,this e,book includes #e papers or      
speeches by ,james ,clerk ,maxwell4     
,the contents are3     ,foramen         
,centrale    ,theory of ,compound       
,colours    ,poinsot's ,theory          
,address to the ,mathematical           
,introductory ,lecture     ,on the      
,unequal ,sensibility of the ,foramen   
,centrale to ,light of different        
,colours4  ,james ,clerk ,maxwell       
,from the ,report of the ,british       
,association1 #ahef4   ,when observing  
the spectrum formed by looking at a long
 ve rtical slit through a simple prism1 
,i noticed an elongated dark spot       
running up and down in the blue1 and    
following the motion of the eye as it   
moved up and down the spectrum1 but     
refusing to pass out of the blue into   
the other colours4  ,it was plain that  
the spot belonged both to the eye and to
 the blue part of the spectrum4  ,the   
result to which ,i have come is1 that   
the appearance is due to the yellow spot
 on the retina1 commonly called the     

,foramen ,centrale of ,soemmering4  ,the
 most convenient method of observing the
 spot is by presenting to the eye in not
 too rapid succession1 blue and yellow  
glasses1 or1 still better1 allowing blue
 and yellow papers to revolve slowly    
before the eye4  ,in this way the spot  
is seen in the blue4  ,it fades rapidly1
 but is renewed every time the yellow   
comes in to relieve the effect of the   
blue4  ,by using a ,nicol's prism along 
with this apparatus1 the brushes of     
,haidinger are well seen in connexion   
with the spot1 and the fact of the      
brushes being the spot analysed by      
polarized light becomes evident4  ,if we
 look steadily at an object behind a    
series of bright bars which move in     
front of it1 we shall see a curious     
bending of the bars as they come up to  
the place of the yellow spot4  ,the part
 which comes over the spot seems to     
start in advance of the rest of the bar1
 and this would seem to indicate a      
greater rapidity of sensation at the    

yellow spot than in the surrounding     
retina4  ,but ,i find the experiment    
difficult1 and ,i hope for better       
results from more accurate observers4   
,on the ,theory of ,compound ,colours   
with reference to ,mixtures of ,blue and
 ,yellow ,light4  ,james ,clerk ,maxwell
   ,from the ,report of the ,british    
,association1 #ahef4   ,when we mix     
together blue and yellow paint1 we      
obtain green paint4 ,this fact is well  
known to all who have handled colours2  
and it is universally admitted that blue
 and yellow make green4  ,red1 yellow1  
and blue1 being the primary colours     
among painters1 green is regarded as a  
secondary colour1 arising from the      
mixture of blue and yellow4 ,newton1    
however1 found that the green of the    
spectrum was not the same thing as the  
mixture of two colours of the spectrum1 
for such a mixture could be separated by
 the prism1 while the green of the      
spectrum resisted further decomposition4
  ,but still it was believed that yellow

 and blue would make a green1 though not
 that of the spectrum4  ,as far as ,i am
 aware1 the first experiment on the     
subject is that of ,m4 ,plateau1 who1   
before #ahai1 made a disc with alternate
 sectors of prussian blue and gamboge1  
and observed that1 when spinning1 the   
resultant tint was not green1 but a     
neutral gray1 inclining sometimes to    
yellow or blue1 but never to green4     
,prof4 ,j4 ,d4 ,forbes of ,edinburgh    
made similar experiments in #ahdi1 with 
the same result4  ,prof4 ,helmholtz of  
,konigsberg1 to whom we owe the most    
complete investigation on visible       
colour1 has given the true explanation  
of this phenomenon4  ,the result of     
mixing two coloured powders is not by   
any means the same as mixing the beams  
of light which flow from each           
separately4  ,in the latter case we     
receive all the light which comes either
 from the one powder or the other4  ,in 
the former1 much of the light coming    
from one powder falls on particles of   

the other1 and we receive only that     
portion which has escaped absorption by 
one or other4  ,thus the light coming   
from a mixture of blue and yellow       
powder1 consists partly of light coming 
directly from blue particles or yellow  
particles1 and partly of light acted on 
by both blue and yellow particles4      
,this latter light is green1 since the  
blue stops the red1 yellow1 and orange1 
and the yellow stops the blue and       
violet4  ,i have made experiments on the
 mixture of blue and yellow light--by   
rapid rotation1 by combined reflexion   
and transmission1 by viewing them out of
 focus1 in stripes1 at a great distance1
 by throwing the colours of the spectrum
 on a screen1 and by receiving them into
 the eye directly2 and ,i have arranged 
a portable apparatus by which any one   
may see the result of this or any other 
mixture of the colours of the spectrum4 
,in all these cases blue and yellow do  
not make green4  ,i have also made      
experiments on the mixture of coloured  

powders4  ,those which ,i used          
principally were mineral blue 7from     
copper7 and chrome-yellow4  ,other blue 
and yellow pigments gave curious        
results1 but it was more difficult to   
make the mixtures1 and the greens were  
less uniform in tint4  ,the mixtures of 
these colours were made by weight1 and  
were painted on discs of paper1 which   
were afterwards treated in the manner   
described in my paper ,on ,colour as    
perceived by the ,eye1 in the           
,transactions of the ,royal ,society of 
,edinburgh1 ,vol4 ,,xxi4 ,part #b4  ,the
 visible effect of the colour is        
estimated in terms of the               
standard-coloured papers3--vermilion    
7,v71 ultramarine 7,u71 and             
emerald-green 7,e74  ,the accuracy of   
the results1 and their significance1 can
 be best understood by referring to the 
paper before mentioned4  ,i shall denote
 mineral blue by ,b1 and chrome-yellow  
by ,y2 and ,b#c ,y#e means a mixture of 
three parts blue and five parts yellow4 

,given ,colour4     ,standard ,colours4 
,coefficient                            
,v4    ,u4    ,e4           of          
brightness4           ,b#h    1 #ajj    
#b    #cf     #g   444444444444   #de   
,b#g  ,y#a1 #ajj     #a    #ah    #ag   
444444444444   #cg              ,b#f    
,y#b1 #ajj     #d    #aa    #cd         
444444444444   #di              ,b#e    
,y#c1 #ajj     #i     #e    #dj         
444444444444   #ed              ,b#d    
,y#d1 #ajj    #ae     #a    #dj         
444444444444   #ef              ,b#c    
,y#e1 #ajj    #bb   - #b    #dd         
444444444444   #fd              ,b#b    
,y#f1 #ajj    #ce   -#aj    #ea         
444444444444   #gf              ,b#a    
,y#g1 #ajj    #fd   -#ai    #fd         
444444444444  #aji                      
,y#h1 #ajj   #ahj   -#bg   #abd         
444444444444  #bgg  ,the columns ,v1 ,u1
 ,e give the proportions of the standard
 colours which are equivalent to #ajj of
 the given colour2 and the sum of ,v1   
,u1 ,e gives a coefficient1 which gives 

a general idea of the brightness4  ,it  
will be seen that the first admixture of
 yellow diminishes the brightness of the
 blue4  ,the negative values of ,u      
indicate that a mixture of ,v1 ,u1 and  
,e cannot be made equivalent to the     
given colour4 ,the experiments from     
which these results were taken had the  
negative values transferred to the other
 side of the equation4  ,they were all  
made by means of the colour-top1 and    
were verified by repetition at different
 times4  ,it may be necessary to remark1
 in conclusion1 with reference to the   
mode of registering visible colours in  
terms of three arbitrary standard       
colours1 that it proceeds upon that     
theory of three primary elements in the 
sensation of colour1 which treats the   
investigation of the laws of visible    
colour as a branch of human physiology1 
incapable of being deduced from the laws
 of light itself1 as set forth in       
physical optics4  ,it takes advantage of
 the methods of optics to study vision  

itself2 and its appeal is not to        
physical principles1 but to our         
consciousness of our own sensations4    
,on an ,instrument to illustrate        
,poinsot's ,theory of ,rotation4  ,james
 ,clerk ,maxwell   ,from the ,report of 
the ,british ,association1 #ahef4   ,in 
studying the rotation of a solid body   
according to ,poinsot's method1 we have 
to consider the successive positions of 
the instantaneous axis of rotation with 
reference both to directions fixed in   
space and axes assumed in the moving    
body4  ,the paths traced out by the pole
 of this axis on the invariable plane   
and on the central ellipsoid form       
interesting subjects of mathematical    
investigation4 ,but when we attempt to  
follow with our eye the motion of a     
rotating body1 we find it difficult to  
determine through what point of the body
 the instantaneous axis passes at any   
time1--and to determine its path must be
 still more difficult4  ,i have         
endeavoured to render visible the path  

of the instantaneous axis1 and to vary  
the circumstances of motion1 by means of
 a top of the same kind as that used by 
,mr ,elliot1 to illustrate precession994
  ,the body of the instrument is a      
hollow cone of wood1 rising from a ring1
 #g inches in diameter and #a inch      
thick4  ,an iron axis1 #h inches long1  
screws into the vertex of the cone4     
,the lower extremity has a point of hard
 steel1 which rests in an agate cup1 and
 forms the support of the instrument4   
,an iron nut1 three ounces in weight1 is
 made to screw on the axis1 and to be   
fixed at any point2 and in the wooden   
ring are screwed four bolts1 of three   
ounces1 working horizontally1 and four  
bolts1 of one ounce1 working vertically4
  ,on the upper part of the axis is     
placed a disc of card1 on which are     
drawn four concentric rings4  ,each ring
 is divided into four quadrants1 which  
are coloured red1 yellow1 green1 and    
blue4  ,the spaces between the rings are
 white4 ,when the top is in motion1 it  

