T HE ST E EL S UARE AND I T S USES Q ,

I NT RODUCT ORY REMAR! S.

DI V I SI ON A .

to I will not attempt in this small treatise , o cc of o t give an hist rical a ount the rigin , grow h a n d o of ct devel pment the square , as the subj e has been treated of at length in my larger wo I to out rks , as do not care pad these pages with matter that is not of a severely practical n ature.

S f to a re fi u fice it say , th t while iron squa s , g ured ori e an d their faces in inch s feet , and small

o E and er divisi ns , have been made in ngland

B f or 200 e elgium y ars or more , the genuine s n ow o teel square, as we kn w it , is a purely

A c has no a n o meri an product , and it equal , s Europea n manufacturer has as yet been able to turn out a square anything like as good or per

e o et-u fe t in finish , graduati n , or general g p, as

S Cc. of Ha e Co . argent , New v n , nn ; Nicholls

Co. Ot u T S o , t mwa , Iowa ; and he Peck , t w 8r

co Cc. So to Co . r Wil x , uthing n , nn Squa es made

one of by any these firms named , may be relied u pon as being as near perfect as it is possible to 3 4 T HE L . A B C OF STEE SQUARE make them in everythin g that pertains to ac

. curacy , durability and general finish The American workman sho uld 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 j oinery and carpentry , than that he should make himself thoroughly conversant with the capabilities of the tools he employs .

i n It may be that , in some of the rules shown 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 whe n others a re witli in 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 kind s continually arising in mechanical work , which by the ordinary meth ods are more difficult to perform .

‘ The great improvement which the art s and manufactureshave attained wi thin the last fifty

i eh years , renders it essent al that every person gaged therein should use his utmost exertion s to obtain a perfect knowledge of the trade he 5 A B c or THE ST EEL SQ UARE

r to . a p ofesses follow It is not enough , now

r days , for a person to have attained the characte of a good workman ; that phrase implies that o quantum of excellence , which consists in w rk d of ing correctly and neatly , under the irections

- others . The workman of to day , to excel , must b e understand the principles of his trade , and 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 o p ssesses a steady manner , and industrious hab

' it s f d. , his e forts cannot fail of being rewarde i s It is no sin not to know much , though it

can ' an d a great one not to know all we , put it

. Yet ow few all to good use , h mechanics there ! are who will know all they can hlen apply f or employment daily who claim to be finished me chan i cs , and profess to be conversant with all

a re the ins and outs of their craft , and who noways backward in demanding the highest

o ~ wages going, who , when tested , are f und want ing in knowledge of the simplest formulas of t . heir trade They may , perhaps , be able to per form a good j ob 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 t o e of heir t ols ; but , generally , their knowledg ends here . Yet some of these men have worked 6 A B C or T H E STEEL SQ UARE

f or c at this trade or that a third of a entury ,

all a i fi and are to appearances , s t s ed with the little they learned when they were apprentices. o so True , mechanical kn wledge was not always easily obtained as at present , for nearly all works on the constructive arts were written bv o s e pr fes ional architects , engine rs , and designers , a n e e t d however un xceptionable in other r spec s , t n hey were generally couched in such la guage , e to e technical and math matical , as be p rfectly u nintelligible to the maj ority of workmen ; and

.n stead of acting as aids to the ordinary

ui rer s q , they enveloped in mystery the simple t s - o olutions of every day problems , disc uraging nine-tenths o f workmen on the very threshold of inquiry , and causing them to abandon further efforts to master the intricacies of their respect ive trades . Of o late years , a number of b oks have been c published , in which the authors and ompilers hav e made commendable eff orts to simplify mat ters pertaining to the arts of carpentry and

- j oinery , and the mechanic of to day has not the difficulties of his predecessors to contend with . The workman of old could excuse his ignorance h of the hig er branches of his trade , by saying that he had no means of acquiring a knowledge of . them Books were beyond his reach , and A B c OF T H E STEEL SQUARE 7

a a t rade secrets were gu rded so j ealously , th t to o m only a limited few were allowed kn w the , a nd unless he was made of better stuff than the

of hi s o - was orced to most fell w workmen , he f plod on in the same groove all his da ys . ' Not so with the mechanic of today ; if he is n all ae ot well up in the minuti of his trade, he has to f or 1 8 but himself blame , although there o royal r ad to knowledge , there are hundreds of Open ways to obtain it ; and the you ng me chanie who does n ot avail himself of one or other e h of thes ways to enric his mind , must lack be e i ff o energy , or altogeth r ind erent ab ut his de tra , and may be put down as one who will nev er make a workman . I have thought tha t it would not be out of l “ ” p ace to preface this work on the Steel Square , w o ith the foregoing remarks , in the h pe that t they may s imulate the young mechanic , and urge him fo rward to conquer what at best are only imaginary difficulties. A willing heart and a clear head will most assuredly win honorable d i n h o 0 istinction any trade, if t ey are nly pr p

. e e erly used Ind ed , during an exp rience of many years in the employment and superintendence of “ e cs m e m chani of every grade , fro the gre n wood ” haggler to the finished and accomplished work I h man , have invariably discovered that t e fin 8 A B C OF T HE STEEL SQUARE i shed workman was the result of persistent o study and application , and not , as is p pularly

o . supposed , a natural or spontane us production It is true that some men possess greater natural o con se mechanical abilities than thers , and quently a greater aptitude in grasping the principles that underlie the constructive arts bu t , as a rule , such men are not reliable ; they r may be expert , equal to any mechanical eme en c e g y , and quick at mastering details , but th y are seldom thorough , and never reliable where long sustained eff orts are requ ired . The mechanic who reaches a fair degree of c perfection by experience , study and appli a who tion is the man rises to the surface , and whose steadiness and trustworthiness force themselves on the notice of employers and su peri n ten den t s. I have said this in order to give encoura gement to those young mechanics who find it u p- hill work to master the intricacies of the various arts they are engaged in , for they may rest assured that in the end wo rk and ap pli ca ti on 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 . A B c OF THE STEEL SQUARE 9

It must not be supposed that the work here presented exhausts the subj ect . The en terpri s ing mechanic will find opportunity for using the square in the solution of many problems that o will crop up during his daily w rk , and the principles herein laid down wi ll aid very much towards correct solutions . In framing roofs .

- t e bridges , trestle work , and constructions of im her A , the Steel Square is a necessity to the mer ican carpenter ; but only a few of the more i ntelligent workmen ever use it for other pur o off p ses than to make measurements , lay the s mortices and tenons , and square over the variou

o . i n j ints Now , framing bevel work of any de scription , the square may be used with great

. advantage and profit Posts , girts , braces , and struts of every imaginable kind may be laid out

r by this wonderful instrument , if the operato will only study the plans with a view of making use of his square for obtaining the various bev els , 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 i s by the square when properly applied , and it t I m f or his fact wish to i press on my readers ,

i n i v it would be impossible , this work , to g ve e ery possible application of the square to work 1 9 A B c or T H E STEEL SQUARE

. I h of this kind have , therefore , only given suc 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 f ew

re t h n hints as to the kind of Jqu a o purchase w e i r t is necessary to buy ; in many cases , howeve , this book will find its way into t he hands of a o l old and mech nics and thers , who wi l have o s favorite squares in their chests or worksh p , “ and who will not care to dispose of a well-tried ” friend for the purpose of filling its place with

I . another , simply because have recommended it To these workmen I would say that I do not

ru advise a change , provided the old square is t e , and the inches and sub - divisions are pmperly and accurately defined . I wish it distinctly

a e understood th t old squares , if true , and mark d

sub— o with inches and divisi ns of inches , will per form nearly every solution presented in this book . The lines and figu res formed on the squares

i ff ma o o of d erent ke , s metimes vary , b th as to os e o their p ition on the square , and th ir m de of

a n t application , but thorough u ders anding of the application of the scales and lines shown on

first - s any class tool , will enable the tudent to comprehend the use of the lines and figures

- hi bited on other first class squares . A B c or TH E STEEL SQUARE 1 1

T o s to o insure go d results , it is nece sary be ca reful in the selection of the tool . T he blade 24 o of the square should be inches l ng , and o 1 4 to 1 8 two inches wide, and the tongue fr m inches long and inches wide. The tongue e should be exactly at right angles with the blad , “ ” or in other words the square Should be per fectly square . s o o 1 2 To test this que tion , get a b ard , ab ut or 1 4 i o e o inches w de, and f ur fe t l ng, dress it on on e S one ide , and true up edge as near straight as it is possible to make it . Lay the

oa s b rd on the bench , with the dres ed side up ,

s ou and the trued edge toward y , then apply the to square , with the blade the left , and mark

the bo enknif across prepared ard with a p e blade , pressing close a gainst the edge of the tongue ; o o to o c this pr cess d ne y ur satisfa tion , reverse the o o c o square , and m ve it until the t ngue is l se up to the knife mark ; if you find that the edge of o co c oo the t ngue and mark in ide, it is pr f that the tool is correct enough f or your purposes .

on l o b ow h Later , I wil sh w y diagram h t is test is performed . o This , o f c urse, relates to the outside edge of the o i blade , and the uts de edge of the tongue .

s s o not s ra o If these edge h uld be t ight , r should n ot ro c o p ve perfe tly true , they sh uld be filed 1 2 A B c or THE STEEL SQUARE 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 proc ess should be gone through on the tongue . As m a rule , squares ade by firms of repute are per

. feet and require no adj usting ; nevertheless , it is well to make a critical examination before purchasing . The next thing to be considered is the use of o the figures , lines , and scales , as exhibited n the square . It is supposed that the ordinary

s — s n s division and sub divi io of the inch , into

s halve , quarters , eighths , and sixteenths are understood by the student ; and that he al so under stands how to use that part of the square that i s subdivided into twelfths of an inch . s o d Thi being c ncede , we now proceed to de scribe the variou s rules as shown on all good s r quares ; but befo e proceeding further , it may not be out of place to state , that on the squares recommended in this book , one edge is sub — divided into thirty seconds of an inch . Thi s fin e sub —division will be found very u se ful , particularl y so when used as a scale to

on eh u a rter on e measure drawings made in half, q , eighth or one - sixteenth of an inch to the foot . PRACTICAL USE S OF THE STEEL SQUARE

We now take up a Square void of any attach ments , and one which has become quite popular in the west and the middle southern states . I “ ” refer to the Nicholls Square , a representa ‘ tion of one side of which is Shown at Fig. 1 . i Th s square is a new one on the market , and presents some advantages over many now being Sold . The manufacturers direct special atten tion to the f a ct that the board mea sure has l b s been rep aced y a imple 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 1 square is % inches wide , thus making it con v en i en t for spacing , as much of the dimension 3 lumber is 1 4 inches thick . The general dirce ‘ — tions 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 j udge of the merits of the tool . T hese squares are numbered or graded accord ing to the graduation marks and quality of finish . 1 4 A B c or TH E STEEL SQUARE

c s The fa e of a quare is the side 0 1 !

which we sta mp our name . The reverse

is the back. The longer arm is the o o b dy , the ther is the tongue . — Frami ng E ula 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 ra fters f or one foot run . The third line of figures gi ves the length of first j ack rafter and the dif ference i n the length of the others spaced 1 6 inches on centers . The fourth line of figu res gives the length of first j ack rafters and the dif ference in the length of the others

spa ced 2 feet on centers . The fifth line of figures gives the side cut of j ack rafters against hip or alley rafters . Flg 1 . The sixth li ne of figures gives the side cut of hip or valley rafter against ridge board or deck . A B C or T H E STEEL SQUARE 1 5

The seventh line of figures gi ves the cuts of sheathing and shingles in valley or hip , for example

1 . o If your roof is raised 8 inches to the f ot ,

h e 8 t. or, as it is called , t ird pitch , und r on the firs line are the figures This is the length of common rafters for one foot run . If the bui lding is 1 6 feet wide half the width of building would be the run of common rafter. In this case it 8 8 would be ; multiply by , you have

. inches , or 9 feet inches

2. T o obta in the bottom and top cuts of common rafter use the figures 1 2 on body and 8 on o 1 2 o 8 t ngue ; side gives b ttom cut , side gives top cut ; the sa me figures give bottom and top cuts f or j ack .

