531 
- 35 - 
Thus, when pa = 0,2 we obtain the following results 
ba = 0.2 
t/T, = c/2a = 0.067 0.250 0.500 0.750 0.933 1.000 
ur 
Pm/P = 0.029 0.188 0.460 0.707 0.818 0.825 
i 
Ouring this interval the recorded pressure is rising practically the whole time. When t exceeds To 
the recorded pressure must necessarily fal? and will follow the law 
Pn = Pm e™ {t - 7) . (5) 
where Pm. is the value of Pm when t = Ue and m gives the rate of decay of the true pressure with time, 
As a first approximation we may take the maximum pressure as occurring at t = T,and as given by the formyla 
roo = P(1— ua + 0.02 we a’) (6) 
We will now obtain a more accurate expression for P since the time to reach the maximum is slightly 
less than 7+ Assuming the maximum to occur when @ differs from 7 by 2 small angle put P= 7-wW 
in equations (4) and expand in ascending powers of yz then 
3 3 
ete Ga eer 4 te leigsi-al VO OOet: 
Z¥ v7] 
BOF Sr Wigan ene to order p * (7) 
Ch a eee to order w 
Bot ceeees 
Frey Bea bt 0 
D (coefficient of u° a~) = mq to order unity, 
Substituting in (3) 
Pm = See ee a ee Toe (8) 
in the neighbourhood of ¢= 7 
To find the maximum, differentiate with respect to w and equate to zero. The maximum occurs when 
ye Fa and has the value 
2 
. 5a 2ne ze tors a7 
Pray come fem tautaty piesa +t Pp 2 ssa} (9) 
and occurs at a time T such that 
Tae nw 2.2 
es Sage a (10) 
Equation (9) gives the following values for Trax and T 
pa 0 0.05 0.10 0.15 0,20 0.25 0.30 0.35 0.40 
Pcie 0.951 0.906 0.864 0.826 0.791 0.759 0.731 0.708 
SN ee ee 
TIT a 0.998 0,994 0.986 0.976 0.962 0.946 0926 0.90% 
