New-York Tribune account.
Gen. Fremont left Franklin on Sunday, May twenty-fifth. His troops were exhausted by previous forced marches to relieve Schenck and Milroy, from which they had not had time to recruit, and were weak from want of food. The first seven miles of road were only just not absolutely impassable by wagons. It was just such a road as cannot be found in the East, nor where an army has not passed. Wounded and sick were left at Franklin, because an attempt to carry them would have killed them. Nevertheless, with all its train of wagons, the army marched fifteen miles the first day. The next it reached Petersburgh, thirty miles from Franklin, at noon, and halted till Tuesday morning. Orders were then issued that knapsacks, tents, and baggage of every description that could possibly be dispensed with should be left behind. The knapsacks were stored in houses; officers were allowed a single valise. Five days rations of hard bread were issued to the troops, and on Tuesday the army advanced to Moorefield. It encamped in a valley five times broader, and infinitely more beautiful, than the valley at Franklin. On Wednesday the march was ten miles, the roads growing continually more difficult, and rain falling steadily. Col. Cluseret, commanding the rearguard, brought up his men with admirable rapidity, having remained in Franklin till Monday, reached Petersburgh at four o'clock Tuesday, and starting again at midnight, brought his troops to Moorefield by seven o'clock. Thursday, the troops remained in camp, too much exhausted by their extraordinary fatigues and want of supplies to continue their march to any advantage. The delay was the result of a careful inspection of each brigade and regiment by the staff of Gen. Fremont, approved by the Medical Director, Dr. George Suckley. Refreshed by the halt, the army on Friday advanced to Wardensville, twenty miles distant. A reconnoissance had been made the day before by Lieut.-Col. Downey, of the Third Maryland regiment, Potomac Home Brigade, who, with one company of Indiana cavalry, explored both roads and the village. On his return he was halted by a rebel within thirty feet, and challenged. As he drew his pistol to reply, the soldier raised his carbine and fired. The ball struck the horse of Colonel Downey, and then passed through his coat at the shoulder. The horse fell, and with him the Colonel, who was stunned by the shock. Recovering, he charged at the head of his men, and drove through the town a large body of rebel cavalry which had posted itself to intercept his passage. Two of the rebels were killed, and several wounded, without loss on our side. On Saturday, May thirty-first, the last of the intervening mountain ranges was crossed, and the western barrier of the Shenandoah Valley alone remained to be traversed. The troops pushed on twelve miles through the rain, and halted at night where the Winchester and Strasburgh roads divide. On the narrow ridges along which the path wound in constant ascent, there was no plain or table-land for camp. By the side of the road the tired troops dropped and slept under the partial shelter of open forests, many of them too wet and tired even to build fires. The General and his staff spent the night in a deserted and ruinous house at the angle of the roads, and shared together the floor, which, because a roof was over it, was a comfort and a luxury. For the troops, especially, it was rough preparation for the expected battle on to-morrow, but the spirit of the men was most admirable. It was nine o'clock in the evening before the main column came by the house, but they passed with elastic step, which only the depth of the mud made unsteady, and whole regiments went by singing as they marched, and sometimes cheering as they passed headquarters. Next morning the sun came out. The advance moved at six o'clock, and by eight the whole column was in motion. An hour and a half after-ward, while the General and his staff, riding next the cavalry, were ascending one of the long hills which anywhere else would be mountains, suddenly came the sound of a gun from the front. In a moment a succession of quick reports followed, and announced unerringly that Col. Cluseret's brigade was engaged with the enemy. The skirmish in advance is not very serious Cluseret's position is a good one for infantry, but Col. Pilsen sees at a glance that his artillery cannot be advantageously posted, and in the hope of inducing the enemy to advance, Cluseret is ordered to withdraw slowly. Four companies--two of the Sixtieth Ohio and two of the Eighth Virginia--were thrown out as skirmishers, and the contest was for a while rather eager. An effort of the enemy to flank the position was repulsed with a loss of seven wounded, five of the Eighth Virginia and two of the Sixtieth Ohio, whose names are given below, with other casualties since occurred. The cannonade ceased about eleven o'clock, and was not renewed. It was soon known that only the rear-guard or flanking column of Jackson had been engaged, while his main force passed hurriedly on over the Winchester and Strasburgh road. But the wily rebel meant to run — not fight — and had succeeded in reaching Strasburgh just in season to pass between McDowell on the one side and Fremont on the other. I know nothing of the movements of the former, except that his advance-guard reached Strasburgh next morning, twelve