"I must ask you to allow me yet leave to reply to the objections you make to two statements in my catalogue, as those objections would otherwise diminish its usefulness. I have asserted that, in a given drawing (named as one of the chief in the series), Turner's pencil did not move over the thousandth of an inch without meaning; and you charge this expression with extravagant hyperbole. On the contrary, it is much within the truth, being merely a mathematically accurate description of fairly good execution in either drawing or engraving. It is only necessary to measure a piece of any ordinary good work to ascertain this. Take, for instance, Finden's engraving at the 180th page of Rogers' poems; in which the face of the figure, from the chin to the top of the brow, occupies just a quarter of an inch, and the space between the upper lip and chin as nearly as possible one-seventeenth of an inch. The whole mouth occupies one-third of this space, say one- fiftieth of an inch, and within that space both the lips and the much more difficult inner corner of the mouth are perfectly drawn and rounded, with quite successful and sufficiently subtle expression. Any artist will assure you that in order to draw a mouth as well as this, there must be more than twenty gradations of shade in the touches; that is to say, in this case, gradations changing, with meaning, within less than the thousandth of an inch. "But this is mere child's play compared to the refinement of a first- rate mechanical work--much more of brush or pencil drawing by a master's hand. In order at once to furnish you with authoritative evidence on this point, I wrote to Mr. Kingsley, tutor of Sidney-Sussex College, a friend to whom I always have recourse when I want to be precisely right in any matter; for his great knowledge both of mathematics and of natural science is joined, not only with singular powers of delicate experimental manipulation, but with a keen sensitiveness to beauty in art. His answer, in its final statement respecting Turner's work, is amazing even to me, and will, I should think, be more so to your readers. Observe the successions of measured and tested refinement: here is No. 1:-- "'The finest mechanical work that I know, which is not optical, is that done by Nobert in the way of ruling lines. I have a series ruled by him on glass, giving actual scales from .000024 and .000016 of an inch, perfectly correct to these places of decimals, and he has executed others as fine as .000012, though I do not know how far he could repeat these last with accuracy.' "This is No. 1 of precision. Mr. Kingsley proceeds to No. 2:-- "'But this is rude work compared to the accuracy necessary for the construction of the object-glass of a microscope such as Rosse turns out.'