462 Geological Society : — 



This volume contains Chapters XII-XIX of the whole work, 

 and the chapters deal successively with definitions of compound 

 and compartite matrices and other introductory matter (p. 1) ; 

 relations between the elements and minor determinants of a 

 matrix (p. 37); some properties of square matrices (p. 107); 

 ranks of matrix products and matrix factors (p. 165); equi- 

 gradent transformations of a matrix whose elements are 

 constants (p. 228); some matrix equations of the second degree 

 (p. 309); the extravagances of matrices and of spacelets in homo- 

 geneous space (p. 378) ; and the paratomy and orthotomy of two 

 matrices and of two spacelets of homogeneous space (p. 463). 

 There are also Appendixes and an Index. 



The ideas and language are frequently geometrical : for ex- 

 ample, we have "spacelets" (pp. vi, 78), but there seem to be — 

 quite naturally, after what has been said above — no geometrical 

 applications in this volume, and the only physical application 

 seems to be the interesting treatment (pp. 330-332) of the 

 rotation of a rigid body. 



XLI. Proceedings of Learned Societies. 



GEOLOGICAL SOCIETY. 



[Continued from vol. xxxvi. p. 488.] 



November 6th, 1918.— Mr. G. IV. Lamplugh, F.H.S., President, 

 in the Chair. 



The President read a communication that he had received 

 from Prof. Charles Barrois, D.Sc, F.M.G.S., in reply to con- 

 gratulations sent o» the occasion of the evacuation of Lille by the 

 enemy forces. 



A Discussion on the Antarctic Ice-Cap and its Borders 

 was introduced by Sir Douglas Mawsojst, D.Sc, B.E., F.Gr.S. 



Sir Douglas Mawson said that at the last Meeting of the 

 Society the subject of the Antarctic Ice-Cap was reviewed in its 

 broader aspects, chiefly with the view of promoting a discussion 

 among those specially interested in Grlaciology. The present 

 occasion had been reserved for the Discussion, and he proposed to 

 show certain lantern -slides in order to bring the salient features 

 freshly to mind. 



Though much of the foundation of the Antarctic Ice- Cap is cer- 

 tainly elevated land, it is quite possible that elsewhere the dome 

 rests upon a floor actually below sea-level. In any case it is most 

 probable that the smooth ice-surface masks a very irregular rock- 

 basement. The thickness of the ice may, therefore, be expected to 

 be extremely variable, no doubt reaching a maximum of several 

 thousands of feet. 



An ice-formation of such magnitude introduces questions relating 

 to the flow of its substance and the abrasion of its foundations which 

 do not enter into the physics of ice-masses of smaller dimensions. 



