^ ' Mr Adamson on Rail-Roads. 



rope, rollers, &c. -it will have 147 ft), as the friction of the rope, 

 and the smaller rollers on which it rests. This is at the rate of 

 S62 tb. per mile, and equal to about one-fifth of the strain to 

 which the rope was exposed ; and therefore the utmost strain to 

 which, from this example, a similar rope ought to be exposed, 

 is the friction of 5 miles of rope of the same thickness, resting 

 on the same proportion of rollers of the same weight. If we 

 make m represent the distance at which the expenditure of 

 power. in overcoming the friction of the rope by the fixed en- 

 gine is equal to that expended by the locomotive engines, in 

 moving themselves, and let t represent the strain upon the rope, 

 or power of the fixed engine, independent of its own friction, 



— will be, in this case, the resistance of the rope of the fixed 

 5 



engine, and will represent the friction of the locomotive engines ; 



and, assuming that their friction is half the power available to 



move the load, or one-third of the power of the engine, then 



-— =- ; hence w — II, the distance in miles. As the un- 



certain amount of the friction of the fixed engine and its rope^ 

 roll has not [been taken into account, we may perhaps con- 

 clude, that the moving of goods by means of a rope of a greater 

 length than 1^ miles, will always be more expensive than their 

 conveyance by locomotive engines, when there is no ascent on 

 the line. To find the more general formula for an ascent, we 

 must make the gravitating force of the load and of the rope to 

 become elements in the equation. Now, as the weight of the 

 rope per mile is nearly three times the strain to which it is sub- 

 jected, making sin i to represent the inclination, 3 ^ sin i wiU be 



\he gravitating force of the rope ; hence m' x f - + 3 f sin i 1 



will represent the whole loss of force incident to the fixed en- 



gine, from the weight and friction of the rope. Now, as ^j ^ is 



the progressive effort or adhesion of the locomotive engines, 



^5 X ai will be their weight; and the loss of power incident tb 



.them, which is to be equal to that lost by the fixed engines, ac- 



coi'ding to the foregoing deductions, will be ^ f 1 -)- 50 sin « ); 



