Chapter XIV: Measuring Machines, Tools, and Devices (1)

Measurements are primarily derived in Great Britain and her colonies, and in the United States, from the English Imperial or standard yard. This yard is marked upon a bar of "Bailey's metal" (composed of 16 parts copper, 2-1/2 parts tin, and 1 part zinc), an inch square and 38 inches long. One inch from each end is drilled a hole about three-quarters through the whole depth of the bar, into which are fitted gold plugs, whose upper end faces are level with the axis of the bar. Across each plug is marked a fine line, and the distance between these lines was finally made the standard English yard by an Act of Parliament passed in 1855. A copy of this bar is in the possession of the United States Government at Washington, and all the standard measuring tools for feet, inches, &c., are derived from subdivisions of this bar.

The standard of measurement in France and her colonies, Italy, Germany, Portugal, British India, Mexico, Roumania, Greece, Brazil, Peru, New Granada, Uruguay, Chili, Venezuela, and the Argentine Confederation, is the French mètre, which is also partially the standard in Austria, Bavaria, Wurtemberg, Baden, Hesse, Denmark, Turkey, and Switzerland. It consists of a platinum bar, called the "mètre des archives," whose end faces are parallel, and the length of this bar is the standard mètre. But as measuring from the ends of this bar would (from the wear) impair its accuracy, a second bar, composed of platinum and iridium, has been made from the "mètre des archives." This second bar has ruled upon it two lines whose distance apart corresponds to the length of the "mètre des archives," and from the distance between these lines the subdivisions of the mètre have been obtained.

As all metals expand or contract under variations of temperature, it is obvious that these standards of length can only be accurate when at some given temperature: thus the English bar gives a standard yard when it is at a temperature of 62° Fahr., while the French standard bar is standard at a temperature of 32° Fahr., which corresponds to 0 in the centigrade thermometer. But if a bar is copied from a standard, and is found to be too short, it is obvious that if its amount of expansion under an increase of temperature be accurately known, it will be an accurate standard at some higher temperature, or in other words, at a temperature sufficiently higher to cause it to expand enough to compensate for its error, and no more.

As all bars of metal deflect from their own weight, it is obvious that the bar must be supported at the same points at which it rested when the lines were marked, and it has been determined by Sir George Airy, that the best position for the points of support for any bar may be obtained as follows: Multiply the number of the points of support by itself (or, as it is commonly called, "square it"), and from the sum so obtained subtract 1. Then subtract the square root of the remainder, which gives a sum that divided into the length of the bar will represent the distance apart for the points of support. It will be obvious that the points of support must be at an equal distance from each end of the bar.

Measurement may be compared in two ways, by sight and by the sense of feeling. Measurement by sight is made by comparing the coincidence of lines, and is called "line measurement." Measurement by feeling or touch is called "end measurement," because the measurement is taken at the ends. If, for example, we measure the diameter of a cylindrical bar, it is an end measurement, because the measurement is in a line at a right angle to the axis of the bar, and the points of touch on each side of the bar are the ends of the measurement, which is supposed to have no width.

In measuring by sight we may, for rude measurements, trust to the unaided eye, as in using the common foot rule, but for such minute comparisons as are necessary in subdividing or transferring a standard, we may call in the aid of the microscope.

The standard gauges, &c., in use in the United States have been obtained from Sir Joseph Whitworth, or duplicated from those made by him with the aid of measuring and comparing machines. It has been found, however, that different sets of these gauges did not measure alike, the variations being thus given by Mr. Stetson, superintendent of the Morse Twist Drill and Machine Co.

At the time the Government established the use of the standard system of screw threads in the navy yards, ten sets of gauges were ordered from a manufacturer. His firm procured a duplicate set of these and took them to the navy yard in Boston and found that they were practically interchangeable. He also took them to the Brooklyn Yard Navy. The following tabular statement shows the difference between them:--

---------------------------------------------------------------
| |Morse Twist|
|Navy Yard |Drill and | Morse Twist Drill and
Size. |Male Gauge. |Machine Co.| Machine Co.
| |Male Gauge.| Female Gauge.
-------+------------+-----------+------------------------------
1/4 | 0.25 | 0.25 | Interchanged
5/16 | .313 | .313 | "
3/8 | .375 | .3759 |
7/16 | .437 | .437 | Interchanged
1/2 | .505 | .505 | "
9/16 | .562 | .564 (-)| "
5/8 | Damaged | .626 | "
3/4 | .7505 | .751 | "
7/8 | .876 | .8758 | "
1 | 1.00075 | 1.00075 | "
| | | { Navy Yard M. T. D. & M. Co.
1-1/8 | 1.125 (+)| 1.125 (-)| { --------- -----------------
| | | { (+) (-)
1-1/4 | 1.25 | 1.25 | Interchanged
1-3/8 | 1.375 | 1.375 | "
1-1/2 | 1.5 | 1.5 (-)| (-)
1-5/8 | 1.6245 | 1.624 | (-)
1-3/4 | 1.749 | 1.749 | Interchanged
1-7/8 | 1.8745 | 1.874 | (-)
2 | 1.999 | 1.999 |
---------------------------------------------------------------

The sign (-) means that the piece is small, but not enough to measure.
The sign (+) means that the piece is large, but not enough to measure.

