SECT. 8.] Origin, or Process of Causation of the Series. 61 



and the intention of aiming at a given point. These we 

 must of course suppose to remain unchanged, if we are 

 to obtain any such uniformity as we are seeking. The 

 minor and variable causes are all those innumerable little 

 disturbing influences referred to in the last chapter. It 

 might conceivably be the case that we were only able to 

 ascertain that these acted as often in one direction as in 

 the other; what we should then find was that the quoit 

 tended to fall short of the mark as often as beyond it. 

 But owing to these little causes being mostly independent 

 of one another, and more or less equal in their influence, 

 we find also that every amount of excess and defect presents 

 the same general characteristics, and that in a large number 

 of throws the quantity of divergences from the mark, of any 

 given amount, is a tolerably determinate function, according 

 to a regular law, of that amount of divergence 1 . 



8. The necessity of the conditions just hinted at 

 will best be seen by a reference to cases in which any of 



1 &quot;It would seem in fact that in having been till then masked and 



coarse and rude observations the overshadowed by the graver errors 



errors proceed from a very few prin- which had been now approximately 



cipal causes, and in consequence our removed There were errors of 



hypothesis [as to the Exponential graduation, and many others in the 



Law of Error] will probably repre- contraction of instruments ; other 



sent the facts only imperfectly, and errors of their adjustments ; errors 



the frequency of the errors will only (technically so called) of observation ; 



approximate roughly and vaguely to errors from the changes of tempera- 



the law which follows from it. But ture, of weather, from slight irregular 



when astronomers, not content with motions and vibrations; in short, the 



the degree of accuracy they had thousand minute disturbing influ- 



reached, prosecuted their researches ences with which modern astrono- 



into the remaining sources of error, mers are familiar.&quot; (Extracted from 



they found that not three or four, a paper by Mr Crofton in the Vol. of 



but a great number of minor sources the Philosophical Transactions for 



of error of nearly co-ordinate import- 1870, p. 177.) 

 ance began to reveal themselves, 



