Later from New Mexico., Bra«t°. N*w Me*co, Aug. 5,1857. Mr. Editor—I lie express from that portion of the army under Col. Dixon H. Miles, stationed on the (Jila river, brings the gratifyi ng intelligence that a severe battle had been fought between our troops and the Apaches, in which the enemy were completely routed, losing forty-eight killed upon the spot,and some thirty odd taken prisoners. This is decidedly the severest chastisement the Indians have received since New Mexico has been attached to the United States, and it is to be hoped it will be long remembered by them. Lieuts. Steen, Lazalle and Cook are said to have distinguished themselves, having fought the Indians in a hand to hand fight. The command, it is thought, will return to the val-l«y the Rio Grande by the last of this month.There is considerable difficulty existing between the revenue department of Paso del Nor*e and the contractors for army supplies—the contractors refusing to pay duties upon grain and flour brought • I? _exico* bY setting up the plea that the county ot Li Paso, Texas, has been detaphed from the revenue district of Paso del Norte, by an act of Congress passed the 3d March, 1857, and the contractor are supported in this view of the matter by the officers of the army stationed at Fort Bliss, Texas. Indeed, eo warm has been the dispute, and so determined are the contractors not to pay duties, as to have caused the collector of the department (CalebSherman) to go on to Washington to have the mat-ter adjusted, leaving Col. A. B. O'Banncn, late of South Carolina, a gentleman of great intelligence, popularity and firmness, at the head of the depart ment until his return.The election oame off on the 3d inst, for State officers, with the following result: J. Cresbv, Judge ; A. C. Hyde, Senator, and Stephen Ilale, Representative to the Legislature.Fine crops of com aud wheat have been mad# this year all along the valley of the Rio Grande, and the Jjpalth of the country never better.—Cor. of the jV. O. Picayune.