,,the ,,beautiful ,,necessity    ,seven 
,essays on ,theosophy and ,architecture 
by ,,claude ,,bragdon1 ,f4,a4,i4,a4     
,,mcmxxii                  ,let us build
 altars to the ,beautiful ,necessity    
--,,emerson        ,by the ,same        
,author3    ,episodes ,from ,an         
,unwritten ,history    ,the ,golden     
,person ,in ,the ,heart    ,architecture
 ,and ,democracy    ,a ,primer ,of      
,higher ,space    ,four ,dimensional    
,vistas    ,projective ,ornament        
,oracle          ,,contents      ,i     
,,the ,,art ,,of ,,architecture         
,,ii   ,,unity ,,and ,,polarity         
,,iii  ,,changeless ,,change      ,,iv  
,,the ,,bodily ,,temple      ,v         
,,latent ,,geometry      ,,vi   ,,the   
,,arithmetic ,,of ,,beauty      ,,vii   
,,frozen ,,music           ,,conclusion 
,,preface ,,to ,,the ,,second ,,edition 
,the ,beautiful ,necessity was first    
published in #aiaj4 ,save for a slim    
volume of privately printed verse it was
 my first book4 ,i worked hard  on it4  

,fifteen years elapsed between its      
beginning and completion2  it was twice 
published serially--written1 rewritten  
and  tre-written--before it reached its 
ultimate incarnation in book form4      
,confronted now with the opportunity to 
revise the text again1 ,i find  myself  
in the position of a surgeon who feels  
that the operation he  is called upon to
 perform may perhaps harm more than it  
can help4  ,prudence therefore prevails 
over my passion for dissection3 warned  
by  eminent examples1 ,i fear that any  
injection of my more mature and less    
cocksure consciousness into this book   
might impair its unity--that ,i  never  
could recapture the first fine careless 
rapture4    ,the text stands therefore  
as originally published save for a few  
verbal changes1 and whatever            
reservations ,i have about it shall  be 
stated in this preface4 ,these are not  
many nor important3 ,the  ,beautiful    
,necessity contains nothing that ,i need
 repudiate or care to  contradict4      

,its thesis1 briefly stated1 is that art
 in all its manifestations is  an       
expression of the cosmic life1 and that 
its symbols constitute a  language by   
means of which this life is published   
and represented4 ,art  is at all times  
subject to the ,beautiful ,necessity of 
proclaiming  the world order4    ,in    
attempting to develop this thesis it was
 not necessary 7nor as  ,i now think1   
desirable7 to link it up in so definite 
a manner with  theosophy4 ,the          
individual consciousness is colored by  
the particular  medium through which it 
receives truth1 and for me that medium  
was  theosophy4 ,though the book might  
gain a more unprejudiced hearing1  and  
from a larger audience1 by the removal  
of the theosophic  color-screen1 it     
shall remain1 for its removal now might 
seem to  imply a loss of faith in the   
fundamental tenets of theosophy1 and    
such  an implication would not be true4 
,the ideas in regard to time and space  
are those commonly current  in the world

 until the advent of the ,theory of     
,relativity4 ,to a  generation brought  
up on ,einstein and ,ouspensky they are 
bound to  appear lower dimensional4     
,merely to state this fact is to deal   
with it to the extent it needs to be    
dealt with4 ,the integrity of my        
argument is not impaired by these new   
views4    ,the one important influence  
that has operated to modify my opinions 
concerning the mathematical basis of the
 arts of space has been the  discoveries
 of ,mr4 ,jay ,hambidge with regard to  
the practice of the  ,greeks in these   
matters1 as exemplified in their temples
 and their  ceramics1 and named by him  
,dynamic ,symmetry4    ,in tracing      
everything back to the logarithmic      
spiral 7which embodies  the principle of
 extreme and mean ratios7 ,i consider   
that ,mr4 ,hambidge  has made one of    
those generalizations which reorganizes 
the old  knowledge and organizes the    
new4 ,it would be only natural if in his
  immersion in his idea he overworks it1

 but ,mr4 ,hambidge is a man of  such   
intellectual integrity and thoroughness 
of method that he may be  trusted not to
 warp the facts to fit his theories4    
,the truth of the  matter is that the   
entire field of research into the       
mathematics of  ,beauty is of such      
richness that wherever a man plants his 
metaphysical  spade he is sure to come  
upon pay dirt4 ,the ,beautiful          
,necessity  represents the result of my 
own prospecting2 ,dynamic ,symmetry     
represents the result of his4 ,if at any
 point our findings appear to  conflict1
 it is less likely that one or the other
 of us is mistaken  than that each is   
right from his own point of view4 ,be   
that as it may1  ,i should be the last  
man in the world to differ from ,mr4    
,hambidge1  for if he convicted me of   
every conceivable error his work would  
still  remain the greatest justification
 and confirmation of my fundamental     
contention--that art is an expression of
 the world order and  is therefore      

orderly1 organic2 subject to            
mathematical law1 and  susceptible of   
mathematical analysis4    ,,claude      
,,bragdon    ,rochester1 ,n4,y4         
,april1 #aibb          ,i    ,,the ,,art
 ,,of ,,architecture      ,one of the   
advantages of a thorough assimilation of
 what may be called  the theosophic idea
 is that it can be applied with         
advantage to every  department of       
knowledge and of human activity3 like   
the key to a  cryptogram it renders     
clear and simple that which before      
seemed  intricate and obscure4 ,let us  
apply this key to the subject of art1   
and to the art of architecture in       
particular1 and see if by so  doing we  
may not learn more of art than we knew  
before1 and more of  theosophy too4     
,the theosophic idea is that everything 
is an expression of the  ,self--or      
whatever other name one may choose to   
give to that immanent  unknown reality  
which forever hides behind all          
phenomenal life--but  because1 immersed 

as we are in materiality1 our chief     
avenue of  knowledge is sense           
perception1 a more exact expression of  
the  theosophic idea would be3          
,everything is the expression of the    
,self  in terms of sense4 ,art1         
accordingly1 is the expression of the   
,self in  terms of sense4 ,now though   
the ,self is one1 sense is not one1 but 
manifold3 and therefore there are arts1 
each addressed to some  particular      
faculty or group of faculties1 and each 
expressing some  particular quality or  
group of qualities of the ,self4 ,the   
white light  of ,truth is thus broken up
 into a rainbow-tinted spectrum of      
,beauty1  in which the various arts are 
colors1 each distinct1 yet merging one  
into another--poetry into music2        
painting into decoration2 decoration    
becoming sculpture2                     
sculpture--architecture1 and so on4     
,in such a spectrum of the arts each one
 occupies a definite place1 and  all    
together form a series of which music   

and architecture are the two  extremes4 
,that such is their relative position   
may be demonstrated in  various ways4   
,the theosophic explanation involving   
the familiar idea  of the pairs of      
opposites would be something as follows4
 ,according  to the ,hindu-,aryan       
theory1 ,brahma1 that the world might be
 born1 fell  asunder into man and       
wife--became in other words name and    
form,a  ,the two universal aspects of   
name and form are what philosophers call
  the two modes of consciousness1 one of
 time1 and the other of space4  ,these  
are the two gates through which ideas   
enter phenomenal life2 the  two boxes1  
as it were1 that contain all the toys   
with which we play4  ,everything1 were  
we only keen enough to perceive it1     
bears the mark of  one or the other of  
them1 and may be classified accordingly4
 ,in such a  classification music is    
seen to be allied to time1 and          
architecture to  space1 because music is
 successive in its mode of              

manifestation1 and  in time alone       
everything would occur successively1 one
 thing following  another2 while        
architecture1 on the other hand1        
impresses itself upon  the beholder all 
at once1 and in space alone all things  
would exist  simultaneously4 ,music1    
which is in time alone1 without any     
relation to  space2 and architecture1   
which is in space alone1 without any    
relation  to time1 are thus seen to     
stand at opposite ends of the art       
spectrum1  and to be1 in a sense1 the   
only pure arts1 because in all the      
others  the elements of both time and   
space enter in varying proportion1      
either actually or by implication4      
,poetry and the drama are allied to     
music inasmuch as the ideas and images  
of which they are made up are  presented
 successively1 yet these images are for 
the most part  forms of space4          
,sculpture on the other hand is clearly 
allied to  architecture1 and so to      
space1 but the element of action1       

suspended  though it be1 affiliates it  
with the opposite or time pole4         
,painting  occupies a middle position1  
since in it space instead of being      
actual has become ideal--three          
dimensions being expressed through  the 
mediumship of two--and time enters into 
it more largely than into  sculpture by 
reason of the greater ease with which   
complicated action  can be indicated3 a 
picture being nearly always time        
arrested in  midcourse as it were--a    
moment transfixed4    ,in order to form 
a just conception of the relation       
between music and  architecture it is   
necessary that the two should be        
conceived of not  as standing at        
opposite ends of a series represented by
 a straight  line1 but rather in        
juxtaposition1 as in the ancient        
,egyptian symbol  of a serpent holding  
its tail in its mouth1 the head in this 
case  corresponding to music1 and the   
tail to architecture2 in other words1   
though in one sense they are the        

most-widely separated of the arts1 in   
another they are the most closely       
related4    ,music being purely in time 
and architecture being purely in space1 
each is1 in a manner and to a degree not
 possible with any of  the other arts1  
convertible into the other1 by reason of
 the  correspondence subsisting between 
intervals of time and intervals of      
space4 ,a perception of this may have   
inspired the famous saying  that        
architecture is frozen music1 a poetical
 statement of a  philosophical truth1   
since that which in music is expressed  
by means  of harmonious intervals of    
time and pitch1 successively1 after the 
manner of time1 may be translated into  
corresponding intervals of              
architectural void and solid1 height and
 width4    ,in another sense music and  
architecture are allied4 ,they alone of 
all the arts are purely creative1 since 
in them is presented1 not  a likeness of
 some known idea1 but a thing-in-itself 
brought to  a distinct and complete     

expression of its nature4 ,neither a    
musical  composition nor a work of      
architecture depends for its            
effectiveness  upon resemblances to     
natural sounds in the one case1 or to   
natural  forms in the other4 ,of none of
 the other arts is this to such a degree
  true3 they are not so much creative as
 re-creative1 for in them all  the      
artist takes his subject ready made from
 nature and presents it  anew according 
to the dictates of his genius4    ,the  
characteristic differences between music
 and architecture are the  same as those
 which subsist between time and space4  
,now time and space  are such abstract  
ideas that they can be dealt with best  
through  their corresponding            
correlatives in the natural world1 for  
it is a  fundamental theosophic tenet   
that nature everywhere abounds in such  
correspondences2 that nature1 in its    
myriad forms1 is indeed the  concrete   
presentment of abstract unities4 ,the   
energy which everywhere  animates form  

is a type of time within space2 the mind
 working in  and through the body is    
another expression of the same thing4   
,correspondingly1 music is dynamic1     
subjective1 mental1 of one  dimension2  
while architecture is static1 objective1
 physical1 of three  dimensions2        
sustaining the same relation to music   
and the other  arts as does the human   
body to the various organs which        
compose1 and  consciousnesses which     
animate it 7it being the reservatory of 
these  organs and the vehicle of these  
consciousnesses72 and a work of         
architecture in like manner may and     
sometimes does include all of the  other
 arts within itself4 ,sculpture         
accentuates and enriches1 painting      
adorns1 works of literature are stored  
within it1 poetry and the drama  awake  
its echoes1 while music thrills to its  
uttermost recesses1 like  the very      
spirit of life tingling through the     
body's fibres4    ,such being the       
relation between them1 the difference in

 the nature of  the ideas bodied forth  
in music and in architecture becomes    
apparent4  ,music is interior1 abstract1
 subjective1 speaking directly to the   
soul  in a simple and universal language
 whose meaning is made personal and     
particular in the breast of each        
listener3 ,music alone of all the  arts1
 says ,balzac1 has power to make us live
 within ourselves4  ,a work of          
architecture is the exact opposite of   
this3 existing  principally and         
primarily for the uses of the body1 it  
is like the  body a concrete organism1  
attaining to esthetic expression only in
  the reconciliation and fulfilment of  
many conflicting practical              
requirements4 ,music is pure beauty1 the
 voice of the unfettered  and           
perpetually vanishing soul of things2   
architecture is that soul  imprisoned in
 a form1 become subject to the law of   
causality1 beaten  upon by the elements1
 at war with gravity1 the slave of man4 
,one is  the ,ariel of the arts2 the    

other1 ,caliban4    ,coming now to the  
consideration of architecture in its    
historical  rather than its             
philosophical aspect1 it will be shown  
how certain  theosophical concepts are  
applicable here4 ,of these none is more 
familiar and none more fundamental than 
the idea of reincarnation4 ,by          
reincarnation more than mere physical   
re-birth is meant1 for physical         
re-birth is but a single manifestation  
of that universal law of  alternation of
 state1 of animation of vehicles1 and   
progression  through related planes1 in 
accordance with which all things move1  
and as it were make music--each cycle   
complete1 yet part of a larger  cycle1  
the incarnate monad passing through     
correlated changes1  carrying along and 
bringing into manifestation in each     
successive arc  of the spiral the       
experience accumulated in all preceding 
states1  and at the same time unfolding 
that power of the ,self peculiar to the 
plane in which it is momentarily        

manifesting4    ,this law finds         
exemplification in the history of       
architecture in the  orderly flow of the
 building impulse from one nation and   
one country  to a different nation and a
 different country3 its new vehicle of  
manifestation2 also in the continuity   
and increasing complexity of  the       
development of that impulse in          
manifestation2 each incarnation         
summarizing all those which have gone   
before1 and adding some new  factor     
peculiar to itself alone2 each being a  
growth1 a life1 with  periods           
corresponding to childhood1 youth1      
maturity and decadence2  each also      
typifying in its entirety some single   
one of these  life-periods1 and         
revealing some special aspect or power  
of the ,self4    ,for the sake of       
clearness and brevity the consideration 
of only one  of several architectural   
evolutions will be attempted3 that      
which1  arising in the north of ,africa1
 spread to southern ,europe1 thence to  

