In Fig. 31 is illustrated a case of a crooked line from which a considerable saving of curvature was made, although at a very large expenditure for earthwork, by eliminating the reverse curvature and all that part of the direct curvature which is necessary to balance the reversed curvature. This change of location was recently made by the Pennsylvaina Railroad, and involved not only the elimination of some very sharp curves, which prevented very high speed, but also eliminated about 494° of curvature and incidentally reduced the length of line by about 4700 feet. The total number of degrees of central angle in the original line is approximately 582, of which about 335° is in one direction and about 247° in the other. The new line therefore eliminates all of the curvature in one direction (247°), but likewise as much curvature in the other direction.

This problem also involves the reduction in the length of the line by about 4700 feet. The cost of this improvement was very great, since it involved the construction of four new bridges crossing the Conemaugh, and also some very heavy earthwork, four of the cuts having a depth at the highest point of 80, 105, 106, and 120 feet. The improvement was also combined with the widening of the road-bed for four tracks instead of two. On account of the very large amount of through competitive traffic hauled over the Pennsylvania lines, this reduction in distance is of benefit to the railroad to its full value on such traffic. It is not to be supposed that this reduction of 4700 feet in distance has the slightest effect in reducing the revenue received by the road.

In order to compute numerically the value and justification of the above improvement, it is necessary to know the number of trains actually using those tracks, and also the cost of the improvement. The determination of the number of trains is not easy, since the number of passenger-trains, which alone run by regular schedule, is but a small proportion of the total. The number of freight-trains is not even a constant quantity, since it varies from day to day with fluctuations of the traffic. The author has been unable to obtain any statement of the total number of trains on this division. Even the cost of the reduction of curvature and distance is so bound up with the cost of widening the road-bed for four tracks instead of two that it is impracticable to test, even by the above method, whether the improvements were justified. According to the curvature formula the saving on each regular train operating that stretch of track every day for one year would be 494° x 82 cents = \$405.08.

Fig. 31. Revision of alinement, Pennsylvania Railroad between Portage and Lilly.

The added saving per train per year on account of the reduction of distance would be 4700 x 6.91 cents = \$324.77.

The sum of these gives \$729.85, the annual saving on each regular daily train. To allow for fluctuations, the average number of trains per day should be used as a multiplier. On the basis that this average number is 100, we have a computed annual saving of \$72,985. Capitalized at 5%, this indicates a justifiable expenditure of \$1,459,700.

If the original line in the above case had been constructed on a uniform grade, and if that grade had been the ruling grade, then since the new line is considerably shorter, the question of the grade of the new line would have been a very important one. In fact the improvement would have lost all of its value if its accomplishment had required an increase in the ruling grade of the road. But the new line has been put in with a ruling grade of 1.15% against east-bound traffic. Even this will doubtless be operated by pusher-engines for all heavy trains.

## 178. Reliability And Value Of The Above Estimate

No extreme accuracy is claimed for the above method of estimating the effect of curvature. The effect of curvature depends on so many conditions, some of which are variable, that an estimate which might be mathematically perfect at one time would be somewhat altered during the succeeding year, on account of a change in operating conditions. Therefore the value obtained by any such calculations must be only considered as approximate. Nevertheless, it does give a value for the proposed change which is far better than a mere guess as to the desirability of an improvement. The real value of these figures may be tested as follows: If you vary some of the very important items very largely, it has a comparatively small influence on the final result. As an illustration, suppose that the item of renewals of rails is assumed to be affected 500% rather than 226%. The effect on the value of the reduction of 1° of curvature is increased less than 7%, which of course means that the justifiable expenditure to effect this result might and would be increased by the same percentage, but after all the real question is not whether the improvement in an ordinary case is worth, say, \$10,000, or \$10,700, seven per cent more. Possibly the extra work may be done for \$3000 or it may require \$25,000. In the first case there is but little question that the improvement will be justified in view of the probable growth in the business of the road. In the second case it would probably show that the improvement should be delayed until the amount of actual traffic will furnish a better justifica- , tion for the work. If the estimated cost of the improvement very nearly equals the computed operating value of the change, the final decision on the question would depend very largely on the financial ability of the road to make such an improvement.