SECT. 7.] Arrangement and Formation of the Series. 33 



to tend in the same direction, instead of, as in the other 

 cases, more or less neutralizing one another s work. But 

 the aggregate effect of such causes may well be supposed 

 to be limited. The man will not discharge his shot nearly 

 at right angles to the true line, of fire unless some entirely 

 new cause comes in, as by some unusual circumstance 

 having distracted his attention, or by his having had some 

 spasmodic seizure. But influences of this kind were not 

 supposed to have been available before ; and even if they 

 were we are taking a bold step in assuming that these 

 occasional great disturbances are subject to the same kind 

 of laws as are the aggregates of innumerable little ones. 



We cannot indeed lay much stress upon an example 

 of this last kind, as compared with those in which we 

 can see for certain that there is a fixed limit to the range 

 of error. It is therefore offered rather for illustration than 

 for proof. The enormous, in fact inconceivable magnitude 

 of the numbers expressive of the chance of very rare com 

 binations, such as those in question, has such a bewildering 

 effect upon the mind that one may be sometimes apt to con 

 found the impossible with the higher degrees of the merely 

 mathematically improbable. 



7. At the time the first edition of this essay was com 

 posed writers on Statistics were, I think, still for the most 

 part under the influence of Quetelet, and inclined to over 

 value his authority on this particular subject: of late however 

 attention has been repeatedly drawn to the necessity of 

 taking account of other laws of arrangement than the binomial 

 or exponential. 



Mr Galton, for instance, to whom every branch of the 

 theory of statistics owes so much, has insisted 1 that the 

 &quot; assumption which lies at the basis of the well-known law of 

 1 Proc. E. Soc. Oct. 21, 1879. 



v. 3 



