A new invasion of Cuba, somewhat more formidable, but less successful even, than the former, has absorbed public attention during the past month. Immediately after the return of Lopez from his first expedition, rumors were rife that he was making preparations for another attempt. These reports, however, attracted comparatively little attention, and no effective measures were taken to put a stop to proceedings which were so palpably in violation of our treaty engagements with Spain. The reported rising of the inhabitants of Cuba at Puerto Principe, which was noticed in our last Number, and which was grossly exaggerated in public prints throughout the country, had evidently been regarded by the Cubans in the United States as eminently favorable to the prosecution of their purposes. A party of about 480 men, led by Lopez himself, and commanded by subordinate officers, accordingly embarked on board the steamer Pampero, at New Orleans, and set out for Cuba. They intended to land in the central department of the island upon the southern coast, where the disaffection had been represented as most rife, and where they were, therefore, most sure of a favorable reception. But on touching at Key West for supplies, they were informed that a revolt had taken place in the Vuelta de Abajo, and Lopez accordingly resolved to land in that district. By some mistake, the nature of which has not been clearly explained, they missed their point of destination, and landed on the northern coast of the western department of the Island on the night of the 11th of August. The shore was deserted and they met no opposition.

General Lopez left Colonel Crittenden at this point with about 100 men in charge of the stores and unnecessary arms, and advanced with the remainder of his command to the town of Las Pozas: the inhabitants, however, fled as he approached, neither joining his standard nor furnishing him with provisions or encouragement of any sort. The day after landing, Col. Crittenden was attacked by the Spanish troops—two bodies of infantry and one company of horse. This force was too strong for them. After struggling as long as possible, they withdrew from the field, and finding that neither Lopez himself, who was only three miles off, nor any of the inhabitants came to their aid, they resolved to return to the United States. They procured small boats, and had just got to sea when they were followed and captured on the 15th by the Spanish steamer Habanero. They were taken to Havana, and, on the 17th, were shot. It was at first reported that they had no trial, but were shot immediately, and that their bodies were horribly mutilated and every possible insult offered to their remains by the Cuban populace. These statements were, however, afterward contradicted. It was stated that they were properly tried, and condemned, and that after their execution they were decently interred. Several of them, and Colonel Crittenden among the number, wrote letters to their friends at home, all of which agreed that they had been grossly deceived as to the state of public feeling in Cuba, and that, so far as could be perceived, not the slightest disposition prevailed among the inhabitants of the Island to overthrow the Spanish government.

General Lopez was attacked on the 13th by a large body of Spanish troops at Las Pozas; the action was severe, and the Spaniards were repulsed. The loss of Lopez was considerable, and among those who fell was Colonel Pragay, an officer who had served with distinction in Hungary. He lost in all about fifty men, but retained possession of the place. He soon perceived that all his hopes of aid from the inhabitants were groundless, and that it would be impossible to maintain himself against the Spanish troops; and determined to conceal himself in the mountains. On their march thither they met several Spanish detachments with whom they had successive engagements, suffering severely in each, and inflicting losses more or less serious upon their opponents. Among the Spaniards who fell was General Enna, a distinguished officer, who was buried at Havana on the 21st, with military pomp. At Martitorena on the 24th, while the remaining body of the invaders were breakfasting, they were surprised by an overwhelming Spanish force, and completely scattered; and from that time forward they seem to have been zealously hunted by the inhabitants of all classes, and by every means. The official reports of the Spanish officers state that the peasants pursued them with dogs, that the negroes aided in their capture, and that every part of the population evinced the most active and devoted loyalty to the Spanish government. On the 28th, Lopez with only six followers, was endeavoring to conceal himself and escape to the sea coast, and on the 29th, he was captured in the Pinos de Rangel, by a guide named Jose Antonio Castañeda, with fifteen peasants. He was at once handed over to a military force under Colonel Ramon de Sago, who had him conveyed by a night march to Havana, where orders were immediately issued for his execution, which took place at 7 o'clock on the morning of September 1st. He perished by the garrote vil, an instrument in common use among the Spaniards. It consists of an iron chair, with a back, upon which, at a point even with the head of the person sitting in it, is the instrument of death. This consists of iron clasps made to fit the sides of the head, and a clasp to pass round the throat. From behind is a long iron bar attached to a screw, which put in motion by the executioner giving it a single turn, draws the throat and side pieces tight and at the same time sends an iron rod into the spinal marrow at the neck from behind, causing instantaneous death. This machine was placed upon a scaffold about ten feet high, in the middle of a large square, surrounded by troops. An eyewitness has given an account of the execution. He states that Lopez behaved like a brave man throughout—and walked, surrounded by a guard, to the steps of the scaffold, as coolly as if he were at the head of his troops. He was dressed in a long white gown, and a white cap; his wrists were tied in front and above his elbows behind, with the cords held by soldiers. He ascended the steps with two civilians, friends, but without a priest. He faced round and looked upon the soldiers, and the immense throng of people outside of the square, and then turned round and knelt in prayer for about one minute. He then rose and turned toward the front, and in a clear, manly voice, and in tones loud enough to be heard by the thousands present (for it was still as night), spoke as follows:—"Countrymen, I most solemnly, in this last awful moment of my life, ask your pardon for any injury I have caused you. It was not my wish to injure any one, my object was your freedom and happiness;" here he was interrupted by the commanding officer in front. He concluded, by saying, "My intention was good, and my hope is in God." He then bowed, and turned round and took his seat, apparently with as much coolness as if he were taking a chair in a room with friends. He placed his head back, between the iron grasps, the negro hangman then adjusted the iron throat clasp and tied his feet to bolts on each side of the seat. During this preparation, Lopez was in conversation with his friends. The executioner, then took his place at the iron bar behind. Lopez kissed the cross handed to him by his friend; the negro then gave one turn of the wrench, and Lopez died instantly without the least struggle. The military at once returned to the city, the band playing a quick step; the thousands dispersed with little or no noise; and thus ended the second invasion of Cuba.

