka from Berings ifland.

North of the fo often mentioned Berings ifland,
there is another ifland, in length from 80 to 100,
verftes, which lies parallel to it, /. e. from the fouth-
eaft to the north-weft. The ftreights between thefe
two iflands, at the north-weft, meafure 20 verftes, and
at the fouth-eaft about 40. The mountains upon it
are lower than the ridge [of mountains] in Berings
ifland. At both ends of it, there are, in the fea,
many rocks at [low] water mark, and perpendicular
rocks like pillars.

With regard to the weather, it differs from that
at Kamtchatka only in this, that it is more fevere and
fharp : for the ifland has no (belter from any quarter j.
and, befides that, it is narrow, and without woods.

Moreover, the force of the winds increafes to fuch
a degree, in thofe deep and narrow vallies, that one
can fcarce ftand upon one’s legs. In February and
April months, were obferved the lharpeft winds,
which blew from the fouth-eaft and from the north-
weft. In the former cafe, the weather was clear,
but tolerable ; but in the latter cafe, it was clear, in-
deed, but extremely cold.

The higheft riling of the water happened in the
beginning of February month, during north-weft
winds : the other inundation was in the middle of
May, occafioned by great rains, and by the fudden
thawing of the fnows. Neverthelefs, thofe floods
were moderate, in comparifon with thofe, of which
there [ftill] remained undoubted marks: for there

[ 493 3

have been carried many trees, and whole jfkeletons
of fea animals, to the height of 30 fathoms, or
more, above the furface of the fea [above the com-
mon water mark, or level] : from which our author
judges, that, in the year 1 737, there happened,
likewife, here [in this iftand] fuch an inundation as
that at Kamtchatka.

Earthquakes happen [here] feveral times in the
year. The moil violent, that was obferved, was in
the beginning of February, which, during a wefterlv
wind, iafted exactly fix minutes ; and before it was
heard a noife, and a ftrong wind, under ground,
with a hiding, which went from fouth to north.

Among mineral things, which are found in that
illand, one may reckon, as the molt remarkable, the
fine waters, which, upon account of their purenefs
and lightnefs, are very wholfome : and this virtue of
them was obferved upon fick people, with advantage,
and the defired fatisfadtion. With regard to the plen-
tifulnefs of them, there is not a valley but what has a
flream running through it; and the number of them all
together exceeds fixty j among which there are fome,
which are from 8 to 1 1 fathoms broad 3 and fome
are two, and fome even 5 fathoms deep, when the
water is high 3 but there are few fuch, and the greater
part of them is extremely fhallow at the mouth 3 be-
caufe that they have a very rapid courle, on account
of the deep dopes of the vallies, and that near the
fea they divide into many rivulets.

S s s 2

Explication

[ 494 ]

'Explication of feme Words, which occur in the Reife-

Befchreibung, &c.

Page

6. Promyfchleni properly fignifies thofe, that
make a trade or profeffion of hunting in
Siberia.

7- Goftinna fotna , the merchants of the firft

clafs in Ruffia.

Ibid. Semeon Iwanow fin Defchnew. When the
Ruffians fpeak of a man of quality, they
add to his Chriftian name that of his fa-
ther ; ex. gr. Simon Ivanowitfch Defchnejj ’•
but if of a common man, they fay, as
here, Simon Ivanoff fin ( i. e. fon of)
Defchnefi], Simon the fon of John Defch-
neffi.

& Cofacke. The Cofacks are properly the fol-
diers, of whom confifts the Ukrain. militia,
or that of the neighbourhood of the Dom
Thefe laft began the conqueft of Siberia.
Their pofterity is ftill employed in railing
the taxes laid on the Siberian nations, which
have fubmitted to the Ruffian empire.

Ibid. Zimmer , is a bundle of furs, confining of

40 fkins.

11. Simowie [zimovie], properly, is an habita-
tion, or quarters, for the winter; a hut or
huts, built haliily, in fome defert place,
in order to fpend a winter there. When
the number of thofe huts has fo increafed,
as to become a village, it has often ltill
retained the old name of zimovie. Zimay
in Ruffian, is winter.

Ofirog.

[ 495 ]

Page

ii. Oflrog, See page 484 above.

14. Narte , a kind of fmall fledge, very light,
drawn by dogs. See the reprefentation of
it in the Defcription of Kamtchatka.

1 9. Werchnei , nifchnei , ferednte , bolfche ; thefe

words fignify, high, low, middle, and
greater $ as ‘werchnei OJirog , the upper
Oftrog, &c.

24. Swaetoi, fignifies holy, faint $ as Sivaetoi nofs>
cape Holy.

26. Piaetidefaetnifs , an officer, who has 50 men

under his command, and who may be
called a lieutenant. In Rufs, pietderiat is
fifty.

27. Woewood is the governor of a town, of a

diftridt, or of a province.

33. Stolnik was an officer, formerly, who fet

the difhes upon the tfar’s table. Sto/y a
table.

Ibid . Knjaes , a prince.

34. Dwvraen^ a gentleman.

Ibid . mouth. UJt Jana, the name of a place

fituated at or near the mouth of the river
Jana.

Ibid . No/s, cape, promontory, nefs, neefe. The
The proper fignification of the word is
nofe.

40. Sc hi kit i , fewed, from fchit , to few.

41. We r fie, an itinerary meafure in Ruffia, con-
fiding of 500 fajens, or fathoms, each of
which makes 7 feet Englifh.

Sin

<

Page

42.

90.

121.

Ibid .
Ibid.

[ 496 ]

Sin bojarjkoiy a title which is conferred, in
Siberia, upon low people, in order to raife
them to a degree nearer to that of a noble
or a gentilhomme.

59. Vielfrafs , a German word, which fignifies a

glutton. It is a wild beaft of a fmall lize,
about the bignefs of a fox, but more re-
fembling a bear. This creature, called in
French, glouton , is extremely voracious,
from whence it had its name.

Ibid. Steinfuchs , is a kind of fox.

86. Baidar , canoe.

Ibid . Nejfel , a nettle, in general, in German ; here

a kind of nettles, of which a particular fluff
is made.

Ibid. 1 Levkajhenuiu pofudu , fignifies a veffel or pot
//«** / made of levkas, a kind of alabafter. Here
penul- f it probably was intended to exprefs China
tima. J ware, or porcelaine.

Rietgrafs , a German word, fignifying the
fame as bamboo.

JudotnJkot krejiy Judoma’s-crofs, the name
of a village near the river Judoma, in a
place on which was eredted a crofs, when
it was firft difcovered.

Beljkoi pereivofs , the ferry of Bela.

linen >Jiujnoi , foutherly, to the fouth.
penult. J

143. Krepoft , fignifies a caftle, or a fort.

Ibid. Sawody a manufactory, pr fabrique.

Ibid. Wofkrefenjkeiy belonging to the rcfurredtion.

Plot-

7

[ 497 ]

Page

165.

181.

1S2.

I5I*
*5 !*

linea
antep.
250.
lin. 6.
249.
lin. 16.

Plotbifchtfche , the place where are built the
(plotui) floats, or fmall boats.

Buxiren , a German word, which fignifies to
tow, to take in tow.

Dannen (or tannen) knofpe , the buds of fir-
trees.

Bu 'tkowjkoi muis , parvum promontorium bc~
vinwn.

j.Read korova morjkaid , the fea-cow.

^Read viporotki ...

| Read kotui morJkiey fea-cats.

a gulf, or bay.

Matrofs , a failor*.

IVo'Utf Zemla , New Land, jfrra* Nova.

Gorodock , a fmall town, oppidulum.

Sloboda. See the introduction to the
Rujjicus , in which many Ruffian names of.
places, are explained.

I

XL VII. I&v

[ 49s J

XLVII. Remarks on the Mutations of the
Stars \ by Th o. Barker, Efq\ Lyndon,
in Rutland : Communicated by the Rev .
W. Stukcley, M. D. F. R. S .

Rcadi^6o’ 3I,TT *s we^ known there have been feve-
X ral alterations among the fixed ftars : for
inftance, Ptolemy’s ultima jluvn , a firft magnitude ftar,
is in Dr.Halley’s catalogue of the fouthern conflellations
only a third magnitude : and in much lefs time, the
of the Great Bear, which Bayer feems to have
judged juft of the fame fize with the other fix, is
grown far duller than any of them. Some ftars alio
have quite difappeared, while again new ones, not
feen before, have been difcovered : and there are
others periodically larger and fmaller. Two very
remarkably bright, yet Ihort-lived, ftars, have been
alfo feen, one in Cafiiopeia, the other in Serpen-
tariusj which breaking out, at once, with greater
luftre than any other fixed ftar, gradually faded, and
changing to different colours, in about a year and
half were no longer vifible. But, I think, no one
has yet remarked, that any lafting ftar was of a dif-
ferent colour in different ages : Greaves, on the con-
trary, takes notice, that the colours of the ftars and
planets are the fame now as the antients obferved ;
which is, I believe, very true in general : for Pto-
lemy, in his catalogue of ftars, fays, Ardturus, AI-
debaran, Pollux, Cor Scorpii, and Orion’s Shoulder
(with another to be mentioned prefently), are J7 ro-
xippos, reddilh : and the five here mentioned are ftill

of

[ 499 ]

of that colour, and, I think, the only considerable
liars which are fo.

But, to this rule there feems to be one exception,
and that in a remarkable ftar : for old authors men-
tion the Dog ftar, which is now white, and not at
all inclined to rednefs, as being then very much fo-;
as in the following places :

T oios KOLl (ppVpOS CLiipQfJLiVCt) V7TO J'WTW
QctivBTca ccfjLtpoTepoicn y.vo)v vtto 7rocrai fiefirwus
TlolXlAoS " • ApotTB (pOUVQ[JiZVGC . 326.

Which Cicero thus turns Sec Gruter’s Cicero,

359 •

Namque pedes fubter rutilo cum lumine claret
Fervidus ille Cams ftellarum luce refulgens.

Seu rubra Canicula findet
Infantes ftatuas— Hor. Sat. II. y, 3 9,

Acrior ft Caniculas rubor, Martis remifiior Jo vis
nullus. Se?ieca Qutfft. Nat. I. 1 .

’O 6V TW <?0]XCtTL ?,0LfJL7rp0TCt,T9S XCtXBfJLeVOS XU60V V7T0-

xippos. Ptolemy. Kvvos ct^eptafxos.

UoikiXgsj in the quotation from Aratus, does not
exprefly mean red; but is always ufed of fomething
fhewy, glittering as gold, various-coloured, &c. as
in the following places.

„ Tei^icc ToiKtha. •yyx.hKw. Homer' s II. y. 181.
llccpSccAey pxiv TrpooToc cceppevov' evpi kolAv-^s
YloixiAn - — — IA. ?c. 36.

Os k<xAA/$-'os eyy 7roLxi?iyLa.cnv OA 0. 107*

BuTtiy g is OSvayct Sotupporcc 7roiKihofAimn'. OS' . 102.

Vol. LI. Ttt Aratus

[ $<*> ]

Aratus therefore, I think, thews at leafl, that the
Dog dar was not then of the lame colour as other
dars: and, as Cicero turns it rutilus , it appears he
either underdood the word to mean red, or knowings
by his own view it was fo, thought it the proper inter-
pretation ; for rutilus is ufed of what is reddilh, and
often of the red glare of a lire, or the dawn, as be-
low :

rutilum vomit ille cruorem, Ovid, Met, IV. 33*.

Promiffje et rutilatas comas. Livy. XXXVIII. iy.

Arma inter nubem, ceeli in regione ferena.

Virg . JEneid . VIII. 728..

Per fudum rutilare vident.

Sin maculae incipient rutilo immifcerier igni.

Georg. L 454,

Auroram rutilare procul cerno.

, Varro , de Ling. Lat, VI.

Rubra , in Horace, will, I think, bear no other
fenfe than red, or elfe it is the heat he there chiefly
fpeaks of : and though, I think, Latin authors con-
found Canicula , fome uling the word for Sirius ,
others for Procyon ; yet it plainly appears, that
Sirius is here meant, flnce Horace always calls it
Canicula, and never ufes the word Sirius : but Ara-
tus and Ptolemy leave no room to doubt what dar it
was, being exprefly fpeaking about the Dog dar.

Seneca fays, the rednefs was fo drong as to exceed
that of Mars, to which no dar now approaches.
None of the notes on Seneca clear up this matter:
Fromondus, indeed, obferved the place, and de-
clared his adonilhment at it 5 but does not attempt

50r

to folve the difficulty. Ptolemy’s is, however, the
moft undeniable evidence, who, when direCtly de-
ferring the ffars, and particularly mentioning the
Dog ftar, fays, exprefly, it was of the fame colour
as Cor Scorpii, and the other ffars, which are ffill
red ; fo that I do not fee how his evidence can be dis-
puted.

There is, however, one objection to what I have
faid, but I, think, not an unanfwerable one ; which
is, that, at firft fight, Hyginus feems to call Sirius
white : but fince, if fo, he contradicts the other
authors I have above quoted to prove it red, and,
becaufe he there fays fomething I do not well under-
ffand, I ffiall quote the whole.

Hygini Poetic jdftron. II. 3 3.

Canis habet in lingua ftellam unam, quae ipfa Canis
appellatur; in capite autem alteram, quam Ills fuo
nomine ffatuifle exiffimatur, et Sirion appellaflc
propter flammae candorem ; quod ejufmodi fft, ut
prater caeteras lucere videatur, itaque quo magis earn
cognofcerent, Sirion appellafl'e.

He again diffinguiflies thefe two ffars, lib. III. 34.

Canis habet in lingua ffellam unam, quae Canis
appellatur, in capite autem alteram, quam nonnulli
Sirion appellant, de quo prius diximus.

Of two ffars in the Dog’s head, Ifis and Sirius,
Eratoffhenes alfo fpeaks :

KctTctc?e(>ic[j.os A y. Kvwv E%ei Se oc^epa^ eiti

fjiBv x.t(pa A)?s a bs I o-ls teyeTca-, t m yXoTTviG a. op xca
Xeipoov xaAso-f [xeyccs Si £<re % Ao'.y.Tpos, tbs Si toibtbg

T 1 1 2 ctf-epcct

3

C

[ 5°* j

oi cl<? poXoyoi csipms xaA uci Six tw tvs tpA o^’C?

Kivticrip.

Hyginus, in diftinguiflhing Canis from Sirius as
two different ffars, feems, to me, to contradid all
other writers, who fpeak of them as one, except,
perhaps, two or three latter ones, who diredly quote
Hyginus’s words.. Sirius, or Canis, the brighteft ffar
in the heavens, is that, which Ptolemy calls in the
mouth ; Eratofthenes and Hyginus, in the tongue :
but whether Bayer y , which Flamftead calls a third
magnitude ftar, Ptolemy only a fourth, was in more
antient times larger, I will not pretend to fay ; fince,
Eratofthenes and Hyginus both fpeak of two ftars in
the Dog’s head, as thought worthy of particular names.
If, in Hyginus, jiammce candor em means the white-
nefs of its light, as candor often does, he exprefly
contradids what I have quoted above from others •
yet ftill I think Ptolemy’s authority is greater than
that of Hyginus. But that candor is alfo ufed for in-
nocence, beauty, brightnefs, &c. take the following
examples. &

Bis fenis equis candore eximio trahentibus. Suet.
Ccef. Ottav. p4.

Si tamen ille prior, quo me line crimine gefli

Candor Ow'd. Epift. IV. 3i.

forma: nifi candor* Metam. I. 743 , .

Candore noto reddas judicium peto.

P hccdrus. III. Prol. 64.

Pendebant ex auribus infignes candore et magni-
tudine Lapilli, Quint. Curt . IX. 4.

• 3 Us

C 5° 3 1

Ut cum videmus fpeciem primum, candoremquc
coeli. Cic. TuJ'c. I. 28.

Solis candor illudrior quam ullus ignis, j De Nat .
Dear. II. if.

In the fecond or third lad quotation, candor is
ufed in the fame fenfe as in Hyginus, for brightnefs,
without regard to colour 3 for fo, I think, he mud
be underdood, not only to avoid contradiction be-,
tween him and Ptolemy, but from the name Sirius
which it could not be called from its whitenefs, Xti-
pios bearing no relation to that, but to brightnefs,
heat, or drynefs 3 all which the antients fpeak of, as
properties of the Dog liar. Again, it is brightnefs,
wherein it excells all other liars, and not in white-
nefs 3. for Orion’s foot and others are as white, but
there is none fo bright as the Dog dar. All this is
faid, on fuppolition there was but one remarkable
liar in the Dog’s head, that in the mouth : for if
there were two, as Hyginus fays, we are not here
concerned with either the brightnefs or colour of his
Sirion, which was in the head, as it certainly faded
before Ptolemy’s time, who mentions only one, that
in the mouth, and which, he fays, was then red,
but is now white.

To conclude the whole 5 however remarkable and
without precedent it may be, that fo noted and lading
a dar as the Great Dog fhould have changed its co-
lour, yet as at lead five different writers affirm it,
fome fo exprefly, and where their fubjeCt required
them to fpeak particularly about it, it appears to me
to have been certainly the cafe. If, however, , any-
one, dartled at the drangenefs of the thing, thinks.

[ 5°4 ]

the evidence I have brought inefficient to prove it,
he is defired to invalidate what I have here faid, by
a dedudion of frefh evidence, and to account5 for
thefe feveral expreffions in old authors, which feem
to prove, that fuch a change has really happened.

XL VIII. The Method of making Sal Ammo-
tiiac in Egypt ; as communicated by Dr.
Linnceus, f? o?n his Pupil Dr. Haflelquift,
who had been lately in thofe Parts • By
John Ellis, Efr, F. R. S.

Reader,. 3>.QAL Ammoniac is made from the foot
. 1^3 arifing from the burnt dung of four-
footed animals, that feed only on vegetables.

This dung is cohered in the four firft months of
the year, when all their cattle, fuch as oxen, cows,
buffaloes, camels, (beep, goats, horfes, and affes,
feed on frefh fprmg grafs, which, in Egypt, is a kind
° t! eroil, or clover: for when they are obliged to
feed their cattle on hay, and their camels on bruifed
date kernels, their excrements are not fit for this
purpofe ; but when they feed on grafs, the poor
people of Egypt are very careful to colled the dunt*
qmte frefh, and, for that purpofe, follow the cattle
all day long, m order to colled it as it falls from
tht-m ; and, if it is too moift, they mix it with chaff
inibble, fliort ftraw, or duff, and make it up in the

form of cakes, about the fame fize and fhape as it
lies on the ground. 1

Then

Philos. Trans. Vo /.LI TAB.Xl.jo. 505.

L 5°5 ]

Then they fix it to a wall to dry, till it is fit to be-
burnt.

For want of wood, which none but the rich in
Egypt can afford to buy, they burn this dung through
the whole country, and fell a vaft quantity of it to th<*
falt-makers.

The excrements of the camel are not found at all
preferable to any other 3 and its urine is never ufed
for this purpofe, although generally reported fo by
authors.

The falt-workers pretend, that the human excre-
ments, and thofe of goats and fheep, are preferable
to any other.

The months of March and April is the only time
they make the fait.

Sal ammoniac is made in the following manner :

They build an oblong oven, about as long again:
as broad, of brick and moift dung, of fuch a fize,
that the outfide, or flat part of the top of the arch,
may hold fifty glafs veffels, ten in length, and five
in breadth, each veffel having a cavity left for it in
the brick-work of the arch. See Tab. XI.

Thefe glafs veffels are globular, with a neck an
inch long, and two inches wide.

Thefe veffels are of different fizes, in different fait-
works, containing from a gallon to two gallons 3 but,
in general, are about 1 8 inches diameter.

They coat each veffel over with a fine clay (which
they find in the Nile), and afterwards with ftraw3.
they then fill them two-thirds full of foot, and put
them into their holes on the top of the oven.

They make the fire gentle at firfi, and ufe the
afore-mentioned dried dung for the fuel 3 they in-

creafe

1

[ S°6 ]

creafe the heat gradually, till they bring it to die
higheft degree, which the workmen call hell-fire,
and continue it fo for three days and three nights to-
gether.

When the heat is come to its due degree, the
fmoke fliews itfelf, with a fourifh fmell, that is not
unpleafant; and, in a little time, the fait flicks to
the glaftes, and covers the whole opening. The fait
continues fubliming, till the above-mentioned time
is expired ; then they break the glades, and take out
the fait, juft in the fame form, and of the fame fub-
ftance, that it is fent all over Europe.

At each falt-work, they have a glafs furnace, to
melt the old glaftes, and make new ones.

XLIX. Mont turn quor undam prcealtorum ,
tnagna ligni fojjilis copia quaft infarElorum ,
brevis defer iptio Sam. Chrift. Hollmanni,
Philofophice Profejfor. Goettingeniis, et
S. R. Sodalis .

Rea^J6e^-I4. ^<UNT in Haftite et principals Goet-
tingenfis confiniis montes quidam pras-
alti, qui tanta ligni fojjilis copia abundant, ut fidem
fere fuperet. Horum alter non procul Mundenfi
oppido, circa Werram Fuldamque confluentes pofito,
verfus meridionalem plagam ad tantam altitudinem
affurgit, ut mercurius barometricus in eodem ad
i" 25'" pedis Lond. ab illo gradu defeendat, quern
ad Werras Fuldaeque, ipfiufque adeo ex iifdem ori-
undi Vilurgis, ripas habet : unde ex repetitis in

utroque

[ 5°7 ]

utroque loco obfervationibus, mercuriique adeo alti-
tudine media, utrobique, quam maxime fieri potuif,
determinata, montis, de quo nunc pluribus dicendum
efl, altitudinem ad 1150 circiter pedes Parifinos re-
vocare licebit. In hujus montis fummo fere vertice
planities qutedam, fi ita appellare fas eft, reperitur,
quae ad fexcentarum circiter orgyarum latitudinem,
feptingentarum vero longitudinem, excurrit, fubcujus
fuperficie, ad 5, 10, 15 pedum profunditatem ingentia
lignorum foffilium ftrata reperiuntur, quas in illis
locis, ubi ligna ifta foffilia ad fuos, quibus deftinata
erant, ufus eruebantur, 20 circiter pedum altitudi-
nem tunc temporis, quando ante paucos annos ibi-
dem aderam, habebant. Quoniam ftratorum vero
iftorum fundus, cui infiftebant, lapideus, die Johla
metallifoflores noftri vocant, dimidium circiter pedem
craffus folum erat, Dominufque fundi refcire cupiebat,
num infra fundum iftum lapideum ejufdem ligni co-
pia aliqua forfan fupereftet ; terebra quadam, quali ad
exploranda montium vifcera uti metallifoffores non-
nunquam folent, periculum fadlum eft, repertumque,
infra fundum iftum lapideam ejufdem ligni copiam ad
30 circiter pedum profunditatem adhuc fuperefte, ne-
que ad novum tamen ejufdem fundum perventum
adbuc erat; eandemque ligni iftius foftilis altitudinem
in aliis etiam ejufdem montis locis, ubi inquirere in
eafdem licuit, reperiri, mihi confirmatum eft. Place
ligna in ftratis fuis ita fibi incumbunt, ut in febtione
ipforum perpendiculari, qualis tunc temporis, quum
ibidem adeflem, ad fundum ipforum lapideum uf-
.que ad 20 circiter et plurimum pedum latitudinem
fabta erat, ligna ipfa lapidum, in lapicidinis fibi in-
xumbentium, fitumque horizonti parallelum fervan-
V" o l. LI. U u u tium*

C 508 3

tium, formam fere referens, adeo arde etiam fibi
invicem quafi impada fint, ut vix terra interlabentis
quicquam obfervare liceat : unde difficillimum cog-
nitu evadit, num arbores integrce , an arborum jam
fiftarum divilarumque partes folum, fuerint, ex qui-
bus ifta enata Tint. Temporis etiam, quo hunc fitum
procul dubiojamobtinuerunt, longinquitate, terraque
fimul incumbentis et aquas interlabentis humiditate*
adeo fragilia fada funt, ut non in naturali fuo fitu
folum rimarum, verfus omnes fere dirediones excur-
rentium, plena Tint, fed loco etiam fuo mota in ma-
jores facile minorefve portiones dilabantur. Color
omnium horum lignorum a fufco ad nigrum fere
tendit, quo etiam terra ilia pauca paffim intermixta
non folum, fed eidem etiam incumbens, ad pedis
unius et ultra altitudinem, fimul tinda eft : unde et
hac, licet caute remota, ne in extrema quidem fuper-
ficie juftam lignorum iftorum faciem, imo ne fitus
quidem diredionem veram, cognofcere fatis diftinde
licet. Terra enim ifta humida ligni femiputridi
rimas et intervalla omnia adeo oblita repletaque funt,
ut vifum omnem fallant confundantque. Quae huic
vero terra incumbit, humus eft intermixto fabulo, in
qua optimae paffim argillae bolique, alibi vero arenas
etiam fubtiliffimas, varieque coloratas, reperire ftrata
licet. Ex his ipfis terrarum circumjacentium ftratis
vero novus quafi adhuc afturgit in fummo cacuminis
vertice mons, quingentorum et quod excurrit pafiuum
ambitum circiter habens, lapidibus ingentibus fere
totus conftratus, arboribufque prxterea proceris con-
fitus, fub quo ipfo quoque lignorum iftorum ftrata>
quaedam adhuc excurrunt*

[ 5°9 ]

Ligna, quae ex dratis hifce eruantur, limo humo-
que interkbente ita plerumque inquinata et obdu&a
funt, ut a gleba quadam terredri primo adfpedtu
non in ul turn differant : unde et a fofloribus et ope-
rariis, qui iifdem eruendis adhibentur, carboncs fojjiles
plerumque appellantur. Quando aqua vero leviter
ablutaet purgatafunt, aerique ficciori per breve tern-
poris fpatium expofita, naturam indolemque fuam
genuinam adeo clare datim produnt, ut vel imperi-
tiflimus et dupididimus quifque ne per momentum
quidem temporis dubitare podit, num ligna vere talia
fint, an minus. Quod nudo vero oculo in iifdem ita
jam agnofcitur, illud ipfum vel leviter armato magis
adhuc patefcit : fiquidem et tubuli lignorum perpen-
diculares , cum fibris ipforum tra?ifverfis et horizon-
talibus , facilliine in iifdem dignofcuntur, et lucre-
inenta ipforum annua clariffime in iifdem apparent ;
ut alia ejufmodi plura taceamus. Quando fruftra
etiam ilia lignea in judas magnitudinis acervos conve-
huntur, hique eadem ilia enchirefi tradantur, qua
carbonarii nodri in parandis ex ligno recenti carboni-
bus utuntur, optimas notae carbones lignci inde pro-
deunt ; qui ab acido vero, quod magna copia in iif*
•dem adhuc reddet, minerali non eofdem ubivis cum
aliis carbonibus ligneis ufus prasdant. Ligna enim
haecce fodila, quorum formam dtumque hadenuS
defcripfi, tanta bituminis aluminifque copia imprasg-
nata funt, ut non ignem folum facile concipiant,
alantque, fed et cineres, quiabillorum fub diu fada
combudione fuperfunt, magnam aluminis copiam
fundant : quod ex iifdem etiam in peculiari huic
ufui dedinata odicina, magna copia, in eodem montis
•-vertice adhuc excoquitur. Atque base caufa etiam

U u u 2 ede

[5io]

efle videtur, cur elegantiffimi inter ligna iffa non raro
reperiantur pyrita , qui aliorum fimilium more fcin*-
tillas ex chalybe copioffimas eliciant j aeri vero libe*-
riori per aliquod tempus expofiti, primum dehifcere,
mox in pulverem refolvi, toti quanti foleant, qui alu-
mnus fulphurifque vulgaris fioribus quad, paucaque
terra martiali, vel nudo oculo conftare cbfervatur.
Quoniam inter eofdem vero nonnunquam reperiun-
tur, qui arborum fruticumque ramentis circumfud
formas elegantiffimas refertint, quos ab interitu fuo,
fi fieri poffet, confervare cupiebam, aquam ferventem
aliquoties dngulis diebus iplis tamdiu affudi, donee
©dore et colore fere omni- carens ab iifdem rediret :
atque hac equidem ratione fadfum eff, ut illorum
nonnulli, probe prrus exficcati, atque chartis thecif-
que ficcis involuti, et ab aeris humidioris accefTu de-
fend, jam lex fere annos perdurent, parumque mu*
tationis adhuc pafli lint. Horum nonnulli media
fruffi cujufdam lignei fubffantia ita depe occultantur,
ut non nifi illo fra&o, fiffoque, in confpedfuin pre-
deant.

Alter horum montium, de quibus dicere conffi-
tum elf, in ipfa Hadia, prope Allendorfiium, quod
a fontibus et officinis fuis falaribus longe lateque his
in regionibus celebratur, fitus, atque ab accolis prop-
terea procul dubio der IVyfzner, mons albus, appella-
tus efr, quod cacumen ipfius diu adhuc ab incum*-
bente nive albefcit, quando in reliquorum montium
circumjacentium verticibus dudum ilia difparuit.
Hie mons priorem iff um altitudine multum adhuc
vincit, atque ex obfervationibus barometricis, in eo*
dem etiam aliquoties repetitis, fupra Werrce, ipfum
quoque proxime praeterl abends, ripam ad 1970 c i

citer

[ 5ii ]

citer pedum Parifinorum altitudinem quam proxime
afcendit. In montis hujus vifcera, circa i 5x0 cir-
citer pedum inde a bafi ipfius altitudinem, ab orien-
tali, meridionali, et occidentali ejufdem plaga cuni-
€uli , quos mellen Germani noftri vocant, per durif-
ftmum partim lapidem dudti funt, quos magna bitu-
minis foffilis lignorumque foffilium copia undique
ambit. Horum unum, fubftrudtionibus fuis muni-
tum, fumto metallifofforis habitu, ad quingentarum
circiter orgy arum , quarum lingulae hexapedam Gal-
licam paulum adhuc fuperant, longitudinem, finem-
que adeo ipfum illius cuniculi, fubii, nihil ab omni
latere, tedtoque. incumbente, quam bituminum ligno-
rumque foffilium immenfam copiam, poll; fubftrudli-
ones illas ligneas, ad lampadum flammam cum co-
mitibus meis videns. Atque bitumen quidem, quod
hie reperitur, et eruitur, nigredine et fplendore fuo
ad gagatem ipfum quam proxime accedit, duritie vero
parum per ab eodem difFert. Lignum vero foftile
ejufdem cum altero illo, quod modo defcripfi, eta.
cujus antea indicata fede hie mons etiam paucis mil-
liaribus Germanicis folum diftat, videtur efte generis ;
aluminis vero, aut alius falis mineralis, bituminifque,
quantum adhuc conftat, parum admodum continet,
coloris etiam minus fufei, et nigricantis eft. Per hoc
lignum cuniculus ille, quern fubii, ita dueftus erat, ut
hunc ipfum undique ambiret, cuniculique ipfius fub-
ftru&ionibus in fttu fuo naturali confervaretur, ejuf-
que altitudinem ab utroque cuniculi latere 4 aut q or-
gy arum plerumque efte foffores confirmabant. Hifce
lignis bi tumults illius, quod modo indicavi, ftratum,.
ad duarum circiter orgy; arum altitudinem, adeo exadte
ubivis incumbit, ut fuperfufum quaft eidem efte vi~

* deatur

[5*2]

deatun unde et proxime eidem fubjacentium fupe»
riorum lignorum fruftra multum eodem impreegnata
funt, propiufve ad colorem ipfius nigricantein acce-»
dunt. Quum hujus igitur bituminis tanta intra montis
hujus viicera reperiatur copia, ut a cucentis fere annis
jam ad excoquenda falia Allendorffienfia fit adhibi-
turn, illoque ipfo, quum ibidem adefTem, tempore
vel fingulis annis ultra ducenties mille modios, men-
furte Goettingenfis, ex eodem adhuc erui, earundem-
que falinarum ufibus impendi, dicerentur; ligna ifta
foffilia, quas eodem bitumine imbuta non funt, in-
tadta fere a foffibus relinquuntur, futurorum faecu-
lorum ufibus demum infervitura* Quemadmodum
haec vero bitumina lignis fubjacentibus foffilibus, ita
bituminis hujus fuperficiei tedium^ quod ipfum pro-
xime excipit, lapideum adeo ardte ubivis incumbit ct
cohasret, ac fi vel ipfum infufum eidem efiet, adeo
ut lapidum bituminumque fubftantioe fibi invicem
quad permixtae ibidem multis in locis appareant.
Quanta tecli hujus incumbentis lapidei craffities ht,
non fatis equidem conftat, neque in omnibus forfan
locis eft eadem. A tedti vero hujus cum fubjacenti-
bus bituminibus confinio ad fummum montis, ad
quod per acclivitatem ejus paffim afeenditur, cacu-
men, quingentorum circiter pedum Parifinorum alti-
tudo adhuc multis in locis eft : hoeque montis cacu-
men procerarum arborum fylvis paffim tegitur, fu-
perius vero, ubi in ampliffimam tandem planitiem
obit, prato quodam fatis fpatiofo et udofo fimul in-
fternitur. Ligna ergo hsecce, cum incumbente bitu-
minum ftrato fatis craffo, mediis fere montis ingentis
vifeeribus inclufa funt ; quum priorum iftorum magna
pars, non admodum profunde, plerifque in locis, humo

cooperta

[ 5i3 ]

cooperta fit, parfque folum illorum aliqua fub accum-
bentis fupremi montis verticem, quantum adhuc con-
flat, excurrat. Utrumque tamen tantum naturae efl
miraculum, ut fatis vivis depingi coloribus vix queat,
neque parum ad illuflrandam globi noflri terraquei
hifloriam conferre vel maxime aliquando poffit.

Ejufdem forfan generis efl, quod ex Societatis Reg.
Goettingenfis Comment arior urn tom. II. paucis hie re-
petere liceat. Reperta nempe ante aliquot annos, et
ex marga eruta, in montium noflrorum Hercynico-
rum vicinia, funt ofTa quaedam ingentis, et fere mon-
flrofae, magnitudinis, quae Elephantis cujufdam reli-
quiae primo intuitu efie fere omnibus videbantur.
Paulo accuratiore vero illorum inflituto examine, fa-
cile apparebat, oda ifla animalis cujufdam fragmenta
effe, minoris quidem elephante altitudinis, ejufdem
tamen, fi non majoris, cum eodem molis et ponderis.
Quum eodem vero in loco paulo pofl etiam dentes
eruerentur, inufitatae magis forms, quam magnitudi-
nis, qui vivi iflius, per nonnullas Germanise Galliae-
que provincias tunc temporis peregrinatis, rhinoce-
rotis dentibus exadte fimiles reperiebantur effe ; rbi-
nocerotis offa ifla foflilia effe, eo minus relinquebatur
dubii, quod nullius adhuc cogniti, five terreflris, five
aquatilis, animalis fimilitudinem ifla ullam referrent.
Tot vero eorum odium eodem in loco reperta funt
fragmenta, ex quibus clariffime patet, qnatuor mini-
mum adult a, unumque minus adultum , ejufdem ge-
neris individua eodem in loco fepulta fuiffe : id quod
occafionem mihi poflea dedit, viam quandam novain-
tentandi, qua corporum hujufmodi peregrinorum,
ipforumque marinorum, in terrae continentis diverfis
regionibus origo intelligi forfan melius poffet : de quo-

in

[ 5 r4 ]

in iifdem Societatis noftrae ■■ Commentary or um tom. IV,
jam fuiius didtum eft.

L. Experiments in Ele&ricity : hi a Eetter
from Father Beccaria, Profejfor of Expe-
rimental Philofophy at Turin, to Benjamin
Franklin, L. L. D. F. R. S.

Benj amino Franklin viro de re electric a meritijjimo
“Joannes Baptijla Beccaria ex fcholis piis S.P.D.

Read Feb. 14, £''iOfpitem ex America Londinum te

appulifte gaudeo, vir praclarif-
fime. Offero tibi de motibus eledtricis, qualem expe-
rimentis excudi, hypotheftn : partior banc in duas
partes, quemadmodum ipfa poftulare videtur motuum
hujufmodi differentia: ago parte prima de acceftioni-
bus, de difeeflionibus dico parte altera.

2. Et continuo univerfam de acceftionibus pertrac-
tationem meam ita paucis comprehendo: “ Quum
<£ ignis eledfricus copiofior in corpore altero vi ex-
“ pandendi fe ad asqualitatem trajicit in alterum,
££ partem interjedti aeris dimovet e loco pro majore
t£ fua copia majorem : fit inde, ut aer a tergo cor-
<£ poribus adjacens deficiente fulcro aeris intermedii
££ ruat verfus ipfum medium locum ; ruit vero non
<£ circumeundo corpora, quae via eft longior, atque
££ impedita abs igne proffuente, fed ipfa trudendo a
££ tergo : bac aeris trufione accedunt corpora inasqua-
££ liter eledtrica; dum accedunt, accelerantur, quia
cc pro acceflione majore copiofior ignis interfluit, co-

“ piofior

-

1

/

Philos. Trans YclLI TAB XU jj.5i5.

B

« X .l/ytt./s fc .

[ 5I5 ]

ft plofior intermedius aer disjicitur, augeturque adeo
“ momentum aeris a tergo trudentis.”

Experimentum I.

3. Aerem disjici ab interfluente eledrico igne,
fcintillas experimento demonftratur, quas excitatur in
medio tubulo, hinc claufo hermetice, inde imped ito
abs liquore aliquo, ipfa enim, disjiciens liquorem, dif-
jedum aerum teftatur. s

4. Neque vero interfluens ignis aeris intermedii
disjedi fulcrum poteft fupplere, quo aer corporibus a
tergo adjacens fuftineatur ; is enim liberrime effluit,
et effunditur per alterum corpus : quare cum non
fulciatur ipfe, nec fulcri vices poteft agere.

Experimentum II.

5. Experimento res confirmatur plane luculentif-

fimo : vittam ex charta inaurata longam pollices odo,
latam lineas quatuor convolvo circa fefe, ut cylindrum
folidum D [Vide T^^.XII.] efFormet : hunc fufpendo
ferico filo D G fub fornice vitri pneumatici IHK, per
cujus verticem H init virga metallica B C deftnens in
metallicam fphasram C : figo in lance I K virgam me-
tallicam LE fimili fphaera ornatam ; nempe fphserae C
et E funt in eodem piano cum pendulo D, atque ab
ipfo diftant ambae aequaliter ; turn nexa catena A B,
qus pertinet ad machinam eledricam virgae B C, et
confequenter immiflo eledrico igne in virgam B C,
obfervo : 1. ante fubdudum aerem chartaceum cylin-
drum D agitari vehementiftimis vibrationibus inter
duas fphasras EC: 2. dum aer fubducitur, minui earn
agitationem plane pro copia fubdudi aeris : 3. omni,
quantus poteft, aere fubdudo, cylindrum D vix
‘ Vol, LI. Xxx nutare.

\

C 516 ]

nutare. His obfervatis aerem reftituo particulatim >
atque pro aere admifio video vibrationes iterum au-
gejfcere, et fieri, quemadmodum antea, vehementifii-
mas : qux dum contemplor fingula, atque omnia'
iimul comprehendo animo, intelligo magnitudinem
motuum eledricorum aeri, vel toti, vel refiduo prc-
portione refpondere.

Experimentu m III.

6. Quod leviora corpufcula, bradeolte, et pulvii-
culi, motu adhuc fatis fenfili agitentur in rarefado
aere, id in caufa fuit, cur cenfuerim a principio cum
phyficis aliis eledricos motus adioni ignis eledrici in
aerem acceptos referri non debere; quod, Fe nunc
accuratius collata, refiduos videam in refiduo aere
motus non majorem habere ad primos motus, qui
fiunt in toto aere atmofpherico, proportionem, quam
ea fit, qua? inter refiduum et primum aerem inter-
cede, id nunc facit, ut ilium meum, et alienum er-
rorem agnofcam, atque in contrariam veniam, quam
verifiima tefiatur experientia, fententiam.

7. Neque omittam partem obfervationis opportunif-
fimam rei confirmandas : foleo enim allatum ultima
loco experimentum perfiepe capere in cubiculo obte-
nebrato, atque turn obfervo ignem vibrantem pendu-
lum ante aerem fubdudum micare hinc inde crepi-
tantibus quidem, ac lucidifiimis, fed ardis, atque
brevibus prope fphasram utramque fcintillis : deinceps
ignem hunc pro fubdudo aere, adeoque pro minutis
penduli vibrationibus effiuere magis amplo radio*
magis tranquillo, magis continuo, quanquam non ita
micante>

8* Atque

[ SJ7 ]

8. Atque hasc ipfa res certe readtionem aeris de-
monftrat ignem eledtricum cohibentis in denfitate
quadam, quae denfitati fuae proportioni refpondeat j
haec autem aeris readtio non poteft adtioni non refpon-
dere ignis eledtrici aerem nitentis disjicere, ac plane
disjicientis, ubi neceftaria is igni vi polleat.

9. Atque his plura non adferam tibi pro accefiio-
nibus explicandis corporum eledtricorum insqualiter,
attuli in datis ad Beccarium litteris, in quibus tamen
non nift dubitanter plura admodum differebam de
mechanica acceffionum cauffa: accuratior conlidera-
tio experimentorum facit nunc, ut de acceffionum
cauffia dicam fidentius.

10. Corpora aequaliter eledlrica difcedunt j qua
cauffa id efficiatur, nunc perfequar.

11. “ Ignis eledtricus, qui quoquomodo inlidet in
<c corporibus, nititur, ut libretur cum igne eledtrico,
<c qui infidet in aere. Si uterque” [finito me ilium
deinceps proprium dicere hunc aereum] <c aequalem
“ habet proportionem ad nativam corporum atque
“ aeris capacitatem, corpora accedunt, aut in nativa
“ quiefcunt diredtione ; alter ft fuperat proprius, vel
“ aereus, corpora explicat ftmiliter, compellitque ad
“ difceffionem.” Haec rei narratio.

Experimentum IV.

12. Quoties in cubiculo quodam meo amplo ipfo
quidem at claufo pergo diutius urgere alium, atque
alium in catenam eledtricum ignem, experior partem
ejus ignis effundi in aerem ambientem, ipfumque
etiam, quantufcumque in cubiculo eft [dum a tem-
peftate ficcus fit, vel abs igne] facere exceffu eledtri-
cum. Duo enim tenuia ex lino fila, quae vel fummis

X x x 2 digitis

t S*s 3

digitis prehenfa, vel arundine fufpenfa deffero quoli-
bet, in quodlibet cubiculi fpatium, mutuo difcedunt.
Atque, five in eodem ipfa contineam loco, five in loco
transferam alia atque alia, pergunt divergere ad femi-
horam, ad horam quandoque, et ultra.

Experimentum V.

13. Si ea fila ope vitri feparentur ab arundine^
adeoque a folo, principio divergunt, turn ad nativam
veniunt diredlionem : obtingunt autem hasc omnia
pofl omnes elicitas, quants poffunt, a catena fcintil-
las, pofl omnem ab ipfa fubdudlum redundantem ig-
nem, pofl catenam nexam cum folo*

Experimentum VI.

14. Ex diuturna eledlricitate machine phenomena
experior omnino eadem. At, fi diuturna eledlricitas
machinas continuo confequitur diuturnam eledtrici-
tatem catenas, aut contra, fila, quas arundine fufpenfa
conflanter divergere videbam ex alterius eledlricitate,
video principio accedere mutuo incipiente eledlricitate
alterius, turn iterum divergere quemadmodum antea.

1 f. His inquam experimentis doceri nos arbitror.
tc i* Dum alium atque alium ignem congerimus in
“ catenam, aliam atque aliam ipfius partem difce*
“ dere quam latiffime in ambientem aerem, ipfique
u adhasrefcere, atque ita omnem contentum in cubi-
“ Culo aerem evadere exceffu eledtricum : fimiliter
“ dum alium atque alium ignem fubtrahimus a ma-
“ china, aliam atque aliam ignis partem machinam
“ haurire abs aere ambiente ; atque ita omnem con-

tentum in cubiculo aerem fieri defedu eledtricum.
u Eila vel manu, vel arundine delata difcedere

" in.

[ 519 ]

■ c in aere, vel eledrico exceffu ex catena, vel eledrico
* defedu ex machina, vel vi proprii nativi ignis fu-
*c perantis aereum, fi merguntur in acre eledrico ex
w machina, vel vi ignis aerei fuperantis nativum pro-
“ prium filorum ignem, fi merguntur in aere eledrico
“ ex catena. 3. Fila hujufmodi divergentia ex elec-
“ tricitate catenas, ex confequente eledricitate ma-
“ chins (vel contra) primo accedere, quia machina
w primo hauriat abs aere exceffu m inditum a catena,
" vel catena ignem reffituat aeri fublatum a machina ;
ce atque ita ignis in aere ad nativam menfuram re.-
<c dudus librari deb'eat cum igne nativo permancnte
<c in filis. 4. At deinceps ex diuturniore eledricitate
" machine confequente eledricitatem catenae, vel
u contra, fila iterum divergere, quia vel machina per-
“ gat haurire partem ignis nativi, vel catena pergat
“ addere alium ultra nativum aeri ignem. 5. De-
nique ffla eadem cum vitro feparantur, principio
“ divergere, quia ipfa, quae folum ignem nativum
" habeant, mergantur in aerem vel exceffu, vel de-
** fedu eledricum. At dein, cum funt vitro fepa-
“ rata, venire ad nativam diredionem, quia vel pars
<c ignis aerei, fi aer eft exceffu eledricus a catena, in
“ ipfa fe denique effundat ad aequalitatem, quin ultro
'c praeterfiuat ob cohibens vitrum j vel pars ignis na-
<c tivi et proprii filorum fe effundat in aerem, fi aer
“ eft eledricus defedu, quia fuppleri aliunde poflit
“ ob interdicens vitrum.”

16. Quare haec videntur univerfe conftare :
“ 1. Aerem fuum continere nativum ipfi fibi ignem.
<c 2. Nativo aeris igni ignem alium addi pofte, 11a-
“ tivi abs aere ignis partem poffe fubtrahi, fed lente,
f* et quafi per vim. 3. Aerem dimittere redundan-

“ tern,.

[ 520 ]

li tem, haurire ignem deficientem, fed quam lentif-
<c fime. 4. Si aer aeque ac contenta corpora habeant
“ nativum ignem fuum, confiftere hasc in nativo
“ ftatu ; fi aer, manente nativo in corporibus igne,

“ ignem habeat nativo aut copiofiorem, aut parcio-
“ rem, corpora difcedere.” Verum fingula baec tbeo-
remata experimentis aiiis illuftrari mirum in modum
pofliint, et demonftrari latius.

Experimentum VII.

1 7. Duo fila nexa catena poll paucas globi conver-
fones divergunt maxime ; deinceps a diuturniore ca-
tenae eledlricitate incipiunt minus divergere j atque
baec divergentia ad certum ufque gradum minuitur,
lit quandoque angulus divergentia3 poll continuatam
diutius globi fricationem fiat fubduplus anguli diver-
gentiae, qui extiterat ab eledtricitate eadem primo ex-
citata. Quum banc filorum divergentiam video mi-
nutam fatis, turn globum non frico ulterius, fed fti-
lum acutiffimum catenae admoveo pedetentim, quo
lente redundantem omnem abs ipfa ignem bauriam.
Id dum fit, lente fila accedunt, turn continenter
lente iterum divergunt ad angulum primo quidem
minorem, fed fatis magnum, quae quandoque vix
metiantur gradus quadraginta quinque ; turn vero
pergunt divergere ad diuturnum tempus.

18. Videlicet maximus abs eledlricitate primo ex-
citata angulus, quia turn fatis ingens immiflus in ca-
tenam, et in nexa fila, ignis j nullus, vel minimus, in
aerem. Fit deinceps minor angulus, prout augefcit
ignis, qui confequenter immittitur in aerem, con-
ftante codem ignis cxcefi'u in catena. Dum admoto
flilo lente minuitur ignis in catenam immiflus, mi-
nuitur

C 5 21 ]

irmtur adhuc angulus prout accedunt ad squalitafem
ignis in catena refiduus, atque ignis in aerem immif-
fus, ipfique affixus j ubi uterque ignis pertingit ad
aequalitatem, fila attingunt ad diredtionem fuam na-
tivam ; cum deinceps minuitur ulterius ignis red un-
dans adhuc in catena, nec fimiliter minuitur ignis re-
dundans in aere [aeri enim, uti vidimus, adhaerefcit,
atque ab ipfo lente dimittitur] fila iterum difcedunt
pro excefiu ignis aerei fupra ignem in catena ; qui
denique aereus ignis, quoniam lentifiime dimittitur,
diutiffime pergunt divergere fila.

Experimentum VIII.

ip. Si fila fint nexa machinae, eadem omnia in iia
contingunt phaenomena ex diuturna eledtricitate ma-
chine, quae in iis contingebant catenae nexis ex diu-
tuna eledtricitate catenae.

20. Quare univerfe, quemadmodum confiitui a
principio, “ Si ignis proprius corporum, quantuf-
“ cumque is fit, libratur cum igne ambientis aeris,
<e corpora vel confiftunt in nativo ftatu, vel ad ipfum
cc redeunt; fi alter ignis fuperat alterum, corpora dif-
4C cedunt vi ignis fuperantis.”

21. Atque hinc rationem vides, ni fallor, vir prae®
fiantifiime, cur aeque difcedant turn quae a catena,
turn quae a machina funt eledtrica corpora.. “ Ignis
“ proprius in corporibus a catena eledtricis vincit
<c aereum, aereus vincit aeque proprium in eledtricis
ie a machina.”

Experimentum IX.

22. Quoties fila mutuo difcedunt a fe invicem,
atque divergunt ex audto in ipfis, vel minuto igne

nativo

5

[5*0

native ad meutn accedunt admotum digitum : quoties
difeedunt, atque divergunt fervantes ignem fuum na-
tivum ex audio, vel minuto igne nativo aeris, a di-
gito refugiunt meo.

23. Hac vero res primo quidem notiffimis legibus
acceffionum atque difeeffionum eledricarum eft con-
fentanea ; quum enim nativus in fills ignis audus eft,
vel minutus, ipfa funt inaequaliter ac digitus eledrica,
qui habet nativum ignem fuurn : quum vero nativus
ignis perftat in filis, et ipfa diicedunt mutuo ob ignem
audum, vel minutum in aere ; turn, quemadmo-
dum difeedunt ambo alterum abs altero, ita difeedant
oportet a digito meo ipfo etiam habente ignem na-
tivum, vi aeris, in quo nativus ignis minutus eft, aut
audus. Sed praeterea haec filorum a digito difcefiio
ipfa hanc probat etiam, quam affero, difeeffionis
caufam : nam et digitus, et fila cum folo communi-
cant, adeoque alium in fe certe non habent ignem,
nifi nativum, quo quoniam non difeedunt, reftat ipfa
difeedere ex nativo igne in aere audo, vel minuto.

24. Cum in hanc primo incidi difeeffionum elec-
tricarum theoriam, ea me ancipitem tenuit fufpicio,
ne ignis aereus difeeffiones facere non poffiet in ma-
china iis asquales in pernicitate, et magnitudine, quas
facit in catena ignis proprius : haec inde fubibat ani-
mum fufpicio, quod ignis in machina, et catena (uni-
verfe in corporibus omnibus deferentibus) menfura
mutetur quam perniciffime, lentiffime autem auge-
atur, aut minuatur menfura ignis in aere ambiente.
Alia praeterea fufpicionem exagerabat confideratio ;
tantum me nunquam abs aere, quantum a machina,
fubtrahere ignem potuiffie, tantum potuifle nunquam
aeri addere, quantum catenae j nunquam enim eo veni,

ut

[ 523 ]

-ut omnem aerea fob eledWcitate fuftukrim filoram
oivergentiam, quanta exiftebat ex Integra macbina;
aut catenae eledricitate.

Fadtum inde eft, ut experirnenta ha:c eadem, imo
et alia, in literis attulerim ad praeclarifllmum inftituti
ifonomenfis pratidem dads, quin banc in iis fatis late
theoriam dilcefiionum conftituercm.

Verum re maturius perpenfa intellexi pernicitatem
dilceliionum, quae fiant abs igne aereo, non ipfi per-
mciuti refpondere debere, qua vel augeatur ipfius
copia, vel minuatur ; fed pernicitati, qua agat copia
inhaerens; et magnitudinem difcefilonum, qu$ fiant
ab igne eodeirq non ablolutae, fed comparative ipfius
rnagnitudini refpondere debere utrumque autem fa-
cile vidi pro re obvenire.

%

Experimentum X.

2f. Si in experimento VI. poll minufcam ex diu-
turniore eledricitate catenae filorum divergentiam,
non jente, led protinus (manu nempe in catenam
immifla) omnem fubtraho a catena redundantem i«r.
nem, contmuo incipiunt quidem accedere fila quam
velocillime ; verum velocitate aequali refiliunt repente,
antequam pertingant ad nativam diredionem. Hec
autem altera difcefiio quoniam fit ex aereo igne fu-
perante proprium in fills refiduum, video inde ignem
aereum (quamquam mutetur lentifiime ipfius copia)
lplum tamen difcefiiones facere iis aeque veloces, que
abs igne proprio efiiciuntur. ’ 1

Experimentum XI.

26. Sed et ip fas ex igne aereo obvenire eque mag.
nas ita mtelligo. Pod ignem inditum in aerem, qui

1 yy catenam

[ 524- ]

catenam ambit quantus poteft, dempto red andante
omni ab catena igne, atque aaeo difcedentibus jam
fills ex igne aereo, vitreo globo fubftituo faiphureum,
atque ex hujus fundione, video, principio augeri
angulum divergentiae, quern effecerat ignis aereus,

turn ipfum continenter minui. . .

2 7 . Id autem certum : prirnas globi fulphurei iricti-
ones demere partem nativi ignis a catena, neque pa-
riter demere exceftivum ignem ambientis aeris (aer
enim lente, ut vidimus, accipit ignem alienum, lente
acceptum exuit) ; quare augefcit magnitudo diver-
gentiae, quae fit abs igne aereo, non mutata magnitu-
dine abfoluta ignis aerei, fed mutata folum magnitu-
dine ipfius comparativa, minuto nempe igne piopno;
adeoque auda proportione aerei ad proprium. Igitiu
quoniam quantum ignis ingeritur in catenam, tan-
tundem fubtrahitur a machina ; pioportio ignis aerei
circa machinam ad refiduum in machina eadem ent
ac proportio ignis in catena redundantis ad aereum
circa catenam : quamobrem aereus circa machinam
difceffiones faciet non aeque veloces folum, fed et
aeque magnas, ac eae funt, quas facit ignis propnus

in catena. . 1

28. Itaque, ut omnia demum paucis complettar,
quae pertinere videntur ad motus eledricos univerfe
omnes explicandos (fufpenfiones enim, adhaefiones,
vibrationes, infinitofque alios compofitiores quail u-
dos eledricos, tu ipfe probe videre vifus es difcemom-
bus omnes, atque accefhonibus contineri) h^c eni-
que eft fumma hypothefis meae. <c Accefliones cor-*
“ porum inaequaliter eledricorum efficiuntur ab igne
<c eledrico a corpore altero, in quo copiofior eft, cr-
*« fluente in alterum per aerem interjedum, ipfum-

t 525 ]

° que disjiciente. Difceffiones autem vel igne pro-
ec prio corporum efficiuntur fe expandente contra
tf aereum, vel aereo fe expandente valentius contra
tc propriumj” qua? tamen expanfio ignis alterius al-
terutn iiiperantis fine mixtione mutua alterius cum
altero videtur contingere. Aer enim ignem continet
fuum quantuncumque, ne dilcedat; arcet proprium
deferentium corporum ignem, ne adhairefcat fibi.

2p. Hanc, inquam, hypothefim offero tibi, vir praa-
clariffime, quo tu earn facias ineliorem. Si tanti in-
terea ipfam ducas, lit Regia? iffi fcientiarum Societati
exhibenda videatur, res ex meo obtinget defiderio,
qui quando ornamentum ipfi adferre nullum poffum,
diligentiam faltem nolim defiderari meam. Tu vero
cura, ut valeas. Servari enim te decet quam diutil-
fime utiliffime, fcientiae perficienda? amplificanda?-
que, quam certiflimam inftituifti. Dat. Taurini,
24. Decembris, 1757.

Remarks on the preceding Paper , by Benja-
min Franklin, L. L. Z). F. R. S.

Read Feb. 14, pOR the better understanding this pa-

1760. JF per, *s ncce{fary t0 know, that

Father Beccaria ufes a large chain, fufpended by filk
lines, for the purpofe of a prime condudtor ; and that
his machine for turning the glafs globe is fo con-
trived, as that he can, on occafion, readily ifolate it,
(/. e. place it on glafs or wax) together with the per-
fon that works it. When the communication is thus
cut off between the earth and the chain, and alfo
between the earth and the machine, he obferves,
that the globe being turned, both the chain and the

Y y y 2 machine

[ 526 ]

machine fhow figns of electricity ; and as thefe figns,
when examined, appear to be different in the chain,
and in the machine, and the globe having, as he
fuppofes, drawn from the machine part of its natural
or common quantity of electricity, and given it to
the chain, he calls the electricity appearing in the
chain, electricity by excefs 5 and the electricity ap-
pearing in the machine, electricity by defedt ; which
anfwer to our terms of pofitive and negative electri-
city, or eleCtricity plus and minus. And thus his
expreffions, electrifying by the chain, and eledlrijying
by the machhie , are to be underftood, electrifying po -
fitively , and electrifying negatively .

LI. An imcommon Cafe of an Hcemoptyfs j
hy Erafmus Darwin, M. D.

To the very Honourable and Learned the Frefident ,
and Members of the Royal Society .

Gentlemen,

Feb. *4./- g 'HE following cafe of a difeharge
1 of blood from the pulmonary ar-
tery, appears to have been owing to a caufe different
from any mentioned amongft the writers of medicine :
and as, from the knowlege of that caufe, the cure,
was fo eafily deduced, I flatter myfelf, you will not
elteem it unworthy your attention.

A gentleman, reflding near this place, between,
forty and fifty years of age, of a pale and meagre
habit, has been daily afflicted with violent liead-achs

foe

. [ 527 ]

for feveral years paft ; and, about four years ao-0,
after having taken a confiderable quantity of Peruvian!
bark, became fuddenly paralytic. The ufe, however,
ot his right limbs was fo much reftored, as only to
remain weaker than the other ; when, upon fuddenly
awaking from his deep about two o’clock in the
morning, (May 7, 1779), he fpit up four or five
ounces of florid blood.

fie immediately loft twelve or fourteen ounces
from the arm, had elixir of vitriol given him, and
in the evening had a glyfter, and loft blood again to
about ten ounces.

On the 8th, about the fame hour, he again fud-
denly awaked, and fpit about the fame quantity of
blood as before. He was now advifed to increafe
the quantity of elixir of vitriol, had a bolus of ex-
trattum CampechenJ'e every fix hours, and had a leech,
applied to a blind pile, that had long appeared after
going to ftool.

On the 9th, at the fame hour, he had again the.
fame difcharge as before. That thcfe hemorrhages
were from the pulmonary artery, rather than the
bronchial, appears from the fudden exfpuition, the
quantity, the fioridity, and from the difcharge being,
without pain, and unmixed with phlegm.

As he had no feverifh fymptoms, either when he
firft awaked, or during the day, no more blood was
taken from him ; and as he conftantly flept pro-
foundly from ten o’clock till two, when the com-
plaint feized him, he was now advifed to be awa-
kened, and rife out of his bed, at one in the morn-
ing, and remain awake till three, omitting all me-
dicines.

He

[ 528 ]

't'Te continued to rife from bed for a week, and

baS ever fince ufed himfelf to awake at the fame
time ; and has not only been entirely free from this
complaint, and that without any lurthei diichaige
from the hemorrhoidal veffels ; ' but has got. more
flefh, and his head-achs arc become even incon-

fidcrable.

I ought not here to omit, that he haci a vomit
given him on the 12th, and twice repeated, at the

intervals ot three or four days.

As the patient, from a former htemiplagia, had,
in all probability, many parts of his body rendered
lei's irritable than is natural j and as he conftantly
ilept profoundly, and the haemoptoe always awaked
him after four hours ilcep ; I was led to conclude,
that, during this ileep, the lungs were not fufliciently
fenfible to pufli forwards the whole circulation ; and
and that hence the blood, gradually accumulated,
ruptured fome minute branches of the pulmonary
artery, before the uneafinefs became great enough to
awake the patient. And, as much as the evidence
of a fugle cafe in medicine may be eftimated, the
fiaccefsful cure would feem to evince the truth of this
doCtrine.

I have only to add, that the anxiety, with which
patients reduced to great weaknefs awake from their
lleep, and the hurried pulle, have, by others, been
obferved to be owing to an accumulation of blood in
the lungs, during their (late of decrcafed ienfibility .
And how detrimental, in thefe cafes, might be the
adminiftration of opium, or nitre j whilft the want
of fleep, or the recurring haemorrhage, might feem,
to the unwary practitioner, to need their abidance.

[ 529 ]

After a few days, obferving fome cough remain,
it feemed advifeable to give two or three vomits 3 as,
from late experience, they do not endanger a renewal
of the difcharge, and muft promote the expedora-
tion of the efchar, or any extravafated blood 3 which
otherwife, by its delay acquiring a putrid acrimony,
perhaps moft frequently erodes the contiguous velfels>
and, forming new ulcerations, becomes the general
caufe of coniumptiofts, fubfequent to accidental fpit-
tings of blood.

I am, Gentlemen,

Your very humble fervant,

Lichfield, Dec. 17. 1759. Erafmus Darwin.

L1I. An Account of the late Earthquakes in
Syria : In a Letter from Dr. Patrick
Ruffell, to his Brother, Alexander Ruffell,
M.D. F.R.S .

Aleppo, Dec. 2, 1759.

Read Feb. zi, S I recoiled nothing in the way of
176°. bufinefs, which I have not already

wrote you about 3 and as I know not when this
letter may get away, I (hall, in the mean time, give
you fome account of the earthquakes here, which
have thrown the people into a terrible confternation.

The fpring of this year was unufually dry, the
fummer temperate, and the autumn, though the

rains came on towards the end of September, might

be

[ 53° ]

be efleemed much drier than in other years. The
Aleppo river has been very low all the dimmer; and
its bed, from the firft to the fecond mill, is, I be-
lieve, even now dill without water. This pheno-
menon I, at fir ft, thought remarkable j but have
been informed, that the fcarcity of water complained
ol, during ad the fummer, was cccafioned by driving
the river into fome rice-grounds lately formed to-
wards Antab.

On the morning of the loth of June, a flight
fliock of an earthquake was felt here, and, as ufual,
loon forgot ; having, fo far as we know, been felt in
no other place, in any degree of feverity.

October the 30th, about four in the morning,, we
had a pretty fevere fliock (indeed the mod violent I
had ever felt), which laded fomewhat more than a
minute, but did no damage in Aleppo. In about
ten minutes after this firfl, there was a fecond fliock ;
but the tremulous motion was lefs violent, and did
not lad above fifteen feconds. It had rained a little
in the preceding evening ; and when the earthquake
happened, the wed wind blew frefli, the Iky was
cloudy, and it lightened.

This earthquake occafioned little alarm amongfl
the natives, and even with the Europeans was the
topic only for a day. But the fubjedt was foon re-
vived, by letters from Damafcus, .where the fame
fliock felt by us at Aleppo, and feveral other fuccef-
flve ones, had done confiderable damage. F:om
this time, we had daily accounts of earthquakes from
Damafcus, Tripoly, Seidon, Acri, and all along the
coad of Syria ; but fo exaggerated in fome circum-
stances, and fo inaccurate in all, that we only knew

in

[ 53i ]

in general, that Damafcus, Acri, and Seidon, have
differed injury from the earthquake, though lefs than
was at fird given out.

Such (lories circulating among the people, ren-
dered them more lufceptible of alarm ; and an occa-
fion foon offered, where they feared, that the word
of their apprehenfions were to be realized.

This happened the 25-th of November. Tire
morning had been ferene, fome clouds arofe after
noon, and the evening was remarkably hazy, with
little or no wind. About half an hour after feven at
night, the earthquake came on : the motion, at firff,
was gently tremulous, increadng by degrees, till the
vibrations became more didin<d, and, at the fame
time, fo ffrong, as to (hake the walls of the houfes
with condderable violence; they again became more
gentle, and thus changed alternately feveral times
during the (hock, which laded in all about two mi-
nutes. In about eight minutes after this was over,
a (light (hock, of a few feconds duration, fucceeded.
The thermometer was at $0, and the barometer dood
at 28-9, the mercury differing no alteration. There
was little or no wind in the night, the (ky clear,
excepting fome heavy clouds, that hung about the
moon. At a quarter after four next morning, we
had another (hock, which laded fomewhat lefs than
a minute, and was hardly fo drong as that of the
preceding night. The night of the 26th was rainy
and cloudy. At nine o’clock we had a (light (hock,
of a few feconds. The motion here appeared to be
very deep, and was rather undulatory than tremulous.
The 27th, cloudy and rainy. From midnight of the
25th, befides thefe now mentioned, four or dve dighter
V ol. LI. Z z z lhocks

[ 532 ]

fiiocks were felt ; but I myfelf was fendble of none;,
till the morning of the 28th, when we had a diort
pulfatory fhock. The fame day, at two o’clock,
we had a pretty fmart fhock, lading about forty fe-
conds. From this time, I was fenfible of no more,,
though others either felt or imagined feveral flight
vibrations every day.

However violent this earthquake was, or rather, by
the frightened people of Aleppo, imagined to be, it
is certain, that, excepting in a very few old walls,
the city bears no fredi marks of ruin j none of the
oldeft minorets have differed. Its effects at Antioch
were more formidable ; many houfes have been
thrown down, and fome few people killed.

December 7 h.

HJ£ earthquake of the evening of the 25th has

proved fatal to Damafcus ; one-third of the city
was thrown down, and of the people, numbers yet
unknown perifhed in the ruins. The greater part
ef the furviving inhabitants fled to the fields, where
they dill continued, being hourly alarmed by dighter
ihocks, which deterred them from re-entering the
city, or attempting the relief of fuch as might yet be
faved, by clearing away the rubbidi. Such was the
purport of a letter I read this day, which was wrote
from Damafcus three days after the earthquake.
Other accounts we have at this place, make the lofs
of the inhabitants amounts to 20,000; but, in cir-
cumdances of fuch general horror and confudon,.
little accuracy can be expedted, and the eadern dif-
podtion to exaggeration reigns, at prefent, univerfally.

Tripoly has differed rather more than Aleppo;
three minorets, and two or three houfes, were thrown

down,

[ 533 ]

down, while the walls of numbers of the houfes
were rent. The Franks, and many of the natives,
have deferted the city, and remain in the fields.

At Seidon, great part of the Frank kane was over-
thrown, and fome of the Europeans narrowly efcaped
with their lives. Acri and Latakea have fuffered
little, befides rents in fome of the walls : but Saphet
(eight hours from Acri) was totally deftroyed, toge-
ther with the greater part of the inhabitants.

Such are the moft authentic accounts we have
from abroad ; how much they contribute to calm the
minds of the people at Aleppo, you may eafily ima-
gine. Since the afternoon of the 28th, feveral flight
fhocks have been every day felt, and many more
formed by the power of imagination : for my own
part, 1 have fince that time perceived none, except-
ing one the evening of the 5th, which was pretty
fixong, but lafted not above twenty feconds. The
weather, for thefe two days, has been gloomy and
rainy ; a change which people are willing to flatter
themfelves is favourable. It often lightens in the
night, and thunder is heard at a great diftance.

ExtraS 1 from another Letter of Dr. Patrick
Ruffell, to Dr. Alexander Ruffell, dated
at Aleppo, 29 March 1760.

TN my lafi:, of the 7th of December, I gave you a full
account of the earthquakes, which have occafioned
an univerfal panic all over Syria. There were feveral
other fhocks in December, and a few very flight ones
in January : fince which time, all has been quiet.

Z z z 2 Except-

[ 534 3

Excepting a few old houfes, none of the buildings
in Aleppo were actually thrown down ; but the walls
of a confiderable number of houfes have been rent.

We have had the wetted winter 1 ever faw in this
country. The Coic has every-where overflowed its
banks, and is juft now much higher than it has been
known to rife for many years.

LI II. Remarks on the Bovey Coal: In a
Reiter to the Right Honourable George
Earl of Macclesfield, Proficient of the Royal
Society . By Jeremiah Milles, ZX ZX
F. R. S.

Vi (

My Lord,

Read Feb. HE defcription, which the learned

176°. profeftor Hollman has given the

Society *, of two remarkable ftrata of foftil wood in
Germany, one in the neighbourhood of Munden, in
the duchy of Grubenhagen, and the other near AL
lendorf in Hefte, correfponds, in fo many particulars,
with fome ftrata, difcovered about fifteen years ago,
in Devonfhire, that it fuggefted to me a doubt, whe-
ther thofe German ftrata were really (what the
learned profeftor fuppofes them) foftil wood, and
formerly a vegetable fubftance, or (what he fays the
miners call them) foftil coal. The reafons, on which
this doubt is founded, are fubmitted to the judgment
of your Lordfhip, and the Society, in the following

* See the above, N° xlix. p. 5g6.

4

account

[ 535 ]

account of the Devonshire foffil, which is commonly
known by the name of the Bovey coal. It is found
on a common furrounded with hills, called Bovey
Heathfield, in the parifh of South-Bovey, 13 miles
fouth-weft of Exeter, and 3 miles weft of Chud-
leigh. The uppermoft of thefe ftrata rifes within a
foot of the furface, under a fharp white fand, inter-
mixed with an afh coloured clay, and underlies to
the fouth about 20 inches in a fathom.

The perpendicular thicknefs of thefe ftrata, in-
cluding the beds of clay, with which they are inter-
mixed, is about 70 feet. There are about fix of
each, and they are found to continue eaftward, in an
uninterrupted courfe, to the village of Little-Bovey,
a mile diftant, and probably extend much further.
The ftrata of coal near the furface are from 1 8 inches
to 4 feet thick, and are feparated by beds of a brownifh
clay, nearly of the fame dimensions, but diminishing
in thicknefs downwards, in proportion as the ftrata
of coal grew larger ; and both are obferved to be
of a more compact and folid fubftance in the lower
beds. The lowermoft ftratum of coal is 16 feet
thick ; it lies on a bed of clay, under which is a
Sharp green fand, not unlike fea fand, 17 feet thick,
and under that, a bed of hard clofe clay, into which
they bored, but found no coal. From the fand arifes
a fpring of clear blue water, which the miners call
mundic water, and a moifture of the fame kind
trickling through the crevices of the coal tinges the
outfide of it with a blue caft.

Some fmall and narrow veins of coal are found in-
termixed with, and Shooting through, the beds of
clay, forming impreffions like reeds and grafs, and

very

[ 536 ]

very fimilar to thofe, which are generally found on
the top of coal mines. The clay all'o (at lead: that
part of it, which lies neared: to the coal) feems to
partake of its nature, having fomewhat of a laminous
texture, and being in a fmall degree inflammable j and
amongft this clay, but adhering to the veins of coal,
are found lumps of a bright yellow loam, extremely
light, and fo faturated with petroleum, that they
burn like fealing wax, emitting a very agreeable and
aromatic fcent.

Though the fubftance and quality of this coal, in
its feveral ftrata, are much alike, and it is all indif-
criminately ufed for the fame purpofes j yet there is
fome difference in the colour, form, and texture, of
the feveral veins. The exterior parts, which lie
neared: to the clay, have a greater mixture of earth,
and are generally of a dark brown, or chocolate
colour ; fome of them appear like a mafs of coal and
earth mixed ; others have a laminous texture, but
the laminae run in fuch oblique, waving, and undu-
lating forms, that they bear a ftrong refemblance to
the roots of trees, of which kind I have feen fome
fpecimens from Lough Neagh in Ireland, which feem
to be the fame fort of foflil.

There are other veins of this coal, which lie more
in the center of the ftrata, and abound mod: in the
lowed: and thickeft bed, the fubftance of which is
more compact and folid : thefe are as black, and al-
moft as heavy, as pit coal ; they do not fo eaflly di-
vide into laminae, and feem to be more ftrongly im-
pregnated with bitumen ": thele are diftinguifhed by
the name of ftone coals, and the fire of them is more
ftrong and lafting than that of other veins.

But

[ 537 ]

But the moft remarkable and curious vein in thefe
fh ata is that, which they call the wood coal, or board
coal, from the refemblance which the pieces have to
the gi ain of deal boards. It is fometimes of a choco-
late colour, and fometimes of a fhining black. The
formei fort feems to be lefs impregnated with bitu-
men, is not fo folid and heavy as the latter, and has
more the appearance of wood. It lies in ftrait and
even veins, and is frequently dug in pieces of three
or four feet long, and, with proper care, might be
taken out of a much greater length. Other pieces
ot the fame kind are found lying upon them, in all
irections,. but without the lead: intermixture of
eaith, or any other interflices, except fome fmall
crevices, by which the pieces are divided from each
other, m all directions. When it is firft dug, and
moift, the thin pieces of it will bend like horn, but
w en diy, it lofes its elafticity, and becomes fhort
and cnfp. At all times,, it is eafily to be feparated.
into very thin laminae, or fplinters, efpecially if it lie
any time expofed to the heat of the fun, which, like
tne fire, makes it crackle, feparate, and fall to pieces..
The texture of this loffil confhls of a number of la-
minae, or very thin plates, lying upon each other ho-
rizontally, in which fmall protuberancies fometimes-
appeal, like the knots of trees • but,- upon examina-
tion, they are only mineral nuclei, which occafion.
this interruption m the courfe of the lamime ; and
pieces of ipar have been fometimes found in the
middle of this wood coal.

. Though the texture of this coal is laminated yet
it does not appear to have any of thofe fibrous inter-
jections,. which are obferved in the grain of all wood..

This

[ 53s ]

This coal eafily breaks tranfverfely, and the feparated
parts, inftead of being rugged and uneven, are ge-
nerally fmooth and (hilling, in which even the courfie
of the laminae is hardly differ nable.

They dig this coal in an open pit, together with
the clay that is mixed with it ; and though it lies very
clofe and compact in its original bed, yet it is fo eafily
feparated, that they can afford to fell it for half a
crown a ton at the pit. The 1 mailer coal is leparated
from the clay by a fkreen, or grated fhovel ; the
larger, which riles fometimes in pieces of above an
hundred weight, is piled up by hand. There is hardly
any other ufe made of it at prefent, but to bake the
earthen ware of a manufacture ereCted at South-
Bovey, and for burning of limeftone, which riling in
great quantities at the neighbouring town of Chud-
leigh, the coal is carried thither, and they return
with limeftone to the pit ; which they burn theie, foi
the ufe of the northern parifhes, to whom it lies more
convenient than the kilns of Chudleigh.

The fire made by this coal is more or lefs ftrong
and lafting, according to its different veins: thofe
which lie neareft tp the clay, having a greater mixture
of earth, burn heavily, leaving a large quantity of
brownifh allies ; that, which they call the wood coal,
is faid to make as ftrong a fire as oaken billets, efpe-
cially if it be let on edge, fo that the fire, as it afcends,
may infinuate itfelf between, and feparate the laminae.
But that of the ftone coal is accounted moft ftiong
and durable, being apparently more folid and heavy,
and probably alfo more ftrongly impregnated with bi-
tumen. One of the proprietors of this coal made an
experiment of burning it in the fire-engines of Corn-

[ 539 ]

wall, to which it might have been tranfported, with-
out much trouble or expence, being only four miles
diflant from the navigable river Teign; but the heat
of the coal was not fufficiently intenfe, and the con-
fumption of it too great, to anfwer the purpofe.
When this coal is put into the fire, it crackles, and
feparates into laminae, as the cannel coal into ir-
regular pieces, burns for fome time with a heavy
flame, becomes red-hot, and gradually confumes to
light white afhes. Though the tranfverfe crevices
made in it by the fire give it the external appearance
of a wooden brand, yet, if quenched when red-hot,
the unconfumed part does not look like charcoal, 'but
feems to be almofl as fmooth and folid, as when firfl
put into the fire.

The thick heavy fmoak, which arifes from this
coal when burnt, is very foetid and difagreeable ;
entirely different from that aromatic fcent of the bi-
tuminous loam, which is found adhering to it, but
much refembling that of the afphaltum, or bitumen
of the Dead Sea. The whole neighbourhood is in-
fected with the flench, which is wafted by the wind
to the diflance of three or four tniles. When burnt
in a chimney (as it is fometimes in the neighbour-
hood), the offenfivenefs is leffened by the draught :
however, it is found, by thofe, who live continually
in the fmoak of it, not to be unwholfome ; nor is it
in the leafl prejudicial to the eyes, like the fmoak of
wood. The mofl fhining and folid pieces of this
coal have not the leafl degree of eleCtrical attraction.

Notwithflanding the refemblance, which this foffil
bears to wood, efpecially when viewed in detached
pieces, yet the following obfervations on its fituation,
V o l. LI. 4 A its

[ 54° ]

its form and properties, will prove it to be not of a
vegetable, but of a mineral origin.

In the fird place, there does not feem to be any
imaginable caufe in nature, which could bring toge-
ther fuch a mafs of foffil wood, as is found in this,
and other drata of the like kind in different parts of
Europe. It extends here to the depth of 70 feet :
in that near Munden they have funk yo feet, with-
out coming to the bottom. Foffil trees, though fre-
quently found fingle, or in fmall numbers, are ge-
nerally difcovered in moraffes and foft ground, where
they have either buried themfelves by their own
weight, or been overwhelmed by fome accidental
caufe : but the Bovey ftrata are found in a dry foil,
intermixed with clay and fand, and, by their regular
courfe and continuance, carry the mod; undoubted
marks of never having been didurbed fince their ori-
ginal formation. Foffil trees likewife preferve their
form and dze, their length and roundnefs, their
branches and roots, their fibrous texture and drength,
and are either found entire, or in fuch large pieces,
that there is no room to doubt of their nature, fince
the very fpecies of wood is frequently didinguifhable
in them ; whereas the Bovey coal comes out only in
flat pieces, of a few feet long, like the fplinters of
large mads ; and on them we difcover no figns of
roots, branches, or bark, no round pieces, or con-
centric circles, which didinguifh the annual growth
of trees ; the laminae, which have the appearance of
wood, being always horizontal, according to the fi-
tuation of the pieces in the drata : or could we fup-
pofe a number of foffil trees to be brought together,
and ranged in this regular manner in the fevcral

drata..

[ 54i ]

firata, yet,- by the form and roundnefs of their
trunks, they muft be, in a great meafure, encom-
palfed by the foil, in which they are buried ; whereas
there is not the lead: mixture of earth, or any other
aperture, in the Bovey ftrata of coal, except a few
crevices, common to this fort of foffil, which divide
the pieces from each other in ail directions, and feem
to be inconfiftent with the nature and fibrous texture
of wood.

If the balls or matrix of this fofiil were wood, it
Would acquire, by being impregnated with bitumen,
a greater degree of inflammability ; whereas it neither
kindles nor confumes fo fall as wood.

The inflammability and laminated texture of this
foffil, which have been the only reafons for fuppofing
it of vegetable origin, may be accounted for from the
nature of its principles, and their difpofition, when
united, to afiume certain forms. The bituminous
matter uniting with various kinds of earth, in certain
proportions, will form an inflammable fubfiance ; and
a fimilar mixture of thefe will generally affume a
fimilar texture and form, as will appear from the ac-
counts given us of this foffil both by the antients
and moderns, moll of whom fpeak of it as a mineral
fubfiance.

Theophraftus * mentions <c a fione on the pro-
cc montory of Erineas in Peloponefus, and another
(c in the mines of Bina3 in Thrace, which being
<f burnt, emitted a bituminous odour j and another
ct fione in the mines of Scaptilulae, not unlike to rotten

* De Lapidibus, p. 4.

4 A 2

cc

wood,

[ 542 ]

“ wood, which would burn, if oil was poured on it,
“ but would ceafe burning as boon as the oil was
“ conl'umed.”

Diofcorides * obferves of the lapis gagates, which
is certainly a fpecies of this foffil, “ that the fort,
“ which kindles quickly, and gives a bituminous
41 odour, is the belt.” He defcribes it as generally
of a black colour, and uneven fubflance, broad and
flat, and very light. He mentions -f alfo a black
earth, found at Seleucia in Syria, called terra Ampe-
litis, which refembled long pieces of foffil coal, fplit-
ting eafily, of an uniform glofly fuperficies, which
being pounded, and immerfed in oil, immediately
liquified.

Pliny X defcribes the gagates as black, porous, and
flat, not much unlike wood, brittle, of a difagree-
able fmell when rubbed, and emitting a fulphureous
odour when burnt.

Galen || calls it “ a black flone, which, when put
“ in the fire, fends forth a bituminous odour.” And
he fpeaks of fome other black ftones, brought by
him out of Ccelofyria, “ which were broad like a
“ board, and, being put into the fire, burnt with a
“ flender flame : they were generated in the hills on
« the eaft fide of the Dead Sea, where the bitumen
<c is produced, and the fmell of the flone was like
“ bitumen.” I cannot but obferve on this paflage,
that the fmell of the Bovey coal, when burnt, is the

* Lib. v. cap. 103.
t Lib. v. cap. 138.
t Hift. Nat. lib. xxxvi. cap. 19.

|j De Simplicium Medicamentorum Facultat. lib. ix, de CU-

gate.

fame

C 543 ]

/

fame with that of the afphaltum, and of a done im-
pregnated with it, which is found at a fmall diftance
from the Dead Sea.

Agricola * mentions thefe, and feveral other kinds
of bituminous foflils, taken notice of by the antients,
and points out feveral places in Europe where they
are now found. Later writers defcribe it under the
name of metallophyton, or lignum foible; and moft
of them fuppofe it to be a mineral fubftance. Fran-*
cifco Stelluti, in a treatife printed at Rome 1637, has
accurately defcribed fome very curious ftrata of this
kind, near Todi and Aqua Sparta in Umbria : he fays,
“ they confift of large oval and comprefled pieces,
" lying horizontally, refembling the trunks of trees,
fC but larger: he mentions one above 3 feet broad:
£C they have neither roots, branches, nor fibres, but
“ fomething like bark; and the heart of the tree,
<c which in fome is as hard as a bone, in others as
t{ black as a coal. The extremity of thefe pieces is
“ as fmooth, as if they had been divided by a faw. It
“ is full of veins of a dark brown colour, which, in-
“ Read of running ftrait like the fibres of wood, are
“ undulated and irregular, taking a variety of forms,
“ and are only fuperficial ; for, upon taking oft one
“ of the thin laminae, of which this fofiil is com-
“ pofed, the veins underneath appear in a different
“ direction. This fofiil, when firft taken out of the
« earth, bends like a bow ; and when put into the
“ fire confumes fiowly, with a great fmoak, and dif-
“ agreeable fmell ; but, if burnt when dry, thefmell
“ is more pleafing. The heat is more intenfe than

* De Natura Fofiilium, lib, iv. p. 596,

ic wood,,

[ 544 ]

“ wood, and it does not confume To faft. Many of
<£ thefe pieces are fprinkled with marcafite, and there
cc exfudes from it a white bituminous fubftance, like
££ rofin. It is full of crevices, in all directions, and the
£c pieces appear in a variety of forms,” which the au-
thor has exhibited, together with a reprefentation of the
veins of the foffil, in feveral copper-plates accompany-
ing his work. He is clearly of opinion, ££ that this
cc fubftance is not generated from the feed or roots of
££ any plant, but from a cretaceous earth transform-
tc ing itfelf into wood, by the afliftance of fulphu-
££ reous water minerals, and fubterraneous heat,
££ which appears there in a thick ftnoak, and fome-
£C times in flames, particularly in rainy weather.”
He forms his fuppolition on the different appear-
ances of this foffil, £C fome pieces of it being like
£C chalk, others like wood, and again others like
££ coal ; fome are either totally or partially petrified,
££ being ftone without and wood within, or vice
££ verfa ” But thefe various appearances may be
eaffly accounted for, from the different kinds and
proportions of earthy matter, with which the bitu-
men is mixed.

Of the fame kind are the foffil ftrata in Iceland,
mentioned in the Mufaeum Wormianum, and by
Horrebow, in his natural hiftory of that ifland. The
former of thefe authors * defcribes it as ££ a laminated
£C fubftance, generally of a black, but fometimes only
<£ of a dark colour, heavy, and, when dry, brittle ;
£C though the merchant, who gave the fpecimen,
££ affured him, that when it was firft dug out of the

* Lib. ii. cap. 16. p. 169.

t£ earth

C 545 ]

“ earth it would bend like a twig. It confids of
“ oblique fibres, and here and there fome knots
“ like the roots of a great tree. A carpenter, who
“ was a judge of wood, thought it to be the root
“ of a walnut-tree grown black with age. It was
<c not eafily to be polished, too brittle to be ufed
“ in cabinet work, and was full of crevices. This
tc dratum is found fome yards under the earth, in a
“ mountain fo high and perpendicular, that thofe
“ only who have been accudomed to climb fucli
“ precipices can venture to dig for it. There is not
!{ the lead; appearance, that trees ever grew where this
“ fbffil is found, notwithstanding this author fup-
tc pofes them to be roots of trees turned black, by a
“ Subterraneous vitriolic juice. The dud of this dra-
<c turn is accounted, by the Icelanders, an excellent
<£ prefervative of cloaths from moths and worms.”

Horrebow * fays, <£ it is an extraordinary fort of
<£ wood, which they call fortebrand, or black brand,.
££ very hard, heavy, and black like ebony. It is
t£ found deep in the ground, in broad, thin, and
£C pretty large pannels, or leaves, fit for a moderate
£c Sized table. It is generally wavy, undulated ; and
tc is always found between the rocks, or great dones,
££ wedged, as it were, clofe in.” He was doubtful,
whether it were wood, or a petrification ; but in-
clined to the former opinion, becaufe it could be
planed and managed like wood.

The fame fort of fofiil, according to Wormius f,

<£ is found in the islands of Faro. It does not eafily

* Page 33-

t Mufseum Wormianum, p. 31. cap. 13, de Bitumine.

t£ take

[ 546 ]

« take fire, but has a fplendor like gagates. It is
« found in the joints of the rock, and is taken out
“ in laminae, or fplinters, of 3 or 4 inches thick.”

Of the like kind is the ftratum of foffil wood near
Thun in Swiflerland, mentioned by Schentzer, in
his Itinera Alpina * j which he defcribes as lying
under feveral ftrata of flints, clay, and afli coloured
marie. Being expofed to the air, parts of it grew
hard, and others broke to pieces. “ It is (he fays)
“ obfervable of this foffil wood, that the trunks and
<£ branches are not round, but comprefled; yet, in
{< fome places, cloathed with their bark, and here
“ and there adorned with their leaves. The wood
is inflammable, making a ftrong fire, and ferves
*c inftead of foffil coals.” The author fuppofes the
compreffion of this flratum to be owing to the great
fuperincumbent weight ; but others, he fays,, ima-
gine it to be fo formed by nature, from clay, in the
bowels of the earth. I would obferve here, that
the cruftaceous appearance, fo common to thefe bi-
tuminous foffils, might eafily be miftaken by this
author for the bark of the tree, the fame appearance
being obferved by Stelluti, in that of Umbria ; but
it is not fo eafy to account for the leaves, which cer-
tainly have no connection with a mineral fubftance.

John George Liebnecht, in his Hajjia J'ubterranea ,
quotes Pillingius’s treatife on bitumen and lignum
fojjile , for the following defcription of a fir a turn
of this latter kind. He fays, that at Meiflibitz, in
the duchy of Altenburg in Saxony, there is a moun-
tain, with a gradual afcent and fertile fummit, the

* Quarto, 1724. p. 604.

s>

outward

[ 547 ]

outward ftratum of which is vegetable earth, three
feet deep ; and under it a ftratum of clay, two fathom
thick j then a ftratum of fand, made blackifli by bi-
tuminous fumes : Jubtus lignum putridum , fiammam
concipiem , pedlines annuos ref ere ns, it a a naturd na-
tum , ut nec aqua aqua, nec lac laSfi fimilius , quant
ligno huic miner ali lignum vegetabile putridum.

Our Englifh naturalifls have likewife defcribed
this foffil, as found in feveral parts of the kingdom,
and always in or near ftrata of clay.

Dr. Plott, in his natural hiftory of Oxfordshire %
obferves, cc that the fcarcity of firing in fome parts
“ of that county has induced people to burn a fort
“ of black fubftance, of a grain fome what like rotten
<c wood half burnt, partaking alfo of a mineral na-
tc ture, and therefore by authors called metallophy-
tc ton, or lignum fofiile. Put into water, it will not
<c fwim ; and into fire, it confumes but {lowly, and
“ fends forth very unpleafant fumes. A vein of it
ec at Duchlington looked like wood ; yet broken,
cc fhewed a fmooth and fiiining fuperficies, not un-
cc like to ftone pitch; and put into the fire, has not
tc near fo ill a fmell. As to the fubftance of lignum
<£ fofiile, it is thought to be a cretaceous earth, turned
“ to what it is by fubterraneous heats ; for that it was
<c never formerly wood, notwithftanding its fpecious
<c and outward likenefs, is plain from its never being
cc found with roots or boughs, or any other figns of
<c wood.” And, in his hiftory of Staffordfhire, he
quotes Scoochius’s opinion, £C that many of the
€£ flumps and trunks of trees found in Holland, Zea-

* Page 65.

V 0 l. LI. 4 B

<£ land.

[ 548 ]

“ land, and Friezland, are of this mineral wood,

“ chiefly becaufe moft of them are found without
“ knots or roots/’

Dr. Morton, in his natural hiftory of Northamp-
tonfhire *, mentions two or three varieties of this
metallophyton ; one of which he defcribes, as of
« a dark colour, and having a gram ; for in one di-
“ redtion (which is ufually according to the length
“ of the pieces), it cleaves or parts pretty readily
« into plates and fplinters, the other way it fnaps
<c into fliorter pieces, and will not cleave at all.
“ There is another fort, which does not fo readily
*{ part into flakes. None of thefe are found in any
« large maffes. They are all, more or lefs, of a
<( gloffy black, and have a denfity or fmoothnefs within
“ like that of bitumen, or jet. In that alio, they
“ refemble the true bitumen, or piffaphalton. They
*c are not fo firm and hard as the common coal, and
*c are much brittler than canal or jet. They like-
« wife all of them agree pretty nearly in the fame
« properties. In water they fink. They are all in-
<c flammable, but confume flowly in the fire, and
emit a fomewhat unpleafant fume, not unlike that
“ of bitumen, only fainter.”

Of the fame kind is the inflammable date, or coal,
of Dorfetfhire, found in the cliffs at the north-weft
corner of the ifle of Portland, near the cattle, of
which I have received the following account from a
gentleman of that county. The upper ftratum is the
natural black earth 1 4 fee* deep ; the next is a gieyifh,
foft, paving done, 6 inches thick j then follows the vein

* Page 32ii

of

[ 549 ]

of coal, of io inches; under which is a black earth,
and at the bottom of the clift, clay. It rifes in la-
minae, and is difcovered in the outermoft part of the
clift, whence it is taken, by digging horizontally :
fome is black,-' and fome of a redifh colour; which
latter is reputed the worft, and does not burn fo
well. The afhes of both are reckoned very good
manure for clay ground. It is made ufe of to heat
ovens ; and when piled up as turff, gives a clear light,
and yields a ftrong bituminous fmell. It is found
more to the weft, at Chickerel and Fleet, in the
fands, the fhore being open.

The Kimendge coal, which, in all refpedts, re-
fembles that before-mentioned, and is fo called from
the place where it is dug, appears in moft of the
cliffs of the ifle of Purbeck, from St. Aldhelm’s cha-
pel to Eaft-Lulworth, and at Ofmington, oppofite to
that part of Portland where the coal is dug. It is
found 1 6 feet below the top of the rock, in great
lumps ; but the ftratum does not exceed a feet in
thicknefs, nor extend far from the fhore. It emits,
when burnt, a ftrong fulphureous fmell, and has a
great many yellow ftrokes and fpots on it, which
feem to be marcafite. It is almoft wholly ufed by
the poor, in their ovens and chimneys, and is fold
for nine pence per hogfhead, or fix fhillings per ton.
Under water, and in the cliffs, it is very hard ; but
when expofed to the air it fhivers into pieces like
flate.

At Kimendge are found fmall round pieces of this
coal, from one to three inches in diameter, one fide
of which is flat, the other tapering, like the lower
part of a cone. In fome there is a fquare hole in

4 B 2 the

[ 55° ]

the center on the flat fide j in moft of them two, or
fometimes four holes, near the edge, but they do not
penetrate quite through the piece. They are fome-
times found at the top of the cliff's, between two
ffones fet on edge, and covered with a third, mingled
with human bones. Sometimes they are found by
themfelves, but always in made ground. The com-
mon people call them coal money. I think it can
fcarce be doubted, that they are Britifli antiquities.

To thefe, I Avail add Dr. Hoffman’s * account of a
ffratum of the fame kind in Pruflia, in the neigh-
bourhood of Filchaufen, &c. where they dig. for
amber. “ The upper ffratum is fand, under it a
“ bed of clay, and then a woody ffratum, eonfifting
“ of a fubftance like old wood, but inflammable j
« under this was a vitriolic mineral ; and, laftly, a
“ bed of fand, in which a great quantity of amber was
“ found.” There is a remarkable refemblance be-
tween the order of thefe ffrata, and thole at Bovey ;
and though no amber has been difcovered at the latter
place, yet it would feem, as if there were fome con-
nection between that and thefe bituminous ffrata ; for
it ^remarkable, that Theophraffus +, fpeaking of an
eairthy inflammable fubffance in Liguria of tnis kind,
adds, that amber is found there.

The refemblance likewife, which the ffrata of
Munden and Allendorf bear to thefe of Bovey, is
re mar kable, the foil in which they lie con fitting of
clays, boles, and fand. This is fo much the cale at
Bovey, that they have large beds of a very fine pipe

* Obfervationes Phylico-chemicalcs, lib. ii. obf, 23. p. 199*

4 De Lapidibus, p. 4.

clay

[ S5i ]

clay in the neighbourhood, which has for many
years been exported to Liverpool, and manufactured
there into earthen ware ; but there is one now erected
at Bovey. The depth of the ftrata is likewife much
the fame ; for at Munden they have funk 50 feet,
without coming to the bottom. The pieces, that
form thefe ftrata, feem to lie much in the fame man-
ner; they are compreifed, without any intermixture
of earth, full of cracks and fiftiires, and lying fo clofe
upon each other, that the profeffor fays, “ it could
“ not be difcovered, whether they were entire trees,
tc or only parts of them,” and when taken out, they
eafily fell to pieces. The German ftrata referable
thofe of Bovey in colour. That of Allendorf, which
Dr. Hollman calls bitumen, and which he diftin-
guifhes from the foffil wood lying under it, is faid to
be little inferior in blacknefs, fplendor, and hardnefs,
to jet ; and he adds, that the foffil wood approaches
very nearly to the fame colour. He obferves, indeed,,
that the ftratum of Allendorf is not fo ftrongly im-
pregnated with bitumen, and. therefore left by the
workmen for future ages; and, no doubt, fome
fpecies of this foffil have fo much earth, and fo little
bitumen, that they are not at all, or only in a fmall
degree, inflammable. I ffiall only obferve further,
that the layer of hone, which divides the two ftrata
in the quarry of Munden, is a ftrong objection to the
notion of their being foffil wood, properly fo called ;
and that the vein of the ftratum at Allendorf, being
taken in the adit of a mine, could not give an oppor-
tunity of examining the nature and difpofition of its
parts, with the fame advantage, that we can view the
ftrata at Bovey.

I ffiall

[ 552 ]

I £hall conclude this paper with obferving the fe-
veral particulars, in which all the fpecies of the bitu-
minous foffils before-mentioned refemble each other.
They feem to be generally found between beds of
clay, or flone; are of a dark brown, or black co-
lour, of a laminated texture : pliable when moifl,
and frelli dug, but crifp and brittle when dry ; full
of cracks, and eafily breaking tranfverfely ; they all
link in water, and emit the fame naufeous and bi-
tuminous fmell ; they differ in being more or lets
folid, heavy, and inflammable, according to the pro-
portions and principles of which they confift ; and if
any doubt could remain of their being a mineral
fubftance, it muft be removed by the following ana-
lyfis.

One pound of Bovcy coal, of the woody kind,
powdered, put into a glafs retort, and diflilled in fand,
yielded four ounces and a half of phlegm, which had
the appearance of common water, but fomewhat of a
bituminous fmell and tafle ; near four ounces of a
turbid whitifh bituminous liquor, of an intolerable
fcetid fmell, and extremely pungent to the tongue;
about two drachms of a heavy bituminous matter,
which would not mix with the liquor above-men-
tioned, but funk entirely to the bottom, and (which
is very remarkable) there was not the leaf! appear-
ance of any light oil floating on the bituminous li-
quor. There remained in the retort about feven
ounces of a very black powder, which had the fame
bituminous fmell, not very heavy ; fome of which
being put on a red-hot iron, emitted a little fmoak,
but no flame.

4

[ 553 ]

The afhes of this foflil, when burnt, being boiled
in water, and the water evaporated, there remained
no fait behind.

I am, my Lord, &c.
Grofvenot-Street, Feb. 28, 1760.

LIV. A new Method of computing the Sums
of certain Series ; by Mr. John Landen :
Communicated by Mr. Thomas Simplon,

F. R . S.

Read Feb. 28,
1760.

AS the improving the analytic art,
efpecially any branch of it that re-
lates to the fummation of feries, may, by facilitating
computations, conduce to the improvement of feveral
branches of fcience; it is prefumed, that this paper,
which exhibits a new and eafy method of computing
the fums of a great number of infinite feries, may be
acceptable to the mathematical world, and deemed
worthy to be inferted in the Britifh Philofophical
Tranfadtions.

1.

Suppofing x to be the fine of the circular arc

whofe radius is 1,

x

Vi—,

X

will be = z-j and,, con-
From whence, by

fequently, • — ,

^ y/ x7, — 1 v/— I

taking the corredt fluents, we have hyp. log.
a* -f- V — 7

z

Hence*

V — 1

[ 554 ]

Hence, writing a for one fourth of the periphery
of the circle whofe radius is i, and taking x equal

to the faid radius, we find hyp. log.

V— i

and, confequently, hyp. log. s/ — i =

a

V — i

v7—

and

hyp. log. — i = +

2 a

V-

2.

The hyp. log. of - being - ^ + y + &c'

I * J X*"

F = fluent of ^ hyp. log. is = x -f- + p

+ &c-

F = fluentofiF = x + ^+^+5. Se.

F = fluent of F = *+ |j + ^+ ^> <*•

F — fluent of-F = ^ + "T+^r+^T>

&c.

X

&C.

3s
&c.

By writing, in the firft equation in the preceding
article, - inftead of *, we have

Hyp. log. _1_ = *-• + ^ &c.

I -

X

But the hyp. log. of is = hyp. log. ^ q —

i

*

hyp.

a

[ 555 ]

hyp. log. -JL- -f hyp. log. Af + hyp. log. -

i 2 b -j- X + hyp. log. — j--, b being put for

1 * V— i

and X for the hyp. log. of x.

It is evident, therefore, that

Hyp. log. — — is = -ip + ^ &C'

■where, of the two figns prefixed to 2 b, the upper
one takes place, when the hyp. log. of — i is taken

equal to ~ 2 likewife when x is taken equal to

v — I

n/~ i ; and the lower one takes place, when the

hyp. log. of — i is taken equal to — =, alfo when

v — I

x is taken equal to : wherefore, if we obferve
to take the value of hyp. log. of — i , as lad: men-
tioned, and x equal to — 1 ■ , inftead of s/ — i, we

V— i

need retain only the lower of the faid figns.

For brevity fake, we fhall, in what follows, put
the feries i + ~ + -p + &c. = P,

i + —t + ~ 4. 2L, — p,

2 3 4

1 4" Th -f —t 5 + 70> &C‘

2 3 4

&c.

1 + ~ + p + &c:

Vol. LI. 4 C

vx

= p,

&c .

