SATURDAY, JAN. 30. The long-looked for intelligence has come at last in an authentic shape. The American forces, commanded by Com. Stockton, aided by Gen. Kearny, broke camp at San Diego on the 29th ult., and took up the line of march for los Angeles. Their route lay through a rugged country of one hundred and forty miles, drenched with the winter rains, and bristling with the lances of the enemy. Through this the commodore led our seamen and marines, sharing himself, with the general at his side, all the hardships of the common sailor. The stern engagements with the enemy derive their heroic features from the contrast existing in the condition of the two. The Californians were well mounted, are the most expert horsemen in the world, and whirled their flying-artillery to the most commanding positions. Our troops were on foot, mired to the ankle, and with no resource except in their own indomitable resolution and courage. Their exploits may be lost in the shadow of the clouds which roll up from the plains of Mexico, but they are realities here, which impress themselves with a force which reaches the very foundations of social order. The march of the American forces from San Diego to the Pueblo below, and their engagements with the enemy, are vividly described in a letter to me from one of the officers attached to the expedition. This writer says: “Com. Stockton, at the head of a force amounting to about six hundred men, including a detachment of the 1st regiment of U. S. dragoons, under Gen. Kearny, left San Diego on the morning of the 29th of December, for los Angeles. Our line of march lay through a rough and mountainous country of nearly one hundred and fifty miles, with impediments on every side, and constant apprehensions of an attack from the enemy: our progress was nevertheless rapid; and though performed mostly by sailor troops, would have done credit to the best disciplined army.