THE STEEL SQUARE AND ITS USES.
INTRODUCTORY REMARKS.
Division A.
I will not attempt in this small treatise, to give an historical account
of the origin, growth and development of the square, as the subject has
been treated of at length in my larger works, as I do not care to pad
out these pages with matter that is not of a severely practical nature.
Suffice it to say, that while iron squares, figured on their faces in
inches and feet, and smaller divisions, have been made in England and
Belgium for 200 years or more, the genuine steel square, as we now know
it, is a purely American product, and it has no equal, as no European
manufacturer has as yet been able to turn out a square anything like as
good or perfect in finish, graduation, or general get-up, as Sargent &
Co., of New Haven, Conn.; Nicholls Co., Ottumwa, Iowa; and The Peck,
Stow & Wilcox Co., Southington, Conn. Squares made by any one of these
firms named, may be relied upon as being as near perfect as it is
possible to make them in everything that pertains to accuracy,
durability and general finish. The American workman should feel proud of
the fact that he possesses a Steel Square of purely Home production
which has no equal in the world.
There is nothing of more importance to a young man who is learning the
business of house-joinery and carpentry, than that he should make
himself thoroughly conversant with the capabilities of the tools he
employs. It may be that, in some of the rules shown in this work, the
result could be attained much readier with other aids than the square;
but the progressive mechanic will not rest satisfied with one method of
performing operations when others are within his reach.
In the hand of the intelligent mechanic the square becomes a simple
calculating machine of the most wonderful capacity, and by it he solves
problems of the kinds continually arising in mechanical work, which by
the ordinary methods are more difficult to perform.
The great improvement which the arts and manufactures have attained
within the last fifty years, renders it essential that every person
engaged therein should use his utmost exertions to obtain a perfect
knowledge of the trade he professes to follow. It is not enough,
nowadays, for a person to have attained the character of a good workman;
that phrase implies that quantum of excellence, which consists in
working correctly and neatly, under the directions of others. The
workman of to-day, to excel, must understand the principles of his
trade, and be able to apply them correctly in practice. Such a one has a
decided advantage over his fellow-workman; and if to his superior
knowledge he possesses a steady manner, and industrious habits, his
efforts cannot fail of being rewarded.
It is no sin not to know much, though it is a great one not to know all
we can, and put it all to good use. Yet, how few mechanics there are who
will know all they can? Men apply for employment daily who claim to be
finished mechanics, and profess to be conversant with all the ins and
outs of their craft, and who are noways backward in demanding the
highest wages going, who, when tested, are found wanting in knowledge of
the simplest formulas of their trade. They may, perhaps, be able to
perform a good job of work after it is laid out for them by a more
competent hand; they may have a partial knowledge of the uses and
application of their tools; but, generally, their knowledge ends here.
Yet some of these men have worked at this trade or that for a third of a
century, and are to all appearances, satisfied with the little they
learned when they were apprentices. True, mechanical knowledge was not
always so easily obtained as at present, for nearly all works on the
constructive arts were written by professional architects, engineers,
and designers, and however unexceptionable in other respects, they were
generally couched in such language, technical and mathematical, as to be
perfectly unintelligible to the majority of workmen; and instead of
acting as aids to the ordinary inquirer, they enveloped in mystery the
simplest solutions of every-day problems, discouraging nine-tenths of
workmen on the very threshold of inquiry, and causing them to abandon
further efforts to master the intricacies of their respective trades.
Of late years, a number of books have been published, in which the
authors and compilers have made commendable efforts to simplify matters
pertaining to the arts of carpentry and joinery, and the mechanic of
to-day has not the difficulties of his predecessors to contend with. The
workman of old could excuse his ignorance of the higher branches of his
trade, by saying that he had no means of acquiring a knowledge of them.
Books were beyond his reach, and trade secrets were guarded so
jealously, that only a limited few were allowed to know them, and unless
he was made of better stuff than the most of his fellow-workmen, he was
forced to plod on in the same groove all his days.
