,,clerk ,,maxwell',s                    
,,electromagnetic ,,theory              
,the ,rede ,lecture for #aibc           
,,by                            ,h4 ,a4 
,,lorentz                               
,,cambridge                     ,,at    
,,the ,,university ,,press              
#aibc          ,,clerk ,,maxwell',s     
,,electromagnetic ,,theory      ,,when  
,i had the honour to be invited to      
deliver a lecture in the ,rede          
,foundation1 ,i thought ,i might perhaps
 present to you a brief review of  the  
electromagnetic theory of your great    
physicist ,james ,clerk ,maxwell4  ,the 
choice seemed the more appropriate as it
 is now exactly fifty years  ago that   
the work which raised him at once to the
 very first rank of  investigators of   
all ages1 the ,treatise on ,electricity 
and ,magnetism1  was published4 ,in this
 work it was proved beyond all doubt    
that electric  and magnetic actions can 
be conceived as being transmitted       
through a  medium and the theory was    

crowned by the wonderful revelation that
 light  is an electromagnetic           
phenomenon4    ,maxwell's theory was    
also a great simplification4 ,indeed1   
before his  time there was much         
uncertainty and confusion in this part  
of physics  and many contending theories
 were in the field4 ,in electrodynamics1
 for  instance1 we had the laws of      
,ampre and ,grassmann for the actions   
between elements of current1 and1 when  
we went further1 we found the           
speculations of ,weber1 ,riemann and    
,clausius about the mutual actions of   
particles of electricity4 ,in connexion 
with these theories there was a  good   
deal of discussion on the phenomena that
 were to be expected in the  case of    
closed and in that of open circuits4 ,it
 was thought in those  days that the    
current in a wire by means of which a   
metallic conductor  is charged1 ends on 
that conductor1 and even the discharge  
current of a  condenser was considered  
not to be closed2 there was a gap in the

  circuit1 because we had no idea that  
something is going on in the  insulating
 layer between the coatings4    ,in     
optics we had no less trouble4 ,it is   
true that the general principles  of the
 undulatory theory of light had been    
firmly established and  physicists were 
justly proud of the success that had    
been achieved in  the explanation of    
interference and diffraction1 double    
refraction and  polarization4 ,yet1 when
 we tried to penetrate somewhat deeper1 
we were  confronted with serious        
difficulties4 ,when we wanted to account
 for the  different optical properties  
of various substances1 of air and water 
for  instance1 we had the choice between
 two assumptions4 ,fresnel had sought   
the cause of the difference in an       
inequality of the density of the ether  
in the two substances1 the elasticity   
being the same in both4 ,f4 ,e4         
,neumann1 on the other hand1 had        
supposed the densities to be the same1  
but the elasticities to be different4   

,on either of these suppositions1  and  
in no other way1 it had been found      
possible to deduce the right  value for 
the ratio between the amplitude of the  
reflected and that of  the incident     
light4 ,you know that in this problem   
two principal cases  must be            
distinguished1 the vibrations being     
normal to the plane of  incidence in the
 one case and parallel to that plane in 
the other4 ,the  two values for the     
ratio in question are          sin 7i --
 r7 _/ sin 7i  r7    and        tg 7i - 
r7 _/ tg 7i  r71      if i is the angle 
of incidence and r the angle of         
refraction2 and it  is remarkable that1 
of the two rival theories1 one led to   
the expression  with the sines when the 
other required that with the tangents1  
and  conversely4 ,in connexion with this
 ,fresnel supposed the vibrations of    
plane polarized light to be at right    
angles to the plane of  polarization1   
whereas ,neumann wanted them to be      
parallel to that plane4    ,here was a  