On the - second line under 8 are the figures 8 w multiply these figures by , hich is the ru n of the common rafter. This gives or

1 2 feet inches . Thi s is the correct length of hip or valley rafter. To obtain the bottom to c t and p uts for hip or valley raf ers , use the figures 1 7 on body and 8 on tongue ; 1 7 side _

e tto 8 S giv s bo m cut , ide gives top cut.

This is all the figuring necessa ry to be done . The reason f or giving the lengths f or one foot of common and hip or valley rafters is that it 6 A B c or THE STEEL SQUARE will work in all cases regardle ss of width of buildings .

3 . On the third line under 8 are the figures 1 1 9 A inches . This is the length of first j ack i f rafter , also the d f erence in the length of the others spaced 1 6 inche s on centers . For ex s bem the ample , the fir t j ack g inches , second j ack would be 3 feet inches ; make each one inches longer than the other . On the fourth line under 8 are the fig ures 2 feet. inches . This i s the length of the first f j ack rafter , and the dif erence in the length of the others spaced 2 feet centers . On the fifth line under 8 are the figures 1 0 and 1 2 . By placing square on stock to be cut 1 0 1 2 o at these figures on body , on t ngue , and marking on 1 2 side this gives side cut of j acks against hip or vallev rafter . On the sixth line under 8 are the figures 9 and 1 0. By placing square on stock to be cut at

9 1 0 u these figures , on body and on tong e , and 1 0 marking on the side , this gives side cut of hip or valley rafter against ridge board or deck . On the seventh line under 8 are figures 1 2 and 1 0. By placing square on stock to be cut at 1 2 1 0 on these figures on body , tongue , and marking on the 1 0 side this gives the cut of sheathing and shingles in valley or hip . 1 7 A B c or THE STEEL SQUARE

— Rema rks. To obtain the lengths and cuts be careful to use the figures under whatever figure your roof raises to the foot . If your roof 1 2 raises inches to the foot , or half pitch , look

1 2 i n . under , and so on all cases In cutting j ack rafters allow for half the thickn ess of hip or valley rafters as lengths given 0 1 1 squ are are to center lines .

Neta — S The figures on the quare , giving side cu t s l t of j acks , wi l also give the correct mi er cuts for moulding in the valley at the j unction of two gables , also miter cuts for gable mould ings 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 wi o th gable planceer , als the miter cuts where

lan ceers two gable p intersect , also the cut for planceer on gable end . To obtain the bottom and top cuts of hip or 1 7 valley rafter use the figure on body , and whatever figure your roof raises to the foot on tongue . This will give you the correct cuts in a ll cases . To obtain the bottom and top cuts of common rafters and j ack rafters use the figure 1 2 on o b dy , and whatever figure your roof raises to the foot on ton gue . This gives correct cuts i n 1 8 A B C or T H E STEEL SQUARE all cases . Always remember that the cut comes

. is (in the tongue , or last named figure It so arranged in all cases . “ cta on Ei ht- s u are Scale. - T c O g , g q his s ale c o is along the middle of the fa e of the t ngue , “ and is used f or laying of lines to cut an eight ” square or octagon stick of timber from a square .

o A . 2 Supp se the figures , B , C , D , Fig , is the butt of a square stick of timber 6 x6 inches . Through the center draw the lines AB and CD parallel with the sides and at right angles to each other. With the di viders take as many spaces ( 6 ) from the scale as there are inches in the width of la off the stick , and y 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 C f and Cg and Db and De. Then draw the ‘

ef h. off lines ab, cd , and g Cut the solid angle E also G H , F , and ; there is left an octagon , or “ ” eight square stick . This is nearly exact . — Brace Mmam a This is along the center of “ ” back o the of the t ngue , and gives the length of the common brace. 1 8-1 8 in the scale means that if the run is 1 8 inches on the post and the same on the

c 25 45- 1 00 beam , then the bra e will be inches.

20 A B C OF T HE STEEL SQUARE

o m every expert w rk an , the

square pure and simple , like this of Nicholls or simi lar s ones , hould never be absent “ ” from the kit of the ordi if nary workman , for with it , he thoroughly understands

it , he can accomplish all that is possible even with a com bination Square . If he is not “ ” posted the workman should procure some one or more of the many devices or helps for s getting bevels , angle , lengths

and cuts , for rafters , braces , hips and j acks as advertised Ri esman n o s by , W od , and others .

Fig. 3.

With these aids and a good tru e and honest steel square the workman can accomplish al

all most all that can be done with this tool , or A B C or T H E STEEL SQUARE 1 that he will be called upon to execute by aid of the square . These squares are furnished by the manu fac t u rers S either in polished teel , nickel plate or oxidized copper . The latter style is quite pop ular with some workmen , because of its not get tin g so hot when exposed to the rays of the sun .

s . 3 The two side of the square , shown at Fig , ’ . represent the carpenters popular square , No

1 00. Thi s square has been a special favorite with workmen for nearly thirty years , and is still looked upon by many as being the ne plu s u ltra 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 . L ike the Nicholls square , this may be obtained in polished Fig. 4. steel , nickel plated , or oxidized copper as purchaser may desire . 22 A B C or TH E STEEL SQUARE

I o Sh w the complete square , reduced to page

' size. Sometimes this squ are is catalogued by e No 1 000 d alers as . , practically , however , it is the sa me square as the No. 1 00. If we examine this square we will find on the tongue near its _ j u nction with the blade a series of lines and cross lines ( see Fig. making a figure known “ ” the diagonal scale . This is drawn to .scale

Fig. 5 .

a larger size at Fig . 5 and is shown alone an d is used for taking off the hundredths of an inch .

ab o The line is here an inch l ng , and is divided into ten equal parts ; the line cd being also divi ded o into ten equal parts , and diag nal lines are then drawn connecting the points as shown in the diagram . Suppose we wish to take off

7 6 -1 00 o : Co of an inch , we proceed as foll ws unt Os A B c or T H E STEEL SQUARE 251 of a c c e 7 0 seven sp es from , , g, which equals 1 00 of an inch ; then count up the diagonal line

6 e until the sixth horizontal line , , is reach d , when (3 f will equal the required distance of

- 1 00 r f 7 6 of an inch , which is a t i le over of an inch.

F ig . 6 .

Quoting from the table of di rections given in ’ a we S rgent s circular describing this square , o o have , for rafter cuts , the foll wing explanati n This run of a rafter Set up in place is the hori zontal measure from the extreme end of the foot to a plumb -line from the ridge end— from A

B . . to , Fig 6

q -o

Fig . 7 .

The rise is the distance from the top of the ridge end of the rafter to the level of the foot .

o C to D . 7 . Fr m , Fig A B C OF T HE STEEL SQUARE

The pitch is the proportion that the rise bears to the whole width of the building . The

o . 8 - illustrati n , Fig , shows one third pitch ; the rise of 8 feet being one - third of the W idth of the building.

Fig. 8.

The cuts or angles of a rafter are obtained by applying the square so that the 1 2 - inch mark on the body and the mark on the tongue

Fig. 9. that represent the rise shall both be at the edge

. . 9 8 of the rafter The illustration , Fig , shows l A foot rise , the ine the cut for the ridge end ” of the rafter and B the cut for foot end . The portion of square shown at Fig. 1 0 exhibits the tool having on its face a table of A B c or THE STEEL SQUARE 25

r s c of the run , i e and pit h rafters , being spe ci all for o y figured this purp se , 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 bui ldi ng from the center to the outside . oll i The f ow ng table , which was prepared es

eci all for o p y this square , sh ws the manner of working the square :

RAFTER TAB LE DI RECTI ONS.

The rafter table and the outside edge of the

o . back of the square , both on body and t ngue are in twelfths . The inch marks may represent i nches or feet , and the twelfth marks may rep resent twelfths of an inch or twelfths of a foot

(that is , inches) as a scale . The rafter table is used in connection with the marks and figures on the outside edge of the square 26 A B C or T H E STEEL SQUARE

At the left end of the table are figures repre

run the rise i tch. senting the , and the p 1 2 In the first column the figures are all , which 1 2 e 1 2 may be used as inch s or feet , and they represent a run of 1 2 . The second column of figures is to represent various ri ses.

‘ rI he third col u mn of figures in fractions rep resents the va rious pi tches. These three columns of figures show that a rafter

1 2 of 4 1 - with a run of and a rise has 6 pitch , — 1 2 1 4~ with a run of and a rise of 6 has pitch ,

1 8 1 - 3 with a run of 2 and a rise of has pitch , and so on to the bottom of the figures . — T o Find the L ength of a Rafter . For a roof with 1 - 6 pitch ( or the rise 1 - 6 the width of the

i a 1 2 ow build ng ) and h ving a run of feet , foll

1 - in the rafter table the upper 6 pitch ruling , find under the graduation figure 1 2 the rafter 1 2 7 1 0 1 2 t length required , which is , or fee and 7 1 0- 1 2 inches . For 15 pitch ( or the rise the width of the 1 2 e the building) and run fe t , rafter length is

- 1 1 1 8 1 1 1 8 1 2 . 6 , or 6 feet inches 25 h If the run is feet , add the rafter lengt for run of 23 feet to the rafter length for run of 2 feet .

28 A B (3 OF THE STEEL SQUARE

The octagon scale on this square runs 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 one.

Fig. 1 1 . Fig. 1 2.

Suppose the figure ABCD (see Fig 2 ) is butt of a square stick of timber 6 x6 inches. 25 A B c or TH E STEEL SQUARE

Through the center draw the lines AB and CD parallel with the sides and at right angles to each other . With a pair of compasses take m s

many spaces (6 ) from the scale as there are inches in the width of the stick , and lay off thi s

e A Aa space on ither side of the point , as and ‘ 30 A B c or T H E STEEL SQUARE

Ab ; lay off in the same way the same space from t he as Bd C C . point B , Be ; also f, g and Db , Dc

T l ef h. off hen draw ines ab , cd , and g Cut the

E G H . solid angle , also F , and This will leave

a - an oct gon , or eight sided stick , which will be found nearly exact on all sides . “E The board measure , known as the ssex ” . 1 3 fi Board Measure , Fig , is made use of in g

e s: uring thes squares , and is used as follow Fig ures 1 2 and 1 7 in the graduation marks on the outer edge represent a one- inch board 1 2 inches wide , which is the starting point for all calcula tions . The smaller figures under the 1 2 repre sent the length . A board 1 2 inches wide and 8 feet long meas clres 8 a the . squ re feet , and so on down table 8 Therefore , to get the square feet of a board 8 feet long and 6 inches wide , find the figure in the scale under the 1 2 - inch graduation mark and pass the pencil along to the left on the same line to a point below the graduation mark 6 ( repre s o on enting the width of the b ard ) , and you stop 4 4 e o the scale at , which is f et , the b ard meas ure required . If the board is the same length an d 1 0 e t inch s wide , look under he grad ua tion mark 1 0 on a line with the figure 8 before

o 8 - 1 menti ned , and you will find 6 2 feet board measure; if 1 8 inches wide then to the right n u A B C OF T H E STEEL SQUARE 31 der the graduation mark 1 8 and 1 2 feet is found t o be the board measure . If 1 3 feet long an d 7

1 3 inches wide , find in the scale under the 1 2 - inch graduation and on the same line under the 7 - inch grad n ation will be found 7 7 - 1 2 feet

board measure . If the board is

s half this length , take half of thi

result ; i f double this length , then double this result For stuff 2

inches thick double the figure . In this way the scale covers all

lengths of boards , the most common

from 8 fee t to 1 5 feet being given . This compan y also manufactures “ ” a. u sq are that is blued , or appar o ently xidized , with all the figures on it enameled in white . This is s really a hand ome tool , and the white figures on a d ark blue ground enable the operator to see what fig o Fig. 1 4 . ures he is l oking for without waste of time and straining of eyesight . ’ The bridge builders steel square , which is z“ . 1 4 o a h astrated in Fig , is als m de by t is com 32 A B c or THE STEEL SQUARE

pany . This square has a blade three inches wide , which is made with a slot down the center one inch wide . The tongue is the same as in the

