,transcrib]'s ,notes3 ,und]scores 80 be=e & aft] a ^w or phrase indicate italics 9 ! orig9al text4 ,equal signs 80 be=e & aft] a ^w or phrase indicate bold 9 ! orig9al text4 ,small capitals h be5 conv]t$ to ,,solid capitals4 ,illu/rations h be5 mov$ s !y d n break up p>agraphs4 ,old or antiquat$ spell+s h be5 pres]v$4 ,typographical & punctuation errors h be5 sil5tly correct$4 ,! li/ ( works by ,sir ,david ,brew/] has be5 mov$ =m ! fir/ page to ! end ( ! text4 ,illu/ration ,,! ,,kaleidoscope1 ,,its ,,hi/ory1 ,,!ory1 ,,& ,,con/ruction4 ,,) ,,its ,,application ,,to ,,! ,,f9e ,,& ,,useful ,,arts4 ,,by ,,sir ,,david ,,brew/]1 ,k4,h41 ,m4,a41 ,d4,c4,l41 ,f4,r4,s41 ,v4,p4,r4,s41 ,,ed941 ,m4,r4,i4,a41 ,f4,g4,s41 ,f4,r4,a4,s41 ,,associate ,,( ,,! ,,imp]ial ,,in/itute ,,( ,,france1 ,,honor>y ,,or ,,correspond+ ,,memb] ,,( ,,! ,,academies ,,( ,,pet]sburgh1 ,,vi5na1 ,,b]l91 ,,cop5hag51 ,,/ockholm1 ,,brussels1 ,,gott+51 ,,mod5a1 ,,& ,,( ,,! ,,national ,,in/itute ,,( ,,wa%+ton1 ,,& ,,pr9cipal ,,( ,,! ,,unit$ ,,colleges ,,( ,,/4 ,,salvator ,,& ,,/4 ,,leon>d1 ,,/4 ,,&rews4 ,nihil tangit quod non ornat4 ,illu/ration ,?ird ,edition1 greatly enl>g$4 ,,) ,,fifty-,,six ,,wood ,,engrav+s ,,& ,,"o ,,plate4 ,,london3 ,,john ,,camd5 ,,hott51 ,,piccadilly4 #ahgj4 ,,cont5ts4 ,,page ,,introduction--,,hi/ory ,,( ,,! ,,kaleidoscope1 #a ,,*ap4 ,i4--,,prelim9>y ,,pr9ciples ,,respect+ ,,! ,,effects ,,( ,,comb9+ ,,two ,,pla9 ,,mirrors1 #i ,,ii4--,,on ,,! ,,pr9ciples ,,( ,,! ,,kaleidoscope1 ,,& ,,! ,,=mation ,,( ,,symmetrical ,,pictures ,,by ,,! ,,comb9ation ,,( ,,direct ,,& ,,inv]t$ ,,images1 #af ,,iii4--,,on ,,! ,,effects ,,produc$ ,,by ,,! ,,motion ,,( ,,! ,,object ,,& ,,! ,,mirrors1 #bf ,,iv4--,,on ,,! ,,effects ,,produc$ ,,^u ,,! ,,symmetry ,,( ,,! ,,picture ,,by ,,v>y+ ,,! ,,position ,,( ,,! ,,eye1 #cg ,v4--,,on ,,! ,,effects ,,produc$ ,,^u ,,! ,,symmetry ,,( ,,! ,,picture ,,by ,,v>y+ ,,! ,,position ,,( ,,! ,,object1 #df ,,vi4--,,on ,,! ,,int5sity ,,( ,,! ,,light ,,9 ,,diff]5t ,,p>ts ,,( ,,! ,,field1 ,,& ,,on ,,! ,,effects ,,produc$ ,,by ,,v>y+ ,,! ,,l5g? ,,& ,,bread? ,,( ,,! ,,reflectors1 #ea ,,vii4--,,on ,,! ,,con/ruction ,,& ,,use ,,( ,,! ,,simple ,,kaleidoscope1 #ei ,,viii4--,,on ,,! ,,selection ,,( ,,objects ,,= ,,! ,,kaleidoscope1 ,,& ,,on ,,! ,,mode ,,( ,,con/ruct+ ,,! ,,object-,,box1 #fg ,,ix4--,,on ,,! ,,illum9ation ,,( ,,transp>5t ,,objects ,,9 ,,! ,,kaleidoscope1 #gf ,x4--,,on ,,! ,,con/ruction ,,& ,,use ,,( ,,! ,,telescopic ,,kaleidoscope1 ,,= ,,view+ ,,objects ,,at ,a ,,di/ance1 #ha ,,xi4--,,on ,,! ,,con/ruction ,,& ,,use ,,( ,,polyangul> ,,kaleidoscopes1 ,,9 ,,:i* ,,! ,,reflectors ,,c ,,be ,,fix$ ,,at ,,any ,,angle1 #hh #a4 ,bate's ,polyangul> ,kaleidoscope ) ,metallic ,reflectors1 #hi #b4 ,bate's ,polyangul> ,kaleidoscope ) ,glass ,reflectors1 #id ,,xii4--,,on ,,! ,,con/ruction ,,& ,,use ,,( ,,annul> ,,& ,,p>allel ,,kaleidoscopes1 #ih #a4 ,mr4 ,dollond's ,univ]sal ,kaleidoscope1 #ajj #b4 ,ru?v5's ,univ]sal ,kaleidoscope1 #ajb ,,xiii4--,,on ,,! ,,con/ruction ,,& ,,use ,,( ,,polyc5tral ,,kaleidoscopes1 #aje #a4 ,on comb9ations ( f\r mirrors =m+ a squ>e1 #ajg #b4 ,on comb9ations ( f\r mirrors =m+ a rectangle1 #aji #c4 ,on comb9ations ( ?ree reflectors at angles ( #fj1 #aji #d4 ,on comb9ations ( ?ree reflectors at angles ( #ij1 #de1 & #de1 #aaa #e4 ,on comb9ations ( ?ree reflectors at angles ( #ij1 #fj1 & #cj1 #aab ,,xiv4--,,on ,,kaleidoscopes ,,9 ,,:i* ,,! ,,effect ,,is ,,produc$ ,,by ,,total ,,reflexion ,,f ,,! ,,int]ior ,,surfaces ,,( ,,transp>5t ,,solids1 #aad ,,xv4--,,on ,,! ,,application ,,( ,,! ,,kaleidoscope ,,to ,,! ,,magic ,,lant]n1 ,,sol> ,,microscope1 ,,& ,,cam]a ,,obscura1 #aag ,,xvi4--,,on ,,! ,,con/ruction ,,( ,,kaleidoscopes ,,:i* ,,comb9e ,,! ,,col\rs ,,& ,,=ms ,,produc$ ,,by ,,pol>iz$ ,,light1 #abb ,,xvii4--,,on ,,! ,,con/ruction ,,( ,,/]eoscopic ,,kaleidoscopes1 #abf ,,xviii4--,,on ,,! ,,con/ruction ,,( ,,microscopic ,,kaleidoscopes1 #abh ,,xix4--,,on ,,! ,,*anges ,,produc$ ,,by ,,! ,,kaleidoscope1 #aca ,,xx4--,,on ,,! ,,application ,,( ,,! ,,kaleidoscope ,,to ,,! ,,f9e ,,& ,,useful ,,arts1 #acd #a4 ,ar*itectural ,ornam5ts1 #acg #b4 ,ornam5tal ,pa9t+1 #ada #c4 ,designs = ,c>pets1 #add ,,xxi4--,,on ,,! ,,photographic ,,del9eation ,,( ,,! ,,pictures ,,creat$ ,,by ,,! ,,kaleidoscope1 #adh ,,xxii4--,,on ,,! ,,advantages ,,( ,,! ,,kaleidoscope ,,z ,,an ,,in/rum5t ,,( ,,amusem5t1 #aed ,,xxiii4--,,hi/ory ,,( ,,! ,,comb9ations ,,( ,,plane ,,mirrors ,,:i* ,,h ,,be5 ,,suppos$ ,,to ,,resemble ,,! ,,kaleidoscope1 #afb #a4 ,bapti/a ,porta's multiply+ speculum1 #afd #b4 ,kir*]'s comb9ation ( plane mirrors1 #afh #c4 ,bradley's comb9ation ( plane mirrors1 #age ,,app5dix1 #ahe ,,on ,,! ,,kaleidoscope4 ,,introduction4 ,,hi/ory ,,( ,,! ,,kaleidoscope4 ,! "n ,kaleidoscope1 :i* ,i h giv5 to a new ,optical ,in/rum5t1 = creat+ & exhibit+ beautiful =ms1 is d]iv$ f ! ,greek words 1 beautiful2 1 a =m2 & 1 to see4 ,! fir/ idea ( ?is in/rum5t pres5t$ itself to me 9 ! ye> #ahad1 9 ! c\rse ( a s]ies ( exp]im5ts on ! pol>ization ( light by successive reflexions betwe5 plates ( glass1 :i* 7 publi%$ 9 ! ,philosophical ,transactions = #ahae1 & :i* ! ,royal ,society did me ! hon\r to di/+ui% by ! adjudication ( ! ,copley ,m$al4 ,9 ^! exp]im5ts1 ! reflect+ plates 7 necess>ily incl9$ to ea* o!r dur+ ! op]ation ( plac+ _! surfaces 9 p>allel planes2 & ,i 0 !re=e l$ to rem>k ! circul> arrangem5t ( ! images ( a c&le r\nd a c5tre1 & ! multiplication ( ! sectors =m$ by ! extremities ( ! plates ( glass4 ,9 consequ5ce1 h[ev]1 ( ! di/ance ( ! c&les1 c41 f ! ends ( ! reflectors1 _! arrangem5t 0 s de/itute ( symmetry1 t ,i 0 n induc$ to give any f>!r att5tion to ! subject4 ,on ! #g? ( ,febru>y #ahae1 :5 ,i discov]$ ! developm5t ( ! complem5t>y col\rs1 by ! successive reflexions ( pol>iz$ light betwe5 two plates ( gold & silv]1 ! effects ( ! ,kaleidoscope1 ?\gh rudely exhibit$1 7 aga9 =c$ ^u my notice2 ! multipli$ images 71 h[ev]1 col\r$ ) ! mo/ spl5did t9ts2 & ! :ole effect1 ?\gh inconceivably inf]ior to ! creations ( ! ,kaleidoscope1 0 /ill f> sup]ior to any?+ t ,i _h previ\sly witness$4 ,9 giv+ an acc\nt ( ^! exp]im5ts to ,m4 ,biot on ! #f? ( ,m>* #ahae1 ,i rem>k$ to him1 8t :5 ! angle ( incid5ce 7on ! plates ( silv]7 0 ab\t #he or #hf1 & ! plates almo/ 9 contact1 & incl9$ at a v small angle1 ! two s]ies ( reflect$ images appe>$ at once 9 ! =m ( two curves2 & t ! succession ( spl5did col\rs =m$ a ph5om5on :i* ,i _h no d\bt w\ld be consid]$1 by e p]son :o saw x to advantage1 z "o ( ! mo/ beautiful 9 optics40 ,^! exp]im5ts 7 aft]w>ds repeat$ ) m p]fectly poli%$ plates ( diff]5t metals1 & ! effects 7 proportionally m brilliant3 b not)/&+ ! beauty aris+ f ! multiplication ( ! images1 & ! additional spl5d\r :i* 0 communicat$ to ! picture by ! ri*ness ( ! pol>iz$ t9ts1 x 0 :olly de/itute ( symmetry1 z ,i 0 !n ignorant ( ^? positions = ! eye & ! objects1 :i* are absolutely necess>y to produce t magical union ( p>ts1 & t ma!matical symmetry ?r\gh\t ! :ole picture1 :i*1 indep5d5tly ( all col\r+1 give to ! visions ( ! ,kaleidoscope ! peculi> *>m :i* di/+ui%es !m f all artificial creations4#a #a ,an acc\nt ( ! exp]im5ts above allud$ to 0 giv5 9 ! ,analyse des ,travaux de la ,classe des ,sci5ces ,ma?matiques et ,physiques de l',in/itut ,royal de ,france1 p5dant l'anne #ahae1 p> ,m4 le ,*ev4 ,delambre1 p4 #bi1 c4 ,! col\rs produc$ by repeat$ reflexions f plates ( silv] are ^? ( ,elliptical ,pol>ization1 & are expla9$ at great l5g? 9 my pap] on t subject1 publi%$ 9 ! ,philosophical ,transactions = #ahcj4 ,al?\gh ,i _h ?us comb9$ two pla9 mirrors1 s z to produce highly pleas+ effects1 f ! multiplication & circul> arrangem5t ( ! images ( objects plac$ at a di/ance f _! extremities1 yet ,i _h sc>cely made a /ep t[>ds ! inv5tion ( ! ,kaleidoscope4 ,! effects1 h[ev]1 :i* ,i _h obs]v$1 7 suffici5t to prep>e me = tak+ advantage ( any sugge/ion :i* exp]im5t might aft]w>ds ?r[ 9 ! way4 ,9 repeat+1 at a subsequ5t p]iod1 ! v beautiful exp]im5ts ( ,m4 ,biot1 on ! action ( homog5e\s fluids ^u pol>iz$ light1 & 9 ext5d+ !m to o!r fluids :i* he _h n tri$1 ,i f\nd x mo/ conv5i5t to place !m 9 a triangul> tr\gh1 =m$ by two plates ( glass cem5t$ toge!r by two ( _! sides1 s z to =m an acute angle4 ,! ends be+ clos$ up ) pieces ( plate glass cem5t$ to ! o!r plates1 ! tr\gh 0 fix$ horizontally1 = ! reception ( ! fluids4 ,! eye be+ necess>ily plac$ )\t ! tr\gh1 & at "o end1 "s ( ! cem5t1 :i* _h be5 press$ ?r\gh betwe5 ! plates at ! object end ( ! tr\gh1 appe>$ to be arrang$ 9 a mann] f> m regul> & symmetrical ?an ,i _h be=e obs]v$ :5 ! objects1 9 my e>ly exp]im5ts1 7 situat$ at a di/ance f ! reflectors4 ,f ! approximation to p]fect symmetry :i* ! figure n[ display$1 comp>$ ) ! great deviation f symmetry :i* ,i _h =m]ly obs]v$1 x 0 obvi\s t ! progression f ! "o effect to ! o!r mu/ take place dur+ ! passage ( ! object f ! "o position to ! o!r2 & x became highly probable1 t a position w\ld be f\nd :]e ! symmetry 0 ma!matically p]fect4 ,by inve/igat+ ?is subject optically1 ,i discov]$ ! lead+ pr9ciples ( ! ,kaleidoscope1 9 s f> z ! incl9ation ( ! reflectors1 ! position ( ! object1 & ! position ( ! eye1 7 conc]n$4 ,i f\nd1 t 9 ord] to produce p]fectly beautiful & symmetrical =ms1 ?ree conditions 7 necess>y4 #a4 ,t ! reflectors %\ld be plac$ at an angle1 :i* 0 an ev5 or an odd aliquot "p ( a circle1 :5 ! object 0 regul>1 & simil>ly situat$ ) respect to bo? ! mirrors2 or ! ev5 aliquot "p ( a circle :5 ! object 0 irregul>1 & _h any position :atev]4 #b4 ,t out ( an inf9ite numb] ( positions = ! object1 bo? )9 & )\t ! reflectors1 !re 0 only "o :]e p]fect symmetry c\ld be obta9$1 namely1 :5 ! object 0 plac$ 9 contact ) ! ends ( ! reflectors4 ,?is 0 precisely ! position ( ! cem5t 9 ! prec$+ exp]im5t ) ! triangul> tr\gh4 #c4 ,t out ( an inf9ite numb] ( positions = ! eye1 !re 0 only "o :]e ! symmetry 0 p]fect1 namely1 z ne> z possible to ! angul> po9t1 s t ! circul> field c\ld be di/9ctly se52 & t ?is po9t 0 ! only "o out ( an inf9ite numb] at :i* ! uni=mity ( ! light ( ! circul> field 0 a maximum1 & f :i* ! direct & ! reflect$ images _h ! same =m & ! same magnitude1 9 consequ5ce ( be+ plac$ at ! same di/ance f ! eye4 ,?is1 also1 0 ! position 9 :i* ! eye 0 necess>ily plac$ :5 look+ ?r\gh ! fluid ) :i* ! glass tr\gh 0 p>tially fill$4 ,^u ^! pr9ciples ,i con/ruct$ an in/rum5t1 9 :i* ,i fix$ p]man5tly1 across ! ends ( ! reflectors1 pieces ( col\r$ glass1 & o!r irregul> objects2 & ,i %[$ ! in/rum5t 9 ?is /ate to "s memb]s ( ! ,royal ,society ( ,ed9burgh1 :o 7 mu* /ruck ) ! beauty ( its effects4 ,9 ?is case1 h[ev]1 ! =ms 7 ne>ly p]man5t2 & slight1 ?\gh beautiful1 v>iations 7 produc$ by v>y+ ! position ( ! in/rum5t ) respect to ! s\rce ( light4 ,! great /ep1 h[ev]1 t[>ds ! completion ( ! in/rum5t rema9$ yet to be made2 & x 0 n till "s "t aft]w>ds t ! idea occurr$ to me ( giv+ motion to objects1 su* z pieces ( col\r$ glass1 c41 :i* 7 ei!r fix$ or plac$ loosely 9 a cell at ! end ( ! in/rum5t4 ,:5 ?is idea 0 c>ri$ into execution1 & ! reflectors plac$ 9 a tube1 & fitt$ up on ! prec$+ pr9ciples1 ! ,kaleidoscope1 9 its simple =m1 0 complet$4 ,9 ?is =m1 h[ev]1 ! ,kaleidoscope c\ld n be consid]$ z a g5]al philosophical in/rum5t ( univ]sal application4 ,! lea/ deviation ( ! object f ! position ( symmetry at ! end ( ! reflectors1 produc$ a deviation f beauty & symmetry 9 ! figure1 & ?is deviation increas$ ) ! di/ance ( ! object4 ,! use ( ! in/rum5t 0 !re=e limit$ to objects 9 contact ) ! ends ( ! reflectors1 or held close to !m1 & consequ5tly to objects1 or gr\ps ( objects1 ^: magnitudes 7 less ?an its triangul> ap]ture4 ,! next1 & by f> ! mo/ important /ep ( ! inv5tion1 0 to remove ?is limitation1 & to ext5d indef9itely ! use & application ( ! in/rum5t4 ,?is effect 0 obta9$ by employ+ a draw tube1 conta9+ a convex l5s1 or1 :at is bett]1 an a*romatic object-glass ( su* a focal l5g?1 t ! images ( objects1 ( all magnitudes & at all di/ances1 might be di/9ctly =m$ at ! end ( ! reflectors1 & introduc$ into ! pictures creat$ by ! in/rum5t 9 ! same mann] z if !y _h be5 r$uc$ 9 size1 & plac$ 9 ! true position 9 :i* alone p]fect symmetry c\ld be obta9$4 ,:5 ! ,kaleidoscope 0 br\ght to ?is degree ( p]fection1 x 0 impossible n to p]ceive t x w\ld prove ( ! highe/ s]vice 9 all ! ornam5tal arts1 & w\ld1 at ! same "t1 become a popul> in/rum5t = ! purposes ( rational amusem5t4 ,) ^! views ,i ?\ght x advisable to secure ! exclusive prop]ty ( x by a ,pat5t2#b b 9 consequ5ce ( "o ( ! pat5t in/rum5ts hav+ be5 exhibit$ to "s ( ! ,london opticians1 ! rem>kable prop]ties ( ! ,kaleidoscope became kn[n be=e any numb] ( !m c\ld be prep>$ = sale4 ,! s5sation excit$ by ?is premature exhibition ( its effects is incapable ( description1 & c be conceiv$ only by ^? :o witness$ x4 8,x v quickly became popul>10 says ,dr4 ,roget1 9 8 excell5t article on ! ,,kaleidoscope 9 ! ,encyclopdia ,britannica1 8& ! s5sation x excit$ 9 ,london ?r\gh\t all ranks ( p 0 a/oni%+4 ,x af=d$ delight to ! poor z well z ! ri*2 to ! old z well z ! "y4 ,l>ge c>goes ( !m 7 s5t abroad1 p>ticul>ly to ! ,ea/ ,indies4 ,!y v soon became kn[n ?r\gh\t ,europe1 & h be5 met ) by travell]s ev5 9 ! mo/ obscure & retir$ villages 9 ,switz]l&40 ,accord+ to ! computation ( ^? :o 7 be/ able to =m an op9ion on ! subject1 no few] ?an two hundr$ ?\s& in/rum5ts 7 sold 9 ,london & ,p>is dur+ ?ree mon?s4 ,out ( ?is imm5se numb] !re 7 p]haps n "o ?\s& con/ruct$ ^u sci5tific pr9ciples1 & capable ( giv+ any?+ l a correct idea ( ! p[] ( ! ,kaleidoscope2 & ( ! millions :o h witness$ its effects1 !re is p]haps n a hundr$ individuals :o h any idea ( ! pr9ciples ^u :i* x is con/ruct$1 :o are capable ( di/+ui%+ ! spuri\s f ! real in/rum5t1 or :o h suffici5t k ( its pr9ciples to be able to apply x to ! num]\s bran*es ( ! useful & ornam5tal arts4 ,"u ^! circum/ances ,i h ?\ght x necess>y to draw up ! foll[+ %ort treatise1 = ! purpose ( expla9+1 9 z popul> a mann] z ,i c\ld1 ! pr9ciples & con/ruction ( ! ,kaleidoscope2 ( describ+ ! diff]5t =ms 9 :i* x is fitt$ up2 ( po9t+ out ! v>i\s me?ods ( us+ x z an in/rum5t ( recreation2 & ( in/ruct+ ! arti/ h[ to employ x 9 ! num]\s bran*es ( ! useful & ornam5tal arts to :i* x is applicable4 #b ,z ?is ,pat5t1 9 s f> z ! simple ,kaleidoscope is conc]n$1 0 to a great ext5t infr+$1 x has be5 suppos$ t x 0 r$uc$ 9 a ,c\rt ( ,law4 ,! validity ( ! ,pat5t 0 nev] que/ion$ by any lawy]1 or any philosoph] acqua9t$ ) its !ory & con/ruction1 z w appe> f ! op9ion ( f\r compet5t judges1 giv5 9 ! ,app5dix4 ,9 a trial = ! infr+em5t ( a ,pat5t sev]al ye>s ago1 a di/+ui%$ judge 7we believe x 0 ,judge ,ald]son7 /at$ x z a fact1 t ! ,pat5t = ! ,kaleidoscope _h be5 set aside 9 a ,c\rt ( ,law4 ,! p>ty ^: case 0 prejudic$ by ?is errone\s ass]tion1 appli$ to me = an affidavit1 by :i* he 0 enabl$ to contradict x 9 ,c\rt1 & remove any unfav\rable impression x might h made ^u ! jury4 ,,*apt] ,i4 ,,prelim9>y ,,pr9ciples ,,respect+ ,,! ,,effects ,,( ,,comb9+ ,,two ,,pla9 ,,mirrors4 ,! pr9cipal p>ts ( ! ,kaleidoscope are two reflect+ planes1 made ( glass1 or metal1 or any o!r reflect+ sub/ance gr\nd p]fectly flat & highly poli%$4 ,^! reflectors1 :i* are g5]ally made ( plate glass1 ei!r r\gh gr\nd on _! out] side1 or cov]$ ) black v>ni%1 may be ( any size1 b 9 g5]al !y %\ld be f f\r or five to t5 or twelve in*es long2 _! greate/ bread? be+ ab\t an in* :5 ! l5g? is six in*es1 & increas+ 9 proportion z ! l5g? increases4 ,:5 ^! two plates are put toge!r at an angle ( #fj1 or ! six? "p ( a circle1 z %[n 9 ,fig4 #a1 & ! eye plac$ at ! n>r[ end ,e1 x w obs]ve ! op5+ ,a ,o ,b multipli$ six times1 & arrang$ r\nd ! c5tre ,o1 z %[n 9 ,fig4 #b4 ,illu/ration3 ,,fig4 #a4 ,illu/ration3 ,,fig4 #b4 ,9 ord] to und]/& h[ ?is effect is produc$1 let u take a small sector ( :ite pap] ( ! %ape ,a ,o ,b1 ,fig4 #b1 & hav+ laid x on a black gr\nd1 let ! extremity ,a ,o ( "o ( ! reflectors be plac$ ^u ! edge ,a ,o ( ! sector4 ,x is !n obvi\s t an image ,a ,o b ( ?is :ite sector ( pap] w be =m$ beh9d ! mirror ,a ,o1 & w h ! same magnitude & ! same situation beh9d ! mirror z ! sector ,a ,o ,b _h be=e x4 ,9 l mann]1 if we place ! edge ,b ,o ( ! o!r reflector ^u ! o!r side ,b ,o ( ! pap] sector1 a simil> image ,b ,o a w be =m$ beh9d x4 ,! orig9 ( ?ree ( ! sectors se5 r\nd ,o is !re=e expla9$3 ! fir/1 ,a ,o ,b1 is ! :ite pap] sector se5 by direct vision2 ! second1 ,a ,o b1 is an image ( ! fir/ =m$ by "o reflexion f ! mirror ,a ,o2 & ! ?ird is ano!r image ( ! fir/ =m$ by "o reflexion f ! o!r mirror ,b ,o4 ,b x is well kn[n1 t ! reflect$ image ( any object1 :5 plac$ be=e ano!r mirror1 has an image ( itself =m$ beh9d ?is mirror1 9 ! v same mann] z if x 7 a new object4 ,h5ce x foll[s1 t ! image ,a ,o b be+1 z x 71 a new object plac$ be=e ! mirror ,b ,o1 w h an image a ,o ( itself =m$ beh9d ,b ,o2 & = ! same reason ! image ,b ,o a w h an image b ,o ( itself1 =m$ beh9d ! mirror ,a ,o1 & bo? ^! new images w occupy ! same position beh9d ! mirrors z ! o!r images did be=e ! mirrors4 ,a difficulty n[ pres5ts itself 9 acc\nt+ = ! =mation ( ! la/ or six? sector1 ,o 4 ,mr4 ,h>ris1 9 ! ,x,v,i,ith ,prop4 ( 8 ,optics1 has evad$ ?is difficulty1 & giv5 a false demon/ration ( ! proposition4 ,he rem>ks1 t ! la/ sector1 ,o is produc$ 8by ! reflexion ( ! rays =m+ ei!r ( ! two la/ images0 7namely1 b ,o & a ,o 72 b ?is is cle>ly absurd1 = ! sector ,o w\ld ?us be =m$ ( two images ly+ above ea* o!r1 :i* is impossible4 ,9 ord] to und]/& ! true cause ( ! =mation ( ! sector ,o 1 we mu/ recollect t ! l9e ,o ,e is ! l9e ( junction ( ! mirrors1 & t ! eye is plac$ any :]e 9 ! plane pass+ ?r\gh ,o ,e & bisect+ ,a ,o ,b4 ,n[1 if ! mirror1 ,b ,o1 _h ext5d$ z f> z ,o 1 ! sector ,o w\ld h be5 ! image ( ! sector b ,o 1 reflect$ f ,b ,o2 & 9 l mann]1 if ! mirror ,a ,o _h ext5d$ z f> z ,o 1 ! sector ,o w\ld h be5 ! image ( ! sector a ,o reflect$ f ,a ,o2 b z ?is ov]lapp+ or ext5sion ( ! mirrors is impossible1 & z !y mu/ necess>ily jo9 at ! l9e ,o ,e1 x foll[s1 t an image ,o e1 ( only half ! sector b ,o 1 viz41 b ,o r1 c be se5 by reflexion f ! mirror ,b ,o2 & t an image ,o e1 ( only half ! sector a ,o 1 viz41 a ,o s1 c be se5 by reflexion f ! mirror ,a ,o4 ,h5ce x is manife/1 t ! la/ sector1 ,o 1 is n1 z ,mr4 ,h>ris supposes1 a reflexion f ei!r ( ! two la/ images1 b o 1 a o 1 b is compos$ ( ! images ( two half sectors1 "o ( :i* is =m$ by ! mirror ,a ,o1 & ! o!r by ! mirror ,b ,o4 ,mr4 ,h>ris repeats ! same mi/ake 9 a m s]i\s =m1 9 8 second ,s*olium1 #bdj1 :]e he %[s t ! images are arrang$ 9 ! circumf]5ce ( a circle4 ,! two images ,d1 d1 says he1 co9cide & make b "o image4 ,mr4 ,wood has committ$ ! v same mi/ake 9 8 second ,coroll>y to ,prop4 ,,xiv41 & 8 demon/ration ( t ,coroll>y is decid$ly errone\s4 ,?is ,coroll>y is /at$ 9 ! foll[+ mann]3--8,:5 a 7! angle ( ! mirrors7 is a measure ( #ahj two images co9cide10 & x is demon/rat$1 t s9ce two images ( any object ,x 7,fig4 #b7 mu/ be =m$1 viz41 "o by ea* mirror1 & s9ce ^! two images mu/ be =m$ at #ahj f ! object ,x1 plac$ betwe5 ! mirrors1 t is1 at ! same po9t x1 x foll[s t ! two images mu/ co9cide4 ,n[1 x w appe> f ! simple/ consid]ations1 t ! assumption1 z well z ! conclusion1 is errone\s4 ,! image x is se5 by ! la/ reflexion f ! mirror ,b ,o ,e1 & ano!r image w\ld be se5 at x1 if ! mirror ,a ,o ,e _h ext5d$ z f> z x2 b z ?is is impossible1 )\t cov]+ ! "p ( ! mirror ,b ,o ,e1 :i* gives ! fir/ image x1 !re c be only "o image se5 at x4 ,:5 ! object ,x is equidi/ant f ,a & ,b1 !n "o-half ( ! la/ reflect$ image x w be =m$ by ! la/ reflexion f ! mirror ,b ,o1 & ! o!r half by ! la/ reflexion f ! mirror ,a ,o1 & ^! two half images w jo9 ea* o!r1 & =m a :ole image at e1 z p]fect z any ( ! re/4 ,9 ?is la/ case1 :5 ! angle ,a ,o ,b is a little diff]5t f an ev5 aliquot "p ( #cfj1 ! eye at ,e w p]ceive at e an appe>ance ( two inco9cid5t images2 b ?is arises f ! pupil ( ! eye be+ p>tly on "o side ( ,e & p>tly on ! o!r2 &1 !re=e1 ! app>5t duplication ( ! image is remov$ by look+ ?r\gh a v small ap]ture at ,e4 ,z ! prec$+ rem>ks are equally true1 :atev] be ! incl9ation ( ! mirrors1 provid$ x is an ev5 aliquot "p ( a circle1 x foll[s1-- #a4 ,t :5 ,a ,o ,b is 1 1 1 1 _/1 etc41 ( a circle1 ! numb] ( reflect$ images ( any object ,x1 is #d - #a1 #f - #a1 #h - #a1 #aj - #a1 #ab - #a4 #b4 ,t :5 ,x is ne>] "o mirror ?an ano!r1 ! numb] ( images se5 by reflexion f ! mirror to :i* x is ne>e/ w be _/1 _/1 _/1 _/1 _/1 :ile ! numb] ( images =m$ by ! mirror f :i* ,x is mo/ di/ant w be _/ - #a1 _/ - #a1 _/ - #a1 _/ - #a2 t is1 an image m always rea*es ! eye f ! mirror ne>e/ ,x1 ?an f ! mirror f>!/ f x4 #c4 ,t :5 ,x is equidi/ant f ,a ,o & ,b ,o1 ! numb] ( images :i* rea*es ! eye f ea* mirror is equal1 & is always #d - #a1 #f - #a1 #h - #a1 #aj - #a1 #ab - #a ----- ----- ----- ------ ------ #b #b #b #b #b :i* are fractional values1 %[+ t ! la/ image is compos$ ( two half images4 ,:5 ! incl9ation ( ! mirrors1 or ! angle ,a ,o ,b1 ,fig4 #c1 is an odd aliquot "p ( a circle1 su* z 1 1 1 1 etc41 ! diff]5t sectors :i* compose ! circul> image are =m$ 9 ! v same mann] z has be5 already describ$2 b z ! numb] ( reflect$ sectors mu/ 9 ?is case always be ev51 ! l9e ,o ,e1 :]e ! mirrors jo91 w sep>ate ! two la/ reflect$ sectors1 b ,o e1 a ,o e4 ,h5ce x foll[s1-- ,illu/ration3 ,,fig4 #c4 #a4 ,t :5 ,a ,o ,b is 1 1 1 1 etc41 ( a circle1 ! numb] ( reflect$ images ( any object is #c - #a1 #e - #a1 #g - #a1 etc41 &1-- #b4 ,t ! numb] ( images :i* rea* ! eye f ea* mirror is #c - #a #e - #a #g - #a1 -----1 -----1 -----1 #b #b #b :i* are always ev5 numb]s4 ,hi!rto we h suppos$ ! incl9ation ( ! mirrors to be exactly ei!r an ev5 or an odd aliquot "p ( a circle4 ,we %all n[ proce$ to consid] ! effects :i* w be produc$ :5 ?is is n ! case4 ,if ! angle ,a ,o ,b1 ,fig4 #b1 is made to increase f be+ an ev5 aliquot "p ( a circle1 su* z ?1 till x becomes an odd aliquot "p1 su* z ?1 ! la/ reflect$ image ,o 1 compos$ ( ! two halves ,o e1 ,o e1 w gradually increase1 9 consequ5ce ( ea* ( ! halves increas+2 & :5 ,a ,o ,b becomes ? ( ! circle1 ! sector ,o w become d\ble ( ,a ,o ,b1 & ,o e1 ,o e w become ea* complete sectors1 or equal to ,a ,o ,b4 ,if ! angle ,a ,o ,b is made to v>y f ? to ? ( a circle1 ! la/ sector ,o w gradually dim9i%1 9 consequ5ce ( ea* ( its halves1 ,o e1 ,o e1 dim9i%+2 & j :5 ! angle becomes ? ( a circle1 ! sector ,o w h become inf9itely small1 & ! two sectors1 b ,o 1 a ,o 1 w jo9 ea* o!r exactly at ! l9e ,o e1 z 9 ,fig4 #c4 ,,*apt] ,,ii4 ,,on ,,! ,,pr9ciples ,,( ,,! ,,kaleidoscope1 ,,& ,,! ,,=mation ,,( ,,symmetrical ,,pictures ,,by ,,! ,,comb9ation ,,( ,,direct ,,& ,,inv]t$ ,,images4 ,! pr9ciples :i* we h laid d[n 9 ! prec$+ *apt] mu/ n be consid]$ z 9 any respect ! pr9ciples ( ! ,kaleidoscope4 ,!y are m]ely a s]ies ( prelim9>y d$uctions1 by means ( :i* ! pr9ciples ( ! ,in/rum5t may be illu/rat$1 & !y g no f>!r ?an to expla9 ! =mation ( an app>5t circul> ap]ture by means ( successive reflexions4 ,all ! v>i\s =ms :i* nature & art pres5t to u1 may be divid$ into two classes1 namely1 simple or irregul> =ms1 & comp\nd or regul> =ms4 ,to ! fir/ class belong all ^? =ms :i* are call$ picturesque1 & :i* _c be r$uc$ to two =ms simil>1 & simil>ly situat$ ) reg>d to a giv5 po9t2 & to ! second class belong ! =ms ( animals1 ! =ms ( regul> ar*itectural build+s1 ! =ms ( mo/ articles ( furniture & ornam5t1 ! =ms ( _m natural productions1 & all =ms1 9 %ort1 :i* are compos$ ( two =ms1 simil> & simil>ly situat$ ) reg>d to a giv5 l9e or plane4 ,n[1 x is obvi\s t all comp\nd =ms ( ?is k9d are compos$ ( a direct & an inv]t$ image ( a simple or an irregul> =m2 &1 !re=e1 e simple =m c be conv]t$ into a comp\nd or beautiful =m1 by skilfully comb9+ x ) an inv]t$ image ( itself1 =m$ by reflexion4 ,! image1 h[ev]1 mu/ be =m$ by reflexion f ! fir/ surface ( ! mirror1 9 ord] t ! direct & ! reflect$ image may jo91 & con/itute "o unit$ :ole2 = if ! image is reflect$ f ! po/]ior surface1 z 9 ! case ( a look+-glass1 ! direct & ! inv]t$ image c nev] coalesce into "o =m1 b mu/ always be sep>at$ by a space equal to ! ?ickness ( ! mirror-glass4 ,if we arrange simple =ms 9 ! mo/ p]fect mann] r\nd a c5tre1 x is impossible by any art to comb9e !m into a symmetrical & beautiful picture4 ,! regul>ity ( _! arrangem5t may give "s satisfaction to ! eye1 b ! adjac5t =ms c nev] jo91 & mu/ !re=e =m a picture compos$ ( disunit$ p>ts4 ,! case1 h[ev]1 is q diff]5t ) comp\nd =ms4 ,if we arrange a succession ( simil> =ms ( ?is class r\nd a c5tre1 x necess>ily foll[s t !y w all comb9e into "o p]fect :ole1 9 :i* all ! p>ts ei!r are or may be unit$1 & :i* w delight ! eye by its symmetry & beauty4 ,9 ord] to illu/rate ! prec$+ obs]vations1 we h repres5t$ 9 ,figs4 #d & #e ! effects produc$ by ! multiplication ( s+le & comp\nd =ms4 ,! l9e a b c d1 = example1 ,fig4 #d1 is a simple =m1 & is arrang$ r\nd a c5tre 9 ! same way z x w\ld be done by a p]fect multiply+ glass1 if su* a ?+ c\ld be made4 ,! consecutive =ms are all disunit$1 & d n compose a :ole4 ,fig4 #e repres5ts ! v same simple =m1 a b c d1 conv]t$ into a comp\nd =m1 & !n1 z x 71 multipli$ & arrang$ r\nd a c5tre4 ,9 ?is case e "p ( ! figure is unit$1 & =ms a :ole1 9 :i* !re is no?+ r$undant & no?