II

I —

[ 55& ]

1 “? + ?“■? +’

! + £ + £+.£. ®*=Q-

1-T+?“?+* ®‘-“*

&C. &C.

• • X

Multiplying the laft equation in art. 3. by and
taking the correct fluents, we have

t II VI v — 2 v— 3

F = 2 P + zbX — — — *-• — 4- — &c.

2Z

X

From whence, by multiplying by and taking

*Y

the fluents, we get
F = 2PX + £X2'

X3 , . .

b x-1 + -1

2.3 2 3

+ — . ®f.

X

Again, multiplying the laft equation by -, and

taking the corred fluents, we find

1U

F=aP+PX2ft

bX3 x+

, — 3

— x

— 1

&c.

3 2.3.4 2* 3

And, by proceeding in the fame manner, we find

iv

f=2PX+^Px‘

X5 . _ . . x-i

&C.

f A?-1 ft -"tF— T“J &c*

3.4 2.34.5 1 1 25 3s

&c.

6 .

Now, it is obvious, that x + — + p:> the

» 11

"value of F in art. 2. mult be equal to 2 P -fi 2 ^X

[ «7 ]

— &c. the value of F

X

in art. y. when both feries converge.

Therefore, *-±p. + + x±±fl, &c.

is then = 2 P -f- 2 b¥L — — .

2

From which equation, by taking x equal to — 1,

we have t + *t — “ + == P + b1 —

2 3 4

n ^ j

P — az ; and, by taking x equal to we have

v — 1

_L+.L

I1 * 2*

£ + ~ — , &C. = 4P + 3 =

3 4

4P — ja2.

Therefore 4P — 3 a2 is = P — a2 :

II

Hence P is found =

2 a

Moreover ~ ^ being = P> by

1 z 3 4

fuppofition ; and — ~-+ =

II

P — az , as found above ; we, by fubtradtion, get
~ + |r + -jr. ©c. (= zQ_) = a2, and, confe-

quently Q_— 1.

Scholium.

The hyp. log. of being 5=-Jf+“ + ^> .Gta

we, by writing i — ■ x inftead of x, have

4 C 2 Hyp.

C 558 ]

Hyp. log. of - — 1 — x -{- i

EH! + EE!, ev.

and confequently X = — 1 — -a: — ~

3

1 -

, &c.

\ X •

Moreover the fluent of x hyp. log. of is =

A X 1 ■ A*

x -4- — 4- &c. which vanifhes when x vanifhes ;

1 2 1 3

and the fluent of x X is = 1 — * + - — 1

1-x 2‘ ' 3

— P, being corredled fo as to vanifh when x
vanifhes.

But the fluent of ~ x hyp. log. of — - f fluent

of _L_ x X is = X x hyp. log. of — - — , which
alfo vanifhes when x vaniflies.

Therefore X x hyp. log. of is = x Jr ~

&c. -j- 1 — x — ■—

A' I

, &C. — P.

2 < 3

From whence, by taking x equal to 4> we And

— fquare of hyp. log. of 2 = 2 x -T

X 1 i

1 ±. 1

2*. 2a 1 3Z.23’
2 a1

C5fr.

— P : hence, P being before found = — , it appears

xx ^ X3

that, when x is = the feries x + — + — > is.

2 3

= j — \ x hyp. log. of 2I2.

X~ X 3 *

Furthermore, x -f -3 -f ~3i &c. the value of F in

2 3

11 j'j

art. 2. mufl be equal to 2 P X -f- ^X2 — — + a*”1

^ 3

[ 559 ]

y ^ 3 J I

4 — s- + value of F in art. y. when

II

both feries converge.
Therefore ~~ .A {_

A* X~~x

4"

J

•, &c. is

ir

then = 2 P X 4- £ X* — — .

' 2.3

From whence, by taking x equal to — i, we have

11 8 bz 11

4 ^ P + 4 — — -Oj and, confequently, P =

2-3

2 a

, as before found.

And, by taking x equal to -L=, we find

v — i

2 111 j p - i2. b3 a. a3 a 3 a 3

'1/ — - lbV\b — - y= /=• + 1 , —

V - i 2’3 3 V - 1 V - I 2.3 — I

Q3

v~

m cr

Therefore <7 is — — .

7 4

8.

From what is done above, it evidently follows, that

£ . 2£’~P . 2.8

P IS ,

3 34-5

II

— P

&C.

2b*P . Sb*P 3.32 b6

' “ ' + T~T +

3-4-5 3•4•5•&•7,

&c.

IV

— Q_ = £!P +

3-4

VI

IV

— Q_ = b1 P + + 5'8 ^

&e.

3-4 3-4-5-^

[ s6o ]

V

9

V— i

VII

9

. J3P , 9 bs

IS ~ b P H ,

2.3 2.2. 3.4.5

3P + ~+r^r +

13^

vr

V7— 1 ‘ 2 3 2-3-4-5 2. 2. 3. 4. 5. 6. 7*

ev.

IV VI IV

From whence the values of P, P, &c. G , Q_»

v vu

&c. q , q> &c. may be eafily obtained, in terms of a.
9- . .

1 4“ .. 1 *3

Hyp. log. -

I ^ J

G = fluent of hyp. log. -

II

1 being = x + — h — , 6?f .
I 3 5

I 4- • 1 A'3 I

IS _ X\ — -j- p,

x'

x ' *' &C.

G = fluent of-G = ^4- — + — , fife.

* 3 53

in <• n *3 v-S

G = fluent of-G = * + — +— ©V.

&c.

&c.

3 1

efr.

10.

By writing, in the firft equation in the preceding
article, - inftead of a*, we have

1 + -

Hyp. log

I

X

= r>+- + — , G?r.
3 5

But the hyp. log. of

1

1 X

is = hyp. log. iEj5

= hyp. log. 1 + hyp* l°g* — 1 = 4- ^ -p

hyp- los- 7“

it

[ 56i ]

It is manifeft, therefore, that
Hyp. log. i

i 4- *

is = + b + #-i + ~ e?r.

where, with refped to the two figns prefixed to b,
the fame obfervation may be made as in art. 3.

11,

Multiplying the laft equation by -, and taking the
correct fluents, we have

II

G = 2QJ- 6X - *-» _ £ _ 11s, &c.

From whence, by multiplying by -, and taking

A*

the fluents, we get

g = 2clx-i-^: + *-. + 9 + 9. &c.

Again, multiplying the laft equation by -, and
taking the corred fluents, we find

HI IV II 7 -KTo

G=2CL-f QX^ + i|-.v-.

X J A--5

1_ &c

34 5+ ’ ^ L‘

And, by proceeding in the fame manner, we find

IV

IV

*-5

g = *Q3c + 2£+ ££ + *-. +

3 3 5

&C.

1 2.

Now, it is obvious, that x 4- — 4- — , &c. the

3 5*

value of G in art. 5?. muft be equal to 2 QJ- b X

— — IF ~ V' &c’ va*U€ ^ *n art‘ 1 T'

when both feries converge.

There-

4

[ 562 ]

Therefore tilL \- - ■ * — j- is

5*

then = 2 Qj- ^ X.

From whence, by taking x equal to ;—===, we

n «

have 2 QJ- ^ = o ; and, confequemly, q>

as in art. 6.

!3*

Likewife at 4- ^ -4- ~ > ^ie v^ue °f G

1 33 1 53

tl £ X1 X ~ 3

art. 9. muft be equal to 2 QX + — + + -jr

-j- t — , Gfr . the value of G in art. 1 1 . when both
feries converge.

- X X~' , X1 X~* , A' 5 A1-5

Therefore — ^ — -) }- — ^ 18

n /. Y*

then = 2QX + y*

Hence, by taking x = --l=r, we find ^ — _

2 m

x q

II HI

= 2 £ Q -j — === — 7= ; and, confequently, q =
1 2 2 v— 1

— , as in art. 7.
4 7

14.

From what is done in the laid five articles, it evi-
dently follows, that

. £*Q. ,

— *Q__is = +

2

IV

6*

2.2.3’

=iQ^+^ + _il_,

y/Z-T 2-3 » 2.2.34’

[ 563 ]

-0Js = 4+^- +

b6

VII

7

2

VI

b 7

V— i

&c.

2.3.4. n 2... 3.4.5’

= 3cL+tjl + i± + .

2.3 2.34.5 2.2.34.5.6*

&c.

From whence (as well as from the theorems in

art. 8.) may the values of qt Q^, q] &c. be
readily found, in terms of a.

15.

G being ~ x ~r ~r + p> &c. by art. 9.

H = fluent of x xG is A ' A

H = fluent of-H

y.3 AS XT

4- + 4- + 4~,

i -3 3“-5 5 *7

.v ia.3z

A”* . A'

-r

H = fluent of x iH =

z ^ + 4-, &c.

3-5 S' -7

x 1 x 1 x*

"i z —■ " i _a ;■ T 71 _x — ) CS>f.

1 ’3 ’5 3 -5 •/ 5 •/ -9

H = fluent of-H = 4. 4. _i!_

* ^Sz ?f-7z 5"-7"-9"’

&C. &c. &c.

&c.

1 6.

Moreover, G being — 2 Q^-f- bX — x-' ^

5 ^ 3

by ai"t* 1 1 • we, by multiplying by xx,
and taking the correct fluents, get H = ,v2Q— . 0

44 Ti-3iT3F

+ — S being put for the feries ~z 4. _L_
r ^ '3 3 c5

— &c
S\f' *

6. LI. 4 D

~h

Now,

r 564 ]

r

Now, it is obvious, that this value of H mud be

equal to the value of H in the preceding article*
when both feries converge.

n *3 v~l . Cl'! O X~3 . n X1 C X~S

Therefore 2 — 1 1 *

1-.3-

n b x'TL Jx' .

4*4

&c. is then s= *2 CZr~ 2

~f* 1 "f* 2 s* »

Hence, by taking # equal to — 1, we find 2 S
= -f- 2 -f 2 S j. and, confequently, S = — h

And, by taking x equal to -7=) we hnd

V‘-

2 x _J l ! — l 3 &c.

^zn 1 3i-sz ^ 5z-r

— — — — {- ’T=== “b 1 "f" 2 S —

*> ' ^ y — »

/:

and, confequently, -p—i — ■ -rjz 5;-. 7

— 2Q,

•W

&c+ =

a
~~ %
4

17-

Seeing that Qjs = ~, and S = ^ — h it follows,
from the laft article, that

H is — a;2 Qj 'ZT’TJ * i-3z

4. Z.3 4- Zi, &c.

3-52 r 5-7z

From whence, by multiplying by — , ajid taking
the correct fluent, we get

fT

H

C 56s ]

El

H

rr

**Q.

bxrX bx* , l , bX

-—3

X

— 5

4 +?+ 4
&c.

x 4- —

' 4

i2-32 32-52 52-72'

And hence, by multiplying by a? x, and taking
the correct fluents, we have

nr

II

A4 Q_ . bx*X

+

8

16

5 b A4 b x* X , 4

64 ‘ 16 ' 8 ~7~ 64

y-f + 4 +

G1 X~

8

16 1 8

o nt- nr

^- + +3 +

. — 3

, — 5

J-32-52

- ~r S5V. S being put for the feries

1 1 ,

*z-32-52

32-52-7:

— , &c.

52*72*92

ill

Now, this value of H being equal to the value of H
in art, 1 5. when both feries converge, it follows, that

5 *5

X

+ 4. 94!

o2 r2 ^2 *

5 *'

1 *-32-52 ' 3-5-7

A"4 1 b AT4 X 5 b X (

8 16 64 ' 16

2-72 92

4 b x%

_L

bx*X

, G’e is then
b

..3

K + 6*

+ 4 +

1 3 aZ Q

+ T6-- +b-

9 • - - 8

Hence, by taking x equal to — 1 , we hnd — 4 S

m

O h 2 111 111 O n't

— — + -§ -j- 4 S j and, confequently, S = ~-

r

9"

Many other instances of the ulc of this method
might be given ; but thefe may fuffice to enable the
intelligent reader to purfue the {peculation farther, at
his pleafure.

4 D 1

LV. Cor*>

[ 566 ]

LV. Conjectures concerning the Caufe , and
Observations upon the Phenomena of
Earthquakes ; particularly of that great
Earthquake of the Firft of November,
17 55, which proved fo fatal to the City of
Lifbon, and whofe EffeCls were felt as far
as Africa, and more or lefs throughout
almcft all Europe; by the Reverend john
Michel 1, M. A. Fellow of Queen's Collegey
Cambrid ge-

INTRODUCTION.

Art. i.TT has been the general opi-
| men of philolophers, that
earthquakes o we their origin to fome
fudden explolion in the internal parts of the earth.
This opinion is very agreeable to the phenomena,
which feem plainly to point out fomething of that
kind. The conjectures, however, concerning the
caufe of fuch an explofion, have not been yet, I think,
fufficiently fupported by fads; nor have the more
particular effeds, which will arife from it, been
traced out; and the connexion of them with the
phenomena explained. To do this, is the intent of
the following pages; and this we are now the better
enabled to do, as the late dreadful earthquake of the
1 ft of November 1755 fupplies us with more * fads,

and

* Many of thefe fa£ts are collected together in the 49th »'oIume
of the Pinlofophical Tranfa£tions. The fame are alfo to be found.

With

Read Feb. 28. 1
March 6. 1 3. >
20. 27. i/bo )

C 567 ]

and thofe better related, than any other earthquake
of which we have an account.

2. That thefe concuffions fhould owe their origin to
fomething in the air, as it has fometimes been imagined,
feems very ill to correfpond with the phenomena.
This, I apprehend, will fufficiently appear, as thofe
phenomena are hereafter recounted j nor does there
appear to be any fuch certain and regular connexion
between earthquakes and the ftate of the air, when
they happen, as is fuppofed by thofe who hold this
opinion. It is faid, for inftance, that earthquakes
always happen in calm ftill weather : but that this is
not always fo, may be feen in an account of the
* earthquakes in Sicily of 165)3, where we are told,
“ the fouth winds have blown very much, which
“ f ill have been impetuous in the mod fenfible
<c earthquakes, and the like has happened at other
tc times.”

3. Other examples to the fame purpofe we have
in an account of the earthquakes that happened in
New England in 1727 and 17283 the author of

with fome additional ones, in “ The Hiftory and Philofophy of
“ Earthquakes,” (a work well worth the perufal of thofe, who
are defirous of being acquainted with this fubjedb). The author
of it has given us, befuies the aforefaid fadbs, a very judicious
abndgment of ten of the moft confiderable writers upon the fub-
ject. I have taken the greateft part of my authorities either from
this author, or the Philofophicai Tranfaciions, that thofe who
would w.fh to examine them, may have 2n opportunity of doing
it the more eafily 3 fome things only, which were not to be met
with in thefe, and which yet were neceflary to my purpofe, I*
have been obliged to feek for elfewhere.

* See Philof. Tranf. N° 207. or vol. ii. p. 408. Lowthorp’s
Abridgment.

which

' [ 568 ]

which fays, that he could neither obferve any coii'
nexion between the weather and the eaithcjuak^s,
nor any prognoftic of them ; for that they happened
alike in all kinds of weather, at all times of the tides,

and at all times of the moon *.

.p. If, however, it fhould hill be fuppofed, not-
withftanding thefe inftances to the contraiy, that
there is fome general connexion between earthquakes
and the weather, at the time when they happen,
yet, furely, it is far more probable, that the air
fhould be affefted by the caufes of earthquakes, than
that the earth fhould be affefted in fo extraordinary
a manner, and to fo great a depth ; and that this,

* See Philof. Tranf. N° 4°9- or vol. vi. part 11. 2C2.

Eames’s Abridgment.— To thefe authorities, we may add the
opinion of Mor.f. Bertrand, who exprelles himfelf, upon this
occafion, in the following manner. “ Ariftotle, i liny, and
“ Seneca, tell us, that earthquakes are preceded by a calm and
“ ferene air. This is, indeed, often the cafe, but not always.
“ I don’t know, upon an examination of the whole, if there are
“ not as many exceptions to this rule, as examples that conn. m
“ it. Some authors again have thought, that they might look on
“ a dark fky, lightenings, and iudden ftorms, as the forerunne.s
“ of earthquakes.” Then relating fome inftances of {hocks that
happened in calm and ferene weather, he adds, “ On the other
“ ‘hand, it appears, from the examples, which we have before
“ related, that many earthquakes have happened at the time of
“ great rains, violent winds, and with a cloudy fky ; fo that one
“ cannot find any certain prognoftic of them in the ftate of the
“ atmofphcre.” See Memoires Hijlonques ct Phyf.ques Juries
tremblemcns de Terre, par Monf. Bertrand , a la Ha)c ll57' . 1IS

author, in thefe fenfible memoiis, has obliged the public with a
circu mftantial account of all the facls he couid collect, relating to
the earthquakes of Switzerland, or thofe of other places, that
feemed to be conneaed with them. The whole feems to be done
with care and fidelity, and without the leaft attachment to any
particular fyftem. ^

[ S69 1

and all the other circumftances attending thefe mo-
tions, fliould be owing to fome caufe redding in
the air.

f. Let us then, rejecting this hypothefis, fuppofe,
that earthquakes have their origin under ground, and
we need not go far in fearch of a caufe, whofe real
exigence in nature we have certain evidence of, and
which is capable of producing all the appearances of
thefe extraordinary motions. The caufe I mean is
fubterraneous fires. Thefe fires, if a large quantity
of water fhould be let out upon them fuddenly, may
produce a vapour, whofe quantity and elaftic force
may be fully fufficient for that purpofe. The prin-
cipal fadts, from which I would prove, that thefe
fires are the real, caufe of earthquakes, are as follow.

Section I.

6. Firjl , The fame places are fubjedt to re-
turns of earthquakes, not only at fmall inter-
vals for fome time after any confiderable one
has happened, but alfo at greater intervals of
fome ages.

7. Both thefe fadls fufiiciently appear, from the
accounts we have of earthquakes. The tremblings
and fhocks of the earth at * Jamaica in 1692, at
* Sicily in 1693, and at * Lilbon in 1 7ff, were re-
peated fometimes at larger, and fometimes at fmaller
intervals, for feveral months. The fame thing has
been obferved in all other very violent earthquakes.
At “f- Lima, from the 28th October 1746, to the

* See the accounts of thefe in the Philof. Tranf.

t, See Antonio d’Uiloa’s Voyage to Peru, part ii. book i. ch. 7.

9 24th

r 570 1

24th February 1747 (f^e ^me w^en the account of
them was fcnt from thence), there had been num-
bered no lefs than 45 1 fhocks, many of them littie in-
ferior to the fin ft great one, which deftroyed that city.

8. The returns of earthquakes alfo, in the fame
places, at larger diftances of time, are confirmed by
all hiftory. Conftantinople, and many parts of Afia
Minor, have fuffered by them, in many different
ages : Sicily has been fubjedt to them, as far back as
the remains even of fabulous hiftory can inform us
of: Lifbon did not feel the effedts of them for the
firft time in 1 755 : Jamaica has frequently been
troubled with them, iince the Englifh firft fettled
there ; and the Spaniards, who were there before,
ufed to build their houfes of wood, and only one
ftory high, for fear of them : * Lima, Callao, and
the parts adjacent, were almoft totally deftroyed by
them twice, within the compafs of about fix ty years,
fcarce any building being left ftanding, and the latter
being both times overflowed by the fea : nor were
thefe the only inftances of the like kind, which have
happened there; for, from the year 1582 to 1746,
they have had no lefs than fifteen very violent earth-
quakes, befides an infinity of lefs confiderable ones ;
and the Spaniards, at their firft fettling there, were
told by the old inhabitants, when they faw them
building high houfes, that they were building their
own fepulchres •f*.

, p. Secondly ,

* See the place above-quoted.

f What is here (aid, is taken from d’UHoa’s Voyage to Peru,
the Hiftory and Pbilofophy of Earthquakes, the fhilof. Tianf. &c.

where

[571]

5). Secondly , Thofe places that are in the neigh-
bourhood of burning mountains, ..are always
fubjedt to frequent earthquakes ; and the erup-
tions of thofe mountains, when violent, are ge-
nerally attended with them.

10. Afia Minor and Conftantinople may be looked
upon as in the neighbourhood of Santerini. The
countries alfo about * * /Etna, Vefuvius, mount Hascla,
&c. afford us fufficient proofs to the fame purpofe.
But, of all the places in the known world, I fuppofe,
no countries are fo fubjedl to earthquakes, as -f* Peru,
Chili, and all the weftern parts of South America ;
nor is there any country in the known world fo full
of volcanos : for, throughout all that long range
of mountains, known by the name of the Andes,
from 4y degrees fouth latitude, to feveral degrees
north of the line, as alfo throughout all Mexico,
being about 5 coo miles in extent, there is a con^-
tinned chain of them £.

11. Thirdly, The motion of the earth in earth-
quakes is partly tremulous, and partly propa-
gated by waves, which fucceed one another
iometimes at larger and fometimes at fmaller

where many more examples, to the fame purpofe, are to be met
with. See alfo Metnoires fur les tremblemens de Terre ; in which
are mentioned above 130 repetitions of earthquakes, that have
happened, within the compafs of 960 yeais, in Switzetland.

* See many inflances of this in vol. ii. of Lowthorp’s Abr. of
the Philof. Tranf.

f Monf. Bouguer fays, that fcarce a week paffes without earth-
quakes in fome part of Peru. See Hiflr. of Earthq, p. 205.

t See the Maps of thefe countries, Condamine’s Voyage down
the Maranon, Axofta’s Nat. Hift. of the Indies, tefc.

Vol, LI. 4E diflances;

[ 572 ]

didances ; and this latter motion is generally
propagated much farther than the former.

12. The former part of this proportion wants no
confirmation : for the proof of the latter, roiz. the
wave-like motion of the earth, we may appeal to
many accounts of earthquakes : it was very remark-
able in the tw7o, which happened at Jamaica in
* 1687-8 and * 1692. In an account of the former,
it is faid, that a gentleman there faw the ground rife
like the fea in a wave, as the earthquake palled
along, and that he could didinguidi the effects of it,
to fome miles didance, by the motion of the tops of
the trees on the hills. Again, in an account of the
latter, it is faid, “ the ground heaved and fwelled,
“ like a rolling fwelling fea,” infomuch, that people
could hardly Hand upon their legs by reafon of it.

13. The fame has been oblerved in the earth-
quakes of *f* New England, where it has been very
remarkable. A gentleman giving an account of one,
that happened there the 18th November 1755, fays,
the earth rofe in a wave, which made the tops of the
trees vibrate ten feet, and that he was forced to fup-
port himfelf, to avoid falling, whild it was palling.

14. The fame all'o was obferved at J Lifbon, in
the earthquake of the id November 1755, as may

be

* See Phil. Tranf. N° 209. or vol. ii. Lowthorp’s Abridgment,
p. 410.

t See Philof. Tranf. vol. 1. p. 1, b'c.

I See the accounts collected together, in the 49th volume of the
Philof. 1 rant, or in Hift. and Philof. of Earthq. and particularly
p. 315. where it is faid, « A molt dreadful earthquake Ihook by

“ fliort.

[ 573 ]

he plainly collected from many of the accounts that
have been published concerning it, fome of which
affirm it exprefly : and this wave-like motion was
propagated to far greater diflances than the other
tremulous one, being perceived by the motion of wa-
ters, and the hanging branches in churches, through
all Germany, amongft the Alps, in Denmark, Swe-
den, Norway, and all over the Britifh ifles.

15. Fourthly , It is obferved in places, which are
fubjedt to frequent earthquakes, that they ge-
nerally come to one and the fame place, from
the fame point of the compafs. I may add
alfo, that the velocity, with which they pro-
ceed, (as far as one can collect it from the ac-
counts of them) is the fame j but the velocity
of the earthquakes of different countries is very
different.

16. Thus all the Shocks, that fucceeded the firft
great one atLilbon in 1755, as well as the flrfl; itfelf,
came from the * * north- weft. This is afferted by
the perlon, who fays, he was about writing a hiftory
of the earthquakes there : all the other accounts alfo
confirm the fame thing 5 for what fome fay, that they
came from the north, and others, that they came

“ fhort, but quick vibrations, the foundations of all Lifbon ;
<c then, with a fcarcely perceptible paufe, the nature of the mo-

*c tion changed, and every building was tolled like a waggon
“ driven violently over rough ftones, which laid in ruins almoft
“ every houfe, church, GV.”

For the wave-like motion at Oporto, fee Phil. Trarif. vol. xlix.
p. 418. for the fame at Gibraltar, fee Hi ft. and Philof. of Farthq.
p. 322.

* See Philof. Tranf. vol. xlix. p. 410.

4 E 2

from

[ 57+ ]

from the weft, cannot be looked on as any reafonable
obje&ion to this, but rather the contrary. The ve-
locity alfo, with which they were all propagated, was
the fame, being at leaft equal to that of found ; for
they all followed * immediately after the noife that
preceded them, or rather the noife and the earthquake
came together : and this velocity agrees very well with
the intervals between the time when the firft (hock
was felt at Lilbon, and the time when it was felt at
other diftant places, from the comparifon of which,
it feems to have travelled at the rate of more than
•f* twenty miles per minute.

17. An hiftorical account of the earthquakes, which
have happened in J New England, fays, that, of
five confiderable ones, three are known to have come
from the fame point of the com pals, viz. the north-
weft : it is uncertain from what point the other two
came, but it is fuppofed that they came from the fame
with the former. The |j velocity of thefe has been
much lefs than that of the Lifbon earthquakes : this
appears from the interval between the preceding noife,
and the fhock, as well as from the wave-like motion
before- mentioned.

* See Piiilof. Tranf vol. xlix. p. 414. or Hift. and Philof. of
Earthq. p. 315.

f See Art. 97.

j See Philof. Tranf. vol. 1. p. 9.

|j As in feme earthquakes the velocity, with which they are
propagated, is much lefs than in others, it is evident, that they can
by no means be owing to any caufe refiding in the air : for any
fhock communicated to the air, mud neceHarily move with a ve-
locity neither greater nor lefs than that of founds ; that is, at the
rate of about thirteen miles per minute.

18. All

[ 575 ]

l8. All the greater earthquakes, that have been
felt at * Jamaica, feem, by the accounts given of
them, to have come from the fea, and, palling by
Port-Royal, to have gone northwards. The velocity
of thefe alfo was far fhort of the velocity of the Lif.
bon earthquakes.

ip. The earthquake of -f London, on the 8th of
March 1750, was fuppofed to move from eaft to
weft. I have been credibly informed, that the fame
thing happened in a flight fhock, which was felt
there in the laft century, as the perfon, who told me
this, had an opportunity of obferving; for being, by
accident, in a lcalemaker’s fhop at the time when it
happened, he found that all the fcales vibrated from
eaft to weft.

20. All the fhocks that have been lately felt at
Brigue in Valais, have likewife come from the fame
point of the compafs, viz. the louth ;j\

2 r . Fifthly , The great Lisbon earthquake lias been
fucceeded by feveral local ones ftnce, the extent
of which has been much lefs.

22. Such were the earthquakes in Switzerland ;
thole on the borders of France and Germany j thofe
in Barbary, &c. ||

* See the accounts of them in Philof. Tranf. N° 209. cr vol. ii.
Lowthorp’s Abr. p. 410, &c.

t See Hill, and Philof. of Earthq. p. 250. or Philof. Tranf.
vol. x. Martyn’s Abr. Meteorology, paffim.

•f- See Philof. Tranf. vol. xlix. p. 620. The fame has been
obferved at Smyrna alfo, fee Philof. Tranf. N° 495, or Martyn’s
Abr. vol. x. p. 526.

(I See the accounts of thefe collected together in Philof. Tranf.
vol. xlix. or in the Hilt, and Philof. of Earthq,

Sect,

[ 576 ]

Sect. II.

23. How well foever thefe fads may agree with

the fuppofition before laid down, That fubterraneous
fires are the caufc of earthquakes, one doubt, how-
ever, may perhaps remain ; viz. how it is pofilblc
that fires fhould fubfift, which have no communica-
tion with the outward air ? I11 anfwer to this, I

might alledge the example of green plants, which take
fire by fermentation, when laid together in heaps ;
where the ad million of the outward air is fo far from
being neceflary, that it will effiedually prevent their
doing fo. But, to pafs by this, we have many in-
fiances more immediately to the purpofe.

24. It can hardly be fuppofed, that the fires of the
generality of volcanos receive any fupply of frelh air
(for this mufl effedually be prevented by that vapour,
which is continually rufhing out at all their vents),
and yet they fubfilf , and frequently even increafe, for
many ages. Now, thefe are fires of the very fame
kind with thofe, which I fuppofe to be the caufe
of earthquakes. Other fads, ffill more exprefiy to
the purpofe, are as follow:

ay. In the earthquake of the 1 ft of November
1 755, we are told, that both fmoke and light flames
were feen on the coafl of Portugal, near Colares ; and
that, upon occafion of fome of the fucceeding fhocks,
a flight fmell of fulphur was perceived to accompany
a “ fog, which came from the fea, from the fame
“ quarter, whence the fmoke appeared

* Sec Philof. Tranf. vol. xlix. p.414,

26. Ill

[ 577 ]

26. In an account of an earthquake in New Eng-
land, it is faid, that at Newbury, forty miles from
Bofton, the earth opened, and threw up feveral cart-
loads of fand and allies ; and that the fand was alfo
Hightly impregnated with fulphur, emitting a blue
flame, when laid on burning coals *.

27. One of the relaters of the earthquake in Ja-
maica in 1692, has thefe words: “ In Port-Royal,
“ and in many places all over the ifland, much ful-
“ phureous combuftible matter hath been found
“ (Ihppofed to have been thrown out upon the
“ opening of the earth), which, upon the firft touch
“ of fire, would flame and burn like a candle.

28. “ St. Chriftopher’s was heretofore much
“ troubled with earthquakes, which, upon the erup-
<c tion there of a great mountain of combuftible mat-
“ ter, which ftill continues, wholly ceafed, and have
,c never been felt there fince

29. Again, we are told, that, on the 20th No-
vember 1720, a burning J ifland was railed out of
the fea, near Tercera, one of the Azores, at which
place, feveral houfes were Ihaken down by an earth-
quake, which attended the eruption of it. This
ifland was about three leagues in diameter, and nearly
round ; from whence it is manifeft, that the quan-
tity of pumice ftones and melted matter, which mull
have been requifite to form it, was amazingly great :

See Pnilof. Tranf. N° 409. or vol. vi. part ii. p. 201.
Eames’s Abr.

t See Philof, Tranf. N° 209. or vol. ii. p. 418. Lowthorn’s
Abr.

t ^ee Philof. Tranf. N3 372, or vol. vi. part ii. p. 203^
Eames’s Abr.

C 578 ]

iii all probability, it mud have far exceeded all that
has been thrown out of /Etna and Vefuvius together
within the 1 a ft two thoufand years. This may i'erve
to latisfy us, that the fire which occafioned all this,
tnuft have fubffed for many years, not to fay ages,
and this without any communication with the exter-
nal air. It is worth obferving, that ^ feveral Al-
liances of this kind have happened amongft the
Azores. There are befides many marks of lubter-
raneous fires about thefe ifiands, feveral places lend-
ing up fmoke or flames. Thefe iflands are alio lub-
je£t to violent and frequent earthquakes.

30. We have more inflances to the fame purpofe,
near the illand of Santerini in the Archipelago, where
there have been feveral little iflands railed out of the
fea by a fubmarine volcano. The eruption of one of
thefe in the year 1708, with all the circumflances
that attended it, we have a very good account of in
the + Philofophical Tranfadtions. It was raifed in a
place where the fea had been formerly 100 fathoms
deep, and was attended with earthquakes before it
lliewgd ltfelf above water, as well as after. It is le-
ported, that the illand of Santerini itfelf was origi-
nally raifed out of the fea in the fame manner ; but,
be that as it will, we have certain accounts of new
iflands raifed there, or additions made to the old ones,
from time to time, for above ipoo years backwards,
and there have always been earthquakes at the time
of thefe eruptions.

* See Hift. and Philof. of Earthquakes, under the titles Azores,

Elands raifed, b ’c. ,

t See N° 314, 317, and 332. or vol. v. part 11. p. 190. Jones s

4

C 579 ]

51. Another example of the fame kind happened
at' * Manila, one of the Philippine iflands, in the
year 1750. This alfo was attended with violent
earthquakes, to which that illand, as well as the reft
of the Philippines, is very much fubjedh

32. We may add to thefe, the many inftances of
V&ft quantitive of -f* pumice ftones, which have been
fometimes found floating upon the fea, at fo great a
diftance from the fhore, as well as from any known
Volcano, that there can be little doubt of their being
thrown up by fires fubfifting under the bottom of the
Ocean.

33. From thefe inftances, we may, with great
probability, conclude, that the fires of volcanos pro-
duce earthquakes : I do not, however, fuppofe, that
the earthquakes, which are frequently felt in the
neighbourhood of volcanos, are owing to the fires
of thofe volcanos themfelves ; for volcanos, giving
paflage to the vapours that are there formed, fhould
rather prevent them, as in the inftance at St. Chri-
ftopher’s, before-mentioned.

34. We alfo meet with frequent inftances con-
firming the fame thing amongft the Andes. Antonio
d’Ulloa (fpeaking of what happens amongft thefe
mountains) fays, tc Experience thews us, that, upon
(C the frefti breaking out of any volcano, it occafions
ct fo violent a thock to the earth, that all the villages,
c< which are near it, are overthrown and deftroyed,

* See Philof. Tranf. vol. xlix. p. 459.

t See Philof. Tranf. N° 372. or vol. vi. part ii, p. 204. and
N° 402. or vol. vii, part ii. p, 43. Earnest Abr.

Vol, LI. 4 F

(C

as

[ 58° 3

u as it happened in the cafe of the mountain 7rr Car-
“ guayrafo. This fhock, which we may, without
“ the lead; impropriety, call an earthquake, is fel-
“ dom found to accompany the eruptions, after an
<{ opening is once made ; or, if fome imall trembling
14 is perceived, it is very inconfiderable ; fo that,
“ after the volcano has once found a vent, the fhocks
<{ ceafe, notwithftanding the matter of it continues
« to be on fire.” The greater earthquakes, there-
fore, feem rather to be occafioned by other fires, that
lie deeper in the fame trad: of country ; and the erup-
tions of volcanos, which happen at the fame time
with earthquakes, may, with more probability, be
afcribed to thofe earthquakes, than the earthquakes
to the eruptions, whenever, at leaf!:, the earthquakes
are of any confiderable extent. If this don t appear
fufficiently manifeft at prefent, it will, perhaps, be
better underftood, by applying to the prefent pur-
pofe, what will be faid hereafter concerning local
earthquakes.

* It does not appear altogether certain, from the expreffion
made ufe of in the French tranflation (from whence I have taken
this), that Carguayrafo might not have been a volcano in former
times, which is aflerted to have been the cafe by Monf. Conda-
mine. It is poffible alfo, that the fame may be true of thofe four
mentioned in the next article ; and, indeed, it is difficult to know
it to be otherwife, in any inftance, among the Andes, where the
volcanos are generally found at inacceffible heights. But allowing,
that all thefe were only old volcanos, which broke out afrtfh, yet
they will ferve at leaft to fwell the number of them in the fame
neighbourhood, as well as to fhew us, that there may, very7 pro-
bably, be many more, which lie hid : for thefe fhewed no marks
of their exiftence, till, by their eruption, they melted a vaft quan-
tity of fnow, with which they were before covered, and which,
being reduced to water, did great damage, by overflowing the
country round about.

[ 5§* ]

Sect. Ill

35". It may be afked, perhaps, why we fhould
fuppofe, that feveral fubterraneous fires exift in the
neighbourhood of volcanos ? In evidence of this,
we have frequent inftances of new volcanos breaking
out in the neighbourhood of old ones : Carguayrafo,
juft mentioned, may fupply us with one example to
this purpofej and, in the night of the 28th of Octo-
ber 1746, in which Lima and Callao were deftroyed,
no lefs than four * new ones burft forth in the ad-
jacent mountains.

36. To the fame purpofe, we may allege the in-
ftances of many volcanos lying together in the fame
trad; of country : as for example, the many places,
“ not fo few as forty,” amongft the Azores, which
either do now or have formerly fent forth fmoke and
flames ; the many volcanos alfo amongft the Andes,
already mentioned : thus /Etna, Strombolo, and Ve-
fuvius, I may add Solfatara too, are all in the fame
neighbourhood : and Monf. Condamine fays, he has
traced -f4 lavas, exadly like thofe of Vefuvius, all the
way from Florence to Naples. In f Iceland alfo, we
have, befides Haecla, not only feveral other volcanos,
but alfo a great number of places, that fend up ful-

* See d’Ulloa’s Voyage to Peru, part ii. book i. chap. y.
f See Phil. Tranf. vol. xlix. p. 624. All thefe lavas, as well
as the volcanos juft mentioned, lie in a continued line. The fame
thing holds good in the volcanos of the Andes alfo. This is a fadt
I muft defire the reader to attend to, as it ferves to Confirm a very
material dodlrine, which I (hall have occaiion to mention here-
after. See art. 44, 45, and 46.

+ See Horrebow’s Natural Hiftory of Iceland.

4F 2

phureous

C 582 ]

phureous vapours. But the examples of this kind are
fo frequent, that there are few inftances to be pro-
duced of fingle volcanos, without evident marks,
either that there have been others formerly in their
neighbourhood, or that there are, at prefent, fub-
terraneous fires near them.

37. This frequency of fubterraneous fires, in the
neighbourhood of volcanos, will appear fiill more
probable, if we confider the internal ftrudture of the
earth ; and, as it will be neceffary alfo, in order to
underhand what follows, to know a little more of
this matter, than what falls under common obferva-
tion, I fhall endeavour to give the reader fome ac-
count of it.

38. The earth then (as far as one can judge from
the appearances), is not compofed of heaps of matter
cafually thrown together, but of regular and uniform
ftrata. Thefe ftrata, though they frequently do not
exceed a few feet, or perhaps a few inches, in thick-
nefs, yet often extend in length and breadth for
many miles, and this without varying their thick-
nefs confiderably. The fame ftratum alfo preferves
a uniform character throughout, though the ftrata
immediately next to each other are very often totally
different. Thus, for inftance, we fhall have, per-
haps, a ftratum of potters clay; above that, a ftra-
tum of coal ; then another ftratum of fome other kind
of clay ; next, a fharp grit fand ftone ; then clay
again ; next, perhaps, fand ftone again ; and coal
again above that; and it frequently happens, that
none of thefe exceed a few yards in thicknefs. There
are, however, many inftances, in which the fame
kind of matter is extended to the depth of fome

hundreds

[ 583 ]

hundreds of yards ; but in all thefe, a very few only
excepted, the whole of each is not one continued
nrnis, but is again fubdivided into a great number
of thin laminae, that feldom are more than one, two,
or three feet thick, and frequently not fo much.

39. Befide the horizontal divifion of the earth into
firata, thefe firata are again divided and Blattered by
many perpendicular fiffures, which are in fome places
few and narrow, but oftentimes many, and of con-
fiderable width. There are alfo many inftances,
where a particular firatum fliall have almoft no
fiffures at all, though the firata both above and be-
low it are confiderably broken: this happens fre-
quently in clay, probably on account of the foftnefs
of it, which may have made it yield to the preffure
of the fuperincumbent matter, and fill up thofe fif-
fures which it originally had ; for we fometimes meet
with infiances in mines, where the correfpondent
fi fibres in an upper and lower firatum are interrupted
in an intermediate firatum compofed of clay, or fome
fuch foft matter.

40. Though thefe fifihres do fometimes correfpond
to one another in the upper and lower firata, yet this
is not generally the cafe, at leaft not to any great di-
fiance : thofe clefts, however, in which the larger
veins of the ores of metals are found, are an excep-
tion to this obfervation ; for they fometimes pafs
through many firata, and thofe of different kinds, to
unknown depths.

41. From this conftitution of the earth, viz. the
want of correfpondence in the fiffures of the upper
and lower firata, as well as on account of thofe firata
which are little or not at all fhattered, it will come to

pafs.

4

[ 5H ]

pufs, that the earth cannot eafily be Separated in a
direction * perpendicular to the horizon, if we ta*e
any confiderable portion of it together j but m the
horizontal direction, as there is little or no adhefion
between one ftratum and another, it may be fepaiated

without difficulty. , . . ,

42. Thofe fiffures which arc at fome depth below

the fur face of the earth, are generally found full of
water : but all thofe that are below the level of
fea, muft always be fo, either from the oozing of the
fea or rather of the land waters between the ftrata.

The ftrata of the earth are frequently very
much bent, being raifed in fome places, and de-
prefled in others, and this fometimes with a very
quick afeent or defeent ; but as thefe afeents and
feents, in a great meafure, compenfate one another,
if we take a large extent of country together, we may
look upon the whole fet of ftrata, as ying neatly ho-
rizontally. What is very remarkable, howeve, , m
their fituation, is, that from mod, if not all large
trafts of high and mountainous countries, the ftrata
lie in a fituation more inclined to the horizon, than
the country itfelf, the + mountainous countries bemg

* What I laid before of thofe deep clefts, in which metals are
found wdl not .0* «KU conduf.on , for ^ a - -M -b.y

dirt'erent from either ' t other foft matter ;

are frequently interrupted by ft ra a o *y» ^ rubbl(h? or wllh

ores 'and Spar’s, '"hTadhe're ’as firmly to ^ roefcs on both tides, as

if they compofed one continue ^tum not only that

+ b feems very Probable> out oPf the lower ftrata of the

the mountainous countries arc :fon?wl out o h ^ ^ formeJ

earth, but that fomelimes the 'g, out

—

C 585 ]

generally, if not always, formed out of the lower
rtrata of earth. This fituation of the rtrata may be
not unaptly reprefented in the following manner.
Let a number of leaves of paper, of feveral different
forts or colours, be parted upon one another; then
bending them up together into a ridge in the middle,
conceive them to be reduced again to a level lurface,
by a plane fo parting through them, as to cut off all
the part that had been raifed ; let the middle now be
again raifed a little, and this will be a good general
reprefentation of moft, if not of all, large tradls of
mountainous countries, together with the parts ad-
jacent, throughout the whole world * *.

44. From this formation of the earth, it will fol-
low, that we ought to meet with the fame kinds of
earths, ftones, and minerals, appearing at the furface,
in long narrow flips, and lying parallel to the greateft
rife of any long ridges of mountains ; and fo, in fadt,
we find them. The Andes in South America, as it
has been faid before, have a chain of volcanos, that
extend in length above 5000 miles : thefe volcanos,
in all probability, are all derived from the -f- fame

out of ftrata ftill lower than the reft, which, perhaps, may always
be the cafe, where they have volcanos in them. [See a repre-
fentation of this in Tab. XIII. Fig. 3 J In other inftances, how-
ever, it often happens, that the hills, to which thefe high lands
ferve as a bafe, are not only formed out of the ftrata next above
them, but they ftand, as it were, in a difti, as if they had deprefled
the ground, on which they reft, by their weight.

* Fig.. 1. reprefents a fe&ion of a fett of ftrata, lying in the
fituation juft defcribed: the feilion is fuppofed to be made at right
angles to the length of the ridge, and perpendicular to the ho-
rizon.

f See the notes to art. 36 and 53. See alfo Fig. 3.

rtraturru

[ 586 ]

ftratum. Parallel to the Andes, is the Sierra, another
long ridge of mountains, that run between the Andes
and the fea ; and “ thefe two ridges of mountains run
" within fight of one another, and aknoft equally,
“ for above a thoufand leagues together being
each, at a medium, about twenty leagues wide. The
gold and filver mines wrought by the Spaniards, are
found in a tradl of country parallel to the direction of
thefe, and extending through a great part of the length
of them.

4f. The fame thing is found to obtain in North
America alfo. The great lakes, which give rife to
the river St. Laurence, are kept up by a long ridge of
mountains, that run nearly parallel to the eaftern coaft.
In defcending from thefe towards the fea, the fame
fets -f- of ftrata, and in the fame order, are generally
met with throughout the greateft part of their length.

46. In Great Britain, we have another inftance to
the fame purpofe, where the direction of the ridge
varies about a point from due north and fouth, lying
nearly from t- N. by E. to S. by W. There are many
more inflances of this to be met with in the world, if
we may judge from circumftances, which make it
highly probable, that it obtains in a great number of
places, and in feveral they feem to put it almoft: out
of doubt.

47. The reader is not to fuppofe, however, that,
in any inftances, the higheft rife of the ridge, and

* See Acofla’s Natural Hiftory of the Indies.

+ See Lewis Evans’s Map and Account of North America.

J Of this I could give many undoubted proofs, if it would not
too far exceed the limits of my piefent defign, and which, for that
reafon, I am obliged to omit.

the

L 587 ]

tlie inclination of the firata from thence to the coun-
tries on each fide, is perfectly uniform ; for they have
frequently very confiderable inequalities, and thefe
inequalities are fometimes fo great, that the firata are
bent for fome fmall difiance, even the contrary way
from the general inclination of them. This often
makes it difficult to trace the appearance I have been
relating, which, without a general knowlege of the
foffil bodies of a large trad of country, it Is hardly
poffible to do.

48. At confiderable difiances from large ridges of
mountains, the firata, for the rnofi part, alfume a
iituation nearly level; and as the mountainous coun-
tries are generally formed out of the lower firata, fo
the more level countries are generally formed out of
the upper firata of the earth.

49. Hence it comes to pafs, that, in countries of
this kind, the lame firata are found to extend them-
felves a great way, as well in breadth as in length :
we have an infiance of this in the chalky and flinty
countries of England and France, which (excepting
the interruption of the Channel, and the clays, fandsl
&c. of a few counties) compofe a trad of about three
hundred miles each way.

50. Befides the railing of the firata in a ridge,
there is another very remarkable appearance in the
firudure of the earth, though a very common one;
and this is what is ufually called bv miners, the
trapping down of the firata; that is/ the whole fet
of firata on one fide a cleft are funk down below the
level of the correfponding firata on the other fide.
If, in fome cafes, this difference in the level of the
firata, on the different Tides of the cleft, fhould be

Vol. LI, 4G very

[ 588 j

very confiderable, it may have a great erFedt in pro-
ducing fome of the fingularities of particular earth-
quakes

PART II.

5 1 . T N the former part of this effay, I have re-
counted fome of the principal appearances of
earthquakes, as well as thofe particulars in the druc-
ture of the earth, upon which I fuppofe thefe ap-
pearances to depend. From what has been already
faid, I think it is fufficiently manifed, that, in fome
indances at lead:, earthquakes are actually produced
by fubterraneous fires ; it now, therefore, remains to
be fhewn, how all the appearances above- recited, as
well as many other minuter circumdances attending
earthquakes, may be accounted for from the fame
caufe.

Sect. I.

f2. The returns of earthquakes in the fame places,,
either at fmall or large intervals of time, are very
confident with the caufe affigned : fubterraneous fires,
from their analogy to volcanos, might reafonably be
fuppofed to fubfid for many ages, though we had not
thofe indances •f' already mentioned, which put the

* Fig. 2. reprefents a fe&ion of the ftrata trapping down after
the manner juft defcribed. The fedfion is fuppofed to be made
perpendicularly to the horizon, and at right angles to the dire&ion
of the cleft : an inftance of this kind, amongft the coal miners of
Mendip in Somerfetfhire, is mentioned in thePhilof. Tranf. See
the account of it, together with a drawing, in N° 360. or Jones's
Abr. vol. iv. part ii. p. 260.
f See art. 28 to 32 inclufive.

matter

r s®9 ]

matter out of doubt. And, as it frequently happens,
that volcanos rage for a time, and then are quiet
again for a number of years j fo we fee earthquakes
alfo frequently repeated for fome fmall time, and
then ceafing again for a long term, excepting, per-
haps, now and then fome flight ftiock. And this
analogy between earthquakes, and the effects of vol-
canos, is fo great, that I think it cannot but appear
ftriking to any one, who will read the accounts of
both, and compare them together. The raging of
volcanos is not one continued and uniform effedt;
but an effedt, that is repeated at unequal intervals,
and with unequal degrees of force : thus, for in-
ftance, we fhall have, perhaps, two or three blafts
difcharged from a volcano, fucceeding one another
at the interval of a few feconds only : fometimes the
intervals are of a quarter of an hour, an hour, a day, or
perhaps feveral days. And as thefe intervals are very-
unequal, fo is the violence of the blafts alfo : fome-
times ftones, &c. are thrown, by thefe blafts, to the
diftance of fome miles ; at other times, perhaps, not
to the diftance of a hundred yards. The fame dif-
ference is obferved in the intervals and violence of
the fhocks of earthquakes, which are repeated at
fmall intervals for fome time.

Sect. II.

. The great frequency of earthquakes in the
neighbourhood of burning mountains, is a ftrong
argument of their proceeding from a caufe of the
fame kind : and the analogy of feveral volcanos lying
together in the fame tradt of country, as well as new
ones breaking out in the neighbourhood of old ones,

4 G 2 tends

C 59° ]

tends greatly to confirm this opinion ; but what makes
it flill the more probable, is that peculiarity in the
ftrudture of the earth, already mentioned. I obferved-
before, that the fame ftrata are generally very exten-
five, and that they commonly lie more inclining from
the mountainous countries, than the countries them-
selves : thefe circumftances make it very probable,,
that thofe * ftrata of combuflible materials,, which

break

* I has been imagined by fome authors, that volcanos are pro-
duced by the pyrites of veins, and that they do not owe their origin
to the matter of ftrata. In order to prove this, it is alleged, that
volcanos are generally found on the tops of mountains, and that
thofe are the places in which veins of pyrites are generally lodged.
This argument being taken from observations that have their
foundation in nature, ought not to go unanfwered.. In the firft
place, then, the pyrites of veins, or fiilures, are not found in fuf-
ficient quantities, or extending to a fufficient breadth, to be fup-
pofed capable of producing the fires of volcanos : it very rarely
happens, that we meet with a vein or fiffure five or fix yards wide j.
and when we meet with fuch an one, yet, perhaps, not a twentieth
part of it at moft fhall be filled with pyrites ; but the fires of vol-
canos, inftead of being long and narrow, as if the matter that fup-
plied them was depofited in veins, are generally round, and of far
greater breadth than veins can be fuppofed to be. Monf. Bouguer
fays, that the mouth of the volcano Cotopaxi is, at this time, five
or fix hundred fathoms wide; [fee Hift. and Phil, of Earthquakes,
p. 195 ] and the burning ifland that was raifed out of the fea near
Tercera, as before-mentioned, was almoft three leagues in diameter,
and nearly round. [See art; 29.]

Befides this, it is very difficult to conceive how any matters
lodged in veins can ever take fire ; for, excepting where the veins
are extremely narrow, they are almoft always drowned in a very
great quantity of water, which has free accefs to every part of
them : neither are the pyrites of veins, by any means, fo apt to
take fire of themfelves, as thofe of ftrata ; and if, indeed, there are
any of them that will do fo, yet they are but few in companion of
thofe which will not : all thofe, which, befide iron and fulphur,
contain copper, or arfenic, even in a very fjnall proportion, are not

at

[ 59i ]

break out in volcanos on the tops of the hill's, are to be:
found at a confiderable depth under ground in the level
and low countries near them. If this lhould be the cafe,

at all fubjedf to inflame of themfelves. On the other hand, moft of
the pyrites of ftrata, if not all of. them, have this property more or
lefs. There are alfo two forts of ftrata, in which pyrites are
lodged in the greateft abundance, that have the fame property,
and that frequently in as great a degree as themfelves : thefe are-
coals and aluminous earths, or (hale. There are fome kinds of.
both thefe, that, upon being expofed to the external air for a few
months, will take fire of themfelves, and bum. Thefe two forts
of ftrata are alfo near akin to each other; they are generally found
to accompany each other; they are both of them generally inter-
mixed with, or accompanied by ftrata of iron ore; and they both
of them, for the moft part, either contain, or are lodged amongft,
the remains of vegetable bodies ; and thefe remains of vegetable
bodies, in the aluminous earths, are frequently either wholly, or.
in part, converted into pyrites, or coal, or both. Numberlefs, in-
ftances of this are to be met with in the aluminous (hale of Whitby
and other places.

It is very probable, that to fome ftratum of this kind the fires of
volcanos are owing ; and this feems to be confirmed by the fimi-
larity of the materials, which are thrown up or fublimated by the
fires- of volcanos, to the matter of the aluminous earths. Solfatara-
produces fulphur, alum, and fal ammoniac. The two former of thefe
are very eafily to be obtained from the aluminous earths, and, I.
fuppofe,. the latter alfo ; at leaft it is procurable from the foot of
common foffil coals, and probably, therefore, from the foot of that
coaly matter which is intermixed with fuch earths.

The aluminous earths, moreover, not only have feveral ftrata of.
iron ore lying in them, but they alfo contain a confiderable propor-
tion of iron in their compofition. In correfpondence to this, we find
the lavas of volcanos, and other matters thrown out from thence,,
frequently containing a great deal of iron, the finall duft of them,
readily adhering to the magnet.

As to the pyrites of veins, I much doubt whether they ever con-
tain alum, or fal ammoniac; at leaft they are very rarely found to
contain either the one or the other.

andi

6>

[ 592 ]

and if the fame * ftrata fhould be on fire in any places
under fuch countries, as well as on the tops of the hills*
all vapours, of whatfoever kind, raifed from thefe
fires, muft be pent up, unlefs fo far as they can open
themfelves a paflage between the ftrata; whereas the
vapours raifed from volcanos find a vent, and are dis-
charged in blafts from the mouths of them. Now,
if, when they find fuch a vent, they are yet capable
of fhaking the country to the diftance of ten or twenty
miles round, what may we not expedt from them,
when they are confined ? We may form fome idea
of the force and quantity of thefe vapours from their
effedts: it is no uncommon thing to fee them throw
up, at once, fuch clouds of fand, allies, and pumice
ftones, as are capable of darkening the whole air,
and covering the neighbouring country with a fhower
of duff, &c. to fome miles diftance: great ftones
alfo, of fome tons weight, are often thrown to the
diftance of two or three miles by thefe explofions :
and Monf. Bouguer tells us, that he met with ftones

* It may be afked, perhaps, why a ftratum liable to take fire
in fome places, fhould not take fire throughout the whole extent
of it ? In anfwer to this, it may be faid, that the fame ftratum
may differ a little in the richnefs of its combuflible principles in
different places ; or, perhaps, the frequency of the fifliires, either
in the combuflible ftratum itfelf, or the ftratum next to it, may let
in fo much water, as to prevent its taking fire, excepting in a few
places ; but, if this once happens, the fire will not eafily be put out
again, but it will fpread itfelf, notwithftanding the fiflures that lie in
its way, though they are filled with water ; for the matter on fire
will be, in fome degree at leaft, in a fluid ftate; and, for this reafon,
it muft neccflarily expel the water from the fiflures, both on ac-
count of the extenfion of its own dimenfions by the heat, and of
the weight of the fuperincumbent earth, which, prefling it, will
make it fpread laterally.

ill

[ 593 ]

m South America, of eight or nine feet diameter,
that had been thrown from the volcano Cotopaxi, by
one of thefe blafts, to the diftance of more than
* three leagues.

54. If we fuppofe that thefe vapours, when pent
up, are the caufe of earthquakes, we muft naturally
expetfr, from what has been juft laid, that the moft
extenfive earthquakes fhould take their rife from the
level and low countries ; but more efpecially from the
lea, which is nothing elfe than waters covering fuch
countries. Accordingly we find, that the great earth-
quake of the 1 ft November 1757, which was felt at
places near three thoufand miles diftant from each
other, took its rife from under the fea ; this is mani-
feft, from that wave which accompanied it, as fhall
be fhewn hereafter. The fame thing is to be under-
wood of the earthquake that deftroyed Lima in the
year 1746, which, it has been faid, was felt as far as
Jamaica ; and, as it was more violent than the Lifbon
earthquake, fo, if this be true, it muft, in all pro-
bability, have been more extenfive alfo. There have
been many other very extenfive earthquakes in South
America: Acofta fays, that they have been often
known to extend themfelves one, two, or three hun-
dred, and fome even five hundred leagues, along the
eoaft. Thefe have been generally, if not always, at-
tended with waves from the fea$ but any minuter

* See Hift. and Philof. of Earthq. p. 19.5. Don Antonio d’Ulloa,
an author of great veracity, fpeaking of the fame thing, fays, that
w whole plain [near Latacunga] is full of large pieces of rocks,
fome of them thrown from the volcano Cotopaxi, by one of its
ft eruptions, to the diftance of five leagues.” See his Voyage to
Peoj, part L book vi. chap. 1,

circum-

C 59+ ]

circumftances accompanying them are not related.
Indeed it is hardly to be expected that they fhould
be observed, much lefs that they fhould be related,
when they happened in a country fo thinly inhabited,
and where one may reafonably fuppofe, that, in ge-
neral, only the grofler and more violent effedts would
be taken notice of.

Sect. III.

I have faid before, that I imagined earth-
quakes were caufed by vapours raifed from waters
luddenly let out upon fubterraneous fires. It is not
eafy to find any other caufe capable of producing
fuch hidden and violent effedts, or of railing fuch ail
amazing quantity of vapour in fo fmall a time. That
the blahs, difcharged from volcanos, are always pro-
duced from this caufe, is highly probable j that they
are often fo.,* cannot admit of the leah doubt. There
can be no doubt, that confiderable quantities of water
muh be often let out upon the fires of thefe volcanos,
and whenever this happens, it will be immediately
raifed by the heat of them into a vapour, whofe
elahic force is capable of producing the moh violent
effedts *.

y6. Both

* There are many effedts produced by the vapour of water,
when intenfely heated, which make it probable, that the force of
gunpowder is not near equal to it. The effedts of an exceeding
fmall quantity of water, upon which melted metals are acci-
dentally poured, are fuch, as, I think, could in no wife be ex-
pected from the like quantity of gunpowder. Founders, if they
are not careful, often experience thefe effedts to their coft. An
accident of this kind happened about forty years fince, at the cart-
ing of two brafs cannon at Windmill-hill, Moorfields. The

“ heat

[ 595 ]

5 6 « Both the tremulous and wave-like motion ob-
ferved in earthquakes, may be very well accounted

for

“ heat ofr the metal of the firft gun drove fo much damp into the
mould of the fecond, whicn was near it, that as foon as the
metal was Jet into it, it blew up with the greateft violence, tear-
“ ing. UP the ground fome feet deep, breaking down the furnace,
“ untiling the houfe, killing many fpedtators on the fpot, with the
ftreams oi melted metal, and fealding many ethers in a moft mi-
“ ferabIe manner.” [See the note at the end of procefs 44th of the
Englifh tranflation of Cramer’s Art of aJTaying Metals, j'

Other inftances of the violence of vapours raifed from water, are
frequently to be met with : one of Papin’s digefters being placed
between the bars of a grate, where there was a fire, was, after
fome time, burft by the violence of the fleam, the fire was all
blown out of the grate, and a piece of the digefler was driven
again ft the leaf of a flrong oak table, which it broke to pieces.
[See Philof.. Tranf. N 454’ or Martyn’s Abr. vol. viii. p. 465.]
The marquis of Worcefter alfo, in his Century of Inventions, tells
us, that he burft a cannon by the fame means.

It has been fometimes imagined, that the vapours, which occa-
fion earthquakes, were of the fame kind with thofe fulminating
damps, of which we often meet with inftances in coal mines.
iNow, there are feveral things which make it very probable, that
this is not the cafe . it is true, the force of fuch vapours is very
great; we have had inftances, where large beams of timber have
been thrown to the diftance of an hundred yards by them : [fee
Philof. Tranf. N° 136. or vol. ii. p. 381. Lowthorp’s Abr.l but
what is this to the force of that vapour, which could throw ftones
of twenty or thirty ton weight to the diftance of three leaoues?
Nor, indeed, is it at all probable, that any vapour, already in the
form of a vapour, can, by fuddenly taking fire, increafe its dimen-
fions fo much, as to produce that immenfe quantity of motion,
which we obferve in fome earthquakes : but this is rather to be
expected from fome folid body, fuch as water, which is capable of
being converted, and that almoft inftantly, into one of the lighteft,
and perhaps one of the moll elaftic, vapours in the world. Air*
when heated to the greateft degree that it is capable of receiving
from the hotteft fires we can make, acquires a degree of elafticity
about five times as great as that of common air: the vapour of
Vol. LI. a H

C 596 ]

for from fticli a vapour. In order to trace a little
more particularly the manner in which thefe two

motions

gunpowder, whilft it is inflamed, has alfo about five times the
elaftic force which it has when cold. [See Robins’s excellent
tract on Gunnery.] Now, if vve fuppofe a fulminating damp, of
any kind, to increafe its el aflicity, when inflamed in the fame pro-
portion, this will be abundantly fufficient to make it produce any
effects, which we have ever feen produced by any of the damps of
mines, l2c. And, indeed, whoever carefully examines the effects,
either of the damps of mines, or of thofe fulminating damps, that
are raifed from fome metals, when in fufion, or when they are
difTolving in acids, will rather be inclined to think, that the force
of inflamed vapours is fo far from exceeding the proportion of five
to one, that it falls confiderably fhort of it.

But though we fhould fuppofe that this proportion holds good,
where {hall we find a place capable of containing a fufficient quan-
tity of fuch a vapour, to produce the great effedts of earthquakes ?
It will be faid, perhaps, in fubterraneous caverns. To this we
may anfwer, that he, who is but moderately acquainted with the
ftru&ure of the earth, and the materials of which it is compofed,
will be little inclined to allow of any great or extenfive caverns in
it. But, though this fhould be admitted, how can it come to pafs
that thefe caverns fhould not be filled with water ? If it is alleged,
that the water is expelled, as the vapour is formed, why fhould
not the vapour, as it is fuppofed to be the lighter, be expelled,
rather than the water, by the fame paflages by which the water is
to be expelled ? But let us fuppofe this difficulty alfo to be got
over, and the water to be removed, and we fhall then have a gage
for the denfity of the vapour ; for it muff be juft fufficient to make
it capable of fuftaining a column of water, whofe height is equal
to that of the furface of the fea above the bottom of the cavern, in
which the vapour is fuppofed to be contained. Now, fince the
mean weight of earth, ftones, &c. is not lefs than two and a half
times the weight of water, this vapour muft be incrcafcd to two
and half times its original elafticity, before it can, in any wife,
raife the earth above it; and if we fuppofe it to be increafed to five
times its original elafticity, it will then be no more than twice able
to do fo ; in which cafe, fo much vapour only can be chfeharged
from the cavern, to produce an earthquake, as is equal to the

content

[ 597 ]

motions will be brought about, let us fuppofe the
roof over fome fubterraneous fire to fall in. If this
fhould be the cafe, the earth, Hones, &c. of which
it was compofed, would immediately link in the
melted matter of the fire below : hence all the water
contained in the fi (lures and cavities of the part fall-
ing in, would come in contad: with the fire, and be
almoft infbantly railed into vapour. From the firft
effort of this vapour, a cavity would be formed (be-
tween the melted matter and fuperincumbent earth)
filled with vapour only, before any motion would be
perceived at the furface of the earth : this mull ne-
ceffarily happen, on account of the * comprelfibility

content of the cavern : and what mud the fize of that cavern
be, which could contain vapour enough to produce the earthquake
of the ift of November 1755, in which an extent of earth of near
three thoufand miles diameter was conliderably moved ? or how can
we fuppofe, that the roof of fuch a cavern, when fo violently
(liaken, fhould avoid falling in? efpecially, as it is hardly to be
fuppofed, that any inflamed vapour whatfoever fhould be able to
move the earth over thefe caverns, if they lay at any great depth,
fince the weight of lefs than three miles depth of earth is capable
of retaining the inflamed vapour of gunpowder within the original
dimenfions of the gunpowder itfelf ; and common air, comprefled
by the fame weight (fuppofing the known law of its compreflion to
hold fo far), would be of greater denfity than water.

We may afk {fill farther, whence fuch vaft quantities of vapour
fhould be formed, or what fources they muff be, which would
not be exhaufted (if they were not again replenifhed) by a very few
repetitions of fuch immenfe difeharges.

* The compreflibility and elafticity of the earth, are qualities
which don’t fhow themfelves in any great degree in common in-
ftances, and therefore are not commonly attended to. On this
account it is, that few people are aware of the great extent of
* them, or the effects that may arife from them, where exceeding
large quantities of matter are concerned, and where the compref-

4 H 2 five

[ 59§ ]

of all kinds of earth, ftones, &c. but as the com*
preffion of the materials immediately over the cavity,

would

jive force is immenfely great. The compreflibility and elafticity
of the eaith may be collected, in fome meafure, from the vibration
of the walls of houfes, occafioned by the pafllng of carriages in the
ftreets next to them. Another inftance to the fame purpofe, may
ne taken from the vibrations of fteeples, occafioned by the ringing
of bells, or by gufts of wind: not only fpires are moved very con-
fiderably by this means, but even ftrong towers will, fometimcs, be
made to vibrate feveral inches, without any disjointing of the mor-
tar, or rubbing of the {tones againft one another. Now, it is ma-
mfeft, that this could not happen, without a conftderable decree of
compreflibility and elafticity in the materials, of which they arty
compofed : and if fuch fmall things as the weight of fceeples, and
the motion of bells in them, or a guft of wind, are capable of pro-
ducing fuch effe&s, what may we not expert from the weight of
great depths of earth ? There are fome circumftances, which feem
to make it not altogether improbable, that the form and internal
ftrudfure of the earth depend, in a great meafure, upon the com-
preffibility and elafticity of it. There are feveral things that feem
to argue a confiderably greater denfity in the internal, than the ex-
ternal part of the earth; and why may not this greater denfity be
owing to the compreflion of the internal parts arifmg from the
weight of the fuperincumbent matter, fince it is probable, that
the matter, of which the earth is compofed, is pretty much
of the fame kind throughout ? There is a ftill ftronger ar-
gument for the earth’s owing its form, in fome meafure, to
the fame caufe ; for it is found to be higher [fee the French
accounts of the meafures of a degree of the meridian in France,
Sweden, and America] at the equator, than at the poles, in a
greater proportion than it would be on account of the centrifugal
force, if it was of uniform denfity ; but, if we fuppofe the earth
to be of lefs denfity in an equatorial diameter than in the axis, the
whole will then be eafily accounted for, from the riftng of the earth
a little by its elafticity, the weight being in part taken off by the
diurnal rotation : and that the earth is really a little denfer in the
axis, than in the equatorial diameter, feems highly probable, from
the experiments of pendulums compared with aftronomical obferva-
tions ; for the forms of the earth derived from thefe, cannot be

reconciled

[ 599 ]

would be more than fufficient to make them bear the
weight of the fuperincumbent matter, this compref-
fion mull be propagated on account of the elafticity of
the earth, in the fame manner as a pulfe is propa-
gated through the air ; and again the materials im-
mediately over the cavity, reftoring themfelves be-
yond their natural bounds, a dilatation will fucceed to
the compreffion j and thefe two following each other
alternately, for fome time, a vibratory motion will be.
produced at the furface of the earth. If thefe alter-
nate dilatations and compreftions fhould fucceed one
another at very fmall intervals, they would excite a.
like motion in the air, and thereby occafion a con-
fiderable noife. The noife that is ufually obferved-
to precede or accompany earthquakes, is probably
owing partly to this ca-ufe, and partly to the grating
of the parts of the earth together, occafioned by that
wave-like motion before-mentioned.

5-7. After the water, that firft came in contact
with the fire, has formed a cavity, all the reft of the
water contained in the fi ftures, immediately commu-
nicating with the hollow left by the part that fell in,.

reconciled with each other, but upon this fuppofition. [See Mac-
laurin’s Fluxions, art. 681, fcfc.] It appears, from fome late and
accurate obfervations, that the ^equatorial parts of the planet Jupiter
alfo, as well as thofe of the earth, are a little higher than they would
be, if their rife was owing to the centrifugal force, and he was of.
uniform denfity ; but if we fuppofe him to be of lefs denfity in the
aequatorial, than the polar regions, then the form may be fuch as
he would afturne from the refpedlive gravitation of the feveral parts ;
and any fluid like our ocean, would not overflow the polar parts,
(which, upon any other fuppofition, it mud neceflarily do) hut
would follow his general form, as our ocean does that of the
sarth.

£

mu ft.

[ 600 ]

muft run out upon the fire, the fleam taking its
place. From hence may be generated a vaft quantity
of vapour, the effedts of which Shall be confidered
prefently. This fleam will continue to be generated,
fuppofing the fire to be fufficiently great, till the fif-
fures before-mentioned are evacuated, or till the wa-
ter begins to flow very flowly ; when the fleam al-
ready formed will be removed by the elafticity of
the earth, which will again fubfide, and, prefling
upon the furface of the melted matter, will force it
up a little way into all the clefts, by which the water
might continue to flow out. By this means, all com-
munication between the fire and the water will be
prevented, excepting at thefe clefts, where the water,
dripping flowly upon the melted matter, will gra-
dually form a cruft upon it, that will foon ftop all
farther communication in thefe places likewife; and
the fiflures, that had been before evacuated, will be
again gradually replenifhed by the oozing of the water
between the ftrata.

58. As a fmall quantity of vapour almoft inftantly
generated at fome considerable depth below the fur-
face of the earth, will produce a vibratory motion,
fo a very large quantity (whether it be generated al-
moft inftantly, or in any fmall portion of time) will
produce a wave-like motion^ The manner in which
this wave-like motion will be propagated, may, in
fome meafure, be reprefented by the following expe-
riment. Suppofe a large cloth, or carpet, (Spread
upon a floor) to be railed at one edge, and then
Suddenly brought down again to the floor, the air
under it, being by this means propelled, will pafs
along, till it efcapes at the oppofite fide, railing the

cloth

[ 601 ]

doth in a wave all the way as it goes. In like man-
ner, a large quantity of vapour may be conceived to
raife the earth in a wave, as it paffes along between the
ftrata, which it may eafily feparate in an horizontal
direction, there being, as I have faid before, little or
no cohefion between one ftratum and another. The
part of the earth that is firft railed, being bent from
its natural form, will endeavour to reftore itfelf by
its elafticity, and the parts next to it beginning to
have their weight fupported by the vapour, which
will infinuate itfelf under them, will be raifed in their
turn, till it either finds fome vent, or is again con-
denfed by the cold into water, and by that means
prevented from proceeding any farther.

59. If a large quantity of vapour fhould continue
to be generated for fome time, feveral waves might
be produced' by it; and this would be, in fome mea-
fure, the cafe, if the quantity at firft generated was
exceedingly great, though the whole of it was gene-
rated in lefs time, than whilft the motion was propa-
gated through the diftance between two waves.

60. Thefe waves muft rife the higher, the nearer
they are to the place from whence they have their
fource ; but, at great diftances from thence, they
may rife fo little, and fo flowly, as not to be per-
ceived, but by the motions of waters, hanging branches
in churches, &c.

61. The vibratory motion occafioned by the firft
impulfe of the vapour, will be propagated through
the folid parts of the earth, and therefore, it will
much fooner become too weak to be perceived, than
the wave-like motion ; for this latter, being occa-
fioned by the vapour infinnating itfelf between the

ftrata, .

[ 602 ]

drata, may be propagated to very great didances-;
and even after it has ceafed to be perceived by the
the fenfes, it may dill difcover itfelf by the appear-
ances before-mentioned.

Sect. IV.

62. All earthquakes derived from the fame fub-
terraneous fire, mud come to the fame place in the
fame direction ; and thofe only which are derived
from different fires, will come from different points
of the compafs ; but as, in all probability, it feldom
happens that earthquakes, cauled by different fires,
affed the fame place, we therefore find in general,
that they come from the fame quarter : it is not,
however, to be fuppofed, that this diould always be
the cafe, for it will, probably, fometimes happen to
be otherwife : and this is to be expeded in fuch
places as are fituated in the neighbourhood of feveral
iubterraneous fires; or where, being fubjed to the
fhocks of fome local earthquake of fmall extent, they
now and then are affeded by an earthquake, produced
by fome more didant, but much more confiderable
caufe. Of this lad cafe, we feem to have had fome
indances in the earthquake of the id of November
1 7ff, and thofe local ones, before-mentioned, which
fucceeded it.

63. As we may reafonably infer from many earth-
quakes coming to the fame place, from the fame point
of the compafs, that they are all derived from the
fame caufe, and that a permanent one; fo we may
reafonably infer the fame thing all'o, from their being
propagated with the fame velocity ; but this argu-
ment will dill come with the greater force, if it be

conlidered.

[ 6o3 ]

-conMered, that the velocity of any vapour, which
infinuatcs itfelf between the firata of the earth, de-
pends upon the depth of it below the furface 5 for
the deeper it lies, the greater will be its * velocity.
We may therefore conclude, from the famenefs of the
velocity of the earthquakes of the fame place, that
the caufe of them lies at the fame depth) and from
the inequality of the velocity of the earthquakes of
different places, that their caufes lie at different
depths. Both thefe are perfectly confident with the
fuppofition, that earthquakes owe their origin to fub-
terraneous fires, fince the firata in which thefe fuhfift,
may be eafily conceived to lie at different depths in
different parts of the world.

Sect. V.

64. From the fame caufe, we may eafily account
for thofe local earthquakes, which fucceed the greater
and more ex ten five ones. If there are many fubter-
raneous fires fubfifting in different parts of the world,
the vapour coming from one fire may very well be
fuppofed, as it paffes, to difturb the roof over fome
other fire, and, by that means, occafion earthquakes
by the falling in of fome part of it : and this may be
the cafe, in fome meafure, even where the vapour
paffes at fome fmall difiance over the fire ; but it will
be mofi likely to take place, where the vapour either

* The velocity of fuch a vapour, depending intirely upon the
elafticity of the earth which is over it, will be, catsris paribus , (if I
am not miftaken) in the ratio of the depth below the furface. This
feems to follow from a known law of all elaftic bodies, according
to which they tend to return to their ftate of reft, when either di-
lated or comprefled, with forces proportionable to the quantity by
which they differ from their natural bounds.

Vol.LI. , 4 1 paffes

[ 6°4 ]

pafiss at feme diftance under it, or between the

iatum, in which the fire lies, and that next above-
or below it.

PART HI..

Sect. I.

6f. TN the former part of this trad, I fuppofed'*
part of the roof over fome fubterraneous fire
to fall in . this is an event that cannot happen merely
accidentally • tor fo long as the roof refts on the mat-
ter on fire, no part of it can fall in, unlefs the matter
elow could rife and take its place : now, it is very
difficult to conceive how this ffiould happen, unlefs it
was to rife by fome larger palfages than the ordinary
finures of the earth, which feem much too narrow
for that purpofej for, befides that the melted matter
cannot be fuppofed to have any very great degree of
fluidity, it mufl neceffarily have a hard cruft formed:
upon it, at all the fiffures, by the long continued con-
tad of the water contained in them : thefe impede
ments feem too great to be overcome by the difference
of the fpecific gravities of the part that is to fall in,
and the melted matter, which is the only caufe that
can tend to make it defcend j the manner therefore,
in which, I fuppofe, this event may be brought
about, is as follows :

66. The matter of which any fubterraneous fire is
compofed, mufl be greatly * extended beyond its ori-
ginal

. j al! bodi?s we are acquainted with are liable to be ex-
tended by heat, there can he no doubt of its being fo in this cafe

likewife

[ 6o5 3

ginal dlmenfions by the heat. As this will be brought
about gradually, whilft the matter fpreads itfelf, or
grows hotter, the parts over the fire will be gradually
raifed and bent ; and this bending will, for fome
time, go on without any other confequence ; but, as
the fire continues to increafe, the earth will at laft
begin to be raifed fomewhat beyond the limits of it.
By this means, an annular fpace will be formed at the
edges next to the fire, and furrounding it, a vertical
lection of which fpace, through a diameter of the
fire, will be two long triangles, the fiiortefi: fide or
bafe of each lying next the fire, and the two longer
fides being formed by the upper and lower ftrata,
which will be feparated for a confiderable extent,
proportionably to the diftance through which they
are raifed from each other * *. This fpace will be

gradually

likewife; but the matter of fubterraneous fires is yet much more
extended, than thofe bodies which are only capable of being melted
into a folid glafs, if we may judge of it from what we fee of vol-
canos ; for the lavas, fciari, and pumice ftones, thrown out from
thence, even after they are cold, are commonly of much lefs fpe-
cific gravity, on account of their porous fpongy texture, than the
generality of earth, ftones, &c. and they frequently are even
lighter than water, which is itfelf lighter than any known foflil
bp dies, that compofe ftrata in their natural ftate.

* In Fig. 4. A is fuppofed to reprefent a vertical feffion of the
matter on fire ; B B, parts of the fame ftratum yet unkindled ;
C C, the two feftions of the annular fpace, (furrounding the fire)
which is fuppofed to be filled with water, as far as the ftrata are
feparated ; D, the feveral fijts of earth, ftones, dSV. lying over
the fire, which are raifed a little, and bent, by the expanlion of
the matter at A. As it is not eafy to reprefent the things above
defcribed in their due proportions, it may not be amifs, in order to
prevent the figure here given from mifleading the reader, to give
fome random meaftjres of the feveral parts, fucb as may probablv

4 1 2 approach

[ M ]

i

gradually filled with water, as it is formed, the
melted matter being prevented from filling it, by
its want of fluidity, as well as on account of the
other circum fiances, under which it is to fpread.
itfelfj for the lentor and fluggifhnefs of this kind
of matter is inch, that, when fomewhat cooled on
the furface by the contad of the air only, it will not
flow, perhaps, ten feet in a month, though in a very
large body ; infiances of which we have in the lavas ,
of fEtna, Vefuvius, &c. It is not to be expcded
tnen, that it fhould i oread tar, when it comes in con-
oid with water at its edges, as foon as it is formed,
and when it is, perhaps, feveral months in acquiring
a thicknefs of a few inches ; but it muff, by degrees,
form a kind of wall between the fire and the open-
ing into the annular fprxe befpre defcribed. This
wall will gradually increafe in height, till it becomes
too tall in proportion to its thicknefs, to bear any
longer the preflure of the melted matter ; which

approach towards thofe which are fometimes found in nature : we
may fuppofe then the flratum B to he, perhaps, from ten or twenty
to a hundred yards in thicknefs; the greateft height of the annular
fpace next the fire, to be from four or five to ten or fifteen
feet, and its greateft extent, horizontally, from ten or twenty to
fi!ty or fixty feet; the horizontal extent' of the fire at A, may be
from half a mile to ten or twenty miles ; [See art. 29. and the note
to art. 5 3. ] and the thicknefs of the fuperincumbent matter at D,
may be from a quarter or half a mile to two or three miles ; the
number of tne lamin;e a!fo, into which it is divided, may he many
times more than thofe in the figure. As to the perpendicular
fiffures, they muff be fo numerous, and fo fin all, in proportion
to the other parts, that I chofe rather to leave them, to be fupplied
by the imagination of the reader, than attempt to exprefs them in a
manner, that could give no adequate idea of them at all.

mull

C 6o7 ]

mud neceflfarily happen at laft, becaufe the thick-
ness of it will not exceed a certain * limit.

67. Befides the giving way of this wall, the fire
may undermine the lpace containing the water, and,
by that means, open a communication between them.
Let us fuppofe one of thefe come to pafs, and the
time arrived when the partition begins to yield. If
then the water had any way to efcape readily, the
breach would be made, and the melted matter would
burd: forth immediately, and flow out in large quan-
tities at once amongft it j but as this is not the cafe,
and it can only efcape by oozing flowly between the
Strata, and through the fl flares, the way that it came,
the breach will be made gradually, from whence we
may account for Some appearances that have preceded
great earthquakes.

68. We are told, that two or three days before
an f earthquake in New England, the waters of Some
wells were rendered muddy, and flank intolerably

T his limit will depend upon the thicknefs of the matter necef-
fary to prevent fo quick a communication of the heat or cold
through it, as that the water (hould be able to diminifh the heat
of the lire confiderably. The thicknefs requifite to do this, is very
different in different kinds of bodies. Metals of all kinds tranfmit
heat and cold extremely readily ; but bricks and vitrified fubftances
(witii wmch laft we may clafs the matter under our prefent confi-
deration) tranfmit them very flowly : the walls of the hotteft of our
furnaces, when built of bricks, and eighteen inches thick, will not
tranfmit more heat than a living animal can bear without injurv,
though the fires are continued in them for ever fo long a time •
probably, therefore, if we allow two feet for the thicknefs of the
matter, cooled and rendered hard by the contact of the water, we
/hall not underdo it.

t See Philo f. Tranf. N° 437. or Martyn’s Abridgm. vol. viii.
p. 689.

why

[ 608 J

why might not this be occafioned by the waters con-
tained in the fpaces before defcribed, which, being
impregnated with fulphureous fleams, were driven
up, and mixed with the waters of the fprings ? At
leall, theie can be no doubt, by whatfoever means it
was bi ought about, that this phenomenon was owing
■to .the fame caufe, already beginning to exert itfelf,

which afterwards gave rife to the fucceeding earth-
quake.

69. Something like this happened before the
great Lilbon * earthquake of 1755. We are
told, that at -Colares, about twenty miles from
thence, “ in the afternoon preceding the ift of No-
vember, the water of a fountain was greatly de-
creafed : on the morning of the ifl of November,
it ran very muddy, and after the earthquake, it re-
turned to its ufual flate, both in quantity and clear-
nefs.” The fame author fays, a little lower, « in
the afternoon of the 24th, I was much apprehen-
five, that the following days we fhould have an-
other great earthquake; for I obferved the fame

“ prognoftics as in the afternoon of the 31ft Odlober;

that is,” &c. “ And I farther obferved, that the

“ water of a fountain began to be diflurbed to fuch
a degree, that in the night it ran of a yellow clay
<c colour; and from midnight to the morning of the
25th, I felt five (hocks, one of which feemed to
me as violent as that of the 1 ith of December.”

70. But the mod extraordinary appearance of any
»that preceded this earthquake, was that of the agita-

* S-PhUof. Tranf. vol. xlix, p. 416 and 417.— or Hift. and
Fhilof. of Earthq. p. 313.

tion

6

r 6o9 ]

tion of the waters of * * Lochnefs, and feme others of
the lochs in Scotland, about half an hour before any
motion was felt at Litbon, notwithftanding the caufe
of all thefe great effefts could not lie far from thence,
and, I think, certainly lay to the fouth of Oporto-
Nor is it probable, that there fliould be any-miftake
in the time, not only becaufe the difference is too
great,, as well as the concurrent teftimonies too many,
to admit of fuch a folution ; but becaufe they men-
tion another greater agitation, that happened about
an hour and half after the former j. which latter agrees
with the times, when the agitations of the waters-
were obferved in England, if we allow only a proper
interval for the motion to be propagated fo far north-
ward, proportionably to the time it took up in tra-
velling from its original fource near Lifbon.

71. Thefe appearances feem to be connected with
that mentioned in the preceding article, and they
may both, I think, be accounted for, by fuppofing
a confiderable quantity of vapour to be raifed^
whillt the partition before-mentioned was begin-
ning to give way • during which time, a partial

arc TSee PhiIof- Tranf- vol. xlix. — or Hift. and Philof. of Earthq;

* i,r ^le&’ fJ°Ch0rf m°nd’ &c- The thing alfo fee ms
to have taken place in Switzerland ; for Monf. Bertrand fays, that

■3 1 k n xTf th£ ?'aterS in the lakes there’ which were ob-

ferved on the ift November 1755, happened between nine and tea

tat Jn rr,llngi PrartlcularJy at lake Leman, he fays, the agU
on happened juft before ten ; which, allowing for the difference
of longitude muff have been juft before nine at Lifbon; and con-

Preceded “ u° m,ft£ke in the times» a11 thefe agitations

preceded the earthquake, at this laft place, by near three quarters

iTr cT' fSeC Memoircs fur les trembkmens de Terre, p. ic7

commum-

[ 610 ]

communication between the water and fire would be
brought on, and that by degrees only. Hence the
vapour, not being produced at once but gradually,
might creep * filently between the ffrata, towards
that quarter where the fuperincumbent mat's of earth
was lighted: ; and, by this means, fome places very
near the fource of the vapour might be little, or not
at all, affected by it, whilft others might be greatly
affsdted, though they lay at a great diftance ; and
even thofe places, which lay immediately over the
part where the vapour was paffing, might not per-
ceive any effedt, on account of the gentienefs of the
motion, occafioned by the fmall quantity of it. This
might continue to be the cafe, till it came to fome
country where, the fet of ftrata above being much
thinner, the vapour would not only be hurried for-
ward, but collected alfo into a much narrower com-
pafs; and therefore, raffing the earth more, would
produce more fenfible effedts j and this we ought

* Some appearances that have been obferved in New England
feem to confirm this, and make it probable, that a fmall quantity
of vapour is often found to creep filently between the ftrata, before
a general communication between the water and the fire gives rife
to the greater and more fenfible efFedts of earthquakes. See Philof.
T'ran f. N° 462. or Martyn’s Abr. vol. viii. p. 693. where we are
told, that, at Newbury, a little before any noife or fhock was per-
ceived, the bricks of an hearth were obferved to rife, and, falling
down again, to lean another way. In the fame account, it is alfo
faid, that “ a few minutes before any fhock came, many people
“ could foretell it by an alteration in their ftomachs:” an effeft,
which feems to be of the fame kind with fea-ficknefs, and which
always accompanies the wave-like motion of earthquakes, when it
is fo weak, as to be uncertainly diftinguifhable.

chiefly

I 611 i

chiefly to expert in the moft mountainous countries,
according to the idea before given of them *.

72.. To make this fomething clearer, let us fup-
pofe, in Fig. 1. the vapour to be pafllng between
the ftrata in the dotted line C, and to go forwards,
till it ai lives at A : whilft, then, it pafles under the
deeper parts at E, it will raife the earth over it but
little, as well becaufe it will be fpread broader and
thinner, as becaufe it will be more compreffed by the
weight of the fuperincumbent matter; but as it ar-
lives towards A, not only the latter part will be
driven forwards with greater velocity, but the fore-
mod will travel flower, on account of its travelling-
under a f thinner fet of ftrata ; and, befides this, the
load being much lefs, it will greatly expand itfelf.
From all thefe caufes taken together, the wave at the
iuiface of the earth, occafioned by the palling of the
vapour under it, will not only be much higher, but
alfo much fhorter, and, confequently, the tides of it,
on both thefe accounts, will be much more inclined
to the honzon . and, moreover, becaule the pro°Tefs
of the wave will be flower, it will give more time to
any waters fituated on one fide of it, to flow one
way ; and on this account alfo, the apparent agitation

of them will be increafed.

\

Sect. II.

73. We are told, that, in the Lifbon earthquake
of 1777, “ the bar [at the mouth of the Tagus] was
“ feen dry from fhore to fhore ; then fuddenly the fea.

* See art. 43.
f See art. 63. the note.

Vol. LI,

«

i c

like

t * * * 612 ]

tc like a mountain, came rolling in ; and about Bel-
<c lem caftle, the water rofe fifty feet almofl: in an
<c inftant ; and, had it not been for the great bay
“ oppofite to the city, which received and fpread
<c the great flux, the low part of it muft have been
<c under water The fame phenomena were ob—
ferved to accompany the fame earthquake at the Aland
of Madeira ; where we are told, that, at the city of
Funchal, “ the fea, which was quite calm, was ob-
“ ferved to retire fuddenly fome paces ; then rifing
“ with a great fwell, without the leafl: noife, and as
<£ fuddenly advancing, it overflowed the fhore, and*
“ entered the city. It rofe full fifteen feet perpen-
“ dicular above high-water mark, although the tide,
“ which ebbs and flows there feven feet, was then
<c at half ebb. In the northern part of the Aland,
te the inundation was more violent, the fea retiring
<c there above one hundred paces at firff, and fud-
<c denly returning, overflowed the fhore, forcing
“ open doors, breaking down the walls of feveral-
tc magazines and ftorehoufes, and carrying away, in
<£ its recefs, a confiderable quantity of grain, and
“ fome hundred pipes of wine •f*.”

74. Both thefe appearances (which have been
obierved to attend feveral other earthquakes, as
well as this) feem to admit of an eafy folution, fup-
pofing the caufe of them to lie under the bed of the
ocean ; for, in the farther progrefs of the communi-
cation between the fire and water, the vapour, that is

* See Hift. and Philof. of Earthq. p. 316.

t See Philof. Tranf. vol. xflx. p. 432, &f<\— - or Hift. and Philof.

Of Earthq. p. 329.

6 gradually

[ 6i3 ]

gradually raifed at firft, will at lad begin to raife the
roof over the fire, which, being fupported by lb light
a vapour, there will now be no want of fiuidity in the
matter it reds upon, and the difference of fpecific
gravity between the two, indead of being fmall, will
be very great : hence, if any part of the roof gives
way, it mud: immediately fail in, the vapour readily
rifing, and taking its place; and a beginning being
once made, a communication will be opened with
numberlefs clefts and fiffures, that mud occafion the
falling in of vad quantities of matter, which, as foon
as the vapour can pafs round them, will want their
fupport ; then will follow the great * effects already
defcribed.

75. Now, whild the roof is railing, the waters of
the ocean, lying over it, mud retreat, and flow from
thence every way ; this, however, being brought
about flowly, they will have time to retreat fo gently,
as to occafion no great didurbance : but as foon as fome
part of the roof falls in, the cold water contained in
the fiflures of it, mixing with the deam, will imme-
diately produce a vacuum, in the fame manner as
the water injedted into the cylinder of a deam engine,
and the earth fubfiding, and leaving a hollow place
above, the waters will flow every way towards it,
and caufe a retreat of the fea on all the fhores round
about : then prefently, the waters being again con-
verted by the contadl of the fire into vapour, together
with all the additional quantity, which has now an
open communication with it, the earth will be raifed,
and the waters over it will be made to flow every

* See art. 56 to 60 inclufive.

4K 2

wa\v

0 9

\

[ 6i4 ]

way, and produce a great wave immediately fucceed-
ing the previous retreat

Sect. III.

76. That great quantity of water, which we have
iuppofed to be let out upon fubterraneous fires, and,,
by that means, to produce earthquakes, will fupply
us with a reafon, why they obferve a fort of periodi-
cal return. This water muff extinguish a great por-
tion of the burning matter, in confequence of which,
it will be contracted within much narrower bounds ;
and though the eftedts before defcribed could not
take place at fir ft, but by the great extenfion of the
heated matter, yet, after they have once taken place,.

* It may, perhaps, be objected, that thefe phaenomena may asf
eafily be occafioned by a vapour generated under the dry land,
which, by firft raifing the earth upon the fea-fhore, would make
the waters retreat ; and that the return of them again, upon its
fubfiding into its place, might caufe the fubfequent wave. That
this may be the cafe, in fome inftances, is not impoffible, but, I
believe, upon examining the particular circumftances, it will ge-
nerally be found to,be otherwise; and there cannot be any doubt
about it, in the cafe of the Lifbon earthquake; for the retreat was
obferved to precede the wave, not only on the coaft of Portugal,
but alfo at the ifland of Madeira, and feveral other places : now,
if the retreat had been caufed by the raifing of the earth on the
coaft of Portugal, the motion of the waters occafioned by this
means, when propagated to Madeira, muft have produced a wave
there previous to the retreat, contrary to what happened ; nor
could the motion of the waters at Madeira be caufed by the earth-
quake at that place, becaufe it did not happen till above two hours
after; whence it is manifeft, that it muft have been owing to the
continuation of a motion propagated from the place, where the
earthquake exerted its firft efforts. And we may obferve, in gene-
ral, that this muft always be the cafe, whenever the retreat does
not happen till fome confiderable time after the earthquake.

[ 6i5 ]

they may well continue to do fo for fome time j for
the great difturbance in the firft inflance, by the
falling in of a great part of the roof, rauft render the
frequent communication between the fire and water
not only very eafy, but almoft unavoidable : and this
will continue to be fo, till the roof is well fettled,
and the furface of the melted matter fufficiently
cooled, after which, it may require a long time for
the fire to heat it again fo much, as will be neceffary
to make it produce the former effedts. Now, as the
matter has been more or lefs cooled, or as the com-
buffible materials are with more or lefs difficulty fet
on fire again, as well as on account of other circum-
ffances, the returns of thefe effedts will be later or
earlier j but though they will not, for this reafon,
obferve any exadt period, yet they will generally fall
within fome fort of limits, till either the matter that
occafions them is confumed, (which, probably, will
feldom happen in lefs than many ages) or till the
fires open themfelves a paffage, and become vol-
canos.

Sect. IV.

77. I have already intimated, that the mod: exten-
five earthquakes frequently take their rife from the
fea. According to the description of the * ffrudture
of the earth before given, any combuftible ftratum
muff lie at greater depths in places under the ocean,
than elfewhere; hence far more extenfive fires may
fubfift there, than where the quantity of matter over
them is lefs ; for any vapour raifed from fuch fires.

* See art. 43.

having

[ 616 ]

having both a ftronger roof over it, and being prefled
by a greater weight, (befide the additional weight of
the water) will not only be lefs at liberty to expand
itfelf, and confequently of lefs bulk, but it will alfo
be eafily driven away towards the parts round about,
where the fuperincumbent matter is lefs, and there-
fore lighter. On the other hand, any vapour raifed
from fires, where the fuperincumbent matter is
lighter, finding a weaker roof over it, and being not
fo eafily driven away under flrata, that are thicker
and heavier, will be very apt to break through, and
open a mouth to a volcano ; and it muff neceflarily do
this long before the fires can have fpread themfelves
fufficiently, to be near equal to thofe which may
fubfift in places that lie deeper. All this feems to
be greatly confirmed by the fituation of volcanos,
which are almoft always found on the * tops of
mountains, and thofe often fome of the highefl in
the world.

78. If, then, the largefl fires are to be fuppofed
to fubfift under the ocean, it is no wonder that the

* Perhaps this may fupply us with a hint (if the conjecture is
not thought extravagant) concerning the manner in which thefe
mountains have been raifed, and why the ftrata lie generally more
inclining from the mountainous countries, than thofe countries
themfelves ; an appearance not eafily to be accounted for, but
upon the fuppofition, that the upper parts of the earth reft upon
matter, in fome degree, though not perfectly fluid, and that this
matter is lighter than the earth that refts upon it. ^ his conjecture,
however, will probably be thought lefs ftrange, if it be confldered,
that the new iflands, formed about Santerini and the Azores, have
fome of them been raifed from 200 to 300 yards, and upwards ; a
height which might well enough intitle them to the denomination
of mountains, if they had been raifed from lands not lying under
the, ocean. [See Fig. 3.]

molt

[ 6 1 7 ]

mod extenfive earthquakes fhould take their rife from
thence : the great earthquake of Lifbon has been
* fhewn to have done fo 3 and that the caufe of it was
alfo at a greater depth, than that of many others, ap-
pears from the greater -f* velocity with which it was
propagated.

79. The great earthquake that deftroyed Lima
and Callao in 1746, feems alfo to have come from
the fea 5 for feveral of the ports upon the coaft were
overwhelmed by a great wave, which did not arrive till
four or five minutes after the earthquake began, and
which was preceded by a J retreat of the waters, as
well as that at Lifbon. Againfi: this, it may, perhaps,
be alleged, that there were four || volcanos broke out
fuddenly, in the neighbouring mountains, when this
earthquake happened, and that the fires of thefe
might be the occafion of it. This however, I think,
is not very probable 5 for, to omit the argument of
the wave, and previous retreat of the waters, already
mentioned, it is not very likely, that more than one
fire was concerned : befides, the vapour, opening it-
felf a paflage at thefe places, could not well be fup-
pofed, if it took its rife from thence, to fpread itfelf
far 5 efpecially towards the fea, where it is manifeft.

* See art. 54. See alfo art. 94 to 97 inclufive,

+. See the note to art. 63..

% Both the wave and previous retreat have been obferved in the
other great earthquakes, which have happened at Lima, and in the
neighbouring country. See d’Ulloa’s Voyage to Petu, part ii,
book i. chap. 7.

|| If thefe volcanos were not new ones, but only <51d ones which
broke out afrelh, [See the note to art, 34. ] the argument will come
with ifill greater force,

that

,[618]

that the firata over it were of great thicknefs, as ap-
pears from the great velocity with which the earth-
quake was propagated there: the (hocks alfo con-
tinued with equal, or nearly equal violence, for fome
months after the openings were made ; whereas, if
thefe fires had been the caufe of them, they mufi
immediately have ceafed, upon the fires finding
a vent, as it has happened in other * cafes. It is
therefore much more probable, that a very large
quantity of vapour, taking its rife from fome far
more extenfive fire under the fea, fpread itfelf from
thence; and as it pafled in places, where the roof
over it was naturally much thinner, as well as greatly
weakened by the undermining of thefe fires, it opened
itfelf a pafiage, and burft forth.

80. As the moft extenfive earthquakes generally
proceed from the lowed; countries, but efpeciallv
from the fea, fo thofe of a fmaller extent are gene-
rally found amongfi the mountains: hence it almofi
always happens, that earthquakes, which are felt near
the fea, if at all violent, are felt alfo in the higher
lands; whereas there are many amongfi; the hills,
and thofe very violent ones, which never extend
themfelves to the lower countries. Thus we are
told, that, at Jamaica, “ •f* (hakes often happen in
“ the country, not felt at Port-Royal ; and fome-
<c times are felt by thofe that live in and at the foot

* See art. 28.

t This is taken from an account of the earthquake that hap-
pened at Jamaica in the year 1692, which, as well as fome others
before- mentioned, was attended with the wave and previous re-
treat. See Philof. Tranf. N° 209. or Lowthorp’s Abr, vol. ii.
p. 417 and 418.

“ of

[ 6i9 3

ec of the mountains, and by no body elfe.” On the
other hand, the earthquake that deftroyed Port-
Royal extended itfelf all over the ifland : and the
fame was obferved of a fmaller earthquake, that hap-
pened there in 1687-83 which latter undoubtedly
came from the fea, as appears by Sir * Hans Sloane’s
account of it.

8 1 . Earthquakes of fmall extent are alfo very com-
mon amongft the mountains of Peru and Chili. An-
tonio d’Ulloa fays, “ Whilft we were preparing for
** our departure from the mountain Chichi-Choco,

<c there was an earthquake which was felt four
“ leagues round about : our field tent was tolled to
<( and fro by it, and the earth had a motion like
“ that of waves ; this earthquake, however, was
<c one of the fmalleft, that commonly happen in that
“ country.” The fame author tells us, in- another ’
place, that, “ during his ftay at the city of Quito,

“ or in the neighbourhood of it, there were two
“ earthquakes, violent enough to overturn fome
“ houfes in the country, which buried feveral perfons
“ under their ruins.”

Sect. V.

82. It is generally found, that earthquakes in hilly
countries, are much more violent than thofe, which
happen elfewhere; and this is obferved to be the
cafe, as well when they take their rife from the
lower countries, as amongfi: the hills thernfelves.
This appearance being fo eafily to be accounted for,
from the firudture of the earth already deferibed, I

*

See Phil. Tranf. N° 2C9, or Lowthorp’s Abr. vol. ii. p. 410.

V o l. LI. 4 L Ifiall

[ 620 ]

fliall content myfelf with eftablifhing the certainty of
a facft, which tends fo greatly to confirm it.

