TRACT 29.

BIVISION OP THE QUADRANT.

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sub-divisions by the moderns, among various uses, servesfor trigonometrical and other mathematical operations, by-adapting to those divisions of the arc, certain lines ex-pressed in equal parts of the radius, as chords, sines, tan-gents, &c. But among all the improvements in this usefulbranch of science, I have long wished to see a set of tablesof sines, tangents, secants, &c, constructed to the arcs ofthe quadrant, as divided into the like equal parts of the ra-dius as those lines themseives. In this natural way, the arcswould not be expressed by divisions of 60tbs, in degrees,minutes, &c, but by the common decimal scale of num-bers ; and the real lengths of the arcs, expressed in suchcommon numbers, would then stand opposite their respec-tive sines, tangents, &c. The uses of such an alterationwould be many and great, but are too obvious and import-ant to need pointing out or enforcing. I have therefore hadfor a long time a great desire to commence this arduoustask; but continual interruptions have hitherto preventedme from making any considerable progress, in so desirablean undertaking. But I am not without hopes that somefuture occasion may prove more propitious to my ardentwishes. It is not however to be expected, that this workcan, be accomplished by the labours of one person only ; itwill require rather the united endeavours of many. I shalltherefore explain a few particulars relative to my project ofthis work, with a view to obtain from others, who may haveleisure and abilities for it, their kind assistance, either byrcominunicat.ing hints of improvements, or by undertakingsome part of the computations, to which they may be ex-cited by their zeal for the accomplishment of so importanta work, and by the extreme facility with which the calcula-tions in this way are made.

2. In the first place then I would observe, that I think itwill be sufficient to print the sines, tangents, &c, to 7 placesof figures; and that therefore it will be necessary to com-pute them to 10 places, in order effectually to secure thetruth of the 7th place to the nearest unit.