It was after nine o'clock when the French streamed over the brow of the hill on our right--Chasseurs d'Orleans, Tirailleurs, Indigènes, Zouaves, Infantry of the Line, and Artillery--and fell upon the flank of the Russians. On visiting the spot it was curious to observe how men of all arms--English, French, and Russians--lay together, showing that the ground must have been occupied by different bodies of troops. The French were speedily engaged, for the Russians had plenty of men for all comers. Their reserves in the valley and along the road to Sebastopol received the shattered columns which were driven down the hill, allowed them to re-form and attack again, or furnished fresh regiments to assault the Allies again and again. This reserve seems to have consisted of three large bodies--probably of 5,000 men each. The attacking force could not have been less than 20,000 men, and it is a very low estimate indeed of the strength of the Russians to place it at from 45,000 to 50,000 men of all arms. Some say there were from 55,000 to 60,000 men engaged on the side of the enemy; but I think that number excessive, and there certainly was not ground enough for them to show front upon. Captain Burnett, R. N., states that he saw fresh bodies of Russians marching up to the attack on three successive occasions, and that their artillery was relieved no less than four times. The Minié rifle did our work, and Lord Hardinge is entitled to the best thanks of the country for his perseverance in arming this expedition as far as he could with every rifle that could be got, notwithstanding the dislike with which the weapon was received by many experienced soldiers. Three battalions of the Chasseurs d'Orleans rushed by, the light of battle on their faces. Their trumpets sounded above the din of battle, and when we watched their eager dash on the flank of the enemy we knew the day was safe. They were followed by a battalion of Chasseurs Indigènes. At twelve o'clock they were driven pell-mell down the hill towards the valley, where pursuit was impossible, as the roads were commanded by artillery. The day, which cleared up about eleven, again became obscured. Rain and fog set in, and we could not pursue. We formed in front of our lines, the enemy, covering his retreat by horse on the slopes, near the Careening Bay, and by artillery fire, fell back upon the works, and across the Inkerman Bridge. Our cavalry, the remnant of the Light Brigade, were moved into a position where it was hoped they might be of service, but they were too few to attempt anything, and lost several horses and men. Cornet Cleveland, was struck by a piece of shell and expired. General Canrobert, who was wounded in the early part of the day, directed the French, ably seconded by General Bosquet, whose devotion was noble. Nearly all his escort were killed, wounded, or unhorsed.