,,popular ,,scientific ,,lectures4      
,,by ,,the ,,same ,,author4   ,,the     
,,science ,,of ,,mechanics4 ,translated 
from the ,second ,german ,edition     by
 ,t4 ,j4 ,mc,cormack4 #bej ,cuts and    
,illustrations4 #ecd ,pages4 ,half      
,morocco1 ,gilt ,top4 ,price1 #b4ej4    
,,contributions ,,to ,,the ,,analysis   
,,of ,,the ,,sensations4 ,translated by 
,c4 ,m4     ,williams4 ,with ,notes and 
,new ,additions by the ,author4 #bjj    
,pages4     #cf ,cuts4 ,price1 #a4jj4   
,,popular ,,scientific ,,lectures4      
,translated by ,t4 ,j4 ,mc,cormack4     
,third     ,revised and ,enlarged       
,edition4 #daa ,pages4 #ei ,cuts4       
,cloth1 #a4ej2     ,paper1 #ej cents4   
,,the ,,open ,,court ,,publishing ,,co41
 #cbd ,,dearborn ,,st41 ,,chicago4      
,,popular ,,scientific ,,lectures       
,,by ,,ernst ,,mach    ,,formerly       
,,professor ,,of ,,physics ,,in ,,the   
,,university ,,of ,,prague1 ,,now       
,,professor ,,of ,,the ,,history ,,and  
,,theory ,,of ,,inductive ,,science ,,in

 ,,the   ,,university ,,of ,,vienna     
,,translated ,,by ,,thomas ,j4          
,mc,c,o,r,m,a,c,k    ,,third ,,edition1 
,,revised ,,and ,,enlarged    ,,with    
,,fifty-,,nine ,,cuts ,,and ,,diagrams  
,,chicago ,,the ,,open ,,court          
,,publishing ,,company    ,,for ,,sale  
,,by    ,,kegan ,,paul1 ,,trench1       
,,truebner  ,,co41 ,,london    #ahih    
,,copyright    ,,by ,,the ,,open ,,court
 ,,publishing ,,co4    ,pages   #a-beh  
in #ahid4   ,pages #cch-cgd    ,pages   
#bei-bha in #ahif4   ,pages #bhb-cjh in 
#ahig4   ,pages #cji-ccg in #ahih4      
,,author',s ,,preface ,,to ,,the ,,first
 ,,edition4   ,popular lectures1 owing  
to the knowledge they presuppose1 and   
the time they occupy1 can afford only a 
modicum of instruction4 ,they must      
select for this purpose easy subjects1  
and restrict themselves to the          
exposition of the simplest and the most 
essential points4 ,nevertheless1 by an  
appropriate choice of the matter1 the   
charm and the poetry of research can be 

conveyed by them4 ,it is only necessary 
to set forth the attractive and the     
alluring features of a problem1 and to  
show what broad domains of fact can be  
illuminated by the light radiating from 
the solution of a single and ofttimes   
unobtrusive point4  ,furthermore1 such  
lectures can exercise a favorable       
influence by showing the substantial    
sameness of scientific and every-day    
thought4 ,the public1 in this way1 loses
 its shyness towards scientific         
questions1 and acquires an interest in  
scientific work which is a great help to
 the inquirer4 ,the latter1 in his turn1
 is brought to understand that his work 
is a small part only of the universal   
process of life1 and that the results of
 his labors must redound to the benefit 
not only of himself and a few of his    
associates1 but to that of the          
collective whole4  ,i sincerely hope    
that these lectures1 in the present     
excellent translation1 will be          
productive of good in the direction     

indicated4      ,e4 ,,mach4  ,,prague1  
,december1 #ahid4     ,,translator',s   
,,note ,,to ,,the ,,third ,,edition4    
,the present third edition of this work 
has been enlarged by the addition of a  
new lecture1 ,on ,some ,phenomena       
,attending the ,flight of ,projectiles4 
,the additions to the second consisted  
of the following four lectures and      
articles3 ,professor ,mach's ,vienna    
,inaugural ,lecture1 ,the ,part ,played 
by ,accident in ,invention and          
,discovery1 the lecture on ,sensations  
of ,orientation1 recently delivered and 
summing up the results of an important  
psychological investigation1 and two    
historical articles 7see ,appendix7 on  
,acoustics and ,sight4  ,the lectures   
extend over a long period1 from #ahfd to
 #ahih1 and differ greatly in style1    
contents1 and purpose4 ,they were first 
published in collected form in ,english2
 afterwards two ,german editions were   
called for4  ,as the dates of the first 
five lectures are not given in the      

footnotes they are here appended4 ,the  
first lecture1 ,on the ,forms of        
,liquids1 was delivered in #ahfh and    
published with that ,on ,symmetry in    
#ahgb 7,prague74 ,the second and third  
lectures1 on acoustics1 were first      
published in #ahfe 7,graz72 the fourth  
and fifth1 on optics1 in #ahfg 7,graz74 
,they belong to the earliest period of  
,professor ,mach's scientific activity1 
and with the lectures on electrostatics 
and education will more than realise the
 hope expressed in the author's         
,preface4  ,the eighth1 ninth1 tenth1   
eleventh1 and twelfth lectures are of a 
more philosophical character and deal   
principally with the methods and nature 
of scientific inquiry4 ,in the ideas    
summarised in them will be found one of 
the most important contributions to the 
theory of knowledge made in the last    
quarter of a century4 ,significant hints
 in psychological method1 and exemplary 
specimen-researches in psychology and   
physics1 are also presented2 while in   

physics many ideas find their first     
discussion that afterwards1 under other 
names and other authorship1 became      
rallying-cries in this department of    
inquiry4  ,all the proofs of this       
translation have been read by ,professor
 ,mach himself4      ,t4 ,j4            
,,mccormack4  ,,la ,,salle1 ,,ill41     
,may1 #ahih4     ,,table ,,of           
,,contents4     ,the ,forms of ,liquids 
#a   ,the ,fibres of ,corti             
#ag   ,on the ,causes of ,harmony       
#cb   ,the ,velocity of ,light          
#dh   ,why ,has ,man ,two ,eyes8        
#ff   ,on ,symmetry                     
#hi   ,on the ,fundamental ,concepts of 
,electrostatics                  #ajg   
,on the ,principle of the ,conservation 
of ,energy                 #acg   ,on   
the ,economical ,nature of ,physical    
,inquiry                   #ahf   ,on   
,transformation and ,adaptation in      
,scientific ,thought         #bad   ,on 
the ,principle of ,comparison in        
,physics                      #bcf   ,on

 the ,part ,played by ,accident in      
,invention and ,discovery      #bei     
,on ,sensations of ,orientation         
#bhb   ,on ,some ,phenomena ,attending  
the ,flight of ,projectiles             
#cji   ,on ,instruction in the ,classics
 and the ,mathematico-,physical         
,sciences                               
#cch   ,appendixes4       ,i4 ,a        
,contribution to the ,history of        
,acoustics              #cge       ,,ii4
 ,remarks on the ,theory of ,spatial    
,vision                #chf   ,index    
#cic     ,,the ,,forms ,,of ,,liquids4  
,what thinkest thou1 dear ,euthyphron1  
that the holy is1 and the just1 and the 
good8 ,is the holy holy because the gods
 love it1 or are the gods holy because  
they love the holy8 ,by such easy       
questions did the wise ,socrates make   
the market-place of ,athens unsafe and  
relieve presumptuous young statesmen of 
the burden of imaginary knowledge1 by   
showing them how confused1 unclear1 and 
self-contradictory their ideas were4    

,you know the fate of the importunate   
questioner4 ,so called good society     
avoided him on the promenade4 ,only the 
ignorant accompanied him4 ,and finally  
he drank the cup of hemlock--a lot which
 we ofttimes wish would fall to modern  
critics of his stamp4  ,what we have    
learned from ,socrates1 however1--our   
inheritance from him1--is scientific    
criticism4 ,every one who busies himself
 with science recognises how unsettled  
and indefinite the notions are which he 
has brought with him from common life1  
and how1 on a minute examination of     
things1 old differences are effaced and 
new ones introduced4 ,the history of    
science is full of examples of this     
constant change1 development1 and       
clarification of ideas4  ,but we will   
not linger by this general consideration
 of the fluctuating character of ideas1 
which becomes a source of real          
uncomfortableness1 when we reflect that 
it applies to almost every notion of    
life4 ,rather shall we observe by the   

study of a physical example how much a  
thing changes when it is closely        
examined1 and how it assumes1 when thus 
considered1 increasing definiteness of  
form4  ,the majority of you think1      
perhaps1 you know quite well the        
distinction between a liquid and a      
solid4 ,and precisely persons who have  
never busied themselves with physics    
will consider this question one of the  
easiest that can be put4 ,but the       
physicist knows that it is one of the   
most difficult4 ,i shall mention here   
only the experiments of ,tresca1 which  
show that solids subjected to high      
pressures behave exactly as liquids do2 
for example1 may be made to flow out in 
the form of jets from orifices in the   
bottoms of vessels4 ,the supposed       
difference of kind between liquids and  
solids is thus shown to be a mere       
difference of degree4  ,the common      
inference that because the earth is     
oblate in form1 it was originally fluid1
 is an error1 in the light of these     

facts4 ,true1 a rotating sphere1 a few  
inches in diameter will assume an oblate
 form only if it is very soft1 for      
example1 is composed of freshly kneaded 
clay or some viscous stuff4 ,but the    
earth1 even if it consisted of the      
rigidest stone1 could not help being    
crushed by its tremendous weight1 and   
must perforce behave as a fluid4 ,even  
our mountains could not extend beyond a 
certain height without crumbling4 ,the  
earth may once have been fluid1 but this
 by no means follows from its           
oblateness4  ,the particles of a liquid 
are displaced on the application of the 
slightest pressure2 a liquid conforms   
exactly to the shapes of the vessels in 
which it is contained2 it possesses no  
form of its own1 as you have all learned
 in the schools4 ,accommodating itself  
in the most trifling respects to the    
conditions of the vessel in which it is 
placed1 and showing1 even on its        
surface1 where one would suppose it had 
the freest play1 nothing but a polished1

 smiling1 expressionless countenance1 it
 is the courtier par excellence of the  
natural bodies4  ,liquids have no form  
of their own6 ,no1 not for the          
superficial observer4 ,but persons who  
have observed that a raindrop is round  
and never angular1 will not be disposed 
to accept this dogma so unconditionally4
  ,it is fair to suppose that every man1
 even the weakest1 would possess a      
character1 if it were not too difficult 
in this world to keep it4 ,so1 too1 we  
must suppose that liquids would possess 
forms of their own1 if the pressure of  
the circumstances permitted it1--if they
 were not crushed by their own weights4 
,an astronomer once calculated that     
human beings could not exist on the sun1
 apart from its great heat1 because they
 would be crushed to pieces there by    
their own weight4 ,the greater mass of  
this body would also make the weight of 
the human body there much greater4 ,but 
on the moon1 because here we should be  
much lighter1 we could jump as high as  

the church-steeples without any         
difficulty1 with the same muscular power
 which we now possess4 ,statues and     
plaster casts of syrup are undoubtedly  
things of fancy1 even on the moon1 but  
maple-syrup would flow so slowly there  
that we could easily build a maple-syrup
 man on the moon1 for the fun of the    
thing1 just as our children here build  
snow-men4  ,accordingly1 if liquids have
 no form of their own with us on earth1 
they have1 perhaps1 a form of their own 
on the moon1 or on some smaller and     
lighter heavenly body4 ,the problem1    
then1 simply is to get rid of the       
effects of gravity2 and1 this done1 we  
shall be able to find out what the      
peculiar forms of liquids are4  ,the    
problem was solved by ,plateau of       
,ghent1 whose method was to immerse the 
liquid in another of the same specific  
gravity4#a ,he employed for his         
experiments oil and a mixture of alcohol
 and water4 ,by ,archimedes's well-known
 principle1 the oil in this mixture     

loses its entire weight4 ,it no longer  
sinks beneath its weight2 its formative 
forces1 be they ever so weak1 are now in
 full play4  ,as a fact1 we now see1 to 
our surprise1 that the oil1 instead of  
spreading out into a layer1 or lying in 
a formless mass1 assumes the shape of a 
beautiful and perfect sphere1 freely    
suspended in the mixture1 as the moon is
 in space4 ,we can construct in this way
 a sphere of oil several inches in      
diameter4  ,if1 now1 we affix a thin    
plate to a wire and insert the plate in 
the oil sphere1 we can1 by twisting the 
wire between our fingers1 set the whole 
ball in rotation4 ,doing this1 the ball 
assumes an oblate shape1 and we can1 if 
we are skilful enough1 separate by such 
rotation a ring from the ball1 like that
 which surrounds ,saturn4 ,this ring is 
finally rent asunder1 and1 breaking up  
into a number of smaller balls1 exhibits
 to us a kind of model of the origin of 
the planetary system according to the   
hypothesis of ,kant and ,laplace4       

,illustration3 ,fig4 #a4  ,still more   
curious are the phenomena exhibited when
 the formative forces of the liquid are 
partly disturbed by putting in contact  
with the liquid's surface some rigid    
body4 ,if we immerse1 for example1 the  
wire framework of a cube in our mass of 
oil1 the oil will everywhere stick to   
the wire framework4 ,if the quantity of 
oil is exactly sufficient we shall      
obtain an oil cube with perfectly smooth
 walls4 ,if there is too much or too    
little oil1 the walls of the cube will  
bulge out or cave in4 ,in this manner we
 can produce all kinds of geometrical   
figures of oil1 for example1 a          
three-sided pyramid1 a cylinder 7by     
bringing the oil between two wire       
rings71 and so on4 ,interesting is the  
change of form that occurs when we      
gradually suck out the oil by means of a
 glass tube from the cube or pyramid4   
,the wire holds the oil fast4 ,the      
figure grows smaller and smaller1 until 
it is at last quite thin4 ,ultimately it

 consists simply of a number of thin1   
smooth plates of oil1 which extend from 
the edges of the cube to the centre1    
where they meet in a small drop4 ,the   
same is true of the pyramid4            
,illustration3 ,fig4 #b4  ,the idea now 
suggests itself that liquid figures as  
thin as this1 and possessing1 therefore1
 so slight a weight1 cannot be crushed  
or deformed by their weight2 just as a  
small1 soft ball of clay is not affected
 in this respect by its weight4 ,this   
being the case1 we no longer need our   
mixture of alcohol and water for the    
production of figures1 but can construct
 them in the open air4 ,and ,plateau1 in
 fact1 found that these thin figures1 or
 at least very similar ones1 could be   
produced in the air1 by dipping the wire
 nets described in a solution of soap   
and water and quickly drawing them out  
again4 ,the experiment is not difficult4
 ,the figure is formed of itself4 ,the  
preceding drawing represents to the eye 
the forms obtained with cubical and     

pyramidal nets4 ,in the cube1 thin1     
smooth films of soap-suds proceed from  
the edges to a small1 quadratic film in 
the centre4 ,in the pyramid1 a film     
proceeds from each edge to the centre4  
,these figures are so beautiful that    
they hardly admit of appropriate        
description4 ,their great regularity and
 geometrical exactness evokes surprise  
from all who see them for the first     
time4 ,unfortunately1 they are of only  
short duration4 ,they burst1 on the     
drying of the solution in the air1 but  
only after exhibiting to us the most    
brilliant play of colors1 such as is    
often seen in soap-bubbles4 ,partly     
their beauty of form and partly our     
desire to examine them more minutely    
induces us to conceive of methods of    
endowing them with permanent form4 ,this
 is very simply done4#b ,instead of     
dipping the wire nets in solutions of   
soap1 we dip them in pure melted        
colophonium 7resin74 ,when drawn out the
 figure at once forms and solidifies by 

contact with the air4  ,it is to be     
remarked that also solid fluid-figures  
can be constructed in the open air1 if  
their weight be light enough1 or the    
wire nets of very small dimensions4 ,if 
we make1 for example1 of very fine wire 
a cubical net whose sides measure about 
one-eighth of an inch in length1 we need
 simply to dip this net in water to     
obtain a small solid cube of water4     
,with a piece of blotting paper the     
superfluous water may be easily removed 
and the sides of the cube made smooth4  
,yet another simple method may be       
devised for observing these figures4 ,a 
drop of water on a greased glass plate  
will not run if it is small enough1 but 
will be flattened by its weight1 which  
presses it against its support4 ,the    
smaller the drop the less the           
flattening4 ,the smaller the drop the   
nearer it approaches the form of a      
sphere4 ,on the other hand1 a drop      
suspended from a stick is elongated by  
its weight4 ,the undermost parts of a   

drop of water on a support are pressed  
against the support1 and the upper parts
 are pressed against the lower parts    
because the latter cannot yield4 ,but   
when a drop falls freely downward all   
its parts move equally fast2 no part is 
impeded by another2 no part presses     
against another4 ,a freely falling drop1
 accordingly1 is not affected by its    
weight2 it acts as if it were           
weightless2 it assumes a spherical form4
  ,a moment's glance at the soap-film   
figures produced by our various wire    
models1 reveals to us a great           
multiplicity of form4 ,but great as this
 multiplicity is1 the common features of
 the figures also are easily            
discernible4      ,all forms of ,nature 
are allied1 though none is the same as  
the other2     ,thus1 their common      
chorus points to a hidden law4  ,this   
hidden law ,plateau discovered4 ,it may 
be expressed1 somewhat prosily1 as      
follows3  #a7 ,if several plane liquid  
films meet in a figure they are always  

three in number1 and1 taken in pairs1   
form1 each with another1 nearly equal   
angles4  #b7 ,if several liquid edges   
meet in a figure they are always four in
 number1 and1 taken in pairs1 form1 each
 with another1 nearly equal angles4     
,this is a strange law1 and its reason  
is not evident4 ,but we might apply this
 criticism to almost all laws4 ,it is   
not always that the motives of a        
law-maker are discernible in the form of
 the law he constructs4 ,but our law    
admits of analysis into very simple     
elements or reasons4 ,if we closely     
examine the paragraphs which state it1  
we shall find that their meaning is     
simply this1 that the surface of the    
liquid assumes the shape of smallest    
area that is possible under the         
circumstances4  ,if1 therefore1 some    
extraordinarily intelligent tailor1     
possessing a knowledge of all the       
artifices of the higher mathematics1    
should set himself the task of so       
covering the wire frame of a cube with  

cloth that every piece of cloth should  
be connected with the wire and joined   
with the remaining cloth1 and should    
seek to accomplish this feat with the   
greatest saving of material1 he would   
construct no other figure than that     
which is here formed on the wire frame  
in our solution of soap and water4      
,nature acts in the construction of     
liquid figures on the principle of a    
covetous tailor1 and gives no thought in
 her work to the fashions4 ,but1 strange
 to say1 in this work1 the most         
beautiful fashions are of themselves    
produced4  ,the two paragraphs which    
state our law apply primarily only to   
soap-film figures1 and are not          
applicable1 of course1 to solid         
oil-figures4 ,but the principle that the
 superficial area of the liquid shall be
 the least possible under the           
circumstances1 is applicable to all     
fluid figures4 ,he who understands not  
only the letter but also the reason of  
the law will not be at a loss when      

confronted with cases to which the      
letter does not accurately apply4 ,and  
this is the case with the principle of  
least superficial area4 ,it is a sure   
guide for us even in cases in which the 
above-stated paragraphs are not         
applicable4  ,our first task will now   
be1 to show by a palpable illustration  
the mode of formation of liquid figures 
by the principle of least superficial   
area4 ,the oil on the wire pyramid in   
our mixture of alcohol and water1 being 
unable to leave the wire edges1 clings  
to them1 and the given mass of oil      
strives so to shape itself that its     
surface shall have the least possible   
area4 ,suppose we attempt to imitate    
this phenomenon4 ,we take a wire        
pyramid1 draw over it a stout film of   
rubber1 and in place of the wire handle 
insert a small tube leading into the    
interior of the space enclosed by the   
rubber 7,fig4 #c74 ,through this tube we
 can blow in or suck out air4 ,the      
quantity of air in the enclosure        

represents the quantity of oil4 ,the    
stretched rubber film1 which1 clinging  
to the wire edges1 does its utmost to   
contract1 represents the surface of the 
oil endeavoring to decrease its area4   
,by blowing in1 and drawing out the air1
 now1 we actually obtain all the oil    
pyramidal figures1 from those bulged out
 to those hollowed in4 ,finally1 when   
all the air is pumped or sucked out1 the
 soap-film figure is exhibited4 ,the    
rubber films strike together1 assume the
 form of planes1 and meet at four sharp 
edges in the centre of the pyramid4     
,illustration3 ,fig4 #c4  ,illustration3
 ,fig4 #d4  ,the tendency of soap-films 
to assume smaller forms may be directly 
demonstrated by a method of ,van der    
,mensbrugghe4 ,if we dip a square wire  
frame to which a handle is attached into
 a solution of soap and water1 we shall 
obtain on the frame a beautiful1 plane  
film of soap-suds4 7,fig4 #d47 ,on this 
we lay a thread having its two ends tied
 together4 ,if1 now1 we puncture the    

part enclosed by the thread1 we shall   
obtain a soap-film having a circular    
hole in it1 whose circumference is the  
thread4 ,the remainder of the film      
decreasing in area as much as it can1   
the hole assumes the largest area that  
it can4 ,but the figure of largest area1
 with a given periphery1 is the circle4 
,illustration3 ,fig4 #e4  ,similarly1 by
 the principle of least superficial     
area1 a freely suspended mass of oil    
assumes the shape of a sphere4 ,the     
sphere is the form of least surface for 
a given content4 ,this is evident4 ,the 
more we put into a travelling-bag1 the  
nearer its shape approaches the         
spherical form4  ,the connexion of the  
two above-mentioned paragraphs with the 
principle of least superficial area may 
be shown by a yet simpler example4      
,picture to yourselves four fixed       
pulleys1 a1 b1 c1 d1 and two movable    
rings f1 g 7,fig4 #e72 about the pulleys
 and through the rings imagine a smooth 
cord passed1 fastened at one extremity  

to a nail e1 and loaded at the other    
with a weight h4 ,now this weight always
 tends to sink1 or1 what is the same    
thing1 always tends to make the portion 
of the string e h as long as possible1  
and consequently the remainder of the   
string1 wound round the pulleys1 as     
short as possible4 ,the strings must    
remain connected with the pulleys1 and  
on account of the rings also with each  
other4 ,the conditions of the case1     
accordingly1 are similar to those of the
 liquid figures discussed4 ,the result  
also is a similar one4 ,when1 as in the 
right hand figure of the cut1 four pairs
 of strings meet1 a different           
configuration must be established4 ,the 
consequence of the endeavor of the      
string to shorten itself is that the    
rings separate from each other1 and that
 now at all points only three pairs of  
strings meet1 every two at equal angles 
of one hundred and twenty degrees4 ,as a
 fact1 by this arrangement the greatest 
possible shortening of the string is    

attained2 as can be easily proved by    
geometry4  ,this will help us to some   
extent to understand the creation of    
beautiful and complicated figures by the
 simple tendency of liquids to assume   
surfaces of least superficial area4 ,but
 the question arises1 ,why do liquids   
seek surfaces of least superficial area8
  ,the particles of a liquid cling      
together4 ,drops brought into contact   
coalesce4 ,we can say1 liquid particles 
attract each other4 ,if so1 they seek to
 come as close as they can to each      
other4 ,the particles at the surface    
will endeavor to penetrate as far as    
they can into the interior4 ,this       
process will not stop1 cannot stop1     
until the surface has become as small as
 under the circumstances it possibly can
 become1 until as few particles as      
possible remain at the surface1 until as
 many particles as possible have        
penetrated into the interior1 until the 
forces of attraction have no more work  
to perform4#c  ,the root of the         

principle of least surface is to be     
sought1 accordingly1 in another and much
 simpler principle1 which may be        
illustrated by some such analogy as     
this4 ,we can conceive of the natural   
forces of attraction and repulsion as   
purposes or intentions of nature4 ,as a 
matter of fact1 that interior pressure  
which we feel before an act and which we
 call an intention or purpose1 is not1  
in a final analysis1 so essentially     
different from the pressure of a stone  
on its support1 or the pressure of a    
magnet on another1 that it is           
necessarily unallowable to use for both 
the same term--at least for well-defined
 purposes4#d ,it is the purpose of      
nature1 accordingly1 to bring the iron  
nearer the magnet1 the stone nearer the 
centre of the earth1 and so forth4 ,if  
such a purpose can be realised1 it is   
carried out4 ,but where she cannot      
realise her purposes1 nature does       
nothing4 ,in this respect she acts      
exactly as a good man of business does4 

,it is a constant purpose of nature to  
bring weights lower4 ,we can raise a    
weight by causing another1 larger weight
 to sink2 that is1 by satisfying        
another1 more powerful1 purpose of      
nature4 ,if we fancy we are making      
nature serve our purposes in this1 it   
will be found1 upon closer examination1 
that the contrary is true1 and that     
nature has employed us to attain her    
purposes4  ,equilibrium1 rest1 exists   
only1 but then always1 when nature is   
brought to a halt in her purposes1 when 
the forces of nature are as fully       
satisfied as1 under the circumstances1  
they can be4 ,thus1 for example1 heavy  
bodies are in equilibrium1 when their   
so-called centre of gravity lies as low 
as it possibly can1 or when as much     
weight as the circumstances admit of has
 sunk as low as it can4  ,the idea      
forcibly suggests itself that perhaps   
this principle also holds good in other 
realms4 ,equilibrium exists also in the 
state when the purposes of the parties  

are as fully satisfied as for the time  
being they can be1 or1 as we may say1   
jestingly1 in the language of physics1  
when the social potential is a          
maximum4#e  ,you see1 our miserly       
mercantile principle is replete with    
consequences4#f ,the result of sober    
research1 it has become as fruitful for 
physics as the dry questions of         
,socrates for science generally4 ,if the
 principle seems to lack in ideality1   
the more ideal are the fruits which it  
bears4  ,but why1 tell me1 should       
science be ashamed of such a principle8 
,is science#g itself anything more      
than--a business8 ,is not its task to   
acquire with the least possible work1 in
 the least possible time1 with the least
 possible thought1 the greatest possible
 part of eternal truth8     ,,footnotes3
    ,footnote #a3 ,statique exprimentale
 et thorique des liquids1   #ahgc4 ,see 
also ,the ,science of ,mechanics1 p4    
#chd et seqq41 ,the ,open   ,court      
,publishing ,co41 ,chicago1 #ahic4      

,footnote #b3 ,compare ,mach1 ,ueber die
 ,molecularwirkung der   ,flssigkeiten1 
,reports of the ,vienna ,academy1 #ahfb4
    ,footnote #c3 ,in almost all        
branches of physics that are well worked
   out such maximal and minimal problems
 play an important part4    ,footnote   
#d3 ,compare ,mach1 ,vortrge ber        
,psychophysik1 ,vienna1   #ahfc1 page   
#da2 ,compendium der ,physik fr         
,mediciner1 ,vienna1 #ahfc1   page #bcd2
 and also ,the ,science of ,mechanics1  
,chicago1 #ahic1 pp4 #hd   and #dfd4    
,footnote #e3 ,like reflexions are found
 in ,qutelet1 ,du systme   sociale4     
,footnote #f3 ,for the full development 
of this idea see the essay ,on   the    
,economical ,nature of ,physical        
,inquiry1 p4 #ahf1 and the chapter   on 
,the ,economy of ,science1 in my        
,mechanics 7,chicago3 ,the ,open        
,court ,publishing ,company1 #ahic71 p4 
#dha4    ,footnote #g3 ,science may be  
regarded as a maximum or minimum        
problem1 exactly as the business of the 

merchant4 ,in fact1 the   intellectual  
activity of natural inquiry is not so   
greatly different   from that exercised 
in ordinary life as is usually supposed4
     ,,the ,,fibres ,,of ,,corti4       
,whoever has roamed through a beautiful 
country knows that the tourist's        
delights increase with his progress4    
,how pretty that wooded dell must look  
from yonder hill6 ,whither does that    
clear brook flow1 that hides itself in  
yonder sedge8 ,if ,i only knew how the  
landscape looked behind that mountain6  
,thus even the child thinks in his first
 rambles4 ,it is also true of the       
natural philosopher4  ,the first        
questions are forced upon the attention 
of the inquirer by practical            
considerations2 the subsequent ones are 
not4 ,an irresistible attraction draws  
him to these2 a nobler interest which   
far transcends the mere needs of life4  
,let us look at a special case4  ,for a 
long time the structure of the organ of 
hearing has actively engaged the        

attention of anatomists4 ,a considerable
 number of brilliant discoveries has    
been brought to light by their labors1  
and a splendid array of facts and truths
 established4 ,but with these facts a   
host of new enigmas has been presented4 
,whilst in the theory of the            
organisation and functions of the eye   
comparative clearness has been attained2
 whilst1 hand in hand with this1        
ophthalmology has reached a degree of   
perfection which the preceding century  
could hardly have dreamed of1 and by the
 help of the ophthalmoscope the         
observing physician penetrates into the 
profoundest recesses of the eye1 the    
theory of the ear is still much shrouded
 in mysterious darkness1 full of        
attraction for the investigator4  ,look 
at this model of the ear4 ,even at that 
familiar part by whose extent we measure
 the quantity of people's intelligence1 
even at the external ear1 the problems  
begin4 ,you see here a succession of    
helixes or spiral windings1 at times    

very pretty1 whose significance we      
cannot accurately state1 yet for which  
there must certainly be some reason4    
,illustration3 ,fig4 #f4  ,the shell or 
concha of the ear1 a in the annexed     
diagram1 conducts the sound into the    
curved auditory passage b1 which is     
terminated by a thin membrane1 the      
so-called tympanic membrane1 e4 ,this   
membrane is set in motion by the sound1 
and in its turn sets in motion a series 
of little bones of very peculiar        
formation1 c4 ,at the end of all is the 
labyrinth d4 ,the labyrinth consists of 
a group of cavities filled with a       
liquid1 in which the innumerable fibres 
of the nerve of hearing are imbedded4   
,by the vibration of the chain of bones 
c1 the liquid of the labyrinth is       
shaken1 and the auditory nerve excited4 
,here the process of hearing begins4 ,so
 much is certain4 ,but the details of   
the process are one and all unanswered  
questions4  ,to these old puzzles1 the  
,marchese ,corti1 as late as #ahea1     

added a new enigma4 ,and1 strange to    
say1 it is this last enigma1 which1     
perhaps1 has first received its correct 
solution4 ,this will be the subject of  
our remarks to-day4  ,corti found in the
 cochlea1 or snail-shell of the         
labyrinth1 a large number of microscopic
 fibres placed side by side in          
geometrically graduated order4          
,according to ,klliker their number is  
three thousand4 ,they were also the     
subject of investigation at the hands of
 ,max ,schultze and ,deiters4  ,a       
description of the details of this organ
 would only weary you1 besides not      
rendering the matter much clearer4 ,i   
prefer1 therefore1 to state briefly what
 in the opinion of prominent            
investigators like ,helmholtz and       
,fechner is the peculiar function of    
,corti's fibres4 ,the cochlea1 it seems1
 contains a large number of elastic     
fibres of graduated lengths 7,fig4 #g71 
to which the branches of the auditory   
nerve are attached4 ,these fibres1      

called the fibres1 pillars1 or rods of  
,corti1 being of unequal length1 must   
also be of unequal elasticity1 and1     
consequently1 pitched to different      
notes4 ,the cochlea1 therefore1 is a    
species of pianoforte4  ,illustration3  
,fig4 #g4  ,what1 now1 may be the office
 of this structure1 which is found in no
 other organ of sense8 ,may it not be   
connected with some special property of 
the ear8 ,it is quite probable2 for the 
ear possesses a very similar power4 ,you
 know that it is possible to follow the 
individual voices of a symphony4        
,indeed1 the feat is possible even in a 
fugue of ,bach1 where it is certainly no
 inconsiderable achievement4 ,the ear   
can pick out the single constituent     
tonal parts1 not only of a harmony1 but 
of the wildest clash of music           
imaginable4 ,the musical ear analyses   
every agglomeration of tones4  ,the eye 
does not possess this ability4 ,who1 for
 example1 could tell from the mere sight
 of white1 without a previous           

experimental knowledge of the fact1 that
 white is composed of a mixture of other
 colors8 ,could it be1 now1 that these  
two facts1 the property of the ear just 
mentioned1 and the structure discovered 
by ,corti1 are really connected8 ,it is 
very probable4 ,the enigma is solved if 
we assume that every note of definite   
pitch has its special string in this    
pianoforte of ,corti1 and1 therefore1   
its special branch of the auditory nerve
 attached to that string4 ,but before ,i
 can make this point perfectly plain to 
you1 ,i must ask you to follow me a few 
steps into the dry domain of physics4   
,look at this pendulum4 ,forced from its
 position of equilibrium by an impulse1 
it begins to swing with a definite time 
of oscillation1 dependent upon its      
length4 ,longer pendulums swing more    
slowly1 shorter ones more quickly4 ,we  
will suppose our pendulum to execute one
 to-and-fro movement in a second4  ,this
 pendulum1 now1 can be thrown into      
violent vibration in two ways2 either by

 a single heavy impulse1 or by a number 
of properly communicated slight         
impulses4 ,for example1 we impart to the
 pendulum1 while at rest in its position
 of equilibrium1 a very slight impulse4 
,it will execute a very small vibration4
 ,as it passes a third time its position
 of equilibrium1 a second having        
elapsed1 we impart to it again a slight 
shock1 in the same direction with the   
first4 ,again after the lapse of a      
second1 on its fifth passage through the
 position of equilibrium1 we strike it  
again in the same manner2 and so        
continue4 ,you see1 by this process the 
shocks imparted augment continually the 
motion of the pendulum4 ,after each     
slight impulse1 the pendulum reaches out
 a little further in its swing1 and     
finally acquires a considerable         
motion4#h  ,but this is not the case    
under all circumstances4 ,it is possible
 only when the impulses imparted        
synchronise with the swings of the      
pendulum4 ,if we should communicate the 

second impulse at the end of half a     
second and in the same direction with   
the first impulse1 its effects would    
counteract the motion of the pendulum4  
,it is easily seen that our little      
impulses help the motion of the pendulum
 more and more1 according as their time 
accords with the time of the pendulum4  
,if we strike the pendulum in any other 
time than in that of its vibration1 in  
some instances1 it is true1 we shall    
augment its vibration1 but in others    
again1 we shall obstruct it4 ,our       
impulses will be less effective the more
 the motion of our own hand departs from
 the motion of the pendulum4  ,what is  
true of the pendulum holds true of every
 vibrating body4 ,a tuning-fork when it 
sounds1 also vibrates4 ,it vibrates more
 rapidly when its sound is higher2 more 
slowly when it is deeper4 ,the standard 
,a of our musical scale is produced by  
about four hundred and fifty vibrations 
in a second4  ,i place by the side of   
each other on this table two            

tuning-forks1 exactly alike1 resting on 
resonant cases4 ,i strike the first one 
a sharp blow1 so that it emits a loud   
note1 and immediately grasp it again    
with my hand to quench its note4        
,nevertheless1 you still hear the note  
distinctly sounded1 and by feeling it   
you may convince yourselves that the    
other fork which was not struck now     
vibrates4  ,i now attach a small bit of 
wax to one of the forks4 ,it is thrown  
thus out of tune2 its note is made a    
little deeper4 ,i now repeat the same   
experiment with the two forks1 now of   
unequal pitch1 by striking one of them  
and again grasping it with my hand2 but 
in the present case the note ceases the 
very instant ,i touch the fork4  ,what  
has happened here in these two          
experiments8 ,simply this4 ,the         
vibrating fork imparts to the air and to
 the table four hundred and fifty shocks
 a second1 which are carried over to the
 other fork4 ,if the other fork is      
pitched to the same note1 that is to    

say1 if it vibrates when struck in the  
same time with the first1 then the      
shocks first emitted1 no matter how     
slight they may be1 are sufficient to   
throw the second fork into rapid        
sympathetic vibration4 ,but when the    
time of vibration of the two forks is   
slightly different1 this does not take  
place4 ,we may strike as many forks as  
we will1 the fork tuned to ,a is        
perfectly indifferent to their notes2 is
 deaf1 in fact1 to all except its own2  
and if you strike three1 or four1 or    
five1 or any number whatsoever1 of forks
 all at the same time1 so as to make the
 shocks which come from them ever so    
great1 the ,a fork will not join in with
 their vibrations unless another fork ,a
 is found in the collection struck4 ,it 
picks out1 in other words1 from all the 
notes sounded1 that which accords with  
it4  ,the same is true of all bodies    
which can yield notes4 ,tumblers resound
 when a piano is played1 on the striking
 of certain notes1 and so do window     

panes4 ,nor is the phenomenon without   
analogy in other provinces4 ,take a dog 
that answers to the name ,nero4 ,he lies
 under your table4 ,you speak of        
,domitian1 ,vespasian1 and ,marcus      
,aurelius ,antoninus1 you call upon all 
the names of the ,roman ,emperors that  
occur to you1 but the dog does not stir1
 although a slight tremor of his ear    
tells you of a faint response of his    
consciousness4 ,but the moment you call 
,nero he jumps joyfully towards you4    
,the tuning-fork is like your dog4 ,it  
answers to the name ,a4  ,you smile1    
ladies4 ,you shake your heads4 ,the     
simile does not catch your fancy4 ,but  
,i have another1 which is very near to  
you3 and for punishment you shall hear  
it4 ,you1 too1 are like tuning-forks4   
,many are the hearts that throb with    
ardor for you1 of which you take no     
notice1 but are cold4 ,yet what does it 
profit you6 ,soon the heart will come   
that beats in just the proper rhythm1   
and then your knell1 too1 has struck4   

,then your heart1 too1 will beat in     
unison1 whether you will or no4  ,the   
law of sympathetic vibration1 here      
propounded for sounding bodies1 suffers 
some modification for bodies incompetent
 to yield notes4 ,bodies of this kind   
vibrate to almost every note4 ,a high   
silk hat1 we know1 will not sound2 but  
if you will hold your hat in your hand  
when attending your next concert you    
will not only hear the pieces played1   
but also feel them with your fingers4   
,it is exactly so with men4 ,people who 
are themselves able to give tone to     
their surroundings1 bother little about 
the prattle of others4 ,but the person  
without character tarries everywhere3 in
 the temperance hall1 and at the bar of 
the public-house--everywhere where a    
committee is formed4 ,the high silk hat 
is among bells what the weakling is     
among men of conviction4  ,a sonorous   
body1 therefore1 always sounds when its 
special note1 either alone or in company
 with others1 is struck4 ,we may now go 

a step further4 ,what will be the       
behaviour of a group of sonorous bodies 
which in the pitch of their notes form a
 scale8 ,let us picture to ourselves1   
for example 7,fig4 #h71 a series of rods
 or strings pitched to the notes c d e f
 g4444 ,on a musical instrument the     
accord c e g is struck4 ,every one of   
the rods of ,fig4 #h will see if its    
special note is contained in the accord1
 and if it finds it1 it will respond4   
,the rod c will give at once the note c1
 the rod e the note e1 the rod g the    
note g4 ,all the other rods will remain 
at rest1 will not sound4  ,illustration3
 ,fig4 #h4  ,we need not look about us  
long for such an instrument4 ,every     
piano is an instrument of this kind1    
with which the experiment mentioned may 
be executed with splendid success4 ,two 
pianos stand here by the side of each   
other1 both tuned alike4 ,we will employ
 the first for exciting the notes1 while
 we will allow the second to respond2   
after having first pressed upon the loud

 pedal1 so as to render all the strings 
capable of motion4  ,every harmony      
struck with vigor on the first piano is 
distinctly repeated on the second4 ,to  
prove that it is the same strings that  
are sounded in both pianos1 we repeat   
the experiment in a slightly changed    
form4 ,we let go the loud pedal of the  
second piano and pressing on the keys c 
e g of that instrument vigorously strike
 the harmony c e g on the first piano4  
,the harmony c e g is now also sounded  
on the second piano4 ,but if we press   
only on one key g of one piano1 while we
 strike c e g on the other1 only g will 
be sounded on the second4 ,it is thus   
always the like strings of the two      
pianos that excite each other4  ,the    
piano can reproduce any sound that is   
composed of its musical notes4 ,it will 
reproduce1 for example1 very distinctly1
 a vowel sound that is sung into it4    
,and in truth physics has proved that   
the vowels may be regarded as composed  
of simple musical notes4  ,you see that 

by the exciting of definite tones in the
 air quite definite motions are set up  
with mechanical necessity in the piano4 
,the idea might be made use of for the  
performance of some pretty pieces of    
wizardry4 ,imagine a box in which is a  
stretched string of definite pitch4     
,this is thrown into motion as often as 
its note is sung or whistled4 ,now it   
would not be a very difficult task for a
 skilful mechanic to so construct the   
box that the vibrating cord would close 
a galvanic circuit and open the lock4   
,and it would not be a much more        
difficult task to construct a box which 
would open at the whistling of a certain
 melody4 ,sesame6 and the bolts fall4   
,truly1 we should have here a veritable 
puzzle-lock4 ,still another fragment    
rescued from that old kingdom of fables1
 of which our day has realised so much1 
that world of fairy-stories to which the
 latest contributions are ,casselli's   
telegraph1 by which one can write at a  
distance in one's own hand1 and ,prof4  

,elisha ,gray's telautograph4 ,what     
would the good old ,herodotus have said 
to these things who even in ,egypt shook
 his head at much that he saw8 ,greek3  
emoi men ou pista1 just as              
simple-heartedly as then1 when he heard 
of the circumnavigation of ,africa4  ,a 
new puzzle-lock6 ,but why invent one8   
,are not we human beings ourselves      
puzzle-locks8 ,think of the stupendous  
groups of thoughts1 feelings1 and       
emotions that can be aroused in us by a 
word6 ,are there not moments in all our 
lives when a mere name drives the blood 
to our hearts8 ,who that has attended a 
large mass-meeting has not experienced  
what tremendous quantities of energy and
 motion can be evolved by the innocent  
words1 ,liberty1 ,equality1 ,fraternity4
  ,but let us return to the subject     
proper of our discourse4 ,let us look   
again at our piano1 or what will do just
 as well1 at some other contrivance of  
the same character4 ,what does this     
instrument do8 ,plainly1 it decomposes1 

it analyses every agglomeration of      
sounds set up in the air into its       
individual component parts1 each tone   
being taken up by a different string2 it
 performs a real spectral analysis of   
sound4 ,a person completely deaf1 with  
the help of a piano1 simply by touching 
the strings or examining their          
vibrations with a microscope1 might     
investigate the sonorous motion of the  
air1 and pick out the separate tones    
excited in it4  ,the ear has the same   
capacity as this piano4 ,the ear        
performs for the mind what the piano    
performs for a person who is deaf4 ,the 
mind without the ear is deaf4 ,but a    
deaf person1 with the piano1 does hear  
after a fashion1 though much less       
vividly1 and more clumsily1 than with   
the ear4 ,the ear1 thus1 also decomposes
 sound into its component tonal parts4  
,i shall now not be deceived1 ,i think1 
if ,i assume that you already have a    
presentiment of what the function of    
,corti's fibres is4 ,we can make the    

matter very plain to ourselves4 ,we will
 use the one piano for exciting the     
sounds1 and we shall imagine the second 
one in the ear of the observer in the   
place of ,corti's fibres1 which is a    
model of such an instrument4 ,to every  
string of the piano in the ear we will  
suppose a special fibre of the auditory 
nerve attached1 so that this fibre and  
this alone1 is irritated when the string
 is thrown into vibration4 ,if we strike
 now an accord on the external piano1   
for every tone of that accord a definite
 string of the internal piano will sound
 and as many different nervous fibres   
will be irritated as there are notes in 
the accord4 ,the simultaneous           
sense-impressions due to different notes
 can thus be preserved unmingled and be 
separated by the attention4 ,it is the  
same as with the five fingers of the    
hand4 ,with each finger ,i can touch    
something different4 ,now the ear has   
three thousand such fingers1 and each   
one is designed for the touching of a   

different tone4#i ,our ear is a         
puzzle-lock of the kind mentioned4 ,it  
opens at the magic melody of a sound4   
,but it is a stupendously ingenious     
lock4 ,not only one tone1 but every tone
 makes it open2 but each one            
differently4 ,to each tone it replies   
with a different sensation4  ,more than 
once it has happened in the history of  
science that a phenomenon predicted by  
theory1 has not been brought within the 
range of actual observation until long  
afterwards4 ,leverrier predicted the    
existence and the place of the planet   
,neptune1 but it was not until sometime 
later that ,galle actually found the    
planet at the predicted spot4 ,hamilton 
unfolded theoretically the phenomenon of
 the so-called conical refraction of    
light1 but it was reserved for ,lloyd   
some time subsequently to observe the   
fact4 ,the fortunes of ,helmholtz's     
theory of ,corti's fibres have been     
somewhat similar4 ,this theory1 too1    
received its substantial confirmation   

from the subsequent observations of ,v4 
,hensen4 ,on the free surface of the    
bodies of ,crustacea1 connected with the
 auditory nerves1 rows of little hairy  
filaments of varying lengths and        
thicknesses are found1 which to some    
extent are the analogues of ,corti's    
fibres4 ,hensen saw these hairs vibrate 
when sounds were excited1 and when      
different notes were struck different   
hairs were set in vibration4  ,i have   
compared the work of the physical       
inquirer to the journey of the tourist4 
,when the tourist ascends a new hill he 
obtains of the whole district a         
different view4 ,when the inquirer has  
found the solution of one enigma1 the   
solution of a host of others falls into 
his hands4  ,surely you have often felt 
the strange impression experienced when 
in singing through the scale the octave 
is reached1 and nearly the same         
sensation is produced as by the         
fundamental tone4 ,the phenomenon finds 
its explanation in the view here laid   

down of the ear4 ,and not only this     
phenomenon but all the laws of the      
theory of harmony may be grasped and    
verified from this point of view with a 
clearness before undreamt of4           
,unfortunately1 ,i must content myself  
to-day with the simple indication of    
these beautiful prospects4 ,their       
consideration would lead us too far     
aside into the fields of other sciences4
  ,the searcher of nature1 too1 must    
restrain himself in his path4 ,he also  
is drawn along from one beauty to       
another as the tourist from dale to     
dale1 and as circumstances generally    
draw men from one condition of life into
 others4 ,it is not he so much that     
makes the quests1 as that the quests are
 made of him4 ,yet let him profit by his
 time1 and let not his glance rove      
aimlessly hither and thither4 ,for soon 
the evening sun will shine1 and ere he  
has caught a full glimpse of the wonders
 close by1 a mighty hand will seize him 
and lead him away into a different world

 of puzzles4  ,respected hearers1       
science once stood in an entirely       
different relation to poetry4 ,the old  
,hindu mathematicians wrote their       
theorems in verses1 and lotus-flowers1  
roses1 and lilies1 beautiful sceneries1 
lakes1 and mountains figured in their   
problems4  ,thou goest forth on this    
lake in a boat4 ,a lily juts forth1 one 
palm above the water4 ,a breeze bends it
 downwards1 and it vanishes two palms   
from its previous spot beneath the      
surface4 ,quick1 mathematician1 tell me 
how deep is the lake6  ,thus spoke an   
ancient ,hindu scholar4 ,this poetry1   
and rightly1 has disappeared from       
science1 but from its dry leaves another
 poetry is wafted aloft which cannot be 
described to him who has never felt it4 
,whoever will fully enjoy this poetry   
must put his hand to the plough1 must   
himself investigate4 ,therefore1 enough 
of this6 ,i shall reckon myself         
fortunate if you do not repent of this  
brief excursion into the flowered dale  

of physiology1 and if you take with     
yourselves the belief that we can say of
 science what we say of poetry1         
,who the song would understand1         
,needs must seek the song's own land2   
,who the minstrel understand     ,needs 
must seek the minstrel's land4          
,,footnotes3    ,footnote #h3 ,this     
experiment1 with its associated         
reflexions1 is due   to ,galileo4       
,footnote #i3 ,a development of the     
theory of musical audition   differing  
in many points from the theory of       
,helmholtz here   expounded1 will be    
found in my ,contributions to the       
,analysis of the   ,sensations 7,english
 translation by ,c4 ,m4 ,williams71     
,chicago1 ,the   ,open ,court           
,publishing ,company1 #ahig4     ,,on   
,,the ,,causes ,,of ,,harmony4   ,we are
 to speak to-day of a theme which is    
perhaps of somewhat more general        
interest--the causes of the harmony of  
musical sounds4 ,the first and simplest 
experiences relative to harmony are very

 ancient4 ,not so the explanation of its
 laws4 ,these were first supplied by the
 investigators of a recent epoch4 ,allow
 me an historical retrospect4           
,pythagoras 7#ehf ,b4 ,c47 knew that the
 note yielded by a string of steady     
tension was converted into its octave   
when the length of the string was       
reduced one-half1 and into its fifth    
when reduced two-thirds2 and that then  
the first fundamental tone was consonant
 with the two others4 ,he knew generally
 that the same string under fixed       
tension gives consonant tones when      
successively divided into lengths that  
are in the proportions of the simplest  
natural numbers2 that is1 in the        
proportions of #a3b1 #b3c1 #c3d1 #d3e4  
,pythagoras failed to reveal the causes 
of these laws4 ,what have consonant     
tones to do with the simple natural     
numbers8 ,that is the question we should
 ask to-day4 ,but this circumstance must
 have appeared less strange than        
inexplicable to ,pythagoras4 ,this      

philosopher sought for the causes of    
harmony in the occult1 miraculous powers
 of numbers4 ,his procedure was largely 
the cause of the upgrowth of a numerical
 mysticism1 of which the traces may     
still be detected in our oneirocritical 
books and among some scientists1 to whom
 marvels are more attractive than       
lucidity4  ,euclid 7#cjj ,b4 ,c47 gives 
a definition of consonance and          
dissonance that could hardly be improved
 upon1 in point of verbal accuracy4 ,the
 consonance 7,greek3 symphnia7 of two   
tones1 he says1 is the mixture1 the     
blending 7,greek3 krasis7 of those two  
tones2 dissonance 7,greek3 diaphnia71 on
 the other hand1 is the incapacity of   
the tones to blend 7,greek3 amixia71    
whereby they are made harsh for the ear4
 ,the person who knows the correct      
explanation of the phenomenon hears it1 
so to speak1 reverberated in these words
 of ,euclid4 ,still1 ,euclid did not    
know the true cause of harmony4 ,he had 
unwittingly come very near to the truth1

 but without really grasping it4        
,leibnitz 7#afdf-agaf ,a4 ,d47 resumed  
the question which his predecessors had 
left unsolved4 ,he1 of course1 knew that
 musical notes were produced by         
vibrations1 that twice as many          
vibrations corresponded to the octave as
 to the fundamental tone1 etc4 ,a       
passionate lover of mathematics1 he     
sought for the cause of harmony in the  
secret computation and comparison of the
 simple numbers of vibrations and in the
 secret satisfaction of the soul at this
 occupation4 ,but how1 we ask1 if one   
does not know that musical notes are    
vibrations8 ,the computation and the    
satisfaction at the computation must    
indeed be pretty secret if it is        
unknown4 ,what queer ideas philosophers 
have6 ,could anything more wearisome be 
imagined than computation as a principle
 of sthetics8 ,yes1 you are not utterly 
wrong in your conjecture1 yet you may be
 sure that ,leibnitz's theory is not    
wholly nonsense1 although it is         

difficult to make out precisely what he 
meant by his secret computation4  ,the  
great ,euler 7#agjg-aghc7 sought the    
cause of harmony1 almost as ,leibnitz   
did1 in the pleasure which the soul     
derives from the contemplation of order 
in the numbers of the vibrations4#aj    
,rameau and ,d',alembert 7#agag-aghc7   
approached nearer to the truth4 ,they   
knew that in every sound available in   
music besides the fundamental note also 
the twelfth and the next higher third   
could be heard2 and further that the    
resemblance between a fundamental tone  
and its octave was always strongly      
marked4 ,accordingly1 the combination of
 the octave1 fifth1 third1 etc41 with   
the fundamental tone appeared to them   
natural4 ,they possessed1 we must admit1
 the correct point of view2 but with the
 simple naturalness of a phenomenon no  
inquirer can rest content2 for it is    
precisely this naturalness for which he 
seeks his explanations4  ,rameau's      
remark dragged along through the whole  

modern period1 but without leading to   
the full discovery of the truth4 ,marx  
places it at the head of his theory of  
composition1 but makes no further       
application of it4 ,also ,goethe and    
,zelter in their correspondence were1 so
 to speak1 on the brink of the truth4   
,zelter knew of ,rameau's view4         
,finally1 you will be appalled at the   
difficulty of the problem1 when ,i tell 
you that till very recent times even    
professors of physics were dumb when    
asked what were the causes of harmony4  
,not till quite recently did ,helmholtz 
find the solution of the question4 ,but 
to make this solution clear to you ,i   
must first speak of some experimental   
principles of physics and psychology4   
#a7 ,in every process of perception1 in 
every observation1 the attention plays a
 highly important part4 ,we need not    
look about us long for proofs of this4  
,you receive1 for example1 a letter     
written in a very poor hand4 ,do your   
best1 you cannot make it out4 ,you put  

together now these1 now those lines1 yet
 you cannot construct from them a single
 intelligible character4 ,not until you 
direct your attention to groups of lines
 which really belong together1 is the   
reading of the letter possible4         
,manuscripts1 the letters of which are  
formed of minute figures and scrolls1   
can only be read at a considerable      
distance1 where the attention is no     
longer diverted from the significant    
outlines to the details4 ,a beautiful   
example of this class is furnished by   
the famous iconographs of ,giuseppe     
,arcimboldo in the basement of the      
,belvedere gallery at ,vienna4 ,these   
are symbolic representations of water1  
fire1 etc43 human heads composed of     
aquatic animals and of combustibles4 ,at
 a short distance one sees only the     
details1 at a greater distance only the 
whole figure4 ,yet a point can be easily
 found at which1 by a simple voluntary  
movement of the attention1 there is no  
difficulty in seeing now the whole      

figure and now the smaller forms of     
which it is composed4 ,a picture is     
often seen representing the tomb of     
,napoleon4 ,the tomb is surrounded by   
dark trees between which the bright     
heavens are visible as background4 ,one 
can look a long time at this picture    
without noticing anything except the    
trees1 but suddenly1 on the attention   
being accidentally directed to the      
bright background1 one sees the figure  
of ,napoleon between the trees4 ,this   
case shows us very distinctly the       
important part which attention plays4   
,the same sensuous object can1 solely by
 the interposition of attention1 give   
rise to wholly different perceptions4   
,if ,i strike a harmony1 or chord1 on   
this piano1 by a mere effort of         
attention you can fix every tone of that
 harmony4 ,you then hear most distinctly
 the fixed tone1 and all the rest appear
 as a mere addition1 altering only the  
quality1 or acoustic color1 of the      
primary tone4 ,the effect of the same   

harmony is essentially modified if we   
direct our attention to different tones4
  ,strike in succession two harmonies1  
for example1 the two represented in the 
annexed diagram1 and first fix by the   
attention the upper note e1 afterwards  
the base e-a2 in the two cases you will 
hear the same sequence of harmonies     
differently4 ,in the first case1 you    
have the impression as if the fixed tone
 remained unchanged and simply altered  
its timbre2 in the second case1 the     
whole acoustic agglomeration seems to   
fall sensibly in depth4 ,there is an art
 of composition to guide the attention  
of the hearer4 ,but there is also an art
 of hearing1 which is not the gift of   
every person4  ,music3 ,fig4 #i4  ,the  
piano-player knows the remarkable       
effects obtained when one of the keys of
 a chord that is struck is let loose4   
,bar #a played on the piano sounds      
almost like bar #b4 ,the note which lies
 next to the key let loose resounds     
after its release as if it were freshly 

struck4 ,the attention no longer        
occupied with the upper note is by that 
very fact insensibly led to the upper   
note4  ,music3 ,fig4 #aj4  ,any         
tolerably cultivated musical ear can    
perform the resolution of a harmony into
 its component parts4 ,by much practice 
we can go even further4 ,then1 every    
musical sound heretofore regarded as    
simple can be resolved into a           
subordinate succession of musical tones4
 ,for example1 if ,i strike on the piano
 the note #a1 7annexed diagram17 we     
shall hear1 if we make the requisite    
effort of attention1 besides the loud   
fundamental note the feebler1 higher    
overtones1 or harmonics1 #b 444 #g1 that
 is1 the octave1 the twelfth1 the double
 octave1 and the third1 the fifth1 and  
the seventh of the double octave4       
,music3 ,fig4 #aa4  ,the same is true of
 every musically available sound4 ,each 
yields1 with varying degrees of         
intensity1 besides its fundamental note1
 also the octave1 the twelfth1 the      

double octave1 etc4 ,the phenomenon is  
observable with special facility on the 
open and closed flue-pipes of organs4   
,according1 now1 as certain overtones   
are more or less distinctly emphasised  
in a sound1 the timbre of the sound     
changes--that peculiar quality of the   
sound by which we distinguish the music 
of the piano from that of the violin1   
the clarinet1 etc4  ,on the piano these 
overtones can be very easily rendered   
audible4 ,if ,i strike1 for example1    
sharply note #a of the foregoing series1
 whilst ,i simply press down upon1 one  
after another1 the keys #b1 #c1 444 #g1 
the notes #b1 #c1 444 #g will continue  
to sound after the striking of #a1      
because the strings corresponding to    
these notes1 now freed from their       
dampers1 are thrown into sympathetic    
vibration4  ,as you know1 this          
sympathetic vibration of the            
like-pitched strings with the overtones 
is really not to be conceived as        
sympathy1 but rather as lifeless        

mechanical necessity4 ,we must not think
 of this sympathetic vibration as an    
ingenious journalist pictured it1 who   
tells a gruesome story of ,beethoven's  
,f minor sonata1 ,op4 #b1 that ,i cannot
 withhold from you4 ,at the last ,london
 ,industrial ,exhibition nineteen       
virtuosos played the ,f minor sonata on 
the same piano4 ,when the twentieth     
stepped up to the instrument to play by 
way of variation the same production1 to
 the terror of all present the piano    
began to render the sonata of its own   
accord4 ,the ,archbishop of ,canterbury1
 who happened to be present1 was set to 
work and forthwith expelled the ,f minor
 devil4  ,although1 now1 the overtones  
or harmonics which we have discussed are
 heard only upon a special effort of the
 attention1 nevertheless they play a    
highly important part in the formation  
of musical timbre1 as also in the       
production of the consonance and        
dissonance of sounds4 ,this may strike  
you as singular4 ,how can a thing which 

is heard only under exceptional         
circumstances be of importance generally
 for audition8  ,but consider some      
familiar incidents of your every-day    
life4 ,think of how many things you see 
which you do not notice1 which never    
strike your attention until they are    
missing4 ,a friend calls upon you2 you  
cannot understand why he looks so       
changed4 ,not until you make a close    
examination do you discover that his    
hair has been cut4 ,it is not difficult 
to tell the publisher of a work from its
 letter-press1 and yet no one can state 
precisely the points by which this style
 of type is so strikingly different from
 that style4 ,i have often recognised a 
book which ,i was in search of from a   
simple piece of unprinted white paper   
that peeped out from underneath the heap
 of books covering it1 and yet ,i had   
never carefully examined the paper1 nor 
could ,i have stated its difference from
 other papers4  ,what we must remember1 
therefore1 is that every sound that is  

musically available yields1 besides its 
fundamental note1 its octave1 its       
twelfth1 its double octave1 etc41 as    
overtones or harmonics1 and that these  
are important for the agreeable         
combination of several musical sounds4  
#b7 ,one other fact still remains to be 
dealt with4 ,look at this tuning-fork4  
,it yields1 when struck1 a perfectly    
smooth tone4 ,but if you strike in      
company with it a second fork which is  
of slightly different pitch1 and which  
alone also gives a perfectly smooth     
tone1 you will hear1 if you set both    
forks on the table1 or hold both before 
your ear1 a uniform tone no longer1 but 
a number of shocks of tones4 ,the       
rapidity of the shocks increases with   
the difference of the pitch of the      
forks4 ,these shocks1 which become very 
disagreeable for the ear when they      
amount to thirty-three in a second1 are 
called beats4  ,always1 when one of two 
like musical sounds is thrown out of    
unison with the other1 beats arise4     

,their number increases with the        
divergence from unison1 and             
simultaneously they grow more           
unpleasant4 ,their roughness reaches its
 maximum at about thirty-three beats in 
a second4 ,on a still further departure 
from unison1 and a consequent increase  
of the number of beats1 the unpleasant  
effect is diminished1 so that tones     
which are widely apart in pitch no      
longer produce offensive beats4  ,to    
give yourselves a clear idea of the     
production of beats1 take two metronomes
 and set them almost alike4 ,you can1   
for that matter1 set the two exactly    
alike4 ,you need not fear that they will
 strike alike4 ,the metronomes usually  
for sale in the shops are poor enough to
 yield1 when set alike1 appreciably     
unequal strokes4 ,set1 now1 these two   
metronomes1 which strike at unequal     
intervals1 in motion2 you will readily  
see that their strokes alternately      
coincide and conflict with each other4  
,the alternation is quicker the greater 

the difference of time of the two       
metronomes4  ,if metronomes are not to  
be had1 the experiment may be performed 
with two watches4  ,beats arise in the  
same way4 ,the rhythmical shocks of two 
sounding bodies1 of unequal pitch1      
sometimes coincide1 sometimes interfere1
 whereby they alternately augment and   
enfeeble each other's effects4 ,hence   
the shock-like1 unpleasant swelling of  
the tone4  ,now that we have made       
ourselves acquainted with overtones and 
beats1 we may proceed to the answer of  
our main question1 ,why do certain      
relations of pitch produce pleasant     
sounds1 consonances1 others unpleasant  
sounds1 dissonances8 ,it will be readily
 seen that all the unpleasant effects of
 simultaneous sound-combinations are the
 result of beats produced by those      
combinations4 ,beats are the only sin1  
the sole evil of music4 ,consonance is  
the coalescence of sounds without       
appreciable beats4  ,illustration3 ,fig4
 #ab4  ,to make this perfectly clear to 

you ,i have constructed the model which 
you see in ,fig4 #ab4 ,it represents a  
claviatur4 ,at its top a movable strip  
of wood aa with the marks #a1 #b 444 #f 
is placed4 ,by setting this strip in any
 position1 for example1 in that where   
the mark #a is over the note c of the   
claviatur1 the marks #b1 #c 444 #f1 as  
you see1 stand over the overtones of c4 
,the same happens when the strip is     
placed in any other position4 ,a second1
 exactly similar strip1 bb1 possesses   
the same properties4 ,thus1 together1   
the two strips1 in any two positions1   
point out by their marks all the tones  
brought into play upon the simultaneous 
sounding of the notes indicated by the  
marks #a4  ,the two strips1 placed over 
the same fundamental note1 show that    
also all the overtones of those notes   
coincide4 ,the first note is simply     
intensified by the other4 ,the single   
overtones of a sound lie too far apart  
to permit appreciable beats4 ,the second
 sound supplies nothing new1            

consequently1 also1 no new beats4       
,unison is the most perfect consonance4 
,moving one of the two strips along the 
other is equivalent to a departure from 
unison4 ,all the overtones of the one   
sound now fall alongside those of the   
other2 beats are at once produced2 the  
combination of the tones becomes        
unpleasant3 we obtain a dissonance4 ,if 
we move the strip further and further   
along1 we shall find that as a general  
rule the overtones always fall alongside
 each other1 that is1 always produce    
beats and dissonances4 ,only in a few   
quite definite positions do the         
overtones partially coincide4 ,such     
positions1 therefore1 signify higher    
degrees of euphony--they point out the  
consonant intervals4  ,these consonant  
intervals can be readily found          
experimentally by cutting ,fig4 #ab out 
of paper and moving bb lengthwise along 
aa4 ,the most perfect consonances are   
the octave and the twelfth1 since in    
these two cases the overtones of the one

 sound coincide absolutely with those of
 the other4 ,in the octave1 for example1
 #a;b falls on #b;a1 #b;b on #d;a1 #c;b 
on #f;a4 ,consonances1 therefore1 are   
simultaneous sound-combinations not     
accompanied by disagreeable beats4      
,this1 by the way1 is1 expressed in     
,english1 what ,euclid said in ,greek4  
,only such sounds are consonant as      
possess in common some portion of their 
partial tones4 ,plainly we must         
recognise between such sounds1 also when
 struck one after another1 a certain    
affinity4 ,for the second sound1 by     
virtue of the common overtones1 will    
produce partly the same sensation as the
 first4 ,the octave is the most striking
 exemplification of this4 ,when we reach
 the octave in the ascent of the scale  
we actually fancy we hear the           
fundamental tone repeated4 ,the         
foundations of harmony1 therefore1 are  
the foundations of melody4  ,consonance 
is the coalescence of sounds without    
appreciable beats6 ,this principle is   

competent to introduce wonderful order  
and logic into the doctrines of the     
fundamental bass4 ,the compendiums of   
the theory of harmony which 7,heaven be 
witness67 have stood hitherto little    
behind the cook-books in subtlety of    
logic1 are rendered extraordinarily     
clear and simple4 ,and what is more1 all
 that the great masters1 such as        
,palestrina1 ,mozart1 ,beethoven1       
unconsciously got right1 and of which   
heretofore no text-book could render    
just account1 receives from the         
preceding principle its perfect         
verification4  ,but the beauty of the   
theory is1 that it bears upon its face  
the stamp of truth4 ,it is no phantom of
 the brain4 ,every musician can hear for
 himself the beats which the overtones  
of his musical sounds produce4 ,every   
musician can satisfy himself that for   
any given case the number and the       
harshness of the beats can be calculated
 beforehand1 and that they occur in     
exactly the measure that theory         

determines4  ,this is the answer which  
,helmholtz gave to the question of      
,pythagoras1 so far as it can be        
explained with the means now at my      
command4 ,a long period of time lies    
between the raising and the solving of  
this question4 ,more than once were     
eminent inquirers nearer to the answer  
than they dreamed of4  ,the inquirer    
seeks the truth4 ,i do not know if the  
truth seeks the inquirer4 ,but were that
 so1 then the history of science would  
vividly remind us of that classical     
rendezvous1 so often immortalised by    
painters and poets4 ,a high garden wall4
 ,at the right a youth1 at the left a   
maiden4 ,the youth sighs1 the maiden    
sighs6 ,both wait4 ,neither dreams how  
near the other is4  ,i like this simile4
 ,truth suffers herself to be courted1  
but she has evidently no desire to be   
won4 ,she flirts at times disgracefully4
 ,above all1 she is determined to be    
merited1 and has naught but contempt for
 the man who will win her too quickly4  

,and if1 forsooth1 one breaks his head  
in his efforts of conquest1 what matter 
is it1 another will come1 and truth is  
always young4 ,at times1 indeed1 it     
really seems as if she were well        
disposed towards her admirer1 but that  
admitted--never6 ,only when ,truth is in
 exceptionally good spirits does she    
bestow upon her wooer a glance of       
encouragement4 ,for1 thinks ,truth1 if  
,i do not do something1 in the end the  
fellow will not seek me at all4  ,this  
one fragment of truth1 then1 we have1   
and it shall never escape us4 ,but when 
,i reflect what it has cost in labor and
 in the lives of thinking men1 how it   
painfully groped its way through        
centuries1 a half-matured thought1      
before it became complete2 when ,i      
reflect that it is the toil of more than
 two thousand years that speaks out of  
this unobtrusive model of mine1 then1   
without dissimulation1 ,i almost repent 
me of the jest ,i have made4  ,and think
 of how much we still lack6 ,when1      

several thousand years hence1 boots1    
top-hats1 hoops1 pianos1 and bass-viols 
are dug out of the earth1 out of the    
newest alluvium as fossils of the       
nineteenth century2 when the scientists 
of that time shall pursue their studies 
both upon these wonderful structures and
 upon our modern ,broadways1 as we      
to-day make studies of the implements of
 the stone age and of the prehistoric   
lake-dwellings--then1 too1 perhaps1     
people will be unable to comprehend how 
we could come so near to many great     
truths without grasping them4 ,and thus 
it is for all time the unsolved         
dissonance1 for all time the troublesome
 seventh1 that everywhere resounds in   
our ears2 we feel1 perhaps1 that it will
 find its solution1 but we shall never  
live to see the day of the pure triple  
accord1 nor shall our remotest          
descendants4  ,ladies1 if it is the     
sweet purpose of your life to sow       
confusion1 it is the purpose of mine to 
be clear2 and so ,i must confess to you 

a slight transgression that ,i have been
 guilty of4 ,on one point ,i have told  
you an untruth4 ,but you will pardon me 
this falsehood1 if in full repentance ,i
 make it good4 ,the model represented in
 ,fig4 #ab does not tell the whole      
truth1 for it is based upon the         
so-called even temperament system of    
tuning4 ,the overtones1 however1 of     
musical sounds are not tempered1 but    
purely tuned4 ,by means of this slight  
inexactness the model is made           
considerably simpler4 ,in this form it  
is fully adequate for ordinary purposes1
 and no one who makes use of it in his  
studies need be in fear of appreciable  
error4  ,if you should demand of me1    
however1 the full truth1 ,i could give  
you that only by the help of a          
mathematical formula4 ,i should have to 
take the chalk into my hands and--think 
of it6--reckon in your presence4 ,this  
you might take amiss4 ,nor shall it     
happen4 ,i have resolved to do no more  
reckoning for to-day4 ,i shall reckon   

now only upon your forbearance1 and this
 you will surely not gainsay me when you
 reflect that ,i have made only a       
limited use of my privilege to weary    
you4 ,i could have taken up much more of
 your time1 and may1 therefore1 justly  
close with ,lessing's epigram3      ,if 
thou hast found in all these pages      
naught that's worth the thanks1     ,at 
least have gratitude for what ,i've     
spared thee4    ,,footnotes3            
,footnote #aj3 ,sauveur also set out    
from ,leibnitz's idea1 but arrived   by 
independent researches at a different   
theory1 which was very near   to that of
 ,helmholtz4 ,compare on this point     
,sauveur1 ,mmoires de   l',acadmie des  
,sciences1 ,paris1 #agjj-agje1 and ,r4  
,smith1   ,harmonics1 ,cambridge1 #agdi4
 7,see ,appendix1 p4 #cdf47     ,,the   
,,velocity ,,of ,,light4   ,when a      
criminal judge has a right crafty knave 
before him1 one well versed in the arts 
of prevarication1 his main object is to 
wring a confession from the culprit by a

 few skilful questions4 ,in almost a    
similar position the natural philosopher
 seems to be placed with respect to     
nature4 ,true1 his functions here are   
more those of the spy than the judge2   
but his object remains pretty much the  
same4 ,her hidden motives and laws of   
action is what nature must be made to   
confess4 ,whether a confession will be  
extracted depends upon the shrewdness of
 the inquirer4 ,not without reason1     
therefore1 did ,lord ,bacon call the    
experimental method a questioning of    
nature4 ,the art consists in so putting 
our questions that they may not remain  
unanswered without a breach of          
etiquette4  ,look1 too1 at the countless
 tools1 engines1 and instruments of     
torture with which man conducts his     
inquisitions of nature1 and which mock  
the poet's words3      ,mysterious even 
in open day1     ,nature retains her    
veil1 despite our clamors2     ,that    
which she doth not willingly display    
,cannot be wrenched from her with       

levers1 screws1 and hammers4  ,look at  
these instruments and you will see that 
the comparison with torture also is     
admissible4#aa  ,this view of nature1 as
 of something designedly concealed from 
man1 that can be unveiled only by force 
or dishonesty1 chimed in better with the
 conceptions of the ancients than with  
modern notions4 ,a ,grecian philosopher 
once said1 in offering his opinion of   
the natural science of his time1 that it
 could only be displeasing to the gods  
to see men endeavoring to spy out what  
the gods were not minded to reveal to   
them4#ab ,of course all the             
contemporaries of the speaker were not  
of his opinion4  ,traces of this view   
may still be found to-day1 but upon the 
whole we are now not so narrow-minded4  
,we believe no longer that nature       
designedly hides herself4 ,we know now  
from the history of science that our    
questions are sometimes meaningless1 and
 that1 therefore1 no answer can be      
forthcoming4 ,soon we shall see how man1

 with all his thoughts and quests1 is   
only a fragment of nature's life4       
,picture1 then1 as your fancy dictates1 
the tools of the physicist as           
instruments of torture or as engines of 
endearment1 at all events a chapter from
 the history of those implements will be
 of interest to you1 and it will not be 
unpleasant to learn what were the       
peculiar difficulties that led to the   
invention of such strange apparatus4    
,galileo 7born at ,pisa in #aefd1 died  
at ,arcetri in #afdb7 was the first who 
asked what was the velocity of light1   
that is1 what time it would take for a  
light struck at one place to become     
visible at another1 a certain distance  
away4#ac  ,the method which ,galileo    
devised was as simple as it was natural4
 ,two practised observers1 with muffled 
lanterns1 were to take up positions in a
 dark night at a considerable distance  
from each other1 one at ,a and one at   
,b4 ,at a moment previously fixed upon1 
,a was instructed to unmask his lantern2

 while as soon as ,b saw the light of   
,a's lantern he was to unmask his4 ,now 
it is clear that the time which ,a      
counted from the uncovering of his      
lantern until he caught sight of the    
light of ,b's would be the time which it
 would take light to travel from ,a to  
,b and from ,b back to ,a4              
,illustration3 ,fig4 #ac4  ,the         
experiment was not executed1 nor could  
it1 in the nature of the case1 have been
 a success4 ,as we now know1 light      
travels too rapidly to be thus noted4   
,the time elapsing between the arrival  
of the light at ,b and its perception by
 the observer1 with that between the    
decision to uncover and the uncovering  
of the lantern1 is1 as we now know1     
incomparably greater than the time which
 it takes light to travel the greatest  
earthly distances4 ,the great velocity  
of light will be made apparent1 if we   
reflect that a flash of lightning in the
 night illuminates instantaneously a    
very extensive region1 whilst the single

 reflected claps of thunder arrive at   
the observer's ear very gradually and in
 appreciable succession4  ,during his   
life1 then1 the efforts of ,galileo to  
determine the velocity of light remained
 uncrowned with success4 ,but the       
subsequent history of the measurement of
 the velocity of light is intimately    
associated with his name1 for with the  
telescope which he constructed he       
discovered the four satellites of       
,jupiter1 and these furnished the next  
occasion for the determination of the   
velocity of light4  ,the terrestrial    
spaces were too small for ,galileo's    
experiment4 ,the measurement was first  
executed when the spaces of the         
planetary system were employed4 ,olaf   
,rmer1 7born at ,aarhuus in #afdd1 died 
at ,copenhagen in #agaj7 accomplished   
the feat 7#afge-afgf71 while watching   
with ,cassini at the observatory of     
,paris the revolutions of ,jupiter's    
moons4  ,illustration3 ,fig4 #ad4  ,let 
,,ab 7,fig4 #ad7 be ,jupiter's orbit4   

,let ,s stand for the sun1 ,e for the   
earth1 ,j for ,jupiter1 and ,t for      
,jupiter's first satellite4 ,when the   
earth is at ,e we see the satellite     
enter regularly into ,jupiter's shadow1 
and by watching the time between two    
successive eclipses1 can calculate its  
time of revolution4 ,the time which     
,rmer noted was forty-two hours1        
twenty-eight minutes1 and thirty-five   
seconds4 ,now1 as the earth passes along
 in its orbit towards ,e1 the           
revolutions of the satellite grow       
apparently longer and longer3 the       
eclipses take place later and later4    
,the greatest retardation of the        
eclipse1 which occurs when the earth is 
at ,e1 amounts to sixteen minutes and   
twenty-six seconds4 ,as the earth passes
 back again to ,e1 the revolutions grow 
apparently shorter1 and they occur in   
exactly the time that they first did    
when the earth arrives at ,e4 ,it is to 
be remarked that ,jupiter changes only  
very slightly its position during one   

revolution of the earth4 ,rmer guessed  
at once that these periodical changes of
 the time of revolution of ,jupiter's   
satellite were not actual1 but apparent 
changes1 which were in some way         
connected with the velocity of light4   
,let us make this matter clear to       
ourselves by a simile4 ,we receive      
regularly by the post1 news of the      
political status at our capital4        
,however far away we may be from the    
capital1 we hear the news of every      
event1 later it is true1 but of all     
equally late4 ,the events reach us in   
the same succession of time as that in  
which they took place4 ,but if we are   
travelling away from the capital1 every 
successive post will have a greater     
distance to pass over1 and the events   
will reach us more slowly than they took
 place4 ,the reverse will be the case if
 we are approaching the capital4  ,at   
rest1 we hear a piece of music played in
 the same tempo at all distances4 ,but  
the tempo will be seemingly accelerated 

if we are carried rapidly towards the   
band1 or retarded if we are carried     
rapidly away from it4#ad  ,illustration3
 ,fig4 #ae4  ,picture to yourself a     
cross1 say the sails of a wind-mill     
7,fig4 #ae71 in uniform rotation about  
its centre4 ,clearly1 the rotation of   
the cross will appear to you more slowly
 executed if you are carried very       
rapidly away from it4 ,for the post     
which in this case conveys to you the   
light and brings to you the news of the 
successive positions of the cross will  
have to travel in each successive       
instant over a longer path4  ,now this  
must also be the case with the rotation 
7the revolution7 of the satellite of    
,jupiter4 ,the greatest retardation of  
the eclipse 7#af minutes71 due to the   
passage of the earth from ,e to ,e1 or  
to its removal from ,jupiter by a       
distance equal to the diameter of the   
orbit of the earth1 plainly corresponds 
to the time which it takes light to     
traverse a distance equal to the        

diameter of the earth's orbit4 ,the     
velocity of light1 that is1 the distance
 described by light in a second1 as     
determined by this calculation1 is      
#caa1jjj kilometres1#ae or #aic1jjj     
miles4 ,a subsequent correction of the  
diameter of the earth's orbit1 gives1 by
 the same method1 the velocity of light 
as approximately #ahf1jjj miles a       
second4  ,the method is exactly that of 
,galileo2 only better conditions are    
selected4 ,instead of a short           
terrestrial distance we have the        
diameter of the earth's orbit1 three    
hundred and seven million kilometres2 in
 place of the uncovered and covered     
lanterns we have the satellite of       
,jupiter1 which alternately appears and 
disappears4 ,galileo1 therefore1        
although he could not carry out himself 
the proposed measurement1 found the     
lantern by which it was ultimately      
executed4  ,physicists did not long     
remain satisfied with this beautiful    
discovery4 ,they sought after easier    

methods of measuring the velocity of    
light1 such as might be performed on the
 earth4 ,this was possible after the    
difficulties of the problem were clearly
 exposed4 ,a measurement of the kind    
referred to was executed in #ahdi by    
,fizeau 7born at ,paris in #ahai74  ,i  
shall endeavor to make the principle of 
,fizeau's apparatus clear to you4 ,let s
 7,fig4 #af7 be a disk free to rotate   
about its centre1 and perforated at its 
rim with a series of holes4 ,let l be a 
luminous point casting its light on an  
unsilvered glass1 a1 inclined at an     
angle of forty-five degrees to the axis 
of the disk4 ,the ray of light1         
reflected at this point1 passes through 
one of the holes of the disk and falls  
at right angles upon a mirror b1 erected
 at a point about five miles distant4   
,from the mirror b the light is again   
reflected1 passes once more through the 
hole in s1 and1 penetrating the glass   
plate1 finally strikes the eye1 o1 of   
the observer4 ,the eye1 o1 thus1 sees   

the image of the luminous point l       
through the glass plate and the hole of 
the disk in the mirror b4               
,illustration3 ,fig4 #af4  ,if1 now1 the
 disk be set in rotation1 the unpierced 
spaces between the apertures will       
alternately take the place of the       
apertures1 and the eye o will now see   
the image of the luminous point in b    
only at interrupted intervals4 ,on      
increasing the rapidity of the rotation1
 however1 the interruptions for the eye 
become again unnoticeable1 and the eye  
sees the mirror b uniformly illuminated4
  ,but all this holds true only for     
relatively small velocities of the disk1
 when the light sent through an aperture
 in s to b on its return strikes the    
aperture at almost the same place and   
passes through it a second time4        
,conceive1 now1 the speed of the disk to
 be so increased that the light on its  
return finds before it an unpierced     
space instead of an aperture1 it will   
then no longer be able to reach the eye4