problem that long baffled the efforts of
 physicists1 and many  attempts were    
made to determine experimentally the    
direction of the  vibrations4 ,one      
cannot say that the result has been very
 satisfactory  and the question remained
 open until ,maxwell's theory settled it
 once  for all4    ,i have enumerated   
some only of the difficulties with which
 we had to  struggle4 ,i could have     
mentioned similar problems that arose in
 the  theory of double refraction and ,i
 may add that in some cases             
longitudinal vibrations intruded        
themselves and complicated the theory4  
,maxwell relieved us of all these doubts
 and uncertainties4 ,by his bold        
assumption that in a non-conducting     
body1 in a dielectric as he called  it1 
there can exist what is truly a motion  
of electricity1 and that1 if  this      
motion1 the dielectric displacement1 is 
taken into account1  electricity can    
always be said to move as an            
incompressible fluid1 the  open currents

 and the longitudinal vibrations that   
were closely allied  to them were made  
to vanish from the scene4 ,further1 the 
optical  behaviour of non-conducting    
substances was shown to depend on two   
properties1 each characterized by a     
physical constant1 the dielectric       
constant1 or ,faraday's specific        
inductive capacity1 and the magnetic    
permeability4 ,it is true that the way  
in which these constants are  determined
 by the constitution of matter1 by the  
structure of molecules  and atoms1 was  
not considered and that1 so far1 they   
were no less  inaccessible than the     
ethereal density and elasticity of the  
old  theories1 but there was this       
important difference that1 whereas these
  latter constants had no connexion with
 any other phenomena1 the  dielectric   
constant and the magnetic permeability  
can be measured by  means of statical   
experiments1 so that1 at least in       
certain simple  cases1 we can deduce the
 optical properties of a substance from 

wholly  different data4 ,it was found   
that in the new theory the treatment of 
the  reflexion problem was much like    
that in the old one2 one is led to the  
two formulae which ,i recalled to you1  
if one supposes either the  dielectric  
constant or the magnetic permeability to
 be the same in the  two substances4    
,the choice between these alternative   
suppositions again  entailed a decision 
concerning the direction of the         
vibrations with  respect to the plane of
 polarization1 but the choice was not   
doubtful  now1 as it had been           
ascertained experimentally that the     
ratios between  the magnetic            
permeabilities of transparent substances
 are little  different from unity1      
whereas the dielectric constants diverge
 to a much  greater extent4 ,it was     
therefore at once established that the  
electric  vibrations are normal to the  
plane of polarization4 ,this implies    
that  the magnetic vibrations are in    
that plane1 so that1 in a sense1 the    

contending parties both had their will4 
,in the case of crystals it became      
certain that their double refraction  is
 due to an inequality of the dielectric 
properties in different  directions4    
,so1 many difficulties and outstanding  
problems melted away as snow  before the
 sun4 ,indeed1 a reviewer in ,nature    
actually compared  ,maxwell's work to   
the sun1 his only criticism being that  
there are spots  on the sun itself1     
which1 however1 are not visible save to 
those whose  eyes can bear the full     
glare of the glowing orb4 ,my eyes      
certainly were  not as strong as that4  
,i could not see the spots1 but what ,i 
could see  was that the sun was not     
entirely unclouded2 what sun always was8
 ,it was  not always easy to grasp      
,maxwell's ideas1 and one feels a want  
of unity  in his book1 due to the fact  
that it faithfully reproduces his       
gradual  transition from old to new     
ideas4 ,when we read what ,maxwell says 
of  ,ampre and ,faraday1 of the former  

having removed all traces of the        
scaffolding by which he had built up a  
perfect demonstration of his law1       
whereas ,faraday shews us his           
unsuccessful as well as his successful  
experiments1 and his crude ideas as well
 as his developed ones1 we feel  that1  
great though the difference may be      
between the ,experimental  ,researches  
and ,maxwell's largely mathematical     
,treatise1 yet the two  works were      
written in the same spirit4 ,in fact1   
,maxwell repeatedly  expresses his      
indebtedness to ,faraday1 from whom he  
had borrowed part of  his fundamental   
ideas1 so that1 when there is question  
of ,maxwell's  theory1 we must often    
think of ,faraday also4    ,maxwell's   
followers1 of whom there were many1 in  
this country and  elsewhere1 have       
perfected the theory in its form and    
extended it by the  introduction of new 
ideas4 ,think1 for instance1 of         
,poynting's beautiful  and important    
theorem on the flow of energy1          

