There are many disputes between divisions as the result of a proud and natural rivalry, which was possibly too energetically promoted by the staff in order to force each to its utmost before it staggered in its tracks from wounds and exhaustion. One division might have done the pioneer hammering and thrusting which gave a succeeding division its opportunity. A daring patrol of one division may have entered a position and been ordered to fall back; troops of another division may have taken the same position later. There was nothing so irritating as having to withdraw from hard-won ground because an adjoining unit could not keep up with the advance. Towns and villages were the landmarks on the map, with which communiqués and dispatches conjured; but often the success which made a village on low ground tenable was due to the taking of commanding hills in the neighborhood. Sometimes troops, in their eagerness to overcome the fire on their front, found themselves in the sector of an adjoining division, and mixed units swept over a position at the same time. In cases of controversy I have tried to adjust by investigation and by comparing reports. I must have made errors, whose correction I welcome. To illustrate the full detail of each division's advance would require several maps as large as a soldier's blanket. The maps which I have used are intended to indicate in a general way the movement of each division, and our part on the western front in relation to our Allies. There may be surprise that I have not mentioned the names of individuals below the rank of division commander, and that I have not identified units lower than divisions. The easy and accepted method would have been to single out this and that man who had won the Medal of Honor or the Cross, and this or that battalion or company which had a theatric part. Indeed, the author could have made his own choices in distinction. I knew the battle too well; I had too deep a respect for my privilege to set myself up in judgment, or even to trust to the judgment of others. Not all the heroes won the Medal or the Cross. The winners had opportunities; their deeds were officially observed. How many men deserved them in annihilated charges in thickets and ravines, but did not receive them, we shall not know until our graves in France yield their secrets.