The advantages to be derived from having universally accepted standard subdivisions of the yard into inches and parts of an inch are as follows:--

When a number of pieces of work of the same shape and size are to be made to fit together, then, if their exact size is not known and there is no gauge or test piece to fit them to, each piece must be fitted by trial and correction to its place, with the probability that no two pieces will be of exactly the same size. As a result, each piece in a machine would have to be fitted to its place on that particular machine, hence each machine is made individually.

Furthermore, if another lot of machines are afterwards to be made, the work involved in fitting the parts together in the first lot of machines affords no guide or aid in fitting up the second lot. But suppose the measurements of all the parts of the first lot are known to within the one ten-thousandth part of an inch, which is sufficiently accurate for practical purposes, then the parts may be made to measurement, each part being made in quantities and kept together throughout the whole process of manufacture, so that when all the parts are finished they may go to the assembling or erecting room, and one piece of each part may be taken indiscriminately from each lot, and put together to make a complete machine. By this means the manufacture of the machine may be greatly simplified and cheapened, and the fit of any part may be known from its size, while at the same time a new part may be made at any time without reference to the machine or the part to which it is to fit.

Again, work made to standard size in one shop will fit to that made to standard size in another, providing the standard gauges agree.

The Pratt and Whitney Company, of Hartford, Connecticut, in union with Professor Rogers, of Cambridge University, in Massachusetts, determined to inspect the Imperial British yard, to obtain a copy of it, and to make a machine that would subdivide this copy into feet and inches, as well as transfer the line measurements employed in the subdivisions into end measures for use in the workshops, the degree of accuracy being greater than is necessary in making the most refined mechanism, made under the interchangeable or standard gauge system. The machine made under these auspices is the Rogers-Bond Universal Comparator; Mr. Bond having been engaged in conjunction with Professor Rogers in its construction.

The machine consists of two cylindrical guides, upon which are mounted two heads, carrying microscopes which may be reversed in the heads, so as to be used at the front of the machine for line measurements and on the back for end measurements.

Fig. 1348 is a front, and Fig. 1349 a rear view of the machine, whose details of construction are more clearly shown in the enlarged views, Fig. 1350 and 1352.

Fig. 1350 is a top view, and Fig. 1352 a front view, the upper part of the machine being lifted up for clearness of illustration. X, X, are the cylindrical guides, upon which are the carriages I, K, for the microscopes. The construction of these carriages is more fully seen in Fig. 1351, which represents carriage K. It is provided with a hand-wheel R, operating a pinion in a rack (shown at T in the plan view figure of the machine) and affording means to traverse the carriage along the cylindrical guides. The microscope may be adjusted virtually by the screw M^{4}. The base upon which the microscope stands is adjustable upon a plate N, by means of the two slots and binding screws shown, and the plate N fits in a slideway running across the carriage. U is one of the stops used in making end measurements, the other being fixed upon the frame of the machine at V in the plan view, Fig. 1350. The micrometric arrangement for the microscope is shown more clearly in Fig. 1353. The screw B holds the box in position, the edge of the circular base on which it sits being graduated, so that the position of M may be easily read. In the frame M is a piece of glass having ruled upon it the crossed lines, or in place of this a frame may be used, having in it crossed spider web lines. These lines are so arranged as to be exactly in focus of the upper glass of the microscope, this adjustment being made by means of the screw S. The lines upon the bar are in the focus of the lower glass; hence, both sets of lines can be seen simultaneously, and by suitable adjustment of the microscope can be brought to coincide.

Beneath the cylindrical guides, and supported by the rack T that runs between and beneath them, are the levers P, in Fig. 1352, upon which weights may be placed to take up the flexure or sag of the cylindrical guides.

In Fig. 1352, H, H, are heads that may be fixed to the cylindrical guides at any required point, and contain metallic stops, against which corresponding stops on the microscope carriages may abut, to limit and determine the amount to which these carriages may be moved along the cylindrical guides.

The pressure of contact between the carriage and the fixed stops is found to be sufficiently uniform or constant if the carriage is brought up to the stops (by means of the hand-wheel R, Fig. 1351) several times, and a microscope reading taken for each time of contact. But this pressure of contact may be made uniform or constant for all readings by means of an electric current applied to the carriage through the metallic stops on heads H, H, and those on the carriage.

We have now to describe the devices for supporting the work and adjusting it beneath the microscopes.

