Mr. HOPKINS, ON THE TRANSPORT OF ERRATIC BLOCKS. 227 



miles an hour, and we are justified in concluding by induction, that the expression will hold for 



still greater velocities. Hence (p ( — j = 1. It also results from experiment that the value of (p{9) 



is very nearly unity for all values of 9 not exceeding 45"*, and therefore, since the applications 

 I shall make of the above expressions are in cases where is less than that value, we may assume 

 generally 



and 



R'=-p^Ssia^e. 



13. Let us first take the case of a prism, of which the axis is perpendicular to the current, 

 and the section a triangle ABC- 



If this section bisect the prism, it is manifest that the resultant 

 of the whole pressure upon it produced by the current will pass 

 through the middle point of AC. If therefore a perpendicular to 

 AC through this middle point meet AB in B, or between A and B, 

 it is manifest that the force of the current can have no tendency to 

 make the prism turn over about the edge through B. Suppose the 

 triangle equilateral; then on whichever side the prism may rest, the 

 above perpendicular will pass through the opposite angular point, 

 and the prism will not roll; and if the triangle be not equilateial, it is easily seen that there must 

 necessarily be one side which, when the prism rests on it, will be met by the perpendicular. Con- 

 sequently no triangular prism can continue to roll by the force of a current round each edge in 

 succession. 



To find under what conditions the prism will slide, I shall assume, as the most favorable 

 condition for such motion, that the water has access to the lower side of the prism. In this 

 case, taking p for the specific gravity of the prism, and ^j for that of water, we shall have the 

 weight of the body in water 



= (p- Pi) gU, 

 U = volume of the prism, and g = accelerating force of gravity. Let AB = a, AC = c, the length 

 of the prism = b, and CAB = Q. Then if /? = the normal force on the side of which AC is the 

 section due to the current, and R' the horizontal force, we have (supposing Q not much less 

 than 45°) 



v" 

 R = — pxSsin" 9, , 



R' = - 



or, since S = 6c, 



-p^S sin" 9; 



R = ~ p, be siiv' 9, 



' The most dctailnl experiments I have seen on this point are 

 contained in a work, entitled Nnuvrlles Experiences sur la 

 HeiiMlunce ilei I'luides, par MM. U'Alemberl, le Marquis de 

 Condorcet, ctrAI/lii Uossut^ Memhre de r Academic des Sciences, 

 ^c.Sic. Par M. liossut, Rajiporteur, 1777. It was intended to 

 appear in the Transactions of the Academy; but, on account of 



Vol. VIII. Pabt II. 



it3 length it was deemed better to publish it separately. M'hen 

 = 45% these experiments give (/j{y)= l,01i, and values approxi- 

 mating to unity as their limit, for smaller values of (J. For greater 

 values of 0, unity is no longer a near approximation to the value of 



