2 14 THE GRAMMAR OF SCIENCE 



on the horizontal line through P, the number of minutes 



o 1 



that the train takes from Aldgate to each of the other 

 stations. Thus the times of a vertical column of Brad- 

 shaw are in our case arranged horizontally. But we will 

 place these times at such distances that ^-th of an inch 

 shall represent a minute, or the minutes between any pair 

 of stations may be at once read off by aid of an inch- 

 scale. To connect each station with its corresponding 

 time we will draw a horizontal line PQ through the 

 station, and vertical line /Q through the corresponding 

 time. These meet in a point Q, and we obtain a series 

 of points Q^, Q^, . . . Q^,,, in our diagram, corresponding 

 to the sixteen stations. Now at first sight it may seem 

 rather an inconvenient form of Bradshaw, when each train 

 takes up an entire page.^ The reader, however, must 

 wait till we have seen whether our page may not be made 

 to convey a great deal more information as to the motion 

 of the train than Bradshaw' s single column. 



Now it is clear that what we have done for the stations 

 may be done for every signal-box, S^, Sg, S3, etc., on the 

 line, and not only for every signal-box, but for every 

 position along the whole line at which we choose to 

 observe the time at which the train passes. We thus 

 obtain a series of points : Q^, Q^, Q3, Q^, Q^, S^, Og, Q^, 

 Q , Og, Sg, etc., which are seen to take more and more the 

 form of a curve as we increase their number. We will 

 join this series of points by a continuous curve, and to 

 simplify matters we will suppose our train to be a 

 luggage train running from Aldgate to South Kensington 

 without stopping, otherwise our curve would have a small 

 straight horizontal piece at each station. This curve must 

 be carefully distinguished from the map of the path in 

 Fig. 9 ; it tells us nothing about the direction in which the 

 train is moving at a given time — that is to say, whether 

 it is going northwards, or southwards, or what. But with 



^ Such geometrical Bradskazvs with, however, many train -curves on a 

 page are used by the traffic managers of several French railways. I possess 

 a facsimile of that for the Paris- Lyons route containing between 30 and 40 

 train-curves, and showing the passing places, stoppages and speeds of the 

 corresponding trains. 



