,,scientific ,,romances4                
,,by                             ,c4 ,h4
 ,,hinton1 ,b4,a4      ,what is the     
,fourth ,dimension8    ,the ,persian    
,king4    ,a ,plane ,world4    ,a       
,picture of ,our ,universe4    ,casting 
,out the ,self4      ,illustration3     
,,first ,,series4                       
,london4                       ,,swan   
,,sonnenschein  ,,co41 ,,lim41          
,paternoster ,square4                   
#ahhf4                                  
,what is the ,fourth ,dimension8        
,,chapter ,i4    ,at the present time   
our actions are largely influenced by   
our theories4  ,we have abandoned the   
simple and instinctive mode of life of  
the earlier  civilisations for one      
regulated by the assumptions of our     
knowledge and  supplemented by all the  
devices of intelligence4 ,in such a     
state it is  possible to conceive that a
 danger may arise1 not only from a want 
of  knowledge and practical skill1 but  
even from the very presence and         

possession of them in any one           
department1 if there is a lack of       
information in other departments4 ,if1  
for instance1 with our present          
knowledge of physical laws and          
mechanical skill1 we were to build      
houses  without regard to the conditions
 laid down by physiology1 we should     
probably--to suit an apparent           
convenience--make them perfectly        
draught-tight1 and the best-constructed 
mansions would be full of  suffocating  
chambers4 ,the knowledge of the         
construction of the body and  the       
conditions of its health prevent it from
 suffering injury by the  development of
 our powers over nature4    ,in no      
dissimilar way the mental balance is    
saved from the dangers  attending an    
attention concentrated on the laws of   
mechanical science by  a just           
consideration of the constitution of the
 knowing faculty1 and the  conditions of
 knowledge4 ,whatever pursuit we are    
engaged in1 we are  acting consciously  

or unconsciously upon some theory1 some 
view of  things4 ,and when the limits of
 daily routine are continually narrowed 
by  the ever-increasing complication of 
our civilisation1 it becomes doubly     
important that not one only but every   
kind of thought should be shared  in4   
,there are two ways of passing beyond   
the domain of practical certainty1  and 
of looking into the vast range of       
possibility4 ,one is by asking1  8,what 
is knowledge8 ,what constitutes         
experience80 ,if we adopt this  course  
we are plunged into a sea of            
speculation4 ,were it not that the      
highest faculties of the mind find      
therein so ample a range1 we should     
return to the solid ground of facts1    
with simply a feeling of relief at      
escaping from so great a confusion and  
contradictoriness4    ,the other path   
which leads us beyond the horizon of    
actual experience is  that of           
questioning whatever seems arbitrary and
 irrationally limited in  the domain of 

knowledge4 ,such a questioning has often
 been successfully  applied in the      
search for new facts4 ,for a long time  
four gases were  considered incapable of
 being reduced to the liquid state4 ,it 
is but  lately that a physicist has     
succeeded in showing that there is no   
such  arbitrary distinction among gases4
 ,recently again the question has been  
raised1 8,is there not a fourth state of
 matter80 ,solid1 liquid1 and  gaseous  
states are known4 ,mr4 ,crookes attempts
 to demonstrate the  existence of a     
state differing from all of these4 ,it  
is the object of  these pages to show   
that1 by supposing away certain         
limitations of the  fundamental         
conditions of existence as we know it1 a
 state of being can  be conceived with  
powers far transcending our own4 ,when  
this is made  clear it will not be out  
of place to investigate what relations  
would  subsist between our mode of      
existence and that which will be seen to
 be  a possible one4    ,in the first   

place1 what is the limitation that we   
must suppose away8    ,an observer      
standing in the corner of a room has    
three directions  naturally marked out  
for him2 one is upwards along the line  
of meeting  of the two walls2 another is
 forwards where the floor meets one of  
the  walls2 a third is sideways where   
the floor meets the other wall4 ,he can 
proceed to any part of the floor of the 
room by moving first the right  distance
 along one wall1 and then by turning at 
right angles and walking  parallel to   
the other wall4 ,he walks in this case  
first of all in the  direction of one of
 the straight lines that meet in the    
corner of the  floor1 afterwards in the 
direction of the other4 ,by going more  
or less  in one direction or the other1 
he can reach any point on the floor1 and
  any movement1 however circuitous1 can 
be resolved into simple movements  in   
these two directions4    ,but by moving 
in these two directions he is unable to 
raise himself in  the room4 ,if he      

wished to touch a point in the ceiling1 
he would have to  move in the direction 
of the line in which the two walls meet4
 ,there are  three directions then1 each
 at right angles to both the other1 and 
entirely independent of one another4 ,by
 moving in these three directions  or   
combinations of them1 it is possible to 
arrive at any point in a  room4 ,and if 
we suppose the straight lines which meet
 in the corner of  the room to be       
prolonged indefinitely1 it would be     
possible by moving in  the direction of 
those three lines1 to arrive at any     
point in space4  ,thus in space there   
are three independent directions1 and   
only three2  every other direction is   
compounded of these three4 ,the question
 that  comes before us then is this4    
8,why should there be three and only    
three  directions80 ,space1 as we know  
it1 is subject to a limitation4    ,in  
order to obtain an adequate conception  
of what this limitation is1 it  is      
necessary to first imagine beings       

existing in a space more limited  than  
that in which we move4 ,thus we may     
conceive a being who has been           
throughout all the range of his         
experience confined to a single straight
  line4 ,such a being would know what it
 was to move to and fro1 but no  more4  
,the whole of space would be to him but 
the extension in both  directions of the
 straight line to an infinite distance4 
,it is evident  that two such creatures 
could never pass one another4 ,we can   
conceive  their coming out of the       
straight line and entering it again1 but
 they  having moved always in one       
straight line1 would have no conception 
of  any other direction of motion by    
which such a result could be effected4  
,the only shape which could exist in a  
one-dimensional existence of this  kind 
would be a finite straight line4 ,there 
would be no difference in  the shapes of
 figures2 all that could exist would    
simply be longer or  shorter straight   
lines4    ,again1 to go a step higher in

 the domain of a conceivable existence4 
,suppose a being confined to a plane    
superficies1 and throughout all the     
range of its experience never to have   
moved up or down1 but simply to  have   
kept to this one plane4 ,suppose1 that  
is1 some figure1 such as a  circle or   
rectangle1 to be endowed with the power 
of perception2 such a  being if it moves
 in the plane superficies in which it is
 drawn1 will  move in a multitude of    
directions2 but1 however varied they may
 seem to  be1 these directions will all 
be compounded of two1 at right angles to
  each other4 ,by no movement so long as
 the plane superficies remains          
perfectly horizontal1 will this being   
move in the direction we call up  and   
down4 ,and it is important to notice    
that the plane would be  different1 to a
 creature confined to it1 from what it  
is to us4 ,we think  of a plane         
habitually as having an upper and a     
lower side1 because it is  only by the  
contact of solids that we realize a     

plane4 ,but a creature  which had been  
confined to a plane during its whole    
existence would have  no idea of there  
being two sides to the plane he lived   
in4 ,in a plane  there is simply length 
and breadth4 ,if a creature in it be    
supposed to  know of an up or down he   
must already have gone out of the plane4
    ,is it possible1 then1 that a       
creature so circumstanced would arrive  
at  the notion of there being an up and 
down1 a direction different from  those 
to which he had been accustomed1 and    
having nothing in common with  them8    
,obviously nothing in the creature's    
circumstances would tell him  of it4 ,it
 could only be by a process of reasoning
 on his part that he  could arrive at   
such a conception4 ,if he were to       
imagine a being  confined to a single   
straight line1 he might realise that he 
himself  could move in two directions1  
while the creature in a straight line   
could only move in one4 ,having made    
this reflection he might ask1 8,but  why

 is the number of directions limited to 
two8 ,why should there not be  three80  
,a creature 7if such existed71 which    
moves in a plane would be much more     
fortunately circumstanced than one which
 can only move in a straight  line4     
,for1 in a plane1 there is a possibility
 of an infinite variety of  shapes1 and 
the being we have supposed could come   
into contact with an  indefinite number 
of other beings4 ,he would not be       
limited1 as in the  case of the creature
 in a straight line1 to one only on each
 side of  him4    ,it is obvious that it
 would be possible to play curious      
tricks with a  being confined to a      
plane4 ,if1 for instance1 we suppose    
such a being to  be inside a square1 the
 only way out that he could conceive    
would be  through one of the sides of   
the square4 ,if the sides were          
impenetrable1  he would be a fast       
prisoner1 and would have no way out4    
,what his case would be we may          
understand1 if we reflect what a similar

  case would be in our own existence4   
,the creature is shut in in all the     
directions he knows of4 ,if a man is    
shut in in all the directions he  knows 
of1 he must be surrounded by four walls1
 a roof and a floor4 ,a  two-dimensional
 being inside a square would be exactly 
in the same  predicament that a man     
would be1 if he were in a room with no  
opening on  any side4 ,now it would be  
possible to us to take up such a being  
from  the inside of the square1 and to  
set him down outside it4 ,a being to    
whom this had happened would find       
himself outside the place he had been   
confined in1 and he would not have      
passed through any of the boundaries  by
 which he was shut in4 ,the astonishment
 of such a being can only be  imagined  
by comparing it to that which a man     
would feel1 if he were  suddenly to find
 himself outside a room in which he had 
been1 without  having passed through the
 window1 doors1 chimney or any opening  
in the  walls1 ceiling or floor4        

,another curious thing that could be    
effected with a two-dimensional  being1 
is the following4 ,conceive two beings  
at a great distance from  one another on
 a plane surface4 ,if the plane surface 
is bent so that  they are brought close 
to one another1 they would have no      
conception of  their proximity1 because 
to each the only possible movements     
would seem  to be movements in the      
surface4 ,the two beings might be       
conceived as so  placed1 by a proper    
bending of the plane1 that they should  
be absolutely  in juxtaposition1 and yet
 to all the reasoning faculties of      
either of  them a great distance could  
be proved to intervene4 ,the bending    
might be  carried so far as to make one 
being suddenly appear in the plane by   
the  side of the other4 ,if these beings
 were ignorant of the existence of a    
third dimension1 this result would be as
 marvellous to them1 as it would  be for
 a human being who was at a great       
distance--it might be at the  other side

 of the world--to suddenly appear and   
really be by our side1  and during the  
whole time he not to have left the place
 in which he was4                       
,,chapter ,,ii4    ,the foregoing       
examples make it clear that beings can  
be conceived as  living in a more       
limited space than ours4 ,is there a    
similar limitation  in the space we     
know8    ,at the very threshold of      
arithmetic an indication of such a      
limitation  meets us4    ,if there is a 
straight line before us two inches long1
 its length is  expressed by the number 
#b4 ,suppose a square to be described on
 the line1  the number of square inches 
in this figure is expressed by the      
number #d1  i4e41 #b  #b4 ,this #b  #b  
is generally written #b1 and named 8#b  
square40    ,now1 of course1 the        
arithmetical process of multiplication  
is in no  sense identical with that     
process by which a square is generated  
from  the motion of a straight line1 or 
a cube from the motion of a square4     

,but it has been observed that the units
 resulting in each case1 though         
different in kind1 are the same in      
number4    ,if we touch two things twice
 over1 the act of touching has been     
performed four times4 ,arithmetically1  
#b  #b  #d4 ,if a square is  generated  
by the motion of a line two inches in   
length1 this square  contains four      
square inches4    ,so it has come to    
pass that the second and third powers of
 numbers are  called 8square0 and       
8cube40    ,we have now a straight line 
two inches long4 ,on this a square has  
been  constructed containing four square
 inches4 ,if on the same line a cube be 
constructed1 the number of cubic inches 
in the figure so made is #h1  i4e41 #b  
#b  #b or #b4 ,here1 corresponding to   
the numbers #b1 #b1 #b1  we have a      
series of figures4 ,each figure contains
 more units than the  last1 and in each 
the unit is of a different kind4 ,in the
 first figure a  straight line is the   
unit1 viz41 one linear inch2 it is said 

to be of  one dimension4 ,in the second 
a square is the unit1 viz41 one square  
inch4 ,the square is a figure of two    
dimensions4 ,in the third case a cube   
is the unit1 and the cube is of three   
dimensions4 ,the straight line is  said 
to be of one dimension because it can be
 measured only in one way4  ,its length 
can be taken1 but it has no breadth or  
thickness4 ,the square  is said to be of
 two dimensions because it has both     
length and breadth4  ,the cube is said  
to have three dimensions1 because it can
 be measured in  three ways4    ,the    
question naturally occurs1 looking at   
these numbers #b1 #b1 #b1 by  what      
figure shall we represent #b1 or #b  #b 
#b  #b4 ,we know that in the  figure    
there must be sixteen units1 or twice as
 many units as in the  cube4 ,but the   
unit also itself must be different4 ,and
 it must not differ  from a cube simply 
in shape4 ,it must differ from a cube as
 a cube  differs from a square4 ,no     
number of squares will make up a cube1  

because  each square has no thickness4  
,in the same way1 no number of cubes    
must  be able to make up this new unit4 
,and here1 instead of trying to find    
something already known1 to which the   
idea of a figure corresponding to  the  
fourth power can be affixed1 let us     
simply reason out what the  properties  
of such a figure must be4 ,in this      
attempt we have to rely1  not on a      
process of touching or vision1 such as  
informs us of the  properties of bodies 
in the space we know1 but on a process  
of thought4  ,each fact concerning this 
unknown figure has to be reasoned out2  
and it  is only after a number of steps 
have been gone through1 that any        
consistent familiarity with its         
properties is obtained4 ,of all         
applications of the reason1 this        
exploration is perhaps the one which    
requires1 for the simplicity of the data
 involved1 the greatest exercise  of the
 abstract imagination1 and on this      
account is well worth patient           

attention4 ,the first steps are very    
simple4 ,we must imagine a finite       
straight line to generate a square by   
moving on the plane of the paper1  and  
this square in its turn to generate a   
cube by moving vertically  upwards4     
,fig4 #a represents a straight line2    
,fig4 #b represents a square  formed by 
the motion of that straight line2 ,fig4 
#c represents  perspectively a cube     
formed by the motion of that square ,a  
,b ,c ,d  upwards4 ,it would be well1   
instead of using figure #c1 to place a  
cube on  the paper4 ,its base would be  
,a ,b ,c ,d1 its upper surface ,e ,f ,g 
,h4      ,illustration3 ,generating a   
line1 square1 and cube4    ,the straight
 line ,a ,b gives rise to the square ,a 
,b ,c ,d by a movement at  right angles 
to itself4 ,if motion be confined to the
 straight line ,a ,b1  a backward and   
forward motion is the only one possible4
 ,no sideway  motion is admissible4 ,and
 if we suppose a being to exist which   
could  only move in the straight line ,a

 ,b1 it would have no idea of any other 
movement than to and fro4 ,the square ,a
 ,b ,c ,d is formed from the straight   
line by a movement in a direction       
entirely different from the direction   
which exists in ,a ,b4 ,this motion is  
not expressible by means of any         
possible motion in ,a ,b4 ,a being which
 existed in ,a ,b1 and whose  experience
 was limited to what could occur in ,a  
,b1 would not be able to  understand the
 instructions we should give to make ,a 
,b trace out the  figure ,a ,b ,c ,d4   
,in the figure ,a ,b ,c ,d there is a   
possibility of moving in a variety of   
directions1 so long as all these        
directions are confined to one plane4   
,all directions in this plane can be    
considered as compounded of two1  from  
,a to ,b1 and from ,a to ,c4 ,out of the
 infinite variety of such  directions   
there is none which tends in a direction
 perpendicular to  ,fig4 #b2 there is   
none which tends upwards from the plane 
of the paper4  ,conceive a being to     

exist in the plane1 and to move only in 
it4 ,in all  the movements which he went
 through there would be none by which he
  could conceive the alteration of ,fig4
 #b into what ,fig4 #c represents in    
perspective4 ,for #b to become #c it    
must be supposed to move                
perpendicularly to its own plane4 ,the  
figure it traces out is the cube ,a  ,b 
,c ,d ,e ,f ,g ,h4    ,all the          
directions1 manifold as they are1 in    
which a creature existing  in ,fig4 #c  
could move1 are compounded of three     
directions4 ,from ,a to ,b1  from ,a to 
,c1 from ,a to ,e1 and there are no     
other directions known to it4    ,but if
 we suppose something similar to be done
 to ,fig4 #c1 something of  the same    
kind as was done to ,fig4 #a to turn it 
into ,fig4 #b1 or to ,fig4 #b  to turn  
it into ,fig4 #c1 we must suppose the   
whole figure as it exists to  be moved  
in some direction entirely different    
from any direction within  it1 and not  
made up of any combination of the       

directions in it4 ,what is  this8 ,it is
 the fourth direction4    ,we are as    
unable to imagine it as a creature      
living in the plane ,fig4 #b  would be  
to imagine a direction such that moving 
in it the square #b  would become the   
cube #c4 ,the third dimension to such a 
creature would be  as unintelligible as 
the fourth is to us4 ,and at this point 
we have to  give up the aid that is to  
be got from any presentable object1 and 
we  have simply to investigate what the 
properties of the simplest figure in    
four dimensions are1 by pursuing further
 the analogy which we know to  exist    
between the process of formation of #b  
from #a1 and of #c from #b1 and  finally
 of #d from #c4 ,for the sake of        
convenience1 let us call the figure  we 
are investigating--the simplest figure  
in four dimensions--a  four-square4     
,first of all we must notice1 that if a 
cube be formed from a square by  the    
movement of the square in a new         
direction1 each point of the  interior  

of the square traces out part of the    
cube4 ,it is not only the  bounding     
lines that by their motion form the     
cube1 but each portion of  the interior 
of the square generates a portion of the
 cube4 ,so if a cube  were to move in   
the fourth dimension so as to generate a
 four-square1  every point in the       
interior of the cube would start de     
novo1 and trace  out a portion of the   
new figure uninterfered with by the     
other points4    ,or1 to look at the    
matter in another light1 a being in     
three dimensions1  looking down on a    
square1 sees each part of it extended   
before him1 and  can touch each part    
without having to pass through the      
surrounding  parts1 for he can go from  
above1 while the surrounding parts      
surround  the part he touches only in   
one plane4    ,so a being in four       
dimensions could look at and touch every
 point of a  solid figure4 ,no one part 
would hide another1 for he would look at
 each  part from a direction which is   

perfectly different from any in which it
  is possible to pass from one part of  
the body to another4 ,to pass from  one 
part of the body to another it is       
necessary to move in three  directions1 
but a creature in four dimensions would 
look at the solid  from a direction     
which is none of these three4    ,let us
 obtain a few facts about the fourth    
figure1 proceeding according  to the    
analogy that exists between #a1 #b1 #c1 
and #d4 ,in the ,fig4 #a there  are two 
points4 ,in #b there are four           
points--the four corners of the  square4
 ,in #c there are eight points4 ,in the 
next figure1 proceeding  according to   
the same law1 there would be sixteen    
points4    ,in the ,fig4 #a there is one
 line4 ,in the square there are four    
lines4 ,in  the cube there are twelve   
lines4 ,how many lines would there be in
 the  four-square8 ,that is to say that 
there are three numbers--#a1 #d1 and    
#ab4  ,what is the fourth1 going on     
accordingly to the same law8    ,to     

answer this question let us trace out in
 more detail how the figures  change    
into one another4 ,the line1 to become  
the square1 moves2 it  occupies first of
 all its original position1 and last of 
all its final  position4 ,it starts as  
,a ,b1 and ends as ,c ,d2 thus the line 
appears  twice1 or it is doubled4 ,the  
two other lines in the square1 ,a ,c1 ,b
 ,d1  are formed by the motions of the  
points at the extremities of the moving 
line4 ,thus1 in passing from the        
straight line to the square the lines   
double themselves1 and each point traces
 out a line4 ,if the same  procedure    
holds good in the case of the change of 
the square into the  cube1 we ought in  
the cube to have double the number of   
lines as in the  square--that is        
eight--and every point in the square    
ought to become a  line4 ,as there are  
four points in the square1 we should    
have four lines  in the cube from them1 
that is1 adding to the previous eight1  
there  should be twelve lines in the    

cube4 ,this is obviously the case4      
,hence we  may with confidence1 to      
deduce the number of lines in a         
four-square1  apply this rule4 ,double  
the number of lines in the previous     
figure1 and  add as many lines as there 
are points in the previous figure4 ,now 
in  the cube there are twelve lines and 
eight points4 ,hence we get #b  #ab     
#h1 or thirty-two lines in the          
four-square4    ,in the same way any    
other question about the four-square can
 be  answered4 ,we must throw aside our 
realising power and answer in           
accordance with the analogy to be worked
 out from the three figures we  know4   
,thus1 if we want to know how many plane
 surfaces the four-square has1 we  must 
commence with the line1 which has none2 
the square has one2 the  cube has six4  
,here we get the three numbers1 #j1 #a1 
and #f4 ,what is the  fourth8           
,consider how the planes of the cube    
arise4 ,the square at the beginning  of 
its motion determines one of the faces  

of the cube1 at the end it is  the      
opposite face1 during the motion each of
 the lines of the square  traces out one
 plane face of the cube4 ,thus we double
 the number of  planes in the previous  
figure1 and every line in the previous  
figure  traces out a plane in the       
subsequent one4    ,apply this rule to  
the formation of a square from a line4  
,in the line  there is no plane surface1
 and since twice nothing is nothing1 we 
get1  so far1 no surface in the square2 
but in the straight line there is one   
line1 namely itself1 and this by its    
motion traces out the plane surface  of 
the square4 ,so in the square1 as should
 be1 the rule gives one  surface4       
,applying this rule to the case of the  
cube1 we get1 doubling the  surfaces1   
#ab2 and adding a plane for each of the 
straight lines1 of  which there are #ab1
 we have another #ab1 or #bd plane      
surfaces in all4  ,thus1 just as by     
handling or looking at it1 it is        
possible to describe a  figure in space1

 so by going through a process of       
calculation it is  within our power to  
describe all the properties of a figure 
in four  dimensions4    ,there is       
another characteristic so remarkable as 
to need a special  statement4 ,in the   
case of a finite straight line1 the     
boundaries are  points4 ,if we deal with
 one dimension only1 the figure #a1 that
 of a  segment of a straight line1 is   
cut out of and separated from the rest  
of  an imaginary infinitely long        
straight line by the two points at its  
extremities4 ,in this simple case the   
two points correspond to the  bounding  
surface of the cube4 ,in the case of a  
two-dimensional figure an  infinite     
plane represents the whole of space4    
,the square is separated  off by four   
straight lines1 and it is impossible for
 an entry to be made  into the interior 
of the square1 except by passing through
 the straight  lines4 ,now1 in these    
cases1 it is evident that the boundaries
 of the  figure are of one dimension    

less than the figure itself4 ,points    
bound  lines1 lines bound plane figures1
 planes bound solid figures4 ,solids    
then must bound four dimensional        
figures4 ,the four-square will be       
bounded in the following manner4 ,first 
of all there is the cube which1  by its 
motion in the fourth direction1         
generates the figure4 ,this1 in  its    
initial position1 forms the base of the 
four-square4 ,in its final  position it 
forms the opposite end4 ,during the     
motion each of the faces  of the cube   
give rise to another cube4 ,the         
direction in which the cube  moves is   
such that of all the six sides none is  
in the least inclined in  that          
direction4 ,it is at right angles to all
 of them4 ,the base of the  cube1 the   
top of the cube1 and the four sides of  
the cube1 each and all  of them form    
cubes4 ,thus the four-square is bounded 
by eight cubes4  ,summing up1 the       
four-square would have #af points1 #cb  
lines1 #bd surfaces1  and it would be   

bounded by #h cubes4    ,if a           
four-square were to rest in space it    
would seem to us like a cube4    ,to    
justify this conclusion we have but to  
think of how a cube would  appear to a  
two-dimensional being4 ,to come within  
the scope of his  faculties at all1 it  
must come into contact with the plane in
 which he  moves4 ,if it is brought into
 as close a contact with this plane as  
possible1 it rests on it by one of its  
faces4 ,this face is a square1 and  the 
most a two-dimensional being could get  
acquainted with of a cube  would be a   
square4    ,having thus seen how it is  
possible to describe the properties of  
the  simplest shape in four dimensions1 
it is evident that the mental           
construction of more elaborate figures  
is simply a matter of time and          
patience4    ,in the study of the form  
and development of the chick in the egg1
 it is  impossible to detect the        
features that are sought to be observed1
 except  by the use of the microscope4  

,the specimens are accordingly hardened 
by  a peculiar treatment and cut into   
thin sections4 ,the investigator going  
over each of these sections1 noticing   
all their peculiarities1  constructs in 
his mind the shape as it originally     
existed from the  record afforded by an 
indefinite number of slices4 ,so1 to    
form an idea  of a four-dimensional     
figure1 a series of solid shapes bounded
 on every  side differing gradually from
 one another1 proceeding1 it may be1 to 
the  most diverse forms1 has to be      
mentally grasped and fused into a       
unitary  conception4    ,if1 for        
instance1 a small sphere were to appear1
 this to be replaced by  a larger one1  
and so on1 and then1 when the largest   
had appeared1  smaller and smaller ones 
to make their appearance1 what would be 
witnessed would be a series of sections 
of a four-dimensional sphere4  ,each    
section in space being a sphere4        
,again1 just as solid figures can be    
represented on paper by perspective1    

four-dimensional figures can be         
represented perspectively by solids4 ,if
  there are two squares1 one lying over 
the other1 and the underneath one  be   
pushed away1 its sides remaining        
parallel with the one that was over  it1
 then if each point of the one be joined
 to the corresponding point  of the     
other1 we have a fair representation on 
paper of a cube4 ,fig4 #c  may be       
considered to be such a representation  
if the square ,c ,d ,g ,h be  considered
 to be the one that has been pushed away
 from lying originally  under the square
 ,a ,b ,e ,f4 ,each of the planes which 
bound the cube is  represented on the   
paper4 ,the only thing that is wanting  
is the  three-dimensional content of the
 cube4 ,so if two cubes be placed with  
their sides parallel1 but one somewhat  
diagonally with regard to the  other1   
and all their corresponding points be   
supposed joined1 there will  be found a 
set of solid figures1 each representing 
7though of course  distortedly7 the     

bounding cubes of the four-dimensional  
figure1 and  every plane and line in the
 four-dimensional figure will be found  
to be  represented in a kind of solid   
perspective4 ,what is wanting is of     
course  the four-dimensional content4   
,,chapter ,,iii4    ,having now passed  
in review some of the properties of     
four-dimensional  figures1 it remains to
 ask what relations beings in four      
dimensions1 if  they did exist1 would   
have with us4    ,and in the first      
place1 a being in four dimensions would 
have to us  exactly the appearance of a 
being in space4 ,a being in a plane     
would  only know solid objects as       
two-dimensional figures--the shapes     
namely in  which they intersected his   
plane4 ,so if there were                
four-dimensional  objects1 we should    
only know them as solids--the solids1   
namely1 in which  they intersect our    
space4 ,why1 then1 should not the       
four-dimensional  beings be ourselves1  
and our successive states the passing of

 them  through the three-dimensional    
space to which our consciousness is     
confined8    ,let us consider the       
question in more detail4 ,and for the   
sake of  simplicity transfer the problem
 to the case of three and two dimensions
  instead of four and three4    ,suppose
 a thread to be passed through a thin   
sheet of wax placed  horizontally4 ,it  
can be passed through in two ways4      
,either it can be  pulled through1 or it
 can be held at both ends1 and moved    
downwards as a  whole4 ,suppose a thread
 to be grasped at both ends1 and the    
hands to be  moved downwards            
perpendicularly to the sheet of wax4 ,if
 the thread  happens to be perpendicular
 to the sheet it simply passes through  
it1  but if the thread be held1         
stretched slantingwise to the sheet1 and
 the  hands are moved perpendicularly   
downwards1 the thread will1 if it be    
strong enough1 make a slit in the sheet4
    ,if now the sheet of wax were to    
have the faculty of closing up behind   

the thread1 what would appear in the    
sheet would be a moving hole4           
,suppose that instead of a sheet and a  
thread1 there were a straight line  and 
a plane4 ,if the straight line were     
placed slantingwise in reference  to the
 plane and moved downwards1 it would    
always cut the plane in a  point1 but   
that point of section would move on4 ,if
 the plane were of  such a nature as to 
close up behind the line1 if it were of 
the nature  of a fluid1 what would be   
observed would be a moving point4 ,if   
now there  were a whole system of lines 
sloping in different directions1 but all
  connected together1 and held          
absolutely still by one framework1 and  
if  this framework with its system of   
lines were as a whole to pass slowly    
through the fluid plane at right angles 
to it1 there would then be the          
appearance of a multitude of moving     
points in the plane1 equal in number  to
 the number of straight lines in the    
system4 ,the lines in the  framework    

will all be moving at the same          
rate--namely1 at the rate of the        
framework in which they are fixed4 ,but 
the points in the plane will have       
different velocities4 ,they will move   
slower or faster1 according as the      
lines which give rise to them are more  
or less inclined to the plane4 ,a       
straight line perpendicular to the plane
 will1 on passing through1 give  rise to
 a stationary point4 ,a straight line   
that slopes very much  inclined to the  
plane will give rise to a point moving  
with great  swiftness4 ,the motions and 
paths of the points would be determined 
by  the arrangement of the lines in the 
system4 ,it is obvious that if two      
straight lines were placed lying across 
one another like the letter ,x1  and if 
this figure were to be stood upright and
 passed through the  plane1 what would  
appear would be at first two points4    
,these two points  would approach one   
another4 ,when the part where the two   
strokes of the ,x  meet came into the   

plane1 the two points would become one4 
,as the upper  part of the figure passed
 through1 the two points would recede   
from one  another4      ,illustration3  
,rectangle ,a ,b ,c ,d1 crossed by two  
interlinked lines ,x    and ,y two      
lines4    ,if the line be supposed to be
 affixed to all parts of the framework1 
and  to loop over one another1 and      
support one another1#a it is obvious    
that  they could assume all sorts of    
figures1 and that the points on the     
plane  would move in very complicated   
paths4 ,the annexed figure represents a 
section of such a framework4 ,two lines 
,x ,x and ,y ,y are shown1 but there    
must be supposed to be a great number of
 others sloping backwards and  forwards 
as well as sideways4    ,let us now     
assume that instead of lines1 very thin 
threads were attached  to the framework3
 they on passing through the fluid plane
 would give  rise to very small spots4  
,let us call the spots atoms1 and regard
 them  as constituting a material system

 in the plane4 ,there are four          
conditions which must be satisfied by   
these spots if they are to be  admitted 
as forming a material system such as    
ours4 ,for the ultimate  properties of  
matter 7if we eliminate attractive and  
repulsive forces1  which may be caused  
by the motions of the smallest          
particles71 are--#a1  ,permanence2 #b1  
,impenetrability2 #c1 ,inertia2 #d1     
,conservation of energy4    ,according  
to the first condition1 or that of      
permanence1 no one of these  spots must 
suddenly cease to exist4 ,that is1 the  
thread which by sharing  in the general 
motion of the system gives rise to the  
moving point1 must  not break off before
 the rest of them4 ,if all the lines    
suddenly ended  this would correspond to
 a ceasing of matter4    #b4            
,impenetrability4--,one spot must not   
pass through another4 ,this  condition  
is obviously satisfied4 ,if the threads 
do not coincide at any  point1 the      
moving spots they give rise to cannot4  

#c4 ,inertia4--,a spot must not cease to
 move or cease to remain at rest        
without coming into collision with      
another point4 ,this condition gives    
the obvious condition with regard to the
 threads1 that they1 between the  points
 where they come into contact with one  
another1 must be straight4  ,a thread   
which was curved would1 passing through 
the plane1 give rise to  a point which  
altered in velocity spontaneously4 ,this
 the particles of  matter never do4     
#d4 ,conservation of energy4--,the      
energy of a material system is never    
lost2 it is only transferred from one   
form to another1 however it may  seem to
 cease4 ,if we suppose each of the      
moving spots on the plane to be  the    
unit of mass1 the principle of the      
conservation of energy demands  that    
when any two meet1 the sum of the       
squares of their several  velocities    
before meeting shall be the same as the 
sum of the squares of  their velocities 
after meeting4 ,now we have seen that   

any statement  about the velocities of  
the spots in the plane is really a      
statement  about the inclinations of the
 threads to the plane4 ,thus the        
principle  of the conservation of energy
 gives a condition which must be        
satisfied  by the inclinations of the   
threads of the plane4 ,translating this 
statement1 we get in mathematical       
language the assertion that the sum of  
the squares of the tangents of the      
angles the threads make with the  normal
 to the plane remains constant4         
,hence1 all complexities and changes of 
a material system made up of  similar   
atoms in a plane could result from the  
uniform motion as a whole  of a system  
of threads4    ,we can imagine these    
threads as weaving together to form     
connected  shapes1 each complete in     
itself1 and these shapes as they pass   
through  the fluid plane give rise to a 
series of moving points4 ,yet1 inasmuch 
as  the threads are supposed to form    
consistent shapes1 the motion of the    

points would not be wholly random1 but  
numbers of them would present the       
semblance of moving figures4 ,suppose1  
for instance1 a number of threads  to be
 so grouped as to form a cylinder for   
some distance1 but after a  while to be 
pulled apart by other threads with which
 they interlink4  ,while the cylinder   
was passing through the plane1 we should
 have in the  plane a number of points  
in a circle4 ,when the part where the   
threads  deviated came to the plane1 the
 circle would break up by the points    
moving away4 ,these moving figures in   
the plane are but the traces of the     
shapes of threads as those shapes pass  
on4 ,these moving figures may be        
conceived to have a life and a          
consciousness of their own4    ,or1 if  
it be irrational to suppose them to have
 a consciousness when the  shapes of    
which they are momentary traces have    
none1 we may well suppose  that the     
shapes of threads have consciousness1   
and that the moving  figures share this 

consciousness1 only that in their case  
it is limited  to those parts of the    
shapes that simultaneously pass through 
the plane4  ,in the plane1 then1 we may 
conceive bodies with all the properties 
of a  material system1 moving and       
changing1 possessing consciousness4     
,after a  while it may well be that one 
of them becomes so disassociated that it
  appears no longer as a unit1 and its  
consciousness as such may be lost4  ,but
 the threads of existence of such a     
figure are not broken1 nor is the  shape
 which gave it origin altered in any    
way4 ,it has simply passed on  to a     
distance from the plane4 ,thus nothing  
which existed in the  conscious life on 
the plane would cease4 ,there would in  
such an  existence be no cause and      
effect1 but simply the gradual          
realisation in  a superficies of an     
already existent whole4 ,there would be 
no progress1  unless we were to suppose 
the threads as they pass to interweave  
themselves in more complex shapes4      

,can a representation1 such as the      
preceding1 be applied to the case of    
the existence in space with which we    
have to do8 ,is it possible to  suppose 
that the movements and changes of       
material objects are the  intersections 
with a three-dimensional space of a     
four-dimensional  existence8 ,can our   
consciousness be supposed to deal with a
 spatial  profile of some higher        
actuality8    ,it is needless to say    
that all the considerations that have   
been brought  forward in regard to the  
possibility of the production of a      
system  satisfying the conditions of    
materiality by the passing of threads   
through a fluid plane1 holds good with  
regard to a four-dimensional  existence 
passing through a three-dimensional     
space4 ,each part of the  ampler        
existence which passed through our space
 would seem perfectly  limited to us4   
,we should have no indication of the    
permanence of its  existence4 ,were such
 a thought adopted1 we should have to   

imagine some  stupendous whole1 wherein 
all that has ever come into being or    
will come  co-exists1 which passing     
slowly on1 leaves in this flickering    
consciousness of ours1 limited to a     
narrow space and a single moment1 a     
tumultuous record of changes and        
vicissitudes that are but to us4 ,change
  and movement seem as if they were all 
that existed4 ,but the appearance  of   
them would be due merely to the         
momentary passing through our           
consciousness of ever existing          
realities4    ,in thinking of these     
matters it is hard to divest ourselves  
of the habit  of visual or tangible     
illustration4 ,if we think of a man as  
existing in  four dimensions1 it is hard
 to prevent ourselves from conceiving   
him as  prolonged in an already known   
dimension4 ,the image we form resembles 
somewhat those solemn ,egyptian statues 
which in front represent well  enough   
some dignified sitting figure1 but which
 are immersed to their  ears in a smooth

 mass of stone which fits their contour 
exactly4    ,no material image will     
serve4 ,organised beings seem to us so  
complete  that any addition to them     
would deface their beauty4 ,yet were we 
creatures confined to a plane1 the      
outline of a ,corinthian column would   
probably seem to be of a beauty         
unimprovable in its kind4 ,we should be 
unable to conceive any addition to it1  
simply for the reason that any  addition
 we could conceive would be of the      
nature of affixing an  unsightly        
extension to some part of the contour4  
,yet1 moving as we do in  space of three
 dimensions1 we see that the beauty of  
the stately column  far surpasses that  
of any single outline4 ,so all that we  
can do is to  deny our faculty of       
judging of the ideal completeness of    
shapes in four  dimensions4             
,,chapter ,,iv4    ,let us now leave    
this supposition of framework and       
threads4 ,let us  investigate the       
conception of a four-dimensional        

existence in a simpler  and more natural
 manner--in the same way that a         
two-dimensional being  should think     
about us1 not as infinite in the third  
dimension1 but  limited in three        
dimensions as he is in two4 ,a being    
existing in four  dimensions must then  
be thought to be as completely bounded  
in all four  directions as we are in    
three4 ,all that we can say in regard to
 the  possibility of such beings is1    
that we have no experience of motion in 
four directions4 ,the powers of such    
beings and their experience would be    
ampler1 but there would be no           
fundamental difference in the laws of   
force and motion4    ,such a being would
 be able to make but a part of himself  
visible to us1  for a cube would be     
apprehended by a two-dimensional being  
as the square  in which it stood4 ,thus 
a four-dimensional being would suddenly 
appear  as a complete and finite body1  
and as suddenly disappear1 leaving no   
trace of himself1 in space1 in the same 

way that anything lying on a  flat      
surface1 would1 on being lifted1        
suddenly vanish out of the  cognisance  
of beings1 whose consciousness was      
confined to the plane4 ,the  object     
would not vanish by moving in any       
direction1 but disappear  instantly as a
 whole4 ,there would be no barrier1 no  
confinement of our  devising that would 
not be perfectly open to him4 ,he would 
come and go  at pleasure2 he would be   
able to perform feats of the most       
surprising  kind4 ,it would be possible 
by an infinite plane extending in all   
directions to divide our space into two 
portions absolutely separated  from one 
another2 but a four-dimensional being   
would slip round this  plane with the   
greatest ease4    ,to see this clearly1 
let us first take the analogous case in 
three  dimensions4 ,suppose a piece of  
paper to represent a plane4 ,if it is   
infinitely extended in every direction1 
it will represent an infinite  plane4   
,it can be divided into two parts by an 

infinite straight line4 ,a  being       
confined to this plane could not get    
from one part of it to the  other       
without passing through the line4 ,but  
suppose another piece of  paper laid on 
the first and extended infinitely1 it   
will represent  another infinite plane4 
,if the being moves from the first plane
 by a  motion in the third dimension1 it
 will move into this new plane4 ,and in 
it it finds no line4 ,let it move to    
such a position that when it goes  back 
to the first plane it will be on the    
other side of the line4 ,then  let it go
 back to the first plane4 ,it has       
appeared now on the other side  of the  
line which divides the infinite plane   
into two parts4    ,take now the case of
 four dimensions4 ,instead of bringing  
before the  mind a sheet of paper       
conceive a solid of three dimensions4   
,if this  solid were to become infinite 
it would fill up the whole of           
three-dimensional space4 ,but it would  
not fill up the whole of                

four-dimensional space4 ,it would be to 
four-dimensional space what an  infinite
 plane is to three-dimensional space4   
,there could be in  four-dimensional    
space an infinite number of such solids1
 just as in  three-dimensional space    
there could be an infinite number of    
infinite  planes4    ,thus1 lying       
alongside our space1 there can be       
conceived a space also  infinite in all 
three directions4 ,to pass from one to  
the other a  movement has to be made in 
the fourth dimension1 just as to pass   
from  one infinite plane to another a   
motion has to be made in the third      
dimension4    ,conceive1 then1          
corresponding to the first sheet of     
paper mentioned  above1 a solid1 and as 
the sheet of paper was supposed to be   
infinitely  extended in two dimensions1 
suppose the solid to be infinitely      
extended  in its three dimensions1 so   
that it fills the whole of space as we  
know  it4    ,now divide this infinite  
solid in two parts by an infinite plane1

 as the  infinite plane of paper was    
divided in two parts by an infinite     
line4 ,a  being cannot pass from one    
part of this infinite solid to another1 
on  the other side of this infinite     
plane1 without going through the        
infinite plane1 so long as he keeps     
within the infinite solid4    ,but      
suppose beside this infinite solid a    
second infinite solid1 lying  next to it
 in the fourth dimension1 as the second 
infinite plane of  paper was next to the
 first infinite plane in the third      
dimension4 ,let  now the being that     
wants to get on the other side of the   
dividing plane  move off in the fourth  
dimension1 and enter the second infinite
 solid4  ,in this second solid there is 
no dividing plane4 ,let him now move1 so
  that coming back to the first infinite
 solid he shall be on the other  side of
 the infinite plane that divides it into
 two portions4 ,if this is  done1 he    
will now be on the other side of the    
infinite plane1 without  having gone    

through it4    ,in a similar way a      
being1 able to move in four dimensions1 
could get out  of a closed box without  
going through the sides1 for he could   
move off  in the fourth dimension1 and  
then move about1 so that when he came   
back  he would be outside the box4      
,is there anything in the world as we   
know it1 which would indicate the       
possibility of there being an existence 
in four dimensions8 ,no definite  answer
 can be returned to this question4 ,but 
it may be of some interest  to point out
 that there are certain facts which     
might be read by the  light of the      
fourth dimensional theory4    ,to make  
this clear1 let us suppose that space is
 really four  dimensional1 and that the 
three-dimensional space we know is1 in  
this  ampler space1 like a surface is in
 our space4    ,we should then be in    
this ampler space like beings confined  
to the  surface of a plane would be in  
ours4 ,let us suppose that just as in   
our  space there are centres of         

attraction whose influence radiates out 
in  every direction1 so in this ampler  
space there are centres of attraction   
whose influence radiates out in every   
direction4 ,is there anything to be     
observed in nature which would          
correspond to the effect of a centre of 
attraction lying out of our space1 and  
acting on all the matter in it8  ,the   
effect of such a centre of attraction   
would not be to produce motion  in any  
known direction1 because it does not lie
 off in any known  direction4    ,let us
 pass to the corresponding case in three
 and two dimensions1  instead of four   
and three4 ,let us imagine a plane lying
 horizontally1  and in it some creatures
 whose experience was confined to it4   
,if now  some water or other liquid were
 poured on to the plane1 the creatures1 
becoming aware of its presence1 would   
find that it had a tendency to  spread  
out all over the plane4 ,in fact it     
would not be to them as a  liquid is to 
us--it would rather correspond to a gas4

