460 Notices respecting Neiv Books. 



of AB is /3 + S. If R, S' do not intersect at all, the most 

 general space destroyed by AB is obviously B/; and the nullity 

 of AB is therefore @. 



We have now to distinguish cases : I assume a + ft < n. 

 which gives a<n—ft. An a-point and an (n— /3)-point in 

 the same w-point will in general intersect in an (a— /3)-point: 

 therefore if a < ft, R, S' will not intersect at all, but may cut 

 in anything up to an a -point. If a > ft they may intersect in 

 anything from an (a— /3)-point to an a-point. We therefore 

 have the following theorem : — Let A, B be two matrices of 

 nullities a, ft respectively: then, if a < ft, the nullity of AB 

 is in general ft, but may be anything from u to ex. + ft inclusive; 

 if « > ft, the nullity of AB is in general u, but may be anything 

 from «upto« + j& inclusive. 



The Grammar School, Manchester, 

 October 6, 1884. 



LII. Notices respecting New Books. 



Geology of Wisconsin. Survey of 1873-79. Vol. IV. Accompanied 

 by an Atlas of Maps. Large 8vo, pages xxiv & 779. With 

 numerous maps, plans, plates, and woodcuts. [Madison.] 1882. 



npHlS handsome, well-stored, and richly illustrated volume of 

 -*- the Wisconsin Geological Survey Eeports is a worthy successor 

 to the Volumes II. and III., already noticed in the Philosophical 

 Magazine for April 1880 and September 1882. It is divided 

 into nine Parts, being reports and memoirs by members of the 

 Survey and other competent workers. 



In Part I. (pages 1-98) Moses Strong gives the " Geology of the 

 Mississippi region north of the Wisconsin River :" noting, first 

 (pp. 3-6), the field-work in general, during 1873-6; then (pp. 7-36), 

 the Physical Geography and Surface-Geology of the district, accord- 

 ing to the Townships in their order; thirdly (pp. 38-98), the 

 local Geological Formations are described. These stand thus : — 





Periods. 



Epochs. 



Epochs in Western Wisconsin. 





( Eecent 



\ Champlain . . . 



Recent. 



Quaternary . . . 



Champlain. 





^Glacial 



[ Cincinnati . . . 



Glacial. 







Wanting. 







\ Utica 



Wanting. 



Galena, and Blue and Buff Limestones 



fe j 





[Trenton 





f Chazy 



St. -Peter's Sandstone. 



J J 



Canadian 



\ Quebec 



Wanting. 





[ Oalciferous... 



Lower Magnesian Limestone. 





Primordial or "1 

 Cambrian... J 



I Potsdam 



\ Acadian 



Potsdam Sandstone. 





Wanting. 





Archaean 



Archaean 



Not exposed. 



