Suppose in Fig. 1438 a a represents a piece of wrought-iron tube that has been heated to a bright red and immersed in cold water c c from the end b to d, until that end is cold. The part submerged and cold will be contracted to its normal diameter and have regained its normal strength, while the part above the water, remaining red-hot, will be expanded and weak. There will be, then, a narrow section of the tube, joining the heated and expanded part to the cooled and contracted part, and its form will be conical, as shown at d d. Now, suppose the tube to be slowly lowered in the water, the cold metal below will compress the heated metal immediately above the water-line, the cone section d being carried up into the metal before it has had time to cool; and the tube removed from the water when cold will be as shown in Fig. 1438, from c to d, representing the part first immersed and cooled. To complete the operation the tube must be heated again from the end c to a short distance past d, and then immersed from e nearly to d, and held still until the submerged part is cold, when the tube must be slowly lowered to compress the end c d, making the tube parallel, but smaller in diameter and in bore, while leaving it of its original length, but thickening its wall.
This process may, in many cases, be artificially assisted. Suppose, for example, a washer is too large in its bore; it should have its hole and part of its radial faces filled with fire-clay, as shown in Fig. 1439, in which a is the washer and b b the clay, c c being pieces of wire to hold the fire-clay and prevent its falling off. The washer should be heated to a clear red and plunged in the water d d, which will cool and shrink the exterior and exposed metal in advance of the interior, which will compress to accommodate the contraction of the outer metal, hence the hole will be reduced. This operation may be repeated until the hole be entirely closed.
Another method of closing such a piece as an eye of large diameter compared to its section, is shown in Fig. 1440; first dipping the heated eye at a and holding it there till cold and then slowly lowering it into the water, which would close the diameter across c, and, after reheating, dipping at d till cold, and then slowly immersing, which would close the eye across e. To shrink a square ring, the whole ring would require to be heated and a side of the square dipped, as shown in Fig. 1441, until quite cold, and then immersed slowly for about an inch, the operation being performed with a separate heating for each side. Connecting rod straps, wheel-tires, and a large variety of work may be refitted by this process, but in each case the outside diameter will be reduced.
For what may be termed the length measurements of lathe work it is obvious that caliper gauges, such as shown in Fig. 1402, may be employed. Since, however, these length measurements rarely require to be so accurate as the diametrical measurements, the ordinary lineal rule is very commonly employed in work not done under the standard gauge system. It is obvious, however, that when a number of pieces are to be turned to corresponding lengths, a strip of sheet iron, or of iron rod made to the required length, may be employed; a piece of sheet iron filed to have the necessary steps being used where there are several steps in the work; but if the lineal measuring rule is used, and more than one measurement of length is to be taken, some one point, as one end of the work, should be taken wherefrom to measure all the other distances. Suppose, for example, that Fig. 1442 represents a crank pin requiring to have its end collar 1⁄4 inch thick, the part a 2 inches long, part b 3 inches long, collar c 1⁄2 inch thick, and the part d 7 inches long. If the length of each piece were taken separately and independently of the others, any errors of measurement would multiply; whereas, if some one point be taken as a point wherefrom to measure all the other distances, error is less liable to occur, while at the same time an error in one measurement would not affect the correctness of the others. In the case of the crank pin shown, the collar c would be the best point wherefrom to take all the other measurements. First, it would require to be made to its proper thickness, and the lengths of b, a, and the end collar should be measured from its nearest radial face. The length of d should then be measured from the same radial face, the thickness of the collar being added to the required length of d, or d may be measured from the nearest radial face of c, providing c be of its exact proper thickness. In measuring the length of the taper part d, a correct measurement will not be obtained by laying the rule along its surface, because that surface does not lie parallel to its axis, hence it is necessary to apply the measuring rule, as shown in Fig. 1443, in which s is a straight-edge held firmly against the radial face of the crank pin (the radial face being of course turned true), and r is the measuring rule placed true with the axial line of the crank pin. Whenever the diameters of the lengths to be measured vary, this mode of measuring must be employed. On small work, or on short distances requiring to be very exact, a gauge such as shown in Fig. 1444 at a may be employed, which will not only give more correct results, but because it is more convenient, as it can be conveniently held or tried to the work with one hand while the other hand is applied to the feed screw handle to withdraw the cutting tool at the proper moment, and to the feed nut to unlock it and stop the feed.
