CHAPTER XVI. PHILOSOPHICAL PROBLEMS- TIME-PIECES MICROMETER AND DIVIDINGSCREW MICROMETERS FOR SURVEYING QUADRANT - BAROMETERS MEASURING DISTANCES - HISTORY OF THE INVENTION OF MICROMETERS BESIDES all his surveying and civil-engineering, and the manifold alterations he devised in both his condensing and his wheel engines, Mr. Watt bestowed, during the years of which we have now been speaking, in concert with his friend Small, a good deal of thought on various other ingenious mechanical contrivances, which supplied pleasant amusement to their inventive and reflective brains. "We have "abundance of matter to discuss," says the great engineer; "though the damned engine sleep in quiet!" "The French, 66 66 you know," says Small, "offer large præmia for time-keepers. "Were I idle, I should try to win one of these. But physic "exhausts my whole faculties, and pays but indifferently. I "am so made that I suffer no fatigue from thinking ever so "long and attentively on a subject in which I can get for"ward; but if I am absolutely puzzled, and see no clue, my "head turns round, and I speedily become more tired than a galley-slave. Physic very fortunately furnishes abundance "of these profitable points." "I have perfected my clock "with one wheel of nine inches diameter, which is to tell "hours, minutes, and seconds, and strike, and repeat, and be "made for thirty shillings." And again, "My clock of one "wheel, that shows hours, minutes, and seconds, and strikes "the hours and repeats them, is nearly finished. The striking "and repetition are good, the rest is gimcrack." § 7 November, 1772. † 5 October, 1770. 14 February, 1771. § 16 December, 1771. "You wrote me before," says Mr. Watt,* "of your clock "with one wheel. Did I ever mention to you a striking 66 66 part, regulated by a balance pendulum with live scapement, "which had only one wheel?" But some months later,† Everybody," says Small, "is too much engaged for the "prosecution of schemes, so that even my clock is not prose"cuted, and I have only one, which I cannot send to you; "I have just ordered a pendulum clock to be made with no "wheel at all;"-and, "when my clock with one wheel," he afterwards adds,§ "was finished, I found it too complicated, " and have now got one with no wheel, and only one sector "with seventy-five teeth. It strikes, repeats, shows hours, "minutes, and seconds, and goes eight days, with the usual "descent of the weight. This is to be ranked in mechanics, "as riddles and rebuses are ranked in poetry." 66 66 On which comes this comment of the sagacious Watt:"As to clocks, I do not fully conceive how you can make yours go eight days with the ordinary descent of the weight, "unless by pulleys or something equivalent, which would only "be a quibble upon a wheel; "-thus answered by the inventor:-"there is no quibble in my clock, and we have "now found a tolerable workman for the execution of it. "One is now making, which will show with much more accuracy than any other clock has hitherto done, the spheric "phenomena relating to astronomy, sidereal and mean time, "hours, minutes, and seconds, with only one wheel and one "sector. It will also strike and repeat the hours. The wheel "has 72 teeth and the sector 75 only; "-" I have had a new "scapement made for watches, of such marvellous virtue, that "if the maintaining power is quadrupled, or decupled, the "number of the vibrations will be lessened, but not above ten "in twenty-four hours." ** And—" I have taken out a patent "for improvement on clocks and other time-pieces, and want "you vastly to help me to draw up the specification, which * 24 December, 1771. 17 January, 1773. 27 January, 1773. **15 March, 1773. 66 "must be given in soon. I have made a church-clock, con"sisting only of one wheel of 126 pins, and one sector of 75 "pins, and a hammer, with a scapement for the sector and "another for the hammer. It strikes the hours, shows hours, minutes, and 20th parts of minutes, and goes eight days. “And I have given drawings of a pocket-watch, which is to "consist of one wheel and two sectors, and is to show hours, "minutes, and seconds, and to have only 142 pins in the "whole watch, and to have no chain nor fuzee, the kind of scapement rendering them unnecessary. But I have had "hitherto villainous bad workmen. The axis of the pendulum "of my clock is a cylinder, and rolls upon curves, which "render the vibrations isochronous, and it has two rolls for "one impulse." 