MEMOIR OF EATON HODGKINSON. 217 



subject was mentionedto 'Mr. Fuiii»airn, wlio at once, with liis cliaracterisac liber- 

 ality, supplied his friend witli ample means for investigatin;:^ experimenlally the 

 strength of cast-iron pillars. For this paper the council for the Roya Society 

 •awarded Mr. Hodgkinson the royal medal as a mark of their apprt 'jiation of 

 his labors, the value and importance of which are confirmed by every ngineer's 

 pocket-book in Europe during a period of 20 years. 



The inquiry is natm-ally divided into two parts, viz., long pillars and short 

 pillars. 



LONG PILLARS. 



The first object was to supply the deficiencies of Euler's theory of the strength 

 of pillars, if it should appear capable of being rendered practically useful, and if 

 not, to endeavor to adai)t the experiments so as to lead to useful results. For 

 this purpose solid cast-iron [)illars were broken, of various dimensions, from five 

 feet to one inch in length, and from half an inch to three inches in diameter. In 

 hollow pillars the length was increased to seven feet six inches, and the diameter 

 to three inches and a half. 



With pillars c)f cast-iron J wrought iron, steel, and timher, whose length is upivarcls 

 of 30 times tlieir diameter, the strength of those with flat ends is three times as 

 great as those tvith rounded ends. 



Experiments were next made upon pillars with one end flat and the other end 

 rounded, and the result is summed up in the following interesting and impor- 

 tant law : 



With xyillars of tJie same diameter and length, both ends rounded, one end rounded 

 and the other flat, and both ends flat, their strengths are as 1, 2, 3, respectively/. 



When the pillars were uniform, and the same shape at both ends, the fracture 

 took place in the middle. This was not the case when one end was flat and the 

 other rounded, as the fracture then took place at about one-third of the length 

 from the rounded end. Hence, in these pillars, the metal may be economized 

 by increasing the thickness in the point of fracture. 



' It follows, from Eulei-'s theory, that the strength of pillars to bear incipient 

 flexure is directly as the fourth power of the diameter, and inversely as the square 

 of the length. 



This incipient flexure was sought for by Mr. Hodgkinson without success, 

 and he states his conviction that flexure commences with very small weights, 

 such as could be of little use to load pillars ^vith in practice. Although Mr. 

 iro<lgkinson was unable to find the point to which Euler's computations refer, 

 still he has shown that Eider's formula is not widely from the truth when ajiplied 

 to the breaking point of the pillar. From a great number of experiments Mr. 

 Hodgkinson deduced the following formula for pillars with rounded ends: 

 D := diameter of pillar in inches. 

 L = length of jiillar iu feet. 

 W = breaking-weight iu tons. 



])376 



Then, W = 14.9 j^ • 



The above rule applies to pillars tlie length of which is 15 times the diametei' 

 and upwards. Perhaps not quite so low as 15 times the diameter in large pillars, 

 as there is a reduction of the strength of such pillars, owing to tlie softness of 

 the metal in large castings. This remark is significant, and gave rise to many 

 interesting experiments at rortsmoiith dockyard by the royal commissioners, 

 conducted by Colonel Sir Henry James. 



When the pillars are flat at the ends, the formula becomes 



T^3.55 



W=44.16^j-^-. 



This rule applies to pilhirs whose lengths vary from 30 to 121 times the diameter. 



