,the ,growth of a ,crystal              
,,being ,,the                           
,,eighteenth ,,robert ,,boyle ,,lecture 
,,delivered ,,before                    
,,the ,,oxford ,,university ,,junior    
,,scientific ,,club                     
,on the #bjth of ,may1 #aiaa            
,,by                  ,,henry ,a4       
,,miers1 ,m4,a41 ,d4,,sc4 7,,oxon471    
,f4,r4,s4                               
,,principal ,,of ,,london ,,university  
,,london3 ,,henry ,,frowde1 ,,amen      
,,corner1 ,e4,c4        ,,edinburgh3 #ab
 ,,frederick ,,street4 ,,glasgow3 #ajd  
,,west ,,george ,,street                
,,oxford3 #aaf ,,high ,,street          
,,new ,,york3 #bi-ce ,,west #cb,,nd     
,,street                    ,,toronto3  
#be-bg ,,richmond ,,street ,,west       
,,melbourne3 ,,cathedral ,,buildings1   
#bje ,,flinders ,,lane                  
#aiaa                                   
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--------------------------------        
,,oxford3 ,,horace ,,hart               

,,printer ,,to ,,the ,,university       
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--------------------------------        
,,the ,,growth ,,of ,a ,,crystal        
,when this date was fixed by your       
,secretary for the delivery of the      
,,boyle  ,lecture1 ,i discovered that it
 happened to be the fifteenth           
anniversary  of the very day on which ,i
 was first called upon to address a     
general  audience in ,oxford4 ,on ,may  
#bj1 #ahif1 ,i delivered an inaugural   
lecture as  ,waynflete ,professor of    
,mineralogy2 when ,i look back upon the 
happy years  spent here in teaching and 
studying a science which is dear to me1 
,i  feel that the present lecture should
 be an opportunity for expressing       
gratitude for those peaceful years1 not 
unmingled with regret that they  led to 
no such worthy achievement on my part as
 might have brought great  credit to the
 ,university and so have repaid         
something of the debt which  ,i owe to  
her4    ,looking back from the busier   

world of ,london1 it is easy to see how 
ideal are the conditions under which an 
,oxford ,professor conducts his  work2  
especially if his subject be one which  
does not overwhelm him with  students   
who pursue it only for the purpose of   
passing an examination4  ,those who are 
attracted to his ,laboratory probably   
come because they  have some natural    
taste for the subject2 he finds it a    
pleasure to  devote his time to them2   
while his vacations and the conditions  
of  ,oxford life give him unique        
opportunities for his own researches4   
,it is true that those who have most    
leisure not infrequently waste most     
time4 ,it is true also that the custom  
of ,oxford is to burden her  students   
and scholars in addition to their       
teaching1 with the conduct of  affairs  
which could be managed as well by       
persons specially appointed  for the    
purpose4 ,still it is also certain that 
to those who enter into  the genius of  
the place1 and are animated by the      

spirit of ,learning1  ,oxford is        
prodigal of opportunity1 and enables    
them to live the ,academic  ,life in a  
way which is scarcely possible          
elsewhere4    ,i know that the doors of 
the ,university are being opened to all 
the  newer studies1 and that many a     
student spends most of his time in      
acquiring the useful knowledge that is  
to equip him for his profession  and for
 the direct purpose of that profession2 
knowledge which is to fit  him to become
 lawyer1 doctor1 minister1 engineer1 or 
teacher2 yet an  ,oxford ,professor may 
always maintain the pursuit of ,learning
 for its own  sake and keep this purpose
 before his students even in their most 
technical work4    ,now ,mineralogy is  
one of those sciences whose practical   
applications are  clear2 it is necessary
 to the miner and the engineer2 indeed1 
it sprang  from their needs2 even       
,crystallography 7that is1 the study of 
,crystals71  which has always hitherto1 
though with little reason1 been treated 

for  ,university purposes as a branch of
 ,mineralogy1 has also become part of   
the necessary equipment of the practical
 chemist and geologist2 but both        
,sciences are1 in their general aspects1
 very far removed from the  turmoil of  
practical life2 it is with these aspects
 that ,i would fain  deal1 and          
especially in relation to the study of  
crystals4    ,in this connexion1 a      
passage which ,i quoted from ,,goethe   
fifteen years  ago will bear repetition3
 #8,there is a flavour1' he says1 #8of  
the ,monk  or of the old ,bachelor about
 ,crystallography and therefore it is   
self-sufficient4 ,practical application 
in life it has none2 its rarest         
objects1 the crystallized precious      
stones1 have to be cut and polished     
before we can adorn our ladies with     
them4'    ,in fact1 this lecture1 which 
,i was constrained to prepare during a  
brief  holiday in ,italy1 was written in
 the midst of surroundings where it was 
easier to think of ,science as          

cultivated in the quiet of the          
,laboratory1  rather than in the        
restless scenes of its practical        
applications1  although ,i am familiar  
with both4 ,writing at a window         
overlooking the  mediaeval town and     
ancient walls of ,perugia1 with the view
 of peaceful  ,assisi and the snowy cap 
of ,monte ,subasio across the plain1 it 
was  easier to recall the hours of quiet
 toil and reflection spent in one's     
,laboratory at ,oxford than visits to   
,mining ,camp1 or ,metallurgical ,works4
    ,accordingly when1 under these      
circumstances1 ,i set about choosing a  
subject for the present occasion1 it    
occurred to me that ,i might be  allowed
 to take up my discourse where ,i laid  
it down in #ahif and in some  sense to  
continue and conclude the remarks which 
,i then made to the  ,university2 and1  
considering how recently ,i have left   
you1 ,i might  regard this as my        
farewell address corresponding to the   
opening lecture  which ,i then          

delivered4    ,in that address1 ,i      
recollect1 ,i began with an inquiry into
 the  resemblances and differences      
between minerals and other objects of   
nature in respect of their beauty1      
especially as regards the beauty of     
form which is so specially              
characteristic of minerals4 ,some       
minerals1  indeed1 are found in delicate
 fronds and leaflets1 and in mossy      
tufts1  which1 in their form and        
texture1 in their sheen and lustre1 so  
closely  resemble plants that they are  
often mistaken for them4 ,those who     
heard  ,,ruskin',s lectures will        
remember the delight with which he      
described  these beauties of the mineral
 kingdom and the affection which he felt
  for them4 ,i pointed out1 ,i remember1
 that these delicate forms are1  like   
the frost patterns on a window-pane1    
really expressions of the  crystalline  
shape and symmetry of the mineral2 each 
mineral consists of  crystals1 and      
therefore has its own peculiar          

