TRANSACTIONS OF THE SECTIONS. 425 



applied to the bottom end of the lever. If this lower cord be 

 drawn horizontally in the same vertical plane, but in the op- 

 posite direction to that in which the former one was pulled, 

 then the top of the lever or axis of the wheel will be moved 

 in the same direction as before, three times the distance that 

 the cord passes through : thus, if the cord be pulled one inch, 

 the axis will be moved three inches, because the leverage is 

 in this case as three to one. Let the pulley be made to roll 

 along a horizontal plane, and the cord be passed around a 

 wheel concentrically attached to the pulley by the side of the 

 plane, the radius of which wheel is equal to the whole lever, 

 as was the wheel of Case 1 . ; then the cord being passed around 

 that wheel, and pulled, the pulley will run along the plane with 

 three times the velocity of the cord that draws the wheel, but 

 the motion will be in a direction opposite to the pull. 



Case 3rd. Let both the cords of Case L and Case 2. be 

 pulled at the same time, (say each one inch,) then the fulcrum 

 will necessarily be removed to a point exactly half-way between 

 the two cords, which fulcrum will be at one eighth of the length 

 of the lever from the bottom end ; and the top of the lever or 

 common axis of the wheel and pulley will, in this case, be 

 moved seven inches, being seven times the distance through 

 which the cords pass. The ratio of the velocity of the axis to 

 the cord is as the sum of the two radii of the pulley and wheel 

 divided by their difference. 



Now fix a spindle in the axis, and support it on a four- 

 wheeled travelling carriage, or on a vessel afloat upon water, 

 and make a groove in the wheel to constitute it a pulley, and 

 pass a cord around each pulley in opposite directions, and 

 pull both cords with equal speed, then the carriage or floating 

 vessel will be propelled with seven times the velocity of the 

 cords, in the direction in which the cord of the smaller pulley 

 is drawn, because the axis of the pulleys or top of the lever 

 is seven eighths of the whole length of the lever above the 

 fulcrum, and the two cords act at one eighth of the length of the 

 lever above and below the fulcrum, which, in every part of the 

 revolution of the pulleys, remains perpendicularly under the axis, 

 at a height half-way between the bottom ends of the radii of 

 the two pulleys. But if instead of the two cords being at- 

 tached to the pulleys, an endless cord be stretched around two 

 riggers, placed at some considerable distance from each other, 

 and one side of the cord be made to take one turn around one 

 pulley, and the other side of the cord one turn also around the 

 other pulley, then the cord being drawn at either side or either 

 end will cause the pulleys to revolve, and the carriage or vessel 