 ,we then see the mirror b only when no 
light is emitted from it1 but only when 
light is sent to it2 it is covered when 
light comes from it4 ,in this case1     
accordingly1 the mirror will always     
appear dark4  ,if the velocity of       
rotation at this point were still       
further increased1 the light sent       
through one aperture could not1 of      
course1 on its return pass through the  
same aperture but might strike the next 
and reach the eye by that4 ,hence1 by   
constantly increasing the velocity of   
the rotation1 the mirror b may be made  
to appear alternately bright and dark4  
,plainly1 now1 if we know the number of 
apertures of the disk1 the number of    
rotations per second1 and the distance  
sb1 we can calculate the velocity of    
light4 ,the result agrees with that     
obtained by ,rmer4  ,the experiment is  
not quite as simple as my exposition    
might lead you to believe4 ,care must be
 taken that the light shall travel back 
and forth over the miles of distance sb 

and bs undispersed4 ,this difficulty is 
obviated by means of telescopes4  ,if we
 examine ,fizeau's apparatus closely1 we
 shall recognise in it an old           
acquaintance3 the arrangement of        
,galileo's experiment4 ,the luminous    
point l is the lantern ,a1 while the    
rotation of the perforated disk performs
 mechanically the uncovering and        
covering of the lantern4 ,instead of the
 unskilful observer ,b we have the      
mirror b1 which is unfailingly          
illuminated the instant the light       
arrives from s4 ,the disk s1 by         
alternately transmitting and            
intercepting the reflected light1       
assists the observer o4 ,galileo's      
experiment is here executed1 so to      
speak1 countless times in a second1 yet 
the total result admits of actual       
observation4 ,if ,i might be pardoned   
the use of a phrase of ,darwin's in this
 field1 ,i should say that ,fizeau's    
apparatus was the descendant of         
,galileo's lantern4  ,a still more      

refined and delicate method for the     
measurement of the velocity of light was
 employed by ,foucault1 but a           
description of it here would lead us too
 far from our subject4  ,the measurement
 of the velocity of sound is easily     
executed by the method of ,galileo4 ,it 
was unnecessary1 therefore1 for         
physicists to rack their brains further 
about the matter2 but the idea which    
with light grew out of necessity was    
applied also in this field4 ,koenig of  
,paris constructs an apparatus for the  
measurement of the velocity of sound    
which is closely allied to the method of
 ,fizeau4  ,the apparatus is very       
simple4 ,it consists of two electrical  
clock-works which strike simultaneously1
 with perfect precision1 tenths of      
seconds4 ,if we place the two           
clock-works directly side by side1 we   
hear their strokes simultaneously1      
wherever we stand4 ,but if we take our  
stand by the side of one of the works   
and place the other at some distance    

from us1 in general a coincidence of the
 strokes will now not be heard4 ,the    
companion strokes of the remote         
clock-work arrive1 as sound1 later4 ,the
 first stroke of the remote work is     
heard1 for example1 immediately after   
the first of the adjacent work1 and so  
on4 ,but by increasing the distance we  
may produce again a coincidence of the  
strokes4 ,for example1 the first stroke 
of the remote work coincides with the   
second of the near work1 the second of  
the remote work with the third of the   
near work1 and so on4 ,if1 now1 the     
works strike tenths of seconds and the  
distance between them is increased until
 the first coincidence is noted1 plainly
 that distance is travelled over by the 
sound in a tenth of a second4  ,we meet 
frequently the phenomenon here          
presented1 that a thought which         
centuries of slow and painful endeavor  
are necessary to produce1 when once     
developed1 fairly thrives4 ,it spreads  
and runs everywhere1 even entering minds

 in which it could never have arisen4   
,it simply cannot be eradicated4  ,the  
determination of the velocity of light  
is not the only case in which the direct
 perception of the senses is too slow   
and clumsy for use4 ,the usual method of
 studying events too fleet for direct   
observation consists in putting into    
reciprocal action with them other events
 already known1 the velocities of all of
 which are capable of comparison4 ,the  
result is usually unmistakable1 and     
susceptible of direct inference         
respecting the character of the event   
which is unknown4 ,the velocity of      
electricity cannot be determined by     
direct observation4 ,but it was         
ascertained by ,wheatstone1 simply by   
the expedient of watching an electric   
spark in a mirror rotating with         
tremendous known velocity4              
,illustration3 ,fig4 #ag4               
,illustration3 ,fig4 #ah4  ,if we wave a
 staff irregularly hither and thither1  
simple observation cannot determine how 

quickly it moves at each point of its   
course4 ,but let us look at the staff   
through holes in the rim of a rapidly   
rotating disk 7,fig4 #ag74 ,we shall    
then see the moving staff only in       
certain positions1 namely1 when a hole  
passes in front of the eye4 ,the single 
pictures of the staff remain for a time 
impressed upon the eye2 we think we see 
several staffs1 having some such        
disposition as that represented in ,fig4
 #ah4 ,if1 now1 the holes of the disk   
are equally far apart1 and the disk is  
rotated with uniform velocity1 we see   
clearly that the staff has moved slowly 
from a to b1 more quickly from b to c1  
still more quickly from c to d1 and with
 its greatest velocity from d to e4  ,a 
jet of water flowing from an orifice in 
the bottom of a vessel has the          
appearance of perfect quiet and         
uniformity1 but if we illuminate it for 
a second1 in a dark room1 by means of an
 electric flash we shall see that the   
jet is composed of separate drops4 ,by  

their quick descent the images of the   
drops are obliterated and the jet       
appears uniform4 ,let us look at the jet
 through the rotating disk4 ,the disk is
 supposed to be rotated so rapidly that 
while the second aperture passes into   
the place of the first1 drop #a falls   
into the place of #b1 #b into the place 
of #c1 and so on4 ,we see drops then    
always in the same places4 ,the jet     
appears to be at rest4 ,if we turn the  
disk a trifle more slowly1 then while   
the second aperture passes into the     
place of the first1 drop #a will have   
fallen somewhat lower than #b1 #b       
somewhat lower than #c1 etc4 ,through   
every successive aperture we shall see  
drops in successively lower positions4  
,the jet will appear to be flowing      
slowly downwards4  ,illustration3 ,fig4 
#ai4  ,now let us turn the disk more    
rapidly4 ,then while the second aperture
 is passing into the place of the first1
 drop #a will not quite have reached the
 place of #b1 but will be found slightly

 above #b1 #b slightly above #c1 etc4   
,through the successive apertures we    
shall see the drops at successively     
higher places4 ,it will now look as if  
the jet were flowing upwards1 as if the 
drops were rising from the lower vessel 
into the higher4  ,you see1 physics     
grows gradually more and more terrible4 
,the physicist will soon have it in his 
power to play the part of the famous    
lobster chained to the bottom of the    
,lake of ,mohrin1 whose direful mission1
 if ever liberated1 the poet ,kopisch   
humorously describes as that of a       
reversal of all the events of the world2
 the rafters of houses become trees     
again1 cows calves1 honey flowers1      
chickens eggs1 and the poet's own poem  
flows back into his inkstand4         99
       99       99       99       99    
,you will now allow me the privilege of 
a few general remarks4 ,you have seen   
that the same principle often lies at   
the basis of large classes of apparatus 
designed for different purposes4        

,frequently it is some very unobtrusive 
idea which is productive of so much     
fruit and of such extensive             
transformations in physical technics4   
,it is not otherwise here than in       
practical life4  ,the wheel of a waggon 
appears to us a very simple and         
insignificant creation4 ,but its        
inventor was certainly a man of genius4 
,the round trunk of a tree perhaps first
 accidentally led to the observation of 
the ease with which a load can be moved 
on a roller4 ,now1 the step from a      
simple supporting roller to a fixed     
roller1 or wheel1 appears a very easy   
one4 ,at least it appears very easy to  
us who are accustomed from childhood up 
to the action of the wheel4 ,but if we  
put ourselves vividly into the position 
of a man who never saw a wheel1 but had 
to invent one1 we shall begin to have   
some idea of its difficulties4 ,indeed1 
it is even doubtful whether a single man
 could have accomplished this feat1     
whether perhaps centuries were not      

necessary to form the first wheel from  
the primitive roller4#af  ,history does 
not name the progressive minds who      
constructed the first wheel2 their time 
lies far back of the historic period4   
,no scientific academy crowned their    
efforts1 no society of engineers elected
 them honorary members4 ,they still live
 only in the stupendous results which   
they called forth4 ,take from us the    
wheel1 and little will remain of the    
arts and industries of modern life4 ,all
 disappears4 ,from the spinning-wheel to
 the spinning-mill1 from the            
turning-lathe to the rolling-mill1 from 
the wheelbarrow to the railway train1   
all vanishes4  ,in science the wheel is 
equally important4 ,whirling machines1  
as the simplest means of obtaining quick
 motions with inconsiderable changes of 
place1 play a part in all branches of   
physics4 ,you know ,wheatstone's        
rotating mirror1 ,fizeau's wheel1       
,plateau's perforated rotating disks1   
etc4 ,almost the same principle lies at 

the basis of all these apparatus4 ,they 
differ from one another no more than the
 pen-knife differs1 in the purposes it  
serves1 from the knife of the anatomist 
or the knife of the vine-dresser4       
,almost the same might be said of the   
screw4  ,it will now perhaps be clear to
 you that new thoughts do not spring up 
suddenly4 ,thoughts need their time to  
ripen1 grow1 and develop in1 like every 
natural product2 for man1 with his      
thoughts1 is also a part of nature4     
,slowly1 gradually1 and laboriously one 
thought is transformed into a different 
thought1 as in all likelihood one animal
 species is gradually transformed into  
new species4 ,many ideas arise          
simultaneously4 ,they fight the battle  
for existence not otherwise than do the 
,ichthyosaurus1 the ,brahman1 and the   
horse4  ,a few remain to spread rapidly 
over all fields of knowledge1 to be     
redeveloped1 to be again split up1 to   
begin again the struggle from the start4
 ,as many animal species long since     

conquered1 the relicts of ages past1    
still live in remote regions where their
 enemies cannot reach them1 so also we  
find conquered ideas still living on in 
the minds of many men4 ,whoever will    
look carefully into his own soul will   
acknowledge that thoughts battle as     
obstinately for existence as animals4   
,who will gainsay that many vanquished  
modes of thought still haunt obscure    
crannies of his brain1 too faint-hearted
 to step out into the clear light of    
reason8 ,what inquirer does not know    
that the hardest battle1 in the         
transformation of his ideas1 is fought  
with himself4  ,similar phenomena meet  
the natural inquirer in all paths and in
 the most trifling matters4 ,the true   
inquirer seeks the truth everywhere1 in 
his country-walks and on the streets of 
the great city4 ,if he is not too       
learned1 he will observe that certain   
things1 like ladies' hats1 are          
constantly subject to change4 ,i have   
not pursued special studies on this     

subject1 but as long as ,i can remember1
 one form has always gradually changed  
into another4 ,first1 they wore hats    
with long projecting rims1 within which1
 scarcely accessible with a telescope1  
lay concealed the face of the beautiful 
wearer4 ,the rim grew smaller and       
smaller2 the bonnet shrank to the irony 
of a hat4 ,now a tremendous             
superstructure is beginning to grow up  
in its place1 and the gods only know    
what its limits will be4 ,it is not     
otherwise with ladies' hats than with   
butterflies1 whose multiplicity of form 
often simply comes from a slight        
excrescence on the wing of one species  
developing in a cognate species to a    
tremendous fold4 ,nature1 too1 has its  
fashions1 but they last thousands of    
years4 ,i could elucidate this idea by  
many additional examples2 for instance1 
by the history of the evolution of the  
coat1 if ,i were not fearful that my    
gossip might prove irksome to you4      
99       99       99       99       99  

,we have now wandered through an odd    
corner of the history of science4 ,what 
have we learned8 ,the solution of a     
small1 ,i might almost say              
insignificant1 problem--the measurement 
of the velocity of light4 ,and more than
 two centuries have worked at its       
solution6 ,three of the most eminent    
natural philosophers1 ,galileo1 an      
,italian1 ,rmer1 a ,dane1 and ,fizeau1 a
 ,frenchman1 have fairly shared its     
labors4 ,and so it is with countless    
other questions4 ,when we contemplate   
thus the many blossoms of thought that  
must wither and fall before one shall   
bloom1 then shall we first truly        
appreciate ,christ's weighty but little 
consolatory words3 ,many be called but  
few are chosen4  ,such is the testimony 
of every page of history4 ,but is       
history right8 ,are really only those   
chosen whom she names8 ,have those lived
 and battled in vain1 who have won no   
prize8  ,i doubt it4 ,and so will every 
one who has felt the pangs of sleepless 

nights spent in thought1 at first       
fruitless1 but in the end successful4   
,no thought in such struggles was       
thought in vain2 each one1 even the most
 insignificant1 nay1 even the erroneous 
thought1 that which apparently was the  
least productive1 served to prepare the 
way for those that afterwards bore      
fruit4 ,and as in the thought of the    
individual naught is in vain1 so1 also1 
it is in that of humanity4  ,galileo    
wished to measure the velocity of light4
 ,he had to close his eyes before his   
wish was realised4 ,but he at least     
found the lantern by which his successor
 could accomplish the task4  ,and so ,i 
may maintain that we all1 so far as     
inclination goes1 are working at the    
civilisation of the future4 ,if only we 
all strive for the right1 then are we   
all called and all chosen6              
,,footnotes3    ,footnote #aa3          
,according to ,mr4 ,jules ,andrieu1 the 
idea that nature   must be tortured to  
reveal her secrets is preserved in the  

name   crucible--from the ,latin crux1 a
 cross4 ,but1 more probably1   crucible 
is derived from some ,old ,french or    
,teutonic form1 as   cruche1 kroes1     
krus1 etc41 a pot or jug 7cf4 ,modern   
,english   crock1 cruse1 and ,german    
,krug74--,trans4    ,footnote #ab3      
,xenophon1 ,memorabilia iv1 #g1 puts    
into the mouth of   ,socrates these     
words3 ,greek3 oute gar heureta         
anthrpois auta   enomizen einai1 oute   
chaoizesthai theois an hgeito ton       
ztounta ha   ekeinoi saphnisai ouk      
eboulthsan4    ,footnote #ac3 ,galilei1 
,discorsi e dimostrazione matematiche4  
,leyden1 #afch4 ,dialogo ,primo4        
,footnote #ad3 ,in the same way1 the    
pitch of a locomotive-whistle is        
higher as the locomotive rapidly        
approaches an observer1 and lower   when
 rapidly leaving him than if the        
locomotive were at   rest4--,trans4     
,footnote #ae3 ,a kilometre is #j4fba or
 nearly five-eighths of a   statute     
mile4    ,footnote #af3 ,observe1 also1 

the respect in which the wheel is held  
in ,india1 ,japan and other ,buddhistic 
countries1 as the emblem of   power1    
order1 and law1 and of the superiority  
of mind over matter4   ,the             
consciousness of the importance of this 
invention seems to have   lingered long 
in the minds of these nations4--,tr4    
,,why ,,has ,,man ,,two ,,eyes8   ,why  
has man two eyes8 ,that the pretty      
symmetry of his face may not be         
disturbed1 the artist answers4 ,that his
 second eye may furnish a substitute for
 his first if that be lost1 says the    
far-sighted economist4 ,that we may weep
 with two eyes at the sins of the world1
 replies the religious enthusiast4  ,odd
 opinions6 ,yet if you should approach a
 modern scientist with this question you
 might consider yourself fortunate if   
you escaped with less than a rebuff4    
,pardon me1 madam1 or my dear sir1 he   
would say1 with stern expression1 man   
fulfils no purpose in the possession of 
his eyes2 nature is not a person1 and   

consequently not so vulgar as to pursue 
purposes of any kind4  ,still an        
unsatisfactory answer6 ,i once knew a   
professor who would shut with horror the
 mouths of his pupils if they put to him
 such an unscientific question4  ,but   
ask a more tolerant person1 ask me4 ,i1 
,i candidly confess1 do not know exactly
 why man has two eyes1 but the reason   
partly is1 ,i think1 that ,i may see you
 here before me to-night and talk with  
you upon this delightful subject4       
,again you smile incredulously4 ,now    
this is one of those questions that a   
hundred wise men together could not     
answer4 ,you have heard1 so far1 only   
five of these wise men4 ,you will       
certainly want to be spared the opinions
 of the other ninety-five4 ,to the first
 you will reply that we should look just
 as pretty if we were born with only one
 eye1 like the ,cyclops2 to the second  
we should be much better off1 according 
to his principle1 if we had four or     
eight eyes1 and that in this respect we 

are vastly inferior to spiders2 to the  
third1 that you are not just in the mood
 to weep2 to the fourth1 that the       
unqualified interdiction of the question
 excites rather than satisfies your     
curiosity2 while of me you will dispose 
by saying that my pleasure is not as    
intense as ,i think1 and certainly not  
great enough to justify the existence of
 a double eye in man since the fall of  
,adam4  ,but since you are not satisfied
 with my brief and obvious answer1 you  
have only yourselves to blame for the   
consequences4 ,you must now listen to a 
longer and more learned explanation1    
such as it is in my power to give4  ,as 
the church of science1 however1 debars  
the question ,why8 let us put the matter
 in a purely orthodox way3 ,man has two 
eyes1 what more can he see with two than
 with one8  ,i will invite you to take a
 walk with me8 ,we see before us a wood4
 ,what is it that makes this real wood  
contrast so favorably with a painted    
wood1 no matter how perfect the painting

 may be8 ,what makes the one so much    
more lovely than the other8 ,is it the  
vividness of the coloring1 the          
distribution of the lights and the      
shadows8 ,i think not4 ,on the contrary1
 it seems to me that in this respect    
painting can accomplish very much4  ,the
 cunning hand of the painter can conjure
 up with a few strokes of his brush     
forms of wonderful plasticity4 ,by the  
help of other means even more can be    
attained4 ,photographs of reliefs are so
 plastic that we often imagine we can   
actually lay hold of the elevations and 
depressions4  ,illustration3 ,fig4 #bj4 
,but one thing the painter never can    
give with the vividness that nature     
does--the difference of near and far4   
,in the real woods you see plainly that 
you can lay hold of some trees1 but that
 others are inaccessibly far4 ,the      
picture of the painter is rigid4 ,the   
picture of the real woods changes on the
 slightest movement4 ,now this branch is
 hidden behind that2 now that behind    

this4 ,the trees are alternately visible
 and invisible4  ,let us look at this   
matter a little more closely4 ,for      
convenience sake we shall remain upon   
the highway1 ,i1 ,,ii4 7,fig4 #bj47 ,to 
the right and the left lies the forest4 
,standing at ,i1 we see1 let us say1    
three trees 7#a1 #b1 #c7 in a line1 so  
that the two remote ones are covered by 
the nearest4 ,moving further along1 this
 changes4 ,at ,,ii we shall not have to 
look round so far to see the remotest   
tree #c as to see the nearer tree #b1   
nor so far to see this as to see #a4    
,hence1 as we move onward1 objects that 
are near to us seem to lag behind as    
compared with objects that are remote   
from us1 the lagging increasing with the
 proximity of the objects4 ,very remote 
objects1 towards which we must always   
look in the same direction as we        
proceed1 appear to travel along with us4
  ,if we should see1 therefore1 jutting 
above the brow of yonder hill the tops  
of two trees whose distance from us we  

were in doubt about1 we should have in  
our hands a very easy means of deciding 
the question4 ,we should take a few     
steps forward1 say to the right1 and the
 tree-top which receded most to the left
 would be the one nearer to us4 ,in     
truth1 from the amount of the recession 
a geometer could actually determine the 
distance of the trees from us without   
ever going near them4 ,it is simply the 
scientific development of this          
perception that enables us to measure   
the distances of the stars4  ,hence1    
from change of view in forward motion   
the distances of objects in our field of
 vision can be measured4  ,rigorously1  
however1 even forward motion is not     
necessary4 ,for every observer is       
composed really of two observers4 ,man  
has two eyes4 ,the right eye is a short 
step ahead of the left eye in the       
right-hand direction4 ,hence1 the two   
eyes receive different pictures of the  
same woods4 ,the right eye will see the 
near trees displaced to the left1 and   

the left eye will see them displaced to 
the right1 the displacement being       
greater1 the greater the proximity4     
,this difference is sufficient for      
forming ideas of distance4  ,we may now 
readily convince ourselves of the       
following facts3  #a4 ,with one eye1 the
 other being shut1 you have a very      
uncertain judgment of distances4 ,you   
will find it1 for example1 no easy task1
 with one eye shut1 to thrust a stick   
through a ring hung up before you2 you  
will miss the ring in almost every      
instance4  #b4 ,you see the same object 
differently with the right eye from what
 you do with the left4  ,place a        
lamp-shade on the table in front of you 
with its broad opening turned downwards1
 and look at it from above4 7,fig4 #ba47
 ,you will see with your right eye the  
image #b1 with your left eye the image  
#a4 ,again1 place the shade with its    
wide opening turned upwards2 you will   
receive with your right eye the image   
#d1 with your left eye the image #c4    

,euclid mentions phenomena of this      
character4  #c4 ,finally1 you know that 
it is easy to judge of distances with   
both eyes4 ,accordingly your judgment   
must spring in some way from a          
co-operation of the two eyes4 ,in the   
preceding example the openings in the   
different images received by the two    
eyes seem displaced with respect to one 
another1 and this displacement is       
sufficient for the inference that the   
one opening is nearer than the other4   
,illustration3 ,fig4 #ba4  ,i have no   
doubt that you1 ladies1 have frequently 
received delicate compliments upon your 
eyes1 but ,i feel sure that no one has  
ever told you1 and ,i know not whether  
it will flatter you1 that you have in   
your eyes1 be they blue or black1 little
 geometricians4 ,you say you know       
nothing of them8 ,well1 for that matter1
 neither do ,i4 ,but the facts are as ,i
 tell you4  ,you understand little of   
geometry8 ,i shall accept that          
confession4 ,yet with the help of your  

two eyes you judge of distances8 ,surely
 that is a geometrical problem4 ,and    
what is more1 you know the solution of  
this problem3 for you estimate distances
 correctly4 ,if1 then1 you do not solve 
the problem1 the little geometricians in
 your eyes must do it clandestinely and 
whisper the solution to you4 ,i doubt   
not they are fleet little fellows4      
,what amazes me most here is1 that you  
know nothing about these little         
geometricians4 ,but perhaps they also   
know nothing about you4 ,perhaps they   
are models of punctuality1 routine      
clerks who bother about nothing but     
their fixed work4 ,in that case we may  
be able to deceive the gentlemen4  ,if  
we present to our right eye an image    
which looks exactly like the lamp-shade 
for the right eye1 and to our left eye  
an image which looks exactly like a     
lamp-shade for the left eye1 we shall   
imagine that we see the whole lamp-shade
 bodily before us4  ,you know the       
experiment4 ,if you are practised in    

squinting1 you can perform it directly  
with the figure1 looking with your right
 eye at the right image1 and with your  
left eye at the left image4 ,in this way
 the experiment was first performed by  
,elliott4 ,improved and perfected1 its  
form is ,wheatstone's stereoscope1 made 
so popular and useful by ,brewster4  ,by
 taking two photographs of the same     
object from two different points1       
corresponding to the two eyes1 a very   
clear three-dimensional picture of      
distant places or buildings can be      
produced by the stereoscope4  ,but the  
stereoscope accomplishes still more than
 this4 ,it can visualise things for us  
which we never see with equal clearness 
in real objects4 ,you know that if you  
move much while your photograph is being
 taken1 your picture will come out like 
that of a ,hindu deity1 with several    
heads or several arms1 which1 at the    
spaces where they overlap1 show forth   
with equal distinctness1 so that we seem
 to see the one picture through the     

other4 ,if a person moves quickly away  
from the camera before the impression is
 completed1 the objects behind him will 
also be imprinted upon the photograph2  
the person will look transparent4       
,photographic ghosts are made in this   
way4  ,some very useful applications may
 be made of this discovery4 ,for        
example1 if we photograph a machine     
stereoscopically1 successively removing 
during the operation the single parts   
7where of course the impression suffers 
interruptions71 we obtain a transparent 
view1 endowed with all the marks of     
spatial solidity1 in which is distinctly
 visualised the interaction of parts    
normally concealed4 ,i have employed    
this method for obtaining transparent   
stereoscopic views of anatomical        
structures4  ,you see1 photography is   
making stupendous advances1 and there is
 great danger that in time some         
malicious artist will photograph his    
innocent patrons with solid views of    
their most secret thoughts and emotions4

 ,how tranquil politics will then be6   
,what rich harvests our detective force 
will reap6         99       99       99 
99       99  ,by the joint action of the
 two eyes1 therefore1 we arrive at our  
judgments of distances1 as also of the  
forms of bodies4  ,permit me to mention 
here a few additional facts connected   
with this subject1 which will assist us 
in the comprehension of certain         
phenomena in the history of             
civilisation4  ,you have often heard1   
and know from personal experience1 that 
remote objects appear perspectively     
dwarfed4 ,in fact1 it is easy to satisfy
 yourself that you can cover the image  
of a man a few feet away from you simply
 by holding up your finger a short      
distance in front of your eye4 ,still1  
as a general rule1 you do not notice    
this shrinkage of objects4 ,on the      
contrary1 you imagine you see a man at  
the end of a large hall1 as large as you
 see him near by you4 ,for your eye1 in 
its measurement of the distances1 makes 

remote objects correspondingly larger4  
,the eye1 so to speak1 is aware of this 
perspective contraction and is not      
deceived by it1 although its possessor  
is unconscious of the fact4 ,all persons
 who have attempted to draw from nature 
have vividly felt the difficulty which  
this superior dexterity of the eye      
causes the perspective conception4 ,not 
until one's judgment of distances is    
made uncertain1 by their size1 or from  
lack of points of reference1 or from    
being too quickly changed1 is the       
perspective rendered very prominent4    
,on sweeping round a curve on a rapidly 
moving railway train1 where a wide      
prospect is suddenly opened up1 the men 
upon distant hills appear like dolls4#ag
 ,you have at the moment1 here1 no known
 references for the measurement of      
distances4 ,the stones at the entrance  
of a tunnel grow visibly larger as we   
ride towards it2 they shrink visibly in 
size as we ride from it4  ,usually both 
eyes work together4 ,as certain views   

are frequently repeated1 and lead always
 to substantially the same judgments of 
distances1 the eyes in time must acquire
 a special skill in geometrical         
constructions4 ,in the end1 undoubtedly1
 this skill is so increased that a      
single eye alone is often tempted to    
exercise that office4  ,permit me to    
elucidate this point by an example4 ,is 
any sight more familiar to you than that
 of a vista down a long street8 ,who has
 not looked with hopeful eyes time and  
again into a street and measured its    
depth4 ,i will take you now into an     
art-gallery where ,i will suppose you to
 see a picture representing a vista into
 a street4 ,the artist has not spared   
his rulers to get his perspective       
perfect4 ,the geometrician in your left 
eye thinks1 ,ah ha6 ,i have computed    
that case a hundred times or more4 ,i   
know it by heart4 ,it is a vista into a 
street1 he continues2 where the houses  
are lower is the remote end4 ,the       
geometrician in the right eye1 too much 

at his ease to question his possibly    
peevish comrade in the matter1 answers  
the same4 ,but the sense of duty of     
these punctual little fellows is at once
 rearoused4 ,they set to work at their  
calculations and immediately find that  
all the points of the picture are       
equally distant from them1 that is1 lie 
all upon a plane surface4  ,what opinion
 will you now accept1 the first or the  
second8 ,if you accept the first you    
will see distinctly the vista4 ,if you  
accept the second you will see nothing  
but a painted sheet of distorted images4
  ,it seems to you a trifling matter to 
look at a picture and understand its    
perspective4 ,yet centuries elapsed     
before humanity came fully to appreciate
 this trifle1 and even the majority of  
you first learned it from education4  ,i
 can remember very distinctly that at   
three years of age all perspective      
drawings appeared to me as gross        
caricatures of objects4 ,i could not    
understand why artists made tables so   

broad at one end and so narrow at the   
other4 ,real tables seemed to me just as
 broad at one end as at the other1      
because my eye made and interpreted its 
calculations without my intervention4   
,but that the picture of the table on   
the plane surface was not to be         
conceived as a plane painted surface but
 stood for a table and so was to be     
imaged with all the attributes of       
extension was a joke that ,i did not    
understand4 ,but ,i have the consolation
 that whole nations have not understood 
it4  ,ingenuous people there are who    
take the mock murders of the stage for  
real murders1 the dissembled actions of 
the players for real actions1 and who   
can scarcely restrain themselves1 when  
the characters of the play are sorely   
pressed1 from running in deep           
indignation to their assistance4        
,others1 again1 can never forget that   
the beautiful landscapes of the stage   
are painted1 that ,richard ,,iii4 is    
only the actor1 ,mr4 ,booth1 whom they  

have met time and again at the clubs4   
,both points of view are equally        
mistaken4 ,to look at a drama or a      
picture properly one must understand    
that both are shows1 simply denoting    
something real4 ,a certain preponderance
 of the intellectual life over the      
sensuous life is requisite for such an  
achievement1 where the intellectual     
elements are safe from destruction by   
the direct sensuous impressions4 ,a     
certain liberty in choosing one's point 
of view is necessary1 a sort of humor1  
,i might say1 which is strongly wanting 
in children and in childlike peoples4   
,let us look at a few historical facts4 
,i shall not take you as far back as the
 stone age1 although we possess sketches
 from this epoch which show very        
original ideas of perspective4 ,but let 
us begin our sight-seeing in the tombs  
and ruined temples of ancient ,egypt1   
where the numberless reliefs and        
gorgeous colorings have defied the      
ravages of thousands of years4  ,a rich 

and motley life is here opened to us4   
,we find the ,egyptians represented in  
all conditions of life4 ,what at once   
strikes our attention in these pictures 
is the delicacy of their technical      
execution4 ,the contours are extremely  
exact and distinct4 ,but on the other   
hand only a few bright colors are found1
 unblended and without trace of         
transition4 ,shadows are totally        
wanting4 ,the paint is laid on the      
surfaces in equal thicknesses4          
,shocking for the modern eye is the     
perspective4 ,all the figures are       
equally large1 with the exception of the
 king1 whose form is unduly exaggerated4
 ,near and far appear equally large4    
,perspective contraction is nowhere     
employed4 ,a pond with water-fowl is    
represented flat1 as if its surface were
 vertical4  ,human figures are portrayed
 as they are never seen1 the legs from  
the side1 the face in profile4 ,the     
breast lies in its full breadth across  
the plane of representation4 ,the heads 

of cattle appear in profile1 while the  
horns lie in the plane of the drawing4  
,the principle which the ,egyptians     
followed might be best expressed by     
saying that their figures are pressed in
 the plane of the drawing as plants are 
pressed in a herbarium4  ,the matter is 
simply explained4 ,if the ,egyptians    
were accustomed to looking at things    
ingenuously with both eyes at once1 the 
construction of perspective pictures in 
space could not be familiar to them4    
,they saw all arms1 all legs on real men
 in their natural lengths4 ,the figures 
pressed into the planes resembled more  
closely1 of course1 in their eyes the   
originals than perspective pictures     
could4  ,this will be better understood 
if we reflect that painting was         
developed from relief4 ,the minor       
dissimilarities between the pressed     
figures and the originals must gradually
 have compelled men to the adoption of  
perspective drawing4 ,but               
physiologically the painting of the     

,egyptians is just as much justified as 
the drawings of our children are4  ,a   
slight advance beyond the ,egyptians is 
shown by the ,assyrians4 ,the reliefs   
rescued from the ruined mounds of       
,nimrod at ,mossul are1 upon the whole1 
similar to the ,egyptian reliefs4 ,they 
were made known to us principally by    
,layard4  ,painting enters on a new     
phase among the ,chinese4 ,this people  
have a marked feeling for perspective   
and correct shading1 yet without being  
very logical in the application of their
 principles4 ,here1 too1 it seems1 they 
took the first step but did not go far4 
,in harmony with this immobility is     
their constitution1 in which the muzzle 
and the bamboo-rod play significant     
functions4 ,in accord with it1 too1 is  
their language1 which like the language 
of children has not yet developed into a
 grammar1 or1 rather1 according to the  
modern conception1 has not yet          
degenerated into a grammar4 ,it is the  
same also with their music which is     

satisfied with the five-toned scale4    
,the mural paintings at ,herculaneum and
 ,pompeii are distinguished by grace of 
representation1 as also by a pronounced 
sense for perspective and correct       
illumination1 yet they are not at all   
scrupulous in construction4 ,here still 
we find abbreviations avoided4 ,but to  
offset this defect1 the members of the  
body are brought into unnatural         
positions1 in which they appear in their
 full lengths4 ,abridgements are more   
frequently observed in clothed than in  
unclothed figures4  ,a satisfactory     
explanation of these phenomena first    
occurred to me on the making of a few   
simple experiments which show how       
differently one may see the same object1
 after some mastery of one's senses has 
been attained1 simply by the arbitrary  
movement of the attention4              
,illustration3 ,fig4 #bb4  ,look at the 
annexed drawing 7,fig4 #bb74 ,it        
represents a folded sheet of paper with 
either its depressed or its elevated    

side turned towards you1 as you wish4   
,you can conceive the drawing in either 
sense1 and in either case it will appear
 to you differently4  ,if1 now1 you have
 a real folded sheet of paper on the    
table before you1 with its sharp edges  
turned towards you1 you can1 on looking 
at it with one eye1 see the sheet       
alternately elevated1 as it really is1  
or depressed4 ,here1 however1 a         
remarkable phenomenon is presented4     
,when you see the sheet properly1       
neither illumination nor form presents  
anything conspicuous4 ,when you see it  
bent back you see it perspectively      
distorted4 ,light and shadow appear much
 brighter or darker1 or as if overlaid  
thickly with bright colors4 ,light and  
shadow now appear devoid of all cause4  
,they no longer harmonise with the      
body's form1 and are thus rendered much 
more prominent4  ,in common life we     
employ the perspective and illumination 
of objects to determine their forms and 
position4 ,hence we do not notice the   

lights1 the shadows1 and the            
distortions4 ,they first powerfully     
enter consciousness when we employ a    
different construction from the usual   
spatial one4 ,in looking at the planar  
image of a camera obscura we are amazed 
at the plenitude of the light and the   
profundity of the shadows1 both of which
 we do not notice in real objects4  ,in 
my earliest youth the shadows and lights
 on pictures appeared to me as spots    
void of meaning4 ,when ,i began to draw 
,i regarded shading as a mere custom of 
artists4 ,i once drew the portrait of   
our pastor1 a friend of the family1 and 
shaded1 from no necessity1 but simply   
from having seen something similar in   
other pictures1 the whole half of his   
face black4 ,i was subjected for this to
 a severe criticism on the part of my   
mother1 and my deeply offended artist's 
pride is probably the reason that these 
facts remained so strongly impressed    
upon my memory4  ,you see1 then1 that   
many strange things1 not only in the    

life of individuals1 but also in that of
 humanity1 and in the history of general
 civilisation1 may be explained from the
 simple fact that man has two eyes4     
,change man's eye and you change his    
conception of the world4 ,we have       
observed the truth of this fact among   
our nearest kin1 the ,egyptians1 the    
,chinese1 and the lake-dwellers2 how    
must it be among some of our remoter    
relatives1--with monkeys and other      
animals8 ,nature must appear totally    
different to animals equipped with      
substantially different eyes from those 
of men1 as1 for example1 to insects4    
,but for the present science must forego
 the pleasure of portraying this        
appearance1 as we know very little as   
yet of the mode of operation of these   
organs4  ,it is an enigma even how      
nature appears to animals closely       
related to man2 as to birds1 who see    
scarcely anything with two eyes at once1
 but since their eyes are placed on     
opposite sides of their heads1 have a   

separate field of vision for each4#ah   
,the soul of man is pent up in the      
prison-house of his head2 it looks at   
nature through its two windows1 the     
eyes4 ,it would also fain know how      
nature looks through other windows4 ,a  
desire apparently never to be fulfilled4
 ,but our love for nature is inventive1 
and here1 too1 much has been            
accomplished4  ,placing before me an    
angular mirror1 consisting of two plane 
mirrors slightly inclined to each other1
 ,i see my face twice reflected4 ,in the
 right-hand mirror ,i obtain a view of  
the right side1 and in the left-hand    
mirror a view of the left side1 of my   
face4 ,also ,i shall see the face of a  
person standing in front of me1 more to 
the right with my right eye1 more to the
 left with my left4 ,but in order to    
obtain such widely different views of a 
face as those shown in the angular      
mirror1 my two eyes would have to be set
 much further apart from each other than
 they actually are4  ,illustration3     

,fig4 #bc4  ,squinting with my right eye
 at the image in the right-hand mirror1 
with my left eye at the image in the    
left-hand mirror1 my vision will be the 
vision of a giant having an enormous    
head with his two eyes set far apart4   
,this1 also1 is the impression which my 
own face makes upon me4 ,i see it now1  
single and solid4 ,fixing my gaze1 the  
relief from second to second is         
magnified1 the eyebrows start forth     
prominently from above the eyes1 the    
nose seems to grow a foot in length1 my 
mustache shoots forth like a fountain   
from my lip1 the teeth seem to retreat  
immeasurably4 ,but by far the most      
horrible aspect of the phenomenon is the
 nose4  ,interesting in this connexion  
is the telestereoscope of ,helmholtz4   
,in the telestereoscope we view a       
landscape by looking with our right eye 
7,fig4 #bd7 through the mirror a into   
the mirror ,a1 and with our left eye    
through the mirror b into the mirror ,b4
 ,the mirrors ,a and ,b stand far apart4

 ,again we see with the widely separated
 eyes of a giant4 ,everything appears   
dwarfed and near us4 ,the distant       
mountains look like moss-covered stones 
at our feet4 ,between1 you see the      
reduced model of a city1 a veritable    
,liliput4 ,you are tempted almost to    
stroke with your hand the soft forest   
and city1 did you not fear that you     
might prick your fingers on the sharp1  
needle-shaped steeples1 or that they    
might crackle and break off4            
,illustration3 ,fig4 #bd4  ,liliput is  
no fable4 ,we need only ,swift's eyes1  
the telestereoscope1 to see it4         
,picture to yourself the reverse case4  
,let us suppose ourselves so small that 
we could take long walks in a forest of 
moss1 and that our eyes were            
correspondingly near each other4 ,the   
moss-fibres would appear like trees4 ,on
 them we should see strange1 unshapely  
monsters creeping about4 ,branches of   
the oak-tree1 at whose base our         
moss-forest lay1 would seem to us dark1 

immovable1 myriad-branched clouds1      
painted high on the vault of heaven2    
just as the inhabitants of ,saturn1     
forsooth1 might see their enormous ring4
 ,on the tree-trunks of our mossy       
woodland we should find colossal globes 
several feet in diameter1 brilliantly   
transparent1 swayed by the winds with   
slow1 peculiar motions4 ,we should      
approach inquisitively and should find  
that these globes1 in which here and    
there animals were gaily sporting1 were 
liquid globes1 in fact that they were   
water4 ,a short1 incautious step1 the   
slightest contact1 and woe betide us1   
our arm is irresistibly drawn by an     
invisible power into the interior of the
 sphere and held there unrelentingly    
fast6 ,a drop of dew has engulfed in its
 capillary maw a manikin1 in revenge for
 the thousands of drops that its big    
human counterparts have quaffed at      
breakfast4 ,thou shouldst have known1   
thou pygmy natural scientist1 that with 
thy present puny bulk thou shouldst not 

joke with capillarity6  ,my terror at   
the accident brings me back to my       
senses4 ,i see ,i have turned idyllic4  
,you must pardon me4 ,a patch of        
greensward1 a moss or heather forest    
with its tiny inhabitants have          
incomparably more charms for me than    
many a bit of literature with its       
apotheosis of human character4 ,if ,i   
had the gift of writing novels ,i should
 certainly not make ,john and ,mary my  
characters4 ,nor should ,i transfer my  
loving pair to the ,nile1 nor to the age
 of the old ,egyptian ,pharaohs1        
although perhaps ,i should choose that  
time in preference to the present4 ,for 
,i must candidly confess that ,i hate   
the rubbish of history1 interesting     
though it may be as a mere phenomenon1  
because we cannot simply observe it but 
must also feel it1 because it comes to  
us mostly with supercilious arrogance1  
mostly unvanquished4 ,the hero of my    
novel would be a cockchafer1 venturing  
forth in his fifth year for the first   

time with his newly grown wings into the
 light1 free air4 ,truly it could do no 
harm if man would thus throw off his    
inherited and acquired narrowness of    
mind by making himself acquainted with  
the world-view of allied creatures4 ,he 
could not help gaining incomparably more
 in this way than the inhabitant of a   
small town would in circumnavigating the
 globe and getting acquainted with the  
views of strange peoples4         99    
99       99       99       99  ,i have  
now conducted you1 by many paths and    
by-ways1 rapidly over hedge and ditch1  
to show you what wide vistas we may     
reach in every field by the rigorous    
pursuit of a single scientific fact4 ,a 
close examination of the two eyes of man
 has conducted us not only into the dim 
recesses of humanity's childhood1 but   
has also carried us far beyond the      
bourne of human life4  ,it has surely   
often struck you as strange that the    
sciences are divided into two great     
groups2 that the so-called humanistic   

sciences1 belonging to the so-called    
higher education1 are placed in almost a
 hostile attitude to the natural        
sciences4  ,i must confess ,i do not    
overmuch believe in this partition of   
the sciences4 ,i believe that this view 
will appear as childlike and ingenuous  
to a matured age as the want of         
perspective in the old paintings of     
,egypt does to us4 ,can it really be    
that higher culture is to be gotten only
 from a few old pots and palimpsests1   
which are at best mere scraps of nature1
 or that more is to be learned from them
 alone than from all the rest of nature8
 ,i believe that both these sciences are
 simply parts of the same science1 which
 have begun at different ends4 ,if these
 two ends still act towards each other  
as the ,montagues and ,capulets1 if     
their retainers still indulge in lively 
tilts1 ,i believe that after all they   
are not in earnest4 ,on the one side    
there is surely a ,romeo1 and on the    
other a ,juliet1 who1 some day1 it is   

hoped1 will unite the two houses with a 
less tragic sequel than that of the     
play4  ,philology began with the        
unqualified reverence and apotheosis of 
the ,greeks4 ,now it has begun to draw  
other languages1 other peoples and their
 histories1 into its sphere2 it has1    
through the mediation of comparative    
linguistics1 already struck up1 though  
as yet somewhat cautiously1 a friendship
 with physiology4  ,physical science    
began in the witch's kitchen4 ,it now   
embraces the organic and inorganic      
worlds1 and with the physiology of      
articulation and the theory of the      
senses1 has even pushed its researches1 
at times impertinently1 into the        
province of mental phenomena4  ,in      
short1 we come to the understanding of  
much within us solely by directing our  
glance without1 and vice versa4 ,every  
object belongs to both sciences4 ,you1  
ladies1 are very interesting and        
difficult problems for the psychologist1
 but you are also extremely pretty      

phenomena of nature4 ,church and ,state 
are objects of the historian's research1
 but not less phenomena of nature1 and  
in part1 indeed1 very curious phenomena4
 ,if the historical sciences have       
inaugurated wide extensions of view by  
presenting to us the thoughts of new and
 strange peoples1 the physical sciences 
in a certain sense do this in a still   
greater degree4 ,in making man disappear
 in the ,all1 in annihilating him1 so to
 speak1 they force him to take an       
unprejudiced position without himself1  
and to form his judgments by a different
 standard from that of the petty human4 
,but if you should ask me now why man   
has two eyes1 ,i should answer3  ,that  
he may look at nature justly and        
accurately2 that he may come to         
understand that he himself1 with all his
 views1 correct and incorrect1 with all 
his haute politique1 is simply an       
evanescent shred of nature2 that1 to    
speak with ,mephistopheles1 he is a part
 of the part1 and that it is absolutely 

unjustified1      ,for man1 the         
microcosmic fool1 to see     ,himself a 
whole so frequently4    ,,footnotes3    
,footnote #ag3 ,this effect is          
particularly noticeable in the size of  
workmen on high chimneys and            
church-steeples--steeple ,jacks4 ,when  
the cables were slung from the towers of
 the ,brooklyn bridge 7#bgg   feet      
high71 the men sent out in baskets to   
paint them1 appeared1   against the     
broad background of heaven and water1   
like   flies4--,trans4    ,footnote #ah3
 ,see ,joh4 ,mller1 ,vergleichende      
,physiologie des   ,gesichtssinnes1     
,leipsic1 #ahbf4     ,,on ,,symmetry4#ai
   ,an ancient philosopher once remarked
 that people who cudgelled their brains 
about the nature of the moon reminded   
him of men who discussed the laws and   
institutions of a distant city of which 
they had heard no more than the name4   
,the true philosopher1 he said1 should  
turn his glance within1 should study    
himself and his notions of right and    

wrong2 only thence could he derive real 
profit4  ,this ancient formula for      
happiness might be restated in the      
familiar words of the ,psalm3           
,dwell in the land1 and verily thou     
shalt be fed4  ,to-day1 if he could rise
 from the dead and walk about among us1 
this philosopher would marvel much at   
the different turn which matters have   
taken4  ,the motions of the moon and the
 other heavenly bodies are accurately   
known4 ,our knowledge of the motions of 
our own body is by far not so complete4 
,the mountains and natural divisions of 
the moon have been accurately outlined  
on maps1 but physiologists are just     
beginning to find their way in the      
geography of the brain4 ,the chemical   
constitution of many fixed stars has    
already been investigated4 ,the chemical
 processes of the animal body are       
questions of much greater difficulty and
 complexity4 ,we have our ,mcanique     
cleste4 ,but a ,mcanique sociale or a   
,mcanique morale of equal               

trustworthiness remains to be written4  
,our philosopher would indeed admit that
 we have made great progress4 ,but we   
have not followed his advice4 ,the      
patient has recovered1 but he took for  
his recovery exactly the opposite of    
what the doctor prescribed4  ,humanity  
is now returned1 much wiser1 from its   
journey in celestial space1 against     
which it was so solemnly warned4 ,men1  
after having become acquainted with the 
great and simple facts of the world     
without1 are now beginning to examine   
critically the world within4 ,it sounds 
absurd1 but it is true1 that only after 
we have thought about the moon are we   
able to take up ourselves4 ,it was      
necessary that we should acquire simple 
and clear ideas in a less complicated   
domain1 before we entered the more      
intricate one of psychology1 and with   
these ideas astronomy principally       
furnished us4  ,to attempt any          
description of that stupendous movement1
 which1 originally springing out of the 

physical sciences1 went beyond the      
domain of physics and is now occupied   
with the problems of psychology1 would  
be presumptuous in this place4 ,i shall 
only attempt here1 to illustrate to you 
by a few simple examples the methods by 
which the province of psychology can be 
reached from the facts of the physical  
world--especially the adjacent province 
of sense-perception4 ,and ,i wish it to 
be remembered that my brief attempt is  
not to be taken as a measure of the     
present state of such scientific        
questions4         99       99       99 
99       99  ,it is a well-known fact   
that some objects please us1 while      
others do not4 ,generally speaking1     
anything that is constructed according  
to fixed and logically followed rules1  
is a product of tolerable beauty4 ,we   
see thus nature herself1 who always acts
 according to fixed rules1 constantly   
producing such pretty things4 ,every day
 the physicist is confronted in his     
workshop with the most beautiful        

vibration-figures1 tone-figures1        
phenomena of polarisation1 and forms of 
diffraction4  ,a rule always presupposes
 a repetition4 ,repetitions1 therefore1 
will probably be found to play some     
important part in the production of     
agreeable effects4 ,of course1 the      
nature of agreeable effects is not      
exhausted by this4 ,furthermore1 the    
repetition of a physical event becomes  
the source of agreeable effects only    
when it is connected with a repetition  
of sensations4  ,an excellent example   
that repetition of sensations is a      
source of agreeable effects is furnished
 by the copy-book of every schoolboy1   
which is usually a treasure-house of    
such things1 and only in need of an ,abb
 ,domenech to become celebrated4 ,any   
figure1 no matter how crude or poor1 if 
several times repeated1 with the        
repetitions placed in line1 will produce
 a tolerable frieze4  ,illustration3    
,fig4 #be4  ,also the pleasant effect of
 symmetry is due to the repetition of   

sensations4 ,let us abandon ourselves a 
moment to this thought1 yet not imagine 
when we have developed it1 that we have 
fully exhausted the nature of the       
agreeable1 much less of the beautiful4  
,first1 let us get a clear conception of
 what symmetry is4 ,and in preference to
 a definition let us take a living      
picture4 ,you know that the reflexion of
 an object in a mirror has a great      
likeness to the object itself4 ,all its 
proportions and outlines are the same4  
,yet there is a difference between the  
object and its reflexion in the mirror1 
which you will readily observe4  ,hold  
your right hand before a mirror1 and you
 will see in the mirror a left hand4    
,your right glove will produce its mate 
in the glass4 ,for you could never use  
the reflexion of your right glove1 if it
 were present to you as a real thing1   
for covering your right hand1 but only  
for covering your left4 ,similarly1 your
 right ear will give as its reflexion a 
left ear2 and you will at once perceive 

that the left half of your body could   
very easily be substituted for the      
reflexion of your right half4 ,now just 
as in the place of a missing right ear a
 left ear cannot be put1 unless the     
lobule of the ear be turned upwards1 or 
the opening into the concha backwards1  
so1 despite all similarity of form1 the 
reflexion of an object can never take   
the place of the object itself4#bj  ,the
 reason of this difference between the  
object and its reflexion is simple4 ,the
 reflexion appears as far behind the    
mirror as the object is in front of it4 
,the parts of the object1 accordingly1  
which are nearest the mirror will also  
be nearest the mirror in the reflexion4 
,consequently1 the succession of the    
parts in the reflexion will be reversed1
 as may best be seen in the reflexion of
 the face of a watch or of a manuscript4
  ,it will also be readily seen1 that if
 a point of the object be joined with   
its reflexion in the image1 the line of 
junction will cut the mirror at right   

angles and be bisected by it4 ,this     
holds true of all corresponding points  
of object and image4  ,if1 now1 we can  
divide an object by a plane into two    
halves so that each half1 as seen in the
 reflecting plane of division1 is a     
reproduction of the other half1 such an 
object is termed symmetrical1 and the   
plane of division is called the plane of
 symmetry4  ,if the plane of symmetry is
 vertical1 we can say that the body is  
vertically symmetrical4 ,an example of  
vertical symmetry is a ,gothic          
cathedral4  ,if the plane of symmetry is
 horizontal1 we can say that the object 
is horizontally symmetrical4 ,a         
landscape on the shores of a lake with  
its reflexion in the water1 is a system 
of horizontal symmetry4  ,exactly here  
is a noticeable difference4 ,the        
vertical symmetry of a ,gothic cathedral
 strikes us at once1 whereas we can     
travel up and down the whole length of  
the ,rhine or the ,hudson without       
becoming aware of the symmetry between  

objects and their reflexions in the     
water4 ,vertical symmetry pleases us1   
whilst horizontal symmetry is           
indifferent1 and is noticed only by the 
experienced eye4  ,whence arises this   
difference8 ,i say from the fact that   
vertical symmetry produces a repetition 
of the same sensation1 while horizontal 
symmetry does not4 ,i shall now show    
that this is so4  ,let us look at the   
following letters3    d b   q p  ,it is 
a fact known to all mothers and         
teachers1 that children in their first  
attempts to read and write1 constantly  
confound d and b1 and q and p1 but never
 d and q1 or b and p4 ,now d and b and q
 and p are the two halves of a          
vertically symmetrical figure1 while d  
and q1 and b and p are two halves of a  
horizontally symmetrical figure4 ,the   
first two are confounded2 but confusion 
is only possible of things that excite  
in us the same or similar sensations4   
,figures of two flower-girls are        
frequently seen on the decorations of   

gardens and of drawing-rooms1 one of    
whom carries a flower-basket in her     
right hand and the other a flower-basket
 in her left4 ,all know how apt we are1 
unless we are very careful1 to confound 
these figures with one another4  ,while 
turning a thing round from right to left
 is scarcely noticed1 the eye is not at 
all indifferent to the turning of a     
thing upside down4 ,a human face which  
has been turned upside down is scarcely 
recognisable as a face1 and makes an    
impression which is altogether strange4 
,the reason of this is not to be sought 
in the unwontedness of the sight1 for it
 is just as difficult to recognise an   
arabesque that has been inverted1 where 
there can be no question of a habit4    
,this curious fact is the foundation of 
the familiar jokes played with the      
portraits of unpopular personages1 which
 are so drawn that in the upright       
position of the page an exact picture of
 the person is presented1 but on being  
inverted some popular animal is shown4  

,it is a fact1 then1 that the two halves
 of a vertically symmetrical figure are 
easily confounded and that they         
therefore probably produce very nearly  
the same sensations4 ,the question1     
accordingly1 arises1 why do the two     
halves of a vertically symmetrical      
figure produce the same or similar      
sensations8 ,the answer is3 ,because our
 apparatus of vision1 which consists of 
our eyes and of the accompanying        
muscular apparatus is itself vertically 
symmetrical4#ba  ,whatever external     
resemblances one eye may have with      
another they are still not alike4 ,the  
right eye of a man cannot take the place
 of a left eye any more than a left ear 
or left hand can take the place of a    
right one4 ,by artificial means1 we can 
change the part which each of our eyes  
plays4 7,wheatstone's pseudoscope47 ,but
 we then find ourselves in an entirely  
new and strange world4 ,what is convex  
appears concave2 what is concave1       
convex4 ,what is distant appears near1  

and what is near appears far4  ,the left
 eye is the reflexion of the right4 ,and
 the light-feeling retina of the left   
eye is a reflexion of the light-feeling 
retina of the right1 in all its         
functions4  ,the lense of the eye1 like 
a magic lantern1 casts images of objects
 on the retina4 ,and you may picture to 
yourself the light-feeling retina of the
 eye1 with its countless nerves1 as a   
hand with innumerable fingers1 adapted  
to feeling light4 ,the ends of the      
visual nerves1 like our fingers1 are    
endowed with varying degrees of         
sensitiveness4 ,the two retin act like a
 right and a left hand2 the sensation of
 touch and the sensation of light in the
 two instances are similar4  ,examine   
the right-hand portion of this letter   
,t3 namely1 ,t4 ,instead of the two     
retin on which this image falls1 imagine
 feeling the object1 my two hands4 ,the 
,t1 grasped with the right hand1 gives a
 different sensation from that which it 
gives when grasped with the left4 ,but  

if we turn our character about from     
right to left1 thus3 ,t1 it will give   
the same sensation in the left hand that
 it gave before in the right4 ,the      
sensation is repeated4  ,if we take a   
whole ,t1 the right half will produce in
 the right hand the same sensation that 
the left half produces in the left1 and 
vice versa4  ,the symmetrical figure    
gives the same sensation twice4  ,if we 
turn the ,t over thus3 ,t1 or invert the
 half ,t thus3 ,l1 so long as we do not 
change the position of our hands we can 
make no use of the foregoing reasoning4 
,the retin1 in fact1 are exactly like   
our two hands4 ,they1 too1 have their   
thumbs and index fingers1 though they   
are thousands in number2 and we may say 
the thumbs are on the side of the eye   
near the nose1 and the remaining fingers
 on the side away from the nose4  ,with 
this ,i hope to have made perfectly     
clear that the pleasing effect of       
symmetry is chiefly due to the          
repetition of sensations1 and that the  

effect in question takes place in       
symmetrical figures1 only where there is
 a repetition of sensation4 ,the        
pleasing effect of regular figures1 the 
preference which straight lines1        
especially vertical and horizontal      
straight lines1 enjoy1 is founded on a  
similar reason4 ,a straight line1 both  
in a horizontal and in a vertical       
position1 can cast on the two retin the 
same image1 which falls moreover on     
symmetrically corresponding spots4 ,this
 also1 it would appear1 is the reason of
 our psychological preference of        
straight to curved lines1 and not their 
property of being the shortest distance 
between two points4 ,the straight line  
is felt1 to put the matter briefly1 as  
symmetrical to itself1 which is the case
 also with the plane4 ,curved lines are 
felt as deviations from straight lines1 
that is1 as deviations from symmetry4#bb
 ,the presence of a sense for symmetry  
in people possessing only one eye from  
birth1 is indeed a riddle4 ,of course1  

the sense of symmetry1 although         
primarily acquired by means of the eyes1
 cannot be wholly limited to the visual 
organs4 ,it must also be deeply rooted  
in other parts of the organism by ages  
of practice and can thus not be         
eliminated forthwith by the loss of one 
eye4 ,also1 when an eye is lost1 the    
symmetrical muscular apparatus is left1 
as is also the symmetrical apparatus of 
innervation4   ,it appears1 however1    
unquestionable that the phenomena       
mentioned have1 in the main1 their      
origin in the peculiar structure of our 
eyes4 ,it will therefore be seen at once
 that our notions of what is beautiful  
and ugly would undergo a change if our  
eyes were different4 ,also1 if this view
 is correct1 the theory of the so-called
 eternally beautiful is somewhat        
mistaken4 ,it can scarcely be doubted   
that our culture1 or form of            
civilisation1 which stamps upon the     
human body its unmistakable traces1     
should not also modify our conceptions  

of the beautiful4 ,was not formerly the 
development of all musical beauty       
restricted to the narrow limits of a    
five-toned scale8  ,the fact that a     
repetition of sensations is productive  
of pleasant effects is not restricted to
 the realm of the visible4 ,to-day1 both
 the musician and the physicist know    
that the harmonic or the melodic        
addition of one tone to another affects 
us agreeably only when the added tone   
reproduces a part of the sensation which
 the first one excited4 ,when ,i add an 
octave to a fundamental tone1 ,i hear in
 the octave a part of what was heard in 
the fundamental tone4 7,helmholtz47 ,but
 it is not my purpose to develop this   
idea fully here4#bc ,we shall only ask  
to-day1 whether there is anything       
similar to the symmetry of figures in   
the province of sounds4  ,look at the   
reflexion of your piano in the mirror4  
,you will at once remark that you have  
never seen such a piano in the actual   
world1 for it has its high keys to the  

left and its low ones to the right4     
,such pianos are not manufactured4  ,if 
you could sit down at such a piano and  
play in your usual manner1 plainly every
 step which you imagined you were       
performing in the upward scale would be 
executed as a corresponding step in the 
downward scale4 ,the effect would be not
 a little surprising4  ,for the         
practised musician who is always        
accustomed to hearing certain sounds    
produced when certain keys are struck1  
it is quite an anomalous spectacle to   
watch a player in the glass and to      
observe that he always does the opposite
 of what we hear4  ,but still more      
remarkable would be the effect of       
attempting to strike a harmony on such a
 piano4 ,for a melody it is not         
indifferent whether we execute a step in
 an upward or a downward scale4 ,but for
 a harmony1 so great a difference is not
 produced by reversal4 ,i always retain 
the same consonance whether ,i add to a 
fundamental note an upper or a lower    

third4 ,only the order of the intervals 
of the harmony is reversed4 ,in point of
 fact1 when we execute a movement in a  
major key on our reflected piano1 we    
hear a sound in a minor key1 and vice   
versa4  ,it now remains to execute the  
experiments indicated4 ,instead of      
playing upon the piano in the mirror1   
which is impossible1 or of having a     
piano of this kind built1 which would be
 somewhat expensive1 we may perform our 
experiments in a simpler manner1 as     
follows3  #a7 ,we play on our own piano 
in our usual manner1 look into the      
mirror1 and then repeat on our real     
piano what we see in the mirror4 ,in    
this way we transform all steps upwards 
into corresponding steps downwards4 ,we 
play a movement1 and then another       
movement1 which1 with respect to the    
key-board1 is symmetrical to the first4 
#b7 ,we place a mirror beneath the music
 in which the notes are reflected as in 
a body of water1 and play according to  
the notes in the mirror4 ,in this way   

also1 all steps upwards are changed into
 corresponding1 equal steps downwards4  
#c7 ,we turn the music upside down and  
read the notes from right to left and   
from below upwards4 ,in doing this1 we  
must regard all sharps as flats and all 
flats as sharps1 because they correspond
 to half lines and spaces4 ,besides1 in 
this use of the music we can only employ
 the bass clef1 as only in this clef are
 the notes not changed by symmetrical   
reversal4  ,you can judge of the effect 
of these experiments from the examples  
which appear in the annexed musical cut4
 7,page #ajb47 ,the movement which      
appears in the upper lines is           
symmetrically reversed in the lower4    
,the effect of the experiments may be   
briefly formulated4 ,the melody is      
rendered unrecognisable4 ,the harmony   
suffers a transposition from a major    
into a minor key and vice versa4 ,the   
study of these pretty effects1 which    
have long been familiar to physicists   
and musicians1 was revived some years   

ago by ,von ,oettingen4#bd  ,music3     
,fig4 #bf4  7,see pages #aja and #ajc47 
,now1 although in all the preceding     
examples ,i have transposed steps upward
 into equal and similar steps downward1 
that is1 as we may justly say1 have     
played for every movement the movement  
which is symmetrical to it1 yet the ear 
notices either little or nothing of     
symmetry4 ,the transposition from a     
major to a minor key is the sole        
indication of symmetry remaining4 ,the  
symmetry is there for the mind1 but is  
wanting for sensation4 ,no symmetry     
exists for the ear1 because a reversal  
of musical sounds conditions no         
repetition of sensations4 ,if we had an 
ear for height and an ear for depth1    
just as we have an eye for the right and
 an eye for the left1 we should also    
find that symmetrical sound-structures  
existed for our auditory organs4 ,the   
contrast of major and minor for the ear 
corresponds to inversion for the eye1   
which is also only symmetry for the     

mind1 but not for sensation4  ,by way of
 supplement to what ,i have said1 ,i    
will add a brief remark for my          
mathematical readers4  ,our musical     
notation is essentially a graphical     
representation of a piece of music in   
the form of curves1 where the time is   
the absciss1 and the logarithms of the  
number of vibrations the ordinates4 ,the
 deviations of musical notation from    
this principle are only such as         
facilitate interpretation1 or are due to
 historical accidents4  ,if1 now1 it be 
further observed that the sensation of  
pitch also is proportional to the       
logarithm of the number of vibrations1  
and that the intervals between the notes
 correspond to the differences of the   
logarithms of the numbers of vibrations1
 the justification will be found in     
these facts of calling the harmonies and
 melodies which appear in the mirror1   
symmetrical to the original ones4       
99       99       99       99       99  
,i simply wish to bring home to your    

minds by these fragmentary remarks that 
the progress of the physical sciences   
has been of great help to those branches
 of psychology that have not scorned to 
consider the results of physical        
research4 ,on the other hand1 psychology
 is beginning to return1 as it were1 in 
a spirit of thankfulness1 the powerful  
stimulus which it received from physics4
  ,the theories of physics which reduce 
all phenomena to the motion and         
equilibrium of smallest particles1 the  
so-called molecular theories1 have been 
gravely threatened by the progress of   
the theory of the senses and of space1  
and we may say that their days are      
numbered4  ,i have shown elsewhere#be   
that the musical scale is simply a      
species of space--a space1 however1 of  
only one dimension1 and that1 a         
one-sided one4 ,if1 now1 a person who   
could only hear1 should attempt to      
develop a conception of the world in    
this1 his linear space1 he would become 
involved in many difficulties1 as his   

space would be incompetent to comprehend
 the many sides of the relations of     
reality4 ,but is it any more justifiable
 for us1 to attempt to force the whole  
world into the space of our eye1 in     
aspects in which it is not accessible to
 the eye8 ,yet this is the dilemma of   
all molecular theories4  ,we possess1   
however1 a sense1 which1 with respect to
 the scope of the relations which it can
 comprehend1 is richer than any other4  
,it is our reason4 ,this stands above   
the senses4 ,it alone is competent to   
found a permanent and sufficient view of
 the world4 ,the mechanical conception  
of the world has performed wonders since
 ,galileo's time4 ,but it must now yield
 to a broader view of things4 ,a further
 development of this idea is beyond the 
limits of my present purpose4  ,one more
 point and ,i have done4 ,the advice of 
our philosopher to restrict ourselves to
 what is near at hand and useful in our 
researches1 which finds a kind of       
exemplification in the present cry of   

inquirers for limitation and division of
 labor1 must not be too slavishly       
followed4 ,in the seclusion of our      
closets1 we often rack our brains in    
vain to fulfil a work1 the means of     
accomplishing which lies before our very
 doors4 ,if the inquirer must be        
perforce a shoemaker1 tapping constantly
 at his last1 it may perhaps be         
permitted him to be a shoemaker of the  
type of ,hans ,sachs1 who did not deem  
it beneath him to take a look now and   
then at his neighbor's work and to      
comment on the latter's doings4  ,let   
this be my apology1 therefore1 if ,i    
have forsaken for a moment to-day the   
last of my specialty4    ,,footnotes3   
,footnote #ai3 ,delivered before the    
,german ,casino of ,prague1 in the      
winter of #ahga4    ,a fuller treatment 
of the problems of this lecture will be 
found in   my ,contributions to the     
,analysis of the ,sensations 7,jena1    
#ahhf71   ,english ,translation1        
,chicago1 #ahie4 ,j4 ,p4 ,soret1 ,sur la

 perception   du beau 7,geneva1 #ahib71 
also regards repetition as a principle  
of   sthetics4 ,his discussions of the  
sthetical side of the subject   are much
 more detailed than mine4 ,but with     
respect to the   psychological and      
physiological foundation of the         
principle1 ,i am   convinced that the   
,contributions to the ,analysis of the  
,sensations   go deeper4--,,mach        
7#ahid74    ,footnote #bj3 ,kant1 in his
 ,prolegomena zu jeder knftigen         
,metaphysik1 also refers to this fact1  
but for a different purpose4            
,footnote #ba3 ,compare ,mach1 ,fichte's
 ,zeitschrift fr ,philosophie1   #ahfd1 
p4 #a4    ,footnote #bb3 ,the fact that 
the first and second differential       
coefficients of a curve are directly    
seen1 but the higher   coefficients not1
 is very simply explained4 ,the first   
gives the   position of the tangent1 the
 declination of the straight line from  
the position of symmetry1 the second the
 declination of the curve   from the    

straight line4 ,it is1 perhaps1 not     
unprofitable to remark   here that the  
ordinary method of testing rulers and   
plane surfaces   7by reversed           
applications7 ascertains the deviation  
of the object   from symmetry to itself4
    ,footnote #bc3 ,see the lecture ,on 
the ,causes of ,harmony4    ,footnote   
#bd3 ,a4 von ,oettingen1 ,harmoniesystem
 in dualer   ,entwicklung4 ,leipsic and 
,dorpat1 #ahff4    ,footnote #be3       
,compare ,mach's ,zur ,theorie des      
,gehrorgans1 ,vienna   ,academy1 #ahfc4 
,,on ,,the ,,fundamental ,,concepts ,,of
 ,,electrostatics4#bf   ,the task has   
been assigned me to develop before you  
in a popular manner the fundamental     
quantitative concepts of                
electrostatics--quantity of electricity1
 potential1 capacity1 and so forth4 ,it 
would not be difficult1 even within the 
brief limits of an hour1 to delight the 
eye with hosts of beautiful experiments 
and to fill the imagination with        
numerous and varied conceptions4 ,but we

 should1 in such a case1 be still far   
from a lucid and easy grasp of the      
phenomena4 ,the means would still fail  
us for reproducing the facts accurately 
in thought--a procedure which for the   
theoretical and practical man is of     
equal importance4 ,these means are the  
metrical concepts of electricity4  ,as  
long as the pursuit of the facts of a   
given province of phenomena is in the   
hands of a few isolated investigators1  
as long as every experiment can be      
easily repeated1 the fixing of the      
collected facts by provisional          
description is ordinarily sufficient4   
,but the case is different when the     
whole world must make use of the results
 reached by many1 as happens when the   
science acquires broader foundations and
 scope1 and particularly so when it     
begins to supply intellectual           
nourishment to an important branch of   
the practical arts1 and to draw from    
that province in return stupendous      
empirical results4 ,then the facts must 

be so described that individuals in all 
places and at all times can1 from a few 
easily obtained elements1 put the facts 
accurately together in thought1 and     
reproduce them from the description4    
,this is done with the help of the      
metrical concepts and the international 
measures4  ,the work which was begun in 
this direction in the period of the     
purely scientific development of the    
science1 especially by ,coulomb 7#aghd71
 ,gauss 7#ahcc71 and ,weber 7#ahdf71 was
 powerfully stimulated by the           
requirements of the great technical     
undertakings manifested since the laying
 of the first transatlantic cable1 and  
brought to a brilliant conclusion by the
 labors of the ,british ,association1   
#ahfa1 and of the ,paris ,congress1     
#ahha1 chiefly through the exertions of 
,sir ,william ,thomson4  ,it is plain1  
that in the time allotted to me ,i      
cannot conduct you over all the long and
 tortuous paths which the science has   
actually pursued1 that it will not be   

possible at every step to remind you of 
all the little precautions for the      
avoidance of error which the early steps
 have taught us4 ,on the contrary1 ,i   
must make shift with the simplest and   
rudest tools4 ,i shall conduct you by   
the shortest paths from the facts to the
 ideas1 in doing which1 of course1 it   
will not be possible to anticipate all  
the stray and chance ideas which may and
 must arise from prospects into the     
by-paths which we leave untrodden4      
99       99       99       99       99  
,here are two small1 light bodies 7,fig4
 #bg7 of equal size1 freely suspended1  
which we electrify either by friction   
with a third body or by contact with a  
body already electrified4 ,at once a    
repulsive force is set up which drives  
the two bodies away from each other in  
opposition to the action of gravity4    
,this force could accomplish anew the   
same mechanical work which was expended 
to produce it4#bg  ,illustration3 ,fig4 
#bg4  ,illustration3 ,fig4 #bh4         

,coulomb1 now1 by means of delicate     
experiments with the torsion-balance1   
satisfied himself that if the bodies in 
question1 say at a distance of two      
centimetres1 repelled each other with   
the same force with which a             
milligramme-weight strives to fall to   
the ground1 at half that distance1 or at
 one centimetre1 they would repel each  
other with the force of four            
milligrammes1 and at double that        
distance1 or at four centimetres1 they  
would repel each other with the force of
 only one-fourth of a milligramme4 ,he  
found that the electrical force acts    
inversely as the square of the distance4
  ,let us imagine1 now1 that we         
possessed some means of measuring       
electrical repulsion by weights1 a means
 which would be supplied1 for example1  
by our electrical pendulums2 then we    
could make the following observation4   
,the body ,a 7,fig4 #bh7 is repelled by 
the body ,k at a distance of two        
centimetres with a force of one         

milligramme4 ,if we touch ,a1 now1 with 
an equal body ,b1 the half of this force
 of repulsion will pass to the body ,b2 
both ,a and ,b1 now1 at a distance of   
two centimetres from ,k1 are repelled   
only with the force of one-half a       
milligramme4 ,but both together are     
repelled still with the force of one    
milligramme4 ,hence1 the divisibility of
 electrical force among bodies in       
contact is a fact4 ,it is a useful1 but 
by no means a necessary supplement to   
this fact1 to imagine an electrical     
fluid present in the body ,a1 with the  
quantity of which the electrical force  
varies1 and half of which flows over to 
,b4 ,for1 in the place of the new       
physical picture1 thus1 an old1 familiar
 one is substituted1 which moves        
spontaneously in its wonted courses4    
,adhering to this idea1 we define the   
unit of electrical quantity1 according  
to the now almost universally adopted   
centimetre-gramme-second 7,c4 ,g4 ,s47  
system1 as that quantity which at a     

distance of one centimetre repels an    
equal quantity with unit of force1 that 
is1 with a force which in one second    
would impart to a mass of one gramme a  
velocity-increment of a centimetre4 ,as 
a gramme mass acquires through the      
action of gravity a velocity-increment  
of about #iha centimetres in a second1  
accordingly1 a gramme is attracted to   
the earth with #iha1 or1 in round       
numbers1 #ajjj units of force of the    
centimetre-gramme-second system1 while a
 milligramme-weight would strive to fall
 to the earth with approximately the    
unit force of this system4  ,we may     
easily obtain by this means a clear idea
 of what the unit quantity of           
electricity is4 ,two small bodies1 ,k1  
weighing each a gramme1 are hung up by  
vertical threads1 five metres in length 
and almost weightless1 so as to touch   
each other4 ,if the two bodies be       
equally electrified and move apart upon 
electrification to a distance of one    
centimetre1 their charge is             

approximately equivalent to the         
electrostatic unit of electric quantity1
 for the repulsion then holds in        
equilibrium a gravitational             
force-component of approximately one    
milligramme1 which strives to bring the 
bodies together4  ,vertically beneath a 
small sphere suspended from the         
equilibrated beam of a balance a second 
sphere is placed at a distance of a     
centimetre4 ,if both be equally         
electrified the sphere suspended from   
the balance will be rendered apparently 
lighter by the repulsion4 ,if by adding 
a weight of one milligramme equilibrium 
is restored1 each of the spheres        
contains in round numbers the           
electrostatic unit of electrical        
quantity4  ,in view of the fact that the
 same electrical bodies exert at        
different distances different forces    
upon one another1 exception might be    
taken to the measure of quantity here   
developed4 ,what kind of a quantity is  
that which now weighs more1 and now     

weighs less1 so to speak8 ,but this     
apparent deviation from the method of   
determination commonly used in practical
 life1 that by weight1 is1 closely      
considered1 an agreement4 ,on a high    
mountain a heavy mass also is less      
powerfully attracted to the earth than  
at the level of the sea1 and if it is   
permitted us in our determinations to   
neglect the consideration of level1 it  
is only because the comparison of a body
 with fixed conventional weights is     
invariably effected at the same level4  
,in fact1 if we were to make one of the 
two weights equilibrated on our balance 
approach sensibly to the centre of the  
earth1 by suspending it from a very long
 thread1 as ,prof4 von ,jolly of ,munich
 suggested1 we should make the gravity  
of that weight1 its heaviness1          
proportionately greater4  ,let us       
picture to ourselves1 now1 two different
 electrical fluids1 a positive and a    
negative fluid1 of such nature that the 
particles of the one attract the        

particles of the other according to the 
law of the inverse squares1 but the     
particles of the same fluid repel each  
other by the same law2 in non-electrical
 bodies let us imagine the two fluids   
uniformly distributed in equal          
quantities1 in electric bodies one of   
the two in excess2 in conductors1       
further1 let us imagine the fluids      
mobile1 in non-conductors immobile2     
having formed such pictures1 we possess 
the conception which ,coulomb developed 
and to which he gave mathematical       
precision4 ,we have only to give this   
conception free play in our minds and we
 shall see as in a clear picture the    
fluid particles1 say of a positively    
charged conductor1 receding from one    
another as far as they can1 all making  
for the surface of the conductor and    
there seeking out the prominent parts   
and points until the greatest possible  
amount of work has been performed4 ,on  
increasing the size of the surface1 we  
see a dispersion1 on decreasing its size

 we see a condensation of the particles4
 ,in a second1 non-electrified conductor
 brought into the vicinity of the first1
 we see the two fluids immediately      
separate1 the positive collecting itself
 on the remote and the negative on the  
adjacent side of its surface4 ,in the   
fact that this conception reproduces1   
lucidly and spontaneously1 all the data 
which arduous research only slowly and  
gradually discovered1 is contained its  
advantage and scientific value4 ,with   
this1 too1 its value is exhausted4 ,we  
must not seek in nature for the two     
hypothetical fluids which we have added 
as simple mental adjuncts1 if we would  
not go astray4 ,coulomb's view may be   
replaced by a totally different one1 for
 example1 by that of ,faraday1 and the  
most proper course is always1 after the 
general survey is obtained1 to go back  
to the actual facts1 to the electrical  
forces4  ,illustration3 ,fig4 #bi4      
,illustration3 ,fig4 #cj4  ,we will now 
make ourselves familiar with the concept

 of electrical quantity1 and with the   
method of measuring or estimating it4   
,imagine a common ,leyden jar 7,fig4    
#bi71 the inner and outer coatings of   
which are connected together by means of
 two common metallic knobs placed about 
a centimetre apart4 ,if the inside      
coating be charged with the quantity of 
electricity q1 on the outer coating a   
distribution of the electricities will  
take place4 ,a positive quantity almost 
equal#bh to the quantity q flows off to 
the earth1 while a corresponding        
quantity-q is still left on the outer   
coating4 ,the knobs of the jar receive  
their portion of these quantities and   
when the quantity q is sufficiently     
great a rupture of the insulating air   
between the knobs1 accompanied by the   
self-discharge of the jar1 takes place4 
,for any given distance and size of the 
knobs1 a charge of a definite electric  
quantity q is always necessary for the  
spontaneous discharge of the jar4  ,let 
us insulate1 now1 the outer coating of a

