298 Royal Society, 



certain narrow limits. At Upsala he met with the usual indications 

 of a former elevation of the sea, from the presence of littoral shells 

 of the same species as those now found in the Baltic. Certain plants, 

 as the Glauca maritima and the Triglochin maritimus, which naturally 

 inhabit salt marshes bordering the sea, flourish in a meadow to the 

 south of Upsala ; a fact which corroborates the supposition that the 

 whole of the lake Maelar and the adjoining low lands have, at no 

 very remote period of history, been covered with salt water. 



The author examined minutely certain marks which had at different 

 times been cut artificially in perpendicular rocks, washed by the sea, 

 in various places ; particularly near Oregrund, Gefle, Lofgrund, and 

 Edskosund ; all of which concur in showing that the level of the sea, 

 when compared with the land, has very sensibly sunk. A similar con- 

 clusion was deduced from the observations made by the author on 

 the opposite, or western coast of Sweden, between Uddevalla and 

 Gotenburg ; and especially from the indications presented by the 

 islands of Orust, Gulholmen, and Marstrand. 



Throughout the paper a circumstantial account is given of the geo- 

 logical structure and physical features of those parts of the country 

 which the author visited : and the general result of the comparison he 

 draws of both the eastern and western coasts and their islands, with 

 the interior, is highly favourable to the hypothesis of a gradual rise 

 of the land ; every tract having, in its turn, been first a shoal in the 

 sea, and then, for a time, a portion of the shore. This opinion is 

 strongly corroborated by the testimony of the inhabitants, (pilots and 

 fishermen more especially,) of the increased extension of the land, 

 and the apparent sinking of the sea. The rate of elevation, however, 

 appears to be very different in difl'erent places : no trace of such a 

 change is found in the South of Scania. In those places where its 

 amount was ascertained with greatest accuracy, it appears to be about 

 three feet in a century. The phaenomenon in question having ex- 

 cited increasing interest among the philosophers of Sweden, and es- 

 pecially in the mind of Professor Berzelius, it is to be hoped that the 

 means of accurate determination will be greatly multiplied. 



January 15. — Second Essay on a general Method in Dynamics. 

 By William Rowan Hamilton, Esq., Andrew's Professor of Astronomy 

 in the University of Dublin, and Royal Astronomer of Ireland. Com- 

 municated by Captain Beaufort, R.N., F.R.S. 



This essay is a sequel of the one which appeared in the last volume 

 of the Philosophical Transactions, and which contained a general me- 

 thod for reducing all the most important problems of dynamics to the 

 study of one characteristic function, or one central or radical relation. 

 It was there remarked that many eliminations required by this me- 

 thod might be avoided by a general transformation, introducing the 

 lime explicitly into a part (S) of the whole characteristic function (V) ; 

 and the first object of the present essay is to examine and develope 

 the properties of this part (S), which the author designates by the 

 term Principal Function. This function is applied by the author to 

 problems of perturbation, in which he finds it dispenses with many 

 laborious and circuitous processes, and furnishes accurate expressions 



