───────────┬───────────────────────┬───────────┬───────────┬─────────── Height. │ Area. │ Weight of │ Weight of │ Ratio of Feet. │ │ the │the Train. │the Weight │ │Embankment.│ Tons. │ of 1 Foot │ │ Tons per │ │ Lineal of │ │ Lineal │ │ an │ │ Foot. │ │Embankment │ │ │ │ to the │ │ │ │ Weight of │ │ │ │the Train. ───────────┼───────────────────────┼───────────┼───────────┼─────────── │Square Lineal Ton. │ │ │ │ Feet. Foot. │ │ │ 10 │ 330 × 1 × 0·05 = │ 16·5│ 100 │0·165 to 1 20 │ 960 × 1 × 0·05 = │ 48·0│ 100 │0·480 to 1 30 │1,890 × 1 × 0·05 = │ 94·5│ 100 │0·945 to 1 40 │3,120 × 1 × 0·05 = │ 156·0│ 100 │1·560 to 1 50 │4,650 × 1 × 0·05 = │ 232·5│ 100 │2·325 to 1 60 │6,480 × 1 × 0·05 = │ 324·0│ 100 │3·240 to 1 ───────────┴───────────────────────┴───────────┴───────────┴─────────── NOTE.—For the purpose of a comparison of ratios it is not necessary to consider the length of the train. A simple inspection of the above ratios would lead to a supposition that the effects of vibration would be no less than 3·210/0·165 = 19·6 times greater in a 10 feet than in a 60 feet embankment. Merely comparing the weight of a train with that of an embankment, and assuming that the results of vibration at the same rate of speed are so governed is incorrect, for the effect of vibration at the formation level is not regulated by the height of an embankment or the depth of a cutting. The weight of a train may bear a very small relation to that of the quantity of earth slipped, yet the soil may have gradually become in such a state of delicate equilibrium that at last the least vibration will destroy it, even a little of the top soil falling upon the slope; and it frequently occurs that a slip commences by the detachment of a few small lumps and increases until it becomes of serious dimensions; therefore, the area of a cutting or embankment cannot necessarily be considered as reducing vibration although the source of disturbance may be more distant; but, of course, the heavier the mass the greater the weight and speed required to cause the whole to vibrate.