On the 7th of June the Meerut force joined that from Umballah, at Alipore, a short march from Delhi; and the next morning the little army, now under the command of Sir H. Barnard--for General Anson, overwhelmed by work and responsibility, had died a few days before advanced upon the capital of India, After four miles march they came at Badulee-Ka-Serai upon the enemy's first line of defense, a strong intrenched position, held by three thousand Sepoys with twelve guns. These pieces of artillery were much heavier than the British field guns, and as they opened a heavy fire, they inflicted considerable damage upon our advancing troops. The British, however, were in no humor for distant fighting; they panted to get at the murderers of women and children--these men who had shot down in cold blood the officers, whose only fault had been their too great kindness to, and confidence in them. Orders were given to the Seventy-fifth to advance at once and take the position; and that regiment, giving a tremendous cheer, rushed forward with such impetuosity through the heavy fire that, as at Ghazee-ud-deen-Nugghur, the Sepoys were seized with a panic, and fled in wild haste from their intrenchments, leaving their cannon behind them. At the foot of the steep hill on which the signal tower stands, another and stronger line of defense had been prepared; but the mutineers stationed here were infected by the wild panic of the fugitives from the first position, and so, deserting their position, joined in the flight into the city.