,transcriber's ,notes3      ,underscores
 80 before and after a word or phrase   
indicate italics      in the original   
text4    ,equal signs 80 before and     
after a word or phrase indicate bold    
in the original text4    ,small capitals
 have been converted to ,,solid         
capitals4    ,illustrations and         
footnotes have been moved so they do not
 break up      paragraphs4              
,antiquated spellings have been         
preserved4    ,typographical and        
punctuation errors have been silently   
corrected4    ,in the ,table of         
,contents1 ,chapters ,,xv and ,,xvi were
 corrected from page      #bjj to #baa  
and #baf respectively4    ,figure #df   
was incorrectly labelled ,figure #de1   
this has been corrected4                
,,the ,,stereoscope                     
,,its ,,history1 ,,theory1 ,,and        
,,construction                 ,,with   
,,its ,,application ,,to ,,the ,,fine   
,,and ,,useful ,,arts                   
,,and ,,to ,,education4                 

,,by              ,,sir ,,david         
,,brewster1 ,k4,h41 ,d4,c4,l41          
,f4,r4,s41 ,m4,r4,i4,a41                
,,vice-,,president ,,of ,,the ,,royal   
,,society ,,of ,,edinburgh1 ,,one ,,of  
,,the ,,eight        ,,associates ,,of  
,,the ,,imperial ,,institute ,,of       
,,france1 ,,officer ,,of ,,the          
,,legion ,,of ,,honour1 ,,chevalier ,,of
 ,,the ,,prussian ,,order ,,of ,,merit1 
,,honorary ,,or ,,corresponding ,,member
 ,,of ,,the ,,academies                 
,,of ,,petersburgh1 ,,vienna1 ,,berlin1 
,,copenhagen1                           
,,stockholm1 ,,brussels1 ,g,,ttingen1   
,,modena1                       ,,and   
,,of ,,the ,,national ,,institute ,,of  
,,washington1 ,,etc4                    
,,with ,,fifty ,,wood ,,engravings4     
,,london3                        ,,john 
,,murray1 ,,albemarle ,,street4         
#ahef4                  ,the ,right of  
,translation is reserved4               
,,edinburgh3                     ,t4    
,,constable1 ,,printer ,,to ,,her       

,,majesty4                              
,,contents                              
,,page      ,,introduction1             
#a      ,,chap4 ,i4--,,history ,,of     
,,the ,,stereoscope1                    
#e           ,,ii4--,,on ,,monocular    
,,vision1 ,,or ,,vision ,,with ,,one    
,,eye1         #ch          ,,iii4--,,on
 ,,binocular ,,vision1 ,,or ,,vision    
,,with ,,two ,,eyes1        #dg         
,,iv4--,,description ,,of ,,the         
,,ocular1 ,,reflecting1                 
,,and ,,lenticular ,,stereoscopes1      
#ec            ,v4--,,on ,,the ,,theory 
,,of ,,the ,,stereoscopic ,,vision1     
#gf           ,,vi4--,,on ,,the ,,union 
,,of ,,similar ,,pictures ,,in          
,,binocular ,,vision1                   
#ij          ,,vii4--,,description ,,of 
,,different ,,stereoscopes1             
#ajg         ,,viii4--,,method ,,of     
,,taking ,,pictures ,,for ,,the         
,,stereoscope1      #aca                
,,ix4--,,on ,,the ,,adaptation ,,of     
,,the ,,pictures ,,to                   

,,the ,,stereoscope4--,,their ,,size1   
,,position1                 ,,and       
,,illumination1                         
#aei            ,x4--,,application ,,of 
,,the ,,stereoscope ,,to ,,painting1    
#aff           ,,xi4--,,application ,,of
 ,,the ,,stereoscope ,,to ,,sculpture1  
,,architecture1 ,,and ,,engineering1    
#ahc          ,,xii4--,,application ,,of
 ,,the ,,stereoscope ,,to ,,natural     
,,history1  #ahi                        
,,xiii4--,,application ,,of ,,the       
,,stereoscope ,,to                      
,,educational ,,purposes1               
#aic          ,,xiv4--,,application ,,of
 ,,the ,,stereoscope ,,to ,,purposes    
,,of ,,amusement1                       
#bjd           ,,xv4--,,on ,,the        
,,production ,,of ,,stereoscopic        
,,pictures ,,from ,a ,,single ,,picture1
                   #baa                 
,,xvi4--,,on ,,certain ,,fallacies ,,of 
,,sight ,,in ,,the                      
,,vision ,,of ,,solid ,,bodies1         
#baf         ,,xvii4--,,on ,,certain    

,,difficulties ,,experienced ,,in       
,,the ,,use ,,of ,,the ,,stereoscope1   
#bca          ,,on ,,the ,,stereoscope4 
,,introduction4      ,the ,stereoscope1 
a word derived from 1 solid1 and  1 to  
see1 is an optical instrument1 of modern
 invention1 for  representing1 in       
apparent relief and solidity1 all       
natural objects and  all groups or      
combinations of objects1 by uniting into
 one image two  plane representations of
 these objects or groups as seen by each
 eye  separately4 ,in its most general  
form the ,stereoscope is a binocular    
instrument1 that is1 is applied to both 
eyes2 but in two of its  forms it is    
monocular1 or applied only to one eye1  
though the use  of the other eye1       
without any instrumental aid1 is        
necessary in the  combination of the two
 plane pictures1 or of one plane picture
 and its  reflected image4 ,the         
,stereoscope1 therefore1 cannot1 like   
the telescope  and microscope1 be used  
by persons who have lost the use of one 

eye1  and its remarkable effects cannot 
be properly appreciated by those  whose 
eyes are not equally good4    ,when the 
artist represents living objects1 or    
groups of them1 and  delineates         
buildings or landscapes1 or when he     
copies from statues or  models1 he      
produces apparent solidity1 and         
difference of distance from  the eye1 by
 light and shade1 by the diminished size
 of known objects as  regulated by the  
principles of geometrical perspective1  
and by those  variations in distinctness
 and colour which constitute what has   
been  called aerial perspective4 ,but   
when all these appliances have been     
used in the most skilful manner1 and art
 has exhausted its powers1  we seldom1  
if ever1 mistake the plane picture for  
the solid which it  represents4 ,the two
 eyes scan its surface1 and by their    
distance-giving  power indicate to the  
observer that every point of the picture
 is  nearly at the same distance from   
his eye4 ,but if the observer closes    

one eye1 and thus deprives himself of   
the power of determining  differences of
 distance by the convergency of the     
optical axes1 the  relief of the picture
 is increased4 ,when the pictures are   
truthful  photographs1 in which the     
variations of light and shade are       
perfectly  represented1 a very          
considerable degree of relief and       
solidity is  thus obtained2 and when we 
have practised for a while this species 
of  monocular vision1 the drawing1      
whether it be of a statue1 a living     
figure1 or a building1 will appear to   
rise in its different parts from  the   
canvas1 though only to a limited extent4
    ,in these observations we refer     
chiefly to ordinary drawings held in the
  hand1 or to portraits and landscapes  
hung in rooms and galleries1 where  the 
proximity of the observer1 and lights   
from various directions1  reveal the    
surface of the paper or the canvas2 for 
in panoramic and  dioramic              
representations1 where the light1       

concealed from the observer1  is        
introduced in an oblique direction1 and 
where the distance of the  picture is   
such that the convergency of the optic  
axes loses much of  its distance-giving 
power1 the illusion is very perfect1    
especially  when aided by correct       
geometrical and aerial perspective4 ,but
 when  the panorama is illuminated by   
light from various directions1 and the  
slightest motion imparted to the canvas1
 its surface becomes distinctly         
visible1 and the illusion instantly     
disappears4    ,the effects of          
stereoscopic representation are of a    
very different  kind1 and are produced  
by a very different cause4 ,the singular
 relief  which it imparts is independent
 of light and shade1 and of geometrical 
as well as of aerial perspective4 ,these
 important accessories1 so  necessary in
 the visual perception of the drawings  
in plano1 avail  nothing in the         
evolution of their relievo1 or third    
dimension4 ,they  add1 doubtless1 to the

 beauty of the binocular pictures2 but  
the  stereoscopic creation is due solely
 to the superposition of the two  plane 
pictures by the optical apparatus       
employed1 and to the distinct  and      
instantaneous perception of distance by 
the convergency of the  optic axes upon 
the similar points of the two pictures  
which the  stereoscope has united4      
,if we close one eye while looking at   
photographic pictures in the            
stereoscope1 the perception of relief is
 still considerable1 and  approximates  
to the binocular representation2 but    
when the pictures are  mere diagrams    
consisting of white lines upon a black  
ground1 or black  lines upon a white    
ground1 the relief is instantly lost by 
the shutting  of the eye1 and it is only
 with such binocular pictures that we   
see the  true power of the stereoscope4 
,as an amusing and useful instrument the
 stereoscope derives much of  its value 
from photography4 ,the most skilful     
artist would have been  incapable of    

delineating two equal representations of
 a figure or a  landscape as seen by two
 eyes1 or as viewed from two different  
points  of sight2 but the binocular     
camera1 when rightly constructed1       
enables  us to produce and to multiply  
photographically the pictures which we  
require1 with all the perfection of that
 interesting art4 ,with this            
instrument1 indeed1 even before the     
invention of the ,daguerreotype and  the
 ,talbotype1 we might have exhibited    
temporarily upon ground-glass1  or      
suspended in the air1 the most perfect  
stereoscopic creations1 by  placing a   
,stereoscope behind the two dissimilar  
pictures formed by the  camera4         
,,chapter ,i4    ,,history ,,of ,,the   
,,stereoscope4      ,when we look with  
both eyes open at a sphere1 or any other
 solid  object1 we see it by uniting    
into one two pictures1 one as seen by   
the  right1 and the other as seen by the
 left eye4 ,if we hold up a thin book   
perpendicularly1 and midway between both

 eyes1 we see distinctly the  back of it
 and both sides with the eyes open4     
,when we shut the right  eye we see with
 the left eye the back of the book and  
the left side of  it1 and when we shut  
the left eye we see with the right eye  
the back of  it and the right side4 ,the
 picture of the book1 therefore1 which  
we see  with both eyes1 consists of two 
dissimilar pictures united1 namely1 a   
picture of the back and the left side of
 the book as seen by the left  eye1 and 
a picture of the back and right side of 
the book as seen by  the right eye4     
,in this experiment with the book1 and  
in all cases where the object is  near  
the eye1 we not only see different      
pictures of the same object1  but we see
 different things with each eye4 ,those 
who wear spectacles  see only the       
left-hand spectacle-glass with the left 
eye1 on the left  side of the face1     
while with the right eye they see only  
the right-hand  spectacle-glass on the  
right side of the face1 both glasses of 

the  spectacles being seen united midway
 between the eyes1 or above the  nose1  
when both eyes are open4 ,it is1        
therefore1 a fact well known to  every  
person of common sagacity that the      
pictures of bodies seen by  both eyes   
are formed by the union of two          
dissimilar pictures formed by  each4    
,this palpable truth was known and      
published by ancient mathematicians4    
,euclid knew it more than two thousand  
years ago1 as may be seen in the  #bfth1
 #bgth1 and #bhth theorems of his       
,treatise on ,optics4#a ,in these       
theorems he shews that the part of a    
sphere seen by both eyes1 and  having   
its diameter equal to1 or greater or    
less than the distance  between the     
eyes1 is equal to1 and greater or less  
than a hemisphere2  and having          
previously shewn in the #bc;d and #bdth 
theorems how to find  the part of any   
sphere that is seen by one eye at       
different distances1  it follows1 from  
constructing his figure1 that each eye  

sees different  portions of the sphere1 
and that it is seen by both eyes by the 
union  of these two dissimilar pictures4
    #a ,edit4 of ,pena1 pp4 #ag1 #ah1   
,paris1 #aegg2 or ,opera1 by ,gregory1  
pp4  #fai1 #fbj4 ,oxon4 #agjc4    ,more 
than fifteen hundred years ago1 the     
celebrated physician ,galen  treated the
 subject of binocular vision more fully 
than ,euclid4 ,in  the twelfth chapter  
of the tenth book of his work1 ,on the  
use of  the different parts of the      
,human ,body1 he has described with     
great  minuteness the various phenomena 
which are seen when we look at  bodies  
with both eyes1 and alternately with the
 right and the left4  ,he shews1 by     
diagrams1 that dissimilar pictures of a 
body are seen  in each of these three   
modes of viewing it2 and1 after         
finishing his  demonstration1 he adds1--
        8,but if any person does not    
understand these      demonstrations by 
means of lines1 he will finally         
give his assent to them when he has made

 the      following                     
experiment3--,standing near a column1   
and      shutting each of the eyes in   
succession2--when the      right eye is 
shut1 some of those parts of the        
column which were previously seen by the
 right eye      on the right side of the
 column1 will not now be      seen by   
the left eye2 and when the left eye is  
shut1 some of those parts which were    
formerly seen      by the left eye on   
the left side of the column1      will  
not now be seen by the right eye4 ,but  
when we1      at the same time1 open    
both eyes1 both these will be      seen1
 for a greater part is concealed when we
 look      with either of the two eyes1 
than when we look with      both at the 
same time40#b    #b ,de ,usu ,partium   
,corporis ,humani1 edit4 ,lugduni1      
#aeej1 p4 #eic4    ,in such distinct and
 unambiguous terms1 intelligible to the 
meanest  capacity1 does this illustrious
 writer announce the fundamental law  of
 binocular vision--the grand principle  

of the ,stereoscope1 namely1  that the  
picture of the solid column which we see
 with both eyes is  composed of two     
dissimilar pictures1 as seen by each eye
 separately4  ,as the vision of the     
solid column1 therefore1 was obtained by
 the union  of these dissimilar         
pictures1 an instrument only was wanted 
to take  such pictures1 and another to  
combine them4 ,the ,binocular           
,photographic  ,camera was the one      
instrument1 and the ,stereoscope the    
other4    ,the subject of binocular     
vision was studied by various optical   
writers  who have flourished since the  
time of ,galen4 ,baptista ,porta1 one of
  the most eminent of them1 repeats1 in 
his work ,on ,refraction1 the           
propositions of ,euclid on the vision of
 a sphere with one and both  eyes1 and  
he cites from ,galen the very passage   
which we have given  above on the       
dissimilarity of the three pictures seen
 by each eye and  by both4 ,believing   
that we see only with one eye at a time1

 he denies  the accuracy of ,euclid's   
theorems1 and while he admits the       
correctness  of the observations of     
,galen1 he endeavours to explain them   
upon other  principles4                 
,illustration3 ,,fig4 #a4    ,in        
illustrating the views of ,galen on the 
dissimilarity of the three  pictures    
which are requisite in binocular vision1
 he employs a much  more distinct       
diagram than that which is given by the 
,greek physician4  8,let ,a10 he says1  
8be the pupil of the right eye1 ,b that 
of the left1  and ,,dc the body to be   
seen4 ,when we look at the object with  
both eyes  we see ,,dc1 while with the  
left eye we see ,,ef1 and with the right
 eye  ,,gh4 ,but if it is seen with one 
eye1 it will be seen otherwise1 for when
  the left eye ,b is shut1 the body     
,,cd1 on the left side1 will be seen in 
,,hg2 but when the right eye is shut1   
the body ,,cd will be seen in ,,fe1     
whereas1 when both eyes are opened at   
the same time1 it will be seen  in      

,,cd40 ,these results are then explained
 by copying the passage from  ,galen1 in
 which he supposes the observer to      
repeat these experiments  when he is    
looking at a solid column4    ,in       
looking at this diagram1 we recognise at
 once not only the  principle1 but the  
construction of the stereoscope4 ,the   
double  stereoscopic picture or slide is
 represented by ,,he2 the right-hand    
picture1 or the one seen by the right   
eye1 by ,,hf2 the left-hand  picture1 or
 the one seen by the left eye1 by ,,ge2 
and the picture of the  solid column in 
full relief by ,,dc1 as produced midway 
between the other  two dissimilar       
pictures1 ,,hf and ,,ge1 by their union1
 precisely as in the  stereoscope4#c    
#c ,joan4 ,baptist ,port ,neap41 ,de    
,refractione ,optices parte1 lib4 v4  p4
 #acb1 and lib4 vi4 pp4 #adc-e4 ,neap4  
#aeic4    ,galen1 therefore1 and the    
,neapolitan philosopher1 who has        
employed  a more distinct diagram1      
certainly knew and adopted the          

fundamental  principle of the           
stereoscope2 and nothing more was       
required1 for  producing pictures in    
full relief1 than a simple instrument   
for uniting  ,,hf and ,,ge1 the right   
and left hand dissimilar pictures of the
 column4    ,illustration3 ,,fig4 #b4   
,in the treatise on painting which he   
left behind him in ,,ms41#d  ,leonardo  
da ,vinci has made a distinct reference 
to the dissimilarity  of the pictures   
seen by each eye as the reason why 8a   
painting1 though  conducted with the    
greatest art1 and finished to the last  
perfection1  both with regard to its    
contours1 its lights1 its shadows1 and  
its  colours1 can never shew a relievo  
equal to that of the natural  objects1  
unless these be viewed at a distance and
 with a single  eye10#e which he thus   
demonstrates4 8,if an object ,c be      
viewed by a  single eye at ,a1 all      
objects in the space behind             
it--included1 as it  were1 in a shadow  
,,ecf1 cast by a candle at ,a--are      

invisible to an eye at  ,a2 but when the
 other eye at ,b is opened1 part of     
these objects become  visible to it2    
those only being hid from both eyes that
 are included1  as it were1 in the      
double shadow ,,cd1 cast by two lights  
at ,a and ,b and  terminated in ,d2 the 
angular space ,,edg1 beyond ,d1 being   
always visible  to both eyes4 ,and the  
hidden space ,,cd is so much the shorter
 as the  object ,c is smaller and nearer
 to the eyes4 ,thus he observes that    
the object ,c1 seen with both eyes1     
becomes1 as it were1 transparent1       
according to the usual definition of a  
transparent thing1 namely1 that  which  
hides nothing beyond it4 ,but this      
cannot happen when an object1  whose    
breadth is bigger than that of the      
pupil1 is viewed by a single  eye4 ,the 
truth of this observation is1 therefore1
 evident1 because a  painted figure     
intercepts all the space behind its     
apparent place1 so  as to preclude the  
eyes from the sight of every part of the

 imaginary  ground behind it4 ,hence10  
continues ,dr4 ,smith1 8we have one help
 to  distinguish the place of a near    
object more accurately with both eyes   
than with one1 inasmuch as we see it    
more detached from other objects  beyond
 it1 and more of its own surface1       
especially if it be roundish40    #d    
,trattata della ,pictura1 ,scultura1 ed 
,architettura4 ,milan1 #aehd4    #e ,dr4
 ,smith's ,compleat ,system of ,opticks1
 vol4 ii41 ,remarks1 pp4 #da  and #bdd4 
,we have quoted this passage1 not from  
its proving that ,leonardo da  ,vinci   
was acquainted with the fact that each  
eye1 ,a1 ,b1 sees dissimilar  pictures  
of the sphere ,c1 but because it has    
been referred to by ,mr4  ,wheatstone as
 the only remark on the subject of      
binocular vision which  he could find   
8after looking over the works of many   
authors who might  be expected to have  
made them40 ,we think it quite clear1   
however1 that  the ,italian artist knew 
as well as his commentator ,dr4 ,smith1 

that each  eye1 ,a and ,b1 sees         
dissimilar parts of the sphere ,c4 ,it  
was not his  purpose to treat of the    
binocular pictures of ,c1 but his figure
 proves  their dissimilarity4    ,the   
subject of binocular vision was         
successfully studied by ,francis        
,aguillon or ,aguilonius1#f a learned   
,jesuit1 who published his ,optics  in  
#afac4 ,in the first book of his work1  
where he is treating of the  vision of  
solids of all forms1 7de genere illorum 
qu   ta  sterea nuncupantur17 he has    
some difficulty in explaining1 and fails
  to do it1 why the two dissimilar      
pictures of a solid1 seen by each  eye1 
do not1 when united1 give a confused and
 imperfect view of it4  ,this discussion
 is appended to the demonstration of the
 theorem1 8that  when an object is seen 
with two eyes1 two optical pyramids are 
formed  whose common base is the object 
itself1 and whose vertices are in the   
eyes10#g and is as follows3--    #f     
,opticorum ,libri ,sex ,philosophis     

juxta ac ,mathematicis utiles4  ,folio4 
,antverpi1 #afac4    #g ,in ,,fig4 #a1  
,,ahf is the optical pyramid seen by the
 eye ,a1 and ,,bge  the optical pyramid 
seen by the eye ,b4    8,when one object
 is seen with two eyes1 the angles at   
the vertices of  the optical pyramids   
7namely1 ,,haf1 ,,gbe1 ,fig4 #a7 are not
 always equal1  for beside the direct   
view in which the pyramids ought to be  
equal1  into whatever direction both    
eyes are turned1 they receive pictures  
of  the object under inequal angles1 the
 greatest of which is that which  is    
terminated at the nearer eye1 and the   
lesser that which regards the  remoter  
eye4 ,this1 ,i think1 is perfectly      
evident2 but ,i consider it as  worthy  
of admiration1 how it happens that      
bodies seen by both eyes are  not all   
confused and shapeless1 though we view  
them by the optical axes  fixed on the  
bodies themselves4 ,for greater bodies1 
seen under greater  angles1 appear      
lesser bodies under lesser angles4 ,if1 

therefore1 one  and the same body which 
is in reality greater with one eye1 is  
seen  less on account of the inequality 
of the angles in which the pyramids  are
 terminated1 7namely1 ,,haf1 ,,gbe1#h7  
the body itself must assuredly  be seen 
greater or less at the same time1 and to
 the same person that  views it2 and1   
therefore1 since the images in each eye 
are dissimilar  7minime sibi congruunt7 
the representation of the object must   
appear  confused and disturbed 7confusa 
ac perturbata7 to the primary sense40   
#h ,these angles are equal in this      
diagram and in the vision of a  sphere1 
but they are inequal in other bodies4   
8,this view of the subject10 he         
continues1 8is certainly consistent with
  reason1 but1 what is truly wonderful  
is1 that it is not correct1 for  bodies 
are seen clearly and distinctly with    
both eyes when the optic  axes are      
converged upon them4 ,the reason of     
this1 ,i think1 is1 that  the bodies do 
not appear to be single1 because the    

apparent images1  which are formed from 
each of them in separate eyes1 exactly  
coalesce1  7sibi mutuo exacte           
congruunt17 but because the common sense
 imparts  its aid equally to each eye1  
exerting its own power equally in the   
same manner as the eyes are converged by
 means of their optical axes4  ,whatever
 body1 therefore1 each eye sees with the
 eyes conjoined1 the  common sense makes
 a single notion1 not composed of the   
two which  belong to each eye1 but      
belonging and accommodated to the       
imaginative  faculty to which it 7the   
common sense7 assigns it4 ,though1      
therefore1  the angles of the optical   
pyramids which proceed from the same    
object  to the two eyes1 viewing it     
obliquely1 are inequal1 and though the  
object appears greater to one eye and   
less to the other1 yet the same         
difference does not pass into the       
primary sense if the vision is made     
only by the axes1 as we have said1 but  
if the axes are converged on  this side 

or on the other side of the body1 the   
image of the same body  will be seen    
double1 as we shall shew in ,book iv41  
on the fallacies of  vision1 and the one
 image will appear greater and the other
 less on  account of the inequality of  
the angles under which they are seen40#i
    #i ,aguilonius1 ,opticorum1 lib4 ii4
 book xxxviii4 pp4 #adj1 #ada4    ,such 
is ,aguilonius's theory of binocular    
vision1 and of the union  of the two    
dissimilar pictures in each eye by which
 a solid body is  seen4 ,it is obviously
 more correct than that of ,dr4 ,whewell
 and ,mr4  ,wheatstone4 ,aguilonius     
affirms it to be contrary to reason that
 two  dissimilar pictures can be united 
into a clear and distinct picture1  as  
they are actually found to be1 and he is
 therefore driven to call  in the aid of
 what does not exist1 a common sense1   
which rectifies  the picture4 ,dr4      
,whewell and ,mr4 ,wheatstone have cut  
the ,gordian knot  by maintaining what  
is impossible1 that in binocular and    

stereoscopic  vision a long line is made
 to coincide with a short one1 and a    
large  surface with a small one2 and in 
place of conceiving this to be done by  
a common sense overruling optical laws1 
as ,aguilonius supposes1 they  give to  
the tender and pulpy retina1 the        
recipient of ocular pictures1  the      
strange power of contracting or         
expanding itself in order to  equalize  
inequal lines and inequal surfaces6     
,illustration3 ,,fig4 #c4    ,in his    
fourth and very interesting book1 on the
 fallacies of distance1  magnitude1     
position1 and figure1 ,aguilonius       
resumes the subject of the  vision of   
solid bodies4 ,he repeats the theorems  
of ,euclid and ,gassendi  on the vision 
of the sphere1 shewing how much of it is
 seen by each  eye1 and by both1        
whatever be the size of the sphere1 and 
the distance  of the observer4 ,at the  
end of the theorems1 in which he        
demonstrates  that when the diameter of 
the sphere is equal to the distance     

between  the eyes we see exactly a      
hemisphere1 he gives the annexed drawing
  of the mode in which the sphere is    
seen by each eye1 and by both4 ,in  this
 diagram ,e is the right eye and ,d the 
left1 ,,chfi the section of  that part  
of the sphere ,,bc which is seen by the 
right eye ,e1 ,,bhga the  section of the
 part which is seen by the left eye ,d1 
and ,,blc the half  of the great circle 
which is the section of the sphere as   
seen by both  eyes4#aj ,these three     
pictures of the solids are all          
dissimilar4 ,the  right eye ,e does not 
see the part ,,blcif of the sphere2 the 
left eye  does not see the part ,,blcga1
 while the part seen with both eyes is  
the  hemisphere ,,blcgf1 the dissimilar 
segments ,,bfg1 ,,cgf being united in   
its  vision4#aa    ,after demonstrating 
his theorems on the vision of spheres   
with one  and both eyes1#ab ,aguilonius 
informs us1 before he proceeds to the   
vision of cylinders1 that it is agreed  
upon that it is not merely true  with   

the sphere1 but also with the cylinder1 
the cone1 and all bodies  whatever1 that
 the part which is seen is comprehended 
by tangent rays1  such as ,,eb1 ,,ec for
 the right eye1 in ,fig4 #c4 8,for10    
says he1 8since  these tangent lines are
 the outermost of all those which can be
 drawn  to the proposed body from the   
same point1 namely1 that in which the   
eye is understood to be placed1 it      
clearly follows that the part of  the   
body which is seen must be contained by 
the rays touching it on  all sides4 ,for
 in this part no point can be found from
 which a right  line cannot be drawn to 
the eye1 by which the correct visible   
form is  brought out40#ac    #aj ,it is 
obvious that a complete hemisphere is   
not seen with both  eyes4    #aa        
,aguilonius1 ,opticorum1 lib4 iv4 pp4   
#cjf1 #cjg4    #ab ,in the last of these
 theorems ,aguilonius describes and     
explains1  we believe for the first     
time1 the conversion of relief in the   
vision  of convex and concave surfaces4 

,see ,prop4 xciv4 p4 #cab4    #ac ,id41 
p4 #cac4    ,optical writers who lived  
after the time of ,aguilonius seem to   
have  considered the subject of         
binocular vision as exhausted in his    
admirable work4 ,gassendi1#ad though he 
treats the subject very  slightly1 and  
without any figures1 tells us that we   
see the left side  of the nose with the 
left eye1 and the right side of it with 
the  right eye1--two pictures           
sufficiently dissimilar4 ,andrew        
,tacquet1#ae  though he quotes          
,aguilonius and ,gassendi on the subject
 of seeing  distances with both eyes1   
says nothing on the binocular vision of 
solids2 and ,smith1 ,harris1 and        
,porterfield1 only touch upon the       
subject  incidentally4 ,in commenting on
 the passage which we have already      
quoted from ,leonardo da ,vinci1 ,dr4   
,smith says1 8,hence we have one help   
to distinguish the place of a near      
object more accurately with both  eyes  
than with one1 inasmuch as we see it    

more detached from other  objects beyond
 it1 and more of its own surface1       
especially if it be  roundish40#af ,if  
any farther evidence were required that 
,dr4 ,smith  was acquainted with the    
dissimilarity of the images of a solid  
seen by  each eye1 it will be found in  
his experiment with a 8long ruler placed
  between the eyebrows1 and extended    
directly forward with its flat  sides1  
respecting the right hand and the left40
 8,by directing the eyes  to a remote   
object10 he adds1 8the right side of the
 ruler seen by  the right eye will      
appear on the left hand1 and the left   
side on the  right hand1 as represented 
in the figure40#ag    #ad ,opera1 tom4  
ii4 p4 #cid4 ,lugduni1 #afeh4    #ae    
,opera ,mathematica ,optica1 tribus     
libris exposita1 p4 #acf4    #af        
,opticks1 vol4 ii41 ,remarks1 pp4 #da   
and #bde4    #ag ,id41 vol4 i4 p4 #dh1  
,fig4 #aif4    ,in his ,treatise on     
,optics1 published in #agge1 ,mr4       
,harris1 when speaking  of the visible  

or apparent figures of objects1         
observes1 that 8we have  other helps for
 distinguishing prominences of small    
parts besides  those by which we        
distinguish distances in general1 as    
their degrees  of light and shade1 and  
the prospect we have round them40 ,and  
by  the parallax1 on account of the     
distance betwixt our eyes1 we can       
distinguish besides the front part of   
the two sides of a near object  not     
thicker than the said distance1 and this
 gives a visible relievo  to such       
objects1 which helps greatly to raise or
 detach them from the  plane in which   
they lie4 ,thus the nose on a face is   
the more remarkably  raised by our      
seeing both sides of it at once48#ah    
,that is1 the  relievo is produced by   
the combination of the two dissimilar   
pictures  given by each eye4    ,without
 referring to a figure given by ,dr4    
,porterfield1 in which he  actually     
gives drawings of an object as seen by  
each eye in binocular  vision1#ai the   

one exhibiting the object as seen       
endwise by the right  eye1 and the other
 the same object as seen laterally by   
the left eye1  we may appeal to the     
experience of every optical1 or even of 
every  ordinary observer1 in support of 
the fact1 that the dissimilarity of  the
 pictures in each eye1 by which we see  
solid objects1 is known to  those who   
have never read it in ,galen1 ,porta1 or
 ,aguilonius4 ,who has  not observed the
 fact mentioned by ,gassendi and        
,harris1 that their left  eye sees only 
the left side of their nose1 and their  
right eye the  right side1 two pictures 
sufficiently dissimilar8 ,who has not   
noticed1  as well as ,dr4 ,smith1 that  
when they look at any thin1 flat body1  
such  as a thin book1 they see both     
sides of it--the left eye only the left 
side of it1 and the right eye only the  
right side1 while the back1 or  the part
 nearest the face1 is seen by each eye1 
and both the sides and  the back by both
 the eyes8 ,what student of perspective 

is there--master  or pupil1 male or     
female--who does not know1 as certainly 
as he knows  his alphabet1 that the     
picture of a chair or table1 or anything
 else1  drawn from one point of sight1  
or as seen by one eye placed in that    
point1 is necessarily dissimilar to     
another drawing of the same  object     
taken from another point of sight1 or as
 seen by the other eye  placed in a     
point #b inches distant from the first8 
,if such a person is  to be found1 we   
might then admit that the dissimilarity 
of the pictures  in each eye was not    
known to every student of               
perspective4#bj    #ah ,treatise on     
,optics1 p4 #aga2 see also sect4 #fd1 p4
 #aac4    #ai ,treatise on the ,eye1 vol
 i4 p4 #dab1 ,plate #e1 ,fig4 #cg4      
#bj ,as ,mr4 ,wheatstone himself        
describes the dissimilar pictures or    
drawings as 8two different projections  
of the same object seen from  two points
 of sight1 the distance between which is
 equal to the  interval between the eyes

 of the observer10 it is inconceivable  
on what  ground he could imagine himself
 to be the discoverer of so palpable and
  notorious a fact as that the pictures 
of a body seen by two eyes--two  points 
of sight1 must be dissimilar4    ,such  
was the state of our knowledge of       
binocular vision when two  individuals1 
,mr4 ,wheatstone1 and ,mr4 ,elliot1 now 
,teacher of ,mathematics  in ,edinburgh1
 were directing their attention to the  
subject4 ,mr4  ,wheatstone communicated 
an important paper on the ,physiology of
 ,vision  to the ,british ,association  
at ,newcastle in ,august #ahch1 and     
exhibited  an instrument called a       
,stereoscope1 by which he united the two
  dissimilar pictures of solid bodies1  
the  1 7ta sterea of  ,aguilonius17 and 
thus reproduced1 as it were1 the bodies 
themselves4  ,mr4 ,wheatstone's paper on
 the subject1 which had been previously 
read at the ,royal ,society on the #bast
 of ,june1 was printed in their         
,transactions for #ahch4ba    #ba ,phil4

 ,trans41 #ahch1 pp4 #cga-cid4    ,mr4  
,elliot was led to the study of         
binocular vision in consequence  of     
having written an ,essay1 so early as   
#ahbc1 for the ,class of ,logic  in the 
,university of ,edinburgh1 8,on the     
means by which we obtain  our knowledge 
of distances by the ,eye40 ,ever since  
that date he was  familiar with the     
idea1 that the relief of solid bodies   
seen by the  eye was produced by the    
union of the dissimilar pictures of them
 in  each eye1 but he never imagined    
that this idea was his own1 believing   
that it was known to every student of   
vision4 ,previous to or during the  year
 #ahcd1 he had resolved to construct an 
instrument for uniting two  dissimilar  
pictures1 or of constructing a          
stereoscope2 but he delayed  doing this 
till the year #ahci1 when he was        
requested to prepare an  original       
communication for the ,polytechnic      
,society1 which had been  recently      
established in ,liverpool4 ,he was thus 

induced to construct  the instrument    
which he had projected1 and he exhibited
 it to his  friends1 ,mr4 ,richard      
,adie1 optician1 and ,mr4 ,george       
,hamilton1 lecturer  on chemistry in    
,liverpool1 who bear testimony to its   
existence at that  date4 ,this simple   
stereoscope1 without lenses or mirrors1 
consisted of  a wooden box #ah inches   
long1 #g broad1 and #d deep1 and at the 
bottom  of it1 or rather its farther    
end1 was placed a slide containing two  
dissimilar pictures of a landscape as   
seen by each eye4 ,photography did  not 
then exist1 to enable ,mr4 ,elliot to   
procure two views of the same  scene1 as
 seen by each eye1 but he drew the      
transparency of a landscape  with three 
distances4 ,the first and most remote   
was the moon and  the sky1 and a stream 
of water from which the moon was        
reflected1 the  two moons being placed  
nearly at the distance of the two eyes1 
or #b  inches1 and the two reflected    
moons at the same distance4 ,the second 

distance was marked by an old cross     
about a hundred feet off2 and the  third
 distance by the withered branch of a   
tree1 thirty feet from the  observer4   
,in the right-hand picture1 one arm of  
the cross just touched  the disc of the 
moon1 while1 in the left-hand one1 it   
projected over  one-third of the disc4  
,the branch of the tree touched the     
outline of a  distant hill in the one   
picture1 but was 8a full moon's-breadth0
 from  it on the other4 ,when these     
dissimilar pictures were united by the  
eyes1 a landscape1 certainly a very     
imperfect one1 was seen in relief1      
composed of three distances4    ,owing1 
no doubt1 to the difficulty of procuring
 good binocular  pictures1 ,mr4 ,elliot 
did not see that his contrivance would  
be very  popular1 and therefore carried 
it no farther4 ,he had never heard of   
,mr4  ,wheatstone's stereoscope till he 
saw his paper on ,vision reprinted in   
the ,philosophical ,magazine for ,march 
#aheb1 and having perused it1 he  was   

convinced not only that ,mr4            
,wheatstone's theory of the instrument  
was incorrect1 but that his claim to the
 discovery of the dissimilarity  of the 
images in each eye had no foundation4   
,he was1 therefore1 led  to communicate 
to the same journal the fact of his     
having himself1  thirteen years before1 
constructed and used a stereoscope1     
which was  still in his possession4 ,in 
making this claim1 ,mr4 ,elliot had no  
intention of depriving ,mr4 ,wheatstone 
of the credit which was justly  due to  
him2 and as the claim has been publicly 
made1 we have described  the nature of  
it as a part of scientific history4     
,in ,mr4 ,wheatstone's ingenious paper  
of #ahch1 the subject of binocular      
vision is treated at considerable       
length4 ,he gives an account of  the    
opinions of previous writers1 referring 
repeatedly to the works  of ,aguilonius1
 ,gassendi1 and ,baptista ,porta1 in the
 last of which  the views of ,galen are 
given and explained4 ,in citing the     

passage  which we have already quoted   
from ,leonardo da ,vinci1 and inserting 
the figure which illustrates it1 he     
maintains that ,leonardo da ,vinci  was 
not aware 8that the object 7,c in ,fig4 
#b7 presented a different  appearance to
 each eye40 8,he failed10 he adds1 8to  
observe this1  and no subsequent writer1
 to my knowledge1 has supplied the      
omission4  ,the projection of two       
obviously dissimilar pictures on the two
 retin1  when a single object is viewed1
 while the optic axes converge1 must    
therefore be regarded as a new fact in  
the theory of vision40 ,now1  although  
,leonardo da ,vinci does not state in so
 many words that he was  aware of the   
dissimilarity of the two pictures1 the  
fact is obvious in  his own figure1 and 
he was not led by his subject to state  
the fact  at all4 ,but even if the fact 
had not stared him in the face he must  
have known it from the ,optics of       
,euclid and the writings of ,galen1     
with which he could not fail to have    

been well acquainted4 ,that the         
dissimilarity of the two pictures is not
 a new fact we have already  placed     
beyond a doubt4 ,the fact is expressed  
in words1 and delineated  in drawings1  
by ,aguilonius and ,baptista ,porta4 ,it
 was obviously known  to ,dr4 ,smith1   
,mr4 ,harris1 ,dr4 ,porterfield1 and    
,mr4 ,elliot1 before it  was known to   
,mr4 ,wheatstone1 and we cannot         
understand how he failed  to observe it 
in works which he has so often quoted1  
and in which he  professes to have      
searched for it4    ,this remarkable    
property of binocular vision being thus 
clearly  established by preceding       
writers1 and admitted by himself1 as the
 cause  of the vision of solidity or    
distance1 ,mr4 ,wheatstone1 as ,mr4     
,elliot  had done before him1 thought of
 an instrument for uniting the two      
dissimilar pictures optically1 so as to 
produce the same result that is         
obtained by the convergence of the      
optical axes4 ,mr4 ,elliot thought of   

doing this by the eyes alone2 but ,mr4  
,wheatstone adopted a much better       
method of doing it by reflexion4 ,he was
 thus led to construct an  apparatus1 to
 be afterwards described1 consisting of 
two plane mirrors1  placed at an angle  
of #ij1 to which he gave the name of    
stereoscope1  anticipating ,mr4 ,elliot 
both in the construction and publication
 of his  invention1 but not in the      
general conception of a stereoscope4    
,after describing his apparatus1 ,mr4   
,wheatstone proceeds to consider  7in a 
section entitled1 8,binocular vision of 
objects of different  magnitudes07 8what
 effects will result from presenting    
similar images1  differing only in      
magnitude1 to analogous parts of the    
retina40 8,for  this purpose10 he says1 
8two squares or circles1 differing      
obviously  but not extravagantly in     
size1 may be drawn on two separate      
pieces of  paper1 and placed in the     
stereoscope1 so that the reflected image
 of  each shall be equally distant from 

the eye by which it is regarded4 ,it    
will then be seen that notwithstanding  
this difference they coalesce  and      
occasion a single resultant perception40
 ,the fact of coalescence  being        
supposed to be perfect1 the author next 
seeks to determine the  difference      
between the length of two lines which   
the eye can force  into coalescence1 or 
8the limits within which the single     
appearance  subsists40 ,he1 therefore1  
unites two images of equal magnitude1 by
  making one of them visually less from 
distance1 and he states that1  8by this 
experiment1 the single appearance of two
 images of different  size is           
demonstrated40 ,not satisfied with these
 erroneous assertions1  he proceeds to  
give a sort of rule or law for          
ascertaining the  relative size of the  
two unequal pictures which the eyes can 
force  into coincidence4 ,the           
inequality1 he concludes1 must not      
exceed the  difference 8between the     
projections of the same object when seen

 in the  most oblique position of the   
eyes 7i4e41 both turned to the extreme  
right or the extreme left7 ordinarily   
employed40 ,now1 this rule1 taken  in   
the sense in which it is meant1 is      
simply a truism4 ,it merely  states that
 the difference of the pictures which   
the eyes can make to  coalesce is equal 
to the difference of the pictures which 
the eyes do  make to coalesce in their  
most oblique position2 but though a     
truism  it is not a truth1 first1       
because no real coincidence ever can    
take  place1 and1 secondly1 because no  
apparent coincidence is effected when   
the difference of the picture is greater
 than what is above stated4    ,from    
these principles1 which will afterwards 
be shewn to be erroneous1  ,mr4         
,wheatstone proceeds 8to examine why two
 dissimilar pictures  projected on the  
two retin give rise to the perception of
 an object  in relief40 8,i will not    
attempt10 he says1 8at present to give  
the  complete solution of this question1

 which is far from being so easy  as at 
first glance it may appear to be1 and   
is1 indeed1 one of great  complexity4 ,i
 shall1 in this case1 merely consider   
the most obvious  explanations which    
might be offered1 and shew their        
insufficiency to  explain the whole of  
the phenomena4    8,it may be supposed  
that we see only one point of a field of
 view  distinctly at the same instant1  
the one1 namely1 to which the optic     
axes are directed1 while all other      
points are seen so indistinctly that    
the mind does not recognise them to be  
either single or double1 and  that the  
figure is appreciated by successively   
directing the point of  convergence of  
the optic axes successively to a        
sufficient number of  its points to     
enable us to judge accurately of its    
form4    8,that there is a degree of    
indistinctness in those parts of the    
field  of view to which the eyes are not
 immediately directed1 and which        
increases with the distance from that   

point1 cannot be doubted2 and  it is    
also true that the objects there        
obscurely seen are frequently  doubled4 
,in ordinary vision1 it may be said1    
this indistinctness and  duplicity are  
not attended to1 because the eyes       
shifting continually  from point to     
point1 every part of the object is      
successively rendered  distinct1 and the
 perception of the object is not the    
consequence  of a single glance1 during 
which a small part of it only is seen   
distinctly1 but is formed from a        
comparison of all the pictures          
successively seen1 while the eyes were  
changing from one point of an  object to
 another4    8,all this is ,,in ,,some  
,,degree true1 but were it entirely so  
no  appearance of relief should present 
itself when the eyes remain  intently   
fixed on one point of a binocular image 
in the stereoscope4  ,but in performing 
the experiment carefully1 it will be    
found1 provided  the picture do not     
extend far beyond the centres of        

distinct vision1  that the image is     
still seen single1 and in relief1 when  
in this  condition40#bb    #bb ,phil4   
,trans41 #ahch1 pp4 #cia1 #cib4    ,in  
this passage the author makes a         
distinction between ordinary  binocular 
vision1 and binocular vision through the
 stereoscope1  whereas in reality there 
is none4 ,the theory of both is exactly 
the  same4 ,the muscles of the two eyes 
unite the two dissimilar pictures1  and 
exhibit the solid1 in ordinary vision2  
whereas in stereoscopic  vision the     
images are united by reflexion or       
refraction1 the eyes in  both cases     
obtaining the vision of different       
distances by rapid and  successive      
convergences of the optical axes4 ,mr4  
,wheatstone notices  the degree of      
indistinctness in the parts of the      
picture to which  the eyes are not      
immediately directed2 but he does not   
notice the  8confusion and incongruity0 
which ,aguilonius says ought to exist1  
in consequence of some parts of the     

