PHYSICAL AND MATHEMATICAL SCIENCES. 1 <)3

mirificus Logarithmoram” in the form he had originallyplanned in 1614; and left to Briggs the task, which hesubsequently brought to perfection, of calculating a newset of tables, upon another system or series, with a dif-ferent base, which presented many practical advan-tages.

The great principle of Napier’s invention is of sucha nature as must always claim admiration for its sin-gular combination of simplicity and power; but wecannot appreciate his full merit without recollecting thestate of algebra in his time. The general theory ofindices was hardly at all understood: nor were theforms of series investigated so as to afford him anyfacilities for his calculations. Hence, to conceivethe fundamental idea that all numbers might be re-garded as some powers of one given number, and todevise the actual means of finding the indices qf thosepowers, must be allowed to have been indications ofgenius of the highest order. The existing state ofknowledge had by no means prepared the way for anysuch conceptions; and all the means of perfectingthem were supplied from the original resources of theinventor’s powerful mind. In another respect, too, thisinvention has been remarkable: most other discoverieshave been produced at first in a comparatively crudestate from the hands of their inventors, and have sub-sequently received their perfection from the successivelabours of those who trod in the footsteps of the ori-ginal discoverers; but the system of logarithms cameout of the hands of its author so perfect, that it neverreceived but one material improvement; and that itderived, as has been just remarked, from the ingenioussuggestions of the illustrious inventor’s friend, in con-junction with his own. Subsequent advances in science,instead of superseding this invention by better methods,have only enlarged the circle of its applications, andgiven more extensive confirmation of its utility.

The originality of the conception by which Napierillustrated his idea, and on which he founded hiso