CHAP. XVI.] OF THE THEORY OF PROBABILITIES. 245 



blance to the past ; that under the same circumstances the same 

 event will tend to recur with a definite numerical frequency ; not 

 upon any attempt to submit to calculation the strength of human 

 hopes and fears. 



Now experience actually testifies that events of a given species 

 do, under given circumstances, tend to recur with definite fre- 

 quency, whether their true causes be known to us or unknown. 

 Of course this tendency is, in general, only manifested when the 

 area of observation is sufficiently large. The judicial records of 

 a great nation, its registries of births and deaths, in relation to 

 age and sex, &c., present a remarkable uniformity from year to 

 year. In a given language, or family of languages, the same 

 sounds, and successions of sounds, and, if it be a written lan- 

 guage, the same characters and successions of characters recur 

 with determinate frequency.'" The key to the rude Ogham in- 

 scriptions, found in various parts of Ireland, and in which no 

 distinction of words could at first be traced, was, by a strict ap- 

 plication of this principle, recovered.* The same method, it is 

 understood, has been appliedf to the deciphering of the cuneiform 

 records recently disentombed from the ruins of Nineveh by the 

 enterprise of Mr. Layard. 



4. Let us endeavour from the above statements and defini- 

 tions to form a conception of the legitimate object of the theory 

 of Probabilities. 



Probability, it has been said, consists in the expectation 

 founded upon a particular kind of knowledge, viz., the know- 

 ledge of the relative frequency of occurrence of events. Hence 

 the probabilities of events, or of combinations of events, whether 

 deduced from a knowledge of the particular constitution of 

 things under which they happen, or derived from the long-con- 

 tinued observation of a past series of their occurrences and fai- 

 lures, constitute, in all cases, our data. The probability of some 



* The discovery is due to the Rev. Charles Graves, Professor of Mathematics 



in the University of Dublin Vide Proceedings of the Royal Irish Academy, 



Feb. 14, 1848. Professor Graves informs me that he has verified the principle 

 by constructing sequence tables for all the European languages. 



t By the learned Orientalist, Dr. Edward Hincks. 



