82 Memoir of John Napier, 



enthusiasm, as a wonderful assistance in the composition of 

 his Rudolphine Tables, was unacquainted with it till 1617 ; 

 and even then, possessed but an imperfect knowledge of it, 

 having only seen Napier's book at Prague, without being 

 able to study it ; so that, unfortunately for him, he did not 

 appreciate it, as may be learned from a remarkable passage 

 in a letter written by Kepler to his friend Schikkart, dated 

 11th March, 1618. The passage is, " Extitit Scotus Baro, 

 cujus nomen mihi excidit qui praeclari quid prsestitit, 

 necessitate omni multiplicationum et divisionum in meras 

 additiones et substractiones commutata ; nee sinibus utitur. 

 Attamen opus est ipsi tangentium canone ; et varietas, cre- 

 britas difficultasque additionum, substractionumque alicubi 

 laborem multiplicandi et dividendi superat" (Epist. ad Kep- 

 lerum Lipsiae 1718, in fol. p. 672). The last part of this 

 passage shews us that Kepler, at first sight, had formed an 

 erroneous opinion of Napier's method. The objection, 

 attamen opus est ipsi tangentium canone, requires some expla- 

 nation. In the original publication of his discovery, in 

 1614, of which I have examined a copy, from the library 

 of Walknaer, Napier does not give a special table for 

 logarithms of natural numbers, but only for sines, co-sines, 

 and tangents of arcs. Thus, when it is necessary to find the 

 logarithm of a given number, he supposes that it maybe 

 considered as a natural sine if it is included between & 1, 

 and as a natural tangent if it exceeds these limits. In the 

 first case, the logarithm sought is found immediately among 

 those of the sines which the table of Neper gives ; in the 

 second case, it is necessary to find first in a table of natural 

 tangents the arc which corresponds to the given number, 

 and with this arc the table of Neper gives the logarithm. 



Having soon after, however, met accidentally with a short 

 and clear exposition of this discovery, " I learned" said he, 

 " its nature, and scarcely had I tried an example of the 

 process, when I found, to my great delight, that it far sur- 

 passed all the attempts at abbreviation which I had attempted 

 for a long time past." He set one of his pupils to the work 

 immediately, and made him calculate logarithmic tables 

 after the method of Napier ; employed them with success 

 in completing the calculation of his Rudolphine Tables, 

 which had hitherto cost him immense labour; and even 



