,,abc                                   
,,of ,,the                              
,,steel ,,square                        
,,and ,,its ,,uses        being a       
condensed compilation from the          
copyrighted works of ,fred ,t4          
,hodgson1 author of 8,,the ,,steel      
,,square ,,and ,,its ,,uses10           
8,,practical    ,,carpentry0 and        
numerous other works on building and    
construction    ,the present compilation
 and new matter is made up into three   
divisions--,a1 ,b and ,c4               
,,division ,a    ,this ,division        
describes the various kinds of squares1 
their markings1  their uses1 and        
application in the solution of simple   
problems4                               
,,division ,b    ,this ,division shows  
how the ,square may be used for         
obtaining the cuts1  bevels1 and lengths
 of all sorts of rafters for roofs of   
every  description4 ,it also shows      
methods for finding ,hopper and other   
bevels1  brace cuts and lengths1 and    

raking cornices4                        
,,division ,c    ,this shows what no    
other work on the ,steel ,square does1 a
 number of easy  solutions of           
,handrailing ,problems1 by the square4  
,something that has not  been done or   
attempted in book form before4 ,this    
division is made up  mostly of questions
 and answers from practical mechanics4  
,,compiled ,,and ,,brought ,,down ,,to  
,,date ,,by                             
,,fred ,t4 ,,hodgson                    
,,wilmette1 ,,illinois                  
,,frederick ,j4 ,,drake  ,,co4          
,,publishers                    ,printed
 in the ,united ,states of ,america     
,,the ,,steel ,,square ,,and ,,its      
,,uses4                                 
,,introductory ,,remarks4               
,division ,a4      ,i will not attempt  
in this small treatise1 to give an      
historical account  of the origin1      
growth and development of the square1 as
 the subject has  been treated of at    
length in my larger works1 as ,i do not 

care to pad  out these pages with matter
 that is not of a severely practical    
nature4    ,suffice it to say1 that     
while iron squares1 figured on their    
faces in  inches and feet1 and smaller  
divisions1 have been made in ,england   
and  ,belgium for #bjj years or more1   
the genuine steel square1 as we now know
  it1 is a purely ,american product1 and
 it has no equal1 as no ,european       
manufacturer has as yet been able to    
turn out a square anything like as  good
 or perfect in finish1 graduation1 or   
general get-up1 as ,sargent   ,co41 of  
,new ,haven1 ,conn42 ,nicholls ,co41    
,ottumwa1 ,iowa2 and ,the ,peck1  ,stow 
,wilcox ,co41 ,southington1 ,conn4      
,squares made by any one of these  firms
 named1 may be relied upon as being as  
near perfect as it is  possible to make 
them in everything that pertains to     
accuracy1  durability and general       
finish4 ,the ,american workman should   
feel proud of  the fact that he         
possesses a ,steel ,square of purely    

,home production  which has no equal in 
the world4    ,there is nothing of more 
importance to a young man who is        
learning the  business of house-joinery 
and carpentry1 than that he should make 
himself thoroughly conversant with the  
capabilities of the tools he  employs4  
,it may be that1 in some of the rules   
shown in this work1 the  result could be
 attained much readier with other aids  
than the square2  but the progressive   
mechanic will not rest satisfied with   
one method of  performing operations    
when others are within his reach4    ,in
 the hand of the intelligent mechanic   
the square becomes a simple  calculating
 machine of the most wonderful capacity1
 and by it he solves  problems of the   
kinds continually arising in mechanical 
work1 which by  the ordinary methods are
 more difficult to perform4    ,the     
great improvement which the arts and    
manufactures have attained  within the  
last fifty years1 renders it essential  
that every person  engaged therein      

should use his utmost exertions to      
obtain a perfect  knowledge of the trade
 he professes to follow4 ,it is not     
enough1  nowadays1 for a person to have 
attained the character of a good        
workman2  that phrase implies that      
quantum of excellence1 which consists in
  working correctly and neatly1 under   
the directions of others4 ,the  workman 
of to-day1 to excel1 must understand the
 principles of his  trade1 and be able  
to apply them correctly in practice4    
,such a one has a  decided advantage    
over his fellow-workman2 and if to his  
superior  knowledge he possesses a      
steady manner1 and industrious habits1  
his  efforts cannot fail of being       
rewarded4    ,it is no sin not to know  
much1 though it is a great one not to   
know all  we can1 and put it all to good
 use4 ,yet1 how few mechanics there are 
who  will know all they can8 ,men apply 
for employment daily who claim to be    
finished mechanics1 and profess to be   
conversant with all the ins and  outs of

 their craft1 and who are noways        
backward in demanding the  highest wages
 going1 who1 when tested1 are found     
wanting in knowledge of  the simplest   
formulas of their trade4 ,they may1     
perhaps1 be able to  perform a good job 
of work after it is laid out for them by
 a more  competent hand2 they may have a
 partial knowledge of the uses and      
application of their tools2 but1        
generally1 their knowledge ends here4   
,yet some of these men have worked at   
this trade or that for a third of a     
century1 and are to all appearances1    
satisfied with the little they  learned 
when they were apprentices4 ,true1      
mechanical knowledge was not  always so 
easily obtained as at present1 for      
nearly all works on the  constructive   
arts were written by professional       
architects1 engineers1  and designers1  
and however unexceptionable in other    
respects1 they were  generally couched  
in such language1 technical and         
mathematical1 as to be  perfectly       

unintelligible to the majority of       
workmen2 and instead of  acting as aids 
to the ordinary inquirer1 they enveloped
 in mystery the  simplest solutions of  
every-day problems1 discouraging        
nine-tenths of  workmen on the very     
threshold of inquiry1 and causing them  
to abandon  further efforts to master   
the intricacies of their respective     
trades4    ,of late years1 a number of  
books have been published1 in which the 
authors and compilers have made         
commendable efforts to simplify matters 
pertaining to the arts of carpentry and 
joinery1 and the mechanic of  to-day has
 not the difficulties of his            
predecessors to contend with4 ,the      
workman of old could excuse his         
ignorance of the higher branches of his 
trade1 by saying that he had no means of
 acquiring a knowledge of them4  ,books 
were beyond his reach1 and trade secrets
 were guarded so  jealously1 that only a
 limited few were allowed to know them1 
and unless  he was made of better stuff 

than the most of his fellow-workmen1 he 
was  forced to plod on in the same      
groove all his days4    ,not so with the
 mechanic of today2 if he is not well up
 in all the  minuti of his trade1 he has
 but himself to blame1 for although     
there is  no royal road to knowledge1   
there are hundreds of open ways to      
obtain  it2 and the young mechanic who  
does not avail himself of one or other  
of  these ways to enrich his mind1 must 
lack energy1 or be altogether           
indifferent about his trade1 and may be 
put down as one who will never  make a  
workman4    ,i have thought that it     
would not be out of place to preface    
this work on  the 8,steel ,square10 with
 the foregoing remarks1 in the hope that
 they  may stimulate the young mechanic1
 and urge him forward to conquer what   
at best are only imaginary difficulties4
 ,a willing heart and a clear  head will
 most assuredly win honorable           
distinction in any trade1 if they  are  
only properly used4 ,indeed1 during an  

experience of many years in  the        
employment and superintendence of       
mechanics of every grade1 from the      
green 8wood-haggler0 to the finished and
 accomplished workman1 ,i have          
invariably discovered that the finished 
workman was the result of  persistent   
study and application1 and not1 as is   
popularly supposed1 a  natural or       
spontaneous production4 ,it is true that
 some men possess  greater natural      
mechanical abilities than others1 and   
consequently a  greater aptitude in     
grasping the principles that underlie   
the  constructive arts2 but1 as a rule1 
such men are not reliable2 they may  he 
expert1 equal to any mechanical         
emergency1 and quick at mastering       
details1 but they are seldom thorough1  
and never reliable where long  sustained
 efforts are required4    ,the mechanic 
who reaches a fair degree of perfection 
by experience1  study and application is
 the man who rises to the surface1 and  
whose  steadiness and trustworthiness   

force themselves on the notice of       
employers and superintendents4 ,i have  
said this in order to give              
encouragement to those young mechanics  
who find it up-hill work to  master the 
intricacies of the various arts they are
 engaged in1 for they  may rest assured 
that in the end work and application    
will be sure  to win2 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 occupation4    ,it must not be    
supposed that the work here presented   
exhausts the  subject4 ,the enterprising
 mechanic will find opportunity for     
using the  square in the solution of    
many problems that will crop up during  
his  daily work1 and the principles     
herein laid down will aid very much     
towards correct solutions4 ,in framing  
roofs1 bridges1 trestle-work1 and       

constructions of timber1 the ,steel     
,square is a necessity to the ,american 
carpenter2 but only a few of the more   
intelligent workmen ever use it  for    
other purposes than to make             
measurements1 lay off the mortices and  
tenons1 and square over the various     
joints4 ,now1 in framing bevel work  of 
any description1 the square may be used 
with great advantage and  profit4       
,posts1 girts1 braces1 and struts of    
every imaginable kind may be  laid out  
by this wonderful instrument1 if the    
operator will only study  the plans with
 a view of making use of his square for 
obtaining the  various bevels1 lengths  
and cuts required to complete the work  
in hand4  ,tapering structures--the most
 difficult the framer meets with--do not
  contain a single bevel or length that 
can not be found by the square  when    
properly applied1 and it is this fact ,i
 wish to impress on my  readers1 for it 
would be impossible1 in this work1 to   
give every  possible application of the 

square to work of this kind4 ,i have1   
therefore1 only given such examples as  
will enable any one to apply some  one  
of them to any work in hand4    ,in the 
foregoing sketch ,i have given a few    
hints as to the kind of  square to      
purchase when it is necessary to buy2 in
 many cases1 however1  this book will   
find its way into the hands of mechanics
 and others1 who  will have old and     
favorite squares in their chests or     
workshops1 and who  will not care to    
dispose of a 8well-tried friend0 for the
 purpose of  filling its place with     
another1 simply because ,i have         
recommended it4 ,to  these workmen ,i   
would say that ,i do not advise a       
change1 provided the  old square is     
true1 and the inches and sub-divisions  
are properly and  accurately defined4 ,i
 wish it distinctly understood that old 
squares1 if  true1 and marked with      
inches and sub-divisions of inches1 will
 perform  nearly every solution         
presented in this book4    ,the lines   

and figures formed on the squares of    
different make1 sometimes  vary1 both as
 to their position on the square1 and   
their mode of  application1 but a       
thorough understanding of the           
application of the  scales and lines    
shown on any first-class tool1 will     
enable the student  to comprehend the   
use of the lines and figures exhibited  
on other  first-class squares4    ,to   
insure good results1 it is necessary to 
be careful in the selection  of the     
tool4 ,the blade of the square should be
 #bd inches long1 and two  inches wide1 
and the tongue from #ad to #ah inches   
long and #a inches  wide4 ,the tongue   
should be exactly at right angles with  
the blade1 or in  other words the       
8square0 should be perfectly square4    
,to test this question1 get a board1    
about #ab or #ad inches wide1 and four  
feet long1 dress it on one side1 and    
true up one edge as near straight  as it
 is possible to make it4 ,lay the board 
on the bench1 with the  dressed side up1

 and the trued edge towards you1 then   
apply the square1  with the blade to the
 left1 and mark across the prepared     
board with a  penknife blade1 pressing  
close against the edge of the tongue2   
this  process done to your satisfaction1
 reverse the square1 and move it until  
the tongue is close up to the knife     
mark2 if you find that the edge of  the 
tongue and mark coincide1 it is proof   
that the tool is correct  enough for    
your purposes4 ,later on1 ,i will show  
by diagram how this test  is performed4 
,this1 of course1 relates to the outside
 edge of the blade1 and the  outside    
edge of the tongue4 ,if these edges     
should not be straight1 or  should not  
prove perfectly true1 they should be    
filed or ground until  they are straight
 and true4 ,the outside edge of the     
blade should also be  8trued0 up and    
made exactly parallel with the inside   
edge1 if such is  required4 ,the same   
process should be gone through on the   
tongue4 ,as a  rule1 squares made by    

firms of repute are perfect1 and require
 no  adjusting2 nevertheless1 it is well
 to make a critical examination  before 
purchasing4    ,the next thing to be    
considered is the use of the figures1   
lines1 and  scales1 as exhibited on the 
square4 ,it is supposed that the        
ordinary  divisions and sub-divisions of
 the inch1 into halves1 quarters1       
eighths1  and sixteenths are understood 
by the student2 and that he also        
understands how to use that part of the 
square that is subdivided into  twelfths
 of an inch4 ,this being conceded1 we   
now proceed to describe the  various    
rules as shown on all good squares2 but 
before proceeding  further1 it may not  
be out of place to state1 that on the   
squares  recommended in this book1 one  
edge is subdivided into thirty-seconds  
of  an inch4    ,this fine sub-division 
will be found very useful1 particularly 
so when  used as a scale to measure     
drawings made in half1 one-quarter1     
one-eighth or one-sixteenth of an inch  

to the foot4                            
,,practical ,,uses ,,of ,,the           
,,steel ,,square    ,we now take up a   
square void of any attachments1 and one 
which has  become quite popular in the  
west and the middle southern states4 ,i 
refer  to the 8,nicholls ,square10 a    
representation of one side of which is  
shown  at ,fig4 #a4 ,this square is a   
new one on the market1 and presents some
  advantages over many now being sold4  
,the manufacturers direct special       
attention to the fact that the board    
measure has been replaced by a  simple  
rule for framing1 and that there is to  
be found the lengths and  figures giving
 the cuts for an entire roof1 also the  
cuts for cornice of  the same4 ,the     
tongue on the square is #a inches wide1 
thus making it  convenient for spacing1 
as much of the dimension lumber is #a   
inches  thick4 ,the general directions  
for using this square--a copy of which  
is  given to every purchaser of a       
square--are presented herewith1 so that 

the  reader will be able himself to     
judge of the merits of the tool4 ,these 
squares are numbered or graded according
 to the graduation marks and  quality of
 finish4    ,illustration3 ,fig4 #a4    
8,the face of a square is the side on   
which we stamp our name4 ,the  reverse  
is the back4 ,the longer arm is the     
body1 the other is the  tongue4         
,framing ,rule4--,the first line of     
figures gives the length of common      
rafters for one foot run4    ,the second
 line of figures gives the length of hip
 or valley rafters for  one foot run4   
,the third line of figures gives the    
length of first jack rafter and the     
difference in the length of the others  
spaced #af inches on centers4    ,the   
fourth line of figures gives the length 
of first jack rafters and  the          
difference in the length of the others  
spaced #b feet on centers4    ,the fifth
 line of figures gives the side cut of  
jack rafters against hip  or valley     
rafters4    ,the sixth line of figures  

gives the side cut of hip or valley     
rafter  against ridge board or deck4    
,the seventh line of figures gives the  
cuts of sheathing and shingles in       
valley or hip1 for example3    #a4 ,if  
your roof is raised #h inches to the    
foot1 or1 as it is called1  third pitch1
 under #h on the first line are the     
figures #ad4db4 ,this is  the length of 
common rafters for one foot run4 ,if the
 building is #af  feet wide half the    
width of building would be the run of   
common rafter4  ,in this case it would  
be #h2 multiply #ad4db by #h1 you have  
#aae4cf inches1  or #i feet #g inches4  
#b4 ,to obtain the bottom and top cuts  
of common rafter use the figures #ab  on
 body and #h on tongue2 #ab side gives  
bottom cut1 #h side gives top cut2  the 
same figures give bottom and top cuts   
for jack4    ,on the second line under  
#h are the figures #ah4gh2 multiply     
these figures  by #h1 which is the run  
of the common rafter4 ,this gives       
#aej4bd1 or #ab  feet #f inches4 ,this  

