possible way to decrease the value of t by B5* and cause an in- 
erease in the value of the argument by 27. This is the reason 
why T,* is imaginary for certain values of t'. 
The derivation given above applies only to values of t>ty 
(or t'>- Be + tig) and X,> 0. For the other three possible com-= 
binations of inequalities, similar derivations can be carried 
out. One of the two quantities T,* or T5*, will always exist 
for the entire range of applicability. The other will be imagi- 
nary only over a very short range. 
Although S(7) ) is not periodic, it now becomes convenient 
to define a term which is somewhat analogous to the period of 
a periodic function. This term will be denoted by T* and it 
will be defined to be the average value of T,* and T5*e wee 
be called the apparent local period of S(7 ). 
It has been shown that the maximum value of the envelope 
occurs for t' = 0, and therefore T* is most important near t' 
= 0. For the values ofa , xy and T employed in Tables 1 through 
4, 8 ot x40°/enD is always less than 1077, and it can be shown 
from the expansion of the radicals in the expressions for t* 
and T5* that T* depends essentially only on the square of this 
term as a slight correction factor. Therefore T* can be given 
by equation (4.23) to four significant figures in the neighbor- 
nood, of t' = 0% 
The apparent local periods which correspond to the times 
and distances given in Tables 1 through 4 are given in Tables 5 
through 13. The apparent local periods are given to three sig- 
nificant places. Table 5 can be interpreted as follows with 
S155 
