PRINCIPLES OF MECHANICS. 541 



are achievements which have, in the ages in which they occurred, been 

 received with great admiration and applause ; but in those cases the 

 principle of the structure had been tried and verified for ages upon a 

 smaller scale. Here not only was the space thus spanned wider than 

 any ever spanned before, but the principle of such a beam with a cel- 

 lular structure of its parts, was invented for this very purpose, experi- 

 mentally verified with care, and applied with the most exact calcula- 

 tion of its results. 



Roof s> — Arches — Vaults. 



The calculations of the mechanical conditions of structures consist- 

 ing of several beams, as for instance, the frames of roofs, depends upon 

 elementary principles of mechanics ; and was a subject of investigation 

 at an early period of the science. Such frames may be regarded as 

 assemblages of levers. The parts of which they consist are rigid beams 

 which sustain and convey force, and Ties which resist such force by 

 their tension. The former parts mast be made rigid in the way just 

 spoken of with regard to iron beams ; but ties may be rods merely. 

 The wide structures of many of the roofs of railway stations, compared 

 with the massive wooden roofs of ancient buildings, may show us how 

 boldly and how successfully this distinction has been carried out in 

 modern times. The investigation of the conditions and strength of 

 structures consisting of wooden beams has been cultivated by Mathe- 

 maticians and Engineers, and is often entitled Carpentry in our Me- 

 chanical Treatises. In our own time, Dr. Robison and Dr. Thomas 

 Young have been two of the most eminent mathematicians who have 

 written upon this subject. 



The properties of the simple machines have been known, as we have 

 narrated, from the time of the Ancient Greeks. But it is plain that 

 such machines are prevented from producing their full effect by vari- 

 ous causes. Among the rest, the rubbing of one part of the machine 

 upon another produces an obstacle to the effectiveness of a machine : 

 for instance, the rubbing of the axle of a wheel in the hole in which it 

 rests, the rubbing of a screw against the sides of its hollow screw; the 

 rubbing of a wedge against the sides of its notch ; the rubbing of a 

 cord against its pulley. In all these cases, the effect of the machine 

 to produce motion is diminished by the friction. And this Friction 

 may be measured and its effects calculated ; and thus we have a new- 

 branch of mechanics, which has been much cultivated. 