+ defici5t2 & ?is is ! precise effect :i* is produc$ by ! application ( ! ,kaleidoscope to ! simple =m a b c4 ,illu/ration3 ,,fig4 #d4 ,illu/ration3 ,,fig4 #e4 ,! fundam5tal pr9ciple1 !re=e1 ( ! ,kaleidoscope is1 t x produces symmetrical & beautiful pictures1 by conv]t+ simple into comp\nd or beautiful =ms1 & arrang+ !m1 by successive reflexions1 into "o p]fect :ole4 ,?is pr9ciple1 x w be readily se51 _c be discov]$ by any exam9ation ( ! lum9\s sectors :i* compose ! circul> field ( ! ,kaleidoscope1 & is n ev5 allud$ to 9 any ( ! propositions giv5 by ,mr4 ,h>ris & ,mr4 ,wood4 ,9 look+ at ! circul> field compos$ ( an ev5 & an odd numb] ( reflexions1 ! arrangem5t ( ! sectors is p]fect 9 bo? cases2 b :5 ! numb] is odd1 & ! =m ( ! object simple1 & :5 ! object is n simil>ly plac$ ) reg>d to ! two mirrors1 a symmetrical & unit$ picture _c possibly be produc$4 ,h5ce x is manife/1 t nei!r ! pr9ciples nor ! effects ( ! ,kaleidoscope c\ld possibly be d$uc$ f any practical k respect+ ! lum9\s sectors4 ,9 ord] to expla9 ! =mation ( ! symmetrical picture %[n 9 ,fig4 #e1 we mu/ consid] t ! simple =m m n1 ,fig4 #b1 is se5 by direct vision ?r\gh ! op5 sector ,a ,o ,b1 & t ! image n o1 ( ! object m n1 =m$ by "o reflexion 9 ! sector ,b ,o a1 is necess>ily an inv]t$ image4 ,b s9ce ! image o p1 9 ! sector a ,o 1 is a reflect$ & consequ5tly an inv]t$ image ( ! inv]t$ image1 m t1 9 ! sector ,a ,o b1 x foll[s1 t ! :ole n o p is an inv]t$ image ( ! :ole n m t4 ,h5ce ! image n o w unite ) ! image o p1 9 ! same mann] z m n unites ) m t4 ,b z ^! two la/ unite into a regul> =m1 ! two fir/ w also unite into a regul> or comp\nd =m4 ,n[1 s9ce ! half ,o e ( ! la/ sector ,o 0 =m]ly %[n to be an image ( ! half sector a ,o s1 ! l9e q v w also be an image ( ! l9e o z1 & = ! same reason ! l9e v p w be an image ( t y4 ,b ! image v p =ms ! same angle ) ,b ,o or n q t t y does1 & is equal & simil> to t y2 & q v =ms ! same angle ) ,a ,o t o z does1 & is equal & simil> to o z4 ,h5ce1 ,o o o q1 & ,o y ,o v1 & !re=e q v & v p w =m "o /raight l9e1 equal & simil> to t q1 & simil>ly situat$ ) respect to ,b ,o4 ,! figure m n o p q t1 !re=e1 compos$ ( "o direct object1 & sev]al reflect$ images ( t object1 w be symmetrical4 ,z ! same reason+ is applicable to e object ext5d+ across ! ap]ture ,a ,o ,b1 :e!r simple or comp\nd1 & to e angle ,a ,o ,b1 :i* is an ev5 aliquot "p ( a circle1 x foll[s1-- #a4 ,t :5 ! incl9ation ( ! mirror is an ev5 aliquot "p ( a circle1 ! object se5 by direct vision across ! ap]ture1 :e!r x is simple or comp\nd1 is s unit$ ) ! images ( x =m$ by repeat$ reflexions1 z to =m a symmetrical picture4 #b4 ,t ! symmetrical picture is compos$ ( a s]ies ( p>ts1 ! numb] ( :i* is equal to ! numb] ( times t ! angle ,a ,o ,b is conta9$ 9 #cfj4 ,&-- #c4 ,t ^! p>ts are alt]nately direct & inv]t$ pictures ( ! object2 a direct picture ( x be+ always plac$ betwe5 two inv]t$ ones1 &1 vice v]sa1 s t ! numb] ( direct pictures is equal to ! numb] ( inv]t$ ones4 ,:5 ! incl9ation ( ! mirrors is an odd aliquot "p ( #cfj1 su* z ?1 z %[n 9 ,fig4 #c1 ! picture =m$ by ! comb9ation ( ! direct object & its reflect$ images is symmetrical only "u p>ticul> circum/ances4 ,if ! object1 :e!r simple or comp\nd1 is simil>ly situat$ ) respect to ea* ( ! mirrors1 z ! /raight l9e #a1 #b ( ,fig4 #f1 ! comp\nd l9e #c1 #d1 ! incl9$ l9es #e1 #f1 ! circul> object #g1 ! curv$ l9e #h1 #i1 & ! radial l9e #aj1 ,o1 !n ! images ( all ^! objects w also be simil>ly situat$ ) respect to ! radial l9es t sep>ate ! sectors1 & w !re=e =m a :ole p]fectly symmetrical1 :e!r ! numb] ( sectors is odd or ev54 ,illu/ration3 ,,fig4 #f4 ,b :5 ! objects are n simil>ly situat$ ) respect to ea* ( ! mirrors1 z ! comp\nd l9e #a1 #b1 ,fig4 #h1 ! curv$ l9e #c1 #d1 & ! /raight l9e #e1 #f1 &1 9 g5]al1 z all irregul> objects t are pres5t$ by accid5t to ! in/rum5t1 !n ! image =m$ 9 ! la/ sector a ,o e1 ,fig4 #g1 by ! mirror ,b ,o1 w n jo9 ) ! image =m$ 9 ! la/ sector b ,o e1 by ! mirror ,a ,o4 ,9 ord] to expla9 ?is ) suffici5t p]spicuity1 let u take ! case :]e ! angle is #gb1 or ? "p ( ! circle1 z %[n 9 ,fig4 #g4 ,let ,a ,o1 ,b ,o1 be ! reflect+ planes1 & m n a l9e1 incl9$ to ! radius :i* bisects ! angle ,a ,o ,b1 s t o m o n2 !n m n1 n m1 w be ! images =m$ by ! fir/ reflexion f ,a ,o & ,b ,o1 & n m1 m n1 ! images =m$ by ! second reflexion2 b by ! pr9ciples ( catoptrics1 o m o m ,o m1 & ,o n ,o n ,o n1 consequ5tly s9ce ,o m is by hypo!sis great] ?an ,o n1 we %all h ,o m great] ?an ,o n2 t is1 ! images m n1 n m1 w n co9cide4 ,z ,o n approa*es to an equality ) ,o m1 ,o n approa*es to an equality ) ,o m1 & :5 ,o m ,o n1 we h ,o n ,o m1 & at ?is limit ! images are symmetrically arrang$1 :i* is ! case ( ! /raight l9e #a1 #b 9 ,fig4 #f4 ,by trac+ ! images ( ! o!r l9es1 z is done 9 ,fig4 #h1 x w be se51 t 9 e case ! picture is de/itute ( symmetry :5 ! object has n ! same position ) respect to ! two mirrors4 ,illu/ration3 ,,fig4 #g4 ,illu/ration3 ,,fig4 #h4 ,?is result may be d$uc$ 9 a m simple mann]1 by consid]+ t ! symmetrical picture =m$ by ! ,kaleidoscope conta9s half z _m pairs ( =ms z ! numb] ( times t ! incl9ation ( ! mirrors is conta9$ 9 #cfj2 & t ea* pair consi/s ( a direct & an inv]t$ =m1 s jo9$ z to =m a comp\nd =m4 ,n[ ! comp\nd =m made up by ea* pair obvi\sly con/itutes a symmetrical picture :5 multipli$ any numb] ( times1 :e!r ev5 or odd2 b if we comb9e s _m pair & half a pair1 two direct images w come toge!r1 ! half pair _c possibly jo9 bo? ) ! direct & ! inv]t$ image on ea* side ( x1 & !re=e a symmetrical :ole _c be obta9$ f su* a comb9ation4 ,f ^! obs]vations we may conclude1-- #a4 ,t :5 ! incl9ation ( ! mirrors is an odd aliquot "p ( a circle1 ! object se5 by direct vision ?r\gh ! ap]ture unites ) ! images ( x =m$ by repeat$ reflexions1 & =ms a complete & symmetrical picture1 only 9 ! case :5 ! object is simil>ly situat$ ) respect to bo? ! mirrors2 ! two la/ sectors =m+1 9 e o!r position ( ! object1 an imp]fect junction1 9 consequ5ce ( ^! be+ ei!r bo? direct or bo? inv]t$ pictures ( ! object4 #b4 ,t ! s]ies ( p>ts :i* compose ! symmetrical z well z ! unsymmetrical picture1 consi/s ( direct & inv]t$ pictures ( ! object1 ! numb] ( direct pictures be+ always equal to half ! numb] ( sectors increas$ by "o1 :5 ! numb] ( sectors is #e1 #i1 #ac1 #ag1 #ba1 etc41 & ! numb] ( inv]t$ pictures be+ equal to half ! numb] ( sectors dim9i%$ by "o1 :5 ! numb] ( sectors is #c1 #g1 #aa1 #ae1 #ai1 etc41 & vice v]sa4 ,h5ce1 ! numb] ( direct pictures ( ! object mu/ always be odd1 & ! numb] ( inv]t$ pictures ev51 z appe>s f ! foll[+ table3-- ,incl9ation ,numb] ,numb] ( ,numb] ( ( ! ( ,inv]t$ ,direct ,mirrors4 ,sectors4 ,pictures4 ,pictures4 #abj #c #b #a #gb #e #b #c #ea_/ #g #d #c #dj #i #d #e #cb_/ #aa #f #e #bg_/ #ac #f #g #bd #ae #h #g #ba_/ #ag #h #i #ah_/ #ai #aj #i #ag #ba #aj #aa #c4 ,t :5 ! numb] ( sectors is #c1 #g1 #aa1 #ae1 #ai1 etc41 ! two la/ sectors are inv]t$2 & :5 ! numb] is #e1 #i1 #ac1 #ag1 #ba1 etc41 ! two la/ sectors are direct4 ,:5 ! incl9ation ( ! mirrors is n an aliquot "p ( #cfj1 ! images =m$ by ! la/ reflexions d n jo9 l e o!r pair ( images1 & !re=e ! picture :i* is creat$ mu/ be imp]fect4 ,x has already be5 %[n at ! end ( ,*ap4 ,i4 t :5 ! angle ( ! mirrors becomes great] ?an an ev5 or less ?an an odd aliquot "p ( a circle1 ea* ( ! two incomplete sectors :i* =m ! la/ sector becomes great] or less ?an half a sector4 ,! image ( ! object compreh5d$ 9 ea* ( ! incomplete sectors mu/ !re=e be great] or less ?an ! images 9 half a sector2 t is1 :5 ! la/ sector ,o 1 ,fig4 #b1 is great] ?an ,a ,o ,b1 ! "p q v 9 "o half mu/ be ! image ( m ?an o z1 & v p ! image ( m ?an t y1 & vice v]sa1 :5 ,o is less ?an ,a ,o ,b4 ,h5ce x foll[s t ! symmetry is imp]fect f ! image 9 ! la/ sector be+ great] or less ?an ! o!r images4 ,b besides ?is cause ( imp]fection 9 ! symmetry1 !re is ano!r1 namely1 ! disunion ( ! two images q v & v p4 ,! angles ,o q v & ,o o p are obvi\sly equal1 & also ! angles ,o p v1 ,o p o2 b s9ce ! angle ,o 1 or q ,o p1 is by hypo!sis great] or less ?an p ,o o1 x foll[s t ! angles ( ! triangle q ,o p are ei!r great] or less ?an two "r angles1 because !y are great] or less ?an ! ?ree angles ( ! triangle p ,o o4 ,b z ?is is absurd1 ! l9es q v1 v p1 _c jo9 s z to =m "o /raight l9e1 & !re=e ! completion ( a p]fect figure by means ( two mirrors1 ^: incl9ation is n an aliquot "p ( a circle1 is impossible4 ,:5 ! angle ,o is great] ?an p ,o o1 or ,a ,o ,b1 ! l9es q v1 v p1 w =m a re-ent]+ angle t[>ds ,o1 & :5 x is less ?an ,a ,o ,b1 ! same l9es w =m a sali5t angle t[>ds ,o4 ,,*apt] ,,iii4 ,,on ,,! ,,effects ,,produc$ ,,by ,,! ,,motion ,,( ,,! ,,object ,,& ,,! ,,mirrors4 ,hi!rto we h consid]$ bo? ! object & ! mirrors z /ation>y1 & we h contemplat$ only ! effects produc$ by ! union ( ! diff]5t p>ts ( ! picture4 ,! v>iations1 h[ev]1 :i* ! picture exhibits1 h a v s+ul> "*1 :5 ei!r ! objects or ! mirrors are put 9 motion4 ,let u1 fir/1 consid] ! effects produc$ by ! motion ( ! object :5 ! mirrors are at re/4 ,illu/ration3 ,,fig4 #i4 ,if ! object moves f ,x to ,o1 ,fig4 #i1 9 ! direction ( ! radius1 all ! images w likewise move t[>ds ,o1 & ! patt]ns w h ! appe>ance ( be+ absorb$ or ext+ui%$ 9 ! c5tre4 ,if ! motion ( ! object is f ,o to ,x1 ! images w also move outw>ds 9 ! direction ( ! radii1 & ! patt]n w appe> to develop itself f ! c5tre ,o1 & to be lo/ or absorb$ at ! circumf]5ce ( ! lum9\s field4 ,! objects t move p>allel to ,x ,o w h _! c5tre ( developm5t1 or _! c5tre ( absorption1 at ! po9t 9 ! l9es ,a ,o1 ,b ,o1 a ,o1 b ,o1 etc4 :]e ! direction 9 :i* ! images move cuts ^! l9es4 ,:5 ! object passes across ! field 9 a circle conc5tric ) ,a ,b1 & 9 ! direction ,a ,b1 ! images 9 all ! sectors =m$ by an ev5 numb] ( reflexions w move 9 ! same direction ,a ,b1 namely1 9 ! direction b1 a 2 :ile ^? t h be5 =m$ by an odd numb] ( reflexions w move 9 an opposite direction1 namely1 9 ! directions a ,b1 ,a b4 ,h5ce1 if ! object moves f ,a to ,b1 ! po9ts ( absorption w be 9 ! l9es ,b ,o1 ,o1 & b ,o1 & ! po9ts ( developm5t 9 ! l9es ,a ,o1 a ,o1 & ,o1 & vice v]sa1 :5 ! motion ( ! object is f ,b to ,a4 ,if ! object moves 9 an oblique direction m n1 ! images w move 9 ! directions m t1 o n1 o p1 q t1 q p1 & m1 o1 q1 w be ! c5tres ( developm5t1 & n1 p1 t1 ! c5tres ( absorption2 :]eas1 if ! object moves f n to m1 ^! c5tres w be int]*ang$4 ,^! results are susceptible ( ! simple/ demon/ration1 by suppos+ ! object 9 "o or two successive po9ts ( its pa? m n1 & consid]+ t ! image mu/ be =m$ at po9ts simil>ly situat$ beh9d ! mirrors2 ! l9e pass+ ?r\gh ^! po9ts w be ! pa? ( ! image1 & ! ord] 9 :i* ! images succe$ ea* o!r w give ! direction ( _! motion4 ,h5ce1 we may conclude 9 g5]al1 #a4 ,t :5 ! pa? ( ! object cuts bo? ! mirrors ,a ,o & ,b ,o l m n1 ! c5tre ( absorption w be 9 ! radius pass+ ?r\gh ! section ( ! mirror to :i* ! object moves1 & 9 e alt]nate radius2 & t ! c5tre ( developm5t w be 9 ! radius pass+ ?r\gh ! section ( ! mirror f :i* ! object moves1 & 9 all ! alt]nate radii3 &1 #b4 ,t :5 ! pa? ( ! object cuts any "o ( ! mirrors & ! circumf]5ce ( ! circul> field1 ! c5tre ( absorption w be 9 all ! radii :i* sep>ate ! sectors1 & ! c5tre ( developm5t 9 ! circumf]5ce ( ! field1 if ! motion is t[>ds ! mirror1 b vice v]sa if ! motion is t[>ds ! circumf]5ce4 ,:5 ! objects are at re/1 & ! ,kaleidoscope 9 motion1 a new s]ies ( appe>ances is pres5t$4 ,:atev] be ! direction 9 :i* ! ,kaleidoscope moves1 ! object se5 by direct vision mu/ always be /ation>y1 & x is easy to det]m9e ! *anges :i* take place :5 ! ,kaleidoscope has a progressive motion ov] ! object4 ,a v curi\s effect1 h[ev]1 is obs]v$ :5 ! ,kaleidoscope has a rotatory motion r\nd ! angul> po9t1 or r r\nd ! common section ( ! two mirrors4 ,! picture creat$ by ! ,in/rum5t seems to be compos$ ( two pictures1 "o 9 motion r\nd ! c5tre ( ! circul> field1 & ! o!r at re/4 ,! sectors =m$ by an odd numb] ( reflexions are all 9 motion 9 ! same direction z ! ,kaleidoscope1 :ile ! sector se5 by direct vision1 & all ! sectors =m$ by an ev5 numb] ( reflexions1 are at re/4 ,9 ord] to und]/& ?is1 let ,m1 ,fig4 #aj1 be a plane mirror1 & ,a an object ^: image is =m$ at a1 s t a ,m ,a ,m4 ,let ! mirror ,m advance to ,n1 & ! object ,a1 :i* rema9s fix$1 w h its image b =m$ at su* a di/ance beh9d ,n1 t b ,n ,a ,n2 !n x w be f\nd t ! space mov$ ?r\gh by ! image is d\ble ! space mov$ ?r\gh by ! mirror2 t is1 a b #b ,m ,n4 ,s9ce ,m ,n ,a ,m - ,a ,n1 & s9ce ,a ,m a ,m1 & ,a ,n b ,n1 we h ,m ,n a ,m - b ,n2 & add+ ,m ,n or its equal b ,m b ,n to bo? sides ( ! equation1 we obta9 #b,m ,n a ,m - b ,n b ,n b ,m2 b -b ,n b,n #j1 & a ,m b ,m a b2 h5ce #b,m ,n a b4 ,?is result may be obta9$ o!rwise1 by consid]+1 t if ! mirror ,m advances "o in* t[>ds ,a1 "o in* is add$ to ! di/ance ( ! image a1 & "o subtract$ f ! di/ance ( ! object2 t is1 ! diff]5ce ( ^! di/ances is n[ two in*es1 or twice ! space mov$ ?r\gh by ! mirror2 b s9ce ! new di/ance ( ! object is equal to ! di/ance ( ! new image1 ! diff]5ce ( ^! di/ances1 :i* is ! space mov$ ?r\gh by ! image1 mu/ be two in*es1 or twice ! space describ$ by ! mirror4 ,illu/ration3 ,,fig4 #aj4 ,let u n[ suppose t ! object ,a advances 9 ! same direction z ! mirror1 & ) twice its velocity1 s z to describe a space ,a #b ,m ,n a b1 9 ! same "t t ! mirror moves ?r\gh ,m ,n1 ! object be+ at :5 ! mirror is at ,n4 ,!n1 s9ce ,a a b & b ,n ,a ,n1 ! :ole ,n is equal to ! :ole a ,n1 t is1 a w /ill be ! place ( ! image4 ,h5ce x foll[s1 t if ! object advances 9 ! same direction z ! mirror1 b ) twice its velocity1 ! image w rema9 /ation>y4 ,illu/ration3 ,,fig4 #aa4 ,if ! object ,a moves 9 a direction opposite to t ( ! mirror1 & ) d\ble its velocity1 z is %[n 9 ,fig4 #aa2 !n1 s9ce b w\ld be ! image :5 ,a 0 /ation>y1 & :5 ,m _h mov$ to ,n1 9 :i* case a b #b ,m ,n1 & b ! image :5 ,a _h advanc$ to ?r\gh a space ,a #b ,m ,n1 we h b ,n ,a ,n1 & b ,n ,n1 &1 !re=e1 b b ,a ,n - ,n ,a #b ,m ,n1 & a b b b or its equal a b #d ,m ,n4 ,h5ce x foll[s1 t :5 ! object advances t[>ds ! mirror ) twice its velocity1 ! image w move ) f\r times ! velocity ( ! mirror4 ,if ! mirror ,m moves r\nd a c5tre1 ! v same results w be obta9$ f ! v same reason+1 only ! angul> motion ( ! mirror & ! image w !n be m conv5i5tly measur$ by p>ts ( a circle or degrees4 ,illu/ration3 ,,fig4 #ab4 ,n[1 9 ,fig4 #ab1 let ,x be a fix$ object1 & ,a ,o1 ,b ,o1 two mirrors plac$ at an angle ( #fj & moveable r\nd ,o z a c5tre4 ,:5 ! eye is appli$ to ! end ( ! mirrors 7or at ,e1 ,fig4 #a71 ! fix$ object ,x1 ,fig4 #ab1 se5 by direct vision w1 ( c\rse1 be /ation>y1 :ile ! mirrors describe an ar* ,x ( #aj = example2 b s9ce ,a ,o has approa*$ ,x by #aj1 ! image ( ,x =m$ beh9d ,a ,o mu/ h approa*$ ,x by #bj1 & consequ5tly moves ) twice ! velocity 9 ! same direction z ! mirrors4 ,9 l mann]1 s9ce ,b ,o has rec$$ #aj f ,x1 ! image ( ,x =m$ by ,b ,o mu/ h rec$$ #bj f ,x1 & consequ5tly mu/ h mov$ ) twice ! velocity 9 ! same direction z ! mirrors4 ,n[1 ! image ( ,x 9 ! sector b ,o is1 z x 71 an image ( ! image 9 ,b ,o a reflect$ f ,a ,o4 ,b ! image 9 ,b ,o a advances 9 ! same direction z ! mirror ,a ,o & ) twice its velocity1 h5ce ! image ( x 9 ! sector b ,o w be /ation>y4 ,9 l mann] x may be %[n1 t ! image 9 ! sector a ,o w be /ation>y4 ,s9ce ,o e is an image ( b ,o r reflect$ f ! mirror ,b ,o1 & s9ce all images 9 t sector are /ation>y1 ! correspond+ images 9 ,o e w move 9 ! same direction z ! mirrors2 & = ! same reason ! images 9 ! o!r half-sector ,o e w move 9 ! same direction2 h5ce1 ! image ( any object =m$ 9 ! la/ sector ,o w move 9 ! same direction1 & ) ! same velocity z ! images 9 ! sectors ,a ,o b1 ,b ,o a4 ,by a simil> process ( reason+1 ! same results w be obta9$1 :atev] be ! numb] ( ! sectors1 & :e!r ! angle ,a ,o ,b be ! ev5 or ! odd aliquot "p ( a circle4 ,h5ce we may conclude1 #a4 ,t dur+ ! rotatory motion ( ! mirrors r\nd ,o1 ! objects 9 ! sector se5 by direct vision1 & all ! images ( ^! objects =m$ by an ev5 numb] ( reflexions are at re/4 #b4 ,t all ! images ( ^! objects1 =m$ by an odd numb] ( reflexions1 move r\nd ,o 9 ! same direction z ! mirrors1 & ) an angul> velocity d\ble t ( ! mirrors4 #c4 ,t :5 ! angle ,a ,o ,b is an ev5 aliquot "p ( a circle1 ! numb] ( mov+ sectors is equal to ! numb] ( /ation>y sectors1 a mov+ sector be+ plac$ betwe5 two /ation>y sectors1 & vice v]sa4 #d4 ,t :5 ! angle ,a ,o ,b is an odd aliquot "p ( a circle1 ! two la/ sectors adjac5t to ea* o!r are ei!r bo? 9 motion or bo? /ation>y1 ! numb] ( mov+ sectors be+ great] by "o :5 ! numb] ( sectors is #c1 #g1 #aa1 #ae1 etc41 & ! numb] ( /ation>y sectors be+ great] by "o :5 ! numb] ( sectors is #e1 #i1 #ac1 #ag1 etc4 ,&1 #e4 ,t z ! mov+ sectors correspond ) ^? 9 :i* ! images are inv]t$1 & ! /ation>y ones ) ^? 9 :i* ! images are direct1 ! numb] ( ea* may be f\nd f ! table giv5 9 page #bd4 ,:5 "o ( ! mirrors1 ,a ,o1 is /ation>y1 :ile ! o!r1 ,b ,o1 is mov$ r\nd1 & s z to enl>ge ! angle ,a ,o ,b1 ! object ,x1 & ! image ( x se5 9 ! /ation>y mirror ,a ,o1 rema9 at re/1 b all ! o!r images are 9 motion rec$+ f ! object ,x1 & its /ation>y image2 & :5 ,b ,o moves t[>ds ,a ,o1 s z to dim9i% ! angle ,a ,o ,b1 ! same effect takes place1 only ! motion ( ! images is t[>ds ! object ,x1 on "o side1 & t[>ds its /ation>y image on ! o!r4 ,^! images w obvi\sly move 9 pairs2 =1 s9ce ! fix$ object & its /ation>y image are at an inv>iable di/ance1 ! exi/5ce ( a symmetrical arrangem5t1 :i* we h =m]ly prov$1 requires t simil> pairs be arrang$ at equal di/ances r\nd ,o1 & ea* ( ! images ( ^! pairs mu/ be /ation>y ) reg>d to ! o!r4 ,n[1 z ! fix$ object is plac$ 9 ! sector ,a ,o ,b1 & its /ation>y image 9 ! sector ,a ,o b1 x w be f\nd t 9 ! semicircle ,m b e1 conta9+ ! fix$ mirror1 ! #a/ reflect$ image & direct object1 #b;d #c;d reflect$ image #d? #e? are /ation>y ) #f? #g? respect to ea* o!r4 #h? #i? :ile 9 ! same semicircle ,m b e1 ! #a/ reflect$ image & #b;d reflect$ image #c;d #d? #e? #f? are movable ) #g? #h? respect to ea* o!r4 #i? #aj? ,on ! o!r h&1 9 ! semicircle ,m a e1 conta9+ ! movable mirror1 ! ph5om5a are rev]s$1 ! images :i* 7 =m]ly /ation>y ) respect to ea* o!r be+ n[ movable1 & vice v]sa4 ,9 consid]+ ! velocity ) :i* ea* pair ( images revolves1 x w be readily se5 t ! pair on ea* side1 & ne>e/ ! fix$ pair1 w h an angul> velocity d\ble t ( ! mirror ,b ,o2 ! next pair on ea* side w h a velocity f\r times z great z t ( ! mirror2 ! next pair w h a velocity eight times z great1 & ! next pair a velocity sixte5 times z great z t ( ! mirror1 ! velocity ( any pair be+ always d\ble ! velocity ( ! pair :i* is adjac5t to x on ! side ( ! fix$ pair4 ,! reason ( ?is w be manife/1 :5 we recollect :at has already be5 demon/rat$1 t ! velocity ( ! image is always d\ble t ( ! mirror1 :5 ! mirror alone moves t[>ds ! object1 & quadruple t ( ! mirror :5 bo? are 9 motion1 & :5 ! object approa*es ! mirror ) twice ! velocity4 ,:5 ,b ,o moves f ,a ,o1 ! image 9 ! sector ,b ,o a moves ) twice ! velocity ( ! mirror2 b s9ce ! image 9 b ,o is an image ( ! image 9 ,b ,o a reflect$ f ! fix$ mirror ,a ,o1 x also w move ) ! same velocity1 or twice t ( ! mirror ,b ,o4 ,aga91 ! image 9 ! sector a ,o 1 be+ a reflexion ( ! /ation>y image 9 ,a ,o b f ! mov+ mirror1 w itself move ) d\ble ! velocity ( ! mirror4 ,b ! image 9 ! next sector ,o is a reflexion ( ! image 9 b ,o f ! mov+ mirror ,b ,o2 & z ?is latt] image has be5 %[n to move 9 ! direction b 1 ) twice ! velocity ( ! mirror ,b ,o1 :ile ! mirror ,b ,o itself moves t[>ds ! image1 x foll[s t ! image 9 ,o w move ) a velocity f\r times t ( ! mirror4 ,! same reason+ may be ext5d$ to any numb] ( sectors1 & x w be f\nd t 9 ! semicircle ,m b e1 conta9+ ! fix$ mirror1 ,! #b & #c #b times ! images #d & #e reflexions1 move ) #d velocity ( =m$ #f & #g #h ! mirror2 by #h & #i #af :]eas 9 ! semicircle ,m a e1 conta9+ ! movable mirror1-- ,! #a & #b #b times ! images #c & #d reflexions1 move ) #d velocity ( =m$ #e & #f #h ! mirror2 by #g & #h #af a progression :i* may be cont9u$ to any l5g?4 ,be=e conclud+ ?is *apt]1 x may be prop] to m5tion a v rem>kable effect produc$ by mov+ ! two pla9 mirrors along "o ( two l9es plac$ at "r angles to ea* o!r4 ,:5 ! ap]ture ( ! mirrors is cross$ by ea* ( ! two l9es1 ! figure creat$ by reflexion consi/s ( two polygons ) sali5t & re-ent]+ angles4 ,by mov+ ! mirrors along "o ( ! l9es1 s t x may always cross ! ap]ture at ! same angle1 & at ! same di/ance f ! angul> po9t1 ! polygon =m$ by ?is l9e w rema9 /ation>y1 & ( ! same =m & magnitude2 b ! polygon =m$ by ! o!r l9e1 at fir/ em]g+ f ! c5tre1 w gradually increase till its sali5t angles t\* ! re-ent]+ angles ( ! /ation>y polygon2 ! sali5t angles becom+ m acute1 w enclose ! apices ( ! re-ent]+ angles ( ! /ation>y polygon1 & at la/ ! polygon w be de/roy$ by truncations f its sali5t angles4 ,:5 ! l9es cross ea* o!r at a "r angle1 ! sali5t angles ( ! op5+ polygon c nev] t\* ! sali5t angles ( ! /ation>y polygon1 b always its re-ent]+ angles4 ,if ! l9es1 h[ev]1 =m a less angle ?an ! complem5t ( ! angle =m$ by ! mirrors1 !n ! sali5t angles ( ! op5+ polygon may t\* ! sali5t angles ( ! /ation>y polygon1 by plac+ ! mirrors s z to =m re-ent]+ angles 9 ! polygon4 ,:5 ! l9es =m an angle betwe5 #ij & ! complem5t ( ! angle =m$ by ! mirrors1 ! sali5t angle ( ! op5+ polygon may be made to t\* ! sali5t angles ( ! /ation>y "o1 b 9 ?is case ! /ation>y polygon c h no re-ent]+ angles4 ,! prec$+ effects are f9ely exemplifi$ by ! use ( a ,kaleidoscope ) a draw-tube & l5s describ$ 9 ,*apt] ,x41 & by employ+ ! v]tical & horizontal b>s ( a w9d[1 :i* may be set at diff]5t angles1 by view+ !m 9 p]spective4 ,,*apt] ,,iv4 ,,on ,,! ,,effects ,,produc$ ,,^u ,,! ,,symmetry ,,( ,,! ,,picture ,,by ,,v>y+ ,,! ,,position ,,( ,,! ,,eye4 ,x has be5 tak5 = grant$ 9 ! prec$+ *apt]s1 n only t ! object se5 by direct vision is 9 a /ate ( p]fect junction ) ! images ( x =m$ by reflexion2 b t ! object & its images h ! same app>5t magnitude1 & ne>ly ! same int5sity ( light4 ,z ^! conditions are absolutely necess>y to ! production ( symmetrical & beautiful =ms1 & may be all effect$ by p>ticul> me?ods ( con/ruction1 we %all proce$ to inve/igate ! pr9ciples ^u :i* ^! me?ods are f\nd$1 9 s f> z ! position ( ! eye is conc]n$4 ,:5 any object is made to t\* a common look+-glass 9 "o or m po9ts1 ! reflect$ image does n t\* ! object 9 ^! po9ts1 b is always sep>at$ f x by a space equal to ! ?ickness ( ! glass1 9 consequ5ce ( ! reflexion be+ p]=m$ by ! po/]ior surface ( ! mirror4 ,! image & ! object mu/ !re=e be always disunit$2 & z ! int]val ( sep>ation mu/ be int]pos$ betwe5 all ! reflect$ images1 !re _c possibly exi/ t union ( =ms :i* con/itutes ! v ess5ce ( symmetry4 ,9 mirror-glass !re is a s]ies ( images reflect$ f ! fir/ surface1 :i* unite p]fectly ) ! object1 & ) "o ano!r4 ,:5 ! angles ( incid5ce are n great1 ?is s]ies ( images is v fa9t1 & does n mu* int]f]e ) ! m brilliant images =m$ by ! metallic surface4 ,z ! angles ( incid5ce increase1 ! "o s]ies ( images de/roys ! effect ( ! o!r1 f _! ov]lapp+ or imp]fect co9cid5ce--an effect :i* increases ) ! ?ickness ( ! glass2 b :5 ! reflexions are made at v oblique incid5ces1 ! images =m$ by ! metallic surface become almo/ invisible1 :ile ^? =m$ by ! fir/ surface are z brilliant & ne>ly z p]fect z if ! effect ( ! po/]ior metallic surface _h be5 entirely remov$4 ,9 ! foll[+ obs]vations1 !re=e1 x is und]/ood t ! images are reflect$ ei!r f a poli%$ metallic surface1 or f ! fir/ surface ( glass4 ,illu/ration3 ,,fig4 #ac4 ,9 ord] to expla9 ! effects produc$ ^u ! symmetry ( ! picture by a v>iation 9 ! position ( ! eye1 we mu/ suppose ! object to be plac$ at a small di/ance f ! end ( ! mirror4 ,?is position is repres5t$ 9 ,fig4 #ac1 :]e ,a ,e is a section ( ! mirror 9 ! direction ( its l5g?2 ,m ,n ,o ,p an object plac$ at a di/ance f ! extremity ,a ( ! mirror1 & m n o p1 its image se5 by an eye to ! "r h& ( ,e1 & :i*1 by ! pr9ciples ( catoptrics1 w be simil> to ! object & simil>ly situat$ ) respect to ! mirror ,a ,e4 ,n[1 if ! eye is plac$ at 1 x w see di/9ctly ! :ole object ,m ,n ,o ,p1 b x w only see ! portion n r s o ( ! image cut (f by draw+ ! l9e ,a r ?r\gh ! extremity ( ! mirror1 s t !re _c be a symmetrical =m produc$ by obs]v+ at ! same "t ! object ,m ,n ,o ,p & ?is portion ( its image2 & ! deviation f symmetry w be /ill great]1 if ,m ,n ,o ,p is br\ght ne>] ! l9e ,b ,a1 = ! image m n o p w be entirely includ$ betwe5 ! l9es ,a r & ,a ,b1 s t no "p :atev] ( ! image w be visible to an eye at 4 ,z ! eye ( ! obs]v] moves f to e1 ! l9e ,a r w move into ! position e ,a x1 & :5 x has rea*$ ! po9t e1 ! :ole ( ! image m n o p w be visible4 ,! symmetry1 !re=e1 aris+ f ! simultane\s contemplation ( ! object & its image w be improv$2 b x w /ill be imp]fect1 z ! image w appe> to be di/ant f ! plane ( ! mirror1 only by ! space m x1 :ile ! di/ance ( ! object is ,m x4 ,z ! eye moves f e to ,e1 ! l9e e ,a x w move into ,e ,a ,b1 & ! object & its image w seem to be plac$ at ! equal di/ances ,m ,b1 m ,b f ! plane ( ! mirror1 & w !re=e =m a symmetrical comb9ation4 ,:5 ! object is mov$1 & arrives at ,b ,a ! image w t\* ! object1 & !y w =m "o p]fect & unit$ :ole1 :atev] be ! %ape ( ! l9e ,m ,p4 ,h5ce we conclude1 t :5 an object is plac$ at a little di/ance f ! extremity ( a pla9 mirror1 its image =m$ by reflexion f ! mirror _c unite ) ! object 9 =m+ a conjo9$ & symmetrical picture1 unless ! eye is 9 ! plane ( ! mirror4 ,illu/ration3 ,,fig4 #ad4 ,:5 two mirrors1 !re=e1 are comb9$1 z 9 ,fig4 #ad1 ! eye mu/ be 9 ! plane ( bo?1 9 ord] t ! object & its image may h a symmetrical co9cid5ce1 & !re=e x mu/ be at ! po9t ,e :]e ! two planes cut ea* o!r4 ,! necessity ( ?is position1 & ! effects ( any consid]able deviation f x1 w be und]/ood f ,fig4 #ad1 :]e ,a ,o ,b is ! angle =m$ by ! mirrors1 & ,m ,n ! place ( ! object4 ,!n if ! eye is plac$ at 1 ! ap]ture ,a ,o ,b w be project$ into a b ^u a plane pass+ ?r\gh ,m ,n & at "r angles to ,e ,o2 b ! or?ographic projection ( ,a ,b ,o ^u ! same plane is ,a ,b ,o1 or1 :at is ! same ?+1 ! reflect+ surfaces ( :i* ,a ,o1 ,b ,o are sections1 w1 :5 prolong$1 cut ! plane pass+ ?r\gh ,m ,n 9 ! l9es ,a ,o1 ,b ,o2 h5ce1 rays f ! objects situat$ betwe5 ,a ,o ,b & a b _c fall ^u ! mirrors ,a ,o ,e1 ,b ,o ,e1 or images ( ^! objects _c be =m$ by ! mirrors4 ,! images1 !re=e1 9 ! diff]5t sectors =m$ by reflexion r\nd ,o z a c5tre1 _c include any objects )\t ,a ,o ,b2 & s9ce ! eye at sees all ! objects betwe5 ,a ,o ,b & a b1 !re c be no symmetry & uni=mity 9 ! picture =m$ by ! comb9ation ( su* an object ) ! images 9 ! sectors4 ,:5 ! eye desc5ds to e1 ! ap]ture ,a ,o ,b is project$ into a o b1 :i* approa*es ne>] to ,a ,o ,b2 b = ! reasons already assign$1 ! symmetry ( ! picture is /ill imp]fect4 ,z ! eye desc5ds1 ! l9es a o1 b o approa* to ,a ,o1 ,b ,o1 & :5 ! eye arrives at ,e1 a po9t 9 ! plane ( bo? ! reflect+ surfaces1 ! projection ( ! ap]ture ,a ,o ,b w be ,a ,o ,b1 & ! images 9 all ! sectors w be exactly simil> to ! object pres5t$ to ! ap]ture4 ,h5ce we conclude 9 g5]al1 t :5 an object is plac$ at any di/ance be=e two mirrors incl9$ at an angle1 :i* is an ev5 aliquot "p ( #cfj1 ! symmetry ( ! picture is p]fect1 :5 ! eye1 consid]$ z a ma!matical po9t1 is plac$ at ,e1 & t ! deviation f symmetry increases z ! eye rec$es f ,e t[>ds 4 ,if ! object 7 a ma!matical surface1 all ! p>ts ( :i* 7 9 contact ) ! extremities ,a ,o1 ,b ,o ( ! mirrors1 !n x is easy to see t ! symmetry ( ! picture w n be affect$ by ! deviation ( ! eye f ! po9t ,e1 &1 9 consequ5ce ( ! enl>gem5t ( ! sector1 se5 by direct vision4 ,! symmetry ( ! picture1 is1 h[ev]1 affect$ 9 ano!r way1 by ! deviation ( ! eye f ! po9t ,e4 ,we h already se51 t1 9 ord] to possess p]fect symmetry1 an object mu/ consi/ ( two p>ts 9 complete contact1 "o ( :i* is an inv]t$ image ( ! o!r4 ,b 9 ord] t an object possess+ p]fect symmetry may appe> p]fectly symmetrical1 f\r conditions are requir$4 ,! two halves ( ! object mu/ be s plac$ ) respect to ! eye ( ! obs]v]1 t no "p ( ! "o half %all conceal any "p ( ! o!r2 t :atev] p>ts ( ! "o half are se51 ! correspond+ p>ts ( ! o!r mu/ also be se52 & t ! correspond+ p>ts ( bo? halves1 & bo? halves !mselves1 mu/ subt5d ! same angle at ! eye4 ,:5 we /& be=e a look+-glass1 & hold out "o h& s z to t\* x1 ! h& w be f\nd to conceal v>i\s p>ts ( its image2 &1 9 "s positions ( ! eye1 ! :ole image w be conceal$1 s t a symmetrical picture _c possibly be =m$ by ! union ( ! two4 ,if ! eye is plac$ s obliquely to ! look+-glass1 t ! h& no long] int]f]es ) its image1 x w /ill be se51 t p>ts ( ! h& :i* are n directly visible1 are visible 9 its reflect$ image1 & !re=e t a symmetrical picture _c be creat$ by ! union ( two p>ts app>5tly dissimil>4 ,if ! eye ( ! obs]v] is plac$ ne> 8 h&1 s t he c see di/9ctly bo? ! h& & its image1 ! angul> magnitude ( 8 h& is mu* great] ?an t ( its image2 & !re=e1 :5 ! two are unit$1 !y _c =m a symmetrical object4 ,?is w be bett] und]/ood f ,fig4 #ae4 ,:5 ! eye is plac$ at 1 ! object ,m ,n ,o ,p is obvi\sly ne>] ?an its image m n o p1 & mu/ !re=e appe> l>g]2 & ?is diff]5ce 9 _! app>5t magnitudes w increase z ! eye rises above ! plane ( ! mirror ,a ,e4 ,z ! eye approa*es to ,e1 ! di/ances ( ! object & its image approa* to an equality2 & :5 ! eye is at ,e1 ! object ,m ,n ,o ,p1 & its image m n o p1 are situat$ at exactly ! same di/ance f ! eye1 & !re=e h ! same angul> magnitude4 ,h5ce x foll[s1 t :5 !y are unit$1 !y w =m a p]fectly symmetrical comb9ation4 ,illu/ration3 ,,fig4 #ae4 ,:5 ! eye is plac$ 9 ! plane ( bo? ! mirrors1 ! field ( view aris+ f ! multiplication ( ! sector ,a ,o ,b1 ,fig4 #ad1 w be p]fectly circul>2 b z ! eye rises above ! plane ( bo? ! mirrors1 ?is circle w become a sort ( ellipse1 becom+ m & m ecc5tric z ! eye comes 9 front ( ! mirrors1 or rises 9 ! direction ,e 4 ,if ! obs]v] 7 inf9itely di/ant1 ^! figures w\ld be correct ellipses2 b z ! eye1 p>ticul>ly :5 ! mirrors are broad1 mu/ be ne>ly twice z f> f ! la/ reflect$ sector z f ! sector se5 by direct vision1 ! field ( view1 & consequ5tly e patt]n :i* x conta9s1 mu/ be di/ort$ & de/itute ( beauty1 f ?is cause alone4 ,hi!rto we h allud$ only to symmetry ( =m1 b x is manife/ t be=e ! union ( two simil> =ms c give pleasure to ! eye1 !re mu/ be also a symmetry ( light4 ,if ! object ,m ,n ,o ,p1 ,fig4 #ae1 is :ite1 & its image m n o p black1 !y _c possibly =m1 by _! comb9ation1 an agreeable picture4 ,z any consid]able diff]5ce 9 ! int5sity ( ! light w de/roy ! beauty ( ! patt]ns1 x becomes a matt] ( indisp5sable importance to det]m9e ! position ( ! eye1 :i* w give ! greate/ possible uni=mity to ! diff]5t images ( :i* ! picture is compos$4 ,x has be5 asc]ta9$ by ! accurate exp]im5ts ( ,b\gu]1 t :5 light is reflect$ p]p5dicul>ly f good plate glass1 only #be rays are reflect$ out ( #ajjj2 t is1 ! int5sity ( ! light ( any object se5 p]p5dicul>ly 9 plate glass1 is to ! int5sity ( ! light ( its image z #ajjj to #be1 or z #dj is to #a4 ,:5 ! angle ( incid5ce is #fj1 ! numb] ( reflect$ rays is #aab1 & ! int5sities are ne>ly z #i to #a4--,:5 ! angle ( incid5ce is #hg1 ! numb] ( reflect$ rays is #ehd1 & ! int5sities are ne>ly z #ag to #aj1 s t ! lum9\sness ( ! object & its image approa* rapidly to an equality4 ,x is !re=e cle>1 t1 9 ord] to h ! greate/ uni=mity ( light 9 ! diff]5t images :i* compose ! figure1 ! eye mu/ be plac$ z ne>ly z possible 9 ! plane ( bo? ! mirrors1 t is1 z ne> z possible to ! angul> po9t4--,b z x is impracticable to h ! eye exactly 9 ! plane ( bo? mirrors1 ! images =m$ by "o reflexion mu/ always be less bright ?an ! direct object1 ev5 at ! "p ne>ly 9 contact ) ! object4 ,! second & ?ird reflexions1 etc41 :]e ! rays fall ) less obliquity1 w be /ill d>k] ?an ! fir/2 ?