On long work a wooden strip is the best, especially if the work has varying diameters and a number of pieces of work require to be made exactly alike. In Fig. 1445 s represents the wooden strip, and w the work. The strip is marked across by lines representing the distances apart the shoulders of the work require to be; thus the lines a, b, c, d, e, f, g, represent the distances apart of the radial faces a, b, c, d, e, f, g, on the work, and these lines will be in the same plane as the shoulders if the latter are turned to correct lengths. To compare the radial faces with the lines, a straight-edge must be held to each successive shoulder (as already described) that is of smaller diameter than the largest radial face on the work.
If the wooden strip be made the full length of the work the dog or clamp driving the work will require to be removed every time the wooden gauge is applied, and since the work must be turned end for end in the lathe to be finished, it would be as well to let the length of the wood gauge terminate before reaching the work driver, as, say, midway between e and f.
When a lineal distance is marked by lines, and this distance is to be transferred to another piece of work and marked thereon by lines, the operation may be performed, for short distances or radii, by the common compasses employed to mark circles, but for greater distances where compasses would be cumbersome, the trammels are employed.
Fig. 1446 represents a pair of trammels made entirely of metal, and therefore suitable for machinists’ use, in which the points require to be pressed to the work to mark the lines. a a represents a bar of square steel; or for very long trammels wood may be used. b represents a head fastened tightly to one end, and through b passes the leg or pointer c, which is thus adjustable as to its projecting distance, as c can be fastened in any position by the thumb-screw d. The head e is made to a good sliding fit upon the bottom and two side faces of a a; but at the top there is sufficient space to admit a spring, which passes through e. f is the leg screwed into e, which is locked in position by the thumb-screw g. The head e is thus adjustable along the whole length of the bar or rod a a. The object of the spring is as follows:—If the head e were made to fit the bar a a closely on all four sides, the burrs raised upon the top side of the rod a a by the end of the thumb-screw g would be likely to impede its easy motion. Then again, when the sliding head e has worn a trifle loose upon the bar a a, and is loosened for adjustment, it would be liable to hang on one side, and only to right itself when the screw g brought it to a proper bearing upon the under side of the bar a a, and thus tightening the head e would alter the adjustment of the point. The spring, however, always keeps the lower face of the square hole through e bearing evenly against the corresponding face of the bar, so that tightening the screw g does not affect the adjustment, and, furthermore, the end of the set-screw, bearing against the spring instead of against the top of the rod, prevents the latter from getting burred.
The flat place at i i is to prevent the burrs raised by the thumb-screw end from preventing the easy sliding of leg c through b.
In some cases a gib is employed, as shown at a in Fig. 1447, instead of a spring, the advantage being that it is less liable to come out of place when moving the head along the bar.
The trammels should always be tried to the work in the same relative position as that in which they were set, otherwise the deflection of the bar may vitiate the correctness of the measurement; thus, if the rod or bar stood vertical when the points were adjusted for distance to set them to the required distance, it should also stand vertical upon the work when applied to transfer that distance, otherwise the deflection of the bar from its own weight will affect the correctness of the operation. Again, when applied to the work the latter should be suspended as nearly as convenient in the same position as the work will occupy when erected to its place.
Thus, suppose the trammels be set to the crank pin centres of a locomotive, then the bar will stand horizontally. Now the side rod, or coupling rod, as it may be more properly termed, should be stood on edge and should rest on its ends, because its bearings wherever it will rest when on the engine are at the ends; thus the deflection of the trammel rod will be in the same direction when applied to the work as it was when applied to the engine, and the deflection of the coupling rod will be in the same direction when tried by the trammel as when on the engine. The importance of this may be understood when it is mentioned that if the coupling rod be a long one, resting it on its side and supporting it in the middle instead of at its ends will cause a difference of 1⁄50th inch in its length.
Another lineal measuring gauge employed in the machine shop is shown in Fig. 1448. It is employed to measure the distance between two faces, and therefore in place of inside calipers, in cases where from the extreme distance to be measured it would require the use of inside calipers too large to be conveniently handled. Its application is more general upon planing machine work than any other, although it is frequently used by the lathe hand or turner, and by the vice hand and erector. It consists of two legs a and b, held together by the screws c d, which screw into nuts. These nuts should have a shoulder fitting into the slots in both legs, so as to form a guide to the legs. The screws are set up so as to just bind both legs together but leaving them free enough to move under a slight friction. The gauge is then set to length by lightly striking the ends e, and when adjusted the screws c d are screwed firmly home. The ends e are rounded somewhat, as is shown, to prevent them from swelling or burring by reason of the blows given to adjust them.