determined at every point  by the       
electric and the magnetic force existing
 in the field1 a theorem  that has      
produced more clearness perhaps than any
 other and which is now  so essential   
that we can hardly recall the state in  
which physics was  when we did not know 
it4 ,yet1 notwithstanding all           
innovations of this  kind1 we always    
speak1 and with full justice1 of        
,maxwell's ,theory4 ,we  continue to do 
so now that we have been led to         
introduce electric  charges supposed to 
exist in the interior of molecules and  
atoms1 by  which we have come to the    
theory of electrons4 ,and when we refer 
to  those wonderfully simple equations  
in which the fundamental laws of        
electromagnetism are embodied with a    
conciseness that could never have  been 
dreamed of before1 we call them         
,maxwell's ,equations4 ,surely1  though 
,maxwell did not use them in their      
modern form1 no name could be  more     
appropriate1 for the general relations  

which they express are those  that were 
constantly in his mind4    ,time does   
not permit me to dwell at length on the 
verifications of  ,maxwell's theory1 but
 ,i should like to make an exception for
 two of  them4    ,allow me1 in the     
first place1 to say some words on the   
optical  properties of metals4    ,if   
the medium1 so we read in ,maxwell1     
instead of being a perfect  insulator1  
is a conductor1 the disturbance 7viz4   
that which is produced  by an incident  
beam of light7 will consist not only of 
electric  displacements but of currents 
of conduction1 in which electric energy 
is  transformed into heat1 so that the  
undulation is absorbed by the  medium4  
,after having stated in these words one 
of the most important  consequences     
drawn from his theory1 ,maxwell goes on 
to calculate the  coefficient of        
absorption as a function of the         
conductivity1 and he  proceeds3 ,gold1  
silver and platinum are good conductors1
 and yet1 when  formed into very thin   

plates1 they allow light to pass through
 them4  ,from experiments which ,i have 
made on a piece of gold leaf1 it appears
  that its transparency is very much    
greater than is consistent with our     
theory1 unless we suppose that there is 
less loss of energy when the            
electromotive forces are reversed for   
every semi-vibration of light than  when
 they act for sensible times1 as in our 
ordinary experiments4 ,later  researches
 have amply confirmed what ,maxwell says
 here2 obviously1  bodies1 both         
conductors and dielectrics1 behave in   
general differently  towards rapidly    
alternating electric forces and towards 
stationary ones4  ,yet1 ,hagen and      
,rubens have been able to show that     
when1 instead of  working with visible  
light1 one uses infra-red rays of       
sufficiently  great wave-length1 the    
properties of metals will1 in the limit1
 exactly  conform to the theory1 if we  
reckon with the ordinary conductivity4  
,hagen and ,rubens did not measure the  

amount of radiation that is  transmitted
 through a thin plate but the           
coefficient of reflexion of a  thick    
mirror4 ,for the case of normal         
incidence1 this coefficient and         
therefore also the loss of energy1 i4e4 
the quantity that is absorbed by  the   
mirror1 can easily be calculated as a   
function of the conductivity4  ,for the 
residual rays of sylvin1 whose          
wavelength is #ab 1 and for  silver1    
copper1 gold and platinum1 the absorbed 
energy was found to be  respectively    
#aae1 #af1 #ba and #ce per cent1 of the 
incident  energy1 whereas it ought to   
have been #ac1 #ad1 #af1 and #ce per    
cent1 according to the theoretical      
formula4    ,the agreement became still 
better when the residual rays of        
fluorite  with a wave-length of #bee    
were used4 ,since1 however1 for waves of
  this length the reflexion becomes     
nearly complete1 it was not possible  to
 determine the loss of energy with      
sufficient precision4 ,hagen and        

