,transcriber's note3 ,a few             
typographical errors have been          
corrected3 they are listed at the end of
 the text4         99       99       99 
99       99   ,,the ,,earl ,,of         
,,pembroke ,,to ,,the ,,abbess ,,of     
,,wilton4  ,go spin1 you jade6 go spin6 
,illustration3 ,,magnetism1 ,,light1    
,,and ,,molecular ,,spinning ,,tops4    
,page #abb4  ,,the ,,romance ,,of       
,,science4  ,,spinning ,,tops4  ,,the   
,,operatives' ,,lecture ,,of ,,the      
,,british ,,association ,,meeting ,,at  
,,leeds1 #fth ,,september1 #ahij4  ,,by 
,,professor ,,john ,,perry1 ,m4,e41     
,d4,sc1 ,,ll4,d41 ,f4,r4,s4  ,with      
,numerous ,illustrations4  ,,reprint    
,,of ,,new ,,and ,,revised ,,edition1   
,with an ,illustrated ,appendix on the  
,use of ,gyrostats4  ,,london ,,society 
,,for ,,promoting ,,christian           
,,knowledge1 ,northumberland ,avenue1   
,w4,c42 #dc1 ,queen ,victoria ,street1  
,e4,c4 ,,brighton3 #abi1 ,north ,street4
 ,,new ,,york3 ,e4 ,s4 ,,gorham4  #aiaj 

,,published ,,under ,,the ,,direction   
,,of ,,the ,,general ,,literature       
,,committee  ,date of last impression1  
,april #aijh  ,this ,report of an       
,experimental ,lecture ,,was ,,inscribed
 ,,to ,,the ,,late ,,lord ,,kelvin1 ,,by
 ,,his ,,affectionate ,,pupil1 ,,the    
,,lecturer1 ,,who ,,hereby ,,took ,a    
,,convenient ,,method ,,of              
,,acknowledging ,,the ,,real ,,author   
,,of ,,whatever ,,is ,,worth            
,,publication ,,in ,,the ,,following    
,,pages4         99       99       99   
99       99   ,,preface4  ,this is not  
the lecture as it was delivered4        
,instead of two pages of letterpress and
 a woodcut1 the reader may imagine that 
for half a minute the lecturer played   
with a spinning top or gyrostat1 and    
occasionally ejaculated words of        
warning1 admonition1 and explanation    
towards his audience4 ,a verbatim report
 would make rather uninteresting        
reading1 and ,i have taken the liberty  
of trying1 by greater fullness of       

explanation1 to make up to the reader   
for his not having seen the moving      
apparatus4 ,it has also been necessary  
in a treatise intended for general      
readers to simplify the reasoning1 the  
lecture having been delivered to persons
 whose life experiences peculiarly      
fitted them for understanding scientific
 things4 ,an argument has been added at 
the end to make the steps of the        
reasoning clearer4    ,,john ,,perry4   
99       99       99       99       99  
#i  ,,spinning ,,tops4  --------  ,at a 
,leeds ,board ,school last week1 the    
master said to his class1 ,there is to  
be a meeting of the ,british            
,association in ,leeds4 ,what is it all 
about8 ,who are the members of the      
,british ,association8 ,what do they do8
 ,there was a long pause4 ,at length it 
was broken by an intelligent shy boy3   
,please1 sir1 ,i know--they spin tops6#a
  ,now ,i am sorry to say that this     
answer was wrong4 ,the members of the   
,british ,association and the           

,operatives of ,leeds have neglected    
top-spinning since they were ten years  
of age4 ,if more attention were paid to 
the intelligent examination of the      
behaviour of tops1 there would be       
greater advances in mechanical          
engineering and a great many industries4
 ,there would be a better general       
knowledge of astronomy4 ,geologists     
would not make mistakes by millions of  
years1 and our knowledge of ,light1 and 
,radiant ,heat1 and other #aj           
,electro-magnetic ,phenomena would      
extend much more rapidly than it does4  
,i shall try to show you towards the end
 of the lecture that the fact of our    
earth's being a spinning body is one    
which would make itself known to us even
 if we lived in subterranean regions    
like the coming race of an ingenious    
novelist4#b ,it is the greatest and most
 persistent cause of many of the        
phenomena which occur around us and     
beneath us1 and it is probable that even
 ,terrestrial ,magnetism is almost      

altogether due to it4 ,indeed there is  
only one possible explanation of the    
,vril-ya ignorance about the earth's    
rotation4 ,their knowledge of mechanics 
and dynamics was immense2 no member     
attending the meeting of the ,british   
,association can approach them in their 
knowledge of1 ,i will not say1 ,vril1   
but even of quite vulgar electricity and
 magnetism2 and yet this great race     
which expresses so strongly its contempt
 for ,anglo-,saxon ,koom-,poshery was   
actually ignorant of the fact that it   
had existed for untold generations      
inside an object that spins about an    
axis4  ,can we imagine for one instant  
that the children of that race had never
 spun a top or trundled a hoop1 and so  
had had no chance of being led to the   
greatest study of nature8 ,no2 the only 
possible explanation lies in the great  
novelist's never #aa having done these  
things himself4 ,he had probably as a   
child a contempt for the study of       
nature1 he was a baby ,pelham1 and as a 

man he was condemned to remain in       
ignorance even of the powers of the new 
race that he had created4  ,the ,vril-ya
 ignorance of the behaviour of spinning 
bodies existing as it does side by side 
with their deep knowledge of magnetism1 
becomes even more remarkable when it    
comes home to us that the phenomena of  
magnetism and of light are certainly    
closely connected with the behaviour of 
spinning bodies1 and indeed that a      
familiar knowledge of the behaviour of  
such bodies is absolutely necessary for 
a proper comprehension of most of the   
phenomena occurring in nature4 ,the     
instinctive craving to investigate these
 phenomena seems to manifest itself soon
 after we are able to talk1 and who     
knows how much of the intellectual      
inferiority of woman is due to her      
neglect of the study of spinning tops2  
but alas1 even for boys in the pursuit  
of top-spinning1 the youthful mind and  
muscle are left with no other guidance  
than that which is supplied by the      

experience of young and not very        
scientific companions4 ,i remember      
distinctly that there were many puzzling
 problems presented to me every day4    
,there were tops which nobody seemed    
able to spin1 and there were others1    
well #ab prized objects1 often studied  
in their behaviour and coveted as       
supremely valuable1 that behaved well   
under the most unscientific treatment4  
,and yet nobody1 even the makers1 seemed
 to know why one behaved badly and the  
other well4  ,i do not disguise from    
myself the fact that it is rather a     
difficult task to talk of spinning tops 
to men who have long lost that skill    
which they wonder at in their children2 
that knowingness of touch and handling  
which gave them once so much power over 
what ,i fear to call inanimate nature4  
,a problem which the child gives up as  
hopeless of solution1 is seldom attacked
 again in maturer years2 he drives his  
desire for knowledge into the obscure   
lumber-closets of his mind1 and there it

 lies1 with the accumulating dust of his
 life1 a neglected and almost forgotten 
instinct4 ,some of you may think that   
this instinct only remains with those   
minds so many of which are childish even
 to the limit of life's span2 and       
probably none of you have had the       
opportunity of seeing how the old dust  
rubs off from the life of the ordinary  
man1 and the old desire comes back to   
him to understand the mysteries that    
surround him4  ,but ,i have not only    
felt this desire myself1 ,i have seen it
 in the excited eyes of the crowd of    
people who stand by the hour under the  
dropping cherry-blossoms beside the     
red-pillared temple of #ac ,asakusa in  
the ,eastern capital of ,japan1 watching
 the tedzu-mashi directing the          
evolutions of his heavily rimmed ,koma4 
,first he throws away from him his great
 top obliquely into the air and catches 
it spinning on the end of a stick1 or   
the point of a sword1 or any other      
convenient implement2 he now sends it   

about quite carelessly1 catching it as  
it comes back to him from all sorts of  
directions2 he makes it run up the      
hand-rail of a staircase into a house by
 the door and out again by the window2  
he makes it travel up a great corkscrew4
 ,now he seizes it in his hands1 and    
with a few dexterous twists gives it a  
new stock of spinning energy4 ,he makes 
it travel along a stretched string or   
the edge of a sword2 he does all sorts  
of other curious things with his tops1  
and suddenly sinks from his masterful   
position to beg for a few coppers at the
 end of his performance4  ,how tame all 
this must seem to you who more than half
 forget your childish initiation into   
the mysteries of nature2 but trust me1  
if ,i could only make that old          
top-spinner perform those magical       
operations of his on this platform1 the 
delight of the enjoyment of beautiful   
motion would come back4 ,perhaps it is  
only in ,japan that such an exhibition  
is possible2 the land where the waving  

bamboo1 and the circling hawk1 and the  
undulating summer sea1 and every        
beautiful motion of nature #ad are      
looked upon with tenderness2 and perhaps
 it is from ,japan that we shall learn  
the development of our childish         
enthusiasm4  ,the devotees of the new   
emotional art of beautiful motion and   
changing colour are still in the main   
beggars like ,homer1 and they live in   
garrets like ,johnson and ,savage2 but  
the dawn of a new era is heralded1 or   
rather the dawn has already come1 for   
,sir ,william ,thomson's achievements in
 the study of spinning tops rank already
 as by no means the meanest of his great
 career4  ,if you will only think of it1
 the behaviour of the commonest spinning
 top is very wonderful4 ,when not       
spinning you see that it falls down at  
once1 ,i find it impossible to balance  
it on its peg2 but what a very different
 object it is when spinning2 you see    
that it not only does not fall down1 it 
offers a strange resistance when ,i     

strike it1 and actually lifts itself    
more and more to an upright position4   
,once started on scientific observation1
 nature gives us facts of an analogous  
kind in great plenty4  ,those of you who
 have observed a rapidly moving heavy   
belt or rope1 know that rapid motion    
gives a peculiar quasi-rigidity to      
flexible and even to fluid things4      
,here1 for example1 is a disc of quite  
thin paper 7,fig4 #a71 and when ,i set  
it in rapid rotation you observe that it
 resists the force exerted by my #ae    
hand1 the blow of my fist1 as if it were
 a disc of steel4 ,hear how it resounds 
when ,i strike it with a stick4 ,where  
has its flexibility gone8               
,illustration3 ,,fig4 #a4  ,here again  
is a ring of chain which is quite       
flexible4 ,it seems ridiculous to       
imagine that this #af could be made to  
stand up like a stiff hoop1 and yet you 
observe that when ,i give it a rapid    
rotation on this mandril and let it     
slide off upon the table1 it runs over  

the table just as if it were a rigid    
ring1 and when it drops on the floor it 
rebounds like a boy's hoop 7,fig4 #b74  
,illustration3 ,,fig4 #b4  ,here again  
is a very soft hat1 specially made for  
this sort of experiment4 ,you will note 
that it collapses to the table in a     
shapeless mass when ,i lay it down1 and 
seems quite incapable of resisting      
forces which tend to alter its shape4   
,in fact1 there is almost a complete    
absence of rigidity2 but when this is   
spun on the end of a stick1 first note  
#ag how it has taken a very easily      
defined shape2 secondly1 note how it    
runs along the table as if it were made 
of steel2 thirdly1 note how all at once 
it collapses again into a shapeless heap
 of soft material when its rapid motion 
has ceased4 ,even so you will see that  
when a drunken man is not leaning       
against a wall or lamp-post1 he feels   
that his only chance of escape from     
ignominious collapse is to get up a     
decent rate of speed1 to obtain a       

quasi-sobriety of demeanour by rapidity 
of motion4  ,the water inside this glass
 vessel 7,fig4 #c7 is in a state of     
rapid motion1 revolving with the vessel 
itself4 ,now observe the piece of       
paraffin wax ,a immersed in the water1  
and you will see when ,i push at it with
 a rod that it vibrates just as if it   
were surrounded with a thick jelly4 ,let
 us now apply ,prof4 ,fitzgerald's      
improvement on this experiment of ,sir  
,william ,thomson's4 ,here is a disc ,b 
stuck on the end of the rod2 observe    
that when ,i introduce it1 although it  
does not touch ,a1 ,a is repelled from  
the disc4 ,now observe that when ,i     
twirl the disc it seems to attract ,a4  
,illustration3 ,,fig4 #c4c  ,at the     
round hole in front of this box a rapid 
motion is given to a small quantity of  
air which is mixed with smoke that you  
may see it4 ,that smoke-ring moves      
through the air almost like a solid body
 for a considerable distance unchanged1 
and ,i am not sure that it may not be   

possible yet #ah to send as a projectile
 a huge poisoned smoke-ring1 so that it 
may destroy or stupefy an army miles    
away4 ,remember that it is really the   
same air all the time4 ,you will observe
 that two smoke rings sent from two     
boxes have curious actions #ai upon one 
another1 and the study of these actions 
has given rise to ,thomson's smoke-ring 
or vortex theory of the constitution of 
matter 7,fig4 #d74  ,illustration3      
,,fig4 #d4  ,it was ,rankine1 the great 
guide of all engineers1 who first       
suggested the idea of molecular vortices
 in his explanations of heat phenomena  
and the phenomena of elasticity--the    
idea that every particle of matter is   
like a little spinning top2 but ,i am   
now speaking of ,thomson's theory4 ,to  
imagine that an atom of matter is merely
 a #bj curiously shaped smoke-ring      
formed miraculously in a perfect fluid1 
and which can never undergo permanent   
alteration1 looks to be a very curious  
and far-fetched hypothesis4 ,but in     

spite of certain difficulties1 it is the
 foundation of the theory which will    
best explain most of the molecular      
phenomena observed by philosophers4     
,whatever be the value of the theory1   
you see from these experiments that     
motion does give to small quantities of 
fluid curious properties of elasticity1 
attraction and repulsion2 that each of  
these entities refuses to be cut in two2
 that you cannot bring a knife even near
 the smoke-ring2 and that what may be   
called a collision between two of them  
is not very different in any way from   
the collision between two rings of      
india-rubber4  ,another example of the  
rigidity given to a fluid by rapid      
motion1 is the feeling of utter         
helplessness which even the strongest   
swimmers sometimes experience when they 
get caught in an eddy underneath the    
water4  ,i could1 if ,i liked1 multiply 
these instances of the quasi-rigidity   
which mere motion gives to flexible or  
fluid bodies4 ,in ,nevada a jet of water

 like the jet from a fireman's hose1    
except that it is much more rapid1 which
 is nearly as easily projected in       
different directions1 is used in mining1
 and huge masses of earth and rock are  
rapidly disintegrated #ba by the running
 water1 which seems to be rather like a 
bar of steel than a jet of water in its 
rigidity4  ,it is1 however1 probable    
that you will take more interest in this
 box of brass which ,i hold in my hands4
 ,you see nothing moving1 but really1   
inside this case there is a fly-wheel   
revolving rapidly4 ,observe that ,i rest
 this case on the table on its sharp    
edge1 a sort of skate1 and it does not  
tumble down as an ordinary box would do1
 or as this box will do after a while1  
when its contents come to rest4 ,observe
 that ,i can strike it violent blows1   
and it does not seem to budge from its  
vertical position2 it turns itself just 
a little round1 but does not get tilted1
 however hard ,i strike it4 ,observe    
that if ,i do get it tilted a little it 

does not fall down1 but slowly turns    
with what is called a precessional      
motion 7,fig4 #e74  ,you will1 ,i hope1 
allow me1 all through this lecture1 to  
use the term precessional for any motion
 of this kind4 ,probably you will object
 more strongly to the great liberty ,i  
shall take presently1 of saying that the
 case precesses when it has this kind of
 motion2 but ,i really have almost no   
option in the matter1 as ,i must use    
some verb1 and ,i have no time to invent
 a less barbarous one4  ,illustration3  
,,fig4 #e4  ,when ,i hold this box in my
 hands 7,fig4 #f71 ,i find that if ,i   
move it with a motion of mere           
translation in any direction1 it feels  
just as it would do #bb if its contents 
were at rest1 but if ,i try to turn it  
in my hands ,i find the most curious    
great resistance to such a motion4 ,the 
result is that when you hold this in    
your hands1 its readiness to move so    
long as it is not turned round1 and its 
great resistance to turning round1 and  

its unexpected tendency to turn in a    
different way from that in which you try
 to turn it1 give one the most uncanny  
sensations4 ,it seems almost as if an   
invisible being had hold of the box and 
exercised forces capriciously4 ,and #bc 
indeed there is a spiritual being       
inside1 what the algebraic people call  
an impossible quantity1 what other      
mathematicians call an operator4        
,illustration3 ,,fig4 #f4  ,nearly all  
the experiments1 even the tops and other
 apparatus you have seen or will see    
to-night1 have been arranged and made by
 my enthusiastic assistant1 ,mr4        
,shepherd4 ,the following experiment is 
not only his in arrangement2 even the   
idea of it is his4 ,he said1 you may    
grin and contort your body with that    
large gyrostat in your hands1 but many  
of your audience will simply say to #bd 
themselves that you only pretend to find
 a difficulty in turning the gyrostat4  
,so he arranged this pivoted table for  
me to stand upon1 and you will observe  

that when ,i now try to turn the        
gyrostat1 it will not turn2 however ,i  
may exert myself1 it keeps pointing to  
that particular corner of the room1 and 
all my efforts only result in turning   
round my own body and the table1 but not
 the gyrostat4  ,now you will find that 
in every case this box only resists     
having the axis of revolution of its    
hidden flywheel turned round1 and if you
 are interested in the matter and make a
 few observations1 you will soon see    
that every spinning body like the       
fly-wheel inside this case resists more 
or less the change of direction of its  
spinning axis4 ,when the fly-wheels of  
steam-engines and dynamo machines and   
other quick speed machines are rotating 
on board ship1 you may be quite sure    
that they offer a greater resistance to 
the pitching or rolling or turning of   
the ship1 or any other motion which     
tends to turn their axes in direction1  
than when they are not rotating4  ,here 
is a top lying on a plate1 and ,i throw 

it up into the air2 you will observe    
that its motion is very difficult to    
follow1 and nobody could predict1 before
 it falls1 exactly how it will alight on
 the plate2 it may come down peg-end    
foremost1 or hindmost1 or sideways4 ,but
 when ,i spin it 7,fig4 #g71 and now    
throw it up into the air1 there is no   
doubt whatever #be as to how it will    
come down4 ,the spinning axis keeps     
parallel to itself1 and ,i can throw the
 top up time after time1 without        
disturbing much the spinning motion4    
,illustration3 ,,fig4 #g4               
,illustration3 ,,fig4 #h4  ,if ,i pitch 
up this biscuit1 you will observe that  
,i can have no certainty as to how it   
will come down1 but if ,i give it a spin
 before it leaves my hand there is no   
doubt whatever 7,fig4 #h74 ,here is a   
hat4 ,i throw it up1 and ,i cannot be   
sure as to how it will move1 but if ,i  
give it a spin1 you see that1 as #bf    
with the top and the biscuit1 the axis  
about which the spinning takes place    

keeps parallel to itself1 and we have   
perfect certainty as to the hat's       
alighting on the ground brim downwards  
7,fig4 #i74  ,illustration3 ,,fig4 #i4  
,i need not again bring before you the  
very soft hat to which we gave a        
quasi-rigidity a few minutes ago2 but   
you will remember that my assistant sent
 that off like a projectile through the 
air when it was spinning1 and that it   
kept its spinning axis parallel to      
itself just like this more rigid hat and
 the biscuit4  ,illustration3 ,,fig4    
#aj4  ,illustration3 ,,fig4 #aa4  ,i    
once showed some experiments on spinning
 tops to a coffee-drinking1             
tobacco-smoking audience in that most   
excellent institution1 the ,victoria    
,music ,hall in ,london4 ,in that music 
hall1 things are not very different from
 what they are at any other #bg music   
hall except in beer1 wine1 and spirits  
being unobtainable1 and in short        
scientific addresses being occasionally 
given4 ,now1 ,i impressed my audience as

 strongly as ,i could with the above    
fact1 that if one wants to throw a quoit
 with certainty as to how it will       
alight1 one gives it a spin2 if one     
wants to throw a hoop or a hat to       
somebody to catch upon a stick1 one     
gives the hoop or hat a spin2 the       
disinclination of a spinning body to let
 its axis get altered in direction can  
always be depended upon4 ,i told them   
that this was why smooth-bore guns      
cannot be depended upon for accuracy2#d 
that the spin which an ordinary bullet  
took depended greatly on how it chanced 
to touch the muzzle as it just left the 
gun1 whereas barrels are now rifled1    
that is1 spiral grooves are now cut     
inside the barrel of a gun1 and         
excrescences from the bullet or         
projectile fit into these grooves1 so   
that as it is forced along the barrel of
 the gun by the explosive force of the  
powder1 it must also spin about its     
axis4 ,hence it leaves the gun with a   
perfectly well-known spinning motion    

about which there can be no doubt1 and  
we know too that ,fig4 #aj shows the #bh
 kind of motion which it has afterwards1
 for1 just like the hat or the biscuit1 
its spinning axis keeps nearly parallel 
to itself4 ,well1 this was all ,i could 
do1 for ,i am not skilful in throwing   
hats or quoits4 ,but after my address   
was finished1 and after a young lady in 
a spangled dress had sung a comic song1 
two jugglers came upon the stage1 and ,i
 could not have had better illustrations
 of the above principle than were given 
in almost every trick performed by this 
lady and gentleman4 ,they sent hats1 and
 hoops1 and plates1 and umbrellas       
spinning from one to the other4 ,one of 
them threw a stream of knives into the  
air1 catching them and throwing them up 
again with perfect precision and my now 
educated audience shouted with delight1 
and showed in other unmistakable #bi    
ways that they observed the spin which  
that juggler gave to every knife as it  
left his hand1 so that he might have a  

perfect knowledge as to how it would    
come back to him again 7,fig4 #aa74 #cj 
,it struck me with astonishment at the  
time that1 almost without exception1    
every juggling trick performed that     
evening was an illustration of the above
 principle4 ,and now1 if you doubt my   
statement1 just ask a child whether its 
hoop is more likely to tumble down when 
it is rapidly rolling along1 or when it 
is going very slowly2 ask a man on a    
bicycle to go more and more slowly to   
see if he keeps his balance better2 ask 
a ballet-dancer how long she could stand
 on one toe without balancing herself   
with her arms or a pole1 if she were not
 spinning2 ask astronomers how many     
months would elapse before the earth    
would point ever so far away from the   
pole star if it were not spinning2 and  
above all1 ask a boy whether his top is 
as likely to stand upright upon its peg 
when it is not spinning as when it is   
spinning4  ,illustration3 ,,fig4 #ab4   
,we will now examine more carefully the 