Not so with the mechanic of today; if he is not well up in all the
minutiæ of his trade, he has but himself to blame, for although there is
no royal road to knowledge, there are hundreds of open ways to obtain
it; and the young mechanic who does not avail himself of one or other of
these ways to enrich his mind, must lack energy, or be altogether
indifferent about his trade, and may be put down as one who will never
make a workman.
I have thought that it would not be out of place to preface this work on
the “Steel Square,” with the foregoing remarks, in the hope that they
may stimulate the young mechanic, and urge him forward to conquer what
at best are only imaginary difficulties. A willing heart and a clear
head will most assuredly win honorable distinction in any trade, if they
are only properly used. Indeed, during an experience of many years in
the employment and superintendence of mechanics of every grade, from the
green “wood-haggler” to the finished and accomplished workman, I have
invariably discovered that the finished workman was the result of
persistent study and application, and not, as is popularly supposed, a
natural or spontaneous production. It is true that some men possess
greater natural mechanical abilities than others, and consequently a
greater aptitude in grasping the principles that underlie the
constructive arts; but, as a rule, such men are not reliable; they may
he expert, equal to any mechanical emergency, and quick at mastering
details, but they are seldom thorough, and never reliable where long
sustained efforts are required.
The mechanic who reaches a fair degree of perfection by experience,
study and application is the man who rises to the surface, and whose
steadiness and trustworthiness force themselves on the notice of
employers and superintendents. I have said this in order to give
encouragement to those young mechanics who find it up-hill work to
master the intricacies of the various arts they are engaged in, for they
may rest assured that in the end _work_ and _application_ will be sure
to win; and I am certain that a thorough study of the Steel Square and
its capabilities will do more than anything else to aid the young
workman in mastering many of the mechanical difficulties that will
confront him from time to time in his daily occupation.
It must not be supposed that the work here presented exhausts the
subject. The enterprising mechanic will find opportunity for using the
square in the solution of many problems that will crop up during his
daily work, and the principles herein laid down will aid very much
towards correct solutions. In framing roofs, bridges, trestle-work, and
constructions of timber, the Steel Square is a necessity to the American
carpenter; but only a few of the more intelligent workmen ever use it
for other purposes than to make measurements, lay off the mortices and
tenons, and square over the various joints. Now, in framing bevel work
of any description, the square may be used with great advantage and
profit. Posts, girts, braces, and struts of every imaginable kind may be
laid out by this wonderful instrument, if the operator will only study
the plans with a view of making use of his square for obtaining the
various bevels, lengths and cuts required to complete the work in hand.
Tapering structures—the most difficult the framer meets with—do not
contain a single bevel or length that can not be found by the square
when properly applied, and it is this fact I wish to impress on my
readers, for it would be impossible, in this work, to give every
possible application of the square to work of this kind. I have,
therefore, only given such examples as will enable any one to apply some
one of them to any work in hand.
In the foregoing sketch I have given a few hints as to the kind of
square to purchase when it is necessary to buy; in many cases, however,
this book will find its way into the hands of mechanics and others, who
will have old and favorite squares in their chests or workshops, and who
will not care to dispose of a “well-tried friend” for the purpose of
filling its place with another, simply because I have recommended it. To
these workmen I would say that I do not advise a change, provided the
old square is true, and the inches and sub-divisions are properly and
accurately defined. I wish it distinctly understood that old squares, if
true, and marked with inches and sub-divisions of inches, will perform
nearly every solution presented in this book.
The lines and figures formed on the squares of different make, sometimes
vary, both as to their position on the square, and their mode of
application, but a thorough understanding of the application of the
scales and lines shown on any first-class tool, will enable the student
to comprehend the use of the lines and figures exhibited on other
first-class squares.
To insure good results, it is necessary to be careful in the selection
of the tool. The blade of the square should be 24 inches long, and two
inches wide, and the tongue from 14 to 18 inches long and 1½ inches
wide. The tongue should be exactly at right angles with the blade, or in
other words the “square” should be perfectly square.
