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Such investigations bomg purely matlicmatical, and involving the use of the 
differential calculus, are of little practical value, as they camiot take into account 
the numerous variables that ought to be considered. Not only do the stresses in 
a truss vary with the depth, but also the intensities of working- stress in the com- 
pression members. These, ngaiu, vary witli tbc uumber of panels ; ami this 
variation is according to a law or laws altoge tlier too complicated to be handled by 
the calculus. Again : the iutensity of working- stress varies, or should vary, accord- 
ing to tho position and importance of the member. 
In view of the complexity of the question, and wishing to determine the most 
economic depths for Pratt ami Whipple trusses, the author, a year or two ago, under- 
took to solve the problem in a practical manner by figuring out a number of dia- 
grams of stresses, and bills of materials. At first lie considered that it would be 
necessary to calculate the total actual cost for every case, but upon further inves- 
tigation found that it would be sufticient to figure out tho sections and weights per 
lineal foot of. tho different members of ono truss, multiply these by their respective 
lea jfchs, ami sum up tlio products, neglecting all consideration of details, because the 
differences in the weights of the latter balance each other. Thus, if the depth of a 
truss bo increased by 0110 foot, thefo would be a little increase in the weights of the 
lattice bars aud rivets and a decrease in that of the pins and eye-bar heads. These 
may bo taken as balancing each other, without making any appreciable error. 
Tho most economic length of panel was at the same time invostigatetl, and was 
determined, without preparing complete bills of materials, by considering only those 
portions of the structure which arc affected by the variation in the number of panels. 
Economy in pony trasses is an element which ought seldom to influence the 
design, for a good bridge of this kind will generally require more iron than the or- 
dinary calculations demand. Instead of trying to avoid a little expense, regard 
should be paid to obtaining a good distribution of plenty of material, in order to 
partly compensate for the lack of rigidity which is characteristic of the pony truss. 
In very wide pony-truss bridges, especially when the length of span approaches its 
superior economic ifc might be well to make a few calculations concerning tho 
economic depth ； bufc tJie number of panels should bo regulated by the slope of the 
batter braces, which should never bo less than two horizontal to one vertical. 
The superior economic limit of tho pony truss is not a fixed quantity, but 
decreases as the width of the bridge and the load increase. 
After making oufe diagrams of stresses, and bills of materials, for over one 
lumdred spans, tho author came to the following conclusions : 一 
That if the economic depth be calculated for any span, where the panel length 
is iu the neighbourhood of twenty feofc, and if the economic depth for the same span, 
bufc with ono panel les.^, be calculated, the latter mil exceed the former by one or 
two feet. 
The principal objections to the use of the double intersection for short spans are, 
that, as the rods are long and slender, they will vibrate more than the shorter and 
larger 0110s of the single intersection. Auy Haw in a small rod will have a propor- 
tionately greater injurious effect than the same sized flaw in a larger rod. Long 
