396 J. H. ROHRS, ESQ. ON THE 



tension at the ends of chains of bridges of wide span seems a fatal obstacle to the employment 

 of such modes of attachment ; and probably it would be less costly to increase to a sufficien t 

 amount the thickness of the chains, than to adopt a complex mode of spring attachment, even 

 if it were possible to construct one. 



Mr. Homersham Cox has, I believe, shewn that by the use of oblique tension rods to 

 support the platform, the same load could be sustained as by suspension chains of the same 

 amount of material as the oblique rods; and for bridges of narrow span at least this would 

 seem to be the preferable construction, as it would be less liable probably to vibration. 



ADDENDA. 



In the solution of the equation 



d* dV 2s d 2 „ d 2 _ <PV 



d?-d7 + sd¥ M ° + dF LlS = cg 'd?> 



d*V 

 we assumed in the first instance that — - could be expanded in a convergent series, 



CIS 



_ , 2fl + l T 2tl + \ ITS 

 2, . A. — COS , 



2 a 2 a 



and shewed that in the majority of the kinds of disturbance arising from ordinary causes 



our assumption was true. It is curious, though practically useless, to examine some kinds of 



disturbance in which this is not the case. 



d V 

 Let us, for instance, suppose that — — could be expanded in a convergent series 



CIS 



2,A„ sin , so that also 2 A n cos 7r — 



a a a 



was convergent, and let us suppose the chain free at its ends. The motion being supposed, 



as hitherto, to be always symmetrical about the vertical axis. Then, as before, we should 



have 



dV 2s . j — 



— + — M + L x s = h sinp Vcgt sin (ps + a), 

 tts c 



d?V _ 2 



-r-j + L x = 0, .•. = - — M Q + hp sin p vcgt cos (pa + a) ; 



— - «= 0, .\ = h sin a ; 



as 



V o = 0. 



Hence, = — -M + hp sin py/cgt cos pa, 

 c 



which determines M and L x , when p is given. 



2a t 



= — X-^o + A« + Asinp y/cgt sin pa, 



