362 PHILOSOPHICAL TRANSACTIONS. [aNNO J 7 18. 



If other curves were desired which should exhibit other series, it inight easily 

 be done by means either of a circle or a right line; for by the one of them all 

 the curves may be constructed, in which s : i/ :: o" : r", by taking bsr to bsl as 



1 to n, and sn X sr = a~T~ X sl w, if the problem is to be solved by means 

 of the circle, fig. 5 ; for the equation of the curve drawn through all the points 

 n, will be * t^r :: a": r". In like manner, by means of the right line, may be 

 constructed the curves whose equation is * :^ :: r": a". 



We have exhibited two infinite series of curves commensurable to right lines : 

 we have demonstrated another commensurable to circular arcs, another to para- 

 bolic, another to hyperbolic arcs with right lines. But these seem reducible 

 to the measure of right lines by infinite art only, as they are expressed in right 

 lines only by an infinite equation. 



Remarks on a Fragment of an old Roman Inscription lately found in the North 

 of England. By Dr. James Jurin, M.D.F.R.S. N° 356, p. 8 1 3. 



Dr. Jurin, having resided for some time at Newcastle upon Tyne, had the 

 curiosity to travel the country between that town and Carlisle, to observe what 

 might occur worth notice in the remains of the ruins of the famous Picts-wall, 

 built by the Romans to secure themselves against the incursions of the natives 

 of that part of Britain which they did not care to conquer. In this perambu- 

 lation, besides many other valuable observations, Dr. 



Jurin saw and transcribed no less than '20 Roman in- civitate cat 

 scriptions, many of them wholly new; among them the willava' 



following, which, though broken, and in great part ille- orvm'[*o[5 



gible, suffices to fix the name of one of the ancient na- cdio^ 



tions of Britain, which has hitherto been greatly miscalled. 



It is thus, as annexed, and is to be seen on the wall, about 2 miles west of 

 Lenecross Abbey, near the confines of the two northernmost counties. 



Here it is observable, that the last A of the second line has a mark that 

 follows it, not unlike the last stroke of an N ; and if instead of A' we put N, 

 we shall read it civitate catvvillavnorvm, which we cannot doubt to 

 have been the true name of that people which Dion. Cassius, lib. 6o, calls 

 KaTBiXAavoi, and Ptolomy, in his geography, lib. 2, cap. 3, more falsly, 

 KaTu£up^Xavo» ; the first >, by producing the transverse stroke, having been mis- 

 taken for p^. This nation appears by Dion to have been more potent than their 

 neighbours the Dobuni, whom he calls Boduni, and had, according to Ptolomy, 

 Verolamium for their capital, which was probably the Cassivellauni oppidum of 

 Caesar. So that it should seem Cassivellaunus, king of these Catuvillauni, 



