Lever force F at a point "A" located by the coordinate vector r on the bar. The lever then exerts an output force F at the point "B" located by r. The rotation of the lever about the fulcrum "P" is defined by the rotation angle "θ" in radians. Let the coordinate vector of the point "P" that defines the fulcrum be r, and introduce the lengths which are the distances from the fulcrum to the input point "A" and to the output point "B", respectively. Now introduce the unit vectors e and e from the fulcrum to the point "A"
Darcy Lever that Levers daughter had inherited them and thus they passed to her husband John Bradshaw. However the land came to them, the family estate grew and today they continue to hold large parts of the Bolton area. At this time, 1666, Robert Lever had eight hearths liable to tax, James Bradshaw and John Crompton had seven each and Lawrence Fogg six. The rest of the township was made up of 12 more heaths. The land-tax return of 1786 shows that James Bradshaw and John Peploe Birch were the chief proprietors of Darcy Lever, between them they paid about half the