the northwest of ,europe and to         
,england--the architecture1 in short1 of
  the so-called civilized world4        
,this architecture1 anterior to the     
,christian era1 may be broadly  divided 
into three great periods1 during which  
it was successively  practiced by three 
peoples3 the ,egyptians1 the ,greeks and
 the ,romans4  ,then intervened the     
,dark ,ages1 and a new art arose1 the   
,gothic1 which  was a flowering out in  
stone of the spirit of ,christianity4   
,this was  in turn succeeded by the     
,renaissance1 the impulse of which      
remains  to-day unexhausted4 ,in each of
 these architectures the peculiar genius
  of a people and of a period attained  
to a beautiful1 complete and  coherent  
utterance1 and notwithstanding the      
considerable intervals  of time which   
sometimes separated them they succeeded 
one another  logically and inevitably1  
and each was related to the one which   
preceded and which followed it in a     
particular and intimate manner4    ,the 

power and wisdom of ancient ,egypt was  
vested in its priesthood1  which was    
composed of individuals exceptionally   
qualified by birth  and training for    
their high office1 tried by the severest
 ordeals  and bound by the most solemn  
oaths4 ,the priests were honored and    
privileged above all other men1 and     
spent their lives dwelling  apart from  
the multitude in vast and magnificent   
temples1 dedicating  themselves to the  
study and practice of religion1         
philosophy1 science  and art--subjects  
then intimately related1 not widely     
separated as  they are now4 ,these men  
were the architects of ancient ,egypt3  
theirs  the minds which directed the    
hands that built those time-defying     
monuments4    ,the rites that the       
priests practiced centered about what   
are known  as the ,lesser and the       
,greater ,mysteries4 ,these consisted of
  representations by means of symbol and
 allegory1 under conditions  and amid   
surroundings the most awe-inspiring1 of 

those great truths  concerning man's    
nature1 origin and destiny of which the 
priests--in  reality a brotherhood of   
initiates and their pupils--were the    
custodians4 ,these ceremonies were made 
the occasion for the initiation  of     
neophytes into the order1 and the       
advancement of the already  initiated   
into its successive degrees4 ,for the   
practice of such rites1  and others     
designed to impress not the elect but   
the multitude1 the  great temples of    
,egypt were constructed4 ,everything    
about them was  calculated to induce a  
deep seriousness of mind1 and to inspire
  feelings of awe1 dread and even       
terror1 so as to test the candidate's   
fortitude of soul to the utmost4    ,the
 avenue of approach to an ,egyptian     
temple was flanked on both  sides1      
sometimes for a mile or more1 with great
 stone sphinxes--that  emblem of man's  
dual nature1 the god emerging from the  
beast4 ,the  entrance was through a     
single high doorway between two towering

  pylons1 presenting a vast surface     
sculptured and painted over with  many  
strange and enigmatic figures1 and      
flanked by aspiring obelisks  and seated
 colossi with faces austere and calm4   
,the large court thus  entered was      
surrounded by high walls and colonnades1
 but was open  to the sky4 ,opposite the
 first doorway was another1 admitting to
 a  somewhat smaller enclosure1 a forest
 of enormous carved and painted  columns
 supporting a roof through the apertures
 of which sunshine  gleamed or dim light
 filtered down4 ,beyond this in turn    
were other  courts and apartments       
culminating in some inmost sacred       
sanctuary4    ,not alone in their       
temples1 but in their tombs and pyramids
 and  all the sculptured monuments of   
the ,egyptians1 there is the same       
insistence upon the sublimity1 mystery  
and awefulness of life1  which they seem
 to have felt so profoundly4 ,but more  
than this1 the  conscious thought of the
 masters who conceived them1 the        

buildings of  ,egypt give utterance also
 to the toil and suffering of the       
thousands  of slaves and captives which 
hewed the stones out of the heart of the
  rock1 dragged them long distances and 
placed them one upon another1 so  that  
these buildings oppress while they      
inspire1 for there is in them  no       
freedom1 no spontaneity1 no             
individuality1 but everywhere the felt  
presence of an iron conventionality1 of 
a stern immutable law4    ,in ,egyptian 
architecture is symbolized the condition
 of the human soul  awakened from its   
long sleep in nature1 and become        
conscious at once  of its divine source 
and of the leaden burden of its fleshy  
envelope4  ,egypt is humanity new-born1 
bound still with an umbilical cord to   
nature1 and strong not so much with its 
own strength as with the  strength of   
its mother4 ,this idea is aptly         
symbolized in those  gigantic colossi   
flanking the entrance to some rock-cut  
temple1 which  though entire are yet    

part of the living cliff out of which   
they were  fashioned4    ,in the        
architecture of ,greece the note of     
dread and mystery yields to  one of pure
 joyousness and freedom4 ,the terrors of
 childhood have been  outgrown1 and man 
revels in the indulgence of his unjaded 
appetites  and in the exercise of his   
awakened reasoning faculties4 ,in ,greek
 art  is preserved that evanescent      
beauty of youth which1 coming but once  
and continuing but for a short interval 
in every human life1 is yet  that for   
which all antecedent states seem a      
preparation1 and of  which all          
subsequent ones are in some sort an     
effect4 ,greece typifies  adolescence1  
the love age1 and so throughout the     
centuries humanity  has turned to the   
contemplation of her1 just as a man all 
his life  long secretly cherishes the   
memory of his first love4    ,an        
impassioned sense of beauty and an      
enlightened reason characterize  the    
productions of ,greek architecture      

during its best period4 ,the  perfection
 then attained was possible only in a   
nation whereof the  citizens were       
themselves critics and amateurs of art1 
one wherein  the artist was honored and 
his work appreciated in all its beauty  
and subtlety4 ,the ,greek architect was 
less bound by tradition and  precedent  
than was the ,egyptian1 and he worked   
unhampered by any  restrictions save    
such as1 like the laws of harmony in    
music1 helped  rather than hindered his 
genius to express itself--restrictions  
founded on sound reason1 the value of   
which had been proved by  experience4   
,the ,doric order was employed for all  
large temples1 since it possessed  in   
fullest measure the qualities of        
simplicity and dignity1 the  attributes 
appropriate to greatness4 ,quite        
properly also its formulas  were more   
fixed than those of any other style4    
,the ,ionic order1  the feminine of     
which the ,doric may be considered the  
corresponding  masculine1 was employed  

for smaller temples2 like a woman it was
 more  supple and adaptable than the    
,doric1 its proportions were more       
slender  and graceful1 its lines more   
flowing1 and its ornament more delicate 
and profuse4 ,a freer and more elaborate
 style than either of these1  infinitely
 various1 seeming to obey no law save   
that of beauty1 was  used sometimes for 
small monuments and temples1 such as the
 ,tower of  the ,winds1 and the monument
 of ,lysicrates at ,athens4             
,illustration #a    ,because the ,greek 
architect was at liberty to improve upon
 the work of  his predecessors if he    
could1 no temple was just like any      
other1  and they form an ascending scale
 of excellence1 culminating in the      
,acropolis group4 ,every detail was     
considered not only with relation  to   
its position and function1 but in regard
 to its intrinsic beauty as  well1 so   
that the merest fragment1 detached from 
the building of which  it formed a part1
 is found worthy of being treasured in  

our museums  for its own sake4    ,just 
as every detail of a ,greek temple was  
adjusted to its position  and expressed 
its office1 so the building itself was  
made to fit  its site and to show forth 
its purpose1 forming with the           
surrounding  buildings a unit of a      
larger whole4 ,the ,athenian ,acropolis 
is an  illustration of this3 it is an   
irregular fortified hill1 bearing       
diverse monuments in various styles1 at 
unequal levels and at  different angles 
with one another1 yet the whole         
arrangement seems as  organic and       
inevitable as the disposition of the    
features of a face4  ,the ,acropolis is 
an example of the ideal architectural   
republic  wherein each individual       
contributes to the welfare of all1 and  
at the  same time enjoys the utmost     
personal liberty 7,illustration #a74    
,very different is the spirit bodied    
forth in the architecture of  ,imperial 
,rome4 ,the iron hand of its sovereignty
 encased within the  silken glove of its

 luxury finds its prototype in buildings
 which were  stupendous crude brute     
masses of brick and concrete1 hidden    
within a  covering of rich marbles and  
mosaics1 wrought in beautiful but often 
meaningless forms by clever degenerate  
,greeks4 ,the genius of ,rome  finds its
 most characteristic expression1 not in 
temples to the high  gods1 but rather in
 those vast and complicated             
structures--basilicas1  amphitheatres1  
baths--built for the amusement and      
purely temporal  needs of the people4   
,if ,egypt typifies the childhood of the
 race and ,greece its beautiful  youth1 
,republican ,rome represents its strong 
manhood--a soldier filled  with the lust
 of war and the love of glory--and      
,imperial ,rome its  degeneracy3 that   
soldier become conqueror1 decked out in 
plundered  finery and sunk in           
sensuality1 tolerant of all who minister
 to his  pleasures but terrible to all  
who interfere with them4    ,the fall of
 ,rome marked the end of the ancient    

,pagan world4 ,above  its ruin          
,christian civilization in the course of
 time arose4 ,gothic  architecture is an
 expression of the ,christian spirit2 in
 it is  manifest the reaction from      
licentiousness to asceticism4 ,man's    
spiritual nature1 awakening in a body   
worn and weakened by  debaucheries1     
longs ardently and tries vainly to      
escape4 ,of some such  mood a ,gothic   
cathedral is the expression3 its        
vaulting1 marvelously  supported upon   
slender shafts by reason of a nicely    
adjusted  equilibrium of forces2 its    
restless1 upward-reaching pinnacles and 
spires2 its ornament1 intricate and     
enigmatic--all these suggest the        
over-strained organism of an ascetic2   
while its vast shadowy interior  lit by 
marvelously traceried and jeweled       
windows1 which hold the eyes  in a      
hypnotic thrall1 is like his soul3      
filled with world sadness1  dead to the 
bright brief joys of sense1 seeing only 
heavenly visions1  knowing none but     

mystic raptures4    ,thus it is that the
 history of architecture illustrates and
 enforces  the theosophical teaching    
that everything of man's creating is    
made in  his own image4 ,architecture   
mirrors the life of the individual and  
of  the race1 which is the life of the  
individual written large in time  and   
space4 ,the terrors of childhood2 the   
keen interests and appetites  of youth2 
the strong stern joy of conflict which  
comes with manhood2  the lust1 the      
greed1 the cruelty of a materialized old
 age--all these  serve but as a         
preparation for the life of the spirit1 
in which the  man becomes again as a    
little child1 going over the whole      
round1 but  on a higher arc of the      
spiral4    ,the final1 or fourth state  
being only in some sort a repetition of 
the first1 it would be reasonable to    
look for a certain correspondence       
between ,egyptian and ,gothic           
architecture1 and such a correspondence 
there is1 though it is more easily      

divined than demonstrated4 ,in  both    
there is the same deeply religious      
spirit2 both convey1 in some  obscure   
yet potent manner1 a sense of the soul  
being near the surface  of life4 ,there 
is the same love of mystery and of      
symbolism2 and in  both may be observed 
the tendency to create strange composite
 figures  to typify transcendental      
ideas1 the sphinx seeming a             
blood-brother to  the gargoyle4 ,the    
conditions under which each architecture
 flourished  were not dissimilar1 for   
each was formulated and controlled by   
small  well-organized bodies of         
sincerely religious and highly          
enlightened  men--the priesthood in the 
one case1 the masonic guilds in the     
other--working together toward the      
consummation of great undertakings  amid
 a populace for the most part oblivious 
of the profound and subtle  meanings of 
which their work was full4 ,in ,medival 
,europe1 as in  ancient ,egypt1         
fragments of the ,ancient               

,wisdom--transmitted in the  symbols and
 secrets of the cathedral               
builders--determined much of  ,gothic   
architecture4    ,the architecture of   
the ,renaissance period1 which succeeded
 the  ,gothic1 corresponds again1 in the
 spirit which animates it1 to ,greek    
architecture1 which succeeded the       
,egyptian1 for the ,renaissance as  the 
name implies was nothing other than an  
attempt to revive ,classical  antiquity4
 ,scholars writing in what they         
conceived to be a ,classical  style1    
sculptors modeling ,pagan deities1 and  
architects building  according to their 
understanding of ,vitruvian methods     
succeeded  in producing works like1 yet 
different from the originals they       
followed--different because1 animated by
 a spirit unknown to the  ancients1 they
 embodied a new ideal4    ,in all the   
productions of the early ,renaissance1  
that first  transcendent springtide of  
the modern world1 there is the          
evanescent  grace and beauty of youth   

which was seen to have pervaded ,greek  
art1  but it is a grace and beauty of a 
different sort4 ,the ,greek artist      
sought to attain to a certain abstract  
perfection of type2 to build  a temple  
which should combine all the            
excellencies of every similar  temple1  
to carve a figure1 impersonal in the    
highest sense1 which  should embody     
every beauty4 ,the artist of the        
,renaissance on the other  hand         
delighted not so much in the type as in 
the variation from it4  ,preoccupied    
with the unique mystery of the          
individual soul--a sense of  which was  
,christianity's gift to ,christendom--he
 endeavored to portray  that wherein a  
particular person is unique and         
singular4 ,acutely  conscious also of   
his own individuality1 instead of       
effacing it he  made his work the       
vehicle and expression of that          
individuality4 ,the  history of         
,renaissance architecture1 as ,symonds  
has pointed out1  is the history of a   

few eminent individuals1 each one       
moulding and  modifying the style in a  
manner peculiar to himself alone4 ,in   
the  hands of ,brunelleschi it was stern
 and powerful2 ,bramante made  it       
chaste1 elegant and graceful2 ,palladio 
made it formal1 cold1  symmetrical2     
while with ,sansovino and ,sammichele it
 became sumptuous  and bombastic4    ,as
 the ,renaissance ripened to decay its  
architecture assumed more and  more the 
characteristics which distinguished that
 of ,rome during the  decadence4 ,in    
both there is the same lack of          
simplicity and sincerity1  the same     
profusion of debased and meaningless    
ornament1 and there is  an increasing   
disposition to conceal and falsify the  
construction by  surface decoration4    
,the final part of this second or modern
 architectural cycle lies still  in the 
future4 ,it is not unreasonable to      
believe that the movement  toward       
mysticism1 of which modern theosophy is 
a phase and the  spiritualization of    

science an episode1 will flower out into
 an  architecture which will be in some 
sort a reincarnation of and a  return to
 the ,gothic spirit1 employing new      
materials1 new methods1  and developing 
new forms to show forth the spirit of   
the modern world1  without violating    
ancient verities4    ,in studying these 
crucial periods in the history of       
,european  architecture it is possible  
to trace a gradual growth or unfolding  
as of a plant4 ,it is a fact fairly well
 established that the ,greeks  derived  
their architecture and ornament from    
,egypt2 the ,romans in  turn borrowed   
from the ,greeks2 while a ,gothic       
cathedral is a lineal  descendant from a
 ,roman basilica4    ,illustration #b   
,illustration #c    ,the ,egyptians in  
their constructions did little more than
 to place  enormous stones on end1 and  
pile one huge block upon another4 ,they 
used many columns placed close together3
 the spaces which they spanned  were    
inconsiderable4 ,the upright or         

supporting member may be said to  have  
been in ,egyptian architecture the      
predominant one4 ,a vertical  line      
therefore may be taken as the simplest  
and most abstract symbol  of ,egyptian  
architecture 7,illustration #b74 ,it    
remained for the ,greeks  fully to      
develop the lintel4 ,in their           
architecture the vertical  member1 or   
column1 existed solely for the sake of  
the horizontal  member1 or lintel2 it   
rarely stood alone as in the case of an 
,egyptian  obelisk4 ,the columns of the 
,greek temples were reduced to those    
proportions most consistent with        
strength and beauty1 and the            
intercolumnations were relatively       
greater than in ,egyptian examples4  ,it
 may truly be said that ,greek          
architecture exhibits the perfect       
equality and equipoise of vertical and  
horizontal elements and these  only1 no 
other factor entering in4 ,its graphic  
symbol would therefore  be composed of a
 vertical and a horizontal line         