crystalline shape which is  one of its  
inherent properties2 moreover1 this     
persists unchanging  through the ages1  
and under all conditions1 and is in no  
way dependent  upon the environment in  
which the mineral is situated4    ,the  
shape of a crystal does not depend like 
that of the animal or the  plant upon   
the life which its forefathers have led 
or the conditions  under which they have
 grown4    ,there are indeed other      
features in which a mineral or any      
crystal may  resemble a living thing in 
a way even more surprising than in its  
form4  ,two of the most remarkable are  
these3 it grows out of a solution as    
though it were alive2 and1 if it is     
wounded or broken1 it heals itself  and 
replaces the missing part just as a     
living organism may do4 ,but1 as  ,i    
pointed out1 there is this radical      
difference4 ,the crystal is not         
responsive to the change of its         
surroundings2 its form is not the result
  of external forces2 it does not adapt 

itself to its environment2 it is  not   
undergoing any progressive evolution2   
but remains fixed and  unchanging4 ,its 
form is the expression of its permanent 
composition1 and  so far as we know has 
always been the same4 ,indeed1 until it 
has been  converted into its constituent
 elements and destroyed1 it is in a     
sense  not only unchanging1 but         
imperishable4 ,for1 take a crystal and  
break or  dissolve it away until only   
the tiniest fragment remains2 that      
fragment  7e4 g4 sugar71 though it may  
be only an invisible speck1 will1 if    
immersed in the appropriate solution1   
continue to grow again and will  once   
more assume the form of a perfect       
crystal4 ,neither does it make any      
difference if the crystal fragment has  
been kept for years or even  centuries2 
it will1 when supplied with nourishment 
from the appropriate  solution1 heal    
itself and continue to grow as though   
the process had  never been suspended4  
,in a sense it is immortal1 for1 if not 

destroyed1  it never loses the          
mysterious power of growth1 and is      
therefore more  imperishable than any   
seed or germ of life4    ,the main      
conclusion of my lecture was that1      
having been led by analogy  to compare  
the growing crystal with the growing    
plant1 one finds the  growth and life of
 the crystal to be totally unlike the   
growth and life  of any organism4 ,its  
life is only an unchanging persistence  
without the  display of any struggle for
 existence1 any movement1 any           
adaptation1 or  response to environment2
 its growth is only the addition of new 
material  on the surface of the old1    
without assimilation1 so that the       
crystal  remains uniform and increases  
in size2 there is no distinction of any 
one part from any other2 the crystal    
grows1 therefore1 without the           
development of any organs4    ,one      
appears to be left with the conclusion  
that the crystal should be  regarded    
rather as a type of death than of       

immortality4    ,,schopenhauer expressed
 this idea when he said3 #8,the crystal 
has only  one manifestation of life1    
crystallization1 which afterwards has   
its  fully adequate and exhaustive      
expression in the rigid form--the corpse
 of  that momentary life4'    ,this1    
however1 is not the conclusion which ,i 
would have you draw from  the facts2 and
 ,i shall ask you on the present        
occasion to accompany me  in pursuing a 
little further the inquiry into what we 
may call the  vitality of a crystal and 
the manner in which it is displayed2    
although  this vitality is not to be    
confounded in any way with that of a    
living  plant or creature4    ,it is1 ,i
 hope1 not unfitting that the subject of
 crystal growth should  be dealt with in
 a ,,boyle ,lecture1 for ,,robert       
,,boyle was himself one of  the first to
 treat it in a scientific spirit4 ,he   
was the exact  contemporary of ,,nicolas
 ,,steno1 the famous ,danish physician  
who laid the  foundation of modern      

crystallography2 and ,,boyle1 in his    
treatise on the  origin and virtues of  
gems1 was the first to express the      
conviction  which was almost            
simultaneously expressed by             
,,steno--that gems must have  solidified
 from the liquid state4 ,one of his     
reasons for thinking so was  their      
crystalline form1 which resembles that  
of salts which crystallize  from        
solutions4 ,let me quote his exact      
words3 #8,the origin assigned to  gems  
may be countenanced by the external     
figuration of divers of them4  ,for we  
plainly see that the corpuscles of      
nitre1 alum1 vitriol1 and even  common  
salt1 being suffered to coagulate in the
 liquors they swam in  before1 will     
convene into crystals of curious and    
determinate shapes4'  ,and then he      
points out that when a salt such as     
nitre crystallizes in a  vessel it is   
only where it is free to grow in the    
liquid1 and away from  contact with the 
sides of the vessel1 that it can acquire

 this shape4  ,these crystals 7he says71
 #8having a fluid ambient to shoot in1  
will  have those parts of their bodies  
that are contiguous to the liquor       
curiously formed into such prismatical  
shapes as are proper to nitre4'    ,when
 ,,boyle wrote these words he had not   
seen the work of ,,steno1 which  had    
just been published4    ,i may1         
therefore1 claim that he was the first  
person to deal in a  scientific spirit  
with the subject which ,i have chosen   
for this lecture1  the #8,growth of a   
,crystal4'    ,three years before ,i    
came back to ,oxford--on ,may #afth1    
#ahic1 the subject  of crystal structure
 had been treated in the second ,,boyle 
,lecture in a  most original and        
masterly manner by no less a person than
 ,,lord ,,kelvin4  ,i well remember that
 ,lecture1 at which ,i had the good     
fortune to be  present2 and to one who  
was already interested in crystals it   
was a  wonderfully illuminating and     
inspiring address4    ,on that occasion 

my venerable predecessor and teacher1   
,professor ,,story  ,,maskelyne1        
conducted ,,lord ,,kelvin to the lecture
 table4#a      ,footnote #a3 ,it is with
 the deepest regret that ,i add that my 
old friend  and revered teacher died on 
the very day on which these words were  
spoken4--,h4 ,a4 ,m4      ,at that time1
 however1 there was no laboratory in    
,oxford for  mineralogical and          
crystallographical research2 the        
,professor only had a  lecture-room1 he 
did not reside in ,oxford1 and his      
scientific work was  necessarily carried
 on elsewhere4 ,to-day ,i am more       
fortunate in being  able to draw upon   
the resources of the well-equipped      
laboratory of my  successor1 and former 
pupil1 ,professor ,,bowman1 and upon his
 still more  valuable personal          
assistance and that of ,mr4 ,,barker2 so
 that1 though ,i  only have to deal with
 ideas that are simple compared with    
those which  issued with fiery vigour   
from the fertile brain of the ,,boyle   