Referring, then, to Fig. 1352, E is a bed or frame that may be raised or lowered by means of the hand-wheel C, so as to bring the plate S (on which rests the bar whose line measure is to be compared) within range of the microscopes. The upper face of E is provided with raised [V] slideways, which are more clearly seen in the end view of this part of the machine shown in Fig. 1354. Upon these raised [V]s are the devices for adjusting the height of the eccentric rollers S^{3}, upon which the bars to be tested are laid, S^{2} representing one of these bars. To adjust the bars in focus under the microscope, these eccentric rollers are revolved by means of levers S^{4}. At S^{5} is a device for giving to the table a slight degree of longitudinal movement in the base plate that rests upon the raised [V]s; on the upper face of E and at S^{6} is a mechanism for adjusting the height of that end of the plate S. The base plate may be moved along the raised [V]s of E by the hand-wheel D.

To test whether the cylindrical guides are deflected by their own weight or are level, a trough of mercury may be set upon the eccentric rollers S^{3}, Fig. 1352, and the fine particles of dust on its surface may be brought into focus in the microscope, whose carriage may then be traversed to various positions along the cylindrical guides, and if these dust particles remain in focus it is proof that the guides are level with the mercury surface.

The methods of using the machine are as follows: The standard bar has marked upon its upper face (which is made as true as possible and highly polished) a line B (Fig. 1355), which is called the horizontal line, and is necessary in order to set the bar parallel to the cylindrical guides of the machine. The lines A, A, are those defining the measurement as a yard, a foot, or whatever the case may be, and these are called the vertical lines or lines of measurement. Now, suppose we require to test a bar with the standard and the lines on its face are marked to correspond to those on the standard.

The first operation will be to set the standard bar on the eccentric rollers S^{3} in Fig. 1352, and it and the microscopes are so adjusted that the spider web lines in the microscope exactly intersect the lines A and B on the standard, when the microscope carriage abuts against the heads H, Fig. 1352. The standard bar is then replaced by the bar to be tested, which is adjusted without altering the microscope adjustment or the heads H, and if the spider web lines in the microscope exactly coincide with and intersect the lines A and B, the copy corresponds to the standard. But if they do not coincide, then the amount of error may be found by the micrometer wheel G, Fig. 1353.

In this test the carriage is moved up against the stops H several times, and several readings or tests are made, so as to see that the force of the contact of the carriage against the stops H is uniform at each test, and if any variation is found, the average of a number of readings is taken. It is found, however, that with practice the carriage may be moved against the head H by means of the hand-wheel with such an equal degree of force that an error of not more than one fifty-thousandth of an inch is induced. It is found, however, that if too much time is occupied in this test, the heat of the operator's body will affect the temperature of the bars, and therefore expand them and vitiate the comparison. But in this connection it may be noted that if a bar is at a temperature of 40°, and is placed in an ice bath, it does not show any contraction in less than one minute, and that when it does so, the contraction is irregular, taking place in sudden movements or impulses.

Professor Rogers' methods of testing end measures are as follows: To compare a line with an end measure, a standard bar is set upon the machine, its horizontal and vertical lines being adjusted true to the cylindrical guides by the means already described, and the microscope carriage is so adjusted that the spider web lines of the microscope coincide with the horizontal and vertical lines marked on the standard, while at the same time the stop (U, Fig. 1350) on the carriage K has contact with the fixed stop (V, Fig. 1350.) Carriage K is then moved along the cylindrical guides so as to admit the bar (whose end measure is to be compared with the lines on the standard) between the two stops, and if, with the bar touched by both stops U and V, the microscope spider lines intersect the vertical and horizontal line on the standard bar, then the end measure corresponds to the line measure; whereas, if such is not the case, the amount of error may be found by noting how much movement of the micrometer wheel of the microscope is required to cause the lines to intersect.

It is obvious that in this test, if the cylindrical guides had a horizontal curvature, the test would not be perfect.

THE HORIZONTAL CURVATURE.--The copy or bar to be tested may be set between the stops, and the standard bar may be placed on one side of it, as in Fig. 1356, and the test be made as already described. It is then set the same distance from the bar to be tested, but on the other side of it, as in figure, and again adjusted for position and tested, and if the readings on the standard bar are the same in both tests, it is proof that the measurements are correct.

Suppose, for example, that the cylindrical guides were curved as in Fig. 1356, it is evident that the vertical lines would appear closer together on the standard bar when in the first position than when in the second position.

In the Rogers machine the amount of error due to curvature in the cylindrical guides in this direction is found to be about 1/5000 part of an inch in 39 inches, corresponding to a radius of curvature of five miles.

Another method of testing an end with a line measure is as follows: The bar to be measured is shaped as in Fig. 1357, the end measurement being taken at A, and the projection B at each end serving to preserve the end surfaces A from damage. The standard bar is then set upon the machine and its horizontal and vertical lines adjusted in position as before described. In connection with this adjustment, however, the bar to be tested is set as in Fig. 1358; C being a block of metal (having marked centrally upon it horizontal and vertical lines), placed between the bar and the fixed stop U, its vertical line being in line with the vertical line on the standard. This adjustment being made, the block C is removed and placed at the other end of the bar, as shown in Fig. 1359, when, if the end measure on the bar corresponds with the line measure on the standard, the vertical line at the other end of the standard will correspond with the vertical line on block C.

