The public doubts of the peace are at length settled. A note has been sent from the Foreign Office to the Lord Mayor, announcing that the definitive treaty had been finally settled at Amiens, on the 27th of March, by the plenipotentiaries of England, France, Spain, and the Batavian Republic. The treaty, as it transpires, is the source of general cavil. It leaves to France all her conquests, while England restores every thing except Ceylon and Trinidad; the one a Dutch colony, and the other a Spanish; both powers having been our Allies at the commencement of the war. The Cape is to be given back to the Dutch; but Malta, the principal bone of contention, is to be garrisoned by a Neapolitan force, until a Maltese garrison can be raised, and the island is then to be declared independent, under the guarantee of all the great powers of Europe. The French government affected to display great reluctance to conclude even this treaty, which has thus taken six months of negotiation since the exchange of preliminaries. At one time, orders were sent for the Channel fleet to put to sea. Yet there can be no question that France desired this Peace, whether as a resting time for a fresh attack, or from the mere exhaustion of war. She had already gained every object that she could hope to obtain by arms in her present condition, and her natural policy was to secure what she had thus attained. The two grand prizes of her ambition, Egypt and the command of the Mediterranean, had been boldly aimed at, but she had lost both, and both were now evidently hopeless. Some of those straws, too, had been thrown up, which, if they show nothing else, show the direction of the wind; and there were evident signs in the almost royal pomp of the First Consul, in the appointments of officers of state for ten years, and the constituting the Consulate an office for life; in the preparations for the return of the emigrants, and in the superb receptions at the Tuilleries--that Bonaparte already contemplated the last days of the republic. To what new shape of power his ambition looks is yet only in conjecture. But he is ambitious, daring, and unscrupulous--the idol of the army, and the wonder of the people. He may shrink, like Caesar, from the diadem, or he may assume, like Cromwell, the power of a king, without the name; but the field is open before him, and France can offer no competition.