invariably found, and a consideration of the various sets of calculations resulted in the following empirical rule for the stresses in the diagonals: "The horizontal component of the greatest stress in any diagonal, which will be both compressive and tensile, and is the same for every diagonal brace in the girder, is equal to the amount of the live load per bay multiplied by the span of the girder, and divided by sixteen times the depth of girder at center." The following formulæ will give all the stresses in the bowstring girder, without the necessity of any diagrams, or basing any calculations on the assumed action of any of the members of the girders: Let S = span of girder. D = depth at center. B = length of one bay. N = number of bays. L = length of any bay of top flange. l = length of any diagonal. w = dead load per bay of girder. w¹= live load per bay of girder. W = total load per bay of girder = w + w¹. Then: S/B = N. Bottom Flange. WNS/8D = maximum stress throughout. (1) Top Flange.--In any bay the maximum stress = + WNS/8D × L/B = + WLN²/8D (2) _Verticals._--The maximum stress = -W. (3) _Diagonals._--The maximum stress is ± w¹lS/16DB = ± w¹lN/16D (4) These results show that the method generally adopted in the construction of bowstring girders is erroneous; and one consequence of the method is the observed looseness and rattling of the long embraced ties referred to at the commencement of the article during the passage of the live load; the fact being that they have at such times to sustain a compressive stress, which slightly buckles them, and sets them vibrating when they recover their original position. Another necessity of the common method of construction is the use of an unnecessary quantity of metal in the diagonals; for, by leaving them unbraced, the set of diagonals which does act is subjected to exactly twice the stress which would be caused in it if the bridge was properly constructed. A comparison of the results of a set of calculations on the common plan with those given in this paper, shows at once that this is the case; for the ordinary system of calculation the stresses, in addition to showing compression in the verticals, gives exactly twice the amount of tension in the diagonals which they should have.