is the correct length of hip or valley  
rafter4 ,to  obtain the bottom and top  
cuts for hip or valley rafters1 use the 
figures #ag on body and #h on tongue2   
#ag side gives bottom cut1 #h side      
gives top cut4    ,this is all the      
figuring necessary to be done4 ,the     
reason for giving the  lengths for one  
foot of common and hip or valley rafters
 is that it will  work in all cases     
regardless of width of buildings4    #c4
 ,on the third line under #h are the    
figures #ai inches4 ,this is the  length
 of first jack rafter1 also the         
difference in the length of the  others 
spaced #af inches on centers4 ,for      
example1 the first jack being  #ai      
inches1 the second jack would be #c feet
 #b inches2 make each one #ai  inches   
longer than the other4    ,on the fourth
 line under #h are the figures #b feet  
#d inches4 ,this is the  length of the  
first jack rafter1 and the difference in
 the length of the  others spaced #b    
feet centers4    ,on the fifth line     

under #h are the figures #aj and #ab4   
,by placing square  on stock to be cut  
at these figures #aj on body1 #ab on    
tongue1 and  marking on #ab side this   
gives side cut of jacks against hip or  
valley  rafter4    ,on the sixth line   
under #h are the figures #i and #aj4 ,by
 placing square on  stock to be cut at  
these figures1 #i on body and #aj on    
tongue1 and  marking on the #aj side1   
this gives side cut of hip or valley    
rafter  against ridge board or deck4    
,on the seventh line under #h are       
figures #ab and #aj4 ,by placing square 
on  stock to be cut at these figures #ab
 on body1 #aj on tongue1 and marking  on
 the #aj side this gives the cut of     
sheathing and shingles in valley or     
hip4    ,remarks4--,to obtain the       
lengths and cuts be careful to use the  
figures  under whatever figure your roof
 raises to the foot4 ,if your roof      
raises  #ab inches to the foot1 or half 
pitch1 look under #ab1 and so on in all 
cases4 ,in cutting jack rafters allow   

for half the thickness of hip or  valley
 rafters as lengths given on square are 
to center lines4    ,note4--,the figures
 on the square1 giving side cuts of     
jacks1 will also  give the correct miter
 cuts for moulding in the valley at the 
junction  of two gables1 also miter cuts
 for gable mouldings where it intersects
  with level mouldings at the end of    
building4    ,the figures giving cuts of
 sheathing in valley or hip also give   
cuts for  mitering level planceer with  
gable planceer1 also the miter cuts     
where  two gable planceers intersect1   
also the cut for planceer on gable end4 
,to obtain the bottom and top cuts of   
hip or valley rafter use the figure  #ag
 on body1 and whatever figure your roof 
raises to the foot on tongue4  ,this    
will give you the correct cuts in all   
cases4    ,to obtain the bottom and top 
cuts of common rafters and jack rafters 
use  the figure #ab on body1 and        
whatever figure your roof raises to the 
foot  on tongue4 ,this gives correct    

cuts in all cases4 ,always remember that
  the cut comes on the tongue1 or last  
named figure4 ,it is so arranged in  all
 cases4    ,octagon1 8,eight-square0    
,scale4--,this scale is along the middle
 of the  face of the tongue1 and is used
 for laying off lines to cut an 8eight  
square0 or octagon stick of timber from 
a square4    ,suppose the figures ,a1   
,b1 ,c1 ,d1 ,fig4 #b1 is the butt of a  
square stick of  timber #ff inches4     
,through the center draw the lines ,,ab 
and ,,cd parallel  with the sides and at
 right angles to each other4    ,with   
the dividers take us many spaces 7#f7   
from the scale as there are  inches in  
the width of the stick1 and lay off this
 space on either side  of the point ,a  
as ,aa and ,ab2 lay off in the same way 
the space from the  point ,b as ,bd and 
,be2 also ,cf and ,cg and ,db and ,de4  
,then draw the lines  ab1 cd1 cf and gh4
 ,cut off the solid angle ,e1 also ,f1  
,g and ,h2 there is  left an octagon1 or
 8eight square0 stick4 ,this is nearly  

exact4    ,brace ,measure4--,this is    
along the center of the back of the     
8tongue10  and gives the length of the  
common brace4    #ah-ac #be4de in the   
scale means that if the run is #ah      
inches on the post  and the same on the 
beam1 then the brace will be #be #de-ajj
 inches4    ,if the run is #ba inches on
 both beam and post1 then the brace will
 be #bi  #gj-ajj inches4    ,care of    
,square4--,never use emery or sand paper
 on nickel or black  finished squares4  
,when through using put on a few drops  
of oil4 ,do not  put your square away   
with finger marks on it2 nothing rusts  
it so  quickly as perspiration40        
,illustration3 ,fig4 #b4    ,it will be 
seen that these squares adapt themselves
 to other work as  well as to framing1 a
 quality very few of the combination    
squares  possess1 and while combination 
squares have their special uses and     
should be in the tool chest of every    
expert workman1 the square pure and     
simple1 like this of ,nicholls or       

similar ones1 should never be absent    
from the 8kit0 of the ordinary workman1 
for with it1 if he thoroughly           
understands it1 he can accomplish all   
that is possible even with a            
combination square4 ,if he is not       
8posted0 the workman should procure     
some one or more of the many devices or 
helps for getting bevels1  angles1      
lengths and cuts1 for rafters1 braces1  
hips and jacks as  advertised by        
,riesmann1 ,woods1 and others4          
,illustration3 ,fig4 #c4    ,with these 
aids and a good true and honest steel   
square the workman can  accomplish      
almost all that can be done with this   
tool1 or all that he  will be called    
upon to execute by aid of the square4   
,these squares are furnished by the     
manufacturers either in polished  steel1
 nickel plate or oxidized copper4 ,the  
latter style is quite  popular with some
 workmen1 because of its not getting so 
hot when  exposed to the rays of the    
sun4    ,illustration3 ,fig4 #d4    ,the

 two sides of the square1 shown at ,fig4
 #c1 represent the carpenters'  popular 
square1 ,no4 #ajj4 ,this square has been
 a special favorite with  workmen for   
nearly thirty years1 and is still looked
 upon by many as  being the ne plus     
ultra of steel squares4 ,i show both    
sides of the  square in order to enable 
the workman to see1 before he buys1 the 
kind  of tool he will get4 ,like the    
,nicholls square1 this may be obtained  
in  polished steel1 nickel plated1 or   
oxidized copper as the purchaser may    
desire4    ,illustration3 ,fig4 #e4     
,i show the complete square1 reduced to 
page size4 ,sometimes this square  is   
catalogued by dealers as ,no4 #ajjj1    
practically1 however1 it is the  same   
square as the ,no4 #ajj4 ,if we examine 
this square we will find on  the tongue 
near its junction with the blade a      
series of lines and cross  lines 7see   
,fig4 #d71 making a figure known as the 
8diagonal scale40 ,this  scale is drawn 
to a larger size at ,fig4 #e and is     

shown alone and is used  for taking off 
the hundredths of an inch4 ,the line ab 
is here an inch  long1 and is divided   
into ten equal parts2 the line cd being 
also  divided into ten equal parts1 and 
diagonal lines are then drawn           
connecting the points as shown in the   
diagram4 ,suppose we wish to take  off  
#gf-ajj of an inch1 we proceed as       
follows3 ,count off seven spaces  from  
c1 e1 g1 which equals #gj-ajj of an     
inch2 then count up the  diagonal line  
until the sixth horizontal line1 e1 is  
reached1 when e  f will equal the       
required distance of #gf-ajj of an inch1
 which is a  trifle over  of an inch4   
,illustration3 ,fig4 #f4    ,quoting    
from the table of directions given in   
,sargent's circular  describing this    
square1 we have1 for rafter cuts1 the   
following  explanation3 8,this run of a 
rafter set up in place is the horizontal
  measure from the extreme end of the   
foot to a plumb-line from the ridge     
end--from ,a to ,b1 ,fig4 #f4           

,illustration3 ,fig4 #g4    8,the rise  
is the distance from the top of the     
ridge end of the rafter to  the level of
 the foot4 ,from ,c to ,d1 ,fig4 #g4    
8,the pitch is the proportion that the  
rise bears to the whole width of  the   
building4 ,the illustration1 ,fig4 #h1  
shows one-third pitch2 the rise  of #h  
foot being one-third of the width of the
 building4    ,illustration3 ,fig4 #h4  
8,the cuts or angles of a rafter are    
obtained by applying the square so  that
 the #ab-;inch mark on the body and the 
mark on the tongue that  represent the  
rise shall both be at the edge of the   
rafter4 ,the  illustration1 ,fig4 #i1   
shows #h foot rise1 the line ,a the cut 
for the  ridge end of the rafter and ,b 
the cut for foot end40    ,illustration3
 ,fig4 #i4    ,the portion of square    
shown at ,fig4 #aj exhibits the tool    
having on its  face a table of the run1 
rise and pitch of rafters1 being        
specially  figured for this purpose1 and
 shows the measure of the rafter for any

  one of seven pitches of roof based    
upon the length of the horizontal       
measurement of the building from the    
center to the outside4    ,the following
 table1 which was prepared especially   
for this square1  shows the manner of   
working the square3    ,illustration3   
,fig4 #aj4                              
,,rafter ,,table ,,directions4    ,the  
rafter table and the outside edge of the
 back of the square1 both on  body and  
tongue1 are in twelfths4 ,the inch marks
 may represent inches or  feet1 and the 
twelfth marks may represent twelfths of 
an inch or  twelfths of a foot 7that is1
 inches7 as a scale4 ,the rafter table  
is  used in connection with the marks   
and figures on the outside edge of the  
square4    ,at the left end of the table
 are figures representing the run1 the  
rise and the pitch4    ,in the first    
column the figures are all #ab1 which   
may be used as #ab  inches or #ab feet1 
and they represent a run of #ab4    ,the
 second column of figures is to         

represent various rises4    ,the third  
column of figures in fractions          
represents the various  pitches4        
,these three columns of figures show    
that a rafter        with a run of #ab  
and a rise of #d has #a-f pitch1        
with a run of #ab and a rise of #f has  
#a-d pitch1        with a run of #ab and
 a rise of #h has #a-c pitch1    and so 
on to the bottom of the figures4    ,to 
,find the ,length of a ,rafter4--,for a 
roof with #a-f pitch 7or the rise  #a-f 
the width of the building7 and having a 
run of #ab feet1 follow in  the rafter  
table the upper #a-f pitch ruling1 find 
under the graduation  figure #ab the    
rafter length required1 which is #ab #g 
#aj1 or #ab feet and #g  #aj-ab inches4 
,for  pitch 7or the rise  the width of  
the building7 and run #ab feet1  the    
rafter length is #af #aa #h1 or #af feet
 #aa #h-ab inches4    ,if the run is #be
 feet1 add the rafter length for run of 
#bc feet to the  rafter length for run  
of #b feet4    ,when the run is in      

inches1 then in the rafter table read   
inches and  twelfths instead of feet and
 inches4 ,for instance3    ,if with     
pitch the run is #ab feet #d inches1 add
 the rafter length of #ab  feet to that 
of #d inches1 as follows3      ,for run 
of #ab feet the rafter length is        
#af feet #aa #h-ab inches4    ,for run  
of #d inches the rafter length is       
#e #h-ab inches4       ,total           
#ag feet #e #d-ab inches4    ,the brace 
measure on these squares is along the   
center of the back of  the tongue1 and  
gives the length of the common braces as
 shown in ,fig4  #aa4 ,examples are     
shown in the blade as at the point      
marked #bd #cj1 which  means #bd inches 
on the post and #ah inches on the beam  
or girt1 which  make the brace #cj      
inches long from point to point         
according to the rule  given4 ,an       
application of this rule is shown at    
,fig4 #ab1 where #cf inches  are laid   
off on both post and beam1 which gives  
the length of the brace  from point to  

point #ej4ia inches1 or very nearly #d  
feet #c inches4 ,other  dimensions are  
shown in the square4 ,there is also a   
scale of  one-hundredths1 or one inch   
divided into #ajj equal parts4    ,the  
octagon scale on this square runs along 
the middle of the face of  the tongue1  
and is used for laying off lines to cut 
an 8eight square0 or  octagon stick of  
timber from a square one4               
,illustration3 ,fig4 #aa4               
,illustration3 ,fig4 #ab4               
,illustration3 ,fig4 #ac4    ,suppose   
the figure ,,abcd 7see ,fig4 #b7 is the 
butt of a square stick of  timber #fx#f 
inches4 ,through the center draw the    
lines ,,ab and ,,cd parallel  with the  
sides and at right angles to each other4
 ,with a pair of  compasses take as many
 spaces 7#f7 from the scale as there are
 inches in  the width of the stick1 and 
lay off this space on either side of the
  point ,a1 as ,aa and ,ab2 lay off in  
the same way the same space from the    
point ,b as ,bd1 ,be2 also ,cf1 ,cg and 

,db1 ,dc4 ,then draw lines ab1 cd1 ef   
and gh4 ,cut off the solid angle ,e1    
also ,f1 ,g and ,h4 ,this will leave an 
octagon1 or eight-sided stick1 which    
will be found nearly exact on all       
sides4    ,the board measure1 known as  
the 8,essex ,board ,measure10 ,fig4 #ac1
 is made  use of in figuring these      
squares1 and is used as follows3        
,figures #ab and  #ag in the graduation 
marks on the outer edge represent a     
one-inch board  #ab inches wide1 which  
is the starting point for all           
calculations4 ,the  smaller figures     
under the #ab represent the length4     
,a board #ab inches wide and #h feet    
long measures #h square feet1 and so on 
down the table4 ,therefore1 to get the  
square feet of a board #h feet long  and
 #f inches wide1 find the figure #h in  
the scale under the #ab-;inch           
graduation mark and pass the pencil     
along to the left on the same line  to a
 point below the graduation mark #f     
7representing the width of the  board71 

and you stop on the scale at #d1 which  
is #d feet1 the board  measure required4
 ,if the board is the same length and   
#aj inches wide1  look under the        
graduation mark #aj on a line with the  
figure #h before  mentioned1 and you    
will find #f #h-ab feet board measure2  
if #ah inches  wide then to the right   
under the graduation mark #ah and #ab   
feet is found  to be the board measure4 
,if #ac feet long and #g inches wide1   
find #ac in  the scale under the        
#ab-;inch graduation and on the same    
line under the  #g-;inch graduation will
 be found #g #g-ab feet board measure4  
,if the board  is half this length1 take
 half of this result2 if double this    
length1  then double this result4 ,for  
stuff #b inches thick double the figure4
    ,in this way the scale covers all   
lengths of boards1 the most common from 
#h feet to #ae feet being given4        
,this company also manufactures a square
 that is 8blued10 or apparently         
oxidized1 with all the figures on it    

enameled in white4 ,this is really a    
handsome tool1 and the white figures on 
a dark blue ground enable the  operator 
to see what figures he is looking for   
without waste of time and  straining of 
eyesight4    ,illustration3 ,fig4 #ad4  
,the bridge builders' steel square1     
which is illustrated in ,fig4 #ad1 is   
also made by this company4 ,this square 
has a blade three inches wide1  which is
 made with a slot down the center one   
inch wide4 ,the tongue is  the same as  
in the ,no4 #ajj square1 but has no     
figures for brace or  octagon rules4 ,it
 is not so handy for general purposes as
 the regular  square1 but for special   
purposes in bridge building1 or for     
laying out  very heavy timber structures
 it has special advantages1 as #c-;inch 
shoulders and #c-;inch tenons and       
mortises can be readily laid out with   
it4 ,another square1 shown in ,fig4 #ae1
 known as the 8machinists' square10  is 
made by this company4 ,it has a blade #f
 inches and a tongue #d inches  long1   

and is very finely finished4 ,this      
square is found very useful for  pattern
 makers1 piano and organ builders1 and  
where other especially  close work is   
required4 ,a number of other squares are
 made by this firm1  but as they are not
 intended for woodworkers' use1 ,i will 
not describe  them here4                
,illustration3 ,fig4 #ae4    ,i would   
not complete this description of        
,sargent's make of squares if ,i  failed
 to make mention of their 8bench        
square40 ,i give this name to it        
because of its fitness for bench        
purposes4 ,the square referred to has a 
blade #ab inches long and #a inches     
wide1 and a tongue #i inches long and   
#a inch wide4 ,the figuring on it is    
divided into inches1 half inches1       
quarter inches1 eighths and sixteenths  
of an inch4 ,this is a very handy       
square for bench and jobbing purposes1  
and can be used in many places  where   
the larger tool is unavailable1 and may 
on emergency be employed  for laying out

 rafters1 braces and similar work4 ,a   
square that was quite  popular some     
sixteen or eighteen years ago known as  
8,the ,crenalated  ,square10 an         
illustration of which is shown in ,fig4 
#af1 is still  preferred by many        
workmen4 ,the peculiarity of this square
 is that the  inner edge of the tongue  
is notched or crenalated1 as shown in   
the  illustration1 the notches being    
intended as 8gauge-points10 where a     
sharpened pencil may be inserted1 then  
the square may be drawn along the       
timber or board1 with the blade held    
snug against the edge1 as shown1  and   
mortises or tenons can be laid out at   
will4    ,besides being crenalated1     
these squares have all the advantages of
 other  squares1 and are well made and  
pleasant to handle4 ,they are made by   
the  manufacturers1 ,the ,peck1 ,stowe  
,wilcox ,co41 of ,southington1 ,conn41  
in  polished steel1 copper plated1      
blued1 with enameled white figures1 and 
in nickel plate4    ,illustration3 ,fig4