behaviour of this common top 7,fig4     
#ab74 ,it is not #ca spinning1 and you  
observe that it tumbles down at once2 it
 is quite unstable if ,i leave it       
resting upright on its peg4 ,but now    
note that when it is spinning1 it not   
only will remain upright resting on its 
peg1 but if ,i give it a blow and so    
disturb its state1 it goes circling     
round with a precessional motion which  
grows gradually less and less as time   
goes on1 and the top lifts itself to the
 upright position again4 ,i hope you do 
not think that time spent in careful    
observation of a phenomenon of this kind
 is wasted4 ,educated observation of the
 commonest phenomena occurring in our   
everyday life is never wasted1 and ,i   
often feel that if workmen1 who are the 
persons most familiar with inorganic    
nature1 could only observe and apply    
simple scientific laws to their         
observations1 instead of a great        
discovery every century we should have a
 great discovery every year4 ,well1 to  

return to our top2 there are two very   
curious observations to make4 ,please   
neglect for a short time the slight     
wobbling motions that occur4 ,one       
observation we make is1 that the top    
does not at first bow down in the       
direction of the blow4 ,if ,i strike    
towards the south1 the top bows towards 
the west2 if ,i strike towards the west1
 the top bows down towards the north4   
,now the reason of this is known to all 
scientific men1 and the principle       
underlying the top's behaviour is of    
very great #cb importance in many ways1 
and ,i hope to make it clear to you4    
,the second fact1 that the top gradually
 reaches its upright position again1 is 
one known to everybody1 but the reason  
for it is not by any means well known1  
although ,i think that you will have no 
great difficulty in understanding it4   
,the first phenomenon will be observed  
in this case which ,i have already shown
 you4 ,this case 7,fig4 #e71 #cc with   
the fly-wheel inside it1 is called a    

gyrostat4 ,when ,i push the case it does
 not bow down1 but slowly turns round4  
,this gyrostat will not exhibit the     
second phenomenon2 it will not rise up  
again if ,i manage to get it out of its 
upright position1 but1 on the contrary1 
will go precessing in wider and wider   
circles1 getting further and further    
away from its upright position4         
,illustration3 ,,fig4 #ac4              
,illustration3 ,,fig4 #ad4  ,the first  
phenomenon is most easily studied in    
this balanced gyrostat 7,fig4 #ac74 ,you
 here see the fly-wheel ,g in a strong  
brass frame ,f1 which is supported so   
that it is free to move about the       
vertical axis ,a ,b1 or about the       
horizontal axis ,c ,d4 ,the gyrostat is 
balanced by a weight ,w4 ,observe that  
,i can increase the leverage of ,w or   
diminish it by shifting the position of 
the sleeve at ,a so that it will tend to
 either lift or lower the gyrostat1 or  
exactly balance it as it does now4 ,you 
must observe exactly what it is that we 

wish to study4 ,if ,i endeavour to push 
,f downwards1 with the end of this stick
 7,fig4 #ad71 it really moves           
horizontally to the right2 now ,i push  
it to the right 7,fig4 #ae71 and it only
 rises2 now push it up1 and you see that
 it goes to the left2 push it to the    
left1 and it only goes downwards4 ,you  
will notice that if ,i clamp the        
instrument so that it cannot move       
vertically1 it moves at once            
horizontally2 if ,i prevent mere        
horizontal motion it readily moves      
vertically when ,i push it4 ,leaving it 
free as #cd before1 ,i will now shift   
the position of the weight ,w1 so that  
it tends continually to lift the        
gyrostat1 and of course the instrument  
does not lift1 it moves horizontally    
with a slow precessional motion4 ,i now 
again shift the weight ,w1 so that the  
gyrostat would fall if it were not      
spinning 7,fig4 #af71 and it now moves  
horizontally with a slow precessional   
motion which is in a direction opposed  

to the last4 ,these phenomena are easily
 explained1 but1 #ce as ,i said before1 
it is necessary first to observe them   
carefully4 ,you all know now1 vaguely1  
the fundamental fact4 ,it is that if ,i 
try to make a very quickly spinning body
 change the direction of its axis1 the  
direction of the axis will change1 but  
not in the way ,i intended4 ,it is even 
more curious than my countryman's pig1  
for when he wanted the pig to go to     
,cork1 he had to pretend that he was    
driving the pig home4 ,his rule was a   
very #cf simple one1 and we must find a 
rule for our spinning body1 which is    
rather like a crab1 that will only go   
along the road when you push it         
sidewise4  ,illustration3 ,,fig4 #ae4   
,illustration3 ,,fig4 #af4e             
,illustration3 ,,fig4 #aj4  ,as an      
illustration of this1 consider the      
spinning projectile of ,fig4 #aj4 ,the  
spin tends to keep its axis always in   
the same direction4 ,but there is a     
defect in the arrangement1 which you are

 now in a #cg position to understand4   
,you see that at ,a the air must be     
pressing upon the undersurface ,a ,a1   
and ,i have to explain that this        
pressure tends to make the projectile   
turn itself broadside on to the air4 ,a 
boat in a current not allowed to move as
 a whole1 but tied at its middle1 sets  
itself broadside on to the current4     
,observe this disc of cardboard which ,i
 drop through the air edgewise1 and note
 how quickly it sets itself broadside on
 and falls more slowly2 and some of you 
may have thrown over into the water at  
,aden small pieces of silver for the    
diving boys1 and you are aware that if  
it were not for this slow falling of the
 coins with a wobbling motion broadside 
on1 it would be nearly impossible for   
any diving boy to get possession of     
them4 ,now all this is a parenthesis4   
,the #ch pressure of the air tends to   
make the projectile turn broadside on1  
but as the projectile is spinning it    
does not tilt up1 no more than this     

gyrostat does when ,i try to tilt it up1
 it really tilts out of the plane of the
 diagram1 out of the plane of its       
flight2 and only that artillerymen know 
exactly what it will do1 this kind of   
windage of the projectile would give    
them great trouble4  ,you will notice   
that an experienced child when it wants 
to change the direction of a hoop1 just 
exerts a tilting pressure with its      
hoop-stick4 ,a man on a bicycle changes 
his direction by leaning over so as to  
be out of balance4 ,it is well to remind
 you1 however1 that the motion of a     
bicycle and its rider is not all        
rotational1 so that it is not altogether
 the analogue of a top or gyrostat4 ,the
 explanation of the swerving from a     
straight path when the rider tilts his  
body1 ultimately comes to the same      
simple principle1 ,newton's second law  
of motion1 but it is arrived at more    
readily4 ,it is for the same reason--put
 briefly1 the exercise of a centripetal 
force--that when one is riding he can   

materially assist his horse to turn a   
corner quickly1 if he does not mind     
appearances1 by inclining his body      
towards the side to which he wants to   
turn2 and the more slowly the horse is  
going the greater is the tendency to    
turn for a given amount of tilting of   
one's body4 ,circus-riders1 when        
galloping in a circle1 assist their     
horses greatly by the position of their 
bodies2 it is #ci not to save themselves
 from falling by centrifugal force that 
they take a position on a horse's back  
which no riding-master would allow his  
pupil to imitate2 and the respectable   
riders of this country would not scorn  
to help their horses in this way to     
quick turning movements1 if they had to 
chase and collect cattle like ,american 
cowboys4  ,very good illustrations of   
change of direction are obtained in     
playing bowls4 ,you know that a bowl1 if
 it had no bias1 that is1 if it had no  
little weight inside it tending to tilt 
it1 would roll along the level          

bowling-green in a straight path1 its   
speed getting less and less till it     
stopped4 ,as a matter of fact1 however1 
you know that at the beginning1 when it 
is moving fast1 its path is pretty      
straight1 but because it always has bias
 the path is never quite straight1 and  
it bends more and more rapidly as the   
speed diminishes4 ,in all our examples  
the slower the spin the quicker is the  
precession produced by given tilting    
forces4  ,now close observation will    
give you a simple rule about the        
behaviour of a gyrostat4 ,as a matter of
 fact1 all that has been                
incomprehensible or curious disappears  
at once1 if instead of speaking of this 
gyrostat as moving up or down1 or to the
 right or left1 ,i speak of its motions 
about its various axes4 ,it offers no   
resistance to mere motion of            
translation4 ,but when ,i spoke of its  
moving #dj horizontally1 ,i ought to    
have said that it moved about the       
vertical axis ,a ,b 7,fig4 #ac74 ,again1

 what ,i referred to as up and down     
motion of ,f is really motion in a      
vertical plane about the horizontal axis
 ,c ,d4 ,in future1 when ,i speak of    
trying to give motion to ,f1 think only 
of the axis about which ,i try to turn  
it1 and then a little observation will  
clear the ground4  ,illustration3 ,,fig4
 #ag4  ,illustration3 ,,fig4 #ah4  ,here
 is a gyrostat 7,fig4 #ag71 suspended in
 gymbals so carefully that neither      
gravity nor any frictional forces at the
 pivots constrain it2 nothing that ,i   
can do to this frame which ,i hold in my
 hand will affect the direction of the  
axis ,e ,f of the gyrostat4 ,observe    
that ,i whirl round on my toes like a   
ballet-dancer while this is in my hand4 
,i move it about in all sorts of ways1  
but if it was pointing to the pole star 
at the beginning it remains pointing to 
the pole star2 if it pointed towards the
 moon at the beginning it still points  
#da towards the moon4 ,the fact is1 that
 as there is almost no frictional       

constraint at the pivots there are      
almost no forces tending to turn the    
axis of rotation of the gyrostat1 and ,i
 can only give it motions of            
translation4 ,but now ,i will clamp this
 vertical spindle by means of a screw   
and repeat my ballet-dance whirl2 you   
will note that ,i need not whirl round1 
a very small portion of a whirl is      
enough to cause this gyrostat 7,fig4    
#ah7 to set its spinning axis vertical1 
to set its axis parallel to the vertical
 axis of rotation which ,i give it4 ,now
 ,i whirl in the opposite direction1 the
 gyrostat at once turns a somersault1   
turns completely round and remains again
 with its axis vertical1 and if you were
 to carefully note the direction of the 
spinning of the #db gyrostat1 you would 
find the following rule to be generally 
true3--,pay no attention to mere        
translational motion1 think only of     
rotation about axes1 and just remember  
that when you constrain the axis of a   
spinning body to rotate1 it will        

endeavour to set its own axis parallel  
to the new axis about which you rotate  
it2 and not only is this the case1 but  
it will endeavour to have the direction 
of its own spin the same as the         
direction of the new rotation4 ,i again 
twirl on my toes1 holding this frame1   
and now ,i know that to a person looking
 down upon the gyrostat and me from the 
ceiling1 as ,i revolved in the direction
 of the hands of a clock1 the gyrostat  
is spinning in the direction of the     
hands of a clock2 but if ,i revolve     
against the clock direction 7,fig4 #ai7 
the gyrostat tumbles over so as again to
 be revolving in the same direction as  
that in which ,i revolve4               
,illustration3 ,,fig4 #ai4  ,this then  
is the simple rule which will enable you
 to tell beforehand how a gyrostat will 
move #dc when you try to turn it in any 
particular direction4 ,you have only to 
remember that if you continued your     
effort long enough1 the spinning axis   
would become parallel to your new axis  

of motion1 and the direction of spinning
 would be the same as the direction of  
your new turning motion4  ,now let me   
apply my rule to this balanced gyrostat4
 ,i shove it1 or give it an impulse     
downwards1 but observe that this really 
means a rotation about the horizontal   
axis ,c ,d 7,fig4 #ac71 and hence the   
gyrostat turns its axis as if it wanted 
to become parallel to ,c ,d4 ,thus1     
looking down from above 7as shown by    
,fig4 #bj71 ,o ,e was the direction of  
the spinning axis1 ,o ,d was the axis   
about which ,i endeavoured to move it1  
and the instantaneous effect was that ,o
 ,e altered to the position ,o ,g4 ,a   
greater impulse of the same kind would  
have caused the spinning axis instantly 
to go to ,o ,h or ,o ,j1 whereas an     
upward opposite impulse would have      
instantly made the spinning axis point  
in the direction ,o ,k1 ,o ,l or ,o ,m1 
depending on how great the impulse was  
and the rate of spinning4 ,when one     
observes these phenomena for the first  

time1 one says1 ,i shoved it down1 and  
it moved to the right2 ,i shoved it up1 
and it moved to the left2 but if the    
direction of the spin were opposite to  
what it is1 one would say1 ,i shoved it 
down1 and it moved to the left2 ,i      
shoved it up1 and it moved to the right4
 ,the simple #dd statement in all cases 
ought to be1 ,i wanted to rotate it     
about a new axis1 and the effect was to 
send its spinning axis towards the      
direction of the new axis4 ,and now if  
you play with this balanced gyrostat as 
,i am doing1 shoving it about in all    
sorts of ways1 you will find the rule to
 be a correct one1 and there is no      
difficulty in predicting what will      
happen4  ,illustration3 ,,fig4 #bj4  #de
  ,if this rule is right1 we see at once
 why precession takes place4 ,i put this
 gyrostat 7,fig4 #ac7 out of balance1   
and if it were not rotating it would    
fall downwards2 but a force acting      
downwards really causes the gyrostat to 
move to the right1 and so you see that  

it is continually moving in this way1   
for the force is always acting          
downwards1 and the spinning axis is     
continually chasing the new axes about  
which gravity tends continually to make 
it revolve4 ,we see also why it is that 
if the want of balance is the other way1
 if gravity tends to lift the gyrostat1 
the precession is in the opposite       
direction4 ,and in playing with this    
gyrostat as ,i do now1 giving it all    
sorts of pushes1 one makes other        
observations and sees that the above    
rule simplifies them all2 that is1 it   
enables us to remember them4 ,for       
example1 if ,i use this stick to hurry  
on the precession1 the gyrostat moves in
 opposition to the force which causes   
the precession4 ,i am particularly      
anxious that you should remember this4  
,at present the balance-weight is so    
placed that the gyrostat would fall if  
it were not spinning4 ,but it is        
spinning1 and so it precesses4 ,if      
gravity were greater it would precess   

faster1 and it comes home to us that it 
is this precession which enables the    
force of gravity to be inoperative in   
mere downward motion4 ,you see that if  
the precession is hurried1 it is more   
than sufficient to balance gravity1 #df 
and the gyrostat rises4 ,if ,i retard   
the precession1 it is unable to balance 
gravity1 and the gyrostat falls4 ,if ,i 
clamp this vertical axis so that        
precession is impossible1 you will      
notice that the gyrostat falls just as  
if it were not spinning4 ,if ,i clamp   
the instrument so that it cannot move   
vertically1 you notice how readily ,i   
can make it move horizontally2 ,i can   
set it rotating horizontally like any   
ordinary body4  ,in applying our rule to
 this top1 observe that the axis of     
spinning is the axis ,e ,f of the top   
7,fig4 #ab74 ,as seen in the figure1    
gravity is tending to make the top      
rotate about the axis ,f ,d1 and the    
spinning axis in its chase of the axis  
,f ,d describes a cone in space as it   

precesses4 ,this gyrostat1 which is     
top-heavy1 rotates and precesses in much
 the same way as the top2 that is1 if   
you apply our rule1 or use your         
observation1 you will find that to an   
observer above the table the spinning   
and precession occur in the same        
direction1 that is1 either both with the
 hands of a watch1 or both against the  
hands of a watch4 ,whereas1 a top like  
this before you 7,fig4 #ba71 supported  
above its centre of gravity1 or the     
gyrostat here 7,fig4 #bb71 which is also
 supported above its centre of gravity1 
or the gyrostat shown in ,fig4 #ef1 or  
any other gyrostat supported in such a  
way that it would be in stable          
equilibrium if it were not spinning2 in 
all these #dg cases1 to an observer     
placed above the table1 the precession  
is in a direction opposite to that of   
the spinning4  ,illustration3 ,,fig4    
#ba4  ,illustration3 ,,fig4 #bb4  #dh   
,if an impulse be given to a top or     
gyrostat in the direction of the        

precession1 it will rise in opposition  
to the force of gravity1 and should at  
any instant the precessional velocity be
 greater than what it ought to be for   
the balance of the force of gravity1 the
 top or gyrostat will rise1 its         
precessional velocity diminishing4 ,if  
the precessional velocity is too small1 
the top will fall1 and as it falls the  
precessional velocity increases4  ,now  
,i say that all these facts1 which are  
mere facts of observation1 agree with   
our rule4 ,i wish ,i dare ask you to    
remember them all4 ,you will observe    
that in this wall sheet ,i have made a  
list of them4 ,i speak of gravity as    
causing the precession1 but the forces  
may be any others than such as are due  
to gravity4  ,,wall ,,sheet4  ,i4       
,,rule4 ,when forces act upon a spinning
 body1 tending to cause rotation about  
any other axis than the spinning axis1  
the spinning axis sets itself in better 
agreement with the new axis of rotation4
 ,perfect agreement would mean perfect  

parallelism1 the directions of rotation 
being the same4  ,,ii4 ,hurry on the    
precession1 and the body rises in       
opposition to gravity4 #di  ,,iii4      
,delay the precession and the body      
falls1 as gravity would make it do if it
 were not spinning4  ,,iv4 ,a common top
 precesses in the same direction as that
 in which it spins4  ,v4 ,a top         
supported above its centre of gravity1  
or a body which would be in stable      
equilibrium if not spinning1 precesses  
in the opposite direction to that of its
 spinning4  ,,vi4 ,the last two         
statements come to this3--,when the     
forces acting on a spinning body tend to
 make the angle of precession greater1  
the precession is in the same direction 
as the spinning1 and vice versa4        
,having by observation obtained a rule1 
every natural philosopher tries to make 
his rule a rational one2 tries to       
explain it4 ,i hope you know what we    
mean when we say that we explain a      
phenomenon2 we really mean that we show 

the phenomenon to be consistent with    
other better known phenomena4 ,thus when
 you unmask a spiritualist and show that
 the phenomena exhibited by him are due 
to mere sleight-of-hand and trickery1   
you explain the phenomena4 ,when you    
show that they are all consistent with  
well-observed and established mesmeric  
influences1 you are also said to explain
 the phenomena4 ,when you show that they
 can be effected by means of telegraphic
 messages1 or by reflection of light    
from mirrors1 you explain the #ej       
phenomena1 although in all these cases  
you do not really know the nature of    
mesmerism1 electricity1 light1 or moral 
obliquity4  ,the meanest kind of        
criticism is that of the man who        
cheapens a scientific explanation by    
saying that the very simplest facts of  
nature are unexplainable4 ,such a man   
prefers the chaotic and indiscriminate  
wonder of the savage to the reverence of
 a ,sir ,isaac ,newton4  ,illustration3 
,,fig4 #bc4  ,the explanation of our    

rule is easy4 ,here is a gyrostat 7,fig4
 #bc7 something like the earth in shape1
 and it is at rest4 ,i am sorry to say  
that ,i am compelled to support this    
globe in a very visible manner by gymbal
 rings4 ,if this globe were just        
floating in the air1 if it had no       
tendency to fall1 my explanation would  
be easier to understand1 and ,i could   
illustrate it better experimentally4    
,observe the point ,p4 ,if ,i move the  
globe slightly about the axis ,a1 the   
point ,p moves to ,q4 ,but suppose      
instead of this that the globe and inner
 gymbal #ea ring had been moved about   
the axis ,b2 the point ,p would have    
moved to ,r4 ,well1 suppose both those  
rotations took place simultaneously4    
,you all know that the point ,p would   
move neither to ,q nor to ,r1 but it    
would move to ,s2 ,p ,s being the       
diagonal of the little parallelogram4   
,the resultant motion then is neither   
about the axis ,o ,a in space1 nor about
 the axis ,o ,b1 but it is about some   

such axis as ,o ,c4  ,to this globe ,i  
have given two rotations simultaneously4
 ,suppose a little being to exist on    
this globe which could not see the      
gymbals1 but was able to observe other  
objects in the room4 ,it would say that 
the direction of rotation is neither    
about ,o ,a nor about ,o ,b1 but that   
the real axis of its earth is some line 
intermediate1 ,o ,c in fact4  ,if then a
 ball is suddenly struck in two         
different directions at the same        
instant1 to understand how it will spin 
we must first find how much spin each   
blow would produce if it acted alone1   
and about what axis4 ,a spin of three   
turns per second about the axis ,o ,a   
7,fig4 #bd71 and a spin of two turns per
 second about the axis ,o ,b1 really    
mean that the ball will spin about the  
axis ,o ,c with a spin of three and a   
half turns per second4 ,to arrive at    
this result1 ,i made ,o ,a1 #c feet long
 7any other scale of representation     
would have been right7 #eb and ,o ,b1 #b

 feet long1 and ,i found the diagonal ,o
 ,c of the parallelogram shown on the   
figure to be #c-a_/b feet long4         
,observe that if the rotation about the 
axis ,o ,a is with the hands of a watch 
looking from ,o to ,a1 the rotation     
about the axis ,o ,b looking from ,o to 
,b1 must also be with the hands of a    
watch1 and the resultant rotation about 
the axis ,o ,c is also in a direction   
with the hands of a watch looking from  
,o to ,c4 ,fig4 #be shows in two        
diagrams how necessary it is that on    
looking from ,o along either ,o ,a or ,o
 ,b1 the rotation should be in the same 
direction as regards the hands of a     
watch4 ,these constructions are well    
known to all who have studied elementary
 mechanical principles4 ,obviously if   
the rotation about ,o ,a is very much   
greater than the rotation about ,o ,b1  
then the position of the new axis ,o ,c 
must be much nearer ,o ,a than ,o ,b4   
,illustration3 ,,fig4 #bd4              
,illustration3 ,,fig4 #be4  ,we see then