83. The earthquakes that have infefted fome of
the^owns in the neighbourhood of Quito, have not
only been incomparably more violent than that which
deftroyed Lifbon, but they feem to have exceeded
that alfo which deftroyed Lima and Callao. In
* Lifbon, many of the houfes were left Handing,
although few of them were lei's than four or five
ftories high. At Lima alio, it is only faid, that <c all
“ the buildings, great and fmall, or at leaft the
“ greateft part of them, were deftroyed.” Callao
likewife, as it appears from the accounts we have of
it, had many houfes left unhurt by the earthquake,
till the wave came, which overwhelmed the whole
town, and threw down every thing that lay in its
way. All thefe effedls feem to be greatly fhort of
thofe produced by an earthquake that happened at
Latacunga, in the year ] 6pS, when the whole town,
confifting of more than fix hundred houfes, was en-
tirely deftroyed in lefs than three minutes time, a
part of one only efcaping; notwithftanding that the
houfes there are never built more than one ftory high,
in order, if poftible, to avoid thefe dangers. Am-
bato, a village about the fame fize as Latacunga, to-
gether with a great part of Riobamba, another town
in the ‘ fame neighbourhood, were alfo entirely de-
ftroyed by the fame earthquake, and fome others
were either deftroyed, ©r received confiderable damage

* See Philof. Tranf. vol. xlix. p. 403. where it is faid, “ ot
“ the dwelling-houfes, there might be about one fourth of them
“ that tumbled.”

from

[ 62i ]

from it. At the fame time, a volcano burft out fud-
denly in the neighbouring mountain of Carguayrafo,
as before-mentioned ; and, cc near Ambato, the earth
“ opened itfelf in feveral places, and there yet re-
« mains, to the fouth of that town, a cleft of four
tc or five feet broad, and about a league in length,
<c lying north and fouth; there are alfo feveial other
“ like^clefts on the other fide of the river.” The city
of * Quito was affedted at the fame time, but re-
ceived no damage, though it is no more than fort\~
two geographical miles from Latacunga, not tai from
whence the greateft violence of the £hock feems to
have exerted itfelf. Thefe towns are fuppofed. to
Hand by far the highefl of any in the world, ^being
as high above the level of the fea, as the tops or fomc
of the highelf mountains in Europe; and the giound
upon which Riobamba Hands,. wants but f ninety
yards of being three times as high as Snowdon, the
higheH mountain in Wales.

84. The country upon which thefe towns Hand,
ferves as a bafe, from whence ariie another fet of
hio-h lands and mountains, which are much the
higheH in the known world. Amongft thefe moun-
tains there are no lefs than fix volcanos, if not moie.

* The city of Quito {lands lower than the level of Riobamba,
by about 500 yards perpendicular. Though it efcaped t is, 1
has lately, however, been deftroyed by another violent earthquake,

that happened on the 28th April 1756, of which I have no ye

feen any other particulars worth notice. . r

f This is according to Antonio d’Ufloa’s account ; hut Monf.
Condamine makes it exadly three times the height of Snowdon,
computing it at 1770 toifes. [See his meafure of a degree o
meridian.] . .

4L 2 within

[ 622 ]

within an extent of 120 miles long, and lefs than
thirty broad, the loweft of which exceeds the height
of Riobamba by above two thirds of a mile, and the
higheft by more than twice that quantity. Now, as
the earthquakes have been more violent at the foot of
thefe mountains, than in the lower lands, fo they
have been ftill more violent towards the tops of them :
this is lufficiently manifeft, from the many * rents
made in them, and the rocks that have been broken
oft from them, upon fuch occafions : but it appears
ftill more manifeftly, and beyond all difpute, in the
burfting forth of volcanos, which are almoft always
at the very fummit of the mountains, where they
are found. In thefe inftances, the earth, ftones, &c.
which lay over the nre, are generally fcattered by the
violence of the vapour, that breaks its way through,
to the diftance of iome miles round about.

8y. The great earthquake of the 1 ft November
1 7fS» was a’i'° more violent amongft the mountains,
than at the city of Lifbon. We are told, that “ the
“ mountains of Arrabida, Eftrella, Julio, Marvan,
and Cintra, being fome of the largeft in Portugal,

“ were impetuoufly fhaken, as it were, from their
** very foundations; and mod of them opened at
“ their fummits, fplit and rent in a wonderful man-
“ ner, and huge maftes of them were thrown down
<c into the fubjacent vallies J.”

* See d’Ulloa’s Voyage to Peru, part i. book vi. chap. 2.
t 1 he only exceptions that I know of to this rule, are in thofq.
cafes, where the higheft part having an opening already, fome
frefli mouth opens itfelf in the fide of the mountain.

X See Hift. andPhilof. of Earthq. p. 317.

86. The

[ 62 3 ]

86. The fame was obferved at Jamaica likewife.
In the earthquake that deftroyed Port-Royal in 165)2,
we are told, that “ more houfes were left Handing
“ at that town, than in all the ifland belides. It was
“ fo violent in other places, that people were violently
tc thrown down on the ground, where they lay with
“ their legs and arms i'pread out, to prevent being
“ tumbled about by the incredible motion of the
“ earth. It fcarce left a planter’s houfe or fugar-

work ftanding all over the ifland : I think it left
<c not a houfe ftanding at Palfage fort, and but one
“ in all Liganee, and none in St. lago, except a few
“ low houles, built by the wary Spaniards. In Cla-
“ rendon precindt, the earth gaped, and fpouted up,
“ with a prodigious force, great quantities of water
“ into the air, twelve miles from the fea ; and all
“ over the ifland, there were abundance of openings
“ of the earth, many thoufands. But in the moun-
<{ tains, are faid to be the moll violent lhakes of allj
<c and it is a generally received opinion, that the
“ nearer to the mountains, the greater the fhake ;
“ and that the caufe thereof, whatever it is, lies
“ there. Indeed they are llrangely torn and rent,
<c efpecially the blue, and other highell mountains,
<e which feem to be the greatell fufferers, and which,
“ during the time that the great drakes continued,
“ bellowed out prodigious loud noifes and echo-
“ ings.

87. <c Not far from Ya Howes, a mountain, after
“ having made feveral moves, overwhelmed a whole
“ family, and a great part of a plantation, lying a
“ mile off ; and a large high mountain near Port-

“ moran t.

41 [ 6a+ ]

“ morant, near a day’s journey over, is faid to be
£f quite fvvallowed up.

88. “ In the blue mountains, from whence came
<£ thofe dreadful roarings, may reafonably be fup-
££ pofed to be many flrange alterations of the like
££ nature; but thofe wild defart places being very
<£ rarely, or never vifited by any body, we are yet
££ ignorant of what happened there ; but whereas
££ they ufed to afford a fine green profpedt, now one
££ half part of them, at lead:, feem to be wholly de-
££ prived of their natural verdure

Sect. VI.

89. I have fuppofed, that fires lying at the greatefl
depths generally produce the moil extenfive earth-
quakes, we muft, however, except from this rule
thofe cafes where the depths are very great : for, as
the weight of three miles perpendicular of common
earth is capable of abfolutely reprefiing the vapour of
inflamed gunpowder, fo we may well fuppofe, that

* See Pbilof. Tranf. N° 209. or Lowthorp’s Abridg. vol. ii.
p. 416, where there is a great deal more to the fame purpofe.
See alfo Hift. and Philof. of Earthq. p. 286 and 287.

From the authorities quoted in this fe£tion, it appears, how
little reafon there is for the notion, that either large cities, or
towns fituated near the fea-coaft, are more fubjeit to violent
earthquakes than others : it is not, however, much to be won-
dered at, that fuch a notion fhould have prevailed, after the great
deftrudtion that happened in fo large and populous a city as Lifbon ;
fince the demolition of a few ruinous houfes only, in fuch a place,
would have affe&ed the imaginations of men more, and would
have been more talked of, than the fubverfion of whole mountains
in fome wild and defart country, where at moft half a dozen un-
known fhepherds might feel the effects of it, or perhaps only fee it at
a diftance.

there

C 625 ]

there may be a quantity of earth fufhcient to reprefs
the vapour of water, and keep it within its original
limits, though ever fo much heated. Now, when-
ever this is the cafe, it is manifeft, that it can pro-
duce no effeCt : or, it may happen, that though the
quantity of earth may not be fufhcient abfolutely to
reprefs the vapour, yet it may be fo great, as to fuffer
it to expand but very little : in this cafe, an earth-
quake arifing from it would be but of fmall extent j
the wave-like motion would be little or nonej the
vibratory motion would be felt every-where ; and
the propagation of the motion would be very quick.
Th is laft circumftance being almoft the only one,
by which thefe earthquakes can be known from thofe
which owe their origin to fhallower fires, it muff be
very difficult to diftinguifh them with certainty, as
it is almoft impofiible to diftinguifh the difference of
the time of their happening in different places, when
the whole, perhaps, is comprehended within the fpace
of two or three minutes ; poflibiy, however, fome of
the earthquakes, which we have had in England, may
have been of this clafs.

Sect. VII.

90. If we would inquire into the place of the ori-
gin of any particular earthquake, we have the fol-
lowing grounds to go upon.

5>i. Firfti The different directions, in which it
arrives at feveral diftant places : if lines be drawn in
thefe directions, the place of their common inter-
section muft be nearly the place fought : but this is
liable to great difficulties ; for there muft neceffarily
be great uncertainty in observations, which cannot, at

C 626 ]

beft, be made with any great precifion, and which arc
generally made by minds too little at eafe to be nice
obfervers of what paffes j moreover, the directions
themfelves may be l'omewhat varied, by the inequali-
ties in the weight of the fuperincumbent matter, un-
der which the vapour paffes, as well as by other
caufes.

92. Secondly , We may form fome judgment con-
cerning the place of the origin of a particular earth-
quake, from the time of its arrival at different places ;
but this alfo is liable to great difficulties. In both
thefe methods, however, we may come to a much
greater degree of exadtnefs, by taking a medium
amongft a variety of accounts, as they are related by
different obfervers. But,

93. Thirdly , We may come to the greatest degree
of exadtnefs in thofe cafes, where earthquakes have
their fource from under the ocean ; for, in thefe in-
ftances, the proportional diftance of different places
from that fource may be very nearly afeertained, by
the interval between the earthquake and the fucceed-
ing wave: and this is the more to be depended on,
as people are much lefs likely to be miftaken in de-
termining the time between two events, which fol-
low one another at a fmall interval, than in obferving
the precife time of the happening of fome fingle
event.

94. Let us now, by way of example, endeavour
to inquire into the fituation of the caufe, that gave
rife to the earthquake of the iff of November lyff,
the place of which feems to have been under the
ocean, fomewhere between the latitudes of Lifbon
and Oporto, (though probably fomewhat nearer to

[ 627 ]

the former) and at the diftance, perhaps, of ten or
fifteen leagues from the coaft. For,

95. Firji , The direction, in which the earthquake
arrived at Lifbon, was from the north-weft ; at Ma-
deira it came from the north-eaft ; and in England
it came from the fouth-weft ; all of which perfectly
agree with the place aflumed *.

9 6. Secondly , The times in which the earthquake
arrived at different places, agree perfectly well alfo
with the fame point. And,

97. Thirdly, The interval between thefe, and the
time of the arrival of the fubfequent wave, concur in
confirming it. That all this might appear the better,
I have fubjoined the following table, affuming the
point, from whence I compute, at the diftance of
about a degree of a great circle from Lifbon, and
a degree and half from Oporto. In confequence of
this fuppofition, I have added three minutes to the
interval between the time when the fliock was felt
at Lifbon, and at the feveral other places. The firft:
column in the table contains the names of places ;
the fecond, the diftances from the aflumed point,
reckoned in half degrees ; the third, the time that
the earthquake took up in travelling to each, ex-
preffed in minutes ; and the fourth contains the time
in which the wave was propagated, from its fource to
the refpedtive places, exprefled in minutes likewife.

* All thefe dire&ions, together with the times when the earth-
quake, as well as the fucceedirg wave, arrived at different places,
(two or three only excepted) are taken from the 49^ volume of the
Philof. Tranf. and the Hift. and Philof. of Earthq. To thefe, I
muft refer the reader for the particular authorities, which, as they
are very numerous, I was not willing to quote at length.

V ol. LI. 4 M

Lilbon

Lifbon * - - -

Oporto * - -

Ayamonte -
Cadiz - - -

Madrid -
Gibraltar -
Madeira - - -

Mountfbay - -

Plymouth
Portfmouth - -

Kingfale
Swanfea -
The Hague - -

Lochnefs -
Antigua - - -

Barbadoes - -

[ 628 ]

Half deg.

Min.

-

-

2

3

-

-

3

5

mm mm

-

6

-

-

9

12

-

-

9

1 1

-

-

1 1

18

-

-

1 9

25

-

-

20

-

-

21

-

••

23

29

-

-

23

-

-

24

%m —

-

30

32

-

-

33

66

-

-

98

-

-

IOI

Min.
I 2

53

82

152

267

360

290

53°

565

485

98. In computing the times in the preceding table,
allowance was made for the difference of longitude,
as it is laid down in the common maps, which are

'* It appears, by all the accounts, that the interval between the
earthquake and wave, either at Oporto or Lifbon, was not long :

I have met with no account yet, however, which tells us how long
it was at the former, and only one which mentions it at the latter,
where it is faid to have been nine minutes. [See Memoires fur Us
iremblemens de Terre , p. 245. compared with Hift. of Earthquakes,
P- 3* I5<] Thefe intervals, if we knew them exadlly, might have
ferved, perhaps, to afeertain the diftance of thofc two places from
the original fource a little more accurately ; but, as the diflance of
neither from thence could be very great, a fmall difference in them
would hardly fenfibly affedt any of the others ; from which, there-
fore, we may draw the fame general conclufions, as if they were
♦■xadt.

not

[ 6z9 3

not always greatly to be depended on. The times
thernfelves alio are often fo carelefly obferved, as
well as vaguely related, that they are many of them
fubjedt to coniiderable errors ; the concurrent telli-
monies, however, are fo many, that there can be
no doubt about the main point ; and, that the errors
might be as frnall as poffible, I have not only en-
deavoured to feledt thole accounts that had the sxeatefl

m O

appearance of accuracy, but, in all cafes where it was
to be had, I have always taken a mean amongfl them.
In many of the accounts, the relaters fay only be-
tween fuch hours, or about fuch an hour: of this
kind were the accounts of the times of the agitation
of the waters at The Hague and Lochnefs, which
vary the moll from a medium of the reft, the former
erring about feven minutes in defect, and the latter
about twenty minutes in excels ; with regard to
the latter, however, I mull obferve, that, from the
account itfelf, it is probable the agitation happened
fooner than eleven o’clock, which is the time men-
tioned. The accounts alfo of the time of the agita-
tion of the waters in the northern parts of England,
feem to confirm the fame thing *.

5?p. It is obfervable, in the preceding table, that
the times, which the wave took up in travelling, are

* As the Ihorteft way that the vapour could pafs from near Lifoon
to Lochnefs was under the ocean, poffibly it might, on that ac-
count, be fomewhat retarded ; for the wTater adding to the weight
of the fuperincumbent mafs, and not to its elafticity, muft produce
this effecl in fome degree; it is probable, however, that this could
make no great difference, as the motion feems to have been very
little retarded in its paffage from the original fource to Madeira, to
which place, I fuppofe, it muft have paffed under deeper feas than
would be found in its road to Scotland.

4M 2

not

[ 630 3

not in the fame proportion with the diftances of the
refpe&ive places from the fuppofed fource of the
motion ; this, however, is no objection againft the
point affumed, fince it is manifeft, wherever it was,
that it could not be far from Lifbon, as well becaufe
the wave arrived there fo very foon after the earth-
quake, as becaufe it was fo great, riling, as -we are
told, at the diftance of three miles from Lifbon, to
the height of fifty or fixty feet. The true reafon of
this difproportion, feems to be the difference in the
depth of the water ; for, in every inftance in the above
table, the time will be found to be proportionably
fhorter or longer, as the water through which the
wave palTed was * deeper or fhallower. Thus the
motion of the wave to Kingfale or Mountfbay (through
waters not deeper in general than 200 fathoms) was
flower than that to Madeira, (where the waters are
much deeper) in the proportion of about three to
five ; and it was flower than that to Barbadoes,
(where its courfe lay through the deepefl part of the
Atlantic ocean) nearly in the proportion of one to
three : fo likewife the motion of it from the Scilly
iflands to Swanfea in Wales (where the depth gra-
dually diminifhes from about fixty or feventy fa-
thoms to a very fmall matter) was fill flower than
that to Kingfale, in the proportion of lefs than one
to three : the fame thing is obfervable with regard to

* We have an inftance to this purpofe in the tides, which, in
deep waters, move with a velocity that would carry them round
the whole earth in a Tingle day; but as they get into fhallower
waters, they are greatly retarded : and we are told, that in the
river of Amazons, the fame tide is found running up to the tenth
or twelfth day, before it is entirely fpent. [See Condaminc s Voyage
down the Mara non.]

Plymouth

[ 631 ]

Plymouth alfo, where the wave arrived about ninety
minutes later than at Mountfbay, though the difference
of their diftance from the firft fource could not, upon
any fuppofition, be more than forty or fifty miles.

Sect. VIII.

ioo. If we would inquire into the depth, at which
the caufe lies, that occafions any particular earth-
quake, I know of no method of determining it, which
does not require obfervations not yet to be had j but
if fuch could be procured, and they were made with
fufficient accuracy, I think fome kind of guefs might
be formed concerning it : for,

i o i , Firji , In thofe inftances, where the vapour
difcharges itfelf at the mouths of volcanos, (as in the
cafe of the earthquake at Lima) it might, perhaps,
be poffible for a careful obferver to trace the * thick-
nefs of the feveral ftrata from thence to the place
where the earthquake took its rife, or at lead; as far
as the fhore, if it took its rife from under the fea.
If this could be once done in any one inftance, and
the velocity of fuch an earthquake nicely determined,
we might then guefs at the depth of the caufe in
other earthquakes, where we knew their velocity, by
taking the ft* depths proportional to thofe velocities,
which probably would anfwer very nearly.

102. Secondly, If, in any inftance, it fhould be
poffible to know how much the motion of any earth-
quake was retarded by palling under the ocean, the

* This is upon the fuppofition, that the under ftrata, in afcend-
ing up the hills, come to the day in the manner before defcribed.
See art. 43. and Fig. 3.
t See the note to art. 63.

depth

[ 63 2 ]

depth of the ocean being known, the depth at which
the vapour pafled would be known alfo ; for the ve-
locity under the water would be to the velocity, if
there had been no water, in the fubduplicate ratio of
the weight in the latter cafe to the weight in the
former ; hence allowing earth to be about two and
half times the weight of water, the depth will be
•readily found.

io3 • thirdly. Let us conceive the earth to be
termed according to the idea before given of it, and
that tiie fame ffrata are at a medium of the fame
thicknefs for a very great extent, as well in thofe
places, where feveral of the upper ones are wanting,
as where they are not. Upon this luppofition, we
ina> on cover the depth, at which the vapour paffes,
by coinparing the feveral velocities of the fame earth-
quake in places, where the * thicknefles of the fuper-
incumbent mafs are different. It mult be acknow-
deged, indeed, that fuch obfervations with regard to
time, as would enable us to determine thefe veloci-
ties, are in general much too nice to be expeded :
the matter, however, is not altogether defperate, as
we may colled: them, in fome meafure perhaps, from
other circumffances, fuch, for inffance, as the degree
of f agitation in different waters, the proportional
t fuddennefs, with which the earth is lifted in dif-
ferent places, &c.

104. As

* In order to know this difference, it will be neceflary to trace
the thicknefs of thofe ffrata, which are found in fome of the places
but are wanting in others. r

t See art. 71 and 72.

r ,i/hlS n?ay ,be known from the diftance to which the mercury
fublides in the barometer, upon the firft raifing of the earth by the

vapour.

C 633 ]

104. As the obfervations relating to the earthquake
of the 1 ft of November 1755 are too grofs, it would
be in vain to attempt, by any of the foregoing me-
thods, to determine with any certainty the depth at
which the caufe of it lay ; but, if I might be allowed
to form a random guefs about it, I fhould fuppofe,
(upon a comparifon of all circumftances) that it could
not be much lefs than a mile, or a mile and half, and
I think it is probable, it did not exceed three miles.

CONCLUSION.

105. Thus have I endeavoured to lhew how the
principal phenomena of earthquakes may be pro-
duced, by a caufe with which none, that I have feen,
appear to me to be incompatible. As I have not
knowingly mifreprefented any fad:, fo neither have I
defignedly omitted any that appeared to affed the main
queftion ; but, that I might not unneceffarily fwell
what had already much exceeded the limits at frit in-
tended for it, I have omitted,

106. Fir//, Thofe minuter appearances, which
almoft every reader would ealily account for, from
what has been laid already, and which did not feem
to lead to any thing farther : inch, for inftance, are
the fudden Hopping and gufhing out of fountains, oc-
casioned by the opening or contrading of fiftures; the
dizzinefs and ficknefs people feel, from the almoft
imperceptible wave-like motion, &c.

vapour. I don’t find, that this phenomenon, which is a common
attendant on earthquakes, was obferved any-where, at the time of
the earthquake of the ift of November 1755, except at Amfter-
dam, where the mercury fubfided more than an inch. See Hift.
and Philof. of Earthq. p. 309.

107. dV-

V

[ 63+ ]

107. Secondly , Thofe appearances which feemed
to depend upon particular circumftances, and of
which, therefore, unlefs we had a more exaCt know-
lege of the countries where they happened, it would
have been impoffible to give any account, without
having recourfe to uncertain conjectures ; of this kind,
was the greater agitation of the waters in the lakes of
Switzerland, at the time of the earthquake of the ift
of November 175*5:, than during the * earthquake of
the 9th of December following, though the houfes
upon the borders of them were more violently fhaken
by the latter. And,

108. Laftly , Thofe appearances, which only feem
to have an accidental connection with earthquakes, or
the caufes of them ; of this kind, are the effeCts which,
in fome inftances perhaps, they produce on the wea-
ther ; the diftempers which are fometimes faid to fuc-
ceed them ; the difturbance which, we are told, they
have fometimes occalioned, during the fhocks, in the
direction of the magnetic needle, &c. none of which
are obferved to be conftant attendants on earthquakes,
nor do they feem materially to affeCt the folution given
either one way or other.

* See Monfieur Bertrand’s Memoires fur Us tremblemens de
Terre.

LVI. An

C 63S ]

LVI. An Extra & of a Letter from Abbe De
la Caille, F. R. S. and Member of the
Royal Academy of Sciences at Paris, to
Matthew Maty, M. D. and F. R. S .

Paris, Feb. 18, 1760.

’LL venture to fend yon fome of my
obfervations on the prefent comet,
becaufe bad weather may have prevented it from
being feen in England.

Read March 6,
1760.

I

Feb. 8.

Equal time.

h / //

Longitude.

0 1 n

North latitude.

0 / //

3 26 42

9 29 28

SI 20 17 22

9-

8 48 50

l8 49 l8

4 46 28

1 1.

7 22 35

16 5 3

7 -i4 fo

7 47 4

14 43 21

8 24 18

14*

641 0

12 20 l8

10 30 9

Thefe obfervations, together with another made
at Marfeilles, (on the fird day) at 911 55' 38" equal
time, when the longitude of the comet was found in
Si 230 29' 46", and its north latitude 31' 20", have
enabled me to compute the elements of its orbit.
Its motion is diredt. The afcending node is in
1 p° 42' o ', and the place of the perihelion in
26° 41' 22". The inclination of the orbit is
8o° 5T 30", and the didance of the perihelion JUJJJL
of the radius of the orbit of the earth. The comet
paffed the perihelion Nov. 25, 1759, at 2°b 55*
mean time, at Paris. Thefe computations will be
further improved by the obfervations I dill hope to
make; but they are fudicient to find the comet’s
place in the heavens.

V 0 l. LI, 4 N

LVII. Ex-

[ 636 ]

LVII. ExtraS} s of fome Letters from Signor
Abbatc de Venuti, F. R. S. to J. Nixon,
A. M. and F. R. S. relatmg to feveral
Antiquities in Italy.

Dear Sir,

Rome, Sept. 27, 1759.

Read March 20, — .
1760.

SOME days ago a fire accidentally
broke out, where the Antonine
column lay, near the Curia Innocenziana on Monte
Citorio. It burnt the wooden props or fcaffolding,
which fupported the column, and did fuch confider-
able damage to the column itfelf, by caufing its fur-
face to fhell off, that it will be very difficult to fet it
up, if any attempt fhould be made for that purpofe
hereafter.

A certain Greek epigram, lately dug up at Naples,
relating to a boy, has occafioned feveral grammatical
altercations among the literati in that part of the
world ; and thefe again have produced fome fmart
lampoons and fatirical writings on each fide of the
quefiion.

Many lingular fiatues and relievos, lately difco-
vered, have been fet up in the gardens of Cardinal
Albani, without the Porta Salaria. Thefe, if you
were among us, would afford a very agreeable enter-
tainment to your curiofity.

LETTER

[ 63 7 ]

LETTER II.

Rome, Dec. 31, 1759.

. — I have already met with fome differtations of
Mr. Swinton, which fhew his acute judgment, and
excellent learning in the oriental languages; and
therefore, I do not question his accuracy in treating
of the epocha of the Sidonians. Your extradd of his
eflay upon that fubjedt has induced me to examine
fome coins ifampt at Sidon, which I think it need-
lefs to defcribe, as the world is already in poffeffion
of their hiftory. However, I have taken particular
notice of one of that kind, of the fmalleft fize, which,
I think, has never been publifhed. It exhibits the
trunk of a palm-tree, or rather the laferiptium of
Cyrene, with this legend, OJ7 On the reverfe,

there is a caldron, or vafe, with thefe letters round
it, If Mr. Swinton thinks this

com will be of any fervice to him in his inquiry, I
will fend a more exad copy of it.

I come now (in compliance with your requefl) to
give you fome infcriptions lately dug up among the
ruins of antient Rome.

The firft was difcovered without the Porta Latina,
two miles from the city, and runs thus :

LIBERTI. LIBERTAE
PRISCI. AVG. L. GAMIANI
EX. TESTAMENTO. DESCRIPTV. ITA. VT
CAVTVM. ERAT. SVBSCIPSER
M)CVS. MONIMENTI. SIVE. AGER. EST. VIA. LATIN
AD. MILLIARIVM. V. SVPRA. PONTEM. AD
MONIMENTVM. GAME CAESARIS. AGATHOCLIAN

4 N 2 DO.

[ 638 ]

DO. LEGO. LIBERTIS. MEIS. VTRIVSQVE. SEXSVS
POSTERISQVE. EORVM. ET. IIS. QVOS. MANV
MITTI. ROGAVI. IBIQVE. TABERNAM. FIERI.
INQVE. EAM. REM. CONSVMI. HS. N.
ARBITRATV. AGATHANGELI. COLLIB.

II.

The fecond is in my pofleflion ; and is as follows :

D. M.

SOTER. SERVOS. PVBLICVS.
CASTELLAR. AQVAE. ANNIONIS
VETERIS. FECIT. CONGVGI. BENE
MERENTI. ET. L. CALPVRNIVS
FLAVIANVS. MATRI. BENE K
MERENTI. SIBI. ET. SVIS
POSTERISQVE. EORVM.

III.

On a Hermes, without a head.

D. M. V. F.

SEX. SAMNIVS
SEX. F. VVLTVR
APER.

DOMO. NEMAVSO
IIIIVIR. IVREDICVND
PONTIFEX. PVBLICORV
SACRIFICIORVM
PRAEFECTVS. VIGILVM
ET. ARMORVM.

IV.

On the bafis of a ftatue dreffed in a toga, are the
following letters ;

EVENTIVS
P. D. S. C.

I have

[ 639 ]

I have lately bought a relievo, which, in my opi-
nion, is very lingular. It is of marble, two palms
wide, and one high, and reprefents, in a neat tafte,
a Faun, with a tail, and wings j which latter circum-
ftance has never occured to my obfervation before.
He feems to be dancing, and his dog at his feet is in
the fame attitude. Near him is a tree, to which is
tied a very elegant open chariot, ( thenfa ) and beneath
it there appears a table, fuch as are ufed in entertain-
ments, with a goblet upon it, charged with relievo
in embolfed work.

I have likewife, a few days ago, met with a cor-
nelian, on which was engraved a man cloathed with
a pallium, and fitting on a chair : before him there
appeared a lighted furnace, and upon it a veflel of
glafs, or earthen ware. The artift himfelf held in
his hand a pair of iron pincers, with handles, to take
off the veflel from the fire, without burning himfelf.
They demanded ten fequins for it, which I thought
too great a price, and therefore did not purchafe it.

Remarks on the preceding Extra&s ; in a
Letter to Charles Morton, M. D. Secre-
tary to the Royal Society : By John Nixon,
A. M. F. R. S.

Dear Sir,

Kead March 27, T Heg leave, in purfuance of my pro-
mife, to tranfmit to you fome ob-
fervations, which tend, in my opinion, to illuftrate
the preceding extracts of the Abbate de Venuti’s let-
ters to me.

The

[ 640 ]

The column, mentioned in Letter I. is of red
granite, and was dug up (together with its pedeftal)
by Clement XI. out of the ruins on Monte Citorio,
yl. D. 1705. Innocent XII. intended to have let it
up ; but the great damage it had fuftered in clearing
the rubbilh from it, hindered that defign from being
effected.

In 174.5, Benedict XIV. removed it from the
Piazza di Monte Citorio to its prefent lituation on the
fame hill, and alfo caufed the pedeftal, that belonged
to it, to be eredted where it now hands, being the
fpot deligned for it by his predecellors, mentioned
above.

The relievi on the lides of the pedeftal refer to
the apotheofis of Antoninus Pius; as the infeription
fhews, that the column was eredted to the memory
of that emperor by M. Aurelius (ftiled in this, as in
fome other antient monuments *, Antoninus) and
L. Verus, his adopted fons, and alfociates in the go-
vernment.

Letterll. infcript.2. 1. 2. — SERVOS. PVBLICVS.]
i. e. One of thole officers, who were to atteft the fign-
ing of all public inftruments — Cen fores extemplo jam
atrium libertatis afeenderunt , et ibi Jignatis tabelhs
public is, claufoque tabulario , et dimijjis Jervis public! s,
negarunt J'e prius quidquam negotii public i gefturos ,
quam judicium populi de J'e jaclum efet. Liv. Hift.
1. xliii. c. 16. A. U. 584. Vid. Marcell. Donat, in
loc.

* Vid. Bianchim apud Vafi delle Magnif. di Rcma, lib. ii.
p. *3> J4*

[ 64i ]

L. 3. — CASTELLAR.] For explaining this title,
it is to be obferved, that the refervoirs, which re-
ceived the waters brought by aqueduds into the city
of Rome, were called caftella.

■Agrippa in cedilitate Jua adjeftd virgine aqua , c ce-
teris corrivatis atque emendatis , lacus feptingentos
fecit: prceterea falientes centum quinque-, castella
centum triginta , complura etiam cultu magnifica.
Plin. Hift. Nat. 1. xxxvi. c. 15.

There are ftill extant very confiderable remains of
fome of thefe caftellai viz. that of Aqua Claudia at
Porta Maggiore ; and another of Aqua Marcia, com-
monly called I Trofei di Mario, near Sto Eufebio in
Rome.

From hence it is obvious to colled, that the office
of the caflellarius was to fuperintend the public refer-
voirs above-mentioned, to diftribute the waters in due
proportion into the feveral quarters of the city,
Fabretti has preferved an infcription, relating to one
of thefe officers, viz. the cajtellarius of the Aqua
Marcia. Fid. Bianchini apud Vafi delle Magnif. di
Roma , lib. i. ^.31.

lb. L. 3. — AQyAE. ANNIONIS. VETER IS.]
This water was brought to Rome A. U. 481. It
was taken up from the Anio, or Teverone, above
Tibur, (Tivoli) about twenty miles from Rome, and
entered the city by the fame aquedud, which con-
veyed the Aqua Appia, near the Porta Capena (Sto
Sebaftiano). From thence it palled along between
M. Aventinus and Caslius, to the end of the Vicus
Publicius, near the modern Scola Greca, where it
had its refervoir contiguous to that of the Aqua Appia

above-

[ 642 ]

above-mentioned. M. Angel. Rojjt Roma Antic a,
p. 229. 231.

The epithet vetus diftinguifhes this water from that
of the Anio nevus , which was brought to Rome from
the diftance of fixty-two miles, by the emperor Clau-
dius, in the twelfth year of his reign, about A. U. 803,
as appears from an infcription in Vafi, lib. i. p. 32.
To which we may add the testimony of Suetonius —
(Claudius) Rivum Anienis novi lap idee opere in urbem
perduxit , divijitque in plunmos et ornatijjimos lacus .
Suet. Claud, c. xx.

Infcript. 3. 1. 7, 8. — PONTIFEX. PVBLICO-
RV. SACRIFICIORVM.] If this title implies the
fame as that of the Sacerdotes Publici in Livy, it
comprehended the feveral orders of Pontifex Maxi-
mus, Pontifex, Augur, Decemvir Sacrorum, &c .
Liv. Hift. lib. xxv. c. 2. xxvi. 23. xli. 2 1, &c. But
to which of thel'e clafles SAMNIVS, mentioned in
this infcription, belonged, we cannot determine.

lb. 1. 9. — PRAEFECTVS. VIGILVM.] Some
writers refer the firlf inftitution of a night-watch, for
the fafeguard of the city of Rome from fires, to Au-
gufius. Augujlus adverfus incendia excubias noSlur-
nas , vigilefque commentus ejl. Suet. Aug. c. xxx.

E.7raSv ’tv t co ^povoj 'tutcc'^ Cum €0 te?npore rnulta
effent in urbe incendiis vafiata , libertinos J'eptem locis
t idea curanda injlituit (Auguflus). Dion. Calf. 1. lv.
A. U. 759. But Livy mentions an office fubfifiing
in Rome, in the time of the republic, as early as
A. U. 449, viz. the Triumviratus noElurnus, (Liv.
HifL lib. ix. c. 46. ) which mud have been the

fame

[ 6+3 ]

fame in effect with that defcribed above : for it mud
have been undoubtedly the province of thofe Tri-
umviri to prevent all manner of diforders and acci-
dents in the night, efpecially that mod: calamitous
one of fires. This conclufion, in general, refults
from the nature of things ; as the particular circum-
flance relating to fires may be collected from Tacitus.
— Triumviri , quod ad incendium in Jacrd via orturn
tarde venerant , d tribuno plebis die dibid damnati.
[Tac. apud Godeler. not. in Liv. fupra.] Now, in
order to reconcile thefe accounts, in fome degree, we
may fay, that, as the inhabitants of Rome were be-
come more numerous and wealthy, and (confe-
quently) more licentious, in Auguftus’s time, that
emperor found it requifite to new model the night-
watch, by making feveral additional improvements
in it, with regard, probably, to the number and con-
dition of the perfons, of whom it confided ; the qua-
lity of the officer, who prefided over it ; the appoint-
ment of the proper places of rendezvous in the mod
commodious parts of the city, & c. And, upon ac-
count of thefe regulations made by Auguftus in the
night-watch, fome hiftorians may have been induced
to conlider him as the founder of this police in the
city of Rome.

I am,

J. Nixon.

Vol, LI.

+0

LVIII. A

[ 644 ]

LVIII. A Catalogue of the Fifty Plants from
Chelfea Garden, prefented to the Royal
Society by the worf hipful Company of Apo-
thecaries , for the Tear 1759, purfuant to
the DireElion of Sir Hans Sloane, Baronet ,
Med. Reg. & Soc. Reg. nuper Prcefes , by
John Wilmer, M. D. clariff. Societatis
Pharmaceut. Lond. Socius , Hort. Chelfean.
Pr&fe&us & PrceleElor . Botanic .

Rcad^March z7> 7 1 8 f i /l CER foliis trilobis integerri-
S f~\ mis. Flor.Leyd. Prod. 459.

Acer trifolium. C. B. P. 431.

1852 Alfine marina foliis portulacas. FI. Pruff*. P. 12.

Ic. 2.

Anthyllis maritima centifolia. C. B. P. 282.

Alfine centifolia, feu Alfine cruciata marina.

Ger. Emac. 622.

1853 After foliis lanceolatis acutis fcabris, caule fim-

plici, floribus umbellatis terminalibus. Did:.

Hort.

After ramofus annuus Canad. Mor. Hift.

I^54 Azalea ramis infra flores foliofis. Flor. Virg.

iSyy Brafiica foliis infiinis ovato-lanceolatis, ferrato-

dentatis, fummis linearibus integerrimis.

18 56 Bromos panicula nutante, foliis utrinque fub-

pilofis, glumis ciliatis. Lin. Sp. PI. j6.

1 8 57 Calendula foliis obverfe ovatis denticulatis, caule

fruticofo perenni. Flor. Leyd. Prod. 531.

i8y8 Ceralus foliis ovatis. Virg. Hort. Cliff*. 43.

Cerafus

5*

[ 645 3

Cerafus Sylveftris amara Mahaleb putata. I.

1.227.

i8yp Chelidonium maximum Canadenfe acaulon
Cornuti.

Sanguinaria. Hort. Eltham*

1860 Clematis compofitis et decompofitis foliolis

ternatis ferratis. Gmel.

1861 Clematis purpurea repens, petalis florum co

riaceis. Banifter.

1862 Crataegus ; folio fubrotundo, ferrato, fubtus in-

cano. Aria multis. Tourn. 633.

1863 Crataegus; Cerali folio, floribus magnis. Am-

man. Ruth. 274.

1864 Crataegus ; folio laciniato. Tourn. 633.
Sorbus torminalis. Dod. 803.

1 86 5 Dens canis latiore; rotundioreque folio, flore
ex purpura rubente. C. B. 87.

1 866 Elymus fpica eredta, fpicula involucro lorn*

giore. Hort. Upfal. 22*

1867 Erigeron foliis bafi revolutis. Lin. Sp. PL 863.
Senecio Bonarienfis purpurafcens, foliis imis

coronopi. Hort. Eltham. 344.

1868 Eruca latifolia, alba fativa, Dofcoridis. C. B.

98. OfHcin. i8f.

1869 Euonymus floribus omnibus quinquefidis. Lin«

Sp. PI. 197.

Euonymus Virginianus pyracanthae foliis, cap-
ful a verrucarum inftar exafperata. Pluk.
Almag. 139.

1870 Gypfophylla foliis lanceolato-linearibus obfo-

lete triquetris laevibus obtulis. Lin. Gem
noY. 1103.

4O z

Saponaria

[ 646 ]

Saponaria petalis ovatis, foliis glaucis pulpofis.
Hall. Jen. 1 17.

1871 Hypericum foetidum frutefcens maj us. Tourn.
Hypericum frutefcens Canarienfe multiflorum.

Hort. Amft.

1872 Hypericum foetidum frutefcens. Tourn.
Tragium legitimum veterum. Ponas Baldo 88.

1873 Hypericum orientale fcetido fimile fed inodo-

rum. T. Cor.

1874 Jafminum foliis lanceolatis oppofitis integerri-

mis calvcibus acutioribus. Miller’s Icons.

*

1 875 Ixia planifolia, caule multiflora, fpatha brevif-

fima. Miller.

1876 Lunaria major) filiqua rotundiore. I. B. 2.

881.

1877 Lycopus foliis asqualiter ferratis. Lin. Sp.

Plant. 2 1.

Lycopus foliis lanceolatis tenuiflime ferratis.
Flor. Virg. 8.

1878 Majorana rotundifolia fcutellata exotica. H. R.

Par.

1875) Ortega. Laefl. epift. viii. Lin. Sp. PI. 560.
Juncaria Salmatica. Cluf. Hifl. 1. P. 174.

1880 Ofteofpermum foliis oppofitis palmatis. Lin.
Chryfanthemum perenne Virginianum maj us

platani folio orientale. Mor. Hifl:.

1881 Oxalisfcapo umbellifero, foliis ternatis biparti-

te. Lin. Sp. PI. 434.

Oxalis bulbofa pentaphylla et hexaphylla, flo-
ribus magnis luteis et copiofis. Burman.
Plant. Afric. 80.

1882 Peucedanum Germanicum. C. B. P. i4P*

Mor. Umb, 36.

Fceniculum

[ 6+7 ]

Foeniculum porcinum. Lobel. Adverf. 350.

1883 Potentilla foliis bipinnatis, fegmentis integer-

rimis diftantibus fubtus tomentofis, caule
decumbente. Lin. Sp. PI. 496.
Pentaphylloides fupinum minus, folio glabro
non ferrato. Amman. Ruth. 1 16.

1884 Robiniapedunculis fimplicifhmis, foliis abrupte

pinnatis. Hort. Upfal. 212.

Caragana Siberica. Flor. Leyd. 53 7.

1885 Salvia foliis oblongo-ovatis integerrimis caly-

cibus patulis coloratis. Fig. Tab. 2 2y.
F. 2.

1886 Scabiofa Africana frutefcens, foliis rugofis, et

crenatis minor. Par. Bat.

1887 Sefeli caule alto rigido, foliolis linearibus faf-

ciculatis. Lin. Sp. PI. 260.

Oenanthe fixiata rigida. Hort. Cliff. 99.

1888 Silene floribus fafciculatis, calycibus tomen-

tofis. FI. Virg.

1889 Silene foliis quaternis. Flor. Virg.

Lychnis Caryophylleus Virginianus, Gentians

foliis glabris quatuor ex fineulis geniculis
caulem amplexantibus, flore an: plo fimbriato.
Raii Hift. tom. ii. p. 1895.

1890 Siler montanum, foliis Aquilegias. Mor. HifL

3. 276.

Angelica montana perennis, Aquilegias folio.
Tourn. 3 13.

1891 Sifyrinchium foliis gladiolatis amplexicaulibus

pedunculis brevioribus. Dtdt. Hort.
Bermudiana iridis folio fibrofa radice. T . Inft.

338-

1892 Soli-

[ 648 ]

iSj?2 Solidago paniculata, racemis recurvatis, flori-
bus erectis, foliis lanceolatis integerrimis
glabris. Miller’s Icons.

i $93 Sorbus Sylveftris foliis domefticse limilis. C. B.
P. 415.

Sylveftris live Fraxinus bubula. Ger. 1290.
1B94 Styrax; folio Mali Cotonei. C. B. 452. Of-
ficin. 473.

1 0 95 Thaplia montana omnium maxima, foliis lo-
batis, umbellis luteis. Micheli Hort. Flor.

1 896 Tithymalus arboreus. Alpini.

1897 Tithymalus Cypariflias. Alpini Exotic.

1898 Veronica; flofculis oblongis pediculis inlidenti-

bus, Chamasdryos folio. Hid:. Ox. 2. 322.

1899 Viburnum Mathioli. C. B. 429.

1900 Vitex foliis ternatis quinatifque pinnato incilis,

fpicis verticillatis terminalibus. Didt. Hort.

LIX. Some Account of the Animal fent fr 0, t
the Eafl: Indies, by General Clive, to k s
Royal Highnefs the Duke of Cumberland,
which is now in the Tower of London : In
a Letter from James Parfons, M. D.
F. R, S. to the Rev . Tho. Birch, D . Z).
Secretary to the Royal Society .

&ead March 27,
1760.

AT the requelt of the Reverend
Dr. Littleton, dean of Exeter, I
went to obferve this creature, in order to find what
clafs of animals he belonged to ; and made the draw*

I

I Parsons _M) . ad vttfttm del. mart 25 //d'o.

J Afyndt. Sc,

Tbilos Trans. Foi.LI. TAB ,JW.p.64y

\

[ 649 ]

ing, now before the Royal Society, for its infpedion.
[See Tab. XIV.] I have endeavoured to make it as
accurate as poflible in all its proportion ; yet am afraid
I have made the ears a fmall matter too long. There
is a figure of it in the London Magazine for December
laft, which has no refemblance at all to it, except in
the ears, which the engraver, who drew it, has made
to turn forwards, contrary to nature. However, the
following defcription will, I believe, be the proper
account of it.

It is fomething taller than the larged fized cat,
being about fifteen inches high at the fhoulders ;
fender and light, though firong. The head is fmall
in proportion to the reft, and the neck flender. It
has nothing fierce in its afpedf, but is mild, and very
tame. It is exadtly of a fawn-colour, having its ears
black on their outfides, and lined with white hairs,
and fome white round the root of each ear ; it is alfo
white under the throat and belly, and a little fo on
the backs of its limbs. Its eyes are fmall, and its
head like that of a cat, but fomewhat llenderer; its
legs are genteel and ftrait, with the paws of a cat,
having the power of dilating and contracting its toes,
which are armed with ftrong crooked nails, in the
fame manner as a cat or tyger does ; and its adtions
are like thofe of a cat. I fat and watched its mo-
tions, and faw it lick its foot, and rub it over its
face feveral times, exadtly like a cat ; and was told
by the man who fhewed it me, that, if it is offended,
it hiftes. I examined its teeth, and find them in the
fame number and manner with thofe of a cat. And
as to its food, they give it raw mutton every day;
and when it is fick, which it often is, they give it a

live

[ 65° ]

live fowl, or rabbit, which it feizes eagerly, and lies
upon it without motion, for a confiderable time, to
fuck the blood, and this proves a certain cure. The
figure fhews it to have alio a tail like that of a
cat.

None of the natural historians have any account of
this animal, that I have yet feen, except the learned
Dr. Walter Charleton who has a bad figure of it,
engraved at the expence of Dr. John Lawfon, his
cotemporary, of the college of phyficians, as it ap-
pears in an infcription at the bottom of the plate,
wherein the head is, contrary to truth, very large
and ftrong in appearance, the tail like that of a fox,
and the whole as flrong as a maftiff dog : the name
given it in the plate is the fame with this, but dif-
ferently fpelled, thus, Siyah-ghujh .

This author very juftly ranks it among the cats,
and has given fuch an account of this animal, as well
deferves the notice of this learned Society, of which
I have made the following Englifh extradt.

“ Among the wild cats, which vary according to
tc the difference of climate, manner of living, and
*c the like, none is more worthy of notice than that
“ which is now kept in the park of our fovereign
<J King Charles II. It was fent to the king by an
c< Englifh gentleman, who was governor of our mer-
“ cantile affairs in the dominion of Surat, and is called,
“ among other names, in the Perfian language, Sty ah -

* See his Exercitationes de Differentiis et Nominibus Ani-
snalium.

“ Ghujh,

[ 6S» ]

cc ghujh, that is, Black-ear *, all along the coaft of
“ Coromandel, and indeed all over India. It is about
cc the fize of a fox, but like a cat in its form and
“ has the cunning and cruelty of a leopard, with
“ the limbs of a cat, but longer and ftronger ; having
“ fo much ftrength, that I law it kill a hound, that
<c came in its way, in a moment. The legs are
£c thick fet with hair, and its nails concealed under
“ them, which are never extended but upon feizing
" its prey, which is common to lions, panthers, and
<c domeftic cats. But what feems peculiar to this
“ animal is, that, having jumped upon his prey, he
“ lies upon it unmoved, holding his bite, as if he
<c was dead, whether for joy, or in order to drink the
<c blood of the creature. The great men in India
<c have them bred up tame, becaufe of their dex-
“ terity in catching birds, hares, rabbits, and fuch-
tc like i and fuch is their craft and fiercenefs, that
cc they will feize even a fox ; but their keepers will
“ not fuffer them to attack any thing above their
“ ftrength, and therefore they only fet them at cranes,
“ geefe, ducks, pheafants, partridges, peacocks, and
“ fuch-like game, which they feize by many kinds
<c of deceit, to the great pleafure of the fpedtators j
tc and catch thofe timid animals, the hare, rabbit, fawn,
“ goat, &c. by fwift running, and fometimes by
“ craft.

“ When they are lick (which, from over-gorging
<c their ftomachs, they often are) their keepers fteep

* Dr. Charleton fays, that he was obliged to his good friend tl e
learned Dr. Thomas Hyde, then principal librarian to the Bocleian
library, for this interpretation, who was well verfed in the oriental
languages.

Vol. LI. 4 P <c apiece

[ 652 ]

w a piece of tender meat in human urine, and feed
“ them with if, and being bruifed or tired by over-
“ hunting, they give them fome Mummy, wrapped up
“ in their meat, and a warm place to reft in till they
“ recover.”

It is faid of this animal, that he follows the lion at a
diftance, in order to feed on what he leaves of the
animals he deftroys. To illuftrate this, Dr. Charleton
quotes a palfage from the Apolog. of Sbeich Saadiy
which was written five hundred years before, and
publifhed in Perfic and Latin by Georgius Gentius ;
which is in Englifh as follows :

— This Black-Ear is afked, u What makes him
“ keep company with the lion, and feems fo officious
“ to pleafe him ?” to which he anfwers, “ That I
fc may feed on his leavings, and lead my life fafely
<c under his protection.” To which it is replied,
“ Since you live under the fhadow of his protection,
“ and draw fuch benefit from him, why do not you
“ approach nearer to him ?” He anfwers, “ If I took
“ your counfel, and come near to him, 1 fhould not
“ be fafe from his fury a moment.”

Now from this particular account by the learned
Charleton, and my own obfervations on him and his
adtions, I am inclined to rank this animal among the
cats ; and join with Linnceusy who, in his Or do fecund.
has a fifth lpecies of Felts, which agrees well with the
principal characters of the animal before us : his
words are,

“ Felis cauda ekngata , auribus

“ — — — penicilliformibus.”

LX. An

#

4

[ 6S3 ]

LX. An Account of the Frog - fflo of Surinam,
addrejjed to the Royal Society , by Mr.
George Edwards, F. R . S.

Read^March 27>T' Have now the honour to lay before
X this Royal Society an animal not to
be found in the Britifh Mufeum, nor in any other col-
lection that I have feen in England, and which, per-
haps, deferves attention, in regard to what is laid of
its ftrange metamorphofes, as much as any part of na-
tural hiftory whatever. It was brought from Suri-
nam in South America, by the way of Barbadoes, to
John Fothergill, M. D. of London, and is the ani-
mal, which Merian and Seba defcribe as changing
from a frog into a fifh.

In the appendix to Merian’s Nat. Hiftory of the
InfeCts of Surinam, where fhe treats of thetrans form-
ation of fifhes into frogs, and of frogs into fifhes, af-
ter explaining, how the European frog is changed
from a minute fifh (or tadpole *) into a perfect frog,
fhe proceeds to defcribe the gradual transformation of
a fpecies of frogs found in great numbers in the ri-
ver of Surinam, into perfeCt fifhes, and gives five
figures to illuftrate her defcription j the fubjeCts
whereof, fhe fays, were then in the collection of Al-
bert Seba at Amfterdam, from whom fine alio had her

* I have grofsly copied Mrs. Merian’s five figures from Plate
LXXI, the better to explain her defcriptions, which figures are
herewith prefented. Linnaeus calls this animal Paradoxa, Laft
Edit, of his Syftema Nature, p. 2 1 2.

4 P 2 figures

[ 654 ]

figures and information, as appears fince by the ac-
*■ count publifhed by Mr* Seba of his curious cabinet
of natural hiftory, in two pompous folio volumes, a
copy of which, finely illuminated, is now in the
Britifti Mufeum.

t

Mrs. Merian's Description is as follows.

tc The firft figure fhews the perfect frog, brown,
“ yellow, and green, in fpots, but paler on the belly,
“ the hinder feet webbed like thofe of a goofe, the
“ fore feet without webs : the fecond figure repre-
“ fents the firft change the frog undergoes, by the
“ growing out of a tail; after which it gradually ac-
“ quires thefhapeof a fifth, the two fore feet decreaf*
“ ing and perfthing by degrees, as is ftiewn by figure
€t 3. alfo the decreafe of the hinder legs, as is
“ fhewn by figure 4. and, laftly, the frog is changed
“ to a perfect ffth, as at figure 5.

■ u The Indians and Europeans of Surinam call
“ thefe fifties Jakies; they are cartilaginous, of
<c a fubftance like our Muftela -f, and very deli-
<£ cate food. A bone (or cartilage) runs down the
<( back, with fmall bones all over the body, which
“ is divided into equal parts; they are adorned with
“ tender beautiful fcales, are firft of a darkilh co-
<c lour, and afterwards grey.”

The frogs of Afia and Africa are defcribed by this
author, plate 72. to change gradually from fifties into
frogs, as the European frogs do ; but then fhe tells

f A fith of the cartilaginous kind : See Willoughby de Pifcibus,
Tab. B. 5. and Edwards’s Gleanings, Tab. 288.

US

■

Fbilos.Tans.Vo/LI. TAB. XV (a )y>.%

I

I

4 >

Pbilos. Trans. Yol. LI. TAB. XV (b) p.6'55-

. K , VtrttJs

[ 655 ]

us that, after many years growth, they change again
into fifhes, tho’ the manner of their change is un-
known.

The natural fubjed before us, two views of which
I have given in a print annexed, fee Tab. XV.
Letters F G. They are drawn and engraved imme-
diately from nature, of the fize of life, which, on
comparifon, I find to be more than double the fize of
what Merian has figured in her book, plate 71.
which inclines me to think this before us to be fpe-
cifically different from Merians : her figure expreffes
the fin, which paffes round the tail, fcalloped, where-
as in this before us the edge of the fin is perfedly
even, without any indentures : the hinder feet in her
figures have only four toes each, whereas this before
us hath five, webbed together, befides a fmall rudi-
ment of a toe, as may be feen in the natural fubjed,
as well as in my print. The fore feet, both in Meri-
an’s and my figures, exprefs four toes, unwebbed, tho’
I find the four toes to ftand, three of them in the form
of fingers, and one oppofite to them, which ferves as
a thumb, which is not expreffed in Merian’s figure.
The general fhape of it is expreffed by the figures F.
G, in my print. The fkin is foft, without any thing
of fcalinefs, and the fin round the tail is like thin wet
leather, without any fibres to fupport it, as is com-
mon to mofl fifhes. The toes in all the feet end in
points, but are without nails or claws. On piercing
the tail, or hinder part, with a needle, I found no
bony refiftance ; but on piercing the thighs and
head the bones flrongly refilled. Its colour in the
ipirits appeared dark brown, with dufky fpots, the
under fide lighter, and without fpots*

There

[ 656 ]

There came in the fame glafs of fpirits with the
above-defcribed frog-fifh (as I have chofe to call it), a
parcel of fmall tadpoles, in their different changes from
the fpawn to near the perfect frog : fee them expreffed
on the plate of their natural fize at letter A B C D.
Doubtlefs thefe produce a fpecies of frogs different
from the European, and perhaps are the fame that
Merian and Seba defcribe as changing into fifhes. I
think, however, that our affent to fuch an opinion
may reafonablybe fufpended, till we are confirmed in
it by farther obfervations of the real fadt ; for it feems
ffrange, that a tadpole fhould firft be changed into
a frog, and that the felf-fame frog, by a reverfed pro-
cefs of nature, fhould change again into a very large
tadpole, as figured at G in the plate, and finally
change into a fifh, as in Merian, tab. 71. fig. y. It
feems very ffrange, that another tail fhould grow from
the frog that hath lately loft one, and that he fhould
gradually lofe his legs, and become a perfect fifh.
Nature, in her ordinary courfe, is not accuftomed to
adt in fuch a manner backwards and forwards, to
feem to perfedt a work, and then to reverfe it by a
procefs diredtly oppofite.

The little tadpoles on the plate A B C D, are fpe-
cifically different from the large one F G, as is ma-
nifeft by the difference of their feet : fee the hinder
foot of one of the fmall ones magnified at E, which
fhews, that the ends of their toes are round and flat on
their underfides, both in the hinder and fore feet :
forwards they have four toes in each foot, unwebbed ;
the hinder feet have five toes, each webbed together.

As to thefpecimen before us, whether it is already
in its perfedt ffate, a fpecies of frog having a tail, or a

kind

[ 657 ]

kind of water' lizard, I fhall not pretend to deter-
mine : but, considering its fize, if it Should be deem-
ed a tadpole, as firft produced from a fpawn, and in
its progrefs towards a frog, fuch a frog, when full-
grown, if it bears the fame proportion to its tadpole
that the frogs in Europe do, it muft be of an enor-
mous fize ; for our full-grown frogs exceed the tad-
poles, and young fry of perfect frogs, at lead fifty
times in magnitude.

London, March 27, 1760.

LXL An Account of a re??tar liable Operation
on a broken Ann ; by Mr . Charles White,
Surgeon at Manchefler, com?nunicated by
George Lloyd, Efq\ F. R. S.

Read March 27, Tjj Obert Elliot, of Eyam, in Derby-
17601 XV Ihire, a very healthful boy of nine
years old, had the misfortune, about midfummer
in the year 1/59, by a fall, to fra&ure the Hu-
merus, near the middle of the bone. He was imme-
diately taken to a bone-fetter in that neighbourhood,
who applied a bandage and fplints to his arm, and
treated him as properly, as, I fuppofe, he was capable
of, for two or three months. His endeavours, how-
ever, were by no means productive of the defired
effeCt, the bones not being at all united. A furgeon
of eminence in Bakewell was afterwards called in >
but as he foon found he could be of no fervice to him,
and, as the cafe was very curious, he advifed the lad’s

friends

[ 65s ]

friends to fend him to the infirmary at Manchefter :
he was accordingly brought thither the Chriftmas
following, and admitted an in-patient. Upon ex-
amination, we found it to have been a fimple oblique
fradture, and that the ends of the bone rode over each
other. His arm was become not only entirely ufelefs,
but even a burthen to him, and not likely to be
otherwife, as there was little probability, that it would
ever unite, it being now near fix months fince the
accident happened.

Amputation was therefore propofed as the only
method of relief ; but I could not give my content to
that j for, as the boy was young, and had a good
conftitution, it was hardly poflible that it could be
owing to any fault in the folids or fluids, but that
cither nature was difappointed in her work by frequent
fridtion, while the callus was forming, or rather that
the oblique ends of the bone being ftiarp, had divid-
ed a part of a mufcle, and fome portion of it had
probably infinuated itfelf betwixt the two ends of the
bone, preventing their union. Which ever of thefe
might be the cafe, I was of opinion, that he might be
relieved by the following operation ; m. to make a
longitudinal incifion down to the bone, to bring out
one of the ends of it (which might be done with
great eafe, as the arm was very flexible), and cut off
the oblique end, either by the faw or cutting pincers,
then to bring out the other end of the bone, and cut
oft that likewife; afterwards to replace them end to
end, and then treat it intirely as a compound frac-
ture.

The objections, made by the other gentlemen con-
cerned to this propofal were, iff, The danger of

wounJing

[ 6S9 ]

wounding the humeral artery by the knife; id, the
laceration of the artery by bringing out the ends of
the bones; and, 3d, that we had no authority for
fuch an operation. As to the firft, that was eafily
obviated, by making the incifion on the fide of the
arm oppofite to the humeral artery. The place of
election appeared to me, to be at the external and
lower edge of the deltoid mufcie, as the fradture was
very near to the infertion of that mufcie into the hu-
merus, the danger of wounding the veffel not only
being by that means avoided, but after the operation,
while the patient was confined to his bed, the matter
would be prevented from lodging, and the wound be
eafily come at, to renew the dreffings. The fecond
objection will not appear to be very great, when we
confider, that in compound fractures, the bone is fre-
quently thruft with great violence through the inte-
guments, and feldom attended with the laceration of
any confiderable artery, and as this would be done
with great care and caution, that danger would ap-
pear very trifling. The third and laft Objection is no
more than a general one to all improvements.

This method, which I have been propofing, was at
lafi: refolved upon, and I aflifted in the operation, which
was performed by a gentleman of great abilities in his
profeffion, on the third of January, in the prefent year.
The patient did not lofe above a fpoonful of blood
in the operation, though the tourniquet was not made
ufe of. When the operation and dreffings were
finifhed, the limb was placed in a fradlu re-box con-
trived on purpofe, the lad confined to his bed, and
the reft of the treatment nothing different from that
of a compound fradture.

Vol. LI.

The

[ 66o ]

The wound was nearly healed in a fortnight’s
time, when an erifipelas came on, and fpread itfelf
all over the arm, attended with fome degree of fwell-
ing : this by fomentations and the antiphlogiftic me-
thod loon went off, and the cure proceeded happily
without any other interruption. In about fix weeks
alter the operation, the callus began to form, and is
now grown quite firm : that arm is as long as the
other, but fomewhat fmaller by fuch long continued
bandage ; he daily acquires ftrength in it, and will
foon be fit to be difcharged.

Manchcfter,
March 17, 1760.

C. White,

Surgeon to the Infirmary
at Manchefter.

LX 1 1. An Account of a Bone found in the
Pelvis of a Man at BruiTels; by Terence
Brady, M. D. In a Better to the Rev.
Tho. Birch, D. D. Secretary to the Royal
Society.

Revd. Sir,

Read Apr. 29, V Send you here inclofed a draught of a
JL bone found in the pelvis or bafon of a
man, that died in the military hofpital of this town
the rath of March 1760, of a feven days inflamma-
tory diftemper. This extraordinary concretion weighs
about 20 ounces, has all the external appearances of
a bone, with the hardnefs, folidity, and fpccifick gra-
vity

*

Tb/los Trans. Yol. LI. 'VA&LSifMi

I

J-iMyrutt /■'

[ ]

vity of common ftone. It is chequered or marbled, as
you fee in the figure, Tab. XVI. by which you can
diftinguifh the primitive particles of the bone whiter
and harder than the darker part: it was formed on the
lower extremity of the mefocolon, and probably as
it grew big was carried down by its own weight into
the bafon, where it had no adherence to, nor connec-
tion with, any of the adjacent parts, but lay in its own
very thin membrane or jftrioftium, betwixt the os
pubis and ,the bladder, fomewhat to the right fide.
It was joined to the mefenterium by a tough, com-
pact, membranaceous, glandulous fubftance, in the
form of an inverted cone, whofe point was firmly
inferted in the cavity obferved on the top : here the
membranaceous fibres were turned into bones, or,

‘ vice verfa , the fibres of bones degenerated into flefhy
membranes: there was no intermediate cartilaginous
fubflance to be obferved. By drawing up this conic
body with very little effort, the bone followed, to the
great furprife of all the fpedlators ; after which there
was no farther inquiry made, in regard of the other
vifcera of the abdomen. It w7as only taken notice
of, that the omentum was quite confumed, and the
mefenterium very much fwelled and fchirrous.

The man, that bred this monfixous bone, was called
Stralzet, was born in Bavaria, and lived to the age of
45, of w'hich he was 28 years a mufketeer in Ba-
reitlfs imperial regiment. He was always ftrong and
healthy till about five years ago, w7hen he began to
complain of the hardnefs of his belly, and now and
then of a fupprefilon of urine, of which laid incon-
veniency he could help himfelf, by turning on his
right fide, and lying a little on his face : by that po-

4 Q^2 fition,

C 662 ]

fition, the ffone did no more prefs on his bladder.
He never miffed doing foldier’s duty till his laft
ficknefs, about feven days before his death.

We have examples of membranes, and of feveral
foft parts of the body, being offified ; but I believe
there is not fuch a monftrous production as this to
be fee nany- where.

About 20 years ago I faw at Mantua, two inches
of the aorta near the heart turned to bone, in a man
that was a long time tormented with a violent palpi-
tation of heart.

I know. Sir, relations of fuch extraordinary appear-
ances are often, and with reafon, fufpeCted of exag-
geration, but you may depend upon the veracity of
this. I am,

Reverend Sir,

Your moff humble, and

Bruffels, March 29,
1760.

moff obedient Servant.

Terence Brady, M. 2).

LXIII. An Account of an extraordinary Cafe
of a Lady , who fw allowed Euphorbium.
By Dr. Willis, of Lincoln : Communicated
by Sir Francis Dafhwood, Bart .

Read Apr. 24>1T N December 1758, Mrs. Willis of
JL Lincoln fell into a flow fever, occa-
sioned by too fmall a difeharge of the lochia after

lying-in.

[ 663 ]

lying-in, and a redundancy of milk, the confequence
of her not fuckling her child. On the 1 8th day
after her delivery, by the miftake of her nurfe, fhe
took, inftead of a draught that was ordered for her,
two ounces of the tindture of euphorbium *. The
fhocking fymptoms, which immediately enfued, vio-
lent fuffocation, and an intolerable burning pain in
the mouth, throat, and ftomach, foon difcovered
the horrible miftake. I was in the room in about
four or five minutes after the accident happened,
unapprifed of the nature of it, and therefore the
more fhocked, when I found every body in tears of
defpair, offering at no means of relief, as they had
no hopes of fuccefs.

As foon as I was made acquainted with what had
happened, it occurred to me, that warm water and
oil were the likelieft things to corredt and expei the
poifon. I imagined a large quantity of warm water
might probably make the patient vomit, and in fome
meafure help to difcharge the cauftic tindture. I was
fure the water would at the fame time mitigate its
violence, by diluting it; and by precipitating the acrid
gum from the fpirit, whereby it would neceftarily be
hindered from touching the membranes of the fto-
mach and bowels in fo many points, and from pene-
trating into their fubftance.

There was happily a large tea-kettle of water on
the fire, of which, being firft qualified with a proper

* The tindture was thus made ;

lx Gum. Eupborb. 5ij. Spt. Vin. rcctif §ij. Sol. add. Campb. Si j.
The camphor was ordered to weaken the cauftic quality of the
tindiure, which being applied to a horfe’s leg without the camphor
had made a blemifti.

quantity

C 66+ ]

quantity of cold water, I immediately gave the pa-
tient a bafin lukewarm, and repeated it as faft as pof-
fible. conjuring her to ufe her utmoft refolution to
fwailow; which fhe certainly did in a moft furpriling
manner. After the third bafin, fhe vomited very
freely : what was brought up fmelt very ftrong of the
camphor, and feemed to contain a good deal of the
tin&ure, with the gum feparated from the fpirit.
She hill drank on, but complained of excefiive
burning and torture in her ftomach, crying out con-
tinually, fhe was burnt to death.

I had then recourfe to oil between whiles, in the
quantity of two or three ounces at a time ; and
drenched her plentifully fometimes with oil and
fometimes with water. She vomited very copioufly,
and I repeated the oil and water interchangeably, till
fire had taken, as well as I could guefs by the vef-
fels, two gallons of water and a flafk of oil in a very
fhort time -f*.

Imagining

t Dr. Sydenham, being called to a man, who had taken Mercur.
fublim. corrof about an hour before the doblor faw him, the poifon
having affedted his lips, &c. only ordered water to be taken in a
large quantity, and thrown up copioufly in glifters. But as the
corrofive fublimate of mercury is to be confidered as a poifon, whofe
cauftic acrimony confifts in a faline principle, and water is the pro-
per folvent, diluent, and vehicle of all faline fubftances, the pro-
priety of Sydenham’s ordering water alone is fufficiently apparent.
Poifons of a faline nature being diflolved in the fluids of the ftomach
and inteftines, do not confine their ravages to thefe parts only, but
are apt to enter the abforbent veffels, and infinuatc thetnfelves into
the road of the circulation. Water is here a good antidote, as it di-
lutes fuch fubftances, vvafhes them off the fenfible membranes, de-
ftroys their acrimony, and readily pafling through all forts of canals,

foe a

[ 66S ]

Imagining the deleterious draught had not had fuf-
flcient time to bring on any violent inflammation or
excoriation, or to make its way into the blood, vo-
miting and purging, with plenty of diluents and
fheathing fubftances, feemed the likelieft means to
fave the patient, if any thing could be hoped to fuc-
ceed in fo perilous a fltuation. I therefore ordered a
mild but operative emetic of Pith. Rad. lpecacuan.
and a mixture with Sperm. Ceti and oil to be taken
occaflonally ; ftill following up the patient with oil
and water. I had reafon to expeCt the emetic would
alfo purge as well as vomit, and not only clear the
ftomach of the remains of the poifonous draught, but
likewife carry downwards what portion of it might
have pafled through the pylorus by the contraction
and agitation of the ventricle on the preceding vomit-
ing. The apothecary demurred at the emetic, and

foon carries them out of the body. But the cafe is otherwife with
gummy refinous poifons, fuch as euphorbium. Thefe being indif-
i'oluble in water, are not fo apt to enter the abforbent veflels, and pafs
into the blood, but, by their acrimony, fhut up the orifices of thofe
canals, and preclude a paflage. Therefore oil here fhould be called
in to the afliftance of water. For the cauftic refinous fubftance of
euphorbium being precipitated or feparated from the fpirit, and
formed into clots by the water, would ftill be apt to ftick to the
tender nervous membranes of the ftomach and bowels, and by its
intolerable acrimony caufe violent vellications, inflammations, and
gangrene. But the oil contributes greatly to prevent thefe fatal ef-
fects, by fheathing the corrofive acrimony of the poifon, prevent-
ing its adhefion to the delicate lining membranes of thefe firft paf-
f'ages, and defending them from the violence of its attacks ; while
at the fame time it promotes the difcharge of their contents.

Thefe qualities of oil alfo render it very ferviceable in other
fpecies of poifon.

objedted

[ 666 ]

objected the danger of its aggravating the effeCts of
the poifon by its dimulus and irritation. Though I
was not in the lead convinced by the objection, yet,
from an apprehenflon of the reflections, which might
probably be made after the tragical fcene, which
feemed to be inevitable, I was daggered in my pro-
ceeding, and wiflied the objection had not been dart-
ed. My brother, obferving my uneafinefs, afked
me, it die diould fend for Dr. Dymock. I glaalv
accepted this offer, as it rid me of my perplexity, and
would give fatisfaCtion to all concerned to have had
the bed advice. In the mean time, I plied the pa-
tient with oil and water alternately, with which die
vomited ; but dill grievoufly complained of a burn-
ing heat in the domach and bowels. Her breath and
all die vomited fmelt very drong of the camphor.
Her pulfe was moderate, and not much quickened.
1 had now given her about a gallon more of water,
and half a flafk more of oil, when Dr. Dymock ar-
rived. Upon informing him of all the particulars of
the cafe, lie, without hefltation, ordered an emetic
of Vin. Ipecacuan . f . which was immediately given :
but the patient complained more and more of an in-
ward burning heat, which made it neceffary to lup-
ply her with more water before the emetic oper-
ated. It had however in a diort time the defired ef-
fect, and operated plentifully both by vomit and
dool, efpecially the latter way. The ltools, which
continued to be difcharged for near an hour, without
any griping pain, very manifedly difcovered both
camphor and oil being mixed with them. fne
purging now began gradually to abate, and foon after
the burning heat in the region of the donlach became

more

[ 667 ]

more tolerable, and infenfibly grew better, the cam-
phor being no longer perceptible in the breath or
evacuations. Her drink now was water with the
addition of a little milk.

The patient’s fpirits, which, by means of the great
irritation and feveridi tumult the caudic tindure had
excited, kept up furpridngly, now began to fail her,
and die was with difficulty got into bed : where, after
complaining for a ffiort time only of a forenefs in
the fird paffages, ffie lay fweating profufely for four
hours in a very low defponding condition.

A gentle opiate was exhibited, which took effed >
and after a found fleep of five hours the patient
waked very eafy, took dome of the fperma ceti mix-
ture, and had another fleep of three hours. She
now found herfelf free from all her complaints ; the
previous dow fever, as well as the effeds of the
poifonous tindure, being entirely carried off.

It is remarkable, that the patient found herfelf,
for four days fucceffively, in fo happy a date of eafe
and tranquillity, as fhe had never before experienced,
and to this day enjoys a perfed date of health.

Thus have I laid before you the true hilfory of
this cafe ; for the dmple relation of which I datter
myfelf I need make no apology, when I reded,
that the pradice of phydc mud derive much greater
advantages from plain hidories of matter of fad, and
jud dedudions drawn from them, than from the
mod ingenious hypothefes and fpeculative theories.
Thefe were of baneful induence to the progrefs of
true knowlege, till your illudrious Society taught the
world the true method of invedigating the laws of

Vol. LI. 4R nature.

[ 668 ]

nature, by observation of fad:, experiment, and ra-
tional deduction.

The following observations, which this caSe natu-
rally fuggefts, Seem to deServe our attention.

i ft, That in any fimilar accidents of Swallowing
corrolive poiSonous fubftances, a quick and reSolute
administration of thefe fimple bodies, water and oil,
in a large quantity, Seems to be the moSt effectual
method of preventing any bad conSequences, and far
preferable to the numerous boafted antidotes, which
have been handed down to us.

2 dly. That an emetic may be more fafely and
effectually adminiStred, and its operation waited for,
after the acrimony of the poifon hath been fheathed
and blunted, and the coats of the Stomach defended
from its attacks, by a liberal ufe of water and oil,
than immediately after it is Swallowed.

3 dly, That as the flow fever and redundancy of
milk, as well as the poifon, were carried off by the
copious discharge excited in the eaSy manner above-
mentioned ; might we not often hope for Succefs in
fevers occafioned by fimilar caufes, plenitude and
obstruction, from plentiful evacuations, brought on
after the fame manner, by fimple, diluent, and fheath-
ing medicines ?

4 thly. The camphor was * undoubtedly of great
Service in curbing the deftruCtive effeCts of the
euphorbium, by blunting its acrimony, and Soothing
the nerves into an infenfibility of irritation, and con-
sequently an incapacity of fpafmodic affeCtions. I
have tried the tinft. cuphorb. cum c amphora on a

horfe’s-

[ 669 ]

horfe’s leg feveral times, and find it not near fo caufiic
as without the camphor. And it is well known how
much camphor involves the fpicula, corrects the acri-
mony, and mitigates the effects of cantharides, fac-
charum Saturni, and rough, mercurial, and anti-
monial preparations.

§tbly> To water and oil therefore we may juftly
add camphor as a powerful corrector and expeller of
poifons in general. This it probably effectuates, ift,
by blunting the acrimony; adly, by calming the
nervous fyftem, and fecuring it from fpafmodic tu-
mult and convulfion, which may be a confequence
of its fheathing quality ; 3dly, by its extreme fub-
tilty and volatility, whereby it freely penetrates the
fmalleft recedes of the body, and powerfully pro-
motes a diaphorefis. Some late inftances of the ef-
fects of camphor in poifonous cafes greatly confirm
this account.

Thefe three fimple bodies then, water, oil, and
camphor, challenge the firft place among the anti-
dotes hitherto difcovered, both for internal and ex-
ternal ufe, and are much more to be depended upon
than any of the elaborate compofitions calculated for
this purpofe by the ancients, as the Theriac. Androm.
Mithridat, Conf, Paulin, &c.

4 R z

LXIV,

I

[ 67b ]

LXIV. An Account of artificial Cold pro-
duced at Peterfburg : By Dr. Himfel. In
a Letter to Dr. De Caftro, F. R. S.
Tranjlated from the French by James Par-

fonsj M. D. F. R. S.

Read May i. the 14th of December [i7f9l wc

1760. had, at Peterfburg, the moft ex-

ceffive cold weather that ever was known, even to
205 degrees of De Lifle’s thermometer. At that time
Profeffor Braun repeated Fahrenheit’s experiments,
in order to produce exceffive cold by means of fpirit
of nitre combined with fnow. He faw, with fur-
prize, the quickfilver fall considerably in the ther-
mometer, and defcend even to 4 7° degrees at laft 1
there the quickfilver remained fixed in the open air
for the fpace of a quarter of an hour, and did not
begin to rife till it was carried into a warm room.
He repeated the fame experiment, firft with the fame,
and then with another thermometer, with the fame
fuccefs. The immobility of the quickfilver made
him conjecture, that it might be frozen, or become
a folid body. But as Mr. Braun had not broken
the glaffes, he could only at that time form a con-
jecture. On the 17th he produced, again, cold
equal to that of the 14th ; but on that day there
was no experiment made; and Mr. Braun commu-
nicated his difeovery at a meeting of the academy*
On the 25th of December in the morning, between
nine and ten, De Lifle’s thermometer was at the 199th
degree of cold ; and Mr. Braun, as well as Profeffor
^ /Epinus,

[ 67i ]

iEpinus, then repeated this experiment. As foon as
the former had obferved the quickfilver immoveable
in the thermometer, he broke the glafs ; and he
found, to his amazement, the quickfilver frozen, but
not intirely ; for in the middle of the glafs ball there
was a fmall portion yet remaining fluid. Mr. A£-
pinus’s thermometer fell, with extreme rapidity, al-
mofl to the 500th degree, and in breaking the glafs
from below, he found the quickfilver contained in it
abfolutely frozen. Both the gentlemen found, that
the quickfilver, thus rendered folid, bore hammering
and extenfion, like other metals j but being aftewards
expofed to the open air, it recovered its former-fluidity
in a little time.

Mr. j®pinus went fomewhat farther, in order to
examine the quickfilver, when it was made folid.
He poured quickfilver into a glafs tube as thick as
one’s finger, clofed at bottom, but open at top. The
quickfilver in this cylinder, which was about one inch
and half long, froze in three quarters of a minute ;
and he obferved, that it became folid, perfectly re-
fembling other metals, except iron : it continually
contracted, and its furface, which was at firfl pretty
high, foon funk very low. This cylinder of frozen
quickfilver funk to the bottom of fluid quickfilver,
in the fame manner, as is obferved of other metals,
except iron. We know the contrary happens with
regard to water frozen and other fluids, which ex-
tend as they become folid, and their ice fwims in
the fluid matter, of which they were produced.

On the a 6th of December in the morning, be-
tween nine and ten, the cold became extremely fharp
at a 1 1 de grees, and fuch as exceeded the greatefl
3 degree

[ 672 ]

degree of artificial cold fixed by Fahrenheit; for 40
degrees below zero, in Fahrenheit’s thermometer, is
equal to 210 degrees of that of De Lille.

Mr. Braun repeated this experiment again, exactly
with the fame fuccefs with that of the day before.
The counfellor and profefi'or Lomonolfow made the
fame experiment on the fame day ; and by means ot
aqua fortis the cold came to 495 degrees. He then
poured in fpirit of common or fea fait, and the
quickfilver fell down in the thermometer to 55*4 de-
grees ; and in taking the thermometer from the mix-
ture, the quickfilver continued to fall in the open
air to the y 5- 2d degree. He threw yet into the glafs
a little more fnow, pouring on it fome oil of vitriol,
and fuddenly the quickfilver fell to 1260 degrees.
Then he broke the ball, and found the mercury
changed to a folid body. The quickfilver, which
yet remained in the tube, was alfo become folid, and
appeared like a loofe filver wire, attached to the ball,
which was flexible every way. He gave the ball of
quickfilver feveral blows with a turned ax, and it
became flat like a half-ruble, or Englifli half-crown ;
but receiving thereby fome cracks, it diflblved in
about 20 minutes. Thefe experiments were made
when the air was at about 208 degrees of cold.

Mr. Krafe, Mr. Zeicher, and the firfl: apothecary
Model, and again Mr. ^Epinus, repeated the fame
experiment with the very fame fuccefs. It is to be
oblerved, that at the fecond experiment by profeflor
Zeicher, on the 3 1 ft of December, as the air was
then only at the 183d degree of cold, in taking
the thermometer from the mixture, in which the
quickfilver was at 300 degrees, it fell yet 100 de-
grees

[ 673 ]

grees more in the open air. The teftimony of fo
many philofophers, each of whom had refpedtively
made the experiment, will, no doubt, be fufficient
to prove the truth of it. But in order to remove all
doubt about it, it mud be remarked, that diftilled
quickfilver only was made ufe of in every experi-
ment ; nay, in fome, the quick hi ver was revivified
from fublimation. There can therefore be no fufpi-
cion, that what they ufed was impure, or mixed with
any heterogeneous matter. This appears to have
happened to Mr. De Lille de la Croyere, when he
fays, that in Siberia he found the quicklilver con-
gealed in the barometer : and even his papers, which
are in the academy, fhew that he made a miftake in
his remarks j for, according to them, the mercury
became folid as foon as it fell to about ipy or 100
degrees : but the mercury, which is pure, does not
congeal at that degree j for otherwife it would not be
very extraordinary with us to fee it take a folid form,
becaufe it is not rare to find the cold at this degree
here. We may believe, that the quickfilver ufed by
Mr. De la Croyere was impure, and therefore might
fooner become an amalgama than pure mercury.

Now there are two things we cannot reafon upon
with any certainty : As to the hardnefs of the quick-
filver congealed, it appeared to have had, in fome
efiays, lefs hardnefs than lead, and in others more :
alfo we cannot be very lure of the degree of cold, by
which the mercury is confolidated. The greateft
part of the experiments agree in this, that the quick-
filver becomes folid, when it falls in the thermo-
meter to yoo degrees, more or lefs. Neverthelefs,
they do not fo fufficiently agree as to deduce any
thing certain about it.

Although.

C 674 ]

Although in the experiment made by Mr. Lomo-
noffow the quickfilver fell to 1260 degrees, this phi-
lofopher neverthelefs fays, that he could not fufficient-
ly obferve, in his hurry, whether the ball might not
have received fome crack, and the quickfilver thereby
perhaps might have had liberty to fall the lower,
which otherwife would not have happened j for the
fame thing happened to Mefl. Braun, Zeicher, and
/Epinus, that the balls of their thermometers were
cracked and broken. By the experiment of Mr.
jEpinus, made on the 25-th of December, in which
the quickfilver fell fuddenly in the thermometer, and
the cylinder of quickfilver of the thicknefs of one s
finger becoming folid fo quickly, it may be obferved,
that the degree of cold then produced ought to ex-
ceed 300 degrees. Neverthelefs, whatever the de-
gree be, we cannot determine how the common ther-
mometer ceafes to be of ufe as loon as the mercuiy
begins to become folid.

Here follows an account of the manner, in which
thefe experiments may be made, that other philolo-
phers may be capable of repeating them. It is
therefore to be obferved, that it is neceffary to ufe
fuming fpirit of nitre, or of fuch as is evaporated till
the fumes become red * for the common aqua fortis,
which is ufed, had not the defired effe<ff. Mr. iE-
pinus has found, that this experiment is very eafily
and fpeedily made in the following manner. Take
fpirit of nitre, cooled as much as poffible, and with
it half fill a wine-glafs, throwing -in as much fnow
at the fame time, and ffirring it till it becomes of the
confidence of pap : then you have almofl in an in-
flant the neceffary degree for the congelation of the

quickfilver.

[ 675 ]

quickfilver : not only Mr. iEpinus ufed this method,
but alfo Meff. Krafe, Zeicher, and Model, who fol-
lowed Mr. iEpinus, and found it the mod conve-
nient method. Now, in reflecting upon the proce-
dure of other philofophers, efpecially of Meff. Muf-
chenbroek and Reaumur, for producing artificial
cold, by the commixtion of fnow with aquafortis, as
the former has mentioned in his edition of the expe-
riments of the academy of Florence, tom. i. p. 174.
and Mr. Reaumur, in the memoirs of the academy
of fciences of Paris for the year 1734. it is aftonifh-
ing how it happens, that thefe learned men have not
obtained, by a great deal, the degree of cold produced
by the gentlemen of the academy of Peterflburg ; for
their manner of making the experiments does not
feem to differ much from that of Mr. Braun, as to
what relates to any eflential circumftances, nor from
the manner mentioned before, fo as to hinder them
from producing effects nearly equal. Perhaps they
may, in time, and by continued refearches, be able
to find out the circumftances, that prevented their
fuccefs in the experiments of thefe great men : it
may be, becaufe the fpirit of nitre was not endowed
with its proper quality. In fine, I muft further ob~
ferve, that a certain degree of external cold appears
abfolutely necefiary to the experiment. Mr. ./Epinus,
who made it the 2§th of December, in a room where
De Lille’s thermometer fhewed 1 2 2 degrees of cold,
cooled the fpirit of nitre in liquifying fnow to 1 so de-
grees, and the fnow, which they ufed, came to the
fame degree ; in making the mixture, the refult
wras an augmentation of cold to 300 degrees. It muft
then happen, that they had obtained the furprizing
Vol, LI. 4 S degree

C 676 ]

degree neceffary to congeal the mercury ; which Mr.
Zeicher alfo at length obtained ; the degree of cold
of the air being the 175th degree of De Lille’s ther-
mometer, or the 30th of that of Fahrenheit.

LXV. An Account of a complete Luxation
of the Thigh Bone , in an adult Perfon , by
external Violence *, by Mr. Charles White,
Surgeon , at Manchester. Com?nunicated
by George Lloyd, Ffq\ F. R. S.

Read May 1, A S Robert Hogg, (a farmer in Clyfton,

1 76o‘ 21 about four miles from Manchester)

a Strong, robuSt, middle-aged man, was taking a load
of wheat from off a horle, on the 20th of March
1759, his foot flipping, he fell backwards; his breech
upon the pavement, and the load of wheat upon his
belly and thighs. The fervants carried him into the
houfe, and laid him upon a bed, where he remained
in the molt racking torture, when I came to him,
which was about two hours after the accident hap-
pened. I found his right buttock as large again as
the other 5 the knee and foot of the fame fide turned
inwards ; and the thigh much Shortened. Upon en-
deavouring to make the thigh perform its rotatory mo-
tion, there was not the leaft crackling to be heard.
This convinced me, that the head of the bone was
thrown out of the acetabulum ; and, upon examina-
tion, I could diftindly feel it under the glutaei
muScles: to which Situation of it, and not to any

bruife,

[ 677 ]

bruife, I was now fatisfied that the fize of the buttock
was owing.

I foon reduced it, by the following eafy, and very
fimple method.

Some napkins being firft lapped round one of the
pofts at the foot of the bed, to prevent its galling
him, I ordered the patient to be laid upon his back,
with one leg on each fide the poft, and then directed
three or four afiiftants to pull at the diflocated limb,
the pofi now placed to his groin being a fixed point
to pull againft. Whilft they were making this ex-
tenfion, I clapped my left hand upon the head of the
bone, to help it into its place ; and, at the fame in-
fant, with my right hand, turning the knee out-
wards, threw the bone into the focket, with the
greateft facility imaginable, but with fuch an un-
commonly loud noife, as greatly aftonifhed all who
were prefcnt.

He was perfectly eafy from that moment ; the en-
largement of the buttock entirely fubfided. In a
fortnight, he was able to move about, without ai-
fi fiance ; and in two months afterwards walked as
far as Manchefter, being then quite found ; and the
limb, that had been dillocated, of the fame length
with the other.

Remarks.

Both antients and moderns have fallen into great
errors, in regard to the treatment of accidents, that
have happened to the hip joint. The antients, who,
for want of frequent opportunities of diffedting bodies,
were ignorant, that the neck of the femur was often
broken, always imagined it to be luxated. Their

4. S 2 patients

[ 678 ]

patients were, therefore, fometimes tormented, (in
hopes of a redudtion) without any advantage j and
this want of fuccefs made the furgeons, at other
times, abandon their patients, when they might have
been relieved. The moderns have fallen into a con-
trary extreme, but attended with as bad confe-
quences. Boerhaave, in particular, was of opinion,
that there never was a dillocation of the thigh bone
by any external violence, but that the head of it was
commonly broken off" at its neck, near the great
trochanter. The opinion of fo learned a man has
had fuch weight with the generality of the profeflion,
that it has been taken for granted, that, in thefe
cafes, the neck of the bone was always broken : con-
fequently, the reduction was feldom attempted, and
the unfortunate patients remained cripples during the
reft of their lives. But the point is now, I think,
cleared up, beyond the pofiibility of a doubt.

In the fecond volume of the memoirs of the royal
academy of furgery at Paris, there are two cafes re-
lated, to fhew the refources of nature, where luxa-
tions of the thigh bone have not been reduced. Here
it appears, (from examination after death) that, in
the hrft cafe, the bone was thrown out upwards
and outwards, the cotyloid cavity greatly diminifhed
in fize, and its figure changed from round to oval.
The head of the femur was received into another
cavity formed upon the os ileum, under the glutaeus
minimus, which ferved it as a capfula, to fecure it
within this preternatural cavity. This accident was
occafioned by a fall, when the patient was a child.
She was afterwards able to walk about, though fhe
continued a cripple to the time of her death, which

happened

[ 679 ]

happened at the age of fixty-eight. In the other
cafe, the bone was luxated downwards and inwards,
and the head fixed upon the foramen ovale.

There is a cafe too related, and very well attefted,
in the Edinburgh effays, philofophical and literary,
vol. 2d, of a man at Worcefter, who had the head
of the bone thrown out of the acetabulum, and
lodged in the groin. It was with fome difficulty re-
duced, and the man fuffered no other inconvenience,
than that of the leg’s being about a quarter of an inch
longer than the other.

To thefe, let me add, that, about thirty years ago,
my father was fent for to a man, who had luxated
his thigh bone three or four days before. The head
of it lay in the groin, which the furgeon, who was
firfi: employed, did not difcover. However, it was
immediately replaced, and the patient recovered the
ufe of his limb, in a very ffiort time.

From what I have faid, I would by no means have
it concluded, that the neck of the bone is not fome-
times broken, or that it is not even oftener broken
than luxated : but, from the cafe, which has fallen
diredtly under my notice, joined to thofe, which I
have above recited, Lthink it muft appear very clear,
that it has been frequently luxated, and that two dif-
ferent wrays.

C. White,

LXVI. Con-

[ 68o ]

LX VI. Conjectures upon an inedited Parthian
Coin. By the Rev . John Swinton, B. D.
of Chrift- Church, Oxon. F. R. S.

To the Rev. Thomas Birch, D. D. Secretary to the

Royal Society.

Good Sir,

Read May i, "T" Some time fince met with a Parthian
1 coin, nearly of the fize of the middle
Roman brafs, that feems to merit the attention of
..he curious. For though the piece itfelf is in very
indifferent confervation, yet it has not been hitherto
publifhed, and may perhaps ferve to illuffrate an ex-
ceeding rare coin, with a draught of which the learned
world has been obliged by M. Bouteroue. As therefore
it may poflibly be deemed not altogether unworthy the
notice of the Royal Society, I have taken the liberty
to trouble them with a few conjectures upon it ; ef’pe-
cially, as they have done me the honour to order the
publication of two papers, a few years fince, upon
fimilar fubjects. To this I have likewife been farther
excited by part of a letter, written lately to my worthy
friend the Reverend Mr. John Nixon, a learned mem-
ber of the Society, by Sig. Abate Venuti ; who
therein mentions the famous F. Corfini’s approbation
of my remarks upon MonnefesJs coin, inferted in the
fiftieth volume of the Philofophical Tran factions,
excepting that he fufpeded the Victory on the re-
verfe to allude to the Parthian monarch’s devaftation
of the neighbouring provinces, and ufurpation of the

Parthian

Tbit os. Tram VolLI. TAB.XVII^k 6'8o.

Apud Joanne m S wmton, S.T.E . Oxoniens . R.S.S .

i A

l T

,y

I

« . t > Yj V

♦

[ 68 1 ]

Parthian throne. I have therefore endeavoured to
remove the fufpicion F. Corfini has entertained, and
attempted to prove, that the impreffion of this
Victory , fo utterly repugnant to the Parthian genius,
muft have been occafioned by fome remarkable ad-
vantage, gained by the Parthian forces over the Ro-
mans. In order to which, I have at lealt in fome
meafure evinced the Romans to have adorned with
fuch a Victory the reverfes of their coins, not only
after a battle had been won, as F. Corfini would
feem to maintain, but likewife on certain occafions
after other profperous military exploits. It is alfo
here rendered probable, that the ViSiory was im-
preffed on Monnefes’s medal, in allufion to the man-
ner in which the Romans treated the Parthians, on
their coins, after any favourable military event ; that
F. Corfini is not quite confiftent with himfelf, the
reafon by him aligned for differing from me, on the
principle he has advanced, being fubverfive of his own
opinion ; and that, as the reverfes of the other Par-
thian medals never exhibit a Victory in the Ro-
man tafte, the coin before me could have been {truck
only to perpetuate the memory of fome fignal at-
chievement, performed by the Parthian arms againft
the Romans.

If the conjectures now fubmitted to the confidera-
tion of the Royal Society fhould meet with the ap-
probation of that molt learned and illuftrious body,
they will undoubtedly be allowed to throw fome
light on the lingular and valuable medal above-men-
tioned, publifhed by (t) M. Bouteroue, never hi-

fi) Recherches Curieufes des Monoyes de France &c. Par Claude
Bouteroue, p. 33. A Baris, 1666.

therto

[ 682 ]

therto explained. I therefore judged it not improper
to tranfmit you an accurate draught of this coin, as
well as one of the medal here fo particularly de-
fcribed ; [Vide Tab. XVII.] which may probably be
the more acceptable to many, who have a tade for
this kind of literature, as M. Bouteroue s book itfelf
cannot now without great difficulty be found.

With regard to the language of the paper in which
my remarks are contained, I (hall only beg leave to
hint, that it is underflood by all who are proper
judges of the performance. For this therefore I ffiall
offer no other apology, than that the letter from Sig.
Abate Venuti to Mr. Nixon, which occafioned it,
is penned in the Latin tongue ; and that the famous
F. Corfini, the removal of whofe doubt or fufpicion
was one of the principal objects I had in view, writes
for the mofl part at lead in the fame language. I
might however add, that many learned foreigners,
who are particularly pleafed with fuch difquifitions,
are much better acquainted with Latin than any
other tongue, except their own; and that it were
to be wifhed the ufe of this noble language, in the
republic of letters, were more general than it at pre-
lent (2) feems to be. You will give me leave only
farther to fugged, that there can be no impropriety
in communicating to the Royal Society the following
remarks, the (3) paper they are intended to fuppoit
not only authorizing but even requiring fuch a com-

(2) Nov. An. Eruditor. Lipf. Menfts Mali A. 1755. p. 252.

(3) Pbilofoph.Tranfaft. Vol. L. p. 184 187.

munication ;

C 6*3 ]

munication j and to allure you that I am, with the
moll perfect attachment and refped.

Chrift-Church, Oxon.
Apr. 24th, 1760.

S I R,

Your moll faithful,
and moll obedient,

humble fervant,

J. Swinton.

In Nummum Parthicum haSlenus hieditum

conjefturce.

v I.

NUmifma plane incognitum, quod vulgavit ( 1) D.

Bouteroue, in adverfa parte regis cujufdam im-
berbis exhibet caput, tiara margaritis five unionibus
fulgente ornatum j in averfa verb binos racemos, ut
et trinas inulitata forma literas, quarum poteftas eti—
amnum ignoratur. Aliud item haud parum detri-
menti a tempore perpelfum, cujus edtypum Regise
Societati jam vifendum filto, capite regis tali mitra

(1) Recherches Curieufes des Monoyes de France iffc. Par Claude
Bouteroue, p. 33. A Paris, 1666. Si Gamma pone Vologefis III.
caput Gazam, vel Gazacam, Mediae Atropatiae urbem, indigitet,
ut exiftimat Vaillantius (1); trina elementa incognita, in nummo
Bouteriano confpicua, eandem forfan urbem defignent. Quod et
ipfae eorundem formae fuadere videntur. Primum enim Gimel
Phoenicium figuia refert, fecundum Z am Chaldaico et Palmyreno
non eft abfimile, tertium verb ipfiflimum Phoenicium Ain fe facile
fatetur. Ain autem (2) nunc Alepb, nunc Gimel (3) fonuit. Hinc
igitur vox Gaza, Straboni (4) ufitata, Gazag, vel Gazaca, quae
Stephano (5) Byzantino magis placuit, fortafle fit enata.

(1) J. F. Vail!, drfactd. Imper. p. 366. Parifiis, 1718. (2) Boch. Cban, p. Sit,

813. Francof. ad Man. l65i. (3) Id. ibid. p. 561. (4) Strab, Lib, xi. p. 523

(5.) Steph. Byzar.t. in voc. F A Z A K. A. -

Vol. Lh 4T feu

[ 684 ] '

feu tiara confpicui nobilitatum, fupellex mea anti-
quaria fuppeditat. Hoc ante caput fceptrum often-
tat, pone autem figuram, quas Graecum elementum
Gamma referre videtur. Caetera nummus nofrer Bou-
terouiano non difiimilis jure haud iniquo cenfendus.
Quare altero aliquantulum illuftrato, nonnihil etiam
lucis alteri forfan afpergatur.

II.

Tiaram quod attinet, noftro in numifmate de-
pidum, eum e redis unum efle, quos, Xenophonte
(2) tefte, Cyrus accepit a Medis, et ad fucceffores
tranfmifit, fummae majeftatis infignia, ita ut nemini
liceret gerere, nifi regibus, ex audoribus hie lauda-
tis abunde fit perfpicuum. ‘c Solos (ait (3) V. C.
Theophilus Sigefridus Bayerus) “ reges geflifle ad-
“ firmant nobis Ariftophanes et ejus Scholiafta de
“ Perfis, Jofephus autem et Dio Prufieus de Parthis.”
Pergit Cel. Bayerus, “ Quos igitur (tiaras) dicemus
“ redos nifi eos, qui non lunatum in orbem circum
“ tempora flederentur, fed rigidiores eflent apices et
“ altiores ? — Neque aufi funt (ft eundem audiamus
Bayerum) {t Edefifeni reges iis uti, potentia et ma-
“ jeftate inferiors Parthis.” Quandoquidem igitur
hie nummus ante everfum ab Artaxerxe Parthorum
imperium videtur procufus, ac proinde ad Perfas,
faltem pofteriores, vix referendus; eum a Parthias
quodam rege fuifie percuflum, etfi tiarae figura parti
adverfas infculpta complurium Parthicorum formas non
ad amuffim congruat, omnino certe par eft arbitrari.

(2) Xcn. Cyrop. L. viii. c. 3.

(3) Theoph. Sig. Bayer. Hjl, Ofrboen. & Edejfen. &c, p. 1 35*
13b. Petropoli, 1734.

[ 685 ]

III.

His rite perpenfis, tiaram nobis Parthorum regem
indigitare, cordatum quemque vix inficias exiftimo
iturum. Quo concefio, Vologefem III. numifma
noftrum cudifie, indicio erunt, forfan certiffimo,
in priori facie ante caput fceptrum et pone litera
Gamma , fi modo figura fuperius memorata pro ifto
elemento commode fatis accipi poflit. Etenim hujufce
principis nummum, a (4) Cl. Vaillantio publici juris
fadtum,five typum, five modulum refpiciamus, noftrum
plurimum referre, vel caecutienti fat dare innotefcat.
Nil interim mirandum, quod caput regis imberbis,
feu potius mediocriter barbati, antica primum cften-
taverit; cum (5) Mannus, regulus finitimus Parthis,
in nummulo fine barba depingatur, et nonnulli Par-
thorum (6) reges (quorum numero ipfe forfan Volo-
gefes III. accenfeatur) mediocriter tantum barbati in
numifmatis interdum confpiciantur.

IV.

Quod ad binos racemos fpedlat, quibus pars num-
mi nofiri pofterior cernitur fignata, id quoque quic-
quid fit fymboli Parthorum regem ante oculos ponere
fortafle reperietur. Numifma enim argenteum majori
forma penes fpedlatiflimum virum, Henricum March,
armigerum, a V. C. Arthuro Pullinger ex Oriente

(4) J. F. Vaill. Jrfacid. Impcr. p. 364 — 369. Parifiis, 1728.

(5) Nicol. Fran. Haym Roman. Del Tcfor. Britan. Vol. Second,
p. 57, 58. In Londra, 1720. Numifm. Antiqn. Collett, a Thom.
Pembr. et Mont. Gom. Com. P, 2. T. 72. Wife Epijl. ad V.
Cl. Joannem MaJJon de num. Abgari Regis. Oxon. 1750.

(6) J. F. Vaill. Arfaeid. Imper. p. 31, 58, 105, 321, 364,
366, &c.

4 T 2 feciun

[ 6S6 ]

fecurn in Britanniam reportatum, in antica typum
oftentat, Parthico (quo complures nummi (7) infig-
niuntur) non diflimilem : principem nempc fellae in-
fidentem, manibufque fagittam geftantem, ante cujus
pedes vifitur arcus ; in poftica vero fenem, dniftra
tenentem racemum. Si igitur numifma noftrum ad
Vologefem HI. pertinuiffe autumemus, a vero forlan
non multum abludemus. Interim ii coidatus quil-
piam aliter fenferit, integrum lit ipfi fua gaudere l'en-
tentia, eandem quoque nobis largiatur veniam.

V.

Si fuperius annotatis fuffragentur eruditi, et a Vo-
Ioaefe III. nummulus nofter habeatur revera percuffus,
rogitet forfan aliquis, “ qul fit ut princeps ifte ®reos
<< cuderit nummos, cum argentei fere ioli (fi ex iis
« q^ii nobis fuperfunt hac de re judicium faciamus)
<< fub ejus in imperio antecefloribus prodierint ? ”
Cui refpondeamus licet, “ Monnefis nummus, te-
“ tradrachmarum magnitudine (8), a Cl. Vaillantio
“ evulgatus, pariter ac nofler, aereus eft ; quin ct
“ alium Vologefis II. rariflimum ad aereorum mediae
“ formae numerum idem adfcripfit (9) Vaillantius-
“ Quidni igitur Vologefis III. numifmata interdum
“ ex sere cernantur conflata ? Hoc enim fadtum
tc fuiffe propter res Parthiae difficillimas, eo imperii
“ clavum tenente, fummamque argenti penuriam,
<l cum jam laudato (10) Vaillantio arbitramui.

(7) J. F. Vaill. ubi fup. pafT.

