From NEW MEXICO we have news to the end of September. Colonel Sumner's expedition against the Navajo Indians had reached Cyrality, in the very heart of the Indian country, and intended to erect a fort there. The Indians were swarming on his rear, threatening hostilities. News had reached Santa Fé that five of Colonel Sumner's men had perished for want of water, before reaching Laguna. The troops were scattered along the road for forty miles, and horses were daily giving out. Colonel Sumner will establish a post at St. Juan, one in the Navajo country, and one at Don Ana. Quite an excitement had been raised at Santa Fé by the demand of the Catholic Bishop for the church edifice commonly known as the Military Church. Under the Mexican Government it was used exclusively as the chapel of the army. Since the conquest it had been used by the United States army as an ordnance house. After the departure of the troops, Chief Justice Baker obtained from Col. Brooks permission to occupy the house as a court room. The Catholic clergy considered this as a desecration of the house, and consequently objected to its being thus appropriated. The commotion was quelled by the Governor's surrendering the key to the Bishop, formally putting the possession of the building into the hands of the Church.--Major Weightman is certain to be elected delegate to Congress.--Much misunderstanding exists between the Judges in construing the laws in regard to holding the courts, and some fear a good deal of delay in administering justice in consequence, as the lawyers are refusing to bring suits until there shall be unanimity among the Judges.--The difficulty between Mr. Bartlett and Colonel Graham, of the Boundary Commission, is still unsettled. The former was progressing with the survey. Rain had fallen to some extent throughout New Mexico, and vegetation was consequently beginning to revive. MEXICO. Late advices from the City of Mexico state that the Cabinet resigned in a body on the 2d of September, and much disaffection prevailed throughout the country, which was in the most deplorable and abject condition.