Numerical solutions have been obtained of the equations governing the steady motion of a viscous fluid in a tube of circular cross-section coiled in the form of a circle. Results are presented for the range 96 to 5000 of the parameter D = 4R√(2a/L). Here R = Ga3/4μν, where G is the constant pressure gradient maintaining the motion, a the radius of the cross-section of the tube, and L the radius of the circle in which the tube is coiled. The solutions have been carefully checked for accuracy and the results are compared with previous work on this problem. Substantial discrepancies are found to exist with a recent set of calculations over approximately the same range of D.