is easy to see in which quadrant the    
instantaneous axis is at any moment and 
the distance between it and the axis of 
the instrument2 and we observe1--#ast4  
,that the instantaneous axis travels in 
a closed curve1 and returns to its      
original position in the body4  #bndly4 
,that by working the vertical bolts1 we 
can make the axis of the instrument the 
centre of this closed curve4  ,it will  
then be one of the principal axes of    
inertia4 #crdly4 ,that1 by working the  
nut on the axis1 we can make the order  
of colours either red1 yellow1 green1   
blue1 or the reverse4  ,when the order  
of colours is in the same direction as  
the rotation1 it indicates that the axis
 of the instrument is that of greatest  
moment of inertia4  #dthly4 ,that if we 
screw the two pairs of opposite         
horizontal bolts to different distances 
from the axis1 the path of the          
instantaneous pole will no longer be    
equidistant from the axis1 but will     
describe an ellipse1 whose longer axis  

is in the direction of the mean axis of 
the instrument4  #ethly4 ,that if we now
 make one of the two horizontal axes    
less and the other greater than the     
vertical axis1 the instantaneous pole   
will separate from the axis of the      
instrument1 and the axis will incline   
more and more till the spinning can no  
longer go on1 on account of the         
obliquity4  ,it is easy to see that1 by 
attending to the laws of motion1 we may 
produce any of the above effects at     
pleasure1 and illustrate many different 
propositions by means of the same       
instrument4  99 ,transactions of the    
,royal ,scottish ,society of ,arts1     
#ahee4     ,address to the ,mathematical
 and ,physical ,sections of the ,british
 ,association4  ,james ,clerk ,maxwell  
,from the ,british ,association ,report1
 ,vol4 ,,xl4  ,liverpool1 ,september    
#ae1 #ahgj4   ,at several of the recent 
,meetings of the ,british ,association  
the varied and important business of the
 ,mathematical and ,physical ,section   

has been introduced by an ,address1 the 
subject of which has been left to the   
selection of the ,president for the time
 being4  ,the perplexing duty of        
choosing a subject has not1 however1    
fallen to me4  ,professor ,sylvester1   
the ,president of ,section ,a at the    
,exeter ,meeting1 gave us a noble       
vindication of pure mathematics by      
laying bare1 as it were1 the very       
working of the mathematical mind1 and   
setting before us1 not the array of     
symbols and brackets which form the     
armoury of the mathematician1 or the dry
 results which are only the monuments of
 his conquests1 but the mathematician   
himself1 with all his human faculties   
directed by his professional sagacity to
 the pursuit1 apprehension1 and         
exhibition of that ideal harmony which  
he feels to be the root of all          
knowledge1 the fountain of all pleasure1
 and the condition of all action4  ,the 
mathematician has1 above all things1 an 
eye for symmetry2 and ,professor        

,sylvester has not only recognized the  
symmetry formed by the combination of   
his own subject with those of the former
 ,presidents1 but has pointed out the   
duties of his successor in the following
 characteristic note3--  ,mr            
,spottiswoode favoured the ,section1 in 
his opening ,address1 with a combined   
history of the progress of ,mathematics 
and ,physics2 ,dr4 ,tyndall's address   
was virtually on the limits of ,physical
 ,philosophy2 the one here in print1    
says ,prof4 ,sylvester1 is an attempted 
faint adumbration of the nature of      
,mathematical ,science in the abstract4 
,what is wanting 7like a fourth sphere  
resting on three others in contact7 to  
build up the ,ideal ,pyramid is a       
discourse on the ,relation of the two   
branches 7,mathematics and ,physics7 to1
 their action and reaction upon1 one    
another1 a magnificent theme1 with which
 it is to be hoped that some future     
,president of ,section ,a will crown the
 edifice and make the ,tetralogy        

7symbolizable by ,a,a'1 ,a1 ,a'1 ,,aa'7 
complete4  ,the theme thus distinctly   
laid down for his successor by our late 
,president is indeed a magnificent one1 
far too magnificent for any efforts of  
mine to realize4  ,i have endeavoured to
 follow ,mr ,spottiswoode1 as with      
far-reaching vision he distinguishes the
 systems of science into which          
phenomena1 our knowledge of which is    
still in the nebulous stage1 are        
growing4  ,i have been carried by the   
penetrating insight and forcible        
expression of ,dr ,tyndall into that    
sanctuary of minuteness and of power    
where molecules obey the laws of their  
existence1 clash together in fierce     
collision1 or grapple in yet more fierce
 embrace1 building up in secret the     
forms of visible things4  ,i have been  
guided by ,prof4 ,sylvester towards     
those serene heights      ,where never  
creeps a cloud1 or moves a wind1        
,nor ever falls the least white star of 
snow1      ,nor ever lowest roll of     

thunder moans1      ,nor sound of human 
sorrow mounts to mar      ,their sacred 
everlasting calm4  ,but who will lead me
 into that still more hidden and dimmer 
region where ,thought weds ,fact1 where 
the mental operation of the             
mathematician and the physical action of
 the molecules are seen in their true   
relation8  ,does not the way to it pass 
through the very den of the             
metaphysician1 strewed with the remains 
of former explorers1 and abhorred by    
every man of science8  ,it would indeed 
be a foolhardy adventure for me to take 
up the valuable time of the ,section by 
leading you into those speculations     
which require1 as we know1 thousands of 
years even to shape themselves          
intelligibly4  ,but we are met as       
cultivators of mathematics and physics4 
,in our daily work we are led up to     
questions the same in kind with those of
 metaphysics2 and we approach them1 not 
trusting to the native penetrating power
 of our own minds1 but trained by a     

long-continued adjustment of our modes  
of thought to the facts of external     
nature4  ,as mathematicians1 we perform 
certain mental operations on the symbols
 of number or of quantity1 and1 by      
proceeding step by step from more simple
 to more complex operations1 we are     
enabled to express the same thing in    
many different forms4  ,the equivalence 
of these different forms1 though a      
necessary consequence of self-evident   
axioms1 is not always1 to our minds1    
self-evident2 but the mathematician1 who
 by long practice has acquired a        
familiarity with many of these forms1   
and has become expert in the processes  
which lead from one to another1 can     
often transform a perplexing expression 
into another which explains its meaning 
in more intelligible language4  ,as     
students of ,physics we observe         
phenomena under varied circumstances1   
and endeavour to deduce the laws of     
their relations4 ,every natural         
phenomenon is1 to our minds1 the result 

of an infinitely complex system of      
conditions4  ,what we set ourselves to  
do is to unravel these conditions1 and  
by viewing the phenomenon in a way which
 is in itself partial and imperfect1 to 
piece out its features one by one1      
beginning with that which strikes us    
first1 and thus gradually learning how  
to look at the whole phenomenon so as to
 obtain a continually greater degree of 
clearness and distinctness4  ,in this   
process1 the feature which presents     
itself most forcibly to the untrained   
inquirer may not be that which is       
considered most fundamental by the      
experienced man of science2 for the     
success of any physical investigation   
depends on the judicious selection of   
what is to be observed as of primary    
importance1 combined with a voluntary   
abstraction of the mind from those      
features which1 however attractive they 
appear1 we are not yet sufficiently     
advanced in science to investigate with 
profit4  ,intellectual processes of this

 kind have been going on since the first
 formation of language1 and are going on
 still4  ,no doubt the feature which    
strikes us first and most forcibly in   
any phenomenon1 is the pleasure or the  
pain which accompanies it1 and the      
agreeable or disagreeable results which 
follow after it4  ,a theory of nature   
from this point of view is embodied in  
many of our words and phrases1 and is by
 no means extinct even in our deliberate
 opinions4  ,it was a great step in     
science when men became convinced that1 
in order to understand the nature of    
things1 they must begin by asking1 not  
whether a thing is good or bad1 noxious 
or beneficial1 but of what kind is it8  
and how much is there of it8  ,quality  
and ,quantity were then first recognized
 as the primary features to be observed 
in scientific inquiry4  ,as science has 
been developed1 the domain of quantity  
has everywhere encroached on that of    
quality1 till the process of scientific 
inquiry seems to have become simply the 

measurement and registration of         
quantities1 combined with a mathematical
 discussion of the numbers thus         
obtained4  ,it is this scientific method
 of directing our attention to those    
features of phenomena which may be      
regarded as quantities which brings     
physical research under the influence of
 mathematical reasoning4  ,in the work  
of the ,section we shall have abundant  
examples of the successful application  
of this method to the most recent       
conquests of science2 but ,i wish at    
present to direct your attention to some
 of the reciprocal effects of the       
progress of science on those elementary 
conceptions which are sometimes thought 
to be beyond the reach of change4  ,if  
the skill of the mathematician has      
enabled the experimentalist to see that 
the quantities which he has measured are
 connected by necessary relations1 the  
discoveries of physics have revealed to 
the mathematician new forms of          
quantities which he could never have    

imagined for himself4  ,of the methods  
by which the mathematician may make his 
labours most useful to the student of   
nature1 that which ,i think is at       
present most important is the systematic
 classification of quantities4  ,the    
quantities which we study in mathematics
 and physics may be classified in two   
different ways4  ,the student who wishes
 to master any particular science must  
make himself familiar with the various  
kinds of quantities which belong to that
 science4  ,when he understands all the 
relations between these quantities1 he  
regards them as forming a connected     
system1 and he classes the whole system 
of quantities together as belonging to  
that particular science4  ,this         
classification is the most natural from 
a physical point of view1 and it is     
generally the first in order of time4   
,but when the student has become        
acquainted with several different       
sciences1 he finds that the mathematical
 processes and trains of reasoning in   