To test this question, get a board, about 12 or 14 inches wide, and four
feet long, dress it on one side, and true up one edge as near straight
as it is possible to make it. Lay the board on the bench, with the
dressed side up, and the trued edge towards you, then apply the square,
with the blade to the left, and mark across the prepared board with a
penknife blade, pressing close against the edge of the tongue; this
process done to your satisfaction, reverse the square, and move it until
the tongue is close up to the knife mark; if you find that the edge of
the tongue and mark coincide, it is proof that the tool is correct
enough for your purposes. Later on, I will show by diagram how this test
is performed.
This, of course, relates to the outside edge of the blade, and the
outside edge of the tongue. If these edges should not be straight, or
should not prove perfectly true, they should be filed or ground until
they are straight and true. The outside edge of the blade should also be
“trued” up and made exactly parallel with the inside edge, if such is
required. The same process should be gone through on the tongue. As a
rule, squares made by firms of repute are perfect, and require no
adjusting; nevertheless, it is well to make a critical examination
before purchasing.
The next thing to be considered is the use of the figures, lines, and
scales, as exhibited on the square. It is supposed that the ordinary
divisions and sub-divisions of the inch, into halves, quarters, eighths,
and sixteenths are understood by the student; and that he also
understands how to use that part of the square that is subdivided into
twelfths of an inch. This being conceded, we now proceed to describe the
various rules as shown on all good squares; but before proceeding
further, it may not be out of place to state, that on the squares
recommended in this book, one edge is subdivided into thirty-seconds of
an inch.
This fine sub-division will be found very useful, particularly so when
used as a scale to measure drawings made in half, one-quarter,
one-eighth or one-sixteenth of an inch to the foot.
PRACTICAL USES OF THE
STEEL SQUARE
We now take up a square void of any attachments, and one which has
become quite popular in the west and the middle southern states. I refer
to the “Nicholls Square,” a representation of one side of which is shown
at Fig. 1. This square is a new one on the market, and presents some
advantages over many now being sold. The manufacturers direct special
attention to the fact that the board measure has been replaced by a
simple rule for framing, and that there is to be found the lengths and
figures giving the cuts for an entire roof, also the cuts for cornice of
the same. The tongue on the square is 1¾ inches wide, thus making it
convenient for spacing, as much of the dimension lumber is 1¾ inches
thick. The general directions for using this square—a copy of which is
given to every purchaser of a square—are presented herewith, so that the
reader will be able himself to judge of the merits of the tool. These
squares are numbered or graded according to the graduation marks and
quality of finish.
[Illustration: Fig. 1.]
“The face of a square is the side on which we stamp our name. The
reverse is the back. The longer arm is the body, the other is the
tongue.
_Framing Rule._—The first line of figures gives the length of common
rafters for one foot run.
The second line of figures gives the length of hip or valley rafters for
one foot run.
The third line of figures gives the length of first jack rafter and the
difference in the length of the others spaced 16 inches on centers.
The fourth line of figures gives the length of first jack rafters and
the difference in the length of the others spaced 2 feet on centers.
The fifth line of figures gives the side cut of jack rafters against hip
or valley rafters.
The sixth line of figures gives the side cut of hip or valley rafter
against ridge board or deck.
The seventh line of figures gives the cuts of sheathing and shingles in
valley or hip, for example:
1. If your roof is raised 8 inches to the foot, or, as it is called,
third pitch, under 8 on the first line are the figures 14.42. This is
the length of common rafters for one foot run. If the building is 16
feet wide half the width of building would be the run of common rafter.
In this case it would be 8; multiply 14.42 by 8, you have 115.36 inches,
or 9 feet 7⅜ inches.
2. To obtain the bottom and top cuts of common rafter use the figures 12
on body and 8 on tongue; 12 side gives bottom cut, 8 side gives top cut;
the same figures give bottom and top cuts for jack.
