444 . THE PRINCIPLES OF SCIENCE. 



between permutations and combinations, a subject upon 

 which I may seem to have dwelt with unnecessary pro- 

 lixity in previous pages (pp. 200-216). The order in 

 which we add quantities together does not affect the 

 amount of the sum, so that if there be three positive 

 and five negative causes of error in operation, it does not 

 matter in which order they are considered as acting. 

 They may be indifferently intermixed in any arrange- 

 ment, and yet the result will be the same. The reader 

 should not fail to notice how laws or principles which 

 appeared to be absurdly simple and evident when first 

 noticed, reappear in the most complicated and mysterious 

 processes of scientific method. The fundamental Laws 

 of Identity and Difference gave rise to the Logical Abe- 

 cedarium, which, after abstracting the character of the 

 differences, led to the Arithmetical Triangle (p. 214). 

 The Law of Error is defined by an infinitely high line 

 of that triangle, and the law proves that the mean is the 

 most probable result, and that divergencies from the 

 mean become much less probable as they increase in 

 amount. Now the comparative greatness of the numbers 

 towards the middle of each line of the Arithmetical 

 Triangle is entirely due to the indifference of order in 

 space or time, which was first prominently pointed out 

 as a condition of logical relations, and the symbols in- 

 dicating them (pp. 40-42), and which was afterwards 

 shown to attach equally to numerical symbols, the deri- 

 vatives of logical ferms (pp. 180, 181). 



Verification of the Law of Error. 



The theory of error which we have been considering 

 rests entirely upon an assumption, namely that when 

 known sources of disturbances are allowed for, there yet 

 remain an indefinite, possibly an infinite number of other 



