Numbers 22:41

and brought him up to Bamoth-Baal] See on Numbers 21:19. The name indicates that it was a sanctuary.

the end of the people Not the whole body of Israelites to their furthest extremity but only the nearest end or fringe in the valley immediately below him, the bulk of them being hidden by the hills.

It seems clear that Bamoth-Baal was north and not south of the Arnon, otherwise the Israelites would be many miles away. But the country north of the Arnon was then in possession not of the Moabites but of the Amorites. If we knew more of the facts the difficulty might be explained; but it is not impossible that the narrative is to be considered in the light of a popular tradition which was poetical, and that the details must not be rigidly pressed.