evening, when the nearest land was two miles off, and the northern
hummock on Smoky Cape bore S. 4° W. nine leagues. I had before seen the
coast further northward, as far as 29° 20'; and having therefore no
inducement to lose a night's run for its examination, we steered onward,
passing without side of the Solitary Isles. At three in the morning
[SUNDAY 25 JULY 1802], hove to until day-light; and at eight o'clock made
the south head of a bay discovered in the Norfolk (Introd. Vol I, "In
latitude 29° 43', we discovered a small opening like a river, with an
islet lying in the entrance; and at sunset, entered a larger, to which I
gave the name of SHOAL BAY, an appellation which it but too well
merited."), and named _Shoal Bay_. One of the marks for finding this
small place is a peaked hummock on the low land, thirteen miles distant;
and it was now set over the south head of the bay at S. 20° W. In
steering northward close along the coast, we passed two small reefs, and
the water shoaled to 10 fathoms; they lie two miles off the land, and
there did not seem to be any safe passage within them. Our latitude at
noon was 29° 4', and longitude by time keepers 153° 31'; the shore was
three miles off but until we came up with Cape Byron at five in the
evening, there was no projection worthy of being particularly noticed.
From Shoal Bay to Cape Byron is fifty miles, where the coast, with the
exception of two or three rocky heads, is mostly low and sandy; and the
soundings, at from two to four miles off, vary between 10 and 32 fathoms,
on a sandy bottom. A few miles back the land rises to hills of moderate
elevation, which were poorly covered with wood in the southern part, but
towards the cape had a more fertile appearance.

Cape Byron is a small steep head, projecting about two miles from the low
land, and in coming along the coast makes like an island; its latitude is
28° 38', and longitude 153° 37', or 7' east of the situation assigned to
it by captain Cook. There are three rocks on its north side; and in the