(8) J. F. Vaill. Arfacicl. Imfer. p. 341.

(9) Idem ibid. p. 345.

(10) Id. ibid. p. 341.

VI.

[ 687 ]

|

VI.

Parthorum res fub Vologefelll. baud parum fuifle
turbatas, bello iis a Severo tunc temporis illato,

( 1 1 ) ex Herodiano, Spartiano, et Dione abunde con-
ftat. Anno enim Arfacidarum serae vulgaris 4 56°. vel
4570. feu potius, ft meam eatur in fententiam (12),
429°. Severus Parthos inopinato eft aggreftus ; quin
et caefts primo quicmique obvii ei Jujit faffii, non
quicwiqiie rejiitiffent , ut Herodiani (13) verba,
ttccvtx TS r i/x7Tt7rlo.i'1ci, perpetam Latine vertit An-
gelus Politianus, regiam Cteftphontem trajedo Tigri
cepit, atque militibus diripiendam conceffit. Illinc
ipfo rege cum paucis tantum equitibus elapfo, the-
fauris illius ornatuque omni et fupelledile potiti vic-
tores regrediuntur. Quanquam autem, profpere fuc-
cedentibus rebus, literas ad Senatum Populumque Ro-
manum de fe magnificas dederit, ac depidas in tabu -
lis pugnas, vidoriafque fuas, ft Herodiano (14) fides
ftt habenda, expofuerit Severus, nihil non honorum
decernente Senatu, et fuper his cognomina imponente
gentium devidarum ; “ ullam (15) tamen, eodem
4‘ anno, Romanos inter et Barbaros revera interfuifte
<c pugnam,” ex ifto hiftorico haud facile colligamus.
Neque ab Herodiano hac in re diflentit Spartianus
(16), qui nullius Severum inter et Vologefum praslii,

( 1 1 ) Herodian. Lib. iii. JEl. Spartian. in Sever. Dio, Lib. lxxv..
p. 854.

(12) Pbilofopb. Tranfali. Vol. L. p. 183 — 187..

(13) Herodian. ubi Tup. c. 30. Oxon. 1678.

(14) Idem ibid. c. 31 .

(15) Venut. ad V. C. ‘Joamem Nixonum , A. M. & R. S. S.
Epiji. Vid. etiam Adi. Pbilofopb . Anglican. Vol. LI. p. 205.

^16) JLl. Spartian. ubi Tup.

dido

[ 688 ]

didto anno commifti, ufquam meminit. Quod quidem
filentium calculo fuo egregie confirmat Dio (17), cujus
fic fe ferme habent verba : “ Item Seluciam et
“ Babylonem defertas celeriter occupavit , ac paulo
“ poft Ctefiphontem ; quam urbem diripiendam re-
<c liquit militibus, et in ea caedem maximam fecit,

“ cepitque fuperftitum hominum ad centum millia.

“ V ologefum tamen non eft infecutus, neque Ctefi-
“ pbontem retinuit j fed tanquam ob id folum ve-
<( niftet, ut earn &c.” Unde veriftnile admodum
videtur, nullam Romanos inter et Barbaros bac for-
tuita in Parthiam expeditione interfuiffe pugnam ;
cum Seleuciam et Babylonem ab hoftibus fuifle de r-
Jertas , et a Severo celeriter oc cup at as , celeberrimus
ille fcriptor diferte monuit. Celeberrimus, inquam,
ille fcriptor j cum Dioni Severi comiti et familiari
omnino fidendum, praefertim ft fuo teftimonio didti
duo hiftorici, Spartianus et Herodianus, fcriptis ejus
etiam fidem adftruxerint. Aft quanquam in fua ad
Senatum epiftola praslia quaedam tantummodo com-
mentus fit Severus, Vifforiam in averfa parte Gradien -
tem pras fe ferentes (18), denarios tamen, in perpetuam
rei memoriam, fignari juflit. Unde quodammodo
patet, Romanorum imperatores Viftoriam in num-
mis Gradientem' interdum fcalplift'e, licet nulla “ in-
<c ter eos gentemque devidtam interfuift'et (19) pugna.”
Quod et alio forfan exemplo, ex hiftoria Romano-
Partbica petito, clarius elucefcet. In belli adverfus ,
Parthos ab Antonino Caracalla gefti memoriam, prin-

(17) Dio, Lib. Ixxv. p. 854.

(18) J. F. Vaill. ubi fup. p. 361.

(19) Vrenut. ubi fup.

ceps

[ &8g ]

ceps ifte (20) nummos argenteos percuffit, Victories
Parthicce typum exhibentes. Incruentam tamen a
Parthis reportavit vibtoriam. Etenim, “ ingenti caede
“ Parthorum fadta, praedaque et hominibus magna
<c copia captisj difeedit, teftante Herodiano (21),
“ fxri^evos ccutm ccv^re^oo t^>, rejijlente millo , vicilque
“ et urbibus incenfis, data poteftate militibus ra-
<c piendi, quod quifque poflet, aut vellet.” Cum
Herodiano item, bac in re (22), concinit Dio; ei
enim h fidem tribuamus, Antoninus regionem, quae
Mediam attingit, in quam de improvifo irruerat,
magna ex parte vaftavit, multa caftella diruit, Arbela
fubegit, ac fepulchra regum Parthorum, abje&is obi-
bus, fubvertit. “ Verum (23), ait hiftoricus, quia
“ Parthi cum eo non venerunt ad mantis , nihil de re-
“ bus tunc geflis feribi a me eximium poteft.”

VII.

Sed et fententias noftras hie in medium prolate cal-
culum quoque fuum appofuit praeftantidimus Span-
hemius. Inter alia enim hue fpedtantia erudite an-
notavitVir (24) Clariffimus, “ VICTORIAM PAR-
“ THICAM, cum in M. Antonini ac L. Veri, turn
<c Severi, Caracallse, ac Macrini nummis legi, immo
<c in Severi nummis etiam VICTORIAM PAR-
“ THICAM MAXIMAM : a quibus utique prin-
<f cipibus bella feliciter contra Parthos gejla me-

(20) J. F. Vaill. ubi Tup. p. 375.

(21 ) Herodian. ubi fup. Lib. iv. c. 20. p. 163. Edit. Oxon. 1678.

(22) Dio, Lib. Ixxvii. p. 881.

(23) Idem ibid.

(24) . Ez. Spanhem. De Prajiant. fcf Uf, Numifm. Antiquor .
Pol, Alter, p. 635, Amftelaedamij 1717.

(C

morant

[ 69o ]

xc morant Romanarum rerum fcriptores, ac firmant
« infuper, cum iidem nummi, turn additum in iis
<« PARTHICI, et quidem fubinde PARTHICI
“ MAXIMI, cognomentum.” Notatu hie non in-
dignum, numifmata RomanaVICT. PART, voci-
bus dimidiatis in averfa parte exornata Victoria iti-
dem figuram pras (25) fe ferre. Unde omnino
patet, Romanos in nummis VICTORIAM PAR-
THICAM, audore Cel. Vir. Ezech. Spanhemio,
fcalpfifte (26), fi bella feliciter contra Part bos 3 vel
praslio fecundo, vel alio quoquo modo, gererentur .

VIII.

Haic de monetam Vittorio, fignandi more, Ro-
manis diu ufitato, dida funto. Ad Parthos quod
attinet, ex nummis talem apud eos confuetudinem
{27) non invaluifle conftat. Vittoria igitur, five
potius Vittorio Gradicns3 Latinum ad modum in-
fculpta, certiffimo eft indicio, Monnefen numifma
banc oftentans (28), a me fufius olim atque ube-
rius explicatum, in rerum contra Romanos, felici-
ter geftarum memoriam, utque iis par pari refer-
ret, praefertlm ob fignatam fimili typo pecuniam
a M. Aurelio Antonino et L. Vero vidoribus (25?),

(25) J. F. Vaill. ubi fup. p. 333* 375> &c- Uancifc.

Mediobarb. Birag. Imperator. Romanor. Numifm. <3c. pall.

(26) F.z. Spanhem. ubi fup.

(27) T. F. Vaill. Arfacidar. Imper. Nicol. Fran. Haym Ro-
man. W. Tefor. Britan. Vol. Second, p. 30—37. Muf. 1 heupol.
p. 1221, 1222. Numifm. Antiqu. &c. 'I hem. Pembr. & Mont,
bom. Com. &c. P. II. T. 76. Claude Bouteroue, ubi fup.

aliique Scriptor. pafT.

(28) Pbilofoph. Tranfaft. Vol. L. p. 1 75— 18b.

(29) J. F. Vaill. ubi fup. p. 333.

percuftiffe.

1 691 ]

percuffiffe. At praelium exinde tunc temporis Ro-
manos inter et Parthos fuiffe commiffum, propter
rationes fuperius allatas, haud aequo jure colligamus.
Quare leviter faltem lapfus videtur (30) V. C. Ed-
vardus Corfinus, (31) cc ubi dubitat, ad epocham
“ ftatuendam, de Vidlorid in poftica (regis Mon-

(3°) V. C. Edv. Corfin. apud Venut. in Latin, ad Joan. Ni~
xonum Epijl.

(31) Perpenfo (quod fequitur) Cl. Nixoni apographo, ab eo
mecum quam humaniffime communicato, de vero hie fenfus acu-
mine cordatus lector liquidius judicare poflit. 44 Cl. Corfino doc-
44 tiflimas Cl. Swintom conjedturas de nummo Monnefis Partho-
44 rum regis communicavi : ille vero comprobavit, admiratulque
44 eft folertiam authoris, ingeniique acumen ; tantummodo ubi
44 dubitat , ad epocham ftatuendam, de ViRorid in poftica ex-
44 culpta, cum eo anno nulla interfuerit pugna inter Romanos et
44 Barbaros : fed cum Monnefes regnum ufurpaverit, legitimofque
44 fpoliaverit haeredes, vicinaque devaftaverit regna, nil mirum ii
44 ViRoriam in nummis infculpferit, atque ad Barbaricam, non
44 ad Romanam, referri debet.” Hinc abunde conftat, Coriinum,
non me, ut voluit Cl. Nixonus, 44 ad epocham ftatuendam, de
44 ViRorid in poftica exculpta dubitaffe.” Nemini enim non
liquet, meam de vera Arfacidarum aera, hujufee Victoria typi
ope, felicius enodanda fententiam, quanquam immerito, in du-
bium vocafle Cl. Coriinum ; 44 cum eo anno nulla, ft ilium audi-
44 amus, interfuerit pugna inter R.omanos et Barbaros.” En caufa,
cur, 44 ad epocham ftatuendam, de ViRorid in poftica excel ptA
44 dubitaverit” Corftnus, ab ipfo Corfino, vel, ft malimus, v e-
nuto, in medium prolata. Quinimo ViRorits ft guru, in roc
Monnefis numifmate fealpta, seram Parthorum Corfinianam (vel
invito Corfino) fine ulla dubitatione ftrmandam duxi, ut ex noftris
ARis Pbilofophicis omnino fit perfpicuum. Voces igitur tantmn-
rnod'o ubi dubitat minus redte but excepted a little to that part , where
he [ Mr. Swinton] exprejjes a doubt , fiquid judico, Anglice vertit
Cl. Nixonus. Neque meo folo, hac in re, nixus fum judicio;
cum prrecellentes, quotquot confului, eruditione amici, inter quos
eminet reverendus ac dobliffimus vir, Jofephus Sanford, S. T. . B
Collegii Ballioleniis Oxon Socius, milft ccrtatim adftipularentur.
Philofoph. TranfaR, Vol. L. p. 185.

Vol. LI., 4U w nefis

[ 692 ]

nefis nummi ) exculpta, cum eo anno nulla
“ interfuerit pugna inter Romanos et Barbaras;”
tametfi meam hujufce numifmatis explicationem,
quod fummo mihi honori duco, tefte Cl. Ve-
nuto (3a), comprobavit-

IX.

Sed et minus fibi conftare, fi non aperte Tecum
pugnare, quoque videtur vel Cel. Corfinus, vel doc-
tiffiinus Venutus ; cujus hue fpedtantia, in pereru-
dita fua ad V. C. Joannem (33) Nixonum epiftola,
ita fe habent verba. “ Sed cum Monnefes regnum
“ ufurpaverit, legitimofque fpoliaverit hasredes, vi-
t£ cinaque devaftaverit regna, nil mirum fi Vitto-
“ riam in nummis infculpferit, atque ad Barba-
“ ricam, non ad Romanam, referri debet.” Hinc
enim abunde conflat, docente nos vel Corfino, vel
Venuto, Monnefen monetam fuam Vittorio fig-
naffe, propterea quod “ regnum ufurpaverat, legi-
“ timofque fpoliaverat hasredes, vicinaque devafia-
“ verat regna,” quanquam de praslio inter eum et
Barbaras commiffo omnino fileat hiftoria. Aft hoc
minime patitur inftituti Corfiniani ratio, quandoqui-
dem antea “ dubitaverat de Vittorio, in poftica
** exculpta ” Vir dodtiffimus, “ cum eo anno nulla
“ interfuerit pugna inter Romanos et Barbaras,” fi
ex hiftoricorum filentio id evinci poflit. Pari igitur
jure ViBoriam Barbaricam, fi hujufmodi valeat ratio,
ac Romanam repudiemus.

(32) Vcnut. ubi fup.

(33) Idem ibid.

C 693 ]

X.

Sed lit verutn aperte atque ingenue fateamur, id
genus argumenta, ex hidoriae filentio du&a, facile
' et nullo negotio, advocata prsefertim nummorum
fide, haud raro refelluntur. Vidorias Romanorum
copiis partas prasdantiora interdum memorant numif-
mata, ab eorum fcriptoribus filentio penitus praeter-
miffas ; cujus, ut alia nunc non in medium proferam,
nobis exemplo fit VICTORIA GOTTHI. P. (34)
a Taciti imperatoris nummo ante oculos pofita, et
ca3teroquin (ut opinor) minimum nota. Parthos igitur
Romanorum aciem non profligaffe, eodem quo Me-
fopotamire urbes ceperunt anno, utcunque de pugna
taceat hidoria, pro certo dicere non aufim. Imrao
Parthos cum Romanis turn dimicafle a vero non uf-
que adeo forfan alienum reperietur, fi Vaillantium,
cujus de Monnefe fenfa prefle fatis fequitur (35) Cl.
Cordnus, perpendamus (3d) innuide, cc hunc prin-
“ cipem SQTHPOX epitheton fibi adrogavide, ob
cc egregium quoddam adverfus Romanos facinus bel-
“ licum j quo populorum omnium fibi benevolen-
<c tiam atque amorem conciliavit, quoque in turbu-
“ lento illo rerum datu ad Parthicum folium viam
cc fibi patefecit.” Utut tamen ed, nil mirum fi
Vittoriam , more Romano Gradient cm , Monnefis
nummus jam odentet; cum bella (37) contra Roma-
nos feliciter gelferit, et totam fere Mefopotamias pro-
vinciam, fecundum (38) Dionem, perdomuerit.

(34) Francifc. Mediobarb. Birag. ubi fup. p. 410. Mediol. 1683.

(35) Edv. Corfin. apud Venut. ubi fup.

(36) J. F. Vaill. ubi fup. p. 34O.

(37) Idem ibid.

(38) Dio, Lib.Ixxv. p. 853 Pbllof.TranfVo l.L. p. 184, 185.

4. U 2 L XVII. An

[ 694 ]

LXVII. An Account of a Jlony Concretion
t alien from the Colon of an Horfe ; by Mr.
H. Baker, F. R. S.

Read May 8, I Have now the honour to lay before this

1760.

Royal Society one half of a flony con-
cretion, formed in the colon of an horfe, which was
lately fent me from Norwich, by my very curious
friend Mr. William Arderon, F. R. S. This horfe,
he informs me, was twenty-five years old, had been
often ill, and under the farrier’s care j which made
him defire to have it opened, when dead.

The whole fione, when firfi: taken out, weighed
ten pounds and half ; and he caufed it to be fawed
in two, that a better judgment might be made of the
manner of its formation. Several fmaller concretions
were alio found in the colon, fome whereof are fhewn
herewith j but they are much lefs folid, and more
irregular, than the large one.

This ball is full feven inches in diameter, and con-
fifts of many laminae, or coats, which form a num-
ber of concentric circles, around a nucleus in the
center, which leems to be a fmall fhiver of black
flint. Fifteen or fixteeen of thefe coats are eafily di-
ftinguifhable, and fome have been broken off : they
vary fomething in colour, and are, in general, fo
ftony, that they v/ould probably take a pretty good
polifh. The coats differ in thicknefs, according, per-
haps, to the time they were in forming : for it fhould
feem, if conjedture may be allowed, that each coat
was formed in a longer or fliorter time, according to
2 its

[ 695 ]

its thicknefs ; and that, between the finifhing of one
coat and the beginning of the next, there was fome
interval of time, and fome fufpenfion of that attractive
power whereby, or of that component matter whereof,
the feveral coats are refpeCtively formed.

Strand, May 8, 1760. H. Baker.

LXVIII. An Explanatio?i of the Modes or
' Tones in the antient Graecian Mufc ; by
Sir Francis Hafkins Eyles Stiles, Bart .

R R. S.

Read Decem- “l Otwithftanding the valuable edi-

ber 1750, and I I I . r , 0 r ,

January, &c. f ^1 tions or the antient mulical and

1760. J harmonic writers, given by Meibomius

and Wallis, and the great pains thofe two learned
editors have bellowed on the correcting the tables,
and throwing light on the difficult paffages of thofe
works, there are fome of the doCtrines delivered in
them, that feem dill to require a more perfeCt ex-
planation. Thofe, that refpeCt the tones or modes,
in particular, feem to have been ill underftood : and
as it was on thefe, that the effeCts of the antient
mufic were fuppofed principally to depend, I have
thought, that the fubjeCt might well merit a re-
examination.

Concerning thefe modes, we find two diftinCt, and
feemingly contradictory doCtrines delivered by the
antients 5 and this it is, which has perplexed the fub-
jeCt;

[ 696 ]

je<5t j for fome, not aware of the diftinCtion, have
charged the antients with contradictions j and others,
who perceived the two doCtrines, not being able to
reconcile them, have either adopted one, and rejected
the other, • or given up the fubjeCt as hopelefs : but,
as they were both admitted by the antients, they mull:
both have been true, in lome fenfe. What, therefore,
I have principally in view in thefe fheets, is to drew,
that the difference between the doCtrines arofe only
from the different way of confidering one and the
fame objeCt ; and that therefore there was fuch an
agreement betwixt them, as that, under certain re-
ftriCtions, they may be embraced under one common
interpretation.

For diftinCtion fake, 1 fhall call one of thefe doc-
trines the harmonic, and the other the mufical doc-
trine ; the reafon of which will fufficiently appear,
when I come to treat of the diftinCtion between the
fcience of harmonic and that of melopceia or mufical
compofition.

According to the harmonic doCtrine, the number
of the modes had been augmented to fifteen ; but as
Ptolemey, who appears to have favoured the mufical,
reduces them to feven, and as it is on the principles
of that writer, that I propofe to fhew an agreement
between the doCtrines, it will be neceffary for me, in
treating of the harmonic modes, to difiinguifh the
feven he admits from the eight he has excluded.

This being premifed, I fhall be underftood in
making the diftribution of what I have to offer upon
this fubjeCt, which I propofe to treat under the fol-
io wine fix heads.

Fir ft.

[ 697 ]

Firft, To explain the harmonic docffrine, as far as
concerns the feven modes admitted by Pto-
lemey.

Secondly , To explain the mufical dodrine of the
fame modes, and fhew its agreement with the
harmonic.

■ Thirdly , To explain the eight harmonic modes re-
jected by Ptolemey, and give at large his reafons
for excluding them.

Fourthly , To point out fomething of the origin of
the two doctrines.

Fifthly , To drew how far the preceding explana-
tions may be fupported by arguments, or war-
ranted by the teftimony of antient writers.

Laflly, To confider how this fubject has been un-
derftood by Meibomius, Wallis, and fome few
others that have wrote fince, and in what refpect
their explanations differ from my own.,

I now proceed to the firff head ; viz.

FtrJ? , To explain the harmonic doctrine, as far as
concerns the feven modes admitted by Pto-
lemey.

The harmonic doctrine of the tones we find ex-
prefiy delivered in the harmonic treatifes -y which,
probably, is the reafon, why, among the moderns, the
later writers at leaff have, for the moll part, deter-
mined themfelves in its favour : how juffly it is in-
titled to the preference, I fhall have fufficient occafion
to examine. The treatifes on harmonic, that are come
down to us, are moffly Ariffoxenian, which fchool
feems to have treated the fcience, if not better, at

leaff

[ 698 ]

leaft more methodically than any other, of which we
can now form a judgment j and hence we find their
divifions often adopted by antient writers, who might
not, perhaps, be ready to admit all their principles.
In confidering the phyficai properties of found, and
the ratios of intervals, the Ariftoxenians appear to
have been lefs exadt than the Pythagoreans, the doc-
trines of the former being more adapted to the grofs
and familiar notions of the practical muiician, than
to the accurate fpeculations of the philofopher. But,
however exceptionable their treatifes may have been
in this refpedt, they are the more valuable to us, on
this very account, as they give more light into the an-
tient practice of mufic ; which is what is chiefly de-
iired, the philofophic principles of the fcience being
better underftood. By this fchool harmonic was di-
vided into thefe feven parts ; I. of founds, 2 . of in-
tervals, 3. of genera, 4* °f fyftems, y* of tones,
6. of mutations, 7. of melopceia. The propriety of
their adding this laft divifion I fhall have occaiion to
confider. Of thefe divifions, it was the fifth, which
contained the dodtrine in queftion ; but, to complete
it, the fixth mud alfo be taken in ; for, amongft
other mutations, that of the tones was there treated
of, and was indeed the moft confideraole objedt of
that divifion. This dodtrine taught, that the dif-
ference between one tone and another lay in the ten-
fion or pitch of the fyftem. dhe fyftem (by which
I mean the greater perfedt one, exclufive of the lets,
of which I fhall have little occafion to fpeak) con-
fifted of fifteen founds, extending to a difdiapafon, or
double odtave. How thefe founds were denominated,

* and at what intervals they fucceeded each other, in

the

[ 699 ]

the diatonic genus, to which I /hall coniine this ex-
planation, is fo well known, that I need fay no more
concerning the ftru&ure of the fyftem, than that it
anfwered to that of our natural fcale, beginning with
Are, and ending with Alamire. This fyftem was
held immutable, as to the relation of its parts one to
another ; that is, the order of founds and intervals,
by which it proceeded, was in the fame genus to be
always the fame; but the teniion or pitch of the
whole was variable, a different one being affigned
for each mode. The explanation, therefore, ufually
given of the iyftem, by comparing it, as I have done,
to a double ocftave, from A in our natural fcale, is
not to be underftood as fixing its pitch, but as {hew-
ing its fuccefiion only; which might as well be done
by a double odtave from B, taking C# and F # into
the fcale, or from any other note, taking in the flats
and /harps neceflary to make the tones and femitones
follow in the fame order.

The relation of the parts to each other in the fyftem
being immutable, the fixing the pitch of any one
found in it, for any mode, was fufficient to deter-
mine that of all the reft. For this purpofe, the found
mefe was commonly ufed ; which, by its fituation,
was well adapted to it, being the middle found of
the fyftem. If, therefore, we fettle the pofition of
the mefe for each mode, we /hall do all, that is re-
quifite for the clearing up and eftabli/hing the har-
monic dodtrine, which confidered the modes as dif-
fering only in the pitch of the fyftem.

The modes admitted by the Ariftoxenians were
thirteen in number ; to which two more were added
by later harmonicians ; and to the mefe of each of
Vo_l. LI. 4 X thefe

[ 700 3

thefe fifteen a diftindt pitch wasaffigned; but, as
Ptolemey has rejected eight of them, I fhall, as I
have propofed firft, feparately confider the portions
cf the mefe for the feven modes he admits.

Concerning the relative pitch of the refpedtive
mefes for thefe feven modes, I f nd no difagreement
amongft the harmonic writers. There are not want-
ing, indeed, who charge the antients with giving,
in refpedt thereto, contradictory accounts. Amongft
others, the learned Dr. Gregory aflerts, that Ariftides
Quintilianus inverts the order of the modes ( i ) : but
what led the dodtor into this miftake, was his not
diftinguifhing the double dodtrine. Ariftides, in the
paftage cited, is not fpeaking of the pitch of the
fyftem for the feven modes in queftion, but of the
feven fpecies of diapafon, as they lay in the fyftem $
which was, indeed, in the inverted order of the
mefes of the feven modes, as will appear, when we
come to confider the other dodtrine. This, then, is
no contradiction in the Greek writer, nor, if it weie,
would it be chargeable fingly on himj fince,. if the
dodtor had but caft his eye on his own Euclid (a),
he would have met with the very fame dodtrine he
found in Ariftides. But his remark is, indeed, en-
tirely without foundation ; and I make no fcruple to
aftert, that the antients agree in their accounts of the
relative pitch of the mefes, for thefe feven modes ;

(1) Atque Ariftides Quintilianus (pag. 18. editionis Meibo-
mianae) tonum Hypodorium acutiorem tacit quam Dorium, et
Hypophrygium quam Phrygium, et Hypolydium quam Lydium.
Vide Praefat. ad Opera Euclid.

(2) Pag. 540. verf. 6. et feq. feu pag. 15* ver^ J5*
Meibom.

[ 70i ]

for though many of the harmonic writers treat of the
thirteen or fifteen modes all together, without diftin-
guifhing the feven in queftion, yet they have given
them in fuch order, and at fuch difiances, that the
feven fiand at the fame intervals from each other, as
are afligned for them by thofe, who have treated of
them feparately ; fo that all the accounts agree in this
particular. The direction we may conveniently take
from Bacchius (3), where it is clearly and concifely
delivered ; and where it appears, that the Mixolydian
was the moft acute 5 the Lydian, graver by a femi-
tone; the Phrygian, graver than the Lydian by a
tone ; the Dorian, graver than the Phrygian by a
tone 5 the Hypolydian, graver than the Dorian by a
femitone; the Hypophrygian, graver than the Hypo-
lydian by a tone ; and the Llypodorian, graver than
the Hypophrygian by a tone. Now, as the Guido-
nian fcale, in ufe amongfi the moderns, when firipped
of Guido’s additions, anfwers to the fyftem of the
antients, in its natural fituation, which was in the
Dorian mode, and our Alamire confequently an-
fwers to the pitch of the Dorian mefe, we have a
plain direction for finding the abfolute pitch of the
mefes, for all the feven in our modern notes, and
they will be found to fiand thus :

Mixolydian mefe in d
Lydian in - - - c#

Phrygian in - - b

Dorian in - - - a

Hypolydian in - - g#

Hypophrygian in - f#
Hypodorian in - - e

But to underftand this dodtrine, as it is delivered by
the antients, it will be neceflary alfo to examine, how

(3) Pag. edit. Meibom.

4X2

the

[ 702 ]

the mefes of the feven modes were Rationed uporr
the lyre; and, in order to this, we mull: confider the
ftrudture of that inftrument. The lyre, after its laft en-
largement, confifted of fifteen fixings, which took in
the compafs of a difdiapafon, or double odtave. Thefe
firings were called by the lame names as the fifteen
founds of the fyftem, and when tuned for the Dorian
mode, correfponded exactly with them. Indeed them
can be no doubt, but that the theory of the fyfiem
had been originally drawn from the practice of the
lyre in this mode,* which was the favourite one of
the Greeks, as the lyre was alfo their favourite in*
firument. In this mode, then, the mel'e of the fyfiem
was placed in the mele of the lyre ; but in eveiy one
of the reft, it was applied to a different firing, and
every found of the lyftem tranfpofed accordingly.
Hence arofe the diftindtion between a found in power
and a found in polition for when the fyfiem was
tranfpofed from the Dorian to any other, mode, (fup-
pofe, for inftance, to the Phrygian)' the mefe of the
lyre, though ftill mefe in polition, acquired, in this
cafe, the power of the lichanos mcfon ; and the pa-
ramefe of the lyre, though ftill paramefe in polition;
acquired the power of the mefe. In thefe tranfpo-
litions, one or more of the firings always required
new tunings , to preferve the relations of the fyfiem;
but, notwithftanding this alteration or their pitch;
they retained their old names-, when fpoken of, in
refpedt to their pofitions only ; for the name implied
not any particular pitch of the firing, but only its
place upon the lyre, in the numerical order, reckoning

the prollambanomenos for the firft*

r I thought:

[ 7°3 ]

1 thought this remark the more neceffary, as I
fufpedt it was the not attending to this circumflance,
that led Dr. Wallis to affign c and g natural, for the
places of the mefe in the Lydian and Hypolydian
modes, inftead of c# and^#, where I have placed
them (4). But, to return.

We are now to give the places of the mefe for
thefe feven modes upon the lyre, which are thus
fettled by Ptolemey (.5)*

Mixolydian

Lydian'

Phrygian

Dorian

Hypolydian

Hypophrygian

Hypodorian

"Paranetediezeugmenon
Tritediezeugmenon
Paramefe - - - -

) Mefe in( Mefe - -

Lichanos mefon - -

Parhypate mefon - -
Hypate mefon - - -

String

1 1
10

9

8

7

6

The portions affigned for the mefes of thefe feven-
modes, by the harmonic dodtrine, being thus fettledr
both in our modern fcale, and upon the lyre, I come
now,.

Secondly, To explain the mufical dodtrine of tha
fame modes, and fhew its agreement with the
harmonic.

The mufical dodtrine taught, that the difference
between one mode and another confifted in the man-
ner of dividing an odtave,. or, as the antients- exprefs
it, in the different fpecies of diapafcn. The ele-
mentary principles of thefe fpecies we find delivered'

(4) See his edition of Ptolemey, p, 137

(5) Ibidem,

[ 7°4 ]

in the harmonic writers ; but as in the Ariftoxenian
treatifes, they are not found under the fifth divifion,
of tones ; nor under the fixth, of mutations, where
it was natural to expedt them ; but under the fourth,
of fyftems ; and it not being there exprelly affirmed,
that the lpecies had a relation to the tones, though,
from their denominations, and other circumftances,
it might well be inferred, this has created a difficulty
in admitting their connexion with the fubjedt. The
obviating of this objection I fhall referve for my fifth
head ; where I ffiall take occafion, particularly, to
juflify this dodtrine, and the ule I ffiall have made
of it ; and I ffiall therefore proceed to explain it, as
I find it in the harmonic writers.

To underftand how this dodtrine of the fpecies of
diapafon came to be treated under the head of fyftems,
it will be neceffary to confider the definition given
of the term fyftem by the Ariftoxenians, and their
fubdivifion of this branch of harmonic.

With this fchool, whatever confided of more than
one interval, was a fyftem. So comprehenfive a de-
finition could not but make this branch a very large
one ; and fo we accordingly find it. It was fubdivided
in the manner following : fyftems were there con-
fidered as differing in refpedt, firft, to magnitude ;
fecondly, to genus j thirdly, to the being confonant
or diffonant; fourthly, to the being rational or irra-
tional ; fifthly, to the being fequent or tranfgreffive ;
fixthly, to the being conjundt ordisjundt; feventhly,
to the being mutable or immutable. Now, of thefe
feven differences, it was under the third that the doc-
trine of the fpecies of diapafon came to be treated,
the confonant fyftems being there enumerated, and

explained.

[ 7°S ]

explained. By a confonant fyftem was underflood
a fyftem, whofe extreme or comprehending founds
were confonant : of thefe, there were fix within the
compafs of the immutable fyftem, viz. the diateffa-
ron, diapente, diapafon, diapafon and diateffaron,
diapafon and diapente, and difdiapafon. Thefe con-
fonant fy items were confidered as admitting each of
a variety in the order of the intervals, of which it was
compofed. A fyftem of a determined magnitude,
compofed of the fame intervals, and of the fame
number of them, might, if the component intervals
were not equal, differ in refpedt to their order or
fucceftion- Thefe variations of each fyftem they called
eiS'os, its fpecies, or its figure, for thefe terms

were fynonymous (6). The fpecies of diateffaron
were three 3 thofe of the diapente four, and thofe
of the diapafon feven, being the fum of the fpecies
of the other two confonances, of which the diapafon
itfelf was compofed: and here the dodtrine of the
fpecies flopped 3 for, in the three larger confonant
fyftems, they feem not to have confidered the fpecies
of the whole magnitude, but only thofe of the three
fmaller fyftems, of which they were compofed, and
which are called, by Ptolemey, the firft confonances
(7). As the fpecies of diateffaron and diapente do
not immediately concern this dodtrine, the explaining
them will be unneceffary 3 and I fhall therefore pro-
ceed to thofe of the diapafon.

(6) Msra J'e tal net AiKTtov, T/f er/, ka) ttoia r/<, » ' xar’ tri/of

S'lctqoty. j c P/apifti ^ ryiv iS'iv, eiS'o; Aiyeiv ij %7iyA' y<xg

ay^oTi^r. ta ovcy-ATA taut a iiri to auto. Ariftox. p. 74. v. 9.

(7) n^cT/oe^Ol' T At KATA TO KAKvy.tl’OV Uj'of TMV JpWTUV GVy.VCJ-

yiuv J'tApgf.t, Ptol. lib. ii. c. 3,

Concerning;

5

[ 706 ]

Concerning thefe, I find no difagreement amongft
the writers of antiquity: they all agree, that they
were feven in number, and had the denominations
of Mixolvdian, Lydian, Phrygian, Dorian, Hypo-
lydian, Hypophrygian, and Hypodonan ; circum-
fiances, which leave no doubt of their connexion
with the modes. The fucceffion of intervals, or
manner of dividing the diapafon for each fpecies, has
been varioufly explained by the antient waters ; but
the refult of thefe explanations is the fame,, except-
ins; the generic differences. It will be fufhcient here
to give what refpeds the diatonic genus only, as the
queftion concerning the tones does not turn upon the
diftindion of the genera.

In the diatonic genus, the diapafon conlilting
of five tonic and two femitomc intervals, the Ari-
ftoxenians fixed the fucceffion for each fpecies, by
the pofition of the two femitones ; fhewrng, at
the fame time, between which of the founds of
the immutable fyftem the fpecies in queftion was
comprehended: for this fyftem confiftmg of fifteen
founds, contained eight odaves, two of which
•viz. that from proflambanomenos to mele, anrt
that from mefe again to netehyperboleon, were
divided after the fame manner, and therefore con-
flicted the fame fpecies: but the fix others were
all differently divided ; fo that the fyftem con-
tained within itfelf the feven fpecies of diapafon,
and thence obtained the denomination of perfect 5
the leffer perfed fyftem, which reached only to
a diapafon and diateffaron, being improperly lo
called for want of this qualification, as Ptolen^

[ 7°7 ]

has fhewn (8). According to this method of ex-
plaining the fpecies of diapafon, they /land as fol-
lows :

Species,

i. Mixolydian

*

2. Lydian

3. Phrygian

4. Dorian

5. Hypolydian

rFrom hypate hypaton to para-
\ mefe.

J Semitones, firft interval in the
l grave, fourth in the acute.

rFrom parhypate hypaton to trite
\ diezeugmenon.
j Semitones, third interval in the
L grave, firft in the acute.

rFrom lichanos mefon to paranete
l diezeugmenon.

,1 Semitones, fecond interval in the
L grave, fecond in the acute.

rFrom hypate mefon to nete die-
J zeugmenon.

I Semitones, firft interval in the
L grave, third in the acute.

rFrom parhypate mefon to trite hy-
\ perbolaeon.

1 Semitones, fourth interval in the
L grave, firft in the acute.

6.

Hypophrygian

rFrom lichanos mefon to paranete
\ hyperbolason.

"j Semitones, third interval in the
L grave, fecond in the acute.

(8) '/0-3ii' to GWTiSiy.zvov tK J' i&'&o.ffav 39 cT/oe najafuv trvrn/xa.

7iheiov i H-&A uf KctAetr r a f/Xv irfd « V'tt tS cf/«.'3r£t<r&>V soH-

«wo7« Ptol. Harm. p. 106. v. 3.

Vol. LI. 4Y 7, Hypo-

Species.

7. Hypodorian

C 708 ]

SFronrmefe t§ nete hyperbolaeon,
or profl. to mefe.

Semitones, fecond interval in the
. grave,, third in the acute.

It mud be here obferved, that thefe fpecies, as
they hand in the fyftem, are, with refpe<& to acute-
nefs and gravity, in the inverted order of the feven
modes, as fettled by the harmonic do&rine, which
will account for the miftake, which Dr. Gregory (as
was {hewn above) and others have fallen into, in
imagining the antients did not agree in their accounts
of the modes ; fince it is plain thefe writers did not
obferve, that, in the one cafe, the modes were fpoken.
of with refpedt to the pofition of the fyftem itfelf,
and in the other, with refpedt to the pofition of the.
feven fpecies within the fyftem.

Thefe fpecies may alfo be more readily {hewn, by
examples out of theGuidonian fcale, where, keeping
die natural notes, they will ft and thus :

Mixolydian

Lydian

Phrygian

Dorian

Hypolydian

Hypophrygian>

Hypodorian

B to b .

C to c.

D to d.

E to e.

Fto /.

G to 'g.

e to a a3 or A to a.

But as well this, as the former way of {hewing
them, we are to underftand only as exemplifications
of the fucceftion of the intervals, and not as an affign-
ment of the pitch for each, which was to depend on

*hat of the fyftem, out of which they are exemplified ;

and

[ 7°9 ]

and it may not be amifs therefore, in order to pre-
vent any limited conception of thefe fpecies, to date
generally the order of the intervals, of which each is
compofed ; which will be as follows, proceeding in
each from grave to acute.

Mixolydian,

Lydian.

Phrygian.

Dorian.

Hypolydian.'

Hypophrygian.

Hypodorian.

Semitone, tone, tone, femitone, tone, tone, tone.
Tone, tone, femitone, tone, tone, tone, femitone*
Tone, femitone, tone, tone, tone, femitone, tone.
Semitone, tone, tone, tone, femitone, tone, tone.
Tone, tone, tone, femitone, tone, tone, femitone.
Tone, tone, femitone, tone, tone, femitone, tone.
Tone, femitone, tone, tone, femitone, tone, tone.

Befides the manner above-mentioned of explaining
the fpecies of diapafon, the antients have given us
another, the refult of which is the fame j and that
is, by the pofition of the diazeudtic tone, or interval
from mefe to paramefe. In the Mixolydian fpecies,
the diazeu&ic tone was the firft interval, reckoning
from acute to grave ; in the Lydian, it was the fe-
cond j in the Phrygian, the third ; in the Dorian,
the fourth $ in the Hypolydian, the fifth j in the
Hypophrygian, the fixth; and in the Hypodorian,
the laft.

Now, either of thefe methods fixes the fucceffion
of intervals peculiar to each fpecies j but as the
examples are taken from a fyftem, whofe pitch was
variable, we are ftill to feek, at what abfolute pitch
the feveral fpecies were taken in the modes, to which
we fuppofe them to have been refpedtively fubfer-
vient ; and it is, perhaps, the feeming difficulty of
fettling this, that has induced fo many to rejedt this
dodtrine entirely, and fall in with the harmonic
writers, who confidered the modes as differing only

4 Y 2 n

[ 7™ J

in the pitch of the fydem : but, by taking in the
abidance of the harmonic dodrine, we fhall not only
gain the true pitch for each fpecies in the mufical,
but be led to fee the agreement between the two
dodrines, which, I have already faid, was my prin-
cipal view in thefe fheets, and which, having gone
through the explanation of each dodrine feparately,
as far as concerns the feven modes, we are now ripe
for confidering ; for the eight modes, whofe expla-
nation I have deferred, have no concern in this agree-
ment, being rejeded by Ptolemey, as will appear,
for this very reafon, in fubdance, that they would
fiand the trial of the harmonic dodrine only, whereas
the red had the fupport of both. Let’ us then con-
fider how the two dodrines, as I have explained',
them, may be made to agree.

By the harmonic dodrine, we are told the pitch
of the fydem for each mode ; and by the mufical,
in wbat part of the fydem to take the fpecies of dia-
pafon : now, by combining thefe two diredions, we'
gain the following plain canon, for finding any mode,
required. -

Canon.

Fird pitch the fydem for the mode, as dirededf
by the harmonic dodrine ; then feled from it.
the diapafon, direded by the mufical; and we
have the charaderidic fpecies of the. mode in its
true pitch.

To make this more plainly appear, and alfo to
avoid the length of particular explanations, I have
annexed a. diagram of the feven lpecies, which will

fhew at what pitch of the Guidonian fcale each found

of,

Diagram I. Of the Species of Diapafon in the Seven Modes admitted by Ptolemev.

c

.2

*5

0

Paramefe.

e

c

•3

Trite diez.

e

c

"Si

-C

P-i

Paran. diez.

£

a

.2

0

Q

Nete diez.

e

d*

c

.2

•3

0

CL.

Trite hyperb.

c

*&

£

§•

a.

X

Paran. hyperb.

c

rt

O

T3

O

CL,

X'

aj

c

0

N

d*

Paramefe.

Nete diez.

6

6

s

Mefe.

O

c

0

d

Trite diez.

d

Paran. diez.

d

r*

Trite hyperb.

d

Paran. hyperb.

c*

rt

Q

Mefe.

c*

Paramefe.

r#

Paran. diez.

Nete diez.

Lich. mef.

oj

c

0

c

Trite diez.

Trite hyperb.

b

Lich. mef.

b

s

Mefe.

b

Paramefe.

b

Trite diez.

U

Paran. diez.

b

Nete diez.

Parhyp. mef.

R

0

a*

Paramefe.

n

Hyp. mef.

a

Parhyp. mef.

a

Lich. mef.

a

Q

Mefe.

u

c

a

g*

Trite diez.

a

Paran. diez.

g*

Hvp. mef.

g*

Q

Mefe.

Paramefe.

«J

Lich. hyp.

g

Parhyp. mef.

g

Lich. mef.

0

g

Trite diez.

N

f*

Lich. hyp.

r

Hyp. mef.

f*

Lich. mef.

f*

Q

Mefe.

f*

Paramefe.

Parhyp. hyp.

f

e

Parhyp. mef.

ci

c

0

Hyp. hyp.

e

Parhyp. hyp.

e

Lich. hyp.

Hyp. mef.

e

Parhyp. mef.

e

Lich. mef.

e

g

Q

Mefe.

Vol, LI. Page 710.

f

[ 7» J

of the diapafon is brought out by the canon for each
of the feven modes. As in the conftruCtion of this
diagram, the directions of the canon have, been
flriCtly purfued, fo it will appear, that the refult of
it is, in all refpeCts, conformable to the principles of
both doCtrines. Thus in the Dorian, for inftance, it
will be feen, that the mefe is placed in Alamire, and
that the reft of the founds exhibited in that diapafon,
are placed at the proper diftances, for preferving the
order of the fyftem, as required by the harmonic
doCtrine. It will be alfo feen, that the diapafon fe-
leCted lies between hypate mefon and nete diezeug-
menon; that the femitones are the firft interval in'
the grave, and third in the acute ; and that the dia-
zeuCtic tone is in the fourth interval, reckoning from'
the acute; all which circumftances were alfo required
by the mufical doCtrine for this mode; and, in the
reft of the modes, all the circumftances required by
each doCtrine will, in like manner, be found to ob-
tain: fo that no objection can well be raifed to the
principles, on which the diagram has been framed, by
the favourers of either doCtrine feparately; and the
very coincidence of the two doCtrines therein, might
furnifh a probable argument in juftification of the
manner, in which I have combined them in the
canon. But as I propofe to confider this under the
fifth head, where the proofs will be collected, I fhall
leave this argument for the prefent, and proceed to
explain, ,

1 Thirdly , The eight harmonic modes rejected by
Ptolemey, and give at large his reafons for ex-
cluding them,.

Six

[ 712 3

Six of thefe modes, with the feven Ptolemey al-
lowed, made up the thirteen allowed by the Arifto-
xenians : the other two feem to have been added
afterwards, more with a view to regularity in the
names and pofitions of the modes, than to any par-
ticular ufe, as will appear in the courfe of the ex-
planation. For the lettling thefe eight modes,. I
fhall have no occafion to go farther than the fixing
the pofition of the mefe for each, according to the
harmonic dodtrine : the refult of applying the mufi-
cal do&rine to them will lufficiently appear, when
I come to explain the reafons, which Ptolemey has
affigned for rejecting tnem.

The old Dorian, Phrygian, and Lydian modes,
having, as we have feen, their mefes refpedtively in
a , by c# , at the diflance of a tone from each other,
thefe tonic fpaces were afterwards divided, to make
room for the Ionian mefe in b flat, and the Aeolian in
c natural. To thefe five modes, whofe mefes fuc-
ceeded each other at the interval of a femitone, and
which came, in time, to be called the middle modes,
five others were made to correfpond, that . lay re-
fpedtively graver by a fourth, and took their deno-
minations from them, but compounded with the
prepofition hypo , to diftinguifh them. Of thefe, we
have already fhewn the Hypodorian mefe to have
been in et the Hypophrygian mj#, and the Hypo-
lydian in g# . Now, the two tonic fpaces between
e, y#, and g #, being likewife divifible, the Hypo-
ionian mefe was inferted in f natural, and the Hypo-
32olian in g natural, at a fourth refpedfively from the
Ionian and ALolian. To thefe ten modes, it was con-
ceived that five more might properly be ranged

towards

C 713 ]

towards the acute, at the diftances of a fourth re-
flectively from the five firft mentioned, and taking
their denominations from them alfo, but compounded
with the prepofition hyper 3 which would complete
them to fifteen, divided into five grave, five middle,
and five acute. But the Arifioxenians limiting the
pofitions of the mefe to the com pals of an odtave,
had eftablifhed only three out of thefe lall five, viz.
the old Mixolydian, whofe mefe we have fhewn to
Be in dy at a fourth from the Dorian, and which
was therefore afterwards called Hyperdorian ; the
Hyperionian, whofe mefe was in e flat, at a fourth
from the Ionian ; and the Hypermixolydian (for fo it
had been originally named, the prepofition being taken
in a different fenfe), the mefe of which was in e, at
a fourth from the Phrygian, and which was there-
fore afterwards called the Hyperphrygian. To make
thefe acute modes therefore five in number, as well
as the grave and middle ones, two new modes were
added, viz. the Hyperaeolian, whofe mefe was in f
and the Hyperlydian, whofe mefe was in f#3 at a
fourth refpeCtively from the Aiolian and Lydian.

The modes being thus augmented to fifteen, upon
the Angle principle of the harmonic doCtrine, their
mefes will be found to ftand all together in the fol-
lowing order..

r

Hyperlydian - - - - - in jf#

Hyperasolian - - - - - - - f

Acute ( Hyperphrygian, or Hypermixolydian - e
Hyperionian - - - - - e b

Hyperdorian, or Mixolydian - - - d

Middle

3

Lydian -
j^Eolean -
Middle Phrygian
Ionian -
Dorian -

[ 7*4 3

- in e*

- - - c

- - - b

_ _ - A

a

Hypolydian - -

- in g

#

/

Grave /

§

/#

/

- e

Hypoaeolian - - - - -

Hypophrygian ------

Hypoionian ------

Hypodorian - - - - -

Having now fhewn, how thefe fifteen modes were
iituated according to the harmonic dodtrine, I come
to the objedtions raifed by Ptolemey againft the eight
laft explained- For the right understanding of which,
it will be neceffary to give an account of all that he
lias delivered on the lubjedt of the modes, a talk of
fome difficulty i for though his reafoning appears to
me moft clear and methodical, it is rather too prolix
to be given exadtly in his own words, as this, with
the neceffary explanations of thofe paffiages, of which
the fenfe is lefs obvious, would carry me to too great
a length. I muff therefore endeavour to abridge his
dodtrmes, though at the hazard of leaving out iorne
of the fubftantial parts, and thereby doing mjuffice

to his argument.

It will be expedient to premife fomething con-
cerning his apparent intention, and method of reafon-
ing in this part of his work, which will ferve as a
key to his argument : and this feems ^ the more
neceffary, as he has been thought by fome (9) to

(q) So obfcurely has the beft of all the antient writers (Ftolcnu ) )

delivered himfelf on this article (the tones), that de ferve o ave
.been moft clearly handled. Malcolm’s Trcatife on Munc, p. 539-

[ 7\5 ]

have written very obfcurely upon the fubjedl. His
chief view was to reduce the fifteen modes, admitted,
upon the principle of the harmonic dodtrine, to thofe
feven, which had the fupport alfo of the mufical:
but this reformation was to be attempted with great
precaution, on account of the obflinate prejudices it
was likely to meet with, from the harmonicians of
his own time : And we fhall therefore find him firfl
artfully treating the modes upon the foot of the har-
monic dodtrine only, and arguing ad homines for the
reduction of the modes, even upon their own prin-
ciples ; but, before he drops the fubjedl, his true
reafons will appear ; and, indeed, it will eafily be
feen, that he had them conflantly in view from the
firfl, though he does not argue openly upon them.
This will account for that mixture of the two doc-
trines, which is found in his writings, and will, with
the affiflance of a few explanations, render intel-
ligible what he has delivered upon the fubjedl.

The tones he confiders, after the harmonic doc-
trine, as mutations by whole conflitutions, which, he
tells us, are therefore properly called tones, as they
are differences in refpedl to tenfion. Thefe differences
he admits to be infinite in poflibility, but argues,
that in efficacy, and in refpedl to fenfe, they are finite,
and liable to certain limitations. Thefe limitations he
derives from the theory of the confonances, by which
means, he lays a foundation for his future argument,
for reducing the modes to the number of fpecies of
the confonance diapafon. The limitations of the tones,
which he propofes to regulate by thofe of the con-
fonances, are, as he tells us, threefold ; viz,

Vol, LI, 4 Z

i. As

C 7>6 3

1. As to the diftance, or ratio, as he expreffes it,
of the extreme tones ; for the Pythagoreans, whole
method he adopts with fome improvements of hi*
own, meafured intervals by the ratios of the com-
prehending founds.

2. As to the number of tones to be admitted be-
tween thefe extremes. And,

3. As to the intervals, at which they were to hand
in fuccefiion, which he calls their exceffes..

Thus in the diatelfaron confonance, which he in-
{lances, thcle three circumftances are obfervabie;
firh, That the ratio of the extreme founds is fefqui-
tertian ; fecondly, That the component intervals, or
ratios, are three j and thirdly, That hich and fuch.
are the differences of thofe ratios,, meaning the inter-
vals in fuccefiion. But here he obferves, that, in
the confonances, thefe limitations have each their
diftindt caufe ; whereas in the tones, the firft being;
determined, the other two neceffarily followed, as
being dependent on the fame conditions. This re-
mark will hardly be intelligible, without fome ex-
planation. The interval, or ratio of the extreme
founds in each confonance, though differently treated
by the Arilloxenian and Pythagorean fchools, were
yet determined, both by the one and the other,
upon principles, which concerned not their inter-
mediate divilion : their intermediate divifion again
was fettled by a dodtrine, that required, in the com-
polition of intervals, either that every fourth found
Ihould complete the diateffaron, or every filth the
diapente ; without one or other of which cir-
cumftances, the compofition was held inconcin-

nous

[ 717 ]

tig us (10) j and hence the diateftaron could not be di-
vided into more than three ratios, nor the diapente into
more than four ; and again, the exceffes of the ratios,
or intervals in fucceffion, were affigned bv the doc-
trine of the genera ; fo that in the confonances, each
of the three limitations had a feparate caufe ; but in
applying the fame limitations to the tones, there was
a connection between them ; fo that the determining
the firft, determined the reft. Thus, for inftance,
if the interval diateftaron, or fequitertian ratio, lhould
be affigned for the limitation of the extreme tones,
the other limitations could only be fuch, as were
affigned for that confonance j that is, the component
ratios muft be three, and the exceffes of thofe ratios
fuch, as were eftabliffied for the diateftaron by the
doCtrine of the genera. But the not knowing the
neceffity of this confequence, he tells us, had occa-
fioned a great difagreement amongft the harmonicians
in determining thefe points, fome making the inter-
val of the extreme tones lefs than a diapafon, others
equal to it, and others again exceeding it ; the later
harmonicians, in particular, being fond of adding
fomething to what had been admitted by thofe, who
went before them. To bring thefe various opinions
to fome determination, he propofes the reftitution of
fimilitude in the hermofmenon, or harmonifed melos,
as the chief circumftance, by which to regulate the

2 Z 2

[ 7*8 ]

flrft limitation ; and this, he fays, is effected by the
diapafon, for, at that diftance, there was always a
return of fimilar harmony ; fo that the tone, that was
a diapafon diftant from that flrft taken, was a repeti-
tion of it ; and the tone {till farther diftant, as for in-
stance, at a diapafon and diateflaron, the fame with
the tone diftant a diateflaron only, and fo of the reft.
For a proof of this, he appeals to the practice of
mufic ; where it was well known, that in fuch mu-
tations, as were at the interval of a diapafon, no one of
the firings required new tuning, though in all other
mutations fome alterations were neceflary. And
hence he concludes, that thofe, who make the diftance
of the extreme tones lefs than the diapafon, do not
reftitute the hermofmenon, there being ftill other
tones beyond the limit they aflign, unlike to thofe
before taken 5 and that thofe, who exceed the diapa-
fon, admit redundancies, by repeating fome of the
harmonies before taken ; and further inflfts, that even
they, who proceeded no farther than the diapafon,
were yet to blame, inafmuch as they took in the
tone, that was a diapafon diftant from the firft, fince,
in fo doing, they admitted one redundancy, and
thereby gave a handle to thofe, whom they charged
with pafling the proper limits for the modes, to accufe
them, in turn, with being really the authors of this
licence, fince, if one ufelefs tone be admitted, the
fame privilege may be fairly claimed for a greater
number. This laft argument feems levelled at the
Ariftoxenians, who admitted no more than thirteen
modes ; bccaufe they would not exceed the diapafon ;
but whofe Hyperphrygian was, according to this

argument, a repetition of the Hypodorian. The

author

C 7*9 3

author fupports this argument flill farther, by an
appeal to the circumffance of the fpecies of diapafon,
the founds of which were eight, but the number of
the fpecies feven only, anfwering not to the number
of terms in the divifion, but to that of the component
ratios : for that the diapafon taken from the graved;
found towards the grave, yielded the fame fpecies
with the firft diapafon taken from the acuteft found
towards the fame parts, was out of difpute, it hold-
ing true univerfally, that whatever takes its beginning
in the fame manner from either of the extremes of the
diapafon, produces the fame power. And here he
leaves the firft limitation, without exprelly affigning
the interval for the extreme tones ; for the title of the
chapter, which' feems to fix it to a diapafon, ought
to be underftood only in this fenfe, that it fhould not
exceed it 5 which agrees with the i-eafoning in the
chapter itfelf. As to the conclufion, which depended
on the two other limitations, if I may venture to-
draw it for him, it will fiand thus, that into what
number foever of terms the diapafon be divided, the
diftance for the extreme tones fhould be the interval
between the firft term and the laft but one.

The firft limitation being thus far considered, he
proceeds to determine the next, upon which de-
pended the number of the tones ; and here he again
oppofes the Ariftoxenians, rejecting, by his theory of
this limitation, five of their thirteen modes, befides
the Hyperphrygian, which flood condemned by the
former one, and leaving only feven, according to the
number of the fpecies of diapafon, which he pro-
pofes as the properefl rule, by which to govern this
limitation 3 and affigns for this the following reafons.

The-

[ 720 3

The number of the fpecles of diapafon was equal to
that of the fpecies of the two firft confonances taken
together, and the fpecies of thefe laft were taken ac-
cordin°' to the condition of the ratios in each, the
number of which the very nature of them would
not permit to be either increafed or dimimftied. Now
the tones contained within the diapafon following
the nature of the confonances, and being indeed efta-
bliihcd on their account, viz. that the whole fyitems
might have confonant differences, he argues, that
thofe, who were either for admitting more than feven,
which was the number both of the fpecies and of the
ratios in the diapafon, or for making all the excefles
of the tones equal, were not to be affented to, lince
they could not affign any fatisfadtory reafon either
for the equality of the increments in general, which, in
the harmonic genus, was particularly inconvenient,
or for fixing either on the tone, hemitone, or dieiis,
in particular, for the common excefs, (from the fiip-
pofition of one or other of which, they determined
the number of tones, according to the number of
fuch intervals contained within the diapafon). roi
what was there to determine fuch a preference, when
the confonance (meaning the diapafon) was, as they
themfelves allowed, fufceptible not only of all thefe
excefles, but of many others, in the orders both of
the genera and of the diftances? Nor could they fay,
that fuch a magnitude divides the diapafon exactly,
and fuch another not exaftly, or one, perhaps, into
an even number of parts, and another into an uneven :
for though the diapafon was divided into fix by the
tone, into twelve by the hemitone, into eighteen by

the third of the tone, and into twenty-four by the

quarter.

[ 721 ]

quarter ; yet, in all thefe divifions, there was a varL
ation from the exa£t truth, even perceptible to the
ear. All this reafoning is again manifedly levelled
at the Aridoxenians, who, falfely edeeming the dia-
pafon to confid exactly of fix tones, or twelve hemi-
tones, had admitted thirteen modes, at the didance
of a femitone from each other : and here we fee the
author dill combats them fairly on the principles of
the harmonic dodtrine. But, to go on with his ar-
guments j having thus fixed the number of the modes
to feven only, he proceeds to confider the third li-
mitation. It will be alked, fays he, what are to be
the excefles chofen for thefe feven modes, fince the
diapafon cannot be divided into feven equal parts
and , if unequal intervals be ’ admitted, there is
dill room for variety in the choice? In anfwer to
this, he propofes, that the intervals in quedion diall
be taken by means of the fird confonances, diateffa-
ron and diapente, and their differences or exceffes,
whatfoever they may be : for he argues, that the
mutations, by confonant intervals, ought to be fird
edablifhed; and next to thefe, the mutations, by
concinnous intervals. Thole, who admitted eight
tones, he tells uSj had found their pofitions after the
following manner. The Dorian, Phrygian, and
Lydian, the three mod antient, being fird fet at the
didance of a tone from each other, they made the
next mutation confonant, at a diateffaron from the
Dorian, towards the acute, and at a limma from the
Lydian, calling it Mixolydian ; becaufe it lay not at
the didance of a tone from the Lydian, but only
at the didance of a limma, or difference between
ditonus and diateffaron 5 then this new mode having

the

[ 722 ]

the Dorian graver than it by a diate Aaron, that the
reft of the four might be attended with the like cir-
cumftance, they edablilhed the Hypolydian, Hypo-
phrygian, and Hypodorian, a diateffiiron giavei re-
fpedavely than the Lydian, Phrygian, and Dorian ;
and ladly, they placed the Hypermixolydian at a
diapafon from the Hypodorian, towards the acute,
o-iving it that denomination from its pofition above
the Mixolydian, mifufing, as he tells us, the prepo-
lition hypo to fignify the grave, and hyper to expreis
the acute. But though the refult of this method is
the fame with that of his own, excepting as to the
Hypermixolydian, (which he excludes for the reafon
afligned in treating of the fird limitation) yet he ob-
jects to it j becaufe the concinnous intervals are fird
aflumed, which ought to be taken by the confo-
nances ; and gives his own, which is by the con-
tinual addition of the confonance diatefiaron, but,
however, within the compafs of the diapafon.
Wherefore, when fuch addition would exceed it, he
directs taking the diapente in its dead, the contrary
way 5 whereby the divifion will be kept within the
limits afligned. This method, and its lefult, will
perhaps be better underflood, and will alfo be more
fuccinCtly couched in our modern expiedions, in
which I (hall therefore give it, applying to it the cor-
refponding characters of the Guidonian lcale.

Having fird taken the Mixolydian tone, which
was the acutefl of the feven, fuppofe in D, fall a
fourth to A, for the Dorian ; another fourth to C,
for the Hypodorian j then, to avoid pading the
bounds of the diapafon, rife a fifth to B, foi t ic

Phrygian; fall a fourth again to/#, for the Hypo-
J phrygian ;

3

[ 723 J

Phrygian; rife a fifth to c# , for the Lydian; and
fall a fourth to G#, for the Hypolydian.

By this method, the pofitions of the feven modes
come out exadtly, as I fixed them from Bacchius, in
explaining the harmonic doctrine ; and we fee, that,
for fettling them, Ptolemey has really recourfe to no
other theory of the modes, than that admitted by thofe
he contends with, though he makes the fpecies of the
confonances, and thofe of the diapafon more particu-
larly, the governing rule for fixing their pofitions, as
the only means, by which the two dodtrines could be
made to coincide. But it remained, after thus fettling
the feven modes, to (hew more fully the confequence
of following the method of the Ariftoxenians, and
others, who divided the tonic fpaces found by his
method, and placed the modes in a femitonic fuccef-
fion, by which their number had been raifed to thir-
teen, even within the compafs of the diapafon ; and,
in doing this, we {hall find he ventures to afiign the
true reafon for his reduction, which was grounded
on the mufical dodtrine. This argument, which is
contained in the eleventh chapter of his fecond book,
being very remarkable, and feeming ftrongly to fup-
port the combination of the two dodtrines in the dia-
gram I have given of the feven modes, I {hall give a
tranflation of the whole chapter, left I fhould be
thought to ftrain his arguments in favour of the mu-
fical dodtrine, which has been thought by many to
have little or no relation to the modes, and which,
if we except what this author has delivered, feems
indeed, upon a flight examination, and comparifon
of the evidence, to have the weaker fupport.

Vol.LI. 5 A Now,

[ 724 ]

Now, thefe being the tones we have eftablifhed,
it is plain, that. a certain found of the diapafon is ap-
propriated to the mefe, in power of each, by reafon
of their being equal in number to the fpecies. For a
diapafon being feleded out of the middle parts of the
perfect fyftem ; that is, the parts from hypate mefon
in pofition to nete diezeugmenon, (becaufe the voice
is moll pleafed to be exercifed about the middle me-
lodies, feldom running to the extremes, becaufe of
the difficulty and conftraint in immoderate intentions
and remiffions), the mefe in power of the Mixo-
lydian will be fitted to the place of paranete diezeug-
menon, that the tone may, in this diapafon, make
the fir ft fpecies ; that of the Lydian, to the place of
trite diezeugmenon, according to the fecond fpecies ;
that of the Phrygian, to the place of paramefe, ac-
cording to the third fpecies; that of the Dorian, to
the place of the mefe, making the fourth and middle
fpaces of the diapafon; that of the Hypolydian to
the place of lichanos mefon, according to the fifth
fpecies; that of the Hypophrygian, to the place of
parhvpate mefon, according to the fixth fpecies ; that
of the Hypodorian, to the place of hypate mefon, ac-
cording to the fcventh fpecies ; that fo it may be pof-
fible, in the alterations required for the tones, to keep
fome of the founds of the fyftem unmoved, for pre-
ferving the magnitude of the voice (meaning the pitch
of the diapafon), it being impoffible for the fame
powers, in different tones, to fall upon the places o
the fame founds. But, fhould we admit more tones
than thefe, as they do, who augment their excefles
by hemitones, the mefes of two tones muft, of ne-
ceffity, be applied to the place of one found ; fo that,

C 725 3

in interchanging the tunings of thofe two tones, die
whole fyftem in each mud be removed, not pre-
fervingany one of the preceding tenfions in common,
by which to regulate the proper [pitch] of the voice.
For the mefe in power of the Hypodorian, for in-
ftance, being fixed to hypate mefon by pofition, and
that of the Hypophrygian to parhypate mefon, the
tone taken between thefe two, and called by them
the graver Hypophrygian, to diftinguifh it from the
other acuter one, mud have its mefe either in hypate,
as the Hypodorian, or in parhypate, as the acuter
Hypophrygian ; which being the cafe, when we in-
terchange the tuning of two fuch tones, which ufe
one common found, this found is indeed altered a
hemitone in pitch, by intention or remifiion; but
having the fame power in each of the tones, *vi&.
that of the mefe, all the reft of the founds are in-
tended or remitted in like manner, for the fake of
preferving the ratios to the mefe, the fame with thofe
taken before the mutation, according to the genus
common to both tones ; fo that this tone is not to be
held different in fpecies from the former, but the
Hypodorian again, or the fame Hypophrygian, only
fomewhat acuter or graver in its pitch. That thefe
feven tones, therefore, are fufficient, and fuch as the
ratios require, be it thus far declared (1 1).

With

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vizi TrtV yipas yuhtra yiKwf'ia.r ohiyaKts i-ji tuc uk^ IkCu\v*-

5 A z ffav-.

[ 726 ]

With this chapter he ends his doCtrine of the
modes, and of their reduction ; and we fee he here
makes the mufical dodtrine of the fpecies the bafis of
his theory, as far as concerns the rejecting the eight
redundant modes ; though, out of caution, and to
obviate objections, he had eftablifhed the feven
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•jrtenri7detv. Ukei'ovuv c Pi tuv t'ovuv tta£A ™T«f uoroTiStfitvuv o ttoiv-
CIV 01 tv Tolf Y\[ll\WlOlf TAf VTSt^yAf AVTUV TO Agjf. V^ Ot'jif A VAyKAl OV
\fAl, c No TOVUV [V.'tTAf tVof (fd’O') f« T07TU TVAvjuf ttfiApUo'elV Ui •& OArf
KIVel&At Td TVTr)[AA7A, KATA Ti'lV ilf rfAAnAK? TUV S'vO TVTUV TOVUV
fltd-AplAOyvV’ [VMKiTl Tlip«^]rf KOIVW JtVA TVV TAG IV* A TSA£C/-

y.{]n${)<T,i)Ai to iS'tov t~\$ tpuvnt. T«f fi,' y> tv vTsoS'attv, ,<ptp t tiTr&t vf
rli' J'vvduei [/tani, ffvvz^tvyy.tvnt tm kata tht &teiv tuv pitAuv vtsatw
J'i rk ■Cvro'ppvyi* tm tuv [itauv TTApunrATn' tov A Ay.C Avopj.tvovjv.il a~u

TXTUV TOVQV, KAhiS[JtVOV J'i \Au' AVTUV &ApvTi£CV VBrOfpvy/OV, ATA? fK^VoV*
C^VTt^pV, S'iUAtl 7 t)V AVTYIV [ItAIJV, ilTOl KATA T l)v yZTATIIV i'/J-l?, UP KAl
C \&roS'ueiOf n KATA T TVApVTTATiV, UP KAl 0 o’coTifyi \&TOppvyi&.
Ov <7V[J.£a'iV0v]&, tTVilJ'AV ilf A AAllA«< jUsSrfp [VO^Ufli^A T«f T KOIVOV
5/AH^OTrfJ TOVVf KlVH^HAt']AI [V.tV t<TS [Jay Sttf t] 'yA\A§Stlf

nflf)ov'w ToS J'i TtlV AVTtIV, OV tKATtpu TOVUV, JuVAfllV tyilV TK-
Ttf l % f [JAW AKOKt^naWlV Al ffi Konruv ATTAv\uV qS-b^UViAglTA-
Cilf » yjA Aatrc-if ivZKA TV Al/]nptiV TVf TfpOf T [AtVlIV AoJ/Vf, TUf AVJVf
TOl f TSpO f [iJIaCoMP, KATA TO KOIVOVA[A<pOTtpUV TOVUV ytV&,* A/A-
Cavo[1))voi f. "Up Tt [/mJI av 'tTt&v \ti Jo^ai ttJ hJ'&t r Toyov ^
esf'oTtpjv rfAA’ vsroj'ueiov TSTrfA/V, l r AVTOV xs&oypvyiov, °Zy<puVoTt*pV
Tivof ii CApv<puvoTt£pv [j.ovov. T o "po «(' tuAoyov Tt kai dvjupytf JyJ tor1] A
rovuv, [Atyti t\stuv \s&o\<c]\jTru&u. Ptol. lib. ii. c. n.

fyftem

[ 727 ]

fyftem. That the force of his arguments in this
chapter, and the refult of admitting the eight modes,
may be more plainly feen, I have annexed a fecond
diagram of the fpecies, as they lay in the fpurious
modes ; by which it will appear, to which fpecies in
the genuine ones they feverally anfwered; and the
objection, raifed againll each of them by Ptolemey
will become intelligible.

There is, however, an objection, to which this
fecond diagram feems liable. It may be afked, if
the Hypoionian mode, inftanced by Ptolemey, could
give either Hypodorian or Hypophrygian harmony,
according as either the eighth or the ninth firing was
employed for its mefe ? and if the reft of the fpurious
modes were liable to a like alternative, what was it
determined me in my choice of the two fpecies, in
the conftrudtion of the diagram ? To which I an-
fwer, that the antients have decided for me as to five
of them j for we find (12), that the Hypoionian was
called the graver Hypophrygian ; the Hypoaeolian,
the graver Hypolydian j the Ionian, the graver Phry-
gian j the ALolian, the graver Lydian ; and the Hy-
perionian, the acuter Mixolydian. And this, by the
way, furnifhes us with an unanfwerable argument of
the antiquity of the dodtrine enforced by Ptolemey,
that the number of the modes ought not to exceed
that of the fpecies of the diapafon ; for thefe appella-
tions, which were given to the modes long enough
before Ptolemey flourifhed, can be accounted for on
no other principle, but the fuppofing the fpecies of

(12) Vide Euclid. Introduft, Harm. p. 19. v. 29. & feq. Arift.
Quint, p. 23. v. 7. & feq.

diapafon.

C 728 ]

diapafon to have been confidered as the eflential cha-
radlers of the modes ; and that thefe five modes
therefore, though they had a difference in pitch,
were thought to be the fame, as to their effedts, with
thofe, after which they were thus named. As to the
other three, the Hyperphrygian, Hyperasolian, and
Hyperlydian, their mefes being refpedtively at the
diftance of an octave from the Hypodorian, Uypo-
ionian, and Hypophrygian, it was necelTary to give
them the fame fpecies with thofe three modes ; for a
tranfpofition of an odtave was always underflood to
give a return of the fame harmony, as has been al-
ready fhewn.

This fecond diagram, and that of the feven ge-
nuine modes, may be thought fufficient to render the
fubjedt intelligible: however, as the fifteen modes
are parted in the two diagrams, and confined alfo to
the compafs of a diapafon, for {hewing the fpecies,
I have added a table, (hewing the tuning of the
fifteen firings of the lyre for all the modes. The
letters of Guido’s fcale, placed within the fquares,
{hew, in their horizontal orders, the tunings of all
the firings for each mode 5 the two broader lines
include the fpecies of diapafon ; and the mefes are
diftinguifhed by capital letters, by which means, the
cafes, where the fame firing is employed for the
mefes of two modes, appear at the firft view 5 and tne
reafoning, upon which Ptolemey rejedts the eight
modes, is illuflrated, fo as to need no farther explana-
tion.

Having now gone through with what I propofol
to explain under the three full heads, I come,

Fourthly ,

S t r i n c s of the LYRE.

/

A TABLE, fliewing the Tuning of the Strings of the LYRE for every Mode.

X

c o

>5

Nete hyperbolaeon.

a

d

a

d

a

a

d

a

d

a

a*

a

a

d

a

14

Paranete hyperbolaeon.

g*

g

g

d

g

g*

g

g

£

g

g#

g

g *

g

g

>3

Trite hyperbolaeon.

F#

F

r

f

f*

f

f*

f

f

f*

f

f*

f

f*

12

Nete diezeugmenon.

e

*

E

f

e

e

ek

e

d

e

e

d

e

d

e

II

Paranete diezeugmenon.

d

dk

d

El

D

d*

d

d

dk

d

d*

d

d

dk

d

10

Trite diezeugmenon.

c*

c

c

dk

c

c*

C

c*

c

c

c

c*

c

c

9

Paramefe.

b

d

b

d

d

b

d

B

Bl

b

b

d

b

d

b

8

Mefe.

a

d

a

d

a

a

d

a

d

A

a*

a

a

d

a

7

Lichanos mefon.

g*

g

g

d

g

g*

g

g

£

g

G#

G

g*

g

g

6

Parhypate melon.

f*

f

f*

£

f

f *

f

f *

f

f

f*

f

F*

F

f*

5

Hypate melon.

e

d

e

f

e

e

d

e

d

e

e

d

e

d

E

4

Lichanos hypaton.

d

dh

d

ek

d

d*

d

d

dk

d

d*

d

d

dk

d

3

Parhypate hypaton.

c*

c

c

dk

c

c *

c

c*

c

c

c*

c

c*

c

c

2

Hypate hypaton.

b

bk

b

&

d

b

d

b

d

b

b

d

b

d

b

1

Proflambanomenos.

a

d

a

d

a-

a

d

a

d

a

a *

a

a

d

a

Vol. LI. Page 728,

Diagram II. Of the Species of Diapafon in the Eight Modes rejected by Ptolemey.

d

f

f*

tS.

•s w

c .§

5 op

'■t ir

s §•

6 $

^ c

c .2n

yperphrygian M.

ypodorian Sp.

/

l .§

1 s-

Q.

S' %

Paramefe.

Lich. mef.

'■% “

s -a

u 0

X

Mefe.

e

0

d

X X

Lich. mef.

d

N

6

Mefe.

Parhyp. mef.

d

Lich. mef.

Hyp. mef.

dk

Parhyp. mef.

dk

Lich. mef.

Hyp. mef.

c

Parhyp. mef.

Lich. hyp.

b

Hyp. mef.

d

Parhyp. mef.

d

Lich. hyp.

d

Hyp. mef.

Parhyp. hyp.

a

Lich. hyp.

Hyp. hyp.

d

Parhyp. hyp.

d

Lich. hyp.

O

c

0

N

Q

Proflamb.

g

Hyp. hyp.

g

f*

Parhyp. hyp

U

c

0

Hyp. hyp.

£

f

Parhyp. hyp.

f

Q

Proflamb.

cJ

c

0

Hyp. hyp.

Paran. hyper.

Q

Proflamb.

d

Paran. hyperb.

e

d

b Trite diez.

d

d

£

/

Paramefe.

Q

Mefe.

Lich. mef.

Parhyp. mef.

Hyp. mef.

Lich. hyp.

Parhyp. hyp.

sJ a

S To

J £

J3 Paran. diez.

dh

c

d

d

£

f

Trite diez.

Paramefe.

Q

Mefe.

Parhyp. mef.

Hyp. mef.

Lich. mef.

.§ 5

H J-

a a

X S'

L Trite hyp.

d

a

£

f

Nete diez.

Paran. diez.

Trite diez.

Paramefe.

Q

Mefe.

Lich. mef.

X a

^,b Paran. hyp.

Parhyp. mef.

&

c

d

d

&

f

Trite hyp.

Nete diez.

Paran. diez.

Trite diez.

Paramefe.

Q

Mefe.

Lich. mef.

% XL

[ 729 ]

Fourthly , To point out fomething of the origin of
the two dodtrines.

The harmonic dodtrine was, as I have fhewn, ex-
prefly taught in harmonic; and therefore, to account
for its reception, it will be neceflary to conlider the
fcope of that icience.

The muflcal dodtrine I have alfo fhewn to have
been explained in harmonic, as far as concerned the
elementary principles of the fpecies of diapafon ; but
the application of thofe principles to the dodtrine of
the modes was not taught therein, being referved for
melopoeia, a fcience, that looked higher than har-
monic, and confidercd the ufe of the elements, when
in the hands of the poet or mufician. It is to this
fcience, therefore, that we muff look for the origin df
the muflcal dodtrine.

But, before I conflder the fcope of either of thefe
fciences, it will be neceflary to fhew my reafons for
feparating them, flnce they were blended by the
Ariftoxenians, as has been fhewn above. For this
purpofe, we mufl have recourfe to the divifion of
muflc, the mother fcience ; which, as treated by the
antients, comprehended all, that the moderns now
underhand by muflc and poetry. Its firh general
divifion, according to Ariflides Quintilianus (13), was
into theoretic and pradtic. The theoretic was fub-
divided into natural and artificial ; the latter of which
was again fubdivided into harmonic, rhythmic, and

metric ;

(13) De Mufica, p. 7. See alfo Meibomius on the paffage,
who has embraced the divifion of Ariflides, in the following table.

Mu s i.c JE

[ 730 ]

metric; which three fciences more particularly con-
tained the poets elements, as teaching the grounds of
tune, time, and verfe. But nothing lefs than a com-
petent knowlege of every branch of the . mothei^
l'cience could carry with it the refpeded title of o
aao-»co5, the mufician. To harmonic, rhythmic,
and metric, in the theoretic, refpedtiyely anfwered
melopoei'a, rhythmopceia, and poetic, in the piadtic.
In this author’s divifion therefore, we lee, that har-
monic and melopoei’a are diftinguilhed, even by the
firft general divifion. Of the propriety of this even
the Arilfoxenians feem to have been fenfible ; lincc,
in order to juftify their blending them, they have
defined harmonic as a fcience, both theoretic and
pra&ic (14). And Ariftoxenus himfelf, in the frag-
ments we have under the falfe title of his three books
of harmonic elements, feems to afiign fuch bounds
to harmonic, as might well be underftood to exclude

ijusdividitur in \ Phyficam generi cognominem.

^ alia

Pra&ica

cujus item
partes dux

TTr Vo C Melopoei’a,

Ulualis, > Rhythmopceia,

cujus panes £ ?q^

melopceia (15). We have Plutarch alfo on our fide,
who, in a paffage of his dialogue on mufic, which
I fhall have occalion to cite, amongft other proofs,
enumerates only the firft fix parts of harmoniac,
leaving melopce'ia out of his divifion. For this Mei-
bomius blames him (16), but too haftily ; for had
the learned critic confidered the whole paflage, he
muft have feen, that the omiffion was not through
ignorance, but defign, the author being there ex-
prefly arguing for the confining of harmonic within
its proper bounds. However, whether the Arifto-
ocenians were right or wrong, in including melopoei'a
in harmonic, my argument feems not materially af-
fe&ed by it j for they gave it only as a lafh divifion,
to be taught after all the reft had been inculcated ;
and they agreed in defining it to be the ufe of the
harmonic elements, according to the propriety of
each F ubj e<fb (17): which is diftin&ion enough for
the ufe I propofe to make of it.

Having thus far juftified my dividing thefe fci-
ences, I fhall now confider the fcope of each ; which

(15) Tlif 'TVZeA f/AKHS l©7S‘M(t/>K 'TtroWy.Zp^i aft)?, KOA ZK

'nrAiisf ril'd dwffi v'trohetCeiy Ah, t;'v dp//.oVt)ctiv K&h\s(j.zvnt',

eivcti 'srgy.y petrel ctv, rrirz rcc^m nrpurw Ireiy, zyj,acLV rz J'vva.utv rot-
y&:uJ'n. Tt tyyjLvet jS xra mfurn foapiijiKav' rxv]ct Ji zriv
cuvrzivzi ntpoi r ruv ffvrvip-drav rz > ut) rbvvv ■'rzeonetv. Ilfprn kzi ip

[j.nS'zv froffurtpa) rirew d?ivv ‘vu.f dim ri r h ptty.ivnv ohrti-

[adv’ rzh'Q' y6 rira'zri f rrM.ypi-&r'ii&<; rc/.vrtw. Ariftox. p i. init.

(16) Plutarchus dialogo de Mufica fex tantum priores turbato
etiam ordine recenfet, cum tamen crebrana [/.thoTouat mentionem
injiciat, adeoque, non una ratione excufari ill ud poteft. Not. in
Gaudientium, p. 30.

(17) MzAo'zrc/tci S'z \n \mroKZtyXvuv tm Jp/MviM rsp&y-

fi.ctreid, r5?fos rb ont&ov ZKeLrnt xzso&z'jzwz. Euclid. Introd, Harmon.

[ 732 ]

will lead us to the origin of the doCtrines they con-
tained.

The objeCt of melopoeia was propriety in the ufe
of the harmonic elements, as appears from the de-
finition juft cited. In what this propriety confifted, it
is difficult to know, as no collection of the rules of
this fcience is come down to us : it is not to be learnt
from the harmonic writers, who treat very fiightly
of this branch; and thofe of them, who are the
fulleft upon it, as Ariftides Quintilianus and Manuel
Briennius, wrote in later times, when the faffiion of
mufic was changed, and a new kind of melopoeia
prevailed, with the rules of which the earlier mu-
licians could hardly have been acquainted; as, on
the other hand, many of the earlier rules muft have
been forgot, or, in a great meafure, difufed. There
is more light to be procured from the dialogue of
Plutarch, and fome others, who fpeak occafionally
of the practice of mufic. I do not propofe to colleCt
any thing here upon this fubjeCt, as, indeed, there
does not feem to be fufficient materials left us for a
thorough explanation of it, which would require no
lefs than a complete hiftory of the fcience of its
mufic, and its improvements : it is fufficient for my
purpofe to fay, that, in the earlier times, when the
beft mufic is fuppofed to have prevailed, the genera,
modes, rhythmi, metres, &c. were not employed
indifcriminately, nor even left to the difcretion of the
mufician, but were under particular reftriCtions, which
confined them to the arguments, to which they were
held refpeCtively the beft adapted; and that it was
from the mixture of thefe ingredients, that arofe the
ethic character of the compofition. Hence the feveral

nomi

C 733 3

nomi took their rife j of which there is, in the dia-
logue of Plutarch, an ample account. As what I
am now advancing cannot but be well known, I
need look no farther for the proof of it, than to a
paflage of Plato’s third book of laws, where he com-
plains of a licence beginning even in his time to the
prejudice of the fcience. Speaking of times paft,.

Our inufic (fays he) was then divided according
to certain fpecies, and figures thereof. Prayers to
the gods were one fpecies of fong, to which they
gave the name of hymns: 6ppofed to this was an-
other fpecies, which, in particular, might be called
threni; another, paeones ; and another, the birth of
Dionyfius, which I hold to be the dithyrambus :
there were alfo citharoedic nomi, fo called, as being
ftill another fong. Thefe, and fome others, being
prefcribed, it was not allowable to ufe one fpecies of

melos for another. But afterwards, in procefs of

time, the poets fil'd: introduced an unlearned licence,
being poetic by nature, but unfkilled in the rules of
the fcience, trampling upon its laws, over attentive
to pleafe, mixing the threni with the. hymns, and
the pseones with the dithyrambi, imitating the mu fie
of the flute upon the cithara, and confounding all

things with all, &c. (18).

° This

(i 8) A/HPH/wint $ t'otz rlv Yifiv tS fxmxtl xat #S» rz zavT a. tJa xai
M/xrfA' Mi 71 fo «S& acNf ofofM SivjXM <-™ka-

kwlo’ xa'i TXTW, c H to zvavtiov w oSns ztz&v Spnv*f S. tk

AV AVTdf utiklTA ZxAkZtTZ' Ka'i 'KAtcovZS, ZTZ&VMl atAAO £U0VVtfd yiVZ-
cr/f, ol iiA,y vby-«f TZ auto T670

aSnv W( TIVA ZTZ£A.V Z'ttZkzyov Si K/&Ap aSiKtsf. Tutvv Sz Stetli^Ay-
UAVUV KAl AkkWV TIVUV dK ViyiV AkkU Ztf AkkO XAjA^piftAi [Aikdi « '

H-M VTA SI TAUT A V&lbvT& T6 XfJVd, WX,0^

5 B 2 V0{xi*f

[ 734 ]

This paflage, with what has been faid, being fuf-
ficient to give a general idea of the fcope of melo-
poeia, I fhall pafs to that of harmonic.

We have already feen, that the theoretic divifion
of mufic was by the author, whofe diftribution I
have followed, fubdivided into natural and artificial,
and that harmonic came under the latter. The an-
tients, indeed, feem not all to have treated the fci-
ence under fuch narrow limits, the phyfical proper-
ties of found, the ratios of intervals, &c. appearing
to have been confidered therein, by the Pythagorean
and other fchools, as well as the ftrudure of the
fyflems in ufe. But not to flop at this objection,
which is not very material, thus far muff be allowed,,
that harmonic, as to the greateff part of its fcope, was
an artificial fcience, its moft considerable objed being
to explain and teach the denominations, pofitions,
powers, &c. of the founds of the fyftem, and all
other inventions in ufe, for facilitating the jftudy of
mufic, or bringing it to greater perfedion. Now, in
this fhort view of the fcience, which is fufficient for
our purpofe, we may already begin to account for
the difference between its dodrines and thofe of me-
lopce'ia, artificial fciences being but too prone to ad-
mit dodrines for convenience, that are repugnant to
the truth. This was indeed the cafe with harmonic,
as the two dodrines of the tones fufficiently teflify^.
the origin of which I fhall now confider.

wy'iAs 'sronfjeii i y\yvoVTv, potrs/ pi Tironil/noi, etyffoyol’H S'i to <Ti-
hcuov f yntrnt kaI to topsy-W, iW]s<, ha\ y.AWav 78

v'<p' WsToW, Ki££AVUv{lit J'i Sfill vy.VOIf KAt TXAlttV Af
J'ldv^J.y.Cotf kai duhtoJ'tAs V Ki-^AfuJ'iAii y.iyi^zyoi, KAI tva i*]a

nf 'BayjA %vyuyoy]i{. Plat, de Legibus, lib. iii.

The

C 735 ]

The mufical do£trine I look upon as the moll
antient, and that which exhibited the modes in their
proper character ; for which reafon, it could not
avoid making a part, and probably the mod; effential
one, of the doctrines of melopceia. The precife time
when it firfl came into ufe, I pretend not, in the
midfl of uncertainties, to be able to determine j but
we may, perhaps, be near the truth, if we refer its
origin to the age of Pythagoras, if the eighth firing of
the lyre was really, as we are told, the addition of that
philofopher. The flory of his difcovering, at a forge,
the ratios of hypate, mefe, paramefe, and nete, is
well known. Thefe ratios, which gave rife to the
harmonic proportion, and the numbers of which
were fo vainly applied afterwards, by philofophers,
to all the parts of the univerfe, were drawn from the
Dorian fpeciesof diapafon, which we cannot fuppofe
to have been well understood, till its form exifted
upon the inflruinent. What dodtrine of the modes
prevailed, before -the addition of the eighth firing, we
can only guefs at ; for it was a queflion, even with
Ariflotle ( 19), how the heptachord lyre had been ad-
iufled 3 and Nichomachus fpeaks of that inflruinent fo

{19) ti 0! dpyctiot dppcovlctf Troiv/Jzf t v&sithp,

dkk B T v'nYW K&TihtlSeV, T70Ti£pV TV TO ''Fii' d& r d[J.$0TtfC£? KAT.~

kiTzov, «r dz renw e^itpar 5 » b, dkk fa ‘t n CapvTZfjf. iyvet t d 04- v-
Ti&if pdoyfov, <yrs p/.3Lkkov n \jsrdm d-zrzdidu 7 b o.vt\$uvov >} u 1 4th •
TO %d dvvd/xzoot y.dk'kov, To dz Cetpv gcf.ov <$$zy%<t&eu‘. AriHot.
Pro’bl. fed. ig. qu. 7-

&td ti oi ctpydioi ZT/jaybpdvf vzoix]!]is T&t r 'dzrd,TAV dkk'

* T Vr\T)lV KATtklTTOV y /') B T)J V •$Sr<&TW, dkkd TnV vvy KctkK/AwV
fj-iaw dzmp-aV Kttl T3 TOVld/CV dlCtTUfjt.a,. \ypWljo di T« Z%el7.H [XiOil T«

cm too'v 'zrvr.vd, dib x.cti fjiianv ct’urw rsr&tniybpzvtTsLV ; Jj S77 tiv tv p'
a.vo) Tijfc/.yipd a TikivTn, dv dz katu doyj, K4t) ij/ztov £yj kbyov t bva>

‘ffld uKpav, Probl. fed. 19. qu. 48.

confuiedly,.

4

[ 736 ]

confufedly, as to have given room for a fuppofition
(20), that it had received two forms, the feven firings
anfwering, in the oldefl form, to our notes e,f, gy
b b, C, d, and in the new one, to e,f, g, by d, e.
However this may have been, neither the mufical
nor the harmonic doCtrines could be then in ule,
exadly as they were taught in after times ; and the
probability feems to be, that the modes were in thole
days characterized by the fpecies of the leflei con-
fonances, diateffaron and diapente ; but the theory of
the Dorian fpecies of diapafon, we may be fure, too*
place about the time, when the lyre was brought to
that compafsj and the other fpecies, though they
might have exifted before, in the melody of parti-
cular inftruments; as for inftance, the barbarous
Phrygian, upon its flute, could hardly have been
taken into the Greek theories of the Science, till the
extenfion of their own favourite inflrument had
brought the diapafon under confideration : fo that
the origin of the mufical doCtrine of the modes,, is,
with great probability, to be referred to this im-
provement of the lyre. . r ,

I come now to the harmonic doCtrine, for the
origin of which we mud look to the invention of
the fyflem. The greater perfect fyflem, upon whole
pitch the modes depended, by the harmonic doctrine,
con filled, as I have already fhewn, of fifteen founds,
anfwerable to thofe of the lyre ; and it is reafonable

(20) Ut ex his difficultatibus nos expediamus, duas, non opi-
niones, fed aetates ftatuere debemus, quibus aliter obtinuerint in-
terval^ in feptem chordis. Meibomius in Nichomachum, p. 52-
See alfo Nichomachus, p. 9. v. 14. & kq. & P- 1 7* v* 24"
feq.

to

[ 737 ]

to think, that the flrudture of it was not fettled, till
the inflrument had been again extended to the com-
pafs of a difdiapafon, by the additions of the tetra-
chords hyperbolaeon and hypaton, and of the found
proflambanomenos : for this change the age of Ale-
xander the Great may, perhaps, be a probable asra ;
for, in the mufical problems of Ariflotle, I obferve
no mention of the new tetrachords, though many of
the queflions concern the firings of the lyre; and
yet there is no doubt of their being in ufe in the time
of Arifloxenus, his difciple. Should I be near the
truth in this, the mufical dodlrine will then appear
to have been earlier than the harmonic, by the whole
period from Pythagoras to Alexander. But, without
being follicitous about the precife time when the har-
monic dodlrine was introduced, I fhall, with more
certainty, endeavour to point <3ut what mufl have
given occafion to it.

The fludy of the mufic of the antients, though
they feem not to have much ufed compofition in
parts, mufl yet have been very perplexing, from the
variety only of the tones and genera ; and fome help
might well be thought neceffary, even in the time of
the odtachord lyre. But when feven new firings were
given to the inflrument, and thefe placed not all at
one end, but three at the acute, and four at the
grave, the eight old firings, upon which the cha-
radleriflic fpecies of melody for each mode had
been always exhibited, became confounded by thefe
additions ; and poffeffing now the center of the lyre,
it was difficult to diflinguifh them, and to preferve for
each mode its proper charadter as before. This dif-
ficulty mull alfo have been increafed, by the change

introduced

[ 738 ]

introduced in the praflice of the fcience ; for both
the players and compofers, having now a greater la-
titude would not fail to take advantage of the en-
largement; and though the fkilful among them
mio-ht, in their excurfions upon the new firings, pre-
ierve a due attention to the proper characters of the
feveral modes, yet the melody peculiar to each could
not be fo eafily comprehended, when carried beyond
its ufual limits. An artificial help, therefore, to the
learner, was now become indilpenfably necenary ;
and with this view, 1 make no doubt, but that the
fyftem was invented. It was, indeed, admirably well
contrived for the purpoie ; for its fuccefiion being the
fame with that of the lyre, in its Dorian tuning, with
which the Greeks mufl have been the befl acquainted,
as being the proper mode of their favourite inftrument,
it was the mod eafy to be learnt and retained, and the
knowlege of this fucceffion was all now required ; foi ,
by imagining only the fyftem removed to fome other
pitch, and tuning all the firings in the fame relations
to a new mefe, the melody ot the old ei^it firings
was thereby changed, and a new fpecies of diapafon
gained thereon, without the trouble of ftudying the
the mufical dodtrine, which was now left to the mu-
fician, or melopcefus, who was anfwerable foi the
choice of the fucceffiions he feledted for his various
fubjedts, whilft the harmonician followed him through
the intricacies of his compofitions, by the eafier me-
thod of the tranfpofition of the fyftem. And this .1
apprehend to have been the origin, both of the
fyftem itfelf, and of the harmonic dodtrine of the
tones. But now, as it often happens, what was de-
figned for the improvement of the fcience, became,

[ 739 ]

in time, the ruin of it ; for, after the reception of
the difdiapafon fyftem, the elementary treatifes, as
we fee by what is left to us of them, became filled
with this new dodtrine of the parts and relations of
the fyftem, of its tranfpofitions, of the pofitions of
the mefe, of founds in power, and found by pofition,
and many other dodtrines flowing from the fame
fource, till, in time, the fyftem itfelf came to be
confidered as the true type of a mode ; and a
number of new modes were introduced, that were
grounded on no other principle than this, which I
fcruple not to call a falfe dodtrine of them, though
the antients admitted it for convenience, as I have
fhewn, and thereby almoft loft their impreflions of
the new one.

Having thus pointed out the origin of thefe two
dodtrines, as far as was poftible, from a general view
of them, and without entering into a critical exami-
nation of the many paflages of the antients, that
might help us to greater certainty, I ihall now pro-
ceed.

Fifthly , To fhew how far the preceding explana-
tions may be fupported by arguments, or war-
ranted by the teftimony of antient writers.

Here I muft repeat, that the harmonic dodtrine of
the tones, as I have explained it, is found, exprefly
delivered under its proper head, in almoft every
writer on the fubjedt; and that the dodtrine of the
fpecies of diapafon is found alfo in the harmonic
treatifes, though not under the head of tones, nor ex-
prefly applied to them. Now, this being the cafe,
I lhall have no occafion to wafte time in bringing
Vol. LL 5 C particular

[ 74° ]

particular proofs, to lupport the explanations I have
«riven of thefe two dodtrines feparately. What imme-
diately lies upon me is, to prove, that the dodtrine of
the fpecies of diapafon had a connexion with the
modes ; and to juftify the manner, in which I have
combined the two dodtrines in the canon, and in the
diagrams framed from it. With this view, therefore,

I {hall diredt my arguments to the proving of the five
following points.

1. That the dodtrine of the fpecies of diapafon
was a dodtrine of the modes.

2. That this dodtrine was not diftindt from, nor
independent of, the harmonic, but fo connedted with
it, that a mutation, according to the one, produced
the alteration required by. the other.

3. That the fpecies of diapafon, as taken pradti-
cally on the lyre, lay all at the fame pitch.

4. That this pitch was the diapafon, between the
firings hypate mefon and nete diezeugmenon, as they
ftand in the diagram.

y. I Khali endeavour to drew, that it was the mufi-
cal dodtrine, and not the harmonic, that exhibited
the true character of the modes, as confidered in re-
fpedt to their effedts.

To begin with the firft point. That the dodtrine
of the fpecies of diapafon was a dodtrine of the
modes, might,, perhaps, be inferred from fome of
the definitions given of a mode ; but as thefe defini-
tions are moftly intermixed with, if not drawn folely
from, the harmonic dodtrine, and hence have given
room for difputes, I fhall reft this point upon three
arguments, in which the definitions are not con-
cerned.

Firft.;,

t 74i ]

Firft, Becaufe the fpecies are denominated after
feven of the modes, which could hardly have arifen
from any other caufe, than their connection with
them.

2dly, Becaufe the whole reafoning of Ptolemey,
in the fixth, feventh, eighth, ninth, tenth, and ele-
venth chapters, of his fecond book, tends to leuuce
the modes to the number of the fpecies of the dia-
pafonj which, as far as his opinion goes, is an ex-
prefs confirmation, that the mufical doCtrine was a
doCtrine of the modes.

gdly, Becaufe Ptolemey is not fingle in this opi-
nion, as fome may have thought, but is fupported
in it by the Ariftoxenian writers, who, though they
admitted thirteen modes, upon the falfe principle of
the harmonic doCtrine, did, in faCt, reduce them to
eight, on the very principle of Ptolemey, calling the
Hyperionian mode, which gave the fame fpecies with
the Mixolydian, the acuter Mixolydian j and calling
alfo the y&olian, the graver Lydian j the Ionian, the
graver Phrygian ; the Hypoasolian, the graver Hypo-
lydian j and the Hypoionian, the graver Hypophry-
gian ; the former of all which modes gave, re-
fpeCtively, the fame fpecies with the latter. So that,
to make their dodrine anfwer to that of Ptolemey,
there wanted but the reduction of one mode moie,
which was their Hyperphrygian. And it is not to be
conceived, but that they faw this mode alfo to be a re-
petition of the Hypodorian ; but as this repetition was
at the diftance of an oCtave, and the other five were
repeated at the difference only of a femitone in pitch,
they could not have called this the acuter Hypodorian,
without uling the fame expreflion in too great a lati-

5 C 2 tude

C 742 ]

tilde of fenfe. And this might be the reafon why they
omitted taking notice of that circumftance attending
this mode ; though we might perhaps* with fafety to
the argument, go a fiep farther, and fuppofe, that
the Ariftoxenians might think a difference of an
odtave in pitch worthy of a diftindt denomination,
though they would not allow it to that of a femi-
tone. And this is the more probable,, as we find they
did not abfolutely rejedt thefe modes, as Ptolemey
did, but admitted them upon the principles of the
harmonic dodtrine, though, by their denominating
five of them from the genuine modes, it is plain
they acknowleged them to be fuperfluous, in refpedt
to the mufical. I cannot fay more to this point,
without defrauding the lubfequent ones j and I fhall
therefore leave it, with this rerfiark, that whatever is
proved of the fubfequent points, and efpecially of the
fifth, muff hold true of this, a fortiori ; fo that it
may really be faid to have the fupport of the whole
tefiimony.

2. To the fecond point, the firft diagram fpeaks
very firongly ; for had the two dodtrines no relation
to each other, no fuch coincidence, as is there found,
could have been expedted, in the refult of their com-
bination; and this proof, from the coincidence of the
dodtrines in the diagram, becomes much ftronger, if
we attend to thefe two circumftances. Firfi, That in
the canon, upon which the diagram has been con-
ftrudted, there is no ftrain of either dodtrine, but a
plain and natural combination of them, as they are
fiated feparately by the antient writers. And fecondly,
That the fpecies of diapafon, as brought out by this
combination, all Fill upon the firings of the old

odtachord

C 743 ]

octachord lyre, where it was natural to exped them;
for when the lyre had but eight firings, the fpecies
could be taken no where elfe ; and it cannot be
thought, but that, after the extenfion of the inftru-
ment, they were taken at the fame pitch as before,
unlefs we fhould fuppofe, that the new firings
brought with them an immediate change, both of
the theory and pradice of the fcience, which is moft
improbable. We fee our modern harpfichords have
more keys given to them than thofe of the laft cen-
tury ; and yet neither the portions of the cliffs, nor
any other circumflances attending our theories of the
fcience, have been altered by them. But that this
point may not reft wholly on the circumflances of
the diagram, I fhall produce four paffages, that plainly
fbew the relation between the two dodrines. The
firffc from Ariftoxenus.

“ Now, as fome of thofe [fyftems] which we employ
in mufic, are fimple, and others mutable, we muft treat
of mutation ; and firfl of this, what mutation is, and
how it is accomplifhed ; now, I fay, there happens,
as it were, a pathos in the melody ; afterwards, how
many mutations there are in all, and according to
what intervals (21).”

In this paffage, the author is fpeaking of the fixth
divifion of harmonic, which was mutation 3 and
more particularly of mutation with helped to tone,
which, in this divifion, was always treated upon the

(21) ’E-sth S'i r y.zKo^ay.iVav Z7i Tci y cLzrka, 7 a 3 ttuZTctCoAct ,
[corrige, zyyi7 dQahA] 'Sfi yzlaCohrif dv ini hZKTzar ^r/>arov fie cLyro,
71 '707 Zfiv n yilaCoAri, kai vAf yivbyzvov. Azyco

Tivli

<ruyCau>oS]& zv ra f yihuS'ias ra'£«. "E-sr &Ja. 7707A1 \uxiv cJ tsa-
pxi yi]ciCo\cti} Kct} Kci7u 7707 a fiasnyet}*,. Ariftox. p.38. v. 7.

principle

3

[ 74+ ]

principle of the harmonic dodrine, and is fo here ;
but he tells us, there was a pathos in the melody,
which can only relate to the mufical dodrine, and
therefore (hews their connection. In the next paff-
age, from Ariftides Quintilianus, it is more plainly

hinted at. , . r .. u

“ For if a certain type of the voice follows each

fyftem, it is manifeft, that the. fpecies of the melos
will be altered with the harmonics (22).

