The energy spent in pulling a train over its track may be roughly divided into five elements: work against gravity; work of acceleration; internal resist ance that due to friction within the rolling-stock); external resistances, due to interaction between rolling-stock and track; and air resistance. Of these several items the first two, as such, are pretty definite in character and can be figured in a given case with reasonable precision. The last three are extremely hard to separate and have been the source of many difficulties.