For striking circles we have the compasses or dividers, which are made in various forms.
Thus, Fig. 1449 represents a pair of spring dividers, the bow spring at the head acting to keep the points apart, and the screw and nut being employed to close and to adjust them.
Another form is shown in Fig. 1450, the legs being operated by a right and left-hand screw, which may be locked in position by the set-screw shown.
For very small circles the fork scriber shown in Fig. 1451 is an excellent tool, since it may be used with great pressure so as to cut a deep line in the surface of the work. This tool is much used by boiler makers, but is a very useful one for the machinist for a variety of marking purposes, which will be described with reference to vice work.
For larger work we have the compasses, a common form of which is shown in Fig. 1452, in which the leg a is slotted to receive the arc piece c, which has a threaded stem passing through e, and is provided with a nut at b; at d is a spring which holds the face of the nut b firmly against the leg e; at a is a thumb-screw for securing the leg to the arm c. The thumb-screw a being loosened, the compass legs may be rudely adjusted for distance apart, and a is then tightened. The adjustment is finally made by operating the nut b, which, on account of its fine thread, enables a very fine adjustment to be easily made.
It is often very convenient to be able to set one leg of a pair of dividers to be longer than the other, for which purpose a socket b, Fig. 1453, is provided, being pierced to receive a movable piece a, and split so that by means of a set-screw c the movable piece a may be gripped or released at pleasure.
For finding the centres of bodies or for testing the truth of a centre already marked, the compass calipers shown in Fig. 1454, are employed. It is composed of one leg similar to the leg of a pair of compasses, while the other is formed the same as the leg of an inside caliper. The uses of the compass calipers are manifold, the principal being illustrated as follows:—
Let it be required to find the centre of a rectangular block, and they are applied as in Fig. 1455, the curved leg being rested against the edge and a mark being made with the compass leg. This being done from all four sides of the work gives the centre of the piece.
In the case of a hole its bore must be plugged and the compass calipers applied as in Fig. 1456.
For marking a line true with the axial line of a cylindrical body, we have the instrument w in Fig. 1457, which is shown applied to a shaft s. The two angles of the instrument are at a right angle one to another, so that when placed on a cylindrical body the contact will cause the edge of w to be parallel with the axis of the shaft. The edge is bevelled, as shown, so that the lines of division of inches and parts may come close to the work surface, and a scriber may be used to mark a line of the required length. A scriber is a piece of steel wire having a hardened sharp point wherewith to draw lines.
On account of the instrument w finding its principal application in marking key seats upon shafts, it is termed the “key-seat rule.”
For marking upon one surface a line parallel to another surface, the scribing block or surface gauge shown in Fig. 1458 is employed. It consists of a foot piece or stand d, carrying a stem. In the form shown this stem contains a slot running centrally up it. Through this slot passes a bolt whose diameter close to the head is larger than the width of the slot, so that it is necessary to file flat places on the side of the slot to permit the bolt to pass through it.
On the stem of the bolt close to the head, and between the bolt head and the stem of the stand, passes the piece shown at f. This consists of a piece of brass having a full hole through which the bolt passes clear up to the bolt head. On the edge view there is shown a slot, and on each side of the slot a section of a hole to receive a needle. A view of the bolt is given at e, the flat place to fit the slot in the stem being shown in dotted lines, and the space between the flat place and the bolt head is where the piece of brass, shown in figure, passes. This piece of brass being placed on the bolt, and the bolt being passed through the slot in the stem, the needle is passed through the split in the brass, and the thumb-nut is screwed on so that tightening up the thumb-nut causes the needle to be gripped in the brass split in any position in the length of the stem slot in which the bolt may be placed. The advantage of this form over all others is that the needle may be made of a simple piece of wire, and therefore very readily. Again, the piece of brass carrying the needle may be rotated upon the pin any number of consecutive rotations backwards and forwards, and there is no danger of slacking the thumb-nut, because the needle is on the opposite side of the stem to what the thumb-nut is, and the flat place prevents the bolt from rotating. Furthermore, the needle can be rotated on the bolt for adjustment for height without becoming loosened, whereas when the thumb-nut is screwed up firmly the needle is held very fast indeed, and finally all adjustments are made with a single thumb-nut.
The figure represents a view of this gauge from the bolt head and needle side of the stem, the thumb-nut being on the opposite side.
