Mr. HOPKINS, ON THE TRANSPORT OF ERRATIC BLOCKS. 235 



"= h.+ H 



x -a + l V {h,-h) V H , V + V, 



i7^-r-^°s.—-^ (5). 



I V2 ^1 "3 *i ' "2 



h + H 



V+ , 

 Equations (4) and (5) give the two relations between .v, a,' and h. Our object is to determine 



the value of a; when the motion of the block ceases, when we have the condition — — = 0, which 



at 



gives from (1) 



n^J-''^ = ' («)• 



From (4) (5) and (6) the required value of a; can be determined, and thence x - a, the space 

 through which the block will be transported, will be known. 



Equation (6) gives 



and we have from Art. 3, 



Also from (4), 



Substituting this value of w' in (5) we obtain 



F-«3 



V - v^ 





"2 A, 



V hj vl h, »' _ v^ h- 



V+v'H 



Since — i will always be less than unity and -^ will generally be a small fraction, we shall obtain 



a near approximate value of — - — if we expand the logarithm. We shall thus have, preserving 

 terms of the second order. 



_ «2 / h\ I hj + h hi - 



Omitting -^; and substituting the above values of h and A,, we obtain finally 



1 ("1 - ■"^f , 

 s = a>-a =-~ r--l, (7), 



which gives the space through which the block will be transported. 

 If we put Uj = we have 



*«=^-'^=iT?i;:-^ ('^' 



which gives the whole space through which each particle of the fluid is carried by the wave from its 

 original position. 



Vol. VIII. Pakt II. Hh 