\gh ?is diff]5ce w n be v p]ceptible :5 ! incl9ation ( ! mirrors is #cj or upw>ds1 & ! eye plac$ 9 ! position already describ$4 ,x is a curi\s circum/ance1 t ! positions ( ! eye :i* are necess>y to effect a complete union ( ! images--to repres5t simil> p>ts ( ! object & its images--to obs]ve ! object & its image "u ! same angul> magnitude1 & to give a maximum int5sity ( light to ! reflect$ images--%\ld all unite 9 ! same po9t4 ,_h ?is n be5 ! case1 ! con/ruction ( ! ,kaleidoscope w\ld h be5 impracticable1 & h5ce x w be se5 h[ va9 is ! attempt to produce beautiful & symmetrical =ms f any comb9ation ( pla9 mirrors 9 :i* ?is position ( ! eye is n a radical & ess5tial pr9ciple4 ,,*apt] ,v4 ,,on ,,! ,,effects ,,produc$ ,,^u ,,! ,,symmetry ,,( ,,! ,,picture ,,by ,,v>y+ ,,! ,,position ,,( ,,! ,,object4 ,hav+ asc]ta9$ ! prop] position ( ! eye1 we %all n[ proce$ to det]m9e ! position ( ! object4 ,if ! object is plac$ )9 ! reflectors at any po9t ,d1 ,fig4 #af1 betwe5 _! object end ,o1 & _! eye-end ,e1 a p]fectly symmetrical picture w obvi\sly be =m$ f x2 b ! c5tre ( ?is picture w n be at ,o1 ! c5tre ( ! lum9\s sectors1 b at ! po9t ,d1 :]e ! object is plac$1 or its projection d1 s t we %all h a circul> lum9\s field enclos+ an ecc5tric circul> patt]n4 ,su* a position ( ! object is !re=e entirely unfit = ! production ( a symmetrical picture1 unless ! object %\ld be su* z :olly to exclude ! view ( ! circul> field1 =m$ by ! reflect$ images ( ! ap]ture ,a ,o ,b4 ,z ! po9t ,d approa*es to ,o1 ! c5tre d ( ! symmetrical picture w approa* to ,o1 & :5 ,d co9cides ) ,o1 ! c5tre ( ! picture w be at ,o1 & all ! images ( ! object plac$ 9 ! plane ,a ,o ,b w be simil>ly dispos$ 9 all ! sectors :i* compose ! circul> field ( view4 ,h5ce we may conclude1 t a p]fectly symmetrical patt]n _c be exhibit$ 9 ! circul> field ( view1 :5 ! object is plac$ betwe5 ,o & ,e1 or any:]e )9 ! reflectors4 ,if ! eye c\ld be plac$ exactly at ! angul> po9t ,e1 s t e po9t ( ! l9e ,e ,o %\ld be project$ ^u ,o1 !n ! images w\ld be symmetrically arrang$ r\nd ,o2 b ?is is obvi\sly impossible1 = ! object w\ld1 9 su* circum/ances1 cease to become visible :5 ?is co9cid5ce took place4 ,b indep5d5t ( ! ecc5tricity ( ! patt]n1 ! position ( ! object )9 ! mirrors prev5ts t motion ( ! objects1 )\t :i* a v>iation ( ! patt]n _c be produc$4 ,an object betwe5 ! reflectors mu/ always be expos$ to view1 & we _c re/rict our view to "o-half1 "o-?ird1 or "o-f\r? ( x1 z :5 we h x 9 our p[] to move ! objects across ! ap]ture1 or ! ap]ture ov] ! objects4 ,illu/ration3 ,,fig4 #af4 ,ano!r evil aris+ f ! plac+ ( ! objects )9 ! mirrors1 is1 t we are prev5t$ f giv+ !m ! prop] degree ( illum9ation :i* is s ess5tial to ! di/9ctness ( ! la/ reflexions4 ,! portions ( ! mirrors1 too1 beyond ! objects1 or ^? betwe5 ,d & ,o1 are :olly unnecess>y1 z !y are n conc]n$ 9 ! =mation ( ! picture4 ,h5ce x foll[s1 t ! effects ( ! ,kaleidoscope _c be produc$ by any comb9ation ( mirrors1 9 :i* ! objects are plac$ )9 !m4 ,let u n[ consid] :at w happ51 by remov+ ! object beyond ! plane pass+ ?r\gh ,a ,o ,b4 ,9 ?is case ! patt]n w lose its symmetry f two causes4 ,9 ! fir/ place1 x is manife/1 z already expla9$1 t z ! eye is necess>ily rais$ a little above ! po9t ,e1 & also above ! planes ,a ,o ,e1 ,b ,o ,e1 x mu/ see ?r\gh ! ap]ture ,a ,o ,b a portion ( ! object situat$ bel[ bo? ( ^! planes4 ,?is "p ( ! object w !re=e appe> to project beyond ! po9t1 or bel[ ! plane :]e ! direct & reflect$ images meet4 ,if we suppose1 !re=e1 t all ! reflect$ images 7 symmetrical1 ! :ole picture w\ld lose its symmetry 9 consequ5ce ( ! irregul>ity ( ! sector ,a ,o ,b se5 by direct vision4 ,b ?is supposition is n correct2 = s9ce ! image m n1 ,fig4 #c1 se5 by direct vision does n co9cide ) ! fir/ reflect$ images mn1 nm1 x is cle> t all ! o!r images w likewise be inco9cid5t1 &1 !re=e1 t ! figure =m$ by _! comb9ation mu/ lose its symmetry1 &1 consequ5tly1 its beauty4 ,z ! eye mu/ necess>ily be plac$ above a l9e p]p5dicul> to ! plane ,a ,b ,o at ! po9t ,o1 x w see a portion ( ! object situat$ bel[ t p]p5dicul> cont9u$ to ! object4 ,?us1 9 ,fig4 #af1 if ! eye is plac$ at e above ,e1 & if ,m ,n is ! object plac$ at ! di/ance ,p ,o1 !n ! eye at e w obs]ve ! portion ,p ,o ( ! object situat$ bel[ ! axis ,p ,o ,e1 & ?is portion1 :i* may be call$ ! ab]ration1 w v>y ) ! height ,e e ( ! eye1 & ) ! di/ance ,o ,p ( ! object4 ,illu/ration3 ,,fig4 #ag4 ,let u n[ suppose ,e e & ,o ,p to be con/ant1 & t a polygonal figure is =m$ by "s l9e plac$ at ! po9t ,q ( ! object ,m ,n4 ,!n if ,p ,q is v great comp>$ ) ,p ,o1 ! polygonal figure w be tol]ably regul>1 ?\gh all its angles w exhibit an imp]fect junction1 & its l[] half w be actually1 ?\gh n v p]ceptibly1 less ?an its upp] half4 ,b if ,q approa*es to ,p1 ,p ,o rema9+ ! same1 s t ,p ,o be>s a consid]able ratio to ,p ,q1 !n ! polygonal figure w lose all symmetry1 ! upp] sectors be+ decid$ly ! l>ge/1 & ! l[e/ sectors ! smalle/4 ,:5 ,q arrives ne> ,p1 ! ab]ration becomes enorm\s1 & ! figure is s di/ort$1 t x c no long] be recognis$ z a polygon4 ,! deviation f symmetry1 !re=e1 aris+ f ! removal ( ! object f ! extremity ( ! reflectors1 increases z ! object approa*es to ! c5tre ( ! lum9\s sectors or ! circul> field1 & ?is deviation becomes s p]ceptible1 t an eye accu/om$ to obs]ve & admire ! symmetry ( ! comb9$ objects1 w in/antly p]ceive x1 ev5 :5 ! di/ance ( ! object or ,p ,o is less ?an ! tw5tie? "p ( an in*4 ,:5 ! object is v di/ant1 ! defect ( symmetry is s enorm\s1 t ?\gh ! object is se5 by direct vision1 & 9 "s ( ! sectors1 x is entirely invisible 9 ! re/4 ,! pr9ciple :i* we h n[ expla9$ is ( prim>y importance 9 ! con/ruction ( ! ,kaleidoscope1 & x is only by a c>eful att5tion to x t ! in/rum5t c be con/ruct$ s z to give to an exp]i5c$ & fa/idi\s eye t high delight :i* x nev] fails to d]ive f ! exhibition ( =ms p]fectly symmetrical4 ,f ^! obs]vations x foll[s1 t a picture possess$ ( ma!matical symmetry1 _c be produc$ unless ! object is plac$ exactly at ! extremity ( ! reflectors1 & t ev5 :5 ?is condition is compli$ )1 ! object itself mu/ consi/ ( l9es all ly+ 9 ! same plane1 & 9 contact ) ! reflectors4 ,h5ce x is obvi\s1 t objects ^: ?ickness is p]ceptible1 _c give ma!matically symmetrical patt]ns1 = "o side ( !m mu/ always be at a c]ta9 di/ance f ,o4 ,! deviation 9 ?is case is1 h[ev]1 s small1 t x c sc>cely be p]ceiv$ 9 objects ( mod]ate ?ickness4 ,9 ! simple =m ( ! ,kaleidoscope1 ! production ( symmetrical patt]ns is limit$ to objects :i* c be plac$ close to ! ap]ture ,a ,o ,b2 b x w be se5 9 ! sequel ( ?is treatise1 t ?is limitation may be remov$ by an optical contrivance1 :i* ext5ds indef9itely ! use & application ( ! in/rum5t4 ,,*apt] ,,vi4 ,,on ,,! ,,int5sity ,,( ,,! ,,light ,,9 ,,diff]5t ,,p>ts ,,( ,,! ,,field1 ,,& ,,on ,,! ,,effects ,,produc$ ,,by ,,v>y+ ,,! ,,l5g? ,,& ,,bread? ,,( ,,! ,,reflectors4 ,:5 we look ?r\gh a ,kaleidoscope 9 :i* ! mirrors are plac$ at an angle ( #ah or #bb1 ! eye w p]ceive a v obvi\s diff]5ce 9 ! int5sity ( ! light 9 diff]5t p>ts ( ! field4 ,if ! incl9ation ( ! mirrors be ab\t #cj1 & ! eye prop]ly plac$ ne> ! angul> po9t1 ! int5sity ( ! light is tol]ably uni=m2 & a p]son :o is unaccu/om$ to ! comp>ison ( diff]5t lights1 w f9d x extremely difficult to di/+ui% ! direct sector f ! reflect$ ones4 ,?is difficulty w be /ill great] if ! mirrors are made ( f9ely poli%$ /eel1 or ( ! be/ speculum metal1 & ! obs]v] w n hesitate 9 believ+ t he is look+ ?r\gh a tube ^: diamet] is equal to t ( ! circul> field4 ,?is approximation to uni=mity 9 ! int5sity ( ! light 9 all ! sectors1 :i* arises :olly f ! det]m9ation ( ! prop] position ( ! eye1 is "o ( ! mo/ curi\s & unexpect$ prop]ties ( ! ,kaleidoscope1 & is "o :i* c\ld n h be5 anticipat$ f any !oretical views1 or f any exp]im5tal results obta9$ f ! anci5t mode ( comb9+ pla9 mirrors4 ,x is t prop]ty1 too1 :i* gives x all its value2 =1 if ! eye obs]v$ ! direct sector ) its includ$ objects di/+ui%$ f all ! re/ by sup]ior brilliancy1 n only w\ld ! illusion vani%1 b ! picture itself w\ld cease to af=d pleasure1 f ! want ( symmetry 9 ! light ( ! field4 ,illu/ration3 ,,fig4 #ah4 ,be=e we proce$ to inve/igate ! effects produc$ by a v>iation 9 ! l5g? ( ! reflect+ planes1 x w be necess>y to consid] ! v>iation ( ! int5sity ( ! light 9 diff]5t p>ts ( ! reflect$ sectors4 ,9 ! direct sector ,a ,o ,b1 ,fig4 #b1 ! int5sity ( ! light is uni=m 9 e "p ( its surface2 b ?is is f> f be+ ! case 9 ! images =m$ by reflexion4 ,9 ,fig4 #ag1 take any two po9ts m1 o1 & draw ! l9es m n1 o p1 p]p5dicul> to ,a ,o1 & meet+ ,o 9 n & p4 ,let ,o ,e1 ,fig4 #ah1 be a section ( ! reflector ,a ,o se5 edgewise1 & let ,o p1 ,o n1 be tak5 equal to ! l9es m n1 o p1 or ! height ( ! po9ts n1 p1 above ! plane ( ! reflector ,a ,o4 ,make ,o ,r to ,r ,e z ,o p is to ,e e ! con/ant height ( ! eye above ! reflect+ plane1 & ,o r to r ,e z ,o n to ,e e1 & ! po9ts ,r1 r1 w be ! po9ts ( incid5ce ( ! rays issu+ f p & n2 = 9 ?is case ,o ,r p ,e ,r e1 & ,o r n ,e r e4 ,h5ce x is obvi\s1 t ,e ,r e is less ?an ,e r e1 & t ! rays issu+ f p1 by fall+ m obliquely ^u ! reflect+ surface1 w be m copi\sly reflect$4 ,x foll[s1 !re=e1 t ! int5sity ( ! light 9 ! reflect$ sector ,a ,o is n uni=m1 ! l9es ( equal brightness1 or ! isophotal l9es1 z !y may be call$1 be+ p>allel to ! reflect+ surface ,a ,o1 & 9 e sector p>allel to ! radius1 betwe5 ! giv5 sector & ! reflect+ surface by :i* ! sector is =m$4 ,z x is easy f ! prec$+ con/ruction to det]m9e ! angles at :i* ! light f any po9ts m1 n1 is reflect$1 :5 ! l5g? ,o ,e ( ! reflectors1 & ! position ( ! eye at ,e is giv51 we may calculate ! int5sity ( ! light 9 any po9t ( ! circul> field by means ( ! foll[+ table1 :i* %[s ! numb] ( rays reflect$ at v>i\s angles ( incid5ce1 ! numb] ( incid5t rays be+ suppos$ to be #ajjj4 ,"p ( ?is table 0 comput$ by ,b\gu] = plate glass n quicksilv]$1 by means ( a =mula d$uc$ f 8 exp]im5ts4 ,by ! aid ( ! same =mula ,i h ext5d$ ! table consid]ably4 ,table %[+ ! quantity ( light reflect$ at v>i\s angles ( incid5ce f plate glass4 ------------------------------ ,complem5t ( ,rays ,reflect$ ! ,angles out ( ,incid5ce4 ( #ajjj4 ------------------------------ #b #ehd #e #edc #g #dgd #aj #dab #ab #cef #ae #bii #bj #bbb #ba #baj #be #aeg #bf #adi #cj #aab #ca #aje #cd #he #ce #gi #cf #gd #cg #fi #ch #fe #ci #fa #dj #eg #df #dj #ej #cd #ee #bi #fj #bg #gj #be #hj #be #ij #be ------------------------------ ,9 ord] to expla9 ! me?od ( us+ ! table1 let u suppose t ! angle ( incid5ce1 or ,o ,r p1 ,fig4 #ai1 is #he3 !n ! numb] ( rays 9 ! correspond+ po9t ( ! reflect$ sector ,a ,o b 7,fig4 #ag7 w be #edc4 ,by lett+ fall p]p5dicul>s f ! po9ts 1 1 ^u ! mirror ,b ,o1 & tak+ ,o p1 ,o n1 ,fig4 #ai1 equal to ^! p]p5dicul>s1 we may asc]ta9 ! angles at :i* ! light f ! po9ts 1 1 suff] a second reflexion f ! mirror ,b ,o4 ,let ! angle = ! po9t be #aj1 !n ! numb] ( rays out ( #ajjj reflect$ at ?is angle1 accord+ to ! table1 is #dab2 b z ! numb] ( rays emanat+ f 1 & incid5t ^u ,b ,o1 is n #ajjj1 b only #edc1 we mu/ say z #ajjj3 #dab #edc3 #bbd1 ! numb] ( rays reflect$ f ,b ,o1 or ! int5sity ( ! light 9 a po9t 9 ! l9e ,o b correspond+ to 4 ,illu/ration3 ,,fig4 #ai4 ,! prec$+ me?od ( calculation is applicable only ) /rictness to ! two sectors ,a ,o b1 ,b ,o a1 =m$ by "o reflexion1 = ! int5sity ( ! light 9 ! o!r sectors :i* are =m$ by m ?an "o reflexion1 mu/ be affect$ by ! pol>ization :i* ! light exp]i5ces aft] successive reflexions2 = light :i* has acquir$ ?is prop]ty is reflect$ accord+ to laws diff]5t f ^? :i* regulate ! reflexion ( direct light4 ,:5 ! mirrors are metallic1 ! quantity ( reflect$ light is also affect$ by its pol>ization1 b x is regulat$ by m complicat$ laws4 ,9 ,kaleidoscopes made ( plates ( glass1 ! la/ reflect$ image ,o 1 ,fig4 #b1 is m pol>iz$ ?an any ( ! re/1 & is pol>iz$ 9 a plane p]p5dicul> to ,x ,e1 or 9 ! same mann] z if x _h be5 reflect$ at ! pol>iz+ angle f a v]tical plane p>allel to ,x ,e4 ,illu/ration3 ,,fig4 #bj4 ,let u n[ consid] :at w take place by a v>iation 9 ! l5g? ( ! reflect+ planes1 ! angul> ext5t ( ! field ( view rema9+ always ! same4 ,if ,a ,o ,e1 ,a ,o ,e1 ,fig4 #bj1 be two reflect+ plates ( ! same bread? ,a ,o1 b ( diff]5t l5g?s1 x is manife/ t ! light :i* =ms ! direct sector mu/ be incid5t ne>] ! p]p5dicul>1 or reflect$ at less obliquities 9 ! %ort plate ?an 9 ! long "o1 &1 !re=e1 t a simil>ly situat$ po9t 9 ! circul> field ( ! %ort] in/rum5t1 w h less int5sity ( light ?an a simil>ly situat$ po9t 9 a l>g] in/rum5t4 ,b 9 ?is case1 ! field ( view 9 ! %ort in/rum5t is proportionally enl>g$1 s t ! comp>ison betwe5 ! two is incorrect4 ,:5 ! long & ! %ort in/rum5t h equal app>5t ap]tures1 :i* w be ! case :5 ! plates are ,a ,o ,e1 ,a ,o ,e1 !n simil>ly situat$ po9ts ( ! two fields w h exactly ! same int5sity ( light4 ,?is w be bett] und]/ood f ,fig4 #ai1 :]e ,o ,e may repres5t ! long reflector & ,o ,e ! %ort "o4 ,!n1 if ^! two h exactly ! same ap]ture1 or a circul> field ( ! same angul> magnitude1 ! rays ( light :i* fl[ f two giv5 po9ts1 p1 n1 ( ! long in/rum5t1 w be reflect$ at a c]ta9 angle f ! po9ts ,r1 r2 b z ! po9ts p1 n1 are ! correspond+ po9ts 9 ! field ( ! %ort] in/rum5t1 ! rays :i* issue f !m w be reflect$ at ! same angles f ! po9ts ,r1 r1 ! eye be+ 9 bo? cases plac$ at ! same po9t e4 ,h5ce x is obvi\s1 t ! quantity ( reflect$ light w 9 bo? cases be ! same1 &1 !re=e1 t !re is no peculi> advantage to be d]iv$1 9 s f> z ! light ( ! field is conc]n$1 by increas+ ! l5g? ( ! reflectors1 unless we raise ! eye above e1 till e "p ( ! pupil receives ! reflect$ rays4 ,!re is1 h[ev]1 "o advantage1 & a v important "o1 to be d]iv$ f an increase ( l5g? 9 ! mirrors1 namely a dim9ution ( ! deviation f symmetry :i* arises f ! small height ( ! eye above ! plane ( ! mirrors1 & ( ! small di/ance ( ! objects f ! extremity ( ! mirrors4 ,z ! height ( ! eye mu/ always be a c]ta9 quantity1 ,e e1 ,fig4 #ag1 above ! angul> po9t ,e1 :atev] be ! l5g? ( ! reflectors1 x is obvi\s1 t :5 ! l5g? ( ! reflectors is e ,o1 ! deviation f symmetry w be only ,p o1 :]eas :5 ! l5g? ( ! reflectors is r$uc$ to e ,o1 ! height ( ! eye e ,e be+ /ill equal to e ,e1 ! ab]ration w be increas$ to ,p o4 ,?is advantage is c]ta9ly ( consid]able consequ5ce2 b 9 practice ! difficulty ( con/ruct+ a p]fect in/rum5t1 increases ) ! l5g? ( ! reflectors4 ,:5 ! plates are long1 x is m difficult to get ! surface p]fectly flat2 ! risk ( a b5d+ 9 ! plates is also increas$1 :i* creates ! additional difficulty ( =m+ a good junction1 on :i* ! excell5ce ( ! in/rum5t s mu* dep5ds4 ,by augm5t+ ! l5g? ( ! reflectors1 ! quantity ( du/ :i* collects betwe5 !m is also increas$1 & x is !n v difficult to remove ?is du/1 )\t tak+ ! in/rum5t to pieces4 ,f ^! causes x is advisable to limit ! greate/ l5g? ( ! reflectors to sev5 or eight in*es4 ,,*apt] ,,vii4 ,,on ,,! ,,con/ruction ,,& ,,use ,,( ,,! ,,simple ,,kaleidoscope4 ,9 ord] to con/ruct ! ,kaleidoscope 9 its mo/ simple =m1 we mu/ procure two reflectors1 ab\t five1 six1 sev51 or eight in*es long4 ,^! reflectors may be ei!r rectangul> plates1 or plates %ap$ l ^? repres5t$ 9 ,fig4 #a1 hav+ _! broade/ ends ,a ,o1 ,b ,o1 f "o to two in*es wide1 & _! n>r[e/ ends a ,e1 b ,e1 half an in* wide4 ,if ! reflectors are ( glass1 ! newe/ plate glass %\ld be us$1 z a great deal ( light is lo/ by employ+ old plate glass1 ) scrat*es or imp]fections ^u its surface4 ,! plate glass may be ei!r quicksilv]$ or n1 or its po/]ior surface may be gr\nd1 or cov]$ ) black wax1 or black v>ni%1 or any?+ else t removes its reflective p[]4 ,?is1 h[ev]1 is by no means absolutely necess>y1 = if ! eye is prop]ly plac$1 ! reflexions f ! po/]ior surface w sc>cely affect ! di/9ctness ( ! picture1 unless 9 v int5se lights4 ,if x %\ld be ?\ght necess>y to ext+ui%1 z completely z possible1 all extrane\s light t may be ?r[n into ! tube f ! po/]ior surface ( ! glass plates1 t surface %\ld be coat$ ) a v>ni% ( ! same refractive & disp]sive p[] z ! glass4 ,if ! plates ( glass h be5 skilfully cut ) ! diamond1 s z to h _! edges p]fectly /raight1 & free f *ips1 two ( ! edges may be plac$ toge!r1 z 9 ,fig4 #ag 7p4 #di71 or "o edge ( "o plate may be plac$ aga9/ ! surface ( ! o!r plate1 z %[n 9 ! section ( ,mr4 ,bates's ,kaleidoscope4 ,b if ! edges are r\gh & unev51 "o ( !m may be made q /raight1 & fre$ f all imp]fections1 by gr9d+ x ^u a flat surface1 ) v f9e em]y1 or ) ! p[d] scrap$ f a hone4 ,:5 ! two plates are laid toge!r1 s z to =m a p]fect junction1 !y are !n to be plac$ 9 a brass or any o!r tube1 s z to =m an angle ( #de1 #cf1 #cj1 or any ev5 aliquot "p ( a circle4 ,9 ord] to d ?is ) p]fect accuracy1 direct ! tube conta9+ ! reflectors to any l9e1 su* z m n1 ,fig4 #b1 plac$ v obliquely to "o ( ! reflectors ,a ,o1 & op5 or %ut ! plates till ! figure ( a /> is =m$1 compos$ ( #h1 #aj1 or #ab sectors1 or ) #d1 #e1 or #f po9ts1 correspond+ to angles ( #de1 #cf1 & #cj4 ,:5 all ! po9ts ( ! /> are equally p]fect1 & none ( ! l9es :i* =m ! sali5t & re-ent]+ angles disunit$1 ! reflectors mu/ be fix$ 9 t position by small ar*es ( brass or wood ,a ,b1 a b1 ,fig4 #ba1 fil$ d[n till !y exactly fit ! space betwe5 ! op5 ends ( ! plates4 ,! plates mu/ !n be kept 9 ?is position by pieces or w$ges ( cork or wood1 or any o!r sub/ance pu%$ betwe5 !m & ! tube4 ,! greate/ c>e1 h[ev]1 mu/ be tak5 t ^! w$ges press lightly ^u ! reflectors1 = a v slight =ce is capable ( b5d+ & alt]+ ! figure ev5 ( v ?ick plates ( glass4 ,:5 ! reflectors are ?us plac$ 9 ! tube1 z 9 ,fig4 #ba1 _! extremities a ,e1 b ,e1 next ! eye1 mu/ rea* to ! v end ( ! tube1 z x is ( ! greate/ importance t ! eye get z ne> z possible to ! reflectors4 ,! o!r ends ( ! reflectors ,a ,o1 ,b ,o1 mu/ also ext5d to ! o!r extremity ( ! tube1 9 ord] t !y may be br\ght into contact ) ! objects :i* are to be appli$ to ! in/rum5t4 ,9 us+ transp>5t objects ! cell or box :i* conta9s !m may be screw$ into ! end ( ! tube1 s z to rea* ! ends ( ! reflectors1 if !y happ5 to t]m9ate )9 ! tube2 b an in/rum5t ?us con/ruct$ is incapable ( be+ appli$ to opaque objects1 or to transp>5t objects se5 by reflect$ light4 ,illu/ration3 ,,fig4 #ba4 ,if ! plates are n>r[] at ! eye-end1 z 9 ,fig4 #ba1 ! angul> po9t ,e %\ld be a little on "o side ( ! axis ( ! tube1 9 ord] t ! ap]ture 9 ! c5tre ( ! brass cap next ! eye may be br\ght z ne> z possible to ,e4 ,:5 ! plates h ! same bread? at bo? ends1 ! angul> po9t ,e w be ne> ! l[] circumf]5ce ( ! tube1 z x is at ,o2 & 9 ?is case x is necess>y to place ! eye-hole out ( ! c5tre1 s z to be a little above ! angul> po9t ,e4 ,?is con/ruction is less elegant ?an ! prec$+2 b x has ! advantage ( giv+ m room = ! introduction ( a fea!r1 or a piece ( ?9 wood cov]$ ) lea!r1 = ! purpose ( remov+ ! du/ :i* is con/antly accumulat+ betwe5 ! reflectors4 ,9 "s in/ances ! plates h be5 put toge!r 9 su* a mann] t !y may be tak5 out ( ! tube1 = ! purpose ( be+ clean$2 b ?\gh ?is con/ruction has its advantages1 yet x requires "s +5uity to replace ! reflectors ) facility1 & to fix !m at ! exact incl9ation :i* is requir$4 ,"o ( ! mo/ conv5i5t me?ods is to support ! reflector 9 a groove cut out ( a solid cyl9d] ( dry wood ( ne>ly ! same diamet] z ! tube2 & aft] a slip ( wood1 or any o!r sub/ance1 is plac$ along ! op5 edges ( ! plates1 to keep !m at ! prop] angle giv5 by ! groove1 ! :ole is slipp$ into ! tube1 :]e x rema9s firm & secure f all accid5t4 ,if ! l5g? ( ! reflectors is less ?an ! %orte/ di/ance at :i* ! eye is capable ( see+ objects ) p]fect di/9ctness1 x w be necess>y to place at ! eye-end ,e a convex l5s1 ^: focal l5g? is equal to1 or an in* or two great] ?an1 ! l5g? ( ! reflectors4 ,by ?is means ! obs]v] w see ) p]fect di/9ctness ! objects plac$ at ! object end ( ! ,kaleidoscope4 ,?is l5s1 h[ev]1 mu/ be remov$ :5 ! in/rum5t is to be us$ by p]sons :o are %ort-sight$4 ,! prop] application ( ! objects at ! end ( ! reflectors is n[ ! only /ep :i* is requir$ to complete ! simple ,kaleidoscope4 ,! me?od ( =m+1 select+1 & mix+ ! objects1 w be describ$ 9 ! next *apt]4 ,at pres5t1 we %all conf9e our att5tion to ! v>i\s me?ods :i* may be employ$ 9 apply+ !m to ! end ( ! reflectors4 ,illu/ration3 ,,fig4 #bb4 ,! fir/ & mo/ simple me?od consi/s 9 br++ ! tube ab\t half an in* beyond ! ends ( ! reflectors4 ,a circul> piece ( ?9 plane glass ( ! same diamet] z ! tube1 is !n pu%$ into ! tube1 s z to t\* ! reflectors4 ,! pieces ( col\r$ glass be+ laid ^u ?is piece ( glass :5 ! tube is held 9 a v]tical position1 ano!r simil> disc ( plane glass1 hav+ its out] surface gr\nd ) f9e em]y1 is next plac$ above ! glass fragm5ts1 be+ prev5t$ f press+ ^u !m1 or approa*+ too ne> ! fir/ plane glass by a r+ ( copp] or brass2 & is kept 9 its place by burni%+ d[n ! end ( ! tube4 ,! eye be+ plac$ at ! o!r end ( ! in/rum5t1 ! obs]v] turns ! :ole r\nd 9 8 h&1 & p]ceives an inf9ite v>iety ( beautiful figures & patt]ns1 9 consequ5ce ( ! succession ( new fragm5ts1 :i* are br\ght opposite ! ap]ture by _! own gravity1 & by ! rotatory motion ( ! tube4 ,9 ?is rude /ate1 h[ev]1 ! in/rum5t is by no means susceptible ( af=d+ v pleas+ exhibitions4 ,a v disagreeable effect is produc$ by br++ ! d>ke/ sectors1 or ^? =m$ by ! greate/ numb] ( reflexions1 to ! upp] "p ( ! circul> field1 & ?\gh ! v>iety ( patt]ns w be v great1 yet ! in/rum5t is limit$ to ! same s]ies ( fragm5ts1 & _c be appli$ to ! num]\s objects :i* are p]petually pres5t+ !mselves to our notice4 ,^! evils c be remov$ only by adopt+ ! con/ruction %[n 9 ,fig4 #bb1 9 :i* ! reflectors rea* ! v end ( ! tube4 ,^u ! end ( ! tube a b1 c d1 ,fig4 #bb1 is plac$ a r+ ( brass1 m n1 :i* moves easily ^u ! tube a b c d1 & is kept 9 its place by a %\ld] ( brass on ea* side ( x4 ,a brass cell1 ,m ,n1 is !n made to slip tightly ^u ! moveable r+ m n1 s t :5 ! cell is turn$ r\nd by means ( ! mill$ end at ,m ,n1 ! r+ m n may move freely ^u ! tube4 ,! fragm5ts ( col\r$ glass1 etc41 are n[ plac$ 9 a small object-box1 z x may be call$1 consi/+ ( two glasses1 ! inn]mo/ ( :i*1 m n1 is transp>5t1 & ! o!r gr\nd on ! outside ,p1 & kept at ! di/ance ( ? or ? ( an in* by a brass rim3 ?is brass rim g5]ally consi/s ( two pieces1 :i* screw into "o ano!r1 s t ! object-plate c be op5$ by unscrew+ x1 & ! fragm5ts *ang$ at pleasure4 ,?is object-box is plac$ at ! bottom ( ! cell ,m ,n1 z %[n at ,o ,p1 & ! dep? ( ! cell is su* z to all[ ! side ,o to t\* ! end ( ! reflectors1 :5 ! cell is slipp$ ^u ! r+ m n4 ,:5 ?is is done1 ! in/rum5t is held 9 "o h& ) ! angul> po9t ,e1 ,fig4 #ba1 d[nw>ds1 :i* is kn[n by a m>k on ! upp] side ( ! tube betwe5 a & b1 & ! cell is turn$ r\nd ) ! o!r h&1 s z to pres5t diff]5t fragm5ts ( ! includ$ glass be=e ! ap]ture ,a ,o ,b4 ,! tube may be direct$ to ! brighte/ "p ( ! sky 9 ! day-"t1 or 9 ! ev5+ to a c&le1 or an ,arg& ,lamp1 s z to transmit ! light directly ?r\gh ! col\r$ fragm5ts2 b x w always be f\nd to give ri*] & m brilliant effects if ! tube is direct$ to ! w9d[-%utt]1 a little to "o side ( ! light1 or is held to "o side ( ! c&le--or1 :at is /ill bett]1 betwe5 two c&les or lamps plac$ z ne> ea* o!r z possible4 ,9 ?is way ! picture creat$ by ! in/rum5t is n compos$ ( ! h>% t9ts =m$ by transmitt$ light2 b ( ! v>i\s reflect$ & s(t5$ col\rs :i* are ?r[n into ! tube f ! sides & angles ( ! glass fragm5ts4 ,:5 ! patt]n rema9s fix$ 9 any position ( ! in/rum5t1 a v>iety ( beautiful *anges may be effect$ by mak+ ! end ( ! tube revolve r\nd a c&le or a bright gas flame1 plac$ ne> ! object-plate4 ,! g5]al patt]n rema9s ! same1 b its col\rs v>y bo? 9 _! position & int5sity1 z ! light falls ^u diff]5t sides ( ! fragm5ts ( glass4 ,9 ! prec$+ me?od ( apply+ ! objects to ! reflectors1 ! fragm5ts ( col\r$ glass are introduc$ be=e ! ap]ture1 & pass across x 9 conc5tric circles2 & z ! fragm5ts always desc5d by _! own gravity1 ! *anges 9 ! picture1 ?\gh inf9ite 9 numb]1 con/antly take place 9 a simil> mann]4 ,?is defect may be rem$i$1 & a great degree ( v>iety exhibit$ 9 ! motion ( ! fragm5ts1 by mak+ ! object-plates rectangul> in/ead ( circul>1 & mov+ !m ?r\gh a groove cut 9 ! cell at ,m ,n1 9 ! same mann] z is done ) ! pictures or slid]s = ! magic lant]n & sol> microscope4 ,by ?is means ! diff]5t fragm5ts t pres5t !mselves to ! ap]ture may be made to pass across x 9 e possible direction1 & v int]e/+ effects may be produc$ by a comb9ation ( ! rotatory & rectil9eal motions ( ! object-plate4 ,:5 ! object or objects are fix$1 & ! tube ) ! reflectors mov$ r\nd a c5tre1 z describ$ 9 ,*apt] ,,ii41#c we h ! same succession ( symmetrical pictures2 b 9 ?is case e alt]nate sector is /ation>y1 & ! same numb] 9 motion1 ! mov+ figures always *ang+ _! =m1 & assum+ t ( ! figures 9 ! /ation>y sectors1 :i* ( c\rse *ange1 :ile ! ends ( ! mirror pass ov] ! fix$ objects4 #c ,see ,*apt] ,x4 ,:5 ! simple ,kaleidoscope is appli$ to opaque objects1 su* z a seal1 a wat*-*a91 ! seconds h&s ( a wat*1 co9s1 pictures1 gems1 %ells1 fl[]s1 leaves1 & petals ( plants1 impressions f seals1 etc41 ! object1 in/ead ( be+ held betwe5 ! eye & ! light1 mu/ be view$ 9 ! same mann] z we view objects ?r\gh a microscope1 be+ always plac$ z ne> ! in/rum5t z possible1 & s z to all[ ! light to fall freely ^u ! object4 ,! object-plates1 & all transp>5t objects1 may be view$ 9 ?is mann]2 b ! mo/ spl5did exhibition ( ?is k9d is to view m9ute fragm5ts ( col\r$ glass1 & objects ) opaque col\rs1 etc41 plac$ 9 a flat box1 ! bottom ( :i* is made ( mirror-glass4 ,! light reflect$ f ! mirror-glass1 & transmitt$ ?r\gh ! transp>5t fragm5ts1 is comb9$ ) ! light reflect$ bo? f ! transp>5t & opaque fragm5ts1 & =ms an effect ( ! f9e/ k9d4 ,z du/ is apt to collect 9 ! angle =m$ by ! reflectors1 x may be remov$ :5 ! reflectors are fix$1 ei!r by ! end ( a /rong fea!r1 or bl[n away ) a pair ( bell[s4 ,:5 ! du/ is lodg$ ^u ! face ( ! reflectors1 x %\ld be remov$ by a piece ( s(t lea!r4 ,,*apt] ,,viii4 ,,on ,,! ,,selection ,,( ,,objects ,,= ,,! ,,kaleidoscope1 ,,& ,,on ,,! ,,mode ,,( ,,con/ruct+ ,,! ,,object-,,box4 ,al?