 ,lane's unit jar ,l1 the jar just      
described1 and put in connexion with it 
the inner coating of a jar ,f exteriorly
 connected with the earth 7,fig4 #cj74  
,every time that ,l is charged with q1 a
 like quantity q is collected on the    
inner coating of ,f1 and the spontaneous
 discharge of the jar ,l1 which is now  
again empty1 takes place4 ,the number of
 the discharges of the jar ,l furnishes 
us1 thus1 with a measure of the quantity
 collected in the jar ,f1 and if after  
#a1 #b1 #c1 444 spontaneous discharges  
of ,l the jar ,f is discharged1 it is   
evident that the charge of ,f has been  
proportionately augmented4              
,illustration3 ,fig4 #ca4  ,let us      
supply now1 to effect the spontaneous   
discharge1 the jar ,f with knobs of the 
same size and at the same distance apart
 as those of the jar ,l 7,fig4 #ca74 ,if
 we find1 then1 that five discharges of 
the unit jar take place before one      
spontaneous discharge of the jar ,f     
occurs1 plainly the jar ,f1 for equal   

distances between the knobs of the two  
jars1 equal striking distances1 is able 
to hold five times the quantity of      
electricity that ,l can1 that is1 has   
five times the capacity of ,l4#bi       
,illustration3 ,fig4 #cb4  ,we will now 
replace the unit jar ,l1 with which we  
measure electricity1 so to speak1 into  
the jar ,f1 by a ,franklin's pane1      
consisting of two parallel flat metal   
plates 7,fig4 #cb71 separated only by   
air4 ,if here1 for example1 thirty      
spontaneous discharges of the pane are  
sufficient to fill the jar1 ten         
discharges will be found sufficient if  
the air-space between the two plates be 
filled with a cake of sulphur4 ,hence1  
the capacity of a ,franklin's pane of   
sulphur is about three times greater    
than that of one of the same shape and  
size made of air1 or1 as it is the      
custom to say1 the specific inductive   
capacity of sulphur 7that of air being  
taken as the unit7 is about #c4cj ,we   
are here arrived at a very simple fact1 

which clearly shows us the significance 
of the number called dielectric         
constant1 or specific inductive         
capacity1 the knowledge of which is so  
important for the theory of submarine   
cables4  ,let us consider a jar ,a1     
which is charged with a certain quantity
 of electricity4 ,we can discharge the  
jar directly4 ,but we can also discharge
 the jar ,a 7,fig4 #cc7 partly into a   
jar ,b1 by connecting the two outer     
coatings with each other4 ,in this      
operation a portion of the quantity of  
electricity passes1 accompanied by      
sparks1 into the jar ,b1 and we now find
 both jars charged4  ,illustration3     
,fig4 #cc4  ,illustration3 ,fig4 #cd4   
,it may be shown as follows that the    
conception of a constant quantity of    
electricity can be regarded as the      
expression of a pure fact4 ,picture to  
yourself any sort of electrical         
conductor 7,fig4 #cd72 cut it up into a 
large number of small pieces1 and place 
these pieces by means of an insulated   

rod at a distance of one centimetre from
 an electrical body which acts with unit
 of force on an equal and               
like-constituted body at the same       
distance4 ,take the sum of the forces   
which this last body exerts on the      
single pieces of the conductor4 ,the sum
 of these forces will be the quantity of
 electricity on the whole conductor4 ,it
 remains the same1 whether we change the
 form and the size of the conductor1 or 
whether we bring it near or move it away
 from a second electrical conductor1 so 
long as we keep it insulated1 that is1  
do not discharge it4  ,a basis of       
reality for the notion of electric      
quantity seems also to present itself   
from another quarter4 ,if a current1    
that is1 in the usual view1 a definite  
quantity of electricity per second1 is  
sent through a column of acidulated     
water2 in the direction of the positive 
stream1 hydrogen1 but in the opposite   
direction1 oxygen is liberated at the   
extremities of the column4 ,for a given 

quantity of electricity a given quantity
 of oxygen appears4 ,you may picture the
 column of water as a column of hydrogen
 and a column of oxygen1 fitted into    
each other1 and may say the electric    
current is a chemical current and vice  
versa4 ,although this notion is more    
difficult to adhere to in the field of  
statical electricity and with           
non-decomposable conductors1 its further
 development is by no means hopeless4   
,the concept quantity of electricity1   
thus1 is not so aerial as might appear1 
but is able to conduct us with certainty
 through a multitude of varied          
phenomena1 and is suggested to us by the
 facts in almost palpable form4 ,we can 
collect electrical force in a body1     
measure it out with one body into       
another1 carry it over from one body    
into another1 just as we can collect a  
liquid in a vessel1 measure it out with 
one vessel into another1 or pour it from
 one into another4  ,for the analysis of
 mechanical phenomena1 a metrical       

notion1 derived from experience1 and    
bearing the designation work1 has proved
 itself useful4 ,a machine can be set in
 motion only when the forces acting on  
it can perform work4  ,illustration3    
,fig4 #ce4  ,let us consider1 for       
example1 a wheel and axle 7,fig4 #ce7   
having the radii #a and #b metres1      
loaded respectively with the weights #b 
and #a kilogrammes4 ,on turning the     
wheel and axle1 the #a                  
kilogramme-weight1 let us say1 sinks two
 metres1 while the #b kilogramme-weight 
rises one metre4 ,on both sides the     
product  ,,kgr4 ,m4 ,,kgr4 ,m4  #a  #b  
#b  #a4  is equal4 ,so long as this is  
so1 the wheel and axle will not move of 
itself4 ,but if we take such loads1 or  
so change the radii of the wheels1 that 
this product 7kgr4  metre7 on           
displacement is in excess on one side1  
that side will sink4 ,as we see1 this   
product is characteristic for mechanical
 events1 and for this reason has been   
invested with a special name1 work4  ,in

 all mechanical processes1 and as all   
physical processes present a mechanical 
side1 in all physical processes1 work   
plays a determinative part4 ,electrical 
forces1 also1 produce only changes in   
which work is performed4 ,to the extent 
that forces come into play in electrical
 phenomena1 electrical phenomena1 be    
they what they may1 extend into the     
domain of mechanics and are subject to  
the laws which hold in this domain4 ,the
 universally adopted measure of work1   
now1 is the product of the force into   
the distance through which it acts1 and 
in the ,c4 ,g4 ,s4 system1 the unit of  
work is the action through one          
centimetre of a force which would impart
 in one second to a gramme-mass a       
velocity-increment of one centimetre1   
that is1 in round numbers1 the action   
through a centimetre of a pressure equal
 to the weight of a milligramme4 ,from a
 positively charged body1 electricity1  
yielding to the force of repulsion and  
performing work1 flows off to the earth1

 providing conducting connexions exist4 
,to a negatively charged body1 on the   
other hand1 the earth under the same    
circumstances gives off positive        
electricity4 ,the electrical work       
possible in the interaction of a body   
with the earth1 characterises the       
electrical condition of that body4 ,we  
will call the work which must be        
expended on the unit quantity of        
positive electricity to raise it from   
the earth to the body ,k the potential  
of the body ,k4#ca  ,we ascribe to the  
body ,k in the ,c4 ,g4 ,s4 system the   
potential #a1 if we must expend the unit
 of work to raise the positive          
electrostatic unit of electric quantity 
from the earth to that body2 the        
potential -#a1 if we gain in this       
procedure the unit of work2 the         
potential #j1 if no work at all is      
performed in the operation4  ,the       
different parts of one and the same     
electrical conductor in electrical      
equilibrium have the same potential1 for

 otherwise the electricity would perform
 work and move about upon the conductor1
 and equilibrium would not have existed4
 ,different conductors of equal         
potential1 put in connexion with one    
another1 do not exchange electricity any
 more than bodies of equal temperature  
in contact exchange heat1 or in         
connected vessels1 in which the same    
pressures exist1 liquids flow from one  
vessel to the other4 ,exchange of       
electricity takes place only between    
conductors of different potentials1 but 
in conductors of given form and position
 a definite difference of potential is  
necessary for a spark1 which pierces the
 insulating air1 to pass between them4  
,on being connected1 every two          
conductors assume at once the same      
potential4 ,with this the means is given
 of determining the potential of a      
conductor through the agency of a second
 conductor expressly adapted to the     
purpose called an electrometer1 just as 
we determine the temperature of a body  

with a thermometer4 ,the values of the  
potentials of bodies obtained in this   
way simplify vastly our analysis of     
their electrical behavior1 as will be   
evident from what has been said4  ,think
 of a positively charged conductor4     
,double all the electrical forces       
exerted by this conductor on a point    
charged with unit quantity1 that is1    
double the quantity at each point1 or   
what is the same thing1 double the total
 charge4 ,plainly1 equilibrium still    
subsists4 ,but carry1 now1 the positive 
electrostatic unit towards the          
conductor4 ,everywhere we shall have to 
overcome double the force of repulsion  
we did before1 everywhere we shall have 
to expend double the work4 ,by doubling 
the charge of the conductor a double    
potential has been produced4 ,charge and
 potential go hand in hand1 are         
proportional4 ,consequently1 calling the
 total quantity of electricity of a     
conductor ,q and its potential ,v1 we   
can write3 ,q  ,,cv1 where ,c stands for

 a constant1 the import of which will be
 understood simply from noting that ,c  
,q_/,v4#cb ,but the division of a number
 representing the units of quantity of a
 conductor by the number representing   
its units of potential tells us the     
quantity which falls to the share of the
 unit of potential4 ,now the number ,c  
here we call the capacity of a          
conductor1 and have substituted1 thus1  
in the place of the old relative        
determination of capacity1 an absolute  
determination4#cc  ,in simple cases the 
connexion between charge1 potential1 and
 capacity is easily ascertained4 ,our   
conductor1 let us say1 is a sphere of   
radius r1 suspended free in a large body
 of air4 ,there being no other          
conductors in the vicinity1 the charge q
 will then distribute itself uniformly  
upon the surface of the sphere1 and     
simple geometrical considerations yield 
for its potential the expression ,v     
q_/r4 ,hence1 q_/,v  r2 that is1 the    
capacity of a sphere is measured by its 

radius1 and in the ,c4 ,g4 ,s4 system in
 centimetres4#cd ,it is clear also1     
since a potential is a quantity divided 
by a length1 that a quantity divided by 
a potential must be a length4  ,imagine 
7,fig4 #cf7 a jar composed of two       
concentric conductive spherical shells  
of the radii r and r1 having only air   
between them4 ,connecting the outside   
sphere with the earth1 and charging the 
inside sphere by means of a thin1       
insulated wire passing through the      
first1 with the quantity ,q1 we shall   
have ,v  7r-r7_/7rr7,q1 and for the     
capacity in this case 7rr7_/7r-r71 or1  
to take a specific example1 if r  #af   
and r  #ai1 a capacity of about #ajj    
centimetres4  ,illustration3 ,fig4 #cf4 
,we shall now use these simple cases for
 illustrating the principle by which    
capacity and potential are determined4  
,first1 it is clear that we can use the 
jar composed of concentric spheres with 
its known capacity as our unit jar and  
by means of this ascertain1 in the      

manner above laid down1 the capacity of 
any given jar ,f4 ,we find1 for example1
 that #cg discharges of this unit jar of
 the capacity #ajj1 just charges the jar
 investigated at the same striking      
distance1 that is1 at the same          
potential4 ,hence1 the capacity of the  
jar investigated is #cgjj centimetres4  
,the large battery of the ,prague       
physical laboratory1 which consists of  
sixteen such jars1 all of nearly equal  
size1 has a capacity1 therefore1 of     
something like #ej1jjj centimetres1 or  
the capacity of a sphere1 a kilometre in
 diameter1 freely suspended in          
atmospheric space4 ,this remark         
distinctly shows us the great           
superiority which ,leyden jars possess  
for the storage of electricity as       
compared with common conductors4 ,in    
fact1 as ,faraday pointed out1 jars     
differ from simple conductors mainly by 
their great capacity4  ,illustration3   
,fig4 #cg4  ,for determining potential1 
imagine the inner coating of a jar ,f1  

the outer coating of which communicates 
with the ground1 connected by a long1   
thin wire with a conductive sphere ,k   
placed free in a large atmospheric      
space1 compared with whose dimensions   
the radius of the sphere vanishes4      
7,fig4 #cg47 ,the jar and the sphere    
assume at once the same potential4 ,but 
on the surface of the sphere1 if that be
 sufficiently far removed from all other
 conductors1 a uniform layer of         
electricity will be found4 ,if the      
sphere1 having the radius r1 contains   
the charge q1 its potential is ,v  q_/r4
 ,if the upper half of the sphere be    
severed from the lower half and         
equilibrated on a balance with one of   
whose beams it is connected by silk     
threads1 the upper half will be repelled
 from the lower half with the force ,p  
q_/#hr  #a_/h,v4 ,this repulsion ,p may 
be counter-balanced by additional       
weights placed on the beam-end1 and so  
ascertained4 ,the potential is then ,v  
sqrt7#h,p74#ce  ,that the potential is  

proportional to the square root of the  
force is not difficult to see4 ,a       
doubling or trebling of the potential   
means that the charge of all the parts  
is doubled or trebled2 hence their      
combined power of repulsion quadrupled  
or nonupled4  ,let us consider a special
 case4 ,i wish to produce the potential 
#dj on the sphere4 ,what additional     
weight must ,i give to the half sphere  
in grammes that the force of repulsion  
shall maintain the balance in exact     
equilibrium8 ,as a gramme weight is     
approximately equivalent to #ajjj units 
of force1 we have only the following    
simple example to work out3 #djdj  #h   
#ajjj4x1 where x stands for the number  
of grammes4 ,in round numbers we get x  
#j4b gramme4 ,i charge the jar4 ,the    
balance is deflected2 ,i have reached1  
or rather passed1 the potential #dj1 and
 you see when ,i discharge the jar the  
associated spark4#cf  ,the striking     
distance between the knobs of a machine 
increases with the difference of the    

potential1 although not proportionately 
to that difference4 ,the striking       
distance increases faster than the      
potential difference4 ,for a distance   
between the knobs of one centimetre on  
this machine the difference of potential
 is #aaj4 ,it can easily be increased   
tenfold4 ,of the tremendous differences 
of potential which occur in nature some 
idea may be obtained from the fact that 
the striking distances of lightning in  
thunder-storms is counted by miles4 ,the
 differences of potential in galvanic   
batteries are considerably smaller than 
those of our machine1 for it takes fully
 one hundred elements to give a spark of
 microscopic striking distance4       99
       99       99       99       99    
,we shall now employ the ideas reached  
to shed some light upon another         
important relation between electrical   
and mechanical phenomena4 ,we shall     
investigate what is the potential       
energy1 or the store of work1 contained 
in a charged conductor1 for example1 in 

a jar4  ,if we bring a quantity of      
electricity up to a conductor1 or1 to   
speak less pictorially1 if we generate  
by work electrical force in a conductor1
 this force is able to produce anew the 
work by which it was generated4 ,how    
great1 now1 is the energy or capacity   
for work of a conductor of known charge 
,q and known potential ,v8  ,imagine the
 given charge ,q divided into very small
 parts q1 q1 q 4441 and these little    
parts successively carried up to the    
conductor4 ,the first very small        
quantity q is brought up without any    
appreciable work and produces by its    
presence a small potential ,v'4 ,to     
bring up the second quantity1           
accordingly1 we must do the work q',v'1 
and similarly for the quantities which  
follow the work q'',v''1 q''',v'''1 and 
so forth4 ,now1 as the potential rises  
proportionately to the quantities added 
until the value ,v is reached1 we have1 
agreeably to the graphical              
representation of ,fig4 #ch1 for the    

total work performed1  ,w  #a_/b,,qv1   
which corresponds to the total energy of
 the charged conductor4 ,using the      
equation ,q  ,,cv1 where ,c stands for  
capacity1 we also have1  ,w  #a_/b;,,cv1
 or ,w  ,q_/#b;,c4  ,it will be helpful1
 perhaps1 to elucidate this idea by an  
analogy from the province of mechanics4 
,if we pump a quantity of liquid1 ,q1   
gradually into a cylindrical vessel     
7,fig4 #ci71 the level of the liquid in 
the vessel will gradually rise4 ,the    
more we have pumped in1 the greater the 
pressure we must overcome1 or the higher
 the level to which we must lift the    
liquid4 ,the stored-up work is rendered 
again available when the heavy liquid   
,q1 which reaches up to the level h1    
flows out4 ,this work ,w corresponds to 
the fall of the whole liquid weight ,q1 
through the distance h_/#b or through   
the altitude of its centre of gravity4  
,we have  ,w  #a_/b,qh4  ,further1 since
 ,q  ,kh1 or since the weight of the    
liquid and the height h are             

proportional1 we get also  ,w  #a_/b,kh 
and ,w  ,q_/#b,k4  ,illustration3 ,fig4 
#ch4  ,illustration3 ,fig4 #ci4  ,as a  
special case let us consider our jar4   
,its capacity is ,c  #cgjj1 its         
potential ,v  #aaj2 accordingly1 its    
quantity ,q  ,,cv  #djg1jjj             
electrostatic units and its energy ,w   
#a_/b,,qv  #bb1che1jjj ,c4 ,g4 ,s4 units
 of work4  ,the unit of work of the ,c4 
,g4 ,s4 system is not readily           
appreciable by the senses1 nor does it  
well admit of representation1 as we are 
accustomed to work with weights4 ,let us
 adopt1 therefore1 as our unit of work  
the gramme-centimetre1 or the           
gravitational pressure of a             
gramme-weight through the distance of a 
centimetre1 which in round numbers is   
#ajjj times greater than the unit       
assumed above2 in this case1 our        
numerical result will be approximately  
#ajjj times smaller4 ,again1 if we pass1
 as more familiar in practice1 to the   
kilogramme-metre as our unit of work1   

our unit1 the distance being increased a
 hundred fold1 and the weight a thousand
 fold1 will be #ajj1jjj times larger4   
,the numerical result expressing the    
work done is in this case #ajj1jjj times
 less1 being in round numbers #j4bb     
kilogramme-metre4 ,we can obtain a clear
 idea of the work done here by letting a
 kilogramme-weight fall #bb centimetres4
  ,this amount of work1 accordingly1 is 
performed on the charging of the jar1   
and on its discharge appears again1     
according to the circumstances1 partly  
as sound1 partly as a mechanical        
disruption of insulators1 partly as     
light and heat1 and so forth4  ,the     
large battery of the ,prague physical   
laboratory1 with its sixteen jars       
charged to equal potentials1 furnishes1 
although the effect of the discharge is 
imposing1 a total amount of work of only
 three kilogramme-metres4  ,in the      
development of the ideas above laid down
 we are not restricted to the method    
there pursued2 in fact1 that method was 

selected only as one especially fitted  
to familiarise us with the phenomena4   
,on the contrary1 the connexion of the  
physical processes is so multifarious   
that we can come at the same event from 
very different directions4 ,particularly
 are electrical phenomena connected with
 all other physical events2 and so      
intimate is this connexion that we might
 justly call the study of electricity   
the theory of the general connexion of  
physical processes4  ,with respect to   
the principle of the conservation of    
energy which unites electrical with     
mechanical phenomena1 ,i should like to 
point out briefly two ways of following 
up the study of this connexion4  ,a few 
years ago ,professor ,rosetti1 taking an
 influence-machine1 which he set in     
motion by means of weights alternately  
in the electrical and non-electrical    
condition with the same velocities1     
determined the mechanical work expended 
in the two cases and was thus enabled1  
after deducting the work of friction1 to

 ascertain the mechanical work consumed 
in the development of the electricity4  
,i myself have made this experiment in a
 modified1 and1 as ,i think1 more       
advantageous form4 ,instead of          
determining the work of friction by     
special trial1 ,i arranged my apparatus 
so that it was eliminated of itself in  
the measurement and could consequently  
be neglected4 ,the so-called fixed disk 
of the machine1 the axis of which is    
placed vertically1 is suspended somewhat
 like a chandelier by three vertical    
threads of equal lengths l at a distance
 r from the axis4 ,only when the machine
 is excited does this fixed disk1 which 
represents a ,prony's brake1 receive1   
through its reciprocal action with the  
rotating disk1 a deflexion alpha and a  
moment of torsion which is expressed by 
,d  7,pr_/l7alpha1 where ,p is the      
weight of the disk4#cg ,the angle alpha 
is determined by a mirror set in the    
disk4 ,the work expended in n rotations 
is given by #bnpi,d4  ,if we close the  

machine1 as ,rosetti did1 we obtain a   
continuous current which has all the    
properties of a very weak galvanic      
current2 for example1 it produces a     
deflexion in a multiplier which we      
interpose1 and so forth4 ,we can        
directly ascertain1 now1 the mechanical 
work expended in the maintenance of this
 current4  ,if we charge a jar by means 
of a machine1 the energy of the jar     
employed in the production of sparks1 in
 the disruption of the insulators1 etc41
 corresponds to a part only of the      
mechanical work expended1 a second part 
of it being consumed in the arc which   
forms the circuit4#ch ,this machine1    
with the interposed jar1 affords in     
miniature a picture of the transference 
of force1 or more properly of work4 ,and
 in fact nearly the same laws hold here 
for the economical coefficient as obtain
 for large dynamo-machines4  ,another   
means of investigating electrical energy
 is by its transformation into heat4 ,a 
long time ago 7#ahch71 before the       

mechanical theory of heat had attained  
its present popularity1 ,riess performed
 experiments in this field with the help
 of his electrical air-thermometer or   
thermo-electrometer4  ,illustration3    
,fig4 #dj4  ,if the discharge be        
conducted through a fine wire passing   
through the globe of the                
air-thermometer1 a development of heat  
is observed proportional to the         
expression above-discussed ,w           
#a_/b,,qv4 ,although the total energy   
has not yet been transformed into       
measurable heat by this means1 in as    
much as a portion is left behind in the 
spark in the air outside the            
thermometer1 still everything tends to  
show that the total heat developed in   
all parts of the conductor and along all
 the paths of discharge is the          
equivalent of the work #a_/b,,qv4  ,it  
is not important here whether the       
electrical energy is transformed all at 
once or partly1 by degrees4 ,for        
example1 if of two equal jars one is    

charged with the quantity ,q at the     
potential ,v the energy present is      
#a_/b,,qv4 ,if the first jar be         
discharged into the second1 ,v1 since   
the capacity is now doubled1 falls to   
,v_/#b4 ,accordingly1 the energy        
#a_/d,,qv remains1 while #a_/d,,qv is   
transformed in the spark of discharge   
into heat4 ,the remainder1 however1 is  
equally distributed between the two jars
 so that each on discharge is still able
 to transform #a_/h,,qv into heat4      
99       99       99       99       99  
,we have here discussed electricity in  
the limited phenomenal form in which it 
was known to the inquirers before       
,volta1 and which has been called1      
perhaps not very felicitously1 statical 
electricity4 ,it is evident1 however1   
that the nature of electricity is       
everywhere one and the same2 that a     
substantial difference between statical 
and galvanic electricity does not exist4
 ,only the quantitative circumstances in
 the two provinces are so widely        

different that totally new aspects of   
phenomena may appear in the second1 for 
example1 magnetic effects1 which in the 
first remained unnoticed1 whilst1 vice  
versa1 in the second field statical     
attractions and repulsions are scarcely 
appreciable4 ,as a fact1 we can easily  
show the magnetic effect of the current 
of discharge of an influence-machine on 
the galvanoscope although we could      
hardly have made the original discovery 
of the magnetic effects with this       
current4 ,the statical distant action of
 the wire poles of a galvanic element   
also would hardly have been noticed had 
not the phenomenon been known from a    
different quarter in a striking form4   
,if we wished to characterise the two   
fields in their chief and most general  
features1 we should say that in the     
first1 high potentials and small        
quantities come into play1 in the second
 small potentials and large quantities4 
,a jar which is discharging and a       
galvanic element deport themselves      

somewhat like an air-gun and the bellows
 of an organ4 ,the first gives forth    
suddenly under a very high pressure a   
small quantity of air2 the latter       
liberates gradually under a very slight 
pressure a large quantity of air4  ,in  
point of principle1 too1 nothing        
prevents our retaining the              
electrostatical units in the domain of  
galvanic electricity and in measuring1  
for example1 the strength of a current  
by the number of electrostatic units    
which flow per second through its       
cross-section4 ,but this would be in a  
double aspect impractical4 ,in the first
 place1 we should totally neglect the   
magnetic facilities for measurement so  
conveniently offered by the current1 and
 substitute for this easy means a method
 which can be applied only with         
difficulty and is not capable of great  
exactness4 ,in the second place our     
units would be much too small1 and we   
should find ourselves in the predicament
 of the astronomer who attempted to     

measure celestial distances in metres   
instead of in radii of the earth and the
 earth's orbit2 for the current which by
 the magnetic ,c4 ,g4 ,s4 standard      
represents the unit1 would require a    
flow of some #cj1jjj1jjj1jjj            
electrostatic units per second through  
its cross-section4 ,accordingly1        
different units must be adopted here4   
,the development of this point1 however1
 lies beyond my present task4           
,,footnotes3    ,footnote #bf3 ,a       
lecture delivered at the ,international 
,electrical   ,exhibition1 in ,vienna1  
on ,september #d1 #ahhc4    ,footnote   
#bg3 ,if the two bodies were oppositely 
electrified they   would exert          
attractions upon each other4            
,footnote #bh3 ,the quantity which flows
 off is in point of fact less   than q4 
,it would be equal to the quantity q    
only if the inner   coating of the jar  
were wholly encompassed by the outer    
coating4    ,footnote #bi3 ,rigorously1 
of course1 this is not correct4 ,first1 

it   is to be noted that the jar ,l is  
discharged simultaneously with   the    
electrode of the machine4 ,the jar ,f1  
on the other hand1 is   always          
discharged simultaneously with the outer
 coating of the jar   ,l4 ,hence1 if we 
call the capacity of the electrode of   
the machine   ,e1 that of the unit jar  
,l1 that of the outer coating of ,l1    
,a1 and that of the principal jar ,f1   
then this equation would   exist for the
 example in the text3 7,f  ,a7_/7,l  ,e7
  #e4 ,a cause of   further departure   
from absolute exactness is the residual 
charge4    ,footnote #cj3 ,making       
allowance for the corrections indicated 
in the   preceding footnote1 ,i have    
obtained for the dielectric constant of 
sulphur the number #c4b1 which agrees   
practically with the results   obtained 
by more delicate methods4 ,for the      
highest attainable   precision one      
should by rights immerse the two plates 
of the   condenser first wholly in air  
and then wholly in sulphur1 if the      

ratio of the capacities is to correspond
 to the dielectric constant4   ,in point
 of fact1 however1 the error which      
arises from inserting   simply a plate  
of sulphur that exactly fills the space 
between the   two plates1 is of no      
consequence4    ,footnote #ca3 ,as this 
definition in its simple form is apt to 
give   rise to misunderstandings1       
elucidations are usually added to it4   
,it   is clear that we cannot lift a    
quantity of electricity to ,k1   without
 changing the distribution on ,k and the
 potential on ,k4   ,hence1 the charges 
on ,k must be conceived as fixed1 and so
 small a   quantity raised that no      
appreciable change is produced by it4   
,taking   the work thus expended as many
 times as the small quantity in         
question is contained in the unit of    
quantity1 we shall obtain the           
potential4 ,the potential of a body ,k  
may be briefly and precisely   defined  
as follows3 ,if we expend the element of
 work d,w to raise   the element of     

positive quantity d,q from the earth to 
the   conductor1 the potential of a     
conductor ,k will be given by ,v        
d,w_/d,q4    ,footnote #cb3 ,in this    
article the solidus or slant stroke is  
used   for the usual fractional sign of 
division4 ,where plus or minus signs    
occur in the numerator or denominator1  
brackets or a vinculum is   used4--,tr4 
,footnote #cc3 ,a sort of agreement     
exists between the notions of   thermal 
and electrical capacity1 but the        
difference between the two   ideas also 
should be carefully borne in mind4 ,the 
thermal capacity   of a body depends    
solely upon that body itself4 ,the      
electrical   capacity of a body ,k is   
influenced by all bodies in its         
vicinity1   inasmuch as the charge of   
these bodies is able to alter the       
potential of ,k4 ,to give1 therefore1 an
 unequivocal significance to   the      
notion of the capacity 7,c7 of a body   
,k1 ,c is defined as   the relation     
,q_/,v for the body ,k in a certain     

given position of   all neighboring     
bodies1 and during connexion of all     
neighboring   conductors with the earth4
 ,in practice the situation is much     
simpler4 ,the capacity1 for example1 of 
a jar1 the inner coating of   which is  
almost enveloped by its outer coating1  
communicating with   the ground1 is not 
sensibly affected by charged or         
uncharged   adjacent conductors4        
,footnote #cd3 ,these formul easily     
follow from ,newton's theorem that   a  
homogeneous spherical shell1 whose      
elements obey the law of the   inverse  
squares1 exerts no force whatever on    
points within it but   acts on points   
without as if the whole mass were       
concentrated at its   centre4 ,the      
formul next adduced also flow from this 
proposition4    ,footnote #ce3 ,the     
energy of a sphere of radius r charged  
with the   quantity q is #a_/b7q_/r74   
,if the radius increase by the space    
dr a loss of energy occurs1 and the work
 done is   #a_/b7q_/r7dr4 ,letting p    

denote the uniform electrical   pressure
 on unit of surface of the sphere1 the  
work done is also   #drpipdr4 ,hence p  
7#a_/hrpi77q_/r74 ,subjected to the     
same superficial pressure on all sides1 
say in a fluid1 our half   sphere would 
be an equilibrium4 ,hence we must make  
the pressure p   act on the surface of  
the great circle to obtain the effect on
 the   balance1 which is rpip           
#a_/h7q_/r7  #a_/h,v4    ,footnote #cf3 
,the arrangement described is for       
several reasons not   fitted for the    
actual measurement of potential4        
,thomson's absolute   electrometer is   
based upon an ingenious modification of 
the   electrical balance of ,harris and 
,volta4 ,of two large plane parallel    
plates1 one communicates with the earth1
 while the other is brought   to the    
potential to be measured4 ,a small      
movable superficial portion   f of this 
last hangs from the balance for the     
determination of the   attraction ,p4   
,the distance of the plates from each   

other being ,d   we get ,v              
,dsqrt7#hpi,p_/f74    ,footnote #cg3    
,this moment of torsion needs a         
supplementary   correction1 on account  
of the vertical electric attraction of  
the   excited disks4 ,this is done by   
changing the weight of the disk by      
means of additional weights and by      
making a second reading of the   angles 
of deflexion4    ,footnote #ch3 ,the jar
 in our experiment acts like an         
accumulator1   being charged by a dynamo
 machine4 ,the relation which obtains   
between the expended and the available  
work may be gathered from the           
following simple exposition4 ,a ,holtz  
machine ,h 7,fig4 #dj7 is   charging a  
unit jar ,l1 which after n discharges of
 quantity q   and potential v1 charges  
the jar ,f with the quantity ,q at the  
potential ,v4 ,the energy of the        
unit-jar discharges is lost and   that  
of the jar ,f alone is left4 ,hence the 
ratio of the available   work to the    
total work expended is  ,,qv_/,,qv      

7n_/#b7qv and as ,q  nq1 also ,v_/7,v   
v74    ,if1 now1 we interpose no unit   
jar1 still the parts of the machine     
and the wires of conduction are         
themselves virtually such unit jars     
and the formula still subsists ,v_/7,v  
sumv71 in which sumv   represents the   
sum of all the successively introduced  
differences of   potential in the       
circuit of connexion4     ,,on ,,the    
,,principle ,,of ,,the ,,conservation   
,,of ,,energy4#ci   ,in a popular       
lecture1 distinguished for its charming 
simplicity and clearness1 which ,joule  
delivered in the year #ahdg1dj that     
famous physicist declares that the      
living force which a heavy body has     
acquired by its descent through a       
certain height and which it carries with
 it in the form of the velocity with    
which it is impressed1 is the equivalent
 of the attraction of gravity through   
the space fallen through1 and that it   
would be absurd to assume that this     
living force could be destroyed without 

some restitution of that equivalent4 ,he
 then adds3 ,you will therefore be      
surprised to hear that until very       
recently the universal opinion has been 
that living force could be absolutely   
and irrevocably destroyed at any one's  
option4 ,let us add that to-day1 after  
forty-seven years1 the law of the       
conservation of energy1 wherever        
civilisation exists1 is accepted as a   
fully established truth and receives the
 widest applications in all domains of  
natural science4  ,the fate of all      
momentous discoveries is similar4 ,on   
their first appearance they are regarded
 by the majority of men as errors4 ,j4  
,r4 ,mayer's work on the principle of   
energy 7#ahdb7 was rejected by the first
 physical journal of ,germany2          
,helmholtz's treatise 7#ahdg7 met with  
no better success2 and even ,joule1 to  
judge from an intimation of ,playfair1  
seems to have encountered difficulties  
with his first publication 7#ahdc74     
,gradually1 however1 people are led to  

see that the new view was long prepared 
for and ready for enunciation1 only that
 a few favored minds had perceived it   
much earlier than the rest1 and in this 
way the opposition of the majority is   
overcome4 ,with proofs of the           
fruitfulness of the new view1 with its  
success1 confidence in it increases4    
,the majority of the men who employ it  
cannot enter into a deep-going analysis 
of it2 for them1 its success is its     
proof4 ,it can thus happen that a view  
which has led to the greatest           
discoveries1 like ,black's theory of    
caloric1 in a subsequent period in a    
province where it does not apply may    
actually become an obstacle to progress 
by its blinding our eyes to facts which 
do not fit in with our favorite         
conceptions4 ,if a theory is to be      
protected from this dubious rle1 the    
grounds and motives of its evolution and
 existence must be examined from time to
 time with the utmost care4  ,the most  
multifarious physical changes1 thermal1 

electrical1 chemical1 and so forth1 can 
be brought about by mechanical work4    
,when such alterations are reversed they
 yield anew the mechanical work in      
exactly the quantity which was required 
for the production of the part reversed4
 ,this is the principle of the          
conservation of energy2 energy being the
 term which has gradually come into use 
for that indestructible something of    
which the measure is mechanical work4   
,how did we acquire this idea8 ,what are
 the sources from which we have drawn   
it8 ,this question is not only of       
interest in itself1 but also for the    
important reason above touched upon4    
,the opinions which are held concerning 
the foundations of the law of energy    
still diverge very widely from one      
another4 ,many trace the principle to   
the impossibility of a perpetual motion1
 which they regard either as            
sufficiently proved by experience1 or as
 self-evident4 ,in the province of pure 
mechanics the impossibility of a        

perpetual motion1 or the continuous     
production of work without some         
permanent alteration1 is easily         
demonstrated4 ,accordingly1 if we start 
from the theory that all physical       
processes are purely mechanical         
processes1 motions of molecules and     
atoms1 we embrace also1 by this         
mechanical conception of physics1 the   
impossibility of a perpetual motion in  
the whole physical domain4 ,at present  
this view probably counts the most      
adherents4 ,other inquirers1 however1   
are for accepting only a purely         
experimental establishment of the law of
 energy4  ,it will appear1 from the     
discussion to follow1 that all the      
factors mentioned have co-operated in   
the development of the view in question2
 but that in addition to them a logical 
and purely formal factor1 hitherto      
little considered1 has also played a    
very important part4   ,i4 ,,the        
,,principle ,,of ,,the ,,excluded       
,,perpetual ,,motion4  ,the law of      

energy in its modern form is not        
identical with the principle of the     
excluded perpetual motion1 but it is    
very closely related to it4 ,the latter 
principle1 however1 is by no means new1 
for in the province of mechanics it has 
controlled for centuries the thoughts   
and investigations of the greatest      
thinkers4 ,let us convince ourselves of 
this by the study of a few historical   
examples4  ,illustration3 ,fig4 #da4    
,s4 ,stevinus1 in his famous work       
,hypomnemata mathematica1 ,tom4 ,,iv1   
,de statica1 7,leyden1 #afje1 p4 #cd71  
treats of the equilibrium of bodies on  
inclined planes4  ,over a triangular    
prism ,,abc1 one side of which1 ,,ac1 is
 horizontal1 an endless cord or chain is
 slung1 to which at equal distances     
apart fourteen balls of equal weight are
 attached1 as represented in            
cross-section in ,figure #da4 ,since we 
can imagine the lower symmetrical part  
of the cord ,,abc taken away1 ,stevinus 
concludes that the four balls on ,,ab   

hold in equilibrium the two balls on    
,,bc4 ,for if the equilibrium were for a
 moment disturbed1 it could never       
subsist3 the cord would keep moving     
round forever in the same direction1--we
 should have a perpetual motion4 ,he    
says3       ,but if this took place1 our
 row or ring of balls would come once   
more into their original position1 and  
from the same cause the      eight      
globes to the left would again be       
heavier than the six to the      right1 
and therefore those eight would sink a  
second time and these      six rise1 and
 all the globes would keep up1 of       
themselves1 a      continuous and       
unending motion1 which is false4#da     
,stevinus1 now1 easily derives from this
 principle the laws of equilibrium on   
the inclined plane and numerous other   
fruitful consequences4  ,in the chapter 
,hydrostatics of the same work1 page    
#aad1 ,stevinus sets up the following   
principle3 ,aquam datam1 datum sibi     
intra aquam locum servare1--a given mass

 of water preserves within water its    
given place4  ,illustration3 ,fig4 #db4 
,this principle is demonstrated as      
follows 7see ,fig4 #db73       ,for1    
assuming it to be possible by natural   
means1 let us suppose      that ,a does 
not preserve the place assigned to it1  
but sinks down      to ,d4 ,this being  
posited1 the water which succeeds ,a    
will1 for the      same reason1 also    
flow down to ,d2 ,a will be forced out  
of its      place in ,d2 and thus this  
body of water1 for the conditions in it 
are everywhere the same1 will set up a  
perpetual motion1 which is              
absurd4#db  ,from this all the          
principles of hydrostatics are deduced4 
,on this occasion ,stevinus also first  
develops the thought so fruitful for    
modern analytical mechanics that the    
equilibrium of a system is not destroyed
 by the addition of rigid connexions4   
,as we know1 the principle of the       
conservation of the centre of gravity is
 now sometimes deduced from             

,d',alembert's principle with the help  
of that remark4 ,if we were to reproduce
 ,stevinus's demonstration to-day1 we   
should have to change it slightly4 ,we  
find no difficulty in imagining the cord
 on the prism possessed of unending     
uniform motion if all hindrances are    
thought away1 but we should protest     
against the assumption of an accelerated
 motion or even against that of a       
uniform motion1 if the resistances were 
not removed4 ,moreover1 for greater     
precision of proof1 the string of balls 
might be replaced by a heavy homogeneous
 cord of infinite flexibility4 ,but all 
this does not affect in the least the   
historical value of ,stevinus's         
thoughts4 ,it is a fact1 ,stevinus      
deduces apparently much simpler truths  
from the principle of an impossible     
perpetual motion4  ,in the process of   
thought which conducted ,galileo to his 
discoveries at the end of the sixteenth 
century1 the following principle plays  
an important part1 that a body in virtue

 of the velocity acquired in its descent
 can rise exactly as high as it fell4   
,this principle1 which appears          
frequently and with much clearness in   
,galileo's thought1 is simply another   
form of the principle of excluded       
perpetual motion1 as we shall see it is 
also in ,huygens4  ,galileo1 as we know1
 arrived at the law of uniformly        
accelerated motion by a priori          
considerations1 as that law which was   
the simplest and most natural1 after    
having first assumed a different law    
which he was compelled to reject4 ,to   
verify his law he executed experiments  
with falling bodies on inclined planes1 
measuring the times of descent by the   
weights of the water which flowed out of
 a small orifice in a large vessel4 ,in 
this experiment he assumes as a         
fundamental principle1 that the velocity
 acquired in descent down an inclined   
plane always corresponds to the vertical
 height descended through1 a conclusion 
which for him is the immediate outcome  

of the fact that a body which has fallen
 down one inclined plane can1 with the  
velocity it has acquired1 rise on       
another plane of any inclination only to
 the same vertical height4 ,this        
principle of the height of ascent also  
led him1 as it seems1 to the law of     
inertia4 ,let us hear his own masterful 
words in the ,dialogo terzo 7,opere1    
,padova1 #agdd1 ,tom4 ,,iii74 ,on page  
#if we read3       ,i take it for       
granted that the velocities acquired by 
a body in      descent down planes of   
different inclinations are equal if the 
heights of those planes are equal4#dc   
,then he makes ,salviati say in the     
dialogue3#dd       ,what you say seems  
very probable1 but ,i wish to go further
 and by      an experiment so to        
increase the probability of it that it  
shall      amount almost to absolute    
demonstration4 ,suppose this sheet of   
paper to be a vertical wall1 and from a 
nail driven in it a ball of      lead   
weighing two or three ounces to hang by 

a very fine thread      ,,ab four or    
five feet long4 7,fig4 #dc47 ,on the    
wall mark a      horizontal line ,,dc   
perpendicular to the vertical ,,ab1     
which      latter ought to hang about   
two inches from the wall4 ,if now the   
thread ,,ab with the ball attached take 
the position ,,ac and the      ball be  
let go1 you will see the ball first     
descend through the arc      ,,cb and   
passing beyond ,b rise through the arc  
,,bd almost to the      level of the    
line ,,cd1 being prevented from reaching
 it exactly by      the resistance of   
the air and of the thread4 ,from this we
 may truly      conclude that its       
impetus at the point ,b1 acquired by its
 descent      through the arc ,,cb1 is  
sufficient to urge it through a similar 
arc ,,bd to the same height4 ,having    
performed this experiment and           
repeated it several times1 let us drive 
in the wall1 in the      projection of  
the vertical ,,ab1 as at ,e or at ,f1 a 
nail five      or six inches long1 so   

that the thread ,,ac1 carrying as before
 the      ball through the arc ,,cb1 at 
the moment it reaches the position      
,,ab1 shall strike the nail ,e1 and the 
ball be thus compelled to      move up  
the arc ,,bg described about ,e as      
centre4 ,then we shall      see what the
 same impetus will here accomplish1     
acquired now as      before at the same 
point ,b1 which then drove the same     
moving body      through the arc ,,bd to
 the height of the horizontal ,,cd4 ,now
      gentlemen1 you will be pleased to 
see the ball rise to the      horizontal
 line at the point ,g1 and the same     
thing also happen if      the nail be   
placed lower as at ,f1 in which case the
 ball would      describe the arc ,,bj1 
always terminating its ascent precisely 
at      the line ,,cd4 ,if the nail be  
placed so low that the length of        
thread below it does not reach to the   
height of ,,cd 7which would      happen 
if ,f were nearer ,b than to the        
intersection of ,,ab with      the      

horizontal ,,cd71 then the thread will  
wind itself about the      nail4 ,this  
experiment leaves no room for doubt as  
to the truth of      the supposition4   
,for as the two arcs ,,cb1 ,,db are     
equal and      similarly situated1 the  
momentum acquired in the descent of the 
arc      ,,cb is the same as that       
acquired in the descent of the arc ,,db2
      but the momentum acquired at ,b by
 the descent through the arc      ,,cb  
is capable of driving up the same moving
 body through the arc      ,,bd2 hence  
also the momentum acquired in the       
descent ,,db is equal      to that which
 drives the same moving body through the
 same arc from      ,b to ,d1 so that in
 general every momentum acquired in the 
descent of an arc is equal to that which
 causes the same moving      body to    
ascend through the same arc2 but all the
 momenta which      cause the ascent of 
all the arcs ,,bd1 ,,bg1 ,,bj1 are equal
 since      they are made by the same   
momentum acquired in the descent ,,cb1  

as      the experiment shows3 therefore 
all the momenta acquired in the         
descent of the arcs ,,db1 ,,gb1 ,,jb are
 equal4  ,illustration3 ,fig4 #dc4  ,the
 remark relative to the pendulum may be 
applied to the inclined plane and leads 
to the law of inertia4 ,we read on page 
#abd3de       ,it is plain now that a   
movable body1 starting from rest at ,a  
and      descending down the inclined   
plane ,,ab1 acquires a velocity         
proportional to the increment of its    
time3 the velocity possessed      at ,b 
is the greatest of the velocities       
acquired1 and by its      nature        
immutably impressed1 provided all causes
 of new acceleration      or retardation
 are taken away3 ,i say acceleration1   
having in view      its possible further
 progress along the plane extended2     
retardation1 in view of the possibility 
of its being reversed and      made to  
mount the ascending plane ,,bc4 ,but in 
the horizontal plane      ,,gh its      
equable motion1 according to its        

velocity as acquired in      the descent
 from ,a to ,b1 will be continued ad    
infinitum4      7,fig4 #dd47            
,illustration3 ,fig4 #dd4  ,huygens1    
upon whose shoulders the mantel of      
,galileo fell1 forms a sharper          
conception of the law of inertia and    
generalises the principle respecting the
 heights of ascent which was so fruitful
 in ,galileo's hands4 ,he employs the   
latter principle in the solution of the 
problem of the centre of oscillation and
 is perfectly clear in the statement    
that the principle respecting the       
heights of ascent is identical with the 
principle of the excluded perpetual     
motion4  ,the following important       
passages then occur 7,hugenii1          
,horologium oscillatorium1 pars         
secunda74 ,hypotheses3       ,if gravity
 did not exist1 nor the atmosphere      
obstruct the motions      of bodies1 a  
body would keep up forever the motion   
once impressed      upon it1 with       
equable velocity1 in a straight line4#df

  ,in part four of the ,horologium de   
centro oscillationis we read3       ,if 
any number of weights be set in motion  
by the force of gravity1      the common
 centre of gravity of the weights as a  
whole cannot      possibly rise higher  
than the place which it occupied when   
the      motion began4       ,that this 
hypothesis of ours may arouse no        
scruples1 we will state      that it    
simply imports1 what no one has ever    
denied1 that heavy      bodies do not   
move upwards4--,and truly if the        
devisers of the new      machines who   
make such futile attempts to construct a
 perpetual      motion would acquaint   
themselves with this principle1 they    
could      easily be brought to see     
their errors and to understand that the 
thing is utterly impossible by          
mechanical means4#dg  ,there is possibly
 a ,jesuitical mental reservation       
contained in the words mechanical means4
 ,one might be led to believe from them 
that ,huygens held a non-mechanical     

perpetual motion for possible4  ,the    
generalisation of ,galileo's principle  
is still more clearly put in ,prop4 ,,iv
 of the same chapter3       ,if a       
pendulum1 composed of several weights1  
set in motion from      rest1 complete  
any part of its full oscillation1 and   
from that      point onwards1 the       
individual weights1 with their common   
connexions      dissolved1 change their 
acquired velocities upwards and ascend  
as      far as they can1 the common     
centre of gravity of all will be        
carried up to the same altitude with    
that which it occupied before      the  
beginning of the oscillation4#dh  ,on   
this last principle now1 which is a     
generalisation1 applied to a system of  
masses1 of one of ,galileo's ideas      
respecting a single mass and which from 
,huygens's explanation we recognise as  
the principle of excluded perpetual     
motion1 ,huygens grounds his theory of  
the centre of oscillation4 ,lagrange    
characterises this principle as         

precarious and is rejoiced at ,james    
,bernoulli's successful attempt1 in     
#afha1 to reduce the theory of the      
centre of oscillation to the laws of the
 lever1 which appeared to him clearer4  
,all the great inquirers of the         
seventeenth and eighteenth centuries    
broke a lance on this problem1 and it   
led ultimately1 in conjunction with the 
principle of virtual velocities1 to the 
principle enunciated by ,d',alembert in 
#agdc in his ,trait de dynamique1 though
 previously employed in a somewhat      
different form by ,euler and ,hermann4  
,furthermore1 the ,huygenian principle  
respecting the heights of ascent became 
the foundation of the law of the        
conservation of living force1 as that   
was enunciated by ,john and ,daniel     
,bernoulli and employed with such signal
 success by the latter in his           
,hydrodynamics4 ,the theorems of the    
,bernoullis differ in form only from    
,lagrange's expression in the           
,analytical ,mechanics4  ,the manner in 

which ,torricelli reached his famous law
 of efflux for liquids leads again to   
our principle4 ,torricelli assumed that 
the liquid which flows out of the basal 
orifice of a vessel cannot by its       
velocity of efflux ascend to a greater  
height than its level in the vessel4    
,let us next consider a point which     
belongs to pure mechanics1 the history  
of the principle of virtual motions or  
virtual velocities4 ,this principle was 
not first enunciated1 as is usually     
stated1 and as ,lagrange also asserts1  
by ,galileo1 but earlier1 by ,stevinus4 
,in his ,trochleostatica of the         
above-cited work1 page #gb1 he says3    
,observe that this axiom of statics     
holds good here3       ,as the space of 
the body acting is to the space of the  
body acted      upon1 so is the power of
 the body acted upon to the power of the
      body acting4#di  ,galileo1 as we  
know1 recognised the truth of the       
principle in the consideration of the   
simple machines1 and also deduced the   

laws of the equilibrium of liquids from 
it4  ,torricelli carries the principle  
back to the properties of the centre of 
gravity4 ,the condition controlling     
equilibrium in a simple machine1 in     
which power and load are represented by 
weights1 is that the common centre of   
gravity of the weights shall not sink4  
,conversely1 if the centre of gravity   
cannot sink equilibrium obtains1 because
 heavy bodies of themselves do not move 
upwards4 ,in this form the principle of 
virtual velocities is identical with    
,huygens's principle of the             
impossibility of a perpetual motion4    
,john ,bernoulli1 in #agag1 first       
perceived the universal import of the   
principle of virtual movements for all  
systems2 a discovery stated in a letter 
to ,varignon4 ,finally1 ,lagrange gives 
a general demonstration of the principle
 and founds upon it his whole           
,analytical ,mechanics4 ,but this       
general demonstration is based after all
 upon ,huygens and ,torricelli's        

remarks4 ,lagrange1 as is known1        
conceives simple pulleys arranged in the
 directions of the forces of the system1
 passes a cord through these pulleys1   
and appends to its free extremity a     
weight which is a common measure of all 
the forces of the system4 ,with no      
difficulty1 now1 the number of elements 
of each pulley may be so chosen that the
 forces in question shall be replaced by
 them4 ,it is then clear that if the    
weight at the extremity cannot sink1    
equilibrium subsists1 because heavy     
bodies cannot of themselves move        
upwards4 ,if we do not go so far1 but   
wish to abide by ,torricelli's idea1 we 
may conceive every individual force of  
the system replaced by a special weight 
suspended from a cord passing over a    
pulley in the direction of the force and
 attached at its point of application4  
,equilibrium subsists then when the     
common centre of gravity of all the     
weights together cannot sink4 ,the      
fundamental supposition of this         

demonstration is plainly the            
impossibility of a perpetual motion4    
,lagrange tried in every way to supply a
 proof free from extraneous elements and
 fully satisfactory1 but without        
complete success4 ,nor were his         
successors more fortunate4  ,the whole  
of mechanics1 thus1 is based upon an    
idea1 which1 though unequivocal1 is yet 
unwonted and not coequal with the other 
principles and axioms of mechanics4     
,every student of mechanics1 at some    
stage of his progress1 feels the        
uncomfortableness of this state of      
affairs2 every one wishes it removed2   
but seldom is the difficulty stated in  
words4 ,accordingly1 the zealous pupil  
of the science is highly rejoiced when  
he reads in a master like ,poinsot      
7,thorie gnrale de l'quilibre et du     
mouvement des systmes7 the following    
passage1 in which that author is giving 
his opinion of the ,analytical          
,mechanics3       ,in the meantime1     
because our attention in that work was  

first      wholly engrossed with the    
consideration of its beautiful          
development of mechanics1 which seemed  
to spring complete from a      single   
formula1 we naturally believed that the 
science was      completed or that it   
only remained to seek the demonstration 
of the      principle of virtual        
velocities4 ,but that quest brought back
 all      the difficulties that we had  
overcome by the principle itself4 ,that 
law so general1 wherein are mingled the 
vague and unfamiliar ideas      of      
infinitely small movements and of       
perturbations of equilibrium1      only 
grew obscure upon examination2 and the  
work of ,lagrange      supplying nothing
 clearer than the march of analysis1 we 
saw      plainly that the clouds had    
only appeared lifted from the course of 
mechanics because they had1 so to speak1
 been gathered at the very      origin  
of that science4       ,at bottom1 a    
general demonstration of the principle  
of virtual      velocities would be     

equivalent to the establishment of the  
whole of      mechanics upon a different
 basis3 for the demonstration of a law  
which embraces a whole science is       
neither more nor less than the          
reduction of that science to another law
 just as general1 but      evident1 or  
at least more simple than the first1 and
 which1      consequently1 would render 
that useless4#ej  ,according to         
,poinsot1 therefore1 a proof of the     
principle of virtual movements is       
tantamount to a total rehabilitation of 
mechanics4  ,another circumstance of    
discomfort to the mathematician is1 that
 in the historical form in which        
mechanics at present exists1 dynamics is
 founded on statics1 whereas it is      
desirable that in a science which       
pretends to deductive completeness the  
more special statical theorems should be
 deducible from the more general        
dynamical principles4  ,in fact1 a great
 master1 ,gauss1 gave expression to this
 desire in his presentment of the       

principle of least constraint 7,crelle's
 ,journal fr reine und angewandte       
,mathematik1 ,vol4 ,,iv1 p4 #bcc7 in the
 following words3 ,proper as it is that 
in the gradual development of a science1
 and in the instruction of individuals1 
the easy should precede the difficult1  
the simple the complex1 the special the 
general1 yet the mind1 when once it has 
reached a higher point of view1 demands 
the contrary course1 in which all       
statics shall appear simply as a special
 case of mechanics4 ,gauss's own        
principle1 now1 possesses all the       
requisites of universality1 but its     
difficulty is that it is not immediately
 intelligible and that ,gauss deduced it
 with the help of ,d',alembert's        
principle1 a procedure which left       
matters where they were before4         
,whence1 now1 is derived this strange   
part which the principle of virtual     
motion plays in mechanics8 ,for the     
present ,i shall only make this reply4  
,it would be difficult for me to tell   

the difference of impression which      
,lagrange's proof of the principle made 
on me when ,i first took it up as a     
student and when ,i subsequently resumed
 it after having made historical        
researches4 ,it first appeared to me    
insipid1 chiefly on account of the      
pulleys and the cords which did not fit 
in with the mathematical view1 and whose
 action ,i would much rather have       
discovered from the principle itself    
than have taken for granted4 ,but now   
that ,i have studied the history of the 
science ,i cannot imagine a more        
beautiful demonstration4  ,in fact1     
through all mechanics it is this        
self-same principle of excluded         
perpetual motion which accomplishes     
almost all1 which displeased ,lagrange1 
but which he still had to employ1 at    
least tacitly1 in his own demonstration4
 ,if we give this principle its proper  
place and setting1 the paradox is       
explained4  ,the principle of excluded  
perpetual motion is thus no new         

discovery2 it has been the guiding idea1
 for three hundred years1 of all the    
great inquirers4 ,but the principle     
cannot properly be based upon mechanical
 perceptions4 ,for long before the      
development of mechanics the conviction 
of its truth existed and even           
contributed to that development4 ,its   
power of conviction1 therefore1 must    
have more universal and deeper roots4   
,we shall revert to this point4   ,,ii4 
,,mechanical ,,physics4  ,it cannot be  
denied that an unmistakable tendency has
 prevailed1 from ,democritus to the     
present day1 to explain all physical    
events mechanically4 ,not to mention    
earlier obscure expressions of that     
tendency we read in ,huygens the        
following3#ea       ,there can be no    
doubt that light consists of the motion 
of a      certain substance4 ,for if we 
examine its production1 we find that    
here on earth it is principally fire and
 flame which engender it1      both of  
which contain beyond doubt bodies which 

are in rapid      movement1 since they  
dissolve and destroy many other bodies  
more      solid than they3 while if we  
regard its effects1 we see that when    
light is accumulated1 say by concave    
mirrors1 it has the property      of    
combustion just as fire has1 that is to 
say1 it disunites the      parts of     
bodies1 which is assuredly a proof of   
motion1 at least      in the true       
philosophy1 in which the causes of all  
natural      effects are conceived as   
mechanical causes4 ,which in my judgment
      must be accomplished or all hope  
of ever understanding physics           
renounced4#eb  ,s4 ,carnot1#ec in       
introducing the principle of excluded   
perpetual motion into the theory of     
heat1 makes the following apology3      
,it will be objected here1 perhaps1 that
 a perpetual motion proved              
impossible for purely mechanical        
actions1 is perhaps not so when      the
 influence of heat or of electricity is 
employed4 ,but can      phenomena of    

heat or electricity be thought of as due
 to anything      else than to certain  
motions of bodies1 and as such must they
 not      be subject to the general laws
 of mechanics8#ed  ,these examples1     
which might be multiplied by quotations 
from recent literature indefinitely1    
show that a tendency to explain all     
things mechanically actually exists4    
,this tendency is also intelligible4    
,mechanical events as simple motions in 
space and time best admit of observation
 and pursuit by the help of our highly  
organised senses4 ,we reproduce         
mechanical processes almost without     
effort in our imagination4 ,pressure as 
a circumstance that produces motion is  
very familiar to us from daily          
experience4 ,all changes which the      
individual personally produces in his   
environment1 or humanity brings about by
 means of the arts in the world1 are    
effected through the instrumentality of 
motions4 ,almost of necessity1          
therefore1 motion appears to us as the  

most important physical factor4         
,moreover1 mechanical properties may be 
discovered in all physical events4 ,the 
sounding bell trembles1 the heated body 
expands1 the electrified body attracts  
other bodies4 ,why1 therefore1 should we
 not attempt to grasp all events under  
their mechanical aspect1 since that is  
so easily apprehended and most          
accessible to observation and           
measurement8 ,in fact1 no objection is  
to be made to the attempt to elucidate  
the properties of physical events by    
mechanical analogies4  ,but modern      
physics has proceeded very far in this  
direction4 ,the point of view which     
,wundt represents in his excellent      
treatise ,on the ,physical ,axioms is   
probably shared by the majority of      
physicists4 ,the axioms of physics which
 ,wundt sets up are as follows3  #a4    
,all natural causes are motional causes4
  #b4 ,every motional cause lies outside
 the object moved4  #c4 ,all motional   
causes act in the direction of the      

straight line of junction1 and so forth4
  #d4 ,the effect of every cause        
persists4  #e4 ,every effect involves an
 equal countereffect4  #f4 ,every effect
 is equivalent to its cause4  ,these    
principles might be studied properly    
enough as fundamental principles of     
mechanics4 ,but when they are set up as 
axioms of physics1 their enunciation is 
simply tantamount to a negation of all  
events except motion4  ,according to    
,wundt1 all changes of nature are mere  
changes of place4 ,all causes are       
motional causes 7page #bf74 ,any        
discussion of the philosophical grounds 
on which ,wundt supports his theory     
would lead us deep into the speculations
 of the ,eleatics and the ,herbartians4 
,change of place1 ,wundt holds1 is the  
only change of a thing in which a thing 
remains identical with itself4 ,if a    
thing changed qualitatively1 we should  
be obliged to imagine that something was
 annihilated and something else created 
in its place1 which is not to be        

reconciled with our idea of the identity
 of the object observed and of the      
indestructibility of matter4 ,but we    
have only to remember that the ,eleatics
 encountered difficulties of exactly the
 same sort in motion4 ,can we not also  
imagine that a thing is destroyed in one
 place and in another an exactly similar
 thing created8 ,after all1 do we really
 know more why a body leaves one place  
and appears in another1 than why a cold 
body grows warm8 ,granted that we had a 
perfect knowledge of the mechanical     
processes of nature1 could we and should
 we1 for that reason1 put out of the    
world all other processes that we do not
 understand8 ,on this principle it would
 really be the simplest course to deny  
the existence of the whole world4 ,this 
is the point at which the ,eleatics     
ultimately arrived1 and the school of   
,herbart stopped little short of the    
same goal4  ,physics treated in this    
sense supplies us simply with a diagram 
of the world1 in which we do not know   

reality again4 ,it happens1 in fact1 to 
men who give themselves up to this view 
for many years1 that the world of sense 
from which they start as a province of  
the greatest familiarity1 suddenly      
becomes1 in their eyes1 the supreme     
world-riddle4  ,intelligible as it is1  
therefore1 that the efforts of thinkers 
have always been bent upon the reduction
 of all physical processes to the       
motions of atoms1 it must yet be        
affirmed that this is a chimerical      
ideal4 ,this ideal has often played an  
effective part in popular lectures1 but 
in the workshop of the serious inquirer 
it has discharged scarcely the least    
function4 ,what has really been achieved
 in mechanical physics is either the    
elucidation of physical processes by    
more familiar mechanical analogies1 7for
 example1 the theories of light and of  
electricity17 or the exact quantitative 
ascertainment of the connexion of       
mechanical processes with other physical
 processes1 for example1 the results of 

thermodynamics4   ,,iii4 ,,the          
,,principle ,,of ,,energy ,,in          
,,physics4  ,we can know only from      
experience that mechanical processes    
produce other physical transformations1 
or vice versa4 ,the attention was first 
directed to the connexion of mechanical 
processes1 especially the performance of
 work1 with changes of thermal          
conditions by the invention of the      
steam-engine1 and by its great technical
 importance4 ,technical interests and   
the need of scientific lucidity meeting 
in the mind of ,s4 ,carnot led to the   
remarkable development from which       
thermodynamics flowed4 ,it is simply an 
accident of history that the development
 in question was not connected with the 
practical applications of electricity4  
,in the determination of the maximum    
quantity of work that1 generally1 a     
heat-machine1 or1 to take a special     
case1 a steam-engine1 can perform with  
the expenditure of a given amount of    
heat of combustion1 ,carnot is guided by

 mechanical analogies4 ,a body can do   
work on being heated1 by expanding under
 pressure4 ,but to do this the body must
 receive heat from a hotter body4 ,heat1
 therefore1 to do work1 must pass from a
 hotter body to a colder body1 just as  
water must fall from a higher level to a
 lower level to put a mill-wheel in     
motion4 ,differences of temperature1    
accordingly1 represent forces able to do
 work exactly as do differences of      
height in heavy bodies4 ,carnot pictures
 to himself an ideal process in which no
 heat flows away unused1 that is1       
without doing work4 ,with a given       
expenditure of heat1 accordingly1 this  
process furnishes the maximum of work4  
,an analogue of the process would be a  
mill-wheel which scooping its water out 
of a higher level would slowly carry it 
to a lower level without the loss of a  
drop4 ,a peculiar property of the       
process is1 that with the expenditure of
 the same work the water can be raised  
again exactly to its original level4    

,this property of reversibility is also 
shared by the process of ,carnot4 ,his  
process also can be reversed by the     
expenditure of the same amount of work1 
and the heat again brought back to its  
original temperature level4  ,suppose1  
now1 we had two different reversible    
processes ,a1 ,b1 such that in ,a a     
quantity of heat1 ,q1 flowing off from  
the temperature t to the lower          
temperature t should perform the work   
,w1 but in ,b under the same            
circumstances it should perform a       
greater quantity of work ,w  ,w'2 then1 
we could join ,b in the sense assigned  
and ,a in the reverse sense into a      
single process4 ,here ,a would reverse  
the transformation of heat produced by  
,b and would leave a surplus of work    
,w'1 produced1 so to speak1 from        
nothing4 ,the combination would present 
a perpetual motion4  ,with the feeling1 
now1 that it makes little difference    
whether the mechanical laws are broken  
directly or indirectly 7by processes of 

heat71 and convinced of the existence of
 a universal law-ruled connexion of     
nature1 ,carnot here excludes for the   
first time from the province of general 
physics the possibility of a perpetual  
motion4 ,but it follows1 then1 that the 
quantity of work ,w1 produced by the    
passage of a quantity of heat ,q from a 
temperature t to a temperature t1 is    
independent of the nature of the        
substances as also of the character of  
the process1 so far as that is          
unaccompanied by loss1 but is wholly    
dependent upon the temperature t1 t4    
,this important principle has been fully
 confirmed by the special researches of 
,carnot himself 7#ahbd71 of ,clapeyron  
7#ahcd71 and of ,sir ,william ,thomson  
7#ahdi71 now ,lord ,kelvin4 ,the        
principle was reached without any       
assumption whatever concerning the      
nature of heat1 simply by the exclusion 
of a perpetual motion4 ,carnot1 it is   
true1 was an adherent of the theory of  
,black1 according to which the sum-total

 of the quantity of heat in the world is
 constant1 but so far as his            
investigations have been hitherto       
considered the decision on this point is
 of no consequence4 ,carnot's principle 
led to the most remarkable results4 ,w4 
,thomson 7#ahdh7 founded upon it the    
ingenious idea of an absolute scale of  
temperature4 ,james ,thomson 7#ahdi7    
conceived a ,carnot process to take     
place with water freezing under pressure
 and1 therefore1 performing work4 ,he   
discovered1 thus1 that the freezing     
point is lowered #jjjge ,celsius by     
every additional atmosphere of pressure4
 ,this is mentioned merely as an        
example4  ,about twenty years after the 
publication of ,carnot's book a further 
advance was made by ,j4 ,r4 ,mayer and  
,j4 ,p4 ,joule4 ,mayer1 while engaged as
 a physician in the service of the      
,dutch1 observed1 during a process of   
bleeding in ,java1 an unusual redness of
 the venous blood4 ,in agreement with   
,liebig's theory of animal heat he      

connected this fact with the diminished 
loss of heat in warmer climates1 and    
with the diminished expenditure of      
organic combustibles4 ,the total        
expenditure of heat of a man at rest    
must be equal to the total heat of      
combustion4 ,but since all organic      
actions1 even the mechanical actions1   
must be set down to the credit of the   
heat of combustion1 some connexion must 
exist between mechanical work and       
expenditure of heat4  ,joule started    
from quite similar convictions          
concerning the galvanic battery4 ,a heat
 of association equivalent to the       
consumption of the zinc can be made to  
appear in the galvanic cell4 ,if a      
current is set up1 a part of this heat  
appears in the conductor of the current4
 ,the interposition of an apparatus for 
the decomposition of water causes a part
 of this heat to disappear1 which on the
 burning of the explosive gas formed1 is
 reproduced4 ,if the current runs an    
electromotor1 a portion of the heat     

again disappears1 which1 on the         
consumption of the work by friction1    
again makes its appearance4             
,accordingly1 both the heat produced and
 the work produced1 appeared to ,joule  
also as connected with the consumption  
of material4 ,the thought was therefore 
present1 both to ,mayer and to ,joule1  
of regarding heat and work as equivalent
 quantities1 so connected with each     
other that what is lost in one form     
universally appears in another4 ,the    
result of this was a substantial        
conception of heat and of work1 and     
ultimately a substantial conception of  
energy4 ,here every physical change of  
condition is regarded as energy1 the    
destruction of which generates work or  
equivalent heat4 ,an electric charge1   
for example1 is energy4  ,in #ahdb      
,mayer had calculated from the physical 
constants then universally accepted that
 by the disappearance of one            
kilogramme-calorie #cfe                 
kilogramme-metres of work could be      

performed1 and vice versa4 ,joule1 on   
the other hand1 by a long series of     
delicate and varied experiments         
beginning in #ahdc ultimately determined
 the mechanical equivalent of the       
kilogramme-calorie1 more exactly1 as    
#dbe kilogramme-metres4  ,if we estimate
 every change of physical condition by  
the mechanical work which can be        
performed upon the disappearance of that
 condition1 and call this measure       
energy1 then we can measure all physical
 changes of condition1 no matter how    
different they may be1 with the same    
common measure1 and say3 the sum-total  
of all energy remains constant4 ,this is
 the form that the principle of excluded
 perpetual motion received at the hands 
of ,mayer1 ,joule1 ,helmholtz1 and ,w4  
,thomson in its extension to the whole  
domain of physics4  ,after it had been  
proved that heat must disappear if      
mechanical work was to be done at its   
expense1 ,carnot's principle could no   
longer be regarded as a complete        

expression of the facts4 ,its improved  
form was first given1 in #ahej1 by      
,clausius1 whom ,thomson followed in    
#ahea4 ,it runs thus3 ,if a quantity of 
heat ,q' is transformed into work in a  
reversible process1 another quantity of 
heat ,q of the absolute#ee temperature  
,t is lowered to the absolute           
temperature ,t4 ,here ,q' is dependent  
only on ,q1 ,t1 ,t1 but is independent  
of the substances used and of the       
character of the process1 so far as that
 is unaccompanied by loss4 ,owing to    
this last fact1 it is sufficient to find
 the relation which obtains for some one
 well-known physical substance1 say a   
gas1 and some definite simple process4  
,the relation found will be the one that
 holds generally4 ,we get1 thus1        
,q'_/7,q'  ,q7  7,t-,t7_/,t 7#a7  that  
is1 the quotient of the available heat  
,q' transformed into work divided by the
 sum of the transformed and transferred 
heats 7the total sum used71 the         
so-called economical coefficient of the 

process1 is1  7,t-,t7_/,t4   ,,iv4 ,,the
 ,,conceptions ,,of ,,heat4  ,when a    
cold body is put in contact with a warm 
body it is observed that the first body 
is warmed and that the second body is   
cooled4 ,we may say that the first body 
is warmed at the expense of the second  
body4 ,this suggests the notion of a    
thing1 or heat-substance1 which passes  
from the one body to the other4 ,if two 
masses of water m1 m'1 of unequal       
temperatures1 be put together1 it will  
be found1 upon the rapid equalisation of
 the temperatures1 that the respective  
changes of temperatures u and u' are    
inversely proportional to the masses and
 of opposite signs1 so that the         
algebraical sum of the products is1  mu 
m'u'  #j4  ,black called the products   
mu1 m'u'1 which are decisive for our    
knowledge of the process1 quantities of 
heat4 ,we may form a very clear picture 
of these products by conceiving them    
with ,black as measures of the          
quantities of some substance4 ,but the  

essential thing is not this picture but 
the constancy of the sum of these       
products in simple processes of         
conduction4 ,if a quantity of heat      
disappears at one point1 an equally     
large quantity will make its appearance 
at some other point4 ,the retention of  
this idea leads to the discovery of     
specific heat4 ,black1 finally1         
perceives that also something else may  
appear for a vanished quantity of heat1 
namely3 the fusion or vaporisation of a 
definite quantity of matter4 ,he adheres
 here still to this favorite view1      
though with some freedom1 and considers 
the vanished quantity of heat as still  
present1 but as latent4  ,the generally 
accepted notion of a caloric1 or        
heat-stuff1 was strongly shaken by the  
work of ,mayer and ,joule4 ,if the      
quantity of heat can be increased and   
diminished1 people said1 heat cannot be 
a substance1 but must be a motion4 ,the 
subordinate part of this statement has  
become much more popular than all the   

rest of the doctrine of energy4 ,but we 
may convince ourselves that the motional
 conception of heat is now as           
unessential as was formerly its         
conception as a substance4 ,both ideas  
were favored or impeded solely by       
accidental historical circumstances4 ,it
 does not follow that heat is not a     
substance from the fact that a          
mechanical equivalent exists for        
quantity of heat4 ,we will make this    
clear by the following question which   
bright students have sometimes put to   
me4 ,is there a mechanical equivalent of
 electricity as there is a mechanical   
equivalent of heat8 ,yes1 and no4 ,there
 is no mechanical equivalent of quantity
 of electricity as there is an          
equivalent of quantity of heat1 because 
the same quantity of electricity has a  
very different capacity for work1       
according to the circumstances in which 
it is placed2 but there is a mechanical 
equivalent of electrical energy4  ,let  
us ask another question4 ,is there a    

mechanical equivalent of water8 ,no1    
there is no mechanical equivalent of    
quantity of water1 but there is a       
mechanical equivalent of weight of water
 multiplied by its distance of descent4 
,when a ,leyden jar is discharged and   
work thereby performed1 we do not       
picture to ourselves that the quantity  
of electricity disappears as work is    
done1 but we simply assume that the     
electricities come into different       
positions1 equal quantities of positive 
and negative electricity being united   
with one another4  ,what1 now1 is the   
reason of this difference of view in our
 treatment of heat and of electricity8  
,the reason is purely historical1 wholly
 conventional1 and1 what is still more  
important1 is wholly indifferent4 ,i may
 be allowed to establish this assertion4
  ,in #aghe ,coulomb constructed his    
torsion balance1 by which he was enabled
 to measure the repulsion of electrified
 bodies4 ,suppose we have two small     
balls1 ,a1 ,b1 which over their whole   

extent are similarly electrified4 ,these
 two balls will exert on one another1 at
 a certain distance r of their centres1 
a certain repulsion p4 ,we bring into   
contact with ,b now a ball ,c1 suffer   
both to be equally electrified1 and then
 measure the repulsion of ,b from ,a and
 of ,c from ,a at the same distance r4  
,the sum of these repulsions is again p4
 ,accordingly something has remained    
constant4 ,if we ascribe this effect to 
a substance1 then we infer naturally its
 constancy4 ,but the essential point of 
the exposition is the divisibility of   
the electric force p and not the simile 
of substance4  ,in #ahch ,riess         
constructed his electrical              
air-thermometer 7the                    
thermoelectrometer74 ,this gives a      
measure of the quantity of heat produced
 by the discharge of jars4 ,this        
quantity of heat is not proportional to 
the quantity of electricity contained in
 the jar by ,coulomb's measure1 but if  
,q be this quantity and ,c be the       

capacity1 is proportional to ,q_/#b;,c1 
or1 more simply still1 to the energy of 
the charged jar4 ,if1 now1 we discharge 
the jar completely through the          
thermometer1 we obtain a certain        
quantity of heat1 ,w4 ,but if we make   
the discharge through the thermometer   
into a second jar1 we obtain a quantity 
less than ,w4 ,but we may obtain the    
remainder by completely discharging both
 jars through the air-thermometer1 when 
it will again be proportional to the    
energy of the two jars4 ,on the first1  
incomplete discharge1 accordingly1 a    
part of the electricity's capacity for  
work was lost4  ,when the charge of a   
jar produces heat its energy is changed 
and its value by ,riess's thermometer is
 decreased4 ,but by ,coulomb's measure  
the quantity remains unaltered4  ,now   
let us imagine that ,riess's thermometer
 had been invented before ,coulomb's    
torsion balance1 which is not a         
difficult feat1 since both inventions   
are independent of each other2 what     

would be more natural than that the     
quantity of electricity contained in a  
jar should be measured by the heat      
produced in the thermometer8 ,but then1 
this so-called quantity of electricity  
would decrease on the production of heat
 or on the performance of work1 whereas 
it now remains unchanged2 in that case1 
therefore1 electricity would not be a   
substance but a motion1 whereas now it  
is still a substance4 ,the reason1      
therefore1 why we have other notions of 
electricity than we have of heat1 is    
purely historical1 accidental1 and      
conventional4  ,this is also the case   
with other physical things4 ,water does 
not disappear when work is done4 ,why8  
,because we measure quantity of water   
with scales1 just as we do electricity4 
,but suppose the capacity of water for  
work were called quantity1 and had to be
 measured1 therefore1 by a mill instead 
of by scales2 then this quantity also   
would disappear as it performed the     
work4 ,it may1 now1 be easily conceived 

that many substances are not so easily  
got at as water4 ,in that case we should
 be unable to carry out the one kind of 
measurement with the scales whilst many 
other modes of measurement would still  
be left us4  ,in the case of heat1 now1 
the historically established measure of 
quantity is accidentally the work-value 
of the heat4 ,accordingly1 its quantity 
disappears when work is done4 ,but that 
heat is not a substance follows from    
this as little as does the opposite     
conclusion that it is a substance4 ,in  
,black's case the quantity of heat      
remains constant because the heat passes
 into no other form of energy4  ,if any 
one to-day should still wish to think of
 heat as a substance1 we might allow    
that person this liberty with little    
ado4 ,he would only have to assume that 
that which we call quantity of heat was 
the energy of a substance whose quantity
 remained unaltered1 but whose energy   
changed4 ,in point of fact we might much
 better say1 in analogy with the other  

terms of physics1 energy of heat1       
instead of quantity of heat4  ,when we  
wonder1 therefore1 at the discovery that
 heat is motion1 we wonder at something 
that was never discovered4 ,it is       
perfectly indifferent and possesses not 
the slightest scientific value1 whether 
we think of heat as a substance or not4 
,the fact is1 heat behaves in some      
connexions like a substance1 in others  
not4 ,heat is latent in steam as oxygen 
is latent in water4   ,v4 ,,the         
,,conformity ,,in ,,the ,,deportment    
,,of ,,the ,,energies4  ,the foregoing  
reflexions will gain in lucidity from a 
consideration of the conformity which   
obtains in the behavior of all energies1
 a point to which ,i called attention   
long ago4#ef  ,a weight ,p at a height  
,h represents an energy ,w  ,,ph4 ,if we
 suffer the weight to sink to a lower   
height ,h1 during which work is done1   
and the work done is employed in the    
production of living force1 heat1 or an 
electric charge1 in short1 is           

transformed1 then the energy ,w  ,,ph is
 still left4 ,the equation subsists     
,w_/,h  ,w_/,h1 7#b7  or1 denoting the  
transformed energy by ,w'  ,w-,w and the
 transferred energy1 that transported to
 the lower level1 by ,w  ,w1  ,w'_/7,w' 
,w7  7,h-,h7_/,h1 7#c7  an equation in  
all respects analogous to equation 7#a7 
at page #afe4 ,the property in question1
 therefore1 is by no means peculiar to  
heat4 ,equation 7#b7 gives the relation 
between the energy taken from the higher
 level and that deposited on the lower  
level 7the energy left behind72 it says 
that these energies are proportional to 
the heights of the levels4 ,an equation 
analogous to equation 7#b7 may be set up
 for every form of energy2 hence the    
equation which corresponds to equation  
7#c71 and so to equation 7#a71 may be   
regarded as valid for every form4 ,for  
electricity1 for example1 ,h1 ,h signify
 the potentials4  ,when we observe for  
the first time the agreement here       
indicated in the transformative law of  

the energies1 it appears surprising and 
unexpected1 for we do not perceive at   
once its reason4 ,but to him who pursues
 the comparative historical method that 
reason will not long remain a secret4   
,since ,galileo1 mechanical work1 though
 long under a different name1 has been a
 fundamental concept of mechanics1 as   
also a very important notion in the     
applied sciences4 ,the transformation of
 work into living force1 and of living  
force into work1 suggests directly the  
notion of energy--the idea having been  
first fruitfully employed by ,huygens1  
although ,thomas ,young first called it 
by the name of energy4 ,let us add to   
this the constancy of weight 7really the
 constancy of mass7 and we shall see    
that with respect to mechanical energy  
it is involved in the very definition of
 the term that the capacity for work or 
the potential energy of a weight is     
proportional to the height of the level 
at which it is1 in the geometrical      
sense1 and that it decreases on the     

lowering of the weight1 on              
transformation1 proportionally to the   
height of the level4 ,the zero level    
here is wholly arbitrary4 ,with this1   
equation 7#b7 is given1 from which all  
the other forms follow4  ,when we       
reflect on the tremendous start which   
mechanics had over the other branches of
 physics1 it is not to be wondered at   
that the attempt was always made to     
apply the notions of that science       
wherever this was possible4 ,thus the   
notion of mass1 for example1 was        
imitated by ,coulomb in the notion of   
quantity of electricity4 ,in the further
 development of the theory of           
electricity1 the notion of work was     
likewise immediately introduced in the  
theory of potential1 and heights of     
electrical level were measured by the   
work of unit of quantity raised to that 
level4 ,but with this the preceding     
equation with all its consequences is   
given for electrical energy4 ,the case  
with the other energies was similar4    

,thermal energy1 however1 appears as a  
special case4 ,only by the peculiar     
experiments mentioned could it be       
discovered that heat is an energy4 ,but 
the measure of this energy by ,black's  
quantity of heat is the outcome of      
fortuitous circumstances4 ,in the first 
place1 the accidental slight variability
 of the capacity for heat c with the    
temperature1 and the accidental slight  
deviation of the usual thermometrical   
scales from the scale derived from the  
tensions of gases1 brings it about that 
the notion quantity of heat can be set  
up and that the quantity of heat ct     
corresponding to a difference of        
temperature t is nearly proportional to 
the energy of the heat4 ,it is a quite  
accidental historical circumstance that 
,amontons hit upon the idea of measuring
 temperature by the tension of a gas4   
,it is certain in this that he did not  
think of the work of the heat4#eg ,but  
the numbers standing for temperature1   
thus1 are made proportional to the      

tensions of gases1 that is1 to the work 
done by gases1 with otherwise equal     
changes of volume4 ,it thus happens that
 temperature heights and level heights  
of work are proportional to one another4
  ,if properties of the thermal         
condition varying greatly from the      
tensions of gases had been chosen1 this 
relation would have assumed very        
complicated forms1 and the agreement    
between heat and the other energies     
above considered would not subsist4 ,it 
is very instructive to reflect upon this
 point4 ,a natural law1 therefore1 is   
not implied in the conformity of the    
behavior of the energies1 but this      
conformity is rather conditioned by the 
uniformity of our modes of conception   
and is also partly a matter of good     
fortune4   ,,vi4 ,,the ,,differences    
,,of ,,the ,,energies ,,and ,,the       
,,limits ,,of ,,the ,,principle ,,of    
,,energy4  ,of every quantity of heat ,q
 which does work in a reversible process
 7one unaccompanied by loss7 between the

 absolute temperatures ,t1 ,t1 only the 
portion  7,t-,t7_/,t  is transformed    
into work1 while the remainder is       
transferred to the lower                
temperature-level ,t4 ,this transferred 
portion can1 upon the reversal of the   
process1 with the same expenditure of   
work1 again be brought back to the level
 ,t4 ,but if the process is not         
reversible1 then more heat than in the  
foregoing case flows to the lower level1
 and the surplus can no longer be       
brought back to the higher level ,t     
without some special expenditure4 ,w4   
,thomson 7#aheb71 accordingly1 drew     
attention to the fact1 that in all      
non-reversible1 that is1 in all real    
thermal processes1 quantities of heat   
are lost for mechanical work1 and that  
accordingly a dissipation or waste of   
mechanical energy is taking place4 ,in  
all cases1 heat is only partially       
transformed into work1 but frequently   
work is wholly transformed into heat4   
,hence1 a tendency exists towards a     

diminution of the mechanical energy and 
towards an increase of the thermal      
energy of the world4  ,for a simple1    
closed cyclical process1 accompanied by 
no loss1 in which the quantity of heat  
,q is taken from the level ,t1 and the  
quantity ,q is deposited upon the level 
,t1 the following relation1 agreeably to
 equation 7#b71 exists1  -7,q_/,t7      
7,q_/,t7  #j4  ,similarly1 for any      
number of compound reversible cycles    
,clausius finds the algebraical sum     
sum,q_/,t  #j1  and supposing the       
temperature to change continuously1     
integrald,q_/,t  #j 7#d7  ,here the     
elements of the quantities of heat      
deducted from a given level are reckoned
 negative1 and the elements imparted to 
it1 positive4 ,if the process is not    
reversible1 then expression 7#d71 which 
,clausius calls entropy1 increases4 ,in 
actual practice this is always the case1
 and ,clausius finds himself led to the 
statement3  #a4 ,that the energy of the 
world remains constant4  #b4 ,that the  

entropy of the world tends toward a     
maximum4  ,once we have noted the       
above-indicated conformity in the       
behavior of different energies1 the     
peculiarity of thermal energy here      
mentioned must strike us4 ,whence is    
this peculiarity derived1 for1 generally
 every energy passes only partly into   
another form1 which is also true of     
thermal energy8 ,the explanation will be
 found in the following4  ,every        
transformation of a special kind of     
energy ,a is accompanied with a fall of 
potential of that particular kind of    
energy1 including heat4 ,but whilst for 
the other kinds of energy a             
transformation and therefore a loss of  
energy on the part of the kind sinking  
in potential is connected with the fall 
of the potential1 with heat the case is 
different4 ,heat can suffer a fall of   
potential without sustaining a loss of  
energy1 at least according to the       
customary mode of estimation4 ,if a     
weight sinks1 it must create perforce   

kinetic energy1 or heat1 or some other  
form of energy4 ,also1 an electrical    
charge cannot suffer a fall of potential
 without loss of energy1 i4 e41 without 
transformation4 ,but heat can pass with 
a fall of temperature to a body of      
greater capacity and the same thermal   
energy still be preserved1 so long as we
 regard every quantity of heat as       
energy4 ,this it is that gives to heat1 
besides its property of energy1 in many 
cases the character of a material       
substance1 or quantity4  ,if we look at 
the matter in an unprejudiced light1 we 
must ask if there is any scientific     
sense or purpose in still considering as
 energy a quantity of heat that can no  
longer be transformed into mechanical   
work1 7for example1 the heat of a closed
 equably warmed material system74 ,the  
principle of energy certainly plays in  
this case a wholly superfluous rle1     
which is assigned to it only from       
habit4#eh ,to maintain the principle of 
energy in the face of a knowledge of the

 dissipation or waste of mechanical     
energy1 in the face of the increase of  
entropy is equivalent almost to the     
liberty which ,black took when he       
regarded the heat of liquefaction as    
still present but latent4#ei ,it is to  
be remarked further1 that the           
expressions energy of the world and     
entropy of the world are slightly       
permeated with scholasticism4 ,energy   
and entropy are metrical notions4 ,what 
meaning can there be in applying these  
notions to a case in which they are not 
applicable1 in which their values are   
not determinable8  ,if we could really  
determine the entropy of the world it   
would represent a true1 absolute measure
 of time4 ,in this way is best seen the 
utter tautology of a statement that the 
entropy of the world increases with the 
time4 ,time1 and the fact that certain  
changes take place only in a definite   
sense1 are one and the same thing4      
,,vii4 ,,the ,,sources ,,of ,,the       
,,principle ,,of ,,energy4  ,we are now 

prepared to answer the question1 ,what  
are the sources of the principle of     
energy8 ,all knowledge of nature is     
derived in the last instance from       
experience4 ,in this sense they are     
right who look upon the principle of    
energy as a result of experience4       
,experience teaches that the            
sense-elements alpha beta gamma delta   
444 into which the world may be         
decomposed1 are subject to change4 ,it  
tells us further1 that certain of these 
elements are connected with other       
elements1 so that they appear and       
disappear together2 or1 that the        
appearance of the elements of one class 
is connected with the disappearance of  
the elements of the other class4 ,we    
will avoid here the notions of cause and
 effect because of their obscurity and  
equivocalness4 ,the result of experience
 may be expressed as follows3 ,the      
sensuous elements of the world 7alpha   
beta gamma delta 4447 show themselves to
 be interdependent4 ,this               

interdependence is best represented by  
some such conception as is in geometry  
that of the mutual dependence of the    
sides and angles of a triangle1 only    
much more varied and complex4  ,as an   
example1 we may take a mass of gas      
enclosed in a cylinder and possessed of 
a definite volume 7alpha71 which we     
change by a pressure 7beta7 on the      
piston1 at the same time feeling the    
cylinder with our hand and receiving a  
sensation of heat 7gamma74 ,increase of 
pressure diminishes the volume and      
increases the sensation of heat4  ,the  
various facts of experience are not in  
all respects alike4 ,their common       
sensuous elements are placed in relief  
by a process of abstraction and thus    
impressed upon the memory4 ,in this way 
the expression is obtained of the       
features of agreement of extensive      
groups of facts4 ,the simplest sentence 
which we can utter is1 by the very      
nature of language1 an abstraction of   
this kind4 ,but account must also be    

taken of the differences of related     
facts4 ,facts may be so nearly related  
as to contain the same kind of a alpha  
beta gamma 4441 but the relation be such
 that the alpha beta gamma 444 of the   
one differ from the alpha beta gamma 444
 of the other only by the number of     
equal parts into which they can be      
divided4 ,such being the case1 if rules 
can be given for deducing from one      
another the numbers which are the       
measures of these alpha beta gamma 4441 
then we possess in such rules the most  
general expression of a group of facts1 
as also that expression which           
corresponds to all its differences4     
,this is the goal of quantitative       
investigation4  ,if this goal be reached
 what we have found is that between the 
alpha beta gamma 444 of a group of      
facts1 or better1 between the numbers   
which are their measures1 a number of   
equations exists4 ,the simple fact of   
change brings it about that the number  
of these equations must be smaller than 

the number of the alpha beta gamma 4444 
,if the former be smaller by one than   
the latter1 then one portion of the     
alpha beta gamma 444 is uniquely        
determined by the other portion4  ,the  
quest of relations of this last kind is 
the most important function of special  
experimental research1 because we are   
enabled by it to complete in thought    
facts that are only partly given4 ,it is
 self-evident that only experience can  
ascertain that between the alpha beta   
gamma 444 relations exist and of what   
kind they are4 ,further1 only experience
 can tell that the relations that exist 
between the alpha beta gamma 444 are    
such that changes of them can be        
reversed4 ,if this were not the fact all
 occasion for the enunciation of the    
principle of energy1 as is easily seen1 
would be wanting4 ,in experience1       
therefore1 is buried the ultimate       
well-spring of all knowledge of nature1 
and consequently1 in this sense1 also   
the ultimate source of the principle of 

energy4  ,but this does not exclude the 
fact that the principle of energy has   
also a logical root1 as will now be     
shown4 ,let us assume on the basis of   
experience that one group of sensuous   
elements alpha beta gamma 444 determines
 uniquely another group lambda mu nu    
4444 ,experience further teaches that   
changes of alpha beta gamma 444 can be  
reversed4 ,it is then a logical         
consequence of this observation1 that   
every time that alpha beta gamma 444    
assume the same values this is also the 
case with lambda mu nu 4444 ,or1 that   
purely periodical changes of alpha beta 
gamma 444 can produce no permanent      
changes of lambda mu nu 4444 ,if the    
group lambda mu nu 444 is a mechanical  
group1 then a perpetual motion is       
excluded4  ,it will be said that this is
 a vicious circle1 which we will grant4 
,but psychologically1 the situation is  
essentially different1 whether ,i think 
simply of the unique determination and  
reversibility of events1 or whether ,i  

exclude a perpetual motion4 ,the        
attention takes in the two cases        
different directions and diffuses light 
over different sides of the question1   
which logically of course are           
necessarily connected4  ,surely that    
firm1 logical setting of the thoughts   
noticeable in the great inquirers1      
,stevinus1 ,galileo1 and the rest1      
which1 consciously or instinctively1 was
 supported by a fine feeling for the    
slightest contradictions1 has no other  
purpose than to limit the bounds of     
thought and so exempt it from the       
possibility of error4 ,in this1         
therefore1 the logical root of the      
principle of excluded perpetual motion  
is given1 namely1 in that universal     
conviction which existed even before the
 development of mechanics and           
co-operated in that development4  ,it is
 perfectly natural that the principle of
 excluded perpetual motion should have  
been first developed in the simple      
domain of pure mechanics4 ,towards the  

transference of that principle into the 
domain of general physics the idea      
contributed much that all physical      
phenomena are mechanical phenomena4 ,but
 the foregoing discussion shows how     
little essential this notion is4 ,the   
issue really involved is the recognition
 of a general interconnexion of nature4 
,this once established1 we see with     
,carnot that it is indifferent whether  
the mechanical laws are broken directly 
or circuitously4  ,the principle of the 
excluded perpetual motion is very       
closely related to the modern principle 
of energy1 but it is not identical with 
it1 for the latter is to be deduced from
 the former only by means of a definite 
formal conception4 ,as may be seen from 
the preceding exposition1 the perpetual 
motion can be excluded without our      
employing or possessing the notion of   
work4 ,the modern principle of energy   
results primarily from a substantial    
conception of work and of every change  
of physical condition which by being    

reversed produces work4 ,the strong need
 of such a conception1 which is by no   
means necessary1 but in a formal sense  
is very convenient and lucid1 is        
exhibited in the case of ,j4 ,r4 ,mayer 
and ,joule4 ,it was before remarked that
 this conception was suggested to both  
inquirers by the observation that both  
the production of heat and the          
production of mechanical work were      
connected with an expenditure of        
substance4 ,mayer says3 ,ex nihilo nil  
fit1 and in another place1 ,the creation
 or destruction of a force 7work7 lies  
without the province of human activity4 
,in ,joule we find this passage3 ,it is 
manifestly absurd to suppose that the   
powers with which ,god has endowed      
matter can be destroyed4  ,some writers 
have observed in such statements the    
attempt at a metaphysical establishment 
of the doctrine of energy4 ,but we see  
in them simply the formal need of a     
simple1 clear1 and living grasp of the  
facts1 which receives its development in

 practical and technical life1 and which
 we carry over1 as best we can1 into the
 province of science4 ,as a fact1 ,mayer
 writes to ,griesinger3 ,if1 finally1   
you ask me how ,i became involved in the
 whole affair1 my answer is simply this3
 ,engaged during a sea voyage almost    
exclusively with the study of           
physiology1 ,i discovered the new theory
 for the sufficient reason that ,i      
vividly felt the need of it4  ,the      
substantial conception of work 7energy7 
is by no means a necessary one4 ,and it 
is far from true that the problem is    
solved with the recognition of the need 
of such a conception4 ,rather let us see
 how ,mayer gradually endeavored to     
satisfy that need4 ,he first regards    
quantity of motion1 or momentum1 mv1 as 
the equivalent of work1 and did not     
light1 until later1 on the notion of    
living force 7mv_/#b74 ,in the province 
of electricity he was unable to assign  
the expression which is the equivalent  
of work4 ,this was done later by        