No . 1 00 square , but has no figures for brace or octagon rules . It is not so hand y for general p u r p o s e s as the r e gu l a r

s q u a r e , but for s p e c i a l

purposes in bridge building, or for laying out very heavy timber strue 3 tures it has special advantages , as inch shoulders and 33- inch tenons and morti ses can be readily laid out with

. A n 1 5 it nother square , show in Fig. “ ’ known as the machinists square ,

is made by this company . It has a blade 6 inches and a tongue 4 inches

. long , and is very finely finished This square is found very useful for pat

u tern makers , piano and organ b ild e ers , and where other especially clos work is required . A number of other Fig. 1 5. squares are made by this firm , but ’ as they are not intended for woodworkers use,

I will not describe them here . I would not complete this description of Sar ’ gent s make of squares if I failed to make men 33 A B c or THE STEEL SQUARE

“ ” ti on of their bench squ are . I give thi s name to it because of its fitness for bench purposes . The square referred to has a blade 1 2 inches 9 long and inches wide , and a tongue inches long and 1 inch wide . The figuring on it is di v ided into inches , half inches , quarter inches , eighths and sixteenths of an inch . This is a very handy square for bench and j obbing purposes , and can be used in many places where the larger tool is unavailable , and may on emergency be employed for laying out rafters , braces and similar work . A square that was quite popular some sixteen or eighteen years ago known as “ Cren alated The Square , an illustration of

. 1 6 which is shown in Fig , is still preferred by many workmen . The peculiarity of this square is that the inner edge of the tongue is notched

cren alated or , as shown in the illustration , the

‘ “ ” s - notches being intended a gauge points , where a sharpened pencil may be inserted , then the square may be drawn along the timber or board , with the blade held snug against the edge , as s - or hown , and mortises tenons can be laid out at will .

cren alated Besides being , these squares have he of all t advantages other squares , and are well made and pleasant to handle. They are made

8: by the manufacturers , The Peck , Stowe Wil

Co. . e cox , of Southington , Conn , in polished ste l , 34 B C or TH E STEEL SQUARE

copper plated , blued , with enameled

. ures , and in nickel plate

Fig . 1 6

de It is the simplest of tools , and may be scribed as the mechanical embodi ment of a right angle . It must necessarily ha ve some breadth

3 6 A B c or THE STEEL SQUARE

t to o righ angle , or use common terms , if the to l “ ” ou t is of square , that is , if it is in the least

. inaccurate , its usefulness is destroyed When the square is inaccurate instead of solving i n t ri categeomet ri cal' problemscorrectly itbecomes a snare and a delusion , leading to false results and misfits in general . It is somewhat remark able how few workmen test their squares . I am disposed to believefrom long experience that comparatively few mechanics who buy ste el squares are cogn izant of the possible defect s that the tool may have and of the tests which may be applied for the purpose of demon strat

. ing its accuracy Before proceeding further , of therefore , in the discussion of the use this instrument let us give brief attention to s ome of the simple methods that may be employed for determining the accuracy of the tool . By way of making practical application of these tests I suggest that at the next dinner hour the reader borrow from his fellow carpenters as

many squares as may be convenient , and apply

or ' less to them more of the tests which follow , the merely for the purpose of practice , and at same time to show to what extent the squares in use are correct . Fig . 1 7 shows a very common method of test ing the exterior angle of a steel square . Two A B C OF T HE STEEL SQUARE squares are placed against ea ch other an d a

- e straight edge , or against the blad of a third square . If the edges of the squares exactly coincide through out the squares may be con sidered co rrect .

o o Supp se , h wever , that there is a discrepancy s s hown by this test , and that as the two square h are placed in the general position , shown in t e illustration , they part at the heel , while touch i ing at the ends of the blades , or touch ng at the heel that they part at the ends of the blade s. 38 A B c or TH E STEEL SQUARE

Thi s evidently shows that on e of the squares is o inaccurate, or possibly that b th are inaccurate. H ow is the inaccuracy to be located ! The two c squares may be pla ed face to face , with the t blades upward from an even surface, say he face of the third square or the j ointed edge of o a b ard , and so held that their

heels, for exam c ple, shall oin

cide . Then glance at the edges of

the blad es . If they exactly coincide it would indicate that the error is evenly divided between the two

squares , a very improbable occur

rence . Compare the two squares in

os the the reverse p ition , that is, with tongues extending upward . Then

. 1 8 and apply the test shown in Fig ,

finally that shown in Fig . 1 9. By trying the squares one inside

of . 1 8 the other, as shown in Fig , e Fi g, 1 3 , the ext rior angle is compared with

the interior angle. If the edges

one throughout fit together tightly , first using s d o quare insi e and then the other , it is alm st con elusive evidence that both the squares are accu rate. A B C or T H E STE EL SQUARE 39

By tests of the kinds j ust described among sev e n soo eral squares , the m cha ic will n perceive from the several ascertained results that one or the other of the several squares that he is hand

n ot ling is more accurate than all the others , if accurate . There still remains the

Fig . 1 9 .

ne of o o ed a test , however , to pr ve the abs lute accuracy of the particular square which he be lieves o . On to be ab ut right a drafting table , or o o a smooth b ard , let him next perf rm the f ol

o i one of l wing exper ment , which is the several that might be mentioned in this connection 40 A B C or THE STEEL SQUARE

A i n Draw a straight line , B , say three feet

. 1 9 . T length , as shown in Fig his may be done by a straight - edge . Use a hard pencil sharp

. ened to a chisel point With the compasses , us : A ing and B as centers , and with a radius long er than one - half of AB strike the arcs CD an d EF. Then with the straight -edge draw a GH of straight line , , through the intersection the arcs . If the work is accurately done the re su lti n AOH HOB BOG GOA g angles , , , and will be right angles . Lay the square to be tested onto one of these angles , as shown in the illus t rati on - , and with a chisel pointed pencil scribe along the blade and along the tongue . If the lines thus drawn exactly coincide with those first drawn it is satisfactory proof that the square is accurate , and in the same way the square may be placed against one or the other of these right angles in a way to test its interior angle . The method shown in Fig. 1 9 anticipates the use of another tool besides the square in making

. A the test right angle , however , may be drawn for the purpose described by a method which

re uses only the square , and which does not

v of quire the ser ices any other tool , or what is tool i tself the same thing, consider the to be the o figure drawn , and then measure for the purp se of determining the accu racv of the figure . A B c or THE STEEL SQUARE 41

V arious writers have discussed the proper of - ties the right angled triangle , but we all know that a square erected on a hypothenuse of a right - angled triangle is equal to the sum of the squares erected on the base and perpon

- di cu la r. This is a well known mathematical

r t uth , and it may be applied in the tests we are making . Those carpenters who have had occasion to lay out the foundations of house s are well acquainted with the old rule f requ en tlv “ 6 8 u known as the , and which depends p on the relationship of the squares of the perpen di cula r and the base to the square of the hypoth

n u se. u 6 36 e Th s the square of is , the square o f

8 is 6 4 . The sum of 36 and 6 4 is 1 00. And the square of 1 0 is 1 00. Now let us make applica tion of this rule to test the steel square . For the sake of accuracy we want to take to figures which are as large as possible , so as reduce the possible error in measurement to the smallest possible dimensions . Let us take for

s 9 1 2 1 5 . dimen ions , , and inches That these Will serve is easily demon strated . The square of 9 is The square of 1 2 is 1 44 . The sum 22 5 5 of these squares is , and the square of 1 22 5 is . Therefore , if the tool that we are test ing shows a dimension of exactly 1 5 inches meas u red from 9 on the outside of the tongue to 1 2 42 A B c or THE STEEL SQUARE

o of o i n . on the utside the blade , as sh wn Fig

2 0 l . , it wi l be proof that the square is correct It may be somewhat difficult to make a meas u remen t f of this kind on the instrument itsel , with sufficient accuracy to be beyond dispute . I fl at suggest , therefore , that the square be laid o up n an even surface , like a drawing table , and that with a chisel- pointed pencil lines he scribed

Fig. 20. along the tongue and along the blade . Mark accurately the di stance of 9 inches from the 1 2 e heel up the tongue , and inches from the he l along the blade . Then measure diagonally and see if the distance is exactly 1 5 inches . In what has preceded there has been a su gges tion that the error due to lack of precision in measurement is diminished if the figures are i n

44 A B c or THE STEEL SQUARE

2 1 XG In Fig. there is shown a quarter circle , , described from the center C . Along the horizon A tal line , B , the blade of the square is laid with 1 2 o of the blade against the center C , fr m which the quadrant was stru ck . Now if we di vide this quadrant into halves , thus establishing E E the point , and if from we draw a line to i s 1 2 the center C , which of the blade , it will be

Fig. 2 1 .

found that it cuts al so 1 2 of the tongue . If we complete the figure by erecting a perpendicular line from the point X , and intersecting it with G a horizontal line from , thus establishing the 0 CE the point , it becomes very evident that is miter line of a square . XE o If we bisect , thus establishing the p int A B C OF T H E STEEL SQUARE

off D , and by the conditions existing setting in the quadrant a space equal to one - quarter of its extent , and if from D we draw a line to the center , C , corresponding , as already mentioned , 1 2 with on the blade , we shall find that this line (DC ) cuts the tongue on the point 5 (very

4 3 1 - 32 nearly , the exact figures being inches)

The line DC , as above explained , bisects the

. eighth of a circle In other words , it is the line e of an octagon miter , and therefore , w say that for an octagon miter we take 1 2 on the blade and 5 on the tongue . By dividing the quadrant into three equal

b y XG GH HG oh parts , as shown , and , we tain by drawing GC the line corresponding to the hexagon miter . This , it will be observed , cuts the tongue of the square at 7 (very near l 6 1 5 - 1 6 y , the exact figures being inches ) , and , therefore , we sav for hexagon miters we take 1 2 of the blade and 7 of the tongue .

The question sometimes arises , can the square be employed to describe a circle ! While the Square may be used for describing a circle of an y the diameter , providing the capacity of square is not exceeded , still those who attempt to perform the work will very likely conclude before they a re through that other means are more sati sfa c t orv for regu lar use . The way to proceed i s i n 46 A B C OF TH E STEEL s Q UARE di cated in Fig. 22 . Let it be required to de scribe

e of to ED . a circle, the diamet r which is equal Drive pins or nails at these points and place the square as shown in the sketch. Place a pencil o of in the interi r angle the square , as shown at F . T hen gradually shift the square so that the e o t p ncil will m ve in the direc ion of D ,

Fi g. 22. being careful to keep the inside of the blade and inside of the tongue in contact with the pins or

i s E . A are na l , D fter having described the from F to D reverse the direction describing the are from F to E . Then turn the square over and by similar means complete the other hal f of the circle. T H E ST EEL SQUARE AND I T S USES .

DIV I SION B .

INTRODU C T ORY .

Having dealt with the more simple matters the that can be dealt with by aid of Steel Square , we n ow take up some of the more di ficult prob lems that can be solved by aid of this useful tool .

A o he o off are m ng t pr blems and solutions ered , c or those of laying out bra es , having regular i s oo n . rregular run , rafters , and r fing ge erally

s r h s e s. a ce taining the length of ip , their bev ls , cut pitches and angles ; j acks , cripples , ridges , pur o e lins , collar beams , and much th r matter per ta ining to hip or cottage roofs. G e o s abl s , or saddle ro fs are dealt with , al o

e a odd mansard roofs , tap r fr ming , bevels , spla y s and other similar work . I introduce in this division a f ew remarks regarding the fence made use of when laying out

e . ~ rafters , stairs or oth r bevelled work The , de partmen t also shows how to lay -out stair strings

and o e by aid of the square , many th r things that will be found useful to the general workman . 47 48 A B c OF THE STEEL SQUARE

A very good fence for the square may readily be made from a stick of hardwood (Fig . 23 ) a bout two inches wide , one and a half inches

. A kcrf thick and two and a half feet long saw , into which the square will slide , is cut from both ends leaving about 8 inche s of solid wood near

DOUBLE SLOTTE D FENCE

Fig . 23. the middle . The tool is clamped to the square by means of screws at convenient points as s A hown . nother style of fence , which is made of a piece of hardwood , has a single slot only as shown in Fig . 2 4 . The square is slipped in and fastened in place b v screws similar to the first .

