NEW HOPE CHURCH.

The casualties thus far in my division are-1 officer killed and 9 wounded; privates, 9 killed and 57 wounded.

The officer killed was the gallant Colonel A. C. Riley, commanding First and Fourth Missouri Infantry, Cockrell's brigade. His loss will be irreparable to his regiment and to the brigade, and the country will mourn the loss of one of her most valuable soldiers.

Lieutenant Stewart, of Hoskins' battery, had his leg carried away by a cannon shot while standing by his gun, but I am pleased to learn he is recovering. He, too, is a gallant officer.

Very respectfully,

S. G. FRENCH,

Major-General, Commanding.

Lieutenant General L. POLK,

Commanding Army of Mississippi.

HEADQUARTERS FRENCH'S DIVISION,
Kenesaw Mountain, June 28, 1864.

GENERAL: I have the honor to report to you that yesterday morning (27th), between the hours of 8 and 9 a. m., the enemy in my front and that portion of Major-General Walker's front, on my let, were seen forming in lines of battle behind their intrenchments, and at the same time their batteries opened on my line with all their guns. Soon after the enemy's line of skirmishers rose from their works and were followed by two lines of infantry. They were soon seen to be in an almost hand-to-hand conflict with the skirmishers on General Walker's right, and after a short but spirited contest most of those skirmishers appeared to have been killed or captured. Soon after my skirmishers in General Cockrell's front were forced from their pits on the right of the road by an attack in front and on their left and rear, and many were killed and captured. From my position on the west extremity of the mountain I could see but little of my line to the left in the woods, but observing the enemy in force on the right of Walker's front, I directed the artillery to be run down to the west end of the Kenesaw Mountain, and it opened on the enemy to the south of the road in Walker's front with such effect that they were driven back.

In the mean time the enemy on the right of the road and in my front advanced and attacked the line of intrenchments occupied by Brigadier General F. M. Cockrell, commanding the Missouri brigade, nd a portion of the left of the line occupied by General Sears' brigade, and after a spirited contest of an hour were signally repulsed with severe loss. The killed of the enemy that fell nearest our line were left on the field. So severe and continuous was the cannonading that the volleys of musketry could scarcely be heard at all on the line. My impression is that my artillery, almost enfilading the lines of the enemy on the left of the Marietta road, drove them back, and thus frustrated the attack intended on General Walker's right. General Cockrell sent an officer to inform the brigade commander on my left that we were being hotly pressed by the enemy, but from some cause the artillery that could command my front in part was not fired.