approximation to which there can be no end but, as a matter of
fact, there is. The process may be compared with a rapidly
converging series meaning by this, not rapid in the sense of
time, for the work is slow and tedious, but rapid in the sense



32 METHODS OF MACHINE SHOP WORK

that, if the work is intelligently done, Comparatively few passes
around the circle will bring the plates to a condition in which
no further error can be discovered.

It will be observed that this is a perfect illustration of the
definition of precision work, as the result obtained is in no way
dependent upon anything previously done. Given a scraper
and a pot of paint, it might, if necessary, be done in the wilder-
ness with just as good final results as if done in the best machine
shop in the world.

There is a high degree of satisfaction in doing work of this
character. When finished, one feels that he has really made
something made it himself and without dependence upon
others or the work of others.

Plates made in this manner are called original plates. It
is not to be understood that all plates are original and, as a
matter of fact, but few of them are. With three plates origi-
nated in this manner, they may be used as standards and be
copied indefinitely, provided they are occasionally tested and
corrected by another application of the process by which they
were made.

When long and narrow, surface plates become straight edges
and in this form they illustrate Dr. Sweet's classical definition:
"A perfect straight edge is one of three, any two of which,
when placed together, coincide throughout their length."
This is a mechanical definition of a straight line. It is funda-
mental and is at least as satisfactory as any geometrical defini-
tion that has ever been given.

APPLICATIONS OF SCRAPED STANDARDS

One application of such straight edges is to the making of
the V's and cross rails of planing machines and this applica-
tion is a perfect illustration of the manner in which precision
workmanship establishes a standard and sets a limit to the
degradation of commercial workmanship. Were the V's
and cross rails of planing machines made on existing planing

1 There is no class of work in which good judgment on the part of the workman
is more important than this.



PRECISION WORK AND WORKMANSHIP 33

machines and were this process repeated indefinitely, the
accumulation of errors, which has been explained, would ob-
viously be in full operation and there would be no limit to
the process of degradation. By scraping the V's and cross
rails, however, every planer begins its life with a certain
standard of accuracy, and the work which comes from it is
only once removed from precision workmanship. 1

Figs. 10 and n show the application of a straight edge to
the testing of the vertical parallelism of the ways of a lathe bed,
as practised at the works of the Hendey Machine Company.
Six blocks which are flat on their tops and have V notches to
fit the V's of the lathe bed, are placed upon the V's and across
them are laid three parallel strips all these parts being ac-
curately made so that, the lathe bed V's being individually
straight, the straight edge will make contact with all three of
the parallels in the position shown in Fig. 10. If, now, the lathe
bed V's are not parallel vertically the tops of the parallels
become three elements of a warped surface containing no
straight lines except one set parallel with the parallels and
another set parallel with the lathe V's. Consequently, if the
straight edge is swung diagonally across the lathe bed as in
Fig. ii it will ride upon the end parallels and fail to make con-
tact with the center one, or it will ride upon the center one and
fail to make contact with the end ones and, the direction of
the error being determined, the lathe bed V's may be scraped
to correct it.

Another application of the same principle is shown in Fig. 1 2,
which illustrates the process of erecting a long planer bed
in the shops of the American Tool Works Company on which
the work is finished but which, by reason of its length fifty-
five feet and flexibility, must be set in its permanent position
with great care. The planer V's being inverted from those of
the lathe, the V blocks used in the former case are here re-

1 The author is well aware that some planer manufacturers succeed in making
planer V's of a satisfactory degree of accuracy without scraping them, but this
does not alter the fact that the work was begun with scraped V's and that the
scraping process must be reverted to again from time to time if a suitable standard
is to be maintained.
3



34



METHODS OF MACHINE SHOP WORK




FIG. 10. Testing a lathe bed for straightness.




FIG. ii. Testing a lathe bed for wind.



