310 Mr Sang on the Construction of Oblique Arches. 



The horizontal plan of the jomt is still a double logarithmic 

 curve ; and its delineation, including, of course, that for the 

 circular arch, is as follows. 



EF being, as before, the plan of one of the lines of pres- 

 sure, find HQ a F's- 3- 

 third proportional 

 to the horizontal 

 and the vertical 

 semi-axis; through 

 Q draw Q'E paral- 

 leltoHG. Describe 

 then logarithmics 

 having E'G for 

 their common sub- 

 tangent, and having their ordinates parallel to E'H, the bisec- 

 tion of the interval between these Avill give the horizontal pro- 

 jection of the joint. Similarly, the side and end projections 

 are modifications of those belonging to the circular arch : — 

 they are fully investigated in the appendix. 



Having obtained a tolerable approximation to the forms of 

 the arch-stones, it is not uncommon for bridge-builders to 

 throw the remaining responsibility on the abutments, which, 

 besides transmitting the pressure, have to continue its distri- 

 bution among the parts of the pier. In truth, the principles 

 of equilibrium seem never, even in the case of the right arch, 

 to have penetrated beyond the facing stones of the piers ; and 

 the effect of the arrangement in every bridge which I have seen, 

 or the drawings for which I have inspected, is to throw the 

 whole weight of the arch on the outside stones of the pier 

 and on the outer row of piles in the 

 foundation. To see this clearly, let us 

 draw one of the abutment stones of a 

 right bridge. The oblique face AB re- 

 ceives the pressure of the lowest vous- 

 soir ; and it ought to receive that pres- 

 sure perpendicularly. But the stone 

 is prevented from yielding by resistances against the sur- 

 faces CD. DE : the pressm-e of the voussoir is thus decom- 

 posed into two pressures, one against CD, well known to 