,lecturer of  #ahic1 ,i have a better   
opportunity of showing to an ,oxford    
audience  to-day the actual things of   
which ,i am speaking1 and may help to   
make my  meaning clear to those who     
cannot know much from personal          
experience  concerning the growth of    
crystals4#b ,when ,i delivered my own   
inaugural  lecture ,i had no means of   
making visible to an audience the       
astonishing  features of crystal growth4
 ,beautiful effects may easily be       
witnessed by  anyone with a few drops of
 common solution and a magnifying glass1
 yet ,i  believe that they are witnessed
 by comparatively few persons4          
,footnote #b3 ,this lecture was         
beautifully illustrated by excellent    
slides showing the actual growth of     
crystals4--,,ed4      ,i have alluded to
 laws of crystalline structure1 to which
 ,,lord ,,kelvin  had directed          
attention3 these are the laws of        
geometrical arrangement  which prove    
crystals to be constructed in an        

entirely different manner  from the     
living plants which they may so closely 
resemble2 these laws1  however1 were not
 established by observations or         
experiments upon the  growth of         
crystals4 ,they were the result of a    
century of patient  measurements of the 
external shape of countless crystals2   
more than a  century of accurate        
determinations of what happens when heat
 and light  are transmitted through them
 and of numberless other experiments    
made by  physicists2 and1 added to this1
 the labours of mathematicians who      
studied the manner in which solid       
particles could be arranged so as to    
correspond to the geometrical and       
physical proportions thus determined  by
 experiment4    ,but all these were     
experiments and reasoning upon matter   
which appears  to be as nearly as       
possible inert2 they entirely ignore the
 power of  growth possessed by crystals2
 indeed1 no such power is contemplated  
by  the ordinary theories of crystal    

structure or could be predicted from    
them4    ,so far1 then1 we may regard   
the comparison of crystals with plants  
and  all the fanciful ideas concerning  
their connexion with the origin of  life
 which were suggested by that comparison
 as only one more example of  the       
dangers of reasoning from analogy4 ,the 
recollections that ,i retain  of the    
allusions to that process--in text-books
 of logic and treatises on  ,science    
alike--give me the impression that      
examples of reasoning from  analogy are 
generally quoted only as instances of   
its danger and  futility4 ,that1 indeed1
 might seem to be the conclusion of my  
own  inaugural lecture2 for1 when we    
come to examine the growth and structure
  of crystals1 so far from finding that 
there is any real likeness to the  life 
and structure of the plants which they  
resemble1 we find nothing  but a        
profound difference4    ,that1 however1 
is not my real opinion1 and was not my  
opinion fifteen  years ago4 ,on the     

contrary1 ,i have the greatest belief in
 analogy as one  of the most useful     
guides to discovery1 and as the means by
 which in  practice new lines of        
investigation are most frequently opened
 and new  hypotheses suggested4 ,in     
fact1 ,i think that most of the advances
 which  are made in science1 and        
especially in scientific theory1 have   
been made  with the help of analogies4  
,if an explanation of any fact in       
,nature consists in correlating it with 
some apparently distinct fact1 and      
showing that the two have a common      
cause1 or are connected in a definite   
manner1 how often has the  explanation  
of a new occurrence been suggested by   
the analogy of some  other known        
occurrence which is brought to mind by  
the memory2 not by a  conscious effort  
of the reason1 but by the recollection  
of a  resemblance4 ,do not some of the  
standard methods which are familiar in  
the descriptions or criticisms of       
scientific discovery1 such as           

#8reasoning from the known to the       
unknown'1 #8the adoption of a working   
hypothesis'1 #8the scientific use of the
 imagination'1 often resolve  themselves
 on analysis into the simple process of 
being struck by an  analogy and being   
led by it to adopt an explanation or to 
try an  experiment suggested by it8     
,i daresay that scientific discoverers  
are ashamed to confess that they  may   
have been led to a theory by a          
superficial analogy just as they are    
ashamed to confess that they have hit   
upon a discovery or an invention  by    
chance1 and have found one thing when   
they were looking for another4  ,but    
there is no need to be ashamed1 for the 
discoveries only come to  those who have
 the eyes to see1 or the knowledge which
 enables them to  remember a            
resemblance1 and who have further the   
intellectual power to  make use of it4  
,science grows on the acquisition of new
 knowledge and we  must not hesitate to 
grasp it where we can4 ,there is a      

danger lest the  formulation of the     
methods of science may deter the        
inquisitive student  from seeking       
knowledge wherever it is to be found1   
and make him believe  that it is only by
 the orthodox processes of reasoning    
based upon a  lifetime of training that 
he is to discover anything new4 ,rather 
let him  be encouraged to seek any      
resemblance or analogy that may point a 
way in  the gloom4    ,it is true that  
in the past the argument from analogy   
has often proved  dangerous when1       
because the things possess certain      
attributes in common1  it was inferred  
that they are alike in other respects4  
,yet even here it  may prove useful4    
,,newton only asserted that the diamond 
is inflammable  because it resembles    
other inflammable substances in         
possessing a high  refractive power2 and
 yet he turned out to be right1 although
 his  analogy was wrong4 ,moreover1 it  
was the analogy which prompted the      
experiment4 ,to detect an analogy1 to   

test it1 and to find that it cannot  be 
maintained1 may be as useful an addition
 to knowledge as the  establishment of a
 real causal relationship3 it has had   
the effect of  setting the worker on to 
new experiments or observations1 and    
every such  step is necessarily an      
advance4 ,the conscientious search for  
one thing  almost invariably leads to   
the discovery of another2 and1 even if  
it  does not1 who shall say that it may 
not be as important and useful1 say1  to
 establish a difference as to prove the 
resemblance which has been  suspected8  
,if1 however1 reasoning from an analogy 
may be fallacious when inferences  are  
drawn from the fact that two things     
possess the same attributes in  common1 
it is1 ,i think1 a safer guide when it  
is used to suggest a new  hypothesis2 a 
corpuscular theory of light may be      
suggested by the  analogy between the   
reflexion of light and the rebounding of
 elastic  bodies2 an undulatory theory  
by the analogy of a wave propagated     

