,transcrib]'s ,notes ,conv5tional ma!matical notation requires specializ$ fonts & typesett+ conv5tions4 ,i h adopt$ mod]n comput] programm+ notation us+ only ,,ascii *>act]s4 ,! squ>e root ( #i is ?us r5d]$ z squ>eroot7#i7 & ! squ>e ( #i is squ>e7#i74 #aj divid$ by #e is 7#aj_/e7 & #aj multipli$ by #e is 7#aj 99 #e 74 ,by ! "t ,i f9i%$ eng9e]+ s*ool 9 #aifc1 ! slide rule 0 a well worn tool ( my trade4 ,i did n use an electronic calculator = ano!r t5 ye>s4 ,consid] t my pr$ecessors _h little else to use--?9k ,b\ld] ,dam 7) all its electrical1 me*anical & con/ruction calculations74 ,r ?an deal+ ) elaborate rules = position+ ! decimal po9t1 ,i 0 taught to fir/ scale ! factors & deal ) ! decimal position sep>ately4 ,= example3 #abcj 99 4#jjjjic #a4bc;,e#c 99 #i4c;,e-#e #a4bc;,e#c means multiply #a4bc by #aj to ! p[] #c4 #i4c;,e-#e means multiply #i4c by #j4a to ! p[] #e or #aj to ! p[] -#e4 ,! computation is ?us #a4bc 99 #i4c 99 #a;,e#c 99 #a;,e-#e ,! expon5ts are simply add$4 #a4bc 99 #i4c 99 #a;,e-#b #aa4d 99 #a;,e-#b 4#aad ,:5 tak+ roots1 divide ! expon5t by ! root4 ,! squ>e root ( #a;,e#f is #a;,e#c ,! cube root ( #a;,e#ab is #a;,e#d4 ,:5 tak+ p[]s1 multiply ! expon5t by ! p[]4 ,! cube ( #a;,e#e is #a;,e#ae4 ,end ,transcrib]'s ,notes ,,in/ructions = us+ a ,,slide ,,rule ,,save ,,"t6 ,,d ,,! ,,foll[+ ,,in/antly ,,)\t ,,pap] ,,& ,,p5cil ,,multiplication ,,division ,,reciprocal ,,values ,,squ>es ,,cubes ,,extraction ,,( ,,squ>e ,,root ,,extraction ,,( ,,cube ,,root ,,diamet] ,,or ,,area ,,( ,,circle ,illu/ration3 ,two images ( a slide rule4 ,,in/ructions ,,= ,,us+ ,a ,,slide ,,rule ,! slide rule is a device = easily & quickly multiply+1 divid+ & extract+ squ>e root & cube root4 ,x w also p]=m any comb9ation ( ^! processes4 ,on ?is acc\nt1 x is f\nd extremely useful by /ud5ts & tea*]s 9 s*ools & colleges1 by eng9e]s1 ar*itects1 draftsm51 surveyors1 *emi/s1 & _m o!rs4 ,acc\ntants & cl]ks f9d x v helpful :5 approximate calculations mu/ be made rapidly4 ,! op]ation ( a slide rule is extremely easy1 & x is well wor? :ile = anyone :o is call$ ^u to d mu* num]ical calculation to le>n to use "o4 ,x is ! purpose ( ?is manual to expla9 ! op]ation 9 su* a way t a p]son :o has nev] be=e us$ a slide rule may tea* himself to d s4 ,,description ,,( ,,slide ,,rule ,! slide rule consi/s ( ?ree p>ts 7see figure #a74 ,b is ! body ( ! rule & c>ries ?ree scales m>k$ ,a1 ,d & ,k4 ,s is ! slid] :i* moves relative to ! body & also c>ries ?ree scales m>k$ ,b1 ,,ci & ,c4 ,r is ! runn] or indicator & is m>k$ 9 ! c5t] ) a hair-l9e4 ,! scales ,a & ,b are id5tical & are us$ 9 problems involv+ squ>e root4 ,scales ,c & ,d are also id5tical & are us$ = multiplication & division4 ,scale ,k is = f9d+ cube root4 ,scale ,,ci1 or ,c-inv]se1 is l scale ,c except t x is laid (f f "r to left in/ead ( f left to "r4 ,x is useful 9 problems involv+ reciprocals4 ,,multiplication ,we w />t ) a v simple example3 ,example #a3 #b 99 #c #f ,to prove ?is on ! slide rule1 move ! slid] s t ! #a at ! left-h& end ( ! ,c scale is directly ov] ! l>ge #b on ! ,d scale 7see figure #a74 ,!n move ! runn] till ! hair-l9e is ov] #c on ! ,c scale4 ,read ! answ]1 #f1 on ! ,d scale "u ! hair-l9e4 ,n[1 let u consid] a m complicat$ example3 ,example #b3 #b4ab 99 #c4af #f4gj ,z be=e1 set ! #a at ! left-h& end ( ! ,c scale1 :i* we w call ! left-h& index ( ! ,c scale1 ov] #b4ab on ! ,d scale 7,see figure #b74 ,! hair-l9e ( ! runn] is n[ plac$ ov] #c4af on ! ,c scale & ! answ]1 #f4gj1 read on ! ,d scale4 ,,me?od ,,( ,,mak+ ,,sett+s ,9 ord] to und]/& j :y #b4ab is set :]e x is 7figure #b71 notice t ! int]val f #b to #c is divid$ into #aj l>ge or major divisions1 ea* ( :i* is1 ( c\rse1 equal to "o-t5? 7#j4a7 ( ! am\nt repres5t$ by ! :ole int]val4 ,! major divisions are 9 turn divid$ into #e small or m9or divisions1 ea* ( :i* is "o-fif? or two-t5?s 7#j4b7 ( ! major division1 t is #j4jb ( ! :ole int]val4 ,!re=e1 ! index is set above #b #a major division #a m9or division #b #j4a #j4jb #b4ab4 ,9 ! same way we f9d #c4af on ! ,c scale4 ,:ile we are on ?is subject1 notice t 9 ! int]val f #a to #b ! major divisions are m>k$ ) ! small figures #a to #i & ! m9or divisions are #j4a ( ! major divisions4 ,9 ! int]vals f #b to #c & #c to #d ! m9or divisions are #j4b ( ! major divisions1 & = ! re/ ( ! ,d 7or ,c7 scale1 ! m9or divisions are #j4e ( ! major divisions4 ,read+ ! sett+ f a slide rule is v mu* l read+ measurem5ts f a rul]4 ,imag9e t ! divisions betwe5 #b & #c on ! ,d scale 7figure #b7 are ^? ( a rul] divid$ into t5?s ( a foot1 & ea* t5? ( a foot divid$ 9 #e p>ts #j4jb ( a foot long4 ,!n ! di/ance f "o on ! left-h& end ( ! ,d scale 7n %[n 9 figure #b7 to "o on ! left-h& end ( ! ,c scale w\ld he #b4ab feet4 ,( c\rse1 a foot rule is divid$ into p>ts ( uni=m l5g?1 :ile ^? on a slide rule get small] t[>d ! "r-h& end1 b ?is example may help to give an idea ( ! me?od ( mak+ & read+ sett+s4 ,n[ consid] ano!r example4 ,example #c;a3 #b4ab 99 #g4ce #ae4f ,if we set ! left-h& index ( ! ,c scale ov] #b4ab z 9 ! la/ example1 we f9d t #g4ce on ! ,c scale falls out beyond ! body ( ! rule4 ,9 a case l ?is1 simply use ! "r-h& index ( ! ,c scale4 ,if we set ?is ov] #b4ab on ! ,d scale & move ! runn] to #g4ce on ! ,c scale we read ! result #ae4f on ! ,d scale "u ! hair-l9e4 ,n[1 ! "q imm$iately arises1 :y did we call ! result #ae4f & n #a4ef8 ,! answ] is t ! slide rule takes no acc\nt ( decimal po9ts4 ,?us1 ! sett+s w\ld be id5tical = all ( ! foll[+ products3 ,example #c3 a-- #b4ab 99 #g4ce #ae4f b-- #ba4b 99 #g4ce #aef4j c-- #bab 99 #gc4e #aefjj4 d-- #b4ab 99 4#jgce 4#aef e-- 4#jjbab 99 #gce 4#jaef ,! mo/ conv5i5t way to locate ! decimal po9t is to make a m5tal multiplication us+ only ! fir/ digits 9 ! giv5 factors4 ,!n place ! decimal po9t 9 ! slide rule result s t its value is ne>e/ t ( ! m5tal multiplication4 ,?us1 9 example #c;a above1 we c multiply #b by #g 9 our heads & see imm$iately t ! decimal po9t mu/ be plac$ 9 ! slide rule result #aef s t x becomes #ae4f :i* is ne>e/ to #ad4 ,9 example #c;b 7#bj 99 #g #adj71 s we mu/ place ! decimal po9t to give #aef4 ,! read] c readily v]ify ! o!r examples 9 ! same way4 ,s9ce ! product ( a numb] by a second numb] is ! same z ! product ( ! second by ! fir/1 x makes no diff]5ce :i* ( ! two numb]s is set fir/ on ! slide rule4 ,?us1 an alt]native way ( work+ example #b w\ld be to set ! left-h& index ( ! ,c scale ov] #c4af on ! ,d scale & move ! runn] to #b4ab on ! ,c scale & read ! answ] "u ! hair-l9e on ! ,d scale4 ,! ,a & ,b scales are made up ( two id5tical halves ea* ( :i* is v simil> to ! ,c & ,d scales4 ,multiplication c also be c>ri$ out on ei!r half ( ! ,a & ,b scales exactly z x is done on ! ,c & ,d scales4 ,h[ev]1 s9ce ! ,a & ,b scales are only half z long z ! ,c & ,d scales1 ! accuracy is n z good4 ,x is sometimes conv5i5t to multiply on ! ,a & ,b scales 9 m complicat$ problems z we %all see lat] on4 ,a gr\p ( examples foll[ :i* cov] all ! possible comb9ation ( sett+s :i* c arise 9 ! multiplication ( two numb]s4 ,example #d3 #bj 99 #c #fj #e3 #he 99 #b #agj #f3 #de 99 #ce #aege #g3 #aea 99 #db #fcdb #h3 #f4e 99 #ae #ig4e #i3 4#cd 99 4#jh 4#jbgb #aj3 #ge 99 #bf #aiej #aa3 4#jjjed 99 #a4d 4#jjjgef #ab3 #aa4a 99 #b4g #bi4ig #ac3 #a4ja 99 #ed #ed4e #ad3 #c4ad 99 #be #gh4e ,,division ,s9ce multiplication & division are inv]se processes1 division on a slide rule is done by mak+ ! same sett+s z = multiplication1 b 9 rev]se ord]4 ,suppose we h ! example3 ,example #ae3 7#f4gj _/ #b4ab7 #c4af ,set indicator ov] ! divid5d #f4gj on ! ,d scale4 ,move ! slid] until ! divisor #b4ab on ! ,c scale is "u ! hair-l9e4 ,!n read ! result on ! ,d scale "u ! left-h& index ( ! ,c scale4 ,z 9 multiplication1 ! decimal po9t mu/ be plac$ by a sep>ate process4 ,make all ! digits except ! fir/ 9 bo? divid5d & divisor equal z]o & m5tally divide ! result+ numb]s4 ,place ! decimal po9t 9 ! slide rule result s t x is ne>e/ to ! m5tal result4 ,9 example #ae1 we m5tally divide #f by #b4 ,!n we place ! decimal po9t 9 ! slide rule result #caf s t x is #c4af :i* is ne>e/ to #c4 ,a gr\p ( examples = practice 9 division foll[3 ,example #af3 #cd _/ #b #ag #ag3 #di _/ #g #g #ah3 #acb _/ #ab #aa #ai3 #dhj _/ #af #cj #bj3 #a4je _/ #ce 4#jc #ba3 #d4cb _/ #ab 4#cf #bb3 #e4bc _/ #f4ae 4#he #bc3 #ag4a _/ #d4e #c4h #bd3 #ahie _/ #f4jf #cac #be3 #de _/ 4#jag #bfdg ,,! ,,ci ,,scale ,if we divide "o 7#a7 by any numb] ! answ] is call$ ! reciprocal ( ! numb]4 ,?us1 "o-half is ! reciprocal ( two1 "o-qu>t] is ! reciprocal ( f\r4 ,if we take any numb]1 say #ad1 & multiply x by ! reciprocal ( ano!r numb]1 say #b1 we get3 ,example #bf3 #ad 99 7#a_/b7 #g :i* is ! same z #ad divid$ by two4 ,?is process c be c>ri$ out directly on ! slide rule by use ( ! ,,ci scale4 ,numb]s on ! ,,ci scale are reciprocals ( ^? on ! ,c scale4 ,?us we see t #b on ! ,,ci scale comes directly ov] #j4e or #a_/b on ! ,c scale4 ,simil>ly #d on ! ,,ci scale comes ov] #j4be or #a_/d on ! ,c