one science resemble those in another so
 much that his knowledge of the one     
science may be made a most useful help  
in the study of the other4  ,when he    
examines into the reason of this1 he    
finds that in the two sciences he has   
been dealing with systems of quantities1
 in which the mathematical forms of the 
relations of the quantities are the same
 in both systems1 though the physical   
nature of the quantities may be utterly 
different4  ,he is thus led to recognize
 a classification of quantities on a new
 principle1 according to which the      
physical nature of the quantity is      
subordinated to its mathematical form4  
,this is the point of view which is     
characteristic of the mathematician2 but
 it stands second to the physical aspect
 in order of time1 because the human    
mind1 in order to conceive of different 
kinds of quantities1 must have them     
presented to it by nature4  ,i do not   
here refer to the fact that all         
quantities1 as such1 are subject to the 

rules of arithmetic and algebra1 and are
 therefore capable of being submitted to
 those dry calculations which represent1
 to so many minds1 their only idea of   
mathematics4  ,the human mind is seldom 
satisfied1 and is certainly never       
exercising its highest functions1 when  
it is doing the work of a calculating   
machine4  ,what the man of science1     
whether he is a mathematician or a      
physical inquirer1 aims at is1 to       
acquire and develope clear ideas of the 
things he deals with4  ,for this purpose
 he is willing to enter on long         
calculations1 and to be for a season a  
calculating machine1 if he can only at  
last make his ideas clearer4  ,but if he
 finds that clear ideas are not to be   
obtained by means of processes the steps
 of which he is sure to forget before he
 has reached the conclusion1 it is much 
better that he should turn to another   
method1 and try to understand the       
subject by means of well-chosen         
illustrations derived from subjects with

 which he is more familiar4  ,we all    
know how much more popular the          
illustrative method of exposition is    
found1 than that in which bare processes
 of reasoning and calculation form the  
principal subject of discourse4  ,now a 
truly scientific illustration is a      
method to enable the mind to grasp some 
conception or law in one branch of      
science1 by placing before it a         
conception or a law in a different      
branch of science1 and directing the    
mind to lay hold of that mathematical   
form which is common to the             
corresponding ideas in the two sciences1
 leaving out of account for the present 
the difference between the physical     
nature of the real phenomena4  ,the     
correctness of such an illustration     
depends on whether the two systems of   
ideas which are compared together are   
really analogous in form1 or whether1 in
 other words1 the corresponding physical
 quantities really belong to the same   
mathematical class4  ,when this         

condition is fulfilled1 the illustration
 is not only convenient for teaching    
science in a pleasant and easy manner1  
but the recognition of the formal       
analogy between the two systems of ideas
 leads to a knowledge of both1 more     
profound than could be obtained by      
studying each system separately4  ,there
 are men who1 when any relation or law1 
however complex1 is put before them in a
 symbolical form1 can grasp its full    
meaning as a relation among abstract    
quantities4  ,such men sometimes treat  
with indifference the further statement 
that quantities actually exist in nature
 which fulfil this relation4  ,the      
mental image of the concrete reality    
seems rather to disturb than to assist  
their contemplations4 ,but the great    
majority of mankind are utterly unable1 
without long training1 to retain in     
their minds the unembodied symbols of   
the pure mathematician1 so that1 if     
science is ever to become popular1 and  
yet remain scientific1 it must be by a  

profound study and a copious application
 of those principles of the mathematical
 classification of quantities which1 as 
we have seen1 lie at the root of every  
truly scientific illustration4  ,there  
are1 as ,i have said1 some minds which  
can go on contemplating with            
satisfaction pure quantities presented  
to the eye by symbols1 and to the mind  
in a form which none but mathematicians 
can conceive4  ,there are others who    
feel more enjoyment in following        
geometrical forms1 which they draw on   
paper1 or build up in the empty space   
before them4  ,others1 again1 are not   
content unless they can project their   
whole physical energies into the scene  
which they conjure up4  ,they learn at  
what a rate the planets rush through    
space1 and they experience a delightful 
feeling of exhilaration4  ,they         
calculate the forces with which the     
heavenly bodies pull at one another1 and
 they feel their own muscles straining  
with the effort4  ,to such men momentum1

 energy1 mass are not mere abstract     
expressions of the results of scientific
 inquiry4  ,they are words of power1    
which stir their souls like the memories
 of childhood4  ,for the sake of persons
 of these different types1 scientific   
truth should be presented in different  
forms1 and should be regarded as equally
 scientific whether it appears in the   
robust form and the vivid colouring of a
 physical illustration1 or in the       
tenuity and paleness of a symbolical    
expression4  ,time would fail me if ,i  
were to attempt to illustrate by        
examples the scientific value of the    
classification of quantities4  ,i shall 
only mention the name of that important 
class of magnitudes having direction in 
space which ,hamilton has called        
vectors1 and which form the             
subject-matter of the ,calculus of      
,quaternions1 a branch of mathematics   
which1 when it shall have been          
thoroughly understood by men of the     
illustrative type1 and clothed by them  

with physical imagery1 will become1     
perhaps under some new name1 a most     
powerful method of communicating truly  
scientific knowledge to persons         
apparently devoid of the calculating    
spirit4  ,the mutual action and reaction
 between the different departments of   
human thought is so interesting to the  
student of scientific progress1 that1 at
 the risk of still further encroaching  
on the valuable time of the ,section1 ,i
 shall say a few words on a branch of   
physics which not very long ago would   
have been considered rather a branch of 
metaphysics4  ,i mean the atomic theory1
 or1 as it is now called1 the molecular 
theory of the constitution of bodies4   
,not many years ago if we had been asked
 in what regions of physical science the
 advance of discovery was least         
apparent1 we should have pointed to the 
hopelessly distant fixed stars on the   
one hand1 and to the inscrutable        
delicacy of the texture of material     
bodies on the other4  ,indeed1 if we are

 to regard ,comte as in any degree      
representing the scientific opinion of  
his time1 the research into what takes  
place beyond our own solar system seemed
 then to be exceedingly unpromising1 if 
not altogether illusory4  ,the opinion  
that the bodies which we see and handle1
 which we can set in motion or leave at 
rest1 which we can break in pieces and  
destroy1 are composed of smaller bodies 
which we cannot see or handle1 which are
 always in motion1 and which can neither
 be stopped nor broken in pieces1 nor in
 any way destroyed or deprived of the   
least of their properties1 was known by 
the name of the ,atomic theory4  ,it was
 associated with the names of           
,democritus1 ,epicurus1 and ,lucretius1 
and was commonly supposed to admit the  
existence only of atoms and void1 to the
 exclusion of any other basis of things 
from the universe4  ,in many physical   
reasonings and mathematical calculations
 we are accustomed to argue as if such  
substances as air1 water1 or metal1     

which appear to our senses uniform and  
continuous1 were strictly and           
mathematically uniform and continuous4  
,we know that we can divide a pint of   
water into many millions of portions1   
each of which is as fully endowed with  
all the properties of water as the whole
 pint was2 and it seems only natural to 
conclude that we might go on subdividing
 the water for ever1 just as we can     
never come to a limit in subdividing the
 space in which it is contained4  ,we   
have heard how ,faraday divided a grain 
of gold into an inconceivable number of 
separate particles1 and we may see ,dr  
,tyndall produce from a mere suspicion  
of nitrite of butyle an immense cloud1  
the minute visible portion of which is  
still cloud1 and therefore must contain 
many molecules of nitrite of butyle4    
,but evidence from different and        
independent sources is now crowding in  
upon us which compels us to admit that  
if we could push the process of         
subdivision still further we should come

 to a limit1 because each portion would 
then contain only one molecule1 an      
individual body1 one and indivisible1   
unalterable by any power in nature4     
,even in our ordinary experiments on    
very finely divided matter we find that 
the substance is beginning to lose the  
properties which it exhibits when in a  
large mass1 and that effects depending  
on the individual action of molecules   
are beginning to become prominent4  ,the
 study of these phenomena is at present 
the path which leads to the development 
of molecular science4  ,that superficial
 tension of liquids which is called     
capillary attraction is one of these    
phenomena4  ,another important class of 
phenomena are those which are due to    
that motion of agitation by which the   
molecules of a liquid or gas are        
continually working their way from one  
place to another1 and continually       
changing their course1 like people      
hustled in a crowd4  ,on this depends   
the rate of diffusion of gases and      

liquids through each other1 to the study
 of which1 as one of the keys of        
molecular science1 that unwearied       
inquirer into nature's secrets1 the late
 ,prof4 ,graham1 devoted such arduous   
labour4  ,the rate of electrolytic      
conduction is1 according to ,wiedemann's
 theory1 influenced by the same cause2  
and the conduction of heat in fluids    
depends probably on the same kind of    
action4  ,in the case of gases1 a       
molecular theory has been developed by  
,clausius and others1 capable of        
mathematical treatment1 and subjected to
 experimental investigation2 and by this
 theory nearly every known mechanical   
property of gases has been explained on 
dynamical principles2 so that the       
properties of individual gaseous        
molecules are in a fair way to become   
objects of scientific research4  ,now   
,mr ,stoney has pointed out#a that the  
numerical results of experiments on     
gases render it probable that the mean  
distance of their particles at the      

ordinary temperature and pressure is a  
quantity of the same order of magnitude 
as a millionth of a millimetre1 and ,sir
 ,william ,thomson has since#b shewn1 by
 several independent lines of argument1 
drawn from phenomena so different in    
themselves as the electrification of    
metals by contact1 the tension of       
soap-bubbles1 and the friction of air1  
that in ordinary solids and liquids the 
average distance between contiguous     
molecules is less than the              
hundred-millionth1 and greater than the 
two-thousand-millionth of a centimetre4 
#a ,phil4 ,mag41 ,aug4 #ahfh4 #b        
,nature1 ,march #ca1 #ahgj4  ,these1 of 
course1 are exceedingly rough estimates1
 for they are derived from measurements 
some of which are still confessedly very
 rough2 but if at the present time1 we  
can form even a rough plan for arriving 
at results of this kind1 we may hope    
that1 as our means of experimental      
inquiry become more accurate and more   
varied1 our conception of a molecule    

