Mr. Haworth's Sixth Decade of new Succulent Plants. 125 



purpose of showing the nature of the mutations which the 

 theorem undergoes when we take the trapezium successively 

 salient (fig. 8), re-entrant (fig. 9), and intersectant (fig. 10). 

 The number of figures, however, which a complete exhibition 

 of all the cases of the theorem would require, is not less than 

 a hundred and twenty; perhaps even more, which have escaped 

 my notice. These three figures are sufficient to show, also, 

 that had we defined AC, FG, DE, the three diagonals of 

 the trapezium in fig. 8, an elegant enunciation might be 

 formed for the combination of them in pairs in reference to 

 this theorem. 



It is easy by a similar train of investigation to discover se- 

 veral analogous and equally beautiful properties of the trape- 

 zium : but as this paper has already exceeded the limits which 

 I originally proposed to myself, I shall defer them to a future 

 but not distant period. In conclusion, I shall just remark, 

 that from the properties already given a series of interesting 

 properties of the conic-sections are immediately deducible. 

 August 5, 1825. 



XVII. Decas sexta novarum Plantarum Succulentarum ; 

 Autore A. H. Haworth, Soc. Linn. Lond. — Soc. Horticult. 

 Lond. — necnon Soc. Cces. Nat. Curios. Mosc. Socio, fyc. Sfc. 



To the Editor of the Philosophical Magazine and Journal. 



Sir, 

 TJAVING just finished my sixth Decade of new Succulent 

 *••*■ Plants, I lose no time in sending it for insertion in the 

 next Number of your Magazine. 



All the plants included in this deeade, appear to me, after 

 the most diligent research, to be entirely nondescript, and be- 

 long to the vast genus Mesembryanthemum ; to which they form 

 a conspicuous addition : for some of them are not only new 

 as species, but constitute new and unrecorded sections. They 

 are all flourishing and flowering in the royal and unrivalled 

 gardens at Kew ; and were sent thither by our most assiduous 

 friend Bowie, whose adventurous and discriminating eye de- 

 tected them growing spontaneously in the remote and arid 

 regions of Southern Africa, whither this enterprising travel- 

 ler is again about to repair. And he proposes to go not only 

 with the intention of collecting plants, seeds and roots, but 

 also, as heretofore, in almost all the branches of animated na- 

 ture. 



And now, sir, most heartily wishing this extensive disco- 

 verer of succulent plants every possible success in his laborious 



undertakings, — 



