March 13, 1879] 



NATURE 



441 



haps astonish many of you by saying that the speed of a 

 vehicle is one of the things most miperfectly known. It 

 is generally believed to be sufficiently expressed by stating 

 how much way has been made and how much time has 

 been occupied for that. I have come, you may say, from 

 the Pont de Sevres to the Madeleine in 41^ minutes ; the 



road is well mile-stoned, I possess a good watch ; what 

 greater precision do you require? Assuredly you have 

 measured accurately the space traversed and the time 

 employed, but that constitutes only the expression of a 

 mean speed resulting from a series of variable speeds, of 

 accelerations, of retardations, and sometimes of stoppages 



I 



Fig. s- — Graphic of the progress of trains upon a railway, after Ibry's method. — When we place the figure before us we read finom the left, on the 

 axU of the ordinates. the series of stations, that is, the divisions to be run over ; the distance between the stations on the papter is proportional to the 

 kilometric distances which separate them. In the horizontal direction, that is. on the axis of the abscissse, are coimted the divisions of time in hours, 

 themselves subdivided into spaces of ten minutes each. The breadth of the taljle is such that the_ twenty fotir 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 Une 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 diTis:on of time. A 

 single point of the table satisfies the^e 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 descending and oblique from left to right for trains coming from Paris, while it will be ascending and obHque in 

 the sam e direction for trains going to Paris. The line which corresponds to each of the trains expresses the h >urs 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 fi-om the station at Paris at ii a..m. ; if we f jUow this train in its progress, we find that it has seven stoppages (during which it is 

 BOt displaced in space, but only in time). These stoppages arc 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 6 P.M. ; but, if we reckon the distance on the axis of the onLnates, we see that 512 kilometres have been traversed in eleTcn hours ten 

 minutes, stoppages included, which g^ves a mean rate of abcut 46 kilometres per hcur. 



where time is quite unknown. A rigorous measurement 

 of rates supposes the road traversed by the vehicle at each 

 instant ; in other words, the position which it occupies 

 upon the road. It is thus that physicists have determmed 

 the accelerated motion of the fall of bodies — Galileo and 

 Atwood, by means of successive measurements, Poncelet 

 and Morin by means of that admirable apparatus which 

 traces by a single stroke the curve of a movement. 



This machine is now too well known to need descrif>- 

 tion ; 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 

 position 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 departiu-e 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 practice. An engineer named Ibry has devised a 

 method of representing graphically the progress of trains 

 upon a railway. This mode of representation, incom- 

 parably more explicit than the tables of figures of our 

 railway indicators, has not yet got into the hands of the 

 public ; and this is to be regretted, for it gives a genuine 



interest to a journey, as you may see by inspection of one 

 of these graphics. 



Fig. 6. — Odograph, reduced to one-third of its diameter. 



The table which you see (Fig. 5) is prepared by- 

 engineers according to the regulation progress of trains 



