130 MR. GWYTHER ON THE LAGRANGIAN FORM OF 



determining a Permian from a Triassic sandstone by 

 external characters. 



In some places in Lancashire the Coal Measures are 

 covered by Triassic beds without the occurrence of the 

 intermediate Permian beds; but near Manchester the latter 

 are generally met with either as the upper deposits^ the 

 marls and the conglomerate (Nos. 2 and 3) most frequently 

 together, or with all the three beds of the series. 



XVI. On an Adaptation of the Lagrangian Form of the 

 Equations of Fluid-Motion. — Part I. By R. F. 



GWYTHERj M.A. 



Eead April 20th, 1880. 



I. 



The object of the Lagrangian form of equation is to follow 

 the motion of a particular element ; and although the 

 Eulerian forms suit the general purposes of fluid-motion 

 best, there are certain cases, as that of vortex motion in a 

 perfect fluid (which may be termed steadily progressive), 

 where the course of an element may be investigated with 

 advantage. 



For this purpose I propose investigating the course of a 

 fluid element, defined by means of surfaces moving with 

 the fluid, and expressing the results as far as possible in 

 terms of the parts of the element. 



This method leads to a more general integral form than 

 that of Weber, and finally exhibits some of the known 

 properties of fluid-motion in a novel manner'^. 



* A similar method with the ordinary coordinates has previously (Q. J, 

 of Math. Feb. 1880) been used by Mr. Hill to obtain some similar results, 

 which will be referred to later. 