On the second line under 8 are the figures 18.78; multiply these figures
by 8, which is the run of the common rafter. This gives 150.24, or 12
feet 6¼ inches. This is the correct length of hip or valley rafter. To
obtain the bottom and top cuts for hip or valley rafters, use the
figures 17 on body and 8 on tongue; 17 side gives bottom cut, 8 side
gives top cut.
This is all the figuring necessary to be done. The reason for giving the
lengths for one foot of common and hip or valley rafters is that it will
work in all cases regardless of width of buildings.
3. On the third line under 8 are the figures 19¼ inches. This is the
length of first jack rafter, also the difference in the length of the
others spaced 16 inches on centers. For example, the first jack being
19¼ inches, the second jack would be 3 feet 2½ inches; make each one 19¼
inches longer than the other.
On the fourth line under 8 are the figures 2 feet 4⅞ inches. This is the
length of the first jack rafter, and the difference in the length of the
others spaced 2 feet centers.
On the fifth line under 8 are the figures 10 and 12. By placing square
on stock to be cut at these figures 10 on body, 12 on tongue, and
marking on 12 side this gives side cut of jacks against hip or valley
rafter.
On the sixth line under 8 are the figures 9 and 10. By placing square on
stock to be cut at these figures, 9 on body and 10 on tongue, and
marking on the 10 side, this gives side cut of hip or valley rafter
against ridge board or deck.
On the seventh line under 8 are figures 12 and 10. By placing square on
stock to be cut at these figures 12 on body, 10 on tongue, and marking
on the 10 side this gives the cut of sheathing and shingles in valley or
hip.
_Remarks._—To obtain the lengths and cuts be careful to use the figures
under whatever figure your roof raises to the foot. If your roof raises
12 inches to the foot, or half pitch, look under 12, and so on in all
cases. In cutting jack rafters allow for half the thickness of hip or
valley rafters as lengths given on square are to center lines.
_Note._—The figures on the square, giving side cuts of jacks, will also
give the correct miter cuts for moulding in the valley at the junction
of two gables, also miter cuts for gable mouldings where it intersects
with level mouldings at the end of building.
The figures giving cuts of sheathing in valley or hip also give cuts for
mitering level planceer with gable planceer, also the miter cuts where
two gable planceers intersect, also the cut for planceer on gable end.
To obtain the bottom and top cuts of hip or valley rafter use the figure
17 on body, and whatever figure your roof raises to the foot on tongue.
This will give you the correct cuts in all cases.
To obtain the bottom and top cuts of common rafters and jack rafters use
the figure 12 on body, and whatever figure your roof raises to the foot
on tongue. This gives correct cuts in all cases. Always remember that
the cut comes on the tongue, or last named figure. It is so arranged in
all cases.
_Octagon, “Eight-square” Scale._—This scale is along the middle of the
face of the tongue, and is used for laying off lines to cut an “eight
square” or octagon stick of timber from a square.
Suppose the figures A, B, C, D, Fig. 2, is the butt of a square stick of
timber 6×6 inches. Through the center draw the lines AB and CD parallel
with the sides and at right angles to each other.
With the dividers take us many spaces (6) from the scale as there are
inches in the width of the stick, and lay off this space on either side
of the point A as Aa and Ab; lay off in the same way the space from the
point B as Bd and Be; also Cf and Cg and Db and De. Then draw the lines
ab, cd, cf and gh. Cut off the solid angle E, also F, G and H; there is
left an octagon, or “eight square” stick. This is nearly exact.
_Brace Measure._—This is along the center of the back of the “tongue,”
and gives the length of the common brace.
18-13 25.45 in the scale means that if the run is 18 inches on the post
and the same on the beam, then the brace will be 25 45-100 inches.
If the run is 21 inches on both beam and post, then the brace will be 29
70-100 inches.