 ,for a gas1 as we  know it1 tends to   
expand in every direction1 and gradually
 increase so  as to fill the whole of   
space4 ,it exercises a pressure on the  
walls of  any vessel in which we confine
 it4    ,the liquid on the plane expands
 in all the dimensions which the        
two-dimensional creatures on the plane  
know1 and at the same time  becomes     
smaller in the third dimension1 its     
absolute quantity remaining  unchanged4 
,in like manner we might suppose that   
gases 7which by  expansion become larger
 in the dimensions that we know7 become 
smaller  in the fourth dimension4       
,the cause in this case would have to be
 sought for in an attractive  force1    
acting with regard to our space as the  
force of gravity acts with  regard to a 
horizontal plane4    ,can we suppose    
that there is a centre of attraction    
somewhere off in the  fourth dimension1 
and that the gases1 which we know are   
simply more  mobile liquids1 expanding  
out in every direction under its        

influence4  ,this view receives a       
certain amount of support from the fact 
proved  experimentally that there is no 
absolute line of demarcation between a  
liquid and a gas4 ,the one can be made  
to pass into the other with no  moment  
intervening in which it can be said that
 now a change of state  has taken place4
    ,we might then suppose that the     
matter we know extending in three       
dimensions has also a small thickness in
 the fourth dimension2 that  solids are 
rigid in the fourth as in the other     
three dimensions2 that  liquids are too 
coherent to admit of their spreading out
 in space1 and  becoming thinner in the 
fourth dimension1 under the influence of
 an  attractive centre lying outside of 
our space2 but that gases1 owing to  the
 greater mobility of their particles1   
are subject to its action1 and  spread  
out in space under its influence1 in the
 same manner that  liquids1 under the   
influence of gravity1 spread out on a   
plane4    ,then the density of a gas    

would be a measure of the relative      
thickness  of it in the fourth          
dimension3 and the diminution of the    
density would  correspond to a          
diminution of the thickness in the      
fourth dimension4  ,could this          
supposition be tested in any way8       
,suppose a being confined to a plane2 if
 the plane is moved far off from  the   
centre of attraction lying outside it1  
he would find that liquids  had less    
tendency to spread out than before4     
,or suppose he moves to a distant part  
of the plane so that the line from  his 
position to the centre of attraction    
lies obliquely to the plane2 he  would  
find that in this position a liquid     
would show a tendency to  spread out    
more in one direction than another4     
,now our space considered as lying in   
four-dimensional space1 as a plane  does
 in three-dimensional space1 may be     
shifted4 ,and the expansive force  of   
gases might be found to be different at 
different ages4 ,or1 shifting  as we do 

our position in space during the course 
of the earth's path  round the sun1     
there might arise a sufficient          
difference in our position  in space1   
with regard to the attractive centre1 to
 make the expansive  force of gases     
different at different times of the     
year1 or to cause  them to manifest a   
greater expansive force in one direction
 than in  another4    ,but although this
 supposition might be worked out at some
 length1 it is  hard to suppose that it 
could afford any definite test of the   
physical  existence of a fourth         
dimension4 ,no test has been discovered 
which is  decisive4 ,and1 indeed1 before
 searching for tests1 a theoretical     
point  of the utmost importance has to  
be settled4 ,in discussing the          
geometrical properties of straight lines
 and planes1 we suppose them to  be     
respectively of one and two dimensions1 
and by so doing deny them any  real     
existence4 ,a plane and a line are mere 
abstractions4 ,every portion  of matter 

is of three dimensions4 ,if we consider 
beings on a plane not  as mere          
idealities1 we must suppose them to be  
of some thickness4 ,if  their experience
 is to be limited to a plane this       
thickness must be very  small compared  
to their other dimensions4 ,transferring
 our reasoning to  the case of four     
dimensions1 we come to a curious result4
    ,if a fourth dimension exists there 
are two possible alternatives4    ,one  
is1 that there being four dimensions1 we
 have a three-dimensional  existence    
only4 ,the other is that we really have 
a four-dimensional  existence1 but are  
not conscious of it4 ,if we are in three
 dimensions  only1 while there are      
really four dimensions1 then we must be 
relatively  to those beings who exist in
 four dimensions1 as lines and planes   
are in  relation to us4 ,that is1 we    
must be mere abstractions4 ,in this case
 we  must exist only in the mind of the 
being that conceives us1 and our        
experience must be merely the thoughts  

of his mind--a result which has         
apparently been arrived at1 on          
independent grounds1 by an idealist     
philosopher4    ,the other alternative  
is that we have a four-dimensional      
existence4 ,in  this case our           
proportions in it must be infinitely    
minute1 or we should  be conscious of   
them4 ,if such be the case1 it would    
probably be in the  ultimate particles  
of matter1 that we should discover the  
fourth  dimension1 for in the ultimate  
particles the sizes in the three        
dimensions are very minute1 and the     
magnitudes in all four dimensions  would
 be comparable4    ,the preceding two   
alternative suppositions are based on   
the hypothesis  of the reality of       
four-dimensional existence1 and must be 
conceived to  hold good only on that    
hypothesis4    ,it is somewhat curious  
to notice that we can thus conceive of  
an  existence relative to which that    
which we enjoy must exist as a mere     
abstraction4    ,apart from the interest

 of speculations of this kind they have 
considerable value2 for they enable us  
to express in intelligible terms  things
 of which we can form no image4 ,they   
supply us1 as it were1 with             
scaffolding1 which the mind can make use
 of in building up its  conceptions4    
,and the additional gain to our power of
 representation is  very great4    ,many
 philosophical ideas and doctrines are  
almost unintelligible because  there is 
no physical illustration which will     
serve to express them4 ,in  the         
imaginary physical existence which we   
have traced out1 much that  philosophers
 have written finds adequate            
representation4 ,much of  ,spinoza's    
,ethics1 for example1 could be          
symbolized from the preceding  pages4   
,thus we may discuss and draw perfectly 
legitimate conclusions with  regard to  
unimaginable things4    ,it is1 of      
course1 evident that these speculations 
present no point of  direct contact with
 fact4 ,but this is no reason why they  

should be  abandoned4 ,the course of    
knowledge is like the flow of some      
mighty  river1 which1 passing through   
the rich lowlands1 gathers into itself  
the  contributions from every valley4   
,such a river may well be joined by a   
mountain stream1 which1 passing with    
difficulty along the barren  highlands1 
flings itself into the greater river    
down some precipitous  descent1         
exhibiting at the moment of its union   
the spectacle of the  utmost beauty of  
which the river system is capable4 ,and 
such a stream is  no inapt symbol of a  
line of mathematical thought1 which1    
passing  through difficult and abstract 
regions1 sacrifices for the sake of its 
crystalline clearness the richness that 
comes to the more concrete  studies4    
,such a course may end fruitlessly1 for 
it may never join the  main course of   
observation and experiment4 ,but1 if it 
gains its way to  the great stream of   
knowledge1 it affords at the moment of  
its union the  spectacle of the greatest

 intellectual beauty1 and adds somewhat 
of  force and mysterious capability to  
the onward current4                     
,the ,persian ,king4                    
,,part ,i4                              
,,chapter ,i4    ,in ,persia there was  
once a king4 ,on one occasion when he   
was out hunting  he came to the narrow  
entrance of a valley4 ,it was shut in on
 either  side by vast hills1 seemingly  
the spurs from the distant mountains4   
,these great spurs spread out including 
a wide tract of land4 ,towards the      
entrance where he stood they approached 
one another1 and ended in abrupt        
cliffs4 ,across the mouth of the valley 
stretched a deep ravine4 ,the  king1    
followed by courtiers1 galloped along1  
searching a spot where the  deep fissure
 might be shallower1 so that descending 
into it he might  reach the valley by   
ascending on the opposite side4    ,but 
at every point the ravine stretched     
downwards dark and deep1 from  cliff to 
cliff1 shutting off all access to the   

valley4    ,at one point only was there 
a means of crossing4 ,there were two    
masses  of rocks1 jutting out one from  
either side like the abutments of a     
natural bridge1 and they seemed to meet 
in mid air4    ,the mass trembled and   
shook as the king spurred his horse over
 it1 and  the dislodged stones          
reverberated from side to side of the   
chasm till  the noise of their falling  
was lost4    ,before the first of his   
courtiers could follow him one of the   
great  piers or abutments gave way--the 
whole mass fell crashing down4 ,the king
  was alone in the valley4    8,so ho10 
he cried1 8the kingdom of ,persia is    
shrunk to this narrow  spot60 and       
without troubling himself for the moment
 how he should  return1 he sped onward4 
,but when he had ridden far into the    
valley on his steed that could          
outnumber ten leagues in an hour1 and   
had returned to the entrance of  it1 he 
saw no trace of a living soul on the    
opposite brink of the cleft4  ,no sign  

was left1 save a few reeds bent down by 
the passage of the  mounted train1 that 
any human being had stood on the        
opposite side for  ages4    ,the evening
 came on apace4 ,yet no one returned4   
,again he rode far into  the valley4    
,for the most part it was covered with  
long grass1 but here  and there a thick 
and tangled mass of vegetation attested 
to a great  luxuriance of soil1 while   
the surface was intersected here and    
there  with rivulets of clear water1    
which finally lost their way in the dark
  gorge over which he had just so rashly
 adventured4 ,but on no side did  the   
steep cliffs offer any promise of       
escape4    ,when the night came on he   
stretched himself beneath one of the few
 trees  not far from the ravine1 while  
his faithful horse stood tranquilly at  
his head4    ,he did not awake till the 
moon had risen4 ,but then suddenly he   
started  to his feet1 and walking to the
 edge of the cleft1 peered over to the  
land from whence he had come4 ,for he   

thought he heard sounds of some  kind   
that were not the natural ones of the   
rustling wind or the falling  water4    
,looking out he saw clearly opposite to 
him an old man in ragged  clothing1     
leaning against a rock1 holding a long  
pipe in his hands1 on  which he now and 
again played a few wild notes4    8,oho1
 peasant60 cried the king4 8,run and    
tell the head man of your  village that 
the king bids him come directly1 and    
will have him bring  with him the       
longest ropes and the strongest throwers
 under him40    ,but the old man did not
 seem to give heed4 ,then the king      
cried1  8,hearken1 old man1 run quickly 
and tell your master that the king is   
confined here1 and will reward him      
beyond his dreams if he deliver him     
quickly40    ,then the old man rose1 and
 coming nearer to the edge of the ravine
 stood  opposite1 still playing at      
intervals some notes on his long pipe4  
,and  the king cried1 8,canst thou hear8
 ,dost thou dare to refuse to carry my  

commands8 ,for ,i am the king of        
,persia4 ,who art thou80    ,then the   
old man made answer1 putting his pipe   
aside3 8,i am he who  appears only when 
a man has passed for ever beyond the ken
 of all that  have known him4 ,i am     
,demiourgos1 the maker of men40    ,then
 the king cried1 8,mock me not1 but obey
 my commands40    ,the old man made     
answer1 8,i do not mock thee2 and oh1 my
 ,lord1 thou hast  moved the puppets ,i 
have made1 and driven them so to dance  
on the  surface of the earth that ,i    
would willingly obey thee4 ,but it is   
not  permitted me to pass between thee  
and the world of men thou hast known40  
,then the king was silent4    ,at length
 he said1 8,if thou art really what thou
 sayest1 show me what  thou canst do2   
build me a palace40    ,the old man     
lifted his pipe in both his trembling   
hands1 and began to  blow4    ,it was a 
strange instrument1 for it not only     
produced the shriller  sounds of the    
lute1 and the piercing notes of the     

trumpet1 but resounded  with the hollow 
booming of great organ pipes1 and       
amongst all came ever  and again a sharp
 and sonorous clang as of some metal    
instrument  resounding when it was      
struck4    ,and then the king was as one
 who enjoys the delights of thought4    
,for in  thought1 delicate shades1      
impalpable nuances are ever passing4 ,it
 is as  the blended strains of an       
invisible orchestra1 but more subtle    
far1 that  come and go in unexpected    
metres1 and overwhelm you with their    
beauty  when all seemed silent4 ,and lo1
 as the strains sound1                  
outside--palpable1  large as the        
firmament1 or real as the smallest thing
 you can take up  and know it is        
there--outside stands some existence    
revealed--to be known  and returned to  
for ever4    ,so the king1 listening to 
this music1 felt that something was     
rising  behind him4 ,and turning1 beheld
 course after course of a great         
building4  ,almost as soon as he had    

looked it had risen completed1 finished 
to the  last embossure on the windows1  
the tracery on the highest pinnacles4   
,all  had happened while the old man was
 blowing on his pipe1 and when he       
ceased all was perfect4    ,and yet the 
appearance was very strange1 for a      
finished and seemingly  habitable       
building rose out of waste unreclaimed  
soil1 strewn with rocks  and barren4 ,no
 dwellings were near the palace to wait 
on it1 no roads  led to it or away from 
it4    8,there should be houses around  
it1 and roadways10 said the king2 8make 
them1 and fields sown with corn1 and all
 that is necessary for a state40        
,blowing on his pipe in regular         
recurrent cadences1 the old man called  
up  houses close together1 than         
scattered singly along roads which      
stretched  away into the distance1 to be
 seen every here and there perfectly    
clearly where they ascended a rising    
ground4 ,and near at hand could be      
distinguished fields of grain and       

pasture land4    ,yet as the king turned
 to walk towards the new scene1 the old 
man  laughed4 8,all this is a dream10 he
 cried2 8so much ,i can do1 but not at  
once40 ,and breathing peals of music    
from his pipe1 he said1 8,this can  be1 
but is not yet40    8,what10 asked the  
king1 8is all a delusion80 and as he    
asked everything  sank down4 ,there was 
no palace1 no houses or fields1 only the
 steep  precipice-locked valley1 whither
 the king had ridden2 and his horse     
cowering behind him4    ,then the king  
cried1 8,thou art some moonstruck       
hermit1 leading out a  life of folly    
alone4 ,get thee to the village thou    
knowest1 and bring me  help40    ,but   
the old man answered him saying1 8,great
 king1 ,i am bound to obey  thee1 and   
all the creative might of my being ,i   
lay at thy feet2 and lo1  in the midst  
of this valley ,i make for thee beings  
such as ,i can  produce4 ,and all that  
thou hast seen is as nothing to what ,i 
can do for  thee4 ,the depths of the    

starry heavens have no limit1 nor what  
,i do for  thee4 ,hast thou ever in thy 
life looked into the deep still ocean1  
and  lost thy sight in the unseen       
depths8 ,even so thou wilt find no end  
in  what ,i will give thee4 ,hast thou  
ever in thy life sought the depths of   
thy love's blue eyes1 and found therein 
a world which stretched on  endlessly8  
,even so ,i bring all to thy feet4 ,now 
that all the gladness of  the world has 
departed from thee1 behold1 ,i am a more
 willing servant  than ever thou hast   
had40    ,and again he played1 and a hut
 rose up with a patch of cleared soil   
around it1 and a spring near by4        
,then the king said1 8,here will ,i     
dwell1 and if ,i am to be cut off from  
the rest of the world1 ,i will lead a   
peaceful life in this valley40    ,the  
sun was rising1 the sounds had ceased1  
and the old man had  disappeared4       
,,chapter ,,ii4    ,he made his way     
slowly to the patch of cultivated       
ground1 he knocked at  the door of the  

hut1 and then he called out4 ,no answer 
was made to the  sound of his voice1 he 
entered1 and saw a rude1 plain interior4
 ,there  were two forms half lying1 half
 propped up by the walls1 and some      
domestic implements lay about4 ,but when
 he spoke to the beings they did  not   
answer1 and when he touched their arms  
they fell powerless on the  ground and  
remained there4 ,a terrible fear came on
 the king lest he  should become such as
 these4 ,he left them and again sought a
 possible  outlet1 but fruitlessly4 ,and
 that evening he sought the old man     
again  and inquired what sort of beings 
these were4    8,for though in form and 
body like children outwardly10 said the 
king1  8they do nothing and seem unable 
to move2 are they in an enchanted       
slumber80    ,then the old man came near
 to the edge of the ravine and1 speaking
  solemnly and low1 said3    8,o king1  
thou dost not yet know the nature of the
 place wherein thou  art4 ,for these    
children are like the children thou hast

 known always  both in form and body4 ,i
 have worked on them as far as is within
 my  power4 ,but here in this valley a  
law reigns which binds them in          
sleepfulness and powerlessness4 ,for    
here in everything that is done  there  
is as much pain as pleasure4 ,if it is  
pleasant to tread a downward  slope     
there is as much pain in ascending the  
upward slope4 ,and in every  action     
there is a pleasant part and a painful  
part1 and in the tasting  of every herb 
the beings feel a bitter taste and a    
sweet taste1 so  indistinguishably      
united that the pleasure and the pain of
 eating it are  equally balanced4 ,and  
as hunger increases the sense of the    
bitterness in  the taste increases1 so  
it is never more pleasant to eat than   
not to  eat4 ,everything that can be    
done here affords no more pleasure than 
it  does pain1 from the greatest action 
down to the least movement4 ,and the    
beings as ,i can make them1 they follow 
pleasure and avoid pain4 ,and if  the   

pleasure and the pain are equal they do 
not move one way or the  other40        
8,this is impossible10 said the king4   
8,nay10 said the old man1 8that it is as
 ,i have said ,i will prove to  thee40  
,and he explained to the king how it    
would be possible to  stimulate the     
children to activity1 for he showed him 
how he could  divest anything that was  
done of part of its pain and render it  
more  pleasurable than painful4 8,in    
this way thou canst lead the beings ,i  
have  given thee to do anything10 said  
the old man1 8but the condition is that 
thou must take the painful part that    
thou sparest them thyself40 ,and he     
bade the king cut himself of the reeds  
that grew by the side of the  ravine1   
and told him that putting them between  
himself and any being  would enable him 
to take a part of the pain and leave in 
their feeling  the whole of the pleasure
 and the pain diminished by that part   
which he  bore himself4    ,then the    
king cut of the reeds that grew by the  

side of the ravine4 ,he  went to the hut
 where these beings lay1 and1 taking the
 reeds in his  hand1 he placed one      
between the child's frame and himself4  
,and the child  rose up and walked1     
while he himself felt a pain in his     
limbs4 ,and he  found that by taking a  
pain in each part of him the child would
 exercise  that part2 if he wished the  
child to look at anything he1 by bearing
 a  pain in his eyes1 made looking at it
 pleasurable to the child1 and          
accordingly the child did look at the   
object he wished him to regard4  ,and   
again1 by bearing a bitter taste in his 
mouth he made the child feel  eating as 
pleasant1 and the child gathered fruits 
and ate them4    ,then the king by using
 two reeds made both the children move1 
and they  went together wheresoever he  
wished them4 ,but they had not the      
slightest  idea of the king's action on 
them4 ,they recognized each other1 and  
played with each other4 ,they saw the   
king and had a certain regard for  him1 

but of his action on them they knew     
nothing4 ,for they felt his  bearing the
 pain as this thing or that being       
pleasurable4 ,they felt his  action as a
 motive in themselves4    ,and all day  
long the king went with them1 leading   
them through the  valley1 bearing the   
pain of each step1 so that the children 
felt nothing  but pleasure4 ,but at     
nightfall he led them back to the rude  
dwelling  where he had found them4 ,he  
led them by taking the pain from their  
steps  in that direction1 and not taking
 any of the pain from steps in any      
other direction4    ,and when they had  
entered the dwelling-place he removed   
his reeds from  them4 ,immediately they 
sank down into the state of apathy in   
which he  had found them4 ,they did not 
move4    ,and the king at nightfall     
sought again the side of the ravine4    
,gazing across it he saw the sandy waste
 of the land from which he had  come1 he
 saw the great stones which were        
scattered about1 looking pale  and grey 

in the moonlight4 ,and presently in the 
shadow of a rock near  the opposite     
brink he discerned the form of the old  
man4    ,and he cried out to him1 and   
bade him come near4 ,and when the old   
man  stood opposite to him1 he besought 
him to tell him how he could make the   
beings go through their movements of    
life without his bearing so much  pain4 
,and the old man took his staff in his  
hand1 and he held it out towards  the   
king1 over the depth4    8,behold1 ,o   
king1 thy secret10 he cried4 ,and with  
his other hand he smote  the staff which
 was pointing down into the depths4 ,the
 staff swung to  and fro many times1 and
 at last it came to rest again4    ,then
 the king besought him to explain what  
this might signify4    8,thou hast      
been10 replied the old man1 8as one who1
 wishing to make a  staff swing to and  
fro1 has made every movement separately1
 raising it  up by his hand each time   
that it falls down4 ,but1 behold1 when  
,i set it  in movement it goes through  

many swings of itself1 both downward and
  upward1 until the movement ,i imparted
 to it is lost4 ,even so thou must  make
 these beings go through both pleasure  
and pain1 thyself bearing but  the      
difference1 not taking all the pain40   
8,must ,i then10 asked the king1 8by    
bearing pain give these beings a        
certain store of pleasure1 and then let 
them go through their various  actions  
until they have exhausted this store of 
pleasure80    ,then the old man made    
answer4 8,can ,i have any secrets from  
thee8  ,hearken1 ,o king1 and ,i will   
tell thee what lies behind the shows of 
the  world4 ,what ,i have shown thee is 
an outward sign and symbol of what thou 
shouldst do1 but it lies far outside    
those recesses whither ,i shall lead    
thee4 ,thou couldst indeed give these   
beings a store of pleasure1 and  they   
would go through their actions until it 
was all spent2 but then  thou wouldst be
 as one of themselves4 ,thou wouldst    
have to perform the  painful part of    

some action and let them perform the    
pleasant part1 and  thus thou wouldst be
 immersed in the same chain of actions  
wherein they  were4 ,for regard my staff
 as it begins to swing4 ,it is not ,i   
that make  the movement that is imparted
 to it2 that movement lay stored up in  
my  arm1 and when ,i struck the staff   
with my arm it was as if ,i had let     
another staff fall which in its falling 
gave up its movement to the one  ,i held
 in my hand40    8,where1 then1 does the
 movement go to when the staff ceases to
 swing10  asked the king4    8,it goes  
to the finer particles of the air1 and  
passes on and on4 ,there  is an endless 
chain4 ,it is as if there were          
numberless staffs1 larger  and smaller1 
and when one falls it either raises     
itself or passes on its  rising to      
another or to others4 ,there is an      
endless chain of movement to  and fro1  
and as one ceases another comes4 ,but1  
,o king1 ,i wish to take  thee behind   
this long chain and to place thee where 

thou mayest not say1  ,i will do this or
 that2 but where thou canst say1 ,this  
whole chain of  movement shall be or    
shall not4 ,for as thou regardest this  
staff  swinging thou seest that it moves
 as much up as it does down1 as much to 
right as to left4 ,and if the movements 
which it goes through came  together it 
would be at rest4 ,its motion is but    
stillness separated into  equal and     
opposite motions4 ,and in what thou     
callest rest there are vast  movements4 
,it shall be thine1 ,o king1 to strike  
nothingness asunder and  make things be4
 ,nay1 ,o king1 ,i have not given thee  
these beings in the  valley for thee to 
move by outward deeds1 but ,i have given
 them to thee  such that thou canst     
strike their apathy asunder and let them
 live4 ,and  know1 ,o king1 that even as
 those beings are whom thou hast found1 
so are  all things in the valley down to
 the smallest4 ,the smallest particle   
there is in the valley lies1 unless it  
were for me1 without motion4 ,each      

particle has the power of feeling pain  
and of feeling pleasure1 but by  the law
 of the valley these are equal4 ,hence  
of itself no particle  moves4 ,but ,i   
make it move1 and all things in the     
valley sooner or later  move back to    
whence they came4 ,the streams which    
gather far off in the  valley ,i lead   
along to where they fall into the depths
 between us4 ,there  they shiver        
themselves into the smallest fragments1 
and each fragment ,i  cause to return   
whence it first came4 ,and1 ,o king1 in 
all this movement1  since it ends where 
it began1 there is no more pleasure than
 pain4 ,it is  but the apathy of rest   
broken asunder4 ,but the particles will 
not go  through this round of           
themselves4 ,i bear the pain to make    
them go  through1 each one the round ,i 
appoint it40    8,how then10 exclaimed  
the king1 thinking of the pain he had   
felt in  directing the movements of the 
children1 8canst thou bear all this     
pain80    8,it is not much10 answered   

the old man2 8and were it more ,i would 
willingly bear it for thee4 ,for think  
of a particle which has made the  whole 
round of which ,i spoke to you--it will 
make this journey if on the  whole there
 is the slightest gain of pleasure over 
pain2 and thus1  although for each      
particle in its movement at every moment
 ,i bear the  difference of pain1 the   
pain for each particle is so minute that
 the  whole course of natural movements 
in the valley weighs upon me but        
little4 ,and behold all lies ready for  
thee1 ,o king4 ,i have done all that  ,i
 can do4 ,i can perfect each natural    
process1 each quality of the  ground1   
each plant and herb ,i make1 up to the  
beings whom thou hast  found4 ,they are 
my last work1 and into your hands ,i    
give them40    ,and when he had said    
this1 the old man let drop his staff1   
and placing  both hands to his breast he
 seemed to draw something therefrom1 and
 with  both hands to fling it to the    
king4    ,for some moments' space the   

king could distinguish nothing1 but soon
 he  became aware of a luminousness over
 the mid ravine4 ,something palely      
bright was floating towards him4 ,as the
 brightness came nearer he saw  that it 
was a centre wherein innumerable bright 
rays met1 and from which  innumerable   
bright rays went forth in every         
direction4    8,take that10 the old man 
cried4 8,the rays go forth unto         
everything in  the valley4 ,they pass   
through everything unto everything4     
,through them  thou canst touch         
whatsoever thou wilt40    ,the king took
 the rays and placed them on his breast2
 thence they went  forth1 and through   
them he touched and knew every part of  
the valley4  ,and thinking of the hut   
where the children lay1 the king        
perceived  through the rays that went   
thither that the walls were tottering1  
and  like to fall on the children4 ,and 
through his rays he knew that the       
children perceived this in a dull kind  
of way2 but since in their life  there  

was no more pleasure than pain1 they did
 not feel it more pleasant  to rise up  
and move than to be still and be buried4
    ,but the king through the rays1 as  
before through the reeds1 took the  pain
 of moving1 and the children rose and   
came out of the hut2 and soon  they were
 with the king1 running and bounding as 
never children leapt  and ran1 with     
ecstasy of movement and unlimited       
exuberance of spirit4  ,but as they     
leapt and ran the king felt an          
increasing pain in all his  limbs4      
,still he liked to see them in their    
full and joyous activity1 and  he wished
 them to cast off that dull apathy in   
which they lay4 ,so all  through the    
night he roamed about with them thinking
 of all the wildest  things for them to 
do1 and leading them through dance and  
play1 every  movement and activity he   
could think of4    ,at length the rising
 sun began to warm the air1 and the     
king1 exhausted  with pain1 left off    
bearing it for them4    ,after a few    

languid movements the children sank down
 on a comfortable  bank into a state of 
absolute torpor4 ,the king looked at    
them2 it seemed  inconceivable that they
 could be the same children who had been
 running  about so merrily a few moments
 ago4 ,thus far he had received no      
advantage from the rays the old man had 
given him1 except that he could  touch  
the children more easily4    ,he turned 
wearily and looked around4 ,his horse   
stood there4 ,but instead  of whinnying 
and running up to greet him1 the        
faithful animal stood  still1 looking   
across the ravine4    8,perchance       
without my burden1 and with the strength
 these rays may  impart10 thought the   
king1 8he might manage the leap40       
,the horse was standing opposite the    
remains of the natural bridge over      
which the two had so rashly crossed the 
day before4 ,the king touched the  horse
 with his rays4 ,as with a sudden thrust
 of the spur1 the noble  animal rushed  
forward and leapt madly from the        

fragments of the arch4  ,his fore feet  
gained the opposite brink1 and with a   
terrible struggle he  raised himself on 
the firm ground4 ,then he stood still4  
,with a crash the  remaining fragments  
of the bridge fell into the gulf1       
leaving the vast  gap unnarrowed at any 
part4 ,the horse stood looking over the 
ravine4 ,but  though the king called him
 by name1 the faithful creature who used
 to  come to him at the slightest       
whisper paid no heed4 ,in a few moments 
he  galloped off along the track the    
courtiers had pursued4                  
,,chapter ,,iii4    ,the king being left
 thus with the children1 applied himself
 to thought4  ,he directed his rays to  
one of the children and caused it to    
stand up1  and1 following the counsel of
 the old man1 he thought of an action4  
,the  action he thought of was that of  
walking1 and he separated it into two   
acts2 the one act moving the right foot1
 the other act moving the left  foot4   
,and he separated the apathy in which   

the child was into pleasure  and pain2  
pleasure connected with the act of      
moving the right foot1 pain  connected  
with the act of moving the left foot4   
,immediately the child  moved forward   
its right foot1 but the left foot       
remained motionless4 ,the  child had    
taken the pleasure1 but the pain was    
left2 or1 since the king  had connected 
the pleasure and pain with two acts1 it 
may be said1 had  done the pleasant act 
and left the painful act undone4        
,after waiting some time to see if the  
child would move1 the king took  the    
pain of moving the left foot2 instantly 
the child moved it1 and as  soon as it  
had come to the ground again it moved   
the right foot1 which  was the pleasant 
act4 ,but then it stopped4 ,and by no   
amount of taking  pains in the matter of
 the left foot could the king get the   
child into  the routine of walking4 ,as 
soon as he ceased to take the pain of   
moving  the left foot1 the child        
remained with the right foot forward4   

,at last  he removed his attention from 
the movement of the child1 and it sunk  
back again torpor4    ,the rest of the  
day the king spent in reflection1 and in
 making  experiments with the children4 
,but he did not succeed any better4     
,whatever action he thought of they went
 through the pleasant act1 but  made no 
sign of going through the painful act4  
,when darkness came the king perceived  
the faint luminousness of his  rays3    
unless he had known of them he would    
hardly have perceived it4    ,and now he
 tried a new experiment4 ,he took one of
 the rays1 and1  detaching it from the  
rest1 he put it upon the body of one of 
the  children1 going out from its body  
and returning again to its body1 so     
that it went forth from the child and   
returned to the child again4 ,he  then  
caused the child to stand up1 and again 
tried it with the action of  walking4   
,his idea was this3 the child required a
 power of bearing its  own pain in order
 to go through a painful act1 and as the

 rays enabled  him to bear their pain1  
the ray proceeding from the child and   
coming  back to it might enable it to   
bear its own pain4 ,and now he separated
  the apathy into pleasure and pain as  
before4 ,the child moved the right      
foot1 and then when it had moved it1 he 
saw that it actually began to  move the 
left foot4 ,but it did not move it a    
complete step1 and after  the next      
movement of the right foot the left foot
 did not stir4    ,again and again the  
king tried the children1 but his        
attempts came to  nothing4 ,one halting 
step of the left foot he could get them 
to go  through1 but no more4    ,he     
spent many hours4 ,suddenly the cause of
 his failure flashed upon him4  8,of    
course10 he said to himself1 8they don't
 move1 for ,i have forgotten  to take   
part of the pain4 ,if they went on      
moving their left feet they  would have 
no balance of pleasure40    ,and he     
tried one of them again4 ,the child     
moved the right foot1 then  began to    

move the left foot4 ,the king now by    
means of his rays took part  of the pain
 of the movement of the left foot1 and  
the child completed  the step with it4  
,then of course it moved the right foot1
 for that was  pleasant1 and again the  
king took part of the pain of moving the
 left  foot1 and the child completed its
 second step4 ,it walked4    ,the       
difficulty was surmounted4 ,soon both   
the children were moving hither  and    
thither like shifting shadows in the    
night1 and the king felt just a  shade  
of pain4    ,the children would come up 
to him and talk with him1 if he took the
  difference of pain which made it      
pleasant for them to do so4 ,but they   
had no idea of his action on them1 for  
by his taking the difference of  pain   
they found an action pleasant1 and felt 
a motive in themselves to  do it1 which 
they did not in the least connect with  
the being outside  themselves to whom   
they spoke4 ,they looked on him as some 
one more  powerful than themselves1 and 

friendly to them4    ,as soon as he was 
assured of the practical success of his 
plans1 the  king let the children       
relapse into their apathy while he      
thought4 ,he  conceived the design of   
forming with these children a state such
 as he  had known on earth--a state with
 all the business and affairs of a      
kingdom1 such as he had directed before4
 ,the vision of the palace which  the   
old man had shown him rose up4 ,he saw  
in imagination the fertile  fields1 with
 the roads stretching between them2 he  
saw all the varied  life of a great     
state4 ,accordingly from this time he   
was continually  directing their        
existence1 developing their powers1 and 
learning how to  guide them4 ,and just  
as on first learning to read whole words
 are learnt  which are afterwards split 
up into letters by the combinations of  
which  other words are formed2 so at    
first he thought of actions of a        
complicated nature1 such as walking1 and
 associated the moments of  pleasure and

 pain with the acts of which such       
actions were composed4 ,but  afterwards 
he came to regard the simpler actions by
 the combination of  many of which the  
beings were made to walk1 and with the  
separate acts  of these simple actions  
he associated pleasure and pain4    ,and
 at first the beings were conscious of  
these simple acts and nothing  else1 but
 in order that they might carry out more
 complicated actions1  he developed the 
dim apprehension which they had1 and led
 it on to the  consciousness of more    
complicated actions4 ,the simplest      
actions became  instinctive to these    
beings1 and they went through them      
without knowing  why4 ,but if at any    
time the king ceased to take the        
difference of pain1  these actions1     
seemingly automatic as they were1       
ceased4    ,at certain intervals the    
king found his plans inconvenienced4    
,every now  and then the beings went off
 into a state of apathy4 ,enough pain   
was  borne for them to make it just     

worth their while to go through the     
actions of each routine4 ,but any       
additional complication or hindrance    
unforeseen by the king was too much for 
them1 and they sank under it4 ,to       
remedy this he took in every action a   
slight portion of pain more than  he had
 done at first4 ,thus he expended a     
certain portion of pain-bearing  power  
to give stability to the routines4 ,and 
the margin of pleasure over  pain thus  
added was felt by the beings as a sort  
of diffused pleasure in  existence1     
which made them cling to life4    ,now  
in guiding these beings towards the end 
he wished to obtain1 the  king had to   
deal with living moving beings1 and     
beings whose state was  continually     
changing4 ,and this led him to adopt as 
the type of the  activity of these      
beings not a single action1 but a       
succession of  actions of the same kind1
 coming the one after the other4 ,thus a
 being  having been given a certain     
activity1 it continued going on in a    

uniform  manner until the king wished to
 alter it4    ,again it was important to
 keep the beings together1 to prevent   
their  being lost in the remote parts of
 the valley1 and consequently the king  
took1 other things being equal1 a       
certain amount of the pain of motion    
towards the centre1 and took none of the
 pain in any movement away from  the    
centre of the valley4 ,thus the         
inhabitants had a tendency to come      
towards the centre1 for there was a     
balance of pleasure in doing so1 and    
thus they were continually presenting   
themselves to his notice1 and not       
getting lost4    ,of course1 if there   
was any reason why he wanted them away  
from the  centre1 the king ceased his   
bearing of the pain of motion towards   
the  centre1 and then they were under   
the other tendency solely1 which he     
imparted to them1 in virtue of his      
bearing pain in another respect4 ,and   
in everything that he did the king had  
regard to the circumstances in  which   

the beings were placed1 and the objects 
which he wanted to obtain4  ,he did not 
spare any of his pain-bearing power to  
give them pleasure  purely as a feeling1
 but always united the pleasure he      
obtained for them  by his suffering with
 some external work4    ,and as time    
went on and the number of the           
inhabitants increased1 he  introduced   
greater order and regularity into the   
numberless activities  which he         
conceived for them4 ,the activities     
formed regular routines1  conditioned by
 the surroundings of the being and the  
routines of those  around it4 ,a routine
 did not suddenly cease without         
compensation2 but if  the king wished it
 to stop he let another activity spring 
up at once in  place of it1 so that     
there was no derangement4 ,the beings   
gradually  became more intelligent1 so  
that they could be entrusted with more  
difficult routines1 and carried them out
 successfully1 the king1 of  course1    
always taking the difference of pain    

necessary to make it worth  their while4
 ,and they even became able to carry out
 single activities on  a large scale1   
involving the co-operation of many      
single routines4 ,for  they had a sense 
of analogy1 and observing some activity 
which the king  had led them through on 
a small scale1 and in which they had    
found a  balance of pleasure1 they were 
ready to try a similar one on a larger  
scale4    ,there was one feature        
springing from the advanced intelligence
 of the  inhabitants which it is worth  
while to mention4 ,many of the possible 
activities which the beings could go    
through1 instead of consisting of a     
pleasurable part first and a less       
painful part afterwards1 consisted of  a
 painful part first and a pleasurable   
part afterwards4 ,this might  happen by 
the particular arrangement of the acts  
of which the compounded  activity       
consisted1 the acts having already      
moments of pain or pleasure  affixed to 
them1 and happening to occur in such    

dispositions that the  first part of the
 activity was painful1 the next part    
pleasurable4    ,now when the           
intelligence of the inhabitants was     
developed1 the king1 by  leading them to
 think of such an activity1 could induce
 them to go  through with it4 ,for the  
idea of the pleasure which would        
accompany the  second part of the       
activity lightened the pain of the      
first4 ,and this1  combined with the    
portion of the pain which the king bore1
 almost  counterbalanced the pain       
connected with the first part of the    
activity4  ,thus the beings were enabled
 to go through the painful part of the  
activity4 ,but when they came to the    
second part of the activity the         
creatures were much disappointed4 ,for  
by the law of the valley pleasure  and  
pain were equal 7except for the small   
part which the king bore74 ,now  the    
pleasures of expectation had been so    
great that when the time came  for the  
act usually associated in their minds   

with pleasure1 the  pleasure due had    
most of it been used up4    ,from this  
circumstance a saying arose amongst the 
inhabitants which was  somewhat         
exaggerated1 but which had a kernel of  
truth in what has just  been described4 
,the saying was that 8,the pleasure for 
which a labour has  been undertaken     
flies away as soon as the labour has    
been finished1 and  nothing is left but 
to begin a new labour40 ,and1 again1    
another saying3  8,the enjoyment of a   
thing lies in its anticipation1 not in  
its  possession40    ,all this which has
 been so briefly described had in       
reality taken a long  time4 ,and now    
fields were cultivated1 better houses   
were built4 ,the  inhabitants of the    
valley had increased greatly in number1 
and were  divided up into several       
tribes1 inhabiting different parts of   
the  valley4 ,but the most favoured     
position was the centre1 and for the    
possession of the centre there were     
contentions and struggles4 ,there the   

king's activity in bearing was greatest1
 and the life was most  developed4      
,all around the outskirts of the valley 
dwelt the ruder and less advanced       
people1 who were called barbarians and  
savages by those nearer the  centre4    
,,chapter ,,iv4    ,now when the king   
saw the inhabitants becoming more like  
the human  beings he had known1 he felt 
that he was solitary1 and he desired to 
have some intercourse with them4 ,but   
when he appeared amongst them they      
recognized him at once as some one more 
powerful than themselves1 and  were     
afraid of him4 ,in their alarm they     
tried to lay hands on him4 ,when  he1 to
 prevent their attacks1 withdrew his    
continued bearing the  difference of    
pain in their actions1 those who were   
attacking him sank  into apathy and     
became as the children whom he had first
 found4    ,and a horrible report sprang
 up amongst the inhabitants of a        
terrible  being who came amongst them1  
and who struck all who looked on him    

with  torpor and death4 ,so the king    
ceased to walk amongst them4 ,still it  
was  long since he had heard the sound  
of a voice speaking to him1 and he      
wished for a companion4 ,he sought again
 the old man1 and standing at the  edge 
of the chasm he called upon him4    ,and
 the old man appeared4 8,art thou weary1
 ,o king1 of thy task80    8,nay10      
replied the king2 8but ,i wish to make  
myself known to the  inhabitants that ,i
 may speak with them and they with me40 
,and the old man counselled him to give 
some of his rays to one amongst  the    
beings1 for then this being having these
 rays and the power of  bearing pain for
 another other than himself1 would be   
like the king1 and  being like him would
 understand him4    ,now the king sought
 over the whole of the valley1 and of   
all the  inhabitants he found one most  
perfect in form and in mind4 ,he was the
  son of a king1 and destined to reign  
in his turn over a numerous people4     
,and the king gave him some of his rays1

 straight rays going forth from  the    
prince to others4    ,and immediately   
the prince awoke as it were from a      
dream4 ,and he  comprehended existence1 
and saw that in reality the pain and the
  pleasure were equal4 ,and when he had 
seen this1 and knew the power of  the   
rays1 and how by bearing pain he could  
make others pass through  pleasure and  
pain1 and call those sleeping into      
activity2 when the  prince knew this1 he
 cried out3    8,one thing succeeds     
another in the valley2 pain follows     
pleasure1 and  pleasure follows pain4   
,but the cause of all being is in       
bearing pain4  ,wherefore10 he cried1   
8let us seek an end to this show4 ,let  
us pray to  be delivered1 that at last1 
pain ceasing1 we may pass into          
nothingness40    ,thus the prince1      
apprehending the cause of existence1    
felt that it was  pain1 and dimly       
comprehending how the king was bearing  
pain1 and himself  feeling the          
strenuousness of the effort of using the

 rays for which the  frame of the       
inhabitants was unstrung1 longed that   
existence itself  might cease4    ,yet  
all his life his deeds were noble1 and  
he passed from tribe to  tribe1 bearing 
the burdens and calling forth the       
sleeping to activity4                   
,,chapter ,v4    ,it is now the place in
 which to give a clear account of the   
king's  activity1 and explain how he    
maintained the varied life of the       
valley4    ,and the best plan is to take
 a typical instance1 and to adopt the   
,arabic  method of description4 ,by the 
,arabic method of description is meant  
the  same method which the ,arabs used  
for the description of numerical        
quantities4 ,for instance1 in the       
,arabic notation1 if we are asked the   
number of days in the year1 we answer   
first #cjj1 which is a false  answer1   
but gives the nearest approximation in  
hundreds2 then we say  sixty1 which is a
 correction2 last of all we say five1   
which makes the  answer a correct one1  

namely1 #cfe4 ,in this simple case the  
description  is given so quickly that we
 are hardly conscious of the nature of  
the  system employed4 ,but the same     
method when applied to more difficult   
subjects presents the following         
characteristics4 ,firstly1 a certain    
statement is made about the subject to  
be described1 and is impressed  upon the
 reader as if it were true4 ,then1 when 
that has been grasped1  another         
statement is made1 generally somewhat   
contradictory1 and the  first notion    
formed has to be corrected4 ,but these  
two statements taken  together are given
 as truth4 ,then when this idea has been
 formed in the  mind of the reader1     
another statement is made which must    
likewise be  received as a correction1  
and so on1 until by successive          
statements and  contradictions1 or      
corrections1 the idea produced          
corresponds to the  facts1 as the       
describer knows them4    ,thus the      
activity of the king will be here       

described by a series of  statements1   
and the truth will be obtained by the   
whole of the  statements and the        
corrections which they successively     
bring in4    ,when the king wished to   
start a being on the train of activity  
he  divided its apathy into pleasure and
 pain4 ,the pleasure he connected  with 
one act which we will call ,a4 ,the pain
 he associated with another  act which  
we will call ,b4    ,these two 8acts10  
,a and ,b1 which together form what we  
call an 8action10  were of such a nature
 that the doing of ,a first and then of 
,b was a  process used in the           
organization of the life in the valley4 
,thus the act ,a may be represented by  
moving the right foot1 ,b by moving  the
 left foot1 then ,,ab will be the action
 of taking a step4 ,this however  is but
 a superficial illustration1 for the    
acts which we represent by ,a  and ,b   
were fundamental acts1 of which great   
numbers were combined  together in any  
single outward act which could be       

observed or described4    ,suppose for  
the present that there is only one      
creature in the valley4  ,the king      
separates his apathy with regard to the 
action ,,ab4 ,let us say  he separates  
his apathy into #ajjj pleasure and #ajjj
 pain4 ,of the  pleasure he lets the    
being experience the whole1 of the pain 
he bears an  amount which we will       
represent by #b4 ,thus the being has    
#ajjj pleasure  and #iih of pain1 and   
the action is completed4 ,his sensation 
is measured  by the number #ajjj in the 
first act1 and by #iih in the second    
act4    ,but the king did not choose to 
make the fundamental actions of this    
limited and finishing kind4 ,as the type
 of the fundamental activity1 he  chose 
an action1 and made the being go through
 it again and again4 ,thus  the being   
would go through the act ,a1 then the   
act ,b4 ,when the action ,,ab  was      
complete it would go through an act of  
the kind ,a again1 then  through an act 
of the kind ,b4 ,thus the creature would

 be engaged in a  routine of this kind1 
,,ab1 ,,ab1 ,,ab1 and so on4    ,and if 
the creature had been alone1 and this   
had been the sole activity  in which it 
was concerned1 the king would have gone 
on bearing #b of pain  in each of these 
actions4 ,the king would have kept the  
routine going on  steadily1 the creature
 bearing #ajjj of pleasure in each ,a1  
and #iih of  pain in each ,b4    ,at    
this point it may be asked that an      
example should be given of one of  these
 elementary routines which the king set 
going4 ,and this seems a  reasonable    
request1 and yet it is somewhat too     
peremptory4 ,for in the  world we may   
know of what nature the movements of the
 atoms are without  being able to say   
exactly what the motion of any one is4  
,in such a case  a type is the only     
possible presentation4 ,again1 take the 
example of a  crystal4 ,we know that a  
crystal has a definite law of shape1 and
 however  much we divide it we find that
 its parts present the same             

conformation4  ,we cannot isolate the   
ultimate crystalline elements1 but we   
infer that  they must be such as to     
produce the crystal by their            
combination4    ,now life on the valley 
was such in its main features as would  
be  produced by a combination of        
routines of the kind explained4 ,there  
were  changes and abrupt transitions1   
but the general and prevailing plan of  
life was that of a routine of           
alternating acts of a pleasurable and a 
painful kind4 ,it was just such as would
 be built up out of elementary          
routines1 on which the king could count1
 and which1 unless he modified  their   
combinations1 tended to produce rhythmic
 processes of a larger  kind4 ,and even 
the changes and abruptnesses had a      
recurrent nature about  them1 for if any
 routine in the valley altered suddenly1
 it was found  that there were cases of 
other routines altering in like manner1 
when  the conditions under which they   
came were similar4 ,thus the fundamental

  type of the action which the king     
instituted was that of a routine ,,ab1  
,,ab1 as described above4 ,but there    
were two circumstances which caused a   
variation1 so that this simple routine  
was modified4    ,firstly1 there was not
 one being only but many4    ,secondly1 
the king wished to have some of his     
pain-bearing power set  free from time  
to time4 ,he did not wish to have to be 
continually  spending it all in         
maintaining the routines he had started 
at first1 and  those immediately        
connected with them4    ,when he first  
began to organize the life of the beings
 he did not  consciously keep back any  
of his pain-bearing power1 but threw it 
all in  the activities which he started4
 ,still from time to time he wished to  
start new activities quite unconnected  
with the old1 and for this reason  he   
withdrew some of his pain-bearing power1
 as will be shown afterwards4    ,there 
were many beings4 ,the king chose that  
the type of activity in each  should be 

a routine4 ,in that way he could        
calculate on the activity1 and  hold it 
in his mind as a settled process on     
whose operation he could  count4 ,but as
 the routines of the beings proceeded   
they came into  contact with one        
another1 and made1 even by their simple 
co-existence1  something different from 
what a routine by itself was4 ,they     
interwove in  various ways4 ,then1 in   
order to take advantage of the          
combinations of  these routines1 or to  
modify them1 it was necessary to set    
going other  routines4    ,in order to  
be able to originate these connected    
routines the king  adopted the following
 plan4    ,in the first action ,,ab he  
separated the creatures' apathy into    
#ajjj  pleasure and #ajjj pain1 bearing 
#b of the pain himself4 ,the creature   
thus  went through #ajjj of pleasure and
 #iih of pain4 ,in the next action ,,ab 
he  did not separate the beings' apathy 
up into so much pleasure and pain4  ,he 
separated it up into #ihj pleasure and  

