112 Observations on Inclined Planes, 



" Experiment 27th.~ Boulton and Watt's low pressure condensing 

 engine, with two thirty inch cylinders, steam 4^ lbs. per square inch 

 above the pressure of the atmosphere, weight of rope 6967 lbs., 

 sheaves 10278 lbs., rope-roll 8960 lbs., length of plane 2646 feet, 

 height 154-J feet. Time of drawing up seven loaded carriages, each 

 weighing 9408 lbs., six hundred and twenty seconds, the engine 

 making three hundred and seventy four single strokes, five feet each." 

 Here we have/=294, and 'F=^^\{k-{-m-\-p)=^Q^b, or more accu- 

 rately, by a previous experiment on a plane precisely similar, we 

 have F=6861bs. Hence by (M) the resistance overcome by the 

 engine is R= 1288960 lbs., the power of the engine is 4988738 lbs. 

 whence we have the effective power of the engine upon the load, 

 compared with the pressure of the steam upon the piston, equal to 

 25.8 per cent., nearly the same as obtained by the author. 



" Example. — Suppose an inclined plane, one thousand yards in 

 length, height sixty feet, up which a train of eight loaded carriages, 

 each weighing 9408 lbs., is required to be drawn by an engine on 

 the summit, in three hundred seconds, with a rope weighing 4065 

 lbs., sheaves 6000 lbs., rope-roll 4500 lbs., while at the same time 

 the same number of empty carriages, each weighing 3472 lbs. are 

 descending j required the power of the engine." Here we have 

 /=515, and by (K) F=315 lbs., hence by (S) we have P=32^ 

 horses' power. Mr. Wood gives in this case P=33^ for the power 

 of the engine, the two results differing by | of a horse power. 



It will be seen from the above examples, that the results of the 

 equations given, do not differ greatly from those derived from the 

 equations of Mr. Wood ; and the facility of using them is much great- 

 er. Strict accuracy is unattainable in questions of the above kind. 

 The friction of the moveable parts of the apparatus on an inclined 

 plane, and other circumstances may so vary, that it would be impos- 

 sible to give equations that would meet with accuracy every case that 

 may be presented in practice. 



The reduction of friction is of the greatest importance in rail road 

 improvements. We have had no accurate experiments for ascertain- 

 ing the amount of friction on curved rail ways. In order to reduce 

 this kind of friction, various plans have been proposed and tried. 

 The exterior wheel has been enlarged by causing it to run on its 

 flange while passing a curve ; sometimes the conical wheel has been 

 adopted to answer the same purpose ; and it has been proposed, in 

 order to avoid the inconvenience of the conical wheel, to suffer one 

 of a pair of wheels to turn freely on its axle. That the first method 



