that of the exhaust gases does not exceed
180 deg.F.--_Industries._

[Illustration: Diagram from cylinder--25 in. diam, 18 in. stroke.
I.H.P., 63. Scale, 1/30 in. Mean pressure, 28.2 lb. FIG. 5.]

[Illustration: Diagram from air pump--15 in. diam., 18 in. stroke.
I.H.P., 23. Scale, 1/30 in--Mean pressure, 28.5 lb. FIG. 6.

DIAGRAMS FROM CYLINDER AND AIR PUMP.

Net indicated horse power, 40; revolutions per minute, 100; coal tar
consumed per hour, 20.5 lb.; coal tar per I.H.P. per hour, 0.512 lb.]

* * * * *

AN INVESTIGATION INTO THE INTERNAL STRESSES OCCURRING IN CAST IRON
AND STEEL.

BY GENERAL NICHOLAS KALAKOUTZKY.

NO. I.

_Determination of the Influence of Internal Stresses on the Strength of
Materials._--We call internal stresses those which exist within the mass
of any hollow cylinder or other body, when it appears to be in a state
of repose, or not under the influence of external forces. When pressure
is applied to a hollow cylinder, either externally or internally, the
interior layers into which its walls may be conceived to be divided are
subjected to a new series of stresses, the magnitude of which is
independent of those already existing. These additional stresses combine
with the former in such a manner that at every point of the thickness of
the cylinder they have common resultants acting in various directions.
Thus, if we call t the internal stress existing at a distance r_x
from the axis of the cylinder, and in a direction tangential to its
cross section, and T the additional stress due to pressure inside the
cylinder acting at the same point and in the same direction, then the
newly developed stress will be t + T.

If R and r0 be the external and internal radii of the cylinder, and
if we suppose the external pressure _nil_, then, if the pressure inside
the bore be P0, the stress on the radius r_x is determined by the
following expression deduced from the well-known fundamental formulae of
Lame:[1]

r0 squared R squared + (r_x) squared
T = P0 ------- . -------------
R squared-r0 squared (r_x) squared

From which we see that T is a maximum when r_x = r0, i.e., for
the layer immediately next to the bore of the cylinder. Calling t0
the internal stress in this layer, and T0 the stress resulting from
the action inside the bore of the pressure P0, and allowing that the
sum of both these quantities must not exceed the elast