DESERT SAND-DUNES 53 



of surface waves. The idea of a lateral boundary, 

 or third dimension, is not, however, revolutionary 

 in wave theory. F.or instance, in examining crystals 

 by means of a convergent beam of polarized light 

 we have a cone-shaped wave-front. 



I have pointed out that crescentic dunes or 

 barchans were left as scattered mounds where 

 there had once been continuous sand in consecu- 

 tive ridges. This part of the sandbank, now partly 

 bare, was, however, receiving a shower of sand 

 from the cloud which formed a haze 20 or 30 

 feet high over the sandbank. The freshly 

 deposited sand collected in patches, and I saw 

 that they were beginning to shape themselves so 

 as to produce barchans. The profile was at first 

 symmetrical, with a gentle slope fore and aft, 

 but after a time the lee slope began to steepen. 

 In plan the patches had the same convex end 

 to windward as the barchan, and to leeward 

 a nearly straight tra^nsverse front correspond- 

 ing to a line drawn from horn to horn of the 

 barchan. I thought that a cliff would soon form, 

 and cusps be produced, and this conclusion I subse- 

 quently confirmed by observations of the production 

 of similar forms in snow. Thus, if loose sand lies 

 in patches the wind produces crescentic dunes. 



On the day of my first visit to the sandbank I 