#ihj pain1 that is1 each moment  of     
feeling was #bj less in sensation than  
the moments of feeling were in  the     
first action4    ,now it is obvious that
 if the bearing #b of pain will make it 
worth while  for a being to go through  
#ajjj pleasure and #iih pain1 then the  
bearing  on the king's part of #a of    
pain would make it worth while for the  
being  to go through #ejj pleasure and  
#dii of pain4    ,and a similar relation
 would hold for different amounts of    
pleasure and  pain4 ,thus clearly for   
the being to go through #ihj of pleasure
 and the  corresponding amount of pain1 
it would not be necessary for the king  
to  bear so much as when the being went 
through #ajjj of pleasure and the       
corresponding amount of pain4           
,consequently when the king divided the 
beings' apathy into #ihj pleasure  and  
#ihj pain1 it would not be necessary for
 him to bear #b of pain to  make it     
worth the beings' while to go through   
the action4 ,the king would  not bear so

 much as #b of pain1 and thus he would  
have some of his  pain-bearing power set
 free4 ,he would have exactly as much as
 would  enable him to make it worth a   
being's while to go through an action   
with  the moments of #bj of pleasure and
 #bj of pain4    ,and this--with a      
correction which will come later--is    
what the king did4  ,he employed the    
pain-bearing power thus set free in     
starting other  routines4 ,thus in the  
routine ,,ab1 ,,ab1 ,,ab there would be 
first of all the  action ,,ab4 ,then    
along with the second action ,,ab1 the  
king 7with the  pain-bearing power set  
free7 started an action ,,cd--the       
beginning of a  routine ,,cd1 ,,cd1     
,,cd4 ,thus as the first routine went on
 and came into  connection with other   
routines1 new and supplementary routines
 sprang up  which regulated and took    
advantage of the combinations of the old
  routines4    ,the amount of the       
moments of pleasure in the routine ,,cd1
 was 7with a  slight correction         

explained below7 measured in sensation1 
equal to #bj4  ,thus the moment of      
pleasure in the first ,a being #ajjj1   
the moment of  pleasure in the second ,a
 was #ihj1 the moment of pleasure in the
 first ,c  was #bj 7subject to the      
correction spoken of74 ,thus the total  
amount of  sensation in the second ,a   
and the associated act ,c1 taken        
together 7but  for a small correction7  
was equal to the sensation in the first 
,a4 ,hence  the three points which were 
characteristic of the activity of the   
beings  in the valley are obvious       
enough4    #a4 ,there is as fundamental 
type a routine ,,ab1 ,,ab1 ,,ab1 the    
sensation  involved in which goes on    
diminishing4    #b4 ,there are routines 
,,cd1 ,,cd1 c41 connected with ,,ab1    
,,ab1 in which the  sensation which     
disappears in the routine ,,ab1 ,,ab    
seems to reappear4    #c4 ,in the action
 ,,ab itself there is a disappearance of
 sensation4 ,the  sensation connected   
with ,a is #ajjj1 that connected with ,b

 is #iih4 ,thus #b  of sensation seems  
to have disappeared4 ,this #b of        
sensation is of course  the pain which  
the king bore1 and which was the means  
whereby the  creature was induced to go 
through the action at all4 ,but looked  
at from  the point of view of sensation1
 it seems like a diminution of amount4  
,this diminution of amount1 owing to the
 correction spoken of above1 was  to be 
found regularly all through the routine4
    ,and now1 with the exception of the 
final correction1 the theory of the     
king's activity is complete4 ,there are 
certain mathematical difficulties  which
 render an exhaustive account somewhat  
obscure in expression4 ,when  we take a 
general survey of a theory we want to   
see roughly how it all  hangs together2 
but if we mean to adopt it1 the         
exactitude of the  numerical relations  
becomes a matter of vital importance4   
,it must be added that the numbers taken
 above were taken simply for  purposes  
of illustration4 ,in reality the pain   

born by the king was less  in           
proportion4    ,the exhaustive account  
which follows deals with small numerical
  quantities4 ,it had better be omitted 
for the present1 and turned to  later on
 for reference4                         
,,exhaustive ,,account4    ,we keep for 
the time being to the numbers used      
above4 ,when the king had  enough       
pain-bearing power set free in the      
second action of the routine  ,,ab1 ,,ab
 to start another routine ,,cd1 of #bj  
pleasure #bj pain1 he did not  use it   
all4 ,he only used enough of it to set a
 routine going the moments  of pleasure 
and pain in which were #af in sensation4
 ,the routine ,,cd was  made up of acts 
with #af of pleasure and #af of pain4   
,the sensation in the first ,a was      
#ajjj1 in the first ,b it was #iih1     
giving  a disappearance of #b4 ,in the  
second ,a it was #ihj1 and in ,c1 which 
starts  concurrently with the second ,a1
 it was not #bj as might have been      
expected1 but #af1 giving a loss of #d4 

,the second ,a is less than the  first  
,a by #bj4 ,searching for that #bj we   
find #af in ,c4 ,but there has been  a  
disappearance of #d4    ,looking now at 
the successive acts in the series we    
have in ,a #ajjj  sensation1 in ,b #iih 
sensation1 in ,a and ,c together #iif   
sensation4    ,the cause of the loss    
between ,a and ,b has already been      
explained4 ,that  between ,b and the    
second ,a with ,c remains to be         
accounted for4    ,it has been already  
said that the king withdrew some of his 
pain-bearing  power from the routine    
,,ab and all routines connected with it1
 thus he  was enabled to start          
activities altogether unconnected with  
those which  he had originated1 and was 
with regard to the products of his own  
activity as he had been at first1 with  
regard to the beings in the  valley     
before he started them on the path of   
life4 ,and it was in  consequence of his
 withdrawal of his pain-bearing power   
that the amount  of sensation in ,c was 

not #bj but was less4 ,this loss of #d  
of sensation  to the being corresponded 
to a setting free of a certain portion  
of  pain-bearing power on the part of   
the king4 ,and thus as the process went 
on1 a portion of his power was          
continually being returned to him4      
,in the table below the first line of   
figures contains the amount of          
sensation in the actions ,,ab1 ,,ab4    
,the second line of figures contains the
  amount of sensation in the actions    
,,cd1 ,,cd4 ,the third line of figures  
relates to another connected routine    
,,ef1 ,,ef1 which originates in a       
manner similar to ,,cd4 ,the fourth line
 of figures represents the amount  of   
pain borne by the king1 the fifth line  
represents his pain-bearing  power set  
free4     7#a7   #ajjj   #iih   #ihj    
#igh-dj_/ajjj      #ifj                 
#ieh-hj_/ajjj          ,a      ,b     ,a
         ,b            ,a               
,b   7#b7                 #af           
#ae-iih_/ajjj  #ae-fcj_/ajjj            

#ae-fehfdj_/ajjjjjj                     
,c         ,d            ,c             
,d   7#c7                          #af  
#ae-iih_/ajjj                           
,e               ,f   7#d7       #b     
#a-iib_/ajjj        #a-iia_/ajjj        
#cfj_/ajjjjjj   7#e7       #j           
#h_/ajjj           #h_/ajjj             
#fdj_/ajjjjjj    ,if the total amount of
 sensation which is experienced by the  
being in  the original routine and the  
connected routines in the consecutive   
stages be summed up1 it will be found to
 be                     #ajjj1 #iih1    
#iif1 #iid-hh_/ajjj1 #iia-fhj_/ajjj1    
and so on4    ,finally1 the proportion  
of pain borne by the king was so small  
compared  with the sensation experienced
 by the being1 that ,a and ,b were      
apparently equal in sensation4 ,thus the
 sensation in the second ,a and in  ,c  
together becomes apparently equal to    
that in ,b4 ,and instead of the         
sensation diminishing quickly as shown  
above1 it was only after a great  many  

acts of the primary and connected       
routines had been gone through  that any
 diminution of sensation in the form    
which the being could  experience it was
 to be detected4 ,thus1 as before       
stated1 there was3    #a4 ,a routine of 
continually diminishing sensation4      
#b4 ,connected routines the sensation in
 which was apparently equal to  that    
lost in ,a4    #c4 ,there was a         
continuous disappearance of sensation   
from the experience  of the beings      
accompanying every step of the routine4 
,the sensation  which they could        
experience was less in every subsequent 
step and  connected steps than in any   
one in which it was measured4           
,,chapter ,,vi4    ,the history of the  
events which took place in the valley in
 their due  order and importance must be
 sought elsewhere4 ,but let us return   
and  look at the condition of the valley
 and its inhabitants4 ,let us see what  
has become of them after a great lapse  
of time4    ,it is a fair1 a beautiful  

land4 ,the greater part of it is        
cultivated4  ,there is no war--even to  
the extremest confines of the valley    
there is  peace4 ,passing from the      
remote confines where still dwell a     
barbarous  race1 we come1 as we approach
 the metropolis1 amongst a more and more
  polite and refined people4 ,in the    
metropolis itself the buildings are     
numerous and of great size4 ,the palace 
which the king saw rise under the  old  
man's music is there1 but another ruler 
dwells in it4 ,near the  palace are two 
vast buildings standing on each side of 
a wide open  court4 ,there is no other  
building near save one between them1 a  
comparatively small edifice of brick4   
,these buildings are the assembly  halls
 of the two most important councils in  
the valley4 ,in the one on  the         
left-hand side of the palace met the    
most distinguished of the  inhabitants  
who from a special inclination or       
fitness were entrusted  with the        
regulations about the pleasure and pain 

of the inhabitants4  ,they framed the   
rules according to which each inhabitant
 must conform in  his pursuit of        
pleasure1 and they made the regulations 
whereby the whole  body of inhabitants  
were supposed to gain an increase in    
pleasure and to  avoid pain4    ,in the 
building on the right hand of the palace
 met those of the  inhabitants who had  
studied the nature of feeling most      
deeply1 and who  from temperament or for
 other reasons had in their course of   
study not  paid so much attention to    
whether feelings were painful or        
pleasurable1  but who had studied their 
amount and regularity of their          
recurrence4  ,they were the thinkers    
from whom all the practical inhabitants 
derived  their rules of business4 ,they 
devised the means and manner of putting 
into execution what was decided on in   
the other assembly4 ,they did not  often
 propose any positive enactment         
themselves1 but were always able to     
show how the proposals of the other     

council could be carried into  effect4  
,their power was derived in this manner4
 ,the king had connected the  feelings  
of pleasure and pain with certain acts1 
and had given each  being a routine4    
,now as he himself made use of this     
routine and combined  the routines of   
different individuals to bring about the
 results he  desired1 so also did the   
rulers of the valley4 ,the routines of  
the  individuals were studied and       
classified1 and if any work was required
 to  be done1 those individuals whose   
routines were appropriate were selected 
and brought to the required spot4 ,now  
to effect this a careful study of  the  
different routines was necessary1 and   
also a knowledge of what stage  they    
were at4 ,for it would be no use        
bringing an individual whose  routine   
was almost at an end to a work which was
 just beginning4 ,hence  the most       
delicate instruments and processes had  
been devised for  measuring the amount  
of feeling experienced by any           

individual1 whether  of pleasure or of  
pain1 and a careful classification had  
been made of  all routines4    ,but it  
is best to study the constitution of the
 state in a regular  order1 and the     
questions of pleasure and pain          
considered as such were  esteemed the   
most important4    ,the inhabitants knew
 that they sought pleasure and avoided  
pain1 and the  great object was to make 
their life more pleasurable4 ,two means 
were  adopted1 the banishing of the     
causes of pain1 and the obtaining causes
  of pleasure4    ,by causes of pain and
 pleasure they meant those objects with 
which the  king had associated the      
feelings of pleasure and pain in the    
equal and  opposite moments into which  
he had divided their apathy4    ,but in 
this respect they were in error to a    
certain extent1 for it was  not so much 
in respect to things as in respect to   
actions that the king  separated their  
apathy into pleasure and pain4 ,for     
instance1 there was a  peculiar species 

of shell which was found in many parts  
of the valley1  covered with strange and
 involved lines and marks4 ,now the king
 had  struck the apathy of the          
inhabitants into two moments with regard
 to  this shell1 one of pain connected  
with tracing out the twistings and      
interweavings of the hues on the shell1 
one of pleasure in contemplating  the   
shell when the twistings and            
interweavings had been deciphered4 ,now 
it was the custom of the inhabitants to 
call the shell in its  undeciphered     
condition a painful object1 in its      
deciphered condition a  pleasant object4
 ,and whoever could1 would get as many  
deciphered shells  as possible and      
experience the wave of pleasure in      
looking at them4    ,now in the earlier 
ages those who deciphered the shells1 or
 did work of  a similar kind1 had been  
forced to do it2 they were a kind of    
slaves  dependent on the will of their  
masters1 who took away all the pleasures
  of their life4 ,but in these earlier  

ages a great danger arose1 for when  all
 the pleasure was taken away by their   
masters1 great masses of these  slaves  
sank into apathy1 and it seemed as if   
the valley was sinking into  deadness4  
,now this was a great terror with the   
inhabitants whose life was  pleasurable1
 and at length they determined that     
there should not be any  more of these  
slaves4 ,but each of the inhabitants    
when he worked for  another had to have 
it made worth his while4    ,in this way
 a great diminution took place in the   
pleasure-giving power  of the so-called 
pleasurable things4 ,for if a man had   
had it made worth  his while to decipher
 one of these shells1 he had had a great
 deal or  nearly all of the pain he     
spent in doing it counterbalanced by the
  pleasure given him to induce him to do
 it4 ,hence when the shell was  handed  
over there was not much to enjoy in it2 
for by the law of the  valley the       
pleasure and the pain were equal1 and   
the decipherer1 not  having gone through

 so much pain on the whole1 there was   
but little  pleasure to be got4    ,in  
fact1 at this time the fashion of       
filling the houses of the more  powerful
 of the inhabitants with the so-called  
pleasurable things had  somewhat gone   
out1 and it had passed into a proverb1  
8,it is better to  decipher your own    
shells40    ,now it may be considered   
strange how it was that some of the     
inhabitants  could get other of the     
inhabitants to decipher the shells for  
them at  all1 or1 at any rate1 to       
decipher them so that there was any     
balance of  pleasure left with the      
shells at all4 ,but this power on the   
part of some  of the inhabitants        
depended on the general action of the   
king4 ,for by  bearing the difference of
 pain in innumerable respects in the    
life of  each he made life a pleasure   
7on the whole7 to each1 and they strove 
each to preserve their own life which   
was a source of pleasure4 ,and some  of 
the more powerful inhabitants had the   

power of denying to the rest1  unless   
they laboured for them1 the means of    
continuing to exist4  ,consequently it  
was possible for things to be obtained  
by the more  powerful which had a       
balance of pleasure in them4    ,but the
 authorities who had studied the life of
 the valley in relation  to pleasure and
 pain1 saw that there was a danger in   
this relation of  the more powerful to  
the less powerful4 ,for as the numbers  
of the  inhabitants increased the power 
grew more and more concentrated in the  
hands of a few1 and there was a tendency
 for the inhabitants in general  to be  
compelled more and more to go through   
the painful part of actions1  leaving   
the pleasurable parts for the more      
powerful4 ,and every now and  then1     
before the council of wise men regulated
 the matter1 great masses  of the       
inhabitants passed off in a state of    
apathy4 ,so they had many  laws to      
restrict the action of the more powerful
 of the inhabitants2  and1 indeed1 the  

more powerful of the inhabitants were   
ready to frame  these laws themselves1  
and were willing to obey them1 for they 
did not  like to see portions of the    
inhabitants going off into a state of   
apathy4    ,but not only in this        
respect1 but also in every other1 the   
wise men  regulated the affairs of the  
valley so as to make life more          
pleasurable4  ,they had severe laws     
against any one who deprived another of 
pleasure  without his consent1 by       
violence or deceit4 ,they did all they  
could to  ward off a state of apathy4   
,but in one respect beyond all others   
they  were full of care and precaution4 
,and this was in guarding against such  
sources of trouble1 anxiety1 and pain   
which could be removed from the         
community as a whole4 ,anything tending 
to lower the standard of comfort  as a  
whole was carefully removed4            
,irregularities were reduced as much as 
possible2 and1 in one respect1 a great  
step had been taken4 ,it had not  been  

carried in the council of wise men      
without great opposition1 but it  had at
 length been passed into law4    ,any   
child born in the valley which had any  
incurable disease1 or any  gross        
deformity1 or which by its delicacy     
seemed likely to cause more  pain than  
pleasure in the valley1 was at once put 
out of existence4 ,the  gain to the     
inhabitants of the valley of this was in
 their eyes immense2  for their sight   
was offended by no deformities1 and the 
painful offices  of attending to the    
sick had undergone a considerable       
diminution since  this edict had been   
passed into law4    ,the important duty 
of deciding on the claims of every      
infant that was  born to a painless     
extinction was confined to a band of    
inspectors1 who  stayed for a short time
 only in any one part of the valley1    
lest they  should become biassed by     
personal acquaintance with the          
individuals for  whose children their   
offices were called into requisition4   

,,chapter ,,vii4    ,passing on to the  
other great building1 where the other   
wise men meet1  it is right to describe 
what may be called the intellectual     
development--as the foregoing was the   
moral development of the valley4  ,the  
course which the opinions of the        
thinkers in the valley had gone  through
 was the following4    ,at first they   
had no clear ideas1 but all manner of   
mere opinions and  fancies4 ,at last    
they apprehended certain general        
tendencies--such as  that towards the   
centre of the valley1 and they explained
 many  inclinations which had before    
been puzzling to them by this4 ,and     
stimulated by this great discovery they 
examined more and more closely4  ,and   
they found many special tendencies like 
that towards the centre of  the valley1 
which the king had called into          
existence1 and which he let  go on as a 
general rule1 unless he wished the      
contrary4 ,and they also  succeeded in  
nearly isolating the simplest routines1 

and so practically  could observe the   
type of the king's plan4    ,they saw   
that one act ,a was succeeded by another
 act ,b4 ,and not taking  into account  
that one was pleasant the other painful1
 they measured the  amount of sensation 
present in the two acts4 ,and then they 
took the next  pair of acts1 namely1 ,a 
and ,b over again1 and measured the     
amount of  sensation present in them2   
and they found that the amount of       
sensation  gradually diminished4 ,and at
 first they thought that sensation      
gradually  came to a stop2 but          
afterwards they noticed that other      
actions were  started in the            
neighbourhood of the routine ,a ,b as   
that diminished in  point of feeling4   
,now1 of course1 these other actions    
were started by the king with the       
pain-bearing power set free from the    
routine ,a ,b1 as above described4  ,but
 not knowing anything about this action 
on the part of the king1 or  about the  
king at all1 the conclusion arrived at  

was this3 ,that  sensation transmits    
itself4 ,if it does not continue in the 
routine ,a ,b1  that part which does not
 continue passes on to the other        
routines1 ,c ,d1  ,e ,f1 c4    ,then    
they measured very carefully2 and they  
found1 as nearly as they  could measure1
 the routines which sprang up as the    
routine ,a ,b died away  were equal in  
sensation to the loss in the routine ,a 
,b1 ,a ,b4 ,and from  this they         
concluded that the amount of sensation  
or feeling was  constant4 ,they called  
it living force1 and said that it must  
transmit  itself and1 wherever it       
appeared1 be equal in its total amount  
to what  it was at first4 ,but after a  
time1 with more delicate measurements   
and  more patient thought1 they found   
that some of the sensation was still    
unaccounted for4    ,for consider any   
routine consisting of the acts ,a1 ,b2  
,a1 ,b2 ,a1 ,b4 ,in  order to make any  
pair of acts ,a1 ,b worth while1 the    
king bore a certain  amount of pain4    

,referring to the numbers which we took 
before1 if there  were #ajjj of pleasure
 in ,a there would only be #iih of pain 
in ,b4 ,thus  the sensation was not     
equal in the two acts ,a and ,b4 ,some  
of the  sensations had gone1 and the    
portion of sensation we are now         
considering--the portion by which ,b was
 less than ,a--had not gone in  starting
 other routines4 ,this loss could not be
 accounted for as they  accounted for   
the difference in sensation between the 
first action ,a ,b  and the second      
action1 consisting of the acts ,a and ,b
 in the routine4  ,there was a loss of  
sensation which was counterbalanced by  
the gain in  sensation in other         
routines4    ,but besides this there was
 a further loss4 ,some sensation went   
off1 not  to be recovered in any routine
 they knew4    ,now it was the bearing  
on the part of the king which produced  
the  appearance of the passing away of  
sensation altogether1 so that the act   
,b was less in amount of sensation than 

the act ,a4 ,but the inhabitants--at    
least the wise ones--were firmly        
convinced that sensation could not be   
annihilated or lessened4 ,so they came  
to the conclusion that sensation  was   
passing off into a form from which it   
never reappeared1 so that it  could     
affect them4 ,they conceived it still to
 exist1 but to be  irrecoverably gone   
from the life of the inhabitants of the 
valley4    ,taking the numbers we have  
taken1 and the simple instances we have 
supposed1 this course of reasoning      
appears straightforward enough4 ,but  in
 reality so complicated was the state of
 things in the valley1 and the          
proportion of pain which the king bore  
in each single action so minute1  that  
to have arrived at this result implied  
powers of investigation of  no mean     
order4    ,it is interesting to mention 
the names which these investigators gave
 in  the valley4 ,in the performance of 
the pleasant act ,a1 they said that the 
being acquired greater animation4 ,in   

going through the painful act ,b1  they 
said that he passed into a position of  
advantage4 ,they used the  term         
advantage because1 having completed the 
painful act ,b1 he was ready  to begin  
the pleasant part of the action ,a over 
again4 ,and in this part  he manifested 
more animation4    ,and now although    
acts of greater animation and greater   
advantage  succeeded one another1 and   
although the new total of the sensation 
in  the act of a being was very nearly  
equalled by that in a subsequent act1   
still there was not--they had to confess
 there was not--a complete  equality4   
,some of the sensation had certainly    
gone from the sphere in  which the      
inhabitants could feel it4    ,we see   
that this sensation which was gone was  
in reality the  pain-bearing of the     
king1 which set all their life going4   
,but they knew nothing of this1 and     
formed a very different conclusion4     
,they said3 8,if some of the sensation  
is continually going and  disappearing  

from the life of the inhabitants of the 
valley--if this is  the case1 although  
the sensation may not be destroyed1 it  
is certainly  lost to us40    ,and then 
they thought3 8,surely the amount of    
sensation must be always  the same2 if  
some of it continually goes off into a  
form in which we  cannot feel it1 that  
portion which is left behind1 and which 
we feel1  must be continually growing   
less40    ,hence they concluded that the
 sensation in the valley was gradually  
running down4 ,less and less was being  
felt4 ,after a time1 which they         
calculated with some show of precision1 
all feeling will have left the          
inhabitants and gone off in some        
irrecoverable form4 ,all the beings of  
the valley will sink into apathy4       
,thus coming in the course of their     
investigations upon the action of the   
king1 which was the continual cause of  
all life1 they apprehended it as  the   
gradual annihilation of life4    ,the   
small building between the two council  

halls remains to be noticed4    ,now    
when the king had connected pleasure and
 pain with different acts to  be        
performed by the inhabitants of the     
valley1 he had of necessity to  let the 
pleasant one be the one that came first 
in the order of its  possible           
performance4 ,and then by the device of 
the curved rays he had  brought it about
 that the inhabitants went through the  
painful act  consequent on the          
pleasurable one1 the two together       
forming the complete  action which the  
king had designed4 ,but this chain was  
not very secure4  ,the inhabitants had a
 tendency to go through the pleasurable 
act and  leave the painful act undone4  
,now in things which necessarily        
concerned their life1 the king would1 by
  repeatedly bearing the pain of the    
painful act1 continually set the  beings
 going again2 for when they had         
performed the pleasant act they  were   
landed in a state of torpor1 until the  
pain of the painful act had  been borne 

by them or for them4 ,now if this act of
 which they took the  pleasant and left 
the painful part undone was in the main 
current of  their lives1 the king would 
over and over again1 by bearing the     
pain1  bring those who had shirked the  
painful part into a position of         
advantage again1 so that they could     
begin the routine afresh with  another  
pleasant act4 ,and often when thus      
started again they would take  to the   
routine1 and bear the pain in the       
painful act themselves4 ,but  many1     
after assisting them again and again1   
the king was obliged to let  sink into  
apathy1 such namely as always left the  
painful part of the  action undone4     
,now the little building was the council
 hall or investigation chamber of  the  
searchers out of new pleasures4 ,and by 
new pleasures they meant  something of  
the following kind4 ,with the pleasant  
and painful acts  which made up the main
 routines of their life1 it was not safe
 to take  the pleasant and leave the    

painful acts1 for that gradually led to 
their  sinking into apathy4 ,but there  
were many routines which the king had   
instituted besides the main ones4 ,and  
if the pleasant part of the action      
constituting these secondary routines   
were taken1 then there followed no      
tendency to lethargy in the main current
 of their lives1 but they simply  had a 
pleasure the more4 ,of course the pain  
of the painful act had to be  borne1 but
 they not going through with it left it 
for the king to bear4    ,long ago1     
through one of the inhabitants of the   
valley with whom he had  communicated1  
the king had sent a message1 asking the 
inhabitants not to  take the pleasant   
part of an action without the connected 
painful part4  ,but now all memory of   
this message was lost1 and the little   
building had  been built1 as a council  
hall or investigation chamber for the   
searching  out of pleasurable acts4 ,in 
it all possible novelties of action were
  discussed4 ,and the pleasant parts of 

them being described1 exactly how  far  
they were pleasurable1 and in what      
degree they were pleasurable1 the       
information was made public throughout  
the land4                               
,,chapter ,,viii4    ,besides these two 
principal buildings in the metropolis1  
there were  other public buildings      
devoted to various purposes4 ,and some  
of the most  important were colleges    
devoted to the education of the young   
inhabitants4    ,now there was in the   
college of applied sensations a student 
who1 though  outwardly as proficient as 
the average of his companions1 was in   
reality  the most backward of all4 ,he  
learned by a kind of rote all the       
doctrines  they understood1 and he could
 explain apparently how one feeling     
caused  another4 ,but in himself he had 
no particle of understanding4 ,he seemed
  deficient in the sense of cause and   
effect which the others had4 ,of this   
the following instance will suffice to  
show the nature4    ,the king had1 in   

order to prevent the inhabitants from   
straying too far  from the metropolis1  
kept a constant watchfulness over their 
movements1  and had uniformly taken     
somewhat of the pain from any effort    
which they  made to move towards the    
metropolis1 and had not taken any of the
 pain  in efforts whose tendency was to 
remove them to a distance from the      
metropolis4 ,if there was any purpose to
 be served in going away from the       
metropolis1 he took enough pain from    
these movements to make it worth  the   
beings' while to go away from the       
metropolis4 ,but when other things  were
 equal1 it was a pleasurable thing to go
 towards the metropolis4 ,the  king made
 this general inclination1 because if it
 had not been so1  beings lying out of  
the way of his immediate attention might
 have  drifted away and gone to the     
confines of the valley1 away from where 
the  busy life he was calling out was   
manifested1 and so have been lost to    
others and themselves4 ,as it was by    

imparting this general  pleasurableness 
of moving towards the metropolis he held
 all the  inhabitants together1 and knew
 the direction in which each would tend1
  unless for any special reason he had  
made it more pleasurable for the  person
 to move away from the metropolis4      
,now1 as has been mentioned above1 this 
general tendency had been  observed by  
the inhabitants2 and they knew quite    
well that every  individual tended      
towards the metropolis1 and was only    
prevented from  coming into it by strong
 local interests1 or by all available   
positions  in it or near it being       
already occupied4 ,if any situation was 
vacant in  the metropolis1 it was easily
 filled up by those from the surrounding
  country1 for they all felt this       
tendency to press in4    ,now1 the      
learned men in the valley had long      
recognized this as one of  the most     
important laws of the valley4 ,and the  
students in the college  of applied     
sensations felt this law to be true law1

 and anything which  followed from it   
they felt to be self-evident4 ,but the  
student of whom  we speak had not this  
happy1 settled feeling with regard to   
this law4 ,he  could not feel as if it  
were necessarily true4    ,one day the  
head of the college was talking to the  
foremost  students--those who had nearly
 finished their course and who would    
take  their places in the valley        
shortly--and he said incidentally in the
  course of his remarks1 that those who 
were moving away from the  metropolis   
were as much attracted to it as those   
who were moving towards  it4    8,why do
 they move away1 then80 asked the       
backward student1 who had by  great     
diligence1 after a long time1 plodded   
his way by force of  remembering by     
heart into the top class4 ,he forgot his
 usual caution and  his acquired habit  
of only asking questions he had heard   
asked before in  order to refresh his   
memory with the answers he had heard    
given before4    ,the professor frowned 

at the stupid question4 8,the supposed  
being10 he  answered1 8while he is      
attracted to the metropolis in          
accordance with  the general law1 may   
yet have some stronger inducement at the
 time to  move away from the metropolis4
 ,that he does move away shows of course
  that his temporary inducement to move 
away is stronger than his  permanent    
attraction towards the metropolis40     
,the student said that he was obliged   
for the explanation4 8,but----0         
8,well80 said the professor4    8,the   
only reason you have for supposing that 
the being is attracted  towards the     
metropolis is that he does move towards 
the metropolis4 ,i  don't see why you   
should say it was pleasant for him to   
move towards the  metropolis when he    
does not do so40    8,but we know10 said
 the professor4    8,no10 said the      
student1 8you only suppose2 because you 
find it so on a  great many occasions1  
you suppose it is so always4 ,you are   
like a savage  who attacks the house of 

a civilized man4 ,and he tries the      
window1 the  civilized man meets him    
there2 so he tries the door1 the        
civilized man  meets him there2 so he   
goes back to the window1 and is met     
there again4  ,and he concludes there   
are two men in the house2 and after a   
time he  concludes there are as many men
 in the house as there are ways by which
  he tries to get in40    ,the student  
had forgotten himself in speaking like  
this2 and the  comparison to a savage1  
though made in haste and in good part as
 an  illustration1 offended the         
professor1 so he said3    8,you do not  
believe that the law of attraction      
towards the metropolis is  universal1   
and affects all the inhabitants80    8,i
 cannot10 said the student4    8,then   
you shall go to a place where you will  
feel it10 said the  professor4 8,you    
will go to-morrow to the extreme        
confines of the valley1  and stop there 
until you are of a different mind40     
,he said this in a superior and gentle  

manner4 ,but it was a terrible blow  to 
the prospects of any student to be thus 
exiled4 ,and yet the professor  was     
within his strict legal right1 and the  
student knew it4 ,he had  avoided this  
danger all through his college course1  
and now it came with  crushing effect on
 him4 ,for just as long ago in the      
valley they had had  doctrines about the
 king1 and had punished any one who did 
not feel them  as true1 and who was     
found out1 so now when all the ideas    
about the king  had been disproved1 they
 had severe regulations about the belief
 in the  laws4 ,the learned class was a 
sect of priests1 and whoever threatened 
to  bring confusion and trouble by      
denying any of the known laws1 and to   
lead the ignorant people to disregard   
them and deny them1 was subject to      
severe punishments4 ,in the case of this
 student1 the error did not so  much    
matter1 because he had committed his    
offence in the presence of              
well-instructed people1 who would only  

smile at his folly4 ,but he had in  his 
presumption insulted the head of the    
college1 and his punishment was         
universally considered to be mild and   
just4 ,and yet he was not  altogether in
 the wrong4 ,for it was not as though   
the king 7when he  wanted a being to    
move away from the metropolis7 took as  
usual a portion  of his effort in going 
there2 and at the same time             
counterbalanced this  by taking a still 
larger portion of the pain involved in  
his moving away  from the metropolis4   
,by no means4 ,when the king willed a   
man to move  away from the metropolis1  
he let him start afresh1 as it were1    
according  to the conditions which every
 being was subject to in the            
valley--that it  was just as pleasant as
 painful to move in any way1 and he took
 a  portion of the pain involved in     
moving away from the city4    ,now the  
student1 when he was sent away1 tried   
earnestly to see wherein  he had been   
wrong4 ,the place where he was exiled   

was on the confines of  the valley1     
where a peaceable race of savages lived1
 engaged in  agriculture4 ,in the quiet1
 monotonous life of the place he thought
 over  his whole course of life1 but    
could not obtain any different feeling4 
,and while thus buried in thought1 he   
fell into the way of going about  with  
the savages and doing as they did4 ,much
 to his surprise1 when his              
preoccupation of mind passed away1 he   
found himself singularly at home  with  
them4 ,their tastes seemed to agree with
 his4 ,and he came to the  conclusion   
that he was in reality a savage who by  
some mistake had been  admitted to the  
college4 ,having formed this conclusion1
 he threw himself  into the life around 
him heartily4 ,in course of time he won 
the  confidence of the rude1            
uncultivated people1 and they talked to 
him  unreservedly4    ,many curious     
traditions were handed down amongst     
them4 ,there were some  which proceeded 
from the time when the king had walked  

and talked with  the children he called 
into activity4 ,there were others       
proceeding from  times when there had   
appeared amongst them one to whom the   
king had  given some of his rays1 so    
that that person had the power of making
 the  pain less in actions for others1  
and of giving them motives to act1 and  
of rousing them thus to an active state4
 ,and all these traditions they  told to
 the exiled student4    ,now their own  
belief was this4 ,they thought that     
there was a power over  them1 and in    
this they recognized the king2 but how  
it was that this  power prompted them   
they did not know4 ,yet they connected  
him in some  way with pleasure and pain4
 ,they thought it pained him when they  
had  pleasure1 but not in the way in    
which was really the case4 ,they thought
  simply that it was pain to him to see 
them taking pleasure4 ,they  thought1   
moreover1 that he would1 if they        
displeased him much1 take away  all     
their pleasure and leave them nothing   

but pain4    ,now the student saw       
clearly some errors1 some contradictions
 in their  belief4 ,for instance1 he    
knew that beings only followed pleasure1
 and  directly pleasure was equalled by 
pain1 sank into apathy1 and then        
gradually vanished away4 ,hence he knew 
there need be no apprehension of  the   
power's acting as they thought4 ,but the
 thing they said1 that their  taking    
pleasure pained this power1 struck him4 
,he did not approve the  results in     
their life1 for it was in consequence   
very gloomily framed1  though with a    
good deal of unconscious cheeriness4    
,but he knew as a  scientific fact that 
there was a constant diminution of      
feeling2 and  since he also knew that   
beings in the valley did nothing except 
it was  more pleasant1 he concluded that
 although pleasure and pain might both  
be disappearing1 still pain must be     
disappearing to a greater extent4  ,now 
since the feeling did not become        
nothing1 but passed away out of the     

perception of the inhabitants1 it       
followed that it must pass to some      
being4 ,it did not disappear as feeling1
 but passed away from the  sensation of 
the inhabitants4 ,is there a being1     
then1 he asked  himself--the power of   
whom these simple folks tell--who bears 
the  difference of pain1 and so makes   
existence pleasant to us8 ,and is that  
the meaning of what they say that our   
pleasure pains him8 ,is it just the     
truth read backwards--the truth1 namely1
 that by his taking pain we have        
pleasures1 which they have had handed   
down to them as this--that our  taking  
pleasure pains him4    ,when he had     
thought thus far he remembered one of   
his books in which the  ancient beliefs 
of the valley were discussed4 ,it       
happened to be one of  the books which  
he had brought into his exile with him4 
,he took it down1  and in the evening   
set himself to search through it4 ,and  
in a footnote  towards the end of the   
book he read3    8,the existence of a   

power shaping the valley for the good of
 the beings  in it is clearly disproved4
 ,first1 by the amount of suffering     
there is  in the valley4 ,secondly1 by  
the fewness of the types of life1 and   
the  constant modification of one plan  
to secure different results--which      
would be much better achieved by the use
 of radically different types  and      
means4 ,thirdly1 by the absence of any  
indication of such a power1  except in  
the traditions of uncultivated tribes40 
,when the student had read this he rose 
up and paced his chamber4 ,for he  saw  
clearly that if it was in bearing part  
of the pain that the power of  the being
 lay1 the first of these arguments fell 
to the ground4 ,the  presence of the    
pain in the valley would prove that this
 power took only  some of the pain and  
not all4 ,as to the second argument1 all
 it would  come to was that the being   
who1 bearing pain1 gave existence to the
  inhabitants1 used economy in his      
actions--he chose to effect his objects 

with the least possible expenditure of  
means4    ,reflecting thus he went out4 
,now it may be considered surprising    
that the king did not communicate in    
some way with the student1 for by means 
of his rays he was in possession  of all
 that had gone on in his mind4 ,but the 
king had found over and  over again that
 if he manifested himself to any one of 
the inhabitants  of the valley1 the     
effect1 though good at the immediate    
time1 was most  disastrous for the      
following time4 ,for the ends he was    
working towards1  and leading the       
inhabitants towards1 were much greater  
than any one of  them could grasp or    
conceive4 ,and the inhabitants1 as soon 
as they had  communication with him1 at 
once thought they knew his final will4  
,and  they were a set most peculiarly   
stiff in their notions1 and with the    
kind of sanction which communication    
with him gave them1 even the most       
absurd ideas if once conceived took a   
very long time to eradicate4    ,so when

 the student went out into the open air 
he saw nothing except the  stars1 and   
heard nothing except the wind4 ,the way 
was so well known to  him1 however1 that
 he walked on quickly without stumbling 
in the  darkness4 ,he had not gone far  
when he saw a kind of luminousness4 ,is 
it  the moon beginning to rise8 he      
thought4 ,but he found he had passed the
  light and was leaving it behind4 ,he  
could not have passed the moon thus4    
,he went towards the light1 and when he 
had reached it1 it seemed like a        
slender staff of light4 ,he touched it  
with his hand1 and although he did  not 
feel anything1 yet he could take hold of
 it1 and he walked on with  the slender 
beam in his hand4    ,he had not gone   
very far when in his walk he touched on 
something lying  in the path4 ,bending  
down and touching it with his hand he   
found that it  was the form of a fellow 
creature4 8,he is overcome with fatigue2
 can ,i  help him along80 he thought4   
,he rose up to look round1 and let the  

beam  of light which he held in his hand
 touch the prostrate form4 8,i wish he  
could get up by himself10 he thought4   
,no sooner had he felt this wish  than  
he had a sensation of pain in his limbs1
 and the figure rose up4    8,i could   
not move10 it said1 8until you came1    
with all my reasons to get  along2 the  
pain was as much as the pleasure40      
8,who are you80    8,i am a wanderer1   
and am trying to reach the place where  
,i was born2  they will help me there40 
,now in the valley there was a certain  
set of people called wanderers1  who had
 proved themselves unfit for any real   
work4 ,these1 if  inoffensive1 were     
allowed to roam about subsisting on     
charity4 ,the  student walked alongside 
this wanderer2 and every step the       
wanderer made  he felt a sensation of   
pain in his limbs4 ,but the two walked  
quickly on  till they came to the       
dwelling he had left so shortly before4 
,the  student led him in and let him    
rest in his chamber4 ,and then he       

himself  left the dwelling again1 taking
 with him a few necessaries4            
,,chapter ,,ix4    ,when he had seen the
 wanderer safely housed he determined to
 go and  visit a friend who had lived in
 a town not very far from the           
metropolis4  ,this friend had been his  
most intimate companion when he first   
became a  student1 but being older had  
finished his studies sooner1 and had    
left  the metropolis before the         
student's misfortune4 ,in leaving his   
place of  exile the student rendered    
himself liable to punishment1 and he    
gave up  the means of subsistence which 
had been provided for him there4 ,he was
  obliged to go as a wanderer1 and trust
 to the liberality of the people  on the
 way4    ,he was hospitably received as 
a rule4 ,the region was remote from the 
metropolis1 the inhabitants were glad to
 talk with a stranger--and the          
wanderers were1 in general1 held to have
 a stock of exchangeable talk  and news4
 ,but he did not speak with any one of  

what lay present to his  mind1 till one 
occasion4    ,as he was walking along   
early in the day1 he was hailed by an   
inhabitant  who looked like a well-to-do
 farmer4 ,something in the student's    
appearance attracted him1 for1 learning 
that he was on his way to a  distant    
town1 he asked him to stay and take the 
first meal of the day  with him4 ,this  
inhabitant had been a clerk employed in 
the council of  pleasure and pain4 ,but 
the sedentary life had been too trying  
for him2  he had come to live in the    
country on a small possession of his    
till he  had overcome the strain4       
8,did you not find it very dull in the  
part you come from80    8,no2 ,i found  
that the people had much of interest to 
tell me40    8,they have singular       
traditions4 ,i remember when a          
deliberation was held  in our council as
 to whether they were pernicious or     
harmless2 it was  decided that they were
 harmless and little likely to spread40 
8,i have talked a good deal with them   

