As shown in the figure, _z_ and _x_, the latter locating the section at which the bending moments are to be found, are measured to the right from _A_. Equation (_a_) shows that if the quantity _g_(l-_x_) be laid off, by any convenient scale, as _BK_ at right angles to _AB_, _XC_ will represent the moment _M_ by the same scale when _x = z_ or when _z_ has any value between 0 and _x_. Similarly will _AD_ be laid off at right angles to _AB_ by the same scale as before, to represent _gx_. Then when _x = z_ the expression for _M′_ will have the same value _XC_ as before. Hence if the lines _AC_ and _CB_ be drawn as parts of _AK_ and _DB_, any vertical intercept between _AB_ and _ACB_ will represent the bending at _X_ produced by the load _g_ when placed at the point from which the intercept is drawn. The lines _AC_ and _CB_ are the influence lines for the bending moments produced by the load _g_ in its passage across the span _AB_. It is to be observed that the influence lines are continuous only when the positions of the moving load are consecutive. In case those positions are not consecutive the influence lines are polygonal in form. If there are a number of loads _g_ resting on the span at the same time, the total bending moments produced at _X_ will be found by taking the sum of all the vertical intercepts between _AB_ and _ACB_, drawn at the various points where those loads rest. The influence lines drawn for a single load, therefore, may be at once used for any number of loads. The load _g_ is considered as a unit load. If the vertical intercepts representing the bending moments by the scale used are themselves represented by _y_, and if _W_ represent any load whatever, the general expression for the bending moment at _X_, produced by any system of loads, will be _l_ ---- ∑_Wy._ (_c_) _g_ If this expression be written as a series, the general value of the bending moment will be the following: _l_ _M_ = --- (_W₁y₁ + W₂y₂ + W₃y₃_ + etc.). (_d_) _g_ The effect of a moving train upon the bending moment at any given section is thus easily made apparent by means of influence lines. It is obvious that there will be as many influence lines to be drawn as there are sections to be considered. In the case of a truss-bridge there will be such a section at every panel-point. A slight modification of the preceding results is to be made when the loads are applied to the beam or truss at panel-points only. In Fig. 25 let 1, 2, 3, 4, 5, 6, and 7 be panel-points at which loads are applied, and let the load _g_ be located at the distance _z′_ to the right of panel-point 5, also let the panel length be _p_. The reactions at 5 and 6 will then be _p-z′_ _z′_ _R₅ = g_ -------- and _R₆ = g_ ------. _p_ _p_ The reactions at _A_ will then be _l-z_ _R = g_ ------. _l_