Unstiffened Roadway in a Suspension Bridge. 447 



and, since 



: AA / =AQ + QN' + N f A' = (AN-QN) + (QN' + N^A'), 



■. 2ft=clo S /+ ^+g +,JW V+ jjggjgB^ SW+F) (14) 



s+ \/s 2 + c 2 c 12 



Here are fourteen equations connecting the fifteen quantities 

 ss 1 ax 1 ccf W hh' kk' yy' and / ; each of the first fourteen can there- 

 fore be determined in terms of t, which measures the position of 

 the train upon the bridge. 

 By (1), (5), and (11), 



/3 2 (s 2 + c 2 )=s ,2 + c' 2 ; 

 .'.by (10), 



/3s=s', also/Sc^; , . ♦ . , (15) 

 .♦. by (12) and (13), 



or by (2) and (6), 



•F + 2?#=2m + (£--l)*--£ Vh* + 2ch; . . \(16) 



.-. by (is), •'",:„'. - 



h' + c'=^/^ + (2m-r (/3- 1)^-/3 V^ 2 + 2cA) 2 . (17) 

 By (9), (1), (5), (12), (13), (15), 



h + c-^c 2 +{^h 2 + 2ch-^=h ! + c ! -\/^c 2 +^\/¥^^h'-t) 2 , 

 or, substituting from (17), 



his a small quantity, and c a large one ; I shall therefore expand 

 these expressions in descending powers of c. This gives 



, n iv f 1 f2h f- 3th /2h 



3/ 2 A 

 2c 2 



where 



/» /2A ^\ 



+ 2?VT~8 C 3 J 



of i * * /M /r* Srh A / 



n <+ *- r V7 + 2; + iv 



+ 2c 2 V c 8c 3 J' 



2A 3r 2 £ 



. , 2m— t 



(3 