To prove that the vertical line is exactly equidistant from each end of the block C, all that is necessary is to place it between the bar and the fixed stop U, Fig. 1350, adjust the microscope to it and then turn it end for end, and if its vertical line is still in line with the spider web of the microscope it is proof that it is central on the block, while if it is not central the necessary correction may be made. It is obvious that it is no matter what the length of C may be so long as its vertical line is central in its length.

In this process the coincidence of the vertical lines on the standard and on the piece C are employed to test the end measure on the bar with the line measure on the standard.

Figs. 1360 and 1361 represent the Whitworth Millionth Measuring Machine, in which the measurement is taken by the readings of an index wheel, and the contact is determined from the sense of touch and the force of gravity.

It is obvious that in measuring very minute fractions of an inch one of the main difficulties that arise is that the pressure of contact between the measuring machine and the surfaces measured must be maintained constant in degree, because any difference in this pressure vitiates the accuracy of the measurement. This pressure should also be as small as is consistent with the assurance that contact actually exists, otherwise the parts will spring, and this would again impair the accuracy of the measurement.

If the degree of contact is regulated by devices connected with the moving mechanism of the machine it is indirect, and may vary from causes acting upon that mechanism. But if it is regulated between the work and the moving piece that measures it, nothing remains but to devise some means of making its degree or amount constant for all measurements; so that if a duplicate requires to be compared with a standard, the latter may first be measured and the duplicate be afterwards measured for comparison.

All that is essential is that the two be touched with an equal degree of contact, and the most ingenious and delicate method yet devised to accomplish this result is that in the Whitworth machine, whose construction is as follows:--

In a box frame A, is provided a slide-way for two square bars, B, C, which are operated by micrometer screws, one of which is shown at J (the cap over B being removed to expose B and J to view). The bars B, C, are made truly square, and each side a true plane. The groove or slide-way in which they traverse is made with its two sides true planes at a right angle to each other; so that the bars in approaching or receding from each other move with their axes in a straight line. At the two ends of the frame the micrometer screws are afforded journal bearings. The ends of the bars B, C, are true planes at a right angle to the axes of B, C. Bar B is operated as follows: Its operating screw J has a thread of 1/20 inch pitch; or in other words, there are twenty threads in an inch of its length. It is rotated by the hand-wheel F, whose rim-face is graduated by 250 equidistant lines of division. Moving F through a distance equal to that between, or from centre to centre of its lines of division, moves B through a distance equal to one five-thousandth part of an inch.

The screw in head I for operating bar C also has a pitch of 1/20 inch (or twenty threads in an inch of its length), and is driven by a worm-wheel W, having 200 teeth. This worm-wheel W is driven by a worm or tangent-screw H, having upon its stem a graduated wheel G, having 250 equidistant lines marked upon the face of its rim.

Suppose, then, that wheel G be moved through a distance equal to that between its lines of division, that is 1/250th of a rotation, then the worm H will move through 1/250th of a rotation, and the worm-wheel on the micrometer screw will be rotated 1/250th part of its pitch expressed in inches; because a full rotation of G would move the worm one rotation, and thus would move the worm-wheel on the screw one tooth only, whereas it has 200 teeth in its circumference; hence it is obvious that moving graduated wheel G, through a distance equal to one of its rim divisions will move the bar C the one-millionth of an inch; because:

Pitch of Rotation of Rotation of
thread worm-wheel graduated wheel
1/20 inch × 1/200 × 1/250 = 1/1000000

Fixed pointers, as K, Fig. 1362, enable the amount of movement or rotation of the respective wheels F, G, to be read.

A peculiarly valuable feature of this machine is the means by which it enables an equal pressure of contact to be had upon the standards, and the duplicates to be tested therewith. This feature is of great importance where fine and accurate measurements are to be taken. The means of accomplishing this end are as follows:--

In the figures, D is a piece in position to be measured, and between it and the bar C is a feeler consisting of a small flat strip of steel, E E, having parallel sides, which are true planes.

When the pressure of contact upon this piece E E is such that if one end be supported independently the other will just be supported by friction, and yet may be easily moved between D and C by a touch of the finger, the adjustment is complete. At the sides of the frame A are two small brackets, shown at K, in the end view, Fig. 1362, E E being shown in full lines resting upon them, and in dotted lines with one end suspended. The contact-adjustment may thus be made with much greater delicacy and accuracy than in those machines in which the friction is applied to the graduated wheel-rim, because in the latter case, whatever friction there may be is multiplied by the difference in the amount of movement of the graduated rim and that of the bar touching the work.

