In the particular case where the motion is of the kind known as simple harmonic the disturbing force on the frame due to the reciprocation of the weight is equal to the component of the centrifugal force in the line of stroke due to a weight equal to the reciprocated weight supposed concentrated at the crank pin.
He bases all moral phenomena on five facts: - (i) Man is susceptible to pleasure (and pain); (2) he likes (or dislikes) their causes; (3) he desires to reciprocate pleasure and pain received; (4) he expects such reciprocation from others; (5) he feels more or less sympathy with the same feelings in his fellows (Letters, 3rd series).
In practice reciprocation is usually effected through a connecting rod, as in the case of steam engines.
Although this method balances the pistons in the horizontal plane, and thus allows the pull of the engine on the train to be exerted without the variation due to the reciprocation of the pistons, yet the force balanced horizontally is introduced vertically and appears as a variation of pressure on the rail.
A focus or directrix is equal to two conditions; hence such problems as: given a focus and three points; a focus, two points and one tangent; and a focus, one point and two tangents are soluble (very conveniently by employing the principle of reciprocation).