40 ZEILON, ON TIDAL BOUNDARY-WAVES. 



There is an interesting agreement between the above conclusions from the author's 

 experiments and the mechanism advanced by Pettersson as being of fundamental im- 

 portance for the circulation of the Baltic. In Nature, of course, circumstances generally de- 

 part very much from the idealized ones of the experiments; moreover, for the Hydrograph- 

 er, a complication will ensue from the necessity of taking account of frictional effects. 

 A closer comparison would scarcely enter into the scope of this paper; for that subject, 

 the reference to the named work mav suffice. 1 



In conclusion I want to acknowledge my indebtedness to all those who in a way or 

 other have assisted me in the researches here presented. The experiments were made at 

 the Swedish Hydrographic Station of Bornö, almost exclusively at the expense of the 

 Swedish Hydrographo-Biological Commission; for the ample opportunity thus afforded 

 me I here present my sincere thanks. Prof. O. Pettersson, member of the Commission, 

 has throughout my work taken a great interest in it and helped me with much and valuable 

 advice. Thanks to the kindness of Prof. I. Fredholm of Stockholms Högskola, I had the 

 fortune of having access to a magnificent kinematographic camera. Prof. V. Carlheim- 

 Gyllensköld having placed at my disposal for the photographing a suitable room in the 

 Physical Institute of Stockholms Högskola, I was able to obtain very beautiful and inte- 

 resting records of the experiments. 2 



Appendix. 



On the direct treatment of the jixed-ridge problem. 



The indirect method of the text may seem somewhat artificial, and anyhow a 

 direct verification of the solution obtained ought to possess some interest. With a view 

 to formål simplification, I will assume the disturbance to be imperceptible in the upper 

 surf ace, a supposition that does not avoid any real difficulty. 



As a plausible assumption to correspond to the bottom-corrugation of wave-length 



-^ we take for the displacement of the boundary: 



rC 



/ = (p cos kx + «/' sin kx, 



'/ and i/' being certain functions of time. Introducing the velocity potentials 



Q)' ! ficoshkiy — h') . , \ cosh k(y — h!) ,- . , . , , 



- = cos o t\ — x — ' . . f T , — sin kx] ■ . , ,, {<p sin kx — «/' cos kx) 



c \ smh kh I sinh kh 



*l> , , , , , . . . . . 7 . cosh&(w + h) . . , . , . 



= cos at (— x + (a cosh ky + ji sinh ky) sin ta;) + . ' , , — - (rp sin kx — «/' cos kx), 



c sinn te fi 



1 loc. cit. p.3. Also, in amorecondensed form: O. Pettersson, »Ubor Meeresströmungen », Veröffentlichungen 

 des Instituts fiir Meereskunde. Berlin 1908. 



2 Originally I intended to utilize. individual kinematographic pictures for the plates of this paper. However, 

 the necessary strong enlargement did not give very satisfactory results. The present photographs were therefore 

 obtained by means of a special apparatus, constructed on a sort of rough kinematographic principle, and apphcable 

 in the form of a casette to a folding camera of the usual type. In this way up to 4 pictures pro second could 

 easily be taken on an ordinary Kodak film (7 inchea broad). 