will become more definite1 so that we   
may be able at no distant period to     
estimate its weight with a greater      
degree of precision4  ,a theory1 which  
,sir ,w4 ,thomson has founded on        
,helmholtz's splendid hydrodynamical    
theorems1 seeks for the properties of   
molecules in the ring vortices of a     
uniform1 frictionless1 incompressible   
fluid4  ,such whirling rings may be seen
 when an experienced smoker sends out a 
dexterous puff of smoke into the still  
air1 but a more evanescent phenomenon it
 is difficult to conceive4  ,this       
evanescence is owing to the viscosity of
 the air2 but ,helmholtz has shewn that 
in a perfect fluid such a whirling ring1
 if once generated1 would go on whirling
 for ever1 would always consist of the  
very same portion of the fluid which was
 first set whirling1 and could never be 
cut in two by any natural cause4  ,the  
generation of a ring-vortex is of course
 equally beyond the power of natural    
causes1 but once generated1 it has the  

properties of individuality1 permanence 
in quantity1 and indestructibility4  ,it
 is also the recipient of impulse and of
 energy1 which is all we can affirm of  
matter2 and these ring-vortices are     
capable of such varied connexions and   
knotted self-involutions1 that the      
properties of differently knotted       
vortices must be as different as those  
of different kinds of molecules can be4 
,if a theory of this kind should be     
found1 after conquering the enormous    
mathematical difficulties of the        
subject1 to represent in any degree the 
actual properties of molecules1 it will 
stand in a very different scientific    
position from those theories of         
molecular action which are formed by    
investing the molecule with an arbitrary
 system of central forces invented      
expressly to account for the observed   
phenomena4  ,in the vortex theory we    
have nothing arbitrary1 no central      
forces or occult properties of any other
 kind4  ,we have nothing but matter and 

motion1 and when the vortex is once     
started its properties are all          
determined from the original impetus1   
and no further assumptions are possible4
  ,even in the present undeveloped state
 of the theory1 the contemplation of the
 individuality and indestructibility of 
a ring-vortex in a perfect fluid cannot 
fail to disturb the commonly received   
opinion that a molecule1 in order to be 
permanent1 must be a very hard body4    
,in fact one of the first conditions    
which a molecule must fulfil is1        
apparently1 inconsistent with its being 
a single hard body4  ,we know from those
 spectroscopic researches which have    
thrown so much light on different       
branches of science1 that a molecule can
 be set into a state of internal        
vibration1 in which it gives off to the 
surrounding medium light of definite    
refrangibility--light1 that is1 of      
definite wave-length and definite period
 of vibration4  ,the fact that all the  
molecules 7say1 of hydrogen7 which we   

can procure for our experiments1 when   
agitated by heat or by the passage of an
 electric spark1 vibrate precisely in   
the same periodic time1 or1 to speak    
more accurately1 that their vibrations  
are composed of a system of simple      
vibrations having always the same       
periods1 is a very remarkable fact4  ,i 
must leave it to others to describe the 
progress of that splendid series of     
spectroscopic discoveries by which the  
chemistry of the heavenly bodies has    
been brought within the range of human  
inquiry4  ,i wish rather to direct your 
attention to the fact that1 not only has
 every molecule of terrestrial hydrogen 
the same system of periods of free      
vibration1 but that the spectroscopic   
examination of the light of the sun and 
stars shews that1 in regions the        
distance of which we can only feebly    
imagine1 there are molecules vibrating  
in as exact unison with the molecules of
 terrestrial hydrogen as two            
tuning-forks tuned to concert pitch1 or 

two watches regulated to solar time4    
,now this absolute equality in the      
magnitude of quantities1 occurring in   
all parts of the universe1 is worth our 
consideration4  ,the dimensions of      
individual natural bodies are either    
quite indeterminate1 as in the case of  
planets1 stones1 trees1 c41 or they vary
 within moderate limits1 as in the case 
of seeds1 eggs1 c42 but even in these   
cases small quantitative differences are
 met with which do not interfere with   
the essential properties of the body4   
,even crystals1 which are so definite in
 geometrical form1 are variable with    
respect to their absolute dimensions4   
,among the works of man we sometimes    
find a certain degree of uniformity4    
,there is a uniformity among the        
different bullets which are cast in the 
same mould1 and the different copies of 
a book printed from the same type4  ,if 
we examine the coins1 or the weights and
 measures1 of a civilized country1 we   
find a uniformity1 which is produced by 

careful adjustment to standards made and
 provided by the state4  ,the degree of 
uniformity of these national standards  
is a measure of that spirit of justice  
in the nation which has enacted laws to 
regulate them and appointed officers to 
test them4  ,this subject is one in     
which we1 as a scientific body1 take a  
warm interest2 and you are all aware of 
the vast amount of scientific work which
 has been expended1 and profitably      
expended1 in providing weights and      
measures for commercial and scientific  
purposes4  ,the earth has been measured 
as a basis for a permanent standard of  
length1 and every property of metals has
 been investigated to guard against any 
alteration of the material standards    
when made4  ,to weigh or measure any    
thing with modern accuracy1 requires a  
course of experiment and calculation in 
which almost every branch of physics and
 mathematics is brought into            
requisition4  ,yet1 after all1 the      
dimensions of our earth and its time of 

rotation1 though1 relatively to our     
present means of comparison1 very       
permanent1 are not so by any physical   
necessity4  ,the earth might contract by
 cooling1 or it might be enlarged by a  
layer of meteorites falling on it1 or   
its rate of revolution might slowly     
slacken1 and yet it would continue to be
 as much a planet as before4  ,but a    
molecule1 say of hydrogen1 if either its
 mass or its time of vibration were to  
be altered in the least1 would no longer
 be a molecule of hydrogen4  ,if1 then1 
we wish to obtain standards of length1  
time1 and mass which shall be absolutely
 permanent1 we must seek them not in the
 dimensions1 or the motion1 or the mass 
of our planet1 but in the wave-length1  
the period of vibration1 and the        
absolute mass of these imperishable and 
unalterable and perfectly similar       
molecules4  ,when we find that here1 and
 in the starry heavens1 there are       
innumerable multitudes of little bodies 
of exactly the same mass1 so many1 and  

no more1 to the grain1 and vibrating in 
exactly the same time1 so many times1   
and no more1 in a second1 and when we   
reflect that no power in nature can now 
alter in the least either the mass or   
the period of any one of them1 we seem  
to have advanced along the path of      
natural knowledge to one of those points
 at which we must accept the guidance of
 that faith by which we understand that 
that which is seen was not made of      
things which do appear4  ,one of the    
most remarkable results of the progress 
of molecular science is the light it has
 thrown on the nature of irreversible   
processes--processes1 that is1 which    
always tend towards and never away from 
a certain limiting state4  ,thus1 if two
 gases be put into the same vessel1 they
 become mixed1 and the mixture tends    
continually to become more uniform4  ,if
 two unequally heated portions of the   
same gas are put into the vessel1       
something of the kind takes place1 and  
the whole tends to become of the same   

temperature4  ,if two unequally heated  
solid bodies be placed in contact1 a    
continual approximation of both to an   
intermediate temperature takes place4   
,in the case of the two gases1 a        
separation may be effected by chemical  
means2 but in the other two cases the   
former state of things cannot be        
restored by any natural process4  ,in   
the case of the conduction or diffusion 
of heat the process is not only         
irreversible1 but it involves the       
irreversible diminution of that part of 
the whole stock of thermal energy which 
is capable of being converted into      
mechanical work4  ,this is ,thomson's   
theory of the irreversible dissipation  
of energy1 and it is equivalent to the  
doctrine of ,clausius concerning the    
growth of what he calls ,entropy4  ,the 
irreversible character of this process  
is strikingly embodied in ,fourier's    
theory of the conduction of heat1 where 
the formulae themselves indicate1 for   
all positive values of the time1 a      

possible solution which continually     
tends to the form of a uniform diffusion
 of heat4  ,but if we attempt to ascend 
the stream of time by giving to its     
symbol continually diminishing values1  
we are led up to a state of things in   
which the formula has what is called a  
critical value2 and if we inquire into  
the state of things the instant before1 
we find that the formula becomes absurd4
  ,we thus arrive at the conception of a
 state of things which cannot be        
conceived as the physical result of a   
previous state of things1 and we find   
that this critical condition actually   
existed at an epoch not in the utmost   
depths of a past eternity1 but separated
 from the present time by a finite      
interval4  ,this idea of a beginning is 
one which the physical researches of    
recent times have brought home to us1   
more than any observer of the course of 
scientific thought in former times would
 have had reason to expect4  ,but the   
mind of man is not1 like ,fourier's     

heated body1 continually settling down  
into an ultimate state of quiet         
uniformity1 the character of which we   
can already predict2 it is rather like a
 tree1 shooting out branches which adapt
 themselves to the new aspects of the   
sky towards which they climb1 and roots 
which contort themselves among the      
strange strata of the earth into which  
they delve4  ,to us who breathe only the
 spirit of our own age1 and know only   
the characteristics of contemporary     
thought1 it is as impossible to predict 
the general tone of the science of the  
future as it is to anticipate the       
particular discoveries which it will    
make4  ,physical research is continually
 revealing to us new features of natural
 processes1 and we are thus compelled to
 search for new forms of thought        
appropriate to these features4  ,hence  
the importance of a careful study of    
those relations between mathematics and 
,physics which determine the conditions 
under which the ideas derived from one  