,rubens overcame this difficulty by     
measuring the emissivity of the         
different metals1 or rather the ratio   
between this emissivity and that  of a  
perfectly black body at the same        
temperature1 a ratio which1 by          
,kirchhoff's law1 is equal to that      
between the absorbed and the incident   
energy for a beam falling on the metal  
from the outside1 so that it can  be    
calculated by the same formula as this  
latter ratio4 ,for the four  metals just
 mentioned 7at a temperature of #agj    
,c47 the ratio in  question was found to
 be 7after multiplication by #ajj7 #aac1
 #aag1  #aef and #bhb4 ,the theoretical 
values were #aae1 #abi1 #aci and  #bif4 
,these numbers show conclusively that1  
however complicated things may be  for  
shorter waves1 we can calculate the     
optical properties of metals in  the    
extreme infra-red by means of ,maxwell's
 equations1 simply  substituting for the
 conductivity the value that has been   
deduced from  experiments with constant 

or slowly alternating currents4 ,this is
  certainly a most splendid             
confirmation1 the counterpart to the    
verification1 which for gaseous bodies  
at least has been very  satisfactory1 of
 ,maxwell's relation of the dielectric  
constant to the  index of refraction4   
,the phenomenon of the pressure of      
radiation may serve as a second  example
 of verification4 ,that a beam of light 
falling1 say in the normal  direction1  
on a mirror exerts on it a pressure     
proportional to the  intensity of the   
beam was deduced by ,maxwell from his   
formulae1 and he  calculated the force  
that may be expected in the case of     
sunlight4 ,it  lasted a quarter of a    
century before ,lebedew succeeded in    
observing this  small force1 which1 for 
sunlight1 amounts to no more than about 
a ten  millionth part of a gramme weight
 per cm4#b1 and which it is therefore   
difficult to disentangle from other     
forces that are caused by the           
surrounding gas1 even when this is      

highly rarefied4 ,some years later ,e4  
,f4 ,nichols and ,hull repeated the     
experiment with the utmost care and     
were able to measure the pressure and to
 prove that its intensity agrees  with  
,maxwell's calculation4    ,we are now  
quite sure of this phenomenon which has 
come to play a great  part in stellar   
physics4 ,when we are concerned with    
very small particles  near or in a star1
 the radiation pressure may very well   
become greater  than the force of       
gravitation1 and it is taken into       
account by many  astronomers in their   
speculations about the state of heavenly
 bodies4    ,the forces exerted by rays 
of light or heat are a special case of  
what  we call ponderomotive forces1 i4e4
 of the forces with which the           
electromagnetic field acts on material  
bodies4 ,maxwell showed how1 in         
general1 these forces can be deduced    
from the values of the  electromagnetic 
energy corresponding to different       
positions of a system  of bodies1 or    

from a consideration of certain stresses
 which exist in  the electromagnetic    
field and of which he taught us to      
determine the  direction and the        
intensity4 ,every student1 even of      
rather elementary  physics1 now knows   
that the mutual attraction of two       
conducting plates  between which there  
is a difference of potential1 e4g4 of   
the plates of  an absolute electrometer1
 may be considered as due to stresses   
along the  lines of force1 that the same
 may be said of the attraction between a
  magnetic pole and a piece of iron1 and
 that in the case of an  electromagnetic
 motor we are concerned with the        
tangential stresses  acting at the      
surface of the revolving system4 ,here  
again there has been  a great deal of   
later development1 but we continue to   
speak of  ,maxwell's stresses4    ,the  
notion of the electromagnetic momentum1 
which ,maxwell seems not to  have had1  
though he was quite near it1 has also   
proved very fruitful4 ,a  beam of light 

has a definite momentum1 much like a    
moving ball1 and when  the beam is      
normally reflected by a mirror1 so that 
the momentum is  inverted1 we can deduce
 the force acting on the mirror from the
 change  of the momentum1 exactly as we 
can do in the case of the ball or of a  
stream of material particles4    ,in    
modern theory--,i allude to the theory  
of relativity--one has found  good      
reasons for combining into one unity1   
which we call the  stress-energy-tensor1
 all these quantities of which ,i have  
spoken1 viz4  the energy1 the flow of   
energy1 ,maxwell's stresses and the     
electromagnetic momentum4 ,in           
,einstein's theory of gravitation this  
tensor determines the gravitation field 
that is produced by an  electromagnetic 
system and in virtue of which such a    
system has an  influence on the motion  
of material particles1 unfortunately    
much too  small to be observed4    ,i   
should be led too far astray if ,i dwelt
 on these questions1 but what ,i  want  