hours after it had been entered by Col. Cluseret, but it is certain no efforts could have accelerated the march of the column under Gen. Fremont. Cluseret was ordered on, entered Strasburgh in the evening, marching in a storm of rain, and thunder and lightning, such as only the mountains know. A reconnoissance was immediately sent out. The force advanced three or four miles  beyond Strasburgh, and was stopped at midnight, in perfect darkness, by an ambush and a barricade. Col. Figyelmesi, of Fremont's staff, who was in advance with the cavalry, went through the one and over the other, not without severe injury to himself by the fall of his horse As he felt his way along through the blinding storm, and over roads which were rivers of mire, a quick challenge came out of the darkness, and was answered with a demand for the countersign. “If you are Ashby's cavalry,” replied the rebel leader, “it is all right, come on.” Recognizing Ashby's voice, Colonel Figyelmesi did “come on,” and answered with instant order to charge. One officer and fifteen men followed him, and with this handful he rode straight into the famous rebel cavalry, and scattered it with the shock. Ashby gave the order to retreat at the first moment, yet in the brief contest three or four rebels were killed. It was impossible in the darkness and tremendous storm of that night to send forward the main column. General Fremont, therefore, encamped his troops where his lines had been formed, and at six next morning advanced again upon Strasburgh. A mile from camp a courier met him with the news that the head of McDowell's column was approaching the train from the other side. The General instantly put spurs to his horse, and dashing over four miles of frightful roads, passed infantry, artillery, and cavalry, and, with only his staff for body-guard, entered the main street of Strasburgh just as Gen Bayard, commanding the advance brigade of McDowell, rode in. The First New-Jersey cavalry, Col. Halstead, came up shortly afterward, and with his regiment and the rest of his force, Gen. Bayard was ordered to press forward as rapidly as possible on the rear of the flying enemy. Stewart's Indiana and Sixth Ohio cavalry, under Col Zagonyi, who arrived very soon after, were also sent on, and in a few minutes Buell's and Schirmer's batteries, and the rest of the light artillery under Col. Pilsen, as fast as it could be brought to the front, were hurried ahead at full gallop. After a brief conference with Gen. Bayard, Gen. Fremont rode on with his staff. The morning for once was clear and beautiful, and the pursuit had every element of interest and excitement. The troops ordered forward came up in quick succession, and as we rode on, cavalry and flying artillery constantly overtook and passed us, tearing furiously along the road in their eagerness to reach the front in time for the expected fight. Very soon came the sound of guns rapidly served, and we knew that the enemy had halted with his rear-guard, in hope of making a stand long enough to delay the pursuit. From a hill at the side of the road we saw the smoke of the guns and exploding shells, and then the cavalry, forming just below the crest of a hill a mile beyond us, in the endeavor to charge the battery in flank, rode over the summit, but were stopped by the timber and could not reach the guns. As Col. Pilsen brought up more guns, it soon became too hot for the rebels, and they hastily abandoned their position and retreated. A second stand was attempted some miles further on, but with no better success. Col. Pilsen's excellent judgment in placing his batteries, and the rapidity and accuracy with which they were served, again compelled the enemy to fly, closely pursued each time by the New-Jersey cavalry, which, during the whole day, were in the advance. A third time Gen. Ewell, who was in command of the rebel rear-guard, halted and turned his guns on his pursuers. It was his strongest position, and he doubtless hoped that here, at least, a few hours might be gained for the main body. So close was our pursuit, and so near the hostile forces, that Col. Pilsen, while reconnoitring the ground, in order to get his artillery most effectively planted, suddenly found himself within thirty paces of a body of rebel cavalry. They fired; his horse was shot under him, and horse and rider went down together. The Colonel's arm was badly crushed, but he was otherwise unhurt, though two bullets passed through his boots. A squadron of cavalry opportunely appearing, the rebels retreated, and Col. Pilsen was rescued and carried to an ambulance. His wound, though painful, was not serious; and in spite of it, he was next morning on horseback, and again in charge of the artillery. All along the road, and in the woods on either side, were strewn the relics which a fugitive army had left in its trail. Arms, clothing, stores of all kinds, were profusely scattered. A caisson of ours which had broken down and been left by Cluseret on his reconnaissance the night before, was passed within three or four miles of Strasburgh. Dead, wounded, and exhausted soldiers lay by the side of the road. Numerous prisoners were taken, and they gave themselves up often with evident willingness. In one group were men from the Forty-second Virginia, Sixth Alabama, and a Louisiana regiment. One captain was taken in Strasburgh. He had ridden back for his sabre, which