294 The Differential Invariants of Space. [June 18, 



Sorghum vulgare and the consequent production of prussic acid by this 

 plant, have led to the examination by J. C. Brunnich,* Chemist to 

 the Agricultural Department, Brisbane, of the varieties of this plant 

 grown in Queensland, which have been long known to be poisonous 

 to cattle under certain conditions, although the nature and origin of 

 the poison had not been discovered. Brunnich has now determined 

 the amounts of hydrocyanic acid produced when weighed quantities 

 of the plants grown under different conditions are crushed with water. 

 The results thus obtained confirm those already recorded by the 

 authors in the case of sorghum grown in Egypt, and show that the 

 amount of cyanogenetic glucoside contained in the stem and leaves 

 of the plant increases until the seeds are ripe, after which it rapidly 

 diminishes until the glucoside finally disappears. Brunnich finds that 

 cultivation of sorghum on land heavily manured with sodium nitrate 

 leads to an increased production of the cyanogenetic glucoside in the 

 stem and leaves. 



"The Differential Invariants of Space." By Professor A. It. 

 FORSYTH, Sc.D., LL.D., F.RS. Received June 18, Head 

 June 18, 1903. 



(Abstract.) 



The memoir is devoted to the consideration of the differential 

 invariants of ordinary space and of a surface or surfaces in that space ; 

 they are the functions of the fundamental magnitudes of space and 

 of quantities connected with the surface or surfaces which remain 

 unaltered in value through all changes of the independent variables of 

 position. 



The method used arises through the obviously natural development 

 of the method used for the corresponding investigations concerned 

 with a surface and with curves upon the surface, which formed the 

 subject of an earlier memoir by the author. The partial differential 

 equations, characteristic of the invariance, are formed, and then the 

 most general solution of these equations is constructed. At a certain 

 stage in the latter process, the equations then remaining unsolved can 

 be transformed, so that they become the invariants and the contra- 

 variants of a set of simultaneous ternary forms. The results of the 

 latter theory are then used to complete the solution of the equations. 



The main part of the memoir is devoted to obtaining the invariants ; 

 and the explicit expressions of the invariants, up to the third order 

 inclusive as associated with a single surface, are given. Further, 



* ' Trans. Chern. Soc.,' 1903. 