7,illustration #c74 ,the  ,romans1 while
 retaining the column and lintel of the 
,greeks1 deprived  them of their        
structural significance and subordinated
 them to the  semicircular arch and the 
semi-cylindrical and hemispherical      
vault1  the truly characteristic and    
determining forms of ,roman             
architecture4  ,our symbol grows        
therefore by the addition of the arc of 
a circle  7,illustration #d74 ,in       
,gothic architecture column1 lintel1    
arch and  vault are all retained in     
changed form1 but that which more than  
anything else differentiates ,gothic    
architecture from any style which       
preceded it is the introduction of the  
principle of an equilibrium of  forces1 
of a state of balance rather than a     
state of rest1 arrived at  by the       
opposition of one thrust with another   
contrary to it4 ,this fact  can be      
indicated graphically by two opposing   
inclined lines1 and  these united to the
 preceding symbol yield an accurate     

abstract of the  elements of ,gothic    
architecture 7,illustration #e74        
,illustration #d    ,illustration #e    
,all this is but an unusual application 
of a familiar theosophic  teaching1     
namely1 that it is the method of nature 
on every plane and  in every department 
not to omit anything that has gone      
before1 but to  store it up and carry it
 along and bring it into manifestation  
later4  ,nature everywhere proceeds like
 the jingle of ,the ,house that ,jack   
,built3 she repeats each time all she   
has learned1 and adds another  line for 
subsequent repetition4    ,footnote ,a3 
,the quaint ,oriental imagery here      
employed should not  blind the reader to
 the precise scientific accuracy of the 
idea of  which this imagery is the      
vehicle4 ,schopenhauer says3 ,polarity1 
or  the sundering of a force into two   
quantitively different and opposed      
activities striving after re-union1444  
is a fundamental type of almost  all the
 phenomena of nature1 from the magnet   

and the crystal to man  himself4        
,,ii    ,,unity ,,and ,,polarity        
,theosophy1 both as a philosophy1 or    
system of thought1 which discovers      
correlations between things apparently  
unrelated1 and as a life1  or system of 
training whereby it is possible to gain 
the power to  perceive and use these    
correlations for worthy ends1 is of     
great value  to the creative artist1    
whose success depends on the extent to  
which  he works organically1 conforming 
to the cosmic pattern1 proceeding       
rationally and rhythmically to some     
predetermined end4 ,it is of value  no  
less to the layman1 the critic1 the art 
amateur--to anyone in  fact who would   
come to an accurate and intimate        
understanding and  appreciation of every
 variety of esthetic endeavor4 ,for the 
benefit of  such ,i shall try to trace  
some of those correlations which        
theosophy  affirms1 and indicate their  
bearing upon art1 and upon the art of   
architecture in particular4    ,one of  

the things which theosophy teaches is   
that those transcendent  glimpses of a  
divine order and harmony throughout the 
universe  vouchsafed the poet and the   
mystic in their moments of vision are   
not  the paradoxes--the paronomasia as  
it were--of an intoxicated state of     
consciousness1 but glimpses of reality4 
,we are all of us participators  in a   
world of concrete music1 geometry and   
number--a world of  sounds1 odors1      
forms1 motions1 colors1 so              
mathematically related and  coordinated 
that our pigmy bodies1 equally with the 
farthest star1  vibrate to the music of 
the spheres4 ,there is a ,beautiful     
,necessity  which rules the world1 which
 is a law of nature and equally a law of
  art1 for art is idealized creation3   
nature carried to a higher power  by    
reason of its passage through a human   
consciousness4 ,thought and  emotion    
tend to crystallize into forms of beauty
 as inevitably as does  the frost on a  
window pane4 ,art therefore in one of   

its aspects is the  weaving of a        
pattern1 the communication of an order  
and a method to  the material or medium 
employed4 ,although no masterpiece was  
ever  created by the conscious following
 to set rules1 for the true artist      
works unconsciously1 instinctively1 as  
the bird sings or as the bee  builds its
 honey-cell1 yet an analysis of any     
masterpiece reveals the  fact that its  
author 7like the bird and the bee7 has  
followed the  rules without knowing     
them4    ,helmholtz says1 ,no doubt is  
now entertained that beauty is subject  
to laws and rules dependent on the      
nature of human intelligence4 ,the      
difficulty consists in the fact that    
these laws and rules1 on whose          
fulfilment beauty depends1 are not      
consciously present in the mind of  the 
artist who creates the work1 or of the  
observer who contemplates  it4          
,nevertheless they are discoverable1 and
 can be formulated1  after a fashion4   
,we have only to read aright the lessons

 everywhere  portrayed in the vast      
picture-books of nature and of art4     
,the first truth therein published is   
the law of ,unity--oneness2 for  there  
is one ,self1 one ,life1 which1 myriad  
in manifestation1 is yet  in essence    
ever one4 ,atom and universe1 man and   
the world--each is  a unit1 an organic  
and coherent whole4 ,the application of 
this law to  art is so obvious as to be 
almost unnecessary of elucidation1 for  
to  say that a work of art must possess 
unity1 must seem to proceed from a      
single impulse and be the embodiment of 
one dominant idea1 is to state  a       
truism4 ,in a work of architecture the  
cordination of its various  parts with  
one another is almost the measure of its
 success4 ,we  remember any             
masterpiece--the cathedral of ,paris no 
less than the  pyramids of ,egypt--by   
the singleness of its appeal2 complex it
 may be1  but it is a coordinated       
complexity2 variety it may possess1 but 
it is  a variety in an all-embracing    

unity4    ,the second law1 not          
contradicting but supplementing the     
first is the  law of ,polarity1 i4e41   
duality4 ,all things have sex1 are      
either  masculine or feminine4 ,this too
 is the reflection on a lower plane  of 
one of those transcendental truths      
taught by the ,ancient ,wisdom1  namely 
that the ,logos1 in his voluntarily     
circumscribing his infinite  life in    
order that he may manifest1 encloses    
himself within his  limiting veil1 maya1
 and that his life appears as spirit    
7male71 and  his maya as matter         
7female71 the two being never disjoined 
during  manifestation4 ,the two terms of
 this polarity are endlessly repeated   
throughout nature3 in sun and moon1 day 
and night1 fire and water1 man  and     
woman--and so on4 ,a close              
inter-relation is always seen to subsist
  between corresponding members of such 
pairs of opposites3 sun1 day1  fire1 man
 express and embody the primal and      
active aspect of the  manifesting deity2

 moon1 night1 water1 woman1 its         
secondary and  passive aspect4          
,moreover1 each implies or brings to    
mind the others  of its class3 man1 like
 the sun1 is lord of day2 he is like    
fire1 a  devastating force2 woman is    
subject to the lunar rhythm2 like water1
  she is soft1 sinuous1 fecund4    ,the 
part which this polarity plays in the   
arts is important1 and the  constant and
 characteristic distinction between the 
two terms is a  thing far beyond mere   
contrast4    ,in music they are the     
major and minor modes3 the typical1 or  
representative chords of the dominant   
seventh1 and of the tonic 7the  two     
chords into which ,schopenhauer says all
 music can be resolved73 a  partial     
dissonance1 and a consonance3 a chord of
 suspense1 and a chord  of satisfaction4
 ,in speech the two are vowel1 and      
consonant sounds3  the type of the first
 being a1 a sound of suspense1 made with
 the  mouth open2 and of the second m1 a
 sound of satisfaction1 made by  closing

 the mouth2 their combination forms the 
sacred syllable ,om  7,aum74 ,in        
painting they are warm colors1 and cold3
 the pole of  the first being in red1   
the color of fire1 which excites2 and of
 the  second in blue1 the color of      
water1 which calms2 in the ,arts of     
design  they are lines straight 7like   
fire71 and flowing 7like water72 masses 
light 7like the day71 and dark 7like    
night74 ,in architecture they are  the  
column1 or vertical member1 which       
resists the force of gravity2  and the  
lintel1 or horizontal member1 which     
succumbs to it2 they are  vertical      
lines1 which are aspiring1 effortful2   
and horizontal lines1  which are restful
 to the eye and mind4    ,it is         
desirable to have an instant and keen   
realization of this sex  quality1 and to
 make this easier some sort of          
classification and  analysis must be    
attempted4 ,those things which are      
allied to and  partake of the nature of 
time are masculine1 and those which are 

allied to and partake of the nature of  
space are feminine3 as  motion1 and     
matter2 mind1 and body2 etc4 ,the       
,english words masculine  and feminine  
are too intimately associated with the  
idea of physical  sex properly to       
designate the terms of this polarity4   
,in ,japanese  philosophy and art       
7derived from the ,chinese7 the two are 
called ,in  and ,yo 7,in1 feminine2 ,yo1
 masculine72 and these little words1    
being  free from the limitations of     
their ,english correlatives1 will be    
found  convenient1 ,yo to designate that
 which is simple1 direct1 primary1      
active1 positive2 and ,in1 that which is
 complex1 indirect1 derivative1         
passive1 negative4 ,things hard1        
straight1 fixed1 vertical1 are ,yo2     
things soft1 curved1 horizontal1        
fluctuating1 are ,in--and so on4        
,illustration #f3 ,,wild ,,cherry2      
,,maple ,,leaf    ,illustration #g3     
,,callas ,,in ,,yo    ,in passing it may
 be said that the superiority of the    

line1 mass1 and  color composition of   
,japanese prints and kakemonos to that  
exhibited  in the vastly more           
pretentious easel pictures of modern    
,occidental  artists--a superiority now 
generally acknowledged by               
connoisseurs--is  largely due to the    
conscious following1 on the part of the 
,japanese1  of this principle of        
sex-complementaries4    ,nowhere are ,in
 and ,yo more simply and adequately     
imaged than in the  vegetable kingdom4  
,the trunk of a tree is ,yo1 its        
foliage1 ,in2 and  in each stem and leaf
 the two are repeated4 ,a calla1        
consisting of  a single straight and    
rigid spadix embraced by a soft and     
tenderly  curved spathe1 affords an     
almost perfect expression of the        
characteristic differences between ,yo  
and ,in and their reciprocal  relation  
to each other4 ,the two are not often   
combined in such  simplicity and        
perfection in a single form4 ,the       
straight1 vertical  reeds which so often

 grow in still1 shallow water1 find     
their  complement in the curved         
lily-pads which lie horizontally on its 
surface4 ,trees such as pine and        
hemlock1 which are excurrent--those in  
which the branches start successively   
7i4e41 after the manner of time7  from a
 straight and vertical central stem--are
 ,yo2 trees such as  the elm and willow1
 which are deliquescent--those in which 
the trunk  dissolves as it were         
simultaneously 7after the manner of     
space7 into  its branches--are ,in4 ,all
 tree forms lie in or between these two 
extremes1 and leaves are susceptible of 
a similar classification4 ,it  will be  
seen to be a classification according to
 time and space1  for the characteristic
 of time is succession1 and of space1   
simultaneousness3 the first is expressed
 symbolically by elements  arranged with
 relation to axial lines2 the second1 by
 elements  arranged with relation to    
focal points 7,illustrations #f1g74     
,the student should train himself to    

recognize ,in and ,yo in all  their     
,protean presentments throughout        
nature--in the cloud upon the  mountain1
 the wave against the cliff1 in the     
tracery of trees against  the sky--that 
he may the more readily recognize them  
in his chosen  art1 whatever that art   
may be4 ,if it happens to be painting1  
he will  endeavor to discern this law of
 duality in the composition of every    
masterpiece1 recognizing an instinctive 
obedience to it in that  favorite device
 of the great ,renaissance masters of   
making an  architectural setting for    
their groups of figures1 and he will    
delight to trace the law in all its     
ramifications of contrast between       
complementaries in line1 color1 and mass
 7,illustration #h74    ,illustration   
#h3 ,,the ,,law ,,of ,,polarity         
,,cleopatra ,,melting ,,the ,,pearl4    
,,by  ,,tiepolo    ,with reference to   
architecture1 it is true1 generally     
speaking1  that architectural forms have
 been developed through necessity1 the  

function seeking and finding its        
appropriate form4 ,for example1 the     
buttress of a ,gothic cathedral was     
developed by the necessity of  resisting
 the thrust of the interior vaulting    
without encroaching upon  the nave2 the 
main lines of a buttress conform to the 
direction of the  thrust1 and the       
pinnacle with which it terminates is a  
logical shape  for the masonry necessary
 to hold the top in position            
7,illustration  #i74 ,research along    
these lines is interesting and fruitful 
of result1  but there remains a certain 
number of architectural forms whose     
origin  cannot be explained in any such 
manner4 ,the secret of their undying    
charm lies in the fact that in them ,in 
and ,yo stand symbolized and            
contrasted4 ,they no longer obey a law  
of utility1 but an abstract  law of     
beauty1 for in becoming sexually        
expressive as it were1 the  construction
 itself is sometimes weakened or        
falsified4 ,the familiar  classic       

console or modillion is an example3     
although in general  contour it is well 
adapted to its function as a supporting 
bracket1  embedded in1 and projecting   
from a wall1 yet the scroll-like        
ornament  with which its sides are      
embellished gives it the appearance of  
not entering the wall at all1 but of    
being stuck against it in some          
miraculous manner4 ,this defect in      
functional expressiveness is  more than 
compensated for by the perfection with  
which feminine  and masculine           
characteristics are expressed and       
contrasted in the  exquisite double     
spiral1 opposed to the straight lines of
 the moulding  which it subtends        
7,illustration #aj74 ,again1 by fluting 
the shaft of a  column its area of      
cross-section is diminished but the     
appearance of  strength is enhanced     
because its masculine character--as a   
supporting  member resisting the force  
of gravity--is emphasized4              
,illustration #i3 ,,cross ,,section ,,of