department of physics may be safely used
 in forming ideas to be employed in a   
new department4  ,the figure of speech  
or of thought by which we transfer the  
language and ideas of a familiar science
 to one with which we are less          
acquainted may be called ,scientific    
,metaphor4  ,thus the words ,velocity1  
,momentum1 ,force1 c4 have acquired     
certain precise meanings in ,elementary 
,dynamics4  ,they are also employed in  
the ,dynamics of a ,connected ,system in
 a sense which1 though perfectly        
analogous to the elementary sense1 is   
wider and more general4  ,these         
generalized forms of elementary ideas   
may be called metaphorical terms in the 
sense in which every abstract term is   
metaphorical4  ,the characteristic of a 
truly scientific system of metaphors is 
that each term in its metaphorical use  
retains all the formal relations to the 
other terms of the system which it had  
in its original use4  ,the method is    
then truly scientific--that is1 not only

 a legitimate product of science1 but   
capable of generating science in its    
turn4  ,there are certain electrical    
phenomena1 again1 which are connected   
together by relations of the same form  
as those which connect dynamical        
phenomena4  ,to apply to these the      
phrases of dynamics with proper         
distinctions and provisional            
reservations is an example of a metaphor
 of a bolder kind2 but it is a          
legitimate metaphor if it conveys a true
 idea of the electrical relations to    
those who have been already trained in  
dynamics4  ,suppose1 then1 that we have 
successfully introduced certain ideas   
belonging to an elementary science by   
applying them metaphorically to some new
 class of phenomena4  ,it becomes an    
important philosophical question to     
determine in what degree the            
applicability of the old ideas to the   
new subject may be taken as evidence    
that the new phenomena are physically   
similar to the old4  ,the best instances

 for the determination of this question 
are those in which two different        
explanations have been given of the same
 thing4  ,the most celebrated case of   
this kind is that of the corpuscular and
 the undulatory theories of light4  ,up 
to a certain point the phenomena of     
light are equally well explained by     
both2 beyond this point1 one of them    
fails4  ,to understand the true relation
 of these theories in that part of the  
field where they seem equally applicable
 we must look at them in the light which
 ,hamilton has thrown upon them by his  
discovery that to every brachistochrone 
problem there corresponds a problem of  
free motion1 involving different        
velocities and times1 but resulting in  
the same geometrical path4  ,professor  
,tait has written a very interesting    
paper on this subject4  ,according to a 
theory of electricity which is making   
great progress in ,germany1 two         
electrical particles act on one another 
directly at a distance1 but with a force

 which1 according to ,weber1 depends on 
their relative velocity1 and according  
to a theory hinted at by ,gauss1 and    
developed by ,riemann1 ,lorenz1 and     
,neumann1 acts not instantaneously1 but 
after a time depending on the distance4 
,the power with which this theory1 in   
the hands of these eminent men1 explains
 every kind of electrical phenomena must
 be studied in order to be appreciated4 
,another theory of electricity1 which ,i
 prefer1 denies action at a distance and
 attributes electric action to tensions 
and pressures in an all-pervading       
medium1 these stresses being the same in
 kind with those familiar to engineers1 
and the medium being identical with that
 in which light is supposed to be       
propagated4  ,both these theories are   
found to explain not only the phenomena 
by the aid of which they were originally
 constructed1 but other phenomena1 which
 were not thought of or perhaps not     
known at the time2 and both have        
independently arrived at the same       

numerical result1 which gives the       
absolute velocity of light in terms of  
electrical quantities4  ,that theories  
apparently so fundamentally opposed     
should have so large a field of truth   
common to both is a fact the            
philosophical importance of which we    
cannot fully appreciate till we have    
reached a scientific altitude from which
 the true relation between hypotheses so
 different can be seen4  ,i shall only  
make one more remark on the relation    
between ,mathematics and ,physics4  ,in 
themselves1 one is an operation of the  
mind1 the other is a dance of molecules4
  ,the molecules have laws of their own1
 some of which we select as most        
intelligible to us and most amenable to 
our calculation4  ,we form a theory from
 these partial data1 and we ascribe any 
deviation of the actual phenomena from  
this theory to disturbing causes4  ,at  
the same time we confess that what we   
call disturbing causes are simply those 
parts of the true circumstances which we

 do not know or have neglected1 and we  
endeavour in future to take account of  
them4  ,we thus acknowledge that the    
so-called disturbance is a mere figment 
of the mind1 not a fact of nature1 and  
that in natural action there is no      
disturbance4  ,but this is not the only 
way in which the harmony of the material
 with the mental operation may be       
disturbed4  ,the mind of the            
mathematician is subject to many        
disturbing causes1 such as fatigue1 loss
 of memory1 and hasty conclusions2 and  
it is found that1 from these and other  
causes1 mathematicians make mistakes4   
,i am not prepared to deny that1 to some
 mind of a higher order than ours1 each 
of these errors might be traced to the  
regular operation of the laws of actual 
thinking2 in fact we ourselves often do 
detect1 not only errors of calculation1 
but the causes of these errors4  ,this1 
however1 by no means alters our         
conviction that they are errors1 and    
that one process of thought is right and

 another process wrong4  ,i  ,one of the
 most profound mathematicians and       
thinkers of our time1 the late ,george  
,boole1 when reflecting on the precise  
and almost mathematical character of the
 laws of right thinking as compared with
 the exceedingly perplexing though      
perhaps equally determinate laws of     
actual and fallible thinking1 was led to
 another of those points of view from   
which ,science seems to look out into a 
region beyond her own domain4  ,we must 
admit1 he says1 that there exist laws   
7of thought7 which even the rigour of   
their mathematical forms does not       
preserve from violation4  ,we must      
ascribe to them an authority1 the       
essence of which does not consist in    
power1 a supremacy which the analogy of 
the inviolable order of the natural     
world in no way assists us to           
comprehend4     ,introductory ,lecture  
on ,experimental ,physics4  ,james      
,clerk ,maxwell   ,the ,university of   
,cambridge1 in accordance with that law 

of its evolution1 by which1 while       
maintaining the strictest continuity    
between the successive phases of its    
history1 it adapts itself with more or  
less promptness to the requirements of  
the times1 has lately instituted a      
course of ,experimental ,physics4  ,this
 course of study1 while it requires us  
to maintain in action all those powers  
of attention and analysis which have    
been so long cultivated in the          
,university1 calls on us to exercise our
 senses in observation1 and our hands in
 manipulation4  ,the familiar apparatus 
of pen1 ink1 and paper will no longer be
 sufficient for us1 and we shall require
 more room than that afforded by a seat 
at a desk1 and a wider area than that of
 the black board4  ,we owe it to the    
munificence of our ,chancellor1 that1   
whatever be the character in other      
respects of the experiments which we    
hope hereafter to conduct1 the material 
facilities for their full development   
will be upon a scale which has not      

hitherto been surpassed4  ,the main     
feature1 therefore1 of ,experimental    
,physics at ,cambridge is the           
,devonshire ,physical ,laboratory1 and  
,i think it desirable that on the       
present occasion1 before we enter on the
 details of any special study1 we should
 consider by what means we1 the         
,university of ,cambridge1 may1 as a    
living body1 appropriate and vitalise   
this new organ1 the outward shell of    
which we expect soon to rise before us4 
,the course of study at this ,university
 has always included ,natural           
,philosophy1 as well as ,pure           
,mathematics4  ,to diffuse a sound      
knowledge of ,physics1 and to imbue the 
minds of our students with correct      
dynamical principles1 have been long    
regarded as among our highest functions1
 and very few of us can now place       
ourselves in the mental condition in    
which even such philosophers as the     
great ,descartes were involved in the   
days before ,newton had announced the   

true laws of the motion of bodies4      
,indeed the cultivation and diffusion of
 sound dynamical ideas has already      
effected a great change in the language 
and thoughts even of those who make no  
pretensions to science1 and we are daily
 receiving fresh proofs that the        
popularisation of scientific doctrines  
is producing as great an alteration in  
the mental state of society as the      
material applications of science are    
effecting in its outward life4  ,such   
indeed is the respect paid to science1  
that the most absurd opinions may become
 current1 provided they are expressed in
 language1 the sound of which recals    
some well-known scientific phrase4  ,if 
society is thus prepared to receive all 
kinds of scientific doctrines1 it is our
 part to provide for the diffusion and  
cultivation1 not only of true scientific
 principles1 but of a spirit of sound   
criticism1 founded on an examination of 
the evidences on which statements       
apparently scientific depend4  ,when we 

shall be able to employ in scientific   
education1 not only the trained         
attention of the student1 and his       
familiarity with symbols1 but the       
keenness of his eye1 the quickness of   
his ear1 the delicacy of his touch1 and 
the adroitness of his fingers1 we shall 
not only extend our influence over a    
class of men who are not fond of cold   
abstractions1 but1 by opening at once   
all the gateways of knowledge1 we shall 
ensure the association of the doctrines 
of science with those elementary        
sensations which form the obscure       
background of all our conscious         
thoughts1 and which lend a vividness and
 relief to ideas1 which1 when presented 
as mere abstract terms1 are apt to fade 
entirely from the memory4  ,in a course 
of ,experimental ,physics we may        
consider either the ,physics or the     
,experiments as the leading feature4    
,we may either employ the experiments to
 illustrate the phenomena of a          
particular branch of ,physics1 or we may

 make some physical research in order to
 exemplify a particular experimental    
method4  ,in the order of time1 we      
should begin1 in the ,lecture ,room1    
with a course of lectures on some branch
 of ,physics aided by experiments of    
illustration1 and conclude1 in the      
,laboratory1 with a course of           
experiments of research4  ,let me say a 
few words on these two classes of       
experiments1--,experiments of           
,illustration and ,experiments of       
,research4 ,the aim of an experiment of 
illustration is to throw light upon some
 scientific idea so that the student may
 be enabled to grasp it4  ,the          
circumstances of the experiment are so  
arranged that the phenomenon which we   
wish to observe or to exhibit is brought
 into prominence1 instead of being      
obscured and entangled among other      
phenomena1 as it is when it occurs in   
the ordinary course of nature4  ,to     
exhibit illustrative experiments1 to    
encourage others to make them1 and to   

