These notes show that the major obervable features of a whirlpool galaxy can be explained by fundamental kinematics. The orbit in the r infinity limit must be a hyperbolic spiral. The orbit is totally non Newtonian and non Einsteinian because the gravitational potential does not depend on M, the mass that is assumed to be at the centre of a whirlpool galaxy. The kinematics of plane polar coordinates is an example of Cartan geometry because the axes are rotating and there is a spin connection present. The geometry is more fundamental than Newton and Einstein, both of whom fail completely in a whirlpool galaxy. I am not sure whether the general public is even aware of this fact, having been fed a diet of crass dogma. I am well aware that the whirlpool galaxy is an enormously complicated system, but this kinematic theory explains it major features with great elegance and simplicity. Robert Cheshire has analyzed a whirlpool galaxy in great detail, and I am prepared to publish his findings in any format he wishes. I am also aware that the plasma theory has contributed greatly to galactic theory, for example the recent ECE papers on the Beltrami theory. However UFT262 is a beautiful result – geometry is perfect beauty. I will go on developing UFT262 in the next few notes.