Figs. 1382, 1383, and 1384 represent a method adopted to divide a circle by the Pratt and Whitney Company. The principle of the device is to enable the wheel to be marked, to be moved through a part of a revolution equal to the length of a division, and to test the accuracy of the divisions by the coincidence of the line first marked with that marked last when the wheel has been moved as many times as it is to contain divisions. By this means any error in the division multiplies, so that the last division marked will exhibit it multiplied by as many times as there are divisions in the whole wheel. The accuracy of this method, so long as variations of temperature are avoided, both in the marking and the drilling of the wheel, appears to be beyond question. In the figures, w represents a segment of the wheel to be divided, and c what may be termed a dividing chuck. The wheel is mounted on an arbor in a gear-cutting machine. On the hub of the wheel (which has been turned up for the purpose) there is fitted, to a close working fit, a bore at the end of an arm, the other end of the arm being denoted by a in the figures. The dividing chuck is fitted to the slide s of the gear-cutting machine, and is of the following construction.

Between two lugs, b and b′, it receives the end of arm a. These lugs are provided with set-screws, the distance between the ends of which regulate the amount of movement of the end of arm a. Upon a is the slide d, carrying the piece e, in which is the marking tool f, the latter being lifted by a spring g, and, therefore, having no contact with the wheel surface until the spring is depressed. h is an opening through the arm a to permit the marking tool f to meet the wheel face, as shown in Fig. 1384, which is an end view of the slide showing the arm a in section. The face of the wheel rests upon the chuck on each side of the arm at the points i, j, and may be clamped thereto by the clamps k. The arm may be clamped to the wheel by the clamp shown dotted in at l, the bolt passing up and through the screw handle m. n is simply a lever with which to move the arm a, or arm a and the wheel. Suppose all the parts to be in the position shown in the cuts, the clamps being all tightened up, the slide d may be moved forward towards k, while the spring is depressed, and f will mark a line upon the wheel. The handle m may then be released and arm a moved until it touches the set-screw in b′, when m may be tightened and another line marked. Clamps k are then tightened, and the wheel, with the arm a fast to it, moved back to the position shown in the cut, when the clamps may be tightened again and another line marked, the process being continued all round the wheel. To detect and enable the correction of any discoverable error in a division, there is provided the plate p, having upon it three lines of division (which have been marked simultaneously with three of the lines marked on the wheel). This plate is supported by an arm or bracket q, on the rear edge of which are three notches r to hold a microscope, by means of which the lines on p may be compared with those on the wheel face, so that if any discrepancy should appear it may be determined which line is in error. The labor involved in the operation of marking a large wheel is very great. Suppose, for example, that a wheel has 200 lines of division, and that after going round the wheel as described it is found that the last division is 100th inch out; then in each division the error is the two-hundredth part of this 100th inch, and that is all the alteration that must be made in the distance between set-screws b and b′.

Figs. 1385 and 1386 represent a method of originating an index wheel, adopted by R. Hoe and Co., of New York City.

In this method the plan was adopted of fitting round a wheel 180 tapering blocks, which should form a complete and perfect circle. These blocks were to serve the same purpose as is ordinarily accomplished by holes perforated on the face of an index wheel. In their construction, means of correcting any errors that might be found, without the necessity of throwing away any portion of the work done, would also be provided. Further, this means would provide for taking up wear, should any occur in the course of time, and thus restore the original truth of the wheel.

Fig. 1385 of the engravings shows the originating wheel mounted upon a machine or cutting engine. Upon the opposite end of the shaft is the worm-wheel in the process of cutting. After the master worm-wheel has been thus prepared by means of the originating wheel, it is used upon the front end of the shaft, in the position now occupied by the originating wheel, and operated by a worm in the usual manner. Subdivisions are made by change wheels. The construction of the originating wheel will be understood by the smaller engravings.

Fig. 1386 is an enlarged section of a segment of the wheel, while Fig. 1387 is an edge view of this segment. Fig. 1388 is a view of one of the blocks employed in the construction of the wheel, drawn to full size.