\gh ! ,kaleidoscope is capable ( creat+ beautiful =ms f ! mo/ ugly & %apeless objects1 yet ! comb9ations :i* x pres5ts1 :5 obta9$ f c]ta9 %apes & col\rs1 are s sup]ior to ^? :i* x produces f o!rs1 t no idea c be =m$ ( ! p[] & effects ( ! in/rum5t1 unless ! objects are judici\sly select$4 ,:5 ! incl9ation ( ! reflectors is great1 ! objects1 or ! fragm5ts ( col\r$ glass1 %\ld be l>g] ?an :5 ! incl9ation is small2 = :5 small fragm5ts are pres5t$ be=e a l>ge ap]ture1 ! patt]n :i* is creat$ has a spott$ appe>ance1 & d]ives no beauty f ! inv]sion ( ! images1 9 consequ5ce ( ! outl9e ( ea* sep>ate fragm5t n jo9+ ) ! inv]t$ image ( x4 ,! objects :i* give ! f9e/ outl9es by inv]sion1 are ^? :i* h a curvil9eal =m1 su* z circles1 ellipses1 loop$ curves l ! figure #h1 curves l ! figure #c & ! lett] ,s2 spirals1 & o!r =ms1 su* z squ>es1 rectangles1 & triangles1 may be appli$ ) advantage4 ,glass1 bo? spun & twi/$1 & ( all col\rs1 & %ades ( col\rs1 %\ld be =m$ into ! prec$+ %apes2 & :5 ^! are mix$ ) pieces ( flat col\r$ glass1 blue vitriol1 native sulphur1 yell[ orpim5t1 diff]5tly col\r$ fluids1 enclos$ & mov+ 9 small vessels ( glass1 etc41 !y w make ! f9e/ transp>5t objects = ! ,kaleidoscope4 ,:5 ! objects are to be laid ^u a mirror plate1 fragm5ts ( opaquely-col\r$ glass %\ld be add$ to ! transp>5t fragm5ts1 along ) pieces ( brass wire1 ( col\r$ foils1 & gra9s ( spelt]4 ,9 select+ transp>5t objects1 ! greate/ c>e mu/ be tak5 to reject fragm5ts ( opaque glass1 & d>k col\rs t d n transmit mu* light2 & all ! pieces ( spun glass1 or col\r$ plates1 %\ld be z ?9 z possible4 ,:5 ! objects are ?us prep>$1 ! next /ep is to place !m 9 ! object-box4 ,! di/ance betwe5 ! int]ior surfaces ( ! two plane glasses1 ( :i* ! object-plates are g5]ally compos$1 %\ld be z small z possible1 n exce$+ ? ( an in*4 ,! out]mo/ ( ^! glasses has its ext]nal surface r\gh gr\nd1 or is :at is call$ a grey glass1 ! pr9cipal use ( :i* is to prev5t ! l9es ( ext]nal objects1 su* z ! b>s ( ! w9d[1 or ! outl9es ( ! illum9at+ flame f be+ introduc$ into ! picture4 ,:5 a /rong light is us$1 a circul> disk ( f9e ?9 pap] plac$ outside ( ! object-box may be advantage\sly employ$ 9 place ( ! gr\nd glass4 ,! ?ickness ( ! transp>5t glass plate next ! reflectors %\ld be j suffici5t to keep ! glass f break+2 & ! int]ior diamet] ( ! brass r+s into :i* ! transp>5t & ! grey or gr\nd plates ( glass are burni%$1 %\ld be s great t no "p ( ! brass rim may be opposite ! angul> "p ( ! reflectors dur+ ! rotatory motion ( ! cell4 ,if ?is precaution is n att5d$ to1 ! c5tral "p ( ! patt]n1 :]e ! developm5t ( new =ms is g5]ally ! mo/ beautiful1 w be entirely oblit]at$ by ! int]position ( ! brass rim4 ,in/ead ( us+ transp>5t or grey glasses on ! sides ( e object-box1 "s ( ! boxes %\ld be made ) disks ( fl9t glass1 ! int]ior surface ( :i* h be5 /amp$ :ile 9 a /ate ( fusion ) a sort ( patt]n1 or ) curv$ l9es ( a pleas+ =m4 ,9 o!rs1 ! out] surface alone ( ! plate next ! reflectors might be ?us =m$4 ,an object-box might also be =m$ ( disks ( glass1 "o side ( :i* is col\rless1 & ! o!r col\r$1 "s ( ! col\r$ portions be+ gr\nd away irregul>ly1 z 9 c]ta9 ,bohemian articles ( glass2 & ! col\r 9 "o disk may be complem5t>y to t 9 ! o!r4 ,9 object-boxes ( ?is k9d1 pieces ( col\r$ glass may also be plac$4 ,:5 ! two p>ts ( ! object-boxes ?us con/ruct$ are screw$ or fix$ toge!r1 ! box %\ld be ne>ly two-?irds fill$ ) ! mixture ( regul> & irregul> objects1 already m5tion$4 ,if !y fall ) difficulty dur+ ! rotation ( ! cell1 two or ?ree turns ( ! screw backw>d1 :5 !re is a screw1 w relieve !m2 & if !y fall too easily1 & accumulate1 by slipp+ beh9d "o ano!r1 ! space betwe5 ! glasses may be dim9i%$ by plac+ )9 ! box ano!r glass 9 contact ) ! grey glass4 ,:5 ! object-box1 n[ describ$1 is plac$ 9 ! cell1 & exam9$ by ! ,kaleidoscope1 ! pictures :i* x =ms are 9 a /ate ( p]petual *ange1 & c nev] be fix$1 & %[n to ano!r p]son4 ,to obviate ?is disadvantage1 an object-box ) fix$ objects g5]ally accompanies ! in/rum5t2 ! pieces ( spun & col\r$ glass are fix$ by a transp>5t cem5t to ! inn] side ( ! glass ( ! object-plate1 next ! eye1 s t ! patt]ns are all p]man5t1 & may be exhibit$ to o!rs4 ,aft] ! cell has p]=m$ a complete rotation1 ! same patt]ns aga9 recur1 & may !re=e be at any "t recall$ at ! pleasure ( ! obs]v]4 ,! same patt]ns1 x is true1 w h a diff]5t appe>ance1 if ! light falls 9 a diff]5t mann] ^u ! objects1 b its g5]al "* & outl9e w1 9 mo/ cases1 rema9 ! same4 ,! object-boxes :i* h n[ be5 describ$1 are made to fit ! cell1 b at ! same "t to slip easily into x1 s t !y !mselves h no motion sep>ate f t ( ! cell4 ,an object-plate1 h[ev]1 ( a less diamet]1 call$ ! vibrat+ object-plate1 & conta9+ loose objects1 is an int]e/+ addition to ! in/rum5t4 ,:5 ! ,kaleidoscope is held horizontally1 ?is small object-plate vibrates on its l[] edge1 ei!r by a g5tle motion ( ! tube1 or by /rik+ x slightly ) ! f+]2 & ! effect ( ?is vibration is s+ul>ly f9e1 p>ticul>ly :5 x is comb9$ ) ! motion ( ! col\r$ fragm5ts4 ,ano!r ( ! object-boxes1 9 sev]al ( ! in/rum5ts1 conta9s ei!r fragm5ts ( col\rless glass1 or an irregul> surface ( transp>5t v>ni% or indurat$ ,canada balsam4 ,?is object-box gives v f9e col\rless figures :5 us$ alone2 b its pr9cipal use is to be plac$ 9 ! cell betwe5 an object-box ) bright col\rs & ! end ( ! in/rum5t4 ,:5 ?is is done1 ! outl9e ( ! pieces ( col\r$ glass are s(t5$ d[n by ! refraction ( ! transp>5t fragm5ts1 & ! patt]n displays ! f9e/ effects ( s(t & brilliant col\r+4 ,! col\rless object-box supplies ! outl9e ( ! patt]n1 & ! mass ( col\r beh9d fills x up ) ! s(te/ t9ts4 ,"s ( ! object-boxes are fill$ ) iron or brass wires1 twi/$ into v>i\s =ms1 & r5d]$ broad] & flatt] 9 "s places by hamm]+4 ,^! wires1 :5 int]mix$ ) a few small fragm5ts ( col\r$ glass1 produce a v f9e effect4 ,o!r object-plates h be5 made ) pit*1 balsam ( tolu1 gum lac1 & ?ick transp>5t pa9ts2 & :5 ^! sub/ances are laid on ) judgm5t1 !y =m excell5t objects = ! ,kaleidoscope4 ,lace has be5 introduc$ ) consid]able effect1 & also fe/oons ( beads /rung ^u wire or ?read2 b pieces ( glass1 ) cut & poli%$ faces1 are ill fitt$ = objects4 ,:5 ! object-box is wide1 c]ta9 insects may be introduc$ tempor>ily1 )\t kill+ or injur+ !m1 & ! cry/allization ( c]ta9 salts f _! solution1 & o!r *emical *anges1 may be curi\sly exhibit$4 ,hi!rto we h suppos$ all col\rs to be indiscrim9ately adopt$ 9 ! selection ( objects2 b x w be f\nd f exp]i5ce1 t ?\gh ! eye is pleas$ ) ! comb9ation ( v>i\s objects1 yet x d]ives ?is pleasure f ! beauty & symmetry ( ! outl9e1 & n f ! union ( _m diff]5t t9ts4 ,^? :o are accu/om$ to ?is k9d ( obs]vation1 & :o are acqua9t$ ) ! pr9ciples ( ! h>mony ( col\rs1 w soon p]ceive ! h>%ness ( ! effect :i* is produc$ by ! pr$om9ance ( "o col\r1 by ! juxtaposition ( o!rs1 & by ! accid5tal union ( a numb]2 & ev5 ^? :o are ignorant ( ^! pr9ciples1 w ackn[l$ge ! sup]ior effect :i* is obta9$ by ! exclusion ( all o!r col\rs except ^? :i* h>monize ) ea* o!r4 ,9 ord] to enable any p]son to f9d :at col\rs h>monize ) ea* o!r1 ,i h drawn up ! foll[+ table1 :i* conta9s ! h>monic col\rs4 ,deepe/ ,r$1 ,blue & ,gre5 equally mix$4 ,r$1 ,blue & ,gre51 ) mo/ ,blue1 mix$4 ,orange ,r$1 ,blue mix$ ) mu* ,indigo4 ,orange1 ,blue & ,indigo1 ! ,indigo pr$om9at+4 ,orange-,yell[1 ,indigo unmix$4 ,yell[1 ,violet & ,indigo ne>ly 9 equal portions4 ,gre5i% ,yell[1 ,pale ,violet4 ,gre51 ,violet4 ,gre5i% ,blue1 ,violet & ,r$ 9 equal portions4 ,blue1 ,orange ,r$1 ,r$4 ,indigo1 ,orange-,yell[4 ,violet1 ,gre54 ,x appe>s f ! prec$+ table t ,blui% ,gre5 h>monizes ) ,r$1 or1 9 o!r words1 ,r$ is said to be ! accid5tal col\r ( ,blui% ,gre51 & vice v]sa4 ,^! col\rs are also call$ complem5t>y col\rs1 because ! "o is ! complem5t ( ! o!r1 or :at ! o!r wants ( :ite light2 t is1 :5 ! two col\rs are mix$1 !y w always =m :ite by _! comb9ation4#d #d ,see ! article ,accid5tal ,col\rs1 9 ! ,,ed9burgh ,,encyclop,,dia1 vol4 i4 p4 #hh4 ,! foll[+ g5]al me?od ( f9d+ ! h>monic col\rs w enable ! read] to det]m9e !m = t9ts n conta9$ 9 ! prec$+ table4 ,let ,a ,b1 ,fig4 #bc1 be ! prismatic spectrum1 conta9+ all ! sev5 col\rs1 namely1 ,r$1 ,orange1 ,yell[1 ,gre51 ,blue1 ,indigo1 & ,violet1 9 ! proportion assign$ to !m by ,sir ,isaac ,newton1 & m>k$ by ! dott$ l9es4 ,bisect ! ,a ,b at m1 s t ,a m is equal to ,b m1 & let x be requir$ to asc]ta9 ! col\r :i* h>monizes ) ! col\r 9 ! ,indigo space at ! po9t p4 ,take ,a m1 & set x f p to o1 & ! col\r opposite o1 or an orange-yell[1 w be t :i* h>monizes ) ! indigo at p4 ,if p is betwe5 m & ,a1 !n ! di/ance ,a m mu/ be set (f f m t[>ds n4 ,illu/ration3 ,,fig4 #bc ,9 ord] to %[ ! me?od ( con/ruct+ object-boxes on ! prec$+ pr9ciples1 we %all suppose t ! h>monic col\rs ( orange-yell[ & indigo are to be employ$4 ,f\r or five regul> figures1 su* z ^? already describ$1 mu/ be made out ( indigo-col\r$ glass1 "s ( !m be+ pla91 & o!rs twi/$4 ,! same numb] ( figures mu/ also be made out ( an orange-yell[ glass2 & "s ( ^! may be drawn ( less diamet] ?an o!rs1 9 ord] t t9ts ( v>i\s int5sities1 b ( ! same col\r1 may be obta9$4 ,"s ( ^! pieces ( spun glass1 ( an indigo col\r1 may be int]twi/$ ) fibres ( ! orange-yell[ glass4 ,a few pieces ( :ite fl9t-glass1 or cry/al spun 9 a simil> mann]1 & int]twi/$1 "s ) fibres ( orange-yell[1 & o!rs ) fibres ( indigo glass1 %\ld be add$2 & :5 all ^! are jo9$ to "s flat fragm5ts ( orange-yell[ glass1 & indigo-col\r$ glass1 & plac$ 9 ! object-plate1 !y w exhibit1 :5 appli$ to ! ,kaleidoscope1 ! mo/ *a/e comb9ations ( =ms & col\rs1 :i* w n only delight ! eye by ! beauty ( _! outl9e1 b also by ! p]fect h>mony ( _! t9ts4 ,by us+ ! ?9 & highly-col\r$ films or flakes ( decompos$ glass1 v brilliant & beautiful patt]ns are produc$4 ,^! films may be plac$ ei!r ^u a mirror plate or ^u black wax1 & !y may be plac$ among o!r objects1 or fix$ 9 movable cells4 ,by apply+ ! ,kaleidoscope to cry/als 9 ! act ( =mation1 %oot+ out 9 diff]5t directions1 symmetrical patt]ns are in/antane\sly creat$4 ,! effect produc$ by objects ( only "o col\r is p]haps ev5 sup]ior to ! comb9ation ( two h>monic col\rs4 ,9 con/ruct+ object-plates ( ?is k9d1 v>i\s %ades ( ! same col\r may be adopt$2 & :5 su* objects are mix$ ) pieces ( col\rless glass1 twi/$ & spun1 ! mo/ *a/e & delicate patt]ns are produc$2 & ^? eyes :i* suff] pa9 f ! contemplation ( v>i\s col\rs1 are able to look )\t uneas9ess ^u a patt]n 9 :i* !re is only "o4 ,9 ord] to %[ ! p[] ( ! in/rum5t1 & ! ext5t to :i* ^! comb9ations may be c>ri$1 ,i h sometimes con/ruct$ a long object-plate1 l ! slid] ( ! magic lant]n1 9 :i* comb9ations ( all ! pr9cipal h>monic col\rs foll[$ "o ano!r 9 succession1 & pres5t$ to ! eye a s]ies ( brilliant visions no less gratify+ to "s p]sons1 & to "s o!rs ev5 m gratify+1 ?an ^? successions ( musical s\nds f :i* ! e> d]ives su* int5se delight4 ,we _c conclude ?is *apt] )\t notic+ ! f9e effects :i* are produc$ by ! introduction ( c>v$ gems1 & figures ( all k9ds1 :e!r !y are drawn or engrav$ on opaque1 or transp>5t gr\nds4 ,! p>ticul> mode ( comb9+ ^! figures w be po9t$ out 9 a subsequ5t *apt]4 ,,*apt] ,,ix4 ,,on ,,! ,,illum9ation ,,( ,,transp>5t ,,objects ,,9 ,,! ,,kaleidoscope4 ,:5 ! ,kaleidoscope is direct$ to ! sky1 or to a lum9\s object1 su* z a gas flame1 or ! flame ( a c&le1 a uni=m t9t is se5 ?r\gh ! pieces ( glass1 or o!r transp>5t fragm5ts t h flat surfaces1 & !re is a c]ta9 degree ( h>dness 9 _! outl9es4 ,:5 ! in/rum5t is n opposite ! flame1 b direct$ to "o side ( x1 ! light ent]s ! transp>5t fragm5ts obliquely1 & a mu* f9] effect is produc$4 ,! patt]n1 inde$1 *anges v consid]ably by mak+ ! ,kaleidoscope move r\nd ! flame4 ,an excell5t effect is obta9$1 z we h already /at$1 by direct+ ! tube betwe5 two bright lights2 & ! ri*ness ( ! symmetrical patt]n increases ) ! numb] ( lights :i* illum9ate ! objects4 ,z x w\ld be inconv5i5t to adopt su* a mode ( illum9ation1 x becomes ( importance to h "s contrivance atta*$ to ! in/rum5t1 by :i* we c illum9ate ! objects by light fall+ ^u !m 9 diff]5t directions4 ,illu/ration3 ,,fig4 #bd4 ,! simple/ me?od ( ?us illum9at+ ! objects1 is to fix on ! end ( ! ,kaleidoscope ! portion ( a metallic or silv]$-glass cone4 ,! light ( a bright flame1 plac$ 9 front ( ! cone1 w be reflect$ f its int]ior surface1 & fall obliquely on ! fragm5ts ( col\r$ glass4 ,9 _m cases ! effect w be increas$ by plac+ 9 ! base or m\? ( ! cone a circul> /op1 or opaque disk1 9 ord] to prev5t any light f fall+ directly ^u ! objects1 _! oblique illum9ation be+ produc$ solely by ! rays reflect$ f ! int]ior surface ( ! cone4 ,?is w be und]/ood f ! annex$ figure1 :]e ,m ,a ,n ,c is a portion ( ! cone1 fix$ to ! end ,e ,f ( ! ,kaleidoscope1 & m n o p ! object-box4 ,if ! angle =m$ by ! sides ( ! cone is su* t a ray ( ! sun's light fall+ ^u ,m1 ! upp] m>g9 ( ! reflect+ surface ( ! cone1 is reflect$ to o1 ! l[] side ( ! object-box1 !n all ! rays ( a beam ( ! sun's light incid5t ^u ! upp] half ( ! conical surface1 w be reflect$ ^u ! object-box2 &1 = ! same reason1 if a ray fall+ on ,n is reflect$ to m1 all ! o!r rays fall+ on ! l[] half ( ! conical surface w be reflect$ ^u ! object-box1 & illum9ate obliquely ! objects :i* x conta9s4 ,9 ! ,kaleidoscopes ( m rec5t con/ruction1 ! object-box is made transp>5t ?r\gh\t1--! plates ( glass m n1 o p be+ fix$ 9 a cyl9drical case ( glass m n o p1 s t rays ,r ,r1 ei!r p>allel or div]g+1 may be reflect$ f ! cone ,a ,b ,c ,d1 & aft] pass+ ?r\gh ! transp>5t cyl9drical rim m n o p1 illum9ate ! objects4 ,ano!r cone ,a ,m ,n ,c1 ) its angle less ?an a "r angle1 may be jo9$ to ,a ,b ,d ,c1 s z to ?r[ ! rays obliquely1 into m n & o p1 & also1 if desir$1 ^u ! front glass m o ( ! object-box1 ! direct rays be+ exclud$ by an opaque disk ,s ,s4 ,9 ?is con/ruction1 ! out] face ( ! glass m o %\ld n be gr\nd1 z x w\ld prev5t ! admission ( ! light to ! objects1 ! exclusion ( ext]nal objects1 ! purpose = :i* ! grey glass is requir$1 be+ effect$ by ! /op ,s ,s4 ,! illum9at+ cone may be ( t91 or1 :at is mu* bett]1 ( plat$ copp]1 :i* reflects m light ?an any o!r metal1 & x mu/ be s atta*$ to ! tube conta9+ ! reflectors1 z to h a rotatory motion4 ,! same k9d ( lat]al illum9ation may be obta9$ f polyh$ral cones or hemisph]es ( solid glass4 ,if ,a ,b ,c ,d1 ,fig4 #be1 is ! section ( a polyh$ral cone ( fl9t or plate glass1 a portion m n o p is cut out ( its base ,a ,b1 to =m an object-box = ! reception ( ! pieces ( col\r$ glass1 or o!r objects4 ,! sides m n1 m o1 o p1 be+ highly poli%$1 rays ( light1 ei!r p>allel1 z emanat+ f ! sun1 or div]g+ f artificial s\rces ( light1 w be refract$ & fall obliquely ^u ! faces ( ! object-box1 & illum9ate its cont5ts ) ! irregul> prismatic spectra :i* are =m$ by refraction4 ,! apex ,d ,c ,e may1 9 "s cases1 be cut (f1 & ! polygonal section ,d ,e black5$ 9 ord] to prev5t ! introduction ( direct light1 & act z ! /op ,s ,s 9 ! prec$+ figure4 ,illu/ration3 ,,fig4 #be4 ,a simil> effect w be obta9$ f a polyh$ral solid1 ( a hemisph]ical =m1 z %[n 9 ,fig4 #bf1 :]e ,a ,c1 ,c ,d1 ,d ,e1 ,b ,f1 ,f ,g1 ,g ,e1 are poli%$ facets1 by :i* p>allel or div]g+ rays imm$iately be=e x1 or incid5t 9 any lat]al direction1 may be refract$ s z to illum9ate by ! prismatic rays ! objects 9 ! box m n o p4 ,! front ,d ,e ,c may h an apex1 z 9 ,fig4 #be1 or may be made sph]ical to act z a cond5s+ l5s1 ! surface ( :i* may be black5$ :5 necess>y1 = ! purpose ( exclud+ ! direct light4 ,^! illum9ators may be atta*$ 9 v>i\s ways to ! tube conta9+ ! reflectors1 s to h a rotatory motion 9 front ( !m4 ,illu/ration3 ,,fig4 #bf4 ,:5 ! light is /rong1 a circul> disk ( f9e gra9$ :ite pap] may be advantage\sly plac$ ^u ! out] face m o ( ! object-box4 ,,*apt] ,x4 ,,on ,,! ,,con/ruction ,,& ,,use ,,( ,,! ,,telescopic ,,kaleidoscope1 ,,= ,,view+ ,,objects ,,at ,a ,,di/ance4 ,we h already se51 9 expla9+ ! pr9ciples ( ! ,kaleidoscope1 t a symmetrical picture _c be =m$ f objects plac$ at any di/ance f ! in/rum5t4 ,if we take ! simple ,kaleidoscope1 & hold+ an object-box 9 contact ) ! reflectors1 gradually )draw x to a di/ance1 ! picture1 :i* is at fir/ p]fect 9 e "p1 w1 at ! di/ance ( "o-t5? ( an in*1 beg9 to be di/ort$ at ! c5tre1 f ! disunion ( ! reflect$ images2 ! di/ortion w gradually ext5d itself to ! circumf]5ce1 & at ! di/ance ( eighte5 in*es1 or less1 f ! reflectors1 all ! symmetry & beauty ( ! patt]n w disappe>4 ,an inexp]i5c$ eye may /ill admire ! circul> arrangem5t ( ! imp]fect & dissimil> images2 b no p]son acqua9t$ ) ! in/rum5t c\ld endure ! defects ( ! picture1 ev5 :5 ! slighte/ di/ortion only is visible at ! c5tre4 ,z ! p[] ( ! ,kaleidoscope1 !re=e1 9 its simple =m1 is limit$ to transp>5t objects1 or to ! outl9e ( opaque objects held close to ! ap]ture ( ! reflectors1 x becomes a matt] ( consequ5ce to ext5d its p[] by enabl+ x to produce p]fectly symmetrical patt]ns f opaque objects1 f movable or immovable objects at a di/ance1 or f objects ( su* a magnitude t !y _c be introduc$ be=e ! op5+ ( ! reflectors4 ,)\t su* an ext5sion ( its p[]1 ! ,kaleidoscope might only be reg>d$ z an in/rum5t ( amusem5t2 b :5 x is made to embrace objects ( all magnitudes1 & at all di/ances1 x takes its place z a g5]al philosophical in/rum5t1 & becomes ( ! greate/ use 9 ! f9e1 z well z ! useful arts4 ,illu/ration3 ,,fig4 #bg4 ,9 consid]+ h[ ?is *ange might be effect$1 x occurr$ to me1 t if ,m ,n1 ,fig4 #bg1 7 a di/ant object1 ei!r opaque or transp>5t1 x might be introduc$ into ! picture by plac+ a l5s ,l ,l1 s+le or a*romatic1 at su* a di/ance be=e ! ap]ture ,a ,o ,b1 t ! image ( ! object may be di/9ctly =m$ 9 ! air1 or ^u a plate ( glass1 ! inn] side ( :i* 0 f9ely gr\nd1 & 9 contact ) ! ends ,a ,o1 ,b ,o ( ! reflectors1 ! plane pass+ ?r\gh ,a ,o ,b4 ,by submitt+ ?is idea to exp]im5t1 ,i f\nd x to answ] my mo/ sangu9e expectations4 ,! image =m$ by ! l5s at ,a ,o ,b became a new object1 z x 71 & 0 multipli$ & arrang$ by successive reflexions 9 ! v same mann] z if ! object ,m ,n _h be5 r$uc$ 9 ! ratio ( ,m ,l to ,l ,a1 & plac$ close to ! ap]ture4 ,illu/ration3 ,,fig4 #bh4 ,! ,comp\nd or ,telescopic ,kaleidoscope is !re=e fitt$ up z %[n 9 ,fig4 #bh1 ) two tubes1 ,a ,b1 ,c ,d4 ,! inn] tube1 ,a ,b1 conta9s ! reflectors z 9 ,fig4 #bg1 & at ! extremity ,c1 ( ! out] tube ,c ,d1 is plac$ a l5s :i*1 along ) ! tube1 may be tak5 (f or put on at pleasure4 ,! focal l5g? ( ?is l5s %\ld always be mu* less ?an ! l5g? ( ! out] tube ,c ,d1 & %\ld 9 g5]al be su* t x is capable ( =m+ an image at ! end ( ! reflectors1 :5 ,a ,b is pull$ out z mu* z possible1 & :5 ! object is )9 ?ree or f\r in*es ( ! l5s4 ,:5 x is requir$ to introduce into ! picture v l>ge objects plac$ ne> ! l5s1 ano!r l5s ( a less focal l5g? %\ld be us$2 & :5 ! objects are di/ant1 & n v l>ge1 a l5s1 ^: pr9cipal focal l5g? is ne>ly equal to ! greate/ di/ance ( ! l5s f ! reflectors1 %\ld be employ$4 ,:5 ?is comp\nd ,kaleidoscope is us$ z a simple in/rum5t = view+ objects held close to ! ap]ture1 ! tube ,a ,b is pu%$ 9 z f> z x w g1 ! cell ) ! object-plate is slipp$ ^u ! end ,c ( ! out] tube1 & ! in/rum5t is us$ 9 ! same way z ! simple ,kaleidoscope4 ,9 apply+ ! comp\nd ,kaleidoscope to di/ant objects1 ! cell is remov$ & ! l5s sub/itut$ 9 its place4 ,! in/rum5t is !n direct$ to ! objects1 & ! tube ,a ,b drawn out till ! inv]t$ images ( ! objects are se5 p]fectly di/9ct1 or 9 focus1 & ! patt]n consequ5tly p]fectly symmetrical4 ,:5 ?is is done1 ! patt]n is v>i$1 bo? by turn+ ! in/rum5t r\nd its axis1 & by mov+ x 9 any direction ov] ! object to :i* x is po9t$4 ,:5 ! object is ab\t f\r in*es f ! l5s1 ! tube requires to be pull$ out z f> z possible1 & = great] di/ances x mu/ be pu%$ 94 ,! po9ts suit$ to diff]5t di/ances c easily be det]m9$ by exp]im5t1 & m>k$ on ! inn] tube1 if x %\ld be f\nd conv5i5t4 ,9 mo/ ( ! in/rum5ts !re is1 ne> ! middle ( ! tube ,a ,b1 a m>k :i* is ne>ly suit$ to all di/ances beyond ?ree feet4 ,! object-plates held 9 ! h&1 or ! mirror-box plac$ ^u a table1 at a di/ance great] ?an five or six in*es1 may be also us$ :5 ! l5s ,l is 9 ! tube4 ,! furniture ( a room1 books & pap]s ly+ on a table1 pictures on ! wall1 a blaz+ fire1 ! mov+ bran*es & foliage ( trees & %rubs1 bun*es ( fl[]s1 horses & cattle 9 a p>k1 c>riages 9 motion1 ! curr5ts ( a riv]1 wat]falls1 mov+ insects1 ! sun %9+ ?r\gh cl\ds or trees1 &1 9 %ort1 e object 9 nature may be introduc$ by ! aid ( ! l5s into ! figures creat$ by ! in/rum5t4 ,! patt]ns :i* are ?us pres5t$ to ! eye are ess5tially diff]5t f ^? exhibit$ by ! simple ,kaleidoscope4 ,"h ! objects are indep5d5t ( ! obs]v]1 & all _! movem5ts are repres5t$ ) ! mo/ s+ul> effect 9 ! symmetrical picture1 :i* is z mu* sup]ior to :at is giv5 by ! simple in/rum5t1 z ! sight ( liv+ or mov+ objects is sup]ior to an imp]fect portrait ( !m4 ,:5 ! flame ( a blaz+ fire is ! object1 ! ,kaleidoscope creates f x ! mo/ magical fireworks1 9 :i* ! curr5ts ( flame :i* compose ! picture c be turn$ into e possible direction4 ,9 ord] to m>k ) accuracy ! po9ts on ! tube ,a ,b1 suit$ to diff]5t di/ances1 ! in/rum5t %\ld be direct$ to a /raight l9e1 incl9$ l m n1 ,fig4 #c1 to ! l9e bisect+ ! angul> ap]ture ,a ,o ,b1 & br\ght ne>] to ! c5tre ,o ( ! field4 ,! p]fect junction ( ! reflect$ images ( ! l9e at ! po9ts m n1 c41 s z to =m a />1 or a polygon ) sali5t & re-ent]+ angles1 w indicate ) great nicety1 t ! tube has be5 pull$ out ! prop] l5g? = ! giv5 di/ance4 ,9 ?is way1 a scale = diff]5t di/ances1 & scales = diff]5t l5ses1 may be m>k$ on ! tube4 ,9 ! con/ruction ( ! ,tele-,kaleidoscope1 z x may be call$1 ! greate/ c>e mu/ be tak5 to h ! l5s ( suffici5t magnitude4 ,if x is too small1 ! field ( view w n co9cide ) ! circul> patt]n1 t is1 ! c5tre ( ! circul> patt]n w n co9cide ) ! c5tre ( ! field2 & ?is ecc5tricity w increase z ! di/ance ( ! l5s f ! reflectors is increas$1 or z ! object introduc$ into ! picture approa*es to ! in/rum5t4 ,! b\nd>y ( ! lum9\s field is also an irregul> outl9e1 consi/+ ( disunit$ curves4 ,^! irregul>ities are easily expla9$4 ,:5 ! l5s is too small1 ! lum9\s field is b\nd$ by ! brass rim 9 :i* ! glass is fix$2 & z ?is brass rim is at a di/ance f ! reflectors1 ! portion ( x pres5t$ to ! angul> ap]ture _c be =m$ by successive reflexions into a cont9u\s curve2 & = ! same reason1 ! upp] sectors ( ! lum9\s field are l>g] ?an ! l[] ones1 & consequ5tly ! c5tre ( ! patt]n _c co9cide ) t ( ! field4 ,9 ord] to avoid ^! defects1 !re=e1 ! diamet] ( ! l5s %\ld be su*1 t :5 x is at its greate/ di/ance f ! reflectors1 ! field ( view may be b\nd$ by ! ar* ,a ,b1 ,fig4 #ac1 & n by ! brass rim :i* holds ! l5s4 ,?is may be readily kn[n by remov+ ! eye-glass1 & apply+ ! eye at ,e :5 ! l5s is at its greate/ di/ance4 ,if ! eye _c see ! brass rim1 !n ! l5s is suffici5tly l>ge2 b if ! brass rim is visible1 ! l5s is too small1 & mu/ be enl>g$ till x ceases to become visible4 ,sometimes ! l5s has be5 made s small t ! brass rim is se5 n only at ,a ,b1 b appe>s also above ! angul> po9t ,o1 & produces a d>k spot 9 ! c5tre ( ! picture4 ,in/ead ( us+ two tubes1 a l5s is sometimes fitt$ into a tube ab\t an in* long] ?an ! focal l5g? ( ! glass1 & ?is tube is slipp$ ^u ! object end ,a ,b ,o1 ,fig4 #ba4 ,?is mode ( apply+ ! l5s is1 h[ev]1 inf]ior to ! fir/ me?od1 z !re is little room = adju/+ x to diff]5t di/ances2 :]eas ) ! long tube all objects at a great] di/ance ?an f\r in*es f ! l5s may be introduc$ into ! picture--a prop]ty :i* possesses v peculi> advantages4 ,! ext5sion ( ! in/rum5t to di/ant objects is n ! only advantage :i* is d]iv$ f ! use ( ! l5s4 ,z ! position = giv+ p]fect symmetry is r )9 ! extremities ( ! reflectors ?an )\t !m2 & z x is impossible to place movable objects )9 ! reflectors1 we are compell$ to admit a small error1 aris+ pr9cipally f ! ?ickness ( ! objects1 & f ! ?ickness ( ! plate ( glass :i* is necess>ily int]pos$ betwe5 ! objects & ! reflectors4 ,! comp\nd ,kaleidoscope1 h[ev]1 is entirely free f ?is defect4 ,! image ( a di/ant1 or ev5 ( a ne> object1 c be =m$ )9 ! reflectors1 & 9 ! ma!matical position ( symmetry2 :ile1 at ! same "t1 ! sub/itution ( ! image = ! object itself1 enables u to produce all ! *anges 9 ! picture :i* ! motion ( ! object c\ld h effect$1 m]ely by turn+ ! in/rum5t r\nd its axis1 or by mov+ x horizontally1 or 9 any o!r direction across ! object4 ,?is in/rum5t may be advantage\sly plac$ ^u a /& l a telescope1 & may ei!r h a p>tial motion ( rotation by means ( a ball & socket1 z %[n 9 ! figure1 or :at is bett]1 a complete motion ( rotation r\nd ! axis ( ! tube ,c ,d1 )9 a brass r+1 occupy+ ! place ( ! ball & socket4#e #e ,an in/rum5t call$ ,! ,improv$ ,kaleidoscope has be5 rec5tly br\ght out 9 ,p>is4 ,x is m]ely ! ,telescopic ,kaleidoscope det]iorat$4 ,x consi/s ( a l5s fix$ at ! di/ance ( ab\t two in*es 9 front ( ! reflectors1 & c !re=e give symmetrical pictures ( objects only at "o di/ance1 :ile x _c be us$ z an ord9>y ,kaleidoscope4 ,! in/rum5t describ$ 9 ! prec$+ page1 ) a l5s t c be slipp$ (f1 is a mu* bett] ,kaleidoscope4 ,,*apt] ,,xi4 ,,on ,,! ,,con/ruction ,,& ,,use ,,( ,,polyangul> ,,kaleidoscopes1 ,,9 ,,:i* ,,! ,,reflectors ,,c ,,be ,,fix$ ,,at ,,any ,,angle4 ,9 all ! prec$+ in/rum5ts1 ! reflect+ planes are fix$ at an inv>iable angle1 :i* is "s ev5 aliquot "p ( #cfj2 & !re=e1 ?\gh ! =ms or patt]ns :i* !y create are lit]ally inf9ite 9 numb]1 yet !y h all ! same "*1 9 s f> z !y are compos$ ( z _m pairs ( direct & inv]t$ images z half ! numb] ( times t ! incl9ation ( ! reflectors is conta9$ 9 #cfj4 ,x is !re=e ( ! greate/ importance1 9 ! application ( ! ,kaleidoscope to ! arts1 to h x con/ruct$ 9 su* a mann]1 t patt]ns compos$ ( any numb] ( pairs ( direct & inv]t$ images may be creat$ & drawn4 ,) ?is view1 ! in/rum5t may be fitt$ up 9 v>i\s ways1 ) pap]1 clo?1 & metallic jo9ts1 by means ( :i* ! angle c be v>i$ at pleasure2 b ! mo/ conv5i5t me?ods are %[n 9 ! ,figures f ,fig4 #bi to #ce1 inclusive1 :i* repres5t two diff]5t k9ds ( ,polyangul> ,kaleidoscopes1 z made by ! late ,mr4 ,r4 ,b4 ,bate1 ,optician1 ,london1 :o _h devot$ mu* "t & att5tion to ! p]fection ( ?is species ( ,kaleidoscope4 ,bate's ,polyangul> ,kaleidoscope ) ,metallic ,reflectors4 ,illu/ration3 ,,fig4 #bi4 ,illu/ration3 ,,fig4 #cj4 ,! ?ree ,figures1 viz41 #bi1 #cj1 & #ca1 repres5t ! ,polyangul> ,kaleidoscope ) metallic reflectors1 z made by ,mr4 ,bate4 ,fig4 #bi %[s ! complete in/rum5t1 :5 m\nt$ ^u a /&2 ,fig4 #cj is a section ( x 9 ! direction ( its l5g?2 ,fig4 #ca is a transv]se section ( x ?r\gh ! l9e ,s ,t1 ,fig4 #cj1 & ,fig4 #cb %[s ! l5s ( ! eye-hole ,e4 ,! tube ( ?is in/rum5t is compos$ ( two cones1 ,m ,m1 ,n ,n1 ,fig4 #cj1 connect$ toge!r by a middle piece or r+1 ,r ,r1 into :i* !y are bo? screw$4 ,^! two cones enclose two highly poli%$ metallic reflectors1 ,a ,o1 ,b ,o1 ,fig4 #ca1 only "o ( !m1 viz41 ,b ,o ,e1 be+ se5 9 ,fig4 #cj4 ,"o ( ^! reflectors1 ,b ,o ,e1 is fix$ to ! r+ ,r ,r1 by ! int]m$iate piece ,k ,g ,l4 ,! reflector is screw$ to ?is piece by ! adju/able screws ,k1 ,l2 & ! piece ,k ,g ,l is aga9 fix$ to ! r+ ,r ,r1 by two screws se5 above & bel[ ,g1 9 ,fig4 #ca4 ,h5ce ! tube1 consi/+ ( ! cones ,m ,m1 ,n ,n1 & ! r+ ,r ,r1 are immovably connect$ ) ! mirror ,b ,o ,e4 ,! surface ( ! reflector ,b ,o ,e is adju/$ by ! screws at ,k & ,l1 till x passes accurately ?r\gh ! axis ( ! cones & r+ z se5 9 ,fig4 #ca4 ,! o!r reflector ,a ,o1 is fix$ to an out] r+ r r1 by means ( an int]m$iate piece1 simil> to ,k ,g ,l1 ! arm ,f ( :i*1 correspond+ to ,g1 passes ?r\gh an annul> space or op5 ar*1 ( m ?an #ij1 cut out ( ! circumf]5ce ( ! inn] r+ ,r ,r4 ,! arm ,f is fix$ to ! out] r+ r r by two screws1 se5 above & bel[ ,f2 & ! reflector ,a ,o is fix$ to ! b> correspond+ to ,k ,l1 ,fig4 #cj1 by simil> screws1 = ! purpose ( adju/+ x4 ,illu/ration3 ,,fig4 #ca4 ,illu/ration3 ,,fig4 #cb4 ,! l[] edge ,o ,e ( ! reflector ,b ,o ,e ext5ds ab\t ! #ae? ( an in* bel[ ! axis ( ! cones1 z repres5t$ by ! dott$ l9e 9 ,fig4 #cj2 b ! l[] edge ,o ,e ( ! o!r reflector ,a ,o ,e1 :i* is f9ely gr\nd to an acute angle1 =m+ a p]fectly /raight & smoo? l9e1 is plac$ exactly 9 ! axis ( ! cones1 s z j to t\* a l9e 9 ! reflector ,a ,o ,e1 :i* co9cides ) ! axis ( ! cone1 & to =m a junction ) t l9e 9 e "p ( ! two meet+ planes4 ,! v nice adju/m5ts :i* are necess>y to produce s exact a motion are effect$ by ! screws correspond+ to ,k & ,l4 ,if we n[ fix ! out] r+ r r into ! r+ ( a /& ,s ,t1 s z to be held fa/1 & turn ! cones ) ! h&1 we %all give motion to ! reflector ,b ,o1 s z to place x at any angle we please1 f #j to #ij2 & dur+ its motion ?r\gh ?is ar*1 ! junction ( ! two reflectors mu/ rema9 p]fect1 if ! t\*+ l9es are adju/$1 z we h describ$ !m1 to ! axis ( motion1 :i* mu/ also be ! axis ( ! cones & r+s4 ,if1 on ! contr>y1 we take away ! /&1 &1 hold+ ! in/rum5t 9 ! h& by ei!r ( ! cones ,m1 ,n1 turn ! r+ ,r ,r ) ! o!r1 we %all give motion to its reflector ,a ,o1 & produce a v>iation 9 ! angle 9 ! same mann] z be=e4 ,! same effect may be produc$ by an endless screw work+ 9 tee?1 cut ^u ! circumf]5ce ( ! out] r+ r r4 ,9 ord] to enable ! obs]v] to set ! reflectors at once to any ev5 aliquot "p ( a circle1 or s z to give any numb] ( pairs ( direct & inv]t$ images1 ! mo/ conv5i5t ( ! ev5 aliquot p>ts ( ! circle are engrav5 ^u ! r+ r r2 s t we h only to set ! index to any ( ^! p>ts1 to ! numb] #ab1 = example1 & ! reflectors w !n be plac$ at an angle ( #cj 7#ab #cj #cfj71 & w =m a circul> field ) twelve lum9\s sectors1 or a /> ) six po9ts1 & consequ5tly a patt]n compos$ ( six pairs ( direct & inv]t$ images4 ,z ! l5g? ( ! plates is only ab\t five in*es1 x is necess>y1 except+ = p]sons v %ort-sight$1 to h a convex l5s plac$ 9 front ( ! eye-hole ,e1 z %[n 9 ,figs4 #cj & #cb4 ,a brass r+ conta9+ a plane glass screws into ! out] r+ ,c ,d1 :5 ! in/rum5t is n 9 use2 & !re is an object-box conta9+ fragm5ts ( diff]5tly col\r$ glass4 ,?is object-box consi/s ( two plates ( glass1 "o gr\nd & ! o!r transp>5t1 set 9 brass rims4 ,! transp>5t "o goes ne>e/ ! reflector1 & ! brass rim :i* conta9s x screws into ! o!r1 s z to enclose betwe5 !m ! col\r$ fragm5ts1 & regul> figures ( col\r$ & twi/$ glass4 ,a loose r+ surr\nds ?is object-box2 & :5 ?is r+ is screw$ into ! circul> rim ,c ,d1 ! object-box c be turn$ r\nd s z to produce a v>iety ( patt]ns1 )\t any risk ( its be+ deta*$ f ! out] cone4 ,9 apply+ ?is in/rum5t to opaque objects1 su* z engrav+s1 co9s1 gems1 or fragm5ts ( col\r$ glass laid ^u a mirror1 ! ap]ture ( ! mirrors is laid directly ov] !m1 ! l>ge cone ,m ,m hav+ be5 previ\sly unscrew$1 = ! purpose ( all[+ ! light to fall freely ^u ! objects4 ,?is prop]ty ( ! ,kaleidoscope is ( great importance1 z 9 e o!r =m ( ! in/rum5t opaque objects mu/ be held obliquely1 & !re=e at su* a di/ance f ! reflectors z mu/ affect ! symmetry ( ! patt]n4 ,z ! p]fection ( ! figures dep5ds on ! reflectors be+ kept completely free ( du/1 p>ticul>ly at _! junction1 :]e x naturally accumulates1 ! greate/ facility is giv5 by ! prec$+ con/ruction 9 keep+ !m clean4 ,= ?is purpose1 ! l>ge cone mu/ be unscrew$2 ! reflectors hav+ be5 previ\sly clos$1 by turn+ ! index to #fj on ! r+4 ,!y are next to be op5$ to ! utmo/1 & ! du/ may 9 g5]al be remov$ by means ( a f9e po9t wrapp$ 9 clean & dry wa%-lea!r4 ,if any