SETTLEMENT OF THE TRENT DIFFICULTY – FAVORABLE EFFECT ON THE PUBLIC MIND. – The decision arrived at by the government to restore Mason, Slidell & Co. to the British authorities had a very marked and favorable effect on the public mind in this city yesterday. It removed a load of care from men’s spirits, and restored a degree of elasticity which was noticeable in every department of trade. The public pulse beat more evenly than it had done for the last five or six weeks. The Stock Exchange felt the influence, and gave evidence of it in an advance in the price of government securities and a general movement in stocks. Even those who held that the action of Commodore Wilkes was legal and justifiable felt gratified that the administration entertained a somewhat different idea, and that it found a mode of postponing war without subjecting the nation to humiliation and disgrace. Now that this trouble has passed over, let us look forward with confidence to a speedy throttling of the rebellion.