scale1 & s on4 ,to d example #bf by use ( ! ,,ci scale1 proce$ exactly z if y 7 go+ to multiply 9 ! usual mann] except t y use ! ,,ci scale in/ead ( ! ,c scale4 ,fir/ set ! left-h& index ( ! ,c scale ov] #ad on ! ,d scale4 ,!n move ! indicator to #b on ! ,,ci scale4 ,read ! result1 #g1 on ! ,d scale "u ! hair-l9e4 ,?is is really ano!r way ( divid+4 ,,! ,,read] ,,is ,,advis$ ,,to ,,"w ,,examples #af ,,to #be ,,ov] ,,aga9 ,,by ,,use ,,( ,,! ,,ci ,,scale4 ,,squ>+ ,,& ,,squ>e ,,root ,if we take a numb] & multiply x by itself we call ! result ! squ>e ( ! numb]4 ,! process is call$ squ>+ ! numb]4 ,if we f9d ! numb] :i*1 :5 multipli$ by itself is equal to a giv5 numb]1 ! =m] numb] is call$ ! squ>e root ( ! giv5 numb]4 ,! process is call$ extract+ ! squ>e root ( ! numb]4 ,bo? ^! processes may be c>ri$ out on ! ,a & ,d scales ( a slide rule4 ,= example3 ,example #bg3 #d 99 #d squ>e7 #d 7 #af ,set indicator ov] #d on ,d scale4 ,read #af on ,a scale "u hair-l9e4 ,example #bh3 squ>e7 #be4d 7 #fdf4j ,! decimal po9t mu/ be plac$ by m5tal survey4 ,we "k t squ>e7 #be4d 7 mu/ be a little l>g] ?an squ>e7 #be 7 #fbe s t x mu/ be #fdf4j4 ,to extract a squ>e root1 we set ! indicator ov] ! numb] on ! ,a scale & read ! result "u ! hair-l9e on ! ,d scale4 ,:5 we exam9e ! ,a scale we see t !re are two places :]e any giv5 numb] may be set1 s we mu/ h "s way ( decid+ 9 a giv5 case :i* half ( ! ,a scale to use4 ,! rule is z foll[s3 7a7 ,if ! numb] is great] ?an "o4 ,= an odd numb] ( digits to ! left ( ! decimal po9t1 use ! left-h& half ( ! ,a scale4 ,= an ev5 numb] ( digits to ! left ( ! decimal po9t1 use ! "r-h& half ( ! ,a scale4 7b7 ,if ! numb] is less ?an "o4 ,= an odd numb] ( z]os to ! "r ( ! decimal po9t be=e ! fir/ digit n a z]o1 use ! left-h& half ( ! ,a scale4 ,= none or any ev5 numb] ( z]os to ! "r ( ! decimal po9t be=e ! fir/ digit n a z]o1 use ! "r-h& half ( ! ,a scale4 ,example #bi3 squ>eroot7 #aeg 7 #ab4e ,s9ce we h an odd numb] ( digits set indicator ov] #aeg on left-h& half ( ,a scale4 ,read #ab4e on ! ,d scale "u hair-l9e4 ,to *eck ! decimal po9t ?9k ( ! p]fect squ>e ne>e/ to #aeg4 ,x is #ab 99 #ab #add1 s t squ>eroot7#aeg7 mu/ be a little m ?an #ab or #ab4e4 ,example #cj3 squ>eroot7 4#jjcg 7 4#jfjh ,9 ?is numb] we h an ev5 numb] ( z]os to ! "r ( ! decimal po9t1 s we mu/ set ! indicator ov] #cg on ! "r-h& half ( ! ,a scale4 ,read #fjh "u ! hair-l9e on ,d scale4 ,to place ! decimal po9t write3 squ>eroot7 4#jjcg 7 squ>eroot7 #cg_/ajjjj 7 #a_/ajj squ>eroot7 #cg 7 ,! ne>e/ p]fect squ>e to #cg is #f 99 #f #cf1 s ! answ] %\ld be a little m ?an #j4jf or 4#jfjh4 ,all ( :at has be5 said ab\t use ( ! ,a & ,d scales = squ>+ & extract+ squ>e root applies equally well to ! ,b & ,c scales s9ce !y are id5tical to ! ,a & ,d scales respectively4 ,a numb] ( examples foll[ = squ>+ & ! extraction ( squ>e root4 ,example #ca3 squ>e7 #b 7 #d #cb3 squ>e7 #ae 7 #bbe #cc3 squ>e7 #bf 7 #fgf #cd3 squ>e7 #ai4fe 7 #chf #ce3 squ>eroot7 #fd 7 #h #cf3 squ>eroot7 #f4d 