1055 
= 9 
(y= 1) 0 + (y+ 1) > 
e SS en (16) 
Py Po (y + 1) ae (y= 1) 0) 
where the suffix o refers to the undisturbed yas. 
using (12)-(16) we can eliminate from (11) all quantities witn the suffix 1 exceot 04. 
When tnis is done we cbtain the result 
Gop ne es (peed) yee y= ye eee 
= + eS bY 
dt Ovey {yy -1+y (57% ~y+ 2 + y* (2¥°+y~- 1) } R yi R 
(17) 
where a,/ hs is denoted by y. 
Sincs aR = p,dt we may write (17) in the form 
co (y-1) {y+ 1+ (ly- 1) y} Oo uy oy 
eles = ty + 1) Se ee at 
aR (yeasty BY -y+ Dey AY ry-1) | OR yea R 
(18) 
The formula for olane waves is cbtained by going to the limit as R~®, The term 
containing R is simply dropoea from equations (17) and (18). Taylor's formula fcr the plane 
wave is 
do Bo 
Fauna te lame eae or 
CO a EES Ne eee) 8 
ot ay f y-1+ \y+ 1) y eee Y Neder 
(15) 
which differs from (17). The discrepancy is due to Taylor's assumption that a given value of 
pressure just behind the shock front is cropajated forward with a velocity cy relative to tne gas. 
{f instead of au we nad eliminates oo from (8) ana (9) we snoula nave found 
r r 
dp au 3 2 p,c,2u 
1 = 1h u a 2 dete 
ea es a ris, UG SAM) Soils ge 4 
or 
Decline, eee Bet vO ae x 
dt Cig ae { sy +1) +5y- 3} R JP, 
aya iat) Vey eee yeaa) 
BAe ee (21) 
{ x (y+ 1)+5y-3} 
or 
Oo dine Bg ee Oral ey lyn. ely et) ye Tae someway 
aR eR c¢, By (Y+-1) + Sy - 3 i Got e aye? 
(22) 
If we omit from (18) ana (22) the terms deoending on the form of the wave, we obtain 
two different rates of decay. These agree, however, when Oy is small, ano reduce to the 
ordinary result for small waves. when 0, is large, equation (18) gives 
a0, uy (y= 1) oy 
aR (2y-1) +1) & 
Integrating eevee 
