78 
examples of this plant discovered in the British Carhoniferons 
Strata. M. Lesquereux has figured and described (Coal Flora 
of Pennsylvania, p. 557, pi. 83, fig. 5, and 84, fig. 1) under 
the name of Lepidoxylon anonialum, a plant which he is 
inclined to regard as identical with Brongniart’s plant — but 
my specimens incline me to doubt the identity. Though 
the specimens described by M. Lesquereux have dichoto- 
mous leaves, none of them show the globular terminations so 
characteristic of Brongniart’s examples as well as of mine. 
According to M. Lesquereux, Geinitz obtained another 
example of the plant, but not having his figure within 
reach I am uncertain whether or no his specimen is identical 
with that of M. Brongniart. Anyhow, the plant is one of 
extreme rarity. It is further interesting to discover examples 
of so rare a form at points so remote from each other as 
Saarbruck and Ashton-under-Lyne. 
The diffraction of a plane polarised wave of light.” By 
B. F. Gwyther, M.A. 
The possibility of representing a wave of light in all its 
effects by a system of secondary waves arising from all 
points in a wave front seems to be a consequence of the 
j)rinciple of the super-position of small motions, but we may 
consider it purely as a mathematical question, and enquire 
whether it is possible that the vibrations of a plane polarised 
wave may be represented at all portions of space in advance 
of any position of the wave front, by the resultant displace- 
ments due to spherical waves emanating from a continuous 
system of sources over the wave front, and conforming with 
some law. It is this mathematical question which I have 
proposed to myself in this paper, and I find that the form 
of the law of displacement in the secondary wave is not 
made determinate by the conditions : that the form is such 
that all the differential coefficients in the integrated form 
give the same values as the corresponding differential co- 
