THE METHOD OF MEANS. 421 



earth, it is exceedingly unlikely that there is any part of 

 the earth exactly of that density, and, as the crust is only 

 about half the mean density, there must be other parts of 

 greater density. I may also determine the mean specific 

 gravity of a body composed of iron and gold, so that 

 there will certainly be no portion possessing the mean 

 density. 



The very different signification of the word 'mean' in 

 these two uses has been fully explained by M. Quetelet 11 , 

 and the importance of the distinction has moreover been 

 pointed out by Sir John Herschel in reviewing his work \ 

 It is much to be desired that scientific men would mark 

 the difference by using the word mean only in the former 

 sense when it denotes approximation to a definite exist- 

 ing quantity ; and average, when the mean is only a 

 fictitious quantity, used for the convenience of thought 

 and expression. The etymology of this word ' average ' is 

 somewhat obscure ; but according to De Morgan k it comes 

 from averia, ' havings or possessions/ especially applied to 

 farm stock. By the accidents of language averagium 

 came to mean the labour of farm horses to which the lord 

 was entitled, and it probably acquired in this manner the 

 notion of distributing a whole into parts, a sense in which 

 it was very early applied to maritime averages or contri- 

 butions of the other owners of cargo to those whose goods 

 have been thrown overboard or used for the safety of the 

 vessel. 



1> ' Letters on the Theory of Probabilities,' transl. by Downes, Part ii. 

 i Herschel's 'Essays,' &c. pp. 404, 405. 



fc ' On the Theory of Errors of Observations/ ' Cambridge Philosophical 

 Transactions/ vol. x. Part ii. 416. 



