688 BARBER AND TUCKER [CHAP. 19 



buoy which rises and falls with the wave surface may have a pressure meter 

 suspended from it (Fig. 11). If the pressure meter is deep enough to be below 

 the action of the waves, it will measure pressure fluctuations corresponding to 

 its vertical displacement. Variations of these principles are possible. In one 

 American instrument, the pole and drogue is replaced by a single long articu- 

 lated buoy (Farmer et al., 1955 : the theory given in this paper has since been 

 revised, see Chase et al., 1957, p. 73). In a Russian instrument seen by the 

 authors, the pressure gauge of the second type was replaced by a propeller 

 device measuring the integral of the vertical velocity. 



In general, instruments of this class are not very satisfactory. They tend to 

 be difficult to handle from a ship, particularly in rough weather. If the device 

 is attached to the ship by a cable, great care must be taken that the cable be 

 kept slack. The buoys may be tilted by a strong wind, or currents may drag 

 the suspended drogue or pressure meter to one side. If the longest wind-wave 

 components (about 25 sec period) are to be effectively measured, long vertical 

 suspensions at least 100 m are required. Thus, the present tendency is away 

 from this class of instrument. 



The second class of deep-sea wave recorders measure the vertical acceleration 

 of a buoy on the sea surface (Dorrestein, 1957). The spectrum of wave accelera- 

 tion A' (a) is simply related to the height spectrum by 



A'{a) = a^E'{a). (15) 



If only the spectrum is required, this conversion can be done after A' {a) has 

 been computed. However, if a wave-height record is required, the output of the 

 accelerometer must be integrated twice either electronically before recording, 

 or digitally after recording. In principle, the vertical acceleration can be 

 integrated mechanically in the buoy, but the authors know of no successful 

 instrument which does this. 



Ideally, the axis of the accelerometer should be kept truly vertical (by means 

 of a gyroscope, for example), but this is somewhat difficult and expensive and 

 in most instruments the accelerometer is either hung in gimbals to form a 

 short-period pendulum, or fixed to a flat float so that it remains perpendicular 

 to the local water surface. The water surface sets itself perpendicular to the 

 direction of the vector sum G{t) of the vertical and horizontal accelerations of 

 the water particles and gravity because, since it is effectively a constant 

 pressure surface, there can be no component forces parallel to it. A short- 

 period pendulum in a small buoy also sets itself in the direction oiO{t), so that 

 the two methods of mounting are equivalent. 



Thus, the magnitude of G{t) is measured and is given by 



\G{t)\^ = {g + z)^ + x^ + r, (16) 



where g is the acceleration due to gravity, x, y and z are the three components 

 of the acceleration of a particle in the water surface. Expanding for \G{t)\ to 

 the second approximation gives 



\G{t)\ =g + z + {r^ + y^^)l2g. (17) 



