162 
two surfaces, as accurate as the planing tool could make 
them, I coated one of them thinly with colouring matter 
and rubbed the other over it. Had the two surfaces been 
true, the colouring matter would have spread itself uniformly 
over the upper one. It never did so, but appeared in spots 
and patches. These marked the eminences, which I removed 
with a scraping tool till the surfaces became gradually more 
nearly coincident. But the coincidence of two surfaces 
would not prove them to be planes. If the one were 
concave and the other convex they might still coincide. I 
got over this difficulty by taking a third surface and 
adjusting it to both of the others. Were one of the latter 
concave and the other convex, the third plane could not 
coincide with both of them. By a series of comparisons 
and adjustments, I made all three surfaces coincide, and then, 
and not before, knew that I had true planes. When they 
were perfect, I took them one Sunday morning to a fellow- 
workman who had laughed at my attempts and thought I 
was mad. When I showed him what I had done he was 
thunderstruck, but he rejoiced over the work.” The impor- 
tance of this discovery cannot be overestimated, and it laid 
the foundation for the present accuracy with which 
mechanism can be constructed. From this time it became 
possible to construct surfaces such as the valves of steam 
engines, the tables of printing presses, and all kinds of slides 
requiring a high degree of truth, with an accuracy practi- 
cally perfect. The first set of true planes having been 
obtained, the work of producing copies of them sufficiently 
accurate for all practical purposes of the woi’kshops became 
comparatively easy. Quite recently a planing machine has 
been made in Sir Joseph Whitworth’s own shop, whose bed 
is fifty feet long, and the grooves in which the table works 
are probably the longest true planes ever made. So exactly 
are these surface plates now made that if one of them be 
placed upon the other, both being clean and dry, the upper 
