10 THE LIFE OF SCIENCE 



more than eighteen centuries) between Archimedes and Galileo. In 

 the year 1585 Stevin published, in both a Dutch and French edi- 

 tion, a little booklet entitled 7be lithe, wherein he gave for the 

 first time a systematic account of decimal fractions. Though he 

 was not the first to think of such fractions, he showed such a deep 

 understanding and gave such a masterly exposition of them, that 

 we will not be far wrong if we call him their inventor. His manner 

 of representing them was rather clumsy, however, and that might 

 have delayed their diffusion, had this brilliant innovation not been 

 reinforced a little later by another invention at least equally im- 

 portant, that of the logarithms. The logarithms, like the decimals, 

 made it possible to increase considerably the speed of computa- 

 tion. It has been justly said that the discovery of logarithms dou- 

 bled the lives of the astronomers. They were introduced at the be- 

 ginning of the following century (1614, 1619) by John Napier, 

 laird of Merchiston, who showed us at the same time a far sim- 

 pler method of representing the decimal fractions, the very one we 

 use today. The triumph of the logarithms was immediate — no 

 amount of prejudice could have prevented the astronomers from 

 doubling their years! — and the decimals shared the triumph as a 

 matter of course. But here again our surprise is not that these frac- 

 tions were accepted so readily, but that they were offered so late. 

 Indeed what did they stand for? Just as the main idea of the 

 decimal system was to collect the objects to be counted in tens, 

 tens of tens, or hundreds, and so on; so the gist of the decimal frac- 

 tions was to count fragments of unity similarly in tenths, tenths of 

 tenths or hundredths, etc. When this was consistently done it was 

 found that those fractions could be written and used almost as 

 simply as ordinary numbers. The decimal fractions, so to say, 

 drove the fractions out of our calculations and the more so that 

 one could always suppress them altogether if one wished. If it an- 

 noyed you too much to speak of $3.53, you could say, without 

 changing a single figure, 353 cents. The decimal fractions are so 

 simple that most people handle them without being aware of their 



