On the Triads made with Fifteen Things. 



169 



If this inference be admitted, it follows that the excess of 

 sulphuric acid beyond that required to saturate the oxide of 

 lead, is, together with the arsenic and phosphoric acids, com- 

 bined with sesquioxide of iron, of which there is much more 

 than sufficient to neutralize those acids. The mineral may 

 therefore be considered as a mixture of sulphate of lead, and of 

 arseniate and sulphate of sesquioxideof iron with excessof base. 



The sulphate of lead cannot be regarded as in combination 

 with the salts of iron, because no analogous combination is 

 known. Nor is it more probable that arseniate and sulphate 

 of sesquioxide of iron should exist in combination with each 

 other. Hence the mineral would appear to be a simple mix- 

 ture of three distinct salts. But it is crystallized ; and the 

 crystalline form certainly is very similar to, if not identical 

 with, that of cube-ore. Levy maintained that it was an ob- 

 tuse rhombohedron with the vertical angle truncated. Descloi- 

 zeaux, on the other hand, asserts that the crystals are cubes 

 similar in all respects to those of cube-ore from Cornwall. 

 {Ann. de C/iim. et de Phys., vol. x, p. 77.) 



Professor Miller, however, has not been able to obtain sa- 

 tisfactory measurements of the crystals. Now, as Beudantite 

 contains in very sensible proportion the elements of cube-ore, — 

 as the form of the crystals, to say the least, very nearly re- 

 sembles that of cube-ore, — and as neither sulphate of lead nor 

 sulphate of sesquioxide of iron forms crystals at all similar to 

 those of cube-ore, the most probable conclusion seems to be 

 that of Damour, namely, that Beudantite is nothing more than 

 cube-ore containing an accidental mixture of much foreign matter. 

 Such mixtures, as Damour observes, are frequently met with 

 in the mineral kingdom, and present a very interesting subject 

 of inquiry. An extended investigation to determine the 

 amount of foreign matter which may enter into the composi- 

 tion of crystals, and its power of distorting or modifying the 

 crystalline form, would certainly yield many valuable results. 



XIX. On the Triads made with Fifteen Things. 

 By the Rev. Thomas P. Kirkman, M.A.* 



THE neatest method of writing the solution of the problem 

 mentioned at page 52 of this volume is the following: — 



a l a 2 a 3 

 h t b 2 b 3 



C \ c 1 c 3 

 d l d 2 d 3 

 e \ e i e 3 



a \b\ c \ a l d l e l 

 a 2 b 2 c 2 a 2 d 2 e 2 

 a 3 d 8 c 3 



h d \ c z 

 c 3 d 2 c ] 



a ih d i 



aj? 3 d 3 



a 3 b 3 c 3 a 3 c^e x 



df)^ 

 e 3 bcf x 



b x c 3 e, 

 d.Co e. 



a \ c i e o 



a 2 c 3 e 3 

 a 3 b l d 1 



c i b A 



a x b 3 e 3 



a 3 c 2 d 2 

 bcf 3 d x 



e 2 C \ d 3 



Y c 3 d 3 



*\ d \ 



a x c 



a*c 



a 3 b 2 e 2 



C 1°3 G \ 



dj) x e 3 



Communicated by the Author. 