along a  string or on the surface of    
water4 ,the one theory may be found to  
fit  the facts and the other may be     
condemned2 but without some analogy as a
  guide how are such theories to be     
devised8 ,what we require in science    
are continual stimuli to start us on new
 experiments1 new observations1  and new
 ideas1 and prevent us1 especially those
 who are teachers1 from  constantly     
repeating the old ones4    ,i shall be  
satisfied if the present lecture is     
regarded as a plea for  the use of      
reasoning from analogy1 and as an       
illustration of its value4    ,let me1  
then1 after this exhortation1 return to 
my problem of the growth  of crystals1  
and show how ,i still think that we may 
be guided by analogy  in seeking to     
understand it4    ,so far from regarding
 the growth of a crystal as of no       
further  importance after it has been   
proved to be quite different from the   
growth of a plant1 we must still think  
of it as one of the most  interesting   

and mysterious events1 and the one      
through which we may hope  to get the   
clearest insight into the nature of the 
crystal itself4    ,for1 after all1 when
 after making physical experiments upon 
the solid  crystal and studying its     
action upon heat and light we are led to
  speculate upon the manner in which it 
is constructed1 we must not forget  that
 it grew1 and that the material was laid
 down under conditions which  we can    
only understand by studying what happens
 on the surface as it  grows4    ,,lord 
,,curzon devoted his ,,romanes ,lecture 
to the consideration of  ,frontiers1 and
 explained their interest and importance
 in the growth of  nations4 ,in the     
study of ,science also nothing is more  
interesting and  important than frontier
 problems4 ,in two senses is this true4 
,the  problems which lie on the         
borderland between two sciences are the 
most  fruitful of all1 because they     
throw light upon each science1 and1 by  
bringing into harmony things that were  

previously distinct and separate1  lead 
to an immediate extension of knowledge4 
,and also in a more restricted sense4   
,you will find1 ,i think1 that the      
scenes of the most interesting events in
 ,nature are generally those  places    
where different things come into contact
 and where there is  consequently stir  
and action2 where two substances meet to
 form a new  chemical compound2 where   
two bodies touch and react upon each    
other2 at  the surface of a solid or a  
liquid2 these are the regions in which  
events are taking place that we can     
study and measure with the prospect  of 
discovery4    ,impressed by the analogy 
between the growth of crystals and of   
living  things1 ,i have always felt     
that1 for a proper understanding of the 
things themselves1 the study of their   
growth is as important for the one  as  
for the other2 that to obtain this      
understanding it is necessary to  study 
what is happening on the surface of the 
growing crystal where the  advancing    

solid is in actual contact with the     
solidifying liquid4 ,if you  wish to    
understand a plant or an animal it is   
not enough to study dried  specimens or 
specimens in spirits1 but to watch the  
living organisms  growing under natural 
conditions2 and in the same way it is   
surely worth  while to study the growing
 crystal surrounded by the solution     
which  feeds it1 and even to make under 
these conditions the measurements and   
observations which are usually made upon
 crystals only after they have  been    
taken out of the solution and have      
ceased to grow4    ,in the case of      
living things1 we know that growth takes
 place by  internal processes and not   
only by new material added on the       
surface4  ,how much easier1 then1 should
 it be to study the growth of a crystal 
when we have found that it is only a    
surface activity1 and does not  involve 
internal changes8    ,as ,i have already
 said1 when ,i came to ,oxford there was
 no laboratory of  ,mineralogy nor any  

apparatus for research1 but ,i brought  
with me a piece  of apparatus which ,i  
had constructed a few years previously  
for this  exact purpose2 to measure the 
angles of crystals while they are       
growing  in the solution and to         
ascertain whether any changes take place
 in those  angles1 in the hope of       
getting some insight into the nature of 
the  surface and what ,i have called the
 frontier problem4 ,many days and also  
nights had ,i spent with this apparatus 
in the absorbing pursuit of  measuring  
growing crystals1 watching the curious  
changes that take place  in the position
 of their facets1 excited by the        
knowledge that ,i was  looking at things
 that had certainly not been seen       
before1 and by the  expectation of what 
they might disclose4    ,i need not     
weary this audience with any description
 of these  experiments1 which doubtless 
seem more interesting and important to  
their author than to anyone else4 ,but  
,i wish to draw your attention to  the  

result that came out of them4 ,i found  
that it was possible with the  same     
apparatus to measure the refractive     
power of the liquid in absolute  contact
 with the growing crystal and from this 
to calculate the exact  strength of the 
solution at that spot4 ,it was thus     
possible to prove  that the solution in 
contact with the crystal is rather      
stronger than at  a very short distance 
from it1 and to know exactly how much   
stronger4 ,in  other words1 while a     
crystal of1 say1 alum is growing1 the   
liquid in  contact with it contains more
 particles of alum and less particles of
  water1 or is richer in alum1 than the 
liquid at a short distance from  it4 ,i 
will ask you to bear this in mind in    
what follows4 ,there is  another curious
 fact connected with this subject4      
,crystals of nitrate of  soda have      
almost exactly the same shape and almost
 the same physical  properties as       
crystals of the common mineral calcite1 
which1 in its  purest and most perfect  

form of transparent glassy crystals1 is 
known as  ,iceland spar4 ,now1 when a   
perfectly clean crystal of ,iceland spar
 is  immersed in a strong solution of   
nitrate of soda1 although it is not     
dissolved by the liquid itself and      
therefore cannot crystallize out of  it1
 the ,iceland spar actually continues to
 grow1 and becomes enveloped  by the    
nitrate of soda so as to form what is   
apparently a single  crystal4    ,it    
appears1 therefore1 highly probable that
 a crystal of nitrate of soda  and a    
crystal of ,iceland spar behave alike in
 this respect when placed  in a strong  
solution of the nitrate2 each draws to  
itself the liquid  nitrate in the       
solution1 then draws it out of the      
solution in the solid  state1 and       
further arranges the particles upon its 
own surface in a  perfectly regular     
manner1 so that the arrangement of the  
particles in  the shell of nitrate is   
the same as the arrangement of the      
particles in  the spar which it         

surrounds2 just as a bricklayer sets    
upon the rising  wall new bricks        
arranged in the same way as those which 
he has already  laid4 ,i remember that  
on ,,lord ,,kelvin',s last visit to     
,oxford1 shortly  before his death1     
mindful of his ,,boyle ,lecture1 ,i     
showed him1 in company  with my pupil1  
,mr4 ,,barker1 this beautiful           
experiment1 with which he was  at that  
time not familiar1 and ,i shall never   
forget the interest and  enthusiasm with
 which he witnessed the beautifully     
regular and  instantaneous growth of the
 nitrate crystals4 ,he always was as    
enthusiastic and inquiring as a boy1 and
 these characteristics were  exhibited  
on that occasion in his old age4 ,it is 
an experiment which  sets one thinking1 
and ,i have no doubt that1 if ,,lord    
,,kelvin1 even at  that advanced age1   
had set his mind to consider it1 he     
would have been  able to deduce far more
 than it has yet suggested to those who 
have  witnessed it4#c      ,footnote #c3