since ,i have lived amongst them1  and  
have come to the conclusion that in what
 they believe a great deal  is true40   
8,indeed6 you cannot surely believe that
 our pleasure is distasteful to  any    
being outside us40    8,no2 but ,i go   
back to the old notion of which you have
 heard1 that there  is a being who calls
 us into being1 and who is over us2 and 
,i believe  that this being takes pain1 
and so makes life pleasurable to us4    
,you  know that some sensation is       
passing away1 and you know that there   
must  be more pain that passes away than
 pleasure40    8,how can ,i know that80 
8,we know that there is not such a very 
great excess of pleasure over  pain4    
,now if in all the course of time that  
has been1 the sensation that  has been  
passing away was pleasure1 there would  
by this time have been  left an excess  
of pain1 and before now we should all   
have sunk into  apathy4 ,so it is either
 pleasure and pain mixed which passes   
away1 or  pain alone4 ,i conceive that  

it is pain alone4 ,these strange        
doctrines  are true1 only curiously     
expressed4 ,the being over us is        
continually  bearing pain and so making 
existence pleasant to us1 thus causing  
us to  move and live4 ,so the pain of   
our life is that remaining pain which he
  does not take40    8,this seems to me 
a very dismal doctrine4 ,i can imagine  
some poetry in  the idea of a being of  
infinite power1 strong and glorious1 but
 none in  the idea of a suffering       
being40    8,when you were a child you  
thought your father could do everything2
 but  as you grew up and found that he  
too had his difficulties1 was your      
regard for him lessened1 or your        
thankfulness for that which he did for  
you80    8,no4 ,and you mean that if we 
do not regard this being in the same    
way1  granting his existence1 still we  
should feel gratitude towards him40     
8,certainly we should feel gratitude to 
him2 and1 considering the  attitude we  
have taken towards him1 this feeling of 

gratitude comes over  us with a kind of 
revulsion4 ,but besides gratitude ,i do 
not see why we  must lose any other     
feeling such as you seem to miss4 ,do   
you not  remember how1 in the course of 
the studies we have all been through1 we
  were told that there were two parts in
 knowledge--one corresponding to        
reality1 one introduced by the action of
 our own minds--so that certain         
characteristics which we at first think 
to be due to the nature of  things in   
themselves we find out on reflection are
 only our apprehension  of our own      
mental action80    8,yes2 we do not     
perceive the reality absolutely1 we     
apprehend it subject  to the mind's mode
 of perceiving40    8,and of course the 
mode of the mind's action makes it      
perceive certain  qualities as parts of 
the real existence1 which do not belong 
to real  existence at all4 ,these       
qualities spring from our mind's own    
action4 ,in  old times these qualities  
were considered to be qualities of the  

reality  instead of introduced there4   
,and much of the impressiveness of the  
idea  formed of the being of whom we    
speak was due to a mere magnification   
and  extension of these                 
qualities--qualities which do not       
correspond to  anything in reality4 ,so 
the impressiveness of the idea of this  
being was  due to the magnification of  
qualities which originate solely in our 
minds40    8,this accounts for the idea 
having faded away4 ,but tell me         
definitely in  an instance4 ,explain by 
taking some particular quality what you 
mean40    8,i cannot do that1 the       
thought but floats in my mind2 still it 
is always  good to embody4 ,something of
 this sort4 ,when we observe any object 
we  always attribute to it a certain    
power4 ,everything has its own powers of
  resistence1 of moving1 of affecting us
 in certain ways4 ,thus whatever we     
apprehend1 we apprehend as powerful4    
,now since this quality of powerful     
comes in with regard to everything1 it  

is probably introduced by the  mind1 and
 is rather a part of the mental action  
in giving an idea of  reality than a    
quality of reality4 ,if so1 when we     
suppose a being to  have the quality of 
#8all powerful1' we are not supposing   
anything at all  about the being1 but   
are only extending a quality quite      
barren of any  correspondence with the  
absolute nature of things4 ,we have left
 off  talking about the being1 and are  
extending a conception which springs    
solely from the only way in which we can
 perceive40    8,surely you would say   
that this being was powerful40    8,of  
course1 if we think of him at all1 we   
must conceive of him as  powerful2 the  
nature of our mental action demands     
this4 ,but to dwell on  the notion of   
his powerfulness is quite barren1 the   
only subject of  thought which has      
content is to inquire what kind of power
 he has4 ,there  has been a tendency on 
the part of those who have thought about
 this  being to represent his greatness 

in every respect4 ,but they have not    
always been judicious in so doing1      
because being unable to separate his    
real qualities from those which they    
attribute to him in virtue of their  own
 mode of perception1 they have come to  
lay stress on descriptions  which on the
 one hand correspond to nothing in      
reality1 and on the other  hand fail to 
move those whom they are intended to    
impress4 ,a cloak has  been woven4 ,the 
nature of this being is hidden4 ,his    
nature has been  connected with         
introspective questions about the       
origin--of1 of all  things1 the way in  
which we perceive4 ,all this must be    
dashed aside4  ,this being is the cause 
of all our life1 and yet he needs your  
help as  you understand help40    8,i   
should like to accompany you to your    
friend and hear what he has to  say40   
8,come1 certainly40    ,so they went    
together to the town4 ,on the way the   
clerk felt a  brightness of existence   
such as he had not enjoyed for a long   

time4 ,they  talked together1 and       
confided in one another4 ,at length they
 came near  the town where the student's
 friend lived4 ,they separated1 the     
clerk  going into the town1 the student 
to the house of his friend4 ,on his way 
there the path led through a small wood 
of very thick growth4 ,passing  along1  
he found that he had left the path4     
,pausing to reflect in which  direction 
he ought to go1 he thought he heard a   
sound4 ,it was repeated4  ,penetrating  
deep into the obscurest part of the     
wood1 he searched till  at length he    
found--carefully concealed--a child1 a  
mere infant4    ,the child was nearly   
perished with exposure4 ,he took it up  
and warmed  it4 ,when the child was a   
little better the cause of its having   
been  hidden away was apparent4 ,its    
breathing was distressed and laboured4  
,it  suffered under some affection of   
the lungs1 which made it gasp at every  
breath4 ,still in other respects the    
child was well developed and seemed     

strongly made4 ,it seemed to have been  
left too long without care to  recover4 
,the pain of exhaustion from the        
neglect1 and added to this the  pain of 
its breathing1 was too much for it1 it  
was sinking4    8,if ,i could bear the  
pain of its breathing10 thought the     
student1 8it  might not sink till ,i    
could get some nourishment for it40     
,he looked up1 for it seemed to him as  
if some one struck him in the  chest4   
,there was no one there4 ,the pain      
continued4 ,he did not drop the  child  
but continued on his way to the house of
 his friend4 ,when he got  there he     
noticed a stillness unusual in the      
houses of the inhabitants4  ,he entered1
 and was met by his friend's sister4 ,he
 saw at once that  something must have  
happened4 ,she took him into a dimly    
lighted room1  where he saw his friend  
lying motionless and his face quite     
white4    8,he has been suffering great 
pain for long10 she said2 8it was hoped 
that if he could bear up the pain would 

have run its course and he would  not   
sink4 ,but all we could do was no use40 
,the room was full of all  things       
accounted pleasurable1 and she looked   
round as she spoke4 8,it was  no good40 
,taking the child from his arms she left
 him with the form of  her brother4     
,sitting down by his side the student   
felt the strange oppression on his      
chest continue4 ,he went out and found  
that the child had completely  revived4 
,it had still the appearance of being   
agonized in its breathing1  but its eyes
 were bright1 and it laughed4    8,it   
will be all right soon10 said his       
friend's sister4    8,tell me what was  
the matter with your brother40    ,when 
he had heard about his malady he        
returned to the room4 ,after he had  sat
 there for some time he felt more and   
more the sorrow for the loss of  his    
friend1 and the need of his counsel4    
,this aimless1 inert form1 this         
lifeless mass1 was that which he had    
come to seek--was the being with  whom  

he had longed to confer4    ,he bent    
over him4 8,could ,i but snatch him back
 into life2 could ,i but  have one      
hour's intercourse with him4 ,if ,i had 
been with him ,i might  have borne some 
of the pain of his complaint before he  
was overpowered  with it40 ,he touched  
the lifeless hands1 they were cold and  
damp4 ,he  gazed into the expressionless
 face4 ,he seemed to feel the pain of   
the  inner struggle his friend had waged
 against the disease4 ,the quiet of     
that still chamber was gone for him2 in 
his own person he felt the pangs  of the
 struggle for life4 ,a mist came over   
his eyes1 and he sank down  holding his 
friend's hands4 ,suddenly he heard a    
voice4 ,he rose and  looked about him4  
,the sound came faintly from the lips of
 his friend4    8,i have been very ill10
 were the words he caught4 8,i am so    
glad you have  come2 ,i was thinking of 
you in my worst moments4 ,you have come 
just as ,i  am getting better40         
,indeed the features were regaining     

expression1 the hands were warm4 ,it    
was his living friend again4    ,after a
 few hours he was sufficiently recovered
 to hear about all that  had happened4  
,they talked together long and          
earnestly4 ,his friend was  convinced4  
8,let us go to your companion10 he said4
    ,they went into the town together4  
,they found that the clerk had gone to  
the magistrates' hall where a trial was 
being held4 ,they did not see the  clerk
 at first1 so they listened to the      
proceedings4 ,a woman was brought  in   
who had been kept in prison for some    
days1 accused of concealing her  child4 
,the case was clearly proved4 ,the woman
 received her sentence with  an         
appearance of apathy4    8,she will not 
come out of prison alive10 said the     
student's friend1  noting her           
expression4    ,but he called out to her
 from where they stood in the body of   
the court1  8,do not fear1 your child is
 safe40    ,the woman's face brightened1
 and she went with her jailers          

buoyantly4    ,the magistrate had       
remarked who it was that had spoken1 and
 was about to  give orders for the      
disturber of order to be brought up for 
punishment4  ,but the clerk1 who was    
sitting near to the magistrate with whom
 he was  acquainted1 said3    8,this is 
the one ,i have told you about2 pray do 
not punish him40    ,the magistrate     
accordingly contented himself with      
warning the audience  in general terms4 
,but he said to the clerk1 8,something  
about him is very repulsive to me1  do  
not tell me anything more about him40   
,the three returned together1 and       
together they deliberated as to how the 
new idea about the king could be made   
known4 ,it seemed best to go to the     
metropolis and talk with the wisest and 
most learned there4    ,the student     
asked about the child4 ,his friend's    
sister came and told him  that its      
breathing was not any better1 but that  
the child itself was  strong and        
playful4    8,it belongs to the woman   

who was tried to day10 said the student1
 8and  must be kept safely till she is  
out of prison40    ,his friend after    
some deliberation gave it in charge to a
 faithful  servant to take to the       
metropolis4 ,a suffering child there    
would be much  more likely to be        
overlooked1 8and you10 he said1 8will be
 able to look  after it40    ,as the    
student and the clerk were about to set 
out on their way to the  metropolis his 
friend took him apart4    8,my sister   
tells me that ,i had sunk into apathy   
when you came40    8,yes40    8,and that
 you called me back80    8,yes40        
8,how can ,i thank you6 had it not been 
for you ,i should never have  enjoyed   
life again4 ,i am grateful to you40     
8,do not say grateful to me1 but rather 
to that power which does for you  all   
your life that which ,i do for you      
momentarily now4 ,and even now it  is   
not to me that you should be grateful1  
but to him1 for it is only  because he  
has enabled me to do so that ,i have    

taken of your pain40    ,with this he   
took farewell of his friend1 and with   
the clerk proceeded  on their way4      
,they had not got very far when a train 
of servants came up behind them4  ,they 
stood by on one side1 but from the midst
 of his attendants a youth  stepped     
forward4    8,i have learned what you   
have done1 and ,i have overtaken you    
with great  haste40    8,what is your   
wish80    8,i want to come with you4 ,i 
know that you have restored your friend 
from  apathy to life4 ,no power is so   
great as that4 ,i have riches in        
abundance4 ,all that ,i have is at your 
service2 teach me your power40    ,now  
in the valley riches meant abundance of 
pleasant things4 ,at the time  the      
student was bearing the constant pain   
which he took of the child's  breathing1
 and the pain also of his friend's      
illness4 ,he felt that  before beginning
 to take pleasure--which was the meaning
 of having  pleasant things--it would be
 necessary to give up the power which he

 was  exercising1 so he said to the     
youth somewhat harshly3    8,you cannot 
compare riches and that which ,i do1 nor
 can you exchange the  one for the      
other4 ,first give up all your riches1  
then you can begin to  learn what ,i    
do40    ,the youth turned back1 but once
 again spoke1 saying3    8,i will give  
up a great part of my riches if you will
 teach me40    8,if you want to keep    
any1 however small a portion1 you cannot
 do what ,i  do40    ,then the youth    
with all his attendants passed away4    
,,chapter ,x4    ,when they came to the 
metropolis the clerk brought many of his
  acquaintances to see the student4     
,from his position in the council       
chamber1 he was able to address and     
induce many of the ablest of the        
councillors to come and inquire4 ,but as
 soon as they came into the  presence of
 the student a sort of constraint sprang
 up between them4  ,they did not take   
his words as having any real meaning4   
,they were  occupied all the time on    

speculating what motive it was that made
 him  say these things1 and as to what  
kind of difference it was which they    
felt existing between him and them4     
,in fact1 as time passed on1 no one of  
any position or power would be  brought 
into any sort of approximation to him4  
,on the other hand he used  to speak    
continually with the poorer people4     
,those that were sick  especially       
delighted in his presence4 ,there seemed
 to be in him a power  of stimulating   
those that were sinking into apathy back
 again into life4  ,those who were worst
 off in the city seemed to feel when he 
spoke to  them a promise of an          
alleviation of their sufferings4    ,one
 day the clerk asked him    8,how is the
 child80    8,it is well40    8,but it  
still seems to breathe with as much     
difficulty40    8,yes1 but see how      
happily it runs about40    8,how do you 
manage to preserve it8 ,any child which 
,i have seen would be  pining miserably 
with such an affliction4 ,what is the   

power which the  being you tell of has  
given you80    8,it is no power in the  
sense you mean40    8,surely it must be4
 ,have ,i not followed you faithfully   
and done all ,i  could to get the wisest
 in the city to listen to you8 ,surely  
the time  has now come when you will    
tell me what this power is1 and1 if you 
can1  let me share it40    8,you do not 
know what you ask40    8,tell me1 ,i    
pray40    8,it is simply this1 when ,i  
became aware through thought of the     
being  that is over us ,i had no message
 or command from him4 ,but ,i found that
 ,i  could when ,i stood by any         
suffering being take some of the        
suffering and  bear it myself4 ,so as he
 of whom ,i tell does with us each      
moment of our  lives ,i do occasionally 
and in a little manner40    8,but what  
pleasure do you get that makes all this 
worth your while80    8,there is no     
pleasure4 ,i am glad to see the being   
freed from suffering1  and living       
instead of sinking40    8,do you mean to

 say that there is nothing to hope for80
    8,i hope the time will come when ,i 
shall have a fuller knowledge of the    
being ,i know40    ,the clerk was       
silent4 ,he went out4 ,while he was     
still thinking over what  he had heard  
in answer to his inquiries1 a messenger 
came to him from  the chief of the      
councillors of pleasure and pain1 asking
 him to an  interview4    ,when the     
clerk had been ushered into the presence
 of the chief  councillor1 and was alone
 with him1 the latter said3    8,i      
should like a little quiet conversation 
with you about your  companion40    8,i 
shall be glad40    8,when you gave up   
your office and retired you had no      
expectation of  being concerned in      
affairs of state again so soon40    8,i 
did not expect1 certainly1 and ,i do not
 know what your meaning may be  about my
 being concerned in affairs of state40  
8,what ,i mean is very simple4 ,the     
continued deliberations1 generation     
after generation1 of the wise men who   

assemble in the council chamber  have   
been the cause of the continued progress
 of the inhabitants4  ,nothing is done  
by them hurriedly or violently1 but     
gradually  improvement after improvement
 is worked out4 ,but besides this1 there
  have always been at every age certain 
disturbances in the state2 certain      
doctrines are brought forward1 and      
sometimes these tend to good1 and       
should be encouraged2 sometimes they are
 of unknown import1 and must be         
studied2 sometimes they are against the 
happiness of the state1 and then  the   
grave responsibility rests upon us of   
checking them4 ,now from your  position 
you have more opportunity of knowing    
than any one else in what  direction    
your companion's doctrines tend4 ,i have
 sent for you to ask  you to share with 
me this grave responsibility40    8,i do
 not think ,i can help you4 ,i am sure  
he does not wish to do any  harm4 ,what 
harm can there be in his doctrines80    
8,it is not so much about his doctrines 

which ,i want to speak to you as  about 
another subject4 ,many of those who have
 talked with him have  agreed with one  
another in ascribing a singular         
oppressiveness to his  presence4 ,the   
expression was even used by a very      
worthy friend of mine1  #8,he made me   
feel like a puppet4' ,now what right had
 he to inflict such a  sensation on a   
very worthy individual8 ,i want to ask  
you yourself if you  have ever felt     
this80    ,the clerk hesitated4    8,at 
least1 tell me1 have you ever found it  
easy to influence him80    8,no2 ,i do  
not feel as if ,i could influence him in
 the least4 ,he seems to  lack the      
ordinary springs of motive40    8,now1  
should you say that it would be a gain  
to the community if many  should become 
like him8 ,would not they be difficult  
to govern80    8,certainly they would be
 difficult to govern40    8,would it be 
a gain in pleasure to the rest of the   
inhabitants or to  themselves80    8,it 
would not be a gain to themselves10 said

 the clerk1 recalling the  pain which   
his companion bore1 8but it might be    
good for the rest of the  inhabitants40 
8,yes10 said the chief councillor1 8that
 is where his strength lies2 he  is a   
very skilful physician or an impostor1  
and he has the people on his  side from 
the cures he has effected4 ,can you tell
 me anything about his  life80    8,i   
have heard from him that he was a       
student1 and was exiled2 and that  in   
his place of exile he found out the new 
doctrines1 and he left the  place he was
 sentenced to4 ,on his way ,i joined    
him40    8,so much we know1 and it is   
within our power1 according to the      
regulations1 to compel him to go back1  
and to punish him for having left  the  
region he was banished to40    8,if you 
have that power1 why do you not send him
 back if you think it  would be best for
 the state for him to disappear80       
8,ah1 my good friend1 you have heard a  
great deal of our public  deliberations 
from your place in the council2 but now 

that we are  consulting together1 ,i    
must tell you that there are deeper     
secrets in  the art of government1 which
 you will readily apprehend4 ,suppose we
  arrested this individual and sent him 
away1 the people would not see the      
justice of it4 ,they want him now1 and  
they would say that the forms of  law   
were being used to get rid of him4 ,of  
course if his partizans became  violent 
something of this kind would have to be 
done4 ,but it is only a  decree that    
seems just in the eyes of the people    
that we can prudently  carry out in such
 a case without attracting even more    
attention to him  than there is at      
present40    ,the clerk said nothing4   
,the chief councillor went on3    8,i am
 sorry that our conference has come to  
so little4 ,i was hoping that  ,i might 
have found in you a successor to the    
vacant seat in the chamber4  ,i know you
 have the ability to fill it well4 ,but 
before the advancements  are made some  
proof of the wisdom of the successor is 

required4 ,hitherto  you have not had   
the chance1 but ,i thought that in this 
difficult case1  where you have so much 
better opportunities of observation than
 any one  else has1 you might have shown
 your mental power and confirmed my     
opinion of you4 ,still1 no doubt1 on    
some future occasion you will have      
another opportunity when this affair1   
difficult as it is1 is forgotten40      
,the chief councillor made a sign that  
the interview was at an end1 but  the   
clerk remained4    8,all that we want10 
the chief councillor resumed1 8is to    
form an opinion  from inside knowledge  
of whether this innovator is likely to  
cause more  pain or more pleasure if he 
gains a hearing4 ,can you advise us8 any
  particle of knowledge of his inner    
life1 apart from his public             
professions1 is valuable40    8,there is
 a singular fact which ,i should like to
 tell you of1 as it has  been somewhat  
of a burden to me40    ,the chief       
councillor made a sign of assent1 and   

the clerk told him about  the child1 and
 how it had been preserved4    8,and    
with this child10 he said1 8he and ,i   
sit when the day's work is  done40      
8,it is indeed a strange story10 said   
the chief councillor2 8you are  quite   
right in telling me4 ,i was sure you    
were one on whose discretion  confidence
 might be placed4 ,you have given me the
 highest proof ,i could  have expected4 
,the bearings of this matter must be    
thought over40    ,that evening1 as the 
clerk entered the room where they lived1
 the  student was leaning over the child
 with a wearied expression4 ,he went up 
to him and laid his hand on his         
shoulder4 ,the child looked up at them  
and laughed4 ,it was quite happy despite
 the apparent struggles of its          
breathing4 ,the student looked at his   
companion's face4 ,his weariness        
vanished at once1 and a strong warm     
light came into his eyes4    8,you seem 
oppressed1 my friend4 ,i know you regret
 the way in which all  the wise and     

important people you have brought here  
look on me1 and you  must feel some     
sorrow for the partial loss of esteem   
they have showed  you in consequence4   
,can ,i help you to bear it80    ,at    
that moment the door opened1 and a      
messenger came in and gave the  clerk a 
sealed packet4 ,he opened it and saw    
that it was his appointment  to the     
vacant seat in the council chamber4 ,but
 his face did not  brighten4 ,he        
answered his companion moodily1 and thus
 the day ended4                         
,,chapter ,,xi4    ,on the next day the 
student rose early and went forth alone4
 ,he did not1  as was his wont1 go      
amongst the people1 but he passed       
through the  streets towards the open   
country4 ,on his way he was stopped by  
an old  woman1 bent with age and many   
infirmities4 ,she had no place amongst  
the  people1 and had so many pains and  
such a barrenness of existence that  any
 one who had thought of her would have  
wondered that she remained  alive4      

,she stopped him and said1 8,master1 ,i 
have heard that you can take my  pain4  
,help me40    ,but he answered1 looking 
at her1 8,no1 ,i cannot1 but ,i have a  
message for  you40    ,and she said1 8,a
 message for me8 ,i do not know any one 
who would send me  a message40    ,but  
he answered1 8,nevertheless1 ,i have a  
message to you from my lord1  and he    
bids me thank you40    ,she answered1   
8,it cannot be4 ,you must have made a   
mistake40    ,but he said1 8,i have made
 no mistake2 he thanks you40    ,he     
could not explain to her how by her     
bearing pain1 according to the  law of  
the valley1 she took it from that which 
the king bore4 ,instead of  saying that1
 he gave her the message1 and somehow   
the old woman believed  it4    ,the rest
 of the day he spent in the open        
country4 ,when he returned it  was      
getting towards dusk4 ,there was an     
unusual movement in the streets4  ,on   
passing into the public market-place he 
saw a crowd collected2 and  when he had 

penetrated to their midst1 he saw lying 
on the ground the  child he had kept so 
long4 ,it had been lying uncared for and
 exposed for  many hours2 and the want  
of food1 the fright1 and its gasping    
breathing  made it the most pitiable    
object4 ,he at once stepped towards it  
and took  it up in his arms4    8,is    
that your child80 said one of the crowd4
    8,it is not my own10 he answered1   
8but ,i take care of it40    8,then it  
is you that are bringing pain upon us   
all10 shouted several  voices from the  
back of the crowd4 ,and some one shouted
 out3    8,i know you4 ,you pretend to  
take pain away and you really bring much
  more in secret40    ,and moved with a 
feeling of indignation against the one  
who had caused  such a painful object to
 exist as the child was1 the crowd      
closed on  him1 and barred his way to   
his own place4 ,but they did not lay    
hands on  him4 ,as he stood with the    
child it gradually began to regain its  
composure4 ,but with a sudden movement  

the crowd swept towards the  council    
chamber4 ,and when they had come there  
they demanded that this  cruel and      
wicked act of keeping pain in existence 
should be punished4    ,there happened  
to be several of the chief magistrates  
on the spot1 and  in obedience to the   
voices of the crowd they proceeded to   
sit in  judgment at once4 ,it was not   
known how the child had come into the   
streets2 but it was admitted by the     
prisoner to be his doing that it had    
been kept alive4 ,the doctors           
unanimously said that it ought to have  
been  put out of existence directly it  
was born4 ,there was practically no     
defence4 ,the charge of subverting the  
laws was established4 ,the people       
clamoured for the extreme penalty4 ,the 
judges passed sentence on the  student4 
,before morning he was put to death4    
,he met his fate without sorrow1 even   
with gladness4 ,the pain in his life    
had for long been as much as he could   
bear4 ,he did not1 like the prince  of  

long ago1 look upon nothingness as the  
desired end of existence4 ,he  felt the 
presence of the one whom he had         
discerned through thought1 and  this    
seemed more real to him than life or    
death4    ,on the following day1 whether
 in reaction from the excitement of the 
previous evening1 or from some other    
cause1 an unusual quiet pervaded  the   
streets of the city4 ,there was not much
 discussion as to the event  which had  
happened4 ,the prevailing feeling was   
one of wonder that there  should have   
been so much commotion about an         
unimportant affair4 ,for the  most part 
before the next evening the whole       
circumstances were on the  way to be    
forgotten4 ,and yet every here and there
 were persons in whose  lives the loss  
of their friend was deeply felt4 ,the   
joy and spring of  life seemed gone4    
,the poor child lay pale and motionless1
 save when  every now and then it gasped
 convulsively for breath4 ,none felt the
  despondency more than the clerk4 ,the 

interest and value of life seemed  to   
have gone4 ,he did not care for his new 
honours4    ,that day some most         
unexpected news went through the town4  
,the chief of  the council of sensation 
had sunk into apathy4 ,he was in the    
prime of  his life4 ,it was most        
unexpected4 ,every one was astonished at
 the news1  but were still more         
astonished at how little they felt      
concerned4    ,following on these       
tidings came others4 ,many of the       
inhabitants of the  metropolis whose    
lives were most strenuous suddenly      
succumbed4 ,the clerk  had made up his  
mind to go into the country4 ,but       
tidings came from there  also that the  
poorer labourers1 and those who were    
exposed to the  fatigue of long journeys
 or exposure were in many cases sinking4
 ,the  wave of torpor seemed passing    
over the whole valley and not to be     
confined to the metropolis4 ,the rich   
and unoccupied classes only were        
comparatively unaffected4 ,they betook  

themselves to the store of  enjoyable   
things at their service1 and so replaced
 the natural spring of  life which      
seemed tending to fail in every one4    
,on the confines of the valley1 where   
the ravine struck its vast depth        
between this land and that1 vast and    
endless as the sea stretched the  plain 
whence the king had come4 ,it was struck
 silvery grey by the light  of the moon1
 dark shadows marked the nearer strands1
 and gradually the  rocks which cast    
them showed their sharp outlines1 hardly
  distinguishable from the ground out of
 which they rose4    ,over the great    
gulf floated the sounds of a pipe1 the  
strains were low1  winning the soul with
 the sweetness of an unearthly melody1  
throbbing as  with a call to a distant  
land away and beyond4    ,and when the  
eye found the source of the sounds1     
there stood1 once more1  solitary in the
 untenanted vast1 the king's devoted    
friend1 the same old  man who before had
 hailed him4 ,gradually the music sank  

lower and lower1  till at length silence
 spread in folds unruffled4 ,then on the
 edge of  the valley a form appeared4   
,it came and seemed to gaze across the  
gulf1  standing motionless and intent4  
,at length a voice came4    8,art thou  
there80    8,yea1 ,o king1 what wouldst 
thou8 ,art weary80    ,no answer came4  
,then the old man spoke4 8,behold the   
roads where they stretch gleaming  white
 in the moonlight2 behold the fields1   
the villages2 see in the  distance the  
great walls of the palace4 ,have not    
these risen up for  thee1 ,o king80     
,then the king made answer3 8,i am      
weary40    ,suddenly the old man raised 
his pipe with both his hands to his     
lips4  ,wave after wave of triumphant   
sound pealed forth4 ,great harmonies    
such  as marching nations might hear and
 rejoice1 noble notes of unbounded      
gladness4    ,then1 crossing by an      
unknown way1 he came and stood by the   
king's side4  ,after a while the two    
moved on together1 and by a secret path 

passed  away from the valley--whither ,i
 know not4    ,as soon as the king had  
departed from the valley the beings in  
it began  to sink into the same state of
 apathy as those were whom he had first 
found there4 ,those who sank first were 
the ones in whose lives the  stress of  
labour or thought was the most intense1 
for they first felt  the loss of that   
bearing of pain by one beyond themselves
 which gave  them a difference of       
pleasure4 ,and slowly as the accumulated
 enjoyment  was exhausted1 a chill death
 in life crept over the land4 ',tis     
useless  to ask after the fate of any   
one of those that were there1 for each  
was  involved in the same calamity that 
overwhelmed all4 ,every hand forgot  its
 cunning4 ,the busy hum of life in the  
streets was hushed4 ,in the  country the
 slowly moving forms gradually sank to  
rest4 ,at every spot  was such unbroken 
quiet as might have been had all the    
inhabitants gone  to some great         
festival4 ,but there was no return of   

life4 ,no watchful  eye1 no ready hand  
was there to stay the slight but        
constant inroads of  ruin and decay4    
,the roads became choked with grass1 the
 earth encroached  on the buildings1    
till in the slow consuming course of    
time all was  buried--houses1 fields1   
and cities vanished1 till at length no  
trace was  left of aught that had been  
there4                                  
,,part ,,ii4                            
,,chapter ,i4    ,there are certain     
respects in which our world resembles   
the valley4  ,instead of regarding      
pleasure1 pain1 and feeling1 let us     
examine the  world we live in with      
regard to motion in one direction and   
another1 and  in respect of energy4     
,if we observe the movements which go on
 in the world1 we find that in  great   
measure they consist of movements which 
if put together would  neutralize each  
other4    ,a pendulum swings to and fro4
 ,if the two movements took place at the
  same time the pendulum would be still4

 ,taking a more ample motion--that  of  
the earth round the sun4 ,the earth     
moves in the course of its orbit  as    
much towards the sun as away from it1   
and as much towards the east as  towards
 the west4 ,if all the motion were to be
 gone through at one and  the same time 
the earth would not move with regard to 
the sun4    ,again1 if we notice what   
goes on on the surface of the earth1 we 
see  that there is a motion of rising up
 and of sinking down4 ,there is an      
approximation of the chemical elements  
into some compounds1 and a  separation  
of them again4 ,of all the myriad       
processes which go on1 the  swing of a  
pendulum is the type4 ,but the downward 
swing may be very  different to the     
upward swing4 ,it may be that the       
downward swing is  represented by the   
violent action of the chemical          
affinities in a charge  of gunpowder    
when exploded1 and the upward swing may 
be represented by  the swift motion     
imparted to a cannon ball1 and the swift

 motion of the  cannon ball in its turn 
comes to rest1 and as it comes to rest  
slowly or  quickly other changes take   
place4    ,and what we notice in our    
world is similar to what the inhabitants
 of  the valley noticed about pleasure  
and pain--that they do not neutralize   
one another as a matter of fact4    ,the
 contrary motions on the earth which1 if
 they were put together1  would         
neutralize one another1 do not as a     
matter of fact neutralize one  another4 
,we call motion in one direction        
positive--in the opposite  direction    
negative4 ,but in the world as a matter 
of fact positive and  negative motion do
 not together come to nothing4    ,as in
 the valley the states of pleasure and  
of pain did not coalesce  into a state  
of apathy1 but always succeeded one     
another1 in simple or  complicated      
fashion1 so on the earth it is          
impossible from two opposite  moving    
bodies to get stillness4 ,if the two    
come into contact in opposite           

directions the movement does not stop1  
but makes its appearance in an          
alteration of the shape of the bodies1  
in a disturbance of their  particles1 or
 in some such fashion4    ,again in the 
valley1 by measuring the pleasure and   
pain simply as  feeling1 and not taking 
into account whether it was pleasure or 
pain1  the inhabitants found that the   
feeling was always the same in amount4  
,so we on the earth1 measuring the      
amount of movement1 and leaving out of  
account whether it is positive or       
negative1 come to the conclusion that   
the quantity of movement1 reckoned in   
the way in which we call it  energy1 is 
always the same4 ,the principle of the  
conservation of energy  has become a    
fundamental one in science4    ,but     
besides the discovery that the amount of
 sensation as such was  always constant1
 the inhabitants of the valley          
discovered that a portion  of the       
sensation was passing away from a form  
in which they could feel  it4    ,and   

there is an analogous discovery in      
science4 ,we know that a portion  of the
 energy of our system is passing away4  
,it is not being  annihilated1 but is   
disappearing4 ,with the energy which can
 be collected  from the falling of a    
stone1 the same stone cannot be raised  
to its  former level again4 ,some of the
 energy has disappeared from the form in
  which it can be known as the energy of
 moving masses4 ,the energy has in  some
 measure irrecoverably passed off in the
 form of heat4    ,hence1 just as the   
inhabitants of the valley came to the   
conclusion that  in point of sensation  
they were 8running down10 and that after
 a time  all sensation would have passed
 away from the form in which they could 
feel it1 so we have come to the         
conclusion that the energy of the system
  in which we live is running down1 that
 the energy is passing out of the  form 
in which it can be manifested as moving 
masses1 that finally all  movement of   
masses will come to a standstill1 and   

there be nothing left  save motionless  
matter1 with warmth equally diffused    
through it4    ,now in coming to the    
conclusion about the valley1 that the   
amount of  sensation was gradually      
passing away1 the inhabitants1 as we    
have seen1  had come upon the very      
secret and cause of all the life in the 
valley4  ,but coming upon it from the   
outside they had not recognized the     
significance of what they had found4    
,the cause and prime mover of all  their
 existence indicated itself to them1    
coming thus upon it1 as a  process      
whereby all that went on was doomed to a
 distant but certain  extinction4       
,now1 is this process of the passing of 
mechanical energy into the form  of heat
 to be interpreted by us in a way       
analogous to that in which the          
inhabitants of the valley could have    
interpreted the process they found8     
,in this cessation of sensation in the  
form in which they could  experience it 
lay the central fact of the life of the 

valley4 ,has this  passing away of      
energy from the form in which we can    
experience it an  analogous significance
 to us8    ,in order to examine into the
 possibility thus suggested there are   
four  convergent lines of thought which 
it will be well to follow up            
separately4 ,each of these lines of     
thought bears in an independent  manner 
on the central question--the            
significance of the passing away of     
energy4 ,these lines of thought may be  
connected with the following  words1    
which indicate their significance3 7#a7 
,permission2 7#b7 ,causation2  7#c7     
,conservation of ,energy2 7#d7 ,level4  
,,chapter ,,ii4    ,when we observe any 
movement taking place we ask what is the
 cause of  it8 what is the force which  
produces it8 ,but surely1 if we confine 
our  inquiry to this point1 we have made
 an omission4 ,that we are not          
conscious of having made an omission may
 perhaps come from our living in  the   
air which yields so easily to any moving

 body4 ,if we lived in a  rigid medium  
we should1 when we became aware of any  
moving body1 ask two  questions4 ,first1
 what urges it along8 secondly1 what    
prepared the  channel for its motion8   
,but seriously1 without laying any      
stress on the above illustration1 we    
see that to every movement two          
conditions are necessary3 a pushing and 
a  yielding1 a force and a permission4  
,if the particles of the air could  not 
yield1 a pendulum could not swing       
through it4 ,if again the air could  not
 pass on the motion it has received1 it 
could not yield to the motion  of the   
pendulum4    ,now since every motion    
requires a permission1 we are led to ask
 the  question1 ,what is the ultimate   
permission8 ,what again is that which by
  yielding allows motion at all to take 
place8    ,if we trace any movement     
scientifically we find an indication of 
what  the ultimate permission is4    ,a 
body swings through the air4 ,currents  
in the air are set up4 ,these  currents 

impinge on the objects with which the   
air is in contact1 and in  them produce 
heat--producing heat also by friction   
with other portions of  the same air4   
,every motion thus passes off finally1  
at however long an  interval1 in the    
form of heat4 ,motion may reappear as   
motion through  myriads of phases1 but  
at each change of form some of it passes
 off into  the form of heat1 and finally
 all passes off into the form of heat4  
,thus1 unless matter admitted of being  
warmed1 there would be no ultimate      
permission4 ,a motion once started would
 never come to rest4 ,or1 rather1  no   
motion could take place at all4    ,the 
tendency of the above remarks is to     
avoid the conception of there  being    
absolute laws of motion1 true of bodies 
when surrounded by no  medium1 modified 
when a medium is present4 ,surely such a
 conception is  an instrument of the    
mind for exploring nature1 not an       
absolute fact in  nature4 ,the abstract 
laws of motion are mental aids in       

creating  knowledge2 like scaffolding   
for the builder1 even from their very   
usefulness they have probably but little
 to do with the permanent  edifice4     
,this passing into the form of heat     
supplies a place analogous to that of   
the 8void0 in the speculations of the   
,epicurean philosophers4 ,they  argued  
that motion was not possible without a  
void4 ,given a void1  somewhere into    
which matter could move1 then any amount
 of motion could  be accounted for4 ,but
 without a void into which a portion of 
matter  could move1 how was it possible 
for motion to begin8    ,thus repeating 
their inquiry with our altered          
conceptions1 we ask this  question about
 motion1 or energy 7which is a          
particular way of reckoning  motion74   
,unless motion can in some way pass off1
 how can there be all these             
transformations of energy8    ,now the  
ultimate transformation of all energy of
 motion is into the form  of heat4 ,in  
this change into the form of heat is to 

be sought the  ultimate permission which
 makes all transformations of energy1   
all  motions1 possible4 ,it is this     
being acted on of the finer particles of
  matter which permits the movements of 
the larger masses4    ,this passing of  
energy into the form of heat must not be
 regarded as a  side circumstance1 as   
less essential to the laws of nature    
than that law  which we call the        
conservation of energy4 ,it is at the   
same time the end  of every motion1 and 
that which makes every motion possible4 
,the passing of energy into the form of 
heat takes place in that which we  call 
friction1 and in all those modes in     
which any movement is brought  to a     
standstill4 ,but so far from these being
 simply 8hindrances0 to  motion1 it is  
through them that we learn that which   
makes motion  possible4 ,it is with us  
as with the inhabitants of the valley1  
the  gradual cessation of feeling from  
their life and the modes in which it    
ceased were the way in which they       

regarded the action of the king who  was
 the cause of all4 ,we have thought of  
motion as a thing in itself  impaired by
 the multitudinous obstacles it meets in
 the world4 ,let us  look on the        
circumstances more impartially4 ,let us 
look on them as  something co-equal with
 motion4 ,let us find in that mode      
whereby all  motion comes to an end the 
originating cause also whereby all      
motion  comes to be4    ,the passing of 
the motion of masses into the form of   
heat is the  ultimate permission4       
,,chapter ,,iii4    ,if we reflect      
cautiously on the history of our        
opinions1 we find that we  often fall   
into error in respect to our freedom in 
attributing causes4  ,if we are         
unfortunate we are apt to look on our   
neighbours1 or the  world1 or1 if we are
 of a self-depreciatory turn of mind1   
ourselves as  the cause4    ,again in   
past times people really felt sure about
 certain things being  causes which we  
now know had a very slight connection   

with the result4  ,incantations have    
been supposed to have an effect on      
physical phenomena1  such as eclipses4  
,numbers and their properties have      
really been  conceived as the causes of 
the modes of existence4 ,ideas have been
  supposed to have causative power over 
the order of the world4    ,we should be
 very careful in attributing the notion 
of causation4 ,if we  see a stone lying 
on the ground1 and proceed to pick it up
 by the  strength of the arm1 we say    
that the exertion of the arm is the     
cause of  the stone being lifted4 ,but  
in this respect even we are too hasty4  
,the  arm may exert itself and yet the  
stone not be lifted up--if it is too    
heavy4 ,all that we can say about it is 
that if the stone is lifted1 a  certain 
set of muscular actions has gone on in  
the arm1 and a certain  movement of the 
stone has taken place4 ,if we look      
closely at the matter1  the movements in
 the arm are related to the movements in
 the stone in a  strictly measurable    

way4 ,there has been so much exertion   
corresponding  to the weight of the     
stone4 ,but suppose the arm had done    
anything else1  there would have been   
the same relation traceable between the 
movements  in the arm and the actions   
which followed its movements4 ,the      
energy  spent by the arm would be equal 
to the energy imparted to the object    
moved1 whether it be a stone sent flying
 through the air1 or one lifted  to a   
higher position 7bearing in mind always 
the small quantity of  energy passing   
off in the form of heat74    ,it does   
not seem advisable that the notion of   
cause should be brought in  to denote   
the relation of the movement of the arm 
and the movement of  the stone4 ,these  
are two sets of actions between which   
the regular  relations which hold good  
between the consecutive states of moving
  systems hold good4    ,the notion of  
8cause0 should rather be applied to that
 act of the will  whereby the movements 
of the arm are connected with the       

movement of that  particular stone      
rather than the movement of any other   
object4    ,we are the cause of the     
actions we will4 ,the notion of cause is
 derived  from our 8will0 action1 and   
the notion of cause ought to be kept to 
this  connection4    ,all that goes on  
outside us can only be apprehended as   
consecutive  states following on one    
another4 ,between certain sets of       
consecutive  events we notice that the  
same relation holds good which we have  
observed in other consecutive states4   
,if some water is heated in ,england  it
 passes off into steam2 if water is     
heated in another part of the  world it 
also passes off into steam4 ,there is an
 exact analogy in the  behaviour of     
water under the action of heat wherever 
we observe it4 ,but  all that we have   
obtained as knowledge is the fact that  
we may  practically be confident of an  
analogous behaviour on the part of water
  wherever circumstances are similar4   
,we may use the expression that heat  is

 the cause of water boiling for         
convenience4 ,but the expression should 
not be used as containing any deep      
meaning4 ,to say one external event is  
the cause of another is to put an       
absolutely unknown and spiritual        
relation in place of impartial          
observation4    ,to cause a motion is   
the name for the action of our soul on  
matter--a  thing shrouded in mystery4   
,to be the antecedent in a chain of     
movements  is the fact which we can     
observe about any movement in the       
external  world4 ,we cannot strictly say
 what movements of gases1 water1 c41    
cause  this volcano4 ,we can only say   
what movements of gases1 water1 c41     
precede this volcanic eruption analogous
 to movements which have  preceded other
 volcanoes4    ,there are invariable    
sequences in the external world to which
 we do not  affix the notion of cause   
and effect--day and night1 summer and   
winter4  ,why we should do so in any    
case is not clear1 except that by       

familiarity  and mystery the sequences  
have become to us something like our own
 will  action4 ,indeed1 is it not the   
case that when we can trace intermediate
  links we say so and so comes from so  
and so in such a manner4 ,but when  no  
intermediate links can be traced we say 
one event causes another4    ,if1       
however1 we omit the feeling of         
causation from the external chain of    
events1 it does not follow that there is
 no causation to be apprehended  in the 
external world4    ,let us not introduce
 the notion of causation at haphazard4  
,but if we  find in the external world  
signs of an action like our own will    
action1  let us then say1 ,here is      
causation4    ,the inhabitants of the   
valley would not have been right in     
saying that  one act of a routine caused
 another3 ,but they were right in saying
 that  the amount of sensation was      
constant1 and that some of it passed off
 in  a form in which they could not feel
 it4    ,and so let us not say that one 

action causes another4 ,let us not say1 
for example1 that the downward swing of 
a pendulum is the cause of its  upward  
swing4 ,but let us simply say that the  
one follows the other2 that  the amount 
of energy present is the same except for
 the small portion  that passes off into
 the form of heat4                      
,,chapter ,,iv4    ,suppose certain sets
 of numbers were being presented to us  
one after the  other1 and amongst these 
three consecutive sets were the         
following4  ,first set3 #c1 #e1 #f4     
,second set3 #h1 -#b1 -#a1 #a4 ,third   
set3 #g1 #d1 #b1 -#a4    ,a little      
consideration will show us that there is
 a certain uniformity  in these sets4   
,take the square of each of the numbers 
in the first set and add them  together1
 the result is #gj4 ,thus #c  #e  #f  #i
  #be  #cf  #gj4    ,the sums of the    
squares of the numbers in the second set
 come to the  same4 #h  7-#b7  7-#a7  #a
  #fd  #d  #a  #a  #gj4 ,also in the    
third1  #g  #d  #b  7-#a7  #di  #af  #d 

