The elements Li, Na, K, Rb, Cs, Ba, La and Tl, having their strongest atomic lines in the wavelength range from 500 to 1000 nm, are exited in a Grimm glow discharge lamp. The radiation is detected by a silicon photodiode array which shows a good spectral response in the mentioned region. Electrically non-conductive rock powders (NIM samples) serve as sample materials which contain the elements named above as trace elements only, in the majority of cases. The standard deviation which is essential for the intensity measurement can be determined by the measuring system and by fluctuations of the radiation, and it is investigated examplary in some analysis. The influence of the graininess gathering particular signification in the analysis of heterogeneous samples is shown, and the effect on precision and accuracy is proven experimentally and by means of Wilson's theory. Furthermore, calibration curves, limits of detection and the weight tractions of the elements Li, Rb, Ba and partially Na, K and La in rock samples are reported.