38 MOVEMENT 



glance. The direction of the curve indicates the 

 destination of the train. Lines descending towards 

 the right represent trains going away from Paris, 

 while those which ascend towards the right correspond 

 to trains going towards the capital. The intersections 

 of lines on the chart signify the places and the hours 

 at which trains cross one another en route. This 

 admirable mode of representation is the only one 

 which should be employed to express in a graphic 

 form the trajectory of a moving point. In such tables 

 the rate of progress of the trains is supposed to be 

 uniform, and is represented by straight lines instead 

 of irregular curves. The latter are employed to 

 express a change of speed as it occurs from moment 

 to moment. This is the only way in which such a 

 mode of graphic representation deviates from what 

 actually occurs. It is improbable, however, that any 

 serious difficulty would arise from this cause. 



The Curve of a Prolonged Movement should be re- 

 corded in Sections. — Charts used to express the move- 

 ments on a railway are crowded with detail, because 

 they record the progress of every train which moves 

 in one or other direction along a more or less extensive 

 section of the line. The surface of the paper is thi>s 

 completely utilized. But this would not be the case 

 if we had to record the progress of one train only 

 during a long run extending over many hours. On 

 referring back to Fig. 25 it will be noticed that the 

 diagonal of the square expresses a journey of six 

 hectometres completed in six minutes. Now, for a 

 journey twice as long, and taking twice the time, the 

 diagonal would be double the length, and the square 

 containing it four times as large. According to this 

 geometrical progression, we should have to use a sheet 

 of paper a metre square if we wanted to record the 

 progress of a moving body for twenty kilometres. 