In the rim of the originating wheel there was turned a shoulder, c, Fig. 1387, 5 feet in diameter. Upon this shoulder there were clamped 180 blocks, of the character shown in Fig. 1386, as indicated by the section, Fig. 1387. These blocks were secured to the face of the wheel d by screws e, and were held down to the shoulder by the screw and clamp g f, shown in Fig. 1387. (They are omitted in Fig. 1385 for clearness of illustration.) In the preparation of these blocks each was fitted to a template t, in Fig. 1388, and was provided with a recess b, to save trouble in fitting and to insure each block seating firmly on the shoulder c. The shoulder, after successive trials, was finally reduced to such a diameter that the last block exactly filled the space left for it when it was fully seated on the shoulder c. The wheel thus prepared was mounted on a Whitworth cutting engine, as shown in Fig. 1385. The general process of using this wheel is as follows: The blocks forming the periphery of the originating wheel are used in place of the holes ordinarily seen in the index plates. One of them is removed to receive a tongue, shown in the centre of Fig. 1385, which, exactly filling the opening or notch thus made, holds the wheel firmly in place. After a tooth has been cut in the master worm-wheel, shown at the back of Fig. 1385, the block in the edge of the originating wheel corresponding to the next tooth to be cut is removed. The tongue is withdrawn from the first notch, the wheel is revolved, and the tongue is inserted in the second position. The block first removed is then replaced, and the cutting proceeds as before. This operation is repeated until all the teeth in the master wheel have been cut. The space being a taper, the tongue holds the originating wheel more firmly than is possible by means of cylindrical pins fitting into holes. The number of blocks in the originating wheel being 180, the teeth cut in the master wheel may be 180 or some exact divisor of this number.

The advantages of this method of origination are quite evident. Since 180 blocks were made to fill the circle, the edges of each had 2° taper. This taper enabled the blocks to be fitted perfectly to the template, because any error in fit would be remedied by letting the block farther down into the template. Hence, it was possible to correct any error that was discovered without throwing the block away. Further, as the blocks themselves are removed to form a recess for locking the originating wheel in position while cutting the worm-wheel, the truth of the work is not subject to the errors that creep in when holes or notches require to be pierced in the originating wheel. Such errors arise from the heating due to the drilling or cutting, from the wear of the tools or from their guides, from soft or hard spots in the metal and other similar causes. To avoid any error from the heating due to the cut on the worm-wheel, in producing master wheels, Messrs. Hoe and Co. allowed the wheel to cool after each cut. The teeth were cut in the following order: The first three were cut at equidistant points in the circumference of the wheel. The next three also were at equidistant points, and midway between those first cut. This plan was continued until all the teeth were cut, thus making the expansion of the wheel from the heat as nearly equal as possible in all directions.

There is one feature in this plan that is of value. It is that a certain number of blocks, for example six, may be taken out at two or three different parts of the originating wheel and interchanged, thus affording a means of testing that does not exist in any other method of dividing.

The tools applied by the workmen to measure or to test work may be divided into classes.

1st. Those used to determine the actual size or dimension of the work, which may be properly termed measuring tools.

2nd. Those used as standards of a certain size, which may be termed gauges.

3rd. Those used to compare one dimension with another, as in the common calipers.

4th. Those used to transfer measurements or distances defined by lines.

5th. Those used to test the accuracy of plane or flat surfaces, or to test the alignment of one surface to another.

Referring to the first, their distinctive feature is that they give the actual dimensions of the piece, whether it be of the required dimension or not.

The second determine whether the piece tested is of correct size or not, but do not show what the amount of error is, if there be any.

The third show whatever error there may be, but do not define its amount; and the same is true of the fifth and sixth.