cultivate in every way the ideas on     
which they throw light1 forms an        
important part of our duty4  ,the       
simpler the materials of an illustrative
 experiment1 and the more familiar they 
are to the student1 the more thoroughly 
is he likely to acquire the idea which  
it is meant to illustrate4  ,the        
educational value of such experiments is
 often inversely proportional to the    
complexity of the apparatus4  ,the      
student who uses home-made apparatus1   
which is always going wrong1 often      
learns more than one who has the use of 
carefully adjusted instruments1 to which
 he is apt to trust1 and which he dares 
not take to pieces4  ,it is very        
necessary that those who are trying to  
learn from books the facts of physical  
science should be enabled by the help of
 a few illustrative experiments to      
recognise these facts when they meet    
with them out of doors4  ,science       
appears to us with a very different     
aspect after we have found out that it  

is not in lecture rooms only1 and by    
means of the electric light projected on
 a screen1 that we may witness physical 
phenomena1 but that we may find         
illustrations of the highest doctrines  
of science in games and gymnastics1 in  
travelling by land and by water1 in     
storms of the air and of the sea1 and   
wherever there is matter in motion4     
,this habit of recognising principles   
amid the endless variety of their action
 can never degrade our sense of the     
sublimity of nature1 or mar our         
enjoyment of its beauty4  ,on the       
contrary1 it tends to rescue our        
scientific ideas from that vague        
condition in which we too often leave   
them1 buried among the other products of
 a lazy credulity1 and to raise them    
into their proper position among the    
doctrines in which our faith is so      
assured1 that we are ready at all times 
to act on them4  ,experiments of        
illustration may be of very different   
kinds4  ,some may be adaptations of the 

commonest operations of ordinary life1  
others may be carefully arranged        
exhibitions of some phenomenon which    
occurs only under peculiar conditions4  
,they all1 however1 agree in this1 that 
their aim is to present some phenomenon 
to the senses of the student in such a  
way that he may associate with it the   
appropriate scientific idea4  ,when he  
has grasped this idea1 the experiment   
which illustrates it has served its     
purpose4  ,in an experiment of research1
 on the other hand1 this is not the     
principal aim4  ,it is true that an     
experiment1 in which the principal aim  
is to see what happens under certain    
conditions1 may be regarded as an       
experiment of research by those who are 
not yet familiar with the result1 but in
 experimental researches1 strictly so   
called1 the ultimate object is to       
measure something which we have already 
seen--to obtain a numerical estimate of 
some magnitude4  ,experiments of this   
class--those in which measurement of    

some kind is involved1 are the proper   
work of a ,physical ,laboratory4  ,in   
every experiment we have first to make  
our senses familiar with the phenomenon1
 but we must not stop here1 we must find
 out which of its features are capable  
of measurement1 and what measurements   
are required in order to make a complete
 specification of the phenomenon4 ,we   
must then make these measurements1 and  
deduce from them the result which we    
require to find4  ,this characteristic  
of modern experiments--that they consist
 principally of measurements1--is so    
prominent1 that the opinion seems to    
have got abroad1 that in a few years all
 the great physical constants will have 
been approximately estimated1 and that  
the only occupation which will then be  
left to men of science will be to carry 
on these measurements to another place  
of decimals4  ,if this is really the    
state of things to which we are         
approaching1 our ,laboratory may perhaps
 become celebrated as a place of        

conscientious labour and consummate     
skill1 but it will be out of place in   
the ,university1 and ought rather to be 
classed with the other great workshops  
of our country1 where equal ability is  
directed to more useful ends4  ,but we  
have no right to think thus of the      
unsearchable riches of creation1 or of  
the untried fertility of those fresh    
minds into which these riches will      
continue to be poured4  ,it may possibly
 be true that1 in some of those fields  
of discovery which lie open to such     
rough observations as can be made       
without artificial methods1 the great   
explorers of former times have          
appropriated most of what is valuable1  
and that the gleanings which remain are 
sought after1 rather for their          
abstruseness1 than for their intrinsic  
worth4  ,but the history of science     
shews that even during that phase of her
 progress in which she devotes herself  
to improving the accuracy of the        
numerical measurement of quantities with

 which she has long been familiar1 she  
is preparing the materials for the      
subjugation of new regions1 which would 
have remained unknown if she had been   
contented with the rough methods of her 
early pioneers4  ,i might bring forward 
instances gathered from every branch of 
science1 shewing how the labour of      
careful measurement has been rewarded by
 the discovery of new fields of         
research1 and by the development of new 
scientific ideas4  ,but the history of  
the science of terrestrial magnetism    
affords us a sufficient example of what 
may be done by ,experiments in ,concert1
 such as we hope some day to perform in 
our ,laboratory4  ,that celebrated      
traveller1 ,humboldt1 was profoundly    
impressed with the scientific value of a
 combined effort to be made by the      
observers of all nations1 to obtain     
accurate measurements of the magnetism  
of the earth2 and we owe it mainly to   
his enthusiasm for science1 his great   
reputation and his wide-spread          

influence1 that not only private men of 
science1 but the governments of most of 
the civilised nations1 our own among the
 number1 were induced to take part in   
the enterprise4  ,but the actual working
 out of the scheme1 and the arrangements
 by which the labours of the observers  
were so directed as to obtain the best  
results1 we owe to the great            
mathematician ,gauss1 working along with
 ,weber1 the future founder of the      
science of electro-magnetic measurement1
 in the magnetic observatory of         
,gottingen1 and aided by the skill of   
the instrument-maker ,leyser4  ,these   
men1 however1 did not work alone4       
,numbers of scientific men joined the   
,magnetic ,union1 learned the use of the
 new instruments and the new methods of 
reducing the observations2 and in every 
city of ,europe you might see them1 at  
certain stated times1 sitting1 each in  
his cold wooden shed1 with his eye fixed
 at the telescope1 his ear attentive to 
the clock1 and his pencil recording in  

his note-book the instantaneous position
 of the suspended magnet4  ,bacon's     
conception of ,experiments in concert   
was thus realised1 the scattered forces 
of science were converted into a regular
 army1 and emulation and jealousy became
 out of place1 for the results obtained 
by any one observer were of no value    
till they were combined with those of   
the others4  ,the increase in the       
accuracy and completeness of magnetic   
observations which was obtained by the  
new method1 opened up fields of research
 which were hardly suspected to exist by
 those whose observations of the        
magnetic needle had been conducted in a 
more primitive manner4  ,we must reserve
 for its proper place in our course any 
detailed description of the disturbances
 to which the magnetism of our planet is
 found to be subject4  ,some of these   
disturbances are periodic1 following the
 regular courses of the sun and moon4   
,others are sudden1 and are called      
magnetic storms1 but1 like the storms of

 the atmosphere1 they have their known  
seasons of frequency4  ,the last and the
 most mysterious of these magnetic      
changes is that secular variation by    
which the whole character of the earth1 
as a great magnet1 is being slowly      
modified1 while the magnetic poles creep
 on1 from century to century1 along     
their winding track in the polar        
regions4  ,we have thus learned that the
 interior of the earth is subject to the
 influences of the heavenly bodies1 but 
that besides this there is a constantly 
progressive change going on1 the cause  
of which is entirely unknown4  ,in each 
of the magnetic observatories throughout
 the world an arrangement is at work1 by
 means of which a suspended magnet      
directs a ray of light on a preparred   
sheet of paper moved by clockwork4  ,on 
that paper the never-resting heart of   
the earth is now tracing1 in telegraphic
 symbols which will one day be          
interpreted1 a record of its pulsations 
and its flutterings1 as well as of that 

slow but mighty working which warns us  
that we must not suppose that the inner 
history of our planet is ended4  ,but   
this great experimental research on     
,terrestrial ,magnetism produced lasting
 effects on the progress of science in  
general4  ,i need only mention one or   
two instances4  ,the new methods of     
measuring forces were successfully      
applied by ,weber to the numerical      
determination of all the phenomena of   
electricity1 and very soon afterwards   
the electric telegraph1 by conferring a 
commercial value on exact numerical     
measurements1 contributed largely to the
 advancement1 as well as to the         
diffusion of scientific knowledge4  ,but
 it is not in these more modern branches
 of science alone that this influence is
 felt4  ,it is to ,gauss1 to the        
,magnetic ,union1 and to magnetic       
observers in general1 that we owe our   
deliverance from that absurd method of  
estimating forces by a variable standard
 which prevailed so long even among men 

of science4  ,it was ,gauss who first   
based the practical measurement of      
magnetic force 7and therefore of every  
other force7 on those long established  
principles1 which1 though they are      
embodied in every dynamical equation1   
have been so generally set aside1 that  
these very equations1 though correctly  
given in our ,cambridge textbooks1 are  
usually explained there by assuming1 in 
addition to the variable standard of    
force1 a variable1 and therefore        
illegal1 standard of mass4  ,such1 then1
 were some of the scientific results    
which followed in this case from        
bringing together mathematical power1   
experimental sagacity1 and manipulative 
skill1 to direct and assist the labours 
of a body of zealous observers4  ,if    
therefore we desire1 for our own        
advantage and for the honour of our     
,university1 that the ,devonshire       
,laboratory should be successful1 we    
must endeavour to maintain it in living 
union with the other organs and         

faculties of our learned body4  ,we     
shall therefore first consider the      
relation in which we stand to those     
mathematical studies which have so long 
flourished among us1 which deal with our
 own subjects1 and which differ from our
 experimental studies only in the mode  
in which they are presented to the mind4
  ,there is no more powerful method for 
introducing knowledge into the mind than
 that of presenting it in as many       
different ways as we can4 ,when the     
ideas1 after entering through different 
gateways1 effect a junction in the      
citadel of the mind1 the position they  
occupy becomes impregnable4  ,opticians 
tell us that the mental combination of  
the views of an object which we obtain  
from stations no further apart than our 
two eyes is sufficient to produce in our
 minds an impression of the solidity of 
the object seen2 and we find that this  
impression is produced even when we are 
aware that we are really looking at two 
flat pictures placed in a stereoscope4  

