205 



War. Cornelius Nepos, from his brevity, and Appian, from his in- 

 accuracy, were not worthy to be taken into account. No modern 

 historian appeared to have visited the place. The principal points 

 to be determined were (1) the situation of Scipio's camp after he 

 had abandoned his position in the immediate vicinity of Placentia, 

 and (2) the identification of the deep watercourse where Hannibal 

 placed Mago with two thousand men in ambush on the morning of 

 the battle. 



Scipio's camp was, beyond doubt, at or near Itivalta, a castle and 

 hamlet situated on a 'high bank' (as the name imports) on the 

 further side of the Trebbia, about nine miles south-west of Piacenza. 

 The ambuscade was placed in the watercourse called the Trebbiola, 

 a small stream, of which the banks were from 6 to 8 feet high, about 

 six miles from Piacenza, above the place called ' La Volta di Settirna. 5 



The passages of Polybius, to which reference was made in the 

 lecture, are in Book III. chapters 60' sqq. ; those of Livy, in Book 

 XXI. chapters 47, 48, 52-56. 



The rude plan given below may make this abstract more intel- 

 ligible. 



December 6, 1858. 



" Suggestion of a proof of the Theorem that every Algebraic Equa- 

 tion has a Root." By G. B. Airy, Esq., Astronomer Royal. 



In this paper the equation to be discussed is expressed under the 

 form 



««*•£+ vr'+ •• • +m„.=0, 



where «„=«(cosa-(- V — 1 sin a), r 9 =r(cos0 + V — 1 sin 0), . . . or, 