PRECISION WORK AND WORKMANSHIP



35



placed by short cylinders which may be easily made of the same
diameter. Across these cylinders are laid three parallels of
precisely the same thickness and to these the straight edge is
applied in the manner shown in connection with the lathe bed
the straight edge in this case being eight feet long. Below the
planer bed at regular intervals adjustable wedges are placed




FIG. 12. Erecting a long planer bed.

and by suitable adjustment of these in accordance with the
indications of the spirit level shown and of the straight edge,
the planer bed may be brought to a position in which it is level
and without wind.



ORIGINATING SQUARES BY THE SCRAPING PROCESS

Other things besides surface plates and straight edges may
be originated by the scraping process and among these are



36



METHODS OF MACHINE SHOP WORK



right angles or squares. The customary form of shop square is
not satisfactory. The surface of the blade edge is inadequate
and the blade is not well secured in the head. Few shop squares
which have seen much use will satisfactorily stand a test for
accuracy.

Figs. 13-16 show a form of square due to Dr. John E. Sweet
which is far more permanent than the usual form. The hy-





FIG. 13.



FIG. 14.




FIG. 15. FIG. 1 6.

A superior machine shop square.

pothenuse and other braces insure that, once made correct, it
will stay so, while the surfaces are large enough to endure
much use without appreciable wear. The hypothenuse gives
angles of thirty and sixty degrees and the short brace has raised
pads near its ends by which angles of forty-five degrees may be
determined. Small plates, slightly longer than the width of
the faces of the square and shown each side the square in Fig.



PRECISION WORK AND WORKMANSHIP



37



13, are fitted with small bolts and thumb nuts by which they
may be attached to the square as indicated in the various figures.
Fig. 15 shows the instrument in use for obtaining a right angle,
Fig. 14 for obtaining angles of forty-five degrees, and Fig. 16
for obtaining angles of thirty and sixty degrees.

The method of originating these squares which was used by
Whitworth is shown in Figs. 17-19. A straight edge is first
provided and here we have an illustration of the fundamental
importance of straight surfaces for, without them, the originat-
ing of the squares would be impossible. As in the case of the
surface plates and straight edges the squares are made in sets of
three. These are first planed as correctly as possible and, as in
the case of the surface plates, two of them are first scraped to
make their sum equal to two right angles but, as indicated in
Fig. 17, when this has been done the probabilities are all




FIG. 17. FIG. 18.

First method of originating squares.



FIG. 19.



against their being true squares, one of them being slightly over
and the other slightly under ninety degrees. When agreement
has been secured, one of the squares, as &,is removed and square
c is substituted for it and scraped to agree with a no scraping
being done on a at this stage in order to insure that b and c shall
have the same degree of untruth. When the agreement be-
tween a and c is obtained, as indicated in Fig. 18, a is removed
and b and c are placed together as in Fig. 19, when they are
scraped into agreement, the aim at this stage being, as in the
case of the surface plates, to divide the scraping equally between
the two squares as nearly as can be done. The result is a large
improvement, but when b and c have been brought to agreement
there will still be an error similar to that between a and b in
Fig. 17 but smaller. The process of correcting this is exactly



38 METHODS OF MACHINE SHOP WORK

parallel with that followed in the case of the surface plates
and it seems unnecessary to explain it in detail at greater length.
The final result is three squares which, by the nature of the
process by which they were made, are known to be correct.
Uses of such squares are shown in Figs. 82-85.

OTHER METHODS OF ORIGINATING SQUARES

Other methods exist for originating squares, one of which is
illustrated in Fig. 20. A square in this case having an in-
ternal angle is first made as accurately as possible by mechani-
cal means. A rectangular plate of sheet metal is then fitted to
this square at one of its angles, as a, and then at b and c in order.




FIG. 20. Second method of originating squares.

This done, the square is applied to the angle at d when the error
will be shown at e multiplied by four three times for the
rectangular plate and once for the square. The direction of the
error being now known, the square is corrected, as nearly as may
be, and the angles of the plate are corrected to agreement with
it. The process is continued until the error at e disappears
when, obviously, both the square and the plate are correct.
The work once done, the square may be put into use and the
plate may be preserved for making future squares.

