498 Theory of the Average. [CHAP. xix. 



In the above example we were supposed to know that 

 the calibre of the guns was likely to run in English inches or 

 in some other recognized units. But if the battery .were in 

 China or Japan, and we knew nothing of the standards of 

 length in use there, we could no longer appeal to this 

 principle. It is doubtless highly probable that those calibres 

 are not of the nature of continuously varying magnitudes; 

 but in an entire ignorance of the standards actually adopted, 

 we are to all intents and purposes in the same position as if 

 they were of that continuous nature. When this is so the 

 objections to trusting to the average would no longer hold 

 good, and if we had only one opportunity, or a very few 

 opportunities, we should do best to adhere to the customary 

 practice. 



34. When however we are able to collect and compare 

 a large number of measurements of various objects, this 

 consideration of the probable discontinuity of the objects we 

 thus measure, that is, their tendency to assume some one or 

 other of a finite number of distinct magnitudes, instead of 

 showing an equal readiness to adapt themselves to all inter 

 mediate values, again assumes importance. In fact, given 

 a sufficient number of measurable objects, we can actually 

 deduce with much probability the standard according to 

 which the things in question were made. 



This is the problem which Mr Flinders Petrie has at 

 tacked with so much acuteness and industry in his work on 

 Inductive Metrology, a work which, merely on the ground of 

 its speculative interest, may well be commended to the 

 student of Probability. The main principles on which the 

 reasoning is based are these two: (1) that all artificers are 

 prone to construct their works according to round numbers, 

 or simple fractions, of their units of measurement; and (2) 

 that, aiming to secure this, they will stray from it in toler- 



