316 Cambridge Philosophical Society. 



CAMBRIDGE PHILOSOPHICAL SOCIETY. 

 [Continued from vol. ii. p. 500.] 



Dec. S, 1851. — On the Oscillations of Suspension Bridges. By 

 J. H. Rohrs, Esq., M.A. 



In this paper the oscillations of a chain suspended at two points 

 were discussed, with a view to explain the causes of fracture in sus- 

 pension-bridges, by vibration arising from the tramping of troops, 

 gusts of wind, &c, as well as to suggest means for obviating the 

 mischief under those circumstances. The following were some of 

 the most remarkable results arrived at : — 



1st. That if the tension at the ends of the chain where it is sus- 

 pended be kept constant by allowing play at those points, the varia- 

 tion of tension due to vibration at any other point of the chain will 

 be but small. 



2ndly. That if the chain be tied at the points of suspension so 

 that it can have no motion there, a slight extent of vibration will 

 produce comparatively a great increase of tension. 



3rdly. That periodic forces, such as may be taken, for instance, to 

 represent the effect of tramping in time of troops moving across the 

 bridge, are dangerous in the extreme, as if they happen to coincide 

 in period with any of the possible types of vibration, the extent of 

 vibration will increase continuously, till it ceases to be represented 

 approximately by a linear or even an equation of the second order ; 

 in this case, the chain will be divided by nodal points where there is 

 no vertical motion. 



4thly. That the mere transit, without tramping, of ordinary loads 

 at an ordinary pace would not cause sensible vibration in a bridge 

 of wide span ; but that terms not periodic might be introduced by the 

 variable pressure of wind sweeping in rapid gusts along the platform. 



Feb. 16, 1852. — On the Composition and Resolution of Streams 

 of Polarized Light from different Sources. By Professor Stokes. 



In this paper the author investigates the nature of the light result- 

 ing from the union of several independent streams of polarized light. 

 The refrangibility of the several streams is supposed to be the same, 

 and the polarization to be of the most general nature, that is, to be 

 elliptic. The following proposition is established. 



When any number of independent polarized streams, of given 

 refrangibility, are mixed together, the nature of the mixture is com- 

 pletely determined by the values of four constants, A, B, C, D, de- 

 nned in the following manner : — Let J be the intensity of one of the 

 elliptically-polarized streams, a the azimuth of its plane of maximum 

 polarization, tan ft the ratio of the axes of the ellipse described by 

 the sethereal particles ; then 



A=S(J); B = 2(Jsin2/3); C = 2(J cos 2/3 cos 2a) ; 

 D=2(Jcos2/3sin2a). 

 Two groups of polarized streams, of the same refrangibility, which 

 are such as to give the same values to each of the four constants 

 A, B, C, D, are denned to be equivalent; and the author has shown, 





