6 TJie Realm of Nature CHAP. 



correct measurement of mass, space, or time, by means of 

 suitable instruments. Accuracy is always to be striven 

 for, but it can never be attained. This fact is only fully 

 realised by scientific workers. The banker can be accurate 

 because he only counts or weighs masses of metal which 

 he assumes to be exactly equal. The Master of the Mint 

 knows that two coins are never exactly equal in weight, 

 although he strives by improving machinery and processes 

 to make the differences as small as possible. When the 

 utmost care is taken the finest balances which have been 

 constructed can weigh i Ib. of a metal with an uncertainty 

 less than the hundredth part of a grain. In other words, 

 the weight is not accurate but the inaccuracy is very small, 

 and its greatest possible amount is known to 'less than 

 To o~o o P ar * f ^ e mass weighed. In weighing out tea 

 or sugar a grocer is content if the inaccuracy is not more 

 than about ^-^ of the mass. No person is so stupid as 

 not to feel sure that the height of a man he sees is between 

 3 ft. and 9 ft. ; some are able by the eye to estimate 

 the height as between 5 ft. 6 in. and 5 ft. 8 in. ; measure- 

 ment may show it to be between 5 ft. 6| in. and 5 ft. 7 

 in., but to go closer than that requires many precautions. 

 Training in observation and the use of delicate instruments 

 thus narrow the limits of approximation. Similarly with 

 regard to space and time, there are instruments with which 

 one-millionth of an inch, or of a second, can be measured, but 

 even this approximation, although far closer than is ever 

 practically necessary, is not accuracy. In the statement of 

 measurements there is no meaning in more than six signifi- 

 cant figures, and only the most careful observations can be 

 trusted so far. The height of Mount Everest is given as 

 29,002 ft. ; but here the fifth figure is meaningless, the 

 height of that mountain not being known so accurately 

 that two feet more or less would be detected. Similarly 

 the radius of the Earth is sometimes given as 3963-295833 

 miles, whereas no observation can get nearer the truth than 

 3963-30 miles. 



11. Definiteness in thought and description does not 

 require perfect accuracy in observation. We must always 



