It is very desirable, in a topographical and historical point of view, that the site of this remarkable contest between the Anglo-Saxons and the allied Scandinavians and British _reguli_ under Anlaff, should be determined on satisfactory data; and the allusion to it by MR. HESLEDEN, in a recent communication to "NOTES AND QUERIES" (Vol. iv., p. 180.), induces me to call the attention of your readers, and of that gentleman in particular, to some mention of this battle, topographically not unimportant, which is to be found in Egil's _Saga_; the hero of which was himself a combatant at Brunanburgh, under the standard of Athelstan, and which appears to have escaped the observation of those who have discussed the probable site of this deadly encounter. The circumstantial account to be found in the _Saga_, chap. lii. and liii., has not been overlooked by Sharon Turner, who however does not quote the passages having a special topographical interest. It is remarkable that the name of Wendune, for which among Anglo-Saxon writers there appears the single authority of Simeon of Durham, is confirmed by the testimony of the _Saga_: at least there can be little doubt, that the _Vinheida_ of the _Saga_ is but a Norse form for the Wendun or Weondune of the Anglo-Saxon chronicler. The natural and other features of the locality are not neglected by the author of the _Saga_, who describes it as a wild and uncultivated spot, surrounded by woods, having the town of _Vinheida_ not far distant on the north. These particulars I take from the Latin of the _Saga_; but the reader of the Icelandic would possibly find more minute characteristics, which may have been lost in the process of translation. As, by his residence in the neighbourhood, MR. HESLEDEN is favourably situated for the further prosecution of this inquiry, I should be glad to find whether his conclusion as to the site of the battle received confirmation, or otherwise, from the passages of the _Saga_ to which I have now ventured to direct attention. I may here observe, that if we consider the situation of _Jorvik_, or York, the capital of the then Norse kingdom of Northumbria, we shall perhaps conclude that it was on the Yorkshire rather than on the Lincolnshire side of the Humber, that-- "Athelstan, king, of earls the Lord, of heroes the bracelet-giver, And his brother eke, Edmund etheling, life-long-glory in battle won with edges of swords near Brumby."