In the above cases the original squares were intended for
shop use. More frequently the aim is to make a test square by



PRECISION WORK AND WORKMANSHIP



39



which to test and correct the working squares. An example of
this kind, from the works of the Ingersoll Milling Machine Com-
pany, is shown in Fig. 21. A scraped surface plate of suitable
form is first made and then a skeleton cylinder is ground on a
grinding machine to be truly parallel and cylindrical and to




FIG. 21. Third method of originating squares.

have at least one end truly square with its center line the
making of such a cylinder with a good grinding machine being
an easy and simple matter. The cylinder is then placed upon
the surface plate as shown when, by the nature of the work,
the angle between the surface plate and the side of the cylinder
is truly square. The illustration shows also the manner of test-



40



METHODS OF MACHINE SHOP WORK





FIGS. 22 and 23. Fourth method of originating squares.



PRECISION WORK AND WORKMANSHIP 41

ing shop squares by the test square. Placed in position as
shown, small pieces of paper are placed between the cylinder
and the blade of the shop square and, if the pieces of paper
are all pinched alike, the truth of the shop square is proven.

Pieces of paper used in this way are commonly called tissues,
although actual tissue paper is seldom or never used. Good
printing paper is surprisingly uniform in thickness and, in use,
is very sensitive and satisfactory. It has many applications.

It will be observed that this process does not conform to the
definition of precision work, as the result depends on the ac-
curacy of the grinding machine. It is the cheapest method of
making a correct square and is in wide use.

Another form of test square, from the works of Ludwig Loewe
and Company, is shown in Figs. 22 and 23. l The base of
the instrument is a narrow surface plate having at its rear a
vertical arm from which there is suspended a blade of hardened
steel of which the two edges are truly parallel. In use, the shop
square resting upon the surface plate has its blade applied to the
blade of the instrument as indicated in the dotted outline of the
plan view. The instrument blade is now adjusted to make con-
tact with the blade of the shop square and the shop square is
turned bodily around and applied to the, opposite edge of the
instrument blade. If the shop square is correct, it will, of course,
make perfect contact in the second position whereas, if in-
correct, the error will appear, multiplied by two, as an angle
between the two blades. To facilitate the use of the instrument,
long narrow mirrors a and b are placed as shown, together with a
row of incandescent lights c and a suitable shield d the instru-
ment being used in a darkened room.

Another very satisfactory form of square for some purposes
is an application of the spirit level. A false impression of the
accuracy of this instrument prevails because, in the form most
commonly seen that used by masons and carpenters it
makes no pretension to accuracy. For this use, in fact, a really
accurate level would be practically useless. Every surveying
instrument carries precision levels and should prevent the

1 The two illustrations do not agree in all details because made from different
instruments. They are, however, identical in all essentials.



42



METHODS OF MACHINE SHOP WORK



formation of this impression. In the present use the level used
is of surveying-instrument grade.

A shop square in which dependence is place upon a spirit
level is shown in use in Fig. 24, the operation being that of testing
the squareness of a boring mill housing with its bed. The
application of the instrument is obvious and self-explanatory.




FIG. 24.- The spirit level square.

ORIGINATING ANGLES OTHER THAN RIGHT ANGLES BY THE
SCRAPING PROCESS

Certain angles other than right angles may be originated by
the scraping process and among these are angles of forty-five
degrees for which the process is indicated in Fig. 25. As
always, we begin with a surface plate to which must be added
two straight edges. In order to originate angles of forty-five
degrees we must first have, also, a right angle as one angle of a
triangle of which the forty-five-degree angles desired are the
others. The straight edges are laid upon the surface plate and
adjusted to fit one of the forty-five-degree angles, a, of the



PRECISION WORK AND WORKMANSHIP



43



square. The square is then removed and, without disturbing
the straight edges, it is replaced with the angle b in the angle
between the straight edges. The angle c being already a right
angle, if the test shows angles a and b to be equal, they are
necessarily of forty-five degrees and if they are unequal, the
direction in which scraping must be done on the hypothenuse
in order to make them equal will be shown by the tests.

