374 PROCEEDINGS OF THE AMERICAN ACADEMY 



Upon seeing the enormous strength thus given to the iron, Captain 

 Rodman merely remarks that the bursting pressures are greater in the 

 whole series than required by the tenacity of the iron, " even suppos- 

 ing the whole thickness of metal to resist uniformly as in tensile 

 strain." But no doubt seems to cross his mind as to the accuracy 

 of his instrument or his measures ; he therefore proceeds forthwith 

 to compute the force on the hypothesis " that the strain diminishes 

 as the square ' of the distance from the axis increases." This 

 means to reduce the power of the metal to sustain pressure, at 

 different thicknesses, according to Barlow's formula. I have given his 

 numbers in the third column above. 



I confess I was puzzled for a long time to find out what these num- 

 bers meant. The tenacity of the iron used was 27,000 pounds to the 

 inch ; Barlow's formula gives for a cylinder 2 inches in internal diam- 

 eter and 1 inch thick, made of such iron, just half of this tenacity, or 

 13,500 pounds. I then went over all the different thicknesses accord- 

 ing to Barlow's formula, and found even stronger cases of discrepancy 

 than that here cited ; and as I do not profess to be a mathematician of 

 a very high order, while Captain Rodman has the calculus " familiar 

 as his garter," I thought it was possible, after all, that I had misunder- 

 stood Barlow's rule. I therefore laid down, in section, each of the 

 cylinders in full size, and requested three of the distinguished mathe- 

 maticians of Cambridge to tell me what must be the strength of each 

 according to Barlow's rule. They all calculated separately, and all 

 agreed with each other and with me exactly, and I here give the 

 whole matter in a tabular form. 



1st column in this table, gives the thickness of the several cylinders. 



2d column, the pressure per square inch, as measured by Captain 

 Rodman's instrument, under which each cylinder burst. 



3d. The pressure which the cylinders ought to have sustained 

 according to Captain Rodman's computations, from Barlow's formula. 



4th. The true pressure of burstings according to Barlow's formula 

 as computed and "applied by me, on iron having 27,000 pounds per 

 inch tenacity, — this being the mean tenacity of these specimens, as 

 stated on p. 192. 



5th. The errors of Captain Rodman's experiments, or of his instru- 

 ment. 



6th. The errors of Captain Rodman's computations. 