But the two following paffages from Ptolemey wi

put the matter out of difpute. > . c

il For we are not to imagine this conftitution o
the mutation, according to. the tone, eftablifhed for
fake of graver or acuter voices, (fince the intennon,
or again the remiflion of whole inftruments, fumces
for fuch a difference, no alteration being produced in
refped of the melos, the whole being executed by
performers of graver or acuter voices) ; but with this
view, that the fame melos, begun by the fame voice,
now from acuter places, and now from graver,, may
produce a certain change of ethos; becaufe that in the
permutations of the tones, the extremities o the voice
do not anfwer to both the extremities of the melos;
but in one, the extremity of the voice always falls lhoit
of that of the melos ; and in the other, the extremity
of the melos of that of the voice : fo as that the fame
melos, which at fir ft (meaning in the Dorian) 1 an-
fwered to the compafs of the voice, now falling Ihort

(22) ’E/ >8 Hufra *5 lU0l>0< ^

Quintil. p. 24. v. ult. Q£

C 745 ]

of it, and now again exceeding it, may give to the
ear the impreflion of another mode (23).”

“ For of the mutations in refpedt to tone, fo called,
there are two principal differences, the one by which
we run through the whole melos in an acuter tenfion,
or again in a graver, preferving always the fucceffion
of the fpecies. The other, by which there is an al-
teration, not of the whole melos in its tenfion, but
only of a part thereof, from the fucceffion it fet out
with. Wherefore, this laft might be called rather a
mutation of the melos, than of the tone ; for, ac-
cording to the former, the melos is not altered, but
the tone (tenfion) of the whole; whereas, according
to the latter, the melos varies from its proper order,
and the tenfion varies not as tenfion, but as on ac-
count of the melos. Hence the former does not
ftrike the fenfe with an idea of that alteration, ac-
cording to power, by which the ethos is changed,
but only of an alteration in refpedt to the being acuter
or graver; whereas the latter caufes the fenfe to drop
from the ufual and expedted melos, the fucceffion
being preferved fome time, and then making a tran-

(23) ’OuJ'i $ biHiV T CctpvTipaV ?] b^VTifW (puVuV Iv&tpfy AV TnV
tuta-oiv Hard r r bvov [azIaCoKvt ysyentifAznr o-stots mpos tm toiav-

Tin/ J'lcttpogc/A’ h r opydvuv oAcuv amTATis, « ttaKiv ivz<ns att Ap/oe. , y.n-
fzy.iAf yz <3^51 Wetytif ^ i to &srrv\zK xy.ivnf, otav o\ov byoio/f

vtso t Q'ApvouvoTzpcov n t o^vfuvoTzpcoy dyovtsuv J'iAvfy’&iviija.r «AA
ZVZKct TV X-ATA TtjV [At A V fyuviiv TO AVTO [AZK& TTOTi y ^ffTV T b^VTtpuT
TOTUV dp'yj/[J^J0Vf 7T0TZ cPs T CApvTZffiJ", T&>7T 11V TIVA TV AVnfji'

A«l' TT>7 y.tlX.ZTl TSfoi iXATZgA TA TTi^A TV [Aihvi AWAIT ApTl^Z&Al TA
tptovris iv ¥ t t'ovmv Lv&hKctycii (’ «aa’ dbi TT^oKccjA^nyen', hrm y i vof-
T«£J t, TO f tpcoviii; TTi£Ai; TV TV [AZ AVJ1 C//7J 0 TA CVAVTlA , TO TV [AiKvf

Ts‘z^f.i tv $ Wfiif cba'ji ro z^Apyjif iqApy'uAAV th J'lATatA&t f own f y\-
Ko$, tty! y a/mK&Trov iv r [/.{IaGoAaIs, tt h q amKAyCdvoVt trips n$n{
ft o/Jaalav TTApzyjv t ama! f . Ptol, Harm. lib. ii. c. 7.

fificn

[ 7+6 ]

fition to another fpecies, whether according to genus
or tenfion (24)-’’

o The third point will receive much fupport from
thefe two confiderations ; firft, That diapafons, va-
rioully divided and varioufly bounded, alfo feem to
form a more complicated theory, than can well be
fuppofed to have prevailed in early times, when mufic
had not yet loft its natural fimplicity ; and fecondly,
That the compafs of the inftrument, in its odtachord
ftate, would not admit of any variation, in refped to
the bounding founds. But there is teftimony to this
point alio : I fliall cite one pretty remarkable paflage,
from Ariftides Quintilianus, which will be fufficient,
as the proof of the next point neceftarily carries this
along with it. Ariftides, who, in his explanations
of the harmonic doctrines, follows the method of the
Ariftoxenians, coming under the head of fyftems, to
treat of the fpecies of diapafon, after explaining their
fituation in the immutable fyftem, and afligning their
denominations, immediately fubjoins :

<c Hence it is plain, that if we make our nrft ngn
the fame, though denominated in different cafes from

(24.) E k-f'nxL va&**t* Kiy'o/t&Jov tow, pel rt&Jjit Mo ‘bp»t<u
AtL. uU% KdJ\v OKOV TO oMpct TAffH

.. . ..kxlfa. a.WAas£\Al T» T eLcki, ^ Tt '&&&• T"v

TAOlf, Of
T Al&MSOJ

a retv twv 3, to y

Ttto7f, aAA’ Ivika rk yitof o$tv ,

Wncur’icLV rw/vvctyev, uV

£*4 ukmc T n< KATA TO » C* WTt&r

7$ elKKd yom T«{ KATA TO btvTiepV » CAfV Ti&V; AVj

Umvlttv AVTfo ««« n kai^Uko^vh

— y <TVVbip\)lAI TO AKQhvSoV, y{\ACAlV* o TtS <T3f0f _ •

tret to ytyQ', it kata f Tamr. Ftol. Harm, lib- “•

<VKiOV
HTOt kata

[ 747 ]

a different power of found, the quality of the har-
mony will become manifest, from the fucceffton of
the founds in order (25).

In this paffage, it is to be obferved, that the term
tmjjLUQVi a Sign, Signifies a muSical charader, fuch as
the antients ufed to write over the words of a fong,
to exprefs the air, or tune ; and that each of thefe
characters reprefented not a found of the fyftem, fub-
jedt to tranfpoSition, but, like the notes of our gamut,
a found of a certain pitch, or at lead liable to very
fmall variations only, from the generic differences.
The term, therefore, is properly ufed here by Arifti-
des, in opposition to <p£royy©~, a found of the fyftem,
whofe pitch depended on the mode in which it was
employed. As to the expreflion, quality of the har-
mony, it evidently refpeds the fpecies of diapafon ;
fo that the author plainly means to tell us, that if we
begin a diapafon always with the fame note, the
fucceflion of its founds, that is, the manner in which
it is divided, will determine the fpecies: and fo far
he fpeaks to our purpofe. But this point will re-
ceive farther proof, from what we Shall fay upon the
next.

4. The fourth point being the natural refult of the
combination of the two dodrines, carries a fort of
convidion with it ; and the Stronger, as not only the
feven modes, but the whole fifteen, affift the proof,
as will appear, on examining the table I have given
of them : for there the founds lying between the

(25) ha rara tpavifiv, ut ^ 7cl<jtov \zro§zy.'ivo:s atiy-tn ev rspwTov,
aKhn S'vvdfjt.M Qd-oyfu x.ci}oi>oy.ct^oy$/M', chtij( r <p&o''yfv v

dx.cK**yia.{ Tin • tvs a.yy.ona.$ '~ci'n>{]ct <p&vtpg.v ’fptSreu avy-Gdtvzi. Arift.
Quint p. 18. v. 7.

Vol.LI. 5D Strings

[ 74§ ]

firings hypate melon and nete diezeugmenon fall out
fo, as to give the proper fpecies for every mode ;
which circumftance will not attend any other boun-
daries, common or varying, without altering the po-
rtions of the mefe, and thereby difturbing the har-
monic dodrine. But we have from Ptolemey iut-
ficient teftimony to this point. In the eleventh chap-
ter of his fecond book, of which I have given a tranl-
lation above, we fee, that the diapafon in question is
chofen by him, to exhibit the divifions, that belong
to the feveral fpecies. ’Tis true, he feems to m-
finuate, that any other diapafon might have been
chofen, were it not for the difficulty the voice finds
in running to the extremes : and in this, as a theorifr,
he is right ; for muficai relations and proportions,
confidered as objeds of mere fpeculation, may be
conceived at any pitch ; but in the cafe before us, it
was die pradice of the inftrument, that governed
the theory. The pitch of the lyre had been made
to anfwer to the double odave of the human voice ;
the pitch of the fyflem, in the Dorian mode, anfwei ed
to that of the lyre; and, in every other mode, the
difference in pitch from that of the Dorian was de-
termined. Now, under fuch limitations, that tooK
their rife from pradical mufic, it is evident, that no
other diapafon, but that inftanced by Ptolemey, could

have ferved his purpofe. . . . . , ,

But that the boundary of the fpecies is rightly act-

iufled in the diagram, there is yet another ftrong tefti-
mony, from the tables of Ptolemey, annexed to the
fifteenth chapter of book fecond. T o make this pi ooi
evident, it will be neceffary to give fome account ot
this part of his work.

In

[ 749 ]

In the twelfth chapter of book fecond, he begins
to treat of the fedtions of the harmonic canon, for
proving, by experiment, the truth of the ratios he
had delivered for the genera, and propofes to exhibit
thefe fedtions for each genus, in all the feven tones.
Then, after (hewing the defeats of the monochord
canon in ufe, and (chapter thirteenth) the infufficiency
of the improvements made thereon by Didymus, he
propofes, and explains, his own method of applying
the canon to eight firings tuned in unifon. But, be-
fore he proceeds to give the fedtions upon all the
tones, he thinks it neceffary to fhew, by experiment,
the advantage of his own numbers, above thofe of
preceding harmonicians ; for which purpofe, the ex-
pofition of them in one tone, that is, in the immu-
table fyflem, was fufficient. Accordingly, in chaptcr
fourteenth, (the greatefl part of which has been lofl,
and is fupplied from conjecture by Wallis) and in the
tables annexed, he gives the fedtions of the Dorian
fpecies of diapafon ; where the diazeudtic tone, lying
in the middle, left a complete tetrachord on each
fide, for the expofition of the generic numbers ; and
compares his own ratios with thofe of Archytas,
Eratoflhenes, Ariftoxenus, and Didymus. Then, in
the fifteenth chapter, he proceeds, as he propofed, to
give the fedtions according to his own ratios, for the
genera moil in ufe in all the feven tones : thefe fec-
tions he has included in two fets of tables, each fet
containing feven, viz. one for each mode; and each
table being again fubdivided into five, for the generic
differences. Now, of thefe two fets of tables, the
firfl juftifies the diagram; for here he has given his
numbers upon the eight firings, from nete diezeug-

5 D 2 menon

C 75° 3

menon to hypate mefonj fo that the diagram and
the tables agree in every refpedt, except the generic
differences, which I had no occafion to confider. In
the fecond fet, indeed, the numbers are applied to
the diapafon, from mefe to proffambanomenos > and
there being no explanation in this chapter of the
diftindt ufe of this fecond fet, nor any reafon affigned
for giving it, but the convenience of having the op-
tion, to begin the tuning from nete or mefe (26), this
may feem to furnifh an objection to the proof pro-
pofed to be gained from thefe tables : but if we look
forward to the fecond chapter of his third book, we
fhall there fee his meaning j which I fhall proceed
to explain.

Having, in the fixteenth chapter, fhewn how the
numbers, given in the two fets of tables, are to be
applied to an odlachord canon, he propofes, in the
firff chapter of the third book, to drew, how the di-
viffons for the fifteen founds of the whole difdiapafon
fyffem might, if required, be found, according to
the fame ratios he had already affigned for the
extent of a diapafon. Now, for the doing this, two
inconveniences were to be obviated. Firff, If the in-
ftrument, on which this experiment was to be tried,
was to receive an addition of feven firings, to com-
plete the difdiapafon, and thefe additional firings
were all to be in unifon with the eight before applied,
it would happen, that, in fhifting the moveable ma-
gas, or bridge, to the fedtions required, thofe firings,
which were to exhibit the acute fedtions of the tetra-

(26) '1/ 'iyufjUfJ ct’p’ o7roTi£$f aV T 'XfjcLifvy.lScL tas

«p//o^ccV. Ptol. Harm. p. 174. v. ult.

chord

C 751 ]

chord hyperbolseon, would have fo little fpace left
between the magas and the extremity of the firing,
that it would be difficult for them to yield a diflindt
found. And fecondly, The canon mud be crowded
with thefe additional divifions, which would alfo
have its inconvenience. To remedy this, he propofes
feveral methods ; the firfl of which is, to fit the in-
flrument with fifteen firings, of which the eight, that
were to receive the divifions from mefe to nete hyper-
bolason, ffiould be in unifon, at the pitch of mefe,
and the other feven in unifon, at the pitch of prof-
lambanomenos. Now, as the fucceffion from the
firing proflambanomenos to the firing mefe, though
it varied with the modes, was yet, in the fame mode,
always the fame with that from mefe to nete hyper-
bolaeon, the difference of a diapafon in pitch excepted,
it is plain, that, under this adjuflment, a canon di-
vided for the one diapafon would ferve equally for
the other, the difference in pitch being eftablifhed
before in the open firings. By this method, there-
fore, the divifions for the acuter diapafon would be
as large as thofe for the graver, and the canon needed
not to be crowded with a greater number of divifions,
than had been ufed for the fingle diapafon, by reafon
of its double application. The other methods, which
he propofed, I need not go through the explanation of,
farther than to remark, that, for thofe, as well as for
this, a freffi fet of numbers was neceffary, thofe con-
trived for the fucceffion of the diapafon, from hypate
mefon to nete diezeugmenon, being no-ways appli-
cable to a fucceffion, which began from proflamba-
nomenos or mefe. And this, it feems, was his reafon
for giving the fecond fet of tables in his fifteenth

chapter,

[ 752 3

chapter, as appears from his own words, in the fe*

cond chapter of the third book.

In general, for fuch ufes, as comprehend a diapa-
fon only, it behoves us to employ, out of the numbers
exhibited, thofe which contain the fedion from nete
diezeugmenon, that the melos may be taken in the
middle tenfions ; but for fuch as comprehend the dtf-
diapafon, thofe exhibited from nete hyperbohuon, or
mefe, that the tuning may be adjufted at both extie-
mities alike (27).

Here we fee he fully explains his former mean-
ing; ; and, in recommending his firft fet of tables or
the ufes of a diapafon, gives the fame reafon for the
choice of that diapafon in particular, as he a igns
for it in the eleventh chapter of the fecond book,
viz. that the melos may poflefs the middle of the
inftrument. But it muft be obferved, that when the
whole difdiapafon has been adjufted by the fccond
fet of tables, the tunings of the eight filings, fiom
note diezeugmenon to hypate mefon, will come out,
for every mode and genus, the very fame, as if they
had been tuned by the firft fet : fo that no inference
can poffibly be drawn from thence, either that the
author has varied as to his own meaning, 01 t a e
diagram, which 1 have given, does not correipon

with it.

TO J'lf 6't'X 'THO.TUV, T8J bOT ™ T'< ' J'tiv/IeU.

1 vet y.&r djj.tpoTifeov T axfcov optiwv -? f. • C

Ptol. Harm. p. 228. v. 15. t

J* 1

[ 753 3

y. I come now to the fifth point, which has been
the fubjedt of much difpute, and which might well
afford an endlefs controverfy, whilft the union of the
two dodtrines was not underftood ; for whatever rea-
fons, from probability or teftimony, might be urged
in favour of the mufical, the harmonic dodtrine ap-
pearing to be ftill better fupported, and feeming to
eontradidt the other, was fure to fufpend the deci-
fion, at leaft, if not gain one in its own favour. But
the agreement between the two dodtrines being fhewn,
and their views diftinguifhed, the teftimony borne to
the harmonic dodtrine will no longer be in the way
of the mufical, and we may fafely allow whatever
appears favourable to the latter, its full weight. I
fhall therefore offer, in fupport of this point, the fix
following arguments.

Firft, No one accuftomed to hear and judge of the
effedts of mufic, can conceive, that a mere alteration
in pitch of the fame melody, though in the hands of
the moft artful mafter, can have fo powerful an effedt,
to change the mode or ftyle of compofttion, as an
alteration of the melodious fucceflion : or, if this
fhould be aflerted, it might be difproved, by an ap-
peal to the works of all the compofers of eminence
among the moderns j who having, in all the variety
of their modulations, but one change, that truly an-
fwers to the mufical dodtrine of the modes, viz. the
change of the fucceflion of the fame key, from the
major third to the minor, have all referved this change
for their pathetic paffages. I fhall give but one in-
ftance of it, from our countryman Purcell, who,
in his Mad Befsr has fo happily introduced this
change, upon the words, “ Cold and hungry am I

“ grown/'

[ 754 ]

“ *rown,” that if the performer does juflice to the
compolition, the hearer can fcarce help fancying him-
felf affeCted with the very fenfations, with wliich the
Marts’ of frenzy are there pictured.

2dlv If I have been right in aligning a greater
antiquity to the mufical doctrine, than to the har-
monic, the effeds of the modes muft, in earlier
times at lead, be referred to the former. And this
carries with it an argument for later times alfo; for
the old principle of the modes could not be fudden y
changed. And though it may be urged, from the in-
troduction of the eight fpurious modes, that the har-
monic doCtrine came, in time, to be confidered as a
principle independent of the other, _ this will only
prove a corruption of the better dodrine, which may
fafely be admitted ; though that the mufical dodrine
was ever quite difufed, unlefs in very late times in-
deed, I much doubt, as fome traces of it are found in

almoft all the writers come down to us.

-dly, Ptolemey’s rejeding the eight modes, that
wanted the fupport of the mufical dodrine, is an-
other proof. For, if the harmonic dodrine had been
the more effential of the two, thofe modes ought to
have been preferved. Nor does the ad million of ix
of them, by the Ariftoxenians in earlier times, weaken
the force of this argument : for though the rejecting
them is conclufive, againft the harmonic dodrine, as
•far as any weight is allowed to the opinion of the re-
ieder, the argument from their admiflion will not
conclude in its favour, till it be proved, that in the
■life the fpecies of diapafon aflbrded by thefe modes
was not attended to, but only the order from the proi-

■lambanomenos, in power of each, as the favouiers o

the

C 755 3

the harmonic dodtrine feem to fuppofe : and this
proof it would not be eafy to obtain, fince each of
thefe modes had its fpecies belonging to it, and was
only exceptionable, becaufe it repeated the melody of
one or other of the feven.

4thly, The denominations given by the Arifto-
xenians to five of the fpurious modes, after the ge-
nuine ones, whofe fpecies they afforded, furnifli an-
other ffrong proof j for this could fcarce have hap-
pened, if the pitch of the fyftem had been the prin-
cipal diftindtion.

ythly, We find in Plutarch, Pliny, and other
authors, the invention of particular modes afcribed
to particular muficians ; which may be accounted
for, on the fuppofition, that the modes were fo many
different fpecies of diapafon; fince it requires great
art and fkill to introduce agreeably melodies, to
which the ear has not been accuflomed : but the
taking the fame melody at a different pitch is a va-
riety, for which the inventor would hardly have had
his name fo carefully delivered to pofterity.

But 6thly, there are paffages, that ftrongly con-
firm the preceding arguments. Ariftoxenus fpeaks
of modes of the melopcei (28), by which I under-
ffand him to mean the fpecies of diapafon, in contra-
diftindtion to the modes of the harmonicians ; for I
fufpedt the modes of melopcei'a, mentioned by Ari-
ff ides Quintilianus (29), and divided by him into
three kinds, viz. nomic, which was netoidesj di~
thyrambic, which was mefoides ; and tragic, which

(28) Pag. 40. v. 21.

(29) Pag. 29. v. ult.

Vol. LI.

was

[ 756 ]

was hypatoides; and which are alfo mentioned by
other writers, of a low age (30) ; thefe modes, I lay,

I fufped to be founded on diftindions not in ufe fo
early. The ufe of the fpecies of diapafon in melo-
pceia is confirmed alfo by Bacchius, who, imme-
diately after explaining them, exprefles himfelf thus :

£t So many, therefore, in the art of mufic, are the
fpecies of the confonances, by which every melopoeia
is formed (31)-”

And alfp by Ariftides Quintilianus, who concludes
his dodrine of the fpecies, with thefe words :

<c And thus much fuffices concerning fyftems,
which the antients alfo ftyled the ethic princi-
ples (32).”

For, by fyftems, we are here to underftand fyftems
in the general fenfe, as defined and treated by the
Ariftoxenians, whom Ariftides follows in this part of
his work, and more particularly the three confonant
fyftems, whofe fpecies he had juft been defcribing.

The paflage I have already cited from Plato, ferves
alfo ftrongly to fupport this point ; for the terms,
fpecies, and figure, are there ufed in the ftrid technic
fenfe, and not merely to exprefs variety, as appears
from his fpeaking, in the fame paftage, afterwards
of the fpecies of melos, the fenfe of which cannot
be miftaken j and that he is fpeaking of mufic, in

(30) Martianus Capclla, p. 189. v. 21. Manuel Bryennius in

Oper. Wallifii, p. 503. v. 1 4^ , w ,

(31) Toffc’JjTCC y z?t T GVU.$UVtMV TO, flftTl) Ci' TH [AX 07 KYI

J'i' go v 71 a ace fAihcTroticc <ruvjret]cLi. Bacch. Son. Introd. Art. Mufic.
p. 19. v. 1 8. ^ w , ,

(32) riiet' (a y ffvrtt/AUTUv, ct Tr&heMOt T i&P&v

dfKtira tc/jjtcc, Ariftid. Quintil. p. 18. v. 12.

refped

[ 757 ]

refpedt to its effedls, is manifefl, from the whole
paifage : fo that, though the modes are not diredtly
mentioned, they are necelfarily to be implied. But
Ptolemey is ftill more exprefs ; for, in the paifage
cited above, from book fecond, chapter feventh, he
diredtly affirms, that the ethos, or character or the
mode, depended on the mufical dodtrine, and not
on the harmonic 5 and is ftill more explicit, to the
fame purpofe, in the paifage cited alfo from the fixth
chapter of the fame book. Thefe two palfages are
fo clear, that there is no evading their teftimony,
but by fuppoling the author to be lingular in Ins
opinion j which there is, indeed, room to think was
his cafe, with refpedt to many of the muficians, his
contemporaries ; for the pains he has taken to clear up
and diftinguifh the two dodtrines, is a fufficient proof,
that miftakes had prevailed concerning them 5 but
that what he has advanced is not repugnant to the
dodtrines held in earlier antiquity, has, I think, been
amply Ihewn. I lhall now dole thefe proofs with
three remarkable palfages from Plutarch’s dialogue
on mulic, which will all become intelligible from
the explanation given of this fubjedt, at the lame
time, that they will ferve to confirm it. The firlt
refpedtts the invention of the Mixolydian mode,
which we fhall fee he treats as a fpecies of diapafon,
telling us between what founds of the fyftem it lay,
and in what part of the diapafon the diazeudtic tone
was fituated ; in both which circumftances, the
paifage agrees with the preceding explanation, and
with the firft diagram.

<c Lyfis informs us, that Lamprocles the Athenian,
feeing, that it (the Mixolydian harmony) had not the

y E 2 disjundtion

/

C 758 ]

disjunction (diazcuCtic tone), where almoft every one
imagined (meaning in the middle of the diapafon,
for fo it was in the Dorian, which was moft familiar
to the Greeks), but at the acute, made the figure of it
fuch as that from paramefe to hypate mefon (33). ’
The next pafiage informs us of a very remarkable
circumftance, viz. that, after the addition made to
the lyre of the tetrachord hypaton, no ufe was made
of thole firings in the Dorian mode, though they
were employed in the reft. Speaking of the earlier
times, and arguing, that the antients had omitted
many things, rather from choice than ignorance 5
“ It is manifeft (fays he), that, in refpeCt to the
[tetrachord] hypaton, it was not through ignorance,
that they abftained, in their Dorian [compofitions],
from this tetrachord ; for they employed it in the
reft of the tones, as plainly knowing it ; but, for the
fake of preferving the ethos, they left it out in the
Dorian tone, as refpeCting the beauty thereof (34).”

From this pafiage it is evident, that the Dorian
melody, which, in its proper character, according
to the mufical doCtrine, was terminated by hypate
mefon, was in fuch efteem with the Greeks, from
a long habit of hearing their beft pieces com-
pofed in that fucceflion, and within that compafs,

(33) Ajtsif 0 (own) A&piyoKKict <f ’ \$m’cuoV trvy/fovJaoTl Zx. h -

TaijT&cL V/jH t J oxa V c o'. lo, aAA cm Too

to /a tov dv 7<k a.zTfyuTA^a.1 to yet to 'arc cm \£irct]>l

xsttatuv. Plutarch. Dial, de Mufica. ^

(34) A»Ao V j )0 T Tiei \X70Tuv, ot i a JV ctyvoictv dLTH-yov}o If Toii
•Papio/f T6 T^j^cf.yip^n tZt*, avtikcl ctj T honroov xcr*’i' typai’] o, S'nKo-
moi 1 uJ'oTif S'to q t rns iiSvf <pv\ctK>)v dtpZpvv cm tv Suti a toi'k, ti-
y-wi’ln to KuKov turns . Ibidem.

that

C 759 ]

that the additional firings could not be ventured
upon in that mode, though in the rell they were
admitted.

The laft paflage is that, which I have mentioned
above to have been cenfured by Meibomius : we
ftiall fee here, that the author is exprefly arguing for
confining harmonic within its proper fphere, and not
fufFering it to encroach on melopoeia, by engaging
with the rules of propriety, in the ufe of the ele-
ments ; fo that it both justifies and explains the di-
ftindtion I have made above, between the two fci-
ences, and turns the cenfure of Meibomius upon
himfelf, who feems, indeed, without excufe, unlels
we fuppofe him to mean only, that Plutarch, in
giving the Ariftoxenian divifion, ought not to have
funk any part of it : which remark would have been
juft, if Plutarch had given the divifion as fiich 5
but he does not name the fchool, though he adopts
their diftribution of the fcience as far as the fix di-
vifions he approved 5 fo that no inconfiftence can be
charged upon him. The latter part of this paflage
alfo confirms the diftindtion I have made between
the two dodtrines, and their ufe in the two fciences ;
fo that it aflifts moll of the preceding arguments and
proofs : and here I fhall therefore reft this point,
which will fcarce be thought to need farther fup-
port.

For it is evident, that the immediate objedts of
harmonic are genera, viz. thofe of the hermofme-
non, intervals, fyftems, founds, tones, and fyftematic
mutations ; and farther than this it cannot go : fo
that we ought not to expect it ftiouid determine how
far the poet, in his mufic, has properly aflumed the

Hypo-

[ 76° ]

Hypodorian tone, for inftance, for the outfet ; or the
Mixolydian and Dorian, for the conclufion ; or the
Hypophrygian and Phrygian, for the middle; fince
the harmonic treatife does not extend fo far, but has
need of many others. For of the force of propriety
it cannot judge, lince neither the chromatic nor the
enharmonic genus will ever contain a perfedt force of
propriety, fuch as to difcover the ethos of the com-
pofition, that being the bufinefs of the artift. And
again, it is plain, that the voice [pitch] of the iyftem
is to be diftinguifhed from the melopce'ia wrought in
the fyftem, the confederation whereof does not be-
long to the harmonic treatife (35)- Having now
finifhed my head of proofs, I come,

Lnjlly , To confider how far this fubjedt has been
underftood by Meibomius, Wallis, and fome
few others that have wrote fince ; and in what
reipedt their explanations differ from my own.

In refpedt to the opinion of Meibomius, Malcolm
tells us,- that that writer, in his notes on Arillides
Quintilianus, affirms the differences of the modes.

(35) •$> oti n /X ctpyovotri 'fivuv tzt ra npyoyyzvis Ka S'ttcTyy.a-

ruv 10 ffvTtiya'Tu v >y tp&b'yfap )y Toiav jl, y{ja£ohav ayTiiy-ojiKup t<rt
y put ToppuTzpu q fozTi Tdvjtiv '&f>o(re\$£v o/jifjr mtz QiiTetP
Tdv]m to S'lttyvuvai J'foa.S cu vroTi&v otxiiuy uyimvo arotrmif,
ouoto v znreiv, dv yfoa.it r xaroj'uewv Tovov ai n r " ,T

jtov TZ >y S'ueiov am r tx.Ca.mp, » r vsrotppvyibp n (ppvyiop am r
lAanv. O v $ J'la.T&vet w dpyovix.ii 7r&.yy*T*a. Tsfbt to. tokwta,

TreoeJ'jTcLi 0 itohhuv fotpar r $ f J'vva.piv^a.yvoei.

GClrz TO ypuydJ/Kfo yiv&, V/e to Ivapyopiop yoTzyxcvri‘
o/x.MTt{]& S'vv'.iyiv Ttheicty >y KO.& fo to th rwrojnyiv* yt^f
cm<p<up{ja.i, d\Kd raro Ttxy'i7* hyov- $<*-vzc?v Q oti tTZ&t. to
(rvrnya]@j » $upyi f dv ttJ avT.iya]t Kx]a.<rx.nja.<Se!o>y yz^oTroita.;, lie*
fo »x. tTi diupmat f dpy'.vuiif ‘vpa.yyaT&a.s* Plutarch. Dial, de
Mufica.

upon

5

[ 76r I

upon which all the different effcdts depended, to have
been only in the tendon, or acutenefs and gravity of
the whole fyftem (3 6). And indeed, in the note on
page 13 verfe 4. of that author (37), which, I pre-
fume, Malcolm had under his eye, Meibomius clearly
decides tor the harmonic dodurine, as he does alfo in
his note on page 2. verfe r. of Euclid’s Harmonic
Introduction (38). But in this laft note, he had juft
before told us, that tone was by the antients alfo called
harmonia, and fpecies of diapafon (39). And, in
the conclufion of his note on page 1 . verfe io. of the
fame author, he delivers himfelf more fully to the
fame purpofe.

“ The antients (fays he) having confidered feveral
fpecies of diapafon in the bifdiapafon, called thefe alfo
harmonics. Whence we read Dorian, Phrygian har-
mony, in the beff writers. The fame were again
called tones and tropes, or modes (40).”

In

(36) Malcolm’s Treatife on Mufic, p. 540.

(37) ^'c autem locus oppidd notandus eft contra recentiorum
de tonorum effectibus opiniones, illorum enim varietates, fo , la ,
acuminis atque gravitatis differentia veteres unanimi confenfu defini-
unt — Acumen autem ac gravitatem nihil varietatis cantilenae adf'erre
contra omnem eruditam vetuftatem, imo communem fenfum exif-
timant. Meibom, in Arift.,Quint. p.219.

(38) Tonus feu modus eft totius fyftematis harmonici, hoc eft
bifdiapafon aut fimpliciter diapafon differentia; ut Phrygius tonus
a Dorio nulla alia re differt, quam quod totum Phrygii fyftema
acutius fit toto .Dorii fyftemate, tono, qui eft in ratione fuper-
oftava. Meibom, in Euclid. Intro, di Harm. p. 46.

(39) T oni vocabulum quatuor modis accipitur ; — hie idem eft
quod modus ; cum dicimus tonus, five modus Dorius, Lydius,
Mixolydius ; veteribus quoque harmonia adpellalur, et fpecies dia-
pafon. Ibidem.

(40) Cum autem plures diapafon fpecies in bifd'apafon antlqui
fpedlarent, illas quoque adpellarunt harmonias. Unde Doria, Phry-
gia

[ 7&2 ]

In his note alfo on the paffage I have cited above,
from Ariftides, page 18. verfe II. he explains the
cxpreffion, quality of the harmony, to iignify the
fpecies of diapafon, or tone (41), which is the fenfc
\ have put upon it. We fee therefore, that though
he haltily afcribes to the harmonic dodtrine alone the
effedts, which I have luppofed to arife only from the
mufical, yet he clearly admits both the dodtiines to
be warranted from antiquity ; and I am glad to have
fo far the fupport of this learned critic’s opinion : but
of the connection between the two dodtrines, as I
have explained it, I fee no trace in his notes j noi is
it to be imagined, but that, if he had feen it, he
Would have enlarged upon it.

In relpedt to Dr. Wallis, though he had the ad-
vantage of the notes of Meibomius, who had cleared
up fo many difficulties, and had alfo taken under his
own management the text of Ptolemev, the author,
of all others, the moft likely to have given him a
thorough in light into this fubjedt, yet we find him
not only defective in his explanations of it, but, con-
trary to his ufual accuracy, even in milleading his
readers by falle dodtrines. With refpedt to the mu-
fical dodtrine, if we may judge by his filence, he ap-
pears to have feen lefs of it than Meibomius ; for, in
the appendix to his edition of Ptolemey, wherein he

eia harmonia, apud optimos autores legimus. Deinde eaedem toni
et tropi, feu modi funt adpellati. Meibom, in Euclid. Introduc .

Harm. p. 42. .

(41) Id eft quae fit fpecies otachordi, feu quis tonus; nam duo-

bus modis ufurpatur vox «p y.ovict, uno pro genere enarmonio, a-
tero pro tono, feu tropo, feu modo ; quae fignificatio eft buic oco
propria. Meibom, in Arift. Quint, p. 230.

under-

[ 763 ]

'undertakes to explain the harmonic elements, after
treating of the fpecies of diapafon, he gives not the lead:
hint, that they had any relation to the modes, except
by giving their denominations ; and in doing this, he
expreffes himfelf (42) as if he thought thefe denomi-
nations rather affigned for fome feparate reafon, than
on account of their connection with the modes ;
though, as he was going immediately to the doCtrine
of the tones, this was the place, where he might have
been expeCted to have taken notice of the connection
between the two doCtrines, if he had obferved it. In
treating of the modes, indeed, though he explains
them on the foot of the harmonic doCtrine only (43),
he affigns fome of his author’s reafons for reducing
them to feven (44). And his note alfo on the be-
ginning

(42) Atque has quidem diapafon fpecies feptem fua fingulae
fortiebantur nomina ; prima di£ta eft Mixolydia ; fecunda, Lydia ;
tertia, Phrygia; quarta, Doria; quinta, Hypolydia; fexta, Hy-
pophrygia; feptima, tum Locrenfis turn Hypodoria. Tandem de
modis, -feu tonis dicendum reftat. App. ad Ptol. p. 31 1.

(43) Modus itaque, feu tonus, prout hie fumitur, denotat vocis
locum, non quo una vox, fed quo tota vocum feries, feu fyftema
canitur; acutiorem puta, gravioremve. Utpote prout apud nos mi
canitur, nunc in b f b mi , nunc in elami , nunc in alamire , See :
Sic apud illos verbi gratia, paramefe poteftate (quod tantumdem
eft atque noftrum ?ni), pofita erat nunc in paramefe pofitione,
nunc in pofitione nete diezeugmenon, nunc in mefe. Sec. Ibid,
p. 312.

(44) Contra hos, qui tonos, feu modos, fic augent per hemi-
tonia difputat Ptolemaeus, cap. 7, 8, 9, 10, II. lib. ii. docetque
modorum variorum ufum non in hunc folum finem introdiuftum,
ut acutior graviorve fit totius cantus tenor; quippe huic fufficeret
cantoris vox acutior graviorve ; aut mulici organi ad hofee tenores
accommodatio. — Sed eo potiftimum fine fuille introdutftum, ut in
ipfius cantus curriculo tranfitus fiat de modo in modum, quam vo-

V.ol, LI. 5F cant

[ 764 ]

ginning of chapter eleventh, book fecond (45)) rightly
explains the fpecies of diapafon, as they lay between
hypate melon and nete diezeugmenon : but this in-
terpretation is formally introduced with a nernpe hoc
*vult , as if he thought his author fingulai in tuis doc-
trine, and looked upon the dodtrine itfelf, as flated
in that paffage, rather as explanatory of an incidental
circumftance attending the harmonic dodtiine, than
meant to affign the true dodrine of the modes. This
is manifeft, from his drawing the fame inference,
both in this note and elfewhere (46), from this mu-
fical dodtrine of the fpecies, as he had drawn before
from the harmonic one, ‘viz. that the tones thus

cant (//sIctCoAM' KcCja, tci'oi') mutationem fecundum tonum : quou a
noftris fit mutata clavis fignatura adhibitis mollis et dun notis, c:c.
— Et propterea tonos diftin&os ponendos efle docet ommno leptcm,
Mixolydium, Lydiura, Phrygium, Donum, Hypolyd.um, Hypo-
phrygium, et Hypodorium. Totidemque admittit hodieina mUica

pro varia clavis fignatura. Ibid, p* 3r3*

Or) Nempe hoc vult : diapafon illud expofitum ab hypate me-
fon ad neten diezeugmenon; hoc eft (in mufica hodicrna), ab
elami ad elami, his vocibus port primam cam m tono INnxolydio,
fa, fol , la, fa, fol, la, mi-, quae eft pnma fpecies diapafon, ha-
bens mi, feu tonum diazeu£licum in loco precedents, teu acut.f-
fimo: his in Lydio, fol, la , fa, fol, la, mi, fa-, quae eft fpecies
fecunda diapafon, habens mi, in loco fecundo ab acutiihmo : in
Phrygio, la, fa, fol , la, mi, fa, fol: in Dono , fa, Jol, la, mi, fa,
fol, /!: in Hypolydio, fol, la, mi, fa, Jol, la, fa: in Hypop.irygio,
la, mi, fa, fol , la, fa , fol: in Hypodono, mi, fa, fol, la, fa, fol,
la-, qu* funt tcrtia, quarta, quinta, fexta, ct feptima fpecies dia-
pafon ; habentes mi, in loco tertio, quarto, quuVo, cxto, et
fep’imo, ab acutiffimo: quae omnia in mufica noftra mo bs ct dun
notis varie pofitis indicantur, ut mox dicemus. ac 0

P* U6) Ut foli fuperfint Ptolemaei feptem, Hypodoriu?, Hypo-
phrygius, &c. tot'demque agnofcit hodierna mniica poino mi in
F, G, A, b, c, cl, e. Ibid; p. 15 4, ad finem. ^

[ 765 ]

fettled by Ptolemey are acknowleged by the moderns,
in their feven pofitions of the mi. For nothing favours
lefs of the muiical dodtrine, than what the moderns
hold in this refpedt. And it is manifeft alfo, from
his negledting to affid the explanation of this doc-
trine of Ptolemey, by any citations from other au-
thors, that fpeak to the fame purpofe ; which he
would not have failed to do, if it had druck him as
an antient and genuine theory of the modes. But it
is plain to me, that, however he may have penetrated
the fenfe of thefe particular paffages, he did not grafp
their confequences. This the miftakes he has fallen
into fudiciently (hew ; which I (hall now proceed to
point out, and which a thorough comprehenlion of
the fubjedt could not but have prevented.

In fpeaking of the mefe of the Hypophrygian
mode, he explains it by f #, indead of f # (47), a
midake, which, I think, mud be imputed to his
hade.

In the table of the modes, which he has given
from Meibomius (48), he has placed the letters in
ufe with the moderns, againd the Hypodorian, as
well as the Dorian, making A anfwer to the proflam-
banomenos of the former, as well as the latter j by
which, it is to be prefumed, he means them to exprefs
the abfolute pitch of the founds in the Dorian, and
in the Hypodorian, to denote only the general rela-
tions of the fydem j but this fhould have been far-
ther explained.

(47) Not. ad Ptol. p. 154. lin. 41.

(48) P. 155.

But

[ 766 ]

But his greateft mifiake, and which I know not
how to reconcile to his ufual caution, is in the me-
thod he gives for finding the places of the mefes for
the feven modes. Not only is this method erroneous,
but he gives it exprefly as the method of Ptolemey
(49), though no l'uch direction is to be found in his
work. As I have already given Ptolemey’s method,
in our modem terms, for the fake of brevity, from
his tenth chapter, where it is delivered, I fhall here
give that of Wallis, in the fame terms, that the dif-
ference between the two may more eafily be feen.

“ Firffc pitch the Dorian, which is the middle
tone, fuppofe in A ; rife a fourth to D, for the
Mixolydian ; fall a fifth to G, for the Hypolydian ;
rife a fourth to C, for the Lydian. Then begin from
the Dorian again, and fall a fourth to E, for the
Hypodorian ; rife a fifth to B, for the Phrygian ; and
fall a fourth to F#, for the Hypophrygian (50).”

By this method, we fee the mefes of the Lydian
and Hypolydian are brought out at c and J natural ;
whereas, by Ptolemey’s, they come out at c # and
f #, where I have placed them.

This mifiake, I apprehend, the dodtor was .led
into by the eleventh chapter of Ptolemey’s fecond
book, where the mefes of the Lydian and Hypo-
lydian are fettled in trite diezeugmenon and lichanos
mefon ; which firings, in their natural iituation, in
the Dorian mode, were tuned to c and g natural ;

(49) Hanc autem methodum adhibet Ptolemseus in tonis fuis
feptem defignandis, Sec. — primum omnium facit, &c. fecundo
tonum fumit, See. App. ad Ptol. p. 3 1 3 ^ 3I4*

(50) Ibid, p. 313. lin. uit. ufque ad p. 315. lin. 20.

but,.

[ 767 ]

but, in this chapter, the author means only to fix
the numerical firing allotted for each mefe, without
regard to its pitch, which was to be regulated by
the diftances afiigned for the tones in the tenth
chapter. And by thefe difiances, and all other con-
curring circumftances, it is manifeft, that the two
firings in queftion were, in thefe modes, to be made
a femitone, more acute than their natural fituation,
as I have already obferved, in explaining the har-
monic doCtrine. How, therefore, the doCtor could
fo far wander from the true theory, which lay before
him in the text of his author’s tenth chapter, as to
fubftitute a different method, and deliver it. with
great prolixity of explanation, as the method of his
author, is what I know not how to account for,
much lefs reconcile to his accufiomed care and fide-
lity. What is ftill more extraordinary, is, that, after
finifhing the directions and explanations of his own
method, he, in the very next paragraph, cites the
very tenth chapter of Ptolemey, where the method
is given (5 1), in order to infer with his author, that
the Mixolydian tone was diftant from the Lydian a
hemitone ; the Lydian from the Phrygian, a tone,
&c. though this inference, which is true only from
Ptolemey’s method, direCtly contradicts all he had
been delivering. Could he overlook the falfenefs of
this inference, whilfi he was taking fo much pains

(51) His pofitis, inde colligitur (ut cap. 10.) toni Mixolvdii
a Lydio diftantiam limma, feu craflius loquendo hemitonium ;
hujus a Phrygio, tonum; hujus a Dorio, tonum ; Dorii ab Hypo-
lydio limma; Hypolydii ab Hypophrygio, tonum; hujufque ab
Hypodorio, itidem tonum. App. p. 315. Jin. 21.

with

[ 768 ]

with the fubjed? But not to inlift farther on the
flips of a writer, to whom the learned world Hands
fo highly indebted, I fhall take leave of him, with
this remark only, that whatever he may have feen of
the truth of thefe dodrines himfelf, his explanations
have not fucceeded in making the fubjed clear to
fucceeding writers ; thofe I have feen having either
adopted the harmonic dodrine only, or been fo con-
founded between the two, as to give a right account
of neither. This has, in particular, been the cafe
with Malcolm, who, in his i reatiie on Mufic, ex-
plains that of the antients, and has taken fome pains
to reconcile the two dodrines of the modes. 1 he
greateft part of what this writer delivers is not only
falfe, in refped to the order, pofitions, and, indeed,
almoft every other circumftance attending the modes,
but, at the fame time, fcarce intelligible ; or, if any
meaning can be put upon it, it is too foreign to the
truth of either of the dodrines, to be worth con-
fidering. I fhall content myfelf with citing apaffage
from him, where his reafoning is the clearcfl, and
where we may fee, that, after all the pains he has
taken to reconcile the tv/o dodrines, he owns himfelf
unable to make any fure deciflon upon t.ie fubjed.

“ He (Ptolemey) fays, in the beginning of that
chapter (cap. y. lib. ii.), the mutations, which aie
made by whole fyftems (which we propeily call
tones, bccaufe thefe differences confift in tenfion),
are infinite, with refped to poflibility, as founds aie;
but adually, and with refped to fenfe, they are finite.
All this feems plainly to put the difference of the
tones only in the acutcnefs or gravity of the w hole ;
elfe, how do their differences confift in tcnlion, w hicli

, lignifies

[ 769 ]

fignifies a certain tenor or degree of tune ? and how
can they be called infinite, if they depend on the
confritution of the odtave? Yet, elfewhere, he argues,
that they are no other than the fpecies of odtaves, and
as fuch, makes their number feven • and accordingly,
in all his fchemes, fets down their different modula-
tions. But, in chapter fixth, he feems more plainly
to take in both thefe differences 3 for he fays, there are
two principal differences with refpedt to the change
of the tone, one, whereby the whole fong is fung
higher or lower, the other wherein there is a change
of the melody to another fpecies than it was begun
in 3 but this, he thinks, is rather a change of the
long, or melos, than of the tone 5 as if again he
would have us think, this depended only on the
acutenefs and gravity of the whole. So obfcurely
has the bed of all the antient writers delivered him-
felf on this artic'e, that deferved to have been mod
clearly handled. But, that I may have done with
it, I fhall only fay, it mud be taken in one or other
of the fenfes mentioned, if not in both 3 for another,
I think, cannot be found (52).”

Notwithdanding the confufion in this author’s ex-
planations, and his leaving the quedion thus unde-
cided, it is his account of the modes, that feems
chiefly to have been adopted by compilers fince.
And hence we find nothing better in the Cyclopaedia
of Chambers, or the Mufical Dictionary of Grafli-
neau, than a repetition of thefe doubts and perplexi-
ties. Amongd the French writers, Brodard, in his
Ditfionaire de Mujique , throws no light upon this fub-

(52) Malcolm’s Treatife on Mufic, p. 538. lin. ult.

jedt,

6

[ 770 3

ieft, his account of the modes refpe&ing chiefly thofe
of much later times, which were diftinguilhed into
plao-al and authentic, and with which the prelcnt
queftion has very little concern. Nor have I met
with any thing fatisfa&ory from their academicians,
though fome of them appear to have taken great pains
with the fubjea. The writer amongft thefe who
feems the moll converfant with the mufic of the an-
antients, is Monfieur Burette, who, m the Memoirs
of literature, has furnilhed many pieces on the va-
rious branches of the fcience. Amongft others, there
is a differtation of his on the melopceia of the antient
mufic, which the learned academician flrould rather
have intituled a differtation on harmonic; for it con-
tains an explanation of the elements of that fcience.
This author feems little apprized of the mufical doc-
trine ; nor has he given a right account even of nc
harmonic one, having followed Wallis in his miftake
in refpedt to the method, by which Ptolemey fixed
the po fit ions of his feven modes (53)1 an^ ev^n
drawn the fame contradictory conclufion ( 54 ) •

fro) Ou’ainfton devoit renfermer dans l’efpace d’une oclave toTs

153; ^ , , Dorien devoit occuper, comme le centre, ks

les modes, dont *efU°rlen, def^"n F j’ Mixolydien fut d’une
fix autres etant difpofez de ff?o , g > inte plus

quarte plus haut que le Donen , ,11 plus\aut Fque

rHvpolidicn , PHypodorien d’une q««Fdus barque le Dorien;

bas “«A Phrygien. Differtation fur

• 'e M^paroit, qu’a compter de PHypodorien, qui eft le

mode e plus bas it y a de celui ci a 1’Hypophryg.en 1 intervals
mode le plus bas, > l’Hypolydien un autre ton; dc

d un ton ; de 1 Hypophrygien a i y\> y Phrvcien,

lHypolydien au Dorien, un demiton ; de ce dern « £6

un ton-; du Phrygien au Lydien encore un ton; ct du Lyd.cn

Mixolydien, un demiton. Ibidem. whence

C 771 ]

whence it appears, that he relied on the doctor’s ap-
pendix for this part at leaft of his explanations. In
his notes on the dialogue of Plutarch, printed alfo in
the fame memoirs, the not underftanding the mufical
doCtrine has led him into a very falfe explanation of
the paflage cited above, concerning the invention of
the Mixolydian mode. He fets out (5-5-) with ex-
cluding the only fuppofition, that could lead him to
the fenfe of his author, by denying, that the octa-
chord fyftem could havq any thing to do with this
invention; and then flies (56) to two other fuppofi-
tions, viz. that either the hendecachord or difdia-
pafon' was here meant, both which are equally wide
of the truth. The public is much indebted to this
writer, for the laborious collections he has made in
thefe notes, concerning the antient muficians ; but
his harmonic explanations are not always to be re-
lied on.

(55) Lamprocle n’eft point ici donne comme 1’auteur de Phar-
monie Mixolydienne, il en eft regarde feulement comme le re-
formateur. Mais en quoi pouvoit confifter cette reforme? C’etoit,
comme le dit Plutarque, a determiner le veritable fyfteme de cette
harmonie, ou de ce mode, quant a fa disjonCtion, ou a Parrange-
ment des divers tetrachordes, qui compofoient ce fyfteme. En le
reduifant a Petendue de Po&ave, ou de 1’oCtachorde, c’eftadiredu
double tetrachorde disjoint; le lieu de cette disjon&ion eft unique,
et par confequent n’eft point equivoque, comme on le peut voir par
la progreffion de ce fyfteme, que void, mi, fa , fol , la , ft, ut , re,
ml ; il ne s’agit done point ici du double tetrachorde disjoint.
Note 1 1 4.

(56) Mais Phendecachorde, ou le triple tetrachorde disjoint,
pouvoit etre le fyfteme, dont parle icy Plutarque — fuppofe qu’il foit
icy queftion du fyfteme complet de l’ancienne mufique, &c.
Ibidem.

jG

Vol. LI.

The

[ 77* ]

The laft writer, that I have feen, who has treated
this fubjedt, and with whofe opinion I fhall conclude
thefe Sheets, is the anonymous author of a letter to
Mr. Avilon, concerning the mufic of the antients,
pub! ilhed with the effay of the latter on mufical ex-
preffion, in 1753. This author, who profeffes but
a (lender knowlege of the theory, either of modern
or antient mufic, has, in a few pages, difcovered him -
felf to be poffeffed of more than his modefty will
permit him to lay claim to. In the matter of the
tones, however, (fuch is the fatality, that feems to
have conftantly attended this dodtrine) he does not
appear to have fucceeded better than the writers that
have gone before him. He blames Sanadon and
Cerceau, for affirming, in their obfervations on Ho-
race, carm. 5. 9. that the Dorian mode anfwered
exactly to our A-mi-la with a minor third, and the
Phrygian to our A-mi-la with a major third. Now,
that thefe French critics, though right, inafmuch as
they feem to confider the modes as different fpecies
of diapafon, are, neverthelefs, miftaken in their ap-
plication of them, does, indeed, appear from my firff
diagram, where it may be immediately feen, that
what they affert of the Dorian and Phrygian modes,
is true only of the Hypodorian and Lydian ; and had
the anonymous writer gone no farther in his cenfure
of them, I (hould readily have joined with him : but
he reje£s the mufical dodtrine entirely, and admits
only of the harmonic. “ Surely (fays he (57), fpeak-
ing of what thefe critics advance) this is a mufical
error, and a dream from the ivory gate. Two modes

(57) Pa£e 6*

with

t 773 ]

with the fame tonic note, the one neither acuter nor
graver than the other, make no part of the old
fyftem of modes.” And, agreeably to this opinion,
he had before (58) deicribed the feven modes, as
reducible to one mode, taken higher or lower ; which,
he fays, may be be called the mode of A, and mult
have had a minor third, as c natural is a minor third
to A-mi-la. Whether this be a juft account of the
nature of the modes, I muft now fubmit, having
faid already what has occurred to me, in fupport of
the contrary opinion.

To conclude, if what has been faid fhould be
thought to eftablifh any certainty concerning this
matter, I lhould hope it might tend to revive an in-
quiry into the mufic of the antients, which feems to
have fuffered an interruption from the difficulty of
arriving at a right underftanding of this material
branch of it. Such an inquiry may, perhaps, be
judged well worth purfuing, not only from the ad-
vantages, which modern mufic might derive from it,
but alfo for the fake of improving the art of poetry,
and of better underftanding and tafting the noble re-
mains we have of the antient poets j the greateft
beauties of whofe works, efpecialiy the lyric and
dramatic, are probably loft to us, for want of feeing
their connection with this fcience.

(58) Page 5.

5g 2

LXIX. An

[ 774 ]

LXIX. An Enquiry into the Meafure of the
Roman Foot ; by Matthew Raper, Efq\
F. R. S.

Read May 15, 22, g ~AHE methods that have hitherto
une 5.1/60. been t0 difcover the mea-

fure of the Roman foot, will, upon examination,
be found fo unfatisfaftory, that it is no wonder the
learned are not yet agreed in that point.

The antient foot-rules now remaining ; the repre-
fentations of the foot in fculpture ; and the meafure
of it, derived from the congius, differ fo much among
themfelves, and from each other, as to be infuffi-
cient evidences feparately : and the great difagree-
ment of the foot from the congius, with the reft,
has not hitherto been fatisfaftorily accounted for.

The foot-rules found in old ruins at Rome, are
of various lengths j and the age of none of them
being certainly known, no precife meafure can be
determined from them, otherwife than by taking a
mean from fuch as appear to be mod; perfeft. But
though this may have been the foot in ufe at fome
time or other, yet as thefe rules are probably of dif-
ferent ages, both the greateft and the lead: of them
may have anfwered to the ftandards of their times.

For though we have no account of any alteration
ever made in the ftandard of the Roman foot, yet
the wear of a ftandard meafure by ufe, and the
making new to replace the old ones, mud:, in all
probability, create a difference ; efpeciallv, as the
Romans had not thofe inducements to fo precife an

accuracy

C 775 ]

accuracy in thefe matters, as the later difcoveries in
natural philofophy (particularly the invention of the
pendulum) have introduced among the moderns.
Add to this, that the different ftate of Europe, which
has, for fome ages, been divided into many confider-
able kingdoms and fovereign hates, independent on
each other, equally civilized, and carrying on a more
conftant and regular mercantile commerce with each
other, than was known to the Romans, muff ne-
ceffarily introduce more frequent enquiries into the
weights and meafures of the different hates, and a
more careful examination of the refpedtive handards
of each, than the Romans could have any occafion
for : and ufe in thefe matters, is the parent of ac-
curacy.

We can arrive at no greater certainty from the
marbles, than from the foot-rules. Thefe, indeed,
do not differ fo widely from each other, as the rules ;
which feems to be the reafon why moh of the writers
on this fubjedt have given them the preference : but
of the four that are extant, no two agree in the fame
meafure ; nor is the age of any one of them known :
and as they were intended for reprefentations only,
and not for ufe, their accuracy may reafonably be
doubted.

Feffus, Frontinus, and Rhemnius Fannius, fay,
the fide of the quadrantal (which contained 8 congii)
was a Roman foot (i). A ftandard congius of

Vefpafian

( i ) Quadrantal vocabant antiqui quam ex Graeco v

dicunt, quod vas pedis quadrati odto et quadraginta capit fextarios.
Feftus in v. Quadrantal. Fes quadratus concavus capit amphora

trimodia

[ 776 1

Vefpafian is {till in being, and has been meafured by
fever al learned men ; but the foot derived from it
exceeds thofe on the marbles, and the greateft num-
ber of the foot-rules, fo much, that Mr. Greaves
could find no better way of accounting for fo great a
difference, than by fuppofing what Feftus and Fan-
nius fay (for he does not quote Frontinus), to be a
vulgar error (2) : whereas the name of this ftandard
fhews its figure to have been a cube (?) ; which adds
probability to their teftimony, that its fide was intended
for the meafure of the foot.

The meafures of public roads in the itineraries,
can be of little ufe in this enquiry ; for they omit
fra&ions, and we do not know whether the diftances
of the towns are reckoned from the market-places 01
from the gates $ but a difference of half a mile in
fixty, is equivalent to the tenth part of an inch in
the foot : therefore, no exadt meafure is to be ex-
pected from thence, even though the modern men-
surations of Caffini, Riccioli, and others, were more
unexceptionable than they really are.

trimodia [read, amphoram trimodiam]. Frontinus, in Expofi-
tione Formarum. Though the paflage is corrupt, there can be no
doubt of the meaning.

Pes longo fpatio latoque notetur in anglo,

Angulus ut par fit quern claudit linea triplex ;

Quattuor ex quadris medium cingatur inane.

Amphora fit cubus : quern ne violare liceret,

Sacravere Jovi, Tarpeio in monte, Quirites.

Rh. Fannius, de Pond, et Menf.

(2) See Dr. Birch’s edition of Greaves’s Works, p.7.28.

(3) Quse illi KvCvf, nos quadrantalia dicimus. A.Gellius, hi.

c. 20.

The

C in ]

The distances between the antient mile-Hones are
not liable to thefe obiedfions ; and if a fufficient num-
ber of fuch as Hand neared; to Rome were carefully
meafured, their authority would be confiderable.
But I do not find that any are now Handing within
thirty miles of that city, nor that any of thefe have
been meafured, or even any in Italy ; and provincial
meafures are not of equal authority.

There is Hill another method, whereby we may
difcover the meafure of the Roman foot ; which is,
from the remains of the antient buildings now Hand-
ing at Rome : and though many have made ufe of
fome fingle parts of them for this purpofe, yet
no one hath hitherto compared the meafures of the
principal parts of any one of them with each other,
which is the only way to difcover the meafure whereby
a building was conHrudfed.

With this view, therefore, I Hiall carefully exa-
mine the meafures of the buildings contained in that
ineflimable treafury of antient Roman architecture,
intituled, Les Edifices antiques de Rome, and pub-
lished at Paris, by Monf. Defgodetz, in the year
1682.

In order to this, it will firfi be neceflary to afcer-
tain the proportion of the Paris foot (the meafure ufed
by this author) to fome known EngliSh Handard.

The Paris foot is one fixth part of the toife in the
Chatelet; which was renewed in the year 1668 (4),
and the new Handard has continued in ufe ever Since.

(4) See De la Hire’s Differtation on the Roman Foot, in the
Memoirs of the Academy of Sciences for the year 1714 ; where he
gives an account of this renewal of the ftandard in the Chatelet.

In

C 778 ]

In the year 1742 (5), the Royal Academy of
Sciences at Paris, at the requefl of the Royal Society
of London, fent over a meafure of half the toife of
the Chateletj from which Mr. Graham determined
the proportion of the Paris foot to that of London,
to be as io6y,4.i-f to 1000. Monf. Le Monnier, of
the Royal Academy of Sciences, from the fame ori-
ginals, found their proportion as 864, to 811, or as
ioby^yi to 1000. The difference is inconfidei-
ab’e, and we may, without injuflice to Mr. Graham’s
known fkill and accuracy in thefe matters, fuppofe
their true proportion to be as iotfy, 4 to 1000.

Mr. Graham’s meafure of the London yard, to-
gether with that of half the toife of the Chatelet, aic
depofited in the archives of the Royal Society at Lon-
don, and of the Royal Academy of Sciences at Paris j
and whenever I fhall mention the London foot, with-
out fpecifying any particular ffandard of it, 1 would
be underflood to mean this meafure.

In this enquiry, we are to fcek a common mea-
fure to the feveral parts of each building, that final 1
not differ very widely from fome aflumed magnitude
of the Roman foot : and though we might take this
alfumption from any of the antient foot-rules now
remaining, yet the nearer it is taken to the truth,
the better guide it will be to us, and the more it
will facilitate our enquiry. Now, as a mean mea-
fure, derived from thefe rules, will, probably, be
nearer the truth, than either the greatefl or the leaf!
of them, fo one that fhall include fuch othei remains
of antiquity, as have hitherto been made of to difcovei

(5) See Philof. Tranf. N° 465.

the

[ 779 ]

the meafure of the Roman foot, will be fiill more
unexceptionable, as the writers on this fubjeCt are
not agreed, which of the different authorities is to be
preferred.

The reprefentations of this foot in fculpture, are
four in number ; one on the fepulchral monument of
Cofiutius, formerly in the Colotian gardens at Rome ;
another on that of Statilius, in the Belvedere j a third
on that of M. Ebutius, in the Villa Mattei (6) ; and
the fourth on a marble, without infeription, dug up
of late years in the Via Aurelia, which, being in the
pofTeffion of the Marquis Capponi, is called, by P.
Revillas, the Capponian foot.

Moft of the early writers on this fubjeCt have ex-
preffed their meafure of the Roman foot by a dia-
gram ; and Snellius (7) obferving, that the paper con-
tracted in drying, after the impreffion was taken off,
endeavoured to make a proper allowance for it. But
Greaves, finding the meafures of thefe figures to dif-
fer in different copies of the fame impreffion, took
another method ; and feems to have been the firft
that compared the original figures on the monuments
of Coffutius and Statilius with a modern ftandard.
This he did with fuch care and diligence, that his
meafures deferve a particular examination.

The London foot, which he ufed upon this occa-
fion, was taken from the iron fiandard of 3 feet in

(6) Picard and Auzout (in a paper called De Menfuris, here-
after quoted) have given the meafure of the foot on this monument
of Ebutius for the Colotian foot.

(7) See his Diflertation on the Roman Foot, in the 3d vol. of
Sagai di Diftertazioni Academiche di Cortona.

Vol. LI. 5 H the

[ ?8o ]

the Guild-hall, London (8) ; which having been
long fince loft, or deftroyed, we have nothing left
whereby to difcover its true magnitude, but the mea-
fures others have taken of it, and thofe which have
fmce been taken of fuch magnitudes as Greaves had
compared with his copy of it.

Snellius, from a meafure fent him of this iron
ftandard (9), determined the proportion of the Rhyn-
land to the London foot, as icoo to 968. The
Rhynland foot, according to Picard (1), contains
696 fuch parts as the Paris foot contains 720 :
whence the proportion of the latter to this meafure
from the iron ftandard, is as 1 065,4 to 997 nearly.
Eifenfchmid found the Rhynland foot to contain
1391,3 fach Parts as the Paras f°ot contains *44° (* 1 2 3 4) >
which gives 1065,4. to lefs than 9967, for the pro-
portion of the Paris foot to that of the iron ftandard.
Huyghens makes the Paris to the Rhynland foot as
144 to 139 (3); whence the proportion of the for-
mer to Snellius’s London foot, will be nearly as
1 06534. to 995 L But there is reafon to believe,
that Huyghens’s meafure of the Rhynland foot was
too final 1 (4).

(8) Greaves, p. 223.

(9) Kratofthenes Batavus, p. 125. 141.

( 1 ) See a paper intituled De Menfuris, in Divers Ouvrages de
Mathematique et de Phyfique, par Meflrs. de l’Academie Royale
des Sciences, Paris 1693, in folio, and afterwards printed in the
4th vol. of Ouvrages adoptez.

(2) Eifenfchmid de Pond, et Menf. vett. p. 94.

(3) Horolog. Ofcill. part iv. prop. 25.

(4) Picard, in his Voyage d’Uranibourg, p. 64. edit. Amff.
fays, “ Paflant par Holland je pris l’occalion de verifier la pro-
portion

[ 78* ]

By thefe companions it appears, that Snellius’s
meafure of the London foot, from this iron ftandard,
was at lead: 3 parts in 1000 fhorter than Graham’s
London foot.

Our countryman Norwood, in the year 1635,
meafured the diftance between London and York,
in order to determine the length of a degree on the
meridian j which he found to contain 367196 Lon-
don feet of this iron ftandard ( 5-). The French found
the meafure of a degree, in the latitude 66° 20', to
be 57438 toifes, and at the equator 56783. Hence
the meafure of a degree in 52 0 44' (the middle lati-
tude between London and York) will be found to
be 57276 toifes, or 343656 Paris feet. Thefe num-
bers give the proportion of the Paris foot to that of
the iron ftandard, as 1065,4 to 997,1 — , wanting
fomewhat lefs than 3 parts in 1000 of Graham’s
London foot.

Picard’s paper De Menfuris, quoted above, and
another on the fame fubjedt by Auzout, printed with
it, contain fome meafures, which Greaves had before
compared with his London foot. Both thefe papers
were written after the renewal of the ftandard of the
Chatelet, in 1668. The former is fo full of inac-
curacies and miftakes, that little ufe can be made of
it ; but Auzout’ s meafures appear to be accurate ;
and as he feems to have taken his Paris foot from the

portion du pied de Paris a celui du Rhin, dont l’original eft a
Leyde ; laquelle proportion me parut eftre exadlement comme
720 a 696, au lieu de 720 a 695, que j’avois fuppofee dans la me*
fure de la terre.” This latter is Huyghens’s proportion.

(5) See Norwood’s Seaman’s Pradlice.

5 h 2

toife

C 782 3

toife in the Chatelet for this purpofe, it was probably
a correct meafure of that ftandard.

Such of his meafures as anfwer to Greaves’s, are
here reduced to thoufandth parts of the London
foot, reckoning his Paris foot to contain 1065,4
parts.

Greaves.

Auzout.

Diff.

Diff. per foot.

The Statilian foot

972.

969,96

— 2,04

2,1

The braccio of Florence

1913*

1908,84

— 4,16

2,l8

The braccio of Siena

1974.

i973>2i

— 0,79

0,4

Paetus’s palm

732-

7 3 1 >35

— 0,65

0,89

All thefe differences fall the fame way, and fliew,
that Greaves’s London foot bore a lefs proportion ta
Auzout’s Paris foot, than that of 1000 to 1065,4.
The Statilian foot, and the braccio of Florence, give
the greateft differences ; one is carved in relievo, and
the other is a rod ; fo that both are fubjed to dimi-
nution, by time and ufe. The palm is engraved;
and Auzout, from the deviation of Pastus’s Greek
and Roman foot, from the common received pro-
portion of 25 to 24, fufpeded, that the latter was
lengthened by wear ; if fo, the like muft have hap-
pened to the palm. How their meafures of the
braccio of Siena come to differ fo little, I cannot ac-
count for. But we can draw no certain conclufion
from this comparifon, till we know whether any,
and what, allowance is to be made for the di-
minution or increafe of thefe magnitudes, in the
interval between Greaves’s and Auzout’s meafuring
them.

For this purpofe, I fhall compare Auzout’s mea-
fures, with thofe taken by P. Revillas, with a cor-

red

[ 783 ]

redt London foot (6), between fifty and fixty years
after. Thefe he has converted into Paris meafure,
by the proportion of 864 to 81 i; and I have re-
duced them back again, according to the fame pro-
portion.

Auzout.

Revillas.

Diff.

Diff. ptr foot.

The Statilianfoot

969,96

969,79

— 0,17

0,18

TheEbutian foot

972, 9r

972,22

— 0,69

0,71 —

Pastus’s palm

73G35

732^5

+ G3

1,78

Pastus’s foot

966,26

968,74

“b 2,48

2»57

or

967 —

or 1,75

1,81

Hence the carvings appear to have fuffered very-
little diminution in this interval; but Pastus’s mea-
fures, which are engraved, and in conftant ufe as
public ftandards, have been confiderably lengthened.
Therefore, allowing for both thefe circumstances,
we may conclude, that Greaves’s London foot wanted
2 parts in 1 000, to be to Auzout’s Paris foot, in the
proportion of 1000 to 1065,4.

Greaves’s meafure of the door-cafe of the Pantheon,
9 inches within the jambs, is 19,602 of his London
feet and decimal parts (7). Defgodetz found the
meafure of the fame on the infide 1 8 feet 4-f inches
Paris meafure, and on the outfide 1 8 feet 4-3 inches,
their difference is of a Paris inch ; the depth of
the jambs is 4 feet io£ inches Paris meafure; and

(6) Efattiflimo piede Tnglefe. See Saggi di Diflertazioni Aca-
demiche di Cortona, vol. iii. p. 113. I have been credibly in-
formed, that this London foot was given him by the late Martin
Folkes, Efq; and that it was made by SifTon, according to Graham’s
meafure.

(7) Greaves, p. 348.

5) Lon-

[ 74 ]

9 London inches are equal to 8,447 Paris inches and
decimals. Hence the meafure of this door-cafe 9 Lon-
don inches within the jambs, fliould, according to
Defgodetz, be 18,3676 Paris feet and decimals. But
19,602 is to this number, as 1065,4 to 998,3 ; and
Greaves’s London foot wanted Itq to be to Defgo-
detz’s Paris foot, in the proportion of 1000 to 1065,4.

Greaves fays, mod of the white marble hones on
the pavement of the Pantheon contained exactly 3 of
thofe Roman feet on Coffutius’s monument (8).
Their Paris meafure, according to Defgodetz, is
2 feet 81 inches, which is equal to 2885,46 London
parts. This number divided by 3, gives but 961,82
fuch parts ; whereas Greaves’s meafure of the Codu-
tian foot was 967 parts of his London foot; which
mud therefore have wanted above y parts in 1000 of
the proportion before-mentioned. But it is probable
they meafured different ranges of thefe dones.

The meafure of the Paris foot, which Greaves re-
ceived from Monf. Hardy, was taken from the old
dandard in the Chatelet (9)* and contained 1008
fuch parts as his London foot contained 1000. Thefe
numbers are in the proportion of 1065,4 to 997T7 »
therefore, if the new dandard did not differ from
this old one (and no fuch difference appears to have
been intended), Greaves’s London foot mud have
been 2,43 parts in 1000 fhorter than Grahams.

(8) Greaves, p. 21 1.

(9) See Monf. Hardy’s Letter, in Greaves’s Works, p. 44-7-
rIhe meafure he fent was only half the Paris foot; but he tells
Greaves, it was taken from the ftandard, under his own in<pe£tionv
with great care.

All

[ 7§5 ]

All thefe companions fhew Greaves’s meafure of
the Londonjfoot to have been fhorter than Graham’s,
But they are not all of equal authority. The mea-
fures of Sneilius depend upon the corredtnefs of three
feveral feet ; that is to fay, his copy of the iron ftan-
dard, the Rhynland, and the Paris foot; whereas
the reft (except Norwood’s) depend only on the
Paris foot, applied to the fame magnitudes that
Greaves himfelf had meafured. Norwood’s meafure
is rather to be wondered at, that, notwithftanding all
the difficulties he had to encounter, it ffiould come
fo near to the true magnitude of a degree, than to
be depended on for the exadt meafure of the iron
ftandard ; and is an inftance of what the diligence
and fagacity of a private and obfcure man, unaffifted
by the public purfe, or the contributions of friends,
could accomplifh ; whofe labours may, perhaps, be
forgotten, when the meafures of the French, taken
under a royal commiffion, fhall be known to the lateft
pofterity.

The three more immediate comparifons of Greaves’s
meafure with the Paris foot, are by the meafures of
Auzout, Defgodetz, and Hardy, which afford as clear
a proof as can well be expedted in this matter, that his
meafure of the iron ftandard was about 2 parts in 1000
deficient of Graham’s London foot.

Mr. Greaves found the foot on the monument of
Statilius to contain 972 fuch parts as his London foot
contained 1000 ; and that on the monument of Cof-
futius 967 ( 1 ). Thefe meafures reduced to Graham’s
foot, are 970, and 967.

(1) G/eavcs, p. 208, 209,

Auzout’s

[ 786 ]

♦ Auzout’s meafure of the foot on the monument of
M. Ebutius, is nearly equal to 973 London parts.
Revillas makes this 972L and the Capponian foot

The mean of thefe meafures of the Roman foot on
the marbles, is nearly 969 thoufandth parts of the
London foot.

Philander, in his notes on Vitruvius (2), fays, the
foot from a porphyry column, inlcribed nOA> ©•
exceeded the Coffutian foot by the ninth pait of an
inch ; therefore it contained nearly 974 London parts.
This column feems to have been a more authentic
meafure of the Roman foot, than the figures on the
monuments; fince the infcription fiiews it was in-
tended for fuch, whereas they were only reprefenta-
tions of it. And notwithftanding the inlcription was
Greek, the foot mull have been Roman ; for Philan-
der’s meafure of it exceeds the mean meafuie of thofe
on the marbles, by lefs than the fixteenth part of a
London inch, and is lefs than fome of the antient
foot-rules, hereafter mentioned; whereas it wants
above the third part of an inch to be equal to the
Greek foot. It might, perhaps, be ufed by fome
Greek mafon at Rome, to adjull his workmens rules
by; for when the Romans began to be expenfive in
their buildings, they had moll of their maions from
Greece. And though this column is not now to be
found, and the accuracy of Philander’s meafure of it
may be doubted, it is Hill a proof, that, at one time
or other, the meafure of the Roman foot was feniibly
greater than that on the monument of Cofiutius.

(2) P. 117- of the Lyons edit. 1552.

Lucas

[ 787 ]

Lucas Psetus compared five antient foot-rules with
the marbles; he feems not to have been a perfon of
great accuracy; for though in one place he allows
there was fome fmall difference between the Stati-
lian foot and that on the monument of Coffutius (3),
yet he every-where elfe fpeaks of them as equal, and
has given but one figure for the meafure of both.
His comparifons feem to have been made only with
the latter, the meafure of which he had before fet
up in the Capitol, as the true Roman foot (4). Three
of thefe rules, which, he fays, were exactly equal to
each other, were fhorter than the Coffutian foot by
one feventh part of a Coffutian inch ; they mull then
have been nearly py 3! London parts. Of the other
two, one appears to have been 9)8, and the other
974, equal to that from Philander’s column. He
decides in favour of the three fhortefl, to which
perhaps he was induced, partly by their agreement
with each other, and partly by his opinion, that the
Roman foot had been continually increafing ; whence
it mu ft follow, that the fhortefl meafure of it was
the mod antient.

(3) Cum quo fane convenit modico difcrimine hie Statilianus.
Paetus de Menf. et Pond. lib. i.

(4) Greaves, p. 209. fays, the Roman foot engraved by Paetus
in the Capitol, agreed exa&ly with that on the monument of Cof-
futius. Paetus therefore feems at that time to have acquiefced
in the opinion of Portius, which, he fays, was generally received.
(Leonardus Portius Vicentinus, vir fane dodfus, primus omnium
noftrae tetatis qui de hac re feripferit, menfuram Colotiani. pedis
pro vera tradidit.— Quern juniores quoque fecuti funt.) But he
changed his opinion when he wrote his book, which was after he
had fet up the meafures in the Capitol.

Vol. LI. 5 *

Greaves

[ 788 ]

Greaves fays, the Coflutian foot exa&ly agreed
with fome very antient and perfect Roman feet in
brafsj and from his companion of two that differed
from it (which feem to be the greateft and leaft he
had met with), one of them appears to contain nearly
972! London parts, and the other 962-} (5).

P. Revillas has given the meafures of three foot-
rules of an uncommon length ; one of which con-
tains 972 London parts, another 976, and the third
5)83 (6).

There are many more of thefe rules in being, that
we have no account of; lor moft of the writers on
this fubjedt, preferring the authority of the marbles,
have been negligent in their accounts of the foot-
rules ; therefore I think a mean meafure from thefe
above-mentioned of no great authority, efpecially as
fome of them have been produced only on account
of their difference from the more common meafure
of the reft.

If a cubic Roman foot contained a quadrantal of
wine, the cube of half a foot muft have contained a
congius, which was the eighth part of the quadran-
tal. Paetus, Villalpandus, and Auzout meafured the
ftandard congius of Vefpafian with water ; and have

(5) Greaves, p. 222. But, p. 227. he fays, there is not one
of ten meafures of the Roman foot (befides thofe on the monu-
ments), that arrive to the proportion of that deduced by Villalpan-
dus from the congius, by 27 parts in 200c ; whereas the greater
of the two here mentioned contained 9741 parts of his London
foot, and he makes the foot from the congius of Villalpandus, hut
986 fuch parts; their difference is but 23 two thoufandth parts of
the latter.

(6) Saggi di DifL Academ. di Cortona, vol. iii.

given

[ 7«9 ]

given the weight of its contents. The two firft differ
from each other by almoft 5! modern Roman ounces,
which is nearly the one-and-twentieth part of the
whole weight, though they both meafured up to the
fame part of the neck. The weight of water given
by Psetus, is deficient of the mean weight of Auzouf s
meafures by 3 Troy ounces; and that given by Vil-
lalpandus exceeds the fame by a ; therefore they
muff both have ufed bad ballances.

Auzout meafured this vefiel twice, with the water
of Trevi. His greater weight of the water is 63024
Paris grains, his leffer 62760 (7).

Picard found a cubic Paris foot of fpring water to
weigh 641326 Paris grains (8); and that foot con-
taining 2o8p,6p cubic London inches, Auzoufs
greater weight will give 205,36 fuch inches for the
Solid content of the congius, his leffer 204!.

According to Picard’s experiment, a cubic London
inch of fpring water fhould weigh but 251! Troy
grains ; whereas, according to Snellius, it fhould
weigh above 254 (p).

Our countryman Wybard made many experiments
to difcover the weight of water (1), from which the
weight of a cubic inch of rain water fhould be 253
Troy grains. His experiments feem to have been
made with great attention, and his inch muff have
been that of the iron ftandard, which I have already

(7) See the paper De Menfuris, above quoted, p. 366. 377%

of the folio edit, where Picard gives thefe weights as Auzout s,
without any farther account of them. , _ ?

(8) Ibidem.

(9) Snellius, in Eratofthene Batavo, p. 155.

(1) See Wybard’s Tadtometria, from p. 269 to p. 287.

5 1 2 .--{hewn

[ 79° ]

(hewn to be lefs than Graham s ; therefore, I think
a cubic inch of Graham’s meafure of the water of
Trevi, cannot weigh lefs than 253 Troy grains. This
will reduce xAuzout’s two meafures of the congius to
204,35 and 203,4 p cubic London inches; which
give 5)81,7 and 5)80,3 for the meafure of the Roman
foot.

Greaves meafured the congius with millet feed (2),
and comparing it with our mealures of capacity,
found it to contain y\ pints wine meafure, and
6^ pints corn meafure. When he wrote, the wine
gallon was univerfally allowed to contain 231 cubic
inches (3); and the dimenfions of the bufhel were
published yearly, by the Lord Mayor of London,
to be 15) inches in diameter, and y\ in depth (4).
But Greaves’s inches were according to the iron
ftandard in the Guildhall, and were 2 parts in 1000
Shorter than Graham’s. Therefore reducing thefe
meafures in that proportion, the wine gallon will be
found to contain 2 2p,62 cubic London inches, and
the corn gallon 264,22. . Hence by the wine mea-
fure, the congius contained 204,5 cubic London
inches, and by the corn meafure 2 03 >7 > which give
5)8 1, p and 5)80,6 for the meafure of the Roman

foot.

Thefe meafures agree fo well with thofe of Au-
zout, that I think a mean between them mull be
very near the truth, and that we may reckon the

(2) Greaves, note f. p. 303. _

(3) See Wybard’s Ta&ometria, p. 264. Oughtred s Circles
©f Proportion, p. 57. who quotes Gunter and Briggs for the fame
©pinion.

(4.) Wybard’s Ta&ometria, p. 282.

foot*

[ 7S1 ]

foot from the congius to contain about yo. on-
don parts.

Greaves took likewife another rr 'afure of i ' us
congius, by the cube of his Cofiutian foot, which
he found to contain 7 congii, and about an half, of
millet (5). Now, the quadrantal fhould contain 8>
hence the fide of the quadrantal to this congius will
contain 988 parts of the iron ftandard: for 988 is to
o6y (Greaves’s meafure of the Coffutian foot) in the
fubtriplicate proportion of 8 to 7!* But this is a greater
meafure than even that of Villalpandus, and was pro-
bably owing to an erroneous cube of the Coffutian,
foot ; for the joiners at Rome might be as bad work-
men as the fcalemakers and Greaves fays, he could
not get a ballance there, fit to examine the congius
by weight (6).

Monf. Aftruc, in his Natural Hiftory of Langue-
doc, fays, he had caufed the diftance between the
ninth and tenth mile-fiones on the road from Nifmes
to Beaucaire to be meafured, and that it was found
to be 7 54 Paris toifes. They were both fet up by
Tiberius, and the road lies in a ftrait line between
them. This meafure gives a Roman foot of 964
London parts. He does not fay he took this meafure
himfelf (7), nor has he given any account how it
was taken. Perhaps by a provincial meafure, and

(5) Greaves, p. 225.

(6) Ibid, note f.

(7) Memoires pour l’Hiftoire Naturelle de Languedoc, p. 225.
His expreffion is, “ J’ai fait mefurer la diftance de l’un a l’autre,
et elle s’eft trouvee de 754 toifes de Paris.” Where he fpeaks of
the Marquis Maffbei, he fays, “ II amefure;” but, in the fame
paragraph, fpeaking of himfelf, he again fays, « J’ai fait mefurer.”

C 792 ]

afterwards reduced to Paris toifes ; or by a wheel,
which is liable to great errors : therefore we cannot
allow much authority to it, unlefs we were better
affured of its accuracy. He quotes the Marquis Maf-
fei for a mcafure of 756 toifes between two other
mile-ftones on the fame road ; but obferves, that they
were fet up by different emperors, Auguftus and Ti-
berius, and that the road formerly made an elbow
between them, whole pofition is now not certainly
known. Therefore this meafure, which gives a
foot of y66i London parts, is likevvife of fmall au-
thority.

All that can be determined from fuch uncertain
and difcordant data, as I have here collected, is a
meafure that fhall probably be neither the greateft
nor the lead: magnitude of the Roman foot. And
for this, 1 fhall take a mean from all the meafures
above recited, which is nearly p68 thoufandth parts
of the London foot.

Before I enter upon the examination of the antient
buildings, it may be proper to fay fomething con-
cerning the nature of the evidence to be expected from
them.

All buildings are planned and executed by fome
meafure of the country where they are built. At
Rome this meafure was the foot, which was divided
by the workmen into 4 palms, and each palm into
4 digits (8).

(8) Vitruvius, lib. iii. c. r. Frontinus de Agrorum Qualit.
Both thefe authors are technical writers, and give this as the di-
vilion ufed by workmen; and the antient foot-rules are fo divided.

They

3

[ 793 ]

If the Roman buildings were correCtly executed,
and we had the true dim'enfions of their feveral parts
in any known meafure, fome divifors confifting of
Roman feet, and parts of thofe feet, applied to thefe
meafures, muft, in the fame building, give the faille
quotient to all ; and this quotient will be the meafure
of the foot, by which that building was conftruCted,
in parts of the known meafure. Therefore, where
a range of fimple divifors, applied to the principal
parts of any building, give as nearly the fame quo-
tient as can be expected from the common inaccu-
racies of workmanlhip, we may reafonably conclude,
that thefe divifors were the architects numbers ; and
the foot derived from them, that by which the build-
ing was conftruCted.

As an architect cannot be fuppofed to be limited to
a few digits in the extent of the front, or of the depth
of large buildings, it is probable fuch meafures con-
lifted of whole feet. Thefe, and the diameters of cir-
cular buildings, I call prime meafures.

In all large prime meafures, the preference is to
be given to a round number for the divifor; as it is
more probable a building fhould be defigned for i oc
feet in front, than for pp or ioi : and becaufe the
paffus was 5 feet, I reckon any multiple of 5 a round
number.

The diameters of columns are of lefs authority
than any other horizontal meafures ; not only on ac-
count of the difficulty of meafuring them correCtly,

They both mention the duodecimal divifion, which Teems to have
been ufed by the vulgar.; for the Romans divided every integer into.
12 uncice.

but

[ 79+ ]

but becaufe errors of workmanfhip, to which they
are more liable than fquare members, moie fenfioly
affe£t the magnitude of the foot in fmall meafures,

than in large ones. . . r . r

Uprights, of any confiderable height, are of lets

authority than horizontal meafures, fiom the dif-
ficulty of taking them correctly ; and being defigned
by modules, few of them anfwer well to the toot
meafure. But here we muft except fuch fhafts of
columns as are of one block of marble; which feem
to be as good authority as any part of a building . foi
the neceffity of making them all exactly of the fame
length, muft produce accuracy ; and the doing this
was no difficult piece of workmanfhip. Being like-
wife commonly (if not always) wrought at the
quarry, to fave expence in the carriage, they were
probably befpoke to fome Ample meafure; and we
lhall find all fuch fhafts anfwer to fome number of

whole palms. . c

In the following enquiry, I fuppofe that Delgo-

detz’s Paris foot contained 1065,4. fuch parts, as
our London foot contains 1000 : fince it appears,
from the comparifon of his meafure of the door-cafe
of the Pantheon with Greaves’s, that if Greaves’s
London foot was not above 2 parts in 1000 fhorter
than Graham’s, Defgodetz’s Paris foot was but
3 of the London foot fhorter than that in the
archives of the Royal Scociety. This difference (if
fuch there was) does not amount to the 277th part
of an inch ; which is much nearer than we can expert
to find the meafure of the Roman foot, from all the
remains of antiquity now in being,

The

[ 795 ]

The temple of Fortuna virilis.

When this temple was built, is not known j but
It is commonly thought, from the poornefs of the
materials, and the flyle of the architecture, to be
one of the moft antient buildings now remaining in
Rome. The great fimplicity of its parts, and their
near agreement with each other, afford fo clear an
evidence of the meafure by which it was conftruCted,
that I have chofen to begin with it, as an introduction
to the reft.

It has four Ionic columns in front, and feven in
depth.

The depth, taken between the centers of the an-
gular columns, is 54, feet 8f inches Paris meafure,
equal to 58264,06 thoufandth parts of the London
foot; which contain juft 60 Roman feet of 971 -j-
fuch parts each.

The diftance between the centers of the columns
in this range, is 9 feet if inches, equal to 9710,6
London parts ; containing 10 Roman feet of the fame
meafure with the former.

The extent of the front, taken between the centers
of the angular columns, is 28 feet 83- inches, =.
3°SS^32S y which contain 31-j Roman feet of

970 -|- London parts each.

The diftance between the centers of the angular
columns, and thofe on each fide the entrance, is
exaCtly equal to the diftance between the centers of
the columns on the fides; being 10 Roman feet of

97 1 + parts each.

There remain therefore nf Roman feet, for the
diftance between the centers of the columns on each

Vo l, LI. 5 K fide

[ 796 ]

fide the entrance. This meafures io feet 5— inches
(p), equal to 11134,5?; which, divided by n\y
gives for the Roman foot.

This difagreement between the meafures in the
front, cannot be reconciled by any probable divifors ;
therefore it muft be owing to an error in workman-
fhip. And if the diftance between the centers of the
middle columns were but a little more than | of a
London inch greater, both that, and the whole extent
of the front, wrould anfwer to the fame meafure of
the foot with the fides. Now, as the middle inter-
columniation was intended to be greater than the reft,
the workman might be lefs exadt in laying out the
front, than the fides, where they were all to be equal ;
for the front intercolumniations next the angles being
kept equal to thofe on the fides, the fymmetry of the
building would be preferved, and the whole error fall
on the middle intercolumniation, where it could not
be difcovered.

Or if, on the other hand, we fuppofe the meafure
of the extent in front to have been corredt, and the
error to have lain in the fides, the workman muft ftill
have made the intercolumniations on the fides equal
to each other, and thofe in the front next the angles,
equal to them : and, in this cafe, 5)70 would be the
true meafure of the foot, inftead of 971.

Therefore, I think, it cannot be doubted, that one
or the other of them was the meafure by which this
building was conftrudted.

(9) Defgodetz has figured this io feet 5 A inches; which will
be found to be a miftake, by comparing the corrcfpondent num-
bers, and by his meafure of this interval in modules.

The

t 797 )

The temple of Vefta, at Rome.

This building is remarkable for the ftyle of its archi-
tecture, and the elegance of its workmanfhip. The
pointed abacus fhews the architecture to be Greek ;
which is a ftrong prefumption in favour of its anti-
quity, as it is the only example of the kind now re-
maining at Rome (i).

None of the diameters will anfwer to the fame
mealure of the foot with the other parts, by probable
divifors. This was likely enough to be the cafe, if
the circles of the plan were defcribed by a cord,
whofe ftretching might increafe their diameters be-
yond the intended meafures. But the reft of the
meafures agree pretty nearly with each other, by as
limple divifors as ,can be expeCted in fo fmall a
building.

At the door-cafe, the arch of the wall is difcon-
tinued, and the groundfil is ftrait. The width be-
tween the jambs is p feet i-| inches, equal to 573 6,6
which, divided by 10, gives a foot of <737 London
parts.

From the wall to the centers of the columns, is
8 feet 8-g- inches, = ^244, 6; which, divided by p|,
gives a foot of 573,1 parts.

From the wall to the extremity of the bafement,
is 10 feet 6 inches, — 11 186,7 ; which, divided by
a 1 7, gives p727*

(1) That is to fay, it is probably older than the Pantheon; for,
according to Pliny, in his thirty-fixth book, there feems to have
been no marble temple in Rome above fixty years older than that
building. And his hiftory of marble is confirmed by the faying of
Auguftus, “ That he found Rome brick, and left it marble.’*
Sueton. in Aug. c. 28.

5 K 2

From

[ 798 ]

From the top of the furbafe within, to the pave-
ment of the cell, is 7 feet p£ inches, = 827 1,65 >
which, divided by 8{, gives 5)73,1.

From the top of the furbafe without, to the outer
pavement, is p feet i{- inches, = p/f 1,4; which,
divided by 10, gives p7f, 1.

The fhafts of the columns are 27 feet 5 inches,
= 2p2op,8 ; which, divided by 30, gives p73,7*

The columns, with their bafes and capitals, are
32 feet o inch, = 34op2,8; which, divided by 35s
gives a foot of P74 London parts.

The mean meafure of the foot from this building,
is P73,6; which agrees nearly with the foot of Phi-
lander’s porphyry column above-mentioned, and with
one derived from Greaves’s meafure of the monument
of Ceftius, whofe fide within the city (as he fays in
p. 151 of his works) is completely 78 feet Englifh;
which, reduced to Graham’s meafure, is 77,84, and
contains 80 Roman feet of P73 London parts each.

The temple of Veda, at Tivoli.

The meafures of the parts of this building difagree
fo much with each other, by any probable divifors,
that I fhall only mention the width of the door-way
between the jambs, which is 7 feet 3! inches, =
77po,7, and anfwers to 8 Roman feet of p73>8 parts
each*

The Pantheon.

This is a circular building, with a portico before
the entrance; which, having been added after the
body of the work was finifhed (a), has induced many

(2) See Defgodetz, p. 3. & p. 14.

to

[ 799 ]

to think the temple was more antient, and that
Agrippa only adorned it with marble, and added the
portico. But the infcription on the freze, “ M.
** Agrippa L. F.. Cof. tertium fecit,” feems to refer
to the whole. And Pliny, enumerating the mod:
magnificent buildings in Rome, fays, “ Pantheon
ct Jovi ultori ab Agrippa fa&um ; cum Theatrum
“ ante texerit Romas Valerius Odienfis archite&us,
ft ludis Libonis (3).’' If the latter part of this paflage
alludes to the dome of the Pantheon (as it feems to
do), it will imply, that Agrippa built it. In another
place (4), Pliny calls this building Agrippa’s Pan-
theurm Now, temples of this form were ufually
peripteres ; that is to fay, encompafled with co-
lumns (.5), as the two temples of Veda 3 but fuch a
colonnade to this building (fuppofing the entablature,
to reach up to the top of the wall) could not con fid:
of fewer than twenty-fix columns of 9 London feet
in diameter; which, with their entablature, mud:
have cod much more than the whole building, as it
now dands. Therefore, it feems as if no columns
were at fil'd intended on the outfide, and that the
portico was an after-thought.

This temple is faid to have been burnt in that
great conflagration, which happened in the reign of
Titus (6); and again by lightning, in the thirteenth
vear of Trajan (7), and to have been redored. by

(3-) Fliny, lib. xxxvi. c. 15.

(4) Ibid. c. 5.

(5) Vitruvius, lib. iv. c. 7.

(6) Xiphilin. in Tito. Suetonius likewife m*ntions this hre;
but does not fay what buildings were burnt by it. Titus, c. S.

(7) Eufebius in.Chronico,

Adrian.

[ ^00 ]

Adrian (8). But it does/not feem to have been to-
tally deflroyed either time ; for the infcription of Se-
verus fays, it was “ vetuftate corruptum;” which
could hardly be true, if it was entirely rebuilt by
Adrian, who began his reign but feventy-fix years be-
fore Severus; but is very applicable to a building that
had flood above 200 years, and been twice damaged
by fire. Neither does ic feem poffible, that a building
of this fize and folidity, without any timber in it,
except the roofing of the portico, fhould be totally
conlumed by the fire of the neighbouring buildings.
Therefore, we may fuppofe the meafures of the prin-
cipal parts of it to be according to the foot of the
Auguftan age.

If the execution of this noble building had been
anfwerable to the beauty of the defign ; the multi-
plicity of its parts, and the accuracy with which
Defgodetz has mealured them, would have afforded
ample materials for the difcovery of the foot^ by
which it was conftrudted : but the dimenlions of fuch
parts of it as fhould be equal to each other, differ lo
widely, that fcarce any but the prime meafures are
to be depended on.

Thefe were, probably, the diameter of the circle
palling through the centers of the columns within ;
for on this, the diameter of the cupola depended j
and the diameter of the whole building, from out to
out.

Defgodetz has given twelve meafures of the dia-
meter within the fhafts of the columns. The mean
from them all, is 133 feet ij inches Paris meafure:

(8) Spartianus in Adriano.

to

[ ^0I 3

to this, add the mean diameter of the columns, 3 feet
4I inches, their fum, 13 6 feet 7-f inches, equal to
14 5533,6 London parts, is the diameter of the circle
paffing through the centers of the columns ; which,
divided by 150 (as round a number as can be defired),
gives 5)70,2 fuch parts for the mealure of the Roman
foot.

The mean depth of the four long chapels, be-
tween the fhafts of the columns and the wall, is
9 feet 1 inch, = 9764,3 ; which, divided by 10,
gives a foot of 976,4 London parts ; but by io|, one
of 952,6 ; which is certainly too fmall. And if this
was an arbitrary meafure, we cannot admit the frac-
tion of a palm in it. Therefore, we may fuppofe
thefe chapels were intended to be 10 Roman feet
deep in the clear between the columns and the wall.

The mean diameter of the columns, 3 feet
4! inches, = 3622,3d London parts, divided by 3-f,
gives a foot of 966 parts. The fhafts of thefe co-
lumns meafure 27 feet i| inches, whofe eighth
part (reckoning the fhaft at 16 modules) is 3 feet
4! inches ; which is fomewhat lefs than the mean
of their diameters. Yet even this meafure (which is
equal to 3610,5 London parts) does not want half a
Roman digit of 34 feet of 970,2 parts each ; which
the architect might fafely negleft, and allow 3-I feet
for thefe diameters, in his general plan.

Now, if to twice the depth of thefe chapels, or
20 Roman feet, we add twice the femidiameter of
the columns, or 3-| fuch feet; and to their fum, the
diameter of the circle pafhng through the centers of
the columns, 150 feet; we fhall have 1 73-J Romaji

6

[ 802 ]

feet for the diameter from wall to wall of the op-
polite chapels.

Defgodetz has given four meafures of this dia-
meter,&whofe mean, 1 58 feet 2-f inches, is equal to
168570 London parts, which, divided by i73i>
give 970,2*—, for the meafure of the Roman foot;
agreeing with that found from the diameter of the
circle palling through the centers of the columns.

Or if, inftead of taking a mean of the four dia-
meters from wall to wall, we add twice the mean
depth of thefe chapels, and twice the mean femi-
diameter of the columns, to the mean diameter of
the circle palling through their centers, we lhall have
158 feet 4 inches for the diameter from wall to wall,
equal to 168688 London parts; which, divided by
175.3 give 970,9, for the meafure of the foot.

But if this diameter from wall to wall was a prime
meafure, as well as that of the circle palling thiough
the centers of the columns, the depth of thefe chapels
mull have been a refiduary meafure, and might be
more or lefs than 10 Roman feet. And if we divide
the diameter laft mentioned by 174 (which being
compofed of 150, and twice 12, may here be rec-
koned a round number), it will give a foot of 969a.
London parts. But if, inllead of twice the mean
depth of thefe chapels, we take twice the greatell
depth, 1 8 feet 6 inches, for part of this diameter,
the fame divifor will give a foot of 97°^ fuc^ pa*ts.

The meafure of the diameter from out to out can-
not be fo well determined as either of the foi mci ;
for Defgodetz has given but one meafure of the outer
wall, which is 5 feet 4a. inches ; to this we mull add
i foot io-j inches, for the mean depth of the niches

m

«

[ 8o3 ]

in the long chapels; and twice their fum, 14 feet
j-f inches, added to 1 58 feet inches, the infide
diameter between the walls of thefe chapels, will
give 172 feet 84- inches for the diameter from out
to out. This is equal to 1 835)88,6 London parts;
which anfwer to ipo Roman feet, of ^68,4 fuch
parts each. But this diameter being got by the ad-
dition of many fmall parts, one of which is a fingle
meafure, is of fmall authority. Though if the outer
wall is 5 feet 4!' inches thick in brick-work, and
the backs of the niches in the long chapels' are in-
crufted with marble (as I fuppofe they are), a proper
allowance for the incrudation will make this diameter
anfwer to a foot of ^70 London parts.

The principal parts of the circular range within,
are too unequal to anfwer to any regular divifion into
compartments; and the two larged meafures in it
fufficiently evince, how little ufe is to be made of the
red; : for the width of the grand chapel oppodte the
entrance, and the width of the entrance between the
piladers in the range, will not anfwer to the fame
meafure of the foot, by any probable divifors.

But the inequality of the faces of the piladers, that
terminate the folids in this range, affords the cleared;
proof, that no certain meafure of the foot is to be ob-
tained from the leffer parts of this building : for two
of them, at the extremities of the fame folid, differ
in breadth by a Paris inch and three quarters. One
of the two on each fide the grand chapel exceeds the
other in breadth, by a Paris inch and a quarter ; and
it exceeds the lead in the circular range, by no lefs
than qi fuch inches, though the diameter of the co-
lumn before it is lefs than that of fome in the range.
Vol. LI. 5 L The

[ 804 ]

The diameter of the circular light at top is 27 feet
5 inches, equal to 29209,7 ; which, divided by 30,
gives 5>73t for the Roman foot. Whether Defgodetz
took more meafures than one of this diameter, does
not appear, nor how he took it. It is probable, that
30 Roman feet was the meafure here intended, being
a round number, and one fifth of the diameter be-
tween the centers of the columns : but the making
this light a tiue circle, precifely anfwering to. a
given meafure, was a difficult piece of workmanfhip.
Therefore, this meafure is of lmal 1 authority.

The fquare compartments on the pavement mea-
fure 9 feet of inch, or 9647,79 London parts;
which, divided by 10, give a foot of 964,8 parts.
But Defgodetz obferves (9), that this is not the ori-
ginal pavement : and this meafure of the foot anfwers
to the age of S. Severus, as I (hall fliew hereafter.

This pavement being confiderably raifed above the
old one, no meafures of uprights taken from it are
of any authority.

The height of the attic, above the cornice it Rands
upon, iss 27 feet 2 1 inches, equal to 29010 ; which,
divided by 30, gives a foot of 967 parts. But the
walls of this building being brick, this meafure may
have been diminifhed by their fettling, as the whole
error occafioned by it might be made to fall on this
part, rather than on the order below.

The length of the fhafts of the columns in the cir*-
cular range, is 27 feet if inches, == 28884,18;
which anfwers to 29^ feet, of 970,9 parts each.

(9) Defgodetz, p. 41.