 that if a body is spinning about an    
axis ,o ,a1 and we apply forces to it   
which #ec would1 if it were at rest1    
turn it about the axis ,o ,b2 the effect
 is to cause the spinning axis to be    
altered to ,o ,c2 that is1 the spinning 
axis sets itself in better agreement    
with the new axis of rotation4 ,this is 
the first statement on our wall sheet1  
the rule from which all our other       
statements are derived1 assuming that   
they were not really derived from       
observation4 ,now ,i do not say that ,i 
have here given a complete proof for all
 cases1 for the fly-wheels in these     
gyrostats are running in bearings1 and  
the bearings constrain the axes to take 
the new positions1 whereas there is no  
such #ed constraint in this top2 but in 
the limited time of a popular lecture   
like this it is not possible1 even if it
 were desirable1 to give an exhaustive  
proof of such a universal rule as ours  
is4 ,that ,i have not exhausted all that
 might be said on this subject will be  

evident from what follows4  ,if we have 
a spinning ball and we give to it a new 
kind of rotation1 what will happen8     
,suppose1 for example1 that the earth   
were a homogeneous sphere1 and that     
there were suddenly impressed upon it a 
new rotatory motion tending to send     
,africa southwards2 the axis of this new
 spin would have its pole at ,java1 and 
this spin combined with the old one     
would cause the earth to have its true  
pole somewhere between the present pole 
and ,java4 ,it would no longer rotate   
about its present axis4 ,in fact the    
axis of rotation would be altered1 and  
there would be no tendency for anything 
further to occur1 because a homogeneous 
sphere will as readily rotate about one 
axis as another4 ,but if such a thing   
were to happen to this earth of ours1   
which is not a sphere but a flattened   
spheroid like an orange1 its polar      
diameter being the one-third of one per 
cent4 shorter than the equatorial       
diameter2 then as soon as the new axis  

was established1 the axis of symmetry   
would resent the change and would try to
 become again the axis of rotation1 and 
a great wobbling motion would ensue4 #ee
 ,i put the matter in popular language  
when ,i speak of the resentment of an   
axis2 perhaps it is better to explain   
more exactly what ,i mean4 ,i am going  
to use the expression ,centrifugal      
,force4 ,now there are captious critics 
who object to this term1 but all        
engineers use it1 and ,i like to use it1
 and our captious critics submit to all 
sorts of ignominious involution of      
language in evading the use of it4 ,it  
means the force with which any body acts
 upon its constraints when it is        
constrained to move in a curved path4   
,the force is always directed away from 
the centre of the curve4 ,when a ball is
 whirled round in a curve at the end of 
a string its centrifugal force tends to 
break the string4 ,when any body keyed  
to a shaft is revolving with the shaft1 
it may be that the centrifugal forces of

 all the parts just balance one another2
 but sometimes they do not1 and then we 
say that the shaft is out of balance4   
,here1 for example1 is a disc of wood   
rotating4 ,it is in balance4 ,but ,i    
stop its motion and fix this piece of   
lead1 ,a1 to it1 and you observe when it
 rotates that it is so much out of      
balance that the bearings of the shaft  
and the frame that holds them1 and even 
the lecture-table1 are shaking4 ,now ,i 
will put things in balance again by     
placing another piece of lead1 ,b1 on   
the side of the spindle remote from ,a1 
and when ,i again rotate the disc 7,fig4
 #bf7 there #ef is no longer any shaking
 of the framework4 ,when the crank-shaft
 of a locomotive has not been put in    
balance by means of weights suitably    
placed on the driving-wheels1 there is  
nobody in the train who does not feel   
the effects4 ,yes1 and the coal-bill    
shows the effects1 for an unbalanced    
engine tugs the train spasmodically     
instead of exerting an efficient steady 

pull4 ,my friend ,professor ,milne1 of  
,japan1 places earthquake measuring     
instruments on engines and in trains for
 measuring this and other wants of      
balance1 and he has shown unmistakably  
that two engines of nearly the same     
general design1 one balanced properly   
and the other not1 consume very         
different amounts of coal in making the 
same journey at the same speed4         
,illustration3 ,,fig4 #bf4  ,if a       
rotating body is in balance1 not only   
does the axis of rotation pass through  
the centre of gravity 7or rather centre 
of mass7 of the body1 but #eg the axis  
of rotation must be one of the three    
principal axes through the centre of    
mass of the body4 ,here1 for example1 is
 an ellipsoid of wood2 ,a ,a1 ,b ,b1 and
 ,c ,c 7,fig4 #bg7 are its three        
principal axes1 and it would be in      
balance if it rotated about any one of  
these three axes1 and it would not be in
 balance if it rotated about any other  
axis1 unless1 indeed1 it were like a    

homogeneous sphere1 every diameter of   
which is a principal axis4              
,illustration3 ,,fig4 #bg4  ,every body 
has three such principal axes through   
its centre of mass1 and this body 7,fig4
 #bg7 has them2 but ,i have here        
constrained it to rotate about the axis 
,d ,d1 and you all observe the effect of
 the unbalanced centrifugal forces1     
which is nearly great enough to tear the
 framework in pieces4 ,the higher the   
speed the more important this want of   
balance is4 ,if the speed is doubled1   
the centrifugal forces become four times
 as great2 and modern mechanical        
engineers with their quick speed        
engines1 some of which revolve1 like the
 fan-engines of torpedo-boats1 at #agjj 
revolutions per minute1 require to pay  
great attention to this subject1 which  
the older engineers never troubled their
 #eh heads about4 ,you must remember    
that even when want of balance does not 
actually fracture the framework of an   
engine1 it will shake everything1 so    

that nuts and keys and other fastenings 
are pretty sure to get loose4  ,i have  
seen1 on a badly-balanced machine1 a    
securely-fastened pair of nuts1 one     
supposed to be locking the other1       
quietly revolving on their bolt at the  
same time1 and gently lifting themselves
 at a regular but fairly rapid rate1    
until they both tumbled from the end of 
the bolt into my hand4 ,if my hand had  
not been there1 the bolts would have    
tumbled into a receptacle in which they 
would have produced interesting but most
 destructive phenomena4 ,you would have 
somebody else lecturing to you to-night 
if that event had come off4  ,suppose1  
then1 that our earth were spinning about
 any other axis than its present axis1  
the axis of figure4 ,if spun about any  
diameter of the equator for example1    
centrifugal forces would just keep      
things in a state of unstable           
equilibrium1 and no great change might  
be produced until some accidental cause 
effected a slight alteration in the     

spinning axis1 and after that the earth 
would wobble very greatly4 ,how long and
 how violently it would wobble1 would   
depend on a number of circumstances     
about which ,i will not now venture to  
guess4 ,if you #ei tell me that on the  
whole1 in spite of the violence of the  
wobbling1 it would not get shaken into a
 new form altogether1 then ,i know that 
in consequence of tidal and other       
friction it would eventually come to a  
quiet state of spinning about its       
present axis4  ,you see1 then1 that     
although every body has three axes about
 which it will rotate in a balanced     
fashion without any tendency to wobble1 
this balance of the centrifugal forces  
is really an unstable balance in two out
 of the three cases1 and there is only  
one axis about which a perfectly stable 
balanced kind of rotation will take     
place1 and a spinning body generally    
comes to rotate about this axis in the  
long run if left to itself1 and if there
 is friction to still the wobbling4  ,to

 illustrate this1 ,i have here a method 
of spinning bodies which enables them to
 choose as their spinning axis that one 
principal axis about which their        
rotation is most stable4 ,the various   
bodies can be hung at the end of this   
string1 and ,i cause the pulley from    
which the string hangs to rotate4       
,observe that at first the disc 7,fig4  
#bh a7 rotates soberly about the axis ,a
 ,a1 but you note the small beginning of
 the wobble2 now it gets quite violent1 
and now the disc is stably and smoothly 
rotating about the axis ,b ,b1 which is 
the most important of its principal     
axes4 #fj  ,illustration3 ,,fig4 #bh4   
,again1 this cone 7,fig4 #bh b7 rotates 
smoothly at first about the axis ,a ,a1 
but the wobble begins and gets very     
great1 and eventually the cone rotates  
smoothly about the axis ,b ,b1 which is 
the most important of its principal     
axes4 ,here again is a rod hung from one
 end 7,fig4 #bh d74  ,see also this     
anchor ring4 ,but you may be more       

interested in this limp ring of chain   
7,fig4 #bh c74 ,see how at first it     
hangs from the cord vertically1 and how 
the wobbles and vibrations end in its   
becoming a perfectly circular ring lying
 all in a horizontal plane4 ,this       
experiment illustrates also the         
quasi-rigidity given to a flexible body 
by rapid motion4  ,to return to this    
balanced gyrostat of ours 7,fig4 #ac74  
,it is not precessing1 so you know that 
the weight ,w just balances the gyrostat
 ,f4 ,now if ,i leave the instrument to 
itself after ,i give a downward impulse 
to ,f1 not exerting merely a steady     
pressure1 you will notice that ,f swings
 to the right for the reason already    
given2 but it swings too fast and too   
far1 just like any other swinging body1 
and it is easy from what ,i have already
 said1 to see that this wobbling motion 
7,fig4 #bi7 should be the result1 and   
that it should continue until friction  
stills it1 and ,f takes its permanent   
new position only after some time       

elapses4  ,you see that ,i can impose   
this wobble or nodding #fb motion upon  
the gyrostat whether it has a motion of 
precession or not4 ,it is now nodding as
 it processes round and round--that is1 
it is rising and falling as it          
precesses4  ,illustration3 ,,fig4 #bi4  
,perhaps ,i had better put the matter a 
little more clearly4 ,you see the same  
phenomenon in this top4 ,if the top is  
precessing too fast for the force of    
gravity the top rises1 and the          
precession diminishes in consequence2   
the precession being now too slow to    
balance gravity1 the top falls a little 
and the #fc precession increases again1 
and this sort of vibration about a mean 
position goes on just as the vibration  
of a pendulum goes on till friction     
destroys it1 and the top precesses more 
regularly in the mean position4 ,this   
nodding is more evident in the nearly   
horizontal balanced gyrostat than in a  
top1 because in a top the turning effect
 of gravity is less in the higher       

positions4  ,when scientific men try to 
popularize their discoveries1 for the   
sake of making some fact very plain they
 will often tell slight untruths1 making
 statements which become rather         
misleading when their students reach the
 higher levels4 ,thus astronomers tell  
the public that the earth goes round the
 sun in an elliptic path1 whereas the   
attractions of the planets cause the    
path to be only approximately elliptic2 
and electricians tell the public that   
electric energy is conveyed through     
wires1 whereas it is really conveyed by 
all other space than that occupied by   
the wires4 ,in this lecture ,i have to  
some small extent taken advantage of you
 in this way2 for example1 at first you 
will remember1 ,i neglected the nodding 
or wobbling produced when an impulse is 
given to a top or gyrostat1 and1 all    
through1 ,i neglect the fact that the   
instantaneous axis of rotation is only  
nearly coincident with the axis of      
figure of a precessing gyrostat or top4 

,and indeed you may generally #fd take  
it that if all one's statements were    
absolutely accurate1 it would be        
necessary to use hundreds of technical  
terms and involved sentences with       
explanatory1 police-like parentheses2   
and to listen to many such statements   
would be absolutely impossible1 even for
 a scientific man4 ,you would hardly    
expect1 however1 that so great a        
scientific man as the late ,professor   
,rankine1 when he was seized with the   
poetic fervour1 would err even more than
 the popular lecturer in making his     
accuracy of statement subservient to the
 exigencies of the rhyme as well as to  
the necessity for simplicity of         
statement4 ,he in his poem1 ,the        
,mathematician in ,love1 has the        
following lines--   ,the lady loved     
dancing2--he therefore applied     ,to  
the polka and waltz1 an equation2   ,but
 when to rotate on his axis he tried1   
,his centre of gravity swayed to one    
side1     ,and he fell by the earth's   

gravitation4  ,now ,i have no doubt that
 this is as good dropping into poetry as
 can be expected in a scientific man1   
and ----'s science is as good as can be 
expected in a man who calls himself a   
poet2 but in both cases we have         
illustrations of the incompatibility of 
science and rhyming4  ,illustration3    
,,fig4 #ag4  ,the motion of this        
gyrostat can be made even more          
complicated than it was when we had #fe 
nutation and precession1 but there is   
really nothing in it which is not       
readily explainable by the simple       
principles ,i have put before you4      
,look1 for example1 at this             
well-balanced gyrostat 7,fig4 #ag74     
,when ,i strike this inner gymbal ring  
in any way you see that it wriggles     
quickly just as if it were a lump of    
jelly1 its rapid vibrations dying away  
just like the rapid vibrations of any   
yielding elastic body4 ,this strange    
elasticity is of very great interest    
when we consider it in relation to the  

molecular properties of matter4 ,here   
again 7,fig4 #cj7 we have an example    
which is even more interesting4 ,i have 
supported the cased #ff gyrostat of     
,figs4 #e and #f upon a pair of stilts1 
and you will observe that it is moving  
about a perfectly stable position with a
 very curious staggering kind of        
vibratory motion2 but there is nothing  
in these motions1 however curious1 that 
you cannot easily explain if you have   
followed me so far4  ,illustration3     
,,fig4 #cj4  ,some of you who are more  
observant than the others1 will have    
remarked that all these precessing      
gyrostats gradually fall lower and      
lower1 just as they would do1 only more 
quickly1 if they were not spinning4 ,and
 if you cast your eye upon the third    
statement of our wall sheet 7p4 #di7 you
 will readily understand why it is so4  
,delay the precession and the body      
falls1 as gravity would make it do if it
 were not spinning4 #fg ,well1 the      
precession of every one of these is     

resisted by friction1 and so they fall  
lower and lower4  ,i wonder if any of   
you have followed me so well as to know 
already why a spinning top rises4       
,perhaps you have not yet had time to   
think it out1 but ,i have accentuated   
several times the particular fact which 
explains this phenomenon4 ,friction     
makes the gyrostats fall1 what is it    
that causes a top to rise8 ,rapid rising
 to the upright position is the         
invariable sign of rapid rotation in a  
top1 and ,i recollect that when quite   
vertical we used to say1 ,she sleeps6   
,such was the endearing way in which the
 youthful experimenter thought of the   
beautiful object of his tender regard4  
,all so well known as this rising       
tendency of a top has been ever since   
tops were first spun1 ,i question if any
 person in this hall knows the          
explanation1 and ,i question its being  
known to more than a few persons        
anywhere4 ,any great mathematician will 
tell you that the explanation is surely 

to be found published in ,routh1 or that
 at all events he knows men at          
,cambridge who surely know it1 and he   
thinks that he himself must have known  
it1 although he has now forgotten those 
elaborate mathematical demonstrations   
which he once exercised his mind upon4  
,i believe that all such statements are 
made in error1 but ,i cannot #fh be     
sure4#f ,a partial theory of the        
phenomenon was given by ,mr4 ,archibald 
,smith in the ,cambridge ,mathematical  
,journal many years ago1 but the problem
 was solved by ,sir ,william ,thomson   
and ,professor ,blackburn when they     
stayed together one year at the seaside1
 reading for the great ,cambridge       
mathematical examination4 ,it must have 
alarmed a person interested in          
,thomson's success to notice that the   
seaside holiday was really spent by him 
and his friend in spinning all sorts of 
rounded stones which they picked up on  
the beach4  ,and ,i will now show you   
the curious phenomenon that puzzled him 

that year4 ,this ellipsoid 7,fig4 #ca7  
will represent a waterworn stone4 ,it is
 lying in its most stable state on the  
table1 and ,i give it a spin4 ,you see  
that for a second or two it was inclined
 to go on spinning about the axis ,a ,a1
 but it began to wobble violently1 and  
after a while1 when these wobbles       
stilled1 you saw that it was spinning   
nicely with its axis ,b ,b vertical2 but
 then a new series of wobblings began   
and became more violent1 and when they  
ceased you saw that the object had at   
length reached a settled state of #fi   
spinning1 standing upright upon its     
longest axis4 ,this is an extraordinary 
phenomenon to any person who knows about
 the great inclination of this body to  
spin in the very way in which ,i first  
started it spinning4 ,you will find that
 nearly any rounded stone when spun will
 get up in this way upon its longest    
axis1 if the spin is only vigorous      
enough1 and in the very same way this   
spinning top tends to get more and more 

upright4  ,illustration3 ,,fig4 #ca4  ,i
 believe that there are very few        
mathematical explanations of phenomena  
which may not be given in quite ordinary
 language to people who have an ordinary
 amount of experience4 ,in most cases   
the symbolical algebraic explanation    
must be given first by somebody1 and    
then comes the time for its translation 
into ordinary language4 ,this is the    
foundation of the new thing called      
,technical ,education1 which assumes    
that a #gj workman may be taught the    
principles underlying the operations    
which go on in his trade1 if we base our
 explanations on the experience which   
the man has acquired already1 without   
tiring him with a four years' course of 
study in elementary things such as is   
most suitable for inexperienced children
 and youths at public schools and the   
universities4  ,illustration3 ,,fig4    
#cb4  ,illustration3 ,,fig4 #cc4  ,with 
your present experience the explanation 
of the rising of the top becomes        

ridiculously simple4 ,if you look at    
statement two on this wall sheet 7p4    
#dh7 and reflect a little1 some of you  
will be able1 without any elaborate     
mathematics1 to give the simple reason  
for this that ,thomson gave me sixteen  
years ago4 ,hurry on the precession1 and
 the body rises in opposition to        
gravity4 ,well1 as ,i am not touching   
the top1 and as the body does rise1 we  
look at once for something that is      
hurrying on the precession1 and we      
naturally look to the way in which its  
peg is rubbing on the table1 for1 with  
the exception of the atmosphere this top
 is touching nothing else than the      
table4 ,observe carefully how any of    
these objects precesses4 ,fig4 #cb shows
 the way in which a top spins4 ,looked  
at from above1 if the top is spinning in
 the direction of the hands of a watch1 
we know from the fourth statement of our
 wall sheet1 or by mere observation1    
that it also precesses in the direction 
of the hands #ga of a watch2 that is1   

its precession is such as to make the   
peg roll at ,b into the paper4 ,for you 
will observe that the peg is rolling    
round a circular path on the table1 ,g  
being nearly motionless1 and the axis ,a
 ,g ,a describing nearly a cone in space
 whose vertex is ,g1 above the table4   
,fig4 #cc #gb shows the peg enlarged1   
and it is evident that the point ,b     
touching the table is really like the   
bottom of a wheel ,b ,b'1 and as this   
wheel is rotating1 the rotation causes  
it to roll into the paper1 away from us4
 ,but observe that its mere precession  
is making it roll into the paper1 and   
that the spin if great enough wants to  
roll the top faster than the precession 
lets it roll1 so that it hurries on the 
precession1 and therefore the top rises4
 ,that is the simple explanation2 the   
spin1 so long as it is #gc great enough1
 is always hurrying on the precession1  
and if you will cast your recollection  
back to the days of your youth1 when a  
top was supported on your hand as this  

is now on mine 7,fig4 #cd71 and the spin
 had grown to be quite small1 and was   
unable to keep the top upright1 you will
 remember that you dexterously helped   
the precession by giving your hand a    
circling motion so as to get from your  
top the advantages as to uprightness of 
a slightly longer spin4  ,illustration3 
,,fig4 #cd4  ,i must ask you now by     
observation1 and the application of     
exactly the same argument1 to explain   
the struggle for uprightness on its     
longer axis of any rounded stone when it
 spins on a table4 ,i may tell you that 
some of these large rounded-looking     
objects which ,i now spin before you in 
illustration1 are made hollow1 and they 
are either of wood or zinc1 because ,i  
have not the skill necessary to spin    
large solid objects1 and yet ,i wanted  
to have objects which you would be able 
to see4 ,this small one 7,fig4 #ca7 is  
the largest solid one to which my       
fingers are able to give sufficient     
spin4 ,here is a very interesting object

 7,fig4 #ce71 spherical #gd in shape1   
but its centre of gravity is not exactly
 at its centre of figure1 so when ,i lay
 it on the table it always gets to its  
position of stable equilibrium1 the     
white spot touching the table as at ,a4 
,some of you know that if this sphere is
 thrown into the air it seems to have   
very curious motions1 because one is so 
apt to forget that it is the motion of  
its centre of gravity which follows a   
simple path1 and the boundary is        
eccentric to the centre of gravity4 ,its
 motions when set to roll upon a carpet 
are also extremely curious4             
,illustration3 ,,fig4 #ce4  ,now for the
 very reasons that ,i have already      
given1 when this sphere is made to spin 
on the table1 it always endeavours to   
get its white spot uppermost1 as in ,c1 
,fig4 #ce2 to get into the position in  
which when not spinning it would be     
unstable4  ,illustration3 ,,fig4 #cf4   
,the precession of a top or gyrostat    
leads us at once to think of the        

precession of the great spinning body on
 which we live4 ,you know that the earth
 #ge spins on its axis a little more    
than once every twenty-four hours1 as   
this orange is revolving1 and that it   
goes round the sun once in a year1 as   
this orange is now going round a model  
sun1 or as is shown in the diagram      
7,fig4 #cf74 ,its spinning axis points  
in the direction shown1 very nearly to  
the star which is called the pole star1 
almost infinitely far away4 ,in the     
figure and model ,i have greatly        
exaggerated the elliptic nature of the  
earth's path1 as is quite usual1        
although it may be a little misleading1 
because the earth's path is much more   
nearly circular than many people        
imagine4 ,as a matter of fact the earth 
is about three million miles nearer the 
sun in winter than it is in summer4     
,this seems at first paradoxical1 but we
 get to understand it when we reflect   
that1 because of the slope of the       
earth's axis to the ecliptic1 we people 

who live in the northern hemisphere have
 the sun less vertically above us1 and  
have a shorter day in the winter1 and   
hence each square foot of our part of   
the earth's surface receives much less  
heat every day1 and so we feel colder4  
,now in about #ac1jjj years the earth   
will have precessed just half a         
revolution 7see ,fig4 #ch72 the axis    
will then be sloped towards the sun when
 it is nearest1 instead of away from it 
as it is now2 consequently we shall be  
much warmer in summer and colder in     
winter than we are now4 ,indeed we shall
 then be much worse off than the        
southern #gg hemisphere people are now1 
for they have plenty of oceanic water to
 temper their climate4 ,it is easy to   
see the nature of the change from       
figures #cf1 #cg1 and #ch1 or from the  
model as ,i carry the orange and its    
symbolic knitting-needle round the model
 sun4 ,let us imagine an observer placed
 above this model1 far above the north  
pole of the earth4 ,he sees the earth   

rotating against the direction of the   
hands of a watch1 and he finds that it  
precesses with the hands of a watch1 so 
that spin and precession are in opposite
 directions4 ,indeed it is because of   
this that we have the word precession1  
which we now apply to the motion of a   
top1 although the precession of a top is
 in the same direction as that of the   
spin4  ,illustration3 ,,fig4 #cg4       
,illustration3 ,,fig4 #ch4  ,the        
practical astronomer1 in explaining the 
luni-solar precession of the equinoxes  
to you1 will not probably refer to tops 
or gyrostats4 ,he will tell you that the
 longitude and right ascension of a star
 seem to alter2 in fact that the point  
on the ecliptic from which he makes his 
measurements1 namely1 the spring        
equinox1 is slowly travelling round the 
ecliptic in a direction opposite to that
 of the earth in its orbit1 or to the   
apparent path of the sun4 ,the spring   
equinox is to him for heavenly          
measurements what the longitude of      

