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Abstract of Proceedings. 
1906. 
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GENERAL MEETINGS. 
Friday, January 5th. Sir Samuel Wilks, Bart., M.D., F.RS., 
President, in the Chair. 
Mr. Walter Baily, M.A., gave a lecture entitled «‘ Patterns 
in Space,’’ illustrated with models. In the simplest kind of 
pattern, he said, such as occurs in ribbons, borders, or friezes, 
there is a direction such that, if a point is taken and a certain 
distance measured in that direction, the same state of things is 
found at each end of this distance. A line, straight or crooked, 
can be drawn across the pattern, and similar lines at the proper 
distance from one another. These lines will divide the pattern 
into enclosures, exactly like one another, and the design in all 
the enclosures will be exactly the same. Passing on to patterns 
in which the recurrence of the same state of things occurs in more 
than one direction, so as to cover a surface of any extent (of which 
the patterns of wall-papers are a familiar example), we have to 
inquire how to divide a flat surface into enclosures, all exactly alike, 
and in similar positions; and, this being done, it only remains 
to draw some design in one of the enclosures, and to repeat it in 
all the others, for a pattern to be formed. The simplest enclosures 
are the square and the hexagon. These may be altered by lengthen- 
ing any pair of opposite edges, and again by sloping the sides, 
maintaining opposite sides always equal and parallel. Any amount 
of complication may be introduced by cutting out a piece from 
one side of the figure and sticking it on to the corresponding part 
of the opposite side, and repeating the same process with the other 
pairs of opposite sides. A designer of wall-papers might first 
prepare a very complicated form of enclosure, and then invent a 
design to fill it. He would find much more scope for his imagination 
than if he worked from a simple oblong. The same method may 
be applied to find enclosures of space of three dimensions. The 
simplest form is the cube. This may be altered as before, by 
lengthening and sloping into variously-shaped bricks, which may 
