OF ]R01« BEAMS. 410 



to advert to a matter which seems to strike at 

 the root of the theory we have just laid down. 

 M. Duleau, (Essai theorique et experimentaJ 

 sur la resistance du fer forge), speaking (page 

 2nd) of a body fixed horizontally by one end, 

 and bent by a weight at the other, after having 

 observed that the top fibres will be elongated, 

 and the lower ones compressed, proceeds thus : 

 ** Coulomb has supposed that when the cur- 

 vature of the elastic piece is very small, the 

 neutral line is so placed, that the sum of the 

 moments of the tensions of the superior 

 fibres is equal to that which is obtained by 

 adding together the moments of the com- 

 pressions of the inferior ones. This principle, 

 which has not been demonstrated in a rigorous 

 manner, has been adopted by all the authors* 

 who have treated on this subject." He further 

 mentions, '* It is useless to have recourse to 

 it, if the inquiry is respecting a solid, whose 

 transverse section is divisible by an horizontal 

 line into two symmetrical portions. This right 

 line is then, evidently, that in which the passage 

 from tension to compression lies," (the neutral 

 line.) " It is very rare that in practice one 

 has to consider bodies of any other form.*' 



* Mr. Duleau perhaps means In France, those in England 

 hare till lately snppoted bodies to be incompre«8ible. 



3o2 