66 "A patent," he again writes, "has been taken out for my "clocks and watches, and there is reason to hope they may "become an article of commerce. I am ready to make over "to you all my interest in the patent, provided that can be "done so as to benefit all concerned, which, if you can be "established in this country, might be the case.' 66 66 "As to gimcracks," writes Mr. Watt, "I have contrived a new micrometer, made by drawing two converging lines upon glass. I believe from trial it will answer. I men"tioned a dividing-screw; it has a wheel fixed upon it with "150 teeth and only 14 inch diameter: it is moved any 66 portion of a turn or number of turns by a straight-line rack, "the teeth of which fit it, without shake, and is moved by "the hand or foot. It divides distinctly an inch into 400 "equal parts." Of the micrometer, we shall soon give a full history. "As to your doubts about the screw," he writes to Small, "I intend to annihilate them when I see you:"-" my 66 dividing-screw can divide an inch into 1000 tolerably equal "and distinct parts on glass;"-" I had occasion to use my "last dividing-screw for the first time the other day. It "divided 9 inches into 20ths, and did not err the 20th of an * 27 October, 1773. 29 March, 1774. 24 November, 1772. "inch in the whole 9 inches. I did not find that there was "the least inequality among the divisions, though I subjected "them to the most severe trial, and I have found a way by "which I can divide a foot into Tooths of an inch without "erring above 200th of an inch in the whole length, and the "divisions shall be equal among themselves; so that I reckon "that machine exceeding near perfect, and find it very useful, "as it saves much needless compass work, and, moreover, can "divide lines into the ordinates of any curve whatsoever." "I rejoice in all your improvements," replies Dr. Small,* "but have many optical difficulties that lessen my confidence "in observations made with the most accurately divided instru"ments. For example, no optical instrument hitherto constructed, catoptric or dioptric, or catadioptric, produceth an "exact copy of any object; so that all the visible points of "every object of sensible apparent diameter are represented "in the field of the instrument in situations in relation to "each other very different from what they ought to occupy, "&c. &c. The unsteady refractions of light passing through "the atmosphere are also vile things; not those mentioned by astronomers only, but others I will show you when "we meet." 66 66 "I am making a new surveying quadrant by reflection," writes Mr. Watt, "having the uses of a semicircle as "taking angles to 180°; the principle, that of Bird's octant, "in which the objects are only once reflected. In this I am making, the fixed glass stands at 45° to the first radius; "and by shifting the place of the eye, the head is never in "the way. I am going to make another altogether of glass, "with nonius of the same." 66 On which, Dr. Small observes:-" I remember to have "much admired your schemes about improving instruments "for measuring angles by reflected light. Dollond has lately, "as I have heard, made some inconsiderable but saleable "alterations of Hadley's Quadrant, as it is called, though the "invention is Newton's, which you no doubt know." Dr. 29 March, 1774. 17 January, 1773. 66 Small was quite correct in his account of the history of the invention of that most valuable instrument; for Sir John Herschel speaks, in his Treatise on Astronomy,' of "the "sextant, or quadrant, commonly called Hadley's, from its reputed inventor, though the priority of invention belongs "undoubtedly to Newton, whose claims to the gratitude of "the navigator are thus doubled, by his having furnished at "once the only theory by which his vessel can be securely "guided, and the only instrument which has ever been found "to avail, in applying that theory to its nautical uses. "Newton communicated it to Dr. Halley, who suppressed "it. The description of the instrument was found, after the "death of Halley, among his papers, in Newton's own hand"writing, by his executor, who communicated the papers to "the Royal Society, twenty-five years after Newton's death, "and eleven after the publication of Hadley's invention; "which might be, and probably was, independent of any "knowledge of Newton's, though Hutton insinuates the " contrary."* 66 So also Oltmanns has said, "John Hadley made the first "reflecting sextant be constructed; of which the invention belonged to Newton."† 66 Small then continues: -" I am attempting the improve"ment of telescopes, and still more anxiously of microscopes, "because the present microscopes deceive their users; but "I find it very difficult to procure good lenses. Could you "make an achromatic lens of half an inch focal distance? "Dollond's patent is out." In return says Mr. Watt: §-"I have invented two problems "for clearing the observed distance of the moon from a star "of the effects of refraction and parallax; one trigonometrical, by Mercator's sailing,—the other instrumental, by a "sector having a line of chords on each limb and a moveable portion of a circle of the same radius, which, if of three 66 |