The invention is related to a method of determininng the instantaneous rotation speed of a drill string or a drill bit in a borehole or the lateral shocks applied to the string or bit. The centripetal acceleration of the drill string is measured at at least two opposite ends of a drill string diameter so as to obtain two centripetal acceleration signals ac1 and ac2; the signals ac1 and ac2 are combined and the instantaneous rotation speed or the lateral shocks are derived from said combined signal. The accelerometers must be of the type delivering a signal with a DC component. An important application of the invention is to transform drill string rotation speed dependent data acquired versus time with a constant sampling time increment T.sub.c separating successive data, into compensated data which would be obtained for a substantially constant drill string rotation speed S.sub.c. The compensated data are obtained either by adjusting the constant sampling time interval T.sub.c into a variable sampling time increment T.sub.v, using the measured instantaneous rotation speed S, or by selecting the data which have been acquired during periods of time during which the instantaneous rotation speed of the drill string varied within predetermined limits only.