resulting relievo being seen of  one    
size by the left eye alone1--other parts
 of a different size by the  right eye  
alone1 and other parts by both eyes4    
,this confusion1 however1  ,aguilonius1 
as we have seen1 found not to exist1 and
 he ascribes it to  the influence of a  
common sense overruling the operation of
 physical  laws4 ,erroneous as this     
explanation is1 it is still better than 
that of  ,mr4 ,wheatstone1 which we     
shall now proceed to explain4    ,in    
order to disprove the theory referred to
 in the preceding extract1  ,mr4        
,wheatstone describes two experiments1  
which he says are equally  decisive     
against it1 the first of them only being
 subject to rigorous  examination4 ,with
 this view he draws 8two lines about two
 inches long1  and inclined towards each
 other1 on a sheet of paper1 and having 
caused them to coincide by converging   
the optic axes to a point nearer  than  
the paper1 he looks intently on the     
upper end of the resultant  line without

 allowing the eyes to wander from it for
 a moment4 ,the  entire line will appear
 single1 and in its proper relief1 c4444
  ,the eyes10 he continues1 8sometimes  
become fatigued1 which causes the  line 
to become double at those parts to which
 the optic axes are not  fixed1 but in  
such case all appearance of relief      
vanishes4 ,the same  experiment may be  
tried with small complex figures1 but   
the pictures  should not extend too far 
beyond the centre of the retin40    ,now
 these experiments1 if rightly made and 
interpreted1 are not  decisive against  
the theory4 ,it is not true that the    
entire line  appears single when the    
axes are converged upon the upper end of
 the  resultant line1 and it is not true
 that the disappearance of the  relief  
when it does disappear arises from the  
eye being fatigued4  ,in the combination
 of more complex figures1 such as two   
similar  rectilineal figures contained  
by lines of unequal length1 neither the 
inequalities nor the entire figure will 

appear single when the axes are         
converged upon any one point of it4     
,in the different passages which we have
 quoted from ,mr4 ,wheatstone's  paper1 
and in the other parts of it which      
relate to binocular vision1  he is      
obviously halting between truth and     
error1 between theories  which he partly
 believes1 and ill-observed facts which 
he cannot  reconcile with them4         
,according to him1 certain truths 8may  
be supposed0  to be true1 and other     
truths may be 8in some degree true10 but
 8not  entirely so20 and thus1 as he    
confesses1 the problem of binocular and 
stereoscopic vision 8is indeed one of   
great complexity10 of which 8he  will   
not attempt at present to give the      
complete solution40 ,if he had  placed a
 proper reliance on the law of visible  
direction which he  acknowledges ,i have
 established1 and 8with which10 he says1
 8the laws  of visible direction for    
binocular vision ought to contain       
nothing  inconsistent10 he would have   

seen the impossibility of the two eyes  
uniting two lines of inequal length2 and
 had he believed in the law of  distinct
 vision he would have seen the          
impossibility of the two eyes  obtaining
 single vision of any more than one     
point of an object at a  time4 ,these   
laws of vision are as rigorously true as
 any other physical  laws1--as          
completely demonstrated as the law of   
gravity in ,astronomy1  or the law of   
the ,sines in ,optics2 and the moment we
 allow them to be  tampered with to     
obtain an explanation of physical       
puzzles1 we convert  science into       
legerdemain1 and philosophers into      
conjurors4    ,such was the state of our
 stereoscopic knowledge in #ahch1 after 
the  publication of ,mr4 ,wheatstone's  
interesting and important paper4        
,previous to this ,i communicated to the
 ,british ,association at  ,newcastle1  
in ,august #ahch1 a paper1 in which ,i  
established the law  of visible         
direction already mentioned1 which1     

though it had been  maintained by       
preceding writers1 had been proved by   
the illustrious  ,d',alembert to be     
incompatible with observation1 and the  
admitted  anatomy of the human eye4 ,at 
the same meeting ,mr4 ,wheatstone       
exhibited  his stereoscopic apparatus1  
which gave rise to an animated          
discussion  on the theory of the        
instrument4 ,dr4 ,whewell maintained    
that the  retina1 in uniting1 or causing
 to coalesce into a single resultant    
impression two lines of different       
lengths1 had the power either of        
contracting the longest1 or lengthening 
the shortest1 or what might  have been  
suggested in order to give the retina   
only half the trouble1  that it         
contracted the long line as much as it  
expanded the short one1  and thus caused
 them to combine with a less exertion of
 muscular power6  ,in opposition to     
these views1 ,i maintained that the     
retina1 a soft  pulpy membrane which the
 smallest force tears in pieces1 had no 

such  power1--that a hypothesis so      
gratuitous was not required1 and that   
the  law of visible direction afforded  
the most perfect explanation of all  the
 stereoscopic phenomena4    ,in         
consequence of this discussion1 ,i was  
led to repeat my experiments1  and to   
inquire whether or not the eyes in      
stereoscopic vision did  actually unite 
the two lines of different lengths1 or  
of different  apparent magnitudes4 ,i   
found that they did not1 and that no    
such union  was required to convert by  
the stereoscope two plane pictures into 
the apparent whole from which they were 
taken as seen by each eye4  ,these views
 were made public in the lectures on the
 ,philosophy of the  ,senses1 which ,i  
occasionally delivered in the ,college  
of ,st4 ,salvator  and ,st4 ,leonard1   
,st4 ,andrews1 and the different        
stereoscopes which ,i  had invented were
 also exhibited and explained4    ,in   
examining ,dr4 ,berkeley's celebrated   
,theory of ,vision1 ,i saw the vast     

importance of establishing the law of   
visible direction1 and of proving  by   
the aid of binocular phenomena1 and in  
opposition to the opinion of  the most  
distinguished metaphysicians1 that we   
actually see a third  dimension in      
space1 ,i therefore submitted to the    
,royal ,society of  ,edinburgh1 in      
,january #ahdc1 a paper ,on the law of  
visible position in  single and         
binocular vision1 and on the            
representation of solid figures  by the 
union of dissimilar plane pictures on   
the retina4 ,more than  twelve years    
have now elapsed since this paper was   
read1 and neither  ,mr4 ,wheatstone nor 
,dr4 ,whewell have made any attempt to  
defend the  views which it refutes4     
,in continuing my researches1 ,i        
communicated to the ,royal ,society of  
,edinburgh1 in ,april #ahdd1 a paper ,on
 the knowledge of distance as  given by 
binocular vision1 in which ,i described 
several interesting  phenomena produced 
by the union of similar pictures1 such  

as those  which form the patterns of    
carpets and paper-hangings4 ,in carrying
 on  these inquiries ,i found the       
reflecting stereoscope of little        
service1  and ill fitted1 not only for  
popular use1 but for the application  of
 the instrument to various useful       
purposes4 ,i was thus led to the        
construction of several new             
stereoscopes1 but particularly to the   
,lenticular ,stereoscope1 now in        
universal use4 ,they were constructed   
in ,st4 ,andrews and ,dundee1 of various
 materials1 such as wood1  tin-plate1   
brass1 and of all sizes1 from that now  
generally adopted1  to a microscopic    
variety which could be carried in the   
pocket4 ,new  geometrical drawings were 
executed for them1 and binocular        
pictures  taken by the sun were         
lithographed by ,mr4 ,schenck of        
,edinburgh4  ,stereoscopes of the       
lenticular form were made by ,mr4       
,loudon1 optician1  in ,dundee1 and sent
 to several of the nobility in ,london1 

and in other  places1 and an account of 
these stereoscopes1 and of a binocular  
camera  for taking portraits1 and       
copying statues1 was communicated to the
  ,royal ,scottish ,society of ,arts1   
and published in their ,transactions4   
,it had never been proposed to apply the
 reflecting stereoscope to  portraiture 
or sculpture1 or1 indeed1 to any useful 
purpose2 but it was  very obvious1 after
 the discovery of the ,daguerreotype and
 ,talbotype1  that binocular drawings   
could be taken with such accuracy as to 
exhibit in the stereoscope excellent    
representations in relief1 both  of     
living persons1 buildings1 landscape    
scenery1 and every variety of           
sculpture4 ,in order to shew its        
application to the most interesting of  
these purposes1 ,dr4 ,adamson of ,st4   
,andrews1 at my request1 executed  two  
binocular portraits of himself1 which   
were generally circulated  and greatly  
admired4 ,this successful application of
 the principle to  portraiture was      

communicated to the public1 and         
recommended as an art  of great domestic
 interest4    ,after endeavouring in    
vain to induce opticians1 both in       
,london and  ,birmingham1 7where the    
instrument was exhibited in #ahdi to the
  ,british ,association17 to construct  
the lenticular stereoscope1 and         
photographers to execute binocular      
pictures for it1 ,i took with me  to    
,paris1 in #ahej1 a very fine           
instrument1 made by ,mr4 ,loudon in     
,dundee1 with the binocular drawings and
 portraits already mentioned4  ,i shewed
 the instrument to the ,abb ,moigno1 the
 distinguished author  of ,l',optique   
,moderne1 to ,m4 ,soleil and his        
son-in-law1 ,m4 ,duboscq1  the eminent  
,parisian opticians1 and to some members
 of the ,institute  of ,france4 ,these  
gentlemen saw at once the value of the  
instrument1  not merely as one of       
amusement1 but as an important auxiliary
 in the  arts of portraiture and        
sculpture4 ,m4 ,duboscq immediately     

began to make  the lenticular           
stereoscope for sale1 and executed a    
series of the most  beautiful binocular 
,daguerreotypes of living individuals1  
statues1  bouquets of flowers1 and      
objects of natural history1 which       
thousands of  individuals flocked to    
examine and admire4 ,in an interesting  
article  in ,la ,presse1#bc the ,abb    
,moigno gave the following account of   
the  introduction of the instrument into
 ,paris3--    #bc ,december #bh1 #aeej4 
8,in his last visit to ,paris1 ,sir     
,david ,brewster intrusted the models   
of his stereoscope to ,m4 ,jules        
,duboscq1 son-in-law and successor of   
,m4  ,soleil1 and whose intelligence1   
activity1 and affability will extend    
the reputation of the distinguished     
artists of the ,rue de l',odeon1 #ce4   
,m4 ,jules ,duboscq has set himself to  
work with indefatigable ardour4         
,without requiring to have recourse to  
the binocular camera1 he has1  with the 
ordinary ,daguerreotype apparatus1      

procured a great number  of dissimilar  
pictures of statues1 bas-reliefs1 and   
portraits of  celebrated individuals1 c4
 ,his stereoscopes are constructed with 
more  elegance1 and even with more      
perfection1 than the original ,english  
7,scotch7 instruments1 and while he is  
shewing their wonderful effects  to     
natural philosophers and amateurs who   
have flocked to him in crowds1  there is
 a spontaneous and unanimous cry of     
admiration40    ,while the lenticular   
stereoscope was thus exciting much      
interest in  ,paris1 not a single       
instrument had been made in ,london1 and
 it was not  till a year after its      
introduction into ,france that it was   
exhibited in  ,england4 ,in the fine    
collection of philosophical instruments 
which ,m4  ,duboscq contributed to the  
,great ,exhibition of #ahea1 and for    
which he  was honoured with a ,council  
medal1 he placed a lenticular           
stereoscope1  with a beautiful set of   
binocular ,daguerreotypes4 ,this        

instrument  attracted the particular    
attention of the ,queen1 and before the 
closing  of the ,crystal ,palace1 ,m4   
,duboscq executed a beautiful           
stereoscope1  which ,i presented to ,her
 ,majesty in his name4 ,in consequence  
of this  public exhibition of the       
instrument1 ,m4 ,duboscq received       
several orders  from ,england1 and a    
large number of stereoscopes were thus  
introduced  into this country4 ,the     
demand1 however1 became so great1 that  
opticians  of all kinds devoted         
themselves to the manufacture of the    
instrument1  and photographers1 both in 
,daguerreotype and ,talbotype1 found it 
a most  lucrative branch of their       
profession1 to take binocular portraits 
of  views to be thrown into relief by   
the stereoscope4 ,its application to    
sculpture1 which ,i had pointed out1 was
 first made in ,france1 and an  artist  
in ,paris actually copied a statue from 
the relievo produced by  the            
stereoscope4    ,three years after ,i   

had published a description of the      
lenticular  stereoscope1 and after it   
had been in general use in ,france and  
,england1 and the reflecting stereoscope
 forgotten1#bd ,mr4 ,wheatstone         
printed1 in the ,philosophical          
,transactions for #aheb1 a paper on     
,vision1 in which he says that he had   
previously used 8an apparatus in  which 
prisms were employed to deflect the rays
 of light proceeding from  the pictures1
 so as to make them appear to occupy the
 same place20 and  he adds1 8,i have    
called it the refracting                
stereoscope40#be ,now1  whatever ,mr4   
,wheatstone may have done with prisms1  
and at whatever time  he may have done  
it1 ,i was the first person who         
published a description  of stereoscopes
 both with refracting and reflecting    
prisms2 and  during the three years that
 elapsed after he had read my paper1 he 
made  no claim to the suggestion of     
prisms till after the great success of  
the lenticular stereoscope4 ,the reason 

why he then made the claim1 and  the    
only reason why we do not make him a    
present of the suggestion1  will appear 
from the following history3--    #bd    
8,le fait est10 says the ,abb ,moigno1  
8que le stroscope par  rflexion tait    
presque compltement oubli1 lorsque ,sir 
,david  ,brewster construisit son       
stroscope par refraction que nous allons
  dcrire40--,cosmos1 vol4 i4 p4 #d1     
#aheb4    #be ,phil4 ,trans41 #aheb1 p4 
#f4    ,in the paper above referred to1 
,mr4 ,wheatstone says1--8,i recommend1  
as  a convenient arrangement of the     
refracting stereoscope for viewing      
,daguerreotypes of small dimensions1 the
 instrument represented1 7,fig4  #d17   
shortened in its length from #h inches  
to #e1 and lenses #e inches  focal      
distance1 placed before and close to the
 prisms40#bf ,although  this refracting 
apparatus1 which is simply a            
deterioration of the  lenticular        
stereoscope1 is recommended by ,mr4     
,wheatstone1 nobody  either makes it or 

uses it4 ,the semi-lenses or            
quarter-lenses of the  lenticular       
stereoscope include a virtual and       
absolutely perfect  prism1 and1 what is 
of far more consequence1 each lens is a 
variable  lenticular prism1 so that1    
when the eye-tubes are placed at        
different  distances1 the lenses have   
different powers of displacing the      
pictures4  ,they can thus unite pictures
 placed at different distances1 which   
cannot be done by any combination of    
whole lenses and prisms4    #bf ,ibid41 
pp4 #i1 #aj4    ,in the autumn of #ahed1
 after all the facts about the          
stereoscope  were before the public1 and
 ,mr4 ,wheatstone in full possession of 
all  the merit of having anticipated    
,mr4 ,elliot in the publication of  his 
stereoscopic apparatus1 and of his      
explanation of the theory of            
stereoscopic relief1 such as it was1 he 
thought it proper to revive  the        
controversy by transmitting to the ,abb 
,moigno1 for publication in  ,cosmos1 an

 extract of a letter of mine dated #bgth
 ,september #ahch4 ,this  extract was   
published in the ,cosmos of the #aeth   
,august #ahed1bg with  the following    
illogical commentary by the editor4     
8,nous avons eu tort mille fois         
d'accorder  notre      illustre ami1    
,sir ,david ,brewster1 l'invention du   
stroscope par rfraction4 ,m4            
,wheatstone1 en effet1      a mis entre 
nos mains une lettre date1 le croirait  
on1 du #bg ,septembre #ahch1 dans lequel
 nous avons      l ces mots crits par   
l'illustre savant ,ecossais3      #8,i  
have also stated that you promised to   
order      for me your stereoscope1 both
 with reflectors and      ,,prisms4     
,j'ai aussi dit 7 ,lord ,rosse#bh7      
que vous aviez promis de commander pour 
moi votre      stroscope1 celui avec    
rflecteurs et celui avec      prismes4' 
,le stroscope par rfraction est donc1   
aussi bien que le stroscope par         
rflexion1 le      stroscope de ,m4      
,wheatstone1 qui l'avait invent      en 

#ahch1 et le faisait construire  cette  
poque      pour ,sir ,david ,brewster   
lui-mme4 ,ce que ,sir      ,david       
,brewster a imagine1 et c'est une ide   
trs      ingnieuse1 dont ,m4 ,wheatstone
 ne lui disputt      jamais la gloire1  
c'est de former les deux prismes      du
 stroscope par rfraction avec les deux  
moitis      d'une mme lentille40    #bg 
,vol4 v4 livre viii4 p4 #bda4    #bh    
,mr4 ,andrew ,ross1 the celebrated      
optician6    ,that the reader may form a
 correct idea of the conduct of ,mr4    
,wheatstone in making this claim        
indirectly1 and in a foreign journal1   
whose editor he has willingly misled1 ,i
 must remind him that ,i  first saw the 
reflecting stereoscope at the meeting of
 the ,british  ,association at          
,newcastle1 in the middle of ,august    
#ahch4 ,it is proved  by my letter that 
he and ,i then conversed on the subject 
of prisms1  which at that time he had   
never thought of4 ,i suggested prisms   
for  displacing the pictures1 and ,mr4  

,wheatstone's natural reply was1 that   
they must be achromatic prisms4 ,this   
fact1 if denied1 may be proved  by      
various circumstances4 ,his paper of    
#ahch contains no reference to  prisms4 
,if he had suggested the use of prisms  
in ,august #ahch1 he would  have        
inserted his suggestion in that paper1  
which was then unpublished2  and if he  
had only once tried a prism stereoscope1
 he never would  have used another4 ,on 
my return to ,scotland1 ,i ordered from 
,mr4 ,andrew  ,ross one of the          
reflecting stereoscopes1 and one made   
with achromatic  prisms2 but my words do
 not imply that ,mr4 ,wheatstone was the
 first  person who suggested prisms1 and
 still less that he ever made or used  a
 stereoscope with prisms4 ,but however  
this may be1 it is a most  extraordinary
 statement1 which he allows the ,abb    
,moigno to make1 and  which1 though made
 a year and a half ago1 he has not      
enabled the ,abb  to correct1 that a    
stereoscope with prisms was made for me 

7or for  any other person7 by ,mr4      
,ross4 ,i never saw such an instrument1 
or  heard of its being constructed3 ,i  
supposed that after our conversation    
,mr4 ,wheatstone might have tried       
achromatic prisms1 and in #ahdh1 when ,i
  described my single prism stereoscope1
 ,i stated what ,i now find is not      
correct1 that ,i believed ,mr4          
,wheatstone had used two achromatic     
prisms4 ,the following letter from ,mr4 
,andrew ,ross will prove the main  fact 
that he never constructed for me1 or for
 ,mr4 ,wheatstone1 any  refracting      
stereoscope3--                          
0#b1 ,,featherstone ,,buildings1        
#bhth ,september #ahed4        8,,dear  
,,sir1--,in reply to yours of the #aath 
instant1 ,i beg to state that ,i never  
supplied you      with a stereoscope in 
which prisms were employed in      place
 of plane mirrors4 ,i have a perfect    
recollection      of being called upon  
either by yourself or ,professor        
,wheatstone1 some fourteen years since1 

to make      achromatized prisms for the
 above instrument4 ,i also              
recollect that ,i did not proceed to    
manufacture them      in consequence of 
the great bulk of an achromatized       
prism1 with reference to their power of 
deviating a      ray of light1 and at   
that period glass sufficiently      free
 from stri could not readily be         
obtained1 and      was consequently very
 high-priced4--,i remain1 c4 c4         
8,,andrew ,,ross4      8,to ,sir ,david 
,brewster40    ,upon the receipt of this
 letter ,i transmitted a copy of it to  
the ,abb  ,moigno1 to shew him how he   
had been misled into the statement1     
8that  ,mr4 ,wheatstone had caused a    
stereoscope with prisms to be           
constructed  for me20 but neither he nor
 ,mr4 ,wheatstone have felt it their    
duty to  withdraw that erroneous        
statement4    ,in reference to the      
comments of the ,abb ,moigno1 it is     
necessary to  state1 that when he wrote 
them he had in his possession my printed

  description of the single-prism1 and  
other stereoscopes1#bi in which  ,i     
mention my belief1 now proved to be     
erroneous1 that ,mr4 ,wheatstone  had   
used achromatic prisms1 so that he had1 
on my express authority1  the           
information which surprised him in my   
letter4 ,the ,abb also must  bear the   
responsibility of a glaring             
misinterpretation of my letter  of      
#ahch4 ,in that letter ,i say that ,mr4 
,wheatstone promised to order  certain  
things from ,mr4 ,ross1 and the ,abb    
declares1 contrary to the  express terms
 of the letter1 as well as to fact1 that
 these things  were actually constructed
 for me4 ,the letter1 on the contrary1  
does  not even state that ,mr4          
,wheatstone complied with my request1   
and it  does not even appear from it    
that the reflecting stereoscope was made
  for me by ,mr4 ,ross4    #bi ,the ,abb
 gave an abstract of this paper in the  
,french journal ,la  ,presse1 ,december 
#bh1 #ahej4    ,such is a brief history 

of the lenticular stereoscope1 of its   
introduction into ,paris and ,london1   
and of its application to  portraiture  
and sculpture4 ,it is now in general use
 over the whole  world1 and it has been 
estimated that upwards of half a million
  of these instruments have been sold4  
,a ,stereoscope ,company has  been      
established in ,london#cj for the       
manufacture and sale of the  lenticular 
stereoscope1 and for the production of  
binocular pictures  for educational and 
other purposes4 ,photographers are now  
employed  in every part of the globe in 
taking binocular pictures for the       
instrument1--among the ruins of ,pompeii
 and ,herculaneum--on the glaciers  and 
in the valleys of ,switzerland--among   
the public monuments in the  ,old and   
the ,new ,world--amid the shipping of   
our commercial harbours--in  the museums
 of ancient and modern life--in the     
sacred precincts of  the domestic       
circle--and among those scenes of the   
picturesque and the  sublime which are  

so affectionately associated with the   
recollection of  our early days1 and    
amid which1 even at the close of life1  
we renew1  with loftier sentiments and  
nobler aspirations1 the youth of our    
being1  which1 in the worlds of the     
future1 is to be the commencement of a  
longer and a happier existence4    #cj  
,no4 #ed1 ,cheapside1 and #cac1 ,oxford 
,street4 ,the prize of twenty  guineas  
which they offered for the best short   
popular treatise on the  ,stereoscope1  
has been adjudged to ,mr4 ,lonie1       
,teacher of ,mathematics in  the ,madras
 ,institution1 ,st4 ,andrews4 ,the      
second prize was given to the  ,rev4 ,r4
 ,graham1 ,abernyte1 ,perthshire4       
,,chapter ,,ii4    ,,on ,,monocular     
,,vision1 ,,or ,,vision ,,with ,,one    
,,eye4      ,in order to understand the 
theory and construction of the          
stereoscope  we must be acquainted with 
the general structure of the eye1 with  
the  mode in which the images of visible
 objects are formed within it1 and  with

 the laws of vision by means of which we
 see those objects in  the position     
which they occupy1 that is1 in the      
direction and at the  distance at which 
they exist4    ,every visible object    
radiates1 or throws out in all          
directions1  particles or rays of light1
 by means of which we see them either   
directly by the images formed in the    
eye1 or indirectly by looking at  images
 of them formed by their passing through
 a small hole1 or through  a lens placed
 in a dark room or camera1 at the end of
 which is a  piece of paper or          
ground-glass to receive the image4      
,in order to understand this let ,h be a
 very small pin-hole in a shutter  or   
camera1 ,,mn1 and let ,,ryb be any      
object of different colours1 the  upper 
part1 ,r1 being red1 the middle1 ,y1    
yellow1 and the lower  part1 ,b1 blue4  
,if a sheet of white paper1 br1 is      
placed behind  the hole ,h1 at the same 
distance as the object ,,rb is before   
it1 an  image1 br1 will be formed of the

 same ray and the same colours as the   
object ,,rb4 ,as the particles or rays  
of light move in straight lines1  a red 
ray from the middle part of ,r will pass
 through the hole ,h and  illuminate the
 point r with red light4 ,in like       
manner1 rays from  the middle points of 
,y and ,b will pass through ,h and      
illuminate with  yellow and blue light  
the points y and b4 ,every other point  
of the coloured spaces1 ,r1 ,y1 and ,b1 
will1 in the same manner1 paint  itself1
 as it were1 on the paper1 and produce a
 coloured image1 byr1  exactly the same 
in form and colour as the object ,,ryb4 
,if the hole ,h  is sufficiently small  
no ray from any one point of the object 
will  interfere with or mix with any    
other ray that falls upon the paper4    
,if the paper is held at half the       
distance1 at by for example1 a  coloured
 image1 byr1 of half the size1 will be  
formed1 and if we  hold it at twice the 
distance1 at br for example1 a coloured 
image1  byr1 of twice the size1 will be 

painted on the paper4    ,illustration3 
,,fig4 #d4    ,as the hole ,h is        
supposed to be so small as to receive   
only one ray  from every point of the   
object1 the images of the object1 viz41 
br1  br1 br1 will be very faint4 ,by    
widening the hole ,h1 so as  to admit   
more rays from each luminous point of   
,,rb1 the images would  become brighter1
 but they would become at the same time 
indistinct1  as the rays from one point 
of the object would mix with those from 
adjacent points1 and at the boundaries  
of the colours ,r1 ,y1 and ,b1 the  one 
colour would obliterate the other4 ,in  
order1 therefore1 to obtain             
sufficiently bright images of visible   
objects we must use lenses1  which have 
the property of forming distinct images 
behind them1 at a  point called their   
focus4 ,if we widen the hole ,h1 and    
place in it a  lens whose focus is at y1
 for an object at the same distance1    
,,hy1 it  will form a bright and        
distinct image1 br1 of the same size as 

the  object ,,rb4 ,if we remove the     
lens1 and place another in ,h1 whose    
focus  is at y1 for a distance ,,hy1 an 
image1 br1 half of the size of  ,,rb1   
will be formed at that point2 and if we 
substitute for this lens  another1 whose
 focus is at y1 a distinct image1 br1   
twice the  size of the object1 will be  
formed1 the size of the image being     
always  to that of the object as their  
respective distances from the hole or   
lens at ,h4    ,with the aid of these   
results1 which any person may confirm by
 making  the experiments1 we shall      
easily understand how we see external   
objects  by means of the images formed  
in the eye4 ,the human eye1 a section   
and a front view of which is shewn in   
,fig4 #e1 ,a1 is almost a sphere4  ,its 
outer membrane1 ,,abcde1 or ,,mno1 ,fig4
 #e1 ,b1 consists of a tough  substance1
 and is called the sclerotic coat1 which
 forms the white  of the eye1 ,a1 seen  
in the front view4 ,the front part of   
the eyeball1  ,cx,d1 which resembles a  

small watch-glass1 is perfectly         
transparent1  and is called the cornea4 
,behind it is the iris1 cabe1 or ,c in  
the front view1 which is a circular     
disc1 with a hole1 ab1 in its  centre1  
called the pupil1 or black of the eye4  
,it is1 as it were1  the window of the  
eye1 through which all the light from   
visible  objects must pass4 ,the iris   
has different colours in different      
persons1 black1 blue1 or grey2 and the  
pupil1 ab1 or ,h1 has  the power of     
contracting or enlarging its size       
according as the light  which enters it 
is more or less bright4 ,in sunlight it 
is very small1  and in twilight its size
 is considerable4 ,behind the iris1 and 
close  to it1 is a doubly convex lens1  
df1 or ,,ll in ,fig4 #e1 ,b1 called the 
crystalline lens4 ,it is more convex or 
round on the inner side1 and  it is     
suspended by the ciliary processes at   
,,lc1 ,,lc1 by which it  is supposed to 
be moved towards and from ,h1 in order  
to accommodate  the eye to different    

distances1 or obtain distinct vision at 
these  distances4 ,at the back of the   
eye is a thin pulpy transparent         
membrane1  rr ,o rr1 or vvv1 called the 
retina1 which1 like the ground  glass of
 a camera obscura1 receives the images  
of visible objects4  ,this membrane is  
an expansion of the optic nerve ,o1 or  
,a in ,fig4 #e1 ,a1  which passes to the
 brain1 and1 by a process of which we   
are ignorant1  gives us vision of the   
objects whose images are formed on its  
expanded  surface4 ,the globular form of
 the eye is maintained by two fluids    
which  fill it1--the aqueous humour1    
which lies between the crystalline lens 
and the cornea1 and the vitreous humour1
 ,,zz1 which fills the back of  the eye4
    ,illustration3 ,,fig4 #e1 ,a4       
,illustration3 ,,fig4 #e1 ,b4    ,but   
though we are ignorant of the manner in 
which the mind takes  cognizance through
 the brain of the images on the retina1 
and may  probably never know it1 we can 
determine experimentally the laws by    

which we obtain1 through their images on
 the retina1 a knowledge of the         
direction1 the position1 and the form of
 external objects4    ,if the eye ,,mn  
consisted only of a hollow ball with a  
small aperture ,h1  an inverted image1  
ab1 of any external object ,,ab would be
 formed on  the retina r,or1 exactly as 
in ,fig4 #d4 ,a ray of light from ,a    
passing  through ,h would strike the    
retina at a1 and one from ,b would      
strike  the retina at b4 ,if the hole ,h
 is very small the inverted image  ab   
would be very distinct1 but very        
obscure4 ,if the hole were the  size of 
the pupil the image would be            
sufficiently luminous1 but very         
indistinct4 ,to remedy this the         
crystalline lens is placed behind the   
pupil1 and gives distinctness to the    
image ab formed in its focus4  ,the     
image1 however1 still remains inverted1 
a ray from the upper part  ,a of the    
object necessarily falling on the lower 
part a of the  retina1 and a ray from   

the lower part ,b of the object upon the
 upper  part b of the retina4 ,now1 it  
has been proved by accurate experiments 
that in whatever direction a ray ,,aha  
falls upon the retina1 it gives  us the 
vision of the point ,a from which it    
proceeds1 or causes us to  see that     
point1 in a direction perpendicular to  
the retina at a1 the  point on which it 
falls4 ,it has also been proved that the
 human eye is  nearly spherical1 and    
that a line drawn perpendicular to the  
retina  from any point a of the image ab
 will very nearly pass through the      
corresponding point ,a of the object    
,,ab1#ca so that the point ,a is1 in    
virtue of this law1 which is called the 
,law of visible direction1  seen in     
nearly its true direction4    #ca       
,edinburgh ,transactions1 vol4 xv4 p4   
#cdi1 #ahdc2 or ,philosophical          
,magazine1 vol4 xxv4 pp4 #cef1 #dci1    
,may and ,june #ahdd4    ,when we look  
at any object1 ,,ab1 for example1 we see
 only one point  of it distinctly4 ,in  

,fig4 #e the point ,d only is seen      
distinctly1 and  every point from ,d to 
,a1 and from ,d to ,b1 less distinctly4 
,the point of  distinct vision on the   
retina is at d1 corresponding with the  
point ,d  of the object which is seen   
distinctly4 ,this point d is the centre 
of  the retina at the extremity of the  
line ,,aha1 called the optical axis  of 
the eye1 passing through the centre of  
the lens ,lh1 and the centre  of the    
pupil4 ,the point of distinct vision d  
corresponds with a small  hole in the   
retina called the ,foramen centrale1 or 
central hole1  from its being in the    
centre of the membrane4 ,when we wish to
 see the  points ,a and ,b1 or any other
 point of the object1 we turn the eye   
upon  them1 so that their image may fall
 upon the central point d4 ,this  is    
done so easily and quickly that every   
point of an object is seen  distinctly  
in an instant1 and we obtain the most   
perfect knowledge  of its form1 colour1 
and direction4 ,the law of distinct     

vision may be  thus expressed4 ,vision  
is most distinct when it is performed by
 the  central point of the retina1 and  
the distinctness decreases with the     
distance from the central point4 ,it is 
a curious fact1 however1 that  the most 
distinct point d is the least sensitive 
to light1 and that  the sensitiveness   
increases with the distance from that   
point4 ,this is  proved by the          
remarkable fact1 that when an astronomer
 cannot see a  very minute star by      
looking at it directly along the optical
 axis d,d1  he can see it by looking    
away from it1 and bringing its image    
upon a  more sensitive part of the      
retina4    ,but though we see with one  
eye the direction in which any object or
  point of an object is situated1 we do 
not see its position1 or the  distance  
from the eye at which it is placed4 ,if 
a small luminous point  or flame is put 
into a dark room by another person1 we  
cannot with one  eye form anything like 
a correct estimate of its distance4     

,even in good  light we cannot with one 
eye snuff a candle1 or pour wine into a 
small  glass at arm's length4 ,in       
monocular vision1 we learn from         
experience to  estimate all distances1  
but particularly great ones1 by various 
means1  which are called the criteria of
 distance2 but it is only with both     
eyes that we can estimate with anything 
like accuracy the distance of  objects  
not far from us4    ,the criteria of    
distance1 by which we are enabled with  
one eye to  form an approximate estimate
 of the distance of objects are five in 
number4    #a4 ,the interposition of    
numerous objects between the eye and the
 object  whose distance we are          
appreciating4 ,a distance at sea appears
 much  shorter than the same distance on
 land1 marked with houses1 trees1 and   
other objects2 and for the same reason1 
the sun and moon appear more  distant   
when rising or setting on the horizon of
 a flat country1 than  when in the      
zenith1 or at great altitudes4    #b4   

,the variation in the apparent magnitude
 of known objects1 such as  man1        
animals1 trees1 doors and windows of    
houses4 ,if one of two men1  placed at  
different distances from us1 appears    
only half the size of  the other1 we    
cannot be far wrong in believing that   
the smallest in  appearance is at twice 
the distance of the other4 ,it is       
possible that  the one may be a dwarf1  
and the other of gigantic stature1 in   
which  case our judgment would be       
erroneous1 but even in this case other  
criteria might enable us to correct it4 
#c4 ,the degree of vivacity in the      
colours and tints of objects4    #d4    
,the degree of distinctness in the      
outline and minute parts of  objects4   
#e4 ,to these criteria we may add the   
sensation of muscular action1 or  rather
 effort1 by which we close the pupil in 
accommodating the eye to  near          
distances1 and produce the              
accommodation4    ,with all these means 
of estimating distances1 it is only by  

binocular  vision1 in which we converge 
the optical axes upon the object1 that  
we  have the power of seeing distance   
within a limited range4    ,but this is 
the only point in which ,monocular is   
inferior to  ,binocular vision4 ,in the 
following respects it is superior to it4
    #a4 ,when we look at oil paintings1 
the varnish on their surface reflects   
to each eye the light which falls upon  
it from certain parts of the  room4 ,by 
closing one eye we shut out the quantity
 of reflected light  which enters it4   
,pictures should always be viewed by the
 eye farthest  from windows or lights in
 the apartment1 as light diminishes the 
sensibility of the eye to the red rays4 
#b4 ,when we view a picture with both   
eyes1 we discover1 from the  convergency
 of the optic axes1 that the picture is 
on a plane surface1  every part of which
 is nearly equidistant from us4 ,but    
when we shut one  eye1 we do not make   
this discovery2 and therefore the effect
 with which  the artist gives relief to 

the painting exercises its whole effect 
in  deceiving us1 and hence1 in         
monocular vision1 the relievo of the    
painting is much more complete4    ,this
 influence over our judgment is         
beautifully shewn in viewing1  with one 
eye1 photographs either of persons1 or  
landscapes1 or solid  objects4 ,after a 
little practice1 the illusion is very   
perfect1 and  is aided by the correct   
geometrical perspective and chiaroscuro 
of  the ,daguerreotype or ,talbotype4   
,to this effect we may give the name of 
,monocular ,relief1 which1 as we shall  
see1 is necessarily inferior to         
,binocular ,relief1 when produced by the
 stereoscope4    #c4 ,as it very        
frequently happens that one eye has not 
exactly the same  focal length as the   
other1 and that1 when it has1 the vision
 by one eye  is less perfect than that  
by the other1 the picture formed by     
uniting a  perfect with a less perfect  
picture1 or with one of a different     
size1  must be more imperfect than the  

single picture formed by one eye4       
,,chapter ,,iii4    ,,on ,,binocular    
,,vision1 ,,or ,,vision ,,with ,,two    
,,eyes4      ,we have already seen1 in  
the history of the stereoscope1 that in 
the binocular vision of objects1 each   
eye sees a different picture  of the    
same object4 ,in order to prove this1 we
 require only to look  attentively at   
our own hand held up before us1 and     
observe how some  parts of it disappear 
upon closing each eye4 ,this experiment 
proves1 at  the same time1 in opposition
 to the opinion of ,baptista ,porta1    
,tacquet1  and others1 that we always   
see two pictures of the same object     
combined  in one4 ,in confirmation of   
this fact1 we have only to push aside   
one  eye1 and observe the image which   
belongs to it separate from the other1  
and again unite with it when the        
pressure is removed4    ,it might have  
been supposed that an object seen by    
both eyes would be  seen twice as       
brightly as with one1 on the same       

principle as the light  of two candles  
combined is twice as bright as the light
 of one4 ,that  this is not the case has
 been long known1 and ,dr4 ,jurin has   
proved  by experiments1 which we have   
carefully repeated and found correct1   
that the brightness of objects seen with
 two eyes is only _/th part  greater    
than when they are seen with one eye4#cb
 ,the cause of this  is well known4     
,when both eyes are used1 the pupils of 
each contract  so as to admit the proper
 quantity of light2 but the moment we   
shut  the right eye1 the pupil of the   
left dilates to nearly twice its size1  
to compensate for the loss of light     
arising from the shutting of the        
other4#cc    #cb ,smith's ,opticks1 vol4
 ii41 ,remarks1 p4 #ajg4 ,harris makes  
the  difference _/th or _/th2 ,optics1  
p4 #aag4    #cc ,this variation of the  
pupil is mentioned by ,bacon4           
,illustration3 ,,fig4 #f4    ,this      
beautiful provision to supply the proper
 quantity of light when  we can use only

 one eye1 answers a still more important
 purpose1 which  has escaped the notice 
of optical writers4 ,in binocular       
vision1 as we  have just seen1 certain  
parts of objects are seen with both     
eyes1 and  certain parts only with one2 
so that1 if the parts seen with both    
eyes  were twice as bright1 or even much
 brighter than the parts seen with  one1
 the object would appear spotted1 from  
the different brightness of  its parts4 
,in ,fig4 #f1 for example1 7see p4 #ad17
 the areas ,,bfi and ,,cgi1  the former 
of which is seen only by the left eye1  
,d1 and the latter  only by the right   
eye1 ,e1 and the corresponding areas on 
the other side  of the sphere1 would be 
only half as bright as the portion      
,,figh1 seen  with both eyes1 and the   
sphere would have a singular appearance4
    ,it has long been1 and still is1 a  
vexed question among philosophers1  how 
we see objects single with two eyes4    
,baptista ,porta1 ,tacquet1 and  others1
 got over the difficulty by denying the 

fact1 and maintaining  that we use only 
one eye1 while other philosophers of    
distinguished  eminence have adopted    
explanations still more groundless4 ,the
 law of  visible direction supplies us  
with the true explanation4              
,illustration3 ,,fig4 #g4    ,let us    
first suppose that we look with both    
eyes1 ,r and ,l1 ,fig4 #g1 upon  a      
luminous point1 ,d1 which we see single1
 though there is a picture  of it on the
 retina of each eye4 ,in looking at the 
point ,d we turn or  converge the       
optical axes d,,hd1 d,h ,d1 of each eye 
to the point ,d1  an image of which is  
formed at d in the right eye ,r1 and at 
d in  the left eye ,l4 ,in virtue of the
 law of visible direction the point  ,d 
is seen in the direction d,d with the   
eye ,r1 and in the direction  d,d with  
the eye ,l1 these lines being           
perpendicular to the retina  at the     
points d1 d4 ,the one image of the point
 ,d is therefore  seen lying upon the   
other1 and consequently seen single4    

,considering  ,d1 then1 as a single     
point of a visible object ,,ab1 the two 
eyes will  see the points ,a and ,b     
single by the same process of turning or
  converging upon them their optical    
axes1 and so quickly does the point  of 
convergence pass backward and forward   
over the whole object1 that  it appears 
single1 though in reality only one point
 of it can be seen  single at the same  
instant4 ,the whole picture of the line 
,,ab1 as seen  with one eye1 seems to   
coincide with the whole picture of it as
 seen  with the other1 and to appear    
single4 ,the same is true of a surface  
or area1 and also of a solid body or a  
landscape4 ,only one point of  each is  
seen single2 but we do not observe that 
other points are  double or indistinct1 
because the images of them are upon     
parts of the  retina which do not give  
distinct vision1 owing to their distance
 from  the foramen or point which gives 
distinct vision4 ,hence we see the      
reason why distinct vision is obtained  

only on one point of the retina4  ,were 
it otherwise we should see every other  
point double when we look  fixedly upon 
one part of an object4 ,if in place of  
two eyes we had  a hundred1 capable of  
converging their optical axes to one    
point1  we should1 in virtue of the law 
of visible direction1 see only one      
object4    ,the most important advantage
 which we derive from the use of two    
eyes is to enable us to see distance1 or
 a third dimension in  space4 ,that we  
have this power has been denied by ,dr4 
,berkeley1 and  many distinguished      
philosophers1 who maintain that our     
perception of  distance is acquired by  
experience1 by means of the criteria    
already  mentioned4 ,this is undoubtedly
 true for great distances1 but we  shall
 presently see1 from the effects of the 
stereoscope1 that the  successive       
convergency of the optic axes upon two  
points of an object  at different       
distances1 exhibits to us the difference
 of distance when  we have no other     

possible means of perceiving it4 ,if1   
for example1 we  suppose ,g1 ,d1 ,fig4  
#g1 to be separate points1 or parts of  
an object1  whose distances are ,,go1   
,,do1 then if we converge the optical   
axes ,,hg1  ,h ,g upon ,g1 and next turn
 them upon ,d1 the points will appear to
 be  situated at ,g and ,d at the       
distance ,,gd from each other1 and at   
the  distances ,,og1 ,,od from the      
observer1 although there is nothing     
whatever  in the appearance of the      
points1 or in the lights and shades of  
the  object1 to indicate distance4 ,that
 this vision of distance is not  the    
result of experience is obvious from the
 fact that distance is  seen as         
perfectly by children as by adults2 and 
it has been proved  by naturalists that 
animals newly born appreciate distances 
with the  greatest correctness4 ,we     
shall afterwards see that so infallible 
is  our vision of near distances1 that a
 body whose real distance we can        
ascertain by placing both our hands upon

 it1 will appear at the greater  or less
 distance at which it is placed by the  
convergency of the  optical axes4    ,we
 are now prepared to understand         
generally1 how1 in binocular vision1  we
 see the difference between a picture   
and a statue1 and between a  real       
landscape and its representation4 ,when 
we look at a picture of  which every    
part is nearly at the same distance from
 the eyes1 the  point of convergence of 
the optical axes is nearly at the same  
distance  from the eyes2 but when we    
look at its original1 whether it be a   
living man1 a statue1 or a landscape1   
the optical axes are converged  in rapid
 succession upon the nose1 the eyes1 and
 the ears1 or upon  objects in the      
foreground1 the middle and the remote   
distances in the  landscape1 and the    
relative distances of all these points  
from the eye  are instantly perceived4  
,the binocular relief thus seen is      
greatly  superior to the monocular      
relief already described4    ,since     

objects are seen in relief by the       
apparent union of two  dissimilar plane 
pictures of them formed in each eye1 it 
was a  supposition hardly to be         
overlooked1 that if we could delineate  
two  plane pictures of a solid object1  
as seen dissimilarly with each  eye1 and
 unite their images by the convergency  
of the optical axes1  we should see the 
solid of which they were the            
representation4 ,the  experiment was    
accordingly made by more than one       
person1 and was found  to succeed2 but  
as few have the power1 or rather the    
art1 of thus  converging their optical  
axes1 it became necessary to contrive an
  instrument for doing this4    ,the    
first contrivances for this purpose     
were1 as we have already  stated1 made  
by ,mr4 ,elliot and ,mr4 ,wheatstone4 ,a
 description of these1  and of others   
better fitted for the purpose1 will be  
found in the  following chapter4        
,,chapter ,,iv4    ,,description ,,of   
,,the ,,ocular1 ,,the ,,reflecting1     

