274 Proceedings of the Royal Society of Edinburgh. [Sess. 
were this explanation correct, that the etched glass would scatter least of 
all, which, of course, is contrary to the fact. The explanation is that an 
etched pit, unlike a pit due to grinding, is always of a depth proportional 
to its width, and hence in etched glass the steepness of the sides of even the 
largest pits is maintained. Lord Rayleigh, in a paper published in the Pro- 
ceedings of the Optical Convention, p. 73, 1905, puts the matter thus : “ Some 
very curious observations were also made upon the effect of hydrofluoric 
acid upon glass originally finely ground. The acid acts in such a way as 
to eliminate from the roughened surface all the finer irregularities, leaving 
only those of longer periodicity. It is not difficult to form a theory, and 
to illustrate that theory by drawing, especially if one takes the case of two 
dimensions. If one assumes, as seems reasonable, that the hydrofluoric 
acid always eats in normally to the surface, then if we start with any 
particular surface and imagine that from every point of that surface 
spheres are drawn having their centres in the surface and a radius pro- 
portioned to the time during which the hydrofluoric acid acts, then the 
envelope of all those surfaces will be the surface to be expected at the 
close of the operation. You see the ultimate result will be to leave the 
surface in the form of spherical segments, the centres of the spheres corre- 
sponding to the deepest places in the original roughly ground surface. I 
have a slide showing the appearance of such a piece of ground glass after 
treatment. It appears to be divided into a number of cells, and the wall 
of each spherical segment separated from its neighbour is of the nature of 
a ridge. Each cell is of itself absolutely devoid of structure ; it appears 
finely polished.* Although the surface was originally finely ground all over^ 
all the minor irregularities are gone, and we are left with the surface 
which in a sense might be called polished, although of course it is far 
from flat. In each case, if we are looking down upon the surface, the 
middle of these segments will be the deepest place ; the ridges are raised 
and exceedingly sharp. According to the theory here briefly sketched 
they would be mathematically sharp, and such they appear to be.” As 
regards the ground glass experimented on, the nature of the operation by 
which it is produced is well understood. See, for example, a paper by 
* Following Lord Rayleigh, I tested the smoothness of the pits on the surface of the 
etched glass (no. 8) by using the pits as lenses, and the photomicrographs, Plate II. figs. 6 and 7, 
show the images thus obtained when the object was (1) a luminous point, and (2) a luminous 
cross. The definition is sufficiently good to leave little doubt as to the smoothness of the 
pits ; and indeed the perfection of the images is somewhat surprising, in view of the fact 
that the pits are for the most part of a decidedly elongated shape, the length along the 
surface of the plate being often several times as great as the breadth, as appears clearly in 
the photomicrograph, Plate II. fig. 5. This fact, no doubt, accounts, partly at least, for the: 
marked astigmatism shown by many of the images when thrown slightly out of focus. 
