[79] The question whether the centre of the axle or the point of contact with the rail is the fulcrum of the lever in this case has been the subject of much animated discussion and contention. As the word _fulcrum_ means “a point about which a lever moves,” it is believed that the dispute is due simply to a difference in the meaning assigned to the word fulcrum. If we regard the fulcrum as the point which is fixed in relation to the locomotive, then it is at the centre of the axle, but if we refer it to the surface of the earth, then it is at the top of the rail. As the pressure against the axle in the opposite direction, _b_, is only 10,000 pounds, there will be an unbalanced force of 3,333 pounds acting in the direction of the dart _c_, and tending to move it that way. As the axle is attached to the locomotive frame, this force will of course have a tendency to move the whole machine, and is really the tractive force of the engine. If, on the other hand, we regard the point of contact _B_ of the wheel with the rail as a fulcrum, we have a force of 10,000 pounds acting against a lever, _E G B_, four feet long. There would therefore be a force, _c_, of 10,000 × 4 ---------- = 13,333 pounds 3 exerted at _G_, and as the pressure in the direction of the dart _b_ is only 10,000, there would be an unbalanced strain of 13,333 - 10,000 = 3,333 pounds acting against the axle in the direction of the dart _c_, or, in other words, there is 3,333 pounds more of force pulling the axle forward than there is pushing it backward. When the crank-pin is below the axle, in the position shown in fig. 193, then if the centre of the axle is regarded as the fulcrum we have a pressure of 10,000 pounds pushing against the front cylinder-head, which is transferred to the axle by the frames, and acts in the direction of the dart _c_, and we also have a pressure against the crank-pin _E_ in the direction of the dart _a_. Now 10,000 pounds at _E_ would exert a force of 10,000 × 1 ---------- = 3,333 pounds 3 at _B_ and 10,000 × 2 ---------- = 6,666 pounds 3 at _G_ in the direction of _b_. But the pressure on the cylinder-head pulls against the axle _G_ in the direction c with a force of 10,000, so that the excess of strain in the direction _b_ will be equal to 10,000 - 6,666 = 3,333 pounds. If we regard _B_ as the fulcrum, the calculation is exactly the same, as 10,000 pounds at _E_ exerts a force at _G_ equal to 10,000 × 2 ---------- = 6,666 pounds, 3 and the difference between it and the pressure exerted by the strain against the front cylinder-head is the force which urges the axle and with it the locomotive forward. It will be seen, then, that it is immaterial which point is regarded as the fulcrum, as the result of the calculations is exactly the same. [Illustration: _Fig. 193._ Scale ¹⁄₄ in. = 1 foot.]