KITNUL. SV. VET. AKADEMIENS HANDLINGAR. BAND 47. \.<) 4. 23 



giving 



ioy = k (a sinli kh — t i cosh kh j. 



The other conditions will be exactly of the same form as equations 2 — 5 of pp. 7 !>. Ii 

 now: 



rj = (S cos &£ . e* *, 

 \ve only need in the formula, there found to determine ,>', replace 



ioy 

 ;'by- ^ - 



and put c = l, to obtain the solution of our actual problem. Tims \ve find: 



y_ '/"'yigh — o 2 coth kh') 

 '' sinh ä*å . D 



To the bottom-motion: 



y = — Ä + y cos &(.£ — Ä)e'" , '-' ) 



will then correspond the boundary displacement : 



yo 2 o(qk— a 2 cothkh') ,. ,. . ,, . 

 sin h kh . D 



and the free-surfaee displacement: 



This now may be generalised in various ways, by summing up with respect to /, 

 or to r, or to both at once. The most important application for our purposes will be 

 that the above formulse will pennit to construct the ivave-motion caused hy a ridge. 

 moving along the bottom according to any assigned laiv of motion. 



The simple case of summation only with respect to /., however, also is of some 

 interest for ns. The equation of the moving bottom being: 



y-=— h + f(x)e ir > 1 , 



f(.r) being a function of the same kind as before was used to rej)resent the fixed bottom- 

 ridge, we at once obtain an integral-representation of the resulting wave-motion. Re- 

 ducing those integrals in the manner shown in a previous chapter, we have for some di- 

 stance from the centre of disturbance: 



) itJ = Be' {at -' <J:) -h be i{nt - xx) , 



x being positive. Here the second term gives the boundary-wave in the proper sense of 

 the word. Again, in our original problem, we found: 



