The Paris line is built with the standard gauge of 4 ft 82 in., but its tunnels are designedly made of such a small crosssection that ordinary main line stock cannot pass through them.
The crosssection of a tube of induction may vary in different parts, but the total induction across any section is everywhere the same.
This is represented in crosssection and in position in fig.
Let S be the area of the crosssection at distance x from the plane A.
In the case, therefore, of any solid whose cross-section at distance x from one end is a quadratic function of x, the position of the crosssection through the centroid is to be found by determining the position of the centre of gravity of particles of masses proportional to So, S2, and 4S 1, placed at the extremities and the middle of a line drawn from one end of the solid to the other.
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