,greenwich is to the navigator4 ,he will
 tell you that aberration of light1 and 
parallax of the stars1 #hj but more than
 both1 this precession of the equinoxes1
 are the three most important things    
which prevent us from seeing in an      
observatory by transit observations of  
the stars1 that the earth is revolving  
with perfect uniformity4 ,but his way of
 describing the precession must not     
disguise for you the physical fact that 
his phenomenon and ours are identical1  
and that to us who are acquainted with  
spinning tops1 the slow conical motion  
of a spinning axis is more readily      
understood than those details of his    
measurements in which an astronomer's   
mind is bound up1 and which so often    
condemn a man of great intellectual     
power to the life of drudgery which we  
generally associate with the idea of the
 pound-a-week cheap clerk4              
,illustration3 ,,fig4 #bb4  ,the        
precession of the earth is then of the  
same nature as that of a gyrostat       

suspended above its centre of gravity1  
of a body which would be stable and not 
top-heavy if it were not spinning4 ,in  
fact the precession of the earth is of  
the same nature as that of this large   
gyrostat 7,fig4 #bb71 which is suspended
 in gymbals1 so that it has a vibration 
like a pendulum when not spinning4 ,i   
will now spin it1 so that looked at from
 above it goes against the hands of a   
watch1 and you observe that it precesses
 with the hands of a watch4 ,here again 
is a hemispherical wooden ship1 in which
 there is a gyrostat with its axis      
vertical4 ,it is in stable #ha          
equilibrium4 ,when the gyrostat is not  
spinning1 the ship vibrates slowly when 
put out of equilibrium2 when the        
gyrostat is spinning the ship gets a    
motion of precession which is opposite  
in direction to that of the spinning4   
,astronomers1 beginning with            
,hipparchus1 have made observations of  
the earth's motion for us1 and we have  
observed the motions of gyrostats1 and  

we naturally seek for an explanation of 
the precessional motion of the earth4   
,the equator of the earth makes an angle
 of #bc-a_/b;deg with the ecliptic1     
which is the plane of the earth's orbit4
 ,or the spinning axis of the earth is  
always at angle of #bc-a_/b;deg with a  
perpendicular to the ecliptic1 and makes
 a complete revolution in #bf1jjj years4
 ,the surface of the water on which this
 wooden ship is floating represents the 
ecliptic4 ,the axis #hb of spinning of  
the gyrostat is about #bc-a_/b;deg to   
the vertical2 the precession is in two  
minutes instead of #bf1jjj years2 and   
only that this ship does not revolve in 
a great circular path1 we should have in
 its precession a pretty exact          
illustration of the earth's precession4 
,the precessional motion of the ship1 or
 of the gyrostat 7,fig4 #bb71 is        
explainable1 and in the same way the    
earth's precession is at once explained 
if we find that there are forces from   
external bodies tending to put its      

spinning axis at right angles to the    
ecliptic4 ,the earth is a nearly        
spherical body4 ,if it were exactly     
spherical and homogeneous1 the resultant
 force of attraction upon it1 of a      
distant body1 would be in a line through
 its centre4 ,and again1 if it were     
spherical and non-homogeneous1 but if   
its mass were arranged in uniformly     
dense1 spherical layers1 like the coats 
of an onion4 ,but the earth is not      
spherical1 and to find what is the      
nature of the attraction of a distant   
body1 it has been necessary to make     
pendulum observations all over the      
earth4 ,you know that if a pendulum does
 not alter in length as we take it about
 to various places1 its time of         
vibration at each place enables the     
force of gravity at each place to be    
determined2 and ,mr4 ,green proved that 
if we know the force of gravity at all  
places on the surface of the earth1     
although we may know nothing about the  
#hc state of the inside of the earth1 we

 can calculate with absolute accuracy   
the force exerted by the earth on matter
 placed anywhere outside the earth2 for 
instance1 at any part of the moon's     
orbit1 or at the sun4 ,and hence we know
 the equal and opposite force with which
 such matter will act on the earth4 ,now
 pendulum observations have been made at
 a great many places on the earth1 and  
we know1 although of course not with    
absolute accuracy1 the attraction on the
 earth1 of matter outside the earth4    
,for instance1 we know that the         
resultant attraction of the sun on the  
earth is a force which does not pass    
through the centre of the earth's mass4 
,you may comprehend the result better if
 ,i refer to this diagram of the earth  
at midwinter 7,fig4 #ci71 and use a     
popular method of description4 ,a and ,b
 may roughly be called the protuberant  
parts of the earth--that protuberant    
belt of matter which makes the #hd earth
 orange-shaped instead of spherical4 ,on
 the spherical portion inside1 assumed  

roughly to be homogeneous1 the resultant
 attraction is a force through the      
centre4  ,illustration3 ,,fig4 #ci4  ,i 
will now consider the attraction on the 
protuberant equatorial belt indicated by
 ,a and ,b4 ,the sun attracts a pound of
 matter at ,b more than it attracts a   
pound of matter at ,a1 because ,b is    
nearer than ,a1 and hence the total     
resultant force is in the direction ,m  
,n rather than ,o ,o1 through the centre
 of the earth's mass4 ,but we know that 
a force in the direction ,m ,n is       
equivalent to a force ,o ,o parallel to 
,m ,n1 together with a tilting couple of
 forces tending to turn the equator edge
 on to the sun4 ,you will get the true  
result as to the tilting tendency by    
imagining the earth to be motionless1   
and the sun's mass to be distributed as 
a circular ring of matter #ahd millions 
of miles in diameter1 inclined to the   
equator at #bc-a_/b;deg4 ,under the     
influence of the attraction of this ring
 the earth would heave like a great ship

 on a calm sea1 rolling very slowly2 in 
fact1 making one complete swing in about
 three years4 ,but the earth is         
spinning1 and the tilting couple or     
torque acts upon it just like the forces
 which are always tending to cause this 
ship-model to stand upright1 and hence  
it has a precessional motion whose      
complete period is #bf1jjj years4 ,when 
there is no spin in the ship1 its       
complete oscillation takes place in     
three seconds1 and #he when ,i spin the 
gyrostat on board the ship1 the complete
 period of its precession is two        
minutes4 ,in both cases the effect of   
the spin is to convert what would be an 
oscillation into a very much slower     
precession4  ,there is1 however1 a great
 difference between the earth and the   
gyrostat4 ,the forces acting on the top 
are always the same1 but the forces     
acting on the earth are continually     
altering4 ,at midwinter and midsummer   
the tilting forces are greatest1 and at 
the equinoxes in spring and autumn there

 are no such forces4 ,so that the       
precessional motion changes its rate    
every quarter year from a maximum to    
nothing1 or from nothing to a maximum4  
,it is1 however1 always in the same     
direction--the direction opposed to the 
earth's spin4 ,when we speak then of the
 precessional motion of the earth1 we   
usually think of the mean or average    
motion1 since the motion gets quicker   
and slower every quarter year4          
,further1 the moon is like the sun in   
its action4 ,it tries to tilt the       
equatorial part of the earth into the   
plane of the moon's orbit4 ,the plane of
 the moon's orbit is nearly the same as 
that of the ecliptic1 and hence the     
average precession of the earth is of   
much the same kind as if only one of the
 two1 the moon or the sun1 alone acted4 
,that is1 the general phenomenon of     
precession of the #hf earth's axis in a 
conical path in #bf1jjj years is the    
effect of the combined tilting actions  
of the sun and moon4  ,you will observe 

here an instance of the sort of untruth 
which it is almost imperative to tell in
 explaining natural phenomena4 ,hitherto
 ,i had spoken only of the sun as       
producing precession of the earth4 ,this
 was convenient1 because the plane of   
the ecliptic makes always almost exactly
 #bc-a_/b;deg with the earth's equator1 
and although on the whole the moon's    
action is nearly identical with that of 
the sun1 and about twice as great1 yet  
it varies considerably4 ,the superior   
tilting action of the moon1 just like   
its tide-producing action1 is due to its
 being so much nearer us than the sun1  
and exists in spite of the very small   
mass of the moon as compared with that  
of the sun4  ,as the ecliptic makes an  
angle of #bc-a_/b;deg with the earth's  
equator1 and the moon's orbit makes an  
angle #e-a_/b;deg with the ecliptic1 we 
see that the moon's orbit sometimes     
makes an angle of #bi;deg with the      
earth's equator1 and sometimes only     
#ah;deg1 changing from #bi;deg to       

#ah;deg1 and back to #bi;deg again in   
about nineteen years4 ,this causes what 
is called ,nutation1 or the nodding of  
the earth1 for the tilting action due to
 the sun is greatly helped and greatly  
modified by it4 ,the result of the      
variable nature of the moon's action is 
then that the earth's axis #hg rotates  
in an elliptic conical path round what  
might be called its mean position4 ,we  
have also to remember that twice in     
every lunar month the moon's tilting    
action on the earth is greater1 and     
twice it is zero1 and that it           
continually varies in value4  ,on the   
whole1 then1 the moon and sun1 and to a 
small extent the planets1 produce the   
general effect of a precession1 which   
repeats itself in a period of about     
#be1fie years4 ,it is not perfectly     
uniform1 being performed at a speed     
which is a maximum in summer and winter2
 that is1 there is a change of speed    
whose period is half a year2 and there  
is a change of speed whose period is    

half a lunar month1 the precession being
 quicker to-night than it will be next  
,saturday1 when it will increase for    
about another week1 and diminish the    
next4 ,besides this1 because of         
#e-a_/b;deg of angularity of the orbits1
 we have something like the nodding of  
our precessing gyrostat1 and the        
inclination of the earth's axis to the  
ecliptic is not constant at             
#bc-a_/b;deg1 but is changing1 its      
periodic time being nineteen years4     
,regarding the earth's centre as fixed  
at ,o we see then1 as illustrated in    
this model and in ,fig4 #dj1 the axis of
 the earth describes almost a perfect   
circle on the celestial sphere once in  
#be1hff years1 its speed fluctuating    
every half year and every half month4   
,but it is not a perfect circle1 it is  
really a wavy #hh line1 there being a   
complete wave every nineteen years1 and 
there are smaller ripples in it1        
corresponding to the half-yearly and    
fortnightly periods4 ,but the very cause

 of the nutation1 the nineteen-yearly   
period of retrogression of the moon's   
nodes1 as it is called1 is itself really
 produced as the precession of a        
gyrostat is produced1 that is1 by       
tilting forces acting on a spinning     
body4  ,illustration3 ,,fig4 #dj4       
,imagine the earth to be stationary1 and
 the sun and moon revolving round it4   
,it was ,gauss who found that the       
present action is the same as if the    
masses of the moon and sun were         
distributed all #hi round their orbits4 
,for instance1 imagine the moon's mass  
distributed over her orbit in the form  
of a rigid ring of #dhj1jjj miles       
diameter1 and imagine less of it to     
exist where the present speed is        
greater1 so that the ring would be      
thicker at the moon's apogee1 and       
thinner at the perigee4 ,such a ring    
round the earth would be similar to     
,saturn's rings1 which have also a      
precession of nodes1 only ,saturn's     
rings are not rigid1 else there would be

 no equilibrium4 ,now if we leave out of
 account the earth and imagine this ring
 to exist by itself1 and that its centre
 simply had a motion round the sun in a 
year1 since it makes an angle of        
#e-a_/b;deg with the ecliptic it would  
vibrate into the ecliptic till it made  
the same angle on the other side and    
back again4 ,but it revolves once about 
its centre in twenty-seven solar days1  
eight hours1 and it will no longer swing
 like a ship in a ground-swell1 but will
 get a motion of precession opposed in  
direction to its own revolution4 ,as the
 ring's motion is against the hands of a
 watch1 looking from the north down on  
the ecliptic1 this retrogression of the 
moon's nodes is in the direction of the 
hands of a watch4 ,it is exactly the    
same sort of phenomenon as the          
precession of the equinoxes1 only with a
 much shorter period of #fgih days      
instead of #be1hff years4  ,i told you  
how1 if we knew the moon's mass or the  
sun's1 we could tell the amount of the  

forces1 or #ij the torque as it is more 
properly called1 with which it tries to 
tilt the earth4 ,we know the rate at    
which the earth is spinning1 and we have
 observed the precessional motion4 ,now 
when we follow up the method which ,i   
have sketched already1 we find that the 
precessional velocity of a spinning body
 ought to be equal to the torque divided
 by the spinning velocity and by the    
moment of inertia#g of the body about   
the polar axis4 ,hence the greater the  
tilting forces1 and the less the spin   
and the less the moment of inertia1 the 
greater is the precessional speed4      
,given all of these elements except one1
 it is easy to calculate that unknown   
element4 ,usually what we aim at in such
 a calculation is the determination of  
the moon's mass1 as this phenomenon of  
precession and the action of the tides  
are the only two natural phenomena which
 have as yet enabled the moon's mass to 
be calculated4  ,i do not mean to       
apologize to you for the introduction of

 such terms as ,moment of ,inertia1 nor 
do ,i mean to explain them4 ,in this    
lecture ,i have avoided1 as much as ,i  
could1 the introduction of mathematical 
expressions and the use of technical    
terms4 ,but ,i want you to #ia          
understand that ,i am not afraid to     
introduce technical terms when giving a 
popular lecture4 ,if there is any       
offence in such a practice1 it must1 in 
my opinion1 be greatly aggravated by the
 addition of explanations of the precise
 meanings of such terms4 ,the use of a  
correct technical term serves several   
useful purposes4 ,first1 it gives some  
satisfaction to the lecturer1 as it     
enables him to state1 very concisely1   
something which satisfies his own weak  
inclination to have his reasoning       
complete1 but which he luckily has not  
time to trouble his audience with4      
,second1 it corrects the universal      
belief of all popular audiences that    
they know everything now that can be    
said on the subject4 ,third1 it teaches 

everybody1 including the lecturer1 that 
there is nothing lost and often a great 
deal gained by the adoption of a casual 
method of skipping when one is working  
up a new subject4  ,some years ago it   
was argued that if the earth were a     
shell filled with liquid1 if this liquid
 were quite frictionless1 then the      
moment of inertia of the shell is all   
that we should have to take into account
 in considering precession1 and that if 
it were viscous the precession would    
very soon disappear altogether4 ,to     
illustrate the effect of the moment of  
inertia1 ,i have hung up here a number  
of glasses--one a filled with sand1     
another b with treacle1 a third c with  
oil1 the fourth d with water1 #ib       
,illustration3 ,,fig4 #da4  #ic and the 
fifth e is empty 7,fig4 #da74 ,you see  
that if ,i twist these suspending wires 
and release them1 a vibratory motion is 
set up1 just like that of the balance of
 a watch4 ,observe that the glass with  
water vibrates quickly1 its effective   

moment of inertia being merely that of  
the glass itself1 and you see that the  
time of swing is pretty much the same as
 that of the empty glass2 that is1 the  
water does not seem to move with the    
glass4 ,observe that the vibration goes 
on for a fairly long time4  ,the glass  
with sand vibrates slowly2 here there is
 great moment of inertia1 as the sand   
and glass behave like one rigid body1   
and again the vibration goes on for a   
long time4  ,in the oil and treacle1    
however1 there are longer periods of    
vibration than in the case of the water 
or empty glass1 and less than would be  
the case if the vibrating bodies were   
all rigid1 but the vibrations are       
stilled more rapidly because of         
friction4  ,boiled 7f7 and unboiled 7g7 
eggs suspended from wires in the same   
way will exhibit the same differences in
 the behaviour of bodies1 one of which  
is rigid and the other liquid inside2   
you see how much slower an oscillation  
the boiled has than the unboiled4  ,even

 on the table here it is easy to show   
the difference between boiled and       
unboiled eggs4 #id ,roll them both2 you 
see that one of them stops much sooner  
than the other2 it is the unboiled one  
that stops sooner1 because of its       
internal friction4  ,i must ask you to  
observe carefully the following very    
distinctive test of whether an egg is   
boiled or not4 ,i roll the egg or spin  
it1 and then place my finger on it just 
for an instant2 long enough to stop the 
motion of the shell4 ,you see that the  
boiled egg had quite finished its       
motion1 but the unboiled egg's shell    
alone was stopped2 the liquid inside    
goes on moving1 and now renews the      
motion of the shell when ,i take my     
finger away4  ,it was argued that if the
 earth were fluid inside1 the effective 
moment of inertia of the shell being    
comparatively small1 and having1 as we  
see in these examples1 nothing whatever 
to do with the moment of inertia of the 
liquid1 the precessional motion of the  

earth ought to be enormously quicker    
than it is4 ,this was used as an        
argument against the idea of the earth's
 being fluid inside4  ,we know that the 
observed half-yearly and half-monthly   
changes of the precession of the earth  
would be much greater than they are if  
the earth were a rigid shell containing 
much liquid1 and if the shell were not  
nearly infinitely rigid the phenomena of
 the tides would not occur1 but in      
regard to the general precession of the 
earth there is now #ie no doubt that the
 old line of argument was wrong4 ,even  
if the earth were liquid inside1 it     
spins so rapidly that it would behave   
like a rigid body in regard to such a   
slow phenomenon as precession of the    
equinoxes4 ,in fact1 in the older line  
of argument the important fact was lost 
sight of1 that rapid rotation can give  
to even liquids a quasi-rigidity4 ,now  
here 7,fig4 #db a7 is a hollow brass top
 filled with water4 ,the frame is light1
 and the water inside has much more mass

 than the outside frame1 and if you test
 this carefully you will find that the  
top spins in almost exactly the same way
 as if the water were quite rigid2 in   
fact1 as if the whole top were rigid4   
,here you see it spinning and precessing
 just like any rigid top4 ,this top1 ,i 
know1 is not filled with water1 it is   
only partially filled2 but whether      
partially or wholly filled it spins very
 much like a rigid top4  ,illustration3 
,,fig4 #db4  #if  ,this is not the case 
with a long hollow brass top with water 
inside4 ,i told you that all bodies have
 one axis about which they prefer to    
rotate4 ,the outside metal part of a top
 behaves in a way that is now well known
 to you2 the friction of its peg on the 
table compels it to get up on its longer
 axis4 ,but the fluid inside a top is   
not constrained to spin on its longer   
axis of figure1 and as it prefers its   
shorter axis like all these bodies ,i   
showed you1 it spins in its own way1 and
 by friction and pressure against the   

case constrains the case to spin about  
the shorter axis1 annulling completely  
the tendency of the outside part to rise
 or keep up on its long axis4 ,hence it 
is found to be simply impossible to spin
 a long hollow top when filled with     
water4  ,illustration3 ,,fig4 #dc4      
,illustration3 ,,fig4 #dd4  ,here1 for  
example1 is one 7,fig4 #db b7 that only 
differs from the last in being longer4  
,it is filled1 or partially filled1 with
 water1 and you observe that if #ig ,i  
slowly get up a great spin when it is   
mounted in this frame1 and ,i let it out
 on the table as ,i did the other one1  
this one lies down at once and refuses  
to spin on its peg4 ,this difference of 
behaviour is most remarkable in the two 
hollow tops you see before you 7,fig4   
#dc74 ,they are both nearly spherical1  
both filled with water4 ,they look so   
nearly alike that few persons among the 
audience are able to detect any         
difference in their shape4 ,but one of  
them 7a7 is really slightly oblate like 

an orange1 and the other 7b7 is slightly
 prolate like a lemon4 ,i will give them
 both a gradually increasing rotation in
 this frame #ih 7,fig4 #dd7 for a time  
sufficient to insure the rotation of the
 water inside4 ,when just about to be   
set free to move like ordinary tops on  
the table1 water and brass are moving   
like the parts of a rigid top4 ,you see 
that the orange-shaped one continues to 
spin and precess1 and gets itself       
upright when disturbed1 like an ordinary
 rigid top2 indeed ,i have seldom seen a
 better behaved top2 whereas the        
lemon-shaped one lies down on its side  
at once1 and quickly ceases to move in  
any way4  ,illustration3 ,,fig4 #de4    
,and now you will be able to appreciate 
a fourth test of a boiled egg1 which is 
much more easily seen by a large        
audience than the last4 ,here is the    
unboiled one 7,fig4 #de b74 ,i try my   
best to spin it as it lies on the table1
 but you see that ,i cannot give it much
 spin1 and so there is nothing of any   

importance to look at4 ,but you observe 
that it is quite easy to spin the boiled
 #ii egg1 and that for reasons now well 
known to you it behaves like the stones 
that ,thomson spun on the sea-beach2 it 
gets up on its longer axis1 a very      
pretty object for our educated eyes to  
look at 7,fig4 #de a74 ,you are all     
aware1 from the behaviour of the        
lemon-shaped top1 that even if1 by the  
use of a whirling table suddenly        
stopped1 or by any other contrivance1 ,i
 could get up a spin in this unboiled   
egg1 it would never make the slightest  
effort to rise on its end and spin about
 its longer axis4  ,i hope you don't    
think that ,i have been speaking too    
long about astronomical matters1 for    
there is one other important thing      
connected with astronomy that ,i must   
speak of4 ,you see1 ,i have had almost  
nothing practically to do with          
astronomy1 and hence ,i have a strong   
interest in the subject4 ,it is very    
curious1 but quite true1 that men       

