MECHANICS. 165 



of the sine of the angle which the direction of that 

 strain makes with the direction of the longitudi- 

 nal fibres of the wood. 



According to this, the strength of the beam to resist 

 a force applied to it endwise is infinite. This is no 

 doubt false ; but the force in the case of a longitu- 

 dinal pull or thrust is so great, that no practical 

 error will arise from it. The cause of the error 

 in this extreme case is, that the beam does not, nor 

 cannot, obey the law of continuity, which would re- 

 quire, that when, by varying its inclination, it be- 

 comes quite upright, its longitudinal section should 

 be infinitely extended. 



From this theorem, it is evident, that great advantage 

 is obtained by making the strain on all timber as 

 oblique or as nearly longitudinal as possible. This 

 is the great principle in the construction of roofs 

 and centres of bridges. The principle of the Arch 

 should also be combined with it, so that pressure 

 downwards may be so applied as to produce a pull 

 or thrust upward. See the article by Professor Ko- 

 fi ISON 07i the Strength of Timber, in the Encyclo- 

 padia Britannica. 



In the preceding theorems, no account is made of the 

 weight of the beams, a circumstance that is often 

 necessary to be considered. This may always be 

 done by supposing the weight of the beam to be 

 an addition to its load, collected in its centre of 

 gravity. On this the following theorem is found- 

 ed. 



246. If 