7 #b4ec #cg3 squ>eroot7 #dih 7 #bb4e #ch3 squ>eroot7 #bejj 7 #ej #ci3 squ>eroot7 4#af 7 4#jd #dj3 squ>eroot7 4#jc 7 4#agc ,,cub+ ,,& ,,cube ,,root ,if we take a numb] & multiply x by itself1 & !n multiply ! result by ! orig9al numb] we get :at is call$ ! cube ( ! orig9al numb]4 ,?is process is call$ cub+ ! numb]4 ,! rev]se process ( f9d+ ! numb] :i*1 :5 multipli$ by itself & !n by itself aga91 is equal to ! giv5 numb]1 is call$ extract+ ! cube root ( ! giv5 numb]4 ,?us1 s9ce #e 99 #e 99 #e #abe1 #abe is ! cube ( #e & #e is ! cube root ( #abe4 ,to f9d ! cube ( any numb] on ! slide rule set ! indicator ov] ! numb] on ! ,d scale & read ! answ] on ! ,k scale "u ! hair-l9e4 ,to f9d ! cube root ( any numb] set ! indicator ov] ! numb] on ! ,k scale & read ! answ] on ! ,d scale "u ! hair-l9e4 ,j z on ! ,a scale1 :]e !re 7 two places :]e y c\ld set a giv5 numb]1 on ! ,k scale !re are ?ree places :]e a numb] may be set4 ,to tell :i* ( ! ?ree to use1 we mu/ make use ( ! foll[+ rule4 7a7 ,if ! numb] is great] ?an "o4 ,= #a1 #d1 #g1 #aj1 etc41 digits to ! left ( ! decimal po9t1 use ! left-h& ?ird ( ! ,k scale4 ,= #b1 #e1 #h1 #aa1 etc41 digits to ! left ( ! decimal po9t1 use ! middle ?ird ( ! ,k scale4 ,= #c1 #f1 #i1 #ab1 etc41 digits to ! left ( ! decimal po9t use ! "r-h& ?ird ( ! ,k scale4 7b7 ,if ! numb] is less ?an "o4 ,we n[ tell :i* scale to use by c\nt+ ! numb] ( z]os to ! "r ( ! decimal po9t be=e ! fir/ digit n z]o4 ,if !re are #b1 #e1 #h1 #aa1 etc41 z]os1 use ! left-h& ?ird ( ! ,k scale4 ,if !re are #a1 #d1 #g1 #aj1 etc41 z]os1 !n use ! middle ?ird ( ! ,k scale4 ,if !re are no z]os or #c1 #f1 #i1 #ab1 etc41 z]os1 !n use ! "r-h& ?ird ( ! ,k scale4 ,= example3 ,example #da3 cuberoot7 #ahe 7 #e4gj ,s9ce !re are #c digits 9 ! giv5 numb]1 we set ! indicator on #ahe 9 ! "r-h& ?ird ( ! ,k scale1 & read ! result #egj on ! ,d scale4 ,we c place ! decimal po9t by ?9k+ ( ! ne>e/ p]fect cube1 :i* is #abe4 ,!re=e1 ! decimal po9t mu/ be plac$ s z to give #e4gj1 :i* is ne>e/ to #e1 ! cube root ( #abe4 ,example #db3 cuberoot7 4#jcd 7 4#cbd ,s9ce !re is "o z]o betwe5 ! decimal po9t & ! fir/ digit n z]o1 we mu/ set ! indicator ov] #cd on ! middle ?ird ( ! ,k scale4 ,we read ! result #cbd on ! ,d scale4 ,! decimal po9t may be plac$ z foll[s3 cuberoot7 4#jcd 7 cuberoot7 #cd_/ajjj 7 #a_/aj cuberoot7 #cd 7 ,! ne>e/ p]fect cube to #cd is #bg1 s our answ] mu/ be close to "o-t5? ( ! cube root ( #bg or ne>ly #j4c4 ,!re=e1 we mu/ place ! decimal po9t to give #j4cbd4 ,a gr\p ( examples = practice 9 extraction ( cube root foll[s3 ,example #dc3 cuberoot7 #fd 7 #d #dd3 cuberoot7 #h 7 #b #de3 cuberoot7 #cdc 7 #g #df3 cuberoot7 4#jjjgae 7 4#jhid #dg3 cuberoot7 4#jjgae 7 4#aic #dh3 cuberoot7 4#jgae 7 4#dae #di3 cuberoot7 4#eaf 7 4#hjc #ej3 cuberoot7 #bg4h 7 #c4jc #ea3 cuberoot7 #e4di 7 #a4gf #eb3 cuberoot7 #hg4a 7 #d4dc ,,! #a4e ,,& #b_/c ,,p[] ,if ! indicator is set ov] a giv5 numb] on ! ,a scale1 ! numb] "u ! hair-l9e on ! ,k scale is ! #a4e p[] ( ! giv5 numb]4 ,if ! indicator is set ov] a giv5 numb] on ! ,k scale1 ! numb] "u ! hair-l9e on ! ,a scale is ! #b_/c p[] ( ! giv5 numb]4 ,,comb9ations ,,( ,,processes ,a slide rule is especially useful :]e "s comb9ation ( processes is necess>y1 l multiply+ #c numb]s toge!r & divid+ by a ?ird4 ,op]ations ( ?is sort may be p]=m$ 9 su* a way t ! f9al answ] is obta9$ imm$iately )\t f9d+ int]m$iate results4 #a4 ,multiply+ sev]al numb]s toge!r4 ,= example1 suppose x is desir$ to multiply #d 99 #h 99 #f4 ,place ! "r-h& index ( ! ,c scale ov] #d on ! ,d scale & set ! indicator ov] #h on ! ,c scale4 ,n[1 leav+ ! indicator :]e x is1 move ! slid] till ! "r-h& index is "u ! hairl9e4 ,n[1 leav+ ! slid] :]e x is1 move ! indicator until x is ov] #f on ! ,c scale1 & read ! result1 #aib1 on ! ,d scale4 ,?is may be cont9u$ indef9itely1 & s z _m numb]s z desir$ may be multipli$ toge!r4 ,example #ec3 #b4cb 99 #aed 99 4#jcge 99 4#ef #g4ed #b4 ,multiplication & division4 ,suppose we wi% to d ! foll[+ example3 ,example #ed3 7#d 99 #ae7 _/ #b4e #bd ,fir/ divide #d by #b4e4 ,set indicator ov] #d on ! ,d scale & move ! slid] until #b4e is "u ! hair-l9e4 ,! result ( ?is division1 #a4f1 appe>s "u ! left-h& index ( ! ,c scale4 ,we d n ne$ to write x d[n1 h[ev]1 b we c imm$iately move ! indicator to #ae on ! ,c scale & read ! f9al result #bd on ! ,d scale "u ! hair-l9e4 ,let u consid] a m complicat$ problem ( ! same type3 ,example #ee3 7#cj_/g4e7 99 7#b_/d7 99 7#d4e_/e7 99 7#a4e_/c7 4#i ,fir/ set indicator ov] #cj on ! ,d scale & move slid] until #g4e on ! ,c scale comes "u ! hairl9e4 ,! int]m$iate result1 #d1 appe>s "u ! "r-h& index ( ! ,c scale4 ,we d n ne$ to write x d[n b m]ely note x by mov+ ! indicator until ! hair-l9e is ov] ! "r-h& index ( ! ,c scale4 ,n[ we want to multiply ?is result by #b1 ! next factor 9 ! num]ator4 ,s9ce two is out beyond ! body ( ! rule1 transf] ! slid] till ! o!r 7left-h&7 index ( ! ,c scale is "u ! hair-l9e1 & !n move ! indicator to #b on ! ,c scale4 ,?us1 successive division & multiplication is cont9u$ until all ! factors h be5 us$4 ,! ord] 9 :i* ! factors are tak5 does n affect ! result4 ,) a little practice y w le>n to take !m 9 ! ord] :i* w require ! fewe/ sett+s4 ,! foll[+ examples are = practice3 ,example #ef3 7#f_/c4e7 99 7#d_/e7 99 7#c4e_/b4d7 99 7#b4h_/g7 4#h ,example #eg3 #ceb 99 7#bgc_/bed7 99 7#gfj_/gfh7 #cgd ,an alt]native me?od ( do+ ^! examples is to proce$ exactly z ?\gh y 7 multiply+ all ! factors toge!r1 except t :5ev] y come to a numb] 9 ! d5om9ator y use ! ,,ci scale in/ead ( ! ,c scale4 ,! read] is advis$ to practice bo? me?ods & use :i*ev] "o he likes be/4 #c4 ,! area ( a circle4 ,! area ( a circle is f\nd by multiply+ #c4adaf,,pi by ! squ>e ( ! radius or by "o-qu>t] ! squ>e ( ! diamet] ,=mula3 ,a ,,pi 99 squ>e7 ,r 7 ,a ,,pi 99 7 squ>e7 ,d 7 _/ #d 7 ,example #eh3 ,! radius ( a circle is #j4be in*es2 f9d its area4 ,area ,,pi 99 squ>e7#j4be7 #j4aif squ>e in*es4 ,set left-h& index ( ,c scale ov] #j4be on ,d scale4 