#a  #gj1 and so on4    ,having noticed  
this we should regard it as a purely    
formal law1 having  nothing to do with  
why the numbers were presented to us4   
,but we should  consider it likely that 
it would characterize all the numbers   
that were  presented to us4 ,and if this
 expectation were found to be realized1 
we  should after a time feel a certain  
assurance that the next set of  numbers 
presented would satisfy the same law4   
,if this assurance was  indefinitely    
satisfied we should get to regard the   
satisfying this law  as an invariable   
condition of the numbers presented4 ,but
 we should never  regard this purely    
formal law--that is1 a law about the    
particular  characteristics of the      
numbers--we should never regard this    
formal law as  the cause of the next set
 of numbers appearing after the first   
had gone4    ,when1 however1 we talk    
about the conservation of energy we are 
apt to  think of it as more than a      
merely formal law1 more than a statement

  about numbers which has been found to 
hold true4    ,yet it is no more4 ,the  
law of the conservation of energy       
asserts that in  any system in motion   
the sum of the squares of the velocities
 of the  particles at any one moment is 
equal to the sum of the squares of the  
velocities of the particles at the next 
moment4    ,the conservation of energy  
is but a mode of reckoning motion1 by   
which  it is found to be constant in all
 changes of a system4 ,the system must  
embrace all the particles concerned in  
the motion4 ,it may be made as  large as
 we like4    ,the principle of the      
conservation of energy as here stated is
 confined  to the case of moving bodies4
 ,sometimes the energy is said to       
disappear  from the form of motion and  
become potential energy4 ,that case will
 be  treated under the fourth           
consideration of level1 but it          
introduces no  alteration in what has   
been said4    ,as to the practical truth
 of the law of conservation of energy   

there can  be no doubt2 nor as to the   
value of the results obtained from      
tracing  its validity in obscure        
actions4 ,but there is nothing final    
about it4 ,it  is a numerical statement 
of extreme value1 and it introduces a   
mode of  reckoning by which motion can  
be looked upon as indestructible as     
matter  is4    ,there is a possible     
objection to the law of conservation of 
energy4    ,it is no less a law in      
nature that in every one of a series of 
changes  some of the energy passes off  
into the form of heat4 ,now heat is     
reckoned as a mode of energy4 ,and there
 is in science a method of  calculating 
how much energy any given quantity of   
heat is the equivalent  of4 ,and this   
equivalence is calculated on the        
supposition that no energy  is lost4    
,when heat is produced and motion passes
 away1 the proportion  between the      
motion that disappears and the heat that
 appears is  represented by a number    
calculated on the assumption that no    

energy is  lost4 ,thus whenever any     
quantity of energy takes the form of    
heat1 the  quantity of heat which is    
produced is exactly given by the        
calculation4  ,but the reverse process  
is not possible4 ,it is not possible to 
turn back  all the energy in the form of
 heat into the form of motion4          
,consequently  it cannot be proved that 
the energy in the form of heat would1 if
 all  turned into motion1 produce as    
much motion as that from which it was   
produced4 ,there may be an absolute loss
 of energy--only a very small one4  ,the
 law of the conservation of energy may  
be the expression that this  loss is a  
minimum4    ,this objection is not      
essential to the line of argument       
pursued above  with regard to the       
conservation of energy4 ,it forms no    
necessary part of  the line of thought  
we are pursuing4 ,it merely tends to    
show that the  law of the conservation  
of energy is no axiom which we cannot   
suppose  not true4 ,the real conclusion 

to which this part of our line of       
thought  tends is that the conservation 
of energy is a purely formal law4       
,,chapter ,v4    ,the most apparently   
simple movements are those which we see 
taking place  on the surface of the     
earth1 connected with the agency which  
we call  gravitation4 ,we see the rivers
 flowing from a higher to a lower level1
  rocks when loosened from a mountain   
side rolling down1 rain falling1 and    
many minor changes of this sort4    ,but
 there are many actions besides these4  
,for instance1 suppose before  us a     
spring coiled up4 ,when it unwinds it   
8exerts force10 it transmits  movement4 
,in its first state it is like a stone  
at the top of a  mountain4 ,in its      
second state it is like a stone which   
has fallen to the  bottom of the        
mountain4 ,it had a power of movement   
and of communicating  movement1 now it  
has lost that power4    ,again1 the     
powder in a gun when it explodes expands
 and imparts movement  to the shot4     

,when the gun has been fired off the    
powder enters a  different state4       
,before1 the chemical affinities of its 
constituents  were in a state of        
tension1 now that it is fired off1 they 
have formed  fresh combinations4 ,the   
power of transmitting movement has been 
lost by  that which was the powder4 ,it 
is like a portion of water at the top of
 a  fall of water4 ,if it remains at the
 top it has at any time the power of    
producing a shock1 and of effecting1    
say1 the movement of a water-wheel      
under it4 ,but if it falls it has       
exerted and lost that power4    ,the    
difference of level associated with     
gravity is familiar to us4 ,but  we have
 no right1 other than our own           
familiarity with it1 to look on  gravity
 as less in need of explanation than any
 other phenomenon of the  external      
world4 ,newton did not suppose that     
there was any force inherent  in matter 
which attracted other matter inversely  
as the square of the  distance4 ,he     

showed that a great many astronomical   
facts were capable of  being explained  
and calculated on this hypothesis4 ,he  
left the  explanation of how it is that 
matter gravitates unsolved1 and it      
remains  unsolved to the present day4   
,but gravitation affords us a useful    
term--8,level40    ,let us agree to call
 the following on a high level--a stone 
at the top of  a precipice1 a wound-up  
spring1 oxygen and hydrogen mixed in the
  proportion to form water4 ,let us call
 the following at a low level--the      
stone at the foot of the precipice1 a   
spring straightened so far as it  tends 
to straighten1 oxygen and hydrogen      
united in the form of water4    ,in     
passing from their first state to their 
last all these have  manifested a power 
of movement and of communicating        
movement4 ,they have  now relatively to 
their former state lost that power4     
,difference of level in this general    
sense is the most universal  distinction
 of matter4    ,no motion takes place   

unless matter passes from a higher to a 
lower  level4    ,the universal cause of
 motion is that which produces this     
difference of  8level0 in the general   
sense4    ,if there were no difference  
of level the state of things in nature  
would  be as if one spring in order to  
unwind had to wind up an exactly equal  
spring of the same amount2 as if a stone
 falling from a height had to  raise an 
exactly equal stone to the same height  
from which it fell4  ,under such        
conditions of things no motion would    
begin4 ,in such a state  of things all  
nature would be like the inhabitants of 
the valley when  the king bore no pain1 
for no course would be preferable to any
 other  course4    ,what is the cause of
 the 8,difference of ,level80 ,whenever 
matter passes  from a higher to a lower 
level some of the energy which is given 
out  passes away in the form of heat4   
,this passing away of some of the energy
  into the form of heat is an invariable
 accompaniment of the transition  from a

 higher to a lower level4 ,is it the    
cause of the difference of  level8      
,in the valley the king by bearing some 
pain made action worth while4 ,is  there
 any indication in nature of the        
production of a lower level which  makes
 the course of things run on8    ,it is 
certain that energy in every action     
passes off into the form of  heat1 and  
unless it is through the power of the   
finer particles of  matter to absorb the
 energy1 it is difficult to see how any 
action can  take place4    ,as with the 
other lines of thought1 this line also  
terminates with a  possibility4 ,nothing
 has been proved1 but a place has been  
provided4    ,in the first part of this 
paper a possible mode of action was     
exhibited  in the imaginary relations of
 a world subject to certain laws of     
pleasure and pain4    ,in the second    
part it has been shown that something is
 wanting in our  conception of the      
natural processes4 ,there is room for a 
central idea4  ,no scientific doctrines 

properly understood would clash with one
  properly located4    ,can the mode of 
action exhibited in terms of sensation  
in the fictitious  world be applied to  
the case of the world of force and      
matter8    ,before passing on1 however1 
it is worth while to examine a little   
more  closely into what is meant by the 
expression so often used3 8,passing off 
into the form of heat40    ,the modes in
 which energy passes off into the form  
of heat are in  general those modes by  
which movement is brought to a          
standstill such as  friction4 ,and we   
are apt to think motion the primary     
fact1 the cessation  of motion a        
secondary and disagreeable fact4 ,but   
both are equally  existent phenomena1   
and the convenience to ourselves is not 
to mislead  us as to their relative     
importance4    ,but what is this passing
 off of energy into the form of heat8   
,the phrase  is unsatisfactory1 for we  
are told by science almost in the same  
breath  that heat is the motion1 the    

mechanical motion1 of the particles of  
matter4 ,so the statement resolves      
itself into this4 ,only when some of    
the motion passes off into the form of  
motion of the smaller particles  of     
matter does motion take place in larger 
masses4    ,as a corollary it follows   
that at some date1 however distant1 all 
the  motion of masses will have passed  
away into the form of motion of  smaller
 masses4    ,it may be urged that when  
the larger masses move1 the smaller     
particles  also move4 ,this is true2 but
 motion in this sense is used to denote 
change of position amongst the smaller  
particles with regard to one  another4  
,the particles in a flying cannon-ball  
are relatively still with  regard to one
 another as far as the motion of the    
cannon-ball as a whole  is concerned4   
,we thus arrive at the following        
principle3 ,the condition of the motion 
of masses taking place is that some of  
the motion passes off into the  motion  
of the smaller particles4    ,but if the

 motion of the smaller particles is just
 the same as that of  the larger        
portions1 we are obviously not at the   
end4 ,the very same  principle just     
applied must be applied again4    ,these
 motions of the small particles of      
matter cannot take place unless  some of
 their movement is transmitted and      
passed on1 and transformed  into the    
motion of still finer particles of      
matter4    ,but here obviously we are   
brought to the beginning of an infinite 
series4 ,an infinite series passing from
 finer matter to still finer  matter1   
and so on endlessly4    ,the assumption 
by which we are led to this endless     
series of  transmissions must be clearly
 apprehended4 ,we take the law--that the
  motion of masses only takes place when
 some of the motion passes off  into the
 motion of the finer particles of       
matter1 and we assume that it  holds    
always4    ,in a lever there is a fixed 
point1 the fulcrum1 which supports it1  
and  the power raises the weight2 but   

the weight may be fixed1 and then the   
fulcrum can be lifted by the power4 ,so 
we obtained this law from the           
consideration of material relations2 and
 now we suppose this law to be  the     
fixed point1 and shift our notions of   
material relations4    ,thus we are     
landed on an endless series4 ,before    
proceeding1 however1 to  inquire what   
the significance of this endless series 
may be1 let us  assume an end to it4    
,let us assume that we come at last to a
 final  transmission4 ,let us assume    
that the energy is transmitted to the   
ultimate particles of matter4    ,or1 if
 we have gone beyond matter1 let us     
suppose an ultimate medium  which by its
 modifications builds up matter1 and    
which is the last and  ultimate         
substance4    ,let us suppose this      
ultimate medium absolutely to receive   
some of the  energy4 ,let it absolutely 
receive and absorb some of the energy1  
and  thereby give rise to the difference
 of level1 to give the ultimate         

permission which sets all things going4 
,what are the properties of this medium8
 ,we obtain an indication of what  they 
are when we examine the properties of   
the finer kinds of matter4  ,compared   
with the motions of masses1 motions     
which affect the smaller  particles of  
bodies are infinitely quick4 ,light and 
electricity are  actions affecting the  
smaller particles of bodies1 and by them
 distances  are speedily traversed1     
which relatively to moving masses are   
very  great4    ,now in point of speed  
of transmission the properties of this  
ultimate  medium must be infinitely     
beyond those of luminiferous ether4     
,to this ultimate medium all movements  
at any distance from each other  must be
 almost equally present at every part4  
,at whatever distance from  one another 
two affections of this ultimate medium  
be supposed to take  place1 the effect  
of the one will travel to the place of  
action of the  other instantaneously4   
,such a medium is a kind of visible     

symbol of the universe1 being one       
system in which all motions should be   
co-determined4    ,to make this clear1  
suppose a transformation of energy was  
produced in  one part of space of an    
absorption of energy on the part of this
  ultimate medium1 this transformation  
of energy would be produced by a  medium
 in instantaneous contact with every    
other part of space1 and the            
transformation of energy thus originated
 would harmonize with1 and have         
reference to1 the transformations of    
energy in every other part of  space4   
,there are two infinities--the infinite 
of space extending out each way1  the   
infinite of the smaller and smaller     
divisions of matter4 ,the  ultimate     
medium we have supposed partakes of both
 infinities4 ,it is  infinite in extent1
 and infinitely fine in its particles4  
,now this medium by absorbing energy    
sets movements going4 ,and that         
movements do not neutralize one         
another--i4e41 that movements in        

opposite directions do not mutually     
destroy one another--has this result1   
that a given amount of this absorption  
produces the greatest possible  amount  
of motion4 ,if motion came to a rest in 
any other way1 more of  this absorption 
by the ultimate medium would be needed4 
,hence1 by a  given amount of absorption
 in the ultimate medium the greatest    
possible  amount of motion is produced4 
,that is1 the absorption of motion into 
the  ultimate medium is a minimum1 and  
the law of the conservation of energy   
is the expression of this being a       
minimum4    ,but here again a further   
remark is called for4 ,we start by      
assuming  energy to be an absolute      
existence4 ,but why not assume this     
action on  the part of the ultimate     
medium to be the real action1 and       
consider the  phenomena of motion and   
energy as the mode of its action4       
,what this action of the ultimate medium
 may be needs examination4 ,all  that we
 can say at present is that relatively  

to that which we call  energy1 the      
action of this medium is that of being  
acted on4                               
,,chapter ,,vi4    ,in the preceding1   
however1 it must be remembered that this
 conception of  an ultimate medium was  
merely a supposition to enable us to see
 and  roughly map out the relations of  
the things we are investigating4 ,where 
we were really landed was in an infinite
 series--we were brought  logically to  
the conception of an infinite series of 
media1 one behind  the other4    ,what  
does an infinite series indicate8       
,let us turn to a region of thought     
where infinite series are familiar      
objects1 and we can learn about them4   
,in algebra infinite series are common4 
,thus take series #a - x_/#b   x_/#d and
 so on for ever4 ,this is the attempt in
 algebra to represent a  trigonometrical
 idea4 ,in trigonometry it is expressed 
as cos4 x4 ,but  in algebra it needs    
this infinite series4    ,in algebra    
infinite series occur when the object   

which it is wanted to  represent in     
algebraical terms cannot be grasped by  
algebra4 ,when there  is no single term 
or set of them in algebra which will    
serve1 the object  is represented by    
means of an infinite series4 ,thus we   
may say that in  any calculus1 when the 
object to be treated of cannot be       
expressed in  the terms of the calculus1
 it is represented by means of an       
infinite  series4    ,now1 dealing with 
material considerations1 going on in the
 calculus of  matter1 we have come to an
 infinite series4 ,this indicates that  
we have  gone as far as the material    
calculus will carry us4 ,we have now to 
bring  in an idea from a different      
quarter if we will simplify our         
expression4    ,it may well be that     
within our experience there is nothing  
which will  serve4 ,but let us suppose  
that that which in material terms we    
represent  as an infinite series is a   
will--a will in contact with all        
existence1 as  shown by the properties  

it had when we conceived it as an       
ultimate  medium4 ,for1 regarding it as 
an ultimate substance1 we found that it 
would be affected by pulsations         
infinitely quicker than light and       
electricity2 considered as a substance1 
it was such that distance to it  tended 
to be annihilated4 ,hence as a will we  
must say of it that to it  all that is  
is present--a will which by a fiat that 
to our notions is  being acted on rather
 than acting1 accepting pain rather than
 taking  pleasure1 sets the course of   
the world in motion1 which holds all in 
one  system1 which creates all          
activities4 ,for although we apprehend  
this  will relatively to the appearances
 which we suppose we know1 mechanical   
energy and feeling1 still we see that   
both are caused by it1 and that  the sum
 of both is nothing1 save for that which
 this will is in them4    ,is there any 
other way of apprehending this will than
 through the  external world8    ,we    
have two apprehensions of nature--one of

 external things1 the other of  our own 
wills4    ,does this will not exist in  
those who are true personalities1 and   
not  mere pleasure-led creatures8--have 
they not some of this power1 the power  
of accepting1 suffering1 of determining 
absolutely what shall be8--a  creative  
power which1 given to each who possesses
 it1 makes him a true  personality1     
distinct1 and not to be merged in any   
other--a power which  determines the    
chain of mechanical actions1 of material
 sequences--which  creates it in the    
very same way in which it seems to be   
coming to an  end--by that which1       
represented in material terms1 is the   
absorption of  energy into an ultimate  
medium2 which1 represented in terms of  
sensation1 is suffering2 but which in   
itself is absolute being1 though  only  
to be known by us as a negation of      
negations4                              
,,chapter ,,vii4    ,in conclusion let  
us remark that we have supposed two     
different  worlds--one of sensation in  

the first part1 one of motion in the    
second  part4 ,and these have been      
treated as distinct from one another4   
,and  especially in the first part1 by  
this avoidance of questions of          
movement1 an appearance of artificiality
 was produced1 and occasionally         
inconsistencies1 for sometimes          
sensations were treated as independent  
of  actions1 sometimes as connected with
 them4 ,but it remains to be decided  if
 these inconsistencies are in themselves
 permanent1 or whether1 when  we remove 
the artificial separation1 and let the  
world of sensation and  the world of    
motion coalesce1 the inconsistencies    
will not disappear1  thereby showing    
that their origin was merely in the     
treatment1 not in  the fact2 that they  
came from the particular plan adopted of
 writing  about the subject and are not 
inherent in the arguments themselves4   
,the king in the first part was supposed
 to have all the material  problems of  
existence solved4 ,there was a complete 

mechanism of nature4  ,he took up the   
problem of the sentient life4 ,but this 
problem can only  artificially be       
separated from that of the material     
world4 ,the gap  between our sensations 
and matter can never be bridged1 because
 they are  really identical4    ,let us 
then allow this separation to fall      
aside4 ,let us suppose the king  to have
 all the reins of power in his own      
hands4 ,let us moreover suppose  that he
 imparts his rays to the inhabitants so 
that they have each a  portion of his   
power4 ,and let us suppose that the     
inhabitants have  arrived at a state of 
knowledge about their external world    
corresponding  to that which we have    
about the world which we know4    ,let  
us listen to a conversation between two 
of them4    ,a4 ,the energy of the whole
 state of things is running down4    ,b4
 ,how do you prove that8    ,a4         
,whenever any motion of masses takes    
place a certain portion of the  energy  
passes irrecoverably into the form of   

heat1 and it is not  possible to make so
 large a movement with those same masses
 as before1  do all that is possible to 
obtain the energy back again from the   
heat  into which it has passed4    ,b4  
,well1 what about the heat8 ,energy in  
the form of the motions of the  masses  
passes off into the energy of heat4 ,but
 what is heat8    ,a4 ,it is the motion 
of the finer particles of matter4    ,b4
 ,well1 ,i would put forward this       
proposal4 ,we have by observation got   
hold of a certain principle that where  
any movement takes place some of  the   
energy goes in working on the finer     
particles of matter4 ,let us now  take  
this principle as a universal one of    
motion1 and apply it to the  motions of 
the finer particles of matter           
themselves1 which are simply  movements 
of the same kind as the movements of the
 larger ones4 ,this  principle would    
show that these movements are only      
possible inasmuch as  they hand over a  
portion of their energy to work on still

 finer matter4    ,a4 ,then you would   
have to go on to still finer matter4    
,b4 ,yes1 and so on and on2 but to fix  
our thoughts1 suppose there is an       
ultimate fine matter which is the last  
worked on4 ,now ,i say that we may      
either suppose that this is being       
gradually worked on and all the energy  
is dissipating1 or else we may put it in
 this way4 ,when we regard so  much     
energy we are apt to think that it is   
the cause of the next  manifestation in 
which it shows itself4 ,but this is     
really an  assumption4 ,energy is a     
purely formal conception1 and all that  
we do is  to trace in the actions that  
go on a certain formal correspondence1  
which we express by saying that the     
energy is constant4    ,a4 ,but ,i feel 
my own energy4    ,b4 ,allow me to put  
your feeling to one side4 ,if we take   
then the  conservation of energy to be  
merely a formal principle1 may we not   
look  for the cause of the movements in 
the invariable accompaniment of them1   

namely1 in the fact that a certain      
portion of the energy is expended       
irrevocably on the finer portions of    
matter4 ,if now we take this  ultimate  
medium which suffers the expenditure of 
energy on it1 may we  not look on it as 
the cause1 and the setter in action of  
all the  movements that there are4 ,by  
its submitting to be acted on in the way
 in  which it does submit1 it determines
 all the actions that go on4 ,for what  
is all else than a great vibration1 a   
swinging to and fro4 ,when we count  it 
as energy1 we by reckoning it in a      
particular manner make it seem to  be   
indestructible1 but that the energy     
should be indestructible would be  a    
consequence from the supposition which  
we could very well make1 that  to       
produce a given series of effects the   
submitting to be worked on of  this     
ultimate medium must be a minimum4 ,if  
it were a minimum no  movements could   
neutralize one another when once set    
going1 for if they  did there would be a

 waste of the submission of this        
ultimate medium4    ,a4 ,but what do you
 suppose this ultimate medium would be8 
,b4 ,that ,i cannot tell1 but we seem to
 have indications4 ,for the more  fine  
the matter which we investigate1 the    
more its actions seem to  annihilate    
distance3 light and electricity produce 
their effects with  far greater rapidity
 than do the movements of masses4 ,we   
might suppose  that to this ultimate    
matter all parts were present in their  
effects1 so  that anything emanating    
from the ultimate matter would have the 
appearance of a system comprehending    
everything4    ,a4 ,but you have not got
 any evidence of an ultimate matter4    
,b4 ,no1 all that we can think of is an 
endless series of finer and  finer      
matter4 ,but is that not an indication  
rather1 not that the  direction of our  
thoughts is false1 but that there are   
other  characteristics of this ultimate1
 so that when looked at under the form  
of matter it can only be expressed as an

 infinite series4    ,let us omit the   
considerations brought forward in the   
preceding  conversation and examine more
 closely the philosophy of the          
inhabitants  of the valley in so far as 
it corresponds with ours4    ,they laid 
great stress on a notion of vis viva1 or
 what we should term  energy1 but said  
it was gradually passing away from the  
form of  movements of large bodies to   
that of movements of small bodies4 ,so  
that  in the course of time the whole   
valley would consist of nothing but an  
evenly extended mass of matter moving   
only in its small particles--and  this  
motion of the small particles they      
called heat4 ,now they had very  clearly
 arrived at the conviction that with    
every mechanical motion  there was a    
certain transference of vis viva to the 
smaller particles  of matter1 so that it
 did not appear again as mechanical     
motion4 ,but  they did not accept this  
as a principle to work by4 ,they did not
  consider that the motions of the      

smaller particles of matter were just   
the same as those of the larger masses4 
,they did not see that if a  condition  
held universally for the movements of   
the visible world1 it  must also hold   
for the smaller motions which they      
experienced as heat4  ,so the conclusion
 which they should logically have come  
to that there  was a transference of vis
 viva on and on was not held4 ,but the  
step  was a very little one for them to 
take from regarding an invariable       
condition as always there to regarding  
it as a cause4 ,for the causes  they    
assigned were all purely formal         
relations1 and only got to assume  an   
appearance of effective causes by       
familiarity with them1 and a  throwing  
over them of that feeling of            
effectiveness which they derived  from  
the contact which they had with the     
king4    ,they might have reasoned4     
,this universal condition of anything   
happening  must be the cause4 ,energy   
goes from a higher to a lower level4    

,that  which causes the difference of   
level is the cause1 and the cause of the
  difference of level must be that which
 invariably accompanies such a          
transference of energy from a higher to 
a lower level4 ,now this  invariable    
condition is the passing of a portion of
 the energy into the  form of motions of
 the finer parts of matter4 ,hence there
 is an  apparently endless series4 ,but 
to realize the matter1 suppose an       
ultimate medium1 suppose there is a kind
 of matter of infinite fineness         
distributed everywhere which let itself 
be worked on1 and so determines         
differences and wakens the sleeping     
world4 ,what are the qualities of  this 
fine matter8 ,we see them in the        
properties of the finer kind of  matter 
which we know1 such as light1           
electricity4 ,the property of the  finer
 kind of matter is in general that it   
tends to bring distant places  together1
 so that a change in one part is rapidly
 communicated to every  other part4 ,if 

they followed this indication they would
 have supposed  that the ultimate fine  
matter was of such a nature as to make  
all parts  of the valley as one1 so that
 there was no distance1 and any         
determination of a difference of level  
on the part of this ultimate  matter    
would have reference to all the         
conditions everywhere4 ,it would  be in 
immediate contact with every part1 so   
that anything springing  therefrom would
 present the appearance of a system     
having regard to the  whole4 ,now if    
they had imagined such an ultimate      
medium doing that which  to them would  
seem bearing rather than exerting force1
 suffering rather  than acting1 they    
would not have been far from a true     
conception of the  king who directed    
them all4 ,for he himself by reason of  
his very  omnipresence could not be seen
 by them4 ,there was nothing for them to
  distinguish him by4 ,but they could   
have discovered somewhat of the means   
by which he acted on them1 which can    

only be described from the  appearances 
they present to the creatures whom the  
king calls into life4    ,but of truth  
they would have had another and perhaps 
a truer  apprehension of the king in a  
different way4 ,for when he acted on    
them  so that they took one course      
rather than another1 it was his action  
in  themselves that they felt4 ,if they 
were mere pleasure-led creatures then   
they were shaped outwardly1 but if in   
their inner souls he acted and  through 
them suffered1 then they were true      
personalities conscious of  being true  
selves1 the oneness of all of them lying
 in the king1 but  each spontaneous in  
himself and absolute will1 not to be    
merged in any  other4    ,thus they had 
two modes of access to the king1 one    
through their own  selves where he had  
made them exist1 one through the outer  
world4 ,and in  the outer world it was  
but a direction in which they could     
look4 ,they  could never behold the     
personality of the king1 but only an    

infinite  series of different kinds of  
matter1 one supporting the other as it  
were  and underlying it1 but doing more 
also than this1 for in proportion as    
they considered the kinds of matter that
 lay deeper they found that  distant    
became near1 absent1 present1 that time 
gave no longer such  distinctions1 but  
from the phenomenal side they seemed by 
a gradual  diminution of the limitations
 of experience to arrive at an external 
presentation of that absolute which     
exists in the fulness of things1  which 
they knew more immediately in themselves
 when they truly were4                  
,,the ,,end4                            
,,introduction4      ,in the next two or
 three of these papers certain questions
 connected  with the subject of a space 
higher than our own will be treated4 ,it
 is  well1 therefore1 first to recede   
and to form definite conceptions about  
a world of plane space1 about a world in
 which the beings can only move  in two 
independent directions4 ,then1          

proceeding thence to our own world1  we 
may gain the means of passing on to a   
higher world4 ,and ,i should have       
wished to be able to refer the reader   
altogether to that ingenious work1      
8,flatland40 ,but on turning over its   
pages again1 ,i find that the author    
has used his rare talent for a purpose  
foreign to the intent of our  work4 ,for
 evidently the physical conditions of   
life on the plane have  not been his    
main object4 ,he has used them as a     
setting wherein to place  his satire and
 his lessons4 ,but we wish1 in the first
 place1 to know the  physical facts4    
,with this aim it is necessary to form a
 clear idea of what matter would  be in 
a world of two dimensions1 and the      
following illustration is a  convenient 
one4    ,place on the smooth surface of 
a table a half-crown piece1 and suppose 
it to slide on the table perfectly      
freely4 ,imagine it to exercise an      
attractive force along the surface of   
the table in all directions round       

itself4 ,by it and near it place a      
sixpence1 and let the sixpence also     
slide freely on the table4 ,it will1    
however1 not be so free to move  equally
 in all directions as the half-crown    
was1 for it will be  attracted by the   
half-crown4 ,it will slip over the      
surface of the table  under the         
influence of this supposed force1 and   
will come into contact  with the        
half-crown4 ,now if we suppose that both
 the half-crown and the  sixpence are   
very thin1 that they are both of them   
only the thickness of  the ultimate     
particles of matter1 then we shall have 
a representation of  what material      
bodies will be in a plane world4    ,we 
must suppose that the particles cannot  
lift themselves or be lifted  up from   
the plane so as to lie upon each other4 
,under no circumstances  can they quit  
the surface of the plane4    ,moreover1 
at no point must the particles adhere to
 the plane1 nor must  there be any      
friction impeding their movements over  

it4 ,the only purpose  which the support
 serves is to keep them on the same     
level surface and  to convey influences 
from one particle to another4 ,the      
gravity which we  know1 and which acts  
at right angles to the table on which   
the coins  rest1 will not have any      
effect on the particles in their motions
 on the  plane1 but will simply keep    
them to the plane4 ,any force of        
attraction  which concerns their motions
 proceeds from one particle to another4 
,thus1 conceive the half-crown to be a  
very large disk of matter1 and the      
sixpence to be a sentient being4 ,this  
being would feel a force of  attraction 
towards the centre of the half-crown1   
and this force of  attraction would keep
 him to the rim of the half-crown4 ,if  
he weighed  anything it would be by     
balancing it with his weight against the
 force  which tended to pull it to the  
centre of the half-crown4 ,he would not 
feel the gravity which keeps him against
 the surface of the table2 he  would not

 know that there was a hard1 smooth     
surface on which he rested4  ,he would  
always have been in contact with it1 and
 so he could not tell  what it would be 
like to be free from it4 ,he would have 
no contrast  whereby to apprehend its   
effect on him4 ,moreover1 he would only 
know of  movements in directions along  
the plane4 ,he would not conceive that  
such  a thing was possible as movement  
in another direction than to and fro1   
hither and thither on the plane4 ,it is 
difficult to suppose that a being  would
 be supported on one side by a plane1   
and not be in contact with  anything on 
the other side1 even atmosphere4 ,yet if
 we suppose a being  of real matter free
 to move on the plane1 this is what must
 be  conceived4 ,if the sixpence is     
conceived as such a being1 it must      
receive  its impressions through its    
rim4 ,the rim represents its skin4      
,and if it be supposed to be surrounded 
by air for its respiration1 this  air   
must not be able1 any more than the     

particles of solid matter1 to  rise away
 from the plane4 ,the plane being must  
be conceived to have a  different air to
 that which we know4 ,the particles of  
its air1 however  free to move amongst  
themselves1 must not have the power of  
moving away  from the surface of the    
plane1 as if so they would be able to   
pass to  the interior of the body       
without passing through the skin4 ,any  
passage  leading to the interior of the 
body would have to terminate in an      
opening in the rim1 otherwise it would  
be completely shut up from the          
exterior4    ,now it is obvious that if 
the table is struck so that it quivers1 
this  movement will be communicated to  
the coins lying on it4 ,either the coins
  as a whole will move1 or their        
particles will be disturbed4    ,again1 
if we suppose there to be some particles
 loosely cohering  together1 lying on a 
smooth sheet of iron1 it is evident that
 the  quivering and jostling of the     
iron1 if it is struck1 would have an    

effect on the particles1 and may cause  
the breaking up of the thin  masses in  
which the particles cohere4 ,thus1 if   
the material of which the  sheet is     
composed be very dense and rigid1       
compared to the substances  lying on it1
 they may undergo many alterations1     
being broken up and  coming together    
again while the supporting matter which 
bears them all  up simply moves and     
vibrates4      ,illustration3 ,diagram  
,i4    ,it is evident that just as the  
particles are affected by the vibration 
and shaking of the sheet of metal on    
which we suppose them1 so they  might in
 turn possibly affect the sheet of metal
 and cause vibrations  and shakings in  
it4 ,these shakings and vibrations would
 go forth from a  particle which excited
 them in every direction along the      
sheet4 ,they  would not pass out into   
the air1 except secondarily and in a    
very minute  degree4 ,the shake would be
 transmitted in the sheet4 ,and the     
effect on  neighbouring particles would 

be great1 on more distant particles it  
would be less1 and on those at a great  
distance barely perceptible4    ,the    
following is a good plan for obtaining  
in a definite way the feeling  of what  
existence in a plane would be like2 it  
enables us to realize the  conditions in
 such a way as to lay the basis for     
subsequent thought4    ,let the reader  
take a sheet of note-paper and hold it  
before himself  edgewise1 so that he    
sees it with one eye as a single line4  
,and let him  hold it so that this line 
runs downwards from his eyebrows to his 
mouth1  as shown in ,diagram ,i4 ,now on
 this sheet of paper1 on one side of it1
  let a straight line be drawn running  
across it1 away from the observer4      
,suppose all below this line to be a    
thin layer of particles which1  keeping 
compactly together1 form a solid sheet  
of particles1 every one  of which       
touches the paper4 ,this would be the   
solid earth to a being in  the plane    
world4    ,let the surface of the paper 

above this be covered by a layer of     
particles which move freely amongst each
 other1 but which do not rise  from the 
surface of the paper4 ,these particles  
form the air of such a  world4    ,on   
the surface of the earth draw a line    
standing upright4 ,let this line        
represent a man4 ,another line will     
represent a wall which the man could    
not pass except by getting over it4     
,it will be found that the objects on   
the paper are felt to be subject to  the
 action of gravity4 ,the question will  
occur1 ,why will not this thin  layer of
 particles slip off the paper8    ,now1 
the sense of gravity must not be got rid
 of1 but it must be  connected with the 
matter in the sheet of paper4           
,suppose1 then1 that the sheet were to  
grow bigger and bigger till it  filled  
out reaching through the whole world and
 cutting the globe in  two4 ,then let   
all the earth be removed except a thin  
layer on one side  of this enlarged     
sheet of paper4 ,this thin layer will be

 the only  portion of matter left4 ,and 
such a thin layer will represent a plane
  world4 ,the force of gravity must be  
conceived as remaining1 but as  coming  
from a large and thin disk4    ,now to  
keep this thin layer on the paper it    
would be necessary to have  some force  
acting sideways1 so as to keep the      
particles to the paper4    ,and the     
paper itself may be conceived to        
exercise such a force3 it is  many      
particles thick1 while the thin layer of
 matter is only one  particle thick1 and
 thus it will keep the layer of matter1 
which covers  one side of it1 in its    
place by virtue of its own attraction4  
,we suppose that the paper exerts an    
attractive force which keeps the  thin  
layer of matter to it4 ,this attractive 
force is not felt by the  sentient      
beings on the paper1 nor does it        
influence the movements of the          
particles of matter amongst themselves4 
,we also suppose another  attractive    
force proceeding from particle to       

particle of the matter on  the plane4   
,this would be felt by the beings and   
produce movements of  matter4    ,thus  
the conception of a plane world         
necessarily involves that of  something 
on which it is4                         
,a ,plane ,world4      ,where the sun's 
rays grazing the earth in ,january pass 
off and merge  into darkness lies a     
strange world4    ',tis a vast bubble   
blown in a substance something like     
glass1 but harder  far and              
untransparent4    ,and just as a bubble 
blown by us consists of a distended     
film1 so this  bubble1 vast beyond      
comparison1 consists of a film distended
 and  coherent4    ,on its surface in   
the course of ages has fallen a thin    
layer of space  dust1 and so smooth is  
this surface that the dust slips over it
 to and  fro and forms densities and    
clusters as its own attractions and     
movements determine4    ,the dust is    
kept on the polished surface by the     
attraction of the vast  film2 but1      

except for that1 it moves on it freely  
in every direction4    ,and here and    
there are condensations wherein have    
fallen together  numbers of these       
floating masses1 and where the dust     
condensing for ages  has formed vast    
disks4    ,and these disks are glowing  
hot--yet no light comes from them into  
our  universe4    ,for this world lies  
beyond the ther--far beyond4 ,and       
however hot or  glowing the masses are1 
if there is no medium to transmit the   
vibrations  of heat the influence cannot
 travel4    ,thus the only directions in
 which the heat can travel are on the   
film4  ,from each of these glowing disks
 the luminous influence streams forth   
carried by the vibrations of the film   
which supports everything4 ,for the     
heat and intense agitation of these     
glowing disks shakes and disturbs  the  
bubble1 and just as a thin soap bubble  
quivers and shakes1 so this  film       
quivers and shakes4 ,and so elastic is  
it1 and so rigid1 that it  carries the  

light and heat to all surrounding       
regions4 ,yet so vast is  the bubble1 so
 tremendous in its dimensions1 that the 
agitation from  these glowing disks     
travels almost in straight lines1 till1 
spreading  out on every side1 it merges 
into darkness--like the ripples in the  
centre of a vast calm lake gradually    
become indistinguishable4    ,and round 
these central orbs of fire--for orbs of 
fire they are1 though  they only        
transmit their fire along the film of   
the bubble--round these  orbs pass in   
due order and succession other disks1   
which1 cold or warm1  have not that     
energy of light and heat which the      
central orbs possess4    ,these disks1  
though large1 are so immeasurably small 
compared with the  vast surface of the  
all-supporting bubble1 that their       
movements seem to  lie on a plane flat  
surface2 the curving of the film on     
which they rest  is so slight compared  
to their magnitude1 that they sail round
 and round  their central fires as on a 

perfect level surface4    ,and one of   
these orbs is fitted by nature to be the
 habitation and home  of living beings4 
,for it is neither so hot as it was for 
long ages after  it had condensed from  
the film of dust wherefrom all orbs are 
made1 nor  has it so cooled down as to  
render life unsupportable4    ,and1     
moreover1 it is full of vast crevices   
and channels1 for in many  places the   
interior in cooling after the rim had   
set from its molten  condition has left 
long caverns and passages1 not only in  
one layer1 but  in many4    ,and on the 
rim and in these passages and caverns   
live the inhabitants of  whom ,i speak4 
,they do not rise from the surface of   
the film1 but as all matter lies on  the
 smooth surface but one particle deep1  
so their bodies formed out of  matter   
lie1 as we should say1 on this smooth   
surface4    ,yet of this they know      
nothing4 ,they say that they stand and  
walk4    ,for this orb has an attractive
 force4      ,illustration3 ,diagram    

