A second imperfection is that in order to loosen the pattern in the sand or mould, and enable its extraction by hand from the mould, the pattern requires to be _rapped_ in the mould, the blows forcing back the sand of the mould and thus loosening the pattern. In ordinary practice the amount of this rapping is left entirely to the judgment of the moulder, who has nothing to guide him in securing an equal amount of pattern movement in each direction in the mould; hence, the finished mould may be of increased radius at the circumference in the direction in which the wheel moved most during the rapping. Again, the wood pattern is apt in time to shrink and become _out of round_, while even iron patterns are not entirely free from warping. Again, the cast metal is liable to contract in cooling more in one direction than in another. The amount of clearance usually allowed for pattern-moulded cast gearing is given by Professor Willis as follows:--Whole depth of tooth 7/10, of the pitch working depth 6/10; hence 1/10 of the pitch is allowed for top and bottom clearance, and this is the amount shown at B in Fig. 143. The amount of side clearance given by Willis as that ordinarily found in practice is as follows:--"Thickness of tooth 5/11 of the pitch; breadth of space 6/11; hence, the side clearance equals 1/11 of the pitch, which in a 3-inch pitch equals .27 of an inch in each wheel." Calling this in round figures, which is near enough for our purpose, 1/4 inch, we have thickness of tooth 1-1/4, width of space 1-3/4, or 1/2 inch of clearance in a 3-inch pitch, an amount which on wheels of coarse pitch is evidently more than that necessary in view of the accuracy of modern moulding, however suitable it may have been for the less perfect practice of Professor Willis's time. It is to be observed that the rapping of the pattern in the founder's mould reduces the thickness of the teeth and increases the width of the spaces somewhat, and to that extent augments the amount of side clearance allowed on the pattern, and the amount of clearance thus obtained would be nearly sufficient for a small wheel, as say of 2 inches diameter. It is further to be observed that the amount of rapping is not proportionate to the diameter of the wheel; thus, in a wheel of 2 inches diameter, the rapping would increase the size of the mould about 1/32 inch. But in the proportion of 1/32 inch to every 2 inches of diameter, the rapping on a 6-foot wheel would amount to 1-1/16 inches, whereas, in actual practice, a 6-foot wheel would not enlarge the mould more than at most 1/8 inch from the rapping.