Fig. 24.

An application of the fence and square combined 25 is shown at Fig . , where the combination is used as a pitch -board for laying out stair strings . In this example the blade is set off at 1 0 inches , which makes the tread , and the tongue s off . hows the riser , which is set at 7 inches The 4 A B c or THE STEEL SQUARE 9

cc o of dotted line , , sh ws the edge the plank from

it which the string is cut , and shows the fence , a shows the bottom tread and riser . In this ex ample the riser shows the same height as the riser

. above it , namely , 7 inches This is wrong, as the first riser should always be cut the thi ckn ess of

Fig. 2 5. the tread less o o o than th se ab ve it , as sh wn by the dotted lines on the bottom of the string, then when the tread is in place it will be the

Fig. 26 . same height from the top of the flo or to the top of the first tread , that the top of first tread is to top of second one and so on . Suppose we wish to lay out a rafter having eight inches rise and twelve inches run . Set the 0 A B C or rH E STEEL SQUARE

' 8 a . 2 fence at the m rk on the blade , Fig 6 , and 1 2” m at the ark on the tongue , clamping it to 1 ” the square with 1 4 screws . Applying the square and fence at the upper end of the rafter we get the plumb- cut P at once . By -applying the square as shown twelve times successively the required length of the rafter and foot- cut B is obtained . In this case the twelve applications of the square are made between the points P and B . Run and rise must also be measured be tween these points . If run is measured from the . point B , which will be the outer edge of the

i l c a to wall plate, it w l be ne ess ry run a gauge o l the line thr ugh B para lel to the edge of rafter , and subtract a distance from the height of the ridge to give us the correct rise . The square must then be applied to the line L . A rafter of any desired rise an d run m y be laid off in this manner by selecting p roportional parts of the iri se and ru n for the blade and tongue of the square . For a half - pitch roof use 1 2 in . on both

o - c u se . t ngue and blade , for a quarter pit h 6 in

1 2 i n . - 8 . 1 2 and , for a third pitch use in and i n. . - t - , etc The terms half pi ch , quarter pitch , etc e , refer to the height of the ridge expr ssed as a fraction of the span . The line L is supposed to represent the path of the fence as it i s sli d along the edge of the

52 A B c or THE STEEL SQUARE the twelve -inch mark on both sides of the square carefully on the backing line , and marking off the rafter on the outside edges of the square . Repeat this until you have fiftee n s d off paces marke , then set back from your last

- mark half the thickness of the ridge board , and with the square as before mark of the rafte r. This will be the exact length and also the plumb - cut to fit the ridge - board . Or if we take 1 2 1 2 1 the diagonal of by , which is 7 , and mark of 1 5 1 7 i n . spaces of , making the necessary allowan ce for the half thickness of the ridge . hoard , it will amount to the same thing, every 1 7 in . on the rafter being nearly equal to one foot on the level .

30 ft . 9 . i Should the building measure , in n — — 1 5 ft . i h . we width the half of which is , take the fifteen spaces of 1 2 by 1 2 and then the in . on both sides of the square on the back ing line as before . This will give us the extra length required . The same rule will apply to any portion of a foot there may be .

A S fence , sometimes called a tair gauge , is manufactured of metal by the Cheney Towe r

A s I . Company , thol , Mas , which show at Fig 28 o i of , and is c nsidered about the best th ng the kind . It consists of a piece of polished

. On e angle metal , each side being inch wide 3 A B 0 OF THE STEEL SQUARE 5 side 1 8 slotted to accommodate the heads of the set - screws and to allow the slides to be fastened at the desired points . The gauge is fastened to

Fig. 28 . any square and is useful for laying out stairs , cutting in rafters , cutting bevels or other angles . In marking of stairs with an 8 - inch rise and an

1 1 % - inch tread the gauge would be fastened at 8 inches on one end of the square and 1 1 % 54 A B c or TH E STEEL SQUARE at the other end . The square would then be laid on the plank wi th the face of the gauge against i ts edge and the mark made around the point of the square . Thi s would be repeated until the required number of steps were marked. The two 1 8 8 gauges are made in sizes , and 2 inches long. It is stated that mechanics who have used it find it one of the handiest tools in their kits.

Another style of fence is shown at Fig . 29 in

o ct o . h c nj un ion with a sl tted square T is , per h the e aps , is the handiest of all d vices for a

n o s r fence , but it is expe sive , and as c n tructed e

a r o quires squa e with a sl t in each arm , and as a rule workmen do not take kindly to squares

o . A r with sl ts in them shows the squa e , B the 8 8 s o the c o o fence , set crews to h ld fen e in p siti n , and if the points of the square .

The application of the square and fence com bi ned f or laying out a housed string for stairs is shown at Fig. In this example the fence is a single slotted one , and three screws are em ployed to hold the square in position . The rise is seven inches and the tread is laid off n in e inches on the blade . The square at the foot of the strin g shows how the latter shou ld be fin — i shed to make the floor and the base board. In th case no tc - o r r re is pi h b a d is equired , as the squa AB C OF T HE STEEL SQUARE 55 56 A B c or THE STEEL SQUAR E

w when adj usted with fence , as sho n , does the

- work of the pitch board . There are many other applications of the fence in connection with the square that I may have cause to refer to as I proceed , as it is my desire to present in this work everything I can collect regarding the square that I think will be of service to the workman . Doubtless there will be many descriptions and illustration s some of my readers will have met with before , or which they have been acquainted with for a long time .

s n ew The great bulk of reader , however , will be hand s and unacquainted with the u se of the square bex’ on d its simple application as a squ a r

s ing tool , and what may appear to be a useles rule to the expert or old hand w ill prove a choice tidbit to the beginner and will whet hi s appetite for further knowledge on the subj ect . Indeed this book is prepared more particularly for the younger members of the craft , although a ma j ori ty of the older workers will find much in it

. that will interest , amuse and instruct It will be seen that the fence or guide used in

v er connection with the square is , after all , a v it simple matter , and would , no doubt , suggest self to any clever workman who was laying off rafters with the square . f 5 1 A B c or THE STEEL SQUARE

B RACE RU LE S.

It will now be in order to show how the squa re can be used for getting the lengths and bevel s for braces of regular and irregular runs . If we

wish to lay out a brace having a three - foot run o on b th post and beam , the matter is quite snn le 1 2 i p , for we can take nches on the tongue and 1 2 inches on the blade and transfer this dis t ance three times on a straight line and we have A B C OF T H E STEEL SQUARE

the extreme length of the brace from point to point. and by marking along the blade at one end of this length and along the tongue at the other end we also get the bevels . This is easy and o simple enough , and with ut further refinement will give the lengths and bevels ex actly for a flat - footed brace. When the run is diff erent

than the rise , as in the ex

so n . 3 1 the ample show at Fig ,

' square is applied in a some what diff erent manner . Here

we have a ru n of three feet. and a rise of four feet . To get the proper length and bevels for a brace to fit in this Situation we must u se 1 2 inches on the tongue and

1 6 inches on the blade , then the bevel of the upper end of the brace will be fou nd f along the line o the tongue , and the line of the bl ade wi ll

f . gi ve the bevel for the foot o the brace In this

6 0 A B c or THE STEEL SQUARE

4 tern , dress up a piece of wood to inches wide if the braces are to be made of 4x 44- inch stuff ; if for larger or smaller stuff then make the pat tern the width of brace to suit . H ave the pat tern of sufficien t length ; if for a 4 - foot run and rise it will require to be not le ss than 6 feet long . Run a gauge line three - eighths of an inch from 0000 the straight or front edge , as shown at ,

set 1 2 - and the two inch marks on this line , then screw the fence tight. on the square with its slid ing edge against the edge of the pattern , and then slide and mark as shown four times , when the length and bevels of the brace will be oh t ai n ed . Provide for ' the tenons beyond the lines “ ” s fl a t - hown by the square , or for a foot brace , s aw the timber off on the lines shown on the edge of the square . After the pattern is made the

s fence and square may be laid a ide , as the pat tern can be used for any number of braces , and when finished with on one j ob , may be safely placed away to use again for the same run and ” rise when occasion arises . The pattern may be any thickness from half an inch to one in ch . The same rules ma y be observed in making pat terns for any regu lar or irregular runs and rises . With regard to the b ra ceru le as given on steel

u a res q , I mav sa v that there is some slight dif A B c or T HE STEEL SQUARE 6 1 ference in the lengths given by different makers — though nearly all modern makes figure up alike— but this diff erence is so small that in soft wood framing it has no eff ect . In hardwood framing the framer never applies these rules , but gets his lengths with the square and fence . The length of a u v brace simply represents the hypothenuse of a right - angled triangle . To

find the hypothenuse , extract the square root of the sum of the square of the perpendicular and

. 6 horizontal runs For instance , if feet is the 8 6 horizontal run and feet the perpendicular , 3 6 8 6 4 3 6 s squared equals , squared equals , plu

6 4 1 00 1 0. equals , the square root of which is These are the figures gen erallv used for squ a r ing the frame of a building or foundation wall . 42 42 1 6 4 If the run is inches , squared is 7 , double that amount , both sides being equal , 3528 gives , the square root of which is , in feet 4 and inches , feet , inches . In cutting braces always allow in length from a sixteenth to an eighth of an inch more than the exact measurement calls for . Directly under the half- inch marks on the outer edge of the back of the tongue will be n . oticed two figures , one above the other These represent the run of the brace , or the length of two sides of a right - angled triangle ; the 62 A B c or TH E STEEL SQUARE

figures immediately to the right represent the

" length of the brace or the hypothenuse . For

s c the 3 - 3 5 - 1 o t a in tan e , figures 6 6 9 9 sh w h t the run os 3 on the p t and beam is 6 inches , and the length of the brace is inches . Upon some squares will be found brace meas u remen ts as given where the run is not equal , 1 8 - 24 30. It will be noticed that the last set of figures are each j ust three times those mentioned in the set that are usually used i n squaring a building . So if the student or mechanic will fix in hi s mind the measurements of a few runs . with the length of braces , he can readily work almost any length required .

Take a run , for instance , of 9 inches on the beam and 1 2 inches on the post . The length of

1 5 . A 2 3 20 brace is inches run , therefore , of , , , m e or any other nu ber of tim s the above figures , the length of the brace will bear the same pro portion to the run as the multiple used . Thus . if you multiply all the figures by 4 you will have

3 48 the run 0 6 and inches for , and 6 inches for

a 3 4 the br ce , or to remember still more easily , ,

5 S 1 0 e . and feet , or 6 , and f et There are other runs that are j ust as easilv

x the . 51 - fi ed in mind inch run , brace 6 feet .

1 2 s 8 3 - hundredth of an inch ; feet , inch run 1 1 e 8 brace f et , inches , etc . A B C OF T H E STEEL SQUARE 63

T he following examples and explanations on i e t roof fram ng are simple and asily unders ood , and cannot fail of being valuable to the young mechanic who aspires to become an expert roof

. s s s framer The e examples will erve as starter , h e and in the following volume , whic will b issued

S o t v h r ly , more ad anced examples will be pre sented

ROOF FRAMING.

Roof framing can be done about as many

different ways as there are mechanics . But

an d undoubtedly the easiest , most rapid most “ ” practical is framing with the squ are . The fol lowing cuts will illustrate several applications

the and of square as applied to roof framing , all

who are interested in the subj ect can , by giving

it a careful study , be able to frame any ordinary

roof the mechanic comes in contact with . Fig 33 is an illustration that could well be

given much thought and study . It not only s o o l gives the mo t c mm n pitches , but a so gives the

degrees. Most carpenters know that hal f - pitch is 45 o h 4 degrees , yet few kn w t ird pitch is nearly 3 , and qua rter- pitch about 27 degrees . A bu ilding 24 feet wide ( as the rafters come 64 A B C or TH E STEEL SQUARE to the center ) has a 1 2 - foot run and half-pitch

u 1 2 the rise wo ld also be feet , and the length of the rafter would be 1 7 feet (the diagonal of

L t . be o the eng h , cuts , etc , could all figured fr m on e illustration .

