14,8 Measurement of Belief. [CHAP. vi. 



if we form a series by taking successively a number out of 

 totally distinct kinds. 



It is in this circumstance that we find an extension of the- 

 practical justification of the measure of our belief. A man r 

 say, buys a life annuity, insures his life on a railway journey, 

 puts into a lottery, and so on. Now we may make a series 

 out of these acts of his, though each is in itself a single event 

 which he may never intend to repeat. His conduct, and there 

 fore his belief, measured by the result in each individual 

 instance, will not be justified, but the reverse, as shewn in 

 19. Could he indeed repeat each kind of action often 

 enough it would be justified ; but from this, by the conditions 

 of life, he is debarred. Now it is perfectly conceivable that 

 in the new series, formed by his successive acts of different 

 kinds, there should be no regularity. As a matter of fact, 

 however, it is found that there is regularity. In this way the 

 equalization of his gains and losses, for which he cannot hope 

 in annuities, insurances, and lotteries taken separately, may 

 yet be secured to him out of these events taken collectively. 

 If in each case he values his chance at its right proportion 

 (and acts accordingly) he will in the course of his life neither 

 gain nor lose. And in the same way if, whenever he has the 

 alternative of different courses of conduct, he acts in accord 

 ance with the estimate of his belief described above, i.e. 

 chooses the event whose chance is the best, he will in the end 

 gain more in this way than by any other course. By the ex 

 istence, therefore, of these cross-series, as we may term them, 

 there is an immense addition to the number of actions which 

 may be fairly considered to belong to those courses of con -I 

 duct which offer many successive opportunities of equalizing- 

 gains and losses. All these cases then may be regarded as 

 admitting of justification in the way now under discussion. 



25. In the above remarks it will be observed that we 