 ,the experiment was then shown1 exactly
 as it was shown to  ,lord              
,kelvin4--,,ed4      ,some two years or 
so before the time of which ,i am       
speaking1 ,mr4 ,,barker  had at my      
suggestion made an exhaustive study of a
 great number of  different substances  
in order to ascertain which of them     
behave towards  one another like nitrate
 of soda and calcite1 and why they do   
so1 and he  has really discovered the   
secret4 ,when two substances like       
nitrate of  soda and calcite have nearly
 the same shape and resemble one another
  closely in their physical properties1 
the geometrical laws of  crystalline    
structure of which ,i have already      
spoken make it certain  that they       
consist of particles arranged in the    
same way4 ,we do not know  what these   
particles are or what is their shape or 
size1 but we may be  sure that they are 
arranged in the same way4 ,i am perhaps 
using the word  particles in a loose    
sense1 for they might be hollow cells or

 they might  be the space occupied by   
moving particles1 or anything else1 but 
whatever they may be it is pretty       
certain that they are arranged in the   
same way4    ,well1 ,mr4 ,,barker has   
proved that1 if two crystals grow       
together like  nitrate of soda and      
calcite1 their particles are not only   
arranged in  the same way1 but they must
 be of the same size1 or at any rate    
occupy  the same space4 ,in more        
scientific language1 the two crystals   
not only  have the same molecular       
structure1 but the same molecular       
volume4 ,it is1  therefore1 mainly a    
question of fitting together1 and1 if   
the two  structures do not fit1 they    
cannot grow together1 like nitrate of   
soda  and ,iceland spar1 as a continuous
 crystal4    ,let me illustrate by a    
suggestive comparison4 ,the bee's cell  
is one of  the most remarkable and      
symmetrical structures in nature4 ,its  
regularity  is probably due to the fact 
that bees of the same size are1 in      

making  it1 so closely crowded together2
 there is one bee's head in each cell1  
and therefore you may say that the      
arrangement of the bees is the same  as 
that of the cells4 ,for example1 if you 
place in each cell a ball  which exactly
 fits it and then take away the cells1  
you have an  arrangement of balls which 
is the same as that of the cells1 each  
being  in contact with six neighbours4  
,it may be called a hexagonal           
arrangement4 ,you have only to push     
together a number of balls on a  table1 
and they will fall into this            
arrangement4 ,it was a contemporary  and
 associate of ,,boyle1 and an ,oxford   
man1 ,dr4 ,,robert ,,hooke1 who pointed 
out that with balls piled together in   
this way you can build up the  shapes of
 crystals1 and that1 for example1 a     
pyramid of cannon-balls  stacked        
together in the manner that ,i have just
 shown1 has the shape and  angles of an 
alum crystal4 ,now1 if two such         
arrangements are to fit  together1 they 

must be of the same size1 whether they  
consist of bees1  or cells1 or balls1 or
 molecules4 ,in the same way ,mr4       
,,barker has proved  that ,iceland spar 
and nitrate of soda must consist of     
materials which  are not only arranged  
in the same way1 but are of the same    
size1  although we do not know in the   
least what that material is1 nor what   
its  actual size may be4    ,but this1  
of course1 is not the end of the whole  
mystery3 for not only  do two such      
structures fit together1 as might be    
expected1 but each has  the remarkable  
property of making the other crystallize
 and grow1 and  that means1 as ,i have  
just explained1 that it draws the other 
out of the  solution where it is liquid 
into the crystal where it becomes part  
of a  solid structure and lays it down  
in the exact position in which it fits1 
just as one bee's cell is added to      
another in the growth of the comb4 ,we  
have advanced a step1 but only one step1
 towards the better  understanding of   

the mystery1 and ,i would beg you to    
note how we are  continually led on by  
analogies which may be quite false1 but 
which are  at any rate fruitful4    ,now
 let me pass to another series of       
researches which were conducted by      
,miss ,,isaac and myself for a few years
 before ,i left ,oxford and have  since 
been carried on by her with conspicuous 
success4 ,still  experimenting with the 
same apparatus1 and endeavouring to     
trace how a  solution changes in        
strength while it is crystallizing1 we  
came across  some curious and unexpected
 results4 ,it is1 of course1 well known 
that  if a crystal1 say of alum1 is     
placed in a weak solution of alum it is 
dissolved1 and only has the effect of   
making the solution stronger1 but  that 
at last a stage is reached at which the 
solution becomes  #8saturated' and can  
dissolve no more1 just as a stage is    
reached at  which a soaking sponge will 
hold no more water4 ,at this point a    
crystal1  if put into it1 remains       

unchanged4 ,but it is quite easy to make
 the  solution still stronger1 not by   
adding alum to it1 but by taking water  
away from it by evaporation3 it then    
becomes oversaturated or                
#8supersaturated'1 and now a crystal of 
alum dipped into the liquid will  at    
once begin to grow and to make the      
solution weaker4 ,in fact1 this is  an  
unfailing test by which we can tell     
whether a solution is saturated  or     
supersaturated2 and1 more than this1    
until a bit of solid crystal  gets into 
it the liquid does not crystallize4     
,keep it in a closed vessel  so that no 
speck of alum can fall into it1 and it  
will remain liquid for  weeks or years  
or as long as you please4 ,but let the  
smallest possible  grain of an alum     
crystal fall into it1 and               
crystallization will be  started2       
inoculate it with an invisible germ of  
alum dust1 such as must  be flying about
 in the air of any room where dry alum  
is or has been  kept1 and you will see  