,helmholtz4 ,the formal need1 therefore1
 is first present1 and our conception of
 nature is subsequently gradually       
adapted to it4  ,the laying bare of the 
experimental1 logical1 and formal root  
of the present principle of energy will 
perhaps contribute much to the removal  
of the mysticism which still clings to  
this principle4 ,with respect to our    
formal need of a very simple1 palpable1 
substantial conception of the processes 
in our environment1 it remains an open  
question how far nature corresponds to  
that need1 or how far we can satisfy it4
 ,in one phase of the preceding         
discussions it would seem as if the     
substantial notion of the principle of  
energy1 like ,black's material          
conception of heat1 has its natural     
limits in facts1 beyond which it can    
only be artificially adhered to4        
,,footnotes3    ,footnote #ci3          
,published in ,vol4 #e1 ,no4 ,i1 of ,the
 ,monist1 ,october1   #ahid1 being in   
part a re-elaboration of the treatise   

,ueber die   ,erhaltung der ,arbeit1    
,prague1 #ahgb4    ,footnote #dj3 ,on   
,matter1 ,living ,force1 and ,heat1     
,joule3   ,scientific ,papers1 ,london1 
#ahhd1 ,i1 p4 #bfe4    ,footnote #da3   
,atqui hoc si sit1 globorum series sive 
corona eundem   situm cum priore        
habebit1 eademque de causa octo globi   
sinistri   ponderosiores erunt sex      
dextris1 ideoque rursus octo illi       
descendent1 sex illi ascendent1 istique 
globi ex sese continuum et   aeternum   
motum efficient1 quod est falsum4       
,footnote #db3 ,a igitur1 7si ullo modo 
per naturam fieri possit7   locum sibi  
tributum non servato1 ac delabatur in   
,d2 quibus positis   aqua quae ipsi ,a  
succedit eandem ob causam deffluet in   
,d1 eademque   ab alia istinc           
expelletur1 atque adeo aqua haec 7cum   
ubique eadem   ratio sit7 motum         
instituet perpetuum1 quod absurdum      
fuerit4    ,footnote #dc3 ,accipio1     
gradus velocitatis ejusdem mobilis super
   diversas planorum inclinationes      

acquisitos tunc esse aequales1 cum      
eorundum planorum elevationes aequales  
sint4    ,footnote #dd3 ,voi molto      
probabilmente discorrete1 ma oltre al   
veri   simile voglio con una esperienza 
crescer tanto la probabilit1 che   poco 
gli manchi all'agguagliarsi ad una ben  
necessaria   dimostrazione4 ,figuratevi 
questo foglio essere una parete eretta  
all'orizzonte1 e da un chiodo fitto in  
essa pendere una palla di   piombo      
d'un'oncia1 o due1 sospesa dal sottil   
filo ,,ab lungo due1 o   tre braccia    
perpendicolare all'orizzonte1 e nella   
parete segnate una   linea orizontale   
,,dc segante a squadra il perpendicolo  
,,ab1 il   quale sia lontano dalla      
parete due dita in circa1 trasferendo   
poi il   filo ,,ab colla palla in ,,ac1 
lasciata essa palla in libert1 la       
quale primieramente vedrete scendere    
descrivendo l'arco ,,cbd1 e di   tanto  
trapassare il termine ,b1 che scorrendo 
per l'arco ,,bd   sormonter fino quasi  
alla segnata parallela ,,cd1 restando di

 per   vernirvi per piccolissimo        
intervallo1 toltogli il precisamente    
arrivarvi dall'impedimento dell'aria1 e 
del filo4 ,dal che possiamo             
veracemente concludere1 che l'impeto    
acquistato nel punto ,b dalla   palla   
nello scendere per l'arco ,,cb1 fu      
tanto1 che bast a   risospingersi per un
 simile arco ,,bd alla medesima altezza2
 fatta1   e pi volte reiterata cotale   
esperienza1 voglio1 che fiechiamo nella 
parete rasente al perpendicolo ,,ab un  
chiodo come in ,e1 ovvero in   ,f1 che  
sporga in fuori cinque1 o sei dita1 e   
questo acciocch il   filo ,,ac tornando 
come prima a riportar la palla ,c per   
l'arco   ,,cb1 giunta che ella sia in   
,b1 inoppando il filo nel chiodo ,e1    
sia costretta a camminare per la        
circonferenza ,,bg descritta in   torno 
al centro ,e1 dal che vedremo quello1   
che potr far quel   medesimo impeto1 che
 dianzi concepizo nel medesimo termine  
,b1   sospinse l'istesso mobile per     
l'arco ,,ed all'altezza                 

dell'orizzonale ,,cd4 ,ora1 ,signori1   
voi vedrete con gusto condursi   la     
palla all'orizzontale nel punto ,g1 e   
l'istesso accadere1   l'intoppo si      
metesse pi basso1 come in ,f1 dove la   
palla   descriverebbe l'arco ,,bj1      
terminando sempre la sua salita         
precisamente nella linea ,,cd1 e quando 
l'intoppe del chiodo fusse   tanto      
basso1 che l'avanzo del filo sotto di   
lui non arivasse   all'altezza di ,,cd  
7il che accaderebbe1 quando fusse pi    
vicino al   punto ,b1 che al segamento  
dell' ,,ab coll'orizzontale ,,cd71      
allora il filo cavalcherebbe il chiodo1 
e segli avolgerebbe intorno4   ,questa  
esperienza non lascia luogo di dubitare 
della verit del   supposto3 imperocch   
essendo li due archi ,,cb1 ,,db equali e
   similmento posti1 l'acquisto di      
momento fatto per la scesa nell'arco    
,,cb1  il medesimo1 che il fatto per la 
scesa dell'arco ,,db2 ma il   momento   
acquistato in ,b per l'arco ,,cb        
potente a risospingere   in su il       

medesimo mobile per l'arco ,,bd2 adunque
 anco il momento   acquistato nella     
scesa ,,db  eguale a quello1 che        
sospigne   l'istesso mobile pel medesimo
 arco da ,b in ,d1 sicche               
universal-mente ogni memento acquistato 
per la scesa d'un arco    eguale a      
quello1 che pu far risalire l'istesso   
mobile pel medesimo   arco3 ma i momenti
 tutti che fanno resalire per tutti gli 
archi   ,,bd1 ,,bg1 ,,bj sono eguali1   
poich son fatti dal istesso medesimo    
momento acquistato per la scesa ,,cb1   
come mostra l'esperienza3   adunque     
tutti i momenti1 che si acquistano per  
le scese negli archi   ,,db1 ,,gb1 ,,jb 
sono eguali4    ,footnote #de3 ,constat 
jam1 quod mobile ex quiete in ,a        
descendens   per ,,ab1 gradus acquirit  
velocitatis juxta temporis ipsius       
incrementum3 gradum vero in ,b esse     
maximum acquisitorum1 et suapte   natura
 immutabiliter impressum1 sublatis      
scilicet causis   accelerationis novae1 
aut retardationis3 accelerationis       

inquam1 si   adhuc super extenso plano  
ulterius progrederetur2 retardationis   
vero1 dum super planum acclive ,,bc fit 
reflexio3 in horizontali   autem ,,gh   
aequabilis motus juxta gradum           
velocitatis ex ,a in ,b   acquisitae in 
infinitum extenderetur4    ,footnote    
#df3 ,si gravitas non esset1 neque ar   
motui corporum   officeret1 unumquodque 
eorum1 acceptum semel motum             
continuaturum   velocitate aequabili1   
secundum lineam rectam4    ,footnote    
#dg3 ,si pondera quotlibet1 vi          
gravitatis suae1 moveri   incipiant2 non
 posse centrum gravitatis ex ipsis      
compositae altius1   quam ubi incipiente
 motu reperiebatur1 ascendere4    ,ipsa 
vero hypothesis nostra quominus         
scrupulum moveat1 nihil aliud   sibi    
velle ostendemus1 quam1 quod nemo unquam
 negavit1 gravia nempe   sursum non     
ferri4--,et sane1 si hac eadem uti      
scirent novorum operum   machinatores1  
qui motum perpetuum irrito conatu       
moliuntur1 facile   suos ipsi errores   

deprehenderent1 intelligerentque rem eam
 mechanica   ratione haud quaquam       
possibilem esse4    ,footnote #dh3 ,si  
pendulum e pluribus ponderibus          
compositum1 atque e   quiete dimissum1  
partem quamcunque oscillationis integrae
   confecerit1 atque inde porro         
intelligantur pondera ejus singula1     
relicto communi vinculo1 celeritates    
acquisitas sursum convertere1   ac      
quousque possunt ascendere2 hoc facto   
centrum gravitatis ex   omnibus         
compositae1 ad eandem altitudinem       
reversum erit1 quam ante   inceptam     
oscillationem obtinebat4    ,footnote   
#di3 ,notato autem hic illud staticum   
axioma etiam locum   habere3      ,ut   
spatium agentis ad spatium patientis    
,sic potentia patientis ad potentiam    
agentis4    ,footnote #ej3 ,cependant1  
comme dans cet ouvrage on ne fut d'abord
   attentif qu' considrer ce beau       
dveloppement de la mcanique qui         
semblait sortir tout entire d'une seule 
et mme formule1 on crut   naturellement 

que la science etait faite1 et qu'il ne 
restait plus   qu' chercher la          
dmonstration du principe des vitesses   
virtuelles4   ,mais cette recherche     
ramena toutes les difficults qu'on avait
   franchies par le principe mme4 ,cette
 loi si gnrale1 o se mlent   des ides   
vagues et trangres de mouvements        
infinement petits et de   perturbation  
d'quilibre1 ne fit en quelque sorte que 
s'obsurcir    l'examen2 et le livre de  
,lagrange n'offrant plus alors rien de  
clair   que la marche des calculs1 on   
vit bien que les nuages n'avaient paru  
lev sur le cours de la mcanique que     
parcequ'ils taient1 pour   ainsi dire1  
rassembls  l'origine mme do cette       
science4    ,une dmonstration gnrale du 
principe des vitesses virtuelles        
devait au fond revenir a tablir le      
mcanique entire sur une autre   base3   
car la demonstration d'une loi qui      
embrasse toute une science   ne peut tre
 autre chose qua la reduction de cette  
science  une   autre loi aussi gnrale1  

mais vidente1 ou du moins plus simple   
que   la premire1 et qui partant la     
rende inutile4    ,footnote #ea3 ,trait 
de la lumire1 ,leyden1 #afij1 p4 #b4    
,footnote #eb3 ,l'on ne saurait douter  
que la lumire ne consiste   dans le     
mouvement de certaine matire4 ,car soit 
qu'on regarde sa   production1 on trouve
 qu'iy sur la terre c'est principalement
 le   feu et la flamme qui l'engendrent1
 lesquels contient sans doute des       
corps qui sont dans un mouvement rapide1
 puis qu'ils dissolvent et   fondent    
plusieurs autres corps des plus solides3
 soit qu'on regarde   ses effets1 on    
voit que quand la lumire est ramasse1   
comme par des   miroires concaves1 elle 
a la vertu de brler comme le feu4       
c-est--dire qu'elle desunit les parties 
des corps2 ce qui marque   assurment du 
mouvement1 au moins dans la vraye       
,philosophie1   dans laquelle on conoit 
la cause de tous les effets naturels par
   des raisons de mechanique4 ,ce qu'il 
faut faire  mon avis1 ou bien   renoncer

  tout esprance de jamais rien          
comprendre dans la   ,physique4         
,footnote #ec3 ,sur la puissance motrice
 du feu4 7,paris1 #ahbd47    ,footnote  
#ed3 ,on objectra peut-tre ici que le   
mouvement perptuel1   dmontr impossible 
par les seules actions mcaniques1 ne    
l'est   peut-tre pas lorsqu'on emploie  
l'influence soit de la chaleur1   soit  
de l'lectricit2 mais pent-on concevoir  
les phnomnes de la   chaleur et de      
l'lectricit comme dus  autre chose qu'  
des   mouvements quelconques des corps  
et comme tels ne doivent-ils pas   tre  
soumis aux lois gnrales de la mcanique8 
,footnote #ee3 ,by this is meant the    
temperature of a ,celsius scale1   the  
zero of which is #bgc below the         
melting-point of ice4    ,footnote #ef3 
,i first drew attention to this fact in 
my treatise   ,ueber die ,erhaltung der 
,arbeit1 ,prague1 #ahgb4 ,before this1  
,zeuner   had pointed out the analogy   
between mechanical and thermal energy4  
,i   have given a more extensive        

development of this idea in a           
communication to the ,sitzungsberichte  
der ,wiener ,akademie1   ,december1     
#ahib1 entitled ,geschichte und ,kritik 
des ,carnot'schen   ,wrmegesetzes4      
,compare also the works of ,popper      
7#ahhd71 ,helm   7#ahhg71 ,wronsky      
7#ahhh71 and ,ostwald 7#ahib74          
,footnote #eg3 ,sir ,william ,thomson   
first consciously and   intentionally   
introduced 7#ahdh1 #ahea7 a mechanical  
measure of   temperature similar to the 
electric measure of potential4          
,footnote #eh3 ,compare my ,analysis of 
the ,sensations1 ,jena1 #ahhf3          
,english translation1 ,chicago1 #ahig4  
,footnote #ei3 ,a better terminology    
appears highly desirable in the   place 
of the usual misleading one4 ,sir       
,william ,thomson 7#aheb7   appears to  
have felt this need1 and it has been    
clearly expressed by   ,f4 ,wald        
7#ahhi74 ,we should call the work which 
corresponds to a   vanished quantity of 
heat its mechanical substitution-value2 

while   that work which can be actually 
performed in the passage of a   thermal 
condition ,a to a condition ,b1 alone   
deserves the name of   the energy-value 
of this change of condition4 ,in this   
way the   arbitrary substantial         
conception of the processes would be    
preserved and misapprehensions          
forestalled4     ,,the ,,economical     
,,nature ,,of ,,physical ,,inquiry4#fj  
,when the human mind1 with its limited  
powers1 attempts to mirror in itself the
 rich life of the world1 of which it is 
itself only a small part1 and which it  
can never hope to exhaust1 it has every 
reason for proceeding economically4     
,hence that tendency1 expressed in the  
philosophy of all times1 to compass by a
 few organic thoughts the fundamental   
features of reality4 ,life understands  
not death1 nor death life4 ,so spake an 
old ,chinese philosopher4 ,yet in his   
unceasing desire to diminish the        
boundaries of the incomprehensible1 man 
has always been engaged in attempts to  

understand death by life and life by    
death4  ,among the ancient civilised    
peoples1 nature was filled with demons  
and spirits having the feelings and     
desires of men4 ,in all essential       
features1 this animistic view of nature1
 as ,tylor#fa has aptly termed it1 is   
shared in common by the                 
fetish-worshipper of modern ,africa and 
the most advanced nations of antiquity4 
,as a theory of the world it has never  
completely disappeared4 ,the monotheism 
of the ,christians never fully overcame 
it1 no more than did that of the ,jews4 
,in the belief in witchcraft and in the 
superstitions of the sixteenth and      
seventeenth centuries1 the centuries of 
the rise of natural science1 it assumed 
frightful pathological dimensions4      
,whilst ,stevinus1 ,kepler1 and ,galileo
 were slowly rearing the fabric of      
modern physical science1 a cruel and    
relentless war was waged with firebrand 
and rack against the devils that        
glowered from every corner4 ,to-day     

even1 apart from all survivals of that  
period1 apart from the traces of        
fetishism which still inhere in our     
physical concepts1#fb those very ideas  
still covertly lurk in the practices of 
modern spiritualism4   ,by the side of  
this animistic conception of the world1 
we meet from time to time1 in different 
forms1 from ,democritus to the present  
day1 another view1 which likewise claims
 exclusive competency to comprehend the 
universe4 ,this view may be             
characterised as the physico-mechanical 
view of the world4 ,to-day1 that view   
holds1 indisputably1 the first place in 
the thoughts of men1 and determines the 
ideals and the character of our times4  
,the coming of the mind of man into the 
full consciousness of its powers1 in the
 eighteenth century1 was a period of    
genuine disillusionment4 ,it produced   
the splendid precedent of a life really 
worthy of man1 competent to overcome the
 old barbarism in the practical fields  
of life2 it created the ,critique of    

,pure ,reason1 which banished into the  
realm of shadows the sham-ideas of the  
old metaphysics2 it pressed into the    
hands of the mechanical philosophy the  
reins which it now holds4  ,the         
oft-quoted words of the great           
,laplace1#fc which ,i will now give1    
have the ring of a jubilant toast to the
 scientific achievements of the         
eighteenth century3 ,a mind to which    
were given for a single instant all the 
forces of nature and the mutual         
positions of all its masses1 if it were 
otherwise powerful enough to subject    
these problems to analysis1 could grasp1
 with a single formula1 the motions of  
the largest masses as well as of the    
smallest atoms2 nothing would be        
uncertain for it2 the future and the    
past would lie revealed before its eyes4
 ,in writing these words1 ,laplace1 as  
we know1 had also in mind the atoms of  
the brain4 ,that idea has been expressed
 more forcibly still by some of his     
followers1 and it is not too much to say

 that ,laplace's ideal is substantially 
that of the great majority of modern    
scientists4  ,gladly do we accord to the
 creator of the ,mcanique cleste the    
sense of lofty pleasure awakened in him 
by the great success of the             
,enlightenment1 to which we too owe our 
intellectual freedom4 ,but to-day1 with 
minds undisturbed and before new tasks1 
it becomes physical science to secure   
itself against self-deception by a      
careful study of its character1 so that 
it can pursue with greater sureness its 
true objects4 ,if ,i step1 therefore1   
beyond the narrow precincts of my       
specialty in this discussion1 to        
trespass on friendly neighboring        
domains1 ,i may plead in my excuse that 
the subject-matter of knowledge is      
common to all domains of research1 and  
that fixed1 sharp lines of demarcation  
cannot be drawn4  ,the belief in occult 
magic powers of nature has gradually    
died away1 but in its place a new belief
 has arisen1 the belief in the magical  

power of science4 ,science throws her   
treasures1 not like a capricious fairy  
into the laps of a favored few1 but into
 the laps of all humanity1 with a lavish
 extravagance that no legend ever dreamt
 of6 ,not without apparent justice1     
therefore1 do her distant admirers      
impute to her the power of opening up   
unfathomable abysses of nature1 to which
 the senses cannot penetrate4 ,yet she  
who came to bring light into the world1 
can well dispense with the darkness of  
mystery1 and with pompous show1 which   
she needs neither for the justification 
of her aims nor for the adornment of her
 plain achievements4  ,the homely       
beginnings of science will best reveal  
to us its simple1 unchangeable          
character4 ,man acquires his first      
knowledge of nature half-consciously and
 automatically1 from an instinctive     
habit of mimicking and forecasting facts
 in thought1 of supplementing sluggish  
experience with the swift wings of      
thought1 at first only for his material 

welfare4 ,when he hears a noise in the  
underbrush he constructs there1 just as 
the animal does1 the enemy which he     
fears2 when he sees a certain rind he   
forms mentally the image of the fruit   
which he is in search of2 just as we    
mentally associate a certain kind of    
matter with a certain line in the       
spectrum or an electric spark with the  
friction of a piece of glass4 ,a        
knowledge of causality in this form     
certainly reaches far below the level of
 ,schopenhauer's pet dog1 to whom it was
 ascribed4 ,it probably exists in the   
whole animal world1 and confirms that   
great thinker's statement regarding the 
will which created the intellect for its
 purposes4 ,these primitive psychical   
functions are rooted in the economy of  
our organism not less firmly than are   
motion and digestion4 ,who would deny   
that we feel in them1 too1 the elemental
 power of a long practised logical and  
physiological activity1 bequeathed to us
 as an heirloom from our forefathers8   

,such primitive acts of knowledge       
constitute to-day the solidest          
foundation of scientific thought4 ,our  
instinctive knowledge1 as we shall      
briefly call it1 by virtue of the       
conviction that we have consciously and 
intentionally contributed nothing to its
 formation1 confronts us with an        
authority and logical power which       
consciously acquired knowledge even from
 familiar sources and of easily tested  
fallibility can never possess4 ,all     
so-called axioms are such instinctive   
knowledge4 ,not consciously gained      
knowledge alone1 but powerful           
intellectual instinct1 joined with vast 
conceptive powers1 constitute the great 
inquirer4 ,the greatest advances of     
science have always consisted in some   
successful formulation1 in clear1       
abstract1 and communicable terms1 of    
what was instinctively known long       
before1 and of thus making it the       
permanent property of humanity4 ,by     
,newton's principle of the equality of  

pressure and counterpressure1 whose     
truth all before him had felt1 but which
 no predecessor had abstractly          
formulated1 mechanics was placed by a   
single stroke on a higher level4 ,our   
statement might also be historically    
justified by examples from the          
scientific labors of ,stevinus1 ,s4     
,carnot1 ,faraday1 ,j4 ,r4 ,mayer1 and  
others4  ,all this1 however1 is merely  
the soil from which science starts4 ,the
 first real beginnings of science appear
 in society1 particularly in the manual 
arts1 where the necessity for the       
communication of experience arises4     
,here1 where some new discovery is to be
 described and related1 the compulsion  
is first felt of clearly defining in    
consciousness the important and         
essential features of that discovery1 as
 many writers can testify4 ,the aim of  
instruction is simply the saving of     
experience2 the labor of one man is made
 to take the place of that of another4  
,the most wonderful economy of          

communication is found in language4     
,words are comparable to type1 which    
spare the repetition of written signs   
and thus serve a multitude of purposes2 
or to the few sounds of which our       
numberless different words are composed4
 ,language1 with its helpmate1          
conceptual thought1 by fixing the       
essential and rejecting the unessential1
 constructs its rigid pictures of the   
fluid world on the plan of a mosaic1 at 
a sacrifice of exactness and fidelity   
but with a saving of tools and labor4   
,like a piano-player with previously    
prepared sounds1 a speaker excites in   
his listener thoughts previously        
prepared1 but fitting many cases1 which 
respond to the speaker's summons with   
alacrity and little effort4  ,the       
principles which a prominent political  
economist1 ,e4 ,hermann1#fd has         
formulated for the economy of the       
industrial arts1 are also applicable to 
the ideas of common life and of science4
 ,the economy of language is augmented1 

of course1 in the terminology of        
science4 ,with respect to the economy of
 written intercourse there is scarcely a
 doubt that science itself will realise 
that grand old dream of the philosophers
 of a ,universal ,real ,character4 ,that
 time is not far distant4 ,our numeral  
characters1 the symbols of mathematical 
analysis1 chemical symbols1 and musical 
notes1 which might easily be            
supplemented by a system of color-signs1
 together with some phonetic alphabets  
now in use1 are all beginnings in this  
direction4 ,the logical extension of    
what we have1 joined with a use of the  
ideas which the ,chinese ideography     
furnishes us1 will render the special   
invention and promulgation of a         
,universal ,character wholly            
superfluous4  ,the communication of     
scientific knowledge always involves    
description1 that is1 a mimetic         
reproduction of facts in thought1 the   
object of which is to replace and save  
the trouble of new experience4 ,again1  

to save the labor of instruction and of 
acquisition1 concise1 abridged          
description is sought4 ,this is really  
all that natural laws are4 ,knowing the 
value of the acceleration of gravity1   
and ,galileo's laws of descent1 we      
possess simple and compendious          
directions for reproducing in thought   
all possible motions of falling bodies4 
,a formula of this kind is a complete   
substitute for a full table of motions  
of descent1 because by means of the     
formula the data of such a table can be 
easily constructed at a moment's notice 
without the least burdening of the      
memory4  ,no human mind could comprehend
 all the individual cases of refraction4
 ,but knowing the index of refraction   
for the two media presented1 and the    
familiar law of the sines1 we can easily
 reproduce or fill out in thought every 
conceivable case of refraction4 ,the    
advantage here consists in the          
disburdening of the memory2 an end      
immensely furthered by the written      

preservation of the natural constants4  
,more than this comprehensive and       
condensed report about facts is not     
contained in a natural law of this sort4
 ,in reality1 the law always contains   
less than the fact itself1 because it   
does not reproduce the fact as a whole  
but only in that aspect of it which is  
important for us1 the rest being either 
intentionally or from necessity omitted4
 ,natural laws may be likened to        
intellectual type of a higher order1    
partly movable1 partly stereotyped1     
which last on new editions of experience
 may become downright impediments4      
,when we look over a province of facts  
for the first time1 it appears to us    
diversified1 irregular1 confused1 full  
of contradictions4 ,we first succeed in 
grasping only single facts1 unrelated   
with the others4 ,the province1 as we   
are wont to say1 is not clear4 ,by and  
by we discover the simple1 permanent    
elements of the mosaic1 out of which we 
can mentally construct the whole        

province4 ,when we have reached a point 
where we can discover everywhere the    
same facts1 we no longer feel lost in   
this province2 we comprehend it without 
effort2 it is explained for us4  ,let me
 illustrate this by an example4 ,as soon
 as we have grasped the fact of the     
rectilinear propagation of light1 the   
regular course of our thoughts stumbles 
at the phenomena of refraction and      
diffraction4 ,as soon as we have cleared
 matters up by our index of refraction  
we discover that a special index is     
necessary for each color4 ,soon after we
 have accustomed ourselves to the fact  
that light added to light increases its 
intensity1 we suddenly come across a    
case of total darkness produced by this 
cause4 ,ultimately1 however1 we see     
everywhere in the overwhelming          
multifariousness of optical phenomena   
the fact of the spatial and temporal    
periodicity of light1 with its velocity 
of propagation dependent on the medium  
and the period4 ,this tendency of       

obtaining a survey of a given province  
with the least expenditure of thought1  
and of representing all its facts by    
some one single mental process1 may be  
justly termed an economical one4  ,the  
greatest perfection of mental economy is
 attained in that science which has     
reached the highest formal development1 
and which is widely employed in physical
 inquiry1 namely1 in mathematics4       
,strange as it may sound1 the power of  
mathematics rests upon its evasion of   
all unnecessary thought and on its      
wonderful saving of mental operations4  
,even those arrangement-signs which we  
call numbers are a system of marvellous 
simplicity and economy4 ,when we employ 
the multiplication-table in multiplying 
numbers of several places1 and so use   
the results of old operations of        
counting instead of performing the whole
 of each operation anew2 when we consult
 our table of logarithms1 replacing and 
saving thus new calculations by old ones
 already performed2 when we employ      

determinants instead of always beginning
 afresh the solution of a system of     
equations2 when we resolve new integral 
expressions into familiar old integrals2
 we see in this simply a feeble         
reflexion of the intellectual activity  
of a ,lagrange or a ,cauchy1 who1 with  
the keen discernment of a great military
 commander1 substituted for new         
operations whole hosts of old ones4 ,no 
one will dispute me when ,i say that the
 most elementary as well as the highest 
mathematics are economically-ordered    
experiences of counting1 put in forms   
ready for use4  ,in algebra we perform1 
as far as possible1 all numerical       
operations which are identical in form  
once for all1 so that only a remnant of 
work is left for the individual case4   
,the use of the signs of algebra and    
analysis1 which are merely symbols of   
operations to be performed1 is due to   
the observation that we can materially  
disburden the mind in this way and spare
 its powers for more important and more 

difficult duties1 by imposing all       
mechanical operations upon the hand4    
,one result of this method1 which       
attests its economical character1 is the
 construction of calculating machines4  
,the mathematician ,babbage1 the        
inventor of the difference-engine1 was  
probably the first who clearly perceived
 this fact1 and he touched upon it1     
although only cursorily1 in his work1   
,the ,economy of ,manufactures and      
,machinery4  ,the student of mathematics
 often finds it hard to throw off the   
uncomfortable feeling that his science1 
in the person of his pencil1 surpasses  
him in intelligence1--an impression     
which the great ,euler confessed he     
often could not get rid of4 ,this       
feeling finds a sort of justification   
when we reflect that the majority of the
 ideas we deal with were conceived by   
others1 often centuries ago4 ,in great  
measure it is really the intelligence of
 other people that confronts us in      
science4 ,the moment we look at matters 

in this light1 the uncanniness and      
magical character of our impressions    
cease1 especially when we remember that 
we can think over again at will any one 
of those alien thoughts4  ,physics is   
experience1 arranged in economical      
order4 ,by this order not only is a     
broad and comprehensive view of what we 
have rendered possible1 but also the    
defects and the needful alterations are 
made manifest1 exactly as in a well-kept
 household4 ,physics shares with        
mathematics the advantages of succinct  
description and of brief1 compendious   
definition1 which precludes confusion1  
even in ideas where1 with no apparent   
burdening of the brain1 hosts of others 
are contained4 ,of these ideas the rich 
contents can be produced at any moment  
and displayed in their full perceptual  
light4 ,think of the swarm of           
well-ordered notions pent up in the idea
 of the potential4 ,is it wonderful that
 ideas containing so much finished labor
 should be easy to work with8  ,our     

first knowledge1 thus1 is a product of  
the economy of self-preservation4 ,by   
communication1 the experience of many   
persons1 individually acquired at first1
 is collected in one4 ,the communication
 of knowledge and the necessity which   
every one feels of managing his stock of
 experience with the least expenditure  
of thought1 compel us to put our        
knowledge in economical forms4 ,but here
 we have a clue which strips science of 
all its mystery1 and shows us what its  
power really is4 ,with respect to       
specific results it yields us nothing   
that we could not reach in a            
sufficiently long time without methods4 
,there is no problem in all mathematics 
that cannot be solved by direct         
counting4 ,but with the present         
implements of mathematics many          
operations of counting can be performed 
in a few minutes which without          
mathematical methods would take a       
lifetime4 ,just as a single human being1
 restricted wholly to the fruits of his 

own labor1 could never amass a fortune1 
but on the contrary the accumulation of 
the labor of many men in the hands of   
one is the foundation of wealth and     
power1 so1 also1 no knowledge worthy of 
the name can be gathered up in a single 
human mind limited to the span of a     
human life and gifted only with finite  
powers1 except by the most exquisite    
economy of thought and by the careful   
amassment of the economically ordered   
experience of thousands of co-workers4  
,what strikes us here as the fruits of  
sorcery are simply the rewards of       
excellent housekeeping1 as are the like 
results in civil life4 ,but the business
 of science has this advantage over     
every other enterprise1 that from its   
amassment of wealth no one suffers the  
least loss4 ,this1 too1 is its blessing1
 its freeing and saving power4  ,the    
recognition of the economical character 
of science will now help us1 perhaps1 to
 understand better certain physical     
notions4  ,those elements of an event   

which we call cause and effect are      
certain salient features of it1 which   
are important for its mental            
reproduction4 ,their importance wanes   
and the attention is transferred to     
fresh characters the moment the event or
 experience in question becomes         
familiar4 ,if the connexion of such     
features strikes us as a necessary one1 
it is simply because the interpolation  
of certain intermediate links with which
 we are very familiar1 and which        
possess1 therefore1 higher authority for
 us1 is often attended with success in  
our explanations4 ,that ready experience
 fixed in the mosaic of the mind with   
which we meet new events1 ,kant calls an
 innate concept of the understanding    
7,verstandesbegriff74  ,the grandest    
principles of physics1 resolved into    
their elements1 differ in no wise from  
the descriptive principles of the       
natural historian4 ,the question1 ,why8 
which is always appropriate where the   
explanation of a contradiction is       

concerned1 like all proper habitudes of 
thought1 can overreach itself and be    
asked where nothing remains to be       
understood4 ,suppose we were to         
attribute to nature the property of     
producing like effects in like          
circumstances2 just these like          
circumstances we should not know how to 
find4 ,nature exists once only4 ,our    
schematic mental imitation alone        
produces like events4 ,only in the mind1
 therefore1 does the mutual dependence  
of certain features exist4  ,all our    
efforts to mirror the world in thought  
would be futile if we found nothing     
permanent in the varied changes of      
things4 ,it is this that impels us to   
form the notion of substance1 the source
 of which is not different from that of 
the modern ideas relative to the        
conservation of energy4 ,the history of 
physics furnishes numerous examples of  
this impulse in almost all fields1 and  
pretty examples of it may be traced back
 to the nursery4 ,where does the light  

go to when it is put out8 asks the      
child4 ,the sudden shrivelling up of a  
hydrogen balloon is inexplicable to a   
child2 it looks everywhere for the large
 body which was just there but is now   
gone4  ,where does heat come from8      
,where does heat go to8 ,such childish  
questions in the mouths of mature men   
shape the character of a century4  ,in  
mentally separating a body from the     
changeable environment in which it      
moves1 what we really do is to extricate
 a group of sensations on which our     
thoughts are fastened and which is of   
relatively greater stability than the   
others1 from the stream of all our      
sensations4 ,absolutely unalterable this
 group is not4 ,now this1 now that      
member of it appears and disappears1 or 
is altered4 ,in its full identity it    
never recurs4 ,yet the sum of its       
constant elements as compared with the  
sum of its changeable ones1 especially  
if we consider the continuous character 
of the transition1 is always so great   

that for the purpose in hand the former 
usually appear sufficient to determine  
the body's identity4 ,but because we can
 separate from the group every single   
member without the body's ceasing to be 
for us the same1 we are easily led to   
believe that after abstracting all the  
members something additional would      
remain4 ,it thus comes to pass that we  
form the notion of a substance distinct 
from its attributes1 of a               
thing-in-itself1 whilst our sensations  
are regarded merely as symbols or       
indications of the properties of this   
thing-in-itself4 ,but it would be much  
better to say that bodies or things are 
compendious mental symbols for groups of
 sensations--symbols that do not exist  
outside of thought4 ,thus1 the merchant 
regards the labels of his boxes merely  
as indexes of their contents1 and not   
the contrary4 ,he invests their         
contents1 not their labels1 with real   
value4 ,the same economy which induces  
us to analyse a group and to establish  

special signs for its component parts1  
parts which also go to make up other    
groups1 may likewise induce us to mark  
out by some single symbol a whole group4
  ,on the old ,egyptian monuments we see
 objects represented which do not       
reproduce a single visual impression1   
but are composed of various impressions4
 ,the heads and the legs of the figures 
appear in profile1 the head-dress and   
the breast are seen from the front1 and 
so on4 ,we have here1 so to speak1 a    
mean view of the objects1 in forming    
which the sculptor has retained what he 
deemed essential1 and neglected what he 
thought indifferent4 ,we have living    
exemplifications of the processes put   
into stone on the walls of these old    
temples1 in the drawings of our         
children1 and we also observe a faithful
 analogue of them in the formation of   
ideas in our own minds4 ,only in virtue 
of some such facility of view as that   
indicated1 are we allowed to speak of a 
body4 ,when we speak of a cube with     

trimmed corners--a figure which is not a
 cube--we do so from a natural instinct 
of economy1 which prefers to add to an  
old familiar conception a correction    
instead of forming an entirely new one4 
,this is the process of all judgment4   
,the crude notion of body can no more   
stand the test of analysis than can the 
art of the ,egyptians or that of our    
little children4 ,the physicist who sees
 a body flexed1 stretched1 melted1 and  
vaporised1 cuts up this body into       
smaller permanent parts2 the chemist    
splits it up into elements4 ,yet even an
 element is not unalterable4 ,take      
sodium4 ,when warmed1 the white1 silvery
 mass becomes a liquid1 which1 when the 
heat is increased and the air shut out1 
is transformed into a violet vapor1 and 
on the heat being still more increased  
glows with a yellow light4 ,if the name 
sodium is still retained1 it is because 
of the continuous character of the      
transitions and from a necessary        
instinct of economy4 ,by condensing the 

vapor1 the white metal may be made to   
reappear4 ,indeed1 even after the metal 
is thrown into water and has passed into
 sodium hydroxide1 the vanished         
properties may by skilful treatment     
still be made to appear2 just as a      
moving body which has passed behind a   
column and is lost to view for a moment 
may make its appearance after a time4   
,it is unquestionably very convenient   
always to have ready the name and       
thought for a group of properties       
wherever that group by any possibility  
can appear4 ,but more than a compendious
 economical symbol for these phenomena1 
that name and thought is not4 ,it would 
be a mere empty word for one in whom it 
did not awaken a large group of         
well-ordered sense-impressions4 ,and the
 same is true of the molecules and atoms
 into which the chemical element is     
still further analysed4  ,true1 it is   
customary to regard the conservation of 
weight1 or1 more precisely1 the         
conservation of mass1 as a direct proof 

of the constancy of matter4 ,but this   
proof is dissolved1 when we go to the   
bottom of it1 into such a multitude of  
instrumental and intellectual           
operations1 that in a sense it will be  
found to constitute simply an equation  
which our ideas in imitating facts have 
to satisfy4 ,that obscure1 mysterious   
lump which we involuntarily add in      
thought1 we seek for in vain outside the
 mind4  ,it is always1 thus1 the crude  
notion of substance that is slipping    
unnoticed into science1 proving itself  
constantly insufficient1 and ever under 
the necessity of being reduced to       
smaller and smaller world-particles4    
,here1 as elsewhere1 the lower stage is 
not rendered indispensable by the higher
 which is built upon it1 no more than   
the simplest mode of locomotion1        
walking1 is rendered superfluous by the 
most elaborate means of transportation4 
,body1 as a compound of light and touch 
sensations1 knit together by sensations 
of space1 must be as familiar to the    

physicist who seeks it1 as to the animal
 who hunts its prey4 ,but the student of
 the theory of knowledge1 like the      
geologist and the astronomer1 must be   
permitted to reason back from the forms 
which are created before his eyes to    
others which he finds ready made for    
him4  ,all physical ideas and principles
 are succinct directions1 frequently    
involving subordinate directions1 for   
the employment of economically          
classified experiences1 ready for use4  
,their conciseness1 as also the fact    
that their contents are rarely exhibited
 in full1 often invests them with the   
semblance of independent existence4     
,poetical myths regarding such          
ideas1--for example1 that of ,time1 the 
producer and devourer of all things1--do
 not concern us here4 ,we need only     
remind the reader that even ,newton     
speaks of an absolute time independent  
of all phenomena1 and of an absolute    
space--views which even ,kant did not   
shake off1 and which are often seriously

 entertained to-day4 ,for the natural   
inquirer1 determinations of time are    
merely abbreviated statements of the    
dependence of one event upon another1   
and nothing more4 ,when we say the      
acceleration of a freely falling body is
 #ihaj metres per second1 we mean the   
velocity of the body with respect to the
 centre of the earth is #ihaj metres    
greater when the earth has performed an 
additional #hfdjjth part of its         
rotation--a fact which itself can be    
determined only by the earth's relation 
to other heavenly bodies4 ,again1 in    
velocity is contained simply a relation 
of the position of a body to the        
position of the earth4#fe ,instead of   
referring events to the earth we may    
refer them to a clock1 or even to our   
internal sensation of time4 ,now1       
because all are connected1 and each may 
be made the measure of the rest1 the    
illusion easily arises that time has    
significance independently of all4#ff   
,the aim of research is the discovery of

 the equations which subsist between the
 elements of phenomena4 ,the equation of
 an ellipse expresses the universal     
conceivable relation between its        
co-ordinates1 of which only the real    
values have geometrical significance4   
,similarly1 the equations between the   
elements of phenomena express a         
universal1 mathematically conceivable   
relation4 ,here1 however1 for many      
values only certain directions of change
 are physically admissible4 ,as in the  
ellipse only certain values satisfying  
the equation are realised1 so in the    
physical world only certain changes of  
value occur4 ,bodies are always         
accelerated towards the earth4          
,differences of temperature1 left to    
themselves1 always grow less2 and so on4
 ,similarly1 with respect to space1     
mathematical and physiological          
researches have shown that the space of 
experience is simply an actual case of  
many conceivable cases1 about whose     
peculiar properties experience alone can

 instruct us4 ,the elucidation which    
this idea diffuses cannot be questioned1
 despite the absurd uses to which it has
 been put4  ,let us endeavor now to     
summarise the results of our survey4 ,in
 the economical schematism of science   
lie both its strength and its weakness4 
,facts are always represented at a      
sacrifice of completeness and never with
 greater precision than fits the needs  
of the moment4 ,the incongruence between
 thought and experience1 therefore1 will
 continue to subsist as long as the two 
pursue their course side by side2 but it
 will be continually diminished4  ,in   
reality1 the point involved is always   
the completion of some partial          
experience2 the derivation of one       
portion of a phenomenon from some other4
 ,in this act our ideas must be based   
directly upon sensations4 ,we call this 
measuring4#fg ,the condition of science1
 both in its origin and in its          
application1 is a great relative        
stability of our environment4 ,what it  

teaches us is interdependence4 ,absolute
 forecasts1 consequently1 have no       
significance in science4 ,with great    
changes in celestial space we should    
lose our co-ordinate systems of space   
and time4  ,when a geometer wishes to   
understand the form of a curve1 he first
 resolves it into small rectilinear     
elements4 ,in doing this1 however1 he is
 fully aware that these elements are    
only provisional and arbitrary devices  
for comprehending in parts what he      
cannot comprehend as a whole4 ,when the 
law of the curve is found he no longer  
thinks of the elements4 ,similarly1 it  
would not become physical science to see
 in its self-created1 changeable1       
economical tools1 molecules and atoms1  
realities behind phenomena1 forgetful of
 the lately acquired sapience of her    
older sister1 philosophy1 in            
substituting a mechanical mythology for 
the old animistic or metaphysical       
scheme1 and thus creating no end of     
suppositious problems4 ,the atom must   

remain a tool for representing          
phenomena1 like the functions of        
mathematics4 ,gradually1 however1 as the
 intellect1 by contact with its         
subject-matter1 grows in discipline1    
physical science will give up its mosaic
 play with stones and will seek out the 
boundaries and forms of the bed in which
 the living stream of phenomena flows4  
,the goal which it has set itself is the
 simplest and most economical abstract  
expression of facts4         99       99
       99       99       99  ,the       
question now remains1 whether the same  
method of research which till now we    
have tacitly restricted to physics1 is  
also applicable in the psychical domain4
 ,this question will appear superfluous 
to the physical inquirer4 ,our physical 
and psychical views spring in exactly   
the same manner from instinctive        
knowledge4 ,we read the thoughts of men 
in their acts and facial expressions    
without knowing how4 ,just as we predict
 the behavior of a magnetic needle      

placed near a current by imagining      
,ampre's swimmer in the current1        
similarly we predict in thought the acts
 and behavior of men by assuming        
sensations1 feelings1 and wills similar 
to our own connected with their bodies4 
,what we here instinctively perform     
would appear to us as one of the        
subtlest achievements of science1 far   
outstripping in significance and        
ingenuity ,ampre's rule of the swimmer1 
were it not that every child            
unconsciously accomplished it4 ,the     
question simply is1 therefore1 to grasp 
scientifically1 that is1 by conceptional
 thought1 what we are already familiar  
with from other sources4 ,and here much 
is to be accomplished4 ,a long sequence 
of facts is to be disclosed between the 
physics of expression and movement and  
feeling and thought4  ,we hear the      
question1 ,but how is it possible to    
explain feeling by the motions of the   
atoms of the brain8 ,certainly this will
 never be done1 no more than light or   

heat will ever be deduced from the law  
of refraction4 ,we need not deplore1    
therefore1 the lack of ingenious        
solutions of this question4 ,the problem
 is not a problem4 ,a child looking over
 the walls of a city or of a fort into  
the moat below sees with astonishment   
living people in it1 and not knowing of 
the portal which connects the wall with 
the moat1 cannot understand how they    
could have got down from the high       
ramparts4 ,so it is with the notions of 
physics4 ,we cannot climb up into the   
province of psychology by the ladder of 
our abstractions1 but we can climb down 
into it4  ,let us look at the matter    
without bias4 ,the world consists of    
colors1 sounds1 temperatures1 pressures1
 spaces1 times1 and so forth1 which now 
we shall not call sensations1 nor       
phenomena1 because in either term an    
arbitrary1 one-sided theory is embodied1
 but simply elements4 ,the fixing of the
 flux of these elements1 whether        
mediately or immediately1 is the real   

object of physical research4 ,as long   
as1 neglecting our own body1 we employ  
ourselves with the interdependence of   
those groups of elements which1         
including men and animals1 make up      
foreign bodies1 we are physicists4 ,for 
example1 we investigate the change of   
the red color of a body as produced by a
 change of illumination4 ,but the moment
 we consider the special influence on   
the red of the elements constituting our
 body1 outlined by the well-known       
perspective with head invisible1 we are 
at work in the domain of physiological  
psychology4 ,we close our eyes1 and the 
red together with the whole visible     
world disappears4 ,there exists1 thus1  
in the perspective field of every sense 
a portion which exercises on all the    
rest a different and more powerful      
influence than the rest upon one        
another4 ,with this1 however1 all is    
said4 ,in the light of this remark1 we  
call all elements1 in so far as we      
regard them as dependent on this special

 part 7our body71 sensations4 ,that the 
world is our sensation1 in this sense1  
cannot be questioned4 ,but to make a    
system of conduct out of this           
provisional conception1 and to abide its
 slaves1 is as unnecessary for us as    
would be a similar course for a         
mathematician who1 in varying a series  
of variables of a function which were   
previously assumed to be constant1 or in
 interchanging the independent          
variables1 finds his method to be the   
source of some very surprising ideas for
 him4#fh  ,if we look at the matter in  
this unbiassed light it will appear     
indubitable that the method of          
physiological psychology is none other  
than that of physics2 what is more1 that
 this science is a part of physics4 ,its
 subject-matter is not different from   
that of physics4 ,it will unquestionably
 determine the relations the sensations 
bear to the physics of our body4 ,we    
have already learned from a member of   
this academy 7,hering7 that in all      

probability a sixfold manifoldness of   
the chemical processes of the visual    
substance corresponds to the sixfold    
manifoldness of color-sensation1 and a  
threefold manifoldness of the           
physiological processes to the threefold
 manifoldness of space-sensations4 ,the 
paths of reflex actions and of the will 
are followed up and disclosed2 it is    
ascertained what region of the brain    
subserves the function of speech1 what  
region the function of locomotion1 etc4 
,that which still clings to our body1   
namely1 our thoughts1 will1 when those  
investigations are finished1 present no 
difficulties new in principle4 ,when    
experience has once clearly exhibited   
these facts and science has marshalled  
them in economic and perspicuous order1 
there is no doubt that we shall         
understand them4 ,for other             
understanding than a mental mastery of  
facts never existed4 ,science does not  
create facts from facts1 but simply     
orders known facts4  ,let us look1 now1 

a little more closely into the modes of 
research of physiological psychology4   
,we have a very clear idea of how a body
 moves in the space encompassing it4    
,with our optical field of sight we are 
very familiar4 ,but we are unable to    
state1 as a rule1 how we have come by an
 idea1 from what corner of our          
intellectual field of sight it has      
entered1 or by what region the impulse  
to a motion is sent forth4 ,moreover1 we
 shall never get acquainted with this   
mental field of view from               
self-observation alone4                 
,self-observation1 in conjunction with  
physiological research1 which seeks out 
physical connexions1 can put this field 
of vision in a clear light before us1   
and will thus first really reveal to us 
our inner man4  ,primarily1 natural     
science1 or physics1 in its widest      
sense1 makes us acquainted with only the
 firmest connexions of groups of        
elements4 ,provisorily1 we may not      
bestow too much attention on the single 

constituents of those groups1 if we are 
desirous of retaining a comprehensible  
whole4 ,instead of equations between the
 primitive variables1 physics gives us1 
as much the easiest course1 equations   
between functions of those variables4   
,physiological psychology teaches us how
 to separate the visible1 the tangible1 
and the audible from bodies--a labor    
which is subsequently richly requited1  
as the division of the subjects of      
physics well shows4 ,physiology further 
analyses the visible into light and     
space sensations2 the first into colors1
 the last also into their component     
parts2 it resolves noises into sounds1  
these into tones1 and so on4            
,unquestionably this analysis can be    
carried much further than it has been4  
,it will be possible in the end to      
exhibit the common elements at the basis
 of very abstract but definite logical  
acts of like form1--elements which the  
acute jurist and mathematician1 as it   
were1 feels out1 with absolute          

certainty1 where the uninitiated hears  
only empty words4 ,physiology1 in a     
word1 will reveal to us the true real   
elements of the world4 ,physiological   
psychology bears to physics in its      
widest sense a relation similar to that 
which chemistry bears to physics in its 
narrowest sense4 ,but far greater than  
the mutual support of physics and       
chemistry will be that which natural    
science and psychology will render each 
other4 ,and the results that shall      
spring from this union will1 in all     
likelihood1 far outstrip those of the   
modern mechanical physics4  ,what those 
ideas are with which we shall comprehend
 the world when the closed circuit of   
physical and psychological facts shall  
lie complete before us1 7that circuit of
 which we now see only two disjoined    
parts17 cannot be foreseen at the outset
 of the work4 ,the men will be found who
 will see what is right and will have   
the courage1 instead of wandering in the
 intricate paths of logical and         

historical accident1 to enter on the    
straight ways to the heights from which 
the mighty stream of facts can be       
surveyed4 ,whether the notion which we  
now call matter will continue to have a 
scientific significance beyond the crude
 purposes of common life1 we do not     
know4 ,but we certainly shall wonder how
 colors and tones which were such       
innermost parts of us could suddenly get
 lost in our physical world of atoms2   
how we could be suddenly surprised that 
something which outside us simply       
clicked and beat1 in our heads should   
make light and music2 and how we could  
ask whether matter can feel1 that is to 
say1 whether a mental symbol for a group
 of sensations can feel8  ,we cannot    
mark out in hard and fast lines the     
science of the future1 but we can       
foresee that the rigid walls which now  
divide man from the world will gradually
 disappear2 that human beings will not  
only confront each other1 but also the  
entire organic and so-called lifeless   

world1 with less selfishness and with   
livelier sympathy4 ,just such a         
presentiment as this perhaps possessed  
the great ,chinese philosopher ,licius  
some two thousand years ago when1       
pointing to a heap of mouldering human  
bones1 he said to his scholars in the   
rigid1 lapidary style of his tongue3    
,these and ,i alone have the knowledge  
that we neither live nor are dead4      
,,footnotes3    ,footnote #fj3 ,an      
address delivered before the anniversary
 meeting of   the ,imperial ,academy of 
,sciences1 at ,vienna1 ,may #be1 #ahhb4 
,footnote #fa3 ,primitive ,culture4     
,footnote #fb3 ,tylor1 loc4 cit4        
,footnote #fc3 ,essai philosophique sur 
les probabilits4 #fth ,ed4   ,paris1    
#ahdj1 p4 #d4 ,the necessary            
consideration of the initial            
velocities is lacking in this           
formulation4    ,footnote #fd3          
,principien der ,wirthschaftslehre1     
,vienna1 #ahgc4    ,footnote #fe3 ,it is
 clear from this that all so-called     

elementary   7differential7 laws involve
 a relation to the whole4    ,footnote  
#ff3 ,if it be objected1 that in the    
case of perturbations   of the velocity 
of rotation of the earth1 we could be   
sensible of   such perturbations1 and   
being obliged to have some measure of   
time1   we should resort to the period  
of vibration of the waves of sodium     
light1--all that this would show is that
 for practical reasons we   should      
select that event which best served us  
as the simplest   common measure of the 
others4    ,footnote #fg3 ,measurement1 
in fact1 is the definition of one       
phenomenon by another 7standard7        
phenomenon4    ,footnote #fh3 ,i have   
represented the point of view here taken
 for   more than thirty years and       
developed it in various writings        
7,erhaltung der ,arbeit1 #ahgb1 parts of
 which are published in the   article on
 ,the ,conservation of ,energy in this  
collection2 ,the   ,forms of ,liquids1  
#ahgb1 also published in this           

collection2 and the                     
,bewegungsempfindungen1 #ahge74 ,the    
idea1 though known to   philosophers1 is
 unfamiliar to the majority of          
physicists4 ,it is a   matter of deep   
regret to me1 therefore1 that the title 
and author of   a small tract which     
accorded with my views in numerous      
details and   which ,i remember having  
caught a glance of in a very busy period
   7#ahgi-ahhj71 have so completely     
disappeared from my memory that all     
efforts to obtain a clue to them have   
hitherto been fruitless4     ,,on       
,,transformation ,,and ,,adaptation ,,in
 ,,scientific ,,thought4#fi   ,it was   
towards the close of the sixteenth      
century that ,galileo with a superb     
indifference to the dialectic arts and  
sophistic subtleties of the ,schoolmen  
of his time1 turned the attention of his
 brilliant mind to nature4 ,by nature   
his ideas were transformed and released 
from the fetters of inherited prejudice4
 ,at once the mighty revolution was     

felt1 that was therewith effected in the
 realm of human thought--felt indeed in 
circles far remote and wholly unrelated 
to the sphere of science1 felt in strata
 of society that hitherto had only      
indirectly recognised the influence of  
scientific thought4  ,and how great and 
how far-reaching that revolution was6   
,from the beginning of the seventeenth  
century till its close we see arising1  
at least in embryo1 almost all that     
plays a part in the natural and         
technical science of to-day1 almost all 
that in the two centuries following so  
wonderfully transformed the facial      
appearance of the earth1 and all that is
 moving onward in process of such mighty
 evolution to-day4 ,and all this1 the   
direct result of ,galilean ideas1 the   
direct outcome of that freshly awakened 
sense for the investigation of natural  
phenomena which taught the ,tuscan      
philosopher to form the concept and the 
law of falling bodies from the          
observation of a falling stone6 ,galileo

 began his investigations without an    
implement worthy of the name2 he        
measured time in the most primitive way1
 by the efflux of water4 ,yet soon      
afterwards the telescope1 the           
microscope1 the barometer1 the          
thermometer1 the air-pump1 the steam    
engine1 the pendulum1 and the electrical
 machine were invented in rapid         
succession4 ,the fundamental theorems of
 dynamical science1 of optics1 of heat1 
and of electricity were all disclosed in
 the century that followed ,galileo4    
,of scarcely less importance1 it seems1 
was that movement which was prepared for
 by the illustrious biologists of the   
hundred years just past1 and formally   
begun by the late ,mr4 ,darwin4 ,galileo
 quickened the sense for the simpler    
phenomena of inorganic nature4 ,and with
 the same simplicity and frankness that 
marked the efforts of ,galileo1 and     
without the aid of technical or         
scientific instruments1 without physical
 or chemical experiment1 but solely by  

the power of thought and observation1   
,darwin grasps a new property of organic
 nature--which we may briefly call its  
plasticity4#gj ,with the same directness
 of purpose1 ,darwin1 too1 pursues his  
way4 ,with the same candor and love of  
truth1 he points out the strength and   
the weakness of his demonstrations4     
,with masterly equanimity he holds aloof
 from the discussion of irrelevant      
subjects and wins alike the admiration  
of his adherents and of his adversaries4
  ,scarcely thirty years have elapsed#ga
 since ,darwin first propounded the     
principles of his theory of evolution4  
,yet1 already we see his ideas firmly   
rooted in every branch of human thought1
 however remote4 ,everywhere1 in        
history1 in philosophy1 even in the     
physical sciences1 we hear the          
watchwords3 heredity1 adaptation1       
selection4 ,we speak of the struggle for
 existence among the heavenly bodies and
 of the struggle for existence in the   
world of molecules4#gb  ,the impetus    

given by ,galileo to scientific thought 
was marked in every direction2 thus1 his
 pupil1 ,borelli1 founded the school of 
exact medicine1 from whence proceeded   
even distinguished mathematicians4 ,and 
now ,darwinian ideas1 in the same way1  
are animating all provinces of research4
 ,it is true1 nature is not made up of  
two distinct parts1 the inorganic and   
the organic2 nor must these two         
divisions be treated perforce by totally
 distinct methods4 ,many sides1 however1
 nature has4 ,nature is like a thread in
 an intricate tangle1 which must be     
followed and traced1 now from this      
point1 now from that4 ,but we must never
 imagine1--and this physicists have     
learned from ,faraday and ,j4 ,r4       
,mayer1--that progress along paths once 
entered upon is the only means of       
reaching the truth4  ,it will devolve   
upon the specialists of the future to   
determine the relative tenability and   
fruitfulness of the ,darwinian ideas in 
the different provinces4 ,here ,i wish  

simply to consider the growth of natural
 knowledge in the light of the theory of
 evolution4 ,for knowledge1 too1 is a   
product of organic nature4 ,and although
 ideas1 as such1 do not comport         
themselves in all respects like         
independent organic individuals1 and    
although violent comparisons should be  
avoided1 still1 if ,darwin reasoned     
rightly1 the general imprint of         
evolution and transformation must be    
noticeable in ideas also4  ,i shall     
waive here the consideration of the     
fruitful topic of the transmission of   
ideas or rather of the transmission of  
the aptitude for certain ideas4#gc ,nor 
would it come within my province to     
discuss psychical evolution in any form1
 as ,spencer#gd and many other modern   
psychologists have done1 with varying   
success4 ,neither shall ,i enter upon a 
discussion of the struggle for existence
 and of natural selection among         
scientific theories4#ge ,we shall       
consider here only such processes of    

transformation as every student can     
easily observe in his own mind4         
99       99       99       99       99  
,the child of the forest picks out and  
pursues with marvellous acuteness the   
trails of animals4 ,he outwits and      
overreaches his foes with surpassing    
cunning4 ,he is perfectly at home in the
 sphere of his peculiar experience4 ,but
 confront him with an unwonted          
phenomenon2 place him face to face with 
a technical product of modern           
civilisation1 and he will lapse into    
impotency and helplessness4 ,here are   
facts which he does not comprehend4 ,if 
he endeavors to grasp their meaning1 he 
misinterprets them4 ,he fancies the     
moon1 when eclipsed1 to be tormented by 
an evil spirit4 ,to his mind a puffing  
locomotive is a living monster4 ,the    
letter accompanying a commission with   
which he is entrusted1 having once      
revealed his thievishness1 is in his    
imagination a conscious being1 which he 
must hide beneath a stone1 before       

venturing to commit a fresh trespass4   
,arithmetic to him is like the art of   
the geomancers in the ,arabian          
,nights1--an art which is able to       
accomplish every imaginable             
impossibility4 ,and1 like ,voltaire's   
ingnu1 when placed in our social world1 
he plays1 as we think1 the maddest      
pranks4  ,with the man who has made the 
achievements of modern science and      
civilisation his own1 the case is quite 
different4 ,he sees the moon pass       
temporarily into the shadow of the      
earth4 ,he feels in his thoughts the    
water growing hot in the boiler of the  
locomotive2 he feels also the increase  
of the tension which pushes the piston  
forward4 ,where he is not able to trace 
the direct relation of things he has    
recourse to his yard-stick and table of 
logarithms1 which aid and facilitate his
 thought without predominating over it4 
,such opinions as he cannot concur in1  
are at least known to him1 and he knows 
how to meet them in argument4  ,now1    

wherein does the difference between     
these two men consist8 ,the train of    
thought habitually employed by the first
 one does not correspond to the facts   
that he sees4 ,he is surprised and      
nonplussed at every step4 ,but the      
thoughts of the second man follow and   
anticipate events1 his thoughts have    
become adapted or accommodated to the   
larger field of observation and activity
 in which he is located2 he conceives   
things as they are4 ,the ,indian's      
sphere of experience1 however1 is quite 
different2 his bodily organs of sense   
are in constant activity2 he is ever    
intensely alert and on the watch for his
 foes2 or1 his entire attention and     
energy are engaged in procuring         
sustenance4 ,now1 how can such a        
creature project his mind into futurity1
 foresee or prophesy8 ,this is not      
possible until our fellow-beings have1  
in a measure1 relieved us of our concern
 for existence4 ,it is then that we     
acquire freedom for observation1 and not

 infrequently too that narrowness of    
thought which society helps and teaches 
us to disregard4  ,if we move for a time
 within a fixed circle of phenomena     
which recur with unvarying uniformity1  
our thoughts gradually adapt themselves 
to our environment2 our ideas reflect   
unconsciously our surroundings4 ,the    
stone we hold in our hand1 when dropped1
 not only falls to the ground in        
reality2 it also falls in our thoughts4 
,iron-filings dart towards a magnet in  
imagination as well as in fact1 and1    
when thrown into a fire1 they grew hot  
in conception as well4  ,the impulse to 
complete mentally a phenomenon that has 
been only partially observed1 has not   
its origin in the phenomenon itself2 of 
this fact1 we are fully sensible4 ,and  
we well know that it does not lie within
 the sphere of our volition4 ,it seems  
to confront us rather as a power and a  
law imposed from without and controlling
 both thought and facts4  ,the fact that
 we are able by the help of this law to 

prophesy and forecast1 merely proves a  
sameness or uniformity of environment   
sufficient to effect a mental adaptation
 of this kind4 ,a necessity of          
fulfilment1 however1 is not contained in
 this compulsory principle which        
controls our thoughts2 nor is it in any 
way determined by the possibility of    
prediction4 ,we are always obliged1 in  
fact1 to await the completion of what   
has been predicted4 ,errors and         
departures are constantly discernible1  
and are slight only in provinces of     
great rigid constancy1 as in astronomy4 
,in cases where our thoughts follow the 
connexion of events with ease1 and in   
instances where we positively forefeel  
the course of a phenomenon1 it is       
natural to fancy that the latter is     
determined by and must conform to our   
thoughts4 ,but the belief in that       
mysterious agency called causality1     
which holds thought and event in unison1
 is violently shaken when a person first
 enters a province of inquiry in which  

he has previously had no experience4    
,take for instance the strange          
interaction of electric currents and    
magnets1 or the reciprocal action of    
currents1 which seem to defy all the    
resources of mechanical science4 ,let   
him be confronted with such phenomena   
and he will immediately feel himself    
forsaken by his power of prediction2 he 
will bring nothing with him into this   
strange field of events but the hope of 
soon being able to adapt his ideas to   
the new conditions there presented4  ,a 
person constructs from a bone the       
remaining anatomy of an animal2 or from 
the visible part of a half-concealed    
wing of a butterfly he infers and       
reconstructs the part concealed4 ,he    
does so with a feeling of highest       
confidence in the accuracy of his       
results2 and in these processes we find 
nothing preternatural or transcendent4  
,but when physicists adapt their        
thoughts to conform to the dynamical    
course of events in time1 we invariably 

surround their investigations with a    
metaphysical halo2 yet these latter     
adaptations bear quite the same         
character as the former1 and our only   
reason for investing them with a        
metaphysical garb1 perhaps1 is their    
high practical value4#gf  ,let us       
consider for a moment what takes place  
when the field of observation to which  
our ideas have been adapted and now     
conform1 becomes enlarged4 ,we had1 let 
us say1 always seen heavy bodies sink   
when their support was taken away2 we   
had also seen1 perhaps1 that the sinking
 of heavier bodies forced lighter bodies
 upwards4 ,but now we see a lever in    
action1 and we are suddenly struck with 
the fact that a lighter body is lifting 
another of much greater weight4 ,our    
customary train of thought demands its  
rights2 the new and unwonted event      
likewise demands its rights4 ,from this 
conflict between thought and fact the   
problem arises2 out of this partial     
contrariety springs the question1 ,why8 

,with the new adaptation to the enlarged
 field of observation1 the problem      
disappears1 or1 in other words1 is      
solved4 ,in the instance cited1 we must 
adopt the habit of always considering   
the mechanical work performed4  ,the    
child just awakening into consciousness 
of the world1 knows no problem4 ,the    
bright flower1 the ringing bell1 are all
 new to it2 yet it is surprised at      
nothing4 ,the out and out ,philistine1  
whose only thoughts lie in the beaten   
path of his every-day pursuits1 likewise
 has no problems4 ,everything goes its  
wonted course1 and if perchance a thing 
go wrong at times1 it is at most a mere 
object of curiosity and not worth       
serious consideration4 ,in fact1 the    
question ,why8 loses all warrant in     
relations where we are familiar with    
every aspect of events4 ,but the capable
 and talented young man has his head    
full of problems2 he has acquired1 to a 
greater or less degree1 certain         
habitudes of thought1 and at the same   

time he is constantly observing what is 
new and unwonted1 and in his case there 
is no end to the questions1 ,why8       
,thus1 the factor which most promotes   
scientific thought is the gradual       
widening of the field of experience4 ,we
 scarcely notice events we are          
accustomed to2 the latter do not really 
develop their intellectual significance 
until placed in contrast with something 
to which we are unaccustomed4 ,things   
that at home are passed by unnoticed1   
delight us when abroad1 though they may 
appear in only slightly different forms4
 ,the sun shines with heightened        
radiance1 the flowers bloom in brighter 
colors1 our fellow-men accost us with   
lighter and happier looks4 ,and1        
returning home1 we find even the old    
familiar scenes more inspiring and      
suggestive than before4  ,every motive  
that prompts and stimulates us to modify
 and transform our thoughts1 proceeds   
from what is new1 uncommon1 and not     
understood4 ,novelty excites wonder in  

persons whose fixed habits of thought   
are shaken and disarranged by what they 
see4 ,but the element of wonder never   
lies in the phenomenon or event         
observed2 its place is in the person    
observing4 ,people of more vigorous     
mental type aim at once at an adaptation
 of thought that will conform to what   
they have observed4 ,thus does science  
eventually become the natural foe of the
 wonderful4 ,the sources of the         
marvellous are unveiled1 and surprise   
gives way to calm interpretation4  ,let 
us consider such a mental transformative
 process in detail4 ,the circumstance   
that heavy bodies fall to the earth     
appears perfectly natural and regular4  
,but when a person observes that wood   
floats upon water1 and that flames and  
smoke rise in the air1 then the contrary
 of the first phenomenon is presented4  
,an olden theory endeavors to explain   
these facts by imputing to substances   
the power of volition1 as that attribute
 which is most familiar to man4 ,it     

asserted that every substance seeks its 
proper place1 heavy bodies tending      
downwards and light ones upwards4 ,it   
soon turned out1 however1 that even     
smoke had weight1 that it1 too1 sought  
its place below1 and that it was forced 
upwards only because of the downward    
tendency of the air1 as wood is forced  
to the surface of water because the     
water exerts the greater downward       
pressure4  ,again1 we see a body thrown 
into the air4 ,it ascends4 ,how is it   
that it does not seek its proper place8 
,why does the velocity of its violent   
motion decrease as it rises1 while that 
of its natural fall increases as it     
descends4 ,if we mark closely the       
relation between these two facts1 the   
problem will solve itself4 ,we shall    
see1 as ,galileo did1 that the decrease 
of velocity in rising and the increase  
of velocity in falling are one and the  
same phenomenon1 viz41 an increase of   
velocity towards the earth4             
,accordingly1 it is not a place that is 

assigned to the body1 but an increase of
 velocity towards the earth4  ,by this  
idea the movements of heavy bodies are  
rendered perfectly familiar4 ,newton1   
now1 firmly grasping this new way of    
thinking1 sees the moon and the planets 
moving in their paths upon principles   
similar to those which determine the    
motion of a projectile thrown into the  
air4 ,yet the movements of the planets  
were marked by peculiarities which      
compelled him once more to modify       
slightly his customary mode of thought4 
,the heavenly bodies1 or rather the     
parts composing them1 do not move with  
constant accelerations towards each     
other1 but attract each other1 directly 
as the mass and inversely as the square 
of the distance4  ,this latter notion1  
which includes the one applying to      
terrestrial bodies as a special case1   
is1 as we see1 quite different from the 
conception from which we started4 ,how  
limited in scope was the original idea  
and to what a multitude of phenomena is 

not the present one applicable6 ,yet    
there is a trace1 after all1 of the     
search for place in the expression      
attraction4 ,and it would be folly1     
indeed1 for us to avoid1 with           
punctilious dread1 this conception of   
attraction as bearing marks of its      
pedigree4 ,it is the historical base of 
the ,newtonian conception and it still  
continues to direct our thoughts in the 
paths so long familiar to us4 ,thus1 the
 happiest ideas do not fall from heaven1
 but spring from notions already        
existing4  ,similarly1 a ray of light   
was first regarded as a continuous and  
homogeneous straight line4 ,it then     
became the path of projection for minute
 missiles2 then an aggregate of the     
paths of countless different kinds of   
missiles4 ,it became periodic2 it       
acquired various sides2 and ultimately  
it even lost its motion in a straight   
line4  ,the electric current was        
conceived originally as the flow of a   
hypothetical fluid4 ,to this conception 

was soon added the notion of a chemical 
current1 the notion of an electric1     
magnetic1 and anisotropic optical field1
 intimately connected with the path of  
the current4 ,and the richer a          
conception becomes in following and     
keeping pace with facts1 the better     
adapted it is to anticipate them4       
,adaptive processes of this kind have no
 assignable beginning1 inasmuch as every
 problem that incites to new adaptation1
 presupposes a fixed habitude of        
thought4 ,moreover1 they have no visible
 end2 in so far as experience never     
ceases4 ,science1 accordingly1 stands   
midway in the evolutionary process2 and 
science may advantageously direct and   
promote this process1 but it can never  
take its place4 ,that science is        
inconceivable the principles of which   
would enable a person with no experience
 to construct the world of experience1  
without a knowledge of it4 ,one might   
just as well expect to become a great   
musician1 solely by the aid of theory1  

and without musical experience2 or to   
become a painter by following the       
directions of a text-book4  ,in glancing
 over the history of an idea with which 
we have become perfectly familiar1 we   
are no longer able to appreciate the    
full significance of its growth4 ,the   
deep and vital changes that have been   
effected in the course of its evolution1
 are recognisable only from the         
astounding narrowness of view with which
 great contemporary scientists have     
occasionally opposed each other4        
,huygens's wave-theory of light was     
incomprehensible to ,newton1 and        
,newton's idea of universal gravity was 
unintelligible to ,huygens4 ,but a      
century afterwards both notions were    
reconcilable1 even in ordinary minds4   
,on the other hand1 the original        
creations of pioneer intellects1        
unconsciously formed1 do not assume a   
foreign garb2 their form is their own4  
,in them1 childlike simplicity is joined
 to the maturity of manhood1 and they   

are not to be compared with processes of
 thought in the average mind4 ,the      
latter are carried on as are the acts of
 persons in the state of mesmerism1     
where actions involuntarily follow the  
images which the words of other persons 
suggest to their minds4  ,the ideas that
 have become most familiar through long 
experience1 are the very ones that      
intrude themselves into the conception  
of every new fact observed4 ,in every   
instance1 thus1 they become involved in 
a struggle for self-preservation1 and it
 is just they that are seized by the    
inevitable process of transformation4   
,upon this process rests substantially  
the method of explaining by hypothesis  
new and uncomprehended phenomena4 ,thus1
 instead of forming entirely new notions
 to explain the movements of the        
heavenly bodies and the phenomena of the
 tides1 we imagine the material         
particles composing the bodies of the   
universe to possess weight or gravity   
with respect to one another4 ,similarly1

 we imagine electrified bodies to be    
freighted with fluids that attract and  
repel1 or we conceive the space between 
them to be in a state of elastic        
tension4 ,in so doing1 we substitute for
 new ideas distinct and more familiar   
notions of old experience--notions which
 to a great extent run unimpeded in     
their courses1 although they too must   
suffer partial transformation4  ,the    
animal cannot construct new members to  
perform every new function that         
circumstances and fate demand of it4 ,on
 the contrary it is obliged to make use 
of those it already possesses4 ,when a  
vertebrate animal chances into an       
environment where it must learn to fly  
or swim1 an additional pair of          
extremities is not grown for the        
purpose4 ,on the contrary1 the animal   
must adapt and transform a pair that it 
already has4  ,the construction of      
hypotheses1 therefore1 is not the       
product of artificial scientific        
methods4 ,this process is unconsciously 

carried on in the very infancy of       
science4 ,even later1 hypotheses do not 
become detrimental and dangerous to     
progress except when more reliance is   
placed on them than on the facts        
themselves2 when the contents of the    
former are more highly valued than the  
latter1 and when1 rigidly adhering to   
hypothetical notions1 we overestimate   
the ideas we possess as compared with   
those we have to acquire4  ,the         
extension of our sphere of experience   
always involves a transformation of our 
ideas4 ,it matters not whether the face 
of nature becomes actually altered1     
presenting new and strange phenomena1 or
 whether these phenomena are brought to 
light by an intentional or accidental   
turn of observation4 ,in fact1 all the  
varied methods of scientific inquiry and
 of purposive mental adaptation         
enumerated by ,john ,stuart ,mill1 those
 of observation as well as those of     
experiment1 are ultimately recognisable 
as forms of one fundamental method1 the 

method of change1 or variation4 ,it is  
through change of circumstances that the
 natural philosopher learns4 ,this      
process1 however1 is by no means        
confined to the investigator of nature4 
,the historian1 the philosopher1 the    
jurist1 the mathematician1 the artist1  
the sthetician1#gg all illuminate and   
unfold their ideas by producing from the
 rich treasures of memory similar1 but  
different1 cases2 thus1 they observe and
 experiment in their thoughts4 ,even if 
all sense-experience should suddenly    
cease1 the events of the days past would
 meet in different attitudes in the mind
 and the process of adaptation would    
still continue--a process which1 in     
contradistinction to the adaptation of  
thoughts to facts in practical spheres1 
would be strictly theoretical1 being an 
adaptation of thoughts to thoughts4     
,the method of change or variation      
brings before us like cases of          
phenomena1 having partly the same and   
partly different elements4 ,it is only  

by comparing different cases of         
refracted light at changing angles of   
incidence that the common factor1 the   
constancy of the refractive index1 is   
disclosed4 ,and only by comparing the   
refractions of light of different       
colors1 does the difference1 the        
inequality of the indices of refraction1
 arrest the attention4 ,comparison based
 upon change leads the mind             
simultaneously to the highest           
abstractions and to the finest          
distinctions4  ,undoubtedly1 the animal 
also is able to distinguish between the 
similar and dissimilar of two cases4    
,its consciousness is aroused by a noise
 or a rustling1 and its motor centre is 
put in readiness4 ,the sight of the     
creature causing the disturbance1 will1 
according to its size1 provoke flight or
 prompt pursuit2 and in the latter case1
 the more exact distinctions will       
determine the mode of attack4 ,but man  
alone attains to the faculty of         
voluntary and conscious comparison4 ,man

 alone can1 by his power of abstraction1
 rise1 in one moment1 to the            
comprehension of principles like the    
conservation of mass or the conservation
 of energy1 and in the next observe and 
mark the arrangement of the iron lines  
in the spectrum4 ,in thus dealing with  
the objects of his conceptual life1 his 
ideas unfold and expand1 like his       
nervous system1 into a widely ramified  
and organically articulated tree1 on    
which he may follow every limb to its   
farthermost branches1 and1 when occasion
 demands1 return to the trunk from which
 he started4  ,the ,english philosopher 
,whewell has remarked that two things   
are requisite to the formation of       
science3 facts and ideas4 ,ideas alone  
lead to empty speculation2 mere facts   
can yield no organic knowledge4 ,we see 
that all depends upon the capacity of   
adapting existing notions to fresh      
facts4  ,over-readiness to yield to     
every new fact prevents fixed habits of 
thought from arising4 ,excessively rigid

 habits of thought impede freedom of    
observation4 ,in the struggle1 in the   
compromise between judgment and         
prejudgment 7prejudice71 if we may use  
the term1 our understanding of things   
broadens4  ,habitual judgment1 applied  
to a new case without antecedent tests1 
we call prejudgment or prejudice4 ,who  
does not know its terrible power6 ,but  
we think less often of the importance   
and utility of prejudice4 ,physically1  
no one could exist1 if he had to guide  
and regulate the circulation1           
respiration1 and digestion of his body  
by conscious and purposive acts4 ,so1   
too1 no one could exist intellectually  
if he had to form judgments on every    
passing experience1 instead of allowing 
himself to be controlled by the         
judgments he has already formed4        
,prejudice is a sort of reflex motion in
 the province of intelligence4  ,on     
prejudices1 that is1 on habitual        
judgments not tested in every case to   
which they are applied1 reposes a goodly

 portion of the thought and work of the 
natural scientist4 ,on prejudices       
reposes most of the conduct of society4 
,with the sudden disappearance of       
prejudice society would hopelessly      
dissolve4 ,that prince displayed a deep 
insight into the power of intellectual  
habit1 who quelled the loud menaces and 
demands of his body-guard for arrears of
 pay and compelled them to turn about   
and march1 by simply pronouncing the    
regular word of command2 he well knew   
that they would be unable to resist     
that4  ,not until the discrepancy       
between habitual judgments and facts    
becomes great is the investigator       
implicated in appreciable illusion4     
,then tragic complications and          
catastrophes occur in the practical life
 of individuals and nations--crises     
where man1 placing custom above life1   
instead of pressing it into the service 
of life1 becomes the victim of his      
error4 ,the very power which in         
intellectual life advances1 fosters1 and

 sustains us1 may in other circumstances
 delude and destroy us4         99      
99       99       99       99  ,ideas   
are not all of life4 ,they are only     
momentary efflorescences of light1      
designed to illuminate the paths of the 
will4 ,but as delicate reagents on our  
organic evolution our ideas are of      
paramount importance4 ,no theory can    
gainsay the vital transformation which  
we feel taking place within us through  
their agency4 ,nor is it necessary that 
we should have a proof of this process4 
,we are immediately assured of it4  ,the
 transformation of ideas thus appears as
 a part of the general evolution of     
life1 as a part of its adaptation to a  
constantly widening sphere of action4 ,a
 granite boulder on a mountain-side     
tends towards the earth below4 ,it must 
abide in its resting-place for thousands
 of years before its support gives way4 
,the shrub that grows at its base is    
farther advanced2 it accommodates itself
 to summer and winter4 ,the fox which1  

overcoming the force of gravity1 creeps 
to the summit where he has scented his  
prey1 is freer in his movements than    
either4 ,the arm of man reaches further 
still2 and scarcely anything of note    
happens in ,africa or ,asia that does   
not leave an imprint upon his life4     
,what an immense portion of the life of 
other men is reflected in ourselves2    
their joys1 their affections1 their     
happiness and misery6 ,and this too1    
when we survey only our immediate       
surroundings1 and confine our attention 
to modern literature4 ,how much more do 
we experience when we travel through    
ancient ,egypt with ,herodotus1 when we 
stroll through the streets of ,pompeii1 
when we carry ourselves back to the     
gloomy period of the crusades or to the 
golden age of ,italian art1 now making  
the acquaintance of a physician of      
,molire1 and now that of a ,diderot or  
of a ,d',alembert4 ,what a great part of
 the life of others1 of their character 
and their purpose1 do we not absorb     

through poetry and music6 ,and although 
they only gently touch the chords of our
 emotions1 like the memory of youth     
softly breathing upon the spirit of an  
aged man1 we have nevertheless lived    
them over again in part4 ,how great and 
comprehensive does self become in this  
conception2 and how insignificant the   
person6 ,egoistical systems both of     
optimism and pessimism perish with their
 narrow standard of the import of       
intellectual life4 ,we feel that the    
real pearls of life lie in the ever     
changing contents of consciousness1 and 
that the person is merely an indifferent
 symbolical thread on which they are    
strung4#gh  ,we are prepared1 thus1 to  
regard ourselves and every one of our   
ideas as a product and a subject of     
universal evolution2 and in this way we 
shall advance sturdily and unimpeded    
along the paths which the future will   
throw open to us4#gi    ,,footnotes3    
,footnote #fi3 ,inaugural ,address1     
delivered on assuming the ,rectorate    

of the ,university of ,prague1 ,october 
#ah1 #ahhc4    ,the idea presented in   
this essay is neither new nor remote4 ,i
 have   touched upon it myself on       
several occasions 7first in #ahfg71 but 
have never made it the subject of a     
formal disquisition4 ,doubtless1        
others1 too1 have treated it2 it lies1  
so to speak1 in the air4   ,however1 as 
many of my illustrations were well      
received1 although   known only in an   
imperfect form from the lecture itself  
and the   newspapers1 ,i have1 contrary 
to my original intention1 decided to    
publish it4 ,it is not my intention to  
trespass here upon the domain   of      
biology4 ,my statements are to be taken 
merely as the expression   of the fact  
that no one can escape the influence of 
a great and   far-reaching idea4        
,footnote #gj3 ,at first sight an       
apparent contradiction arises from   the
 admission of both heredity and         
adaptation2 and it is undoubtedly   true
 that a strong disposition to heredity  

precludes great   capability of         
adaptation4 ,but imagine the organism to
 be a plastic   mass which retains the  
form transmitted to it by former        
influences   until new influences modify
 it2 the one property of plasticity     
will then represent capability of       
adaptation as well as power of          
heredity4 ,analogous to this is the case
 of a bar of magnetised steel   of high 
coercive force3 the steel retains its   
magnetic properties   until a new force 
displaces them4 ,take also a body in    
motion3 the   body retains the velocity 
acquired in 7inherited from7 the        
interval of time just preceding1 except 
it be changed in the next   moment by an
 accelerating force4 ,in the case of the
 body in motion   the change of velocity
 7,abnderung7 was looked upon as a      
matter   of course1 while the discovery 
of the principle of inertia 7or         
persistence7 created surprise2 in       
,darwin's case1 on the contrary1        
heredity 7or persistence7 was taken for 

granted1 while the   principle of       
variation 7,abnderung7 appeared novel4  
,fully adequate views are1 of course1 to
 be reached only by a study   of the    
original facts emphasised by ,darwin1   
and not by these   analogies4 ,the      
example referring to motion1 if ,i am   
not mistaken1 ,i   first heard1 in      
conversation1 from my friend ,j4        
,popper1 ,esq41 of   ,vienna4    ,many  
inquirers look upon the stability of the
 species as something   settled1 and    
oppose to it the ,darwinian theory4 ,but
 the stability of   the species is      
itself a theory4 ,the essential         
modifications which   ,darwin's views   
also are undergoing will be seen from   
the works of   ,wallace and ,weismann1  
but more especially from a book of ,w4  
,h4   ,rolph1 ,biologische ,probleme1   
,leipsic1 #ahhb4 ,unfortunately1 this   
last talented investigator is no longer 
numbered among the living4    ,footnote 
#ga3 ,written in #ahhc4    ,footnote    
#gb3 ,see ,pfaundler1 ,pogg4 ,ann41     