The intelligence of these proceedings, as it reached the United States, caused an intense excitement throughout the country. In the Southern States, and especially in New Orleans, where the expedition had been planned and prepared, the popular agitation was overwhelming. When the news of the execution of the fifty men under Colonel Crittenden reached New Orleans, with the report of the indignities shown to their dead bodies, a mob destroyed the office of a Spanish newspaper in that city, menaced and injured the shops of sundry Spanish inhabitants, and even sacked the house of the Spanish consul. Large meetings were held in all the principal cities of the United States, at which the conduct of the Spanish authorities was denounced, and active preparations were made for sending fresh reinforcements to the invaders. Subsequent accounts, however, and the interference of the Government, prevented the execution of these designs. The failure of Lopez cooled the ardor of that class of our population whose opinions of the morality and legality of any action, depend upon its success or failure; while the slightest reflection was sufficient to show the great mass of our people, that without a declaration of war against Spain by our Government, we had no right to invade her colonies. If a revolution had existed there, our people, as in the case of Texas, could have emigrated thither, and after becoming Cubans and abandoning all claims to American citizenship, have taken such part as they might see fit in the affairs of the island. But no such revolution existed. Lopez and those who acted with him were undoubtedly deceived as to the state of public sentiment in Cuba. No one can fail to regret the loss of so many noble spirits; but they put their lives upon the hazard of the die, and expected, in case of failure, the fate which they met. About 150 prisoners still remain in the hands of the colonial government; it is understood that their punishment will be commuted to imprisonment and transportation.

Political conventions have been held in several States during the past month, to nominate officers for the coming elections. In Massachusetts the Whigs assembled at Springfield on the 10th of September, above one thousand delegates being in attendance. Hon. Robert C. Winthrop was nominated for Governor, receiving 811 out of 1033 votes, and George Grinnell, of Greenfield County, was nominated for Lieutenant-Governor. Edward Everett, George Ashmun, and Seth Sprague were chosen delegates from the State at large to the National Convention. A series of resolutions was adopted, declaring substantially, that the Constitution of the United States and the laws made in pursuance thereof, are the supreme law of the land, any thing in the constitution or laws of any State to the contrary notwithstanding, and that no citizen or State has any right to resist their execution, except in such extreme cases as justify violent resistance to the laws, on the principle of the natural and indefeasible prerogative of self-defense against intolerable oppression;—that the preservation of the Union transcends in importance any and all other political questions;—that the Whigs of Massachusetts will faithfully perform every duty imposed upon them by the Constitution of the United States, and they call upon their brethren in every section of the State to respect and observe all its provisions;—that they "cordially support the national administration in all its just and patriotic measures; in its generous sympathy with oppressed nations struggling for liberty in every part of the world; in its able and vigorous management of our foreign affairs; in its unwavering purpose to maintain inviolate our public faith with all nations; and in its sworn resolve to vindicate the integrity of the Union against all assaults from whatever quarter;"—that they have undiminished confidence in the comprehensive statesmanship of Daniel Webster;—that they cordially approve the agreement entered into by the Whigs of New York;—that they disapprove very decidedly of the present administration of State affairs in Massachusetts, and that they will use every exertion to secure the election of the Whig candidates put in nomination. The Democratic party held their Convention on the 20th of August. A series of resolutions was adopted declaring that "the Democratic party is preëminently national, anti-sectional, and for the Union as a whole Union—that it has always sustained, and can only regain its supremacy in the Union, by adhering to its own men and measures; reposing on its fundamental principle of excluding all tests marked by sectional lines, South or North, East or West; and by leaving to the sound sense of the people of each State and Territory their domestic policy and institutions;"—that they recommend a National Democratic Convention to be held at Baltimore in May, 1852;—that they "deprecate as disunion in its worst form the attempts of any party or class of men to stigmatize and denounce one portion of the Union for its domestic institutions with which the Constitution does not interfere, and of the propriety of which each State is its own independent judge;"—that they approve the resolutions adopted in the National Democratic Convention of 1848;—and that they "go for a faithful execution of and acquiescence in all the Compromise measures settled by the last Congress." Charles G. Greene, Henry H. Childs, and Isaac Davis were appointed delegates to the National Convention. George S. Boutwell was nominated for Governor, and Henry W. Cushman for Lieutenant-Governor.

