184 . REPORT—1862. 
sectional area, and the large permanent set which they exhibit. These com- 
parative values are as follows :—- 
Statical resistance in Dynamical resistance in 
tons per square inch. foot-pounds per square inch. 
Cast iron, flat ends........-+. = OD:D2. sbisscielategeleh Xe 7768 
Cast iron, round ends ...... =26°8i7iqa.oasians lamar 821:9 
Steel, round ends .......-+. ==O0°AG/latieinthia tak 2515:0 
From the experiments on the wrought iron, the flat-ended steel specimens, 
and the lead, no definite conclusion was arrived at, the material being more 
or less compressed without the appearance of fracture. The mean resistance 
of the cast iron is 800 foot-pounds per square inch, whilst that of steel is 
2515 foot-pounds, or more than three times as much. The conditions which 
appear to be derivable from these facts, in order that the greatest amount of 
force may be expended on the iron plate, are therefore :—Very high statical 
resistance to rupture by compression. In this respect wrought iron and steel 
are both superior to cast iron; in fact, the statical resistance of steel is more 
than three times that of cast iron, and more than two and a half times that 
of wrought iron. Lead is inferior to all the other materials experimented 
upon in this respect. Again, resistance to change of form under severe 
pressure and impact is an important element in the material of shot. In this 
respect hardened steel is infinitely superior to wrought iron. Cast iron is 
inferior to both. In fact, the shot which would produce the greatest damage 
on armour-plates would be one of adamant, incapable of change of form, and 
perfect in its powers of resistance to impact. Such a shot would yield up the 
whole of its vis viva on the plate struck, and, so far as experiment yet proves, 
those projectiles which approach nearest to that condition are the most 
effective. 
Report on the Progress of the Solution of certain Special Problems of 
Dynamics. By A. Cayuny, F.R.S., Correspondent of the Institute. 
My “Report on the Recent Progress of Theoretical Dynamics” was pub- 
lished in the Report of the British Association for the year 1857. The 
present Report (which is in some measure supplemental thereto) relates to 
the Special Problems of Dynamics: to give a general idea of the contents, I 
will at once mention the heads under which these problems are considered ; 
viz., relating to the motion of a particle or system of particles, we haye 
Rectilinear Motion ; 
Central Forces, and in particular 
Elliptic Motion ; 
The Problem of two Centres ; 
The Spherical Pendulum ; 
Motion as affected by the Rotation of the Earth, and Relative Motion in 
general ; 
Miscellaneous Problems : 
The Problem of three bodies. 
And relating to the motion of a solid body, we have 
The Transformation of Coordinates ; 
Principal Axes, and Moments of Inertia ; 
