AUGUST 26TH.—What a number of cavalry companies are daily tendered in the letters received at this department. Almost invariably they are refused; and really it is painful to me to write these letters. This government must be aware, from the statistics of the census, that the South has quite as many horses as the North, and twice as many good riders. But for infantry, the North can put three men in the field to our one. Ten thousand mounted men, on the border of the enemy’s country, would be equal to 30,000 of the enemy’s infantry; not in combat: but that number would be required to watch and guard against the inroads of 10,000 cavalry. It seems to me that we are declining the only proper means of equalizing the war. But it is my duty to obey, and not to deliberate.