420 
Sincew is positive and w*is negative, J an J ¥ are initially positive 
quantities of order of magnitude unity. If oscillations of the gas sphere, 
which occur only after a long period of time are ignored, a ee pos= 
itive, but v may become negative, though never sufficiently so to make 
dp/at positive. 
From Eqs. 4.7, we infer that Dp/Dt is initially large 
in absolute magnitude and negative in sign. Although decreasing somewhat 
in magnitude, it remains negative during the initial phase of the motion. 
The peak approximation is therefore appropriate for p as well as for the 
17/ 
functions W and o-, The derivative bu At may initially have either 
sign, depending upon the equations of state of the twomediums. For a boundary 
between water and typical gas mixtures resulting from explosion products, 
Du/. Dt is initially large and positive, but diminishes rapidly to zero 
and becomes negative. As a more detailed investigation will show, UL depends 
a A function F(t), described by the peak approximation, is supposed to 
have an exponential decay of the form, 
F(t)= Fevt/e 
where Fi =F (0) » and ep is the 7 value of the loga- 
eabinie. derivative of F with respect Kay e 
“Op = [bboy F(t LE] 
Or may be called the time constant. The function oe (s is thus 
represented by a two parameter curve, an approximation that is ap- 
propriate when F ( t) is initially a rapidly decreasing function 
Of tie 
33 