The

[ 8°5 ]

The width of the door-cafe, between the jambs,
has been fuppofed, by Picard, De la Hire, Eifenfch-
mid, and others, to have been a meafure of whole
feet ; for this reafon, becaufe they thought it an ar-
bitrary one, and therefore not likely to contain a
fraction (i). But in this, I think, they were mis-
taken ; for it appears to have been determined by the
width of the paflage within, of which it takes up
juft three fourths. The proportion is too Simple,
and too exactly executed, to be accidental 3 and it is
highly improbable, that the width of this palTage,
which is a principal part of the plan of the inlide,
Should be determined by that of the door-cafe.
The width of the paflage, is 24 feet 5|| inches, ==
26098,6 3 that of the door-way, next the paflage, is
1 8 feet 4! inches, = ip6i o 3 next the portico, 1 8 feet
4-j inches, = 15)561,93 none of which will give a
meafure of the foot, anfwering to the reft of the
building, by whole divifors. The width of the door-
way next the portico (which has been fuppofed to be
juft 20 Roman feet), divided by 20, gives 5)78. But
the diameters of the temple (taking either the greateft
or the leaft, inftead of a mean), will not anfwer to a
foot of this meafure, by probable divifors.

The principal meafures in the portico are, its ex-
tent in front and depth, and the Shafts of the columns.

(1) Mr. Greaves fays, this door-cafe is one entire marble ftone.
See p. 348. and p. 494* And Ficoroni (a late writer), in his
Veftigia di Roma antica, p. 132. fpeaking of this door-cafe, fays,
<* Efiendo amendue i lati, col di fopra, e il di fotto di un folo pezzo
di marmo.” But Defgodetz, p. 18. fays, that each fide of the ar-
chitrave confifts of two ftones, and the top, of one 3 and corredts
Serlio, for faying the whole was of one piece.

5L 2 The

[ 8o6 ]

The extent in front, taken between the centers of
the angular columns, is 5)8 feet qf inches, equal to
10475)7,6; which contain 108 Roman feet of 5)70,3
parts each. Its depth on the right-hand lide of the
entrance (2), from the center of the angular column
to the center of the pilafter, is 41 feet Jj inches, =
44136,4, and contains 45-7 feet of 970 -3- parts. The
fhafts of the columns, which are each of one fingle
hone, meafure 36 feet inches (3), equal to
35>°53,6 ; which anfwer to 40-p Roman feet of
5)70,3 London parts.

I can find no meafures in this building of equal
authority with the diameters, the fhafts of the co-
lumns in the circular range, and thefe meafures in
the portico. All of which give the meafure of the
Roman foot greater than 970 fuch parts as the Lon-
don foot contains 1 000.

In the refl of the buildings, where the meafures
do not require a particular explanation, I fhall firffc
give Defgodetz’s meafures, with their reductions to
thoufandth parts of the London foot, and then let
down the divifors and quotients with two hooks be-
tween them ; the divifor on the left-hand, exprefiing

(2) By fome expreffions of Defgodetz, his plans feem to be in-
verted, as gravings commonly are. I fpeak according to the plan,
fuppofing the reader to view it in front.

(3) Defgodetz, p. 19. has figured the fhafts of the pilafters in
the portico 36 feet 73- inches, and in modules 16 mod. 81 parts;
which is fomewhat too great for his foot meafure, his module being
27 Paris inches. But p. 16. he has figured the fhafts of thefe co-
lumns 16 mod. 8| parts, which is 36 feet 7^ inches. And that
this is no miftake, appears from his meafures of the capitals of
each.

a num-

[ &07 ]

a number of Roman feet ; and the quotient on the
right, their magnitude in parts of the London foot.

The temple of Peace.

The length on one fide within the
walls, including the pronaus or
porch, is 269 feet 8-f inches, —

28734.7,26 —

The width of the nave 77 feet 5-f-
inches, = 82524,1 (twice)

The width of the fide-building 48 feet

o inch, = 51139,2 (thrice)

The length of the firft divifion of the
fide 71 feet 5 inches, — 76087,3
The length of the lecond divifion
71 feet 8 inches, = 76353,87
The length of the third 70 feet 3-

inches, == 74888,75

The width of two of the paflages in
the crofs walls, is 22 feet 4 inches,

— 23793,9

The width of the exedra in the middle

divifion of the fide 53 feet 11

inches, = 57442,82 .

Its depth is equal to the width of the
paffages in the crofs walls.

The two middle entrances through
the porch, 15 feet 3 inches, =

16247,35

The fide entrances 14 feet 4.1 inches,

— i53i5,i3 --

5

296) . . . (970,8 —
85) . . . (970,9 —

52f) • . • (969,5 —
78 {)... (969,3 —
7 8f) • • • (969,6 —

77?) « • • (969,4

24?) • • • (97 r52

59?) • • • (969y5

i6j) . . . (970 —

15I) • • • (S72?4 —
Tffc

[ 808 ]

The entrance into the porch on the
right-hand 14 feet 4 inches, —

* 527°»74 ’ " r “ “

The (haft of the column (or one itone)

49 feet 3 inches, = 52470,9 *

The diameter of the column 5 feet
8^ inches, = 6058,47 '

The height of the order 71 feet
o-i- inch, = 75687»79

15I) •;*(969>5
54) • • • (97 1 5 7 "

6^)...(969»4 —
78) . . • (97°> 4

A mean from thefe twenty-one meafuies gives a

Roman foot of 970,3 Parts' But *e meafllres 111
this building feem to be very incorrectly executed.

The temples of Bacchus, and of Faunus.

I {hall not particularly recite the meafures of thefe
buildings, becaufe they feem to be the works of a
much later age than any of the reft. By trie different
workmanfhip of the fliafts of the columns m tire
temple of Bacchus (4), it fce'ns to have been com-
piled out of the ruins of other buildings. In the
temple of Faunus, moft of the columns are of gra-
nge, but fome of them of white marble ; the crofs
wall was evidently defigned to fupport a flat loot,
the outer wall being too weak to bear a cupola (5) ;
and the windows (which I take to be as old as
reft of the building) are in the Gothic ftyle : a l
which are marks of a late age. Therefore both
thefe temples feem to be more modern than they are
commonly thought to be. The temple of Bacchus

(4) See Defgodetz, p. 68.

(5) Ibid- P* 79*

anfwcrs

[ 8og ]

anfwers to a foot of 5*68 parts, that of Faunus to one
lefs than 5)67.

The amphitheatre of Vefpafian.

The plan of this building is elliptical ; and the area
in the middle being allotted to the exhibition of the
fhews, feems to be the part on which the magnitude
of the whole depended. Therefore one of its axes
mud; be the prime meafure.

The greater axis meafures 263 feet 11 inches, =
281176,8 London parts; the leffer 165 feet 1 inch,
= 1 75875,7. Thefe numbers are fo nearly in the
proportion of 8 to 5, that there is little reafon to doubt
their being intended for it.

The only two whole numbers in this proportion
that will anfwer our purpofe are 288 and 180, by
which the greater axis will give 5)76,3 London parts
for the meafure of the foot; the leffer, 5*77,1.

Either the diftance from the inner to the outer wall,
or that from the inner wall to the extremity of the
upper ftep, was probably a prime meafure too. The
former is 155 feet 53- inches, = 165610,5; which,
divided by 170, gives 574,2. The latter is 158 feet
oTV inch, ~ 168340,6; which, divided by 172,
gives 5)78,7.

But the axes will admit of other divifors, which
are in my opinion as probable at lead:, as thofe above-
mentioned. For if we fuppofe the greater axis to have
been the prime meafure from which the leffer was
determined in the proportion of 5 to 8, and affume
25)0 Roman feet for it (which is a more probable
meafure than 288), the leffer axis muff then be
18 1 ~ fuch feet. And the meafure of the foot by

the

[ 8io ]

the greater axis will be y6p,6 parts ; by the letter

Tht diftance from the inner to the outer wall will
not anfwer to this meafure of the foot by any whole
divifor. And that from the inner wall to the extre-
mity of the upper flep, divided by 174, gives but
067- But this difagreement will not appear extra-
ordinary, when we confider that thefe diftances are
not Angle meafures, but the fums of nine or ten
fmaller ones (6), and may therefore be liable to an

error of fome inches.

The leffer parts are fo incorredly executed, that
no ufe can be made of them. And the heights of the
four orders, and of their parts, are lo irregular as not
eafily to be accounted for.

The amphitheatre at Verona.

The principal meafures in this building anfwer to
the Greek foot j which is not the fubjedt of the pre-
fent inquiry.

The arch of Titus.

This edifice is fo ruined, that we have not the mea-
fure of the extent of its front.

The depth of the folid is 14 feet

7 inches, = 1 553 7’ 1 —

The width of the entrance, 16 feet

4 inches, = I7401i5 " — *

The fhafts of the columns, 16 feet

2 inches, = 17223,97 —

16). . . (97 1

18) . . • (966,7

i7|)...(97°>9

(6) See the fedtion, PI. 3.

The

t *>'■ ]

r.*:z sviiii Ot Z-.n-.ySl J. 1 •'{ <: id I ■ l'i-.

The arch of Conftantine, n<; ,

The meafures of this elegant delign.are fo incor-
rectly executed, that I can make no ufe of them.
The fronts of the two outermoft folids differ by a
Paris inch and one third > the fide entrances by if;
the diftances of the columns from the pilafters (a
meafure of little more than, 1 8 inches) differ an inch

: folid at one end, ex-

aer lefs than n\ Paris

j: gfliuloj add io

andy~j and the depth of th<
ceeck. that at the other end by
inches, .oaoft -

3-

Jn-'

sT^he temple of Antonine and Fauftina.

foefgodetz has giyen the meafure of no part of this
budding in feet and inches, but the diameters of the
columns j which he fays do not differ from each other;
as in many of the reft.

C r

;inm

The diameter of the columns is 4 feet

6-jViffehes* 4846,09 — « 5) . . . (969,2

The extent of the portico taken be-

t^veeh. the centers of the angular : • «- -

columns, 25 mod. %6-g parts, = •' aft ; - -

61935^7 — 64), . . (967,7

The fhafts of the columns, 1 5 mod.

28 -parts,. z±r$86oji'£- — 40) . (965,2

Thefe fhafts were probably intended for 16 mo-
dules, and their meafure is more to be relied on than
that of the diameters, both on account of its fize,
and becaufe the correct execution of it was not only
more ealy, but more neceffary. Therefore, though
thefe meafures are too few, and too unequal to deter-
mine the exaCl magnitude of the foot ufed in the con-

Vol. LI.

5 M

ftruCtion

¥

[ 8X2 ]

ttru&ion of this building, yet it feems to have been^
lefs than any we have hitherto met with.

The arch of Septimius Severus.

This building deferves our particular attention,,
both on account of the corre&nels of the workman—
fhip, and becaufe it exhibits a different meafure of
the Roman foot from any of the preceding. It is all
of white marble. The ftones are laid without mor-
tar, and fattened together with cramps. And the
fhafts of the colums are each of one ftone.

The whole extent in front, is 7 1 feet

5i inches, = 76161,3

The depth at one end, is 21 feet

inches, = 23150,3 •

The depth at the other end, 21 feet

8£ inches, = 23157,6

The width of the middle entrance,
20 feet 10 inches, ~ 22195,8
The width of the fide entrances,

9 feet 2 inches, = 9766,17

From the middle entrance to the
extremity of the outer folid, on
one fide, is 25 feet 3I inches,

= 26967,9 — *

The like on the other fide, 2 5 feet

inches, — 26997,5

The diftance between the fhafts of the
outermoft columns, is 60 feet
inches, = 64619,5 • — (7)

79)... (964, 1

24) , . • (96416
24) • • • (96459

23)... (965
io|) . . . (964,5.

28) . . (963,1

28) . . . (964,2

67) . . . (964,5

The

(7) This and the two following meafures are inferted only to
(hew the probability, that the diameters of the columns were de-

figned

r 8*3 .3

The diftance between their centers,
63 feet 4-j inches, = 67504,9
The diftance including their fhafts,
66 feet o£ inch, = 70390,4 —
The diameter of the columns, 2 feet
S~ inches, = 2885,46 — -

1

7°) * * * (964>4

73).;. (964, 3
3)... (961, 8

The uprights will not anfwer to any one meafure
of the foot by whole divifors ; nor will they agree
with each other by broken ones, fo nearly as the ho-
rizontal meafures do, which may partly be owing to
the difficulty of taking them corredly.

The fhafts of the columns meafure

21 feet 8i inches, — 23105,9
The pedeftals, 12 feet 37V inches,
= i3* * oS8, 14

The whole order, 33 feet 4^ inches,

= 35535.53

The attic, 15 feet 5-J inches, ==

1 6454.5 1

The blocking, 1 foot 9J inches, =:

! 92 3,64 — - ■

The whole height, 62 feet iof inches,
— 67001,8 ■ ■ —

24).. . (962,7

,3t) • • • (969.5

37) .. . (960,4
1 7)., '.(967, 9
2). . . (961,8
697).. •• (964,1 —

I have produced thefe uprights, rather as an in-
llance how little fuch meafures are to be depended
on, even in buildings corredly executed, than as of
any authority for the meafure of the foot. For they
cannot be reconciled to a common meafure without

figned to he three Roman feet, and not as of any authority in the

determination of the meafure of the foot.

5 M 2 fradions

[ 8*4 ]

fractions of the digit in the divil'ors, by which means
any mealure of the foot might be derived from any

building. [ , .

A mean from the feven firft horizontal meafures

gives a Roman foot of 5)64,3 parts. A mean from

the uprights one of 964,4. •'

But the depth of the folid, and the widths of the
entrances are mod to be depended on,, and thefe give
a foot of 964I London parts j which will be found
to be the greatefl meafure this building will anfwer
to by probable divifors.

For though the extent of the front, or the width
of the middle entrance, mult probably have been the
prime meafure in a building of this kindj yet no
part feems more likely to confift of fome number at
whole feet (or at lead whole palms) than the depth
of the folid j fince there appears no reafon why the
arehitea Ihou-ld ufe odd digits in the meafure of it.
Now if we fuppofe the extent of the front to have
been 78-? Roman feet, they will contain 9 70 parts
each ; but to make the depth agree with this mea-
fure, it mull have been 23| fuch feet, which does
not feem probable, for the reafon above-mentioned.
The middle entrance muff then have been 22^ 111-
ftead of 23 whole feet, and the extent on each fide
2741, indead of 28. And there wdl not be one
whole meafure in the plan of this building, w ic
is improbable. Neither do thefe broken meafures
ferve for the fubdivifion of the fides better, or even

fo well as the whole ones.

The drafts of the columns are fo nearly 1 6 modules,
that they feem to have been defigned for that pro-
portion > and xj of a Paris inch added to the dia-
* meters

[ 8i5 1

meters would make them fo. But this is not fuffi-
eient to make thofe diameters anfwer to 3 feet of
5)64! parts, of which they want almoft fo of a Paris
inch. This may be partly an error in the workman-
ship, and partly in Defgodetz’s meafure ; but if this
quantity were added to them, they would not only
anfwer to the fame foot with the reft of the building,
but all the parts in which their meafure is included*
would agree better with the depth of the folid, and
the widths of the entrances.

The height of the blocking was probably intended
for 2 Roman feet, though it anfwers to no greater
meafure of that foot than the diameters of the co-
lumns do. But meafures of 2, 3, and 4 feet, fel-
dom agree with the larger ones in any of the build-
ings ; for a fmall error, either in the workmanlhipi
or in the meafuring, makes a very fenfible difference
in the length of the foot derived from fuch intervals.
And this blocking does not want the 77 part of a
London inch, of 2 feet of 96 f parts each.

The bankers arch, and the portico of Severus, are
contemporary buildings with this, and feem to agree
with it in the meafure of the foot. The former is a
very fmall building, and its parts will not anfwer to
any one common meafure by divifors of whole digits-.
However, the depth of the folid (which, as I have
before obferved, is moft likely to be a whole mea-
fure) taken at three different parts, is 6 feet 4 inches,
which, answer to 7 Roman feet of 963, p3 London
parts.

There are but few meafures in the portico of Se-
verus. Thofe moft to be depended on are, the whole
extent in front, and the ftiafts of the columns, which

are

[ 8r6 ]

are each of one block. The former meafures y6 Feet
iit7^ inches, == 60708,3 — , which contain 63 Ro-
man feet of 964,6 parts each. The latter meafures
26 feet 11-5- inches, = 28699,22, which contain
2 9! fuch feet of 964,7 parts. The whole column,
with the bafe and capital, meafures 32 feet 6~ inches,
= 34669,9 London parts, which contain 36 Roman
feet of 963 parts each.

It appears by the infcription on the architrave of
the portico of the Pantheon (8), that Severus repaired
that temple j and Defgodetz obfcrves, that the pave-
ment is not fo old as the building. That it was laid
by Severus is probable, from the corredtnefs of its
meafures, which is a remarkable charadteriftic of the
workmanfhip of that age. The fquare compartments
on this pavement anfwer to 10 Roman feet, of
964,78 parts, agreeing with a mean from the depth
of the folid of this arch, and the widths of the en-
trances, which are the moft unexceptionable mea-
fures in it. The breadth of the ftrait bands between
thefe compartments, is equal to the meafure Defgo-
detz has given of the diameters of the columns of this
arch, and anfwers to 3 feeet of 961,8 parts. But
thefe bands might be purpofely made fomewhat fhort
of the full meafure, to leave room for one of the
fame breadth with the reft between the outermoft
compartments and the circular range-} for notwith-
ftanding this, the workmen found themfelves obliged
to diminifh both the outermoft compartment, and
the band beyond it.

(8) Imp. Csef. Septimius Severus et Imp. Caef. M. Aurelius

Antoninus Pantheum vetuftate corruptum cum omni cultu

retfituerunt.

The

6

[ 8*7 J

The concurring teftimonies of thefe contemporary
works, though not of fufficient authority to eftablifh
any meafure of the foot by themfelves, are yet very
iirong evidence in favour of the meafure above de-
rived from this arch. And we fhall find a farther
confirmation of it in Diocletian’s baths.

The baths of Diocletian.

The whole length of this building is
439 feet 3 inches, = 4 67977
The length of the great hall, 1 80 feet

inches, = 192497 +

The breadth at one end, 74 feet 31-

inches, = 79179,9 ■

Its breadth at the other end, 74 feet

Si inches, = 79327,9 .

The diftance between the middle fo-
lids on the fide, 49 feet 8| inches,

= 52937+ *

The depth of the recefs out of the
great hall between thefe folids, is
33 feet 6i inches, = 35705,7
The diftance between one of thefe
folids and the neareft angular folid,

32 feet ii|- inches, = 35124,9
The diftance between the other of

them and the other angular folid,

33 feet 1 ^ inch, = 35276,57
Entrance at one end of the hall,

36 feet 2| inches, = 38546,8
Entrance at the other end, 36 feet
*4 inch, = 38465,4 — (twice)

485) . r. (964,8
200) . , . (962,5
82) . . . (965,6
82) . . . (967

55) -» • • (962,5
37) ■ • • (965

36 ^ ... .(962,3

367) . . . (966,4

40) . . >(963,7

4°) • . . (961,6

P adage

[ Si8 ]

Pafiage From the circular veftibule,
30 feet 9! inches, == 32783,2

(twice) -

Side entrance into the veftibule, 20

feet 9! inches, = 22166,2

A meafure from 4 feet 6 inches to

rr

34) • • • (9s4

23)...(963»7 1

* ; ^ -****•
. JWV -v-.* -

4 feet 6| inches, repeated 1 2 times,
the mean from all of them is 4 feet

6Jft inehes, =4818,03 5) • f

A meafure from 5 feet 5' inches to

5 feet 5 1 inches, repeated 1 1 times,

the mean from all is 5 feet 577
inches, = 5787,05 — 6) •

A meafure from 2 feet 8-| inches to * ...
2 feet 8£ inches, repeated 4 times,
the mean from all is 2 feet 8/-

inches, =2892,86 3).*?

A multiple of 6 feet on the wall,
where this meafure of '3 feet is
thrice repeated, is 43 feet 5 j inches,

■ — 46267,2 * 4-8) • •

t—

, . : ' T

- (963?9

The diameter of the circular veftibule is too prin-
cipal a part to be negleaed. It anfwers to 65 Ro-
man feet of 969,1 parts, which the other meafures
in this building will not come up to by probable di-
vifors. It anfwers likewife to 657 feet of 965,4 Parts »
but an odd palm in fo large a meafure is not pro-
bable. Therefore it feems to have been incorrealy
executed, and perhaps this circle was defcribed by a
cord.

The

(963>6

[ 8I9 3

The fhafts of the columns, each of
one block, meafure 35 feet iiy-

inches, = 38302,6 39?) • • •

The whole column is 43 feet inches,

= 46359,7 48)... (965, 3

Thefe are the principal meafures in this building,
and a mean taken from all of them, except the dia-
meter of the veftibule, gives a foot of 96 4, 1 London
parts.

But the three fmall meafures, of y, 6, and 3 Ro-
man feet (the firft of which is the paffus) are alone
fufficient to difcover the meafure of the foot by which
this building wa? conftruCted. For, being fo often
repeated with fo little variation, they muft afford a
mean very near the truth, if their divifors be rightly
affumed 5 and that thefe are fo, can hardly be doubted.
For, were the two largefF to be encreafed but by a
fingle digit, they would give different meaiures of
the foot from each other ; and that from the pafiusf
fo encreafed, would fall fhort of 952 London parts;
which is lefs than the leaf! of the antient foot-rules.
On the other hand, were they diminished by the
fame quantity, they would not agree together fa
nearly in the meafure of the foot as they now do,
nor give fuch a meafure of it as the reft of the build-
ing will anfwer to by probable divifors. Befides, I
have here reckoned only fuch of thefe meafures as
Defgodetz has figured on his plan ; whereas they are
much oftener repeated, and that not in the diameters
of columns, or the members of an order, but in
tyeaks, projections, and thickneffes of walls, where
a digit or two more or lefs could make no vifible
Vol, LI. 5 N difference.

n

[ 820 ]

difference, provided the correfpondent parts were
made to anfwer to each other : and it is highly im-
probable that fuch odd meafures as the paffus want-
ing a digit, 6 feet wanting the fame, and 3 feet
wanting half a digit, fhould be fo often repeated in
fo large a building, and in places that do not feem
to require any fuch precife exadtnefs. Therefore thefe
meafures muff have been whole feet, and the divifors
are rightly affumed.

Their mean is 5)64,1 London parts, which exactly
agrees with that found above from all the meafures
taken together.

The other remains of antiquity contained in this
work are fuch fragments as can be be of little ule in
the prefent enquiry.

CONCLUSION.

It appears from the meafures of thefe buildings,
that the Roman foot before the reign of Titus ex-
ceeded 970 parts in 1000 of the London foot, and
in the reigns of Severus and Diocletian fell fhort of

9<>v

Whether this difference pr'oceded from any al-
reration in the ftandard, or from a falfe meafure of
it being got into common ufe, either before the reign
of Titus or after, is uncertain.

We have no account of any alteration made by
law in the Roman ftandards after the Plebifcitum
Silianum, quoted by Feftus (9); but as great a dif-
ference as this might arife from their having been loft
or deftroyed.

(9) Cnder the words Publica pondera,

4

They

>

C 82* ]

They were kept in the Capitol (i), and Rigaltius,
from a pafifage in Hyginus, obferves that the ftandard
of the foot was depoiited in the temple of Juno Mo*
neta (2). Now the Capitol was burnt no lefs than three
times; fir ft in the civil war of Sylla (3); then again
when Sabinus was befieged in it by the troops of Vi-
tellius (4) ; and the third time in that dreadful con-
flagration which happened in the reign of Titus (y).
Whether the ftandards were deftroyed in the firft of
thefe fires is uncertain ; but they could hardly efcape
the fury and confufion of the fecond, when, accord-
ing to Pliny, the temple of Juno Moneta feems to
have been burnt to the ground (6). And, if we
may credit Xiphilin (whole account of the third is in
fome meafure confirmed by Spartian), not only the
temple of Jupiter Capitolinus, but thofe adjoining to
it, were burnt down in the laft (7).

Vefpafian

(1) This appears from the infcription on Vefpafian’s congius,
and from R. Fannius. And Jul. Capitolinus in Maximinis, men-
tions the amphora Capitolina.

(2) Hyginus de Limit, conftituend. near the end, diftinguifhes
the Roman foot by the name of Pes Monetalis. That this temple
was in the Capitol, appears from Livy, lib. vii. c. 28. Cicero
de Divin. lib. i. and Pliny, lib. xxxiv. cap. 7. Suidas (v. Movnr*)
tells us the mint was kept here.

(3) Taciti Hift. lib. iii. This fire is likewife mentioned by
Plutarch and Appian.

(4) Tacitus, ibid.

(5) Xiphilin in Tito. Sueton. in Domit. c. 5.

(6) Pliny, lib. xxxiv. c. 7. fays, “ ./Etas noftra vidit in Ca-
pitolio, priufquam id noviflime conflagravit, a Vitellianis incenfum,
in cella Junonis canem ex nere, See.” And if the donatives were
deftroyed, it is not likely the ftandards fhould be faved in a feene
of fuch confufion.

(7) Toy ts \"iu)V rH A lot rk KrtT/raAiK, r ay avvvduv dvri,

HccTiKaveiV' Xiphilin in Tito. Spartian, enumerating the public

5 N 2 buildings

[ 822 ]

Vefpaftan rebuilt the Capitol after the fecond con-
flagration, and reftored the antient records from
copies of them that were got abroad (8), and pro-
bably the ftandards at the lame time. The congius
was reftored by weight, according to the Plebilci-
tum Silianum, as the inscription on it teftifies. The
quadrantal was too cumberfome a veffel for common
ufe, to which the congius (like our gallon) was well
adapted * fo that I do not fee what other purpofe it
could ferve, but to adjuft the congius to its capacity,
and the foot to its fide : but here we fee the congius
adj ufted by weight, and it is not very likely that a
new quadrantal fhould be made for no other end but
to adjuft the foot by, when fo many copies of the
old ftandard were extant.

Therefore it is not improbable, that the ftandard
of the foot was at this time reftored, without any
regard to its relation to the quadrantal.

But as to the difference between the foot derived
from the congius, and that found from other autho-
rities, I muft farther obferve, that the correct adjuft-
ment of weights to meafures, is a very difficult mat-
ter, even in this age, and in this kingdom, where
workmanfhip is arrived at a high pitch of accuracy*
And what errors rude workmanfhip is liable to, fuf-
ficiently appears from the weights Paetus and Villal-
pandus have given of the congius. Therefore I fee
no reafon to rejedt the teftimonies of thofe authors.

buildings reftored by Adrian, mentions moft of thofe that Xiphihn
fays were burnt in this fire. JDomitian rebuilt the Capitol. Suet,
in Domit. c. 5.

(8) Sueton. in Vefpaf. c. 8.

wh$

[ 823 ]

who fay that the cubic foot contained a quadrantal
of wine ; and as little to believe that thefe two
ftandards were ever truly adjufted to each other.

But had the original ftandard of the Roman foot
been truly adjufted to the quadrantal, and continued
invariable from the time of its firft eftablifhment, yet
a falfe meafure of it might at one time or other have
got into common ufe at Rome, as well as a falfe
meafure of the French foot did at Paris; where in
the year 1668, the mafon’s foot was found to exceed
the foot of the Chatelet by of a Paris inch (p),
which is above of a London inch : and the unac-
countable negligence which appears in the Roman
coinage, gives fufficient ground to fufpeCt they were
not more accurate in their meafures.

LXX. A Defcription of a metalline "Ther-
mometer ; by Keane Fitzgerald, FJ/y;
jF. R . S. Communicated by the Right Hon .
George Earl of Macclesfield, P ref dent of
the Royal Society .

Read May 22, "TT js univerfally allowed, that all bodies,
I whether folid or fluid, are expanded
and contracted by heat and cold • and, as far as ex-
periments of this kind have yet reached, it appears,
that fcarce any two bodies of different natures, or
even of the fame ; are expanded, or contracted equally
by the fame degrees.

(9) Picard, in the paper De Menfuris, quoted above.

The

[ 824 ]

The advantages that may be derived from being
able, by proper inftruments, to afcertain the degrees
of natural and artificial beat and cold, with refpett
to philofophical inquiries; and alfo to feveral uleful,
and common purpofes in life; have induced many
ingenious perfons to apply their thoughts that way ;
and endeavour to form fome certain ftandard, or
gage, by which this may be obtained. The three
principal bodies that have been made ufe of for this
purpofe ; are air, alcohol, and mercury. _

Mr. Boyle, the great promoter of experimental
philofophy, made a thermometer on the principle of
air, which, to a certain degree of heat or cold, an-
fwered very minutely. Alcohol, or fpirit of wine,
has been more generally ufed ; but has been found
to lofe, in time, much of its expanding quality ; and
alio to be frozen by an intenfe degree of cold.. Mer-
cury, as not deemed fubjeft to thefe inconvemencies,
has therefore been allowed the mod proper for the

^ The learned Dr. Halley has obferved, . that mer-
cury expands very fenfibly at fir ft, attaining very
nearly the fame height, fome time before thewater
boils, in which it is placed; that it does on the
ftrongeft boiling : whereas fpirit of wine expands
gradually, as the heat increafes; but flower at hilt,
and falter after it is well warm ; and, at a certain
degree of heat, which wants much of boiling water,
being almoft tolerable to the touch, it boils vehe-
mently ; emitting bubbles, which, coming into t le
neck of the thermometer, lift the incumbent fpirit

to the top : from whence he concludes, that the
r cxpaniion

F/iilos. Transyol.U. TAB . .Will p. 825.

.z.i

[ 825 ]

expanfion of fluids graduated by equal parts, is not
a fuflicient flandard of heat and cold.

Mr. Fahrenheit has flnce improved the mercurial
thermometer to a great degree, and brought it to as
much perfection as, perhaps, it will bear. Fie has
remarked, that when the barometer thews a greater
degree of preflure of the atmofphere ; the fame liquor
will receive eight, or nine degrees of heat, more than
when the barometer is at the lowed:. But whether
this proceeds entirely from the liquor’s receiving a
greater degree of heat, by the preflure of the atmo-
fphere, may be a matter of fome doubt; as it feerns,
by comparing the mercurial, with other thermometers;
to be affeCted, in fome meafure, by the preflure of
the atmofphere, in all degrees of heat and cold.

The making of metalline thermometers has been
hinted at by many; particularly by Mr. Smeaton, in
his curious obfervations on the expanfion of metals,
who recommends zink, or fpelter, as mod capable
of expanfion, and fitted: for the purpofe. I have en-
deavoured to make one on this principle, which I
take the liberty of laying before this Society, with a
defeription of its conftru&ion, and an account of the
few obfervations I have been as yet able to make on
it. [Vide Tab. XVIII.]

It is compofcd of four metal bars, which aCt by a
combination of levers, and pullies. The upper end
of the bar A, which is 2 feet long, is oppofed by a
flat piece of metal x, fere wed fad: to a piece of deal
board ; y, y, y} y, and its lower end refts on a
fmall hemifphere, placed on the fhorter arm of the
lever B, which is fixed to the board y.

By

[ 826 ]

By the expanfion of the bar A, the fhorter aim
of the lever B is prefled down : and as the fpace
defcribed by each of the points of a lever is as
the diftance from the fulcrum ; fo the longer arm
of the lever B, which is 27 as long as the other ;
is railed proportionably ; and the fecond bar C,
2 feet 2 inches long, the lower end of which
is placed to the point of the lever B, by a final 1 pin,
round which it is moveable j and the upper end, in
like manner, to the Ihorter arm of the iecond lever
D 3 is raifed accordingly ; and thereby the longer
arm of the lever D, which is as long as the other,
is proportionably prefled down; to which is added
the expanflon of the bar C, increafed, in like man-
ner, by the lever D. , . . ,

The third bar E, 2 feet 4 inches long, is placed

to the point of the longer arm of the lever D, and
the fhorter arm of the third lever F, which it prefles
down accordingly ; and the longer arm of this lever,
whiGh is four times as long as the other, is thereby
proportionably raifed ; to which is alfo added the ex-
panflon of the third bar E, increafed by the lever F

There is an arch-head d9 fixed to the point of the
longer arm of the lever F, to which the fourth bar
G 2 feet long, is fixed by two chains, which raile
and lower it, as that arm rifes or falls ; and, at the
diftance of 2 feet 6 inches, there is a pulley H,
a inches diameter. There are two cords fixed to
this pulley, furrounding it different ways, one lead-
ing upwards, the other downwards, which pa s
through the bar G, and are fixed to two fprmgs b b
which keep them equally tight; and the bar clofe to

C 827 ]

the pulley H, which is turned different ways, as the
bar G is moved upwards or downwards.

There is a pulley p fixed on the other fide of the
bar G, oppolite the arch-head of the lever F, on
which the bar rolls ; and which, by the help of a
flender fpring, keeps it clofe to the arch-head ; to-
wards the upper end, there is another pulley y, on
which it alfo moves.

The expanfion of the bar G, from the place where
it is fixed to the arch-head d , to the place where it is
fixed by the firings to the pulley H, is to be added to
the expanfion of the other three bars, increafed by the
feveral levers.

There are two fmall pullies h and /, the pulley h
one inch diameter, and the pulley i a quarter of an
inch diameter, whofe axis paffes through that of
the pulley b, like the hands of a clock j and on thefe
are placed, in like manner, two indexes k and /,
which move round the dial I, that is 1 2 inches dia-
meter. Thefe pullies are lurrounded by cords, which
alfo furround, and are faflened to fprings within the
pulley H. The index /, which may be called the
minute-hand, is moved 4, times round for once the
index k is moved round ; the index / ranges at its
extreme point 48 times as much as the bar G riles
or falls ; and the index £12 times.

As the powers of thefe levers are all reverfed, with
refpedt to the preffure by the expanfion of the bars;
there are two counterbalance fprings e and /’ placed
under the longer arms of the levers B and D, which
help to raife the bars eafily ; and there is another fpring
g, adting on a fmall roller, placed on the top of the

.V ol. LI. y O bar

[ 828 ]

bar G, which returns all the bars on their con-
tra&ion.

On the dial-plate I, there are three circles defcribed.
The inward circle is divided into 240°, according to
Fahrenheit’s fcale. The middle circle is divided into
360°, which is intended to mark the expanfion of
different metals. The outward circle is divided into
2080 parts, to which the longer index / points, which
marks 18 divifions for each degree of the inward circle ;
and 1 2 for each degree of the middle circle, pointed to
by the index k.

The quarter divifions of the dial are marked I, II,
III, II1I, to fhew, by the index k3 how often the
index / has gone round.

There is a fcrew-hole towards the point, in the
index k, to fix a fmall pencil in ; which is moved by
the index on a circle of wood, or ivory, and maiks.
the higheft and lowed; degrees it has pointed to, for
any time; which laves the continual examination le-
quifite to form obfervations of this kind; and the
mark of the pencil is eaiily rubbed out, when any
new obfervation is intended.

The fil'd bar A of this indrument may readily be
taken out, and replaced ; or any other bar of equal*
length and thicknefs applied ; by which means, the
indrument may be ufed as a pyrometer, to mealure
the expanfion of any bar 1 feet long,, with great
exaftnefs, to the 73,840th part of an inch per foot ;
and, as a thermometer, it marks the alterations in
the temperature of the air, much more fenfibly than
any other indrument for the purpofe; the lange of
the minute index / being 74 inches, by the common
degrees of heat and cold of this climate.

if

[ ]

If the greatete expanteon, from freezing to boiling
water, of the metal bars to be made ule of in an
internment of this kind, is certainly known ; it may
be made to mark any minute degree intended. But
to anfwer a calculation of this kind the levers, and
pullies, mute be made with the greatete exadtnefs;
which I could not prevail on the workman that made
mine to be fo careful of as I could wifh. It is eafy,
however, to come to a certain knowlege of the ex-
panfion, mechanically. I took a thick book, and
preteing the leaves between my finger and thumb
gently 5 meafured off an inch exadtly, with a pair of
compaffes, from the 1 ft page, which made 568 pages.
I cut off feveral flips from different leaves, each of
which I placed between two bits of watch-fpring,
which were marked, in order to place them in the
fame pofition exadtly, on each trial. On examining
thefe with the internment, I found but few of an
exadt thicknefs ; but that, on a medium, each leaf
raifed the minute index 1 30 divisions. So that the
number of pages, each leaf of which is the 284th
part of an inch, multiplied by the number of divi-
lions it raifes the index ; teiews, that each divifion
marks the 73,840th part of an inch expanfion per
foot of the bar A, which is 2 feet long.

This bar is made of fpelter, which is of fo brittle
a nature, as makes it difficult to file one of that
length without breaking. If it is not well cate, it
will be extremely hollow j as was the cafe of a bar
I made ufe of, which did not expand near as much,
nor as uniformly, as another of the fame metal, and
contracted much more readily -y which I could not
well account for, until it broke by accident ; when

y O 2 it

[ 830 ]

it appeared full of large cavities on the infide, though
the outfide feemed as fair as any other. Some of
thefe cavities were above an inch long, and the fur-
rounding metal, after filing, not above the thickneis
of a card. I would therefore recommend the weigh-
ing bars of this metal, in order to obferve the dif-
ference of expanfion.

The other bars of this inftrument, as the founder
informs me, are made of 1 8 parts fpelter, and 2 of
copper. I fhould imagine, that there is a greater
proportion of copper than he owns, from the ap-
pearance of the metal, and the difproportion in its
expanfion, to what I fuppofe 2 parts in 20 might
occafion.

Since this inftrument has been made, I found, on
looking over the 1 oth volume of Martin’s Abridgment
of the Philofophical Tranfa&ions ; that Dr. Mortimer
had, in 1735, given the Royal Society a defcription
and drawing of an inftrument he invented for the
purpofe j and that Mr. Johnfon had alio given a
drawing of another, invented by Mr. Fothringham.
Although thefe are of a very different conftrudion,
yet, as they were formed on the fame principles, I
ought, in juftice to thefe gentlemen, to mention
them.

I have made what obfervations I could on this in-
ftrument, fince the Ihort time it is made ; by com-
paring it with a Fahrenheit’s, and a fpirit thermo-
meter } and find, that it keeps at a medium between
both ; not riling at firft fo quick as the mercury, and
fomewhat quicker than the fpirit. Qn placing them
together in the fun, when its heat became intenfe,
it rofe at laft fafter than the mercury, and not fo faff

as

[ 83i ]

as the fpirit ; and continued to rife for iome time after
the others became ftationary.

I electrified the bars of the inflrument, to fee if
the electrical fire could produce any degree of heat
fufficient to expand them ; which, on the firft trial,
it feemed to do, by the minute index rifing 6 divi-
fions in a fhort time. But as I had fome reafon to
imagine; that this appearance proceeded rather from
an increafe of heat, occafioned by two gentlemen
being in the room with me, when I made the expe-
riment ; I repeated it alone the next day, leaving the
door open at the time, and could not perceive the
minute index to rife above one divifion ; which I
attribute rather to the warmth that my being in the
room had occafioned.

I tried the expanfion of a few metal bars, from
artificial freezing, with pounded ice, and water that
it diffolved into ; upon which was poured half an
ounce of fpirit of tartar, in which Fahrenheit’s ther-
mometer defcended to within one degree only of the
freezing point: to boiling water, in which it rofe
to 2ii°, though the water did but fcarce boil, for
want of a fufficient number of lamps. The baro-
meter flood at 30 inches, and the natural heat of the
weather at 6o° of Fahrenheit.

Divifion?,

* A bar of fpelter 2 feet long, marked by the
minute index — — ■ — — — —

Spelter 1 8 parts, and copper 2 parts, accord-
ing to the founder’s account — — —

Brafs — — — — — — — —

}'J7°

}n5°

1120

* This was the bar, found, on breaking, to be hollow.

Iron

C 832 ]

Divisions.

Iron — — — — — — — — 7S5

Steel — — — — — — — —

Note. Each divilion marks the 73,840th part of
an inch expanlion per foot.

I find that thefe come fomewhat near Mr. Smea-
ton’s table. They are far from being as complete
as I wifh ; but hope to be able to give a more ac-
curate account hereafter ; as it certainly requires the
natural cold to be added to the artificial, in order
to get at the laft degree of the contraction of metals,
which can be come at in this climate.

If an inftrument of this kind fhould be deemed
worthy the attention of the curious, there is no doubt,
but it may be carried to a much greater degree of per-
fection than this, which is but a rude beginning. The
friction is little or none, as the fpring at the top of the
fourth bar, keeps the feveral levers and bars in the fame
pofition on their axes, whether riling or falling. It
may be made much more eafily, and at a lefs expence,
by making ufe of counterballance weights, inftead of
fprings ; and by a cord palling over a pulley placed
on the top of the fourth bar, with a weight fixed to
it, which returns the bars, on their contraction.

I have one making in this manner. The firft bar of
which is 3 feet long, and by a Aider, which is fixed
by a fcrew, it will meafure the expan fion of any bar,
within that length. The powers of the levers are
all'o greater; and the minute hand goes 12 times
round, for once the other goes round; by which it
marks the 300,000 part of an inch expanlion per
foot, and ranges a 16 inches, by the common degrees
of heat and cold in this climate.

4

Mercury

MWV .»—• ■ 4*0- - *

I. *-— ■ ■ -

im vr v.'-\ ■' i-w a .wv.^s

Fbilos. Trans. VoLZl. TAB.X7X.

Ftpru/s ofZiftr . /'

h j \

^V^vWHfVv','Si

A Bird fnypofrd la It /'red l/ctn/ern a Turkey and a P/ua/unt.

.ZJfyndf

C 833 ]

Mercury cannot be ufeful in trying any degrees of
heat above what makes it boil : and it appears by Dr.
Hinfell's account of the experiments lately made at
Peterfbourg, that it may be frozen by extreme cold ;
which makes it unfit for afcertaining the extreme de-
grees of either.

An inftrument of this kind might be made by the
help of a tin calling, to come between the bars and
the wood, to receive a bar of iron or fteel, heated to
any degree within that of its melting ; without any
detriment to it. And any kind of metal bar will cer-
tainly bear the moft extreme degree of cold, and pro-
bably contract proportionably. I fhould imagine it
might alfo be made very ufeful in trying minutely the
expanfion of different kinds of metals, fit for making
compound pendulums \ and the exadtnefs of the pendu-
lum, when made, might likewife be tried, by artificial
freezing, or in hard frofl, and by boiling it in water.

LXXI. An Account of a Bird fuppofed to be
bred between a Turkey and Pheafant ; by
Mr . George Edwards, F. R. S.

To the Rev. Dr. Birch, Secretary to the Royal Society ..

SIR,

Read May 22, TJp Aving in my hands a bird, that, I
I760' rl believe, may be a curious and en-
tertaining fubjedt to the Royal Society, I prefume, by
your favour, to lay it before them [Vide Tab. XIX.],.
with its defeription, and what other account of it I

could

[ 834 ]

could procure. I received it from the very curious
and worthy Henry Seymer, Efq; of Handford, near
Blandford, Dorfetfhire, with his letter, dated April p,

1760: wherein he fays, “ I have taken the fil'd

« fafe opportunity of fending the two birds. The
“ large one [the fubjedt lying before the Society], I
“ verily believe, is an accidental crols, as we fporti-
“ men term it, between a pheafant and turkey.
tc You are to be told, that, when the bird was juft
“ killed, the fkin round the eyes was of a pale red-
« lead colour, and the eyes like a turkey’s. As I live
« near the wood where they were found, I took
« great pains to get another of them, but was never
« fo lucky as to find one. There were three at firft,
« all of which, I believe, are now deftroyed. You
“ are heartily welcome to it j but I beg the favour of a
« painting of it by your own hand ; this I fhould
« efteem in the higheft degree. I am fenfible it re-
t£ quires a nice hand to copy the feathers of the back
« and tail ; but your judgment and experience have
« long rendered things, extremely difficult to others,
<c eafy to you.”

In the fame letter, Mr. Seymer informs me, that
the bird was fliot in October laft, and he fuppofes it
to be the production of the fpring or fummer imme-
diately preceding, it having not, as he thinks, molted
off all its firft or chicken feathers, as they are called ;
and that it would have required a fomewhat different
defeription, had it been older. My defeription of it,
in its prefent ftate, is as follows.

It is of a middle fize between a pheafant and a
turkey-hen, and fhaped pretty much like a turkey >
the bill, legs, and feet, are black, and fhaped like a

f 835 ]

turkey’s ; it hath a broad fpace of bare fkin round the
eyes, which, when the bird was living, was of a
pale red-lead colour; the eyes like thofe of a turkey ;
the head, and half the neck, is covered with very
fhort feathers, of a whitifh clay colour, with tranf-
verfe dufky bars, though the throat and fore- part of
the neck are wholly of a light clay colour. Thefe fhort
feathers occupy the head and that part of the neck,
which is naturally void of feathers in turkeys. On
the lower part of the neck, the bread, and belly, the
feathers are much longer, and of a black colour, with
a purple and changeable glofs. The thighs and legs,
on their fore-part, a little below the knees, are co-
vered with feathers tranfverfely barred with clay co-
lour and black. The back, covert feathers of the
wings and tail, are of a mixed colour, in very fine
tranfverfe lines of brown and black, though fome of
the coverts of the wings and tail have larger tranfverfe
bars of the abovefaid colours; the greater quills are
dufky, or black, powdered with fmall day-coloured
fpots; the inner coverts of the wings have white tips,
which hide their bottoms, that are dufky. I counted
fixteen feathers in the tail, the outer ones fhorter by
two inches than the middlemoft ; their colour is com-
pofed of brown and black, mixed tranfverfely, like
thofe on the back, though they are more dufky to-
ward their tips ; the very tips being of a bright brown :
the outer borders of the fide feathers of the tail are of
a bay colour ; the covert feathers beneath the tail are
of an orange colour, eroded with black ; about the
vent, the feathers are white, with dufky fpots. 1 he
whole upper fide nearly refembles that of a hen-phea-
fant, but darker coloured. The feathers of the body

Vol. LI. 5P are

[ 83 6 ]

are all double ; that is, two diftindt feathers proceed-
ing from one Item; the outer large, and of a firm
texture j the inner fmaller, and altogether downy.

Whether this bird be produced from a turkey -hen
and a cock-pheafant, or from a turkey-cock and hen-
pheafant, no one knows. I lhould think it rather
from a hen-turkey and cock-pheafant ; becaule their
difparity in fize is not near fo great, as between the
turkey-cock and hen-pheafant, Though the fuppo-
fition, that this bird is from an egg laid by a hen-
turkey trodden by a cock-pheafant, is attended with
a difficulty not eafily reconciled ; for it is not pro-
bable, that a hen-turkey, a domeftic fowl, fhould
betake herfelf to the woods, and bring up her brood
wild, and unobferved 5 which is contrary to the habit
of turkeys in our country, where they are not ori-
ginally natives. Why thefe mixed generations fo
rarely happen, is, I believe, becaufe nature has fixed
the inclination of every diftindt fpecies to the con-
trary fex of its own identical fpecies, from which, in
a wild and natural ftate, it will hardly ever ftray.
The reafon of the mixtures, that we meet with, con-
trary to the ordinary courfe of generation, may pro-
ceed from fome hinderance of the male’s meeting
with his proper female, or female with male, at the
feafons, when they are by nature appointed to propa-
gate their fpecies, which rarely happens j for, in a
wild ftate of nature, moft animals are numerous,
and, at their breeding feafons, eafily meet with males
or females of their own fpecies. Difappointments of
what they naturally feek, and accidental meetings of
different fpecies, near of kin to each other, caufe thefe
unnatural conjunctions, which produce uncommon

5 mixed

[ s37 ]

mixed fpecies of animals. I believe, that two fpecies
widely different from each other, as water-fowl and
land-birds, &c. cannot poffibly conjoin, fo as to
produce a living mixed offspring. I have been in-
formed, and believe it may be true, that a mixed
fpecies has been produced between our common
poultry, and partridges that harbour near farm-
yards.

I am, SIR,

Your mod; humble

and obedient fervant,

London, May 22, 176c. Geo. Edwards.

LXXIL An Account of a late Difcovery of
Afbeflos in France : In a Letter to the
Rev . Tho. Birch, D. D. Secretary to the
Royal Society , from Mr. Turberville Need-
ham, F. R. S.

Reverend Sir,

Read June 5, y Have little to add in the way of litera-
ture, except a fingular difcovery acci-
dentally made, lately, in one of the French pro-
vinces, of the nature of the afbeflos, or amianthus.
The proprietor of a certain forge, upon taking down
his furnaces to repair them, found a great quantity of
this fubftance at the bottom. It anfwered effectually
all the common ufes of the native amianthus, either

5 P 2 manu-

[838]

manufactured into linen, or paper. In fhort, upon a
progrefs in this inquiry, he finds, that both this,
which he obtained from his forge, and the native
afbeftos, is nothing more, as he terms it, than cal-
cined iron, deprived of the phlogiftic ; and that, by
uniting the phlogiftic, either with this, or the foflile
amianthus, he can reftore it, at any time, to its pri-
mitive flate of iron. Does not this, with the dis-
covery of lava, pummice-ftones, iron in a perfect
ftate, and, in fine, many other traces of fire obferved
in moft of the mountains, particularly in all the great
chains, and remarkably in all thofe under the equator,
which are the higheft upon the globe, feem to indi-
cate, that the dry land, with all its eminencies, was
originally raifed out of the waters, by the force of
fubterraneous fire ?

I am.

With great refpeCt and efteem,.

Reverend Sir,

Your moft obedient,

humble fervant,

Paris, May 17, 1760. T. Needham,

LXXIII. An

[ 839 ]

LXXIII. An Account of the hot Baths ofV i-
nadioj in the Province of Coni in Pied-
mont • with the State of the Weather at
Turin in the Year 1759 : In an Ext raff
of a Letter from Dr. Jofeph Bruni,
F. R. S. to Mr. Henry Baker, F. R. S.

Deal* Sir, Turin, Feb. 24, 1760.

Read Junes.r-JpHE warm baths, which have been

fo very ferviceable to the Chevalier
OlTorio, run through the rocks, near the village
called Vinadio, in the province of Coni.

The water is very clear, and fo warm, one cannot
bear the hand in it : the contents are fulphur diffufed
through it, and fome fait almoft like common fait.
By evaporation, you get five, fometimes fix grains,
from a pound of water. I fend you a fmall quan-
tity of the fait, gathered from the ftones by which
the water runs, before the riling of the fun, for in
the day-time it is not found upon them, except in
winter. Where thefe waters run, they depofit oily
particles, which, by degrees, join together, and form
a foft, fpongious, greenifh-vellow fubdance, one inch
almod in thicknefs, which is called muff a : this,
when dry, is wrinkled, takes fire, crackles, and gives
the fmell of brimdone, and when entirely burnt,
leaves a black afh behind, I immerfed a piece of
filver in thefe waters, which, in a few minutes, be-
came black. Their tade is neither fait nor acid, but
difagreeable. The miffa left for two days in common
water, fwells fix times thicker than it was, dinks, and
throws up oily particles on the furface of the water.

The

C 840 ]

The fait does not ferment with acids. If you
diffolve it in common water, and mix it with fyrup
of violets, it gives fome appearance of a green colour
the fame water poured on a folution of filver, it foon
throws down a white fediment. Some fay thefe wa-
ters contain nitre, and particles of other bodies > but
this has not been demonftrated.

The diforder of the Chevalier Offono, for which I
advifed him to the ufe of thefe baths, was, that he
had loft the feeling of his fingers, had a weaknefs in
his hands, and alfo in his legs, infomuch, that fome-
times he could not walk in a ftrait line, but tottered
from fide to fide. He could not extend his toes, and
the foies of his feet feelcd, according to his own ex-
prefiion, as if hard firings were drawn acrofs them.
He tried many medicines to no purpole j but is now
perfectly free from the above complaints, by the ufe
of thefe warm baths ; of which he is fo fully con-
vinced, that he intends to go to them again next fum-
mer, notwithftanding at that time of year the heat is
there excefiive.

He bathed in thefe waters forty times, when the
ftomach was empty, in a morning ; and flayed in
them, at firfl, half an hour, but lengthened the time,
gradually, at lafl, to a full hour. After each bathing,
he was dried with cloths, and put into a warm bed,
where a plentiful fweat came on for about half an
hourj during which, the pulfe beat like that in an
high fever, but became quieter, as the fweating
abated. When the fweating was almoft over, and
the pulfe quite regular, he was dried again with
cloths, his fhirt was changed, and, fitting up in bed,
he was refrefhcd with a glafs of ftrong wine, and a

[ 8+r ]

piece of bread. After this, he rofe, and drefled, and
took a gentle walk.

I obferved, while I was there with the Chevalier
Qfforio, that no patient, who came thither, received
the leaft prejudice by the waters, though all did not
i eceive alike benefit for their refpeCtive diforders. But
one gentleman in particular, who came paralitic, in
the whole inferior extremities of his body, occafioned
by hard drinking, I faw fo far relieved as to walk
without help. I alfo faw others cured of diforders
in the fkin, and relieved in rheumatic and .many other
complaints.

Several perfons drank the waters of a neighbouring
fpring, which is lukewarm, but I cannot fay to any
great advantage : the cures I obferved were by bath-
ing only. Where there is a partial diforder, the
waters of Vinadio are pumped upon the diftempered
part.

Olaus Borrichius mentions a remarkable cure ef-
fected by thefe waters. Vide Medic. Septentrion .

Col/at. tom. II. p. Syy.

I fend you alfo an account of the weather in this
country, in the laft year iyjp. It fhewsthe higheft
and lowdt itate of the barometer and thermometer
in every month.

The firft cypher denotes the day.

Mat. fignines the morning; D. M. the afternoon ;
the following cypher the hour; and the laft cypher
the inches, and parts of inches, divided in 12.

In the thermometer, o denotes the freezing point;
and the laft cypher the degrees above or under the
fame. The thermometer is made according to that
of Monf. De Reaumur.

BARO-

[ 842 ]

BAROMETRO 1759-

Months.

Gennaio

Febbraio

Marzo

Aprile

Maggio

Giugno

Guglio

Agofto

Settembre

Ottobre

Novembre

Dicembre

Days.

Morn, or Aft.

5 3*

D. M.

i 17-

Mat.

r 25*

Mat.

\ 14.

Mat.

i

D. M.

(. 15*

Mat.

V 11.

Mat.

1 15-

Mat.

f !5-

D. M.

-<) 16.

Mat.

1

Mat.

V 4.

D. M.

I 20.

Mat.

y 30-

D. M.

^ 20.

Mat.

r 4-

Mat.

S 9-

Mat.

L IO*

Mat.

D. M.

Mat.
D. M.
Mat.
D. M.
Mat.
Mat.
Mat.
D. M.
Mat.
D. M.
Mat.
D. M.
D. M.
Mat.
D. M.
Mat.

Hours- 1 Inches. Parts.

2

7*

7\

7r

2

*7 I

/ a

7

7

4

7

7

3

7

3

6

6

6

6

3

6

2*

2f

2f

7

2

6

2

2

27 if
27 IO
27 I
27 IO
27 IO
27 IO
2611
27 6

26 1 1

26 1 1

27 6

2611
27 8

27 1

2 7 7t
27 oi

27 8

27 8

27

27

27

27

27

2 7
27

27

27

7

3

3

3

7

7

2

2

7t

2

7 *

27 8f

26 9

27 10
27 10
26 1 1
26 1 1

26 nf

27 6

TERMO-

,|„ Wl» M|l

[ 843 ]

TERMOMETRO 1759.

Months,

Gennaio

Febbraio

Mario

Aprile

Magglo

Giugno

Guglio

Agofto

Settembre

Ottobre

Novembre

Dicembre

{

Days,

M. nr A.

Hours.

Degrees.

7. 26. 31.

Mat.

7 T

O

12, 13, 14.

D.M.

2

6

4> 5*

Mat.

7t

0

17. 22.

D.M.

2

84

*4> *5*

Mat.

7

1

28.

D.M.

13

1.

Mat.

7

4

14. 23, 24.

D.M.

17*

5. 19.

Mat.

9

13. 15, 16.

D.M.

8

21

4. 6.

Mat.

6

r 1

19.

D.M.

3i

2 6f

‘2.

Mat.

6

124

22.

D.M.

3f

284

24.

Mat.

6

I2f

6. 18.

D.M.

3i

26

22, 23.

Mat.

6i

II

9, 10. 12.

D.M.

3

24

6. 25, 26, 30.

Mat.

7

9

.i* 3 •7»8>9*2I*23-

D.M.

24

l7

26.

Mat.

7*

44 Sottolozero.

19. 26. 29.

D.M.

2

1

28.

Mat.

7*

0

2 9*

D.M.

2

2f

5 0.

Vol. LI.

LXXIV. Jh

C 844 ]

LX XIV. An Account of a Specimen of the
Labour of a Kind of Bees , which lay up
their Young in Cafes of Leaves , which they
bury in rotten Wood: In a Letter to
Daniel Wray, Efq\ F. R. S . from Sir
Francis Eyles Styles, Bart . F. R, S .

S I R,

Batterfea, June 11, 1760.

Read June i2,TT Send you by the bearer a fpecimen of
1 of the labour of a kind of bees, who
lay up their young in cafes of leaves, which they bury
in rotten wood. I make no doubt but they are the
fame, which are defcribed in the Tranfacftions of the
Royal Society, by Sir Edmond King, Mr. Francis
Willoughby, and Dr. Lifter. See Lowthorp’s abridg-
ment, vol. ii. p. 772, & feq.

Monf. Reaumur, in his Hiftory of Infecfts, tom. vi.
p. 39. defcribes a kind of bees, which he calls per-
cebois (wood-borers). But thefe, he tells us, form
no cafes for their young, but lay them in the holes
they make in the wood, without other covering, ex-
cept artificial floors, which they make of the fame
wood, to divide the length of the holes into feparate
lodgements, each of which contains a Angle bee. In
p. 97. of the fame volume, he defcribes another kind
of bees, which he calls coupefeuilles (leaf-cutters) ;
and the defcription, which he gives of their work,
feems to anfwer to the fpecimen I fend you. But he
tells us, that all the fpecimens he had ever found, or
been able to collect, of their labours, were taken out

of

[ s45 ]

of the ground ; and feems unwilling to rely on what
he met with in Ray, concerning the depofiting thefe
cafes of leaves in rotten willows. Monf. Reaumur’s
words are as follows.

<c Entre les coupeufes, et meme entre les coupeufes
tc de feuilles de Roller, il y en a, qui fl^avent placer
<c leurs etuis dans des lieux, ou ils peuvent fe con-
iC ferver fains plus longtemps, 11, comme Ray le rap-
<c porte, mais ce qu’il a neglige de dire qu’il avoit
“ vu, les etuis de feuilles, qu’il a decrits, avoient ete
“ reellement tires de trous perces dans du Bois de
tc Saule pourri. Pour moi je n’en ai encore vu
“ qu’en terre, et ceux qui me font venus de divers
“ endroits, ont tous ete tires de terre.”

As Monf. Reaumur quedions the truth of the ac-
count he met with, it may, perhaps, be agreeable to
the Royal Society, to have a fight of the work in
quedion ; and, if you think fo, I lhall be obliged to
you, if you will take the trouble of fhewing it to
them, at their next meeting. I Ihould have told you,
that the fpecimen was found in fome park pales near
Windfor, the latter end of lad: fummer, by fome
workmen, who brought it to Mr. Lee, nurfery-
gardener at Hammerfmith, from whom I received it.
One of the bees hatched, and crawled from his cafe,
under my eye, on Whitfunday lad ; and, by an empty
cafe I faw, that was broke open much in the fame
manner, I imagine another had hatched, and flown
away a little before. The remainder, I prefume, will
not come to life, as I obferve, that fome foreign infeed
has made its way into fome of the cafes ; and others
may have been chilled in the winter, by the fra&ure
of the wood, in which they were inclofed. I have

5 Q_2 dedroyed

[ 846 ]

deftroyed fome of the cafes, in examining them ; but
there are enough left in their original fituation, to
fhew how they are contrived and difpofed.

I am, SIR,

Your moft obedient

humble fervant,

F. H. Eyles Styl cs.

LXXV. An Account of a Cafe of a luxated
Thigh Bone % educed ; by Mr. Charles
Young, Surgeon , at Plymouth : Com-
municated by John Huxham, M. D .
R R. S.

Read June 12,
1760*

AS John Down, a middle fized man,
aged about forty, was, on the 2,1 ft
Auguft harneffing his mafter’s horfes, they

fuddenly took fright, and ran away with the chaife.
He had his back towards the chaife, the wheel of
which, as it rolled very fwiftly along, ftruck him on
the upper and hinder part of the right thigh. He fell
to the ground, and was unable to rife again, and
complained immediately of a violent pain in his right
hip. I came to him foon after the accident, and
caufed him to be put to bed ; when, on examination,
I found his only complaint was the violent pain about
the articulation of the femur with the ifehium, which
was increafed by any even the leaf! motion of the

limb..

[ 8 47 ]

limb. The toe was turned in toward the heel of
the left foot, and the heel of courfe outward j and
the whole limb, from the head of the femur to the
toes end, diflorted in proportion.

I thought it was very evident, at firft fight, that
there muff be either a fradture of the femur, or a
diflocation of its articulation with the ifchium. The
former, I think, would have been eafily difcoverable.
But as by laying my hand on the great trochanter,
while an affiftant turned the foot inward and out-
ward alternately, I could perceive, that the motion
of the great trochanter correfponded exadtly to the
motion of the lowed end of the femur, I concluded,
that, had there been a fradture, it muft have been
between the great trochanter and the head of the
bone. And, had this been the cafe, I expedted to
have been able to difcover it, by the grating, that
is always to be felt, when the two broken ends of a
bone are moved again!! one another. But no fuch
thing being perceivable, and yet the limb fo much
diflorted, and the pain fo violent, and confined to
the parts about the joint, I took it for granted, and.
pronounced the cafe to be a diflocation of the femur ;
and confequently endeavoured to reduce it, by the
ufual method of extenfion. To this end, two men
extended the limb, by pulling on napkins tied round
the ancle, while others counteracted them, by pulling-
on a fheet palled between his legs, and fecured at
the bed’s head, turning the foot outward as they
made the extenfion. This gave him great pain; but
the limb foon became, in every refpedt, parallel to
the other. It appeared as long, and, on laying it
down on the bed, the great toes and heels of both

C 848 ]

feet lay exactly in the fame pofition \ and the only
difference, which I could perceive in the two limbs,
was, that there was a little flatnefs about the hip of
the right fide. In fhort, the difference between the
two limbs was fo little, that I began to think I had
been miflaken in my opinion of a diflocation (for it
was evident there was no reduction made by the ex-
ten fion, for that could not but have been perceived,
both by the patient and myfelf), and that the diftor-
tion of the limb was owing to nothing elfe than an
involuntary contraction of the mufcles, occafioned by
the violence of the blow. I therefore bled him, con-
fined him to lie on his back, and charged him to
move as little as poffible ; imagining, that reft would
be his moll effectual remedy. He continued in much
pain for fome days; but by degrees grew tolerably
eafy, except when the limb was moved ; and at about
twelve days after the accident, he could fuffer the
limb to be lifted to and fro gently, with little or no
pain at all. Notwithftanding which, he could no
more lift it of himfelf than at firft, when it was
much more painful. This embarraffed me a good
deal. I was convinced there was no fraCture of the
limb, in any part ; and I thought, from the circum-
ftances above related, there could hardly be a diflo-
cation. I therefore defired the opinion of two other
furgeons, who, on feeing the pofition of the limb,
and inquiring into all the circumftances, which did
and had attended it, agreed with me in opinion, that
it was no fraCture, and that it was equally unlikely,
under thefe circumftances, there fhould be any diflo-
cation. For the right leg, when placed by the fide
of the other leg, as I have faid already, was exactly
3 parallel

[ 849 ]

parallel to it, and continued io, un!, fs the patient,
eithei when afleep or at any other ume, moved his
body, fo as to drag his leg: in that cafe, the toe
was always found inclining inwards, and the heel
outward ; but never fo, but that it might be replaced,
without the lead; difficulty or pain to him, but juft fo
as one might have done by a limb that was paralytic.
W e therefore recommended reft, hoping that farther
reft and time would recover the perfect eafe and
ftiength of the limb. But fome days palling without
any alteration, I gave him a ftrong purgative, and
repeated it every other or every third day, for feveral
times, in order to reduce the mufcles, that I might
the more plainly feel any thing through them. For
though he was, in point of height, but middle ftzed, he
was pretty flefhy, and the glutsei mufcles confequently
too thick to fuffer any thing to be felt with any de-
gme of diftindneis through them. This anfwered
my expectation fully* for, by repeating the purga-
tive often, and at fhort intervals, his living fparingly,
and being confined to his bed, he became much
emaciated, infomuch, that the head of the femur
was plainly felt through the mufcles, diflocated back-
ward, and lying in the fpace between the os ifchium
and os facrum.

.Of this I acquainted the gentlemen, who had exa-
mined it before, and defired them to examine it a
fecond time; which they did, on the 15th Septem-
ber, and were immediately convinced, that the os
femoris was diflocated, and that it was the head of
the bone we felt through the glutaei mufcles, in the
fpace between the ifchium and facrum,

To.

[ 850 ]

To the head of the bone’s lying in this fpace, it was
probably owing that we were at fird: deceived ; fince its
being there allowed a greater latitude of motion, than
could poffibly have been the cafe any where elfe ;
which may ferve to account tor the parallelifm of
the limb to that of the other, notwithftanding a
luxation.

But, on turning the foot inward and outward by
turns, while an adiftant laid his hand on the head of
the bone, a grating was perceived, both by the pa-
tient and us all. I his fo me what furprized us at fird ;
but, as this grating was never to be perceived, with-
out preding pretty hardly on the head of the bone,
at the time the limb was turned round, and as the
head of the bone was plainly felt to turn round,
whenever the thigh had that motion given to it, we
concluded it could be nothing but the fide of the
head of the femur againft the edge of the ifehium.

Convinced of this, we determined to make an ex-
tenfion ; and, to that end, brought him to the foot
of the bed, and placed him on his back, with the
bed’s poll between his thighs, which was wrapped
round with cloths, to prevent its galling him. . A
napkin was tied round his leg, at the ancle, which
two adiftants pulled on, while a third turned the
knee outward, and I had my hand on the head of
the bone, preding it downward. As foon as the
extendon began, I perceived plainly the bone dnk
under my hand, which I had hardly time to fay,
before it gave a fnap, which was felt by the patient,
and heard by us all, and the bone was reduced.

When he was laid on his back in the bed, the
right leg appeared fomewhat longer than the othei ;

[ $5* ]

but that might poffibly be owing to the mufcles not
immediately overcoming the effedt of the extenfion
fufficiently, to draw the head of the femur to the
bottom of the acetabulum.

In about fix or feven days he was eafy, and able
to walk over the room with crutches, and bear a con-
fiderable weight of his body on the right leg ; and,
from this time, he recovered ftrength very faff, and
is now, and has long been, as ftrong in that leg and
thigh, as in the other, without any even the lead'
difference in length, or any other refpedt.

To Dr. Huxham.

S I R, Plymouth, May 1760.

T Have fent you the above cafe of John Down ; be-
* caufe I know it is afferted by fome furgeons, and
among thofe of the greateff charadter too, that a luxa-
tion of the head of the femur is little lefs than im-
poffible ; and that what is generally taken for a luxa-
tion of this joint, is a fradture of the bone at its neck.

A fradture of the neck of the bone probably hap-
pens more often than a diflocation. But the above
cafe has convinced me, that it may happen, and that
without any extraordinary violence, provided the
force is aptly applied. Indeed any force applied in
the diredtion of the thigh downward can hardly
have any tendency to diflocate it at all ; and any
force from below upward will be fudained by the
bead of the femur bearing againft the upper part of
the acetabulum, till the neck, the weakeft part, gives
way.

Vol. LI. f R But

P

[ 852 ]

But though it may not be poffible, that the femur
fhould be luxated by any force applied in a direction
parallel to that of the thigh, in an ere£t pofture of
the body, it is not equally impofiible it fhould be.
dillocated by a force applied in a contrary direction..
For, in the above cafe, the blow was received on the
upper and hinder part of the thigh, in a dire&ion
forward, from the wheel of the chaile, which muft
neceilarily have a tendency to drive it round forward,
and confequently cant the head of the femur out of
the acetabulum, backwards,, where it is lefs deep
than it is either above or below. On the fore part of
the acetabulum, it is yet more (hallow, and therefore
lefs force is required to diflocate it that way, and more
efpecially, as there is on that fide lefs ftrength of
mufcles to refill.

It was probably a fortunate circumfiance for this
man, that I thought myfelf millaken in my firft
opinion of its being a difiocation ; for, had that beea.
clearly the cafe, I (hould, no doubt, have ufed every
method, and every afiiftance to be had, in order to
have reduced it immediately ; and mod likely, while,
the mufcles remained in their full ftrength, and con-
tradling involuntarily, and that violently too, as they
will fometimes do, upon attempting an extenfion of
them, and under which circumftance, the mufcular
fibres oftentimes rather break than give way, fhould
have failed of being able to reduce it; and, in that
cafe, the man mufl have remained a cripple as long
as he lived : whereas now', though five-and-twenty
days from the time of the accident, the mufcles
were fo much weakened, by his being confined to
his bed, and wafted by his frequently repeated purges,.

T 853 ]

that they very eafily gave way, and the reduction was
efheded with as little difficulty, as ever I faw in a dis-
location of the humerus.

Might not the giving ftrong purgatives, and fre-
quently repeating them, lo as to render the mufcles of
throng mufcular fubjeds more lax and weak, be a
means of reducing luxations of the humerus, which
are not reducible by any method of extenfion, which
is often found the cafe ?

I am, SIR,

Your very humble fervant,

Charles Yonge.

LXXVI. Some Obfervations upon a Samnite-
htrufcan Coin , never before fully explained,
hi a Letter from the Rev. John Swinton,
B.D, of Chrift- Church, Oxon. F. R. S.
to the Rev. Thomas Birch, D. D. Secre-
tary to the Royal Society *

Reverend Sir,

Read June 19, “W" Have in my fmall colledion a filver
JL Etrufcan coin, of the lize of the
confular denarii, limilar to one publiffied by (1) Ful-
vius Urlinus, (2) Patin, (3) Vaillant, (4.) Havercamp,

(1) Fulv. Urfin. in Famil. Romanar. num. incert.

(2) Car. Pat. ibid.

(3) J- V a ‘ H • in Famil Romanar. num. incert.

(4) Sig. Haverc. apud Andr. Morel, in Thefaur . Kumifmat.

p. 459.

5 R 2 and

C 854 ]

and Sig. Annibale degli Abati Olivieri (5), a gentle-
man of Pefaro, who has written two learned diflerta-
tions upon three or four medals of the fame kind ;
all which, with the greateft appearance of truth, he
takes to have been ftruck on occafion of the Social
war. Fulvius Urfinus, Patin, Vaillant, Morel, and
Havercamp affign the medal refembling mine a place
amongft the uncertain, or unknown, confular coins ;
though Havercamp (6), without any manner of
foundation, affirms it to be a medal of Faleria. But
this is not to be wondered at, as he feems to have
been alinoft an intire ftranger to the Etrufcan cha-
racter. Sig. Annibale degli Abati Olivieri has, with
the higheft degree of probability, determined it to be
(7) a Samnite coin; and clearly evinced it to have
firft appeared in (8), or about, the year of Rome
663.

But notwithftanding this moft learned and inge-
nious gentleman has fo perfectly well explained three
very rare filver Etrufcan medals of C. Papius Mutilus,
who commanded the Samnite troops in the Social
war, that not the lead doubt can be entertained of
the truth of his explication ; notwithftanding he has
fufficiently proved the coin I am confidering to have
been adorned with the name of the pretor of the

(5) Saggi di Dijfertazioni Accadetniche pubblicamente lette nella
Nobile Accademia Etrufca dell * antlchijfima Cittd di Cortona.
Tom. II. p. 49—72. h Tom. IV. p. 133—148.

(6) Sig. Haverc. apud Andr. Morel, in Thejaur. Numijmat.
five Sig. °Haverc. Comment, in Famil . Roman, num. emu. b'c.

p. 459.

(7) Annib. degli Abati Olivier, in Saggi &c. ubi fup.

(8) Id. ibid.

Marfi,

[ 8SS ]

Marfi, who likewife diftinguifhed himfelf againd the
Romans, in the fame ruinous and dedruCtive war ;
yet I cannot prevail upon myfelf abfolutely to con-
gratulate him, upon his dilcovery of ail the Etrufcan
characters forming that name. His differtation here
does not come quite up to the point. Of this he
feems himfelf to have been aware, when he informed
the learned world, that, “ after having viewed the
“ Etrufcan infer iption with a very good glafs, and
“■ well confidered it, he thought he could make out
sc the following letters, P. ITEEIV ; and that if fuch
“ another medal fhould hereafter be found, with the
** elements better preferved, it might perhaps con-
“ firm his (9). conjecture.” Having therefore a limi-
lar coin now in my poffeffion, I hope I fhall be in-
dulged the liberty of tranfmitting to the Royal Society
a few brief and concife obfervations upon it > efpe-
cially, as thefe may perhaps throw fome new light:
upon Sig. Annibale degli Abati Olivieri’s difeoveries,
and ferve as a fhort fupplement to his two mod
learned and elaborate differtations.

The laureated head on my Etrufcan denarius is
adorned with an ear-ring, not vifible either on Sig.
Annibale degli Abati Olivieri’s medal, or any of thofe
publifhed by Fulvius Urfinus, Dr. Patin, Dr. Vail-
iant, and Mr. Havercamp.. There is a minute dif-
ference between the lower part of the lance, held in
the right hand of the galeated figure on the reverie
of the piece before me, and the fame part of the
lance, exhibited by the other coins. The drapery
likewife of the galeated figure on the firfh of thefe is

(,o) Sag. di D’.jjertaz . AacuUmich, &c. Tom, II. p. 65, 66.

fome^-

[ 856 ]

Something different from that of the fame figure on
the reff. The foot of the ox or bull feems hairy on
my denarius, but not fo on the others. All which
Angularities, together with the additional Etrufcan
element at the end of the infcription, reprefent-
ing R, and the Etrufcan M on the reverie, will
perhaps intitle the medal I am confidering to the
denomination of an inedited coin. The workman-
fhip is good, but fomewhat different from that of
the confular denarii, particularly thofe of the fame
age. Mr. Havercamp juffly remarks, that the legend,
or infcription, here is Etrufcan (10) ; but by no
means afcertains the forms and powers of the let-
ters, of which it is compofed. He even took the
Etrufcan A in the exergue of his own medal, which
does not appear in that of mine, for an ( 1 1 ) inverted R.
Sig. Annibale degli Abati Olivieri calls thefe fmall
filver pieces (12) Etrufcan medals, becaufe they have
l'carce any thing in common with thofe of Rome,
and are adorned with Etrufcan characters, or fuch as
were in the earlier ages the letters of all Italy, then
fubjeCt to the Etrufcans ; but at the fame time he
oblerves, that they might with greater propriety, not-
withffanding the authority of the Marquis Scipio
Maffei, be termed Italian coins.

As I remember not to have feen an alphabet of the
Samnite-Etrufcan characters, exhibited to the public;
I have taken the liberty to tranffnit one to the Royal
Society, deduced from fome very valuable Samnite-

(10) Sig. Haverc. ubi Tup. p. 459.

( 1 1 ) Id. ibid.

(12) Sag. dl DiJJertaz. Accadcmich. &c, Tom. II. p. 49.

Etrufcan

;

*■-

Philos. Jr mis. Voi.Ll TAB .XJL.jci 8 5 y.

Samnite-Etn i lain r/fZui/o'fi, iZfd/ofJ fro?o/lZi£' Zototo of C.l*apius 3Iutilus<Vetu.rius>
Capua .Accrric .<<t. <//>/? o.hv/ /// ooofrol ytor&j of PfaZy oo lafc tu l/tof /’<//’ of Po/ot’ 6t>,i

RR/CinRIRR /X rRI /I

A

a 3

B

>>>> > 'h >t a >| »>i

C

3 3 a 3 33 3

E

H B B

H

O

TH

1 H'h K l

I

•4 vj H H

L

w w w wt it] m

M

klHHM

N

n/i n n

P

gc<]3 m

K

* * * *

•: s

T T T

T

vs/vva a O 3 q ^

V

8 8 $ $

P H or F

E 1

./

f. ftf/uO /r

[ 857 ]

Etrnfon coins. The doits 0f the letters are drawn
with Jo much accuracy, that they may be intirely
depended upon. [Vide Tab. XX.] *

Hie infcription here mentioned, ftanding behind
ne laureatedi head on this denarius, is drawn from

, right hand to the left, after the Etrufcan manner,
and confifts of eight letters. The firft of thefe is*the
Digamma equivalent to V or F, as it appears on the
celebrated tab,es of Gubbio, and leveral Etrufcan

C0‘ns- , r“e fec°"d JS apparently I, and the fixth will
undoubtedly be taken for the fame element. The third
is raanifeftly T, both on my medal and every ihnilar
one hitherto pubhfhed. The fourth and fifth mull: be E
though the latter of thefe has not been perfefllv well
prelerved on my coin. The feventh will be univerfallv
ronfidered as V, though only part of it is vifible on
he piece before me. The eighth is the Etrufcan R
as prefen ted to our view by one of the medals of
, 1 apius Mutnus, by the tables of Gubbio, and by
other Etrufcan remains of antiquity. It is very per-
ea and intire, and not exhibited by any fuch piece
mat has hitherto appeared ( i j). Sigf Annibale degli
Abati Olivieri feems inclined to take the firft element
of the infcription (14) for P. But this is probably-
done in order to accommodate the name to the cor-
rupted text of Velleius. The form he himfelf has
given us of this letter bears fcarce any refemblance to
tliat of the Etrufcan P, on the medals of C. Papins
Mutilus j. but approaches near enough to that of the

Jtn3^ Pafl: Vid. etiam Gor. Muf. Etrufc Vol H

h Dempft. De Etrur. Regal Tom. I. J ' ' ii*

iH), Sag. ai Differ tax. Accademicb. fcfr. Tom. II. p. 6c.

Digamma *

[ 8S8 ]

Digamma , or Etrufcan V, above-mentioned. ( 1 5) Mr,
Havercamp’s denarius, as well as mine, and that de-
fcribed by M. Morel, fets the point here infilled upon
beyond difpute.

From the foregoing obfervations we may colled:,
that our infcription, in Roman, or modem Latin,
letters, will be FITEEIVR, or VITEEIVR ;
which, in the cacography of the Etrufcans, as their
rude and uncouth manner of writing is termed by
.Sig. Pafferi (16), feems to anfwer to the VETVRI,
or rather VETVRI VS, of the Romans. If this be
admitted, it will be allowed extremely probable, that
the name of the general, who commanded the Marli
in the Italian war, was FITEEIVR, VIFEEIVR,
or VETVRIVS, and neither VETTIVS nor IN-
STEIVS, as Sig. Annibale degli Abati Olivieri feems
inclinable (17) to believe. This general is called
Vettiils, or C. Vettius, by ( 18) Claudius Quadrigarius ;
Infteius, or Infteius Cato, by ( 19) Velleius ; 'O vinos
KaToir, Vetius Cato, by (20) Appian; P. Vettius, or
P. Vettius Scato, by (21) Cicero ; Vellius, or Vellius
Cato, by (22) Florus ; and T. Vettius, T. Vetius,
T. Vetitius, and T. Vietius, in different manufcripts

(15) Sig. Haverc. ubi fup. p. 459.

(16) Jo. Bapt. Pafler. Pifaurenf. De Nurn. Etrufc. Pajlanor.
Differ tat. p. i S. in Symbol. Liter ar. opufc. var. &c. Vol. II.
Florentine, 1748.

(17) Sag. di Dffertaz. Accademich. &c. Tom. II. p. 65, 66.

(18) Claud. Q^iadrigar. apud Sencc. De Benef. Lib. iii. c.. 23.

(19) Veil. Paterc. Lib. ii. c. 16.

(20) Appian. Alexandria p. 375.

(21) Cic. Philip, xii- II.

(22) Flor. apud Sig. Havercamp. in not. ad Eutrop. p. 206.
Lugd. Batavor. 1729.

and

[ *59 ]

and printed editions of (23) Eutropius. From whence
vve may infer, that the name of this general has been
corrupted in moft, if not all, of the texts of thofc
authors ; even upon the fuppofition, that our coin
bears not any relation to him. But as (24) Sig. An-
nibale degli Abati Olivieri has clearly evinced the
truth of the contrary fuppofition, the variety of cor-
ruptions here produced will add no fmall weight to
what is more than fuggefted by the denarius I am con-
fidering; fo that the infcription exhibited by this fmall
medal is even fupported by thofe corruptions, and will
undoubtedly, in the opinion of the moft learned men,
afcertain the name of the general, who commanded
the Marii in the Italian war.

In farther eviction of what is here advanced, it
may be obferved, that the proper name VETVRIVS
itfelf has aifo been indifputably corrupted in other
paftages of antient writers. In one of Cicero (25)
it has been transformed into Betucius, and in one of
Plutarch (26) into BareW, or Butetius. Which
being maturely weighed, it will not appear ftrange,
that this general’s family name ftiould have met
with fo hard a fate. For that the piece I am en-
deavouring to explain is one of his coins, will
be acknowleged more than probable, if we con-
fider with proper attention what has been urged by
Sig. Annibale degli Abati (27) Olivieri in favour of

(23) Eutrop. Hiji. Rom. Lib. v. c. 3. p. 205, 206. Ed. Ha-
vercamp. Lugd. Bat. 1729.

(24) Sag. di Dijfertaz. Accademich. lAc. Tom. II. p. 65, 66.

(25) Cic. in Bruto.

(26) Plutarch, in £>uaj}. Roman.

(27) Sag. di Dijfertaz. Accademich. Tom. II. p. 65, 66.

Vql. LI. f S fuch

[ 860 ]

fuch a notion. He has demonftrated this denarius
and one of C. Papius Mutilus to be of nearly the lame
fize and workmanfhip, to be adorned with infcriptions
conlifting of the fame fort of characters, and to have
the very fame type on the reverfe. He has alfo in-
contelfably proved, from the belt authorities that can
tz produced, that C. Papius Mutilus, mentioned by
the coins he has fo learnedly explained, was cotem-
porary with our Veturius, or, as he denominates him,
P. Iteeius, and the general under whofe conduCt the
Samnites fo greatly diftinguifhed themfelves, in the
aforefaid ruinous war, againlt the Romans.

But this will ftill receive a farther acceliion of
ftrength from another confideration, relative to the
point I am now upon, which ought by no means to
be omitted here. Two (28) medals of the Veturian
family and one of (29) C. Papius Mutilus exhibit
almoft exaClly the fame type on the reverfe, though
the infcriptions they bear confifl of different cha-
racters. This amounts at leaft to a pretty ftrong
prefumption, that Ti. Veturius, whofe name occurs
on one of the Roman denarii, was either the pretor
of the Marfi himfelf or related to fome commander
of the allies of the fame name; as (30) Mr. Haver-
camp takes the piece to have been ftruck not long
after the Italians had the right of fuffrage conferred
upon them by the Romans, in order to perpetuate
the memory of that remarkable event. I fay, “ or
“ related to fome commander of the allies of the lame

(28) J. Vaill. in Num. Fam. Vetur. p. 533*

(29) Sag. di Differ taz. .Accademich. iff c. ubi fup.

(30) Sig. Haverc. Comment, in Famil. Roman, num. omn. <Ac,

P- 438> 439> 440.

“ name;

[ 86i ]

<v name;” becaufe it cannot perhaps be fo eafily proved,
that he was our Veturius himfelf. For we are told by
Claudius (31) Quadrigarius, in a fragment of his pre-
ferved to 11s by Seneca, that one of this general’s Haves
killed him, in order to prevent his falling into the
hands of the Romans ; which feems to intimate, that
he was dead before the cone lull on of the Social war,
or at lead: before the Italians were put upon an equal
foot with the Romans. However, his name might
have been impreffed upon this denarius, after his
death. Whether or no the Veturian family itfelf de-
duced its origin from the Mark, notwithdanding
the blence of Fulvius Urdnus, Dr. Vaillant, and Mr.
Havercamp, on that head, I jfhall not take upon me
to determine.

Be this, however, as it will, from the family name
CVJ33TJ3, FITEEIVR, or VITEEIVR, on the
diver Etrufcan, or Samnite, medal, which at prefent
is the principal objeCt of my attention, we may infer,
that the Etrufcan orthography was very rough and
unpolifhed, at lead in fome of the Italian provinces,
fo late as the 662d, or 66 3d, year of Rome; when
that of the Romans, now called the Latin, was ar-
rived at almoft the lad degree of perfection. It mud
neverthelefs be owned, that the later Latin, or Ro-
man, letters (fo denominated in contradidinCtion to
the antient Latin characters, undoubtedly the fame
with the Etrufcan, and ufed by the Romans them-
felves in the earlied times) as well as the Etrufcan, were
in vogue amongd feveral of the Italian dates, when
the medals of C. Papius Mutilus and Veturius were
druck. This mod evidently appears, from the diver

(31) Claud. Quadrigar, apud Senec. ubi fup.

jS 2

pieces,

[ 862 ]

pieces, with the word ITALIA upon them, explained
hy Sig. (32) Annibale degli Abati Olivieri, in his firft
diflertation ; and from a fimilar one in my little ca-
binet, hitherto unpublilhed, which I lately acquired.
Hence fome learned men may perhaps be inclined to
believe, that both the denarius of the Veturian family
and the coin by me here referred to our Veturius did in
reality exhibit the name of the general of the Marti,
and firft appeared about the 663d year of Rome. With
regard to the word 4V113T\3, or VETVRIVS, men-
tioned in the beginning of this paragraph, I (hall be°-
leave to remark, that it might as eafily have been
transformed into VETTIVS, or VETIVS, in the
manufciipts and printed editions of fome antient
writers, as PAPIVS into APONIVS in tholb of
others; and that the (33) word APONIVS, for
PAPIVS, ftands in the text of Diodorus Siculus, as
cited by Photius. Vv ith which obfervations I ftiall
conclude what I have here to fay, in defence of my
ledtion of this Etrufcan infeription.

y 1 s paper to be a ftiort fupple-

ment to Sig. Annibale degli Abati Olivieri’s two
moft excellent diliertations upon his Samnite coins,
it would be intirely fuperfluous to attempt an explica-
tion of the types exhibited by thofe coins; efpecially,
as. this has already been done in fo ample a manner*
with fo much fagacity and erudition, by that very
ingenious gentleman himfelf, the learned Sig. Bian-
coni, and the moft acute Sig. Pafteri, that fcarce any
thing new or material on that head can be added to
then oblervations. Plowever, it may not be improper

(32) Sag. di Dijertaz. /Iccadsmich, &c. Toni.TlTp. 57.

v ,133) Dl°d. S c. apud Photium, in Myriobibl. p. 1185/1186.
uchot, Rothomagi, 1 653,

juft

[ ^3 ]

juft to remark, that both the denarii of C. Papins
Mutilus and the piece by me attributed to our Vetu-
rius (34.) were coined, in commemoration of the al-
liance entered into by the Italian ftates againft the Ro-
mans, about the time of the commencement of the
Social war ; whereas the Roman medal of Ti. Vetu-
rius (3 5), according to Mr. Plavercamp, was probably
ftruck after the conclusion of that war, and even after
the admiftlon of the Italian allies into the city, the
memory of which it was perhaps intended to perpe-
tuate, by the Romans.

That the Etrufcan pieces here confidered were ftruck
on occafion of the Italian war, or war of the allies,
is likewife abundantly clear, from a mod rare Etruf-
can medal in Lord (3 6) Pembroke’s noble collection,
never hitherto explained. It is adorned with fuch a
laureated head as occurs on Veturius’s coin, and on
the reverfe a bull goring with one of his horns a fu-
rious wild beaft, refembling a monftrous dog, he had
got under him, together with the Etrufcan infcription,

vTKamPtJ d 1 tv hi iniwn >, c. paapi

MVTIL EM BRAT VII, though very indifferently
copied. This is a fourth Etrufcan, or Samnite, coin
of C. Papius Mutilus, the Samnite general; which
Sig. Annibale degli Abati Olivieri had neither feen
nor heard of, when he publifhed thofe two learned
differtations, which this paper is intended to render
a little more complete. The bull on Lord Pembroke’s
medal undoubtedly denoted the ftates of Italy, or rather

(34) Sag. di Dijfertaz. /. Iccadtmicb . Tom. II. p. 65—72.

Si Tom. IV. p. 140 — 148.

(35) Sig. Havercamp. Comment, in Famil. Roman, num. omn .
i3'c. p. 438, 439, 440.

(36) NumiJ'm. Antiqu. &c. Thom. Pembroch, et Mont. Go-
menc. Com. P. 2. T. 87. num. 10.

the

C 864 ]

the union of thofe dates, combined againd the Ro-
mans, as the fierce animal under him did the fenate
and people of Rome j the whole type pointing out to
us the hoped for fuperiority of the former over the
latter, or rather being intended as a prognodication
of fuch fuperiority. That the bull was the fymbol of
feveral Italian cities, or dates (37), appears from the
coins of Pofidonia, Thurium, Arpi, &c. and that
the (38) word ’Ira Italus, or Italian, in the old
Etrufcan tongue, the primitive language of all Italy,
dgnified a bull, whence probably that animal might
become the fymbol of at lead a very confiderable part
of this country, is a point fo exceeding clear, that it
will not admit of a difpute.

To what has been faid we may add, that the Italians
looked upon the Roman republic, about the time of
the Social war, as a receptacle of wolves, always ready,
if not determined, to ravifh their liberty from them.
This we may colled; from the following words of
Pontius Telefinus, in Velleius: (39) — adjicie?2s , nun-
quam defuturos raptores Italicce libertatis lupos , nifi
filva , in quam refugere Jolerent , effet excifa. This
obfervation may pofiiblv throw fome new light upon
Lord Pembroke’s medal, as well as upon the type of
my Etrufcan denarius, and the fimilar one of C. Pa-
pius Mutilus’s coin, which feems to have a little em-
barraficd the learned (40) author I have all along here
had principally in view.

(37) Hubertus Goltzius, in Magn. Grac. Nurnifrn. pafl'.

(38) Apollodor. Lib. ii. lfacius ad Lycophronem, & Tzetzes

in Cbiliadibui.

(39) Veil. Patere. Lib. ii. c. 27.

(40J Sag. di Dijfcrtaz. Aaadmkh. (Ac. Tom. II. p. 66, 67.
hi. Tom. IV. p. 141.

As

[ 86S ]

As the foregoing Etrufcan coins are proved to have
been ftruck about the 662 d or 663d (41) year of
Rome, the Etrufcan alphabet then undoubtedly pre-
vailed over a very confiderable part of Italy ; though
the forms of fome of the characters, particularly thofe
of A, P, and I, were not precifely the fame with
thofe of the equipollent letters ufed in Umbria and
the (42) Proper Etruria. I fhall only at prefent beg
leave farther to remark, that the reverfe of my Etruf-
can denarius has handed down to us a new form of
the Etrufcan M, placed in the exergue, which has
never been before obferved on any of the Etrufcan
remains of antiquity ; and that I am, with fentiments
of the higheft refpeCt and efteem,

S I R,

Your mod: obliged,

Chrift-Church, Oxon. and moft obcdient>

May 19, 1760. humble fervant,

J. Swinton.

LX XVI I. De Proximo Veneris Jub Sole

\ Tranjitu .

Ad Londinenfem Regiam Societatem ,

Read June 19, It 'y’EMO fane ignorat Adronomus,,

quanti interfit ad abfolutam per-
fedtionem Aftronomiae, accurate node diftantiam Terra

(41) Annibal. degli Abat. Olivier, ubi Tup. & alib.

(42) Gor. Mtif Etrufc. Annibal. degli Abat. Olivier, in Sagr
di DiJJerta%. Accadtmhh . &c, Tom. II. & Tom. IV.

5 a Sole*

[ 866 ]

a Sole, a qua reliquorum Planetarum, Cometarumque
pendent abfoluta? diftantiae, moles, ac mafia;, et alia
fane multa, quae notam exigunt parallaxim Solis cum
hac ipfa diftantia tam arde connexam, ut utriuflibet
inveftigatio pro uno eodemque haberi foleat. At hoc
tantum nobiliffimae facultatis fundamentum nondum
intra fatis ardos limites definitum efle cenfetur paffim
vel poll ipfos, utiliffimos illos quidem, Caillii labores,
ex quibus nelcio, an omnino certum intra decimam fui
partem habendum fit. Quamobrem nulla videtur
praeterm ittenda occalio promovendae ulterius nobilif-
fimas atque utiliffimae perquifitionis, quod ad eos
maxime pertinet dodorum hominum coetus, qui
publica audoritate et conftituti et fuftentati multo
facilius, quam privati homines et inire pofiunt, et
vero etiam debcnt, rationes ad rem perficiendam ido-
neas.

2. Una ex occafionibus rei bene gerendae maxime
opportunis habebitur fequenti anno, nimirum ex-
pedatifhmus et rariffimus Veneris Tub Sole tranfitusj
quae occafio ne fine optatiffimo frudu effugiat, id vero
potiflimum ad Anglicanam nationem curare pertinet,
et ad hanc Regiam Societatem in primis. Duplex
autem videtur mihi effe ratio, cur hujus occafionis
non omittendae cura ad Angliam in primis, et ad hunc
dodifiimum coetum, pertineat. Primo quidem, quod
in ejus occafionis fpem jam ab anno 171b, in Phi-
lofophicis Tranfadionibus univerfam primus Eu-
ropam erexit ingens illud Aftronomiae lumen, ac
Anglicans nationis decus, Halleyus, Aftronomos
omnes ad earn rem excitans, quern et illud maxime
doluiffe conftat, quod nullam haberet fpem vitae ufque
ad id tempus produccndae, ut tanto bono frui polfet.
Deinde, quod nufquam alibi inftru.menta ad rem bene

gerendam

[ 867 ]

gerendam apta ad eum perfedionis gradum, quo hie
eft opus, redada lint, ut hie in Anglia.

3. Primum caput per fefe patet; quam enim de-
deceret illud, fi, quod ne fufpiciari quidem pofium,
ea gens tantam opportunitatem negligeret, quae ipfum
detexit prima, quee caeteras nationes ad earn arripen-
dam incitavit, quae tot alia praeclariffima inventa ad
Aftronomiam in primis perficiendam hue ufque pro-
tulit ! Ipfi nimirum debet Literaria Refp. generalem
immortalis Newtoni gravitatem, quae una ad Ccelum
Aftronomis referandum cenfetur jam per univerfam
Europam quaedam veluti clavis certiflima ; ipli Co-
metarum orbitas, et Lunarium aberrationum perio-
dum ab Halleyo definitas ; ipli aberrationem lumi-
nis, et nutationem axis incredibili et patientia, et
fagacitate, et vero etiam felicitate deteftam a Brad-
leyo, a quo uno, definitis jam demum ftellarum fixa-
rum locis ad datum tempus quodcumque intra ardif-
limos unius, vel alterius fecundi limites, Aftronomia
accepit illud, ut perfici demum poflitj ipfi alia in-
numera, quae tantam Anglicanae nationi laudem et
gloriam pepererunt, quibus omnino vel tantummodo
commemorandis nullus adelfet finis. Quamobrem
hue univerfa defixos habet oculos Europa, nihil du-
bitans, quin eadem perftet adhuc ad nobiliflimam
facultatem promovendam alacritas, ac vetuftum om-
nium bonarum artium ftudium perfeverct, et qui
alios ad hanc ipfam rem bene gerendam incitarunt
feriptis, exemplo quoque fuo follicituri lint.

4. Quod autem ad alterum pertinet caput, inftru-
menta omnino necefiaria ad hujufmodi obl'ervationem
funt horologium ofcillatorium et telefcopiam : horum
alterum hie primum fatis perpolitis, et rite difpofitis

Yol. LI. fT tarn

[ 86S ]

tam variis delicatiftimae machinae partibus, ac impe-
dito caloris effedu, idmmam demum aequabilitatem
accepit, nec ufquam alibi nunc etiam majorem habet
perfedionem, quam hie : alterum hinc fere tantum-
modo prodit fatis idoneum ad fubtiliores ejufmodi
obfervationes, live dioptricum adhibendum lit, live
catadioptricum. Illud quidem poll mirum fane re-
centiflimum Dollonii inventum ad eum perfedionis
apicem redadum eft, quern olim nunquam fperare
licuilfet : hoc autem hie primo inventum, eo Shortii
in primis diligentia atque induftria perduxit, ut hinc
potiflimum ejufmodi inftrumenta praecipui omnes per
Europam Aftronomi libi expetant, atque hie, quo—
tiefcumque per fumptus licet, requirant. Sed et re-
liqua ilia, quae ufui efte poflunt ad uberiores certio-
refque ex hoc Veneris tranfitu capiendos frudus hie
vel inventa funt primo, vel ad fummum perfedionis
gradum perduda, quadrantes nimirum, fedorefque,
et micrometra, tam externa ilia, quae ad alidada3 mo-
tum pertinet, quam interna, live ea lint filaria ilia,
vetera, quae ocularia appellantur, live haec nova, quae
objediva dicimus, quorum abfolutam perfedionem
debemus itidem Dollonio, in quibus omnibus, ut
omittam ca3teros, tantam libi laudem Silfonius com-
paravit. Ea fane omnia nulquam alibi ita ad rena
idonea conftruuntur, ut hie. Quamobrem quis illud
plane non agnofeat, earn gentem, quae inftrumenta
ad utiliflimas obfervationes inftituendas prae ceteris
omnibus aptiflima exhibeat, decere itidem ante omnes
alias iifdem uti, et Aftronomos, quos habet plurimos,
ad capiendos ex iifdem frudus ab omni Europa ex-
pedatos adhibere,,

5. Accedit

[ 869 ]

y4 Accedit aemulae nationis conatus. IS am ante
meurn difeedum Parifiis profedtus jam fuerat unus ex
Academicis Pondicherium in India, alter a Petropo-
litana requidtus Academia parabat fe ad difeedendum
Toboldcam in Siberiam : eodem autem, quo difeedi,
die, de tertio ad caput Bonae Spei mittendo delibera-
batur, eratque alius, qui fe offerret ad navigandum in
Cyprum infulam, ac rem urgebat. Ufque adeo ne
in nobiliffima facultate promovenda vinci fe dnet a
Gallis Anglia, quae tanto majorem hoc potidimum
tempore opportunitatem habet tranfvehendorum quo-
cumque oporteat Aftronomorum ?

6. Haec quidem ad Angliam privatim pertinent,
illud vero ad gentes omnes, phaenomeni raritas fumma,
quae hanc vetat occadonem omittere. Id quidem
phaenomenum hue ufque a nullo unquam Ailronomo
elt obfervatum. Nam Horoccius partem vidit tan-
tummodo Sole ante finem demerfo, nec alios longe
podtos obfervatores habuit, cum quibus illam ipiam
fuae obfervationis partem conferret. Idem phaeno-
menum non nid pod: annos odto recurret, turn nun-
quam iterum per totum faeculum, eoque amplius, ha-
bebitur. Quo pauciores fefe occadones ofterunt, eo
ipfas avidius arripiendas ede nemo non videt. Sed
hifee, quae ad incitamenta pertinent, omidis, ea, quae
fpedlant ad ipfam obfervandi rationem, et loca obfer-
vationibus indituendis maxime idonea, paucis evol-
vam.

y. Omnis obfervatio in eo potifdmum ed: dta, ut
accurate determinetur momentum, quo nigricans Ve-
neris difeus lucidum Solis difeum contingit. Horum
contadtuum habentur quatuor, bini in immerdone, bini
in emerfione. Initium immerdonis et finis emerdonis

5 T 2 non

[ 87° ]

non ita accurate definiri poftunt, cum in illo incipiat,
in hoc definat excavari in Solis limbo foveola quae-
dam, quae, ubi fatis exigua eft, facile oculos vel ma-
xime diligentes fallet. Nam centrum Veneris horis
circiter 6 percurret in Sole chordam minutorum cir-
citer 1 5 diftantem a centro Solis minutis circiter
exiftente femidiametro apparenti Solis minutorum pro-
xime 1 6. Calculo inftituto, invenio Venerem debere
impendere fecunda horaria 14-j ad percurrendum in
Sole unum fecundum in diredtione ejus chordae, et in
ipfo ingreflii vel egreflii ob ejufdem chordae obliqui-
tatem, erit tardior in ratione chordae ad diametrum
Solis, adeoque acceftus per unum fecundum requiret
aliquanto etiam plus quam 18 fecunda temporis; cum-
que foveola, quae uno tantummodo fecundo intra
difcum Solis procurrat, fub fenfum cadere aut vix,
aut ne vix quidem, poliit, patet ne intra quartam qui-
dem minuti partem fperari pofte hujus initii et finis
determinationem ex oblervatione immediata. Licebit
illud initium quaerere ex chordis fegmenti obfcuri de-
terminatis per micrometrum objedtivum, ubi jam ipfa
foveola aliquanto major evaferit ; earum enim fingulae,
cum fuam fagittam determinent, deficiunt fimul par-
tem dilci Veneris immerfam, adeoque immerfionis
initium : adhuc tamen fatis vereor, ne ea etiam me-
thodo citra plurium fecundorum errorem fatis definiri
non poflit illud. primum immerfionis initium, et ille
ultimus finis emerfionis.

