partitions of the pyramid are determined in terms of those of the 

 r-gon and r-ace. 



Thus the entire first class of r-gonous ^c-edra is enumerated, with- 

 out descending to any classification of polyedra according to the 

 rank of their faces and summits. The enumeration of the second 

 and higher classes will require such classification, which will in- 

 troduce so vast a complexity as to render the further prosecution of 

 the theory of the polyedra, in the opinion of the author, practically 

 impossible by any method deserving the name of scientific generality. 



III. " Researches on the Cinchona Alkaloids." By W. BIRD 

 HERAPATH, M.D. Lond., F.R.S.E. Communicated by 

 Prof. STOKES, Sec. R.S. Received June 19, 1857. 



(Abstract.) 



PART I. Critical examination of the ordinary methods em- 

 ployed for the discrimination of the Cinchona Alkaloids, 

 viz. Quinine, Quinidin, and Quinicine and Cinchonine, 

 Cinchonidin and Cinchonicine ; together with the optical 

 and chemical characters of their lodo- Sulphates, upon 

 which new methods are founded. 



In consequence of the gradually increasing scarcity of the cortex 

 cinchona calysayce and its chief product quinine, many other barks 

 have been introduced into commerce, which furnish alkaloids having 

 a strong general resemblance in the physical characters of those 

 preparations of them more commonly employed in medicine, but 

 differing widely in medicinal properties and commercial values. 



In order to prevent fraudulent adulterations, it has long been 

 highly desirable to have some ready methods of detecting admixtures 

 of these alkaloids and their salts. The author having discovered 

 several optical salts of these vegetable alkaloids, proposes to make 

 their well-marked optical characters the means of such detection, 

 and in the second part of this paper has fully developed his views 

 upon this ready method of analysis, whilst in the present part 

 he has passed under review the various existing tests for the differ- 

 ent cinchona alkaloids, and the results of his investigations may be 

 enumerated under the following conclusions : 



