^6 M. Biot's Abstract of Mr Napier's 



enthusiastically, as a miraculous aid to his Rudolphine Tables, — 

 Kepler knew nothing of the matter until the year 1617, and 

 then his knowledge of it was but imperfect, having merely 

 seen Napicfs work at Prague, when he had not an opportunity 

 of studying the contents ; so that, unhappily for himsielf, he did 

 not properly appreciate the invention, as is evident from the 

 letter he wrote, about that epoch, in which the author of the lo- 

 garithms is simply designated as " Scotus Baro, cnjus nomen 

 mihi eivcidit,* a Scottish Baron, whose name has escaped me." 

 One year later, however, an abridged, and perhaps plainer ex- 

 position of the discovery having accidentally fallen under his ob- 

 servation, " I comprehended (he exclaims) the nature of his 

 work, and scarcely had I essayed a single example of the pro- 

 cess, when, to my great joy, I became sensible that he had in- 

 finitely surpassed all the attempts at abbreviation which I my- 

 self for a length of time had been labouring to effect." He set 

 one of his pupils instantly to work, made him calculate logarith- 

 mic tables by Napier''s method, availed himself gratefully of their 

 assistance to complete the calculations of his Rudolphine Tables, 

 which hitherto had cost him unimaginable labour, and even 

 changing the whole plan of those tables, though they had been 



• This remarkable passage is to be found in a letter, written by Kepler to 

 his friend Schikkart, 11th March 1018, as follows: « Extitit Scotus Baro, 

 cujus nomen ir.ihi excidit, qui prgeclari quid proestitit, necessitate omni mul- 

 tiplicationum et divisionum in meras additioneset substractiones coramutat^; 

 nee sinibus utitur. Attamen opus est ipsi tangentium canone ; et varietas, 

 crebritas, difficultasque additionum, substractionumque alicubi laborem mul- 

 tiplicandi et dividendi superat." (Epist. ad G. Keplerum, Lipsioe, 1718, in 

 foL p. 672). The last clause of this sentence proves, as we have said, that, 

 at that first inspection^ Kepler had ill appreciated the Neperien method. The 

 objection attamen opus est ipsi tangentitim canone^ appears to us to require some 

 explication ; and it is this, — that in the original publication of his discovery, 

 in 1G14, of which we have before us a copy belonging to the library of M. 

 "Walkanaer, Napier does not furnish a special table for the logarithms of na- 

 tural numbers, but only for the sines, cosines and tangents of arcs. Thus 

 when it is required to find the logarithm of a given number, he supposes it 

 considered as a natural sine, if it be comprehended betwixt and 1, and as a 

 natural tangent, without those limits. In the first case, the logarithm sought 

 is found directly among those of Napier's table of sines; in the second case, 

 it is necessary to begin by seeking, in a table of natural tangents, the arc 

 which corresponds to the given number, and with that arc Napier's table 

 gives the logarithm. — M, Biot. 



