148 Mr Sang on the relation which subsists 



new chain would be one hundred times the strength of that 

 at Trinity, while the load put upon it would be one thousand 

 times greater ; so that the new structure would possess only 

 nine-tenths of the strength necessary to support itself. Of how 

 little importance, then, in bridge-building, whether a model con- 

 structed on a scale of perhaps one to a hundred support its own 

 weight ! Yet, on such grounds, a proposition for throwing a 

 bridge of two arches across the Forth at Queensferry was 

 founded. Putting out of view the roadway and passengers al- 

 together, the weight of the chain alone would have torn it to 

 pieces. The larger species of spiders spin threads much thicker, 

 in comparison with the thickness of their own bodies, than those 

 spun by the smaller ones. And, as if sensible that the whole 

 energies of their systems would be expended in the frequent re- 

 production of such massy webs, they choose the most secluded 

 spots; while the smaller species, dreading no inconvenience 

 from a frequent renewal of theirs, stretch them from branch to 

 branch, and often from tree to tree. I have often been astonished 

 at the prodigious lengths of these filaments, and have mused on 

 the immense improvement which must take place in science, and 

 in the strength of material too, ere we could, individually, under- 

 take works of such comparative magnitude. 



When a beam gives support laterally, its strength is propor- 

 tional to its breadth, and to the square of its depth conjointly. 

 If, then, such a beam were enlarged ten times in each of its 

 linear dimensions, its ability to sustain a weight placed at its 

 extremity would, on account of the increased distance from the 

 point of insertion, be only one hundred times augmented, but 

 the load to be put upon it would be one thousand times greater; 

 and thus, although the parts of the model be quite strong enough, 

 we cannot thence conclude that those of the enlarged machine 

 will be so. 



It may thus be stated as a general principle, that, in similar 

 machines, the strengths of the parts vary as the square, while 

 the weights laid on them vary as the cube of the corresponding 

 linear dimension. 



This fact cannot be two firmly fixed in the minds of machine 

 makers; it ought to be taken into consideration even on the 

 smallest change of scale, as it will always conduce either to the 



