62 
MINUTES OF PIIOCEEDINGS OF 
The elevation for 1228 metres is consequently 
11° 25'+ 15'= 11° 48'. 
This elevation has still to be increased by the ground angle n 2 = 24'., 
which gives 12° 7'. If now the trajectory is raised by half the 
50 per cent, vertical spread, or about 5', the elevation becomes 12° 12', 
which only differs by 1' from that obtained by formula (1). 
Since the practice tables are given for charges at intervals of 
100 grammes, the angles of descent necessitated by the profile pro¬ 
portions are not always to be found in the tables. If the difference is 
only slight the next larger angle of descent should he taken , and rather too 
small a charge used. Should the difference be large we must obtain 
the angle of descent corresponding to an intermediate charge, by 
taking the arithmetic mean of the angles of descent given in the 
practice tables for the given distance. If this mean angle is the same 
as the required angle of descent, or only a little larger, the mean 
charge should be employed. In that case the arithmetical mean of 
the angles of elevation for the two consecutive charges at the given 
distance will be the correct elevation. 
Ex. 2.—The face of a work constructed on an old system has to be 
breached by means of curved fire from the short 15 c.m. gun. From 
plans, and by reconnaissances, the following particulars as to the profiles 
are obtainable :—The work has a ditch 20 metres wide and a covered 
way 10 wide, so that the. crest of the glacis is 30 metres from the 
escarp. The glacis crest is 1 metre above, and the bottom of the ditch 
7’5 metres below, the plane of comparison drawn through the cordon. 
If, on the first examination of the case, the lowest point is taken at 
half the height of the scarp, we shall have 
tan a = 
3-75 + 1 
30 
4*75 
~3CT 
0T5833 ; 
which corresponds to an angle of 9°, which angle must further be 
increased by the ground angle; so that the necessary angle of descent 
may be estimated at 9^°. 
A glance at the practice table shows us that this angle of descent 
can be obtained at a distance of between 900 and 1000 metres with a 
charge of between 0‘8 and 0‘9 kilogrammes, and that the resulting 
final velocity will be between 156 and 167 metres. On account of this 
low velocity it will not do to reduce the charge, and therefore the 
distance cannot be lessened; whilst an increase of the charge by 
increasing the distance is not advisable, owing to some steep rising 
ground opposite the fortress, by which the angle of descent would be 
considerably increased. On the other hand, an advantageous spot is 
found at 909 metres from the crest of the glacis, where the terrain 
angle (n) is only 5'. But with the selection of this spot for placing the 
breaching battery is combined the drawback that the line of fire meets 
the face obliquely at an angle of 60°; this, however, increases the 
distance ( a ) of the crest from the escarp, and thus gives a better angle 
of descent. In selecting the lowest point of impact it has further to 
