to high altitude, wide base line, aerial photographs. The sea 
surface as a function of x and y at an instant of time would 
then be the observed quantity. 
The functions which are observed by these instruments will 
be described in the course of the development of the method for 
the determination of [AC es eile: Of course, [a5 (we) 1° can 
only be estimated for some finite net in the same way that [aC 1° 
was determined by the methods given by Tukey. 
Preliminary investigation 
Consider the airborne altimeter. It yields a graph of the 
height of the sea surface along the path taken by the aircraft. 
Suppose that the aircraft were flying at a speed of 200 mph ina 
dense fog over a perfectly sinusoidal wave system (which does not 
exist in nature). What would the record look like? The disturb- 
ance is given by equation (10.40) where 8, and #, are fixed. Of 
course the pilot does not know the orientation of the x axis, and 
he does not know the direction of orientation of the wave crests. 
{otate the coordinate system with respect to the sea surface so 
that x' is the direction along which the aircraft is flying on a 
straight course. The equations for the rotation are given by 
equations (10.41) and (10.42). The sea surface in the new co- 
ordinate system is given by equation (10.43). Since the aircraft 
is flying so fast, as a first approximation consider t to be fixed 
at an instant of time and since the aircraft is flying in the x' 
direction, y' is fixed. The recorder, if calibrated in distance 
traveled by the aircraft, will then record an observed wavelength, 
L 
5? given in equation (10.44) and (10.45). If the aircraft is 
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