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The study discusses the validity of the law of similarity for the impulse breakdown of gases at low pressure and small inter-electrode distances. The research has been done theoretically, experimentally and numerically. The experiments were conducted under well-controlled laboratory conditions. The combined measurement uncertainty was less than 5%. The experiments were carried out with gases SF6, N2 and He. The electrodes were made of copper, but also of metals with different values of the work function. The obtained results are presented through the impulse characteristics for similar systems. Such a presentation only provided qualitative information. In order to obtain quantitative information, a modified Wilcoxon Rank Sum Test (U test) was performed. The obtained results show that the law of similarity is valid for the DC breakdown of gases, but it is not valid for the impulse breakdown of gases. It can be concluded that the law of similarity is inapplicable for the design of gas-insulated systems under low pressure at small values of the inter-electrode distance.