70 FERGUSON'S LECTURES 



LECT. wedge will not be to the resistance of tne wood, as the 

 ^iJJ^ length of the back of the wedge is to the length of both 

 its sides ; but as half the length of the back is to the 

 length of either side of the cleft, estimated from the top 

 or acting part of the wedge. For, if we suppose the 

 wedge to be lengthened down from b to the bottom of 

 the cleft at E, the same proportion will hold ; namely, 

 that the power will be to the resistance, as half the 

 length of the back of the wedge is to the length of either 

 of its sides : or, which amounts to the same thing, as 

 the whole length of the back is to the length of both 

 the sides. 



In order to prove what is here advanced concerning 

 the wedge, let us suppose the wedge to 

 be divided lengthwise into two equal 

 parts ; and then it will become two equal 

 inclined planes ; one of which, as a b c, may 

 be made use of as a half wedge for sepa- 

 rating the moulding c d from the wainscot 

 A B. It is evident, that when this half 

 wedge has been driven its whole length 

 a c between the wainscot and moulding, 

 its side ac will be at ed; and the mould- 



ing will be separated tofg from the wainscot. Now, 

 from what has been already proved of the inclined 

 plane, it appears, that to have an equilibrium between 

 the power impelling the half wedge, and the re- 

 sistance of the moulding, the former must be to the 

 latter, as ab to ac; that is, as the thickness of the back 

 which receives the stroke is to the length of the side 

 against which the moulding acts. Therefore, since 

 the power upon the half wedge is to the resistance against 

 its side, as the half back a b is to the whole side a c, 

 it is plain, that the power upon which the whole wedge 

 (where the whole back is double the half back) must be 

 to the resistance against both its sides, as the thickness 