Fig. 1389 represents a micrometer caliper for taking minute end measurements. This instrument is capable of being set to a standard measurement or of giving the actual size of a piece, and is therefore strictly speaking a combined measuring tool and a gauge. The U-shaped body of the instrument is provided with a hub a, which is threaded to receive a screw c, the latter being in one piece with the stem d, which envelops for a certain distance the hub a. The thread of c has a pitch of 40 per inch; hence one revolution of d causes the screw to move endways ¹⁄₄₀ of an inch.

The vertical lines of division shown on the hub a are also ¹⁄₄₀ of an inch apart, hence the bevelled edge of the sleeve advances one of the divisions on a at each rotation.

This bevelled edge is divided into 25 equal divisions round its circumference, as denoted by the lines marked 5, 10, &c. If, then, d be rotated to an amount equal to one of its points of division, the screw will advance ¹⁄₂₅ of ¹⁄₄₀ of an inch. In the cut, for example, the line 5 on the sleeve coincides with the zero line which runs parallel to the axial line of the hub. Now suppose sleeve d to be rotated so that the next line of division on the bevelled edge of d comes opposite to the zero line, then ¹⁄₂₅ part of a revolution of d will have been made, and as a full revolution of d would advance the screw ¹⁄₄₀ of an inch, then ¹⁄₂₅ of a revolution will advance it ¹⁄₂₅ of ¹⁄₄₀ inch, which is ¹⁄₁₀₀₀ inch.

The zero line being divided by lines of equal division into 40ths of an inch, then, as shown in the cut, the instrument is set to measure ³⁄₄₀ths and ⁵⁄₂₅ths of a fortieth.

It is to be observed that to obtain correct measurements the work must be held true with the face of the foot b, and the contact between the end of screw c and the work must be just barely perceptible, otherwise the pressure of the screw will cause the U-piece to bend and vitiate the accuracy of the measurement. Furthermore, if the screw be rotated under pressure upon the work, its end will wear and in time impair the accuracy of the instrument. To take up any wear that may occur, the foot-piece b is screwed through the hub, holding it so that it may be screwed through the hub to the amount of the wear.

To avoid wear as much as possible, the screws of instruments of this kind are sometimes hardened, and to correct the error of pitch induced in the hardening, each screw is carefully tested to find in what direction the pitch of the hardened thread has varied, and provision is made for the correction as follows:—

The zero line on the hub a stands, if the thread is true to pitch, parallel to the axis of the screw c, but if the pitch of the thread has become coarser from hardening, this zero line is marked at an angle, as shown in Fig. 1390, in which a a represents the axial line of the screw and b the zero line.

If the screw pitch becomes finer from hardening, the zero line is made at an angle in the opposite direction, as shown in Fig. 1391, the amount of the angle being that necessary to correct the error in the screw pitch. The philosophy of this is, that if the pitch has become coarser a less amount of movement of the screw is necessary, while if it has become finer an increased movement is necessary. It is obvious, also, that if the pitch of the thread should become coarser at one end and finer at the other the zero line may be curved to suit.

Fig. 1392 represents a vernier caliper, in which the measurement is read by the coincidence of ruled lines upon the following principle. The vernier is a device for subdividing the readings of any equidistant lines of division. Its principle of action may be explained as follows: Suppose in Fig. 1393 a to be a rule or scale divided into inches and tenths of an inch, and b a vernier so divided that its ten equidistant divisions are equal to nine of the divisions on a; then the distance apart of the lines of division on a will be ¹⁄₁₀ inch; but, as the whole ten divisions on b measure less than an inch, by ¹⁄₁₀ inch, then each line of division is a tenth part of the lacking tenth less than ¹⁄₁₀ inch apart. Thus, were we to take a space equal to the ¹⁄₁₀ inch between 9 and 10 on a, and divide it into 10 equal parts (which would give ten parts each measuring ¹⁄₁₀₀th of an inch) and add one of said parts to each of the distances between the lines of division on b, then the whole of the lines on a would coincide with those on b. It becomes evident, then, that line 1 on b is ¹⁄₁₀₀ inch below line 1 on a, that line 2 on b is ²⁄₁₀₀ inch below line 2 on a, line 3 on the vernier b is ³⁄₁₀₀ inch below line 3 on the rule a, and so on, until we arrive at line 10 on the vernier, which is ¹⁰⁄₁₀₀ or ¹⁄₁₀ inch below line 10 on a. Suppose, then, the rule or scale to rest vertically on a truly surfaced plate, and a piece of metal be placed beneath b, the thickness of the piece will be shown by which of the lines on b coincides with a line on a. For more minute divisions it is simply necessary to have more lines of division in a given length on a and b. Thus, if the rule be divided into inches and fiftieths, and the vernier is so divided that it has 20 equidistant lines of division to 19 lines on the rule, it will then lack one division, or ¹⁄₅₀ inch in ²⁰⁄₅₀ inch, each division on the vernier will then be the one-twentieth of a fiftieth too short, and as ¹⁄₂₀ of ¹⁄₅₀ is ¹⁄₁₀₀₀, the instrument will read to one-thousandth of an inch.

