RELATING TO THE BREAKING OF RAILWAY BRIDGES. 



723 



TABLE II. 



The form of the trajectory will be sufficiently perceived by comparing this table with the curves 

 represented in the figure. As /3 increases, the first point of intersection of the trajectory with the 

 equilibrium trajectory eee moves towards A. Since xr = 1 at this point, we get from the part of the 

 table headed " ar," for the abscissa of the point of intersection, by taking proportional parts, .3-1, .29, 

 .26, .24, and .22, corresponding to the respective values 3, 5, 8, 12, and 20 of /3. Beyond this point 

 of intersection the trajectory passes below the equilibrium trajectory, and remains below it during 

 the greater part of the remaining course. As /3 increases, the trajectory becomes more and more 

 nearly symmetrical with respect to C : when /3 = 20 the deviation from symmetry may be considered 

 insensible, except close to the extremities J, B, where however the depression itself is insensible. 

 The greatest depression of the body, as appears from the column which gives y', takes place a little 

 beyond the centre; the point of greatest depression approaciies indefinitely to the centre as /3 

 increases. This greatest depression of the body must bo carefully distinguished from the greatest 

 depression of the bridge, which is decidedly larger, and occurs in a diderent ])lace, and at a ditl'ercnt 

 time. The numbers in the columns headed " 7'" shew that T is a maximum for a value of a; greater 

 than that which renders y' a maximum, as in fact inunediately follows from a consideration of the 

 mode in which y is derived from T. The first maximum value of T, wliicli according to what has 

 been already remarked is the only such value that we need attend to, is about 1.5<) for /3 = 3, 1.33 

 for /3 = 5, 1.19 for /i = 8, 1.11 for /3 = 12, and I.06 for ft = 20. 



When ft is equal to or greater than 8, the nmximuni value of T occurs so nearly when j; » .5 