,jubelband1 p4 #ahb4    ,footnote #gc3  
,see the beautiful discussions of this  
point in   ,hering's ,memory as a       
,general ,function of ,organised ,matter
 7#ahgj71   ,chicago1 ,the ,open ,court 
,publishing ,co41 #ahhg4 ,compare also  
,dubois1   ,ueber die ,uebung1 ,berlin1 
#ahha4    ,footnote #gd3 ,spencer1 ,the 
,principles of ,psychology4 ,london1    
#ahgb4    ,footnote #ge3 ,see the       
article ,the ,velocity of ,light1 page  
#fc4    ,footnote #gf3 ,i am well aware 
that the endeavor to confine oneself    
in natural research to facts is often   
censured as an exaggerated   fear of    
metaphysical spooks4 ,but ,i would      
observe1 that1 judged by   the mischief 
which they have wrought1 the            
metaphysical1 of all   spooks1 are the  
least fabulous4 ,it is not to be denied 
that many   forms of thought were not   
originally acquired by the individual1  
but   were antecedently formed1 or      
rather prepared for1 in the development 
of the species1 in some such way as     

,spencer1 ,haeckel1 ,hering1 and        
others have supposed1 and as ,i myself  
have hinted on various   occasions4     
,footnote #gg3 ,compare1 for example1   
,schiller1 ,zerstreute   ,betrachtungen 
ber verschiedene sthetische ,gegenstnde4
    ,footnote #gh3 ,we must not be      
deceived in imagining that the          
happiness of other people is not a very 
considerable and essential   portion of 
our own4 ,it is common capital1 which   
cannot be created by   the individual1  
and which does not perish with him4 ,the
 formal and   material limitation of the
 ego is necessary and sufficient only   
for the crudest practical objects1 and  
cannot subsist in a broad   conception4 
,humanity in its entirety may be likened
 to a   polyp-plant4 ,the material and  
organic bonds of individual union       
have1 indeed1 been severed2 they would  
only have impeded freedom of   movement 
and evolution4 ,but the ultimate aim1   
the psychical   connexion of the whole1 
has been attained in a much higher      

degree   through the richer development 
thus made possible4    ,footnote #gi3   
,c4 ,e4 von ,baer1 the subsequent       
opponent of ,darwin and   ,haeckel1 has 
discussed in two beautiful addresses    
7,das allgemeinste   ,gesetz der ,natur 
in aller ,entwickelung1 and ,welche     
,auffassung der   lebenden ,natur ist   
die richtige1 und wie ist diese         
,auffassung auf   die ,entomologie      
anzuwenden87 the narrowness of the view 
which   regards an animal in its        
existing state as finished and complete1
   instead of conceiving it as a phase  
in the series of evolutionary   forms   
and regarding the species itself as a   
phase of the development   of the animal
 world in general4     ,,on ,,the       
,,principle ,,of ,,comparison ,,in      
,,physics4#hj   ,twenty years ago when  
,kirchhoff defined the object of        
mechanics as the description1 in        
complete and very simple terms1 of the  
motions occurring in nature1 he produced
 by the statement a peculiar impression4

 ,fourteen years subsequently1          
,boltzmann1 in the life-like picture    
which he drew of the great inquirer1    
could still speak of the universal      
astonishment at this novel method of    
treating mechanics1 and we meet with    
epistemological treatises to-day1 which 
plainly show how difficult is the       
acceptance of this point of view4 ,a    
modest and small band of inquirers there
 were1 however1 to whom ,kirchhoff's few
 words were tidings of a welcome and    
powerful ally in the epistemological    
field4  ,now1 how does it happen that we
 yield our assent so reluctantly to the 
philosophical opinion of an inquirer for
 whose scientific achievements we have  
only words of praise8 ,one reason       
probably is that few inquirers can find 
time and leisure1 amid the exacting     
employments demanded for the acquisition
 of new knowledge1 to inquire closely   
into that tremendous psychical process  
by which science is formed4 ,further1 it
 is inevitable that much should be put  

into ,kirchhoff's rigid words that they 
were not originally intended to convey1 
and that much should be found wanting in
 them that had always been regarded as  
an essential element of scientific      
knowledge4 ,what can mere description   
accomplish8 ,what has become of         
explanation1 of our insight into the    
causal connexion of things8         99  
99       99       99       99  ,permit  
me1 for a moment1 to contemplate not the
 results of science1 but the mode of its
 growth1 in a frank and unbiassed       
manner4 ,we know of only one source of  
immediate revelation of scientific      
facts--our senses4 ,restricted to this  
source alone1 thrown wholly upon his own
 resources1 obliged to start always     
anew1 what could the isolated individual
 accomplish8 ,of a stock of knowledge so
 acquired the science of a distant negro
 hamlet in darkest ,africa could hardly 
give us a sufficiently humiliating      
conception4 ,for there that veritable   
miracle of thought-transference has     

already begun its work1 compared with   
which the miracles of the spiritualists 
are rank monstrosities--communication by
 language4 ,reflect1 too1 that by means 
of the magical characters which our     
libraries contain we can raise the      
spirits of the the sovereign dead of old
 from ,faraday to ,galileo and          
,archimedes1 through ages of            
time--spirits who do not dismiss us with
 ambiguous and derisive oracles1 but    
tell us the best they know2 then shall  
we feel what a stupendous and           
indispensable factor in the formation of
 science communication is4 ,not the dim1
 half-conscious surmises of the acute   
observer of nature or critic of humanity
 belong to science1 but only that which 
they possess clearly enough to          
communicate to others4  ,but how1 now1  
do we go about this communication of a  
newly acquired experience1 of a newly   
observed fact8 ,as the different calls  
and battle-cries of gregarious animals  
are unconsciously formed signs for a    

common observation or action1           
irrespective of the causes which produce
 such action--a fact that already       
involves the germ of the concept2 so    
also the words of human language1 which 
is only more highly specialised1 are    
names or signs for universally known    
facts1 which all can observe or have    
observed4 ,if the mental representation1
 accordingly1 follows the new fact at   
once and passively1 then that new fact  
must1 of itself1 immediately be         
constituted and represented in thought  
by facts already universally known and  
commonly observed4 ,memory is always    
ready to put forward for comparison     
known facts which resemble the new      
event1 or agree with it in certain      
features1 and so renders possible that  
elementary internal judgment which the  
mature and definitively formulated      
judgment soon follows4  ,comparison1 as 
the fundamental condition of            
communication1 is the most powerful     
inner vital element of science4 ,the    

zologist sees in the bones of the       
wing-membranes of bats1 fingers2 he     
compares the bones of the cranium with  
the vertebr1 the embryos of different   
organisms with one another1 and the     
different stages of development of the  
same organism with one another4 ,the    
geographer sees in ,lake ,garda a fjord1
 in the ,sea of ,aral a lake in process 
of drying up4 ,the philologist compares 
different languages with one another1   
and the formations of the same language 
as well4 ,if it is not customary to     
speak of comparative physics in the same
 sense that we speak of comparative     
anatomy1 the reason is that in a science
 of such great experimental activity the
 attention is turned away too much from 
the contemplative element4 ,but like all
 other sciences1 physics lives and grows
 by comparison4         99       99     
99       99       99  ,the manner in    
which the result of the comparison finds
 expression in the communication1 varies
 of course very much4 ,when we say that 

the colors of the spectrum are red1     
yellow1 green1 blue1 and violet1 the    
designations employed may possibly have 
been derived from the technology of     
tattooing1 or they may subsequently have
 acquired the significance of standing  
for the colors of the rose1 the lemon1  
the leaf1 the corn-flower1 and the      
violet4 ,from the frequent repetition of
 such comparisons1 however1 made under  
the most manifold circumstances1 the    
inconstant features1 as compared with   
the permanent congruent features1 get so
 obliterated that the latter acquire a  
fixed significance independent of every 
object and connexion1 or take on as we  
say an abstract or conceptual import4   
,no one thinks at the word red of any   
other agreement with the rose than that 
of color1 or at the word straight of any
 other property of a stretched cord than
 the sameness of direction4 ,just so1   
too1 numbers1 originally the names of   
the fingers of the hands and feet1 from 
being used as arrangement-signs for all 

kinds of objects1 were lifted to the    
plane of abstract concepts4 ,a verbal   
report 7communication7 of a fact that   
uses only these purely abstract         
implements1 we call a direct            
description4  ,the direct description of
 a fact of any great extent is an       
irksome task1 even where the requisite  
notions are already completely          
developed4 ,what a simplification it    
involves if we can say1 the fact ,a now 
considered comports itself1 not in one1 
but in many or in all its features1 like
 an old and well-known fact ,b4 ,the    
moon comports itself as a heavy body    
does with respect to the earth2 light   
like a wave-motion or an electric       
vibration2 a magnet1 as if it were laden
 with gravitating fluids1 and so on4 ,we
 call such a description1 in which we   
appeal1 as it were1 to a description    
already and elsewhere formulated1 or    
perhaps still to be precisely           
formulated1 an indirect description4 ,we
 are at liberty to supplement this      

description1 gradually1 by direct       
description1 to correct it1 or to       
replace it altogether4 ,we see1 thus1   
without difficulty1 that what is called 
a theory or a theoretical idea1 falls   
under the category of what is here      
termed indirect description4         99 
99       99       99       99  ,what1   
now1 is a theoretical idea8 ,whence do  
we get it8 ,what does it accomplish for 
us8 ,why does it occupy a higher place  
in our judgment than the mere holding   
fast to a fact or an observation8 ,here1
 too1 memory and comparison alone are in
 play4 ,but instead of a single feature 
of resemblance culled from memory1 in   
this case a great system of resemblances
 confronts us1 a well-known physiognomy1
 by means of which the new fact is      
immediately transformed into an old     
acquaintance4 ,besides1 it is in the    
power of the idea to offer us more than 
we actually see in the new fact1 at the 
first moment2 it can extend the fact1   
and enrich it with features which we are

 first induced to seek from such        
suggestions1 and which are often        
actually found4 ,it is this rapidity in 
extending knowledge that gives to theory
 a preference over simple observation4  
,but that preference is wholly          
quantitative4 ,qualitatively1 and in    
real essential points1 theory differs   
from observation neither in the mode of 
its origin nor in its last results4     
,the adoption of a theory1 however1     
always involves a danger4 ,for a theory 
puts in the place of a fact ,a in       
thought1 always a different1 but simpler
 and more familiar fact ,b1 which in    
some relations can mentally represent   
,a1 but for the very reason that it is  
different1 in other relations cannot    
represent it4 ,if now1 as may readily   
happen1 sufficient care is not          
exercised1 the most fruitful theory may1
 in special circumstances1 become a     
downright obstacle to inquiry4 ,thus1   
the emission-theory of light1 in        
accustoming the physicist to think of   

the projectile path of the              
light-particles as an undifferentiated  
straight-line1 demonstrably impeded the 
discovery of the periodicity of light4  
,by putting in the place of light the   
more familiar phenomena of sound1       
,huygens renders light in many of its   
features a familiar event1 but with     
respect to polarisation1 which lacks the
 longitudinal waves with which alone he 
was acquainted1 it had for him a doubly 
strange aspect4 ,he is unable thus to   
grasp in abstract thought the fact of   
polarisation1 which is before his eyes1 
whilst ,newton1 merely by adapting to   
the observation his thoughts1 and       
putting this question1 ,annon radiorum  
luminis diversa sunt latera8 abstractly 
grasped polarisation1 that is1 directly 
described it1 a century before ,malus4  
,on the other hand1 if the agreement of 
the fact with the idea theoretically    
representing it1 extends further than   
its inventor originally anticipated1    
then we may be led by it to unexpected  

discoveries1 of which conical           
refraction1 circular polarisation by    
total reflexion1 ,hertz's waves offer   
ready examples1 in contrast to the      
illustrations given above4  ,our insight
 into the conditions indicated will be  
improved1 perhaps1 by contemplating the 
development of some theory or other more
 in detail4 ,let us consider a          
magnetised bar of steel by the side of a
 second unmagnetised bar1 in all other  
respects the same4 ,the second bar gives
 no indication of the presence of       
iron-filings2 the first attracts them4  
,also1 when the iron-filings are absent1
 we must think of the magnetised bar as 
in a different condition from that of   
the unmagnetised4 ,for1 that the mere   
presence of the iron-filings does not   
induce the phenomenon of attraction is  
proved by the second unmagnetised bar4  
,the ingenuous man1 who finds in his    
will1 as his most familiar source of    
power1 the best facilities for          
comparison1 conceives a species of      

spirit in the magnet4 ,the behavior of a
 warm body or of an electrified body    
suggests similar ideas4 ,this is the    
point of view of the oldest theory1     
fetishism1 which the inquirers of the   
early ,middle ,ages had not yet         
overcome1 and which in its last         
vestiges1 in the conception of forces1  
still flourishes in modern physics4 ,we 
see1 thus1 the dramatic element need no 
more be absent in a scientific          
description1 than in a thrilling novel4 
,if1 on subsequent examination1 it be   
observed that a cold body1 in contact   
with a hot body1 warms itself1 so to    
speak1 at the expense of the hot body2  
further1 that when the substances are   
the same1 the cold body1 which1 let us  
say1 has twice the mass of the other1   
gains only half the number of degrees of
 temperature that the other loses1 a    
wholly new impression arises4 ,the      
demoniac character of the event         
vanishes1 for the supposed spirit acts  
not by caprice1 but according to fixed  

laws4 ,in its place1 however1           
instinctively the notion of a substance 
is substituted1 part of which flows over
 from the one body to the other1 but the
 total amount of which1 representable by
 the sum of the products of the masses  
into the respective changes of          
temperature1 remains constant4 ,black   
was the first to be powerfully struck   
with this resemblance of thermal        
processes to the motion of a substance1 
and under its guidance discovered the   
specific heat1 the heat of fusion1 and  
the heat of vaporisation of bodies4     
,gaining strength and fixity1 however1  
from these successes1 this notion of    
substance subsequently stood in the way 
of scientific advancement4 ,it blinded  
the eyes of the successors of ,black1   
and prevented them from seeing the      
manifest fact1 which every savage knows1
 that heat is produced by friction4     
,fruitful as that notion was for ,black1
 helpful as it still is to the learner  
to-day in ,black's special field1       

permanent and universal validity as a   
theory it could never maintain4 ,but    
what is essential1 conceptually1 in it1 
viz41 the constancy of the product-sum  
above mentioned1 retains its value and  
may be regarded as a direct description 
of ,black's facts4  ,it stands to reason
 that those theories which push         
themselves forward unsought1            
instinctively1 and wholly of their own  
accord1 should have the greatest power1 
should carry our thoughts most with     
them1 and exhibit the staunchest powers 
of self-preservation4 ,on the other     
hand1 it may also be observed that when 
critically scrutinised such theories are
 extremely apt to lose their cogency4   
,we are constantly busied with          
substance1 its modes of action have     
stamped themselves indelibly upon our   
thoughts1 our vividest and clearest     
reminiscences are associated with it4   
,it should cause us no surprise1        
therefore1 that ,robert ,mayer and      
,joule1 who gave the final blow to      

,black's substantial conception of heat1
 should have re-introduced the same     
notion of substance in a more abstract  
and modified form1 only applying to a   
much more extensive field4  ,here1 too1 
the psychological circumstances which   
impart to the new conception its power1 
lie clearly before us4 ,by the unusual  
redness of the venous blood in tropical 
climates ,mayer's attention is directed 
to the lessened expenditure of internal 
heat and to the proportionately lessened
 consumption of material by the human   
body in those climates4 ,but as every   
effort of the human organism1 including 
its mechanical work1 is connected with  
the consumption of material1 and as work
 by friction can engender heat1         
therefore heat and work appear in kind  
equivalent1 and between them a          
proportional relation must subsist4 ,not
 every quantity1 but the appropriately  
calculated sum of the two1 as connected 
with a proportionate consumption of     
material1 appears substantial4  ,by     

exactly similar considerations1 relative
 to the economy of the galvanic element1
 ,joule arrived at his view2 he found   
experimentally that the sum of the heat 
evolved in the circuit1 of the heat     
consumed in the combustion of the gas   
developed1 of the electro-magnetic work 
of the current1 properly calculated1--in
 short1 the sum of all the effects of   
the battery1--is connected with a       
proportionate consumption of zinc4      
,accordingly1 this sum itself has a     
substantial character4  ,mayer was so   
absorbed with the view attained1 that   
the indestructibility of force1 in our  
phraseology work1 appeared to him a     
priori evident4 ,the creation or        
annihilation of a force1 he says1 lies  
without the province of human thought   
and power4 ,joule expressed himself to a
 similar effect3 ,it is manifestly      
absurd to suppose that the powers with  
which ,god has endowed matter can be    
destroyed4 ,strange to say1 on the basis
 of such utterances1 not ,joule1 but    

,mayer1 was stamped as a metaphysician4 
,we may be sure1 however1 that both men 
were merely giving expression1 and that 
half-unconsciously1 to a powerful formal
 need of the new simple view1 and that  
both would have been extremely surprised
 if it had been proposed to them that   
their principle should be submitted to a
 philosophical congress or              
ecclesiastical synod for a decision upon
 its validity4 ,but with all agreements1
 the attitude of these two men1 in other
 respects1 was totally different4       
,whilst ,mayer represented this formal  
need with all the stupendous instinctive
 force of genius1 we might say almost   
with the ardor of fanaticism1 yet was   
withal not wanting in the conceptive    
ability to compute1 prior to all other  
inquirers1 the mechanical equivalent of 
heat from old physical constants long   
known and at the disposal of all1 and so
 to set up for the new doctrine a       
programme embracing all physics and     
physiology2 ,joule1 on the other hand1  

applied himself to the exact            
verification of the doctrine by         
beautifully conceived and masterfully   
executed experiments1 extending over all
 departments of physics4 ,soon          
,helmholtz too attacked the problem1 in 
a totally independent and characteristic
 manner4 ,after the professional        
virtuosity with which this physicist    
grasped and disposed of all the points  
unsettled by ,mayer's programme and more
 besides1 what especially strikes us is 
the consummate critical lucidity of this
 young man of twenty-six years4 ,in his 
exposition is wanting that vehemence and
 impetuosity which marked ,mayer's4 ,the
 principle of the conservation of energy
 is no self-evident or a priori         
proposition for him4 ,what follows1 on  
the assumption that that proposition    
obtains8 ,in this hypothetical form1 he 
subjugates his matter4  ,i must confess1
 ,i have always marvelled at the sthetic
 and ethical taste of many of our       
contemporaries who have managed to      

fabricate out of this relation of       
things1 odious national and personal    
questions1 instead of praising the good 
fortune that made several such men work 
together and of rejoicing at the        
instructive diversity and idiosyncrasies
 of great minds fraught with such rich  
consequences for us4  ,we know that     
still another theoretical conception    
played a part in the development of the 
principle of energy1 which ,mayer held  
aloof from1 namely1 the conception that 
heat1 as also the other physical        
processes1 are due to motion4 ,but once 
the principle of energy has been        
reached1 these auxiliary and            
transitional theories discharge no      
essential function1 and we may regard   
the principle1 like that which ,black   
gave1 as a contribution to the direct   
description of a widely extended domain 
of facts4  ,it would appear from such   
considerations not only advisable1 but  
even necessary1 with all due recognition
 of the helpfulness of theoretic ideas  

in research1 yet gradually1 as the new  
facts grow familiar1 to substitute for  
indirect description direct description1
 which contains nothing that is         
unessential and restricts itself        
absolutely to the abstract apprehension 
of facts4 ,we might almost say1 that the
 descriptive sciences1 so called with a 
tincture of condescension1 have1 in     
respect of scientific character1        
outstripped the physical expositions    
lately in vogue4 ,of course1 a virtue   
has been made of necessity here4  ,we   
must admit1 that it is not in our power 
to describe directly every fact1 on the 
moment4 ,indeed1 we should succumb in   
utter despair if the whole wealth of    
facts which we come step by step to     
know1 were presented to us all at once4 
,happily1 only detached and unusual     
features first strike us1 and such we   
bring nearer to ourselves by comparison 
with every-day events4 ,here the notions
 of the common speech are first         
developed4 ,the comparisons then grow   

more manifold and numerous1 the fields  
of facts compared more extensive1 the   
concepts that make direct description   
possible1 proportionately more general  
and more abstract4  ,first we become    
familiar with the motion of freely      
falling bodies4 ,the concepts of force1 
mass1 and work are then carried over1   
with appropriate modifications1 to the  
phenomena of electricity and magnetism4 
,a stream of water is said to have      
suggested to ,fourier the first distinct
 picture of currents of heat4 ,a special
 case of vibrations of strings          
investigated by ,taylor1 cleared up for 
him a special case of the conduction of 
heat4 ,much in the same way that ,daniel
 ,bernoulli and ,euler constructed the  
most diverse forms of vibrations of     
strings from ,taylor's cases1 so        
,fourier constructs out of simple cases 
of conduction the most multifarious     
motions of heat2 and that method has    
extended itself over the whole of       
physics4 ,ohm forms his conception of   

the electric current in imitation of    
,fourier's4 ,the latter1 also1 adopts   
,fick's theory of diffusion4 ,in an     
analogous manner a conception of the    
magnetic current is developed4 ,all     
sorts of stationary currents are thus   
made to exhibit common features1 and    
even the condition of complete          
equilibrium in an extended medium shares
 these features with the dynamical      
condition of equilibrium of a stationary
 current4 ,things as remote as the      
magnetic lines of force of an electric  
current and the stream-lines of a       
frictionless liquid vortex enter in this
 way into a peculiar relationship of    
similarity4 ,the concept of potential1  
originally enunciated for a restricted  
province1 acquires a wide-reaching      
applicability4 ,things as dissimilar as 
pressure1 temperature1 and electromotive
 force1 now show points of agreement in 
relation to ideas derived by definite   
methods from that concept3 viz41 fall of
 pressure1 fall of temperature1 fall of 

potential1 as also with the further     
notions of liquid1 thermal1 and electric
 strength of current4 ,that relationship
 between systems of ideas in which the  
dissimilarity of every two homologous   
concepts as well as the agreement in    
logical relations of every two          
homologous pairs of concepts1 is clearly
 brought to light1 is called an analogy4
 ,it is an effective means of mastering 
heterogeneous fields of facts in unitary
 comprehension4 ,the path is plainly    
shown in which a universal physical     
phenomenology embracing all domains1    
will be developed4  ,in the process     
described we attain for the first time  
to what is indispensable in the direct  
description of broad fields of fact--the
 wide-reaching abstract concept4 ,and   
now ,i must put a question smacking of  
the school-master1 but unavoidable3     
,what is a concept8 ,is it a hazy       
representation1 admitting withal of     
mental visualisation8 ,no4 ,mental      
visualisation accompanies it only in the

 simplest cases1 and then merely as an  
adjunct4 ,think1 for example1 of the    
coefficient of self-induction1 and seek 
for its visualised mental image4 ,or is1
 perhaps1 the concept a mere word8 ,the 
adoption of this forlorn idea1 which has
 been actually proposed of late by a    
reputed mathematician would only throw  
us back a thousand years into the       
deepest scholasticism4 ,we must1        
therefore1 reject it4  ,the solution is 
not far to seek4 ,we must not think that
 sensation1 or representation1 is a     
purely passive process4 ,the lowest     
organisms respond to it with a simple   
reflex motion1 by engulfing the prey    
which approaches them4 ,in higher       
organisms the centripetal stimulus      
encounters in the nervous system        
obstacles and aids which modify the     
centrifugal process4 ,in still higher   
organisms1 where prey is pursued and    
examined1 the process in question may go
 through extensive paths of circular    
motions before it comes to relative     

rest4 ,our own life1 too1 is enacted in 
such processes2 all that we call science
 may be regarded as parts1 or middle    
terms1 of such activities4  ,it will not
 surprise us now if ,i say3 the         
definition of a concept1 and1 when it is
 very familiar1 even its name1 is an    
impulse to some accurately determined1  
often complicated1 critical1            
comparative1 or constructive activity1  
the usually sense-perceptive result of  
which is a term or member of the        
concept's scope4 ,it matters not whether
 the concept draws the attention only to
 one certain sense 7as sight7 or to a   
phase of a sense 7as color1 form71 or is
 the starting-point of a complicated    
action2 nor whether the activity in     
question 7chemical1 anatomical1 and     
mathematical operations7 is muscular or 
technical1 or performed wholly in the   
imagination1 or only intimated4 ,the    
concept is to the physicist what a      
musical note is to a piano-player4 ,a   
trained physicist or mathematician reads

 a memoir like a musician reads a score4
 ,but just as the piano-player must     
first learn to move his fingers singly  
and collectively1 before he can follow  
his notes without effort1 so the        
physicist or mathematician must go      
through a long apprenticeship before he 
gains control1 so to speak1 of the      
manifold delicate innervations of his   
muscles and imagination4 ,think of how  
frequently the beginner in physics or   
mathematics performs more1 or less1 than
 is required1 or of how frequently he   
conceives things differently from what  
they are6 ,but if1 after having had     
sufficient discipline1 he lights upon   
the phrase coefficient of               
self-induction1 he knows immediately    
what that term requires of him4 ,long   
and thoroughly practised actions1 which 
have their origin in the necessity of   
comparing and representing facts by     
other facts1 are thus the very kernel of
 concepts4 ,in fact1 positive and       
philosophical philology both claim to   

have established that all roots         
represent concepts and stood originally 
for muscular activities alone4 ,the slow
 assent of physicists to ,kirchhoff's   
dictum now becomes intelligible4 ,they  
best could feel the vast amount of      
individual labor1 theory1 and skill     
required before the ideal of direct     
description could be realised4          
99       99       99       99       99  
,suppose1 now1 the ideal of a given     
province of facts is reached4 ,does     
description accomplish all that the     
inquirer can ask8 ,in my opinion1 it    
does4 ,description is a building up of  
facts in thought1 and this building up  
is1 in the experimental sciences1 often 
the condition of actual execution4 ,for 
the physicist1 to take a special case1  
the metrical units are the              
building-stones1 the concepts the       
directions for building1 and the facts  
the result of the building4 ,our mental 
imagery is almost a complete substitute 
for the fact1 and by means of it we can 

ascertain all the fact's properties4 ,we
 do not know that worst which we        
ourselves have made4  ,people require of
 science that it should prophesy1 and   
,hertz uses that expression in his      
posthumous ,mechanics4 ,but1 natural as 
it is1 the expression is too narrow4    
,the geologist and the palontologist1 at
 times the astronomer1 and always the   
historian and the philologist1 prophesy1
 so to speak1 backwards4 ,the           
descriptive sciences1 like geometry and 
mathematics1 prophesy neither forward or
 backwards1 but seek from given         
conditions the conditioned4 ,let us say 
rather3 ,science completes in thought   
facts that are only partly given4 ,this 
is rendered possible by description1 for
 description presupposes the            
interdependence of the descriptive      
elements3 otherwise nothing would be    
described4  ,it is said1 description    
leaves the sense of causality           
unsatisfied4 ,in fact1 many imagine they
 understand motions better when they    

picture to themselves the pulling       
forces2 and yet the accelerations1 the  
facts1 accomplish more1 without         
superfluous additions4 ,i hope that the 
science of the future will discard the  
idea of cause and effect1 as being      
formally obscure2 and in my feeling that
 these ideas contain a strong tincture  
of fetishism1 ,i am certainly not alone4
 ,the more proper course is1 to regard  
the abstract determinative elements of a
 fact as interdependent1 in a purely    
logical way1 as the mathematician or    
geometer does4 ,true1 by comparison with
 the will1 forces are brought nearer to 
our feeling2 but it may be that         
ultimately the will itself will be made 
clearer by comparison with the          
accelerations of masses4  ,if we are    
asked1 candidly1 when is a fact clear to
 us1 we must say when we can reproduce  
it by very simple and very familiar     
intellectual operations1 such as the    
construction of accelerations1 or the   
geometrical summation of accelerations1 

and so forth4 ,the requirement of       
simplicity is of course to the expert a 
different matter from what it is to the 
novice4 ,for the first1 description by a
 system of differential equations is    
sufficient2 for the second1 a gradual   
construction out of elementary laws is  
required4 ,the first discerns at once   
the connexion of the two expositions4   
,of course1 it is not disputed that the 
artistic value of materially equivalent 
descriptions may not be different4      
,most difficult is it to persuade       
strangers that the grand universal laws 
of physics1 such as apply               
indiscriminately to material1           
electrical1 magnetic1 and other systems1
 are not essentially different from     
descriptions4 ,as compared with many    
sciences1 physics occupies in this      
respect a position of vantage that is   
easily explained4 ,take1 for example1   
anatomy4 ,as the anatomist in his quest 
for agreements and differences in       
animals ascends to ever higher and      

higher classifications1 the individual  
facts that represent the ultimate terms 
of the system1 are still so different   
that they must be singly noted4 ,think1 
for example1 of the common marks of the 
,vertebrates1 of the class-characters of
 ,mammals and ,birds on the one hand and
 of ,fishes on the other1 of the double 
circulation of the blood on the one hand
 and of the single on the other4 ,in the
 end1 always isolated facts remain1     
which show only a slight likeness to one
 another4  ,a science still more closely
 allied to physics1 chemistry1 is often 
in the same strait4 ,the abrupt change  
of the qualitative properties1 in all   
likelihood conditioned by the slight    
stability of the intermediate states1   
the remote resemblance of the           
co-ordinated facts of chemistry render  
the treatment of its data difficult4    
,pairs of bodies of different           
qualitative properties unite in         
different mass-ratios2 but no connexion 
between the first and the last is to be 

noted1 at first4  ,physics1 on the other
 hand1 reveals to us wide domains of    
qualitatively homogeneous facts1        
differing from one another only in the  
number of equal parts into which their  
characteristic marks are divisible1 that
 is1 differing only quantitatively4     
,even where we have to deal with        
qualities 7colors and sounds71          
quantitative characters of those        
qualities are at our disposal4 ,here the
 classification is so simple a task that
 it rarely impresses us as such1 whilst 
in infinitely fine gradations1 in a     
continuum of facts1 our number-system is
 ready beforehand to follow as far as we
 wish4 ,the co-ordinated facts are here 
extremely similar and very closely      
affined1 as are also their descriptions 
which consist in the determination of   
the numerical measures of one given set 
of characters from those of a different 
set by means of familiar mathematical   
operations--methods of derivation4      
,thus1 the common characteristics of all

 descriptions can be found here2 and    
with them a succinct1 comprehensive     
description1 or a rule for the          
construction of all single descriptions1
 is assigned1--and this we call law4    
,well-known examples are the formul for 
freely falling bodies1 for projectiles1 
for central motion1 and so forth4 ,if   
physics apparently accomplishes more by 
its methods than other sciences1 we must
 remember that in a sense it has        
presented to it much simpler problems4  
,the remaining sciences1 whose facts    
also present a physical side1 need not  
be envious of physics for this          
superiority2 for all its acquisitions   
ultimately redound to their benefit as  
well4 ,but also in other ways this      
mutual help shall and must change4      
,chemistry has advanced very far in     
making the methods of physics her own4  
,apart from older attempts1 the         
periodical series of ,lothar ,meyer and 
,mendelejeff are a brilliant and        
adequate means of producing an easily   

surveyed system of facts1 which by      
gradually becoming complete1 will take  
the place almost of a continuum of      
facts4 ,further1 by the study of        
solutions1 of dissociation1 in fact     
generally of phenomena which present a  
continuum of cases1 the methods of      
thermodynamics have found entrance into 
chemistry4 ,similarly we may hope that1 
at some future day1 a mathematician1    
letting the fact-continuum of embryology
 play before his mind1 which the        
palontologists of the future will       
supposedly have enriched with more      
intermediate and derivative forms       
between ,saurian and ,bird than the     
isolated ,pterodactyl1 ,archopteryx1    
,ichthyornis1 and so forth1 which we now
 have--that such a mathematician shall  
transform1 by the variation of a few    
parameters1 as in a dissolving view1 one
 form into another1 just as we transform
 one conic section into another4        
,reverting now to ,kirchhoff's words1 we
 can come to some agreement regarding   

their import4 ,nothing can be built     
without building-stones1 mortar1        
scaffolding1 and a builder's skill4 ,yet
 assuredly the wish is well founded1    
that will show to posterity the complete
 structure in its finished form1 bereft 
of unsightly scaffolding4 ,it is the    
pure logical and sthetic sense of the   
mathematician that speaks out of        
,kirchhoff's words4 ,modern expositions 
of physics aspire after his ideal2 that1
 too1 is intelligible4 ,but it would be 
a poor didactic shift1 for one whose    
business it was to train architects1 to 
say3 ,here is a splendid edifice2 if    
thou wouldst really build1 go thou and  
do likewise4  ,the barriers between the 
special sciences1 which make division of
 work and concentration possible1 but   
which appear to us after all as cold and
 conventional restrictions1 will        
gradually disappear4 ,bridge upon bridge
 is thrown over the gaps4 ,contents and 
methods1 even of the remotest branches1 
are compared4 ,when the ,congress of    

,natural ,scientists shall meet a       
hundred years hence1 we may expect that 
they will represent a unity in a higher 
sense than is possible to-day1 not in   
sentiment and aim alone1 but in method  
also4 ,in the meantime1 this great      
change will be helped by our keeping    
constantly before our minds the fact of 
the intrinsic relationship of all       
research1 which ,kirchhoff characterised
 with such classical simplicity4        
,,footnotes3    ,footnote #hj3 ,an      
address delivered before the ,general   
,session of the   ,german ,association  
of ,naturalists and ,physicians1 at     
,vienna1 ,sept4   #bd1 #ahid4     ,,the 
,,part ,,played ,,by ,,accident ,,in    
,,invention ,,and ,,discovery4#ha   ,it 
is characteristic of the nave and       
sanguine beginnings of thought in       
youthful men and nations1 that all      
problems are held to be soluble and     
fundamentally intelligible on the first 
appearance of success4 ,the sage of     
,miletus1 on seeing plants take their   

rise from moisture1 believed he had     
comprehended the whole of nature1 and he
 of ,samos1 on discovering that definite
 numbers corresponded to the lengths of 
harmonic strings1 imagined he could     
exhaust the nature of the world by means
 of numbers4 ,philosophy and science in 
such periods are blended4 ,wider        
experience1 however1 speedily discloses 
the error of such a course1 gives rise  
to criticism1 and leads to the division 
and ramification of the sciences4  ,at  
the same time1 the necessity of a broad 
and general view of the world remains2  
and to meet this need philosophy parts  
company with special inquiry4 ,it is    
true1 the two are often found united in 
gigantic personalities4 ,but as a rule  
their ways diverge more and more widely 
from each other4 ,and if the            
estrangement of philosophy from science 
can reach a point where data unworthy of
 the nursery are not deemed too scanty  
as foundations of the world1 on the     
other hand the thorough-paced specialist

 may go to the extreme of rejecting     
point-blank the possibility of a broader
 view1 or at least of deeming it        
superfluous1 forgetful of ,voltaire's   
apophthegm1 nowhere more applicable than
 here1 ,le superflu--chose trs          
ncessaire4  ,it is true1 the history of 
philosophy1 owing to the insufficiency  
of its constructive data1 is and must be
 largely a history of error4 ,but it    
would be the height of ingratitude on   
our part to forget that the seeds of    
thoughts which still fructify the soil  
of special research1 such as the theory 
of irrationals1 the conceptions of      
conservation1 the doctrine of evolution1
 the idea of specific energies1 and so  
forth1 may be traced back in distant    
ages to philosophical sources4          
,furthermore1 to have deferred or       
abandoned the attempt at a broad        
philosophical view of the world from a  
full knowledge of the insufficiency of  
our materials1 is quite a different     
thing from never having undertaken it at

 all4 ,the revenge of its neglect1      
moreover1 is constantly visited upon the
 specialist by his committal of the very
 errors which philosophy long ago       
exposed4 ,as a fact1 in physics and     
physiology1 particularly during the     
first half of this century1 are to be   
met intellectual productions which for  
nave simplicity are not a jot inferior  
to those of the ,ionian school1 or to   
the ,platonic ideas1 or to that much    
reviled ontological proof4  ,latterly1  
there has been evidence of a gradual    
change in the situation4 ,recent        
philosophy has set itself more modest   
and more attainable ends2 it is no      
longer inimical to special inquiry2 in  
fact1 it is zealously taking part in    
that inquiry4 ,on the other hand1 the   
special sciences1 mathematics and       
physics1 no less than philology1 have   
become eminently philosophical4 ,the    
material presented is no longer accepted
 uncritically4 ,the glance of the       
inquirer is bent upon neighboring       

fields1 whence that material has been   
derived4 ,the different special         
departments are striving for closer     
union1 and gradually the conviction is  
gaining ground that philosophy can      
consist only of mutual1 complemental    
criticism1 interpenetration1 and union  
of the special sciences into a          
consolidated whole4 ,as the blood in    
nourishing the body separates into      
countless capillaries1 only to be       
collected again and to meet in the      
heart1 so in the science of the future  
all the rills of knowledge will gather  
more and more into a common and         
undivided stream4  ,it is this view--not
 an unfamiliar one to the present       
generation--that ,i purpose to advocate4
 ,entertain no hope1 or rather fear1    
that ,i shall construct systems for you4
 ,i shall remain a natural inquirer4    
,nor expect that it is my intention to  
skirt all the fields of natural inquiry4
 ,i can attempt to be your guide only in
 that branch which is familiar to me1   

and even there ,i can assist in the     
furtherment of only a small portion of  
the allotted task4 ,if ,i shall succeed 
in rendering plain to you the relations 
of physics1 psychology1 and the theory  
of knowledge1 so that you may draw from 
each profit and light1 redounding to the
 advantage of each1 ,i shall regard my  
work as not having been in vain4        
,therefore1 to illustrate by an example 
how1 consonantly with my powers and     
views1 ,i conceive such inquiries should
 be conducted1 ,i shall treat to-day1 in
 the form of a brief sketch1 of the     
following special and limited           
subject--of the part which accidental   
circumstances play in the development of
 inventions and discoveries4         99 
99       99       99       99  ,when we 
,germans say of a man that he was not   
the inventor of gunpowder1#hb we        
impliedly cast a grave suspicion on his 
abilities4 ,but the expression is not a 
felicitous one1 as there is probably no 
invention in which deliberate thought   

had a smaller1 and pure luck a larger1  
share than in this4 ,it is well to ask1 
,are we justified in placing a low      
estimate on the achievement of an       
inventor because accident has assisted  
him in his work8 ,huygens1 whose        
discoveries and inventions are justly   
sufficient to entitle him to an opinion 
in such matters1 lays great emphasis on 
this factor4 ,he asserts that a man     
capable of inventing the telescope      
without the concurrence of accident must
 have been gifted with superhuman       
genius4#hc  ,a man living in the midst  
of civilisation finds himself surrounded
 by a host of marvellous inventions1    
considering none other than the means of
 satisfying the needs of daily life4    
,picture such a man transported to the  
epoch preceding the invention of these  
ingenious appliances1 and imagine him   
undertaking in a serious manner to      
comprehend their origin4 ,at first the  
intellectual power of the men capable of
 producing such marvels will strike him 

as incredible1 or1 if we adopt the      
ancient view1 as divine4 ,but his       
astonishment is considerably allayed by 
the disenchanting yet elucidative       
revelations of the history of primitive 
culture1 which to a large extent prove  
that these inventions took their rise   
very slowly and by imperceptible        
degrees4  ,a small hole in the ground   
with fire kindled in it constituted the 
primitive stove4 ,the flesh of the      
quarry1 wrapped with water in its skin1 
was boiled by contact with heated       
stones4 ,cooking by stones was also done
 in wooden vessels4 ,hollow gourds were 
protected from the fire by coats of     
clay4 ,thus1 from the burned clay       
accidentally originated the enveloping  
pot1 which rendered the gourd           
superfluous1 although for a long time   
thereafter the clay was still spread    
over the gourd1 or pressed into woven   
wicker-work before the potter's art     
assumed its final independence4 ,even   
then the wicker-work ornament was       

retained1 as a sort of attest of its    
origin4  ,we see1 thus1 it is by        
accidental circumstances1 or by such as 
lie without our purpose1 foresight1 and 
power1 that man is gradually led to the 
acquaintance of improved means of       
satisfying his wants4 ,let the reader   
picture to himself the genius of a man  
who could have foreseen without the help
 of accident that clay handled in the   
ordinary manner would produce a useful  
cooking utensil6 ,the majority of the   
inventions made in the early stages of  
civilisation1 including language1       
writing1 money1 and the rest1 could not 
have been the product of deliberate     
methodical reflexion for the simple     
reason that no idea of their value and  
significance could have been had except 
from practical use4 ,the invention of   
the bridge may have been suggested by   
the trunk of a tree which had fallen    
athwart a mountain-torrent2 that of the 
tool by the use of a stone accidentally 
taken into the hand to crack nuts4 ,the 

use of fire probably started in and was 
disseminated from regions where volcanic
 eruptions1 hot springs1 and burning    
jets of natural gas afforded opportunity
 for quietly observing and turning to   
practical account the properties of     
fire4 ,only after that had been done    
could the significance of the fire-drill
 be appreciated1 an instrument which was
 probably discovered from boring a hole 
through a piece of wood4 ,the suggestion
 of a distinguished inquirer that the   
invention of the fire-drill originated  
on the occasion of a religious ceremony 
is both fantastic and incredible4 ,and  
as to the use of fire1 we should no more
 attempt to derive that from the        
invention of the fire-drill than we     
should from the invention of sulphur    
matches4 ,unquestionably the opposite   
course was the real one4#hd  ,similar   
phenomena1 though still largely veiled  
in obscurity1 mark the initial          
transition of nations from a hunting to 
a nomadic life and to agriculture4#he   

,we shall not multiply examples1 but    
content ourselves with the remark that  
the same phenomena recur in historical  
times1 in the ages of great technical   
inventions1 and1 further1 that regarding
 them the most whimsical notions have   
been circulated--notions which ascribe  
to accident an unduly exaggerated part1 
and one which in a psychological respect
 is absolutely impossible4 ,the         
observation of steam escaping from a    
tea-kettle and of the clattering of the 
lid is supposed to have led to the      
invention of the steam-engine4 ,just    
think of the gap between this spectacle 
and the conception of the performance of
 great mechanical work by steam1 for a  
man totally ignorant of the             
steam-engine6 ,let us suppose1 however1 
that an engineer1 versed in the         
practical construction of pumps1 should 
accidentally dip into water an inverted 
bottle that had been filled with steam  
for drying and still retained its steam4
 ,he would see the water rush violently 

into the bottle1 and the idea would very
 naturally suggest itself of founding on
 this experience a convenient and useful
 atmospheric steam-pump1 which by       
imperceptible degrees1 both             
psychologically possible and immediate1 
would then undergo a natural and gradual
 transformation into ,watt's            
steam-engine4  ,but granting that the   
most important inventions are brought to
 man's notice accidentally and in ways  
that are beyond his foresight1 yet it   
does not follow that accident alone is  
sufficient to produce an invention4 ,the
 part which man plays is by no means a  
passive one4 ,even the first potter in  
the primeval forest must have felt some 
stirrings of genius within him4 ,in all 
such cases1 the inventor is obliged to  
take note of the new fact1 he must      
discover and grasp its advantageous     
feature1 and must have the power to turn
 that feature to account in the         
realisation of his purpose4 ,he must    
isolate the new feature1 impress it upon

 his memory1 unite and interweave it    
with the rest of his thought2 in short1 
he must possess the capacity to profit  
by experience4  ,the capacity to profit 
by experience might well be set up as a 
test of intelligence4 ,this power varies
 considerably in men of the same race1  
and increases enormously as we advance  
from the lower animals to man4 ,the     
former are limited in this regard almost
 entirely to the reflex actions which   
they have inherited with their organism1
 they are almost totally incapable of   
individual experience1 and considering  
their simple wants are scarcely in need 
of it4 ,the ivory-snail 7,eburna        
spirata7 never learns to avoid the      
carnivorous ,actinia1 no matter how     
often it may wince under the latter's   
shower of needles1 apparently having no 
memory for pain whatever4#hf ,a spider  
can be lured forth repeatedly from its  
hole by touching its web with a         
tuning-fork4 ,the moth plunges again and
 again into the flame which has burnt   

it4 ,the humming-bird hawk-moth#hg      
dashes repeatedly against the painted   
roses of the wall-paper1 like the       
unhappy and desperate thinker who never 
wearies of attacking the same insoluble 
chimerical problem4 ,as aimlessly almost
 as ,maxwell's gaseous molecules and in 
the same unreasoning manner common flies
 in their search for light and air      
stream against the glass pane of a      
half-opened window and remain there from
 sheer inability to find their way      
around the narrow frame4 ,but a pike    
separated from the minnows of his       
aquarium by a glass partition1 learns   
after the lapse of a few months1 though 
only after having butted himself half to
 death1 that he cannot attack these     
fishes with impunity4 ,what is more1 he 
leaves them in peace even after the     
removal of the partition1 though he will
 bolt a strange fish at once4           
,considerable memory must be attributed 
to birds of passage1 a memory which1    
probably owing to the absence of        

disturbing thoughts1 acts with the      
precision of that of some idiots4       
,finally1 the susceptibility to training
 evinced by the higher vertebrates is   
indisputable proof of the ability of    
these animals to profit by experience4  
,a powerfully developed mechanical      
memory1 which recalls vividly and       
faithfully old situations1 is sufficient
 for avoiding definite particular       
dangers1 or for taking advantage of     
definite particular opportunities4 ,but 
more is required for the development of 
inventions4 ,more extensive chains of   
images are necessary here1 the          
excitation by mutual contact of widely  
different trains of ideas1 a more       
powerful1 more manifold1 and richer     
connexion of the contents of memory1 a  
more powerful and impressionable        
psychical life1 heightened by use4 ,a   
man stands on the bank of a             
mountain-torrent1 which is a serious    
obstacle to him4 ,he remembers that he  
has crossed just such a torrent before  

on the trunk of a fallen tree4 ,hard by 
trees are growing4 ,he has often moved  
the trunks of fallen trees4 ,he has also
 felled trees before1 and then moved    
them4 ,to fell trees he has used sharp  
stones4 ,he goes in search of such a    
stone1 and as the old situations that   
crowd into his memory and are held there
 in living reality by the definite      
powerful interest which he has in       
crossing just this torrent1--as these   
impressions are made to pass before his 
mind in the inverse order in which they 
were here evoked1 he invents the bridge4
  ,there can be no doubt but the higher 
vertebrates adapt their actions in some 
moderate degree to circumstances4 ,the  
fact that they give no appreciable      
evidence of advance by the accumulation 
of inventions1 is satisfactorily        
explained by a difference of degree or  
intensity of intelligence as compared   
with man2 the assumption of a difference
 of kind is not necessary4 ,a person who
 saves a little every day1 be it ever so

 little1 has an incalculable advantage  
over him who daily squanders that       
amount1 or is unable to keep what he has
 accumulated4 ,a slight quantitative    
difference in such things explains      
enormous differences of advancement4    
,the rules which hold good in           
prehistoric times also hold good in     
historical times1 and the remarks made  
on invention may be applied almost      
without modification to discovery2 for  
the two are distinguished solely by the 
use to which the new knowledge is put4  
,in both cases the investigator is      
concerned with some newly observed      
relation of new or old properties1      
abstract or concrete4 ,it is observed1  
for example1 that a substance which     
gives a chemical reaction ,a is also the
 cause of a chemical reaction ,b4 ,if   
this observation fulfils no purpose but 
that of furthering the scientist's      
insight1 or of removing a source of     
intellectual discomfort1 we have a      
discovery2 but an invention1 if in using

 the substance giving the reaction ,a to
 produce the desired reaction ,b1 we    
have a practical end in view1 and seek  
to remove a source of material          
discomfort4 ,the phrase1 disclosure of  
the connexion of reactions1 is broad    
enough to cover discoveries and         
inventions in all departments4 ,it      
embraces the ,pythagorean proposition1  
which is a combination of a geometrical 
and an arithmetical reaction1 ,newton's 
discovery of the connexion of ,kepler's 
motions with the law of the inverse     
squares1 as perfectly as it does the    
detection of some minute but appropriate
 alteration in the construction of a    
tool1 or of some appropriate change in  
the methods of a dyeing establishment4  
,the disclosure of new provinces of     
facts before unknown can only be brought
 about by accidental circumstances1     
under which are remarked facts that     
commonly go unnoticed4 ,the achievement 
of the discoverer here consists in his  
sharpened attention1 which detects the  

uncommon features of an occurrence and  
their determining conditions from their 
most evanescent marks1#hh and discovers 
means of submitting them to exact and   
full observation4 ,under this head      
belong the first disclosures of         
electrical and magnetic phenomena1      
,grimaldi's observation of interference1
 ,arago's discovery of the increased    
check suffered by a magnetic needle     
vibrating in a copper envelope as       
compared with that observed in a        
bandbox1 ,foucault's observation of the 
stability of the plane of vibration of a
 rod accidentally struck while rotating 
in a turning-lathe1 ,mayer's observation
 of the increased redness of venous     
blood in the tropics1 ,kirchhoff's      
observation of the augmentation of the  
,d-line in the solar spectrum by the    
interposition of a sodium lamp1         
,schnbein's discovery of ozone from the 
phosphoric smell emitted on the         
disruption of air by electric sparks1   
and a host of others4 ,all these facts1 

of which unquestionably many were seen  
numbers of times before they were       
noticed1 are examples of the            
inauguration of momentous discoveries by
 accidental circumstances1 and place the
 importance of strained attention in a  
brilliant light4  ,but not only is a    
significant part played in the beginning
 of an inquiry by co-operative          
circumstances beyond the foresight of   
the investigator2 their influence is    
also active in its prosecution4 ,dufay1 
thus1 whilst following up the behavior  
of one electrical state which he had    
assumed1 discovers the existence of two4
 ,fresnel learns by accident that the   
interference-bands received on ground   
glass are seen to better advantage in   
the open air4 ,the                      
diffraction-phenomenon of two slits     
proved to be considerably different from
 what ,fraunhofer had anticipated1 and  
in following up this circumstance he was
 led to the important discovery of      
grating-spectra4 ,faraday's             

induction-phenomenon departed widely    
from the initial conception which       
occasioned his experiments1 and it is   
precisely this deviation that           
constitutes his real discovery4  ,every 
man has pondered on some subject4 ,every
 one of us can multiply the examples    
cited1 by less illustrious ones from his
 own experience4 ,i shall cite but one4 
,on rounding a railway curve once1 ,i   
accidentally remarked a striking        
apparent inclination of the houses and  
trees4 ,i inferred that the direction of
 the total resultant physical           
acceleration of the body reacts         
physiologically as the vertical4        
,afterwards1 in attempting to inquire   
more carefully into this phenomenon1 and
 this only1 in a large whirling machine1
 the collateral phenomena conducted me  
to the sensation of angular             
acceleration1 vertigo1 ,flouren's       
experiments on the section of the       
semi-circular canals etc41 from which   
gradually resulted views relating to    

sensations of direction which are also  
held by ,breuer and ,brown1 which were  
at first contested on all hands1 but are
 now regarded on many sides as correct1 
and which have been recently enriched by
 the interesting inquiries of ,breuer   
concerning the macula acustica1 and     
,kreidel's experiments with magnetically
 orientable crustacea4#hi ,not disregard
 of accident but a direct and purposeful
 employment of it advances research4    
,the more powerful the psychical        
connexion of the memory pictures        
is1--and it varies with the individual  
and the mood1--the more apt is the same 
accidental observation to be productive 
of results4 ,galileo knows that the air 
has weight2 he also knows of the        
resistance to a vacuum1 expressed both  
in weight and in the height of a column 
of water4 ,but the two ideas dwelt      
asunder in his mind4 ,it remained for   
,torricelli to vary the specific gravity
 of the liquid measuring the pressure1  
and not till then was the air included  

in the list of pressure-exerting fluids4
 ,the reversal of the lines of the      
spectrum was seen repeatedly before     
,kirchhoff1 and had been mechanically   
explained4 ,but it was left for his     
penetrating vision to discern the       
evidence of the connexion of this       
phenomenon with questions of heat1 and  
to him alone through persistent labor   
was revealed the sweeping significance  
of the fact for the mobile equilibrium  
of heat4 ,supposing1 then1 that such a  
rich organic connexion of the elements  
of memory exists1 and is the prime      
distinguishing mark of the inquirer1    
next in importance certainly is that    
intense interest in a definite object1  
in a definite idea1 which fashions      
advantageous combinations of thought    
from elements before disconnected1 and  
obtrudes that idea into every           
observation made1 and into every thought
 formed1 making it enter into           
relationship with all things4 ,thus     
,bradley1 deeply engrossed with the     

subject of aberration1 is led to its    
solution by an exceedingly unobtrusive  
experience in crossing the ,thames4 ,it 
is permissible1 therefore1 to ask       
whether accident leads the discoverer1  
or the discoverer accident1 to a        
successful outcome in scientific quests4
  ,no man should dream of solving a     
great problem unless he is so thoroughly
 saturated with his subject that        
everything else sinks into comparative  
insignificance4 ,during a hurried       
meeting with ,mayer in ,heidelberg once1
 ,jolly remarked1 with a rather dubious 
implication1 that if ,mayer's theory    
were correct water could be warmed by   
shaking4 ,mayer went away without a word
 of reply4 ,several weeks later1 and now
 unrecognised by ,jolly1 he rushed into 
the latter's presence exclaiming3 ,es   
ischt aso6 7,it is so1 it is so67 ,it   
was only after considerable explanation 
that ,jolly found out what ,mayer wanted
 to say4 ,the incident needs no         
comment4#ij  ,a person deadened to      

sensory impressions and given up solely 
to the pursuit of his own thoughts1 may 
also light on an idea that will divert  
his mental activity into totally new    
channels4 ,in such cases it is a        
psychical accident1 an intellectual     
experience1 as distinguished from a     
physical accident1 to which the person  
owes his discovery--a discovery which is
 here made deductively by means of      
mental copies of the world1 instead of  
experimentally4 ,purely experimental    
inquiry1 moreover1 does not exist1 for1 
as ,gauss says1 virtually we always     
experiment with our thoughts4 ,and it is
 precisely that constant1 corrective    
interchange or intimate union of        
experiment and deduction1 as it was     
cultivated by ,galileo in his ,dialogues
 and by ,newton in his ,optics1 that is 
the foundation of the benign            
fruitfulness of modern scientific       
inquiry as contrasted with that of      
antiquity1 where observation and        
reflexion ofttimes pursued their        

respective courses like two strangers4  
,we have to wait for the appearance of a
 favorable physical accident4 ,the      
movement of our thoughts obeys the law  
of association4 ,in the case of meagre  
experience the result of this law is    
simply the mechanical reproduction of   
definite sensory experiences4 ,on the   
other hand1 if the psychical life is    
subjected to the incessant influences of
 a powerful and rich experience1 then   
every representative element in the mind
 is connected with so many others that  
the actual and natural course of the    
thoughts is easily influenced and       
determined by insignificant             
circumstances1 which accidentally are   
decisive4 ,hereupon1 the process termed 
imagination produces its protean and    
infinitely diversified forms4 ,now what 
can we do to guide this process1 seeing 
that the combinatory law of the images  
is without our reach8 ,rather let us    
ask1 what influence can a powerful and  
constantly recurring idea exert on the  

movement of our thoughts8 ,according to 
what has preceded1 the answer is        
involved in the question itself4 ,the   
idea dominates the thought of the       
inquirer1 not the latter the former4    
,let us see1 now1 if we can acquire a   
profounder insight into the process of  
discovery4 ,the condition of the        
discoverer is1 as ,james has aptly      
remarked1 not unlike the situation of a 
person who is trying to remember        
something that he has forgotten4 ,both  
are sensible of a gap1 and have only a  
remote presentiment of what is missing4 
,suppose ,i meet in a company a         
well-known and affable gentleman whose  
name ,i have forgotten1 and who to my   
horror asks to be introduced to some    
one4 ,i set to work according to        
,lichtenberg's rule1 and run down the   
alphabet in search of the initial letter
 of his name4 ,a vague sympathy holds me
 at the letter ,g4 ,tentatively ,i add  
the second letter and am arrested at e1 
and long before ,i have tried the third 

letter r1 the name ,gerson sounds       
sonorously upon my ear1 and my anguish  
is gone4 ,while taking a walk ,i meet a 
gentleman from whom ,i receive a        
communication4 ,on returning home1 and  
in attending to weightier affairs1 the  
matter slips my mind4 ,moodily1 but in  
vain1 ,i ransack my memory4 ,finally ,i 
observe that ,i am going over my walk   
again in thought4 ,on the street corner 
in question the self-same gentleman     
stands before me and repeats his        
communication4 ,in this process are     
successively recalled to consciousness  
all the percepts which were connected   
with the percept that was lost1 and with
 them1 finally1 that1 too1 is brought to
 light4 ,in the first case--where the   
experience had already been made and is 
permanently impressed on our thought--a 
systematic procedure is both possible   
and easy1 for we know that a name must  
be composed of a limited number of      
sounds4 ,but at the same time it should 
be observed that the labor involved in  

such a combinatorial task would be      
enormous if the name were long and the  
responsiveness of the mind weaker4  ,it 
is often said1 and not wholly without   
justification1 that the scientist has   
solved a riddle4 ,every problem in      
geometry may be clothed in the garb of a
 riddle4 ,thus3 ,what thing is that ,m  
which has the properties ,a1 ,b1 ,c8    
,what circle is that which touches the  
straight lines ,a1 ,b1 but touches ,b in
 the point ,c8 ,the first two conditions
 marshal before the imagination the     
group of circles whose centres lie in   
the line of symmetry of ,a1 ,b4 ,the    
third condition reminds us of all the   
circles having centres in the straight  
line that stands at right angles to ,b  
in ,c4 ,the common term1 or common      
terms1 of the two groups of images      
solves the riddle--satisfies the        
problem4 ,puzzles dealing with things or
 words induce similar processes1 but the
 memory in such cases is exerted in many
 directions and more varied and less    

clearly ordered provinces of ideas are  
surveyed4 ,the difference between the   
situation of a geometer who has a       
construction to make1 and that of an    
engineer1 or a scientist1 confronted    
with a problem1 is simply this1 that the
 first moves in a field with which he is
 thoroughly acquainted1 whereas the two 
latter are obliged to familiarise       
themselves with this field subsequently1
 and in a measure far transcending what 
is commonly required4 ,in this process  
the mechanical engineer has at least    
always a definite goal before him and   
definite means to accomplish his aim1   
whilst in the case of the scientist that
 aim is in many instances presented only
 in vague and general outlines4 ,often  
the very formulation of the riddle      
devolves on him4 ,frequently it is not  
until the aim has been reached that the 
broader outlook requisite for systematic
 procedure is obtained4 ,by far the     
larger portion of his success1          
therefore1 is contingent on luck and    

instinct4 ,it is immaterial1 so far as  
its character is concerned1 whether the 
process in question is brought rapidly  
to a conclusion in the brain of one man1
 or whether it is spun out for centuries
 in the minds of a long succession of   
thinkers4 ,the same relation that a word
 solving a riddle bears to that riddle  
is borne by the modern conception of    
light to the facts discovered by        
,grimaldi1 ,rmer1 ,huygens1 ,newton1    
,young1 ,malus1 and ,fresnel1 and only  
by the help of this slowly developed    
conception is our mental vision enabled 
to embrace the broad domain of facts in 
question4  ,a welcome complement to the 
discoveries which the history of        
civilisation and comparative psychology 
have furnished1 is to be found in the   
confessions of great scientists and     
artists4 ,scientists and artists1 we    
might say1 for ,liebig boldly declared  
there was no essential difference       
between the two4 ,are we to regard      
,leonardo da ,vinci as a scientist or as

 an artist8 ,if the artist builds up his
 work from a few motives1 the scientist 
discovers the motives which permeate    
reality4 ,if scientists like ,lagrange  
or ,fourier are in a certain measure    
artists in the presentation of their    
results1 on the other hand1 artists like
 ,shakespeare or ,ruysdael are          
scientists in the insight which must    
have preceded their creations4  ,newton1
 when questioned about his methods of   
work1 could give no other answer but    
that he was wont to ponder again and    
again on a subject2 and similar         
utterances are accredited to            
,d',alembert and ,helmholtz4 ,scientists
 and artists both recommend persistent  
labor4 ,after the repeated survey of a  
field has afforded opportunity for the  
interposition of advantageous accidents1
 has rendered all the traits that suit  
with the mood or the dominant thought   
more vivid1 and has gradually relegated 
to the background all things that are   
inappropriate1 making their future      

appearance impossible2 then from the    
teeming1 swelling host of fancies which 
a free and high-flown imagination calls 
forth1 suddenly that particular form    
arises to the light which harmonises    
perfectly with the ruling idea1 mood1 or
 design4 ,then it is that that which has
 resulted slowly as the result of a     
gradual selection1 appears as if it were
 the outcome of a deliberate act of     
creation4 ,thus are to be explained the 
statements of ,newton1 ,mozart1 ,richard
 ,wagner1 and others1 when they say that
 thoughts1 melodies1 and harmonies had  
poured in upon them1 and that they had  
simply retained the right ones4         
,undoubtedly1 the man of genius1 too1   
consciously or instinctively1 pursues   
systematic methods wherever it is       
possible2 but in his delicate           
presentiment he will omit many a task or
 abandon it after a hasty trial on which
 a less endowed man would squander his  
energies in vain4 ,thus1 the genius     
accomplishes#ia in a brief space of time

 undertakings for which the life of an  
ordinary man would far from suffice4 ,we
 shall hardly go astray if we regard    
genius as only a slight deviation from  
the average mental endowment--as        
possessing simply a greater             
sensitiveness of cerebral reaction and a
 greater swiftness of reaction4 ,the men
 who1 obeying their inner impulses1 make
 sacrifices for an idea instead of      
advancing their material welfare1 may   
appear to the full-blooded ,philistine  
as fools2 yet we shall scarcely adopt   
,lombroso's view1 that genius is to be  
regarded as a disease1 although it is   
unfortunately true that the sensitive   
brains and fragile constitutions succumb
 most readily to sickness4  ,the remark 
of ,c4 ,g4 ,j4 ,jacobi that mathematics 
is slow of growth and only reaches the  
truth by long and devious paths1 that   
the way to its discovery must be        
prepared for long beforehand1 and that  
then the truth will make its            
long-deferred appearance as if impelled 

by some divine necessity#ib--;all this  
holds true of every science4 ,we are    
astounded often to note that it required
 the combined labors of many eminent    
thinkers for a full century to reach a  
truth which it takes us only a few hours
 to master and which once acquired seems
 extremely easy to reach under the right
 sort of circumstances4 ,to our         
humiliation we learn that even the      
greatest men are born more for life than
 for science4 ,the extent to which even 
they are indebted to accident--to that  
singular conflux of the physical and the
 psychical life in which the continuous 
but yet imperfect and never-ending      
adaptation of the latter to the former  
finds its distinct expression--that has 
been the subject of our remarks to-day4 
,jacobi's poetical thought of a divine  
necessity acting in science will lose   
none of its loftiness for us if we      
discover in this necessity the same     
power that destroys the unfit and       
fosters the fit4 ,for loftier1 nobler1  

and more romantic than poetry is the    
truth and the reality4    ,,footnotes3  
,footnote #ha3 ,inaugural lecture       
delivered on assuming the               
,professorship of the ,history and      
,theory of ,inductive ,science in the   
,university of ,vienna1 ,october #ba1   
#ahie4    ,footnote #hb3 ,the phrase is1
 ,er hat das ,pulver nicht erfunden4    
,footnote #hc3 ,quod si quis tanta      
industria exstitisset1 ut ex   naturae  
principiis at geometria hanc rem eruere 
potuisset1 eum ego   supra mortalium    
sortem ingenio valuisse dicendum        
crederem4 ,sed hoc   tantum abest1 ut   
fortuito reperti artificii rationem non 
adhuc satis   explicari potuerint viri  
doctissimi4--,hugenii ,dioptrica 7de    
telescopiis74    ,footnote #hd3 ,i must 
not be understood as saying that the    
fire-drill   has played no part in the  
worship of fire or of the sun4          
,footnote #he3 ,compare on this point   
the extremely interesting   remarks of  
,dr4 ,paul ,carus in his ,philosophy of 

the ,tool1 ,chicago1   #ahic4           
,footnote #hf3 ,mbius1                  
,naturwissenschaftlicher ,verein fr     
,schleswig-,holstein1 ,kiel1 #ahic1 p4  
#aac et seq4    ,footnote #hg3 ,i am    
indebted for this observation to        
,professor   ,hatscheck4    ,footnote   
#hh3 ,cf4 ,hoppe1 ,entdecken und        
,finden1 #ahgj4    ,footnote #hi3 ,see  
the lecture ,sensations of ,orientation1
 p4 #bhb et   seq4    ,footnote #ij3    
,this story was related to me by ,jolly1
 and   subsequently repeated in a letter
 from him4    ,footnote #ia3 ,i do not  
know whether ,swift's academy of        
schemers in   ,lagado1 in which great   
discoveries and inventions were made by 
a   sort of verbal game of dice1 was    
intended as a satire on ,francis        
,bacon's method of making discoveries by
 means of huge synoptic   tables        
constructed by scribes4 ,it certainly   
would not have been   ill-placed4       
,footnote #ib3 ,crescunt disciplinae    
lente tardeque2 per varios   errores    

sero pervenitur ad veritatem4 ,omnia    
praeparata esse debent   diuturno et    
assiduo labore ad introitum veritatis   
novae4 ,jam illa   certo temporis       
momento divina quadam necessitate coacta
 emerget4    ,quoted by ,simony1 ,in ein
 ringfrmiges ,band einen ,knoten zu     
machen1   ,vienna1 #ahha1 p4 #da4       
,,on ,,sensations ,,of ,,orientation4#ic
   ,through the co-operation of a       
succession of inquirers1 among whom are 
particularly to be mentioned ,goltz of  
,strassburg and ,breuer of ,vienna1     
considerable advances have been made    
during the last twenty-five years in our
 knowledge of the means by which we     
ascertain our position in space and the 
direction of our motion1 or orient      
ourselves1 as the phrase goes4 ,i       
presume that you are already acquainted 
with the physiological part of the      
processes with which our sensations of  
movement1 or1 more generally speaking1  
our sensations of orientation1 are      
connected4 ,here ,i shall consider more 

particularly the physical side of the   
matter4 ,in fact1 ,i was originally led 
to the consideration of these questions 
by the observation of extremely simple  
and perfectly well-known physical facts1
 before ,i had any great acquaintance   
with physiology and while pursuing      
unbiasedly my natural thoughts2 and ,i  
am of the conviction that the way which 
,i have pursued1 and which is entirely  
free from hypotheses1 will1 if you will 
follow my exposition1 be that of easiest
 acquisition for the most of you4  ,no  
man of sound common sense could ever    
have doubted that a pressure or force is
 requisite to set a body in motion in a 
given direction and that a contrary     
pressure is required to stop suddenly a 
body in motion4 ,though the law of      
inertia was first formulated with       
anything like exactness by ,galileo1 the
 facts at the basis of it were known    
long previously to men of the stamp of  
,leonardo da ,vinci1 ,rabelais1 and     
others1 and were illustrated by them    

with appropriate experiments4 ,leonardo 
knew that by a swift stroke with a ruler
 one can knock out from a vertical      
column of checkers a single checker     
without over-throwing the column4 ,the  
experiment with a coin resting on a     
piece of pasteboard covering a goblet1  
which falls into the goblet when the    
pasteboard is jerked away1 like all     
experiments of the kind1 is certainly   
very old4  ,with ,galileo the experience
 in question assumes greater clearness  
and force4 ,in the famous dialogue on   
the ,copernican system which cost him   
his freedom1 he explains the tides in an
 unfelicitous1 though in principle      
correct manner1 by the analogue of a    
platter of water swung to and fro4 ,in  
opposition to the ,aristotelians of his 
time1 who believed the descent of a     
heavy body could be accelerated by the  
superposition of another heavy body1 he 
asserted that a body could never be     
accelerated by one lying upon it unless 
the first in some way impeded the       

superposed body in its descent4 ,to seek
 to press a falling body by means of    
another placed upon it1 is as senseless 
as trying to prod a man with a lance    
when the man is speeding away from one  
with the same velocity as the lance4    
,even this little excursion into physics
 can explain much to us4 ,you know the  
peculiar sensation which one has in     
falling1 as when one jumps from a high  
springboard into the water1 and which is
 also experienced in some measure at the
 beginning of the descent of elevators  
and swings4 ,the reciprocal             
gravitational pressure of the different 
parts of our body1 which is certainly   
felt in some manner1 vanishes in free   
descent1 or1 in the case of the         
elevator1 is diminished on the beginning
 of the descent4 ,a similar sensation   
would be experienced if we were suddenly
 transported to the moon where the      
acceleration of gravity is much less    
than upon the earth4 ,i was led to these
 considerations in #ahff by a suggestion

 in physics1 and having also taken into 
account the alterations of the          
blood-pressure in the cases in question1
 ,i found ,i coincided without knowing  
it with ,wollaston and ,purkinje4 ,the  
first as early as #ahaj in his ,croonian
 lecture had touched on the subject of  
sea-sickness and explained it by        
alterations of the blood-pressure1 and  
later had laid similar considerations at
 the basis of his explanation of vertigo
 7#ahbj-ahbf74id  ,newton was the first 
to enunciate with perfect generality    
that a body can change the velocity and 
direction of its motion only by the     
action of a force1 or the action of a   
second body4 ,a corollary of this law   
which was first expressly deduced by    
,euler is that a body can never be set  
rotating or made to cease rotating of   
itself but only by forces and other     
bodies4 ,for example1 turn an open watch
 which has run down freely backwards and
 forwards in your hand4 ,the            
balance-wheel will not fully catch the  

rapid rotations1 it does not even       
respond fully to the elastic force of   
the spring which proves too weak to     
carry the wheel entirely with it4  ,let 
us consider now that whether we move    
ourselves by means of our legs1 or      
whether we are moved by a vehicle or a  
boat1 at first only a part of our body  
is directly moved and the rest of it is 
afterwards set in motion by the first   
part4 ,we see that pressures1 pulls1 and
 tensions are always produced between   
the parts of the body in this action1   
which pressures1 pulls1 and tensions    
give rise to sensations by which the    
forward or rotary movements in which we 
are engaged are made perceptible4#ie    
,but it is quite natural that sensations
 so familiar should be little noticed   
and that attention should be drawn to   
them only under special circumstances   
when they occur unexpectedly or with    
unusual strength4  ,illustration3 ,fig4 
#de4  ,thus my attention was drawn to   
this point by the sensation of falling  

and subsequently by another singular    
occurrence4 ,i was rounding a sharp     
railway curve once when ,i suddenly saw 
all the trees1 houses1 and factory      
chimneys along the track swerve from the
 vertical and assume a strikingly       
inclined position4 ,what had hitherto   
appeared to me perfectly natural1       
namely1 the fact that we distinguish the
 vertical so perfectly and sharply from 
every other direction1 now struck me as 
enigmatical4 ,why is it that the same   
direction can now appear vertical to me 
and now cannot8 ,by what is the vertical
 distinguished for us8 7,compare ,figure
 #de47  ,the rails are raised on the    
convex or outward side of the track in  
order to insure the stability of the    
carriage as against the action of the   
centrifugal force1 the whole being so   
arranged that the combination of the    
force of gravity with the centrifugal   
force of the train shall give rise to a 
force perpendicular to the plane of the 
rails4  ,let us assume1 now1 that under 

all circumstances we somehow sense the  
direction of the total resultant        
mass-acceleration whencesoever it may   
arise as the vertical4 ,then both the   
ordinary and the extraordinary phenomena
 will be alike rendered intelligible4#if
  ,i was now desirous of putting the    
view ,i had reached to a more convenient
 and exact test than was possible on a  
railway journey where one has no control
 over the determining circumstances and 
cannot alter them at will4 ,i           
accordingly had the simple apparatus    
constructed which is represented in     
,figure #df4  ,in a large frame ,,bb1   
which is fastened to the walls1 rotates 
about a vertical axis ,,aa a second     
frame ,,rr1 and within the latter a     
third one rr1 which can be set at any   
distance and position from the axis1    
made stationary or movable1 and is      
provided with a chair for the observer4 
,illustration3 ,fig4 #df4  ,from ,mach's
 ,bewegungsempfindungen1 ,leipsic1      
,engelmann1 #ahge4  ,the observer takes 

his seat in the chair and to prevent    
disturbances of judgment is enclosed in 
a paper box4 ,if the observer together  
with the frame rr be then set in uniform
 rotation1 he will feel and see the     
beginning of the rotation both as to    
direction and amount very distinctly    
although every outward visible or       
tangible point of reference is wanting4 
,if the motion be uniformly continued   
the sensation of rotation will gradually
 cease entirely and the observer will   
imagine himself at rest4 ,but if rr be  
placed outside the axis of rotation1 at 
once on the rotation beginning1 a       
strikingly apparent1 palpable1 actually 
visible inclination of the entire paper 
box is produced1 slight when the        
rotation is slow1 strong when the       
rotation is rapid1 and continuing as    
long as the rotation lasts4 ,it is      
absolutely impossible for the observer  
to escape perceiving the inclination1   
although here also all outward points of
 reference are wanting4 ,if the         

observer1 for example1 is seated so as  
to look towards the axis1 he will feel  
the box strongly tipped backwards1 as it
 necessarily must be if the direction of
 the total resultant force is perceived 
as the vertical4 ,for other positions of
 the observer the situation is          
similar4#ig  ,once1 while performing one
 of these experiments1 and after        
rotating so long that ,i was no longer  
conscious of the movement1 ,i suddenly  
caused the apparatus to be stopped1     
whereupon ,i immediately felt and saw   
myself with the whole box rapidly flung 
round in rotation in the opposite       
direction1 although ,i knew that the    
whole apparatus was at rest and every   
outward point of reference for the      
perception of motion was wanting4 ,every
 one who disbelieves in sensations of   
movement should be made acquainted with 
these phenomena4 ,had ,newton known them
 and had he ever observed how we may    
actually imagine ourselves turned and   
displaced in space without the          

assistance of stationary bodies as      
points of reference1 he would certainly 
have been confirmed more than ever in   
his unfortunate speculations regarding  
absolute space4  ,the sensation of      
rotation in the opposite direction after
 the apparatus has been stopped1 slowly 
and gradually ceases4 ,but on           
accidentally inclining my head once     
during this occurrence1 the axis of     
apparent rotation was also observed to  
incline in exactly the same manner both 
as to direction and as to amount4 ,it is
 accordingly clear that the acceleration
 or retardation of rotation is felt4    
,the acceleration operates as a         
stimulus4 ,the sensation1 however1 like 
almost all sensations1 though it        
gradually decreases1 lasts perceptibly  
longer than the stimulus4 ,hence the    
long continued apparent rotation after  
the stopping of the apparatus4 ,the     
organ1 however1 which causes the        
persistence of this sensation must have 
its seat in the head1 since otherwise   

the axis of apparent rotation could not 
assume the same motion as the head4  ,if
 ,i were to say1 now1 that a light had  
flashed upon me in making these last    
observations1 the expression would be a 
feeble one4 ,i ought to say ,i          
experienced a perfect illumination4 ,my 
juvenile experiences of vertigo occurred
 to me4 ,i remembered ,flourens's       
experiments relative to the section of  
the semi-circular canals of the         
labyrinths of doves and rabbits1 where  
this inquirer had observed phenomena    
similar to vertigo1 but which he        
preferred to interpret1 from his bias to
 the acoustic theory of the labyrinth1  
as the expression of painful auditive   
disturbances4 ,i saw that ,goltz had    
nearly but not quite hit the bull's eye 
with his theory of the semi-circular    
canals4 ,this inquirer1 who1 from his   
happy habit of following his own natural
 thoughts without regard for tradition1 
has cleared up so much in science1      
spoke1 as early as #ahgj1 on the ground 

of experiments1 as follows3 ,it is      
uncertain whether the semi-circular     
canals are auditive organs or not4 ,in  
any event they form an apparatus which  
serves for the preservation of          
equilibrium4 ,they are1 so to speak1 the
 sense-organs of equilibrium of the head
 and indirectly of the whole body4 ,i   
remembered the galvanic dizziness which 
had been observed by ,ritter and        
,purkinje on the passage of a current   
through the head1 when the persons      
experimented upon imagined they were    
falling towards the cathode4 ,the       
experiment was immediately repeated1 and
 sometime later 7#ahgd7 ,i was enabled  
to demonstrate the same objectively with
 fishes1 all of which placed themselves 
sidewise and in the same direction in   
the field of the current as if at       
command4#ih ,mller's doctrine of        
specific energies now appeared to me to 
bring all these new and old observations
 into a simple1 connected unity4        
,illustration3 ,fig4 #dg4  ,the         

labyrinth of a dove 7stereoscopically   
reproduced71 from ,r4 ,ewald1 ,nervus   
,octavus1 ,wiesbaden1 ,bergmann1 #ahib4 
,let us picture to ourselves the        
labyrinth of the ear with its three     
semi-circular canals lying in three     
mutually perpendicular planes 7,comp4   
,fig4 #dg71 the mysterious position of  
which inquirers have endeavored to      
explain in every possible and impossible
 way4 ,let us conceive the nerves of the
 ampull1 or the dilated extensions of   
the semi-circular canals1 equipped with 
a capacity for responding to every      
imaginable stimulus with a sensation of 
rotation just as the nerves of the      
retina of the eye when excited by       
pressures1 by electrical or chemical    
stimuli always respond with the         
sensation of light2 let us picture to   
ourselves1 further1 that the usual      
excitation of the ampull nerves is      
produced by the inertia of the contents 
of the semi-circular canals1 which      
contents on suitable rotations in the   

plane of the semi-circular canal are    
left behind in the motion1 or at least  
have a tendency to remain behind and    
consequently exert a pressure4 ,it will 
be seen that on this supposition all the
 single facts which without the theory  
appear as so many different individual  
phenomena1 become from this single point
 of view clear and intelligible4  ,i had
 the satisfaction1 immediately after the
 communication in which ,i set forth    
this idea1#ii of seeing a paper by      
,breuer appear#ajj in which this author 
had arrived by entirely different       
methods at results that agreed in all   
essential points with my own4 ,a few    
weeks later appeared the researches of  
,crum ,brown of ,edinburgh1 whose       
methods were even still nearer mine4    
,breuer's paper was far richer in       
physiological respects than mine1 and he
 had particularly gone into greater     
detail in his investigation of the      
collateral effects of the reflex motions
 and orientation of the eyes in the     

phenomena under consideration4#aja ,in  
addition certain experiments which ,i   
had suggested in my paper as a test of  
the correctness of the view in question 
had already been performed by ,breuer4  
,breuer has also rendered services of   
the highest order in the further        
elaboration of this field4 ,but in a    
physical regard1 my paper was1 of       
course1 more complete4  ,in order to    
portray to the eye the behavior of the  
semi-circular canals1 ,i have           
constructed here a little apparatus4    
7,see ,fig4 #dh47 ,the large rotatable  
disc represents the osseous             
semi-circular canal1 which is continuous
 with the bones of the head2 the small  
disc1 which is free to rotate on the    
axis of the first1 represents the mobile
 and partly liquid contents of the      
semi-circular canal4 ,on rotating the   
large disc1 the small disc as you see   
remains behind4 ,i have to turn some    
time before the small disc is carried   
along with the large one by friction4   