All that is necessary in the Whitworth machine is to let E E be easy of movement under a slight touch, though capable of suspending one end by friction, and to note the position of the lines of graduation on C with reference to its pointer. By reason of having two operative bars, B, C, that which can be most readily moved may be operated to admit the piece or to adjust the bars to suit the length of the work, while that having the finer adjustive motion, as C, may be used for the final measuring only, thus preserving it from use, and therefore from wear as much as possible; or coarser measurements may be made with one bar, and more minute ones with the other.

So delicate and accurate are the measurements taken with this machine, that it is stated by C. P. B. Shelley, C.E., in his "Workshop Appliances," that if well protected from changes of temperature and from dust, a momentary contact of the finger-nail will suffice to produce a measurable expansion by reason of the heat imparted to the metal. In an iron bar 36 inches long, a space equal to half a division on the wheel G having been rendered distinctly measurable by it, this space indicating an amount of expansion in the 36-inch bar equals the one two-millionth part of an inch!

The following figures, which are taken from _Mechanics_, represent a measuring machine made by the Betts Machine Company, of Wilmington, Delaware.

Fig. 1363 shows a vertical section through the length of the machine, which consists of a bed carrying a fixed and an adjustable head, the fixed head carrying the measuring screw and vernier while the adjustable one carries a screw for approximate adjustment in setting the points of the standard bars.

These screws have a pitch of ten threads per inch, and the range of the measuring screw has a range of 4 inches, and the machine is furnished with firm standard steel bars (4-inch, 6-inch, 18-inch, and 24-inch). The measuring points of the screws are of hardened steel, secured axially in line with the screws, and of two forms, with spherical and flat points, one set of each being used at a time. The larger wheel C is indexed to 1000 divisions, each division representing the ten-thousandth of an inch at the points; the smaller wheel has 100 divisions, each representing the one-thousandth part of an inch at the points. Beside, and almost in contact with, the larger wheel is a movable or adjustable pointer E, upon which the error of the screw is indexed for each inch of its length; the screw error is of the utmost importance when positive results are desired. The screw is immersed in oil to maintain a uniform temperature throughout its length, and to avoid particles of dust accumulating on its surface.

As stated above, the readings are indexed to the ten-thousandth part of an inch, but variations to the hundred-thousandth part of an inch can be indicated. The machine will take in pieces to 24 inches in length, and to 4 inches in diameter. In measuring, the points are brought into easy contact and then expanded by turning the larger wheel, counting the revolutions or parts of revolutions to determine the distance between the points or the size of what is to be measured. The smaller machine is constructed so as to indicate by means of vernier attachment to the ten-thousandth part of an inch, and is of value in tool-rooms where standard and special tools are continually being prepared. By its use, gauges and other exact tools can be made, and at the same time keep gauges of all kinds to standard size by detecting wear or derangement. The machine consists of a frame with one fixed head; the other head is moved by a screw; on both heads are hardened steel points. As with the larger machine, the screw error is indicated in such a manner as to permit the operator to guard against reproducing its error in its work. These machines are used for making gauges, reamers, drills, mandrels, taps, and so on.

The errors that may exist in the pitch of the measuring screw are taken into account as follows: The points of the measuring machine should be brought into light contact, the position of index-wheel, vernier, and the adjustable pointer which has the screw error indexed upon it should be as in Fig. 1364; that is, the zeros on index-wheel and vernier should be in exact line, the vernier covering half of the zero line on pointer. To measure 1/2 inch, for illustration, five complete revolutions of index-wheel should produce 1/2 inch, and would if we had a perfect screw, but the screw is not perfect, and we must add to the measurement already obtained one-half of the space, stamped upon corrective devise, 0-1. This space 0-1 represents the whole error in the screw from zero to 1 inch. The backlash of the screw should always be taken up.

The details of this machine are as follows:--

In Fig. 1363 the points G are those between which the measuring is done, and the slide held by the nut K in position is adjusted by means of inch bars to the distance to be measured; H, the hand-wheel for moving one point, and F the wheel which moves the other. Fig. 1366 is a cross section of the movable head through the nut K and stud M, by which the movable head is adjusted, and Fig. 1365 is a cross section through the fixed head. The bars used in setting the machine are shown in Fig. 1367, and in Fig. 1368 the points of the measuring screws are shown on a large scale. The other figures show various details of the machine and their method of construction. The vernier, it will be observed, is a double one. This is shown in Fig. 1364, and is so arranged that the zero is made movable in order to correct the errors of the screw itself. These errors are carefully investigated and a record made of each. Thus, in Fig. 1363 the arm E is graduated so as to show the true zero for different parts of the screw; D can then be adjusted to a correct reading, and the divisions on the large wheel will then be correct to an exceedingly small fraction. This method of construction enables the machine to be used for indicating very minute variations of length.