practically engaged in any pursuit are  
almost unable to see the romance of it4 
,this is what the imaginative outsider  
sees4 ,but the overworked astronomer has
 a different point of view4 ,as soon as 
it becomes one's duty to do a thing1 and
 it is part of one's every-day work1 the
 thing loses a great deal of its        
interest4 ,we have been told by a great 
,american philosopher that the only     
coachmen who ever saw the romance of    
coach-driving are those titled          
individuals who pay nowadays so largely 
for the #ajj privilege4 ,in almost any  
branch of engineering you will find that
 if any invention is made it is made by 
an outsider2 by some one who comes to   
the study of the subject with a fresh   
mind4 ,who ever heard of an old         
inhabitant of ,japan or ,peru writing an
 interesting book about those countries8
 ,at the end of two years' residence he 
sees only the most familiar things when 
he takes his walks abroad1 and he feels 
unmitigated contempt for the ingenuous  

globe-trotter who writes a book about   
the country after a month's travel over 
the most beaten tracks in it4 ,now the  
experienced astronomer has forgotten the
 difficulties of his predecessors and   
the doubts of outsiders4 ,it is a long  
time since he felt that awe in gazing at
 a starry sky that we outsiders feel    
when we learn of the sizes and distances
 apart of the hosts of heaven4 ,he      
speaks quite coolly of millions of      
years1 and is nearly as callous when he 
refers to the ancient history of        
humanity on our planet as a             
weather-beaten geologist4 ,the reason is
 obvious4 ,most of you know that the    
,nautical ,almanac is as a literary     
production one of the most uninteresting
 works of reference in existence4 ,it is
 even more disconnected than a          
dictionary1 and ,i should think that    
preparing census-tables must be ever so 
much more romantic as an occupation than
 preparing the tables of the ,nautical  
,almanac4 ,and yet #aja a particular    

figure1 one of millions set down by an  
overworked calculator1 may have all the 
tragic importance of life or death to   
the crew and passengers of a ship1 when 
it is heading for safety or heading for 
the rocks under the mandate of that     
single printed character4  ,but this may
 not be a fair sort of criticism4 ,i so 
seldom deal with astronomical matters1  
,i know so little of the wear and tear  
and monotony of the every-day life of   
the astronomer1 that ,i do not even know
 that the above facts are specially true
 about astronomers4 ,i only know that   
they are very likely to be true because 
they are true of other professional men4
  ,i am happy to say that ,i come in    
contact with all sorts and conditions of
 men1 and among others1 with some men   
who deny many of the things taught in   
our earliest school-books4 ,for example1
 that the earth is round1 or that the   
earth revolves1 or that ,frenchmen speak
 a language different from ours4 ,now no
 man who has been to sea will deny the  

roundness of the earth1 however greatly 
he may wonder at it2 and no man who has 
been to ,france will deny that the      
,french language is different from ours2
 but many men who learnt about the      
rotation of the earth in their          
school-days1 and have had a plentiful   
opportunity of observing the heavenly   
bodies1 deny the rotation of the earth4 
#ajb ,they tell you that the stars and  
moon are revolving about the earth1 for 
they see them revolving night after     
night1 and the sun revolves about the   
earth1 for they see it do so every day4 
,and really if you think of it1 it is   
not so easy to prove the revolution of  
the earth4 ,by the help of good         
telescopes and the electric telegraph or
 good chronometers1 it is easy to show  
from the want of parallax in stars that 
they must be very far away2 but after   
all1 we only know that either the earth 
revolves or else the sky revolves4#h ,of
 course1 it seems infinitely more likely
 that the small earth should revolve    

than that the whole heavenly host should
 turn about the earth as a centre1 and  
infinite likelihood is really absolute  
proof4 ,yet there is nobody who does not
 welcome an independent kind of proof4  
,the phenomena of the tides1 and nearly 
every new astronomical fact1 may be said
 to be an addition to the proof4 ,still 
there is the absence of perfect         
certainty1 and when we are told that    
these spinning-top phenomena give us a  
real proof of the rotation of the earth 
without our leaving the room1 we welcome
 #ajc it1 even although we may sneer at 
it as unnecessary after we have obtained
 it4  ,illustration3 ,,fig4 #ag4  ,you  
know that a gyrostat suspended with     
perfect freedom about axes1 which all   
pass through its centre of gravity1     
maintains a constant direction in space 
however its support may be carried4 ,its
 axis is not forced to alter its        
direction in any way4 ,now this gyrostat
 7,fig4 #ag7 has not the perfect absence
 of friction at its axes of which ,i    

speak1 and even the slightest friction  
will produce some constraint which is   
injurious to the experiment ,i am about 
to describe4 ,it must be remembered1    
that if there were absolutely no        
constraint1 then1 even if the #ajd      
gyrostat were not spinning1 its axis    
would keep a constant direction in      
space4 ,but the spinning gyrostat shows 
its superiority in this1 that any       
constraint due to friction is less      
powerful in altering the axis4 ,the     
greater the spin1 then1 the better able 
are we to disregard effects due to      
friction4 ,you have seen for yourselves 
the effect of carrying this gyrostat    
about in all sorts of ways--first1 when 
it is not spinning and friction causes  
quite a large departure from constancy  
of direction of the axis2 second1 when  
it is spinning1 and you see that        
although there is now the same friction 
as before1 and ,i try to disturb the    
instrument more than before1 the axis   
remains sensibly parallel to itself all 

the time4 ,now when this instrument is  
supported by the table it is really     
being carried round by the earth in its 
daily rotation4 ,if the axis kept its   
direction perfectly1 and it were now    
pointing horizontally due east1 six     
hours after this it will point towards  
the north1 but inclining downwards1 six 
hours afterwards it will point due west 
horizontally1 and after one revolution  
of the earth it will again point as it  
does now4 ,suppose ,i try the           
experiment1 and ,i see that it points   
due east now in this room1 and after a  
time it points due west1 and yet ,i know
 that the gyrostat is constantly        
pointing in the same direction in space 
all the time1 surely it is obvious that 
the room must #aje be turning round in  
space4 ,suppose it points to the pole   
star now1 in six hours1 or twelve1 or   
eighteen1 or twenty-four1 it will still 
point to the pole star4  ,now it is not 
easy to obtain so frictionless a        
gyrostat that it will maintain a good   

spin for such a length of time as will  
enable the rotation of the room to be   
made visible to an audience4 ,but ,i    
will describe to you how forty years ago
 it was proved in a laboratory that the 
earth turns on its axis4 ,this          
experiment is usually connected with the
 name of ,foucault1 the same philosopher
 who with ,fizeau showed how in a       
laboratory we can measure the velocity  
of light1 and therefore measure the     
distance of the sun4 ,it was suggested  
by ,mr4 ,lang of ,edinburgh in #ahcf1   
although only carried out in #aheb by   
,foucault4 ,by these experiments1 if you
 were placed on a body from which you   
could see no stars or other outside     
objects1 say that you were living in    
underground regions1 you could          
discover--first1 whether there is a     
motion of rotation1 and the amount of   
it2 second1 the meridian line or the    
direction of the true north2 third1 your
 latitude4 ,obtain a gyrostat like this 
7,fig4 #df7 but much larger1 and far    

more frictionlessly suspended1 so that  
it is free to move vertically or        
horizontally4 ,for the vertical motion  
your gymbal pivots ought to be hard     
steel knife-edges4 #ajf  ,illustration3 
,,fig4 #df4  ,as for the horizontal     
freedom1 ,foucault used a fine steel    
wire4 ,let there be a fine scale        
engraved crosswise on the outer gymbal  
ring1 and try to discover if it moves   
horizontally by means of a microscope   
with cross wires4 ,when this is         
carefully done we find that there is a  
motion1 #ajg but this is not the motion 
of the gyrostat1 it is the motion of the
 microscope4 ,in fact1 the microscope   
and all other objects in the room are   
going round the gyrostat frame4  ,now   
let us consider what occurs4 ,the room  
is rotating about the earth's axis1 and 
we know the rate of rotation2 but we    
only want to know for our present       
purpose how much of the total rotation  
is about a vertical line in the room4   
,if the room were at the ,north ,pole1  

the whole rotation would be about the   
vertical line4 ,if the room were at the 
equator1 none of its rotation would be  
about a vertical line4 ,in our latitude 
now1 the horizontal rate of rotation    
about a vertical axis is about          
four-fifths of the whole rate of        
rotation of the earth on its axis1 and  
this is the amount that would be        
measured by our microscope4 ,this       
experiment would give no result at a    
place on the equator1 but in our        
latitude you would have a laboratory    
proof of the rotation of the earth4     
,foucault made the measurements with    
great accuracy4  ,if you now clamp the  
frame1 and allow the spinning axis to   
have no motion except in a horizontal   
plane1 the motion which the earth tends 
to give it about a vertical axis cannot 
now affect the gyrostat1 but the earth  
constrains it to move about an axis due 
north and south1 and consequently the   
spinning axis tries to put itself       
parallel #ajh to the north and south    

direction 7,fig4 #dg74 ,hence with such 
an instrument it is easy to find the    
true north4 ,if there were absolutely no
 friction the instrument would vibrate  
about the true north position like the  
compass needle 7,fig4 #ej71 although    
with an exceedingly slow swing4         
,illustration3 ,,fig4 #dg4  ,it is with 
a curious mixture of feelings that one  
first recognizes the fact that all      
rotating bodies1 fly-wheels of          
steam-engines and the like1 are always  
tending to turn themselves towards the  
pole star2 gently and vainly tugging at 
their foundations #aji to get round     
towards the object of their adoration   
all the time they are in motion4        
,illustration3 ,,fig4 #dh4  ,now we have
 found the meridian as in ,fig4 #dg1 we 
can begin a third experiment4 ,prevent  
motion horizontally1 that is1 about a   
vertical axis1 but give the instrument  
freedom to move vertically in the       
meridian1 like a transit instrument in  
an observatory #aaj about its horizontal

 axis4 ,its revolution with the earth   
will tend to make it change its angular 
position1 and therefore it places itself
 parallel to the earth's axis2 when in  
this position the daily rotation no     
longer causes any change in its         
direction in space1 so it continues to  
point to the pole star 7,fig4 #dh74 ,it 
would be an interesting experiment to   
measure with a delicate chemical balance
 the force with which the axis raises   
itself1 and in this way weigh the       
rotational motion of the earth4#i  ,now 
let us turn the frame of the instrument 
,g ,b round a right angle1 so that the  
spinning axis can only move in a plane  
at right angles to the meridian2        
obviously it is constrained by the      
vertical component of the earth's       
rotation1 and points vertically         
downwards4  ,illustration3 ,,fig4 #di4  
,illustration3 ,,fig4 #ej4  ,this last  
as well as the other phenomena of which 
,i have spoken is very suggestive4 ,here
 is a magnetic needle 7,fig4 #di71      

sometimes called a dipping needle from  
the way in which it is suspended4 ,if ,i
 turn its #aaa frame so that it can only
 move at right angles to the meridian1  
you see that it points vertically4 ,you 
may reflect upon the analogous          
properties of this magnetic needle      
7,fig4 #ej7 and of the gyrostat 7,fig4  
#dg72 they both1 when only capable of   
moving horizontally1 point to the north2
 and you see that a very frictionless   
gyrostat might be used as a compass1 or 
at all events as a corrector of         
compasses4#aj ,i have just put before   
you another analogy1 and ,i want you to 
understand that1 although these are only
 analogies1 they are not mere chance    
analogies1 for there is undoubtedly a   
dynamical connection between the        
magnetic and the gyrostatic phenomena4  
,magnetism depends on rotatory motion4  
,the molecules of matter are in actual  
rotation1 and a certain allineation of  
the axes of the rotations produces what 
we call magnetism4 ,in a steel bar not  

magnetized the little axes of rotation  
are all in different directions4 ,the   
process #aab of magnetization is simply 
bringing these rotations to be more or  
less round parallel axes1 an allineation
 of the axes4 ,a honey-combed mass with 
a spinning gyrostat in every cell1 with 
all the spinning axes parallel1 and the 
spins in the same direction1 would--,i  
was about to say1 would be a magnet1 but
 it would not be a magnet in all its    
properties1 and yet it would resemble a 
magnet in many ways4#aa  ,illustration3 
,,fig4 #ea4  ,illustration3 ,,fig4 #eb4 
,some of you1 seeing electromotors and  
other electric contrivances near this   
table1 may think that they have to do   
with our theories and explanations of   
magnetic phenomena4 ,but ,i must explain
 that this electromotor which ,i hold in
 my hand 7,fig4 #ea7 is used by me      
merely as the #aac most convenient means
 ,i could find for the spinning of my   
tops and gyrostats4 ,on the spindle of  
the motor is fastened a circular piece  

of wood2 by touching this key ,i can    
supply the motor with electric energy1  
and the wooden disc is now rotating very
 rapidly4 ,i have only to bring its rim 
in contact with any of these tops or    
gyrostats to set them spinning1 and you 
see that ,i can set half a dozen        
gyrostats a-spinning in a few seconds2  
this chain of gyrostats1 for instance4  
,again1 this larger motor 7,fig4 #eb71  
too large to move about in my hand1 is  
fastened to the table1 and ,i have used 
#aad it to drive my larger contrivances2
 but you understand that ,i use these   
just as a barber might use them to brush
 your hair1 or ,sarah ,jane to clean the
 knives1 or just as ,i would use a      
little steam-engine if it were more     
convenient for my purpose4 ,it was more 
convenient for me to bring from ,london 
this battery of accumulators and these  
motors than to bring sacks of coals1 and
 boilers1 and steam-engines4 ,but1      
indeed1 all this has the deeper meaning 
that we can give to it if we like4 ,love

 is as old as the hills1 and every day  
,love's messages are carried by the     
latest servant of man1 the telegraph4   
,these spinning tops were known probably
 to primeval man1 and yet we have not   
learnt from them more than the most     
fractional portion of the lesson that   
they are always sending out to an       
unobservant world4 ,toys like these were
 spun probably by the builders of the   
,pyramids when they were boys1 and here 
you see them side by side with the very 
latest of man's contrivances4 ,i feel   
almost as ,mr4 ,stanley might feel if1  
with the help of the electric light and 
a magic-lantern1 he described his       
experiences in that dreadful ,african   
forest to the usual company of a ,london
 drawing-room4  ,the phenomena ,i have  
been describing to you play such a very 
important part in nature1 that if time  
admitted ,i might go on expounding and  
#aae explaining without finding any     
great reason to stop at one place rather
 than another4 ,the time at my disposal 

allows me to refer to only one other    
matter1 namely1 the connection between  
light and magnetism and the behaviour of
 spinning tops4  ,you are all aware that
 sound takes time to travel4 ,this is a 
matter of common observation1 as one can
 see a distant woodchopper lift his axe 
again before one hears the sound of his 
last stroke4 ,a destructive sea wave is 
produced on the coast of ,japan many    
hours after an earthquake occurs off the
 coast of ,america1 the wave motion     
having taken time to travel across the  
,pacific4 ,but although light travels   
more quickly than sound or wave motion  
in the sea1 it does not travel with     
infinite rapidity1 and the appearance of
 the eclipse of one of ,jupiter's       
satellites is delayed by an observable  
number of minutes because light takes   
time to travel4 ,the velocity has been  
measured by means of such observations1 
and we know that light travels at the   
rate of about #ahg1jjj miles per second1
 or thirty thousand millions of         

centimetres per second4 ,there is no    
doubt about this figure being nearly    
correct1 for the velocity of light has  
been measured in the laboratory by a    
perfectly independent method4  ,now the 
most interesting physical work done     
since ,newton's time is the outcome of  
the experiments of ,faraday and the     
theoretical deductions of #aaf ,thomson 
and ,maxwell4 ,it is the theory that    
light and radiant heat are simply       
electro-magnetic disturbances propagated
 through space4 ,i dare not do more than
 just refer to this matter1 although it 
is of enormous importance4 ,i can only  
say1 that of all the observed facts in  
the sciences of light1 electricity1 and 
magnetism1 we know of none that is in   
opposition to ,maxwell's theory1 and we 
know of many that support it4 ,the      
greatest and earliest support that it   
had was this4 ,if the theory is correct1
 then a certain electro-magnetic        
measurement ought to result in exactly  
the same quantity as the velocity of    

light4 ,now ,i want you to understand   
that the electric measurement is one of 
quantities that seem to have nothing    
whatever to do with light1 except that  
one uses one's eyes in making the       
measurement2 it requires the use of a   
two-foot rule and a magnetic needle1 and
 coils of wire and currents of          
electricity4 ,it seemed to bear a       
relationship to the velocity of light1  
which was not very unlike the fabled    
connection between ,tenterden ,steeple  
and the ,goodwin ,sands4 ,it is a       
measurement which it is very difficult  
to make accurately4 ,a number of skilful
 experimenters1 working independently1  
and using quite different methods1      
arrived at results only one of which is 
as much as five per cent4 different from
 the observed velocity of light1 and    
some of them1 #aag on which the best    
dependence may be placed1 agree exactly 
with the average value of the           
measurements of the velocity of light4  
,there is then a wonderful agreement of 

the two measurements1 but without more  
explanation than ,i can give you now1   
you cannot perhaps understand the       
importance of this agreement between two
 seemingly unconnected magnitudes4 ,at  
all events we now know1 from the work of
 ,professor ,hertz in the last two      
years1 that ,maxwell's theory is        
correct1 and that light is an           
electro-magnetic disturbance2 and what  
is more1 we know that electro-magnetic  
disturbances1 incomparably slower than  
red-light or heat1 are passing now      
through our bodies2 that this now       
recognized kind of radiation may be     
reflected and refracted1 and yet will   
pass through brick and stone walls and  
foggy atmospheres where light cannot    
pass1 and that possibly all military and
 marine and lighthouse signalling may be
 conducted in the future through the    
agency of this new and wonderful kind of
 radiation1 of which what we call light 
is merely one form4 ,why at this moment1
 for all ,i know1 two citizens of ,leeds

 may be signalling to each other in this
 way through half a mile of houses1     
including this hall in which we are     
present4#ab  #aah  ,i mention this1 the 
greatest modern philosophical discovery1
 because the germ of it1 which was      
published by ,thomson in #ahef1 makes   
direct reference to the analogy between 
the behaviour of our spinning-tops and  
magnetic and electrical phenomena4 ,it  
will be easier1 however1 for us to      
consider here a mechanical illustration 
of the rotation of the plane of         
polarized light by magnetism which      
,thomson elaborated in #ahgd4 ,this     
phenomenon may1 ,i think1 be regarded as
 the most important of all ,faraday's   
discoveries4 ,it was of enormous        
scientific importance1 because it was   
made in a direction where a new         
phenomenon was not even suspected4 ,of  
his discovery of induced currents of    
electricity1 to which all               
electric-lighting companies and         
transmission of power companies of the  

present day owe their being1 ,faraday   
himself said that it was a natural      
consequence of the discoveries of an    
earlier experimenter1 ,oersted4 ,but    
this magneto-optic discovery was quite  
unexpected4 ,i will now describe the    
phenomenon4  ,some of you are aware that
 when a beam of light is sent through   
this implement1 called a ,nichol's      
,prism1 it becomes polarized1 or        
one-sided--that is1 all the light that  
comes through is known to be propagated 
by vibrations which occur all in one    
plane4 ,this rope 7,fig4 #ec7 hanging   
from the ceiling #aai illustrates the   
nature of plane polarized light4 ,all   
points in the rope are vibrating in the 
same plane4 ,well1 this prism ,a1 ,fig4 
#ed1 only lets through it light that is 
polarized in a vertical plane4 ,and here
 at ,b ,i have a similar implement1 and 
,i place it so that it also will only   
allow light to pass through it which is 
polarized in a vertical plane4 ,hence   
most of the light coming through the    

polarizer1 as the first prism is called1
 will pass readily through the analyzer1
 as the second is called1 and ,i am now 
letting this light enter my eye4 ,but   
when ,i turn the analyzer round through 
a right angle1 ,i find that ,i see no   
light2 there was a gradual darkening as 
,i rotated the analyzer4 ,the analyzer  
will now only allow light to pass       
through which is polarized in a         
horizontal plane1 and it receives no    
such light4  ,illustration3 ,,fig4 #ec4 
,illustration3 ,,fig4 #ed4  ,you will   
see in this model 7,fig4 #ee7 a good    
illustration of polarized light4 ,the   
white1 brilliantly illuminated thread ,m
 ,n is #abj pulled by a weight beyond   
the pulley ,m1 and its end ,n is        
fastened to one limb of a tuning-fork4  
,some ragged-looking pieces of thread   
round the portion ,n ,a prevent its     
vibrating in any very determinate way1  
but from ,a to ,m the thread is free    
from all encumbrance4 ,a vertical slot  
at ,a1 through which the thread passes1 

determines the nature of the vibration  
of the part ,a ,b2 every part of the    
thread between ,a and ,b is vibrating in
 up and down directions only4 ,a        
vertical slot in ,b allows the vertical 
vibration to be communicated through it1
 and so we see the part ,b ,m vibrating 
in the same way as ,a ,b4 ,i might point
 out quite a lot of ways in which this  
is not a perfect illustration of what   
occurs with light in ,fig4 #ed4 ,but it 
is quite good enough for my present     
purpose4 ,a is a polarizer of vibration2
 it only allows up and down motion to   
pass through it1 and ,b also allows up  
and down motion to pass through4 ,but   
now1 as ,b is turned round1 it lets less
 and less of the up and down motion pass
 through it1 until when it is in the    
second position shown in the lower part 
of the figure1 it allows no up and down 
motion to pass through1 and there is no 
visible motion of the thread between ,b 
and ,m4 ,you will observe that if we did
 not know in what plane 7in the present 

case the plane is vertical7 the         
vibrations of the thread between ,a and 
,b occurred1 we should only have to turn
 ,b round until we found no vibration   
#abb passing through1 to obtain the     
information4 ,hence1 as in the light    
case1 we may call ,a a polarizer of     
vibrations1 and ,b an analyzer4         
,illustration3 ,,fig4 #ee4  ,now if     
polarized light is passing from ,a to ,b
 7,fig4 #ed7 through the air1 say1 and  
we have the analyzer placed so that     
there is darkness1 we find that if we   
place in the path of the ray some       
solution of sugar we shall no longer    
have darkness at ,b2 we must turn ,b    
round to get things dark again2 this is 
evidence of the sugar solution having   
twisted round the plane of polarization 
of the light4 ,i will now assume that   
you know something about what is meant  
by twisting the plane of polarization of
 light4 ,you know that sugar solution   
will do it1 and the longer the path of  
the ray through the sugar1 the more     