the life and growth of a crystal begin  
when that  germ is introduced4 ,this is 
the most extraordinarily sensitive test1
 and  one that can easily be applied4   
,in many of our experiments we found    
that during the first day when we  were 
working with some new substance it would
 not crystallize from an  exposed       
solution2 but on the second day1 when   
the air of the laboratory  had become   
impregnated with crystal germs1 an      
exposed solution would  begin to        
crystallize at once4    ,dr4 ,,tutton1  
one of the most accomplished            
investigators of crystals1  whose       
refined and beautiful researches were   
for many years carried on in  ,oxford1  
has fully described these effects in his
 two books on crystals  just published1 
and confirms them from his own          
experience4    ,now1 ,miss ,,isaac and  
,i have found in the course of our      
researches that1  as the solution       
becomes stronger and stronger--say1 by  
the evaporation of  some of its water1  

it continues to be in the ordinary state
 of  supersaturation in which it does   
not crystallize save by inoculation     
with a germ of solid alum crystal1 but  
at last it suddenly reaches a  condition
 in which it can crystallize            
spontaneously1 and at this moment  it is
 enough to stir or shake the solution1  
and you will at once witness  the birth 
of thousands of tiny crystals which     
appear as a cloud in the  liquid and    
begin to grow rapidly4    ,a very easy  
way in which to make this experiment is 
to dip a clean  needle into a drop of   
evaporating solution on a glass plate   
and to  scratch the glass on which the  
drop lies3 for a time nothing happens1  
and then suddenly1 as the liquid passes 
into the new condition1 a chain  of tiny
 crystals appears along the line of     
scratch4    ,that this suspended        
crystallization has a fixed limit was   
suspected1 and  had been predicted by   
the ,german chemist ,,ostwald1 but could
 never be  proved until we made our     

experiments1 and it was ,mr4 ,,hartley  
who first  helped us to interpret our   
results4 ,he has subsequently1 with his 
pupils1 made a number of investigations 
on the same subject4    ,i can show you 
the two conditions in one and the same  
drop by using a  solution of common     
potassium bichromate4 ,crystals begin to
 grow at the  edge of the drop where the
 liquid first becomes sufficiently      
strong1 and  continue to grow slowly in 
the evaporating liquid which is only    
slightly  supersaturated4 ,but in a few 
moments other parts of the drop which   
are  thinner become so strongly         
supersaturated that they begin to       
crystallize  spontaneously2 and there   
you can witness the birth of new        
crystals which  grow rapidly in all     
directions1 because they are growing in 
a solution  which is much stronger than 
that in which the first crystals are    
growing  slowly4    ,does not all this  
set one thinking8 ,what is taking place 
we cannot tell1  but we can only think  

of it as in some way analogous to the   
birth of a  cloud2 and in both instances
 we have to picture to ourselves minute 
invisible particles1 of whose shape and 
size we know nothing1 coming  together  
and coalescing till they grow into a    
drop or a crystal that we  can see4 ,but
 why they do not begin to coalesce as   
soon as the liquid is  supersaturated it
 is difficult to say4 ,we have to       
conceive the alum  solution as made up  
of moving particles of alum and of      
water1 and it may  be that the particles
 are constantly coalescing into minute  
groups1 but  as rapidly being broken up 
again1 until a moment arrives at which  
the  alum particles are sufficiently    
dense to cohere permanently2 but how    
they attract one another and arrange    
themselves into the wonderful  structure
 which makes a crystal1 of this we are  
entirely ignorant4 ,the  question brings
 us back again to our initial mystery1  
how does the  crystal actually grow8    
,but this is not all4 ,i have said that 

all solutions seem to behave in  the    
same way1 and among them nitrate of     
soda1 which we have already seen        
growing in perfect regularity on        
,iceland spar4 ,it appears1 however1    
from  experiments made by ,mr4 ,,barker1
 ,miss ,,isaac1 ,m4 ,,chevalier 7who was
  another of my pupils71 and myself1    
that ,iceland spar behaves in this      
respect also exactly like nitrate of    
soda4 ,in a solution which is           
supersaturated1 but is not strong enough
 to crystallize spontaneously1  not only
 will inoculation with a crystal of     
nitrate produce instant                 
crystallization2 but inoculation with a 
crystal of ,iceland spar produces  the  
same result4 ,so we have a still more   
convincing proof of what ,i  suggested a
 short time ago1 that two crystals1     
which have structures so  nearly        
identical that they can fit together1   
possess also the power of  drawing each 
other from the liquid state into the    
solid form of a  crystal4 ,whatever it  

is which conditions the fitting together
 of two  structures must then also      
confer upon them this extraordinary     
power of  making each other grow4    ,if
 ,i had more time1 ,i should like to    
give an account of some of the more     
important discoveries that have been    
made about crystals during the last     
fifteen years1 for they would make it   
easier to understand the present  state 
of our knowledge concerning them4 ,i    
will only refer to two3 one is  an      
experimental fact1 and the other is a   
theoretical speculation1 and  both are  
connected with the subject that ,i have 
been discussing4    ,it was discovered  
shortly before that time1 and has been  
found by many  experiments since1 that  
there are certain substances which are  
in a real  sense crystals1 although they
 are liquid2 that is to say1 they affect
  light in its passage through them just
 as solid crystals do4    ,these        
extraordinary substances1 which had been
 investigated by ,professor  ,,lehmann1 

were first shown in ,england by ,mr4    
,,bowman and ,mr4 ,,hartley1 who  were  
then working in my laboratory1 at a     
conversazione at the ,royal  ,society1  
not long after their discovery1 and ,i  
can well remember the  interest with    
which they were witnessed by ,sir       
,,george ,,stokes and others4  ,we can  
only picture these liquids as consisting
 of particles which1  while they are    
free to move in all directions1 always  
continue to face  the same way1 like a  
group of dancers who in all their       
evolutions  continue to face the        
audience1 instead of turning as they    
move4 ,when the  mechanism which renders
 possible this remarkable behaviour is  
better  understood1 we may be sure that 
it will bring about a better            
understanding of the manner in which a  
solid crystal is constructed4 ,the      
interesting thing about it is that here 
at any rate the particles are in        
violent movement instead of being       
comparatively stationary1 as they are   

