170 LECTURE XIV. 



port the middle of the rafters. Somethnes a flat or less inclined portion is 

 placed in the middle, forming a kirb or mansard roof, somewhat resembling ai*. 

 arch ; this form has the advantage, when it is properly proportioned, of lessening 

 the transverse strain on the rafters, by making them shorter; but this pur- 

 pose is answered equally well by the addition of the braces which have been 

 already mentioned. A kirb roof aftbrds, however, a greater space within, 

 than a plain roof of the same height, and produces also somewhat less strain 

 on the tie beam or on the abutments: the tie beam may be suspended from it 

 by a king post and two queen posts, descending perpendicularly from the 

 joints ; and the place of the king post may be supplied by a cross beam unitr 

 ing the heads of the queen posts and keeping them at a proper distance; this 

 beam may also be suspended by a shorter kingpost from the summit. Such a 

 roof appears to be more advantageous than it has been commonly supposed, 

 (Plate XIII. Fig. 175.. 177.) 



The angle of inclination of a roof to the horizon usually varies in diiferenf 

 climates: in Italy the height is generally less than one fourth of the breadth; 

 in England it was formerly three fourths, but it now commonly approaches 

 much more to the Italian proportion. In northern climates, a steep roof is 

 required on account of falls of snow, which greatly increase the lateral thrust 

 of the rafters; for the horizontal force exerted by a roof is always pro- 

 portional to the length of a line perpendicular to the rafter, descending from 

 its extremity till it meets another similar line drawn from the opposite rafter; 

 and this perpendicular is obviously much increased when the roof becomes very 

 flat. But for bearing the transverse strain, which tends to break the rafters 

 themselves, a low roof is stronger than a high one, supposing the number of 

 braces and queen posts equal on both : for if we have to support a given weight 

 by a beam or rafter, whether it be placed in the middle, or equally divided through- 

 out the length, we neither gain nor lose force by lengthening the beam and rais- 

 ing it higher, while the horizontal span continues the same, since the obli- 

 quity lessens the effect of tlie weight precisely in the same ratio that the 

 length of the beam diminishes its strength ; but by lengthening the beam we 

 also add to the weight which is to be supported, and we thus diminish the 

 strength of the roof. It must be observed, in calculating the strength of a 

 <rafter, that the slight flexure, produced by the transverse strain, has a material 



