394 J. H. ROHRS, ESQ. ON THE 



/ — 2 25 ,•'< 



.: V ag = - a ; .•. a— — g = 200 feet nearly : 

 5 4 



for a span therefore of 400 feet, .♦. ^24.20^ — is a likely type to become of importance ; for 



2a 



a span of about 150 feet, under the same circumstances, v 8 .2c g — - is the type that would rise. 



/I (I 



Besides there is always a remarkable tendency to adjust one's stepping to the motion of a 

 vibrating floor, and to tread heavier on the floor when it is sinking than when it is rising ; 

 which will of course produce a continually increasing disturbance. 



In the case of the disturbance of which \/24i.2cg — is the type (neglecting terms multi- 



«*\ 



plied by — J , the nodal points, or points of no vertical motion, are at s = .15a, s = .62 a, 



i 

 and s = a 



11. To carry the approximation to the second and higher orders, we should have as 

 before, 



dv d ( dv dy dv\ 



— = — T — + w — + w — 

 dt ds \ ds d s dsl 



• d I „,< 



- = — \T- 

 t ds \ t 



<Fu d I du dx du\ 



d'u d I du dx du\ 



dt ds \ ds ds ds) 



dv dy du dx 1 ( fdu\ 2 /o"tA 2 l 

 ds ds ds ds z\\ds) \ds) J 



/d?v dx rd l u dy (dv dx du dy\ 



dt ds J df ds \ds ds ds ds) 



(dv dx du dy\ 



+ w Yizzr-'j-'-r) 5 



\ds as ds dsj 



sdTV_l( sM ((PU'y 

 ~~cds 3 ~ 2\ 1 + J) * VdV) ' 



du 

 ds 



d 3 T . d 3 V '■ . „ . . 



where -— is -— - found to a first approximation. 



r j sdV 2 ,„ „^ ,, 1 rrt «V (c^vy . 



consequently we should have 

 dV 



* 2 d* ,»,» i « rrf «V«** fd'V'y , , 



-?rf^ + 2elA 1 + ?) d-f[-d?) - d8 