in a solid crystal4    ,one is naturally
 led to imagine that before any solution
 begins to  crystallize in the solid    
form it passes into this liquid state1  
and that  the particles have begun to   
set themselves and all to face the same 
way  before they begin to cohere and to 
build themselves into a solid4 ,but so  
far as ,i know there is no evidence in  
favour of this suggestion--a  solution  
before solid crystals begin to appear   
does not behave like a  liquid crystal1 
but remains an ordinary solution up to  
the last moment  when new crystals are  
born in it or are started by inoculation
 with a  crystal germ4    ,the other    
discovery1 which is in the nature of a  
speculation1 is that of  another person 
whom ,i am proud to reckon among my     
former pupils1 namely1  ,professor      
,,pope of ,cambridge1 working in        
conjunction with ,mr4 ,,barlow4 ,mr4    
,,barlow had already been referred to by
 ,,lord ,,kelvin in his ,,boyle ,lecture
  as the author of ingenious researches 

upon the various ways in which          
materials can be packed together1 and   
the different arrangements and          
structures which result from this       
packing4    ,these two workers have now 
propounded a theory according to which1 
if  the various atoms which constitute a
 substance are represented by  spheres  
whose sizes represent the valency of the
 atoms1 and if these  spheres are packed
 together as closely as they will go1   
the resulting  structure will represent 
very nearly the structure of the        
crystal2 and  so it may be possible for 
the first time from a knowledge of the  
chemical constitution of a substance to 
predict the structure of its  crystals  
and therefore the form in which it will 
crystallize4 ,you  remember the bee's   
cell arrangement and the similar        
arrangement of balls  got by placing a  
ball in each cell and then removing the 
cells4 ,another  way of getting the same
 arrangement is to place a number of    
equal balls  on a table and to squeeze  

them together until they are packed as  
closely  as possible4 ,this arrangement 
of closest packing1 the arrangement of a
  pyramid of cannon-balls1 is precisely 
the same as before1 the one in  which   
each ball on the table is in contact    
with six others4 ,according to  ,,pope  
and ,,barlow the atoms in a crystal     
simply pack themselves together  as     
closely as possible1 but instead of     
being equal in size they have  generally
 to be represented as of different sizes
 according to their  valencies4 ,if we  
imagine the coalescence of atoms to form
 a crystal to  be due to their mutual   
attraction1 it is very reasonable to    
suppose that  they will get as close    
together as is possible1 and therefore  
that the  ways of close packing are the 
ways of crystal structure4 ,the theory  
therefore suggests a reason for the     
growth as well as for the shape of a    
crystal4 ,i may remind you that the     
bee's cell itself1 which is in the      
world of life the thing that most nearly

 resembles crystalline  structure1 is   
due to this same principle of close     
packing2 for in their  efforts to get as
 closely together as possible the bees  
are constrained  to get into the        
hexagonal arrangement4 ,the bees crowd  
their heads  together and to each bee's 
head corresponds one cell4    ,on the   
other hand1 ,professor ,,sollas has     
brought forward some most  suggestive   
and convincing speculations concerning  
certain crystals which  are based upon  
the principle of open1 and not close1   
packing4 ,his model  of silver iodide1  
for example1 is well known in ,oxford4  
,i have mentioned these recent          
contributions to science1 not only with 
the object of indicating that our       
knowledge of crystals is steadily       
increasing1 but also in order to point  
out that little has yet been done  to   
explain the mysteries of their growth4  
,all that has been effected up  to the  
present is an attempt to explain how    
they are constructed1 not  the process  

by which the construction takes place4  
,it is as though we  were to analyse the
 form and structure of animals and      
plants and never  to watch them as they 
grow1 but only to study them from       
fossils or from  museum specimens4 ,and 
,i believe the reason to be this4 ,all  
the  speculations concerning crystals   
persist in regarding the particles of   
which they consist as fixed and         
immovable3 the theories are all         
statical4 ,and yet we know that the     
particles of matter1 whatever they  may 
be1 are really in lively movement4 ,is  
it not possible that in order  to get a 
correct understanding of the growth of a
 crystal we should take  account not    
only of the positions1 but of the       
movements1 of its  particles8 ,without  
some knowledge of these we are not able 
to approach  the problem1 or to         
ascertain how a crystal either of       
nitrate of soda or  of ,iceland spar    
draws the nitrate of soda out of the    
solution and makes  it grow into a      

solid4    ,remember that when we say we 
know how the particles of a crystal are 
arranged we really know nothing about   
their nature1 and can only  represent   
them by spheres1 or solid figures1 or   
cells1 or even points1  in order to get 
a representation of their arrangement4  
,but we might  arrange in the same way a
 number of bodies each of which is      
whirling in  a fixed orbit1 like a      
planet1 about the corresponding point1  
or  vibrating about it like the prong of
 a tuning-fork1 or pulsating like a     
breathing animal2 and so far from the   
arrangement being independent of  the   
movements it may be due to them4    ,if 
,i may seek another analogy1 let me take
 a group of figure skaters2  their      
centre remains fixed at the orange1     
maybe1 about which their  figures are   
executed1 but the group of skaters is at
 one moment extended  when they circle  
out to their furthest sweep1 and at     
another moment  concentrated when they  
converge to the centre2 and this        

alternating  expansion and compression  
occurs in a regular rhythm4    ,imagine 
a pond covered by a number of such      
groups of skaters2 the manner  in which 
they will fit in1 and have to arrange   
themselves1 will depend  both upon the  
dimensions and the rhythm of their      
curves1 and they may  even interlace and
 become part of one great figure system 
covering the  whole pond4 ,may not the  
growth of a crystal be something of this
 sort8    ,all the devices which ,i have
 quoted for picturing to ourselves the  
architecture of a crystal ,i would      
regard as merely models representing    
something that may be really quite      
different4 ,but ,i venture to suggest   
that the time has come when we should   
make use of moving and not  stationary  
models4    ,one need not go further than
 a spinning top for an illustration of  
stability due to movement1 and there is 
nothing unreasonable in the  suggestion 
that the rigidity of a crystal structure
 may be due to the  motion of its parts4

