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rent ; then if R denote the whole normal action of the currentoi^jBjf x>ec«?'* 

 we have " 



R = J!!p, Ssin^O, 



provided 9 do not deviate too much from 90°. When = 90° the 

 truth of this formula has been proved by numerous experiments, for 

 all velocities up to 11 or 1 2 miles an hour, and may be assumed to 

 hold, at least approximately, for still greater velocities. It has also 

 been proved experimentally to be approximately true for any value 

 of 9 not differing by more than 45° from a right angle, as is the case 

 in the applications made of the formula. 



The velocity of the current just sufficient to move a block will de- 

 pend on the volume, the specific gravity, and the form of the block. 

 If the block slide, much will depend on the nature of the surface 

 over which it is transported, and thus a very uncertain element will 

 be introduced into the calculations. This uncertainty, however, will be 

 in a great degree removed if we calculate the force sufficient to make 

 the block roll. Each block would present a separate problem if it 

 were required to find accurately the current necessary to move it, 

 but as great accuracy is not necessary in the cases here contem- 

 plated, it is sufficient to make the calculations for a few determinate 

 and simple forms as those to which more irregular forms may be re- 

 ferred with a sufficient approximation to accuracy. Thus the author 

 has considered the cases of blocks whose sections perpendicular to 

 their length are squares, pentagons, hexagons, &c., and has calcu- 

 lated their dimensions, that a current of about 10 miles an hour 

 might just be sufficient to make them move by rolling. Assuming 

 the specific gravity of the blocks to be 2'5, we have the following 

 results : — 



1. A parallelopiped. 



Side of the square section perpendicular to its length = 2*73 feet. 



2. A pentagonal prism. 



Side of the pentagonal section perpendicular to its length = 2*27 

 feet. 



.3. A hexagonal prism. 



Side of hexagonal section perpendicular to its length = 2'3 feet. 



When the motion takes place, as here supposed, in a direction 

 perpendicular to the length of the block, the efficiency of the cur- 

 rent to move it will evidently be independent of the length of the 

 block. If we suppose the length of the parallelopiped to be equal 

 to the side of a section of it taken as above, it becomes a cube ; and 

 if we take the lengths of the blocks in the other two cases to be 

 equal to twice the length of the sides of their sections respectively, 

 their lengths will not much exceed their heights. Then the weights 

 of the blocks will be 1|- ton in the first, nearly 3 tons in the second, 

 and upwards of 4 tons in the third case. Again, if the block be an 

 oblate spheroid resting with its axis vertical, and the polar axis 

 = fths of the equatorial diameter, the current of about 10 miles an 

 hour will just make it roll if its height be about 2 feet, and its weight 