,,ii4--8,two beings walking round40     
,by that very same impulse of coming    
together whereby it gathered its        
particles out of the dust on the bubble1
 by that very same force it  draws      
towards its centre all that is near it  
or on it4 ,thus 8up0 is to  these       
inhabitants a movement from the centre  
of the disk on the rim of  which they   
live and away from it4 8,down0 is a     
movement from the rim  towards the      
centre4 ,the thin layer which forms the 
mass of the disk is  their solid matter4
 ,they are not able even in thought to  
rise away from  the surface of the      
bubble1 and look from space upon their  
mode of  existence4 ,they ever pass to  
and fro upon a line1 upon a rim2 and no 
two  can walk except after one another4 
,if you look at the rude picture you    
will see that the two beings represented
 by two triangles cannot pass  one      
another if they are unable to lift      
themselves up from lying on the  surface
 of the paper4 ,the surface of the paper

 represents the surface of  the bubble1 
and sliding freely on it1 but unable to 
lift up from it1 are  tenuous shapes    
that are the inhabitants1 and that thin 
layer of  particles that is to them     
solid matter4      ,illustration3       
,diagram ,,iii4--,a section of the film 
of the bubble    showing a disk ,,bd    
lying on it1 and a creature ,,ab on the 
rim of the    disk4 ,,ce is a section of
 the film1 ,,bd is a section of the     
disk1 ,,ab is    a section of the       
creature4 ,the thickness is enormously  
magnified and    also the height ,,ab of
 the creature compared with the diameter
 ,,bd of    the disk4 ,the attraction   
which ,,ab feels keeps him to ,,bd2 both
 ,,ab and    ,,bd1 the being and the    
disk1 slide freely on the film ,,ce     
without    knowing of its existence4    
,now were it not for the fact that the  
orb is reft into these chasms and       
passages1 the only movement that these  
beings would have would be of  passing  
round and round on the rim of their     

world4    ,many words that we have1 to  
them could bear no meaning4 ,thus 8right
 and  left0 is to them unknown4 ,for    
consider their faces bent in one        
direction  along the rim4 ,in following 
this direction1 they go forward1 in     
retracting from it they go backward4 ,if
 they go away from the centre  they go  
up1 towards the centre is down4 ,and by 
no means can they turn1  raising        
themselves from the surface whereon they
 are4 ,they do not even  know that they 
have two sides2 their movements1        
thoughts1 and  imaginations are all     
confined to that surface on which they  
are4 ,this  they call their space1 their
 universe2 nor does aught that lies     
beyond  it1 towards the interior of the 
bubble or away from it1 directed        
outwards1 come into their thoughts1 even
 as an imaginary possibility of         
existence4    ,life is extremely limited
 on such a world4 ,to take a single     
instance1 in  order for two beings to   
pass each other1 a complicated          

arrangement is  necessary1 shown in     
,diagram ,,iv4    ,at intervals along   
the rim recesses and chambers are       
constructed4 ,near  the openings of     
these chambers lay movable plates or    
rods4 ,when two  beings wish to pass1   
one of them descends into the recess2   
the other one  pushes the rod so as to  
form a bridge over the opening1 walks   
across it1  and then removes the plate  
so that the one who has descended can   
get up  and go on his way4              
,illustration3 ,diagram ,,iv4--,two     
beings passing4    ,if by any chance1   
while a being is in the recess1 the     
plate or rod which  acts as a bridge    
gets fixed1 he is in a dangerous        
predicament4 ,for  suppose a being      
confined as shown4 ,if he1 suffering    
from want of air1  cuts through the roof
 at ,,ab1 the whole part to the right of
 ,,ab comes  tumbling down4 ,for its    
only support is severed when ,,ab is cut
 through4  ,it is impossible to make a  
hole which is not the whole width of    

matter  as it lies on the surface4 ,and 
with regard to this all constructions   
have to be made4 ,there cannot be two   
openings in a wall of a house1  unless  
when the one is open the other is so    
fashioned as closing to act  as a rigid 
support to the wall1 which now depends  
for its upholding  entirely on it4      
,illustration3 ,diagram ,v4--,a house4  
,thus1 in the diagram1 the house is held
 up entirely by the side opposite  to   
the doorway ,,ef1 which is now open4    
,the roof is supported by the side      
,,cd4 ,if an opening ,,ab be made in the
 wall ,,cd before the doorway ,,ef is   
closed1 the roof will fall in4 ,so1 in  
order to pass through the house1  ,,ef  
must be firmly shut up before ,,ab is   
opened4 ,the houses are always  built in
 the interior passages so as to leave   
the rim of the disk free  for           
locomotion4    ,and there are many      
things to be said of the inhabitants on 
this disk  with respect to their social 
and political life4 ,it is hardly       

necessary  for me to put down much about
 it here1 for any one by using the      
method  of the historian ,buckle1 and   
deducing the character of a people from 
their geographical influences and       
physical surroundings1 could declare    
what the main features of their life and
 history must be4    ,but one or two    
remarks may be made here4 ,first of all 
they are  characterized by what ,i may  
venture to call a crude kind of         
polarity4    ,in dwellers in our world  
this polarity1 which shows itself       
amongst other  ways in the distinction  
of sexes1 is tempered and modified4     
,in every man there is something of a   
woman1 and in every woman there are     
some of the best qualities of a man4    
,but in the world of which we speak     
there is no physical possibility for    
such interfusion4 ,in a linear existence
 there would be no consciousness  of    
polarity4 ,it makes its appearance first
 in the plane1 and in a hard  and       
unmitigated form4    ,it is impossible  

to do otherwise than caricature these   
beings when we  write of them thus in   
brief4 ,so let us accept the matter     
frankly1 and1  without scruple1 look at 
them in the broadest possible manner4   
,if the reader will cut out the         
triangles in the corners of the two next
  pages he will obtain four plane       
beings1 two of which are men1 two of    
which are women4 ,the lines down which  
the cutting is to be made are  marked   
with a black line4 ,now having cut out  
two men1 whom we will call  ,homo and   
,vir1 draw a line on a piece of paper to
 represent the rim of  the world on     
which they stand1 and1 remembering that 
they cannot slide  over each other1 move
 them about4 ,it must be remembered that
 the figures  cannot leave the plane on 
which they are put4 ,they must not be   
turned  over4 ,the only way in which    
they can pass each other is by one      
climbing  over the other's head4 ,they  
can go forwards or backwards4 ,much can 
be  noticed from an inspection of these 

figures4 ,of course it is only          
symbolical in the rudest way1 but in    
their whole life the facts which  can be
 noticed in these simple figures are    
built up and organized into  complicated
 arrangements4      ,illustration3      
,diagram ,,vi4      ,illustration3      
,diagram ,,vii4    ,it is evident that  
the sharp point of one man is always    
running into  another man's sensitive or
 soft edge4 ,each man is in continual   
apprehension of every other man3 not    
only does each fear each1 but their     
sensitive edges--those on which they are
 receptive of all except the  roughest  
impressions--are turned away from each  
other4    ,on the sensitive edge is the 
face and all the means of expression of 
feeling4 ,the other edge is covered with
 a horny thickening of the skin1  which 
at the sharp point becomes very dense   
and as hard as iron4 ,it will  be       
evident1 on moving the figures about    
that no two men could naturally  come   
face to face with each other4    ,in    

this land no such thing as friendship or
 familiar intercourse between  man and  
man is possible4 ,the very name of it is
 ridiculous to them4 ,for  the only way 
in which one man can turn his sensitive 
edge to another man  is if one of them  
will consent to stand on his head4      
,fathers hold their  male children in   
this way when little1 but the first     
symptom of manhood  is connected with a 
resentment against this treatment4      
,if now two women1 ,mulier and ,femina1 
be looked at1 the same relation  will be
 seen to hold good between them4 ,by    
their nature they are  predisposed1 by  
accident1 to injure one another1 and    
their  impressionable sides are1 by the 
very conditions of their being1 turned  
away from each other4    ,if now1       
however1 ,homo and ,mulier be placed    
together1 a very different  relationship
 manifests itself4 ,they cannot injure  
one another1 and each  is framed for the
 most delightful converse with the      
other4 ,nothing can  be more secure from

 the outside world than a pair of       
approximately the  same height2 each    
protects the sensitive edge of each1 and
 their  armoured edges and means of     
offence are turned against all comers1  
either in one direction or the other4   
,but1 if the pair1 through a mutual     
misunderstanding1 happen to be          
disadjusted1 and1 their feet on the rim1
  turn their sharpnesses against one    
another1 they are absolutely exposed  to
 the harms and arrows of the world4     
,still1 even in this case they cannot   
wound one another--a happy immunity4    
,in the annals of this race which ,i    
have by me ,i find a curious history1   
which1 unintelligible for ages to them1 
admits by us of a simple  explanation4  
,it is said that two beings1 the most   
ideally perfect ,vir and ,mulier1  were 
once living in a state of most perfect  
happiness1 when1 owing to  certain      
abstruse studies of the ,mulier1 she was
 suddenly1 in all outward  respects1    
turned irremediably into a man4 ,vir    

recognized her as the same  true        
,mulier4 ,but she occupied the same     
position with regard to him which  any  
other man would4 ,it was only by        
standing on his head that he could1     
with his sensitive edge1 approach her   
sensitive edge4 ,she refused to  explain
 how it was1 or impart her secret to any
 one1 but she had1 she  said1 undergone 
a great peril4 ,she manifested a strange
 knowledge of the  internal anatomy of  
the race1 and most of their medical     
knowledge dates  from her4 ,but no      
persuasion would induce her to reveal   
her secret2 all  the privacy of         
existence would be gone1 she said1 if   
she revealed it4  ,she was supposed to  
have acquired some magical knowledge4   
,this possession1 however1 did not make 
either of them happy1 and one  day1 with
 fear1 she said that she would either   
die or be restored to the  outward      
semblance of her sex4    ,she           
disappeared--absolutely2 although she   
was surrounded by her friends1  she     

absolutely vanished4 ,and had it not    
been that some days afterwards1  cutting
 through the solid rock for the purposes
 of some excavations1  they accidentally
 came on a chasm1 they would never have 
found her alive  again4 ,for she was    
found in a cavity in the living rock1   
warm and  beautiful--her old self again4
    ,her secret died with her4    ,from 
our point of view it is easy to see what
 had happened4 ,if the  figure ,mulier  
be taken up and turned over it will be  
easy to see that1  though still a woman1
 her configuration has become that of a 
man4 ,to all  intents and purposes she  
is a man4 ,she is rendered incapable of 
that  attitude which is the natural one 
between the men and women in this  land1
 and the happy relationship between her 
and ,vir is necessarily and  entirely   
broken off4 ,move about as you will1    
keeping her figure turned  thus on the  
plane1 you will not be able to make her 
a fitting helpmate  for her unfortunate 
,vir4 ,she must have discovered the     

secret of raising  herself off the      
surface1 and by some accident been      
turned over4 ,perhaps  she had used this
 new position to study anatomy--for to  
an observer thus  situated the interior 
of every body would lie perfectly       
open--and in  prosecuting her studies   
had overbalanced herself4    ,i have    
only mentioned this anecdote1 however1  
for the sake of a curious  observation  
which was made at the time4 ,it was     
found that when she was  in this        
transformed condition she was absolutely
 without atmosphere4 ,to  explain3      
ordinarily1 apart from anything she said
 or did1 there was a  kind of influence 
proceeding from her which made her      
presence agreeable  to ,vir4 ,when she  
was turned over she lost this4 ,now the 
explanation of  this is obvious4 ,to    
these people light is the agitation of  
the surface  of the bubble2 transparent 
objects are those which do not hinder   
this  agitation in its course4 ,but most
 bodies and the physical frame of the   

inhabitants amongst them were not       
transparent1 but stopped and reflected  
these agitations of the film1 thus      
sending off from their outer edge  those
 vibrations which excited sight in their
 fellows4 ,but besides these  vibrations
 of light there were finer ones still   
which were not damped or  deflected by  
the outer edge of the body1 but came    
through the greater  part of their frame
 as if it was transparent4 ,in the      
interior1 however1  of their            
organizations there were certain regions
 which did arrest these  subtler        
vibrations1 and which had 7as the eye of
 light7 the power of  appreciating them4
 ,in connection with these regions there
 were certain  structures1 extremely    
minute1 which had the converse power of 
agitating  the film1 and so sending     
forth through the periphery of the body 
these  same minute vibrations4 ,these   
organs were not of any use1 but they    
formed a sort of means of sympathetic   
communication between the  inhabitants1 

acting in no very defined way1 but      
certainly producing a  sensation of a   
vague kind4 ,now when ,mulier was turned
 in the way  described1 the relation of 
her frame to the film of the bubble was 
disarranged1 and it was no wonder that  
this 8atmosphere0 disappeared4    ,in   
many respects the inhabitants of this   
world are far more advanced  than we    
are1 having a simpler problem--how to   
deal with matter in one  plane--they    
have advanced more nearly to a complete 
knowledge of its  properties4 ,yet great
 as their knowledge is1 their           
performance is small4  ,if you but      
reflect on one single fact1 you will see
 how limited all  their efforts must be4
 ,they cannot fix the centre of a wheel1
 so that  it rotates round an axis4 ,for
 consider a wheel--a small disk lying on
  their plane4 ,the centre on every part
 of it touches the surface of the       
bubble on which all things slide freely4
 ,to fix this point they would  have to 
drive down into the film--a thing which 

they cannot do1 and which  they are far 
from even imagining4    ,if they make an
 opening in the disk they can arrive at 
the centre of it4  ,but then the rod of 
matter which they put in will prevent   
the disk from  revolving4               
,illustration3 ,diagram ,,viii4--,the   
nearest approach to a wheel4    ,the    
nearest approach to a wheel with a fixed
 centre which they can  attain is shown 
in ,diagram ,,viii41 a portion of a     
circular disk which  oscillates about   
the smooth end of a rod built into the  
substance of the  cut-away disk4        
,illustration3 ,diagram ,,ix4--,a cart4 
,their carts are shown in the           
accompanying figure4 ,they are simply   
rods  placed on rollers3 as the rod is  
pulled along1 the rollers turn1 and the 
rod slides along--just as a boat does on
 the rollers whereby sailors help       
themselves in hauling it up the beach4  
,as soon as these rollers roll  from    
under the rod1 as it goes on in its     
forward motion1 they have to be         

secured1 and then lifted over the cart  
and put down in front4 ,thus there  are 
to each cart a set of little disks or   
rollers1 and1 as the cart goes  on1     
these rollers have to be lifted over the
 cart from the back to the  front4      
,there is no means by which this can be 
made a continuous action4 ,each  roller 
has to be waited for1 lifted separately1
 and carried over  separately4 ,and to  
put it down in front1 the rope by which 
the cart is  dragged along has to be    
unfastened and fastened up again4       
,looking at the ,diagram ,,ix4 it will  
be seen that there is a hollow in the   
body of the cart4 ,on the part ,a ,b the
 driver sits4 ,in the hollow from ,b  to
 ,c is put the load4 ,the load cannot   
then slip out over the ends of the      
cart4 ,there is nothing in the cart to  
prevent it from falling out  sideways4  
,but the contents1 as the whole body of 
the cart1 are kept to the smooth        
surface of the bubble1 and are thus     
supported by it on the side remote  from

 the reader's eye1 and also are kept    
from rising away from this  surface by  
the force of attraction exerted by the  
film4    ,thus the surface of the bubble
 and its attractive force supply the    
other  two sides of the cart4    ,but of
 these two sides1 the beings are        
ignorant1 and it seems to them          
perfectly natural that loads of any     
kind1 even of fluids1 should be kept    
securely in a cart with two ends4       
,illustration3 ,diagram ,x4--,how a rope
 is fixed to a cart4    ,the method by  
which the rope is fastened to the cart  
is this3 ,c is the  body of the cart2 ,r
 is the rope ending in a wooden step ,b2
 ,a is an  oblong piece of wood4 ,when  
the rope has to be taken out1 ,a is     
lifted out  by its handle1 ,b is slipped
 back and taken out of the recess in ,c1
 and  then the rope is free from the    
cart4 ,and in a similar way it is       
secured  again4    ,one very ordinary   
way of driving machinery with us is by  
shafting4 ,a  long rod is driven round  

and carries wheels at different places  
along  its length4 ,now with these      
inhabitants it was impossible to do     
this1  because the twisting motion round
 a rod could not be imparted without    
going out of the thin layer in which    
they were4 ,their methods of            
transmitting motion were by long rods1  
by a succession of short rods1 by       
pendulums attached to one another1 or   
finally by wheels which drove one       
another1 but which were held by smooth  
sockets fitting round the rim far       
enough to steady them1 but not so far as
 to hinder them from touching  each     
other4    ,as to their science1 the best
 plan is to give a short account of its 
rise4    ,they discovered that they were
 on a disk rotating round an inner      
centre1  and also proceeding in a path  
round the source of light and heat4     
,they found that they were held in their
 path by a force of attraction4  ,but   
this attractive force was not with them 
as it is with us4 ,with us1  since the  

effect which any particle has on the    
surrounding particles  spreads out in   
our space if the distance is doubled    
from a centre of  attraction1 the force 
it exercises becomes one-quarter of what
 it was  when at the less distance4     
,with them1 however1 when the distance  
doubled1 the force of attraction  became
 only one-half of what it was at the    
less distance4 ,for the light1  or      
attraction1 or force of any kind        
emanating from a particle1 only  spreads
 along the film1 and does not pass out  
into the space above or  beneath4 ,if   
they had been on a thick globe instead  
of a bubble1 the laws  of attraction    
would have been the same as with us4    
,but the bubble on  which they were was 
thin compared with the paths along which
 the radiant  forces spread forth4 ,and 
thus every force being kept to one plane
  diminished as the distance from the   
centre of its action4#b    ,now it was a
 great problem with them how the light  
came from the central  orb4 ,their      

atmosphere1 they knew1 extended but a   
small distance above  the surface of    
their disk4 ,and it was quite incapable1
 moreover1 of  conveying vibrations such
 as those of light and heat4    ,by     
studying the nature of light they became
 convinced that to transmit  it there   
must be a medium of extreme rigidity    
between them and the great  source of   
light4    ,it is easy enough to see that
 what they thought was a medium between 
them and their sun was in reality the   
rigid surface on which they  rested4    
,this elastic film vibrated in a        
direction transverse to the  layer they 
called matter1 and carried the particles
 of matter with it4  ,but they1 having  
no idea but that the surface on which   
they were was the  whole of space1      
thought that space must be filled with a
 rigid medium4  ,they found that the    
vibrations of the medium were at right  
angles to the  direction in which a ray 
was propagated4 ,but they did not       
conceive of a  motion at right angles to

 their plane2 they thought it must be in
 their  plane4    ,it was a puzzle to   
them how their disk glided with so      
little friction  through this medium4   
,they concluded it was infinitely rare4 
,they were  still more puzzled when they
 had reason to believe it was an opaque 
substance2 and yet that it could be     
anything else than a medium which       
filled their space was inconceivable to 
them4 ,they could never get rid  of it  
from a vacuum1 however perfect4 ,indeed 
we see that in producing a  vacuum they 
merely cleaned the surface on which they
 were4    ,in one respect it might have 
been advantageous if they had known1    
for1  their law of attraction being what
 it was1 their movement round their  sun
 was not destined to go on for ever2 but
 they were gradually falling  nearer and
 nearer4 ,now1 if only they had made the
 attempt1 they might by  some means have
 got a hold on the surface on which they
 were1 and1 by  means of a keel which   
tended to furrow it1 have guided their  

world and  themselves in their path     
round their sun4 ,indeed1 it is possible
 to  imagine them navigating themselves 
whither they would through their        
universe--that is1 on the surface of    
their bubble4    ,it was also           
unfortunate in another respect that they
 did not realize the  fact of the       
supporting surface1 for the feeling     
which they came to have  of being       
suspended in space1 absolutely isolated1
 was a very unsettling  one1 and tended 
to cause in them a certain lack of the  
feeling of  solidarity with the rest of 
the universe4    ,we have seen that     
their laws of mechanics were very       
different from ours4  ,but they had     
after all an experience of our          
mechanical principles1  though in a     
curious way4 ,in all motions of any     
magnitude moving bodies  were confined  
to the surface of the plane4 ,but where 
the small particles  were concerned     
there was more liberty of motion4 ,the  
small particles  were free in their     

movement2 although they could not go    
more than a very  small distance away   
from the film on which they rested1     
still they were  capable of motion      
perpendicular to it4 ,thus a long line  
of particles  connected together could  
rotate as a whole1 keeping straight like
 a  twisting wire1 and by means of many 
strings of particles thus connected1    
movements could be transmitted in a way 
which was totally unlike the  mechanical
 movements to be seen in the case of    
large masses4    ,this motion of        
rotation round an axis lying in the     
plane was to them  what electricity is  
to us4 ,it was quite a mysterious force4
 ,but it was  extremely useful in its   
applications4 ,having no idea of a      
rotation which  in taking place went out
 of their surface1 they could not       
conceive a  reason for the results of   
such movements4    ,it can easily be    
seen how many kinds of forces they could
 have4 ,there  was the spinning motion  
of the small particles on the surface4  

,this they  were aware of--it produced  
many appearances1 but it was not fitted 
for  transmission across great          
distances1 as each particle was apt to  
be  hindered in its rotation by its     
neighbour4 ,sometimes1 however1 when    
conditions were favourable1 many of     
these rotations were harmonious1 and    
waves were produced in their matter     
resembling the waves in our ocean4      
,there were only two other kinds of     
motion4 ,one was an up and down         
vibration of the film carrying matter   
with it2 the other was the  twisting of 
strings of particles which were rigidly 
connected together4  ,the up and down   
motion of the film was to them light4   
,those kinds of  matter which did not   
hinder this motion were said to be      
transparent2  those kinds which1 lying  
on the film1 hindered the motion or     
threw it  back were said to be opaque4  
,the twisting motion round an axis was  
to them what electricity is to us4  ,and
 when this twisting motion in one       

direction or another was conveyed  to   
the particles of small masses which were
 free to move1 many curious  effects    
were produced analogous to the movements
 of electrified bodies4  ,there are     
obviously no other rotations or         
vibrations possible2 hence in  that     
world there is nothing corresponding to 
magnetism4 ,their light was  simple1 and
 could not be split into two kinds as   
our light can be--into  two kinds of    
polarized light4    ,was there no sign1 
then1 by which the inhabitants of this  
world could  gain a knowledge of their  
own limitation8 ,there was4 ,there was  
both a  sign and the interpretation of  
it lying before them4 ,they knew that   
they  could have two triangles precisely
 similar1 and yet such as could not be  
turned the one into the other by any    
movement in the plane4 ,how two  things 
could be so alike1 and yet differ in    
some mysterious way1 was to  them a     
puzzle4 ,as an instance of such         
triangles may be taken those used  in   

,diagram ,,vi4 to represent the man and 
the woman4 ,they may be exactly  equal1 
yet the beings in a plane world cannot  
turn them so that one  would coincide   
with the other4    ,yet had they but    
considered the case of a being lower in 
the scale of  space existence than      
themselves1 they would have seen the    
answer to  their riddle4 ,for consider a
 being confined altogether to a line    
,c ,b ,a ,m ,a ,b ,c4    ,let ,m be the 
being1 and let him observe the three    
points ,a ,b ,c1 and let  him form an   
idea of them and their positions with   
regard to each other1  which he measures
 by the distance he has to travel to    
reach one after  passing the other4     
,let him also become aware of the three 
points ,a ,b ,c1 forming a  precisely   
similar set on the other side of him4   
,it may be objected that the being in   
the line could not conceive any  point  
lying beyond ,a1 but that his experience
 would be limited to the  points ,a and 
,a4 ,if ,a and ,a are material particles

 this would be the  case1 but we may    
suppose them to be places in the line   
marked out by  cold and heat1 or some   
such means4 ,then a being could conceive
 a series  of positions in his space    
such as ,a1 ,b and ,c1 ,a1 ,b1 ,c4      
,if now he remembers each set1 and      
thinks about them1 he finds that they   
are alike in every respect4 ,but he     
cannot make them coincide with each     
other4 ,for if he pushes the set ,a ,b  
,c along the line1 when ,a ,b and ,a ,b 
are together ,c is just where it ought  
not to be4 ,it is not on ,c4 ,and if  he
 gets ,c on ,c1 then ,a ,b has gone far 
away4    ,he would neither be able to   
make them coincide nor to conceive their
  coincidence4    ,there would be no    
movement within the realm of his        
experience which  would make them       
coincide4    ,yet the dweller in a plane
 world could easily make these sets of  
points  coincide1 for he would bend the 
whole line round in his plane so that ,a
  coming on ,a1 ,b should come on ,b1   

and ,c on ,c4 ,there would be no        
difficulty to him in doing this4 ,and he
 does it in virtue of there being  to   
him a movement possible which is not    
possible to the being in the  line4 ,he 
has a liberty of motion unknown to the  
linear being4    ,and now why should he 
not reason thus1 8,something which to   
the linear  being is inconceivable1 to  
me is conceivable4 ,then may not things 
inconceivable to me be yet possible8    
,may it not be possible that two        
triangles which are like one another1   
but yet which cannot be thought by  me  
as coinciding--may not these triangles  
be able to be made coincident08    ,in  
this simple fact of his perpetual       
observation was really the proof of  the
 whole matter if he had but looked at   
it1 the sign manual of his  limitation1 
the promise of his liberation from it in
 thought1 the key to  the explanation of
 the mysterious minute actions by which 
he was  surrounded1 and perchance a help
 to the comprehension of a higher life4 

,,appendix4    ,in our world a particle 
of matter which sends forth influence on
 the  surrounding matter does not send  
its radiant energy off along a plane1   
but from the particle all the influence 
spreads out into space4 ,and the  most  
convenient instance in our world to     
consider is that of a luminous  point   
from which rays spread out in every     
direction4 ,let ,m in ,diagram  ,,xi4 be
 such a point--a particle of matter     
sending forth luminous rays in  our     
three-dimensional space4                
,illustration3 ,diagram                 
,,xi4--,particles in space and in a     
plane exerting    force4    ,instead of 
studying how these rays spread out in   
every way all around ,m1  let us only   
consider those which1 passing out from  
,m1 fall on the square  ,a ,b ,c ,d4 ,a 
,b ,c ,d casts a shadow1 and this shadow
 extends1 and is found  to be bigger the
 further off from ,m it is measured4    
,suppose1 at the  distance from ,m1 ,m  
,e1 we put a square in the path of the  

shadow so as  just to receive the shadow
 on it exactly4 ,let ,e ,f ,g ,h be this
 square4 ,as  is shown by the dotted    
lines1 this square will be four times as
 large as  the square ,a ,b ,c ,d4 ,so  
when the distance is doubled1 the shadow
 becomes  four times as big4    ,now    
those rays of light which fall on ,a ,b 
,c ,d would1 if they were not           
interrupted by it1 spread out so as to  
exactly cover ,e ,f ,g ,h4 ,thus the    
same amount of light which falls on the 
small square ,a ,b ,c ,d would1 if  it  
were taken away1 fall on the large      
square ,e ,f ,g ,h4    ,now since the   
large square is four times the size of  
the small square1  and the same amount  
of rays fall on it--for it only receives
 those which  would fall on the small   
square--there must be at any part of it 
an  illumination one-quarter as strong  
as there would be at any point on the   
small square4    ,thus the small square1
 if placed in its position1 would seem  
four times  as bright as the large      

square4    ,thus1 when the distance from
 the origin of light is doubled1 the    
amount  of light received by a surface  
of given area becomes one-fourth of what
  it was at the less distance4    ,this 
is what is meant by varying inversely as
 the square of the  distance4 ,when the 
distance is doubled the intensity of the
 light is not  simply less1 but is      
halved and halved1 and becomes          
one-quarter of its  previous intensity4 
,but in the case of a particle resting  
on a thin sheet of metal1 and  shaking  
the metal--as1 for instance1 a metal    
plate can be made to shake  by a violin 
bow--then this law would not hold4      
,take the second figure4 ,let ,p be the 
particle1 and let the influence         
proceeding from it fall on the rod ,a ,b
 lying on the plane1 and let us  suppose
 the rod to stop the vibrations from    
going beyond it1 to receive  them and to
 turn them back just as a body does the 
light4 ,then the  8shadow0 of ,a ,b     
would spread out away from ,p2 and if   

another rod ,e ,f  were put in at the   
distance ,p ,e1 which is double of ,p   
,a1 then1 to  exactly fit the shadow1 it
 would have to be double the length of  
,a ,b2  and the vibrations which fell on
 ,a ,b would exactly fall on ,e ,f4 ,now
  since ,e ,f is twice as long as ,a ,b1
 the vibrations which fall on any part  
of it will be one-half as intense as the
 vibrations which fall on a  portion of 
matter of the same size lying where ,a  
,b lies4    ,thus in a plane the        
influence or force sent out by any      
particle would  diminish as the         
distance4 ,it would not 8vary inversely 
as the square of  the distance10 but    
would 8vary inversely as the distance40 
,a ,picture of ,our ,universe4          
,,chapter ,i4    ,it seems to me that   
the subject of higher space is becoming 
felt as  serious1 and fraught with much 
that is of the deepest interest1 not    
only  as a scientific problem1 but in   
other ways also4    ,it seems also that 
when we commence to feel the seriousness

 of any  subject we partly lose our     
faculty of dealing with it4 ,the        
intellect  seems to be overweighted     
somehow1 and clogged4 ,perhaps the      
suppositions  we make seem to us of too 
great importance1 and we are not willing
  enough to let them go1 fearing to lose
 the thing itself if we lose our  hold  
of the means by which we have first     
apprehended it4    ,but whatever may be 
the cause1 it does seem undoubtedly the 
fact that  the mind works more clearly  
and more freely on subjects which are of
  slight importance4    ,and ,i propose1
 that without ignoring the real         
importance of the subject  about which  
we are treating1 we should cast aside   
any tension from our  minds1 and look at
 it in a light and easy manner4    ,with
 this object in view let us contemplate 
a certain story which bears  on our     
problem4    ,it is said that once in a  
certain region of ,ireland there took   
place a  curious contest4 ,for in       
,kilkenny there were two cats so alike  

in size1  vigour1 determination1 and    
prowess1 that1 fighting1 they so clawed1
  scratched1 bit1 and finally devoured  
each other1 that nothing was left  of   
either of them save the tail4    ,now1  
on reflecting on this story1 it becomes 
obvious that it originated  when        
looking-glasses were first imported into
 ,ireland from ,italy4 ,for  when an    
,irishman sees for the first time       
anything new1 he always  describes it in
 an unexpected and yet genial and       
interesting manner4  ,moreover1 we all  
know what contentious fellows they are1 
and how all  their thoughts run on      
fighting4 ,and ,i think if we put this  
problem to  ourselves1 how by bringing  
in fighting to describe a looking-glass1
 we  shall see that the story of the    
,kilkenny cats is the only possible     
solution4 ,for consider evidently how it
 arose4 ,depositing his favourite       
shillaly in a corner1 the               
massively-built ,irishman1 to whom the  
possession was a novelty1 saw reflected 

in his looking-glass the image  of his  
favourite cat4 ,with a scrutinizing eye 
he compared the two4 ,point  for point  
they were like4 8,begorra if ,i know    
which of the two would  win60 he        
ejaculates4 ,the combat becomes real to 
him1 and the story of  the ,kilkenny    
cats is made4    ,now1 to our more sober
 mind1 it is obvious that two cats--two 
real  material things--could not        
mutually annihilate each other to such  
an  extent4 ,but it is perfectly        
possible to make a model of the         
,kilkenny  cats--to see them fight1 and 
to mark the issue4    ,and ,i propose to
 symbolize or represent the ,kilkenny   
cat by a twist4  ,take a pencil1 and    
round it twist a strip of paper--a flat 
spill will do4  ,now1 having fastened   
the ends on to the pencil by two pins1  
so that it  will not untwist1 hold the  
paper thus twisted on the pencil at     
right  angles to the surface of a       
looking-glass3 and in the looking-glass 
you  will see its image4 ,in ,diagram   

,i41 ,m represents the mirror1 and on   
the  left hand is shown the twist1 on   
the right hand the image twist4 ,now    
take another pencil and another piece of
 paper1 and make a model of what  you   
see in the glass4 ,you will be able to  
twist this second piece of  paper in a  
spiral round this second pencil so that 
it is an exact copy  of what you see in 
the glass4 ,now put the two pencils     
together end to  end1 as they would be  
if the first pencil were to approach the
 glass  until it touched it1 meeting its
 image3 you have the real copy of the   
image instead of the image itself4 ,now 
pin together the two ends of the  pieces
 of paper1 which are near together1 and 
you have your two ,kilkenny  cats ready 
for the fray4 ,to make them fight       
7remember that the  twists--not the     
paper itself1 but the paper             
twisted--represent the cat71  hold      
firmly and pull the other ends 7the tail
 ends1 so to speak71 so as  to let each 
twist exercise its nature on the other4 

,you will see that the two twists       
mutually annihilate each other4 ,without
  your unwrapping the paper the twists  
both go1 and nothing is left of  them4  
,illustration3 ,diagram ,i4    ,now the 
image of the twist as a real thing was  
made by us4 ,it did not  exist in nature
 other than as a mere appearance4       
,but ,i want you to imagine this process
 of producing a real image as  somehow  
existing4 ,i want you to lay aside for  
the present the question  of how it     
could be done1 and to conceive twists   
and image twists4    ,this is the       
mechanical conception ,i wish you to    
adopt--there are such  things as twists4
 ,suppose by some means to every twist  
there is produced  its image twist4     
,these two1 the twist and its image1 may
 exist  separately2 but suppose that    
whenever a twist is produced its image  
twist is also produced1 and that these  
two when put together annihilate  each  
other4    ,with this conception let us  
explore the domain of those actions     

which  are called electrical4    ,when a
 glass rod is rubbed with silk it       
becomes excited1 its state is           
different4 ,it manifests many           
properties1 such as that of attracting  
light bodies1 giving off a glow of      
light1 c4 ,the silk also with which  it 
was rubbed manifests similar properties4
 ,it also attracts light  bodies1       
appears to glow in the dark1 c4    ,and 
yet there is a difference between the   
state of excitement of the  glass and of
 the silk4 ,the electricity which is in 
them is of different  kinds4 ,and if the
 electricity of the silk and of the     
glass be brought  together1 all         
electrical effect disappears2 they      
become glass and silk  in an ordinary   
condition4    ,it may seem strange that1
 if this is so1 they should become      
electrified  when rubbed together4 ,yet 
this is the case1 and must be taken as a
 fact4  ,it seems to depend partly on   
the circumstance that glass and silk are
  not what is called conductors4 ,in a  

conductor1 if one part receives         
electricity1 this electricity at once   
runs over the whole of the  conductor1  
whether it be an inch long or many feet4
 ,and if any part of  the conductor be  
touched by another conductor which is in
 contact with  the earth1 every trace of
 electricity leaves the conductor1      
flowing1 as  it were1 freely out of it4 
,now both glass and silk do not let the 
electricity run from them so  easily4   
,to discharge a glass rod it has        
practically to be touched in  every     
part4 ,thus1 when by the rubbing with   
silk electricity is produced  on it1 it 
is conceivable that this electricity    
should be kept to a  certain extent1 and
 not combined immediately with the      
electricity on the  silk4    ,besides1  
the same cause--the friction which      
produced the electricity on  the glass1 
and the other kind of electricity on the
 silk--would probably  prevent their    
combination as long as it was applied4  
,now let us suppose that the electrical 

charge which the glass has  consists in 
this4    ,let us suppose that the       
particles of the glass on the surface of
 it are  twisted1 strained out of their 
natural position1 and twisted4    ,let  
us also suppose that the particles of   
the silk are twisted too1 but  let them 
have the image twist4    ,now these two 
twists1 the glass twist and the silk    
twist1 its image1  when brought         
together1 will run down4 ,in unwinding  
each other they will  give off a certain
 amount of energy1 which will manifest  
itself as a  spark1 make a crackling    
sound1 and so on4 ,but when they unwind 
each  other there is no more tension of 
the particles4    ,this does not explain
 in the least why the glass particles   
should  receive a twist in one          
direction1 the silk particles a twist of
 the  image kind4    ,but instead of    
inquiring into this1 it is best to see  
if this  supposition is in accordance   
with other known facts of electrical    
action2 because1 if it is not1 we may   

dismiss it more easily than we  could if
 we had to test it with regard to the   
very inaccessible question  of why some 
bodies1 when rubbed1 get electrified in 
one way1 others in  another4    ,when   
the glass and silk are near together the
 twist on the glass and  that on the    
silk are related to each other as twist 
and image twist1 and  there is no action
 on surrounding bodies from either of   
them1 as they1  so to speak1 satisfy    
each other4    ,but when the glass rod  
and the silk are moved apart1 and       
brought near  other objects1 then each  
of them calls up on those objects near  
which it  is brought a twist of the kind
 which is the image of its own twist4   
,if the glass rod is brought near a mass
 of metal1 which we will call a         
conductor1 the following effect is      
observed3--,the part of the conductor   
near the glass rod becomes charged with 
electricity of the silk kind2  the part 
of the conductor away from the rod      
becomes charged with  electricity of the

 glass kind4    ,now let us bring into  
play the supposition which we made      
before4    ,let us suppose that there is
 some process in nature which1 when     
there is  a twist1 makes a real image of
 that twist come into being4 ,if we     
assume  this process1 we see that1      
opposite to the silk1 on whatever       
objects are  near it1 will be a twist of
 the glass kind1 and opposite the rod   
will be  a twist of the silk kind4 ,that
 is to say1 that on the conductor there 
will be a twist of the silk kind when   
the glass rod is brought near it4       
,but there is nothing to make the       
particles of the conductor twist as a   
whole4 ,the glass rod is not supposed to
 touch the conductor--it is simply      
brought near it1 and no actual          
communication takes place between them4 
,no force is actually applied to it1 nor
 electricity communicated to it4        
,hence1 on the whole1 the particles of  
the conductor will not be twisted4      
,that is to say1 since there is a twist 

of the glass kind on one end1  there    
will be at the other end a twist of the 
image kind--that is1 of the  silk kind4 
,and these two twists are like the two  
twists on the pencil--if  allowed to run
 together they will run each other out4 
,so if the  conductor were removed from 
the neighbourhood of the glass rod it   
would  be found to be no different from 
what it was at first4 ,it would not be  
8charged40    ,now this is what actually
 happens4    ,thus we have1 firstly1 a  
glass rod with its twist2 secondly1 a   
mass of  metal with two twists on       
it--one near the glass rod1 and of the  
image  kind2 the other at the other end 
of the mass of metal1 and related to    
the original twist in the following way4
 ,it is the image of its image4    ,now 
it will be found by using a mirror that 
the image of the image of a  twist is   
the twist itself4    ,hence on the other
 end of the conductor there is a twist  
of the same  kind as that on the glass  
rod4    ,and it is obvious that the rod1

 with its twist1 is connected with the  
twist on the conductor nearest to it1   
and the twist on the other end of  the  
conductor will1 by the same arbitrary   
process which we have assumed  as real1 
call up a twist1 the image of itself1 on
 any object near it4    ,if it is       
touched by the object with this contrary
 twist the two will run  together1 and  
the conductor will1 if it is left free1 
have only one  twist--the silk kind1    
which has come up opposite the rod4     
,if now the rod be moved away1 the      
conductor will be twisted as a whole2   
that is1 all the particles of which it  
is composed will be slightly  twisted   
with a twist of the silk kind4    ,in   
this state it is said to be charged4    
,thus the assumption which we have made1
 that there is some process in  nature  
in virtue of which1 opposite to any     
twist1 its image twist is  produced as a
 real thing--this assumption is in      
harmony with the laws of  induction4    
,instead of working with a glass rod it 

is more convenient to use a metal  rod4 
,suppose we take a poker and attach a   
handle of sealing wax to its  middle4   
,see ,a ,b below4 ,this will be easily  
imagined1 and its two ends1  the handle 
and the black end1 will be easily       
retained in the mind4    ,if now        
electricity be communicated from the    
glass rod to the poker by  touching the 
two together1 what happens is this3 ,the
 particles of the  glass being twisted  
communicate their twist to the particles
 of the  poker4 ,the twist on the poker 
is of the same kind as the twist on the 
glass rod1 and the amount of twisting   
which the glass particles had is        
divided between the glass rod and the   
poker4 ,the use of the sealing-wax      
handle is to keep the twist from        
communicating itself to the body of the 
person holding it1 and1 through him1 to 
the earth4 ,it is found that  certain   
bodies1 8non-conductors10 will not      
communicate the twist and  convey it    
along2 whereas metallic bodies1 and     

conductors generally1 will  communicate 
this twist at once to great distances4  
,we will suppose that a metallic body   
consists of particles so arranged       
together that it easily acts as a set of
 minute threads or chains of  particles 
which will twist1 each thread or chain  
twisting as a whole4  ,thus the         
conception which should be formed of a  
metallic body conducting  electricity   
along it is this3--,conceive a bundle of
 very fine but very  rigid wires1 each  
wire twisting separately but with the   
same kind of  twist as all the others1  
and each1 as it twists1 rotating amongst
 its  fellow threads4 ,if we have a     
metal rod we can twist it between the   
finger and thumb4 ,this is not the kind 
of twist we suppose1 but that  each     
separate string of particles is thus    
twisted1 so that each set  twisting     
remains in the same part of the metal   
rod--but is turning round  in its fixed 
position4 ,this is a body conveying an  
electric current4 ,if  the current will 

not pass1 the set of minute wires must  
be conceived as  held at the far end1   
and given a twist1 starting from the    
point where  the electricity is         
communicated4 ,now if a conductor is    
thus charged and  left1 it is found that
 it retains its charge2 to be discharged
 it must  be touched with another       
conductor4 ,hence this twist of minute  
threads  differs from a twist of a wire 
in that the threads cannot untwist of   
themselves unless other threads come    
into contact with them to which  they   
can impart the twist4 ,that this should 
be the case may depend on  the fact that
 the twisting strings are strings of    
molecules1 and the  ends of them would  
thus be connected with other molecules  
with something  of the same tenacity as 
that with which the strings themselves  
cohere  together1 and are unable to     
unlock themselves from these insulating 
or  untwisting molecules4    ,let us    
consider the state due to these twisting
 strings of particles4    ,place two    

pennies lying on the table before you1  
and suppose them to be  the sections in 
which two strings of a conductor are cut
 across1 so that  you are looking at two
 particles1 represented by the pennies  
in the  interior of a conductor2 the    
strings1 of which the pennies are       
sections1  come up towards your eye4    
,now twist the two pennies each in the  
same  direction--say that of the hands  
of a watch4 ,from the outer edges you   
can  take the motion off2 the edges are 
moving in the same direction4 ,but      
where the two pennies meet you will see 
that the edge of each is going  in a    
contrary direction to the other4 ,and if
 one penny tends to move an  object in  
one way the other tends to move it in   
the contrary direction4  ,hence these   
motions tend to neutralize each other in
 the interior of a  conducting wire4    
,having now formed a conception of the  
state of the particles in an            
electrified poker1 suppose another poker
 likewise held by an insulating  handle 

is brought near the first4 ,let the     
pokers be so arranged that the  handles 
both point one way1 the black ends      
another way1 and let the  second poker  
be in the same line as the first1 with  
its handle towards  the black end of the
 first4    ,now the first poker is      
charged1 it contains electricity1 its   
particles  are twisted4 ,what effect    
will it have on the second poker8    ,it
 is found that the second poker         
undergoes a certain change1 but when  it
 is removed to a distance from the first
 poker all trace of this  change        
disappears4    ,on the end nearest the  
first poker--on the handle--is found    
silk  electricity2 on the end furthest  
from the first poker--on the black      
end--is found glass electricity4        
,a ,b   ,c ,d                           
---   ---                               
-       ,let ,a ,b be one poker1 the    
representing the charge of glass        
electricity4 ,let ,c ,d represent the   
other poker1 the - representing the     

induced silk electricity1 the  the glass
 electricity in it4    ,let ,a be the   
handle of the first1 ,b its black end4  
,let ,c be the handle  of the second1   
and ,d its black end4 ,to explain this  
let us bring in our  imaginary          
principle4 ,let us suppose that when a  
charged body is brought  near an        
uncharged body1 but is separated from it
 by some medium through  which          
electricity cannot pass--let us suppose 
that by some agency the  twist in the   
charged body calls up an image twist in 
the body opposite  it4 ,thus1 due to the
 twist in the first poker there will be 
an image  twist in the handle part of   
the second poker4    ,but the strings of
 particles in the second poker are not  
twisted as a  whole2 they are twisted in
 such a way that if they are removed    
from the  first poker1 the twist1       
whatever it be1 disappears4    ,now this
 would obviously be effected if we      
suppose the same thing to go  on in the 
second poker as took place between the  

first poker and the  second4 ,let the   
twist in the handle end ,c of the second
 poker be  accompanied by the production
 of an image twist in the black end ,d4 
,and  let us take this as a fair account
 of our observations4 ,if a body1 which 
as a whole does not undergo a twist1 has
 one part of it twisted1 then  there    
will be the image twist in the other    
part of it4 ,i say that the  poker as a 
whole is not twisted1 and all that this 
means is that if it  be removed from the
 electrical influence it is found to be 
not charged2  and the idea which we may 
form is this3 the strings of particles  
are  twisted like the two strips of     
paper round the pencil2 they are twisted
  so that they will exactly unwind if   
left alone4    ,now of course all these 
suppositions are merely provisional1 and
 must be  dismissed unless seen to be   
mechanically possible2 but for the      
present  we are trying to see if our    
assumption will fit in with facts4 ,and 
our  assumption is that there is in     

nature a power which amongst the        
molecules produces that as a real thing 
which in our larger mode of  existence  
only occurs as a simulacrum and         
appearance4 ,our looking-glass  images  
are not real1 but we suppose that real  
images are produced  amongst the        
molecules4#c    ,we have seen that if we
 make a certain supposition as to the   
calling up  of an image twist by a twist
 of molecular matter1 then the main     
facts of  electricity are capable of an 
explanation1 which1 involving merely the
  motion of ordinary matter1 is far     
preferable to the idea of there being  a
 mysterious fluid1 and more in harmony  
with our present ideas of  electricity4 
,and yet it is impossible to retain this
 supposition unless a clear  mechanical 
explanation can be given of how a real  
image of itself can be  called up by the
 twist which we suppose electricity to  
be4    ,we can by intelligent agency    
produce a twist which is the real image 
of  a given twist4 ,but it would be     

absurd to suppose amongst the molecules 
an agency which1 acting with prescribed 
aim1 gave in that domain those  real    
simulacra1 those evident images1 those  
phantoms with which we in  our larger   
world of masses are for ever mocked4    
,and yet it would be curious if such an 
hypothesis were to claim a  recognized  
position in our mental apparatus with   
which we think about  nature4    ,for in
 that molecular world1 if we imagine it 
to ourselves1 there would  be a curious 
state4    ,if we consider a twist and   
its image1 they are but the simplest and
 most  rudimentary type of an organism4 
,what holds good of a twist and its     
image twist would hold good of a more   
complicated arrangement also4 ,if a  bit
 of structure apparently very unlike a  
twist1 and with manifold parts  and     
differences in it--if such a structure  
were to meet its image  structure1 each 
of them would instantly unwind the      
other1 and what was  before a complex   
and compound whole1 opposite to an image

 of itself1  would at once be resolved  
into a string of formless particles4 ,a 
flash1  a blaze1 and all would be over4 
,to realize what this would mean we must
 conceive that in our world there  were 
to be for each man somewhere a          
counter-man1 a presentment of  himself1 
a real counterfeit1 outwardly fashioned 
like himself1 but with  his right hand  
opposite his original's right hand4     
,exactly like the  image of the man in a
 mirror4    ,and then when the man and  
his counterfeit met1 a sudden whirl1 a  
blaze1  a little steam1 and the two     
human beings1 having mutually unwound   
each  other1 leave nothing but a        
residuum of formless particles4         
,,chapter ,,ii4    ,what physical       
explanation is possible of this         
production of a real  image8    ,first  
of all we may note that the production  
of a real image of any  disturbance is  
one of the commonest phenomena4    ,if a
 piece of indiarubber lying on the table
 be pressed downwards with  the finger  

it will move up when the finger is      
removed4 ,the yielding and  the resuming
 its original form are movement and     
image movement4    ,if the disturbance  
is simply a displacement in one line1   
then1 if the  medium in which this      
displacement is produced is not         
permanently  displaced1 but on the whole
 maintains its equilibrium1 there       
invariably  accompanies any displacement
 its image displacement4    ,moreover1  
to take the simple example of a wave    
propagated through  water--the particles
 of the water on the whole move about a 
mean  position2 they are not displaced  
permanently in any one direction2 and1  
taking the distance from the crest to   
the hollow of a wave1 then from  the    
hollow to the next crest1 is the real   
image of the first part4 ,thus  in the  
complete movement in the wave measured  
from crest to crest1 there  is          
displacement and its real image4        
,thus there seems some consistency about
 this supposition of an image1  about   

the production of a real image in       
nature4    ,but there are two           
observations which we can make4         
,firstly1 if it is true in these        
complicated cases it ought to be true   
in simpler cases also4 ,that is1 if this
 supposition is in harmony with         
electrical actions1 it ought to fit in  
with other actions of a simpler  kind4  
,secondly1 a supposition of this kind   
has no permanent value2 it is  rather a 
feeler1 by which we trace out our way in
 the darkness1 than any  actual vision  
itself4 ,in default of an actual        
realization of what the  electrical     
relations are we can treat them by means
 of a supposition4  ,but we must be     
ready at any moment to give up the      
supposition if it does  not harmonize   
with the facts4    ,and in the first    
case does the idea of a real image hold 
good about the  simplest possible       
actions8    ,if we push our fist towards
 a glass the image is that of a fist    
moving  in the opposite direction4      