8. At finis immerfionis et emerfionis initium
determinari omnino pcfiunt cum evidentia fumma,
et perquam exadtifiime. Dum enim Venus in im-
merfione progreditur, et jam proxima eft immerfioni
totali, habentur ut in figura I.

Fig. I.

[ 871 ]

O

Fig. I

A.

B

A

bina in Sole veluti cornua A, et B, qua? minimo Ve-
neris motu in fine coeunt, abeunte figura prima in
fecundam, in qua quoddam luminis veluti filum in
A ingricantem Veneris rotundum difcum cingit :
contra in emerfione abrumpitur citiffime filum illud,
et fecunda figura abeunte in primam, bina ilia veluti
cornua enafcuntur. Momentum, quo ipfa cornua
coeunt, vel quo enafcuntur, ob ipfam celeritatem,
qua binte cufpides ad fe invicem vel ultimo accedunt,
vel primo recedunt, definiri poterit admodum ac-
curate.

9. Res facile patebit calculo infiituto, qui eft ad-
modum elementaris. Erit enim diameter Veneris
proxime unius minuti primi, et diftantia cornuum,
quae eft chorda communis difci Solis, et Veneris, erit
in initio et fine media proportionalis inter partem
diametri Veneris extantem extra Solis difcum, et
quadruplum refiduae partis ejufdem diametri quam-
proxime, negledla nimirum curvatura Solaris difci
tanto majoris refpe&u curvature difci Veneris, cujus
Solaris curvaturae ft habeatur ratio, adhuc major eva-
dit chorda. Inde autem eruitur illud, uno lecundo
horario, vel binis, tribus, quatuor ante finem im-
merftonis, vel poft emerlionis initium diftantias cor-
nuum A, B a fe invicem fore proxime fecundorurn
6} 7 ? crefcentes nimirum in ratione temporis

[ 872 J

fubduplicata. Porro vel ipfa prima ex biice qaatuor
diftantiis fecundorum 3.1 feledtioribus telefcopiis ad-
hibitis omnino fub fenfum cadit, fecunda fecundorum
quinque etiam communibus non prorfus ad rem in-
eptis, adeoque optimis telefcopiis intra unum etiam
fecundum, communibus intra duo, ea phaiis poterit
determinari.

10. Quod fi confideretur crafiitudo iili lucidi in A
in fig. II. ea iingulis fecundis horariis augetur per Tj
partem unius fecundi, quae ipfa in tarn vivido Solari
lumine utut repreffo a coloratis vitris, vel faltem ejus
duplum, fatis manifefto deprehendi debet.

11. Videtur igitur illud omnino fperafi pofle, ut
haec temporis momenta intra unum etiam, vel al-
terum fecundum, abfolute determinentur. Verum in
re noftra nec id ipfum necefiarium efl nifi ad ele-
menta Veneris accuratius determinanda. Ut eruatur
id, quod pertinet ad parallaxim, et diflantiam Solis
confideranda efi; fola differentia errorum, quos bini
obfervatores committent ex radiis aberrantibus, qui
inducunt procurfum cornuum, et eorum diflantiam
minuunt, vel ex tenuitate fili lucidi non fatis percel-
lente oculi aciem. At haec differentia et multo minor
efie debet errore integro, ut patet, et in immenfum
imminui potefl, fi bini obfervatores telefcopia adhi-
beant ejufdem vis diligenter inter fe invicem ante col-
lata. Ego fane nullus dubito, quin fi haec adhibeatur
induftria, pofiit errorum differentia detrudi vel infra
unium fecundum temporis, quam etiam fine ilia om-
nino arbitror, modo telefcopia fint fatis bona, ultra
duo fecunda non procurfuram.

12. Ejus rei argumentum praeter ea, quae hue
Ufque diximus, efi mihi et illud, quod eundem

2 Mercurii

I

[ 873 ]

Mercurii tranfitum Pafifiis obfervantes fimul tres vel
quatuor Aftronomi, confenferint in ejufmodi phali
obfervanda intra quinque fecunda, uti in poftremo ex
Parilienlis Academise confefiibus, quibus interfui,
enunciatum fuit fub ipfum meum difceftum. Porro
primo quidem in eo tranlitu Mercurius aliquanto mi-
norem potius habuit celeritatem in Sole, quam Ve-
nus fequenti anno habitura lit 5 deinde cum diameter
apparens Mercurii circiter fextuplo minor, quam Ve-
neris diameter, apparens lit futura, difcelTus cornuam
a fe invicem debuit efte ex eo capite minus celer in
ratione 1 ad 2-f, quam in Venere futurus lit. Quam-
obrem hie multo minus diferimen timeri poteft,
quam ibi : ibi autem nec illud quinque fecundorum
diferimen totum huic caufae tribuendum eft, fed par-
tim etiam errorcuio fortafte alicui in horologiis diri-
gendis, partim diftantiae locorum, in quibus eft ob—
fervatum : unde conftat, jure nos hie inetum diferi —
minis ex telefeopiorum errore orti deprimere infra,
duo fecunda horaria; licet nonnulli et decern, et vi-
ginti fecundorum errorem timendum cenfeant, fed3,
uti abunde demonftravimus, omnino perperam.

13. Jam vero ut ex ejufmodi obfervatione optatus
capiatur frutlus, bina ad rem idonea, et a fe fatis re—
mota, feligenda funt loca, in quibus obfervationes
ftant, quae inter fe comparentur, quod triplici ratione
fieri poteft. Prima ratio, et omnium trium maxime.
idonea, eft ea ut obfervetur utroque in loco et im—
merlio et emerlio, comparando bina tempora dura-
tionum totius phaenomeni j fecunda, ut utrobique-
obfervetur immerlio; tertia, ut emerlio utrobique ob—
fervetur, comparando in hifee poftremis binis me-
thodis horas locorum, in quibus obfervationes fant

inftitut$y.

[ 874 ]

inditutae, ac horam alterius ad alterius horam redu-
cendo.

14. Primam methodum propofuit jam olim Hal-
leyus, qui quidem calculo inito cenfuit ad rem ma-
xime idonea fore bina loca, quae ipfe felegerat, al-
terum in Septentrionali America ad Hudfoniam val-
lem, alterum in Ada Orientali circa odia Gangis,
quibus in locis differentiam durationis totius phaeno-
meni cenfuerat fore minutorum primorum 1 7, quae
cum efdciant plufquam 1000 fecundaj vel 10 fe-
cundorum error e binis obfervationibus coalefcens in
unam fummam, intra centedmam fui partem defi-
niret Solis diftantiam et parallaxim, quo quidem
errore odendimus timed vix pode errorem quintuplo
minorem.

1 j. Is quidem Solis parallaxim horizontalem af-
fumpferat aliquanto majorem, quam nunc cenfeatur,
quod illam ejus differentiam durationum auxit non-
nihilj fed id ejus methodo parum obedet. Aliud
quidpiam, quod gravioris momenti ed, humani paf-
fum dodidimum fane virum afdrmavit Ideus in
Paridends Academiae confedu, quod paullo pod etiam
typis edidit, quo quidem corredto invenitur illud, d
cum Gangis odio conferatur locus in Septentrionali
America maxime idoneus (nam is, quern ipfe Hal-
leyus ibi nominaverat, dednitis aliquanto accuratius
per hofce annos elementis theoris Veneris, reperitur
extra eos limites, intra quos hie ejufdem Veneris
trandtus apparebit) vix haberi 4 minuta ejus diferi-
niinis^ et ejus quidem erroris fe fontem etiam inve-
nide afdrmavit Ideus ejufmodi, cui fummi quoque
viri funt aliquando maxime obnoxii, fubtradtionem
nimirum binorum angulorum adhibitam pro addi-

tione 1

C 875 ]

tione : angulorum alter eft inclinatio orbita* Veneris
ad eclipticam graduum 8° 28*, alter circulatio circuli
latitudinis ad circulum declinationis 6° 10, quos,
ut Ifleus affirmat, oportuit fimul addere j ille autem
alteram ab altero fubtraxit.

1 6. Et mihi quidem ante hofce tres annos in ip-
fum difcrimen inquirenti longe alia methodo, obve-
nerat itidem difcrimen ipfum perquam exiguum.
Confiderabam enim illud, duplicem eife difcriminis
fontem, alterum ex eo, quod fi feligantur bina loca
hinc, et inde a polo diurnae vertiginis, in altero, ni-
mirum in Septentrionali America, motus diurnus de-
beat eife conformis motui Veneris, in altero ex parte
oppofita fito contrarius ; unde fit, ut caeteris paiibus
in priore loco phaenomenum diutius durare debeat,
quam in pofteriore, uti et fi binae naves in eandem pla-
gam tendant, diutius in certa parte littoris ad latus fiti
interior exteriori apparebit, breviore vero tempore, fi
ferantur in partes oppofitas : alterum difcriminis fon-
tem videbam elle viam ipfam, quae intra Solem ap-
parebit percurfa a Venere. Ea enim alteri loco eiit
a centro remotior, adeoque brevior j alteri propior, et
proinde longior. Ii bini difcriminis fontes in unuin
additi Halleyanum mihi tempus fatis proxime exhi-
bebant. Et quidem fi borealis effet Veneris latitudo,
coirent utique ii bini fontes ; nam chorda debita locis
ultra polum borealem fids centro propior appareret,
et longior j at cum Auftralis ea fit, videbam lane
contrarium evenire, et fubtradfionem binorum ter-
mi norum adhibendam, quae mihi vix tria vel qua-
tuor minuta relinqueret. Re aliquandiu perpenfa,
cum aliis turn quidem longe gravioribus curis difli-
nerer, metuerem autem, ne mihi potius admoduin
Vol. LI. S U diftrado.

[ 876 ]

diftra&o, quam tanto et Aftronomo et Geometrae
error aliquis fubrepftflet; meditationem omnem ab-
rupt quam Ifleus per otium perfecutus rem omnem
calculo pluribus vicibus repetito, et conftrudtione ad-
hibita, evolvit : et quidem eft ex ejus difcipulis, qui
Parifiis imprefterit, eum ipfum a fe de errore invento
admonitum diu obftitifte, et calculorum iterationem
praecepifte, donee et ipfe rem diligenter exquirens
idem demum deprehenderit.

17. Verum Ifleus ipfe non errorem tantummodo
invenit, fed uti diximus, et erroris fontem aperuit, et
longe moleftius, at fimul etiam longe utilius opus
aggreftus, mappam binis hemifphaeriis conftantem
delineavit, alteri fimilem, quam pro Mercurii tran-
fitu delineaverat olim, cujus exemplar, cum brevi dif-
fertatiuncula imprefla, hue ad hanc ipfam Regiam So-
eietatem tranfmiftt. In ea diverfis coloribus diftinxit
quatuor totius fuperficiei terreftris partes, in quibus
vel ingreftus tantummodo Veneris in Solem apparebit,.
vel tantum egreftus, vel uterque, vel neuter : adjecit
autem et lineas colore rubro diftineftas, quarum lin-
gulae exprimant loca omnia, quibus vel ingreftus ac-
cidet, vel egreftus eodem aliquo momento temporis,
quod Pariftenfis meridiani horis deftgnavit.

1 8. Is quidem methodum, qua ad ejufmodi deli-
neationem eft ufus, nequaquam expofuerat ante meum
difeeftum Pariftis, fed pluribus id ipfum rationibus
inftitui poteft, nee theoria eft fane diftkilis, fed
praxis admodum laboriofa, et longa. Dom. De la
Lande unam e methodis ad' rem idoneis propofuit in
poftremo ex Academiae conventibus, quibus interfui j
quam dum is in fchemate demonftraret, ego alio
evocatus fatis precipere non potui ; at rem ipfam

meditatus

[ 877 ]

meditatus invenio illud, fingulas ejufmodi lineas in
fuperficie Terrs, efle totidem interfedtiones fuper-
ficiei coni redti cujufdam, qui facile definitur, cum
ipfa Terrs fuperficie. Tres autem diverfi corti ad-
hiberi pofiunt, prout qusrantur loca, in quibus fimui
videri debeat immerfionis initium, vel emerfionis finis,
immerfio, vel emerfio centri, immerfionis finis, vel
emerfionis initium. In primo cafu angulus lateris
coni cum axe eft fumma femidiametri apparentis Solis
vifi e Venere, et Veneris vifs e Sole, in fecundo fola
femidiameter Solis, in tertio earum femidiametrorum
differentia j vertex autem omnium eft in redta jun-
gente centra Solis et Veneris, fed in fecundo cafu in
ipfo Veneris centro, in primo citra centrum Veneris
Solem verfus, in tertio ultra ipfum Veneris centrum
ita, ut ejus diftantia ab ipfo centro Veneris ad diftan-
tiam a centro Solis fit in utroque ex hifce poftremis
cafibus in ratione femidiametri vers Veneris ad femi-
diametrum veram Solis.

19. Ex hoc theoremate, data Veneris pofitione ad
datum tempus, accuratifiime ea omnia definiri pof-
funt j fed ad ejufmodi mappam delineandam, qus rei
fummam quandam unico obtutu confpiciendam ex-
hibeat, fatis eft unum ex ejufmodi conis confiderare ;
quin immo fatis eft ejus fuperficiei partem admodum
exiguam in fuperficiem Terrs incurrentem, et parum
admodum inclinatam ad difcum e Sole vifum afiu-
mere pro piano perpendiculari ipfi difco, cujus inter-
fedtio cum hemifphsrio fuperficiei terreftris affumpts
pro fphsrica obverfo Soli erit femicirculus ipfi difco
perpendiculars, et fedtio cum ipfo difco linea recta.
Circulars enim fedtio ejus coni cum piano difci Terrs
comparata eft multo major ipfo difco. Facile invenio

jU 7, illud :

[ 8y8 ]

illud : ft ab angulo lupra definito lateris coni cum
axe auferatur femidiameter apparens Solis vifi e
Terra, refiduum fore femidiametrum ejus circuli vi-
fam e Sole, quae proinde erit ad femidiametrum
Terras, ut eft numerus ex ilia iubtradtione proveniens
ad parallaxim horizontalem Solis, quae ratio evadet
circiter 40 ad 1, ft ea parallaxis aftumatur circiter
fecundorum 10.

20. Inde autem fit, ut delineatis in terreftri difco
meriaianorum et parallelorum projedtionibus ea ra-
tione, quae in Luns eclipfibus adhiberi folet, admo-
dum facile determinentur loca omnia ad fingulas ejuf-
inodi lineas pertinentiaj et multo facilius in globo
res perfici poflit, invento prius pro fingulis femicir-
culis et polo eorum, et diftantia a polo iplo, quo padto
unico circini dudtu res omnis perficitur. At pro locis,
in quibus ingreflus Veneris vel egrefifus habetur, Sole
in horizonte fito, fatis erit aflumere circulos Terrae
maximos, qui difcum terminant e Sole vifum mo-
mento temporis, quo e centro Terrae loca ingreflus
centri, vel egreflus videretur, quae momenta paucis
tantummodo minutis difterunt ab iis, quibus alia
Terrae loca ingrefium vel egreflum videre debent,
adeoque illi circuli rem fatis pro hoc conftrudtionum
genere accurate determinant. Iidem autem Telluris
ftiperficiem in illas quatuor partes dividunt, quas
iupra expofuimus, quas nimirum videre pofl'unt vel
alterum, vel utrumque, vel neutrum ex iis phaeno-
mems. Sed haec omnia fufiore geometrica illuftratione
indigerent, ubi et operationum compendia fane multa
haberi facile poftunt.

2 1* Ifleus quidem nec elementa motuum Veneris,
quibus eft ulus, adhuc, quod ego fciam, ufpiam

expofuit j.

C 879 1

expofuitj fed illud pro certo habeo, tabulas ab ipfo
effe adhibitas optimae notas, quas adhuc per feledtas
recentiores obfervationes correxerit. Ipfa quidem
elementa, et potiffimum hujufce nodi pofitio non ita.
certa funt adhuc, ut omnimodus expedtari debeat
totalis hujus ipfius delineationis confenfus cum ob-
fervatione ineunda, pofito etiam, quod horizontalis
parallaxis Solis fit ea ipfa, quam Ifleus affumpfit, fed
ita parum a vero aberrare poteft, ut, quod pertinet
ad deledtum locorum inftituendis obfervationibus ido-
neorum, et frustum, qui ex iis fperari poflit, quae-
cumque e tribus fupra propofitis comparationum ra-
tionibus adbibeatur, tuto illi fidere liceat. Ad paral-
laxim ipfam accurate determinandam oportebit ex
ipfis obfervationibus hujufce tranfitus corrigere ele-
menta omnia motuum Veneris circa hunc nodum, et
inde accurato calculo inftituto pro iis ipfis locis, in
quibus obfervatum fuerit, inquirere differentiam tem-
porum iis debitam in hypothefi parallaxeos folaris ad
calculum ineundum adhibitas, quas ad inventam per
obfervationes erit quamproxime in ratione reciproca
differentiae temporis calculo erutae ad differentiam ob-
fervationibus definitam, fiquidem difcrimen earum.
differentiarum exiguum fuerit, uti eft admodum pro-
babile 5 fecus vero ope parallaxeos primo corre&as
reftituto calculo, brevi poterit per feriem admodum
convergentem ad verum ipfius parallaxeos valorem
deveniri.

21. Unum illud ad Iflei mappam pertinens hie
omnino addendum eft, ejus imprefiionem binis fieri
cupris, quorum altero Terras loca nigro colore expri-
mantur, altero lineae ad Veneris tranfitum pertinentes
colore rubro. In pluribus ex exemplaribus imprefiis

non

[ 88o ]

11 on ita diligenter lecundo cupro iderfi chart® folium
efl: impofitum, ut rite omnia congruant, quod qui-
dem ipfi exemplari contigit ad Regiam Societatem
trail fmi ifo, in quo idcirco nonnullis eft vifus ipfius
delineationis error graduum io. At figna quaedam
adfunt in ipfis exemplaribus, per qu® ipfe error de-
prehendi, et corrigi utcumque poftit, et in exemplari,
quod ego ad Societatis praefidem detuli, ita amb®
impreffiones congruunt, ut vix ullus ejufmodi error
fuperfit, nec is generalem rei ideam, quam hie quae-
rim us, quidquam perturbat.

23. Ut vero ex hac ipfa mappa jam inquiramus
in loca tribus illis comparationum methodis idonea,
illud occurrit in primis admodum facile percipien-
dum, primam methodum, quae adhibet durationem
totius phaenomeni, reliquis binis effe multo aptiorem.
Nam in ea multo minus accurate neceftarium eft
node binorum locorum longitudines. Sub eodem
Capricorni Tropico a longitudine graduum ad
longitudinem 130 ubique totius ph®nomeni duratio
ita evadit horarum 6, ut non nifi aliquo fecundorum
numero inde difeedat. Quamobrem error fatis in-
gens in longitudine locorum determinanda nihil ad
fenfum perquifitionem perturbat. Secus evenit in re-
liquis binis, in quibus comparantur inter fe bina tem-
pora immerfionum, vel emerlionum, in quibus ubi
alterum ad alterum reducitur, ad habendam differen-
tiam temporis, quidquid erratur in definienda dif-
ferentia longitudinum binorum locorum, erratur iti-
dem in ilia quasfita differentia temporum, per quam
deinde Solis parallaxis eft definienda. Porro longi-
tudinum differentia multo difficilius accurate dehni-
tur, quanquam illud commode accidit, quod ubi
7 femel

[ 88i ]

femel fatis accurate inftituta fuerit in binis locis ob-
fervatio immerftonis, vel emerlionis Veneris, differen-
tia longitudinum poterit deinde per obfervationes,
quotiefcunque libuerit, repetitas inveffigari.

24. Ut autem ex ipfa mappa definiantur loca ad
hanc obiervationem maxime idonea, pro prima me-
thodo feligenda funt ea loca, in quibus duratio pha3-
nomeni eft maxima, et minima; pro fecunda, et tertia
feligenda funt loca, in quibus immerfto, vel emerfio
accidet celerrime, et tardiffime • verum ejufmodi loca
funt feligenda, ad quae accedi poflit, ut in iis fatis
commode liceat inftituere obfervationem.

25. Durationem omnium breviffimam invenio-
prope Tobolfkam in Siberia, ubi, negledtis fecundis,,
eft proxime horarum 5-, 58'; eft autem Petropoli, et
Pekin i jh 55/. Berolini 61* o'. Longiffirnam omnium
circa auftralem incognitam plagam in longitudine
1 1 o° circiter, ac latitudine 6o°, ubi eft proxime

13'. Si eo adire liceret, haberetur difcrimen cum
Tobolika minutorum fere 13; fed ea regio adiri uti--
que non poteft. Sunt loca in Nova Hollandia ad
maris littus, ubi duratio eft 6^ 6', quod adhuc exhi-
bet cum Tobolfka differentiam minutorum 8, fed
nulla eft fpes eo appellendi. E locis, quas fpem ali—
quanto majorem appulfus exhibeant, Batavia praebet
durationem 4', quod pro differentia exhibet cum
Tobolfka minuta 6, et 5 cum Petropoli, et Pekino,
quibus in locis obfervationes exadtae intra duo, vel
tria fecunda adhuc exhiberent diftantiam Solis, et pa-
rallaxim intra centefimam fui partem accuratas.

26. Immerfto omnium citiftime videri incipiet
circa Tropicum Capricorni in longitudine 235 0 in.
Mari Paciftco hora 2 4° > omnium autem locorum

maxime

[ 882 ]

maxime fero prope Cyprum infulam hoi a 2 57 >
duo loca differential!! exhiberent minutoram 17. In
ea error decern etiam fecundorum adhuc relinqueret
Solis parallaxim et diftantiam definitas intra centeft-
mam fui partem. Et in Cypro quidem obfervatio
admodum facile inftitui poteft, ac erat, uti mcnui, in
Gallia, qui profedionem meditaretur; verum plura
alia ex eadem parte funt loca fere aeque apta, in
quibus obfervationes non deerunt. Adero ego Con-
ffantinopoli, ubi habetur hora 6 f 6 • Habentur Be-
rolini minuta plufquam 55, Stokholmiae, et Petropoli
fere accurate is numerus, Tobolfkae 54 -L <lu^us

locis omnibus obiervatores utique habebuntur. At
alter locus Mari Pacifico fitus non nift infulas habet
omnino defertas longiffime a Continenti Americas fitas
ad diftantiam graduum plufquam 60. Is, qui ali-
quant© facilius id commodi Aftronomiae procurare
poffet, eft, ut arbitror, folus Hifpaniae Rex, qui qui-
dem Ulloam Aftronomum egregium, et Quitenfibus
obfervationibus celeberrimum, nunc habet in Peruvia,
unde in aliquam ex iis infulis navigare poftet, et ac-
curatam obfervationem inftituere, line qua quidqui
Petropoli, Stokbolmiae, Berolini, Conftantinopoli, in
Cypro infulo fiet, erit omnino irritum, et fine ej ul-
modi obfervatione nihil omnino deduci potent le-
cunda hac methodo, ut prima etiam methodus fine
Batavica obfervatione eft ferme prorfus inutilis.

27. Relinquitur methodus tertia, quae ad emertio-
nem pertinet. Loca, in quibus ea primo apparent, lunt
paullo ultra Kamtchkatkam ad extremes Orientals
Aftae fines, ubi id phaenomenum accidet hora o 1 49 ,
loca, in quibus poftremo videri defmet, funt in ip a
incognita Auftrali plaga circa primi Meridiam lamu-

[ 883 ]

dinem graduum 45% ubi definet hora p 6', differen-
tia exiftente iterum 17 minutorum, ut in methodo
iecunda. Sed licet eo deveniri non poflit, adeft in-
fula S. Helens aptiflima fane, in qua id accidit fere
ph 44', et linea, qua? exhibet 9h 4' tranfit prope Fer-
nambucum in Orientali Brafiliae ora fitum, fere per-
vadit extremam ultimas meridionalis Africas oram,
ac tranlit per ipfum caput Bonae Spei, quae idcirco
loca omnia, fi cum Kamchkatka conferantur, exhi-
bent plus, quam 14 minuta difcriminis. Verum cum
habeatur finis Pekini hora fere 8 fi', Tobolfkae 52^ ,
Petropoli 54', Berolini 55', Londini 56', Conftanti-
nopoli 56% ; obfervatio habita in infula S. Helens
cum hifce locis collata exhibet differ entiam majorem
minutis 13, 12, 10, 9, 8-j, 8, quarum priores ad
rem maxime idoneae funt, penultima etiam admodum
opportuna, fi illud confideretur, plures Londini ob-
fervationes futuras, et quidem omnino accuratifli-
mas.

28. Triplex autem generatim haberi potefl: errorum
fons j primus in dirigendo horologio, vel horologii ip-
fius aequabilitate; fecundus in determinando momento
immerfionis, vel emerfionis ; tertius in determinanda
pofitione loci, in quo obfervatio ipfa inftitutur. Ex
primo capite non video, quid timeri poflit, cum intra
eundem diem communia etiam horologia ofcillatoria,
fi bona fint, aequabilitatem retinere foleant potiflimum
circa Solftitia, circa quae minus varia Coeli conftitutio
eflfe folet, et per altitudines correfpondentes Solis et
fixarum repetitas horologium fatis facile ita derigatur,
ut ne unius quidem fecundi error inde timeri poflit.
Saltern adhibitis horologiis accuratiflitnis, et peculiari

Vol, LI. 5X diligentia

[ 884 ]

diligentia in obfervando, omnis error inde oriundus
evitari commode potefl.

ap. Ex fecundo capite juxta ea, quae initio diximus,
major quam duorum fecundorum error meo quidem
judicio in lingulis obfervationilpus timeri omnino non
potefl ; quin immo infra unicum etiam fecundum de-
primi potefl adhibitis telefcopiis ejufdem vis. Quam-
obrem, ii haec adhibeatur diligentia, in cafu maxime
infaufto, in quo bini errores fe mutuo nequaquam
corrigunt, nonnifi duorum fecundorum error timeri
poteft.

30. Et hi quidem foli funt errores, qui in prim a'
methodo timeri poflint, licet duplicandi ibi fint id-
circo, quod et immerfionis et emerhonis obferva-
tionem ea methodus requirat, at pro reliquis viden-
dum prasterea, quid timeri poffit, in determinanda
politione locorum, in quibus obl'ervationes inftituun-
tur. Determinatio latitudinis loci nec requiritur ad-
modum accurata, et admodum facile accuratiflima
obtinetur per culminantium fixarum altitudines, po-
tiflimum fi aliquanto majoris radii quadrantes adhi-
beantur. Longitudinum determinatio eft aliquanto
difficilior. Earn per eclipfes fatellitum Jovis, non
credo, obtineri pofi'e fine periculo erroris plurium fe-
cundorum j. adhuc tamen, fi telefcopia adbibeantur
ejufdem vis, et piures ejufmodi obfervationes inffitu-
antur, credo utique intra fex horaria fecunda poffc
etiam per ipfas differentiam longitudinum definiri.
Verum fi occurrant fixarum occultationes per Lunam,
vel alfumantur per egregium objedtivum micrometrum
piures diflantiae Lunse, a fixis cognitis, iifdem autem
diebus accurate alicubi, ut Londini, et tariffs, ob-
fervetur et tranfitus Lunas per meridianum, et dia-
meter

[ 88S ]

meter apparens Lunge, a qua pendet parallaxis quo-
que, credo utique, intra quatuor etiam horaria fe-
cunda, ingenti habito obfervationum numero, rem
poffe concludi.

3 i. Hinc eruitur pro primo metbodo fperari poffe
determinationem intra quatuor, vel etiam duo fe-
cunda, pro reliquis binis intra fex, vel quinque, at-
que id etiam, fi, quod fere nunquam evenit, erroies
omnes in unam fummam coalefcant, Quare fi in
prima methodo habeatur obfervatio inftituta To-
bolfkae, et in Nova Hollandia, ubi vidimus differen-
tiam expedtari minutorum 8, fperari poteft determi-
natio parallaxeos intra centefimam vigefimam, vel du-
centifimam quadragefimam partem totius ; fi autem
babeatur obfervatio Tobolfkas, et Bataviae, ubi. dif-
ferentia expedtatur minutorum fex, poffe fperari de-
terminationem intra nonagefimam, vel centefimam
odtogefimam partem totius.

32. Pro fecunda methodo, fi habeatur obfervatio
ilia in infulis Maris Pacifici circa loca, quae fupra vi-
dimus, licet, ut recedatur a limitibus, quibus exiguo
calculi errore loco motis, fruftrari poteft obferva-
torem fua fpes, amittatur unum minutum in tem-
pore, ac ea obfervatio conferatur cum obfervationibus
ibidem nominatis, Cypria, Conffantinopobtana, Be-
rolinenfi, Petropolitana, Stokholmienfi, Tobolfkaaana,
ubi differentia haberi debet minutorum 16, if, i4>
1 3-i, admiffa etiam errorum fumma fecundorum 6,
haberi poteft determinatio intra partem centefimam
fexagefimam, vel centefimam quinquagenmam, quau-
ragefimam, trigefimam quintam totius.

33. Pro tertia methodo idem fere frudtus fperari
poteft, fi obfervatio inftituatur in infula S. Helenas,

5X2 vel

[ 886 ]

vel Fernambuci in Brafilia, vel Occidentalem Africa?
oram, uti ex iis, quae fupra diximus patet. Obfer-
vatio autem habita in infula S. Helenas, et comparata
cum Londinenfi, et Conftantinopolitana exhibentibus
differentiam minutorum 8£, et 8, promittunt determi-
nationem intra odtogelimam quintam, et odogefimam
partem totius.

34. Binse quidem tantummodo obfervationes ac-
curatas, et inftitutae in locis fatis idoneis, rem omnino
conficiunt, at plura funt, quas jubeant plures hac iliac
obfervatores dimittere; primo enim collatis pluribus
obfervationibus inter fe, apparebit, intra quos li mites
certi effe poffimus de parallaxi Solis eruta, videndo,
quantum ejufmodi determinationes a fe invicem di-
ftent, ac aflumendo medium certiores erimus, et vero
valori propriores: tanti utem momenti eft id, quod
hie quaeritur, ut nihil, quod ad majorem accura-
tionem, et certitudinem conferre pofiit, omitti de-
beat. Deinde cavendum, ne nubes afpedtum pr$-
ripiant, quod quidem nequaquam accidet, fi multi
obfervatores in locis fuerint admodum diverfis. Et
hinc ego quidem cum in meo poemate de eclipfibus
agerem ante hos odto annos de hoc ipfo Veneris fub
Sole tranfitu, et Halleyanam refpicerem methodum,
illud adjeci.

Credo equidem denfas circum fe quaque cohortes
Effundent late terris, quaque horrida trifti
Squalet humus glacie, quaque uftis ardet arenis,

Nec tantas imo nubes alit fEolus antro,

Ventorumque ciet gens improba, pofiit ut omnes
Obruere aerios tradus, atque omnibus axem
iEtherium velare locis, et condere Divam.

1

Fors

[ 887 ]

Fors et ego Irroquium fedes, et inhofpita regna,

Si tantum fortuna finet, fi vita fuperftes,

(Quid namque hs vires, quid non hsc fpondeat stas,
Dum vix ter quartus ter denis additur annis ?)
Tranfcurram procul et dodtis comes ibo catervis.

Spero equidem, nec me pontus turgentibus undis
Audentem terret, glaciefque nivefque perennes.

35. Et ego quidem commutata nunc obfervatio-
num ineundarum ratione non in American! Septen-
trionalem, fed Conftantinopolim abibo, ubi obferva-
tionem inftituam cum iis inftrumentis, quas mihi
prsfto erunt, non quidem optima, quas maxi me cu-
perem, fed ad rem utcumque perficiendam idonea :
labori certe et diligentis non parcam. Et ea qui-
dem obfervatio maximum fecunda methodo habebit
ufum, fi habeatur obfervator aliquis in iis, quas in-
nuimus, Maris Pacifici infulis ; aliquem autem adhuc
non contemnendum in tertia methodo, ii habeatur
obfervator aliquis in infula S. Helens, vel in ora Oc-
cidental! Meridionalis Africas partis, vel Fernambuci
in Brafilia.

36. Quid autem Anglicana natio, et Regia potif-
fimum Londinenfis Societas, prsftare poffit, fatis con^
Rat ex iis, qus diximus. Maxime omnium videtur
defideranda expeditio in infulam S. Helens, ex qua
habebitur optatus frudtus tertia methodo. Verum fi
smuls nationi Gallics nolit palmam concedere in no-
biliffima facultate promovenda, opus eft plures obfer-
vatores dimittat in plures plagas, et ad alias obferva-
tiones obtinendas alibi fua ofticia interponat.

. 37. Pro ipfa tertia methodo poteft utique curare

bina obfervationum binaria facienda cum inftrumentis

egregiis.

[ 838 ]

egregiis, et inter fe coilatis. Ex altera parte prater
obfervationem in infula S. Helenas, dimittendus cffet
aliquis alius vel illam Africa? oram maritimam, vel
cum bona Lufitani Regis gratia Fernambucum : ex
altera parte habebit omnino Societas obfervationes fuas
Londinenfes.

38. Quoniam tanti a fecunda, et prima metbodo
fructus jure lperantur, poffet utique Regalis Societas
ad Legatum Anglicum Matritenfem literas dare, ut
Regem per fe etiam amantiffimum et bonarnm ar-
tium et fcientiarum omnium, luo nomine impelleret
ad pracipiendam Ulloa? obfervationem illam in Mari
Pacifico, deftinata ad ilium mature tranfvehendum
navi, quod quidem aulae Hifpanicae elfet admodum
facile, Literarias autern Reip. exoptatiffimum. Poffet
et ab Hollandis obfervationem expetere, vel in Nova
Hollandia, vel Batavia? peragendam, vel etiam ali-
quem e fuis eo deftinare, petita ab Hollandis facilitate.
Eo pado Gallos in hanc occalionem intentos vinceret
Anglia, ac ipli Literarius orbis dcberet exoptatifli-
mam determ inationem omnibus tribus methodis fac-
tam. Pudebit fane fuorum avorum nepotes venturo
fasculo, li tantam et adeo raram opportunitatem
negledam viderint, et cum ingenti Aftronomiae
damno pratermiflam eo potidimum tempore, quo
maritimi fuccedus maritimas expeditiones etiam li-
terarias ufque adeo faciliores reddiderant, et omnino
expofcebant.

In lignum animi addididimi

et obfequentidimi,

Rogerius Jofeph Bofcovich, S. I.

LXXVIII. A

[ 889 ]

LXXVIII. A Propofal for difcovering the
Annual Parallax of Sirius ; by the Rev.
Nevil Mafkelyne, A. M. Fellow of Tri-
nity College , Cambridge, and F. R. S .

Read June 26, F W' ^ HE Royal Society having come to
3 a refolution to fend perfons of abi-
lity to proper places, in order to obferve the ap-
proaching paffage of Venus over the Sun, the 6th of
June next year 5 (which phenomenon was firfl pro-
pofed to this Society, by the late excellent Dr. Hal-
ley, forty-four years ago, as a proper means of de-
termining the Sun’s parallax, to a great degree of
exadnefs) I take this opportunity of recommending
to the confideration of this learned body another
very important objed in aftronomy, which, I appre-
hend, may be cleared up at the fame time, by the
aftronomers fent to one of thofe places, which will
probably be judged convenient for the obfervation of
Venus’s tranfit; I mean the ifland of St. Helena.

The aftronomical objed, in favour of which I de-
fire to engage your attention, is no lefs than the de-
termination of the annual parallax of the Orbis
Magnus j the finding out of which, from obferva-
tion, would be the fulled and diredeft proof of the
Copernican fyfiem, as the want of this proof, hi-
therto, has been the ftronged argument made ufe of
by thofe, who have with-held their affent to an hy-
pothefis, which fo fully, and yet fimply, fatisfies all
the other phenomena.

No

[ 8go ]

No one, indeed, at this time of day, will ven-
ture to aflert, that, even if no annual parallax
could be found, after the greateft exertion of human
art and industry, the Copernican fyftem was not,
therefore, true; fince the quantity of this paiallax
may be fo fmall, as to efcape the reach of oui light,
though aflifted to the utmoft. But though the de-
fed: of it would be no juft argument againft the Co-
pernican fyftem, yet the aCtual demonftration of it,
from obfervation, would be a direCt and convincing

proof of the truth of that fyftem.

It remains then to be conlidered, what hope there
is now left, after aftronomy has been brought to fuch
a great degree of perfection, of being able to lind out
an annual parallax in any of the fixed ftars.

I am fenfible I may here feem to be prefumptuous,
in venturing to treat upon this fubjeCt, after the many
accurate obfervations made by the learned Dr. Brad-
ley, with an inftrument conftruded for this veiy
purpofe. No one can have a higher veneration than
I have for the difcernment and exadnefs of this il-
luftrious aftronomer, whofe merit I have the greater
opportunity of being acquainted with, by having the
honour of calling him my friend. I would juft beg
leave to take notice, that the ftars, which this aftio-
nomer obferved, were fuch only as lay within a few
decrees of his zenith : and though his obfervations
do^not feem to Ihew a fenfible parallax in any of
them, yet we cannot thence abfolutely conclude, that,
amongft the great number of vifiblc ftars, there are
none in which it may be perceptible, till they have a
of them, efpecially thofe of the greateft luftre, been
obferved in proper places, near the zenith, with the

[ §91 3

like care and accuracy, which he has uied : for, as
Dr. Bradley has himfelf remarked,, where any Bars
are remote from the zenith, the uncertainties of re-
fraction, and the irregular motions of the air, become
fo great, as to take away from us all hopes of ob-
ferving them to an equal degree of exadtnels.

The particular Bar, which, I propofe, ihould be
carefully obferved, with a view of difcovering its an-
nual parallax, if fenfible, is Sirius, the brighteB of
all the Bars in the firmament, and which is there-
fore, probably, the nearefi to us of them all. With
us, this Bar pafifes the meridian, at the altitude of
a 2°, where the refractions are too irregular to admit
of our difcovering a very minute quantity, by obfer-
vation : but, at the ifland of St. Helena, Sirius pafifes
only half a degree fouth of the zenith ; and, on this
account, I have, for fome time, looked upon that as
the moB proper place to make obfervations at, for

this purpofe.

I fhall now beg leave, with great deference, to lay
before you a particular argument, which has, for
thefe two years, induced me to think it piobable,
that the annual parallax of Sirius is not fo fmall, as
to elude the nice difcernment of our modern aBro-
nomers ; and (hall be glad to be determined by your
opinion, whether it affords a fufiicient prefumption
to us, to undertake a careful and affiduous feries of
obfervations of the diBances of Sinus, fiom the
zenith of the ifland of St. Helena. _ This argument
is drawn from an examination, which I have made,
of the obfervations of the zenith diBances of Sirius,
taken at the cape of Good Hope, in the years 175*
and 1 75a, by that excellent aflronomer, and diligent
Vol. LI. 5y obferver,

[ 892 ]

obferver, the Abbe de la Caille, recited in his Fun-
d-amenta Aftronomire, printed about two years fince,
wherein alfo are contained all the obfervations, which
he has taken of the principal fixed fiars; a work
truly worthy of its name ! Every particular obfer-
vation of the fame fiar is reduced to one epoch, that
of the beginning of the year 17 50, by applying the
equations of aberration, precefiion, and deviation, to
the obferved places ; fo that the places corredted
ought all to agree together, if the obfervations were
perfectly exadt, and the fiar was affedted with no
fenfible motion, that was unaccounted for. Being
fatisfied with the excellence of the obfervations, I
was tempted to examine thofe of fome of the princi-
pal fixed fiars, in hopes of difcovering fome fenfible
differences in the obfervations made at different times
of the year, when a parallax, if there had been any,
would have had the greateft effedt. But I found very
few fiars, the obfervations of which were fufficient
in number, or taken at proper feafons of the year,
to give room for any inference at all. Fortunately,
however, the obfervations of the zenith diftances of
Sirius were more in number, and, what is ftill of
more confequence, in this cafe, made in various, and
fome in oppofite feafons of the year : and, upon look-
ing them over, I was agreeably furprized to find a
very fenfible difference in the obfervations made at
different times, agreeing in diredtion with what a
parallax ought to produce, the zenith difiance of Si-
rius in July coming out no lefs than 8" greater than in
the oppofite feafon of the year, namely in December
and January: the zenith difiance alfo in March and

[ «93 ]

April being of an intermediate quantity, as it ought
to be : for, Sirius being in conjunction with the Sun
in June and July, it is evident he muft be then far-
ther from the Earth than in December and January,
when he is in oppofition to the Sun, and, confe-
quently, his latitude and declination, which are both
fouth, muft be lefs in the former cafe, than in the
latter ; and therefore, as he paffes north of the zenith
at the cape of Good Hope, his zenith diftance muft
be greater in the former feafon, than in the latter, as
the&obfervations indicate: but, in March and April,
when Sirius is in quadrature with the Sun, and equally
diftant from the Sun and Earth, his apparent latitude
and zenith diftance muft be the fame as the true, or
that which would obtain, if the Earth was tranflated
to the Sun, and confequently, a mean between the
zenith diftances in July and December, agreeably to
the obfervations.

I fhall now lay before you the obfervations them-
felves, together with the calculations, which I have
made’of the values of the parallax for each, the ma-
ximum being ailumed q , which I find will beft re-
concile the obfervations with one another.

5 Y 2

1751.

[ «94 ]

Zenith diftancc
of Sirius at Cape,
obfcrved and re-
duced.

Annual
parallax
to reduce
obfervat.
to mean.

Zenith diftance
corrected for an-
nual parallax.

Difference between
each obfervation cor-
related, and the mean
of the diftances cor«
redted.

Of//

II

r 75r- July 12.

17 31 19. 1

- 4-3

17 31 14.8

- 1. 1

J^y 13-

17 31 J9-3

— 4-3

I7 31 I5.O

- 0.9

July 14.

21.7

— 4-3

174

4- 1.5

.My 15-

19.7

- 4-3

154

- 0.5

July 16.

19.0

— 4*3

I4.7

- 1.2

1752. April 5.

16.7

— 1.0

I5-7

— 0.2

April 3.

J5-7

— 0.8

14.9

- 1.0

March 28.

14.0

— 0.4

13.6

- 2<3

March 14.

13 1

4* 0.7

,3.8

- 2.1

March 8.

15.2

4- 1.2

16.4

h °*5

March 5.

18.8

-f- 1.4

20.2

b 4-3

March 4.

*7-3

+ i-5

18.8

- 2.9

March 1 .

15-9

-4- 1.6

17-5

- 1.6

Feb. 17.

12.8

-j- 2.6

15.4

- 0.5

Jan. 21.

11. 1

-f- 4-0

J5-i

- 0.8

1751. Dec. 31.

"•6i

4- 4-5

16.1

-}- 0.2

Mean of zenith diftances corrected ? _ „
for parallax - - - - - *7 31 15,9

The firft column fhews the year and day of the
obfervations j the fecond the zenith diftances of Si-
rius at the cape of Good Hope, as delivered in Abbe
de la Caille’s recital ; the third contains the computed
values of the parallax at different times, taking that
of the maximum 9" j the fourth column gives
obfervations reduced to the mean, by applying
the parallax computed in the third column to the
obfervations in the fecond j which quantities ought
all to agree together, if the obfervations were liable
to no error, and the parallax was rightly aftumed :
but, taking a mean of them all, the laft column
fhews how much each of them differs from that

mean.

C 895 ]

mean, which, in general, is very frnall, and fcarce
exceeds a'f, except in two obfervations, in one of
which it amounts to 3", and the other to 4 : but
thefe differ as much from the mean of the fix otheL
obfervations made at the fame feafon of the yeai .
Thus, affirming a parallax, the obfervations will be
found to agree as well with that fuppofition, as the\
do with one another. But if the obfervations aie con-
fidered in themfelves, without any allowance foi pa-
rallax, they will differ fenfibly from one another :
nor is this difference to be found only in two obler-
vations, in which cafe, it may eafily be attiibuted to
the account of the unavoidable errors; but five ob-
fervations in July oppofed to two in Decembei and
January, make the zenith diftances vary S in the

direction, which a parallax ought to produce.

I am aware, that it may be objected, that two obfei-
vations made in the winter feaion in Decembei and
January, at one of the maxima of the paiallax, aie
too few to determine a point of fuch confequence, and
readily agree, that the argument is weakened in pro-
portion to the paucity of the obiervations : but then,
ft fhould alfo be confidered, that the obfervations
made in March and April concur with the reft in
fupporting the fuppofition of a parallax ; and, upon
the whole, the obfervations will, perhaps, be judged
to afford a fufficient preemption of the exiftence of
a parallax, to encourage the undertaking a careful
trial. It is upon the ftrength of this prefumption,
principally, that I have ventured to lay thefe thoughts
before the Royal Society, whole members may juftly
claim the honour of having made the gieateft at-
tempts towards demonftrating this impoitant, b..i

yet undetermined point in aftronomy.

J RXA IX 0. tor-'

[ 896 ]

LXXIX. Farther Experiments in Electricity ;
hy Mr. Benjamin Wilfon, F. R . S.

To the Right Honourable the Earl of Macclesfield,
P ref dent of the Royal Society.

My Lord,

Read Nov. 13, TN my letter upon the Tourmalin, which
I76°’ X I had the honour of communicating
to the Royal Society in December laft, there are fome
experiments to fhew, that glafs is permeable by elec-
tricity. I have fince made others of the like kind,
which feem to favour the fame opinion.

The high regard your Lordfhip has always fhewn
for experimental philofophy, encourages me to lay
before you thefe experiments, with a few others,
of a very curious nature.

But I beg leave, firft, to take notice, that our
ele&rical apparatus is much improved, by the dis-
covery of Father Windelinus Ammerfm , of Switzer-
land, who, in a Latin treatife publifhed in 175-4, has
fhewn us, that wood , properly dried, till it becomes
very brown, is a non-conduCtor of electricity and
recommends boiling the wood in linfeed oil, or
covering it all over with varnifh, after being dried,
to prevent any return of moifture into its pores. He

* It appears, from the Philofophical Franfaftions, fo early as
the year 1747, that Dr. IVatfon having occafion to fupport a long
wire, in the experiment made near Shooter’s Hill, with a view to
determine the velocity of the electric fluid, ufed flakes of dry wood,
(which, he tells me, were baked ) to prevent the eleClric fluid fioin
efcaping into the ground.

adds,

[ 897 ]

adds, that wood fo treated feems to afford ffronger
appearances than even glafs *.

The following experiments were made, with the
affiftance of wood thus prepared.

Being provided with a large fquare of glals, poliflied
on both fides, and fixed upright upon one edge, I
placed, for a conductor, a {lender piece of ivory,
about one foot long, having one end within two
tenths of an inch from the center of the glafs: at
the other end were fufpended two fmall balls of
pith, by threads four inches long. The ivory was
Supported horizontally by a ftand made of the pre-
pared wood. When the glafs was made a little warmer
than the external air, my finger rubbed that fide
thereof which was fartheff from, and oppofite to, the
ivory. Upon doing this, the two fides of the glafs
were electrified plus , as were likewife the balls ; which
continued plus , even after they were removed from
the glafs into any part of the room.

From the appearance of a plus electricity in the
ivory, as well as on the two fides of the glafs, the
fluid muff have flowed from the finger into the glafs,
and part of it into the ivory : otherwife, permit me
to afk how the ivory fhould be electrified plus f

That the fluid really flowed from the finger into
the glafs, may be inferred from the following expe-
riment.

A piece of filver, being fixed upon a flender rod of
prepared wood, I rubbed the fame glafs with it, as
I had done before with the finger upon which the

* See the Abbe Nollet’s Letters upon EleCkicity, published at
Paris in 1760.

j filver

[ s98 3

filvcr was eledrified minus , and both fides of the
glafs, with the conductor and balls, plus.

There are, therefore, certain circumftances under
which the eledric fluid paffes through glafs ; I repeat
in certain cir cum fiances, my Lord, becaufe in others,
for inftance, the Leyden bottle , the fluid does not pafs
through the glals, but electrifies one fide plus , and
the other fide minus , as my friend Dr. Franklin
hath fhewn, in his letters upon electricity.

This difference, which is caufed by the vitreous
eleCtricity in both cales, may perhaps be explained
from the furrounding medium *, and the different de-
grees of the power with which the eleCtric fluid en-
deavours to enter a bodv.

For the rejifiance owing to the furrounding me-
dium in a polifhed plane, without covering, is not
overcome, but by bringing the power neat the glafs,
whereby the glafs is eleCtrified plus on both tides ;
whereas, when the glafs is properly cove ? ed, and the
power brought upon, it, the covering conduds the
fluid equally to all the parts on that fide, where it
accumulates, that is, eledrifies it plus ; whilft the op-
pofite covering carries off to the communicating earth
an equal quantity of the fluid naturally belonging to
the glafs, that is, eledrifies it minus. .

The fame glafs, without any covering, will be ren-
dered minus on both fides, by removing the power to
a greater diflance, by which it is diminifhed, and the
quantity of intermediate air, and confequently of re-
jifiance, increafed.

* See the former paper upon
Volume, Part I.

the Tourmalin, p. 329. of this

The

[ 899 3

The power therefore which caufes the minus effect,
is lefs than the power which caufes the plus effect :
and that this minus effeCt arifes intirely from the re-
pulfve power of the fluid, appears from this, that
part of the fluid naturally belonging to the glafs, is
driven off, and electrifies plus other bodies placed
beyond it.

From hence I col left, that the three different ef-
fects, viz. the electrifying glafs plus on both fides ;
or plus on one fide , and minus on the other ; or,
laftly, minus on both fides j are occafioned by the
different degrees of the fame power and refinance in
the refpeCtive experiments with the fame glafs.

If, on the other hand, the three laft experiments
are made with the minus , inftead of the plus electri-
city, the appearances, and confequently the reafon-
ing upon them, are inverted : for the phis appearance,
in that cafe, muft be owing to the tendency of the
fluid from the earth, air, and other neighbouring-
bodies, towards the oppofite fide of the glafs, where
the power aCts, which caufes the minus appearance.

This regular converfion ferves to confirm the truth
of the principles afligned.

And here, with your Lordfhip’s leave, I fhall fet
down fome farther experiments, mofl of which have
been made with a view to fhew, that a plus electri-
city may be produced by means of a minus electri-
city.

Having electrified the infide of a large Leyden
bottle plus , by means of a conducting- wire from an
excited glafs globe, I fet it upon a ftand of prepared
wood, and took away the conduCting-wire ; after
which, the mouth of the bottle was elofed with a
Vol. LI, fZ ftopk

[ 9°o ]

ftople of glafs. Then the pointed end of the ivory
conductor was brought oppofite to the middle of the
bottle, and about two inches from it. Upon doing
this, the balls were electrified minus j and more
fo, as the ivory was moved nearer the bottle in an
horizontal direction.

But, on removing the ivory to a greater diftance,
the minus electricity decreafed y and, at a certain di-
ftance, there was not any fign thereof remaining :
and when the diftance was increafed to about eighteen
inches from the bottle, a plus electricity appeared,
which continued, even after the ivory was removed
intirely away.

After uneleCtrifying the bottle, it was fet again
upon the ftand of wood ; and upon another of the
fame kind, was laid a large iron poker, fo that the
pointed end was about two inches from the outfide
coating, and much nearer the bottom than the top
of the bottle. I chofe the lower part thereof, for
no other reafon, than to have the poker out of the
reach of any effed that might happen from the co n<-
duding-wire, which communicated with the ma-
chine, and the infide coating of the bottle. The
other end of the poker, being a large round knob,
was about one inch from a rod of iron, which com*
municated with the earth. Under thefe circumi-
ftances, when the infide of the bottle was eledrified
plus , the outer coating became minus , as ufual.

It is to be obferved here, that th t plus appearance
in the poker was caufed by that portion, of the fluid,
which was driven off from the outfide of the bottle,
by the repulfive force of the fluid conveyed into the
bottle. And this confirms the reafoning upon the rer

markable

[ 9°r ]

markable experiments related in the treatife publilhed
by Dr.Hoadly and myfelf. Seep. 27 to 34, and 46, 47.

Jnftead of electrifying the inflde of the bottle, in
the laft experiment, plus , I electrified it minus , with
the prepared wood, without any other change of cir-
cumftances. In this cafe, the outfide of the bottle
was plus, as ufual, and the poker minus . The fluid,
therefore, which caufed the plus electricity on the
outfide of the bottle, muft, in part at leaft, have
flowed from the poker j becaufe there was no other
open communication with the outfide of the bottle
and the earth to fupply it.

With a cylinder of baked wood, which {hewed
ftronger flgns of electricity, than I have yet been able
to produce from glafs, the balls hanging to the ivory
were electrified minus , at the diftance of four feet, or
more, by holding the cylinder over the middle of the
ivory, and continuing it there : and on moving it
nearer, they were more ftrongly electrified minus j
but the fame cylinder, on removing it back again to
the diftance of two or three feet, or more, electrified
the balls plus.

When another conductor, for inftance metal, with-
out edges or points, was ufed inftead of the ivory, and
without any thing hanging from it, the fame cylinder
held over the metal, as was done in the laft experi-
ment over the ivory, at the diftance of two feet, pro-
duced a plus electricity : and this was rendered weaker,
as the cylinder was moved nearer ; but by leflening
the diftance to about one foot, the minus electricity
took place.

In thefe cafes, the plus appearance arofe from the
earth, air, or other neighbouring bodies.

y Z 2, Whew

[ 902 ]

When the preceding experiments were firft: made,
I was a little embarraffed with the uncertain appear-
ances of a plus eledricity at one time, and a minus
at another, in the fame experiment : but, by repeated
trials and obfervations, I have found that a plus or
minus eledricity may be produced at pleafure, by
carefully attending to the following circumftances,
viz. the form of the bodies, their iudden or gradual
removal, and the degrees of eledrifying.

I fhall now proceed to acquaint your Lordfhip
with fome other circumftances of as nice a nature,
where the flighted, and almoft imperceptible dif-
ferences in the pojition , or in the force of the frittion,
of two bodies, produce in either of them, the plus
eledricity at one time, and the minus at another.

Such are the eflfeds of this fubtile and adive fluid,
when the experiments are carefully made j and there-
fore, they require the moft fcrupulous attention, to
trace out the caufes which occaflon them.

Sealing wax and fllver were the bodies ufed in the
firft two experiments j but many other fubftances feem
to perform as well. The fealing wax was clean, and
undifturbed by any fridion whatever, but that of the
air furrounding it ; and had been fo for fome hours.
The fllver was fixed to a piece of the prepared wood,
which was alfo preferved from fridion for the fame
length of time. Then taking one of thefe fubftances
in each hand, the lilver being at that end of the wood
the fartheft from the hand, I laid the fmootheft part
of the fllver upon the fealing wax, and moved it along
the furface gently, once only , and with a very flight
prefjure ; after which, the fllver was eledrified plus?
and the wax minus.

On

C 9°3 ]

On repeating the experiment, with equal care, and
in the fame manner, except that the Jmootb Jide of
the filver was a little inclined, fo that the edge thereof
preffed againft the wax ; the filver, after moving it
as before, was electrified minus , and the wax plus j
which is contrary to what was obferved in the lad
experiment.

Thefe oppofite effeCts, occafioned by the different
applications of the flat, or edge of the filver, feem
to arife from an alteration made in the furface oi
the wax, by deflroying the polijh in one cafe, and
not in the other : and, in this refpeCt, refembles the
polifhed and rough glafs mentioned in the letter upon
the Tourmalin. See p. 328. of this Volume, Part I.
Experiment 24.

Upon making ufe of prepared wood, inftead of
wax, and employing different degrees of preffure in
the friaion, with the fame edge of the filver, I pro-
duced the like appearances ; the leafl: preffure caufing
a plus, and the greateff: preffure a minus appearance
in the filver.

A flat piece of fleel, well polifhed, and the edges
rounded off, afforded the fame appearances, by only
applying the flat furface to the wood ; but it required
more pnefing to produce the minus effeCt in this cafe,
than it did in the former, where the edge was concerned .

Whether the reafon offered above for explaining
thefe lafl: curious appearances be true or not, I do
not venture to affirm, for want of farther experi-
ments ; but thus much may be fafely advanced, that
we have learned to produce at pleafure the plus or
minus eledricity from the fame bodies, by attending
to the manner of their application an d friction,

-> Mr.

[ 9°4 J

Kir. Dufay, and the Abbe Nollet, have indeed
obferved an inconffancy in the effeds, when they
rubbed fealing wax; but for want of the cautions
above-defcribed, in the choice and treatment of the
bodies, they were not able to anfvver for the event of
any experiment. The Abbe, in particular, who has
taken remarkable pains to find out from whence this
uncertainty arifes, acquaints us, in the thirteenth letter ,
with his difficulties, and how much it perplexed him
to iee, within an hour, in the fame place, and with
the fame inffruments, the effeds changed, and be-
come altogether contrary to thofe he had before ob-
ferved. In another part of the fame letter, he fays :

“ Je me fuis flatte plus d’une fois d’avoir faifi les
“ circonffances qui faifoient tourner a coup fur le re-
“ fultat de l’experience d’un cote ou de l’autre; mais
“ la fuite m’a fait connoitre que je m’etois trompe,
<c ou qu’il manquoit encore quelque chofe a ma de-
“ coverte.”

I might add other quotations of the fame kind,
but, as it would take up too much of your Lordfhip’s
time, I fhall beg leave to refer to the letter itfelf.

From the experience now obtained, it may not be
improper to obferve farther, that fealing wax of dif-
ferent hardnefs, will occafion a difference in the ef-
fects, the hardeff being always plus , and the fofteff
minus j which agrees very well with the rule laid
down in the letter upon the Tourmalin, p. 33 1,
ec that where eledric appearances are produced by
“ the rubbing of any two polifhed bodies together,
*c that body, whole fubftance is hardeff, and eledric
“ power ffrongeff, will be always plus, and the fofteff
xt and weakeff always minus” Now we find that

the

[ 905 ]

the Dutch wax is fofter than the Englifh, and the
Irifli harder : and it is not improbable that the French
wax, which I fuppofe the Abbe Nollet ufed, may
like wife be different.

Whoever, therefore, may be defirous of trying the
preceding experiments, with a view to make them fuc-
ceed, as they are here fet down, muff ufe the beft
Eng lijh fea ling wax.

I fhall conclude with an experiment made by my
friend Mr. Hamilton , profeffor of philofophy in the
univerfity of Dublin, as it feems to illuftrate the
doCtrine of refinances, at leaft, fo far as refpeCts the
air.

Let a flender brafs, or iron wire, five or fix inches
long, and finely pointed at each end, be fitted in the
middle,- with a brafs cap, void of angles ; then let
half an inch at each extremity be bent in oppofite
directions, till they are. perpendicular to the reft of
the wire, and in fuch a manner, that when the wire
is fufpended, by means of its cap,* on a point of
metal, it may lie in. a plane parallel to the horizon.
The pointed metal, which fupports this wire, muft
be two or three inches long, and have its other end ■
fixed into a fmall block of wood. Now, if this block, „
with a wire fufpended, be fet upon an electrified
body, the wire will turn round with a very great ve-
locity, moving always in a direction contrary to that
in which the eleCtric. fluid fifties from its points,
without having any conducting fubftance near it, fave
that of- the air : and if the wire be made to turn round
by any other force, in the oppofite direction, fo that
its points go foremoft, it will, when electrified,- foon

be

[ 906 ]

be deprived of that motion, and made to turn round

the contrary way.

This experiment, he fays, was contrived, in order
to try whether the ele&ric fluid, which ifiues fo freely
from pointed bodies, would have any effedt to move
thefe bodies by its reaction ; and that it has luch an
effedt, feems fufficiently manifeft from the event.

Mr. Hamilton apprehends, that the eledtric par-
ticles, by their elaflic force, iflue diredtly forwards
from the points, and endeavour to expand themfelves ;
but meeting with fome refinance from the air, force
the wire to move backward in a contrary diredtion,
much in the fame manner that a Catherine-wheel is
made to turn round in a diredtion, contrary to that in
which the fmall rockets affixed to its periphery dif-
charge themfelves. And therefore, he is inclined to
think, that it might be made ufe of as an eledlrometer,
by having it to turn round in a plane perpendiculai to
the horizon, and loading the wire with lmall weights
near one of its extremities, which will be raifed to a
greater diftance from the perpendiculai line, as the
eledtric fluid is ftronger.

I am, my Lord,

Your Lordfhip’s

Great Queen- Street,
Nov. 5, 1760.

moll: obliged

and obedient fervant,

Benj. Wilfon.

LXXX. A

PMos. Trans. Vol.U. TABJKI

urar/4

itl0M,'ntyfr

[ 9°7 3

LXXX. A Letter to Mr. Benjamin Wilfon,
F. R. S . concerning EleElricity ; from Mr.
Thorbern Bergman, fl/'Upfal.

Ampliffime atque Celeberrime Domine,

Read Nov. zo, ON mireris, Vir Celeberrime, me
176°. phyiicis addidtum Scientiis tuam

quaerere amicitiam, cujus nomen jam diu in hoc Sci-
entiarum genere orbi erudito inclaruit. Praeterea Do-
minus Profeffor Ferner me certioreni fecit Xe. non
sgre laturum mecum commercium literarium infti—
tuere de rebus eledlricis, a'lijque curiofis phyjicis. Pin-
rima enim apud Vros quotidie inveniuntur, quoium
tempeftiva cognitione laetatur quivis Philofophus na-
turalis j forte etiam varia apud nos prodeunt, quae
Angiis baud ingrata fpero, Itaque conftitui fecun-
dum tuum nutum, eos Pkilofophiae naturalis pro-
gredus, quos in Sue cm. capit, notos facere, a Xe vi-
ciffim expedtans eorum notitiam, quibus in Anglia
locupletatur. Lingua utor Romana, quippe quae mihi
notior Anglica, cujus genius ab exterraneo, qui in
Anglia nunquam fuit, vix ita addifci poteft, quin
multa vitia irrumpant, quae Anglo inter legendurri
naufeam movent.

Dominus Franklin in §. 28. ter tics epi/tola mira -
tur giaciei frujlum non tranfmittere commotioneni
elelilricam , cum aqua idem pei~fAde prcejlet : fed feci
nonnulla experimenta, quae monftrant parvam aqua
quantitatem nec huic fini fujjicere. Scilicet capiatur tu-
bus vitreus trium vel quatuor pedum, qualis barometris
infervit: hie aqua impleatur, et claudatur utrumque
extremum fubere perforato filo metallico aquarn pau-
lulum intrante, uti hgura adpolita indicat,

V o l. LI. 6 A

Si

[ 9°8 ]

^*-A

A— 4t

Si jam duo homines in circulo exploforio conftitutf
teneant extrema filorum metallicorum A, A, et ten-
tetur evacuatio, non tamen perfedta evenit, nam vix
carpus et rarilhime rlexura cubitus hac methodo con-
cutitur, licet deinde idem vas abfque ulteriori cumu-
latione tantum contineat eledtricitatis, ut more con-
fueto evacuatum pedtus valide ferire poffit. Audta
tubi capacitate, magis tranfit, ufque dum ita increve-
rit, ut plenarium tranfitum permittat, nec impedit
aquae quantitas juflo major, quod teftantur commo-
tiones per lacus et flumina propagatae. Convemunt
itaque aqua et glacies in eo> quod parvcz quantitates
concufjionem cegre tramittant .

Hinc fufpicatus fum inagnam glaciei quantitatem
faciliorem concedere tranfitum , quod etiam cxperientia
comprobavity etfi adhuc non majus adhibui fruftum
quam quo commotio fiexuram cubitus attigit. Pras-
terea ex cequalibus aquae et glaciei quantitatibus, gla-
cies minus tranfmittit.

Num Auroras Boreales uti phenomena elctlrica re-
fpicias, nec ne, nefeio j mihi faltem adhuc incertum
videtur. Interea fmgularem obfervationem aehate prae-
terlapfa fadtam commemorabo. Die xx fulii bora xs
poll meridiem vidi in N. IV. nubem A B horizonti in-
fijlentem , in qua copiojce et crebrce julgurationes ab
A verfus B progrediebantur, abfque tamen ullo to-
nitriiy ne quidem minimo murmure. C et D erant
nubeculas rariores forte cum magna non cohaerentes,
nam in eis nulla vidi fulgura. [Vide Dab. XXL]
Hora xi circiter adparuit Aurora Borealis fuo cul-
mine ultra zenith progrediens, et pluries arcus extre-
me tat Hits nubem att ingens. Etfi probe examinarem,

null am

C 909 ]

nullam aliam communicationem inter nubem et auro-
ram obfervare potui, nam i°. in D, cui inftitit alteruni
crus, nullam vidi fulgurationem : 2°. dum in nube ful-
guraret auroras fplendotj nullam variationem pati vide-
batur. Hora xii defierant fulgura, et nubes ita erat dila-
tata, ut totum fere hemifphaerium vilibile occuparet.

Prsterito, et hoc quoque anno , mult as elegantij/imas
ohfervari sluroras Boreales. Si quifpiam tales Lon-
dim attentis confideraverit oculis, per tuum favorem
notitiam me obtenturum fpero, et quando et quomodo
ibi apparuerint, ut fciam num fuerint eaedem, quas
hie vidi. Saltern obfervationum collatione certius
hujus phaenomeni altitudo perpendiculars determina-
retur. Si tibi placuerit, alia occafione lubenter meas
tranfmittam obfervationes.

Interea favori tuo me commendo permanfuius
Ampliffimi atque Celeberrimi Nominis Tui

Cultor obfervantiffimus,

Dabam Upfaiae, Thorbern Bergman.

17 03. 1760.

Quomodo ele&ricitas cumulari pofilt in alns quarn vitens
materiis, ex. gr. lacca figillatoria, fulphure, papyro, aere,
&c adeo ut commotio eleftrica ex eis obtineatur, non
hand ita pridem in adtis Academic Scient Stokhol-
menfis docuit Carolus Vilcke Phy fices Ledtor 5 Me-
thodus forte tibi non ignota.

6 A a

LXXXI. Some

[ 9io ]

LXXXL Some Confederations on a late Treatife
intituled , A new Set of Logarithmic Solar
Tables, c, intended feor a more commo-
dious Method of fending the Latitude at
Sea , hy Two Obfeervations of the Sun ; by
H. Pemberton, M. D. R. SL Lond. et
R. A. Berol. S.

Read Nov. 20, /% s it happens not infrequently at

fea for the unfeafonable intervene
tion of clouds to prevent the ordinary method of de-
termining the fhip’s latitude by the fun’s meridian
altitude, even when it is of primary confequence,
that the true latitude fhould be known ; a problem
for remedying this difappointment is ffated in many
treatifes of navigation, for finding the latitude of a
place by any two altitudes of the fun, with the inter-
val of time between them.

A problem limilar to this is propofed, and lolved
inflrumentaily upon a globe, by a very early writer,
Petrus Nonius (a), namely, to find the latitude by
two altitudes of the fun, and the angle made by the
azimuth circles palling through the fun, when the
altitudes are taken. And fince more commodious
and accurate inftruments for meafuring time have
been invented, than were known to this author, the
Other problem has been propofed for the fame pur-

(tf) In L;br. De Obferv. Rcgul. et Inftm.n. Geometr. lib. ii.
Cj 14.

pofe,

[ 91 1 ]

pofe, of which a conftrudion upon the principles of
the flereographic projection of the fphere is exhibited
by Mr. Collins, in his Mariner’s Plain Scale new
planed (£). And as the direft method of folving both
thefe problems by numbers requires a diveriity of ti i-
gonometrical operations, a fet of tables has lately been
publifhed for a more compendious way of computa.-
tion in the problem, where the interval oi time is
given, whereby the {hip’s true latitude may be very
expeditioully derived from the {hip’s dead reckoning,
provided the obfervations are made within certain li-
mits of time. >

But however worthy of notice this method may

be, new tables for the purpofe are altogether unne-
ceffary. It confifts of two parts : the firft computes,
from the latitude exhibited by the dead reckoning of
the {hip, the diftance from noon of the middle time
between the obfervations, and thence the time of
either: the fecond operation computes, from one of
thefe obfervations, what fhould be the fun s meri-
dian altitude, had the {hip’s reckoning given the true
latitude ; but if the latitude affumed from that reckon-
ing is erroneous, the altitude thus computed will not
be conformable to it j however, if the times for the
obfervations are properly chofen, it will much better
agree to the true latitude, and thereby the affumed s
latitude may be more or leis corteCted.

But both thefe operations are an immediate con-
fequence from the propofition in fpherical trigono-
metry, ufually delivered under the name of the fourth,
axiom, which is this 5 That the fquare of the radius
is to the reCtangle under the fines 01 tne fides con-

(b) Book iii. p. 35.

taming'

[ 912 3

taining any angle, as the verfcd fine of that angle to
the difference between the verfed fines of the third
fide, and of the difference between the fides contain-
tabling the angle.

Hence if A be the zenith of any place j B the ele-
vated pole ; C, D two places of the fun in the parallel
of declination D F •, by this propofition in the tri-
angle ABC,

3

Rad.

[ 9*3 ]

Rad.'i : fin. AB x fin. BC (cof. lat. x cof. decl..©)

; : verf. f. A B C : verf. f. AC — verf. f. A F ;

And, in like manner, in the triangle A B D,

Rad.q : cof. lat. x cof. decl. © : ; verf. f. A B D
: verf. f. A D — verf. f. A F j
Confequently,

Rad.q : cof.lat. x cof.decl. © : : verf.f. ABD — verf.f. ABC
: verf. f. A D — verf. f. AC.

But 4 rad. x verf. f. ABD — verf. f. A B~C is =
„ ABD + ABC ABD — ABC

fin. 7 x 11 n* " “ a

2 2

Therefore, ^

^ r ABD + ABC
Rad.q : cof. lat. x cof. decl. © ; : nn. 7-

ABD -ABC

x fin.

: 4 rad. x verf.f. AD — verf.f. AC.

And this is the firft operation in the treatife, thefe re-

, , - ABD + ABC

marks concern. For intheredtangle, thelin. 2
x the fin. A B D A B C- the firft fide, when the obfer-

vations are both made on the fame fide of noon, and

the fecond fide of this re&angle, when one obferva-

tion is before noon, and the other after, io the fine

of the diflance of the middle time between the ob-

fervations from noon, and the other fide is the fine

of half the diflance between the obfervations. . And

in the new tables one column exhibits the aiithme-

tical complement of the logarithmic fine of half the

elapfed time, and the next* the logarithm or twice

the fine of the middle time. _

But moreover, t rad. x veri. 1. A U vcrl. l. /i C

— ■ * ^ A D — A C

the

, r AD -j- Ae ^
being equal to fin. ~ x

operation may be expreffed more commodioufly thus,
r- ‘ Rad.

[ 914 ]

Radd : cof. lat. x cof. decl. O

fin.

ABD + ABC

2

~ ABD- ABC , AD + AC r AD-AC
x fin. : nn. x fin. ;

2 2 2

now requiring the common logarithmic fines only.

Again, the fquare of the radius being, as above,
to cof. lat. x cof. decl. O, as the verf. f. ABC to
verfi f . A C — verf. f. A F, or as verf. f. ABD to
verf. f. A D — verf. f. A F, thefe analogies exprefs the
fecond operation, which, in this treatife, is unnecef-
farily confined to the leffer angle ABC. The co-
lumn in the table intituled Riling confifts of loga-
rithmic verfed fines, which may be applied to either
of the angles ABC or ABD promilcuoufly ; for
here A F being equal to the excels of B C or B D
above the arch BA, affumed for the complement of
the latitude, the arches A C and A D, in the pre-
ceding analogies, will be the complements of the alti-
tudes obferved, if the latitude were truly affumed,
otherwife not ; but the difference of their verfed fines,
will however be equal to the difference of the verfed
fines of the complements of the true latitudes ; for
this is fuppofed in the firfl operation. Therefore, if
one of the fourth terms of thefe analogies be de-
ducted from the verfed fine of the complement of
the greater altitude, or tire other from the verfed fine
of the complement of the leffer, the remainder will
be the fame, and exhibit a verfed fine for the com-
plement of the funs altitude different from AF,
when B A is alfumed different from the true latitude,
and nearer to the truth, if the times for the obferva-
tions are properly chofen.

But farther, the two preceding analogies may be
reduced to thefe $

Rad.

[ 91 5 ]

Rad.’ : cof. lat. x cof. decl._0_ :: fin. -j All Cl’
: \ rad. x verf. f. AC — verf. f. A F,

And

Rad/* : cof. lat. x cof. decl. Q : : fin. ~ A B D'

: 4- rad. x verf. f. AC — verf. f. At >

Alfo,

Verf. f. AC — verf. f. AF = cof. AF — cof. AC, and
verf. f. AD — verf. f. AF = cof. AF — cof. AD.

And thus the common tables of fines will fupply
the ufe of this column of the new tables, as well as
the preceding.

The firft example of this treatife, wrought by the

common tables.

Here the declination of the fun is {fated at 1 1° 17'
N. the altitude firft taken, being the lefler, 46° 55',
the greater altitude 5-4° 7', and the difference of time
between the obfervations ih 25™, or 85 m ; which,
divided by 4, gives 21 0 15' for the arch of the equi-
noctial correfponding.

Here the obfervations are both before noon ; there-
fore, in fig. 1 . the latitude being affumed 46° jo'.
For the firft operation.

AC = 35
A D = 43
Their fum = 78
Their difference — 7

Sine of | fum (39

/

53

5

58

12

29

36

37

//

o

o

o

o

°)

o)

30)

Sine of r difference ( 3
Arith. com. of the fine of f C BD (— 10
Arith. com. of the fine of B F, or the cof. of the decl. 7

of the fun, - -- -- -- - -- ""j

Sum

Cof. of the lat. affumed

r A BD 4 ABC
Diff. = fin '

9.80336

8.79789

0.73429

0.00848

19.34402

9-835i3

6 B

Vol. LI.

2

9.50889

For

\

%

[ 9l6 ]

For the fecond operation.

o / n

ABD + ABC _ i8 49 ^

A B D — ABC

= io 37 30

ABC = 8 12 20

Sine off ABC (4 6 io)| 0^58

Cof. ofdecl. O 9.99 *52
Cof. of the lat. afiumed 9 ^35*3

. verf.f. AC-verf.f. AF St

Sum -30.00000 = log. of the — — /-535bI

*

Natural cof.
altitude,

Verf. f. A C — verf. f. A F
of AC, the complement of the greater 7

5

Natural cof. of 350 12' 23"

0.00686S

0.810212

0.817080

AKD+ABC + ABD -ABC beir)g = A B D>

Sine of* ABD (.4“ 43' 4°")^

Cof. of the decl. of the fun 9 99' 52
Cof. of the latitude afiumed 9-^35 1 3

Sum - 30.00000 = log. of the

verf f. AD -verf.f AF
2

8.63709

Verf. f. A D — verf f. AF
Natural cof. of AD, the complement of the teller
altitude, -

Natural cof. of 350 12' 23", as before

0.0867 -O
] 0.730361
0.817081

Thus the meridian diftance of the fun from the
zenith is computed at 350 12' 23", and this added
to the fun’s declination 1 1° 17' N. gives 46° 29' 23"
for the latitude, different from that a {Turned, and
nearer to the true latitude j which, by a fecond

operation

4

[ 9*7 3

operation with this latitude now
ftill nearer to the truth, thus :

found, will approach

The fum of the four firft logarithms in the firft of? ,9,34402
the two former operations, ~ j

Cofine of 4°6 29 23 9 83789

Sine of ^ BP 4 ABC __ l8 42 25 9.506.3

ABD — ABC

10 37 3°

ABC =
| ABC =

8

4

4 55

2 2"— ^
'* i

8.84800

8.84800

9 99I5Z
9.83789

Log.

verf. f . A C — verf. f. A r
2

7-5254r

Verf. f. AC - verf. f. A F 0.006704
Natural cof. of AC, as before, 0.8x0212
Natural cof. of 350 13' 21" 0.816916

The declination of the fun added to this, amounts
to 46° 30' 31", the true latitude, as direflly com-
puted, being 46° 30' ip".

However, it muft not be expected, that this me-
thod of computation will always converge thus expe-
ditioufly to the true latitude. Had thefe obfervations
been made about 3 hours fooner in the day, and
with the fame interval between them, if the firft al-
titude of the fun had been found 180 55, and the
fecond 330 11', the latitude computed would come
out wider from the truth, than that afiumed, one
exceeding, and the other falling fhort of the true la-
titude, which will lie between them, and is nearly
the fame, as above. But if the left'er altitude bad

6 B 2 been

[ 9i 8 ]

been 290 13', and the greater 40° j in 9 degrees of
north latitude the interval between the obfcrvations
would have been nearly the fame, as before. But if
this latitude be fought by any latitude affumed near
it, the latitude computed according to the method
above, will fall more remote from the truth, than
that affumed, and err the fame way.

In general, the error in the latitude affumed will
bear to the error in the latitude computed, nearly
the ratio compounded of that of the reCtangle under
the radius and the coline of the diftance from noon
of the middle point of time between the two obfer-
vations to twice fin. ~ ABC x fin. ~ ABD, and
the ratio of rad. x fin. AF to fin. BC x cof. AB;
infomuch that the difiance of the middle point of
time between the two obfervations from noon is
to be confidered, as the limit, where thefe com-
putations fhall ceafe to converge, when the rect-
angle under the radius, and the coline of this
difiance from noon fhall be to twice fin. I ABC
x fin. 7 ABD, (or the cofine of this diftance to the
difference between the verfed fine of this diftance
from the verfed fine of half CBD) as fin. BF x cof. AB
to rad. x fin. A F. And the errors in the affumed
and computed latitudes fall on different fides of the
true latitude, when both the obfervations are on the
fame fide of noon, and the zenith lies between the
meridian fun and the elevated pole ; or when the ob-
ervations are one before, and the other after noon,
if the meridian fun paffes between the zenith amt
the elevated pole : otherwife, they fall on the fame
fide of the true latitude.

However *

[ 9'9 3 . ,

However, the diredt method of computation, by
the abidance of the natural lines, will not be fo much
more operofe than this compendium, as may at hi
fight be imagined. For the arch of a grea circ
being drawn through C and D,

BCD, if the logarithmic cofine of BC or. BD ,
added to the logarithmic tangent of half the an

CBD, and the logarithmic fine of BC 01

added to the logarithmic fine of half this angle,
fiift fum is the logarithmic cotangent of the angle
BCD and the fecond the logarithmic fine of
C D, the bafe of the triangle. Then, m the triangle
A C D, from the fides, now all given, is to be com-

puted the angle ACD, ‘hend®“ceb',"'Ee"';ct
and the angle above found BCD, a the angle B C A

when the zenith kies between the pole, and the
great circle through C, D , but when the zenith es
beyond that circle, the angle BCA is either the
fum of thofe angles, or the Implement of that fum
to a circle. And, in the laft place, >f twice the loga-
rithmic fme of half this angle, and the logarithmic
fines of BC and AC are added together, the fum,
after thrice the logarithm of the radius has been de-
d lifted, is the logarithm of half the excefs of t le
natural cofine of BC cn AC above the natural cofine
of A B or the natural fine of the latitude according
to the trigonometrical axiom, which has been above
referred fo ; for rad. x * veil. f. BCA is equal to

fin. I BCAl' (f).

(0 Vide Neper. Mirif. Canon. Conftruft. Edinburg. 1619,
!>• 59- / The

[ 92° ]

The operation for the preceding example will be

this :

Tang. | C B D — 9.273225
Cof. BC — 9.291504

SinefCBD — 9.265714
SineBC — 9.991524

Cotang. BCD — 9.564729

Sine £ CD — 9.257238

BCD == 87° 53' 52"

1//

11

o

o

A D = 43 5

AC = 35 53
C D = 20 50 5
Sum = 99 48 5

£ Sum = 49 54 2 j

| Sum — AD = 6 49 i\

Sum

i Sum — 9.819519

i CD = io° 25' 2|

0.23200 1 7 ar co Qf the fmes.
0.4489503

9 8836*;] fines.

9.074406 3

9.639038

This half fum is the logarithmic cofine of half
ACD ; therefore, half A C D is = 48° 42' 1 1 ", and
its difference from 7 BCD will give { ACB =

4° 45 1

SineofiACB^g^| 8444

Sine of A C — 9.767999

Sine of BC — 9.991524

0.0039483

2

log.— 7-59&411

0.0078966

0.7333345 — natural cofine of BC — ■ AC, that is, of 42° 50'.
0.7254379 — natural cofine of AB, or fine of the latitude.
Therefore, the latitude is 46° 30' 19".

But farther, as in the cafes, where the above ap-
proximation takes place, it is an advantage, that the
illumed latitude fhould be taken as near the true

one.

[ 921 ]

one, as can be, the dead reckoning of the {hip need
not be intirely relied on for that purpofe; for the
inftrumental conftrudfion propofed by Mr. Collins (d)
will very readily give the true latitude, as nearly as
the inftruments ufed can exprefs : and Ms method
may be defer ibed thus.

Two ftraight lines AB, AC
being drawn in an angle cor-
refponding with the diftance
in time between the obferva-
tions, and in one of the lines,
as AB, the lengths AD, AE
being taken from any fcale of
tangents, one equal to the
tangent of half the fum, and
the other equal to the tangent
of half the difference of the
diftance of the fun from the pole, and from the zenith
of the firft obfervation, and alfo the points F, G, taken
in the other line in the fame manner related to the
other obfervation ; then circles being deferibed on the
two diameters D E, F G, the diftance of A from one
of the interft dtions of thefe circles will be the tan-
aent of half the complement of the latitude. .

° Moreover, as in the treatife, which has given oc-
cafion to this difeourfe, it is propofed fometimes to
take into confideration the fhip s motion during the
time, between the obfervations, but imperfectly, re-
gard being had to the change made by the fhip in
longitude onty j but the change in latitude alfo may
be taken into confideration in the foregoing con-

( d ) In the place above cited.

ftru&ion.

[ 922 ]

ftruction, by making the angle B A C equal to the
fum or difference of the interval of time, and the
change in the (hip’s longitude, according as that
change is made towards the weft, or towards the
eafl, and then drawing a line from A, not to the
interfedion of the circles ; but fc, that the portions
of that line, terminated by each of the circles, may
be the tangents of arches, whofe difference is half
the change in the latitude ; which, if made from
the pole, requires the portion of the line terminated
at the circle, whofe diameter is D E, to be fhorter
than the other; and the contrary is required, when
the motion of the (hip is towards the pole.

For determining the latitude by calculation, if the
diftance of the fun in the firft obfervation from the
zenith of the fecond could be found, this cafe would
be reduced to the firft, wherein the fhip is confidered,
as flationary. And for this purpofe, it has been pro-
pofed to make an additional obfervation, by an azi-
muth compafs, of the angle, the (hip’s courfe makes
with the azimuth of the fun, when the firft altitude
is taken; and, perhaps, the fame angle may be found
with fufficient exadnefs from the latitude in the firft
obfervation affumed, whether from the dead reckon-
ing, or from the foregoing conftrudisn.

Why I have taken no notice of the calculations ex-
hibited by the author of the piece here animadverted
on, as proofs of his method, will readily appear to
thofe, who (hall call their eye upon them.

Scholium.

The axiom in trigonometry, on which the calcu-
lations here difeourfed of have been fhewn imme-
diately

[ 923 J

diately to depend, was introduced by Regiomontanus,
and is dill retained, as the foundation of the prefent
methods of computing logarithmically an angle from
the three fides of a fpherical triangle given, though
they may be demonftrated more diredtly by the fol-
lowing lemma.

In the circle ABC, the chord A C being drawn,
and the arch ABC bifedted in B, if D be taken in
the circle at pleafure, and the lines B E, D F drawn
alfo at pleafure parallel to each other, one terminated
by the circle in E, and the other by the chord A C
in F; then AD, DC being drawn, BE x DF is =
A D x D C.

Draw D H perpendicular to A C, and alfo the
diameter BG, joining EG. Then the angles FDH,
E B G are equal, and the angles D H F, BEG right.
Therefore BE is to BG as DH to DF, and BE x DF
= BG x DH = AD x DC.

Vol. LI.

6 C

Now,

[ 92+ 3

Now, in the
fpherical triangle
ABC, through
B, and to the
poles A, C, let
the femicircles
EBF, GBD be
defcribed , and
the arch A C
completed to a
circle. Then the
femicircles EBF,
GBD will be

both perpendi-

cular to the plane of this circle, cut it in their

diameters E F, G D, and their common interfedtion

B H be alfo perpendicular to it, and confequently

perpendicular to G D, the diameter of the femicircle

GBD, whereby G B, D B being joined, G D x G H

is equal to G Bq, and G D x D H equal to B Dq.

Again, A K being drawn parallel to G D, the arch

ACK is double AC, GCD double CB, EAD

the lum of all the three fides of the triangle, EGr-

ED~DG(aCB),GF = AF(AE)4-CG(CD)-AC

= E D — 2 A C, and FD=r ED — EF(2AB).

Then EG, GF, FD, ED being joined; in the

firfl place, AKistoDGasAKxGH toDGxGH,

alfo AK to D G as AK x DG to D G q, but AK x G H

= EG x GF by the preceding lemma, and DG x GH

— G B q ; whereby AK x DG is to D G q as E G x G b

toGBl Hence A K being twice the fine of the arch

AC, D G twice the fine of the arch G C, equal to

B C, EG twice the fine of half the arch E A G, G F
* •

twice

[ 925 1

twice the fine of half the arch GF, and GB twice
the fine of half the angle ACB to the radws °f t e
circle GBD, which is half GD j fin. AC x lm'
is to rad.q as fin. ^ ED — B C x fin. i ED AC
to fin. 4 ACBlq. And this is Napeir’s. firft method
of finding an angle from the three fides given (f )» as *

is ufually delivered. . nPq

Again, AK is to DG, or AK x DG to DG , as

AKxDH (EDxDF) to DG x D H> 01 Db •
Therefore, D B being twice the fine of ha f the angle
B C D, or twice the cofine of half the angle AC B to
the radius of the circle GBD, as fin. t ~ x in^ —

to rad.’ fois^EDxf,n.f EU-Ab to cof. 1 ACBF.
And this is Napeir’s fecond method (/ ).

And laftly, the cofine of an arch or angle being
to its fine, as radius to the tangent, Jin. ? t. U
x fin. 4- E D — A B will be to fin. ?ED B C
x fin. jED — AC as rad.q to tang. \ ACBlq, which
is a third method added by Gellibrand (#)•

Moreover,

In plain triangles, from the three fides given may
an angle be found by a procefs fimilar to each ox

thefe, as follows :

(*) Mirific. Canon. Log. defcrip. lib. ii. c. 6. § 8.
(/) Ibid. § 9.

U) Trigon. Britan, p. 75.

6 C 2

In

[ 926 ]

In the plain triangle ABC, if on the centers A
and C be defcribed circles through B, cutting AC in
E, b, G, and D, the perpendicular B H being let fall
on A C, E H x H F is equal toGHxHD. There-
fore H F : GH ; : HD : HE, and by compofition
GF : GH :: ED : HE, and ;:ED — G F : EGj
alfo HF : GF : ; HD : ED, and ; : D F : E D- GF. ’
Moreover ED is = AB -F AC + CB, EG —
ED— 2CB, FD--ED — 2 A B, ED — GF
= EG-f FD = 2ED — 2CB — 2 AB = 2 A C.
Hence G b is to G H as 2 A C to E G, whence
GF x EG is == 2 AC xGHj and DII is to ED
as D F to 2 A C, that is, 2 A C x D H will be —
E D x D F.

Thus 2 A C : DG (:: 2 AC x DG : DGi)
: : 2 AC x GH (EG x GF) : D GH (GB*>) and
A C x C B : rad.q ;;|ED — CB x 4 E D~— AC
: tin -AC hi1.

Likewife 2 A C : D G ( : : 2 A C x D G : D GO
:: 2ACxDH(EDxDF):GDH(DBq)j therefore
ACxCB: rad.<) : ; FE D x FE D - A B : cof. F A C B)q.
And in the laft place |EDx \ ED — AB

* 1

ED-CB xJ-ED-AC ; ; rad.*1 ; tang. F A C B]q.

5 ‘ This

[ 927 ]

This lafl proportion was firfb delivered by Gelli-
ferand, and the other two not long after by O ugh tied,
in their refpedtive treatifes of Trigonometry.

But it may farther here be noted, that from two
fides of a plain triangle, as AC, CB, with the angle
between them A C B, the third fide A B may be
found either by the firft or fecond of the foregoing
proportions \ for by the firft may be found EG x G b ,
that is, AFq — A Gq, and by the fecond E D x D F,
or A Dq — A Fq j whence by a table of fquares A F
AB) may be readily found, for AG is equal to
AC — BC, andADrr AC + CB.

In like manner in the fphe-
rical triangle from the fides
AC, CB, and the angle ACB,
may the third fide be expedi-
tioufiy found with the aid of a
table of natural fines, by the
axiom referred to in the be-
ginning of this difeourfe, as modelled for this pur-
pofe by Napeir, in the propofition, which has been
already referred to (/;), whereby the axiom is re-
duced to this analogy,

Rad.q : fin. AC x fin. CB :: lin. 4- A C bp

verf. f. A B — verf. f. A C cn C B ...

; rad. x * ~ vr

May

th) Mirif. Canon. Conftr. p. 59. .

(/) An example of this method has been given above in the tri-
angle A B C in p. 920. And in default of a table of natural fines,
the bafe A B might have been found thus. The fum of twice the

logarithmic fine of i AC B, added to the logarithmic fines of A C

b ana

[ 828 ]

May it here be farther added, that thus all the
cafes of obi que fpherical triangles may be folved
without dividing them into rectangular ? For when
two Tides and the angle included, or when two angles
and the tide between them are given, the two other
angles or tides may be found by the proportions of
Napeir and Briggs, whereby the other two angles or
Tides are found together (*&); the proportions, when
two Tides with the including angle are given, being

theTe,

CoT.

AC -f- CB . ^ AC c/3 C B

.* ; cotang, j- A C B

tang.

CAB + CBA

Sin.

And

AC + C B

Tin.

A C cd C B

; ; cotang. \ A C B

CAB cd CB A
: tang. -

The Tecond of thefe has been demonftrated with
great concifenefs by Dr. Halley, from the principles
of the ftereographic projection of the fphere (/) ; and
the firft is derived by him from the Tecond, but not

and BC amounted to 37.596411. The logarithmic fine of

AC cd BC ^ 562468) deduced from half this fum ( 18.79821 1 )
2

leaves 9-235737. This number fought among the logarithmic
tangents exhibits for its correfpondent fine 9.2294CO, which being
deduced from the forefaid half fum (18.79211) leaves 9.568805,
which is the logarithmic fine of 2i° 44' 50Tb equal to half AB.
(/£) Vide Neper. Mirif. Canon. Conltr. pag. penult.

(/) See Jones’s Synopfis, p.281.

altogether

[ 929 ]

altogether with the fame fuccefs, by his not obferving,
that3 if the bafe and one of the fides be completed to
femicircles, the fecond of the two proportions m the
fupplemental triangle thence formed leads directly to
the fir ft in the original triangle.

And to conclude, if two fides, and the angle op-
pofite to one of them, or two angles with the fide
oppofite to one, were given ; when the other oppofite
part is found from the proportion between the fines
of parts oppofite, the remaining angle, or fide, may
be found by either of the two proportions foregoing.

LXXXII. An Account of the Plants Halelia
and Gardenia : In a Letter from John
Ellis, Ejq\ F. R. S. to Philip Carteret

Webb, Efq\ F.R.S.

Dear Sir,

Read Nov. 20, ^ OU muft have obferved,. that as
176°. the fpirjt pf planting has increafed

in this kingdom, the ftudy of botany has become
more fafhionable j the works of the celebrated Lin-
nreus, heretofore looked on as capricious and ftrange,
are now in the hands of every man, who wifhes to

ftudy the order of nature.

The great variety of plants, which you have in-
troduced into your garden from North America, as
well as from many other parts of the world, mult
give you double pleafure, when you view them ranged
in proper order, and judicioufly named.

[ 9.5° ]

The calling of plants after the names of botanifts,
as well as after the names of thofe, that have been,
or are the promoters and encouragers of this ufeful
fcience, is not without its advantages j and this cuftom
has been followed by Linnaeus, and recommended
by him in his Philofophia Botanica. It has this good
effect ; it Simulates many to the fearching after new
difcoveries, and hill further improvements in agri-
culture and vegetation, a truly wife and laudable
end.

The intent of this letter is to lay before you the
characters of two new genera of plants, now grow-
ing in your garden, which I fhall take the liberty to
call after our worthy friends Dr. Stephen Hales of
Teddington, and Dr. Alexander Garden, phyfician
in Charleftown, South Carolina.

The plant, which I fhall firfb defcribe, is the
Halelia ; and in order to give you a better idea of it,
I fhall tranfcribe the account Dr. Garden lent me of
it, when he fent the fpecimens and feeds.

“ This beautiful tree grows commonly along the
<£ banks of Santee river, and rifes often to the fize
“ of middling mulberry-trees. I have leen it fome-
“ times more foutherly, near the fmall rills of water;
“ but of a much fmaller fize than that which grows
“ on Santee. The wood is hard, and veined; the
“ bark is of a darkdh colour, with many irregular

fhallow fiffiires. The leaves are ovated, and fharp
££ pointed, with the middle depreffed, growing al-
“ ternately on fhort footftalks. The f jwers hang
<c in fmall bunches all along the brancl.es, each gem
“ producing from four to eight or nine flowers, bell—
u shaped, and of a pure fnowy whitenefs. As they

“ blow

-P/i/fos. Trans. Vo/. LI. TAB. JOOIy.,. p;jl.

A. HAXESIA /nr /n/rrem.//rara/n,,, mrm/rranarar-ijrrMt/rariait/a/r.)
^ HaIiJ*. SI A / t/r^t/tv/nyT ti/rr/rlr

[ 931 ]

« blow early in the fpring, before the leaves appear,

« and continue for two or three weeks, they make
« a mod elegant appearance. They are followed
“ by pretty large four-winged fruit, which likewiie
“ hang in bunches, each containing four kernels,

“ that are very agreeable to the tahe.

This tree is mentioned by Catefby, v ok 1. p.
and called Frutex padi foliis non ferratis, floribus mo-
nopetalis albis, campaniformibus, &c. &c-

I have not heard that it was cultivated in England,
till about four years ago, when the Dodor fent me
over from Carolina a large parcel, of the leeds, which
I dihributed among many curious gardeners, and
others : but I cannot find any one that it has fuccceded
fo well with as Mr. James Gordon, gardener at Mile-
end, a man, who feems to be pofTefTed of a knowlege
peculiar to himfelf, in railing all the rarer, and moll
difficult exotics from feeds, layers, or cuttings. He
informs me, that it hands our winter in the open air,
without any fhelter ; which confirms what Mr Clay-
ton of Virginia has lately wrote, that it hands even
the feverity of the winter of that country. So that it
may, in a little time, prove a molt agreeable orna-
ment to our gardens in the fpring.

About two years ago, I received from Governor
Ellis of Georgia another fpecies of this tree, which
was fent him by Mr. De Brahme, from Auguha in
Georgia, three hundred miles up the. river Savannah.

The fruit of this kind has two wings, as defcribed

in the Plate, at B. [ Vide ‘Tab. XXII.]

Vol. LI.

6 D

The

[ 932 ]

, •

The characters of the Halefia are as follows.

CAL. (a) Perianthium monophyllum, fuperum,

minimum, periiftens, quadridentatum :
denticulis acutiufculis, ereCtis.

COR. (b) Petalum campanulatum, magnum,

ventricofum j limbus quadrilobus : lobis
minimis, obtufis, patulis.

ST AM. (c d) Filamenta [d) duodecim, (raro fc-
decim) tubo coroll® inferta, bad con-
nata, fubulata, ereCta, corolla paulo bre-
viora. Anther a (c) oblong®, obtuf®,
ereCt®.

PIST. (e fg) Germen (e) oblongum, inferum.

Stylus (/) filiformis, corolla longior,
perfiftens. Stigma (g) fimplex.

PER. (b) Nux corticata, lub cortice fulcata, ob-

longa, utrinque anguftata, membranis
angulata, quadrilocularis (k).

SEM. (/) folitaria, lineari-oblonga.

The fpecies are,

tetraptera. 1. Halesia fruCtibus membranaceo-

quadrangulatis.

diptera. 2. Halesia frudibus alatis.

The other plant, which J am to defcribe, is known
by the name of the Cape Jafmine, and is the rnoft
rare and beautiful fhrub, that has yet been introduced
into the European gardens, as well for the refrefhing
aromatic fmell of its double milk-white flowers, as-
the perpetual verdure of its leaves, which are like
thofe of the lemon-tree. [Fide Tab. XXIII.]

It

P/jilos. Tra/ut . \ rl.LT. iyiB.XXIJI.jK 932.

Gardenia with a Jot/bL Flowrr.

'A&i/iu/tc?
r Xlif/unf

aoi’f /ns trrr

ryj far/f y //u y/s>/i>tr.

<*%>*

[ 933 ]

It promifes, from the thicknefs and woodinefs of
its ftem, together with its free manner of growing,
to become a lhrub of fix or feven feet high.

It bears but one flower at the end of a branch ,
and the leaves grow oppofite to each other on the
branches.

We are indebted to Capt. Hutchinfon, of the Go-
dolphin Indiaman, for this curious difcovery, who,
about fix years ago, found it growing near the cape
of Good Hope, and, on his arrival here, prefented it
to Richard Warner, Efq; of Woodford in Eflcx ;
who finding great difficulty in propagating this va-
luable plant, either from cuttings or by inarching it
on the yellow Indian jafmine, as he had been advifed,
I recommended him to try Mr. James Gordon, gar-
dener at Mile-end ; and,, at the fame time (Augufl
1 757), by the interefi: of my worthy friend Guftavus
Brander, Efq; F. R. S. I procured two cuttings of it
for Mr. Gordon. Thefe, with two more, which he
afterwards received, he increafed to fo confiderable a
number, that, in order to difpofe of them, he ad-
vertifed them for fale, at five guineas a plant; and
has had fuch fuccefs in the fale, that, reckoning the
value of the plants on hands (with a proper allowance
for the falling of the price, as they become more
plenty), he computes this plant will be worth at leaf!
five hundred pounds fierling to him. I mention this ;
becaufe I am perfuaded it muft give you, and all
lovers of vegetation, great pleafure to fee a man thus
amply and defervedly rewarded for his fuperior merit
in this art.

Having difledted many dried as well as frefii fpeci-
tnens of this rare plant, I found fufficient evidence

6 D 2 (not with-

[ 934 ]

(notwithstanding the flowers being double) to prove,
that it belonged to quite another clafs of plants, as
different from the Jafmine as the Rofe is from the
Peony : that the fruit was below the receptacle, in-
flead of being above it. But, in order to be more
certain, you may remember, in July 1 7 58, I pro-
cured a Specimen from Mr. Warner, for my friend
Dr. Linnams’s opinion. At the fame time I wrote
to the profeflor, that if he found it to be a new genus,
agreeable to the defcription I had fent him, that he
would pleafe to call it Warneria, after its worthy
poffeffor. In his anfwer, he fets forth the impofli-
bility of his being exadt in determining a new genus
from a double flower, agreeable to the rules he has
already laid down in his Fundamenta Botanica. But
thefe objections were foon after fortunately removed,
by accidentally finding, among his dried oriental
plants, a fpecimen of the fame kind with a Angle
flower, whiejh, upon expanding it in warm water,
and differing it, he found it to agree very nearly
with the defcription I had fent him. But Mr. War-
ner refuflng to have it fo called, and chufing that it
Should ftill remain a Jafmine, as it is commonly called,
I have thought no man more worthy, as a botanifl,
than our friend Dr. Garden : accordingly, the pro-
feflor has agreed to adopt this new genus by the name
of Gardenia, which he fays belongs to the natural
order of contorted flowers, that is, to thofe mono-
petalous flowers, whofe lobes, or fedtions of the limb
of their petals, turn all to the right hand ; fuch as
the Nerium, Plumeria, Cerbera, Cameraria, Vinca,
&c. and that it fhould be placed next to the Cerbera.

