it can only assume a stable position if the points of contact 46 48 are on a straight line 52a such line must also always contact the centres of circles 40a 50a since two contacting circles must always have centers on a straight line passing through the contact point then the motion of the centre of ball 50 must always be on a circular locus l2 centred about the centre of circle 40a and of radius r1 r where r1 is the radius of circle 40a and r is the radius of circle 50a it will be seen that as the centre of circle 50a thus moves about the centre of circle 40a and the line 52a which represents the line joining the momentary points of contact 46 48 always passes through the centre of circle 40a the locus l1 of point 46 is also a circle about the centre of circle 40 a this having a radius 2r r1 furthermore since the centre of circle 40a is always on line 52a and distant r2 from point 46 its locus l3 of movement is a circle about the centre of circle 40a locus l3 being distant r2 from point 46 so that its radius is r1 r2 2r the positions of the axes 36 44 are not shown in fig2 but it will be easily appreciated that axis 44 can be positioned to pass through the centre of curvature of circle 40a at a desired fixed angle.