412 



PROCEEDINGS OF THE AMERICAN ACADEMY 



thin side ; in this case the deflection caused by the load will depend on 

 the compression of the thick side; from the greater area subject to 

 compression the amount of the compression, and consequently of the 

 deflection, will be less than if the sides are of equal thickness. In 

 either case, when the inequality in the thickness on opposite sides is 

 not too much, the pillar may support a load as great, or even greater, 

 than if the thickness was equal on all sides. 



Hodfkinson determined a new formula for the breaking weight of 

 hollow cylindrical pillars cast from Low Moor iron, No. 2, from the 

 experiments given in his second paper, viz. : — 



W = 94859 



D' 



73.5 



(3) 



Formula (1) was determined from the experiments given in the first 

 paper, which, from their wider range of dimensions, are much better 

 fitted for such an induction than the experiments given in the second 

 paper. 



Table IV. contains a comparison between the breaking weights by 

 experiment and by formulas (1) and (3). The pillars were all cast 

 from Low Moor iron. No. 2, and are the same as those given in Table 

 I. It will be seen that the computed breaking weights by formula (3) 

 ao-ree best with the breaking weights by experiment in the smaller pil- 

 lars, and the computed breaking weights by formula (1) agree best 

 with experiment in the larger pillars. On the whole there appears to 

 be no doubt that formula (1) is the best determined and the safest to 

 adopt in practice. 



Table IV. 



Designalion of the 



Exiieriments in 



IIoilgkiuson"s Tables. 



Tab. I. Exp. 1 



" " 2 



" " 3 



it II ^ 



" " 5 



" " 6 



ti it fj 



Breaking 



weifjlit by 



experiment. 



Lbs. 



34,804 



39,166 



66,259 



69,932 



110,649 



114,479 



112,127 



Breaking 



weight by 



formula (1). 



Lbs. 



31,334 



33,268 



58,966 



60,627 



110,990 



112,122 



113,149 



Breaking 



wei;iht by 



formula (3). 



Lbs. 



33,289 



35,350 



62,059 



63,798 



115,971 



117,103 



117,362 



In applying the formulas to practice, it is of the greatest importance 

 to determine the proper allowance to be made for possible defects, and 

 to insure complete security against fracture, using no more material 

 than is necessary. In doing this, many things should be considered. 



