While our course as a whole had been almost due north, and sometimes east of north, yet where there were rapids the river had generally, although not always, turned westward.  This seemed to indicate that to the east of us there was a low northward projection of the central plateau across which we had travelled on mule-back.  This is the kind of projection that appears on the maps of this region as a sierra.  Probably it sent low spurs to the west, and the farthest points of these spurs now and then caused rapids in our course (for the rapids generally came where there were hills) and for the moment deflected the river westward from its general downhill trend to the north.  There was no longer any question that the Duvida was a big river, a river of real importance.  It was not a minor affluent of some other affluent.  But we were still wholly in the dark as to where it came out.  It was still possible, although exceedingly improbable, that it entered the Gy-Parana, as another river of substantially the same size, near its mouth.  It was much more likely, but not probable, that it entered the Tapajos.  It was probable, although far from certain, that it entered the Madeira low down, near its point of junction with the Amazon.  In this event it was likely, although again far from certain, that its mouth would prove to be the Aripuanan.  The Aripuanan does not appear on the maps as a river of any size; on a good standard map of South America which I had with me its name does not appear at all, although a dotted indication of a small river or creek at about the right place probably represents it.  Nevertheless, from the report of one of his lieutenants who had examined its mouth, and from the stories of the rubber-gatherers, or seringueiros, Colonel Rondon had come to the conclusion that this was the largest affluent of the Madeira, with such a body of water that it must have a big drainage basin.  He thought that the Duvida was probably one of its head streams—­although every existing map represented the lay of the land to be such as to render impossible the existence of such a river system and drainage basin.  The rubber-gatherers reported that they had gone many days’ journey up the river, to a point where there was a series of heavy rapids with above them the junction point of two large rivers, one entering from the west.  Beyond this they had difficulties because of the hostility of the Indians; and where the junction point was no one could say.  On the chance Colonel Rondon had directed one of his subordinate officers, Lieutenant Pyrineus, to try to meet us, with boats and provisions, by ascending the Aripuanan to the point of entry of its first big affluent.  This was the course followed when Amilcar had been directed to try to meet the explorers who in 1909 came down the Gy-Parana.  At that time the effort was a failure, and the two parties never met; but we might have better luck, and in any event the chance was worth taking.