du/1 h[ev]1 /ill adh]es1 ! small screw 9 ! side ( ! r+ opposite to ! index %\ld be remov$1 & ! small] cone1 ,n ,n1 also unscrew$4 ,by eas+ ! support+ screws ( ei!r ( ! reflectors1 _! t\*+ sides w sep>ate1 s z to all[ a piece ( dry wa%-lea!r to be drawn betwe5 !m4 ,:5 e p>ticle ( du/ has be5 ?us remov$1 ! metals %\ld be re-adju/$ & clos$ be=e ! cones are replac$2 bo? ( :i* %\ld be screw$ firmly into ! r+ ,r ,r4 ,z ! axis ( motion 9 ! prec$+ con/ruction is necess>ily ! axis ( ! cones & r+s1 ! diamet] ( ^! cones & r+s mu/ ev]y:]e be d\ble ! bread? ( ! reflectors4 ,f ?is cause1 ! tube1 & consequ5tly ! object-box1 are wide1 & ! in/rum5t is1 to a c]ta9 degree1 n v portable4 ,?is defect is completely avoid$ 9 ano!r ,polyangul> ,kaleidoscope con/ruct$ by ,mr4 ,bate1 ^u entirely diff]5t pr9ciples1 :i* we %all n[ proce$ to describe4 ,bate's ,polyangul> ,kaleidoscope ) ,glass ,reflectors4 ,illu/ration3 ,,fig4 #cc4 ,illu/ration3 ,,fig4 #cd4 ,illu/ration3 ,,fig4 #ce4 ,illu/ration3 ,,fig4 #cf4 ,a section ( ! :ole ( ?is in/rum5t1 9 ! direction ( its l5g?1 is %[n 9 ,fig4 #cc4 ,a section ?r\gh ,m ,n or ,o ,p1 ne> ! eye-end1 is %[n 9 ,fig4 #ce1 ,fig4 #cd repres5t+ ! mode ( support+ ! fix$ reflector1 & ,fig4 #cf ! mode ( support+ ! movable reflector4 ,! tube ( ! ,kaleidoscope1 9 ,fig4 #cc1 is repres5t$ by b c d e f g h1 & consi/s ( two p>ts1 b c g h1 & c d e f g4 ,! fir/ ( ^! p>ts unscrews f ! second1 & ! second conta9s all ! app>atus = hold+ & mov+ ! reflectors4 ,at ! p>ts ,m ,n ,o ,p1 ( ! tube1 are ins]t$ a %ort tube1 a section ( :i* is %[n 9 ,fig4 #cd4 ,! object ( ^! tubes is to support ! fix$ mirror ,a ,o1 :i* re/s ) its l[] end ,o ^u ! piece ( brass t4 ,x is kept f fall+ =w>ds by ! tongue r1 connect$ ) ! upp] "p s s1 & f fall+ backw>d by ! piece ( cork ,q1 :i* may be remov$ at any "t1 = ! purpose ( tak+ out & clean+ ! reflectors4 ,?is little tube is fix$ to ! out] tube by ! screws s1 s4 ,! contrivance = support+ & mov+ ! second reflector ,b ,o1 is %[n 9 ,fig4 #cf1 9 section2 & a longitud9al view ( x is giv5 9 ,fig4 #cc4 ,! mirror ,b ,o lies 9 an op5+1 cut into two pieces ( brass1 v ,b p1 "o ( :i* is plac$ at ,m ,n1 & ! o!r at ,o ,p4 ,^! two pieces ( brass are connect$ by a rod m n1 ,fig4 #cc2 & 9 ! middle ( ?is rod !re is ins]t$ a screw k1 :i* passes ?r\gh ! ma9 tube c d e f g1 into a broad mill$ r+ w w1 :i* revolves ^u ! tube4 ,z ! screw k1 !re=e1 fa/5s ! r+ w w to ! rod m n1 ! reflector ,b ,o w be support$ 9 ! tube by ! r+ w w4 ,! l[] "p ( ! mirror ,b ,o1 or r ( ! brass piece v ,b p1 re/s at y1 ^u ! piece ( wat*-spr+ x y z1 fa/5$ to ! ma9 tube at z4 ,?is spr+ presses ! face ( ! reflector ,b ,o aga9/ ! gr\nd & /raight edge ( ! o!r reflector ,a ,o1 s z always to effect a p]fect junction 9 e "p ( _! l5g?3--,! app>atus = bo? reflectors is %[n 9 ,fig4 #ce4 ,an ar* ( ab\t #de is cut out ( ! ma9 tube1 s z to p]mit ! screw k to move along x2 & h5ce1 by turn+ ! broad r+ w w1 ! reflector ,b ,o may be br\ght ne>ly to t\* ! reflector ,a ,o1 & to be sep>at$ f x by an ar* ( #de1 s z to =m e possible angle f ne>ly #j to #de1 :i* is a suffici5t range = ! ,kaleidoscope4 ,! ma9 tube t]m9ates 9 a small tube at ,e1 ^u :i* may be screw$1 :5 x is requir$1 a brass cap e f1 conta9+ a convex l5s4 ,a %ort tube1 or cell1 a a a a1 = conta9+ ! object-boxes1 slips ^u ! end ( ! tube1 & %\ld always be mov$ r\nd f "r to left1 9 ord] t ! motion may n unscrew ! portion ( ! tube b c g h1 ^u :i* x moves4 ,:5 ! in/rum5t is us$ = opaque objects1 ! end piece1 b c g h ( ! tube1 screws (f1 s z to admit ! light freely ^u ! objects4 ,! advantages :i* ! ,polyangul> ,kaleidoscopes possess ov] all o!rs are-- #a/1 ,t patt]ns ( any numb] ( sectors1 f ! simple/ to ! mo/ complicat$1 c be easily obta9$4 #b;d1 ,t ! reflectors c be set1 ) ! mo/ p]fect accuracy1 to an ev5 aliquot "p ( a circle4 #c;d1 ,t ! reflectors c be at any "t completely clean$ & fre$ f all ! du/ t accumulates betwe5 !m1 & ! in/rum5t r5d]$ z p]fect z :5 x came f ! h&s ( ! mak]4 ,9 ord] to apply ?is ,kaleidoscope to di/ant objects1 or make x telescopic1#f a piece ( tube ) a l5s at ! end ( x is put ^u ! end piece1 b c g h1 & may be suit$ to diff]5t di/ances )9 a c]ta9 range4 #f ,see ,*apt] ,x4 ,,*apt] ,,xii4 ,,on ,,! ,,con/ruction ,,& ,,use ,,( ,,annul> ,,& ,,p>allel ,,kaleidoscopes4 ,9 ! in/rum5ts already describ$1 ! pictures :i* !y create1 ?\gh !y may be made ( v>i\s outl9es1 h all a c5tre to :i* ! reflect$ images are symmetrically relat$4 ,! same in/rum5ts give an annul> patt]n1 or a patt]n return+ into itself1 & includ$ betwe5 two conc5tric circles1 by keep+ ! objects f ! c5tral "p ( ! ap]ture2 b z su* a patt]n c nev] h its greate/ radius m ?an ! bread? ( ! mirror1 & z annul> patt]ns ( a v great radius1 :]e ! eye c see only a portion ( !m at a "t1 are (t5 requir$1 x becomes ( importance to adapt ! ,kaleidoscope = ?is species ( ornam5t4 ,illu/ration3 ,,fig4 #cg4 ,let ,a ,c ,b ,d1 ,fig4 #cg1 be two plane mirrors1 & let _! incl9ation be measur$ by ! angle ,a ,o ,b2 !n1 if ! eye is plac$ betwe5 ,c & ,d1 x w obs]ve ! reflect$ images ( ! objects :i* are plac$ be=e ! ap]ture ,a ,c ,b ,d1 arrang$1 9 ! annul> segm5t ,m ,a ,b ,n1 r\nd ,o1 z a c5tre4 ,! effect is exactly ! same z if ! reflectors _h be5 cont9u$ to ,o1 ) ?is diff]5ce only1 t ! annul> segm5t c nev] be complete4 ,?is defect 9 ! segm5t arises f two causes3 ,:5 ! c5tre ,o is ne> ,c ,d1 ! defect is occasion$ by ! want ( a reflect+ surface to complete ! r+1 & n f any want ( light 9 ! reflect$ images2 b :5 ! c5tre ,o is remote f ,c ,d1 ! defect arises f ! want ( light 9 ! la/ reflexions1 z well z f ! want ( a reflect+ surface4 ,! !ory ( ! ,annul> ,kaleidoscope is exactly ! same z t ( ! common in/rum5t2 & !re=e all ! contrivances = produc+ symmetrical pictures1 f ne> & di/ant objects1 are applicable to ?is in/rum5t4 ,z ! picture1 h[ev]1 nev] c return into itself1 x is ( no importance t ! angle ,a ,o ,b be ! aliquot "p ( a circle1 ! picture be+ equally complete at all angles4 ,9 ord] to h ! mo/ p]fect symmetry ) ?is ,kaleidoscope1 ! eye %\ld be plac$ at ,e1 betwe5 ! ne>e/ ends ( ! reflectors1 z x w !re be ne>] ! plane ( bo? reflectors ?an 9 any o!r position4 ,if ! two mirrors are br\ght ne>] ea* o!r1 s t _! surfaces always pass ?r\gh ! po9t ,o1 ! deviation f p]fect symmetry w dim9i% z ! eye becomes m & m 9 ! plane ( bo?2 & = ! same reason ! light ( ! field w be m brilliant4 ,:5 ! po9t ,o is inf9itely di/ant1 ! two reflectors become p>allel to ea* o!r1 z 9 ,fig4 #ch1 & ! s]ies ( reflect$ images ext5ds 9 a /raight l9e1 =m+ beautiful rectil9eal patt]ns = bord]s1 c4 ,9 ?is position ( ! reflectors ! eye %\ld be plac$ 9 ! c5tre at ,e1 & ! symmetry ( ! picture & ! light ( ! field w increase z ! di/ance ( ! reflectors dim9i%es1 or z _! l5g? is increas$4 ,illu/ration3 ,,fig4 #ch4 ,two diff]5t k9ds ( in/rum5ts h be5 con/ruct$ on ! prec$+ pr9ciples1 ! "o by ,mr4 ,dollond1 & ! o!r by ,mr4 ,john ,ru?v51 bo? ( :i* possess v valuable prop]ties4 ,mr4 ,dollond's ,univ]sal ,kaleidoscope4 ,illu/ration3 ,,fig4 #ci4 ,illu/ration3 ,,fig4 #dj4 ,! in/rum5t con/ruct$ by ,mr4 ,dollond is repres5t$ 9 ,figs4 #ci1 #dj1 & #da1 9 section1 & is int5d$ to unite ! prop]ties ( a common ,kaleidoscope1 9 :i* ! reflectors are incl9$ at an angle ( #cj1 & also ^? ( an ,annul> & a ,p>allel ,kaleidoscope4 ,fig4 #ci repres5ts ! reflectors1 etc41 :5 !y act z a common ,kaleidoscope2 & ,fig4 #dj %[s !m :5 !y =m a p>allel ,kaleidoscope1 an annul> ,kaleidoscope be+ =m$ :5 !y h an int]m$iate position4 ,! tube ( ! in/rum5t is %[n1 9 section1 by ,t ,t2 & to ?is tube is fix$1 by ! screws s s1 a frame ( metal1 a b1 to :i* ! reflectors are fa/5$4 ,! reflectors1 :i* are made ( ! f9e/ speculum metal1 are %[n at ,a ,o1 ,b ,o1 & are atta*$ to plates ( brass1 c d1 c d1 ^: bread? exce$s t ( ! reflectors s z to all[ _! extremities to desc5d bel[ ! po9t ,o1 ,fig4 #ci4 ,a d\ble spr+1 y x x y1 is plac$ 9 ! tube1 s z to press ^u ! back ( ! reflectors1 & keep !m 9 contact1 z %[n 9 ,fig4 #ci1 & is suffici5tly ela/ic z to all[ !m to op51 z 9 ,fig4 #dj4 ,! mill$ head ,m ,n1 :i* passes ?r\gh ! l[] "p ( ! tube1 c>ries1 at its l[] end1 a v ecc5tric button or :eel1 ! lea/ diamet] ( :i* is se5 at m1 ,fig4 #ci1 & ! greate/ at m1 ,fig4 #dj4 ,9 ! fir/ position x has all[$ ! reflectors to come into contact at ,o4 ,9 ! o!r position x has =c$ !m op5 into ! position ( p>allelism4 ,by turn+ ! mill$ head1 ! l[] ends 7,o ,o7 ( ! reflectors may be br\ght to any di/ance less ?an ,o ,o1 s z to =m an annul> ,kaleidoscope4 ,! eye-end ( ! in/rum5t is %[n 9 ,fig4 #da4 ,! l5s ,e is plac$ 9 a slid]1 ,c ,d1 :i* is to be mov$ accord+ to ! position ( ! reflectors1 be+ a little above ,o1 9 ,fig4 #ci1 opposite ! c5tre ( ! tube 9 ,fig4 #dj1 & at an int]m$iate position 9 ! int]m$iate position ( ! reflectors4 ,illu/ration3 ,,fig4 #da4 ,?is in/rum5t is atta*$ to a /& ) a draw-tube1 :i* screws into ! bottom ( a mahogany box4 ,! object-plates1 & ! l5s = introduc+ di/ant objects1 are plac$ at ! end ( ! in/rum5t1 9 ! same mann] z ^? ( ! usual con/ruction4 ,p>ticul> k9ds ( objects are select$ = giv+ rectil9eal bord]s4 ,ru?v5's ,univ]sal ,kaleidoscope4 ,illu/ration3 ,,fig4 #db4 ,illu/ration3 ,,fig4 #dc4 ,! in/rum5t con/ruct$ by ,mr4 ,ru?v5 is also a ,univ]sal ,kaleidoscope1 :i* unites ! prop]ties ( a ,polyangul> "o ) ^? ( ,annul> & ,p>allel ,kaleidoscopes4 ,its con/ruction w be und]/ood f ,figs4 #db1 #dc1 & #dd1 :]e ,a ,b ,e ,f ,g ,h repres5ts a frame ( iron or brass1 :i* slips into ! tube4 ,! two sides ,a ,b1 ,f ,h1 ( ?is frame1 are kept toge!r by f\r cross pieces1 a b1 c d1 etc41 ! o!r two correspond+ to ^! be+ invisible 9 ! figure4 ,! two reflectors1 ! ends ( :i* are se5 at ,a ,o1 ,b ,o1 are ea* fix$ to a plate ( metal p p1 a section ( :i* is se5 9 ,fig4 #dd4 ,ea* plate ( metal has f\r cyl9drical p9s1 p1 p1 etc41 bo? on its upp] & "u edge4 ,! two p9s ne>e/ ! ends ( ! reflectors pass ?r\gh op5+s 9 ! cross pieces a b1 c d4 ,on ! top ( ! frame is plac$ a plate ( brass ,m ,n ,q ,p1 9 :i* are cut grooves e f1 g h1 k l1 m n2 e f & k l1 & also g h & m n1 be+ p>allel to ea* o!r4 ,?is plate c be mov$ =w>ds & backw>ds betwe5 ! cross pieces a b1 c d1 by means ( a small screw ,s ,s1 work+ 9 a female screw fix$ ^u ! edge ,n ,o ( ! plate1 & z ! middle p9s p p1 atta*$ to ! plates :i* c>ry ! reflectors1 pass ?r\gh ! grooves1 any *ange 9 ! position ( ! plate ,m ,q1 produces a *ange 9 ! di/ance1 p p1 ( ! p9s1 & consequ5tly 9 ! di/ance ( ! upp] edges ( ! reflectors4 ,by turn+ ! screw ,s ,s1 !re=e1 ! upp] edges ( ! reflectors may be ei!r br\ght into contact1 or sep>at$ to a di/ance regulat$ by ! incl9ation ( ! grooves e f g h4 ,a simil> plate ) a simil> screw is plac$ ^u ! l[] edges ( ! reflectors1 s t we are furni%$ ) ! means ( giv+ ! plates any incl9ation to ea* o!r1 or plac+ !m at any di/ance )9 c]ta9 limits4 ,= example1 if ! l[] edges ( ! plates are 9 contact1 we c v>y ! angle ( _! incl9ation by sep>at+ or clos+ _! upp] edges by means ( ! upp] screw4 ,by sep>at+ ! l[] edges1 we give !m ! position = annul> patt]ns1 & by mak+ ! di/ance ( ! l[] & upp] edges ! same1 we obta9 f !m rectil9eal patt]ns2 & ! figures ( ^! annul> & rectil9eal patt]ns may be ei!r contract$ or exp&$1 by alt]+ ! di/ance ( ! plates :5 9 ?is p>allel position4 ,illu/ration3 ,,fig4 #dd4 ,,*apt] ,,xiii4 ,,on ,,! ,,con/ruction ,,& ,,use ,,( ,,polyc5tral ,,kaleidoscopes4 ,hi!rto we h consid]$ ! effects ( comb9+ two reflectors1 by means ( :i* ! reflect$ images are arrang$ ar\nd "o c5tre1 ei!r visible or invisible2 b x mu/ be obvi\s1 f ! pr9ciples already expla9$1 t v s+ul> effects w be obta9$ f ! comb9ation ( ?ree or m reflectors4 ,z 9 in/rum5ts ( ?is k9d ! reflect$ images are arrang$ r\nd sev]al c5tres1 we h di/+ui%$ !m by ! "n ( ,polyc5tral4 ,z #ij is ! greate/ angle :i* is an ev5 aliquot "p ( #cfj1 & z all regul> polygons1 ) a great] numb] ( sides ?an f\r1 mu/ h _! int]ior angles great] ?an #ij1 x foll[s1 t symmetrical pictures _c be creat$ by any numb] ( reflectors great] ?an f\r1 arrang$ l ! sides ( a regul> polygon4 ,if ! polygon is irregul>1 & consi/s ( f\r sides1 or m1 !n "o ( its angles mu/ exce$ #ij1 & consequ5tly x _c give symmetrical patt]ns4 ,9 con/ruct+ ,polyc5tral ,kaleidoscopes1 we are limit$ to comb9ations ( f\r or ?ree reflectors4 ,! only modes 9 :i* we c comb9e f\r reflectors1 are s z to =m a holl[ squ>e1 or a holl[ rectangle2 b ?\gh ^! comb9ations af=d regul> patt]ns1 f _! angles be+ ev5 aliquot p>ts ( #cfj1 yet ^! figures are compos$ m]ely ( a great numb] ( squ>es1 or rectangles1 ! po9t :]e e f\r squ>es or rectangles meet be+ ! c5tre ( a patt]n4 ,^?1 h[ev]1 :o may wi% to con/ruct su* in/rum5ts1 mu/ make ! plates z n>r[ z possible at ! eye-end1 s z to br+ ! eye1 z mu* z c be done1 into ! plane ( all ! f\r reflectors4 ,9 comb9+ ?ree reflectors1 ! limitation is ne>ly z great2 b ! effect ( ! comb9ation is highly pleas+4 ,s9ce ! angles at :i* ! reflectors mu/ be plac$ are ev5 aliquot p>ts ( #cfj1 su* z #ij1 #fj1 #de1 #cf1 #be-_/ #bb1 #bj1 #ah1 etc41 :i* are ! quoti5ts ( #cfj1 divid$ by ! ev5 numb]s1 #d1 #f1 #h1 #aj1 #ab1 #ad1 #af1 #ah1 #bj1 etc42 & s9ce ! reflectors are comb9$ 9 ! =m ( a prism1 ! section ( :i* is ev]y:]e a triangle1 ! sum ( ^: angles is #ahj1 we mu/ select any ?ree ( ! above ev5 aliquot p>ts :i* am\nt to #ahj2 & :5 ! reflectors are comb9$ at ^! angles1 !y w af=d =ms p]fectly symmetrical4 ,n[1 x is obvi\s1 t ^! conditions w be compli$ ) :5 ! angles are-- #ij #de #de #ahj #ij #fj #cj #ahj #fj #fj #fj #ahj ,! ,polyc5tral ,kaleidoscopes are !re=e limit$ to five diff]5t comb9ations1 namely1-- #a4 ,f\r reflectors ( equal bread?1 =m+ a squ>e4 #b4 ,f\r reflectors1 two ( :i* are broad] ?an ! o!r two1 & =m1 a rectangle4 #c4 ,?ree reflectors at angles ( #ij1 #de1 & #de4 #d4 ,?ree reflectors at angles ( #ij1 #fj1 & #cj4 #e4 ,?ree reflectors at angles ( #fj1 #fj1 & #fj4 #a4 ,on comb9ations ( f\r mirrors =m+ a squ>e4 ,illu/ration3 ,,fig4 #de4 ,! fir/ ( ^! ,kaleidoscopes is repres5t$ 9 ,fig4 #de1 :]e ,a ,b1 ,b ,c1 ,c ,d1 ,d ,a1 are ! f\r equal & simil> reflectors plac$ accurately at "r angles to ea* o!r4 ,if we consid] ! effect only ( ! two reflectors ,a ,b1 ,b ,c1 & reg>d ,a ,d1 ,d ,c z only ! limits ( ! ap]ture1 x is obvi\s1 f ! pr9ciples expla9$ 9 ,*ap4 ,,ii41 t we %all h a regul> figure ,d m k h ,d1 compos$ ( f\r squ>es1 "o ( :i* ,d ,b is se5 by direct vision2 o!r two ,a l1 ,c i =m$ by "o reflexion f ea* mirror2 & ! f\r? ,b k compos$ ( two half squ>es1 ea* half be+ =m$ by a second reflexion f ea* mirror4 ,9 l mann]1 if we suppose ,a ,d1 ,d ,c to act alone1 !y w =m a squ>e patt]n ,b b d f1 compos$ l ! la/2 & ! same result w be obta9$ by suppos+ ,b ,a1 ,a ,d1 & ,b ,c1 ,c ,d to act alone4 ,! comb9ation ( ^! effects w produce a squ>e a d g k1 compos$ ( n9e squ>es1 f\r ( :i*1 =m$ by second reflexions1 are plac$ at ! angles2 o!r f\r =m$ by fir/ reflexions 9 ! middle2 & "o1 se5 by direct vision1 9 ! c5tre4 ,h5ce1 x foll[s1 t ! light ( ! diff]5t squ>es is symmetrical z well z ! patt]ns1 a prop]ty :i* does n belong to all polyc5tral in/rum5ts4 ,! patt]n1 h[ev]1 does n t]m9ate ) ! squ>e a d g k1 b ext5ds indef9itely on all sides till ! squ>es become invisible1 f ! ext9ction ( ! light by repeat$ reflexions4 ,9 ord] to discov] ! law accord+ to :i* ! squ>es succe$ ea* o!r1 we %all exam9e 9 :at mann] a /ill l>g] squ>e ,e ,f ,g ,h is complet$ r\nd ! c5tral squ>e1 se5 by direct vision4 ,by consid]+ e squ>e 9 ! l>ge squ>e a d g k z an object plac$ be=e ! f\r reflectors1 & recollect+ t ! reflect$ images mu/ be simil>ly situat$ beh9d ! reflectors1 we %all f9d t ! l>g] squ>e ,e ,f ,g ,h is complet$ by images t h suff]$ two1 ?ree1 & f\r reflexions1 z m>k$ 9 ! figure1 & t all ^! are symmetrically arrang$ ) reg>d to ! c5tral squ>e4 ,! squ>es :i* are cross$ ) a dott$ diagonal l9e1 are ^? compos$ ( two halves1 ea* half be+ =m$ by a diff]5t reflector4 ,:5 a ,kaleidoscope is =m$ out ( ! prec$+ comb9ation1 ! ap]ture1 or ! bread? ( ! plates next ! eye1 %\ld n exce$ "o-six? ( an in*4 ,! effect is v pleas+ :5 ! reflectors are accurately jo9$ & nicely adju/$1 & :5 di/ant objects are introduc$ by means ( a l5s4 #b4 ,on comb9ations ( f\r mirrors =m+ a rectangle4 ,:5 ! reflectors are ( diff]5t bread?s1 s z to =m a rectangle1 ! v same effects are produc$ z 9 ! prec$+ comb9ation1 ) ?is diff]5ce only1 t ! images are all rectangul>1 9 place ( be+ squ>e4 #c4 ,on comb9ations ( ?ree reflectors at angles ( #fj4 ,illu/ration3 ,,fig4 #df4 ,:5 ?ree reflectors are comb9$ at angles ( #fj1 z %[n at ,a ,o ,b1 ,fig4 #df1 !y =m an equilat]al triangle1 & !re=e all ! images w also be equilat]al triangles4 ,! figure ,c ,d ,e ,f ,g ,h1 :i* is a truncat$ equilat]al triangle1 is obvi\sly compos$ ( ?ree hexagonal patt]ns1 ( :i* ! sectors1 or r triangles1 are arrang$ r\nd ! ?ree c5tres ,a1 ,o1 ,b2 ! triangle ,a ,o ,b be+ common to all ! ?ree4 ,! ?ree triangles1 adjac5t to ! sides ( ,a ,o ,b1 are =m$ by "o reflexion f ea* mirror4 ,! ?ree :i* spr+ f ! v]tices ,a1 ,o1 ,b1 ( ! triangle1 consi/ ( two halves1 ea* ( :i* is =m$ by ?ree reflexions1 ! la/ reflexion ( ! "o half be+ made f "o ( ! ne>e/ mirrors1 & t ( ! o!r half f ! o!r ne>e/ mirror4 ,if we consid] ! =mation ( a m ext5d$ figure1 ,i ,l ,m ,p ,n ,k1 :i* is also a truncat$ equilat]al triangle1 ) its truncations correspond+ to ! sides ( ! =m] figure1 we %all f9d t x has be5 complet$ by an addition1 to ea* side ( ! =m]1 ( ?ree equilat]al triangles1 two ( :i* are =m$ by ?ree reflexions1 & ! ?ird1 consi/+ ( two halves1 =m$ by f\r reflexions4 ,?is figure consi/s ( ?ree entirely sep>ate hexagons1 ,i ,c ,a ,o ,h ,k1 ,l ,d ,a ,b ,e ,m1 & ,b ,o ,g ,n ,p ,f1 all ( :i* are =m$ ( reflect$ images2--( "o triangle ,a ,o ,b se5 by direct vision1--& ( ?ree triangles ,a ,c ,d1 ,b ,e ,f1 ,o ,g ,h1 consi/+ ( half sectors4 ,9 con/ruct+ ?is ,kaleidoscope1 :i*1 l ! two =m]1 has ! equally lum9\s images symmetrically arrang$ r\nd ! ap]ture ,a ,o ,b1 x is unnecess>y to %ape all ! reflectors ) accuracy4 ,:5 two ( !m1 bo? ( :i* h a great] bread? ?an is want$1 are plac$ toge!r1 ) ! edge ( ! "o re/+ ^u ! face ( ! o!r1 ! ?ird reflector1 :i* mu/ be gr\nd ) great accuracy to ! desir$ %ape ( ! tap]+ equilat]al prism1 may !n be plac$ s t ea* ( its edges re/s ^u ! faces ( ! o!r two4 ,:5 ?is in/rum5t is nicely execut$ ) metallic plates1 & :5 all ! junctions are p]fect1 ! effects :i* x produces are uncommonly spl5did4 #d4 ,on comb9ations ( ?ree reflectors at angles ( #ij1 #de1 & #de4 ,illu/ration3 ,,fig4 #dg4 ,! effect produc$ by ! comb9ation ( ?ree reflectors at angles ( #ij1 #de1 & #de1 is %[n 9 ,fig4 #dg4 ,! two reflectors ,a ,o1 ,a ,b produce a patt]n ,c ,d ,b ,i1 compos$ ( eight triangles2 ! reflectors ,b ,o1 ,b ,a1 likewise give a patt]n ,a ,f ,g ,h1 compos$ ( eight triangles2 & ! reflectors ,a ,o1 ,o ,b1 give a patt]n ,a ,b ,h ,i1 compos$ ( f\r triangles4 ,! triangle ,i ,h ,k is an image =m$ by ?ree reflexions1 "o half ( x be+ a reflexion ( half ( ,a ,i a1 f ! mirror ,b ,o1 & ! o!r half a reflexion ( half ( ,b ,h b1 f ! mirror ,a ,o2 & ! triangle ,d ,e ,f consi/s ( two half images1 :i* are reflexions ( ! two half images 9 ,i ,o ,h4 ,! rema9+ triangle ,d ,l ,f is a reflexion ( ,i ,k ,h1 f ! mirror ,a ,b1 & is !re=e =m$ by f\r reflexions4 ,z ! ?ree mirrors are n symmetrically plac$1 ) reg>d to ea* o!r1 ! equally lum9\s images are n arrang$ symmetrically r\nd ! op5 triangle ,a ,o ,b1 z 9 ! prec$+ comb9ations4 ,! effect is1 h[ev]1 v pleas+1 & all ! reflect$ images includ$ 9 ! figure ,c ,l ,g ,k are suffici5tly bright4 #e4 ,on comb9ations ( ?ree reflectors at angles ( #ij1 #fj1 & #cj4 ,illu/ration3 ,,fig4 #dh4 ,! mo/ complicat$ comb9ations ( ?ree reflectors is repres5t$ 9 ,fig4 #dh4 ,9 ! fir/ comb9ation1 all ! angles 7 equal2 9 ! second1 two ( ! angles only 7 equal2 b 9 ! pres5t comb9ation1 none ( !m are equal4 ,! field ( view1 repres5t$ 9 ! figure by ,d ,e ,h ,l ,m ,p1 is a truncat$ rhomb1 consi/+ ( no few] ?an ?irty-"o images ( ! ap]ture ,a ,o ,b4 ,! figure is compos$ ( two hexagons ,d ,e ,f ,b ,r ,c1 ,r ,b ,k ,l ,m ,n1 e division ( ! hexagon consi/+ ( two reflect$ images1 & ( two rhombs ,c ,r ,n ,p1 ,f ,b ,k ,h1 ea* ( :i* is compos$ ( f\r reflect$ images4 ,9 ?is comb9ation1 z 9 ! la/1 ! equally lum9\s sectors are n symmetrically arrang$ r\nd ! c5tre ,o ( ! figure4 ,9 ! rhomb ,c ,r ,n ,p1 = example1 ! f\r images are =m$ by ?ree1 f\r1 & five reflexions2 :]eas 9 ! correspond+ rhomb ,f ,h ,k ,b1 !y are =m$ by two1 ?ree1 & f\r reflexions4 ,! effects produc$ by a ,kaleidoscope con/ruct$ 9 ?is mann] are v beautiful1 p>ticul>ly :5 ! reflectors are metallic4 ,9 ! f\r figures :i* repres5t ! diff]5t comb9ations ( ! reflectors1 ! small figures indicate ! numb] ( reflexions by :i* ea* image is produc$4 ,,*apt] ,,xiv4 ,,on ,,kaleidoscopes ,,9 ,,:i* ,,! ,,effect ,,is ,,produc$ ,,by ,,total ,,reflexion ,,f ,,! ,,int]ior ,,surfaces ,,( ,,transp>5t ,,solids4 ,:5 light is incid5t ^u ! mo/ p]fectly poli%$ metals1 a v consid]able quantity ( x is absorb$1 & ev5 :5 ! reflexion is made at ! greate/ obliquities1 !re is a v manife/ diff]5ce 9 ! int5sity ( ! direct & ! reflect$ p5cil4 ,9 ! total reflexion ( light f ! second surfaces ( transp>5t bodies1 ! loss ( light is v inconsid]able1 & ! reflexion is made ) a degree ( brilliancy f> surpass+ t ( ! mo/ respl5d5t metals4 ,illu/ration3 ,,fig4 #di4 ,9 con/ruct+ a ,kaleidoscope ^u ?is pr9ciple1 we mu/ procure a piece ( glass entirely free f ve9s1 & cut x into ! =m %[n 9 ,fig4 #di4g ,! two surfaces ,b ,o ,e1 ,a ,o ,e1 mu/ be incl9$ at an angle :i* is ! ev5 aliquot "p ( a circle4 ,!y mu/ be gr\nd p]fectly flat & highly poli%$1 & ! junction ,o ,e mu/ be made z f9e z possible4 ,! upp] surface ,a ,b ,e %\ld be r\gh-gr\nd1 & ! side ,a ,b ,o1 & ! side at ,e1 %\ld be p>allel & well poli%$4 ,if ! glass is col\rless & good1 ! eye1 :5 plac$ at ,e1 w see ! v same appe>ance z 9 ! simple ,kaleidoscope2 & objects plac$ at ,a ,b ,o w be arrang$ into ! same beautiful figures4 ,! only defects att5d+ ?is =m ( ! ,kaleidoscope1 are ! loss ( light occasion$ by its pass+ ?r\gh a mass ( solid glass1 n p]fectly transp>5t1 & ! difficulty ( obta9+ a p]fect junction ( ! two reflect+ planes4 ,! fir/ ( ^! evils is1 h[ev]1 c\nt]balanc$ by ! great int5sity ( ! light :i* suff]s total reflexion2 & ! second does n exi/ :5 ! ,kaleidoscope is int5d$ to give rectil9eal or annul> patt]ns4 #g ,:5 ?is *apt] 0 writt5 7#ahah71 x 0 v difficult to procure glass suffici5tly homog5e\s = ?is purpose3 b x c n[ be procur$ f ! ,glass ,works ( ,messrs4 ,*ance ,co41 at ,sme?wick1 ne> ,birm+ham4 ,9 ! con/ruction ( in/rum5ts ( ?is k9d1 x is necess>y to make ! prism ( glass long] ?an ! di/ance at :i* ! eye c see objects ) p]fect di/9ctness2 t is1 if ! eye is capable ( see+ objects di/9ctly at ! di/ance ( five in*es1 x w n p]ceive ! same objects di/9ctly :5 !y are plac$ at ! end ( a prism ( glass five in*es long4 ,?is s+ul> effect arises f a prop]ty ( pla9 l5ses or pieces ( pla9 glass1 9 consequ5ce ( :i*1 !y cause div]g5t rays to div]ge f a po9t ne>] ! l5s or plate1 ?an t f :i* !y radiat$4 ,x w !re=e be m conv5i5t1 = _m reasons1 to make ! glass prism only two or ?ree in*es long1 & obta9 di/9ct vision by means ( a l5s plac$ at ! eye-end ( x2 b1 = ! reason already m5tion$1 ! focal l5g? ( ! l5s mu/ be less ?an ! l5g? ( ! glass prism4 ,! l5s may ev5 be jo9$ to ! prism1 by gr9d+ ! eye-end into a sph]ical =m1 b ! degree ( convexity mu/ be calculat$ ^u ! pr9ciples already /at$4 ,! solid =m ( ! ,kaleidoscope is peculi>ly fitt$ = polyc5tral in/rum5ts1 z we h only to poli% ! side1 :i* w\ld o!rwise h be5 left r\gh1 ! prism be+ suppos$ to be cut to ! angles :i* are necess>y to give symmetrical =ms1 accord+ to ! pr9ciples /at$ 9 ,*apt] ,,xiii4 ,,*apt] ,,xv4 ,,on ,,! ,,application ,,( ,,! ,,kaleidoscope ,,to ,,! ,,magic ,,lant]n1 ,,sol> ,,microscope1 ,,& ,,cam]a ,,obscura4 ,illu/ration3 ,,fig4 #ej4 ,9 ! v>i\s =ms ( ! ,kaleidoscope :i* h be5 describ$ 9 ! prec$+ *apt]s1 ! pictures :i* x creates are visible only to "o p]son at a "t2 b x is by no means difficult to fit x up 9 su* a mann] z to exhibit !m ^u a wall to any numb] ( spectators4 ,! necess>y limitation ( ! ap]ture at ! eye-end ( ! in/rum5t1 h[ev]1 is ho/ile to ?is species ( exhibition1 z x requires a v int5se light = ! purpose ( illum9at+ ! objects4 ,! g5]al pr9ciple ( ! app>atus requisite = ?is purpose is %[n 9 ,fig4 #ej1 :]e ,c ,d ,g ,f is ! tube conta9+ ! reflectors ,a ,o ,e1 etc4 ,! objects f :i* ! pictures are to be creat$ are plac$ 9 ! cell ,c ,d1 :i* may be made ei!r to h a rotatory movem5t r\nd ! axis ( ! tube1 or to slide ?r\gh a groove1 l ! slid]s ( a magic lant]n4 ,^! objects are p[]fully illum9at$ by a l5s ,b1 :i* conc5trates ^u !m ! direct light ( ! lamp or c&le ,h1 & also ! "p ( ! light :i* is reflect$ f ! mirror ,m ,n4 ,at ! eye-end ,e ( ! ,kaleidoscope1 is plac$ a l5s ,l ,l1 close to ! end ( ! reflectors1 & hav+ its c5tre co9cid5t ) ! c5tre ( ! ap]ture at ,e4 ,9 ord] t ?is l5s may =m beh9d x an image ,p ,p ( ! objects plac$ 9 ! object-plate ,c ,d1 its focal l5g? mu/ be less ?an ! l5g? ,a ,e ( ! plates4 ,if ! focal l5g? ( ,l ,l is s small z "o-half ( ,a ,e1 !n x foll[s1 f ! pr9ciples ( optics1 t ! di/ance ,l ,p at :i* ! image is =m$ beh9d ! l5s1 w be precisely equal to ! di/ance ,a ,e ( ! object2 b ?is is obvi\sly too small a di/ance1 = ! diamet] ( ,p ,p w\ld be equal only to ! app>5t diamet] ( ! circul> ap]ture ( ! ,kaleidoscope1 or to twice ,a ,o4 ,h5ce x is necess>y1 t ! focal l5g? ( ! l5s ,l ,l be less ?an ,a ,e1 & great] ?an half ( ,a ,e4 ,two-?irds1 or ?ree-f\r?s ( ,a ,e w be f\nd to be a suitable focal l5g?2 = if x is l>g] ?an ?is1 ! image w be =m$ ^u ! wall or scre5 at too great a di/ance f ! in/rum5t4 ,:5 ! in/rum5t is ?us fitt$ up1 an enl>g$ image ( ! patt]n w be ?r[n ^u ! wall1 :i* mu/ be cov]$ ) :ite pap]1 or "s :ite gr\nd1 9 ord] to exhibit ! col\rs to advantage4 ,by turn+ ! object-plate r\nd its c5tre1 or1 if x is a rectil9eal "o1 by pu%+ x ?r\gh ! groove1 & at ! same "t giv+ x a rotatory motion1 ! patt]n on ! wall w und]go e possible trans=mation1 & exhibit to ! spectators1 9 a magnifi$ =m1 all ^? v>iations :i* h be5 obs]v$ by apply+ ! eye to ! ,kaleidoscope4 ,:5 ! prec$+ app>atus is us$ 9 daylight1 s t ! objects are illum9at$ by ! rays ( ! sun1 ! mirror ,m ,n is unnecess>y4 ,! ,kaleidoscope1 etc41 mu/1 h[ev]1 be atta*$ to ! "p ( ! frame ( a ,sol> ,microscope1 :i* goes into ! ap]ture 9 ! w9d[-%utt]4 ,z ! mo/ brilliant light is obta9$ f ! burn+ ( oxyg51 ei!r by itself1 or along ) coal gas1 z 9 ! ,bude light1#h a lamp ( ?is k9d is peculi>ly fitt$ = display+ ! pictures ( ! ,kaleidoscope to a numb] ( spectators4 ,"o ( ,mr4 ,bate's ,polyc5tral ,kaleidoscopes 01 _m ye>s ago1 fitt$ up ) a lamp ( ?is k9d1 = exhibition1 at ! lectures on natural philosophy1 deliv]$ at ,guy's ,hospital1 by t em95t *emi/1 ! late ,william ,all51 ,esq41 ,f4,r4,s4 ,! patt]ns :i* are creat$ by ! ,telescopic ,kaleidoscope f natural objects1 or f objects indep5d5t ( ! in/rum5t1 may1 9 l mann]1 be exhibit$ to sev]al spectators at once4 ,if ! objects are 9 a room1 su* z bun*es ( fl[]s1 /atues1 human figures1 or l>ge pictures1 !y mu/ be plac$ 9 "o ap>tm5t1 & /rongly illum9at$4 ,! l5s mu/ !n be plac$ ^u ! end ,a ,o ( ! ,kaleidoscope1 ! object-plate ,c ,d hav+ be5 remov$1 & mu/ be s adju/$ t ! images ( ! objects may fall exactly ^u ! end ,a ,o ( ! reflectors4 ,! objects may be plac$ at any di/ance f ! l5s1 f six in*es to twelve feet1 accord+ to _! magnitude1 & ! pictures w be exhibit$ ) great di/9ctness & effect ^u ! wall ( ! o!r ap>tm5t4 ,if a blaz+ fire is employ$1 ! mo/ brilliant display ( fireworks may be exhibit$4 ,:5 ! objects are out ( doors1 su* z trees1 %rubs1 etc41 ! ,kaleidoscope1 ) its two l5ses1 mu/ be fix$ 9 ! circul> op5+ ( a w9d[-%utt]1 & ! picture receiv$ ^u :ite pap]1 or any o!r suitable gr\nd1 z 9 ! ,cam]a ,obscura4 #h ,?is light 0 fir/ propos$ by myself4 ,see ,ed9burgh ,review1 ,april #ahcc1 vol4 lvii4 p4 #aib4 ,simil> effects may be produc$ 9 a portable ,cam]a ,obscura1 by plac+ ! app>atus ,c ,f ,l ,l ,g ,d 9 ! moveable draw] ( t in/rum5t4 ,if ! l5s ,l ,l is ( su* a focal l5g? z to admit ! =mation ( ! image )9 ! in/rum5t1 ! picture w be f9ely display$ ^u ! gr\nd glass1 & may be copi$ ) consid]able exactness4 ,9 ! prec$+ applications ( ! ,kaleidoscope1 ! great difficulty to be ov]come arises f ! smallness ( ! ap]ture :i* c be obta9$ at ! eye-end ( ! reflectors4 ,if we take a l>g] ap]ture1 = ! purpose ( ga9+ m light1 ! light ( ! reflect$ images is dim9i%$ by ?is v circum/ance1 & ! picture loses its symmetry at ! c5tre4 ,! only me?od by :i* we c remove ?is evil is to l5g!n ! reflectors1 & consequ5tly increase _! bread? 