126 42 
TaBLE X. 
A = shortening of the copper, in thousandths of an inch. 
E = energy in foot-pounds. 
PPP RO wOWWwWh wrth = 
The fact that the shortening of a copper is entirely determined by the energy of the attacking piston 
can only be explained by supposing that the resistance of the copper at any moment is independent of the 
rate at which it is being shortened, and depends only on the extent to which it has been shortened. On 
this view the resistance of the copper for a given shortening A is 
dE 
da 
and can be determined from the calibration results. If these results are analysed it will be found that for 
small values of A the resistance is approximately r = ro + k A, where ro = 400 Ibs. and & = 62 Ibs, 
per 10-Sinch. For bigber crushings, above A = 50 x 10-3, the resistance is less than this formula 
indicates. ‘The increase of resistance which accompanies shortening of the copper is due almost entirely 
to hardening of the metal, and in only a very small degree to enlargement of girth ; for example, a copper 
emshed 40 x 10—5 inch has a resistance twice as great as a copper crushed 17 x 10-$ inch, though its 
cross-sectional area is ouly 5 per cent. greater. 
For measuring very light impacts, less than 0-5 foot-pound, coppers are too hard and lead cylinders 
must be used. Eley’s lead crushers were calibrated for this purpose, and the results are shown in Table XI. 
These leads are ~500 inch long and -325 inch diameter. The relation bevween E and A is independent 
of the weight of the piston, so that it must be concluded, as in the caze of coppers, that the resistance of 
a lead is independent of the rate at which it is being shortened. Asin the case of coppers, the increase 
of resistance which accompanies shortening of the lead is due mainly to hardening of the metal, but there 
is this difference, that whereas the copper keeps its acquired hardness the lead swiftly reverts to its original 
softness (H. W. R. Mason, Arms and Explosives, Jan. 1, 1918). ‘he self-annealing process occupies 
a matter of seconds or minutes, and it certainly has no time to take effect in the very brief duration of 
the impact of a piston, which is of the order of 10-5 second, but the phenomenon is worth noting since 
it invalidates any statical method for determining the resistance of the lead, and explains the “ creeping ” 
or gradual yielding of the lead which has been observed whenever it has been attempted to apply such 
methods. Calculated from the energy data the resistance of the lead is 
r= = = (for small crushings) approximately r° + 4 A, 
where ro = 130 Ibs. and & = 5-6 Iba. per 10-8 inch. 
Tasie XI. 
4 = shortening of the lead, in thousandths of an inch. 
E = energy in foot-pounds. 