This tool finds its field of application upon lathe work, planer work, and, indeed, for one purpose or another upon all machine tools, and in vice work and erecting, examples of its employment being given in connection with all these operations.
Fig. 1459 represents a scribing block for marking the curves to which to cut the ends of a cylindrical body that joins another, as in the case of a T-pipe. It is much used by pattern-makers. In the figure a is a stem on a stand e. A loose sleeve b slides on a carrying an arm c, holding a pencil at d. A piece of truly surfaced wood or iron w, has marked on it the line j. Two Vs, g, g, receive the work p. Now, if the centres of g, g and of the stand e all coincide with the line j then e will stand central to p, and d may be moved by the hand round p, being allowed to lift and fall so as to conform to the cylindrical surface of p, and a line will be marked showing where to cut away the wood on that side, and all that remains to do is to turn the work over and mark a similar line diametrically opposite, the second line being dotted in at k.
The try square, Fig. 1460, is composed of a rectangular back f, holding a blade, the edges of the two being at a right angle one to the other and as straight as it is possible to make them. The form shown in the figure is an L-square.
Fig. 1461 represents the T-square, whose blade is some distance from the end of the back and is sometimes placed in the middle. When the square edges are at a true right angle the square is said to be true or square, the latter being a technical term meaning at practically a true right angle.
The machinists’ square is in fact a gauge whereby to test if one face stands at a right angle to another. It is applied by holding one edge firmly and fairly bedded against the work, while the other edge is brought to touch at some part against the face to be tested.
If in applying a square it be pressed firmly into the corner of the work, any error in the latter is apt to escape observation, because the square will tilt and the error be divided between the two surfaces tested. To avoid this the back should be pressed firmly against one surface of the work and the square edge then brought down or up to just touch the work, which it will do at one end only if the work surface is out of square or not at a right angle to the face to which the square back is applied.
An application of the T-square is shown in Fig. 1462, in which w is a piece of work requiring to have the face a of the jaw c at a right angle to the face b c. Sometimes the L-square is employed in conjunction with a straight-edge in place of the T-square. This is usually done in cases where the faces against which the square rests are so far apart as to require a larger T-square than is at hand. It is obvious that if the face a of the work is the one to be tested, the edge b is the part pressed to the work; or per contra, if b c is the face to be tested, the edge of the blade is pressed to the work.
The plane of the edges of a square should, both on the blade and on the back, stand at a right angle to the side faces of the body or stock, and the side of the blade should be parallel to the sides of the back and not at an angle to either side, nor should it be curved or bent, because if under these conditions the plane of the square edge is not applied parallel with the surface of the work the square will not test the work properly. This is shown in Fig. 1463, in which w is a piece of work, and s a square having its blade bent or curved and applied slightly out of the vertical, so that presuming the plane of the blade edge to be a right angle to the stock or back of the square the plane of the blade edge will not be parallel with the plane of the work, hence it touches the work at the ends a b only, whereas if placed vertically the blade edge would coincide with the work surface all the way along. It is obvious then that by making the edge of the blade at a right angle, crossways as well as in its length, to the stock, the latter will serve as a guide to the eye in adjusting the surface of the blade edge parallel to that of the work by placing the stock at a right angle to the same.
There are three methods of testing the angle of a square blade to the square back. The first is shown in Fig. 1464, in which a is a surface plate having its edge a true plane. The square s is placed in the position shown by full lines pressed firmly to the edge of the surface plate and a fine line is drawn with a needle point on the face of the surface plate, using the edge of the square blade as denoted by the arrow c as a guide. The square is then turned over as denoted by the dotted lines and the edge is again brought up to the line and the parallelism of the edge with the line denotes the truth, for whatever amount the blade may be out of true will be doubled in the want of coincidence of the blade edge with the line.
A better plan is shown in Fig. 1465, in which a is the surface plate, b a cylindrical piece of iron turned true and parallel in the lathe and having its end face true and cupped as denoted by the dotted lines so as to insure that it shall stand steadily and true. The surface of a and the vertical outline of b forming a true right angle we have nothing to do but make the square s true to them when placed in the position shown.
If we have two squares that are trued and have their edges parallel, we may test them for being at a right angle by trying them together as in Figs. 1466 and 1467, in which a, b, are the two squares which, having their back edges pressed firmly together (when quite clean), must coincide along the blade edges; this being so we may place them on a truly surfaced plate as shown in Fig. 1468, in which s is one square and s′ the other, p being the surface plate. Any want of truth in the right angle will be shown doubled in amount by a want of coincidence of the blade edges.
