OF ARTS AND SCIENCES. 435 



But, it may be asked, is not the shaking of the box by the same indi- 

 vidual in either case a common element in the causes of all the throws ? 



I answer, that we are not to look for the common element in those 

 causes which are concerned only in producing the whole class of 

 effects, the relationship of which we seek ; but in those additional 

 and unknown circumstances which determine why one of these effects 

 should be produced rather than another. 



Now, the shaking of the box is supposed simply to cause the result, 



A side is thrown, 



while the cause of the side six being thrown may be a loading of the 

 die, or an ability in the thrower to cause what side he pleases to turn 

 up, either of which would be a common cause, acting through the sev- 

 eral throws, and having a special relation to the side six. 



The proportionate number of times which an event will occur in a 

 great number of times is called by Laplace its facilittj, which word 

 may be defined as follows : — 



If a constant system of causes is combined within an infinite suc- 

 cession of independent causes ; and if, of the infinite number of effects 

 thus produced, a certain proportion belong to a class A, then is the 

 facility of production of an effect of that class represented by the frac- 

 tion representing the above-mentioned proportion. Or, we might say 

 that the constant system of causes is combined with every possible 

 independent cause, and represents the facility by the fraction expressing 

 the ratio of the effects of the class A to the whole number of effects. 



We easily see that the facility of an event depends on the constant 

 causes alone. It is therefore the probability of the event to a mind 

 acquainted with all the constant causes, or with the laws of their action. 



Owing to the complicated manner in which the constant and the va- 

 riable or independent causes are combined, and the general vagueness 

 and difficulty of definition of the former, we can seldom determine with 

 accuracy the facility of an event, except in a few simple mathematical 

 cases. Thus, if we wish to construct a perfect table of mortality, if we 

 select our lives from individuals of nearly the same place and time, the 

 examples will not be sufficiently numerous to assure us that the inde- 

 pendent causes have acted in every possible way ; and if we select 

 them from many countries, and during a long course of time, the cir- 

 cumstances of climate, general external condition, &c., which ought to 

 be constant, will differ with the different individuals. 



