Memoirs of John Napier of MerchisUm. 271 



only the laborious were and might still have been doomed, but 

 even such geniuses as Copernicus and Kepler; and this, too, 

 without relieving, by that immense and irreparable sacrifice of 

 time, their successors from toil, the very same, or more painful 

 still, in proportion to the advance of applicate science. To libe- 

 rate the mathematical sciences from chains so grovelling — to 

 liberate them for ever — thus to sweep from the path of genius 

 every obstacle to the immediate realization of all her conceptions 

 dependent upon numbers — behold the triumph of the Logarithms ! 

 and that species of emancipation has already had, and will for 

 ever have, an influence over the progress of human knowledge 

 too great not to incite us to the attempt of here rendering intel- 

 ligible, to every attentive mind, how it was that Napier realized 

 an invention so marvellous. 



The Scotch biographer has felt with us the necessity of ful- 

 filling this task. Unfortunately, however, his zeal for his an- 

 cestor and his countryman could derive little aid in this attempt, 

 from the writings of mathematicians, even of those whose special 

 design was the history of mathematics. For by a fatality, al- 

 most inseparable from those inventors whose fortune it has been 

 to awaken the very train of improvement by which their own 

 discoveries are subsequently brought to perfection, no one, now- 

 a-days, reads Napier's original work, entitled Mirifici Logarith- 

 morum Canonis Description published in 1614, wherein he ex- 

 pounds the mode of generation he assigns to those new quantities 

 named by him artificial numbers or logarithms ; to which he 

 adds their affections or numerical properties involved in the defi- 

 nition ; their use in the simplification of arithmetical calculations, 

 when it is necessary to multiply numbers together, or to divide 

 one by the other ; their application in the resolutions of trio-o- 

 nometry and astronomy ; and, lastly, the numerical tables, con- 

 taining the logarithms of the trigonometrical lines, termed si7ius, 

 cosinus, tangentes, secantes, calculated from minute to minute 

 through the whole degrees of the quadrant, which must have 

 cost him an inconceivable physical labour, independently of the 

 invention. All this is given without explication, without any 

 opening as to the train of ideas which had led him to conceive 

 the admirable utility of these tables, no more than he gives us 

 with regard to the means he had employed for the calculations. 