Mr.

[ 935 ]

Mr. George Dionyfius Ehret, F. R. S. has lately
publifhed a moil elegant plate of this plant, by the
name of, Jafminum ? ramo uniflore pleno, petalis co-
riaceis, with a note of interrogation, as a quaere, be-
fore the word Jafminum ; leaving the determination,
whether it is a Jafmine or not, to a future inquiry.

The charadters of the Gardenia are,

[ Vide Tab. XXIII.]

CAL. Perianthium monophyllum, quinquangu-

lare, quinquepartitum : laciniis enfifor-
mibus, verticalibus, ftridtis, eredtiufcu-
lis, perfiftentibus.

COR. Petalurn % hypocrateriforme j tubus fubcy-

lindricus, calyce longior; limbus quin-
quepartitus, planus : /#«Vzmobovatis,lon-
gitudine tubi, altero margine redtiore.
STAM. Filamenta quinque, tubo corollas adnata, in
fauce breviffime libera ; Anther £ lineares
fuberedlas, longitudine dimidii limbi.
PIST. Germen infra receptaculum, oblongum.

Stylus filiformis, longitudine tubi co-
rollae, definens extra faucem in Stigmata
duo, magna, craffa, obtufiffima.

PER. Bacca ficca, oblonga, bilocularis.

SEM. plurima, minima.

There is but one fpecies known.

Jafminoides . i. Gardenia.

I am. Dear Sir,

Your molt affedtionate

humble fervant,

John Ellis.

London, Nov. 20, 176c.

[ 936 ]

LXXXIII. An Account of an Eclipfe of the
Moon , 2 2cl November 1760, ohferved in
Surrey-Street in the Strand, London ; by
James Short, M. A. F. R. S.

h ' "

Read Dec. u, "F^Enumbra very fenfible at 7 26 o
176°. yy Beginning of the eclipfe at 7 3 9 °
Quantity of obfeuration = 17' 36 at - - 8 4p o

Moon’s diameter almoft parallel to the ho- J g Q
rizon = 3' 51 at ----- -3 ^

End of the eclipfe at - - - ---1080

LXXXIV. An Account of the Cafe of a
young Ma /z, who had loft the Cje of his
Hands by cleanfmg Brafs Wire \ by Mr.
Samuel More, Apothecary in Jermyn-
Street. Communicated by Charles Morton,
M. D. Secreta?y to the Royal Society.

Read Dec. u, rpHE diforders, to which mechanics
176°. are linav0idably fubjedted by their

employments, have exercifed the pens of feveral in-
genious writers ; among whom I would not piefume
to appear, but that, I hope, the publishing the fol-
lowing cafe may be of fome fervice: foi I am cei-
tain, every one, who has been in the leah conveilant
with the labouring people of this town, muft fie-
quently have obferved their hands in a condition
1 fomething

C 937 ]

fomething refembling, though perhaps not quite fo
bad as, that of the young man, whofe diforder is the
fubjedt of the following paper.

And as there is great reafon to believe, that the
complaint, herein treated of, frequently happens to
perfons employed in the dyeing bufinefs, they will
hereafter have a method of cure laid before them,
which, with little expence, will probably be of great
fervice to them. And, on that confideration only, I
have been induced to fubmit this account of the dif-
eafe to the infpedtion of the public.

The Cafe of Francis Newman, Nephew and Appre?itice
to Mr. Newman, Dyer , in the Maize, Southwark,
who had loft the UJe of his Hands by cleanfing Bra/s
Wire .

FOR the more readily explaining the following
cafe, it is proper to premife, that, in drawing
brafs wire for the pin-makers, the frequent paffing
it through the fire, to anneal it, covers it with a
cruft, which it is neceffary to take off, before they
can make ufe of it j and, for this purpofe, it is fent
to the dyers, who, letting it lie for fome time in the
liquor, with which they have dyed what they call
Saxon colours, (which liquor is compofed of water,
oil of vitriol, alum, tartar, &c.) and then throwing
it forcibly three or four times again ft the ground,
the cruft is, by degrees, broken off, and the wire
rendered bright, and fit for ufe. The gratuity given
for this is generally allowed to the apprentices ; and
in this work Francis Newman had frequently (at his
leifure hours) employed himfelf, till about the month
cf Auguft 1755?, when the cuticle on the palms of

[ 938 ]

Ills hands, and the infide of his fingers, was become
fo hard and rigid, that he was no longer capable of
doing either this, or any other bufinefs.

For relief of this diforder, he applied to the perfon,
who attends the family in capacity of apothecary,
who gave him feveral dofes of purging phyfic, but
without fuccefs.

He was next admitted an out-patient at St. Tho-
mas’s hofpital, where he attended fix weeks or two
months, but without receiving any benefit.

Somebody then told him, his complaint was owing
to the fcurvy, (to which he had been fubjedt) and he
accordingly applied himfelf to feveral perfons, who
advertife remedies for curing that diftemper, and,
among the reft, to Mr. Ward, of whom he had
fome pills ; and once,*by miftake, took two of them
for a dofe, which operated fo violently, that every
body in the family imagined he could not furvive it :
however, he ftill continued in the fame condition.
And now thinking, that if he was admitted an in-
patient at the hofpital, he fhould be more likely to
obtain a cure, he got himfelf admitted, and was
there about two months longer; at the end of which
time he was difcharged, but in no better condition
than before.

About a fortnight after this, and a twelvemonth
from the beginning of his diforder, viz. Auguft 10,
1760, the perfon, who is foreman to Mr. Newman,
defired leave to write to me, for my opinion of the
cafe; which being very readily granted, he defired
me, by letter, to come and fee a young man, who,
as lie exprefted it “ had poifoned his hands with
brafs and oil of vitriol.”

When

[ 939 J

When I firft vifited him, I found him with his
hands quite ftift, and utterly incapable of any bufi-
nefs whatever ; and having already had fo much ad ~
vice, and taken fo many medicines, he concluded
his diforder was incurable, and that he fhould en-
tirely lofe the ufe of his hands, the Jkin on the palms
of them (the right hand rather the worll of the two)
having the exact appearance of parchment^ full of
chaps ; and when I endeavoured, by force, to
/heighten the fingers, the blood farted fro?n every
joint of them.

After hearing the bed: account I could get of the
caufe of his complaint, I imagined, that, as the dif-
eafe had been contracted by his frequently dipping
his hands into a violently-acid liquor, the mod: pro-
bable method of relieving him would be, by the ap-
plication of an emollient liniment, mixed with an
alkaline lixivium. For this purpofe, I ordered as
follows :

01. Olivar. §iv.

Lixivii. Salis Alkalin. fix. §ii. M.

F. Linimentum.

With this he was ordered to anoint his hands fre-
quently, efpecially going to bed ; and, to prevent the
liniment being too foon rubbed off, conftantly to wear
a pair of gloves.

About four days after, I found the fkin a little
foftened, and I could extend the fingers with lefs pain
than before ; and no blood iffued, upon my endea-
vouring to move them. This would have encouraged
me to have continued the ufe of the fame liniment;
but as he complained much of its making his hands

Vol, LI. 6E fmart

[ 94-0 ]

fmart every time he ufed it, (and, indeed, this was
the firffc application among the many he had tried,
that ever gave him any uneafinefs) I concluded, that
the addition of fome yolk of egg might leften the
acrimony of the alkaline fait, without at all abating
the efficacy of the liniment : I therefore compofcd
the liniment thus :

1 x Ol. Olivar. §iv.

Lixivii. Salis Aik. fix. §ii.

Vitel. Ovor. N°. ii. f. Linimentum ;

to be ufed as before. This mixture not giving him
fo much pain as the former, he had ufed it all
in three days; and then, coming to me for more, I
found his hands hill continue to mend; the fkin that
had grown hard fcaling off, and a new flexible one
appearing underneath ; the chaps were many of them
healed ; and he began to have fome ufc of his fingers.
Encouraged by this luccefs, lie continued the ule of
the laft prefcribed liniment ; and as, from his not
having had the proper ufe of his fingers for fo long a
time, the joints of them had, in a great degree, loft
their motion, I advifed him, alternately to clench his
ft ft, and to ftretch out his fingers, many times a day.

The diforder had been fo long upon him, and (if
I may be allowed the expreffion) had taken fo deep
root, that, although he began very fenfibly to amend,
from the firft application of the liniment, yet it was
full two months before I thought it advifeable to
leave off the ufe of it ; and then, to prevent a relapfe,
I gave him the following ointment :

ft Axung. Porcin. %'u.

Vitcl. Ovi.

01. La vend. g*. v. f. Unguentum.

with

[ 94* ]

with orders to anoint his hands with it every night
going to bed. This ointment he has continued ,to
ufe about a month ; and is now perfectly reftored to
the ufe of his hands, and begins again to work at his
hufinefs.

During this courfe of anointing, he took no inter-
nal medicines, except three dofes of purging phyfic.

LXXXV. A further Account of fame Experi-
ments made on the Bovey Coal *.

Read Jan. 8, ALT of hartfhorn mixed with the
l?6u ^ phlegm that diftilled firft from the
Bovey coal, produced no ebullition, nor air bubbles ;
but when mixed with the watry liquor, which arole
with the thick oil in the latter part of the procefs,
after it had flood fome weeks in a glafs bottle, clofe
flopt, and was become perfectly fine, caufed a very
confiderable ebullition, and the mixture immediately
grew foul and red. In fome days after, it grew
much thicker, and had the colour of tar. The fur-
face of it was covered with a bituminous pellicle, as
were the fides and bottom of the glafs. Eighteen
grains of fait of hartfhorn were not more than Ef-
ficient to faturate the acid falts contained in an ounce
.of the liquor, which was but very little four to the
tafle.

Spirit of nitre dropped into this bituminous liquor,
foon after it was diftilled, and before it had deposited
the oily particles (which rendered it cloudy), changed

* See before, p. 534.

6 E 1

its

[ 942 ]

its colour to a deep brown ; but had not that effect
after the liquor was become tranfparent.

The black gritty powder, which remained after
the former procefs, v/as put into a coated retort, and
didiiled by a naked fire ; fo that the whole body of
the retort continued red-hot for more than two hours.
This brought over to the receiver near an ounce of a
watry bituminous liquor, rather ftronger than that
which diddled with a fand heat, and a few drops
only of a thick bituminous matter, which duck to
that part of the receiver on which they fell. The
neck of the retort was thinly incrudated with fome-
thing that refembled a faline concrete ; but was found
to be only bituminous matter. In the bottom of the
retort there remained a very black gritty powder.

Of this powder, one ounce was put into a crucible,
fet in a melting furnace, and kept in a pretty drong
fire for an hour. The powder, after it was grown
cold, appeared on the furface to be of a pale reddifh
colour ; but was not in the lead altered underneath.
It lod, however, in weight, near three drachms.
Some of the black powder taken out of the crucible,
and thrown upon a red-hot iron, burnt without
flame ; but emitted plentifully a heavy black fmoke.

Two ounces of the black powder, which had been
twice diddled, were fet on a clear fire, in an iron
ladle, and continually dirred from the time that the
ladle grew red-hot, and the matter began to emit a
heavy black ftinking fmoke, till no more fmoke arofe
from it. The calcined matter remaining in the ladle
weighed two fcruples,. and feemed to be a kind of
bole earth. This earth was evaporated in two ounces
of rain water to one ounce, which, fome days after,
was poured oft' clean from the fediment. This water

had:

C 943 ]

had not the leaft faline tafte, nor did it give any fio-n

of effervefcence, when fpirit of nitre was dropped
into it. rr

From tiie preceding experiments it appears, that
the fubftance called foffil-wood confifts, for the
moft part, of water, and that a considerable quantity
of this principle is feparated from it by a gentle heat ;
which Seems to be the reafon, why fuch foffil-wood]
on being expofed to the fun and air, or kept in a dry
place, foon becomes full of fuperficial cracks, re-
sembling a piece of timber, which, by lying long on
the ground in the open air, has begun to decay :
that though the foffil-wood does not, like amber,'
or pit-coal, yield, by distillation, a light oil floating
on its phlegm, and a volatile acid fait in a concrete
form, yet that a light oil, and a volatile acid fait, in
a considerable quantity, are intimately mixed with
the water, which diftils from it : that this foffil-
wood differs, in feveral particulars, from all wood
belonging to the vegetable kingdom, which has been
examined by fire after the fame manner.

iff, Its powder burnt in a clofe veffel, and kept
red-hot for a much longer time, than is fufficient to
reduce the like quantity of vegetable charcoal, emits
(when fprinkled on a red-hot iron.) a thick heavy
black fmoke.

2dly, The fame powder, burnt as before-men-
tioned, doth not eaiily take fire, nor burn of itfelf,
nor confume to affies, even when expofed, in an open
crucible, to a Strong Sire, and kept in it ignited, and!
almoft white, for a considerable time.

3 dly,^ The matter left by this powder, after its
phlogiffic principle has been feparated from it by
time and air, contains no alkaline fait, and appears

4 to>

[ 944 ]

to be an aflringent mineral earth ; whereas charcoal
eafily takes fire,, burns freely without finoke, and
continues burning, till it confumes to an afh ; which
confiifis of an alkaline fait, and a pure earth, fit for
making cuppels ; and, by thefe marks, is fufticiently
diflinguifhad from all mineral fubffances.

Grofvenor-Street, Jan. 8, 1761. I er. Mille-s.

L XXX VI. De Aberratione Luminis> in Su-
perfeiebus £t TLentibus Sphezricis refraclo-
rum *.

§ *•

Read April 2, £■>! I radius luminis AG, incidens in fu-
,76‘* perficiem quameunque refringentem

L E, infledtatur
fecundum rec-
tam G K, et
quffivis redta li-
nea AK occurrat radio incidenti AG in A, refradto
G K in K ; et redtae G D, normali ad fuperficiem re-
fringentem LE, in D; erit redtangulum GKxDA
ad redlangulum GAxDK, ut finus anguli inciden-
ts DGA ad finum anguli refradtionis DGK. Elf
enim DA ad G A, ut fin. DGA ad fin. ADG, et
GK : DK :: fin. GDK ; fin. DGK; quare, ob

* This Paper, though Tent to England in the fummer of the
year 1760, was, by accident, prevented from being read to the
Royal Society, till the 2d of April following.

fin.

[ 9+5 ]

fin. ADG = fin.KDG, erit componendo DAxGK
: G A x D I( ; : fin. D G A : fin. D G K. Qu,a2 ratio,
fi ponatur ut i ad r, erit /.GAxDK = r.GKxDA.

§ »•

Incidat radius luminis A G in fuperficiem fphseri-
cam LG, G

cujus cen-

trum eft D, a
et refringatur fecundum redum GK, quaeritur con-
curfus K radii refradi G K cum axe fphaaras A L D,
poftto arcu L G fatis parvo.

A pundo incidents G cadat GE normalis ad
axem A D, ducaturque radius fphsera? G D. His
fadis eft per elementa, AG q = AD q -j- D G <7
— 2 AD x DE = ADj{DL^-aAD xDL-LE

= .AD — DL^+2ADxLE=AL2+2AD
xLE, adeoque AG rr AL^ + 2 A D x L E =
(ob LE fatis parvam) AL -f- A E quampro-

xime. Similiter KGy = KD^+-DG^-f aKD x DE
= KD? + DL^aKDxDL-LE = KD + DL?
— 2 D K x L E =r KL^ — 2 K D x L E, adeoque

KG = y/RL?- 2KD xLE = KL — - DxLE

K JL

quamproxime.

Jam vero eft (§ i.)/.GAxDK = r.GKxDA,
quare fubfti- G,

tutis valori-

busmodoin- K le 35 "k b

vends ipfarum GA et GK, habetur fKDx (AL
X L E\ _ a . /tz t K D x L E'

AL

;) = r. A D X (K L -

KL

:), et

tranf-

[9+6 j

tranfponendo r.ADxKL — / .KDxAL = AD

x KD x LE x (— £■ + kx)-

Ponatur jam L A = A, L K = K, radius fphaerae
DL — a, adeoque A D == A + a, et D K = K — a .

His in noviftlma sequatione fcriptis, erit rKxA + tf
— xK — «LEx(j + [),

__ ? A a

unde tranfponendo et dividendo, K = - — — — -

i . — »• A — r a

A -f- a X K. — a X L E

(s + k)-

i — r . A — r a
Jam ft radius incidens A G fuerit axi A I) vi-
ciniflimus, evanefcet L E, adeoque et terminus

a + a X Iv ^ x L h Quare in hoc cafu

•, id eft, diftantia foci geometrici

K =

r . A — r a
2 A a

r . A — r a

ipfi A conjugati a vertice L, erit =

* A a

__ unde

i — r . A — r a

aberratio radii refradti G K ab hoc foco erit
A + a X K — a x L E

x (iqll fumendo a foco
.A — ra VA ' K7

contra dire&ionem curfus radiorum. Quoniam vero
aberratio ilia femper eft valde parva, erit

valor prope verus diftantia? L K ftve K, adeoque in
expreflione aberrationis fine fenfibili errore pro K
ufurpari poteft. Sit itaque diftantia L B foci geome-

J A Q

trici B a vertice fuperficiei L, ftve ===== — : = B,

i — r , A

ra

critque

C 947 3

“1“ K r™ LB = B - „(' + {)

quamproxime.

Dimidia latitudo fuperficiei refringentis, five di-
ftantia pundi incidentiae G ab axe, id eft LG, dica-

tur L, erit quamproxime L E == — : quare in for-

L2

mula modo inventa pro L E fcribendo — , et ulterius

concinnando expreffionem aberrationis ope asqua-

tionis B = 1 A a , habetur formula, qua in

i — r . A — r a ^

fequentibus prascipue utemur : LK = B-

r .i—r . B2L2

2

§3-

In formulis jam inventis figna fymbolorum illi
tantum cafui funt accommodata, quern figura expri-
mit, ubi radius luminis ab axe divergens ponitur in-
cidere in fuperficiem convexam, et poft refradionem
ad axem convergere. Accommodantur vero ad re-
liquos problematis cafus, mutando lignum radii
fphasrae a , fi radius luminis incidat in fuperficiem
concavam, et fignum ipfius A, fi radius incidens con-
vergat ad axem. Hoc fadto, fi valor diftantias LB
five B prodit pofitivus, fumenda eft diftantia ilia a
vertice L fecundum diredionem curfus radiorum ; fi
nesativus, contra eandem diredionem. Aberratio
vero radii a foco B, five BIC per formulas compu-
tata, fi fuerit pofitiva, fumenda eft a foco B contra
diredionem curfus radiorum ; fi negativa, fecundum
hanc diredionem. Si radii incidentes fuerint axi pa-

Vol. LI. 6F railed.

[ 94-8 ]

ralleli, facienda eft A infinita, et ft B prodit infinita,
radii refradi erunt axi parallel^ abftrahendo ab illo-
rum aberratione.

Si duo radii luminis AG, HG, in angulo quam

minimo A G H
inter fe inclinati
incidant fere per-
pendicular iter in
idem pundhim G fuperficiei cujufcunque refringentis
L G, et refringantur, prior in G K, pofterior vero in
GB, occurrentes lineae redse cuicunque in pundis
A, H, K, B ; dico effe B K ad A H ut eft r . L B q
ad ALA q , poftta i ad r ut ftnus incidentiae ad finum
refradionis.

Quoniam enim anguli valde parvi funt finibus fuis
quamproxime proportionales, erunt in parvis refrac-
tionibus anguli incidentiae et refradionis eorumque
adeo differentiae finibus incidentiae et refradionis pro-
portionales quamproxime. Eft itaque angulus AGH,
utpote differentia angulorum incidentiae radiorum
A G, H G, ad angulum B G K, five differentiam
angulorum refradionis radiorum GK, GB, ut i ad r.
(^iiare centro G inter hos angulos defcriptis arcubus
HE, KF, erit HD ad KF, ut AGH ad r.GKj

r\ ATT GH.HE 1", -rr- GK.KF
fed eft AH = — q~[~> et BK = — — , quare

pro HE et K F, fcribendo earum proportionales
AGHetrxG K, habetur A FI ad B K ut / x G H q
ad rxGK^, quamproxime, id eft, ut / x L A q ad
r x L B q.

[ 949 ]

§ f-

Data forma lentis refringentis, et data in ejus axe
diftantia foci radiorum incidentium, invenire punduni
ooncurfus radii cujufvis refradi cum axe,

G

j\ KB D C E

Sit locus lentis in L, ejus axis ALBC, dimidia
latitudo L G, live diftantia incidentiae ab axe, — L >
radius convexitatis fuperficiei primae, in quam radii
incidunt, — a ; radius convexitatis fuperficiei fe-
cundae, e qua emergunt, — b, radius luminis quivis
incidens AG, refradus GK. In axe lentis ABC
fit diftantia foci radiorum incidentium, five L A = A,
diftantia foci geometrici ipfi A conjugati, five LB
— ■ B ; diftantia foci geometrici C fuperficiei primae
ipfi A conjugati, five LC = C, et evidens eft, efie
etiam idem pundum C focum geometricum fuper-
ficiei fecundae conjugatum ipfi B. Sit tandem di-
ftantia pundi concurfus K radii refradi GK cum
axe, five L K = K.

Radius AG in prima fuperficie refradus tendat ver-
fus pundum D, et concipiatur a pundo B, quod eft
focus lentis
ipfi A conju-
gatis, radius
BG incidere

in fecundam fuperficiem, et in ea ita refringi, ut di-
vergat a pundo axeos E. Et dabuntur per § 2. aber-
rationes CE et CD, adeoque earum fumma DE.
Sed per § 4. eft D E ad B K ut r . L C q ad / . L B qy

6 F 2 quare

C 95° ]

quare B K = xDE = |?xDE. Jam per

r.i — r. C4Ir4 (\ i \ fr , i + r\

X(s+AiX(a + — )

r.i — r . C2 L*

§ 2. eft CD =
et CE -

2

* G+b) * G+4-r).

i B2

quarum fumma D E, duda in — dat aberrationem

quaefitam BK = i^xDE='

r .B2L2

2

[(;+!)'

yG + 1xI) + (f + ^)’,(T + iTr)J’ i“

poft evolutionem terminorum fubtrada de L B, five
B, relinquit diftantiam pundi concurfus LI( —

r . B4 L4

X1 .

+ Ti

B

2 ix

am vuiiv wi. * jul —

r+i±2:+ii+3r+i±r7

a’ r a a* + A'n T A’ /

r i i±3£ |.»f + 3.r +»:+’•(•

' b3' B bz ' B2 b ' B3 J

Porro quoniam pundum C eft focus ipfi A con-

jugate rcfpedu faciei primsc, erit L C = =

/ A a

r a

i — r . A

et quoniam idem pundum C eft focus ipfi B conju-
gate refpedu fuperficiei fecundas, erit L C ~

i B b i A a

per § 2. Hinc =

r . B — r b
iBb

i — r . B — r b

, adeoque B

■r . A — r a
r A a b

i — r . A , a -p b — r a b

five A + i = - — - x — — (- — . Dato fic valore iplius
A B r a b r

B, cognofcitur diftantia concurfus radii refradi G K

cum axe five LK, ejufque aberratio a foco B five

B K, quas ob fignum — fumenda eft a foco B contra

diredionem

5

[ 951 ]

diredlionem curfus radiorum, li valorem habet po-
fitivum j fecundum vero, li negativum.

Accommodantur vero hae formulae ad reliquos pro-
blematis cafus eadem ratione ac didtum ell § 3. de
aberratione fuperficiei limplicis.

§ 6. '

Expreftio aberrationis jam inventa, ad formam re-
ducitur ufui magis accommodatam, conjungendo ter-
minos, in quibus a et b eafdem habent dimen fiones,

et reducendo lingulas partes ope aequationis — - x

= -^-+^=p ubi P eft diftantia foci principalis*
Hac ratione calculum fubducendo habetur : — 4- 7?

aj

r ( 1! 3r V j_ , 1

— r P P* i — r P a 4- h J 3 A ^

i — r . P
r

i — r . P . a b

b3
B ¥

i — r. P

X

X

i — r. P
r

(-

(a * + B b p . ^fb ) J A1 a + frb ~

P . A +5 ) ’ A1 B=

r 1 . x

x b w

A a

(i — r 3 . i — r \

VTP1- TP . A + B /

i — r. P 'r r P . A +

Singulae harum partium dudtae in fuos refpedfive
coefficientes, r> i + 3r> 2/ + r, i + r, conjungantur
cum fignis propriis, ethabebitur: LK = LB — BK. =
B* IP //3 — 2 i2 r -f- 2 r3 3 i ft- 2 r 2 . / + r A B

B-

2 / P'

r . / + 2 r

>

42. P

A -j- B

vel etiam = B

/ — r . a -\- b
3 i -j- 2 r

+ A 4- B X b + a

B2L2

2TF

x

r . i 4- 2 r \

2 . i -J- r A . B

C 952 ]

§ 7-

Invenire lentem, quse radios luminis a data diftan-
tia advenientis in alia data diftantia colligat cum mi-
nima aberratione, ipfamque aberrationem minimam.
Retentis omnibus fymbolis ut fupra, fumantur dif-

ferentialia aberrationis modo invent®, -r-p x

3*

2 r

a ~p a

« . i + r
A 4- B

(=±r—

Vr= tkp

A , B r . ~ 2 r Y

<2 £ i — r . « -p

• *1. * l

politis a et b variabilibus, et habebitur

AjU ]ldb , r ■ i + 2 r x __ fed o[>

a 1 bx ' 1 — r a frr-

r f*it L_ .

b2

I + I=-

1 A “

a

r. P

+

, eft ~ + ^ = o i quare tollendo

per comparationem harum squationum differentialia,

A — B

invenitur :

b — a 2 . i -f- r . i —

b + a

X

r . i + 2 r

A + B’

ideoque

£ 4 r1 4- r i

b

2 1

4 r

. A + 2 . 2 i -p r . B
— J— 7 ' / 2 2* . B -p i . 2 l p T .A

; unde per aequa-

tionem - + - — x - p colliguntur radii facierum
- 1 b 1 — r A B b

a

lends quaefitae, fcil. a

2.1 — r . j p 2 r . A B

et b — — -

i . 2 i -p r

2 . i — r . 2 -p 2 r
i . 2 i -p r

i . 2i + r . B + 4^ + ri — 21

*P4,’ + n'

i . 2 i ~p r . A + 4 rr -p r 2 — 2 it . B
— ; five — rr

2.1 — r . j P 2 r . A B

a

2.i — r . 2 + 2 r

A

+

2.2 — r . 1
\r2 P ri— 2 i

2 1 1 . 1

— X - ; et 7 ==

2 r A £

— X

2.2 — r . 2 -j- 2 r

B*

riic

[ 953 ]

Kic valorss radiorum a et b fubftituti in formula
aberrationis generaii § 6. dant ipfam aberrationem
i . B1 L2 '

mmimam

X

Va + b !

r . 4.1

§s.

Poftquam in § praecedente formam lends iilve-
nimus, qus in datis circumftantiis aberrationem
minimam producat, et fimul ipfam ejus aberra-
tionem; ration! confentaneum eft, inveftigationem
aberrationis lentium ab hac forma difcendentium ita
aggredi, ut fimul appareat relatio formarum harum
lentium ad illius formam, et aberrationis harum ad
illius aberrationem. Solent enim conclufiones pro-
dire concinniores, fi ad calum inter reliquos maxime
fingularem et unicum referantur, qualis hie eft cafus
aberrationis minims.

l , Q. I —i— V

Scribatur brevitatis caufa b pro — ==, et

A 2 . * — r . 1 -|— 2 r

K pro et erit pro determinandis radiis

A 2 . t — r . i -f- 2 r

. 1 h K

a et b lentis aberrationis minims, - = et

a jj i \

1 TT

l = p per § 7. Ponatur jam generaliter pro

I b K.

radiis a et b faciernm cujufvis alius lentis, - = g + ^ -
4- et ~ = ~ ~ — £ ; quos valores ipfarum

- et 7 tales afiumo, ut earum fumma \ 4- 7 =

a b _______ « 0

MHc x 5 + s> five 4r * f ■+ S’ 9uemadm°-

dum

[ 954 ]

dum oportet. Subftituantur hi valores ipfarum ^ et |

in formula aberrationis general!, x (p — ^ _j_- p-

\

^ § 6. et peradto
p

z + r A , B

x7+x-

r . z -f- 2 r

A -f B « 1 b
calculo invenietur

i — r . « -f- £
/• B1 L2

* + 2 r . P3 V A + B

f — [-

V A 4- B T

z — ?'

2 7

xz) pro aberratione lentis, cujus facies lu-
mini obverfa radium habeat a , et facies a lumine
averfa radium habeat b , exiftentibus - = p -p — + p,

et l ~ -f 5. — t . P didantia foci principalis, A

b A Jj i

diftantia foci radiorum incidentium, et B refradto-
rum.

Commodum itaque hie accidit, ut numerus x ,
qui relationem format lentis ad lentem aberrationis
minims defignat, idem quoque relationem aberra-
tionis ejus ad aberrationem minimam ratione non
minus limplici exhibeat.

§ 9-

Si in formulis § praeced. exhibitis, pro radiis fa-
cierum lentis ejufque aberratione, ftatuatur x = o,
radit lens ad earn formam, quaa aberrationem dat
minimam, et aberratio ejus ad aberrationem mini-
mam. Si vero non fuerit x = o, apparet ex iitdem
formulis, cuivis aberrationis quantitati, quas major
fit aberratione minima, duas diverfas refpondere len-
tis formas, quarum utraque definitur asquationibus
b . K . x i b , K

* ~ B + A

t x I

+ p-) ct ~

a

A 1 B

x

l7’

ubi

x pro
altera

[ 955 ]

altera pofitive, altera negative accipitur. Nam in

i B»L* / P

Va

formula aberrationis

2 . i r . P*

4 ~B

X'lj.! ■

4*

r . r

4.2 — r

4~

; + 2r

rii .

— x1) non comparet nifi quadratum ipfius x ,

quod idem manet, five radix x fumatur pofitive, five
negative.

Quoniam aberratio quaevis

i B1 L*

(:

+

4 *

4 . i — d2,
i Bz L1

2 . / -j- 2 r . P3 ^A + B

i — --4- — x2) eft ad aberrationem minimam

x(

L_ 4.4

A -f- B 4.

i — r.rN .

in rationemajoris

2 . i + 2 r . P3

inaequabilitatis, ftatuatur ilia ratio 1 4- ad 1 ; af-
fumendo m pro numero quovis, et invenitur x =

P

+

m

i +

W(

A+ B

+

4 *

Et fic ex data

ratione aberrationis alicujus lentis ad aberrationem
minimam, datur illi correfpondens numerus x , ad-
eoque et radii facierum ejus, per fuperiora.

Numerus hie x, quoniam fimul et formam et
aberrationem luae lentis jndicat, dicatur index lentis,

et feribatur brevitatis caufa f pro

4*

r . r

I + 2r

, ut aberratio fit

B*L*

2g.V3 \A + B

(;

4„_Xet*Pro

? 4-/+£2*2)-

§ io.

In linea reefta AO, tanquam axe communi, dil-

1 u in

pofitas intelligantur lentes quotcunque P, P, P, P,
&cc. quarum foci conjugati fint refpedive, lentis
V o l. LI. 6 G prim as

C 956 ]

I I II II in

primae A et A; fecundas A et A; tertias A et A ;

III IV

quartae A et A, &c.

11

\Ac

1

p

1

n

m n

IK

P

III

B .

JP

71

1

^>^AC

it

P

B

ill

Ii

Radius luminis, veniens a pundto A, refringatur in.

1 11 in

omnibus his lentibus in pundtis L, L, L, L, &c.

1 u hi

pergens fecundum curfum ALL L.L, et poft fin-

1

gulas refradtiones occurrat axi A O in pundtis B, B,

II III I II III IV

B, B, &c. aberrans a focis A, A, A, A, &c. lon-

I II I HI II IV III

gitudinibus A B, A B, A B, A B, &c. Quasruntur

jam has aberrationes.

1 11 hi

Lentium P, P, P, P, &c. diftantias focorum prin-

1 11 hi

cipalium dicantur refpedtive P, P, P, P, &c. et in-
1 n 111

dices x, xy x , x, &c. Diflantiae focorum conjugal
torum a fuis refpedtive lentibus Tint : pro lente prima

P, P A A, PA = B; pro lente fecunda P, P A

I I II I II II II U II III

= A, PA = B j pro lente tertia P, PA = A, PA

II III III III III III IV III

= B ; pro lente quarta P„ P A — A, et P A = B3

et ita porro : ponatur praeterea P L, five diftantia

pundti incidentias in primam lentem ab axe = L, et

1 1 11 1 ir m

. * 1 A T " 11 A. A _ A. A. A _

ent P L = rr x L, PL = — r x L, PL = r — rr x L,

B B . B- B . B . B

et ita porro,

L

[ 957 ]

I

I. Vidimus in § p. aberrationem A B lends primac

B* Lr / P

x(;

^ efle 2g.P‘ " VA + B

et g = * + *:.
4.7— r?1 ° i

+ / 4- £2 *2). uW / =

II. Concipiatur a foco fecundae lentis A ipfi A

ii 1

conjugato in illam incidere radius A L, qui refradtus

1

fecundum L C, conveniat cum axe in C, aberrans a

i 1

foco A longitudine AC: et erit per § 9. aberratio
^C== IT”] Fjpi * +/+£2*2), fcribendo

. . A 1 1 1

fcilicet g-xL pro L, B pro A, A pro B, et P pro

1

P. Hasc aberratio A C, addita ad aberrationem primae

1

lentis modo inventam, A B, dat fummam B C. Eft

1 a

1 1

1 11

vero B C ad BA ut P A q ad PA q, five A2 ad B2,
id eft quantitates aberrationum a focis conjugatis funt
ut quadrata diftantiarum focorum a lente, quod facile

11 1

probari poteft. Ergo aberratio A B, a refraddone

1 gx

per duas lentes P et P produdta, habetur = 7- x B C

B*LX r B2 f P * .r . _2 IX . A

— 2g X p: (a + B + / + £ * ) +B,_

P3

A -J— B

£ #2)J*

6 G 2

III.

[ 958 ]

ill

HI. Concipiatur fimiliter a foco interiori A lentis

M _ _ XU II

tertiae P incidere in illam radium A L, cumque re-

i

fradum convenire cum axe in pundo C, et aberrare

a hi

a foco exteriore A longitudine A C, quae per § 9. eft

— ^ 1 L„ x f u-~ - + f+ g2 x1). Haec addita
£ . B1 . B1 . P3 \A-fB

ad aberrationem duarum priorum lentium modo .in-

11 1 a 1 n 1 11

ventam> AB, dat fummam AB + AC = BC, de-

11 n 11

inde fiat ut A2 ad B2 ita haec fumma B C ad aber-

, . «« 11 B1 . L* r B1 . B*

lentium AB — — — ■ x ^ j -

2g La^a'.P3

\A + B 1 0 B1. A*.P3 \A-f B

-f ■. A* ' A-.T- ( nZ-7T +f+gl **)]•

B1 . B1 . P3 \A + B

IV. Eadem ratione invenitur aberratio A B poft.

1 11 111

jefradionem per quatuor lente& P, P, P, P, =

in t — 1 i> _

B1 . L* r B1 . B“ , Bz f P , r , ,

— « — r— - x Ca+"b +/+«*)

La*.A‘.A*.P> va ^

11
A

rationem trium
P

IV III

B*.BVA* ( P . r. ,M. B*,A*.A*

-1 — — r- x ( YTT+/+<? * ' R. S

B* . A1 . A* . P3 \A + B B . B“ . A* . P

(irs+/+^'"2)+A^(

hi m

A -f B

4- f 4- £2 a;2)]. Et eadem ratione progredi licet ad
J definiendara

[ 959 ]

definiendam aberrationem radiorum poft tranfitum
per plures lentes.

In his computationibus omnes lentes concipiuntur
convex®, et foci radiorum incidentium ponuntur ja-
cere ante lentes fuas, refradtoruin vero poft lentes re-
fpedtu curfus radiorum, quemadmodum figura exhi-
bet. Formulae autem allatae ad quofvis alios cafus
facile accommodantur, mutando figna fymbolorum,
prout requirit mutatio hypothefeos, quod monuifle
fufficiat.

§ IT*

Datis pofitionibus et focorum principalium diftan-
tiis lentium quotcunque, oporteat invenire formas
earum, qu® efficiant, ut radii luminis, a dato in
communi earum axe puncto advenientes, poft refrac-
t-ionem colligantur in ultimo foco fine abberratione,.
ft fieri poteft.

Solutio problematis generaliter abfolvitur, ponendo
expreftionem aberrationis, dat® multitudini lentium
convenientem, (§ 10.) nihilo ®qualem, quo ipfo ha-
betur ®quatio definiens rationem requifitam indicum

i n in

fingularum lentium x, x , x, x, &c. Et quoniam
relatio omnium indicum unica hac ®quatione conti-
netur, patet multum hie locum efte arbitrari® non-
nullorum afiumtioni, prout requirunt vel fuadent
apertur® lentium ali®que circumftanti® ex fcopo
inftrumenti dijudicand®, de quibus hie non eft fer-
mo, In genere tantum cavendum eft, ne aftumtio
ita fiat, ut aliquis indicum prodeat imaginarius.

i n m

Determinatis fic indicibus x, x, x, x, &c. mvem-
untur radii facierum per § 8. Dicatur fcilicet radius

faciei

[ 9^0 ]

faciei anterioris fingularum lentium a, pofterioris b-
diftantia foci principalis a lente, Pj diftantia foci ra-
diorum incidentium ante lentem, A ; diftantia foci
radiorum refradorum poft lentem, B ; et index ad

lentem pertinens, x j et erit - = ~ -f ~ 4. A et l

Q JtJ A Jr b

_A_l_ £ _ -

A ' B P
4 r* + r i — 2 iz
2 . i ■— r . t 2r
radii a et b.

, ubi h = — J==^-t=L=, et K =*

z.i — r . i 2 r

unde dabuntur fingularum lentium

Si nullus detur valor realis indicum x, x , x, x ,
See. id quod accidit, ft omnes aequationis termini ad
unam partem rejedi fuerint ejufdem figni, caius pm-
pofttus eft; impoflibilis.

§ ia.

Exemplum I. Ex duabus lentibus telefcopiuni
componere, quod lit liberum ab aberratione, et objeda
vifa amplificet in data ratione » ad i. Abftrahitur
autem hie a reliquis boni telefcopii requifttis.

1

Lentes duaa primae P et P reprasfentent binas len-

tes telefcopii quaefiti, P quidem objedivam et P ocu-
larem (vid. fig. § 10.). Aberratio harum duarum
lentium (§ 10. caf. 11.) nihilo acqualis pofita dat

I I

• 1 / B2 x% Aa x2

sequationem generalem : g2 x ( — — 4- —

\ A1 . P3 B1 . P3

+/xf— +— +— A-:

\Al.‘P3 B\PV A\P\A-fB B1 . P1 . A -f- B

= o. Quoniam per conftitutionem telefcopii, radii lu-

minis

[ 96* ]

minis in lentem objedtivam incidentes, et e lente oculari
emergentes, funt axi telefcopii paralleli, erit A infinita,

i i i

adeoque B = P ; item B infinita, adeoque. A — P.
Quare deletis duobus ultimis aequationis terminis,
utpote evanefcentibus, et in reliquis in fcribendo P et

I X

P pro B et A, habetur pro cafu hujus exempli asqua—
tis g2 x (Pa;2 -J- P x2) -\-f x (P + P) — o, relati-

i

onem indicum x et x defihiens, requifitam ad id, ut
aberratio radiorum e lente oculari emergentium nulla

I

fit. Jam fi in hac aequatione P et P ponantur ejuf-
dem figni, five utraque lens convexa, vel utraque

i

concava, null us valor realis haberi poteft pro x et x,
adeoque problema in hoc cafu erit impofiibile. Sta-

i

tuatur itaque P negativa, five lens ocularis concava,
fumendo pro exponente amplification^ objedli telef-
copio vifi, #, numerum quemvis pofitivum, et faci-

* j

endo P = — - P, ut patet ex opticis, Scripto hoc

1 . ■> . ^ / T

valore pro P in aequatione indicum, evadit ilia g 2 x (x2
n xz) x n — i . Horum itaque indicum utrumlibet

X

pro lubitu afiumere licet, modo ne x fiat minor, quam
^r==r7

— quod redderet indicem x imaginarium. .
S'

Altero indicum fic aflumto, alter determinatur per

allatam asquationem g2 x ( x 2 — n x2) —f . n — i.
Quo fadto radii facierum utriufque lentis prodeuntper
§ ll. utfequitur:.

3.

Radius

[ 962 ]

p

Radius faciei anterioris lentis objediva ss «j—— ,
pofterioris = »

Radius faciei anterioris lentis ocularis

t

P

K + x*

pofterioris

T> ubi P fumenda eft negativa, five

h — x

P — — Ip ut didtum eft.

tl

Pro quovis itaque pari valorum correfpondentium

indicum x et .v, quatuor prodeunt diverfae problema-

tis folutiones, ob figna duplicia ipfarum x et ,v, un-
de duae prodeunt form* utriufque lentis, quarutn
quaelibet combinari potcft cum binis formis alterius
lentis.

Si detur vel aftumatur forma alterutrius lentis, for-
ma alterius per fupradidta commode determinatur.
Sit v. gr. lens objediva plano-convexa, habens fa-
ciem convexam antrorfum verfam, planam retrorfum.

P

Radius faciei ejus pofterioris ftatuatur infinitus,

p

et erit x = K, adeoque radius faciei, anterioris
P * -

h+ K

b 4- *

x P. Pro x fcribatur K in aequa-

tione indicum x2 — n x 2 = - et erit x =

* •/

+ n Kd, unde dantur radii facierum lentis

ocularis, idque dupliciter, ob lignum duplex valoiis
ipfius x .

Vidimus

[ 963 3

Vidimus in folutione hujus problematic aberrati-
onem a duabus lentibus produdtam non polfe evanef-
cere, fi utraque fuerit convexa, vel utraque concava,
•cujufcumque fint formas et quomodocunque'compo-
nantur. Idem quoque obtinet in quacunque leiiti—
um multitudine, qua; omnes fint convex®, vel oni-
nes concave. Gmnes enim lentes, quarum facies
fuperficierum fph®ricarum funt fegmenta, abcrratio-
nes a focis fuis eo producunt, quod radios luminis
refra&ione nimium infle&unt; unde facile perfpici-
tur, lentem convexam, convexis additam, vel con-
cavam concavis, errores a prioribus produdtos augere,
Quare ut aberratio a foco ultimo evanefcat, debe-
bunt lentium alias effe convex®, ali® concav®, quo
nimi® radiorum incurvationes in unam partem corri-
gantur per nimias incurvationes fadtas in partem con-
trarians

§ 13*

Exemplum II. Propofitum fit inveftigar-e for-
mas binarum lentium, qu® juxta fe pofit® radios in-
cidentes axi parallel's in data a lentibus difkntia R
colligant, citra aberrationem ex figura facierum
Iph®rica oriundam.

Quoniam in cafu hujus exempli radii incidentes
ponuntur paralleli erit in ®quatione (§ 10. caf. 2.)

pro relatione binorum indicum x et xy A infinita,
adcoque B = P. Et quoniam lentes ponuntur juxta

1 1

fe pofit®, erit earum diftantia B -f- A = o, five A
= — B = — P. Pr®terea eft etiam -r = i + “r»

A o

I

unde B ' — P =
Vol. LI,

6 H

Subftitutis itaque bis

valoribus.

[ 96+ ]

valoribus, erit aequatio pro relatione indicum in cafu
praefenti : gz . (p5 . x* + P3 . x* 1) -\~f> P3 + P3 =

I

P . P . P + P, five P3 x2 + P3 x2 = £-±-^ x (7+7. P P

i J

— f > P2 + P2)> quae aflumto numero quovis n, et

fiatuendo P = n P, evadit x 1 4- nl xz — — L..r.

1 gz

x (n — ft2 — n ~>r i . f). Ne autem cafus propo-
fitus fiat impofiibilis, ob utramque lentem convexam,
vel utramque concavam, per n Temper intelligi debet
numerus negativus. Aflumatur jam pro Cubitu al-

teruter indicum x et x} et dabitur alter per aequa-
tionem allatam.

Determinato vero utroque indice, radii facierum
erunt ut fequitur :

Radius faciei anterioris lends prims = 7—? — ,
„ r b + X*

pofierioris =
lius

r

. p

K — x’

Radius faciei anterioris lentis fecundae

»-f-i . h — ■ « K -f- jc

pofierioris = —

n 1 . K — nb — #

1 >

ubi efi 71 P “ P, pofito n numero negative.

Diftantia foci principalis fyftematis binarum len-
1

tium P et P dicatur R, et quoniam efi i- =

I j

erit P = — ~ R, et P = n -j- 1 • R, quare in ex-
prefiionibus radiorum feribendo hos valores pro P et
P, habebuntur:

9 Mill

5

Radius

[ 965 ]

Radius faciei anterioris lentis primse =

n + r

n

R

n -f-i

h -\r X

pofterioris =

n

- R

anterioris lentis

, K — ^ *
Radius faciei

— — — ... ... i

» + I . R n . .

— , pofterioris

fecund®

R

n -j— i

» + I . ^ H K -}- * » -f- i . K — nh — x

Et hae lentes juxta fe pofitas radios incidentes axi
parallelos in diftantia a lente, R, colligent fine aber-
ratione, fi diftantia foci lentis concavae major fuerit
diftantia foci lentis convexae j fi autem contra difper-
gentur radii fine aberratione a puncfto ante lentem,
cujus diftantia pofitive!fumta eft R.

Pro cafu fingulari hmjus exempli, ponamus requi-
ri formas binarum lentium ita cbmparatarum, ut di-
ftantia foci principalis lentis concavae fit ad diftanti-
am foci principalis lentis convexaa, ut 3 ad a, et ut
radii colligantur in diftantia R a lentibus. Si lens
anterior debet efte convexa, erit n = — -§> et ®qua-
tio definiens relationem indicum lentis convexaa x

l\f : ~*r>/ - f/V> ” ’ ' r j /

ct lentis concavas x, 8 x1 — 27 x2

ig/-f- 6

gz

X

De-

terminatis vero decenter indicibus x et x , radii fa-

cierum erunt, utfequitur: rm )

* 1 • * R

Radius faciei anterioris lentis primae = —j— - — ,

3 * I 3 ^

R

pofterioris = :

_ r- ! 3 K 2X r

Radius faciei anterioris

R *

■7, pofterioris :

if

• 1 r>v

3 K — b -j— 2 x

6 H

lentis lecundae ,
R '

mm,m 1 -*» ■ ■■■ ■ ■■

I

3 h K — - 2 A?

Si

[ 966 J:

Si vero lens anterior debet efte concava, erit n =_
— -j, et relatio indicum 8 x1 — 27 xz =
radii vero facierum ut.fequitur:.

' _ JO •

Radius faciei anterioris lends prim# = — ^

R

pofterioris = — — ^ — ;

r 2 K — 2 *

Radius faciei anterioris lentis fecund#

R 0 • • R

poller ions = —

h 2 K -f 3 at

K + 2 b — 3 x

§ H*

Exemplum III. Propofitum fit, telefcopium ex
tribus lentibus componere, quarum prima P et fe- -

cunda P juxta fe poftt# vitrum objedivum duplex
conftituant, cujus diilantia foci principalis fit R;

tertia vero five ocularis P, habeat diftantiam foci

p — — , ut potentia amplificandi delignetur per nu-

1

merum m. Ponatur praeterea P = n P> intelligendo
per n numerum datum negativum, eumque unitate
majorem, li lens convexa anterior eft collocanda,
minorem ft posterior, ut radii poft refradionem itr
vitro objedivo convergant, quemadmodum expofi-
tum ellin exemplo praecedente. Quaeruntur autem
form# harum trium lentium, ut telefcopium liberum
fit ab omni erratione ex figura illarum fphaerica ori-
unda.

Aberratio a tribus lentibus P, P, P, oriunda (§10.
caf. III.) nihilo sequalis pofita, dat t — V/T+b

Hh

V • J

[ 967 I

'+ /+ fx1), + ' * .Ar ( T^-T +/-f «***!'

T,/ 6 B2 . A2 . P3 V A -f* B

X II /■ II

A2 . A2 ( P , r , i M _ .

4* 7 n- ( n II + / + 5

B2 . B2 . P V A + B

Symbola banc aequationem ingredientia per hypo—

the fin hujus exempli ita determinantur : ob A infr-

P 11

nitam eft x-t-r == °> et B = P- °b B infinitam

II

A + B

eft

II M

A + B

= o, et A = P. Ob lentes P et P juxta

i i

fe pofttas j eft earum diftantia A + B.= o, live A =s

_B= — P. Ob^ —jr + 4-. etP = «P„eft

P = ” ^ -■ R, et ^ == n i . R. Prasterea eft B = R’i

n

et P = — . Hisitaque valoribus fubftitutis, et aequa—

i a

tione ordinata, habetur relatio indicum x, x, x, ex-
prefla ut fequitur: gz x \nz x2 ^ x2 -J — — x2)

/x («* + i + ~ =*■« • 71 + 1» Determ i-

natis indicibus x} x , x, habentur. per § n.- radii,
facierum : videlicet,

.... • ft H- i • R

Radius faciei anterioris . lentis primae = _ ■ => >

tl . u •* "J • A"

n . - n 4- i . R

poftenons = — ;

Radius faciei anterioris lentis fecundae =

71 — i • R

n - f- i . h — n K + ,v

7, pofterioris =

n 4- I • R

I >

»-j- I ,K — nb — *

Radius

r 968 ]

Radius faciei anterioris lentis tertlse = -

- -R

pofterioris

R

m.K + *

in . h

11

x

Ita ft vitriim objedtivum hujus telefcopii compo-
nendum fit ex duabus lentibus, cbnv’exa et concava,
qua rum diftanti® focales fint ut 3 et 2, debeatque
primo lens convexa anterior collocari, oportebit fu-
mere ?i ■=. — et erit aequatio pro indicibus :

g2 X {27 X2 — 8 x2 + +/x (ip + •i) + 6

= o, et radii facierum :

Radius faciei anterioris lentis primae = 5

n . R 3h ~h 3X*

pofterioris =

Radius faciei anterioris lentis fecund# =

R

— r, pofterioris = 5

3K-6 + 2* r

Radius faciei anterioris lentis tertise = R

R.

m K -f - mx

pofterioris =

mb — mx

Si vero lens concava anterior eft coliocanda, debet
lumi n f, unde asquatio pro indicibus prodit

** x (-8** + ^ + |) +/x (,9 + i) + 6
= o, et confequenter : _

Radius faciei anterioris lentis primfe = R

pofterioris = ~R r .

r zK-2^

2 b -j~ 2 x’

Radius

[ 969 1

Radius faciei anterioris lends fecundae

j j j . - ' - A ' ‘ ' *

R n . . R

— ■ — -Y, poi ten oris = ;

b - f- 2K -j- 3^ K -}- 2 £ — 3 #

Radius faciei anterioris lentis terti«£ = R ,

mK + mx

R

pofterioris = r.

1 tnb — J7i *

§ if-

Vidimus in folutione gene.rati novifiimi problema-
tis (§ ii.) et fubjundtis exemplis (§ 12, 13, . 14.) re-

1 ir

lationem indicum x, x, x , &c. unica tantum asqua-
tione defimri, adeoque judicio artificis plurimum efie
relidtum in commoda eorum afiumtione facienda.
Duas autem funt confiderationes, quibus hasc affum-
tio utcunque dirigi poffit. Prima eft, ut nullus in-
dicum fiat nimis magnus, five, quod eodem recidit,
ut formas lentium quamproxime accedant ad eas,
quae in datis circumftantiis aberrationem dant omni-
um minimam. Hac enim ratione errores in forma
lentium forte commiffi minus nocebunt, quemadmo-
dum ex natura minimi notum eft. Altera eft, ut
lingulae lentes, quam fieri poteft, proxime evadant
requaliter utrinque convexas, vel aequaliter concave,
quo fie t, ut majores aperturae lint patientes. Quan-
titates enim aberrationum fupra definite non funt nifi
quamproxime verae, et tanto magis fallunt, quanto
facies lentium fuerint majora fuarum fphaerarum teg-
menta. Binae hs regular, etiamfi fibi invicem faepi-
us adverfuntur, nec facile definiri queat, quantum
in quovis dato cafu uni vel alteri -ipfarum fit tribuen-
dum 5 non dubito tamen, quin judiciofo artifici fint

profuturas

[ 97° ]

profuturas ad mediam viam tenendam inter litram-
que.

Eaedem quoque confiderationes impediunt, quo
minus certi aliquid definire auflm, de maximo pof-
fibili effedtu inftrumentorum opticorum fecundum
base principia compoiitorum, vel de modo perfedtif-
iima componendi. Regulae hue pertinentes tutifii-
me exfpedtantur ab experientia, modo dirigatur a
theoria.

§ 16.

Expofitis jam breviter quas dicenda habuimus de
aberrationibus radiorum homogeneorum refradtorum,
ortis a lentium figura fphaerica, ut et de modo illas
corrigendi in inftrumentis opticis : liceat etiam pauca
addere de altera ilia aberrationis fpecie, quas a diver-
fa radiorum refrangibilitate oritur, quae objedta trans
lentes vifa coloribus inficit, et maximam confufionis
partem producit. Creditum hucufque communiter
fuit hoc vitium nulla arte emendabile, donee ingeni-
ofiffimus artifex Londineniis, Dollandus, experi-
mentis inftitutis feliciter deprehenderet, varia dari
vitrorum genera, quas, licet fere aequaliter refringant
certum quoddam radiorum genus, plurimum tamen
diferepent viribus refringendi reliqua radiorum gene-
ra, adeoque et radios heterogeneos a fe invicem fepa-
randi : quo eximio invento et theoriam et praxim
optices infigniter auxit. Difcimus enim hinc, rati—
ones refradtionem radiorum divert! generis nullo
modo a fe invicem dependere, ut hucufque fuit cre-
ditum ; adeoque fruftra quaeri regulam, qua ex datis
refradtionibus radiorum diverfi generis in uno aliquo
medio inveniantur refradtiones eorumdem in alio ;

vel

C 971 3

vel qua ex data refradtione unius alicujus radii in
quovis medio, inveniuntur refradtiones reliquorum in
eodem medio. Praxis quoque telefcopiorum diop-
tricorum infigne incrementum hujus inventi beneh-
cio nadta eft. Scilicet fagaciffimus inventor modum
inde derivavit corrigendi aberrationes ex ieparatione
radiorum heterogeneorum oriundas, componendo
vitrum objedtivum ex duabus lentibus, una convexa,
altera concava, quae ita Tint comparatae, ut una alte-
rius effedtum in radiis feparandis deftruat, quemad-

niodem in Vol. L. Part. II. p. 73 3* e*LecK ia^r
adlionum Philofophicarum expofuit. Quod artm-

cium ita breviter explicabimus.

§ !7-

Sit P lens quaecunque, habens radios faciei urn
fuarum et b ; diftantiam foci principalis inediocri-
ter refrangibilium P j et a x in redtam O O.

EAC

1 1

B A

—i—i-

Ratio refradtionis radiorum mediocriter refrangibi-
linm ex aere in lentem fit N ad I ; radiorum ma-
xime refrangibilium N + » ad I, et radiorum mi-
nime refrangibilium N — » ad i, exiftente n numeio
valde parvo refpedtu ipfius N. In axe lentis OO
lint pundta A, B, C foci radiorum in lentem V > -
cidentium, A mediocriter refrangibilium B maxime
et C minime refrangibilium, quorum focorum -
ftantiae A B, A C fint valde parva?, et ponantur puntt<

A, B, C, foci conjugati ipforum A, B, C refpedhve,

pro fua quique radiorum fpecie, ita ut fint
F Vol? LI. ** dlfIip

-f Ci

[ 972 ]

diflipationes radiorum heterogeneorum circa focot

i

conjugatos A et A. Quaeratur earum relatio.

Quoniam B et B funt foci conjugati radio-
rum maxime refrangibilium, quorum ratio re-

fradtionis eft N 4- n ad i, erit ^ 4- —■ ==

1 PB

■ — ' i

N-f72 — ■ i . • — f- — . Similiter quoniam pundta C et C

funt foci conjugati radiorum minime refrangibilium,
quorum ratio refradtionis eft N — n ad i, erit

X- + —r = N

PC

PC

n 4- i . - + 7.

‘ a 1 b

Subtrahatur ha:c

pofterior requatio a priore, et habebitur

PB

PC

d — ~y — = 2 + 7, five coniungendo binos

PB PC a b

PC — PB , PC — PB
terminos : H ; r

PB x PC

PBxPC

' qua:

pro PBxPC etPB x PC, fcribendo P A q et

1 r

PA et pro - + r fcribendo rr-~— — , evadit

J F a b N — 1 . P ?A*

= j- -^2. exhibens relationem inter dif-

N — 1 . P 1

1 1

fipationes conjugatas B C et B C.

His pracmidis, intelligantur lentes quotcunque P, P,

It HI

P, P, &c. quarum diftantise focorum principalium
refpedu radiorum mediocriter refrangibilium fint

1 11 hi

P, P, P, P, &c. refpcdtive, ordine difpofitas in axe

earum

RAC

(O

[ 973 ]

1 I (

BAG

I 1 i -

II M II

RAC

— n-v —

ii

P

n.i in in

RAC

— r-H-i—

111

earum communi O O. Rationes refradionum ra-
diorum mediocriter refrangibilium in his lentibus

i ii

ordine fumtis fint refpedive, N ad i, N ad i, N ad J,

N ad i, &c. radiorum maxime refrangibilium N + n
ii ii ii in hi

ad i, N -f- n ad i, N + n ad i, N + n ad t, &c.
et radiorum minime refrangibilium N — n ad i,

N — n ad i, N — n ad i, N — n ad i, &c. runda

111 IV

A, A, A, A, A, &c. fint foci conjugati lentium
refpedu radiorum mediocriter refrangibilium, pun da

1 11 111 1V „ ^

B, B, B, B, B, &c. refpedu radiorum maxime re-

1 II 1U IV

frangibilium, C, C, C, C, C, &c. refpedu minime

° I I II II III III IV IV

refrangibilium, ita ut B C, B C, B C, B C, B C, 6cc.

fint diffipationes fucceffivae radiorum heterogeneorum
in axe lentium. Dicantur tandem diftantias focorum
coniugatorum a fuis refpedive lentibus : P A — A,

’ ° , j I I II 1 II II II II III II

P A = B; PA = A, PA = Bj PA = A, PA = B;

iii hi 111 in iv III

P A = A, P A = B, &c.

Jam fi in sequatione pro relatione diffipationum

conjugatarum modo inventa,

BC 2 n , BC
^“NTZ7.P+PA?J

per B C et B C intelligantur fucceffive fingula paria

diffipationum conjugatorum, et per P A et P A di-
flantiae focorum conjugatorum ipfis refpondentes ;

6 I 2 item

VV IV IV

RAC

-t — r— »-

o

[ 97+ ]

item per P> N et n eorum valores fingulis lends pro-
prii, habebuntur tot aequadones, quot funt lentes :

videlicet ; BC=B!x BC =

B* X B C — B1 X (=—= -

\N — i . P A 2/ \N — i . P

+

II II

B

' XI

A2

it v * hi in inv

C\ f 2» . BC\

) '■> ® ^ ^ X ( 771 m 1

2 J ' \N — i . P A2 /

ita

porro, fi plures fuerint lentes. Ponantur pundla B,
A, C> coincidere, five ex primo foco A prodire ra-
dium compofitum, ut difiipatio prima B C fit nulla,
et reducendo lias aequationes, ponendo BC = o,
habentur valores diffipationum fuccefli varum, pro

quovis lentium numero :

i. B C = B: x

2 n

n n i

2. B C = B2 x

N — i . P

I

2 n

N

nt m ii

3. BC =: B2 x =

11

1 . P

n
2 n

, B2 . B2

: H — 7 — x

2 n

A1

ir

N — 1 . P

N — 1 . P

. B2 . B2

n + -n— *

2 tl

A1

N — i .P

, B2 . B2 . B2

"1 77 ; X

2 «

ir 1

A2 . A2

IV IV

N — i . P

hi

4. BC = B2 x

hi ir 1

, B2 . B2 . B2

— n — X

m nr n

2 n . B* . B2

777 m l J‘‘ *

N — i . P A2

1 m ir 1

2 « , B2 . B2 . B2 . B2

7 + 777—77 7 X

If

2 n

11

N

II

1 . P

2 »

A2. A2 N-i.P A\A\A2.A2 N-x.P
Et ita deinceps, fi plures fuerint lentes.

[ 975 ]

/

§i8.

Datis pofitionibus lentium quotcunque in com-
muni axe, una cum fingularum legibus refradtionum
pro radiis omnis generis, oporteat invenire relatio-
nem inter diftantias focorum principalium earundem
lentium, quse efficiat, ut radii heterogenei a quovis
pundto advenientes vel paralleli, poft refradtionem
in omnibus lentibus emergant, fine difiipatione a
diverfa refrangibilitate ‘radiorum oriunda, fi fieri
poteft.

Solutio problematis generaliter abfolvitur ponendo
expreflionem diflipationis, datas multitudini lentium
convenientem, § 17, nihilo asqualem, quo ipfo ha-
betur asquatio definiens relationum diftantiarum fo-

1 h in

calium, P, P, P, P, &c. requifitam ad id, ut dif-
fipatio in foco ultimo evanefcat. Ita in cafu binarum

lentium habebitur :

x

in cafu trium lentium erit :

II

n

11

p

11

N

+

B1

II

A2

X

I

71

N — 1 .P

, B2 . B2
4— " ~ — x

n

u I

A2. A2

m

n

N — I . P

= o j in cafu quatuor lentium :

II

n

, B2 . B2
Ti + 15 5- x

I

n

11

. IP

Hi m ~i ~n~ 11 1 7, ‘I, 1 1

N — i X P A N — i X P A‘A N — ixP
B2 . B2 . B2 n

d” 51 II I q

A2 . A2 . A2 N — l x P
fuerint lentes.

= o et ita porro, fi plures

Ita

[ 976 ]

I

Ita fi in aaquatione pro binis lentibus, ^ — -

N — i . P

B1 n ...

-|- ~ x — == o, ponatur diftantia lentium

A 2 N — I . P

B -f- A =rr o, ut evadant contiguse, quemadmodum

I

in vitro obie&ivo Dollondiano j habetur — 7

N — 1 . P

4. — = o. Unde patet alterutram lentium P

N — 1 . P r

1

et P faciendam effe concavam, alteram convexam,

1

et diflantias earum focales affirmative fumtas P et P

faciendas effie in ratione - ad , quas ratio

evadit n ad n, fi vires refradtivse media? utriufque
lentis fuerint aequales.

Similiter fit conftruendum telefcopium ex tribus

1

lentibus, quarum duse priores P et P juxta fe pofitai

11

conftituant vitrum objedtivum, tertia P fit ocularis,
et potentia amplificandi exprimatur numero m.

Quoniam lentes priores P et P funt juxta fe pofita:,

1

erit earum diflantia B A = o. Quoniam per pon-
ifitutionem telefcopii radii in primam lentem inci-

dentes funt paralleli, erit B =: P, et 4- = -p* + *£•

Quoniam radii ex ultima lente emergunt paralleli,

erit A = P. Et tandem, quia potentia amplificandi

c indicatur

[ 977 ]

I H

indicator numero m> erit B =r m P. Subftitutis ita~
que his valoribus in aequatione pro tribus lentibus

iiipra allata, tranfit ilia in lianc :

N — i . P

N — i .P

+

ii

n

" ii

N — i . n? P

o. Et haec asquatio una cum asqua-

tione —■ r-j— d L — o, determinat redtationem

m P

i ii

diftantiarum focalium P, P, P, qualis ad id requiri-
tur, ut radiorum emergentium diffipatio a diverfa
refrangibilitate nulla fit. Comparando fcilicet has

ii \ i

• 11 Y nm , n \ * / nm

asquationes, habetur ( ^ -f ~ P -f (

\IN i N — ^ j yN — I

” A n f « n \

u J P — o, et ( -tt ~ •“ i )

N — I y VN — I N — i J

x P = o. Eadem ratione pro-

x m1 P

n

n m . n

4“

^ \N_ i ' N — i
cedendum eft in aliis cafibus.

Stockholm,

20 Aprilis 1760.

S. Klingenftierna.

erratum.

Page 900, Line 28, after as ufual add and the

poker plus.

A N

TO THE

FIFTY-FIRST VOLUME

OF T H E

Philofophical Tranfa&ions.

A

Acorns of the Englijh oak , method of preferving them 207

of the cork tree, D° — 209

Aleppo , account of the late earthquake there
Alteration of the colour in a Negro woman, account thereof

1 75

America , account of that part of it which is neareft to the

land of Kamtchatka « 477

. of its produce and inhabitants 481, 482

Amlwch (in the ifle of Anglefea) account of the vitriolic

waters there — 47°

Animal , fent from the Eaft Indies by General Clive, fome

account thereof 648

Antiquities , account of fome found in Cornwall — 13

extra&s of letters concerning feveral lately dif-

covered in Italy — * 201,636

Antient Grecian mufic , an explanation of the modes or
tones therein. — — — — 695

Arm (broken) remarkable operation thereon — 657

Artificial cold , how produced 670

Jfibejlos , account of a late difcovery of fome in France 837
Y O l. LI. 6 K Aurora

INDEX.

Aurora Borealis , an attempt to account for the irregular va;
nation of the horizontal magnetic needle at the time of

one — page 399

Azores i/lands , many marks of fubterraneous fires near them

- - • 578

, fubjed to frequent earthquakes — ibid,

B

Baker ( Mr. H.) his account of a ftony concretion taken

* from the colon of an horle — — 694.

Barker ( Thomas ) Efq; his remarks on the mutations of

the ftars — — — 49 8

Bash, account of a meteor feen there Obloberzo, 1759, 301
Beccaria (Father) his experiments in eledricity — 514

Bees (a kind of) account of a lpecimen of their labour, 844
Bergman{ Mr. Thorbern) his letter concerning dedricity, 907
Berings ijland, fituation and defcnption of it 1 488

Bevis (John) M. B. his account of the comet feen in May

1759 * — 93

Birch (Rev. Thomas) D. D. letter to him, containing ex-
periments on ieveral pieces of marble ftained — 30

Bird, delcription of one fuppofed to be bred between a
turkey and pheafant — — — 8 39

Blake (Francis ) Efq; on the grcatcft effed of engines with

uniformly accelerated motions 1

Body {human ) concerning the eledricity of it • 340

Bone found in the pelvis of a man, account thereof 660
Borlafe (Rev. William) M. A. his account of antiquities

found in Cornwall ■ — — 1 3

Bovey toal, remarks thereon — — — 534

analyfis thereof — — — 552

further account of fome experiments made

thereon — * . 94 1

Brady ( Terence ) M. D. his account of a bone found in the
pelvis of a man — — * 660

Brakenridge (Rev. William) D. D. his letter concerning the
fedionsof a folid not hitherto confider’d by geometers, 44 5

Broken arm, remarkable operation thereon 65 7

Cam-

INDEX.

C

Camphor , a powerful corrector and expeller of poifons in
general — — — Page 669

Canton (Mr. John ) M. A. his attempt to account for the
regular diurnal variation of the horizontal magnetic needle,
and alfo for its irregular variation at the time of an au-
rora borealis — — 39^

Carey ( (Villi am ) account of his cafe, whofe tendons and

mufcles are turning into bones 89, 92

Cafe of a paralytic patient cured by an eleftrical application

1 79

of an empyema — — • — — 194.

of a very long fuppreflion of urine — — 215

of Thomas Bingham, who had two flones of a remark-
able fhape and fize cut out from his urethra — 305

of an uncommon hremoptyfis — — 526

, a very extraordinary one, of a lady who fwallowed

euphorbium — — 662

of a luxated thigh-bone reduced 676,846

of Francis Newman, dyer, who loft the ufe of his

hands by cleaning brafs-wire — ■ — 937

Catalogue of fifty plants from Chelfea garden, for the year
1 75 8 — — — — 96

— D° for the year 1759 — • 644

Chambers (Mr. Robert) experiments on feveral pieces of

marble ftained by him — 3°

Chelfea Garden , catalogue of fifty plants therefrom, for the
year 1758 and 1759 " " ^44

Chefnuts , methods of preferving them — — 212

Chigwell-row , in Eflfex, account of a meteor feen there Oc-
tober 20, 1759 ' — . — . 302

Clive (General) account of an animal fentby him from the

Eaft-lndies 648

Coal (Bovey) remarks thereon — 53 4

analyfis thereof — — — 552

. further account of fome experiments thereon

941

6 K 2 Cocoon

INDEX.

Cocoon , or Silk pod, account of a particular fpecies thereof
from America — — — Page 54

C oh eft on (eleCtrical) concerning it — 359

concerning the force of it - — 390

Coin (Sidonian) account of one — 637

(Parthian) conjectures on an inedited one — 680

. (Samnite-Etrufean) fome obfervations upon one never

before fully explained — — — 853

Cold fufion, the received opinion thereof uncertain 294
Cold (artificial) how produced — — — 670

Colebrooke (Mr. Jofiah) his experiments concerning the
encauftic painting of the antients — — 40

.. — his letter to Lord Charles Caven-

difh, concerning the fuccefs of the above-mentioned ex-
periments — — — 53

._ » his account of a meteor feen at

Bath, Odtober 20, 1759 301

Collinfon (Mr. Peter) his letter concerning the migration

of fvvallows — — 459

Colon of an horfe , account of a (tony concretion taken

therefrom — ^94-

Colour, remarkable alteration of it in a Negro woman 175
Comet, accounts of that feen in May 1759 — 93, 94

obfervations on that feen in January 1760, by Mr.

Short — — — — 4^5

D° by the Rev. Mr. Michell — — 466

account of the fame, by Nich. Munckley, Efq; 467

obfervations on one, made at Paris in February 1 760,

by the Abbe de Caille 635

Concretion (ltony) account of one taken from the colon of
an horfe — 694

Conjectures, on the caufe of earthquakes 566

on an inedited Parthian coin 680

Conftruttion and effeCts of windmill-fails — 138

Conf derations on a late treatife, intituled, A new fet ol lo-
garithmic folar tables for finding the latitude at fea, 910
Cooper (Mr. Samuel) his account of a ftorm of thunder and

lightning at Norwich — — — 3 8

0 0 Corn-

INDEX.

Cornwall , account of antiquities found there. Page 13

D *

DaCoJla (Mr. Emanuel' Mendez) his remarks on fome ob-
fervations relating to the production of the Terra Tri-
politana, or Tripoli ' — — — 192

Damafcus , account of the late earthquake there 532
Darwin ( Erafmus ) M. D. cafe of an uncommon hasmopty-
fis related by him — — — 526

Dawfon ( Ambrofe ) M. D. cafe of a very long fuppreffion
of urine related by him — — — 215

Day (Mr. Mark) his account of the comet feen in January
1750 — — — — 469

Delaval ( Edward ) M. A. his letter, containing fome elec-
trical experiments and obfervations — — 83

Defcription of a metalline thermometer — — 823

of a bird, fuppofed to be bred between a tur-
key and pheafant — — — 834

Defcriptio montium quorundam ligno foflili infarCtorum

506

De Venuti (Signor Abbate) extracts of fome letters from
him, relating to ieveral antiquities lately difcovered in
Italy — — — — 201

Diapafon , the fpecies thereof explained 706

Difcovery of albedos in France, account thereof 837
Dottrine (harmonic) explained, as far as concerns the feven
modes admitted by Ptolemey — — 697

. — (mufical) of the fame modes explained, and its

agreement with the harmonic fhewn 703

Dottrines , fomething of the origin of the harmonic and
mufical pointed out — — — 729

Dutton (Mr. John) his account of a meteor feen at Chig-
well-row, in Efiex, O&ober 20, 1759 • — 3O2

E

Earth , its ftruClure and compofition • — — 582

3 its ftrata regular and uniform — — ibid .

Earth-

INDEX.

Earthquake, method of finding the place of the origin of
any particular one — — Page 625

, inquiry into the fituation of the caufe which

gave rife to that of November 1, 1755 — 626

. , concerning the depth at which the caufe lies

that occafions any particular one — — 631

, a burning ifland raifed out of the fea by one

near Tercera, one of the Azores — — 577

, ifiands raifed out of the fea thereby, near

Santerini, in the Archipelago, and at Manilla, one of

the Philipine ifiands — . 57s> 579

, Latacunga, Ambato, and Riombambo,

towns in South America, defiroyed by one in 169&

620

, effects of that of November 1, 1755, on

the larged mountains in Portugal — — 622

, account of that which defiroyed Port Royal

in Jamaica, in 1692 623

Earthquakes , account of thofe in Syria in 1 759 — 529

, conjectures concerning the caufe, and ob-

fervations upon the phenomena of them 566

, caufed by fubterraneous fires — 569

, the fame place fubjeCl to returns of them

ibid.

places in the neighbourhood of burning

mountains fubjeft to frequent returns of them 571

, motion of the earth during them partly tre-
mulous, and partly propagated by waves — ibid.

generally come to one and the fame place,

from the fame point of the compafs • 573

, their frequency in the neighbourhood of

burning mountains a firong argument of their proceed-
ing from a fimilar caufe 7 5^9

# why they obferve a fort of periodical return

614

, the moft extenfive ones frequently take

their rife from the fea 6 1 5

Earth -

INDEX.

Earthquakes , thofe of fmall extent generally happen among
the mountains — — — Page6i8

— , , thofe in hilly countries more violent than thofe

which happen elfewhere — 619

* , thofe which have happened in the neighbour-

hood of Quito, incomparably more violent than thofe

which deftroyed Lifbon — — 620

■ very frequent in Berings ifland — 493

Eclipfe of the moon , account of one Nov. 22, 1760 — 936
Edwards (Mr. George ) his account of the frog-filh of Su-
rinam — — 653

his account of a bird, fuppofed to be

833

83

308

359

3 9°

179

fub-

340

348

380

bred between a turkey and pheafant
Electrical experiments and obfervations

• — experiments on the tourmalin

■ Coheft on , concerning it

concerning the force of it

Electricity , a paralytic patient cured thereby
»■ ■ - — of the human body, and of the animal

fiances filk and wool — — —

of black and white filk — —

, two diflinil powers therein —

37 1:

, new experiments therein, 308, 348, 514, 896
a letter concerning it — 907

Ellis {John) Efqj his account of experiments relating to

the prefervation of feeds 206

9 method of making Sal Ammoniac in

Egypt, by him — — — 504

— his account of the plants Halefia and

Gardenia — — — — 929

Empyema , remarkable cafe of one — — 194

Encaujlic painting of the ancients , experiments concern-
ing it — — — — 40

Engines , the greatefl effect of thofe with uniformly accele-
rated motions confidered — — — 1

Enquiry (experimental) concerning the natural powers of
water and wind to turn mills and other machines de-
pending on a circular motion — — 100

Enquiry

index.

Enquiry into the meafure of the Roman Foot —* Page 774
Euphorbium , extraordinary cafe of a lady who fwallowed

r 002

iome — — .

Experiments on feveral pieces of marble flamed by Mr.

Robert Chambers — — , *T 3°

. — — . concerning the encauftic painting or the an-
cients — — - .4®

. letter concerning the luccefs of the preceding

53

on underfoot water-wheels — no— ■ 124

. . on overfoot D° — I27 *3^

... — on windmill- fails ■ “ *4I

— •, account of fome relating to the preservation

■ on the tourmalin — - — 3°^ 339

• in eledricity 3°^» 34^ j 5*4> 89b

■ in magnetifm — 4°°

on the Bovey coal — — 55}-> 9.4 1

of feeds

Explanation of the modes or tones in the antient Grecian

Explication of fome words which occur in the Reife Befe hrei-
buncr — — - — 494

Eyles Stiles (Sir Fr. Hajkins ) his explanation of the modes
or tones in the ancient Grecian mufic 95

Ferentum, a town of Etruria, account of the ruins thereof

203

Fiery meteor , feveral accounts of one which appeared on
Sunday November 26, 175^ 21 2^9

, its velocity — — 2 .J

its magnitude — — 7

-* great light yeilded by it _ — — • did.

? length and confiftence of its tail laid.

Fiery meteors] conjedures on their height and f^flance

_ on their formation — 268

Fires (fubterraneous) the probable caufe ot ea 1 1 hqu ak e s^,5 ^9

5

INDEX.

Fitzgerald (Keane) Efq-, his defcription of a metalline ther-
mometer — — Page 823

Force of electrical cohefion , a letter concerning it 390
Forjler (Rev. Richard) M. A. his account of a meteor feen
at Shefford, in Berkfhire, October 20, 1759, and ob-
fervations on the weather of the preceding winter 299

Fojfile woody account of it —

— — found in Iceland — .

in the ifland of Faro —

- — in Switzerland — —

— in Oxford fhire — . —

• in Northamptonfhire >— — -

— in Dorfetlhire — —

near Fifchaufen in Pruflia

543

544

545

546

547

548
ibid.

550

at Munden and Allendorff in Germany

ibid .

Franklin (Mr. Benjamin) his remarks on father Beccaria’s

electrical experiments — 52 r,

Francey account of a late difcovery of Afbeftos in one of the
provinces of that kingdom — . — 837

Frog-fijh of Surinam y account thereof — — 633

Fufion (cold) the received opinion thereof uncertain 294

Gardenia , account of that plant . — - 932

Grecian mufic (ancient) explanation of the modes and tones

therein — — . 695

Growth of trees , obfervations thereon -■■■ ■ 7

H

HsemoptyfiSy cafe of an uncommon one — — 526

Halefiay account of that plant — — 929

Hartfell-fpawy remarks thereon — — 475

, the waters thereof given with fuccefs in con-

fumptions of the lungs — — — ibid.

Henry (Rev. William) D. D. his account of the cafe of
{, William Carey, whofe tendons and mufcles are turning

into bones — ■ 89

6 L Henry

INDEX.

Henry (Rev. William ) D. D. his further account of the fame

cafe — Page 9 2

Himfel (Dr.) tranflation of his letter concerning a paralytic
patient cured by an electrical application — 1 79

his account of producing artificial cold 670

Hollmanni ( Sam.Cbrifi .) philofophise profeffor. Goettingenf.
et S. R. fodalis, montium quorundam ligno foffili infarc-

torum defcriptio — — 1 5°^

Horizontal magnetic needle, an attempt to account for its
regular diurnal variation, and alio for its irregular varia-
tion at the time of an aurora borealis 39 S

Hot-baths , account of thofe of Vinadio in the province of
Coni, in Piedmont — — — 8 37

I

Impregnation of mineral waters, thoughts thereon 275
Inhabitants of that part of America neareft Kamchatka,
account of them, their drefs, and food 4^2

, of their language, and the refemblance b

tween them and the Kamtchadalians
of their armour

manner of their failing upon the fea,

their canoes defcribed

fome of their cuftoms

Infcription on a patera found in Cornwall
— found at Rome

484

485
and

486

487

16

201

Rome

found in the way to Oftia* eight miles from

— — 202

Infer ip tions found among the ruinsof antientRomc, 637-638
— — — , remarks thereon — — 640

JJlands , feveral railed out ot the fea in the Archipelago, by

a fubmarine volcano ■ — — 1 57 ^

Ifland , a burning one raifed out of the fea near 1 ercera,

one of the Azores, by an earthquake 577

, , D° at Manilla, one of the Philippine iflands 579

K

Kamtchatka , fome account of it, and of that part of Ame-
rica which is neareft to it — 477

Kimendge

X.

I N D E

Kimendge coal , account of it — Page 549

Knight ( Gowin ) M. B. his remarks on Mr. Mountaine’s
account of the extraordinary effeCts of lightning 294

L

Labour of a kind of Bees , account of a fpecirften thereof, 844
Landen (Mr. John) new method of computing the fums

of certain feries, by him — - 553

Latacunga , a town in South America, deftoyed by an
earthquake in 1698 — — * — 620

Lightning and thunder , account of the effects of them at
Rickmanfworth in Hertfordftiire • — — 282

Lightning, account of fome extraordinary effedts of it, 286

Lignum Fofiile , account of it — 547

Lijbon, conjectures and obfervations concerning the great
earthquake there Nov. 1, 1755 — — 5^6

Logarithmic folar tables for finding the latitude at fea , con-
fiderations on a new fet thereof — . ■ — 910

Luminis de abberratione , in fuperficiebus et lentibus fphasri-

cis refraCtorum — — 944

Luxation (complete) of the thigh-bone, account thereof, 676
Luxated thigh-bone reduced , account of one * 846

Lyncurium of the ancients, obfervations thereon • — 394

„ . ,, fuppofed to be what we now

call the tourmalin - — — 39^

Lyttelton (Rev. Charles) LL. D. letter to him, giving an
account of fome antiquities found in Cornwall 13

M

Macclesfield (Earl of) letter to him, containing experi-
ments concerning the encauftic painting of the antients

40

letter to him, containing remarks on

the Bovey coal — — 5-? 4

. defcription of a metalline thermome-
ter communicated by him — ^ 823

letter to him, containing fome further

experiments in ele&ricity -'■■■ — 89^

6 L 2 Mag-

I N D E X.

Magnetic net Me (horizontal) attempt to account for its re-
gular diurnal variation, and aifo for its irregular variation
at the time of aa- aurora borealis — Page 39 8

Marble , experiments on fcveral pieces thereof ftained 30
Marcbmont (Earl of) letter to him, concerning the fedlions
of a folid hitherto not confidered by geometers 446
Marjham ( Robert ) Eiq-, his obfervauons on the growth of
trees — — — — 7

Majkeline (Rev. Nevil ) A M. his propofal for difcovering

the annual parallax of Sirius — 889

Maryland, thermometrical account of the weather there for
one year • — • — — — 58

, D° for three years — ■ — 70

Me a jure of the Roman foot, an inquiry thereinto — - 774

• of the Paris foot alcertained — — * 777

Meafures of the temple of Fortuna Virilis at Rome ex-
amined — — — 795

of the temple of Vella at Rome examined 797

of the temple of Vella at Tivoli examined 798

• of the Pantheon at Rome — — ibid.

of the temple of Peace — — 807

;of the temples of Bacchus and Faunus — ■ 808

• of the amphitheatre at Verona 810

of the arch of 7htus — ibid .

of the arch of Conflantine — — 811

of the temple of Antonine and Faullina ibid.

of the arch ofSeptimius Severus 812

■ of the Banker’s arch and the portico of Severus 815

— — of the baths of Dioclefian — — 817

Meafures of trees , tables thereof — — 7, 10

Metalline thermometer, a deicription of one — 823

Metallotophytott , or Lignum Foffile , accounts of it, and

where found — - — — — 543

Meteor (fiery) feveral accounts of one that appeared on
Sunday the 26th of November 1758 218 — 259

, account of one feen at Sheflord in Berkfhire, on

Saturday Gbtober 20, 1 759 — 299

, account of the fame, as feen at Bath, — 301

Meteor

INDEX.

Meteor , account of one feen at Chigwelbrow in Effex,

Oftober 20, 1759 — Page 302

Method, of making Sal Ammoniac in Egypt — 504

— of computing the Turns of certain feries 553

Michell (Rev. John ) M. A. his obfervations on the comet
feen in January 1760 — — — 466

• his conjectures concerning the

caufe and obfervations upon the phenomena of earth-
quakes — — — — 566

Migration of f wallows , concerning it — ■■ 459

Millepes (the Sea) obfervations thereon 33

Mills and other machines depending on a circular motion , of
the natural powers of water and wind to turn them 100
Mills ( Jeremiah ) D.D. his remarks on the Bovey coal, 534

• * his farther account of fome experi-

ments on D2 — — — 941

Mineral waters, thoughts on the different impregnation of
them — — — — 275

, concerning the exiftence of fulphur in

fome of them ibid.

Mitchell (Dr. John) his letter on the force of electrical co-

hefion — — 390

Modes or 'Tones in the antient Grecian mujic , an expla-
nation thereof 695

, the harmonic doCtrine thereof explained,

as far as concerns the feven admitted by Ptolemy 697
the mufical doCtrine thereof explained,

703

— — , the eight harmonic rejected by Ptolemy

explained, and his reafons for excluding them 71 1
how far the preceding explanations of

and its agreement with the harmonic fhewn

them may be fupported by arguments, or warranted by
the teftimony of antient writers — — 73 9

— , how far this fubjeCt has been underftood

by other writers confidered — 760

Montium quorundam praealtorum, magna ligni foffilis copia
quafi infarCtorum, brevis defcriptio — — 506

Moon , account of an eclipfe thereof, Nov. 22, 1760, 936

More

INDEX.

More (Mr. Samuel) his account of the cafe of a young man
who had loft the ufe of his hands by cleaning brafs-wire

Page 936

Mount aine (Mr. William) his account of force very extraor-
dinary effects of lightning — 286

Munckley ( Nicholas ) Fiqj his account of the comet feen in

May 1759 — 7” 94

Mufcles and tendons of a man turning into bones , account

thereof 89, 92

Mufic (antient Grecian) explanation of the modes or tones

therein — ^95

Mutations of the Stars, remarks thereon 498

N

Needle ( horizontal magnetic ) an attempt to account for the
regular diurnal variation thereof, and for its irregular va-
riation at the time of an aurora borealis 398

Needham (Mr. Turberville ) his account of a late difeovery
of Afbeftos in France — — — ' 837

Negro woman , account of the remarkable alteration of the

colour of one — 175

New-improved Jilk-reel , account of one ■ 2 1

Newman ( Francis ) account of his cafe, who had loft the

ufe of his hands by cleaning brafs-wire 937

Norwich , account of a ftorm of thunder and lightning there

38

O

Obfervations on the growth of trees — — 7

on the Sea Scolopendre, or Sea Millepes 35

relating to the production of the Terra Tri-

politana, cr Tripoli — 186

on the weather — * * 3 00

and experiments, concerning ele&ricity 83

on the Lyncurium of the ancients 394

_ on the phenomena of earthquakes 566

on the comet feen January 1 760 4^6

on a comer, made at Paris in Feb. 1760, by

the Abbe de la Caille — 1 — ‘ (,35

Obferva-

INDEX.

Obfervations upon fome antiquities found in Italy, Page 639

• for finding the annual parallax of Sirius, 894

Oil and Water, efficacious antidotes for expelling poifon

664

Operation on a broken arm , a remarkable one — 667

Over Jhot water-wheels, concerning them 124

* ■, fpecimen of a fet of experiments

thereon — — — 127

- — - , table of the refult of fixteen fets of

experiments thereon — — — 129

— ■, concerning the ratio between their

power and effedt — — — — ibid.

• , concerning their mod proper height,

in proportion to their whole defcent 13 1

* , concerning the velocity of their cir-

cumference, in order to produce the greateft effect 132

, concerning their load, in order to

produce a maximum • — — — 135

concerning their greateft poffible ve-
locity — — — ibid.

— ■■ , concerning the greateft load that they

can overcome • — 136

P

Painting {encauftic) of the antients, experiments concerning

Parallax ( annual ) of Sirius, propofft for difcovering it, 889
Paralytic patient , cafe of one cured by an electrical appli-
cation — — — — — 179

Parfons {James) M D. his account of an animal fent from
the Eaft Indies by General Clive — — 648

. 5 account of artificial cold produced at Pe-

terfburg, tranfluted from the French by him — 670

Parthian coin , conjectures on an inedited one — 680

Patera , defcription or one found in Cornwall 1 5

Pelvis of a man , account of a bone found therein 660
Pemberton (H.) M. D, fome confiderations by him, on a
late treatife, intituled, a New Set of Logarithmic Solar
tables for finding the latitude at fea — * — 910

4 Peterf-

INDEX.

Peter/burg, account of artificial cold produced there by Dr.

Himfel — — — — 670

Peyjfonel ( John Andrew) his obfervations on the Sea Scolo-
pendre, or Sea Millepes — — — 35

Phenomena of earthquakes, obfervations thereon — 566

Pieces of marble Jtained, experiments on feveral — 30

Plana, catalogue of fifty from Chelfea garden, for the year

1758 — — — 96'

, Dp for the year 1759 644

, the Halefia and Gardenia, account of them 929

Poligne (mountain of) in Bretagne, Terra Tripolitana, or

Tripoli, found in it — — 187

. , formerly a volcano 188

Power of water and wind to turn mills and other machines
depending on a circular motion — — 100

Powers , of two diftindt ones in eledtricity — 371, 380

Prefervation of feeds, account of fome experiments relating
thereto — — — — 2°6

Pringle {John) M. D. feveral accounts of the fiery meteor
which appeared on Sunday the 26th of November, 1758,
collected by him — — — 218 — 259

his remarks upon the preceding ac-
counts — ■ — — — 259

Production of the Terra Tripolitana, or Tripoli, account

of fome obfervations relating thereto 186

Propofal for difcovcring the annual parallax of Sirius 889
Pidlein (Rev. Samuel) M. A. on a new-invented filk-reel

2 i

— his account of a particular

fpecies of cocoon, or filk-pod, from America 54

R

Raper {Matthew) Efq*, his enquiry into the meafureofthe

Roman foot — — 774

Remarks on Mr. Hubner’s obfervations relating to the pro-
duction of the Terra Tripolitana, or Tripoli 191
— . — upon feveral accounts of a fiery meteor which ap-
peared

N D

X.

peared on Sunday the 26th of November 1758, and
upon other fuch bodies — paae 259

Remarks on Mr. Mountaine’s account of the effe&s of lieht-

mnS — — — — 294

on the mutations of the flars 494

* (Mr- Franklin’s) on father Beccaria’s electrical ex-

periments 525

* on the Bovey coal — __ 534_94,

* C/ J T* _7 T* x

— upon fome antiquities found in Italy — 639

Rickmanfworth , in Hertfordfhire, account of the effects of
a ftorm of thunder and lightning there on July 1 6. 1 759,

2.82.

Roman foot, an enquiry into the meafure thereof 774

Rome (antient) fome infcriptions lately dug up in the ruins
thereof — — — ^

Ruffe U (Dr. Patrick ) his account of the earthquakes in Sy-
ria in the year 1 759 — —

Rutty {John) M. D. his thoughts on the different impreg-
nation of mineral waters, and concerning the exigence of
fulphur in fome of them - — — 2yr

Sal Ammoniac, method of making it in Egypt 704

Samnite-Etrufian coin , fome obfervations upon one never

before fully explained . . - g^

Sand Martins, manner of building their neffs 463

Sea Scolopendre, or Mi’lepes, obfervations thereon
Sections of a folid, hitherto not confidered by geometers

446

Seeds, account of fome experiments relating to the preferva-

tion of them — — 206

Series , new method of computing the furns of certain s**

Sidonian coin, account of one — (f)~

Shefford, in Berkfhire, account of a meteor feen there Oc-
tober 20, 1759 — 229

Shot t { James) M A. his account of an eclipie of the moon

„ 93 6

6 M Short

INDEX.

Short (James) M. A. his obfervations on the comet feen in
January 1760 — — — Page 465

Silk-reeU a new-improved one — — 21

Silk-pod , or Cocoon, account of a particular fpecies from
America — — — — 54

Silk (black and white) concerning the electricity of it —

340— 3 48

Sirius , a propofal for difcovering the annual parallax thereof

889

Siyah-ghujh , or Black-ear, defcription of an animal fo called

650

Smeaton (Mr. John) his experimental inquiry concerning
the natural powers of water and wind to turn mills and
other machines depending on a circular motion, 100— 1 74
Solid , feftions thereof hitherto not conhder’d by geometers

44b

Specimen of the labour of a kind of bees 844

Stars , remarks on their mutations — — 494

Stones , account of two, of a remarkable fhape and fize, cut

out of the urethra of a young man 304

Stony concretion , account of one taken from the colon of an

horfe — — — 694

Storm of thunder and lightningy account of one at Norwich
on July 13, 1758 — — — 38

, account of the effects of

one at Rickmanfworth, on July 16, 1 759 — 282

Strata of the earthy regular and uniform 582

Subterraneous fires , the probable caule of earthquakes 569
Succefs of fome experiments concerning the encauftic paint-

ing of the ancients — — _ 53

Sulphur^ concerning the exiflence of it in fome mineral

waters — — — — 275

Sums of certain ferieSy new method of computing them 533
Suppreffion of uriney cafe of a very long one — — • 2 1 5

Surinam , account oi the frog-fifli thereof — 653

Swallows y concerning their migration — — * 459

Swinton (Rev. John) B. D. his conje&ures on an inedited

Parthian coin - — • — 6 80

Swinton .

INDEX,

Swinton (Rev. John) his obfervations upon a Samnite-
Extrufcan coin, never before fully explained. Page 853
Symmer ( Robert ) Efq-, new experiments and obfervations
concerning electricity, by him — — 340 — 389* *

Syria, account of the earthquakes there in the year 1 759,

529

T

Table of the meafures of trees — 7

of the monthly increafe of trees — 10

of the refult of twenty-feven fets of experiments on

underfhot water-wheels — — — 1 1 5

-■ - of the refult of fixteen fets of experiments on over-
fhot D° — — — — 129

of the refult of fix fets of experiments on windmill

fails — - — — — 152

of the ratio of the velocity of the extremities of wind-
mill fails to the velocity of the wind ■ 162

— of the velocity and force of wind 165

of obfervations for finding the annual parallax of Si-
rius — — — 894

T endons and mufcles of a man turning into bones , account
thereof — — — — 89

TerraTripolitana , or Tripoli , account of lome obfervations

relating to its prod udtion — 186

Thermometrical account of the weather in Maryland for
one year — — — — 58

_ D° for three years — — 70

Thermometer {metalline) a defcription of one — 823

Thigh-bone , account of a complete luxation thereof in an

adult perfon — — 676

, account of a cafe of a luxated one reduced, 846

Thoughts on the different impregnation of mineral waters

2 75

Thunder and lightning , account of a ftorm thereof at Nor-
wich — — — — 38

• , account of the effedts of them at

Rickmanfworth inHertfordfhire,on July 16, 1759— 282

6 M 2 Tones

INDEX.

Tones or Modes , in the antient Grecian mufic, an explana-
tion thereof — — Page 695

Tourmalin, experiments on it — — 308— 339*

, fuppofed to be the Lyncurium of Theophraltus

369

Tranfitu de proximo veneris fub foie — • — 865

T reatife on a new fet of logarithmic folar tables for finding

the latitude at fea , obfervations thereon 9 10

Trees, obfervations on the growth of them — 7

Turin , account of the weather there for the year 1759 — 842

V

Vapours, their amazing force and effects — 592, 594

Variation (regular diurnal) of the horizontal magnetic needle,.

attempt to account for it - — 398

.... — , (irregular) of D° at the time of an aurora bore-
alis, attempt to account for it — — 399

Veneris fplanetae) de proximo fub foie tranfitu — 8 65.

Vinadio (in the province of Coni in Piedmont) account of.

the hot baths there — — 839

Vitriolic waters , account of thofe at Amlwch in the ifle of

Anglefey — — — 47°

, the analyfis thereof — — 472.

-r, of great efficacy in the cure of many ftub-

born chronical diteales — 477*

Volcanos, many lie together in the fame tradf of country

581.

almoft always found on the tops of the highefb

mountains - — 616

Underfoot water-wheels , concerning them 101

. , fpecimen of a fet of experiments

thereon 110

, table of the refult of twenty-feven

fets of experiments thereon — - — ■ — 115

. , maxims and obfervations deduced

from the foregoing experiments thereon — 11C1

Urethra, account of two Hones, of remarkable fhapes and
fizes, cut out from that of a. young man — 304

Urine 4,

INDEX.

UrinSy cafe of a very long fupprefllon of it Page 215

W.

Warner (Mr. Jofeph ) account of a ftorm of thunder and
lightning at Norwich, communicated by him — 38

-- , remarkable account of an empyema,

by him — — — — rg4

— , his account of two ftones, of remar k-
able lhapes and fizes, cut out from the urethra of a young
man by him — — — 304

Water and oil , efficacious antidotes for expelling poifons

664

Water and wind , concerning their natural powers to turn
mills and other machines depending on a circular motion

100

Water-wheels (underffiot) concerning them — 101

• * , fpecimen of a fet of experiments

thereon — — — — no

■ , table of the refult of twenty-

feven fets of experiments thereor> — — 115

- • , maxims and obfervations de-

duced from the foregoing experiments thereon — 1 16

(over-ffiot) concerning them 124

• , fpecimen of a fet of experiments.

thereon — — — — 127

table of the refult of fixteen fets of

experiments thereon — — 129

— obfervations and deductions from

the foregoing experiments thereon — ibid.

— (horizontal) concerning them — 168.

Waters (mineral) thoughts on the different impregnation

of them — 275

concerning the exiftence of fulphur in

fome of them — — ibid.

- (vitriolic) account of thofe at Almwch in the ifle

of.Ang.ldey — — ■ — 470

Waters-

3

INDEX.

Waters (chalybeat) their ufefulnefs and good effedts io dif-
eafes of the lungs arid other Oubborn diioiders P 475
Watfon ( William ) M. D. his obfervations r dating to the

Lyncurium of the ancients — 394

Weather , a thermometrkal account thereof for one year in
Maryland — — ■ — — 5 8

, D° for three years in D° — — 70

— , obfervations on that of the winter of 1 758 300

— , (late thereof at Turin, tor the year 1759 842

While (Mr. Charles ) h*s account of a remarkable operation

performed by him on a broken arm 657

Ins account of a complete luxation of the

thigh bone in an adult perfon — 676

Whitfield (Mrs. Anne) her account of the effedts of a ftorni
of thunder and lightning at Rickmanfworth in Hertford -
(hire, on July 16, 1759 — — — 282

' Willis (Mrs.) who lwallowed euphorbium, her extraordi-
nary cafe — — 662

Wi Inter {John) M. D. catalogue of fifty plants from Chel-
fea garden for the year 1758, prefented to the Royal

Society by. him — — — 96

„ D° for the year 1759 — 644

Wilfon (Mr. Benjamin ) letter from him to the Rev. Tho-
mas Birch, D. D. — — — 83

— letter to him, containing fome

eledtrical experiments and obfervations ibid.

— . his experiments on the tourmalin

3°8

further experiments in elcdlricity

by him — — — 1 — 896

another letter to him concerning

eledlricity — — — — 907

Wind and Water , concerning the natural powers of them
to turn mills and other machines depending on a circu-
lar motion — 1 too

Windmills (horizontal) concerning them 168

Windmill fails , their conftrudtion and effedls — 138

Wind-

/

index.

IV indmill- fails , fpecimen of a fet of experiments thereon

Page 1 41

'■ 5 table of nineteen fets of experiments thereon

144

* , the beft form and pofition of them 145

the ratio between the velocity of them

when unloaded, and their velocity when loaded 153

— 5 the ratio between the greatefl load that

they will bear without flopping, and the load at the

maximum — _ ibid.

* > their effects, according to the different

velocity of the wind — —

* j the efft-Cts of thofe of different magnitudes,,

their ftructure and pofition being fimilar, and the velo-
city of the wind the fame — 155

, the velocity of their extremities, in the

refpeCt to the velocity of the wind — 161

* » the ablolute effect produced upon thofe of

a given magnitude and conftru&ion by a given velocity

of the wind — — I(5r

Winter , obfervations on the weather of that of 1758 — 300
Wood (foffile) accounts of it, and where found — 543

Wool , concerning the electricity of it — 240

Tonge (Mr. Charles) his account of the cafe of a luxated
thigh bone reduced. — — 3^5

E N ‘D of Vol, LL.

*