144 Geological Society :— 



(2) is a continuation of the author's ' Principles of the Algebra 

 of Physics.' 



It opens with a historical note of the theory and use of V— 1 

 by three classes of Analysts, and goes on to applications of quater- 

 nions to Spherical Trigonometry, to Circular Spirals, and to Hyper- 

 bolic Spirals. En route the hyperbolic non-Euclidian Greometry 

 and some other points which have recently occupied attention are 

 touched upon. This paper and the recent Trigonometries by 

 Levett and Davison and by Hayward show how the ideas of 

 De Morgan's Double Algebra are coming to the front. 



Die Theorie der Beobachtungsf elder und die Methode der Kleinsten 

 Quadrate mit Hirer Anwendung auf die Geod'dsie und die 

 Wassermessungen. Von Otto Koll. (Berlin, Julius Springer, 

 1893; pp. viii + 324 and 31 pages of formulae.) 



" Mansfield Merriman's ' Textbook of the Method of Least Squares ' 

 (Macmillan, 1885) contains 174 pp. + 20 pp. of Appendix and 

 Tables : Dr. Bobek's Lehrbuch der Ausgleichsrechnung nach der 

 Methode der Kleinsten Quadrate (Maier, Stuttgart, 1891) has 

 pp. viii+176; and W. Woolsey Johnson's 'The Theory of Errors 

 and Method of Least Squares' (Wiley, New York, 1892) has 

 pp. x + 174 (and is 12mo, not 8vo). 



Now as Prof. Otto's page is much larger than that of any of the 

 above, it is evident that in quantity of matter it " takes the cake." 



The first part (pp. 1-42) is devoted to the Errors of Observation, 

 and the remainder, in seven divisions, discusses the Method of 

 Least Squares. The author very rarely cites previous writers, and 

 none of these are familiar to us except Hagen. The simple text is 

 perhaps equal in extent to that of the respective works cited at the 

 commencement, the special feature is the great amount of illustra- 

 tive examples which are fully worked out. It is this which makes 

 Prof. Roll's work such a practical one. The formulae at the end 

 will be useful for reference to the student. It only remains to say 

 that the type is very clear, the figures numerous and good, and the 

 arrangement of the page conducive to easy reading. 



XIII. Proceedings of Learned Societies, 



GEOLOGICAL SOCIETY. 



[Continued from vol. xxxv. p. 469.] 



March 22, 1893.— W. H. Hudleston, Esq., M.A., F.R.S., 

 President, in the Chair. 



fTVEIE following communications were read : — 



•*- 1. " On the Jaw of a new Carnivorous Dinosaur from the 



Oxford Clay of Peterborough." By E. Lydekker, Esq., B.A., P.G.S. 



2. On a Mammalian Incisor from the Wealden of Hastings." By 

 R. Lydekker, Esq., B.A., E.G.S. 