Let it now be noted that, instead of making the lines of division closer together to obtain minute measurements, the same end may be obtained by making the vernier longer. For example, suppose it be required to measure to ¹⁄₂₀₀₀ part of an inch, then, if the rule or scale be graduated to inches and fiftieths, and the vernier be graduated to have 40 equidistant lines of division, and 39 of the lines on the scale, the reading will be to the ¹⁄₂₀₀₀ part of an inch. But, in any event, the whole of the readings on the vernier may be read, or will be passed through, while it is traversing a division equal to one of the divisions on the scale or rule.

In Fig. 1392 is shown a vernier caliper, in which the vernier is attached to and carried by a slide operating against the inside edge of the instrument. The bar is marked or graduated on one side by lines showing inches and fiftieths of an inch, with a vernier graduated to have 20 equidistant lines of division in 19 of the lines of division on the bar, and therefore measuring to the ¹⁄₁₀₀₀th of an inch, while the other side is marked in millimètres with a vernier reading to ¹⁄₄₀th millimètre, there being also 20 lines of division on the vernier to 19 on the bar.

The inside surfaces of the feet or jaws are relieved from the bar to about the middle of their lengths, so as to confine the measuring surfaces to dimensions sufficiently small to insure accurate measurement, while large enough to provide a bearing area not subject to rapid wear. If the jaw surface had contact from the point to the bar, it would be impossible to employ the instrument upon a rectangular having a burr, or slight projection, on the edge. Again, by confining the bearing area to as small limits as consistent with the requirements of durability a smaller area of the measured work is covered, and the undulations of the same may be more minutely followed.

To maintain the surface of the movable jaw parallel with that of the bar-jaw, it is necessary that the edge of the slide carrying the vernier be maintained in proper contact with the edge of the instrument, which, while adjusting the vernier, should be accomplished as follows:—

The thumb-screw most distant from the vernier should be set up tight, so that that jaw is fixed in position. The other thumb-screw should be set so as to exert, on the small spring between its end and the edge of the bar, a pressure sufficient to bend that spring to almost its full limit, but not so as to let it grip the bar. The elasticity of the spring will then hold the edge of the vernier slide sufficiently firmly to the under edge of the bar to keep the jaw-surfaces parallel; to enable the correct adjustment of the vernier, and to permit the nut-wheel to move the slide without undue wear upon its thread, or undue wear between the edge of the slide and that of the bar, both of which evils will ensue if the thumb-screw nearest the vernier is screwed firmly home before the final measuring adjustment of the vernier is accomplished.

When the measurement is completed the second thumb-screw must be set home and the reading examined again, for correctness, to ascertain if tightening the screw has altered it, as it would be apt to do if the thumb-screw was adjusted too loose.