 #af4    ,it is the simplest of tools1  
and may be described as the mechanical  
embodiment of a right angle4 ,it must   
necessarily have some breadth in  order 
to give the tool necessary stability1   
and1 therefore1 as the  embodiment of a 
right angle it is of a form to give us  
both the exterior  and interior shape4  
,the blade of the square is made a      
little wider than  the tongue1 more for 
convenience1 ,i think1 than for any     
other reason1  for ,i have seen squares 
somewhat old1 to be sure1 and made long 
before  the tools which are now in most 
common use were sent out from the       
factory1 of which the blade and tongue  
were approximately of the same  width4  
,the blade of the square1 as commonly   
constructed1 is #b feet1 or #bd  inches 
long1 and the tongue somewhat less4 ,i  
have seen squares of which  the tongue  
and blade were of equal lengths1 and    
also those1 the blade of  which were    
considerably longer than those of the   
square of present make1  and still      

others of which the tongues were        
considerably shorter than is  now the   
rule4 ,but this is long ago4 ,the most  
commonly accepted  dimensions for a     
carpenter's square at the present time  
are1 blade #bd  inches long1 tongue #ah 
inches long1 blade #b inches wide and   
tongue #a  inches wide4 ,this gives for 
inside measurements blade1 #bb inches   
and  tongue #af inches4    ,i have      
described the square as the embodiment  
of a right angle4 ,if the  square is not
 a right angle1 or to use common terms1 
if the tool is 8out  of square10 that   
is1 if it is in the least inaccurate1   
its usefulness is  destroyed4 ,when the 
square is inaccurate instead of solving 
intricate  geometrical problems         
correctly it becomes a snare and a      
delusion1  leading to false results and 
misfits in general4 ,it is somewhat     
remarkable how few workmen test their   
squares4 ,i am disposed to believe  from
 long experience that comparatively few 
mechanics who buy steel  squares are    

cognizant of the possible defects that  
the tool may have and  of the tests     
which may be applied for the purpose of 
demonstrating its  accuracy4 ,before    
proceeding further1 therefore1 in the   
discussion of the  use of this          
instrument let us give brief attention  
to some of the simple  methods that may 
be employed for determining the accuracy
 of the tool4  ,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   
convenient1 and apply to them more or   
less of the  tests which follow1 merely 
for the purpose of practice1 and at the 
same  time to show to what extent the   
squares in use are correct4    ,fig4 #ag
 shows a very common method of testing  
the exterior angle of a  steel square4  
,two squares are placed against each    
other and a  straight-edge1 or against  
the blade of a third square4 ,if the    
edges of  the squares exactly coincide  

throughout the squares may be considered
  correct4    ,illustration3 ,fig4 #ag4 
,suppose1 however1 that there is a      
discrepancy shown by this test1 and     
that as the two squares are placed in   
the general position1 shown in the      
illustration1 they part at the heel1    
while touching at the ends of the       
blades1 or touching at the heel that    
they part at the ends of the  blades4   
,this evidently shows that one of the   
squares is inaccurate1 or  possibly that
 both are inaccurate4 ,how is the       
inaccuracy to be located8  ,the two     
squares may be placed face to face1 with
 the blades upward from  an even        
surface1 say the face of the third      
square or the jointed edge of  a board1 
and so held that their heels1 for       
example1 shall coincide4 ,then  glance  
at the edges of the blades4 ,if they    
exactly coincide it would  indicate that
 the error is evenly divided between the
 two squares1 a  very improbable        
occurrence4 ,compare the two squares in 

the reverse  position1 that is1 with the
 tongues extending upward4 ,then apply  
the  test shown in ,fig4 #ah1 and       
finally that shown in ,fig4 #ai4        
,illustration3 ,fig4 #ah4    ,by trying 
the squares one inside of the other1 as 
shown in ,fig4 #ah1 the  exterior angle 
is compared with the interior angle4 ,if
 the edges  throughout fit together     
tightly1 first using one square inside  
and then  the other1 it is almost       
conclusive evidence that both the       
squares are  accurate4    ,illustration3
 ,fig4 #ai4    ,by tests of the kinds   
just described among several squares1   
the mechanic  will soon perceive from   
the several ascertained results that one
 or the  other of the several squares   
that he is handling is more accurate    
than  all the others1 if not absolutely 
accurate4 ,there still remains the need 
of a test1 however1 to prove the        
absolute accuracy of the particular     
square which he believes to be about    
right4 ,on a drafting table1 or a       

smooth board1 let him next perform the  
following experiment1 which is  one of  
the several that might be mentioned in  
this connection3 ,draw a  straight line1
 ,,ab1 say three feet in length1 as     
shown in ,fig4 #ai4 ,this  may be done  
by a straight-edge4 ,use a hard pencil  
sharpened to a chisel  point4 ,with the 
compasses1 using ,a and ,b as centers1  
and with a radius  longer than one-half 
of ,,ab strike the arcs ,,cd and ,,ef4  
,then with the  straight-edge draw a    
straight line1 ,,gh1 through the        
intersection of the  arcs4 ,if the work 
is accurately done the resulting angles 
,,aoh1 ,,hob1 ,,bog1  and ,,goa will be 
right angles4 ,lay the square to be     
tested onto one of  these angles1 as    
shown in the illustration1 and with a   
chisel-pointed  pencil scribe along the 
blade and along the tongue4 ,if the     
lines thus  drawn exactly coincide with 
those first drawn it is satisfactory    
proof  that the square is accurate1 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 angle4    ,the method shown in 
,fig4 #ai anticipates the use of another
 tool besides  the square in making the 
test4 ,a right angle1 however1 may be   
drawn for  the purpose described by a   
method which uses only the square1 and  
which  does not require the services of 
any other tool1 or what is the same     
thing1 consider the tool itself to be   
the figure drawn1 and then measure  for 
the purpose of determining the accuracy 
of the figure4    ,various writers have 
discussed the properties of the         
right-angled  triangle1 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 perpendicular4 ,this is a      
well-known mathematical truth1 and it   
may be applied in the tests we are      
making4 ,those carpenters who have had  
occasion to lay out the foundations of  
houses are well acquainted with  the old

 rule frequently known as 8the #f1 #h   
and #aj10 which depends upon  the       
relationship of the squares of the      
perpendicular and the base to the       
square of the hypothenuse4 ,thus the    
square of #f is #cf1 the square of #h   
is #fd4 ,the sum of #cf and #fd is #ajj4
 ,and the square of #aj is #ajj4 ,now   
let  us make application of this rule to
 test the steel square4    ,for the sake
 of accuracy we want to take figures    
which are as large as  possible1 so as  
to reduce the possible error in         
measurement to the  smallest possible   
dimensions4 ,let us take for dimensions1
 #i1 #ab and #ae  inches4 ,that these   
will serve is easily demonstrated4 ,the 
square of #i is  #ha4 ,the square of #ab
 is #add4 ,the sum of these squares is  
#bbe1 and the  square of #ae is #bbe4   
,therefore1 if the tool that we are     
testing shows a  dimension of exactly   
#ae inches measured from #i on the      
outside of the  tongue to #ab on the    
outside of the blade1 as shown in ,fig4 

#bj1 it will  be proof that the square  
is correct4    ,it may be somewhat      
difficult to make a measurement of this 
kind on the  instrument itself1 with    
sufficient accuracy to be beyond        
dispute4 ,i  suggest1 therefore1 that   
the square be laid flat upon an even    
surface1  like a drawing table1 and that
 with a chisel-pointed pencil lines be  
scribed along the tongue and along the  
blade4 ,mark accurately the  distance of
 #i inches from the heel up the tongue1 
and #ab inches from the  heel along the 
blade4 ,then measure diagonally and see 
if the distance is  exactly #ae inches4 
,illustration3 ,fig4 #bj4    ,in what   
has preceded there has been a suggestion
 that the error due to  lack of         
precision in measurement is diminished  
if the figures are  increased in size4  
,if the size of the drafting table      
permits1 therefore1  extend the line    
drawn along the tongue of the square to 
#c feet4 ,extend  that drawn along the  
blade to #d feet4 ,in doing this care   

must be taken  that the lines thus      
extended are fair to the tool under     
examination1 for  if they are not drawn 
in a way to strictly coincide with the  
edges of  the square then the test is of
 no avail4 ,then measure from the ends  
of  these lines1 that is1 from a point  
#c feet from the heel up the tongue to  
a point #d feet from the heel along the 
blade4 ,if this diagonal distance  is   
exactly #e feet it will show that the   
angle represented by the heel of  the   
square1 as ,i have described it1 is a   
right angle1 and that1  therefore1 the  
test is accurate4    ,now let us next   
examine a little more carefully the     
relationship of the  square to          
frequently required lines4 ,it is a     
common thing among  carpenters to use   
#ab of the blade and #ab of the tongue  
for a right angle  or square miter4 ,why
 are these figures employed1 or to put  
the question  otherwise1 how is it      
determined that #ab and #ab are the     
proper figures8  ,perhaps the question  

can be made still clearer by another    
illustration4  ,it is common to say that
 #ab of the blade and #e of the tongue  
is correct  for the octagon miter4 ,how 
is this determined8 ,in ,fig4 #ba there 
is shown  a quarter circle1 ,,xg1       
described from the center ,c4 ,along the
 horizontal  line1 ,,ab1 the blade of   
the square is laid with #ab of the blade
 against  the center ,c1 from which the 
quadrant was struck4 ,now if we divide  
this  quadrant into halves1 thus        
establishing the point ,e1 and if from  
,e we  draw a line to the center ,c1    
which is #ab of the blade1 it will be   
found  that it cuts also #ab of the     
tongue4 ,if we complete the figure by   
erecting a perpendicular line from the  
point ,x1 and intersecting it with  a   
horizontal line from ,g1 thus           
establishing the point ,o1 it becomes   
very  evident that ,,ce is the miter    
line of a square4    ,illustration3     
,fig4 #ba4    ,if we bisect ,,xe1 thus  
establishing the point ,d1 and by the   

conditions  existing setting off in the 
quadrant a space equal to one-quarter of
 its  extent1 and if from ,d we draw a  
line to the center1 ,c1 corresponding1  
as  already mentioned1 with #ab on the  
blade1 we shall find that this line     
7,,dc7 cuts the tongue on the point #e  
7very nearly1 the exact figures  being  
#d #ca-cb inches74 ,the line ,,dc1 as   
above explained1 bisects the  eighth of 
a circle4 ,in other words1 it is the    
line of an octagon miter1  and          
therefore1 we say that for an octagon   
miter we take #ab on the blade  and #e  
on the tongue4    ,by dividing the      
quadrant into three equal parts1 as     
shown by ,,xg1 ,,gh and  ,,hg1 we obtain
 by drawing ,,gc the line corresponding 
to the hexagon miter4  ,this1 it will be
 observed1 cuts the tongue of the square
 at #g 7very  nearly1 the exact figures 
being #f #ae-af inches71 and1 therefore1
 we say  for hexagon miters we take #ab 
of the blade and #g of the tongue4      
,the question sometimes arises1 can the 

square be employed to describe a        
circle8 ,while the square may be used   
for describing a circle of any          
diameter1 providing the capacity of the 
square is not exceeded1 still  those who
 attempt to perform the work will very  
likely conclude before  they are through
 that other means are more satisfactory 
for regular use4  ,the way to proceed is
 indicated in ,fig4 #bb4 ,let it be     
required to  describe a circle1 the     
diameter of which is equal to ,,ed4     
,drive pins or  nails at these points   
and place the square as shown in the    
sketch4 ,place  a pencil in the interior
 angle of the square1 as shown at ,f4   
,then  gradually shift the square so    
that the pencil will move in the        
direction  of ,d1 always being careful  
to keep the inside of the blade and     
inside of  the tongue in contact with   
the pins or nails1 ,,ed4 ,after having  
described  the arc from ,f to ,d reverse
 the direction describing the arc from  
,f to  ,e4 ,then turn the square over   

and by similar means complete the other 
half of the circle4    ,illustration3   
,fig4 #bb4                              
,,the ,,steel ,,square ,,and ,,its      
,,uses4                                 
,division ,b4                           
,introductory4      ,having dealt with  
the more simple matters that can be     
dealt with by aid  of the ,steel        
,square1 we now take up some of the more
 difficult problems  that can be solved 
by aid of this useful tool4    ,among   
the problems and solutions offered1 are 
those of laying out  braces1 having     
regular or irregular runs1 rafters1 and 
roofing  generally1 ascertaining the    
length of hips1 their bevels1 cuts1     
pitches  and angles1 jacks1 cripples1   
ridges1 purlins1 collar beams1 and much 
other matter pertaining to hip or       
cottage roofs4    ,gables1 or saddle    
roofs are dealt with1 also mansard      
roofs1 taper  framing1 odd bevels1      
splays and other similar work4    ,i    
introduce in this division a few remarks

 regarding the fence made use  of when  
laying out rafters1 stairs or other     
bevelled work4 ,the  department also    
shows how to lay-out stair strings by   
aid of the square1  and many other      
things that will be found useful to the 
general workman4    ,illustration3 ,fig4
 #bc3 ,,double ,,slotted ,,fence4       
,illustration3 ,fig4 #bd4    ,a very    
good fence for the square may readily be
 made from a stick of  hardwood 7,fig4  
#bc7 about two inches wide1 one and a   
half inches thick  and two and a half   
feet long4 ,a saw kerf1 into which the  
square will  slide1 is cut from both    
ends leaving about #h inches of solid   
wood near  the middle4 ,the tool is     
clamped to the square by means of screws
 at  convenient points as shown4        
,another style of fence1 which is made  
of a  piece of hardwood1 has a single   
slot only as shown in ,fig4 #bd4 ,the   
square is slipped in and fastened in    
place by screws similar to the  first4  
,an application of the fence and square 

combined is shown at ,fig4  #be1 where  
the combination is used as a pitch-board
 for laying out stair  strings4 ,in this
 example the blade is set off at #aj    
inches1 which makes  the tread1 and the 
tongue shows the riser1 which is set off
 at #g inches4  ,the dotted line1 ce1   
shows the edge of the plank from which  
the string  is cut1 and h shows the     
fence1 a shows the bottom tread and     
riser4  ,in this example the riser shows
 the same height as the riser above it1 
namely1 #g inches4 ,this is wrong1 as   
the first riser should always be cut    
the thickness of the tread less than    
those above it1 as shown by the  dotted 
lines on the bottom of the string1 then 
when the tread is in  place it will be  
the same height from the top of the     
floor to the top of  the first tread1   
that the top of first tread is to top of
 second one and  so on4                 
,illustration3 ,fig4 #be4               
,illustration3 ,fig4 #bf4    ,suppose we
 wish to lay out a rafter having eight  