,,and ,,the ,,lenticular                
,,stereoscopes4      ,although it is by 
the combination of two plane pictures of
 an object1  as seen by each eye1 that  
we see the object in relief1 yet the    
relief  is not obtained from the mere   
combination or superposition of the two 
dissimilar pictures4 ,the superposition 
is effected by turning each eye  upon   
the object1 but the relief is given by  
the play of the optic axes  in uniting1 
in rapid succession1 similar points of  
the two pictures1  and placing them1 for
 the moment1 at the distance from the   
observer of  the point to which the axes
 converge4 ,if the eyes were to unite   
the two  images into one1 and to retain 
their power of distinct vision1 while   
they lost the power of changing the     
position of their optic axes1 no  relief
 would be produced4    ,this is equally 
true when we unite two dissimilar       
photographic pictures  by fixing the    
optic axes on a point nearer to or      
farther from the eye4  ,though the      

pictures apparently coalesce1 yet the   
relief is given by the  subsequent play 
of the optic axes varying their angles1 
and converging  themselves successively 
upon1 and uniting1 the similar points in
 each  picture that correspond to       
different distances from the observer4  
,as very few persons have the power of  
thus uniting1 by the eyes alone1  the   
two dissimilar pictures of the object1  
the stereoscope has been  contrived to  
enable them to combine the two pictures1
 but it is not  the stereoscope1 as has 
been imagined1 that gives the relief4   
,the  instrument is merely a substitute 
for the muscular power which brings  the
 two pictures together4 ,the relief is  
produced1 as formerly1  solely by the   
subsequent play of the optic axes4 ,if  
the relief were  the effect of the      
apparent union of the pictures1 we      
should see it by  looking with one eye  
at the combined binocular pictures--an  
experiment  which could be made by      
optical means2 but we should look for it

 in  vain4 ,the combined pictures would 
be as flat as the combination of two    
similar pictures4 ,these experiments    
require to be made with a thorough      
knowledge of the subject1 for when the  
eyes are converged on one point  of the 
combined picture1 this point has the    
relief1 or distance from  the eye1      
corresponding to the angle of the optic 
axes1 and therefore  the adjacent points
 are1 as it were1 brought into a sort of
 indistinct  relief along with it2 but  
the optical reader will see at once that
  the true binocular relief cannot be   
given to any other parts of the         
picture1 till the axes of the eyes are  
converged upon them4 ,these  views will 
be more readily comprehended when we    
have explained1 in a  subsequent        
chapter1 the theory of stereoscopic     
vision4      ,the ,ocular ,stereoscope4 
,we have already stated that objects are
 seen in perfect relief when  we unite  
two dissimilar photographic pictures of 
them1 either by  converging the optic   

axes upon a point so far in front of the
 pictures  or so far beyond them1 that  
two of the four images are combined4    
,in both these cases each picture is    
seen double1 and when the two  innermost
 of the four1 thus produced1 unite1 the 
original object is  seen in relief4 ,the
 simplest of these methods is to        
converge the  optical axes to a point   
nearer to us than the pictures1 and this
 may  be best done by holding up a      
finger between the eyes and the         
pictures1  and placing it at such a     
distance that1 when we see it single1   
the two  innermost of the four pictures 
are united4 ,if the finger is held up   
near the dissimilar pictures1 they will 
be slightly doubled1 the two  images of 
each overlapping one other2 but by      
bringing the finger nearer  the eye1 and
 seeing it singly and distinctly1 the   
overlapping images  will separate more  
and more till they unite4 ,we have1     
therefore1 made  our eyes a stereoscope1
 and we may1 with great propriety1 call 

it the  ,ocular ,stereoscope4 ,if we    
wish to magnify the picture in relief1  
we  have only to use convex spectacles1 
which will produce the requisite        
magnifying power2 or what is still      
better1 to magnify the united  pictures 
with a powerful reading-glass4 ,the two 
single images are hid  by advancing the 
reading-glass1 and the other two        
pictures are kept  united with a less   
strain upon the eyes4    ,as very few   
people can use their eyes in this       
manner1 some instrumental  auxiliary    
became necessary1 and it appears to us  
strange that the  simplest method of    
doing this did not occur to ,mr4 ,elliot
 and ,mr4  ,wheatstone1 who first       
thought of giving us the help of an     
instrument4  ,by enabling the left eye  
to place an image of the left-hand      
picture  upon the right-hand picture1 as
 seen by the naked eye1 we should have  
obtained a simple instrument1 which     
might be called the ,monocular          
,stereoscope1 and which we shall have   

occasion to describe4 ,the same         
contrivance applied also to the right   
eye1 would make the instrument          
,binocular4 ,another simple contrivance 
for assisting the eyes would  have been 
to furnish them with a minute           
opera-glass1 or a small  astronomical   
telescope about an inch long1 which1    
when held in the hand  or placed in a   
pyramidal box1 would unite the          
dissimilar pictures with  the greatest  
facility and perfection4 ,this form of  
the stereoscope will  be afterwards     
described under the name of the         
,opera-,glass ,stereoscope4             
,illustration3 ,,fig4 #h4               
,description of the ,ocular             
,stereoscope4    ,a stereoscope upon the
 principle already described1 in which  
the eyes  alone are the agent1 was      
contrived1 in #ahcd1 by ,mr4 ,elliot1 as
 we  have already had occasion to state4
 ,he placed the binocular pictures1     
described in ,chapter ,i41 at one end of
 a box1 and without the aid  either of  

lenses or mirrors1 he obtained a        
landscape in perfect relief4  ,i have   
examined this stereoscope1 and have     
given1 in ,fig4 #h1 an  accurate though 
reduced drawing of the binocular        
pictures executed and  used by ,mr4     
,elliot4 ,i have also united the two    
original pictures by  the convergency of
 the optic axes beyond them1 and have   
thus seen the  landscape in true relief4
 ,to delineate these binocular pictures 
upon  stereoscopic principles was a bold
 undertaking1 and establishes1 beyond   
all controversy1 ,mr4 ,elliot's claim to
 the invention of the ocular            
stereoscope4    ,if we unite the two    
pictures in ,fig4 #h1 by converging the 
optic axes to  a point nearer the eye   
than the pictures1 we shall see         
distinctly the  stereoscopic relief1 the
 moon being in the remote distance1 the 
cross  in the middle distance1 and the  
stump of a tree in the foreground4      
,if we place the two pictures as in     
,fig4 #i1 which is the position they    

had in ,mr4 ,elliot's box1 and unite    
them1 by looking at a point beyond  them
 we shall also observe the stereoscopic 
relief4 ,in this position  ,mr4 ,elliot 
saw the relief without any effort1 and  
even without being  conscious that he   
was not viewing the pictures under      
ordinary vision4  ,this tendency of the 
optic axes to a distant convergency is  
so rare  that ,i have met with it only  
in one person4    ,illustration3 ,,fig4 
#i4    ,as the relief produced by the   
union of such imperfect pictures was    
sufficient only to shew the correctness 
of the principle1 the friends  to whom  
,mr4 ,elliot shewed the instrument      
thought it of little interest1  and he  
therefore neither prosecuted the        
subject1 nor published any  account of  
his contrivance4    ,mr4 ,wheatstone    
suggested a similar contrivance1 without
 either mirrors  or lenses4 ,in order to
 unite the pictures by converging the   
optic axes  to a point between them and 
the eye1 he proposed to place them in a 

box to hide the lateral image and assist
 in making them unite with  the naked   
eyes4 ,in order to produce the union by 
looking at a point  beyond the picture1 
he suggested the use of 8a pair of tubes
 capable  of being inclined to each     
other at various angles10 the pictures  
being  placed on a stand in front of the
 tubes4 ,these contrivances1 however1   
though auxiliary to the use of the naked
 eyes1 were superseded by the           
,reflecting ,stereoscope1 which we shall
 now describe4      ,description of the 
,reflecting ,stereoscope4    ,this form 
of the stereoscope1 which we owe to ,mr4
 ,wheatstone1 is shewn  in ,fig4 #aj1   
and is described by him in the following
 terms3--8,,aa are  two plane mirrors1  
7whether of glass or metal is not       
stated17 about  four inches square1     
inserted in frames1 and so adjusted that
 their  backs form an angle of #ij with 
each other2 these mirrors are fixed  by 
their common edge against an upright ,b1
 or1 which was less easy to  represent  

in the drawing against the middle of a  
vertical board1 cut  away in such a     
manner as to allow the eyes to be placed
 before the  two mirrors4 ,c1 ,c are two
 sliding boards1 to which are attached  
the  upright boards ,d1 ,d1 which may   
thus be removed to different distances  
from the mirrors4 ,in most of the       
experiments hereafter to be detailed  it
 is necessary that each upright board   
shall be at the same distance  from the 
mirror which is opposite to it4 ,to     
facilitate this double  adjustment1 ,i  
employ a right and a left-handed wooden 
screw1 r1 l2  the two ends of this      
compound screw pass through the nuts e1 
e1  which are fixed to the lower parts  
of the upright boards ,d1 ,d1 so that   
by turning the screw pin p one way the  
two boards will approach1  and by       
turning them the other they will recede 
from each other1 one  always preserving 
the same distance as the other from the 
middle line  f2 ,e1 ,e are pannels to   
which the pictures are fixed in such    

manner  that their corresponding        
horizontal lines shall be on the same   
level2  these pannels are capable of    
sliding backwards or forwards in grooves
  on the upright boards ,d1 ,d4 ,the    
apparatus having been described1 it  now
 remains to explain the manner of using 
it4 ,the observer must place  his eyes  
as near as possible to the mirrors1 the 
right eye before the  right-hand mirror1
 and the left eye before the left-hand  
mirror1 and  he must move the sliding   
pannels ,e1 ,e to or from him till the  
two  reflected images coincide at the   
intersection of the optic axes1 and     
form an image of the same apparent      
magnitude as each of the component      
pictures4 ,the picture will1 indeed1    
coincide when the sliding pannels  are  
in a variety of different positions1    
and1 consequently1 when viewed  under   
different inclinations of the optic     
axes1 but there is only one  position in
 which the binocular image will be      
immediately seen single1  of its proper 

magnitude1 and without fatigue to the   
eyes1 because in  this position only the
 ordinary relations between the         
magnitude of the  pictures on the       
retina1 the inclination of the optic    
axes1 and the  adaptation of the eye to 
distinct vision at different distances1 
are  preserved4 ,in all the experiments 
detailed in the present memoir ,i  shall
 suppose these relations to remain      
undisturbed1 and the optic axes  to     
converge about six or eight inches      
before the eyes4    ,illustration3      
,,fig4 #aj4    8,if the pictures are all
 drawn to be seen with the same         
inclination of  the optic axes the      
apparatus may be simplified by omitting 
the screw  rl1 and fixing the upright   
boards ,d1 ,d at the proper distance4   
,the  sliding pannels may also be       
dispensed with1 and the drawings        
themselves  be made to slide in the     
grooves40    ,the figures to which ,mr4 
,wheatstone applied this instrument were
 pairs  of outline representations of   

objects of three dimensions1 such as  a 
cube1 a cone1 the frustum of a square   
pyramid1 which is shewn on  one side of 
,e1 ,e in ,fig4 #aj1 and in other       
figures2 and he employed  them1 as he   
observes1 8for the purpose of           
illustration1 for had either  shading or
 colouring been introduced it might be  
supposed that the  effect was wholly or 
in part due to these circumstances1     
whereas1 by  leaving them out of        
consideration1 no room is left to doubt 
that the  entire effect of relief is    
owing to the simultaneous perception of 
the  two monocular projections1 one on  
each retina40    8,careful attention10  
he adds1 8would enable an artist to draw
 and  paint the two component pictures1 
so as to present to the mind of the     
observer1 in the resultant perception1  
perfect identity with the object        
represented4 ,flowers1 crystals1 busts1 
vases1 instruments of various  kinds1   
c41 might thus be represented1 so as not
 to be distinguished  by sight from the 

real objects themselves40    ,this      
expectation has never been realized1 for
 it is obviously beyond  the reach of   
the highest art to draw two copies of a 
flower or a  bust with such accuracy of 
outline or colour as to produce 8perfect
  identity10 or anything approaching to 
it1 8with the object represented40      
,photography alone can furnish us with  
such representations of natural  and    
artificial objects2 and it is singular  
that neither ,mr4 ,elliot  nor ,mr4     
,wheatstone should have availed         
themselves of the well-known            
photographic process of ,mr4 ,wedgewood 
and ,sir ,humphry ,davy1 which1 as  ,mr4
 ,wedgewood remarks1 wanted only 8a     
method of preventing the unshaded  parts
 of the delineation from being coloured 
by exposure to the day1 to  render the  
process as useful as it is elegant40    
,when the two dissimilar  photographs   
were taken they could have been used in 
the stereoscope in  candle-light1 or in 
faint daylight1 till they disappeared1  

or permanent  outlines of them might    
have been taken and coloured after      
nature4    ,mr4 ,fox ,talbot's beautiful
 process of producing permanent         
photographs  was communicated to the    
,royal ,society in ,january #ahci1 but  
no attempt  was made till some years    
later to make it available for the      
stereoscope4    ,in a chapter on        
binocular pictures1 and the method of   
executing them  in order to reproduce1  
with perfect accuracy1 the objects which
 they  represent1 we shall recur to this
 branch of the subject4    ,upon        
obtaining one of these reflecting       
stereoscopes as made by the  celebrated 
optician1 ,mr4 ,andrew ,ross1 ,i found  
it to be very ill adapted  for the      
purpose of uniting dissimilar pictures1 
and to be imperfect in  various         
respects4 ,its imperfections may be thus
 enumerated3--    #a4 ,it is a clumsy   
and unmanageable apparatus1 rather than 
an instrument  for general use4 ,the one
 constructed for me was #af inches long1

 #f  inches broad1 and #h inches high4  
#b4 ,the loss of light occasioned by    
reflection from the mirrors is  very    
great4 ,in all optical instruments where
 images are to be formed1  and light is 
valuable1 mirrors and specula have been 
discontinued4  ,reflecting microscopes  
have ceased to be used1 but large       
telescopes1  such as those of ,sir ,w4  
and ,sir ,john ,herschel1 ,lord ,rosse1 
and ,mr4  ,lassel1 were necessarily made
 on the reflecting principle1 from the  
impossibility of obtaining plates of    
glass of sufficient size4    #c4 ,in    
using glass mirrors1 of which the       
reflecting stereoscope is  always made1 
we not only lose much more than half the
 light by the  reflections from the     
glass and the metallic surface1 and the 
absorbing  power of the glass1 but the  
images produced by reflection are made  
indistinct by the oblique incidence of  
the rays1 which separates the  image    
produced by the glass surface from the  
more brilliant image  produced by the   

metallic surface4    #d4 ,in all        
reflections1 as ,sir ,isaac ,newton     
states1 the errors are  greater than in 
refraction4 ,with glass mirrors in the  
stereoscope1  we have four refractions  
in each mirror1 and the light           
transmitted  through twice the thickness
 of the glass1 which lead to two sources
  of error4    #e4 ,owing to the        
exposure of the eye and every part of   
the apparatus  to light1 the eye itself 
is unfitted for distinct vision1 and    
the binocular pictures become           
indistinct1 especially if they are      
,daguerreotypes1#cd by reflecting the   
light incident from every part of  the  
room upon their glass or metallic       
surface4    #cd ,mr4 ,wheatstone himself
 says1 8that it is somewhat difficult to
  render the two ,daguerreotypes equally
 visible40--,phil4 ,trans41 #aheb1  p4  
#f4    #f4 ,the reflecting stereoscope  
is inapplicable to the beautiful        
binocular slides which are now being    
taken for the lenticular  stereoscope in

 every part of the world1 and even if we
 cut in two  those on paper and         
silver-plate1 they would give1 in the   
reflecting  instrument1 converse        
pictures1 the right-hand part of the    
picture  being placed on the left-hand  
side1 and vice versa4    #g4 ,with      
transparent binocular slides cut in two1
 we could obtain  pictures by reflection
 that are not converse2 but in using    
them1 we  would require to have two     
lights1 one opposite each of the        
pictures1  which can seldom be obtained 
in daylight1 and which it is            
inconvenient  to have at night4         
,owing to these and other causes1 the   
reflecting stereoscope never came  into 
use1 even after photography was capable 
of supplying binocular  pictures4    ,as
 a set-off against these disadvantages1 
it has been averred that in  the        
reflecting stereoscope we can use larger
 pictures1 but this1 as we  shall shew  
in a future chapter1 is altogether an   
erroneous assertion4      ,description  

of the ,lenticular ,stereoscope4        
,having found that the reflecting       
stereoscope1 when intended to produce   
accurate results1 possessed the defects 
which ,i have described1 and  was ill   
fitted for general use1 both from its   
size and its price1 it  occurred to me  
that the union of the dissimilar        
pictures could be  better effected by   
means of lenses1 and that a considerable
 magnifying  power would be thus        
obtained1 without any addition to the   
instrument4    ,illustration3 ,,fig4    
#aa4    ,if we suppose ,a1 ,b1 ,fig4    
#aa1 to be two portraits1--,a a portrait
 of a  gentleman1 as seen by the left   
eye of a person viewing him at the      
proper distance and in the best         
position1 and ,b his portrait as seen   
by the right eye1 the purpose of the    
stereoscope is to place these two       
pictures1 or rather their images1 one   
above the other4 ,the method of  doing  
this by lenses may be explained1 to     
persons not acquainted with  optics1 in 

the following manner3--    ,if we look  
at ,a with one eye through the centre of
 a convex glass1  with which we can see 
it distinctly at the distance of #f     
inches1 which  is called its focal      
distance1 it will be seen in its place  
at ,a4 ,if  we now move the lens from   
right to left1 the image of ,a will move
  towards ,b2 and when it is seen       
through the right-hand edge of the      
lens1 the image of ,a will have reached 
the position ,c1 half-way between  ,a   
and ,b4 ,if we repeat this experiment   
with the portrait ,b1 and move  the lens
 from left to right1 the image of ,b    
will move towards ,a2 and  when it is   
seen through the left-hand edge of the  
lens1 the image  of ,b will have reached
 the position ,c4 ,now1 it is obviously 
by the  right-hand half of the lens that
 we have transferred the image of ,a  to
 ,c1 and by the left-hand half that we  
have transferred the image of  ,b to ,c4
 ,if we cut the lens in two1 and place  
the halves--one in front of  each       

picture at the distance of #b inches--in
 the same position in which  they were  
when ,a was transferred to ,c and ,b to 
,c1 they will stand as in  ,fig4 #ab1   
and we shall see the portraits ,a and ,b
 united into one at ,c1  and standing   
out in beautiful relief1--a result which
 will be explained  in a subsequent     
chapter4    ,illustration3 ,,fig4 #ab4  
,the same effect will be produced by    
quarter lenses1 such as those shewn  in 
,fig4 #ac4 ,these lenses are cut into a 
round or square form1 and  placed in    
tubes1 as represented at ,r1 ,l1 in     
,fig4 #ad1 which is a drawing  of the   
,lenticular ,stereoscope4               
,illustration3 ,,fig4 #ac4    ,this     
instrument consists of a pyramidal box1 
,fig4 #ad1 blackened inside1  and having
 a lid1 ,,cd1 for the admission of light
 when required4 ,the  top of the box    
consists of two parts1 in one of which  
is the right-eye  tube1 ,r1 containing  
the lens ,g1 ,fig4 #ac1 and in the other
 the left-eye  tube1 ,l1 containing the 

lens ,h4 ,the two parts which hold the  
lenses1  and which form the top of the  
box1 are often made to slide in grooves1
  so as to suit different persons whose 
eyes1 placed at ,r1 ,l1 are more  or    
less distant4 ,this adjustment may be   
made by various pieces of  mechanism4   
,the simplest of these is a jointed     
parallelogram1 moved by  a screw forming
 its longer diagonal1 and working in    
nuts fixed on the  top of the box1 so as
 to separate the semi-lenses1 which     
follow the  movements of the obtuse     
angles of the parallelogram4 ,the tubes 
,r1 ,l  move up and down1 in order to   
suit eyes of different focal lengths1   
but  they are prevented from turning    
round by a brass pin1 which runs in a   
groove cut through the movable tube4    
,immediately below the eye-tubes  ,r1   
,l1 there should be a groove1 ,g1 for   
the introduction of convex or  concave  
lenses1 when required for very          
long-sighted or short-sighted  persons1 
or for coloured glasses and other       

purposes4    ,illustration3 ,,fig4 #ad4 
,if we now put the slide ,,ab1 ,fig4    
#aa1 into the horizontal opening at  ,s1
 turning up the sneck above ,s to       
prevent it from falling out1 and  place 
ourselves behind ,r1 ,l1 we shall see1  
by looking through ,r with  the right   
eye and ,l with the left eye1 the two   
images ,a1 ,b united in  one1 and in the
 same relief as the living person whom  
they represent4  ,no portrait ever      
painted1 and no statue ever carved1     
approximate in  the slightest degree to 
the living reality now before us4 ,if we
 shut  the right eye ,r we see with the 
left eye ,l merely the portrait ,a1 but 
it has now sunk into a flat picture1    
with only monocular relief4  ,by closing
 the left eye we shall see merely the   
portrait ,b1 having1  like the other1   
only monocular relief1 but a relief     
greater than the  best-painted pictures 
can possibly have1 when seen even with  
one eye4  ,when we open both eyes1 the  
two portraits instantly start into all  

the  roundness and solidity of life4    
,many persons experience a difficulty in
 seeing the portraits single  when they 
first look into a stereoscope1 in       
consequence of their eyes  having less  
power than common over their optic axes1
 or from their  being more or less      
distant than two and a half inches1 the 
average  distance4 ,the two images thus 
produced frequently disappear in a few  
minutes1 though sometimes it requires a 
little patience and some  practice to   
see the single image4 ,we have known    
persons who have lost  the power of     
uniting the images1 in consequence of   
having discontinued  the use of the     
instrument for some months2 but they    
have always  acquired it again after a  
little practice4    ,if the portraits or
 other pictures are upon opaque paper or
  silver-plate1 the stereoscope1 which  
is usually held in the left hand1  must 
be inclined so as to allow the light of 
the sky1 or any other  light1 to        
illuminate every part of the pictures4  

,if the pictures are  on transparent    
paper or glass1 we must shut the lid    
,,cd1 and hold up  the stereoscope      
against the sky or the artificial light1
 for which  purpose the bottom of the   
instrument is made of glass finely      
ground on  the outside1 or has two      
openings1 the size of each of the       
binocular  pictures1 covered with fine  
paper4    ,in using the stereoscope the 
observer should always be seated1 and it
  is very convenient to have the        
instrument mounted like a telescope1    
upon a stand1 with a weight and pulley  
for regulating the motion of the  lid   
,,cd4    ,the lenticular stereoscope may
 be constructed of various materials    
and in different forms4 ,i had them made
 originally of card-board1  tin-plate1  
wood1 and brass2 but wood is certainly  
the best material  when cheapness is not
 an object4    ,illustration3 ,,fig4    
#ae4    ,one of the earliest forms which
 ,i adopted was that which is shewn  in 
,fig4 #ae1 as made by ,m4 ,duboscq in   

,paris1 and which may be called         
stereoscopic spectacles4 ,the two-eye   
lenses ,l1 ,r are held by the  handle   
,h1 so that we can1 by moving them to or
 from the binocular  pictures1 obtain   
distinct vision and unite them in one4  
,the effect1  however1 is not so good as
 that which is produced when the        
pictures are  placed in a box4    ,the  
same objection applies to a form        
otherwise more convenient1 which        
consists in fixing a cylindrical or     
square rod of wood or metal to ,c1  the 
middle point between ,l and ,r4 ,the    
binocular slide having a hole  in the   
middle between the two pictures is moved
 along this rod to its  proper distance 
from the lenses4    ,illustration3      
,,fig4 #af4    ,another form1 analogous 
to this1 but without the means of moving
 the  pictures1 is shewn in ,fig4 #af1  
as made by ,m4 ,duboscq4 ,the adjustment
  is effected by moving the eye-pieces  
in their respective tubes1 and by  means
 of a screw-nut1 shewn above the        

eye-pieces1 they can be adapted  to eyes
 placed at different distances from one 
another4 ,the advantage  of this form1  
if it is an advantage1 consists in      
allowing us to use  larger pictures than
 can be admitted into the               
box-stereoscope of the  usual size4 ,a  
box-stereoscope1 however1 of the same   
size1 would have  the same property and 
other advantages not possessed by the   
open  instrument4    ,another form of   
the lenticular stereoscope1 under the   
name of the  cosmorama stereoscope1 has 
been adopted by ,mr4 ,knight4 ,the box  
is  rectangular instead of pyramidal1   
and the adjustment to distinct  vision  
is made by pulling out or pushing in a  
part of the box1 instead  of the common 
and better method of moving each lens   
separately4 ,the  illumination of the   
pictures is made in the same manner as  
in the  ,french instrument1 called the  
cosmorama1 for exhibiting dissolving    
views4 ,the lenses are large in surface1
 which1 without any reason1 is  supposed

 to facilitate the view of the binocular
 pictures1 and the  instrument is       
supported in a horizontal position upon 
a stand4 ,there  is no contrivance for  
adjusting the distance of the lenses to 
the  distance between the eyes1 and     
owing to the quantity of light which    
gets into the interior of the box1 the  
stereoscopic picture is injured  by     
false reflections1 and the sensibility  
of the eyes diminished4 ,the  exclusion 
of all light from the eyes1 and of every
 other light from the  picture but that 
which illuminates it1 is essentially    
necessary to the  perfection of         
stereoscopic vision4    ,when by means  
of any of these instruments we have     
succeeded in forming  a single image of 
the two pictures1 we have only1 as ,i   
have already  explained1 placed the one 
picture above the other1 in so far as   
the  stereoscope is concerned4 ,it is by
 the subsequent action of the two  eyes 
that we obtain the desired relief4 ,were
 we to unite the two  pictures when     

transparent1 and take a copy of the     
combination by the  best possible       
camera1 the result would be a blurred   
picture1 in which  none of the points or
 lines of the one would be united with  
the points  or lines of the other2 but  
were we to look at the combination with 
both  eyes the blurred picture would    
start into relief1 the eyes uniting in  
succession the separate points and lines
 of which it is composed4    ,now1      
since1 in the stereoscope1 when looked  
into with two eyes1 we see  the picture 
in relief with the same accuracy as1 in 
ordinary binocular  vision1 we see the  
same object in relief by uniting on the 
retina two  pictures exactly the same as
 the binocular ones1 the mere statement 
of  this fact has been regarded as the  
theory of the stereoscope4 ,we shall    
see1 however1 that it is not1 and that  
it remains to be explained1 more        
minutely than we have done in ,chapter  
,,iii41 both how we see objects  in     
relief in ordinary binocular vision1 and

 how we see them in the  same relief by 
uniting ocularly1 or in the stereoscope1
 two dissimilar  images of them4        
,before proceeding1 however1 to this    
subject1 we must explain the manner  in 
which half and quarter lenses unite the 
two dissimilar pictures4                
,illustration3 ,,fig4 #ag4    ,in ,fig4 
#ag is shewn a semi-lens ,,mn1 with its 
section ,m,n4 ,if we look  at any object
 successively through the portions      
,,aa,a in the semi-lens  ,,mn1          
corresponding to aaa in the section     
,m,n1 which is the same as  in a        
quarter-lens1 the object will be        
magnified equally in all of them1  but  
it will be more displaced1 or more      
refracted1 towards ,n1 by looking       
through ,a or a than through ,a or a1   
and most of all by looking  through ,a  
or a1 the refraction being greatest at  
,a or a1 less  at ,a or a1 and still    
less at ,a or a4 ,by means of a         
semi-lens1  or a quarter of a lens of   
the size of ,,mn1 we can1 with an       

aperture  of the size of ,a1 obtain     
three different degrees of displacement 
or  refraction1 without any change of   
the magnifying power4    ,if we use a   
thicker lens1 as shewn at ,m,nnm1       
keeping the curvature  of the surface   
the same1 we increase the refracting    
angle at its margin  ,nn1 we can produce
 any degree of displacement we require1 
either for  the purposes of experiment1 
or for the duplication of large         
binocular  pictures4    ,when two half  
or quarter lenses are used as a         
stereoscope1 the  displacement of the   
two pictures is produced in the manner  
shewn in  ,fig4 #ah1 where ,,ll is the  
lens for the left eye ,e1 and ,l,l that 
for  the right eye ,e1 placed so that   
the middle points1 no1 no1  of each are 
#b inches distant1 like the two eyes4   
,the two binocular  pictures which are  
to be united are shewn at ab1 ,,ab1 and 
placed at  nearly the same distance4    
,the pictures being fixed in the focus  
of the  lenses1 the pencils ano1 ,ano1  

bno1 ,bno1 will be refracted  at the    
points n1 o1 n1 o1 and at their points  
of incidence  on the second surface1 so 
as to enter the eyes1 ,e1 ,e1 in        
parallel  directions1 though not shewn  
in the ,figure4 ,the points a1 ,a1 of   
one  of the pictures1 will therefore be 
seen distinctly in the direction of  the
 refracted ray--that is1 the pencils an1
 ao1 issuing from a1  will be seen as if
 they came from a1 and the pencils bn1  
bo1 as  if they came from b1 so that ab 
will be transferred by refraction  to   
ab4 ,in like manner1 the picture ,,ab   
will be transferred by  refraction to   
,a,b1 and thus united with ab4          
,illustration3 ,,fig4 #ah    ,the       
pictures ab1 ,,abb thus united are      
merely circles1 and will  therefore be  
seen as a single circle at ,a,b4 ,but if
 we suppose ab to  be the base of the   
frustum of a cone1 and cd its summit1 as
 seen by  the left eye1 and the circles 
,,ab1 ,,cd to represent the base and    
summit  of the same solid as seen by the

 right eye1 then it is obvious that     
when the pictures of cd and ,,cd are    
similarly displaced or refracted  by the
 lenses ,,ll ,l,l1 so that cc is equal  
to a,a and ,,dd to  ,,bb1 the circles   
will not be united1 but will overlap one
 another  as at ,c,d1 cd1 in consequence
 of being carried beyond their  place of
 union4 ,the eyes1 however1 will        
instantly unite them into one  by       
converging their axes to a remoter      
point1 and the united circles  will rise
 from the paper1 or from the base ,a,b1 
and place the single  circle at the     
point of convergence1 as the summit of  
the frustum of a  hollow cone whose base
 is ,a,b4 ,if cd1 ,,cd had been farther 
from  one another than ab1 ,,ab1 as in  
,figs4 #bj and #ba1 they would still    
have overlapped though not carried up to
 their place of union4 ,the  eyes1      
however1 will instantly unite them by   
converging their axes to  a nearer      
point1 and the united circles will rise 
from the paper1 or  from the base ,,ab1 

and form the summit of the frustum of a 
raised cone  whose base is ,a,b4    ,in 
the preceding illustration we have      
supposed the solid to consist  only of a
 base and a summit1 or of parts at two  
different distances  from the eye2 but  
what is true of two distances is true of
 any number1  and the instant that the  
two pictures are combined by the lenses 
they  will exhibit in relief the body   
which they represent4 ,if the pictures  
are refracted too little1 or if they are
 refracted too much1 so as  not to be   
united1 their tendency to unite is so   
great1 that they are  soon brought      
together by the increased or diminished 
convergency of  the optic axes1 and the 
stereoscopic effect is produced4        
,whenever two  pictures are seen1 no    
relief is visible2 when only one picture
 is  distinctly seen1 the relief must be
 complete4    ,in the preceding diagram 
we have not shewn the refraction at the 
second  surface of the lenses1 nor the  
parallelism of the rays when they enter 

the eye1--facts well known in elementary
 optics4          ,,chapter ,v4    ,,on 
,,the ,,theory ,,of ,,stereoscopic      
,,vision4      ,having1 in the preceding
 chapter1 described the ocular1 the     
reflecting1  and the lenticular         
stereoscopes1 and explained the manner  
in which the  two binocular pictures are
 combined or laid upon one another in   
the  last of these instruments1 we shall
 now proceed to consider the theory  of 
stereoscopic vision4    ,illustration3  
,,fig4 #ai4    ,in order to understand  
how the two pictures1 when placed the   
one above  the other1 rise into relief1 
we must first explain the manner in     
which  a solid object itself is1 in     
ordinary vision1 seen in relief1 and  we
 shall then shew how this process takes 
place in the two forms of  the ocular   
stereoscope1 and in the lenticular      
stereoscope4 ,for this  purpose1 let    
,,abcd1 ,fig4 #ai1 be a section of the  
frustum of a cone1 that  is1 a cone with
 its top cut off by a plane ,ce,dg1 and 

having ,,aebg  for its base4 ,in order  
that the figure may not be complicated1 
it will  be sufficient to consider how  
we see1 with two eyes1 ,l and ,r1 the   
cone  as projected upon a plane passing 
through its summit ,ce,dg4 ,the  points 
,l1 ,r being the points of sight1 draw  
the lines ,,ra1 ,,rb1 which  will cut   
the plane on which the projection is to 
be made in the points  a1 b1 so that ab 
will represent the line ,,ab1 and a     
circle1 whose  diameter is ab1 will     
represent the base of the cone1 as seen 
by the  right eye ,r4 ,in like manner1  
by drawing ,,la1 ,,lb1 we shall find    
that  ,a,b will represent the line ,,ab1
 and a circle1 whose diameter is ,a,b1  
the base ,,aebg1 as seen by the left    
eye4 ,the summit1 ,ce,dg1 of the        
frustum being in the plane of           
projection1 will be represented by the  
circle ,ce,dg4 ,the representation of   
the frustum ,,abcd1 therefore1  upon a  
plane surface1 as seen by the left eye  
,l1 consists of two  circles1 whose     

diameters are ,,ab1 ,,cd2 and1 as seen  
by the right eye1 of  other two circles1
 whose diameters are ab1 ,,cd1 which1 in
 ,fig4 #bj1  are represented by ,,ab1   
,,cd1 and ab1 cd4 ,these plane figures  
being  also the representation of the   
solid on the retina of the two eyes1    
how comes it that we see the solid and  
not the plane pictures8 ,when  we look  
at the point ,b1 ,fig4 #ai1 with both   
eyes1 we converge upon it  the optic    
axes ,,lb1 ,,rb1 and we therefore see   
the point single1 and at  the distances 
,,lb1 ,,rb from each eye4 ,when we look 
at the point ,d1 we  withdraw the optic 
axes from ,b1 and converge them upon ,d4
 ,we therefore  see the point ,d single1
 and at the distances ,,ld1 ,,rd from   
each eye2  and in like manner the eyes  
run over the whole solid1 seeing every  
point single and distinct upon which    
they converge their axes1 and at  the   
distance of the point of convergence    
from the observer4 ,during  this rapid  
survey of the object1 the whole of it is

 seen distinctly  as a solid1 although  
every point of it is seen double and    
indistinct1  excepting the point upon   
which the axes are for the instant      
converged4    ,illustration3 ,,fig4 #bj4
    ,from these observations it is      
obvious1 that when we look with both    
eyes  at any solid or body in relief1 we
 see more of the right side of it  by   
the right eye1 and more of the left side
 of it by the left eye4 ,the  right side
 of the frustum ,,abcd1 ,fig4 #ai1 is   
represented by the line  ,db1 as seen by
 the right eye1 and by the shorter line 
,,db1 as seen by  the left eye4 ,in like
 manner1 the left side ,,ac is          
represented by ,,ca1  as seen by the    
left eye1 and by the shorter line ,ca1  
as seen by the  right eye4    ,when the 
body is hollow1 like a wine glass1 we   
see more of the right  side with the    
left eye1 and more of the left side with
 the right eye4    ,if we now separate1 
as in ,fig4 #bj1 the two projections    
shewn together  on ,fig4 #ai1 we shall  

see that the two summits1 ,,cd1 cd1 of  
the frustum  are farther from one       
another than the more distant bases1    
,,ab1 ab1 and  it is true generally that
 in the two pictures of any solid in    
relief1  the similar parts that are near
 the observer are more distant in the   
two pictures than the remoter parts1    
when the plane of perspective is  beyond
 the object4 ,in the binocular picture  
of the human face the  distance between 
the two noses is greater than the       
distance between the  two right or left 
eyes1 and the distance between the two  
right or left  eyes greater than the    
distance between the two remoter ears4  
,we are now in a condition to explain   
the process by which1 with the  eyes    
alone1 we can see a solid in relief by  
uniting the right and left  eye pictures
 of it1--or the theory ocular           
stereoscope4 ,in order to  obtain the   
proper relief we must place the right   
eye picture on the  left side1 and the  
left eye picture on the right side1 as  

shewn in ,fig4  #ba1 by the pictures    
,,abcd1 abcd1 of the frustum of a cone1 
as obtained  from ,fig4 #ai4            
,illustration3 ,,fig4 #ba4    ,in order 
to unite these two dissimilar           
projections1 we must converge  the      
optical axes to a point nearer the      
observer1 or look at some point  about  
,m4 ,both pictures will immediately be  
doubled4 ,an image of the  figure ab    
will advance towards ,p1 and an image of
 ,,ab will likewise  advance towards ,p2
 and the instant these images are       
united1 the frustum  of a cone1 which   
they represent1 will appear in relief at
 ,,mn1 the  place where the optic axes  
meet or cross each other4 ,at first the 
solid figure will appear in the middle1 
between the two pictures from  which it 
is formed and of the same size1 but     
after some practice it  will appear     
smaller and nearer the eye4 ,its        
smallness is an optical  illusion1 as it
 has the same angle of apparent         
magnitude as the plane  figures1 namely1

 mn,l  ,,abl2 but its position at ,,mn  
is a reality1 for  if we look at the    
point of our finger held beyond ,m the  
solid figure  will be seen nearer the   
eye4 ,the difficulty which we experience
 in  seeing it of the size and in the   
position shewn in ,fig4 #ba1 arises from
  its being seen along with its two     
plane representations1 as we shall      
prove experimentally when we treat in a 
future chapter of the union of  similar 
figures by the eye4    ,the two images  
being thus superimposed1 or united1 we  
shall now see  that the combined images 
are seen in relief in the very same way 
that  in ordinary vision we saw the real
 solid1 ,,abcd1 ,fig4 #ai1 in relief1 by
  the union of the two pictures of it on
 the retina4 ,from the points ,a1  ,b1  
,c1 ,d1 a1 b1 c1 d1 draw lines to ,l and
 ,r1 the centres of visible  direction  
of each eye1 and it will be seen that   
the circles ,,ab1 ab1  representing the 
base of the cone1 can be united by      
converging the  optical axes to points  

in the line mn1 and that the circles    
,,cd1 cd1  which are more distant1 can  
be united only by converging the optic  
axes  to points in the line op4 ,the    
points ,a1 a1 for example1 united by    
converging the axes to m1 are seen at   
that point single2 the points  ,b1 b at 
n single1 the points ,c1 c at o single1 
the points ,d1  d at p single1 the      
centres ,s1 s of the base at ,m single1 
and the  centres ,s1 s of the summit    
plane at ,n single4 ,hence the eyes ,l  
and  ,r see the combined pictures at    
,,mn in relief1 exactly in the same     
manner  as they saw in relief the       
original solid ,,mn in ,fig4 #ai4    ,in
 order to find the height ,,mn of the   
conical frustum thus seen1 let ,d       
distance ,,op2 d  ,ss1 the distance of  
the two points united at ,m2  d  ,ss1   
the distance of the two points united at
 ,n2 and ,c  ,,lr   #b inches1 the      
distance of the eyes4 ,then we have--   
,dd                   ,,mp              
--------------                        ,c

  d                           ,dd       
,,np  -------------- 1 and              
,c  d                           ,dd     
,dd                   ,,mn  ------------
  -  --------------                     
,c  d    ,c  d            ,if   ,d  #ibd
 inches1               ,c  #bej1 then   
d  #bad1            d  #bdb1 and        
,,mn  #jbhc1 the height of the cone4    
,,dc          ,when ,c  d1 ,,mp         
--------                                
#b;,c4    ,as the summit plane op rises 
above the base mn by the successive     
convergency of the optic axes to        
different points in the line o,np1  it  
may be asked how it happens that the    
conical frustum still appears  a solid1 
and the plane op where it is1 when the  
optic axes are  converged to points in  
the line m,mn1 so as to see the base    
distinctly8 ,the reason of this is that 
the rays emanate from op  exactly in the
 same manner1 and form exactly the same 
image of it1  on the two retinas as if  
it were the summit ,,cd1 ,fig4 #ai1 of  

the real  solid when seen with both     
eyes4 ,the only effect of the advance of
 the  point of convergence from ,n to ,m
 is to throw the image of ,n a little   
to the right side of the optic axis of  
the left eye1 and a little to  the left 
of the optic axis of the right eye4 ,the
 summit plane op  will therefore retain 
its place1 and will be seen slightly    
doubled and  indistinct till the point  
of convergence again returns to it4     
,it has been already stated that the two
 dissimilar pictures may be  united by  
converging the optical axes to a point  
beyond them4 ,in order  to do this1 the 
distance ,,ss of the pictures1 ,fig4    
#ba1 must be greatly  less than the     
distance of the eyes ,l1 ,r1 in order   
that the optic axes1  in passing through
 similar points of the two plane        
pictures1 may meet  at a moderate       
distance beyond them4 ,in order to      
explain how the relief  is produced in  
this case1 let ,,ab1 ,,cd1 ab1 cd1 ,fig4
 #bb1 be the  dissimilar pictures of the

 frustum of a cone whose summit is ,,cd1
 as  seen by the right eye1 and cd as   
seen by the left eye4 ,from ,l and ,r1  
as before1 draw lines through all the   
leading points of the pictures1  and we 
shall have the points ,a1 a united at m1
 the points ,b1 b at  n1 the points ,c1 
c at o1 and the points ,d1 d at p1 the  
points  ,s1 s at ,m1 and the points ,s1 
s at ,n1 forming the cone mnop1  with   
its base mn towards the observer1 and   
its summit op more  remote4 ,if the cone
 had been formed of lines drawn from the
 outline of  the summit to the outline  
of the base1 it would now appear hollow1
  the inside of it being seen in place  
of the outside as before4 ,if the       
pictures ,,ab1 ab are made to change    
places the combined picture would  be in
 relief1 while in the case shewn in     
,fig4 #ba it would have been  hollow4   
,hence the right-eye view of any solid  
must be placed on the  left hand1 and   
the left-eye view of it on the right    
hand1 when  we wish to obtain it in     

relief by converging the optic axes to a
 point  between the pictures and the    
eye1 and vice versa when we wish to     
obtain it in relief by converging the   
optic axes to a point beyond the        
pictures4 ,in every case when we wish   
the combined pictures to represent  a   
hollow1 or the converse of relief1 their
 places must be exchanged4              
,illustration3 ,,fig4 #bb4    ,in order 
to find the height ,,mn1 or rather the  
depth of the cone in ,fig4  #bb1 let ,d1
 d1 ,c1 c1 represent the same quantities
 as before1 and we  shall have          
,dd      ,,mp  --------------           
,c - d              ,dd      ,,np       
-------------- 1 and           ,c - d   
,dd       ,dd      ,,op  -------------- 
-  ------------           ,c - d    ,c -
 d    ,when ,d1 ,c1 d1 d have the same  
values as before1 we shall have ,,mn    
#ahg feet6    ,when ,c  d1 ,,mp will be 
infinite4    ,we have already explained 
how the two binocular pictures are      
combined  or laid upon one another in   

the lenticular stereoscope4 ,let us now 
see  how the relief is obtained4 ,the   
two plane pictures abcd1 ,,abcd1 in     
,fig4 #ah1 are1 as we have already      
explained1 combined or simply laid  upon
 one another by the lenses ,,ll1 ,l,l1  
and in this state are shewn by  the     
middle circles at ,aa,bb1 ,cc,dd4 ,the  
images of the bases ,,ab1  ab of the    
cone are accurately united in the double
 base ,,ab1 ab1 but  the summits of the 
conical frustum remain separate1 as seen
 at ,c,d1  cd4 ,it is now the business  
of the eyes to unite these1 or rather to
  make them appear as united4 ,we have  
already seen how they are brought  into 
relief when the summits are refracted so
 as to pass one another1  as in ,fig4   
#ah4 ,let us therefore take the case    
shewn in ,fig4 #bj1 where  the summits  
,,cd1 cd are more distant than the bases
 ,,ab1 ab4 ,the  union of these figures 
is instantly effected1 as shewn in ,fig4
 #bc1 by  converging the optic axes to  
points m and n successively1 and thus   

