420 PROCEEDINGS OF THE AMERICAN ACADEMY 



will be only partially communicated to the pillars or other supports 

 of the bridGfe. 



Formulas (1) and (2) give the breaking weights of cast-iron pillars 

 with the ends carefully fitted, so that the weight will be uniformly dis- 

 tributed on all sides ; in ordinary constructions the ends are frequently 

 unfinished, the inequalities in the bearing surfaces causing the weight 

 to rest on a few points of the ends ; the breaking weight of the pillar, in 

 such case, cannot safely be taken as greater than that of a pillar with 

 rounded ends, which, as we have seen, is about one third that of a pil- 

 lar with flat ends. In cotton-mills, and many other structures largely 

 supported by cast-iron pillars, the ends of the pillars are frequently 

 turned, corresponding in this respect to the experimental pillars with 

 flat ends ; it would generally not be safe, however, to assume that they 

 are as perfectly fitted as they were in the experiments ; when put in 

 place it must frequently happen that they will be canted a little, caus- 

 ing the bearing to fall on one edge ; it will, accordingly, not be safe to 

 assume that formulas (1) and (2) apply to this case without modifica- 

 tion. If the ends are as perfectly fitted as they were in the experi- 

 mental pillars, the breaking weight would be three times as great as in 

 pillars with rounded ends ; if one end is well fitted and the other end 

 rounded, the breaking weight is twice that of pillars with both ends 

 rounded ; it would seem, therefore, that we may safely assume that, 

 when pillars with flat ends are fitted and put up with ordinary care, 

 they will support one and a half times as much as pillars with rounded 

 ends, or, what is equivalent, one half the weight of pillars fitted and put 

 up as perfectly as in the experiments. 



The following tables have been computed by formulas (1) and (2), 

 taking one third of the breaking weight as given by them for the 

 breaking weight of a pillar with rounded ends, and one fifth of this 

 last breaking weight as the safe weight for a pillar with rounded ends, 

 or, what we assume to be equivalent, with the ends not turned. The 

 safe weights for the other cases can be easily deduced from the same 

 tables, as will be seen in the explanation of their use. 



Tredgold's table was generally relied upon by constructors, until the 

 publication of Ilodgkinson's experiments. The same table reappears 

 in the fourth edition of Tredgold's work, edited by Hodgkinson, with 

 the note that " This table has no solid basis." As no other table is 

 given, however, it is probable that its use has been continued by many 

 persons not accustomed to such computations. Table V. contains a 