Fig 3 .

Fig . 3 4 .

Fig 3 4 illustrates a way to cut rafters with the square . A roof 1 4 feet wide would have a run of

7 - o 8 h feet , third pitch w uld rise inc es to every A B C or T H E STEEL SQUARE 65

feot . e the s 8 run Therefore , plac quare on and

1 2 e ou n . s ven times , and y have le gth and cuts

35 . o t Fig . For the c agon rafter, proceed

a o u se 1 3 f or s me as c mmon rafter , only run ( in place of 1 2 for common rafter) .

Fig . 35 .

. 3 . A Fig 6 , hip or valley rafter s these run diagonal with the common rafter the diagonal of 1 foot is practically 1 7 i n u se 1 7 oc ches , for run , and pr eed same as common rafter.

Fig . 8 6 .

t . are Leng h of j acks I f there to be five , the co o divide mm n rafter into six equal parts , use that for a pattern , and it gives the length very nicely . But that will n ot always work . To get all the diff erent lengths might at first look to difficult even many good mechanics , but it is 36 A B C OF T H E STEEL SQ UARE very simple as illustrated in Fig . 37 . If the first j ack was one foot from corner apply the square same as for common rafter, and it gives length and cut ( mark the length f or starting point on 1 o e next) , and if it is 7 inches from the other m v 1 1 5 the square up to 7 , i f the next is move up to

1 5 and so on .

Fig 3 7 .

. 38 . of Fig The side cut j ack to fit hip , if

e o e . laid down l vel would , of c urs , be square miter but the more the hip rises the sharper the angle .

é loeQ T

era a , ws

Fig 8 8 .

o s 8 1 2 Measure acr ss the quare from to , and it nearly which is the length of rafter to

run . one foot of Length and run , cut on length , gives the cut .

68 A B C or T H E STEEL SQUARE

. 42 o h i s Fig is an ther practical way , w ich simply to lay the square on heel or hip . T he illustration explains itsel f .

Fig. 42 .

Perha ps the most practical way of all to frame s to s a roof , the simple t under tand , easiest to e o t to rem mber, and m s rapid to apply is simply

the se ru n always take ri and , measure across the square which gives length . and ru n give

all. cuts , so you have it

Fig . 4

Fig . 43 illustrates a roof 2 5 feet wide and a

1 0 e 9 e 1 2 e . rise f et , inch s , run feet , 6 inch s

Bleasu ri n g across the square from 1 O% to I 2 V; 1 gives or 6 feet , 6 inches is the length of rafter . A B C or T H E STEEL SQUARE 6 9

i s Fig . 44. If the run of common rafter the run of the hi p will be diagonal of

1 8 - 1 lai nlv . which is 7 6 , as is p illustrated

Fig . 4 -i .

3 Fig . 45 . As the rise is 1 0 4 and run 1 7 8 - 1 2

th 20 e 2 s. the leng will be f et , inche

Fig . 4 5 .

Fig . 46 . When a roof must go to a certain height to st rike another building at a given ’ . point, as in additions , porches , etc , don t forget in getting the rise from plate to given point to 70 A B C or T H E STEEL SQUARE allow the squaring up of heel as illustrated and also remember to allow for ridge whenever one is used .

Fig 4 6 .

Flg . 7 illustrates the cut of top of quarter pitch rafter to lay on top of roof j u st men “ tion ed . To applv the square first lav it on 1

Fig . 4 7 .

r - l b and 6 , which is qua ter pitch and gives p um — cu t . From plumb cut lay of pitch of mai n 3 roof 1 0 4 and which gives cut . A B C OF T H E STEEL SQUARE 7}

Anyone that ha s stud ied thi s with determin a ti on will have no trouble in framing any or d i na r o ne y ro f , as the ge ral principles apply to i ll oo So I w r fs , pitches , etc . ill not take up any o more space with ro f framing at this time , but

m n . re ember all sheathing , studding , cor ice , etc , are made on the same cuts . In fact a hopper is al so exactly on the same principle . DIV I SION B.

SOME POINT ERS ON ROOF FRAMING.

I No matter what people may say to the con trar e h has y , th re is no method or methods t at ever been devised that is so effective in roof

s o framing , or result so rapidly achieved , as th se which are obta ined by the use of the steel square . I have shown in some of the earlier pages of this w the be an v ork how rapidly length , and vels of co mmon rafter may be obtained by the simple

i r m appl cation of the square , any dete ined num ber . sa 30 of times Thus for a building of , y ,

. i an v ft in width , wh ch is to have a roof of

a I h given pitch , we rrange the pitch as ave the shown , with so many inches on the blade for ru n a nd so e. , many on the ton gue for the ris

a e This settled , we apply the squ r fifteen times to the a 1 5 e r fter , b ing half of the width of the building . This then gives the length of the o rafter, and a line drawn al ng the edge of the tongue of the square will gi v e the proper bevel for the top or plumb cut . If there is to be a

o a s ridge b ard on the roof , then h lf the thi cknes of such board must be measured back on the

n line draw , and the rafter must be cut at that 72 A B c or T HE STEEL SQUARE 731

i ro o point , th s p vides for the ridge b ard being nailed on the face of the out without i n the least cha nging the pitch. lo e the A line a ng the ed ge of the blade , giv s proper bevel for the level or horizontal cut. If the bottom end of the rafter is to have a crow ~ o to the a o m i l fo t cut on it fit pl te , the w rk an w l have no difficulty whatever in cutting the foot of t the rafter to sui , as all the lines will be at right c o of te angles to each other, and a se ti n the pla

e on of b the may , be mad the line the evel and “ ” cuts laid off to suit the conditions . In reviewing an article of mine on this method

ou t E c e of laying a rafter, an nglish arpent r took exceptions to it on the grounds that it would take too much time to lay out the rafters “ ” f or o i so a wh le build ng by this tire me process , as he called it . Now the Englishman was right

o o of no A fr m his p int view , but merican work man would ever thi nk of layin g out the rafters for a whole buildin g by the process. He would

one e I s o n simply make raft r as have h w , f or a

r use hi e f or patte n , and t s patt rn laying out all the other rafters f or tha t particular pitch amd

s on s oo . o o n o ri e the ame r f M st w rkme , h wever , e o ff of so e make a patt rn fr m thin stu m sort, as it i s lighter and easier handled . The reviewer “ suggested as a better way that the pitch be 4 A B c or T H E STEEL SQ UARE

rr d on e a ange the iron square , then measur across om o of the angle fr the p ints run and pitch , and multiply this measurement by half the width of ” the roo to o . ow all f be c vered N this is right,

' b a at of t o o ut, s a m ter fac , entails m re lab r of “ ” a tiresome sort and would use much more time than the method I have taught n ow f or nearly

o e s. T A c o n o f rty y ar he meri an w rkma , h wever , does not even require a suggestion as to the quicker method . He will see and adopt it at once wi thout argument .

Fig 4 8 .

method the Englishman would adopt is 48 the o of shown , where p ints pitch and o 1 2 8 run are sh wn at and , which makes the di agonal line 1 4% inches . T o get the length

the our o b d of rafter for supp sed uil ing then , 1 we must multiply this 1 4 A; inches fif teen then we must use the square at the h p an

76 A B C or T H E STEEL SQUARE

i the .5 or build ng by decimal 6 ,

s a as can o r 1 a ne r be w rked by the squa e , 3 feet , 5 inches . Let us try the same rule f or a greater width say 60 feet . By finding the hypothenuse we find 33 as near as can be used by the square , feet , 1 6 ) . B o o GOX.56 , A, inches y my meth d it w uld be ‘ 33 . i or equal to feet , 7 inches full By th s method the rafters i n wide buildings are a little

. T 52 i e long hus , i f the building is feet w d , by o o 2 1 c the hyp thenuse it w uld be 9 feet , in h ; my

o c . I co way it w uld be 29 feet , in hes nsider o of the this an advantage , as it leaves the p int rafter very slightly open.

For one- I o o m l o third f ll w the sa e p an , nly using the decimal .6 . Unlike the decimal used for a quarter pitch the lengths are a very small

c o or as f or c a or fra ti n sh t ; , instan e; rafter f a 0 h oth building 6 feet wide , by finding the yp e

u be 3 1 - 1 . nuse, wo ld 6 feet , 6 of an inch By my

0 . =3 . A l t ff n way , 6 X 6 6 feet s igh di ere ce ,

. i 48 truly If build ng is feet wide , then by the e o 28 0 first m th d we find feet , 1 inches full ; b 28 e e . A i rac y my way , f et , inch s l ttle p tice will enable the mechanic to allow j ust enough to ff c o make up for the slight di eren e , s that when rafters are put together the fit will bl perfect. A B 0 OF T H E STEEL SQUARE W

The one- half pitch can be found in the same manner by using the decimal .71 . Taking the — of b h 24 foot building, length rafters y the y

othenu se 1 6 1 1 2-3 ; p , we find feet , inches my 1 e ll. A way they would be 7 f et fu gain , build

n W i f t od i g 60 feet de , rafters by the irs meth w e b 6o ould be 42 feet, inch s ; y my way x

. B h s feet , 6 inches y using t i decimal , c co c the length is so near practi ally rre t , that it may be used in all cases . For a full pitch u se the decimal and as be in the preceding mentioned pitch , and it will found so near correct that it can be practically u sed in all cases. It will be noticed that I have not made au v allowance f or proj ection of rafters over the plate. In this case gauge from the crowning side of your rafter the thickness of your proj cc

f or the tion ; allow enough the latter, and find lower bevel according to the way you described i n your last ; measure the length of your rafte' from where this bevel crosses the gauge line. A little practice will enable the mechanicto la 1 off a rafter in a very short time. I have us d e the above mys lf , and have no trouble whatever. W I l to o hile have no fau t find in y ur methods , I e as know th m to be correct , yet it is j ust as

a o well th t w rkmen should know other methods , 8 A B C OF T H E STEEL SQUARE '

“ as there are many occasions when the only ” method he possesses cannot be appli ed . Hence

I bm o o s . su it the foreg ing, at y ur reque t ” W. H.

A ' i ll this is very true , and right as far as t

o so a o e do g es , but it happens th t many w rkm n not have the necessarv learning to work out these problems in footing on the lines laid down by W .

H . o o n , but , in rder to meet c nditio s of this kind

I have prepared a series of tables which is i a~ sertcd e t o in the larg r volumes , giving the leng h f rafters f or any bu ilding having a width of from five to sixty feet and a rise of roof of from one to eighteen feet to ridge . This will cover

o o o m f or the wh le gr und , and f r a ready table the estimator to take his quantities from . I may be pardoned f or again showing the

' common and simplest method of laying out an o n r f or o s I rdi a y rafter , n twith tanding all have

s on c said and de cribed and explained this subj e t , there will always be some persons who will n ot ‘ to be able to grasp the method , unless it is put them in some other light . I am sure of this from the long experience I have had in the answering of questions of this kind through the columns of di fferent building j ournals . This is no doubt owing to some constitutional peculiar ities of both the person who makes the inquiry A B c OF T H E STEEL SQUARE 79 and the person who attempts to answer it . This is one of the main reasons why I have admitted into this work various methods and descriptions

h s of others t an my elf , so that readers will have the same methods described a nd explained to them in several diff erent ways by several writers .

a h . 4 Let us t ke the diagrams s own at Fig 9 ,

which shows a portion of a roof ha ving a quar ~

. E A thc ter pitch C B showing the height , and B length and inclination of ra fter . D shows the “ ” oo the cut f t of rafter on the plate , flat foot and the line E C the plumb cut . This isquite

. The an : plain building may be y width , let u 30 e say in this case , that it is f et wide from A to 0 . That wi ll make the di stance from A to C 1 5 feet .