inches rise and twelve  inches run4 ,set
 the fence at the #h mark on the blade1 
,fig4 #bf1 and at  the #ab mark on the  
tongue1 clamping it to the square with  
#a screws4  ,applying the square and    
fence at the upper end of the rafter we 
get the  plumb-cut ,p at once4 ,by      
applying the square as shown twelve     
times  successively the required length 
of the rafter and foot-cut ,b is        
obtained4 ,in this case the twelve      
applications of the square are made     
between the points ,p and ,b4 ,run and  
rise must also be measured between      
these points4 ,if run is measured from  
the point ,b1 which will be the  outer  
edge of the wall plate1 it will be      
necessary to run a gauge line  through  
,b parallel to the edge of the rafter1  
and subtract a distance  from the height
 of the ridge to give us the correct    
rise4 ,the square  must then be applied 
to the line ,l4 ,a rafter of any desired
 rise and run  may be laid off in this  
manner by selecting proportional parts  

of the  rise and run for the blade and  
tongue of the square4 ,for a half-pitch 
roof use #ab in4 on both tongue and     
blade1 for a quarter-pitch use #f in4   
and #ab in41 for a third-pitch use #h   
in4 and #ab in41 etc4 ,the terms        
half-pitch1 quarter-pitch1 etc41 refer  
to the height of the ridge  expressed as
 a fraction of the span4    ,the line ,l
 is supposed to represent the path of   
the fence as it is slid  along the edge 
of the rafter4 ,this will be explained  
at greater length  in the following     
pages4    ,illustration3 ,fig4 #bg4     
,at ,fig4 #bg ,i show a method of laying
 out a rafter without making use of  a  
fence4 ,in this case the roof is        
supposed to be half-pitch1 so we take   
#ab and #ab on the square and apply it  
to the rafter as many times as  there   
are feet in half the width of the       
building1 which in this case  will be   
#ae feet1 as we suppose the building to 
be #cj feet wide4 ,as the  lower end of 
the rafter is notched to sit on the     

plate we must gauge off  a backing line1
 as shown1 to run into the angle of the 
notch4 ,this line  will be the line on  
which the gauge points #ab and #ab on   
the square must  start from each time4  
,starting from this notch apply the     
square1 keeping the twelve-inch mark  on
 both sides of the square carefully on  
the backing line1 and marking  off the  
rafter on the outside edges of the      
square4 ,repeat this until you  have    
fifteen spaces marked off1 then set back
 from your last mark half  the thickness
 of the ridge-board1 and with the square
 as before mark off  the rafter4 ,this  
will be the exact length and also the   
plumb-cut to fit  the ridge-board4 ,or  
if we take the diagonal of #ab by #ab1  
which is #ag1  and mark off #ae spaces  
of #ag in41 making the necessary        
allowance for the  half thickness of the
 ridge-board1 it will amount to the same
 thing1  every #ag in4 on the rafter    
being nearly equal to one foot on the   
level4    ,should the building measure  

#cj ft41 #i in4 in width--the half of   
which is  #ae ft41 #d in4--we take the  
fifteen spaces of #ab by #ab and then   
the #d  in4 on both sides of the square 
on the backing line as before4 ,this    
will  give us the extra length required4
 ,the same rule will apply to any       
portion of a foot there may be4         
,illustration3 ,fig4 #bh4               
,illustration3 ,fig4 #bi4    ,a fence1  
sometimes called a stair gauge1 is      
manufactured of metal by the  ,cheney   
,tower ,company1 ,athol1 ,mass41 which  
,i show at ,fig4 #bh1 and is  considered
 about the best thing of the kind4 ,it  
consists of a piece of  polished angle  
metal1 each side being  inch wide4 ,one 
side is slotted  to accommodate the     
heads of the set-screws and to allow the
 slides to be  fastened at the desired  
points4 ,the gauge is fastened to any   
square and  is useful for laying out    
stairs1 cutting in rafters1 cutting     
bevels or  other angles4 ,in marking off
 stairs with an #h-;inch rise and an    

#aa-;inch  tread the gauge would be     
fastened at #h inches on one end of the 
square  and #aa at the other end4 ,the  
square would then be laid on the plank  
with the face of the gauge against its  
edge and the mark made around the  point
 of the square4 ,this would be repeated 
until the required number of  steps were
 marked4 ,the gauges are made in two    
sizes1 #ah and #bh inches  long4 ,it is 
stated that mechanics who have used it  
find it one of the  handiest tools in   
their kits4    ,another style of fence  
is shown at ,fig4 #bi in conjunction    
with a slotted  square4 ,this1 perhaps1 
is the handiest of all the devices for a
 fence1  but it is expensive1 and as    
constructed requires a square with a    
slot in  each arm1 and as a rule workmen
 do not take kindly to squares with     
slots  in them4 ,a shows the square1 ,b 
the fence1 ,,ss set screws to hold the  
fence in position1 and ff the points of 
the square4    ,the application of the  
square and fence combined for laying out

 a housed  string for stairs is shown at
 ,fig4 #cj4 ,in this example the fence  
is a  single slotted one1 and three     
screws are employed to hold the square  
in  position4 ,the rise is seven inches 
and the tread is laid off nine inches   
on the blade4 ,the square at the foot of
 the string shows how the latter  should
 be finished to make the floor and the  
base-board4 ,in case no  pitch-board is 
required1 as the square when adjusted   
with fence1 as  shown1 does the work of 
the pitch-board4    ,illustration3 ,fig4
 #cj4    ,there are many other          
applications of the fence in connection 
with the  square that ,i may have cause 
to refer to as ,i proceed1 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 workman4 ,doubtless there  will  
be many descriptions and illustrations  
some of my readers will have  met with  
before1 or which they have been         
acquainted with for a long  time4 ,the  

great bulk of readers1 however1 will be 
new hands and  unacquainted with the use
 of the square beyond its simple        
application as  a squaring tool1 and    
what may appear to be a useless rule to 
the expert  or old hand will prove a    
choice tidbit to the beginner and will  
whet his  appetite for further knowledge
 on the subject4 ,indeed this book is   
prepared more particularly for the      
younger members of the craft1  although 
a majority of the older workers will    
find much in it that will  interest1    
amuse and instruct4    ,it will be seen 
that the fence or guide used in         
connection with the  square is1 after   
all1 a very simple matter1 and would1 no
 doubt1 suggest  itself to any clever   
workman who was laying off rafters with 
the square4                             
,,brace ,,rules4    ,illustration3 ,fig4
 #ca4    ,illustration3 ,fig4 #cb4      
,it will now be in order to show how the
 square can be used for getting  the    
lengths and bevels for braces of regular

 and irregular runs4 ,if we  wish to lay
 out a brace having a three-foot run on 
both post and beam1  the matter is quite
 simple1 for we can take #ab inches on  
the tongue and  #ab inches on the blade 
and transfer this distance three times  
on a  straight line and we have the     
extreme length of the brace from point  
to  point1 and by marking along the     
blade at one end of this length and     
along the tongue at the other end we    
also get the bevels4 ,this is easy  and 
simple enough1 and without further      
refinement will give the lengths  and   
bevels exactly for a flat-footed brace4 
,when the run is different  than the    
rise1 as in the example shown at ,fig4  
#ca1 the square is applied  in a        
somewhat different manner4 ,here we have
 a run of three feet and a  rise of four
 feet4 ,to get the proper length and    
bevels for a brace to  fit in this      
situation we must use #ab inches on the 
tongue and #af inches  on the blade1    
then the bevel of the upper end of the  

brace will be found  along the line of  
the tongue1 and the line of the blade   
will give the  bevel for the foot of the
 brace4 ,in this case the square is     
transferred  three times1 just as though
 the rise and run were both three feet2 
the  difference being made by dividing  
the odd foot into three equal parts of  
#d inches each and adding one part to   
the blade1 thus making the gauge  point 
on the blade #af inches instead of #ab  
inches1 which regulates the  extra      
length and the change in bevels4 ,a     
little study on the part of the  reader 
will reveal to him how the square may be
 set to gauge points so  as to make a   
brace suitable for any rise and run of  
any right-angled  frame work4    ,a     
brace intended for equal run and rise of
 four feet is shown at  ,fig4 #cb4 ,here
 we have the fence in use1 and the      
square is shown in all  its positions   
from start to finish in the formation of
 the brace4 ,the  gauge line marked     
#jjjj is the line from which the marks  

#ab and #ab are  supposed to measure1   
and this when squared over as shown     
leaves a butt1  or 8heel of the brace10 
which is to rest on a shoulder 8boxed0  
in both  beam and post4 ,the dotted     
lines on the ends of the brace show the 
tenons  for which mortises are made in  
both post and girt or beam4 ,it must be 
understood1 of course1 that this        
operation is only performed once for    
each kind of brace1 and that on a       
pattern made of some kindly wood1 such  
as pine1 cedar or whitewood4 ,for the   
pattern1 dress up a piece of wood  to #d
 inches wide if the braces are to be    
made of #dx#d-;inch stuff2 if for       
larger or smaller stuff then make the   
pattern the width of brace to  suit4    
,have the pattern of sufficient length2 
if for a #d-;foot run and  rise it will 
require to be not less than #f feet     
long4 ,run a gauge line  three-eighths  
of an inch from the straight or front   
edge1 as shown at  #jjjj1 and set the   
two #ab-;inch marks on this line1 then  

screw the fence  tight on the square    
with its sliding edge against the edge  
of the  pattern1 and then slide and mark
 as shown four times1 when the length   
and bevels of the brace will be         
obtained4 ,provide for the tenons beyond
  the lines shown by the square1 or for 
a 8flat-foot0 brace1 saw the  timber off
 on the lines shown on the edge of the  
square4 ,after the  pattern is made the 
fence and square may be laid aside1 as  
the pattern  can be used for any number 
of braces1 and when finished with on one
 job1  may be safely placed away to use 
again for the same 8run and rise0 when  
occasion arises4 ,the pattern may be any
 thickness from half an inch to  one    
inch4 ,the same rules may be observed in
 making patterns for any  regular or    
irregular runs and rises4    ,with      
regard to the brace rule as given on    
steel squares1 ,i may say  that there is
 some slight difference in the lengths  
given by different  makers--though      
nearly all modern makes figure up       

alike--but this  difference is so small 
that in soft wood framing it has no     
effect4 ,in  hardwood framing the framer
 never applies these rules1 but gets his
  lengths with the square and fence4    
,the length of any brace simply         
represents the hypothenuse of a         
right-angled triangle4 ,to find the     
hypothenuse1 extract the square root  of
 the sum of the square of the           
perpendicular and horizontal runs4 ,for 
instance1 if #f feet is the horizontal  
run and #h feet the perpendicular1  #f  
squared equals #cf1 #h squared equals   
#fd1 #cf plus #fd equals #ajj1 the      
square root of which is #aj4 ,these are 
the figures generally used for  squaring
 the frame of a building or foundation  
wall4    ,if the run is #db inches1 #db 
squared is #agfd1 double that amount1   
both  sides being equal1 gives #cebh1   
the square root of which is1 in feet and
  inches1 #d feet1 #aa4dj inches4    ,in
 cutting braces always allow in length  
from a sixteenth to an eighth  of an    

inch more than the exact measurement    
calls for4    ,directly under the       
half-inch marks on the outer edge of the
 back of the  tongue will be noticed two
 figures1 one above the other4 ,these   
represent  the run of the brace1 or the 
length of two sides of a right-angled   
triangle2 the figures immediately to the
 right represent the length of  the     
brace or the hypothenuse4 ,for instance1
 the figures #cf-cf #ei-ia show  that   
the run on the post and beam is #cf     
inches1 and the length of the  brace is 
#ej4ia inches4    ,upon some squares    
will be found brace measurements given  
where the run  is not equal1 as #ah-bd  
#cj4 ,it will be noticed that the last  
set of  figures are each just three     
times those mentioned in the set that   
are  usually used in squaring a         
building4 ,so if the student or mechanic
 will  fix in his mind the measurements 
of a few runs1 with the length of       
braces1 he can readily work almost any  
length required4    ,take a run1 for    

instance1 of #i inches on the beam and  
#ab inches on the  post4 ,the length of 
brace is #ae inches4 ,a run1 therefore1 
of #b1 #c1 #bj1  or any other number of 
times the above figures1 the length of  
the brace  will bear the same proportion
 to the run as the multiple used4 ,thus1
 if  you multiply all the figures by #d 
you will have #cf and #dh inches for the
  run1 and #fj inches for the brace1 or 
to remember still more easily1 #c1 #d   
and #e feet1 or #f1 #h and #aj feet4    
,there are other runs that are just as  
easily fixed in the mind4 #ea-;inch     
run1 brace #f feet1 #ab hundredths of an
 inch2 #h feet1 #c-;inch run1 brace  #aa
 feet1 #h inches1 etc4    ,the following
 examples and explanations on roof      
framing are simple and  easily          
understood1 and cannot fail of being    
valuable to the young  mechanic who     
aspires to become an expert roof framer4
 ,these examples  will serve as         
starters1 and in the following volume1  
which will be  issued shortly1 more     

advanced examples will be presented4    
,,roof ,,framing4    ,roof framing can  
be done about as many different ways as 
there are  mechanics4 ,but undoubtedly  
the easiest1 most rapid and most        
practical is  framing with the 8square40
 ,the following cuts will illustrate    
several  applications of the square as  
applied to roof framing1 and all who are
  interested in the subject can1 by     
giving it a careful study1 be able to   
frame any ordinary roof the mechanic    
comes in contact with4    ,fig4 #cc is  
an illustration that could well be given
 much thought and  study4 ,it not only  
gives the most common pitches1 but also 
gives the  degrees4    ,most carpenters 
know that half-pitch is #de degrees1 yet
 few know third  pitch is nearly #cd1   
and quarter-pitch about #bg degrees4    
,a building #bd feet wide 7as the       
rafters come to the center7 has a       
#ab-;foot run and half-pitch the rise   
would also be #ab feet1 and the  length 
of the rafter would be #ag feet 7the    

diagonal of #ab74 ,length1  cuts1 etc41 
could all be figured from the one       
illustration4    ,illustration3 ,fig4   
#cc4    ,illustration3 ,fig4 #cd4       
,fig4 #cd illustrates a way to cut      
rafters with the square4    ,a roof #ad 
feet wide would have a run of #g feet1  
third-pitch would rise #h  inches to    
every foot run4 ,therefore1 place the   
square on #h and #ab seven  times1 and  
you have length and cuts4    ,fig4 #ce4 
,for the octagon rafter1 proceed same as
 common rafter1 only use  #ac for run   
7in place of #ab for common rafter74    
,illustration3 ,fig4 #ce4    ,fig4 #cf1 
hip or valley rafter4 ,as these rafters 
run diagonal with the  common rafter and
 as the diagonal of #a foot is          
practically #ag inches1  use #ag for    
run1 and proceed same as common rafter4 
,illustration3 ,fig4 #cf4    ,length of 
jacks4 ,if there are to be five1 divide 
the common rafter into  six equal parts1
 use that for a pattern1 and it gives   
the length very  nicely4 ,but that will 

not always work4 ,to get all the        
different lengths  might at first look  
difficult even to many good mechanics1  
but it is  very simple as illustrated in
 ,fig4 #cg4 ,if the first jack was one  
foot  from corner apply the square same 
as for common rafter1 and it gives      
length and cut 7mark the length for     
starting point on next71 and if it  is  
#ag inches from the other move the      
square up to #ag1 if the next is #ae    
move up to #ae and so on4               
,illustration3 ,fig4 #cg4    ,fig4 #ch4 
,the side cut of jack to fit hip1 if    
laid down level would1 of  course1 be   
square miter1 but the more the hip rises
 the sharper the  angle4 ,measure across
 the square from #h to #ab1 and it is   
nearly #ad1  which is the length of     
rafter to one foot of run4 ,length and  
run1 cut on  length1 gives the cut4     
,illustration3 ,fig4 #ch4               
,illustration3 ,fig4 #ci4    ,fig4 #ci1 
octagon jack4 ,as the octagon miter on  
level surface is #e and  #ab1 it must   

raise same as common jack1 and is1      
therefore1 raised to  length1 or #ad1   
and #e cut on length4    ,illustration3 
,fig4 #dj4    ,fig4 #dj1 hip rafter1 is 
also length and run1 cut on length4     
,illustration3 ,fig4 #da4    ,fig4 #da4 
,to bevel top of hip take length and    
rise and mark on rise4    ,fig4 #db is  
another practical way1 which is simply  
to lay the square on  heel or hip4 ,the 
illustration1 explains itself4          
,illustration3 ,fig4 #db4    ,perhaps   
the most practical way of all to frame a
 roof1 the simplest to  understand1     
easiest to remember1 and most rapid to  
apply is simply to  always take the rise
 and run1 measure across the square     
which gives  length4 ,rise and run give 
cuts1 so you have it all4               
,illustration3 ,fig4 #dc4    ,fig4 #dc  
illustrates a roof #be feet wide and a  
rise #aj feet1 #i inches1  run #ab feet1
 #f inches4 ,measuring across the square
 from #aj to #ab gives  #af1 or #af     
feet1 #f inches is the length of rafter4