squ>e7#j4be7 n[ appe>s above ! left-h& index ( ! ,b scale4 ,?is c be multipli$ by ,,pi by mov+ ! indicator to ,,pi on ! ,b scale & read+ ! answ] 4#aif on ! ,a scale4 ,?is is an example :]e x is conv5i5t to multiply ) ! ,a & ,b scales4 ,example #ei3 ,! diamet] ( a circle is #h4a feet4 ,:at is its area8 ,area 7,,pi _/ #d7 99 squ>e7#h4a7 4#ghed 99 squ>e7#h4a7 #ea4g sq4 in*es4 ,set "r-h& index ( ! ,c scale ov] #h4a on ! ,d scale4 ,move ! indicator till hair-l9e is ov] 4#ghed 7! special long m>k ne> #h7 at ! "r h& ( ! ,b scale4 ,read ! answ] "u ! hair-l9e on ! ,a scale4 ,ano!r way ( f9d+ ! area ( a circle is to set #ghed on ! ,b scale to "o ( ! indices ( ! ,a scale1 & read ! area f ! ,b scale directly above ! giv5 diamet] on ! ,d scale4 #d4 ,! circumf]5ce ( a circle4 ,set ! index ( ! ,b scale to ! diamet] & read ! answ] on ! ,a scale opposite ,,pi on ! ,b scale ,=mula3 ,c ,,pi 99 ,d ,c #b 99 ,,pi 99 ,r ,example #fj3 ,! diamet] ( a circle is #a4ed in*es1 :at is its circumf]5ce8 ,set ! left-h& index ( ! ,b scale to #a4ed on ! ,a scale4 ,read ! circumf]5ce #d4he in*es above ,,pi on ! ,b scale4 ,,examples ,,= ,,practice #fa3 ,:at is ! area ( a circle #cb-a_/b in*es 9 diamet]8 ,answ] #hcj sq4 in*es #fb3 ,:at is ! area ( a circle #bd in*es 9 diamet]8 ,answ] #deb sq4 in*es #fc3 ,:at is ! circumf]5ce ( a circle ^: diamet] is #ie feet8 ,answ] #bih ft4 #fd3 ,:at is ! circumf]5ce ( a circle ^: diamet] is #c4fe in*es8 ,answ] #aa4e in*es #e4 ,ratio & ,proportion4 ,example #fe3 #c 3 #g 3 3 #d 3 ,x or 7#c_/g7 7#d_/x7 ,f9d ,x ,set #c on ,c scale ov] #g on ,d scale4 ,read ,x on ,d scale "u #d on ,c scale4 ,9 fact1 any numb] on ! ,c scale is to ! numb] directly "u x on ! ,d scale z #c is to #g4 ,,practical ,,problems ,,solv$ ,,by ,,slide ,,rule #a4 ,disc\nt4 ,a firm buys a typewrit] ) a li/ price ( #aej1 subject to a disc\nt ( #bj & #aj4 ,h[ mu* does x pay8 ,a disc\nt ( #bj means #j4h ( ! li/ price1 & #aj m means #j4h ,x #j4i ,x #aej #ajh4 ,to d ?is on ! slide rule1 put ! index ( ! ,c scale opposite #h on ! ,d scale & move ! indicator to #i on ! ,c scale4 ,!n move ! slid] till ! "r-h& index ( ! ,c scale is "u ! hairl9e4 ,n[1 move ! indicator to #aej on ! ,c scale & read ! answ] #ajh on ! ,d scale4 ,notice t 9 ?is1 z 9 _m practical problems1 !re is no "q ab\t :]e ! decimal po9t %\ld g4 #b4 ,sales ,tax4 ,a man buys an article wor? #ab & he mu/ pay a sales tax ( #a4e4 ,h[ mu* does he pay8 ,a tax ( #a4e means he mu/ pay #a4jae 99 #ab4jj4 ,set index ( ,c scale at #a4jae on ,d scale4 ,move indicator to #ab on ,c scale & read ! answ] #ab4ah on ! ,d scale4 ,a long] b m accurate way is to multiply #ab 99 4#jae & add ! result to #ab4 #c4 ,unit ,price4 ,a motori/ buys #ag gallons ( gas at #ai4e c5ts p] gallon4 ,h[ mu* does he pay8 ,set index ( ,c scale at #ag on ,d scale & move indicator to #ai4e on ,c scale & read ! answ] #c4cb on ! ,d scale4 #d4 ,gasol9e ,mileage4 ,an automobile goes #age miles on #ab gallons ( gas4 ,:at is ! av]age gasol9e consumption8 ,set indicator ov] #age on ,d scale & move slid] till #ab is "u hair-l9e4 ,read ! answ] #ad4f miles p] gallon on ! ,d scale "u ! left-h& index ( ! ,c scale4 #e4 ,av]age ,spe$4 ,a motori/ makes a trip ( #bef miles 9 #g4e h\rs4 ,:at is 8 av]age spe$8 ,set indicator ov] #bef on ,d scale4 ,move slid] till #g4e on ! ,c scale is "u ! hair-l9e4 ,read ! answ] #cd4b miles p] h\r "u ! "r-h& index ( ! ,c scale4 #f4 ,decimal ,p>ts ( an ,in*4 ,:at is #e_/af ( an in* express$ z decimal fraction8 ,set #af on ,c scale ov] #e on ,d scale & read ! result 4#cabe in*es on ! ,d scale "u ! left-h& index ( ! ,c scale4 #g4 ,physics4 ,a c]ta9 quantity ( gas occupies #abjj cubic c5timet]s at a temp]ature ( #ae degrees ,c & #gdj millimet]s pressure4 ,:at volume does x occupy at #j degrees ,c & #gfj millimet]s pressure8 ,volume #abjj ,x 7#gdj_/gfj7 99 7#bgc_/bhh7 #aajj cubic cm4 ,set #gfj on ,c scale ov] #ab on ,d scale4 ,move indicator to #gdj on ,c scale4 ,move slid] till #bhh on ,c scale is "u hair-l9e4 ,move indicator to #bgc on ,c scale4 ,read answ]1 #aaaj1 "u hair-l9e on ,d scale4 #h4 ,*emi/ry4 ,h[ _m grams ( hydrog5 are =m$ :5 #hj grams ( z9c react ) suffici5t hydro*loric acid to dissolve ! metal8 7#hj _/ ,x 7 7 #fe4d _/ #b4ja7 ,set #fe4d on ,c scale ov] #b4ja on ,d scale4 ,read ,x #b4df grams "u #hj on ,c scale4 ,9 conclusion1 we want to impress ^u ^? to :om ! slide rule is a new me?od ( do+ _! ma!matical calculations1 & also ! exp]i5c$ op]ator ( a slide rule1 t if !y w =m a habit (1 & apply !mselves to1 us+ a slide rule at "w1 /udy1 or dur+ recreations1 !y w be well rew>d$ 9 ! sav+ ( "t & en]gy4 ,,always ,,h ,,y\r ,,slide ,,rule ,,& ,,in/ruction ,,book ,,) ,,y1 ! same z y w\ld a f\nta9 p5 or p5cil4 ,! pres5t day wond]s ( ! tw5tie? c5tury prove t !re is no end to :at an individual c accompli%--! same applies to ! slide rule4 ,y w f9d aft] practice t y w be able to d _m specializ$ problems t are n outl9$ 9 ?is in/ruction book4 ,x dep5ds entirely ^u y\r ability to d :at we advocate & to be slide-rule consci\s 9 all y\r ma!matical problems4 ,,conv]sion ,,factors #a4 ,l5g? #a mile #ebhj feet #agfj y>ds #a in* #b4ed c5timet]s #a met] #ci4cg in*es #b4 ,weight 7or ,mass7 #a p\nd #af ounces #j4decf kilograms #a kilogram #b4b p\nds #a long ton #bbdj p\nds #a %ort ton#bjjj p\nds #c4 ,volume #a liquid qu>t #j4ide litres #a litre #a4jf liquid qu>ts #a ,u4 ,s4 gallon #d qu>ts #bca cubic in*es #d4 ,angul> ,measure #c4ad radians ,,pi radians #ahj degrees #a radian #eg4cj degrees #e4 ,pressure #gfj millimet]s ( m]cury #ad4g p\nds p] squ>e in* #f4 ,p[] #a horse p[] #eej foot p\nds p] second #gdf watts #g4 ,miscellane\s #fj miles p] h\r #hh feet p] second #ihj c5timet]s p] second p] second #cb4b feet p] second p] second accel]ation ( gravity4 #a cubic foot ( wat] weighs #fb4d p\nds #a gallon ( wat] weighs #h4cd p\nds ,pr9t$ 9 ,u4 ,s4 ,a4 ,,in/ructions ,,= ,,us+ ,a ,,slide ,,rule ,,copyright$ ,,by ,w4 ,,/anley ,,co4 ,comm]cial ,tru/ ,build+1 ,philadelphia1 ,pa4