twist it gets4 ,this phenomenon is taken
 advantage of in the sugar industries1  
to find the strengths of sugar          
solutions4 ,for the thread illustration 
,i am indebted to ,professor ,silvanus  
,thomson1 and the next piece of         
apparatus which ,i shall show also      
belongs to him4  ,i have here 7see      
,frontispiece7 a powerful armour-clad   
coil1 or electro-magnet4 ,there is a    
central hole through it1 through which a
 beam of light may be passed from an    
electric lamp1 and ,i have a piece of   
,faraday's heavy glass nearly filling   
this hole4 ,i have a polarizer at one   
end1 and an analyzer at the other4 ,you 
see now that the #abc polarized light   
passes through the heavy glass and the  
analyzer1 and enters the eye of an      
observer4 ,i will now turn ,b until the 
light no longer passes4 ,until now there
 has been no magnetism1 but ,i have the 
means here of producing a most intense  
magnetic field in the direction in which
 the ray passes1 and if your eye were   

here you would see that there is light  
passing through the analyzer4 ,the      
magnetism has done something to the     
light1 it has made it capable of passing
 where it could not pass before4 ,when  
,i turn the analyzer a little ,i stop   
the light again1 and now ,i know that   
what the magnetism did was to convert   
the glass into a medium like the sugar1 
a medium which rotates the plane of     
polarization of light4  ,in this        
experiment you have had to rely upon my 
personal measurement of the actual      
rotation produced4 ,but if ,i insert    
between the polarizer and analyzer this 
disc of ,professor ,silvanus ,thomson's1
 built up of twenty-four radial pieces  
of mica1 ,i shall have a means of       
showing to this audience the actual     
rotation of the plane of polarization of
 light4 ,you see now on the screen the  
light which has passed through the      
analyzer in the form of a cross1 and if 
the cross rotates it is a sign of the   
rotation of the plane of polarization of

 the light4 ,by means of this electric  
key ,i can create1 destroy1 and reverse 
the magnetic #abd field in the glass4   
,as ,i create magnetism you see the     
twisting of the cross2 ,i destroy the   
magnetism1 and it returns to its old    
position2 ,i create the opposite kind of
 magnetism1 and you see that the cross  
twists in the opposite way4 ,i hope it  
is now known to you that magnetism      
rotates the plane of polarization of    
light as the solution of sugar did4     
,illustration3 ,,fig4 #ef4              
,illustration3 ,,fig4 #eg4  ,as an      
illustration of what occurs between     
polarizer and analyzer1 look again at   
this rope 7,fig4 #ec7 fastened to the   
ceiling4 ,i move the bottom end sharply 
from east to west1 and you see that     
every part of the rope moves from east  
to west4 ,can you imagine a rope such   
that when the bottom end was moved from 
east to west1 a point some yards up     
moved from east-north-east to           
west-sou'-west1 that a higher point     

moved from north-east to south-west1 and
 so on1 the direction gradually changing
 for higher and higher points8 ,some of 
you1 knowing what ,i have done1 may be  
able to imagine it4 ,we should have what
 we want if this rope were a chain of   
gyrostats such as you see figured in the
 diagram2 gyrostats all spinning in the 
same way looked at from below1 with     
frictionless hinges between them4 ,here 
is such a chain 7,fig4 #ef71 one of many
 that ,i have tried to use in this way  
for several years4 ,but although ,i have
 often believed that ,i saw the         
phenomenon occur in #abf such a chain1  
,i must now confess to repeated         
failures4 ,the difficulties ,i have met 
with are almost altogether mechanical   
ones4 ,you see that by touching all the 
gyrostats in succession with this       
rapidly revolving disc driven by the    
little electromotor1 ,i can get them all
 to spin at the same time2 but you will 
notice that what with bad mechanism and 
bad calculation on my part1 and want of 

skill1 the phenomenon is completely     
masked by wild movements of the         
gyrostats1 the causes of which are      
better known than capable of            
rectification4 ,the principle of the    
action is very visible in this gyrostat 
suspended as the bob of a pendulum      
7,fig4 #eg74 ,you may imagine this to   
represent a particle of the #abg        
substance which transmits light in the  
magnetic field1 and you see by the      
trickling thin stream of sand which     
falls from it on the paper that it is   
continually changing the plane of       
polarization4 ,but ,i am happy to say   
that ,i can show you to-night a really  
successful illustration of ,thomson's   
principle2 it is the very first time    
that this most suggestive experiment has
 been shown to an audience4 ,i have a   
number of double gyrostats 7,fig4 #eh7  
placed on the same line1 joined end to  
end by short pieces of elastic4 ,each   
instrument is supported at its centre of
 gravity1 and it can rotate both in     

horizontal and in vertical planes4      
,illustration3 ,,fig4 #eh4  ,the end of 
the vibrating lever ,a can only get a   
horizontal motion from my hand1 and the 
motion is transmitted from one gyrostat 
to the next1 until it has travelled to  
the very end one4 ,observe that when the
 gyrostats are not spinning1 the motion 
is #abh everywhere horizontal4 ,now it  
is very important not to have any       
illustration here of a reflected ray of 
light1 and so ,i have introduced a good 
deal of friction at all the supports4 ,i
 will now spin all the gyrostats1 and   
you will observe that when ,a moves     
nearly straight horizontally1 the next  
gyrostat moves straight but in a        
slightly different plane1 the second    
gyrostat moves in another plane1 and so 
on1 each gyrostat slightly twisting the 
plane in which the motion occurs2 and   
you see that the end one does not by any
 means receive the horizontal motion of 
,a1 but a motion nearly vertical4 ,this 
is a mechanical illustration1 the first 

successful one ,i have made after many  
trials1 of the effect on light of       
magnetism4 ,the reason for the action   
that occurs in this model must be known 
to everybody who has tried to follow me 
from the beginning of the lecture4  ,and
 you can all see that we have only to   
imagine that many particles of the glass
 are rotating like gyrostats1 and that  
magnetism has partially caused an       
allineation of their axes1 to have a    
dynamical theory of ,faraday's          
discovery4 ,the magnet twists the plane 
of polarization1 and so does the        
solution of sugar2 but it is found by   
experiment that the magnet does it      
indifferently for coming and going1     
whereas the sugar does it in a way that 
corresponds with a spiral structure of  
molecules4 ,you see that in this        
important #abi particular the gyrostat  
analogue must follow the magnetic       
method1 and not the sugar method4 ,we   
must regard this model1 then1 the       
analogue to ,faraday's experiment1 as   

giving great support to the idea that   
magnetism consists of rotation4  ,i have
 already exceeded the limits of time    
usually allowed to a popular lecturer1  
but you see that ,i am very far from    
having exhausted our subject4 ,i am not 
quite sure that ,i have accomplished the
 object with which ,i set out4 ,my      
object was1 starting from the very      
different behaviour of a top when       
spinning and when not spinning1 to show 
you that the observation of that very   
common phenomenon1 and a determination  
to understand it1 might lead us to      
understand very much more               
complex-looking things4 ,there is no    
lesson which it is more important to    
learn than this--,that it is in the     
study of every-day facts that all the   
great discoveries of the future lie4    
,three thousand years ago spinning tops 
were common1 but people never studied   
them4 ,three thousand years ago people  
boiled water and made steam1 but the    
steam-engine was unknown to them4 ,they 

had charcoal and saltpetre and sulphur1 
but they knew nothing of gunpowder4     
,they saw fossils in rocks1 but the     
wonders of geology were unstudied by    
them4 ,they had bits of iron and copper1
 but not one of them thought of any one 
of the fifty simple #acj ways that are  
now known to us of combining those known
 things into a telephone4 ,why1 even the
 simplest kind of signalling by flags or
 lanterns was unknown to them1 and yet a
 knowledge of this might have changed   
the fate of the world on one of the     
great days of battle that we read about4
 ,we look on ,nature now in an utterly  
different way1 with a great deal more   
knowledge1 with a great deal more       
reverence1 and with much less           
unreasoning superstitious fear4 ,and    
what we are to the people of three      
thousand years ago1 so will be the      
people of one hundred years hence to us2
 for indeed the acceleration of the rate
 of progress in science is itself       
accelerating4 ,the army of scientific   

workers gets larger and larger every    
day1 and it is my belief that every unit
 of the population will be a scientific 
worker before long4 ,and so we are      
gradually making time and space yield to
 us and obey us4 ,but just think of it6 
,of all the discoveries of the next     
hundred years2 the things that are      
unknown to us1 but which will be so well
 known to our descendants that they will
 sneer at us as utterly ignorant1       
because these things will seem to them  
such self-evident facts2 ,i say1 of all 
these things1 if one of us to-morrow    
discovered one of them1 he would be     
regarded as a great discoverer4 ,and yet
 the children of a hundred years hence  
will know it3 it will be brought home to
 #aca them perhaps at every footfall1 at
 the flapping of every coat-tail4       
,imagine the following question set in a
 school examination paper of #bjij      
,a4,d4--,can you account for the crass  
ignorance of our forefathers in not     
being able to see from ,england what    

their friends were doing in             
,australia8#ac ,or this--,messages are  
being received every minute from our    
friends on the planet ,mars1 and are now
 being answered3 how do you account for 
our ancestors being utterly ignorant    
that these messages were occasionally   
sent to them8 ,or this--,what metal is  
as strong compared with steel as steel  
is compared with lead8 and explain why  
the discovery of it was not made in     
,sheffield4  ,but there is one question 
that our descendants will never ask in  
accents of jocularity1 for to their     
bitter sorrow every man1 woman1 and     
child of them will know the answer1 and 
that question is this--,if our ancestors
 in the matter of coal economy were not 
quite as ignorant as a baby who takes a 
penny #acb as equivalent for a          
half-crown1 why did they waste our coal8
 ,why did they destroy what never can be
 replaced8  ,my friends1 let me conclude
 by impressing upon you the value of    
knowledge1 and the importance of using  

every opportunity within your reach to  
increase your own store of it4 ,many are
 the glittering things that seem to     
compete successfully with it1 and to    
exercise a stronger fascination over    
human hearts4 ,wealth and rank1 fashion 
and luxury1 power and fame--these fire  
the ambitions of men1 and attract       
myriads of eager worshippers2 but1      
believe it1 they are but poor things in 
comparison with knowledge1 and have no  
such pure satisfactions to give as those
 which it is able to bestow4 ,there is  
no evil thing under the sun which       
knowledge1 when wielded by an earnest   
and rightly directed will1 may not help 
to purge out and destroy2 and there is  
no man or woman born into this world who
 has not been given the capacity1 not   
merely to gather in knowledge for his   
own improvement and delight1 but even to
 add something1 however little1 to that 
general stock of knowledge which is the 
world's best wealth4         99       99
       99       99       99   #acc      

,,argument4      #a4 ,introduction1     
pages #i-ad1 showing the importance of  
the study of     spinning-top behaviour4
      #b4 ,quasi-rigidity induced even  
in flexible and fluid bodies by rapid   
motion1 #ad-ba4      ,illustrations3    
,top1 #ad2 belt or rope1 #ad2 disc of   
thin paper1 #ad2 ring     of chain1 #ae2
 soft hat1 #af2 drunken man1 #af2       
rotating water1 #af2 smoke     rings1   
#ag2 ,thomson's ,molecular ,theory1 #ai2
 swimmer caught in an eddy1     #bj2    
mining water jet1 #bj2 cased gyrostat1  
#ba4      #c4 ,the nature of this       
quasi-rigidity in spinning bodies is a  
resistance to change of direction of the
 axis of spinning1 #ba-cj4              
,illustrations3 ,cased gyrostat1 #ba-bd2
 tops1 biscuits1 hats1 thrown into      
the air1 #bd-bf2 quoits1 hoops1         
projectiles from guns1 #bg2 jugglers at 
the ,victoria ,music ,hall1 #bf-cj2     
child trundling hoop1 man on bicycle1   
ballet-dancer1 the earth pointing to    
pole star1 boy's top1 #cj4      #d4     

,study of the crab-like behaviour of a  
spinning body1 #cj-di4                  
,illustrations3 ,spinning top1 #ca2     
cased gyrostat1 #cb2 balanced gyrostat1 
#cc-cf2 windage of projectiles from #acd
 rifled guns1 #cf-ch2 tilting a     hoop
 or bicycle1 turning quickly on         
horseback1 #ch2 bowls1 #ci2 how to      
simplify one's observations1 #ci1 #dj2  
the illustration which gives us     our 
simple universal rule1 #dj-db2 testing  
the rule1 #db-dd2 explanation     of    
precession of gyrostat1 #dd1 #de2       
precession of common top1 #df2          
precession of overhung top1 #df2 list of
 our results given in a wall     sheet1 
#dh1 #di4      #e4 ,proof or explanation
 of our simple universal rule1 #ej-ed4  
,giving two independent rotations to a  
body1 #ej1 #ea2 composition of          
rotations1 #eb1 #ec4      #f4 ,warning  
that the rule is not1 after all1 so     
simple1 #ed-ff4      ,two independent   
spins given to the earth1 #ed2          
centrifugal force1 #ee2     balancing of

 quick speed machinery1 #ef1 #eg2 the   
possible wobbling of     the earth1 #eh2
 the three principal axes of a body1    
#ei2 the free     spinning of discs1    
cones1 rods1 rings of chain1 #fj2       
nodding motion of a     gyrostat1 #fb2  
of a top1 #fc2 parenthesis about        
inaccuracy of statement     and         
,rankine's rhyme1 #fc1 #fd2 further     
complications in gyrostatic             
behaviour1 #fd2 strange elastic1        
jelly-like behaviour1 #fe2 gyrostat on  
stilts1 #ff4      #g4 ,why a gyrostat   
falls1 #ff1 #fg4      #h4 ,why a top    
rises1 #fg-gd4      ,general ignorance1 
#fg2 ,thomson preparing for the         
mathematical tripos1     #fh2 behaviour 
of a water-worn stone when spun on a    
table1 #fh1 #fi2     parenthesis on     
technical education1 #gj2 simple        
explanation of why a top     rises1     
#gj-gc2 behaviour of heterogeneous      
sphere when spun1 #gd4      #i4         
,precessional motion of the earth1      
#gd-ia4      ,its nature and effects on 

climate1 #ge-hj2 resemblance of the     
precessing     earth to certain models1 
#hj-hb2 tilting forces exerted by the   
sun and     moon on the #ace earth1     
#hb-hd2 how the earth's precessional    
motion is     always altering1 #he-hh2  
the retrogression of the moon's nodes is
 itself     another example1 #hh1 #hi2  
an exact statement made and a sort of   
apology     for making it1 #ij1 #ia4    
#aj4 ,influence of possible internal    
fluidity of the earth on its            
precessional motion1 #ia-ih4            
,effect of fluids and sand in tumblers1 
#ia-ic2 three tests of the     internal 
rigidity of an egg1 that is1 of its     
being a boiled egg1 #ic1     #id2       
quasi-rigidity of fluids due to rapid   
motion1 forgotten in original           
argument1 #ie2 beautiful behaviour of   
hollow top filled with water1 #ie2      
striking contrasts in the behaviour of  
two tops which are very much     alike1 
#ig1 #ih2 fourth test of a boiled egg1  
#ih4      #aa4 ,apology for dwelling    

further upon astronomical matters1 and  
impertinent remarks about astronomers1  
#ii-aja4      #ab4 ,how a gyrostat would
 enable a person living in subterranean 
regions     to know1 #ast1 that the     
earth rotates2 #bnd1 the amount of      
rotation2     #crd1 the direction of    
true north2 #dth1 the latitude1         
#aja-aaa4      ,some men's want of      
faith1 #aja2 disbelief in the earth's   
rotation1 #ajb2     how a free gyrostat 
behaves1 #ajc1 #ajd2 ,foucault's        
laboratory     measurement of the       
earth's rotation1 #aje-ajg2 to find the 
true north1     #ajh2 all rotating      
bodies vainly endeavouring to point to  
the pole star1     #ajh2 to find the    
latitude1 #aaj2 analogies between the   
gyrostat and the     mariner's compass  
and the dipping needle1 #aaj1 #aaa2     
dynamical     connection between        
magnetism and gyrostatic phenomena1     
#aaa4      #ac4 ,how the lecturer spun  
his tops1 using electro-motors1         
#aab-aad4      #ad4 ,light1 magnetism1  

and molecular spinning tops1 #aae-abh4  
,light takes time to travel1 #aae2 the  
electro-magnetic #acf theory of         
light1 #aaf1 #aag2 signalling through   
fogs and buildings by means of a     new
 kind of radiation1 #aag2 ,faraday's    
rotation of the plane of                
polarization by magnetism1 with         
illustrations and models1 #aah-abd2     
chain of gyrostats1 #abd2 gyrostat as a 
pendulum bob1 #abf2 ,thomson's          
mechanical illustration of ,faraday's   
experiment1 #abg1 #abh4      #ae4       
,conclusion1 #abi-acb4      ,the        
necessity for cultivating the           
observation1 #abi2 future discovery1    
#acj2 questions to be asked one hundred 
years hence1 #aca2 knowledge the        
thing most to be wished for1 #acb4      
99       99       99       99       99  
#acg  ,,appendix ,i4  ,,the ,,use ,,of  
,,gyrostats4  ,in #ahgd two famous men  
made a great mistake in endeavouring to 
prevent or diminish the rolling motion  
of the saloon of a vessel by using a    

rapidly rotating wheel4 ,mr4 ,macfarlane
 ,gray pointed out their mistake4 ,it is
 only when the wheel is allowed to      
precess that it can exercise a steadying
 effect2 the moment which it then exerts
 is equal to the angular speed of the   
precession multiplied by the moment of  
momentum of the spinning wheel4  ,it is 
astonishing how many engineers who know 
the laws of motion of mere translation1 
are ignorant of angular motion1 and yet 
the analogies between the two sets of   
laws are perfectly simple4 ,i have set  
out these analogies in my book on       
,applied ,mechanics4 ,the last of them  
between centripetal force on a body     
moving in a curved path1 and torque or  
moment on a rotating body is the simple 
key to all gyrostatic or top            
calculation4 ,when the spin of a top is 
greatly reduced it is necessary to      
remember that the total moment of       
momentum is not about the spinning axis 
7see my ,applied ,mechanics1 page #eid72
 correction for this is1 ,i suppose1    

what introduces the complexity which    
scares students from studying the       
vagaries of tops2 but in all cases that 
are likely to come before an engineer it
 would be absurd to study #ach such a   
small correction1 and consequently      
calculation is exceedingly simple4      
,inventors using gyrostats have         
succeeded in doing the following        
things--  7#a7 ,keeping the platform of 
a gun level on board ship1 however the  
ship may roll or pitch4 ,keeping a      
submarine vessel or a flying machine    
with any plane exactly horizontal or    
inclined in any specified way4#ad ,it is
 easy to effect such objects without the
 use of a gyrostat1 as by means of      
spirit levels it is possible to command 
powerful electric or other motors to    
keep anything always level4 ,the actual 
methods employed by ,mr4 ,beauchamp     
,tower 7an hydraulic method71 and by    
myself 7an electric method71 depend upon
 the use of a gyrostat1 which is really 
a pendulum1 the axis being vertical4    

7#b7 ,greatly reducing the rolling 7or  
pitching7 of a ship1 or the saloon of a 
ship4 ,this is the problem which ,mr4   
,schlick has solved with great success1 
at any rate in the case of torpedo      
boats4  7#c7 ,in ,mr4 ,brennan's        
,mono-rail railway1 keeping the         
resultant force due to weight1 wind     
pressure1 centrifugal force1 etc41      
exactly in line with the rail1 so that1 
however the load on a wagon may alter in
 position1 and although the wagon may be
 going round a curve1 it is quickly     
brought to a position such that there   
are no forces tending to alter its      
angular position4 ,the wagon leans over 
towards the wind or towards the centre  
of the curve of the rail so as to be in 
equilibrium4  7#d7 ,i need not refer to 
such matters as the use of gyrostats for
 the correction of compasses on board   
ship1 referred to in page #aaa4  #aci   
,illustration3 ,,fig4 #a4  #adj         
,problems 7#b7 and 7#c7 are those to    
which ,i wish to refer4 ,for a ship of  

#f1jjj tons ,mr4 ,schlick would use a   
large wheel of #aj to #bj tons1         
revolving about an axis ,e ,f 7fig4 #a7 
whose mean position is vertical4 ,its   
bearings are in a frame ,e ,c ,f ,d     
which can move about a thwart-ship axis 
,c ,d with a precessional motion4 ,its  
centre of gravity is below this axis1 so
 that like the ship itself the frame is 
in stable equilibrium4 ,let the ship    
have rolled through an angle ,r from its
 upright position1 and suppose the axis 
,e ,f to have precessed through the     
angle ,p from a vertical position4 ,let 
the angular velocity of rolling be      
called 4,r1 and the angular velocity of 
precession 4,p2 let the moment of       
momentum of the wheel be m4 ,for any    
vibrating body like a ship it is easy to
 write out the equation of motion2 into 
this equation we have merely to         
introduce the moment m 4,p diminishing  
,r2 into the equation for ,p we merely  
introduce the moment m 4,r increasing   
,p4 ,as usual we introduce frictional   

terms2 in the first place ,f 4,r 7,f    
being a constant co-efficient7 stilling 
the roll of the ship2 in the second case
 f 4,p a fluid friction introduced by a 
pair of dash pots applied at the pins ,a
 and ,b to still the precessional       
vibrations of the frame4 ,it will be    
found that the angular motion ,p is very
 much greater than the roll ,r4 ,indeed1
 so great is ,p that there are stops to 
prevent its exceeding a certain amount4 
,of course so long as a stop acts1      
preventing precession1 the roll of the  
ship proceeds as if the gyrostat wheel  
were not rotating4 ,mr4 ,schlick drives 
his wheels by steam2 he will probably in
 future do as ,mr4 ,brennan does1 drive 
them by electromotors1 and keep them in 
air-tight cases in good vacuums1 because
 the loss of energy by friction against 
an atmosphere is proportional to the    
density of the atmosphere4 ,the solution
 of the equations to find the nature of 
the ,r and ,p motions is sometimes      
tedious1 but requires no great amount of

 mathematical knowledge4 ,in a case     
considered by me of #ada a #f1jjj ton   
ship1 the period of a roll was increased
 from #ad to #bj seconds by the use of  
the gyrostat1 and the roll rapidly      
diminished in amount4 ,there was        
accompanying this slow periodic motion1 
one of a two seconds' period1 but if it 
did appear it was damped out with great 
rapidity4 ,of course it is assumed that1
 by the use of bilge keels and rolling  
chambers1 and as low a metacentre as is 
allowable1 we have already lengthened   
the time of vibration1 and damped the   
roll ,r as much as possible1 before     
applying the gyrostat4 ,i take it that  
everybody knows the importance of       
lengthening the period of the natural   
roll of a ship1 although he may not know
 the reason4 ,the reason why modern     
ships of great tonnage are so steady is 
because their natural periodic times of 
rolling vibration are so much greater   
than the probable periods of any waves  
of the sea1 for if a series of waves    

acts upon a ship tending to make it     
roll1 if the periodic time of each wave 
is not very different from the natural  
periodic time of vibration of the ship1 
the rolling motion may become           
dangerously great4  ,if we try to apply 
,mr4 ,schlick's method to ,mr4          
,brennan's car it is easy to show that  
there is instability of motion1 whether 
there is or is not friction4 ,if there  
is no friction1 and we make the gyrostat
 frame unstable by keeping its centre of
 gravity above the axis ,c ,d1 there    
will be vibrations1 but the smallest    
amount of friction will cause these     
vibrations to get greater and greater4  
,even without friction there will be    
instability if m1 the moment of momentum
 of the wheel1 is less than a certain   
amount4 ,we see1 then1 that no form of  
the ,schlick method1 or modification of 
it1 can be applied to solve the ,brennan
 problem4  #adb  ,illustration3 ,,fig4  
#b4  #adc ,mr4 ,brennan's method of     
working is quite different from that of 

