Theory of Machine
For an isochronous Hartnell governor (where r₁ and r₂ = Maximum and minimum radius of rotation of balls respectively, S₁ and S₂ = Maximum and minimum force exerted on the sleeve respectively, and M = Mass on the sleeve)

S₁/S₂ = r₁/r₂
(m.g - S₁)/(m.g - S₂) = r₂/r₁
(m.g + S₁)/(m.g + S₂) = r₁/r₂
S₂/S₁ = r₁/r₂

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Theory of Machine
Hammer blow

Varies as the square root of the speed
Is the maximum vertical unbalanced force caused by the mass added to balance the reciprocating masses
Varies inversely with the square of the speed
Is the maximum horizontal unbalanced force caused by the mass provided to balance the reciprocating masses.

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