If Kepler, or Herschel, or Fulton, or Ericcson had violated axioms and laws of mathematics and dynamics, their labors would have been as so much chaff and dust. War is mechanism and science, inspiration and rule; a genuine staff for an army is a scientific law, and if this law is not recognized and is violated, then the disasters become a mathematically certain result.

May 8.—The defenders of Hooker call the result a drawn battle. Mr. Lincoln calls it a lost battle. I call it a miscarried, if not altogether lost, campaign.

May 9.—The poorest defence of Hooker is that the terrain was such that he could not manœuvre. If the terrain was so bad, Hooker ought to have known it beforehand, and not brought his army there. The rebels have not been prevented from marching and manœuvring on the same ground, and not prevented from attacking Hooker, all of which ought to have been done by our army.

May 9.—All is again in unspeakable confusion. All seems to crack. This time, more than ever, a powerful mind is necessary to disentangle the country. If all is confirmed concerning Hooker's incapacity, then it is a crime to keep him in command; but who after him? It becomes now only a guess, a lottery.

The acting Chief-of Staff on the battle-field was General Van Alen. Brave and devoted; but Van Alen saw the fire for the first time, and makes no claims to be a scientific soldier.

May 10.—I wrote to Stanton to call his attention to, and explain the reasons of Hooker's so-called miscarriage. The insufficiency, the inadequacy of his staff and of chief-of-staff. Hooker attempted what not even Napoleon would have dared to attempt, to fight an army of more than one hundred thousand men, literally without a staff, or without a thorough, scientific and experienced chief-of-staff. I directed Stanton's attention to evidences from military history. Persons interested in such questions read Battle of Ligny and Waterloo, by Thiers.

Cobden, Cobden the friend of the Union, can no more stand Mr. Seward's confused logomachy, and in a speech sneers at Mr. Seward's dispatches. The New York Times dutifully perverts Cobden's speech; other papers dutifully keep silent.

May 10.—To extenuate Hooker's misconduct, his supporters assert that he was struck, stunned, and his brains affected. Hooker was stunned on Friday, and his campaign was already lost on Tuesday before, when he wrote his silly proclamation, when he subsided with the army in a semi-lunar (the worst form of all) camp, and challenged Lee to come and fight him. Lee did it. Hooker was intellectually stunned on Tuesday. Further: the results of the material stunning on Friday could never have been so fatal if the army had been organized on the basis of common sense, as are all the armies of intelligent governments in Europe. The chief-of-staff elaborates with the commander the plan of the action; he is therefore familiar with the intentions of the commander. When the commander is disabled, the chief-of-staff continues the action. At the storming of Warsaw, in 1831, Prince Paschkewitsch, the commander, was disabled or stunned, and his chief-of-staff, Count Toll, directed the storm for two days, and Warsaw fell into Russian hands.

No more effective is the defence of the defeat, by throwing the fault on the Eleventh Army Corps. The Eleventh Corps was put so much in advance of a very foggishly—if not worse—laid out camp, that it was temptingly exposed to any attack of the enemy. The Eleventh Corps was separated from the rest of the army, as was Casey's division in the Chickahominy. The laying of a camp, the distribution of the corps, in a well organized army, is the work of the staff and of its chief; but Butterfield was not even then in Chancellorsville. Lee, who if caught napping, quickly awoke, wheeled his army as if it were a child's toy, cut his way through woods which amazed Hooker, and arrived before Hooker's semi-lunar camp. We, all the time, as it seems, were ignorant of Lee's movements. A good staff, and what Lee did, we would have accomplished. Lee quietly found out our vulnerable point; and struck the blow. That, if you please, was a stunner. Finally: the Eleventh Corps was eleven or twelve thousand strong. The weakest in the army, equal to a strong division in a European army of one hundred thousand men. The breaking of a division or of twelve thousand men posted at the extreme flank, ought not and could not have been so fatal to the whole campaign. A true captain would have been prepared for such eventuality. Battles are recorded in history when a whole wing broke down and retreated, and nevertheless the true captain restored order and fortunes, and won the battle.

I am told that the rebels attacked in columns, and not in lines. The rebels learn and learned, and are not conceited. The terrain here in Virginia is specially fit for attacks in columns, according to continental European tactics. We will not learn, we know all, we have graduated—at West Point.