52 MINUTES OF PROCEEDINGS OF 
putation must be partly taken from tbe plans,, partly ascertained by 
reconnaissance or calculation. 
Thus, if tbe distance x r be ascertained by measuring, we have 
X 2 — x i + °- 
If, by tbe belp of tbe gun and a quadrant, or by an instrument for 
measuring angles, tbe ground angle n 1 of tbe top of tbe covering mass 
is ascertained, we shall bave 
y 1 = x 1 tan n Xi 
and y 2 = y x — u = x 1 tan n x — u. 
According as tbe difference y x — u happens to be positive or nega¬ 
tive we shall bave, in formula (1), to account tan n 2 = 
y± 
Xo 
positive or 
negative. Some examples further on will illustrate this. 
It is a matter of indifference which of tbe two formulas is employed; 
but it must not be overlooked that tbe first gives tbe angle of descent 
for tbe distance x ly the second that for tbe distance x 2 (= x x + a), and 
that tbe elevation, which has to be taken from the practice tables, will 
bave to be corrected accordingly, as directed in part 7. 
If the angles n x and n 2 are very small we can substitute tbe angles 
themselves for their tangents,. 
For instance, if tbe portion DT (Fig. 1) of tbe trajectory is con¬ 
sidered as part of a circular arc drawn through tbe points if, I), 1\ we 
shall bave (as was shown in Section 4 Part 1 of tbe “ Handbook for 
tbe I.R. Artillery”), 
7i = a + 
and y 2 = a + n x ; 
which formula can easily be deduced from tbe properties of tbe circle 
in accordance with tbe principles of geometry. 
In practice it is of little consequence whether tbe angles or their 
tangents are taken. 
3. Influence of the Nature of the Profiles. 
If tbe ground is nearly level tbe values of n 1 and % are very small 
and bave slight effect on tbe magnitude of tbe angle of descent. If 
the objects of fire are of any considerable height tbe angles of descent 
are less favourable, because tbe ground angles % and n 2 are then posi¬ 
tive and increase with tbe height of tbe cover and of tbe point of 
impact. Therefore, for curved fire, low-lying gun sites are less 
favourable than elevated ones, although at the longer ranges a small 
difference in height in tbe position of tbe battery is of no material 
importance. Thus, for instance, at 1000 metres a difference in height 
of l m in tbe position of the gun gives a difference of ground angle of 
only 34'. 
With curved fire the necessary angle of descent depends, therefore, 
essentially on tbe quotient ^ (== tan a ah), 
Tbe greater tbe distance a 