,but if ,i now stop the large disc the  
small disc as you see continues to      
rotate4  ,illustration3 ,fig4 #dh4      
,model representing the action of the   
semi-circular canals4  ,simply assume   
now that the rotation of the small disc1
 say in the direction of the hands of a 
watch1 would give rise to a sensation of
 rotation in the opposite direction1 and
 conversely1 and you already understand 
a good portion of the facts above set   
forth4 ,the explanation still holds1    
even if the small disc does not perform 
appreciable rotations but is checked by 
a contrivance similar to an elastic     
spring1 the tension of which disengages 
a sensation4 ,conceive1 now1 three such 
contrivances with their mutually        
perpendicular planes of rotation joined 
together so as to form a single         
apparatus2 then to this apparatus as a  
whole1 no rotation can be imparted      
without its being indicated by the small
 mobile discs or by the springs which   
are attached to them4 ,conceive both the

 right and the left ear equipped with   
such an apparatus1 and you will find    
that it answers all the purposes of the 
semi-circular canals1 which you see     
represented stereoscopically in ,fig4   
#dg for the ear of a dove4  ,of the many
 experiments which ,i have made on my   
own person1 and the results of which    
could be predicted by the new view      
according to the behavior of the model  
and consequently according to the rules 
of mechanics1 ,i shall cite but one4 ,i 
fasten a horizontal board in the frame  
,,rr of my rotatory apparatus1 lie down 
upon the same with my right ear upon the
 board1 and cause the apparatus to be   
uniformly rotated4 ,as soon as ,i no    
longer perceive the rotation1 ,i turn   
around upon my left ear and immediately 
the sensation of rotation again starts  
up with marked vividness4 ,the          
experiment can be repeated as often as  
one wishes4 ,a slight turn of the head  
even is sufficient for reviving the     
sensation of rotation which in the      

perfectly quiescent state at once       
disappears altogether4  ,we will imitate
 the experiment on the model4 ,i turn   
the large disc until finally the small  
disc is carried along with it4 ,if1 now1
 while the rotation continues uniform1  
,i burn off a little thread which you   
see here1 the small disc will be flipped
 round by a spring into its own plane   
#ahj1 so as now to present its opposite 
side to you1 when the rotation at once  
begins in the opposite direction4  ,we  
have consequently a very simple means   
for determining whether one is actually 
the subject or not of uniform and       
imperceptible rotations4 ,if the earth  
rotated much more rapidly than it really
 does1 or if our semi-circular canals   
were much more sensitive1 a ,nansen     
sleeping at the ,north ,pole would be   
waked by a sensation of rotation every  
time he turned over4 ,foucault's        
pendulum experiment as a demonstration  
of the earth's rotation would be        
superfluous under such circumstances4   

,the only reason we cannot prove the    
rotation of the earth with the help of  
our model1 lies in the small angular    
velocity of the earth and in the        
consequent liability to great           
experimental errors4#ajb  ,aristotle has
 said that ,the sweetest of all things  
is knowledge4 ,and he is right4 ,but if 
you were to suppose that the publication
 of a new view were productive of       
unbounded sweetness1 you would be       
mightily mistaken4 ,no one disturbs his 
fellow-men with a new view unpunished4  
,nor should the fact be made a subject  
of reproach to these fellow-men4 ,to    
presume to revolutionise the current way
 of thinking with regard to any         
question1 is no pleasant task1 and above
 all not an easy one4 ,they who have    
advanced new views know best what       
serious difficulties stand in their way4
 ,with honest and praiseworthy zeal1 men
 set to work in search of everything    
that does not suit with them4 ,they seek
 to discover whether they cannot explain

 the facts better or as well1 or        
approximately as well1 by the           
traditional views4 ,and that1 too1 is   
justified4 ,but at times some extremely 
artless animadversions are heard that   
almost nonplus us4 ,if a sixth sense    
existed it could not fail to have been  
discovered thousands of years ago4      
,indeed2 there was a time1 then1 when   
only seven planets could have existed6  
,but ,i do not believe that any one will
 lay any weight on the philological     
question whether the set of phenomena   
which we have been considering should be
 called a sense4 ,the phenomena will not
 disappear when the name disappears4 ,it
 was further said to me that animals    
exist which have no labyrinth1 but which
 can yet orientate themselves1 and that 
consequently the labyrinth has nothing  
to do with orientation4 ,we do not walk 
forsooth with our legs1 because snakes  
propel themselves without them6  ,but if
 the promulgator of a new idea cannot   
hope for any great pleasure from its    

publication1 yet the critical process   
which his views undergo is extremely    
helpful to the subject-matter of them4  
,all the defects which necessarily      
adhere to the new view are gradually    
discovered and eliminated4 ,over-rating 
and exaggeration give way to more sober 
estimates4 ,and so it came about that it
 was found unpermissible to attribute   
all functions of orientation exclusively
 to the labyrinth4 ,in these critical   
labors ,delage1 ,aubert1 ,breuer1       
,ewald1 and others have rendered        
distinguished services4 ,it can also not
 fail to happen that fresh facts become 
known in this process which could have  
been predicted by the new view1 which   
actually were predicted in part1 and    
which consequently furnish a support for
 the new view4 ,breuer and ,ewald       
succeeded in electrically and           
mechanically exciting the labyrinth1 and
 even single parts of the labyrinth1 and
 thus in producing the movements that   
belong to such stimuli4 ,it was shown   

that when the semi-circular canals were 
absent vertigo could not be produced1   
when the entire labyrinth was removed   
the orientation of the head was no      
longer possible1 that without the       
labyrinth galvanic vertigo could not be 
induced4 ,i myself constructed as early 
as #ahge an apparatus for observing     
animals in rotation1 which was          
subsequently reinvented in various forms
 and has since received the name of     
cyclostat4#ajc ,in experiments with the 
most varied kinds of animals it was     
shown that1 for example1 the larv of    
frogs are not subject to vertigo until  
their semi-circular canals which at the 
start are wanting are developed 7,k4    
,schfer74 ,a large percentage of the    
deaf and dumb are afflicted with grave  
affections of the labyrinth4 ,the       
,american psychologist1 ,william ,james1
 has made whirling experiments with many
 deaf and dumb subjects1 and in a large 
number of them found that susceptibility
 to giddiness is wanting4 ,he also found

 that many deaf and dumb people on being
 ducked under water1 whereby they lose  
their weight and consequently have no   
longer the full assistance of their     
muscular sense1 utterly lose their sense
 of position in space1 do not know which
 is up and which is down1 and are thrown
 into the greatest                      
consternation1--results which do not    
occur in normal men4 ,such facts are    
convincing proof that we do not         
orientate ourselves entirely by means of
 the labyrinth1 important as it is for  
us4 ,dr4 ,kreidl has made experiments   
similar to those of ,james and found    
that not only is vertigo absent in deaf 
and dumb people when whirled about1 but 
that also the reflex movements of the   
eyes which are normally induced by the  
labyrinth are wanting4 ,finally1 ,dr4   
,pollak has found that galvanic vertigo 
does not exist in a large percentage of 
the deaf and dumb4 ,neither the jerking 
movements nor the uniform movements of  
the eyes were observed which normal     

human beings exhibit in the ,ritter and 
,purkinje experiment4  ,after the       
physicist has arrived at the idea that  
the semi-circular canals are the organ  
of sensation of rotation or of angular  
acceleration1 he is next constrained to 
ask for the organs that mediate the     
sensation of acceleration noticed in    
forward movements4 ,in searching for an 
organ for this function1 he of course is
 not apt to select one that stands in no
 anatomical and spatial relation with   
the semi-circular canals4 ,and in       
addition there are physiological        
considerations to be weighed4 ,the      
preconceived opinion once having been   
abandoned that the entire labyrinth is  
auditory in its function1 there remains 
after the cochlea is reserved for       
sensations of tone and the semi-circular
 canals for the sensation of angular    
acceleration1 the vestibule for the     
discharge of additional functions4 ,the 
vestibule1 particularly the part of it  
known as the sacculus1 appeared to me1  

by reason of the so-called otoliths     
which it contains1 eminently adapted for
 being the organ of sensation of forward
 acceleration or of the position of the 
head4 ,in this conjecture ,i again      
closely coincided with ,breuer4  ,that a
 sensation of position1 of direction and
 amount of mass-acceleration exists1 our
 experience in elevators as well as of  
movement in curved paths is sufficient  
proof4 ,i have also attempted to produce
 and destroy suddenly great velocities  
of forward movement by means of various 
contrivances of which ,i shall mention  
only one here4 ,if1 while enclosed in   
the paper box of my large whirling      
apparatus at some distance from the     
axis1 my body is in uniform rotation    
which ,i no longer feel1 and ,i then    
loosen the connexions of the frame rr   
with ,r thus making the former moveable 
and ,i then suddenly stop the larger    
frame1 my forward motion is abruptly    
impeded while the frame rr continues to 
rotate4 ,i imagine now that ,i am       

speeding on in a straight line in a     
direction opposite to that of the       
checked motion4 ,unfortunately1 for many
 reasons it cannot be proved            
convincingly that the organ in question 
has its seat in the head4 ,according to 
the opinion of ,delage1 the labyrinth   
has nothing to do with this particular  
sensation of movement4 ,breuer1 on the  
other hand1 is of the opinion that the  
organ of forward movement in man is     
stunted and the persistence of the      
sensation in question is too brief to   
permit our instituting experiments as   
obvious as in the case of rotation4 ,in 
fact1 ,crum ,brown once observed while  
in an irritated condition peculiar      
vertical phenomena in his own person1   
which were all satisfactorily explained 
by an abnormally long persistence of the
 sensation of rotation1 and ,i myself in
 an analogous case on the stopping of a 
railway train felt the apparent backward
 motion in striking intensity and for an
 unusual length of time4  ,there is no  

doubt whatever that we feel changes of  
vertical acceleration1 and it will      
appear from the following extremely     
probable that the otoliths of the       
vestibule are the sense-organ for the   
direction of the mass-acceleration4 ,it 
will then be incompatible with a really 
logical view to regard the latter as    
incapable of sensing horizontal         
accelerations4  ,in the lower animals   
the analogue of the labyrinth is shrunk 
to a little vesicle filled with a liquid
 and containing tiny crystals1 auditive 
stones1 or otoliths1 of greater specific
 gravity1 suspended on minute hairs4    
,these crystals appear physically well  
adapted for indicating both the         
direction of gravity and the direction  
of incipient movements4 ,that they      
discharge the former function1 ,delage  
was the first to convince himself by    
experiments with lower animals which on 
the removal of the otoliths utterly lost
 their bearings and could no longer     
regain their normal position4 ,loeb also

 found that fishes without labyrinths   
swim now on their bellies and now on    
their backs4 ,but the most remarkable1  
most beautiful1 and most convincing     
experiment is that which ,dr4 ,kreidl   
instituted with crustaceans4 ,according 
to ,hensen1 certain ,crustacea on       
sloughing spontaneously introduce fine  
grains of sand as auditive stones into  
their otolith vesicle4 ,at the ingenious
 suggestion of ,s4 ,exner1 ,dr4 ,kreidl 
constrained some of these animals to put
 up with iron filings 7ferrum limatum74 
,if the pole of an electro-magnet be    
brought near the animal1 it will at once
 turn its back away from the pole       
accompanying the movement with          
appropriate reflex motions of the eye   
the moment the current is closed1       
exactly as if gravity had been brought  
to bear upon the animal in the same     
direction as the magnetic force4#ajd    
,this1 in fact1 is what should be       
expected from the function ascribed to  
the otoliths4 ,if the eyes be covered   

with asphalt varnish1 and the auditive  
sacs removed1 the crustaceans lose their
 sense of direction utterly1 tumble head
 over heels1 lie on their side or their 
back indifferently4 ,this does not      
happen when the eyes only are covered4  
,for vertebrates1 ,breuer has           
demonstrated by searching investigations
 that the otoliths1 or better1          
statoliths1 slide in three planes       
parallel to the planes of the           
semi-circular canals1 and are           
consequently perfectly adapted for      
indicating changes both in the amount   
and the direction of the                
mass-acceleration4#aje  ,i have already 
remarked that not every function of     
orientation can be ascribed exclusively 
to the labyrinth4 ,the deaf and dumb who
 have to be immersed in water1 and the  
crustaceans who must have their eyes    
closed if they are to be perfectly      
disorientated1 are proof of this fact4  
,i saw a blind cat at ,hering's         
laboratory which to one who was not a   

very attentive observer behaved exactly 
like a seeing cat4 ,it played nimbly    
with objects rolling on the floor1 stuck
 its head inquisitively into open       
drawers1 sprang dexterously upon chairs1
 ran with perfect accuracy through open 
doors1 and never bumped against closed  
ones4 ,the visual sense had here been   
rapidly replaced by the tactual and     
auditive senses4 ,and it appears from   
,ewald's investigations that even after 
the labyrinths have been removed1       
animals gradually learn to move about   
again quite in the normal fashion1      
presumably because the eliminated       
function of the labyrinth is now        
performed by some part of the brain4 ,a 
certain peculiar weakness of the muscles
 alone is perceptible which ,ewald      
ascribes to the absence of the stimulus 
which is otherwise constantly emitted by
 the labyrinth 7the labyrinth-tonus74   
,but if the part of the brain which     
discharges the deputed function be      
removed1 the animals are again          

completely disorientated and absolutely 
helpless4  ,it may be said that the     
views enunciated by ,breuer1 ,crum      
,brown and myself in #ahgc and #ahgd1   
and which are substantially a fuller and
 richer development of ,goltz's idea1   
have upon the whole been substantiated4 
,at least they have exercised a helpful 
and stimulative influence4 ,new problems
 have of course arisen in the course of 
the investigation which still await     
solution1 and much work remains to be   
done4 ,at the same time we see how      
fruitful the renewed co-operation of the
 various special departments of science 
may become after a period of isolation  
and invigorating labor apart4  ,i may be
 permitted1 therefore1 to consider the  
relation between hearing and orientation
 from another and more general point of 
view4 ,what we call the auditive organ  
is in the lower animals simply a sac    
containing auditive stones4 ,as we      
ascend the scale1 #a1 #b1 #c            
semi-circular canals gradually develop  

from them1 whilst the structure of the  
otolith organ itself becomes more       
complicated4 ,finally1 in the higher    
vertebrates1 and particularly in the    
mammals1 a part of the latter organ 7the
 lagena7 becomes the cochlea1 which     
,helmholtz explained as the organ for   
sensations of tone4 ,in the belief that 
the entire labyrinth was an auditive    
organ1 ,helmholtz1 contrary to the      
results of his own masterly analysis1   
originally sought to interpret another  
part of the labyrinth as the organ of   
noises4 ,i showed a long time ago       
7#ahgc7 that every tonal stimulus by    
shortening the duration of the          
excitation to a few vibrations1         
gradually loses its character of pitch  
and takes on that of a sharp1 dry report
 or noise4#ajf ,all the intervening     
stages between tones and noises can be  
exhibited4 ,such being the case1 it will
 hardly be assumed that one organ is    
suddenly and at some given point        
replaced in function by another4 ,on the

 basis of different experiments and     
reasonings ,s4 ,exner also regards the  
assumption of a special organ for the   
sensing of noises as unnecessary4  ,if  
we will but reflect how small a portion 
of the labyrinth of higher animals is   
apparently in the service of the sense  
of hearing1 and how large1 on the other 
hand1 the portion is which very likely  
serves the purposes of orientation1 how 
much the first anatomical beginnings of 
the auditive sac of lower animals       
resemble that part of the fully         
developed labyrinth which does not hear1
 the view is irresistibly suggested     
which ,breuer and ,i 7#ahgd1 #ahge7     
expressed1 that the auditive organ took 
its development from an organ for       
sensing movements by adaptation to weak 
periodic motional stimuli1 and that many
 apparatuses in the lower animals which 
are held to be organs of hearing are not
 auditive organs at all4#ajg  ,this view
 appears to be perceptibly gaining      
ground4 ,dr4 ,kreidl by                 

skilfully-planned experiments has       
arrived at the conclusion that even     
fishes do not hear1 whereas ,e4 ,h4     
,weber1 in his day1 regarded the        
ossicles which unite the air-bladder of 
fishes with the labyrinth as organs     
expressly designed for conducting sound 
from the former to the latter4#ajh      
,strensen has investigated the          
excitation of sounds by the air-bladder 
of fishes1 as also the conduction of    
shocks through ,weber's ossicles4 ,he   
regards the air-bladder as particularly 
adapted for receiving the noises made by
 other fishes and conducting them to the
 labyrinth4 ,he has heard the loud      
grunting tones of the fishes in ,south  
,american rivers1 and is of the opinion 
that they allure and find each other in 
this manner4 ,according to these views  
certain fishes are neither deaf nor     
dumb4#aji ,the question here involved   
might be solved perhaps by sharply      
distinguishing between the sensation of 
hearing proper1 and the perception of   

shocks4 ,the first-mentioned sensation  
may1 even in the case of many           
vertebrates1 be extremely restricted1 or
 perhaps even absolutely wanting4 ,but  
besides the auditive function1 ,weber's 
ossicles may perfectly well discharge   
some other function4 ,although1 as      
,moreau has shown1 the air-bladder      
itself is not an organ of equilibrium in
 the simple physical sense of ,borelli1 
yet doubtless some function of this     
character is still reserved for it4 ,the
 union with the labyrinth favors this   
conception1 and so a host of new        
problems rises here before us4  ,i      
should like to close with a reminiscence
 from the year #ahfc4 ,helmholtz's      
,sensations of ,tone had just been      
published and the function of the       
cochlea now appeared clear to the whole 
world4 ,in a private conversation which 
,i had with a physician1 the latter     
declared it to be an almost hopeless    
undertaking to seek to fathom the       
function of the other parts of the      

labyrinth1 whereas ,i in youthful       
boldness maintained that the question   
could hardly fail to be solved1 and that
 very soon1 although of course ,i had   
then no glimmering of how it was to be  
done4 ,ten years later the question was 
substantially solved4  ,to-day1 after   
having tried my powers frequently and in
 vain on many questions1 ,i no longer   
believe that we can make short work of  
the problems of science4 ,nevertheless1 
,i should not consider an ignorabimus as
 an expression of modesty1 but rather as
 the opposite4 ,that expression is a    
suitable one only with regard to        
problems which are wrongly formulated   
and which are therefore not problems at 
all4 ,every real problem can and will be
 solved in due course of time without   
supernatural divination1 entirely by    
accurate observation and close1         
searching thought4    ,,footnotes3      
,footnote #ic3 ,a lecture delivered on  
,february #bd1 #ahig1 before the        
,verein zur ,verbreitung                

naturwissenschaftlicher ,kenntnisse in  
,wien4    ,footnote #id3 ,wollaston1    
,philosophical ,transactions1 ,royal    
,society1 #ahaj4 ,in the same place     
,wollaston also describes and   explains
 the creaking of the muscles4 ,my       
attention was recently   called to this 
work by ,dr4 ,w4 ,pascheles4--,cf4 also 
,purkinje1 ,prager   medicin4           
,jahrbcher1 ,bd4 #f1 ,wien1 #ahbj4      
,footnote #ie3 ,similarly many external 
forces do not act at once on   all parts
 of the earth1 and the internal forces  
which produce   deformations act at     
first immediately only upon limited     
parts4 ,if   the earth were a feeling   
being1 the tides and other terrestrial  
events would provoke in it similar      
sensations to those of our   movements4 
,perhaps the slight alterations of the  
altitude of the   pole which are at     
present being studied are connected with
 the   continual slight deformations of 
the central ellipsoid occasioned by     
seismical happenings4    ,footnote #if3 

,for the popular explanation by         
unconscious inference   the matter is   
extremely simple4 ,we regard the railway
 carriage as   vertical and             
unconsciously infer the inclination of  
the trees4 ,of   course the opposite    
conclusion that we regard the trees as  
vertical   and infer the inclination of 
the carriage1 unfortunately1 is equally 
clear on this theory4    ,footnote #ig3 
,it will be observed that my way of     
thinking and   experimenting here is    
related to that which led ,knight to the
   discovery and investigation of the   
geotropism of plants4   ,philosophical  
,transactions1 ,january #i1 #ahjf4 ,the 
relations between   vegetable and animal
 geotropism have been more recently     
investigated   by ,j4 ,loeb4            
,footnote #ih3 ,this experiment is      
doubtless related to the   galvanotropic
 experiment with the larv of frogs      
described ten years   later by ,l4      
,hermann4 ,compare on this point my     
remarks in the   ,anzeiger der ,wiener  

,akademie1 #ahhf1 ,no4 #ba4 ,recent     
experiments in   galvanotropism are due 
to ,j4 ,loeb4    ,footnote #ii3 ,wiener 
,akad41 #f ,november1 #ahgc4            
,footnote #ajj3 ,wiener ,gesellschaft   
der ,aerzte1 #ad ,november1 #ahgd4      
,footnote #aja3 ,i have made a          
contribution to this last question in   
my ,analysis of the ,sensations1        
7#ahhf71 ,english translation1 #ahig4   
,footnote #ajb3 ,in my ,grundlinien der 
,lehre von den   ,bewegungsempfindungen1
 #ahge1 the matter occupying lines #d to
 #ac of   page #bj from below1 which    
rests on an error1 is1 as ,i have also  
elsewhere remarked1 to be stricken out4 
,for another experiment   related to    
that of ,foucault1 compare my           
,mechanics1 p4 #cjc4    ,footnote #ajc3 
,anzeiger der ,wiener ,akad41 #cj       
,december1 #ahge4    ,footnote #ajd3    
,the experiment was specially           
interesting for me as ,i   had already  
attempted in #ahgd1 although with very  
little confidence   and without success1

 to excite electromagnetically my own   
labyrinth   through which ,i had caused 
a current to pass4    ,footnote #aje3   
,perhaps the discussion concerning the  
peculiarity of   cats always falling on 
their feet1 which occupied the ,parisian
   ,academy1 and1 incidentally1         
,parisian society a few years ago1 will 
be remembered here4 ,i believe that the 
questions which arose are   disposed of 
by the considerations advanced in my    
,bewegungsempfindungen 7#ahge74 ,i also 
partly gave1 as early as   #ahff1 the   
apparatus conceived by the ,parisian    
scientists to   illustrate the phenomena
 in question4 ,one difficulty was left  
untouched in the ,parisian debate4 ,the 
otolith apparatus of the cat   can      
render it no service in free descent4   
,the cat1 however1 while   at rest1     
doubtless knows its position in space   
and is instinctively   conscious of the 
amount of movement which will put it on 
its feet4    ,footnote #ajf3 ,see the   
,appendix to the ,english edition of my 

,analysis of the ,sensations1 ,chicago1 
#ahig4    ,footnote #ajg3 ,compare my   
,analysis of ,sensations1 p4 #abc ff4   
,footnote #ajh3 ,e4 ,h4 ,weber1 ,de aure
 et auditu hominis et   animalium1      
,lipsiae1 #ahbj4    ,footnote #aji3     
,strensen1 ,journ4 ,anat4 ,phys41       
,london1 ,vol4 #bi   7#ahie74     ,,on  
,,some ,,phenomena ,,attending ,,the    
,,flight ,,of ,,projectiles4#aaj        
,i have led my ragamuffins where they   
were peppered4--,falstaff4       ,he    
goes but to see a noise that he         
heard4--,midsummer ,night's      ,dream4
  ,to shoot1 in the shortest time       
possible1 as many holes as possible in  
one another's bodies1 and not always for
 exactly pardonable objects and ideals1 
seems to have risen to the dignity of a 
duty with modern men1 who1 by a singular
 inconsistency1 and in subservience to a
 diametrically contrary ideal1 are bound
 by the equally holy obligation of      
making these holes as small as possible1
 and1 when made1 of stopping them up and

 of healing them as speedily as         
possible4 ,since1 then1 shooting and all
 that appertains thereto1 is a very     
important1 if not the most important1   
affair of modern life1 you will         
doubtless not be averse to giving your  
attention for an hour to some           
experiments which have been undertaken1 
not for advancing the ends of war1 but  
for promoting the ends of science1 and  
which throw some light on the phenomena 
attending the flight of projectiles4    
,modern science strives to construct its
 picture of the world not from          
speculations but so far as possible from
 facts4 ,it verifies its constructs by  
recourse to observation4 ,every newly   
observed fact completes its             
world-picture1 and every divergence of a
 construct from observation points to   
some imperfection1 to some lacuna in it4
 ,what is seen is put to the test of1   
and supplemented by1 what is thought1   
which is again naught but the result of 
things previously seen4 ,it is always   

peculiarly fascinating1 therefore1 to   
subject to direct verification by       
observation1 that is1 to render palpable
 to the senses1 something which we have 
only theoretically excogitated or       
theoretically surmised4  ,in #ahha1 on  
hearing in ,paris the lecture of the    
,belgian artillerist ,melsens1 who      
hazarded the conjecture that projectiles
 travelling at a high rate of speed     
carry masses of compressed air before   
them which are instrumental in producing
 in bodies struck by the projectiles    
certain well-known facts of the nature  
of explosions1 the desire arose in me of
 experimentally testing his conjecture  
and of rendering the phenomenon1 if it  
really existed1 perceptible4 ,the desire
 was the stronger as ,i could say that  
all the means for realising it existed1 
and that ,i had in part already used and
 tested them for other purposes4  ,and  
first let us get clear regarding the    
difficulties which have to be           
surmounted4 ,our task is that of        

observing a bullet or other projectile  
which is rushing through space at a     
velocity of many hundred yards a second1
 together with the disturbances which   
the bullet causes in the surrounding    
atmosphere4 ,even the opaque solid body 
itself1 the projectile1 is only         
exceptionally visible under such        
circumstances--only when it is of       
considerable size and when we see its   
line of flight in strong perspective    
abridgement so that the velocity is     
apparently diminished4 ,we see a large  
projectile quite clearly when we stand  
behind the cannon and look steadily     
along its line of flight or in the less 
pleasant case when the projectile is    
speeding towards us4 ,there is1 however1
 a very simple and effective method of  
observing swiftly moving bodies with as 
little trouble as if they were held at  
rest at some point in their path4 ,the  
method is that of illumination by a     
brilliant electric spark of extremely   
short duration in a dark room4 ,but     

since1 for the full intellectual        
comprehension of a picture presented to 
the eye1 a certain1 not inconsiderable  
interval of time is necessary1 the      
method of instantaneous photography will
 naturally also be employed4 ,the       
pictures1 which are of extremely minute 
duration1 are thus permanently recorded 
and can be examined and analysed at     
one's convenience and leisure4  ,with   
the difficulty just mentioned is        
associated still another and greater    
difficulty which is due to the air4 ,the
 atmosphere in its usual condition is   
generally not visible even when at rest4
 ,but the task presented to us is to    
render visible masses of air which in   
addition are moving with a high         
velocity4  ,to be visible1 a body must  
either emit light itself1 must shine1 or
 must affect in some way the light which
 falls upon it1 must take up that light 
entirely or partly1 absorb it1 or must  
have a deflective effect upon it1 that  
is1 reflect or refract it4 ,we cannot   

see the air as we can a flame1 for it   
shines only exceptionally1 as in a      
,geissler's tube4 ,the atmosphere is    
extremely transparent and colorless2 it 
cannot be seen1 therefore1 as a dark or 
colored body can1 or as chlorine gas    
can1 or vapor of bromine or iodine4     
,air1 finally1 has so small an index of 
refraction and so small a deflective    
influence upon light1 that the          
refractive effect is commonly           
imperceptible altogether4  ,a glass rod 
is visible in air or in water1 but it is
 almost invisible in a mixture of benzol
 and bisulphuret of carbon1 which has   
the same mean index of refraction as the
 glass4 ,powdered glass in the same     
mixture has a vivid coloring1 because   
owing to the decomposition of the colors
 the indices are the same for only one  
color which traverses the mixture       
unimpeded1 whilst the other colors      
undergo repeated reflexions4#aaa  ,water
 is invisible in water1 alcohol in      
alcohol4 ,but if alcohol be mixed with  

water the flocculent streaks of the     
alcohol in the water will be seen at    
once and vice versa4 ,and in like manner
 the air1 too1 under favorable          
circumstances1 may be seen4 ,over a roof
 heated by the burning sun1 a tremulous 
wavering of objects is noticeable1 as   
there is also over red-hot stoves1      
radiators1 and registers4 ,in all these 
cases tiny flocculent masses of hot and 
cold air1 of slightly differing         
refrangibility1 are mingled together4   
,in like manner the more highly         
refracting parts of non-homogeneous     
masses of glass1 the so-called stri or  
imperfections of the glass1 are readily 
detectible among the less refracting    
parts which constitute the bulk of the  
same4 ,such glasses are unserviceable   
for optical purposes1 and special       
attention has been devoted to the       
investigation of the methods for        
eliminating or avoiding these defects4  
,the result has been the development of 
an extremely delicate method for        

detecting optical faults--the so-called 
method of ,foucault and ,toepler--which 
is suitable also for our present        
purpose4  ,illustration3 ,fig4 #di4     
,even ,huygens when trying to detect the
 presence of stri in polished glasses   
viewed them under oblique illumination1 
usually at a considerable distance1 so  
as to give full scope to the            
aberrations1 and had recourse for       
greater exactitude to a telescope4 ,but 
the method was carried to its highest   
pitch of perfection in #ahfg by ,toepler
 who employed the following procedure3  
,a small luminous source a 7,fig4 #di7  
illuminates a lens ,l which throws an   
image b of the luminous source4 ,if the 
eye be so placed that the image falls on
 the pupil1 the entire lens1 if perfect1
 will appear equally illuminated1 for   
the reason that all points of it send   
out rays to the eye4 ,coarse            
imperfections of form or of homogeneity 
are rendered visible only in case the   
aberrations are so large that the light 

from many spots passes by the pupil of  
the eye4 ,but if the image b be partly  
intercepted by the edge of a small      
slide1 then those spots in the lens as  
thus partly darkened will appear        
brighter whose light by its greater     
aberrations still reaches the eye in    
spite of the intercepting slide1 while  
those spots will appear darker which in 
consequence of aberration in the other  
direction throw their light entirely    
upon the slide4 ,this artifice of the   
intercepting slide which had previously 
been employed by ,foucault for the      
investigation of the optical            
imperfections of mirrors enhances       
enormously the delicacy of the method1  
which is still further augmented by     
,toepler's employment of a telescope    
behind the slide4 ,toepler's method1    
accordingly1 enjoys all the advantages  
of the ,huygens and the ,foucault       
procedure combined4 ,it is so delicate  
that the minutest irregularities in the 
air surrounding the lens can be rendered

 distinctly visible1 as ,i shall show by
 an example4 ,i place a candle before   
the lens ,l 7,fig4 #ej7 and so arrange a
 second lens ,m that the flame of the   
candle is imaged upon the screen ,s4 ,as
 soon as the intercepting slide is      
pushed into the focus1 b1 of the light  
issuing from a1 you see the images of   
the changes of density and the images of
 the movements induced in the air by the
 flame quite distinctly upon the screen4
 ,the distinctness of the phenomenon as 
a whole depends upon the position of the
 intercepting slide b4 ,the removal of b
 increases the illumination but         
decreases the distinctness4 ,if the     
luminous source a be removed1 we see the
 image of the candle flame only upon the
 screen ,s4 ,if we remove the flame and 
allow a to continue shining1 the screen 
,s will appear uniformly illuminated4   
,illustration3 ,fig4 #ej4  ,after       
,toepler had sought long and in vain to 
render the irregularities produced in   
air by sound-waves visible by this      

principle1 he was at last conducted to  
his goal by the favorable circumstances 
attending the production of electric    
sparks4 ,the waves generated in the air 
by electric sparks and accompanying the 
explosive snapping of the same1 are of  
sufficiently short period and           
sufficiently powerful to be rendered    
visible by these methods4 ,thus we see  
how by a careful regard for the merest  
and most shadowy indications of a       
phenomenon and by slight progressive and
 appropriate alterations of the         
circumstances and the methods1          
ultimately the most astounding results  
can be attained4 ,consider1 for example1
 two such phenomena as the rubbing of   
amber and the electric lighting of      
modern streets4 ,a person ignorant of   
the myriad minute links that join these 
two things together1 will be absolutely 
nonplussed at their connexion1 and will 
comprehend it no more than the ordinary 
observer who is unacquainted with       
embryology1 anatomy1 and paleontology   

will understand the connexion between a 
saurian and a bird4 ,the high value and 
significance of the co-operation of     
inquirers through centuries1 where each 
has but to take up the thread of work of
 his predecessors and spin it onwards1  
is rendered forcibly evident by such    
examples4 ,and such knowledge destroys1 
too1 in the clearest manner imaginable  
that impression of the marvellous which 
the spectator may receive from science1 
and at the same time is a most salutary 
admonishment to the worker in science   
against superciliousness4 ,i have also  
to add the sobering remark that all our 
art would be in vain did not nature     
herself afford at least some slight     
guiding threads leading from a hidden   
phenomenon into the domain of the       
observable4 ,and so it need not surprise
 us that once under particularly        
favorable circumstances an extremely    
powerful sound-wave which had been      
caused by the explosion of several      
hundred pounds of dynamite threw a      

directly visible shadow in the sunlight1
 as ,boys has recently told us4 ,if the 
sound-waves were absolutely without     
influence upon the light1 this could not
 have occurred1 and all our artifices   
would then1 too1 be in vain4 ,and so1   
similarly1 the phenomenon accompanying  
projectiles which ,i am about to show   
you was once in a very imperfect manner 
incidentally seen by a ,french          
artillerist1 ,journe1 while that        
observer was simply following the line  
of flight of a projectile with a        
telescope1 just as also the undulations 
produced by candle flames are in a weak 
degree directly visible and in the      
bright sunlight are imaged in shadowy   
waves upon a uniform white background4  
,instantaneous illumination by the      
electric spark1 the method of rendering 
visible small optical differences or    
stri1 which may hence be called the     
striate1 or differential1 method1#aab   
invented by ,foucault and ,toepler1 and 
finally the recording of the image by a 

photographic plate1--these therefore are
 the chief means which are to lead us to
 our goal4  ,i instituted my first      
experiments in the summer of #ahhd with 
a target-pistol1 shooting the bullet    
through a striate field as described    
above1 and taking care that the         
projectile whilst in the field should   
disengage an illuminating electric spark
 from a ,leyden jar or ,franklin's pane1
 which spark produced a photographic    
impression of the projectile upon a     
plate1 especially arranged for the      
purpose4 ,i obtained the image of the   
projectile at once and without          
difficulty4 ,i also readily obtained1   
with the still rather defective dry     
plate which ,i was using1 exceedingly   
delicate images of the sound-waves      
7spark-waves74 ,but no atmospheric      
condensation produced by the projectile 
was visible4 ,i now determined the      
velocity of my projectile and found it  
to be only #bdj metres per second1 or   
considerably less than the velocity of  

sound 7which is #cdj metres per second74
 ,i saw immediately that under such     
circumstances no noticeable compression 
of the air could be produced1 for any   
atmospheric compression must of         
necessity travel forward at the same    
speed with sound 7#cdj metres per       
second7 and consequently would be always
 ahead of and speeding away from the    
projectile4  ,i was so thoroughly       
convinced1 however1 of the existence of 
the supposed phenomenon at a velocity   
exceeding #cdj metres per second1 that  
,i requested ,professor ,salcher1 of    
,fiume1 an ,austrian port on the ,gulf  
of ,quarnero1 to undertake the          
experiment with projectiles travelling  
at a high rate of speed4 ,in the summer 
of #ahhf ,salcher in conjunction with   
,professor ,riegler conducted in a      
spacious and suitable apartment placed  
at their disposal by the ,directors of  
the ,royal ,imperial ,naval ,academy1   
experiments of the kind indicated and   
conforming in method exactly to those   

which ,i had instituted1 with the       
precise results expected4 ,the          
phenomenon1 in fact1 accorded perfectly 
with the a priori sketch of it which ,i 
had drafted previously to the           
experiment4 ,as the experimenting was   
continued1 new and unforeseen features  
made their appearance4  ,it would be    
unfair1 of course1 to expect from the   
very first experiments faultless and    
highly distinct photographs4 ,it was    
sufficient that success was secured and 
that ,i had convinced myself that       
further labor and expenditure would not 
be vain4 ,and on this score ,i am       
greatly indebted to the two gentlemen   
above mentioned4  ,the ,austrian ,naval 
,department subsequently placed a cannon
 at ,salcher's disposal in ,pola1 an    
,adriatic seaport1 and ,i myself1       
together with my son1 then a student of 
medicine1 having received and accepted a
 courteous invitation from ,krupp1      
repaired to ,meppen1 a town in ,hanover1
 where we conducted with only the       

necessary apparatus several experiments 
on the open artillery range4 ,all these 
experiments furnished tolerably good and
 complete pictures4 ,some little        
progress1 too1 was made4 ,the outcome of
 our experience on both artillery       
ranges1 however1 was the settled        
conviction that really good results     
could be obtained only by the most      
careful conduct of the experiments in a 
laboratory especially adapted to the    
purpose4 ,the expensiveness of the      
experiments on a large scale was not the
 determining consideration here1 for the
 size of the projectile is indifferent4 
,given the same velocity and the results
 are quite similar1 whether the         
projectiles are large or small4 ,on the 
other hand1 in a laboratory the         
experimenter has perfect control over   
the initial velocity1 which1 provided   
the proper equipment is at hand1 can be 
altered at will simply by altering the  
charge and the weight of the projectile4
 ,the requisite experiments were        

accordingly conducted by me in my       
laboratory at ,prague1 partly in        
conjunction with my son and partly      
afterwards by him alone4 ,the latter are
 the most perfect and ,i shall          
accordingly speak in detail here of     
these only4  ,illustration3 ,fig4 #ea4  
,picture to yourself an apparatus for   
detecting optical stri set up in a dark 
room4 ,in order not to make the         
description too complicated1 ,i shall   
give the essential features only of the 
apparatus1 leaving out of account       
altogether the minuter details which are
 rather of consequence for the technical
 performance of the experiment than for 
its understanding4 ,we suppose the      
projectile speeding on its path1        
accordingly1 through the field of our   
differential optical apparatus4 ,on     
reaching the centre of the field 7,fig4 
#ea7 the projectile disengages an       
illuminating electric spark a1 and the  
image of the projectile1 so produced1 is
 photographically impressed upon the    

plate of the camera behind the          
intercepting slide b4 ,in the last and  
best experiments the lens ,l was        
replaced by a spherical silvered-glass  
mirror made by ,k4 ,fritsch 7formerly   
,prokesch7 of ,vienna1 whereby the      
apparatus was naturally more complicated
 than it appears in our diagram4 ,the   
projectile having been carefully aimed  
passes in crossing the differential     
field between two vertical isolated     
wires which are connected with the two  
coatings of a ,leyden jar1 and          
completely filling the space between the
 wires discharges the jar4 ,in the axis 
of the differential apparatus the       
circuit has a second gap a which        
furnishes the illuminating spark1 the   
image of which falls on the intercepting
 slide b4 ,the wires in the differential
 field having occasioned manifold       
disturbances were subsequently done away
 with4 ,in the new arrangement the      
projectile passes through a ring 7see   
dotted line1 ,fig4 #ea71 to the air in  

which it imparts a sharp impulse which  
travels forward in the tube r as a      
sound-wave having the approximate       
velocity of #cdj metres per second1     
topples over through the aperture of an 
electric screen the flame of a candle   
situated at the other opening of the    
tube1 and so discharges the jar4 ,the   
length of the tube r is so adjusted that
 the discharge occurs the moment the    
projectile enters the centre of the now 
fully clear and free field of vision4   
,we will also leave out of account the  
fact that to secure fully the success of
 the experiment1 a large jar is first   
discharged by the flame1 and that by the
 agency of this first discharge the     
discharge of a second small jar having a
 spark of very short period which       
furnishes the spark really illuminating 
the projectile is effected4 ,sparks from
 large jars have an appreciable         
duration1 and owing to the great        
velocity of the projectiles furnish     
blurred photographs only4 ,by carefully 

husbanding the light of the differential
 apparatus1 and owing to the fact that  
much more light reaches the photographic
 plate in this way than would otherwise 
reach it1 we can obtain beautiful1      
strong1 and sharp photographs with      
incredibly small sparks4 ,the contours  
of the pictures appear as very delicate 
and very sharp1 closely adjacent double 
lines4 ,from their distance from one    
another1 and from the velocity of the   
projectile1 the duration of the         
illumination1 or of the spark1 is found 
to be #a_/hjjjjj of a second4 ,it is    
evident1 therefore1 that experiments    
with mechanical snap slides can furnish 
no results worthy of the name4          
,illustration3 ,fig4 #eb4  ,let us      
consider now first the picture of a     
projectile in the rough1 as represented 
in ,figure #eb1 and then let us examine 
it in its photographic form as seen in  
,figure #ec4 ,the latter picture is of a
 shot from an ,austrian ,mannlicher     
rifle4 ,if ,i were not to tell you what 

the picture represented you would very  
likely imagine it to be a bird's eye    
view of a boat b moving swiftly through 
the water4 ,in front you see the        
bow-wave and behind the body a          
phenomenon k which closely resembles the
 eddies formed in the wake of a ship4   
,and as a matter of fact the dark       
hyperboloid arc which streams from the  
tip of the projectile really is a       
compressed wave of air exactly analogous
 to the bow-wave produced by a ship     
moving through the water1 with the      
exception that the wave of air is not a 
surface-wave4 ,the air-wave is produced 
in atmospheric space and encompasses the
 projectile in the form of a shell on   
all sides4 ,the wave is visible for the 
same reason that the heated shell of air
 surrounding the candle flame of our    
former experiments is visible4 ,and the 
cylinder of friction-heated air which   
the projectile throws off in the form of
 vortex rings really does answer to the 
water in the wake of a vessel4          

,illustration3 ,fig4 #ec4 ,photograph of
 a blunted projectile4  ,now just as a  
slowly moving boat produces no bow-wave1
 but the bow-wave is seen only when the 
boat moves with a speed which is greater
 than the velocity of propagation of    
surface-waves in water1 so1 in like     
manner1 no wave of compression is       
visible in front of a projectile so long
 as the speed of the projectile is less 
than the velocity of sound4 ,but if the 
speed of the projectile reaches and     
exceeds the velocity of sound1 then the 
head-wave1 as we shall call it1 augments
 noticeably in power1 and is more and   
more extended1 that is1 the angle made  
by the contours of the wave with the    
direction of flight is more and more    
diminished1 just as when the speed of a 
boat is increased a similar phenomenon  
is noticed in connexion with the        
bow-wave4 ,in fact1 we can from an      
instantaneous photograph so taken       
approximately estimate the speed with   
which the projectile is travelling4     

,the explanation of the bow-wave of a   
ship and that of the head-wave of a body
 travelling in atmospheric space both   
repose upon the same principle1 long ago
 employed by ,huygens4 ,conceive a      
number of pebbles to be cast into a pond
 of water at regular intervals in such  
wise that all the spots struck are      
situate in the same straight line1 and  
that every spot subsequently struck lies
 a short space farther to the right4    
,the spots first struck will furnish    
then the wave-circles which are widest1 
and all of them together will1 at the   
points where they are thickest1 form a  
sort of cornucopia closely resembling   
the bow-wave4 7,fig4 #ed47 ,the         
resemblance is greater the smaller the  
pebbles are1 and the more quickly they  
succeed each other4 ,if a rod be dipped 
into the water and quickly carried along
 its surface1 the falling of the pebbles
 will then take place1 so to speak1     
uninterruptedly1 and we shall have a    
real bow-wave4 ,if we put the compressed

 air-wave in the place of the           
surface-waves of the water1 we shall    
have the head-wave of the projectile4   
,illustration3 ,fig4 #ed4  ,you may be  
disposed to say now1 it is all very     
pretty and interesting to observe a     
projectile in its flight1 but of what   
practical use is it8  ,it is true1 ,i   
reply1 one cannot wage war with         
photographed projectiles4 ,and ,i have  
likewise often had to say to medical    
students attending my lectures on       
physics1 when they inquired for the     
practical value of some physical        
observation1 ,you cannot1 gentlemen1    
cure diseases with it4 ,i had also once 
to give my opinion regarding how much   
physics should be taught at a school for
 millers1 supposing the instruction     
there to be confined exactly to what was
 necessary for a miller4 ,i was obliged 
to reply3 ,a miller always needs exactly
 as much physics as he knows4 ,knowledge
 which one does not possess one cannot  
use4  ,let us forego entirely the       

consideration that as a general thing   
every scientific advance1 every new     
problem elucidated1 every extension or  
enrichment of our knowledge of facts1   
affords a better foundation for         
practical pursuits4 ,let us rather put  
the special question1 ,is it not        
possible to derive some really practical
 knowledge from our theoretical         
acquaintance with the phenomena which   
take place in the space surrounding a   
projectile8  ,no physicist who has ever 
studied waves of sound or photographed  
them will have the least doubt regarding
 the sound-wave character of the        
atmospheric condensation encompassing   
the head of a flying projectile4 ,we    
have therefore1 without ado1 called this
 condensation the head-wave4  ,knowing  
this1 it follows that the view of       
,melsens according to which the         
projectile carries along with it masses 
of air which it forces into the bodies  
struck1 is untenable4 ,a forward-moving 
sound-wave is not a forward-moving mass 

of matter but a forward-moving form of  
motion1 just as a water-wave or the     
waves of a field of wheat are only      
forward-moving forms of motion and not  
movements of masses of water or masses  
of wheat4  ,by interference-experiments1
 on which ,i cannot touch here but which
 will be found roughly represented in   
,figure #ee1 it was found that the      
bell-shaped head-wave in question is an 
extremely thin shell and that the       
condensations of the same are quite     
moderate1 scarcely exceeding two-tenths 
of an atmosphere4 ,there can be no      
question1 therefore1 of explosive       
effects in the body struck by the       
projectile through so slight a degree of
 atmospheric compression4 ,the phenomena
 attending wounds from rifle balls1 for 
example1 are not to be explained as     
,melsens and ,busch explain them1 but   
are due1 as ,kocher and ,reger maintain1
 to the effects of the impact of the    
projectile itself4  ,illustration3 ,fig4
 #ee4  ,a simple experiment will show   

how insignificant is the part played by 
the friction of the air1 or the supposed
 conveyance of the air along with the   
moving projectile4 ,if the photograph of
 the projectile be taken while passing  
through a flame1 i4 e41 a visible gas1  
the flame will be seen to be1 not torn  
and deformed1 but smoothly and cleanly  
perforated1 like any solid body4 ,within
 and around the flame the contours of   
the head-wave will be seen4 ,the        
flickering1 the extinction of the flame1
 etc41 take place only after the        
projectile has travelled on a           
considerable distance in its path1 and  
is then affected by the powder gases    
which hurry after the bullet or by the  
air preceding the powder-gases4  ,the   
physicist who examines the head-wave and
 recognises its sound-wave character    
also sees that the wave in question is  
of the same kind with the short sharp   
waves produced by electric sparks1 that 
it is a noise-wave4 ,hence1 whenever any
 portion of the head-wave strikes the   

ear it will be heard as a report4       
,appearances point to the conclusion    
that the projectile carries this report 
along with it4 ,in addition to this     
report1 which advances with the velocity
 of the projectile and so usually       
travels at a speed greater than the     
velocity of sound1 there is also to be  
heard the report of the exploding powder
 which travels forward with the ordinary
 velocity of sound4 ,hence two          
explosions will be heard1 each distinct 
in time4 ,the circumstance that this    
fact was long misconstrued by practical 
observers but when actually noticed     
frequently received grotesque           
explanations and that ultimately my view
 was accepted as the correct one1       
appears to me in itself a sufficient    
justification that researches such as we
 are here speaking of are not utterly   
superfluous even in practical           
directions4 ,that the flashes and sounds
 of discharging artillery are used for  
estimating the distances of batteries is

 well known1 and it stands to reason    
that any unclear theoretical conception 
of the facts here involved will         
seriously affect the correctness of     
practical calculations4  ,it may appear 
astonishing to a person hearing it for  
the first time1 that a single shot has a
 double report due to two different     
velocities of propagation4 ,but the     
reflexion that projectiles whose        
velocity is less than the velocity of   
sound produce no head-waves 7because    
every impulse imparted to the air       
travels forward1 that is1 ahead1 with   
exactly the velocity of sound71 throws  
full light when logically developed upon
 the peculiar circumstance above        
mentioned4 ,if the projectile moves     
faster than sound1 the air ahead of it  
cannot recede from it quickly enough4   
,the air is condensed and warmed1 and   
thereupon1 as all know1 the velocity of 
sound is augmented until the head-wave  
travels forward as rapidly as the       
projectile itself1 so that there is no  

need whatever of any additional         
augmentation of the velocity of         
propagation4 ,if such a wave were left  
entirely to itself1 it would increase in
 length and soon pass into an ordinary  
sound-wave1 travelling with less        
velocity4 ,but the projectile is always 
behind it and so maintains it at its    
proper density and velocity4 ,even if   
the projectile penetrates a piece of    
cardboard or a board of wood1 which     
catches and obstructs the head-wave1    
there will1 as ,figure #ef shows1       
immediately appear at the emerging apex 
a newly formed1 not to say newly born1  
head-wave4 ,we may observe on the       
cardboard the reflexion and diffraction 
of the head-wave1 and by means of a     
flame its refraction1 so that no doubt  
as to its nature can remain4            
,illustration3 ,fig4 #ef4  ,permit me1  
now1 to illustrate the most essential of
 the points that ,i have just adduced1  
by means of a few rough drawings taken  
from older and less perfect photographs4

  ,in the sketch of ,figure #eg you see 
the projectile1 which has just left the 
barrel of the rifle1 touch a wire and   
disengage the illuminating spark4 ,at   
the apex of the projectile you already  
see the beginnings of a powerful        
head-wave1 and in front of the wave a   
transparent fungiform cluster4 ,this    
latter is the air which has been forced 
out of the barrel by the projectile4    
,circular sound-waves1 noise-waves1     
which are soon overtaken by the         
projectile1 also issue from the barrel4 
,but behind the projectile opaque puffs 
of powder-gas rush forth4 ,it is        
scarcely necessary to add that many     
other questions in ballistics may be    
studied by this method1 as1 for example1
 the movement of the gun-carriage4      
,illustration3 ,fig4 #eg4  ,a           
distinguished ,french artillerist1 ,m4  
,gossot1 has applied the views of the   
head-wave here given in quite a         
different manner4 ,the practice in      
measuring the velocity of projectiles is

 to cause the projectile to pass through
 wire screens placed at different points
 in its path1 and by the tearing of     
these screens to give rise to           
electro-magnetic time-signals on falling
 slabs or rotating drums4 ,gossot caused
 these signals to be made directly by   
the impact of the head-wave1 did away   
thus with the wire screens1 and carried 
the method so far as to be able to      
measure the velocities of projectiles   
travelling in high altitudes1 where the 
use of wire screens was quite out of the
 question4  ,the laws of the resistance 
of fluids and of air to bodies          
travelling in them form an extremely    
complicated problem1 which can be       
reasoned out very simply and prettily as
 a matter of pure philosophy but        
practice offers not a few difficulties4 
,the same body having the velocity #b1  
#c1 #d 444 displaces in the same        
interval #b1 #c1 #d 444 times the same  
mass of air1 or the same mass of fluid1 
and imparts to it in addition #b1 #c1 #d

 444 times the same velocity4 ,but for  
this1 plainly1 #d1 #i1 #af 444 times the
 original force is required4 ,hence1 the
 resistance1 it is said1 increases with 
the square of the velocity4 ,this is all
 very pretty and simple and obvious4    
,but practice and theory are at daggers'
 points here4 ,practice tells us that   
when we increase the velocity1 the law  
of the resistance changes4 ,for every   
portion of the velocity the law is      
different4  ,the studies of the talented
 ,english naval architect1 ,froude1 have
 thrown light upon this question4       
,froude has shown that the resistance is
 conditioned by a combination of the    
most multifarious phenomena4 ,a ship in 
motion is subjected to the friction of  
the water4 ,it causes eddies and it     
generates in addition waves which       
radiate outward from it4 ,every one of  
these phenomena are dependent upon the  
velocity in some different manner1 and  
it is consequently not astonishing that 
the law of the resistance should be a   

complicated one4  ,the preceding        
observations suggest quite analogous    
reflexions for projectiles4 ,here also  
we have friction1 the formation of      
eddies1 and the generation of waves4    
,here1 also1 therefore1 we should not be
 surprised at finding the law of the    
resistance of the air a complicated one1
 nor puzzled at learning that in        
actuality the law of resistance changes 
as soon as the speed of the projectile  
exceeds the velocity of sound1 for this 
is the precise point at which one       
important element of the resistance1    
namely1 the formation of waves1 first   
comes into play4  ,no one doubts that a 
pointed bullet pierces the air with less
 resistance than a blunt bullet4 ,the   
photographs themselves show that the    
head-wave is weaker for a pointed       
projectile4 ,it is not impossible1      
similarly1 that forms of bullets will be
 invented which generate fewer eddies1  
etc41 and that we shall study these     
phenomena also by photography4 ,i am of 

opinion from the few experiments which  
,i have made in this direction that not 
much more can be done by changing the   
form of the projectile when the velocity
 is very great1 but ,i have not gone    
into the question thoroughly4           
,researches of the kind we are          
considering can certainly not be        
detrimental to practical artillery1 and 
it is no less certain that experiments  
by artillerists on a large scale will be
 of undoubted benefit to physics4  ,no  
one who has had the opportunity of      
studying modern guns and projectiles in 
their marvellous perfection1 their power
 and precision1 can help confessing that
 a high technical and scientific        
achievement has found its incarnation in
 these objects4 ,we may surrender       
ourselves so completely to this         
impression as to forget for a moment the
 terrible purposes they serve4  ,permit 
me1 therefore1 before we separate1 to   
say a few words on this glaring         
contrast4 ,the greatest man of war and  

of silence which the present age has    
produced once asserted that perpetual   
peace is a dream1 and not a beautiful   
dream at that4 ,we may accord to this   
profound student of mankind a judgment  
in these matters and can also appreciate
 the soldier's horror of stagnation from
 all too lengthy peace4 ,but it requires
 a strong belief in the insuperableness 
of medival barbarism to hope for and to 
expect no great improvement in          
international relations4 ,think of our  
forefathers and of the times when club  
law ruled supreme1 when within the same 
country and the same state brutal       
assaults and equally brutal self-defence
 were universal and self-evident4 ,this 
state of affairs grew so oppressive that
 finally a thousand and one             
circumstances compelled people to put an
 end to it1 and the cannon had most to  
say in accomplishing the work4 ,yet the 
rule of club law was not abolished so   
quickly after all4 ,it had simply passed
 to other clubs4 ,we must not abandon   

ourselves to dreams of the ,rousseau    
type4 ,questions of law will in a sense 
forever remain questions of might4 ,even
 in the ,united ,states where every one 
is as a matter of principle entitled to 
the same privileges1 the ballot         
according to ,stallo's pertinent remark 
is but a milder substitute for the club4
 ,nor need ,i tell you that many of our 
own fellow-citizens are still enamored  
of the old original methods4 ,very1 very
 gradually1 however1 as civilisation    
progresses1 the intercourse of men takes
 on gentler forms1 and no one who really
 knows the good old times will ever     
honestly wish them back again1 however  
beautifully they may be painted and     
rhymed about4  ,in the intercourse of   
the nations1 however1 the old club law  
still reigns supreme4 ,but since its    
rule is taxing the intellectual1 the    
moral1 and the material resources of the
 nations to the utmost and constitutes  
scarcely less a burden in peace than in 
war1 scarcely less a yoke for the victor

 than for the vanquished1 it must       
necessarily grow more and more          
unendurable4 ,reason1 fortunately1 is no
 longer the exclusive possession of     
those who modestly call themselves the  
upper ten thousand4 ,here1 as           
everywhere1 the evil itself will awaken 
the intellectual and ethical forces     
which are destined to mitigate it4 ,let 
the hate of races and of nationalities  
run riot as it may1 the intercourse of  
nations will still increase and grow    
more intimate4 ,by the side of the      
problems which separate nations1 the    
great and common ideals which claim the 
exclusive powers of the men of the      
future appear one after another in      
greater distinctness and in greater     
might4    ,,footnotes3    ,footnote     
#aaj3 ,a lecture delivered on ,nov4 #aj1
 #ahig4    ,footnote #aaa3              
,christiansen1 ,wiedemann's ,annalen1   
,,xxiii4 ,s4 #bih1   ,,xxiv41 p4 #dci   
7#ahhd-ahhe74    ,footnote #aab3 ,the   
,german phrase is ,schlierenmethode1 by 

which   term the method is known even by
 ,american physicists4 ,it is also      
called in ,english the shadow-method4   
,but a term is necessary which   will   
cover all the derivatives1 and so we    
have employed   alternatively the words 
striate and differential4 ,the etymology
   of schlieren1 it would seem1 is      
uncertain4 ,its present use is   derived
 from its technological signification in
 glass-manufacturing1   where by die    
,schlieren are meant the wavy streaks   
and   imperfections in glass4 ,hence its
 application to the method for          
detecting small optical differences and 
faults generally4   ,professor ,crew of 
,evanston suggests to the translator    
that   schlieren may be related to our  
slur 7,l4 ,g41 slren1 to trail1   to    
draggle71 a conjecture which is         
doubtless correct and agrees both   with
 the meaning of schlieren as given in   
the large ,german   dictionaries and    
with the intransitive use of our own    
verb slur1   the faults in question     

being conceived as trailings1           
streakings1   etc4--,trans4     ,,on    
,,instruction ,,in ,,the ,,classics     
,,and ,,the ,,sciences4#aac   ,perhaps  
the most fantastic proposition that     
,maupertuis1#aad the renowned president 
of the ,berlin ,academy1 ever put       
forward for the approval of his         
contemporaries was that of founding a   
city in which1 to instruct and          
discipline young students1 only ,latin  
should be spoken4 ,maupertuis's ,latin  
city remained an idle wish4 ,but for    
centuries ,latin and ,greek institutions
 exist in which our children spend a    
goodly portion of their days1 and whose 
atmosphere constantly surrounds them1   
even when without their walls4  ,for    
centuries instruction in the ancient    
languages has been zealously cultivated4
 ,for centuries its necessity has been  
alternately championed and contested4   
,more strongly than ever are            
authoritative voices now raised against 
the preponderance of instruction in the 

classics and in favor of an education   
more suited to the needs of the time1   
especially for a more generous treatment
 of mathematics and the natural         
sciences4  ,in accepting your invitation
 to speak here on the relative          
educational value of the classical and  
the mathematico-physical sciences in    
colleges and high schools1 ,i find my   
justification in the duty and the       
necessity laid upon every teacher of    
forming from his own experiences an     
opinion upon this important question1 as
 partly also in the special circumstance
 that in my youth ,i was personally     
under the influence of school-life for  
only a short time1 just previous to my  
entering the university1 and had1       
therefore1 ample opportunity to observe 
the effects of widely different methods 
upon my own person4  ,passing now1 to a 
review of the arguments which the       
advocates of instruction in the classics
 advance1 and of what the adherents of  
instruction in the physical sciences in 

their turn adduce1 we find ourselves in 
rather a perplexing position with       
respect to the arguments of the first   
named4 ,for these have been different at
 different times1 and they are even now 
of a very multifarious character1 as    
must be where men advance1 in favor of  
an institution that exists and which    
they are determined to retain at any    
cost1 everything they can possibly think
 of4 ,we shall find here much that has  
evidently been brought forward only to  
impress the minds of the ignorant2 much1
 too1 that was advanced in good faith   
and which is not wholly without         
foundation4 ,we shall get a fair idea of
 the reasoning employed by considering1 
first1 the arguments that have grown out
 of the historical circumstances        
connected with the original introduction
 of the classics1 and1 lastly1 those    
which were subsequently adduced as      
accidental afterthoughts4         99    
99       99       99       99           
,instruction in ,latin1 as ,paulsen#aae 

has minutely shown1 was introduced by   
the ,roman ,church along with           
,christianity4 ,with the ,latin language
 were also transmitted the scant and    
meagre remnants of ancient science4     
,whoever wished to acquire this ancient 
education1 then the only one worthy of  
the name1 for him the ,latin language   
was the only and indispensable means2   
such a person had to learn ,latin to    
rank among educated people4  ,the       
wide-spread influence of the ,roman     
,church wrought many and various        
results4 ,among those for which all are 
glad1 we may safely count the           
establishment of a sort of uniformity   
among the nations and of a regular      
international intercourse by means of   
the ,latin language1 which did much to  
unite the nations in the common work of 
civilisation1 carried on from the       
fifteenth to the eighteenth century4    
,the ,latin language was thus long the  
language of scholars1 and instruction in
 ,latin the road to a liberal           

education--a shibboleth still employed1 
though long inappropriate4  ,for        
scholars as a class1 it is to be        
regretted1 perhaps1 that ,latin has     
ceased to be the medium of international
 communication4 ,but the attributing of 
the loss of this function by the ,latin 
language to its incapacity to           
accommodate itself to the numerous new  
ideas and conceptions which have arisen 
in the course of the development of     
science is1 in my opinion1 wholly       
erroneous4 ,it would be difficult to    
find a modern scientist who had enriched
 science with as many new ideas as      
,newton has1 yet ,newton knew how to    
express those ideas very correctly and  
precisely in the ,latin language4 ,if   
this view were correct1 it would also   
hold true of every living language4     
,originally every language has to adapt 
itself to new ideas4  ,it is far more   
likely that ,latin was displaced as the 
literary vehicle of science by the      
influence of the nobility4 ,by their    

desire to enjoy the fruits of literature
 and science1 through a less irksome    
medium than ,latin1 the nobility        
performed for the people at large an    
undeniable service4 ,for the days were  
now past when acquaintance with the     
language and literature of science was  
restricted to a caste1 and in this step1
 perhaps1 was made the most important   
advance of modern times4 ,to-day1 when  
international intercourse is firmly     
established in spite of the many        
languages employed1 no one would think  
of reintroducing ,latin4#aaf  ,the      
facility with which the ancient         
languages lend themselves to the        
expression of new ideas is evidenced by 
the fact that the great majority of our 
scientific ideas1 as survivals of this  
period of ,latin intercourse1 bear      
,latin and ,greek designations1 while in
 great measure scientific ideas are even
 now invested with names from these     
sources4 ,but to deduce from the        
existence and use of such terms the     

necessity of still learning ,latin and  
,greek on the part of all who employ    
them is carrying the conclusion too far4
 ,all terms1 appropriate and            
inappropriate1--and there are a large   
number of inappropriate and monstrous   
combinations in science1--rest on       
convention4 ,the essential thing is1    
that people should associate with the   
sign the precise idea that is designated
 by it4 ,it matters little whether a    
person can correctly derive the words   
telegraph1 tangent1 ellipse1 evolute1   
etc41 if the correct idea is present in 
his mind when he uses them4 ,on the     
other hand1 no matter how well he may   
know their etymology1 his knowledge will
 be of little use to him if the correct 
idea is absent4 ,ask the average and    
fairly educated classical scholar to    
translate a few lines for you from      
,newton's ,principia1 or from ,huygens's
 ,horologium1 and you will discover at  
once what an extremely subordinate rle  
the mere knowledge of language plays in 

such things4 ,without its associated    
thought a word remains a mere sound4    
,the fashion of employing ,greek and    
,latin designations--for it can be      
termed nothing else--has a natural root 
in history2 it is impossible for the    
practice to disappear suddenly1 but it  
has fallen of late considerably into    
disuse4 ,the terms gas1 ohm1 ,ampre1    
volt1 etc41 are in international use1   
but they are not ,latin nor ,greek4     
,only the person who rates the          
unessential and accidental husk higher  
than its contents1 can speak of the     
necessity of learning ,latin or ,greek  
for such reasons1 to say nothing of     
spending eight or ten years on the task4
 ,will not a dictionary supply in a few 
seconds all the information we wish on  
such subjects8#aag  ,it is indisputable 
that our modern civilisation took up the
 threads of the ancient civilisation1   
that at many points it begins where the 
latter left off1 and that centuries ago 
the remains of the ancient culture were 

the only culture existing in ,europe4   
,then1 of course1 a classical education 
really was the liberal education1 the   
higher education1 the ideal education1  
for it was the sole education4 ,but when
 the same claim is now raised in behalf 
of a classical education1 it must be    
uncompromisingly contested as bereft of 
all foundation4 ,for our civilisation   
has gradually attained its independence2
 it has lifted itself far above the     
ancient civilisation1 and has entered   
generally new directions of progress4   
,its note1 its characteristic feature1  
is the enlightenment that has come from 
the great mathematical and physical     
researches of the last centuries1 and   
which has permeated not only the        
practical arts and industries but is    
also gradually finding its way into all 
fields of thought1 including philosophy 
and history1 sociology and linguistics4 
,those traces of ancient views that are 
still discoverable in philosophy1 law1  
art1 and science1 operate more as       

hindrances than helps1 and will not long
 stand before the development of        
independent and more natural views4  ,it
 ill becomes classical scholars1        
therefore1 to regard themselves1 at this
 day1 as the educated class par         
excellence1 to condemn as uneducated all
 persons who do not understand ,latin   
and ,greek1 to complain that with such  
people profitable conversations are not 
to be carried on1 etc4 ,the most        
delectable stories have got into        
circulation1 illustrative of the        
defective education of scientists and   
engineers4 ,a renowned inquirer1 for    
example1 is said to have once announced 
his intention of holding a free course  
of university lectures1 with the word   
frustra2 an engineer who spent his      
leisure hours in collecting insects is  
said to have declared that he was       
studying etymology4 ,it is true1        
incidents of this character make us     
shudder or smile1 according to our mood 
or temperament4 ,but we must admit1 the 

next moment1 that in giving way to such 
feelings we have merely succumbed to a  
childish prejudice4 ,a lack of tact but 
certainly no lack of education is       
displayed in the use of such            
half-understood expressions4 ,every     
candid person will confess that there   
are many branches of knowledge about    
which he had better be silent4 ,we shall
 not be so uncharitable as to turn the  
tables and discuss the impression that  
classical scholars might make on a      
scientist or engineer1 in speaking of   
science4 ,possibly many ludicrous       
stories might be told of them1 and of   
far more serious import1 which should   
fully compensate for the blunders of the
 other party4  ,the mutual severity of  
judgment which we have here come upon1  
may also forcibly bring home to us how  
really scarce a true liberal culture is4
 ,we may detect in this mutual attitude1
 too1 something of that narrow1 medival 
arrogance of caste1 where a man began1  
according to the special point of view  

of the speaker1 with the scholar1 the   
soldier1 or the nobleman4 ,little sense 
or appreciation is to be found in it for
 the common task of humanity1 little    
feeling for the need of mutual          
assistance in the great work of         
civilisation1 little breadth of mind1   
little truly liberal culture4  ,a       
knowledge of ,latin1 and partly1 also1 a
 knowledge of ,greek1 is still a        
necessity for the members of a few      
professions by nature more or less      
directly concerned with the             
civilisations of antiquity1 as for      
lawyers1 theologians1 philologists1     
historians1 and generally for a small   
number of persons1 among whom from time 
to time ,i count myself1 who are        
compelled to seek for information in the
 ,latin literature of the centuries just
 past4#aah ,but that all young persons  
in search of a higher education should  
pursue for this reason ,latin and ,greek
 to such excess2 that persons intending 
to become physicians and scientists     

should come to the universities         
defectively educated1 or even           
miseducated2 and that they should be    
compelled to come only from schools that
 do not supply them with the proper     
preparatory knowledge is going a little 
bit too far4         99       99        
99       99       99  ,after the        
conditions which had given to the study 
of ,latin and ,greek their high import  
had ceased to exist1 the traditional    
curriculum1 naturally1 was retained4    
,then1 the different effects of this    
method of education1 good and bad1 which
 no one had thought of at its           
introduction1 were realised and noted4  
,as natural1 too1 was it that those who 
had strong interests in the preservation
 of these studies1 from knowing no      
others or from living by them1 or for   
still other reasons1 should emphasise   
the good results of such instruction4   
,they pointed to the good effects as if 
they had been consciously aimed at by   
the method and could be attained only   

through its agency4  ,one real benefit  
that students might derive from a       
rightly conducted course in the classics
 would be the opening up of the rich    
literary treasures of antiquity1 and    
intimacy with the conceptions and views 
of the world held by two advanced       
nations4 ,a person who has read and     
understood the ,greek and ,roman authors
 has felt and experienced more than one 
who is restricted to the impressions of 
the present4 ,he sees how men placed in 
different circumstances judge quite     
differently of the same things from what
 we do to-day4 ,his own judgments will  
be rendered thus more independent4      
,again1 the ,greek and ,latin authors   
are indisputably a rich fountain of     
recreation1 of enlightenment1 and of    
intellectual pleasure after the day's   
toil1 and the individual1 not less than 
civilised humanity generally1 will      
remain grateful to them for all time4   
,who does not recall with pleasure the  
wanderings of ,ulysses1 who does not    

listen joyfully to the simple narratives
 of ,herodotus1 who would ever repent of
 having made the acquaintance of        
,plato's ,dialogues1 or of having tasted
 ,lucian's divine humor8 ,who would give
 up the glances he has obtained into the
 private life of antiquity from         
,cicero's letters1 from ,plautus or     
,terence8 ,to whom are not the portraits
 of ,suetonius undying reminiscences8   
,who1 in fact1 would throw away any     
knowledge he had once gained8  ,yet     
people who draw from these sources only1
 who know only this culture1 have surely
 no right to dogmatise about the value  
of some other culture4 ,as objects of   
research for individuals1 this          
literature is extremely valuable1 but it
 is a different question whether it is  
equally valuable as the almost exclusive
 means of education of our youth4  ,do  
not other nations and other literatures 
exist from which we ought to learn8 ,is 
not nature herself our first            
school-mistress8 ,are our highest models

 always to be the ,greeks1 with their   
narrow provinciality of mind1 that      
divided the world into ,greeks and      
barbarians1 with their superstitions1   
with their eternal questioning of       
oracles8 ,aristotle with his incapacity 
to learn from facts1 with his           
word-science2 ,plato with his heavy1    
interminable dialogues1 with his barren1
 at times childish1 dialectics--are they
 unsurpassable8#aai ,the ,romans with   
their apathy1 their pompous externality1
 set off by fulsome and bombastic       
phrases1 with their narrow-minded1      
philistine philosophy1 with their       
frenzied sensuality1 with their cruel   
and bestial indulgence in animal and man
 baiting1 with their outrageous         
maltreatment and plundering of their    
subjects--are they patterns worthy of   
imitation8 ,or shall1 perhaps1 our      
science edify itself with the works of  
,pliny who cites midwives as authorities
 and himself stands on their point of   
view8  ,besides1 if an acquaintance with

 the ancient world really were attained1
 we might come to some settlement with  
the advocates of classical education4   
,but it is words and forms1 and forms   
and words only1 that are supplied to our
 youth2 and even collateral subjects are
 forced into the strait-jacket of the   
same rigid method and made a science of 
words1 sheer feats of mechanical memory4
 ,really1 we feel ourselves set back a  
thousand years into the dull            
cloister-cells of the ,middle ,ages4    
,this must be changed4 ,it is possible  
to get acquainted with the views of the 
,greeks and ,romans by a shorter road   
than the intellect deadening process of 
eight or ten years of declining1        
conjugating1 analysing1 and             
extemporisation4 ,there are to-day      
plenty of educated persons who have     
acquired through good translations      
vivider1 clearer1 and more just views of
 classical antiquity than the graduates 
of our gymnasiums and colleges4#abj     
,for us moderns1 the ,greeks and the    

,romans are simply two objects of       
archological and historical research    
like all others4 ,if we put them before 
our youth in fresh and living pictures1 
and not merely in words and syllables1  
the effect will be assured4 ,we derive a
 totally different enjoyment from the   
,greeks when we approach them after a   
study of the results of modern research 
in the history of civilisation4 ,we read
 many a chapter of ,herodotus           
differently when we attack his works    
equipped with a knowledge of natural    
science1 and with information about the 
stone age and the lake-dwellers4 ,what  
our classical institutions pretend to   
give can and actually will be given to  
our youth with much more fruitful       
results by competent historical         
instruction1 which must supply1 not     
names and numbers alone1 nor the mere   
history of dynasties and wars1 but be in
 every sense of the word a true history 
of civilisation4  ,the view still widely
 prevails that although all higher1     

ideal culture1 all extension of our view
 of the world1 is acquired by           
philological and in a lesser degree by  
historical studies1 still the           
mathematics and natural sciences should 
not be neglected on account of their    
usefulness4 ,this is an opinion to which
 ,i must refuse my assent4 ,it were     
strange if man could learn more1 could  
draw more intellectual nourishment1 from
 the shards of a few old broken jugs1   
from inscribed stones1 or yellow        
parchments1 than from all the rest of   
nature4 ,true1 man is man's first       
concern1 but he is not his sole concern4
  ,in ceasing to regard man as the      
centre of the world2 in discovering that
 the earth is a top whirled about the   
sun1 which speeds off with it into      
infinite space2 in finding that in the  
fixed stars the same elements exist as  
on earth2 in meeting everywhere the same
 processes of which the life of man is  
merely a vanishingly small part--in such
 things1 too1 is a widening of our view 

of the world1 and edification1 and      
poetry4 ,there are here perhaps grander 
and more significant facts than the     
bellowing of the wounded ,ares1 or the  
charming island of ,calypso1 or the     
ocean-stream engirdling the earth4 ,he  
only should speak of the relative value 
of these two domains of thought1 of     
their poetry1 who knows both4  ,the     
utility of physical science is1 in a    
measure1 only a collateral product of   
that flight of the intellect which      
produced science4 ,no one1 however1     
should underrate the utility of science 
who has shared in the realisation by    
modern industrial art of the ,oriental  
world of fables1 much less one upon whom
 those treasures have been poured1 as it
 were1 from the fourth dimension1       
without his aid or understanding4  ,nor 
may we believe that science is useful   
only to the practical man4 ,its         
influence permeates all our affairs1 our
 whole life2 everywhere its ideas are   
decisive4 ,how differently does the     

jurist1 the legislator1 or the political
 economist think1 who knows1 for        
example1 that a square mile of the most 
fertile soil can support with the solar 
heat annually consumed only a definite  
number of human beings1 which no art or 
science can increase4 ,many economical  
theories1 which open new air-paths of   
progress1 air-paths in the literal sense
 of the word1 would be made impossible  
by such knowledge4         99       99  
99       99       99  ,the eulogists of 
classical education love to emphasise   
the cultivation of taste which comes    
from employment with the ancient models4
 ,i candidly confess that there is      
something absolutely revolting in this  
to me4 ,to form the taste1 then1 our    
youths must sacrifice ten years of their
 life6 ,luxury takes precedence over    
necessity4 ,have the future generations1
 in the face of the difficult problems1 
the great social questions1 which they  
must meet1 and that with strengthened   
mind and heart1 no more important duties

 to fulfil than these8  ,but let us     
assume that this end were desirable4    
,can taste be formed by rules and       
precepts8 ,do not ideals of beauty      
change8 ,is it not a stupendous         
absurdity to force one's self           
artificially to admire things which1    
with all their historical interest1 with
 all their beauty in individual points1 
are for the most part foreign to the    
rest of our thoughts and feelings1      
provided we have such of our own4 ,a    
nation that is truly such1 has its own  
taste and will not go to others for it4 
,and every individual perfect man has   
his own taste4#aba  ,and what1 after    
all1 does this cultivation of taste     
consist in8 ,in the acquisition of the  
personal literary style of a few select 
authors6 ,what should we think of a     
people that would force its youth a     
thousand years from now1 by years of    
practice1 to master the tortuous or     
bombastic style of some successful      
lawyer or politician of to-day8 ,should 

we not justly accuse them of a woful    
lack of taste8  ,the evil effects of    
this imagined cultivation of the taste  
find expression often enough4 ,the young
 savant who regards the composition of a
 scientific essay as a rhetorical       
exercise instead of a simple and        
unadorned presentation of the facts and 
the truth1 still sits unconsciously on  
the school-bench1 and still unwittingly 
represents the point of view of the     
,romans1 by whom the elaboration of     
speeches was regarded as a serious      
scientific 767 employment4         99   
99       99       99       99  ,far be  
it from me to underrate the value of the
 development of the instinct of speech  
and of the increased comprehension of   
our own language which comes from       
philological studies4 ,by the study of a
 foreign language1 especially of one    
which differs widely from ours1 the     
signs and forms of words are first      
clearly distinguished from the thoughts 
which they express4 ,words of the       

closest possible correspondence in      
different languages never coincide      
absolutely with the ideas they stand    
for1 but place in relief slightly       
different aspects of the same thing1 and
 by the study of language the attention 
is directed to these shades of          
difference4 ,but it would be far from   
admissible to contend that the study of 
,latin and ,greek is the most fruitful  
and natural1 let alone the only1 means  
of attaining this end4 ,any one who will
 give himself the pleasure of a few     
hours' companionship with a ,chinese    
grammar2 who will seek to make clear to 
himself the mode of speech and thought  
of a people who never advanced as far as
 the analysis of articulate sounds1 but 
stopped at the analysis of syllables1 to
 whom our alphabetical characters1      
therefore1 are an inexplicable puzzle1  
and who express all their rich and      
profound thoughts by means of a few     
syllables with variable emphasis and    
position1--such a person1 perhaps1 will 

acquire new1 and extremely elucidative  
ideas upon the relation of language and 
thought4 ,but should our children1      
therefore1 study ,chinese8 ,certainly   
not4 ,no more1 then1 should they be     
burdened with ,latin1 at least in the   
measure they are4  ,it is a beautiful   
achievement to reproduce a ,latin       
thought in a modern language with the   
maximum fidelity of meaning and         
expression--for the translator4         
,moreover1 we shall be very grateful to 
the translator for his performance4 ,but
 to demand this feat of every educated  
man1 without consideration of the       
sacrifice of time and labor which it    
entails1 is unreasonable4 ,and for this 
very reason1 as classical teachers      
admit1 that ideal is never perfectly    
attained1 except in rare cases with     
scholars possessed of special talents   
and great industry4 ,without slurring1  
therefore1 the high importance of the   
study of the ancient languages as a     
profession1 we may yet feel sure that   

the instinct for speech which is part of
 every liberal education can1 and must1 
be acquired in a different way4 ,should 
we1 indeed1 be forever lost if the      
,greeks had not lived before us8  ,the  
fact is1 we must carry our demands      
further than the representatives of     
classical philology4 ,we must ask of    
every educated man a fair scientific    
conception of the nature and value of   
language1 of the formation of language1 
of the alteration of the meaning of     
roots1 of the degeneration of fixed     
forms of speech to grammatical forms1 in
 brief1 of all the main results of      
modern comparative philology4 ,we should
 judge that this were attainable by a   
careful study of our mother tongue and  
of the languages next allied to it1 and 
subsequently of the more ancient tongues
 from which the former are derived4 ,if 
any one object that this is too         
difficult and entails too much labor1 ,i
 should advise such a person to place   
side by side an ,english1 a ,dutch1 a   

