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[[right corner]] (148 [[/right corner]]
A computation of the powers in an Eight-Day Clock.

[[indent]]
 [[title over number]] Inches [[/title over number]] 
Put a = 2 =
    b = 3 =
    c = 2 =
    d = 1,9 =
    e = 1,8 =
    α = 3/8 =
    β = 2/8 =
    γ = 1,9/7 =
[[bracketed above, a-γ]] 
the Diameter of the 

[[open bracket, a-e]] 
Barrel & Semidiam. of the line together
1 [[superscript]] st [[/superscript]]
2 [[superscript]] nd [[/superscript]]
3 [[superscript]] rd [[/superscript]]
Swing [[/open bracket, a-e]]
[[bracket 1st-Swing]] Wheel. [[/bracket 1st-Swing]]

[[open bracket, α-γ]]
of the pinion driven by the
[[open bracket]] 
1 [[superscript]] st [[/superscript]]
2 [[superscript]] nd [[/superscript]]
3 [[superscript]] rd [[/superscript]]
[[/open bracket]]
[[bracket 1st-3rd]] Wheel. [[/bracket 1st-3rd]]
[[/open bracket, α-γ]]

[[/bracketed above, a-γ]]

    f = 1,44 =
    g = 3,75 =
[[open bracket, f-g]]
The distance of
[[open bracket]] 
each Palet
the Crutch
[[/open bracket]]
[[bracket Palet,Crutch]] 
from the center of its axis. [[/bracket Palet,Crutch]]
[[/open bracket, f-g]]

n=7½.# The weight supported or acting on the barrel a.

[[/indent]]

Then by Mechanics, reciprocally, 
a:n:b:an/b=5#.  the power on the 1 [[superscript]] st [[/superscript]] Wheel or on the pinion it drives.
α:an/b::c:αan/bc=15/16#=,9375#; the power on the 2 [[superscript]] d [[/superscript]] Wh. or the pinion it drives.
β:αan/bc::d:αβan/bcd=300/2432#=,1234#; the power on the 3 [[superscript]] d [[/superscript]] Wh. or on the pinion D. [[superscript]] o [[/superscript]]
γ:αβan/bcd::e:αβγan/bcde=28500/1532160#=,018601#, the power on the swing Wheel, or on each Palet.
f:αβγan/bcde::g:αβγanf/bcdeg=,0071428#=1,8286 Drams, the power communicated to the Rod of the Pendulum by the Crutch.

Here it is evident, the weight n is decreased by g, the length of the Crutch, exceeding f, the distance of each palet, in the ratio of 3,75 to 1,44 or of 2,604 to 1.(*)  I therefore would [[strikeout]] enlarge the palet wheel & the distance of each palet, but [[/strikeout]] shorten the Crutch, till there was no more [[insertion]] length of [[/insertion]] Spring than just sufficient to permit the pendulum to swing free; [[strikeout]] how long [[/strikeout]] This length of Spring can only be determined by experiment: Hereby a much less weight would serve, & consequently greatly diminish the Friction through the whole Clock.  [[smaller handwriting]] Instead of the common pendulum hanging by a Spring, (which is subject to irregularities by heat & cold, dry and moisture,) I would propose, in the annexed fig. AB, part of the back plate or frame, to which the cock CDEF is screwed: At G & H is triangular holes for [[insertion]] IK [[/insertion]] the axis or arbor of the palets I,M, to work in.  To this arbor IK, [[strikeout]][[?]][[/strikeout]] at N, [[strikeout]][[?]][[/strikeout]] is fixed the Crutch NOP.  That part [[insertion]] QS [[/insertion]] of the pendulum QRSVT [[strikeout]][[?]][[/strikeout]] above the bottom of the crutch OP, is a screw, going tight through a hole at R in the axis IK, and raised or let down by a nut w bearing against the arbor IK, and carrying an index round a plate of divisions to estimate [[strikeout]][[?]][[/strikeout]]  the quantity.  That part SV, below the crutch is circular for the crutch to work upon.  But how far the friction here is greater than the power to bend the spring, experiment can only determine. [[/smaller handwriting]]

[[image of clock]]

[[left margin notes]]
In this computation the power on the swing-wheel is supposed to act upon the pallets and drive them with all that power in a tangent to the circle which the acting point would describe round their arbor: which is not true.

(*)if the center of suspension, from which the rod & ball of the pendulum are pendent, is fixed, no length of the crutch will alter the power. [[/left margin notes]]

Transcription Notes:
# is pounds, I think.