435 



The following Gentlemen were admitted as Ordinary Fel- 

 lows : — 



Horatio Ross, Esq. 



James Black, M.D., Lie. R. Coll. Phys. Lond. F.G.S. 



The following Donations to the Library were announced : — 



An Analysis of the Statistics of the Clearing House during the year 

 1839 ; with an Appendix on the London and New York Clear- 

 ing Houses, and on the London Railway Clearing House. By 

 Charles Babbage, F.R.S. 8vo. — From the Author, 



Sanatory Remarks in connection with Nuisances. By Thomas Wil- 

 liamson, M.D. 8vo. — From the Author. 



Monday, 12th January 1857. 

 Right Reverend BISHOP TERROT in the Chair. 



The following Communications were read : — 



1. On the application of the Theory of Probabilities to the 

 question of the Combination of Testimonies. By Pro- 

 fessor Boole. Communicated by Bishop Terrot. 



The method for the solution of questions in the theory of proba- 

 bilities which is applied in this paper, is that which was developed 

 by the author in a treatise entitled " An Investigation of the Laws 

 of Thought, on which are founded the Mathematical Theories of 

 Logic and of Probabilities." 



The special problems with relation to the combination of testi- 

 monies to which the method is applied are the following, viz. : — 1st, 

 That in which the testimonies to be combined are merely different 

 numerical measures of a physical magnitude, as of the elevation of a 

 star, furnished by different observations taken simultaneously. 2d, 

 That in which the testimonies to be combined relate, not to a nume- 

 rical measure, but to some fact or hypothesis of which it is required 

 to determine the probability ; the probabilities furnished by the 

 separate testimonies being given. 



