THEORY OF PROBABILITIES. 179 



under certain conditions, be larger than those which are retained : 

 and, as the result coincides with that of the general method, the 

 doubt thus suggested appears to extend to the latter. The sub- 

 ject of approximation by means of definite integrals is certainly 

 not free from obscurity. 



The method of this paper extends in . m . to the case in which 

 we seek to determine the degree of improbability that the average 

 length of the reigns of a series of kings shall exceed by a given 

 quantity the average deduced from authentic history. The ap- 

 plication of considerations of this nature to historical criticism 

 appears to have been first made in Sir Isaac Newton's Chrono- 

 logy. They are doubtless entitled to much attention ; but any 

 attempt to evaluate their legitimate influence, would, for more 

 than one reason, be unsatisfactory. 



122 



