340

construction or

TRACT 21.

which ingenious performance, it seems, was lost, for want ofencouragement to publish it.

A small specimen of such numbers was published in thePhilosophical Transactions for the year 1714, by Mr. Longof Oxford; but it was not till 1742 that a complete antiloga-rithmic canon was published by Mr. Janies Dodson, whereinhe has computed the numbers corresponding to every loga-rithm from 1 to 100000, for 11 places of figures.

TIIACT XXf.

THE CONSTRUCTION OF LOGARITHMS , &C.

Having, in the last Tract, described the several kinds oflogarithms, their rise and invention, their nature and proper-ties, and given some account of the principal early cultivatorsof them, with the chief' collections that have been publishedof such tables; proceed we now to deliver a more particularaccount of the ideas and methods employed by each author,and the peculiar modes of construction made use of by them.And first, of the great inventor himself, Lord Napier.

Napier's Construction of Logarithms,

The inventor of logarithms did not adapt them to the seriesof natural numbers 1,2, 3, 4, 5, &c,as it was not his principalidea to extend them to all arithmetical operations in general;but he confined his labours to that circumstance which firstsuorrested the necessity of the invention, and adapted his lo-garithms to the approximate numbers which express the na-tural sines of every minute in the quadrant, as they had beenset down by former writers on trigonometry.

The same restricted idea was pursued through his methodof constructing the logarithms. As the lines of the sines ofall arcs are parts of the radius, or sine of the quadrant, which