The Lord Mayor of York gave a splendid entertainment to the Lord Mayor of London, on the 25th of October, which was attended by a great number of the leading men of England. Prince Albert was present, and made a very sensible and pertinent extempore speech. Its leading feature was a marked and impressive eulogy on Sir Robert Peel. In alluding to the interest taken by Sir Robert in the great Industrial Exhibition, Prince Albert took occasion to say that he had assurances of the most reliable character that the works in preparation for the great Exhibition were "such as to dispel all apprehension for the position which British industry will maintain."

At the meeting of the Canford Estate Agricultural Show on the 22d of October, the lady of Sir John Guest made a brief but most admirable speech, expressing her regard for the laboring classes of England, and her earnest desire that the utmost efforts should be made for their elevation and improvement. This unusual incident, and the admirable spirit which it evinced, elicited great applause.

The Town Council of Manchester are taking vigorous steps to compel the manufacturers of that city to consume the smoke of their furnaces, and thus to rid the city of the dense cloud which has hung over it hitherto. The process is found to be perfectly practicable, and decidedly economical. Some of the heaviest manufacturing establishments in the city testify to a saving of one-third in coal. The issue of the experiment will be important.

The rapid increase of burglaries and thefts in Birmingham has elicited from Mr. D.H. Hill a suggestion for the suppression of crime, which is regarded as pertinent and important by the leading journals. He proposes that whenever a jury is satisfied that an accused party is addicted to theft, he shall be compelled to prove a good character, and to show means of subsistence, on penalty of being adjudged a thief, and punished accordingly, under an old statute.

Emigration from Ireland to the United States continues and increases. A great part of those who leave are described by the Irish papers as being farmers of the most respectable class, and considerable apprehensions are expressed of the injurious effect of the movement on the prosperity of the country.

A letter from Brazil, written by Lieut. Bailey of the royal navy, details some rather prompt proceedings on his part in the capture of slavers. He was sent out to the Brazil station, and arrived off Rio Janeiro June 18th, and in sight of the harbor captured a vessel engaged in slave-trading, and sank her the same night. On the 20th, he captured a second, and sent her to St. Helena for adjudication; and on the 23d, he seized another, taking her out of a Brazilian port, which has hitherto been contrary to law. The affair excited a good deal of feeling in Brazil, and was likely to lead to a misunderstanding with the English government. The effect of such proceedings, in exasperating a government which might be induced by friendly appeals to put an end to slave-trading, is forcibly urged.

The Paris correspondent of the London Times has developed an alleged secret plot of the Red Republicans, to revive the revolutionary fever throughout Europe, and the substance of his statements is also given in the Paris Patrie—both accounts being evidently derived from the same source. It is asserted that the Socialists have leagued themselves together and that a secret congress of their chiefs was held in Paris on the 2d of June, where they planned a gigantic conspiracy, the ramifications of which extend to the whole of Europe, and even to the heart of Russia, where it is said to menace a terrible explosion. The motto which has been adopted is, "Sans pitié ni merci," and it has been resolved that all the chiefs of states shall be assassinated. It is added that in one of the numerous secret meetings held by the initiated under the presidency of the principal agents, the death of the Bonapartists was sworn, and would be the signal for the destruction of all the Bourbons, and of all their friends and supporters. The threat uttered by one of the German chiefs of the conspiracy was to the effect that "on the field of battle we shall spare no one, and we will strike down our dearest friends if they are not unconditional Communists." After indicating the dépôts of arms formed by the Communist conspirators in all the capitals where it has established seats, enumerating the means employed to ensnare the foolish and the ambitious, and, in fact, indicating all its resources and all its plans, the document informs us that the object of the conspiracy is to arrive, by means of general confusion and a sanguinary combat, at the extermination of all those who possess a foot of land, or a coupon of rente, and that it has sworn the oath of Hannibal against all the monarchies of Europe. Plunder and assassination form the basis of the plan. The document terminates thus, "The soil of Europe is undermined, so as to render a frightful catastrophe imminent." The pretended revelation is ridiculed in nearly all quarters.

On the destruction of the Roman Republic, the Roman Representatives appointed a National Committee, of which Mazzini was the head, with extensive political powers. This committee has just issued an address, dated at London, calling on all Italians and all Italian provinces to join their standard, promising them eventual success. In the course of the address they declare that they have effected such an organization of the forces of the movement as circumstances permit, and insist on the necessity of Italy becoming an independent nation.

We have hitherto alluded to the public agitation started in the British Colony of New South Wales in favor of independence, by Dr. Lang, who had organized an association for the purpose of accomplishing the object which he declared to be so desirable. The movement has been represented by the English papers as being unsupported by the colonists, and as, therefore, of no importance. We see, however, that Dr. Lang has recently been elected mayor of the City of Sydney, which shows that the people there, at least, have confidence in his character and respect for his views.