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.]

On the 6th of August, a light breeze from the sea carried us within the islands which lie off the harbour, where we anchored for the night, with the convoy, in 14 fathoms water, clear soft ground, the island Raz (a low flat island) bearing south by west two miles, and Rodondo (a high round island) south-west by south.  The next morning an officer was sent to the town, to wait on the viceroy, and give him information who we were, and for what purpose we had visited that port:  in the afternoon of the 7th, with a breeze from the sea, we weighed, and, with the whole convoy, sailed into the harbour.

As we passed Fort Santa Cruz, we saluted with 13 guns, which was returned by an equal number from the fort; we anchored off the town in 171/2 fathoms water, over a good soft bottom, and moored with best bower to the south-east, and the small bower to the north-west; Fort Santa Cruz south 36 deg. 00’ east; the Sugar Loaf south, 7 deg. 00’ east; and the Flag-Staff, on the Island Cobres, north 78 deg. 00’ west,