RAILWAY CONSTANTS. 235 



In the first experiment the motion was continually accele- 

 rated, until the train passed to the succeeding gradient. The 

 acceleration was rapid at first, but gradually lessened as the 

 speed increased, proving a continual augmentation of the re- 

 sistance. For the last thousand yards of the plane, the accele- 

 ration became very small in amount, showing a tendency to an 

 uniform speed, and therefore to an equality between the moving 

 force and the resistance. 



In the second experiment, the train being started from the 

 fifty-seventh stake, a more extensive space was allowed for the 

 action of the gravity of the inclined plane. Throughout the 

 first 3300 yards the motion, as nearly as possible, corresponded 

 with tlie motion of the train in the first experiment, the velo- 

 city at corresponding posts being neai'ly the same. The rate 

 of acceleration, as before, gradually diminished, until the train 

 arrived at the twenty-eighth stake, from which to the foot of 

 the plane the motion was sensibly uniform. From the twenty- 

 eighth to the eighteenth, the rate of motion is 100 yards in a 

 small fraction above 12 seconds, and from the eighteenth stake 

 to the foot of the plane the motion is uniformly 100 yards in 12 

 seconds, being at the rate of 25 feet per second, or 17 miles an 

 hour. 



Hence it follows, that with this train of five wagons, weigh- 

 ing 30 tons gross, with high sides, and presenting a frontage of 

 47" 8 square feet, the whole resistance, at a speed of 17 miles an 

 hour, was equal to yfiyth part of its weight, or 377 lbs., being 

 at the rate of 12*6 lbs. per ton. 



In the third experiment, in which the high sides of the wa- 

 gons were taken down so as to reduce the frontage or end sur- 

 face of the train to 23*8 square feet, the motion continued to be 

 accelerated to the foot of the plane ; but for the last 1000 yards 

 the acceleration is so little as to be barely sensible. There is 

 a tendency to an imiform velocity of 100 yards in 9 seconds, or 

 33*3 feet per second, being at the rate of 22| miles per hour. 



If this be assumed as ti>e uniform velocity which the train 

 would have attained had the plane preserved an uniform incli- 

 nation for a sufficient distance, it will follow that its resistance 

 at this speed, with the reduced frontage, was equal to its resist- 

 ance at 17 miles an hour with the larger frontage. 



Thus, with the same expenditure of tractive power, a dimi- 

 nution of frontage in the ratio of 2 to 1 nearly gives, in this case, 

 an increase of speed in the ratio of only 25 to 33*3. 



After descending the plane of 1 in 178, the train in each ex- 

 periment moved along the next plane, the average descent of 

 which is 1 in 266. The first 1700 yards of this inclination was 



