2'48 ' O^ THE STRUCTURE OF COVERED WAYS. 



facing of this kind is not distinguished from an arch by the 

 want of a key stone, since the two middle blocks act nearly 

 in the same manner ai if tliey were united, except when they 

 are forced outwards by the pressure of the lower parts ; and 

 a centre is as necessary for rasing a facing of this kind, as if 

 it were an arch of any other form. 



I am, Sir, 



Your very obedient servant, 

 17 Oct, 1807. APSOPHUS. 



Postscripts — The equilibrium of the flattened arches, 

 commonly placed over windows, may be determined in a si- 

 milar manner, the princi|Sles being the same as those which 

 are employed in the construction of Fig. 11 and Fig. 13. 

 Supposing the blocks without friction and of equal height, 

 if their di/isions converge to one point, the lateral thrust 

 will be equal throughout, and the whole will remain in equi- 

 librium,, provided that the ends do not slide outwards. In 

 order to find the breadth which i^ within this limit, let the 

 horizontal line A B (Fig. 19) pass through the centre of gra- 

 vity of the blocks, draw any line C B from the centre of 

 divergence C, make B D — A B, join C D, and let the 

 vertical line B E meet it in E; then E F, drawn to the in- 

 tersection of the semicircle E F G with the lower termina- 

 tion of the blocks, will show the direction of the abutment 

 d, which will afford an equilibrium : and C H parallel to it 

 will determine the greatest breadth that will stand. But 

 since the blocks thus disposed, and supporting a wall, can- 

 not slide away without displacing the superincumbent 

 weight, the whole wall may be considered as adding to the 

 height of the blocks, and the stability in every case that 

 can occur in practice, must be completer it is oiily neces- 

 sary to reduce the horizontal thrust as much as possible, and 

 this must be done by making the point C as near the blocks 

 as convenient : the thrust being equal to the weight of the 

 portion A H, supposing A C H half a right angle. If we 

 wish to estimate also the eiiects of friction, let the segment 

 E I G contain a right angle diminished by the angle of re- 

 pose, then C K, parallel to E I, will be the direction of the 



abutment 