uniting ,c and c and ,d and d1 and      
making these points of the summit  plane
 appear at m and n1 the points of       
convergence of the axes  ,lm1 ,rm1 and  
,ln1 ,rn4 ,in like manner1 every pair of
 points in the  summit plane1 and in the
 sides ,am1 ,bn of the frustum1 are     
converged  to points corresponding to   
their distance from the base ,,ab of the
  original solid frustum1 from which the
 plane pictures ,,abcd1 abcd1  were     
taken4 ,we shall1 therefore1 see in     
relief the frustum of a cone  whose     
section is ,amn,b4    ,illustration3    
,,fig4 #bc4    ,the theory of the       
stereoscope may be expressed and        
illustrated in the  following manner1   
without any reference to binocular      
vision3--    #a4 ,when a drawing of any 
object or series of objects is executed 
on a  plane surface from one point of   
sight1 according to the principles  of  
geometrical perspective1 every point of 
its surface that is visible  from the   
point of sight will be represented on   

the plane4    #b4 ,if another drawing of
 the same object or series of objects is
  similarly executed on the same plane  
from a second point of sight1           
sufficiently distant from the first to  
make the two drawings separate  without 
overlapping1 every point of its surface 
visible from this  second point of sight
 will also be represented on the plane1 
so that  we shall have two different    
drawings of the object placed1 at a     
short  distance from each other1 on the 
same plane4    ,illustration3 ,,fig4    
#bd4    #c4 ,calling these different    
points of the object #a1 #b1 #c1 #d1 c41
 it  will be seen from ,fig4 #bd1 in    
which ,l1 ,r are the two points of      
sight1  that the distances #a1 #a1 on   
the plane ,,mn1 of any pair of points in
  the two pictures representing the     
point #a of the object1 will be to  the 
distance of any other pair #b1 #b1      
representing the point #b1 as the       
distances #a,p1 #b,p of the points of   
the object from the plane ,,mn1         

multiplied inversely by the distances of
 these points from the points  of sight 
,l1 ,r1 or the middle point ,o between  
them4    #d4 ,if the sculptor1          
therefore1 or the architect1 or the     
mechanist1 or  the surveyor1 possesses  
two such pictures1 either as drawn by a 
skilful  artist or taken                
photographically1 he can1 by measuring  
the distances of  every pair of points1 
obtain the relief or prominence of the  
original  point1 or its distance from   
the plane ,,mn or ,,ab2 and without the 
use  of the stereoscope1 the sculptor   
may model the object from its plane     
picture1 and the distances of every     
point from a given plane4 ,in like      
manner1 the other artists may determine 
distances in buildings1 in  machinery1  
and in the field4    #e4 ,if the        
distance of the points of sight is equal
 to the distance of  the eyes ,l1 ,r1   
the two plane pictures may be united and
 raised into  relief by the stereoscope1
 and thus give the sculptor and other   

artists  an accurate model1 from which  
they will derive additional aid in the  
execution of their work4    #f4 ,in     
stereoscopic vision1 therefore1 when we 
join the points #a1 #a by  converging   
the optic axes to #a in the line ,,pq1  
and the points #b1 #b by  converging    
them to #b in the same line1 we place   
these points at the  distances ,o#a1    
,,oo#b1 and see the relief1 or the      
various differences of  distance which  
the sculptor and others obtained by the 
method which we  have described4    #g4 
,hence we infer1 that if the            
stereoscopic vision of relief had never 
been thought of1 the principles of the  
instrument are involved in the          
geometrical relief which is embodied in 
the two pictures of an object  taken    
from two points of sight1 and in the    
prominence of every part of  it obtained
 geometrically4          ,,chapter ,,vi4
    ,,on ,,the ,,union ,,of ,,similar   
,,pictures ,,in ,,binocular ,,vision4   
,in uniting by the convergency of the   

optic axes two dissimilar  pictures1 as 
shewn in ,fig4 #ah1 the solid cone ,,mn 
ought to appear at ,,mn  much nearer the
 observer than the pictures which       
compose it4 ,i found1  however1 that it 
never took its right position in        
absolute space1  the base ,,mn of the   
solid seeming to rest on the same plane 
with its  constituent pictures ,,ab1 ab1
 whether it was seen by converging the  
axes as in ,fig4 #ah or in ,fig4 #bb4   
,upon inquiring into the reason of  this
 ,i found that the disturbing cause was 
simply the simultaneous  perception of  
other objects in the same field of view 
whose distance  was known to the        
observer4    ,in order to avoid all such
 influences ,i made experiments on large
  surfaces covered with similar plane   
figures1 such as flowers or  geometrical
 patterns upon paper-hangings and       
carpets4 ,these figures  being always at
 equal distances from each other1 and   
almost perfectly  equal and similar1 the
 coalescence of any pair of them1       

effected by  directing the optic axes to
 a point between the paper-hanging and  
the  eye1 is accompanied by the         
instantaneous coalescence of them all4  
,if  we1 therefore1 look at a papered   
wall without pictures1 or doors1 or     
windows1 or even at a considerable      
portion of a wall1 at the distance  of  
three feet1 and unite two of the        
figures1--two flowers1 for example1  at 
the distance of twelve inches from each 
other horizontally1 the  whole wall or  
visible portion of it will appear       
covered with flowers as  before1 but as 
each flower is now composed of two      
flowers united at the  point of         
convergence of the optic axes1 the whole
 papered wall with  all its flowers will
 be seen suspended in the air at the    
distance of  six inches from the        
observer6 ,at first the observer does   
not decide  upon the distance of the    
suspended wall from himself4 ,it        
generally  advances slowly to its new   
position1 and when it has taken its     

place it  has a very singular character4
 ,the surface of it seems slightly      
curved4  ,it has a silvery transparent  
aspect4 ,it is more beautiful than the  
real  paper1 which is no longer seen1   
and it moves with the slightest motion  
of the head4 ,if the observer1 who is   
now three feet from the wall1  retires  
from it1 the suspended wall of flowers  
will follow him1 moving  farther and    
farther from the real wall1 and also1   
but very slightly1  farther and farther 
from the observer4 ,when he stands      
still1 he may  stretch out his hand and 
place it on the other side of the       
suspended  wall1 and even hold a candle 
on the other side of it to satisfy      
himself  that the ghost of the wall     
stands between the candle and himself4  
,in looking attentively at this strange 
picture some of the flowers have  the   
aspect of real flowers4 ,in some the    
stalk retires from the plane of  the    
picture4 ,in others it rises from it4   
,one leaf will come farther out  than   

another4 ,one coloured portion1 red1 for
 example1 will be more  prominent than  
the blue1 and the flower will thus      
appear thicker and  more solid1 like a  
real flower compressed1 and deviating   
considerably  from the plane            
representation of it as seen by one eye4
 ,all this  arises from slight and      
accidental differences of distance in   
similar  or corresponding parts of the  
united figures4 ,if the distance1 for   
example1 between two corresponding      
leaves is greater than the distance     
between other two corresponding leaves1 
then the two first when united  will    
appear nearer the eye than the other    
two1 and hence the appearance  of a     
flower in low relief1 is given to the   
combination4    ,in continuing our      
survey of the suspended image another   
curious  phenomenon often presents      
itself4 ,a part of one1 or even two     
pieces  of paper1 and generally the     
whole length of them from the roof to   
the floor1 will retire behind the       

general plane of the image1 as if  there
 were a recess in the wall1 or rise     
above it as if there were a  projection1
 thus displaying on a large scale the   
imperfection in the  workmanship which  
otherwise it would have been difficult  
to discover4  ,this phenomenon1 or      
defect in the work1 arises from the     
paper-hanger  having cut off too much of
 the margin of one or more of the       
adjacent  stripes or pieces1 or leaving 
too much of it1 so that1 in the first   
case1 when the two halves of a flower   
are joined together1 part of  the middle
 of the flower is left out1 and hence1  
when this defective  flower is united   
binocularly with the one on the right   
hand of it1  and the one on the left    
hand united with the defective one1 the 
united or corresponding portion being at
 a less distance1 will appear  farther  
from the eye than those parts of the    
suspended image which are  composed of  
complete flowers4 ,the opposite effect  
will be produced  when the two portions 

of the flowers are not brought together1
 but  separated by a small space4 ,all  
these phenomena may be seen1 though  not
 so conveniently1 with a carpet from    
which the furniture has been  removed4  
,we have1 therefore1 an accurate method 
of discovering defects  in the          
workmanship of paper-hangers1           
carpet-makers1 painters1 and all        
artists whose profession it is to       
combine a series of similar patterns  or
 figures to form an uniformly ornamented
 surface4 ,the smallest defect  in the  
similarity or equality of the figures or
 lines which compose  a pattern1 and any
 difference in the distance of single   
figures is  instantly detected1 and what
 is very remarkable a small inequality  
of distance in a line perpendicular to  
the axis of vision1 or in one  dimension
 of space1 is exhibited in a magnified  
form at a distance  coincident with the 
axis of vision1 and in an opposite      
dimension of  space4    ,a little       
practice will enable the observer to    

realize and to maintain  the singular   
binocular vision which replaces the real
 picture4#ce ,the  occasional retention 
of the picture after one eye is closed1 
and even  after both have been closed   
and quickly reopened1 shews the         
influence  of time over the evanescence 
as well as over the creation of this    
class  of phenomena4 ,on some occasions1
 a singular effect is produced4 ,when   
the flowers or figures on the paper are 
distant six inches1 we may  either unite
 two six inches distant1 or two twelve  
inches distant1  and so on4 ,in the     
latter case1 when the eyes have been    
accustomed to  survey the suspended     
picture1 ,i have found that1 after      
shutting or  opening them1 ,i neither   
saw the picture formed by the two       
flowers  twelve inches distant1 nor the 
papered wall itself1 but a picture      
formed by uniting all the flowers six   
inches distant6 ,the binocular  centre  
7the point to which the optic axes      
converged1 and consequently  the        

locality of the picture7 had shifted its
 place1 and instead of  advancing to the
 real wall and seeing it1 it advanced   
exactly as much  as to unite the nearest
 flowers1 just as in a ratchet wheel1   
when the  detent stops one tooth at a   
time2 or1 to speak more correctly1 the  
binocular centre advanced in order to   
relieve the eyes from their  strain1 and
 when the eyes were opened1 it had just 
reached that point  which corresponded  
with the union of the flowers six inches
 distant4    #ce ,a sheet of ,queen's   
heads may be advantageously used to     
accustom  the eyes to the union of      
similar figures4    ,illustration3      
,,fig4 #be4    ,we have already seen1 as
 shewn in ,fig4 #bb1 that when we fix   
the  binocular centre1 that is1 converge
 the optic axes on a point beyond  the  
dissimilar pictures1 so as to unite     
them1 they rise into relief  as         
perfectly as when the binocular centre1 
as shewn in ,fig4 #ah1 is  fixed between
 the pictures used and the eye4 ,in like

 manner we may  unite similar pictures1 
but1 owing to the opacity of the wall   
and the  floor1 we cannot accomplish    
this with paper-hangings and carpets4   
,the experiment1 however1 may be made   
with great effect by looking  through   
transparent patterns cut out of paper or
 metal1 such as those  in zinc which are
 used for larders and other purposes4   
,particular  kinds of trellis-work1 and 
windows with small squares or rhombs of 
glass1 may also be used1 and1 what is   
still better1 a screen might be         
prepared1 by cutting out the small      
figures from one or more pieces of      
paper-hangings4 ,the readiest means1    
however1 of making the experiment1  is  
to use the cane bottom of a chair1 which
 often exhibits a succession  of        
octagons with small luminous spaces     
between them4 ,to do this1 place  the   
back of the chair upon a table1 the     
height of the eye either when  sitting  
or standing1 so that the cane bottom    
with its luminous pattern  may have a   

vertical position1 as shewn in ,fig4    
#be1 where ,,mn is the  real bottom of  
the chair with its openings1 which      
generally vary from  half an inch to    
three-fourths4 ,supposing the distance  
to be half an  inch1 and the eyes1 ,l1  
,r1 of the observer #ab inches distant  
from ,,mn1  let ,lad1 ,lbe be lines     
drawn through the centres of two of the 
open  spaces a1 b1 and ,rbd1 ,rce lines 
drawn through the centres of  b and c1  
and meeting ,lad1 ,lbe at d and e1 d    
being the  binocular centre to which the
 optic axes converge when we look at it 
through a and b1 and c the binocular    
centre when we look at it  through b and
 c4 ,now1 the right eye1 ,r1 sees the   
opening b at  d1 and the left eye sees  
the opening a at d1 so that the image   
at d of the opening consists of the     
similar images of a and b  united1 and  
so on with all the rest2 so that the    
observer at ,l1 ,r no  longer sees the  
real pattern ,,mn1 but an image of it   
suspended at mn1  three inches behind   

,,mn4 ,if the observer now approaches   
,,mn1 the image  mn will approach to    
him1 and if he recedes1 mn will recede  
also1  being #a inches behind ,,mn when 
the observer is six inches before it1   
and twelve inches behind ,,mn when the  
observer is forty-eight inches  before  
it1 the image mn moving from mn with a  
velocity one-fourth  of that with which 
the observer recedes4    ,the observer  
resuming the position in the figure     
where his eyes1 ,l1  ,r1 are twelve     
inches distant from ,,mn1 let us        
consider the important  results of this 
experiment4 ,if he now grasps the cane  
bottom at ,,mn1  his thumbs pressing    
upon ,,mn1 and his fingers trying to    
grasp mn1  he will then feel what he    
does not see1 and see what he does not  
feel6 ,the real pattern is absolutely   
invisible at ,,mn1 where he feels  it1  
and it stands fixed at mn4 ,the fingers 
may be passed through and  through      
between the real and the false image1   
and beyond it1--now seen  on this side  

of it1 now in the middle of it1 and now 
on the other side  of it4 ,if we next   
place the palms of each hand upon ,,mn1 
the real bottom  of the chair1 feeling  
it all over1 the result will be the     
same4 ,no  knowledge derived from       
touch--no measurement of real           
distance--no actual  demonstration from 
previous or subsequent vision1 that     
there is a real  solid body at ,,mn1 and
 nothing at all at mn1 will remove or   
shake the  infallible conviction of the 
sense of sight that the cane bottom is  
at  mn1 and that d,l or d,r is its real 
distance from the observer4 ,if  the    
binocular centre be now drawn back to   
,,mn1 the image seen at mn  will        
disappear1 and the real object be seen  
and felt at ,,mn4 ,if the  binocular    
centre be brought further back to f1    
that is1 if the optic  axes are         
converged to a point nearer the observer
 than the object1 as  illustrated by    
,fig4 #ah1 the cane bottom ,,mn will    
again disappear1 and  will be seen at   

uv1 as previously explained4    ,this   
method of uniting small similar figures 
is more easily attained  than that of   
doing it by converging the axes to a    
point between the  eye and the object4  
,it puts a very little strain upon the  
eyes1 as we  cannot thus unite figures  
the distance of whose centre is equal to
 or  exceeds #b inches1 as appears from 
,fig4 #bb4    ,in making these          
experiments1 the observer cannot fail to
 be struck with  the remarkable fact1   
that though the openings ,,mn1 mn1 uv1  
have all  the same apparent or angular  
magnitude1 that is1 subtend the same    
angle  at the eye1 viz41 d,lc1 d,re1 yet
 those at mn appear larger1  and those  
at uv smaller1 than those at ,,mn4 ,if  
we cause the image  mn to recede and    
approach to us1 the figures in mn will  
invariably  increase as they recede1 and
 those in uv diminish as they approach  
the eye1 and their visual magnitudes1 as
 we may call them1 will  depend on the  
respective distances at which the       

observer1 whether right  or wrong in his
 estimate1 conceives them to be         
placed1--a result which  is finely      
illustrated by the different size of the
 moon when seen in  the horizon and in  
the meridian4 ,the fact now stated is a 
general one1  which the preceding       
experiments demonstrate2 and though our 
estimate of  magnitude thus formed is   
erroneous1 yet it is one which neither  
reason  nor experience is able to       
correct4    ,it is a curious            
circumstance1 that1 previous to the     
publication of  these experiments1 no   
examples have been recorded of false    
estimates  of the distance of near      
objects in consequence of the accidental
  binocular union of similar images4 ,in
 a room where the paper-hangings  have a
 small pattern1 a short-sighted person  
might very readily turn  his eyes on the
 wall when their axes converged to some 
point between  him and the wall1 which  
would unite one pair of the similar     
images1  and in this case he would see  

the wall nearer him than the real wall1 
and moving with the motion of his head4 
,in like manner a long-sighted  person1 
with his optical axes converged to a    
point beyond the wall1  might see an    
image of the wall more distant1 and     
moving with the motion  of his head2 or 
a person who has taken too much wine1   
which often fixes  the optical axes in  
opposition to the will1 might1 according
 to the  nature of his sight1 witness   
either of the illusions above mentioned4
    ,illusions of both these kinds1     
however1 have recently occurred4 ,a     
friend to whom ,i had occasion to shew  
the experiments1 and who is             
short-sighted1 mentioned to me that he  
had on two occasions been  greatly      
perplexed by the vision of these        
suspended images4 ,having taken  too    
much wine1 he saw the wall of a papered 
room suspended near him in  the air2 and
 on another occasion1 when kneeling1 and
 resting his arms  on a cane-bottomed   
chair1 he had fixed his eyes on the     

carpet1 which  had accidentally united  
the two images of the open octagons1 and
 thrown  the image of the chair bottom  
beyond the plane on which he rested his 
arms4    ,after hearing my paper on this
 subject read at the ,royal ,society of 
,edinburgh1 ,professor ,christison      
communicated to me the following        
interesting case1 in which one of the   
phenomena above described was  seen by  
himself3--8,some years ago10 he         
observes1 8when ,i resided in a  house  
where several rooms are papered with    
rather formally recurring  patterns1 and
 one in particular with stars only1 ,i  
used occasionally  to be much plagued   
with the wall suddenly standing out upon
 me1  and waving1 as you describe1 with 
the movements of the head4 ,i was       
sensible that the cause was an error as 
to the point of union of the  visual    
axes of the two eyes2 but ,i remember it
 sometimes cost me a  considerable      
effort to rectify the error2 and ,i     
found that the best  way was to increase

 still more the deviation in the first  
instance4 ,as  this accident occurred   
most frequently while ,i was recovering 
from a  severe attack of fever1 ,i      
thought my near-sighted eyes were       
threatened  with some new mischief2 and 
this opinion was justified in finding   
that1  after removal to my present      
house1 where1 however1 the papers have  
no very formal pattern1 no such         
occurrence has ever taken place4 ,the   
reason is now easily understood from    
your researches40#cf    ,other cases of 
an analogous kind have been communicated
 to me2 and  very recently ,m4 ,soret of
 ,geneva1 in looking through a          
trellis-work in  metal stretched upon a 
frame1 saw the phenomenon represented in
 ,fig4  #be1 and has given the same     
explanation of it which ,i had published
 long  before4#cg    #cf ,see ,edin4    
,transactions1 #ahdf1 vol4 xv4 p4 #ffc1 
and ,phil4 ,mag41  ,may #ahdg1 vol4 xxx4
 p4 #cje4    #cg ,bibl4 ,universelle1   
,october #ahee1 p4 #acf4    ,before     

quitting the subject of the binocular   
union of similar  pictures1 ,i must give
 some account of a series of curious    
phenomena  which ,i observed by uniting 
the images of lines meeting at an       
angular  point when the eye is placed at
 different heights above the plane of   
the paper1 and at different distances   
from the angular point4                 
,illustration3 ,,fig4 #bf4    ,let ,,ac1
 ,,bc1 ,fig4 #bf1 be two lines meeting  
at ,c1 the plane passing  through them  
being the plane of the paper1 and let   
them be viewed by  the eyes successively
 placed at ,e1 ,e1 ,e1 and ,e1 at       
different heights  in a plane1 ,,gmn1   
perpendicular to the plane of the paper4
 ,let ,r be the  right eye1 and ,l the  
left eye1 and when at ,e1 let them be   
strained  so as to unite the points ,a1 
,b4 ,the united image of these points   
will  be seen at the binocular centre   
,d1 and the united lines ,,ac1 ,,bc1    
will  have the position ,d,c4 ,in like  
manner1 when the eye descends to ,e1 ,e1

  ,e1 the united image ,d,c will rise   
and diminish1 taking the positions      
,d,c1 ,d,c1 ,,dc1 till it disappears on 
the line ,,cm1 when the eyes reach  ,m4 
,if the eye deviates from the vertical  
plane ,,gmn1 the united image  will also
 deviate from it1 and is always in a    
plane passing through the  common axis  
of the two eyes and the line ,,gm4      
,if at any altitude ,,em1 the eye       
advances towards ,,acb in the line ,,eg1
 the  binocular centre ,d will also     
advance towards ,,acb in the line ,,eg1 
and  the image ,,dc will rise1 and      
become shorter as its extremity ,d moves
  along ,,dg1 and1 after passing the    
perpendicular to ,,ge1 it will increase 
in length4 ,if the eye1 on the other    
hand1 recedes from ,,acb in the line    
,,ge1 the binocular centre ,d will also 
recede1 and the image ,,dc will  descend
 to the plane ,,cm1 and increase in     
length4    ,illustration3 ,,fig4 #bg4   
,the preceding diagram is1 for the      
purpose of illustration1 drawn in a     

sort of perspective1 and therefore does 
not give the true positions and  lengths
 of the united images4 ,this defect1    
however1 is remedied in ,fig4  #bg1     
where ,e1 ,e1 ,e1 ,e is the middle point
 between the two eyes1 the  plane ,,gmn 
being1 as before1 perpendicular to the  
plane passing through  ,,acb4 ,now1 as  
the distance of the eye from ,g is      
supposed to be the same1  and as ,,ab is
 invariable as well as the distance     
between the eyes1 the  distance of the  
binocular centres ,,oo1 ,d1 ,d1 ,d1 ,d1 
,p from ,g1 will  also be invariable1   
and lie in a circle ,,odp1 whose centre 
is ,g1 and  whose radius is ,,go1 the   
point ,o being determined by the formula
                   ,,gm  ,,ab      ,,go 
,,gd  ------------------                
,,ab  ,,rl4    ,hence1 in order to find 
the binocular centres ,d1 ,d1 ,d1 ,d1   
c41 at  any altitude1 ,e1 ,e1 c41 we    
have only to join ,,eg1 ,e,g1 c41 and   
the  points of intersection ,d1 ,d1 c41 
will be the binocular centres1  and the 

lines ,,dc1 ,d,c1 c41 drawn to ,c1 will 
be the real lengths and  inclinations of
 the united images of the lines ,,ac1   
,,bc4    ,when ,,go is greater than ,,gc
 there is obviously some angle ,a1 or   
,e,,gm1 at  which ,d,c is perpendicular 
to ,,gc4    ,this takes place when      
,,gc      ,cos4 ,a  --------4           
,,go    ,when ,o coincides with ,c1 the 
images ,,cd1 ,,cd1 c41 will have the    
same  positions and magnitudes as the   
chords of the altitudes ,a of the eyes  
above the plane ,,gc4 ,in this case the 
raised or united images will just  reach
 the perpendicular when the eye is in   
the plane ,,gcm1 for since        ,,gc  
,,go1 ,cos4 ,a  #a and ,a  #j4    ,when 
the eye at any position1 ,e for example1
 sees the points ,a and ,b  united at   
,d1 it sees also the whole lines ,,ac1  
,,bc forming the image  ,d,c4 ,the      
binocular centre must1 therefore1 run   
rapidly along the line  ,d,c2 that is1  
the inclination of the optic axes must  
gradually diminish  till the binocular  

centre reaches ,c1 when all strain is   
removed4 ,the  vision of the image ,d,c1
 however1 is carried on so rapidly that 
the  binocular centre returns to ,d     
without the eye being sensible of the   
removal and resumption of the strain    
which is required in maintaining  a view
 of the united image ,d,c4 ,if we now   
suppose ,,ab to diminish1  the binocular
 centre will advance towards ,g1 and the
 length and  inclination of the united  
images ,,dc1 ,d,c1 c41 will diminish    
also1 and  vice versa4 ,if the distance 
,,rl 7,fig4 #bf7 between the eyes       
diminishes1  the binocular centre will  
retire towards ,e1 and the length and   
inclination of the images will increase4
 ,hence persons with eyes more  or less 
distant will see the united images in   
different places and of  different      
sizes1 though the quantities ,a and ,,ab
 be invariable4    ,while the eyes at ,e
 are running along the lines ,,ac1 ,,bc1
 let us suppose  them to rest upon the  
points ab equidistant from ,c4 ,join ab1

 and  from the point g1 where ab        
intersects ,,gc1 draw the line g,e1 and 
find the point d from the formula       
g,e  ab      gd                         
-----------------------4                
ab  ,,rl    ,hence the two points a1 b  
will be united at d1 and when the  angle
 ,e,,gc is such that the line joining ,d
 and ,c is perpendicular to  ,,gc1 the  
line joining d,c will also be           
perpendicular to ,,gc1 the loci  of the 
points ,dd1 c41 will be in that         
perpendicular1 and the image  ,,dc1 seen
 by successive movements of the         
binocular centre from ,d to ,c1  will be
 a straight line4    ,in the preceding  
observations we have supposed that the  
binocular  centre ,d1 c41 is between the
 eye and the lines ,,ac1 ,,bc2 but the  
points  ,a1 ,c1 and all the other points
 of these lines1 may be united by fixing
  the binocular centre beyond ,,ab4 ,let
 the eyes1 for example1 be at ,e2  then 
if we unite ,a1 ,b when the eyes        
converge to a point1 1 7not seen  in the

 ,figure7 beyond ,g1 we shall have      
,,ge  ,,ab      ,g  --------------2     
,,rl - ,,ab      and if we join the     
point  thus found and ,c1 the line ,c   
will be  the united image of ,,ac and   
,,bc1 the binocular centre ranging from 
to ,c1 in order to see it as one line4  
,in like manner1 we may find the        
position and length of the image ,c1 ,c1
 and ,c1 corresponding to  the position 
of the eyes at ,e,e and ,e4 ,hence all  
the united images  of ,,ac1 ,,bc1 viz41 
,c1 ,c1 c41 will lie below the plane of 
,,abc1 and  extend beyond a vertical    
line ,,ng continued2 and they will grow 
larger  and larger1 and approximate in  
direction to ,,cg as the eyes descend   
from  ,e to ,m4 ,when the eyes are near 
to ,m1 and a little above the plane of  
,,abc1 the line1 when not carefully     
observed1 will have the appearance of   
coinciding with ,,cg1 but stretching a  
great way beyond ,g4 ,this extreme  case
 represents the celebrated experiment   
with the compasses1 described  by ,dr4  

,smith1 and referred to by ,professor   
,wheatstone4 ,he took a pair  of        
compasses1 which may be represented by  
,,acb1 ,,ab being their points1  ,,ac1  
,,bc their legs1 and ,c their joint2 and
 having placed his eyes about  ,e1 above
 their plane1 he made the following     
experiment3--8,having opened  the points
 of a pair of compasses somewhat wider  
than the interval  of your eyes1 with   
your arm extended1 hold the head or     
joint in the  ball of your hand1 with   
the points outwards1 and equidistant    
from your  eyes1 and somewhat higher    
than the joint4 ,then fixing your eyes  
upon  any remote object lying in the    
plane that bisects the interval of the  
points1 you will first perceive two pair
 of compasses1 7each by being  doubled  
with their inner legs crossing each     
other1 not unlike the old  shape of the 
letter ,w74 ,but by compressing the legs
 with your hand the  two inner points   
will come nearer to each other2 and when
 they unite  7having stopped the        

compression7 the two inner legs will    
also entirely  coincide and bisect the  
angle under the outward ones1 and will  
appear  more vivid1 thicker1 and larger1
 than they do1 so as to reach from your 
hand to the remotest object in view even
 in the horizon itself1 if the  points  
be exactly coincident40#ch ,owing to his
 imperfect apprehension  of the nature  
of this phenomenon1 ,dr4 ,smith has     
omitted to notice that  the united legs 
of the compasses lie below the plane of 
,,abc1 and that  they never can extend  
further than the binocular centre at    
which their  points ,a and ,b are       
united4    ,there is another variation  
of these experiments which possesses    
some  interest1 in consequence of its   
extreme case having been made the basis 
of a new theory of visible direction1 by
 the late ,dr4 ,wells4#ci ,let us       
suppose the eyes of the observer to     
advance from ,e to ,n1 and to descend   
along the opposite quadrant on the left 
hand of ,,ng1 but not drawn in  ,fig4   

#bg1 then the united image of ,,ac1 ,,bc
 will gradually descend towards  ,,cg1  
and become larger and larger4 ,when the 
eyes are a very little  above the plane 
of ,,abc1 and so far to the left hand of
 ,,ab that ,,ca  points nearly to the   
left eye and ,,cb to the right eye1 then
 we have the  circumstances under which 
,dr4 ,wells made the following          
experiment3--8,if  we hold two thin     
rules in such a manner that their sharp 
edges 7,,ac1 ,,bc  in ,fig4 #bg7 shall  
be in the optic axes1 one in each1 or   
rather a little  below them1 the two    
edges will be seen united in the common 
axis1 7,,gc  in ,fig4 #bg27 and this    
apparent edge will seem of the same     
length with  that of either of the real 
edges1 when seen alone by the eye in the
  axis of which it is placed40 ,this    
experiment1 it will be seen1 is the     
same with that of ,dr4 ,smith1 with this
 difference only1 that the points  of   
the compasses are directed towards the  
eyes4 ,like ,dr4 ,smith1 ,dr4  ,wells   

has omitted to notice that the united   
image rises above ,,gh1 and  he commits 
the opposite error of ,dr4 ,smith1 in   
making the length of the  united image  
too short4    #ch ,smith's ,opticks1    
vol4 ii4 p4 #chh1  #igg4    #ci ,essay  
on ,single ,vision1 c41 p4 #dd4    ,if  
in this form of the experiment we fix   
the binocular centre beyond  ,c1 then   
the united images of ,,ac1 and ,,bc     
descend below ,,gc1 and vary in  their  
length1 and in their inclination to     
,,gc1 according to the height  of the   
eye above the plane of ,,abc1 and its   
distance from ,,ab4          ,,chapter  
,,vii4    ,,description ,,of ,,different
 ,,stereoscopes4      ,although the     
lenticular stereoscope has every        
advantage that such  an instrument can  
possess1 whether it is wanted for       
experiments on  binocular vision--for   
assisting the artist by the reproduction
 of  objects in relief1 or for the      
purposes of amusement and instruction1  
yet there are other forms of it which   

have particular properties1  and which  
may be constructed without the aid of   
the optician1 and of  materials within  
the reach of the humblest inquirers4    
,the first of  these is--      #a4 ,the 
,tubular ,reflecting ,stereoscope4      
,in this form of the instrument1 shewn  
in ,fig4 #bh1 the pictures are seen  by 
reflexion from two specula or prisms    
placed at an angle of #ij1 as  in ,mr4  
,wheatstone's instrument4 ,in other     
respects the two instruments  are       
essentially different4    ,in ,mr4      
,wheatstone's stereoscope he employs two
 mirrors1 each four  inches square--that
 is1 he employs thirty-two square inches
 of  reflecting surface1 and is         
therefore under the necessity of        
employing  glass mirrors1 and making a  
clumsy1 unmanageable1 and unscientific  
instrument1 with all the imperfections  
which we have pointed out in a          
preceding chapter4 ,it is not easy to   
understand why mirrors of such a  size  
should have been adopted4 ,the reason of

 their being made of common             
looking-glass is1 that metallic or      
prismatic reflectors of such a size     
would have been extremely expensive4    
,illustration3 ,,fig4 #bh4    ,it is    
obvious1 however1 from the slightest    
consideration1 that  reflectors of such 
a size are wholly unnecessary1 and that 
one  square inch of reflecting surface1 
in place of thirty-two1 is quite        
sufficient for uniting the binocular    
pictures4 ,we can1 therefore1 at  a     
price as low as that of the #d-;inch    
glass reflectors1 use mirrors of        
speculum metal1 steel1 or even silver1  
or rectangular glass prisms1  in which  
the images are obtained by total        
reflexion4 ,in this way the  stereoscope
 becomes a real optical instrument1 in  
which the reflexion  is made from       
surfaces single and perfectly flat1 as  
in the second  reflexion of the         
,newtonian telescope and the microscope 
of ,amici1 in  which pieces of          
looking-glass were never used4 ,by thus 

diminishing the  reflectors1 we obtain a
 portable tubular instrument occupying  
nearly  as little room as the lenticular
 stereoscope1 as will be seen from      
,fig4 #bh1 where ,,abcd is a tube whose 
diameter is equal to the largest  size  
of one of the binocular pictures which  
we propose to use1 the  left-eye picture
 being placed at ,,cd1 and the right-eye
 one at ,,ab4 ,if  they are transparent1
 they will be illuminated through paper 
or ground  glass1 and if opaque1 through
 openings in the tube4 ,the image of    
,,ab1  reflected to the left eye ,l from
 the small mirror mn1 and that of  ,,cd 
to the right eye ,r from the mirror op1 
will be united exactly  as in ,mr4      
,wheatstone's instrument already        
described4 ,the distance of  the two    
ends1 n1 p1 of the mirrors should be a  
little greater than  the smallest       
distance between the two eyes4 ,if we   
wish to magnify the  picture1 we may use
 two lenses1 or substitute for the      
reflectors a  totally reflecting glass  

prism1 in which one or two of its       
surfaces are  made convex4#dj    #dj ,we
 may use also the lens prism1 which ,i  
proposed many years ago in  the         
,edinburgh ,philosophical ,journal4     
#b4 ,the ,single ,reflecting            
,stereoscope4    ,this very simple      
instrument1 which1 however1 answers only
 for  symmetrical figures1 such as those
 shewn at ,a and ,b1 which must be      
either two right-eye or two left-eye    
pictures1 is shewn in ,fig4 #bi4  ,a    
single reflector1 ,,mn1 which may be    
either a piece of glass1 or a  piece of 
mirror-glass1 or a small metallic       
speculum1 or a rectangular  prism1 is   
placed at ,,mn4 ,if we look into it with
 the left eye ,l1 we see1  by reflexion 
from its surface at ,c1 a reverted      
image1 or a right-eye  picture of the   
left-eye picture ,b1 which1 when seen in
 the direction  ,,lca1 and combined with
 the figure ,a1 seen directly with the  
right eye  ,r1 produces a raised cone2  
but if we turn the reflector ,l round1  

so  that the right eye may look into it1
 and combine a reverted image of  ,a1   
with the figure ,b seen directly with   
the left eye ,l1 we shall see  a hollow 
cone4 ,as ,,bc  ,,cl is greater than    
,,ra1 the reflected image  will be      
slightly less in size than the image    
seen directly1 but the  difference is   
not such as to produce any perceptible  
effect upon the  appearance of the      
hollow or the raised cone4 ,by bringing 
the picture  viewed by reflexion a      
little nearer the reflector ,,mn1 the   
two pictures  may be made to have the   
same apparent magnitude4                
,illustration3 ,,fig4 #bi4    ,if we    
substitute for the single reflector     
,,mn1 two reflectors such as  are shewn 
at ,m1 ,n1 ,fig4 #cj1 or a prism ,p1    
which gives two internal  reflexions1 we
 shall have a general stereoscope1 which
 answers for  landscapes and portraits4 
,illustration3 ,,fig4 #cj4    ,the      
reflectors ,m1 ,n or ,p may be fitted up
 in a conical tube1 which has  an       

elliptical section to accommodate two   
figures at its farther end1  the major  
axis of the ellipse being parallel to   
the line joining the  two eyes4      #c4
 ,the ,double ,reflecting ,stereoscope4 
,this instrument differs from the       
preceding in having a single  reflector1
 ,,mn1 ,m,n1 for each eye1 as shewn in  
,fig4 #ca1 and the effect  of this is to
 exhibit1 at the same time1 the raised  
and the hollow  cone4 ,the image of ,b1 
seen by reflexion from ,,mn at the point
 ,c1 is  combined with the picture of   
,a1 seen directly by the right eye ,r1  
and  forms a hollow cone2 while the     
image of ,a1 seen by reflexion from     
,m,n at the point ,c1 is combined with  
the picture of ,b1 seen directly  by the
 left eye ,l1 and forms a raised cone4  
,illustration3 ,,fig4 #ca4              
,illustration3 ,,fig4 #cb4    ,another  
form of the double reflecting           
stereoscope is shewn in ,fig4 #cb1      
which differs from that shewn in ,fig4  
#ca in the position of the two          

reflectors and of the figures to be     
united4 ,the reflecting faces of  the   
mirrors are turned outwards1 their      
distance being less than the  distance  
between the eyes1 and the effect of this
 is to exhibit at the  same time the    
raised and the hollow cone1 the hollow  
cone being now  on the right-hand side4 
,if in place of two right or two left   
eye pictures1 as shewn in ,figs4  #bi1  
#ca1 and #cb1 we use one right eye and  
one left eye picture1 and  combine the  
reflected image of the one with the     
reflected image of the  other1 we shall 
have a raised cone with the stereoscope1
 shewn in  ,fig4 #ca1 and a hollow cone 
with the one in ,fig4 #cb4    ,the      
double reflecting stereoscope1 in both  
its forms1 is a general  instrument for 
portraits and landscapes1 and thus      
possesses properties  peculiar to       
itself4    ,the reflectors may be glass 
or metallic specula1 or total reflexion 
prisms4      #d4 ,the ,total            
,reflexion-,stereoscope4    ,this form  

of the stereoscope is a very interesting
 one1 and possesses  valuable           
properties4 ,it requires only a small   
prism and one diagram1  or picture of   
the solid1 as seen by one eye2 the other
 diagram1 or  picture which is to be    
combined with it1 being created by total
  reflexion from the base of the prism4 
,this instrument is shewn in ,fig4  #cc1
 where ,d is the picture of a cone as   
seen by the left eye ,l1 and ,,abc  a   
prism1 whose base ,,bc is so large1 that
 when the eye is placed close  to it1 it
 may see1 by reflexion1 the whole of the
 diagram ,d4 ,the angles  ,,abc1 ,,acb  
must be equal1 but may be of any        
magnitude4 ,great accuracy in  the      
equality of the angles is not necessary2
 and a prism constructed1  by a         
lapidary1 out of a fragment of thick    
plate-glass1 the face ,,bc  being one of
 the surfaces of the plate1 will answer 
the purpose4 ,when  the prism is placed 
at a1 ,fig4 #cd1 at one end of a conical
 tube ,,ld1  and the diagram ,d at the  

other end1 in a cap1 which can be turned
 round  so as to have the line mn1 ,fig4
 #cc1 which passes through the centre   
of the base and summit of the cone      
parallel to the line joining the two    
eyes1 the instrument is ready for use4  
,the observer places his left  eye at   
,l1 and views with it the picture ,d1 as
 seen by total reflexion  from the base 
,,bc of the prism1 ,figs4 #cc and #ce1  
while with his right  eye ,r1 ,fig4 #cc1
 he views the real picture directly4    
,the first of these  pictures being the 
reverse of the second ,d1 like all      
pictures formed  by one reflexion1 we   
thus combine two dissimilar pictures    
into a  raised cone1 as in the figure1  
or into a hollow one1 if the picture  at
 ,d is turned round #ahj4 ,if we place  
the images of two diagrams1  one like   
one of those at ,a1 ,fig4 #ca1 and the  
other like the one at ,b1  vertically   
above one another1 we shall then see1 at
 the same time1  the raised and the     
hollow cone1 as produced in the         

lenticular  stereoscope by the three    
diagrams1 two like those in ,fig4 #ca1  
and a  third like the one at ,a4 ,when  
the prism is good1 the dissimilar image1
  produced by the two refractions at ,b 
and ,c1 and the one reflexion at  ,e1   
is1 of course1 more accurate than if it 
had been drawn by the most  skilful     
artist2 and therefore this form of the  
stereoscope has in this  respect an     
advantage over every other in which two 
dissimilar figures1  executed by art1   
are necessary4 ,in consequence of the   
length of the  reflected pencil ,,db    
,,be  ,,ec  ,,cl being a little greater 
than the  direct pencil of rays ,,dr1   
the two images combined have not exactly
 the  same apparent magnitude2 but the  
difference is not perceptible to the    
eye1 and a remedy could easily be       
provided were it required4              
,illustration3 ,,fig4 #cc4              
,illustration3 ,,fig4 #cd4    ,if the   
conical tube ,,ld is held in the left   
hand1 the left eye must be  used1 and if

 in the right hand the right eye must be
 used1 so that  the hand may not        
obstruct the direct vision of the       
drawing by the eye  which does not look 
through the prism4 ,the cone ,,ld must  
be turned round  slightly in the hand   
till the line mn joining the centre and 
apex of  the figure is parallel to the  
line joining the two eyes4 ,the same    
line  must be parallel to the plane of  
reflexion from the prism2 but this      
parallelism is secured by fixing the    
prism and the drawing4    ,it is        
scarcely necessary to state that this   
stereoscope is applicable  only to those
 diagrams and forms where the one image 
is the reflected  picture of the other4 
,illustration3 ,,fig4 #ce4    ,if we    
wish to make a microscopic stereoscope  
of this form1 or to  magnify the        
drawings1 we have only to cement        
plano-convex lenses1  of the requisite  
focal length1 upon the faces ,,ab1 ,,ac 
of the prism1  or1 what is simpler      
still1 to use a section of a deeply     

convex lens  ,,abc1 ,fig4 #ce1 and apply
 the other half of the lens to the right
 eye1  the face ,,bc having been        
previously ground flat and polished for 
the  prismatic lens4 ,by using a lens of
 larger focus for the right eye1 we  may
 correct1 if required1 the imperfection 
arising from the difference  of paths in
 the reflected and direct pencils4 ,this
 difference1 though  trivial1 might be  
corrected1 if thought necessary1 by     
applying to the  right eye the central  
portion of the same lens whose margin is
 used for  the prism4    ,illustration3 
,,fig4 #cf4    ,if we take the drawing  
of a six-sided pyramid as seen by the   
right eye1  as shewn in ,fig4 #cf1 and  
place it in the total-reflexion         
stereoscope at  ,d1 ,fig4 #cc1 so that  
the line ,,mn coincides with mn1 and is 
parallel to  the line joining the eyes  
of the observer1 we shall perceive a    
perfect  raised pyramid of a given      
height1 the reflected image of ,,cd1    
,fig4 #cf1  being combined with ,,af1   

seen directly4 ,if we now turn the      
figure round  #cj1 ,,cd will come into  
the position ,,ab1 and unite with ,,ab1 
and we shall  still perceive a raised   
pyramid1 with less height and less      
symmetry4 ,if  we turn it round #cj     
more1 ,,cd will be combined with ,,bc1  
and we shall  still perceive a raised   
pyramid with still less height and still
 less  symmetry4 ,when the figure is    
turned round other #cj1 or #ij degrees  
from its first position1 ,,cd will      
coincide with ,,cd seen directly1  and  
the combined figures will be perfectly  
flat4 ,if we continue the  rotation     
through other #cj1 ,,cd will coincide   
with ,,de1 and a slightly  hollow1 but  
not very symmetrical figure1 will be    
seen4 ,a rotation of  other #cj will    
bring ,,cd into coalesence with ,,ef1   
and we shall see a  still more hollow   
and more symmetrical pyramid4 ,a further
 rotation of  other #cj1 making #ahj    
from the commencement1 will bring ,,cd  
into union  with ,,af2 and we shall have

 a perfectly symmetrical hollow pyramid 
of  still greater depth1 and the exact  
counterpart of the raised pyramid  which
 was seen before the rotation of the    
figure commenced4 ,if the  pyramid had  
been square1 the raised would have      
passed into the  hollow pyramid by      
rotations of #de each4 ,if it had been  
rectangular1  the change would have been
 effected by rotations of #ij4 ,if the  
space  between the two circular sections
 of the cone in ,fig4 #ca had been      
uniformly shaded1 or if lines had been  
drawn from every degree of the  one     
circle to every corresponding degree in 
the other1 in place of  from every #ijth
 degree1 as in the ,figure1 the raised  
cone would have  gradually diminished in
 height1 by the rotation of the figure1 
till it  became flat1 after a rotation  
of #ij2 and by continuing the rotation  
it  would have become hollow1 and       
gradually reached its maximum depth     
after  a revolution of #ahj4      #e4   
,the ,single-,prism ,stereoscope4       

