The Tay Bridge. 29 



of view, comparatively unimportant. Its weight tends to 

 increase the moment of stability, while the sides of the 

 carriages partly block up the openings, and so increase the 

 area exposed to the wind. The increase in the overturning 

 moment from the latter cause is rather greater than that of 

 the moment of stability, and the result of the whole when 

 calculated out is to reduce the critical pressure by about 

 3 lbs. per square foot. 



Here, then, we have a perfectly consistent and logical 

 explanation of how the accident might have happened, 

 supposing the structure to have been 'perfectly sound in every 

 other respect. 



An inspection of the wreck, however, leads us to doubt 

 whether this was the precise mode of fracture, for, first, the 

 foundations, as a rule, are quite undisturbed, the columns 

 being broken transversely just above their bases ; and, second, 

 some of the piers yet remain comparatively uninjured for a 

 considerable height, the upper portion only being absent. 

 This could hardly have occurred were it a case of pure 

 overturning. 



4. We are now led to the last, and as is, I think, now 

 generally admitted, the true explanation, and it is this — that 

 the bracing of the piers gave way and allowed each column 

 to turn about its own base as a centre, the columns mean- 

 while remaining parallel like the two bars of a parallel 

 ruler. 



Each pier was composed of six columns, placed at the 

 angles of a hexagon, two sides of which were at right angles 

 to the length of the bridge, while the others were at an 

 angle of 45°. At every 11 feet in height the columns were 

 connected together by massive double channel irons, and the 

 square openings formed by the columns and channel irons 

 were provided each with two diagonal braces, upon which 

 was imposed the duty of keeping the columns vertical under 

 the action of any lateral force. The braces were far too 

 weak, and, giving way, permitted the columns to fall 

 laterally. 



We have first to ascertain, in order to test this view 

 mathematically, what was the pull on each brace under 1 lb. 

 of wind pressure on the structure above. In this case the 

 surface of the train will be added to that of the girder, while 

 its weight will in no way affect the stress on the bracing. 



The total area exposed in each 245 feet length of bridge 

 now becomes, including total area of windward girder, area 