A method of obtaining the bevels f or this rafter is given in Fig . 50 where the steel square 80 A B c or T H E STEEL SQ UARE is shown laid on the pattern with the points 1 6 inches on the blade and 8 inches on the tongue applied to the edge of the stuff . T he line HO on the blade gives the bevel for the foot of the

AC . OP . 50 th rafter The line , Fig gives e bevel for the top of the rafter or the plumb

m o m r i s cut , as ost w rk en call it . Now , the e

’ n o thing in this diagram , which from Bell s

— Carpentry , an excellent work from which the workman can get the length of his rafter , with out complicating matters . Had the figures 1 2 inches and 6 inches on the square been employed 1 8 o instead of 6 and , then the distance acr ss the dia gona l from these two points would ha ve o a equalled on the rafter, one f ot on the b se line 1 5 or seat of the rafter , so that times that length would have been the total length of the rafter. A B C or THE STEEL SQUARE 81

e t b a li B t er still , however , would have een the pp cation of the square 1 5 times on the edge of the rafter pattern with the points 1 2 and 6 on o o e gauge p ints , then b th length and b vels would have been obta ined at one operation .

Of se i n cour , the expert workman will often

or o vent , discover , meth ds of using the square

s o a n ot in certa in pha es of ro f framing, th t can be o a o found in b oks , or th t cann t be taught because of the peculiar circumstances of the par ticu la r case . Having a fair k nowledge of the uses of the steel , the workman will seldom be ove rtaken. by difficulties he cannot overcome if he studi es the problems before him and then employs his knowledge of the square to their so o lution , as a little applicati n on this line will remove all possible troubles . E s to very carpenter know , or ought know , that the run and rise of the rafter taken on the c s square will give the seat and plumb ut , but inasmuch as buildings are not all of the same h ff set widt , it requires a di erent of figures f or

e an each run , and as it requir s extra calcula

. d ru n it tion to first fin the of the hip or valley , — is better to use the full scale f or a on e foot run

the : of common rafter which answers f or any run .

R . 51 o eferring to Fig , we sh w a square

b y A the bounded , B , C , D , sides of which are 82 A B c OF THE STEEL SQUARE

5 h o 1 2 inches . E i s at a point inc es fr m B , and C 1 2 inches from B . B-A represents the - the run of the common rafter . E A represents

Fig. 52 .

of o t hi a C-A the run c agon p or v lley , and

f or o o or t r same the c mm n hip valley , hei lengths ,

1 2 1 3 1 s . ow c being , , and 7 re pectively N sin e

1 2 1 3 1 d m ers m , , and 7 are fixe nu b , we take the on thet s e ho n . 52 . ongue o f the quar , as s w in Fig

A B C OF T H E STEEL SQ UARE

The measurement line of hips and valleys is at a line along the center of its back , and j ust where to place the square on the side of the rafter so as to make the cuts and length come right at that point is a question that taxes the s t kill of most carpenters , especially so when he rafters are so backed . In Fig . 54 I have tried to make the above points clear .

R UN I 7 ” 1

PL AN

Fig. 54.

I S . First , how the plan of the rafter The cross lines on same represent an external corner for the hip and valley respectively . Above the plan is Shown the elevation . The sections 1 42- 34 represent the position of the rafters 85 A B c or THE STEEL SQUARE under the followmg condi tions : No. 1 hip when

. 2 .3 not backed , No hip when backed , No valley

No. 4 . when not backed , valley when backed 1 No . is outlined by heavy lines , and sets lower than the others . By tracing the bottom line of 1 the sections down to the seat of No . , thence up to the second elevation will show j ust how deep the notching should be for each rafter . No . 1 cuts into the right hand vertical line from the plan , which would make it stand at the right v height abo e the plate , but in order to make the seat cut clear the corner of plate , it is necessary to cut into the center line above the plan . No. 2 1 cuts into the same points as No . , but owing i t s c to being ba ked , the seat cut drops accord i n l . . 3 g y No cuts into the center vertical line , and in order to clear the edges of the plate must cut ou t at the sides to the left vertical line . No . 4 cuts in the same as the latter , but as much lower than No . 3 as No .2 is below No . 1 . The outer vertical lines from the plan repre sent the width of the rafter . Therefore if the on e rafter be two inches thick , would be inch off apart , and this amount set along the seat line (or a line parallel with it) will give the gauge point on the side of the rafter . To make thi s clearer refer to Fig.53 1 7 and 9 gives the cuts .

Now leaving the square rest as it is , measure 86 A B C or TH E STEEL SQ UARE

1 one- t i s of the r back from 7 half the h cknes after, and this wi ll be the gauge line point from which to remove the wood back to the center line of hi e e the of p, and the m asurem nt from edge the rafter taken vertically down to the gauge point set off on the plumb cut regulates how far apart the parallel lines of the seat cuts will be under the above condi tions . This rule applies to any roof long as the pitches are regular.

Proceed in like manner f or the hip . the o o e one- variati n , h w ver , is practically half of the above results f or the square cornered bui lding.

. 55 str e 1 2 o n Fig illu at s side cut of the j ack ,

1 5 n of co o the tongue, and ( le gth the mm n rafter) on the blade. A B c or TH E STEEL SQUARE 87

56 illustrates side cut of the octagon 5 on the tongue and 1 5 on the blade .

Fig . 5 7 .

57 illustrates the side cut of the hip or 1 1 1 of the valley , 7 on tongue , 9 4 ( length hip ) on the blade giving the cut in each case .

T e o n he latt r , h wever , is for the u backed ra . fter If it has been previously backed , then 88 A B c OF THE STEEL SQUARE apply the square with the above figures on the

a lower edge at bottom of the plumb cut , or p

l . 56 p v the square as for the j ack , Fig , to the backing line , which will give the same result as 1 7 and It is quite clear that when a workman cuts a m i s co mon rafter, he also cutting a timber that would an swer for a hip for a building of les s e span having the same rise , only taking som adj ustment of the top bevel to fit against a ridge .

. 58 This is quite plain , and if we refer to Fig , we find that the common rafter for a 1 - foot run

hi - becomes a p for an inch run , and that a hip for a 1 - foot run of the building becomes a

1 7 - . common rafter for a inch run Therefore , the rule that applie s to the common rafter al so

i . e a n d a pplies to the hip rafter , the run rise taken on the square will gi v e the seat and plumb cuts . The run and length of the rafter taken on the square will give the side cuts , or taking the s 1 - . 58 1 2 cale for a foot run , Fig , it is on the tong ue and the rise on the blade for the com

1 7 ton u e s mon rafter , and on the g and ri e on the blade for the hip . The tongue giving the seat cut and the blade the plumb cut . For the side cuts we take 1 2 on the tongue and i nches on the blade , and the blade will give the side cut of the j ack . Take 1 7 on the tongue A B c or THE STEEL SQUARE 89

3 an d of 1 9 on the length the hip , 4 inches , the blade and the blade will give the side cut of the hi p. It would also be the side cut of the cor responding j ack if it be a common rafter . Seventeen is used for a foot run of the hip rafter because the diagonal of a 1 2 - inch square is practically 1 7 inches .

l O h c‘. Q é 0 0 s I i l ‘ p : s A 1 i 9 a s I , s ‘ : . ' s 1 ‘ i i l a 3 s 5 1 , I I i s a 1 ‘ g s ” O s J I “ , Q 0 o’ “ s I s 0 \ i s l 90 A B C or T H E STEEL SQUARE

If we were to u se 1 2 on the tongue f or a foot run of the hip the rise to the foot would neces sa rily be less than 1 0 inches. In Fig . 59 I show what the diff erence is in rise to the foot .

Fig . 59 .

From 1 2 to 1 2 is the length of the run of the hip would only ha ve 1 0- 1 7 of an inch to one run i of the common rafter, and an equal r se of

o on r off A the c mm after , set as at , and a line from this to 1 2 on the tongue passes at 7 1 - 1 7

92 A B c or THE STEEL SQUARE follows : The run of the long way of the build 1 4 9 ing is , and for the narrow way , which we take on the blade and tongue respectively , as

o s . 1 sh wn on quare No , and to this apply square

No. 2 s . AD . , a shown equals the run of the hip

Fig. 6 0.

equals the rise and ED equals the length of the hip . The reader will notice that the letters A o l , B , C, D f rm a para lelogram , with side and ends equal to the runs of the common rafters . A B c or T H E STEEL SQUARE 93

Therefore , by taking the runs on the tongue ,

r os. 8 1 i as shown by the squa es N and , will g ve

. their lengths , seat and plumb cuts

I n Fig . 6 1 is Shown the intersection of the rafters at the peak and as the lengths of all “ rafters are scaled to run to a common center it is necessarv that the commo n ‘ rafters must cut

so as to fit in the angle formed by the hips .

Fi g 6 1 .

T he proper deduction for this is shown in Fig . 1 50 by placing two squares on the back of the t raf er, with the heel or corner of the squares resting on the Center line . The distance from the corner of the square to B mea sured square

n v back (at right a gles) from the plumb be el , as 94 A B c or T H E STEEL SQUARE A B c or T H E STEE L SQUARE 95

1 o a of shown in Fig. 6 , will l c te the point the long common rafter at B in Fig . 6 1 . Proce ed in like ma nner for the short common rafter,

i i m tak ng the d stance fro the corner at C , and f or 1 45 on the side cuts , take the tongue and the length of the short common rafter CE on the blade— the blade will give the cut at AC in Fig.

61 . The reader will observe that this angle is the same as that for the side cut of the j ack . Proceed in like manner f or the long common

on an d BE rafter side , using 9 the tongue on the blade . These same figures will give the side cuts of the hip , provided hip has been previously ) backed . Taking the last for example t he reader will observe that 9 on the tongue and B E on the blade the square would lay on the plane of

' the backing and the blade giving the ou t along

. 1 the line BB in Fig 6 , or these cuts may be found by measuring square ba ck from a plumb b A A . 2 c evel at points and , Fig 6 , the distan e AC A e e and B , which will give the pr p r plumb cut at the sides and intersecting the line AA at

. s AC A the center The e same distances , and B , bu t a set off tr ns ferred to opposite sides , on the seat cut or a line parallel with it , will give the gauge points on the side of the hip for the backing. The lengths of the j acks may be found by 96 A B C or T H E STEEL SQUARE di vidi ng the length of the common rafter by the number of the spacings for the j acks ; the quotient will be the comm on diff erence .

E N D OF DIV ISIO N B .

Fig . 6 3 .

L AY -" OU T OF H I P - ROO F W IT H DE C ! . T HE ST EEL SQUAR E AND I T S USES .

DIV I SIO N C

I n trod uctory . During my long experience as Editor of several of the leading building j ournals in. the

United States and Canada , I have been asked and have answered thousands of questions re garding matters concerning building construe

’ o an d tion , builders materials , tools and pr cesses , “ particularly regarding the Steel Square and ” o i a its Uses , and I have c ncluded that the publ c t s r ion of a few of these questions and an we s , a oth i o long with er matter , in this div si n will be a en d ppreciated by my readers , and to this I i nsert a number of the most useful items in thi s manual .

e ue o Besides th se q sti ns and answers , I also o e i publish ther up to dat matter , all of wh ch wi ll make this volume one of the most useful little works to the America n carpenter an d wood worker ever published . I open thi s division with a few hints regard ing the con struct ion rather the laying out of a Hip-Roof where the design has been furnished t c o by an archi ect , and which , of ourse , sh ws the pitch and the lay of the timb ers . W e suzv 97 98 A B c or T H E STEEL SQUARE

Fig . 6 4 .

