Having received positive orders to take a position upon the eastern bank of the Rio Grande, Gen. Taylor commenced his march. At the Rio Colorado he was met with a stern resistance, and assured that an attempt to cross would be followed by actual hostilities. It is scarcely necessary to add that he crossed, notwithstanding. On the 24th, Gen. Taylor left the advancing army, and, with a body of dragoons, repaired to Point Isabel, which place he occupied, and received, from steamboats opportunely arriving, supplies for the army. Gen. Taylor soon rejoined the army; a position was occupied opposite Matamoras, and the army proceeded to fortify their camp. On the 11th of April, Gen. Ampudia, in command at Matamoras, summoned Gen. Taylor to break up his camp, and retire beyond the Neuces within twenty-fours, adding that if he did not, arms alone must decide the question. In reply, Gen. Taylor informed him that his instructions would not permit him to retrograde from the position he occupied. Col. Cross, of our army, having been murdered when absent, and alone, some distance from the camp, a party was, on the 17th, sent to discover and seize the murderers. They were set upon by a large party of Mexicans, and some of them killed. On the 19th, Gen. Taylor blockaded the Rio Grande, a measure which elicited an immediate protest from Ampudia; and it was vindicated by Taylor as the necessary result of the Mexican declaration of a determination to commence, and actually commencing, hostilities. The character of the two letters is in singular contrast, that of Gen. Taylor being high-toned and masterly, but moderate and courteous. A collision had, from the first movement to occupy the western bank of the Rio Grande, been inevitable; and every day precipitated that result. Addresses, over the signature of the Mexican general, were scattered throughout our camp, inviting desertion. The communications between Fort Brown and Point Isabel were forcibly interrupted by large bodies of the enemy. The war had begun. On the first of May Gen. Taylor took up his line of march for Point Isabel, leaving a small but sufficient force at Fort Brown. His departure was the signal for a furious but ineffectual attack, which resulted in the death of the gallant commander, Major Brown, and continued until the glorious return of Gen. Taylor.