laws of attraction or repulsion, and with one predominant mass ; 

 10th, the rigorous transition from the theory of binary to that of mul- 

 tiple systems, by means of the disturbing part of the whole charac- 

 teristic function, and approximate expressions for the perturbations. 



A paper was also read, entitled, " Observations on the Motions of 

 Shingle Beaches." By Henry R. Palmer, Esq., F.R.S. 



The author states that the object of his inquiries is limited to the 

 collection of such facts as may assist in establishing practical rules 

 for controlling the motions of the beach, with a view, on the one hand, 

 to the preservation of clear channels where such are wanted, and on 

 the other, to the obtaining accumulations of shingles in situations 

 where they may be useful. He considers the actions of the sea on 

 the loose pebbles as of three kinds ; the first, which he terms the ac- 

 cumulative action, heaps up or accumulates the pebbles against the 

 shore ; the second, or the destructive action, disturbs and breaks down 

 the accumulations previously made ; and the third, or progressive ac- 

 tion, carries the pebbles forwards in a horizontal direction. The causes 

 of these actions are referable to two kinds of forces ; the one being that 

 of the current, or the motion of the general body of the water in the 

 ebbing and flowing of the tides ; and the other that of the waves, or 

 that undulating motion given to the water by the action of the winds 

 upon it. 



He adduces many facts which show that it is not, as is generally 

 believed, the currents which move the pebbles along the coast, the 

 real agent being the force of the waves, the direction of which is de- 

 termined principally by that of the prevailing winds, which, on the 

 coasts of Kent and Sussex, where the author's observations were 

 chiefly made, is from the westward. Every breaker drives before it 

 the loose materials which it meets, throwing them up on the inclined 

 plane on which they rest, and in a direction corresponding generally 

 with that of the breaker. In all cases, the finer particles descend the 

 whole distance with the returning breaker, unless accidentally de- 

 posited in some interstice ; but the larger pebbles return only a part 

 of the distance, this distance having an inverse ratio to its magnitude. 

 This process constitutes the accumulative action. Under other cir- 

 cumstances, on the contrary, depending on the quickness of succes- 

 sion of the breakers, pebbles of every dimension return the whole 

 distance along which they had been carried up, and are also accom- 

 panied in their recession by other pebbles, which had been previously 

 deposited 5 and this constitutes the destructive action. This latter 

 action is also promoted by a form of coast, such as that produced by 

 rocks, tending to confine the returning waves in particular chan- 

 nels, whereby, being collected into streams instead of being broken 

 and dispersed, they acquire, on the recoil, sufficient force to carry 

 down the pebbles, and deposit them below the general surface. The 

 author gives examples of these effects, from what he has observed in 

 the neighborhood of the harbours of Folkstone, Dover and Sand- 

 gate, and along the coast as far as the bay called Sandwich Flats ; 

 accompanied by illustrative drawings. 



