The copying principle is evident in this machine; for the plane surface results from the combination of the straightness of the bed with the straightness of the transverse slide along which the tools are moved. It should, moreover, be observed that it is precisely this machine which would be employed for preparing the straight sliding surfaces required in the construction of planing and other machines, and thus one of these engines becomes the parent, as it were, of many others having the same family likeness, and so on _ad infinitum_. Thus, having once obtained perfectly true surfaces, we can easily reproduce similar surfaces. But the reader may wish to know how such forms have been obtained in the first instance; how, for example, could a perfectly plane surface be fashioned without any standard for comparison? This was first perfectly done by Sir J. Whitworth, forty-five years ago. Three pieces of iron have each a face wrought into comparatively plane surfaces; they are compared together, and the parts which are prominent are reduced first by filing, but afterwards, as the process approaches completion, by scraping, until the three perfectly coincide. The parts where the plates come in contact with each other are ascertained by smearing one of them with a little oil coloured with red ochre: when another is pressed against it, the surfaces of contact are shown by the transference of the red colour. Three plates are required, for it is possible for the prominences of No. 1 exactly to fit into the hollows of No. 2, but in that case _both_ could not possibly exactly coincide with the surface of No. 3; for if one of them did (say No. 1), then No. 3 must be exactly similar to No. 2, and consequently when No. 2 was applied to No. 3, hollow would be opposed to hollow and prominence to prominence. A little reflection will show that only when the three surfaces are truly plane will they exactly and entirely coincide with each other. The planes, when thus carefully prepared, approach to the perfection of the ideal mathematical form, and they are used in the workshop for testing the correctness of surfaces, by observing the uniformity or otherwise of the impression they give to the surface when brought into contact with it, after being covered by a very thin layer of oil coloured by finely-ground red ochre.