,it is therefore natural to expect that 
the knowledge of physical science       
obtained by the combined use of         
mathematical analysis and experimental  
research will be of a more solid1       
available1 and enduring kind than that  
possessed by the mere mathematician or  
the mere experimenter4  ,but what will  
be the effect on the ,university1 if men
 ,pursuing that course of reading which 
has produced so many distinguished      
,wranglers1 turn aside to work          
experiments8  ,will not their attendance
 at the ,laboratory count not merely as 
time withdrawn from their more          
legitimate studies1 but as the          
introduction of a disturbing element1   
tainting their mathematical conceptions 
with material imagery1 and sapping their
 faith in the formulae of the textbook8 
,besides this1 we have already heard    
complaints of the undue extension of our
 studies1 and of the strain put upon our
 questionists by the weight of learning 
which they try to carry with them into  

the ,senate-,house4  ,if we now ask them
 to get up their subjects not only by   
books and writing1 but at the same time 
by observation and manipulation1 will   
they not break down altogether8  ,the   
,physical ,laboratory1 we are told1 may 
perhaps be useful to those who are going
 out in ,natural ,science1 and who do   
not take in ,mathematics1 but to attempt
 to combine both kinds of study during  
the time of residence at the ,university
 is more than one mind can bear4  ,no   
doubt there is some reason for this     
feeling4  ,many of us have already      
overcome the initial difficulties of    
mathematical training4 ,when we now go  
on with our study1 we feel that it      
requires exertion and involves fatigue1 
but we are confident that if we only    
work hard our progress will be certain4 
,some of us1 on the other hand1 may have
 had some experience of the routine of  
experimental work4  ,as soon as we can  
read scales1 observe times1 focus       
telescopes1 and so on1 this kind of work

 ceases to require any great mental     
effort4  ,we may perhaps tire our eyes  
and weary our backs1 but we do not      
greatly fatigue our minds4  ,it is not  
till we attempt to bring the theoretical
 part of our training into contact with 
the practical that we begin to          
experience the full effect of what      
,faraday has called mental inertia--not 
only the difficulty of recognising1     
among the concrete objects before us1   
the abstract relation which we have     
learned from books1 but the distracting 
pain of wrenching the mind away from the
 symbols to the objects1 and from the   
objects back to the symbols4  ,this     
however is the price we have to pay for 
new ideas4  ,but when we have overcome  
these difficulties1 and successfully    
bridged over the gulph between the      
abstract and the concrete1 it is not a  
mere piece of knowledge that we have    
obtained3 we have acquired the rudiment 
of a permanent mental endowment4  ,when1
 by a repetition of efforts of this     

kind1 we have more fully developed the  
scientific faculty1 the exercise of this
 faculty in detecting scientific        
principles in nature1 and in directing  
practice by theory1 is no longer        
irksome1 but becomes an unfailing source
 of enjoyment1 to which we return so    
often1 that at last even our careless   
thoughts begin to run in a scientific   
channel4  ,i quite admit that our mental
 energy is limited in quantity1 and ,i  
know that many zealous students try to  
do more than is good for them4 ,but the 
question about the introduction of      
experimental study is not entirely one  
of quantity4  ,it is to a great extent a
 question of distribution of energy4    
,some distributions of energy1 we know1 
are more useful than others1 because    
they are more available for those       
purposes which we desire to accomplish4 
,now in the case of study1 a great part 
of our fatigue often arises1 not from   
those mental efforts by which we obtain 
the mastery of the subject1 but from    

those which are spent in recalling our  
wandering thoughts2 and these efforts of
 attention would be much less fatiguing 
if the disturbing force of mental       
distraction could be removed4  ,this is 
the reason why a man whose soul is in   
his work always makes more progress than
 one whose aim is something not         
immediately connected with his          
occupation4  ,in the latter case the    
very motive of which he makes use to    
stimulate his flagging powers becomes   
the means of distracting his mind from  
the work before him4  ,there may be some
 mathematicians who pursue their studies
 entirely for their own sake4  ,most    
men1 however1 think that the chief use  
of mathematics is found in the          
interpretation of nature4  ,now a man   
who studies a piece of mathematics in   
order to understand some natural        
phenomenon which he has seen1 or to     
calculate the best arrangement of some  
experiment which he means to make1 is   
likely to meet with far less distraction

 of mind than if his sole aim had been  
to sharpen his mind for the successful  
practice of the ,law1 or to obtain a    
high place in the ,mathematical ,tripos4
  ,i have known men1 who when they were 
at school1 never could see the good of  
mathematics1 but who1 when in after life
 they made this discovery1 not only     
became eminent as scientific engineers1 
but made considerable progress in the   
study of abstract mathematics4  ,if our 
experimental course should help any of  
you to see the good of mathematics1 it  
will relieve us of much anxiety1 for it 
will not only ensure the success of your
 future studies1 but it will make it    
much less likely that they will prove   
injurious to your health4   ,but why    
should we labour to prove the advantage 
of practical science to the ,university8
  ,let us rather speak of the help which
 the ,university may give to science1   
when men well trained in mathematics and
 enjoying the advantages of a           
well-appointed ,laboratory1 shall unite 

their efforts to carry out some         
experimental research which no solitary 
worker could attempt4  ,at first it is  
probable that our principal experimental
 work must be the illustration of       
particular branches of science1 but as  
we go on we must add to this the study  
of scientific methods1 the same method  
being sometimes illustrated by its      
application to researches belonging to  
different branches of science4  ,we     
might even imagine a course of          
experimental study the arrangement of   
which should be founded on a            
classification of methods1 and not on   
that of the objects of investigation4   
,a combination of the two plans seems to
 me better than either1 and while we    
take every opportunity of studying      
methods1 we shall take care not to      
dissociate the method from the          
scientific research to which it is      
applied1 and to which it owes its value4
  ,we shall therefore arrange our       
lectures according to the classification

 of the principal natural phenomena1    
such as heat1 electricity1 magnetism and
 so on4  ,in the laboratory1 on the     
other hand1 the place of the different  
instruments will be determined by a     
classification according to methods1    
such as weighing and measuring1         
observations of time1 optical and       
electrical methods of observation1 and  
so on4  ,the determination of the       
experiments to be performed at a        
particular time must often depend upon  
the means we have at command1 and in the
 case of the more elaborate experiments1
 this may imply a long time of          
preparation1 during which the           
instruments1 the methods1 and the       
observers themselves1 are being         
gradually fitted for their work4  ,when 
we have thus brought together the       
requisites1 both material and           
intellectual1 for a particular          
experiment1 it may sometimes be         
desirable that before the instruments   
are dismounted and the observers        

dispersed1 we should make some other    
experiment1 requiring the same method1  
but dealing perhaps with an entirely    
different class of physical phenomena4  
,our principal work1 however1 in the    
,laboratory must be to acquaint         
ourselves with all kinds of scientific  
methods1 to compare them1 and to        
estimate their value4  ,it will1 ,i     
think1 be a result worthy of our        
,university1 and more likely to be      
accomplished here than in any private   
laboratory1 if1 by the free and full    
discussion of the relative value of     
different scientific procedures1 we     
succeed in forming a school of          
scientific criticism1 and in assisting  
the development of the doctrine of      
method4  ,but admitting that a practical
 acquaintance with the methods of       
,physical ,science is an essential part 
of a mathematical and scientific        
education1 we may be asked whether we   
are not attributing too much importance 
to science altogether as part of a      

liberal education4  ,fortunately1 there 
is no question here whether the         
,university should continue to be a     
place of liberal education1 or should   
devote itself to preparing young men for
 particular professions4  ,hence though 
some of us may1 ,i hope1 see reason to  
make the pursuit of science the main    
business of our lives1 it must be one of
 our most constant aims to maintain a   
living connexion between our work and   
the other liberal studies of ,cambridge1
 whether literary1 philological1        
historical or philosophical4  ,there is 
a narrow professional spirit which may  
grow up among men of science1 just as it
 does among men who practise any other  
special business4  ,but surely a        
,university is the very place where we  
should be able to overcome this tendency
 of men to become1 as it were1          
granulated into small worlds1 which are 
all the more worldly for their very     
smallness4  ,we lose the advantage of   
having men of varied pursuits collected 

into one body1 if we do not endeavour to
 imbibe some of the spirit even of those
 whose special branch of learning is    
different from our own4  ,it is not so  
long ago since any man who devoted      
himself to geometry1 or to any science  
requiring continued application1 was    
looked upon as necessarily a            
misanthrope1 who must have abandoned all
 human interests1 and betaken himself to
 abstractions so far removed from the   
world of life and action that he has    
become insensible alike to the          
attractions of pleasure and to the      
claims of duty4  ,in the present day1   
men of science are not looked upon with 
the same awe or with the same suspicion4
  ,they are supposed to be in league    
with the material spirit of the age1 and
 to form a kind of advanced ,radical    
party among men of learning4  ,we are   
not here to defend literary and         
historical studies4  ,we admit that the 
proper study of mankind is man4  ,but is
 the student of science to be withdrawn 

