4. From the foregoing it appears that the teeth of two wheels working together tend constantly to assume a form more and more perfect: as they abrade each other while imperfect, and cannot wear themselves beyond perfection.
5. For a similar reason the division of the teeth cannot remain unequal: for those that are too far distant from a given tooth will be attacked behind, and those that are too near before; so that the division also will finally become perfect.
But it must be remembered that these recoveries of form are in their nature very slow; since the nearer the teeth come to perfection the slower is their approach to it: so that in thus dwelling on these properties, we do not advise the making of bad wheels that they may become good; but only wish to destroy an honest prejudice that has already much impeded the progress of the System; namely, that it requires great nicety to adjust them so as to work together at all: which is—(to say the least) a very great error.
In [Plate 14], [fig. 1], I have shewn the apparatus presented at the Exchange, as mentioned in [page 110] preceding. A B is the stand; C D is a disk turning on the centre E; b a is the transparent line cut through the stand, and representing the place of contact of two wheels geering together. It is there seen, (supposing the disk to turn in the direction of the arrow) that the action of the teeth, is always progressive along the transparent line a b; whether the single or double obliquity G or F be used. In reality, the lower end of any tooth c, does not uncover the line a b, till the upper point of the succeeding tooth d has begun to cover it; whereas, observing a few of the common teeth represented at H, as directed to the centre of the disk, they would be seen to pass the line a b all at once; and thus to represent, with a certain exaggeration, the transient manner of acting of the common geering.
Some knowledge of the nature of this geering may be gathered from its very appearance: see [fig. 5] [Plate 14]. To represent these teeth properly, no light must appear between them. The tops of the teeth offer a continued circular line, similar to what it would be if there were no teeth at all: and the latter are distinguished only by a different shading of their front and lateral surfaces. The reason (as has been already observed) is, that they are necessarily so placed, as that the last end of any tooth shall not quit the plane of the centres, until the first end of the succeeding tooth arrives at it; which principle precludes the possibility of any space remaining between the teeth, that an eye directed parallelly to the axes could penetrate. Such a space indeed would introduce a portion of the properties of the old geering, which it is the object of this System to avoid. As this wheel then appears in [fig. 5], so it acts: that is equally and perpetually.
It were well also to observe the appearance of these wheels on their edges; or in the planes which, as wheels they occupy. The [4th. figure] of this [Plate] is outlined with some care, in order to shew the varying, and seemingly anomalous form which the teeth assume as they approach the boundaries of the figure. Although cut as obliquely to the axis there, as any where else, the receding cylindrical surface, thus seen, appears to take this obliquity away; and the very outward teeth seem nearly parallel to the axis of the wheel. But this is only appearance: and we give here one example of it, that we may not be obliged to lose much time hereafter, in drawing correctly, wheels on this principle—a process indeed which in many cases, would be found very difficult, if not impossible.