to point out is this1 that we could     
never have gone so far if we  had       
contented ourselves with the actions at 
a distance1 if we had not  fixed our    
attention on the intervening medium1    
localizing the energy in  it and        
considering it as the seat of momenta   
and stresses which manifest  themselves 
in the observed motions of bodies4 ,all 
these modern ideas  have their origin in
 ,maxwell's work4    ,we are also       
concerned with a stress-energy-tensor1  
similar to the  electromagnetic one1    
when we consider a system of material   
particles1  whether unconnected like the
 molecules of a gas1 or held together by
  internal forces as in an elastic body 
or a fluid4 ,the question naturally     
arises3 are these stress-energy-tensors1
 the electromagnetic and1 let me  say1  
the material one1 wholly independent or 
can one be reduced to the  other8 ,one  
has often tried to do so and1 more      
particularly1 to imagine                
electromagnetic phenomena as produced by

 some invisible mechanism moving        
according to the laws of dynamics4      
,this was a favourite idea of ,maxwell's
 and one of his most brilliant  chapters
 is devoted to the dynamical theory of  
electromagnetism4 ,it is  the more      
important because it shows that such a  
theory can be developed  on very general
 lines1 it not being necessary to make  
definite  assumptions regarding the     
underlying mechanism4 ,maxwell showed   
that in  the case of linear circuits    
carrying electric currents we can       
account  for the ponderomotive forces   
and for the phenomena of self and mutual
  induction by ,lagrange's or           
,hamilton's equations of motion1        
provided that  we introduce1 besides the
 coordinates which determine the        
positions of  the material circuits1 a  
certain number of new coordinates1 one  
for each  circuit1 the velocities       
belonging to these coordinates for the  
several  circuits being proportional to 
the current intensities4 ,in fact1 the  

new  or internal coordinate for each    
circuit represents the total quantity   
of electricity that has traversed some  
section since a fixed instant  that is  
chosen as the origin of time4 ,when the 
internal coordinates are  given this    
meaning1 the magnetic energy becomes the
 kinetic energy of  the system1 whereas 
the electric energy has to be identified
 with the  potential energy and is      
comparable to the energy of deformation 
of an  elastic body4    ,while he was   
applying the laws of dynamics in this   
very general way1  ,maxwell was led to  
discuss certain phenomena that might    
perhaps be  expected to exist and some  
of which have been actually observed in 
our  days though ,maxwell was not able  
to detect them with the means at his    
disposal4    ,in the theory of dynamical
 systems there are as many velocities as
 there  are coordinates and the kinetic 
energy is a homogeneous quadratic       
function of these velocities1 in which  
in general not only the squares  but    

also the products of the velocities     
appear4 ,when we have one or more       
circuits carrying electric currents1 we 
can distinguish in the kinetic  energy  
one part that depends on the material   
velocities only1 and this  is the       
kinetic energy of ordinary mechanics1   
and a second part  containing only the  
velocities corresponding to the internal
  coordinates2 this is the magnetic     
energy that manifests itself in so  many
 ways4 ,now1 is this all8 ,there would  
certainly be a third part of  the       
kinetic energy if an electric current   
consisted in a real motion of  some     
substance along the conducting wire1 for
 if the wire were moving1  say in the   
direction of its length1 with the       
velocity v and if v'  were the internal 
velocity proportional to the current1   
the total  velocity of the moving       
substance would be v  v' and in its     
square  we should have the term #bvv'4  
,one is led to a similar conclusion on  
other less simple assumptions and so1   