,now1 suppose a pressure exerted on a   
wall1 as1 for instance1 a hard  stone   
hitting it4 ,the wall undergoes a       
displacement1 but not as a  whole--only 
that part of it where the stone hits4   
,and this displacement  is followed by  
the image displacement1 for the wall in 
the part where it  has been hit and     
pressed back moves forward1 and by its  
reaction throws  the stone off4         
,every case of action and reaction is a 
case of a motion and its image  motion4 
,if a bullet strikes the wall and goes  
with such velocity that it lodges  in   
it1 then the motion of the ball and the 
image motion of the wall  destroy one   
another1 and the result is a shattering 
of the wall in the  path of the bullet4 
,now in the case of a simple            
displacement of this kind there is a    
rule by  which we can form the image    
displacement4 ,take a point on the wall1
 and  about this point as a centre turn 
the displacement half way round1 so     
that it does not come to be itself      

again1 but is opposite to itself4    ,by
 this turning1 the displacement becomes 
the image of itself2 a  movement into   
the wall becomes a movement out from the
 wall2 and these  follow one another if 
the wall is not injured4 ,it should be  
noticed that  the displacement is moved 
round this point1 using a direction     
which is  not in the displacement       
itself4 ,the displacement goes straight 
into  the wall4 ,the turning motion1    
which we suppose1 needs another         
direction  than this4    ,now suppose1  
instead of a simple displacement like   
this1 we take a  displacement involving 
two directions1 as in the case of a wave
  disturbance--it will be found that the
 conditions are just the same4 ,if a    
wave movement falls on a medium which it
 does not destroy or move as a  whole1  
the displacement calls up its image     
displacement4 ,and the image            
displacement can be found1 as before1 by
 twisting the displacement round  so as 
to become opposite to itself--by        

twisting it half-way round4 ,but in     
this case1 too1 a direction must be used
 which is not used in the  displacement 
itself4      ,illustration3 ,diagram    
,,ii4    ,let us look at the wave       
disturbance more closely4    ,the       
horizontal central line in ,diagram     
,,ii4 will represent the positions      
which a number of particles occupy when 
at rest4 ,that is1 let us suppose  there
 to be a number of particles lying in a 
series forming this line4    ,we can    
think of the portions of an elastic     
cord4 ,an indiarubber tube may  be taken
 as an illustration1 and made to vibrate
 by a motion of the  hand4    ,if now   
one of the particles be deflected from  
its natural  position--suppose it is    
moved to the position ,m--then we should
 have one  particle at ,m out of its    
place1 and all the others in their      
places4    ,but this does not happen4   
,if the particle is pulled to ,m1 the   
particles  near it follow after it1 and 
are also disturbed from their places1   

though not so much as the particle at   
,m4    ,we should have a set of         
particles forming a shape like ,l ,m ,n1
 only much  longer2 in fact1 the        
particles all along the cord would be   
raised4    ,if the cord is struck       
suddenly we do have a set arranging     
themselves  like ,l ,m ,n1 but only for 
a limited distance along the cord4      
,and here we notice a curious thing4    
,if a set of particles is forced to go  
like ,l ,m ,n1 removed from their       
position of repose1 then at once a set  
of particles goes like ,n ,o ,n4    ,a  
displacement is accompanied by another  
displacement which is the  opposite of  
it4 ,and this displacement and opposite 
displacement travels  along the elastic 
cord4    ,but the point of view which is
 the most natural one to regard it from 
is  a little different from this4 ,let  
us consider a single point1 ,p4 ,when   
this is disturbed it moves above its    
original position to ,m1 and below  to  
the other end of the dotted line4 ,its  

complete movement is from one  of these 
extremes to the other4 ,and if we take  
the complete disturbance  as exhibited  
in all its phases by different points1  
we ought to look at  the portion of the 
diagram ,m ,n ,o4 ,for here at ,n we    
have a point not  displaced at all2 at  
,m1 one displaced to its full extent    
upwards2 at ,o1  one displaced to its   
full extent downwards4 ,and intermediate
 particles  have intermediate           
displacements4    ,now when a complex   
displacement of this kind is put into a 
cord1 its  image at once springs up4    
,the displacement represented by ,m ,n  
,o at once  calls up the displacement   
represented by ,o ,n ,m1 and this       
condition of  displacement and image    
displacement continues repeating itself 
till the  cord comes to rest4    ,if the
 diagram be closely looked at1 it will  
be seen that it exhibits  the image     
relationship twice over4 ,for the       
movement of the particle ,p  from ,p to 
,m has its image in the motion of       

another particle from its  place of     
repose to the position ,o4 ,the         
disturbance itself1 ,m ,n ,o1  consists 
of displacements and image              
displacements2 and this disturbance1    
with its image ,o ,n ,m1 makes the wave 
from crest to crest4    ,the 8twist0    
which we consider in these pages is like
 the wave motion1  but with a third     
component added1 so that in the complete
 motion there  is a displacement coming 
out from the plane of the paper1 as well
 as the  displacements in the plane of  
the paper itself4    ,and just as the   
wave displacement produces a real image 
of itself in a  medium which it does not
 distort as a whole1 so there is nothing
  arbitrary in our assuming that an     
electric twist calls up the real image  
of itself in an insulating medium--that 
is1 a medium which it cannot  twist as a
 whole4    ,if ,l ,m ,n ,o is a wave    
motion1 then ,l ,m ,n ,o is its image1  
as produced  by moving it round out of  
the plane of the paper--,diagram ,,ii4  

,if the wave  disturbance is moved round
 in the plane of the paper1 the original
 wave  ,l ,m ,n ,o becomes ,l ,m ,n     
,o--,diagram ,,iii4--a shape which bears
 no  resemblance to the transmitted     
wave4    ,consider ,o ,n ,m ,l to be a  
bent piece of wire lying on the paper2  
if it is  moved round ,o1 keeping on the
 paper1 it becomes ,o ,n ,m ,l4 ,to     
become  like ,o ,n ,m ,l in ,diagram    
,,ii4 it must move up from the paper and
 down  again on the right4    ,thus     
adopting this artificial aid to         
thought--that a displacement calls  up  
an image displacement--we get the rule  
that this displacement1 the  image1 can 
be got from the original displacement by
 moving the original  displacement      
half-way round1 using as the plane in   
which the turning is  made that plane   
which is given us by taking these two   
directions--the  direction in which the 
wave is moving1 and a direction at right
 angles  to the directions in which the 
displacements which form the wave take  

place4    ,thus1 with the wave motion   
shown1 if we take the direction towards 
the  top of the page to be the up       
direction1 and that from left to right  
to  be the sideways direction1 then out 
of the paper towards us is the  8near0  
direction4 ,so1 too1 in this case we    
have to turn the wave  disturbance out  
of the plane of the paper1 and each     
point of it1 to  produce the image1 must
 turn in a circle 7going half-way round 
it7 lying  in a plane which has the two 
directions near and sideways4 ,the      
motions  of the particles themselves are
 in the plane of the paper4 ,so to get  
the  image by turning we use a          
direction--the 8near0 direction1 which  
is not  involved in the wave motion     
itself4      ,illustration3 ,diagram    
,,iii4    ,hence we may state1 as a     
tentative principle1 that when a        
disturbance  takes place in a medium    
which will not be disturbed as a whole1 
then  such disturbance is accompanied by
 a real image of itself2 and this real  

image of itself is the configuration    
which would be obtained by twisting  the
 original disturbance round in a        
direction not contained in the  original
 disturbance4    ,thus the disturbance  
,o ,n ,m ,l is obtained by twisting the 
disturbance  ,l ,m ,n ,o round4 ,the    
direction in which it is twisted is the 
direction  coming out from the plane of 
the paper4    ,now if this plane        
disturbance is in nature accompanied by 
its real  image1 why should not a twist 
such as takes place in the electric     
current also be accompanied by its image
 twist when it impinges on a  medium    
which it cannot twist as a whole--that  
is1 when it comes to an  insulator in   
its path8    ,the reason1 obviously1 is 
that we cannot conceive such an image   
produced  mechanically4 ,and the reason 
of this can be exhibited thus4    ,when 
we had a plane disturbance like ,l ,m ,n
 ,o we only used up two  dimensions of  
space1 and we have a third coming up    
from the plane2 and  this direction     

enables us to imagine a turning which   
will alter ,a ,b into  its image4       
,but when we have a twist proceeding    
along an axis1 as in the case of        
electricity1 we have no direction left  
over in space whereby we may  conceive  
the twist turned round4    ,now when the
 displacement itself involves all these 
directions how will  our rule hold8     
,how shall we get the image             
displacement8 ,we can find what it is by
 using  a looking-glass2 but the same   
rule which served in previous cases     
ought  to work here also4    ,we want a 
direction which is neither up and down1 
right and left1  towards and away4      
,now let us adopt a mathematical device1
 and suppose there is such a  direction1
 and let us call it the ,x direction1   
the unknown direction4    ,then if we   
turn the twist round1 using this ,x     
direction1 we shall get  the image if   
our rule is correct4 ,and as a matter of
 fact1 by twisting a  figure round in   
this way1 using a direction different   

from any of the  three mentioned above1 
we do get its image4    ,hence the rule 
we have formed works consistently4      
,it will be found that if there was     
another direction so that the spiral    
disturbance could be turned             
independently of the directions used up 
in  it1 that just as a plane disturbance
 can be turned into its image           
disturbance1 so the spiral disturbance  
of electricity could be turned  into its
 image spiral by a simple turning4      
,in this argument we have not looked at 
the matter directly1 but from the       
outside4 ,to see it immediately requires
 us to gain a familiarity with  the     
properties of space with four           
independent directions1 and that would  
take too long for the present paper4    
,the same conclusion can be arrived  at 
mathematically2 but in these papers as  
far as possible we avoid  symbolism4 ,we
 want to gain hold of scientific facts  
in a warm and living  way1 to unwrap    
them from conventionalities and formul4 

,thus if we suppose that in the minute  
motions which go on about us there  is a
 possibility of moving in a             
four-dimensional way1 then it is        
perfectly legitimate to assume that in a
 medium which cannot be twisted1  but   
which is elastic1 a twist calls up a    
real image twist4    ,and thus the      
assumptions which we have made as the   
basis of an  electrical theory are      
justified on the assumption of a        
four-dimensional  space1 are untenable  
except on that supposition4    ,the     
matter is of course perfectly open4 ,the
 only way is this1 by  adopting the     
assumption of a higher space to predict 
what the actions of  the molecules will 
be1 then if a number of predictions are 
verified the  evidence will become      
strong4 ,and ,i feel sure that there are
 some very  curious things to be made   
out here4 ,for my own part the evidence 
of the  reality of four-dimensional     
space--in the sense in which we say that
 our  space is real--does not rest on   

the consideration of the molecular      
movements about which it is not easy to 
get clear ideas1 but on the  study of   
the facts of space4 ,i hardly think that
 any one who spent a few  years in      
becoming familiar with the facts of     
space1 not by the means of  symbolism or
 reasoning but by pure observation1     
could doubt that there  are really four 
dimensions4    ,in noticing the simpler 
actions and their image actions we find 
that the  real image does not coexist   
with its original1 but rather follows   
and  succeeds it4 ,if we push against a 
board the board yields1 and springs     
back when we leave off pushing4 ,if the 
original displacement is  permanent as a
 point pressed against an elastic       
surface and making the  surface yield1  
then the image of this displacement is  
potential2 it is  not actually there1   
but comes into play as soon as the      
original  displacement is removed4      
,now in the electrical actions we have  
assumed both the original twist  and the

 image twist as concurrently existing4  
,in certain cases there is no doubt that
 they are coexistent as when a  glass   
rod is rubbed by silk4    ,but if the   
case of the action of a charged poker on
 an uncharged one be  examined it will  
be found that there is nothing to prove 
that the image  twist comes into        
existence until the original one is     
removed4    ,when the charged poker is  
brought near the other1 the remote end  
of the  second is affected with the same
 kind of electricity as is on the       
charged poker4    ,the appearance is    
just the same as if a thin wall were    
exposed to a  pressure on one side1 and 
the other side were to bulge out4 ,the  
displacement is transmitted through the 
conductor4    ,it is only when the      
original charged body is removed that   
the image  charge is found to be in     
existence on the second conductor4      
,there are  some peculiarities1 however1
 which make electrical displacements    
different in their appearances from     

ordinary displacements4    ,no body can 
be made to move in any direction without
 imparting an equal  motion in an       
opposite direction to another           
body--e4g41 the motion of a  cannon ball
 is equalled by the recoil of the       
cannon4    ,and so no twist can be given
 to the particles of a body without an  
image  twist being given to other       
particles4    ,now the image            
displacement or rectilinear motion1 in  
the case of a  rectilinear motion1 in   
straightforward movement seems to remain
 in the  place where it was produced4   
,the recoil of the gun carriage produces
 a  strain on its bearings and friction1
 which produce heat1 which gradually    
dissipates4    ,but the image           
displacement1 in the case of            
electricity1 seems to have a  marvellous
 facility for running through the earth 
and meeting the  original displacement4 
,an indefinitely long line of action    
seems in  electricity to take the place 
of a simple point4 ,our ordinary        

mechanical  forces are located in       
centres1 or points of action4 ,in       
electricity the  line seems to take the 
place of the point4 ,where the ordinary 
engineer  deals with points the         
electrical engineer deals with lines4   
,,chapter ,,iii4                        
,,the ,,ther4    ,there are some        
expressions which1 being somewhat       
vaguely used1 are apt  to cause         
confusion in the mind of those who read 
or hear about higher  space4    ,and    
perhaps the most mischievous is the     
expression1 a curvature of  space4 ,now 
of space as it is generally used1 in its
 accepted  significance1 there can be no
 curvature4 ,for space means a system of
  positions extending uniformly in the  
number of dimensions we choose to  fix  
upon4    ,if we take the straight line  
as our space1 we may call it #a space2  
then  the set of positions follow one on
 after the other without bending4 ,if   
the line is bent it becomes a line1 not 
a straight line4 ,it should not  be     

called #a space1 but a thing in #b      
space4 ,that is1 it is a bent line in  a
 plane4    ,a being who was on the line 
might not perceive the fact of this     
bending1  and it might not affect the   
measurements he made4 ,but if the line  
ran  into itself again1 and he found    
that he was moving on what we should    
call a circle1 this would in no way     
affect his idea of space4 ,he would     
recognize that what he called space1    
namely1 his line1 was not space1  but a 
curved thing in #b space4    ,similarly1
 taking a plane--this is by definition  
not curved in any way1  known or        
unknown1 and it can only be conceived to
 be bent by ampler  space being         
conceived1 and its being imagined as    
having force applied to  it so as to    
become a bent thing in this ampler      
space4 ,in this case the  term 8plane0  
is not the correct name4    ,and so     
about our three-dimensional space2 we   
cannot be robbed of that  idea1 although
 it might conceivably be proved that our

 earth and our  whole universe were on a
 curved thing in #d space4    ,we will  
then keep the term 8space0 for the      
ordinary conception2 and call  it #a1   
#b1 #c1 #d space1 according to the      
number of supposed independent          
directions4    ,a curved line or surface
 or solid we will call a #a1 #b1 or #c  
thing1  according to the number of      
dimensions in it4    ,a straight line is
 a #a thing possible in #a space4 ,a    
circle is a #a thing  possible in #b    
space4 ,at any point of it a being in it
 is limited to  motion in one direction1
 while the circle itself involves two   
dimensions4 ,the surface of a sphere is 
a #b thing possible in #c space4  ,the  
rind of an orange1 or the orange itself1
 is a #c thing possible in #c  space4   
,it will be observed that the surface of
 the sphere1 although only a #b  thing1 
involves the conception of #c space1 and
 cannot be understood  without the use  
of the idea of #c space4 ,it is a #b    
thing because at any  point of the      

surface a being can only move in two    
independent  directions4 ,a crooked line
 drawn on the surface of a sphere is a  
#a thing  in a #b thing in #c space4    
,another very common misconception is   
occasioned by the use of a figure  of   
this kind ,illustration3 symbol to      
represent a 8knot0 in #b space4    ,it  
obviously corresponds in #b space to an 
iron rod welded together at  the        
crossing place of the loop1 so that it  
is indistinguishable which is  the one  
free end1 which the other4 ,at the      
crossing point the two lines            
represented by the two ink marks must be
 absolutely one and the same4    ,if one
 line be supposed to go over the other1 
by however small a  distance1 it would  
leave the plane4 ,it would suddenly     
become invisible  to the creature in the
 plane1 and it would appear again at the
 other  side of the line it crossed as  
if it came from nowhere4    ,it would be
 as extraordinary a sight as if we saw a
 pole going up to a  brick wall1 then   

beyond the brick wall the rest of the   
pole  appearing--not going through the  
brick wall1 nor coming round it--but    
somehow appearing2 part of the same pole
 moving when it moved1 obviously        
connected with it1 and yet with no      
joining part which we could possibly    
discover4    ,again1 it sometimes       
appears to be thought that the fourth   
dimension is  in some way different from
 the three which we know4 ,but there is 
nothing  mysterious at all about it4 ,it
 is just an ordinary dimension tilted up
  in some way1 which with our bodily    
organs we cannot point to4 ,but if it   
is bent down it will be just like any   
ordinary dimension3 a line which  went  
up into the fourth dimension one inch   
will1 when bent down1 lie an  inch in   
any known direction we like to point    
out4 ,only if this line in  the fourth  
dimension be supposed to be connected   
rigidly with any rigid  body1 one of the
 directions in that rigid body must     
point away in the  fourth dimension when

 the line that was in the fourth comes  
into a #c  space direction4    ,if the  
reader will refer back to the paper on  
the plane world he will  find a         
description of the means by which a     
being there might know that  he was in a
 limited world1 and that his conception 
of space was not of  what was really the
 whole of space1 but of the limited     
portion of it to  which he was confined 
by his manner of being4    ,the test by 
which such a being could discover his   
limitation was this4  ,he found two     
things1 each consisting of a multitude  
of parts--two  triangles2 and the       
relationship of the parts of the one was
 the same as  the relationship of the   
parts of the other4 ,for every point in 
the one  there was a corresponding point
 in the other4 ,for every pair of points
  in the one there was a corresponding  
pair of points in the other4 ,in  fact1 
considered as systems made up of        
mutually related parts1 each was  the   
same as the other4    ,yet he could not 

make these two triangles coincide4      
,now this impossibility of bringing     
together two things which he felt  were 
really alike was the sign to him of his 
limitation2 and by  reflecting on the   
similar appearance which would present  
itself to a  being limited to a straight
 line--by thinking of two systems of    
points  which were really identical1 and
 which he could make coincide1 but which
  a line being could not make coincide1 
he would be led to conclude that  he in 
his turn was subject to a limitation4   
,now is there any object which we know  
which1 considered as a whole  consisting
 of parts1 is exactly like another      
whole1 the two having all  their parts  
similarly arranged1 so as to form in    
themselves two  identical systems1 and  
yet the one incapable of being made to  
coincide  with the other1 even in       
thought8    ,let us look at our two     
hands4    ,they are 7except for         
accidental variations7 exactly alike4   
,and yet they  cannot be made to        

coincide4    ,and here1 if we reflect on
 it1 is the sign to us that we are      
limited in  our notions of space--that  
we are really in a four-dimensional     
world4    ,watching a ship as it recedes
 from the shore we see that it becomes  
hull  down before it vanishes1 and know 
that the earth is round4 ,and no less   
certainly do our two hands1 in their    
curious likeness and yet  difference1   
afford to us a perpetual proof of our   
limitation1 and  indicate a larger      
world4    ,this sign really tells us    
more than the mere fact of our          
limitation3 it  tells us where to look  
for the possibility of four-dimensional 
movements4 ,it tells us that movements  
of any degree of magnitude  relative to 
us are not possible in the fourth       
dimension4 ,it tells us to  look for    
four-dimensional movements in the minute
 particles of matter1  not in the       
movements of masses of about our own    
size4    ,the task before us is         
difficult4 ,we have to make up from the 

outside  what the appearances of a      
higher space existence are to us in our 
space1  and then we have to look at the 
facts of nature and see if they         
correspond to these appearances4    ,let
 us take a few isolated points and look 
at them patiently4    ,to a being       
standing on the rim of a plane world a  
straight line  absolutely shuts out the 
prospect before him4 ,if the straight   
line is  infinite it cuts his world in  
two2 he can never hope to get beyond it4
    ,it is to him what an infinite plane
 would be to us1 stretching  impassably 
in front of us1 cutting us off from all 
that lies on the  other side4    ,but we
 know that a point can move round this  
line4 ,it can revolve round  it by going
 out of the plane1 and coming down again
 into the plane on  the other side of   
the line4    ,this movement would be    
inconceivable to a plane being2 for he  
can only  conceive it possible to get to
 the other side of the line by going to 
the end of it and coming back along the 

other side of the line4    ,now take a  
piece of paper and put a dot right in   
the middle and suppose  that it has no  
means of passing through the paper4 ,we 
can only conceive  the dot getting to   
the other side of the paper by passing  
round the edge  and coming back again to
 the position underneath where it was4  
,but by a four-dimensional movement it  
can slip round the paper without  going 
to the edge4    ,a set of words may     
help4 ,in a plane a body rotates round a
  point--rotation takes place round a   
point4 ,in space rotation is always     
round a line--the axis4 ,in             
four-dimensional space rotation takes   
place  round a plane4    ,to take a     
farther consideration of this point--a  
plane being can see one  side or the    
opposite of a straight line4 ,he can    
only see it in one  direction or in the 
reverse direction4 ,but we can look at a
 straight  line from a direction at     
right angles to that in which a plane   
being  looks at it4 ,we can look at a   

straight line from points which go all  
round it4    ,similarly1 a being in     
four-dimensional space can look at a    
plane from a  direction at right angles 
to that in which we look at it4 ,if we  
try to  think of this we shall imagine  
ourselves looking at the thin edge4 ,but
  this is not what a four-dimensional   
being would mean4 ,he would see the     
plane exactly as we see it1 but it would
 be from a direction at right  angles to
 that in which we look4    ,in working  
with four-dimensional models it is a    
curious sensation until  we become used 
to it--that of looking at a plane at one
 time1 and then  looking at it again2   
and1 although it seems just the same--as
 square in  front of us as              
before--realizing that we are looking at
 it from a  direction at right angles to
 that of our former view4    ,and in    
four dimensions a point which is quite  
close to a plane can  revolve round it  
without passing through it1 thus        
presenting to us the  appearance of     

vibrating across the plane1 but not     
passing through it4    ,the appearance  
is as wonderful to us as it would be for
 a plane being to  see a point which was
 in front of a line quickly passing     
behind it  without having gone round the
 end4 ,such a point would appear to the 
plane being to vibrate across his line  
without passing through it4    ,now if  
we stand in front of a mirror we see the
 image of ourselves4 ,if  we were to go 
round the mirror and take behind it the 
position which our  image seemed to     
occupy1 we should not be able to make   
ourselves coincide  with it4 ,in the    
mirror opposite to our left hand is the 
image of our  left hand2 but if we      
passed round1 our right hand would be in
 the place  in which we imagined we saw 
the image of our left hand4 ,and thus we
  cannot make ourselves coincide with   
our image4 ,but by a rotation in        
four-dimensional space we could put     
ourselves so as exactly to coincide     
with our image4 ,this can be seen by    

referring to the case of the  straight  
line1 ,diagram ,,iv4      ,illustration3
 ,diagram ,,iv4      ,illustration3     
,diagram ,v4    ,let ,a ,b ,c be a      
triangle1 and ,g a line4 ,if ,a ,b ,c   
moves round the end of  the line1 it can
 take up the position ,a ,b ,c2 but it  
cannot anyhow be  made to take the      
position shown in ,diagram ,v41 ,a ,b   
,c4    ,but if we move the triangle ,a  
,b ,c out of the plane round the line ,g
 as  axis1 it will1 in the course of its
 twisting round this axis1 come into    
the position ,a ,b ,c4 ,it will come    
into this position when it has  twisted 
half-way round4 ,the point ,a1 for      
instance1 twists round in a  circle     
lying in a plane which contains the     
direction ,a to ,a1 and the  direction  
at right angles to the paper4 ,twisting 
half-way round in this  circle1 it      
becomes ,a1 and so on for the other     
points4 ,now a being who  did not know  
what a direction was which lay out of   
the plane would not  be able to conceive

 this twisting and turning movement4 ,it
 would be as  impossible for him to     
conceive the triangle ,a ,b ,c turned   
into the  triangle ,a ,b ,c1 as it would
 be for us to suppose ourselves turned  
into the looking-glass image of         
ourselves by a simple twisting4    ,yet 
just as a thing inconceivable to the    
plane creature can be done1 so  we could
 be twisted round and turned into our   
image4 ,but this only holds             
theoretically2 our relation to the ther 
is such that we cannot be so  turned1 or
 any bodies of a magnitude appreciable  
to our senses4    ,if we consider the   
case of a being limited to a plane1 we  
see that he  would have two directions  
marked out for him at every point of the
 rim  of matter on which he must be     
conceived as standing4 ,this is up and  
down1 and forwards and backwards--the up
 being away from the attracting  mass on
 which he is4    ,now1 if he were to    
realize that he was in three-dimensional
 space1 but  confined to a plane surface

 in it1 his first conclusion would be   
that  there was a new direction starting
 from every point of matter1 and that   
this new direction was not one of those 
which he knew4 ,this new  direction he  
could not represent in terms of the     
directions with which  he was familiar1 
and he would have to invent new terms   
for it4    ,and so we1 when we conceive 
that from every particle of matter there
 is  a new direction not connected with 
any of those which we know1 but         
independent of all the paths we can draw
 in space1 and at right angles  to them 
all--we also must invent a new name for 
this new direction4 ,and  let us suppose
 a force acting in a definite way in    
this new direction4  ,let there be a    
force like gravitation4 ,if there is    
such a direction1  there will probably  
be a force acting in it2 for in every   
known  direction we find forces of some 
kind or another acting4 ,let us call    
away from this force by the ,greek word 
ana1 and towards the centre of  this    

force kata4 ,then from every point in   
addition to the directions up  and down1
 right and left1 away from and towards  
us1 is the new direction  ana and kata4 
,now we must suppose something to       
prevent matter passing off in the       
direction kata4 ,we must suppose        
something touching it at every point1   
and1 like it1 indefinitely extended in  
three dimensions4    ,but we need not   
suppose it--this unknown--to be         
infinitely extended in the  new         
direction ana and kata4 ,if matter is to
 move freely1 it must be on  the surface
 of this substratum4 ,and when the word 
surface is used it  does not mean       
surface in the sense that a table top is
 a surface2 it is  not a plane surface1 
but a solid space surface4 ,if from     
every point of a  material body a new   
direction goes off1 the matter which    
fills up the  space produced by the     
solid moving in this new direction will 
have the  solid it started from as its  
surface1 and will be to it as a solid   

cube  is to the square which bounds it  
on the top4    ,now this body which     
extends thus1 bearing all solid portions
 of matter  in contact with its surface 
by every point of them1 may be thick in 
the  kata direction or thin4    ,if it  
is thick1 then the influence of any     
point streaming out in radiant  lines   
will pass as in all space directions1 so
 out also in this new  direction4       
,and then if its influence spreads out  
in this new direction1 its effect  on   
any particle near it will diminish as   
the cube of the distance2 for1  besides 
filling all space1 it will have also to 
fill space extended in  this new        
direction4    ,but we know that the     
influence proceeding from a particle    
does not  diminish as the cube of the   
distance1 but as the square of the      
distance4    ,hence the body which1     
touching all solid bodies by every point
 in them1  and supports them extending  
itself in the kata direction--this body 
is  not thick in this direction1 but    

thin4 ,it is so thin that over distances
  which we can measure the influence    
proceeding from a body is not lost by   
spreading in this new kind of depth4    
,thus the supporting body resembles1 as 
far as we know it1 a portion of a  vast 
bubble4 ,but moving on the surface of   
this bubble we can pass up and  down1   
near and far1 right and left1 without   
leaving the surface of the  bubble4 ,the
 direction in which it is thin is in a  
direction which we do  not know1 in     
which we cannot move4 ,but although we  
cannot make any  movements which we can 
observe with our eyes in this direction1
 still  the thin film--thin though      
infinitely extended in any way which we 
can  measure--this thin film vibrates   
and quivers in this new direction1 and  
the effects of its trembling and        
quivering are visible in the results of 
molecular motion4 ,it only affects      
matter by its movement in directions  at
 right angles to any paths which we can 
point to or observe1 and these          

movements are minute2 but still they are
 incessant1 all-pervading1 and  the     
cause of movements of matter4 ,it is    
smooth--so smooth that it hinders  not  
at all the gliding of our earth in its  
onward path4 ,hence it does  not        
transmit a direct pull or push in any   
direction from one particle to  another2
 but by the twistings and vibrations of 
the material particles  it is affected1 
and conveys from one to another these   
movements4 ,yet to  bear up all matter1 
and thus hold it on its vast solid      
surface1 it must  be extremely rigid and
 unshatterable2 and hence it cannot be  
permanently  altered or twisted by any  
force proceeding from matter2 but       
receiving  from matter any push or      
twist1 it is impressed with it for some 
distance2 then1 reasserting itself1 it  
produces an image displacement or       
twist1 and this image it transfers to   
the particles of matter which it        
touches4    ,sometimes1 as when light   
comes from the sun1 this displacement   

and image  is repeated and repeated     
innumerable times before at last we1    
receiving  it1 become aware of the      
origin of the disturbance4    ,but the  
properties and powers of this solid     
sheet--this film quivering  and         
trembling1 yet infinite and solid--are  
too many to begin to  enumerate4 ,the   
ther is more solid than the vastest     
mountain chains1 yet  thinner than a    
leaf2 undestroyed by the fiercest heat  
of any furnace1  for the heat of the    
furnace is but its shaking and          
quivering2 bearing  all the heavenly    
bodies on it1 and conveying their       
influence to all  regions of what we    
call space4    ,and by some mysterious  
action it calls up magnetism from       
electricity2 by  its different movements
 it gives the different kinds of light  
their  being4    ,of itself untrammelled
 and unclogged by matter1 it vibrates   
and shakes  with the speed and rapidity 
of the vibrations of light4 ,but when   
matter  lies on it--when air1 even in   

its rarest condition1 lies on it--its   
proper  movement is damped and some of  
its quick shakings that are light1 slow 
down to the obscure vibrations of heat4 
,thus of itself it will not take  up the
 vibration of a hot body1 but selects   
only those orbs which are  glowing with 
radiant light wherefrom to take its     
thrilling messages4 ,but  when matter   
lies on it1 it takes obediently the less
 vivacious movements  of terrestrial    
fires4    ,a being able to lay hold of  
the ther by any means would1 unless he  
were  instantly lost from amongst us by 
his staying still while the earth       
dashes on--he would be able to pass in  
any space direction in our world4  ,he  
would not need to climb by stairs1 nor  
to pass along resting on the  ground4   
,and such a being1 even as thin as      
ourselves1 and as limited1 if not even  
in physical powers1 but merely in       
thought he became aware of his true     
relation to the ther1 he would see all  
things differently4    ,from all shapes 

would fall that limitation of thought   
which makes us see  them differently to 
what they are2 and in largeness and     
liberty of  possible movement his mind  
would travel where ours but creeps1 and 
soar  and extend where ours journeys and
 diverges4    ,it is impossible in      
contemplating the rudiments of          
four-dimensional  existence to prevent a
 sense of largeness and liberty         
penetrating even  through the           
profoundness of our ignorance4          
,whether we shall find beings other than
 ourselves1 when we have explored  this 
larger space1 cannot be said4    ,but   
there is a path which holds out a more  
distinct promise4    ,when the          
conditions of life on a plane are       
realized it becomes evident  that much  
of that which is to us merely           
natural--obvious from the very          
conditions of our life--could only be   
attained by beings on the plane as  the 
result of artificial contrivances and   
modifications of their natural          

tendencies4 ,in their progress and      
development they would1 as it were1     
represent on the plane the features of  
the normal and undeveloped life  of     
three-dimensional beings1 and they would
 attain1 as a result of moral  labour   
and energy1 a position which children in
 our higher life are born  to without   
trouble or thought4    ,and so we in our
 advancing civilization may to the eyes 
of some higher  beings represent in our 
arrangements and institutions an        
approach to the  simplest matters of    
fact in their existence4 ,we are        
separated from such  a view by our      
bodily conditions1 but we are not to be 
prevented from  taking it with our      
minds4    ,by building up the conception
 of higher space1 by framing the        
mechanics  of such a higher world1 we   
may arrive at a fairly accurate         
knowledge of  the conditions of life in 
it4    ,and then1 with that element in  
our thought1 with the reasoned-out      
characteristics present to our minds of 

what life on a higher physical  basis   
would be1 we may be able to judge amidst
 conflicting tendencies  with more      
certainty and calmness4    ,in one of   
the following papers of this series an  
account will be given  of some of the   
facts which we can discern about the    
machinery and  appliances of            
four-dimensional beings4    ,but the    
work of real discernment belongs to     
those who will from  childhood be       
brought up to the conception of higher  
space4                                  
,,appendix ,i4    ,a supposition can be 
made with regard to the ther which      
renders clearer  an idea often found in 
literature4    ,this idea is that of the
 freedom of the will4 ,if the will is   
free1 then  it must affect the world so 
as to determine chains of actions about 
which the mechanical laws hold true4 ,we
 know that these mechanical laws  are   
invariably true4 ,hence1 if the will is 
an independent cause1 it must  act so   
that its deeds produce to us the        

appearance of a set of events           
determined by our known laws of cause   
and effect4 ,the idea of the  freedom of
 the will is intimately connected with  
the assertion that  apparent importance1
 command of power1 greatness and        
estimation1 are  outside considerations1
 not affecting the real importance and  
value of  any human agent4 ,these ideas 
can easily be represented using the idea
 of  the ther as here given4    ,for    
suppose the ther1 instead of being      
perfectly smooth1 to be  corrugated1 and
 to have all manner of definite marks   
and furrows4 ,then  the earth1 coming in
 its course round the sun on this       
corrugated  surface1 would behave       
exactly like the phonograph behaves4    
,in the case of the phonograph the      
indented metal sheet is moved past the  
metal point attached to the membrane4   
,in the case of the earth it is the     
indented ther which remains still while 
the material earth slips along  it4     
,corresponding to each of the marks in  

the ther there would be a  movement of  
matter1 and the consistency and laws of 
the movements of  matter would depend on
 the predetermined disposition of the   
furrows and  indentations of the solid  
surface along which it slips4    ,the   
sun1 too1 moving along the ther1 would  
receive its extreme energy  of vibration
 from the particular region along which 
it moved1 and the  furrows of the       
intervening distance give the phenomena 
actually observed  of our relationship  
to the sun and other heavenly bodies4   
,thus matter may be entirely passive1   
and the history of nations1 stories  of 
kings1 down to the smallest details in  
the life of individuals1 be             
phonographed out according to           
predetermined marks in the ther4 ,in    
that  case a man would1 as to his       
material body1 correspond to certain    
portions of matter2 as to his actions   
and thoughts he would be a  complicated 
set of furrows in the ther4    ,now what
 the man is in himself may be left      

undetermined2 but he would be  more     
intimately connected with the ther than 
with the matter of his  body4 ,and we   
may suppose that the ther itself is     
capable of movement  and alteration2    
that it moulds itself into new furrows  
and marks4    ,thus the old woman       
smoking a pipe by the wayside years ago1
 and whom ,i  somehow so often remember1
 is not much different from me--we are  
both  corrugations of the same ther4    
,now our consciousness is limited to our
 bodily surroundings4 ,yet it may  be   
supposed that in an action of our wills 
we1 whatever we are 7and for  the       
present let us suppose that we are a    
part of the ther71 we may be  altering  
these corrugations of the ther4 ,a      
single act of our wills1  when we really
 do act1 may be a universal affair with 
quite infinite  relations4 ,thus it may 
be the immediate presentation to us of  
an  alteration proceeding from us of all
 that set of corrugations which         
represents our future life2 it may be   

the whole disposition and lie of        
events1 which are prepared for the earth
 to phonograph out1 being  differently  
disposed4 ,and it evidently is quite    
independent of the  particular furrows  
in which such alteration first occurs4  
,that long  strip of ther which is a    
very humble individual may1 by an act of
  self-configuration1 affect the        
neighbouring long strips and produce    
great changes4 ,at any rate the         
intrinsic value of the will is quite    
independent of the kind of furrows along
 which any material human body  is      
proceeding4                             
,,appendix ,,ii4    ,it is a good plan  
in fixing our attention to give definite
 names to the  directions of space4 ,let
 ,u stand for up4 ,then the up direction
 we will  call the ,u direction1 or     
simply ,u4    ,then sideways1 from left 
to right1 we will call ,v1 so that      
moving in the  ,v direction1 or moving  
,v1 means moving to the right hand4     
,then the away direction we will call   

,w1 so that a motion which goes away    
from us we call a ,w motion1 and its    
direction we call ,w4    ,then any other
 direction which we suppose independent 
of these we will  call the ,x direction4
 ,now the simple push or displacement   
takes place in  direction ,v1 or left to
 right4 ,it is turned into its image by 
turning in  the plane ,u ,v--i4e41 the  
plane of the paper4    ,the wave motion 
takes up the directions ,u ,v1 and it   
can be turned into  its image by a      
turning in the plane ,w ,v--i4e41 by    
turning out of the  paper1 as if the    
paper were folded over about the dotted 
line4 ,then  finally the twisting motion
 takes up the directions ,u ,v ,w1 and  
can be  turned into its image by being  
turned in the plane ,v ,x4 ,that is1 if 
each  point is turned half-way round in 
this plane it becomes the  corresponding
 point in the image twist4 ,thus on the 
supposition of the  preceding pages1 if 
a positively electrified particle could 
be turned in  #d space1 it would become 

a negatively electrified particle4      
,,appendix ,,iii4    ,it remains now to 
examine if the supposition that the     
particles of a  wire are twisting in    
strings fits in with observed facts of  
electricity4    ,and firstly1 if the    
particles are twisting in this manner1  
it is only  reasonable to suppose that  
they would take up a little more room   
than  they did when not subject to this 
movement--that is1 the wire would       
become a little thicker4 ,but its volume
 remaining the same1 if it  becomes     
thicker it must compensate for this     
thickening by becoming  shorter4 ,and it
 is found that a wire through which an  
electric current  is sent tends to      
become shorter when the current comes   
into it4    ,again1 suppose a wire      
through which a current has been sent   
suddenly  isolated4 ,it has a twist in  
it1 and will keep this twist4 ,but if it
 is  connected up with any other wire   
forming a complete circuit through      
which it can untwist itself1 it will    

probably do so1 and in untwisting  would
 very likely overshoot the mark and     
become twisted in the opposite          
direction4 ,thus it would make a series 
of twists1 each less than the  last     
before becoming quiescent4 ,and it is   
observed that a wire if so  isolated    
does produce a rapidly alternating      
series of very minute  currents before  
it comes to rest2 just as if it were    
untwisting itself  and overshot the mark
 each way many times before the         
electrical state  has altogether        
disappeared4    ,the question now comes 
before us1 ,how is it that a wire gets  
twisted8  ,through what agency is a     
current of electricity urged through a  
wire1 or  a twist put into it8    ,this 
is often done by means of an electrical 
battery4 ,we will take a  simple        
instance4    ,suppose a dish of         
sulphuric acid1 and a bit of carbon and 
a piece of  zinc put into it4 ,then the 
carbon and the zinc are connected       
outside the  liquid by a wire4 ,along   

this wire electricity will pass4 ,now   
the twist  put into the wire must come  
from somewhere4 ,and it is found that   
the  sulphuric acid1 which is a very    
lively compound1 and contains a great   
deal of energy1 becomes quieted down1   
and is quite different after the        
battery has finished working4 ,on       
examination afterwards it is found to   
consist of sulphate of zinc4            
,sulphuric acid can be looked upon as   
consisting of two bodies--hydrogen  and 
a sulphur and oxygen compound4 ,this    
sulphur and oxygen compound is  called  
,,so4 ,now the ,,so comes to the zinc1  
and with zinc forms quite a  dead       
compound1 with little energy in it1     
called zinc sulphate1 or ,zn  ,,so4 ,the
 hydrogen1 on the other hand1 comes off 
at the carbon in an  energetic state4   
,hence evidently the ,,so has given up  
its energy1 the hydrogen has not4  ,so  
the twist in the wire probably comes    
from the ,,so and thus the twist  is    
started at the zinc end1 and runs round 

the wire from zinc to carbon4    ,at the
 same time we may suppose that an image 
twist1 starting also from  the zinc1    
runs through the fluid of the battery   
and then along the wire1  till meeting  
the twist the two mutually unwind each  
other4    ,thus the battery will be as  
if one had a loop of thread1 and at one 
point twisted it between one's finger   
and thumb4 ,twist and image twist1      
starting from this point1 unwind each   
other on the opposite part of the  loop4
 ,and if the loop is not joined1 but the
 threads are held1 each will  become    
twisted with increasing tension till    
they can twist no longer4  ,the objects 
which hold the ends of the thread1 and  
prevent them  twisting1 represent       
insulators4    ,it is found that when a 
strong current of electricity passes    
through  some water which has had a     
little sulphuric acid added to it1 two  
effects take place4    ,in the first    
place some of the current passes through
 as through a wire4  ,in the next place 

a part of the current is used up in     
producing an  effect on the water4 ,it  
splits the water up into two parts1 each
 of them  containing very much more     
energy than the water4 ,one part is     
called  hydrogen1 and comes off at the  
wire which comes from the zinc1 which we
  will call the zinc wire4 ,the other   
part of the water comes off at the  wire
 coming from the carbon1 or at the      
carbon wire1 and is called  oxygen4     
,let us now suppose that the twist of   
the zinc wire calls up in the  molecule 
of water next to it an image twist4 ,if 
it could pass on its  twist at once1 the
 water would form an ordinary conductor2
 but the water  is not a conductor4     
,hence we suppose the same relation to  
hold good  between the end of the zinc  
wire and the water molecules as between 
the  zinc wire and any other body to    
which the twist cannot be communicated4 
,now in the part of the molecule nearest
 the zinc wire an image twist is  called
 up4 ,and hence the molecule1 being     

unable to twist as a whole1 in  the end 
of it away from the zinc wire a twist is
 produced4 ,thus the  water molecule is 
strained into image twist and twist4    
,now let us  suppose that by a powerful 
current it is wrenched in two4 ,it is   
separated into a part having an image   
twist 8hydrogen10 which comes off  at   
the zinc wire1 and into a part with the 
twist 8oxygen40    ,but this part with  
the twist calls up an image twist in the
 molecule  next to it1 wrenches it in   
two4 ,thus the oxygen of the first      
molecule  separates up the next molecule
 into hydrogen and oxygen4 ,the oxygen  
has  a twist1 the hydrogen an image     
twist4 ,these twists run each other out1
  and leave an oxygen part free4        
,this oxygen part does the same to the  
next molecule1 and so this action  is   
transmitted through the whole body of   
the water till the carbon wire  is      
reached--when1 the oxygen part finding  
no other molecule to wrench  asunder1 is
 left isolated1 and comes off in the    

form of gas4    ,thus we see that oxygen
 and hydrogen would be bodies having in 
them  twist and image twist--that is1   
that they would have an active rotation 
each of them2 but the rotation would be 
different in the two cases1 and  such   
that if put together they would run each
 other out3 the light and  heat produced
 by the union of the two being probably 
the exhibition of  the effects of this  
running out4    ,if we adopt the        
supposition1 which seems most in        
accordance with facts1  that there are  
in water two different elements         
occurring in distinct  particles1 the   
one called oxygen1 the other hydrogen2  
and if1 moreover1  we suppose that these
 particles are perpetually changing     
places1 and  that each oxygen particle  
is sometimes linked with this hydrogen  
particle1 sometimes with that1 then it  
is obvious that the oxygen and  the     
hydrogen in the water are in such a     
state that1 if collected  together      
separately1 they would form liquid      