 ,,buttress4    ,the importance of the  
so-called orders lies in the fact that  
they  are architecture epitomized as it 
were4 ,a building consists of a wall    
upholding a roof3 support and weight4   
,the type of the first is the  column1  
which may be conceived of as a condensed
 section of wall2 and  of the second1   
the lintel1 which may be conceived of as
 a condensed  section of roof4 ,the     
column1 being vertical1 is ,yo2 the     
lintel1 being  horizontal1 is ,in4 ,to  
mark an entablature with horizontal     
lines in the  form of mouldings1 and the
 columns with vertical lines in the form
  of flutes1 as is done in all the      
classic orders1 is a gain  in functional
 and sex expressiveness1 and            
consequently in art  7,illustration     
#aa74    ,illustration #aj3 ,,corinthian
 ,,modillion2 ,,classic ,,console2      
,,ionic ,,cap    ,the column is again   
divided into the shaft1 which is ,yo2   
and the  capital1 which is ,in4 ,the    
capital is itself twofold1 consisting of

 a  curved member and an angular member4
 ,these two appear in their utmost      
simplicity in the echinus 7,in7 and the 
abacus 7,yo7 of a  ,greek ,doric cap4   
,the former was adorned with painted    
leaf forms1  characteristically         
feminine1 and the latter with the       
angular fret  and meander 7,illustration
 #ab74 ,the ,ionic capital1 belonging to
 a more  feminine style1 exhibits the   
abacus subordinated to that beautiful   
cushion-shaped member with its two      
spirally marked volutes4 ,this1  though 
a less rational and expressive form for 
its particular office  than is the      
echinus of the ,doric cap1 is a far more
 perfect symbol of  the feminine element
 in nature4 ,there is an essential      
identity between  the ,ionic cap and the
 classic console before referred        
to--although  superficially the two do  
not resemble each other--for a straight 
line  and a double spiral are elements  
common to both 7,illustration #aj74     
,the ,corinthian capital consists of an 

ordered mass of delicately  sculptured  
leaf and scroll forms sustaining an     
abacus which though  relatively         
masculine is yet more curved and        
feminine than that of any  other style4 
,in the caulicole of a ,corinthian cap  
,in and ,yo are again  contrasted4 ,in  
the unique and exquisite capital from   
the ,tower of the  ,winds at ,athens1   
the two are well suggested in the       
simple1 erect1 and  pointed leaf forms  
of the upper part1 contrasted with the  
complex1  deliquescent1 rounded ones    
from which they spring4 ,the essential  
identity of principle subsisting between
 this cap and the ,renaissance  baluster
 by ,san ,gallo is easily seen          
7,illustration #ac74    ,illustration   
#aa    ,illustration #ab    ,this law of
 sex-expressiveness is of such          
universality that it can  be made the   
basis of an analysis of the             
architectural ornament of any  style or 
period4 ,it is more than mere opposition
 and contrast4 ,the egg  and tongue     

motif1 which has persisted throughout so
 many centuries and  survived so many   
styles1 exhibits an alternation of forms
 resembling  phallic emblems4 ,yo and   
,in are well suggested in the channeled 
triglyphs and the sculptured metopes of 
a ,doric frieze1 in the  straight and   
vertical mullions and the flowing       
tracery of ,gothic  windows1 in the     
banded torus1 the bead and reel1 and    
other familiar  ornamented mouldings    
7,illustrations #ad1 #ae1 #af74         
,there are indications that at some time
 during the development  of ,gothic     
architecture in ,france1 this           
sex-distinction became a  recognized    
principle1 moulding and modifying the   
design of a cathedral  in much the same 
way that sex modifies bodily structure4 
,the masonic  guilds of the ,middle     
,ages were custodians of the            
esoteric--which is  the theosophic--side
 of the ,christian faith1 and every     
student of  esotericism knows how       
fundamental and how far-reaching is this

 idea of  sex4    ,illustration #ac3    
,,capital ,,from ,,the ,,tower ,,of     
,,the ,,winds1 ,,athens2  ,,corinthian  
,,cap ,,from ,,hadrian ,,buildings1     
,,athens2 ,,rosette ,,from ,,temple ,,of
  ,,mars1 ,,rome2 ,,cauliculus ,,of     
,,corinthian ,,cap2 ,,buluster ,,by     
,,san ,,gallo    ,illustration #ad3     
,,egg ,,and ,,tongue2 ,,bead ,,and      
,,reel2 ,,banded ,,torus    ,the entire 
cathedral symbolized the crucified body 
of ,christ2 its two  towers1 man and    
woman--that ,adam and that ,eve for     
whose redemption  according to current  
teaching ,christ suffered and was       
crucified4 ,the  north or right-hand    
tower 7the man's side7 was called the   
sacred  male pillar1 ,jachin2 and the   
south1 or left-hand tower 7the woman's  
side71 the sacred female pillar1 ,boaz1 
from the two columns flanking  the gate 
to ,solomon's ,temple--itself an        
allegory to the bodily temple4  ,in only
 a few of the ,french cathedrals is this
 distinction clearly  and consistently  

maintained1 and of these ,tours forms   
perhaps the most  remarkable example1   
for in its flamboyant faade1 over and   
above the  difference in actual breadth 
and apparent sturdiness of the two      
towers  7the south being the more       
slender and delicate71 there is a       
clearly  marked distinction in the      
character of the ornamentation1 that of 
the  north tower being more salient1    
angular1 radial--more masculine in      
point of fact 7,illustration #ag74 ,in  
,notre ,dame1 the cathedral of  ,paris1 
as in the cathedral of ,tours1 the north
 tower is perceptibly  broader than the 
south4 ,the only other important        
difference appears to  be in the angular
 label-mould above the north entrance3  
whatever may  have been its original    
function or significance1 it serves to  
define  the tower sexually1 so to speak1
 as effectively as does the beard on  a 
man's face4 ,in ,amiens the north tower 
is taller than the south1 and  more     
massive in its upper stages4 ,the only  

traceable indication of  sex in the     
ornamentation occurs in the spandrels at
 the sides of the  entrance arches3     
those of the north tower containing     
single circles1  and those of the south 
tower containing two in one4 ,this      
difference1  small as it may seem1 is   
significant1 for in ,europe during the  
,middle  ,ages1 just as anciently in    
,egypt and again in ,greece--in fact    
wherever  and whenever the ,secret      
,doctrine was known--sex was attributed 
to  numbers1 odd numbers being conceived
 of as masculine1 and even1 as          
feminine4 ,two1 the first feminine      
number1 thus became a symbol of         
femininity1 accepted as such so         
universally at the time the cathedrals  
were built1 that two strokes of a bell  
announced the death of a woman1  three1 
the death of a man4    ,illustration    
#ae3 ,,frieze ,,of ,,the ,,farnese      
,,palace2 ,,roman ,,console4 ,,vatican  
,,museum2 ,,frieze ,,in ,,the ,,empire  
,,style ,,by ,,percier ,,and ,,fontaine4

  ,,frieze ,,from ,,the ,,temple ,,of   
,,vesta ,,at ,,tivoli4 7,,roman72       
,,roman ,,doric  ,,frieze--,,vignole    
,illustration #af    ,illustration #ag  
,the vital1 organic quality so          
conspicuous in the best ,gothic         
architecture has been attributed to the 
fact that necessity determined  its     
characteristic forms4 ,professor        
,goodyear has demonstrated that  it may 
be due also in part to certain subtle   
vertical leans and  horizontal bends2   
and to nicely calculated variations from
 strict  uniformity1 which find their   
analogue in nature1 where structure is  
seldom rigidly geometrical4 ,the author 
hazards the theory that still  another  
reason why a ,gothic cathedral seems so 
living a thing is  because it abounds in
 contrasts between what1 for lack of    
more  descriptive adjectives1 he is     
forced to call masculine and feminine   
forms4    ,illustration #ah             
,illustration #ai    ,ruskin says1 in   
,stones of ,venice1 ,all good ,gothic is

 nothing more  than the development1 in 
various ways1 and on every conceivable  
scale1  of the group formed by the      
pointed arch for the bearing line below1
  and the gable for the protecting line 
above1 and from the huge1 gray1  shaly  
slope of the cathedral roof1 with its   
elastic pointed vaults  beneath1 to the 
crown-like points that enrich the       
smallest niche of  its doorway1 one law 
and one expression will be found in all4
 ,the  modes of support and of          
decoration are infinitely various1 but  
the  real character of the building1 in 
all good ,gothic1 depends on the  single
 lines of the gable over the pointed    
arch endlessly rearranged  and repeated4
 ,these two1 an angular and a curved    
form1 like the  everywhere recurring    
column and lintel of classic            
architecture1  are but presentments of  
,yo and ,in 7,illustration #ah74 ,every 
,gothic  traceried window1 with straight
 and vertical mullions in the           
rectangle1 losing themselves in the     

intricate foliations of the arch1       
celebrates the marriage of this ever    
diverse pair4 ,the circle and the       
triangle are the ,in and ,yo of ,gothic 
tracery1 its ,eve and ,adam1 as  it     
were1 for from their union springs that 
progeny of trefoil1  quatrefoil1        
cinquefoil1 of shapes flowing like      
water1 and shapes  darting like flame1  
which makes such visible music to the   
entranced  ear4    ,illustration #bj3   
,,san ,,gimignano ,s4 ,,jacopo4    ,by  
seeking to discover ,in and ,yo in their
 myriad manifestations1 by  learning to 
discriminate between them1 and by       
attempting to express  their            
characteristic qualities in new forms of
 beauty--from  the disposition of a     
faade to the shaping of a moulding--the 
architectural designer will charge his  
work with that esoteric  significance1  
that excess of beauty1 by which         
architecture rises  to the dignity of a 
fine art 7,illustrations #ai1 #bj74 ,in 
so doing1  however1 he should never     

forget1 and the layman also should ever 
remember1 that the supreme architectural
 excellence is fitness1                 
appropriateness1 the perfect adaptation 
of means to ends1 and the  adequate     
expression of both means and ends4      
,these two aims1 the one  abstract and  
universal1 the other concrete and       
individual1 can always  be combined1    
just as in every human countenance are  
combined a type1  which is universal1   
and a character1 which is individual4   
,,iii    ,,changeless ,,change          
,,trinity1 ,,consonance1 ,,diversity    
,,in ,,monotony1 ,,balance1 ,,rhythmic  
,,change1  ,,radiation      ,the        
preceding essay was devoted for the most
 part to that inevitable  duality which 
finds concrete expression in countless  
pairs of  opposites1 such as day and    
night1 fire and water1 man and woman2   
in the art of music by two chords1 one  
of suspense and the other of            
fulfilment2 in speech by vowel and      
consonant sounds1 epitomized in a  and  

in m2 in painting by warm colors and    
cold1 epitomized in red  and blue2 in   
architecture by the vertical column and 
the horizontal  lintel1 by void and     
solid--and so on4      ,,trinity        
,this concept should now be modified by 
another1 namely1 that in every  duality 
a third is latent2 that two implies     
three1 for each sex so  to speak is in  
process of becoming the other1 and this 
alternation  engenders and is           
accomplished by means of a third term or
 neuter1  which is like neither of the  
original two but partakes of the nature 
of them both1 just as a child may       
resemble both its parents4 ,twilight    
comes between day and night2 earth is   
the child of fire and water2  in music1 
besides the chord of longing and        
striving1 and the chord of  rest and    
satisfaction 7the dominant seventh and  
the tonic71 there is  a third or        
resolving chord in which the two are    
reconciled4 ,in the  sacred syllable ,om
 7,aum71 which epitomizes all speech1   

the u sound  effects a transition       
between the a sound and the m2 among the
  so-called primary colors yellow comes 
between red and blue2 and in            
architecture the arch1 which is both    
weight and support1 which is  neither   
vertical nor horizontal1 may be         
considered the neuter of the  group of  
which the column and the lintel are     
respectively masculine  and feminine4   
,these are the three1 says ,mr4 ,louis  
,sullivan1 the  only three letters from 
which has been expanded the             
architectural art1  as a great and      
superb language wherewith man has       
expressed1 through  the generations1 the
 changing drift of his thoughts4        
,illustration #ba3 ,,the ,,law ,,of     
,,trinity4 ,a ,,roman ,,ionic ,,arcade1 
,,by  ,,vignole4--,,the ,,column1 ,,the 
,,entablature1 ,,and ,,the ,,arch       
,,correspond ,,to ,,lines  ,,vertical1  
,,horizontal ,,and ,,curved4    ,it     
would be supererogatory to dwell at any 
length on this trinity  of manifestation