independently of an special  conception1
 the question arises whether any part of
 the kinetic energy  consists of        
products of ordinary velocities and     
strengths of electric  currents4        
,maxwell thinks this question to be of  
great importance and  deems it desirable
 that experiments should be made on the 
subject with  great care4    ,he then   
proceeds to examine different ways in   
which the terms in  question might be   
made to reveal themselves1 the first of 
which he  explains as follows3      ,if 
any part of the kinetic energy depends  
on the product of an ordinary  velocity 
and the strength of a current1 it will  
probably be most easily  observed when  
the velocity and the current are in the 
same or in  opposite directions4 ,we    
therefore take a circular coil of a     
great many  windings1 and suspend it by 
a fine vertical wire1 so that its       
windings  are horizontal1 and the coil  
is capable of rotating about a vertical 
axis1 either in the same direction as   

the current in the coil1 or in the      
opposite direction4    ,we shall suppose
 the current to be conveyed into the    
coil by means of  the suspending wire1  
and1 after passing round the windings1  
to complete  its circuit by passing     
downwards through a wire in the same    
line with  the suspending wire and      
dipping into a cup of mercury4 ,a       
vertical mirror  is attached to the coil
 to detect any motion in azimuth4       
,now let a current be made to pass      
through the coil in the direction       
,n4,e4,s4,w4 ,if electricity were a     
fluid like water1 flowing along the     
wire1  then1 at the moment of starting  
the current1 and as long as its velocity
  is increasing1 a force would require  
to be supplied to produce the  angular  
momentum of the fluid in passing round  
the coil1 and as this  must be supplied 
by the elasticity of the suspending     
wire1 the coil  would at first rotate in
 the opposite direction or ,w4,s4,e4,n41
 and this  would be detected by means of

 the mirror4 ,on stopping the current   
there  would be another movement of the 
mirror1 this time in the same direction 
as that of the current4      ,it does   
not appear that ,maxwell actually tried 
the experiment2 he only  says3 no       
phenomenon of this kind has yet been    
observed4    ,now1 if for ,maxwell's    
coil we substitute a rod of iron1 the   
magnetization and demagnetization of    
which are comparable to the  starting   
and stopping of a current in the coil1  
we have exactly the                     
,richardson-,einstein-de ,haas effect   
that was really observed by ,einstein   
and de ,haas and by some other          
physicists4 ,you know that it amounts to
  this1 that a cylindrical rod of iron  
suspended in a vertical direction  is   
set rotating1 with a sudden jerk1 when  
it is rapidly magnetized or             
demagnetized4 ,when the magnetization is
 periodically reversed1 the rod  is made
 to oscillate and the amplitude of this 
motion may be increased  by adjusting   

the frequency of the reversals to that  
of the free  oscillations of the rod4   
,whereas ,maxwell seems not to have     
tried the above experiment with the     
coil1 he tried to observe another       
effect4 ,a coil1 through which a        
current could be passed and which could 
be provided with an iron core1  was     
placed in a system rapidly revolving    
about a vertical axis1 the  arrangement 
being such that the coil was free to    
rotate in the revolving  system1 so that
 the axis of the coil could be inclined 
to different  degrees with respect to   
the vertical axis of rotation4 ,if in   
the formula  for the kinetic energy     
there were terms of the kind which      
,maxwell wanted  to detect1 there would 
be a tendency for the coil to place     
itself with  its axis parallel to the   
axis of rotation2 it would behave as a  
gyroscope and might be called an        
electromagnetic gyroscope4 ,no trace of 
a phenomenon of this kind could1        
however1 be observed4 ,i may insert the 

remark that1 if the tendency of which ,i
 spoke existed to an appreciable        
extent1 a magnetic needle would1 even in
 the absence of the terrestrial         
magnetic field1 still take a definite   
position that would be determined  by   
the rotation of the earth2 in fact1 in  
virtue of its internal motions  the     
magnetic needle would be comparable to a
 gyroscopic compass1 such as  has lately
 come into use in navigation4    ,now   
that we know the intensity of the       
,einstein effect we can say with        
certainty that1 if only his instrumental
 means had been more refined4           
,maxwell's experiment would have had a  
positive result4 ,we can evaluate  the  
magnitude of the effect and we can also 
calculate that the force  which a       
magnetic needle experiences on account  
of its internal motions  and of the     
rotation of the earth is thousands of   
millions of times  smaller than the     
force due to the earth's magnetic field1
 so that you  need not fear from this   