In Fig. 1369 is shown a measuring machine designed by Professor John E. Sweet, late of Cornell University. The bed of the machine rests on three feet, so that the amount of support at each leg may remain the same, whether the surface upon which it rests be a true plane or otherwise. This bed carries a headstock and a tailstock similar to a lathe. The tailstock carries a stationary feeler, and the headstock a movable one, operated horizontally by a screw passing through a nut provided in the headstock, the axial lines of the two feelers being parallel and in the same plane. The diameters of the two feelers are equal at the ends, so that each feeler shall present the same amount of end area to the work. The nut for the screw operating the headstock feeler is of the same length as the screw itself, so that the wear of the screw shall be equalized as near as possible from end to end, and not be the most at and near the middle of its length, as occurs when the thread on the screw is longer than that in the nut.

The pitch of the thread on the screw is 16 threads in an inch of length, hence one revolution of the screw advances the feeler 1/16 inch. The screw carries a wheel whose circumference is marked or graduated by 625 equidistant lines of division. If, therefore, this wheel be moved through a part of a rotation equal to one of these divisions, the feeler will move a distance equal to 1/625 of the 1/16th of an inch, which is the ten thousandth part of an inch, and as the bed of the machine is long enough to permit the feelers to be placed 12 inches apart, the machine will measure from zero to 12 inches by the ten-thousandth of an inch.

To assist the eye in reading the lines of division, each tenth line is marked longer than the rest, and every hundredth, still longer. The pitch of the screw being 16 threads to an inch enables the feeler to be advanced or retired (according to the direction of the rotation of the wheel) a sixteenth inch by a simple rotation of the wheel, an eighth inch by two wheel rotations, a thirty-second inch by a quarter rotation, and so on; and this renders the use of that machine very simple for testing the accuracy of caliper gauges, that are graduated to 1/8, 1/16, 1/32, 1/64th inch, and so on, such a gauge being shown (in the cut) between the feelers.

The bar or arm shown fixed to the headstock and passing over the circumference of the wheel at the top affords a fixed line or point wherefrom to note the motion of the wheel, or in other words, the number of graduations it moves through at each wheel movement. It is evident that in a machine of this kind it is essential that the work to be measured have contact with the feelers, but that it shall not be sufficient to cause a strain or force that will spring or deflect either the work itself (if it be slight) or the parts of the machine. It is also essential that at excessive measurements the feelers shall touch the work with the same amount of force. The manner of attaining this end in Professor Sweet's machine is as follows: Upon the same shaft as the wheel is an arm having contact at both ends with the edge of the wheel rim whose face is graduated. This arm is free to rotate upon the shaft carrying the graduated wheel, which it therefore drives by multiple friction on its edges at diametrically opposite points; by means of a nut the degree of this friction may be adjusted so as to be just sufficient to drive the wheel without slip when the wheel is moved slowly. So long, then, as the feelers have no contact with the piece to be measured, the arm will drive the graduated wheel, but when contact does take place the wheel will be arrested and the arm will slip. The greatest accuracy will therefore be obtained if the arm be moved at an equal speed for all measurements.

Fig. 1370 represents a Brown and Sharpe measuring machine for sheet metal. It consists of a stand A with a slotted upright having an adjusting screw C above, and a screw D, with a milled head and carrying a dial, passing through its lower part. One turn of the screw, whose threads are 1/10th inch apart, causes one rotation of the dial, the edge of which is divided into one hundred parts, enabling measurements to be made to thousandths of an inch. The sheet-metal to be gauged is inserted in the slot of the upright. The adjusting-screw is set so that when the points of the two screws meet, the zero of the dial shall be opposite an index or pointer which shows the number of divisions passed over, and is firmly secured by a set-screw.

Next in importance to line and end measurements is the accurate division of the circle, to accomplish which the following means have been taken.

What is known as "Troughton's" method (which was invented by Edward Troughton about 1809) is as follows: A disk or circle of 4 feet radius was accurately turned, both on its face and its inner and outer edges. A roller was next provided of such diameter that it revolved sixteen times on its own axis, while rolling once round the outer edge of the circle. This roller was pivoted in a framework which could be slid freely, yet tightly, along the circle, the roller meanwhile revolving by frictional contact on the outer edge. The roller was also, after having been properly adjusted as to size, divided as accurately as possible into sixteen equal parts by lines parallel to its axis. While the frame carrying the roller was moved once round along the circle, the points of contact of the roller divisions with the circle were accurately observed by two microscopes attached to the frames, one of which commanded the ring on the circle near its edge, which was to receive the divisions, and the other viewed the roller divisions. The exact points of contact thus ascertained were marked with faint dots, and the meridian circle thereby divided into 256 very nearly equal parts.

