The problem of vertical divergence on the double-crystal spectrometer is treated, both theoretically and experimentally. It is shown that, even in the case of finite vertical divergence, one may get the resulting profile of the measured spectral line as a convolution of the true spectral line and the instrumental smearing function. The general method of calculating this smearing function is given. Further, the influence of the vertical divergence is separated, and some general features are derived. In the experimental part, a double-crystal spectrometer for the fluorescent method of excitation and the precise adjustment of the instrument is described in detail. The theoretical formulas concerning instrumental smearing, the dependence of the peak intensity and the shift of the maximum on the vertical divergence are verified experimentally. © 1968 Czechoslovak Academy of Sciences.