,.«osV\^Mr. J. P. Hennessy on the Theory of Parallels. 283 



It appears, therefore, that in passing into perchlororubian, 

 chlororubian loses 9 equivalents of water and 9 of hydrogen, 8 

 of the latter being substituted by chlorine, since ». 



C44H27ci024 + l7Cl = C'*4H9CFOi^ + 9HO + 9ClH. 



It is a singular circumstance, that the 9 equivalents of chlorine 

 in this compound are much more firmly combined with the other 

 constituents than the 1 equivalent contained in chlororubian, 

 which the mere action of alkali is sufficient to separate. 



From the experiments just described it may be inferred, that 

 chlororubian is a conjugate compound containing sugar. It 

 resembles Piria^s chlorosalicine, which, by the action of acids, 

 yields chlorosaligenine and sugar, just as chlororubian gives 

 chlororubiadine and sugar. Though chlororubian is not, strictly 

 speaking, a product of substitution of rubian, still it retains some 

 of the properties of the latter ; for instance, that of giving, with 

 alkalies, products of decomposition differing from those formed 

 by acids. In all the processes of decomposition previously 

 described, rubian is decomposed in no less than three different 

 modes, just as if it were a compound or mixture of three dif- 

 ferent bodies, whereas, when acted on by chlorine, it yields 

 only one series of products. It behaves in the latter case 

 as if it were simply a conjugate compound containing sugar. 

 It splits up into sugar and a chlorinated body, and the latter, by 

 the action of acids, again splits up into sugar and a second chlo- 

 rinated compound. This series of products corresponds exactly 

 with one of the three series in the other processes of decompo- 

 sition, the bodies belonging to the two other series not making 

 their appearance even in the form of products of substitution. 



XXXVI. A Note on Professor Stevelly^s Paper on the Theory of 

 Parallels. By J. P. Hennessy*. 



LEGENDRE solves the so-called difficulty of parallel lines by 

 introducing, as it appears to me, the very same principle as 

 that which is employed by Mr. Stevelly. In his Elements de Geo- 

 metrie, douzieme edition, p. 20, he shows that every property of 

 parallel lines can be easily estabhshed if the proposition, that the 

 three angles of every triangle are equal to two right angles, be first 

 proved. This proposition, the thirty-second of Euclid, he accord- 

 ingly makes his first theorem, and he demonstrates it in two dif- 

 ferent ways. He first gives an elaborate proof of it in the text, and 

 he afterwards deduces it in his notes from the principle of homo- 

 geneity. His first and most important demonstration is rigorous 



* Communicated by the Author. 



