THE 

 LONDON, EDINBURGH and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FOURTH SERIES.] 



MAY 1851. 



XLVII. On certain Questions relating to the Theory of Probabi- 

 lities. Bij W. F. DoNKiN, M.A., F.R.S., F.R.A.S., Savilian 

 Professor of Astronomy in the University of Oxford^. 



WITHIN the last year three papers have been published on 

 subjects connected with the theory of probabilities^ all 

 discussing or suggesting questions of more or less importance 

 and difficulty ; namely, an article in the Edinburgh Review for 

 July 1850; remarks on certain parts of this article by Mr. R. L. 

 Ellis, in the last November Number of this Journal ; and a paper 

 by Prof. J. D. Forbes in the December Number of the same. In 

 what follows, I am not going to attempt anything like a detailed 

 examination of any of these papers, but merely to offer some 

 considerations which may, I hope, contribute something, however 

 little, towards a settlement of the cpiestions treated in them, so 

 far as they invol\e matters of doubt or controversy. How far 

 there may be any originality, either of substance or form, in 

 anything that I shall say, I hope I may be allowed to leave the 

 reader to settle for himself, if he care about it ; though of course 

 I shall not intentionally make unacknowledged use of the labours 

 of others, unless in so far as their results may be considered to 

 have become conmion property. 



1 . It will, I suppose, be generally admitted, and has often been 

 more or less exj)licitly stated, that the subject-matter of calcula- 

 tion in the mathematical theory of jjrobabilities is quantity of 

 belief. Every probUnn with wliieh the theory is concerned is of the 

 following kind. A certain number of hypotheses are presented to 

 the mind, along with a certain quantity of information relating to 

 thciu : In what way ought belief to be distrilmted among them ':* 

 And the law which must always be made the foundation of the 

 * Coimnuiiicated by the Author. 



Phil. May. S. 4. Vol. 1. No. 5. May 1851. 2 B 