For some purposes, as for marking out work on a surface plate, it is better that the square be formed of a single piece having the back and blade of equal thickness, as shown in Fig. 1469, which represents a side and edge view of an L-and T-square respectively.
For angles other than a right angle we have the bevel or bevel square (as it is sometimes called), shown in Fig. 1470, a representing the stock or back, and b the blade, the latter being provided with a slot so that it may be extended to any required distance (within its scope) on either side of the stock. c is the rivet, which is made sufficiently tight to permit of the movement by hand of the blade, and yet it must hold firmly enough to be used without moving in the stock. Instead of the rivet c, however, a thumb-screw and nut may be employed, in which case, after the blade is set to the required angle, it may be locked in the stock by the thumb-screw.
Fig. 1471 represents a Brown and Sharpe bevel protractor, with a pivot and thumb-nut in the middle of the back with a half-circle struck from the centre of the pivot and marked to angular degrees. The pointer for denoting the degrees of angle has also a thumb-screw and nut so that the blade may, by loosening the pivot and pointer, be moved to project to the required distance on either side of the back.
Swasey’s improved protractor, however, is capable of direct and easy application to the work, forming a draughtsman’s protractor, and at the same time a machinist’s bevel or bevel square, while possessing the advantage that there is no protruding back or set-screw to prevent the close application of the blade to the work. This instrument is shown in Fig. 1472. The blade a is attached to the circular piece d, the latter being recessed into the square b b, and marked with the necessary degrees of angle, as shown, while the mark f upon the square b serves as an index point. The faces of a, b b, and d are all quite level, so that the edges will meet the lines upon the work and obviate any liability to error. The piece d is of the shape shown in section at g, which secures it in b b, the fit being sufficient to permit of its ready adjustment and retain it by friction in any required position. The dotted lines indicate the blade as it would appear when set to an angle, the point e being the centre of d, and hence that from which the blade a operates.
On account, however, of the numerous applications in machine work of the hexagon (as, for instance, on the sides of both heads and nuts), a special gauge for that angle is requisite, the usual form being shown in Fig. 1473. The edges a, b, form a hexagon gauge, and edges c, d, form a square, while the edge e serves as a straight-edge.
All these tools should be made of cast steel, the blades being made of straight saw blade, so that they will not be apt to permanently set from an ordinary accidental blow; while, on the other hand, if it becomes, as it does at times, necessary to bend the blade over to the work, it will resume its straightness and not remain bent.
For testing the straightness, in one direction only, of a surface the straight-edge is employed. It consists in the small sizes of a piece of steel whose edges are made straight and parallel one to the other. When used to test the straightness of a surface without reference to its alignment with another one, it is simply laid upon the work and sighted by the eye, or it may have its edge coated with red marking, and be moved upon the work so that its marking will be transferred to the high spots upon the work. The marking will look of the darkest colour in the places where the straight-edge bears the hardest. The most refined use of the straight-edge is that of testing the alignment of one surface to the other, and as this class of work often requires straight-edges of great length, as six or ten feet, which if made of metal would bend of its own weight, therefore they are made of wood.
Fig. 1474 represents an example of the use of straight-edge for alignment purposes. It represents a fork and connecting rod, and it is required to find if the side faces of the end b are in line with the fork jaws. A straight-edge is held firmly against the side faces of b in the two positions s and s′, and it is obvious that if they are in line the other end will be equidistant from the jaw faces, at the two measurements.
Figs. 1474, 1475, 1476, 1477, and 1478 represent the process of testing the alignment of a link with a straight-edge. First to test if the single eye e is in line with the double eye f at the other end, the straight-edge is pressed against the face of e, as in Fig. 1475, and the distance i is measured. The straight-edge is then applied on the other side of e, as in Fig. 1476, and the distance h is measured, and it is clear that if distances h and i are equal, then e is in line with the double eye. To test if the double eye f is in line with the single eye e, the straight-edge is pressed against the face of the double eye in the positions shown in Figs. 1477 and 1478, and when distances j and k measure equal the jaws of the double eye f are in line with those of the single eye e.
