It continued wavering between the south by east and south-east until we had got another degree to the southward, when it settled at south-east a steady breeze; but the easterly current, which would now have been an advantage to us by keeping the transports to windward, had ceased, and we found a strong westerly one running for several days, from 30 to 45 miles in 24 hours, by which our account was brought back to its original agreement with the time-keeper and lunar observations. The greatest velocity of the westerly current, was between latitude 3 deg. 00' north and the line, and its direction appeared to have been nearly west, for we never found our observations for the latitude materially affected by it; the same was the case with the easterly current, which may account for the ships from the northward, bound to the coast of Brazil, who may have no other way of determining their longitude but by account, scarcely having been sensible of any current; so very nearly does the westerly set, counteract, in the passage, that to the eastward. On the 14th of July, in the evening, we crossed the equator in longitude 26 deg. 10' west, and with 5 deg. 00' of west variation. The south-east trade wind now made us ample amends for the failure of the north-east, for it blew a fresh and steady breeze from east-south-east to east, which I believe is rather uncommon when the sun has so great north declination: if the wind had not favoured us so much, we must have fallen in with the coast of Brazil, far to the northward, which, with this convoy, would have been attended with much loss of time, and some degree of danger; however, with this favourable slant, we carried all the sail possible, and were enabled to keep at a distance from the coast, but not so far as to be able to make the island of Trinidada, which it was Captain Phillip's intention to have done, had the wind permitted. We passed its parallel 4 deg. 30' to the westward of it, and had for several days kept a look out for an island, which the Portuguese call Ascencao, and is said to lie between Trinidada and the coast of Brazil; but the existence of which there is much reason to doubt. We did not see any thing until the 3d of August, when we made Cape Frio; at 12 o'clock at night we were right abreast of it, and had it bearing north half west five or six miles; its longitude, by the time-keeper, is 41 deg. 40' west of the meridian of Greenwich* and its latitude is 22 deg. 58' south. This cape is an island distant two or three miles from the main land; we had very light airs and variable weather between the Cape and Rio Janeiro, which is a distance of 18 or 20 leagues; we never approached the shore nearer than five or six miles, at which distance we had 30 fathoms water over a soft bottom, and at four leagues distance had 42 and 43 fathoms, with the same soft ground. [* It will appear hereafter that we had not the true rate of the watch, and consequently that the above longitude is not correct.]