35.2 Mr. A. Cayley on a Question in the 



Oxygen. 

 SiO 2 . . . 30-47 15-81 



FcO . . . 53G6 11-911 

 MnO. . . 1*40 -31 ^16-33 



CaO . . . 14-47 4r.ll J 



Although these values do not come out exactly equal, they 

 lead evidently to the common chrysolite formula 2(110), SiO . 

 If we adopt, consequently, the assumption on which the above 

 calculation is based, the Lievrite falls naturally into the minera- 

 logical group to which it undoubtedly belongs ; whereas on the 

 other view, founded on the bare results of analysis, not only 

 does the atomic constitution of the mineral remain uncertain, 

 but its composition fails to harmonize with its physical characters 

 and conditions. The suggestion, therefore, embodied in this 

 brief notice may not be found altogether unworthy of considera- 

 tion by those engaged in the study of mineral analogies. 



LI. On a Question in the Theory of Probabilities. 

 By A. Cayley, Esq** 



IT is, I think, very desirable to further consider the question 

 in Probabilities proposed by Prof. Boole in the Cambridge 

 and Dublin Mathematical Journal in the year 1851. The ques- 

 tion was originally stated as follows : — " If an event E can only 

 happen as a consequence of some one or more of certain causes 

 A|, A 2 . . . A n) and if generally c t denote the probability of the 

 cause A;, and p t the probability that if the cause A* exist the 

 event E will happen, then, the series of values c l} c 2 . . . c n , 

 2) v jio • • >p n being given, required the probability of the event E." 



Considering only the causes A and B, the proposed question 

 may be considered as being — 



" If the event E can only happen as a consequence of one or 

 both of the causes A and B ; and if a be the probability of the 

 existence of the cause A, p the probability that, the cause A ex- 

 isting, the event E will (whether or not as a consequence of A) 

 happen ; and in like manner if {3 be the probability of the exist- 

 ence of the cause B, q the probability that, the cause B existing, 

 the event E will (whether or not as a consequence of B) happen : 

 required the probability of the event E." 



This, which is strictly equivalent to Prof. Boole's mode of sta- 

 ting the question, may for convenience be called the Causation 

 statement. But his solution, presently to be spoken of, is rather 

 a solution of what may be termed the Concomitance statement of 



* Communicated by the Author. 



