SECT. 15.] Theory of the Average. 479 



The curve A BCD represents the arrangement of a given 

 number of errors supposed to be disposed according to the 

 binomial law already mentioned, when the angles have been 

 smoothed off by drawing a curve through them. A CD 

 represents the similar arrangement of the same number 

 when given not as simple errors, but as averages of pairs of 

 errors. A&quot;BD&quot;, again, represents the similar arrangement 

 obtained as averages of errors taken three together. They 

 are drawn as carefully to scale as the small size of the figure 

 permits. 



15. A glance at the above figure will explain to the 

 reader, better than any verbal description, the full signi 

 ficance of the statement that the result of combining two or 

 more measurements or observations together and taking the 

 average of them, instead of stopping short at the single 

 elements, is to make large errors comparatively more scarce. 

 The advantage is of the same general description as that of 

 fishing in a lake where, of the same number of fish, there 

 are more big and fewer little ones than in another water : of 