9 ! same proportion4 ,let u suppose1 = example1 t :5 ! reflectors are five in*es long1 we c safely employ an ap]ture "o-f\r? ( an in* 9 diamet]2 !n if ! plates are made t5 in*es long1 we may use an ap]ture two-f\r?s 9 diamet]1 ! symmetry cont9u+ z complete1 & ! light ( ! reflect$ images z int5se1 z :5 _! l5g? 0 only five in*es4 ,by increas+ ! l5g? ( ! reflectors1 !re=e1 we increase also ! quantity ( light2 b1 un=tunately1 ?is increase ( l5g? is unfav\rable to ! o!r prop]ties ( ! in/rum5t2 = we mu/ n[ use a l5s ,l ,l ( a great focal l5g?1 :i* w r5d] x necess>y to receive ! image at a great di/ance f ! in/rum5t4 ,9 ord] to r5d] ! effect z brilliant z possible1 ! incl9ation ( ! reflectors %\ld1 9 ! pres5t case1 nev] exce$ #cj1 & might be ev5 #cf or #de4 ,! objects %\ld be select$ z ?9 z possible1 & none ) d>k t9ts ought to be admitt$ into ! object-boxes4 ,,*apt] ,,xvi4 ,,on ,,! ,,con/ruction ,,( ,,kaleidoscopes ,,:i* ,,comb9e ,,! ,,col\rs ,,& ,,=ms ,,produc$ ,,by ,,pol>iz$ ,,light4 ,9 ! prec$+ *apt]s we h suppos$ t ! objects are illum9at$ by common light1 & t ! =ms :i* compose ! symmetrical figure are ^? ( mat]ial bodies4 ,if we employ pol>iz$ light we may introduce into ! ,kaleidoscopic figures1 ! spl5did col\rs produc$ by cry/alliz$ bodies1 & also ! =ms :i* ^! col\rs assume1 r\nd ! optical axes ( cry/als1 or ?r\gh diff]5t ?icknesses ( ! d\bly-refract+ sub/ance4 ,! "p ( ! pol>iz+ app>atus :i* pol>izes ! light1 may be a l>ge ,nicol's prism1 or a bundle ( ?9 glass plates1 or a s+le plate ( black glass1 fix$ at ! object end ( ! ,kaleidoscope4 ,! analys+ "p ( ! app>atus may be a ,nicol's prism1 or plates ( ! sulphate ( iodo-qu99e1 discov]$ by ,dr4 ,william ,h]apa?1 ( ,bri/ol4 ,ow+ to ! ?ickness ( a ,nicol's prism1 x is n well fitt$ = ! analys]1 z x prev5ts ! eye ( ! obs]v] f gett+ suffici5tly ne> ! small eye-hole ( ! ,kaleidoscope4 ,! plates ( ! sulphate ( ! iodo-qu99e1 are !re=e peculi>ly adapt$ = analys]s2 & :5 !y c be obta9$ ( ! same size z ! angul> ap]ture ( ! ,kaleidoscope1 ) fix$ reflectors1 or ( ! :ole circul> ap]ture :5 ! reflectors are movable1 !y w also =m ! be/ pol>iz]s4 ,! cry/als :i* are to give ! col\rs & =ms produc$ by pol>iz$ light & its subsequ5t analysis1 may be ei!r uniaxal cry/als1 su* z calc>e\s sp>1 or qu>tz1 or b]yl1 or biaxal cry/als1 su* z sel5ite1 topaz1 mica1 arragonite1 nitre1 etc4#i ,^! cry/als mu/ be plac$ at ! end ( ! reflectors1 & :5 !y transmit pol>iz$ light1 _! brilliant col\rs & =ms w v>y by turn+ ! cell :i* conta9s !m1 or by giv+ a motion ( rotation to ! analys]4 ,?9 films1 or lam9 ( sel5ite ( diff]5t ?icknesses1 & g5]ally ( su* a ?ickness z gives ! bright r+s ( ! second ord] ( col\rs 9 ,newton's scale1 may be plac$ 9 a n>r[ cell or object-box1 & may h _! outl9es ( v>i\s curvatures1 s z to comb9e bo? =m & col\r 9 ! ,kaleidoscopic figure4 ,diff]5t =ms may also be obta9$ by us+ pieces ( col\rless glass ( diff]5t %apes1 or pieces ( ?9 wire b5t into a v>iety ( curves4 ,if ! outl9es ( ! patt]n are to be obta9$ f pieces ( glass or wire1 ! films ( sel5ite might be cem5t$ to "o ( ! glass plates ( ! object-box1 s z to h _! axes ly+ 9 diff]5t directions4 #i ,see my ,treatise on ,optics1 ,edit4 #ahec1 ,*aps4 ,,xxviii1 ,,xxix4 ,! col\r$ figures produc$ by glass quickly cool$1 might also be advantage\sly employ$1 &1 likewise1 ! rem>kable =ms ( circul> cry/als & cry/all9e gr\ps1 :5 !y are suffici5tly l>ge to be se5 by ! nak$ eye4 ,v beautiful objects may be made by cem5t+ a plate ( sulphate ( lime 7sel5ite71 #j4jahah ( an in* ?ick1 to a plate ( glass1 & cutt+ out1 ^u a turn+-la!1 grooves or b&s ( su* diff]5t dep?s1 z to give diff]5t col\rs by pol>iz$ light4 ,beautiful patt]ns may be ?us execut$ 9 b&s or l9es ( diff]5t col\rs2 b = ! purposes ( ! ,kaleidoscope1 x w be suffici5t to h curves or portions ( curves ( su* diff]5t =ms & curvatures1 z w produce agreeable figures by _! comb9ation4 ,^! curves & irregul> =ms ( any k9d1 may be scrat*$ or excavat$ 9 ! plate ( sel5ite by ! po9t ( a %>p knife1 & aft]w>ds poli%$1 or ev5 deep5$1 by ! action ( wat]1 :i* has ! prop]ty ( sl[ly dissolv+ ! sel5ite4 ,9 ord] to obs]ve ! effects produc$ by pol>iz$ light1 x is n necess>y to h ! pol>iz+ & analys+ app>atus atta*$ to ! ,kaleidoscope4 ,! pol>iz]1 9 ! =m ( a plate ( black glass1 or a bundle ( plates ( common w9d[-glass1 may be laid on ! table s z to reflect ! light into ! ,kaleidoscope at an angle ( #ef1 & ! analys] may be held 9 "o h&1 & ! ,kaleidoscope 9 ! o!r4 ,9 ?is case1 h[ev]1 x w\ld be bett] to h ! ,kaleidoscope fix$1 9 ord] t ! obs]v] may h ! use ( 8 left h&1 to turn ! object-box1 :i* conta9s ! d\bly-refract+ cry/al4 ,)\t ! use ( pol>iz$ light1 v f9e =ms1 & ^! spl5didly col\r$1 may be obta9$ by means ( ! col\r$ r+s exhibit$ 9 ! ,iriscope4#aj ,:5 two su* sy/ems ( r+s are =m$ by brea?+ ?r\gh a tube ^u black glass1 ov] :i* soap has be5 rubb$ & subsequ5tly wip$ (f1 by a piece ( *amois lea!r1 !y =m a d\ble sy/em1 simil> to ! biaxial sy/em 9 mica & topaz1 ) curves ( v>i\s %apes1 :i* exhibit beautiful comb9ations 9 ! ,kaleidoscope4 #aj ,treatise on ,optics1 p4 #abj4 ,,*apt] ,,xvii4 ,,on ,,! ,,con/ruction ,,( ,,/]eoscopic ,,kaleidoscopes4 ,if we apply ! ,kaleidoscope to any /atue or ar*itectural ornam5t1 or any o!r solid object repres5t$1 photographically1 on a transp>5t b9ocul> slide1 ! figures w be comb9$ into a flat symmetrical patt]n1 z %[n 9 a future *apt]4 ,b if1 9 ! l5ticul> /]eoscope1 we place a ,kaleidoscope betwe5 ea* ( ! two semi-l5ses & ! /atue1 or o!r object 9 ! b9ocul> slide1 we %all !n see ! /atue or o!r object 9 full relief 9 ! symmetrical figure4 ,?is1 9 a rude =m1 is ! ,/]eoscopic ,kaleidoscope4 ,9 ord] to con/ruct ! in/rum5t indep5d5tly ( ! /]eoscope1 we h only to comb9e two equal ,kaleidoscopes1 ) _! reflect+ mirrors equally incl9$ to ea* o!r1 & place at ! eye-end ( !m two semi-l5ses or qu>t] l5ses1 at ! di/ance ( two & a half in*es1 & hav+ _! focal l5g?s equal to ! l5g? ( ! /]eoscope4 ,if ! two "r & left eye photographs1 to :i* we apply !m1 are opaque1 ^u pap] or silv] plate1 an op5+ mu/ be left above ! object end ( ! reflectors1 ( suffici5t size to all[ light to be ?r[n ^u ! photographs4 ,:5 ! figures are transp>5t1 ?is ap]ture mu/ be clos$4 ,if ! objects 9 ! b9ocul> slides repres5t ei!r bas-reliefs or alto-relievos1 or /atues1 or vases1 or portions ( any solid bodies1 su* z animals1 plants1 or fl[]s1 :i* c be comb9$ into symmetrical patt]ns1 !y w appe> 9 _! true relief 9 ! ,/]eoscopic ,kaleidoscope4 ,9 ?is way ! arti/ may avail himself ( ! in/rum5t 9 design+ circul> ,go?ic w9d[s1 ! circul> decorations ( ceil+s1 & rectil9eal or curvil9eal belts1 t are to be cut out ( metals1 m>ble1 free/one1 or wood1 or =m$ ( pla/] ( ,p>is1 or metals susceptible ( fusion4#aa #aa ,see my ,treatise on ! ,/]eoscope1 ,*ap4 xi4 p4 #hf4 ,if we comb9e two ,telescopic ,kaleidoscopes1 9 ! mann] already describ$1 s t ! c5tres ( _! object-l5ses are di/ant two & a half in*es1 & receive ! "r & left eye pictures ( real objects ^u disks ( gr\nd glass1 ) ! gr\nd side t\*+ ! ends ( ! reflectors1 ^! objects1 ?\gh !mselves 9 true relief1 w be r$uc$ to plane pictures on ! gr\nd glass1 & aga9 br\ght into /]eoscopic relief1 & comb9$ into symmetrical patt]ns by ! in/rum5t4 ,! effect ?us produc$ is diff]5t f :at we %\ld see 7 ! gr\nd glass remov$1 & ! image ( ! object =m$ 9 ! air at ! end ( ! reflectors1 = ! same reason t ! picture ( an object 9 ! /]eoscope is diff]5t f :at x appe>s if view$ directly by ! eyes4 ,,*apt] ,,xviii4 ,,on ,,! ,,con/ruction ,,( ,,microscopic ,,kaleidoscopes4 ,! "n ( ,microscopic ,kaleidoscope may be giv5 to ! in/rum5t1 "u two =ms1 namely1 :5 x is made to produce symmetrical patt]ns f microscopic objects1 or :5 x is made s %ort t a l5s ( a high p[] is necess>y at "o end ( ! reflectors1 to see di/9ctly1 & magnify ! objects at ! o!r end4 ,9 bo? ^! =ms ,i h (t5 con/ruct$ !m s small z "o in* & "o in* & a half 9 l5g?4 ,z ! ,kaleidoscope1 9 ?is m9ute /ate1 has be5 appli$ bo? 9 ?is c\ntry & abroad1 z a female ornam5t1 we %all proce$ to po9t out ! be/ me?od ( con/ruct+ x4 ,s9ce ! ab]ration f symmetry increases1 z ! l5g? ( ! reflectors is dim9i%$1 & s9ce ! light ( ! field dim9i%es f ! same cause1 x becomes extremely difficult to obta9 correct figures1 & uni=mity ( light 9 small in/rum5ts4 ,9 ord] to ov]come ^! difficulties1 z f> z possible1 ! reflectors %\ld be metallic1 & may be ei!r made ( poli%$ /eel or poli%$ speculum metal4 ,! incl9ation at :i* !y are fix$ %\ld n be less ?an #cf or #de2 & ! eye-hole1 :i* %\ld n exce$ _/? ( an in* 9 diamet]1 mu/ be plac$ z ne> z possible to ! angul> po9t4 ,s9ce ! ab]ration f symmetry increases ) ! di/ance ( ! object f ! reflectors1 & is mu* augm5t$ 9 small in/rum5ts1 ! greate/ c>e mu/ be tak5 to h ! objects at ! lea/ possible di/ance f ! reflectors4 ,to accompli% ?is1 ! objects !mselves %\ld be z ?9 & sl5d] z !y c be made2 ! col\rs %\ld be brilliant & n gloomy2 & !y %\ld be sep>at$ f ! reflectors by a ?9 film ( ! mo/ transp>5t mica1 :i* is sup]ior to glass ( equal ?ickness1 ev5 if x c\ld be got1 f its extreme t\ghness & ela/icity4 ,! mica1 inde$1 is easily scrat*$1 b if ?is %\ld take place to any ext5t1 x c easily be replac$ by a new film4 ,x w\ld ev5 be ( consequ5ce to b5d ! mica into a slight concavity1 s z to p]mit ! objects to lie r )9 ?an )\t ! extremity ( ! reflectors4 ,9 ord] to see ! patt]n ) p]fect di/9ctness1 a l5s mu/ be plac$ at ! end ( ! in/rum5t2 ! focal l5g? ( ?is l5s1 h[ev]1 mu/ n be exactly equal to ! di/ance ( ! objects f ! eye1 b z mu* great] z possible1 s t ! eye1 by a little ex]tion1 may be able to obta9 di/9ct vision4 ,! reason ( ?is w be und]/ood1 by consid]+ t ! images ( ! objects1 se5 by reflexions1 are ?r[n to a great] di/ance1 z x 71 f ! eye1 & c\ld n !re=e be se5 di/9ctly by us+ a l5s adju/$ exactly to ! ne>e/ "p ( ! picture4 ,consequ5tly1 ! focal l5g? ( ! l5s mu/ be a mean betwe5 ! di/ances ( diff]5t p>ts ( ! picture1 t is1 a little great] ?an t :i* is suit$ to ! sector se5 by direct vision4 ,:5 small ,kaleidoscopes are made ) f\r or ) ?ree mirrors1 ! prec$+ directions are equally applicable1 ! greate/ c>e be+ tak5 t ! reflectors tap] ne>ly to a po9t at ! eye-end1 s z n to leave an ap]ture great] ?an ? ( an in* 9 diamet]4 ,:5 !y are made ( solid glass1 ! focal l5g? ( ! l5s mu/ be det]m9$ f ! pr9ciples conta9$ 9 ! la/ *apt]4 ,! prec$+ in/rum5ts may be fitt$ up ) a draw-tube & l5s1 & :5 x is requir$ to introduce draw+s ( pictures & /atues1 small microscopic photographs may be employ$4 ,,*apt] ,,xix4 ,,on ,,! ,,*anges ,,produc$ ,,by ,,! ,,kaleidoscope4 ,! prop]ty ( ! ,kaleidoscope1 :i* has excit$ m wond]1 & !re=e m controv]sy ?an any o!r1 is ! numb] ( comb9ations or *anges :i* x is capable ( produc+ f a small numb] ( objects4 ,_m p]sons1 entirely ignorant ( ! nature ( ! in/rum5t1 h calculat$ ! numb] ( =ms :i* may be creat$ f a c]ta9 numb] ( pieces ( glass1 ^u ! ord9>y pr9ciples ( comb9ation4 ,9 ?is way x foll[s1 t tw5ty-f\r pieces ( glass may be comb9$ #a1cia1gbd1bhh1hhg1beb1iii1dbe1abh1dic1d jb1bjj times--an op]ation1 ! p]=mance ( :i* w\ld require hundr$s ( ?\s&s ( millions ( ye>s1 ev5 ^u ! supposition t tw5ty ( !m 7 p]=m$ e m9ute4 ,?is calculation1 surpris+ z x appe>s1 is q false1 n f be+ exagg]at$1 b f be+ f> inf]ior to ! reality4 ,x proce$s ^u ! supposition t "o piece ( glass c exhibit only "o figure1 & t two pieces c exhibit only two figures1 :]eas x is obvi\s t ! two pieces1 ?\gh !y c only be comb9$ 9 two ways1 9 ! same /raight l9e1 yet ! "o c be put above & bel[ ! o!r1 z well z ^u its "r side & its left side1 & may be jo9$1 s t ! l9e connect+ _! c5tres may h an inf9ite numb] ( positions ) respect to a horizontal l9e4 ,x foll[s1 inde$1 f ! pr9ciples ( ! ,kaleidoscope1 t if only "o object is us$1 & if t object is a ma!matical l9e )\t bread?1 ! in/rum5t w =m an inf9ite numb] ( figures f ?is s+le l9e4 ,! l9e may be plac$ at an inf9ite numb] ( di/ances f ! c5tre ( ! ap]ture1 & equally incl9$ to ! extremities ( ! reflectors4 ,x may be incl9$ at an inf9ite v>iety ( angles to ! radii ( ! circul> field1 & x may be plac$ 9 an inf9ite v>iety ( positions p>allel to any radius4 ,9 all ^! cases1 ! ,kaleidoscope w =m a figure diff]+ 9 "* & 9 magnitude4 ,9 ! fir/ case1 all ! figures are polygons ( ! same "*1 b ( diff]5t sizes4 ,9 ! second case1 !y are />s1 diff]+ f ea* o!r 9 ! magnitude ( _! sali5t & re-ent]+ angles2 & 9 ! ?ird case1 !y =m imp]fect figures1 9 :i* ! l9es unite at "o extremity & are op5 at ! o!r4 ,if1 in/ead ( suppos+ a ma!matical l9e to be ! object1 we take a s+le piece ( col\r$ glass1 ) an irregul> outl9e1 we %all h no difficulty 9 p]ceiv+1 f exp]im5t1 t an inf9ite v>iety ( figures may be creat$ f x alone4 ,?is sy/em ( endless *anges is "o ( ! mo/ extraord9>y prop]ties ( ! ,kaleidoscope4 ,) a numb] ( loose objects1 x is impossible to reproduce any figure :i* we h admir$4 ,:5 x is once lo/1 c5turies may elapse be=e ! same comb9ation returns4 ,if ! objects1 h[ev]1 are plac$ 9 ! cell1 s z to h v little motion1 ! same figure1 or "o v ne> x1 may1 )\t difficulty1 be recall$2 & if !y are absolutely fix$1 ! same patt]n w recur 9 e revolution ( ! object-plate4 ,,*apt] ,,xx4 ,,on ,,! ,,application ,,( ,,! ,,kaleidoscope ,,to ,,! ,,f9e ,,& ,,useful ,,arts4 ,if we exam9e ! v>i\s objects ( art :i* h ex]cis$ ! skill & +5uity ( man1 we %all f9d t !y d]ive all _! beauty f ! symmetry ( _! =m1 & t "o "w ( art excels ano!r 9 proportion z x exhibits a m p]fect developm5t ( ?is pr9ciple ( beauty4 ,ev5 ! =ms ( animal1 vegetable1 & m9]al bodies1 d]ive _! beauty f ! same s\rce4 ,! human figure consi/s ( two halves1 "o ( :i* is ! reflect$ image ( ! o!r2 & ! same symmetry ( =m pres5ts itself 9 ! %apes ( almo/ all ! v>i\s tribes ( animat$ be+s4 ,9 ! /ructure ( vegetables1 ! pr9ciple ( symmetry is less p]fectly develop$4 ,f ! extreme delicacy & ela/icity ( its p>ts1 a plant1 regul>ly con/ruct$1 w\ld h lo/ all its symmetry f ! influ5ce ( gravitation1 or f ! slighte/ brea? ( w9d2 & !re=e a symmetrical comb9ation ( p>ts has be5 effect$ only 9 its leaves & fl[]s4 ,:5 ! laws ( cry/allization are all[$ to p]=m _! functions uncontroll$1 ! beautiful geometrical =ms :i* !y create are m>k$ ) ! mo/ p]fect regul>ity4 ,ev5 _! physical prop]ties are symmetrically relat$ to "s axis or fix$ l9e2 & ?\gh all _! functions are p]=m$ 9 utt] sil5ce & repose1 yet _! physiology1 if we may apply t "n to ! actions ( app>5tly dead matt]1 is n less wond]ful ?an t :i* embraces ! busy ag5cies ( animal & vegetable bodies4 ,! irregul> =ms :i* are ! f\ndation ( picturesque beauty con/itute a s+le exception to ! g5]al law1 & !re=e ! l&scape pa9t] is ! only arti/ :o is n pr(essionally l$ to ! /udy ( t species ( beauty :i* arises f ! inv]sion & multiplication ( simple =ms4 ,:5 we consid] ! imm5se v>iety ( pr(essions connect$ bo? ) ! f9e & ! useful arts1 9 :i* ! creation ( symmetrical ornam5ts =ms a necess>y "p1 we _c fail to atta* a high degree ( utility to any in/rum5t by :i* ! op]ations ( ! arti/ may be facilitat$ & improv$4 ,we are dispos$ to imag9e t no ma*9e is really useful1 unless x is directly employ$ 9 provid+ = our m urg5t wants4 ,?is1 h[ev]1 is a vulg> error4 ,an eng9e :i* =ms ! head ( a p91 has1 9 reality1 z mu* importance z an eng9e = rais+ wat]1 or = manufactur+ clo?2 = 9 ^! cases ! ?ree ma*9es h ! same object1 :i* is m]ely t ( abridg+ manual lab\r4 ,! wat] w\ld /ill be rais$1 & ! clo? & p9s manufactur$1 if ! ma*9es did n exi/2 b ! ma*9]y insures u a m regul> supply ( ^! articles1 & enables u to receive !m at a *eap] rate4 ,! op]ations ( ma*9]y h1 h[ev]1 a /ill high] "* 9 comp>ison ) ^? ( individual ex]tion1 :5 !y enable u to obta9 any article1 ei!r ( necessity or ( luxury1 9 a m p]fect /ate4 ,9 ?is case1 ! ma*9e effects :at is beyond ! rea* ( manual lab\r2 & in/ead ( be+ ! m]e repres5tative ( animal =ce1 x exhibits a conc5tration ( tal5t & skill :i* c\ld n h be5 obta9$ by unit+ ! sep>ate ex]tions ( liv+ ag5ts4 ,:5 we consid]1 t 9 ?is busy isl& ?\s&s ( individuals are :olly occupi$ ) ! composition ( symmetrical designs1 & t !re is sc>cely any pr(ession into :i* ^! designs d n ent] z a necess>y "p1 s z to employ a portion ( ! "t ( e arti/1 we %all n hesitate 9 admitt+1 t an in/rum5t mu/ h no small degree ( utility :i* abridges ! lab\r ( s _m individuals4 ,if we reflect fur!r on ! nature ( ! designs :i* are ?us compos$1 & on ! me?ods :i* mu/ be employ$ 9 _! composition1 ! ,kaleidoscope w assume ! "* ( ! highe/ class ( ma*9]y1 :i* improves at ! same "t t x abridges ! ex]tions ( individuals4 ,!re are few ma*9es1 inde$1 :i* rise high] above ! op]ations ( human skill4 ,x w create1 9 a s+le h\r1 :at a ?\s& arti/s c\ld n inv5t 9 ! c\rse ( a ye>2 & :ile x works ) su* unexampl$ rapidity1 x works also ) a correspond+ beauty & precision4 ,! arti/ :o =ms a symmetrical design1 is entirely ignorant ( ! effect till x is complet$--& if ! design is to be embodi$ 9 col\r$ mat]ials1 or 9 /one1 or any o!r solid sub/ance1 he has no means ( pr$ict+ ! f9al effect :i* x is to produce4 ,e result1 9 %ort1 is a matt] ( unc]ta9ty3 & :5 ! "w is complet$1 x mu/ rema9 z x is4 ,! art ( =m+ designs1 !re=e1 is 9 a /ate ( extreme imp]fection2 & a m /rik+ pro( ( ?is c\ld n be obta9$ ?an f ! s]vility ) :i* we copy1 at ! pres5t mom5t1 ! m\ld+s & ornam5ts ( ,greek & ,go?ic ar*itecture1 & ! decorations :i* embelli% ! furniture1 ! dresses1 & ! ut5sils ( ! ,romans4 ,if ! ,kaleidoscope _h be5 an in/rum5t :i* m]ely enabl$ u to project ^u a plane surface a v>iety ( designs ( ! same "* z ^? :i* ! arti/ =ms ) 8 p5cil1 x w\ld /ill h be5 an in/rum5t ( great utility4 ,b x does mu* m ?an ?is4 ,:5 prop]ly con/ruct$1 & rightly appli$1 x exhibits ! f9al effect ( ! design1 :5 execut$ 9 ! be/ mann]2 & x does ?is1 n only by embody+ ! v mat]ials out ( :i* ! reality is to be produc$2 b by exhibit+1 in/ead ( lights & %ades1 ! v em95ces & depressions :i* necess>ily exi/ 9 e design ! p>ts ( :i* lie 9 v>i\s planes4 ,9 proce$+ to po9t out ! practical me?ods ( obta9+ ^! effects f ! ,kaleidoscope1 we take x = grant$ t ! arti/ has "o or o!r ( ! correct in/rum5ts describ$ 9 ! prec$+ *apt]s1 & t !y are m\nt$ ^u a /&1 & furni%$ ) ,dr4 ,wolla/on's ,cam]a ,lucida1 = enabl+ him to copy ! designs :i* he wi%es to p]petuate4 #a4 ,ar*itectural ,ornam5ts4 ,almo/ e public & private edifice1 ) ! exception ( picturesque cottages1 & build+s erect$ = ! purposes ( def5ce1 has a regul> =m1 consi/+ ( two halves1 "o ( :i* is ! inv]t$ image ( ! o!r4 ,! inf]ior p>ts ( ! build+1 su* z ! doors & w9d[s1 h ! same regul> "*2 & h5ce x necess>ily foll[s1 t all ! decorations1 :e!r 9 ! =m ( rectil9eal bord]s1 circul> patt]ns1 or gr\ps ( figures1 %\ld n only h ! same symmetry1 b %\ld also be symmetrically relat$ to ! bisect+ l9e :i* sep>ates ! build+ into two halves4 ,if1 = example1 a rectil9eal bord]1 surr\nd+ a build+ l a belt1 consi/s ( a patt]n1 or ( l9es incl9$ 9 "o direction1 su* a bord] is n symmetrically relat$ to ! v]tical & horizontal l9es ( :i* ! build+ consi/s4 ,h5ce x w foll[1 t sculptures1 repres5t+ an action ( any k9d1 or /atues repres5t+ liv+ objects1 :5 !y are suffici5tly l>ge to be se5 at ! same "t ) ! :ole build+1 c nev] connect !mselves ) its regul> outl9e4 ,if ^! sculptures1 or /atues1 are inv]t$ s z to =m a ,kaleidoscope patt]n1 l ! beautiful sculpture 9 ! door ( ! temple ( ,jun-wassa1#ab !y may !n be employ$ )\t ! risk ( de/roy+ ! g5]al symmetry ( ! edifice4 ,^! rem>ks are equally applicable to e object :i* d]ives its beauty f symmetry2 & x is curi\s to obs]ve ! num]\s deviations f ?is pr9ciple1 & ! bad effects !y produce on "s ( ! f9e/ vases & ornam5ts ( ! ,romans4#ac ,if ,mr4 ,cock]ell's +5i\s !ory#ad ( ! orig9al composition ( ! /atues ( ,niobe & h] *ildr5 be correct1 ! mode ( gr\p+ ! figures w %[ h[ mu* ! arti/ 0 dispos$ to sacrifice e o!r k9d ( effect1 to obta9 some?+ l a symmetrical gr\p )9 ! p$im5t4 ,! gradual increase 9 ! height ( ! /atues t[>ds ! middle ( ! tympanum1 & _! incl9ation on bo? sides t[>ds ! same po9t1 =m /rong pro(s ( ,mr4 ,cock]ell's hypo!sis1 & af=d a s+ul> example1 ! only "o ) :i* we are acqua9t$1 ( an attempt to reconcile ! app>5tly incongru\s effect ( a real picture & a symmetrical gr\p4 ,_h ! /atues be5 conf9$ to "o-half ( ! tympanum1 :ile ! o!r half 0 a reflect$ image ( ! fir/1 we are p]suad$1 t ?\gh ! effect1 z a picture1 w\ld h be5 dim9i%$1 yet ! effect1 z a "p ( ! temple1 w\ld h be5 greatly increas$4 ,a v rem>kable example ( ?is species ( symmetry is %[n 9 ! f9e pa9t+ ( ! ,f\r ,sibyls1 by ,raphael1 :i* is n[ 9 ! *ur* ( ,santa ,m>ia della ,pace1 at ,rome4 #ab ,see ,ed9burgh ,encyclopdia1 ,art4 ,civil ,ar*itecture1 plate ,,cli4 #ac ,see ,hope's ,co/ume ( ! ,anci5ts1 vol4 ii4 plates #bcj1 #bfd1 #bgh1 figs #a & #bih1 fig4 #b4 #ad ,see ,j\rnal ( ! ,royal ,in/itution1 vol4 v4 p4 #ii4 ,aft] ! ar*itect has fix$ ^u ! nature & "* ( 8 ornam5ts1 he mu/ cut1 ^u ! surface ( a l>ge /one1 or place 9 relief ^u x1 ! elem5ts ( a v>iety ( patt]ns4 ,^! elem5ts ne$ n be exact repres5tations ( any object1 or any portion ( x1 ?\gh1 9 "s cases1 an approximation to ?is may be desirable4 ,:5 ?is /one is set 9 a v]tical position1 & s t ! light may fall obliquely ^u its surface1 = ! purpose ( giv+ light & %ade to ! patt]n1 ! ,kaleidoscope %\ld be plac$ exactly opposite ! /one1 & at a di/ance f x correspond+ to ! magnitude ( ! patt]n :i* is want$4 ,! tube conta9+ ! l5s or l5ses1 be+ put on1 or ! inn] tube be+ drawn out1 if ! in/rum5t consi/s ( two complete tubes1 x mu/ be adju/$ to ! di/ance ( ! /one1 or till an image ( ! /one is =m$ at ! end ( ! reflectors4 ,:5 ?is adju/m5t is p]fect1 ! ,kaleidoscope mu/ be direct$ to ! c>v$ "p ( ! /one1 out ( :i* x is propos$ to =m ! patt]n2 & by slight *anges 9 its position1 by turn+ x r\nd its axis1 & by v>y+ ! incl9ation ( ! reflectors1 an imm5se v>iety ( ! mo/ beautiful designs w be exhibit$1 9 ! f9e/ relief1 & z p]fect z if !y _h be5 c>v$ out ( ! /one by ! mo/ skilful workman4 ,! ar*itect has !re=e only to select f ! pr(usion ( designs :i* are ?us pres5t$ to him2 & :5 he has made 8 *oice1 he may ei!r copy x photographically1 or ) 8 eye1 or by means ( ! ,cam]a ,lucida2 or he may trace ^u ! /one ! projection ( ! angul> ap]ture ( ! in/rum5t1 9 ord] t1 9 ! execution ( 8 "w1 he may h con/antly be=e 8 eyes ! real elem5t out ( :i* ! picture is creat$4 ,if1 9 ! c\rse ( ?is selection1 ! picture %\ld become capable ( improvem5t1 ei!r by giv+ x dep? 9 p>ticul> p>ts1 or by alt]+ ! outl9e1 ?is alt]ation c be easily made1 & its effect ?r\gh\t ! :ole ornam5t w be in/antly se54 ,if ! ar*itect is desir\s to introduce into 8 ornam5t a natural object1 su* z a leaf1 he may fir/ try ! effect :i* x w produce :5 appli$ 9 its natural /ate to ! in/rum5t1 & he may !n c>ve ei!r ! :ole or ! half ( x 9 /one1 & !n exam9e :at w be its f9al effect4 ,if "o half ( ! leaf is an inv]t$ image ( ! o!r half1 x is necess>y only to c>ve "o half ( x1 & place ! reflectors at an angle conta9$ z _m times 9 a circle z twice ! numb] ( times t he wi%es ! :ole leaf to be multipli$3 = example1 if ! :ole leaf is to be multipli$ six times1 ! angle ( ! mirrors mu/ be _/? ( #cfj1 or #cj4 ,! v same effect w\ld be obta9$ by apply+ ! :ole leaf to ! in/rum5t :5 ! incl9ation ( ! reflectors is #fj1 or ? ( #cfj4 ,b :5 ! :ole leaf is n symmetrical 9 itself1 or consi/s ( two dissimil> halves1 x mu/ be appli$ 9 its entire /ate to ! in/rum5t4 ,9 ! =mation ( circul> ,go?ic w9d[s1 ! ar*itect w f9d ! ,kaleidoscope a mo/ important auxili>y4 ,by apply+ x to a mullion drawn ^u pap]1 ) a portion ( ! curves :i* he wi%es to introduce1 or by plac+ x ^u v>i\s ornam5tal p>ts ( ! draw+ ( a ,go?ic ca!dral1 he w obta9 comb9ations to :i* he has nev] obs]v$ ! slighte/ approximation4 ,9 design+ ! decorations = ceil+s1 :i* are g5]ally made ( pla/] ( ,p>is1 ! same me?od %\ld be foll[$ z t :i* we h describ$ = ar*itectural ornam5ts4 #b4 ,ornam5tal ,pa9t+4 ,9 ornam5ts c>v$ out ( /one or m>ble1 or =m$ f pla/] ( ,p>is1 ! idea ( col\r does n ent] into ! consid]ation ( ! ar*itect4 ,! =ms1 h[ev]1 :i* are necess>y 9 ornam5tal pa9t+1 are always associat$ ) col\r2 & !re=e1 9 ! inv5tion & selection ( ^! =ms1 ! ,kaleidoscope p]=ms a d\ble task4 ,:ile x creates ! outl9e1 x at ! same "t fills x up ) col\r2 & by repres5t+ ! effect ( ! two 9 a /ate ( comb9ation1 x enables ! arti/ to judge ( ! h>mony ( 8 t9ts1 z well z ( ! proportion ( 8 =ms4 ,9 ! decoration ( public halls & gall]ies1 !re is no species ( ornam5t m appropriate ?an ^? :i* consi/ 9 ! comb9ation ( s+le figures1 or ( gr\ps ( heads1 :i* are ei!r directly or metaphorically associat$ ) ! hi/ory or object ( ! in/itution4 ,regul> hi/orical pa9t+s on ! ceil+ ( a room are q incompatible ) ! symmetrical "* ( a public gall]y4 ,if !y are well execut$1 !y c nev] be se5 to advantage1 & !re=e _! individual effect is lo/1 :ile1 f _! v nature1 !y _c possibly produce t g5]al effect z an ornam5t :i* good ta/e imp]i\sly requires4 ,9 employ+ regul>ly comb9$ gr\ps ( figures1 !re is suffici5t scope giv5 to ! p[]s ( ! arti/1 :ile ! sy/ematic arrangem5t ( 8 "w prev5ts x f int]f]+ ) ! g5]al "* ( ! place :i* x is to embelli%4 ,! effects :i* ! ,kaleidoscope develops1 :5 appli$ to ! repres5tations ( liv+ objects1 w1 we h no d\bt1 give v great surprise to ^? :o h n previ\sly exam9$ !m4 ,9 ord] to enable ! read] to =m "s notion ( !m1 we h giv51 9 ! annex$ ,plate1 a s]ies ( r$uc$ figures1 tak5 pr9cipally f ! antique4 ,9 ord] to sep>ate an individual figure f ! re/1 we h only to cut an op5+ ( ne>ly ! same size 9 a piece ( pap]1 & lay x ^u ! surface ( ! plate1 s z to conceal all ! adjo9+ figures1 & p]mit ! requir$ figure to be se5 ?r\gh ! ap]ture4 ,by apply+ a ,kaleidoscope1 9 :i* ! incl9ation ( ! mirrors does n exce$ #cj1 ! figure w be comb9$ into a f9e patt]n1 exhibit+1 p]haps1 ! head & a "p ( ! body 9 e sector2 :ile ! h&s1 or ! l[] extremities1 are ?r[n into ! /iff "p ( ! design4 ,! s+ul> ease & grace ) :i* ! figure necess>ily rises out ( ! =mal "p ( ! patt]n1 & ) :i* x connects itself ) ! g5]al picture1 produces a new effect1 :i*1 s f> z we c le>n1 no arti/ _h ev] attempt$ to produce4 ,9 ord] to gr\p ^! s+le figures ) p]fect accuracy1 ! ,kaleidoscopes con/ruct$ by ,mr4 ,bate %\ld be employ$1 z bo? 8 in/rum5ts h a contrivance :i* all[s ! light to fall freely ^u ! surface ( ! picture4#ae #ae ,see p4 #ic4 ,illu/ration3 ,,fig4 #ea4 ,:5 ! figures :i* we wi% to introduce are l>g] ?an ! ap]ture ( ! ,kaleidoscope1 we mu/ use ! l5s1 & place !m at su* a di/ance z to r$uce !m to ! prop] magnitude4 ,! effect :i* is produc$ by ^! simple outl9es w convey "s idea ( ! beauty :i* mu/ *>act]ize ! designs :5 ! figures are f9ely %ad$1 or *a/ely col\r$4 ,by ! application ( ! l5s1 pa9t+s or /atues ( any size may be r$uc$ & admitt$ into ! figure4 ,9 ord] to convey to ! read] "s idea ( ! effect produc$ by ! ,kaleidoscope 9 gr\p+ figures1 we h giv5 9 ,fig4 #ea a design creat$ by ! in/rum5t4 ,! incl9ation ( ! mirrors by :i* ! figures 7 arrang$ is #cf1 or ? ( a circle2 & !re=e ! object is multipli$ t5 times1 s z to give five pair ( direct & inv]t$ images4 #c4 ,designs = ,c>pets4 ,!re is none ( ! useful arts to :i* ! creations ( ! ,kaleidoscope are m directly applicable ?an ! manufacture ( c>pets4 ,9 ?is case1 ! manufactur] requires n m]ely ! outl9e ( a design1 b a design fill$ up ) ! mo/ brilliant col\rs2 & ^u ! nature ( ! figure :i* he selects1 & ! t9ts ) :i* he enri*es x1 w dep5d ! beauty ( ! effect :i* is produc$4 ,a c>pet1 inde$1 is 9 g5]al cov]$ ) a numb] ( ,kaleidoscope designs1 arrang$ 9 l9es p>allel to ! sides ( ! ap>tm5t2 & :ile ?is in/rum5t creates an individual patt]n1 x may also be employ$1 by ! assi/ance ( ! l5s1 9 exhibit+ ! effect or arrang+ or gr\p+ ^! individual patt]ns1 accord+ to ! =m ( ! ap>tm5t1 & o!r circum/ances :i* %\ld inv>iably be att5d$ to4 ,:5 a pla/]] ornam5ts ! ceil+ ( a room1 ! figure :i* he *ooses is always relat$ to ! %ape ( ! ceil+1 & v>ies accord+ z x is circul>1 elliptical1 squ>e1 or rectangul>4 ,9 l mann]1 a c>pet %\ld always h a relation to ! =m ( ! ap>tm5t1 n only 9 ! %ape & "* ( ! individual designs1 b 9 ! mode 9 :i* !y are comb9$ into a :ole4 ,al?