394 Mr Russell on the Vibration of 



tual manner. Suppose that stays may be placed below the 

 bridge, as shewn in figures 1 2 and 13, we are to inquire how 

 they may be best arranged so as to stop the vibration which 

 the others do not. First, let us take one stay, and inquire how 

 it may be most advantageously placed. 



Case (1.) One stay. Fig. 14. Let the span of the bridge be 

 divided into five equal parts. Then one stay to any one of these 

 points will be as effectual as five stays, in reducing the extent 

 of equal-timed oscillations. Also it may be thus placed, mul- 



Fig. 14. 



tiply the length of the bridge by itself, halve the product, and 

 extract the square root — the resulting number gives that dis- 

 tance of the stay from one end, which will most effectually pre- 

 vent the parts of the bridge from oscillating together. 



Case (2.) Two stays. Let the first be fixed as in Fig. 14, 

 then divide the length of the bridge into seven equal parts, a 



Fig. 15. 



second stay to one of these parts will still farther reduce the 

 oscillations in the proportion of 5 : 35. 



Case (3.) Four stays. Let the whole length of the bridge 

 be successively divided into 5, 7, 11, and 13 equal parts; then 

 let a pair of stays be fixed on each side, at one of each of these 



