Military Bridges^ and the Passage of Rivers. 295 



To the logarithmic sines of the measured angles A, B, 

 Plate I. Fig. 15, add the logarithmic cosecant of their sum, if, 

 as in the figure referred to, the perpendicular CD falls within 

 the triangle, or the logarithmic cosecant of their difference if it 

 falls without, and the logarithm of the measured base AB ; the 

 sum of these, rejecting tens in the index, will be the logarithm 

 of CD, the perpendicular breadth of the river. We have been 

 thus minute in this particular, because, if the breadth of a river 

 is not accurately known over which a pontoon bridge is to be 

 thrown, the capture of a place, or the loss of an army, may be 

 the consequence. 



" This was abundantly proved in the passage of the Garonne at Grenade, 

 in 1814, by the army of the Duke of Wellington, previous to the battle of 

 Toulouse. That city served the enemy as a double tete de pont. Its ancient 

 walls were in a very defencible state, on both banks of the river ; and th^ 

 communication between these two works was kept up by a good stone-bridge. 

 The inhabitants of the country had been employed, for some time previous 

 to this period, in repairing and strengthening the ancient ramparts, and in 

 mounting the cannon on them. Two attempts had been made, a few days 

 before that at Grenade, to pass the river above Toulouse. The first, at a 

 place called Portel, failed for want of a sufficint number of pontoons to reach 

 across ; there being still about 20 yards of river remaining after they were all 

 placed in the line. This failure arose from not having correctly ascertained 

 the width of the river at the place recommended for effecting the passage." 



This shows in a remarkable manner the necessity of deter- 

 mining the breadth of a river with precision. 



" The second attempt was made at St Roques, a town situated on the 

 enemy's bank. The operation began at dusk. A party of about fifty infantry 

 were rowed across, and they barricaded themselves in a building favourably 

 placed for protecting the operation. The bridge was immediately com- 

 menced, finished before day -light, and the troops passed ; but the roads by 

 which they were to operate were not found to be in a practicable state, on 

 account of the previous rains, and the troops were ordered to return to the 

 left bank." 



It was next determined to pass the river below the city. 

 The bottom here, as well as at St Roques, proved gravelly, and 

 none of the anchors would hold. The cables next the left bank 

 were, therefore, secured to trees ; those next the right bank, at 

 the suggestion of the Duke of Wellington, were made fast to 

 anchors buried on shore. These, and many other interesting 

 topics relative to the passage of rivers by means of pontoon 



