36 Arrangement and Formation of the Series. [CHAP. n. 



9 (II.). The last remarks will suggest another kind of 

 proof which might be offered to establish the invariable nature 

 of the law of error. It is of a direct deductive kind, not 

 appealing immediately to statistics, but involving an enquiry 

 into the actual or assumed nature of the causes by which the 

 events are brought about. Imagine that the event under 

 consideration is brought to pass, in the first place, by some 

 fixed cause, or group of fixed causes. If this comprised all 

 the influencing circumstances the event would invariably 

 happen in precisely the same way : there would be no errors 

 or deflections whatever to be taken account of. But now 

 suppose that there were also an enormous number of very 

 small causes which tended to produce deflections ; that these 

 causes acted in entire independence of one another ; and that 

 each of the lot told as often, in the long run, in one direction 

 as in the opposite. It is easy 1 to see, in a general way, what 

 would follow from these assumptions. In a very few cases 

 nearly all the causes would tell in the same direction; in 

 other words, in a very few cases the deflection would be 

 extreme. In a greater number of cases, however, it would 

 only be the most part of them that would tell in one direc 

 tion, whilst a few did what they could to counteract the rest ; 

 the result being a comparatively larger number of somewhat 

 smaller deflections. So on, in increasing numbers, till we 

 approach the middle point. Here we shall have a very large 

 number of very small deflections: the cases in which the 

 opposed influences just succeed in balancing one another, 

 so that no error whatever is produced, being, though actually 

 infrequent, relatively the most frequent of all. 



1 The above reasoning will proba- selves, involve somewhat of an anti- 

 bly be accepted as valid at this stage cipation. They demand, and in a 

 of enquiry. But in strictness, as- future chapter will receive, closer 

 sumptions are made here, which how- scrutiny and criticism, 

 ever justifiable they maybe in them- 



