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III. A farther Examination of the Machine's ^ f aid 
to he without FriBion, the fame. 
A t the laft Meeting of the Society, I fliew’d the 
Inconveniency of Monf. PerauJf% new kind of 
j 4 xis in Peritrochio^ or Roller fix’d into a large 
Fully ^ Ihewing not only, that by the Ufe of this 
Engine we inuft lofe Force, whofe Value is feldom 
to be recompens’d by the Time we gain, but alfo 
that the Stiffnefs of the additional Ropes which wind 
about the Roller, in the Operation, gives more than 
double ( fometiraes than ’ triple or quadruple )’ the 
Fridion of the fame Engine us’d in the common Way, 
when the Pivot, or Iron Axis, is in Diameter the 
twelfth Part of the Diameter of the Roller, dr wooden 
Axel. 
■ But as fome have endeavour’d to render this En- 
gine more ufeful, by caufing it to roll up an inclin’d 
Plane, inftead of making it rife diredly up in the 
Manner defcrib’d, and condemn’d in my former Paper j 
I thought proper to fhew here what muft be the Lofs 
of the Power in Proportion to the Inclination of the 
Plane. 
I fay therefore, that in every Inclination of the Plane, 
if the Sine of the Angle of Inclination be taken in 
Parts of the Radius of the Axel, or Roller, the Power 
will be to the Weight : : as the Radius of the Roller -f- 
the Sine of Inclination, to the Radius of the Wheel — 
the faid Sine of Inclination that is, in the Figure, P 
(= i) ;W (=: 3) ::dk:ak. (See Fig. 4.) 
In 
