Geological Society. 279 



incompatible unless U = V = 0. However, this was to be 

 expected, as there is, if the lamina be massless, nothing 

 to enable it to disturb the fluid, so that the only possible 

 motion is one which leaves the fluid undisturbed, i.e. for 

 which U = V = 0. Moreover, in consequence of its lack of 

 inertia, any other motion, even if it could be started, would 

 be instantaneously converted into the above type by the 

 action of the finite pressures on the unsubstantial lamina. 



If the lamina be supposed uniform, and of mass M, its 

 kinetic energy Tj is given by 



-':\^M\w+Y 2 + a 2 d 2 + 2a^\d\. . . (13) 

 By transference to a " centre of inertia " C, given by 



value given by 



2T = (A + B + M)U 2 + (A + M)V 2 + A 4 M 



and the motion of C is known (cf. for instance Lamb's 

 'Hydrodynamics,' 4th ed. p. 165), and so is that of the 

 lamina. If coa is sufficiently great compared with the 

 velocity of translation, the path of A (in ng. 6) is looped, 

 otherwise it is, in general, sinuous, 



Loughborough, 

 June 1st, 1918. 



0'G = a 1 rz 1 . , the total energy assumes the 



(14) 



XXVIII. Proceedings of Learned Societies. 



GEOLOGICAL SOCIETY. 

 [Continued from p. 208.] 



March 6th, 1918.— Mr. G. "W. Lamplugh, F.R.S., President, 

 in the Chair. 



Mr. J. F. N. Green delivered a Lecture on the Igneous 

 Rocks of the Lake District. He first drew attention to some 

 of the manuscript 6-inch maps of the Lake District, prepared 

 nearly fifty years ago, by the Geological Survey, and pointed 

 out that, although undoubtedly most accurate, they differed greatly 

 in the volcanic area from his own. He suggested that the reason 



