The article provides an analysis of scientific papers on the study of a hydraulic shock absorber - an air-hydraulic cap, shows that at present there is no consensus on the choice of the numerical value of the polytropic coefficient n. In practice, during the operation of pumping stations with long pressure pipelines, in the event of a sudden power outage, water hammer often occurs to the motors of the main pumps. To prevent this phenomenon, it is convenient to apply a hydraulic shock absorber. The accuracy of calculating the shock absorber depends on the reliable value of the coefficient n. The correct selection of the numerical value of the polytropic coefficient n provides for determining the optimal dimensions of the proposed hydraulic shock absorber. There are different opinions about the choice of the numerical value of n among scientists. N.E. Zhukovsky, when calculating the hydraulic shock absorber, takes n = 1.41. V.S. Dikarevsky accepts n=1.0. Therefore, the rationale for the correct choice of the numerical value of the polytropic coefficient for calculating the absorber in the case of water hammer is very relevant. The paper presents the results of experimental studies of the polytropic coefficient n in a hydraulic shock absorber from a decrease in pressure. When conducting experiments on the study of the absorber, modern scientific instrumentation was used. At the same time, the obtained results of the experiments confirm that the variability of the value of the polytropic coefficient during hydraulic shock in the cap and the correctness of the recommendation of D.A. Fox. The conducted studies prove that the polytropic coefficient has a strictly polytropic character.