divided by the depth of the bowstring girder at the right of the bay, multiplied by the depth of the parallel flanged girder. Thus the horizontal component of the stress in D= _ _ | Stress caused by diagonals Length of right Depth of parallel | | leaning to left. vertical. flanged girder. | | | + |_ 15.75 × 1/4.5 × 10 _| _ _ | Stress caused by diagonals Length of ver- Depth of parallel | | leaning to right. tical to left. flanged girder. | | | |_ 24 × 1/8 × 10 _| = 65; and the vertical component = Horizontal component. Length of bay. 65 × 1/10 × (8.0 - 4.5) = 22.75. In the same way the horizontal and vertical components of the stresses in each of the other bays of the flanges of the bowstring were found; and the stresses in the verticals and diagonals were found by addition, subtraction, and reduction. These calculations are shown on the table, Fig 1B. The result of this is a complete set of stresses in all the members of the bowstring girder--see Fig. 2--which produce a state of equilibrium at each point. The fact that this state of equilibrium is produced proves conclusively that the rule above described and thus applied, although possibly it may be considered empirical, results in the correct solution of the question, and that the stresses shown are actually those which the girder would have to sustain under the given position of the live load. Figs. 2 to 10 inclusive show stresses arrived at in this manner for every position of the live load. An inspection of these diagrams shows: a. That there is no single instance of compression in a vertical member of the bowstring girder, b. That every one of the diagonals is subjected to compression at some point or other in the passage of the live load over the bridge, c. That the maximum horizontal component of the stresses in each of the diagonals is a constant quantity, not only for tension and compression, but for all the diagonals. The diagrams also show the following facts, which are, however, recognized in the common formulæ: d. The maximum stress in any vertical is equal to the sum of the amounts of the live and dead loads per bay of the girder. e. The maximum horizontal component of the stresses in any bay of the top flange is the same for each bay, and is equal to the maximum stress in the bottom flange. Having taken out the stresses in several forms of bowstring girders, differing from each other in the proportion of depth to span, the number of bays in the girder, and the amounts and ratios of the live and dead loads, similar results were