\gh ! designs giv5 by ! ,kaleidoscope are 9 g5]al circul>1 yet1 :5 !y are once drawn1 _! outl9e may be made ei!r triangul>1 squ>e1 rectangul>1 elliptical1 or ( any o!r =m t we please1 )\t de/roy+ _! beauty4 ,! outl9e ( ! patt]n may be v>i$ 9 ! in/rum5t1 by v>y+ ! %ape ( ! "p ( ! tube or ap]ture :i* b\nds ! field ( view at ! wide/ end ( ! angul> ap]ture2 b x is only at c]ta9 incl9ations ( ! reflectors t any ( ! regul> figures c be produc$ 9 ?is way4 ,if ! b\nd+ l9e is circul>1 ! field ( view w be a circle2 if ! b\nd+ l9e is rectil9eal1 & equally incl9$ to ! reflectors1 ! field ( view w be a regul> polygon1 ( z _m sides z ! numb] ( times t ! angle ( ! reflectors is conta9$ 9 #cfj2 if ! b\nd+ l9e is rectil9eal1 b plac$ at "r angles to "o ( ! reflectors1 ! figure w /ill be a regul> polygon1 b its numb] ( sides w be equal to half ! numb] ( times t ! angle ( ! reflectors is conta9$ 9 #cfj4 ,h5ce x foll[s1 t a squ>e field may be obta9$ 9 two ways1 ei!r by plac+ ! mirrors at an angle ( #de1 & mak+ ! b\nd+ l9e p]p5dicul> to "o ( ! reflectors2 or by incl9+ ! mirrors #ij1 & mak+ ! b\nd+ l9e equally incl9$ to bo? reflectors2--& t a triangul> field may be obta9$1 ei!r by incl9+ ! mirrors #fj1 & sett+ ! b\nd+ l9e at "r angles to "o ( ! reflectors1 or by mak+ ! incl9ation #abj1 & plac+ ! b\nd+ l9e at an angle ( #fj & #cj to ! reflectors4 ,an elliptical field may be obta9$1 by giv+ ! b\nd+ l9e ! %ape ( "o qu>t] ( an ellipse1 & plac+ x 9 su* a mann] t ! v]tex ( ! conjugate axis falls ^u "o ( ! reflectors1 & ! v]tex ( ! transv]se axis ^u ! o!r4 ,! =m ( ! patt]n be+ det]m9$1 ! next /ep is to select an outl9e1 & ! col\rs :i* are to ent] into its =mation4 ,9 ord] to d ?is to ! greate/ advantage1 ! diff]5tly col\r$ wor/$s :i* ! manufactur] proposes to employ %\ld be plac$ ^u a plane surface1 ei!r 9 ! /ate ( ?read1 or1 :at is mu* bett]1 :5 !y are wr\ght into clo?4 ,^! diff]5tly col\r$ pieces ( c>pet1 :i* we may suppose to be blue1 gre51 & yell[1 mu/ !n be plac$ at ! di/ance ( a few feet f ! ,kaleidoscope1 s t _! image may1 by means ( ! l5s1 be =m$ at ! end ( ! reflectors4 ,9 ?is /ate a v p]fect patt]n w be creat$ by ! in/rum5t1 & ! blue1 gre51 & yell[ col\r w pr$om9ate accord+ z a great] or a less] portion ( ^! col\rs happ5s to be opposite to ! angul> ap]ture4 ,by %ift+ ! position ( ! ,kaleidoscope1 any "o ( ! col\rs may be made to pr$om9ate at pleasure2 & ! arti/ has x ?us 9 8 p[]1 n only to produce any k9d ( outl9e t he *ooses1 b regulate ! masses ( col\r by :i* x is to be fill$ up2 & to try ! effects :i* w be produc$ by ! juxtaposition ( two col\rs1 by ! sep>ation ( o!rs1 or by ! transf]5ce ( ! sep>ate or comb9$ masses to diff]5t p>ts ( ! design4 ,x w\ld be =eign to our object to describe ! app>atus by :i* ^! *anges 9 ! quantities ( col\r1 & 9 _! relative position1 may be mo/ easily & conv5i5tly effect$2 ! arti/ c h no difficulty 9 con/ruct+ su* an app>atus = himself1 & by means ( x he w be enabl$ to obta9 results f ! ,kaleidoscope :i* he w\ld h s\ght = 9 va9 f any o!r me?od4 ,z ! me?ods we h describ$ ( us+ ! ,kaleidoscope 9 ornam5tal ar*itecture1 or ornam5tal pa9t+1 & 9 ! manufacture ( c>pets1 w apply to ! v>i\s o!r pr(essions 9 :i* ! =mation ( symmetrical designs is a necess>y "p1 ,i %all m]ely /ate1 t x w be f\nd ( ! greate/ advantage to ! jewell] 9 ! arrangem5t ( preci\s /ones2 to ! bookb9d]1 ! wire-work]1 ! pap]-/a9]1 & ! arti/ :o =ms w9d[s ( pa9t$ glass4 ,9 ?is la/ pr(ession1 9 p>ticul>1 ! application ( ! ,kaleidoscope _c fail to indicate comb9ations f> sup]ior to any?+ t has yet be5 se5 9 ?is bran* ( art4 ,f ! uni=mity ( t9t 9 ! sep>ate pieces ( glass :i* are to be comb9$1 ! effect produc$ by ! in/rum5t f portions ( ! v same glass t is to be us$ = ! w9d[s1 may be consid]$ z a p]fect fac-simile ( ! w9d[ :5 well execut$ on a l>ge scale4 ,,*apt] ,,xxi4 ,,on ,,! ,,photographic ,,del9eation ,,( ,,! ,,pictures ,,creat$ ,,by ,,! ,,kaleidoscope4 ,9 a prec$+ *apt] we h ref]r$ to ! del9eation ( ! pictures creat$ by ! ,kaleidoscope1 :5 !y are receiv$ on ! gr\nd glass ( a cam]a obscura1 or :5 a cam]a lucida is plac$ at ! eye-end ( ! in/rum5t4 ,bo? ( ^! me?ods are v imp]fect1 & :5 ! pictures h be5 copi$ = useful purposes1 we believe t !y h g5]ally be5 execut$ by a skilful draughtsman1 :o del9eat$ c>efully "o ( ! sectors ( :i* ! figure is compos$1 & !n repeat$ x s z to complete ! picture4 ,illu/ration3 ,,fig4 #eb4 ,s9ce ! inv5tion ( ! ,kaleidoscope1 ! discov]y ( ! photographic art--( ! ,dagu]reotype & ,talbotype processes1 has giv5 a new value to ! in/rum5t4 ,by means ( a ,kaleidoscope ,cam]a1 ! mo/ complex figures c be almo/ in/antane\sly transf]r$ to pap]1 or to plat$ copp]1 & hundr$s ( designs (f]$ to ! *oice ( ! arti/ :o is to employ !m4 ,! v same figure :i* is obta9$ by "o mode ( illum9ation1 may be alt]$ indef9itely1 by m]ely *ang+ ! direction or ! int5sity ( ! light1 all ! objects :i* give ! figure rema9+ fix$ 9 ! object-box4 ,! optical arrangem5t by :i* ^! figures may be copi$1 photographically1 is sub/antially ! same z t :i* is %[n 9 ,fig4 #eb1 :]e ,c ,g ,d ,f is ! ,kaleidoscope1 ,a ,o ! object-box1 & ,l ,l a small a*romatic l5s1 ( rock cry/al or glass1 a qu>t] ( an in* 9 diamet]1 plac$ 9 contact ) ! extremities ( ! glass or metallic reflectors1 & hav+ its c5tre imm$iately beh9d ! small op5+ at ,e4 ,:5 ! rays ( ! sun1 or any o!r /rong light1 conta9+ ! act9ic rays1 are ?r[n obliquely ^u ! object-box ,a ,o1 an image ( ! ,kaleidoscopic figure1 produc$ by ! objects 9 ! object-box1 w be =m$ at ,p ,p1 9 ! focus ( ! l5s ,l ,l4 ,if ! focal l5g? ( ! l5s ,l ,l is equal to "o-half ,c ,g1 ! l5g? ( ! ,kaleidoscope1 ! image w be =m$ beh9d ,l ,l1 at a di/ance equal to ,c ,g1 & ( ! same size z ! object-box2 b if ! focal l5g? ( ,l ,l is great] ?an ! half ( ,c ,g1 ! image w be =m$ at a great] di/ance ?an ,c ,g1 beh9d ! l5s1 & ! size ( x w be great] ?an t ( ! object-box1 ! di/ance & ! size ( ! picture increas+ z ! focal l5g? ( ! l5s increases2 & :5 x becomes equal to ,c ,g1 ! size & ! di/ance ( ! picture w be inf9itely great4 ,:5 ! focal l5g? ( ! l5s is less ?an half ,c ,g1 ! figure w be small] ?an ! object-box1 & ne>] ! l5s4 ,! ,kaleidoscope ,cam]a4 ,e cam]a employ$ = ! purposes ( photography may be readily adapt$ = tak+ ! pictures =m$ by ! ,kaleidoscope4 ,we h only to take out ! l5s or l5ses :i* belong to x1 & place ! ,kaleidoscope furni%$ ) its l5s ,l ,l1 ,fig4 #eb1 9 ! inn] tube1 :i* is movable by means ( ! rack & p9ion4 ,if ! picture c be made di/9ct on ! grey glass by ! rack & p9ion1 a negative or positive copy ( x may be tak5 on collodion or pap]1 9 ! same mann] z o!r photographs4 ,9 "s cam]as ! end ( ! box :i* conta9s ! grey glass is movable1 backw>ds & =w>ds1 s t ! adju/m5t = r5d]+ ! picture di/9ct may be effect$1 ?\gh ! ,kaleidoscope is fix$ 9 ! front portion ( ! box4 ,:5 ! cam]a is made = ! express purpose ( tak+ ,kaleidoscope pictures1 x becomes a v simple in/rum5t & may be con/ruct$ easily & *eaply4 ,x requires no l5s except+ ! small "o ,l ,l ( rock cry/al or ( glass1 a qu>t] ( an in* 9 diamet]4 ,! ap]ture requir$ = ?is l5s is s small t ! sph]ical & *romatic ab]ration _c injure1 9 any s5sible mann]1 ! di/9ctness ( ! picture4 ,! diff]5ce betwe5 ! *emical & lum9\s focus1 :i* _c be made to co9cide ) a s+le l5s1 may be easily det]m9$ by exp]im5t1 or 9 ord] to avoid ?is1 ! small l5s may be made a*romatic4#af #af ,a ?9 l5s ( rock cry/al w transmit m ( ! act9ic rays ?an "o r5d]$ a*romatic4 ,! =m ( ! cam]a z fitt$ up ) "o ( ,mr4 ,bate's ,kaleidoscopes1 ) metallic reflectors1 is %[n 9 ! annex$ figure1 :]e ,m ,c ,d ,n is ! body ( ! cam]a1 m n o p ! tube :i* is mov$ out & 9 by a mill$ head atta*$ to ! p9ion :i* drives ! rack on ! tube m n o p4 ,! ,kaleidoscope ,a ,b ,l ,l1 exhibit+ ! figure :i* is to be copi$1 is tempor>ily fix$ 9 ?is tube by pieces ( cork or wood1 s t its axis1 or ! l9e ( junction ( ! reflectors1 may be p]p5dicul> to ! surface ( ! grey glass p q1 :i* c be tak5 out1 s z to all[ ! collodion or pap] slide to be plac$ 9 ! same groove4 ,illu/ration3 ,,fig4 #ec4 ,! pictures %\ld always be tak51 :5 x is possible1 by sunlight incid5t obliquely ^u ! object-box1 or ) ! illum9ators already describ$4 ,:5 ?is _c be done1 artificial light1 conta9+ ! act9ic or *emical rays1 may be ?r[n ^u ! object1 z %[n 9 ,fig4 #eb4 ,! light ( coal gas1 :i* may be cond5s$ = any l5g? ( "t ^u ! objects 9 ! object-box1 w be f\nd to answ] ! purpose2 b if a m rapid process is requir$1 we may1 z propos$ by ,mr4 ,m\le1 use ! ,b5gal lights1 :i* conta9 a l>ge quantity ( ! act9ic rays4#ag ,^! lights are compos$ ( six p>ts ( nitre1 two ( sulphur1 & "o ( ! sulphuret ( antimony4 ,! p[d] is made up 9 ! %ape ( a cone1 :i* is ignit$ at ! top2 b x w\ld be bett] to spread x out widely1 9 ord] t x may be cond5s$ ^u ! object-box4 ,! lime-ball light may also be employ$1 b ! ,bude light1 :i* is a coal gas flame1 r5d]$ m int5sely lum9\s by a /ream ( oxyg51 is pref]able to any o!r artificial flame4 ,9 us+ x1 or any o!r ( ! lights already m5tion$1 = obta9+ ,kaleidoscope figures1 x mu/ ei!r be plac$ v ne> ! object-box1 or cond5s$ ^u x by a l>ge l5s1 on acc\nt ( ! small size ( ! ap]ture at ! eye-end ( ! ,kaleidoscope4 #ag ,see ! ,j\rnal ( ! ,photographic ,society1 vol4 iv4 p4 #acg4 ,9 ! =mation ( ! ,kaleidoscope figures1 x is necess>y to pay p>ticul> att5tion to ! col\r ( ! objects ( :i* !y are to be compos$1 r$1 orange1 & d>k yell[ objects1 :i* transmit few1 if any1 act9ic rays1 %\ld n be employ$4 ,blue glasses1 :i* transmit no r$ rays1 are act9ically m lum9\s ?an col\rless glasses1 & !re=e pale blue1 pale gre51 & pale yell[ glasses may be advantage\sly comb9$ ) col\rless glasses z objects = ! object-box4 ,:5 we wi% to copy photographically ! pictures obta9$ f ext]nal objects1 we mu/ use ! ,telescopic ,kaleidoscope ( ,mr4 ,bates1 by :i* ! images ( ^! objects are =m$ at ! extremity ( ! reflectors4 ,^! objects may be fl[]s1 plants1 ar*itectural ornam5ts1 or p>ts ( !m1 pa9t+s1 photographs1 /atues1 or loose & irregul>ly plac$ mat]ials ( any k9d4 ,9 ! figures creat$ by ! common ,kaleidoscope1 we mu/ tru/ to *ance = ! =mation ( ! figures1 & c only *oose ^? :i* we l out ( a l>ge numb] accid5tally =m$2 b :5 we make use ( ext]nal objects1 we c gr\p !m & illum9ate !m 9 any mann] we *oose1 select+ ^? =ms & col\rs :i*1 :5 comb9$1 produce ! effect t we desire4 ,?is p[]1 ( arrang+ ! objects1 :5 9 contact ) ! ends ( ! reflectors1 may be obta9$ ) ! ,kaleidoscope ( ,mr4 ,bates1 %[n 9 ,fig4 #bi1 by remov+ ! ant]ior half ( ! cone :5 ! objects are opaque1 & plac+ ! cam]a 9 a v]tical position4 ,! objects be+ plac$ ^u a horizontal plate1 may1 if opaque1 be illum9at$1 by reflect$ light1 & ! picture ( !m1 :5 comb9$ by ! ,kaleidoscope1 tak5 9 ! same mann] z :5 ! in/rum5t 0 9 ! position %[n 9 ,fig4 #eb4 ,if ! figure is n :at we l1 we c %ift any individual object1 or remove x1 or replace x by ano!r1 till we are satisfi$ ) ! comb9ation4 ,! v same p[] ( alt]+ ! comb9ation1 may be obta9$ = transp>5t objects4 ,we h only to place ^! objects on a horizontal plate ( glass1 n connect$ ) ! ,kaleidoscope1 b capable ( be+ remov$ f x1 & aga9 br\ght close to ! ends ( ! reflectors4 ,:5 ! objects on ! glass plate h be5 put into _! prop] place1 s z to give ! desir$ picture1 ! plate is br\ght z ne> z possible to ! ends ( ! reflectors1 & ! objects are illum9at$ ei!r by sol> or o!r light reflect$ upw>ds ^u ! object-box4 ,,*apt] ,,xxii4 ,,on ,,! ,,advantages ,,( ,,! ,,kaleidoscope ,,z ,,an ,,in/rum5t ,,( ,,amusem5t4 ,! spl5did discov]ies :i* h be5 made ) ! telescope & microscope h inve/$ !m ) a philosophical "* :i* c nev] be atta*$ to any o!r in/rum5t4 ,x is only1 h[ev]1 9 ! h&s ( ! a/ronom] & naturali/ t !y are consecrat$ to ! great objects ( sci5ce2 _! ord9>y possessors employ !m solely z in/rum5ts ( amusem5t1 & x is s+ul> to rem>k h[ soon !y lose _! novelty & int]e/ :5 devot$ to ?is inf]ior purpose4 ,! sol> microscope1 ! cam]a obscura1 & ! magic lant]n1 are equally %ortliv$ 9 _! p[]s ( ent]ta9m5t2 & ev5 ! wond]s ( ! electrical & galvanic app>atus are call$ =?1 at long int]vals1 = ! occasional purposes ( in/ruct+ ! "y1 or a/oni%+ ! ignorant4 ,a s]5ity ( sky v uncommon 9 our nor!rn climate1 is absolutely necess>y = display+ ! p[]s ( "s ( ! prec$+ in/rum5ts2 & ! effects ( ! re/ c only be exhibit$ aft] mu* previ\s prep>ation4 ,f ^! causes1 b pr9cipally f a want ( v>iety 9 _! exhibitions1 !y h con/antly fail$ to excite1 9 ord9>y m9ds1 t int5se & cont9u$ int]e/ :i* might h be5 expect$ f ! +5uity ( _! con/ruction & ! spl5d\r ( _! effects4 ,! pleasure :i* is d]iv$ f ! use ( musical in/rum5ts is ( a diff]5t k9d1 & f> m int5se 9 its effects1 & m g5]al 9 its influ5ce ?an t :i* is obta9$ f any ( ! prec$+ in/rum5ts4 ,!re are1 inde$1 few m9ds t are n alive to ! soo?+ & exhil>at+ influ5ce ( musical s\nds1 or t d n associate !m ) ! de>e/ & mo/ t5d] sympa?ies ( our nature4 ,b ! e> is n ! only av5ue to ! he>t2 & ?\gh sorr[ & di/ress are repres5t$ by notes ( a deep & solemn "*1 & happ9ess & gaiety by m light & playful tones1 ! same k9d ( feel+s may also be excit$ by ! exhibition ( d>k & gloomy col\rs1 & by ! display ( bright & arial t9ts4 ,! association1 inde$1 is n s p[]ful 9 ! "o case z 9 ! o!r1 = we h be5 taught f our infancy1 9 consequ5ce ( ! connexion ( music & poetry1 to associate p>ticul> s5tim5ts ) p>ticul> s\nds2 b !re c be no d\bt t ! association ( col\r is naturally z p[]ful z t ( s\nd1 & t a p]son :o has nev] li/5$ to any o!r music b t ( nature1 nor se5 any o!r col\rs b ^? ( ! mat]ial _w1 might h 8 feel+s z p[]fully excit$ ?r\gh ! m$ium ( ! eye z ?r\gh t ( ! e>4 ,! fir/ p]son :o attempt$ to supply ! organ ( vision ) ! luxuries ( light & col\r1 0 ,fa!r ,ca/el1 a le>n$ ,jesuit1 :o _h di/+ui%$ himself *iefly by 8 opposition to ! spl5did optical discov]ies ( ,newton4 ,ab\t ! ye> #agbe or #agbf1 he publi%$ 9 ! ,m]cure de ,p>is1 8 fir/ ideas ( an organ1 or ocul> h>psi*ord4 ,a full acc\nt ( ?is curi\s in/rum5t 0 aft]w>ds publi%$ at ,hamburgh1 9 #agci1 by ,m4 ,tellemann1 a ,g]man musician1 :o _h se5 "o ( ! h>psi*ords 9 ! possession ( ! inv5tor1 :5 he 0 on a visit to ,p>is4 ,?is acc\nt 0 aft]w>ds translat$ into ,fr5*1 & pr9t$ at ! end ( ,ca/el's ,l',optique des ,c\leurs1#ah :i* appe>$ at ,p>is 9 #agdj4 ,! ocul> h>psi*ord is a common h>psi*ord1 fitt$ up 9 su* a mann]1 t :5 a c]ta9 s\nd is produc$ by /rik+ ! keys1 a col\r relat$ to t s\nd is at ! same in/ant exhibit$ to ! eye 9 a box or frame connect$ ) ! h>psi*ord2 s t :5 a piece ( music is play$ = ! gratification ( ! e>1 ! eye is simultane\sly delight$ by ! display ( correspond+ col\rs4 #ah ,?is "w is entitl$1 ,l',optique des ,c\leurs1 fonde sur les simples obs]vations et t\rn surt\t la pratique de la pe9ture1 de la te9ture1 et des autres arts colori/es4 ,p> le ,r4 ,p4 ,ca/el1 ,jesuite4 ,p>is1 #agdj4 ,9 adju/+ ! col\rs & ! s\nds1 ,ca/el lays d[n ! foll[+ six propositions3-- #a/1--,!re is a fundam5tal & primitive s\nd 9 nature1 :i* may be call$ ut1 & !re is also an orig9al & primitive col\r1 :i* is ! f\ndation ( all o!r col\rs1 namely1 blue4 #b;d1--,!re are ?ree *ords1 or ess5tial s\nds1 :i* dep5d ^u ! primitive s\nd ut1 & :i* compose ) x a primitive & orig9al accord1 & ^! are ut1 mi1 sol4 ,!re are also ?ree orig9al col\rs dep5d+ on ! blue1 :i*1 :ile !y are n compos$ ( any o!r col\rs1 produce !m all1 namely1 blue1 yell[1 & r$4 ,! blue is "h ! note ( ! tone1 ! r$ is ! fif?1 & ! yell[ is ! ?ird4 #c;d1--,!re are five tonic *ords1 ut1 re1 mi1 sol1 la1 & two semitonic *ords1 fa & si4 ,!re are also five tonic col\rs1 to :i* all ! re/ are ord9>ily relat$1 namely1 blue1 gre51 yell[1 r$1 & violet1 & two semitonic or equivocal col\rs1 namely1 aurora & violant 7relat$ to ! orange & indigo ( ,newton74 #d?1--,out ( ^! five entire tones1 & two semitones1 is =m$ ! diatonic scale1 ut1 re1 mi1 fa1 sol1 la1 & si2 &1 9 l mann]1 out ( ! five entire or tonic col\rs1 & ! two demi-col\rs1 are =m$ ! gradation ( col\rs1 blue1 gre51 yell[1 aurora1 r$1 violet1 & violant2 = ! blue leads to gre51 :i* is demi-blue2 ! yell[ to aurora1 :i* is gild$ yell[2 ! aurora leads to r$1 ! r$ to violet1 :i* is two-?irds ( r$1 & "o-?ird ( blue2 & ! violet to violant1 :i* has m blue ?an r$4 #e?1-- ,! entire tones divide !mselves into semitones2 & ! five entire tones ( ! scale or gamut1 compreh5d+ 9 ?is ! two natural semitones1 make twelve semitones1 viz41 ut natural1 ut dieze1 re1 re dieze1 mi1 fa1 fa dieze1 sol1 sol dieze1 la1 la dieze1 & si4 ,9 l mann] !re are twelve demi-col\rs1 or demi-t9ts1 & !re c be nei!r m nor less1 accord+ to ! op9ion ( pa9t]s !mselves1 & z may be demon/rat$ by o!r means4 ,^! col\rs are blue1 sea-gre51 gre51 olive1 yell[1 aurora1 orange1 r$1 crimson1 violet1 aga!1 & violant4 ,blue leads to sea-gre51 :i* is a gre5i% blue2 sea-gre5 leads to gre52 gre5 to olive1 :i* is a yell[i% gre52 olive to yell[2 yell[ to aurora2 aurora to orange2 orange to r$1 ! col\r ( fire2 r$ to crimson1 :i* is r$ mix$ ) a little blue2 crimson to violet1 :i* is /ill m blue2 violet to aga!1 or blui% violet2 & aga! to violant4 #f?1--,! progression ( s\nds is 9 a circle1 sett+ out f ut1 & return+ back3 ?us1 ut1 mi1 sol1 ut1 or ut1 re1 mi1 fa1 sol1 la1 si1 ut4 ,?is is call$ an octave1 :5 ! la/ ut is "o-half m acute ?an ! fir/4 ,! col\rs also h _! progression 9 a circle4 #g?1--,aft] an octave1 ut1 re1 mi1 fa1 sol1 la1 si1 !re recomm5ces a new "o1 :i* is "o-half m acute1 & ! :ole circle ( music produces sev]al octaves4 ,su* are ! pr9ciples ^u :i* ! ocul> h>psi*ord 0 f\nd$2 b ?\gh ! in/rum5t1 f its s+ul>ity1 excit$ great att5tion :5 x 0 fir/ con/ruct$1 we h n be5 able to le>n t x 0 ev] suppos$ to possess ! p[] ( af=d+ pleasure to ! eye4 ,x mu/ be obvi\s1 inde$1 to any p]son :o consid]s ! subject1 t col\r1 indep5d5t ( =m1 is incapable ( yield+ a cont9u$ pleasure4 ,masses ( ri* & h>moni\s t9ts1 foll[+ "o ano!r 9 succession1 or comb9$ accord+ to c]ta9 laws1 w\ld no d\bt give satisfaction to a p]son :o _h n be5 famili> ) ! contemplation ( col\rs2 b ?is satisfaction w\ld n be p]man5t1 & he w\ld cease to admire !m z soon z !y ceas$ to be new4 ,col\r is a m]e accid5t ( light1 :i* communicates ri*ness & v>iety to objects t are o!rwise beautiful2 b p]fection ( =m is a s\rce ( beauty1 indep5d5t ( all col\rs2 & x is !re=e only f a comb9ation ( ^! two s\rces ( beauty t a s5sation ( pleasure c be excit$4 ,^? :o h be5 9 ! habit ( us+ a correct ,kaleidoscope1 furni%$ ) prop] objects1 w h no hesitation 9 admitt+ t ?is in/rum5t realizes1 9 ! fulle/ mann]1 ! =m]ly *im]ical idea ( an ocul> h>psi*ord4 ,! comb9ation ( f9e =ms1 & ev]-v>y+ t9ts1 :i* x pres5ts 9 succession to ! eye1 h already be5 f\nd1 by exp]i5ce1 to communicate to ^? :o h a ta/e = ?is k9d ( beauty1 a pleasure z int5se & z p]man5t z t :i* ! f9e/ e> d]ives f musical s\nds4 ,an eye = admir+ & appreciat+ ! effect ( f9e =ms1 seems1 inde$1 to be mu* m g5]al ?an an e> = music2 & we h he>d ( _m cases :]e ! t$ium ( sev]e & cont9u$ indisposition has be5 remov$1 & :]e _m a dull & solit>y h\r has be5 r5d]$ *e]ful1 by ! unceas+ v>iety ( ent]ta9m5t :i* ! ,kaleidoscope af=d$4 ,9 "o respect1 inde$1 ?is in/rum5t is sup]ior to all o!rs4 ,:5 x is once prop]ly con/ruct$1 its effects are exhibit$ )\t ei!r skill or lab\r2 & s num]\s are its applications1 & s inexhau/ible its /ores1 t ! obs]v] is con/antly flatt]$ ) ! belief t he has obta9$ results :i* 7 nev] se5 be=e1 & t he has ei!r improv$ ! in/rum5t1 or ext5d$ its p[]1 by new applications4 ,su* are ! advantages1 z an in/rum5t ( amusem5t1 :i* ! ,kaleidoscope possesses1 ev5 9 its pres5t imp]fect /ate4 ,to :at degree ( p]fection x may yet arrive1 x is n easy to anticipate2 b we may v5ture to pr$ict1 because we see ! /eps by :i* ! pr$iction is to be fulfill$1 t comb9ations ( =ms & col\rs may be made to succe$ ea* o!r 9 su* a mann] z to excite s5tim5ts & ideas ) z mu* vivacity z ^? :i* are excit$ by musical composition4 ,if x be true t !re are h>monic col\rs :i* inspire m pleasure by _! comb9ation ?an o!rs2 t dull & gloomy masses1 mov+ sl[ly be=e ! eye1 excite feel+s ( sadness & di/ress2 & t ! arial trac]y ( light & evanesc5t =ms1 enri*$ ) lively col\rs1 are capable ( inspir+ u ) *e]fulness & gaiety2 !n x is unque/ionable1 t1 by a skilful comb9ation ( ^! pass+ visions1 ! m9d may d]ive a degree ( pleasure f> sup]ior to t :i* arises f ! imm$iate impression :i* !y make ^u ! organ ( vision4 ,a v simple piece ( ma*9]y is alone necess>y = introduc+ objects ( diff]5t =ms & col\rs1 = v>y+ ! direction ( ! motion across ! angul> ap]ture1 & = accommodat+ ! velocity ( _! motion to ! effect :i* x is int5d$ to produce4 ,^! comb9ations ( col\rs & =ms may be adapt$ to a piece ( music1 & _! succession exhibit$ on a scre5 by means ( ! electric1 or lime-ball1 or o!r lights to :i* we h already _h occasion to ref]4 ,! col\r$ objects might be fix$ betwe5 long /ripes ( glass1 mov$ horizontally or obliquely across ! ends ( ! reflectors2 & ! effects ?us obta9$ might be v>i$ by ! occasional introduction ( revolv+ object-boxes1 conta9+ objects ( v>i\s col\rs & =ms1 p>tly fix$ & p>tly movable4 ,simil> =ms 9 diff]5t col\rs1 & 9 t9ts ( v>y+ int5sity1 los+ & resum+ _! peculi> "* ) diff]5t velocities1 & 9 diff]5t times1 might exhibit a di/9ct relation betwe5 ! optical & ! ac\/ic ph5om5a simultane\sly pres5t$ to ! s5ses4 ,fla%es ( light1 col\r$ & col\rless1 & cl\ds ( diff]5t dep?s ( %ad[1 advanc+ into1 or em]g+ f ! c5tre ( symmetry1 or pass+ across ! radial l9es ( ! figure at diff]5t obliquities1 w\ld assi/ 9 m>k+ m emphatically ! gay or ! gloomy s\nds ) :i* !y are accompani$4 ,a slight idea ( ! effects :i* might be expect$ f an +5i\s piece ( me*anism = creat+ & comb9+ ! v>i\s optical ph5om5a1 & exhibit+ !m 9 connexion ) musical s\nds1 may be obta9$ by a s+le obs]v]1 :o looks into a f9e ,kaleidoscope1 firmly fix$ ^u a /&1 & produces ) 8 two h&s all ! v>iations 9 =m & col\r :i* he c effect by su* inadequate means1 & :i* he consid]s appropriate to ! musical piece t accompanies !m4 ,,*apt] ,,xxiii4 ,,hi/ory ,,( ,,! ,,comb9ations ,,( ,,plane ,,mirrors ,,:i* ,,h ,,be5 ,,suppos$ ,,to ,,resemble ,,! ,,kaleidoscope4 ,x has always be5 ! fate ( new inv5tions to h _! orig9 ref]r$ to "s remote p]iod2 & ^? :o lab\r to enl>ge ! b\nd>ies ( sci5ce1 or to multiply ! means ( improvem5t1 are de/9$ to le>n1 at a v e>ly p]iod ( _! c>e]1 t ! desire ( do+ ju/ice to ! liv+ is a mu* less p[]ful pr9ciple ?an t ( be+ g5]\s to ! dead4 ,?is mode ( di/ribut+ fame1 injuri\s z x is to ! progress ( sci5ce1 by tak+ away "o ( ! /ronge/ excitem5ts ( e>ly g5ius1 has yet ! advantage ( err+ on ! side ( g5]osity2 & !re are few p]sons :o w\ld reclaim aga9/ a decision inve/$ ) su* a "*1 7 x pron\nc$ by ! grave hi/orian ( sci5ce1 :o _h und]/ood & /udi$ ! subject to :i* x ref]r$4 ,! app>5t simplicity1 bo? ( ! !ory & ! con/ruction ( ! ,kaleidoscope1 has deceiv$ v well-mean+ p]sons into ! belief t !y und]/ood its mode ( op]ation2 & x 0 only ^? t possess$ m ?an a mod]ate %>e ( optical k1 :o saw t x 0 n only m difficult to und]/&1 b also m difficult to execute1 ?an mo/ ( ! philosophical in/rum5ts n[ 9 use4 ,! p]sons :o consid]$ ! ,kaleidoscope z an in/rum5t consi/+ ( two reflectors1 :i* multipli$ objects1 :]ev] ^! objects 7 plac$1 & :atev] 0 ! position ( ! eye1 provid$ t x receiv$ only ! reflect$ rays1 7 at no loss to f9d num]\s c&idates = ! inv5tion4 ,all ^?1 inde$1 :o _h obs]v$ ! multiplication & circul> arrangem5t ( a fire blaz+ betwe5 two poli%$ plates ( brass or /eel2 :o _h dress$ !mselves by ! aid ( a pair ( look+-glasses1 or :o _h obs]v$ ! effects ( two mirrors plac$ ^u ! rectangul> sides ( a draw+-room1 7 entitl$1 ^u su* a def9ition1 to be con/itut$ inv5tors ( ! ,kaleidoscope4 ,! same claim might be urg$ = e jewell] :o _h erect$ 9 8 w9d[ two p]p5dicul> mirrors1 & plac$ 8 w>es be=e !m1 9 ord] to be multipli$ & exhibit$ to advantage2 & = e ,dut* toy-mak]1 & deal] 9 optical wond]s1 :o _h manufactur$ %[-boxes1 = ! purpose ( heap+ toge!r1 9 "s sort ( ord]1 a cr[d ( images ( ! same object1 ( diff]5t int5sities1 se5 "u diff]5t angles1 & pres5t+ diff]5t sides to ! eye4 ,?is mode ( gr\p+ images1 dissimil> 9 _! degree ( light1 dissimil> 9 _! magnitude1 & dissimil> 9 _! v outl9es1 produc$ su* a poor effect1 t ! reflect+ %[-boxes h = a long s]ies ( ye>s disappe>$ f among ! numb] ( philosophical toys4 ,f ^! causes1 ! c&idates = ! m]it ( inv5t+ ! ,kaleidoscope h be5 s num]\s1 t !y h />t$ up 9 e "p ( ! _w2 & _m individuals1 :o are sc>cely acqua9t$ ) ! equality ( ! angles ( incid5ce & reflexion1 h n scrupl$ to fav\r ! _w ) an acc\nt ( ! improvem5ts :i* !y fancy !y h made ^u ! in/rum5t4#ai #ai ,x w\ld be an easy matt] to amuse ! read] ) an acc\nt ( ^! improvem5ts4 ,"o ( ! mo/ notable ( !m consi/s 9 cov]+ ! back ( ! reflectors ) :ite pa9t1 = ! purpose ( increas+ ! light ( ! circul> field4 ,?is s*eme is id5tically ! same z if ! au?or _h propos$ to improve ! magnific5t telescopes ( ,h]s*el1 :5 r5d]$ d>k ) a high magnify+ p[]1 by :ite-wa%+ ! int]ior ( ! tube4 ,! e>lie/ writ] :o appe>s to h describ$ ! use ( two plane mirrors1 0 ,bapti/a ,porta1 :o has giv5 an acc\nt ( sev]al exp]im5ts :i* he p]=m$ ) !m1 9 ! second *apt] ( ! sev5? book ( 8 ,magia ,naturalis4 ,z ! comb9ation ( plane mirrors :i* he !re describes has be5 repres5t$ z ! same z ! ,kaleidoscope1 we %all give ! passage at full l5g?3-- ,speculum planis multividum con/ru]e4 8,speculum con/ruitur1 quod polyphaton id e/ multorum visibilium dicitur1 illud enim ap]i5do et claud5do solius digiti vig9ti et plura demon/rat simulacra4 ,sic igitur id p>abis4 rea duo specula vel cry/all9a rectangula sup] basim e&em erigantur1 s9tque 9 hemiolia proportione1 vel alia1 et secundum longitud9is latus unum simul collig5tur1 ut libri in/> apte claudi et ap]iri poss9t1 et anguli div]s5tur1 qualia ,v5etiis factit>i sol5t3 faciem enim unam objici5s1 9 utroque plura c]nes ora1 et hoc quanto arctius claus]is1 m9orique fu]9t angulo3 ap]i5do autem m9u5tur2 et obtusiori c]nes angulo1 pauciora num]o conspici5tur4 ,sic digitum o/5d5s1 non nisi digitos c]nes1 dextra insup] dextra1 et s9i/ra s9i/ra convisuntur2 quod speculis contr>ium e/3 mutuaque id ev5it reflexione1 et pulsatione1 unde imag9um vicissitudo40 --,edit4 ,am/elod1 #affd4 ,! foll[+ is an exact & lit]al translation ( ?is passage3-- ,h[ to con/ruct a multiply+ speculum out ( plane ones4 ,a speculum is con/ruct$1 call$ polyphaton1 t is1 :i* %[s _m objects1 = by op5+ & %utt+ x1 x exhibits tw5ty & m images ( ! f+] alone4 ,y w !re=e prep>e x 9 ! foll[+ mann]3--,let two rectangul> specula ( brass or cry/al be erect$ ^u ! same base1 & let _! l5g? be "o & a half times _! wid?1 or 9 any o!r proportion2 & let two ( _! sides be plac$ toge!r1 s t !y may be op5$ & %ut l a book1 & ! angles v>i$1 z !y are g5]ally made at ,v5ice4 ,= by pres5t+ y\r face1 y w see 9 bo? m faces ! m !y are %ut1 & ! less t ! angle is2 b !y w be dim9i%$ by op5+ x1 & y w see few] z y obs]ve ) a m obtuse angle4 ,if y exhibit y\r f+]1 y w see only f+]s1 ! "r f+]s be+ se5 on ! "r side1 & ! left on ! left side1 :i* is contr>y to :at happ5s 9 look+-glasses1 & ?is arises f ! mutual reflexion & repulsion :i* produce a *ange ( ! images4#bj #bj ,we reque/ t ! read] w take ! tr\ble ( comp>+ ) ! orig9al ! foll[+ translation ( ,bapti/a ,porta's description1 :i* 0 publi%$ 9 ,london1 & copi$ into all ! =eign newspap]s1 etc4 ,we hope ! translator ( x _h no improp] motive 9 alt]+ ! obvi\s mean+ ( ! orig9al2 yet x is s+ul>1 t 9 ! j\rnal :]e ?is translation appe>$1 ! specification ( ! pat5t 0 publi%$ "u ! title ( ,directions = mak+ ! ,kaleidoscope1 purport+ to be an orig9al communication to t j\rnal1 ! "n ( ! pat5tee1 & ! te*nical p>ts ( ! specification hav+ be5 left out1 app>5tly to promote ! belief t !re 0 no pat5t1 & t e p]son might make !m ) impunity4 ,! foll[+ is ! translation allud$ to3-- 8,9 ! foll[+ mann] we may con/ruct a mirror = see+ a multitude ( objects on a pla9 surface4 ,?is k9d ( mirror1 :5 con/ruct$1 is :at is call$ polyphaton1 t is to say1 multiply+1 = by op5+ & %utt+1 x %[s tw5ty & m images ( "o s+le f+]4 ,if1 !re=e1 y wi% to prep>e x1 let two braz5 or cry/al rectangul> mirrors be erect$ on ! same base1 & let ! proportion ( l5g? be "o & a half ( ! wid?1 or any o!r proportion2 & let ea* side = ! :ole ( its l5g? be s connect$ toge!r t !y may easily be %ut & op5$ l a book1 & t ! angles may be v>i$1 z !y are usually con/ruct$ at ,v5ice2 = if y place "o object opposite to ! face ( ea*1 y w see sev]al figures2 & ?is 9 proportion z y %ut x clos]1 & ! angle %all be less4 ,b1 by op5+1 ! objects w be r$uc$ 9 numb]1 & ! m obtuse ! angle "u :i* y see x1 ! few] objects w be se54 ,s if y exhibit y\r f+] z ! object1 y w see no?