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XXI. Analysis of Euclase. By J. W. Mallet, PA.D * 



AN analysis of 19*83 grs. of this mineral gave the following 

 results reduced to 100 parts : — 



99-14 



These numbers are not far from those of Berzelius, and cor- 

 respond nearly to three atoms silica, two alumina, and two glu- 

 cina, assuming the latter earth to be a sesquioxide, and hence 

 we have the formula of the mineral 26^03, SiO^ + 2(APq3, Sip^) ; 

 or, if alumina and glucina be isomorphous, 4(AP0^ + G^O^), 3SiO^. 



The fragments of crystals employed for the analysis were per- 

 fectly clear and transparent, of a very light mountain-green 

 colour, and spec. grav. 3*036. 



Particular care was taken in determining the presence and 

 amount of the oxide of tin, the existence of which in this and 

 some other hard silicates appears very difficult to account for, 

 and in some degree connects itself with the question of the adop- 

 tion of SiO^ or SiO^ as the formula for silicic acid. 



XXII. On some Facts connected with Geometrical Reasoning. 

 By John Pope HENNEssYf. 



IN a late paper on some geometrical demonstrations, I alluded 

 to the peculiar difficulty which has been found to exist 

 when we attempt to give direct proof to certain theorems in ele- 

 mentary geometry ; and I stated my belief that this difficulty 

 arose from a defective premiss on which the proof depended. 

 To discover the precise nature of such defect, I compared the 

 definition of parallel lines, being one of those referred to, with 

 the remaining definitions and axioms. The result arrived at by 

 this comparison I venture to hope will somewhat elucidate the 

 interesting question as to the origin of Euclid's reductio ad 

 absurdum, 



I found that all the definitions prefixed to the first book, which 

 are used in the Elements, are, with one exception, affirmatives ; 

 the negative definition being that in which, according to my 

 supposition, a defect existed. It is as follows : — 



* Communicated by the Author, 

 t Communicated by the Author. 



