466 Royal Society. 



§ 4. In this section, referring the surface of the second order to 

 absolutely general co-ordinates, and after an incidental solution of the 

 problem to determine a section touching three given sections, the 

 author obtains the equations for the solution of Steiner's extensiou 

 of ]VIalfatti's problem. 



§ 5. Contains a separate discussion of a system of equations, in- 

 cluding as a particular case the equations obtained in the preceding 

 section. 



§§ 6 & 7. Contain the application of the formulae for the general 

 system to the equations in § 4, and the development and completion 

 of the solution. 



§ 8. Is an extension of some preceding formulae to quadratic 

 functions of any number of variables. 



" On the Tides, Bed and Coasts of the North Sea or German 

 Ocean." By John Murray, Esq. Communicated by George Rennie, 

 Esq., F.R.S. 



The author commences his paper by remarking that great similarity 

 of outline pervades the western shores of Ireland, Scotland and 

 Norway, and then observes that the great Atlantic flood-tide wave, 

 having traversed the shores of the former countries, strikes with 

 great fury the Norwegian coast between the Lafoden Isles and Stad- 

 land, one portion proceeding to the north, while the other is de- 

 flected to the south, which last has scooped out along the coast, as 

 far as the Sleeve at the mouth of the Baltic, a long channel from 

 100 to 200 fathoms in depth, almost close in shore, and varying 

 from 50 to 100 miles in width. After describing his method of con- 

 touring and colouring the Admiralty chart of the North Sea, he 

 traces the course of the tide-wave among the Orkney and Shetland 

 Islands along the eastern shores of Scotland and England to the 

 Straits of Dover, and along the western shores of Norway, Denmark 

 and the Netherlands, to the same point. He then remarks that the 

 detritus arising from the continued wasting away of nearly the 

 whole line of the eastern coasts of Scotland and England, caused by 

 the action of the flood-tide, is carried by it, and at the present day 

 finds a resting-place in the North Sea ; and that this filling process 

 is increased by the sand, shingle, and other matter brought through 

 the Straits of Dover by the other branch of the Atlantic flood-tide. 

 Hence, he remarks, the gradual shoaling of this sea, and the forma- 

 tion of its numerous sand-banks ; the silting up the mouths of the 

 Rhine, the Meuse, and the Scheldt ; the formation of the numerous 

 islands on the coast of Holland, that country itself, and much of 

 Belgium ; the deposits at the mouth of the Baltic, the islands in the 

 Cattegat, and indeed the whole country of Sleswig, Denmark and 

 Jutland. 



The author then takes a view of the tides, and their effects upon 

 the Baltic and its shores before the course of the tide- wave was 

 checked by these shoals and lowlands. He considers that, previous 

 to these great changes, the flood-tide entering the North Sea between 

 Norway and Scotland, would make directly towards the German 

 coast, and necessarily heap up the waters in the Baltic considerably 



