SECT. 31.] Theory of the Average. 495 



consequence ? The answer surely is that it will not make 

 the slightest difference to either party in the bargain. In 

 the long run, since the same parties are concerned, it will not 

 matter whether the intermediate errors have been small or 

 large. 



Of course nothing of this sort can be regarded as the 

 general rule. In almost every case in which we have to 

 make measurements we shall find that large errors are much 

 more mischievous than small ones, that is, mischievous in a 

 greater ratio than that of their mere magnitude. Even in 

 purchase and sale, where different purchasers are concerned, 

 this must be so, for the pleasure of him who is overserved 

 will hardly equal the pain of him who is underserved. And 

 in many cases of scientific measurement large errors may be 

 simply fatal, in the sense that if there were no reasonable 

 prospect of avoiding them we should not care to undertake 

 the measurement at all. 



31. If we were only concerned with practical con 

 siderations we might stop at this point ; but if we want to 

 realize the full logical import of average-taking as a means 

 to this particular end, viz. of estimating some assigned 

 magnitude, we must look more closely into such an ex 

 ceptional case as that which was indicated in the figure on 

 p. 493. What we there assumed was a state of things in 

 reference to which extremely small errors were very fre 

 quent, but that when once we got beyond a certain small 

 range all other errors, within considerable limits, were equally 

 likely. 



It is not difficult to imagine an example which will aptly 

 illustrate the case in point: at worst it may seem a little far 

 fetched. Conceive then that some firm in England received 

 a hurried order to supply a portion of a machine : , say a 

 steam-engine, to customers at a distant place; and that it 



