206 
MESSRS. A. Ii. H. LOVE AND F. B. PIDDUCK 
in which 
A 0 / ZA 10 
S/ 0 \t 
= ^ > &=-2A 
A, 2K, /2iV“ 
v 9 \y 
-<1 '"2 
<>3 — 2 —r 
2 ! A 2 /2P h \ 2 fti' 
-'l 
y / \y 
^1 / \^2. 
10 
>_ 4 3! A 3 /2Ri\ 3 /Si\ 10 p ,41 A 4 /2R 1 \VS 1 Y° , . 5! A 5 /2RAVSiY 0 
& ;; x a 7 UJW’ ^ vsJvv* * 5 Lr ’ sh s x W’ 
, __ 4 61A./2RA7SA 10 c « 7!A 7 /2RAV^Y° p _ 8! A 8 /2RAV^Y 0 
^•6 45 ^4 / '^/ 5 ^ 3 15 3 I'C I \ s? I 5 315 ^2 \ V / \ J 
wi / \^2/ 
V 2 \ V / W / 
■<1 \ ^1 / \^2/ 
o9 2 8 3 5 
9! A 9 /2EA 9 ^ 10 
2, \ Sj / 
M \ / £1 
The Second Reflected Waves. 
32. Relation between Pressure and Velocity at a Piston .—The relation between pressure 
and velocity at the image of the shot is an equation connecting r and s, which holds at 
£ 0 = 0, and can be interpreted as the equation of a certain locus in the plane of r and s. 
This equation can he written in the form 
(r-R 3 )/2 2 = B'A + BVf+B' 3 <f+ 
where S stands for (s —S L ,)/S 2 , and the coefficients B' are at present undetermined. 
To determine these coefficients we have recourse to the method of Articles 21-23. 
During the progress of the second reflected wave from the left, the value of x 0 at any 
point in the region occupied by it can be expressed in terms of the values r 1 and s' of 
r and s, which occur simultaneously at the point, by the formula 
e 
x 0 — — 5h f (Y /cr) du, 
Jac 
wherein the integral is taken along the locus from the point A, where r — r', to the 
point C, where s = s'. In this integral 
u—VJ 2 
du 
cr = 
Y 
cr 
M(B / 1 -l)<i + BV 3 +By 3 + 
S 2 {(B' 1 -1)+2BV+3B^ 3 + ...}dS, 
s 2 {i + (b / 1 +i)^+bv 2 +b' 3 ^+ ...}, 
+30 +310 C r + 
<r \ (A + s') or (A + s') 2 <A 
-} 
