In Table XVII is given an analysis of the figures furnished for the rail wear on various curves of the Pacific division of the Northern Pacific Railroad. The method adopted was to determine the percentage loss in four years. This percentage was divided by the tonnage (varying between 27,021,227 and 29,862,738 tons) to reduce it to the uniform basis of the wear for 10,000,000 tons' duty. By dividing the quantities in column 3 by the average percentage loss (0.525%) on two tangents subject to the same traffic, of this same division, we have the ratio of the rail wear on a curve to the rail wear on the average tangent. Subtracting one from each one of the quantities in column 4 we have the excess wear, which may be considered due to curvature alone. By dividing these quantities in column 5 by the degree of the curve we have the excess per degree.

## Table XVIII. Rail Wear On Curves - Northern Pacific R.R., Pac. Div

 Degree of curve. Pet. loss in four years. Pct. loss 10,000,000 tons' duty. Col. 3 / .525. Excess over one. Excess per degree. Average excess per degree. 4° 31'..... 2.675 0.964 1.838 0.838 .185 .150 2.970 1.070 2.038 1.038 .230 2.912 1.049 1.999 0.999 .221 1.781 0.642 1.223 0.223 .049 1.877 0.676 1.'288 0.288 .064 5°0'..... 3.500 1.173 2.235 1.235 .247 .270 3.271 1.096 2.087 1.087 .217 4.349 1.450 2.761 1.761 .352 2.857 0.957 1.823 0.823 .165 4.450 1.491 2.840 1.840 .368 10° 0'.... 5.150 1.855 3.534 2.534 .253 .188 4.417 1.590 3.030 2.030 .203 6.205 2.238 4.265 3.265 .326 2.087 0.751 1.430 0.430 .043 3.122 1.124 2.141 1.141 .114 10° 30' ... 6.200 2.080 3.960 2.960 .282 .213 6.022 2.020 3.850 2.850 .272 5.610 1.882 3.588 2.588 .247 3.704 1.241 2.365 1.365 .130 3.795 1.272 2.423 1.423 .136

The average of the five values in each case is given in column 7. The significance of these numbers in column may be interpreted as follows: .150, for example, means that the excess wear per degree of curve on the various rails of the 4° 31' curve averaged 150/1000 of the wear on an average tangent. The other figures in the last column are to be interpreted similarly. The 4° 31' curve was on a 0.525% grade, the 5° curve was on a 0.3% grade, the 10° curve was on a 0.128% grade, and the 10° 30' curve was on a 0.3% grade. The rate of grade on these curves evidently does not account for the variations in these values. It is quite apparent that the rail wear per degree of curve for the sharper curves does not increase with the curvature, and it is more than likely that it diminishes, as was indicated by the diagrams given in § 100. A similar computation was made from the results of the wear on a 3° curve on the Minnesota division. See Table XIX.

## Table XIX. Rail Wear On Curves - Northern Pacific Railroad Minnesota Division

 Degree of curve. Pet. loss in four years. Pct. loss 10,000,000 tons' duty. Col. 3 / .260. Excess over one. Excess per degree. Average excess per degree. 3° 0' . . 1.208 .447 1.718 0.718 .239 .310 1.030 .392 1.507 0.507 .169 1.538 .569 2.188 1.188 .396 1.314 .487 1.872 0.872 .291 1.637 .613 2.358 1.358 .453

Here the average excess per degree amounted to 31% of the rail wear on the tangent. The average percentage of excess per degree on the curves of the Pacific division was 20.5%; for the one curve on the Minnesota division it was 31%; allowing the average for the four curves a weight of four and giving a weight of one for the curve on the Minnesota division, the weighted mean is 22.6%. Anticipating a demand in a future chapter (Chapter XIII (Curvature. 159. General Objections To Curvature)) for the effect of curvature on the cost of the renewal of the rails, we might state, as an approximate average figure, that, since the excess rail wear per degree of curve does not seem to increase with the curvature, it is a safe conclusion to say that it varies with the degree or curvature, and that therefore the excess rail wear on a 10° curve will be 226% of the rail wear on a tangent.