cause any error in measurements in      
terrestrial  magnetism4    ,in the      
experiments just discussed we were      
concerned with forces acting  on the    
material bodies4 ,maxwell next considers
 cases in which1 always on  account of  
the terms in question1 not the material 
system but the  electricity contained in
 it is set in motion4 ,here he reverts  
again to  the suspended circular coil1  
and he points out that when a rotation  
is  suddenly imparted to it there could 
be produced a transient electric        
current4 ,similarly1 there would be a   
current1 but now in the opposite        
direction1 when the motion of the coil  
is stopped4    ,a very simple experiment
 may serve to give you an idea of these 
phenomena4 ,we take a cylindrical       
tumbler1 partly filled with water1 and  
set it suddenly in rotation about its   
vertical axis4 ,then the friction       
between the glass and the water will    
make the fluid rotate likewise1 but     
this will take some time2 during a      

certain period the water will lag       
behind4 ,let us next suppose that the   
motion of the vessel has been kept      
constant for a sufficient length of     
time1 so that the water has acquired    
the full angular velocity and then let  
the vessel be suddenly brought to  rest4
 ,it is clear that the circulation of   
the water will continue for a  certain  
time1 until it is exhausted by the      
friction4    ,similar phenomena could be
 observed with a closed circular tube   
capable  of rotating about its axis1 and
 there must be a corresponding          
electromagnetic phenomenon if a metallic
 wire contains something like  movable  
electricity1 as we are now in a position
 to assert1 because we  have good       
reasons for believing that an electric  
current consists in a  motion of        
negative electrons4 ,though the         
experiment is much more  delicate with  
electricity than with water1 ,tolman and
 ,stewart have  performed it with very  
satisfactory results4 ,using a coil with

 a great  number of windings1 rapidly   
rotating about its axis1 they were able 
to  observe with a sensitive            
galvanometer the transient electric     
current  that was produced on stopping  
the motion by means of a brake4 ,the    
electrons continued to move over some   
distance just as the water did in  the  
experiment with the circular tube4 ,the 
direction of the current  showed that   
the movable particles really have       
negative charges and the  observed      
deflections agreed with what can be     
inferred from the ratio  between the    
charge and the mass of the electrons1 a 
ratio that was found  for the first time
 by ,zeeman and ,sir ,j4 ,j4 ,thomson   
somewhat more than  twenty-five years   
ago and has been repeatedly determined  
in later years4    ,no less remarkable  
than ,tolman and ,stewart's experiments 
are those made  by ,mr and ,mrs         
,barnett4 ,they found that a cylindrical
 rod of iron1  rotating about its       
geometrical axis1 becomes thereby       

magnetized in the  direction of its     
length4 ,like the ,einstein effect1 to  
which it forms a  counterpart1 this new 
phenomenon can be predicated on the     
assumption  that magnetization consists 
in a motion of electrons in the         
molecules of  the metal4 ,this allows us
 to assign the direction of the effects1
 but  for the sake of truth ,i must add 
that both the rotation produced by the  
magnetization of rods and the           
magnetization caused by a rotation are1 
for some reason which we do not yet     
understand1 only about half what the    
theory of electrons had led us to       
expect4    ,in ,maxwell's time the      
electron was unknown and the mechanism  
of  conduction was even more mysterious 
than it is now4 ,it was precisely for   
this reason that he attached so much    
importance to the phenomena to  which ,i
 have drawn your attention4 ,he says in 
this connexion3      ,it appears to me  
that while we derive great advantage    
from the  recognition of the many       

