3H 



THE POPULAR SCIENCE MONTHLY. 



8 1 a m ii .voox i ; ?. ... T| ^ h midk't i t 1 t < e 



Moret. 



MONTEBEATJ. 



Larocke. 



TONNEHRE. 



Nuitssiir-Raviere, 

 Les Laumes. 



DIJON, 



Chayny. 

 C7i alow-ur- Cdme. 



St.-Germain- 

 en-Mont d'Or. 

 lyon Perrache 

 (512 kil.) 



Fig. 5. Graphic of the Progress of Trains upon a Railway, after Ibrt's Method. "When we place 

 the figure before us we read from the left, on the axis of the ordinate?, the series of stations, that is, 

 the divisions to be run over ; the distance between the stations on the paper is proportional to the 

 kilometric distances which separate them. In the horizontal direction, that is, on the axis of the 

 abscissae, are counted the divisions of time in hours, themselves subdivided into spaces of ten minutes 

 each. The breadth of the table is such that the twenty-four hours of the day are represented on it, 

 commencing- at 6 a. m., and ending next day at the same hour. If we wish to express that a train is 

 on a certain point of the line at a certain hour, we shall point out its position on the table, opposite 

 the station or any point of the line which it occupies, and on the properly chosen division of time. A 

 single point of the table satisfies these conditions. At successive instants the train will occupy points 

 on the table always different ; the series of these points will give rise to a line which will be descend- 

 ing and oblique from left to right for trains coming from Paris, while it will be ascending and oblique 

 in the same direction for trains going to Paris. The line which corresponds to each of the trains ex- 

 presses the hours of departure and arrival, the relative and absolute rates of the trains, the instant of 

 passing each of the stations, and the duration of stoppages. In fact, if we consider any particular train, 

 we see that a train starts from the station at Paris at 11 A. m.; if we follow this train in its progress, 

 we find that it has seven stoppages (during which it is not displaced in space, but only in time). These 

 stoppages are translated by the horizontal direction of the line, opposite the station where they take 

 place ; the length of this horizontal line measures the duration of the stoppages. The line of the 

 train, followed to the end, shows that the arrival takes place at 6p.m.; but, if we reckon the distance 

 on the axis of the ordinates, we see that 512 kilometres have been traversed in eleven hours ten 

 minutes, stoppages included, which gives a mean rate of about forty-six kilometres per hour. 



mirable apparatus which traces by a single stroke the curve of a move- 

 ment. 



This machine is now too well known to need description ; however, 

 I shall make it work before you in order to interpret its language and 

 to show how a graphic curve translates all the phases of a movement. 

 The parabolic curve traced expresses for each of its points the posi- 

 tion in which the body is found at each of the instants of its fall ; 

 it thus supplies the most complete information on the nature of the 

 movement. But if, knowing only the space run over and the time 

 employed, we join the two extreme points of departure and arrival by 

 a straight line, that line which will express the mean rate of the fall 

 will not correspond to any of the rates which the body has successively 

 possessed. 



The expression of movement by a curve has been put into prac- 

 tice. An engineer named Ibry has devised a method of representing 

 graphically the progress of trains upon a railway. This mode of rep- 

 resentation, incomparably more explicit than the tables of figures of our 

 railway indicators, has not yet got into the hands of the public ; and 



