It would now be needful to divide the whole into three parts, by the comparison of the spaces from 0 to 16, from 16 to 32, and from 32 to 48, the points 16 and 32, being adjusted until exactly equal, which is the most difficult part of the work; and then these three distances being bisected four times, every point of the 48 would have been examined, and some of them twice over. These adjustments having been repeatedly verified, during which a very frequent recurrence to the total length is imperative; the concluding step is to file off the corners of the 48 slips very carefully, so as to convert them into a line with undulations, slight it is true, but which represent fifty-fold the actual errors in the guide-screw; and therefore shift the table simultaneously with its general traverse, so as to apply the exact corrections for inequality, at every point examined and found to be in error.

But the term error must be received in a very restricted sense, as it deserves to be noticed, that Mr. Donkin first used a screw made by Mr. Maudslay, and the maximum deflection of the curved edge of the compensation bar from a straight line, was very nearly the eighth of an inch, indicating the maximum error of the screw to have been about the 400th part of an inch; and as the curve was nearly limited to a single undulation, or a hill at one end, it may be presumed this minute error was in part attributable to a difference in the material, a source of perplexity from which no care is a sufficient protection. The dividing engine was employed as a traversing lathe in cutting a new screw, and which, although it had the advantage of the compensation, only reduced the error of the new screw to about one-third the quantity of that of the first; as shown by the new curve assumed by the compensation bar, its deflection being 1/20 of an inch, when re-adjusted in the tedious and anxious method described.*

Having at length concluded the remarks on some of the most refined and scientific efforts that have been employed in pro-ducing and perfectioning the screw, I shall in the next and concluding section of this already extensive chapter, proceed to the discussion of a variety of important considerations and con-ditions, which practically influence the proportions, forms, and general character of screws, to adapt them to multifarious purposes in the mechanical and constructive arts.

* In the past year, 1842, Mr. Donkin has made a similar but enlarged dividing engine. The length of traverse of the new machine is 42 inches, the screw has 40 threads in the inch, the compensation bar is as 60 to 1, and the value of one single tooth in the counting wheel is equivalent to the 60,000th part of an inch; that of the first machine having been the 30,000th part.

It is to be hoped that Mr. Donkin will complete his labours, by publishing a detailed account of these machines, the latter of which, in particular, exhibits throughout its structure a most refined contrivance and execution, of which no adequate idea can possibly be conveyed within the limits of this slender notice, nor without exact drawings of the details, to the arrangement of which great attention has been bestowed.