346 SECTIONAL TRANSACTIONS.— A*, B. 



Mr. C. H. H. Franklin. — Hypersolid concepts, and the completeness of 

 objects and phenomena (12.30). 



To picture mentally the Completeness of Things requires a more elaborate 

 geometry than that of three space as directly observed with the eyes ; needing 

 the three Cartesian axes of ordinary space and other axes representing time, 

 mass or any other dimensions to be considered ; all axes mutually at right 

 angles. 



Just as it is possible to represent a three dimensional object by a two 

 dimensional sketch ; so it should be possible to represent a four, five, or 

 more dimensional experience in a two space drawing or three space model : 

 the picturing being regularly distorted but with parallel lines drawn parallel 

 much as in an oblique or isogonal sketch, or, in geometrical perspective, 

 with angular distortion and vanishing parallels such as would be ordinarily 

 used in artistic work or found in a photograph. 



While any group of lines passing through a point may serve as Cartesian 

 axes for drawing or modelling hyperspace figuring (as in drawing three 

 space objects) ; isogonal relation between axes, possible for four, six 

 and ten space modelling, and any dimensional drawing gives minimum 

 distortion and tends to the best representation ; but regular oblique pro- 

 jection may be essential or preferable for five space or higher dimensional 

 modelling. 



Preliminary to picturing hypersolidity, familiarity with simple four and 

 higher space forms, only distorted by the usual perspective or oblique 

 projection of ordinary experience, is helpful. Demonstration of some of 

 these forms, drawn or modelled and also of some Cartesian axial models. 



It is noted that the oblique projections of the hypercube series have 

 envelopes in three space which introduce an infinite series of rhombic 

 semiregular solids, which follow at regular intervals on the rhombic hexa- 

 hedron, rhombic dodecahedron, and rhombic icosahedron, and have polar 

 and equatorial symmetry. 



SECTION B.— CHEMISTRY. 



Thursday, September 2. 



Symposium on Some aspects of chemotherapy (lo.o). 



Presidenti.\l Address by Dr. F. L. Pyman, F.R.S., on Researches in 

 chemotherapy. 



Prof. Dr. H. Horlein. — The chemotherapy of bacterial diseases {11. o). 



Ten years ago investigations began in the Elberfeld laboratories of the 

 I-G Farbenindustrie on the chemotherapy of bacterial diseases. Patents 

 were taken out for the substance now known as Prontosil in 1932. The 

 early results were so encouraging that further experiments were carried 

 out, but the first publication appeared only in February 1935. The action 

 of Prontosil on experimental streptococcal infections in mice was found to 

 be the property of a whole series of compounds characterised by sub- 

 stituents such as sulphonamide or certain other sulphur-containing groups. 

 A soluble variety of Prontosil was next discovered, having in common wath 