,although the idea of uniting the       
binocular pictures by a single  prism   
applied to one eye1 and refracting one  
of the pictures so as  to place it upon 
the other seen directly by the other    
eye1 or by a  prism applied to each eye1
 could hardly have escaped the notice of
  any person studying the subject1 yet  
the experiment was1 so far as ,i  know1 
first made and published by myself4 ,i  
found two prisms quite  unnecessary1 and
 therefore abandoned the use of them1   
for reasons which  will be readily      
appreciated4 ,this simple instrument is 
shewn in ,fig4  #cg1 where ,a1 ,b are   
the dissimilar pictures1 and ,p a prism 
with such  a refracting angle as is     
sufficient to lay the image of ,a upon  
,b1 as  seen by the right eye4 ,if we   
place a second prism before the eye  ,r1
 we require it only to have half the    
refracting angle of the prism  ,p1      
because each prism now refracts the     
picture opposite to it only  half way   
between ,a and ,b1 where they are       

united4 ,this1 at first sight1  appears 
to be an advantage1 for as there must   
always be a certain  degree of colour   
produced by a single prism1 the use of  
two prisms1  with half the refracting   
angle1 might be supposed to reduce the  
colour  one-half4 ,but while the colour 
produced by each prism is thus reduced1 
the colour over the whole picture is the
 same4 ,each luminous edge with  two    
prisms has both red and blue tints1     
whereas with one prism each  luminous   
edge has only one colour1 either red or 
blue4 ,if the picture  is very luminous 
these colours will be seen1 but in many 
of the finest  opaque pictures it is    
hardly visible4 ,in order1 however1 to  
diminish  it1 the prism should be made  
of glass with the lowest dispersive     
power1  or with rock crystal4 ,a single 
plane surface1 ground and polished by  a
 lapidary1 upon the edge of a piece of  
plate-glass1 a little larger  than the  
pupil of the eye1 will give a prism     
sufficient for every  ordinary purpose4 

,any person may make one in a few       
minutes for himself1  by placing a      
little bit of good window glass upon    
another piece  inclined to it at the    
proper angle1 and inserting in the angle
 a drop  of fluid4 ,such a prism will   
scarcely produce any perceptible colour4
    ,illustration3 ,,fig4 #cg4    ,if a 
single-prism reflector is to be made    
perfect1 we have only to  make it       
achromatic1 which could be done         
extempore1 by correcting  the colour of 
the fluid prism by another fluid prism  
of different  refractive and dispersive 
power4    ,with a good achromatic prism 
the single-prism stereoscope is a very  
fine instrument2 and no advantage of any
 value could be gained by  using two    
achromatic prisms4 ,in the article on   
,new ,stereoscopes1  published in the   
,transactions of the ,royal ,society of 
,arts for #ahdi1  and in the            
,philosophical ,magazine for #aheb1 ,i  
have stated in a note  that ,i believed 
that ,mr4 ,wheatstone had used two      

achromatic prisms4  ,this1 however1 was 
a mistake1 as already explained1#da for 
such  an instrument was never made1 and 
has never been named in any work        
previous to #ahdi1 when it was mentioned
 by myself in the note above  referred  
to4    #da ,see ,chap4 i4 pp4 #cc-cf4   
,if we make a double prism1 or join two1
 as shewn at ,p1 ,p in ,fig4  #ch1 and  
apply it to two dissimilar figures ,a1  
,b1 one of which is the  reflected image
 of the other1 so that with the left eye
 ,l and the prism  ,p we place the      
refracted image of ,a upon ,b1 as seen  
by the right eye  ,r1 we shall see a    
raised cone1 and if with the prism ,p we
 place  the image of ,b upon ,a we shall
 see a hollow cone4 ,if we place the    
left eye ,l at ,o1 behind the common    
base of the prism1 we shall see with    
one-half of the pupil the hollow cone   
and with the other half the  raised     
cone4    ,illustration3 ,,fig4 #ch4     
#f4 ,the ,opera-,glass ,stereoscope4    
,as the eyes themselves form a          

stereoscope to those who have the power 
of quickly converging their axes to     
points nearer than the object which     
they contemplate1 it might have been    
expected that the first attempt  to make
 a stereoscope for those who do not     
possess such a power1 would  have been  
to supply them with auxiliary eyeballs  
capable of combining  binocular pictures
 of different sizes at different        
distances from the  eye4 ,this1 however1
 has not been the case1 and the         
stereoscope for this  purpose1 which we 
are about to describe1 is one of the    
latest of its  forms4    ,illustration3 
,,fig4 #ci4    ,illustration3 ,,fig4    
#dj4    ,in ,fig4 #ci1 ,,mn is a small  
inverting telescope1 consisting of two  
convex lenses ,m1 ,n1 placed at the sum 
of their focal distances1 and  ,,op     
another of the same kind4 ,when the two 
eyes1 ,r1 ,l1 look through the  two     
telescopes directly at the dissimilar   
pictures ,a1 ,b1 they will see  them    
with perfect distinctness2 but1 by the  

slightest inclination of  the axes of   
the telescopes1 the two images can be   
combined1 and the  stereoscopic effect  
immediately produced4 ,with the         
dissimilar pictures  in the diagram a   
hollow cone is produced2 but if we look 
at ,b with  the telescope ,m,n1 as in   
,fig4 #dj1 and at ,a with ,o,p1 a raised
 cone  will be seen4 ,with the usual    
binocular slides containing portraits or
  landscapes1 the pictures are seen in  
relief by combining the right-eye  one  
with the left-eye one4    ,the          
instrument now described is nothing more
 than a double opera-glass1  which      
itself forms a good stereoscope4 ,owing1
 however1 to the use of  a concave      
eye-glass1 the field of view is very    
small1 and therefore a  convex glass1   
which gives a larger field1 is greatly  
to be preferred4    ,the little         
telescopes1 ,,mn1 ,,op1 may be made one 
and a half or even  one inch long1 and  
fitted up1 either at a fixed or with a  
variable  inclination1 in a pyramidal   

box1 like the lenticular stereoscope1   
and  made equally portable4 ,one of     
these instruments was made for me some  
years ago by ,messrs4 ,horne and        
,thornthwaite1 and ,i have described it 
in  the ,north ,british ,review#db as   
having the properties of a ,binocular   
,cameoscope1 and of what has been       
absurdly called a ,pseudoscope1  seeing 
that every inverting eye-piece and every
 stereoscope is entitled  to the very   
same name4    ,the little telescope may 
be made of one piece of glass1 convex   
at each end1 or concave at the eye-end  
if a small field is not                 
objectionable1--the length of the piece 
of glass1 in the first  case1 being     
equal to the sum1 and1 in the second    
case1 to the  difference of the focal   
lengths of the virtual lenses at each   
end4#dc    #db ,for #aheb1 vol4 xvii4 p4
 #bjj4    #dc ,these solid telescopes   
may be made achromatic by cementing     
concave  lenses of flint glass upon each
 end1 or of crown glass if they are made

  of flint glass4      #g4 ,the         
,eye-,glass ,stereoscope4    ,as it is  
impossible to obtain1 by the ocular     
stereoscope1 pictures in  relief from   
the beautiful binocular slides which are
 made in every  part of the world for   
the lenticular stereoscope1 it is very  
desirable  to have a portable           
stereoscope which can be carried safely 
in our  purse1 for the purpose of       
examining stereoscopically all such     
binocular  pictures4    ,if placed      
together with their plane sides in      
contact1 a plano-convex  lens1 ,,ab1 and
 a plano-concave one1 ,,cd1 of the same 
glass and the same  focal length1 will  
resemble a thick watch-glass1 and on    
looking through  them1 we shall see     
objects of their natural size and in    
their proper  place2 but if we slip the 
concave lens1 ,,cd1 to a side1 as shewn 
in  ,fig4 #da1 we merely displace the   
image of the object which we view1 and  
the displacement increases till the     
centre of the concave lens comes  to the

 margin of the convex one4 ,we thus     
obtain a variable prism1 by  means of   
which we can1 with the left eye1        
displace one of the binocular  pictures1
 and lay it upon the other1 as seen by  
the right eye4 ,we may  use semi-lenses 
or quarters of lenses1 and we may make  
them achromatic  or nearly so if we     
desire it4 ,double convex and double    
concave lenses  may also be used1 and   
the motion of the concave one regulated 
by a  screw4 ,in one which ,i constantly
 use1 the concave lens slides in a      
groove over a convex quarter-lens4      
,illustration3 ,,fig4 #da4    ,by       
employing two of these variable prisms1 
we have an ,universal  ,stereoscope for 
uniting pictures of various sizes and at
 various  distances from each other1 and
 the prisms may be placed in a pyramidal
  box1 like the lenticular stereoscope4 
#h4 ,the ,reading-,glass ,stereoscope4  
,if we take a reading-glass whose       
diameter is not less than two inches    
and three quarters1 and look through it 

with both eyes at a binocular  picture  
in which the right-eye view is on the   
left hand1 and the  left-eye view on the
 right hand1 as in the ocular           
stereoscope1 we shall  see each picture 
doubled1 and the degree of separation is
 proportional  to the distance of the   
picture from the eye4 ,if the distance  
of the  binocular pictures from each    
other is small1 the two middle images of
  the four will be united when their    
distance from the lens is not very  much
 greater than its focal length4 ,with a 
reading-glass #d inches in  diameter1   
with a focal length of two feet1        
binocular pictures1 in which  the       
distance of similar parts is nine       
inches1 are united without  any exertion
 of the eyes at the distance of eight   
feet4 ,with the same  reading-glass1    
binocular pictures1 at the usual        
distance of #b inches1  will be united  
at the distance of #b or even #b feet4  
,if we advance the  reading-glass when  
the distance is #b or #c feet1 the      

picture in relief  will be magnified1   
but1 though the observer may not notice 
it1 the  separated images are now kept  
united by a slight convergency of the   
optic axes4 ,although the pictures are  
placed so far beyond the anterior  focus
 of the lens1 they are exceedingly      
distinct4 ,the distinctness of  vision  
is sufficient1 at least to long-sighted 
eyes1 when the pictures  are placed     
within #af or #ah inches of the         
observer1 that is1 #f or #h  inches     
nearer the eye than the anterior focus  
of the lens4 ,in this  case we can      
maintain the union of the pictures only 
when we begin to  view them at a        
distance of #b or #c feet1 and then     
gradually advance  the lens within #af  
or #ah inches of the pictures4 ,at      
considerable  distances1 the pictures   
are most magnified by advancing the lens
 while  the head of the observer is     
stationary4      #i4 ,the ,camera       
,stereoscope4    ,the object of this    
instrument is to unite the transient    

pictures of  groups of persons or       
landscapes1 as delineated in two        
dissimilar  pictures1 on the            
ground-glass of a binocular camera4 ,if 
we attach  to the back of the camera a  
lenticular stereoscope1 so that the two 
pictures on the ground-glass occupy the 
same place as its usual  binocular      
slides1 we shall see the group of       
figures in relief under  every change of
 attitude1 position1 and expression4    
,the two pictures  may be formed in the 
air1 or1 more curiously still1 upon a   
wreath of  smoke4 ,as the figures are   
necessarily inverted in the camera1 they
  will remain inverted by the lenticular
 and every other instrument but  the    
opera-glass stereoscope1 which inverts  
the object4 ,by applying  it therefore  
to the camera1 we obtain an instrument  
by which the  photographic artist can   
make experiments1 and try the effect    
which will  be produced by his pictures 
before he takes them4 ,he can thus      
select  the best forms of groups of     

persons and of landscapes1 and thus     
produce  works of great interest and    
value4      #aj4 ,the ,chromatic        
,stereoscope4    ,the chromatic         
stereoscope is a form of the instrument 
in which relief  or apparent solidity is
 given to a single figure with different
 colours  delineated upon a plane       
surface4    ,if we look with both eyes  
through a lens ,,ll1 ,fig4 #db1 about #b
 inches  in diameter or upwards1 at any 
object having colours of different      
degrees of refrangibility1 such as the  
coloured boundary lines on  a map1 a red
 rose among green leaves and on a blue  
background1 or  any scarlet object      
whatever upon a violet ground1 or in    
general any  two simple colours not of  
the same degree of refrangibility1 the  
differently coloured parts of the object
 will appear at different  distances    
from the observer4    ,illustration3    
,,fig4 #db4    ,let us suppose the rays 
to be red and violet1 those which differ
  most in refrangibility4 ,if the red   

rays radiate from the anterior focus    
,r1 or red rays of the lens ,,ll1 they  
will emerge parallel1 and enter the  eye
 at m2 but the violet rays radiating    
from the same focus1 being  more        
refrangible1 will emerge in a state of  
convergence1 as shewn at  mv1 nv1 the   
red rays being mr1 nr4 ,the part of the 
object1  therefore1 from which the red  
rays come1 will appear nearer to the    
observer than the parts from which the  
violet rays come1 and if there  are     
other colours or rays of intermediate   
refrangibilities1 they will  appear to  
come from intermediate distances4    ,if
 we place a small red and violet disc1  
like the smallest  wafer1 beside one    
another1 so that the line joining their 
centres is  perpendicular to the line   
joining the eyes1 and suppose that rays 
from  both enter the eyes with their    
optical axes parallel1 it is obvious    
that the distance between the violet    
images on each retina will be  less than
 the distance between the red images1   

and consequently the  eyes will require 
to converge their axes to a nearer point
 in order  to unite the red images1 than
 in order to unite the violet images4   
,the  red images will therefore appear  
at this nearer point of convergence1    
just as1 in the lenticular stereoscope1 
the more distant pair of points  in the 
dissimilar images appear when united    
nearer to the eye4 ,by the  two eyes    
alone1 therefore1 we obtain a certain1  
though a small degree  of relief from   
colours4 ,with the lens ,,ll1 however1  
the effect is  greatly increased1 and we
 have the sum of the two effects4       
,from these observations1 it is manifest
 that the reverse effect must  be       
produced by a concave lens1 or by the   
common stereoscope1 when  two coloured  
objects are employed or united4 ,the    
blue part of the  object will be seen   
nearer the observer1 and the red part of
 it  more remote4 ,it is1 however1 a    
curious fact1 and one which appeared    
difficult to explain1 that in the       

stereoscope the colour-relief was not   
brought out as might have been expected4
 ,sometimes the red was nearest  the    
eye1 and sometimes the blue1 and        
sometimes the object appeared  without  
any relief4 ,the cause of this is1 that 
the colour-relief given  by the common  
stereoscope was the opposite of that    
given by the eye1  and it was only the  
difference of these effects that ought  
to have  been observed2 and though the  
influence of the eyes was an inferior   
one1 it often acted alone1 and sometimes
 ceased to act at all1 in  virtue of    
that property of vision by which we see 
only with one eye  when we are looking  
with two4    ,in the chromatic          
stereoscope1 ,fig4 #db1 the intermediate
 part mn of  the lens is of no use1 so  
that out of the margin of a lens upwards
 of  #b inches in diameter1 we may cut a
 dozen of portions capable of making  as
 many instruments4 ,these portions1     
however1 a little larger only than  the 
pupil of the eye1 must be placed in the 

same position as in ,fig4 #db4    ,all  
the effects which we have described are 
greatly increased by using  lenses of   
highly-dispersing flint glass1 oil of   
cassia1 and other  fluids of a great    
dispersive power1 and avoiding the use  
of compound  colours in the objects     
placed in the stereoscope4    ,it is an 
obvious result of these observations1   
that in painting1 and in  coloured      
decorations of all kinds1 the red or    
less refrangible colours  should be     
given to the prominent parts of the     
object to be represented1  and the blue 
or more refrangible colours to the      
background and the  parts of the objects
 that are to retire from the eye4       
#aa4 ,the ,microscope ,stereoscope4     
,the lenticular form of the stereoscope 
is admirably fitted for its  application
 to small and microscopic objects4 ,the 
first instruments  of this kind were    
constructed by myself with quarter-inch 
lenses1 and  were #c inches long and    
only #a and #a deep4#dd ,they may be    

carried in  the pocket1 and exhibit all 
the properties of the instrument to the 
greatest advantage4 ,the mode of        
constructing and using the instrument   
is precisely the same as in the common  
stereoscope2 but in taking the          
dissimilar pictures1 we must use either 
a small binocular camera1 which  will   
give considerably magnified             
representations of the objects1 or  we  
must procure them from the compound     
microscope4 ,the pictures may  be       
obtained with a small single camera1 by 
first taking one picture1  and then     
shifting the object in the focus of the 
lens1 through a space  corresponding    
with the binocular angle4 ,to find this 
space1 which we  may call x1 make d the 
distance of the object from the lens1 n 
the number of times it is to be         
magnified1 or the distance of the image 
behind the lens1 and ,d the distance of 
the eyes2 then we shall have            
,d      nd 3 d  ,d 3 x1 and x  ------4  
n    that is1 the space is equal to the 

distance between the eyes divided by    
the magnifying power4    #dd ,phil4     
,mag41 ,jan4 #aheb1 vol4 iii4 p4 #ai4   
,with the binocular microscope of       
,professor ,riddell1#de and the same    
instrument as improved by ,m4 ,nachet1  
binocular pictures are obtained         
directly by having them drawn1 as       
,professor ,riddell suggests1 by the    
camera lucida1 but it would be          
preferable to take them                 
photographically4    ,portraits for     
lockets or rings might be put into a    
very small  stereoscope1 by folding the 
one lens back upon the other4    #de    
,american ,journal of ,science1 #aheb1  
vol4 xv4 p4 #fh4          ,,chapter     
,,viii4    ,,method ,,of ,,taking       
,,pictures ,,for ,,the ,,stereoscope4   
,however perfect be the stereoscope     
which we employ1 the effect which it    
produces depends upon the accuracy with 
which the binocular pictures  are       
prepared4 ,the pictures required for the
 stereoscope may be arranged  in four   

classes3--    #a4 ,the representations  
of geometrical solids as seen with two  
eyes4    #b4 ,portraits1 or groups of   
portraits1 taken from living persons or 
animals4    #c4 ,landscapes1 buildings1 
and machines or instruments4    #d4     
,solids of all kinds1 the productions of
 nature or of art4 99_/    ,geometrical 
,solids4    ,representations of         
geometrical solids1 were1 as we have    
already seen1  the only objects which   
for many years were employed in the     
reflecting  stereoscope4 ,the figures   
thus used are so well known that it is  
unnecessary to devote much space to     
their consideration4 ,for ordinary      
purposes they may be drawn by the hand1 
and composed of squares1  rectangles1   
and circles1 representing quadrangular  
pyramids1 truncated1  or terminating in 
a point1 cones1 pyramids with polygonal 
bases1 or  more complex forms in which  
raised pyramids or cones rise out of    
quadrangular or conical hollows4 ,all   
these figures may be drawn by the  hand1

 and will produce solid forms           
sufficiently striking to illustrate  the
 properties of the stereoscope1 though  
not accurate representations  of any    
actual solid seen by binocular vision4  
,if one of the binocular pictures is not
 equal to the other in its  base or     
summit1 and if the lines of the one are 
made crooked1 it is  curious to observe 
how the appearance of the resulting     
solid is still  maintained and varied4  
,the following method of drawing upon a 
plane the dissimilar  representations of
 solids1 will give results in the       
stereoscope that  are perfectly         
correct3--    ,illustration3 ,,fig4 #dc4
    ,let ,l1 ,r1 ,fig4 #dc1 be the left 
and right eye1 and ,a the middle point  
between them4 ,let ,,mn be the plane on 
which an object or solid whose  height  
is ,,cb is to be drawn4 ,through ,b draw
 ,,lb1 meeting ,,mn in c2 then  if the  
object is a solid1 with its apex at ,b1 
,cc will be the distance  of its apex   
from the centre ,c of its base1 as seen 

by the left eye4  ,when seen by the     
right eye ,r1 ,cc will be its distance1 
c lying  on the left side of ,c4 ,hence 
if the figure is a cone1 the dissimilar 
pictures of it will be two circles1 in  
one of which its apex is placed  at the 
distance ,cc from its centre1 and in the
 other at the distance  ,cc on the other
 side of the centre4 ,when these two    
plane figures are  placed in the        
stereoscope1 they will1 when combined1  
represent a raised  cone when the points
 c1 c are nearer one another than the   
centres  of the circles representing the
 cone's base1 and a hollow cone when    
the figures are interchanged4    ,if we 
call ,e the distance between the two    
eyes1 and h the height of  the solid1 we
 shall have                  ,e         
,,ab3h  ------ 3 ,cc1                #b 
h,e     #e;h      and ,cc  --------1 or 
--------1                  #b;,,ab      
#d;,,ab    which will give us the       
results in the following table1 ,e being
 #b1 and  ,,ac #h inches3--             

,height of       object4       ,,bc  h  
,,ab  ,,ac - h    ,cc                   
,inches4          #a                 #g 
#j4agi          #b                 #f   
#j4daff          #c                 #e  
#j4ge          #d                 #d    
#a4be          #e                 #c    
#b4jhc          #f                 #b   
#c4ge          #g                 #a    
#h4ge          #h                 #j    
,infinite4    ,if we now converge the   
optic axes to a point b1 and wish to    
ascertain  the value of ,cc1 which will 
give different depths1 d1 of the  hollow
 solids corresponding to different      
values of ,cb1 we shall have            
,e      ,ab3----  d3,cc1           #b   
d,e      and ,cc  ---------- ,,ab1      
#b    which1 making ,,ac  #h inches1 as 
before1 will give the following         
results3--           ,depth4      ,cb  d
     ,ab  ,,ac  d       ,cc             
,inches4           #a               #i  
#j4aci           #b              #aj    
#j4be           #c              #aa     

#j4cd           #d              #ab     
#j4daff           #e              #ac   
#j4dh           #f              #ad     
#j4ece           #g              #ae    
#j4eh           #h              #af     
#j4fbe           #i              #ag    
#j4ffc          #aj              #ah    
#j4fif          #aa              #ai    
#j4gbc          #ab              #bj    
#j4ge    ,the values of h and d when    
,cc1 ,cc are known1 will be found  from 
the formul               #b;,,ab  ,cc   
h  ------------------------1            
,e                  #b;,,ab  ,cc        
and d  ------------------------4        
,e4      ,as ,cc is always equal to ,cc 
in each pair of figures or dissimilar   
pictures1 the depth of the hollow cone  
will always appear much  greater than   
the height of the raised one4 ,when ,cc 
,cc  #j4ge1  h3d  #c3ab4 ,when ,cc  ,cc 
#j4daff1 h3d  #b3d1 and when  ,cc  ,cc  
#j4aci1 h3d  #j4h3a4j4    ,when the     
solids of which we wish to have         
binocular pictures are  symmetrical1 the

 one picture is the reflected image of  
the other1 or  its reverse1 so that when
 we have drawn the solid as seen by one 
eye1  we may obtain the other by copying
 its reflected image1 or by simply      
taking a copy of it as seen through the 
paper4    ,when the geometrical solids  
are not symmetrical1 their dissimilar   
pictures must be taken photographically 
from models1 in the same manner  as the 
dissimilar pictures of other solids4    
,portraits of ,living ,persons or       
,animals4    ,although it is possible   
for a clever artist to take two         
portraits1 the  one as seen by his      
right1 and the other as seen by his left
 eye1 yet1  owing to the impossibility  
of fixing the sitter1 it would be a very
  difficult task4 ,a bust or statue     
would be more easily taken by fixing    
two apertures #b inches distant1 as the 
two points of sight1 but even  in this  
case the result would be imperfect4 ,the
 photographic camera is  the only means 
by which living persons and statues can 

be represented  by means of two plane   
pictures to be combined by the          
stereoscope2 and  but for the art of    
photography1 this instrument would have 
had a very  limited application4    ,it 
is generally supposed that photographic 
pictures1 whether in  ,daguerreotype or 
,talbotype1 are accurate representations
 of the human  face and form1 when the  
sitter sits steadily1 and the artist    
knows  the resources of his art4 ,quis  
solem esse falsum dicere audeat8  says  
the photographer1 in rapture with his   
art4 ,solem esse falsum  dicere audeo1  
replies the man of science1 in reference
 to the hideous  representations of     
humanity which proceed from the studio  
of the  photographer4 ,the sun never    
errs in the part which he has to        
perform4  ,the sitter may sometimes     
contribute his share to the hideousness 
of his  portrait by involuntary nervous 
motion1 but it is upon the artist or    
his art that the blame must be laid4    
,if the single portrait of an individual

 is a misrepresentation of his  form and
 expression1 the combination of two such
 pictures into a solid  must be more    
hideous still1 not merely because the   
error in form and  expression is        
retained or doubled1 but because the    
source of error  in the single portrait 
is incompatible with the application of 
the  stereoscopic principle in giving   
relief to the plane pictures4 ,the art  
of stereoscopic portraiture is in its   
infancy1 and we shall therefore  devote 
some space to the development of its    
true principles and  practice4    ,in   
treating of the images of objects formed
 by lenses and mirrors  with spherical  
surfaces1 optical writers have satisfied
 themselves by  shewing that the images 
of straight lines so formed are conic   
sections1  elliptical1 parabolic1 or    
hyperbolic4 ,i am not aware that any    
writer  has treated of the images of    
solid bodies1 and of their shape as     
affected by the size of the lenses or   
mirrors by which they are formed1  or   

has even attempted to shew how a perfect
 image of any object can be  obtained4  
,we shall endeavour to supply this      
defect4    ,in a previous chapter we    
have explained the manner in which      
images are  formed by a small aperture1 
,h1 in the side1 ,,mn1 of a camera1 or  
in the  window-shutter of a dark room4  
,the rectangles br1 br1 and br1  are    
images of the object ,,rb1 according as 
they are received at the  same distance 
from the lens as the object1 or at a    
less or a greater  distance1 the size of
 the image being to that of the object  
as their  respective distances from the 
hole ,h4 ,pictures thus taken are       
accurate  representations of the object1
 whether it be lineal1 superficial1  or 
solid1 as seen from or through the hole 
,h2 and if we could throw  sufficient   
light upon the object1 or make the      
material which receives  the image very 
sensitive1 we should require no other   
camera for giving  us photographs of all
 sizes4 ,the only source of error which 

we can  conceive1 is that which may     
arise from the inflexion of light1 but  
we  believe that it would exercise a    
small influence1 if any1 and it is  only
 by experiment that its effect can be   
ascertained4    ,illustration3 ,,fig4   
#dd4    ,the ,rev4 ,mr4 ,egerton and ,i 
have obtained photographs of a bust1 in 
the  course of ten minutes1 with a very 
faint sun1 and through an aperture  less
 than the hundredth of an inch2 and ,i  
have no doubt that when  chemistry has  
furnished us with a material more       
sensitive to light1 a  camera without   
lenses1 and with only a pin-hole1 will  
be the favourite  instrument of the     
photographer4 ,at present1 no sitter    
could preserve  his composure and       
expression during the number of minutes 
which are  required to complete the     
picture4    ,but though we cannot use   
this theoretical camera1 we may make    
some  approximation to it4 ,if we make  
the hole ,h a quarter of an inch1  the  
pictures br1 c41 will be faint and      

indistinct2 but by  placing a thin lens 
a quarter of an inch in diameter in the 
hole  ,h1 the distinctness of the       
picture will be restored1 and1 from the 
introduction of so much light1 the      
photograph may be completed in a        
sufficiently short time4 ,the lens      
should be made of rock crystal1  which  
has a small dispersive power1 and the   
ratio of curvature of its  surfaces     
should be as six to one1 the flattest   
side being turned to the  picture4 ,in  
this way there will be very little      
colour and spherical  aberration1 and no
 error produced by any stri or want of  
homogeneity  in the glass4    ,as the   
hole ,h is nearly the same as the       
greatest opening of the pupil1  the     
picture which is formed by the enclosed 
lens will be almost  identical with the 
one we see in monocular vision1 which is
 always the  most perfect representation
 of figures in relief4    ,illustration3
 ,,fig4 #de4    ,with this approximately
 perfect camera1 let us now compare the 

expensive and magnificent instruments   
with which the photographer  practises  
his art4 ,we shall suppose his camera to
 have its lens or  lenses with an       
aperture of only three inches1 as shewn 
at ,,lr in ,fig4  #de4 ,if we cover the 
whole lens1 or reduce its aperture to a 
quarter  of an inch1 as shewn at a1 we  
shall have a correct picture of the     
sitter4 ,let us now take other four     
pictures of the same person1 by         
removing the aperture successively to b1
 c1 d1 and e3 ,it is  obvious that these
 pictures will all differ very          
perceptibly from each  other4 ,in the   
picture obtained through d1 we shall see
 parts on the  left side of the head    
which are not seen in the picture       
through c1  and in the one through c1   
parts on the right side of the head not 
seen through d4 ,in short1 the pictures 
obtained through c and d  are accurate  
dissimilar pictures1 such as we have in 
binocular vision1  7the distance cd     
being #b inches17 and fitted for the    

stereoscope4 ,in  like manner1 the      
pictures through b and e will be        
different from  the preceding1 and      
different from one another4 ,in the one 
through b1  we shall see parts below the
 eyebrows1 below the nose1 below the    
upper lip1 and below the chin1 which are
 not visible in the picture  through e1 
nor in those through c and d2 while in  
the picture  through e1 we shall see    
parts above the brow1 and above the     
upper  lip1 c41 which are not seen in   
the pictures through b1 c1 and d4  ,in  
whatever part of the lens1 ,,lr1 we     
place the aperture1 we obtain  a picture
 different from that through any other  
part1 and therefore  it follows1 that   
with a lens whose aperture is three     
inches1 the  photographic picture is a  
combination of about one hundred and    
thirty  dissimilar pictures of the      
sitter1 the similar parts of which are  
not  coincident2 or to express it in the
 language of perspective1 the  picture  
is a combination of about one hundred   

and thirty pictures of  the sitter1     
taken from one hundred and thirty       
different points of  sight6 ,if such is 
the picture formed by a three-inch lens1
 what must  be the amount of the        
anamorphism1 or distortion of form1     
which is  produced by photographic      
lenses of diameters from three to twelve
  inches1 actually used in              
photography8#df    #df ,see my ,treatise
 on ,optics1 #b;d edit41 chap4 vii4 p4  
#fe4    ,but it is not merely by the    
size of the lenses that hideous         
portraits  are produced4 ,in cameras    
with two achromatic lenses1 the rays    
which  form the picture pass through a  
large thickness of glass1 which may  not
 be altogether homogeneous1--through    
eight surfaces which may  not be truly  
spherical1 and which certainly scatter  
light in all  directions1--and through  
an optical combination in which straight
 lines  in the object must be conic     
sections in the picture6                
,photography1 therefore1 cannot even    

approximate to perfection till the      
artist works with a camera furnished    
with a single quarter of an inch  lens  
of rock crystal1 having its radii of    
curvature as six to one1 or  what       
experience may find better1 with an     
achromatic lens of the same  aperture4  
,and we may state with equal confidence1
 that the photographer  who has the     
sagacity to perceive the defects of his 
instruments1 the  honesty to avow it1   
and the skill to remedy them by the     
applications of  modern science1 will   
take a place as high in photographic    
portraiture  as a ,reynolds or a        
,lawrence in the sister art4    ,such   
being the nature of single portraits1 we
 may form some notion of  the effect    
produced by combining dissimilar ones in
 the stereoscope1 so  as to represent   
the original in relief4 ,the single     
pictures themselves1  including         
binocular and multocular representations
 of the individual1  must1 when         
combined1 exhibit a very imperfect      

portrait in relief1--so  imperfect1     
indeed1 that the artist is obliged to   
take his two pictures  from points of   
sight different from the correct points1
 in order to  produce the least         
disagreeable result4 ,this will appear  
after we have  explained the correct    
method of taking binocular portraits for
 the  stereoscope4    ,no person but a  
painter1 or one who has the eye and the 
taste of  a painter1 is qualified to be 
a photographer either in single or      
binocular portraiture4 ,the first step  
in taking a portrait or copying  a      
statue1 is to ascertain in what aspect  
and at what distance from the  eye it   
ought to be taken4    ,in order to      
understand this subject1 we shall first 
consider the  vision1 with one eye1 of  
objects of three dimensions1 when of    
different magnitudes and placed at      
different distances4 ,when we thus  view
 a building1 or a full-length or        
colossal statue1 at a short  distance1 a
 picture of all its visible parts is    

formed on the retina4  ,if we view it at
 a greater distance1 certain parts cease
 to be seen1  and other parts come into 
view2 and this change in the picture    
will go on1 but will become less and    
less perceptible as we retire  from the 
original4 ,if we now look at the        
building or statue from a  distance     
through a telescope1 so as to present it
 to us with the same  distinctness1 and 
of the same apparent magnitude as we saw
 it at our  first position1 the two     
pictures will be essentially different2 
all the  parts which ceased to be       
visible as we retired will still be     
invisible1  and all the parts which were
 not seen at our first position1 but    
became  visible by retiring1 will be    
seen in the telescopic picture4 ,hence  
the parts seen by the near eye1 and not 
by the distant telescope1  will be those
 towards the middle of the building or  
statue1 whose  surfaces converge1 as it 
were1 towards the eye2 while those seen 
by  the telescope1 and not by the eye1  

will be the external parts of the       
object1 whose surfaces converge less1 or
 approach to parallelism4 ,it  will     
depend on the nature of the building or 
the statue which of these  pictures     
gives us the most favourable            
representation of it4    ,if we now     
suppose the building or statue to be    
reduced in the most  perfect manner1--to
 half its size1 for example1--then it is
 obvious that  these two perfectly      
similar solids will afford a different  
picture1  whether viewed by the eye or  
by the telescope4 ,in the reduced copy1 
the  inner surfaces visible in the      
original will disappear1 and the outer  
surfaces become visible2 and1 as        
formerly1 it will depend on the nature  
of the building or the statue whether   
the reduced or the original copy  gives 
the best picture4    ,if we repeat the  
preceding experiments with two eyes in  
place of  one1 the building or statue   
will have a different appearance2       
surfaces and parts1 formerly invisible1 

will become visible1 and the  body will 
be better seen because we see more of   
it2 but then the  parts thus brought    
into view being seen1 generally         
speaking1 with  one eye1 will have less 
brightness than the rest of the picture4
 ,but  though we see more of the body in
 binocular vision1 it is only parts  of 
vertical surfaces perpendicular to the  
line joining the eyes that  are thus    
brought into view1 the parts of similar 
horizontal surfaces  remaining invisible
 as with one eye4 ,it would require a   
pair of eyes  placed vertically1 that   
is1 with the line joining them in a     
vertical  direction1 to enable us to see
 the horizontal as well as the vertical 
surfaces2 and it would require a pair of
 eyes inclined at all possible  angles1 
that is1 a ring of eyes #b inches in    
diameter1 to enable us to  have a       
perfectly symmetrical view of the       
statue4    ,these observations will     
enable us to answer the question1       
whether or  not a reduced copy of a     

statue1 of precisely the same form in   
all  its parts1 will give us1 either by 
monocular or binocular vision1  a better
 view of it as a work of art4 ,as it is 
the outer parts or  surfaces of a large 
statue that are invisible1 its great    
outline and  largest parts must be best 
seen in the reduced copy2 and           
consequently  its relief1 or third      
dimension in space1 must be much greater
 in the  reduced copy4 ,this will be    
better understood if we suppose a sphere
  to be substituted for the statue4 ,if 
the sphere exceeds in diameter the      
distance between the pupils of the right
 and left eye1 or #b inches1 we  shall  
not see a complete hemisphere1 unless   
from an infinite distance4  ,if the     
sphere is very much larger1 we shall see
 only a segment1 whose  relief1 in place
 of being equal to the radius of the    
sphere1 is equal  only to the versed    
sine of half the visible segment4 ,hence
 it is  obvious that a reduced copy of a
 statue is not only better seen from    

more of its parts being visible1 but is 
also seen in stronger relief4      ,on  
the ,proper ,position of the ,sitter4   
,with these observations we are now     
prepared to explain the proper  method  
of taking binocular portraits for the   
stereoscope4    ,the first and most     
important step is to fix upon the       
position of  the sitter1--to select the 
best aspect of the face1 and1 what is of
  more importance than is generally     
supposed1 to determine the best         
distance from the camera at which he    
should be placed4 ,at a short  distance 
certain parts of one face and figure    
which should be seen are  concealed1 and
 certain parts of other faces are       
concealed which should  be seen4        
,prominent ears may be either hid or    
made less prominent by  diminishing the 
distance1 and if the sight of both ears 
is desirable  the distance should be    
increased4 ,prominent features become   
less  prominent by distance1 and their  
influence in the picture is also        

diminished by the increased vision which
 distance gives of the round  of the    
head4 ,the outline of the face and head 
varies essentially with  the distance1  
and hence it is of great importance to  
choose the best4 ,a  long and narrow    
face requires to be viewed at a         
different distance from  one that is    
short and round4 ,articles of dress even
 may have a better  or a worse          
appearance according to the distance at 
which we see them4    ,let us now       
suppose the proper distance to be six   
feet1 and since it  is impossible to    
give any rules for taking binocular     
portraits with  large lenses we must    
assume a standard camera with a lens a  
quarter of  an inch in diameter1 as the 
only one which can give a correct       
picture  as seen with one eye4 ,if the  
portrait is wanted for a ring1 a locket1
  or a binocular slide1 its size is     
determined by its purpose1 and the      
photographer must have a camera 7which  
he has not7 to produce these  different 

pictures4 ,his own camera will1 no      
doubt1 take a picture for a  ring1 a    
locket1 or a binocular slide1 but he    
does this by placing the  sitter at     
different distances1--at a very great   
distance for the ring  picture1 at a    
considerable distance for the locket    
picture1 and at a  shorter distance for 
the binocular one2 but none of these    
distances are  the distance which has   
been selected as the proper one4 ,with a
 single  lens camera1 however1 he       
requires only several quarter-inch      
lenses  of different focal lengths to   
obtain the portrait of the sitter when  
placed at the proper distance from the  
camera4    ,in order to take binocular  
portraits for the stereoscope a         
binocular  camera is required1 having   
its lenses of such a focal length as to 
produce two equal pictures of the same  
object and of the proper size4  ,those  
in general use for the lenticular       
stereoscope vary from #b4a  inches to   
#b4c in breadth1 and from #b4e inches to

 #b4h in height1 the  distance between  
similar points in the two pictures      
varying from #b4cj  inches to #b4eg1    
according to the different distances of 
the foreground  and the remotest object 
in the picture4    ,having fixed upon   
the proper distance of the sitter1 which
 we shall  suppose to be six feet1--a   
distance very suitable for examining a  
bust or a picture1 we have now to take  
two portraits of him1 which1  when      
placed in the stereoscope1 shall have   
the same relief and the  same appearance
 as the sitter when viewed from the     
distance of six  feet4 ,this will be    
best done by a binocular camera1 which  
we shall now  describe4      ,the       
,binocular ,camera4    ,this instrument 
differs from the common camera in having
 two lenses  with the same aperture and 
focal length1 for taking at the same    
instant  the picture of the sitter as   
seen at the distance of six feet1 or any
  other distance4 ,as it is impossible  
to grind and polish two lenses1  whether

 single or achromatic1 of exactly the   
same focal length1 even  when we have   
the same glass for both1 we must bisect 
a good lens1  and use the two           
semi-lenses1 ground into a circular     
form1 in order  to obtain pictures of   
exactly the same size and definition4   
,these  lenses should be placed with    
their diameters of bisection parallel to
  one another1 and perpendicular to the 
horizon1 at the distance of #b  inches1 
as shewn in ,fig4 #de1 where ,,mn is the
 camera1 ,l1 ,l the two  lenses1 placed 
in two short tubes1 so that by the usual
 mechanical  means they can be directed 
to the sitter1 or have their axes       
converged  upon him1 as shewn in the    
,figure1 where ,,ab is the sitter1 ab   
his  image as given by the lens ,l1 and 
ab as given by the lens ,l4 ,these      
pictures are obviously the very same    
that would be seen by the artist  with  
his two eyes at ,l and ,l1 and as       
,,alb  a,lb  a,lb1    the pictures will 
have the same apparent magnitude as the 

original1 and  will in no respect differ
 from it as seen by each eye from ,e1   
,e1 ,ea  being equal to a,l1 and ,ea to 
a,l4    ,illustration3 ,,fig4 #df4      
,since the publication in #ahdi of my   
description of the binocular  camera1 a 
similar instrument was proposed in      
,paris by a photographer1  ,m4 ,quinet1 
who gave it the name of ,quinetoscope1  
which1 as the ,abb  ,moigno observes1   
means an instrument for seeing ,m4      
,quinet6 ,i have not  seen this camera1 
but1 from the following notice of it by 
the ,abb  ,moigno1 it does not appear to
 be different from mine3--8,nous avons t
   la fois surpris et trs-satisfait de  
retrouver dans le ,quinetoscope  la     
chambre binoculaire de notre ami ,sir   
,david ,brewster1 telle que nous        
l'avons dcrite aprs lui il y a dix-huit 
mois dans notre brochure  intitule      
,stroscope40 ,continuing to speak of ,m4
 ,quinet's camera1  the ,abb is led to  
criticise unjustly what he calls the    
limitation  of the instrument3--8,en un 

mot1 ce charmant appareil est aussi bien
  construit qu'il peut tre1 et nous     
dsirons ardemment qu'il se rpand  assez 
pour rcompenser ,m4 ,quinet de son      
habilet et de ses peines4  ,employ dans 
les limites fixes  l'avance par son     
vritable inventeur1  ,sir ,david        
,brewster2 c'est--dire1 employ          
reproduire des objets  de petite et     
moyenne grandeur1 il donnera assez beaux
 rsultats4  ,il ne pourra pas servir1   
evidemment1 il ne donnera pas bien      
l'effet  stroscopique voulu1 quand on   
voudra l'appliquer  de trs-grands       
objets1 on a des vues ou pay sages pris 
d'une trs-grande distance2  mais il est 
de la nature des uvres humaines d'tre   
essentiellement  bornes40#dg ,this      
criticism on the limitation of the      
camera is  wholly incorrect2 and it will
 be made apparent1 in a future part of  
the ,chapter1 that for objects of all   
sizes and at all distances the          
binocular camera gives the very         
representations which we see1 and that  

other methods1 referred to as superior1 
give unreal and untruthful  pictures1   
for the purpose of producing a startling
 relief4    ,in stating1 as he          
subsequently does1 that the angles at   
which the  pictures should be taken 8are
 too vaguely indicated by theory10#dh   
the  ,abb cannot have appealed to his   
own optical knowledge1 but must have    
trusted to the practice of ,mr4         
,claudet1 who asserts 8that there cannot
  be any rule for fixing the binocular  
angle of camera obscuras4 ,it is  a     
matter of taste and artistic            
illusion40#di ,no question of science   
can be a matter of taste1 and no        
illusion can be artistic which is a     
misrepresentation of nature4    #dg ,see
 ,cosmos1 vol4 ii4 pp4 #fbb1 #fbd4      
#dh ,id4 vol4 vii4 p4 #did4    #di ,id4 
vol4 iii4 p4 #feh4    ,when the artist  
has not a binocular camera he must place
 his single  camera successively in such
 positions that the axis of his lens may
  have the directions ,,el1 ,,el making 

an angle equal to ,,lcl1 the angle      
which the distance between the eyes     
subtends at the distance of the  sitter 
from the lenses4 ,this angle is found by
 the following formula3--               
d   #a4be      ,tang4 ,a  --------      
--------                  ,d       ,d   
d being the distance between the eyes1  
,d the distance of the sitter1  and ,a  
the angle which the distance between the
 eyes1  #b4e1 subtends at  the distance 
of the sitter4 ,these angles for        
different distances are  given in the   
following table3--           ,d         
,distance               ,a  ,angle      
formed          of ,camera              
by the two          from the            
directions          ,sitter4            
of the ,camera4              #e inches1 
#bh  #f            #f1                  
#bc  #cb            #g1                 
#bj  #ad            #h1                 
#ag  #df            #i1                 
#ae  #dh           #aj1                 
#ad  #ae           #aa1                 

