For the farther illustration of what has been here advanced, it will
be requisite to observe, that two æra’s were antiently followed at
Sidon; the æra of Seleucus, and another peculiar to the inhabitants
of that city[196]. On the Greek brass coins of Sidon, according to
F. Frœlich[197], both these epochs seem to have been used. However,
the supputation pointed out to us by the date on the Greek medal
above-mentioned was undoubtedly made according to the æra of Seleucus;
since otherwise the year exhibited by that date must have been nearly
coincident with the 266th of CHRIST, which by those versed in this kind
of literature will never be allowed. For had the piece presented to
our view so recent a date, as Sidon first became a Roman colony in the
reign of Elagabalus[198], above forty years before; the reverse ought
to have been adorned with some other letters intimating this, as were
those of the Sidonian[199] coins posterior to that event. As certain
is it that all the Phœnician medals of Sidon, whose numeral characters
have been interpreted here, acknowledge no other epoch than the proper
one of that city, which commenced in the year[200] of Rome 643. This, I
flatter myself, from the following considerations, exclusive of others
that might, with equal facility, be offered, will even to demonstration
appear.
1. The fifth year mentioned by the oldest of these coins cannot be
the fifth year of the æra of Seleucus, because the Sidonians were
then subject to Antigonus[201], in whose territories the supputation
according to that epoch did not take place; and consequently the piece
itself must have been struck in the fifth year of the proper æra of
Sidon, nearly coincident with the 648th of Rome[202].
2. No dates ever occurred upon the medals of the Syrian kings presiding
over the people of Sidon, either to F. Frœlich or Dr. Vaillant[203],
who have so eminently distinguished themselves in this branch of
literature, before the year of Seleucus 112; and therefore neither
the Phœnician dates preserved on the aforesaid Sidonian coins whose
numeral characters do not amount to 112, nor the Greek dates on others
falling short of that number, can rationally be supposed to bear any
relation to the æra of that prince. This certainly must be considered
as a strong presumption, or rather an incontestable proof, that the
last-mentioned Phœnician dates were deduced from the commencement of
the proper Sidonian epoch, as from their genuine cardinal point. Which
reasoning will by analogy extend, as the numeral characters exhibited
by all the coins here explained are of the same kind, to every one of
the rest.
3. None of the medals of the Syrian kings, with Phœnician letters
upon them[204], hitherto published, bear any Phœnician dates. This,
after what has been said, renders it extremely probable, that the
pieces of Sidon I am considering were posterior to those coins; and
even that their Phœnician dates referred to an æra different from that
of Seleucus, followed by the Greek dates on the medals of the Syrian
kings. Which if we admit, this æra could have been no other than the
new one of the Sidonians, that commenced in the seventh century of Rome.
4. That the dates visible on these coins were supputed according to
the latter epoch of Sidon, will be manifest from an examination of
the Greek and Phœnician brass medals of that city explained, in[205]
the beginning of this paper; whose type and workmanship are extremely
similar, if not almost intirely the same. For this circumstance is
to me an evident proof, that they could not have been struck at very
distant times. Now if we take the Greek coin to have followed the æra
of Seleucus, as was undoubtedly the case, and the others that peculiar
to Sidon; the first of the Phœnician dates[206] will not be prior to
the Greek one above fifty-three years, nor the last of them precede it
above forty-three years. Whereas if we suppose the numeral inscriptions
in the exergues of the Phœnician Sidonian coins to have been supputed
according to the Seleucian epoch, the difference between the aforesaid
dates will be five times as much; which with the similarity of
workmanship and type, already observed, will be altogether incompatible.
5. As the Jews[207], about the time that the first of our medals was
struck, denominated the æra of Seleucus, THE ÆRA OF THE KINGDOM OF
THE GREEKS; we cannot well doubt but it went amongst the Sidonians,
who were neighbours to the Jews, under the same denomination. From
whence it will follow, that the epoch styled by them emphatically, THE
ÆRA OF SIDON, must have been different from the æra of Seleucus; and
consequently that which, after the 643d year of Rome, was peculiar to
them.
[Illustration: _Philos. Trans. Vol. L._ TAB. XXXII. _p. 804_
PHŒNICIAN Numerals antiently used at SIDON, from _One_ to a _Thousand_.