analogies between the electric current  
and a  current of a material fluid1 we  
must carefully avoid making any         
assumption not warranted by experimental
 evidence1 and that there is1 as  yet1  
no experimental evidence to shew whether
 the electric current is  really a      
current of a material substance1 or a   
double current1 or  whether its velocity
 is great or small as measured in feet  
per second4    ,a knowledge of these    
things would amount to at least the     
beginning of a  complete dynamical      
theory of electricity1 in which we      
should regard  electrical action1 not1  
as in this treatise1 as a phenomenon due
 to an  unknown cause1 subject only to  
the general laws of dynamics1 but as the
  result of known motions of known      
portions of matter1 in which not only   
the total effects and final results1 but
 the whole intermediate  mechanism and  
details of the motion1 are taken as the 
object of study4      ,maxwell did not  
always express himself so cautiously3 at

 other times he  did not shrink from    
imagining an elaborate mechanical model4
 ,all  physicists know its principal    
features4 ,the magnetic energy is       
considered as a true vis viva1 the      
magnetic field being the seat of        
invisible motions1 rotations of small   
particles about the lines of  force4    
,the system of these particles may be   
compared to a wheelwork1 and  ,maxwell  
has to explain how it can be that all   
the wheels in an element  of volume are 
rotating in the same direction4 ,this   
shows that the motion  is not           
transmitted directly from one wheel to  
the next4 ,so ,maxwell is  led to assume
 that between these wheels of the       
magnetic field and in  contact with     
them1 there are smaller ones which      
transmit the motion in  the manner of   
friction wheels4    ,what ,i called     
wheels might in reality be spheres      
capable of turning  about axes in any   
direction and1 as ,maxwell showed1 a    
system of this  kind is amenable to     

mathematical analysis4 ,in his image the
 friction  wheels represent what we call
 electricity2 in a conductor we must    
conceive them to be freely movable1     
whereas the centres of the larger       
wheels or balls have fixed positions4   
,it is easily seen how a motion of      
translation imparted to the friction    
wheels can give rise to rotations  of   
the larger balls2 this is how a current 
produces a magnetic field4  ,other      
phenomena can be explained on the same  
lines2 it is sufficient for  this that  
,maxwell's equations can be deduced by  
means of the model4    ,similar models  
have been invented1 with more or less   
success1 by other  physicists1 in such  
quantities1 even1 that nearly all that  
could be done  has been tried4 ,the     
outcome of these various attempts is1 in
 my opinion1  this3 that we must admit  
the possibility of mechanical           
representations1  a possibility that is 
already shown by the fact that the      
formulae of the  electromagnetic field  

can be given the form of the general    
equations of  dynamics4 ,on the other   
hand it cannot be denied that1 when we  
desire  them to be applicable to a      
comparatively wide range of phenomena1  
the  theories that have been proposed   
become so complicated that they can     
give us but little satisfaction4 ,so1 ,i
 think1 the majority of physicists  will
 agree to attach less importance to     
mechanical models and even to  the      
general dynamical analogies1 however    
helpful these may be to us1  than to    
,maxwell's equations that summarize so  
admirably all that is  essential4       
,will it be possible to maintain these  
equations8 ,i am not thinking here  of  
the comparatively slight modifications  
that have been found necessary  in the  
theory of relativity2 and by which we   
explain1 for instance1 the  curvature of
 a ray of light in a gravitation field4 
,a greater and really  serious danger is
 threatening from the side of the       
quantum theory1 for  the existence of   

amounts of energy that remain           
concentrated in small  spaces during    
their propagation1 to which several     
phenomena seem to  point1 is in absolute
 contradiction to ,maxwell's equations4 
,however this  may be1 even if further  
development should require profound     
alterations1  ,maxwell's theory will    
always remain a step of the highest     
importance in  the progress of physics4 
,but ,i must not trespass any longer on 
your patience4 ,let me rather thank  you
 for the attention with which you have  
listened to what ,i had to say1  which  
was mainly intended as a tribute to the 
memory of one of the  greatest ,masters 
of ,science4