220 
MESSRS. A. E. H. LOVE AND F. B. PIDDUCK 
(Plate 1, curve 9) (Articles 32-40).—The second reflected wave begins at the base 
of the projectile at time T 2 and pushes back the second middle wave along a junction 
r = R,. Thus cp is known, and the value of $ corresponding to an assigned x 0 is found 
by trial. We find that the junction reaches the middle particles at time t = 0*01023 
sec. The pressure at the breech is 650*0 kg./cm. 2 , at the junction 641*0 kg./cm. 2 . For 
the constants of the second reflected wave we have 
log B'j = 0T8668, 
log Bk = 1-99012, 
log c 4 = B81519, 
log & = 6-01358, 
log Bb = 0-27390, 
log {—Ci) — T'08789, 
log (—c 5 ) = 2-56985, 
log (-&) = 6-85566, 
log B' 3 = 0-82262 
c 2 — 0"10720, 
log A = 3-94418, 
log & = 7-62931. 
log B' 4 = 1-40104, 
log(-c 3 ) = P00167, 
log (-ft) = 5-07447, 
The method of calculation of the pressures in the second reflected wave has been described 
in Article 40. The pressure at the base of the projectile is 581*6 kg./cm. 2 , where the 
displacement is 571 • 9 cm. and the velocity 801 *3 m./sec. 
The projectile is so near the muzzle at time t = 0*01023 that a fresh chart for the 
muzzle epoch (displacement 600 cm.) is unnecessary. We find for the time to the 
muzzle t = 0*01058 sec., for the muzzle velocity 807*7 m./sec., and for the pressure 
at the base of the projectile at this instant 552*6 kg./cm. 2 . 
43. Results. — The pressure results are collected in Table I., from which Plate 1 is 
constructed. Plate 2 shows the pressures at the breech and at the base of the projec¬ 
tile, their ratio, the mean pressure, the displacement and velocity of the projectile, and 
a certain “ energy factor ” as functions of the time. The mean pressure (P in Table I.) 
is that which the cordite gases would have after adiabatic expansion, at uniform density, 
to the volume which they actually occupy at time i. The work of expansion in these 
circumstances will be ecpial, not to the kinetic energy of the projectile, but to a greater 
kinetic energy corresponding to a fictitious mass M + aC, where 
The energy factor ” a may be expected to vary with the distance travelled by the 
projectile : the lower values given are only approximate. 
It is difficult, after a glance at Plate 2, to resist the conclusion that the motion is 
tending to a limiting form, in which the pressure is approximately represented by 
/ (2/o) i> P)> with suitable functions f, </>. The energy factor a oscillates about a mean 
value of approximately 1/3, and the range of oscillation diminishes in time: similarly 
the pressure ratio oscillates about a value of approximately 0*9. Moreover, the latter 
value, like the former, can be obtained from Lagrange’s approximation by suitable 
treatment.* If p' is the pressure at the breech andp that at the base of the projectile, 
* F. Gossot and R. Liouville, ‘ Memorial des Poudres et Salpetres,’ vol. 13, p. 51, 1905. 
