The planes which occupy the position of the wheel spokes will then each represent a rectangle of the size of _FD_. The construction is shown by the dotted lines in Fig. 69.; _c_ being the center of the uppermost circle. [Illustration: Fig. 69.] Within each of the smaller rectangles between the circles, draw the curve _EB_ in perspective, as in Fig. 69. Draw the curve _xy_, touching and inclosing the curves in the rectangles, and meeting the upper circle at _y_.[32] Then _xy_ is the contour of the surface of the cup, and the upper circle is its lip. If the line _xy_ is long, it may be necessary to draw other rectangles between the eight principal ones; and, if the curve of profile _AB_ is complex or retorted, there may be several lines corresponding to _XY_, inclosing the successive waves of the profile; and the outer curve will then be an undulating or broken one. [Illustration: Fig. 70.] III. All branched ornamentation, forms of flowers, capitals of columns, machicolations of round towers, and other such arrangements of radiating curve, are resolvable by this problem, using more or fewer interior circles according to the conditions of the curves. Fig. 70. is an example of the construction of a circular group of eight trefoils with curved stems. One outer or limiting circle is drawn within the square _EDCF_, and the extremities of the trefoils touch it at the extremities of its diagonals and diameters. A smaller circle is at the vertical distance _BC_ below the larger, and _A_ is the angle of the square within which the smaller circle is drawn; but the square is not given, to avoid confusion. The stems of the trefoils form drooping curves, arranged on the diagonals and diameters of the smaller circle, which are dotted. But no perspective laws will do work of this intricate kind so well as the hand and eye of a painter. IV. There is one common construction, however, in which, singularly, the hand and eye of the painter almost always fail, and that is the fillet of any ordinary capital or base of a circular pillar (or any similar form). It is rarely necessary in practice to draw such minor details in perspective; yet the perspective laws which regulate them should be understood, else the eye does not see their contours rightly until it is very highly cultivated. [Illustration: Fig. 71.] Fig. 71. will show the law with sufficient clearness; it represents the perspective construction of a fillet whose profile is a semicircle, such as _FH_ in Fig. 60., seen above the eye. Only half the pillar with half the fillet is drawn, to avoid confusion. _Q_ is the center of the shaft. _PQ_ the thickness of the fillet, sight-magnitude at the shaft’s center. Round _P_ a horizontal semicircle is drawn on the diameter of the shaft _ab_. Round _Q_ another horizontal semicircle is drawn on diameter _cd_. These two semicircles are the upper and lower edges of the fillet.