244 



A SHORT HISTORY OF SCIENCE 



Independent tables were computed by the astronomer Btirgi 

 and published at Prague in 1620. Both Napier and Biirgi, basing 

 their work on the relation which we should express by the equiva- 

 lent equations x = a v and y = log a x, avoid fractional values of y by 

 taking values of a near 1, their actual values being a = .9999999 

 and a = 1 .0001 respectively. In choosing a base less than 1, Napier 

 is also influenced by his desire that sines and cosines as proper 

 Y . fractions shall have positive 



logarithms. If we intro- 

 duce our modern graphical 

 interpretation of y = log a , 

 Biirgi is concerned with the 

 determination of abscissas 

 of points where the exponen- 

 tial curve is met by the 

 horizontal straight lines y 

 = c where c takes successive 

 integral values. Choosing 

 a base a near 1 naturally gives values of x near each other. 

 Napier's choice of a base less than 1 would correspond with the 

 same curve inverted. 



In 1615 Henry Briggs, afterwards Savilian Professor of Geom- 

 etry at Oxford, wrote of Napier " I hope to see him this summer, 

 if it please God, for I never saw book which pleased me better, or 

 made me more wonder." In connection with this and later visits 

 it was soon discovered that great simplification in the practical 

 use of logarithms would result from taking log 1=0 and log 10=1 

 and giving up the restriction of logarithms to integral values, thus 

 making the decimal parts of all logarithms depend wholly on the 

 sequence of digits. Napier had been so predominantly interested in 

 trigonometric applications that his table consisted not of logarithms 

 of abstract numbers, but of 7-place logarithms of the trigonometric 

 functions for each minute. In connection with his change of the 

 base, Briggs developed interesting methods of interpolating and 

 testing the accuracy of logarithms. He gives the logarithms from 

 1 to 20,000 and from 90,000 to 100,000 to 14 places, computing also 

 10-place trigonometric tables with an angular interval of 10 seconds. 



