NAPIER COMMEMORATIVE LECTURE. 45, 
algebra; and there is evidence that he possessed a method 
of extracting roots of any degree. Further it has to be 
remembered that though the decimal notation for integers 
had been introduced in the Tenth Century, it had not yet 
been extended to fractions. Several writers about his 
time had suggested a new notation for fractions. For 
example, Stevin, in 1585, wrote 
3@7@5@9@® and 8090307 © 
for our “3759 and 8°937. If not the first, Napier was at 
least one of the first to use the present notation. It is 
almost safe to say that his tables would not have been 
constructed without it. 
Towards the end of the Sixteenth Century the progress. 
of science was greatly impeded by the _ continually 
increasing complexity of numerical calculation. Astronomy 
was making wonderful advances. Kepler was examining 
the orbits of the planets. Galileo was soon to turn his 
telescope to the stars. And the numerical calculations of 
astronomers involved immense labour with the means at. 
their disposal. The tables of sines, cosines, etc., were, of 
course, already in their hands: though, as we shall see later, 
the language of trigonometry was then somewhat different. 
German mathematicians had constructed the trigono- 
metrical tables to an enormous degree of accuracy. But 
the precision, which the astronomical computations needed, 
greatly increased the work of the calculator. Nor was 
this the case in astronomy alone. 
Napier seems to have laid aside his earlier work in 
arithmetic and algebra, and set out to devise some means 
of lessening this labour. He was not the only worker in 
the same field. To Napier in Merchiston, and to Burgi, in 
Prague or Cassel, a similar inspiration seems to have 
come, at the same time and quite independently. Welearn 
from one of Kepler’s works that Burgi had made some 
