121 



LECTURE XIV. 



ON ARCHITECTURE AND CARPENTRY. 



THE subjects which we have lately examined, are to be considered as 

 preliminary to the particular departments of practical mechanics. The 

 first division of these is to consist of such as are employed in resisting 

 forces of various kinds, but they may almost all be referred, without in- 

 convenience, to the general heads of architecture and carpentry, of which 

 the principal business is to resist the force of gravitation. Architecture, 

 in its most extensive sense, may be understood as comprehending carpen- 

 try, but the term is more usually applied to the employment of those ma- 

 terials, which are only required to resist the effects of a force tending 

 principally to produce compression, while the materials used by carpenters 

 are frequently subjected to the operation of a force which tends to extend 

 or to bend them : the works of architects being commonly executed in stone 

 or brick, and those of carpenters in wood, besides the occasional use of 

 iron and other metals, in both cases. 



The simplest problem in mechanical architecture appears to be, to de- 

 termine the most eligible form for a column. The length and weight being 

 supposed to be given, it is of importance to investigate the form which 

 affords the greatest possible strength ; but it is somewhat difficult to ascer- 

 tain the precise nature and direction of all the forces which are to be 

 resisted. If we consider the column as a beam fixed in the ground, and 

 impelled by a transverse force, it ought to be much tapered, and reduced 

 almost to a point at its extremity ; but it is seldom that any force of this 

 kind can be powerful enough to do more than overcome the weight alone 

 of the column, and it is only necessary to regard the load which presses 

 vertically on it ; and whether we consider the force as tending to bend or 

 to crush it, the forms commonly employed will appear to be sufficiently 

 eligible. Lagrange seems to have been misled by some intricacies of ma- 

 thematical investigation,* 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 thick- 

 ness. The force may therefore be considered as 'tending only to crush the 

 column ; and since the inferior parts must support the weight of the 

 superior parts in addition to the load which presses on the whole column, 

 their thickness ought be somewhat increased ; and it appears from a con- 

 * Melanges de Turin, v. ii. 123. 