 as the concrete expression of that     
unmanifest and  mystical trinity1 that  
three-in-one which under various names  
occurs  in every world-religion1 where1 
defying definition1 it was wont  to find
 expression symbolically in some        
combination of vertical1  horizontal and
 curved lines4 ,the anstated cross of   
the ,egyptians  is such a symbol1 the   
,buddhist wheel1 and the fylfot or      
swastika  inscribed within a circle1    
also those numerous ,christian symbols  
combining the circle and the cross4     
,such ideographs have spelled  profound 
meaning to the thinkers of past ages4   
,we of to-day are not  given to         
discovering anything wonderful in three 
strokes of a pen1  but every artist in  
the weaving of his pattern must needs   
employ these  mystic symbols in one form
 or another1 and if he employs them with
  a full sense of their hidden meaning  
his work will be apt to gain  in        
originality and beauty--for originality 
is a new and personal  perception of    

beauty1 and beauty is the name we give  
to truth we  cannot understand4    ,in  
architecture1 this trinity of vertical1 
horizontal and curved  lines finds      
admirable illustration in the           
application of columns and  entablature 
to an arch and impost construction1 so  
common in ,roman and  ,renaissance work4
 ,this is a redundancy1 and finds no    
justification in  reason1 because the   
weight is sustained by the arch1 and the
 order  is an appendage merely2 yet the 
combination1 illogical as it is1        
satisfies the sense of beauty because   
the arch effects a transition  between  
the columns and the entablature1 and    
completes the trinity  of vertical1     
horizontal and curved lines             
7,illustration #ba74 ,in the  entrances 
to many of the ,gothic cathedrals and   
churches the same  elements are better  
because more logically disposed4 ,here  
the  horizontal lintel and its vertical 
supports are not decorative merely1  but
 really perform their proper functions1 

while the arch1 too1 has  a raison d'tre
 in that it serves to relieve the lintel
 of the  superincumbent weight of       
masonry4 ,the same arrangement sometimes
  occurs in classic architecture also1  
as when an opening spanned by a  single 
arch is subdivided by means of an order 
7,illustration #bb74    ,three is       
pre-eminently the number of             
architecture1 because it is the  number 
of space1 which for us is               
three-dimensional1 and of all the  arts 
architecture is most concerned with the 
expression of spatial  relations4 ,the  
division of a composition into three    
related parts is  so universal that it  
would seem to be the result of an       
instinctive  action of the human mind4  
,the twin pylons of an ,egyptian temple 
with  its entrance between1 for a third 
division1 has its correspondence in  the
 two towers of a ,gothic cathedral and  
the intervening screen  wall of the     
nave4 ,in the palaces of the            
,renaissance a threefold                

division--vertically by means of quoins 
or pilasters1 and horizontally  by means
 of cornices or string courses--was     
common1 as was also the  division into a
 principal and two subordinate masses   
7,illustration  #bc74    ,illustration  
#bb3 ,,the ,,law ,,of ,,trinity4 ,,the  
,,trinity ,,of ,,horizontal ,,vertical  
,,and ,,curved ,,lines4    ,the         
architectural orders are divided        
threefold into pedestal or  stylobate1  
column and entablature2 and each of     
these is again divided  threefold3 the  
first into plinth1 die and cornice2 the 
second into  base1 shaft and capital2   
the third into architrave1 frieze and   
cornice4 ,in many cases these again lend
 themselves to a threefold  subdivision4
 ,a more detailed analysis of the       
capitals already shown to  be twofold   
reveals a third member3 in the ,greek   
,doric this consists  of the annulets   
immediately below the abacus2 in the    
other orders1 the  necking which divides
 the shaft from the cap4                

,,consonance    ,as is the small1 so is 
the great is a perpetually recurring    
phrase  in the literature of theosophy1 
and naturally so1 for it is a succinct  
statement of a fundamental and          
far-reaching truth4 ,the scientist      
recognizes it now and then and here and 
there1 but the occultist  trusts it     
always and utterly4 ,to him the         
microcosm and the macrocosm  are one and
 the same in essence1 and the           
forth-going impulse  which calls a      
universe into being and the indrawing   
impulse which  extinguishes it again1   
each lasting millions of years1 are     
echoed and  repeated in the inflow and  
outflow of the breath through the       
nostrils1  in nutrition and excretion1  
in daily activity and nightly rest1 in  
that longer day which we name a         
lifetime1 and that longer rest in       
,devachan--and so on until time itself  
is transcended4    ,illustration #bc    
,in the same way1 in nature1 a thing is 
echoed and repeated throughout  its     

parts4 ,each leaf on a tree is itself a 
tree in miniature1 each  blossom a      
modified leaf2 every vertebrate animal  
is a complicated  system of spines2 the 
ripple is the wave of a larger wave1 and
 that  larger wave is a part of the     
ebbing and flowing tide4 ,in music this 
law is illustrated in the return of the 
tonic to itself in the octave1  and its 
partial return in the dominant2 also in 
a more extended sense  in the repetition
 of a major theme in the minor1 or in   
the treble and  again in the bass1 with 
modifications perhaps of time and key4  
,in  the art of painting the law is     
exemplified in the repetition with      
variation of certain colors and         
combinations of lines in different      
parts of the same picture1 so disposed  
as to lead the eye to some  focal point4
 ,every painter knows that any important
 color in his  picture must be echoed1  
as it were1 in different places1 for    
harmony  of the whole4    ,illustration 
#bd    ,in the drama the repetition of a

 speech or of an entire scene1 but      
under circumstances which give it a     
different meaning1 is often most        
effective1 as when ,gratiano1 in the    
trial scene of ,the ,merchant  of       
,venice taunts ,shylock with his own    
words1 ,a ,daniel come to  judgment6 or1
 as when in one of the later scenes of  
,as ,you ,like ,it  an earlier scene is 
repeated1 but with ,rosalind speaking in
 her proper  person and no longer as the
 boy ,ganymede4    ,these recurrences1  
these inner consonances1 these          
repetitions with  variations are common 
in architecture also4 ,the channeled    
triglyphs of  a ,greek ,doric frieze    
echo the fluted columns below           
7,illustration #bd74  ,the balustrade   
which crowns a colonnade is a           
repetition1 in some sort1  of the       
colonnade itself4 ,the modillions of a  
,corinthian cornice are  but elaborated 
and embellished dentils4 ,each pinnacle 
of a ,gothic  cathedral is a little     
tower with its spire4 ,as ,ruskin has   

pointed out1  the great vault of the    
cathedral nave1 together with the       
pointed roof  above it1 is repeated in  
the entrance arch with its gable1 and   
the  same two elements appear in every  
statue-enshrining niche of the  doorway4
 ,in classic architecture1 as has been  
shown1 instead of the  arch and gable1  
the column and entablature everywhere   
recur under  different forms4 ,the minor
 domes which flank the great dome of the
  cathedral of ,florence enhance and    
reinforce the latter1 and prepare  the  
eye for a climax which would otherwise  
be too abrupt4 ,the central  pavilion of
 the ,chteau ,maintenon1 with its two   
turrets1 echoes the  entire faade with  
its two towers4 ,like the overture to an
 opera1 it  introduces themes which find
 a more extended development elsewhere  
7,illustration #bf74    ,illustration   
#be    ,illustration #bf                
,illustration #bg    ,this law of       
,consonance is operative in architecture
 more obscurely  in the form of         

recurring numerical ratios1 identical   
geometrical  determining figures1       
parallel diagonals and the like1 which  
will be  discussed in a subsequent      
essay4 ,it has also to do with style and
  scale1 the adherence to substantially 
one method of construction and  manner  
of ornament1 just as in music the key1  
or chosen series of  notes1 may not be  
departed from except through proper     
modulations1 or  in a specific manner4  
,thus it is seen that in a work of art1 
as in a piece of tapestry1  the same    
thread runs through the web1 but goes to
 make up different  figures4 ,the idea  
is deeply theosophic3 one life1 many    
manifestations2  hence1 inevitably1     
echoes1 resemblances--,consonance4      
,,diversity ,,in ,,monotony    ,another 
principle of natural beauty1 closely    
allied to the foregoing1  its complement
 as it were1 is that of ,diversity in   
,monotony--not  identity1 but           
difference4 ,it shows itself for the    
most part as a  perceptible and piquant 

variation between individual units      
belonging  to the same class1 type1 or  
species4    ,no two trees put forth     
their branches in just the same manner1 
and no  two leaves from the same tree   
exactly correspond2 no two persons  look
 alike1 though they have similiar       
members and features2 even the  markings
 on the skin of the thumb are different 
in every human hand4  ,browning says1   
,as like as a hand to another hand6     
,whoever said that foolish thing1       
,could not have studied to understand-- 
,now every principle of natural beauty  
is but the presentment of some  occult  
law1 some theosophical truth2 and this  
law of ,diversity in  ,monotony is the  
presentment of the truth that identity  
does not  exclude difference4 ,the law  
is binding1 yet the will is free3 all   
men  are brothers united by the ties of 
brotherhood1 yet each is unique1 a  free
 agent1 and never so free as when most  
bound by the ,good ,law4 ,this  truth   
nature beautifully proclaims1 and art   

also4 ,in architecture it  is admirably 
exemplified in the metopes of the       
,parthenon frieze3 seen  at a distance  
these must have presented a scarcely    
distinguishable  texture of sunlit      
marble and cool shadow1 yet in reality  
each is  a separate work of art4 ,so    
with the capitals of the columns of the 
wonderful sea-arcade of the ,venetian   
,ducal palace3 alike in general  contour
 they differ widely in detail1 and      
unfold a ,bible story4  ,in ,gothic     
cathedrals1 in ,romanesque monastery    
cloisters1 a teeming  variety of        
invention is hidden beneath apparent    
uniformity4 ,the  gargoyles of ,notre   
,dame make similiar silhouettes against 
the sky1  but seen near at hand what a  
menagerie of monsters6 ,the same spirit 
of  controlled individuality1 of liberty
 subservient to the law of all1 is      
exemplified in the bases of the columns 
of the temple of ,apollo near           
,miletus--each one a separate           
masterpiece of various ornamentation    

adorning an established architectural   
form 7,illustration #bh74               
,illustration #bh    ,illustration #bi  
,the builders of the early ,italian     
churches1 instinctively obeying this    
law of ,diversity in ,monotony1 varied  
the size of the arches in the  same     
arcade 7,illustration #bi71 and that    
this was an effect of art and  not of   
accident or carelessness ,ruskin long   
ago discovered1 and the  ,brooklyn      
,institute surveys have amply confirmed 
his view4 ,although  by these means the 
builders of that day produced effects of
 deceptive  perspective1 of subtle      
concord and contrast1 their sheer hatred
 of  monotony and meaningless repetition
 may have led them to diversify  their  
arcades in the manner described1 for a  
rigidly equal and regular  division     
lacks interest and vitality4            
,,balance    ,if one were to establish  
an axial plane vertically through the   
center  of a tree1 in most cases it     
would be found that the masses of       

foliage1  however irregularly shaped on 
either side of such an axis1 just about 
balanced each other4 ,similarly1 in all 
our bodily movements1 for every  change 
of equilibrium there occurs an          
opposition and adjustment of  members of
 such a nature that an axial plane      
through the center of  gravity would    
divide the body into two substantially  
equal masses1  as in the case of the    
tree4 ,this physical plane law of       
,balance  shows itself for the most part
 on the human plane as the law of       
,compensation1 whereby1 to the vision of
 the occultist1 all accounts  are       
squared1 so to speak4 ,it is in effect  
the law of ,justice1 aptly  symbolized  
by the scales4    ,the law of ,balance  
finds abundant illustration in art3 in  
music by  the opposition1 the answering1
 of one phrase by another of the same   
elements and the same length1 but       
involving a different sequence of       
intervals2 in painting by the           
disposition of masses in such a way that

  they about equalize one another1 so   
that there is no sense of strain  in the
 composition4    ,in architecture the   
common and obvious recognition of the   
law of  ,balance is in the symmetrical  
disposition of the elements1 whether of 
plan or of elevation1 on either side of 
axial lines4 ,a far more subtle  and    
vital illustration of the law occurs    
when the opposed elements do  not       
exactly match1 but differ from each     
other1 as in the case of the  two towers
 of ,amiens1 for example4 ,this sort of 
balance may be said to  be              
characteristic of ,gothic1 as symmetry  
is characteristic of ,classic1          
architecture4      ,,rhythmic ,,change  
,there is in nature a universal tendency
 toward refinement and  compactness of  
form in space1 or contrariwise1 toward  
increment  and diffusion2 and this      
manifests itself in time as acceleration
 or  retardation4 ,it is governed1 in   
either case1 by an exact mathematical   
law1 like the law of falling bodies4 ,it

 shows itself in the widening  circles  
which appear when one drops a stone into
 still water1 in the  convolutions of   
shells1 in the branching of trees and   
the veining  of leaves2 the diminution  
in the size of the pipes of an organ    
illustrates it1 and the spacing of the  
frets of a guitar4 ,more and  more      
science is coming to recognize1 what    
theosophy affirms1 that the  spiral     
vortex1 which so beautifully illustrates
 this law1 both in its  time and its    
space aspects is the universal          
archetype1 the pattern of  all that is1 
has been1 or will be1 since it is the   
form assumed by the  ultimate physical  
atom1 and the ultimate physical atom is 
the physical  cosmos in miniature4      
,this ,rhythmic ,diminution is          
everywhere3 it is in the eye itself1 for
  any series of mathematically equal    
units1 such for example as the  columns 
and intercolumnations of a colonnade1   
become when seen  in perspective        
rhythmically unequal1 diminishing       

according to the  universal law4 ,the   
entasis of a ,classic column is         
determined by this  law1 the spirals of 
the ,ionic volute1 the annulets of the  
,parthenon  cap1 obey it 7,illustration 
#cj74    ,in recognition of the same    
principle of ,rhythmic ,diminution a    
building  is often made to grow1 or     
appear to grow lighter1 more intricate1 
finer1 from the ground upward1 an end   
attained by various devices1  one of the
 most common being the employment of the
 more attenuated  and highly ornamented 
orders above the simpler and sturdier1  
as in the  ,roman ,colosseum1 or in the 
,palazzo ,uguccioni1 in ,florence--to   
mention  only two examples out of a     
great number4 ,in the ,riccardi ,palace 
an effect of increasing refinement is   
obtained by diminishing the  boldness of
 the rustication of the ashlar in       
successive stories2 in  the ,farnese1 by
 the gradual reduction of the size of   
the angle quoins  7,illustration #cj74  
,in an ,egyptian pylon it is achieved   