    ,fig4 #dd4 ,if the run of common    
rafter is #ab1 the run of the hip will  
be  diagonal of #ab which is #ag #h-af1 
as is plainly illustrated4              
,illustration3 ,fig4 #dd4    ,fig4 #de4 
,as the rise is #aj and run #ag #h-ab1  
the length will be #bj feet1  #b inches4
    ,illustration3 ,fig4 #de4    ,fig4  
#df4 ,when a roof must go to a certain  
height to strike another  building at a 
given point1 as in additions1 porches1  
etc41 don't forget  in getting the rise 
from plate to given point to allow the  
squaring up  of heel as illustrated2 and
 also remember to allow for ridge       
whenever  one is used4    ,illustration3
 ,fig4 #df4    ,fig4 #dg illustrates the
 cut of top of quarter-pitch rafter to  
lay on top  of roof just mentioned4 ,to 
apply the square first lay it on #ab and
 #f1  which is quarter-pitch1 and gives 
plumb-cut4 ,from plumb-cut lay off      
pitch of main roof #aj and #ab1 which   
gives cut4    ,illustration3 ,fig4 #dg4 
,anyone that has studied this with      

determination will have no trouble in   
framing any ordinary roof1 as the       
general principles apply to all roofs1  
pitches1 etc4 ,so ,i will not take up   
any more space with roof framing at     
this time1 but remember all sheathing1  
studding1 cornice1 etc41 are made  on   
the same cuts4 ,in fact a hopper is also
 exactly on the same  principle4        
,division ,b4                           
,,some ,,pointers ,,on ,,roof ,,framing4
    ,no matter what people may say to   
the contrary1 there is no method or     
methods that has ever been devised that 
is so effective in roof framing1  or    
results so rapidly achieved1 as those   
which are obtained by the use  of the   
steel square4 ,i have shown in some of  
the earlier pages of this  work how     
rapidly the length1 and bevels of any   
common rafter may be  obtained by the   
simple application of the square1 any   
determined number  of times4 ,thus for a
 building of1 say1 #cj ft4 in width1    
which is to have  a roof of any given   

pitch1 we arrange the pitch as ,i have  
shown1 with so  many inches on the blade
 for the run1 and so many on the tongue 
for the  rise4 ,this settled1 we apply  
the square fifteen times to the rafter1 
#ae  being half of the width of the     
building4 ,this then gives the length of
  the rafter1 and a line drawn along the
 edge of the tongue of the square  will 
give the proper bevel for the top or    
plumb cut4 ,if there is to be a  ridge  
board on the roof1 then half the        
thickness of such board must be         
measured back on the line drawn1 and the
 rafter must be cut at that  point1 this
 provides for the ridge board being     
nailed on the face of the  cut without  
in the least changing the pitch4    ,a  
line along the edge of the blade1 gives 
the proper bevel for the level  or      
horizontal cut4 ,if the bottom end of   
the rafter is to have a  crow-foot cut  
on it to fit the plate1 the workman will
 have no  difficulty whatever in cutting
 the foot of the rafter to suit1 as all 

the lines will be at right angles to    
each other1 and a section of the  plate 
may be made on the line of the bevel and
 the 8cuts0 laid off to  suit the       
conditions4    ,in reviewing an article 
of mine on this method of laying out a  
rafter1  an ,english carpenter took     
exceptions to it on the grounds that it 
would  take too much time to lay out the
 rafters for a whole building by this   
8tiresome process10 as he called it4    
,now the ,englishman was right from  his
 point of view1 but no ,american workman
 would ever think of laying  out the    
rafters for a whole building by the     
process4 ,he would simply  make one     
rafter as ,i have shown1 for a pattern1 
and use this pattern for  laying out all
 the other rafters for that particular  
pitch and rise on  the same roof4 ,most 
workmen1 however1 make a pattern from   
thin stuff of  some sort1 as it is      
lighter and easier handled4 ,the        
reviewer suggested  as a better way     
8that the pitch be arranged on the iron 

square1 then  measure across the angle  
from the points of run and pitch1 and   
multiply  this measurement by half the  
width of the roof to be covered40 ,now  
this  is all right1 but1 as a matter of 
fact1 entails more labor of a  8tiresome
 sort0 and would use much more time than
 the method ,i have  taught now for     
nearly forty years4 ,the ,american      
workman1 however1 does  not even require
 a suggestion as to the quicker method4 
,he will see and  adopt it at once      
without argument4    ,illustration3     
,fig4 #dh4    ,the method the           
,englishman would adopt is shown at     
,fig4 #dh1 where the  points of pitch   
and run are shown at #ab and #h1 which  
makes the diagonal  line #ad inches4 ,to
 get the length of the rafter for our   
supposed  building then1 we must        
multiply this #ad inches fifteen times1 
then we  must use the square at the top 
and bottom of the timber to obtain the  
necessary bevels for the cutting lines4 
,regarding this question of preparing   

rafters for a common roof1 an 8old      
hand0 in the use of the steel square    
writes to me to say3 8,i do not  think  
that any simpler method can be given for
 finding the bevels at the  heel and    
point of rafters than that which you    
have explained in your  books1 but ,i do
 think that the following method for    
obtaining lengths of  rafters1 is       
somewhat better than yours1 particularly
 when employed for  estimating purposes4
 ,the most common width of buildings in 
my locality  is #bd ft41 and with your  
permission ,i purpose to take that width
 for the  practical test of my method4  
,as you have given several ways by which
 the  same result can be obtained1 ,i   
will ask you to compare them with mine4 
,finding the length of the hypothenuse  
by the old rule1 we obtain for          
one-quarter-inch pitch #ac3d4ii1 or1 as 
near as it can be used on the  square   
#ac feet1 #e inches4    ,allowing one   
inch to the foot and trying your method 
we find1 as a  result1 #ac inches and   

#g-af scant1 or #ac feet1 #e inches4    
,this is a very  simple method1 and when
 the rule is kept perfectly straight1   
the results  are very satisfactory4     
,by my way ,i simply multiply the width 
of the building by the decimal  4#ef1   
#bd4efac4dd1 or as near as can be worked
 by the square1 #ac feet1 #e  inches4   
,let us try the same rule for a greater 
width--say #fj feet4 ,by finding the    
hypothenuse we find as near as can be   
used by the square1 #cc feet1 #f        
inches4 ,by my method it would be       
#fj4ef1 or #cc4fj1 equal to #cc feet1 #g
  inches full4 ,by this method the      
rafters in wide buildings are a little  
long4 ,thus1 if the building is #eb feet
 wide1 by the hypothenuse it would  be  
#bi feet1 #a inch2 my way it would be   
#bi feet1 #a inches4 ,i consider  this  
an advantage1 as it leaves the point of 
the rafter very slightly  open4    ,for 
one-third ,i follow the same plan1 only 
using the decimal 4#f4 ,unlike  the     
decimal used for a quarter pitch the    

lengths are a very small  fraction      
short2 as1 for instance1 a rafter for a 
building #fj feet wide1  by finding the 
hypothenuse1 would be #cf feet1 #a-af of
 an inch4 ,by my  way1 #fj4fcf feet4 ,a 
slight difference1 truly4 ,if building  
is #dh feet  wide1 then by the first    
method we find #bh feet1 #aj inches     
full2 by my  way1 #bh feet1 #i inches4  
,a little practice will enable the      
mechanic to  allow just enough to make  
up for the slight difference1 so that   
when  rafters are put together the fit  
will be perfect4    ,the one-half pitch 
can be found in the same manner by using
 the decimal  4#ga4 ,taking the         
#bd-;foot building1 length of rafters by
 the hypothenuse1  we find #af feet1 #aa
 #b-c inches2 my way they would be #ag  
feet full4  ,again1 building #fj feet   
wide1 rafters by the first method would 
be #db  feet1 #f inches2 by my way      
#fj4gadb feet1 #f inches4 ,by using this
  decimal1 the length is so near        
practically correct1 that it may be used

  in all cases4    ,for a full pitch use
 the decimal #a4ab1 and as in the       
preceding mentioned  pitch1 and it will 
be found so near correct that it can be 
practically  used in all cases4    ,it  
will be noticed that ,i have not made   
any allowance for projection of  rafters
 over the plate4 ,in this case gauge    
from the crowning side of  your rafter  
the thickness of your projection2 allow 
enough for the  latter1 and find the    
lower bevel according to the way you    
described in  your last2 measure the    
length of your rafter from where this   
bevel  crosses the gauge line4    ,a    
little practice will enable the mechanic
 to lay off a rafter in a very  short   
time4 ,i have used the above myself1 and
 have no trouble whatever4  ,while ,i   
have no fault to find in your methods1  
as ,i know them to be  correct1 yet it  
is just as well that workmen should know
 other methods1  as there are many      
occasions when the 8only method0 he     
possesses cannot  be applied4 ,hence ,i 

submit the foregoing1 at your request4  
,w4 ,h40    ,all this is very true1 and 
right as far as it goes1 but it so      
happens  that many workmen do not have  
the necessary learning to work out these
  problems in footing on the lines laid 
down by ,w4 ,h41 but1 in order to  meet 
conditions of this kind ,i have prepared
 a series of tables which is  inserted  
in the larger volumes1 giving the length
 of rafters for any  building having a  
width of from five to sixty feet and a  
rise of roof of  from one to eighteen   
feet to ridge4 ,this will cover the     
whole ground1  and form a ready table   
for the estimator to take his quantities
 from4    ,i may be pardoned for again  
showing the common and simplest method  
of  laying out an ordinary rafter1 for  
notwithstanding all ,i have said and    
described and explained on this subject1
 there will always be some  persons who 
will not be able to grasp the method1   
unless it is put to  them in some other 
light4 ,i am sure of this from the long 

experience ,i  have had in the answering
 of questions of this kind through the  
columns  of different building journals4
 ,this is no doubt owing to some        
constitutional peculiarities of both the
 person who makes the inquiry  and the  
person who attempts to answer it4 ,this 
is one of the main  reasons why ,i have 
admitted into this work various methods 
and  descriptions of others than myself1
 so that readers will have the same     
methods described and explained to them 
in several different ways by  several   
writers4    ,illustration3 ,fig4 #di4   
,let us take the diagrams shown at ,fig4
 #di1 which shows a portion of a  roof  
having a quarter pitch4 ,,ceb showing   
the height1 and ,,ab the length  and    
inclination of rafter4 ,d shows the foot
 of the rafter on the plate1  cut 8flat 
foot0 and the line ,,ec the plumb cut4  
,this is quite plain4 ,the  building may
 be any width1 let us say in this case1 
that it is #cj feet  wide from ,a to ,o4
 ,that will make the distance from ,a to

 ,c #ae feet4    ,illustration3 ,fig4   
#ej4    ,a method of obtaining the      
bevels for this rafter is given in ,fig4
 #ej  where the steel square is shown   
laid on the pattern with the points #af 
inches on the blade and #h inches on the
 tongue applied to the edge of  the     
stuff4 ,the line ,,ho on the blade gives
 the bevel for the foot of the  rafter  
,,ac4 ,the line ,,op1 ,fig4 #ej gives   
the bevel for the top of the  rafter or 
the plumb cut1 as most workmen call it4 
,now1 there is nothing  in this diagram1
 which is from ,bell's ,carpentry1 an   
excellent work--from  which the workman 
can get the length of his rafter1       
without complicating  matters4 ,had the 
figures #ab inches and #f inches on the 
square been  employed instead of #af and
 #h1 then the distance across the       
diagonal from  these two points would   
have equalled on the rafter1 one foot on
 the base  line or seat of the rafter1  
so that #ae times that length would have
 been  the total length of the rafter4  

,better still1 however1 would have been 
the application of the square #ae times 
on the edge of the rafter pattern  with 
the points #ab and #f on gauge points1  
then both length and bevels  would have 
been obtained at one operation4    ,of  
course1 the expert workman will often   
invent1 or discover1 methods of  using  
the square in certain phases of roof    
framing1 that can not be  found in      
books1 or that cannot be taught because 
of the peculiar  circumstances of the   
particular case4 ,having a fair         
knowledge of the  uses of the steel1 the
 workman will seldom be overtaken by    
difficulties  he cannot overcome if he  
studies the problems before him and then
  employs his knowledge of the square to
 their solution1 as a little            
application on this line will remove all
 possible troubles4    ,every carpenter 
knows1 or ought to know1 that the run   
and rise of the  rafter taken on the    
square will give the seat and plumb     
cuts1 but  inasmuch as buildings are not

 all of the same width1 it requires a   
different set of figures for each run1  
and as it requires an extra  calculation
 to first find the run of the hip or    
valley1 it is better to  use the full   
scale for a one-foot run of the common  
rafter which answers  for any run4      
,illustration3 ,fig4 #ea4               
,illustration3 ,fig4 #eb4    ,referring 
to ,fig4 #ea1 we show a square bounded  
by ,a1 ,b1 ,c1 ,d1 the sides  of which  
are #ab inches4 ,e is at a point #e     
inches from ,b1 and ,c #ab inches  from 
,b4 ,b-,a represents the run of the     
common rafter4 ,e-,a represents the  run
 of the octagon hip or valley1 and ,c-,a
 the same for the common hip or  valley1
 their lengths1 being #ab1 #ac1 and #ag 
respectively4 ,now since #ab1  #ac1 and 
#ag are fixed numbers1 we take them on  
the tongue of the square1  as shown in  
,fig4 #eb4 ,now suppose we want to find 
the lengths and cuts of  the rafters for
 the  pitch4 ,we take #i on the blade4  
,why8 ,because the  run being #ab       

inches1 the span must be two times #ab1 
which equals #bd1 and  since the pitch  
is reckoned by the span1 we find that   
of #bd is #i1  which represents the rise
 of the foot run4 ,then #ab and #i give 
the seat  and plumb cuts for the common 
rafter1 #ac and #i for the octagon hip  
or  valley1 and #ag and #i gives the    
same for the common hip or valley4 ,in  
,fig4 #ec ,i show each separately4      
,illustration3 ,fig4 #ec4    ,the       
measurement line of hips and valleys is 
at a line along the center  of its back1
 and just 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     
skill of most carpenters1 especially so 
when the  rafters are so backed4 ,in    
,fig4 #ed ,i have tried to make the     
above points  clear4    ,illustration3  
,fig4 #ed4    ,first1 ,i show the plan  
of the rafter4 ,the cross lines on same 
represent  an external corner for the   
hip and valley respectively4 ,above the 

plan  is shown the elevation4 ,the      
sections #a-b-c-d represent the position
 of  the rafters under the following    
conditions3 ,no4 #a hip when not backed1
  ,no4 #b hip when backed1 ,no4 #c      
valley when not backed1 ,no4 #d valley  
when  backed4 ,no4 #a is outlined by    
heavy lines1 and sets lower than the    
others4 ,by tracing the bottom line of  
the sections down to the seat of  ,no4  
#a1 thence up to the second elevation   
will show just how deep the  notching   
should be for each rafter4 ,no4 #a cuts 
into the right hand  vertical line from 
the plan1 which would make it stand at  
the right  height above the plate1 but  
in order to make the seat cut clear the 
corner of plate1 it is necessary to cut 
into the center line above the  plan4   
,no4 #b cuts into the same points as    
,no4 #a1 but owing to its being  backed1
 the seat cut drops accordingly4 ,no4 #c
 cuts into the center  vertical line1   
and in order to clear the edges of the  
plate must cut out  at the sides to the 