he carried in the Mexican war, and valued accordingly. It cost him his liberty. All sorts of reports of Jackson's strength and the condition of his army comes from the prisoners, but it may be gathered from them that he has about twenty-five thousand men, and is greatly in want of subsistence and supplies. In the rear is the famous Ashby's cavalry, fifteen hundred strong. People in the villages through which we passed told us that the army was hurrying on in panic, plundering all houses of provisions, and many of every thing else, and that the men were so exhausted that the officers were driving them on with their swords. Woodstock was reached on Monday night. Lieut-Col. Downey, who again was sent forward to reconnoitre the town, found the rebel pickets on the opposite side, and was twice fired on, but escaped without injury. A negro woman told him that the rebels began to pass through the town at sunrise, and that their rear-guard had just gone on. In other words, Jackson has less than a day's start; and if his bridge-burning  does not save him, must be forced to stand fight. In the saddle again at seven o'clock on Tuesday morning. The troops have been on the march for hours. From Woodstock, which is rather a pleasant village, and, like all the hamlets of this valley, picturesquely planted among the hills, to Edinburgh the advance was without incident. A military bridge, constructed by Banks, crossing Stony Creek — a swift,, wide stream — is half burned by the flying rebels; but they are now so closely pressed that they have no time to do thoroughly even the work essential to their safety. In half an hour it is so far repaired that the infantry cross. The cavalry have already passed through a ford above, which is so deep as to be sufficiently unpleasant for artillery. All the ammunition is taken out and carried over the bridge by hand; then the caissons and guns go through without disaster, aided in their passage by that extraordinary profusion of oaths which is deemed essential to such efforts. Four miles beyond, the rebels have again halted with artillery, and as our guns have been delayed in crossing, the cavalry can only wait for their arrival. At Mount Jackson there is known to be a long bridge over the Shenandoah, a river too swift and deep to be forded. If they mean to fight on this side they must either lose their guns, or leave the bridge unharmed, and if they do the latter, their further retreat is impossible, for their rearguard will be cut to pieces unless supported. Jackson is too good a general to accept either alternative. His artillery remained in position just long enough to delay the advance of Gen. Bayard's cavalry, then crossed the bridge before our guns could be brought up, and burned it in the face of the cavalry, which Gen. Bayard permitted to remain spectators on the hill. When the smoke was seen, they were ordered forward, but arrived too late to save it. Under fire from the opposite side, the First Pennsylvania cavalry lost one man killed. As soon as Col. Pilsen could bring up his guns, they were unlimbered on either side of the road, and opened on the rebel batteries. Beyond the river stretches a broad plain, the further end of which slopes gradually up into an irregular eminence, along which the enemy had placed his artillery. On its further side, and in the neighboring woods, his troops were quietly encamped out of range, and, the Shenandoah River in their rear, were safe for the night, as they supposed, and at any rate too tired to go much further. It was soon found that the distance was too great for our guns. Col. Albert, chief of staff; was in advance, and reconnoitring the position with a soldier's eye, saw that the river bends suddenly half a mile beyond the bridge, and sent Schirmer's battery to a hill on this side, which flanked the rebel camp, and at once forced them to withdraw to a more secure position. Nothing more could be done till the bridge was rebuilt, and the army was, therefore, halted for the night. Twenty prisoners taken by Jackson at Front Royal escaped to-day, and met our troops as they and advanced on the road. They are all of the First Maryland regiment, said to have been cut to pieces in the unequal fight at Front Royal, and report that not more than forty of their regiment were killed, and that all the rest were captured. Jackson had with him two thousand prisoners, taken at different times from Gen. Banks's command. They have been treated with great severity, half-starved, and forced to follow the retreat of his army, whether sick or well. Officers fell by the roadside from exhaustion and illness, and were forced on at the point of the bayonet. They were not allowed to stop on the road even for a swallow of the water which it crosses in frequent streams. I annex a complete list of casualties: wounded in Col. Cluseret's brigade, in skirmish, Sunday, June 1. Eighth Virginia regiment--Rufus Boyer, company A, slightly; Peter Wards, company B, do.; George W. Douglas, company B, do.; Thomas Skelton, company B; Clark W. Card, company E, severely. Sixtieth Ohio--C. Bennington, company A, slightly; Stephen Parris, company B, slightly. June 2, in pursuit. First New-Jersey cavalry--Corporal Charles G. Morsayles, slightly; George Jones, company D, severely; Sergeant George H. Fowler, company E, killed. First Pennsylvania cavalry--George Tegarleir, company F, killed.