INSTRUCTIONS

The general instructions for use of the Robertson three figure
cosine strips apply to case involving a fourier synthesis of a centro-
symmetric projection, but the method can be extended appropriately (by)
expanding the summations to cover the non-centrosymmetric case.

The summation for the electron-density of the type:

$$
\mathcal{L}_{xy} = \sum_{k}^{h} \sum_{\pm}^{k} F_{hk0} \cos 2\pi \frac{hx + ky}{\sqrt{2}}
$$

can be expanded to:

$$
\mathcal{L}_{xy} = \sum_{k}^{h} \sum_{\pm}^{k} F_{hk0} \left\{ \cos 2\pi ky \cdot \cos \frac{2\pi kx}{\sqrt{2}} - \sin 2\pi ky \cdot \sin \frac{2\pi kx}{\sqrt{2}} \right\}
$$

The expansion can be rearranged as the following:

$$
\mathcal{L}_{xy} = \sum_{k=0}^{h} \sum_{\pm}^{k} F_{hk0} \cos 2\pi ky \left\{ \cos 2\pi hx \quad - \sum_{\substack{n \\ S_y}}^{h} F_{hk0} \sin 2\pi ky \sin 2\pi hx \right\}
$$

or by substituting for the bracketed summations:

$$
\mathcal{L}_{xy} = \sum_{0}^{h} c_y \cos 2\pi hx \rightarrow \sum_{0}^{h} s_y \sin 2\pi hx
$$

Given a series of values, $F_{hk0}$ for the amplitudes, where
$h$ varies from 0 to $h$ and $k$ from $-k$ to $k$ (centrosym. case, only), the
amplitudes are arranged in groups of the same $h$ value in order of
increasing $k$. The various amplitudes on their respective strips are
then inserted into the columns of the Perspex board which is numbered
for the various $k$ values when $h$ is held constant, as in this case. The
summations are to be made using the cos and sin stencils for $h$, even
and odd, for $y$ intervals ranging from 0 to 30 and beyond, if necessary.

The cell divisions are in 1/120ths and can be used for 1/60ths by
omitting every other stencil. The summation for a given h and y value
should be recorded preferably on tape, for the purpose of checking.

when the summations for both the sine and cosines over all
values of h and y have been completed, the sums, C<sub>y</sub> and S<sub>y</sub> represent
a set of new coefficients. These coefficients are then chosen from
the same set of amplitude strips and placed in the Perspex board in
order of increasing h values. The stencils are placed over the strips