The jaws are tempered to resist wear, and are ground to a true plane surface, standing at a right angle to the body of the bar. The method of setting the instrument to a standard size is as follows:—

The zero line marked 0 on the vernier coincides with the line 0 on the bar when the jaws are close together; hence, when the 0 line on the vernier coincides with the inch line on the bar, the instrument is set to an inch between the jaws. When the line next to the 0 line on the vernier coincides with the line to the left of the inch line on the bar, the instrument is set to 1¹⁄₁₀₀₀ inches. If the vernier slide then be moved so that the second line on the vernier coincides with the second line, on the left of the inch on the bar, the instrument is set to 1²⁄₁₀₀₀ inches, and so on, the measurement of inches and fiftieths of an inch being obtained by the coincidence of the zero line on the vernier with the necessary line on the bar, and the measurements of one-thousands being taken as described.

But if it is required to measure, or find the diameter of an existing piece of work, the method of measuring is as follows:—

The thumb-screws must be so adjusted as to allow the slide to move easily or freely upon the work without there being any play or looseness between the slide and the bar. The slide should be moved up so as to very nearly touch the work when the latter is placed between the jaws. The thumb-screw farthest from the vernier should then be screwed home, and the other thumb-screw operated to further depress the spring without causing it to lock upon the bar. The nut-wheel is then operated so that the jaws, placed squarely across the work, shall just have perceptible contact with it. (If the jaws were set to grip the work tight they would spring from the pressure, and impair the accuracy of the measurements.) The thumb-screw over the vernier may then be screwed home, and the adjustment of the instrument to the work again tried. If a correction should be found necessary, it is better to ease the pressure of the thumb-screw over the vernier before making such correction, tightening it again afterwards. The reading of the measurement is taken as follows:—

If the 0 line on the vernier coincides with a line on the bar, the measurement will, of course, be shown by the distance of that line from the 0 line on the bar, the measurement being in fiftieths of inches, or inches and fiftieths (as the case may be), but if the 0 line on the vernier does not coincide with any line of division on the bar, then the measurement in inches and fiftieths will be from the next line (on the bar) to the right of the vernier, while the thousandths of an inch may be read by the line on the vernier which coincides with a line on the bar.

Suppose, for example, that the zero line of the vernier stands somewhere between the 1 inch and the 1¹⁄₅₀ inch line of division on the bar, then the measurement must be more than an inch, but less than 1¹⁄₅₀ inches. If the tenth or middle line on the vernier is the one that coincides with a line on the bar, the reading is 1¹⁰⁄₁₀₀₀ inches. If the line marked 5 on the vernier is the one that coincides with a line on the bar, the measurement is an inch and ⁵⁄₁₀₀₀, and so on.

For measuring the diameters of bores or holes, the external edges of the jaws are employed; the width of the jaw at the ends being reduced in diameter to enable the jaw ends to enter a small hole. These edges are formed to a circle, having a radius smaller than the smallest diameter of hole they will enter when the jaws are closed, which insures that the point of contact shall be in the middle of the thickness of each jaw. In this case the outside diameter of the jaws must be deducted from the measurement taken by the vernier, or if it be required to set the instrument to a standard diameter, the zero line on the vernier must be set to a distance on the bar less than that of the measurement required to an amount equal to the diameter of the jaw edges when the jaws are closed. This diameter is, as far as possible, made to correspond to the lines of division on the bar. Thus in the instrument shown in Fig. 1392, these lines of division are ¹⁄₅₀ inch; hence the diameter across the closed bars should, to suit the reading (for internal measurements) on the bar, be measurable also in fiftieths of an inch; but the other side of the bar is divided into millimètres, hence to suit internal measurements (in millimètres or fractions thereof) the width of the jaws, when closed, should be measurable in millimètres; hence, it becomes apparent that the diameter of the jaws used for internal measurements can be made to suit the readings on one side only of the bar, unless the divisions on one side are divisible into those on the other side of the bar. When the diameter of the jaws is measurable in terms of the lines of division on the bar, the instrument may be set to a given diameter by placing the zero of the vernier as much towards the zero on the bar as the width of the jaws when closed. Thus, suppose that width (or diameter, as it may be termed) be ¹⁰⁄₅₀ of an inch, and it be required to set the instrument for an inch interval or bore measurement, then the zero on the vernier must be placed to coincide with the line on the bar which denotes ⁴⁰⁄₅₀ of an inch, the lacking ¹⁰⁄₅₀ inch being accounted for in the diameter or width of the two jaws.