oxygen and liquid hydrogen2  and the    
effect of the electric twist is to give 
them those active image  rotations1 or  
strains1 which make them take the       
gaseous form1 and assume  that peculiar 
relation to each other which exhibits   
itself so strikingly  in combustion4    
,with regard to magnetism1 the same     
phenomenon of a particular state or     
disturbance of matter and its image     
state or disturbance is very  strikingly
 obvious4    ,for take the case of a    
magnet4 ,by the influence of an electric
 current  passing round it1 it can be   
turned into a magnet with opposite      
poles4  ,that is to say1 the small      
particles of the iron have been so      
shifted  that1 whatever their           
disposition was in the first case1 they 
have now  the reverse disposition4 ,if  
we suppose the small particles to be    
magnets  like the whole magnet1 and all 
to have their north poles pointing in   
one  direction1 then after the action of
 the current they have their north      

poles pointing in the opposite          
direction4 ,but they have not turned in 
space1 for1 if they were to turn1 each  
must turn about some axis4 ,but if      
there was some axis then1 with regard to
 this axis1 the magnetic  influence     
would have a definite relation2 the     
turning of the particles  would take    
place in a certain plane1 and there     
would be a certain plane  in the magnet 
which would have special properties4    
,but a magnet is perfectly symmetrical  
in all its properties round its  axis4  
,the magnet which has had its poles     
reversed is1 as an arrangement1  the    
image of itself in its first condition4 
,in the solid mass of iron  which forms 
the magnet1 by the action of            
electricity1 a particular  arrangement  
and its real image are alternately      
produced4    ,there are some very       
important electrical phenomena which    
have been left  out of consideration    
altogether--namely1 the repulsions and  
attractions  exercised by electrified   

bodies4    ,adopting the conceptions    
here laid down with regard to           
electricity--that  the two kinds are in 
the relation of twist and image         
twist--we find that  certain conclusions
 force themselves upon us4    ,a        
positively electrified body attracts a  
negatively electrified body4    ,a      
positively electrified body repels a    
positively electrified body4    ,or1 as 
it is put in a shorter form1 one kind of
 electricity attracts the  opposite     
kind1 and repels the same kind4    ,now1
 if our theory is true1 a twist ought to
 attract its image twist1  and repel a  
twist like itself4    ,and as far as can
 be observed it is always a fact that a 
movement of any  kind taking place in a 
medium does attract its image movement1 
and repel  a movement like itself4      
,some very instructive experiments have 
been made with bodies suspended  in     
water1 and caused to pulsate or twist4  
,it would be found1 on  referring to the
 details of these experiments1 that if  

two spheres are  pulsating or throbbing1
 so that the movements of the one are at
 any  instant what the movements of the 
other would seem like1 if looked at  in 
a mirror1 then these two spheres will   
attract each other4 ,if the one  is a   
real copy of the other1 then they repel 
each other4 ,and this law  holds good   
not only for throbbing movements1 but   
also for twisting  movements4    ,if now
 we supposed that what held good for    
movements held good for  tensions of the
 same nature as the movements1 these    
results would be in  exact accordance   
with our suppositions4 ,if a twisting   
movement attracts  its image twisting   
movement1 will a twist attract its image
 twist by  means of its effect on the   
medium in which it is1 and on which it  
exerts  tension8 ,this point must be    
left undecided4                         
,casting ,out the ,self4      ,the words
 which ,i have chosen as the title of   
this paper are the  expression for a    
process which has been asserted to be   

one that occurs  alike in our mental and
 in our moral life4 ,it has so happened 
that in  certain of my own inquiries ,i 
have applied this process2 and the      
details  may be of interest4 ,but ,i    
must warn the reader not to expect any  
wide  views on life1 or far-reaching    
thoughts1 or any of the warmth of human 
affairs4 ,what ,i think about is ,space2
 and it is the application of the       
principle of casting out the self in    
attaining a knowledge of ,space  about  
which ,i have something to say4    ,and1
 firstly1 as a bit of absolute human    
experience is never without  value1 but 
that which we make up is often so1 ,i   
may as well cast the  fear of ridicule  
aside and enable the reader to take in1 
in a few lines1  the exact commencement 
of my inquiry4    ,the beginning of it  
was this4 ,i gradually came to find that
 ,i had no  knowledge worth calling by  
that name1 and that ,i had never        
thoroughly  understood anything which ,i
 had heard4 ,i will not go into the     

matter  further2 simply this was what ,i
 found1 and at a time when ,i had       
finished  the years set apart for       
acquiring knowledge1 and was far removed
 from  contact with learned men4 ,i     
could not take up my education again1   
but  although ,i regretted my lost      
opportunities ,i determined to know     
something4 ,with this view ,i tried to  
acquire knowledge in various ways1  but 
in all of them knowledge was too        
impalpable for me to get hold of  it4   
,and ,i would earnestly urge all        
students to make haste in acquiring     
real knowledge while they are in the way
 with those that can impart it2  and not
 rush on too quickly1 thinking that they
 can get knowledge  afterwards4 ,for out
 in the world knowledge is hard to find4
    ,at length ,i came to find that the 
only thing ,i could know was of this    
kind4 ,if1 for instance1 there were     
several people in a room1 ,i could not  
know them themselves1 for they were too 
infinitely complicated for my  mind to  

grasp2 but ,i could know if they were at
 right or left hand of  one another1    
close together1 or far apart4 ,and the  
same of1 to take  another instance1     
botanical specimens in a book4 ,i could 
not grasp the  specimens--each was too  
infinitely complicated1 and each part   
too  infinitely complex--but ,i could   
tell which specimen was next which4     
,accordingly1 being desirous to learn   
something thoroughly1 and since1 in  the
 arrangement of any different objects1  
there was such a lot of  ignorance      
introduced by the objects being         
different--each bringing in its  own    
ignorance and feeling of                
bewilderment--,i determined to learn an 
arrangement of a number of objects as   
much alike as possible4    ,accordingly 
,i took a number of cubes1 which were as
 simple objects as ,i  could get1       
arranged them in a large block1 and     
proceeded to learn how  they were placed
 with regard to each other4 ,in order to
 learn them ,i  gave each of them a     

name4 ,the name meant the particular    
cube in the  particular position4       
,thus1 taking any three names1 ,i could 
say1 about the three cubes  denoted1 how
 they were placed with regard to one    
another3 one1 say1  would be straight   
above the first with four intervening1  
the third would  touch the second on the
 right hand1 or some similar            
arrangement4    ,now in this way ,i got 
what ,i conceived to be knowledge4 ,it  
was of no use  or beauty apparently1 but
 ,i had no reason to use it or to show  
it4    ,it is about this bit of         
knowledge that ,i want to speak now--a  
block of  cubes1 and the cubes are known
 each one where it is4    ,sometimes ,i 
have been tempted to call this absolute 
knowledge1 but have  been reminded that 
,i did not know the cube itself4        
,against this ,i have  argued4 ,but in  
argument we say many things which we do 
not understand1  and my conclusion is1  
on the whole1 that the objection is well
 founded4  ,still1 if not knowledge     

absolute1 the knowledge of this block   
approaches  more nearly to knowledge    
absolute than any other with which ,i am
  acquainted1 because each cube is the  
same as its neighbour1 and instead  of  
an arrangement of all sorts of diverse  
ignorances we have only one  kind of    
ignorance--that of the cube4 ,each of   
the cubes was an inch each  way1 and ,i 
learnt a cubic yard of them4 ,that is to
 say1 when the name of  any cube was    
said1 ,i could tell at once those which 
it lay next to2 and  if a set of names  
were said1 ,i could tell at once what   
shape composed of  cubes was denoted4   
,there were #baf primary names1 and     
these1 taken in  pairs1 were enough to  
name the cubic yard4    ,for the        
practical purpose of this paper1        
however1 it will suffice if the  reader 
will imagine a block of twenty-seven    
cubes1 forming a larger  cube1 each cube
 being denoted by a name 7see ,diagram  
,i4 below74 ,then it  is evident that   
two names mean a certain arrangement    

consisting of two  cubes in definite    
places with regard to one another--three
 names denote  three cubes1 and so on4  
,and ,i would ask the reader not to mind
 taking a  little trouble at this point1
 and to look at the diagram for a little
  while4 ,if there is anything about    
which we can form perfectly clear       
ideas1 it is a little heap of cubes4    
,and if the reader will simply look  at 
them for a little space of time1 he will
 realize clearly every word  of what ,i 
have to say2 for ,i am going to talk    
about nothing else than  this little    
block of cubes4    ,thus1 looking at the
 cube with the figure #a upon it1 this  
numeral will  serve for the name of the 
cube1 and similarly the number written  
on  every cube will serve for its name4 
,so if ,i say cubes #a and #b1 ,i mean  
the two which lie next to each other1 as
 shown in the diagram2 and the  numbers 
#a1 #d1 #g1 denote three cubes standing 
above each other4 ,if ,i say  cubes #a  
and #aj1 ,i mean the first cube and one 

behind it hidden by it in  the diagram4 
,illustration3 ,diagram ,i1 a block     
consisting of #bg cubes4                
,illustration3 ,diagram ,,ii4    ,now   
this is the bit of knowledge on which ,i
 propose to demonstrate the  process of 
casting out the self4 ,it is not a high 
form of knowledge1 but  it is a bit of  
knowledge with as little ignorance in it
 as we can have2  and just as it is     
permitted a worm or reptile to live and 
breathe1 so on  this rudimentary form of
 knowledge we may be able to demonstrate
 the  functions of the mind4    ,and    
first of all1 when ,i had learnt the    
cubes1 ,i found that ,i invariably      
associated some with the idea of being  
above others4 ,when two names were      
said1 ,i had the idea of a direction of 
up and down4 ,but with regard to  the   
cubes themselves1 there was no absolute 
direction of up or down4 ,i  only       
conceive of an up and down in virtue of 
being on the earth's  surface1 and      
because of the frequent experience of   

weight4 ,now this  condition affecting  
myself ,i found was present in my       
knowledge of the  cubes4 ,when certain  
of the names were said1 ,i conceived of 
a figure  having an upper part and a    
lower part4 ,now1 considered as a set of
 cubes  related to one another and not  
to me1 the block had nothing to do with 
up and down4 ,as long ago as ,ptolemy1  
men have known that there is no  such   
thing as an absolute up and an absolute 
down4 ,and yet ,i found that  in my     
knowledge of the set of cubes there was 
firmly embedded this  absolute up and   
this absolute down4 ,here1 then1 was an 
element arising  from the particular    
conditions under which ,i was placed1   
and the next  step after recognizing it 
was to cast it out4 ,this was easily    
done4 ,the  block had to be turned      
upside down and learnt over again with  
the cubes  all in their new positions4  
,it was1 ,i found1 quite necessary to   
learn  them all over again1 for1 if not1
 ,i found that ,i simply went over them 

mentally the way first learnt1 and then 
about any particular one made  the      
alteration required1 by a rule4 ,unless 
they were learnt all over  again the new
 knowledge of them was a mere external  
and simulated  affair1 and the up and   
down would be cast out in name1 not in  
reality4  ,it would be a curious kind of
 knowing1 indeed1 if one had to reflect 
what one knew and then1 to get the      
facts1 say the opposite4    ,it may seem
 as if1 when the cubes were known in an 
upright position1  they would be easily 
imagined in an inverted position4 ,but  
practice  shows that this is very far   
from being the case4 ,it requires       
considerable mental effort to determine 
the alterations in position1 and  to get
 an immediate knowledge requires a      
considerable time4    ,it may seem as if
 it were a dubious way of getting rid of
 gravity1 or up  and down1 just to      
reverse the action of it4    ,but this  
way is the only way1 for we1 ,i have    
found1 cannot conceive it  away2 we have

 to conceive it acting every way1 then1 
affecting each view  impartially1 it    
affects none more than another1 and is  
practically  eliminated4    ,the cube   
had not only to be turned upside down1  
but also laid on each of  its sides and 
then learnt4 ,there were a considerable 
number of  positions1 twenty-four in    
number1 which had to be brought close to
 the  mind1 so that the lie of each     
cube1 relative to its neighbours and the
  whole block1 was a matter of immediate
 apprehension in each of the  positions4
    ,if a single cube be taken and moved
 about1 it will be found that there  are
 twenty-four positions in which it can  
be put by turning it1 keeping  one point
 fixed1 and letting each turning be a   
twist of a right angle4  ,the whole     
block had to be turned into each of     
these positions and learnt  in each4    
,thus the block of cubes seemed to be   
thoroughly known4    ,at any rate1 up   
and down was cast out4 ,and we can now  
attach a definite  meaning to the       

expression 8casting out the self40      
,one's own particular  relation to any  
object1 or group of objects1 presents   
itself to us as  qualities affecting    
those objects--influencing our feeling  
with regard to  them1 and making us     
perceive something in them which is not 
really  there4    ,thus up and down is  
not really in the set of cubes4    ,now 
these qualities or apparent facts of the
 objects can be got rid of  one at a    
time4 ,to cast out the self is to get   
rid of them altogether4    ,as soon as  
,i had got rid of ,up and ,down out of  
the set of cubes ,i was  struck by a    
curious fact4    ,if in building up the 
block of cubes one goes to the left     
instead of  to the right1 keeping all   
other directions the same1 a new cube is
 built  up having a curious relation to 
the old cube4 ,it is like the           
looking-glass image of the old cube4    
,every cube in the new block            
corresponds to every cube in the old    
block1 but in the new figure it is  as  

much to the left as before it was to the
 right4 ,and any set of names  in the   
block so put up gives a shape which is  
like the shape denoted by  the same set 
of names in the old block1 but which    
cannot be made to  coincide with it1    
however turned about4 ,it is the        
looking-glass image of  the old shape4  
,the one block was just like the other  
block1 except that  right was changed   
into left4 ,now1 was it necessary to    
cast out right and  left as had been    
done with up and down8 or was right and 
left1 as giving  distinctions in the    
block and in shapes formed of cubes1 to 
remain8 ,it  seemed as if right and left
 belonged more to me than to the set of 
cubes4 ,and yet the right-handed set of 
cubes could not be made by moving  about
 to coincide with the left-handed set of
 cubes4 ,and this power of  coincidence 
was the test which had convinced me of  
the self nature of  8,up and ,down40    
,let ,diagram ,i4 represent a small     
block of cubes4 ,it is itself in the    

form of a cube1 and it contains #bg     
cubes4 ,for purposes of reference we    
will give a number to each cube1 and the
 number will denote the cube  where it  
is4    ,in the front slice are cubes    
numbered from #a up to #i1 in the second
  slice are cubes numbered from #aj to  
#ah1 and so on4 ,thus behind #a is the  
cube #aj4 ,this cube and the cube #aa   
are hidden1 but the cube #ab is shown   
in the perspective4    ,now in this     
block of cubes there is a part which is 
known and a part  which is unknown4 ,the
 part which is known is how they come or
 the  arrangement of them4 ,the part    
that is unknown is the cube itself1     
repetitions of which in different       
positions forms the block4    ,the cube 
itself is unknown1 because1 being a     
piece of matter1 it  possesses endless  
qualities1 each of which grows more     
incomprehensible  the more we study it4 
,it is also unknown in having in it a   
multitude of  positions which are not   
known4 ,the cube itself is1 amongst     

other things1  a vastly complicated     
arrangement of particles4 ,hence1       
putting all  together1 we are justified 
in calling the cube the unknown part2   
the  arrangement1 the known part4       
,the single cube thus is unknown in two 
ways4 ,it is unknown in respect to  the 
qualities of hardness1 density1 chemical
 composition1 c4 ,it is also  unknown as
 a shape4 ,if it really consisted of a  
certain number of parts1  each of which 
was clear and comprehensible in itself1 
then we should  know it if we grasped in
 our minds the relationship of all these
 parts4  ,but there are no definite     
parts of which a cube can be said to be 
made  up4 ,we can suppose it divided    
into a number of exactly similar parts1 
and suppose that all are like one of    
these parts4 ,but this part itself      
remains1 and the problem remains just   
the same about this part as about  the  
whole cube4    ,now there is a double   
perplexity3 one about the nature of the 
matter1  the other about the cube as to 

the arrangement of its parts4 ,we will  
give up any question about the matter of
 which the cube is composed2 to  know   
anything about that is out of the       
question4 ,but1 supposing it to be  of  
some kind of matter1 it presents an     
inexhaustible number of  positions4 ,it 
can be divided again and again4    ,let 
us look at the block again1 and for the 
moment dismiss from our  minds the      
question just raised as to the single   
cubes of which it is  built up4 ,let us 
look on each of these cubes as a unit4  
,then two of the  units1 taken together1
 form a shape2 three or five of them    
would form a  more complicated shape1   
and so on4    ,we can also suppose the  
cubes away1 and think merely of the     
places which  they occupied4 ,in this   
manner1 by first thinking of the #bg    
cubes1 and  then simply by keeping the  
places of them in our minds1 we get #bg 
positions1 and in these positions we can
 suppose placed any small  objects we   
choose4 ,each of these positions may be 

called a unit  position1 and we can form
 different arrangements of small objects
 by  putting them in different ones of  
these positions4 ,now in all this we do 
not divide the cube up4 ,we simply think
 of it as a whole--we think of it  as a 
unit4 ,or if we take the room of the    
cube instead of the cube1 and  think of 
the place it occupies1 which ,i call a  
position1 we do not  divide that        
position up4 ,we take it1 if ,i may use 
the expression1 as a  unit position4    
,and without asking any question as to  
the nature of  these positions1 whether 
they are complicated ideas or not1 we   
have a  kind of knowledge of the whole  
block1 in that it consists of this      
collection of #bg cubes1 or of this set 
of #bg positions4    ,thus in a rough   
and ready manner there is something     
which we can take4  ,if we do not       
inquire about one of the cubes itself1  
we are all right2  that being granted we
 can know the block4    ,but if we look 
into what each of these unit cubes1 or  

what each of these  unit positions is1  
we find quite an infinity opening before
 us4 ,there is  nothing definitely of   
which we can say that the whole unit    
cube is built  up1 and each of the      
positions has a perfectly endless number
 of  positions in it1 if we come to     
examine it closely4 ,all that we can say
  is that our ignorance about each of   
the unit positions is of the same  kind 
as our ignorance about every other1 and1
 taking one as granted1 we  may as well 
take the #bg as granted2 and so out of a
 lot of similar  ignorances we get a    
kind of knowledge of the whole4 ,and    
this knowledge  is not a mere indefinite
 thing1 but it can be worked at1        
improved1 and  made perfect after its   
kind4 ,for suppose we limit ourselves to
 the #bg  positions numbered in ,diagram
 ,i4 ,two of these positions form one   
shape1  three of them will form another 
shape1 and so on4 ,and in going over    
each  of these arrangements we gradually
 get to know the whole set of them      

which form the block4    ,having given  
up for the time any question as to the  
possible  subdivisions of the cube1 and 
looking on each cube as a unit position1
  we have #bg positions4 ,these         
positions can be taken in different     
selections1 and each selection is a     
shape4 ,to know the block or set of     
positions means to form a clear idea of 
every shape1 consisting of  selections  
of positions1 which can be formed out of
 the #bg4    ,but each of the cubes1 #bg
 of which form the whole block1 can be  
divided  up4 ,each of these cubes       
contains a great many positions4 ,there 
must1 for  instance1 be positions in    
each cube for every one of its          
molecules4    ,thus it is evident that  
the cube supplies an inexhaustible      
number of  positions to be learnt4 ,i   
call the cube unknown in the sense that 
there  are a great number of positions  
in it which are not clearly realized by 
the mind4    ,by a very simple device it
 is possible to penetrate a little into 

the  unknown part4 ,the whole set of    
cubes forms a cube4 ,let us consider the
  small cube to be a model of the whole 
cube4 ,let us consider it as  consisting
 of #bg parts1 each related to the other
 as the #bg first cubes  were related   
amongst themselves4 ,thus the unknown   
part1 the material  cube1 which is used 
to build up the whole1 becomes reduced  
in size4  ,diagram ,,ii4 represents such
 a cube4    ,this is the theory4 ,the   
practical work consisted in learning the
 names  denoting these smaller cubes in 
connection with their positions1 so     
that1 the names being said1 the small   
cubes meant were present to the  mind1  
and a set of names being said1 the      
shape1 consisting of a set of  cubes in 
definite relations to each other1 came  
vividly before one4 ,a  complete        
knowledge of the block of cubes would be
 a complete  appreciation of all the    
possible shapes which selections of the 
cubes  would form1 and this ,i strove to
 attain4 ,here at length ,i found real  

knowledge1 and after a time ,i was able 
to reduce the size of the unknown  still
 further1 and to obtain a solid mass of 
knowledge fairly well  worked all       
through4    ,and now it all seemed      
satisfactory enough4 ,there was real    
knowledge in  knowledge of the          
arrangement2 and the material cube1     
which must be  assumed1 could be made   
smaller and smaller1 it could be turned 
into  knowledge1 thus affording a       
prospect of obtaining endless knowledge4
  ,thus ,i found the real home of my    
mind1 the only knowledge ,i had ever    
had1 and ,i hoped always to continue to 
add to it1 and always to reduce  the    
unknown in size4    ,presently1 too1 the
 forms of the outward world began to    
fall in with  this knowledge2 and as the
 mass of known cubes became larger in   
number1  a group of them would fairly   
well represent a wall1 a door1 a house1 
a  simple natural object such as a stone
 or a fruit4    ,yet amidst all this    
delight ,i became conscious1 dimly      

enough1 of a  self-element in the       
knowledge of blocks4    ,if1 putting up 
the block of cubes1 we go to the left   
instead of the  right1 but in all other 
respects build up in the same way1 we   
obtain a  block which has a curious     
relation to the first block4    ,the    
ordinary block is shown over again in   
,diagram ,,iii4 ,diagram ,,iv4 is  the  
new block4 ,the new block is like a     
looking-glass image of the old  block4  
,it is just the same1 but that left and 
right is reversed4    ,also1 if we take 
selections of blocks we get figures     
which are just  reversed4 ,thus #a1 #d1 
#g1 #h1 in ,block ,,iii41 means a figure
 turned to the  right2 in ,block ,,iv4 a
 figure turned to the left4    ,again1  
consider the two figures formed by      
selecting the cubes #a1 #d1 #g1  #h1    
#ag1 from ,diagrams ,,iii4 and ,,iv4    
respectively4 ,we get two figures which 
are just like one another as            
arrangements1 but which we cannot turn  
into  one another by twisting4          

,illustration3 ,diagram ,,iii4 is a     
block4      ,illustration3 ,diagram ,v4 
,considered as arrangements in          
themselves1 these figures and these     
blocks  seem to be identical1 for the   
relationships of cube to cube which are 
present in the one are all present in   
the other4 ,but considered as  shapes   
they are not identical4 ,for they will  
not coincide4    ,the whole matter      
becomes much more clear if we consider  
the relationship  between the individual
 cube used and the block which it forms4
    ,there are two starting-points1     
either of which we can adopt4 ,we can   
start with the real material cube1 or we
 can start with the act of  arranging4  
,when ,i speak of the real material cube
 ,i do not want to call  attention to   
the kind of matter of which it is       
composed1 or to the  nature of matter1  
but to the fact that it is to be a real 
cube such as  can be made1 and which1 if
 one edge or corner be marked1 will     
retain  that mark just where it is--a   

cube which is not a product of the      
imagination1 but an object1 with the    
properties of objects in general4       
,illustration3 ,diagram ,,iv4 is its    
image block4      ,illustration3        
,diagram ,,vi4    ,let us start with the
 real material cube4 ,let us take the   
cube shown in  ,diagram ,v41 which is   
the model on a small scale of the ,block
 ,,iii4 ,the  numbers in it show the    
small cubes of which we suppose it to be
 built up  after the pattern of ,block  
,,iii4 ,the numbers also serve to show  
the  distinction of positions--that is1 
we can refer to the right-hand corner   
or edge1 c41 by saying the numbers of   
the small cube which lies there4        
,now1 using the cube of ,diagram ,v4 to 
build up the block in ,diagram ,,iii4   
we get a perfectly orderly result1 as   
shown in ,diagram ,,vii41 and we can  go
 to bigger and bigger blocks1 or down to
 smaller and smaller ones  without any  
hitch4 ,but if we use the cube of       
,diagram ,v4 to build up the  block of  

,diagram ,,iv41 there is a disadjustment
 which can be discerned in  ,diagram    
,,viii4 ,thus1 when ,v4 is used to build
 up ,,iii41 the small cubes in  ,v41 #a1
 #d1 #g1 lie in same edge as the cubes  
#a1 #d1 #g1 in the big ,cube ,,iii4     
,but when ,v4 is used to build up ,,iv41
 the small cubes #c1 #f1 #i1 lie on the 
edge which is occupied by the cubes #a1 
#d1 #g1 in big ,cube ,,iv4              
,illustration3 ,diagram ,,vii4--,block  
,,iii4 built up with ,cube ,v4          
,illustration3 ,diagram ,,viii4--,block 
,,iv4 built up with ,cube ,v4--a        
disadjustment4    ,thus1 if the same    
material cube is used1 there is a       
disadjustment1 and  the figure ,,iv4    
cannot be considered the same as the    
figure ,,iii4 even as  an arrangement1  
for the same parts of the cubes do not  
lie in an  analogous manner4 ,a certain 
corner of ,cube ,v4 is marked with the  
figure  #g2 this corner would be on the 
outside in ,block ,,iii41 but in        
building up  ,block ,,iv4 it would lie  

on the inside4    ,it is somewhat       
difficult to express this fact1 but if  
the real cubes are  looked at it becomes
 perfectly obvious4    ,imagine the     
whole ,block ,,iii4 to be built up of a 
number of cubes1 every  one of which is 
alike4 ,if the sides of these cubes be  
distinguished by  any markings--if1 for 
instance1 the left-hand side is blue and
 the other  sides are each of some      
special colour1 then on building up the 
whole  block the left-hand side of the  
whole block will be blue4    ,if1 now1  
the same cubes be taken1 and the attempt
 be made to build up  the looking-glass 
image of the block with them1 it will be
 found that  there will be a            
disadjustment4 ,if the blue sides are   
made to go to the  right1 as they must1 
to form an image block1 then some other 
sides will  be in different places to   
what they should be in order to produce 
an  image of the original block4        
,although considered as an arrangement  
of  cubes the new block will be an image

 of the original block1 still1  looking 
at the individual cubes of which it is  
composed1 it will be seen  that the new 
block is not an exact image of the old  
block4    ,if1 however1 we take the     
other starting-point1 and1 not assuming 
any  fixed fundamental cube1 look only  
at the act of arrangement1 the two      
,blocks1 ,,iii4 and ,,iv41 are found to 
be identical in every internal          
relationship4    ,for1 taking the act of
 arrangement as the basis1 if1 when we  
have built  up the ,block ,,iv41 we look
 upon each of the cubes as an           
arrangement of  the same kind as the    
whole1 then the cube #a in ,diag4 ,,iv4 
is represented  in ,diag4 ,,vi4 ,and it 
is evident that if ,diag4 ,,iv4 is built
 up out of  cubes like ,diag4 ,,vi41 the
 small cubes1 #a1 #d1 #g1 lie in the    
same edge as  the cubes #a1 #d1 #g1 in  
,diag4 ,,iv4 ,thus it will be found for 
every  relationship in ,diag4 ,,iii4    
there is an exactly similar relationship
 in  ,diag4 ,,iv4    ,in this case if1  

for the sake of material illustration1  
we use marked  cubes1 it seems that we  
must not suppose each particular cube to
 have a  fixed marking of its own1 but  
that we must suppose the markings to    
spring up on the sides of the cubes in  
accordance with the places into  which  
they are put4    ,there is another      
manner of regarding the matter which may
 help to bring  out the point at issue4 
,if we suppose that we are putting up   
the cubes in one room while another     
person is putting up cubes in an        
adjoining room2 if we can tell him what 
we are doing1 using the words right and 
left1 he will be able to put up  a block
 exactly like ours4 ,but if we do not   
allow ourselves to use the  words right 
and left1 but speak to the other person 
as if he were simply  an intelligence   
without having the same kind of bodily  
organization as  ourselves1 we should   
find that1 supposing he could put up the
 block of  cubes1 it would be a mere    
matter of chance whether he had put up  

the  block as we had put it1 or whether 
he had put it up in an image way4 ,and  
the same with regard to any shape4 ,we  
could tell him that the cubes  should be
 put together1 and we could tell him the
 relationship which  they should have   
with regard to one another2 but the     
figure he put up  would just as likely  
be an image of our shape as not4    ,and
 we could go on for ever building more  
and more complicated shapes  and telling
 him to do the same1 and no hitch or    
difficulty would come4  ,but at the end 
all his shapes might be ours just       
reversed1 as if seen in  a mirror4      
,and if1 having put up the block1 we    
coloured the sides of the cube we  used 
as the fundamental cube1 and told him   
how we had coloured it3 if he  coloured 
his and brought it to us1 and we        
compared them1 his would just  as likely
 be the image of our cube1 and not able 
to be turned into it4  ,so that         
although1 as arrangements1 the          
structures we had put up were  alike1   

still neither of us could use the       
other's fundamental cube2 and  if we    
exchanged the fundamental cubes there   
would be an inconsistency in  each of   
our arrangements4    ,now1 are these    
blocks of cubes really the same8 ,are   
,,iii4 and ,,iv4 really  the same in    
themselves1 as all relationships in the 
one are to be found  in the other8 ,if  
so1 the feeling on my part that they are
 different1 and  the inconceivability of
 their coinciding1 must be due to some  
self-element which is mixed up with my  
apprehension of the cube4    ,the ,block
 ,,iv4 is like the ,block ,,iii4 in its 
known part--in its  arrangement4 ,it is 
unlike ,block ,,iii4 in its unknown     
part--the cube which  must ultimately be
 supposed as the fundamental cube1 by   
using which over  and over again the    
whole is built up4    ,now1 the         
properties of the unknown part--the     
little cube of matter which  of some    
size or another1 we must assume1 are so 
mysterious that one does  not feel any  

argument very safe which rests on it4   
,moreover1 there is a very obvious      
consideration which reduces the         
importance of the part played by the    
material cube very considerably4    ,it 
is possible to consider the ,cube ,v41  
which is used to build up ,,iii41  as   
the total of #bg cubes4    ,but each of 
these cubes--the small cubes in ,diag4  
,v4--can be considered to  be made up of
 #bg still smaller cubes4    ,by going  
on in this way we can get our           
fundamental cube very small  indeed4    
,the difference between the ,cubes      
,,iii4 and ,,iv41 in respect to  this   
fundamental cube1 will still remain4    
,but omitting this difference  they will
 be1 considered as arrangements1        
identical4    ,to state the matter over 
again4 ,we start with a real cube1 one  
inch each  way1 and build up the block  
in ,diagram ,,iii4 with it4 ,if we try  
to build  up the block in ,diagram ,,iv4
 with this same inch cube1 we find that 
there  is a disadjustment4    ,but we   

are not obliged to have our fundamental 
cube one inch in size4 ,we  can take it 
as small as we like1 and build up the   
block1 using a greater  number of such  
cubes4 ,we can take it the              
twenty-seventh of the  twenty-seventh of
 an inch cube2 or1 in fact1 as small as 
ever we like4  ,and if we take a very   
small cube as the fundamental one with  
which we  build up the ,block ,,iii41   
then1 using this same fundamental cube  
to build  up ,block ,,iv41 we should    
find a disadjustment1 although this     
disadjustment would only come in when we
 come down to the very minute  cube1 and
 studied its relationship to the whole  
,block ,,iv4    ,thus1 apparently1 the  
,block ,,iv4 could never be built up    
consistently1  using as its fundamental 
cube the fundamental cube out of ,block 
,,iii4 ,but  in saying this we have     
really made an assumption4    ,it is    
obvious that ,cubes ,v4 and ,,vi41 just 
like ,cubes ,,iii4 and ,,iv41           
considered as shapes made up of matter1 

are very different1 and could  not be   
shifted one on to the other4    ,but all
 our laws and feelings about movements  
and possibilities are  founded on the   
observation of objects having a certain 
degree of  magnitude4    ,but the       
fundamental cube1 which we must assume1 
may be supposed to be of  a degree of   
magnitude less than any known degree4   
,in cubes of a certain size ,v4 and     
,,vi4 are different1 and cannot be made 
to coincide4    ,but we are absolutely  
unable to say anything about cubes      
beyond a  certain degree of smallness4  
,with cubes of a certain degree of      
minuteness1 ,v4 and ,,vi4 might be able 
to be made coincide4    ,thus1 for      
instance1 we feel as if we could divide 
a piece of matter on  and on for ever4  
,but chemists tell us that1 after a     
certain number of  divisions1 the next  
division would split it up into two     
different kinds  of matter4 ,since all  
our reasoning is founded on the         
behaviour of  objects of known size1 we 

can tell nothing at all by inference    
about the  behaviour of very small      
objects4    ,it is obvious that1 from   
our customary experience1 we can assert 
absolutely nothing at all about the     
extremely minute or the extremely       
large4 ,all reasoning which is founded  
on the likeness between the  extremely  
small and the ordinary objects of our   
observation is  absolutely valueless as 
telling us any truth4    ,of course1 by 
saying this we have not got rid of the  
argument for the  difference of ,,iii4  
and ,,iv4 ,but we have put the thing    
from the  observation of which that     
argument is drawn out of the region of  
known  things4 ,we have put it into the 
hazy land of the extremely minute4 ,its 
argument is good1 but it depends on its 
being of a certain size4 ,we  suppose it
 less than that size1 and we can        
consider the subject without  regard to 
its argument4    ,the question then     
before me was1 ,is 8,right and ,left0 to
 be cast out8 ,and  connected with this 

was the consideration of whether it was 
possible for  extremely minute cubes to 
be 8pulled through10 that is1 to be     
treated  somehow which would turn one   
like ,v4 into one like ,,vi4    ,now1 if
 8right and left0 was a self-element1 it
 could be cast out2 if it  was a        
permanent distinction in the cubes      
themselves1 it could not be  cast out4  
,the thing to do was evidently to try4  
,the method was to learn  the cubes over
 again1 in a set of new positions4 ,for 
every one of the  ways in which they    
were learnt before1 there was an        
inverted or pulled  through way to be   
learnt4    ,while ,i was engaged in this
 attempt another inquiry suddenly       
coincided  with this1 and explained it  
all4    ,much has been said about the   
fourth dimension of space and the       
inconceivability of it to us4 ,now1 if  
there are beings who live in a          
four-dimensional world1 they must feel  
as habituated to it as we do to  ours1  
and the conceptions which seem so       

impossible to us must be  every-day     
matters to them4 ,it would be impossible
 for us to try to enter  at once into   
the serious thoughts of these denizens  
of higher space4 ,but  amongst them     
there would probably be some with whose 
occupations we  might become familiar1  
and with whose ideas we might gain some 
acquaintance4 ,amongst these beings     
there must be children1 and just as     
children on the earth gain their        
familiarity with space by means of      
bricks and blocks and toys1 so these    
higher children must have their own     
simple objects wherewith they grow into 
familiarity with their complex  world4  
,now it is easy to make a set of simple 
objects such as these higher  children  
would use4 ,and it seemed a practical   
thing to do with regard to  the         
conceivability or inconceivability of   
the fourth dimension to give  the matter
 a fair trial1 by going through those   
processes and those  experiences which  
must be gone through by the beings in   

higher space to  gain their acquaintance
 with it4    ,when ,i say that it is    
easy to make a set of objects1 such as  
the higher  children use1 ,i do not mean
 to say that they can be made completely
 in  every part at once4 ,but we can    
make the ends and sides of them1 and we 
can look at the ends and sides of them  
as they appear to us in space1  and we  
can make up exactly what sides come into
 space when the simple  objects are     
twisted and moved4    ,just as a being  
living on a plane could tell about all  
the faces and  edges of a cube or other 
simple solid figure by looking at what  
he could  see when the cube was laid on 
his plane1 and when it was twisted and  
laid down again2 so we can tell all     
about the sides1 faces1 and edges of  a 
higher solid4    ,and the project seems 
less uninviting if we reflect on how    
complicated a  matter the formation of  
our own conceptions of a solid are4     
,what a lot  of faces and edges a cube  
has6 ,and1 moreover1 it must be         

remembered that  we never touch or see a
 solid2 we only see the surface and     
touch the  surface4 ,if we cut away the 
surface that we first saw or touched1 we
  come on another surface1 and so on4   
,now1 of course1 the surfaces of a solid
 are given to us by nature in  their    
right connection and relation4 ,each of 
the edges of the cube1 for  instance1   
can be noticed and remarked without any 
difficulty1 and they  are all on the    
same bit of space1 to be looked at one  
at the same time  as another4    ,but   
the sides1 faces1 and edges of a higher 
solid cannot be in our space  all at    
once4 ,they must come separately1 be    
looked at one by one4    ,thus a being  
in a plane could not see the lower side 
and the front of a  cube at once4 ,he   
would first have to look at the lower   
side as the cube  rested on his plane1  
then if the cube were turned over he    
would see the  front1 and the lower side
 would be gone4 ,if he got the set of   
right  appearances which a cube would   

present to him when1 turning about in a 
systematic way1 it came at intervals    
into his plane1 and if1 moreover1  he   
fixed his mind on these appearances1 he 
might at last1 if it was in  him1 rise  
to the conception of a cube as we know  
it4    ,now1 the parts by which a higher
 solid comes into our space are solids1 
and what we have to form is a set of    
solids coming and going in a  systematic
 way1 as the higher figure is moved     
about in a systematic way4    ,this     
afforded a welcome exercise1 for        
conceiving the solid shapes1 and  how   
they went and came1 increased my        
familiarity with the set of cubes4      
,moreover1 in trying to get the piece of
 ignorance--the necessary real  cube--as
 small as possible1 ,i had got the block
 which ,i knew to a  somewhat fine state
 of division1 and could1 by picking out 
a particular  set of cubes from the     
whole number1 obtain a mental model of  
any shape ,i  wanted4 ,the whole block  
of cubes formed a kind of solid paper in

 which  one could mentally put down any 
solid shape one wanted4 ,and just as it 
is a great convenience to have a piece  
of paper for drawing figures one  wants 
to think about1 so it was a great       
convenience to have this solid  paper4  
,the subject1 however1 abounds in       
abysses for stupidity to fall into1 and 
,i had to clamber out of each of them2  
so it took me several years before  ,i  
got quite on the right tack4 ,then it   
was easy enough3 any one in a few  weeks
 could learn to conceive                
four-dimensional figures4 ,not only is  
it  easy1 but there are abundant traces 
that we do it continually without  being
 aware of it4 ,i am sure if the         
loveliness of the work while one is     
doing it1 and the simplicity and        
self-evident nature of the results when 
obtained1 were generally known1 it would
 be a favourite amusement4    ,now one  
of the first things that presented      
itself to my attention when ,i  began to
 move the four-dimensional figures about

 was a fact which bore  curious         
reference to my difficulty about the    
fundamental cube4 ,if the  reader       
remembers1 it seemed to me as if the    
cube out of which the whole  block of   
known cubes was built ought to be able  
to be inverted4 ,that is  to say1 it    
seemed to me that there was a           
self-element present in my  knowledge of
 the cubes4 ,but in order to cast out   
that self-element the  fundamental cube 
which lay at the basis of the whole     
block would have to  be able to be      
inverted1 or pulled through4    ,now ,i 
found that when ,i took a               
four-dimensional figure which came into 
space by a cube--that is1 a figure which
 rested on space by a cube1 or  one of  
whose sides was a cube--when ,i took a  
figure of that sort up in  the fourth   
dimension and twisted it round and      
brought it down again1  this cube would 
sometimes be inverted or pulled         
through--although ,i had  done nothing  
to it1 but had simply twisted the whole 

figure round  without disturbing the    
arrangement of its parts4    ,thus      
evidently to a higher child it would be 
no more difficult to invert  or pull    
through a cube or a figure than it would
 be to me to twist one  round4    ,hence
 it was obvious that right and left was 
really a self-element in my  block of   
cubes4 ,i being in our space was under a
 certain limitation1 and  that          
limitation made me feel as if a         
right-handed arrangement was  different 
from a left-handed arrangement4    ,a   
being who was not limited as ,i was     
would see that they were one and  the   
same4 ,hence1 in knowing the set of     
blocks it was necessary to cast  out    
8right and left10 and the names had to  
be learnt over again in new  positions4 
,thus it is evident that there are three
 expressions which may be  considered in
 reference to a knowledge of a block of 
cubes as almost  identical3 8,casting   
out the self0--8,seeing as a higher     
child0--and  thirdly1 8,acquiring an    

intuitive knowledge of four-dimensional 
space40    ,thus1 taking the simplest   
and most obvious facts--the arrangement 
of a  few cubes--we found that there was
 a known part and an unknown part2 the  
known part corresponding to our act of  
putting1 the unknown part the  cube     
which1 of some size or another1 must be 
taken as given in the  external world4  
,then there was obviously a self-element
 present in the  ,up and ,down felt as  
in the cubes4 ,this being removed1      
,right and ,left had  also to go4 ,so1  
to get the knowledge of this simple set 
of objects clear  of self-elements1 two 
universe transforming thoughts have to  
be used2  and when these thoughts are   
thus incorporated the cubes become      
different4    ,it will be obvious to the
 reader that in these pages ,i have     
merely  touched the surface of the      
subject4 ,but the deeper matters which  
are  contained in the knowledge of a    
block of cubes are difficult to express1
  and are so mixed up with the practical

 work1 as far as ,i conceive them  at   
present1 that it is best to consider in 
some detail the applications  to the    
world about us of those truths of which 
we have already got a  clear            
apprehension from the block of cubes4   
,instead1 then1 of going on1 let us     
conclude the present paper by going     
back1 and taking a simple instance of   
the general truth that progress in  the 
knowledge of a block of cubes is casting
 out the self4    ,let the reader turn  
to ,diagram ,i4 and make out the shape  
which the  following numbers            
denote--namely1 #a1 #d1 #e4 ,if the     
following numbers be  said1 #ah1 #bg1   
#bf1 it will be found that they denote  
the same shape1 but  in a different     
position4 ,now if the block of cubes be 
well known1 these  two sets of names1   
#a1 #d1 #e1 and #ah1 #bg1 #bf1 ought to 
convey instantly to  the mind the same  
idea4 ,however quickly they are         
realized1 it ought to  be evident that  
they are the same shape4    ,and a good 

deal of the practical work in learning a
 block of cubes  consists in gaining    
this faculty of immediate apprehension4 
,but when it  is gained it is seen to   
consist much more of getting rid of an  
imperfection than in being any real     
advance4 ,for if the two shapes are     
identical we need not ask ourselves how 
it is we see them as the same1  but we  
have to ask ourselves what is the reason
 why we do not recognize  their         
identity2 and the answer evidently is   
that1 if we do not recognize  their     
identity1 it is due to the particular   
relationship of each shape  to          
ourselves4 ,one is down on our left     
hand1 another is up on our right1  and  
they are turned relatively to us        
different ways4 ,now these  differences1
 which are merely relative to us1 we    
impress upon the  shapes1 and really    
feel the shapes to be different4 ,the   
practice  consists in getting rid of the
 influence of these self-elements1 so   
that  two shapes1 however complicated1  

being alike1 when their names are said1 
we feel them to be alike without        
calculation or reflection4 ,thus the    
power of seeing likeness and analogy in 
this domain is merely another  name for 
the power of casting out the            
self-elements from our mental           
presentation of any objects with which  
we come into contact4                   
,footnotes      #a;,a ,b ,c ,d          
framework1 ,x and ,y two lines          
interlinked4    #b,see ,appendix4       
#c;,for details1 see ,appendix ,,iii4   
,transcriber's ,notes      --,retained  
publication information from the printed
 edition3 this e,book    is             
public-domain in the country of         
publication4    --,silently corrected a 
few palpable typos2 left intentionally  
nonstandard usage unchanged4    --,in   
the text versions only1 text in italics 
is delimited by    underscores4    --,in
 the text versions only1 superscript    
text is preceded by caret4    --,in the 
text versions only1 subscript text is   

preceded by underscore4