The full equations of motion for the flow of a viscous fluid have proved too complicated for any general solution to be obtained. It is to be doubted if, in. the near future, the problem of fluid motion will be solved in a general manner, although solutions for a few special cases may be found. In view of this it is of some value to investigate experimentally certain cases which are likely to prove of mathematical interest at a later date; this paper deals with such a problem. By means of the results obtained experimentally the mathematical analysis may be guided along the right lines and a satisfactory analytical solutioa of the problem be obtained. The instrument used in exploring the fluid motion has a special interest of its own as it may prove of use in further aerodynamical investigations where the flow is of three–dimensional character. The development of this instrument, and its performance when tested, are described in Part I. The experiments for the measurement of the forces on the spinning sphere are described in Part II.