174 Memoir of John Napier, 



methods are also the simplest. He also planned for abridg- 

 ing common calculations a small piece of mechanism com- 

 posed of rulers divided by squares, in which the products of 

 the first natural numbers were written ; this was called 

 Napier's rods or bones. Its application to common calcula- 

 tion is even very limited. Lastly, the author of the new 

 biography has given some extracts of numerical or alge- 

 braical researches found among his papers ; but they pre- 

 sent, in our opinion, only two points worthy of remark. 

 Tbe first is, that Napier had formed perfectly clear notions 

 of the calculation of decimal fractions, and of the appre- 

 ciation of irrational quantities by numerical valuations, 

 more and more approaching the true value, without always 

 being able to express them exactly in finite numbers. The 

 second peculiarity is, that in studying the elevation of 

 numbers to their different powers, we see that he had re- 

 cognized the triangular form under which the co-efficients of 

 the entire binomial powers are arranged, when they are 

 placed consecutively one below the other in their consecu- 

 tive powers, a remark, which, it was considered, belonged 

 to Pascal, who used it, like Napier, for the elevation of 

 powers, and the extraction of roots. But Pascal did not 

 publish it till 1665; so that in reference to the invention, 

 at least, Napier preceded him. 



The Scotch biographer concludes from this, that if Napier 

 had lived longer, he probably would have discovered before 

 Newton the Binomial theorem, or even the differential 

 calculus, and he pushes this idea of superiority so far 

 that he makes the remark, that Newton having never 

 been married could devote all his life to intellectual labour, 

 while the Scotch philosopher, as he calls him, had two 

 wives and 12 children. We think it sufficient for Napier 

 to have discovered the logarithms. But we shall finish this 

 abstract by a curious enough approximation. We have 

 often occasion to observe in literary history, that the same 

 inventions, the same discoveries, with slight shades of dif- 

 ference, present themselves at the same time to several dis- 

 tinguished minds, without any communication between 

 them. It proceeds from the circumstance, that these new 

 ideas are, so to speak, prepared and produced by the dis- 

 cussion of preceding ideas, from which they are derived. 



