OF ARTS AND SCIENCES : FEBRUARY 14, 1865. 423 



the pillar must be 5^ inches in diameter ; if | inch thick, G^ inches in 

 diameter ; if 1 inch thick, 5f inches in diameter, &c. 



If in the third case, take ^ of 25 tons, which is 8.33 tons; proceeding 

 in the same manner, we find that, if solid, the pillar must be 4|- inches 

 in diameter ; if f inch thick, 4| inches in diameter ; if 1 inch thick, 4^ 

 inches in diameter, &c. 



In the absence of tables specially computed for the purpose, the use 

 of the following tables may be extended to rectangular pillars of cast- 

 iron, and to pillars both cylindrical and rectangular of some other 

 materials. 



Hule for Solid Square Cast-iron Pillars. 



Calling the strength of a cylindrical pillar 100, the strength of a 

 prismatic pillar of square section, whose side is equal to the diameter 

 of the cylindrical pillar, according to different authorities, is as fol- 

 lows : — 

 According to Tredgold, when the distance of the direction of the 



force from the axis of the pillar is ^- of the diameter . . 146 



Also, according to Tredgold, when the neutral axis is at or near 



the axis of the pillar ........ 170 



According to three experiments on square cast-iron pillars with 



rounded ends, given in Table III. of Hodgkinson's paper in Phil. 



Trans, for 1840 158. 



According to experiments on two square cast-iron pillars and 



two cylindrical cast-iron pillars, all with flat ends, given in the 



appendix to Hodgkinson's paper in Phil. Trans, for 1858 . 143 



Assuming the proportion to be as 100 to 150, the safe weight which 

 can be supported by a solid square cast-iron pillar is given by the fol- 

 lowing rule : — 



Determine the weight for a cylindrical cast-iron pillar, of a diameter 

 equal to the side of the square pillar, by the preceding rule for the par- 

 ticular case ; add one half to this weight, the sum will be the weight 

 for the square pillar. 



Hide for Solid Prismatic Cast-iron Pillars, whose Section is a Rectan- 



gidar Parallelogram. 



Find, by the rule for square cast-iron pillars, the weight for a square 

 pillar whose side is equal to the small side of the parallelogram ; multi- 

 ply this weight by the long side of the parallelogram, and divide the 

 product by the small side ; the quotient is the safe weight required. 



