. Field-book for railroad engineers. Containing formulas for laying out curves, determining frog angles, levelling, calculating earth-work, etc., etc., together with tables of radii, ordinates deflections, long chords, magnetic variation, logarithms, logarithmic and natural sines, tangents, etc., etc . nals), making 37. The second line of the quan-tities multiplied by ^6 is obtained in the same way from the columnmarked A. The sum of these numbers is 171, and this multiplied by16=14 gives 2394. We have now for the first line of the formula1389 + 1185, for the second 605 + 639, and for the rema
. Field-book for railroad engineers. Containing formulas for laying out curves, determining frog angles, levelling, calculating earth-work, etc., etc., together with tables of radii, ordinates deflections, long chords, magnetic variation, logarithms, logarithmic and natural sines, tangents, etc., etc . nals), making 37. The second line of the quan-tities multiplied by ^6 is obtained in the same way from the columnmarked A. The sum of these numbers is 171, and this multiplied by16=14 gives 2394. We have now for the first line of the formula1389 + 1185, for the second 605 + 639, and for the remainder 2394. 100By adding these together, and multiplying the sum by 5/ = -g- , we get the contents of the six sections in feet. 124. When the section is partly in excavation and partly in embank-ment, the preceding formula? are still applicable ; but as this applica-tion introduces minus quantities into the calculation, the followingmethod, similar in principle, is preferable. 125. Problem* Given the ividlhs of an excavation at the road-bed 6 106 EARTH-WORK. AF = w and Ai F, = Wi {Jig. 53), the side heights h and h^.the lenfftkof the section /, arid the direction of the diagonal, to find the solidity S ofthe excavation, when the section is partly in excavation and partly in em-bankment. Fig. 53. Solution. Suppose, first, that the surface is divided into two triangles by the diagonal B A^. Through B draw the plane BA^F,,dividing that part of the section which is in excavation into two pyra-mids B-AAiFiF and B-AiB^ F^, the solidities of which are B - A Ai F, F = I h X k ^ {lo + ivi) = ll{ioh -\- wi h), B-AiBiFi =^lx^ioihi =llwihi. The whole solidity is, therefore, S = kl {wh -\- ivi Aj, + iti h). Next, suppose the dividing diagonal to run from Ato Bi. ThroughBi draw a plane BiAF (not represented in the figure), dividing theexcavation again into two pyramids, of which the solidities are Bi-AAiF^F^^hi X hl{io-\-Wi) = \l{ioh + ^o^h)yBi-ABF =^lxh^h =11 wh. The whole solidity is, ther
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectrailroadengineering
