time at the point of observation. The function, W(p), is a 
point set function which will be defined later. The notation 
Van Cp ) at first does not make sense, until the process by which 
the integration is to be carried out is defined. 
The properties of E(/t) are given by equations (7.2) through 
(7.5). It is zero for p less than or equal to zero. It is 
GING OHNE UI 3) non-decreasing for uw greater than zeros; that is, 
if pe 2 is greater than pu ? then E(p 5) is greater than or equal 
to E(u 4) as stated by equation (7.3). Finally, for allp , 
E(u) is less than some positive constant, M, as required by 
equation (7.4). If E(y) is monotonically non-decreasing and 
if it is bounded from above, then it follows that E(p) has a 
definite maximum value E,., (equation (7.5)) which is either 
actually reached at- a finite value of w or which is approached 
asymptotically as w approaches infinity. In statistics, a 
function with similar properties is referred to as the cumula- 
tive frequency function, or ogive, as defined, for example by 
James and James [1949]. 
E() will be referred to as the cumulative power density. 
It measures that part of the averaged square value of 7) (t) 
which is contributed by those spectral frequencies less than 
or equal top . The word "power" in the definition is unfortu- 
nate for wave theory because the averaged squardl value of ee 
is most nearly connected with the potential energy of the record 
averaged over time. In electronic theory where these concepts 
were originally developed, equation (7.1) usually described i 
voltage produced by an alternating current, and the voltage <«. 
ws le ae 
