424 THIRD REPORT 1833, 



Whence the strength of a rectangular piece of cast iron 

 drawn along the side is rather more than one third of 7-§- 

 tons, its strength, as above found, to bear a central strain 



for «;^r > i) ; l>ut from the preceding remarks it ought 



only to be one fourth ; and, therefore, it would appear that a 

 shifting of the neutral line had made the pieces capable of 

 bearing a greater force along the side than in their natural 

 state. 



An Investigation of the Principle of Mr. Saxtons locomotive 

 differential Pulley, and a Description of a Mode of pro- 

 ducing rapid and uninierrii'pted Travelling, by means of a 

 Succession of such Pulleys, set in Motion by Horses or by 

 stationary Steam-engines. By John Isaac Hawkins. 



In order to a clear understanding of the operation of this 

 differential pulley, in the propelling of carriages or vessels, it 

 will be convenient to view the principle under three cases. 



Case 1st. Let the bottom spoke or radius of a wheel, roUing 

 on a horizontal plane, be considered as a lever. 



Let the point of contact of the wheel with the plane be the 

 fulcrum of the lever. 



If a cord be fastened at one fourth of the length of the 

 lever above the fulcrum, and it be pulled a given distance, (say 

 one inch,) then the top of the lever or axis of the wheel will 

 be moved in the same direction four times the distance, or four 

 inches, agreeably with the common doctrine of the lever. 



If now a pulley be concentrically affixed to the wheel, and 

 the circumference made to meet the point in the lever where 

 the cord is fastened ; in other words, if the pulley be three 

 fourths of the diameter of the wheel, and the cord be wound 

 around the pulley, and be drawn horizontally in the vertical 

 plane of the pulley, then the wheel will run along the hori- 

 zontal plane in the direction of the pull with a velocity equal 

 to four times the speed of the cord, because every point of 

 the circumference of the wheel as it comes in contact with the 

 plane becomes a new fulcrum, and the perpendicular line from 

 that point to the axis becomes a new lever, upon which the 

 cord acts at one fourth of the length of the lever above the 

 fulcrum, and thus a repetition of such leverage is continually 

 brought into action as the cord is drawn along. 



Case 2nd. Let the point where the periphery of the pulley 

 meets the spoke or lever, and where the cord of Case 1. was 

 attached, be considered the fulcrum ; and let another cord be 