But when the width of the jaws when closed is not measurable in terms of the lines of division on the bar, the measurement shown by the vernier will, of course, be too small by the amount of the widths of the two jaws, and the measurement shown by the vernier must be reduced to the terms of measurement of the width of the jaws, or what is the same thing, the measurement of the diameter of the jaws must be reduced to the terms of measurement on the bar, in order to subtract one from the other, or add the two together, as the case may require.

For example: Suppose the diameter of the jaws to measure, when they are close together, ²⁵⁰⁄₁₀₀₀ of an inch, and that the bar be divided into inches and fiftieths. Now set the zero of the vernier opposite to the line denoting ⁴⁹⁄₅₀ inch on the bar. What, then, is the measurement between the outside edges of the jaws? In this case we require to add the ²⁵⁰⁄₁₀₀₀ to the ⁴⁹⁄₅₀ in order to read the measurement in terms of fiftieths and thousandths of an inch, or we may read the measurement to one hundredths of an inch, thus: ⁴⁹⁄₅₀ equal ⁹⁸⁄₁₀₀, and ²⁵⁰⁄₁₀₀₀ equal ²⁵⁄₁₀₀, and ⁹⁸⁄₁₀₀₀ added to ²⁵⁄₁₀₀ are ¹²³⁄₁₀₀, or an inch and ²³⁄₁₀₀. To read in ¹⁄₁₀₀₀ths of an inch, we have that ⁴⁹⁄₅₀ of an inch are equal to ⁹⁸⁰⁄₁₀₀₀, because each ¹⁄₅₀ inch contains ²⁰⁄₁₀₀₀ inch, and this added to ²⁵⁰⁄₁₀₀₀ makes ¹²³⁰⁄₁₀₀₀, that is 1²³⁰⁄₁₀₀₀ inches.

The accuracy of the instrument may be maintained, notwithstanding any wear which may in the course of time take place on the inside faces of the jaws, by adjusting the zero line on the vernier to exactly coincide with the zero line on the bar, but the fineness of the lines renders this a difficult matter with the naked eye, hence it is desirable to read the instrument with the aid of a magnifying glass. If the outer edges of the jaws should wear, it is simply necessary to alter the allowance made for their widths.

Fig. 1394 represents standard plug and collar gauges. These tools are made to represent exact standard measurements, and obviously do no more than to disclose whether the piece measured is exactly to size or not. If the work is not to size they will not determine how much the error or difference is, hence they are gauges rather than measuring tools. It is obvious, however, that if the work is sufficiently near to size, the plug or male gauge may be forced in, or the collar or female gauge may be forced on, and in this case the tightness of the fit would indicate that the work was very near to standard size. But the use of such gauges in this way would rapidly wear them out, causing the plug gauge and also the collar to get smaller than its designated size, hence such gauges are intended to fit the work without friction, and at the same time without any play or looseness whatever. Probably the most accurate degree of fit would be indicated when the plug gauge would fit into the collar sufficiently to just hold its own weight when brought to rest while within the collar, and then slowly fall through if put in motion within the collar. It is obvious that both the plug and the collar cannot theoretically be of the same size or one would not pass within the other, but the difference that is sufficient to enable this to be done is so minute that it is practically too small to measure and of no importance.

When these gauges are used by the workmen, to fit the work to their wear is sufficient to render it necessary to have some other standard gauge to which they can be from time to time referred to test their accuracy, and for this purpose a standard such as in Fig. 1395 may be employed. It consists of a number of steel disks mounted on an arbor and carefully ground after hardening each to its standard size.

