Geological Society. 197 



XXII. Integration Theorems of Four-Dimensional 

 Vector Analysis. 



To the Editors of the Philosophical Magazine. 

 Gentlemen, — 



MAY I point out that the theorems given by Mr. H. T. 

 Flint on p. 389, March 1921, of your Magazine were 

 given by me in 1907 ? Each of the theorems is capable of 

 considerable generalization. Such generalized forms, as 

 also the two corresponding ones in Quaternions (which were 

 also given by me in the ' Messenger of Mathematics'' some- 

 where about 1887), are all particular cases of a single 

 theorem occupying less than half a line of the P.R.S.E., 

 1907-8, p. 564, eq. (17). 



I have given the theorem again, and in two forms, 

 together with some applications, in a paper read before the 

 R. S. L. on 9 Dec, 1920— " Multenions and Differential 

 Invariants/' In this last paper I have fortunately, largely 

 due to recommendations of Prof. Knott, done what Mr. Flint 

 does, in making my notation entirely in harmony with 

 Joly's. I am, 



Yours faithfully, 



Alex. McAulay. 



University of Tasmania, 

 18 April, 1921. 



XXIII. Proceedings of Learned Societies. 



GEOLOGICAL SOCIETY. 



[Continued from vol. xli. p. 950.] 



January 19th, 1921.— Mr. E. D. Oldham, F.E.S., President, 

 in the Chair. 



'TTEE following communication was read : — 



' The Lower Palaeozoic Eocks of the Llangollen District, with 

 especial reference to the Tectonics.' By Leonard Johnston Wills, 

 M.A., Ph.D., F.G.S., and Bernard Smith, M.A., F.G.S. 



The field-work on which this paper is based was done by the 

 authors as officers of H.M. Greological Survey. 



The general sequence is : — 

 Silurian. Series. 



Salopian. 



(Denbighshire type). Ludlow. Dinas-Bran Beds. 



Vivod Bods. 

 Nant-y-Bach Beds. 

 Glyn-Dyfrdwy Bods. 



Wenlock. Pen-y-glog- Grit, 



Pen-y-glog Slates. 

 Valentian. Upper or Tarannon. 



Lower or Birkhillian. 