_J. Mynde sc._]
The powers of the Phœnician numeral characters antiently used at Sidon,
which I flatter myself are now discovered, having been for many ages
unknown; the Society will perhaps not be displeased to see accurate
draughts of the principal Phœnician medals, from whence they are
deduced. I have therefore taken the liberty to transmit them[208] such
draughts, which may be intirely depended upon. I have also constructed
a table[209] of the numeral characters themselves, from UNITY TO A
THOUSAND; which will demonstrate, in the clearest manner possible, the
great affinity between them and those of the Palmyrenes.
1. From this table it plainly appears, that the people of Sidon had
no particular character to denote Five, whilst the Phœnician numerals
here explained were in vogue amongst them; that they expressed TWENTY
by a character, during that period, not very different from the
correspondent one used at Tadmor; and that in all other respects the
Phœnician notation then prevailing at Sidon was, in a manner, the same
with that of the[210] Palmyrenes.
2. It may not be improper to observe, that two of the Sidonian coins I
have been considering[211] exhibit the Phœnician word מא, equivalent
to the Hebrew מאה, and Syriac מאא, AN HUNDRED, instead of the centenary
numeral character. This, in conjunction with the appearance of that
character, occupying the very place of the term אמ, on others of those
coins, first induced me to believe, that the inscription preserved by
every one of them in the exergue could be nothing else but a date.
3. I shall beg leave farther to remark, that none of the indubitable
medals of Tyre, adorned with Phœnician letters, as far as I have been
able to discover, present to our view any Phœnician dates at all.
This still more clearly evinces the second element prefixed to the
Phœnician numerals in the exergue to point out to us the city of Sidon,
and not that of Tyre; which[212], indeed, seems already to have been
sufficiently proved.
4. From the foregoing observations we may likewise collect, that
the coin assigned to Demetrius III. by Mr. Masson, F. Frœlich[213],
and Sig. Haym, exhibiting a Phœnician legend, without a Phœnician
date, in the exergue, ought in reality to be attributed to Demetrius
I. Those three learned men therefore have been guilty of a mistake in
this particular. Nor can the head on this medal be denied to bear some
resemblance to that of Demetrius I.[214] with a moderate beard, as it
appears on a coin published by Dr. Vaillant, and in one of F. Frœlich’s
plates. That the letters A K, behind the head, indicate the piece
to have been struck in the twenty-first year of the proper Sidonian
æra[215], as Mr. Masson and F. Frœlich are pleased to assert, can never
be proved. On the contrary, the improbability of such a notion may be
inferred from two similar letters, behind the turrited head of the _Dea
Syria_[216], on a Phœnician coin, which Mr. Masson makes to point out
the forty-first year of the proper epoch of Sidon; whereas, in truth,
that piece seems to have been struck either in the reign of Demetrius
I. or Antiochus IV.[217] many years before. Nay, that it was actually
struck when Demetrius I. sat upon the Syrian throne, is rendered almost
incontestable by a medal of that prince now in my possession, with a
_Beta_ behind the head on the anterior part, and the very reverse of
the last-mentioned coin. From the former of which circumstances it
farther appears, that the alphabetic characters MA, supposed by Mr.
Masson to denote 41, are by no means to be taken for a date. To which
we may add, that the head on a Phœnician medal, with the two Greek
elements AK behind it, published by Mr. Reland[218], is apparently that
of Demetrius I.; and that the posterior part of this coin is nearly
the same, in all respects, with the reverse of that supposed to[219]
appertain to Demetrius III. by Mr. Masson and Sig. Haym. But to wave
all other considerations, relative to the point in view, that may
occur, the features and turns of the face on the medals of Demetrius
III. are so different[220], that no inference of any validity can be
drawn from the pretended identity or similitude of them, in support of
Mr. Masson’s opinion.
5. The Palmyrene and Phœnician numerals, deduced from coins and
inscriptions, may perhaps be thought not unworthy a place amongst the
arithmetical characters of various nations, formerly[221] collected
by Bishop Beveridge; and consequently may be allowed to render
somewhat more complete the chronological institutions, or rather the
chronological arithmetic, of that learned and judicious author.
You will pardon the prolixity of this letter, which the novelty of
the subject may perhaps render a little more excusable than it would
otherwise have been; and believe me to be, with the most perfect
consideration and esteem,
SIR,
Your most obedient humble Servant,
J. Swinton.
Christ Church, Oxon. Nov. 17. 1758.
[Illustration: _Philos. Trans. Vol. L._ TAB. XXXIII. _p. 809_.
