xvi.] THE METHOD OF MEANS. 3G3 



importance of the distinction was pointed out by Sir John 

 Herschel in reviewing his work. 1 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 ap- 

 proximation to a definite existing quantity ; and average, 

 when the mean is only a fictitious quantity, used for con- 

 venience of thought and expression. The etymology of 

 this word " average " is somewhat obscure ; but according 

 to De Morgan 2 it comes from averia, " havings or pos- 

 sessions," especially applied to farm stock. By the acci- 

 dents of language averagium came to mean the labour of 

 farm horses to which the lord was entitled, and it prob- 

 ably acquired in this manner the notion of distributing a 

 whole into parts, a sense in which it was early applied to 

 maritime averages or contributions of the other owners of 

 cargo to those whose goods have been thrown overboard or 

 used for the safety of the vessel. 



On the Average or Fictitious Mean. 



Although the average when employed in its proper 

 sense of a fictitious mean, represents no really existing 

 quantity, it is yet of the highest scientific importance, as 

 enabling us to conceive in a single result a multitude of 

 details. It enables us to make a hypothetical simplifica- 

 tion of a problem, and avoid complexity without committing 

 error. The weight of a body is the sum of the weights of 

 infinitely small particles, each acting at a different place, 

 so that a mechanical problem resolves itself, strictly speak- 

 ing, into an infinite number of distinct -problems. We 

 owe to Archimedes the first introduction of the beautiful 

 idea that one point may be discovered in a gravitating 

 body such that the weight of all the particles may be re- 

 garded as concentrated in that point, and yet the behaviour 

 of the whole body will be exactly represented by the 

 behaviour of this heavy point. This Centre of Gravity 

 may be within the body, as in the case of a sphere, or it 

 may be in empty space, as in the case of a ring. Any two 

 bodies, whether connected or separate, may be conceived 



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



2 On the Theory of Errors of Observations, Cambridge Philosophical 

 Transactions, vol. x. Part ii. 416. 



