Machine and its Model. 267 



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 ma- 

 chines, 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 ma- 

 kers; it ought to be taken into consideration even on the smallest 

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

 the economy of a structure. To enlarge or diminish the parts of a ma- 

 chine all in the same proportion, is to commit a deliberate blunder. 

 Let us compare the wing of an insect with that of a bird ; enlarge a 

 midge till its whole weight be equal to that of the sea-eagle, and, great 

 as that enlargement must be, its wing will scarcely have attained the 

 thickness of writing paper; — the falcon would feel rather awkward with 

 wings of such tenuity. The wings of a bird, even when idle, form 

 a conspicuous part of the whole animal ; but there are insects which 

 unfold, from beneath two scarcely perceived covers, wings many 

 times more extensive than the whole surface of their bodies. 



The larger animals are never supported laterally; their limbs are 

 always in a position nearly vertical : as we descend in the scale of 

 size the lateral support becomes more frequent, till we find whole 

 tribes of insects resting on limbs laid almost horizontally. The 

 slightest consideration will convince any one that lateral or horizon- 

 tal limbs would be quite inadequate to support the weight of the 

 larger animals. Conceive a spider to increase till his body weighed 

 as much as that of a man, and then fancy one of us exhibiting 

 feats of dexterity with such locomotive instruments as the spider 

 would then possess ! 



The objects which 1 have hitherto compared have been remote, 

 that the comparisons might be the more striking ; but the same princi- 

 ple may be exhibited by the contrast of species the most nearly al- 

 lied, or of individuals even of the same species. The larger species 

 of spiders, for instance, rarely have their legs so much extended as 

 the smaller ones ; or, to take an example from the larger animals, 

 the form of the Shetland pony is very different from that of the 

 London dray-horse. 