_Care of Square._—Never use emery or sand paper on nickel or black
finished squares. When through using put on a few drops of oil. Do not
put your square away with finger marks on it; nothing rusts it so
quickly as perspiration.”
[Illustration: Fig. 2.]
It will be seen that these squares adapt themselves to other work as
well as to framing, a quality very few of the combination squares
possess, and while combination squares have their special uses and
should be in the tool chest of every expert workman, the square pure and
simple, like this of Nicholls or similar ones, should never be absent
from the “kit” of the ordinary workman, for with it, if he thoroughly
understands it, he can accomplish all that is possible even with a
combination square. If he is not “posted” the workman should procure
some one or more of the many devices or helps for getting bevels,
angles, lengths and cuts, for rafters, braces, hips and jacks as
advertised by Riesmann, Woods, and others.
[Illustration: Fig. 3.]
With these aids and a good true and honest steel square the workman can
accomplish almost all that can be done with this tool, or all that he
will be called upon to execute by aid of the square.
These squares are furnished by the manufacturers either in polished
steel, nickel plate or oxidized copper. The latter style is quite
popular with some workmen, because of its not getting so hot when
exposed to the rays of the sun.
[Illustration: Fig. 4.]
The two sides of the square, shown at Fig. 3, represent the carpenters’
popular square, No. 100. This square has been a special favorite with
workmen for nearly thirty years, and is still looked upon by many as
being the _ne plus ultra_ of steel squares. I show both sides of the
square in order to enable the workman to see, before he buys, the kind
of tool he will get. Like the Nicholls square, this may be obtained in
polished steel, nickel plated, or oxidized copper as the purchaser may
desire.
[Illustration: Fig. 5.]
I show the complete square, reduced to page size. Sometimes this square
is catalogued by dealers as No. 1000, practically, however, it is the
same square as the No. 100. If we examine this square we will find on
the tongue near its junction with the blade a series of lines and cross
lines (see Fig. 4), making a figure known as the “diagonal scale.” This
scale is drawn to a larger size at Fig. 5 and is shown alone and is used
for taking off the hundredths of an inch. The line _ab_ is here an inch
long, and is divided into ten equal parts; the line _cd_ being also
divided into ten equal parts, and diagonal lines are then drawn
connecting the points as shown in the diagram. Suppose we wish to take
off 76-100 of an inch, we proceed as follows: Count off seven spaces
from _c_, _e_, _g_, which equals 70-100 of an inch; then count up the
diagonal line until the sixth horizontal line, _e_, is reached, when _e
f_ will equal the required distance of 76-100 of an inch, which is a
trifle over ¾ of an inch.
[Illustration: Fig. 6.]
Quoting from the table of directions given in Sargent’s circular
describing this square, we have, for rafter cuts, the following
explanation: “This run of a rafter set up in place is the horizontal
measure from the extreme end of the foot to a plumb-line from the ridge
end—from A to B, Fig. 6.
[Illustration: Fig. 7.]
“The rise is the distance from the top of the ridge end of the rafter to
the level of the foot. From C to D, Fig. 7.
“The pitch is the proportion that the rise bears to the whole width of
the building. The illustration, Fig. 8, shows one-third pitch; the rise
of 8 foot being one-third of the width of the building.
[Illustration: Fig. 8.]
“The cuts or angles of a rafter are obtained by applying the square so
that the 12-inch mark on the body and the mark on the tongue that
represent the rise shall both be at the edge of the rafter. The
illustration, Fig. 9, shows 8 foot rise, the line A the cut for the
ridge end of the rafter and B the cut for foot end.”
[Illustration: Fig. 9.]
The portion of square shown at Fig. 10 exhibits the tool having on its
face a table of the run, rise and pitch of rafters, being specially
figured for this purpose, and shows the measure of the rafter for any
one of seven pitches of roof based upon the length of the horizontal
measurement of the building from the center to the outside.
The following table, which was prepared especially for this square,
shows the manner of working the square:
[Illustration: Fig. 10.]