The equations used in the examples were formulated with the aid of a spiral diagram which represents the result of preliminary scheduling in so far as it assigns each bus to a definite route and indicates how the various branches are geared together. In complicated networks the construction of a suitable spiral diagram may itself become a difficult problem, particularly when the buses flowing into a main branch have to be geared with the buses flowing out of this branch. The following procedure has been found useful in this case. Of the possible arrangements of the buses flowing into and out of the main branch, select the two which present the most symmetric appearance; perform the minimizing calculation on the various ways of fitting these patterns together. The optimum schedule is likely to be one of these combinations.