10 DISSERTATION SECOND. - [part i. 



thor of authors," would have gradually brought to light. 

 Though logarithms had not been invented by Napier, they 

 would have been discovered in the progress of the alge- 

 braick analysis, when the arithmetick of powers and expo- 

 nents, both integral and fractional, came to be fully under- 

 stood. The idea of considering all numbers, as powers of 

 one given number, would then have readily occurred, and 

 the doctrine of series would have greatly facilitated the cal- 

 culations which it was necessary to undertake. Napier 

 had none of these advantages, and they were all supplied 

 by the resources of his own mind. Indeed, as there never 

 was anv invention for which the state of knowledge had less 

 prepared the way, there never was any where more merit 

 fell to the share of the inventor. 



His good fortune, also, not less than his great sagacity, 

 may be remarked. Had the invention of logarithms been 

 delayed to the end of the seventeenth century, it would 

 have come about without effort, and would not have con- 

 ferred on the author the high celebrity which Napier so 

 justly derives from it. In another respect he has also been 

 fortunate. Many inventions have been eclipsed or obscur- 

 ed by new discoveries ; or they have been so altered by 

 subsequent improvements, that their original form can hard- 

 ly be recognised, and, in some instances, has been entirely 

 forgotten. This has almost always happened to the disco- 

 veries made at an early period in the progress of science, 

 and before their principles were fully unfolded. It has been 

 quite otherwise with the invention of logarithms, which 

 came out of the hands of the author so perfect, that it has 

 never received but one material improvement, that which 

 it derived, as has just been said, from the ingenuity of his 

 friend in conjunction with his own. Subsequent improve- 

 ments in science, instead of offering any thing that could 

 supplant this invention, have only enlarged the circle to 



