in the same manner, assuming the second track is split up into sidings equal to the length of trains and distributed throughout the division.

If the length of double track plus the length of sidings is more than half the length of the division, we have assumed that the theoretical track capacity will be expressed in terms of the double track capacity estimating the double track capacity on the basis of trains one train length apart on each track. (See page 745, Proceedings A.R.E.A., Vol. 22, 1921.) That is, the theoretical double track capacity in train-hours is equal to 12 times the number of tracks times the miles of second track and sidings divided by the length of train expressed in miles. On double track sections minimum train spacings may be determined by block signals, in which case the rule should be changed and length of block section substituted for length of train.

Table I gives details of operating statistics necessary for estimating the theoretical track capacity.

Determination of Actual Track Capacity.

When a road reaches the point where train movements are seriously interfered with on account of limited track facilities, we will assume the conditions then existing represent the actual track capacity of the division. The period of greatest movement can then be selected and analyzed to establish a measure of the actual track capacity. Obviously in the beginning a road must have reached this point before its actual track capacity can be determined. When the actual track capacity has been established for a number of different roads it is felt that it will be possible to determine certain criteria and relationships between various factors of train operations which will make it possible to forecast the actual capacity of similar roads before they reach the limit of their present facilities.

The actual track capacity will be very much less than the theoretical for the reason that we have elected to base the theoretical track capacity on the most favorable conditions. In practice, conditions must be taken as we find them. Trains do not run at a uniform speed, passenger trains and freight trains run at different speeds, and when the two services are maintained there will be more or less interference of one with the other, tending to restrict the time when the running tracks can be used.

Furthermore, due to the fact that passing sidings are laid out so that the running time is not uniform between all sidings, it is impossible to obtain full use from all of the track facilities. The section which takes the longest time for a train to run over it in both directions determines the number of trains which can be operated over the division. It will thus be seen that the actual track capacity can often be improved by a rearrangement of sidings.

TABLE 1-COMPARING ACTUAL TRAIN-HOURS OPERATED WITH THE THEORETICAL TRAIN-HOUR CAPACITY

On Divisions A and B, Fig. 1, the longest stretch of single track between sidings is 8.5 and 8.8 miles, respectively. If there were but one class of trains operated over these divisions and the speeds were uniform over the entire division the maximum number of trains which could be on the line at any one time would be the same as if all the sidings were the same distance apart, namely 8.5 and 8.8 miles, respectively; that is, from this cause alone the track capacity is reduced from 600 and 528 train-hours per day to 384 and 213 train-hours per day, respectively. Suppose the trains took eight hours to run between terminals and 3/4 hour to run over the longest section, then there could only be 24 ÷ 34-32 trains operated per day, or a capacity of 8 X 32 = 256 train-hours per day.

The actual sidings at each end of the longest sections may be long enough to accommodate two or more trains at a time, in which case we would expect that actual operations could be adjusted to fit the conditions, and a somewhat greater capacity than 256 train-hours could be obtained.

Table I gives a comparison of the actual with the theoretical track capacity, assuming these divisions are operating up to full capacity. The actual train-hours reported cover operations over the single and double track sections because data could not be obtained which would show the actual train-hours operated over each section. It is much better to con

sider the track capacities of the single and double track sections separately because the capacity of the single track section always limits the capacity of the division. Likewise, if some trains branch off at junction points between terminals the actual train-hours for various sections where the train density is different should be obtained separately.

There is only a light passenger service operated over these divisions and the train-hours consumed by passenger trains on the road are estimated from time-table schedules. On Division A the passenger run is longer than the freight, as indicated by the dotted lines, but the passenger train-hours are estimated to cover only the freight division.

Comparing the actual train-hours per day with the theoretical capacity it will be noted that the single track sections are being operated nearer to capacity than the double track sections. The gross ton-miles per mile of road is greatest for the sections having the greatest amount of double track, but the train-miles per mile of road differs little on any of the sections. There is more passenger service on Division D, particularly on the double track section, than on the other divisions, a fact which no doubt accounts for much of the double track on this division. How much nearer it is possible to approach the theoretical values than are shown by the ratios for the single track sections is problematical. What effect extending the double track will have in reducing the running time of trains would be very interesting to watch, if such plans are being considered.

The comparisons in the above table are based upon the daily average of the maximum month's operation. The maximum movement for a shorter period may show greater utilization of track facilities and it would be interesting to apply these principles to shorter periods of record movements to see what effect limited track facilities have upon train movements under these conditions or how record movements are brought about. On the other hand, the maximum daily movement which can be handled over a given division is of very little value unless nearly equal movement can be repeated day after day without causing congestion.

Usually the best criterion for judging the traffic capacity of a division is the traffic which it can handle regularly for a period of 15 days or a month. In this connection Fig. 2 shows the average road time per train plotted against the average number of trains per day (assuming the number of trains equals train-miles per mile of road per day) for 22 months.

At first glance it would appear that there is no relation between the time taken per train to cover the road and the number of trains on the road per day. However, by symbolizing the various points so as to distinguish between summer and winter operation, Government control period and months of different years, those familiar with the conditions of operation at those times can no doubt explain many of the irregularities.

Without attempting to analyze the charts it will be seen that the road time for 1921 shows improvement over 1920, that operations are appreci