224 



Mr. HOPKINS, ON THE TRANSPORT OF ERRATIC BLOCKS. 



Hence 

 or, for any assigned value of p 



h = \/- .(pip): 



\/r 



Consequently, 



V and i>i cc 



\/r 



5. A diverging wave, such as above described, would manifestly be produced in the midst 

 of the ocean by the elevation of a portion of its bottom. The height and breadth of the 

 wave will depend on the area of the elevated portion, the height through which it is raised, and 

 the time occupied in the process of elevation. Suppose this area to be circular, and its radius = R; 

 and first suppose the elevation to be i7istantaneous, and the height = A,. The resulting wave 

 will have a steep front, liiie that of the tidal wave called a bore, the height of its crest 

 being at first equal to that of the elevated surface of the water above the level of the general 

 surface = A, in the case before us; and the breadth of the wave will be the space through 

 which its front shall have diverged from the boundary of the original disturbance, when that 

 boundary shall have been reached by the inner circular boundary of the wave. 



6. Let us next suppose the elevation to take place gradually, its amount being still = Aj. 

 The surface of the water above the elevated area will be raised to a height less than h^, and 

 consequently the height of the crest of the wave will be less than A,, and the velocity of the 

 current produced by it will be proportionally less than in the former case. If R be small, 

 a small increase in the time occupied by the elevatory movement may make a great difference 

 in Aj, and consequently in the velocity and transporting power of the current; but if R be 

 large, the corresponding diminution in /jj will be much smaller*. 



7. If the elevated area be a parallelogram, of which the length is much greater than the 

 breadth, two waves will proceed in directions perpendicular to the longer sides of the area, to which 

 sides the fronts of the wave (except near to its extremities) will be parallel. The breadth of the 

 wave will depend on that of the elevated area. It is important to remark that the diminution 

 in the height of the wave, and consequently in the velocity of the attendant current, will be 

 much less rapid than in the case above considered of the circular wave. Instances of circular 

 waves would necessarily present themselves in the elevatory movements of such a district as 

 that of the Cumbrian mountains, while wholly or partially beneath the sea ; and examples of 

 the other kind, in the simultaneous elevation of the whole of such a range as the great mountain 

 limestone ridge of the northern part of this kingdom. 



8. In the case first considered the wave was supposed to be propagated along a canal of 

 uniform width and depth. If, on the contrary, the depth or width decrease, the velocity of 

 the current will be increased, as appears from the expression for «;, (Arts. 3 and 4). Thus, if 

 a portion of a great wave pass into the mouth of a channel which gradually contracts, the velocity 



* For example, let R — 2Q miles, and let the elevation be instan- 

 taneous. The depth of the ocean might be such that it should 

 require 15 or 20 minutes for the surface of the water above the 

 elevated area to be reduced again to the level of the general surface. 

 In such cases, the elevatory movement might occupy several 



minutes without reducing A, very materially. But if, on the 

 contrary, R did not exceed a mile or two, then, under the 

 same conditions, h^ would be reduced to a very small quan- 

 tity, and the transporting power of the wave would be almost 

 annihilated. 



