EXECUTIVE DEPARTMENT, Santa Fe, N. Mex., April 20, 1862.

Hon. W. H. SEWARD, &c.:

SIR: In my command of the 11th instant I informed you that a junction had been made between the forces under General Canby and those under Colonel Paul at the place called Gallisteo, 15 miles south of Santa Fe. I have learned since that the main body of the two forces did not unite until they reached the Canon of Carnavel, directly east of and about 15 miles from Albuquerque. General Canby, having left his position on the river below Albuquerque, at which place he had a slight skirmish with a small force of the enemy, left a garrison, and taking the position to which I have referred, in the Canon of Carnavel the two commands were united on the 13th instant.

The fugitive forces of the Texans had meantime reached Albuquerque from this place, and, uniting with the small force there, took up their line of march down the river on the east side, not being able to cross the stream at Albuquerque. They had progressed only 20 miles, when they were overtaken by General Canby at and in full possession of my residence. It being late at night when General Canby arrived within hearing of their position, his ears were saluted with the "sound of revelry by night." The violin was in full blast, accompanied by other and more noisy instruments. The enemy seemed to be entirely unconscious of his approach, nor was his presence known to them until next morning.

My residence is surrounded by quite a dense forest of trees, extending in every direction for at least half a mile, and the only approach for vehicles is by the main road. The ditches (asequias), for the purpose of irrigation, running across and parallel with the road, offer no small impediment to the operation of artillery.

During the day after General Canby had reached the position of the enemy, as related, a cannonading was carried on from both sides without any serious result. The position of the enemy was a strong one and dangerous to be approached by infantry, having high walls, made of adobes, which constitute our inclosures of farming lands. Against this position General Canby did not think prudent to make any demonstration.

During the night, however, the enemy silently left their position, and passed below a mile or two to a ford in the river where they attempted to cross but their teams being weak and the river swollen by the spring floods, the whole of their train, consisting of 60 wagons, was left in the river and on the banks, the mules along having been crossed over to the opposite shore. I am not informed that any of their artillery was either left behind or captured by our forces, with the exception of one piece the day previous, together with seven wagons and the contents.

The latest news from General Canby by Colonel Roberts, who arrived in town this evening, is that our forces were still in pursuit of the enemy, and had taken a position in advance of him at La Joya, 30 miles, where they crossed the river, bu ton the east side, where the enemy could not pass except under the direct fire of our artillery.

Colonel Paul, with the forces from Colorado, was harassing the enemy in the rear, having crossed the river to the west side. There can be no doubt of the entire capture of the Texans, with all their train of artillery, numbering some eighteen pieces,and this closes the scene of this devastating Texan invasion.

I have the honor to remain, very respectfully, your obedient servant,

HENRY CONNELLY.