kct. i.J DISSERTATION SECOND. 39 



gression, and by which he found the places they must oc- 

 cupy, was founded on a most ingenious supposition, — that 

 of two points describing two different lines, the one with a 

 constant velocity, and the other with a velocity always in- 

 creasing in the ratio of the space the point had already 

 gone over : the first of these would generate magnitudes in 

 arithmetical, and the second magnitudes in geometrical pro- 

 gression. It is plain, that all numbers whatsoever would 

 find their places among the magnitudes so generated ; and, 

 indeed, this view of the subject is as simple and profound 

 as any which, after two hundred years, has yet presented 

 itself to mathematicians. The mode of deducing the results 

 has been simplified ; but it can hardly be said that the prin- 

 ciple has been more clearly developed. 



I need not observe, that the numbers which indicate the 

 places of the terms of the geometrical progression are call- 

 ed by Napier the logarithms of those terms. 



Various systems of logarithms, it is evident, may be con- 

 structed according to the geometrical progression assumed ; 

 and of these, that which was first contrived by Napier, 

 though the simplest, and the foundation of the rest, was 

 not so convenient for the purposes of calculation, as one 

 which soon afterwards occurred, both to himself and his 

 friend Briggs, by whom the actual calculation was per- 

 formed. The new system of logarithms was an improve- 

 ment, practically considered ; but in as far as it was con- 

 nected with the principle of the invention, it is only of se- 

 condary consideration. The original tables had been also 

 somewhat embarrassed by too close a connexion between 

 them and trigonometry. The new tables were free from 

 this inconvenience. 



It is probable, however, that the greatest inventor in sci- 

 ence was never able to do more than to accelerate the pro- 

 gress of discovery, and to anticipate what time, " the an- 



