178 



Presents. 



[Feb. 6, 



considered, which is in fact that of fundamental or single- unitary 

 symmetric functions. 



These partition operations possess an algebra also in exact corre- 

 spondence with the algebra of quantity. 



In § 10 the partition obliterating operations are applied to the 

 theory of multiplication. 



In § 12 a transformation is established by means of which func- 

 tions of differences can, with special exceptions, be converted into 

 non-single-unitary symmetric functions. This theorem is the analogue 

 of the transformation of the theory of invariants first given by the 

 author in Vol. 6 of the ' American Journal of Mathematics.' 



§ 15 proves a useful law to which the tabular numbers are subject, 

 connected with the idea of grouping the separations together in a 

 particular manner. 



In conclusion the memoir consolidates and largely generalises the 

 author's recent researches alluded to above at the beginning of the 

 Abstract. 



Presents, February 6, 1890. 



Transactions. 



Brisbane : — Royal Geographical Society of Australia (Queensland 



Branch). Proceedings and Transactions. Vol. IV. 8vo. 



Brisbane 1889. The Society. 



Royal Society of Queensland. Proceedings. Vol. VI. Parts 



2-3. 8vo. Brisbane 1889 ; Report of Annual Meeting, 1889. 



8vo. Brisbane. The Society. 



Copenhagen : — Academie Royale. Bulletin. 1889. No. 2. 8vo. 



Copenhague ; Memoires (Classe des Sciences). Vol. V. Nos. 



1-2. 4to. Copenhague 1889. The Academy. 



Cordoba : — Academia Nacional de Ciencias. Boletin. Tomo XI. 



Bntrega 3. 8vo. Buenos Aires 1888. The Academy. 



Cracow: — Academie des Sciences. Bulletin International. Comptes 



Rendus des Seances de l'Annee 1889. Nos. 5-10. 8vo. 



Croxovie 1889. The Academy. 



Dresden : — Verein fur Erdkunde. Jubilaumsschrift. Litteratur 



der Landes- und Volkskunde des Konigreichs Sachsen. 



Bearbeitet von Pa Emil Richter. 8vo. Dresden 1889. 



The Verein. 



Dublin : — Royal Historical and Archaeological Association of 

 Ireland. Journal. Vol. IX. No. 80. 8vo. Dublin 1889. 



The Association. 



Edinburgh : — Royal Physical Society. Proceedings. Vol. X. 

 Part 1. 8vo. Edinburgh 1889. * The Society. 



