MT. PLEASANT COAL AND IRON COMPANY. 219 4 



The tangent of angle of minimum grade of a self-acting 

 gravity-incline when all resistances of gravity and friction 

 are considered, equals 



C (W + w + r) x - 



cos a 



\V (w + r) 



If there is not much to spare above the necessary grade, 

 there should be a short piece of level track at the bottom of 

 the incline, and if necessary a heavier grade at the top, so that 

 the waggons can start easier. It is best practice to have the 

 grade as nearly uniform as possible. Anyhow, there should not 

 be too sudden a change in level, or else( the waggon, when 

 passing from a steep grade to a lighter one may have the 

 upper wheels lifted off the track by the rope. The frictional 

 resistance encountered in starting from a state of rest mav 



Fig 139. The Quimby Screw Pump. 



be taken as at about twice the friction of motion. If the- 

 grade is made greater at the top and lighter at the bottom, the 

 speed due to acceleration will dimmish, as the motive force- 

 varies with the size of the angle of inclination ; the inertia 

 carries the waggons over the flat portion. 



Ventilation is carried out with the assistance of a 14-foot 

 Walker's fan. 



One of the pumps in this mine is a Quimby screw, driven 

 by electricity. The dynamo for this purpose is also used for 

 generating the light required about the place. The pump, as 

 shown in Fig. 139, consists of four screws mounted in pairs 

 on parallel shafts, and so arranged that in each pair the 

 thread of one screw projects to the bottom of the space be- 

 tween the threads of the opposite screws. The screw threads 



