PROCEEDINGS 
OF THE 
ROYAL SOCIETY OF EDINBURGH. 
vol. vru. 1874-75. No. 91. 
Ninety-Second Session. 
Monday, 1st February 1875. 
Sir WILLIAM THOMSON, President, in the Chair. 
The following Communications were read: — 
1. On the Complete Theory of the Stone Arch. By 
Edward Sang, Esq. 
In the investigations usually given of the equilibrium of the stone 
bridge, it is assumed that the strains follow the same law as in the 
suspension bridge, the one being a case of stable, the other a case 
of instable, equilibrium ; and, resulting from this hypothesis, for- 
mulas are given whereby to determine the extrados suitable to a 
prescribed intrados. 
The load of the chain bridge is suspended by rods, and therefore 
acts only in the direction of gravity ; it cannot influence the hori- 
zontal strain which must be transmitted unaltered from link to link. 
But the weight is imposed on the stone arch in a different manner. 
The stone which rests on the voussoir is not jointed as the suspend- 
ing rod is, and may transmit an oblique as readily as a downward 
strain : hence the fundamental conditions of the two structures 
are essentially different, and require different modes of treatment. 
The mason trusts greatly to the cohesion of the cement, which 
easily makes up for small inaccuracies of arrangement; but the 
maximum stability of a stone structure is attained by so adjusting 
its parts that each would be in equilibrium even although the sur- 
3 Q 
VOL. VIII. 