#ac   #j           #ab1 #a foot1        
#aa  #ed           #ac1                 
#aa   #j           #ad1                 
#aj  #ag           #ae1                 
#i  #cb           #af1                  
#h  #ef           #ag1                  
#h  #bd           #ah1                  
#g  #ef           #ai1                  
#g  #ca           #bj1                  
#g  #aj           #bd1 #b feet1         
#e  #eh           #cj1                  
#d  #df           #cf inches1 #c feet1  
#c  #ei           #db1                  
#c  #be           #dh1 #d feet1         
#b  #ei           #ed1                  
#b  #ci           #fj1 #e feet1         
#b  #bc           #gb1 #f feet1         
#a  #ei           #hd1 #g feet1         
#a  #db           #if1 #h feet1         
#a  #cj          #ajh1 #i feet1         
#a  #bj          #abj1 #aj feet1        
#a  #ab    ,the numbers given in the    
greater part of the preceding table can 
be  of use only when we wish to take    
binocular pictures of small objects     

placed at short distances from cameras  
of a diminutive size4 ,in  photographic 
portraiture they are of no use4 ,the    
correct angle for a  distance of six    
feet must not exceed two degrees1--for a
 distance  of eight feet1 one and a half
 degrees1 and for a distance of  ten    
feet1 one and a fifth degree4 ,mr4      
,wheatstone has given quite  a different
 rule4 ,he makes the angle to depend1   
not on the distance  of the sitter from 
the camera1 but on the distance of the  
binocular  picture in the stereoscope   
from the eyes of the observer6          
,according  to the rule which ,i have   
demonstrated1 the angle of convergency  
for  a distance of six feet must be #a  
#ei1 whereas in a stereoscope of  any   
kind1 with the pictures six inches from 
the eyes1 ,mr4 ,wheatstone  makes it #bc
 #cb6 ,as such a difference is a scandal
 to science1 we  must endeavour to place
 the subject in its true light1 and it  
will  be interesting to observe how the 
problem has been dealt with by  the     

professional photographer4 ,the         
following is ,mr4 ,wheatstone's         
explanation of his own rule1 or rather  
his mode of stating it3--    8,with     
respect10 says he1 8to the means of     
preparing the binocular  photographs1   
7and in this term ,i include both       
,talbotypes and  ,daguerreotypes17      
little requires to be said beyond a few 
directions as  to the proper positions  
in which it is necessary to place the   
camera  in order to obtain the two      
required projections4    8,we will      
suppose that the binocular pictures are 
required to be seen  in the stereoscope 
at a distance of eight inches before the
 eyes1 in  which case the convergence of
 the optic axes is about #ah4 ,to obtain
  the proper projections for this       
distance1 the camera must be placed     
with its lens accurately directed       
towards the object successively in  two 
points of the circumference of a circle1
 of which the object is the  centre1 and
 the points at which the camera is so   

placed must have the  angular distance  
of #ah from each other1 exactly that of 
the optic axes  in the stereoscope4 ,the
 distance of the camera from the object 
may be  taken arbitrarily1 for so long  
as the same angle is employed1 whatever 
that distance may be1 the picture will  
exhibit in the stereoscope  the same    
relief1 and be seen at the same distance
 of eight inches1  only the magnitude of
 the picture will appear different4     
,miniature  stereoscopic representations
 of buildings and full-sized statues    
are1  therefore1 obtained merely by     
taking the two projections of the object
  from a considerable distance1 but at  
the same time as if the object  were    
only eight inches distant1 that is1 at  
an angle of #ah40ej    #ej ,phil4       
,trans41 #aheb1 p4 #g4    ,such is ,mr4 
,wheatstone's rule1 for which he has    
assigned no reason  whatever4 ,in       
describing the binocular camera1 in     
which the lenses  must be only #b inches
 distant for portraits1 ,i have shewn   

that the  pictures which it gives are   
perfect representations of the original1
  and therefore pictures taken with     
lenses or cameras at any other          
distance1 must be different from those  
which are seen by the artist  looking at
 the sitter from his camera4 ,they are1 
doubtless1 both  pictures of the sitter1
 but the picture taken by ,mr4          
,wheatstone's rule  is one which no man 
ever saw or can see1 until he can place 
his eyes  at the distance of twenty     
inches6 ,it is1 in short1 the picture of
 a  living doll1 in which parts are seen
 which are never seen in society1  and  
parts hid which are always seen4    ,in 
order to throw some light upon his      
views1 ,mr4 ,wheatstone got 8a  number  
of ,daguerreotypes of the same bust     
taken at a variety of  different angles1
 so that he was enabled to place in the 
stereoscope  two pictures taken at any  
angular distance from #b to #ah1 the    
former  corresponding to a distance of  
about six feet1 and the latter to a     

distance of about eight inches40 ,in    
those taken at #b1 7the proper  angle17 
there is 8an undue elongation of lines  
joining two unequally  distant points1  
so that all the features of a bust      
appear to be  exaggerated in depth20    
while in those taken at #ah1 8there is  
an undue  shortening of the same lines1 
so that the appearance of a bas-relief  
is  obtained from the two projections of
 the bust1 the apparent dimensions  in  
breadth and height remaining in both    
cases the same40    ,although ,mr4      
,wheatstone speaks thus decidedly of the
 relative effect  produced by combining 
pictures taken at #b and #ah1 yet in the
 very  next paragraph he makes          
statements entirely incompatible with   
his  previous observations4 8,when the  
optic axes10 he says1 8are parallel1  in
 strictness there should be no          
difference between the pictures         
presented to each eye1 and in this case 
there would be no binocular  relief1 but
 ,i find that an excellent effect is    

produced when the  axes are nearly      
parallel1 by pictures taken at an       
inclination of #g or  #h1 and even a    
difference of #af or #ag has no         
decidedly bad effect60    ,that ,mr4    
,wheatstone observed all these          
contradictory facts we do  not doubt1   
but why he observed them1 and what was  
their cause1 is  a question of          
scientific as well as of practical      
importance4 ,mr4  ,wheatstone was not   
aware#ea that the ,daguerreotype        
pictures which  he was combining1 taken 
with large lenses1 were not pictures as 
seen with two human eyes1 but were      
actually binocular and multocular       
monstrosities1 entirely unfit for the   
experiments he was carrying on1  and    
therefore incapable of testing the only 
true method of taking  binocular        
pictures which we have already          
explained4    #ea ,mr4 ,wheatstone's    
paper was published before ,i had       
pointed out the  deformities produced by
 large lenses4 ,see p4 #acj4    ,had    

,mr4 ,wheatstone combined pictures1 each
 of which was a correct  monocular      
picture1 as seen with each eye1 and as  
taken with a small  aperture or a small 
lens1 he would have found no discrepancy
 between  the results of observation and
 of science4 ,from the same cause1 we   
presume1 namely1 the use of multocular  
pictures1 ,mr4 ,alfred ,smee#eb  has    
been led to a singular method of taking 
binocular ones4 ,in one  place he       
implicitly adopts ,mr4 ,wheatstone's    
erroneous rule4 8,the  pictures for the 
stereoscope10 he says1 8are taken at two
 stations1 at  a greater or less        
distance apart1 according to the        
distance at which  they are to be       
viewed4 ,for a distance of #h inches the
 two pictures are  taken at angles of   
#ah1 for #ac inches #aj1 for #ah inches 
#h1 and for #d  feet #d40 ,but when he  
comes to describe his own method he     
seems to know  and to follow the true   
method1 if we rightly understand his    
meaning4  8,to obtain a binocular       

picture of anybody10 he says1 8the      
camera must  be employed to take half   
the impression1 and then it must be     
moved  in the arc of a circle of which  
the distance from the camera to the     
point of sight#ec is the radius for     
about #b inches when a second  picture  
is taken1 and the two impressions       
conjointly form one binocular  picture4 
,there are many ways by which this      
result may be obtained4 ,a  spot may be 
placed on the ground-glass on which the 
point of sight  should be made exactly  
to fall4 ,the camera may then be moved  
#b inches1  and adjusted till the point 
of sight falls again upon the same spot 
on the ground-glass1 when1 if the camera
 has been moved in a true  horizontal   
plane the effect of the double picture  
will be perfect40  ,this is precisely   
the true method of taking binocular     
pictures which we  had given long       
before1 but it is true only when small  
lenses are used4  ,in order to obtain   
this motion in the true arc of a circle 

the camera  was moved on two cones which
 converged to the point of sight1 and   
,mr4  ,smee thus obtained pictures of   
the usual character4 ,but in making     
these experiments he was led to take    
pictures when the camera was in         
continual motion backwards and forwards 
for #b inches1 and he remarks  that 8in 
this case the picture was even more     
beautiful than when the  two images were
 superimposed60 8,this experiment10 he  
adds1 8is very  remarkable1 for who     
would have thought formerly that a      
picture could  possibly have been made  
with a camera in continual motion8      
,nevertheless  we accomplish it every   
day with ease1 and the character of the 
likeness  is wonderfully improved by    
it40 ,we have now left the regions of   
science1 and have to adjudicate on a    
matter of opinion and taste4 ,mr4  ,smee
 has been so kind as to send me a       
picture thus taken4 ,it is a good       
photograph with features enlarged in all
 azimuths1 but it has no other  relief  

than that which we have described as    
monocular4    #eb ,the ,eye in ,health  
and ,disease1 by ,alfred ,smee1 #b;d    
edit4 #ahed1  pp4 #he-ie4    #ec ,this  
expression has a different meaning in   
perspective4 ,we  understand it to mean 
here the point of the sitter or object1 
which is  to be the centre of the       
picture4    ,a singular effect of       
combining pictures taken at extreme     
angles has  been noticed by ,admiral    
,lageol4 ,having taken the portrait of  
one of  his friends when his eyes were  
directed to the object-glass of the     
camera1 the ,admiral made him look at an
 object #de6 to the right1  and took a  
second picture4 ,when these pictures    
were placed in the  stereoscope1 and    
viewed 8without ceasing1 turning first  
to the right  and then to the left1 the 
eyes of the portrait follow this motion 
as  if they were animated40#ed ,this    
fact must have been noticed in common   
stereoscopic portraits by every person  
who has viewed them alternately  with   

each eye1 but it is not merely the eyes 
which move4 ,the nose1 and  indeed every
 feature1 changes its place1 or1 to     
speak more correctly1  the whole figure 
leaps from the one binocular position   
into the  other4 ,as it is unpleasant to
 open and shut the eyes alternately1 the
  same effect may be more agreeably     
produced in ordinary portraits by       
merely intercepting the light which     
falls upon each picture1 or by  making  
an opaque screen pass quickly between   
the eyes and the lens1  or immediately  
below the lens1 so as to give successive
 vision of  the pictures with each eye1 
and with both4 ,the motion of the light 
reflected from the round eyeball has    
often a striking effect4    #ed ,cosmos1
 ,feb4 #bi1 #ahef1 vol4 viii4 p4 #bjb4  
,from these discussions1 our readers    
will observe that the science1 as  well 
as the art of binocular portraiture for 
the stereoscope1 is in a  transition    
state in which it cannot long remain4   
,the photographer who  works with a very

 large lens chooses an angle which gives
 the least  unfavourable results2 his   
rival1 with a lens of less size1        
chooses1  on the same principle1 a      
different angle2 and the public1 who are
 no  judges of the result1 are delighted
 with their pictures in relief1 and     
when their noses are either pulled from 
their face1 or flattened upon  their    
cheek1 or when an arm or a limb         
threatens to escape from their          
articulation1 they are assured that     
nature and not art is to blame4    ,we  
come now to consider under what         
circumstances the photographer may      
place the lenses of his binocular camera
 at a greater distance than #b  inches1 
or his two cameras at a greater angle   
than that which we have  fixed4    #a4  
,in taking family portraits for the     
stereoscope1 the cameras must be  placed
 at an angle of #b for #f feet1 when the
 binocular camera is not  used4    #b4  
,in taking binocular pictures of any    
object whatever1 when we wish  to see   

them exactly as we do with our two eyes1
 we must adopt the same  method4    #c4 
,if a portrait is wanted to assist a    
sculptor in modelling a statue1  a great
 angle might be adopted1 in order to    
shew more of the head4 ,but  in this    
case the best way would be to take the  
correct social likeness1  and then take 
photographs of the head in different    
azimuths4    ,if we wish to have a      
greater degree of relief than we have   
with our  two eyes1 either in viewing   
colossal statues1 or buildings1 or      
landscapes1 where the deviation from    
nature does not1 as in the human  face1 
affect the expression1 or injure the    
effect1 we must increase  the distance  
of the lenses in the binocular camera1  
or the angle of  direction of the common
 camera4 ,let us take the case of a     
colossal  statue #aj feet wide1 and     
suppose that dissimilar drawings of it  
about  three inches wide are required   
for the stereoscope4 ,these drawings    
are forty times narrower than the       

statue1 and must be taken at such  a    
distance1 that with the binocular camera
 the relief would be almost  evanescent4
 ,we must therefore suppose the statue  
to be reduced n  times1 and place the   
semi-lenses at the distance n  #b       
inches4 ,if  n  #aj1 the statue #aj feet
 wide will be reduced to _/1 or to #a   
foot1 and n  #b1 or the distance of the 
semi-lenses will be #be  inches4 ,with  
the lenses at this distance1 the        
dissimilar pictures of  the statue will 
reproduce1 when combined1 a statue one  
foot wide1 which  will have exactly the 
same appearance and relief as if we had 
viewed  the colossal statue with eyes   
#be inches distant4 ,but the reproduced 
statue will have also the same          
appearance and relief as a statue a foot
  wide reduced from the colossal one    
with mathematical precision1 and it     
will therefore be a better or more      
relieved representation of the work  of 
art than if we had viewed the colossal  
original with our own eyes1  either     

under a greater1 an equal1 or a less    
angle of apparent magnitude4    ,we have
 supposed that a statue a foot broad    
will be seen in proper  relief by       
binocular vision2 but it remains to be  
decided whether or  not it would be more
 advantageously seen if reduced with    
mathematical  precision to a breadth of 
#b inches1 the width of the eyes1 which 
gives the vision of a hemisphere #b     
inches in diameter with the most        
perfect relief4#ee ,if we adopt this    
principle1 and call ,b the breadth  of  
the statue of which we require          
dissimilar pictures1 we must make  n    
,b_/#b1 and n  #b  ,b1 that is1 the     
distance of the semi-lenses  in the     
binocular camera1 or of the lenses in   
two cameras1 must be made  equal to the 
breadth of the statue4    ,in concluding
 this chapter1 it may be proper to      
remark1 that unless  we require an      
increased relief for some special       
purpose1 landscapes  and buildings      
should be taken with the normal         

binocular camera1 that  is1 with its    
lenses #b inches distant4 ,scenery of   
every kind1 whether  of the picturesque1
 or of the sublime1 cannot be made more 
beautiful  or grand than it is when seen
 by the traveller himself4 ,to add an   
artificial relief is but a trick which  
may startle the vulgar1 but  cannot     
gratify the lover of what is true in    
nature and in art4      ,the ,single    
,lens ,binocular ,camera4    ,as every  
photographer possesses a camera with a  
lens between #b and #c  inches in       
diameter1 it may be useful to him to    
know how he may convert  it into a      
binocular instrument4    ,in a cover for
 the lens take two points equidistant   
from each other1  and make two          
apertures1 c1 d1 ,fig4 #dc1 _/ths of an 
inch in  diameter1 or of any larger size
 that may be thought proper1 though  _/ 
is the proper size4 ,place the cover on 
the end of the tube1 and  bring the line
 joining the apertures into a horizontal
 position4  ,closing one aperture1 take 

the picture of the sitter1 or of the    
statue1 through the other1 and when the 
picture is shifted aside by  the usual  
contrivances for this purpose1 take the 
picture through the  other aperture4    
,these will be good binocular portraits1
 fitted for  any stereoscope1 but       
particularly for the ,achromatic        
,reading ,glass  ,stereoscope4 ,if      
greater relief is wanted1 it may be     
obtained in larger  lenses by placing   
the two apertures at the greatest       
distance which the  diameter of the lens
 will permit4    #ee ,it is only in a   
horizontal direction that we can see    
#ahj of the  hemisphere4 ,we would      
require a circle of eyes #b inches      
distant to see  a complete hemisphere4  
,the ,binocular ,camera made the        
,stereoscope4    ,if the lenses of the  
binocular camera1 when they are whole   
lenses1 be  made to separate a little1  
so that the distance between the centres
 of  their inner halves may be equal to 
#b inches1 they become a lenticular     

stereoscope1 in which we may view the   
pictures which they themselves  create4 
,the binocular pictures are placed in   
the camera in the very  place where     
their negatives were formed1 and the    
observer1 looking  through the halves of
 his camera lenses1 will see the        
pictures united  and in relief4 ,if the 
binocular camera is made of semi-lenses1
 we  have only to place them with their 
thin edges facing each other to  obtain 
the same result4 ,it will appear1 from  
the discussions in the  following       
chapter1 that such a stereoscope1       
independently of its being  achromatic1 
if the camera is achromatic1 will be the
 most perfect of  stereoscopic          
instruments4    ,the preceding methods  
are equally applicable to landscapes1   
machines1  and instruments1 and to solid
 constructions of every kind1 whether   
they  be the production of nature or of 
art4#ef    #ef ,see ,chapters ,x4 and   
,,xi4          ,,chapter ,,ix4    ,,on  
,,the ,,adaptation ,,of ,,the ,,pictures

 ,,to ,,the ,,stereoscope4    --,,their 
,,size1 ,,position1 ,,and               
,,illumination4      ,having described  
the various forms of the stereoscope1   
and the method  of taking the binocular 
portraits and pictures to which it is to
 be  applied1 we have now to consider   
the relation that ought to exist        
between the instrument and the          
pictures1--a subject which has not been 
noticed by preceding writers4    ,if we 
unite two dissimilar pictures by the    
simple convergency of  the optical axes1
 we shall observe a certain degree of   
relief1 at a  certain distance of the   
eyes from the pictures4 ,if we diminish 
the  distance1 the relief diminishes1   
and if we increase it1 it increases4    
,in like manner1 if we view the         
dissimilar pictures in the lenticular   
stereoscope1 they have a certain degree 
of relief2 but if we use  lenses of a   
higher magnifying power1 so as to bring 
the eyes nearer  the pictures1 the      
relief will diminish1 and if we use     

lenses of a less  magnifying power1 the 
relief will increase4 ,by bringing the  
eyes nearer  the pictures1 which we do  
by magnifying them as well as by        
approaching  them1 we increase the      
distance between similar points of the  
two  pictures1 and therefore the        
distance of these points1 when united1  
from any plane in the picture1 that is1 
its relief will be diminished4  ,for the
 same reason1 the diminution of the     
distance between similar  points by the 
removal of the eyes from the picture1   
will produce an  increase of relief4    
,this will be readily understood if we  
suppose the  eyes ,r1 ,l1 in ,fig4 #bd1 
to be brought nearer the plane ,,mn1 to 
,r,l1 the  points #a1 #a and #b1 #b will
 be united at points nearer ,,mn than   
when the  eyes were at ,r1 ,l1 and      
consequently their relief diminished4   
,now we have seen1 that in taking       
portraits1 as explained in ,fig4 #df1 we
  view the two pictures1 ab1 ab1 with   
the eyes at ,e and ,e1 exactly1  and    

with the same relief in the air1 as when
 we saw the original ,,ab1  from ,l1 ,l1
 and therefore ,ec is the distance at   
which the dissimilar  pictures should be
 viewed in the stereoscope1 in order    
that we may see  the different parts of 
the solid figure under their proper     
relief4 ,but  the distance ,ec  ,lc is  
the conjugate focal length of the lens  
,l1  if one lens is used1 or the        
conjugate equivalent focal length1 if   
two  achromatic lenses are used2 and    
consequently every picture taken for    
the stereoscope should be taken by a    
camera1 the conjugate focal length  of  
whose lens corresponding to the distance
 of the sitter1 is equal to  five       
inches1 when it is to be used in the    
common stereoscope1 which  has generally
 that depth4    ,between the pictures   
and the purely optical part of the      
stereoscope1  there are other relations 
of very considerable importance4 ,the   
exclusion of all external objects or    
sources of light1 excepting that  which 

illuminates the pictures1 is a point of 
essential importance1  though its       
advantages have never been appreciated4 
,the spectacle  stereoscope held in the 
hand1 the reflecting stereoscope1 and   
the  open lenticular stereoscope1 are   
all1 in this respect1 defective4  ,the  
binocular pictures must be placed in a  
dark box1 in order to  produce their    
full effect2 and it would be a great    
improvement on  the lenticular          
stereoscope1 if1 on the left and right  
side of each  eye-tube1 a piece of brass
 were to be placed1 so as to prevent any
  light from entering the left angle of 
the left eye1 and the right angle  of   
the right eye4#eg ,the eyes1 thus       
protected from the action of all        
external light1 and seeing nothing but  
the picture1 will see it with a         
distinctness and brilliancy which could 
not otherwise be obtained4    #eg ,when 
any external light falls upon the eye1  
its picture is  reflected back from the 
metallic surface of the ,daguerreotype1 

and a  negative picture of the part of  
the ,daguerreotype opposite each eye is 
mixed with the positive picture of the  
same part4    ,the proper illumination  
of the picture1 when seen by reflected  
light1  is also a point of essential    
importance4 ,the method universally     
adopted  in the lenticular stereoscope  
is not good1 and is not the one which ,i
  found to be the best1 and which ,i    
employed in the first-constructed       
instruments4 ,the light which falls upon
 the picture is prevented from  reaching
 the observer only by its being incident
 at an angle greater  or less than the  
angle of reflexion which would carry it 
to his eyes4  ,a portion of the         
scattered light1 however1 does reach the
 eye1 and in  ,daguerreotypes           
especially1 when any part of the surface
 is injured1  the injury1 or any other  
imperfection in the plate1 is more      
distinctly  seen4 ,the illumination     
should be lateral1 either by a different
 form of  window in the front1 or by    

openings on the two sides1 or by both   
these  methods4    ,when the lenticular 
stereoscope is thus fitted up1 and the  
pictures  in this manner illuminated1   
the difference of effect is equally     
great  as it is between a picture as    
commonly seen1 and the same picture     
exhibited as a panorama or a diorama1 in
 which no light reaches the  eyes but   
that which radiates from the painting   
itself1 the reflexion  from the varnish 
being removed by oblique or lateral     
illumination4    ,the great value of    
transparent binocular slides1 when the  
picture  is to be upon glass1 is obvious
 from the preceding considerations4     
,the illumination is uniform and        
excellent1 but care must be taken to    
have the ground-glass in front of the   
picture1 or the paper1 when it  is used1
 of a very fine grain1 so that it may   
throw no black specks  upon the sky or  
the lights of the picture4 ,another     
advantage of the  transparent slides is1
 that the pictures are better protected 

from  injury than those upon paper4     
,it is obvious from these considerations
 that the size of the pictures  is      
determined1 as well as the distance at  
which they are to be viewed4  ,much     
ignorance prevails upon this subject1   
both among practical  photographers and 
optical writers4 ,large binocular       
pictures have been  spoken of as        
desirable productions1 and it has been  
asserted1 and  claimed too1 as a        
valuable property of the reflecting     
stereoscope1 that  it allows us to use  
larger pictures than other instruments4 
,there never  was a greater mistake4 ,if
 we take a large picture for the        
stereoscope  we must place it at a great
 distance from the eye1 and consequently
 use  a large stereoscope4 ,a small     
picture1 seen distinctly near the eye1  
is  the very same thing as a large      
picture seen at a greater distance4 ,the
  size of a picture1 speaking optically 
and correctly1 is measured by the  angle
 which it subtends at the eye1 that is  

its apparent magnitude4 ,a  portrait    
three inches high1 for example1 and     
placed in the lenticular  stereoscope   
five inches from the eye1 has the same  
apparent size as a  ,kit ,cat portrait  
in oil the size of life1 three feet     
high1 seen at the  distance of five     
feet1 the distance at which it is       
commonly examined2  and if we increase  
the magnifying power so as to see the   
three-inch  picture at the distance of  
two inches1 it will have the same       
apparent  size as the three feet oil    
portrait seen at the distance of two    
feet4  ,if the pictures used in the     
stereoscope were imperfect pictures that
  would not bear being magnified1 it    
would be improper to use them2 but  the 
,daguerreotypes1 and the transparent    
pictures1 which are taken  by the first 
artists1 for the lenticular stereoscope1
 will bear a  magnifying power ten times
 greater than that which is applied to  
them4    ,if we take a large picture for
 the stereoscope1 we are compelled by   

pictorial truth to place it at a        
distance from the eye equal to the      
equivalent focal distance of the camera4
 ,every picture in every camera  has the
 same apparent magnitude as the object  
which it represents2  whether it be a   
human figure1 or the most distant       
landscape2 and if  we desire to see it  
in its true relief in the stereoscope1  
we must  place it at a distance from the
 eye equal to the focal length of the   
lens1 whether it be an inch or a foot   
high4 ,there is1 therefore1  nothing    
gained by using large pictures4 ,there  
is1 on the contrary1 much  inconvenience
 in their use4 ,they are in themselves  
less portable1 and  require a larger    
stereoscope2 and we believe1 no person  
whatever1 who  is acquainted with the   
perfection and beauty of the binocular  
slides in  universal use1 would either  
incur the expense1 or take the trouble  
of  using pictures of a larger size4    
,in the beautiful combination of        
lenticular stereoscopes1 which was      

exhibited by ,mr4 ,claudet1 ,mr4        
,williams1 and others1 in the ,paris    
,exhibition1 and into which six or eight
 persons were looking at the  same time1
 binocular pictures of a larger size    
could not have been  conveniently used4 
,but1 independently of these reasons1   
the question of large pictures  has been
 practically settled4 ,no such pictures 
are taken by the  ,daguerreotypists or  
,talbotypists1 who are now enriching art
 with  the choicest views of the        
antiquities1 and modern buildings1 and  
picturesque scenery of every part of the
 world2 and even if they could  be      
obtained1 there are no instruments      
fitted for their exhibition4 ,in  the   
magnificent collection of stereoscopic  
pictures1 amounting to above  a         
thousand1 advertised by the ,london     
,stereoscopic ,company1 there are  no   
fewer than sixty taken in ,rome1 and    
representing1 better than a  traveller  
could see them there1 the ancient and   
modern buildings of  that renowned city4

 ,were these sixty views placed on the  
sides of a  revolving polygon1 with a   
stereoscope before each of its faces1 a 
score  of persons might1 in the course  
of an hour1 see more of ,rome1 and see  
it better1 than if they had visited it  
in person4 ,at all events1 those  who   
are neither able nor willing to bear the
 expense1 and undergo the  toil of      
personal travel1 would1 in such a       
panorama1--an analytical view  of       
,rome1--acquire as perfect a knowledge  
of its localities1 ancient  and modern1 
as the ordinary traveller4 ,in the same 
manner1 we might  study the other       
metropolitan cities of the world1 and   
travel from them  to its river and      
mountain scenery1--admiring its noble   
castles in our  descent of the          
,rhine1--its grand and wild scenery on  
the banks of the  ,mississippi1 or the  
,orinoco1--the mountain gorges1 the     
glaciers1 and the  peaks of the ,alps   
and the ,ural1--and the more sublime    
grandeur which  reigns among the        

solitudes of the ,himalaya and the      
,andes4    ,the following general rule  
for taking and combining binocular      
pictures  is the demonstrable result of 
the principles explained in this        
chapter3--    ,supposing that the camera
 obscura employed to take binocular     
portraits1 landscapes1 c41 gives perfect
 representations of them1 the  relief   
picture in the stereoscope1 produced by 
their superposition  and binocular      
union1 will not be correct and truthful1
 unless the  dissimilar pictures are    
placed in the stereoscope at a distance 
from  the eyes1 equal to the focal      
distance1 real or equivalent1 of the    
object-glass or object-glasses of the   
camera1 and1 whatever be the size  of   
the pictures1 they will appear1 when    
they are so placed1 of the same         
apparent magnitude1 and in the same     
relief1 as when they were seen from  the
 object-glass of the camera by the      
photographer himself4          ,,chapter
 ,x4    ,,application ,,of ,,the        

,,stereoscope ,,to ,,painting4          
,having explained the only true method  
of taking binocular portraits  which    
will appear in correct relief when      
placed in the stereoscope1  we shall    
proceed in this chapter to point out the
 application of the  stereoscope to the 
art of painting in all its branches4 ,in
 doing this  we must not forget how much
 the stereoscope owes to photography1   
and  how much the arts of design might  
reasonably expect from the solar        
pencil1 when rightly guided1 even if the
 stereoscope had never been  invented4  
,when the processes of the              
,daguerreotype and ,talbotype1 the      
sister arts  of ,photography1 were first
 given to the world1 it was the         
expectation  of some1 and the dread of  
others1 that the excellence and         
correctness  of their delineations would
 cast into the shade the less truthful  
representations of the portrait and the 
landscape painter4 ,an invention  which 
supersedes animal power1 or even the    

professional labour of man1  might have 
been justly hailed as a social blessing1
 but an art which  should supersede the 
efforts of genius1 and interfere with   
the exercise  of those creative powers  
which represent to us what is beautiful 
and  sublime in nature1 would1 if such a
 thing were possible1 be a social  evil4
    ,the arts of painting1 sculpture1   
and architecture have in every age1  and
 in every region of civilisation1 called
 into exercise the loftiest  genius and 
the deepest reason of man4 ,consecrated 
by piety1 and  hallowed by affection1   
the choicest productions of the pencil  
and the  chisel have been preserved by  
the liberality of individuals and the   
munificence of princes1 while the       
palaces of sovereigns1 the edifices  of 
social life1 the temples of religion1   
the watch-towers of war1 the  obelisks  
of fame1 and the mausolea of domestic   
grief1 stand under the  azure cupola of 
heaven1 to attest by their living       
beauty1 or their  ruined grandeur1 the  

genius and liberality which gave them   
birth4 ,to  the cultivation and         
patronage of such noble arts1 the       
vanity1 the  hopes1 and the holiest     
affections of man stand irrevocably     
pledged2  and we should deplore any     
invention or discovery1 or any tide in  
the  nation's taste1 which should       
paralyse the artist's pencil1 or break  
the  sculptor's chisel1 or divert into  
new channels the genius which wields    
them4 ,but instead of superseding the   
arts of design1 photography will  but   
supply them with new materials1--with   
collections of costume1--with  studies  
of drapery and of forms1 and with scenes
 in life1 and facts  in nature1 which1  
if they possess at all1 they possess    
imperfectly1  and without which art must
 be stationary1 if she does not languish
 and  decline4    ,sentiments analogous 
to these have been more professionally  
expressed  by ,m4 ,delaroche1 a         
distinguished ,french artist1--by ,sir  
,charles  ,eastlake1 whose taste and    

knowledge of art is unrivalled1--and by 
,mr4  ,ruskin1 who has already given    
laws to art1 and whose genius is        
destined  to elevate and to reform it4  
,m4 ,delaroche considers photography 8as
  carrying to such perfection certain of
 the essential principles of  art1 that 
they must become subjects of study and  
observation1 even  to the most          
accomplished artist40444 8,the finish of
 inconceivable  minuteness10 he says1   
8disturbs in no respect the repose of   
the masses1  nor impairs in any way the 
general effect4444 ,the correctness of  
the  lines1 the precision of the forms  
in the designs of ,m4 ,daguerre1 are  as
 perfect as it is possible they can be1 
and yet1 at the same time1  we discover 
in them a broad and energetic manner1   
and a whole equally  rich in hue and in 
effect4 ,the painter will obtain by this
 process  a quick method of making      
collections of studies1 which he could  
not  otherwise procure without much time
 and labour1 and in a style very far    

inferior1 whatever might be his talents 
in other respects40 ,in the same        
spirit1 ,mr4 ,ruskin#eh considers 8the  
art of photography as enabling  us to   
obtain as many memoranda of the facts of
 nature as we need20 and  long before   
,mr4 ,talbot taught us to fix upon paper
 the pictures of the  camera obscura1   
the ,rev4 ,john ,thomson1 one of the    
most distinguished of  our ,scottish    
landscape painters1 studied1 in one of  
these instruments1  the forms and       
colours of the scenes which he was to   
represent4 ,other  artists1 both in     
portrait and in landscape1 now avail    
themselves of  photography1 both as an  
auxiliary and a guide in their          
profession2 but  there are certain      
difficulties and imperfections in the   
art itself1  and so many precautions    
required in its right application1      
whether we  use its pictures single1 as 
representations on a plane1 or take them
  binocularly1 to be raised into relief 
by the stereoscope1 that we must  draw  

from the principles of optics the only  
rules which can be of real  services to 
the arts of design4    #eh ,modern      
,painters1 vol4 iii41 ,preface1 pp4 #aa1
 #ab4    ,in painting a landscape1 a    
building1 a figure1 or a group of       
figures1  the object of the artist is to
 represent it on his canvas just as  he 
sees it1 having previously selected the 
best point of view1 and  marked for     
omission or improvement what is not     
beautiful1 or what would  interfere with
 the effect of his picture as a work of 
high art4 ,his  first step1 therefore1  
is to fix upon the size of his canvas1  
or the  distance at which the picture is
 to be seen1 which determines its size4 
,his own eye is a camera obscura1 and   
the relation between the picture  or    
image on its retina is such1 that if we 
could view it from the  centre of       
curvature of the retina1 7the centre of 
visible direction17  a distance of half 
an inch1 it would have precisely the    
same apparent  magnitude as the object  

of which it is the image4 ,let us now   
suppose  that the artist wishes to avail
 himself of the picture in the camera   
obscura as received either on paper or  
ground-glass1 or of a photograph  of the
 scene he is to paint4 ,he must make use
 of a camera whose focal  length is     
equal to the distance at which his      
picture is to be seen1  and when the    
picture thus taken is viewed at this    
distance 7suppose  two feet7 it will1 as
 a whole1 and in all its parts1 have the
 same  apparent magnitude as the        
original object4 ,this will be          
understood from  ,fig4 #dg1 in which we 
may suppose ,h to be the lens of the    
camera1 ,,rb the  object1 and ,hy the   
distance at which it is to be viewed4   
,the size  of the picture taken with a  
lens at ,h1 whose focal length is ,hy1  
will be br1 and an eye placed at ,h will
 see the picture br  under an angle     
b,hr1 equal to the angle ,,rhb1 under   
which the real  object ,,rb was seen by 
the artist from ,h4 ,in like manner1 a  

larger  picture1 byr1 taken by a camera 
the focal distance of whose lens at  ,h 
is ,hy1 will be an accurate             
representation of the object ,,rb1 when 
viewed from ,h1 and of the same apparent
 magnitude4 ,if either of these         
pictures1 br or br1 are viewed from     
greater or less distances  than ,hy1 or 
,hy1 they will not be correct           
representations of the  object ,,rb1    
either in apparent magnitude or form4   
,that they will be of  a different      
apparent magnitude1 greater when viewed 
at less distances  than ,hy1 ,hy1 and   
less when viewed at greater distances1  
is too  obvious to require any          
illustration4 ,that they will differ in 
form1 or  in the relative apparent size 
of their parts1 has1 so far as ,i know1 
not been conjectured4 ,in order to shew 
this1 let us suppose a man six  feet    
high to occupy the foreground1 and      
another of the same size to be  placed  
in the middle distance1 the distance of 
the two from the artist  being ten and  

twenty feet4 ,the apparent magnitudes of
 these two men  on the photograph will  
be as two to one2 and if we look at it  
at any  distance greater or less than   
the focal length ,hy of the lens1 the   
same proportion of two to one will be   
preserved1 whereas if we look at  the   
original figures at a greater or less   
distance from them than the  place of   
the artist1 the ratio of their apparent 
magnitudes will be  altered4 ,if the    
artist1 for example1 advances five feet1
 the nearest  man will be five feet     
distant and the other fifteen feet1 so  
that their  apparent magnitude will now 
be as three to one4    ,illustration3   
,,fig4 #dg4    ,the same observations   
apply to a portrait of the human face4  
,in looking  at a human profile let us  
suppose the breadth of the nose to be   
one  inch1 that of the ear one inch1 and
 that we view this profile at the       
distance of three feet from the ear1    
which is two inches nearer the  observer
 than the nose4 ,the apparent magnitude 

of the ear and nose will  be as         
thirty-eight to thirty-six inches1      
whereas if we view the profile  from the
 distance of one foot the ratio will be 
as fourteen to  twelve1 that is1 the ear
 will be increased in apparent size more
 than  the nose4 ,hence it follows that 
all pictures should be viewed under  the
 same angle of apparent magnitude under 
which they were seen by the  artist as  
taken photographically1 for if we view  
them at a greater or  less angle than   
this we do not see the same picture as  
when we looked  at the original         
landscape or portrait1 under the same   
angle of apparent  magnitude4    ,from  
the observations made in the preceding  
,chapter on photographic  and           
stereoscopic portraiture1 the reader    
must have already drawn the  inference  
that the same landscape or building1    
seen at different  distances1 varies    
essentially in its character1--beauties 
disclosing  themselves and defects      
disappearing as we approach or recede   

from them4  ,the picture in the camera1 
therefore1 as used by ,mr4 ,thomson1 or1
 what  is still better1 with the        
exception of colour1 the photograph     
obtained  by the same instrument1 will  
supply the artist with all the general  
materials for his picture4 ,the         
photograph will differ considerably     
from any sketch which the artist may    
have himself made1 owing to  certain    
optical illusions to which his eye is   
subject4 ,the hills and  other vertical 
lines in the distance will be lower in  
the photograph  than in his sketch4#ei  
,the vertical lines of buildings will   
converge  upwards in the photograph1 as 
they ought to do1 in receding from the  
eye2 and in the same picture there will 
be a confusion1 as we shall  afterwards 
shew1 in the delineation of near and    
minute objects in the  foreground1      
increasing with the size of the lens    
which he has employed4    #ei ,sir      
,francis ,chantrey1 the celebrated      
sculptor1 shewed me1 many  years ago1 a 

,sketch-,book1 containing numerous      
drawings which he  had made with the    
,camera ,lucida1 while travelling from  
,london to  ,edinburgh by the ,lakes4   
,he pointed out to me the flatness1 or  
rather  lowness1 of hills1 which to his 
own eye appeared much higher1 but       
which1 notwithstanding1 gave to him the 
idea of a greater elevation4  ,in order 
to put this opinion to the test of      
experiment1 ,i had drawings  made by a  
skilful artist of the three ,eildon     
hills opposite my  residence on the     
,tweed1 and was surprised to obtain1 by 
comparing them  with their true         
perspective outlines1 a striking        
confirmation of the  observation made by
 ,sir ,francis ,chantrey4    ,in his    
admirable chapter 8,on ,finish10 ,mr4   
,ruskin has established1  beyond a      
doubt1 the most important principle in  
the art of painting4  8,the finishing of
 nature10 he states1 8consists not in   
the smoothing  of surface1 but the      
filling of space1 and the multiplication

 of life  and thought20 and hence he    
draws the conclusion1 that 8finishing   
means1 in art1 simply telling more      
truth40 ,titian1 ,tintoret1 ,bellini1   
and ,veronese have1 as he has shewn1    
wrought upon this principle1            
delineating vein by vein in the leaf of 
the vine1 petal by petal in  the        
borage-blossoms1 the very snail-shells  
on the ground1 the stripe  of black bark
 in the birch-tree1 and the clusters of 
the ivy-leaved  toad-flax in the rents  
of their walls2 and we have seen that a 
modern  artist1 ,delaroche1 considers a 
finish of inconceivable minuteness  as  
neither disturbing the repose of the    
masses1 nor interfering with  the       
general effect in a picture4    ,the    
,pre-,raphaelites1 therefore1 may appeal
 to high authority for  the cardinal    
doctrine of their creed2 and whatever be
 their errors  in judgment or in taste1 
they have inaugurated a revolution which
  will release art from its fetters1 and
 give it a freer and a nobler  aim4     

