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45)
[[right margin notes not related to text]]
No electric Fire without Air.


Fire goes [[underline]] from [/underline]] the Body Electrified; and acts according to the solid particles and not the Surface of Matter.


Densest bodies contain most Fire, which is confined only by Air; thence the [[underline]] Hutchinsonian [[/underline]] cause of Attraction of Cohesion. V.p. 48.
[[/margin]]

[[left margin]] The Chord of 1°. adapted to several Radii for the Making of a Quadrant
[[/ margin]]

[[Table: read in the following way: "If the [[insertion]] Arch [[/insertion]] [[strikethrough]] Chord [[/strikethrough]] of 1°. be 
[[strikethrough - illegible]]" (number from left column) "The Radius of the Quadrant will be" (number from right column)]]

[[left column header]] Inches [[/header]]
[[right column header]] Inches [[/header]]

[[left column]]---[[right column]]
{,1}---{5,729578}
{,2}---{11,459156}
{,3}---{17,188734}
{,4}---{22,918312}
{,5}---{28,647890}
{,6}---{34,377468}
{,7}---{40,107046}
{,8}---{45,836624}
{,9}---{51,566202}
{1,}---{57,29578}
{1,5}---{85,94367}
{2,}---{114,59156}
{2,5}---{143,23945}

[[Table: read in the following way: "If the chord of 1° be" (number from left column) "the Radius of the Quadrant will be" (number from right column)]]

{,1}---{5,72965}
{,2}---{11,45930}
{,3}---{17,18895}
{,4}---{22,91860}
{,5}---{28,64825}
{,6}---{34,37790}
{,7}---{40,10755}
{,8}---{45,83720}
{,9}---{51,56685}
{1,}---{57,29650}
{1,5}---{85,94475}
{2,}---{114,593..}
{2,5}---{143,24125}
[[/tables]] 

[[left margin]]
Any Space, its No. of Divisions, & ^ [[insertion]] a [[/insertion]] subdivision [[strikethrough]] s [[/strikethrough]] by a Nonius; any two being given to find the third.
[[/margin]]
Let S be = any space AB, n = number of divisions in it, and X = one of the subdivisions which S or the space AB is required to be divided into by a Nonius ^ [[insertion]] CD [[/insertion]] [[strikethrough]] gh [[/strikethrough]]; then S/n = ^ [[insertion]] AB = [[/insertion]] one division of S; and S/(n±1) = [[strikethrough]] ^ [[insertion]] ab = [[/insertion]][[/strikethrough] One division upon the Nonius [[strikethrough]] CD ^ [[insertion]] ag [[/insertion]] [[/strikethrough]] [[insertion]] CD [[/insertion]]; [[three dots indicating "because" ]] S/n ~ S/n±1 = X. whence, by reduction, x = ([[overbar indicating average]]Sn±S [[/overbar]] ~ Sn)/(n^2±n) = S/(n^2±n); S = [[overbar indicating average]] n^2±n [[/overbar]] x X; and n = [[illegible strikethrough]] √ (S/x ± 1/4)  [[inverted ±]] 1/2   •  Q.E.F.
V. page. 41.

[[two diagrams]]
[[red ink]]Limb. Nonius.[[/red ink]]
[[strikethrough]]I.[[superscript]]st[[/superscript]] kind & + [[/red ink]][[/strikethrough]]
[[a rectangle divided into two rows of rectangles, 10 above and 11 below, the top row in red ink and labeled A and B on the left and right ends respectively, and the bottom row in black ink and labeled C and D at the ends]]
[[red ink]]I.[[superscript]]st[[/superscript]] kind & + [[/red ink]]

[[red ink]]Limb Nonius.[[/red ink]]
[[a rectangle divided into two rows of rectangles, 10 above and 9 below, the top row in red ink and labeled A and B on the left and right ends respectively, and the bottom row in black ink and labeled C and D at the ends]]
[[red ink]]II.[[superscript]]nd[[/superscript]] kind & - [[/red ink]]

[[right margin]]
[[red ink]] Subdivisions of a Nonius [[/red ink]]
Each degree of the limb AB, divided into 3 equal parts, each will be 20'. then 19 of these laid upon the index CD, and divided into 20 equal parts, each of these will be 19' – Now the distance of these 19 parts upon the index CD, then 1' more either added or taken away, in the former case as many times 3" must be subtracted, or in the latter added, as the coincident divisions of the Nonius points out to be added to the last 20.'
[[/right margin]]

Various Methods of obtaining a true MERIDIAN LINE.
Sir Christopher Wren's Contrivance (in the Philosop. Trans. No. 291. Vol. IV. p. 464. of Jone's Abridg[men]t) is thus, 
At one end of a ruler, erect a sight, to see the pole star, &c. thro.' At the other end set up two circles of small wire, one within the other; the diameter of the innermost, equal to the double tangent of the distance of the pole-star from the pole, the distance of the sight being radius; and the diameter of the outermost circle, 
Continued on p. 47.

Transcription Notes:
In the paragraph with the mathematical equations, I have added parentheses according to modern convention in order to clarify grouping in numerators and denominators correctly. In the paragraph about the subdivision of the nonius, the writer quite consciously uses a back-sloping apostrophe (i.e, an accent grave) after the numbers sort of like we would use apostrophes for feet and inches (i.e. 5'10"). -edited tables for clarity, please check -megshu (Checked by Heather W.) Everything looks perfect except for one missing semi-colon, now added. HW