THE LAW OF ERROR. 435 



It is perfectly recognised by mathematicians that in 

 each special case a special Law of Error may apply, and 

 should be discovered and adopted if possible. Nothing 

 can be more unlikely than that the errors committed in all 

 classes of observations should follow the same law a / and 

 the special Laws of Error which will apply to certain in 

 struments, as for instance the repeating circle, have been 

 investigated by M. Bravais b . He concludes that every 

 partial and distinct cause of error gives rise to a curve of 

 possibility of errors, which may have any form whatever, 

 a curve which we may either be able or unable to discover, 

 and which in the first case may be determined by con 

 siderations a priori, on the peculiar nature of this cause, 

 or which may be determined d posteriori by observation. 

 Whenever it is practicable and worth the labour, we ought 

 to investigate these special conditions of error ; never 

 theless, when there are a great number of different sources 

 of minute error, the general resultant will always tend to 

 obey that general law which we are about to consider. 



Establishment of the Law of Error. 



Mathematicians agree far better as to the nature of the 

 ultimate Law of Error than they do as to the manner in 

 which it can be deduced and proved. They agree that 

 among a number of discrepant results of observation, that 

 mean quantity is probably the most nearly approximate 

 to the truth which makes the sum of the squares of the 

 errors as small as possible. But there are at least three 

 different ways in which this principle has been arrived at 

 respectively by Gauss, by Laplace, by Quetelet and by 

 Sir John Herschel. Gauss proceeds much upon assump- 



a Philosophical Magazine, 3rd Series, vol. xxxvii. p. 324. 

 b Letters on the Theory of Probabilities, by Quetelet, transl. by 0. G. 

 Dowries, Notes to Letter XXVI. pp. 286-295. 



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