3.2.1 Positive deviations
one type of deviation, in which the route is lengthened in order to collect more freight, here termed positive deviation, has been considered in an early work by Wellington (1887). Wellington, a mining engineer, worked for some time in the third quarter of the nineteenth century on the planning of the railway system in Mexico, and was particularly concerned with alternative routes between the capital, Mexico City, and the gulf port, Vera Cruz (Wellington, 1886). His major difficulty was to estimate the effect of connecting or ignoring smaller centres lying between Mexico City and Vera Cruz along the general line of the route. His dilemma is shown in Figure 3.1. It consists essentially of a problem in optimizing the relationship between length of railroad (the shorter the better) and the amount of trafic (the greater the better). From the data he was able to assemble, Wellington put forward three basic propositions: (i) that if all intermediate points were of equal generating capacity and if they were equally spaced, then traffic varied as the square of the number of points served; (ii) that if the intermediate points were 'small country towns without a competing alternative railway, then the effect of placing the station away from the town (Figure 3.1B) was to reduce gross revenue by 10 per cent for every mile that the station was removed from the town centre: (ui) that if the intermediate points were large industrial cities' with competing railway facilities, then the loss would be still more abrupt: a reduction of 25 percent for every mile that the station was removed from the town centre. Extreme solutions to a hypothetical problem are to minimize length of line