,mr4 ,schlick4 ,fig4 #b shows his model 
car 7about six feet long72 it is driven 
by electric accumulators carried by the 
car4 ,his gyrostat wheels are driven by 
electromotors 7not shown in fig4 #c72 as
 they are revolving in nearly vacuous   
spaces they consume but little power1   
and even if the current were stopped    
they would continue running at          
sufficiently high speeds to be effective
 for a length of time4 ,still it must   
not be forgotten that energy is wasted  
in friction1 and work has to be done in 
bringing the car to a new position of   
equilibrium1 and this energy is supplied
 by the electromotors4 ,should the      
gyrostats really stop1 or fall to a     
certain low speed1 two supports are     
automatically dropped1 one on either    
side of the car2 each of them drops till
 it reaches the ground2 one of them     
dropping1 perhaps1 much farther than the
 other4  ,the real full-size car1 which 
he is now constructing1 may be pulled   
with other cars by any kind of          

locomotive using electricity or petrol  
or steam1 or each of the wheels may be a
 driving wheel4 ,he would prefer to     
generate electropower on his train1 and 
to drive every wheel with an electric   
motor4 ,his wheels are so independent of
 one another that they can take very    
quick curves and vertical inequalities  
of the rail4 ,the rail is fastened to   
sleepers lying on ground that may have  
sidelong slope4 ,the model car is       
supported by a mono-rail bogie at each  
end2 each bogie has two wheels pivoted  
both vertically and horizontally2 it    
runs on a round iron gas pipe1 and      
sometimes on steel wire rope2 the ground
 is nowhere levelled or cut1 and at one 
place the rail is a steel wire rope     
spanning a gorge1 as shown in fig4 #b4  
,it is interesting to stop the car in   
the middle of this rope and to swing the
 rope sideways to see the automatic     
balancing of the car4 ,the car may be   
left here or elsewhere balancing itself 
with nobody in charge of it4 ,if the    

load on the car--great lead weights--be 
dumped about into new positions1 the car
 adjusts itself to the new conditions   
with great #add quickness4 ,when the car
 is stopped1 if a person standing on the
 ground pushes the car sidewise1 the car
 of course pushes in opposition1 like an
 indignant animal1 and by judicious     
pushing and yielding it is possible to  
cause a considerable tilt4 ,left now to 
itself the car rights itself very       
quickly4  ,illustration3 ,,fig4 #c4     
#ade  ,illustration3 ,,fig4 #c;b        
7showing the ground-plan of ,fig4 #c74  
#adf ,fig4 #c is a diagrammatic         
representation of ,mr4 ,brennan's pair  
of gyrostats in sectional elevation and 
plan4 ,the cases ,g and ,g'1 inside     
which the wheels ,f and ,f' are rotating
 in vacuo at the same speed and in      
opposite directions 7driven by          
electromotors not shown in the figure71 
are pivoted about vertical axes ,e ,j   
and ,e' ,j'4 ,they are connected by     
spur-toothed segments ,j ,j and ,j' ,j'1

 so that their precessional motions are 
equal and opposite4 ,the whole system is
 pivoted about ,c1 a longitudinal axis4 
,thus when precessing so that ,h comes  
out of the paper1 so will ,h'1 and when 
,h goes into the paper1 so does ,h'4    
,when the car is in equilibrium the axes
 ,k ,h and ,k' ,h' are in line ,n ,o ,o'
 ,n' across the car in the plane of the 
paper4 ,they are also in a line which is
 at right angles to the total resultant 
7vertical or nearly vertical7 force on  
the car4 ,i will call ,n ,o ,o' ,n' the 
mid position4 ,let #a_/bm be the moment 
of momentum of either wheel4 ,let us    
suppose that suddenly the car finds that
 it is not in equilibrium because of a  
gust of wind1 or centrifugal force1 or  
an alteration of loading1 so that the   
shelf ,d comes up against ,h1 the       
spinning axis 7or a roller revolving    
with the spinning axis7 of the gyrostat4
 ,h begins to roll away from me1 and if 
no slipping occurred 7but there always  
is slipping1 and1 indeed1 slipping is a 

necessary condition7 it would roll1 that
 is1 the gyrostats would precess with a 
constant angular velocity alpha1 and    
exert the moment malpha upon the shelf  
,d1 and therefore on the car4 ,it is to 
be observed that this is greater as the 
diameter of the rolling part is greater4
 ,this precession continues until the   
roller and the shelf cease to touch4 ,at
 first ,h lifts with the shelf1 and     
afterwards the shelf moving downwards is
 followed for some distance by the      
roller4 ,if the tilt had been in the    
opposite direction the shelf ,d' would  
have acted upwards upon the roller ,h'1 
and caused just the opposite kind of    
precession1 and a moment of the opposite
 kind4  ,we now have the spindles out of
 their mid position2 how are they       
brought back from ,o ,q and ,o' ,q' to  
,o ,n and ,o' ,n'1 #adg but with ,h     
permanently lowered just the right      
amount8 ,it is the essence of ,mr4      
,brennan's invention that after a       
restoring moment has been applied to the

 car the spindles shall go back to the  
position ,n ,o ,o' ,n' 7with ,h         
permanently lowered71 so as to be ready 
to act again4 ,he effects this object in
 various ways4 ,some ways described in  
his patents are quite different from    
what is used on the model1 and the      
method to be used on the full-size wagon
 will again be quite different4 ,i will 
describe one of the methods4 ,mr4       
,brennan tells me that he considers this
 old method to be crude1 but he is      
naturally unwilling to allow me to      
publish his latest method4  ,d' is a    
circular shelf extending from the mid   
position in my direction2 ,d is a       
similar shelf extending from the mid    
position into the paper1 or away from   
me4 ,it is on these shelves that ,h' and
 ,h roll1 causing precession away from  
,n ,o ,o' ,n'1 as ,i have just          
described4 ,when ,h' is inside the      
paper1 or when ,h is outside the paper1 
they find no shelf to roll upon4 ,there 
are1 however1 two other shelves ,l and  

,l'1 for two other rollers ,m and ,m'1  
which are attached to the frames        
concentric with the spindles2 they are  
free to rotate1 but are not rotated by  
the spindles4 ,when they are pressed by 
their shelves ,l or ,l' this causes     
negative precession1 and they roll      
towards the ,n ,o ,o' ,n' position4     
,there is1 of course1 friction at their 
supports1 retarding their rotation1 and 
therefore the precession4 ,the important
 thing to remember is that ,h and ,h'1  
when they touch their shelves 7when one 
is touching the other is not touching7  
cause a precession away from the mid    
position ,n ,o ,o' ,n' at a rate alpha1 
which produces a restoring moment malpha
 of nearly constant amount 7except for  
slipping71 whereas where ,m or ,m'      
touches its shelf ,l or ,l' 7when one is
 touching the other is not touching7 the
 pressure on the shelf and friction     
determine the rate of the precession    
towards the mid position ,n ,o ,o' ,n'1 
#adh as well as the small vertical      

motion4 ,the friction at the supports of
 ,m and ,m' is necessary4  ,suppose that
 the tilt from the equilibrium position 
to be corrected is ,r1 when ,d presses  
,h upward4 ,the moment malpha1 and its  
time of action 7the total momental      
impulse7 are too great1 and ,r is       
over-corrected2 this causes the roller  
,m' to act on ,l'1 and the spindles     
return to the mid position2 they go     
beyond the mid position1 and now the    
roller ,h' acts on ,d'1 and there is a  
return to the mid position1 and beyond  
it a little1 and so it goes on1 the     
swings of the gyrostats out of and into 
the mid position1 and the vibrations of 
the car about its position of           
equilibrium getting rapidly less and    
less until again neither ,h nor ,h'1 nor
 ,m nor ,m' is touching a shelf4 ,it is 
indeed marvellous to see how rapidly the
 swings decay4 ,friction accelerates the
 precession away from ,n ,o ,o' ,n'4    
,friction retards the precession towards
 the middle position4  ,it will be seen 

that by using the two gyrostats instead 
of one when there is a curve on the     
line1 although the plane ,n ,o ,o' ,n'  
rotates1 and we may say that the        
gyrostats precess1 the tilting couples  
which they might exercise are equal and 
opposite4 ,i do not know if ,mr4        
,brennan has tried a single gyrostat1   
the mid position of the axis of the     
wheel being vertical1 but even in this  
case a change of slope1 or inequalities 
in the line1 might make it necessary to 
have a pair4  ,it is evident that this  
method of ,mr4 ,brennan is altogether   
different in character from that of ,mr4
 ,schlick4 ,work is here actually done  
which must be supplied by the           
electromotors4  ,one of the most        
important things to know is this3 the   
,brennan model is wonderfully           
successful2 the weight of the apparatus 
is not a large fraction of the weight of
 the wagon2 will this also be the case  
with a car weighing #a1jjj times as #adi
 much8 ,the calculation is not          

difficult1 but ,i may not give it here4 
,if we assume that suddenly the wagon   
finds itself at the angle ,r from its   
position of equilibrium1 it may be taken
 that if the size of each dimension of  
the wagon be multiplied by n1 and the   
size of each dimension of the apparatus 
be multiplied by p1 then for a sudden   
gust of wind1 or suddenly coming on a   
curve1 or a sudden shift of position of 
part of the cargo1 ,r may be taken as   
inversely proportional to n4 ,i need not
 state the reasonable assumption which  
underlies this calculation1 but the     
result is that if n is #aj1 p is #g4e4  
,that is1 if the weight of the wagon is 
multiplied by #a1jjj1 the weight of the 
apparatus is only multiplied by #dbj4   
,in fact1 if1 in the model1 the weight  
of the apparatus is #aj per cent4 of    
that of the wagon1 in the large wagon   
the weight of the apparatus is only     
about #d per cent4 of that of the wagon4
 ,this is a very satisfactory result4#ae
  ,my calculations seem to show that    

,mr4 ,schlick's apparatus will form a   
larger fraction of the whole weight of a
 ship1 as the ship is larger1 but in the
 present experimental stage of the      
subject it is unfair to say more than   
that this seems probable4 ,my own       
opinion is that large ships are         
sufficiently steady already4  ,in both  
cases it has to be remembered that if   
the diameter of the wheel can be        
increased in greater proportion than the
 dimensions of ship or wagon1 the       
proportional weight of the apparatus may
 be diminished4 ,a wheel of twice the   
diameter1 but of the same weight1 may   
have twice the moment of momentum1 and  
may therefore be twice as effective4 ,i 
assume the stresses in the material to  
be the same4         99       99        
99       99       99   #aej  ,,appendix 
,,ii4  ,page #bc2 note at line #c4      
,prof4 ,osborne ,reynolds made the      
interesting remark 7,collected ,papers1 
,vol4 ii41 p4 #aed71 ,that if solid     
matter had certain kinds of internal    

motions1 such as the box has1 pears     
differing1 say1 from apples1 the laws of
 motion would not have been discovered2 
if discovered for pears they would not  
have applied to apples4  ,page #ch2 note
 at line #h4 ,the motion of a rifle     
bullet is therefore one of precession   
about the tangent to the path4 ,the     
mathematical solution is difficult1 but 
,prof4 ,greenhill has satisfied himself 
mathematically that air friction damps  
the precession1 and causes the axis of  
the shot to get nearer the tangential   
direction1 so that fig4 #aj illustrates 
what would occur in a vacuum1 but not in
 air4 ,it is probable that this         
statement applies only to certain       
proportions of length to diameter4      
,page #abi2 note at line #e4 ,many men  
wonder how the ether can have the       
enormous rigidity necessary for light   
transmission1 and yet behave like a     
frictionless fluid4 ,one way of seeing  
how this may occur is to imagine that   
when ordinary matter moves in the ether 

it only tends to produce motion of      
translation of the ether particles1 and 
therefore no resistance4 ,but anything  
such as light1 which must operate in    
turning axes of rotating parts1 may     
encounter enormous elastic resistance4  
,richard ,clay  ,sons1 ,limited1 ,london
 and ,bungay4         99       99       
99       99       99   ,,publications   
,,of ,,the  ,,society ,,for ,,promoting 
,,christian ,,knowledge4  ,,the         
,,romance ,,of ,,science4  ,small post  
#hvo1 cloth boards4      ,,coal1 ,,and  
,,what ,,we ,,get ,,from ,,it4 ,by      
,professor ,r4 ,,meldola1 ,f4,r4,s41    
,f4,i4,c4     ,with several             
,illustrations4 #bs4 #f;d4      ,,colour
 ,,measurement ,,and ,,mixture4 ,by ,sir
 ,w4 ,,de ,w4 ,,abney1 ,k4,c4,b41       
,r4,e41     ,f4,r4,s4 ,numerous         
,illustrations4 #bs4 #f;d4              
,,diseases ,,of ,,plants4 ,by ,professor
 ,,marshall ,,ward4 ,numerous           
,illustrations4     #bs4 #f;d4          
,,our ,,secret ,,friends ,,and ,,foes4  

,by ,,percy ,,faraday ,,frankland1      
,ph4,d41 ,b4,sc4     7,lond471 ,f4,r4,s4
 ,illustrated4 #cs4                     
,,soap-,,bubbles1 ,,and ,,the ,,forces  
,,which ,,mould ,,them4 ,by ,c4 ,v4     
,,boys1 ,a4,r4,s4,m41     ,f4,r4,s4     
,illustrated4 #bs4 #f;d4      ,,sounding
 ,,the ,,ocean ,,of ,,air4 ,by ,a4      
,,lawrence ,,rotch1 ,s4,b41 ,a4,m4      
,numerous     ,illustrations4 #bs4 #f;d4
      ,,spinning ,,tops4 ,by ,professor 
,j4 ,,perry1 ,m4,e4 ,with several       
,illustrations4     #bs4 #f;d4          
,,the ,,making ,,of ,,flowers4 ,by the  
,rev4 ,professor ,,george ,,henslow1    
,m4,a41     ,f4,l4,s41 ,f4,g4,s4 ,with  
,illustrations4 #bs4 #f;d4      ,,the   
,,story ,,of ,a ,,tinder-,,box4 ,by the 
late ,,charles ,,meymott ,,tidy1 ,m4,b41
     ,m4,s41 ,f4,c4,s4 ,numerous        
,illustrations4 #bs4      ,,time ,,and  
,,tide4 ,a ,romance of the ,moon4 ,by   
,sir ,,robert ,s4 ,,ball1 ,,ll4,d4 ,with
     ,illustrations4 #bs4 #f;d4         
,,the ,,birth ,,and ,,growth ,,of       

,,worlds4 ,by the late ,professor       
,,green1 ,f4,r4,s4     ,with            
,illustrations4 #as4      ,,the ,,splash
 ,,of ,a ,,drop4 ,by ,professor ,a4 ,m4 
,,worthington1 ,f4,r4,s4 ,numerous      
,illustrations4 #as4 #f;d4      ,,the   
,,machinery ,,of ,,the ,,universe4 ,by  
,professor ,a4 ,e4 ,,dolbear1 ,a4,b41   
,a4,m41     ,m4,e41 ,ph4,d4             
,illustrated4 #bs4      ,,the ,,new     
,,state ,,of ,,matter4 ,an ,address by  
,professor ,h4 ,,pellat4 ,translated    
by ,,edmund ,,mcclure1 ,m4,a4 #as4      
,,turbines4 ,by ,engineer-,commander ,a4
 ,e4 ,,tompkins1 ,r4,n4 ,illustrated4   
#cs4     #f;d4         99       99      
99       99       99  ,,works ,,by      
,,mrs4 ,,rundle ,,charles1 ,,author ,,of
 ,the ,chronicles of the                
,schoenberg-,cotta ,family4      ,,the  
,,beatitudes4 ,thoughts for ,all        
,saints' ,day4 ,post #hvo4 ,cloth       
boards4     #as4      ,,by ,,the        
,,mystery ,,of ,,thy ,,holy             
,,incarnation4 ,post #hvo4 ,cloth       

boards4 #as4      ,,by ,,thy ,,cross    
,,and ,,passion4 ,thoughts on the words 
spoken around and on     the ,cross4    
,post #hvo4 ,cloth boards4 #as4         
,,by ,,thy ,,glorious ,,resurrection    
,,and ,,ascension4 ,easter ,thoughts4   
,post     #hvo4 ,cloth boards4 #as4     
,,by ,,the ,,coming ,,of ,,the ,,holy   
,,ghost4 ,thoughts for ,whitsuntide4    
,post #hvo4     ,cloth boards4 #as4     
,,the ,,true ,,vine4 ,post #hvo4 ,cloth 
boards4 #as4      ,,the ,,great ,,prayer
 ,,of ,,christendom4 ,thoughts on the   
,lord's ,prayer4 ,post     #hvo4 ,cloth 
boards4 #as4      ,,an ,,old ,,story    
,,of ,,bethlehem4 ,one link in the great
 ,pedigree4 ,fcap4 #dto1     with six   
plates1 beautifully printed in colours4 
,cloth boards4 #bs4      ,,joan ,,the   
,,maid1 ,deliverer of ,england and      
,france4 ,demy #hvo4 ,cloth     boards4 
#bs4 #f;d4      ,,songs1 ,,old ,,and    
,,new4 ,demy #afmo4 ,cloth boards4 #bs4 
#f;d4      ,,ecce ,,ancilla ,,domini4   
,mary the ,mother of our ,lord4 ,studies

 in the ,ideal     of ,womanhood4 ,post 
#hvo4 ,cloth boards4 #as4 #f;d4         
,,ecce ,,homo1 ,,ecce ,,rex4 ,pages from
 the ,story of the ,moral ,conquests of 
,christianity4 ,crown #hvo4 ,cloth      
boards4 #bs4 #f;d4      ,,three         
,,martyrs ,,of ,,the ,,nineteenth       
,,century4 ,studies from the ,lives of  
,gordon1 ,livingstone1 and ,patteson4   
,crown #hvo4 ,cloth boards4 #bs4 #f;d4  
,,martyrs ,,and ,,saints ,,of ,,the     
,,first ,,twelve ,,centuries4 ,studies  
from the     ,lives of the ,black-letter
 ,saints of the ,english ,calendar4     
,crown #hvo4     ,cloth boards4 #bs4    
#f;d4      ,,against ,,the ,,stream4    
,the ,story of an ,heroic ,age in       
,england4 ,with eight     page woodcuts4
 ,crown #hvo4 ,cloth boards4 #bs4 #f;d4 
,,conquering ,,and ,,to ,,conquer4 ,a   
,story of ,rome in the days of ,st4     
,jerome4     ,illustrated4 ,crown #hvo4 
,cloth boards4 #bs4      ,,attila ,,and 
,,his ,,conquerors4 ,a ,story of the    
days of ,st4 ,patrick and ,st4     ,leo 

the ,great4 ,crown #hvo4 ,cloth boards4 
#bs4      ,,te ,,deum ,,laudamus4       
,christian ,life in ,song4 ,cloth #bs4  
#f;d4      ,,early ,,christian          
,,missions ,,of ,,ireland1 ,,scotland1  
,,and ,,england4 ,crown #hvo4     ,cloth
 boards4 #bs4 #f;d4      ,,lapsed1 ,,not
 ,,lost4 ,a ,story of ,roman ,carthage4 
,crown #hvo4 ,cloth boards4     #bs4    
,,within ,,the ,,veil4 ,studies in the  
,epistle to the ,hebrews4 ,post #hvo4   
,cloth boards4 #as4      ,,the ,,book   
,,of ,,the ,,unveiling4 ,studies in the 
,revelation of ,st4 ,john the           
,divine4 ,post #hvo4 ,cloth boards4 #as4
      ,,lady ,,augusta ,,stanley4       
,reminiscences4 #ahmo4 ,limp cloth4     
#f;d4      ,,sketches ,,of ,,the ,,women
 ,,of ,,christendom4 ,crown #hvo4 #bs4  
#f;d4         99       99       99      
99       99  ,,conversion ,,of ,,the    
,,west4  ,,fcap4 #h,,vo1 ,,with ,,map1  
,,cloth ,,boards1 #b,s4 ,,each4         
,,the ,,continental ,,teutons1 by the   
late ,very ,rev4 ,c4 ,,merivale4        

,,the ,,english1 by the late ,rev4 ,g4  
,f4 ,,maclear1 ,d4,d4      ,,the        
,,northmen1 by the late ,rev4 ,g4 ,f4   
,,maclear1 ,d4,d4      ,,the ,,slavs1 by
 the late ,rev4 ,g4 ,f4 ,,maclear1      
,d4,d4         99       99       99     
99       99  ,,early ,,britain4  ,this  
,series has for its aim the presentation
 of ,early ,britain at great historic   
periods4 ,each volume is the work of an 
accredited specialist1 and the whole    
gives the result of recent critical     
examinations of our ,early ,records4    
,,anglo-,,saxon ,,britain4 ,by the late 
,,grant ,,allen4 ,with ,map4 #bs4 #f;d4 
,,celtic ,,britain4 ,by ,professor      
,,rhys4 ,with two ,maps4 #cs4           
,,norman ,,britain4 ,by the ,rev4 ,w4   
,,hunt4 ,with ,map4 #bs4                
,,post-,,norman ,,britain4 ,by ,,henry  
,g4 ,,hewlett4 ,with ,map4 #cs4         
,,roman ,,britain4 ,by the ,rev4 ,e4    
,,conybeare4 ,with ,map4 #cs4 #f;d4     
,,roman ,,roads ,,in ,,britain4 ,by     
,,thomas ,,codrington1 ,m4 ,inst4       