But a set of plug and collar gauges provide within themselves to a certain extent the means of testing them. Thus we may take a collar or female gauge of a certain size and place therein two or three plug gauges whose added diameters equal that of the female or collar gauge.

In Fig. 1396, for example, the size of the female gauge a being 1¹⁄₂ inches, that of the male b may be one inch, and that of c ¹⁄₂ an inch, and the two together should just fit the female. On the other hand, were we to use instead of b and c two males, ⁷⁄₈ and ⁵⁄₈ inches respectively, they should fit the female; or a ¹⁄₂ inch, a ⁵⁄₈ inch and a ³⁄₈ inch male gauge together should fit the female. By a series of tests of this description, the accuracy of the whole set may be tested; and by judicious combinations, a defect in the size of any gauge in the set may be detected.

The wear of these gauges is the most at their ends, and the fit may be tested by placing the plug within the collar, as in Fig. 1397, and testing the same with the plug inserted various distances within the collar, exerting a slight pressure first in the direction of a and then of b, the amount of motion thus induced in the plug denoting the closeness of the fit.

In trying the fit of the plug by passing it well into or through the collar, the axis of the plug should be held true with that of the collar, and the plug while being pressed forward should be slightly rotated, which will cause the plug to enter more true and therefore more easily. The plug should be kept in motion and not allowed to come to rest while in the collar, because in that case the globules of the oil with which the surfaces are lubricated maintain a circular form and induce rolling friction so long as the plug is kept in motion, but flatten out, leaving sliding friction, so soon as the plug is at rest, the result being that the plug will become too tight in the collar to permit of its being removed by hand.

The surfaces of both the plug and the collar should be very carefully cleaned and oiled before being tried together, it being found that a film of oil will be interposed between the surfaces, notwithstanding the utmost accuracy of fit of the two, and this film of oil prevents undue abrasion or wear of the surfaces.

When great refinement of gauge diameter is necessary, it is obvious that all the gauges in a set should be adjusted to diameter while under an equal temperature, because a plug measuring an inch in diameter when at a temperature of, say, 60° will be of more than an inch diameter when under a temperature of, say, 90°.

It follows also that to carry this refinement still farther, the work to be measured if of the same material as the standard gauge should be of the same temperature as the gauge, when it will fit the gauge if applied under varying temperatures; but if a piece of work composed, say, of copper, be made to true gauge diameter when both it and the gauge are at a temperature of, say, 60°, it will not be to gauge diameter, and will not fit the gauge, if both be raised to 90° of temperature, because copper expands more than steel.

To carry the refinement to its extreme limit then, the gauge should be of the same metal as the work it is applied to whenever the two fitting parts of the work are of the same material. But suppose a steel pin is to be fitted as accurately as possible to a brass bush, how is it to be done to secure as accurate a fit as possible under varying temperatures? The two must be fitted at some equal temperature; if this be the lowest they will be subject to, the fit will vary by getting looser, if the highest, by getting tighter; in either case all the variation will be in one direction. If the medium temperature be selected, the fit will get tighter or looser as the temperature falls or rises. Now in workshop practice, where fit is the object sought and not a theoretical standard of size, the range of variation due to temperature and, generally, that due to a difference between the metals, is too minute to be of practical importance. To the latter, however, attention must, in the case of work of large diameter, be paid: thus, a brass piston a free fit at a temperature of 100° to a 12-inch cast-iron cylinder, will seize fast when both are at a temperature of, say, 250°. In such cases an allowance is made in conformity with the co-efficients of expansion.

In the case of the gauges, all that is practicable for ordinary work-shop variation of temperature is to make them of one kind and quality of material—as hard as possible and of standard diameter, when at about the mean temperature at which they will be when in use. In this case the limit of error, so far as variation from temperature is concerned, will be simply that due to the varying co-efficients of expansion of the metals of which the work is composed.

