290 Improvement in the Construction of Bridges, &c. 
Here follow some formule, for the investigation of models, in 
accordance with the best writers on the subject : 
From an experiment, made to ascertain the firmness of the 
model of a bridge, or of an edifice, certain precautions are neces- 
sary, before we can infer the firmness of the structure itself. 
1. If the side of a model be to the corresponding side of the 
structure, as 1 to n, the stress which tends to draw asunder, or to 
break transversely the parts, increases from the smaller to the 
greater scale, as I to n°; while the resistance of those ruptures 
increases only as 1 to n?._ The structure, therefore, will have so 
much less firmness than the model, as » is greater. If w be the 
greatest weight which one of the beams of the model can bear, 
and w the weight or stress which it actually sustains, then the 
limit of » will be n= ~ 
_ 2. The side of the model being to the corresponding side of 
the structure as_1 to , the stress which tends to crush the parts 
by compression, increases from the smaller to the greater scale, as 
1 to n?, while the resistance increases ouly in the ratio of 1to”. 
Hence, if w were the greatest load which a modular wall or col- 
umn could carry, and w the weight with which it is actually 
loaded ; then the greatest limit of increased dimensions would be 
found from the expression n= Va. If, retaining the length ot 
height m A, and the breadth n b, we wished to give to the solid 
such a thickness x ¢, as that it should not break in consequence of 
ve ; : w 
its increased dimensions, we should have =n? 4/ “i In the case 
of a pilaster with a square base, or of acylindrical column, if the 
dimension of the model were d, and of the largest pillar, which 
should not crush with its own weight when m times as high, #4 
we should have r=n Or ee These theorems will often find 
their application in the profession of an architect or an engineer- 
3. Suppose, for an example, it were required to ascertain the 
strength of a bridge on this improvement, from experiments ma 
with a model. In this construction, the truss-work is carried 
across from pier to pier, so that the road-way. entirely across, shall 
be in a horizontal plane, and all the parts shall retain their owB 
respective magnitudes throughout the structure. Now, let / rep" 