left vertical line4 ,no4 #d cuts in the 
same as the  latter1 but as much lower  
than ,no4 #c as ,no4 #b is below ,no4   
#a4    ,the outer vertical lines from   
the plan represent the width of the     
rafter4 ,therefore if the rafter be two 
inches thick1 would be one inch  apart1 
and this amount set off along the seat  
line 7or a line parallel  with it7 will 
give the gauge point on the side of the 
rafter4 ,to make  this clearer refer to 
,fig4 #ec2 #ag and #i gives the cuts4   
,now leaving the  square rest as it is1 
measure back from #ag one-half the      
thickness of the  rafter1 and this will 
be the gauge line point from which to   
remove the  wood back to the center line
 of hip1 and the measurement from the   
edge  of 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 conditions4 ,this rule 
applies to any roof so  long as the     
pitches are regular4    ,proceed in like

 manner for the octagon hip1 the        
variation1 however1 is  practically     
one-half of the above results for the   
square cornered  building4              
,illustration3 ,fig4 #ee4    ,fig4 #ee  
illustrates side cut of the jack1 #ab on
 the tongue1 and #ae  7length of the    
common rafter7 on the blade4            
,illustration3 ,fig4 #ef4    ,fig4 #ef  
illustrates side cut of the octagon     
jack1 #e on the tongue and #ae  on the  
blade4    ,illustration3 ,fig4 #eg4     
,fig4 #eg illustrates the side cut of   
the hip or valley1 #ag on tongue1 #ai   
7length of the hip7 on the blade giving 
the cut in each case4    ,the latter1   
however1 is for the unbacked rafter4 ,if
 it has been  previously backed1 then   
apply the square with the above figures 
on the  lower edge at bottom of the     
plumb cut1 or apply the square as for   
the  jack1 ,fig4 #ef1 to the backing    
line1 which will give the same result as
  #ag and #ai4    ,it is quite clear    
that when a workman cuts a common       

rafter1 he is also  cutting a timber    
that would answer for a hip for a       
building of less span  having the same  
rise1 only taking some adjustment of the
 top bevel to  fit against a ridge4     
,this is quite plain1 and if we refer to
 ,fig4 #eh1 we  find that the common    
rafter for a #a-;foot run becomes a hip 
for an  #h-;inch run1 and that a hip for
 a #a-;foot run of the building becomes 
a  common rafter for a #ag-;inch run4   
,therefore1 the rule that applies to the
  common rafter also applies to the hip 
rafter1 i4 e41 the run and rise  taken  
on the square will give the seat and    
plumb cuts4 ,the run and  length of the 
rafter taken on the square will give the
 side cuts1 or  taking the scale for a  
#a-;foot run1 ,fig4 #eh1 it is #ab on   
the tongue and  the rise on the blade   
for the common rafter1 and #ag on the   
tongue and  rise on the blade for the   
hip4 ,the tongue giving the seat cut and
 the  blade the plumb cut4 ,for the side
 cuts we take #ab on the tongue and #ae 

inches on the blade1 and the blade will 
give the side cut of the jack4  ,take   
#ag on the tongue and the length of the 
hip1 #ai inches1 on the  blade and the  
blade will give the side cut of the hip4
 ,it would also be  the side cut of the 
corresponding jack if it be a common    
rafter4  ,seventeen is used for a foot  
run of the hip rafter because the       
diagonal  of a #ab-;inch square is      
practically #ag inches4                 
,illustration3 ,fig4 #eh4    ,if we were
 to use #ab on the tongue for a foot run
 of the hip the rise to  the foot would 
necessarily be less than #aj inches4 ,in
 ,fig4 #ei ,i show  what the difference 
is in rise to the foot4                 
,illustration3 ,fig4 #ei4    ,from #ab  
to #ab is the length of the run of the  
hip would only have #aj-ag  of an inch  
to one run of the common rafter1 and an 
equal rise of the  common rafter1 set   
off as at ,a1 and a line from this to   
#ab on the tongue  passes at #g #a-ag   
inches on the blade1 because the common 

rafter having a  rise of #aj inches to  
one foot1 for one inch it would have    
#aj-ab of an  inch1 while the hip would 
only have #aj-ag of an inch to one inch 
and for  #ab inches it would be #ab     
times #aj-ag equals #abj-ag1 or #g #a-ag
 inches4  ,therefore the figures given  
in the second illustration would give   
the  same cuts as those in the first1   
but as the latter necessitates a        
calculation that ends in                
fractions--fractions not given on the   
square--and  for that reason #ag is     
generally used for a foot run for the   
hips and  valleys4    ,illustration3    
,fig4 #fj4                              
,,an ,,unequal ,,pitch4    ,in the      
matter of roofing over unequal pitches  
when there is no ridge and  when all    
hips meet1 the building being longer    
than it is wide1 the  backing of hips   
and their lengths and bevels would be a 
very easy matter  if a drawing of the   
whole thing was made1 but1 to obtain    
these by the  use of the square alone1  

is somewhat more difficult4 ,let us     
assume the  building to be #ah feet wide
 and #bh feet long1 and having a rise of
 #i  feet1 then1 by referring to ,fig4  
#fj1 we show to one inch scale the      
length1 run1 rise1 seat1 and plumb cuts 
for the hip and common rafters  as      
follows3 ,the run of the long way of the
 building is #ad1 and #i for the  narrow
 way1 which we take on the blade and    
tongue respectively1 as shown  on square
 ,no4 #a1 and to this apply square ,no4 
#b1 as shown4 ,,ad equals the  run of   
the hip4 ,,ae equals the rise and ,,ed  
equals the length of the hip4  ,the     
reader will notice that the letters ,a1 
,b1 ,c1 ,d form a parallelogram1  with  
side and ends equal to the runs of the  
common rafters4 ,therefore1  by taking  
the runs on the tongue1 as shown by the 
squares ,nos4 #c and #d1  will give     
their lengths1 seat and plumb cuts4     
,illustration3 ,fig4 #fa4               
,illustration3 ,fig4 #fb4    ,in ,fig4  
#fa 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  necessary that the 
common rafters must cut back so as to   
fit in the  angle formed by the hips4   
,the proper deduction for this is shown 
in ,fig4  #fb by placing two squares on 
the back of the rafter1 with the heel or
  corner of the squares resting on the  
center line4 ,the distance from the     
corner of the square to ,b measured     
square back 7at right angles7 from  the 
plumb bevel1 as shown in ,fig4 #fa1 will
 locate the point of the long  common   
rafter at ,b in ,fig4 #fa4 ,proceed in  
like manner for the short  common       
rafter1 taking the distance from the    
corner at ,c1 and for the  side cuts1   
take #ad on the tongue and the length of
 the short common  rafter ,,ce on the   
blade--the blade will give the cut at   
,,ac in ,fig4 #fa4 ,the  reader will    
observe that this angle is the same as  
that for the side cut  of the jack4     
,proceed in like manner for the long    

common rafter side1  using #i on the    
tongue and ,,be on the blade4 ,these    
same figures will give  the side cuts of
 the hip1 provided hip has been         
previously backed4  ,taking the last for
 example the reader will observe that #i
 on the tongue  and ,,be on the blade   
the square would lay on the plane of the
 backing and  the blade giving the cut  
along the line ,,bb in ,fig4 #fa1 or    
these cuts may  be found by measuring   
square back from a plumb bevel at points
 ,a and ,a1  ,fig4 #fb1 the distance    
,,ac and ,,ab1 which will give the      
proper plumb cut at  the sides and      
intersecting the line ,,aa at the       
center4 ,these same  distances1 ,,ac and
 ,,ab1 but transferred to opposite      
sides1 set off on the  seat cut or a    
line parallel with it1 will give the    
gauge points on the  side of the hip for
 the backing4    ,the lengths of the    
jacks may be found by dividing the      
length of the  common rafter by the     
number of the spacings for the jacks2   

the quotient  will be the common        
difference4                             
,,end ,,of ,,division ,b4               
,illustration3 ,fig4 #fc4  ,,lay-,,out  
,,of ,,hip-,,roof ,,with ,,deck4        
,,the ,,steel ,,square ,,and ,,its      
,,uses4                                 
,,division ,c4                          
,introductory4      ,during my long     
experience as ,editor of several of the 
leading building  journals in the       
,united ,states and ,canada1 ,i have    
been asked and have  answered thousands 
of questions regarding matters          
concerning building  construction1      
builders' materials1 tools and          
processes1 and particularly  regarding  
the 8,steel ,square and its ,uses10 and 
,i have concluded that the  publication 
of a few of these questions and answers1
 along with other  matter1 in this      
division will be appreciated by my      
readers1 and to this  end ,i insert a   
number of the most useful items in this 
manual4    ,besides these questions and 

answers1 ,i also publish other up to    
date  matter1 all of which will make    
this volume one of the most useful      
little  works to the ,american carpenter
 and wood-worker ever published4        
,illustration3 ,fig4 #fd4               
,illustration3 ,fig4 #fe4    ,i open    
this division with a few hints regarding
 the construction1 or  rather the laying
 out of a ,hip-,roof where the design   
has been furnished  by an architect1 and
 which1 of course1 shows the pitch and  
the lay of  the timbers4 ,we suppose the
 roof to have a span of #ah feet and a  
rise of  #f feet1 thus giving the roof a
 one-third pitch4 ,the fence is used in 
this example to its full extent1 and    
when placed on the square and  fastened1
 the line of fence shows the slope or   
pitch of roof4 ,fig4 #fd  shows the     
square set to the pitch of the hip      
rafter4 ,the squares as set  give the   
plumb and level cuts4 ,fig4 #fe is the  
rafter plan of a house #ah  by #bd feet2
 the rafters are laid off on the level1 

and measure nine feet  from center of   
ridge to outside of wall2 there should  
be a rafter  pattern with a plumb cut at
 one end1 and the foot cut at the other1
 got  out as previously shown4 ,when the
 rafter foot is marked1 place the end   
of the long blade of the square to the  
wall line1 as in drawing1 and  mark     
across the rafter at the outside of the 
short blade1 and these  marks on the    
rafter pitch will correspond with two   
feet on the level  plan2 slide the      
square up the rafter and place the end  
of the long blade  to the mark last     
made1 and mark outside the short blade  
as before1  repeat the application until
 nine feet are measured off1 and then   
the  length of the rafter is correct2   
remember to mark off one-half the       
thickness of ridge-piece4 ,the rafters  
are laid off on part of plan to  show   
the appearance of the rafters in a roof 
of this kind1 but for  working purposes 
the rafters #a1 #b1 #c1 #d1 #e and #f1  
with one hip rafter1  is all that is    

required4    ,to proceed1 we first lay  
off common rafter1 which has been       
previously  explained2 but deeming it   
necessary to give a formula in figures  
to  avoid making a plan1 we take #a-c   
pitch4 ,this pitch is #a-c the width of 
the building1 to point of rafter from   
wall plate or base4 ,for an  example1   
always use #h1 which is #a-c of #bd1 on 
tongues for altitude2 #ab1   the width  
of #bd1 on blade for base4 ,this cuts   
common rafter4 ,next is  the hip-rafter4
 ,it must be understood that the        
diagonal of #ab and #ab is              
approximately #ag in framing work1 and  
the hip is the diagonal of a  square    
added to the rise of roof2 therefore we 
take #h on the tongue and  #ag on the   
blade2 run the same number of times as  
common rafter which  gives the length of
 hip and plumb and level bevels4    ,to 
cut jack rafters1 divide the number of  
openings for common rafters4  ,suppose  
we have five jacks1 with six openings1  
our common rafter #ab feet  long1 each  

jack would be #b feet shorter4 ,the     
first1 next the hip1 #aj  feet1 the     
second #h feet1 third #f feet1 and so   
on4 ,the top down cut same  as down cut 
for common rafter4 ,for the bevel1 cut  
against hip4 ,take half  the width of   
building on tongue and length of common 
rafter on blade1  and blade gives the   
bevel4 ,now find diagonal of #h and #ab1
 which is #ad  #g-af in4 ,take this     
length on blade and #ab on tongue1 blade
 gives bevels4  ,if the hip-rafter is   
beveled or 8backed0 to suit jacks1 then 
take height  of hip on tongue1 length of
 hip on blade1 and tongue gives bevel4  
,these  figures will cover all bevels   
for cutting1 cornice and sheathing4 ,for
  bed moulds for gable to fit under     
cornice1 take half width of building  on
 tongue1 length of common rafter on     
blade2 blade gives cut4 ,to cut         
planceer to run up valley1 take height  
of rafter on tongue1 length of  rafter  
on blade2 tongue gives bevel4 ,for plumb
 cut1 take height of hip  on tongue1    

length of hip on blade2 tongue gives    
bevel4    ,these figures were specially 
prepared for a hip roof having a        
one-third  pitch1 but will suit other   
pitches equally well if the difference  
in  height of ridge is considered4      
,for a hopper the mitre is cut on the   
same principle4 ,to make a butt  joint1 
take the width of side on blade1 and    
half the flare on tongue3  the latter   
gives the cut4 ,you will observe that a 
hip-roof is the same  as a hopper       
inverted4 ,the cuts for the edges of the
 pieces of a  hexagonal hopper are found
 this way4 ,subtract the width of one   
piece at  the bottom from the width of  
same at top1 take remainder on tongue1  
depth of side on blade2 tongue gives the
 cut4 ,the cut on face of sides3  ,take 
#g-ab of the rise on tongue and the     
depth of side on blade2 tongue  gives   
cut4 ,the bevel of top and bottom3 ,take
 rise on blade1 run on  tongue2 tongue  
gives cut4                              
,,some ,,questions ,,and ,,answers      

,,from ,,various ,,correspondents4      
,the following questions and answers    
from practical workmen are  considered  
among the very best things regarding the
 use of the ,steel  ,square1 as they are
 from men who knew of what they were    
talking about4  ,they are gathered from 
many sources1 but chiefly from the      
columns of  ,technical ,journals with   
which ,i have been connected1 either as 
,editor or  contributor4    ,jas4       
,willis1 ,rochester1 ,n4 ,y41 asks3     
8,how can ,i get the proper bevel for  a
 butt joint on an obtuse or acute angle1
 by the use of the square  only80       
,illustration3 ,fig4 #ff4    ,answer3   
,suppose ,fig4 #ff represents an obtuse 
angle formed by two  parallel boards or 
timbers4 ,to obtain the joint1 ,a1 space
 off equal  distances from the point #a 
to #c1 #c1 then square over from the    
lines1 ,r1  ,r1 keeping the heel of the 
square at the points #c1 #c4 ,at the    
junction of  the lines formed by the    
tongue of the square at #j will be one  

point1 and  #a will be the other by     
which the joint line1 ,a1 is defined4   
,illustration3 ,fig4 #fg4    ,to find   
the line of juncture for an acute angle1
 proceed as follows3  ,fig4 #fg         
represents two parallel boards or       
timbers2 #a the extreme angle1  #c1 #c  
equal distances from the angle #a and   
are the points where the heel  of the   
square must rest to form the lines #j1  
#c2 #j shows the junction of  the lines 
formed by the blade of the square4 ,draw
 a line from #j to #a1  and the line1   
,a1 formed1 is the bevel required4      
,it will be seen1 by these two examples1
 that the bevel of a junction at  any   
angle may be obtained by this method4   
,p4 ,mc,vity1 ,milwaukee1 asks3 8,how   
can ,i draw a circle with the ,steel    
,square80    ,answer3 ,a circle of any  
required diameter may be drawn by means 
of the  square by using it as indicated 
in the accompanying sketch4 ,drive two  
pins or nails1 ,a and ,b1 ,fig4 #fh1 at 
whatever distance apart the circle  is  

to have as its diameter4 ,bring the     
square against them1 as shown1 and  use 
a pencil in the angle as indicated in   
the drawing4 ,this rule is very         
convenient in many instances4 ,suppose  
,a and ,b are two points through  which 
a circle is required to be drawn4 ,by   
bringing the square against  pins or    
nails placed in the points1 it may be   
described as indicated in  the sketch4  
,illustration3 ,fig4 #fh4    ,a         
8,mechanic10 ,tampa1 ,fla41 asks3 8,can 
the steel square be used in laying  out 
a wreath for a handrail1 and if so1     
please describe how80    ,illustration3 
,fig4 #fi4    ,answer3 ,some advance in 
this direction has been made1 but not   
much1 but  the outlook is quite         
encouraging as many experts are trying  
to obtain  all the lines required for   
forming circular handrails4 ,it will be 
accomplished sooner or later4 ,a few    
problems and solutions are given        
herewith3 ,in getting out face-molds it 
has generally been considered  necessary

 first to unfold the tangents and get   
the heights1 and by  construction get   
the bevels4 ,the method shown is        
somewhat different1  though results are 
the same1 but are produced more rapidly4
 ,take for  illustration a side wreath  
mitered into a newel cap4 ,this method  
will  apply no matter where the newel is
 placed1 or whether the easement is     
less or more than the one step of the   
example illustrated4 ,what is meant  by 
one step is1 that the tangent of the    
straight rail continues to the  point   
#b1 ,fig4 #fi4 ,the tangent #b-a is     
level4    ,illustration3 ,fig4 #gj4     
,to produce the face mould1 lay the     
steel square in the position1  indicated
 by the lines #a1 #b1 #c1 #d1 not the   
figure on the square at the  points     
numbered1 and transfer them to a piece  
of thin stuff1 ,fig4 #gj4  ,line #c-d in
 ,fig4 #gj is indefinite4 ,now take the 
length of the long edge  of the pitch   
board in the compasses1 and with #b1    
,fig4 #gj1 as a center1  cut the line   

