Continuing The March
Since Minard’s map is in French, I have provided an English language version for us to use as we discuss the flow of Napoleon’s march in detail. 
On 24 July, Napoleon had reached Kamień, about 95km due west of Vitebsk. Oudinot was based near Dzisna, keeping an eye on Wittgenstein (who was based at the Drissa camp) but prepared to cross the river Dvina if necessary. The 1st Western Army had marched hard, with some of its forces reaching Vitebsk by 23 July. Barclay de Tolly still hoped to link up with Bagration but, aware that Napoleon was looking to force an engagement at Vitebsk, he dispatched Alexander Ivanovich Ostermann-Tolstoy, commander of the 1st Western Army’s 4th Corps, back to Ostrovno to create a screen and slow the Grande Armée’s advance.
On 25 July, Murat came across Ostermann-Tolstoy’s forces stationed in a defensible position near the river Dvina and the modern-day village of Astroüna (Ostrovno) at what was the first major clash between Napoleon forces and the 1st Western Army. As a result of Ostermann-Tolstoy’s limited qualities as a general, the French ambush succeeded in capturing a number of the 4th Corps’ guns. And a rash Russian infantry charge (not this time the general’s fault) was initially successful but eventually overwhelmed, losing 30% of its men. With an additional French division under Alexis Joseph Delzon advancing on the position, Ostermann-Tolstoy retreated back towards Kakuviachino. Although losses were high (about 2,500 killed, wounded or missing), the 4th Corps had succeeded in slowing down the French advance. The task of delaying the Murat’s troops further was handed over to Peter Konovnitsyn, commander in the 3rd Corps. The latter and his troops managed to hold the French off for another day until on 26 July. When however Barclay de Tolly learned that Bagration had been held at Mogilev and was not going to make Vitebsk, possibilities of facing Napoleon at Vitebsk were severely compromised. Russian generals, notably Ermolov, managed then to pursuade Barclay de Tolly that holding the position at Vitebsk risked being outnumbered by the advancing Grande Armée, and there was still the possibility that the 1st and 2nd Western Armies could become cut off from one another. At 4pm on 27 July, the First Western Army’s retreat from Vitebsk began east in direction of Smolensk. With Peter Pahlen, in charge of the rearguard, holding the French at bay and covering the Russian troops’ tracks, the 1st Western Army again succeeded in slipping away from Napoleon. The deft withdrawal, which left nothing to the French forces when they arrived in Vitebsk on 28 July, was a clear sign to some of the Grande Armée’s officers that the Russian forces in front of them were not going to be a pushover. By this point, Napoleon needed to give his troops a rest and Barclay de Tolly’s men were able to make their way on to Smolensk, arriving there on 1 August.
On 2 August, Bagration’s 2nd Western Army and Barclay de Tolly’s 1st Western Army finally convened in Smolensk.
Having arrived in Vitebsk on 28 July, Napoleon decided to offer his troops some much-needed rest. The march, coupled with the heat (the daily temperature was by averaging 28-30° C), meant his troops could not continue any serious pursuit of Barclay de Tolly. That night, the French emperor declared to Murat, Berthier and Eugène that “The first Russian campaign is over… We shall be in Moscow in 1813, [and] in St Petersburg in 1814. The war with Russia is a three-year war.”
On 4 August, the French headquarters was thus in Vitebsk, with Eugene in Surazh (between Velizh, Russia, to the north-east and Janavičy to the south-west in modern-day Ukraine); Murat at Rudnya (just over the border in modern-day Russia, on the road between Vitebsk and Smolensk); Davout at the confluence of the Beresina and the Dnieper; Ney south-east of Vitebsk, at Liozna (Belarus); Junot in Orcha (Belarus); Poniatowski in Mogilev; Oudinot before Polotsk; and Schwarzenberg in Slonim (Belarus).
Next: Polotsk, Smolensk and on to Borodino
 Dr. Daniel Churchill, MITE6323 – Interactivity, Visualization, Emerging Technologies and Paradigms, The University of Hong Kong, February, 2007.
 Mike Stucka, English translation of Minard’s classic chart of Napoleon’s March, Analyticjournalism.com, November 4, 2006, http://www.analyticjournalism.com/2006/11/04/english-translation-of-minards-classic-chart-of-napoleons-march/
 Napoleon’s Russian campaign: From the Niemen to Moscow, Napoleon.org, http://www.napoleon.org/en/Template/chronologie.asp?idpage=481959&onglet=1.