The Tay Bridge. 31 



area so torn through will be (4 \ — 1-|) X J = 1*68 square 

 inches, which, at 60,000 lbs. per square inch, would re- 

 quire 100,800 lbs., or 45 tons, if the stress were uniformly 

 distributed over the whole section. The experimental 

 researches, however, of Sir C. Fox and Mr. Berkley 

 have shown that the stress is unequally distributed in this 

 case, and have determined a certain set of proportions by 

 adopting which an eye of equal strength against all possible 

 kinds of fracture is secured. Following the lines laid out 

 by them, we find that the best eye that can be delineated 

 within the limits of a bar 4 \ inches wide around a lj-inch 

 bolt is one the actual strength of which is equal to that of 

 a uniform straight rod not more than 2 inches wide, and 

 having, therefore, an area of 1 square inch, which would 

 tear through with 60,000 lbs., or 26*7 tons. Having already 

 computed the value of x for each pound of wind pressure, 

 we find that any force exceeding 44'5 lbs. per square foot 

 should destroy the structure on its first application, while 

 any pressure exceeding about half of this, or 22 lbs., would 

 effect the same result after a certain sufficient number of 

 repetitions. This result is without allowing any margin 

 whatsoever for defective material or errors of workmanship. 

 Making the usual allowance, we may confidently say that 

 the structure was unsafe at any pressure above 15 lbs. per 

 square foot. In view of this last result, we may well ask, 

 not why the Tay Bridge fell, but why it stood as long as it 

 did. According to this view, the tendency to fracture should 

 increase but slowly from the top of the pier downward ; so 

 that, while we should anticipate the majority of the columns 

 to break off at their bases, we should be quite prepared to 

 see a higher fracture in some cases, due to local peculiarities 

 of adjustment. It is also interesting to note that in those 

 piers of which parts still exist those braces which, according 

 to the preceding investigation, are most heavily strained are 

 in almost every case fractured, while the others remain intact. 



As a matter of fact, it seems that the cast-iron lugs them- 

 selves have usually fractured, and not the wrought-iron 

 bars. We have not sufficient particulars to calculate the 

 strength of these lugs ; but this only shows that there was a 

 weaker place still even than the eye at the end of the bar. 

 The strength of the latter, however, is calculable, and con- 

 stitutes a gauge of the weakness of the whole structure. 



Thus we have been led to the subjoined conclusions : — 