711 7 0

Fig. 6 5. pose the roof to have a span of 1 8 feet and a

e n the oo one-t rise of 6 f et , thus givi g r f a hird pitch. The fence is used in this example to its

l and h on he fu l extent, w en placed t square and

n m e faste ed , the line of fence shows the p or

1 00 A B C or THE STEEL SQUARE

o 1 - 3 av id making a plan , we take pitch . This 1 - 3 to pitch is the width of the building, point of rafter from wall plate or base . For an 8 1 - 3 2 4 example , always use , which is of , on 1 2 24 tongues for altitude ; , the width of , on blade for base . This cuts common rafter. Next is the hip - rafter . It must be understood that the diagonal of 1 2 and 1 2 is approximate l 1 7 y in framing work , and the hip is the diag onal of a square added to the rise of roof ; therefore we take 8 on the tongue and 1 7 on the blade ; ru n the same number of times as common rafter which gives the length of hip and plumb and level bevels . ” of To cut j ack rafters , divide the number openings for common rafters . Suppose we have five t j acks , with six openings , our common raf er

1 2 2 . feet long , each j ack would be feet shorter 1 0 8 The first , next the hip , feet , the second

6 . feet , third feet , and so on The top down cut same as down cut for common rafter . For

ou t . the bevel , against hip Take half the width of building on tongue and length of common

. rafter on blade , and blade gives the bevel Now

8 1 2 1 4 7 - 1 6 . find diagonal of and , which is in 1 2 Take this length on blade and on tongue , blade gives bevels . If the hip - rafter is beveled “ ” or backed to suit j acks , then take height of 1 A B C or THE STEEL SQUARE 01

hip on tongue , length of hip on blade , and tong ue gives bevel . These figures will cover all

. bevels for cutting, cornice and sheathing For o bed moulds for gable to fit under c rnice , take half width of building on tongue , length of common rafter on blade ; blade gives cut . To of cut planceer to run up valley , take height r ' after on tongue , length of rafter on blade t o i . ngue g ves bevel For plumb cut , take height f o hip on tongue , length of hip on blade ; t ongue gives bevel .

These figures were specially . prepared for a hi - p roof having a one third pitch , but will suit other pitches equally well if the difference in height of ridge is considered . For a hopper the mitre is cut on the same

. principle To make a butt j oint , take the width

on ! of side on blade , and half the flare tongue t the latter gives the cut . You W ill observe tha a.hip - roof is the same as a hopper inverted . The cuts for the edges of the pieces of a hexagonal hopper are found this way . Subtract the width of one piece at the bottom from the width of s ame at top , take remainder on tongue , depth of side on blade ; tongue gives the cut . The cut on face of sides : Take 7 - 1 2 of the rise on tongu e and the depth of side on blade ; tongue gives cut . The bevel of top and bottom : Take

s o n . ri e blade , run on tongue ; tongue gives cut SOME QUE STIONS AND ANSWERS FROM VARIOUS CORRESPOND ENTS .

The following questions and answers from practical workmen are considered among the v ery best things regarding the u se of the Steel who Square , as they are from men knew of what they were talking about . The y are gathered the from many sources , but chiefly from col umu s of Technical Journals with which I have b e Ed . een connected , eith r as itor or contributor “ J . R c . Y . : How as Willis , o hester, N , asks can I get the proper bevel for a butt j oint on an the the obtuse or acute angle , by use of square only !"

Fig . 6 6 .

Answer : Suppose Fig. 66 represents an oh tuse angle formed by two parallel boards or

b . b A a off a tim ers To o tain the j oint , , sp ce equ l

an o the o 1 3 3 dist ces fr m p int to , , then square 1 02

1 04 A B c or THE STEEL SQUARE

“ McVit : I P. y , Milwaukee , asks How can d raw a circle with the Steel Square !” An swer : A circle of any required di ameter m ay be drawn by means of the square by using it as indicated in the accompanying Sketch .

A . 6 8 at Drive two pins or nails , and B , Fig , whatever distance apart the circle is to have as i t s . diameter Bring the square against them ,

shown , and use a pencil in the angle as indi

Fig. 6 8. cate d in the drawing . This rule i s very con v en ien t in many instances . Suppose A and B a e r two points through which a circle is re quired to be drawn . By bringing the square a gainst pins or nails placed in the points , it may be described as indicated in the sketch . A B c or THE STEEL SQUARE 1 05

“ “ A . : Mechanic , Tampa , Fla , asks Can the steel square be used in laying out a wreath for !” a handrail , and if so , please describe how Answer : Some advance in this direction has been made , but not much , but the outlook is quite encouraging as many experts are trying to ob tain all the lines required for forming circular handrails . It will be accomplished sooner or

o O m Q O O M z’

Fig. 6 9 . later . A few problems and solutions are given herewith : In getting out face - molds it has gen erally been considered necessary first to unfold the tangents and get the heights , and by con struction get the bevels . The method shown is o ff s mewhat di erent , though results are the same , but are produced more rapidly . Take for illus t rati on a side wreath mitered into a newel cap . 1 06 A B c or T H E STEEL SQUARE

This method will apply no matter where the

is ' s newel placed , or whether the easement is les or more tha n the one step of the example illus ~ t rated. a the Wh t is meant by one step is , that tangent of the straight rail continues to the

2 . . 2 - 1 . point , Fig 6 9 The tangent is level

Fig . 7 0.

the e l To produce the face mould , lay st e o o b 1 2 square in the p siti n indicated v the lines , .

3 4 r o , , not the figure on the squa e at the p ints numbered , and transfer them to a piece of thin — ff . 0. L ne 3 4 . 0 n e t . stu , Fig 7 i in Fig 7 is i d fini e Now take the len gth of the long edge of the

o ss 2 . pitch b ard in the compa es , and with , Fig

70 e 3- 4 4 , as a cent r, cut the line in and draw

2 - 4. 1 - 2 2 - 4 the Now is the level , and is pitch tangent on the face mold . To get the bevels and width of the face mold

o 3 - 4 at b th ends , take the distance on the blade the of the square, and the height of a riser on tongue of the square. apply to the edge of a

1 08 A B C or T H E STEEL SQUARE

m e t length of a line , fro the corn r of he pitch board squared from its top edge . This bevel will be understood better by placing the pitch boa rd on the line 2 - 4 and applying the smal l

a a n 4- x tri ngle to it with its b se on the li e , and its point even with the tap edge of the pitch board . It will then be at right angles to the top edge of the pitch board .

c a o s In practi e , a p rallel m ld is generally u ed , and the wreath piece is cut out ; both thicknes s of plank and width of molding being equal to the diameter of a circle that will contain a sec tion of finished rail .

' Demou x W Ma m Jacques , innipeg , , wants to

a n d know how to lay out braces , regular irreg ular b v the use of the Steel Square . A nswer ' Braces and trusses are something

i s like rafters and when the run known , there should be no di fficulty in getti n g the length s and proper bevels . In the first place it is always best to make a pattern and then mark out the timber work !f rom the pa ttern . Suppose we want braces hav “ ” - oo - is ing a four f t run that is , the brace to form a diagon al from points four feet from the post and four feet from the girt . Take a piece ’ f stu fl e e o o already prepar d , six fe t l ng: four A B c or T H E STEEL SQUARE 1 09

e - c e inch s wide and half in h thick , gauge it thr e eighths from j ointed edge .

r . 1 Take the square as a ranged at Fig 7 , and place it on the prepa red stuff as shown at Fig .

- 72 . Adj ust the square so that the twelve inch

e 0 lin coincide exactly with the gauge line , o ,

0 . os o , Hold the square firmly in the p ition

Fig . 7 1 . n ow e the a obtained , and slid the fence up Q gue a nd blade until it fits snugly against the j ointed

the St ff c edge of prepared u , screw the fen e tight

the be 1 2 - on square , and sure that the inch marks on both the blade and the tongue are in exact position over the gauge - lin e.

Fig . 7 2

We are now ready to lay out the pattern . to o Slide the square the extreme left , as sh wn on t on the do ted lines at x , mark with a knife 1 1 0 A B c or T H E STEEL SQUARE

the the outside edges of square , cutting the

. R gauge line epeat this process four times , the marking ends , and you have the length and bevels . Square over at each end from the gauge line and you have the toe of the brace . The

s ss . 72 line , Fig , show the tenons left on the end of the braces .

. 3 o s The cut at Fig 7 , sh ws the brace in po i

c . tion , on a redu ed scale The principle on which the square works in the formation of a brace o can easily be understood fr m this cut , as the dotted lines show the position the square was in when the pattern was laid out. “ be s It may neces ary to state that the square , a s n ow c n arranged , will lay out a bra e patter

1 1 2 A B C or THE STEEL SQUARE bevels at the extreme ends . The dotted lines

a s show the position of the square , the pattern is being laid out . 5 Fig . 7 shows the brace in position , the dotted lines Show where the square w a s placed on the pattern . It is well to thoroughly und erstand the method of obtaining the lengths and bevels of irregular braces . A little study will soon enable any person to make all kinds of braces .

wo- oo ru n If we want a brace with a t f t , and - v w a four foot run it must be e ident that , as t o

on is the half of four , so the square take 1 2 6 inches on the tongue , and inches on the bl ade, apply four times , and we have the length , and the bevels of a brace for this run . A B c or THE STEEL SQUARE 1 1 3

re b o oo a e 1 2 c s For a th e y f ur f t run , t k in he on 9 the tongue and inches on the blade , and 3 apply four times , because , as three feet is Aof 3 9 1 2 n . four feet , so inches is 4 of i ches

A e n young carp nter , Toronto , wants to k ow how to find the center of a circle by aid of the Square.

Fig. 76 .

Answer : In Fig. 7 6 is shown how the cente r of a circle may be determined without the use of compasses this is based on the principle that a circle can be drawn through any three point s tha t are not actually in a straight line . Sup

o A . p se we take , B , C , D for four given points A C then draw a line from to D , and from B to 1 1 4 A B c or TH E STEEL SQUARE

c e he o get the ent r of t se lines , and square fr m

s as these center shown , and when the square

o e or er s at cr ss s the line , wh e the line intersect , as

t the . x , here will be the center of circle This i s a very useful rule .

“ Ed . McDonald n O : , Cincin ati , hio , says I want to know how much can be done with the square towards setti n g out stair railin g ! Answer : In a previous page a few remarks on this subj ect will be found and the following is further submitted

Fig. 77 a plan of a stair well having three winders . The rail in this case will have two different pitches . These rails are a little more complicated than those having equal

e as the is pitch s , in the latter maj or axis parallel off the diagonal line B D ( Fig. When

1 1 6 A B C or THE STEEL SQUARE been done is that the plane in which the rail lies has been proj ected to intersect the horizonta l plane which contains the plan of the w reath . The name by which this line is generally known

. 78 is the horizontal trace ( shown at C , Figs and The minor axis (Figs . 78 an d 79 ) i s

Fig. 79 .

a of A lways parallel this , and always touches as in Fig . 77 . The maj or axis (Figs . 78 and 7 9 s A ) also touches thi point , and is always square off the minor axis and off the horizontal trace . It will be seen by this that the rail i s pitched equally both ways ; therefore the face mold will be of equ al width at the ends . 1 1 7 A B C or THE STEEL SQUARE

W a on o hen r ils are cut by bandsaw bed bl cks , bevels are not necessary , as they can always be obtained by applying a bevel as shown at Fig .