The next part of the operation was to find out and tabulate the errors of these dots, which are called apparent errors, because the error of each dot was ascertained on the supposition that all its neighbors were correct. For this purpose two microscopes, which we shall call A and C, were taken with cross-wires and micrometer adjustments, consisting of a screw and head divided into 100 divisions, 50 of which read in the one and 50 in the opposite direction. These microscopes, A and B, were fixed so that their cross-wires respectively bisected the dots 0 and 128, which were supposed to be diametrically opposite. The circle was now turned half way round on its axis, so that dot 128 coincided with the wire of A, and should dot 0 be found to coincide with B, then the dots were sure to be 180° apart. If not, the cross-wire of B was moved till it coincided with the dot 0 and the number of divisions of micrometer head noted. Half this number gave clearly the error of dot 128 and was tabulated plus or minus according as the arcual distance between 0 and 128 was found to exceed or fall short of the removing part of the circumference. The microscope B was now shifted, A remaining opposite dot 0 as before, till its wire bisected dot 64, and by giving the circle one-quarter of a turn on its axis, the difference of the arcs between dots 0 and 64, and between 64 and 128 was obtained. The half of this distance gave the apparent error of dot 64, which was tabulated with its proper sign. With the microscope A still in the same position, the error of dot 192 was obtained, and in the same way, by shifting B to dot 32, the errors of dots 32, 96, 160 and 224 were successively ascertained. By proceeding in this way the apparent errors of all the 256 dots were tabulated.

In order to make this method fully understood, we have prepared the accompanying diagrams, which clearly show the plan pursued.

Fig. 1371 illustrates the plan of dividing the large circle by means of the roller B.

Fig. 1372 shows the general adjustment of the microscope for the purpose of proving the correctness of the divisions.

Fig. 1373 shows the location of the microscope over the points 0 and 128.

Fig. 1374 shows the circle turned half-way round, the points 0 and 128 coinciding with the cross threads of the microscope.

Fig. 1375 shows a similar reading, in which the points do not coincide with the cross threads of the microscope.

Fig. 1376 shows the microscope adjusted for testing by turning the circle a quarter revolution.

Fig. 1377 represents one of the later forms of Ramsden's dividing engine.[21] It consists first of a three-legged table, braced so as to be exceedingly stiff. Upon this is placed a horizontal wheel with deep webs, and a flat rim. The webs stiffen the wheel as much as possible, and one of these webs, which runs round the wheel about half-way between the centre and the circumference, rests upon a series of rollers which support it, and prevent, as far as possible, the arms from being deflected by their own weight. An outer circle, which receives the graduation, is laid upon the rim of the wheel and secured in place. The edge of this circle is made concave. A very fine screw, mounted in boxes and supported independently, is then brought against this hollow edge, and, being pressed against it, the screw, when revolved, of course cuts a series of teeth in the circumference, and this tooth-cutting, facilitated by having the screw threads made with teeth, was continued until perfect [V]-shaped teeth were cut all around the edge of the wheel. This Mr. Ramsden calls ratching the wheel. The number of teeth, the circumference of the wheel, and the pitch of the screw were all carefully adjusted, so that by using 2160 teeth, six revolutions of the screw would move the wheel the space of 1°. When this work was finished, and the adjustment had been made as perfect as possible, a screw without teeth--that is, one in which the thread was perfect--was put in the place of that which had cut the teeth from the wheel, and the machine was perfected. The wheel A B C in the drawings is made of bell metal, and turns in a socket under the stand, which prevents the wheel from sliding from the supporting or friction rolls Z, Z. The centre R, working against the spindle M, is made so as to fit instruments of various sizes. The large wheel has a radius of 45 inches, and has 10 arms. The ring B is 24 inches in diameter by 3 inches deep. The ring C is of very fine brass, fitting exactly on the circumference of the wheel, and fastened by screws, which, after being screwed home, were well riveted. Great care was taken in making the centre on which the wheel worked exceedingly true and perfect, and in making the socket for the wheel fit as exactly as possible. The revolving mechanism is all carried on the pillar P, resting on the socket C´. We may state here that the machine, as shown in the engravings, now in the possession of the Stevens Institute, is in some respects slightly improved on that shown in the original drawings published in "Rees' Cyclopædia" in 1819. After the wheel was put on its stand, and the pulleys in place, the instrument was ready for the turning mechanism. The upper part of this pillar P carries the framework in which the traversing screw revolves.

[21] From _Mechanics_.

