THE DEVELOPMENT OF ARMOUR. 
555 
years. As pointed out, however, Fairbairn and Maitland appear to 
be quite inapplicable to the case of the high velocities that have now 
come in. Consequently the sound plan appears to be to use Maitland 
or Fairbairn up to 1,580 f.s. and Tresidder above. Fig. 29 herewith 
shows the traces of the formulae above mentioned obtained by 
connecting the results dotted in, so that the course suggested would 
adopt the curve dotted A B X Z and at Z shunt on to the Tresidder 
curve so marked. Practically, all important perforations occur at 
higher velocities than 1,580 f.s. and may be simply obtained by the 
Tresidder slide rule, by setting the shots* weight opposite the calibre 
and reading off the perforation for all velocities required. The scale 
happens to stand nearly or quite correct with the sliding shot home in 
its case for the 6-in. gun and 100 lb. shot. 
Tresidder* s formula may be written as follows :— 
2 wjfi _l_ 
. d log—1 8-8410 
Where t = the thickness of wrought iron in inches. 
to = the weight of shot in lbs. 
v = the striking velocity in feet-seconds. 
d = the calibre of gun or diameter of shot in inches. 
Krupp*s formula brought to the same shape and using the same 
notation is 
i* - wv * v 1 
U di log-i 6-V776 
Now to compare these we may disregard all constant factors leaving 
the constant to be determined by practice as it were once for ail. 
Raising Krupp*s formula to the power f we get 
^2 — w lmAL x constant terms. 
Cla 
Now for shot of similar form the weight will be in proportion to the 
cube of the diameter, that is, for w we may substitute d 3 into some 
constant, or for one factor w%, we may substitute df, thus 
df x wt> 3 
fca = .i i nr.—, x constant terms. 
df x d 
which by cancelling df becomes Tresidder* s formula, viz., 
i 2 __ p x constant terms. 
d 
Another curious instance of agreement of independent formuke has 
occurred. Captain J. Gastner, in the article of C( Stahl und Eisen,** of 
April 1st, 1896, gives a newly adopted formula of Krupp’s for use with 
the newest and best plates with hardened faces. In continental units 
this is given as 
pv 2 = 6800 a E 2 
where v is the striking velocity in metre seconds, p the weight of shot 
in kilos, a the diameter of the projectile in centimetres and E the 
