NAPIER COMMEMORATIVE LECTURE. 63 
theory in plane and spherical trigonometry, especially as 
applied in astronomical calculations. In the sections on 
spherical trigonometry, in addition to some new theorems, 
he gives the general theorem of what are now called 
Napier’s Circular Parts, by which in one rule he brought 
together in a form, very easy to remember, the results for 
the different cases of the solution of right-angled spherical 
triangles. 
To Napier’s table of logarithms a cordial reception was 
at once given by the mathematicians of his day. In 1616 
it was translated into English by Wright. Ursinus printed ~ 
it in his Cursus Mathematicus in 1618, and in 1625 published 
the Magnus Canon Triangulorum Logarithmicus, in which 
Napier’s work was carried from eight figures to nine; and 
in addition, the intervals were diminished from minute to 
minute into intervals of 10 seconds. Kepler also immedi- 
ately recognised the power of the instrument which Napier 
had invented. And it is characteristic of him that he 
calculated the tables afresh—or employed his ‘‘ familiar ’’ 
to do so'—for equidistant sines instead of equidistant 
angles. His version of the tables was published in 1624, 
under the title Chilias Logarithmorum ad todidem numeros 
rotundos. A further extension of the original tables from 
sines to natural numbers was made in 1634 by Cruger. 
But in England long before this date, most important 
developments had been made in the original theory of 
Napier. Briggs—Professor of Geometry at Gresham 
College, London, and a graduate of Cambridge; afterwards, 
like other Cambridge graduates, to become Professor of 
Mathematics at Oxford—immediately on the appearance 
of the Descriptio was filled with admiration of the invention 
there explained. Not only so, he recognised that a new 
1 Cf. Kepler’s letter to Napier, published in Mark Napier’s Life, written 
two years after Napier’s death. 
