There is no way for the Germans to fill the gap in their line between First Army and Second Army, and they are in severe danger of being encircled. All along the front, they quickly disengage and withdraw to avoid the rapidly approaching derriere velocite. They must close the gap as soon as possible. And, as was demonstrated earlier during the Great Retreat, when Second Army retires, Third Army has to do so as well to protect their own flank. So too must everyone else along the northern part of the front. The plan has failed. France is saved. The war has not been won, but the Allies have succeeded in not losing, for the moment.
When General von Moltke receives the news, he literally has a nervous breakdown at his headquarters, and it’s up to his army commanders to govern the retirement. Fortunately for them, the ground that they are now about to retire over is favourable to the defender, and although their pace is slow and tired, the attacking forces are equally slow and tired, after nearly a month of continuous marching and fighting. The Germans cannot fully disengage, but the Allies cannot fully press their advantage.
Some Serbs retreat from the Drina to the Jagodnja mountain, and there launch a vicious counter-attack against the Austro-Hungarians. The Battle for Mackov Kamen will be a clear signpost towards the action that will follow in years to come on the Italian front, or at the Carpathians. Mountain passes are natural bottlenecks. It doesn’t matter if you have an army of a million men; only so many men can traverse a given path at once. The vast force multiplication offered by a single machine-gun can defend a single road almost by itself. The attackers simply can’t get enough people forward at once before they’re all cut down by the enemy fire. Artillery needs flat ground to fire, and there’s not much flat ground up a mountain.
German reinforcements have considerably stabilised the situation around the Masurian Lakes. The Russians are now in retreat all along the battlefield.
This is also the day that the drafting of the German Septemberprogramm is finished. It sets out Germany’s war aims in detail. The plan was subsequently lost until rediscovered by historian Fritz Fischer; he made it the centrepiece of a book that challenged the then-existing historiography of the causes of the war.
The Septemberprogramm envisions the creation of something called Mitteleuropa, a German-dominated economic association, envisioned to run from Belgium to Poland. Luxembourg, Poland, the Netherlands and Belgium will all fall under German control (to a greater or lesser degree), and France will be forced to cede to Germany a strip of its northernmost territory, including the Channel ports. Germany will presumably be able to base its Navy here, right at the mouth of the Channel and the corner of the North Sea, rather than at the (relatively) remote ports of Kiel and Wilhelmshaven. France will also pay reparations and cease trading with Britain in favour of Germany. Germany will also be granted greater control of the African colonial states.
(Of course, the question of whether this all formed the German reasoning for going to war, or had been worked out after victory looked likely as an after the fact justification, is a Matter of Some Debate.)