,nature is too grand in her minuteness1 
and too beautiful in her  humility1 to  
be overlooked in the poetry of art4 ,if 
her tenderest and  most delicate forms  
are worthy of admiration1 she will      
demand from the  artist his highest     
powers of design4 ,if the living        
organizations of the  teeming earth1    
upon which we hourly tread1 are         
matchless in structure1  and fascinating
 in colour1 the palette of the painter  
must surrender  to them its choicest    
tints4 ,in the foreground of the highest
 art1 the  snail-shell may inoffensively
 creep from beneath the withered leaf or
  the living blade2 the harebell and the
 violet may claim a place in the  sylvan
 dell2 the moss may display its tiny    
frond1 the gnarled oak or  the twisted  
pine may demand the recognition of the  
botanist1 while the  castle wall rises  
in grandeur behind them1 and the        
gigantic cliffs or  the lofty mountain  
range terminate the scene4    ,if these 
views are sound1 the man of taste will  

no longer endure  slovenliness in art4  
,he will demand truth as well as beauty 
in the  landscape2 and that painter may 
change his profession who cannot        
impress geology upon his rocks1 and     
botany upon his plants and trees1  or   
who refuses to display1 upon his summer 
or his autumn tablet1 the  green crop as
 well as the growing and the gathered   
harvest4 ,thus  enlarged in its powers  
and elevated in its purposes1 the art of
  painting will be invested with a new  
character1 demanding from its  votaries 
higher skill and more extended          
knowledge4 ,in former times1 the  minute
 and accurate delineation of nature was 
a task almost impossible1  requiring an 
amount of toil which could hardly be    
repaid even when  slightly performed2   
but science has now furnished art with  
the most  perfect means of arresting1 in
 their most delicate forms1 every       
object1  however minute1 that can enter 
into the composition of a picture4      
,these  means are the arts of           

photography and stereoscopic            
re-combination1  when rightly directed1 
and it is the object of the present     
chapter  to shew how the artist may best
 avail himself of their valuable and    
indispensable aid4    ,every country and
 district1 and even different parts of  
the same  district1 have a ,flora and   
,geology peculiar to themselves2 and the
  artist who undertakes to represent its
 beauties owes to truth the  same       
obligations as the botanist who is to   
describe its plants1 or  the            
mineralogist its rocks and stones4 ,the 
critic could not1 in  former times1     
expect more details from his unaided    
pencil than it  has generally furnished2
 but with the means now at his command1 
he  must collect1 like the naturalist1  
all the materials for his subject4      
,after the camera has given him the     
great features of his landscape1 he     
must appeal to it for accurate          
delineations of its minuter parts1--the 
trunks1 and stems1 and leafage of his   

trees--the dipping strata of  its       
sandstone beds--the contortions of its  
kneaded gneiss1 or the  ruder features  
of its trap and its granite4 ,for the   
most important of  these details he will
 find the camera1 as at present         
constructed1 of  little service4 ,it is 
fitted only to copy surfaces2 and       
therefore1  when directed to solid      
bodies1 such as living beings1 statues1 
c41  it gives false and hideous         
representations of them1 as ,i have     
shewn  in a preceding chapter4 ,it is   
peculiarly defective when applied to    
parts of bodies at different distances  
from it1 and of a less diameter  than   
the lens4 ,the photograph of a cube     
taken by a lens of a greater  diameter1 
will display five of its sides in a     
position1 when its true  perspective    
representation is simply a single square
 of its surface4  ,when applied to      
trees1 and shrubs1 and flowers1 its     
pictures are still  more unsatisfactory4
 ,every stem and leaf smaller than the  

lens1 though  absolutely opaque1 is     
transparent1 and leaves and stems behind
 and  beyond are seen like ghosts       
through the photographic image4         
,illustration3 ,,fig4 #dh4    ,this will
 be understood from ,fig4 #dh1 in which 
,,ll is the lens of the  camera1 ,,ab   
the breadth of the trunk or stem of a   
tree less than ,,ll in  width4 ,draw    
,,la1 ,,lb1 touching ,,ab in the points 
,a1 ,b1 and crossing at  ,c4 ,objects   
behind ,,ab1 and placed within the angle
 ,,acb1 will not have  any images of    
them formed by the lens ,,ll1 because   
none of the rays  which proceed from    
them can fall upon the lens1 but objects
 placed  within the angle ,,ecf1 however
 remote be their distance1 will have    
images of them formed by the lens4 ,if  
,d1 for example1 be a leaf or a  fruit1 
or a portion of a branch1 the rays which
 it emits will fall  upon the portions  
,lm1 ,ln of the lens1 determined by     
drawing ,dm1  ,dn touching ,,ab1 and an 
image of it will be formed in the centre

 of  the photographic image of ,,ab1 as 
if ,,ab were transparent4 ,this image   
will be formed by all the portions of   
the surface of the lens on which  the   
shadow of ,,ab1 formed by rays emanating
 from ,d1 would not fall4 ,if  the      
object ,d is more remote1 the shadow of 
,,ab will diminish in size1  and the    
image of the object will be formed by a 
greater portion of the  lens4 ,if the   
sun were to be in the direction ,,mn1   
his image would appear  in the centre of
 the trunk or stem1 corresponding to    
,,ab1 ,fig4 #di4    ,illustration3      
,,fig4 #di4    ,if the stem occupies any
 other position1 ab1 ,fig4 #dh1 in the  
landscape1 objects1 such as d1 within   
the angle ecf1 will have  images of them
 formed within the corresponding portion
 of the trunk or  stem4 ,hence1 if ,,ab1
 ,fig4 #di1 represents the shadow of the
 stem across  the lens ,,ll1 the image  
of any object1 which if luminous would  
give this  shadow1 will be formed within
 the photographic image of the stem1 and

  as every part of it may have branches1
 or leaves1 or fruit behind it1  its    
photographs will be filled with their   
pictures1 which will have the  same     
distinctness as other equidistant parts 
of the landscape4    ,these observations
 are applicable to the limbs and slender
 parts of  animate and inanimate        
figures1 when they are of a less size   
than the  lens with which their         
photograph is taken4 ,they will be      
transparent  to all objects behind them1
 and their true forms and shades cannot 
be  taken with the cameras now in       
use4#fj    ,in order1 therefore1 to     
collect from nature the materials of his
  profession1 the artist must use a     
camera with a lens not much larger  than
 the pupil of his eye1 and with such an 
instrument he will obtain  the most     
correct drawings of the trunks and stems
 of trees1 of the  texture and markings 
of their bark1 of the form of their     
leaves1 and  of all those peculiarities 
of structure and of leafage by which    

alone  the trees of the forest can be   
distinguished4 ,in like manner1 he will 
obtain the most correct representations 
of the rocks and precipices1  and the   
individual stones#fa which may enter    
into his picture1--of  the plants which 
spring from their crevices or grow at   
their base1  and of those flowers in    
their native grace and beauty1 which    
hitherto  he has either drawn from      
recollection1 or copied from the formal 
representations of the botanist4    #fj 
,by using large lenses1 we may obtain   
the picture of an object  within the    
picture of an opaque one in front of it2
 and with a  telescope1 we may see      
through opaque objects of a certain     
size4 ,many  singular experiments may be
 made by taking photographs of solid    
objects1 simple or compound1 with lenses
 larger than the objects  themselves4   
#fa ,in a landscape by ,mr4 ,waller     
,paton1 called the 8,highland ,stream10 
now in the ,edinburgh ,exhibition1 the  
foreground consists principally  of a   

bed of water-worn stones1 on the margin 
of a pool at the bottom  of a waterfall4
 ,the stones are so exquisitely painted1
 that nature  only could have furnished 
the originals4 ,we may examine them at a
 few  inches' distance1 and recognise   
forms and structures with which we have 
been long familiar4 ,a water-ousel1     
peculiar to ,scottish brooks and        
rivers1 perched upon one of them1 looks 
as anxiously around as if a  schoolboy  
were about to avail himself of the      
missiles at his feet4    ,in addition to
 their correctness as true              
representations of natural  forms1      
photographs have a peculiar value1 for  
which no labour or skill  on the part of
 the artist can compensate4 ,in drawing 
the sketch of a  landscape1 or          
delineating the trees1 rocks1 and       
foliage which are near  him1 or the     
objects in the middle or remote         
distance1 several hours  must be spent4 
,during this period1 the landscape and  
its individual  parts are undergoing no 

inconsiderable change4 ,a breeze may    
disturb  the masses of his foliage1 and 
bend his tree stems1 and ruffle his     
verdure1 and throw new reflected lights 
upon the waving crops1 while  every     
direct light is changing in intensity   
and direction during the  culmination or
 descent of the sun4 ,what he has       
delineated in the  morning will hardly  
correspond with what he draws at noon1  
and the  distances which at one time are
 finely marked in aerial perspective1   
will disappear1 or even suffer inversion
 by variations in the intensity  and    
position of the haze4 ,if cottages1 or  
castles1 or buildings of  any kind1     
enter into the picture1 the shadows of  
their projections1  and the lights upon 
their walls and roofs will1 in sunshine1
 undergo  still greater variations1 and 
the artist will be perplexed with the   
anachronisms and inconsistencies of his 
choicest materials4 ,the  landscape thus
 composed in patches will1 in its       
photograph1 have a  very different      

aspect1 as much in its forms as in its  
lights and  shadows4 ,the truths of     
nature are fixed at one instant of time2
 the  self-delineated landscape is      
embalmed amid the co-existing events of 
the physical and social world4 ,if the  
sun shines1 his rays throw their        
gilding on the picture4 ,if the         
rain-shower falls1 the earth and the    
trees glisten with its reflexions4 ,if  
the wind blows1 the partially           
obliterated foliage will display the    
extent of its agitation4 ,the  objects  
of still life1 too1 give reality and    
animation to the scene4  ,the streets   
display their stationary chariots1 the  
esplanade its  military array1 and the  
market-place its colloquial groups1     
while  the fields are studded with the  
forms and attitudes of animal life4     
,the incidents of time and the forms of 
space are thus simultaneously  recorded1
 and every picture from the sober       
palette of the sun becomes  an authentic
 chapter in the history of the world4#fb

    #fb ,these views are well           
illustrated by the remarkable           
photographs of  the ,crimean war4       
,but1 however valuable photography has  
become to the artist1 science  has      
recently given him another important    
auxiliary4 ,in order to make  this      
available1 he must employ a small pocket
 binocular camera1 to  take double      
pictures to be united in the            
stereoscope4 ,his trees will  thus      
exhibit the roundness of their trunks   
and stems1 the leaves and  branches will
 place themselves at their proper       
distance1 and he will  discover the     
reason of peculiar effects which in the 
plane photograph  he has been unable to 
understand4 ,seeing that his own picture
 is to be  upon a plane surface1 ,i can 
hardly expect to convince the artist    
that  he will obtain more information by
 reproducing the original in relief4    
,it is a fact1 however1 beyond dispute1 
that effects are produced by  the       
stereoscopic union of two plane         

photographs which are invisible in  the 
single picture4 ,these effects1 which   
are chiefly those of lustre  and shade1 
are peculiarly remarkable in            
,daguerreotype1 and it is by  no means  
easy to explain the cause4 ,in a        
,daguerreotype1 for example1  of two    
figures in black bronze1 with a high    
metallic lustre1 it is  impossible1 by  
looking at the single picture1 to tell  
the material of  which they are made2   
but the moment they are united into     
stereoscopic  relief their true         
character is instantly seen4 ,in a      
,daguerreotype of  ,alexander and       
,bucephalus1 portions of the figure seem
 as if shaded  with ,china ink of a     
nearly uniform tint1 but when seen in   
relief the  peculiar shade entirely     
disappears4 ,the stereoscopic           
combination of  two surfaces of         
different intensities1 though of the    
same colour1  produces effects which    
have not yet been sufficiently studied4 
,but1  independently of these           

peculiarities1 the artist will certainly
 derive  more aid from his landscape in 
relief1 and from the study of its       
individual parts1 in their roundness and
 relative distances1 than when  he      
examines them in their plane            
representations4 ,the shadows which the 
branches of leaves cast upon the trunks 
and stems of his trees he will  be able 
to trace to the causes which produce    
them4 ,effects in outline1  as well as  
in light and shadow1 which may perplex  
him1 will find an  explanation in the   
relative distances and differences of   
apparent  magnitude of individual parts2
 and1 after becoming familiar with his  
landscape in relief1 as it exists in    
,nature1 he cannot fail to acquire  new 
principles and methods of manipulation4 
,nature flattened upon paper  or metal1 
and ,nature round and plump1 as if fresh
 from the chisel of  the ,divine        
sculptor1 must teach very different     
lessons to the aspiring  artist4    ,the
 historical painter1 or the more humble 

artist who delineates the  scenes of    
common or domestic life1 will derive    
from the photographic  camera and the   
stereoscope advantages of equal         
importance4 ,the  hero1 the sage1 and   
the martyr1 drawn from living originals1
 may  be placed in the scenes where they
 suffered1 or in the localities  which  
they hallowed4 ,the lawgiver of ,egypt1 
though he exists only  in the painter's 
eye1 may take his place beside the giant
 flanks of  ,horeb or the awe-inspiring 
summit of ,mount ,sinai2 and ,he whom we
 may  not name may challenge our love   
and admiration amid the sun-painted     
scenes of his youth1 of his miracles1   
and of his humiliation4 ,the  fragments 
of ancient grandeur which time and war  
have spared1 the  relics of bygone ages 
which have resisted the destructive     
elements1  will1 as the materials of    
art1 give reality and truth to the      
pictorial  history of times past1 while 
the painter of modern events can command
  the most accurate representations not 

only of the costume1 but of  the very   
persons of the great men whose deeds he 
is called upon to  immortalize4 ,the    
heroes of the ,crimean war1 whether     
friends or foes1  will be descried in   
the trenches in which they fought1 amid 
the ranks  which they led to victory1 or
 among the wrecks of the fatal encounter
  in which they fell4 ,the sun will thus
 become the historiographer of  the     
future1 and in the fidelity of his      
pencil and the accuracy of  his         
chronicle1 truth itself will be embalmed
 and history cease to be  fabulous4     
,but even in the narrower1 though not   
less hallowed sphere of domestic  life1 
where the magic names of kindred and    
home are inscribed1 the  realities of   
stereoscopic photography will excite the
 most thrilling  interest4 ,in the      
transition forms of his offspring1 which
 link infancy  with manhood1 the parent 
will recognise the progress of his      
mortal  career1 and in the successive   
phases which mark the sunset of life1   

the stripling in his turn will read the 
lesson that his pilgrimage too  has a   
term which must close4 ,nor are such    
delineations interesting  only as works 
of art1 or as incentives to virtue2 they
 are instinct  with associations vivid  
and endearing4 ,the picture is connected
 with  its original by sensibilities    
peculiarly tender4 ,it was the very     
light  which radiated from her          
brow1--the identical gleam which lighted
 up her  eye1--the hectic flush or the  
pallid hue that hung upon her cheek1    
which  pencilled the cherished image1   
and fixed themselves for ever there4    
,,chapter ,,xi4    ,,application ,,of   
,,the ,,stereoscope ,,to ,,sculpture1   
,,architecture1 ,,and ,,engineering4    
,to the arts of sculpture and           
architecture1 the processes of binocular
  photography and stereoscopic          
combination are particularly applicable4
  ,the landscape painter has every day  
within his reach examples of the        
picturesque1 the wild and the sublime in

 nature4 ,in the fields which  surround 
him1 in the river1 or even in the 8brook
 that bubbles by10 on  the shore1 on the
 heath1 or on the mountain side1 he has 
the choice of  materials for every      
department of his art4 ,the sculptor has
 no such  advantage4 ,swathed in        
impenetrable drapery the human figure   
mocks his  eager eye1 and it is only by 
stolen glances1 or during angel visits1 
few and far between1 that he can see    
those divine forms which it is his      
business to portray4 ,he must therefore 
quit his home and seek for the  models  
of ancient and modern art4 ,in the      
,british ,museum1 in the ,louvre1  in   
the ,vatican1 and in the repositories of
 art in ,berlin1 ,munich1 and  other    
,european cities1 he must spend months  
and years in the study of  his          
profession4 ,he must copy1 day after    
day1 those master triumphs of  genius   
which the taste of ages has consecrated1
 and gather from their  study the true  
principles of his art4 ,transferred to  

his own studio1  these copies will be   
his instructor and his guide4 ,they will
 exhibit  to him forms more than human1 
though human still1 embodying all that  
is true and beautiful in what might be  
man4 ,the value of these copies1        
however1 depends on the skill and care  
with which they have been taken2  but no
 labour however great1 and no power of  
drawing however masterly1  can give even
 an approximate idea either of the      
outline or round of  solid figures1     
whether single or in groups4 ,light and 
shade can alone  evolve those muscular  
prominences1 or those soft and          
sphere-like  relievos which give such   
power and beauty to forms1 male and     
female2  but how can an artist catch and
 fix those lights and shades which give 
relief to the parts which they          
illuminate or obscure8 ,the light of    
the sun1 even in a cloudless sky1 is    
ever varying in intensity1 and  the     
breadth and direction of the shadows    
which he casts are varying  from hour to

 hour4 ,in a cloudy day1 the motion of  
the clouds1 and the  varying reflexions 
within his apartment1 subject the lights
 and shadows  to constant change4 ,the  
portions of the drawing executed in the 
morning  will not harmonize with what is
 drawn at noon1 or during the decline   
of day4 ,we consider it1 therefore1     
impossible to execute a drawing of  a   
statue1 or of a group of statues1 from  
which the artist can have  anything like
 an accurate idea of the forms which    
compose them4    ,from all these        
difficulties the sculptor has been      
relieved by the  invention of the       
photographic process4 ,he may thus take 
copies of  statues in a few minutes1 and
 take them in all their aspects1 and as 
seen at various distances1 and in this  
manner he will obtain drawings  with the
 shadows as they existed at a particular
 instant1 so that the  lights and       
shades1 upon every individual part of   
the statue1 will be  correctly related  
to each other4 ,but valuable as these   

drawings are1  compared with those      
executed by the pencil1 their value     
becomes tenfold  greater when they are  
taken with the binocular camera1 and    
with small  lenses1 as already          
described4 ,when combined in the        
stereoscope1 he may  reproduce the      
statue in relief1 in all its aspects1   
and of different  sizes1 and derive from
 its study the same advantages which the
 statue  itself would have furnished4   
,in one respect the creations of the    
stereoscope surpass the original4 ,while
 the artist is surveying and  drawing   
instruction from the marble prototype1  
its lights and shadows1  and            
consequently the delicate forms1 convex 
and concave1 by which they  are         
produced1 are constantly changing1      
whereas1 in the stereoscopic  statue1   
everything is fixed and invariable4#fc  
,in taking busts and  statues from the  
living subject1 the sculptor will derive
 great  advantage from the stereoscope4 
,double pictures of the whole1 or of any

  portion of the subject1 may be taken  
and raised into relief1 and from  such  
binocular pictures1 executed on one side
 of the globe1 an artist1  on the other 
side1 may complete an admirable statue4 
,the dying and the  dead may thus be    
modelled without the rude contact of a  
mask1 and those  noble forms perpetuated
 which affection or gratitude has       
endeared4    #fc ,a ,french sculptor has
 actually modelled a statue from the    
stereoscopic relief of binocular        
pictures4    ,we must warn the sculptor1
 however1 against the employment of     
binocular  pictures taken with large    
lenses4 ,not only will the individual   
picture  be deformed1 but a double      
deformity will be induced by their      
union2 and  whether he copies from a    
statue or from a living figure1 his work
 must  be defective1 even to an ordinary
 eye4    ,in architecture1 and all those
 arts in which ornamental forms are     
given to solid materials1 the binocular 
camera and the stereoscope  will be     

found indispensable4 ,the carvings of   
ancient1 or medival1  or modern art may 
be copied and reproduced in relief1     
whatever be  the material from which    
they have been cut4 ,the rich forms of  
,gothic  architecture1 and the more     
classical productions of ,greek and     
,roman  genius1 will swell the artist's 
portfolio1 and possess all the value  of
 casts4 ,with the aid of the            
,kaleidoscope the modern artist may     
surpass all his predecessors4 ,he may   
create an infinite variety of  those    
forms of symmetry which enter so largely
 into the decorative  arts2 and if the  
individual forms1 which constitute the  
symmetrical  picture1 are themselves    
solid1 the binocular-kaleidoscopic      
pictures1  taken photographically1 will 
be raised into the original relief of   
their component parts1 or they may be   
represented directly to the eye  in     
relief1 by semi-lenses placed at the    
ocular extremities of the  reflecting   
plates4#fd ,if the symmetrical forms are

 taken from lines  in the same plane1 no
 relief will be obtained from the       
kaleidoscopic  pictures4    #fd ,see my 
,treatise on the ,kaleidoscope1 second  
edition1 just  published4    ,but it is 
not merely to the decorative parts of   
architecture that the  stereoscope is   
applicable4 ,the noblest edifices1      
whether of a civil1 a  religious1 or a  
military character1 which he could      
otherwise study only  as a traveller1   
and represent in hurried and imperfect  
sketches1 will1  when taken binocularly1
 stand before him in their full relief  
and  grandeur1 reflecting to his eye the
 very lights and shadows which at a     
given hour the sun cast upon their      
walls4    ,in the erection of public    
buildings1 hourly or daily photographs  
have  been taken of them1 to shew to the
 absent superintendent the progress  of 
his work2 but these pictures will be    
still more expressive if  binocular ones
 are combined in the stereoscope4    ,to
 the engineer and the mechanist1 and the

 makers of instruments of all  kinds1   
the stereoscope will be of inestimable  
value4 ,the difficulty of  representing 
machinery is so great that it is not    
easy to understand  its construction or 
its mode of operation from plans and    
perspective  views of it4 ,the union of 
one or two binocular pictures of it1    
when  thrown into relief1 will1 in many 
cases1 remove the difficulty both  of   
drawing and understanding it4           
,photographs of machinery1 however1     
consisting of a number of minute parts  
at different distances from  the eye1   
have1 when taken by large lenses1 all   
the defects which we  explained in      
reference to trees and their branches   
and leaves4 ,supports  and axles will be
 transparent1 and the teeth of the      
wheels1 and the  small and distant parts
 of the mechanism1 will be seen through 
all the  nearer parts whose width is    
less than the diameter of the lens4     
,in taking a binocular picture of a     
machine or instrument consisting  of    

various parts1 that minute accuracy     
which is necessary to give  the true    
form and expression of the human face is
 not required2  but if it should happen 
that1 in a correct binocular view of the
  object1 parts are concealed which it  
would be useful to see1 we must         
discover the binocular angle which will 
shew these parts in the two  pictures1  
or1 generally speaking1 which will give 
the best view of  the mechanism1 and    
then adjust the lenses of the camera to 
give the  desired representations of it4
 ,these observations will be found      
useful  in obtaining stereoscopic views 
of the structures in carpentry and      
ship-building4          ,,chapter ,,xii4
    ,,application ,,of ,,the            
,,stereoscope ,,to ,,natural ,,history4 
,in treating of those objects of natural
 history which enter into the           
composition of landscape scenery1 such  
as trees1 plants1 and rocks1 we  have   
pointed out the method of having them   
accurately drawn for the  stereoscope2  

but it is to the importance of          
stereoscopic photography  in natural    
history as a science that we propose to 
devote the present  ,chapter4    ,when  
we reflect upon the vast number of      
species which have been  described by   
zoologists1 the noble forms of animated 
nature1 whether  wild or domesticated1  
and the valuable services which many of 
them  perform as the slaves of man1 we  
can hardly attach too much importance   
to the advantage of having them         
accurately delineated and raised into   
stereoscopic relief4 ,the animal        
painters of the present day1--the       
,landseers1 the ,cowpers1 and the       
,ansdells1 have brought this branch of  
their art to a high degree of           
perfection1 but the subjects of their   
pencil have been principally dogs1      
horses1 deer1 and cattle1 and a few     
other animals1 with which they are well 
acquainted1 and specimens of  which were
 within their reach4 ,to give accurate  
representations of  giraffes1 hynas1 and

 the rarer animals which are found alive
 only in  zoological gardens and        
travelling caravans1 is a more difficult
 task1  and one which has been          
necessarily intrusted to inferior hands4
 ,in this  branch of his art the        
photographer is perplexed with the      
difficulty of  arresting his subject in 
a position of repose and in the attitude
 which  he requires4 ,but this          
difficulty will diminish as his         
materials become  more sensitive to     
light2 and means may be found for       
fixing1 without  constraint1 certain    
animals in the desired position4 ,we    
have seen the  portrait of a dog taken  
with such minute accuracy that the      
slightest  trace of any motion could not
 be perceived4 ,its master directed his 
attention to a piece of bread1 and he   
stood firmly waiting for his  reward4   
,considering truth as an essential      
element in all photographs1  we are     
unwilling to counsel the artist to have 
recourse to a large lens  for the       

purpose of accelerating his process by  
seizing his restless  object in a single
 instant of time2 but what cannot be    
tolerated in the  human form may be     
permitted in animal portraiture as a    
necessary evil4  ,the divine lineaments 
and delicate forms which in man the     
intellect  and the affections conspire  
to mould1 are concealed under the shaggy
  drapery of the world of instinct2 and 
even if they existed and were           
perceived1 could hardly be appreciated  
by those who have not studied  its      
manners and submitted to its laws4 ,but 
even in the present state  of           
photography such a celerity of process  
has been attained that a  distinguished 
amateur in ,edinburgh has constructed a 
portable camera1  which1 by pulling a   
trigger1 instantaneously records upon   
its sensitive  retina the surf which is 
hurrying to the shore1 or the stranger  
who  is passing in the street4 ,with    
such an instrument1 in such hands1 the  
denizens of the jungle or of the plains 

may be taken captive in their  finest   
attitudes and in their most restless    
moods4 ,photographs thus  obtained will 
possess a value of no ordinary kind1 and
 when taken in  the binocular camera and
 raised into relief by the stereoscope1 
will be  valuable auxiliaries to the    
naturalist1 and even to the painters and
  the poets whose works or whose lyrics 
may require an introduction to  the     
brutes that perish4    ,in representing 
with accuracy the osteology and         
integuments of the  zoological          
world--the framework which protects     
life1 and to which life  gives activity 
and power1 the aid of the stereoscope is
 indispensable4  ,the repose of death1  
and the sharp pencil which resides in   
the small  lens1 will place before the  
student's eye the skeleton1 clothed  or 
unclothed1 in accurate perspective and  
true relief1 while he  contemplates with
 wonder1 in their true apparent         
magnitude1 the  gigantic ,mastodon1 the 
colossal ,megatherion1 and the huge     

,dinornis1 or  examines the crushed     
remains of the lengthened ,saurian1 or  
the hollow  footsteps which ancient life
 has impressed on the massive sandstone 
or  the indurated clay4    ,in the other
 branches of natural history1           
ichthyology1 ornithology1  conchology1  
c41 the stereoscope will be found       
equally useful4 ,in  entomology1 where  
insects are to be represented1 the      
microscopic  binocular camera must be   
used2 and in order to prevent the legs1 
the  antenn1 and other small parts of   
the object from being transparent1  and 
therefore spotted1 with the images of   
objects or parts beyond them1  as       
explained in a preceding chapter1 the   
smallest lenses should be  employed4    
,the roots and bulbs which are raised by
 the agriculturist and the              
horticulturist1 the turnip1 the beet1   
the carrot1 and the onion2 and  the     
fruits raised in the orchard1 on the    
wall1 or in the hothouse1 may  be       
exhibited in all their roundness and    

solidity in the stereoscope2  and as    
articles of commerce they might be      
purchased on the authority  of their    
pictures in relief4 ,the microscopic    
stereoscope will1 in like  manner1 give 
accurate magnified representations in   
relief of grains and  seeds of all      
kinds1 and by comparing these with the  
representations of  those of a standard 
form and quality1 the purchaser may be  
enabled to  form a better idea of their 
excellence than if he saw them with his 
own  eyes1 or had them in his own hands4
          ,,chapter ,,xiii4             
,,application ,,of ,,the ,,stereoscope  
,,to ,,educational ,,purposes4      ,the
 observations contained in the preceding
 chapters prepare us for  appreciating  
the value of the stereoscope as an      
indispensable auxiliary  in elementary  
as well as in professional education4   
,when the scholar  has learned to read1 
to write1 and to count1 he has obtained 
only the  tools of instruction4 ,to     
acquire a general knowledge of the works

 of  ,god and of man--of things common  
and uncommon--of the miracles of nature 
and of art1 is the first step in the    
education of the people4 ,without  such 
knowledge1 the humblest of our race is  
unfit for any place in the  social      
scale4 ,he may have learned to read his 
,bible1 and he may have  read it after  
he had learned to read2--he may have    
committed to memory  every sentence in  
the ,decalogue2--he may have packed into
 the storehouse  of his brain all the   
wisdom of ,solomon1 and all the divine  
precepts  of a greater than ,solomon1   
while he is utterly ignorant of         
everything  above him1 around him1 and  
within him1--ignorant1 too1 of the form1
 the  magnitude1 and the motions of his 
terrestrial home1--ignorant of the      
gigantic structures which constitute the
 material universe1--ignorant of  the   
fabrics which industry prepares for his 
use1 and of the luxuries  which commerce
 brings from the ends of the earth and  
places at his  door1--ignorant even of  

the wonderful operations of that        
beneficent  commissariat1 which is every
 moment1 while he sleeps and dreams1    
elaborating the materials by which he is
 fed and clothed4    ,were we to say1   
though we do not say it1 that in our own
 country the  teachers1 so penuriously  
endowed by the ,state1 are not much in  
advance  of their pupils1 we should err 
only in stating what is not universally 
true2 and yet there are men of influence
 and character insisting upon  the      
imposition of sectarian tests1 and thus 
barricading our schools  against the    
admission of the wisest and the fittest 
masters6 ,and while  every civilized    
community in the world is eagerly       
teaching their  people1 irrespective of 
religious creeds1 the same bigots1 civil
 and  ecclesiastical1 in our own        
country1 have combined to resist the    
only  system of education which can stem
 the tide of vice and crime which is    
desolating the land4    ,missionary     
labour and reformatory institutions1    

valuable as they are1  presuppose an    
educated community4 ,to instruct and    
reform a race that  can neither read    
their ,bible nor derive knowledge from  
books1 is a  task beyond human          
achievement4 ,the dearest interests of  
society1  therefore1 call loudly for    
,secular ,education1--the greatest boon 
which  philanthropy ever demanded from  
the ,state4 ,the minister who1 in the   
face of sectarian factions1 dares not   
identify himself with a large           
legislative measure for the education of
 the people1 and resigns office  when he
 fails to carry it1 prefers power to    
duty1 and1 if he ever  possessed it1    
divests himself of the character of a   
statesman and a  patriot4 ,he may be    
justified in punishing the law-breaker  
who cannot  read his statutes1 but he is
 himself the breaker of laws of a higher
  order1 and sanctioned by a higher     
tribunal4    ,if the education of the   
people is to be attempted either by     
partial or  comprehensive legislation1  

the existing system is utterly          
inefficient4  ,the teacher1 however     
wisely chosen and well qualified1 has   
not at his  command the means of        
imparting knowledge4 ,he may pour it in 
by the  ear1 or extract it from the     
printed page1 or exhibit it in          
caricature  in the miserable            
embellishments of the school-book1 but  
unless he  teaches through the eye1 the 
great instrument of knowledge1 by means 
of truthful pictures1 or instruments1 or
 models1 or by the direct  exhibition of
 the products of nature and of art1     
which can be submitted  to the scrutiny 
of the senses1 no satisfactory          
instruction can be  conveyed4#fe ,every 
school1 indeed1 should have a museum1   
however  limited and humble4 ,even from 
within its narrow sphere objects of     
natural history and antiquities might be
 collected1 and duplicates  exchanged2  
and we are sure that many a             
chimney-piece in the district  would    
surrender a tithe of its curiosities for

 the public use4 ,were  the ,british    
,museum1 and other overflowing          
collections1 to distribute  among       
provincial museums the numerous         
duplicates which they possess1  they    
would gradually pass into the schools1  
and before a quarter of a  century      
elapsed1 museums would be found in every
 proper locality4    #fe 8,the          
importance of establishing a permanent  
,museum of ,education  in this country1 
with the view of introducing            
improvements in the  existing methods of
 instruction1 and specially directing   
public  attention in a practical manner 
to the question of ,national ,education1
  has been of late generally            
recognised40--,third ,report of the     
,commissioners for the ,exhibition of   
#ahea1 presented to both ,houses of     
,parliament1 p4 #cg4 ,lond41 #ahef4     
,as we cannot indulge in the hope that  
any such boon will be conferred  on our 
educational institutions1 it becomes an 
important question how  far it is       

possible to supply the defect by the    
means within our reach4  ,the           
photographic process may be             
advantageously employed in producing    
accurate representations of those       
objects1 both of nature and of art1     
which it would be desirable to describe 
and explain in the instruction  of      
youth2 but as experience has not yet    
taught us that such pictures  will be   
permanent1 and capable of resisting the 
action of time and the  elements1 it    
would be hazardous to employ them in the
 illustration  of popular works4 ,it is 
fortunate1 however1 that the new art of 
galvanography enables us1 by a cheap    
process1 to give to photographs  the    
permanence of engravings1 and to employ 
them in the illustration of  educational
 works4#ff    #ff ,this fine invention  
we owe to ,mr4 ,paul ,pretsch1 late     
director of  the ,imperial ,printing    
,office at ,vienna4 ,it is secured by   
patent1 and is  now in practical        
operation in ,holloway ,place1          

,islington4    ,but however much we may 
value such an auxiliary1 representations
 or  drawings1 on a plane1 of solids or 
combinations of solids at different     
distances from the eye1 are in many     
cases unintelligible even to  persons   
well informed2 so that1 on this ground  
alone1 we cannot but  appreciate the    
advantages to be derived from binocular 
pictures and  their stereoscopic        
relievo1 not only in the instruction of 
youth1 but  in the diffusion of         
knowledge among all ranks of society4   
,one of the most palpable advantages to 
be derived from the illustration  of    
school-books by pictures in relief1 is  
the communication of correct  knowledge 
of the various objects of natural       
history4 ,if1 as we have  already shewn1
 the naturalist derives important       
assistance in his  studies from correct 
representations of animated nature1 how 
much more  valuable must they be to the 
scholar who never saw1 and may never see
  the objects themselves4 ,in the       

department of zoology1 the picture      
might frequently be taken from the      
living animal1 standing before the      
camera in vigorous life and transcendent
 beauty2 or when this cannot  be done1  
from the fine specimens of zoological   
forms which adorn our  metropolitan and 
provincial museums4 ,the trees and      
plants1 too1 of  distant zones1 whether 
naked in their osteology1 or luxurious  
in their  foliage1 would shew themselves
 in full relief2--the banyan1 clinging  
with its hundred roots to the           
ground1--the bread-fruit tree1 with its 
beneficent burden1--the cow tree1 with  
its wholesome beverage1--the  caoutchouc
 tree1 yielding its valuable juice1--or 
the deadly upas1  preparing its poison  
for the arrow of the savage or the      
poniard of the  assassin4    ,with no   
less interest will the schoolboy gaze on
 the forms of insect  life1 which will  
almost flutter before him1 and on the   
tenants of  the air and of the ocean1   
defective only in the colours which     

adorn  them4 ,the structures of the     
inorganic world will equally command    
his admiration4 ,the minerals which have
 grown in the earth beneath  his feet1  
and the crystals which chemistry has    
conjured into being1  will display to   
him their geometric forms1 infinite in  
variety1 and  interesting from their    
rarity and value4 ,painted by the very  
light  which streamed from them1 he will
 see1 in their retiring and advancing   
facets1 the ,kohinoor and other         
diamonds1 and the huge rubies1 and      
sapphires1 and emeralds1 which have     
adorned the chaplet of beauty1 or       
sparkled in the diadem of kings4 ,the   
gigantic productions of the earth  will 
appeal to him with equal power1--the    
colossal granites1 which have  travelled
 in chariots of ice1 and the rounded    
boulders1 which have  been transported  
in torrents of mud2 and while he        
admires1 in their  strong relief1 the   
precipices of ancient lava--the ,doric  
colonnades  of basalt--the upheaved and 

contorted strata beside them1 and the   
undisturbed beds which no internal      
convulsions have shaken1 he will  stand 
appalled before the fossil giants of the
 primeval world that trod  the earth    
during its preparation for man1 and have
 been embalmed in  stone to instruct and
 to humble him4    ,in acquiring a      
knowledge of physical geography1 in     
which the  grander aspects of nature    
arrest our attention1 their stereoscopic
  representations will be particularly  
instructive4 ,the mountain range1       
whether abrupt in its elevation1 or     
retiring from our view1--whether        
scarred with peaks or undulating in     
outline1--the insulated mountain  tipped
 with snow or glowing with fire1--the   
volcano ejecting its burning            
missiles1#fg--the iceberg fixed in the  
shore1 or floating on the  deep1--the   
deafening cataract1--the glacier and its
 moraines1 sinking  gently to the       
plains1--and even the colossal wave with
 its foaming  crest1 will be portrayed  

in the binocular camera1 and exhibited  
in all  the grandeur and life of nature4
    #fg ,an accomplished traveller1 the 
,rev4 ,mr4 ,bridges1 who ascended       
,mount ,etna for the purpose of taking  
,talbotype drawings of its scenery1     
placed his camera on the edge of the    
crater to obtain a representation  of   
it4 ,no sooner was the camera fixed and 
the sensitive paper  introduced1 than an
 eruption took place1 which forced ,mr4 
,bridges to  quit his camera in order to
 save his life4 ,when the eruption      
closed1 he  returned to collect the     
fragments of his instrument1 when1 to   
his great  surprise and delight1 he     
found that his camera was not only      
uninjured1  but contained a picture of  
the crater and its eruption4    ,the    
works of human hands1--the structures of
 civilisation1 will stand  before the   
historian and the antiquary1 as well as 
the student1 in  their pristine         
solidity1 or in their ruined            
grandeur1--the monuments by  which      

sovereigns and nations have sought to   
perpetuate their names1--the  gorgeous  
palaces of kings1--the garish temples of
 superstition1--the  humbler edifices of
 ,christian faith1--the bastions and    
strongholds of  war1 will display       
themselves in the stereoscope as if the 
observer were  placed at their base1 and
 warmed by the very sun which shone upon
 their  walls4    ,although few of our  
village youth may become sculptors1 yet 
the  exhibition of ancient statues in   
their actual relief1 and real apparent  
magnitude1 cannot fail to give them     
salutary instruction and rational       
pleasure4 ,to gaze upon the ,apollo     
,belvidere1--the ,venus de ,medici1--the
  ,laocoon1 and the other masterpieces  
of ancient art1 standing in the  very   
halls which they now occupy2 or to see  
the chef d'uvres of  ,canova1           
,thorvaldsen1 and ,chantrey1 or the     
productions of living artists  in their 
own studio1 with the sculptor himself   
standing by their side1  will excite an 

interest of no ordinary kind4    ,from  
the works of the architect1 the         
engineer1 and the mechanist1  as        
exhibited in full relief1 the student1  
whether at our schools or  colleges1    
will derive the most valuable           
instruction4 ,the gigantic  aqueducts of
 ancient and modern times1--the viaducts
 and bridges which  span our valleys and
 our rivers1 and the machinery in our   
arsenals1  factories1 and workshops1    
will be objects of deep interest to the 
general as well as the professional     
inquirer4    ,there is yet another      
application of the stereoscope to       
educational  purposes1 not less         
important than those which have been    
mentioned4  ,in the production of       
diagram representing instruments and    
apparatus1  which cannot be understood  
from drawings of them on a plane1 it    
will  be of incalculable use to the     
teacher to have stereoscopic pictures   
of them4 ,in every branch of physical   
science1 diagrams of this kind  are     

required4 ,when they are intended to    
represent apparatus and  instruments1   
either for illustrating known truths1 or
 carrying on  physical researches1      
binocular pictures can be easily        
obtained2 but  when the diagrams have   
not been taken from apparatus1 but are  
merely  combinations of lines1 we can   
obtain binocular photographs of them    
only  from models constructed on        
purpose4 ,these models will give        
binocular  representations in various   
azimuths1 so that the true position of  
planes at different inclinations1 and   
lines at various angles with  each      
other1 and at different distances from  
the eye1 will be readily  apprehended4  
,astronomical diagrams1 in which orbits1
 c41 may be  represented by wires1 and  
optical figures1 in which the rays may  
be  formed by threads or wires1 would be
 thus easily executed4    ,among the    
binocular diagrams1 consisting of white 
lines upon a black  ground1 which have  
been executed in ,paris1 there is one   

representing  the apparatus in which a  
ray of light1 polarized by reflexion    
from a  glass plate1 passes through a   
crystallized film perpendicular to the  
plane of the paper1 and is subsequently 
analysed by reflexion from  another     
plate at right angle to the following   
plate4 ,this diagram1 when  placed in   
relief by the stereoscope1 gives as     
correct an idea of the  process as the  
apparatus itself4    ,as an auxiliary in
 the investigation of questions of      
difficulty and  importance1 both in     
physics and metaphysics1 the stereoscope
 is  peculiarly valuable4 ,it enables us
 to place in its true light the         
celebrated theory of vision on which    
,bishop ,berkeley reared the ideal      
philosophy1 of which he was the founder1
 and it gives us powerful aid  in       
explaining many physical phenomena which
 have long baffled the  ingenuity of    
philosophers4 ,it would be out of place 
to give any account  of these in a work 
like this1 but there is one so          

remarkable1 and at  the same time so    
instructive1 as to merit special notice4
 ,in order to  exhibit1 by means of     
three diagrams1 a solid in relief and   
hollow at  the same time1 which had not 
been previously done1 ,i executed three 
drawings of the frustum of a cone1      
resembling those in ,fig4 #ca1 so  that 
the left-hand one and the middle one    
gave the hollow cone1  while the middle 
one and the right-hand one gave the     
raised  cone4 ,having their summits     
truncated1 as in the figure1 the cones  
exhibit1 in the one case1 a circle at   
the bottom of the hollow cone1  and in  
the other1 a circle on the summit of the
 raised cone4 ,when these  three        
diagrams#fh are placed in an open       
lenticular stereoscope1 or  are united  
by the convergency of the optical axes1 
so that we can not  only see the hollow 
and the raised cones1 but the flat      
drawing on  each side of them1 we are   
enabled to give an ocular and           
experimental  proof of the cause of the 

large size of the horizontal moon1 of   
her  small size when in the meridian or 
at a great altitude1 and of her         
intermediate apparent magnitude at      
intermediate altitudes1--phenomena      
which had long perplexed astronomers1   
and which ,dr4 ,berkeley1 rejecting     
previous and well-founded explanations1 
ascribed to the different  degrees of   
brightness of the moon in these         
different positions4    #fh ,a binocular
 slide1 copied from the one originally  
designed by  myself1 forms ,no4 #bg of  
the ,series of white-lined diagrams upon
 a black  ground executed in ,paris4    
,the drawings1 however1 are too large   
for the  common stereoscope4    ,as the 
circular summit of the raised cone      
appears to be nearest  the eye of the   
observer1 the summit of the hollow cone 
farthest  off1 and the similar central  
circle in the flat drawing on each side1
  at an intermediate distance1 the      
apparent distances from the eye of      
different and equal circles will        

represent the apparent distance of  the 
moon in the zenith1 or very high in the 
elliptical celestial  vault1--the same  
distance when she is in the horizon1 and
 the same  when at an intermediate      
altitude4 ,being in reality of exactly  
the same  size1 and at the same distance
 from the eye1 these circular summits1  
or  sections of the cone1 are precisely 
in the same circumstances as the  moon  
in the three positions already          
mentioned4 ,if we now contemplate  them 
in the lenticular stereoscope1 we shall 
see the circular summit of  the hollow  
cone the largest1 like the horizontal   
moon1 because  it seems to be at the    
greatest distance from the eye1--the    
circular  summit of the raised cone the 
smallest1 because it appears at  the    
least distance1 like the zenith or      
culminating moon1--and the  circular    
summits of the flat cones on each side1 
of an intermediate  size1 like the moon 
at an intermediate altitude1 because    
their  distance from the eye is         

intermediate4 ,the same effect will be  
equally  well seen by placing three     
small wafers of the same size and colour
 on  the square summits of the drawings 
of the quadrangular pyramids1 or  more  
simply1 by observing the larger size of 
the square summit of the  hollow        
pyramid4    ,this explanation of the    
cause of the increased size of the      
horizontal  moon is rigorously correct4 
,if any person should suspect that the  
circles which represent the moon are    
unequal in size1 or are at  different   
distances from the eye1 they have only  
to cut the diagram  into three parts1   
and make each drawing of the frustum of 
the cone  occupy a different place in   
the binocular slide1 and they will      
obtain  the very same results4 ,hence we
 place beyond a doubt the incorrectness 
of ,dr4 ,berkeley's theory of the size  
of the horizontal moon1--a theory  to   
which the stereoscope enables us to     
apply another test1 for if we  make one 
or more of these circles less bright    

than the rest1 no change  whatever will 
be produced in their apparent magnitude4
          ,,chapter ,,xiv4              
,,application ,,of ,,the ,,stereoscope  
,,to ,,purposes ,,of ,,amusement4       
,every experiment in science1 and every 
instrument depending on  scientific     
principles1 when employed for the       
purpose of amusement1 must  necessarily 
be instructive4 8,philosophy in sport0  
never fails to become  8,science in     
earnest40 ,the toy which amuses the     
child will instruct  the sage1 and many 
an eminent discoverer and inventor can  
trace the  pursuits which immortalize   
them to some experiment or instrument   
which  amused them at school4 ,the soap 
bubble1 the kite1 the balloon1 the      
water wheel1 the sun-dial1 the          
burning-glass1 the magnet1 c41 have all 
been valuable incentives to the study of
 the sciences4    ,in a list of about   
#aej binocular pictures issued by the   
,london  ,stereoscopic ,company1 under  
the title of 8,miscellaneous ,subjects  

of the  #8,wilkie' character10 there are
 many of an amusing kind1 in which      
scenes  in common life are admirably    
represented4 ,following out the same    
idea1  the most interesting scenes in   
our best comedies and tragedies might   
be represented with the same            
distinctness and relief as if the actors
  were on the stage4 ,events and scenes 
in ancient and modern history  might be 
similarly exhibited1 and in our day1    
binocular pictures of  trials1          
congresses1 political1 legislative1 and 
religious assemblies1  in which the     
leading actors were represented1 might  
be provided for the  stereoscope4       
,for the purpose of amusement1 the      
photographer might carry us even  into  
the regions of the supernatural4 ,his   
art1 as ,i have elsewhere  shewn1       
enables him to give a spiritual         
appearance to one or more of his        
figures1 and to exhibit them as 8thin   
air0 amid the solid realities of  the   
stereoscopic picture4 ,while a party is 

engaged with their whist or  their      
gossip1 a female figure appears in the  
midst of them with all the  attributes  
of the supernatural4 ,her form is       
transparent1 every object  or person    
beyond her being seen in shadowy but    
distinct outline4 ,she  may occupy more 
than one place in the scene1 and        
different portions  of the group might  
be made to gaze upon one or other of the
 visions  before them4 ,in order to     
produce such a scene1 the parties which 
are  to compose the group must have     
their portraits nearly finished in the  
binocular camera1 in the attitude which 
they may be supposed to take1  and with 
the expression which they may be        
supposed to assume1 if the  vision were 
real4 ,when the party have nearly sat   
the proper length  of time1 the female  
figure1 suitably attired1 walks quickly 
into the  place assigned her1 and after 
standing a few seconds in the proper    
attitude1 retires quickly1 or takes as  
quickly1 a second or even a  third place

 in the picture if it is required1 in   
each of which she  remains a few        
seconds1 so that her picture in these   
different positions  may be taken with  
sufficient distinctness in the negative 
photograph4  ,if this operation has been
 well performed1 all the objects        
immediately  behind the female figure1  
having been1 previous to her            
introduction1  impressed upon the       
negative surface1 will be seen through  
her1 and  she will have the appearance  
of an aerial personage1 unlike the other
  figures in the picture4 ,this         
experiment may be varied in many ways4  
,one body may be placed within another1 
a chicken1 for example1 within  an egg1 
and singular effects produced by        
combining plane pictures  with solid    
bodies in the arrangement of the persons
 and things placed  before the binocular
 camera4 ,any individual in a group may 
appear more  than once in the same      
picture1 either in two or more          
characters1 and  no difficulty will be  