,c4,e41 ,f4,g4,s4     ,with ,maps4      
,second ,edition1 revised4 #es4         
,,scandinavian ,,britain4 ,by ,w4 ,g4   
,,collingwood1 ,m4,a41 ,f4,s4,a4 ,with  
,chapters     ,introductory to the      
subject by the late ,professor ,f4      
,,york ,,powell1 ,m4,a4     #cs4 #f;d4  
99       99       99       99       99  
,,the ,,dawn ,,of ,,european            
,,literature4  ,a set of ,works designed
 to present the chief races of ,europe  
as they emerge out of pre-historic      
darkness into the light furnished by    
their earliest recorded words4  ,,post  
#h,,vo1 ,,cloth ,,boards1 #b,s4 #f;,d4  
,,each4      ,,anglo-,,saxon            
,,literature4 ,by the ,rev4 ,professor  
,,earle4      ,,french ,,literature4 ,by
 the late ,,gustave ,,masson1 ,b4,a4    
,,slavonic ,,literature4 ,by ,w4 ,r4    
,,morfill1 ,m4,a4      ,,the ,,greek    
,,epic4 ,by ,,george ,c4 ,w4 ,,warr1    
,m4,a4 #cs4         99       99       99
       99       99  ,,the ,,fathers     
,,for ,,english ,,readers4  ,a ,series  

of ,monograms on the ,chief ,fathers of 
the ,church1 the ,fathers selected being
 centres of influence at important      
periods of ,church ,history1 and in     
important spheres of action4  ,,fcap4   
#h,,vo1 ,,cloth ,,boards1 #b,s4 ,,each4 
,,boniface4 ,by the ,rev4 ,canon        
,,gregory ,,smith4 #as4 #f;d4           
,,clement ,,of ,,alexandria4 ,by the    
,rev4 ,f4 ,r4 ,,montgomery ,,hitchcock1 
,b4,d4     #cs4      ,,leo ,,the        
,,great4 ,by the ,right ,rev4 ,c4       
,,gore1 ,d4,d4      ,,gregory ,,the     
,,great4 ,by the late ,rev4 ,j4         
,,barmby1 ,b4,d4      ,,saint ,,ambrose3
 his ,life1 ,times1 and ,teaching4 ,by  
the ,rev4 ,r4 ,,thornton1     ,d4,d4    
,,saint ,,athanasius3 his ,life and     
,times4 ,by the ,rev4 ,r4 ,,wheler      
,,bush4 #bs4     #f;d4      ,,saint     
,,augustine4 ,by the late ,rev4 ,e4 ,l4 
,,cutts1 ,d4,d4      ,,saint ,,basil    
,,the ,,great4 ,by the ,rev4 ,r4 ,t4    
,,smith1 ,b4,d4      ,,saint ,,bernard3 
,abbot of ,clairvaux1 ,a4,d4 #ajia-aaec4

 ,by ,rev4 ,s4 ,j4 ,,eales4     #bs4    
#f;d4      ,,saint ,,jerome4 ,by the    
late ,rev4 ,,edward ,l4 ,,cutts1 ,d4,d4 
,,saint ,,hilary ,,of ,,poitiers1 ,,and 
,,saint ,,martin ,,of ,,tours4 ,by the  
,rev4 ,j4     ,,gibson ,,cazenove1      
,d4,d4      ,,saint ,,john ,,of         
,,damascus4 ,by the ,rev4 ,j4 ,h4       
,,lupton4      ,,saint ,,patrick3 his   
,life and ,teaching4 ,by the ,rev4 ,e4  
,j4 ,,newell1 ,m4,a4     #bs4 #f;d4     
,,synesius ,,of ,,cyrene1 ,philosopher  
and ,bishop4 ,by ,,alice ,,gardner4     
,,the ,,apostolic ,,fathers4 ,by the    
,rev4 ,canon ,,scott ,,holland4         
,,the ,,defenders ,,of ,,the ,,faith2   
or1 ,the ,christian ,apologists of the  
,second     and ,third ,centuries4 ,by  
the ,rev4 ,f4 ,,watson1 ,d4,d4          
,,the ,,venerable ,,bede4 ,by the ,right
 ,rev4 ,g4 ,f4 ,,browne4         99     
99       99       99       99  ,,the    
,,history ,,of ,,the ,,ancient ,,peoples
 ,,of ,,the ,,classic ,,east4  ,by      
,professor ,,maspero4 ,edited by the    

,rev4 ,professor ,,sayce4 ,translated by
 ,m4 ,l4 ,,mcclure4 ,each volume        
contains ,maps1 coloured ,plates1 and   
numerous other ,illustrations4  ,,demy  
#d,,to1 ,,cloth1 ,,bevelled ,,boards4   
,volume ,i4 ,,the ,,dawn ,,of           
,,civilization3 ,,egypt ,,and           
,,chaldaea4 ,fourth ,edition4     #bds42
 half-morocco1 #dhs4      ,volume ,,ii4 
,,the ,,struggle ,,of ,,the ,,nations3  
,,egypt1 ,,syria1 ,,and ,,assyria4      
#bes42 half-morocco1 #ejs4      ,volume 
,,iii4 ,,the ,,passing ,,of ,,the       
,,empires1 #hej ,b4,c4-#ccj ,b4,c4      
#bes42     half-morocco1 #ejs4          
99       99       99       99       99  
,,ancient ,,history ,,from ,,the        
,,monuments4  ,,fcap4 #h,,vo1 ,,cloth   
,,boards1 #b,s4 ,,each4      ,,assyria1 
,,from ,,the ,,earliest ,,times ,,to    
,,the ,,fall ,,of ,,nineveh4 ,by the    
late     ,,george ,,smith1 of the       
,british ,museum4 ,a ,new and ,revised  
,edition1 by the     ,rev4 ,professor   
,,sayce4      ,,sinai1 ,,from ,,the     

,,fourth ,,egyptian ,,dynasty ,,to ,,the
 ,,present ,,day4 ,by the late          
,,henry ,s4 ,,palmer4 ,a ,new ,edition1 
revised throughout by the ,rev4         
,professor ,,sayce4 ,with ,map4         
,,babylonia 7,,the ,,history ,,of74 ,by 
the late ,,george ,,smith4 ,edited and  
brought up to date by the ,rev4         
,professor ,,sayce4      ,,persia1      
,,from ,,the ,,earliest ,,period ,,to   
,,the ,,arab ,,conquest4 ,by the late   
,w4     ,s4 ,w4 ,,vaux1 ,m4,a4 ,a ,new  
and ,revised ,edition1 by the ,rev4     
,professor     ,,sayce4         99      
99       99       99       99      ,,the
 ,,higher ,,criticism ,,and ,,the       
,,verdict ,,of ,,the ,,monuments4 ,by   
the ,rev4     ,professor ,a4 ,h4        
,,sayce4 ,demy #hvo4 ,buckram1 bevelled 
boards1 #es4         99       99        
99       99       99  ,,chief ,,ancient 
,,philosophies4  ,this ,series deals    
with the chief systems of ,ancient      
,thought1 not merely as dry matters of  
,history1 but as having a bearing on    

,modern ,speculation4  ,,fcap4 #h,,vo1  
,,cloth ,,boards1 #b,s4 #f;,d4 ,,each4  
,,neoplatonism4 ,by the ,rev4 ,c4       
,,bigg1 ,d4,d4 #cs4      ,,platonism4   
,by the ,rev4 ,,thomas ,b4 ,,strong1    
,m4,a4 #cs4      ,,epicureanism4 ,by the
 late ,professor ,,william ,,wallace4   
,,stoicism4 ,by ,rev4 ,w4 ,w4 ,,capes1  
,fellow of ,hertford ,college4          
,,aristotelianism4 ,,the ,,ethics ,,of  
,,aristotle4 ,by the ,rev4 ,i4 ,,gregory
 ,,smith4     ,the ,logical ,treatises1 
the ,metaphysics1 the ,psychology1 the  
,politics4     ,by the ,rev4 ,w4        
,,grundy4         99       99       99  
99       99  ,,diocesan ,,histories4    
,this ,series furnishes a perfect       
,library of ,english ,ecclesiastical    
,history4 ,each volume is complete in   
itself1 and the possibility of          
repetition has been carefully guarded   
against4  ,,fcap4 #h,,vo1 ,,with ,,map1 
,,cloth ,,boards4      ,,bath ,,and     
,,wells4 ,by the ,rev4 ,w4 ,,hunt4 #bs4 
#f;d4      ,,canterbury4 ,by the late   

,rev4 ,r4 ,c4 ,,jenkins4 #cs4 #f;d4     
,,carlisle4 ,by the late ,,richard ,s4  
,,ferguson4 #bs4 #f;d4      ,,chester4  
,by the ,rev4 ,,rupert ,h4 ,,morris4    
,with ,map4 #cs4      ,,chichester4 ,by 
the late ,very ,rev4 ,w4 ,r4 ,w4        
,,stephens4 ,with ,map and ,plan4       
#bs4 #f;d4      ,,durham4 ,by ,rev4 ,j4 
,l4 ,,low4 ,with ,map and ,plan4 #bs4   
,,hereford4 ,by the late ,rev4 ,canon   
,,phillpott4 #cs4      ,,lichfield4 ,by 
the ,rev4 ,w4 ,,beresford4 #bs4 #f;d4   
,,lincoln4 ,by the late ,rev4 ,canon ,e4
 ,,venables1 and the late ,ven4         
,,archdeacon ,,perry4 ,with ,map4 #ds4  
,,llandaff4 ,by the ,rev4 ,e4 ,j4       
,,newell1 ,m4,a4 ,with ,map4 #cs4 #f;d4 
,,norwich4 ,by the ,rev4 ,a4 ,,jessopp1 
,d4,d4 #bs4 #f;d4      ,,oxford4 ,by the
 ,rev4 ,e4 ,,marshall4 #bs4 #f;d4       
,,peterborough4 ,by the ,rev4 ,g4 ,a4   
,,poole1 ,m4,a4 #bs4 #f;d4              
,,rochester4 ,by the ,rev4 ,a4 ,j4      
,,pearman4 ,with ,map4 #ds4             
,,salisbury4 ,by the ,rev4 ,w4 ,h4      

,,jones4 ,with ,map4 #bs4 #f;d4         
,,sodor ,,and ,,man4 ,by ,a4 ,w4        
,,moore1 ,m4,a4 #cs4      ,,st4 ,,asaph4
 ,by the ,ven4 ,archdeacon ,,thomas4    
#bs4      ,,st4 ,,david',s4 ,by the     
,rev4 ,canon ,,bevan4 ,with ,map4 #bs4  
#f;d4      ,,winchester4 ,by the ,rev4  
,w4 ,,benham1 ,b4,d4 #cs4               
,,worcester4 ,by the ,rev4 ,i4 ,,gregory
 ,,smith and ,rev4 ,,phipps ,,onslow4   
#cs4     #f;d4      ,,york4 ,by the     
,rev4 ,canon ,,ornsby1 ,m4,a41 ,f4,s4,a4
 #cs4 #f;d4         99       99       99
       99       99  ,,early ,,church    
,,classics4  ,,small ,,post #h,,vo1     
,,cloth ,,boards4      ,a ,,homily ,,of 
,,clement ,,of ,,alexandria1 entitled1  
,who is the ,rich ,man that     is      
,being ,saved8 ,by ,rev4 ,p4 ,,mordaunt 
,,barnard4 #as4      ,,bishop           
,,sarapion',s ,,prayer-,,book3 ,an      
,egyptian ,pontifical dated probably    
about #cej-cef ,a4,d4 ,translated from  
the ,edition of ,dr4 ,g4 ,,wobbermin4   
,with ,introduction1 ,notes1 and        

,indices1 by the ,right ,rev4 ,,john    
,,wordsworth1 ,d4,d4 #as4 #f;d4         
,,origen ,,the ,,teacher4 ,being the    
,address of ,gregory the ,wonder-,worker
 to     ,origen1 together with ,origen's
 ,letter to ,gregory4 ,translated1 with 
an     ,introduction and ,notes1 by the 
,rev4 ,w4 ,,metcalfe1 ,d4,d4 #as4 #f;d4 
,,st4 ,,cyprian ,,on ,,the ,,lord',s    
,,prayer4 ,an ,english ,translation1    
with     ,introduction by the ,ven4     
,archdeacon ,t4 ,h4 ,,bindley1 ,d4,d4   
#as4 #f;d4      ,,st4 ,,polycarp1       
,,bishop ,,of ,,smyrna4 ,by the late    
,rev4 ,,blomfield ,,jackson1     ,m4,a4 
#as4      ,,the ,,doctrine ,,of ,,the   
,,twelve ,,apostles4 ,translated into   
,english1 with     ,introduction and    
,notes1 by the ,rev4 ,,charles ,,bigg1  
,d4,d4 #as4      ,,the ,,epistle ,,of   
,,st4 ,,clement1 ,,bishop ,,of ,,rome4  
,by the ,rev4 ,,john ,a4 ,f4            
,,gregg1 ,m4,a4 #as4      ,,st4         
,,augustine',s ,,treatise ,,on ,,the    
,,city ,,of ,,god4 ,by ,rev4 ,f4 ,r4 ,m4

     ,,hitchcock1 ,m4,a41 ,b4,d4 #as4   
#f;d4      ,,st4 ,,chrysostom ,,on ,,the
 ,,priesthood4 ,by the ,rev4 ,t4 ,,allen
 ,,moxom1 ,m4,a4     #bs4      ,,the    
,,apostolical ,,constitutions ,,and     
,,cognate ,,documents1 with special     
reference to their ,liturgical          
,elements4 ,by the ,rev4 ,,de ,,lacy    
,o',,leary1     ,m4,a4 #as4      ,,the  
,,epistle ,,of ,,diognetus4 ,by the     
,rev4 ,l4 ,b4 ,,radford1 ,m4,a4 #as4    
#f;d4      ,,the ,,epistle ,,of ,,the   
,,galilean ,,churches3 ,lugdunum and    
,vienne4 ,with an     ,appendix         
containing ,tertullian's ,address to    
,martyrs and the ,passion of     ,st4   
,perpetua4 ,translated1 with            
,introduction and ,notes1 by ,ven4      
,archdeacon ,t4 ,h4 ,,bindley1 ,d4,d4   
#as4      ,,the ,,epistles ,,of ,,st4   
,,ignatius1 ,,bishop ,,of ,,antioch4 ,by
 ,rev4 ,j4 ,h4 ,,srawley1     ,m4,a4 ,in
 two volumes4 #as4 each4      ,,the     
,,liturgy ,,of ,,the ,,eighth ,,book    
,,of ,,the ,,apostolic ,,constitutions1 

commonly called the ,clementine         
,liturgy4 ,translated into ,english1    
with     ,introduction and ,notes1 by   
,rev4 ,r4 ,h4 ,,cresswell1 ,m4,a4 #as4  
#f;d4      ,,the ,,shepherd ,,of        
,,hermas4 ,by the late ,rev4 ,c4        
,,taylor1 ,d4,d4 ,vols4 ,i4 and         
,,ii4 #bs4 each4         99       99    
99       99       99  ,,non-,,christian 
,,religious ,,systems4  ,fcap4 #hvo1    
cloth boards1 #bs4 #f;d4 each4          
,,buddhism3 being a sketch of the ,life 
and ,teachings of ,gautama1 the         
,buddha4 ,by ,t4 ,w4 ,,rhys ,,davids1   
,m4,a4 ,with ,map4      ,,buddhism ,,in 
,,china4 ,by the ,rev4 ,s4 ,,beal4 ,with
 ,map4      ,,confucianism ,,and        
,,taouism4 ,by ,sir ,,robert ,k4        
,,douglas1 of the ,british     ,museum4 
,with ,map4      ,,hinduism4 ,by the    
late ,sir ,m4 ,,monier-,,williams1      
,m4,a41 ,d4,c4,l4 ,with ,map4           
,,islam ,,and ,,its ,,founder4 ,by ,j4  
,w4 ,h4 ,,stobart4 ,with ,map4          
,,islam ,,as ,a ,,missionary ,,religion4

 ,by ,,charles ,r4 ,,haines4 #bs4       
,,the ,,coran3 its ,composition and     
,teaching1 and the ,testimony it bears  
to     the ,holy ,scriptures4 ,by ,,sir 
,,william ,,muir1 ,k4,c4,s4,i4          
,,the ,,historical ,,development ,,of   
,,the ,,quran4 ,by the ,rev4 ,,edward   
,,sell1 ,d4,d41     ,m4,r4,a4,s4        
,,the ,,religion ,,of ,,the ,,crescent1 
,,or ,,islam3 its ,strength1 its        
,weakness1 its     ,origin1 its         
,influence4 ,by the ,rev4 ,w4 ,,st4     
,,clair ,,tisdall1 ,m4,a4 #ds4          
,,studies ,,of ,,non-,,christian        
,,religions4 ,by ,,eliot ,,howard4      
99       99       99       99       99  
,,colonial ,,church ,,histories4  ,fcap4
 #hvo1 with ,map1 cloth boards4         
,,diocese ,,of ,,mackenzie ,,river1 by  
the ,right ,rev4 ,w4 ,c4 ,,bompas1      
,d4,d41     ,bishop of the ,diocese4    
#bs4      ,,new ,,zealand1 by the late  
,very ,rev4 ,,henry ,,jacobs1 ,d4,d41   
,dean of     ,christchurch4 ,containing 
the ,dioceses of ,auckland1             

,christchurch1     ,dunedin1 ,nelson1   
,waiapu1 ,wellington and ,melanesia4    
#es4      ,,history ,,of ,,the ,,church 
,,in ,,eastern ,,canada ,,and           
,,newfoundland1 by the ,rev4     ,j4    
,,langtry4 #cs4      ,,the ,,church ,,in
 ,,the ,,west ,,indies1 by the ,rev4 ,a4
 ,,caldecott1 ,b4,d4 #cs4 #f;d4         
,,the ,,story ,,of ,,the ,,australian   
,,church1 by the ,rev4 ,e4 ,,symonds4   
#bs4 #f;d4         99       99       99 
99       99  ,,london3 ,,northumberland 
,,avenue1 ,w4,c4 #dc ,,queen ,,victoria 
,,street1 ,e4,c4         99       99    
99       99       99   ,notes  #a ,the  
,operatives' ,lecture is always well    
advertised in the streets beforehand by 
large posters4  #b ,bulwer ,lytton's    
,coming ,race4  #c ,the glass vessel    
ought to be broader in comparison with  
its height4  #d ,in #agdf ,benjamin     
,robins taught the principles of rifling
 as we know them now4 ,he showed that   
the spin of the round bullet was the    
most important thing to consider4 ,he   

showed that even the bent barrel of a   
gun did not deflect the bullet to       
anything like the extent that the spin  
of the bullet made it deflect in the    
opposite direction4  #e ,,note4--,in    
,fig4 #af the axis is shown inclined1   
but1 only that it would have been more  
troublesome to illustrate1 ,i should    
have preferred to show the precession   
occurring when the axis keeps           
horizontal4  #f ,when this lecture      
containing the above statement was in   
the hands of the printers1 ,i was       
directed by ,prof4 ,fitzgerald to the   
late ,prof4 ,jellet's ,treatise on the  
,theory of ,friction1 published in      
#ahgb1 and there at page #ah ,i found   
the mathematical explanation of the     
rising of a top4  #g ,roughly1 the      
,inertia or ,mass of a body expresses   
its resistance to change of mere        
translational velocity1 whereas1 the    
,moment of ,inertia of a body expresses 
its resistance to change of rotational  
velocity4  #h ,it is a very unlikely1   

and certainly absurd-looking1           
hypothesis1 but it seems that it is not 
contradicted by any fact in spectrum    
analysis1 or even by any probable theory
 of the constitution of the interstellar
 ether1 that the stars are merely images
 of our own sun formed by reflection at 
the boundaries of the ether4  #i ,sir   
,william ,thomson has performed this4   
#aj ,it must be remembered that in one  
case ,i speak of the true north1 and in 
the other of the magnetic north4  #aa   
,rotating a large mass of iron rapidly  
in one direction and then in the other  
in the neighbourhood of a               
delicately-suspended magnetic needle1   
well protected from air currents1 ought1
 ,i think1 to give rise to magnetic     
phenomena of very great interest in the 
theory of magnetism4 ,i have hitherto   
failed to obtain any trace of magnetic  
action1 but ,i attribute my failure to  
the comparatively slow speed of rotation
 which ,i have employed1 and to the want
 of delicacy of my magnetometer4  #ab ,i

 had applied for a patent for this      
system of signalling some time before   
the above words were spoken1 but        
although it was valid ,i allowed it to  
lapse in pure shame that ,i should have 
so unblushingly patented the use of the 
work of ,fitzgerald1 ,hertz1 and ,lodge4
  #ac ,how to see by electricity is     
perfectly well known1 but no rich man   
seems willing to sacrifice the few      
thousands of pounds which are necessary 
for making the apparatus4 ,if ,i could  
spare the money and time ,i would spend 
them in doing this thing--that is1 ,i   
think so--but it is just possible that  
if ,i could afford to throw away three  
thousand pounds1 ,i might feel greater  
pleasure in the growth of a great       
fortune than in any other natural       
process4  #ad ,probably first described 
by ,mr4 ,brennan4  #ae ,the weight of   
,mr4 ,brennan's loaded wagon is #cac    
lb41 including gyrostats and storage    
cells4 ,his two wheels weigh #ac lb4 ,if
 made of nickel steel and run at their  

highest safe speed they would weigh much
 less4         99       99       99     
99       99   ,changes made against     
printed original4  ,page #ia4 all that  
we should have to take into account3    
duplicated 'that' in original4  ,page   
#aej4 applied to apples3 'applied to    
applies' in original4  ,advertisements4 
,persia 444 by the ,rev4 ,professor     
,sayce3 ',professsor' in original4