Purpose. The study has two purposes: development of mathematical model of one-axis inclinometer transducer of zenith and sight angles designed in the form of extended floating tube, balanced by the different and with floatation miss in viscous fluid filling in the transducer case; examination of pointing errors and development of the techniques that reduce them. Methodology. The research used the methods of comparative analysis and mathematical modeling. Findings. Mathematical model of one-axis inclinometer transducer of zenith and sight angles on vibrating base has been developed. Sensing inclinometer device has been made as extended cylindrical floating tube balanced by different and on floatation miss in viscous fluid filling in transducer case. Measurement range of zenith and sight angles is 0 - 360^o. The formulae permitting to evaluate measurement errors of zenith, sight angles and floating tube movement on the axis has been obtained. Originality. For the first time we have developed the mathematical model of inclinometer transducer with two degrees of freeness: longitudinal axial movement and rotary movement about symmetry axis. Measurement range of zenith and sight angles is 0 - 360^o. Practical value. The resulted mathematical model may be accepted as a basis for inclinometer transducers with float structure intended to control dimensional orientation of a borehole during drilling process.

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