VOD. XLIV.^ PHILOSOPHICAL TRANSACTIONS. 357 



the former ; and the impression on it is also of the size of a denarius, and of the 

 same time with the rest. 



Some years ago, the earl of Winchelsea had several impressions or moulds of 

 this sort, all joined together side by side, on one flat piece of clay, as if for the 

 making many casts at once ; they were all of the emperor Severus : and he had 

 seen, in the earl of Pembroke's most valuable collection, a clay mould im- 

 pressed on both sides : among these also is one of the sides bearing the head of 

 the same emperor, and the other side a known reverse of his. Four of the 

 above 5 are also of Severus or his wife Julia, and the other is a reverse of Cara- 

 calla, his son and immediate successor ; so that all that we know of may be said 

 to be of the same time very nearly. 



They are seemingly intended for the coinage of money ; though it is very dif- 

 ficult to conceive in what manner they could be employed to that purpose ; espe- 

 cially N° 2, which has an impression on both sides ; unless we should suppose 

 they coined two pieces at the same time, by the help of three moulds, of which 

 this was to be the middle one. 



If, by disposing these into some sort of iron frame or case (as our letter- 

 founders do the brass moulds for casting their types) the melted metal could be 

 poured into them, it would certainly be a very easy method of coining, as such 

 moulds require little time or expence to make, and therefore might be supplied 

 by new ones, as often as they happened to break. 



These moulds seem to have been burnt or baked sufficiently to make them 

 hard, but not so as to render them porous like bricks, by which they would have 

 lost their smooth and even surface ; which in these is plainly so close, that what- 

 ever metal should be formed in them would have no appearances like the sand- 

 holes, by which counterfeit coins or medals are usually detected. 



A Commodious Disposition of Equations for Exhibiting the Relations of Goniome- 

 trical Lines. By Wm. Jones* Esq. F.R.S. N° 483, p. 56o. 

 Theorem. — In a circle whose radius is r, let there be two arcs, ^^the greater, 

 a the less, each in the first quadrant; put s, t,f, and v, for the sine, tangent, 



* Wm. Jones, an excellent mathematician, and the friend of Sir I. Newton, was born l675, in 

 the Isle of Anglesy, North Wales, where his father was a farmer ; which profession not agreeing 

 with our author's studious disposition, he came up to London, where he soon got into a merchant's 

 counting-house ; and so gained the esteem of his master, that he gave him the command of a ship 

 for a West-India voyage. On his return he set up a mathematical school, and published his book on 

 Navigation in 1702 : and afterwards, on the death of the merchant, Mr. Jones married his widow. 

 The son of lord Macclesfield being his pupil, and having rendered some essential service to the Mac- 

 clesfield family, Mr. Jones was rewarded with the office of secretary to the chancellor, as well as 

 that of a deputy teller of the exchequer. Mr. Jones died July 3, 1749, at 74- years of age, being one 

 of the vice-presidents of the Royal Society. At the lira* of his death, he left his widow with chilj 



