OF ARTS AND SCIENCES. 371 



fectly relied upon for hollow pillars of very large size, with very thin 

 walls. He found that his formula, as applied to solid pillars, was 

 applicable to those of a hollow form, by merely changing (p-^ into 

 (p-^ — gs.e^ -j^ which d and e are the external and internal diameters, 

 respectively. 



Mr. Hodgkinson likewise extended his experiments to some other 

 materials than cast-iron, as wood, wrought-iron, and cast-steel. 



Taken altogether, these researches are undoubtedly the most val- 

 uable that have been made upon the subject. But after all, Mr. 

 Hodgkinson's paper must be considered in the light he intended it for ; 

 namely, as a scientific investigation of the strength of pillars, and not 

 a practical treatise, giving to architects and builders rules that they 

 may follow with confidence in their erections. As the matter now 

 stands, each architect or engineer who would follow this paper must, 

 after finding the limit of strength for any proposed column, determine 

 for himself how far he will keep within this limit, or where safety ends 

 and danger begins. To show how far it is required in practice to 

 carry the strength beyond that assigned by inferences founded upon 

 calculation, to obtain security against all disturbances, and the imper- 

 fections of workmanship, I will cite an example or two. A water- 

 pipe 12 inches in diameteiV, and half an inch thick, ought, from deduc- 

 tions made from the tensile strength of cast-ii-on, to sustain a column 

 of water more than 3,000 feet high. But where is the engineer that 

 would dare to load a series of such pipes with a column of 300 feet 

 high ? Again, a steam-boiler 30 inches in diameter and ^ of an inch 

 thick, ought to hold steam of more than 1,000 pounds' elastic force. 

 But in practice 60 pounds is considered enough for such a boiler. 

 These instances should certainly, in the case of cast-iron pillars, teach 

 us to keep widely within the ultimate, or what may be called the theo- 

 retical strength. No practical directions have, as far as I know, been 

 given in any engineering work founded upon Hodgkinson's experi- 

 ments. The tables by which architects in Boston are governed are 

 derived from the formula of Tredgold, to which I have before alluded. 

 I will finish what I have to say, by comparing a few of the numbers of 

 these tables with each other, and with the experiments and formula of 

 Hodgkinson. I take from these tables a solid pillar 2 inches in diam- 

 eter, 6 feet long. To this the load assigned is 61 cwt., while 2 inches' 

 diameter 12 feet long is made to carry 32 cwt. ; numbers very nearly 



