218 
THE VALUE OF A HIGH SITE FOR COAST ARTILLERY. 
Produce DA to meet MR' in E, 
then 
DV=DE cos 8, 
= (a + b tan 8) cos 8, 
— a cos 8 + b sin 8, 
Let 
= ' /{ “ 2+62) (vW) cosS+ 7(^W in8 } • 
a . s 
V(a 2 +& 2 ) ’ 
then 
b 
and 
JDV= *J(a? + 6 2 ) sin (A 4- 8 ), 
which is a maximum when 
A+ 8=90°, 
or when the ratio ^ is such that A, and 8 are complementary angles, in 
which case DV will coincide with DB. 
DV may thus be considered as revolving round D, having, in the 
case of & purely vertical target, a maximum value DA, when 6 = 0; 
and, in the case of a purely horizontal target, a maximum value DC, 
when a = 0. 
Now the ratio - can never be less than 2, a value it might possibly 
have in the case of a torpedo boat, broadside on ; its value will, in 
general, be very much greater: A can, therefore, never be greater than 
tan -1 ^ or 27° say, hence in all practical cases, the higher the site, the 
larger the virtual target, for DV will become greater as 8 increases up 
to about 60°, a value it can never well exceed. 
III. The Effect of Mistakes. 
That the gun thus becomes a more accurate weapon when placed 
upon a high site, is beyond question, but this will not be considered 
in the following investigation of the results of mistakes or faulty gear 
or material: in addition, lateral errors, from whatever cause, are 
generally trifling and, of course, are unaffected by site, so they need 
not here be taken account of. Longitudinal errors alone will be dealt 
with. 
Longitudinal errors may be divided into two classes: 
A. The gun may be fired at the wrong range. 
B. The correct range may be known, but actually, or in effect, the 
wrong elevation may be given. 