+ b f+]s4 ,! "r f+]s w be se5 on ! "r side1 & ! left on ! left side1 :i* is contr>y to ! usual cu/om ) look+-glasses2 b ?is happ5s f ! mutual reflexion & repulsion :i* produce a *ange ( ! images40 ,x is q obvi\s1 f ! prec$+ passage1 t ! multiply+ speculum describ$ by ,porta 0 n an inv5tion ( 8 own1 b _h be5 long made at ,v5ice4 ,9 ! v next *apt]1 inde$1 :]e he describes a speculum !atrale or amphi!atrale 7! %[-box ( ,h>ris & o!r mod]n au?ors71 he expressly /ates1 t a multiply+ speculum 0 inv5t$ by ! anci5ts4--8,speculum autem planis compactum1 cui si unum spectabile demon/rabitur1 plura illius rei simula*ra demon/rabit1 prud5s inv5it vetu/as2 ut ex quibusdam ,ptolemi scriptis qu circumf]untur p]cipitur20 t is1 8a speculum consi/+ ( plane ones1 :i*1 :5 "o object is pres5t$ to x1 w exhibit sev]al images ( x1 0 inv5t$ by skilful antiquity1 z appe>s f "s ( ! writ+s ( ,ptolemy40 ,?is speculum1 :i* consi/s ( sev]al mirrors arrang$ 9 a polygon1 ) ! object )9 x1 is *>act]iz$ by ,porta z pu]ile1 & mu* less wond]ful & agreeable ?an "o ( 8 own1 :i* he proce$s to describe4 ,?is new speculum consi/s ( t5 mirrors1 plac$ )9 a box1 9 a sort ( polygonal =m1 ) "o ( ! sides ( ! polygon op54 ,ar*itectural columns1 pictures1 gems1 pe>ls1 col\r$ birds1 etc41 are all plac$ )9 ! box1 & _! images are se5 heap$ toge!r 9 inextricable disord]1 z a :ole1 b s z to a/oni% ! spectator by _! numb]1 & by ! arrangem5t ( individual gr\ps4 ,porta speaks ( ?is effect z s beautiful1 8ut nil jucundius nil c]te admirabilius oculis occurset no/ris10--t no?+ m agreeable1 & c]ta9ly no?+ m admirable1 0 ev] pres5t$ to our eyes4 ,x w\ld be an insult to ! capacities ( ! mo/ ord9>y read]s to %[ t ! in/rum5ts "h describ$ by ,bapti/a ,porta h no f>!r connexion ) ! ,kaleidoscope ?an t !y are compos$ ( plane mirrors4 ,! sole purpose ( ^! in/rum5ts 0 to multiply objects by reflexion2 & s little did ! idea ( produc+ a symmetrical picture ent] into ,bapti/a ,porta's contemplation1 t he directs ! mirrors to be plac$ at any angle1 because ! multiply+ prop]ty ( ! mirrors is equally develop$1 :atev] be ! angle ( _! incl9ation4 ,! %[-box ( :i* ,porta speaks ) su* admiration1 has s _m mirrors1 & ^! are plac$ at su* angles1 t n "o ( ! effects ( ! ,kaleidoscope c be produc$ f !m4 ,its beauty is entirely d]iv$ f ! accumulation ( individual images4 ,! next competitor = ! inv5tion ( ! ,kaleidoscope is ! celebrat$ ,kir*]1 :o describes1 z an inv5tion ( 8 own1 ! con/ruction ( two mirrors :i* c be op5$ & %ut l ! leaves ( a book4 ,?is in/rum5t is repres5t$ 9 ,fig4 #ed1 & is describ$ 9 ! foll[+ passage3-- ,illu/ration3 ,,fig4 #ed4 ,,p>a/asis ,i4 ,specula plana multiplicativa sunt speci]um unius rei4 ,vide ,fig4 #ed4 ,mira qudam et a nem9e1 quod sciam obs]vata proprietas elucescit 9 duobus speculis ita con/ructis1 ut ad in/> libri claudi et ap]iri poss9t2 ponantur illa 9 plano quopiam1 9 quo semicirculum 9 gradus suos descriptum habeas4 ,si enim punctum1 9 quo specula committuntur1 9 c5tro semicirculi /atuas1 ita ut utrumque speculi latus diametro insi/at1 semel tantam videbitur rei imago1 app>ebuntque du res1 una extra speculum v]a1 alt]a intra1 phanta/ica3 ,si v]o specula ita posu]is1 ut div>icatio lat]um #abj gradus int]cipiat1 videbis rei intra lat]a e/1 quia angulus reflexionis et incid5ti tantus e/1 quantus e/ angulus int]ceptus a lat]ibus1 videlicet #abj grad4 qui cum obtusius sit1 non nisi b9am imag9em caus>e pote/1 ut 9 ,propos4 v4 fol4 #hdh1 o/5sum e/4 ,si v]o specula int]cep]9t angulum #ij graduum1 videbis 9 plano circulum 9 quatuor p>tes divisum1 9 quibus totidem simulacra rei posit comp>abunt1 tria phanta/ica1 et unum v]um2 cum enim reflectio fiat ad angulos rectos utrumque latus reflect5s =mam causabit intra se alias duas =mas1 unde et consequ5tur pro multiplicatione lat]um =m multiplicabuntur1 qu et 9 reflectione lat]um normam s]vabunt uti 9 ,propos4 v4 fol4 #hdh1 o/5dimus4 ,porro si speculorum lat]a int]cep]9t angulum #gb graduum1 videbis 9 plano horizontali ef=m>i p]fectum et regul>e p5tagonum1 9 quo totidem =m app>ebunt1 item1 si sexag9ta graduum int]cep]9t angulum1 videbis hexagonum totidemque =mas qu9que nimirum phanta/icas unam v]am4 ,ita1 si speculorum angulus int]cep]it #ea gradus cum _/ comp>ebit p]fectum heptagonum1 cum totidem rei intra specula collocat =mis2 non secus angulus speculorum #de graduum dabit octogonum2 #dj graduum dabit enneagonum2 #cf graduum decagonum2 #cb graduum angulus cum _/ dabit endecagonum et d5ique angulus #cj graduum ref]et dodecagonum cum totidem =mis1 et sic 9 inf9itum2 ita ut semp] tot lat]um sit futurum polygonum anacampticum totidemque =m>um1 quot polygonum cuivis latus speculorum int]cipit div>icatio1 lat]a habu]it3 quorum omnium rationes dep5d5t a ,propos4 v4 prec$5tis di/9ctionis4 --,kir*]i1 ,ars ,magna ,lucis et ,umbr4 ,rom4 #afdf1 p4 #hij4 ,! foll[+ is a translation ( ! prec$+ passage3-- ,,p>a/asis ,i4 ,plane specula may be made to multiply ! images ( "o object4 ,see ,fig4 #ed4 ,a wond]ful1 &1 s f> z ,i "k1 a new prop]ty1 is exhibit$ by two specula1 s con/ruct$ t !y may be op5$ & %ut l a book4 ,if !y are plac$ ^u any plane1 9 :i* !re is a semicircle divid$ into degrees1 9 su* a mann] t ! po9t :]e ! specula meet is 9 ! c5tre ( ! circle1 & ! edge ( ea* speculum /&s ^u ! diamet] ( ! semicircle1 "o image only w be visible1 & !re w appe> two ?+s1 namely1 a real "o1 )\t ! specula1 & ano!r =m$ by reflexion beh9d !m1#ba & s on1 z 9 ! foll[+ table1 :]e ! fir/ column %[s ! incl9ation ( ! specula1 & ! second ! figure :i* is produc$3-- #ba ,i h ?r[n ! re/ ( ! passage into a tabul> =m1 t ! read] may see1 m readily1 ! effect produc$ by ! v>iation ( ! angle4 ,angle ( ,specula4 ,effect produc$4 #ahj "o image & "o object1 99#abj two images & "o object1 #ij f\r images1 99#gb a p5tagon & five =ms1 #fj a hexagon & six =ms1 99#ea_/ a heptagon & sev5 =ms1 #de an octagon & eight =ms1 99#dj an enneagon & n9e =ms1 #cf a decagon & t5 =ms1 99#cb_/ an endecagon & elev5 =ms1 #cj a dodecagon & twelve =ms1 & s on1 ad inf9itum1 ! polygon =m$ by reflexion hav+ always z _m sides z ! numb] ( times t ! angle ( ! specula is conta9$ 9 #cfj4 ,! comb9ation ( plane mirrors1 :i* ,kir*] describes 9 ! prec$+ extract1 is precisely ! same z t :i* is giv5 by ,bapti/a ,porta4 ,! latt]1 inde$1 only m5tions1 t ! numb] ( images increases by ! dim9ution ( ! angle1 :]eas ,kir*] gives ! numb] ( images produc$ at diff]5t angles1 & enum]ates ! regul> polygons :i* are ?us =m$4 ,x mu/ be q obvi\s to any p]son :o att5ds to ,kir*]'s description1 t ! idea nev] once occurr$ to him ( produc+ beautiful & symmetrical =ms by means ( plane mirrors4 ,8 sole object 0 to multiply a giv5 regul> =m a c]ta9 numb] ( times2 & he nev] imag9$ t1 :5 ! mirrors 7 plac$ at ! angles m>k$ ) an a/]isk1 !re c\ld be no symmetry 9 ! figure1 & no union ( ! two la/ reflect$ images1 unless 9 ! case :]e a regul> object 0 plac$1 ei!r by design or by accid5t1 9 a position symmetrically relat$ to bo? ! reflectors4 ,9 ,kir*]'s mirrors ! eye 0 plac$ 9 front ( !m4 ,! object !re=e 0 mu* ne>] ! eye ?an ! images1 & ! light ( ! diff]5t reflect$ images 0 n only extremely unequal1 b ! diff]5ce 9 _! angul> magnitude 0 su* t !y c\ld n possibly be unit$ into a symmetrical :ole4 ,f ! accid5tal circum/ance ( 8 us+ l9es ^u pap] z an object1 ! di/ortion ( ! pictures aris+ f ! errone\s position ( ! eye 0 prev5t$2 b if ! same comb9ation ( mirrors 7 appli$ to ! object-plates ( ! ,kaleidoscope1 x w\ld be f\nd utt]ly incapable ( produc+ any ( ! f9e =ms :i* are peculi> to t in/rum5t4 ,if x 7 necess>y to prove t ,kir*] & 8 pupils 7 entirely ignorant ( ! positions ( ! eye & ! object :i* are necess>y to ! production ( a picture1 symmetrical 9 all its p>ts1 & uni=mly illum9at$1 & t !y w5t no f>!r ?an ! m]e multiplication ( =ms t 7 previ\sly regul> & symmetrical1 we w\ld ref] ! read] to ,s*ottus' ,magia ,univ]salis ,natur et ,artis1 pr9t$ at ,wurtzb\rg 9 #afeg1 :]e he repeats1 almo/ ^w = ^w1 ! description ( ,kir*]1 & adds ! foll[+ curi\s obs]vation3--8,b x is n only ! objects plac$ 9 ! semicircle 9 ! angle ( ! glasses t are se5 & multipli$1 b also ^? :i* are m di/ant2 = example1 a wall1 ) its w9d[s1 & 9 ?is case ! multiplication produc$ by ! mirrors w create an imm5se public place1 adorn$ ) edifices & palaces40 ,?is passage %[s1 9 ! cle>e/ mann]1 n only t ! multiplication ( an object1 indep5d5t ( ! union ( ! multipli$ objects into a symmetrical :ole1 0 all t ,kir*] & 8 foll[]s propos$ to accompli%2 b also t !y 7 entirely unacqua9t$ ) ! effects produc$ by v>y+ ! di/ance ( ! object f ! mirrors4 ,if any p]son %\ld d\bt ! accuracy ( ?is obs]vation1 we w\ld reque/ him to take ,kir*]'s two mirrors1 to direct !m to a 8wall ) its w9d[s10 ei!r by ,kir*]'s me?od1 or ev5 by any o!r way t he *ooses1 & to contemplate 8! public place adorn$ ) edifices & ) palaces40 ,he w see heaps ( w9d[s & ( walls1 "s ( ! heaps be+ mu* l>g] ?an o!rs2 & "s be+ f>!r f1 & o!rs ne>] to1 ! c5tre2 & "s be+ d>k1 & o!rs lum9\s2 :ile all ( !m are disunit$4 ,let him n[ take a ,telescopic ,kaleidoscope1 & direct x to ! same object2 he w in/antly p]ceive ! mo/ p]fect ord] arise out ( confusion1 & he w n scruple to ackn[l$ge1 t no two ?+s 9 nature c be m diff]5t ?an ! effects :i* are produc$ by ^! two comb9ations ( mirrors4 ,illu/ration3 ,,fig4 #ee4 ,illu/ration3 ,,fig4 #ef4 ,we come n[ to consid] ! claims ( ,mr4 ,bradley1 ,pr(essor ( ,botany 9 ! ,univ]sity ( ,cambridge4 ,9 a "w1 entitl$1 ,new ,improvem5ts 9 ,plant+ & ,g>d5+1 publi%$ 9 #agag1 ?is au?or has drawn & describ$ ,kir*]'s app>atus z an inv5tion ( 8 own2 &1 in/ead ( hav+ 9 any respect improv$ x1 he has actually det]iorat$ x1 9 s f> z he has made ! bread? ( ! mirrors great] ?an _! height4 ,an exact copy ( ! mirrors us$ by ,bradley is %[n 9 ,fig4 #ee1 f :i* x w be at once se51 t x is precisely ! same z ,kir*]'s1 %[n 9 ,fig4 #ed4 ,we are f> f say+ t ,bradley /ole ! inv5tion f ,kir*]1 or t ,kir*] /ole x f ,bapti/a ,porta1 or t ,bapti/a ,porta /ole x f ! anci5ts4 ,!re is reason1 on ! contr>y1 to ?9k t ! app>atus _h be5 entirely =gott51 9 ! long int]vals :i* elaps$ betwe5 ^! diff]5t au?ors1 & !re c be no d\bt t ea* ( !m add$ "s little improvem5t to ! in/rum5t ( _! pr$ecessors4 ,bapti/a ,porta saw ! sup]iority ( two mirrors1 z a multiply+ ma*9e1 to a great] numb] us$ by ! anci5ts4 ,kir*] %[$ ! relation betwe5 ! numb] ( images & ! incl9ation ( ! mirrors2 & ,bradley1 ?\gh he r injur$ ! app>atus1 yet he _h ! m]it ( notic+1 t figures ^u pap]1 :i* _h a c]ta9 degree ( irregul>ity1 l ^? 9 ,fig4 #ef1 c\ld /ill =m a regul> figure4 ,9 ord] t ! read] may fully und]/& ,bradley's me?od ( us+ ! mirrors1 we %all give x 9 8 own words3-- 8,we mu/ *oose two pieces ( look+-glass 7says he71 ( equal bigness1 ( ! figure ( a long squ>e1 five in*es 9 l5g?1 & f\r 9 bread?2 !y mu/ be cov]$ on ! back ) pap] or silk1 to prev5t rubb+ (f ! silv]1 :i* w\ld else be too apt to crack (f by frequ5t use4 ,?is cov]+ = ! back ( ! glasses mu/ be s put on1 t no?+ ( x may appe> ab\t ! edges on ! bright side4 8,! glasses be+ ?us prep>$1 !y mu/ be laid face to face1 & h+$ toge!r1 s t !y may be made to op5 & %ut at pleasure1 l ! leaves ( a book2 & n[ ! glasses be+ ?us fitt$ = our purpose1 ,i %all proce$ to expla9 ! use ( !m4 8,draw a l>ge circle ^u pap]2 divide x into ?ree1 f\r1 five1 six1 sev51 or eight equal p>ts2 :i* be+ done1 we may draw 9 e "o ( ! divisions a figure1 at our pleasure1 ei!r = g>d5-plats or =tifications2 z1 = example1 9 ,fig4 #ee1 we see a circle divid$ into six p>ts1 & ^u ! division m>k$ ,f is drawn "p ( a design = a g>d54 ,n[1 to see t design entire1 :i* is yet confus$1 we mu/ place our glasses ^u ! pap]1 & op5 !m to ! six? "p ( ! circle1 i4e41 "o ( !m mu/ /& ^u ! l9e b1 to ! c5tre1 & ! o!r mu/ be op5$ exactly to ! po9t c2 s %all we discov] an entire g>d5-plot 9 a circul> =m 7if we look into ! glasses71 divid$ into six p>ts1 ) z _m walks lead+ to ! c5tre1 :]e we %all f9d a bas9 ( an hexagonal figure4 8,! l9e ,a1 :]e ! glasses jo91 /&s imm$iately ov] ! c5tre ( ! circle1 ! glass ,b /&s ^u ! l9e drawn f ! c5tre to ! po9t ,c1 & ! glass ,d /&s ^u ! l9e lead+ f ! c5tre to ! po9t ,e3 ! glasses be+ ?us plac$1 _c fail to produce ! complete figure we look =2 & s :atev] equal "p ( a circle y m>k out1 let ! l9e ,a /& always ^u ! c5tre1 & op5 y\r glasses to ! division y h made ) y\r compasses4 ,if1 in/ead ( a circle1 y w\ld h ! figure ( a hexagon1 draw a /raight l9e ) a p5 f ! po9t c to ! po9t b1 &1 by plac+ ! glasses z be=e1 y w h ! figure desir$4 8,s likewise a p5tagon may be p]fectly repres5t$1 by f9d+ ! fif? "p ( a circle1 & plac+ ! glasses ^u ! outl9es ( x2 & ! f\r? "p ( a circle w likewise produce a squ>e1 by means ( ! glasses1 or1 by ! same rule1 w give u any figure ( equal sides4 ,i easily suppose t a curi\s p]son1 by a little practice ) ^! glasses1 may make _m improvem5ts ) !m1 :i*1 p]haps1 ,i may n h yet discov]$1 or h1 = brevity sake1 omitt$ to describe4 8,x next foll[s t ,i expla9 h[1 by ^! glasses1 we may1 f ! figure ( a circle1 drawn ^u pap]1 make an oval2 & also1 by ! same rule1 repres5t a long squ>e f a p]fect squ>e4 ,to d ?is1 op5 ! glasses1 & fix !m to an exact squ>e2 place !m ov] a circle1 & move !m to & fro till y see ! repres5tation ( ! oval figure y l be/2 & s1 hav+ ! glasses fix$1 9 l mann] move !m ov] a squ>e piece ( "w till y f9d ! figure y desire ( a long squ>e4 ,9 ^! trials y w meet ) _m v>ieties ( designs4 ,z = in/ance1 ,fig4 #ef1 al?\gh x seems to conta9 b a confus$ repres5tation1 may be v>i$ into above two hundr$ diff]5t repres5tations1 by mov+ ! glasses ov] x1 :i* are op5$ & fix$ to an exact squ>e4 ,9 a ^w1 f ! mo/ trifl+ designs1 we may1 by ?is means1 produce "s ?\s&s ( good draughts4 8,b t ,fig4 #ef may yet be m intelligible & useful1 ,i h drawn on e side ( x a scale1 divid$ into equal p>ts1 by :i* means we may asc]ta9 ! j proportion ( any design we %all meet )9 x4 8,i h also m>k$ e side ( x ) a lett]1 z ,a1 ,b1 ,c1 ,d1 ! bett] to in=m my read] ( ! use ( ! inv5tion1 & put him 9 ! way to f9d out e design conta9$ 9 t figure4 8,example ,i4--,turn ! side ,a to any c]ta9 po9t1 ei!r to ! nor?1 or to ! w9d[ ( y\r room2 & :5 y h op5$ y\r glasses to an exact squ>e1 set "o ( !m on ! l9e ( ! side ,d1 & ! o!r on ! l9e ( ! side ,c1 y w !n h a squ>e figure f\r times z big z ! engrav$ design 9 ! plate3 b if t repres5tation %\ld n be agreeable1 move ! glasses 7/ill op5 to a squ>e7 to ! numb] #e ( ! side ,d1 s w "o ( !m be p>allel to ,d1 & ! o!r /& ^u ! l9e ( ! side ,c1 y\r fir/ design w !n be v>i$2 & s by mov+ y\r glasses1 9 l mann]1 f po9t to po9t1 ! draughts w diff] by e v>iation ( ! glasses1 till y h discov]$ at lea/ fifty plans1 diff]+ f "o ano!r4 8,example ,,ii4--,turn ! side m>k$ ,b1 ( ,fig4 #ef1 to ! same po9t :]e ,a 0 be=e1 & by mov+ y\r glasses z y did 9 ! =m] example1 y w discov] z great a v>iety ( designs z _h be5 obs]v$ 9 ! =ego+ exp]im5t2 !n turn ! side ,c to ! place ( ,b1 &1 manag+ ! glasses 9 ! mann] ,i h direct$ 9 ! fir/ example1 y may h a great v>iety ( diff]5t plans1 :i* 7 n 9 ! =m] trials2 & ! f\r? side1 ,d1 mu/ be manag$ 9 ! same mann] ) ! o!rs2 s t f "o plan alone1 n exce$+ ! bigness ( a man's h&1 we may v>y ! figure at lea/ two hundr$ times2 & s1 consequ5tly1 f five figures ( ! l nature1 we might %[ ab\t a ?\s& sev]al sorts ( g>d5-plats2 & if x %\ld happ5 t ! read] has any numb] ( plans = p>t]res or wild]ness-works by him1 he may1 by ?is me?od1 alt] !m at 8 pleasure1 & produce su* innum]able v>ieties1 t x is n possible ! mo/ able design] c\ld ev] h contriv$40 ,9 read+ ! prec$+ description1 ! foll[+ conclusions _c fail to be drawn by e p]son :o und]/&s x4 #a4 ,dr4 ,bradley1 l ,kir*]1 consid]s 8 mirrors z applicable to regul> figures1 su* z are repres5t$ 9 ,fig4 #ee1 & 0 entirely unacqua9t$ ) ! fact1 t ! incl9ation ( ! mirrors mu/ be an ev5 aliquot "p ( a circle4 ,?is is obvi\s1 f 8 /at+ t ! mirrors may be set at ! ?ird1 f\r?1 fif?1 six?1 sev5?1 or eigh? "p ( a circle2 = if he _h tri$ to set an irregul> object betwe5 ! mirrors :5 plac$ at ! ?ird1 fif?1 or sev5? "p ( #cfj1 he w\ld h f\nd t a complete figure c\ld n possibly be produc$4 #b4 ,f ! errone\s position ( ! eye 9 front ( ! mirrors1 !re is su* an inequality ( light 9 ! reflect$ sectors1 t ! la/ is sc>cely visible1 & !re=e _c be unit$ into a uni=m picture ) ! real objects4 #c4 ,z ! place ( ! eye 9 ,bradley's in/rum5t is 9 front1 & !re=e mu* ne>] ! object1 or sector1 se5 by direct vision1 ! angul> magnitudes ( all ! diff]5t sectors are diff]5t1 & h5ce !y _c unite into a symmetrical figure4 ,?is is s unavoidable a result ( ! errone\s position ( ! eye--a position too1 r5d]$ necess>y f ! absurd =m ( ! mirrors--t ,bradley actually employs 8 mirrors to conv]t a circle into an ellipse1 & a squ>e into a rectangle6 #d4 ,9 ,bradley's in/rum5t1 ! sectors ?us unequally %ap$1 & unequally illum9at$1 are all sep>at$ f "o ano!r1 by a space equal to ! ?ickness ( ! glass plates2 & f ! same cause1 ! images reflect$ f ! fir/ surface int]f]e ) ^? reflect$ f ! second1 & produce a confusion or ov]lapp+ ( images entirely incompatible ) a symmetrical picture4 ,^! results are d$uc$ ^u ! supposition t ! object consi/s ( l9es drawn ^u ! surface ( pap]1 ! only purpose to :i* ,bradley ev] appli$ 8 mirrors2 b :5 we attempt to use ^! mirrors z a ,kaleidoscope1 & apply !m to ! objects :i* are usually adapt$ to t in/rum5t1 we %all fail entirely1 z ! mirrors are utt]ly incapable ( produc+ ! beautiful & symmetrical =ms :i* belong to t in/rum5t4 ,we come n[ to consid] ! me?od ( apply+ ! mirrors to ! object %[n 9 ,fig4 #ee1 :i* is an exact1 b r$uc$ copy ( ,bradley's figure4 ,because ! angles ( ?is figure are #ij1 he directs t ! mirrors 8be op5$ & fix$ to an exact squ>e2 & t ! edge ( "o ( ! mirrors mu/ always be plac$ s z to co9cide exactly ) "o ( ! sides ( ! rectangle1 & c>efully kept 9 ?is l9e :5 ! position ( ! mirrors is *ang$40 ,h5ce x is manife/1 t ,bradley 0 entirely ignorant ( ! fundam5tal pr9ciple ( ! ,kaleidoscope1 namely1 t if ! incl9ation ( ! mirrors is an ev5 aliquot "p ( a circle1 & if !y are set 9 any position ^u any object or set ( objects1 h[ev] confus$1 or di/ort$1 or irregul>1 !y w create ! mo/ p]fect & symmetrical designs4 ,b ev5 if ,bradley _h be5 aw>e ( ?is pr9ciple 9 !ory1 nei!r he nor any o!r p]son 0 acqua9t$ ) ! mode ( con/ruct+ & fitt+ up ! reflectors1 9 ord] to r5d] !m capable ( produc+ ! effect4 ,! position ( ! eye1 = symmetry ( light1 & = symmetry ( =m2--! position ( ! mirrors1 to produce a p]fect junction ( ! la/ sectors2--! position ( ! object necess>y to produce an equality & p]fect junction betwe5 ! object & ! reflect$ images2--& ! me?od ( accompli%+ ?is = objects at all di/ances1 7 fundam5tal po9ts1 9 ! comb9ation ( plane mirrors1 :i*1 s f> z ,i "k1 h nev] be5 inve/igat$ by any au?or4 ,b ev5 ?\gh a k ( ^! !oretical po9ts _h be5 obta9$1 num]\s difficulties 9 ! practical con/ruction ( ! in/rum5t rema9$ to be surm\nt$2 & x requir$ no slight degree ( lab\r & att5tion to enable ! in/rum5t to develop1 9 ! mo/ simple & efficaci\s mann]1 ! v>i\s effects :i*1 9 !ory1 x 0 f\nd susceptible ( produc+4 ,z ! comb9ation ( mirrors1 describ$ by ,kir*] & ,bradley1 _h be5 long kn[n to opticians1 & _h excit$ s little att5tion t !y _h ev5 ceas$ to be notic$ 9 works on optical in/rum5ts1 x became necess>y to discov] "s o!r orig9 = ! ,kaleidoscope4 ,! ?irte5? & f\rte5? ,propositions ( ,wood's ,optics1 & "s analog\s propositions 9 ,h>ris's ,optics1 7 !re=e presum$ to be an anticipation ( ! inv5tion4 ,pr(essor ,wood gives a ma!matical inve/igation ( ! numb] & arrangem5t ( ! images =m$ by two reflectors1 ei!r incl9$ or p>allel to ea* o!r4 ,^! !orems assign no position to ! eye1 or to ! object1 & d n include ! pr9ciple ( inv]sion1 :i* is absolutely necess>y to ! production ( symmetrical =ms4 ,! !orems1 inde$1 :i* h no connexion :atev] ) any in/rum5t1 are true1 :atev] be ! position ( ! eye or ! object2 & ,mr4 ,wood has frankly ackn[l$g$1 8t ! effects produc$ by ! ,kaleidoscope 7 nev] 9 8 contemplation40#bb #bb ,see ,app5dix1 p4 #ahe4 ,! propositions 9 ,h>ris's ,optics relate1 l ,pr(essor ,wood's1 m]ely to ! multiplication & circul> arrangem5t ( ! ap]tures or sectors =m$ by ! incl9$ mirrors1 & to ! progress ( a ray ( light reflect$ betwe5 two incl9$ or p>allel mirrors2 & no allusion :atev] is made1 9 ! propositions !mselves1 to any in/rum5t4 ,9 ! propositions respect+ ! multiplication ( ! sectors1 ! eye ( ! obs]v] is nev] once m5tion$2 & ! proposition is true1 if ! eye has an inf9ite numb] ( positions2 :]eas1 9 ! ,kaleidoscope1 ! eye c only h "o position4 ,9 ! o!r proposition 7,prop4 ,,xvii47 respect+ ! progress ( ! rays1 ! eye & ! object are actually /at$ to be plac$ betwe5 ! reflectors2 & ev5 if ! eye _h be5 plac$ )\t ! reflectors1 z 9 ! ,kaleidoscope1 ! position assign$ x1 at a great di/ance f ! angul> po9t1 is a demon/ration t ,h>ris 0 entirely ignorant ( ! positions ( symmetry1 ei!r = ! object or ! eye1 & c\ld n h comb9$ two reflectors s z to =m a ,kaleidoscope = produc+ beautiful or symmetrical =ms4#bc ,x is important also to rem>k1 t all ,h>ris's propositions relate ei!r to sectors or to small circul> objects2 & t he supposes ! v same effects to be produc$ :5 ! incl9ation ( ! mirrors is an odd1 z :5 x is an ev51 aliquot "p ( a circle4 ,x is cle>1 !re=e1 t he 0 nei!r acqua9t$ ) ! fundam5tal po9t 9 ! !ory ( ! ,kaleidoscope1 nor ) any ( its practical effects4 ,! only practical "p ( ,h>ris's propositions is ! fif? & six? s*olia to ,prop4 ,,xvii4 ,9 ! fif? s*olium he proposes a sort ( catoptric box1 or ci/ula1 kn[n long be=e 8 "t1 compos$ ( f\r mirrors1 arrang$ 9 a mo/ unsci5tific mann]1 & conta9+ opaque objects betwe5 ! speculums4 8,:atev] !y are10 says he1 :5 speak+ ( ! objects1 8! upright figures betwe5 ! speculums %\ld be sl5d]1 & n too _m 9 numb]1 o!rwise !y w too mu* ob/ruct ! reflect$ rays f com+ to ! eye40 ,?is %[s1 9 a mo/ decisive mann]1 t ,h>ris knew no?+ ( ! ,kaleidoscope1 & t he has n ev5 improv$ ! common catoptric ci/ula1 :i* _h be5 kn[n long be=e4 ,! pr9ciple ( inv]sion1 & ! positions ( symmetry1 7 entirely unkn[n to him4 ,9 ! six? s*olium1 he speaks ( rooms l9$ ) look+-glasses1 & ( lum9\s amphi!atres1 :i* 7 kn[n ev5 to ! anci5ts1 & h be5 describ$ & figur$ by all ! old writ]s on optics4 #bc ,see ,*ap4 ,i4 pp4 #aa1 #ab1 :]e we h %[n t ,h>ris 0 n ev5 acqua9t$ ) ! way 9 :i* ! la/ sector is =m$ by reflexion4 ,,app5dix4 ,al?\gh ,i h no d\bt t ! obs]vations conta9$ 9 ! prec$+ ,*apt]s are suffici5t to satisfy e c&id & intellig5t p]son respect+ ! true nature ( all ! comb9ations ( plane mirrors t prec$$ ! inv5tion ( ! ,kaleidoscope1 yet z !re are _m :o are incapable1 f want ( optical k1 to und]/& ! comp>ison :i* has be5 made betwe5 !m1 ,i %all "h pres5t ! op9ions ( f\r ( ! mo/ em95t ma!maticians & natural philosoph]s4 ,! fir/ ( ^! is conta9$ 9 a note f ! late ,pr(essor ,wood1 ,ma/] ( ,/4 ,john's ,college1 ,cambridge1 writt5 9 reply to a lett]1 9 :i* ,i reque/$ him to say1 if he _h any idea ( ! effects ( ! ,kaleidoscope :5 he wrote ! ?irte5? & f\rte5? ,propositions ( 8 works on ,optics4 8,,/4 ,,john',s1 ,may #ai1 #ahah4 8,,sir1--,! propositions ,i h giv5 relat+ to ! numb] ( images =m$ by plane reflectors1 incl9$ to ea* o!r1 conta9 m]ely ! ma!matical calculation ( _! numb] & arrangem5t4 ,! effects produc$ by ! ,kaleidoscope 7 nev] 9 my contemplation4 ,my att5tion has = "s ye>s be5 turn$ to o!r subjects1 & ,i regret t ,i h n "t to read y\r ,optical ,treatise1 :i* ,i am sure w\ld give me great pleasure4--,i am1 ,sir1 y\r ob$i5t humble s]vant1 8,j4 ,,wood40 ,! foll[+ is ! op9ion ( ! late celebrat$ ,mr4 ,james ,watt3-- 8,x has be5 said "h10 says ,mr4 ,watt1 8t y took ! idea ( ! ,kaleidoscope f an old book on g>d5+4 ,my fri5d1 ! ,rev4 ,mr4 ,corrie1 has procur$ me a sight ( ! book4 ,x is ,bradley's ,improvem5ts ( ,plant+ & ,g>d5+4 ,london1 #agca1 ,"p ,,ii4 ,*ap4 ,i4 ,x consi/s ( two pieces ( look+-glass1 ( equal bigness1 ( ! figure ( a long squ>e1 five in*es long1 & f\r in*es high1 h+$ toge!r ^u "o ( ! n>r[ sides1 s z to op5 & %ut l ! leaves ( a book1 :i*1 be+ set ^u _! edges ^u a draw+1 w %[ x multipli$ by repeat$ reflexions4 ,?is in/rum5t ,i h se5 9 my fa!r's possession sev5ty ye>s ago1 & frequ5tly s9ce1 b :at has become ( x ,i "k n4 ,9 my op9ion1 ! application ( ! pr9ciple is v diff]5t f t ( y\r ,kaleidoscope40 ,! foll[+ is ! op9ion ( ! late ,mr4 ,playfair1 ,pr(essor ( ,natural ,philosophy 9 ! ,univ]sity ( ,ed9burgh3-- 8,,ed9burgh1 ,may #aa1 #ahah4 8,i h exam9$ ! ,kaleidoscope inv5t$ by ,dr4 ,brew/]1 & comp>$ x ) ! description ( an in/rum5t :i* x has be5 said to resemble1 con/ruct$ by ,bradley 9 #agag4 ,i h also comp>$ its effect ) an exp]im5t to :i* x may be ?\ght to h "s analogy1 describ$ by ,mr4 ,wood 9 8 ,optics1 ,prop4 ,,xiii4 & ,,xiv4 8,f bo? ^! contrivances1 & f e optical in/rum5t ) :i* ,i am acqua9t$1 ! ,kaleidoscope appe>s to diff] ess5tially1 bo? 9 its effect & 9 ! pr9ciples ( its con/ruction4 8,z to ! effect1 ! ?+ produc$ by ! ,kaleidoscope is a s]ies ( figures pres5t$ ) ! mo/ p]fect symmetry1 s z always to compose a :ole1 9 :i* no?+ is want+ & no?+ r$undant4 ,x matt]s n :at ! object be to :i* ! in/rum5t is direct$2 if x only be 9 its prop] place1 ! effect j describ$ is sure to take place1 & ) an endless v>iety4 ,9 ?is respect ! ,kaleidoscope appe>s to be q s+ul> among optical in/rum5ts4 ,nei!r ! in/rum5t ( ,bradley1 nor ! exp]im5t or !orem 9 ,wood's book1 h any resemblance to ?is2 !y g no fur!r ?an ! multiplication ( ! figure4 8,next1 z to ! pr9ciple ( con/ruction1 ,dr4 ,brew/]'s in/rum5t requires a p>ticul> position ( ! eye ( ! obs]v]1 & ( ! object look$ at1 9 ord] to produce its effect4 ,if ei!r ( ^! is want+1 ! symmetry vani%es1 & ! figures are irregul> & disunit$4 ,9 ! o!r two cases1 no p>ticul> position1 ei!r = ! eye or ! object1 is requir$4 8,= ^! reasons1 ,dr4 ,brew/]'s inv5tion seems to me q unlike ! o!r two4 ,inde$1 z f> z ,i "k1 x is q s+ul> among optical in/rum5ts2 & x w be matt] ( s9c]e regret1 if any imag9>y or vague analogy1 betwe5 x & o!r optical in/rum5ts1 %\ld be ! means ( depriv+ ! ,doctor ( any "p ( ! rew>d to :i* 8 skill1 +5uity1 & p]sev]ance1 entitle him s well4 8,,john ,,playfair1 ,pr(essor ( ,natural ,philosophy 9 ! ,univ]sity ( ,ed9burgh40 8,p4,s4--,grant+ t !re 7 a resemblance betwe5 ! ,kaleidoscope & ,bradley's in/rum5t1 9 any ( ! p>ticul>s m5tion$ above1 ! introduction ( col\r$ & movable objects1 at ! end ( ! reflectors1 is q peculi> to ,dr4 ,brew/]'s in/rum5t4 ,besides ?is1 a circum/ance highly des]v+ ( att5tion1 is ! use ( two l5ses & a draw-tube2 s t ! action ( ! ,kaleidoscope is ext5d$ to objects ( all sizes1 & at all di/ances f ! obs]v]1 & unit$1 by t means1 to ! advantages ( ! telescope4 8,j4 ,p40 ,pr(essor ,pictet's op9ion is /at$ 9 ! foll[+ lett]3-- 8,,sir1--,among y\r fri5ds1 ,i h n be5 "o ( ! lea/ pa9fully affect$ by ! %ameful invasion ( y\r rights z an inv5tor1 :i* ,i h be5 a witness ( lately 9 ,london4 ,n only none ( ! allegations ( ! invad]s ( y\r pat5t1 gr\nd$ on a pret5d$ simil>ity betwe5 y\r ,kaleidoscope & ,bradley's in/rum5t1 or su* z ,wood's or ,h>ris's !ories might h sugge/$1 appe> to me to h any real f\ndation2 b ,i c affirm1 t1 nei!r 9 any ( ! ,fr5*1 ,g]man1 or ,italian au?ors1 :o1 to my k1 h treat$ ( optics1 nor 9 ,pr(essor ,*>les's ju/ly-celebrat$ & mo/ complete collection ( optical in/rum5ts at ,p>is1 h ,i read or se5 any?+ resembl+ y\r +5i\s app>atus1 :i*1 f its numb]less applications1 & ! pleasure x af=ds1 & w cont9ue to af=d to millions ( behold]s ( its mat*less effects1 may be rank$ among ! mo/ happy inv5tions t sci5ce ev] pres5t$ to ! lov]s ( rational enjoym5t4 8,m4 ,a4 ,,pictet1 ,pr(essor ( ,natural ,philosophy 9 ! ,academy ( ,g5eva40 ,^? :o wi% to exam9e f>!r ! anci5t comb9ations ( plane mirrors1 & o!r subjects connect$ ) ! ,kaleidoscope1 are ref]r$ to ! foll[+ works3-- ,bapti/a ,porta's ,magia ,naturalis4 ,kir*]'s ,ars ,magna ,lucis et ,umbr4 ,s*ottus's ,magia ,univ]salis ,natur et ,artis4 ,bradley's ,treatise on ,plant+ & ,g>d5+4 ,h>ris's ,treatise on ,optics4 ,wood's ,optics4 ,dr4 ,roget on ! ,kaleidoscope1 9 ! ,annals ( ,philosophy1 vol4 xi4 p4 #cge4 ,encyclopdia ,britannica1 ,art4 ,,kaleidoscope1 by ,dr4 ,roget2 & ! ,compte ,r5du des ,travaux de ,l',acadmie de ,dijon1 p\r #ahah1 pp4 #ajh-aag4 ,works by ,,sir ,,david ,,brew/]4 ,,m ,,worlds ,,?an ,,"o3 ! ,cre$ ( ! ,philosoph]1 ! ,hope ( ! ,*ri/ian4 ,cr4 #hvo41 #ds4 #f;d4 ,,! ,,m>tyrs ,,( ,,sci5ce3 ,galileo1 ,ty*o ,brahe1 & ,kepl]4 ,cr4 #hvo41 #ds4 #f;d4 ,,! ,,kaleidoscope ,practically ,describ$4 ,cr4 #hvo41 ) ,illu/rations1 #ds4 #f;d4 ,,! ,,/]eoscope ,practically ,describ$4 ,cr4 #hvo41 ) ,illu/rations1 #ds4 #f;d4 ,,london3 ,,john ,,camd5 ,,hott51 #gd1 ,,piccadilly4