On the 10th December, being by our reckoning in lat. 20° S. and long. 36° 30' W. from London, the Tryal fired a gun to denote soundings. We immediately tried, and found sixty fathoms, the bottom coarse ground with broken shells. The Tryal, which was a-head of us, had at one time thirty-seven fathoms, which afterwards increased to ninety, after which she had no bottom; which happened to us also at our second trial, though we sounded with a line of 150 fathoms. This is the shoal laid down in most charts by the name of the _Abrollos_,[1] and it appeared we were upon its verge; perhaps farther in it may be extremely dangerous. We were then, by our different accounts, from sixty to ninety leagues east of the coast of Brazil. Next day but one we spoke a Portuguese brigantine from Rio Janeiro bound to _Bahia de todos los Santos_, by which we learnt that we were thirty-four leagues from Cape St Thomas, and forty from Cape Frio; which latter bore from us W.S.W. By our own accounts we were nearly eight leagues from Cape Frio; and though, on the information of this brig, we altered our course, standing more southerly, yet, by our coming in with the land afterwards, we were fully convinced that our own reckoning was more correct than that of the Portuguese. After passing lat. 16° S. we found a considerable current setting to the southward. The same took place all along the coast of Brazil, and even to the southward of the Rio Plata, amounting sometimes to thirty miles in twenty-four hours, and once to above forty miles. If, as is most probable, this current be occasioned by the running off of the water which is accumulated on the coast of Brazil by the constant sweeping of the eastern trade-wind over the Ethiopic Ocean, it were then most natural to suppose that its general course must be determined by the bearings of the adjacent shores. Perhaps in every instance of currents the same may hold true, as I believe there are no examples of any considerable currents at any great distance from land. If this could be ascertained as a general principle, it might be easy by their assistance and the observed latitude, to correct the reckoning. But it were much to be wished, for the general interests of navigation, that the actual settings of the different currents in various parts of the world were examined more frequently and more accurately than appears to have been done hitherto. [Footnote 1: In the map of the world by Arrowsmith, the Abrolhos are made a cluster of islands off the coast of Brazil, in lat. 18° 10' S. long. 39° W. from Greenwich.--E.]