most simply by  battering the wall2 in a
 ,gothic cathedral most elaborately by a
  kind of segregation1 or breaking up1  
analogous to that which a tree          
undergoes--the strong1 relatively       
unbroken base corresponding to  the     
trunk1 the diminishing buttresses to the
 tapering limbs1 and  the multitude of  
delicate pinnacles and crockets1 to the 
outermost  branches and twigs1 seen     
against the sky4      ,,radiation       
,the final principle of natural beauty  
to which the author would call          
attention is the law of ,radiation1     
which is in a manner a return  to the   
first1 the law of ,unity4 ,the various  
parts of any organism  radiate from1 or 
otherwise refer back to common centers1 
or foci1  and these to centers of their 
own4 ,the law is represented in its     
simplicity in the star-fish1 in its     
complexity in the body of man2 a  tree  
springs from a seed1 the solar system   
centers in the sun4    ,the idea here   
expressed by the term radiation is a    

familiar one  to all students of        
theosophy4 ,the ,logos radiates his life
 and light  throughout his universe1    
bringing into activity a host of        
entities  which become themselves radial
 centers2 these generate still others1  
and so on endlessly4 ,this principle1   
like every other1 patiently  publishes  
itself to us1 unheeding1 everywhere in  
nature1 and in  all great art as well2  
it is a law of optics1 for example1 that
 all  straight lines having a common    
direction if sufficiently prolonged     
appear to meet in a point1 i4e41 radiate
 from it 7,illustration #ca74  ,leonardo
 da ,vinci employed this principle of   
perspective in his ,last  ,supper to    
draw the spectator's eye to the         
picture's central figure1  the point of 
sight toward which the lines of the     
walls and ceiling  converge centering in
 the head of ,christ4 ,puvis de         
,chavannes1 in his  ,boston ,library    
decoration1 leads the eye by a system of
 triangulation  to the small figure of  

the ,genius of ,enlightenment above the 
central  door 7,illustration #cb72 and  
,ruskin1 in his ,elements of ,drawing1  
has  shown how artfully ,turner arranged
 some of his compositions to attract    
attention to a focal point4    ,this law
 of ,radiation enters largely into      
architecture4 ,the ,colosseum1  based   
upon the ellipse1 a figure generated    
from two points or foci1  and the       
,pantheon1 based upon the circle1 a     
figure generated from a  central point1 
are familiar examples4 ,the distinctive 
characteristic  of ,gothic construction1
 the concentration or focalization of   
the  weight of the vaults and arches at 
certain points1 is another  illustration
 of the same principle applied to       
architecture1  beautifully exemplified  
in the semicircular apse of a cathedral1
 where  the lines of the plan converge  
to a common center1 and the ribs of the 
vaulting meet upon the capitals of the  
piers and columns1 seeming  to radiate  
thence to still other centers in the    

loftier vaults which  finally meet in a 
center common to all4    ,illustration  
#cj    ,illustration #ca                
,illustration #cb    ,the tracery of the
 great roses1 high up in the faades of  
the  cathedrals of ,paris and of        
,amiens1 illustrate ,radiation1 in the  
one  case masculine3 straight1 angular1 
direct2 in the feminine3 curved1        
flowing1 sinuous4 ,the same ,beautiful  
,necessity determined the               
characteristics of much of the ornament 
of widely separated styles  and periods3
 the ,egyptian lotus1 the ,greek        
honeysuckle1 the ,roman  acanthus1      
,gothic leaf work--to snatch at random  
four blossoms from  the sheaf of time4  
,the radial principle still inherent in 
the debased  ornament of the late       
,renaissance gives that ornament a      
unity1 a  coherence1 and a kind of      
beauty all its own 7,illustration #ce74 
,illustration #cc    ,illustration #cd  
,such are a few of the more obvious laws
 of natural beauty and their            

application to the art of architecture4 
,the list is by no means  exhausted1 but
 it is not the multiplicity and         
diversity of these laws  which is       
important to keep in mind1 so much as   
their relatedness and  cordination1 for 
they are but different aspects of the   
,one ,law1 that  whereby the ,logos     
manifests in time and space4 ,a brief   
recapitulation  will serve to make this 
correlation plain1 and at the same time 
fix  what has been written more firmly  
in the reader's mind4    ,illustration  
#ce    ,illustration #cf    ,first comes
 the law of ,unity2 then1 since every   
unit is in its  essence twofold1 there  
is the law of ,polarity2 but this       
duality is  not static but dynamic1 the 
two parts acting and reacting upon one  
another to produce a third--hence the   
law of ,trinity4 ,given this  third     
term1 and the innumerable combinations  
made possible by  its relations to and  
reactions upon the original pair1 the   
law  of ,multiplicity in ,unity         

naturally follows1 as does the law  of  
,consonance1 or repetition1 since the   
primal process of  differentiation tends
 to repeat itself1 and the original     
combinations  to reappear--but to       
reappear in changed form1 hence the law 
of  ,diversity in ,monotony4 ,the law of
 ,balance is seen to be but a           
modification of the law of ,polarity1   
and since all things are waxing  and    
waning1 there is the law whereby they   
wax and wane1 that of  ,rhythmic        
,change4 ,radiation rediscovers and     
reaffirms1 even in the  utmost          
complexity1 that essential and          
fundamental unity from which  complexity
 was wrought4    ,everything1 beautiful 
or ugly1 obeys and illustrates one or   
another of  these laws1 so universal are
 they1 so inseparably attendant upon    
every  kind of manifestation in time and
 space4 ,it is the number of them  which
 finds illustration within small        
compass1 and the aptness and            
completeness of such illustration1 which

 makes for beauty1 because  beauty is   
the fine flower of a sort of sublime    
ingenuity4 ,a work of  art is nothing if
 not artful3 like an acrostic1 the more 
different  ways it can be read--up1     
down1 across1 from right to left and    
from  left to right--the better it is1  
other things being equal4 ,this         
statement1 of course1 may be construed  
in such a way as to appear  absurd2 what
 is meant is simply that the more a work
 of art is  freighted and fraught with  
meaning beyond meaning1 the more secure 
its  immortality1 the more powerful its 
appeal4 ,for enjoyment1 it is not       
necessary that all these meanings should
 be fathomed1 it is only  necessary that
 they should be felt4    ,consider for a
 moment the manner in which ,leonardo da
 ,vinci's ,last  ,supper1 an            
acknowledged masterpiece1 conforms to   
everyone of the laws  of beauty         
enumerated above 7,illustration #cb74   
,it illustrates the law  of ,unity in   
that it movingly portrays a single      

significant episode in  the life of     
,christ4 ,the eye is led to dwell upon  
the central personage  of this drama by 
many artful expedients3 the visible part
 of the  figure of ,christ conforms to  
the lines of an equilateral triangle    
placed exactly in the center of the     
picture2 the figure is separated  by a  
considerable space from the groups of   
the disciples on either  hand1 and      
stands relieved against the largest     
parallelogram of light1  and the        
vanishing point of the perspective is in
 the head of ,christ1  at the apex1     
therefore1 of the triangle4 ,the law of 
,polarity finds  fulfilment in the      
complex and flowing lines of the draped 
figures  contrasted with the simple     
parallelogram of the cloth-covered      
table1  and the severe architecture of  
the room4 ,the law of ,trinity is       
exemplified in the three windows1 and in
 the subdivision of the twelve  figures 
of the disciples into four groups of    
three figures each4 ,the  law of        

,consonance appears in the repetition of
 the horizontal lines  of the table in  
the ceiling above2 and in the central   
triangle before  referred to1 continued 
and echoed1 as it were1 in the          
triangular  supports of the table       
visible underneath the cloth4 ,the law  
of  ,diversity in ,monotony is          
illustrated in the varying disposition  
of the  heads of the figures in the four
 groups of three2 the law of ,balance   
in the essential symmetry of the entire 
composition2 the law of  ,rhythmic      
,change in the diminishing of the wall  
and ceiling spaces2 and  the law of     
,radiation in the convergence of all the
 perspective lines  to a single         
significant point4    ,to illustrate    
further the universality of these laws1 
consider now  their application to a    
single work of architecture3 the ,taj   
,mahal1 one  of the most beautiful      
buildings of the world 7,illustration   
#cf74 ,it is  a unit1 but twofold1 for  
it consists of a curved part and an     

angular  part1 roughly figured as an    
inverted cup upon a cube2 each of these 
7seen in parallel perspective1 at the   
end of the principal vista7 is          
threefold1 for there are two sides and a
 central parallelogram1 and  two lesser 
domes flank the great dome4 ,the        
composition is rich in  consonances1 for
 the side arches echo the central one1  
the subordinate  domes the great dome1  
and the lanterns of the outstanding     
minarets  repeat the principal motif4   
,diversity in ,monotony appears         
abundantly  in the ornament1 which is   
intricate and infinitely various2 the   
law of  ,balance is everywhere operative
 in the symmetry of the entire design4  
,rhythmic ,change appears in the        
tapering of the minarets1 the outlines  
of the domes and their mass relations to
 one another2 and finally1  the whole   
effect is of radiation from a central   
point1 of elements  disposed on radial  
lines4    ,it would be fatuous to       
contend that the prime object of a work 

of  architecture is to obey and         
illustrate these laws4 ,the prime object
 of  a work of architecture is to       
fulfill certain definite conditions in a
  practical1 economical1 and admirable  
way1 and in fulfilling to express  as   
far as possible these conditions1 making
 the form express the  function4 ,the   
architect who is also an artist however 
will do this  and something beyond3     
working for the most part unconsciously1
  harmoniously1 joyously1 his building  
will obey and illustrate natural        
laws--these laws of beauty--and to the  
extent it does so it will be a  work of 
art2 for art is the method of nature    
carried into those higher  regions of   
thought and feeling which man alone     
inhabits3 regions which  it is one of   
the purposes of theosophy to explore4   
,,iv    ,,the ,,bodily ,,temple         
,carlyle says3 ,there is but one temple 
in the world1 and that is the  body of  
man4 ,if the body is1 as he declares1 a 
temple1 it is not less  true that a     

temple or any work of architectural art 
is a larger body  which man has created 
for his uses1 just as the individual    
self is  housed within its stronghold of
 flesh and bones4 ,architectural beauty 
like human beauty depends upon the      
proper subordination of parts  to the   
whole1 the harmonious interrelation     
between these parts1 the  expressiveness
 of each of its function or functions1  
and when these  are many and diverse1   
their reconcilement one with another4   
,this being  so1 a study of the human   
figure with a view to analyzing the     
sources  of its beauty cannot fail to be
 profitable4 ,pursued intelligently1    
such a study will stimulate the mind to 
a perception of those simple  yet subtle
 laws according to which nature         
everywhere works1 and  it will educate  
the eye in the finest known school of   
proportion1  training it to distinguish 
minute differences1 in the same way that
  the hearing of good music cultivates  
the ear4    ,those principles of natural

 beauty which formed the subject of the 
two preceding essays are all exemplified
 in the ideally perfect human  figure4  
,though essentially a unit1 there is a  
well marked division  into right and    
left--,hands to hands1 and feet to feet1
 in one body  grooms and brides4 ,there 
are two arms1 two legs1 two ears1 two   
eyes1  and two lids to each eye2 the    
nose has two nostrils1 the mouth has    
two lips4 ,moreover1 the terms of such  
pairs are masculine and feminine  with  
respect to each other1 one being active 
and the other passive4  ,owing to the   
great size and one-sided position of the
 liver1 the right  half of the body is  
heavier than the left2 the right arm is 
usually  longer and more muscular than  
the left2 the right eye is slightly     
higher than its fellow4 ,in speaking and
 eating the lower jaw and under  lip are
 active and mobile with relation to the 
upper2 in winking it is  the upper      
eyelid which is the more active4 ,that  
inevitable duality  which is exhibited  

in the form of the body characterizes   
its motions  also4 ,in the act of       
walking for example1 a forward movement 
is  attained by means of a forward and a
 backward movement of the thighs  on the
 axis of the hips2 this leg movement    
becomes twofold again below  the knee1  
and the feet move up and down           
independently on the axis of  the ankle4
 ,a similar progression is followed in  
raising the arm and  hand3 motion is    
communicated first to the larger parts1 
through them  to the smaller and thence 
to the extremities1 becoming more rapid 
and  complex as it progresses1 so that  
all free and natural movements of  the  
limbs describe invisible lines of beauty
 in the air4 ,coexistent  with this     
pervasive duality there is a threefold  
division of the  figure into trunk1 head
 and limbs3 a superior trinity of head  
and  arms1 and an inferior trinity of   
trunk and legs4 ,the limbs are divided  
threefold into upper-arm1 forearm and   
hand2 thigh1 leg and foot4 ,the  hand   

flowers out into fingers and the foot   
into toes1 each with a  threefold       
articulation2 and in this way is        
effected that transition  from unity to 
multiplicity1 from simplicity to        
complexity1 which  appears to be so     
universal throughout nature1 and of     
which a tree is  the perfect symbol4    
,illustration #cg3 ,,the ,,law ,,of     
,,rhythmic ,,diminution ,,illustrated   
,,in ,,the  ,,tapering ,,body1 ,,limbs1 
,,fingers  ,,toes4    ,illustration #ch 
,illustration #ci    ,the body is rich  
in veiled repetitions1 echoes1          
consonances4 ,the  head and arms are in 
a sense a refinement upon the trunk and 
legs1  there being a clearly traceable  
correspondence between their various    
parts4 ,the hand is the body in         
little--,your soft hand is a woman of   
itself--the palm1 the trunk2 the four   
fingers1 the four limbs2 and  the thumb1
 the head2-each finger is a little arm1 
each finger tip a  little palm4 ,the    
lips are the lids of the mouth1 the lids

