Solution of a Question in the Theory of Probabilities. 29 



Cleavage, b, very perfect and easily obtained ; c, perfect. 



The crystals are extremely thin in a direction perpendicular 

 to the face c. 



The faces r, m were so 

 imperfect that the angles 

 they make with b and c 

 could not be determined 

 with much accuracy. 



Xanthoxyline is quite insoluble either in cold or hot water, 

 but it readily dissolves in alcohol or aether. Its solutions are 

 quite neutral to test-paper, and do not appear to possess either 

 acid or basic properties. The crystals of xanthoxyline melt at 

 80° C. Their taste is aromatic and resinous, not unlike that of 

 elemi or olibanum. The amount of xanthoxyline in Japanese 

 pepper is very considerable. A quantity of xanthoxyline, after 

 being dried at 100° Centigrade, was subjected to analysis in the 

 usual way. 



I. 0-179 grm. substance gave 0-401 CO^ and 0-10-i water. 



II. 0-1142 grm. substance gave 0-2558 CO^ and 0-07 water. 



I. II. 



Carbon . . 61-09 61-09 



Hydrogen . 6-45 6*8 



I subsequently found that xanthoxyline contains a small 

 quantity of nitrogen, the amount of which I was unable to deter- 

 mine from want of material. I confidently expect to obtain in 

 the course of a few mouths a considerable quantity of Japanese 

 pepper, when I hope to be able to complete its analysis. Not- 

 withstanding that xanthoxyline contains nitrogen, it does not 

 exhibit any basic properties, but in its general properties con- 

 siderably resembles the so-called stcaroptens. 



V. Solution of a Question in the Theory of Probabilities. By 

 Geougk Boole, LL.D., Professor of Mathematics in Queen's 

 CoUcfje, Cork*. 



THE question considered by Mr. Cayley in the Philosophical 

 Magazine for October 1853, p. 259, is a ])articular case of a 

 problem proposed by me in the Cambridge and Dublin Mathe- 



* Communicated by the Autlior. 



