THE VERTICAL FIRE. 93 



Carnot seems to call for a more thorough examination ; 

 but meanwhile we must applaud our illustrious colleague 



least that part which he speaks of, namely the impossibility of 

 breaching Carnot 1 s wall from a distance. In the experiments made 

 at Woolwich, a wall well-built, and having had time to consolidate, 

 was breached with expedition and certainty; though of course with a 

 verv large expenditure of ammunition, on account of the uncertain 

 nature of the fire; that is, throwing heavy shot over an earthen 

 bank, down against the wall on the opposite side. The vertical fire 

 question does not admit of quite so easy a solution; but Carnot cer 

 tainly miscalculated the effect of the very small balls he proposed to 

 shower down, as is immediately evident theoretically, and has been 

 tested practically. He said that, a large ball fired at a certain angle 

 with a certain velocity, being found to penetrate on falling into hard 

 earth, about its own diameter, his small balls fired under like angles 

 and velocities would also penetrate to the amount of their diameters; 

 but this is fallacious, he having forgotten the resistance of the air, 

 which retards balls of different sizes in the proportion of the squares 

 of their diameters, while their force, or power of retaining momentum, 

 is in proportion to the cubes of their diameters. This is an immense 

 difference when it is recollected that Carnot s given experiment was 

 with a ball of some five or six inches diameter, while those he pro 

 posed would have been about one inch; and that in vertical fire this 

 resistance of the air acts on the ball through a lengthened route both 

 ascending and descending. Experiment with the proposed balls at 

 Woolwich, has shown that the wounds inflicted by these balls would 

 be seldom disabling, unless they struck a man on the head : their 

 force being only somewhat greater than the strongest effort of a 

 strong man. It has also been shown, that they are given to scatter 

 so much, that the outworks in the neighbourhood must be abandoned 

 as soon as this fire is used from the body of the place; in fact, by 

 making vertical fire the whole of his defence, Carnot forfeits all the 

 time which the use of direct fire used to cause the assailant to expend 

 in approaching to the summit of the covered way, as a very slight 

 application of raw hides, &c., supported above the approaches, would 

 protect the assailants; and when there, the neighbouring works could 

 not assist in defence, as they must be abandoned from the scattering 

 fire from the body of the place. 



Still vertical fire is often good and effective, especially in the latter 

 parts of sieges; and all writers on fortification recommend its exten 

 sive use both in defence and attack. Its use has been restricted by 



