306 Mr Sang on the Construction of Oblique Arches. 



of the stone must always be insignificant. Those engineers 

 who have experienced a loss on this account, have done so 

 because their bridges were not properly designed. If the 

 stones be obtained in squared blocks from the quarry, there 

 will be a loss on the ends of the stones ; but this, as every 

 builder knows, can be avoided by proper management in the 

 quarry. And thus, on the whole, the loss of material for the 

 skewed bridge need not exceed to any extent worth naming 

 that for the right one. 



The above statements are true of cylindroid oblique arches 

 whatever may be the forms of their principal sections ; they are 

 at variance with the statements and so-called experience of 

 engineers of established reputation : complete demonstrations 

 of them are given in the appendix. They are equivalent to 

 differential equations, and require to be integrated in order to 

 give practical results ; these results vary according to the par- 

 ticular form assumed for the longitudiual section of the vault. 

 I proceed to give a few of these results, commencing, on ac- 

 count of its more frequent occurrence, Avith the circular arch. 



On investigating the form of the projection of a joint of a 

 circular oblique arch upon a horizontal plane, I arrived at a 

 new curve, to which the name Double Logarithmic has been 

 given. 



Having projected the entire semicylinder, of which only a 

 portion can be used with propriety, let AB, CD, be the sides 

 of the projection, and EF, parallel to the parapet, the plan of 

 one of the lines of pressure. Bisect EF at right angles by 

 GHI, and form Fig i- 



two logarithmic 

 curves of which 

 AB, CD, may ho 

 the asymptotes, 

 EG the common 

 subtangent, theii* 

 ordinates being 

 parallel to EF. Then draw lines KL parallel to AB, 

 and intercepted ' between the logarithmics, the middles M of 

 these lines trac^" out the horizontal projection of one of 