    ,one curious observation which ,i   
have made is suggestive4 ,i have many   
times noticed that when the appropriate 
crystal is introduced into a            
supersaturated solution1 which is not   
strong enough to crystallize            
spontaneously1 it may cause crystals to 
grow not only in actual contact  with   
itself1 but at some little distance in  
its neighbourhood4 ,if this  be so1 then
 the crystallizing force1 the power of  
propagating crystal  growth1 is not     
merely a frontier problem1 but can be   
exercised through  the liquid to a      
distance4 ,if ,i try to picture to      
myself what is  happening1 ,i must again
 have recourse to analogy2 ,i can only  
think of  the manner in which a string  
or a tuning-fork is set in vibration and
  responds to a similar string or       
tuning-fork which is giving out its note
  at the other end of the room2 and so  
is it not possible that the  movements1 
whatever they are1 vibrations or        
pulsations or regular  oscillations of  

some sort1 which constitute crystalline 
growth may be  communicated through the 
almost crystallizing liquid1 and        
culminate at  some point where they set 
similar material vibrating1 that is to  
say1  crystallizing1 in the same way8   
,i remember1 when ,i first began to be  
interested in crystals in  undergraduate
 days1 reading in ,nature an account of 
two papers which  seemed to have a      
possible bearing on the subject4 ,one is
 an example of a  stationary arrangement
 of rigid bodies4 ,the other illustrates
 the  principle which ,i am now         
suggesting1 and is an arrangement of    
pulsating  bodies whose positions are   
due to their movements4 ,the first was a
  description of ,,mayer',s experiment  
on floating magnets which was1 if ,i    
remember right1 shown here in a ,,boyle 
,lecture by ,sir ,,joseph ,,thomson a   
few years ago2 an experiment in which   
magnets suspended in water by  corks and
 with their ,north poles projecting so  
that they repel one  another1 are       

brought together by the attraction of a 
large magnet held1  with its ,south pole
 downwards1 above the surface of the    
water2 under the  joint influence of    
this attraction and their own mutual    
repulsions1 they  group themselves into 
a number of interesting geometrical     
figures very  suggestive of the         
geometrical regularity of crystal       
structure4 ,indeed1  attempts have been 
made by ,,lehmann to explain the        
architecture of a  crystal by a grouping
 of magnetic systems4 ,and the other was
 the  experiment of ,,bjerknes in #ahgf 
7described in ,nature in #ahha71 in     
which  a number of hollow elastic balls 
were made to expand and contract by     
means of air tubes attached to them4    
,these pulsating balls1 when placed  in 
water1 attracted and repelled one       
another like magnets1 and arranged      
themselves in a regular manner2 thus    
suggesting that there may be many       
unexpected ways in which rhythmical     
motion can exercise an attractive  and  

directive action such as is required to 
produce a crystal4    ,let me illustrate
 what ,i mean by another crude analogy4 
,take a room full  of dancers2 if they  
are all dancing to different times and  
in different  ways there will be no     
order or arrangement in the crowd1 and  
it will  remain an incoherent jostling  
assembly of independent persons4 ,but if
  there are among them those who are    
moving to the same step and in the  same
 manner1 and if they come together1 they
 can become partners and can  continue  
to dance together2 and if the room be   
filled with such dancers1  then the     
whole assembly can grow together into an
 orderly movement1 and  only those whose
 step does not fit into the dance will  
be ejected and  left out4 ,or take      
another example3 soldiers marching      
together have not  ceased to be         
individual men1 but when they fell into 
step they became in  addition an        
organized body with a structure and a   
coherence that does  not belong to a    

miscellaneous crowd4 ,even so may the   
particles of  dissolved salt be endowed 
with a movement which enables them to   
enter  into partnership and cohere1 and 
so to build themselves into the orderly 
structure which makes up a crystal4 ,and
 even so do crystals grow out of  a     
mixed solution as a pure and homogeneous
 substance and reject the  other        
materials which are dissolved in the    
liquid4    ,one other suggestion4 ,if   
the growth of a crystal is really the   
coming  together of vibrating particles 
which cohere because they are in tune   
with one another and so enter into a    
partnership like that of the  dancers or
 the figure skaters1 then is it not     
possible that we may be  able to        
communicate these vibrations to a       
supersaturated solution1 which  is so   
densely crowded that it is ready to     
crystallize1 by some other  means than  
by inoculating it with the appropriate  
crystal8 ,i think that  the time has    
come when we may be able to get some    

knowledge of the  manner of these       
movements by experimental methods2      
perhaps by studying  the sort of shock  
or movement1 if there be any such1 which
 starts  crystallization in a           
supersaturated solution2 perhaps by     
finding other  substances1 whose        
movements we understand1 which are able 
to start the  crystallization when they 
are introduced into certain solutions4  
,i have said that the frontier problems 
in science are interesting2 and  that   
this is true not only of the events that
 take place when different  bodies meet1
 but in another and more general sense4 
,the most interesting  and fruitful     
problems are those which deal with the  
borderland between  two sciences1 when  
the difficulties of the one are         
enlightened by the  experience of the   
other1 or when the same problem is      
looked at from two  different sides4    
,let me only quote as an illustration   
the work connected  with osmosis1 which 
attracted first the botanists and then  

the physical  chemists1 and remind you  
of the enormous importance which it has 
assumed  by their combined efforts4 ,i  
think it will be found that these       
problems  of crystal growth are of this 
borderland nature4 ,and such problems   
can  only be satisfactorily attacked by 
those who are more than mere            
specialists and can be led by the       
experience or the analogies of other    
sciences4    ,i said that ,i should like
 to regard this lecture as an attempt to
  justify the value of analogy4 ,we poor
 specialists grope within the  confines 
of our own science1 and what little     
advance we make is made in  part by the 
light we borrow from the other sciences4
 ,in these days of  increasing          
specialization what we need is to       
interest in our own  problems1 not only 
those who are tilling the same fields   
with ourselves1  but even more1 those   
who live on the other side of the fence 
which  surrounds us3 to call to them    
across the frontier1 to seek their      

advice  and assistance and the benefit  
of their experience4    ,this is one of 
the great advantages of a ,university1  
that workers and  thinkers in different 
subjects are brought together and can   
make their  difficulties known to each  
other4 ,the connecting links between    
them are  the analogies which they      
perceive and which excite an interest   
that they  would not otherwise feel in  
each other's work4    ,this is the      
reason why ,i have endeavoured to set   
before you a very  special problem in a 
very elementary way and as far as       
possible without  using technical terms4
 ,it is with the hope of attracting the 
interest of  workers in other subjects  
to this fascinating problem of crystal  
growth  which1 from the time of ,,boyle 
to that of ,,ruskin1 and more           
especially1 as  ,i have shown you1 in   
recent years1 has engaged the attention 
of ,oxford  students of crystals4       
----------------------------------------
--------------------------------        

,transcriber's note3    ,page #h1       
#8allum' changed to #8alum1' 8corpuscles
 of nitre1 alum1 vitriol10