 are the  lips of the eyes--and so on4  
,the law of ,rhythmic ,diminution is    
illustrated in the tapering of the      
entire body and of the limbs1 in  the   
graduated sizes and lengths of the palm 
and the toes1 and in  the successively  
decreasing length of the palm and the   
joints of the  fingers1 so that in      
closing the hand the fingers describe   
natural  spirals 7,illustrations #cg1   
#ch74 ,finally1 the limbs radiate as it 
were  from the trunk1 the fingers from a
 point in the wrist1 the toes from  a   
point in the ankle4 ,the ribs radiate   
from the spinal column like the  veins  
of a leaf from its midrib 7,illustration
 #ci74    ,illustration #dj    ,the     
relation of these laws of beauty to the 
art of architecture has  been shown     
already4 ,they are reiterated here only 
to show that man is  indeed the         
microcosm--a little world fashioned from
 the same elements  and in accordance   
with the same ,beautiful ,necessity as  
is the  greater world in which he       

dwells4 ,when he builds a house or      
temple he  builds it not literally in   
his own image1 but according to the laws
 of  his own being1 and there are       
correspondences not altogether fanciful 
between the animate body of flesh and   
the inanimate body of stone4 ,do  we not
 all of us1 consciously or              
unconsciously1 recognize the fact  of   
character and physiognomy in buildings8 
,are they not1 to our  imagination1     
masculine or feminine1 winning or       
forbidding--human1  in point of fact--to
 a greater degree than anything else of 
man's  creating8 ,they are this         
certainly to a true lover and student of
  architecture4 ,seen from a distance   
the great ,french cathedrals appear     
like crouching monsters1 half beast1    
half human3 the two towers stand  like a
 man and a woman1 mysterious and        
gigantic1 looking out over city  and    
plain4 ,the campaniles of ,italy rise   
above the churches and houses  like the 
sentinels of a sleeping camp--nor is    

their strangely human  aspect wholly    
imaginary3 these giants of mountain and 
campagna have  eyes and brazen tongues2 
rising four square1 story above story1  
with  a belfry or lookout1 like a head1 
atop1 their likeness to a man is not    
infrequently enhanced by a certain      
identity of proportion--of ratio1  that 
is1 of height to width3 ,giotto's       
beautiful tower is an example4  ,the    
caryatid is a supporting member in the  
form of a woman2 in the  ,ionic column  
we discern her stiffened1 like ,lot's   
wife1 into a pillar1  with nothing to   
show her feminine but the spirals of her
 beautiful  hair4 ,the columns which    
uphold the pediment of the ,parthenon   
are  unmistakably masculine3 the ratio  
of their breadth to their height is  the
 ratio of the breadth to the height of a
 man 7,illustration #dj74               
,illustration #da3 ,,the ,,body ,,the   
,,archetype ,,of ,,sacred ,,edifices4   
,illustration #db3 ,,the ,,vesica       
,,piscis ,,and ,,the ,,plan ,,of        

,,chartres4    ,at certain periods of   
the world's history1 periods of mystical
  enlightenment1 men have been wont to  
use the human figure1 the soul's        
temple1 as a sort of archetype for      
sacred edifices 7,illustration #da74    
,the colossi1 with calm inscrutable     
faces1 which flank the entrance to      
,egyptian temples2 the great bronze     
,buddha of ,japan1 with its dreaming    
eyes2 the little known colossal figures 
of ,india and ,china--all these  belong 
scarcely less to the domain of          
architecture than of sculpture4  ,the   
relation above referred to however is a 
matter more subtle and  occult than mere
 obvious imitation on a large scale1    
being based upon  some correspondence of
 parts1 or similarity of proportions1 or
 both4  ,the correspondence between the 
innermost sanctuary or shrine of a      
temple and the heart of a man1 and      
between the gates of that temple  and   
the organs of sense is sufficiently     
obvious1 and a relation once            

established1 the idea is susceptible of 
almost infinite development4  ,that the 
ancients proportioned their temples from
 the human figure  is no new idea1 nor  
is it at all surprising4 ,the sculpture 
of the  ,egyptians and the ,greeks      
reveals the fact that they studied the  
body  abstractly1 in its exterior       
presentment4 ,it is clear that the rules
  of its proportions must have been     
established for sculpture1 and it is    
not unreasonable to suppose that they   
became canonical in architecture  also4 
,vitruvius and ,alberti both lay stress 
on the fact that all  sacred buildings  
should be founded on the proportions of 
the human  body4    ,illustration #dc3  
,a ,,gothic ,,cathedral ,,the ,,symbol  
,,of ,,the ,,body ,,of ,,jesus  ,,christ
    ,illustration #dd3 ,,the ,,symbolism
 ,,of ,a ,,gothic ,,cathedral ,,from    
,,the  ,,rosicrucians3 ,,hargrave       
,,jennings    ,in ,france1 during the   
,middle ,ages1 a ,gothic cathedral      
became1 at the  hands of the secret     

masonic guilds1 a glorified symbol of   
the body  of ,christ4 ,to               
practical-minded students of            
architectural history1  familiar with   
the slow and halting evolution of a     
,gothic cathedral  from a ,roman        
basilica1 such an idea may seem to be   
only the  maunderings of a mystical     
imagination1 a theory evolved from the  
inner  consciousness1 entitled to no    
more consideration than the familiar    
fallacy that vaulted nave of a ,gothic  
church was an attempt to imitate  the   
green aisles of a forest4 ,it should be 
remembered however that the  habit of   
the thought of that time was mystical1  
as that of our own age  is utilitarian  
and scientific2 and the chosen language 
of mysticism is  always an elaborate and
 involved symbolism4 ,what could be more
 natural  than that a building devoted  
to the worship of a crucified ,savior   
should be made a symbol1 not of the     
cross only1 but of the body  crucified8 
,illustration #de3 ,,the ,,geometrical  

,,basis ,,of ,,the ,,human ,,figure     
,illustration #df    ,the vesica piscis 
7a figure formed by the developing arcs 
of two  equilateral triangles having a  
common side7 which in so many cases     
seems to have determined the main       
proportion of a cathedral plan--the     
interior length and width across the    
transepts--appears as an aureole  around
 the figure of ,christ in early         
representations1 a fact which  certainly
 points to a relation between the two   
7,illustrations #db1  #dc74 ,a curious  
little book1 ,the ,rosicrucians1 by     
,hargrave ,jennings1  contains an       
interesting diagram which well          
illustrates this conception  of the     
symbolism of a cathedral4 ,a copy of it 
is here given4 ,the apse  is seen to    
correspond to the head of ,christ1 the  
north transept to his  right hand1 the  
south transept to the left hand1 the    
nave to the body1  and the north and    
south towers to the right and left feet 
respectively  7,illustration #dd74      

,illustration #dg    ,the cathedral     
builders excelled all others in the     
artfulness with  which they established 
and maintained a relation between their 
architecture and the stature of a man4  
,this is perhaps one reason why  the    
,french and ,english cathedrals1 even   
those of moderate dimensions  are more  
truly impressive than even the largest  
of the great  ,renaissance structures1  
such as ,st4 ,peter's in ,rome4 ,a      
gigantic order  furnishes no true       
measure for the eye3 its vastness is    
revealed  only by the accident of some  
human presence which forms a basis  of  
comparison4 ,that architecture is not   
necessarily the most  awe-inspiring     
which gives the impression of having    
been built by  giants for the abode of  
pigmies2 like the other arts1           
architecture is  highest when it is most
 human4 ,the medival builders1 true to  
this  dictum1 employed stones of a size 
proportionate to the strength of  a man 
working without unusual mechanical aids2

 the great piers and  columns1 built up 
of many such stones1 were commonly      
subdivided  into clusters1 and the      
circumference of each shaft of such a   
cluster  approximated the girth of a    
man2 by this device the moulding of the 
base and the foliation of the caps were 
easily kept in scale4 ,wherever  a      
balustrade occurred it was proportioned 
not with relation to the  height of the 
wall or the column below1 as in classic 
architecture1  but with relation to a   
man's stature4    ,illustration #dh3    
,,figure ,,divided ,,according ,,to     
,,the ,,egyptian ,,canon    ,it may be  
stated as a general rule that every work
 of architecture1  of whatever style1   
should have somewhere about it something
 fixed and  enduring to relate it to the
 human figure1 if it be only a flight of
  steps in which each one is the measure
 of a stride4 ,in the ,farnese1  the    
,riccardi1 the ,strozzi1 and many       
another ,italian palace1 the stone  seat
 about the base gives scale to the      

building because the beholder  knows    
instinctively that the height of such a 
seat must have some  relation to the    
length of a man's leg4 ,in the ,pitti   
palace the  balustrade which crowns each
 story answers a similar purpose3 it    
stands in no intimate relation to the   
gigantic arches below1 but is  of a     
height convenient for lounging elbows4  
,the door to ,giotto's  campanile       
reveals the true size of the tower as   
nothing else could1  because it is so   
evidently related to the human figure   
and not to the  great windows higher up 
in the shaft4    ,illustration #di3     
,,the ,,medi,,val ,,method ,,of         
,,drawing ,,the ,,figure    ,the        
geometrical plane figures which play the
 most important part in  architectural  
proportion are the square1 the circle   
and the triangle2  and the human figure 
is intimately related to these          
elementary forms4  ,if a man stand with 
heels together1 and arms outstretched   
horizontally  in opposite directions1 he

 will be inscribed1 as it were1 within a
  square2 and his arms will mark1 with  
fair accuracy1 the base of an  inverted 
equilateral triangle1 the apex of which 
will touch the ground  at his feet4 ,if 
the arms be extended upward at an angle1
 and the  legs correspondingly          
separated1 the extremities will touch   
the circumferences of a circle having   
its center in the navel  7,illustrations
 #de1 #df74    ,illustration #ej    ,the
 figure has been variously analyzed with
 a view to establishing  numerical      
ratios between its parts 7,illustrations
 #dg1 #dh1 #di74 ,some  of these are so 
simple and easily remembered that they  
have obtained  a certain popular        
currency2 such as that the length of the
 hand equals  the length of the face2   
that the span of the horizontally       
extended  arms equals the height2 and   
the well known rule that twice around   
the wrist is once around the neck1 and  
twice around the neck is once  around   
the waist4 ,the ,roman architect        

,vitruvius1 writing in the age of       
,augustus ,csar1 formulated the         
important proportions of the statues  of
 classical antiquity1 and except that he
 makes the head smaller than  the normal
 7as it should be in heroic statuary71  
the ratios which  he gives are those to 
which the ideally perfect male figure   
should  conform4 ,among the ancients the
 foot was probably the standard of all  
large measurements1 being a more        
determinate length than that of the     
head or face1 and the height was six    
lengths of the foot4 ,if the head  be   
taken as a unit1 the ratio becomes #a3h1
 and if the face--#a3aj4    ,doctor     
,rimmer1 in his ,art ,anatomy1 divides  
the figure into four  parts1 three of   
which are equal1 and correspond to the  
lengths of  the leg1 the thigh and the  
trunk2 while the fourth part1 which is  
two-thirds of one of these thirds1      
extends from the sternum to the  crown  
of the head4 ,one excellence of such a  
division aside from its  simplicity1    

consists in the fact that it may be     
applied to the face as  well4 ,the      
lowest of the three major divisions     
extends from the tip of  the chin to the
 base of the nose1 the next coincides   
with the height  of the nose 7its top   
being level with the eyebrows71 and the 
last with  the height of the forehead1  
while the remaining two-thirds of one of
  these thirds represents the horizontal
 projection from the beginning  of the  
hair on the forehead to the crown of the
 head4 ,the middle of  the three larger 
divisions locates the ears1 which are   
the same height  as the nose            
7,illustrations #de1 #dg74    ,such     
analyses of the figure1 however         
conducted1 reveals an  all-pervasive    
harmony of parts1 between which definite
 numerical  relations are traceable1 and
 an apprehension of these should assist 
the architectural designer to arrive at 
beauty of proportion by  methods of his 
own1 not perhaps in the shape of rigid  
formul1 but  present in the             

consciousness as a restraining          
influence1 acting and  reacting upon the
 mind with a conscious intention toward 
rhythm and  harmony4 ,by means of such  
exercises1 he will approach nearer to an
  understanding of that great mystery1  
the beauty and significance of  numbers1
 of which mystery music1 architecture1  
and the human figure  are equally       
presentments--considered1 that is1 from 
the standpoint of  the occultist4       
,v    ,,latent ,,geometry               
,illustration #ea3 ,,the ,,hexagram     
,,and ,,equilateral ,,triangle ,,in     
,,nature    ,it is a well known fact    
that in the microscopically minute of   
nature1  units everywhere tend to       
arrange themselves with relation to     
certain  simple geometrical solids1     
among which are the tetrahedron1 the    
cube1  and the sphere4 ,this process    
gives rise to harmony1 which may be     
defined as the relation between parts   
and unity1 the simplicity latent  in the
 infinitely complex1 the potential      

complexity of that which is  simple4    
,proceeding to things visible and       
tangible1 this indwelling  harmony1     
rhythm1 proportion1 which has its basis 
in geometry and  number1 is seen to     
exist in crystals1 flower forms1 leaf   
groups1 and  the like1 where it is      
obvious2 and in the more highly         
organized world  of the animal kingdom  
also2 though here the geometry is latent
 rather  than patent1 eluding though not
 quite defying analysis1 and thus       
augmenting beauty1 which like a woman is
 alluring in proportion as she  eludes  
7,illustrations #ea1 #eb1 #ec74         
,illustration #eb3 ,,proportions ,,of   
,,the ,,horse    ,illustration #ec      
,by the true artist1 in the crystal     
mirror of whose mind the universal      
harmony is focused and reflected1 this  
secret of the cause and source  of      
rhythm--that it dwells in a correlation 
of parts based on an  ultimate          
simplicity--is instinctively            
apprehended4 ,a knowledge of it  formed 

part of the equipment of the painters   
who made glorious the  golden noon of   
pictorial art in ,italy during the      
,renaissance4 ,the  problem which       
preoccupied them was1 as ,symonds says  
of ,leonardo1  to submit the freest play
 of form to simple figures of geometry  
in  grouping4 ,alberti held that the    
painter should above all things have    
mastered geometry1 and it is known that 
the study of perspective and  kindred   
subjects was widespread and popular4    
,illustration #ed    ,the first painter 
who deliberately rather than            
instinctively based  his compositions on
 geometrical principles seems to have   
been ,fra  ,bartolommeo1 in his ,last   
,judgment1 in the church of ,st4 ,maria 
,nuova1  in ,florence4 ,symonds says of 
this picture1 ,simple figures--the      
pyramid and triangle1 upright1 inverted1
 and interwoven like the  rhymes of a   
sonnet--form the basis of the           
composition4 ,this system was  adhered  
to by the ,fratre in all his subsequent 

