158 LECTURE XIV. 



grange seems to have been misled by some intricacies of mathematical investi- 

 gation, too remote from physical accuracy, when he calculated that a cylinder 

 was the strongest form for resisting flexure; that form approaches in reality 

 much more nearly to-an oblong spheroid, of which the outline is elliptical. 

 The consideration of the flexure of a column is, however, of little practical 

 importance in architecture, for upon a rough estimate of the properties of 

 the materials usually employed, it may be computed that a column of stone 

 must be about forty times as high as it is thick, in order to be capable of 

 being bent by any weight which will not crush it ; although a bar of wood 

 or of iron may be bent by a longitudinal force, if its length exceed about 

 twelve times its thickness. The force may therefore be considered as tend- 

 ing only to crush the column ; and since the inferior parts must support 

 the Aveight of the superior parts, in addition to the load which presses on 

 the whole column, their thickness ought to be somewhat increased ; and it 

 appears from a consideration of the direction in which the fracture is most 

 easily effected, that the outline ought to be made a little convex externally, 

 and more curved above than below, which is the usual, althougli not the 

 universal practice ; an elliptic arc is perhaps the most eligible outline, or a 

 curve formed by bending a ruler fixed at the summit of the column ; some- 

 times the form is made to differ little from a cone, but such a figure is very 

 inelegant. The diminution of the thickness amounts in general to about one 

 sixth or one seventh of the whole, and sometimes to one fourth. (Plate XI. 

 Fig. 149.) 



For a light house, where a great force of wind and water was to be resist- 

 ed, Mr. Smeaton chose a curve with its concavity turned outwards. If we 

 calculated what would be the best form for a wooden pillar, intended to re- 

 main always ipimersed >n the water to a certain depth, we should find that a 

 cone or pyramid would possess the greatest possible strength for supporting 

 the motion of the water; and a cone more acute than this would be equally 

 capable of resisting the force of the wind, supposing it to be less active than 

 that of the water ; the part below the water might, therefore, be widened so 

 as to become a portion of a more obtuse cone, the upper part remaining 

 more slender; and the greatest agitation of the sea being near its surface, 

 the basis of the pillar might be a little contracted, so as to have the outline 

 of the lower part a little convex outwards, if the depth of the water were 



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