THE VERTICAL FIRE. 3 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’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 ~ 
very 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 
strongman. 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 