,danish1 a ,swedish1 and a ,german      
,bible1 and to compare a few lines of   
them2 he will be amazed at the multitude
 of suggestions that offer              
themselves4#abb ,in fact1 ,i believe    
that a really progressive1 fruitful1    
rational1 and instructive study of      
languages can be conducted only on this 
plan4 ,many of my audience will         
remember1 perhaps1 the bright and       
encouraging effect1 like that of a ray  
of sunlight on a gloomy day1 which the  
meagre and furtive remarks on           
comparative philology in ,curtius's     
,greek grammar wrought in that barren   
and lifeless desert of verbal quibbles4 
99       99       99       99       99  
,the principal result obtained by the   
present method of studying the ancient  
languages is that which comes from the  
student's employment with their         
complicated grammars4 ,it consists in   
the sharpening of the attention and in  
the exercise of the judgment by the     
practice of subsuming special cases     

under general rules1 and of             
distinguishing between different cases4 
,obviously1 the same result can be      
reached by many other methods2 for      
example1 by difficult games of cards4   
,every science1 the mathematics and the 
physical sciences included1 accomplish  
as much1 if not more1 in this           
disciplining of the judgment4 ,in       
addition1 the matter treated by those   
sciences has a much higher intrinsic    
interest for young people1 and so       
engages spontaneously their attention2  
while on the other hand they are        
elucidative and useful in other         
directions in which grammar can         
accomplish nothing4  ,who cares1 so far 
as the matter of it is concerned1       
whether we say hominum or hominorum in  
the genitive plural1 interesting as the 
fact may be for the philologist8 ,and   
who would dispute that the intellectual 
need of causal insight is awakened not  
by grammar but by the natural sciences8 
,it is not our intention1 therefore1 to 

gainsay in the least the good influence 
which the study of ,latin and ,greek    
grammar also exercises on the sharpening
 of the judgment4 ,in so far as the     
study of words as such must greatly     
promote lucidity and accuracy of        
expression1 in so far as ,latin and     
,greek are not yet wholly indispensable 
to many branches of knowledge1 we       
willingly concede to them a place in our
 schools1 but would demand that the     
disproportionate amount of time allotted
 to them1 wrongly withdrawn from other  
useful studies1 should be considerably  
curtailed4 ,that in the end ,latin and  
,greek will not be employed as the      
universal means of education1 we are    
fully convinced4 ,they will be relegated
 to the closet of the scholar or        
professional philologist1 and gradually 
make way for the modern languages and   
the modern science of language4  ,long  
ago ,locke reduced to their proper      
limits the exaggerated notions which    
obtained of the close connexion of      

thought and speech1 of logic and        
grammar1 and recent investigators have  
established on still surer foundations  
his views4 ,how little a complicated    
grammar is necessary for expressing     
delicate shades of thought is           
demonstrated by the ,italians and       
,french1 who1 although they have almost 
totally discarded the grammatical       
redundancies of the ,romans1 are yet not
 surpassed by the latter in accuracy of 
thought1 and whose poetical1 but        
especially whose scientific literature1 
as no one will dispute1 can bear        
favorable comparison with the ,roman4   
,reviewing again the arguments advanced 
in favor of the study of the ancient    
languages1 we are obliged to say that in
 the main and as applied to the present1
 they are wholly devoid of force4 ,in so
 far as the aims which this study       
theoretically pursues are still worthy  
of attainment1 they appear to us as     
altogether too narrow1 and are surpassed
 in this only by the means employed4 ,as

 almost the sole1 indisputable result of
 this study we must count the increase  
of the student's skill and precision in 
expression4 ,one inclined to be         
uncharitable might say that our         
gymnasiums and classical academies turn 
out men who can speak and write1 but1   
unfortunately1 have little to write or  
speak about4 ,of that broad1 liberal    
view1 of that famed universal culture1  
which the classical curriculum is       
supposed to yield1 serious words need   
not be lost4 ,this culture might1       
perhaps1 more properly be termed the    
contracted or lopsided culture4         
99       99       99       99       99  
,while considering the study of         
languages we threw a few side glances at
 mathematics and the natural sciences4  
,let us now inquire whether these1 as   
branches of study1 cannot accomplish    
much that is to be attained in no other 
way4 ,i shall meet with no contradiction
 when ,i say that without at least an   
elementary mathematical and scientific  

education a man remains a total stranger
 in the world in which he lives1 a      
stranger in the civilisation of the time
 that bears him4 ,whatever he meets in  
nature1 or in the industrial world1     
either does not appeal to him at all1   
from his having neither eye nor ear for 
it1 or it speaks to him in a totally    
unintelligible language4  ,a real       
understanding of the world and its      
civilisation1 however1 is not the only  
result of the study of mathematics and  
the physical sciences4 ,much more       
essential for the preparatory school is 
the formal cultivation which comes from 
these studies1 the strengthening of the 
reason and the judgment1 the exercise of
 the imagination4 ,mathematics1 physics1
 chemistry1 and the so-called           
descriptive sciences are so much alike  
in this respect1 that1 apart from a few 
points1 we need not separate them in our
 discussion4  ,logical sequence and     
continuity of ideas1 so necessary for   
fruitful thought1 are par excellence the

 results of mathematics2 the ability to 
follow facts with thoughts1 that is1 to 
observe or collect experiences1 is      
chiefly developed by the natural        
sciences4 ,whether we notice that the   
sides and the angles of a triangle are  
connected in a definite way1 that an    
equilateral triangle possesses certain  
definite properties of symmetry1 or     
whether we notice the deflexion of a    
magnetic needle by an electric current1 
the dissolution of zinc in diluted      
sulphuric acid1 whether we remark that  
the wings of a butterfly are slightly   
colored on the under1 and the fore-wings
 of the moth on the upper1 surface3     
indiscriminately here we proceed from   
observations1 from individual acts of   
immediate intuitive knowledge4 ,the     
field of observation is more restricted 
and lies closer at hand in mathematics2 
it is more varied and broader but more  
difficult to compass in the natural     
sciences4 ,the essential thing1 however1
 is for the student to learn to make    

observations in all these fields4 ,the  
philosophical question whether our acts 
of knowledge in mathematics are of a    
special kind is here of no importance   
for us4 ,it is true1 of course1 that the
 observation can be practised by        
languages also4 ,but no one1 surely1    
will deny1 that the concrete1 living    
pictures presented in the fields just   
mentioned possess different and more    
powerful attractions for the mind of the
 youth than the abstract and hazy       
figures which language offers1 and on   
which the attention is certainly not so 
spontaneously bestowed1 nor with such   
good results4#abc  ,observation having  
revealed the different properties of a  
given geometrical or physical object1 it
 is discovered that in many cases these 
properties depend in some way upon one  
another4 ,this interdependence of       
properties 7say that of equal sides and 
equal angles at the base of a triangle1 
the relation of pressure to motion17 is 
nowhere so distinctly marked1 nowhere is

 the necessity and permanency of the    
interdependence so plainly noticeable1  
as in the fields mentioned4 ,hence the  
continuity and logical consequence of   
the ideas which we acquire in those     
fields4 ,the relative simplicity and    
perspicuity of geometrical and physical 
relations supply here the conditions of 
natural and easy progress4 ,relations of
 equal simplicity are not met with in   
the fields which the study of language  
opens up4 ,many of you1 doubtless1 have 
often wondered at the little respect for
 the notions of cause and effect and    
their connexion that is sometimes found 
among professed representatives of the  
classical studies4 ,the explanation is  
probably to be sought in the fact that  
the analogous relation of motive and    
action familiar to them from their      
studies1 presents nothing like the clear
 simplicity and determinateness that the
 relation of cause and effect does4     
,that perfect mental grasp of all       
possible cases1 that economical order   

and organic union of the thoughts which 
comes from it1 which has grown for every
 one who has ever tasted it a permanent 
need which he seeks to satisfy in every 
new province1 can be developed only by  
employment with the relative simplicity 
of mathematical and scientific          
investigations4  ,when a set of facts   
comes into apparent conflict with       
another set of facts1 and a problem is  
presented1 its solution consists        
ordinarily in a more refined distinction
 or in a more extended view of the      
facts1 as may be aptly illustrated by   
,newton's solution of the problem of    
dispersion4 ,when a new mathematical or 
scientific fact is demonstrated1 or     
explained1 such demonstration also rests
 simply upon showing the connexion of   
the new fact with the facts already     
known2 for example1 that the radius of a
 circle can be laid off as chord exactly
 six times in the circle is explained or
 proved by dividing the regular hexagon 
inscribed in the circle into equilateral

 triangles4 ,that the quantity of heat  
developed in a second in a wire         
conveying an electric current is        
quadrupled on the doubling of the       
strength of the current1 we explain from
 the doubling of the fall of the        
potential due to the doubling of the    
current's intensity1 as also from the   
doubling of the quantity flowing        
through1 in a word1 from the quadrupling
 of the work done4 ,in point of         
principle1 explanation and direct proof 
do not differ much4  ,he who solves     
scientifically a geometrical1 physical1 
or technical problem1 easily remarks    
that his procedure is a methodical      
mental quest1 rendered possible by the  
economical order of the province--a     
simplified purposeful quest as          
contrasted with unmethodical1           
unscientific guess-work4 ,the geometer1 
for example1 who has to construct a     
circle touching two given straight      
lines1 casts his eye over the relations 
of symmetry of the desired construction1

 and seeks the centre of his circle     
solely in the line of symmetry of the   
two straight lines4 ,the person who     
wants a triangle of which two angles and
 the sum of the sides are given1 grasps 
in his mind the determinateness of the  
form of this triangle and restricts his 
search for it to a certain group of     
triangles of the same form4 ,under very 
different circumstances1 therefore1 the 
simplicity1 the intellectual            
perviousness1 of the subject-matter of  
mathematics and natural science is felt1
 and promotes both the discipline and   
the self-confidence of the reason4      
,unquestionably1 much more will be      
attained by instruction in the          
mathematics and the natural sciences    
than now is1 when more natural methods  
are adopted4 ,one point of importance   
here is that young students should not  
be spoiled by premature abstraction1 but
 should be made acquainted with their   
material from living pictures of it     
before they are made to work with it by 

purely ratiocinative methods4 ,a good   
stock of geometrical experience could be
 obtained1 for example1 from geometrical
 drawing and from the practical         
construction of models4 ,in the place of
 the unfruitful method of ,euclid1 which
 is only fit for special1 restricted    
uses1 a broader and more conscious      
method must be adopted1 as ,hankel has  
pointed out4#abd ,then1 if1 on reviewing
 geometry1 and after it presents no     
substantial difficulties1 the more      
general points of view1 the principles  
of scientific method are placed in      
relief and brought to consciousness1 as 
,von ,nagel1#abe ,j4 ,k4 ,becker1#abf   
,mann1#abg and others have well done1   
fruitful results will be surely         
attained4 ,in the same way1 the         
subject-matter of the natural sciences  
should be made familiar by pictures and 
experiment before a profounder and      
reasoned grasp of these subjects is     
attempted4 ,here the emphasis of the    
more general points of view is to be    

postponed4  ,before my present audience 
it would be superfluous for me to       
contend further that mathematics and    
natural science are justified           
constituents of a sound education1--a   
claim that even philologists1 after some
 resistance1 have conceded4 ,here ,i may
 count upon assent when ,i say that     
mathematics and the natural sciences    
pursued alone as means of instruction   
yield a richer education in matter and  
form1 a more general education1 an      
education better adapted to the needs   
and spirit of the time1--than the       
philological branches pursued alone     
would yield4  ,but how shall this idea  
be realised in the curricula of our     
intermediate educational institutions8  
,it is unquestionable in my mind that   
the ,german ,realschulen and            
,realgymnasien1 where the exclusive     
classical course is for the most part   
replaced by mathematics1 science1 and   
modern languages1 give the average man a
 more timely education than the         

gymnasium proper1 although they are not 
yet regarded as fit preparatory schools 
for future theologians and professional 
philologists4 ,the ,german gymnasiums   
are too one-sided4 ,with these the first
 changes are to be made2 of these alone 
we shall speak here4 ,possibly a single 
preparatory school1 suitably planned1   
might serve all purposes4  ,shall we1   
then1 in our gymnasiums fill out the    
hours of study which stand at our       
disposal1 or are still to be wrested    
from the classicists1 with as great and 
as varied a quantity of mathematical and
 scientific matter as possible8 ,expect 
no such proposition from me4 ,no one    
will suggest such a course who has      
himself been actively engaged in        
scientific thought4 ,thoughts can be    
awakened and fructified as a field is   
fructified by sunshine and rain4 ,but   
thoughts cannot be juggled out and      
worried out by heaping up materials and 
the hours of instruction1 nor by any    
sort of precepts3 they must grow        

naturally of their own free accord4     
,furthermore1 thoughts cannot be        
accumulated beyond a certain limit in a 
single head1 any more than the produce  
of a field can be increased beyond      
certain limits4  ,i believe that the    
amount of matter necessary for a useful 
education1 such as should be offered to 
all the pupils of a preparatory school1 
is very small4 ,if ,i had the requisite 
influence1 ,i should1 in all composure1 
and fully convinced that ,i was doing   
what was best1 first greatly curtail in 
the lower classes the amount of matter  
in both the classical and the scientific
 courses2 ,i should cut down            
considerably the number of the school   
hours and the work done outside the     
school4 ,i am not with many teachers of 
opinion that ten hours work a day for a 
child is not too much4 ,i am convinced  
that the mature men who offer this      
advice so lightly are themselves unable 
to give their attention successfully for
 as long a time to any subject that is  

new to them1 7for example1 to elementary
 mathematics or physics17 and ,i would  
ask every one who thinks the contrary to
 make the experiment upon himself4      
,learning and teaching are not routine  
office-work that can be kept up         
mechanically for long periods4 ,but even
 such work tires in the end4 ,if our    
young men are not to enter the          
universities with blunted and           
impoverished minds1 if they are not to  
leave in the preparatory schools their  
vital energy1 which they should there   
gather1 great changes must be made4     
,waiving the injurious effects of       
overwork upon the body1 the consequences
 of it for the mind seem to me          
positively dreadful4  ,i know of nothing
 more terrible than the poor creatures  
who have learned too much4 ,instead of  
that sound powerful judgment which would
 probably have grown up if they had     
learned nothing1 their thoughts creep   
timidly and hypnotically after words1   
principles1 and formul1 constantly by   

the same paths4 ,what they have acquired
 is a spider's web of thoughts too weak 
to furnish sure supports1 but           
complicated enough to produce confusion4
  ,but how shall better methods of      
mathematical and scientific education be
 combined with the decrease of the      
subject-matter of instruction8 ,i think1
 by abandoning systematic instruction   
altogether1 at least in so far as that  
is required of all young pupils4 ,i see 
no necessity whatever that the graduates
 of our high schools and preparatory    
schools should be little philologists1  
and at the same time little             
mathematicians1 physicists1 and         
botanists2 in fact1 ,i do not see the   
possibility of such a result4 ,i see in 
the endeavor to attain this result1 in  
which every instructor seeks for his own
 branch a place apart from the others1  
the main mistake of our whole system4 ,i
 should be satisfied if every young     
student could come into living contact  
with and pursue to their ultimate       

logical consequences merely a few       
mathematical or scientific discoveries4 
,such instruction would be mainly and   
naturally associated with selections    
from the great scientific classics4 ,a  
few powerful and lucid ideas could thus 
be made to take root in the mind and    
receive thorough elaboration4 ,this     
accomplished1 our youth would make a    
different showing from what they do     
to-day4#abh  ,what need is there1 for   
example1 of burdening the head of a     
young student with all the details of   
botany8 ,the student who has botanised  
under the guidance of a teacher finds on
 all hands1 not indifferent things1 but 
known or unknown things1 by which he is 
stimulated1 and his gain made permanent4
 ,i express here1 not my own1 but the   
opinion of a friend1 a practical        
teacher4 ,again1 it is not at all       
necessary that all the matter that is   
offered in the schools should be        
learned4 ,the best that we have learned1
 that which has remained with us for    

life1 outlived the test of examination4 
,how can the mind thrive when matter is 
heaped on matter1 and new materials     
piled constantly on old1 undigested     
materials8 ,the question here is not so 
much that of the accumulation of        
positive knowledge as of intellectual   
discipline4 ,it seems also unnecessary  
that all branches should be treated at  
school1 and that exactly the same       
studies should be pursued in all        
schools4 ,a single philological1 a      
single historical1 a single             
mathematical1 a single scientific       
branch1 pursued as common subjects of   
instruction for all pupils1 are         
sufficient to accomplish all that is    
necessary for the intellectual          
development4 ,on the other hand1 a      
wholesome mutual stimulus would be      
produced by this greater variety in the 
positive culture of men4 ,uniforms are  
excellent for soldiers1 but they will   
not fit heads4 ,charles ,v4 learned     
this1 and it should never be forgotten4 

,on the contrary1 teachers and pupils   
both need considerable latitude1 if they
 are to yield good results4  ,with ,john
 ,karl ,becker ,i am of the opinion that
 the utility and amount for individuals 
of every study should be precisely      
determined4 ,all that exceeds this      
amount should be unconditionally        
banished from the lower classes4 ,with  
respect to mathematics1 ,becker1#abi in 
my judgment1 has admirably solved this  
question4  ,with respect to the upper   
classes the demand assumes a different  
form4 ,here also the amount of matter   
obligatory on all pupils ought not to   
exceed a certain limit4 ,but in the     
great mass of knowledge that a young man
 must acquire to-day for his profession 
it is no longer just that ten years of  
his youth should be wasted with mere    
preludes4 ,the upper classes should     
supply a truly useful preparation for   
the professions1 and should not be      
modelled upon the wants merely of future
 lawyers1 ministers1 and philologists4  

,again1 it would be both foolish and    
impossible to attempt to prepare the    
same person properly for all the        
different professions4 ,in such case the
 function of the schools would be1 as   
,lichtenberg feared1 simply to select   
the persons best fitted for being       
drilled1 whilst precisely the finest    
special talents1 which do not submit to 
indiscriminate discipline1 would be     
excluded from the contest4 ,hence1 a    
certain amount of liberty in the choice 
of studies must be introduced in the    
upper classes1 by means of which it will
 be free for every one who is clear     
about the choice of his profession to   
devote his chief attention either to the
 study of the philologico-historical or 
to that of the mathematico-scientific   
branches4 ,then the matter now treated  
could be retained1 and in some branches1
 perhaps1 judiciously extended1#acj     
without burdening the scholar with many 
branches or increasing the number of the
 hours of study4 ,with more homogeneous 

work the student's capacity for work    
increases1 one part of his labor        
supporting the other instead of         
obstructing it4 ,if1 however1 a young   
man should subsequently choose a        
different profession1 then it is his    
business to make up what he has lost4   
,no harm certainly will come to society 
from this change1 nor could it be       
regarded as a misfortune if philologists
 and lawyers with mathematical          
educations or physical scientists with  
classical educations should now and then
 appear4         99       99       99   
99       99  ,the view is now           
wide-spread that a ,latin and ,greek    
education no longer meets the general   
wants of the times1 that a more         
opportune1 a more liberal education     
exists4 ,the phrase1 a liberal          
education1 has been greatly misused4 ,a 
truly liberal education is              
unquestionably very rare4 ,the schools  
can hardly offer such2 at best they can 
only bring home to the student the      

necessity of it4 ,it is1 then1 his      
business to acquire1 as best he can1 a  
more or less liberal education4 ,it     
would be very difficult1 too1 at any one
 time to give a definition of a liberal 
education which would satisfy every one1
 still more difficult to give one which 
would hold good for a hundred years4    
,the educational ideal1 in fact1 varies 
much4 ,to one1 a knowledge of classical 
antiquity appears not too dearly bought 
with early death4 ,we have no objection 
to this person1 or to those who think   
like him1 pursuing their ideal after    
their own fashion4 ,but we may certainly
 protest strongly against the           
realisation of such ideals on our own   
children4 ,another1--,plato1 for        
example1--puts men ignorant of geometry 
on a level with animals4#aca ,if such   
narrow views had the magical powers of  
the sorceress ,circe1 many a man who    
perhaps justly thought himself well     
educated would become conscious of a not
 very flattering transformation of      

himself4 ,let us seek1 therefore1 in our
 educational system to meet the wants of
 the present1 and not establish         
prejudices for the future4  ,but how    
does it come1 we must ask1 that         
institutions so antiquated as the       
,german gymnasiums could subsist so long
 in opposition to public opinion8 ,the  
answer is simple4 ,the schools were     
first organised by the ,church2 since   
the ,reformation they have been in the  
hands of the ,state4 ,on so large a     
scale1 the plan presents many           
advantages4 ,means can be placed at the 
disposal of education such as no private
 source1 at least in ,europe1 could     
furnish4 ,work can be conducted upon the
 same plan in many schools1 and so      
experiments made of extensive scope     
which would be otherwise impossible4 ,a 
single man with influence and ideas can 
under such circumstances do great things
 for the promotion of education4  ,but  
the matter has also its reverse aspect4 
,the party in power works for its own   

interests1 uses the schools for its     
special purposes4 ,educational          
competition is excluded1 for all        
successful attempts at improvement are  
impossible unless undertaken or         
permitted by the ,state4 ,by the        
uniformity of the people's education1 a 
prejudice once in vogue is permanently  
established4 ,the highest intelligences1
 the strongest wills cannot overthrow it
 suddenly4 ,in fact1 as everything is   
adapted to the view in question1 a      
sudden change would be physically       
impossible4 ,the two classes which      
virtually hold the reins of power in the
 ,state1 the jurists and theologians1   
know only the one-sided1 predominantly  
classical culture which they have       
acquired in the ,state schools1 and     
would have this culture alone valued4   
,others accept this opinion from        
credulity2 others1 underestimating their
 true worth for society1 bow before the 
power of the prevalent opinion2 others1 
again1 affect the opinion of the ruling 

classes even against their better       
judgment1 so as to abide on the same    
plane of respect with the latter4 ,i    
will make no charges1 but ,i must       
confess that the deportment of medical  
men with respect to the question of the 
qualification of graduates of your      
,realschulen has frequently made that   
impression upon me4 ,let us remember1   
finally1 that an influential statesman1 
even within the boundaries which the law
 and public opinion set him1 can do     
serious harm to the cause of education  
by considering his own one-sided views  
infallible1 and in enforcing them       
recklessly and inconsiderately--which   
not only can happen1 but has1           
repeatedly1 happened4#acb ,the monopoly 
of education by the ,state#acc thus     
assumes in our eyes a somewhat different
 aspect4 ,and to revert to the question 
above asked1 there is not the slightest 
doubt that the ,german gymnasiums in    
their present form would have ceased to 
exist long ago if the ,state had not    

supported them4  ,all this must be      
changed4 ,but the change will not be    
made of itself1 nor without our         
energetic interference1 and it will be  
made slowly4 ,but the path is marked out
 for us1 the will of the people must    
acquire and exert upon our school       
legislation a greater and more powerful 
influence4 ,furthermore1 the questions  
at issue must be publicly and candidly  
discussed that the views of the people  
may be clarified4 ,all who feel the     
insufficiency of the existing rgime must
 combine into a powerful organisation   
that their views may acquire            
impressiveness and the opinions of the  
individual not die away unheard4  ,i    
recently read1 gentlemen1 in an         
excellent book of travels1 that the     
,chinese speak with unwillingness of    
politics4 ,conversations of this sort   
are usually cut short with the remark   
that they may bother about such things  
whose business it is and who are paid   
for it4 ,now it seems to me that it is  

not only the business of the ,state1 but
 a very serious concern of all of us1   
how our children shall be educated in   
the public schools at our cost4         
,,footnotes3    ,footnote #aac3 ,an     
address delivered before the ,congress  
of ,delegates   of the ,german          
,realschulmnnerverein1 at ,dortmund1    
,april #af1 #ahhf4   ,the full title of 
the address reads3 ,on the ,relative    
,educational   ,value of the ,classics  
and the ,mathematico-,physical ,sciences
 in   ,colleges and ,high ,schools4     
,although substantially contained in an 
address which ,i was to have   made at  
the meeting of ,natural ,scientists at  
,salzburg in #ahha   7deferred on       
account of the ,paris ,exposition71 and 
in the   ,introduction to a course of   
lectures on ,physical ,instruction in   
,preparatory ,schools1 which ,i         
delivered in #ahhc1 the invitation of   
the ,german ,realschulmnnerverein       
afforded me the first opportunity   of  
putting my views upon this subject      

before a large circle of   readers4     
,owing to the place and circumstances of
 delivery1 my   remarks apply of course1
 primarily1 only to ,german schools1    
but1   with slight modifications1 made  
in this translation1 are not without    
force for the institutions of other     
countries4 ,in giving here   expression 
to a strong personal conviction formed  
long ago1 it is a   matter of deep      
satisfaction to me to find that they    
agree in many   points with the views   
recently advanced in independent form by
   ,paulsen 7,geschichte des gelehrten  
,unterrichts1 ,leipsic1 #ahhe7 and      
,frary 7,la question du latin1 ,paris1  
,cerf1 #ahhe74 ,it is not my   desire   
nor effort here to say much that is new1
 but merely to   contribute my mite     
towards bringing about the inevitable   
revolution   now preparing in the world 
of elementary instruction4 ,in the      
opinion   of experienced educationists  
the first result of that revolution     
will be to make ,greek and mathematics  

alternately optional subjects   in the  
higher classes of the ,german ,gymnasium
 and in the   corresponding institutions
 of other countries1 as has been done in
   the splendid system of instruction in
 ,denmark4 ,the gap between the         
,german classical ,gymnasium and the    
,german ,realgymnasium1 or between      
classical and scientific schools        
generally1 can thus be bridged   over1  
and the remaining inevitable            
transformations will then be            
accomplished in relative peace and      
quiet4 7,prague1 ,may1 #ahhf47          
,footnote #aad3 ,maupertuis1 ,oeuvres1  
,dresden1 #ageb1 p4 #cci4    ,footnote  
#aae3 ,f4 ,paulsen1 ,geschichte des     
gelehrten ,unterrichts1   ,leipsic1     
#ahhe4    ,footnote #aaf3 ,there is a   
peculiar irony of fate in the fact that 
while ,leibnitz was casting about for a 
new vehicle of universal   linguistic   
intercourse1 the ,latin language which  
still subserved   this purpose the best 
of all1 was dropping more and more out  

of use1   and that ,leibnitz himself    
contributed not the least to this       
result4    ,footnote #aag3 ,as a rule1  
the human brain is too much1 and        
wrongly1   burdened with things which   
might be more conveniently and          
accurately   preserved in books where   
they could be found at a moment's       
notice4   ,in a recent letter to me from
 ,dsseldorf1 ,judge ,hartwich writes3   
,a host of words exist which are out and
 out ,latin or ,greek1 yet are          
employed with perfect correctness by    
people of good education who   never had
 the good luck to be taught the ancient 
languages4 ,for   example1 words like   
'dynasty4' 444 ,the child learns such   
words as   parts of the common stock of 
speech1 or even as parts of his         
mother-tongue1 just as he does the words
 'father1' 'mother1'   'bread1' 'milk4' 
,does the ordinary mortal know the      
etymology of   these ,saxon words8 ,did 
it not require the almost incredible    
industry   of the ,grimms and other     

,teutonic philologists to throw the     
merest   glimmerings of light upon the  
origin and growth of our own            
mother-tongue8 ,besides1 do not         
thousands of people of so-called        
classical education use every moment    
hosts of words of foreign   origin whose
 derivation they do not know8 ,very few 
of them think it   worth while to look  
up such words in the dictionaries1      
although they   love to maintain that   
people should study the ancient         
languages for   the sake of etymology   
alone4    ,footnote #aah3 ,standing     
remote from the legal profession ,i     
should   not have ventured to declare   
that the study of ,greek was not        
necessary for the jurists2 yet this view
 was taken in the debate   that followed
 this lecture by professional jurists of
 high standing4   ,according to this    
opinion1 the preparatory education      
obtained in the   ,german ,realgymnasium
 would also be sufficient for the future
 jurists   and insufficient only for    

theologians and philologists4 ,in       
,england   and ,america not only is     
,greek not necessary1 but the law-,latin
 is so   peculiar that even persons of  
good classical education cannot         
understand it4--,tr4    ,footnote #aai3 
,in emphasising here the weak sides of  
the writings of   ,plato and ,aristotle1
 forced on my attention while reading   
them in   ,german translations1 ,i1 of  
course1 have no intention of underrating
   the great merits and the high        
historical importance of these two      
men4 ,their importance must not be      
measured by the fact that our           
speculative philosophy still moves to a 
great extent in their paths   of        
thought4 ,the more probable conclusion  
is that this branch has   made very     
little progress in the last two thousand
 years4 ,natural   science also was     
implicated for centuries in the meshes  
of the   ,aristotelian thought1 and owes
 its rise mainly to having thrown off   
those fetters4    ,footnote #abj3 ,i    

would not for a moment contend that we  
derive   exactly the same profit from   
reading a ,greek author in a translation
   as from reading him in the original2 
but the difference1 the excess   of gain
 in the second case1 appears to me1 and 
probably will to most   men who are not 
professional philologists1 to be too    
dearly bought   with the expenditure of 
eight years of valuable time4           
,footnote #aba3 ,the temptation1 ,judge 
,hartwich writes1 to regard   the       
'taste' of the ancients as so lofty and 
unsurpassable appears to   me to have   
its chief origin in the fact that the   
ancients were   unexcelled in the       
representation of the nude4 ,first1 by  
their   unremitting care of the human   
body they produced splendid models2     
and secondly1 in their gymnasiums and in
 their athletic games they   had these  
models constantly before their eyes4 ,no
 wonder1 then1 that   their statues     
still excite our admiration6 ,for the   
form1 the ideal   of the human body has 

not changed in the course of the        
centuries4   ,but with intellectual     
matters it is totally different2 they   
change   from century to century1 nay1  
from decennium to decennium4 ,it is     
very natural now1 that people should    
unconsciously apply what is   thus so   
easily seen1 namely1 the works of       
sculpture1 as a universal   criterion of
 the highly developed taste of the      
ancients--a fallacy   against which     
people cannot1 in my judgment1 be too   
strongly   warned4    ,footnote #abb3   
,english3 ,in the beginning ,god created
 the heaven and   the earth4 ,and the   
earth was without form and void2 and    
darkness was   upon the face of the     
deep4 ,and the spirit of ,god moved upon
 the face   of the waters4--,dutch3 ,in 
het begin schiep ,god den hemel en de   
aarde4 ,de aarde nu was woest en ledig1 
en duisternis was op den   afgrond2 en  
de ,geest ,gods zwefde op de            
wateren4--,danish3 ,i   ,begyndelsen    
skabte ,gud ,himmelen og ,jorden4 ,og   

,jorden var ode og tom1   og der var    
morkt ovenover ,afgrunden1 og ,guds     
,aand svoevede ovenover                 
,vandene4--,swedish3 ,i begynnelsen     
skapade ,gud ,himmel och ,jord4 ,och    
,jorden war de och tom1 och mrker war p 
djupet1 och ,gods ,ande   swfde fwer    
wattnet4--,german3 ,am ,anfang schuf    
,gott ,himmel und   ,erde4 ,und die     
,erde war wst und leer1 und es war      
finster auf der   ,tiefe2 und der ,geist
 ,gottes schwebte auf dem ,wasser4      
,footnote #abc3 ,compare ,herzen's      
excellent remarks1 ,de   l'enseignement 
secondaire dans la ,suisse romande1     
,lausanne1 #ahhf4    ,footnote #abd3    
,geschichte der ,mathematik1 ,leipsic1  
#ahgd4    ,footnote #abe3 ,geometrische 
,analyse1 ,ulm1 #ahhf4    ,footnote     
#abf3 ,in his text-books of elementary  
mathematics    ,footnote #abg3          
,abhandlungen aus dem ,gebiete der      
,mathematik1   ,wrzburg1 #ahhc4         
,footnote #abh3 ,my idea here is an     
appropriate selection of readings   from

 ,galileo1 ,huygens1 ,newton1 etc4 ,the 
choice is so easily made   that there   
can be no question of difficulties4 ,the
 contents would be   discussed with the 
students1 and the original experiments  
performed   with them4 ,those scholars  
alone should receive this instruction in
   the upper classes who did not look   
forward to systematical   instruction in
 the physical sciences4 ,i do not make  
this proposition   of reform here for   
the first time4 ,i have no doubt1       
moreover1 that   such radical changes   
will only be slowly introduced4         
,footnote #abi3 ,die ,mathematik als    
,lehrgegenstand des ,gymnasiums1        
,berlin1 #ahhc4    ,footnote #acj3      
,wrong as it is to burden future        
physicians and   scientists with ,greek 
for the sake of the theologians and     
philologists1 it would be just as wrong 
to compel theologians and               
philologists1 on account of the         
physicians1 to study such subjects   as 
analytical geometry4 ,moreover1 ,i      

cannot believe that ignorance of        
analytical geometry would be a serious  
hindrance to a physician that   was     
otherwise well versed in quantitative   
thought4 ,no special   advantage        
generally is observable in the graduates
 of the ,austrian   gymnasiums1 all of  
whom have studied analytical geometry4  
,refers to   an assertion of            
,dubois-,reymond4    ,footnote #aca3    
,compare ,m4 ,cantor1 ,geschichte der   
,mathematik1   ,leipsic1 #ahhj1 ,vol4   
,i4 p4 #aic4    ,footnote #acb3 ,compare
 ,paulsen1 l4 c41 pp4 #fjg1 #fhh4       
,footnote #acc3 ,it is to be hoped that 
the ,americans will jealously   guard   
their schools and universities against  
the influence of the   ,state4          
,,appendix4  ,i4  ,a ,,contribution ,,to
 ,,the ,,history ,,of ,,acoustics4#acd  
,while searching for papers by          
,amontons1 several volumes of the       
,memoirs of the ,paris ,academy for the 
first years of the eighteenth century1  
fell into my hands4 ,it is difficult to 

portray the delight which one           
experiences in running over the leaves  
of these volumes4 ,one sees as an actual
 spectator almost the rise of the most  
important discoveries and witnesses the 
progress of many fields of knowledge    
from almost total ignorance to          
relatively perfect clearness4  ,i       
propose to discuss here the fundamental 
researches of ,sauveur in ,acoustics4   
,it is astonishing how extraordinarily  
near ,sauveur was to the view which     
,helmholtz was the first to adopt in its
 full extent a hundred and fifty years  
later4  ,the ,histoire de l',acadmie for
 #agjj1 p4 #aca1 tells us that ,sauveur 
had succeeded in making music an object 
of scientific research1 and that he had 
invested the new science with the name  
of acoustics4 ,on five successive pages 
a number of discoveries are recorded    
which are more fully discussed in the   
volume for the year following4  ,sauveur
 regards the simplicity of the ratios   
obtaining between the rates of vibration

 of consonances as something universally
 known4#ace ,he is in hope1 by further  
research1 of determining the chief rules
 of musical composition and of fathoming
 the metaphysics of the agreeable1 the  
main law of which he asserts to be the  
union of simplicity with multiplicity4  
,precisely as ,euler#acf did a number of
 years later1 he regards a consonance as
 more perfect according as the ratio of 
its vibrational rates is expressed in   
smaller whole numbers1 because the      
smaller these whole numbers are the     
oftener the vibrations of the two tones 
coincide1 and hence the more readily    
they are apprehended4 ,as the limit of  
consonance1 he takes the ratio #e3f1    
although he does not conceal the fact   
that practice1 sharpened attention1     
habit1 taste1 and even prejudice play   
collateral rles in the matter1 and that 
consequently the question is not a      
purely scientific one4  ,sauveur's ideas
 took their development from his having 
instituted at all points more exact     

quantitative investigations than his    
predecessors4 ,he is first desirous of  
determining as the foundation of musical
 tuning a fixed note of one hundred     
vibrations which can be reproduced at   
any time2 the fixing of the notes of    
musical instruments by the common tuning
 pipes then in use with rates of        
vibration unknown1 appearing to him     
inadequate4 ,according to ,mersenne     
7,harmonie ,universelle1 #afcf71 a given
 cord seventeen feet long and weighted  
with eight pounds executes eight visible
 vibrations in a second4 ,by diminishing
 its length then in a given proportion  
we obtain a proportionately augmented   
rate of vibration4 ,but this procedure  
appears too uncertain to ,sauveur1 and  
he employs for his purpose the beats    
7battemens71 which were known to the    
organ-makers of his day1 and which he   
correctly explains as due to the        
alternate coincidence and               
non-coincidence of the same vibrational 
phases of differently pitched notes4#acg

 ,at every coincidence there is a       
swelling of the sound1 and hence the    
number of beats per second will be equal
 to the difference of the rates of      
vibration4 ,if we tune two of three     
organ-pipes to the remaining one in the 
ratio of the minor and major third1 the 
mutual ratio of the rates of vibration  
of the first two will be as #bd3 #be1   
that is to say1 for every #bd vibrations
 to the lower note there will be #be to 
the higher1 and one beat4 ,if the two   
pipes give together four beats in a     
second1 then the higher has the fixed   
tone of #ajj vibrations4 ,the open pipe 
in question will consequently be five   
feet in length4 ,we also determine by   
this procedure the absolute rates of    
vibration of all the other notes4  ,it  
follows at once that a pipe eight times 
as long or #dj feet in length will yield
 a vibrational rate of #ab1 which       
,sauveur ascribes to the lowest audible 
tone1 and further also that a pipe #fd  
times as small will execute #f1djj      

vibrations1 which ,sauveur took for the 
highest audible limit4 ,the author's    
delight at his successful enumeration of
 the imperceptible vibrations is        
unmistakably asserted here1 and it is   
justified when we reflect that to-day   
even ,sauveur's principle1 slightly     
modified1 constitutes the simplest and  
most delicate means we have for exactly 
determining rates of vibration4 ,far    
more important still1 however1 is a     
second observation which ,sauveur made  
while studying beats1 and to which we   
shall revert later4  ,strings whose     
lengths can be altered by movable       
bridges are much easier to handle than  
pipes in such investigations1 and it was
 natural that ,sauveur should soon      
resort to their use4  ,one of his       
bridges accidentally not having been    
brought into full and hard contact with 
the string1 and consequently only       
imperfectly impeding the vibrations1    
,sauveur discovered the harmonic        
overtones of the string1 at first by the

 unaided ear1 and concluded from this   
fact that the string was divided into   
aliquot parts4 ,the string when plucked1
 and when the bridge stood at the third 
division for example1 yielded the       
twelfth of its fundamental note4 ,at the
 suggestion of some academician#ach     
probably1 variously colored paper riders
 were placed at the nodes 7noeuds7 and  
ventral segments 7ventres71 and the     
division of the string due to the       
excitation of the overtones 7sons       
harmoniques7 belonging to its           
fundamental note 7son fondamental7 thus 
rendered visible4 ,for the clumsy bridge
 the more convenient feather or brush   
was soon substituted4 4 ,while engaged  
in these investigations ,sauveur also   
observed the sympathetic vibration of a 
string induced by the excitation of a   
second one in unison with it4 ,he also  
discovered that the overtone of a string
 can respond to another string tuned to 
its note4 ,he even went further and     
discovered that on exciting one string  

the overtone which it has in common with
 another1 differently pitched string can
 be produced on that other2 for example1
 on strings having for their vibrational
 ratio #c3d1 the fourth of the lower and
 the third of the higher may be made to 
respond4 ,it follows indisputably from  
this that the excited string yields     
overtones simultaneously with its       
fundamental tone4 ,previously to this   
,sauveur's attention had been drawn by  
other observers to the fact that the    
overtones of musical instruments can be 
picked out by attentive listening1      
particularly in the night4#aci ,he      
himself mentions the simultaneous       
sounding of the overtones and the       
fundamental tone4#adj ,that he did not  
give the proper consideration to this   
circumstance was1 as will afterwards be 
seen1 fatal to his theory4  ,while      
studying beats ,sauveur makes the remark
 that they are displeasing to the ear4  
,he held the beats were distinctly      
audible only when less than six occurred

 in a second4 ,larger numbers were not  
distinctly perceptible and gave rise    
accordingly to no disturbance4 ,he then 
attempts to reduce the difference       
between consonance and dissonance to a  
question of beats4 ,let us hear his own 
words4#ada       ,beats are unpleasing  
to the ear because of the unevenness of 
the      sound1 and it may be held with 
much plausibility that the reason       
why octaves are so pleasing is that we  
never hear their beats4#adb       ,in   
following out this idea1 we find that   
the chords whose beats we      cannot   
hear are precisely those which the      
musicians call      consonances and that
 those whose beats are heard are the    
dissonances1 and that when a chord is a 
dissonance in one octave      and a     
consonance in another1 it beats in the  
one and does not beat      in the other4
 ,consequently it is called an imperfect
 consonance4 ,it      is very easy by   
the principles of ,m4 ,sauveur1 here    
established1 to      ascertain what     

chords beat and in what octaves1 above  
or below the      fixed note4 ,if this  
hypothesis be correct1 it will disclose 
the      true source of the rules of    
composition1 hitherto unknown to        
science1 and given over almost entirely 
to judgment by the ear4      ,these     
sorts of natural judgment1 marvellous   
though they may      sometimes appear1  
are not so but have very real causes1   
the      knowledge of which belongs to  
science1 provided it can gain           
possession thereof4#adc  ,sauveur thus  
correctly discerns in beats the cause of
 the disturbance of consonance1 to which
 all disharmony is probably to be       
referred4 ,it will be seen1 however1    
that according to his view all distant  
intervals must necessarily be           
consonances and all near intervals      
dissonances4 ,he also overlooks the     
absolute difference in point of         
principle between his old view1         
mentioned at the outset1 and his new    
view1 rather attempting to obliterate   

it4  ,r4 ,smith#add takes note of the   
theory of ,sauveur and calls attention  
to the first of the above-mentioned     
defects4 ,being himself essentially     
involved in the old view of ,sauveur1   
which is usually attributed to ,euler1  
he yet approaches in his criticism a    
brief step nearer to the modern theory1 
as appears from the following           
passage4#ade       ,the truth is1 this  
gentleman confounds the distinction     
between      perfect and imperfect      
consonances1 by comparing imperfect     
consonances which beat because the      
succession of their short               
cycles#adf is periodically confused and 
interrupted1 with perfect      ones     
which cannot beat1 because the          
succession of their short      cycles is
 never confused nor interrupted4        
,the fluttering roughness above         
mentioned is perceivable in all         
other perfect consonances1 in a smaller 
degree in proportion as      their      
cycles are shorter and simpler1 and     

their pitch is higher2      and is of a 
different kind from the smoother beats  
and      undulations of tempered        
consonances2 because we can alter the   
rate of the latter by altering the      
temperament1 but not of the      former1
 the consonance being perfect at a given
 pitch3 ,and because      a judicious   
ear can often hear1 at the same time1   
both the      flutterings and the beats 
of a tempered consonance2 sufficiently  
distinct from each other4       ,for    
nothing gives greater offence to the    
hearer1 though ignorant      of the     
cause of it1 than those rapid1 piercing 
beats of high and      loud sounds1     
which make imperfect consonances with   
one another4 ,and      yet a few slow   
beats1 like the slow undulations of a   
close shake      now and then           
introduced1 are far from being          
disagreeable4  ,smith is accordingly    
clear that other roughnesses exist      
besides the beats which ,sauveur        
considered1 and if the investigations   

had been continued on the basis of      
,sauveur's idea1 these additional       
roughnesses would have turned out to be 
the beats of the overtones1 and the     
theory thus have attained the point of  
view of ,helmholtz4  ,reviewing the     
differences between ,sauveur's and      
,helmholtz's theories1 we find the      
following3  #a4 ,the theory according to
 which consonance depends on the        
frequent and regular coincidence of     
vibrations and their ease of            
enumeration1 appears from the new point 
of view inadmissible4 ,the simplicity of
 the ratios obtaining between the rates 
of vibration is indeed a mathematical   
characteristic of consonance as well as 
a physical condition thereof1 for the   
reason that the coincidence of the      
overtones as also their further physical
 and physiological consequences is      
connected with this fact4 ,but no       
physiological or psychological          
explanation of consonance is given by   
this fact1 for the simple reason that in

 the acoustic nerve-process nothing     
corresponding to the periodicity of the 
sonant stimulus is discoverable4  #b4   
,in the recognition of beats as a       
disturbance of consonance1 both theories
 agree4 ,sauveur's theory1 however1 does
 not take into account the fact that    
clangs1 or musical sounds generally1 are
 composite and that the disturbance in  
the consonances of distant intervals    
principally arise from the beats of the 
overtones4 ,furthermore1 ,sauveur was   
wrong in asserting that the number of   
beats must be less than six in a second 
in order to produce disturbances4 ,even 
,smith knows that very slow beats are   
not a cause of disturbance1 and         
,helmholtz found a much higher number   
7#cc7 for the maximum of disturbance4   
,finally1 ,sauveur did not consider that
 although the number of beats increases 
with the recession from unison1 yet     
their strength is diminished4 ,on the   
basis of the principle of specific      
energies and of the laws of sympathetic 

vibration the new theory finds that two 
atmospheric motions of like amplitude   
but different periods1 a sin7rt7 and a  
sin7r  rho77t  tau71 cannot be          
communicated with the same amplitude to 
the same nervous end-organ4 ,on the     
contrary1 an end-organ that reacts best 
to the period r responds more weakly to 
the period r  rho1 the two amplitudes   
bearing to each other the proportion a3 
phia4 ,here phi decreases when rho      
increases1 and when rho  #j it becomes  
equal to #a1 so that only the portion of
 the stimulus phia is subject to beats1 
and the portion 7#a-phi7a continues     
smoothly onward without disturbance4    
,if there is any moral to be drawn from 
the history of this theory1 it is that  
considering how near ,sauveur's errors  
were to the truth1 it behooves us to    
exercise some caution also with regard  
to the new theory4 ,and in reality there
 seems to be reason for doing so4  ,the 
fact that a musician will never confound
 a more perfectly consonant chord on a  

poorly tuned piano with a less perfectly
 consonant chord on a well tuned piano1 
although the roughness in the two cases 
may be the same1 is sufficient          
indication that the degree of roughness 
is not the only characteristic of a     
harmony4 ,as the musician knows1 even   
the harmonic beauties of a ,beethoven   
sonata are not easily effaced on a      
poorly tuned piano2 they scarcely suffer
 more than a ,raphael drawing executed  
in rough unfinished strokes4 ,the       
positive physiologico-psychological     
characteristic which distinguishes one  
harmony from another is not given by the
 beats4 ,nor is this characteristic to  
be found in the fact that1 for example1 
in sounding a major third the fifth     
partial tone of the lower note coincides
 with the fourth of the higher note4    
,this characteristic comes into         
consideration only for the investigating
 and abstracting reason4 ,if we should  
regard it also as characteristic of the 
sensation1 we should lapse into a       

fundamental error which would be quite  
analogous to that cited in 7#a74  ,the  
positive physiological characteristics  
of the intervals would doubtless be     
speedily revealed if it were possible to
 conduct aperiodic1 for example         
galvanic1 stimuli to the single         
sound-sensing organs1 in which case the 
beats would be totally eliminated4      
,unfortunately such an experiment can   
hardly be regarded as practicable4 ,the 
employment of acoustic stimuli of short 
duration and consequently also free from
 beats1 involves the additional         
difficulty of a pitch not precisely     
determinable4    ,,footnotes3           
,footnote #acd3 ,this article1 which    
appeared in the ,proceedings of   the   
,german ,mathematical ,society of       
,prague for the year #ahib1 is   printed
 as a supplement to the article on ,the 
,causes of ,harmony1   at page #cb4     
,footnote #ace3 ,the present exposition 
is taken from the volumes for   #agjj   
7published in #agjc7 and for #agja      

7published in #agjd71 and   partly also 
from the ,histoire de l',acadmie and    
partly from the   ,mmoires4 ,sauveur's  
later works enter less into             
consideration   here4    ,footnote #acf3
 ,euler1 ,tentamen novae theoriae       
musicae1 ,petropoli1   #agci4           
,footnote #acg3 ,in attempting to       
perform his experiment of beats   before
 the ,academy1 ,sauveur was not quite   
successful4 ,histoire de   l',acadmie1  
,anne #agjj1 p4 #acf4    ,footnote #ach3
 ,histoire de l',acadmie1 ,anne #agja1  
p4 #acd4    ,footnote #aci3 ,ibid41 p4  
#bih4    ,footnote #adj3 ,histoire de   
l',acadmie1 ,anne #agjb1 p4 #ia4        
,footnote #ada3 ,from the ,histoire de  
l',acadmie1 ,anne #agjj1 p4   #aci4     
,footnote #adb3 ,because all octaves in 
use in music offer too great            
differences of rates of vibration4      
,footnote #adc3 ,les battemens ne       
plaisent pas  l',oreille1  cause   de   
l'ingalit du son1 et l'on peut croire   
avec beaucoup d'apparence   que ce qui  

rend les ,octaves si agrables1 c'est    
qu'on n'y entend   jamais de battemens4 
,en suivant cette ide1 on trouve que les
 accords dont on ne peut   entendre les 
battemens1 sont justement ceux que les  
,musiciens   traitent de ,consonances1  
et que ceux dont les battemens se font  
sentir1 sont les ,dissonances1 et que   
quand un accord est ,dissonance   dans  
une certaine octave et ,consonance dans 
une autre1 c'est qu'il   bat dans l'une1
 et qu'il ne bat pas dans l'autre4      
,aussi est il   trait de ,consonance    
imparfaite4 ,il est fort ais par les    
principes   de ,mr4 ,sauveur qu'on a    
tablis ici1 de voir quels accords       
battent1   et dans quelles ,octaves     
au-dessus on au-dessous du son fixe4 ,si
   cette hypothse est vraye1 elle       
dcouvrira la vritable source des        
,rgles de la composition1 inconnue      
jusqu' prsent  la ,philosophie1   qui   
s'en remettait presque entirement au    
jugement de l',oreille4 ,ces   sortes de
 jugemens naturels1 quelque bisarres    

qu'ils paroissent   quelquefois1 ne le  
sont point1 ils ont des causes trs      
relles1 dont   la connaissance          
appartient  la ,philosophie1 pourvue    
qu'elle s'en   puisse mettre en         
possession4    ,footnote #add3          
,harmonics or the ,philosophy of        
,musical ,sounds1   ,cambridge1 #agdi4  
,i saw this book only hastily in #ahfd  
and drew   attention to it in a work    
published in #ahff4 ,i did not come into
 its   actual possession until three    
years ago and then only did ,i learn    
its exact contents4    ,footnote #ade3  
,harmonics1 pp4 #aah and #bdc4          
,footnote #adf3 ,short cycle is the     
period in which the same phases   of the
 two co-operant tones are repeated4     
,,ii4  ,,remarks ,,on ,,the ,,theory    
,,of ,,spatial ,,vision4#adg            
,according to ,herbart1 spatial vision  
rests on reproduction-series4 ,in such  
an event1 of course1 and if the         
supposition is correct1 the magnitudes  
of the residua with which the percepts  

or representations are coalesced 7the   
helps to coalescence7 are of cardinal   
influence4 ,furthermore1 since the      
coalescences must first be fully        
perfected before they make their        
appearance1 and since upon their        
appearance the inhibitory ratios are    
brought into play1 ultimately1 then1 if 
we leave out of account the accidental  
order of time in which the percepts are 
given1 everything in spatial vision     
depends on the oppositions and          
affinities1 or1 in brief1 on the        
qualities of the percepts1 which enter  
into series4  ,let us see how the theory
 stands with respect to the special     
facts involved4  #a4 ,if intersecting   
series only1 running anteriorly and     
posteriorly1 are requisite for the      
production of spatial sensation1 why are
 not analogues of them found in all the 
senses8  #b4 ,why do we measure         
differently colored objects and         
variegated objects with one and the same
 spatial measure8 ,how do we recognise  

differently colored objects as the same 
in size8 ,where do we get our measure of
 space from and what is it8  #c4 ,why is
 it that differently colored figures of 
the same form reproduce one another and 
are recognised as the same8  ,here are  
difficulties enough4 ,herbart is unable 
to solve them by his theory4 ,the       
unprejudiced student sees at once that  
his inhibition by reason of form and    
preference by reason of form are        
absolutely impossible4 ,think of        
,herbart's example of the red and black 
letters4  ,the help to coalescence is a 
passport1 so to speak1 made out to the  
name and person of the percept4 ,a      
percept which is coalesced with another 
cannot reproduce all others             
qualitatively different from it for the 
simple reason that the latter are in    
like manner coalesced with one another4 
,two qualitatively different series     
certainly do not reproduce themselves   
because they present the same order of  
degree of coalescence4  ,if it is       

certain that only things simultaneous   
and things which are alike are          
reproduced1 a basic principle of        
,herbart's psychology which even the    
most absolute empiricists will not deny1
 nothing remains but to modify the      
theory of spatial perception or to      
invent in its place a new principle in  
the manner indicated1 a step which      
hardly any one would seriously          
undertake4 ,the new principle could not 
fail to throw all psychology into the   
most dreadful confusion4  ,as to the    
modification which is needed there can  
be hardly any doubt as to how in the    
face of the facts and conformably to    
,herbart's own principles it is to be   
carried out4 ,if two differently colored
 figures of equal size reproduce each   
other and are recognised as equal1 the  
result can be due to nothing but to the 
existence in both series of             
presentations of a presentation or      
percept which is qualitatively the same4
 ,the colors are different4             

,consequently1 like or equal percepts   
must be connected with the colors which 
are yet independent of the colors4 ,we  
have not to look long for them1 for they
 are the like effects of the muscular   
feelings of the eye when confronted by  
the two figures4 ,we might say we reach 
the vision of space by the registering  
of light-sensations in a schedule of    
graduated muscle-sensations4#adh  ,a few
 considerations will show the likelihood
 of the rle of the muscle-sensations4   
,the muscular apparatus of one eye is   
unsymmetrical4 ,the two eyes together   
form a system which is vertical in      
symmetry4 ,this already explains much4  
#a4 ,the position of a figure influences
 its view4 ,according to the position in
 which objects are viewed different     
muscle-sensations come into play and the
 impression is altered4 ,to recognise   
inverted letters as such long experience
 is required4 ,the best proof of this   
are the letters d1 b1 p1 q1 which are   
represented by the same figure in       

different positions and yet are always  
distinguished as different4#adi  #b4 ,it
 will not escape the attentive observer 
that for the same reasons and even with 
the same figure and in the same position
 the fixation point is also decisive4   
,the figure seems to change during the  
act of vision4 ,for example1 an         
eight-pointed star constructed by       
successively joining in a regular       
octagon the first corner with the       
fourth1 the fourth with the seventh1    
etc41 skipping in every case two        
corners1 assumes alternately1 according 
to where we suffer the centre of vision 
to rest1 a predominantly architectonic  
or a freer and more open character4     
,vertical and horizontal lines are      
always differently apprehended from what
 oblique lines are4  ,illustration3     
,fig4 #eh4  #c4 ,the reason why we      
prefer vertical symmetry and regard it  
as something special in its kind1       
whereas we do not recognise horizontal  
symmetry at all immediately1 is due to  

the vertical symmetry of the muscular   
apparatus of the eye4 ,the left-hand    
side a of the accompanying              
vertically-symmetrical figure induces in
 the left eye the same muscular feelings
 as the right-hand side b does in the   
right eye4 ,the pleasing effect of      
symmetry has its cause primarily in the 
repetition of muscular feelings4 ,that a
 repetition actually occurs here1       
sometimes sufficiently marked in        
character as to lead to the confounding 
of objects1 is proved apart from the    
theory by the fact which is familiar to 
every one quem dii oderunt that children
 frequently reverse figures from the    
right to the left1 but never from above 
downwards2 for example1 write epsilon   
instead of #c until they finally come to
 notice the slight difference4 ,figure  
#ej shows how pleasing the repetition of
 muscular feelings may be4 ,as will be  
readily understood1 vertical and        
horizontal lines exhibit relations      
similar to symmetrical figures which are

 immediately disturbed when oblique     
positions are chosen for the lines4     
,compare what ,helmholtz says regarding 
the repetition and coincidence of       
partial tones4  ,illustration3 ,fig4    
#ei4  ,i may be permitted to add a      
general remark4 ,it is a quite universal
 phenomenon in psychology that certain  
qualitatively quite different series of 
percepts mutually awaken and reproduce  
one another and in a certain aspect     
produce the appearance of sameness or   
similarity4 ,we say of such series that 
they are of like or of similar form1    
naming their abstracted likeness form4  
#a4 ,of spatial figures we have already 
spoken4       #b4 ,we call two melodies 
like melodies when they present the same
      succession of pitch-ratios2 the   
absolute pitch 7or key7 may be as       
different as can be4 ,we can so select  
the melodies that not even      two     
partial tones of the notes in each are  
common4 ,yet we recognise      the      
melodies as alike4 ,and1 what is more1  

we notice the form of the      melody   
more readily and recognise it again more
 easily than the key      7the absolute 
pitch7 in which it was played4       #c4
 ,we recognise in two different melodies
 the same rhythm no matter      how     
different the melodies may be otherwise4
 ,we know and recognise      the rhythm 
more easily even than the absolute      
duration 7the tempo74  ,these examples  
will suffice4 ,in all these and in all  
similar cases the recognition and       
likeness cannot depend upon the         
qualities of the percepts1 for these are
 different4 ,on the other hand          
recognition1 conformably to the         
principles of psychology1 is possible   
only with percepts which are the same in
 quality4 ,consequently there is no     
other escape than to imagine the        
qualitatively unlike percepts of the two
 series as necessarily connected with   
other percepts which are qualitatively  
alike4  ,since in differently colored   
figures of like form1 like muscular     

feelings are necessarily induced if the 
figures are recognised as alike1 so     
there must necessarily lie at the basis 
of all forms also1 and we might even say
 at the basis of all abstractions1      
percepts of a peculiar quality4 ,and    
this holds true for space and form as   
well as for time1 rhythm1 pitch1 the    
form of melodies1 intensity1 etc4 ,but  
whence is psychology to derive all these
 qualities8 ,have no fear1 they will all
 be found1 as were the sensations of    
muscles for the theory of space4 ,the   
organism is at present still rich enough
 to meet all the requirements of        
psychology in this direction1 and it is 
even time to give serious ear to the    
question of corporeal resonance which   
psychology so loves to dwell on4        
,different psychical qualities appear to
 bear a very intimate mutual relation to
 one another4 ,special research on the  
subject1 as well also as the            
demonstration that this remark may be   
generally employed in physics1 will     

follow later4#aej    ,,footnotes3       
,footnote #adg3 ,this article1 designed 
to illustrate historically   that on    
,symmetry1 at page #hi1 first appeared  
in ,fichte's   ,zeitschrift fr          
,philosophie1 for #ahfe4    ,footnote   
#adh3 ,comp4 ,cornelius1 ,ueber das     
,sehen2 ,wundt1 ,theorie   der          
,sinneswahrnehmung4    ,footnote #adi3  
,comp4 ,mach1 ,ueber das ,sehen von     
,lagen and ,winkeln4   ,sitzungsb4 der  
,wiener ,akademie1 #ahfa4    ,footnote  
#aej3 ,comp4 ,mach1 ,zur ,theorie des   
,gehrorgans4   ,sitsungsber1 der ,wiener
 ,akad41 #ahfc4--,ueber einige          
,erscheinungen   der physiolog4         
,akustik4 ,ibid41 #ahfd4     ,,index4   
,absolute1 temperature1 #afb2     time1 
#bjd2     forecasts1 have no            
signification in science1 #bjf4         
,abstract1 meaning of the term1 #bdj4   
,abstraction1 #ahj1 #bjj1 #bjh1 #bca4   
,acceleration1 organ for forward1 #bii  
et seq4    ,accelerations1 #bjd1 #baf1  
footnote1 #bbe-bbf1 #bec4    ,accident1 

logical and historical1 in science1     
#afj1 #afh1 #agj1 #bac2     in          
inventions and discoveries1 #bfb et seq4
    ,accord1 the pure triple1 #df4      
,accumulators1 electrical1 #abe et seq42
     #acb1 footnote4    ,acoustic color1
 #cf4    ,acoustics1 ,sauveur on1 #cge  
et seq4    ,action and reaction1        
importance of the principle of1 #aia4   
,adaptation1 in organic and inorganic   
matter1 #baf1 #bbi2     in scientific   
thought1 #bad-bce4    sthetics1         
computation as a principle of1 #cd2     
researches in1 #hi1 footnote2           
repetition1 a principle of1 #ia4        
,africa1 #ahf1 #bcd1 #bcg4    ,agreeable
 effects1 due to repetition of          
sensations1 #ib1 #ig et seq4            
,agriculture1 transition to1 #bfe4      
,air-gun1 #ace4    ,alcohol and water1  
mixture of oil and1 in ,plateau's       
experiments1 #d4    ,algebra1 economy   
of1 #aif4    ,alien thoughts in science1
 #aif4    ,all1 the1 #hh4    ,amontons1 
#agd1 #cdf4    ,ampre1 the word1 #cad4  

,ampre's swimmer1 #bjg4    ,analogies1  
mechanical1 #aeg1 #afj2     generally1  
#bcf-beh4    ,analogy1 defined1 #bej4   
,analysis1 #ahh4    ,analytical         
geometry1 not necessary to physicians1  
#cgj1 footnote4    ,anatomic structures1
 transparent stereoscopic views of1 #gd4
    ,anatomy1 character of research in1 
#bee4    ,andrieu1 ,jules1 #di1         
footnote4    ,animals1 the psychical    
activity of1 #aij1 #bca2     the        
language of1 #bch2     their capacity   
for experience1 #bff et seq4            
,animism1 #ahf1 #ahg1 #bdc1 #bed4       
,anisotropic optical fields1 #bbg4      
,apparatus for producing movements of   
rotation1 #bhg et seq4    ,arabesque1 an
 inverted1 #ie4    ,arabian ,nights1    
#bai4    ,arago1 #bgj4    ,aral1 the    
,sea of1 #bci4    ,archopteryx1 #beg4   
,archimedes1 #d1 #bcg4    ,arcimboldo1  
,giuseppe1 #cf4    ,area1 principle of  
least superficial1 #aj et seq4    ,ares1
 the bellowing of the wounded1 #bgb4    
,aristotelians1 #bhc4    ,aristotle1    

#cdh1 #bif4    ,art1 development of1 #bh
 et seq4    ,artillery1 practical1      
#ccd-cce4    ,artistic value of         
scientific descriptions1 #bed4    ,arts1
 practical1 #ajh4    ,ascent1 heights   
of1 #adc-aea4    ,asia1 #bcd4           
,assyrians1 the art of1 #gi4            
,astronomer1 measures celestial by      
terrestrial distances1 #acf4            
,astronomy1 antecedent to psychology1   
#ij2     rigidity of its truths1 #bba4  
,atomic theories1 #ajd4    ,atoms1 #bjg4
    ,attention1 the rle of1 in sensuous 
perception1 #ce et seq4    ,attraction1 
generally1 #bbf2     of liquid          
particles1 #ac-ad2     in electricity1  
#aji et seq4    ,aubert1 #bih4          
,audition4 ,see ,ear4    ,austrian      
gymnasiums1 #cgj1 footnote4    ,axioms1 
instinctive knowledge1 #aij4            
,babbage1 on the economy of machinery1  
#aif4    ,bach1 #bj4    ,backwards1     
prophesying1 #bec4    ,bacon1 ,lord1    
#dh1 #bhj4    ,baer1 ,c4 ,e4 von1 #bce4 
,balance1 electrical1 #abg1 footnote2   

torsion1 #aji1 #afh4    ,balloon1 a     
hydrogen1 #aii4    ,barbarism and       
civilisation1 #cce et seq4              
,bass-clef1 #aja4    ,bass1 fundamental1
 #dd4    ,beats1 #dj-de1 #cgg et seq4   
,beautiful1 our notions of1 variable1   
#ii4    ,beauty1 objects of1 in nature1 
#ia4    ,becker1 ,j4 ,k41 #cfd1 #cfi4   
,beethoven1 #ci1 #dd4    ,beginnings of 
science1 #ahi1 #aia4    ,belvedere      
,gallery at ,vienna1 #cf4    ,bernoulli1
 ,daniel1 on the conservation of living 
force1 #adi2     on the vibrations of   
strings1 #bdi4    ,bernoulli1 ,james1 on
 the centre of oscillation1 #adi4       
,bernoulli1 ,john1 on the conservation  
of living force1 #adi2     on the       
principle of virtual velocities1 #aea4  
,bible1 parallel passages from1 for     
language study1 #cef4    ,binocular     
vision1 #ff et seq4    ,black1 his      
theory of caloric1 #ach1 #afb2     on   
quantity of heat1 #aff1 #agd2     on    
latent heat1 #afg1 #agh2     researches 
in heat generally1 #bdd4    ,blind cat1 

#cjc4    ,bodies1 heavy1 seek their     
places1 #bbd et seq42     rotating1     
#bhe4    ,body1 a mental symbol for     
groups of sensations1 #bjj-bjc2     the 
human1 our knowledge of1 #ij4           
,boltzmann1 #bcf4    ,booth1 ,mr41 #gg4 
,borelli1 #bag4    ,boulder1 a granite1 
#bcc4    ,bow-wave of ships and moving  
projectiles1 #cbc et seq4    ,boys1     
#cag4    ,bradley1 #bgc4    ,brahman1   
the1 #fc4    ,brain1 localisation of    
functions in1 #baj4    ,breuer1 #bgb1   
#bhb et seq41 #bic1 #bih1 #cjj1 #cja1   
#cjc1 #cjf4    ,brewster1 his           
stereoscope1 #gc4    ,bridge1 invention 
of the1 #bfd1 #bfh4    ,british         
,association1 #ajh4    ,brooklyn        
,bridge1 #ge1 footnote4    ,brown1      
,crum1 #bic1 #cja4    ,building1 our    
concepts directions for1 #bec2     facts
 the result of1 #bec2     science       
compared to1 #beg4    ,building-stones1 
metrical units are1 #bec4    ,busch1    
#cbh4    ,business of a merchant1       
science compared to the1 #af4           

,butterfly1 a1 #bb4     ,calculating    
machines1 their economical character1   
#aif4    ,caloric1 theory of1 stood in  
the way of scientific advancement1 #ach1
 #afg4    ,calypso1 the island of1 #cea4
    ,canterbury1 ,archbishop of1 #ci4   
,cantor1 ,m41 #cfa1 footnote4           
,capacity1 electrical1 #aaf et seq41    
#abc2     thermal1 #abc2     specific   
inductive1 #aag4    ,capulets and       
,montagues1 #hg4    ,cards1 difficult   
games of1 #ceg4    ,carnot1 ,s41        
excludes perpetual motion in heat1 #aef1
 #afb2     his mechanical view of       
physics1 #aef2     on thermodynamics1   
#afj et seq42     his principle1 #afb2  
also1 #aia4    ,carus1 ,dr4 ,paul1 #bfe1
 footnote4    ,casselli's telegraph1    
#bf4    ,cassini1 #ea4    ,cauchy1      
character of the intellectual activity  
of a1 #aie4    ,causal insight1 awakened
 by science1 #ceg4    ,causality1       
#aeg-aei1 #aij1 #aih et seq41 #bba et   
seq41 #bcg1 #bec1 #bed4    ,cause and   
effect1 #aih et seq4 ,see also          

,causality4    ,centimetre-gramme-second
 system1 #aaa4    ,centre of gravity1   
must lie as low as possible for         
equilibrium to   subsist1 #ae2          
,torricelli's principle of1 #aej et seq4
    ,centre of oscillation1 #adi4       
,change1 method of1 in science1 #bcj4   
,changeable character of bodies1 #bjb4  
,changes1 physical1 how they occur1     
#bje4    ,character1 a ,universal ,real1
 #aib4    ,character1 like the forms of 
liquids1 #c2     persons of1 #bd4       
,charles the ,fifth1 #cfi4    ,chemical1
 elements1 #bjb2     symbols1 #aib2     
current1 #aah4    ,chemistry1 character 
of research in1 #bee2     the method of 
thermodynamics in1 #beg4    ,child1 a1  
modes of thought of1 #bbc2     looking  
into a moat1 #bjh4    ,child of the     
forest1 his interpretation of new       
events1 #bah-bai4    ,childish          
questions1 #aii-bjj4    ,children1 the  
drawings of1 #bja-bjb4    ,chinese      
language1 economy of1 #aib2     study   
of1 #ced4    ,chinese philosopher1 an   

old1 #ahf4    ,chinese1 speak with      
unwillingness of politics1 #cgd2     the
 art of1 #gi-hj4    ,chosen1 many are   
called but few are1 #fe4    ,christ1    
saying of1 #fe4    ,christianity1 ,latin
 introduced with1 #caa4    ,christians  
and ,jews1 monotheism of the1 #ahg4     
,church and ,state1 #hh4    ,cicero1    
#cah4    ,circe1 #cgb4    ,circle1 the  
figure of least area with given         
periphery1 #ab4    ,circular            
polarisation1 #bdb4    ,civilisation and
 barbarism1 #cce et seq4                
,civilisation1 some phenomena of1       
explained by binocular vision1 #gd4     
,civilised man1 his modes of conception 
and interpretation1 #bai4    ,clapeyron1
 #afb4    ,class-characters of animals1 
#bee4    ,classical1 culture1 the good  
and bad effects of1 #cdg2     scholars1 
not the only educated people1 #cde4     
,classics1 on instruction in1 #cch-cgd2 
the scientific1 #cfh4    ,classification
 in science1 #bee4    ,clausius1 on     
thermodynamics1 #afe2     on reversible 

cycles1 #agf4    ,claviatur1 ,mach's1   
#db-dc4    ,club-law1 #cce4    ,cochlea1
 the1 a species of piano-forte1 #ai4    
,cockchafer1 #hf4    ,coefficient of    
self-induction1 #bej1 #beb4             
,colophonium1 solution of1 #g4          
,color1 acoustic1 #cf4                  
,color-sensation1 #baj4    ,color-signs1
 their economy1 #aib4    ,colors1 origin
 of the names of1 #bci4    ,column1 body
 moving behind a1 #bjb4                 
,communication1 its functions1 import   
and fruits1 #aig1 #bch et seq42     by  
language1 #bcg2     high importance of1 
#aia et seq4    ,comparative physics1   
#bci4    ,comparison in science1 #bca1  
#bch et seq4    ,computation1 a         
principle of sthetics1 #cd4             
,concepts1 abstract1 defined1 #bej-beb2 
metrical1 in electricity1 #ajg et seq4  
,conceptual1 meaning of the term1 #bdj4 
,conceptual thought1 #aib4    ,concha1  
#ah4    ,condensers1 electrical1 #abe et
 seq4 #acb1 footnote4    ,conductors and
 non-conductors4 ,see ,electrical1 etc4 

,conformity in the deportment of the    
energies1 #aga-age4    ,confusion of    
objects1 cause of1 #ie4    ,conic       
sections1 #beg4    ,conical refraction1 
#bi1 #bdb4    ,conservation of energy1  
#acg et seq4 ,see ,energy4              
,conservation of weight or mass1 #bjc4  
,consonance1 connexion of the simple    
natural numbers with1 #cc2     ,euclid's
 definition of1 #cc2     explanation of1
 #db2     scientific definition of1 #dd2
     and dissonance reduced to beats1   
#cgf1 #cgj1 #chc4    ,consonant         
intervals1 #dc4    ,constancy of matter1
 #bjc4    ,constant1 the dielectric1    
#aag4    ,constants1 the natural1 #aic4 
,continuum of facts1 #bef et seq4       
,cornelius1 #chh1 footnote4    ,corti1  
the ,marchese1 his discovery of minute  
rods in the labyrinth of   the ear1 #ai4
    ,coulomb1 his electrical researches1
 #ajh1 #aji1 #aac2     his notion of    
quantity of electricity1 #agc2     his  
torsion-balance1 #afh4    ,crew1 ,prof4 
,henry1 #cag1 footnote4    ,criticism1  

,socrates the father of scientific1 #a1 
#af4    ,critique of ,pure ,reason1     
,kant's1 #ahh4    ,crucible1 derivation 
of the word1 #di1 footnote4             
,crustacea1 auditory filaments of1 #bi1 
#bgb1 #cjb4    ,cube of oil1 #e4        
,culture1 ancient and modern1 #cdd4     
,currents1 chemical1 #aah2              
electrical1 #aah2     galvanic1 #acb2   
measurement of electrical1 #ace-acf2    
of heat1 #bdd1 #bdi-bej2     strength   
of1 #bej4    ,curtius1 #cef4    ,curved 
lines1 their asymmetry1 #ih4    ,curves1
 how their laws are investigated1 #bjf4 
,cycles1 reversible1 ,clausius on1 #agf4
    ,cyclical processes1 closed1 #age4  
,cyclops1 #fg4    ,cyclostat1 #bih4     
,cylinder1 of oil1 #f2     mass of gas  
enclosed in a1 #agi4     ,d',alembert1  
on the causes of harmony1 #cd2     his  
principle1 #adb1 #adi1 #aed2     also   
#bcd1 #bgi4    ,danish schools1 #cch1   
footnote4    ,darwin1 his study of      
organic nature1 #bae et seq42     his   
methods of research1 #baf4    ,deaf and 

dumb1 not subject to giddiness1 #bii4   
,deaf person1 with a piano1 analyses    
sounds1 #bg4    ,death and life1 #ahf4  
,definition1 compendious1 #aig4         
,deiters1 #ai4    ,delage1 #bih1 #cja1  
#cjb4    ,democritus1 his mechanical    
conception of the world1 #aee1 #ahg4    
,demonstration1 character of1 #cfb4     
,deportment of the energies1 conformity 
in the1 #aga-age4    ,derivation1 laws  
only methods of1 #bef4    ,descent1     
,galileo's laws of1 #aic2     generally1
 #adc et seq41 #bjd1 #bae4              
,description1 #ajh1 #aia1 #bcf1 #bcg2   
a condition of scientific knowledge1    
#aic2     direct and indirect1 #bdj2    
in physics1 #aig1 #aii4    ,descriptive 
sciences1 their resemblance to the      
abstract1 #bdh4    ,determinants1 #aie4 
,diderot1 #bcd4    ,dielectric constant1
 the1 #aag4    ,difference-engine1 the1 
#aif4    ,differential coefficients1    
their relation to symmetry1 #ih4        
,differential laws1 #bjd4               
,differential method1 for detecting     

optical imperfections1 #cag4            
,diffraction1 #ia1 #aid4    ,diffusion1 
,fick's theory of1 #bdi4    ,discharge  
of ,leyden jars1 #aad et seq4           
,discoveries1 the gist of1 #bgj1 #cge4  
,discovery and invention1 distinction   
between1 #bfi4    ,dissonance1          
explanation of1 #db2     definition of1 
#cc1 #dd4 ,see ,consonance4             
,distances1 estimation of1 by the eye1  
#fh et seq4    ,dogs1 like tuning-forks1
 #bc2     their mentality1 #aij4        
,domenech1 ,abb1 #ib4    ,dramatic      
element in science1 #bdc4    ,drop of   
water1 on a greased plate1 #h2     on   
the end of a stick1 #h2     in free     
descent1 #h4    ,dubois1 #bah4          
,dubois-,reymond1 #cgj1 footnote4       
,dufay1 #bga4    ,dynamics1 foundations 
of1 #aec et seq4     ,ear1 researches in
 the theory of1 #ag et seq42     diagram
 of1 #ah2     its analysis of sounds1   
#bj et seq42     a puzzle-lock1 #bh2    
reflected in a mirror1 #ic2     no      
symmetry in its sensation1 #ajc4        

,earth1 its oblateness not due to its   
original fluid condition1 #b2           
rotation of1 #bjd2     internal         
disturbances of1 #bhe4    ,economical1  
nature of physical inquiry1 #ahf2       
procedure of the human mind1 #ahf2      
order of physics1 #aig2     schematism  
of science1 #bjf2     tools of science1 
#bjg2     coefficient of dynamos1 #acc4 
,economy1 of the actions of nature1 #ae2
     the purpose of science1 #af2     of
 language1 #aia et seq42     of the     
industrial arts1 #aib2     of           
mathematics1 #aie-aif2     of machinery1
 #aif2     of self-preservation1 our    
first knowledge derived from1 #aig2     
generally1 #ahf et seq41 #bfi4          
,education1 higher1 #hf2     liberal1   
#cda et seq41 #cga4    ,efflux1 liquid1 
#aej4    ,ego1 its nature1 #bcd-bce4    
,egypt1 #bcd4    ,egyptians1 art of1 #gh
 et seq41 #bja4    ,eighteenth century1 
the scientific achievements of1 #ahg1   
#ahh4    ,eleatics1 on motion1 #aeh4    
,electrical1 attraction and repulsion1  

#aji et seq41 #afh2     capacity1 #aaf  
et seq42     force1 #aaj1 #aai1 #afh2   
spark1 #aag1 #abg1 #acb1 #acc1 #aij2    
energy1 measurement of1 #abh et seq41   
#afi2     currents1 conceptions of1     
#aah1 #acb1 #ace-acf1 #bbf-bbg1 #bdi1   
#bej2     fluids1 #aab et seq41 #bbh2   
pendulums1 #aaj2     levels1 #agc2      
potential1 #aba et seq42     quantity1  
#aaa1 #aah1 #aai4    ,electricity1 as a 
substance and as a motion1 #agj2        
difference between the conceptions of   
heat and1 #afh et seq41     rle of work 
in1 #abj et seq42     galvanic1 #acd4   
,see ,electrical4    ,electrometer1 ,w4 
,thomson's absolute1 #abg1 footnote4    
,electrometers1 #abb1 #abg4             
,electrostatic unit1 #aaa4              
,electrostatics1 concepts of1 #ajg et   
seq4    ,elements1 interdependence of   
the sensuous1 #agi2     of bodies1 #bjb2
     of phenomena1 equations between1   
#bje2     of sensations1 #bjj2     used 
instead of sensations1 #bjh-bji4        
,ellipse1 equation of1 #bje2     the    

word1 #cdb4    ,embryology1 possible    
future state of1 #beg4    ,energies1    
conformity in the deportment of1        
#aga-age2     differences of1 #age4     
,energy1 a metrical notion1 #agh2       
conservation of1 #acg et seq42          
defined1 #aci2     metaphysical         
establishment of the doctrine of1 #ahc2 
kinetic1 #agg2     potential1 #abh et   
seq42     substantial conception of1    
#afd1 #ahe1 #bdd et seq42               
conservation of1 in electrical          
phenomena1 #aca et seq42     limits of  
principle of1 #age2     principle of1 in
 physics1 #afj-aff2     sources of      
principle of1 #agi1 #aha2     thermal1  
#agg2     ,thomas ,young on1 #agc4      
,energy-value of heat1 #agh1 footnote4  
,enlightenment1 the1 #ahh4    ,entropy1 
a metrical notion1 #agh4                
,environment1 stability of our1 #bjf4   
,equations for obtaining facts1 #ahj2   
between the elements of phenomena1 #bje4
    ,equilibrium1 conditions of1 in     
simple machines1 #aea2     figures of   

liquid1 #d et seq42     general         
condition of1 #ae2     in the ,state1   
#ae4    ,etymology1 the word1 misused   
for entomology1 #caf4    ,euclid1 on    
consonance and dissonance1 #cc2     his 
geometry1 #cfd4    ,euler1 on the causes
 of harmony1 #cd2     impression of the 
mathematical processes on1 #aif2     on 
the vibrations of strings1 #bdi1 #bhe1  
#cgf4    ,euler and ,hermann's          
principle1 #adi4    ,euthyphron1        
questioned by ,socrates1 #a4            
,evolute1 the word1 #cdb4    ,evolution1
 theory of1 as applied to ideas1 #baf et
 seq4    ,ewald1 #bih1 #cjd4            
,excluded perpetual motion1 logical root
 of the principle of1 #ahb4    ,exner1  
,s41 #cjb1 #cje4    ,experience1        
communication of1 #aia2     our ready1  
#aii2     the principle of energy       
derived from1 #agi2     the wellspring  
of all knowledge of nature1 #aha2       
incongruence between thought and1 #bjf4 
,experimental research1 function of1    
#aha4    ,explanation1 nature of1 #aid1 

#bcg1 #cfb4    ,eye1 cannot analyse     
colors1 #bj2     researches in the      
theory of the1 #ah et seq42     loss of1
 as affecting vision1 #ih4    ,eyes1    
purpose of1 #ff et seq42     their      
structure symmetrical not identical1    
#if4     ,face1 human1 inverted1 #ie4   
,facts and ideas1 necessary to science1 
#bca4    ,facts1 description of1 #ajh2  
agreement of1 #ahj2     relations of1   
#ahj2     how represented1 #bjf2        
reflected in imagination1 #bbj et seq42 
the result of constructions1 #bec2     a
 continuum of1 #bef et seq42            
equations for obtaining1 #ahj4          
,falling bodies1 #bjd1 #bae2            
,galileo on the law of1 #adc et seq41   
#bhd4    ,falling1 cats1 #cjc1 footnote4
    ,falstaff1 #cji4    ,familiar       
intermediate links of thought1 #aih4    
,faraday1 #aia1 #bag1 #bcg2     his     
conception of electricity1 #aad1 #bga4  
,fechner1 theory of ,corti's fibres1 #ai
 et seq4    ,feeling1 cannot be         
explained by motions of atoms1 #bjh et  

seq4    ,fetishism1 #ahf1 #bdc1 #bed2   
in our physical concepts1 #ahg4         
,fibres of ,corti1 #ag et seq4    ,fick1
 his theory of diffusion1 #bdi4         
,figures1 symmetry of1 #ib et seq4      
,figures of liquid equilibrium1 #d et   
seq4    ,fire1 use of1 #bfd4    ,fishes1
 #cjf4    ,fixed note1 determining of a1
 #cgg4    ,fizeau1 his determination of 
the velocity of light1 #ee et seq4      
,flats1 reversed into sharps1 #aja4     
,flouren's experiments1 #bgb1 #bij4     
,flower-girl1 the baskets of a1 #ie4    
,fluids1 electrical1 #aab et seq4       
,force1 electric1 #aaj1 #aai1 #afh2     
unit of #aaa2     living1 #acg1 #adi1   
#ahd2     generally #bec4     ,see the  
related headings4    ,forces1 will      
compared to1 #bed4    ,foreseeing       
events1 #bbj et seq4    ,formal         
conceptions1 rle of1 #ahc4    ,formal   
need of a clear view of facts1 #ahc1    
#bdf2     how far it corresponds to     
nature1 #ahd4    ,formative forces of   
liquids1 #d4    ,forms of liquids1 #c et

 seq4    ,forward movement1 sensation   
of1 #cjj4    ,forwards1 prophesying1    
#bec4    ,foucault1 #eg1 #gj1 #bif4     
,foucault and ,toepler1 method of1 for  
detecting optical faults1 #cac   et     
seq41 #cbj4    ,foundation of scientific
 thought1 primitive acts of knowledge1  
the1 #aij4    ,fourier1 on processes of 
heat1 #bdi1 #bgh4    ,fox1 a1 #bcd4     
,franklin's pane1 #aaf4    ,frary1 #cch1
 footnote4    ,fraunhofer1 #bga4        
,freezing-point1 lowered by pressure1   
#afb4    ,fresnel1 #bga4    ,fritsch1   
#cba4    ,frogs1 larv of1 not subject to
 vertigo1 #bih4    ,froude1 #ccc4       
,frustra1 misuse of the word1 #cde4     
,future1 science of the1 #bac4          
,galileo1 on the motion of pendulums1   
#ba2     his attempted measurement of   
the velocity of light1 #ej et seq42     
his exclusion of a perpetual motion1    
#adc2     on velocities acquired in free
 descent1 #adc-adg2     on the law of   
inertia1 #adf-adg2     on virtual       
velocities1 #aej2     on work1 #agb2    

his laws of descent1 #aic2     on       
falling bodies1 #bbe2     great results 
of his study of nature1 #bad et seq42   
his rude scientific implements1 #bae2   
selections from his works for use in    
instruction1 #cfh2     also #aje1 #ahb1 
#ahg1 #bcg1 #bgb1 #bgd1 #bhc4    ,galle1
 observes the planet ,neptune1 #bi4     
,galvanic1 electricity1 #acd2           
current1 #acb2     dizziness1 #bia2     
vertigo1 #bih4    ,galvanoscope1 #ace4  
,galvanotropism1 #bia4    ,garda1 ,lake1
 #bci4    ,gas1 the word1 #bfd2     mass
 of1 enclosed in a cylinder1 #agi4      
,gases1 tensions of1 for scales of      
temperature1 #agd4    ,gauss1 on the    
foundations of dynamics1 #aed2     his  
principle1 #aed2     also1 #ajh1 #bgd4  
,genius1 #bgi1 #bhj4    ,geography1     
comparison in1 #bci4    ,geometers1 in  
our eyes1 #gb4    ,geotropism1 #bhi4    
,german schools and gymnasiums1 #cgb1   
#cgc1 #cch1 footnote4    ,ghosts1       
photographic1 #gc4    ,glass1 invisible 
in a mixture of the same refrangibility1

 #cab2     powdered1 visible in a       
mixture of the same refrangibility1     
#cab4    ,glove1 in a mirror1 #ic4      
,goethe1 quotations from1 #i1 #ca1 #di1 
#hh2     on the cause of harmony1 #ce4  
,goltz1 #bhb1 #bia4    ,gossot1 #ccb4   
,gothic cathedral1 #id4    ,gravitation1
 discovery of1 #bbe et seq4    ,gravity1
 how to get rid of the effects of1 in   
liquids1 #d2     also #bbh4    ,gray1   
,elisha1 his telautograph1 #bf4         
,greased plate1 drop of water on a1 #h4 
,great minds1 idiosyncrasies of1 #bdg4  
,greek language1 scientific terms       
derivedfrom1 #cdb-cdc2     common words 
derived from1 #cdc1 footnote2     still 
necessary for some professions1 #cdf2   
its literary wealth1 #cdg-cdh2          
narrowness and one-sidedness of its     
literature1 #cdh-cdi2     its excessive 
study useless1 #cdi-cej2     its study  
sharpens the judgment1 #ceg-ceh2     a  
knowledge of it not necessary to a      
liberal education1 #cga4    ,greeks1    
their provinciality and                 

narrow-mindedness1 #cdi2     now only   
objects of historical research1 #cej4   
,griesinger1 #ahd4    ,grimaldi1 #bgj4  
,grimm1 #cdd1 footnote4    ,grunting    
fishes1 #cjf4     ,habitudes of thought1
 #aii1 #bbd1 #bbg1 #bcb4    ,haeckel1   
#bbb1 #bce4    ,hamilton1 deduction of  
the conical refraction of light1 #bi4   
,hankel1 #cfd4    ,harmonics1 #ch1 #dj4 
,harmony1 on the causes of1 #cb et seq42
     laws of the theory of1 explained1  
#cj2     the investigation of the       
ancients concerning1 #cb2     generally1
 #ajc4     ,see ,consonance4    ,harris1
 electrical balance of1 #abg1 footnote4 
,hartwich1 ,judge1 #cdc1 #cec1 footnote4
    ,hat1 a high silk1 #bd4    ,hats1   
ladies'1 development of1 #fd4           
,head-wave of a projectile1 #cbc et seq4
    ,hearing and orientation1 relation  
between1 #cjd et seq4    ,heat1 a       
material substance1 #agg2     difference
 between the conceptions of electricity 
and1 #afh et seq42     substantial      
conception of1 #bdc et seq42     ,carnot

 on1 #aef1 #afj et seq42     ,fourier on
 the conduction of1 #bdi2     not       
necessarily a motion1 #afg1 #agj1 #aga2 
mechanical equivalent of1 #afd1 #afg2   
of liquefaction1 #agh2     quantity of1 
#aff2     latent1 #afg1 #agh1 #bdd2     
specific1 #aff1 #bdd2     the           
conceptions of1 #afj-aga2     machine1  
#afj2     a measure of electrical       
energy1 #acc et seq42     mechanical    
theory of1 #acc2     where does it come 
from8 #bjj4    ,heavy bodies1 sinking   
of1 #bbb4    ,heights of ascent1        
#adc-aea4    ,helm1 #agb4    ,helmholtz1
 applies the principle of energy to     
electricity1 #ahd2     his              
telestereoscope1 #hd2     his theory of 
,corti's fibres1 #ai et seq42     on    
harmony1 #ce1 #ii2     on the           
conservation of energy1 #afe1 #bdg2     
his method of thought1 #bdg2     also   
#ach1 #cje1 #cjg1 #cge1 #chc4           
,hensen1 ,v41 on the auditory function  
of the filaments of ,crustacea1 #bi1    
#cjb4    ,herbart1 #chf et seq4         

