LAND AND WATER. 
September 18, 1915. 
ship, means at the highest possible point on the 
ast. And, unless tne range is extreme, the 
ma 
conditions of visibility poor, or the line of sight is 
obscured by smoke, extraordinarily accurate 
results can be got by spotting. The difficulty, 
then, in naval gunnery is not to find the range, but 
to keep it once it is found, and this difliculty exists 
because the problems of movement can only be 
solved by machinery that is, unfortunately, ex- 
tremely costly. 
The problem of engaging a target in the sky 
is, in many respects, of a totally different charac- 
ter. In certain aspects it is simpler. At sea 
direct hits have to be made at very great distance. 
In firing at aircraft, it is not direct hits that 
are sought. All that one aspires to do is to burst 
a shell as nearly as possible at the right distance 
from the target. It is like the difference between 
shooting with a rifle and shooting with a shot-gun, 
for the bursting shell sends a scattering charge, 
either of bullets or of fragments, in an ever-enlarg- 
ing pattern. No such perfect accuracy of aim is 
required, then, for air warfare. Again, no inte- 
gration of the movements of the firing-point and 
the target is required, because the firing is done 
from a stationary gun. But otherwise the problem 
is almost infinitely more complicated. Unlike a 
ship, aircraft do not move only in one plane, and 
their speed may be three or four times that of the 
fastest ship. Hence they command far greater 
differences of speed and a far wider freedom in 
the choice of courses. The air target may, then, 
be at any range, be going at any speed, on any 
course, and in any plane; and it is certain to be 
travelling in a different plane from that of the 
gun. These facts create great complications. 
The target being in a different plane from the gun, 
for instance, one range scale is no use. The eleva- 
tion of the gun will vary, for the same range, 
according to the positions of the target. For in- 
stance, at 2,000 yards, the gun would be aimed 
point-blank at the target overhead, but at an in- 
creasing elevation, as the target got lower to the 
right or to the left. The maximum elevation would 
be if the target were in the same plane as the gun. 
But this is a small matter compared with the diffi- 
culties which arise from the aircraft's speed, the 
difficulties of ascertaining its course, and the diffi- 
culties of observing fire. 
• 
A PROBLEM IN THREE DIMENSIONS 
A glance at Sketch II. will show the reader 
some of the characteristics of the problem. If 
the spectator supposes himself to be standing in 
the plane ABCD, the lines connecting the four 
angles of the plane with Xl and X2— two succes- 
sive positions of the Zeppelin— will show by 
the two solid figures the relationship of the 
target s course with any point in the plane. Its 
line of flight is XI to X2. Perpendiculars dropped 
from each of these points show its relative course 
plan-wise, Yl to Y2. To the mathematically 
minded, these figures will suggest the character of 
the operations necessary for finding the Zeppelin's 
course and speed, and the range and change of 
range for successive shots. The two chief diffi- 
culties that arise in trying to get a practical solu- 
tion from the target are, first, those that grow out 
of the fact that the observation of fire is of quite 
a different character from spotting at sea, and 
next from the immense speed at which the range 
and deflection angles change. 
Sketch 3 will bring it home to us that spot- 
ting by a single observer does not help at all. The 
shot that misses the sea target hits the water as 
we have seen, and marks its place; but the shot 
12 
that misses an aircraft hits nothing which is 
visible. The only way to record the position of 
the shot is to employ a time fuse and to mark the 
position of the burst. If, in Sketch III., a shot is 
fired from the gun A at the Zeppelin B and the 
shell bursts at C, the man at the gun will see tJie 
explosion immediately between his eye and the 
Zeppelin. It will be impossible for him to form 
any opinion at all as to how near the target it is. 
But the observer at D can see the gap between C 
and B and can suggest a correction. But sup- 
posing a Zeppelin, instead of being at B, was at 
Bl, and the shell had burst at either C or at Cl, 
or, indeed, anywhere along the line of sight DC, 
the result of the observation would have been 
exactly the same, so that the observer D cannot, 
by himself, make any more useful correction than 
an observer at A. Observation, to be effective, 
then, must be made from several points. And it 
is clear that as the Zeppelin may be at any posi- 
tion with regard to A, the gun, the observers will 
have to surround A, so that for every gun or 
group of guns there will have to be at least four 
groups of spotters. 
.When this difficulty has been got out of the 
way, we have to face another arising from the 
immense speed which airships possess. The dia- 
grams 4 and 5 will perhaps bring home to the 
reader how intricate this problem is. I have 
assumed that the Zeppelin has a speed of 2,000 
yards a minute — that is just over 60 miles an 
hour and less than 60 knots. It is supposed that 
it passes a gun at the lateral distance of 1,000 
yards, i.e., the perpendicular dropped from the 
Zeppelin to the ground would be at that distance 
from the gun position at the shortest range. The 
Zeppelin is supposed to be 6,000 feet up in the 
air, and to travel in a straight line. It will be 