experienced by the ingenious            
photographer in  giving to these double 
or triple portraits1 when it is         
required1 the  same appearance as that  
of the other parties who have not       
changed their  place4 ,in groups of this
 kind curious effects might be produced 
by  placing a second binocular slide    
between the principal slide and the     
eye1 and giving it a motion within the  
stereoscope4 ,the figures upon  it must 
be delineated photographically upon a   
plate of glass1 through  which the      
figures on the principal slide are seen1
 and the secondary  slide must be so    
close to the other that the figures on  
both may be  distinctly visible1 if     
distinct vision is required for those   
which are  to move4    ,another method  
of making solid figures transparent in a
 photograph  has been referred to in the
 preceding chapter1 and may be employed 
in  producing amusing combinations4 ,the
 transparency is1 in this case1         
produced by using a large lens1 the     

margin of which receives the rays  which
 issue from bodies1 or parts of bodies1 
situated behind other  bodies1 or parts 
of bodies1 whose images are given in the
 photograph4  ,the body thus rendered   
transparent must be less in superficial 
extent  than the lens1 and the body seen
 through it must be so far behind it    
that rays emanating from it would fall  
upon some part of the lens1 the         
luminosity of this body on the          
photograph being proportional to the    
part of the surface of the lens upon    
which the rays fall4 ,this will be      
readily understood from ,figs4 #dh and  
#di1 and their description1 and  the    
ingenious photographer will have no     
difficulty in producing very  curious   
effects from this property of large     
object-glasses4    ,one of the most     
interesting applications of the         
stereoscope is in  combining binocular  
pictures1 constructed like the plane    
picture1 used  in what has been called  
the cosmorama for exhibiting dissolving 

views4 ,these plane pictures are so     
constructed1 that when we view  them by 
reflected light1 as pictures are        
generally viewed1 we see a  particular  
scene1 such as the ,chamber of ,deputies
 in its external  aspect2 but when we   
allow no light to fall upon it1 but view
 it by  transmitted light1 we see the   
interior of the building brilliantly    
lighted up1 and the deputies listening  
to the debate4 ,in like  manner1 the one
 picture may represent two armies in    
battle array1  while the other may      
represent them in action4 ,a cathedral  
in all its  architectural beauty may be 
combined with the same building in the  
act  of being burned to the ground2 or a
 winter scene covered with snow  may be 
conjoined with a landscape glowing with 
the warmth and verdure  of summer4 ,in  
the cosmorama1 the reflected light which
 falls upon  the front of the one       
picture is obtained by opening a lid    
similar to  that of the stereoscope1 as 
shewn at ,,cd1 ,fig4 #ad1 while another 

lid  opening behind the picture stops   
any light which might pass through  it1 
and prevents the second picture from    
being seen4 ,if1 when the  first picture
 is visible1 we gradually open the lid  
behind it1 and  close the lid ,,cd      
before it1 it gradually disappears1 or  
dissolves1  and the second picture      
gradually appears till the first        
vanishes and  the second occupies its   
place4 ,a great deal of ingenuity is    
displayed  by the ,parisian artists in  
the composition of these pictures1 and  
the  exhibition of them1 either in small
 portable instruments held in the  hand1
 or placed on the table1 or on a great  
scale1 to an audience1  by means of the 
oxygen and hydrogen light1 never fails  
to excite  admiration4    ,the pictures 
thus exhibited1 though finely executed1 
have only that  degree of relief which  
,i have called monocular1 and which     
depends  on correct shading and         
perspective2 but when the dissolving    
views are  obtained from binocular      

pictures1 and have all the high relief  
given  them by their stereoscopic       
combination1 the effect must be         
singularly  fine4    ,very interesting  
and amusing effects are produced by     
interchanging  the right and the left   
eye pictures in the stereoscope4 ,in    
general1  what was formerly convex is   
now concave1 what was round is hollow1  
and  what was near is distant4 ,the     
effect of this interchange is finely    
seen in the symmetrical diagrams1       
consisting of white lines upon black    
ground1 such as ,nos4 #a1 #e1 #i1 #ab1  
#ah and #bg of the ,parisian set2 but   
when the diagrams are not symmetrical1  
that is1 when the one half is  not the  
reflected image of the other1 such as   
,nos4 #bf1 c41 which are  transparent   
polygonal solids1 formed as it were by  
white threads or  wires1 no effect1     
beyond a slight fluttering1 is          
perceived4 ,as the  right and left eye  
pictures are inseparable when on glass  
or silver  plate1 the experiments must  

be made by cutting in two the slides on 
,bristol board4 ,this1 however1 is      
unnecessary when we have the power  of  
uniting the two pictures by the         
convergency of the optic axes to  a     
nearer point1 as we obtain1 in this     
case1 the same effect as if we  had     
interchanged the pictures4 ,the         
following are some of the results       
obtained in this manner from well-known 
slides3--    ,in single portraits no    
effect is produced by the interchange of
 the  right and left eye pictures4 ,if  
any loose part of the dress is in the   
foreground it may be carried into the   
distance1 and vice versa4 ,in  one      
portrait1 the end of the hat-band1 which
 hung down loosely behind  the party1   
was made to hang in front of it4    ,in 
pictures of streets or valleys1 and     
other objects in which the  foreground  
is connected with the middle-ground1 and
 the middle-ground  with the distance1  
without any break1 no effect is produced
 by the  interchange4 ,sometimes there  

is a little bulging out of the middle   
distance1 injurious to the monocular    
effect4    ,in the binocular picture of 
the ,bridge of ,handeck1 the ,chalet in 
the  foreground retires1 and the middle 
distance above it advances4    ,in the  
picture of the sacristy of ,notre ,dame1
 the sacristy retires  within the       
cathedral4    ,in the ,maison des       
,chapiteaux at ,pompeii1 the picture is 
completely  inverted1 the objects in the
 distance coming into the foreground4   
,in the ,daguerreotype of the ,crystal  
,palace1 the water in the  foreground1  
with the floating plants1 retires and   
takes an inclined  position below a     
horizontal plane4    ,in the binocular  
picture of the lower glacier of         
,rosenlaui1 the roof of  the ice-cave   
becomes hollow1 and the whole foreground
 is thrown into a  disordered           
perspective4    ,in ,copeland's ,venus1 
the arm holding the bunch of grapes is  
curiously  bent and thrown behind the   
head1 while the left arm advances before

 the  child4    ,in the picture of the  
,greek ,court in the ,crystal ,palace1  
the wall  behind the statues and columns
 advances in front of them4    ,the     
singular fallacy in vision which thus   
takes place is best seen in  a picture  
where a number of separate articles are 
placed upon a table1  and in other cases
 where the judgment of the spectator is 
not called  upon to resist the optical  
effect4 ,although the nose of the human 
face  should retire behind the ears yet 
no such effect is produced1 as all  the 
features of the face are connected with 
each other1 but if the nose  and ears   
had been represented separately in the  
position which they  occupy in the human
 head1 the nearer features would have   
retired behind  the more remote ones1   
like the separate articles on a table4  
,we shall have occasion to resume this  
subject in our concluding chapter  on   
the fallacies which take place in       
viewing solids1 whether raised or       
hollow1 and whether seen by direct or   

inverted vision4          ,,chapter     
,,xv4    ,,on ,,the ,,production ,,of   
,,stereoscopic ,,pictures ,,from ,a     
,,single ,,picture4      ,those who are 
desirous of having stereoscopic relievos
 of absent or  deceased friends1 and who
 possess single photographic portraits  
of  them1 or even oil paintings or      
miniatures1 will be anxious to know     
whether or not it is possible to obtain 
from one plane picture another  which   
could be combined with it in the        
stereoscope2 that is1 if we  consider   
the picture as one seen by either eye   
alone1 can we by any  process obtain a  
second picture as seen by the other eye8
 ,we have no  hesitation in saying that 
it is impossible to do this by any      
direct  process4    ,every picture1     
whether taken photographically or by the
 eye1 is  necessarily a picture seen by 
one eye1 or from one point of sight2    
and1  therefore1 a skilful artist1 who  
fully understands the principle of  the 
stereoscope1 might make a copy of any   

picture as seen by the other  eye1 so   
approximately correct as to appear in   
relief when united with  the original in
 the stereoscope2 but the task would be 
a very difficult  one1 and if well      
executed1 so as to give a relievo       
without distortion1  the fortune of the 
painter would be made4    ,when the     
artist executes a portrait1 he does it  
from one point of  sight1 which we may  
suppose fixed1 and corresponding with   
that which  is seen with his left eye4  
,if he takes another portrait of the    
same  person1 occupying exactly the same
 position1 from another point of  sight1
 two and a half inches to the right of  
himself1 as seen with  his right eye1   
the two pictures will differ only in    
this1 that  each point in the head1 and 
bust1 and drapery1 will1 in the second  
picture1 be carried farther to the left 
of the artist on the plane  of          
representation4 ,the points which       
project most1 or are most distant  from 
that plane1 will be carried farther to  

the left than those which  project less1
 the extent to which they are carried   
being proportional  to the amount of    
their projection1 or their distance from
 the plane4  ,but since the painter     
cannot discover from the original or    
left-eye  plane picture the degree of   
prominence of the leading points of the 
head1 the bust1 and the drapery1 he must
 work by guess1 and submit his          
empirical touches1 step by step1 to the 
judgment of the stereoscope4 ,in        
devoting himself to this branch of the  
art he will doubtless acquire  much     
knowledge and dexterity from experience1
 and may succeed to a very  considerable
 extent in obtaining pictures in relief1
 if he follows  certain rules1 which we 
shall endeavour to explain4    ,if the  
given portrait1 or picture of any kind1 
is not of the proper  size for the      
stereoscope1 it must be reduced to that 
size1 by taking  a photographic copy of 
it1 from which the right-eye picture is 
to be  drawn4    ,illustration3 ,,fig4  

#ej4    ,in order to diminish the size  
of the diagram1 let us suppose that the 
plane on which the portrait is taken    
touches the back of the head1  and is   
represented in section by ,,ab1 ,fig4   
#ej4 ,we must now assume1  under the    
guidance of the original1 a certain form
 of the head1 whose  breadth from ear to
 ear is ,,ee1 ,n being the point of the 
nose in the  horizontal section of the  
head1 ,e,,nen1 passing through the nose 
,n1 and  the lobes ,,ee of the two ears4
 ,let ,l1 ,r be the left and right eyes 
of  the person viewing them1 and ,,ln   
the distance at which they are viewed1  
and let lines be drawn from ,l and ,r1  
through ,l1 ,n1 ,e and ,e1 meeting  the 
plane ,,ab on which the portrait is     
taken in e1 ,e1 n1 ,n1 e1  and ,e4 ,the 
breadth1 ,ee1 and the distances of the  
nose from the  ears ,n,e1 ,n,e1 being   
given by measurement of the photograph  
suited  to the stereoscope1 the         
distances ,,nn1 ,,ee1 ,e,e may be       
approximately  obtained from the known  

form of the human head1 either by       
projection  or calculation4 ,with these 
data1 procured as correctly as we can1  
we  shall1 from the position of the nose
 n1 as seen by the right eye ,r1  have  
the formula                ,,lr  ,,nn   
,nn  ----------------                   
,,nl4      ,the distance of the right   
ear e1 from the right-eye picture1 will 
be1        ne  e,n - ,nn2               
,,lr  ,,ee      and as ,ee              
------------------                      
,,el4      ,the distance of the left ear
 e1 in the right-eye picture1 from the  
nose n1 will be        ne  ,nn  ,n,e -  
,ee4    ,in order to simplify the       
diagram we have made the original1 or   
left-eye  picture1 a front view1 in     
which the nose is in the middle of the  
face1  and the line joining the ears    
parallel to the plane of the picture4   
,when the position of the nose and the  
ears has been thus approximately        
obtained1 the artist may1 in like       
manner1 determine the place of the      

pupils of the two eyes1 the point of the
 chin1 the summit of the  eyebrows1 the 
prominence of the lips1 and the junction
 of the nose with  the teeth1 by        
assuming1 under the guidance of the     
original picture1  the distance of these
 different parts from the plane of      
projection4  ,in the same way other     
leading points in the figure and drapery
 may be  found1 and if these points are 
determined with tolerable accuracy the  
artist will be able to draw the features
 in their new place with such           
correctness as to give a good result in 
the stereoscope4    ,in drawing the     
right-eye picture the artist will1 of   
course1 employ as  the groundwork of it 
a faint photographic impression of the  
original1  or left-eye picture1 and he  
may1 perhaps1 derive some advantage from
  placing the original1 when before the 
camera1 at such an inclination  to the  
axis of the lens as will produce the    
same diminution in the  horizontal      
distance between any two points in the  

head1 at a mean  distance between ,n and
 ,n1 as projected upon the plane ,,ab4  
,the line  ,n,e1 for example1 which in  
the left-eye photograph is a            
representation  of the cheek ,,ne1 is   
reduced1 in the right-eye photograph1 to
 ne1  and1 therefore1 if the photograph 
on ,,ab1 as seen by the right eye1 were 
placed so obliquely to the axis of the  
lens that ,ne was reduced  to ne1 the   
copy obtained in the camera would have  
an approximate  resemblance to the      
right-eye picture required1 and might be
 a better  groundwork for the right-eye 
picture than an accurate copy of the    
photograph on ,,ab1 taken when it is    
perpendicular to the axis of the  lens4 
,in preparing the right-eye picture1 the
 artist1 in place of using  paint1 might
 use very dilute solutions of           
aceto-nitrate of silver1  beginning with
 the faintest tint1 and darkening these 
with light till  he obtained the desired
 effect1 and1 when necessary1           
diminishing the  shades with solutions  

of the hypo-sulphite of soda4 ,when the 
picture  is finished1 and found         
satisfactory1 after examining its relief
 in the  stereoscope1 a negative picture
 of it should be obtained in the camera1
  and positive copies taken1 to form1   
with the original photographs1 the  pair
 of binocular portraits required4       
,,chapter ,,xvi4    ,,on ,,certain      
,,fallacies ,,of ,,sight ,,in ,,the     
,,vision ,,of ,,solid ,,bodies4      ,in
 a preceding chapter ,i have explained a
 remarkable fallacy of sight  which     
takes place in the stereoscope when we  
interchange the binocular  pictures1    
that is1 when we place the right-eye    
picture on the left  side1 and the      
left-eye picture on the right side4 ,the
 objects in the  foreground of the      
picture are thus thrown into the        
background1 and1  vice versa1 the same  
effect1 as we have seen1 takes place    
when we  unite the binocular pictures1  
in their usual position1 by the ocular  
stereoscope1 that is1 by converging the 

optic axes to a point between  the eye  
and the pictures4 ,in both these cases  
the objects are only the  plane         
representations of solid bodies1 and the
 change which is produced  by their     
union is not in their form but in their 
position4 ,in certain  cases1 however1  
when the object is of some magnitude in 
the picture1  the form is also changed  
in consequence of the inverse position  
of  its parts4 ,that is1 the drawings of
 objects that are naturally convex  will
 appear concave1 and those which are    
naturally concave will appear  convex4  
,in these phenomena there is no mental  
illusion in their production4 ,the  two 
similar points in each picture1 if they 
are nearer to one another  than other   
two similar points1 must1 in conformity 
with the laws of  vision1 appear nearer 
the eye when combined in the common     
stereoscope4  ,when this change of place
 and form does not appear1 as in the    
case of  the human figure1 previously   
explained1 it is by a mental illusion   

that  the law of vision is controlled4  
,the phenomena which we are about to    
describe are1 in several respects1      
different from those to which we have   
referred4 ,they are seen in  monocular  
as well as in binocular vision1 and they
 are produced  in all cases under a     
mental illusion1 arising either from    
causes over  which we have no control1  
or voluntarily created and maintained by
  the observer4 ,the first notice of    
this class of optical illusion was      
given by ,aguilonius in his work on     
optics1 to which we have already  had   
occasion to refer4#fi ,after proving    
that convex and concave  surfaces appear
 plane when seen at a considerable      
distance1 he shews  that the same       
surfaces1 when seen at a moderate       
distance1 frequently  appear what he    
calls converse1 that is1 the concave    
convex1 and the  convex concave4 ,this  
conversion of forms1 he says1 is often  
seen in  the globes or balls which are  
fixed on the walls of fortifications1   

and he ascribes the phenomena to the    
circumstance of the mind being  imposed 
upon from not knowing in what direction 
the light falls upon  the body4 ,he     
states that a concavity differs from a  
convexity only  in this respect1 that if
 the shadow is on the same side as that 
from  which the light comes it is a     
concavity1 and if it is on the opposite 
side1 it is a convexity4 ,aguilonius    
observes also1 that in pictures         
imitating nature1 a similar mistake is  
committed as to the form of  surfaces4  
,he supposes that a circle is drawn upon
 a table and shaded  on one side so as  
to represent a convex or a concave      
surface4 ,when this  shaded circle is   
seen at a great distance1 it appears a  
plane surface1  notwithstanding the     
shadow on one side of it2 but when we   
view it at  a short distance1 and       
suppose the light to come from the same 
side of  it as the part not in shadow1  
the plane circle will appear to be a    
convexity1 and if we suppose the light  

to come from the same side as  the      
shaded part1 the circle will appear to  
be a concavity4    #fi ,see ,chap4 i4 p4
 #ae4    ,more than half a century after
 the time of ,aguilonius1 a member of   
the  ,royal ,society of ,london1 at one 
of the meetings of that body1 when      
looking at a guinea through a compound  
microscope which inverted the  object1  
was surprised to see the head upon the  
coin depressed1 while  other members    
were not subject to this illusion4      
,dr4 ,philip ,gmelin#gj of ,wurtemberg1 
having learned from a friend1  that when
 a common seal is viewed through a      
compound microscope1 the  depressed part
 of the seal appeared elevated1 and the 
elevated part  depressed1 obtained the  
same result1 and found1 as ,aguilonius  
did1 that  the effect was owing to the  
inversion of the shadow by the          
microscope4  ,one person often saw the  
phenomena and another did not1 and no   
effect  was produced when a raised      
object was so placed between two windows

 as  to be illuminated on all sides4    
#gj ,phil4 ,trans4 #agdd4    ,in #aghj  
,mr4 ,rittenhouse1 an ,american writer1 
repeated these experiments  with an     
inverting eye-tube1 consisting of two   
lenses placed at a  distance greater    
than the sum of their focal lengths1 and
 he found that  when a reflected light  
was thrown on a cavity1 in a direction  
opposite  to that of the light which    
came from his window1 the cavity was    
raised  into an elevation by looking    
through a tube without any lens4 ,in    
this  experiment the shadow was         
inverted1 just as if he had looked      
through  his inverting eye-tube4    ,in 
studying this subject ,i observed a     
number of singular phenomena1  which ,i 
have described in my ,letters on        
,natural ,magic1#ga but as  they were   
not seen by binocular vision ,i shall   
mention only some of  the more important
 facts4 ,if we take one of the intaglio 
moulds used  by the late ,mr4 ,henning  
for his bas-reliefs1 and direct the eye 

to it  steadily1 without noticing       
surrounding objects1 we may distinctly  
see  it as a bas-relief4 ,after a little
 practice ,i have succeeded in raising  
a complete hollow mask of the human     
face1 the size of life1 into a          
projecting head4 ,this result is very   
surprising to those who succeed in  the 
experiment1 and it will no doubt be     
regarded by the sculptor who  can use it
 as an auxiliary in his art4    #ga     
,letter v4 pp4 #ih-ajg4 ,see also the   
,edinburgh ,journal of  ,science1 ,jan4 
#ahbf1 vol4 iv4 p4 #ii4    ,till within 
the last few years1 no phenomenon of    
this kind1 either  as seen with one or  
with two eyes1 had been noticed by the  
casual  observer4 ,philosophers alone   
had been subject to the illusion1 or    
had subjected others to its influence4  
,the following case1 however1  which    
occurred to ,lady ,georgiana ,wolff1    
possesses much interest1 as it  could   
not possibly have been produced by any  
voluntary effort4 8,lady  ,georgiana10  

says ,dr4 ,joseph ,wolff in his         
,journal1 8observed a curious  optical  
deception in the sand1 about the middle 
of the day1 when the  sun was strong3   
all the foot-prints1 and other marks    
that are indented  in the sand1 had the 
appearance of being raised out of it4   
,at these  times there was such a glare1
 that it was unpleasant for the eye40#gb
  ,having no doubt of the correctness of
 this observation1 ,i have often        
endeavoured1 though in vain1 to witness 
so remarkable a phenomenon4  ,in        
walking1 however1 in the month of ,march
 last1 with a friend on the  beach at   
,st4 ,andrews1 the phenomenon presented 
itself1 at the same  instant1 to myself 
and to a lady who was unacquainted with 
this class  of illusions4 ,the          
impressions of the feet of men and of   
horses were  distinctly raised out of   
the sand4 ,in a short time they resumed 
their  hollow form1 but at different    
places the phenomenon again presented   
itself1 sometimes to myself1 sometimes  

to the lady1 and sometimes  to both of  
us simultaneously4 ,the sun was near the
 horizon on our  left hand1 and the     
white surf of the sea was on our right1 
strongly  reflecting the solar rays4 ,it
 is very probable that the illusion     
arose  from our considering the light as
 coming from the white surf1 in which   
case the shadows in the hollow          
foot-prints were such as could only  be 
produced by foot-prints raised from the 
sand1 as if they were in  relief4 ,it is
 possible that1 when the phenomenon was 
observed by ,lady  ,georgiana ,wolff1   
there may have been some source of      
direct or reflected  light opposite to  
the sun1 or some unusual brightness of  
the clouds1 if  there were any in that  
quarter1 which gave rise to the         
illusion4    #gb ,journal1 #ahci1 p1    
#ahi4    ,when these illusions1 whether 
monocular or binocular1 are produced by 
an inversion of the shadow1 either real 
or supposed1 they are instantly         
dissipated by holding a pin in the field

 of view1 so as to indicate by  its     
shadow the real place of the            
illuminating body4 ,the figure will     
appear raised or depressed1 according to
 the knowledge which we obtain  of the  
source of light1 by introducing or      
withdrawing the pin4 ,when the          
inversion is produced by the eye-piece  
of a telescope1 or a compound           
microscope1 in which the field of view  
is necessarily small1 we cannot  see the
 illuminating body and the convex or    
concave object 7the  cameo or intaglio7 
at the same time2 but if we use a small 
inverting  telescope1 #a or #b inches   
long1 such as that shewn at ,,mn1 ,fig4 
#cf1 we  obtain a large field of view1  
and may see at the same time the object 
and a candle placed beside it4 ,in this 
case the illusion will take  place      
according as the candle is seen beside  
the object or withdrawn4    ,if the     
object is a white tea-cup1 or bowl1     
however large1 and if it is  illuminated
 from behind the observer1 the reflected

 image of the window  will be in the    
concave bottom of the tea-cup1 and it   
will not rise into  a convexity if the  
illumination from surrounding objects is
 uniform2  but if the observer moves a  
little to one side1 so that the         
reflected  image of the window passes   
from the centre of the cup1 then the cup
  will rise into a convexity1 when seen 
through the inverting telescope1  in    
consequence of the position of the      
luminous image1 which could  occupy its 
place only upon a convex surface4 ,if   
the concave body were  cut out of a     
piece of chalk1 or pure unpolished      
marble1 it would appear  neither convex 
nor concave1 but flat4    ,very singular
 illusions take place1 both with one and
 two eyes1 when  the object1 whether    
concave or convex1 is a hollow or an    
elevation  in or upon a limited or      
extended surface--that is1 whether the  
surface occupies the whole visible      
field1 or only a part of it4 ,if  we    
view1 through the inverting telescope or

 eye-piece1 a dimple or a  hemispherical
 cavity in a broad piece of wood laid   
horizontally on the  table1 and         
illuminated by quaquaversus light1 like 
that of the sky1  it will instantly rise
 into an elevation1 the end of the      
telescope or  eye-piece resting on the  
surface of the wood4 ,the change of form
 is1  therefore1 not produced by the    
inversion of the shadow1 but by another 
cause4 ,the surface in which the cavity 
is made is obviously inverted  as well  
as the cavity1 that is1 it now looks    
downward in place of  upward2 but it    
does not appear so to the observer      
leaning upon the  table1 and resting the
 end of his eye-piece upon the wooden   
surface in  which the cavity is made4   
,the surface seems to him to remain     
where it  was1 and still to look        
upwards1 in place of looking downwards4 
,if the  observer strikes the wooden    
surface with the end of the eye-piece1  
this  conviction is strengthened1 and he
 believes that it is the lower edge  of 

the field of view1 or object-glass1 that
 strikes the apparent wooden  surface or
 rests upon it1 whereas the wooden      
surface has been inverted1  and         
optically separated from the lower edge 
of the object-glass4    ,in order to    
make this plainer1 place a pen upon a   
sheet of paper with  the quill end      
nearest you1 and view it through the    
inverting telescope3  ,the quill end    
will appear farthest from you1 and the  
paper will not  appear inverted4 ,in    
like manner1 the letters on a printed   
page are  inverted1 the top of each     
letter being nearest the observer1 while
 the  paper seems to retain its usual   
place4 ,now in both these cases the     
paper is inverted as well as the quill  
and the letters1 and in reality  the    
image of the quill and of the pen1 and  
of the lower end of the  letters1 is    
nearest the observer4 ,let us next place
 a tea-cup on its  side upon the table1 
with its concavity towards the observer1
 and view  it through the inverting     

telescope4 ,it will rise into a         
convexity1 the  nearer margin of the cup
 appearing farther off than the bottom4 
,if we  place a short pen within the    
cup1 measuring as it were its depth1 and
  having its quill end nearest the      
observer1 the pen will be inverted1  in 
correspondence with the conversion of   
the cup into a convexity1 the  quill end
 appearing more remote1 like the margin 
of the cup which it  touches1 and the   
feather end next the eye like the summit
 of the convex  cup on which it rests4  
,in these experiments1 the conversion of
 the concavity into a convexity  depends
 on two separate illusions1 one of which
 springs from the other4  ,the first    
illusion is the erroneous conviction    
that the surface of  the table is       
looking upwards as usual1 whereas it is 
really inverted2  and the second        
illusion1 which arises from the first1  
is1 that the  nearest point of the      
object appears farthest from the eye1   
whereas  it is nearest to it4 ,all these

 observations are equally applicable to 
the vision of convexities1 and hence it 
follows1 that the conversion of  relief1
 caused by the use of an inverting      
eye-piece1 is not produced  directly by 
the inversion1 but by an illusion       
arising from the  inversion1 in virtue  
of which we believe that the remotest   
side of the  convexity is nearer our eye
 than the side next us4    ,in order to 
demonstrate the correctness of this     
explanation1 let the  hemispherical     
cavity be made in a stripe of wood1     
narrower than the  field of the         
inverting telescope with which it is    
viewed4 ,it will then  appear really    
inverted1 and free from both the        
illusions which formerly  took place4   
,the thickness of the stripe of wood is 
now distinctly seen1  and the inversion 
of the surface1 which now looks         
downward1 immediately  recognised4 ,the 
edge of the cavity now appears nearest  
the eye1 as  it really is1 and the      
concavity1 though inverted1 still       

appears a  concavity4 ,the same effect  
is produced when a convexity is placed  
on a  narrow stripe of wood4    ,some   
curious phenomena take place when we    
view1 at different degrees  of          
obliquity1 a hemispherical cavity raised
 into a convexity4 ,at every  degree of 
obliquity from #j to #ij1 that is1 from 
a vertical to a  horizontal view of it1 
the elliptical margin of the convexity  
will  always be visible1 which is       
impossible in a real convexity1 and the 
elevated apex will gradually sink till  
the elliptical margin becomes  a        
straight line1 and the imaginary        
convexity completely levelled4  ,the    
struggle between truth and error is here
 so singular1 that while  one part of   
the object has become concave1 the other
 part retains its  convexity6    ,in    
like manner1 when a convexity is seen as
 a concavity1 the concavity  loses its  
true shape as it is viewed more and more
 obliquely1 till  its remote elliptical 
margin is encroached upon1 or eclipsed1 

by the  apex of the convexity2 and      
towards an inclination of #ij the       
concavity  disappears altogether1 under 
circumstances analogous to those already
  described4    ,if in place of using an
 inverting telescope we invert the      
concavity1 by  looking at its inverted  
image in the focus of a convex lens1 it 
will  sometimes appear a convexity and  
sometimes not4 ,in this form of the     
experiment the image of the concavity1  
and consequently its apparent  depth1 is
 greatly diminished1 and therefore any  
trivial cause1 such  as a preconception 
of the mind1 or an approximation to a   
shadow1 or a  touch of the concavity by 
the point of the finger1 will either    
produce  a conversion of form or        
dissipate the illusion when it is       
produced4    ,in the preceding ,chapter 
we have supposed the convexity to be    
high and  the concavity deep and        
circular1 and we have supposed them also
 to be  shadowless1 or illuminated by a 
quaquaversus light1 such as that  of the

 sky in the open fields4 ,this was done 
in order to get rid of  all secondary   
causes which might interfere with and   
modify the normal  cause1 when the      
concavities are shallow1 and the        
convexities low and  have distinct      
shadows1 or when the concavity1 as in   
seals1 has the  shape of an animal or   
any body which we are accustomed to see 
in relief4    ,let us now suppose that a
 strong shadow is thrown upon the       
concavity4 ,in this case the normal     
experiment is much more perfect  and    
satisfactory4 ,the illusion is complete 
and invariable when the  concavity is in
 or upon an extended surface1 and it as 
invariably  disappears1 or rather is not
 produced1 when it is in a narrow       
stripe4    ,in the secondary forms of   
the experiment1 the inversion of the    
shadow  becomes the principal cause of  
the illusion2 but in order that the     
result may be invariable1 or nearly so1 
the concavities must be shallow  and the
 convexities but slightly raised4 ,at   

great obliquities1 however1  this cause 
of the conversion of form ceases to     
produce the illusion1  and in varying   
the inclination from #j to #ij the      
cessation takes place  sooner with deep 
than with shallow cavities4 ,the reason 
of this is that  the shadow of a        
concavity is very different at great    
obliquities from  the shadow of a       
convexity4 ,the shadow never can emerge 
out of a cavity  so as to darken the    
surface in which the cavity is made1    
whereas the  shadow of a convexity soon 
extends beyond the outline of its base1 
and  finally throws a long stripe of    
darkness over the surface on which it   
rests4 ,hence it is impossible to       
mistake a convexity for a concavity     
when its shadow extends beyond its base4
    ,when the concavity upon a seal is a
 horse1 or any other animal1 it will    
often rise into a convexity when seen   
through a single lens1 which  does not  
invert it2 but the illusion disappears  
at great obliquities4  ,in this case1   

the illusion is favoured or produced by 
two causes2 the  first is1 that the form
 of the horse or other animal in relief 
is the  one which the mind is most      
disposed to seize1 and the second is1   
that  we use only one eye1 with which we
 cannot measure depths as well as  with 
two4 ,the illusion1 however1 still takes
 place when we employ a  lens three or  
more inches wide1 so as to permit the   
use of both eyes1  but it is less       
certain1 as the binocular vision enables
 us in some  degree to keep in check the
 other causes of illusion4    ,the      
influence of these secondary causes is  
strikingly displayed in the  following  
experiment4 ,in the armorial bearings   
upon a seal1 the shield  is often more  
deeply cut than the surrounding parts4  
,with binocular  vision1 the shallow    
parts rise into relief sooner than the  
shield1 and  continue so while the      
shield remains depressed2 but if we shut
 one eye  the shield then rises into    
relief like the rest4 ,in these         

experiments  with a single lens a slight
 variation in the position of the seal1 
or  a slight change in the intensity or 
direction of the illumination1  or      
particular reflexions from the interior 
of the stone1 if it is  transparent1    
will favour or oppose the illusion4 ,in 
viewing the shield  at the deepest      
portion with a single lens1 a slight    
rotation of the  seal round the wrist1  
backwards and forwards1 will remove the 
illusion1  in consequence of the eye    
perceiving that the change in the       
perspective  is different from what it  
ought to be4    ,in my ,letters on      
,natural ,magic1 ,i have described      
several cases of  the conversion of form
 in which inverted vision is not        
employed4  ,hollows in mother-of-pearl  
and other semi-transparent bodies often 
rise into relief1 in consequence of a   
quantity of light1 occasioned by        
refraction1 appearing on the side next  
the light1 where there should  have been
 a shadow in the case of a depression4  

,similar illusions take  place in       
certain pieces of polished wood1        
calcedony1 mother-of-pearl1  and other  
shells1 where the surface is perfectly  
plane4 ,this arises  from there being at
 that place a knot1 or growth1 or       
nodule1 differing  in transparency from 
the surrounding mass4 ,the thin edge of 
the knot1  c41 opposite the candle1 is  
illuminated by refracted light1 so that 
it takes the appearance of a concavity4 
,from the same cause arises  the        
appearance of dimples in certain plates 
of calcedony1 which have  received the  
name of hammered calcedony1 or agate1   
from their  having the look of being    
dimpled with a hammer4 ,the surface on  
which  these cavities are seen contains 
sections of small spherical formations  
of siliceous matter1 which exhibit the  
same illusion as the cavities  in wood4 
,mother-of-pearl presents similar       
phenomena1 and so common are  they in   
this substance that it is difficult to  
find a mother-of-pearl  button or       

counter which seems to have its surface 
flat1 although it  is perfectly so when 
examined by the touch4 ,owing to the    
different  refractions of the incident  
light by the different growths of the   
shell1 cut in different directions by   
the artificial surface1 like the  annual
 growth of wood in a dressed plank1 the 
surface of the mineral  has necessarily 
an inequal and undulating appearance4   
,in viewing good photographic or        
well-painted miniature portraits in an  
erect and inverted position1 and with or
 without a lens1 considerable  changes  
take place in the apparent relief4      
,under ordinary vision there  is a      
certain amount of relief depending upon 
the excellence of the  picture4 ,if we  
invert the picture1 by turning it upside
 down1 the  relief is perceptibly       
increased4 ,if we view it when erect1   
with a  lens of about an inch in focal  
length1 the relief is still greater2    
but if we view it when inverted with the
 same lens the relief is very           

considerably diminished4                
,illustration3 ,,fig4 #ea4    ,a very   
remarkable illusion1 affecting the      
apparent position of the  drawings of   
geometrical solids1 was first observed  
by the late  ,professor ,neckar1 of     
,geneva1 who communicated it to me      
personally in  #ahcb4gc 8,the rhomboid  
,,ax10 7,fig4 #ea17 he says1 8is drawn  
so that the  solid angle ,a should be   
seen nearest to the spectator1 and the  
solid  angle ,x the farthest from him1  
and that the face ,,acbd should be the  
foremost1 while the face ,,xdc is       
behind4 ,but in looking repeatedly at   
the same figure1 you will perceive that 
at times the apparent position  of the  
rhomboid is so changed that the solid   
angle ,x will appear the  nearest1 and  
the solid angle ,a the farthest1 and    
that the face ,,acdb  will recede behind
 the face ,,xdc1 which will come        
forward1--which effect  gives to the    
whole solid a quite contrary apparent   
inclination40  ,professor ,neckar       

observed this change 8as well with one  
as with both  eyes10 and he considered  
it as owing 8to an involuntary change in
 the  adjustment of the eye for         
obtaining distinct vision4 ,and that    
whenever  the point of distinct vision  
on the retina was directed to the angle 
,a for instance1 this angle1 seen more  
distinctly than the other1 was          
naturally supposed to be nearer and     
foremost1 while the other angles1  seen 
indistinctly1 were supposed to be       
farther away and behind4 ,the  reverse  
took place when the point of distinct   
vision was brought to  bear upon the    
angle ,x4 ,what ,i have said of the     
solid angles 7,a and  ,x7 is equally    
true of the edges1 those edges upon     
which the axis of  the eye1 or the      
central hole of the retina1 are         
directed1 will always  appear forward2  
so that now it seems to me certain that 
this little1 at  first so puzzling1     
phenomenon depends upon the law of      
distinct vision40    #gc ,see ,edinburgh

 ,philosophical ,journal1 ,november     
#ahcb1 vol4 i4 p4  #ccd4    ,in         
consequence of completely               
misunderstanding ,mr4 ,neckar's         
explanation  of this illusion1 ,mr4     
,wheatstone has pronounced it to be     
erroneous1  but there can be no doubt of
 its correctness2 and there are various 
experiments by which the principle may  
be illustrated4 ,by hiding with  the    
finger one of the solid angles1 or      
making it indistinct1 by  a piece of    
dimmed glass1 or throwing a slight      
shadow over it1 the  other will appear  
foremost till the obscuring cause is    
removed4 ,the  experiment may be still  
more satisfactorily made by holding     
above the  rhomboid a piece of finely   
ground-glass1 the ground side being     
farthest  from the eye1 and bringing one
 edge of it gradually down till it      
touches the point ,a1 the other edge    
being kept at a distance from the       
paper4 ,in this way all the lines       
diverging from ,a will become dimmer  as

 they recede from ,a1 and consequently  
,a will appear the most forward  point4 
,a similar result will be obtained by   
putting a black spot upon  ,a1 which    
will have the effect of drawing our     
attention to ,a rather than  to ,x4     
,from these experiments and             
observations1 it will be seen that the  
conversion of form1 excepting in the    
normal case1 depends upon various       
causes1 which are influential only under
 particular conditions1 such as  the    
depth of the hollow or the height of the
 relief1 the distance of  the object1   
the sharpness of vision1 the use of one 
or both eyes1 the  inversion of the     
shadow1 the nature of the object1 and   
the means used  by the mind itself to   
produce the illusion4 ,in the normal    
case1 where  the cavity or convexity is 
shadowless1 and upon an extended        
surface1  and where inverted vision is  
used1 the conversion depends solely on  
the  illusion1 which it is impossible to
 resist1 that the side of the cavity  or

 elevation next the eye is actually     
farthest from it1 an illusion not       
produced by inversion1 but by a false   
judgment respecting the position  of the
 surface in which the cavity is made1 or
 upon which it rests4          ,,chapter
 ,,xvii4    ,,on ,,certain              
,,difficulties ,,experienced ,,in ,,the 
,,use ,,of ,,the ,,stereoscope4         
,there are many persons who experience  
great difficulty in uniting the  two    
pictures in the stereoscope1 and        
consequently in seeing the relief       
produced by their union4 ,if the eyes   
are not equal in focal length1  that is1
 in the distance at which they see      
objects most distinctly2  or if1 from   
some defect in structure1 they are not  
equally good1 they  will still see the  
stereoscopic relief1 though the picture 
will be  less vivid and distinct than if
 the eyes were in every respect equal   
and good4 ,there are many persons1      
however1 whose eyes are equal and       
perfect1 but who are not able to unite  

the pictures in the stereoscope4  ,this 
is the more remarkable1 as children of  
four or five years of age  see the      
stereoscopic effect when the eye-tubes  
are accommodated to the  distance       
between their eyes4 ,the difficulty     
experienced in uniting the  binocular   
pictures is sometimes only temporary4   
,on first looking into  the instrument1 
two pictures are seen in place of one2  
but by a  little perseverance1 and by   
drawing the eyes away from the          
eye-tubes1  and still looking through   
them1 the object is seen single and in  
perfect relief4 ,after having ceased to 
use the instrument for some  time1 the  
difficulty of uniting the pictures      
recurs1 but1 generally  speaking1 it    
will gradually disappear4               
,illustration3 ,,fig4 #eb4    ,in those 
cases where it cannot be overcome by    
repeated trials1 it  must arise either  
from the distance between the lenses    
being greater  or less than the distance
 between the eyes1 or from some         

peculiarity  in the power of converging 
the optical axes1 which it is not easy  
to  explain4    ,if the distance between
 the pupils of the two eyes1 ,e1 ,e1    
,fig4 #eb1  which has been already      
explained on ,fig4 #ah1 is less than the
  distance between the semi-lenses ,l1  
,l1 then1 instead of looking  through   
the middle portions no1 no1 of the      
lenses1 the observer  will look through 
portions between o and ,l1 and o and ,l1
 which  have a greater power of         
refracting or displacing the pictures   
than  the portions no1 no1 and therefore
 the pictures will be too much          
displaced1 and will have so far         
overpassed one another that the         
observer is not able to bring them back 
to their place of union1  half-way      
between the two pictures in the slide4  
,if1 on the other hand1 the distance    
between the pupils of the  observer's   
eyes is greater than the distance       
between the semi-lenses  ,l1 ,l1 then1  
instead of looking through the portions 

no1 no of the  lenses1 the observer will
 look through portions between n and ,l1
 and  n and ,l1 which have a less power 
of refracting or displacing the         
pictures than the portions no1 no1 and  
therefore the pictures will  be so      
little displaced as not to reach their  
place of union1 and will  stand at such 
a distance that the observer is not able
 to bring them  up to their proper      
place1 half-way between the two pictures
 in the  slide4    ,now1 in both these  
cases of over and under displacement1   
many  persons have such a power over    
their optical axes1 that by converging  
them to a point nearer than the picture1
 they would1 in the first  case1 bring  
them back to their place of union1 and  
by converging them  to a point more     
remote than the picture1 would1 in the  
second case1  bring them up to their    
place of union2 but others are very     
defective  in this power of convergence1
 some having a facility of converging   
them  beyond the pictures1 and others   

between the pictures and the eye4 ,this 
last1 however1 namely1 that of near     
convergence1 is by far the most  common1
 especially among men2 but it is of no  
avail1 and the exercise  of it is       
injurious when the under refracted      
pictures have not come up  to their     
place of union4 ,the power of remote    
convergence1 which is  very rare1 and   
which would assist in bringing back the 
over refracted  pictures to their place 
of union1 is of no avail1 and the       
exercise of  it is injurious when the   
pictures have been too much displaced1  
and  made to pass beyond their place of 
union4    ,when the stereoscope is      
perfectly adapted to the eyes of the    
observer1  and the general union of the 
pictures effected1 the remote parts  of 
the picture1 that is1 the objects seen  
in the distance1 may be  under          
refracted1 while those in the foreground
 are over refracted1  so that while eyes
 which have the power of convergence    
beyond the  picture1 unite the more     

distant objects which are under         
refracted1 they  experience much        
difficulty in uniting those in the      
foreground which  are over refracted4   
,in like manner1 eyes which have the    
power of near  convergence will readily 
unite objects in the foreground which   
are over  refracted1 while they         
experience much difficulty in uniting   
objects in  the distance which are under
 refracted4 ,if the requisite power over
 the  optical axes is not acquired by   
experience and perseverance1 when the   
stereoscope is suited to the eyes of the
 observer1 the only suggestion  which we
 can make is to open the eyes wide1 and 
expand the eyebrows1  which we do in    
staring at an object1 or in looking at a
 distant one1  when we wish to converge 
the axes1 as in ,fig4 #bb1 to a point   
beyond  the pictures1 and to contract   
the eyes and the eyebrows1 which we do  
in  too much light1 in looking at a near
 object1 when we wish to converge  the  
optic axes1 as in ,fig4 #ba1 to a point 

between the pictures and  the eye4      
,when the binocular pictures are taken  
at too great an angle1 so as to  produce
 a startling amount of relief1 the      
distance between similar  points in each
 picture1 both in the distance and in   
the foreground1 is  much greater than it
 ought to be1 and hence the difficulty  
of uniting  the pictures is greatly     
increased1 so that persons who would    
have  experienced no difficulty in      
uniting them1 had they been taken at the
  proper angle1 will fail altogether in 
bringing them into stereoscopic  relief4
    ,in these observations1 it is       
understood that the observer obtains    
distinct vision of the pictures in the  
stereoscope1 either by the  adjustment  
of the moveable eye-tubes1 if they are  
moveable1 as they  ought to be1 or by   
the aid of convex or concave glasses for
 both eyes1  either in the form of      
spectacles1 or separate lenses placed   
immediately  above1 or immediately below
 the semi-lenses in the eye-tubes4 ,if  

the  eyes have different focal lengths1 
which is not unfrequently the case1     
lenses differing in convexity or        
concavity should be employed to         
equalize them4    ,,edinburgh3 ,t4      
,,constable1 ,,printer ,,to ,,her       
,,majesty4