from the study of man1 or cut off from  
every noble feeling1 so long as he lives
 in intellectual fellowship with men who
 have devoted their lives to the        
discovery of truth1 and the results of  
whose enquiries have impressed          
themselves on the ordinary speech and   
way of thinking of men who never heard  
their names8  ,or is the student of     
history and of man to omit from his     
consideration the history of the origin 
and diffusion of those ideas which have 
produced so great a difference between  
one age of the world and another8  ,it  
is true that the history of science is  
very different from the science of      
history4  ,we are not studying or       
attempting to study the working of those
 blind forces which1 we are told1 are   
operating on crowds of obscure people1  
shaking principalities and powers1 and  
compelling reasonable men to bring      
events to pass in an order laid down by 
philosophers4  ,the men whose names are 
found in the history of science are not 

mere hypothetical constituents of a     
crowd1 to be reasoned upon only in      
masses4  ,we recognise them as men like 
ourselves1 and their actions and        
thoughts1 being more free from the      
influence of passion1 and recorded more 
accurately than those of other men1 are 
all the better materials for the study  
of the calmer parts of human nature4    
,but the history of science is not      
restricted to the enumeration of        
successful investigations4  ,it has to  
tell of unsuccessful inquiries1 and to  
explain why some of the ablest men have 
failed to find the key of knowledge1 and
 how the reputation of others has only  
given a firmer footing to the errors    
into which they fell4  ,the history of  
the development1 whether normal or      
abnormal1 of ideas is of all subjects   
that in which we1 as thinking men1 take 
the deepest interest4  ,but when the    
action of the mind passes out of the    
intellectual stage1 in which truth and  
error are the alternatives1 into the    

more violently emotional states of anger
 and passion1 malice and envy1 fury and 
madness2 the student of science1 though 
he is obliged to recognise the powerful 
influence which these wild forces have  
exercised on mankind1 is perhaps in some
 measure disqualified from pursuing the 
study of this part of human nature4     
,but then how few of us are capable of  
deriving profit from such studies4  ,we 
cannot enter into full sympathy with    
these lower phases of our nature without
 losing some of that antipathy to them  
which is our surest safeguard against a 
reversion to a meaner type1 and we      
gladly return to the company of those   
illustrious men who by aspiring to noble
 ends1 whether intellectual or          
practical1 have risen above the region  
of storms into a clearer atmosphere1    
where there is no misrepresentation of  
opinion1 nor ambiguity of expression1   
but where one mind comes into closest   
contact with another at the point where 
both approach nearest to the truth4   ,i

 propose to lecture during this term on 
,heat1 and1 as our facilities for       
experimental work are not yet fully     
developed1 ,i shall endeavour to place  
before you the relative position and    
scientific connexion of the different   
branches of the science1 rather than to 
discuss the details of experimental     
methods4  ,we shall begin with          
,thermometry1 or the registration of    
temperatures1 and ,calorimetry1 or the  
measurement of quantities of heat4  ,we 
shall then go on to ,thermodynamics1    
which investigates the relations between
 the thermal properties of bodies and   
their other dynamical properties1 in so 
far as these relations may be traced    
without any assumption as to the        
particular constitution of these bodies4
  ,the principles of ,thermodynamics    
throw great light on all the phenomena  
of nature1 and it is probable that many 
valuable applications of these          
principles have yet to be made2 but we  
shall have to point out the limits of   

this science1 and to shew that many     
problems in nature1 especially those in 
which the ,dissipation of ,energy comes 
into play1 are not capable of solution  
by the principles of ,thermodynamics    
alone1 but that in order to understand  
them1 we are obliged to form some more  
definite theory of the constitution of  
bodies4  ,two theories of the           
constitution of bodies have struggled   
for victory with various fortunes since 
the earliest ages of speculation3 one is
 the theory of a universal plenum1 the  
other is that of atoms and void4  ,the  
theory of the plenum is associated with 
the doctrine of mathematical continuity1
 and its mathematical methods are those 
of the ,differential ,calculus1 which is
 the appropriate expression of the      
relations of continuous quantity4  ,the 
theory of atoms and void leads us to    
attach more importance to the doctrines 
of integral numbers and definite        
proportions2 but1 in applying dynamical 
principles to the motion of immense     

numbers of atoms1 the limitation of our 
faculties forces us to abandon the      
attempt to express the exact history of 
each atom1 and to be content with       
estimating the average condition of a   
group of atoms large enough to be       
visible4  ,this method of dealing with  
groups of atoms1 which ,i may call the  
statistical method1 and which in the    
present state of our knowledge is the   
only available method of studying the   
properties of real bodies1 involves an  
abandonment of strict dynamical         
principles1 and an adoption of the      
mathematical methods belonging to the   
theory of probability4  ,it is probable 
that important results will be obtained 
by the application of this method1 which
 is as yet little known and is not      
familiar to our minds4  ,if the actual  
history of ,science had been different1 
and if the scientific doctrines most    
familiar to us had been those which must
 be expressed in this way1 it is        
possible that we might have considered  

the existence of a certain kind of      
contingency a self-evident truth1 and   
treated the doctrine of philosophical   
necessity as a mere sophism4  ,about the
 beginning of this century1 the         
properties of bodies were investigated  
by several distinguished ,french        
mathematicians on the hypothesis that   
they are systems of molecules in        
equilibrium4  ,the somewhat             
unsatisfactory nature of the results of 
these investigations produced1          
especially in this country1 a reaction  
in favour of the opposite method of     
treating bodies as if they were1 so far 
at least as our experiments are         
concerned1 truly continuous4  ,this     
method1 in the hands of ,green1 ,stokes1
 and others1 has led to results1 the    
value of which does not at all depend on
 what theory we adopt as to the ultimate
 constitution of bodies4  ,one very     
important result of the investigation of
 the properties of bodies on the        
hypothesis that they are truly          

continuous is that it furnishes us with 
a test by which we can ascertain1 by    
experiments on a real body1 to what     
degree of tenuity it must be reduced    
before it begins to give evidence that  
its properties are no longer the same as
 those of the body in mass4             
,investigations of this kind1 combined  
with a study of various phenomena of    
diffusion and of dissipation of energy1 
have recently added greatly to the      
evidence in favour of the hypothesis    
that bodies are systems of molecules in 
motion4  ,i hope to be able to lay      
before you in the course of the term    
some of the evidence for the existence  
of molecules1 considered as individual  
bodies having definite properties4  ,the
 molecule1 as it is presented to the    
scientific imagination1 is a very       
different body from any of those with   
which experience has hitherto made us   
acquainted4  ,in the first place its    
mass1 and the other constants which     
define its properties1 are absolutely   

invariable2 the individual molecule can 
neither grow nor decay1 but remains     
unchanged amid all the changes of the   
bodies of which it may form a           
constituent4  ,in the second place it is
 not the only molecule of its kind1 for 
there are innumerable other molecules1  
whose constants are not approximately1  
but absolutely identical with those of  
the first molecule1 and this whether    
they are found on the earth1 in the sun1
 or in the fixed stars4  ,by what       
process of evolution the philosophers of
 the future will attempt to account for 
this identity in the properties of such 
a multitude of bodies1 each of them     
unchangeable in magnitude1 and some of  
them separated from others by distances 
which ,astronomy attempts in vain to    
measure1 ,i cannot conjecture4  ,my mind
 is limited in its power of speculation1
 and ,i am forced to believe that these 
molecules must have been made as they   
are from the beginning of their         
existence4  ,i also conclude that since 

none of the processes of nature1 during 
their varied action on different        
individual molecules1 have produced1 in 
the course of ages1 the slightest       
difference between the properties of one
 molecule and those of another1 the     
history of whose combinations has been  
different1 we cannot ascribe either     
their existence or the identity of their
 properties to the operation of any of  
those causes which we call natural4  ,is
 it true then that our scientific       
speculations have really penetrated     
beneath the visible appearance of       
things1 which seem to be subject to     
generation and corruption1 and reached  
the entrance of that world of order and 
perfection1 which continues this day as 
it was created1 perfect in number and   
measure and weight8  ,we may be         
mistaken4  ,no one has as yet seen or   
handled an individual molecule1 and our 
molecular hypothesis may1 in its turn1  
be supplanted by some new theory of the 
constitution of matter2 but the idea of 

the existence of unnumbered individual  
things1 all alike and all unchangeable1 
is one which cannot enter the human mind
 and remain without fruit4  ,but what if
 these molecules1 indestructible as they
 are1 turn out to be not substances     
themselves1 but mere affections of some 
other substance8  ,according to ,sir ,w4
 ,thomson's theory of ,vortex ,atoms1   
the substance of which the molecule     
consists is a uniformly dense plenum1   
the properties of which are those of a  
perfect fluid1 the molecule itself being
 nothing but a certain motion impressed 
on a portion of this fluid1 and this    
motion is shewn1 by a theorem due to    
,helmholtz1 to be as indestructible as  
we believe a portion of matter to be4   
,if a theory of this kind is true1 or   
even if it is conceivable1 our idea of  
matter may have been introduced into our
 minds through our experience of those  
systems of vortices which we call       
bodies1 but which are not substances1   
but motions of a substance2 and yet the 

idea which we have thus acquired of     
matter1 as a substance possessing       
inertia1 may be truly applicable to that
 fluid of which the vortices are the    
motion1 but of whose existence1 apart   
from the vortical motion of some of its 
parts1 our experience gives us no       
evidence whatever4  ,it has been        
asserted that metaphysical speculation  
is a thing of the past1 and that        
physical science has extirpated it4     
,the discussion of the categories of    
existence1 however1 does not appear to  
be in danger of coming to an end in our 
time1 and the exercise of speculation   
continues as fascinating to every fresh 
mind as it was in the days of ,thales4