In New York the Whig Convention met on the 11th at Syracuse. Only part of the State officers are to be chosen at the election this fall. George W. Patterson was nominated for Controller, James M. Cook for Treasurer, Samuel A. Foote for Judge of the Court of Appeals, James C. Forsyth for Secretary of State, Daniel Ullman Jr. for Attorney-General, Henry Fitzhugh for Canal Commissioner, and A. H. Wells for State Prison Inspector. Four very brief resolutions were adopted, declaring that the action of the two Whig State Committees at Albany, which was sketched in our last, was "the result of honorable and patriotic devotion to the Constitution, and for the best interests of the whole people, and that it is adopted and approved by this Convention;"—that to the entire completion of the Erie Canal and kindred public works the Whig party is fully pledged;—that those who supported the canal bill rendered a service to the State of such eminent value, that it has obtained for them the gratitude of every friend of the true prosperity of the State; and that the candidates nominated for State offices deserve and will receive the united support of the whole Whig party.—The Democratic Convention met at the same place on the 10th. Two days were spent in effecting an organization. A series of resolutions was adopted reaffirming the views and principles set forth in the resolutions adopted by the State Convention at Syracuse last year. The following gentlemen were nominated as the Democratic candidates for the several state offices:—John C. Wright for Controller; Henry S. Randall for Secretary of State; Levi S. Chatfield for Attorney-General; Benjamin Welch Jr. for Treasurer; Horace Wheaton for Canal Commissioner; W. J. M'Alpine for State Engineer; Gen. Storms for Inspector of State Prisons; and A. S. Johnson for Judge of the Court of Appeals.—In Maryland P. F. Thomas was nominated for Controller, James Murray for Commissioner of the Land Office, and T. R. Stewart for Lottery Commissioner, by the Democratic State Convention held on the 12th of September.

A very severe storm swept over the whole southern coast of the United States and the West India Islands on the 18th of August. The damage to vessels and other property was very great. In the island of Porto Rico a great number of plantations and an immense number of cattle were destroyed, and many persons lost their lives. In the middle of West Florida, Georgia, and Alabama the gale was terribly destructive. The tobacco crop is said to have suffered severely.

Advices from Texas give encouraging accounts of the cotton crop in that State. In both quality and quantity it will exceed that of ordinary years. A new military post has been established in the Clear Fork of the Brazos; and in the immediate vicinity, it is said, very large deposits of iron ore and of coal have been discovered. A very large trade in cattle has sprung up of late between Texas and New Orleans; the net proceeds of the trade this year are estimated at $120,000. The Boundary Commission is progressing slowly. When last heard from it was at the copper mines. The survey had been temporarily suspended, owing to an error in running the Boundary, making it 60 miles above El Paso, instead of 16, as required by the treaty. About 130 persons are attached to the American Commission, while the Mexican Commission has only seven. From El Paso we learn that a conflict occurred early in June between a considerable body of Apache Indians and a party of twelve Americans, on their way to California. The affray took place near the copper mines. The Americans were defeated, with a loss of two men killed and two wounded. Writers in the Texas papers, who have passed over the route to California from San Antonio and El Paso, state that it is far preferable to the usual route by way of Independence, Missouri. It is said to be shorter, cheaper, and less dangerous.

Two more cases of the surrender of fugitive slaves have occurred in the State of New York during the month. A colored person, living at Poughkeepsie, and named John M. Boulding, was arrested there and brought to New York. Evidence was submitted to Mr. Nelson, a Commissioner under the law of 1850, which showed him to be the slave of Mr. Anderson, of South Carolina, whither he was immediately sent. The other case occurred at Buffalo, where a negro called Daniel was brought before Commissioner H. K. Smith. He was claimed under the tenth section of the act of 1850, a certified copy of the records of a court of Kentucky being produced, as required by that section, to prove him the property of a Mr. Rust. The Commissioner decided that the evidence was sufficient, but a habeas corpus was granted by Judge Conklin of the U. S. District Court, and the case was argued before him. He decided that the tenth section of the law of 1850, could not apply to slaves who had escaped previous to the passage of the law; and as Daniel was alleged to have fled before that time, the evidence provided for by that section was insufficient. He was therefore discharged. This decision is one of a good deal of importance, as it essentially modifies the operation of the law.

An election was held in Mississippi, on the 1st and 2d of September, for delegates to a State Convention, to consider what action Mississippi ought to take in regard to the action of the last Congress on the question of slavery. The majority of Union delegates returned was very large; so decisive, indeed, was the result regarded as to the feeling of the State upon the subject, that Gen. Quitman, who was running against Senator Foote, as the secession candidate, immediately withdrew from the canvass.