Angles of thirty and sixty degrees may also be originated in
sets of three. For this we require a straight edge, a square and
three triangles of which the right angles are correct and of which
the other angles are to be the ones required.

With these parts provided, they are grouped in the manner
shown in Fig. 26 and the
triangles are scraped until
the right angle between
the stright edge and the
square is filled by the two
angles of the triangles.
When doing this the scrap-
ing of each triangle is on
its hypothenuse alone in




FIG. 25. Originating angles of forty-five
degrees.



order to avoid disturbing
the correctness of its right
angle. When the right

angle between square and straight edge is completely filled,
the top and bottom lines of the triangles are truly parallel
because of the correctness of the right angles, and we have two
parallel lines cut by a diagonal. Consequently angles a and b
are equal, as are c and d. Moreover a and c are complements,
as are b and d. There is, however, no certainty that a and b
are truly thirty degrees or that c and d are truly sixty degrees
and, without the certainty that they are correct, there is every
probability that they are wrong. Triangle A is now removed
and triangle C is substituted for it and scraped on its hypothe-
nuse until the right angle is again filled no scraping being done
on triangle B at this stage, as the aim is to insure that the three
triangles have the same degree of untruth. This process
completed, we know that the three smaller angles, while in all



44



METHODS OF MACHINE SHOP WORK



probability not of thirty degrees, are, nevertheless, qual.
They are next grouped as shown in Fig. 27 when the error, multi-
plied by three, is at once shown by the three angles added
together failing to fill, or more than filling, the right angle. The
direction of the error being shown, the three triangles are scraped
by the same amount, as nearly as possible, and each upon its
hypothenuse, until the right angle of Fig. 27 is perfectly filled.
In spite of the care used, this scraping will, in all probability,
slightly disturb the equality of the angles, and the triangles are





FIG. 26.



FIG. 27.




FIG. 28.
Originating angles of thirty and sixty degrees.

then grouped again as in Fig. 26 and the error is corrected
by a second application of the first process. This process is
repeated until the triangles satisfy both tests when, the angles
being equal and their sum ninety degrees, they are necessarily
correct.

Two of the angles of each triangle being now known to be of
ninety and thirty, it follows that the third one must be of sixty
degrees but, if desired, an independent test of this fact may be
made by grouping the triangles as shown in Fig. 28 and, should



PRECISION WORK AND WORKMANSHIP



45



they satisfy the test, the correctness of the sixty-degree angles
is obviously proven.

OTHER METHODS OF ORIGINATING ANGLES

There is in the machine shop a surprising lack of appliances
for making pieces of which the surfaces are to have various
angles with one another. Universal milling machines are, of
course, supplied with protractors but these are never fitted
with verniers and can only be read with accuracy for the angles
which actually appear in the graduations.




FIG. 29. Two-disc method of originating angles.

In the absence of provisions of this sort, when correct angles
are required other than those supplied by the milling machine
protractors, it is necessary to resort to various expedients.
One such expedient is shown in Fig. 29, which shows a surface-
grinding machine fitted for producing a correct angle on the
inclined piece below the grinding wheel. This piece is shown
clamped to a plate which, in turn, rests upon the magnetic
chuck of the grinding machine. The plate has two holes
through it, the centers of which are at exactly the same distance
from its bottom and which are at a known distance apart.
Two discs, as shown, are made of different diameters and with
short shanks which fit the holes in the plate. It is obviously



METHODS OF MACHINE SHOP WORK



a simple matter to calculate and to make the discs of such diam-
eters that the angle between their common tangent and the
center line shall be the angle required and, with the piece of
work clamped in the position shown, the result of the grinding is
to produce this angle upon it.

This is called the two-disc method and it has many applica-
tions and variations. More commonly it is so used that the
angle produced is that between the two common tangents of
the discs and not as in the case shown, that between one common
tangent and the center line.

An application of this kind is shown in Fig. 30 in which
the piece a is required to have an angle of 18 deg. 46 min. as




FIG. 30. Second application of the two disc method of originating angles.

shown. The body b of the fixture has a tongue c fitting the
T slot of the planer or milling machine table and a ledge d
to act as an abutment to the discs e and /, the distance be-
tween which is determined by the distance piece g. The piece
of work is drawn snugly against the discs by the bridle k and
the set screw j, a similar set screw h securing the larger disc
in position against the displacing tendency of the pressure of
the piece a against it.

