Proceedings of the Royal Society of Edinburgh. 173 



And if the chains merely sustain themselves at their utmost tenacity, 

 5154 X 9 will give 46,385 feet, or somewhat more than eight miles and 

 three quarters. 



But this case, Mr Gilbert remarks, is purely hypothetical, for the pur- 

 pose of ascertaining a limit, since £, the mass or weight of the chain, must 

 be infinite, and consequently its length : the figure approaching indefi- 

 nitely near to that of a chain sustaining itself from an infinite height, 

 which figure is identical with that of a building, capable, so far as pressure 

 and the strength of materials are alone concerned, of being carried to any 

 elevation whatever. This figure may be determined as follows : 

 Let a = the section of such a building at its base, 



y = the section at any height, 

 and x = that height. 

 Then, since the section and the superincumbent pressure must always 



be in the same proportion to each other, x and V. are in a constant ratio. 



y 



Let then — = — ^, where m is the modulus of pressure in the given ma- 



— m y 



terial. But when x = o, y = a, and therefore - = nat. log. - ; or . — 



m y A.m 



zrztab. log. -, A being 2.3025851. If, however, < and y be the homologous 



y 



sides or diameters of these sections, then will — — = tab. log.-. 



2i A.'7Tl y 



Mr Gilbert in conclusion observes, that in the event of suspension bridges 

 wanting stability to counteract and restrain undulatory motion, the balus- 

 trades may be carried to any required height, and rendered inflexible by 

 diagonal braces ; and if further means were required for imparting stabili- 

 ty, such braces might be adjusted with screws to the suspension rods them- 

 selves, after these rods had acquired their exact positions, on the comple- 

 tion of the work. 



We recommend the entire paper to the particular attention of the en- 

 gineer. 



Art. XXVIIL— PROCEEDINGS OF THE ROYAL SOCIETY OF 

 EDINBURGH. 



November 27. — At a General Meeting of the Society held this day, the 

 following Office-Bearers were elected : 



President. — Sir Walter Scott, Baronet. 

 Vice-Presidents.— Right Hon. Lord Chief-Baron. Lord Glenlee. 



Dr T. C. Hope. Professor Russell. 



Secretary. — Dr Brewster. 



Treasurer. — Thomas Allan, Esq. 



Curator or the Museum. — James Skene, Esq. 



Physical Class. — Lord Newton, President 



John Robison, Esq. Secretary, 



