Monday, Dec. 17.—­The Diadem, which sailed on Saturday, was detained during the whole of yesterday within sight of the island; but, about noon to-day, a fresh wind springing up from the eastward, she was soon out of sight.  A few days since, our gardener, while digging in Paradise, turned up a Spanish copper-coin of Charles III., dated 1774, probably a relic of some ship which had touched here for water.

Tuesday, Dec. 18.—­Anderson, a black soldier of the Royal African Corps, whom I have previously mentioned as an interpreter on our arrival here, was to-day found sleeping on his post, and committed to the guard-house, from whence he contrived to escape into the woods, with a view of seeking protection from the natives.  Another black soldier was punished this morning for having quitted his post, and lost his musket, a few days since, in the following manner.  A party of Kroomen being employed in cutting down wood, some of the natives contrived to steal an axe and bill-hook.  The theft, however, was immediately detected, and a scuffle ensued, during which this soldier, who was a sentinel near the spot, threw down his musket, and ran away.  The musket was taken possession of by a native, but subsequently recovered by a Krooman, not, however, without his first receiving a severe cut on his hand by the knife of the native.  After throwing a few spears, one of which slightly wounded the head Krooman, the natives got clear off with the bill-hook and axe.  A spear was also thrown at Mr. Davis, the master’s assistant, who was accidentally passing at the time, and whom one of the natives had even the audacity to attempt to make prisoner; a fate which he only escaped, from his shirt giving way under the grasp.

When this affair was made known to Captain Harrison, he immediately proceeded to the market-place, and finding some chiefs there, communicated to them what had happened.  Cut-throat, who was present, instantly arose, and, after making a speech to his countrymen, formed them into line, each being armed with the usual number of spears.  After singing a war-song, and making three circular tours, or evolutions, the whole started off in quest of the thieves, and, in less than an hour, returned with the axe and bill-hook.  Some few days after this event, one of the natives, who had taken an active part in it, had the effrontery to enter our lines for the purpose of selling his palm-wine, when he was immediately secured by the Kroomen, and conducted a prisoner to Captain Harrison, who sent him on board the Eden, where he was put into irons; however, this man had committed a previous offence, namely, having struck Mr. Jeffery two severe blows with a stick, about a month since, which compelled him to give up the pursuit of a fellow, who had been endeavouring to impose two calabashes of water upon him, instead of palm-wine.

During the last week, we have had little communication with the natives, and our supplies of palm-wine, &c., have consequently run short.  This circumstance, we are informed, is attributable to their being occupied in the yam-plantations.  I am inclined to infer, that, if the necessity really exists for thus employing the whole of the inhabitants in the culture of this root, the population of the island is not so great as we have been led to consider it.