Again, as before, it is a simple matter to calculate and to make
the discs of proper diameters and the distance piece of proper
length for the angle required and then to produce that angle on
the planer or milling machine by planing or milling the lower
edge of piece a.



PRECISION WORK AND WORKMANSHIP



47



There are in the machine shop certain standard tapers.
The taper shanks of twist drills and the sockets by which they are
held and driven are made to the Morse taper of nominally,
though not exactly, five-eighths of an inch per foot. The work
ends of milling-machine spindles have each a hole for the cutter
arbors made to the Brown and Sharpe taper of one-half inch
per foot and in some other machine spindles the Sellers taper of
three-quarters of an inch per foot will be found. It would




FIG. 31. Third application of the two-disc method of originating angles.

be much better if we had but one taper, but the unfortunate
diversity is too firmly established to be corrected.

Interchangeability of these taper pieces in imperative.
Twist drills must interchange in their sockets and so with mill-
ing-machine arbors. That each milling machine should have
its own complete set of arbors, for example, is unthinkable.
Means for originating these tapers are therefore important,
both for the original production of plug gages by which to test
them and for the detection and correction of wear of the
plug gages.

This may be done by another application of the two-disc



48



METHODS OF MACHINE SHOP WORK




PRECISION WORK AND WORKMANSHIP 49

method shown in Fig. 31, which illustrates the originating of a
taper test gage from which to make the working taper plug
gage shown in the background. The stand at the left has a
slot through it and suitable binding straps by which to hold
the blades shown behind them, which are adjusted to correct
position by means of the parts shown in the right foreground.
These parts consist of a steel block to which are secured two
discs of such size and distance apart that the angle between
their common tangents is the angle desired. The block is
placed in the opening through the stand from behind, the dimen-
sions being such that when thus placed the discs project through
the stand. With the parts thus placed, the blades are adjusted
to contact with the discs, when, the block and discs being with-
drawn, we have a gage with which to compare the taper plug.

Another method of originating angles is by the use of the
sine bar (due to H. P. Camp) shown in Fig. 32. Here we have
the work table of a surface-grinding machine on which is placed
a swiveled magnetic chuck which it is desired to adjust to an
angle such that the wedge shown in the foreground on the work
table may be ground upon it and with a high degree of accuracy.

The sine bar shown upon the chuck is a bar of steel having
its two edges accurately parallel and carrying near its ends two
pins of exactly the same diameter located on a center line which
is exactly parallel with the edges of the strip and which are at a
known distance apart usually ten inches between centers.
At the right is seen a height gage, 1 which is an accurate in-
strument for measuring vertical distances from the bottom
of its base to the lower side of the projecting- finger. The sine
of the required angle is taken from a table and multiplied by the
distance between the centers of the pins, when the chuck is
adjusted on its trunnions by trial until the pin at the right
stands above the pin at the left by an amount equal to the sine
of the angle thus multiplied this difference in height being
determined by the height gage.

The sine bar has many other application's 'of which two are
shown in Figs. 33 and 34. In Fig. 33 the bar is applied to an

1 This instrument is described at greater length in the chapter on Measures
of Length.
4



50



METHODS OF MACHINE SHOP WORK



angle plate and it locates directly the piece of work to be ground
to the desired angle. In Fig. 34 two sine bars and a suitable
stand are so assembled as to provide a taper gage similar to the




FIG. 34. Third application of the sine bar method of originating angles.

one already shown in Fig. 31 the gage being here shown in
the act of gaging a taper reamer.

The sine bar provides, perhaps, the most generally useful
method of originating angles. It is extremely simple, quite




FIG. 35. Adjustable angle plate for originating angles.

accurate and, unlike the two-disc method, does not require
special construction for each case. Against it is the fact that,
in each of the repeated trials necessary to adjust it, the positions