new Divifion of the Quadrant. 23 
who may have leifure and abilities for it, their kind affiftance, 
either by communicating hints of improvements, or by under- 
taking fome part of the computations, to which they may be 
excited by their zeal for the accomplifhment of fo important a 
work, and by the extreme facility with which the calculations 
in this way are made. © 
2. In the firft place then I would obferve, that I think it 
will be fufficient to print the fines, tangents, &c. to: feven 
places of figures; and that therefore it will be neceflary to 
compute them to ten places, m order effeCtually to fecure the 
truth of the feventh place to the neareft unit. 
2. I would affume the radius equal to 100000; or fuppofe it 
to. be divided into 100000 equal parts. Then it is well. 
known, that the femi-circumference will be 314159°26536. 
nearly, and confequently the quadrant nearly. 157079:63268: 
of the fame equal parts, which is lefs than 157080 by 36732, 
er nearly 2 of an unit, or nearer 2=°375;.or nearer {4p =: 
3636, or ftill nearer 7,="3684, or ftill nearer 14 =-36666 
&c. And the half quadrant, or x of the circle, 78539:81634. 
which is lefs than 78540 by only °18366, or nearly 3 only of: 
any of the above-mentioned fradtions. 
4. The table. may confift of five or more columns; the firft- 
column to contain the regular arithmetical feries of arcs differ- 
ing by unity, from the beginning, .in this manner, 1, 2, 3,.45 55. 
&c. up to half the quadrant, the next lefs whole number: 
being 78539; then for the higher numbers, or thofe in the 
latter half quadrant, befides adding 1 continually, there muft: 
be at the firft added the decimal -63268, which will make alt: 
the numbers in this: half become the exaét complements of. the: 
, firft half, which confifts of whole numbers only; and thefe 
will be the lengths of the arcs. Or, in order to include the: 
| Ze quadrantal: 