To provide a standard of lineal measurement which shall not vary under changes of temperature it has been proposed to construct a gauge such as shown in Fig. 1398, in which a and b are bars of different metals whose lengths are in the inverse ratio of their co-efficients of expansion. It is evident that the difference of their lengths will be a constant quantity, and that if the two bars be fastened together at one end, the distance from the free end of b to the free end of a will not vary with ordinary differences in temperature.

Plug and collar gauges may be used for taper as well as for parallel fits, the taper fit possessing the advantage that the bolt or pin may be let farther into its hole to take up the wear. In a report to the Master Mechanics Association upon the subject of the propriety of recommending a standard taper for bolts for locomotive work, Mr. Coleman Sellers says:—

“As the commission given to me calls for a decision as to the taper of bolts used in locomotive work, it presupposes that taper bolts are a necessity. In our own practice we divide bolts into several classes, and our rule is that in every case where a through bolt can be used it must be used. If we cannot use a through bolt we use a stud, and where a stud cannot be used we put in a tap bolt, and the reason why a tap bolt comes last is because it is part and parcel of the machine itself. There are also black bolts and body bound bolts, the former being put into holes ¹⁄₁₆ inch larger than the bolt. It is possible in fastening a machine or locomotive together to use black bolts and body bound bolts. With body bound bolts it is customary for machine builders to use a straight reamer to true the hole, then turn the bolt and fit it into its place. It is held by many locomotive builders that the use of straight bolts is objectionable, on the score that if they are driven in tight there is much difficulty in getting them out, and where they are got out two or three times they become loose, and there is no means of making them tighter.

“There is no difficulty in making two bolts of commercially the same size. But there is a vast difference between absolute accuracy and commercial accuracy. Absolute accuracy is a thing that is not obtainable. What we have to strive for, then, is commercial accuracy. What system can we adopt that will enable workmen of limited capacity to do work that will be practically accurate? The taper bolt for certain purposes presents a very decided advantage. Bolts may be made practically of the same diameter, but holes cannot be made practically of the same diameter. Each one is only an approximation to correctness. We have here an ordinary fluted reamer (showing an excellent specimen of Betts Machine Company’s make). That reamer is intended to produce a straight hole, but having once passed through a hole the reamer will be slightly worn. The next time you pass it through it is a little duller, and every time you pass it through the hole must become smaller. There have been many attempts made to produce a reamer that should be adjustable. That, thanks to the gentlemen who are making such tools a speciality, has added a very useful tool to the machine shop—a reamer where the cutters are put in tapered and can be set up and the reamer enlarged and made to suit the gauge. This will enable us to make and maintain a commercially uniform hole in our work. But the successful use of a reamer of this kind depends upon the drill that precedes this reamer being made as nearly right as possible, so that the reamer will have little work to do. The less you give a reamer to do the longer it will maintain its size.

“The question of tapered bolts involves at once this difficulty: that we have to drill a straight hole, then the tapered reamer must take out all the metal that must be removed in order to convert a straight into a tapered hole. The straight hole is maintained in its size by taking out the least amount of metal. It follows that the tapered reamer would be nearest right which would also take out the least amount of metal.

“Then you come to the question of the shape of the taper. When I was engaged building locomotives in Cincinnati, a great many years ago, we used bolts the taper of which was greater than I shall recommend to you. In regard to the compression that would take place in bolts, no piece of iron can go into another piece of iron without being smaller than the hole into which it is intended to go. If it is in any degree larger, it must compress the piece itself or stretch the material that is round it. So, if you adopt a tapered bolt, you cannot adopt a certain distance that it shall stand out before you begin to drive it, for there will be more material to compress in a large piece than in a small one. Metal is elastic. Within the elastic limit of the metal you may assume the compression to be a spring. In a large bolt you have a long spring, and in a short one you have a short spring. If you drive a half-inch bolt into a large piece of iron, it is the small bolt which you compress; therefore the larger the bolt the more pressure you can give to produce the same result. Hence, if you adopt the taper bolt, you will have to use your own discretion, unless you go into elaborate experiments to show how far the bolt head should be away from the metal when you begin to drive it.