bagatelle compared with the errors caused by the other assumptions.

Candidly, the author has very little faith in even the approximate correctness of the ordinary methods of computing live-load stresses in draw-spans; nor has he much more in the superrefined methods involving the principle of least work, or stretching of the different truss members, or the principle of the Three Moments with varying moments of inertia. In his opinion, there is but one satisfactory method of ascertaining the reactions for both balanced and unbalanced loads, viz., by making large models of a number of spans of various lengths, and weighing therewith the reactions for all kinds of loading. From a series of experiments of this kind there could be prepared a diagram or diagrams, similar to that shown on Plate IX, which would give approximately correct reactions for all spans and all loadings. Such an investigation would require considerable time and money; but if some professor of civil engineering would undertake to make the experiments, he could undoubtedly get the models built free of charge by dividing up the work among several of the leading bridge-manufacturing companies. The results of such experiments would be of great value to both the engineering profession and the railroads of America.

In finding dead-load stresses in draw-spans, it is customary to assume that the draw is open. The author follows this method, but also assumes an upward reaction from the lifting machinery at the ends, and finds the stresses therefrom; then, when any such stress tends to increase the section of any member, it is considered, but, when it tends to decrease the section, it is ignored. This method certainly is liable to involve errors on the side of safety; but they will tend to offset some possible errors on the side of danger due to the method employed in finding the live-load stresses.

There will be no attempt made in this treatise to illustrate the detailing of draw-spans and their operating machinery. There is a little work on "The Designing of Draw-spans," by Charles H. Wright, C.E., which attempts to cover  this  ground,  and  to  which  the reader  is  referred  for  detailing  of