THE ARCH. 



113 



upon it ; so must the thickness of the constructed arch be 

 sufficient to bear the constant dead load of the whole struc- 

 ture, together with the greatest live load that can ever be 

 taken over it. 



Taking first the case of the dead load. In the model arch 

 it has been shown that the thickness required for this 

 pur])OK0 must bo 12,} inches at the crown, and 15 at the 

 springing, tapering proportionally from tlio one to the 

 other. 



This I have termed tlio necessary thickness, for it forms 

 the basis of our reckoning, as well as tlio main consideration, 

 particularly in arches of wide span. If, therefore, on the 

 drawing of tho arch (Plato XVII.) we mark off a middle 

 thickno.ss of 12^ inches at the crown, and of 15 at the 

 springing, and draw lines in the proper curves, — A the upper 

 and B tho lower,— joining these marks (the thickness is at 

 every point directly proportional to the secant of the angle 

 which the equilibrated curve makes with the horizon at 

 that point). Then, this middle space will show the necessary 

 thickness throughout the length of the arch. This is on the 

 assumption that the safe load on the materials should be 

 One-eighth of tho crushing load of cement, as will bo alluded 

 to presently. 



Having now provided for tlie dead load by means of that 

 middle portion of the arch between the lines A and B, let us 

 look more particularly into the effect of the live load. This 

 has been represented by the supposed passage of the very 

 extreme load of a 50-ton engine over the bi-idge, and tho 

 ''esults have been exem])lified jiractically by its effect upon 

 the suspended chain model. We have seen that the chain 

 (which constantly represents the equilibrated curve of 

 tension) was always deflected under the engine as it passed 

 along, until it attained an extreme deflection, in mid span, 