#c-d in #d and draw #b-d4 ,now #a-b is  
the level1 and #b-d is the  pitch       
tangent on the face mold4    ,to get the
 bevels and width of the face mold at   
both ends1 take the  distance #c-d on   
the blade of the square1 and the height 
of a riser on  the tongue of the square1
 apply to the edge of a board and mark  
by the  tongue2 this gives the width of 
the mold at the lower end4    ,next take
 the distance #d-,x on the blade of the 
square1 and the distance  shown on the  
pitch board by the line squared from its
 top edge to the  corner1 on the tongue 
of the square2 apply to the edge of a   
board and  mark by the tongue2 this     
gives the bevels for the top end of the 
wreath4  ,mark the width of the rail on 
the bevel1 and this gives the width of  
the  mold at the top end4 ,an allowance 
of #f inches is made at the top end to  
joint to the straight rail1 and two     
inches at the bottom end to form the    
miter into the newel cap4 ,the springing
 line is taken from the pitch  board4   

,fig4 #fi1 in which are shown the bevels
 and the pitch board will help to  make 
clear the methods used4 ,the bevel at   
the back of the pitch board is  for the 
bottom end of the wreath4 ,the triangle 
has for its base the line  #c-d and for 
its height one riser4 ,the hypothenuse  
is the length of #b-d1  ,fig4 #gj1 and  
,fig4 #gj stands over ,fig4 #fi1 level  
on the line #a-b-c1 and  inclined from  
it in this cast at an angle of nearly   
#de degrees4    ,the top end bevel is   
shown below the pitch board4 ,the angle 
has for its  base the distance #d-x1 and
 for its height not one rise1 but the   
length  of a line1 from the corner of   
the pitch board squared from its top    
edge4  ,this bevel will be understood   
better by placing the pitch board on the
  line #b-d and applying the small      
triangle to it with its base on the line
  #d-x1 and its point even with the top 
edge of the pitch board4 ,it will  then 
be at right angles to the top edge of   
the pitch board4    ,in practice1 a     

parallel mold is generally used1 and the
 wreath piece is  cut out2 both         
thickness of plank and width of molding 
being equal to the  diameter of a circle
 that will contain a section of finished
 rail4      ,jacques ,demoux1 ,winnipeg1
 ,man41 wants to know how to lay out    
braces1  regular and irregular by the   
use of the ,steel ,square4    ,answer3  
,braces and trusses are something like  
rafters and when the run  is known1     
there should be no difficulty in getting
 the lengths and  proper bevels4    ,in 
the first place it is always best to    
make a pattern and then mark out  the   
timber work from the pattern4 ,suppose  
we want braces having a  8four-foot     
run0--that is1 the brace is to form a   
diagonal from points  four feet from the
 post and four feet from the girt4 ,take
 a piece of  stuff already prepared1 six
 feet long1 four inches wide and        
half-inch  thick1 gauge it three-eighths
 from jointed edge4    ,illustration3   
,fig4 #ga4    ,take the square as       

arranged at ,fig4 #ga1 and place it on  
the prepared  stuff as shown at ,fig4   
#gb4 ,adjust the square so that the     
twelve-inch  line coincide exactly with 
the gauge line o1 o1 o1 o4 ,hold the    
square  firmly in the position now      
obtained1 and slide the fence up the    
tongue  and blade until it fits snugly  
against the jointed edge of the prepared
  stuff1 screw the fence tight on the   
square1 and be sure that the #ab-;inch  
marks on both the blade and the tongue  
are in exact position over the          
gauge-line4    ,illustration3 ,fig4 #gb4
    ,we are now ready to lay out the    
pattern4 ,slide the square to the       
extreme  left1 as shown on the dotted   
lines at x1 mark with a knife on the    
outside edges of the square1 cutting the
 gauge line4 ,repeat this process  four 
times1 marking the ends1 and you have   
the length and bevels4 ,square  over at 
each end from the gauge line and you    
have the toe of the brace4  ,the lines  
ss1 ,fig4 #gb1 show the tenons left on  

the end of the braces4    ,illustration3
 ,fig4 #gc4    ,the cut at ,fig4 #gc1   
shows the brace in position1 on a       
reduced scale4 ,the  principle on which 
the square works in the formation of a  
brace can  easily be understood from    
this cut1 as the dotted lines show the  
position the square was in when the     
pattern was laid out4    ,it may be     
necessary to state that the 8square10 as
 now arranged1 will  lay out a brace    
pattern for any length1 if the angle is 
right1 and the  run equal4 ,should the  
brace be of great length1 however1      
additional care  must be taken in the   
adjustment of the square1 for should    
there be any  departure from truth1 that
 departure will be repeated every time  
the  square is moved1 and where it would
 not affect a short run1 it might       
seriously affect a long one4    ,to lay 
out a pattern for a brace where the run 
on the beam is three  feet1 and the run 
down the post four1 proceed as follows3 
,illustration3 ,fig4 #gd4    ,prepare a 

piece of stuff1 same as the one operated
 on for four feet run2  joint and gauge 
it4 ,lay the square on the left-hand    
side1 keep the  #ab-;inch mark on the   
tongue1 over the gauge-line2 place the  
#i-;inch mark  on the blade1 on the     
gauge-line1 so that the gauge-line forms
 the third  side of a right angle       
triangle1 the other sides of which are  
nine and  twelve inches1 respectively4  
,now proceed as on the former occasion1 
and as shown at ,fig4 #gd1 taking  care 
to mark the bevels at the extreme ends4 
,the dotted lines show the  position of 
the square1 as the pattern is being laid
 out4    ,fig4 #ge shows the brace in   
position1 the dotted lines show where   
the  square was placed on the pattern4  
,it is well to thoroughly understand    
the method of obtaining the lengths and 
bevels of irregular braces4 ,a  little  
study will soon enable any person to    
make all kinds of braces4               
,illustration3 ,fig4 #ge4    ,if we want
 a brace with a two-foot run1 and a     

four-foot run it must be  evident that1 
as two is the half of four1 so on the   
square take #ab  inches on the tongue1  
and #f inches on the blade1 apply four  
times1 and  we have the length1 and the 
bevels of a brace for this run4    ,for 
a three by four foot run1 take #ab      
inches on the tongue and #i inches  on  
the blade1 and apply four times1        
because1 as three feet is  of four      
feet1 so #i inches is  of #ab inches4   
,a young carpenter1 ,toronto1 wants to  
know how to find the center of a  circle
 by aid of the ,square4                 
,illustration3 ,fig4 #gf4    ,answer3   
,in ,fig4 #gf is shown how the center of
 a circle may be determined  without the
 use of compasses2 this is based on the 
principle that a  circle can be drawn   
through any three points that are not   
actually in a  straight line4 ,suppose  
we take ,a1 ,b1 ,c1 ,d for four given   
points1 then  draw a line from ,a to ,d1
 and from ,b to ,c2 get the center of   
these lines1  and square from these     

centers as shown1 and when the square   
crosses the  line1 or where the lines   
intersect1 as at x1 there will be the   
center of  the circle4 ,this is a very  
useful rule4      ,ed4 ,mc,donald1      
,cincinnati1 ,ohio1 says3 8,i want to   
know how much can be  done with the     
square towards setting out stair        
railing80    ,answer3 ,in a previous    
page a few remarks on this subject will 
be found  and the following is further  
submitted3    ,illustration3 ,fig4 #gg4 
,illustration3 ,fig4 #gh4    ,fig4 #gg  
shows a plan of a stair well having     
three winders4 ,the rail in  this case  
will have two different pitches4 ,these 
rails are a little more  complicated    
than those having equal pitches1 as in  
the latter the major  axis is parallel  
off the diagonal line ,b ,d 7,fig4 #gg74
 ,when the pitches  differ the major    
axis ceases to be parallel2 and the     
greater the  difference in the pitches1 
the greater will be the difference in   
the  axis and diagonal line4 ,this fact 

can be easily demonstrated by cutting  a
 model bed block out of #b-;inch by     
#b-;inch stuff to equal pitches4        
,procure a board1 and draw a parallel   
line1 say #h inches off the edge4  ,now 
square over a line to cut the first     
line2 set the bed block on1 with  the   
back corner touching the intersection of
 the lines4 ,lay a piece of  cardboard  
on the inclined face of the bed block1  
and let it slide down  until it touches 
the board4 ,make a mark along this edge1
 and it will be  seen1 on removing the  
card1 that this line is equidistant from
 the  corner 7see ,fig4 #gh74 ,in ,fig4 
#gh the cardboard is shown as though it 
were transparent4 ,what has just been   
done is that the plane in which the     
rail lies has been projected to         
intersect the horizontal plane which    
contains the plan of the wreath4 ,the   
name by which this line is  generally   
known is the horizontal trace 7shown at 
,c1 ,figs4 #gh and #gi74  ,the minor    
axis 7,figs4 #gh and #gi7 is always     

parallel off this1 and always  touches  
,a as in ,fig4 #gg4 ,the major axis     
7,figs4 #gh and #gi7 also touches  this 
point ,a1 and is always square off the  
minor axis and off the  horizontal      
trace4 ,it will be seen by this that the
 rail is pitched  equally both ways2    
therefore the face mold will be of equal
 width at the  ends4    ,illustration3  
,fig4 #gi4    ,when rails are cut by    
bandsaw on bed blocks1 bevels are not   
necessary1  as they can always be       
obtained by applying a bevel as shown at
 ,fig4 #hj4  ,the stock should lie solid
 on the block and square off the sides4 
,when  the block is thin it is best to  
apply the bevel near the corner1 when a 
greater surface is obtained4 ,these     
bevels are applied after the joint is   
squared off the tangent lines4 ,to      
demonstrate a rail with unequal         
pitches1 cut another piece of stuff     
#bx#b inches1 as shown in ,fig4 #gi1    
repeat the process with the cardboard as
 before4 ,it will be found that  the    

horizontal trace has departed from the  
angle of #de degrees 7see ,fig4  #gi7   
and has approached nearer one corner and
 gone farther away on the  other4 ,the  
major axis ,b will have done likewise1  
as it is always square  off the         
horizontal trace ,c4 ,the wreath having 
two pitches1 the face mold  will        
obviously be wider at one end than at   
the other2 and if bevels are  required1 
they must be set off on the face of each
 side of the block4  ,the width of the  
face mold is to be applied on the       
tangent line2 this  makes it slightly in
 excess on the joint1 but it is better  
to have a  little margin in thickness   
for working4 ,where thickness of stuff  
is a  secondary consideration1 it is    
preferable to take the rail out of stuff
  which is as thick as the diameter of a
 circle that will enclose the  section  
of rail2 the corners will then be left  
complete4    ,illustration3 ,fig4 #hj4  
,illustration3 ,fig4 #ha4    ,the       
following method shows the least        

thickness the rail can be cut out  of1  
and also gives width of face molds on   
the joint4 ,set the bevel to  the bed   
block as shown at ,fig4 #hj1 and apply  
at the side of the block4  ,draw a      
section of rail level2 apply the bevel  
again1 touching the bottom  corner of   
the section4 ,the distance between the  
marks is the thickness1  a plumb line   
marked on shows the width of the face   
mold on the bevel  line4 ,where the     
pitches are different the foregoing     
method has to be  applied to each side  
of the bed block4    ,the bevels may be 
also obtained by the steel square4 ,take
 the width of  prism face 7shown by     
dotted lines7 by laying the square with 
blade on  the line ,c ,d 7,fig4 #hb7 and
 tongue1 cutting at the center ,a4 ,note
 the  length on the tongue of the       
square4 ,make a mark of this length on  
the  edge of board4 ,now take the width 
of ,a to ,d 7,fig4 #hd7 which is #f     
inches  off the blade2 keep this        
#f-;inch mark fair at the end of this   

line made  on the board 7,fig4 #ha7 and 
push on square until the tongue touches 
the  end of the line2 mark by the       
tongue1 and this gives the bevel        
required4    ,illustration3 ,fig4 #hb4  
,illustration3 ,fig4 #hc4    ,to obtain 
an example of unequal pitches refer to  
,fig4 #hd4 ,to set this  out1 run a line
 parallel off the edge of the board1 and
 off this line  square another4 ,with   
the intersection ,a as a center1        
describe a  semi-circle of #f inches    
radius4 ,this indicates the center of   
the rail4  ,run lines radial from ,a as 
shown2 these are the riser lines4 ,draw 
the  lines ,b ,c and ,c ,d1 which are   
the tangents4 ,draw the diagonal ,b ,d4 
,to  make the bed blocks1 procure a     
piece of one inch stuff2 take it to the 
width shown at ,b ,c2 square on a mark  
about #c inches from the end 7this  is  
to allow for the shank to clear the saw 
table2 the block is shown at  ,fig4 #hc 
without the #c-;inch allowance74 ,take  
on the steel square the rise  on tongue 

and going on blade of the straight      
flight of stairs2 mark on  the inch     
board at tongue2 this is pitch of the   
first tangent4 ,take the  height at ,d1 
which is one and a half risers--#aj     
inches2 deduct the  height of the first 
tangent from #aj inches2 take the       
difference on the  tongue and width from
 ,c to ,d on the blade2 the tongue gives
 the cut for  the second tangent4 ,mark 
the pitch of the first tangent on the   
edge of  the second and cut to this2 the
 pitch of the second tangent gives the  
edge cut of the first4 ,cut and fix     
together with stretcher as previously   
described4    ,illustration3 ,fig4 #hd4 
,to get out the face mold1 procure a    
piece of thin stuff4 ,three-ply wood  is
 excellent1 as though it is liable to   
warp it does not shrink  perceptibly4   
,shoot on edge and gauge on a center    
line2 take the distance  from ,b to ,d  
7,fig4 #hd7 7the hypothenuse of #f and  
#f7 on the blade and the  rise 7#aj7 at 
,d on the tongue2 lay on the edge of the

 board to this4 ,lay  off this length on
 the three-ply at ,b ,d 7,fig4 #hb72    
take the width ,b ,c  7,fig4 #hd7 on the
 blade1 rise at ,c on the tongue2 find  
the hypothenuse1  and apply with a pair 
of compasses at ,fig4 #hb with ,b as a  
center cutting  at ,c4 ,then apply at ,d
 as a center1 cutting at ,a4 ,now find  
the  hypothenuse ,c to ,d 7,fig4 #hd71  
and apply the compasses as before1 with 
,d  and ,b as centers1 cutting at ,a and
 ,c4 ,connect up the points where the   
arcs intersect to ,b and ,d2 this is the
 face of the inclined prism1 and        
contains the true shape of rail4        
,continue the tangent line ,c ,b1 #c    
inches  or whatever is required for the 
shank1 and square the joints of the     
lines ,b and ,d4 ,in order to locate the
 major axis the horizontal trace is  now
 required4 ,stand the bed block on the  
plan 7see ,fig4 #hc74 ,run the  blade of
 the square down until it touches the   
board2 mark this1 and  remove the block4
 ,it will be seen that the bed block has

