Miscellany

The mechanism of Beevers-Lipson strips

Today, when Fourier transforms on several thousand data items for large, three dimensional unit cells at a resolution of about 0.3 Å require less time than it takes to gulp down a cup of coffee, it is difficult to imagine the size of the task confronting early crystallographers, where this operation was almost unthinkable. After all, even a two dimensional summation of: S {A cos 2p (hx+ky) + B sin 2p (hx+ky)} for 500 data items into 2000 points requires 106 summations, let alone any work required to calculate the trigonometric functions! The boxes of strips themselves have virtually disappeared although they were once almost universal in the crystallographic community. A handsome box still survives in the Clarendon Lab at Oxford U. The great contribution of Beevers and Lipson in 1936 was twofold: to simplify the calculations greatly by factorizing the trigonometric expressions to reduce the two dimensional calculations to many fewer one dimensional ones, and to provide a convenient technique for carrying out the summations - the strips themselves.

Some people used mechanical calculators for the sums, but most found it far quicker and more accurate to use mental arithmetic, a skill more widely found then than now.

Bob Gould
From the BCA Newsletter, Dec. 1998