In Fig. 1378 D is the head of this pillar, P the screw which turns the wheel. E^{1} E^{1} are the boxes, which are made conical so as to prevent any shake and to hold the screw firmly. Circles of brass, F and V, are placed on the arbor of the screw, and as their circumference is divided into 60 parts, each division consequently amounts to a motion of the wheel of 10 seconds, and 60 of them will equal 1 minute. Revolution is given to the screw by means of the treadle B´ and the cord Y, which runs over the guiding screw W, Fig. 1379, and is finally attached to the box U. A spring enclosed in the box U causes it to revolve, and winds up the slack of the cord whenever the treadle is relieved. In the original drawing the head of the pillar P was carried in a parallel slip in the piece surrounding its head. The construction as shown in Fig. 1379 is somewhat different. The result attained, however, is identical, and the spindles and attachments are held so as to have no lateral motion. The wheels V and X have stops upon them, so arranged that the screw may be turned definitely to a given point and stopped. These wheels are at the opposite ends of the screw W. A detail of one of them is shown at V in Fig. 1380, where X is the ratchet-wheel. This figure also illustrates the construction of the bearings for the screw arbor. We have not space to explain the method by which the perfection of the screw was obtained, nor to discuss the means by which was obtained the success of so eliminating the errors as to make the division of the instrument more perfect than anything which had been attempted previously. Success, however, was obtained, and by means of the first or tooth-cutting screw the teeth were brought to such a considerable uniformity that, together with the fact that the screw took hold of a number of teeth at one time, most of the errors which would have been expected from this method of operation were eliminated. The method of ruling lines upon the instrument was most ingenious. The frame L L, is connected to the head D, of the pillar P in front, by the clamps I and K, and to the centre M by the block R. A frame N N stiffens the back. The blocks O, O on the frame Q´ are secured to the frame L L, by set-screws C, C.

Fig. 1381 shows a side view of the frame Q´, which it is seen carries a [V]-shaped piece Q, which in turn carries another [V]-shaped piece S, Fig. 1378. The piece Q is supported on pointed screws _d_, _d_, and the piece S is supported on two similar screws _f_, _f_. The point of this piece S carries the cutting tool E, Fig. 1378. Of course S can move only in a radial line from the centre M towards the circumference. If the sextant, octant, or other instrument be fastened to the large wheel A, with its centre at M, and the large wheel be rotated by the screw, all lines drawn upon it by E will be radial, and the distances apart will be governed by the number of turns made by the screw. This improvement, we think, was originated by Mr. Ramsden, and was a very great advance over the old method of the straight-edge, and has been used in some of the Government comparators and dividing engines. The following is Mr. Ramsden's own description of the graduation of the machine, and of his method of operating it. It shows the extreme care which he took in correcting the mechanical errors in the construction:--

"From a very exact centre a circle was described on the ring C, about 4/10 inch within where the bottom of the teeth would come. This circle was divided with the greatest exactness I was capable of, first into five parts, and each of these into three. These parts were then bisected four times; that is to say, supposing the whole circumference of the wheel to contain 2160 teeth, this being divided into five parts, and these again divided into three parts, each third part would contain 144, and this space, bisected four times, would give 72, 36, 18, 9; therefore, each of the last divisions would contain 9 teeth. But, as I was apprehensive some error might arise from quinquesection and trisection, in order to examine the accuracy of the divisions, I described another circle on the ring C, Fig. 1378, 1/10 inch within the first, and divided it by continual bisection, as 2160, 1080, 540, 270, 135, 67-1/2, 33-3/4, and, as the fixed wire (to be described presently) crossed both the circles, I could examine their agreement at every 135 revolutions (after ratching could examine it at every 33-3/4); but not finding any sensible difference between the two sets of divisions, I, for ratching, made choice of the former, and, as the coincidence of the fixed wire with an intersection could be more exactly determined with a dot or division, I therefore made use of intersections on both sides, before described.

"The arms of the frame L, Fig. 1381, were connected by a thin piece of brass, 3/4 inch broad, having a hole in the middle 4/10 inch in diameter; across this hole a silver wire was fixed, exactly in a line to the centre of the wheel; the coincidence of this wire with the intersections was examined by a lens of 1/10 inch focus, fixed in a tube which was attached to one of the arms L. Now (a handle or winch being fixed on the end of the screw) the division marked 10 on the circle F was set to its index, and, by means of a clamp and adjusting-screw for that purpose, the intersection marked I on the circle C´ was set exactly to coincide with the fixed wire. The screw was then carefully pressed against the circumference of the wheel by turning the finger-screw _h_; then, removing the clamp, I turned the screw by its handle nine revolutions, till the intersection marked 240 came nearly to the wire. Then, turning the finger-screw _h_, I released the screw from the wheel, and turned the wheel back till the intersection marked 2 exactly coincided with the wire, and by means of the clamp before mentioned, the division 10 on the circle being set to its index, the screw was pressed against the edges of the wheel by the finger-screw _h_, the clamps were removed, and the screw turned nine revolutions, till the intersection marked I nearly coincided with the fixed wire; the screw was released from the wheel by turning finger-screw _h_ as before, the wheel was turned back till intersection marked 3 coincided with the fixed wire; the division 10 in the circle being set to its index, the screw was pressed against the wheel as before, and the screw turned nine revolutions, till intersection 2 was nearly coincident with the fixed wire, and the screw released, and I proceeded in this manner till the teeth were marked round the whole circumference of the wheel. This was repeated three times round to make the impressions deeper. I then ratched the wheel round continuously in the same direction, without ever disengaging the screw, and, in ratching the wheel about 300 times round, the teeth were finished.