The Philosophical magazine; a journal of theoretical, experimental and applied physics . not worthy to be taken into account. No modernhistorian appeared to have visited the place. The princijial jjointsto be determined were (1) the situation of Scipios camp after hehad abandoned his position iu the immediate vicinity of Placentia,and (2) the identification of the deep watercourse where Hannibalplaced Mago with two thousand men in ambush on the morning ofthe battle. Scipios camp was, beyond doubt, at or near Rivalta, a castle andhamlet situated on a high bank (as the name imports) on thefurthe
The Philosophical magazine; a journal of theoretical, experimental and applied physics . not worthy to be taken into account. No modernhistorian appeared to have visited the place. The princijial jjointsto be determined were (1) the situation of Scipios camp after hehad abandoned his position iu the immediate vicinity of Placentia,and (2) the identification of the deep watercourse where Hannibalplaced Mago with two thousand men in ambush on the morning ofthe battle. Scipios camp was, beyond doubt, at or near Rivalta, a castle andhamlet situated on a high bank (as the name imports) on thefurther side of the Trebbia, about nine miles south-west of ambuscade was planed in the watercourse called the Trebbiola,a small stream, of which the banks were from 6 to 8 feet high, aboutsix miles from Piacenza, above the place called La Volta di Settima. The passages of Polybius, to which reference was made in thelecture, are in Book III. chapters 66 sgq.; those of Livy, in BookXXL chapters 47, 48, 52-5 J. The rude plan given below may make this abstract more Dec. 6— Suggestion of a proof of the Ilicorem that every Algc- 230 Cambridge Philusophical Society:— braic Equation has a Root, By G. B. Airj, Esq., AstronomerRoyal. In this paper the equation to be discussed is expressed under theform ffar2 + *^rp+ . . +m^=0. where CTa=a(cos a+ v — 1 sin a), re = r(cos 9+ v^ —1 sin 6),.. it may be written, P+ v^—1Q = 0; and the object is to showthat there will be at least one value of r between 0 and positive in-finity, and one value of Q between 0 and lir, which, used in combi-nation, will make both P and Q =0. This is effected by constructing two curves whose common ab-scissa is y, and whose ordinates are respectively the correspondingvalues of P and Q, produced by substituting in their expressions thesame value of r, and observing the change which takes place in theform of these curves, and in the position of their points of intersec-tion, as r
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