this procedure had to be repeated about 20 times to compress the bed 

 for one experiment. The edge of the tamper, where it touched the 

 walls of the tank, was made square, while the other three edges were 

 tapered and rounded to provide smooth overlaps. In experiments 52 and 

 54, 6 was 1.51 and 0.83 millimeters, respectively. The pressures 

 needed for these compressions were considerable, requiring in the first 

 case the full weight of a man standing on the tamper frame. Resulting 

 increases in U^ over the U^- for the usual uncompressed bed, represented 

 by experiment 13, are 6.1 percent for 6 = 0.83 millimeters and 12.9 

 percent for 6 =1.51 millimeters (Table A-1). Considering the 

 severity of the compressions, these associated increases in U^. seem 

 small and suggest that compression effects are generally unimportant. 



3. Results for the Three Sands. 



The 24 observations of the initiation of grain motion are shown in 

 Figure 12, where <p(^ is plotted against a/D and r, as in equation (3). 

 The figure shows that the data fall along separate curves for each sand 

 (value of r) with points for the two compressed surfaces falling above 

 the curve for the 0.55-millimeter sand. For comparison with previous 

 observations, the composite curve in Figure 2 has been transcribed. 

 The trends of the data have curvatures opposed to that of the transcribed 

 composite. Also, it is seen that the present data lie somewhat above 

 the composite though not outside the range of earlier data (Fig. 2). 

 Much of the apparent discrepancies probably stem from personal bias as 

 described in Section 111,1. 



4. A pplicability of a Shields Criterion . 



Madsen and Grant (1975; 1976) have stated that a Shields criterion 

 proven useful in unidirectional flow can also be applied in oscillatory 

 flow. By this criterion, grain motion begins when the bottom stress 

 reaches a critical value, x^,, satisfying 



m = 



g(p 



-^„-(/F^ 



where the function T, first sketched by Shields (1936), is fairly 

 constant over much of its useful range. As pointed out by Madsen and 

 Grant (1976), 



V P V 



r^^ (22) 



so that ^ can be replotted more conveniently as function of r alone, 



40 



