122 LECTURE XIV. 



sideration 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, although 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 ; sometimes 

 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 

 resisted, Smeaton chose a curve with its concavity turned outwards.* If 

 we calculated what would be the best form for a wooden pillar, intended 

 to remain always immersed in 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 considerable. But in the case of a building of stone, 

 the strength often depends as much on the weight of the materials as 

 on their cohesive power : and the lateral adhesion, which is materially 

 influenced by the weight, constitutes a very important part of the strength. 

 For resisting a force which tends to overset the building, the form in 

 which the weight gives the greatest strength is that of a conoid, or a solid 

 of which the outline is a parabola, concave towards the axis : and for pro- 

 curing, by means of the weight, a lateral adhesion which is everywhere 

 proportional to the force, the form must be cylindrical. So that in a 

 building circumstanced as we have supposed the pillar to be, there ap- 

 pears to be no reason for making either portion of the outline taken sepa- 

 rately convex towards the axis, although the angular junction of the two 

 portions of cones might very properly be rounded off; and the upper 

 parts might be a little enlarged if it were desirable to reduce the thickness 

 of the walls. But the Eddystone light house is completely above the level of 

 the sea, although in stormy weather every part of it is exposed to the action 

 of the waves, the water being sometimes thrown up to a much greater height 

 than that of the light house : so that it may be considered as exposed to 

 the force of a fluid more and more powerful as it is nearer to the founda- 

 tion ; and in this point of view its form differs but little from that which 

 the most accurate theory would point out ; but it is probably a little weaker 

 about the middle of its height, or somewhat lower, than in any other part. 

 (Plate XI. Fig. 150.) 



A wall must be reduced in thickness as it rises, for the same reason as a 

 column is diminished ; and if the wall is a part of a house, it must Le 

 reduced in a still greater degree, since the load, which is to be supported by 

 * On the Eddystone Lighthouse, fol. Lond. 1791, PI. ix. 



