STRENGTH OF MATERIALS. 



423 



blocks of stone left projecting from a rock that lias 

 been hewn, of which blocks one is twice as long, 

 and deep, and broad, as the other. The larger one 

 will by no means support as much more weight at 

 its end than the other, as it is larger; and for two 

 reasons: 1. In the larger, each particle of the sur- 

 face of attachment, in helping to bear the weight 

 of the block itself, has to support by its cohesion 

 twice as many particles beyond it, in the double 

 extent of projection, as a particle has to support in 

 the shorter block ; and, 2. both the additional sub- 

 stance, and any thing appended at the outer ex- 

 tremity of the larger, are acting with a double lever 

 advantage to break it, that is, to destroy the cohe- 

 sion. Hence, if any such projection be carried out 

 very far, it will break off or fall by its own weight 

 alone. What is thus true of a block supported at 

 one end, is equally true of a block supported at 

 both ends, and, indeed, of all masses, however sup- 

 ported, and of whatever forms. That a large body, 

 therefore, may have proportionate strength to a 

 smaller, it must be made still thicker and more 

 clumsy than it is made longer; and, beyond a cer- 

 tain limit, no proportions whatever will keep it 

 together, in opposition merely to the force of its 

 own weight. This great truth limits the size and 

 modifies the shape of most productions of nature 

 and of art, of hills, trees, animals, architectural or 

 mechanical structures, &c. 



Hills. Very strong or cohesive material may 

 form hills of sublime elevation, with very project- 

 ing cliffs and very lofty perpendicular precipices; 

 and such are seen, accordingly, where the hard 

 granite protrudes from the bowels of the earth, as 

 in the Andes of America, the Alps of Europe, the 

 Himalayas of Asia, and the Mountains of the Moon 

 in Central Africa. But material of inferior strength 

 exhibits more humble risings and more rounded 

 surfaces. The gradation is so striking and constant 

 from granite mountains down to those of chalk, or 

 gravel, or sand, that the geologist can generally tell 

 the substance of which a hill is composed by the 

 peculiarities of its shape. Even in granite itself, 

 which is the strongest of rocks, there is a limit to 

 height and projection ; and if an instance of either, 

 much more remarkable than now remains on earth, 

 were by any chance to be produced again, the law 

 which we are considering would prune the mon- 

 strosity. The grotesque figures of rocks and moun- 

 tains seen in the paintings of the Chinese, or actu- 

 ally formed in miniature for their gardens, to ex- 

 press their notions of perfect sublimity and beauty, 

 are caricatures of nature, for which originals can 

 never have existed. Some of the smaller islands 

 in the Eastern ocean, however, and some of the 

 mountains of the chains seen in the voyage towards 

 China, along the coasts of Borneo and Palawan, 

 exhibit, perhaps, the very limits of possibility in 

 singular shapes. In the moon, where the weight 

 of gravity of bodies is less than on the earth, on 

 account of her smaller size, mountains might be 

 many times higher than on the earth; and observa- 

 tion proves that the lunar mountains are much 

 higher than ours. By the action of winds, rains, 

 currents and frost upon the mineral masses around 

 us, there is unceasingly going on an undermining 

 and wasting of supports, so that every now and 

 then immense rocks, or almost hills, are torn by 

 gravity from the station which they have held 

 since the earth received its present form, and fall 

 in obedience to the law now explained. 



The size of vegetables, of course, is obedient to 



the same law. We have no trees reaching a 

 height of 300 feet, even when perfectly perpendi- 

 cular, and sheltered in forests that have been un- 

 molested from the beginning of time ; and oblique 

 or horizontal branches are kept within very narrow 

 limits by the great strength required to support 

 them. The truth that, to have proper strength. 

 the breadth or diameter in bodies must increase 

 more quickly than the length, is well illustrated by 

 the contrast existing between the delicate and 

 slender proportions of a young oak or elm, while yet 

 in the seedsman's nursery, and its sturdy form when 

 it has braved for centuries all the winds of heaven, 

 and has become the monarch of the park or forest. 



Animals furnish other interesting illustrations of 

 this law. How massive and clumsy are the limbs 

 of the elephant, the rhinoceros, the heavy ox, com- 

 pared with the slender forms of the stag, antelope 

 and greyhound ! And an animal much larger than 

 the elephant would fall to pieces from its own 

 weight alone, unless its bones were made of much 

 stronger materials. Many have questioned whether 

 the mammoth, or antediluvian elephant, could have 

 lived on dry land, or must have been amphibious, 

 that its great body might generally be borne up by 

 water. The whale is the largest of animals, but 

 feels not its mighty weight because lying constantly 

 in the liquid support of the ocean. A cat may fall 

 with impunity where an elephant or ox would be 

 dashed to pieces. The giants of the heathen my- 

 thology could not have existed upon this earth, for 

 the reason which we are now considering ; although 

 on our moon, where, as already stated, weight is 

 much less, such beings might be. In the planet 

 Jupiter, again, which is many times larger than the 

 earth, an ordinary man from hence would be carry- 

 ing, in the simple weight of his body', a load suffi- 

 cient to crush the limbs which supported him. The 

 phrase a little compact man, points to the fact that 

 such a one is stronger in proportion to his size than 

 a taller man. The same law limits the height and 

 breadth of architectural structures. In the houses 

 of fourteen stories, which formerly stood under the 

 castle of Edinburgh, there was danger of the super- 

 incumbent wall crushing the foundation. 



Roofs. Westminster hall approaches the limit 

 of width that is possible without very incon- 

 venient proportions or central supports; and the 

 domes of the churches of St Peter, in Rome, and 

 St Paul, in London, are in the same predicament. 



Arches of a Bridge. A stone arch much larger 

 than those of the magnificent bridges in London, 

 would be in danger of crushing and splintering its 

 material. 



Ships. The ribs of timbers of a boat have 

 scarcely a hundredth part of the bulk of the tim- 

 bers of a ship ten times as long as the boat. A 

 ship's yard of ninety feet contains, perhaps, twenty 

 times as much wood as a yard of thirty feet, and, 

 even then, is not so strong in proportion. If ten 

 men may do the work of a three-hundred-ton ship, 

 many more than three times that number will be 

 required to manage a ship three times as large. 

 Very large ships, such as the two built in Canada 

 in the year 1825, which carried each nearly 10,000 

 tons, are weak from their size alone ; and the loss 

 of these two first specimens of gigantic magnitude 

 will not encourage the building of others like them. 



The degree in which the strength of structures 

 is dependent on the form and position of their parts, 

 will be illustrated by considering the two cases of 

 longitudinal and transverse compression; and the 



