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.