It is obvious, however, that we have here tested the alignment in one direction only. But to test in the other direction we may use a pair of straight-edges termed winding strips, applying them as in Fig. 1479, to test the stem, and as in Fig. 1480 to test the eye e, and finally placing the winding strip c on the eye of f while strip d remains upon e, as in Fig. 1480. The two strips are sighted together by the eye, as is shown in Fig. 1481, in which s and s′′ are the strips laid upon a connecting rod, their upper edges being level with the eye, hence if they are not in line the eye will readily detect the error. Fig. 1482 represents an application to a fork ended connecting rod. Pattern-makers let into their winding strips pieces of light-coloured wood as at c, c, c, c, in Fig. 1483, so that the eye may be assisted in sighting them.
It is obvious that in using winding strips they should be parallel one to the other; thus, for example, the ends a, b, in Fig. 1481, should be the same distance apart as ends c, d.
If less than three straight-edges or parallel strips are to be trued they must be trued to a surface plate or its equivalent, but if a pair are to be made they should have the side faces made true, and be riveted together so that their edges may be trued together, and equal width may be more easily obtained. For this purpose copper rivets should be used, because they are more readily removable, as well as less likely to strain the work in the riveting.
By riveting the straight-edges together the surface becomes broader and the file operates steadier, while the edges of the straight-edge are left more square. Furthermore parallelism is more easily obtained as one measurement at each end of the batch will test the parallelism instead of having to measure each one separately at each end. If three straight-edges are to be made they may be riveted together and filed as true as may be with the testing conveniences at hand, but they should be finally trued as described for the surface plate.
In using straight-edges to set work, the latter is often heated to facilitate the setting, and in this case the straight-edge or parallel strips should be occasionally turned upside down upon the work, for if the heated work heats one side of the straightedge more than the other the increased expansion of the side most heated will bend the straight-edge or strips, and throw them out of true.
In applying a straight-edge to test work it must never be pressed to the work surface, because in that case it will show contact with the work immediately beneath the parts where such pressure is applied. Suppose, for example, a true straight-edge be given a faint marking, and be applied to a true surface, the straight-edge itself being true; then if the hands are placed at each end of the straight-edge, and press it to the work while the straight-edge is given motion, it will leave the heaviest marks at and near the ends as though the work surface was slightly hollow in its length; while were the hand pressure applied to the middle of the length of the straight-edge the marks on the work would show the heaviest in the middle as though the work surface were rounding. This arises from the deflection due to the weakness of the straight-edge.
For testing the truth of flat or plane surfaces the machinist employs the surface plate or planometer. The surface plate is a plate or casting having a true flat surface to be used as a test plate for other surfaces. It is usually made of cast iron, and sometimes of chilled cast iron or hardened cast steel, the surface in either of these two latter cases being ground true because their hardness precludes the possibility of cutting them with steel tools. A chilled or hardened surface plate cannot, however, be so truly surfaced as one that is finished with either the scraper or the file.
The shape of the surface plate is an element of the first importance, because as even the strongest bars of metal deflect from their own weight, it is necessary to shape the plate with a view to make this deflection as small as possible in any given size and weight of plate. In connection, also, with the shape we must consider the effect of varying temperatures upon the metal, for if one part of the plate is thinner than another it will, under an increasing temperature, heat more rapidly, and the expansion due to the heating will cause that part to warp the plate out of its normal form, and hence out of true. The amount that a plate will deflect of its own weight can only be appreciated by those who have had experience in getting up true surfaces, but an idea may be had when it is stated that it can be shown that it is easily detected, in a piece of steel three inches square and a foot long.
Now this deflection will vary in direction according to the points upon which the plate rests. For instance, take two plates, clean them properly, and rest one upon two pieces of wood, one piece under each end, and then place another plate upon the lower one and its face will show hollow, and, if the upper plate is moved backwards and forwards laterally it will be found to move from the ends as centres of motion. Then rest the lower plate upon a piece of wood placed under the middle of its length, and we shall find that (if the plates are reasonably true) the top one will move laterally with the middle of its length as a centre of motion. Now although this method of testing will prove deflection to exist, it will not show its amount, because the top plate deflects to a certain extent, conforming itself to the deflection of the lower one, and if the test is accurately made it will be found that the two plates will contact at whatever points the lower one is supported.
If plates, tested in this manner, show each other to have contact all along however the lower one is supported, it is because they are so light that the upper one will readily bend to suit the deflection of the lower one, and true work is, with such a plate, out of the question.
To obviate these difficulties the body of the plate is heavily ribbed, and these ribs are so arranged as to be of equal lengths, and are made equal in thickness to the plate, so that under variations of temperature the ribs will not expand or contract more quickly or slowly than the body of the plate, and the twisting that would accompany unequal expansion is avoided.