206 



Description of the Newcastle Dynamometer. 



The spring S in the position shown exerts no force, but is 

 capable of being urged forward until the pulley ]M would arrive 

 at e ; and if in the latter position it exerted a force, say of 100 lbs., 

 at a its force would be 20 lbs,, at h 40 lbs., at c 60 lbs., and at 

 d 80 lbs. 



We will suppose that a wire-rope attached to a steam-'engine 

 passes partly round the pulleys A, JNI, and B, dragging a plough 

 or other implement attached to the end of the rope beyond B. It 

 will be at once perceived that the force of the engine and the re- 

 sistance of the implement, acting in opposite directions, will cause 

 the spring S to be deflected towards J", and when the force of the 

 engine, the resistance of the implement, and the resistance of the 

 spring S are in ecjuilibrium, then the slightest further addition to 

 the force employed will cause the implement to move, the spring 

 to yield, antl the pulley j\I to move in the direction M y". For 

 any assigned position of the pulley M, the amount of the forces 

 of traction and resistance may be ascertained by the formula 



a/ 17} " I 7/ " 



' X ^ = F. Where m = the distance A/ (Fig. 2), 



71 = the distance between M and J', at whatever point M may be 

 found ; t = the resistance of the spring S at that point ; and F 

 = the forces of traction and resistance equal the strain on the 

 wire-rope. For example, if M assumes the position c (Fig. 2), 

 in which case the resistance of the spring is GO lbs., then MJ' = 



Then^lQf +/ X00 = 

 2x6 



540*8 lbs. ^ F = the strain on the rope ; and similarly for other 

 positions of M. The following Tabic exhiljits the different magni- 

 tudes ol the strain or tension of the rope corresponding to the 

 various positions a, b, c, d, c. 



6 inches, and Af = 108 inches. 



It is important to observe that the strain of the rope does not 

 Aary proportionally to the distance of ]M from its original posi- 

 tion, or, what is the same thing, proportionally to the resistance 

 of the spring. If a scale of numljers were inserted instead of the 

 letters a, h, c, d, e,f, and an index placed on the spring at JVI, the 



strain 



