The Military Map Elements of Modern Topography French School of War

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And cd = 0'007 m. , then gradient of AB _ Q-Q07 m. __ 1 gradient of CD ~ 0*028 m. = ~ 4' Comparison of Inclines 79 or the incline of CD is four times as great as that of AB. This may be verified if the gradients are ascertained when the maps are supposed to be respectively on the scale of 1/10, 000 and 1/40, 000. For then : gradient of AB - ^t. Equidistance of 1/10, 000 ab x 10, 000 2*50 m. 0*028 m. X 10, 000 250 J^ "28x1000 ~ = 112' and gradient of CD = nat ' equidistance of 1/40, 000 cd x 40,... 000 10m. 0-007 m. X 40, 000 10 _!_ 7x40 ~ 28* Therefore gradient of ^ = ^ = gradient of CD ^ which was shown to be the case when the size of the two scales was left out of consideration. The inclination of the ground at any point is shown by the gradient of the line of greatest slope which passes through that point. It has been proved already that the line of greatest slope of a plane is perpendicular to the intersection of the plane with the horizontal plane of projection. Similarly the line of greatest slope that passes through any point on the ground is perpendicular to the intersections of the ground with the two horizontal 8o Comparison of Inclines planes situated immediately above and below the point in question.

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