- 11 - 689 



when the qth trough is greatest, aamely wh^n 



R = 2 (2q - l) h 



t = 2 (2q - 1) / (2TT h/g) (50) 



Thus from a 2000 ton explosion at depth 235 feet we have that h = 285 feet (See Table l) . The first 

 wave is greatest at r = liuo feet, t = 30 seconds, and the height of the wave is 3* feet. The first 

 trough (not counting the one which leads the distance) is orcattst at R = 17in feet, its depth is 2i* feet, 

 and t = 45 seconds. At this instant, the first wave has reached 2750 feet and its height is 8 feet. 

 Further details are easily calculated from («7), (us) and (19). 



For a 1 oz. charge at 1.56 feet depth the first wave is greatest at t = 1.7 seconds, R = 6.2 feet 

 and the height is 4i inches (probaDly the wave is broken). The following trough is greatest at 2.6 seconds, 

 R = 9.3 feet and the depth is 3 inches. At this time, the first crest is at 11 feet, and its height is 

 1 inch. 



Motion of the Central Poi nt . 



One interestin.j feature of ttie motion is that zt the centre, and this can be obtained without 

 difficulty from the rtsults of Terazawa (l.c). According to him, if thf initial surface elevation at 

 t ime t = is 



K (x) = A//l^^ ♦ r'l (51) 



the motion of the centre is given by 



Z^ (t) = A q/t, 

 where 7} = 1 - 2 T f " ^ ^ J'" ■•'''. Tr (52) 



r^ = gt^/Uh 



Since the initial surface elevation adopted Dy ui, namely that given r>y equation (uu) is related 

 to that of Terazawa by 



A = 2 h'*/3 (55) 



the motion of the central point in our case is given Dy 



Bh 



r (t) = - la l(t) 



o 3 



L (t) = ( 2 - I T' . t" ) - T ( i| - 10 T^ . 2 t")^-^ r e'^ , dr 



Figure t shows the motion of the centre with a 2000 ton cnarcf of H.E. exploded at depth 285 feet 

 in deep water. Of course, no comparison of Figure u with direct rr^asurements would be possible, at least 

 for t < 5 seconds, because what is seen is spray, and this may extend two or three hundred feet above the 

 water surface. In any case, several seconds are required for the surface to becorie reconstituted. 