 not got the #c  inches allowed at the  
bottom1 but the horizontal trace is as  
easily  found with as without the       
allowance2 all that is required in the  
former  case being to turn the blade to 
,b 7still keeping the heel at the top of
  the bed block71 make a mark where the 
square touches and lay on the  square as
 shown at ,fig4 #hc4 ,mark at the blade1
 and slide back the square  until the   
tongue touches at ,b1 and also at the   
center ,a4 ,this gives the  true        
horizontal trace and major axis4 ,note  
the size indicated by the  arrow lines  
on the tongue 7from heel to ,b74        
,transfer the square to the  three-ply  
board 7,fig4 #hb71 placing it as shown1 
with the blade touching  ,a1 and the    
distance of the arrow lines at ,b4 ,mark
 along the inside of  the blade of the  
square and slide the square back until  
the tongue cuts  at ,a4 ,this gives the 
minor axis4 ,now continue this line     
downwards to  guide the position of the 
square shown at ,fig4 #hd4 ,describe a  

circle as  wide as the rail on the minor
 axis 7,fig4 #hb74 ,the distance from ,a
 7,fig4  #hd7 to the center of the rail 
is the distance to apply at ,fig4 #hb   
for  the center of the rail1 as this is 
the point where the center of the  rail 
is fair with the plank4 ,obtain the     
width of the face molds1 and  apply at  
,b and ,d2 lay the square on the major  
and minor axis as shown at  ,fig4 #hd4  
,lay a lath on the square1 with the     
point touching the outside  of the      
circle at ,c2 drive in a nail at the    
heel of the square2 shift the  lath     
until the point lies at ,b1 and drive in
 another nail at the side of  the       
square4 ,this trammel is now ready to   
sweep the outside of the mold1  which is
 done by reversing the square1 as shown 
by dotted lines4 ,pull  out the nails   
and repeat the process for the inside of
 the mold4    ,illustration3 ,fig4 #he4 
,now run parallel lines off the tangent 
,b for the shank2 this completes  the   
face mold1 which is now ready for the   

face of the plank4 ,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 described4 ,the  only difference1  
practically1 is that the bed block is   
made acute or  obtuse to suit plan of   
tangents4 ,the device shown at ,fig4 #he
 has been  found to answer excellently  
for striking out ellipses4 ,to make     
this1  procure two screws  inches long1 
also a piece of brass tube that will    
just slip on the plain part of the screw
 without shaking4 ,counter sink  out the
 ends until the screw heads are flush2  
cut two pieces off the  tube            
three-sixteenths and file up true--these
 pieces are best held by  sinking them  
with a bit in a piece of hardwood4 ,now 
when about to strike  an ellipse1 drive 
these screws in with the collars on to  
half major and  minor1 measured from the
 point of the trammel to the inside of  
the  collar for the major1 and to the   
outside of the collar for the minor4 ,it

  will be found that if the collar has  
been made true1 the trammel will  slip  
around the curve without causing the    
square to slip about1 the  collars      
acting as rollers4      ,w4 ,t4 ,jones1 
,boise ,city1 ,idaho1 would like to know
 of a ready way to  frame hip roofs and 
roofs of irregular or different pitches 
with the  steel square1 including       
lengths and bevels of all rafters4      
,answer3 ,these problems along with many
 others are discussed and  explained at 
length in my larger works on the ,steel 
,square1 but the  following1 which is   
somewhat condensed1 does to some extent 
cover ,mr4  ,jones' inquiries3          
,illustration3 ,fig4 #hf4    ,suppose   
,a1 ,b1 ,c1 ,d1 ,fig4 #hf1 to represent 
one end of a hip roof with a  span of   
#bd feet and a #aj-;foot rise4 ,the side
 rafter ,i ,d shown in top  sketch will 
have a run of #ab feet4 ,the common     
rafter at the end of  building1 ,i ,l1  
has a run of #af feet1 with the same    
rise1 so that the  ends and sides of the

 roofs have different pitches4 ,the     
lengths and cuts  of the common rafters 
are obtained as shown in ,fig4 #hg1 by  
taking #ab on  the blade and #aj on the 
tongue of the square and measuring      
across1  giving the length of the side  
rafter1 from which one-half the         
thickness  of the ridge1 measured square
 back from the plumb cut1 must be       
deducted4  ,the blade gives the foot cut
 and the tongue the plumb cut4 ,the     
length of  the end rafter is obtained by
 taking #af on the blade and #aj on the 
tongue1 which will of course give the   
respective cuts also4 ,the same  results
 may be obtained by applying the square 
to a straight edge and  marking along   
the blade and tongue1 which will give a 
gauge line to  which a bevel may be set4
 ,by taking #af on the blade and #ab on 
the  tongue1 as shown in ,fig4 #ij1 the 
run of the hip rafters1 #bj1 is         
obtained4    ,illustration3 ,fig4 #hg4  
,illustration3 ,fig4 #hh4               
,illustration3 ,fig4 #hi4    ,referring 

to ,fig4 #hh1 it will be seen that #bj  
on the blade and #aj on the  tongue give
 the seat and plumb cuts of the hip     
together with the length1  after        
one-half the thickness of the ridge has 
been deducted from the  side cut4 ,the  
side cut is found in a slightly         
different way from that of  a regular   
hip or valley on an ordinary roof4 ,the 
common method is to  take the length of 
the hip on the blade and run on the     
tongue1 but this  will not work in this 
case1 as the run of the hip does not be 
at an  angle of #de degrees as in       
ordinary roofs4 ,the line ,b ,j in ,fig4
 #hf must  first be obtained1 as shown  
in ,fig4 #hi4 ,joint one edge of a board
 and  square up the line ,b ,l4 ,measure
 one-half the width of building--in     
inches--on this line1 #ab in this case1 
and with the heel of the square at  the 
point ,b1 move the square until #bj on  
the blade touches the edge of  the board
 at ,e4 ,the tongue will then give the  
point ,j #ae inches2 which  is the      

length of the line required4            
,illustration3 ,fig4 #ij4    ,then take 
this line on the tongue and the length  
of the hip on the  blade1 ,fig4 #ij1 and
 the blade will give the bevel of the   
hip to lie  against the ridge4 ,as a    
general rule1 hip rafters are not       
backed1 but if  such is desired the     
lines for backing can be found by       
setting it to the  foot cut of the hip  
rafter4 ,make ,o ,r square with ,s ,o   
and gauge back as  shown in the diagram 
,a4 ,do the same on the other side1     
using the  distance ,t ,r instead of ,p 
,s4 ,the point ,o is of course at the   
center of  the line ,t ,p4              
,illustration3 ,fig4 #ia4    ,for       
lengths and bevels of jacks1 proceed as 
follows3 ,for end of roof1  and set #b  
feet on centers1 take a board and apply 
the square to it1 as  shown in ,fig4    
#ia1 with the length of the end rafter  
on the blade and the  run of the side   
rafter on the tongue4 ,space off #b1 #d1
 #f1 #h and #aj in4 on  the tongue after

 marking along both blade and tongue4   
,the lines1 ,,aa1 ,,bb1  ,,cc1 ,,dd1    
,,ee1 will give the length of the jacks1
 as well as the side cut  to fit the    
side of the hip1 the square being moved 
down along tongue  line1 while the run  
of the end rafter on blade and its rise 
on tongue  will give the seat and plumb 
cuts4 ,for the side jacks1 ,fig4 #ib    
gives the  same method1 only that the   
length of the side rafter is taken on   
the  blade and the run of the end rafter
 on the tongue4 ,if it is so desired1   
the length of the jack rafter ,a ,a may 
be deducted from the length of  the     
common rafter1 which will give the      
difference in the lengths of the  jacks4
    ,illustration3 ,fig4 #ib4           
,illustration3 ,fig4 #ic4    ,the rules 
and diagrams1 given herewith will apply 
to valley as well as  hip rafters1 and  
may be relied upon as being accurate if 
closely  followed4                      
,,rule--,see ,fig4 #hg4       ,tongue4  
,blade4       #ab      #af gives run of 

hip4       #aj      #ab gives length of 
side rafter4       #aj      #af gives   
length of end rafter4       #aj      #bj
 gives length of hip rafter4            
,,rule--,see ,fig4 #ia4       ,blade4   
,tongue4     ,common      ,end          
,rafter      #ai                #ab     
,longest    ,jack       8         #ae   
#aj_/ab        #aj       #dth        8  
8         #ab   #h_/ab         #h       
#c;d         8        8          #i     
#f_/ab         #f       #b;d         8  
8          #f   #d_/ab         #d       
,shortest      8        8          #c   
#b_/ab         #b                       
,blade gives ,side ,cut of ,jacks4      
,,rule--,see ,fig4 #ib4       ,blade4   
,tongue4     ,common     ,side          
,rafter      #ae     #g        #af      
,longest    ,jack       8        #ac    
#h        #ad       #fth        8       
8        #aa     #h        #ab          
#eth        8        8         #i       
#i        #aj       #dth        8       
8         #g     #i         #h          

#c;d         8        8         #e      
#aj         #f       #b;d         8     
8         #c    #aj         #d          
#ast        8        8         #a       
#aa         #b                   ,blade 
gives ,cut of ,jacks1 also ,sheathing4  
,these matters have been discussed at   
length1 in trade journals and also  in  
my larger volumes on ,the ,practical    
,uses of the ,steel ,square1 but the    
foregoing treatment of the subject is on
 somewhat different lines and  will     
prove interesting4      ,john           
,wilberforce1 ,toronto1 ,ont41 wants to 
know if a wreath piece for a            
single-pitch rail with level landing can
 be set out with the ,steel  ,square4   
,answer3 ,yes1 the problem can be solved
 as follows3    ,illustration3 ,fig4    
#id4    ,set out on a board the plan of 
the wreath ,a 7,fig4 #id74 ,draw the    
outside  circle and the inside and      
center line of same1 showing also the   
joints4  ,set out the pitch off the     
shank2 square up the center outside and 

inside  lines from the plan on to the   
pitch4 ,the thickness of the wreath     
piece  is found by drawing a section of 
rail under the pitch line ,b4 ,set out  
again the half-width of the well2 square
 off the pitch lines to the half  width2
 this gives major and minor axes of the 
ellipse1 as shown in the  development   
7,fig4 #id74 ,lay the square on the     
axis4 ,get a light piece of  lath1 drive
 in a nail at the half major1 and one at
 the half minor2  describe the inner    
ellipse line on the piece of timber from
 which the  wreath is to be formed2 pull
 out the nails1 and repeat the process  
for  the center and outside lines4 ,draw
 the shank and also the point as shown  
on the board4    ,illustration3 ,fig4   
#ie4    ,now cut at the joints1 allowing
 an -inch for the fitting of the joint  
after the wreath is cut and roughed out4
 ,use another piece of timber  about #b 
inches thick1 to form the bed block1 and
 cut it to the pitch  accurate and      
square in thickness4 ,screw or pin it to

 the under side of  the wreath piece    
7see ,fig4 #ie71 taking care to get it  
parallel with the  shank1 and the nails 
in clear of the saw4 ,then proceed to   
cut the wreath  with the band saw1      
beginning at the circular part1 and work
 it to the  shank inside and outside4   
,this operation should be performed most
  carefully with a narrow band saw1     
having a strong set and strained  tight1
 feeding very slowly4 ,the wreath should
 require hardly any spoke  shaving4     
,knock off the block and draw a chalk   
mark across the table1  just in front of
 the teeth4 ,the use of this line is to 
assist the  operator to get the outside 
of the wreath always touching this spot 
in  front of the saw4 ,he must carefully
 lower his hand until it is down  level 
at the shank end4 ,the top is cut first1
 and the saw should skim  along the     
outside top arris1 giving a sweep that  
cannot be excelled in  graduation of    
curve4 ,then set a gauge to the         
thickness of the rail1 mark  a line on  

the inside of the wreath1 and cut as    
before4 ,with a little  practice a      
wreath can be turned off the band saw   
ready for molding4 ,when  the shank is  
too long1 it is always better to nail   
the bed block on top  of the wreath1 and
 cut it upside down1 thus getting the   
curve portion  near the table4 ,then the
 shank can be run in with the band saw  
when the  block is knocked off4 ,the    
foregoing is for a single-pitch wreath  
as used  for stairs with level landings 
and narrow wells4 ,where the rails are  
pitched both ways1 the bed block has to 
be cut at the double  inclination4 7,see
 preceding answers47    ,illustration   
,,index                                 
,a4 ,b4 ,c4                ,,steel      
,,square--,,the ,,steel ,,square ,,and  
,,its ,,uses4                           
,division ,a4      ,preface             
#a    ,introductory remarks             
#c    ,some useful advice               
#g    ,framing posts1 girts and braces  
#i    ,testing a steel square           

#aa    ,practical uses of the steel     
square                                  
#ac    ,some rules for roof framing     
#af    ,octagon rules                   
#ai    ,lines on steel square explained 
#bb    ,varieties of squares            
#bi    ,bridge-builder's square         
#ca    ,crenelated square               
#cd    ,test diagrams                   
#cg    ,degrees on the square           
#dd                                     
,division ,b4      ,introductory        
#dg    ,slotted fence                   
#dh    ,laying out stairs               
#di    ,laying out rafters              
#ea    ,metal fences                    
#ec    ,fence adjusted for stair strings
                                    #ee 
,brace rules and diagrams               
#eg    ,regular and irregular runs      
#fj    ,roof framing                    
#fc    ,cutting rafters                 
#fd    ,octagon rafter bevels           
#fe    ,hip and valley rafters          
#fe    ,jack rafters                    

#ff    ,bevels for hips1 valleys and    
jack rafters                            
#ff    ,measuring rafters               
#fh    ,different pitches for roofs     
#gj    ,some pointers in roof framing   
#gb    ,roof diagrams                   
#gi    ,rise and run of rafters1 hips   
and jacks                               
#hb    ,cuts and bevels for rafters     
#hf    ,unequal pitches                 
#ia    ,hip-roof with deck              
#if                                     
,division ,c4      ,introductory        
#ig    ,diagram of hip-roof             
#ih    ,to cut jack rafters             
#ajj    ,hopper miters                  
#aja    ,questions and answers for      
correspondents                          
#ajb    ,joints for obtuse or acute     
angles                                  
#ajb    ,drawing circle with square     
#ajd    ,laying out stair wreath with   
square                                  
#aje    ,bevel for miter cap            
#aje    ,face mould by the square       

#ajf    ,making pitch-board by the      
square                                  
#ajg    ,to lay out braces1 girts and   
trusses                                 
#ajh    ,braces1 regular and irregular  
#aji    ,diagram of braces in position  
#aab    ,finding center of circles      
#aac    ,stair with three windows       
#aad    ,pitches and bevels for         
hand-rail                               
#aae    ,traces for hand-rail bevels    
#aaf    ,cutting out rails with band saw
                                    #aah
    ,diagram of hand-railing            
#aai    ,tangents in hand-railing       
#aba    ,getting horizontal trace of    
hand-railing                            
#abb    ,instrument for laying out      
hand-rails                              
#abd    ,framing a hip-roof             
#abe    ,diagram of hip and rafter lines
                                    #abf
    ,rafter measurement on the square   
#abg    ,bevels and cuts of roof        
#abh    ,plumb and horizontal cuts for  

hips                                    
#abi    ,length of rafters1 hips and    
jacks on square                         
#aca    ,rules for cutting rafters      
#acc    ,stair wreath for level landing 
#acc    ,wreath for single pitch rail   
#acd    ,block for cutting wreath       
#ace    ,square and plumb               
#acf                                    
,transcriber's ,notes      --,retained  
publication information from the printed
 edition3 this e,book    is             
public-domain in the country of         
publication4    --,silently corrected a 
few palpable typos4    --,moved         
illustrations to the nearest paragraph  
break4    --,in the text versions only1 
text in italics is delimited by         
underscores4    --,in the text versions 
only1 superscript text is preceded by   
caret4    --,in the ,,ascii version     
only1 subscripted numbers are preceded  
by    underscore and delimited by       
brackets4