8 0. The stock should lie solid on the block and square off the sides . When the block is thin it is best to apply the bevel near the corner , when a greater surface is obtain ed . These bevels are applied after the j oint is squared off the tangent lines . To demonstrate a rail with unequal ff 2 x 2 pitches , cut another piece of stu inches ,

m . 9 as shown Fig 7 , repeat the process with the cardboard as before . It will be found that the horizontal trace has departed from the angle of

45 degrees (see Fig . 7 9 ) and has , approached nearer one corn er and gone farther away on the other . The maj or axis B will have done like i t off i wise , as is always square the hor zontal

C . trace The wreath having two pitches , the face mold will obviously be wider at one end t than a the other ; and if bevels are required , they must be set off on the face of each side of the block . The width of the face mold is to be applied on the tangent line ; this makes it s n lightly in excess on the j oi t , but it is better to have a little margin in thickness for working . Where thickness of stuff is a secondary con sid o crati n , it is preferable to take the rail out of stuff which is as thick as the diameter of a circle 1 1 8 A B C or T H E STEEL SQUARE that will enclose the section of rail ; the corners will then be left complete. The following method shows the least thick

the cu t ou t o ness rail can be of , and als gives width of face molds on the j oint . Set the bevel

o . 80 to the bed bl ck as shown at Fig , and apply at the side of the block . Draw a section of rai l the e the bot level ; apply b vel again , touching tom corner of the section . The dista nce between

Fig 8 0. Fig . 8 1 .

e r the marks is the thickness , a plumb lin ma ked on shows the width of the face mold on the bevel line. Where the pitches are different the fore going method ha s to be applied to each side of

The bevels may be also obtained by the steel squa re . Take the width of prism face ( shown

1 20 A B C or THE STEEL SQUARE

This indicates the center of the rail . Run lines radi al from A as shown these are the riser lines . the Draw the lines B C and C D , which are tangents . Draw the di agonal B D . To make ff the bed blocks , procure a piece of one inch stu t ake it to the width shown at B C ; squa re on a

mark about 3 inches from the end (this is to allow for the shank to clear the saw table ; the block is shown at Fig . 83 without the 3 - inch allowance) . Take on the steel square the rise on tongue and going on blade of the straight flight of stairs ; mark on the inch board at tongue ; this is pitch of the first tangent . Take the height at D , which is one and a half risers 1 A B C or THE STEEL SQUARE 1 2

1 1 0 A, inches ; deduct the height of the first tan gent from inches ; take the diff e rence on the tongue and width from C to D on the blade ; the tongue gives the cut for the second tangent . Mark the pitch of the first tangent on the edge of the second and cut t o this ; the pitch of the second tangent gives the edge cut of the first . Cut and fix together with stretcher as previous ly described .

Fig. 84 .

To get out the face mold , procure a piece of f - thin stu f . Three ply wood is excellent , as though it is liable to warp it does not shrink perceptibly . Shoot on edge and gauge on a center line ; take the distance from B to D (Fig. 84) (the hy pothen u se of 6 and 6 ) on the blade and the rise at D on the tongu e ; lay on the edge 1 22 A B C or T H E STEEL SQUARE of the board to this . Lay off this length on the — three ply at B D (Fig . 82 ) ta ke the width B C

. 84 (Fig ) on the blade , rise at C on the tongue ; the e find hypothenus , and apply with a pair of compasses at Fig. 82 with B as a center cutting

C . at Then apply at D as a center , cutting at A . Now find the hypothenuse C to D ( Fig . s o and apply the compa ses as bef re , with

A . Con D and B as centers , cutting at and C nect up the points where the arcs intersect to

i the r B and D ; th s is face of the inclined p ism , and contains the true sha pe of rail . Continue

e 3 e a is the tang nt line C B , inch s or wh tever o s of required for the shank , and square the j int the lines B and D . In order to locate the maj or axis the horizontal trace is now required . Stand the bed block on the plan ( see Fig . Run the bla de of the square down until it touches the

o o e o . l b ard ; mark this , and rem v the bl ck It wil be seen that the bed block has n ot got the 3 i nches ‘ allowed the o o l at bottom , but the h riz nta trace is as easily fou nd wi th as without the allowance ; all that is requi red in the former case being to turn the blade to B ( still keeping the the o heel at top of the bed bl ck ) , make a mark where the square touches and lay on the square

' shown at . 83 . the as Fig Mark at blade , and slide back the square until the tongue touches

1 24 A B C or THE STEEL SQUARE

Now run parallel lines off the tangent B for the shank ; this completes the face mold , which is now ready for the face of the plank . Wreaths for stairs with flights which stand at either acute or obtuse angles to each other may be set out by the methods that have been here de ff scribed . The only di erence , practically , is that the bed block is made acute or obtuse to suit

' fig. 85. plan of tangents . The device shown at Fig. 85 has been found to answer excellently for strik

. ing out ellipses To make this , procure two 3 o screws 4 inches long, als a piece of brass tube that will j ust slip on the plain part of the

‘ screw without shaki ng . Counter sink out the ends until the screw heads are flush ; cut two pieces off the tube three - sixteenths and file u p — true these pieces are best held by sinki ng them with a bit in a piece of hardwood . Now . when about to strike an ellipse, drive these sc rews in wi th the collars on to half maj or an d 1 25 A B C or THE STEEL SQUARE

o o of minor, measured fr m the p int the trammel

to the inside of the collar for the maj or , and to the outside of the collar for the minor . It W lll be found that if the collar has been made

t u e r , the trammel will slip around the curve o without causing the square to slip ab ut , the collars acting as rollers .

. . o e. W T Jones , Boise City , Idah , would lik to know of a ready way to frame hi p roofs and roofs of irregular or diff erent pitches with the t s s eel quare , including lengths and bevels of all rafters . Answer : These problems along with many others are discussed and explained at length in k my larger wor s on the Steel Square , but the l fol owing , which is somewhat condensed , does to ’ some extent cover Mr . Jones inquiries

A . 86 Suppose , B , C , D , Fig , to represent one end of a hip roof with a span of 24 feet and a — 1 0 foot rise . The side rafter I D shown in top sketch will have a run of 1 2 feet . The common L rafter at the end of building , I , has a run of 1 6 feet , with the same rise , so that the ends and sides of the roofs have different pitches . The lengths and cuts of the common rafters are ob ~

t a i ned . 8 ' b 1 2 on the as shown in Fig 7 , y taking 1 26 A B C or T H E STEEL SQUARE blade and 1 0 on the tongue of the square and

o s of Sld( measuring acr s , giving the length the

o - s of tin rafter, fr m which one half the thickne s

s s luml ridge, mea ured quare back from the p

u . f ! cut , must be ded cted The blade gives the oo

g. 86 . cut and the tongue the plumb cut . The length of the end rafter is obtained by taking 1 6 on

b 1 0 on the o of the lade and t ngue, which will course give the respective cuts also. The same results may be obtained by appl y in g the square

1 28 A B C OF THE STEEL SQUARE ridge has been deducted from the side cut . The side cut is found in a slightly ‘diff erent way from that of a regular hip or valley on an ordinary roof. The common method is to take the length

on of the hip on the blade and run the tongue ,

as but this will not work in this case , the run of the hip does not be at an angle of 45 degree s

. 86 a s in ordinary roofs The line B J in Fig. ,

. 89 . must first be obtained , as shown in Fig Joint one edge of a board and square up the line B L . Measure one - half the width of build

— i n — ou h 1 2 i n ing inches t is line , this case , and the with heel of the square at the point B , move the square until 20 on the blade touches the edge of the board at E . The tongue wi ll then give the point J 1 5 inches ; which is the 0 ” length 0 1 ac li n e required . Then take thi s line A B c or THE STEEL SQUARE 1 29 on the tongue and the length of the hip on the

a . 90 i bl de, Fig , and the blade w ll give the bevel of the hip to lie against the ridge . As a general rule , hip rafters are not backed , but if such is desired the lines for backing can be found by setting it to the foot cut of the hip rafter . Make

DlAGW Ac.

Fig. 90.

0 R square with S O and gauge back as shown in the diagram A . Do the same on the other

R i P . side , using the distance T nstead of S The point 0 is of course at the center of the li ne

. T P For lengths and bevels of j acks , pro

: oo 2 oeed as follows For end of r f, and set feet on o centers , take a b ard and apply the square 1 30 A B c or T H E STEEL SQUARE

. 91 of to it , as shown in Fig , with the length the end rafter on the blade and the run of the side

a off 2 4 8 rafter on the tongue . Sp ce , , 6 , and

1 0 in . on the tongue after marking along both

o . AA C blade and t ngue The lines , , BB , C ,

DD EE as , , will give the length of the j acks , w to of ell as the side cut side the hip ,

o e n o i the square being m v d dow along t ngue l ne , while the run of the end rafter on blade and its rise on tongue will give the seat and plumb

. e . 2 s cuts For the sid j acks , Fig 9 give the sa o l a of e me meth d, on y th t the length the sid rafter is taken on the blade and the run of the

on o . so end rafter the t ngue If it is desired , 1 I the length of the jack rafter A A may be

1 32 A n c or THE STEEL SQUARE

i i The rules and d agrams , given herew th will

ma apply to valley as well as hip rafters , and y be relied upon as being accurate if closely followed .

— RULE S ee Fig. 87 .

Blade . " 1 6 gi ves run of hip . 1 2 gives length of side 1 6 gives length of end 20 gives length of hip

— RU LE S ee Fig . 9 1

Blade . Common End Rafter 1 9 Lo st Jack 1 5 25; 1 2 3d 9 2d 6 Shortest 3

Blade gives Side Cut of Jacks . A B C OF THE STEEL SQUARE 1 33

— RU LE See Fig . 9 2 .

Blade . ' Common Side Rafter 1 5 ' Longe st Jack 1 3 8 6 th 1 1 ’

' 5th 9 9 4th 7 ’ 3d 5' 1 0 2d 3 ' ' " l st 1 1 1

Blade gives Cut of Jacks , also Sheathing .

These matters have been discussed at length . i n trade j ourn als and also in my larger vol

umes on The Practical Uses of the Steel Square , but the foregoing treatment of the subj ect is on somewhat different lines and will prove i n

teresti n g.

On t John Wilberforce , Toronto , , wants to know if a wreath piece for a single - pitch rail w ith level landing can be set out with the Steel Square .

A : Yes m n swer , the proble can be solved as follows Set out on a board the plan of the wreath A

( Fig . Draw the outside circle and the 1 34 A B c or T H E STEEL SQUARE

e inside and center lin of same , showing also the j oints. Set out the pitch off the shank ; square up the center outside and inside lines from the plan on to the pitch The thickness of the wreath piece is found by drawi ng a section of t rail under the pitch line B . Se ou t again the half- width of the well ; square off the pitch lines to the half width ; this gives m j or and minor

Fig . 9 4

l s w e axes of the e lip e , as sho n in the d velopment

( Fig . Lay the Square on the axis . Get c a light pie e of lath , drive in a nail at the half

at or maj or , and one the half min ; describe the inner ellipse line on the piece of timber from which the wreath is to be formed ; pull out the nails , and repeat the process for the center and outside lines . Draw the shank and also the pot

1 36 A B c or THE STEEL SQUARE hand until it is down level at the shank end . i The top is cut first , and the saw should sk m

long the outside top arris , giving a sweep that cannot be excelled in grad

nation of curve . Then set a gauge

s to the thickne s of the rail , mark a s line on the in ide of the wreath , and

cut as before : With a little practice a wreath can be turned off the band saw ready for molding . When the e shank is too long , it is always bett r to nail the bed block on top of the

n s wreath , and cut it upside dow , thu getting the curve portion near the

table . Then the shank can be run in with the band saw when the block i s knocked off . T he foregoing is for a single - pitch w r e a t h a s u s e d f o r tai rs with level landings and narrow wells . bed W here the rails are pitched both ways , the block has to be cut at the double inclination . ( See preceding answers .) IND EX

A . B . C .

ST EEL SQUARE— T HE ST E EL SQUARE

AND I T S USE S .

DI V I SION A . Preface I ntroductory remarks Some useful advice

. Framing posts , girts and braces Testing a steel square

Practical u ses of the steel square . Some rules for roof Oct agon rules

Line s on Steel square explained . V arieties of squares ’ Bridge- builder s square Crenelated square Test diagrams Degrees on the square .

D IV I SION B . I ntroductory Slotted fence Laying out stairs i i I NDEX

Laying out rafters Meta l fences Fence adj ust ed f or stair strings Brace rules and diagrams Regular and irregular runs Roof framing Cutting rafters Octagon rafter bevels Hip and valley rafters Jack rafters

r Bevels for hips , valleys and j ack rafte s . Measuring raft Diff erent pitches f or roofs Some pointers in roof framing Roof diagrams

R of ra t s . ise and run f ers , hip and j acks Cuts and bevels for rafters Unequal pitches Hip- roof with deck

DI V I SION C.

Introdu ctory Diagram of hip- roof 98 To cu t j ack rafters 1 00 Hopper mi ters 1 01 Questions and answers f or correspondents. 1 02 Joints for obtuse or acute angles 1 02 Drawing circle with squ are . 1 00