552 FORMATION OF A MACKEREL SKY, 



question arose in the mind — How is this wonderful grouping of 

 the clouds pi-oduced ? Presently the close resemblance of the 

 arrangement of the lines of cloud to that of the low crests of sand 

 on the ripple-marked floor of a wide and shallow bay, forced itself 

 upon me, and led me to consider whether there might not be some 

 real analogy between the two phenomena. 



First, then, what are the conditions under which sand ripple- 

 mark is produced 1 We will take the case of ripple-mark formed 

 under water as being more pertinent than that of the ripple 

 marking of blown sand. There are three layers of descendingly 

 denser free particles, a layer of air above, then a layer of water, 

 and a layer of sand grains below. The uppermost layer, of air, 

 moves with a gentle velocity over the surface of the middle layer, 

 of water, and throws this sui^face into a succession of more or less 

 parallel wavelets. In the open these wavelets range themselves 

 at right angles to the direction of the wind, but near land they 

 tend to conform to the shore-line. If the water is shallow, and 

 the particles of sand are small enough, these last, too, acquire the 

 wave-motion, but with a much slower rate of propagation and 

 with a shorter wave-length. 



Have these conditions any correspondence with those under 

 which alto-cumulus clouds are formed ? Here too we have a 

 number of horizontal layers of free particles increasing in density 

 as we descend. If an upper layer of the air be moving horizon- 

 tally over one below it, the lower layer will acquire a wave-motion 

 in precisely the same way as that in which a water surface is 

 thrown into waves by the wind. That this must be the case has 

 been shown mathematically by von Helmholtz. To what vertical 

 depth this wave-motion may extend will depend upon the numbers, 

 depth, density, and the relative motion of the underlying natu- 

 rally defined layers which may be present. 



The wave-lengths of these air-waves will l)e much greater than 

 those of water-waves, and, of course, very much greater than 

 those of sand-ripples. With a strong horizontal movement of the 

 upper stratum or strata, the wave-lengths of the undulations set 

 up in the lower strata will be greater, and will be accompanied 



