It is admitted that with a certain number of teeth of a certain proportionate length as compared with the radii, there may be a segment of a circle drawn from some center which would give “very near” a true figure to the tooth; but “very near” ought to be expunged from the vocabulary of engineers and millwrights; for that “very near” will depend on the chance of hitting the right center and right radius, according to the diameter of the wheel, and the number of teeth; against which hitting, the odds are very great indeed. Among the Mathematical Instrument Makers, Chronometer, Clock and Watch Makers, the answers to the inquiries were, by some, “We have no rule but the eye in the formation of the teeth of our wheels;” by others, “We draw the tooth correctly on a large scale to assist the eye in judging of the figure of the small teeth;” by another, “In Lancashire, they make the teeth of watch wheels of what is called the bay leaf pattern; they are formed altogether by the eye of the workman; and they would stare at you for a simpleton to hear you talk about the epicycloidal curve.” Again, “The astronomical instrument makers hold the bay leaf pattern to be too pointed a form for smooth action; they make the end of the tooth more rounding than the figure of the bay leaf.” It is curious to observe with what accuracy the practiced eye will determine forms.... How important it is, then, that these Lancashire bay leaf fanciers should be furnished with pattern teeth of large dimensions cut accurately in metal or at least in cardboard; and that they should frequently study them, and compare their work with the patterns. These Lancashire workmen are called bay leaf fanciers, because they cannot be bay leaf copiers; since it is notorious that there are not two bay leaves of the same figure. Hawkins then describes a method of generating correctly curved teeth, or rather of truing them after they had been roughly formed, devised by Mr. Saxton of Philadelphia, “who is justly celebrated for his excessively acute feeling of the nature and value of accuracy in mechanism; and who is reputed not to be excelled by any man in Europe or America for exquisite nicety of workmanship.” By this method the faces of the teeth were milled true by a cutter, the side of which lay in a plane through the axis of a describing circle which was rolled around a pitch circle clamped to the side of the gear being cut. It is by this general method that the most accurate gears and gear cutters are formed today. While he by no means originated the system, Hawkins seems first to have grasped the practical advantages of the involute form of teeth. Breaking away from the influence of Camus, the very authority he was translating, who seems to have controlled the thought of everyone else, Hawkins writes the following rather remarkable words:[63] [63] _Ibid._, pp. 160 _et seq._