The separate loads are placed at fixed distances apart, indicated by the letters _a_, _b_, _c_, _d_, etc., _W_₁ being supposed to be at the head of the train, while _W_₏ is the last load having a variable distance _x_ between it and the end of the span. In Fig. 17 this system of moving loads or train is supposed to pass over the span _l_ from right to left. The problem is to determine the position of the loading, so that the bending moment at the section _C_ of the beam or truss will be a maximum, the section _C_ being at the distance _lʹ_ from the left-hand end of the span. The complete analysis of this problem is comparatively simple and may readily be found, but it is not necessary for the accomplishment of the present purpose to give it here. In order to exhibit the formula which expresses the desired condition, let _W_ₙʹ be that weight which is really placed at _C_, but which is assumed to be an indefinitely short distance to the left of that point, for a reason which will presently be explained. The equation of condition or criterion sought will then be the following: _lʹ W₁ + W₂ + ... + Wₙʹ_ ----- = ------------------------. (27) _l W₁ + W₂ + W₃ + ... + Wₙ_ If the loads are so placed as to fulfil the condition expressed in equation (27), the bending moment at section _C_ will be a maximum. If the variation in the train weights is very great, it is possible that there may be more than one position of the train which will satisfy that equation. It is necessary, therefore, frequently to try different positions of the loading by that criterion and then ascertain which of the resulting maximum moments is the greatest. It is not usually necessary to make more than one or two such trials. The application of the equation is therefore simple and involves but little labor. It will usually happen that _W_ₙʹ in equation (27) is not to be taken as the whole of that weight, but only so much of it as may be necessary to satisfy the equation. This is simply assuming that any weight, _W_, may be considered as made up of two separate weights placed indefinitely near to each other, which is permissible. After having found the position of loading which satisfies equation (27), the resulting maximum bending moment will take the following form: _lʹ_ _M₁_ = ----- [_W₁a_ + (_W₁+ W₂_)_b_ + ... + (_W₁ + W₂ + ... + Wₙ_)_x_] _l_ - _W₁a_ - (_W₁ + W₂_)_b_ - ... - (_W₁ + W₂ + ... + W₍ₙʹ₋₁₎_)(?). (28)