,herbartians1 on motion1 #aeh4          
,herculaneum1 art in1 #hj4    ,heredity1
 in organic and inorganic matter1 #baf1 
footnote4    ,hering1 on development1   
#bbb2     on vision1 #baj4    ,hermann1 
,e41 on the economy of the industrial   
arts1 #aib4    ,hermann1 ,l41 #bia4     
,herodotus1 #bf1 #bcd1 #cdg1 #cej4      
,hertz1 his waves1 #bdb2     his use of 
the phrase prophesy1 #bec4    ,herzen1  
#cfa1 footnote4    ,hindu               
mathematicians1 their beautiful         
problems1 #cj4    ,holtz's electric     
machine1 #acb4    ,horse1 #fc4          
,household1 physics compared to a       
well-kept1 #aig4    ,housekeeping in    
science and civil life1 #aih4           
,hudson1 the1 #id4    ,human beings1    
puzzle-locks1 #bg4    ,human body1 our  
knowledge of1 #ij4    ,human mind1 must 
proceed economically1 #ahf4             
,humanity1 likened to a polyp-plant1    
#bce4    ,huygens1 his mechanical view  
of physics1 #aee2     on the nature of  
light and heat1 #aee-aef2     his       

principle of the heights of ascent1     
#adi2     on the law of inertia and the 
motion of a compound pendulum1 #adg-adi2
     on the impossible perpetual motion1
 #adg-adh2     on work1 #agc2           
selections from his works for use in    
instruction1 #cfh2     his view of      
light1 #bbg-bbh1 #bfb4    ,huygens1     
optical method for detecting            
imperfections in optical glasses   #cac4
    ,hydrogen balloon1 #aii4            
,hydrostatics1 ,stevinus's principle of1
 #ada4    ,hypotheses1 their rle in     
explanation1 #bbh et seq4               
,ichthyornis1 #beg4    ,ichthyosaurus1  
#fc4    ,idea8 what is a theoretical1   
#bda4    ,idealism1 #bji4    ,ideas1 a  
product of organic nature1 #bag et seq42
     and facts1 necessary to science1   
#bca2     not all of life1 #bcc2        
their growth and importance1 #bcc2     a
 product of universal evolution1 #bce2  
the history of1 #bbg et seq42     in    
great minds1 #bbh2     the rich contents
 of1 #aig2     their unsettled character

 in common life1 their clarification in 
science1 #a-b4    ,ideography1 the      
,chinese1 #aib4    ,imagery1 mental1    
#bec4    ,imagination1 facts reflected  
in1 #bbj et seq4    ,inclined plane1 law
 of1 #adj-ada4    ,incomprehensible1    
the1 #ahf4    ,indian1 his modes of     
conception and interpretation1 #bah et  
seq4    ,individual1 a thread on which  
pearls are strung1 #bcd-bce4            
,industrial arts1 economy of the1 ,e4   
,hermann on1 #aib4    ,inertia1 law of1 
#adc et seq41 #adf et seq41 #baf1       
footnote1 #bhc et seq4    ,innate       
concepts of the understanding1 ,kant on1
 #aii4    ,innervation1 visual1 #ii4    
,inquirer1 his division of labor1 #aje2 
compared to a shoemaker1 #aje-ajf2      
what constitutes the great1 #aia2       
the true1 seeks the truth everywhere1   
#fc et seq42     the1 compared to a     
wooer1 #de4    ,instinctive knowledge1  
#ahi1 #aij4    ,instruction1 aim of1 the
 saving of experience1 #aia2     in the 
classics1 mathematics1 and sciences1    

#cch-cgd2     limitation of matter of1  
#cfe et seq4    ,insulators1 #acj4      
,integrals1 #aie4    ,intellectual      
development1 conditions of1 #bhf et seq4
    ,intentions1 acts of nature compared
 to1 #ad-ae4    ,interconnexion of      
nature1 #ahb4    ,interdependence1 of   
properties1 #cfa2     of the sensuous   
elements of the world1 #agi4            
,interference experiments with the      
head-wave of moving projectiles1        
#cbg-cbh4    ,international intercourse1
 established by ,latin1 #cda4           
,international measures1 #ajh4          
,invention1 discovery and1 distinction  
between1 #bfi4    ,inventions1          
requisites for the development of1 #bff1
 #bfh et seq4    ,iron-filings1 #bbj1   
#bdc4    ,italian art1 #bcd4            
,jacobi1 ,c4 ,g4 ,j41 on mathematics1   
#bhj4    ,james1 ,w41 #bge1 #bii4       
,java1 #afc4    ,jews and ,christians1  
monotheism of the1 #ahg4    ,jolly1     
,professor von1 #aab1 #bgd4    ,joule1  
,j4 ,p41 on the conservation of energy1 

#afc-afe1 #afg1 #ahc2     his conception
 of energy1 #bde2     his metaphysics1  
#ahc1 #bdf2     his method of thought1  
#bdg2     also #acg1 #ach4    ,journe1  
#cag4    ,judge1 criminal1 the natural  
philosopher compared to a1 #dh4         
,judgment1 essentially economy of       
thought1 #bja-bjb2     sharpened by     
languages and sciences1 #ceg-ceh2       
also #bcb-bcc1 #bch4    ,juliet1 ,romeo 
and1 #hg4    ,jupiter1 its satellites   
employed in the determination of the    
velocity of   light1 #ea et seq4        
,jurisprudence1 ,latin and ,greek       
unnecessary for the study of1 #cdf1     
footnote4     ,kant1 his hypothesis of  
the origin of the planetary system1 #e2 
his ,critique of ,pure ,reason1 #ahh2   
on innate concepts of the understanding1
 #aii2     on time1 #bjd2     also      
footnote1 #ic4    ,kepler1 #ahg1 #bgj4  
,kinetic energy1 #agg4    ,kirchhoff1   
his epistemological ideas1 #beg-beh2    
his definition of mechanics1 #bcf1 #beh1
 #bga1 #bgc4    ,knight1 #bhi4          

,knowledge1 a product of organic nature1
 #bag et seq41 #bce2     instinctive1   
#aij2     made possible by economy of   
thought1 #aih2     our first1 derived   
from the economy of self-preservation1  
#aig2     the theory of1 #bjc2     our  
primitive acts of the foundation of     
science1 #aij4    ,kocher1 #cbh4        
,koenig1 measurement of the velocity of 
sound1 #eg et seq4    ,klliker1 #ai4    
,kopisch1 #fa4    ,kreidl1 #bii1 #cjb1  
#cjf2     his experiments1 #bgb4        
,krupp1 #cai4     ,labels1 the value of1
 #bja4    ,labor1 the accumulation of1  
the foundation of wealth and power1     
#aih2     inquirer's division of1 #aje1 
#beh4    ,labyrinth1 of the ear1 #ah1   
#bia1 #cje4    ,lactantius1 on the study
 of moral and physical science1 #hi4    
,ladder of our abstraction1 the1 #bjh4  
,ladies1 their eyes1 #ga2     like      
tuning-forks1 #bc-bd4    ,lagrange1 on  
,huygens's principle1 #adi2     on the  
principle of virtual velocities1        
#aej-aee2     character of the          

intellectual activity of a1 #aie1 #bgh4 
,lake-dwellers1 #df1 #bga4              
,lamp-shade1 #gj4    ,lane's unit jar1  
#aae4    ,language1 knowledge of the    
nature of1 demanded by a liberal        
education1   #cef2     relationship     
between1 and thought1 #ceh2             
communication by #bcg2     economy of1  
#aia et seq42     human its character1  
#bch2     of animals1 #bch2             
instruction in1 #cch et seq42     its   
methods1 #aib4    ,laplace1 on the atoms
 of the brain1 #ahh2     on the         
scientific achievements of the          
eighteenth century1 #ahh2     his       
hypothesis of the origin of the         
planetary system1 #e4    ,latent heat1  
#afg1 #agh1 #bdd4    ,latin city of     
,maupertuis1 #cci4    ,latin1           
instruction in1 #caa et seq42           
introduced with the ,christian ,church1 
#cdj2     the language of scholars1 the 
medium of international intercourse1    
its power1 utility1 and final           
abandonment1 #cda-cdg2     the wealth of

 its literature1 #cdh2     the excessive
 study of1 #cdf1 #cdi1 #ced1 #cee2      
its power to sharpen the judgment1      
#ceg-ceh4    ,lavish extravagance of    
science1 #ahi4    ,law1 a1 defined1     
#bef2     a natural1 not contained in   
the conformity of the energies1 #age4   
,law-maker1 motives of not always       
discernible1 #i4    ,layard1 #gi4       
,learning1 its nature1 #cff et seq4     
,least superficial area1 principle of1  
accounted for by the mutual             
attractions of liquid particles1 #ac-ad2
     illustrated by a pulley            
arrangement1 #ab-ac2     also #i et seq4
    ,leibnitz1 on harmony1 #cc2     on  
international intercourse1 #cdb1        
footnote4    ,lessing1 quotation from1  
#dg4    ,letters of the alphabet1 their 
symmetry1 #id1 #ig4    ,level heights of
 work1 #agb-agd4    ,lever1 a1 in       
action1 #bbb4    ,leverrier1 prediction 
of the planet ,neptune1 #bi4    ,leyden 
jar1 #aad4    ,liberal education1 a1    
#cda et seq41 #cei1 #cga4    ,libraries1

 thoughts stored up in1 #bcg4           
,lichtenberg1 on instruction1 #bgf1     
#cgj4    ,licius1 a ,chinese            
philosopher1 #bac4    ,liebig1 #afc1    
#bgh4    ,life and death1 #ahf4         
,light1 history of as elucidating how   
theories obstruct research1 #bdb2       
,huygens's and ,newton's views of1      
#bbg-bbh2     its different conceptions1
 #bbf2     rectilinear propagation of1  
#aid2     rle of1 in vision1 #ha2       
spatial and temporal periodicity of1    
explains optical phenomena1 #aid2       
numerical velocity of1 #eh2     where   
does it go to8 #aii2     generally1 #dh 
et seq4    ,like effects in like        
circumstances1 #aii4    ,likeness1 #chh1
 #cia4    ,lilliput1 #hd4    ,lines1    
straight1 their symmetry1 #ih2          
curved1 their asymmetry1 #ih2     of    
force1 #bdi4    ,links of thought1      
intermediate1 #aih4    ,liquefaction1   
latent heat of1 #agh4    ,liquid1       
efflux1 law of1 #aej2     equilibrium1  
figures of1 #d et seq42     the latter  

produced in open air1 #g-h2     their   
beauty and multiplicity of form1 #g1 #h2
     made permanent by melted           
colophonium1 #g4    ,liquids1 forms of1 
#a-af2     difference between1 and      
solids1 #b2     their mobility and      
adaptiveness of form1 #c2     the       
courtiers par excellence of the natural 
bodies1 #c2     possess under certain   
circumstances forms of their own1 #c4   
,living force1 #acg1 #ahd2     law of   
the conservation of1 #adi4    ,lloyd1   
observation of the conical refraction of
 light1 #bi4    ,lobster1 of ,lake      
,mohrin1 the1 #fa4    ,localisation1    
cerebral1 #baj4    ,locke1 on language  
and thought1 #ceh4    ,locomotive1 steam
 in the boiler of1 #bai4    ,loeb1 ,j41 
#bhi1 #bia1 #cjb4    ,logarithms1 #aie1 
#bai2     in music1 #ajc-ajd4           
,logical root1 of the principle of      
energy1 #aha2     of the principle of   
excluded perpetual motion1 #ahb4        
,lombroso1 #bhj4    ,lucian1 #cdg4      
,macula acustica1 #bgb4    ,magic       

lantern1 #if4    ,magic powers of       
nature1 #ahi4    ,magical power of      
science1 belief in the1 #ahi4           
,magnet1 a1 #bbj2     will compared to  
the pressure of a1 #ad2     coercive    
force of a1 #baf4    ,magnetic needle1  
near a current1 #bjg4    ,magnetised bar
 of steel1 #bdb-bdc4    ,major and minor
 keys in music1 #ajj et seq4    ,malus1 
#bdb4    ,man1 a fragment of nature's   
life1 #di2     his life embraces others1
 #bcd4    ,mann1 #cfd4    ,manuscript in
 a mirror1 #ic4    ,maple syrup1 statues
 of1 on ,moon1 #d4    ,marx1 #ce4       
,material1 the relations of work with   
heat and the consumption of1 #bde   et  
seq4    ,mathematical methods1 their    
character1 #aig-aih4    ,mathematics1   
economy of1 #aie2     on instruction in1
 #cch-cgd2     ,c4 ,g4 ,j4 ,jacobi on1  
#bhj4    ,matter1 constancy of1 #bjc2   
its nature1 #bjc2     the notion of1    
#bac4    ,maupertuis1 his ,latin city1  
#cch4    ,maximal and minimal problems1 
their rle in physics1 #ad1 footnote4    

,mayer1 ,j4 ,r41 his conception of      
energy1 #bde1 #bdf2     his methods of  
thought1 #bdg2     on the conservation  
of energy1 #afc1 #afd1 #afe1 #afg1 #ahc1
 #ahd2     his metaphysical utterances1 
#ahc1 #bdf2     also #ach1 #ahd1 #aia1  
#bag1 #bga1 #bgd4    ,measurement1      
definition of1 #bjf4    ,measures1      
international1 #ajh4    ,mcanique       
cleste1 #ij1 #ahh2     sociale1 and     
morale1 the1 #ij4    ,mechanical1       
conception of the world1 #aje1 #aee et  
seq41 #ahh1 #bjg2     energy1 ,w4       
,thomson on waste of1 #age2             
analogies between ---- and thermal      
energy1 #ag et seq42     equivalent of  
heat1 electricity1 etc41 #afd1 #afg et  
seq42     mythology1 #bjg2              
phenomena1 physical events as1 #ahb2    
philosophy1 #ahh2     physics1 #aee-afj1
 #bab2     substitution-value of heat1  
#agh1 footnote4    ,mechanics1          
,kirchhoff's definition of1 #bcf4       
,medicine1 students of1 #cbf4           
,melody1 #aja4    ,melsens1 #caj1 #cbg4 

,memory1 a treasure-house for           
comparison1 #bcj2     common elements   
impressed upon the1 #ahj2     its       
importance1 #bch2     science disburdens
 the1 #aic4    ,mendelejeff1 his        
periodical series1 #bef4    ,mental1    
adaptation1 #bad-bce2     completion of 
phenomena1 #bbj2     imagery1 #bec2     
imitation1 our schematic1 #aii2         
processes1 economical1 #aie2            
reproduction1 #aih2     visualisation1  
#bej4    ,mephistopheles1 #hh4          
,mercantile principle1 a miserly1 at the
 basis of science1 #ae4    ,mersenne1   
#cgg4    ,mesmerism1 the mental state of
 ordinary minds1 #bbh4    ,metaphysical 
establishment of doctrine of energy1    
#ahc4    ,metaphysical spooks1 #bbb4    
,metrical1 concepts of electricity1 #ajg
 et seq42     notions1 energy and       
entropy are1 #agh2     units1 the       
building-stones of the physicist1 #bec4 
,metronomes1 #da4    ,meyer1 ,lothar1   
his periodical series1 #bef4    ,middle 
,ages1 #bdc1 #cdi4    ,midsummer        

,night's ,dream1 #cji4    ,mill1 ,john  
,stuart1 #bcj4    ,millers1 school for1 
#cbf4    ,mill-wheel1 doing work1 #afa4 
,mimicking facts in thought1 #ahi1 #aic4
    ,minor and major keys in music1 #ajj
 et seq4    ,mirror1 symmetrical        
reversion of objects in1 #ib et seq4    
,miserly mercantile principle at the    
basis of science1 #ae4    ,moat1 child  
looking into1 #bjh4    ,modern          
scientists1 adherents of the mechanical 
philosophy1 #ahh4    ,molecular         
theories1 #ajd4    ,molecules1 #bjc1    
#bjg4    ,molire1 #bcd4    ,momentum1   
#ahd4    ,monocular vision1 #ih4        
,monotheism of the ,christians and      
,jews1 #ahg4    ,montagues and          
,capulets1 #hg4    ,moon1 eclipse of1   
#bai2     lightness of bodies on1 #d2   
the study of the1 #ij1 #bhd4    ,moreau1
 #cjg4    ,mosaic of thought1 #aib4     
,motion1 a perpetual1 #aha2     quantity
 of1 #ahd2     the ,eleatics on1 #aeh2  
,wundt on1 #aeh2     the ,herbartians   
on1 #aeh4    ,motions1 natural and      

violent1 #bbf2     their familiar       
character1 #aeg4    ,mountains of the   
earth1 would crumble if very large1 #c2 
weight of bodies on1 #aab4    ,mozart1  
#dd1 #bgi4    ,mller1 ,johann1 #bia4    
,multiplication-table1 #aie4            
,multiplier1 #acb4    ,music1 band of1  
its tempo accelerated and retarded1 #ec2
     the principle of repetition in1 #ii
 et seq42     its notation1             
mathematically illustrated1 #ajc-ajd4   
,musical notes1 reversion of1 #aja et   
seq42     their economy1 #aib4          
,musical scale1 a species of            
one-dimensional space1 #aje4            
,mystery1 in physics1 #bbb2     science 
can dispense with1 #ahi4    ,mysticism1 
numerical1 #cc2     in the principle of 
energy1 #ahd4    ,mythology1 the        
mechanical1 of philosophy1 #bjg4        
,nagel1 von1 #cfd4    ,nansen1 #bif4    
,napoleon1 picture representing the tomb
 of1 #cf4    ,nations1 intercourse and  
ideas of1 #ccf-ccg4    ,natural         
constants1 #aic4    ,natural law1 a1 not

 contained in the conformity of the     
energies1 #age4    ,natural laws1       
abridged descriptions1 #aic2     likened
 to type1 #aic4    ,natural motions1    
#bbe4    ,natural selection in          
scientific theories1 #fc1 #bah4         
,nature1 experience the well-spring of  
all knowledge of1 #aha2     fashions of1
 #fd2     first knowledge of1           
instinctive1 #ahi2     general          
interconnexion of1 #ahb2     has many   
sides1 #bag2     her forces compared to 
purposes1 #ad-ae2     likened to a good 
man of business1 #ae2     the economy of
 her actions1 #ae2     how she appears  
to other animals1 #hc et seq42          
inquiry of1 viewed as a torture1 #dh-di2
     view of1 as something designedly   
concealed from man1 #di2     like a     
covetous tailor1 #i-aj2     magic powers
 of1 #ahi2     our view of1 modified by 
binocular vision1 #hb2     the          
experimental method a questioning of1   
#dh4    ,negro hamlet1 the science of a1
 #bcg4    ,neptune1 prediction and      

discovery of the planet1 #bi4    ,new   
views1 #bif et seq4    ,newton1         
describes polarisation1 #bdb2           
expresses his wealth of thought in      
,latin1 #cda2     his discovery of      
gravitation1 #bbe et seq42     his      
solution of dispersion1 #cfb2     his   
principle of the equality of pressure   
and counterpressure1 #aia2     his view 
of light1 #bbg-bbh2     on absolute     
time1 #bjd2     selections from his     
works for use in instruction1 #cfh2     
also #bgj1 #bgd1 #bgi1 #bhe1 #bhi4      
,nobility1 they displace ,latin1 #cdb4  
,notation1 musical1 mathematically      
illustrated1 #ajc-ajd4    ,numbers1     
economy of1 #aie2     their connexion   
with consonance1 #cb4    ,numerical     
mysticism1 #cc4    ,nursery1 the        
questions of the1 #aii4                 
,observation1 #caj4    ,observation1 in 
science1 #bfa4    ,ocean-stream1 #bgb4  
,oettingen1 ,von1 #ajc4    ,ohm1 on     
electric currents1 #bdi4    ,ohm1 the   
word1 #cdc4    ,oil1 alcohol1 water1    

and1 employed in ,plateau's experiments1
 #d2     free mass of1 assumes the shape
 of a sphere1 #ab2     geometrical      
figures of1 #e et seq4    ,one-eyed     
people1 vision of1 #ih4                 
,ophthalmoscope1 #ah4    ,optic nerves1 
#if4    ,optimism and pessimism1 #bcd4  
,order of physics1 #aig4    ,organ1     
bellows of an1 #ace4    ,organic nature1
 results of ,darwin's studies of1 #bae  
et seq4     ,see ,adaptation and        
,heredity4    ,oriental world of fables1
 #bgc4    ,orientation1 sensations of1  
#bhb et seq4    ,oscillation1 centre of1
 #adg et seq4    ,ostwald1 #agb4        
,otoliths1 #cja et seq4    ,overtones1  
#bh1 #dj1 #cdi4    ,ozone1 ,schbein's   
discovery of1 #bga4     ,painted things1
 the difference between real and1 #fh4  
,palestrina1 #dd4    ,parameter1 #beg4  
,partial tones1 #cij4    ,particles1    
smallest1 #ajd4    ,pascheles1 ,dr4 ,w41
 #bhe4    ,paulsen1 #cch1 #cdj1 #cgc4   
,pearls of life1 strung on the          
individual as on a thread1 #bcd-bce4    

,pencil surpasses the mathematician in  
intelligence1 #aif4    ,pendulum1 motion
 of a1 #add et seq41     increased      
motion of1 due to slight impulses1 #ba2 
electrical1 #aaj4    ,percepts1 of like 
form1 #cij4    ,periodical1 changes1    
#aha2     series1 #bef4    ,permanent1  
changes1 #aha1 #aii2     elements of the
 world1 #aid4    ,perpetual motion1 a1  
#aha2     defined1 #aci2                
impossibility of1 #aci et seq42     the 
principle of the1 excluded1 #adj et     
seq42     excluded from general physics1
 #afb4    ,personality1 its nature1     
#bcd-bce4    ,perspective1 #gf et seq42 
contraction of1 #gd et seq42            
distortion of1 #gg4    ,pessimism and   
optimism1 #bcd4    ,pharaohs1 #he4      
,phenomenology1 a universal physical1   
#bej4    ,philistine1 modes of thought  
of1 #bbc4    ,philology1 comparison in1 
#bci4    ,philosopher1 an ancient1 on   
the moral and physical sciences1 #hi4   
,philosophy1 its character at all times1
 #ahf2     mechanical1 #aee et seq41    

#ahh1 #bjg1 #bei et seq4    ,phonetic   
alphabets1 their economy1 #aib4         
,photography1 by the electric spark1    
#cah et seq4    ,photography of         
projectiles1 #cji-ccg4    ,photography1 
stupendous advances of1 #gd4            
,physical1 concepts1 fetishism in our1  
#ahg2     ideas and principles1 their   
nature1 #bjd2     inquiry1 the          
economical nature of1 #ahf2             
research1 object of #bjg1 #bji4         
,physical phenomena1 as mechanical      
phenomena1 #ahb2     relations between1 
#bje4    ,physico-mechanical view of the
 world1 #aee1 #ahg1 #ahh1 #bjg et seq4  
,physics1 compared to a well-kept       
household1 #aig2     economical         
experience1 #aig2     the principles of1
 descriptive1 #aii2     the methods of1 
#bji2     its method characterised1     
#baa2     comparison in1 #bci2     the  
facts of1 qualitatively homogeneous1    
#bee2     how it began1 #cg2     helped 
by psychology1 #ajd2     study of its   
own character1 #ahi2     the goal of1   

#bjg1 #bji4    ,physiological           
psychology1 its methods1 #baa et seq4   
,physiology1 its scope1 #bab4    ,piano1
 its mirrored counterpart1 #ajj et seq42
     used to illustrate the facts of    
sympathetic vibration1 #be et seq4      
,piano-player1 a speaker compared to1   
#aib4    ,picture1 physical1 a1 #aaj4   
,pike1 learns by experience1 #bfg4      
,pillars of ,corti1 #ai4    ,places1    
heavy bodies seek their1 #bbd et seq4   
,planetary system1 origin of1           
illustrated1 #e4    ,plasticity of      
organic nature1 #baf4    ,plateau1 his  
law of free liquid equilibrium1 #i2     
his method of getting rid of the effects
 of gravity1 #d4    ,plates of oil1     
thin1 #f4    ,plato1 #cdg1 #cga4        
,plautus1 #cdg4    ,playfair1 #ach4     
,pleasant effects1 cause of1 #id et seq4
    ,pliny1 #cdi4    ,poetry and        
science1 #cj1 #ca1 #cea4    ,poinsot1 on
 the foundations of mechanics1 #aeb et  
seq4    ,polarisation1 #ia2             
abstractly described by ,newton1 #bdb4  

,politics1 ,chinese speak with          
unwillingness of1 #cgd4    ,pollak1     
#bii4    ,polyp plant1 humanity likened 
to a1 #bce4    ,pompeii1 #bcd2     art  
in1 #hj4    ,popper ,j41 #agb1 #baf4    
,potential1 social1 #ae2     electrical1
 #aba et seq42     measurement of1 #abf2
     fall of1 #agg2     swarm of notions
 in the idea of1 #aig2     its wide     
scope1 #bej4    ,pottery1 invention of1 
#bfc4    ,prediction1 #bba et seq4      
,prejudice1 the function1 power1 and    
dangers of1 #bcb-bcc4    ,preparatory   
schools1 the defects of the ,german1    
#cdf-cdg2     what they should teach1   
#cfd et seq4    ,pressure of a stone or 
of a magnet1 will compared to1 #ad2     
also #aeg4    ,primitive acts of        
knowledge the foundation of scientific  
thought1 #aij4    ,problem1 nature of a1
 #bbc4    ,problems which are wrongly   
formulated1 #cjh4    ,process1          
,carnot's1 #afa et seq4    ,projectiles1
 the effects of the impact of1 #caj1    
#cbg-cbh2     seen with the naked eye1  

#caa1 #cag2     measuring the velocity  
of1 #ccb2     photography of1 #cji-ccg4 
,prony's brake1 #acb4    ,proof1 nature 
of1 #bhd4    ,prophesying events1 #bbj  
et seq4    ,psalms1 quotation from the1 
#hi4    ,pseudoscope1 ,wheatstone's1    
#if4    ,psychology1 preceded by        
astronomy1 #ij2     how reached1 #ia et 
seq42     helps physical science1 #ajd2 
its method the same as that of physics1 
#bjg et seq4    ,pully arrangement1     
illustrating principle of least         
superficial area1   #ab-ac4             
,purkinje1 #bhd1 #bhe1 #bia1 #bii4      
,purposes1 the acts of nature compared  
to1 #ad-ae2     nature pursues no1 #ff4 
,puzzle-lock1 a1 #bf4    ,puzzles1 #bgg4
    ,pyramid of oil1 #f4    ,pythagoras1
 his discovery of the laws of harmony1  
#cb1 #bei4     ,quality of tones1 #cf4  
,quantitative investigation1 the goal   
of1 #ahj4    ,quantity of electricity1  
#aaa1 #aah1 #aai1 #afg-agj1 #agc2     of
 heat1 #aff1 #afg-aga1 #agd1 #agg1 #bdd2
     of motion1 #ahd4    ,quests made of

 the inquirer1 not by him1 #cj4         
,qutelet1 #ae1 footnote4     ,rabelais1 
#bhc4    ,raindrop1 form of1 #c4        
,rameau1 #cd4    ,reaction and action1  
principle of1 #aia4    ,reactions1      
disclosure of the connexion of1 #bgj et 
seq4    ,realgymnasien1 #cfe4           
,realschulen1 #cfe1 #cgc4    ,reason1   
stands above the senses1 #aje4          
,reflex action1 #baj4    ,reflexion1    
produces symmetrical reversion of       
objects1 #ic et seq4    ,refraction1    
#bi1 #aic1 #aid1 #bjh1 #bcj1 #bca4      
,reger1 #cbh4    ,reliefs1 photographs  
of1 #fh4    ,repetition1 its rle in     
sthetics1 #hi1 footnote1 #ia et seq41   
#ig1 #ih   et seq41 #cij4               
,reproduction of facts in thought1 #ahi1
 #aic1 #aih1 #bec4    ,repulsion1       
electric1 #aji et seq41 #afh4           
,research1 function of experimental     
#aha2     the aim of1 #bje4             
,resemblances between facts1 #bee4      
,resin1 solution of1 #g4    ,resistance1
 laws of1 for bodies travelling in air  

and fluids1 #ccc et seq4    ,resonance1 
corporeal1 #cib4    ,response of        
sonorous bodies1 #be4    ,retina1 the   
corresponding spots of #ih2     nerves  
of compared to fingers of a hand1 #if et
 seq4    ,reversible processes1 #afa et 
seq41 #age1 #agf1 #aha1 #ahb4    ,rhine1
 the1 #id4    ,richard the ,third1 #gg4 
,riddles1 #bgg4    ,riders1 #cgi4       
,riegler1 #cai4    ,riess1 experiment   
with the thermo-electrometer1 #acc et   
seq41 #afi4    ,rigid connexions1 #adb4 
,rind of a fruit1 #aij4    ,rings of    
oil1 illustrating formation of rings of 
,saturn1 #e4    ,ritter1 #bia1 #bii4    
,rods of ,corti1 #ai4    ,rolph1 ,w4    
,h41 #baf4    ,roman ,church1 ,latin    
introduced with the1 #cdj et seq4       
,romans1 their provinciality and        
narrow-mindedness1 #bgj4    ,romeo and  
,juliet1 #hg4    ,rmer1 ,olaf1 #ea et   
seq4    ,roots1 the nature of1 in       
language1 #beb4    ,rosetti1 his        
experiment on the work required to      
develop electricity1 #aca4    ,rotating 

bodies1 #bhe4    ,rotation1 apparatus   
of1 in physics1 #ei et seq42            
sensations of1 #bhh et seq4             
,rousseau1 #ccf4    ,rubber pyramid1    
illustrating the principle of least     
superficial area1   #aj-aa4             
,ruysdael1 #bgi4     ,sachs1 ,hans1     
#ajf4    ,salcher1 ,prof4 #cai4         
,salviati1 #add4    ,saturn1 rings of1  
their formation illustrated1 #e4        
,saurians1 #beg4    ,sauveur1 on        
acoustics1 #cd1 #cge et seq4    ,savage1
 modes of conception and interpretation 
of a1 #bah et seq4    ,schfer1 ,k41     
#bih4    ,schlierenmethode1 #cag4       
,schnbein's discovery of ozone1 #bga4   
,school-boy1 copy-book of1 #ib4         
,schoolmen1 #bad4    ,schools1          
,state-control of1 #cgb et seq4         
,schopenhauer1 #aij4    ,schultze1 ,max1
 #ai4    ,science1 a miserly mercantile 
principle at its basis1 #ae2            
compared to a business1 #af2     viewed 
as a maximum or minimum problem1 #af1   
footnote2     its process not greatly   

different from the intellectual activity
 of     ordinary life1 #af1 footnote2   
economy of its task1 #af2     relation  
of1 to poetry1 #cj1 #ca1 #cea2     the  
church of1 #fg2     beginnings of1 #ahi1
 #aia2     belief in the magical power  
of1 #ahi2     can dispense with mystery1
 #ahi2     lavish extravagance of1 #ahi2
     economy of the terminology of1     
#aib2     partly made up of the         
intelligence of others1 #aif2           
stripped of mystery1 #aig2     its true 
power1 #aig2     the economical         
schematism of1 #bjf2     the object of1 
#bjf2     the tools of1 #bjg2     does  
not create facts1 #baa2     of the      
future1 #bac2     revolution in1 dating 
from ,galileo1 #bad et seq42     the    
natural foe of the marvellous1 #bbd2    
characterised1 #bbg2     growth of1     
#bcg2     dramatic element in1 #bdc2    
described1 #bea2     its function1 #bec2
     classification in1 #bee1 #bei et   
seq42     the way of discovery in1 #caf4
     ,see also ,physics4    ,sciences1  

partition of the1 #hf2     the barriers 
and relations between the #beg-beh2     
on instruction in the1 #cch-cgd4        
,scientific1 criticism1 ,socrates the   
father of1 #a1 #af2     discoveries1    
their fate1 #ach2     knowledge1        
involves description1 #aic2     thought1
 transformation and adaptation in1      
#bad-bce2     thought1 advanced by new  
experiences1 #bbc et seq42     thought1 
the difficulty of1 #cff2     terms1     
#cdb-cdc2     founded on primitive acts 
of knowledge1 #aij4    ,scientists1     
stories about their ignorance1 #cdb4    
,screw1 the1 #fb4    ,sea-sickness1     
#bhd4    ,secret computation1           
,leibnitz's1 #cc4    ,seek their places1
 bodies1 #bbf4    ,self-induction1      
coefficient of1 #bej1 #beb4             
,self-observation1 #baa4                
,self-preservation1 our first knowledge 
derived from the economy of1 #aig2      
struggle for1 among ideas1 #bbh4        
,semi-circular canals1 #bij et seq4     
,sensation of rounding a railway curve1 

#bhf4    ,sensations1 analysed1 #bea2   
when similar1 produce agreeable effects1
 #if2     their character1 #bjj2        
defined1 #bji2     of orientation1 #bhb 
et seq4    ,sense-elements1 #agi4       
,senses1 theory of1 #ajd2     the source
 of our knowledge of facts1 #bcg4       
,seventh1 the troublesome1 #df4         
,shadow method1 #cac et seq41 #cag      
footnote4    ,shadows1 rle of1 in       
vision1 #ha4    ,shakespeare1 #bgh4     
,sharps1 reversed into flats1 #aja4     
,shell1 spherical1 law of attraction for
 a1 #abd1 footnote4    ,shoemaker1      
inquirer compared to1 #aje-ajf4         
,shooting1 #cji4    ,shots1 double      
report of1 #bbi et seq4    ,similarity1 
#bdi4    ,simony1 #bhj4    ,simplicity1 
a varying element in description1 #bed4 
,sines1 law of the1 #aic4    ,sinking of
 heavy bodies1 #bbb4    ,sixth sense1   
#big4    ,smith1 ,r41 on acoustics1 #cd1
 #cha1 #chc4    ,soap-films1 ,van der   
,mensbrugghe's experiment with1 #aa-ab4 
,soapsuds1 films and figures of1 #g4    

,social potential1 #ae4    ,socrates1   
the father of scientific criticism1 #a1 
#af4    ,sodium1 #bjb4    ,sodium-light1
 vibrations of1 as a measure of time1   
#bje4    ,solidity1 conception of1 by   
the eye1 #ga et seq42     spatial1      
photographs of1 #gc4    ,solids1 and    
liquids1 their difference merely one of 
degree1 #b4    ,sonorous bodies1 #bd et 
seq4    ,soret1 ,j4 ,p41 #hi4           
,sounds1 symmetry of1 #ii et seq42      
generally1 #bb-dg1 #bab4    ,sound-waves
 rendered visible1 #cae et seq4         
,sources of the principle of energy1    
#agi et seq4    ,space1 #bje2           
sensation of1 #baj4    ,spark1 electric1
 #aag1 #abg1 #acb1 #acc1 #aij4          
,spatial vision1 #chf4    ,species1     
stability of1 a theory1 #baf4           
,specific energies1 #bia4    ,specific  
heat1 #aff1 #bdd4    ,specific inductive
 capacity1 #aag4    ,spectral analysis  
of sound1 #bg4    ,spectrum1 mental     
associations of the1 #aij4    ,speech1  
the instinct of1 cultivated by          

languages1 #ced4    ,spencer1 #bah1     
#bbb4    ,sphere1 a soft rotating1 #b2  
the figure of least surface1 #ab2       
electrical capacity of1 #abc et seq4    
,spherical shell1 law of attraction for 
#abd1 footnote4    ,spiders1 the eyes   
of1 #fg4    ,spirits1 as explanation of 
the world #ahf1 #bdc4    ,spiritualism1 
modern1 #ahg4    ,spooks1 metaphysical1 
#bbb4    ,squinting1 #gb4    ,stability 
of our environment1 #bjf4    ,stallo1   
#ccf4    ,stars1 the fixed1 #ij4        
,state1 benefits and evils of its       
control of the schools1 #cgb et seq42   
the ,church and1 #hh4    ,statical      
electricity1 #acd4    ,stationary       
currents1 #bdi4    ,statoliths1 #cjc4   
,steam-engine1 #afj1 #bfe4              
,steeple-jacks1 #ge4    ,stereoscope1   
,wheatstone and ,brewster's1 #gc4       
,stevinus1 on the inclined plane1 #adj2 
on hydrostatics1 #ada2     on the       
equilibrium of systems1 #adb2           
discovers the principle of virtual      
velocities1 #aej2     characterisation  

of his thought1 #adb2     also #ahb1    
#ahg1 #aia4    ,stone ,age1 #df1 #cba4  
,strensen1 #cjf4    ,stove1 primitive1  
#bfc4    ,straight line1 a1 its         
symmetry1 #ih4    ,straight1 meaning of 
the word1 #bdj4    ,street1 vista into  
a1 #ge4    ,striae1 in glass1 #cac4     
,striate method1 for detecting optical  
imperfections1 #cag4    ,striking       
distance1 #aae1 #abg4    ,strings1      
vibrations of1 #bdi4    ,struggle for   
existence among ideas1 #bag4            
,substance1 heat conceived as a1 #agg1  
#bdc et seq42     electricity as a1     
#agj2     the source of our notion of1  
#aii2     rle of the notion of1 #bjc1   
#bdd et seq42     energy conceived as a1
 #afd1 #ahe1 #bdd et seq4               
,substitution-value of heat1 #agh1      
footnote4    ,suetonius1 #cdh4          
,sulphur1 specific inductive capacity   
of1 #aag4    ,sun1 human beings could   
not exist on1 #c4    ,swift1 #hd1 #bhj4 
,swimmer1 ,ampre's1 #bjg4    ,symmetry1 
definition of1 #ib2     figures of1 #ib 

et seq42     plane of1 #id2     vertical
 and horizontal1 #id2     in music1 #ii 
et seq4    ,sympathetic vibration1 #bb  
et seq41 #cgi4     ,tailor1 nature like 
a covetous1 #i-aj4    ,tangent1 the     
word1 #bfc4    ,taste1 doubtful         
cultivation of1 by the classics1        
#ceb-cec2     of the ancients1 #cec4    
,taylor1 on the vibration of strings1   
#bdi4    ,teaching1 its nature1 #cff et 
seq4    ,telegraph1 the word1 #bfc4     
,telescope1 #bfb4    ,telestereoscope1  
the1 #hd4    ,temperament1 even1 in     
tuning1 #dg4    ,temperature1 absolute1 
#afb2     differences of1 #bje2         
differences of1 viewed as level         
surfaces1 #afa2     heights of1 #agd2   
scale of1 derived from tensions of      
gases1 #agd4    ,terence1 #cdg4         
,terms1 scientific1 #cdb-cdc4           
,thales1 #bei4    ,theories1 their      
scope1 function1 and power1 #bda-bdb2   
must be replaced by direct description1 
#bdh4    ,thermal1 energy1 #agd1 #agg2  
capacity1 #abc1 footnote4               

,thermodynamics1 #afj et seq4           
,thermoelectrometer1 ,riess's1 #acc1    
#afi4    ,thing-in-itself1 the1 #bjj4   
,things1 mental symbols for groups of   
sensations1 #bjj-bja4    ,thomson1      
,james1 on the lowering of the          
freezing-point of water by   pressure1  
#afb4    ,thomson1 ,w41 his absolute    
electrometer1 #abg1 footnote2     on    
thermodynamics1 #afb2     on the        
conservation of energy1 #afe2     on the
 mechanical measures of temperature1    
#agd1 footnote2     on waste of         
mechanical energy1 #age2     also #ajh1 
#agc1 footnote4    ,thought1 habitudes  
of1 #aii1 #bbd1 #bbg1 #bcb2             
relationship between language and1 #cbi2
     incongruence between experience    
and1 #bjf2     luxuriance of a fully    
developed1 #eh2     transformation in   
scientific1 #bad-bce4    ,thoughts1     
their development and the struggle for  
existence among them1   #fc2            
importance of erroneous1 #fe2     as    
reproductions of facts1 #ajg4           

,thread1 the individual a1 on which     
pearls are strung1 #bcd-bce4    ,tides1 
#bhc4    ,timbre1 #cg1 #ch1 #ci4        
,time1 #agh1 #bjd1 #bje1 footnote4      
,toepler and ,foucault1 method of1 for  
detecting optical faults1 #cac   et     
seq41 #cbj4    ,tone-figures1 #ia4      
,tones1 #bb-dg1 #ii et seq41 #bab4      
,torsion1 moment of1 #acb4              
,torsion-balance1 ,coulomb's1 #aji1     
#afh4    ,torricelli1 on virtual        
velocities1 #aej2     his law of liquid 
efflux1 #aej2     on the atmosphere1    
#bgc4    ,tourist1 journey of1 work of  
the inquirer compared to1 #ag1 #bi1 #cj4
    ,transatlantic cable1 #ajh4         
,transformation and adaptation in       
scientific thought1 #bad-bce4           
,transformation of ideas1 #fc4          
,transformative law of the energies1    
#agb4    ,translation1 difficulties of1 
#ced4    ,tree1 conceptual life compared
 to a1 #bca4    ,triangle1 mutual       
dependence of the sides and angles of a1
 #agi4    ,triple accord1 #df4          

,truth1 wooed by the inquirer1 #de2     
difficulty of its acquisition1 #df4     
,tumblers1 resounding1 #bc4             
,tuning-forks1 explanation of their     
motion1 #bb et seq4    ,tylor1 #ahf4    
,tympanum1 #ah4    ,type1 natural laws  
likened to1 #aic2     words compared to1
 #aia4     ,ulysses1 #cdg4              
,understanding1 what it means1 #baa4    
,uniforms1 do not fit heads1 #cfi4      
,unique determination1 #aha-ahb4        
,unison1 #dc4    ,unit1 electrostatic1  
#aaa4     ,see ,force and ,work4        
,united ,states1 #ccf4    ,universal    
,real ,character1 a1 #aib4    ,utility  
of physical science1 #cea4              
,variation1 the method of1 in science1  
#bcj2     in biology1 #baf4             
,velocity1 of light1 #dh et seq42     of
 the descent of bodies1 #adc et seq42   
meaning of1 #bjd2     virtual1 #adi-aee4
    ,verstandesbegriffe1 #aii4          
,vertical1 perception of the1 #bgb1 #bhf
 et seq42     symmetry1 #chi4           
,vertigo1 #bhe1 #bij4    ,vestibule of  

the ear1 #cjj4    ,vibration1 #bb et    
seq4    ,vibration-figures1 #ia4        
,vinci1 ,leonardo da1 #bgh1 #bhc4       
,violent motions1 #bbe4    ,virtual     
velocities1 #adi-aee4    ,visibility1   
general conditions of1 #cab4    ,vision1
 symmetry of our apparatus of1 #if4     
,see ,eye4    ,visual nerves1 #if4      
,visualisation1 mental1 #bej4    ,volt1 
the word1 #cdc4    ,volta1 #abg1        
footnote1 #acd4    ,voltaire1 #bfj4     
,voltaire's ingnu1 #bai4    ,vowels1    
composed of simple musical notes1 #bf4  
,wagner1 ,richard1 #bgi4    ,wald1 ,f41 
#agh1 footnote4    ,wallace1 #baf4      
,war1 and peace1 reflexions upon1 #cji1 
#cce et seq4    ,waste of mechanical    
energy1 ,w4 ,thomson on1 #age4          
,watches1 experiment with1 #da2     in a
 mirror1 #ic4    ,water1 jet of1        
resolved into drops1 #fj2     free1     
solid figures of1 #h2     objects       
reflected in1 #id1 #aia2     possible   
modes of measurement of1 #agj4    ,watt1
 #bff4    ,wealth1 the foundation of1   

#aih4    ,weapons1 modern1 #cce4        
,weber1 #ajh1 #cjf4    ,weight of       
bodies1 varies with their distance from 
the centre of the   earth1 #aab4        
,weismann1 #baf4    ,wheatstone1 his    
stereoscope1 #gc2     his pseudoscope1  
#if2     also #ei4    ,wheel1 history   
and importance of1 #fa et seq4          
,whewell1 on the formation of science1  
#bca4    ,whole1 the1 #bjd1 footnote4   
,why1 the question1 #aii1 #bbc4         
,will1 ,schopenhauer on the1 #aij2      
man's most familiar source of power1    
#bdc2     used to explain the world1    
#ahf2     forces compared to1 #bed2     
compared to pressure1 #ad4    ,windmill1
 a rotating1 #ec4    ,wire frames and   
nets1 for constructing liquid figures of
 equilibrium1   #d et seq4              
,witchcraft1 #ahg4    ,wollaston1 #bhd1 
#bhe4    ,wonderful1 science the natural
 foe of the1 #bbd4    ,woods1 the       
relative distance of trees in1 #fh4     
,wooer1 inquirer compared to a1 #de4    
,words and sounds1 #cdc4    ,words1     

compared to type1 #aia4    ,work1 of    
liquid forces of attraction1 #ad2     in
 electricity1 #agc2     measure of1 #aai
 et seq41 #acj1 #bbc2     relation of1  
with heat1 #afb1 #bde et seq42          
amount required to develop electricity1 
#aca et seq42     produces various      
physical changes1 #aci2     substantial 
conception of1 #ahc-ahd4     ,see       
,energy4    ,world1 the1 what it        
consists of1 #bjh4    ,world-particles1 
#bjc4    ,wronsky1 #agb4    ,wundt1 on  
causality and the axioms of physics1    
#aeg-aei2 #cei footnote4     ,xenophon1 
#di1 footnote4     ,young1 ,thomas1 on  
energy1 #agc4     ,zelter1 #ce4         
,zeuner1 #aga4    ,zology1 comparison   
in1 #bci4     ,,the ,,works ,,of ,,ernst
 ,,mach4  ,,the ,,science ,,of          
,,mechanics4  ,a ,,critical ,,and       
,,historical ,,exposition ,,of ,,its    
,,principles4  ,by ,,dr4 ,,ernst ,,mach4
  ,,professor ,,of ,,the ,,history ,,and
 ,,theory ,,of ,,inductive ,,science    
,,in ,,the ,,university ,,of ,,vienna4  

,translated from the ,second ,german    
,edition ,by ,,thomas ,j4               
,mc,c,o,r,m,a,c,k4   #bej ,cuts4 #ecd   
,pages4 ,half ,morocco1 ,gilt ,top1     
,marginal ,analyses4  ,exhaustive       
,index4 ,price #b4ej4     ,,table ,,of  
,,contents4   ,,statics4       ,the     
,lever4       ,the ,inclined ,plane4    
,the ,composition of ,forces4           
,virtual ,velocities4       ,statics in 
,their ,application to ,fluids4         
,statics in ,their ,application to      
,gases4   ,,dynamics4       ,galileo's  
,achievements4       ,achievements of   
,huygens4       ,achievements of        
,newton4       ,principle of ,reaction4 
,criticism of the ,principle of         
,reaction and of the ,concept of ,mass4 
,newton's ,views of ,time1 ,space1 and  
,motion4       ,critique of the         
,newtonian ,enunciations4               
,retrospect of the ,development of      
,dynamics4   ,,the ,,extension ,,of     
,,the ,,principles ,,of ,,mechanics4    
,scope of the ,newtonian ,principles4   

,formul and ,units of ,mechanics4       
,conservation of ,momentum1             
,conservation of the ,centre of         
,gravity1      and ,conservation of     
,areas4       ,laws of ,impact4         
,d',alembert's ,principle4              
,principle of ,vis ,viva4               
,principle of ,least ,constraint4       
,principle of ,least ,action4           
,hamilton's ,principle4                 
,hydrostatic and ,hydrodynamic          
,questions4   ,,formal ,,development    
,,of ,,mechanics4       ,the            
,isoperimetrical ,problems4             
,theological1 ,animistic1 and ,mystical 
,points of ,view in ,mechanics4         
,analytical ,mechanics4       ,the      
,economy of ,science4   ,,the ,,relation
 ,,of ,,mechanics ,,to ,,other          
,,departments ,,of ,,knowledge4         
,relations of ,mechanics to ,physics4   
,relations of ,mechanics to ,physiology4
     ,,press ,,notices4   ,the          
appearance of a translation into        
,english of this remarkable book should 

serve to revivify in this country       
,england the somewhat stagnating        
treatment of its subject1 and should    
call up the thoughts which puzzle us    
when we think of them1 and that is not  
sufficiently often4444 ,professor ,mach 
is a striking instance of the           
combination of great mathematical       
knowledge with experimental skill1 as   
exemplified not only by the elegant     
illustrations of mechanical principles  
which abound in this treatise1 but also 
from his brilliant experiments on the   
photography of bullets4444 ,a careful   
study of ,professor ,mach's work1 and a 
treatment with more experimental        
illustration1 on the lines laid down in 
the interesting diagrams of his ,science
 of ,mechanics1 will do much to revivify
 theoretical mechanical science1 as     
developed from the elements by rigorous 
logical treatment4--,prof4 ,a4 ,g4      
,greenhill1 in ,nature1 ,london4  ,those
 who are curious to learn how the       
principles of mechanics have been       

evolved1 from what source they take     
their origin1 and how far they can be   
deemed of positive and permanent value1 
will find ,dr4 ,mach's able treatise    
entrancingly interesting4444 ,the book  
is a remarkable one in many respects1   
while the mixture of history with the   
latest scientific principles and        
absolute mathematical deductions makes  
it exceedingly attractive4--,mechanical 
,world1 ,manchester and ,london1        
,england4  ,mach's ,mechanics is unique4
 ,it is not a text-book1 but forms a    
useful supplement to the ordinary       
text-book4 ,the latter is usually a     
skeleton outline1 full of mathematical  
symbols and other abstractions4 ,mach's 
book has 'muscle and clothing1' and     
being written from the historical       
standpoint1 introduces the leading      
contributors in succession1 tells what  
they did and how they did it1 and often 
what manner of men they were4 ,thus it  
is that the pages glow1 as it were1 with
 a certain humanism1 quite delightful in

 a scientific book4444 ,the book is     
handsomely printed1 and deserves a warm 
reception from all interested in the    
progress of science4--,the ,physical    
,review1 ,new ,york and ,london4  ,mr4  
,t4 ,j4 ,mc,cormack1 by his effective   
translation1 where translation was no   
light task1 of this masterly treatise   
upon the earliest and most fundamental  
of the sciences1 has rendered no slight 
service to the ,english speaking        
student4 ,the ,german and ,english      
languages are generally accounted second
 to none in their value as instruments  
for the expression of scientific        
thought2 but the conversion bodily of an
 abstruse work from one into the other1 
so as to preserve all the meaning and   
spirit of the original and to set it    
easily and naturally into its new form1 
is a task of the greatest difficulty1   
and when performed so well as in the    
present instance1 merits great          
commendation4 ,dr4 ,mach has created for
 his own works the severest possible    

standard of judgment4 ,to expect no more
 from the books of such a master than   
from the elementary productions of an   
ordinary teacher in the science would be
 undue moderation4 ,our author has      
lifted what1 to many of us1 was at one  
time a course of seemingly unprofitable 
mental gymnastics1 encompassed only at  
vast expenditure of intellectual effort1
 into a study possessing a deep         
philosophical value and instinct with   
life and interest4 ',no profit grows    
where is no pleasure ta'en1' and the    
emancipated collegian will turn with    
pleasure from the narrow methods of the 
text-book to where the science is made  
to illustrate1 by a treatment at once   
broad and deep1 the fundamental         
connexion between all the physical      
sciences1 taken together4--,the ,mining 
,journal1 ,london1 ,england4  ,as a     
history of mechanics1 the work is       
admirable4--,the ,nation1 ,new ,york4   
,an excellent book1 admirably           
illustrated4--,the ,literary ,world1    

,london1 ,england4  ,sets forth the     
elements of its subject with a lucidity1
 clearness1 and force unknown in the    
mathematical text-books 444 is admirably
 fitted to serve students as an         
introduction on historical lines to the 
principles of mechanical                
science4--,canadian ,mining and         
,mechanical ,review1 ,ottawa1 ,can4  ,a 
masterly book4444 ,to any one who feels 
that he does not know as much as he     
ought to about physics1 we can commend  
it most heartily as a scholarly and able
 treatise 444 both interesting and      
profitable4--,a4 ,m4 ,wellington1 in    
,engineering ,news1 ,new ,york4  ,the   
book as a whole is unique1 and is a     
valuable addition to any library of     
science or philosophy4444 ,reproductions
 of quaint old portraits and vignettes  
give piquancy to the pages4 ,the        
numerous marginal titles form a complete
 epitome of the work2 and there is that 
invaluable adjunct1 a good index4       
,altogether the publishers are to be    

congratulated upon producing a technical
 work that is thoroughly attractive in  
its make-up4--,prof4 ,d4 ,w4 ,hering1 in
 ,science4  ,there is one other point   
upon which this volume should be        
commended1 and that is the perfection of
 the translation4 ,it is a common fault 
that books of the greatest interest and 
value in the original are oftenest      
butchered or made ridiculous by a clumsy
 translator4 ,the present is a          
noteworthy exception4--,railway ,age4   
,the book is admirably printed and      
bound4444 ,the presswork is unexcelled  
by any technical books that have come to
 our hands for some time1 and the       
engravings and figures are all clearly  
and well executed4--,railroad ,gazette4 
,,testimonials ,,of ,,prominent         
,,educators4   ,i am delighted with     
,professor ,mach's ,science of          
,mechanics4--,m4 ,e4 ,cooley1 ,professor
 of ,mechanical ,engineering1 ,ann      
,arbor1 ,mich4  ,you have done a good   
service to science in publishing ,mach's

 ,science of ,mechanics in ,english4 ,i 
shall take every opportunity to         
recommend it to young students as a     
source of much interesting information  
and inspiration4--,m4 ,i4 ,pupin1       
,professor of ,mechanics1 ,columbia     
,college1 ,new ,york4  ,mach's ,science 
of ,mechanics is an admirable 444       
book4--,prof4 ,e4 ,a4 ,fuertes1         
,director of the ,college of ,civil     
,engineering of ,cornell ,university1   
,ithaca1 ,n4 ,y4  ,i congratulate you   
upon producing the work in such good    
style and in so good a translation4 ,i  
bought a copy of it a year ago1 very    
shortly after you issued it4 ,the book  
itself is deserving of the highest      
admiration2 and you are entitled to the 
thanks of all ,english-speaking         
physicists for the publication of this  
translation4--,d4 ,w4 ,hering1          
,professor of ,physics1 ,university of  
the ,city of ,new ,york1 ,new ,york4  ,i
 have read ,mach's ,science of          
,mechanics with great pleasure4 ,the    

book is exceedingly interesting4--,w4   
,f4 ,magie1 ,professor of ,physics1     
,princeton ,university1 ,princeton1 ,n4 
,j4  ,the ,science of ,mechanics by     
,mach1 translated by ,t4 ,j4            
,mc,cormack1 ,i regard as a most        
valuable work1 not only for acquainting 
the student with the history of the     
development of ,mechanics1 but as       
serving to present to him most favorably
 the fundamental ideas of ,mechanics and
 their rational connexion with the      
highest mathematical developments4 ,it  
is a most profitable book to read along 
with the study of a text-book of        
,mechanics1 and ,i shall take pleasure  
in recommending its perusal by my       
students4--,s4 ,w4 ,robinson1 ,professor
 of ,mechanical ,engineering1 ,ohio     
,state ,university1 ,columbus1 ,ohio4   
,i am delighted with ,mach's            
',mechanics4' ,i will call the attention
 to it of students and instructors who  
have the ,mechanics or ,physics to study
 or teach4--,j4 ,e4 ,davies1 ,university

 of ,wisconsin1 ,madison1 ,wis4  ,there 
can be but one opinion as to the value  
of ,mach's work in this translation4 ,no
 instructor in physics should be without
 a copy of it4--,henry ,crew1 ,professor
 of ,physics in the ,northwestern       
,university1 ,evanston1 ,ill4           
,,popular ,,scientific ,,lectures4  ,a  
,,portrayal ,,of ,,the ,,spirit ,,and   
,,methods ,,of ,,science4  ,by ,,dr4    
,,ernst ,,mach4  ,,professor ,,of ,,the 
,,history ,,and ,,theory ,,of           
,,inductive ,,science ,,in ,,the        
,,university ,,of ,,vienna4  ,translated
 by ,,thomas ,j4 ,mc,c,o,r,m,a,c,k4     
,third ,edition1 ,revised ,throughout   
and ,greatly ,enlarged4   ,cloth1 ,gilt 
,top4 ,exhaustively ,indexed4 ,pages1   
#dae4 ,cuts1 #ei4 ,price1 #a4ej4        
,,titles ,,of ,,the ,,lectures4         
,the ,forms of ,liquids4       ,the     
,fibres of ,corti4       ,on the ,causes
 of ,harmony4       ,on the ,velocity of
 ,light4       ,why ,has ,man ,two      
,eyes8       ,on ,symmetry4       ,on   

the ,fundamental ,concepts of ,static   
,electricity4       ,on the ,principle  
of the ,conservation of ,energy4        
,on the ,economical ,nature of ,physical
 ,inquiry4       ,on the ,principle of  
,comparison in ,physics4       ,on the  
,part ,played by ,accident in ,invention
 and ,discovery4       ,on ,sensations  
of ,orientation4       ,on the ,relative
 ,educational ,value of the ,classics   
and the      ,mathematico-,physical     
,sciences4       ,a ,contribution to the
 ,history of ,acoustics4       ,remarks 
on the ,theory of ,spatial ,vision4     
,on ,transformation and ,adaptation in  
,scientific ,thought4   ,,press         
,,notices4  ,a most fascinating volume1 
treating of phenomena in which all are  
interested1 in a delightful style and   
with wonderful clearness4 ,for lightness
 of touch and yet solid value of        
information the chapter ',why ,has ,man 
,two ,eyes8' has scarcely a rival in the
 whole realm of popular scientific      
writing4--,the ,boston ,traveller4      

,truly remarkable in the insight they   
give into the relationship of the       
various fields cultivated under the name
 of ,physics4444 ,a vein of humor is met
 here and there reminding the reader of 
,heaviside1 never offending one's taste4
 ,these features1 together with the     
lightness of touch with which ,mr4      
,mc,cormack has rendered them1 make the 
volume one that may be fairly called    
rare4 ,the spirit of the author is      
preserved in such attractive1 really    
delightful1 ,english that one is assured
 nothing has been lost by               
translation4--,prof4 ,henry ,crew1 in   
,the ,astrophysical ,journal4  ,a very  
delightful and useful book4444 ,the     
author treats some of the most recondite
 problems of natural science1 in so     
charmingly untechnical a way1 with such 
a wealth of bright illustration1 as     
makes his meaning clear to the person of
 ordinary intelligence and education4444
 ,this is a work that should find a     
place in every library1 and that people 

should be encouraged to read4--,daily   
,picayune1 ,new ,orleans4  ,in his      
translation ,mr4 ,mc,cormack has well   
preserved the frank1 simple1 and        
pleasing style of this famous lecturer  
on scientific topics4 ,professor ,mach  
deals with the live facts1 the salient  
points of science1 and not with its     
mysticism or dead traditions4 ,he uses  
the simplest of illustrations and       
expresses himself clearly1 tersely1 and 
with a delightful freshness that makes  
entertaining reading of what in other   
hands would be dull and                 
prosy4--,engineering ,news1 ,n4 ,y4     
,the general reader is led by plain and 
easy steps along a delightful way       
through what would be to him without    
such a help a complicated maze of       
difficulties4 ,marvels are invented and 
science is revealed as the natural foe  
to mysteries4--,the ,chautauquan4  ,the 
beautiful quality of the work is not    
marred by abstruse discussions which    
would require a scientist to fathom1 but

 is so simple and so clear that it      
brings us into direct contact with the  
matter treated4--,the ,boston ,post4  ,a
 masterly exposition of important       
scientific truths4--,scotsman1          
,edinburgh4  ,these lectures by ,dr4    
,mach are delightfully simple and frank2
 there is no dryness or darkness of     
technicalities1 and science and common  
life do not seem separated by a gulf4444
 ,the style is admirable1 and the whole 
volume seems gloriously alive and       
human4--,providence ,journal1 ,r4 ,i4   
,the non-scientific reader who desires  
to learn something of modern scientific 
theories1 and the reasons for their     
existence1 cannot do better than        
carefully study these lectures4 ,the    
,english is excellent throughout1 and   
reflects great credit on the            
translator4--,manufacturer and ,builder4
  ,we like the quiet1 considerate       
intelligence of these                   
lectures4--,independent1 ,new ,york4    
,professor ,mach's lectures are so      

pleasantly written and illumined with   
such charm of illustration that they    
have all the interest of lively         
fiction4--,new ,york ,com4 ,advertiser4 
,the literary and philosophical         
suggestiveness of the book is very rich4
 ,hartford ,seminary ,record4  ,all are 
presented so skilfully that one can     
imagine that ,professor ,mach's hearers 
departed from his lecture-room with the 
conviction that science was a matter for
 abecedarians4 ,will please those who   
find the fairy tales of science more    
absorbing than fiction4--,the ,pilot1   
,boston4  ,professor ,mach 444 is a     
master in physics4444 ,his book is a    
good one and will serve a good purpose1 
both for instruction and                
suggestion4--,prof4 ,a4 ,e4 ,dolbear1 in
 ,the ,dial4  ,the most beautiful ideas 
are unfolded in the                     
exposition4--,catholic ,world1 ,new     
,york4     ,,the ,,analysis ,,of ,,the  
,,sensations  ,by ,,dr4 ,,ernst ,,mach4 
,,professor ,,of ,,the ,,history ,,and  

,,theory ,,of ,,inductive ,,science ,,in
 ,,the ,,university ,,of ,,vienna4      
,pages1 #bjh4 ,illustrations1 #cg4      
,indexed4  7,price1 ,cloth1 #a4be47     
,,contents4        ,introductory3       
,antimetaphysical4       ,the ,chief    
,points of ,view for the ,investigation 
of the ,senses4       ,the              
,space-,sensations of the ,eye4         
,space-,sensation1 ,continued4          
,the ,relations of the                  
,sight-,sensations to ,one ,another and 
to the      ,other ,psychical ,elements4
       ,the ,sensation of ,time4        
,the ,sensation of ,sound4              
,influence of the ,preceding            
,investigations on the ,mode of         
,conceiving      ,physics4   ,a         
wonderfully original little book4 ,like 
everything he writes a work of          
genius4--,prof4 ,w4 ,james of ,harvard4 
,i consider each work of ,professor     
,mach a distinct acquisition to a       
library of science4--,prof4 ,d4 ,w4     
,hering1 ,new ,york ,university4  ,there

 is no work known to the writer which1  
in its general scientific bearings1 is  
more likely to repay richly thorough    
study4 ,we are all interested in nature 
in one way or another1 and our interests
 can only be heightened and clarified by
 ,mach's wonderfully original and       
wholesome book4 ,it is not saying too   
much to maintain that every intelligent 
person should have a copy of it1--and   
should study that copy4--,prof4 ,j4 ,e4 
,trevor1 ,cornell4  ,students may here  
make the acquaintance of some of the    
open questions of sensation and at the  
same time take a lesson in the charm of 
scientific modesty that can hardly be   
excelled4--,prof4 ,e4 ,c4 ,sanford1     
,clark ,university4  ,it exhibits keen  
observation and acute thought1 with many
 new and interesting experiments by way 
of illustration4 ,moreover1 the style is
 light and even lively--a rare merit in 
a ,german prose work1 and still rarer in
 a translation of one4--,the ,literary  
,world1 ,london4   ,,chicago3 ,the ,open

 ,court ,publishing ,company #cbd       
,,dearborn ,,street4  ,,london3 ,kegan  
,paul1 ,trench1 ,trbner1  ,company4     
,,catalogue ,,of ,,publications  ,,of   
,,the  ,,open ,,court ,,publishing ,,co4
   ,,cope1 ,e4 ,d4       ,,the ,,primary
 ,,factors ,,of ,,organic ,,evolution4  
#aba cuts4 ,pp41 xvi1 #edg4 ,cloth1     
#b4jj1 net4  ,m,,ller1 ,f4 ,,max4       
,,three ,,introductory ,,lectures ,,on  
,,the ,,science ,,of ,,thought4         
,with a correspondence on ,thought      
,without ,words1 between ,f4 ,max       
,mller and ,francis ,galton1 the ,duke  
of ,argyll1 ,george ,j4 ,romanes        
and others4 #abh pages4 ,cloth1 #ge     
cents4 ,paper1 #be cents4       ,,three 
,,lectures ,,on ,,the ,,science ,,of    
,,language4       ,the ,oxford          
,university ,extension ,lectures1 with a
 ,supplement1 ,my      ,predecessors4   
#aab pages4 #bnd ,edition4 ,cloth1 #ge  
cents4 ,paper1 #be;c4  ,,romanes1       
,,george ,,john4       ,,darwin ,,and   
,,after ,,darwin4       ,an ,exposition 

of the ,darwinian ,theory and a         
,discussion of      ,post-,darwinian    
,questions4 ,three ,vols41 #d4jj4       
,singly1 as follows3       #a4 ,,the    
,,darwinian ,,theory4 #dfj pages4 #abe  
illustrations4 ,cloth1      #b4jj4      
#b4 ,,post-,,darwinian ,,questions4     
,heredity and ,utility4 ,pp4 #cch4      
#a4ej4       #c4 ,,post-,,darwinian     
,,questions4 ,isolation and             
,physiological ,selection4      ,pp4    
#aha4 #a4jj4       ,,an ,,examination   
,,of ,,weismannism4       #bcf pages4   
,cloth1 #a4jj4 ,paper1 #ce;c4           
,,thoughts ,,on ,,religion4             
,edited by ,charles ,gore1 ,m4 ,a41     
,canon of ,westminster4 ,third ,edition1
      ,pages1 #ahd4 ,cloth1 gilt top1   
#a4be4  ,,ribot1 ,,th4       ,,the      
,,psychology ,,of ,,attention4          
,,the ,,diseases ,,of ,,personality4    
,,the ,,diseases ,,of ,,the ,,will4     
,authorised translations4 ,cloth1 #ge   
cents each4 ,paper1 #be cents4          
,full set1 cloth1 #a4ge1 net4  ,,mach1  

,,ernst4       ,,the ,,science ,,of     
,,mechanics4       ,a ,,critical ,,and  
,,historical ,,exposition ,,of ,,its    
,,principles4 ,translated      by ,t4   
,j4 ,,mccormack4 #bej cuts4 #ecd pages4 
#a_/b m41 gilt top4 #b4ej4              
,,popular ,,scientific ,,lectures4      
,third ,edition4 #dae pages4 #ei cuts4  
,cloth1 gilt top4 ,net1 #a4ej4          
,,the ,,analysis ,,of ,,the             
,,sensations4       ,pp4 #bjh4 #cg cuts4
 ,cloth1 #a4be1 net4  ,,goodwin1 ,,rev4 
,t4 ,a4       ,,lovers ,,three          
,,thousand ,,years ,,ago4       ,as     
,indicated by the ,song of ,solomon4    
,pp4 #da4 ,boards1 #ej;c4  ,,holyoake1  
,g4 ,j4       ,,english ,,secularism4 ,a
 ,,confession ,,of ,,belief4       ,pp4 
#adf4 ,cloth1 #ej;c41 net4  ,,cornill1  
,,carl ,,heinrich4       ,,the          
,,prophets ,,of ,,israel4       ,popular
 ,sketches from ,old ,testament         
,history4 ,pp41 #bjj4 ,cloth1           
#a4jj4       ,,the ,,rise ,,of ,,the    
,,people ,,of ,,israel4       ,see      

,epitomes of ,three ,sciences1 below4   
,,binet1 ,,alfred4       ,,the ,,psychic
 ,,life ,,of ,,micro-,,organisms4       
,authorised translation4 #ace pages4    
,cloth1 #ge cents2 ,paper1 #be          
cents4       ,,on ,,double              
,,consciousness4       ,studies in      
,experimental ,psychology4 #ic pages4   
,paper1 #ae cents4  ,,wagner1 ,,richard 
,a ,,pilgrimage ,,to ,,beethoven4       
,a ,novelette4 ,frontispiece1 portrait  
of ,beethoven4 ,pp4 #dj4 ,boards1       
#ej;c4  ,,weismann1 ,,august4           
,,germinal ,,selection4 ,,as ,a ,,source
 ,,of ,,definite ,,variation4       ,pp4
 #gc4 ,paper1 #be;c4  ,,noir1 ,,ludwig4 
,,on ,,the ,,origin ,,of ,,language4    
,pp4 #eg4 ,paper1 #ae;c4  ,,freytag1    
,,gustav4       ,,the ,,lost            
,,manuscript4 ,a ,novel4       #b vols4 
#iec pages4 ,extra cloth1 #d4jj4 ,one   
vol41 cl41 #a4jj2 paper1      #ge;c4    
,,martin ,,luther4       ,illustrated4  
,pp4 #acj4 ,cloth1 #a4jj4 ,paper1 #be;c4
  ,,hering1 ,,ewald4       ,,on         

,,memory1 and ,,the ,,specific          
,,energies ,,of ,,the ,,nervous         
,,system4 ,pp4 #ej4      ,paper1 #ae;c4 
,,trumbull1 ,m4 ,m4       ,,the ,,free  
,,trade ,,struggle ,,in ,,england4      
,second ,edition4 #bif pages4 ,cloth1   
#ge cents2 paper1 #be cents4            
,,wheelbarrow3 ,,articles ,,and         
,,discussions ,,on ,,the ,,labor        
,,question4       ,with portrait of the 
author4 #cjc pages4 ,cloth1 #a4jj2      
paper1 #ce      cents4       ,,earl     
,,grey ,,on ,,reciprocity ,,and ,,civil 
,,service ,,reform4       ,with         
,comments by ,gen4 ,m4 ,m4 ,trumbull4   
,price1 #aj cents4  ,,goethe ,,and      
,,schiller',s ,,xenions4       ,selected
 and translated by ,paul ,carus4 ,album 
form4 ,pp41 #afb4 ,cl41      #a4jj      
,,oldenberg1 ,h4       ,,ancient        
,,india3 ,,its ,,language ,,and         
,,religions4       ,pp4 #ajj4 ,cloth1   
#ej;c4 ,paper1 #be;c4  ,,carus1 ,,paul4 
,,the ,,ethical ,,problem4       #ij    
pages4 ,cloth1 #ej cents2 ,paper1 #cj   

cents4       ,,fundamental ,,problems4  
,second edition1 enlarged and revised4  
#cgb pp4 ,cl41 #a4ej4 ,paper1           
#ej;c4       ,,homilies ,,of ,,science4 
#cag pages4 ,cloth1 ,gilt ,top1 #a4ej4  
,,the ,,idea ,,of ,,god4       ,fourth  
edition4 #cb pages4 ,paper1 #ae cents4  
,,the ,,soul ,,of ,,man4       ,with    
#aeb cuts and diagrams4 #deh pages4     
,cloth1 #c4jj4       ,,truth ,,in       
,,fiction4 ,,twelve ,,tales ,,with ,a   
,,moral4       ,fine laid paper1 white  
and gold binding1 gilt edges4 ,pp4 #aaa4
      #a4jj4       ,,the ,,religion ,,of
 ,,science4       ,second1 extra        
edition4 ,price1 #ej cents4 ,r4 ,s4 ,l4 
edition1 #be;c4 ,pp4      #ajc4         
,,primer ,,of ,,philosophy4       #bdj  
pages4 ,second ,edition4 ,cloth1 #a4jj4 
,paper1 #be;c4       ,,three ,,lectures3
 7#a7 ,,the ,,philosophy ,,of ,,the     
,,tool4 ,pages1 #bd4 ,paper1      #aj;c4
 7#b7 ,,our ,,need ,,of ,,philosophy4   
,pages1 #ad4 ,paper1 #e;c4 7#c7         
,,science      ,a ,,religious           

,,revelation4 ,pages1 #ba4 ,paper1 #e;c4
       ,,the ,,gospel ,,of ,,buddha4    
,according to ,old ,records4       #dth 
,edition4 ,pp41 #bge4 ,cloth1 #a4jj4    
,paper1 #ce cents4 ,in ,german1         
#a4be4       ,,buddhism ,,and ,,its     
,,christian ,,critics4       ,pages1    
#caa4 ,cloth1 #a4be4       ,,karma4 ,a  
,,story ,,of ,,early ,,buddhism4        
,illustrated by ,japanese artists4 #bnd 
,edition4 ,crpe paper1 #ge      cents4  
,,garbe1 ,,richard4       ,,the         
,,redemption ,,of ,,the ,,brahman4 ,a   
,,tale ,,of ,,hindu ,,life4       ,laid 
paper4 ,gilt top4 #if pages4 ,price1    
#ge;c4 ,paper1 #be;c4       ,,the       
,,philosophy ,,of ,,ancient ,,india4    
,pp4 #hi4 ,cloth1 #ej;c4 ,paper1 #be;c4 
,,epitomes ,,of ,,three ,,sciences4     
#a4 ,,the ,,study ,,of ,,sanskrit4 ,by  
,h4 ,oldenberg4 #b4 ,,experimental      
,,psychology4 ,by ,joseph ,jastrow4 #c4 
,,the ,,rise ,,of ,,the ,,people ,,of   
,,israel4 ,by ,c4 ,h4 ,cornill4 #adj    
pages4 ,cloth1 reduced to #ej cents4    

,the ,religion of ,science ,library4    
,a collection of bi-monthly             
publications1 most of which are reprints
 of books published by ,the ,open ,court
 ,publishing ,company4 ,yearly1 #a4ej4  
,separate copies according to prices    
quoted4 ,the books are printed upon good
 paper1 from large type4  ,the ,religion
 of ,science ,library1 by its           
extraordinarily reasonable price1 will  
place a large number of valuable books  
within the reach of all readers4  ,the  
following have already appeared in the  
series3       ,no4 #a4 ,the ,religion of
 ,science4 ,by ,,paul ,,carus4 #be;c4   
#b4 ,three ,introductory ,lectures on   
the ,science of ,thought4 ,by ,f4       
,,max ,m,,ller4 #be;c4       #c4 ,three 
,lectures on the ,science of ,language4 
,by ,f4 ,,max ,m,,ller4      #be;c4     
#d4 ,the ,diseases of ,personality4 ,by 
,,th4 ,,ribot4 #be;c4       #e4 ,the    
,psychology of ,attention4 ,by ,,th4    
,,ribot4 #be;c4       #f4 ,the ,psychic 
,life of ,micro-,organisms4 ,by ,,alfred

 ,,binet4 #be;c4       #g4 ,the ,nature 
of the ,state4 ,by ,,paul ,,carus4      
#ae;c4       #h4 ,on ,double            
,consciousness4 ,by ,,alfred ,,binet4   
#ae;c4       #i4 ,fundamental ,problems4
 ,by ,,paul ,,carus4 #ej;c4       #aj4  
,the ,diseases of the ,will4 ,by ,,th4  
,,ribot4 #be;c4       #aa4 ,the ,origin 
of ,language4 ,by ,,ludwig ,,noire4     
#ae;c4       #ab4 ,the ,free ,trade     
,struggle in ,england4 ,by ,m4 ,m4      
,,trumbull4 #be;c4       #ac4           
,wheelbarrow on the ,labor ,question4   
,by ,m4 ,m4 ,,trumbull4 #ce;c4          
#ad4 ,the ,gospel of ,buddha4 ,by ,,paul
 ,,carus4 #ce;c4       #ae4 ,the ,primer
 of ,philosophy4 ,by ,,paul ,,carus4    
#be;c4       #af4 ,on ,memory1 and ,the 
,specific ,energies of the ,nervous     
,system4      ,by ,,prof4 ,,ewald       
,,hering4 #ae;c4       #ag4 ,the        
,redemption of the ,brahman4 ,a ,tale of
 ,hindu ,life4 ,by      ,,richard       
,,garbe4 #be;c4       #ah4 ,an          
,examination of ,weismannism4 ,by ,g4   

,j4 ,,romanes4 #ce;c4       #ai4 ,on    
,germinal ,selection4 ,by ,,august      
,,weismann4 #be;c4       #bj4 ,lovers   
,three ,thousand ,years ,ago4 ,by ,t4   
,a4 ,,goodwin4 #ae;c4       #ba4        
,popular ,scientific ,lectures4 ,by     
,,ernst ,,mach4 #ej;c4       #bb4       
,ancient ,india3 ,its ,language and     
,religions4 ,by ,h4 ,,oldenberg4        
#be;c4       #bc4 ,the ,prophets of     
,ancient ,israel4 ,by ,,prof4 ,c4 ,h4   
,,cornill4 #be;c4       #bd4 ,homilies  
of ,science4 ,by ,,paul ,,carus4 #ce;c4 
#be4 ,thoughts on ,religion4 ,by ,g4 ,j4
 ,,romanes4 #ej cents4       #bf4 ,the  
,philosophy of ,ancient ,india4 ,by     
,,prof4 ,,richard ,,garbe4 #be;c4       
#bg4 ,martin ,luther4 ,by ,,gustav      
,,freytag4 #be;c4       #bh4 ,english   
,secularism4 ,by ,,george ,,jacob       
,,holyoake4 #be;c4       #bi4 ,on       
,orthogenesis4 ,by ,,th4 ,,eimer4 #be;c4
       #cj4 ,chinese ,philosophy4 ,by   
,,paul ,,carus4 #be;c4       #ca4 ,the  
,lost ,manuscript4 ,by ,,gustav         

,,freytag4 #fj;c4         99       99   
99       99       99  ,,the ,,open      
,,court ,,publishing ,,co4  #cbd        
,,dearborn ,,street1 ,,chicago1 ,,ill4  
,,london3 ,kegan ,paul1 ,trench1 ,trbner
  ,co     ,,the ,,open ,,court  ,a      
,,monthly ,,magazine  ,devoted to the   
,science of ,religion1 the ,religion of 
,science1 and the ,extension of the     
,religious ,parliament ,idea4   ,,the   
,,open ,,court does not understand by   
religion any creed or dogmatic belief1  
but man's world-conception in so far as 
it regulates his conduct4  ,the old     
dogmatic conception of religion is based
 upon the science of past ages2 to base 
religion upon the maturest and truest   
thought of the present time is the      
object of ,the ,open ,court4 ,thus1 the 
religion of ,the ,open ,court is the    
,religion of ,science1 that is1 the     
religion of verified and verifiable     
truth4  ,although opposed to irrational 
orthodoxy and narrow bigotry1 ,the ,open
 ,court does not attack the properly    

religious element of the various        
religions4 ,it criticises their errors  
unflinchingly but without animosity1 and
 endeavors to preserve of them all that 
is true and good4  ,the current numbers 
of ,the ,open ,court contain valuable   
original articles from the pens of      
distinguished thinkers4 ,accurate and   
authorised translations are made in     
,philosophy1 ,science1 and ,criticism   
from the literature of ,continental     
,europe1 and reviews of noteworthy      
recent investigations are presented4    
,portraits of eminent philosophers and  
scientists are published1 and           
appropriate illustrations accompany some
 of the articles4  ,terms3 #a4jj a year2
 #a4ce to foreign countries in the      
,postal ,union4 ,single ,copies1 #aj    
cents4   ,,the ,,monist  ,a ,,quarterly 
,,magazine ,,of  ,,philosophy ,,and     
,,science4   ,,the ,,monist discusses   
the fundamental problems of ,philosophy 
in their practical relations to the     
religious1 ethical1 and sociological    

questions of the day4 ,the following    
have contributed to its columns3        
,,prof4 ,,joseph ,,le ,,conte1   ,,dr4  
,w4 ,t4 ,,harris1   ,m4 ,d4 ,,conway1   
,,charles ,s4 ,,peirce1   ,,prof4 ,f4   
,,max ,m,,ller1   ,,prof4 ,e4 ,d4       
,,cope1   ,,carus ,,sterne1   ,,mrs4 ,c4
 ,,ladd ,,franklin1   ,,prof4 ,,max     
,,verworn1   ,,prof4 ,,felix ,,klein1   
,,prof4 ,g4 ,j4 ,,romanes1   ,,prof4 ,c4
 ,,lloyd ,,morgan1   ,,james ,,sully1   
,b4 ,,bosanquet1   ,,dr4 ,a4 ,,binet1   
,,prof4 ,,ernst ,,mach1   ,,rabbi ,,emil
 ,,hirsch1   ,,lester ,f4 ,,ward1       
,,prof4 ,h4 ,,schubert1   ,,dr4 ,,edm4  
,,montgomery1   ,,prof4 ,c4 ,,lombroso1 
,,prof4 ,e4 ,,haeckel1   ,,prof4 ,h4    
,h,,ffding1   ,,dr4 ,f4 ,,oswald1       
,,prof4 ,j4 ,,delboeuf1   ,,prof4 ,f4   
,,jodl1   ,,prof4 ,h4 ,m4 ,,stanley1    
,g4 ,,ferrero1   ,j4 ,,venn1   ,,prof4  
,h4 ,,von ,,holst4  ,per ,copy1 #ej     
cents2 ,yearly1 #b4jj4 ,in ,england and 
all countries in ,u4,p4,u4 per ,copy1   
#bs #f;d2 ,yearly1 #is #f;d4         99 

99       99       99       99  ,,chicago
  ,,the ,,open ,,court ,,publishing     
,,co41  ,monon ,building1 #cbd ,dearborn
 ,st41  ,,london3 ,kegan ,paul1 ,trench1
 ,trbner  ,co4     ,transcriber's note3 
,underscores have been used to indicate 
italic fonts4