742 REPORT—1890. 
that it is unable to interfere with that from the front and produce ‘ darkness,’ ag 
it does in the case of paraftin, &c. 
Other experiments with substances in the state of powder, such as chalk, sand, 
&c., were made. These absorbed but slightly. Lampblack acted more strongly. 
SATURDAY, SEPTEMBER 6. 
The following Papers were read :— 
DEPARTMENT I.—MATHEMATICS. 
1. On the Physical Character of Caustic Surfaces. By J. Larmor. 
The diffraction produced at a caustic is peculiar in that it is not conditioned by 
a beam of light limited by an aperture or otherwise. The theoretical explanation 
why undulations, propagated by unlimited wave-fronts, cannot penetrate beyond a 
certain geometrical surface, was slightly indicated by Thomas Young, and fully 
worked out on Fresnel’s principles by Sir G. B, Airy, for the special case of the 
rainbow. 
It is worth while to formulate the general law of the thicknesses of the bright 
bands which, for any kind of homogeneous light, lie parallel to the principal 
physical caustic. As the beam of light is determined solely by the geometrical 
caustic, or ray-envelope, it is clear that the law must be expressed in terms of 
this surface. It comes out that 
The bands form, along with the geometrical caustic, a system whose relative dis- 
tances apart are in every case the same, and whose absolute distances at any point 
are proportional to the two-thirds power of the radius of curvature of the caustic 
surface at the point, measured in the direction of the rays. 
2. The Buckling of Plates. By G. H. Bryan. 
In this paper are worked out the analogues for a plane plate of the well- 
known conditions of stability of a straight elastic wire under axial force. 
The first case considered is that of a rectangular plate, supported but not 
clamped round its boundary, and acted on by different uniform edge thrusts in its 
plane applied perpendicularly to the sides and ends. The conditions of stability 
are found, and the most interesting point which they lead to is the determination 
of the number of corrugations produced when buckling takes place. If the thrust 
per unit length on the sides be less than half that on the ends, the plate will 
buckle into a series of undulations, whose number will depend on the ratio of the 
length to the breadth of the plate. In the case of an infinitely long strip the 
corrugations will divide the strip into rectangles, which will diminish in length 
as the lateral thrust is diminished, will become squares when there is end 
thrust only, and will become closer and narrower when the lateral force changes 
sign and becomes a tension. This effect may be easily illustrated by wetting the 
middle of a sheet of thin paper, which is then stretched over two rulers. If now 
the rulers be pulled apart with increasing force, the wrinkles will become more 
numerous and finer. 
The undulatory character of the buckling is also analogous to the ‘ collapse into 
rings’ of a boiler flue. 
The paper also contains an investigation of the stability of a circular plate 
clamped round the edges, and acted on by uniform normal edge thrust in its 
plane. This kind of buckling is well illustrated in the circular lid of a canister 
whose rim is in a state of tension. 