_J. Mynde sc._]
CX. _Of the Irregularities in the Motion of a Satellite arising from
the spheroidical Figure of its Primary Planet: In a Letter to the Rev._
James Bradley _D. D. Astronomer Royal, F.R.S. and Member of the Royal
Academy of Sciences at_ Paris; _by Mr._ Charles Walmesley, _F.R.S.
and Member of the Royal Academy of Sciences at_ Berlin, _and of the
Institute of_ Bologna.
[Read Dec. 14, 1758.]
Reverend Sir,
SINCE the time that astronomers have been enabled by the perfection of
their instruments to determine with great accuracy the motions of the
celestial bodies, they have been solicitous to separate and distinguish
the several inequalities discovered in these motions, and to know their
cause, quantity, and the laws according to which they are generated.
This seems to furnish a sufficient motive to mathematicians, wherever
there appears a cause capable of producing an alteration in those
motions, to examine by theory what the result may amount to, though
it comes out never so small: for as one can seldom depend securely
upon mere guess for the quantity of any effect, it must be a blameable
neglect entirely to overlook it without being previously certain of its
not being worth our notice.
Finding therefore it had not been considered what effect the figure
of a planet differing from that of a sphere might produce in the
motion of a satellite revolving about it, and as it is the case of the
bodies of the Earth and Jupiter which have satellites about them, not
to be spherical but spheroidical, I thought it worth while to enter
upon the examination of such a problem. When the primary planet is an
exact globe, it is well known that the force by which the revolving
satellite is retained in its orbit, tends to the center of the planet,
and varies in the inverse ratio of the square of the distance from
it; but when the primary planet is of a spheroidical figure, the
same rule then no longer holds: the gravity of the satellite is no
more directed to the center of the planet, nor does it vary in the
proportion above-mentioned; and if the plane of the satellite’s orbit
be not the same with the plane of the planet’s equator, the protuberant
matter about the equator will by a constant effort of its attraction
endeavour to make the two planes coincide. Hence the regularity of
the satellite’s motion is necessarily disturbed, and though upon
examination this effect is found to be but small in the moon, the
figure of the earth differing so little from that of a sphere, yet in
some cases it may be thought worth notice; if not, it will be at least
a satisfaction to see that what is neglected can be of no consequence.
But however inconsiderable the change may be with regard to the moon,
it becomes very sensible in the motions of the satellites of Jupiter
both on account of their nearer distances to that planet when compared
with its semidiameter, as also because the figure of Jupiter so far
recedes from that of a sphere. This I have shewn and exemplified in
the fourth satellite; in which case indeed the computation is more
exact than it would be for the other satellites: for as my first design
was to examine only how far the moon’s motion could be affected by
this cause, I supposed the satellite to revolve at a distance somewhat
remote from the primary planet, and the difference of the equatoreal
diameter and the axis of the planet not to be very considerable. There
likewise arises this other advantage from the present theory, that
it furnishes means to settle more accurately the proportion of the
different forces which disturb the celestial motions, by assigning the
particular share of influence which is to be ascribed to the figure of
the central bodies round which those motions are performed.
I have added at the end a proposition concerning the diurnal motion
of the earth. This motion has been generally esteemed to be exactly
uniform; but as there is a cause that must necessarily somewhat alter
it, I was glad to examine what that alteration could amount to. If we
first suppose the globe of the earth to be exactly spherical, revolving
about its axis in a given time, and afterwards conceive that by the
force of the sun or moon raising the waters its figure be changed into
that of a spheroid, then according as the axis of revolution becomes a
different diameter of the spheroid, the velocity of the revolution must
increase or diminish: for, since some parts of the terraqueous globe
are removed from the axis of revolution and others depressed towards
it, and that in a different proportion as the sun or moon approaches
to or recedes from the equator, when the whole quantity of motion
which always remains the same is distributed through the spheroid, the
velocity of the diurnal rotation cannot be constantly the same. This
variation however will scarce be observable, but as it is real, it may
not be thought amiss to determine what its precise quantity is.
I am sensible the following theory, as far as it relates to the motion
of Jupiter’s satellites, is imperfect and might be prosecuted further;
but being hindered at present from such pursuit by want of health and
other occupations, I thought I might send it you in the condition it
has lain by me for some time. You can best judge how far it may be of
use, and what advantage might arise from further improvements in it. I
am glad to have this opportunity of giving a fresh testimony of that
regard which is due to your distinguished merit, and of professing
myself with the highest esteem,
Reverend Sir,
Your very humble Servant,
C. Walmesley.
Bath, Oct. 21. 1758.