THE ROYAL ARTILLERY INSTITUTION. 
55 
about this selected point of impact (taken at a fixed height), the calcu¬ 
lation of the angle of descent must be made with reference to a point 
below it. If we wish to utilise half, at least, of the projectiles in the 
lower half of the trajectory pencil for the purpose of breaching, the 
lowest point in fixing the angle of descent must be taken lower by half 
the 50 per cent, vertical spread ( TLohenstreuung ); because for this point 
the chances are even that those projectiles will strike the scarp. If 
the charge and elevation have been determined for this point it is 
self-evident that the trajectory must be raised by just half this 50 per 
cent, vertical spread. If, then, this process is carefully conducted, and 
conditions in other respects are normal, the resulting mean point of 
impact will coincide with the intended one. 
If it is intended to make the horizontal cut at half the height of the 
scarp the lowest point of impact must be half the 50 per cent, vertical 
spread below it. Should, however, the vertical spread for the charge 
to be employed be but slight, and the profile conditions admit of an 
expectation that the masses of earth above the scarp will come down 
in sufficient quantity to produce a practicable breach, the lowest point 
of impact may be fixed at half the height of the escarp, the angle of 
descent calculated for this height, the charge and elevation found, and 
the latter then increased as much as may be necessary to raise the 
mean point of impact by half the 50 per cent, vertical spread. Should, 
however, half the vertical spread be greater than the half height of 
the strikeable surface, it will be advisable to fix the mean point of 
impact at half the height of the latter, because otherwise a consider¬ 
able number of shots would pass over the mark. 
Finally, should the profile conditions be very unfavourable, the ver¬ 
tical spread considerable, and the resulting final velocity insufficient; 
further, should the latter not admit of an increase by increasing the 
range, owing to this entailing other drawbacks, there will be nothing 
gained by raising the trajectory, and we must leave it to the projectiles 
that fall short to cut away part of the crest of the covering mass. If 
this is done to a sufficient extent the succeeding shots will bring the 
mean point of impact to a lower level. 
With profiles like the one represented in Fig. 4 the mean point of 
impact may, from the very first, be taken at a little above half the 
height of the scarp. 
Eig. 4. 
Since in indirect breaching by means of regular outs the scarp has 
to be struck in certain horizontal and vertical lines, it follows that 
in this kind of fire a certain degree of probability of hitting is indis- 
8 