works 7,illustration  #ed74 ,raphael1   
with that power of assimilation which   
distinguishes  him among men of genius1 
learned from ,fra ,bartolommeo this     
method  of disposing figures and        
combining them in masses with almost    
mathematical precision4 ,it would have  
been indeed surprising if  ,leonardo da 
,vinci1 in whom the artist and the man  
of science were  so wonderfully united1 
had not been greatly preoccupied with   
the  mathematics of the art of painting4
 ,his ,madonna of the ,rocks1 and       
,virgin on the ,lap of ,saint ,anne1 in 
the ,louvre1 exhibit the very           
perfection of pyramidal composition4 ,it
 is however in his masterpiece1  ,the   
,last ,supper1 that he combines         
geometrical symmetry and precision  with
 perfect naturalness and freedom in the 
grouping of individually  interesting   
and dramatic figures4 ,michael ,angelo1 
,andrea del ,sarto1  and the great      
,venetians1 in whose work the art of    
painting may be said  to have           

culminated1 recognized and obeyed those 
mathematical laws of  composition known 
to their immediate predecessors1 and the
 decadence  of the art in the ensuing   
period may be traced not alone to the   
false  sentiment and affectation of the 
times1 but also in the abandonment by   
the artists of those obscurely          
geometrical arrangements and groupings  
which in the works of the greatest      
masters so satisfy the eye and  haunt   
the memory of the beholder              
7,illustrations #ee1 #ef74              
,illustration #ee3 ,,the ,,employment   
,,of ,,the ,,equilateral ,,triangle ,,in
  ,,renaissance ,,painting              
,illustration #ef3 ,,geometrical ,,basis
 ,,of ,,the ,,sistine ,,ceiling         
,,paintings    ,illustration #eg3       
,,assyrian2 ,,greek    ,illustration    
#eh3 ,,the ,,geometrical ,,basis ,,of   
,,the ,,plan ,,in ,,architectural       
,,design    ,illustration #ei           
,sculpture1 even more than painting1 is 
based on geometry4 ,the colossi  of     

,egypt1 the bas-reliefs of ,assyria1 the
 figured pediments and  metopes of the  
temples of ,greece1 the carved tombs of 
,revenna1  the ,della ,robbia lunettes1 
the sculptured tympani of ,gothic church
  portals1 all alike lend themselves in 
greater or less degree to a  geometrical
 synopsis 7,illustration #eg74 ,whenever
 sculpture suffered  divorce from       
architecture the geometrical element    
became less  prominent1 doubtless       
because of all the arts architecture is 
the most  clearly and closely related to
 geometry4 ,indeed1 it may be said that 
architecture is geometry made visible1  
in the same sense that music  is number 
made audible4 ,a building is an         
aggregation of the commonest            
geometrical forms3 parallelograms1      
prisms1 pyramids and cones--the         
cylinder appearing in the column1 and   
the hemisphere in the dome4  ,the plans 
likewise of the world's famous buildings
 reduced to their  simplest expression  
are discovered to resolve themselves    

into a few  simple geometrical figures4 
7,illustration #eh74 ,this is the bed   
rock  of all excellent design4          
,illustration #fj3 ,,egyptian2 ,,greek2 
,,roman2 ,,medi,,val    ,illustration   
#fa3 ,,jefferson',s ,,pen ,,sketch ,,for
 ,,the ,,rotunda ,,of ,,the             
,,university ,,of ,,virginia            
,illustration #fb3 ,,application ,,of   
,,the ,,equilateral ,,triangle ,,to     
,,the  ,,erechtheum ,,at ,,athens       
,illustration #fc    ,illustration #fd3 
,,the ,,equilateral ,,triangle ,,in     
,,roman ,,architecture    ,but          
architecture is geometrical in another  
and a higher sense than  this4 ,emerson 
says3 ,the pleasure a palace or a temple
 gives the eye  is that an order and a  
method has been communicated to stones1 
so that  they speak and geometrize1     
become tender or sublime with           
expression4  ,all truly great and       
beautiful works of architecture from the
 ,egyptian  pyramids to the cathedrals  
of ,ile-de-,france--are harmoniously    

proportioned1 their principal and       
subsidiary masses being related1        
sometimes obviously1 more often         
obscurely1 to certain symmetrical       
figures of geometry1 which though       
invisible to the sight and not          
consciously present in the mind of the  
beholder1 yet perform the  important    
function of cordinating the entire      
fabric into one easily  remembered      
whole4 ,upon some such principle is     
surely founded what  ,symonds calls that
 severe and lofty art of composition    
which seeks  the highest beauty of      
design in architectural harmony supreme1
 above  the melodies of gracefulness of 
detail4    ,illustration #fe3 ,,the     
,,equilateral ,,triangle ,,in ,,italian 
,,architecture    ,illustration #ff3    
,,the ,,hexagram ,,in ,,gothic          
,,architecture    ,there is abundant    
evidence in support of the theory that  
the  builders of antiquity1 the masonic 
guilds of the ,middle ,ages1 and  the   
architects of the ,italian ,renaissance1

 knew and followed certain  rules1 but  
though this theory be denied or even    
disproved--if after  all these men      
obtained their results                  
unconsciously--their creations  so lend 
themselves to a geometrical analysis    
that the claim for the  existence of    
certain canons of proportion1 based on  
geometry1 remains  unimpeached4         
,illustration #fg    ,illustration #fh  
,the plane figures principally employed 
in determining architectural  proportion
 are the circle1 the equilateral        
triangle1 and the  square--which also   
yields the right angled isosceles       
triangle4 ,it  will be noted that these 
are the two dimensional correlatives of 
the  sphere1 the tetrahedron and the    
cube1 mentioned as being among the      
determining forms in molecular          
structure4 ,the question naturally      
arises1 why the circle1 the equilateral 
triangle and the square8  ,because1     
aside from the fact that they are of all
 plane figures the  most elementary1    

they are intimately related to the body 
of man1 as  has been shown              
7,illustration #de71 and the body of man
 is as it were  the architectural       
archetype4 ,but this simply removes the 
inquiry to  a different field1 it is not
 an answer4 ,why is the body of man so  
constructed and related8 ,this leads us1
 as does every question1 to  the        
threshold of a mystery upon which       
theosophy alone is able to throw  light4
 ,any extended elucidation would be out 
of place here3 it is  sufficient to     
remind the reader that the circle is the
 symbol of the  universe2 the           
equilateral triangle1 of the higher     
trinity 7atma1  buddhi1 manas72 and the 
square1 of the lower quaternary of man's
  sevenfold nature4    ,illustration #fi
    ,illustration #gj    ,the square is 
principally used in preliminary         
plotting3 it is the  determining figure 
in many of the palaces of the ,italian  
,renaissance2  the ,arc de ,triomphe1 in
 ,paris is a modern example of its use  

7,illustrations #ei1 #fj74 ,the circle  
is often employed in conjunction  with  
the square and the triangle4 ,in ,thomas
 ,jefferson's ,rotunda for  the         
,university of ,virginia1 a single great
 circle was the determining  figure1 as 
his original pen sketch of the building 
shows 7,illustration  #fa74 ,some of the
 best ,roman triumphal arches submit    
themselves to a  circular synopsis1 and 
a system of double intersecting circles 
has  been applied1 with interesting     
results1 to faades as widely different  
as those of the ,parthenon and the      
,farnese ,palace in ,rome1 though  it   
would be fatuous to claim that these    
figures determined the  proportions of  
the faades4    ,by far the most         
important figure in architectural       
proportion1  considered from the        
standpoint of geometry1 is the          
equilateral  triangle4 ,it would seem   
that the eye has an especial fondness   
for  this figure1 just as the ear has   
for certain related sounds4 ,indeed it  

might not be too fanciful to assert that
 the common chord of any key  7the tonic
 with its third and fifth7 is the       
musical equivalent of  the equilateral  
triangle4 ,it is scarcely necessary to  
dwell upon  the properties and unique   
perfection of this figure4 ,of all      
regular  polygons it is the simplest3   
its three equal sides subtend equal     
angles1 each of #fj degrees2 it trisects
 the circumference of a circle2  it is  
the graphic symbol of the number three1 
and hence of every  threefold thing2    
doubled1 its generating arcs form the   
vesica  piscis1 of so frequent          
occurrence in early ,christian art2 two 
symmetrically intersecting equilateral  
triangles yield the figure  known as    
,solomon's ,seal1 or the ,shield of     
,david1 to which mystic  properties have
 always been ascribed4    ,it may be    
stated as a general rule that whenever  
three important  points in any          
architectural composition coincide      
7approximately or  exactly7 with the    

three extremities of an equilateral     
triangle1 it  makes for beauty of       
proportion4 ,an ancient and notable     
example occurs  in the pyramids of      
,egypt1 the sides of which1 in their    
original  condition1 are believed to    
have been equilateral triangles4 ,it is 
a  demonstrable fact that certain       
geometrical intersections yield the     
important proportions of ,greek         
architecture4 ,the perfect little       
,erechtheum would seem to have been     
proportioned by means of the            
equilateral triangle and the angle of   
#fj degrees1 both in general and  in    
detail 7,illustration #fb74 ,the same   
angle1 erected from the central  axis of
 a column at the point where it         
intersects the architrave1  determines  
both the projection of the cornice and  
the height of  the architrave in many of
 the finest ,greek and ,roman temples   
7,illustrations #fg-gj74 ,the           
equilateral triangle used in conjunction
  with the circle and the square was    

employed by the ,romans in  determining 
the proportions of triumphal arches1    
basilicas and  baths4 ,that the same    
figure was a factor in the designing of 
,gothic  cathedrals is sufficiently     
indicated in the accompanying facsimile 
reproductions of an illustration from   
the ,como ,vitruvius1 published in      
,milan in #aeba1 which shows a vertical 
section of the ,milan cathedral  and the
 system of equilateral triangles which  
determined its various  parts           
7,illustration #ga74 ,the vesica piscis 
was often used to  establish the two    
main internal dimensions of the         
cathedral plan3 the  greatest diameter  
of the figure corresponding with the    
width across  the transepts1 the upper  
apex marking the limit of the apse1 and 
the  lower1 the termination of the nave4
 ,such a proportion is seen to be  both 
subtle and simple1 and possesses the    
advantage of being easily  laid out4    
,the architects of the ,italian         
,renaissance doubtless  inherited       

certain of the ,roman canons of         
architectural proportion1  for they seem
 very generally to have recognized them 
as an essential  principle of design4   
,illustration #ga    ,nevertheless1 when
 all is said1 it is easy to exaggerate  
the  importance of this matter of       
geometrical proportion4 ,the designer   
who seeks the ultimate secret of        
architectural harmony in mathematics    
rather than in the trained eye1 is      
following the wrong road to  success4 ,a
 happy inspiration is worth all the     
formul in the world--if  it be really   
happy1 the artist will probably find    
that he has  followed the rules without 
knowing them4 ,even while formulating   
concepts of art1 the author must        
reiterate ,schopenhauer's dictum  that  
the concept is unfruitful in art4 ,the  
mathematical analysis  of spatial beauty
 is an interesting study1 and a useful  
one to the  artist2 but it can never    
take the place of the creative faculty1 
it  can only supplement1 restrain1      

direct it4 ,the study of proportion is  
to the architect what the study of      
harmony is to a musician--it helps  his 
genius adequately to express itself4    
,,vi    ,,the ,,arithmetic ,,of ,,beauty
      ,although architecture is based   
primarily upon geometry1 it is possible 
to express all spatial relations        
numerically3 for arithmetic1 not        
geometry1 is the universal science of   
quantity4 ,the relation of masses  one  
to another--of voids to solids1 and of  
heights and lengths to  widths--forms   
ratios2 and when such ratios are simple 
and harmonious1  architecture may be    
said1 in ,walter ,pater's famous phrase1
 to  aspire towards the condition of    
music4 ,the trained eye1 and not an     
arithmetical formula1 determines what   
is1 and what is not1 beautiful          
proportion4 ,nevertheless the fact that 
the eye instinctively rejects  certain  
proportions as unpleasing1 and accepts  
others as satisfactory1  is an          
indication of the existence of laws of  

space1 based upon number1  not unlike   
those which govern musical harmony4 ,the
 secret of the deep  reasonableness of  
such selection by the senses lies hidden
 in the very  nature of number itself1  
for number is the invisible thread on   
which  the worlds are strung--the       
universe abstractly symbolized4         
,number is the within of all things--the
 first form of ,brahman4 ,it  is the    
measure of time and space2 it lurks in  
the heart-beat and is  blazoned upon the
 starred canopy of night4 ,substance1 in
 a state of  vibration1 in other words  
conditioned by number1 ceaselessly      
undergoes  the myriad transmutations    
which produce phenomenal life4 ,elements
  separate and combine chemically       
according to numerical ratios3  ,moon1  
plant1 gas1 crystal1 are concrete       
geometry and number4 ,by  the           
,pythagoreans and by the ancient        
,egyptians sex was attributed to        
numbers1 odd numbers being conceived of 
as masculine or generating1  and even   

numbers as feminine or parturitive1 on  
account of their  infinite divisibility4
 ,harmonious combinations were those    
involving the marriage of a masculine   
and a feminine--an odd and an           
even--number4    ,illustration #gb3 ,a  
,,graphic ,,system ,,of ,,notation      
,numbers progress from unity to         
infinity1 and return again to unity as  
the soul1 defined by ,pythagoras as a   
self-moving number1 goes forth  from1   
and returns to ,god4 ,these two acts1   
one of projection and the  other of     
recall2 these two forces1 centrifugal   
and centripetal1 are  symbolized in the 
operations of addition and subtraction4 
,within them  is embraced the whole of  
computation2 but because every number1  
every  aggregation of units1 is also a  
new unit capable of being added  or     
subtracted1 there are also the          
operations of multiplication and        
division1 which consists in one case of 
the addition of several equal  numbers  
together1 and in the other1 of the      

subtraction of several  equal numbers   
from a greater until that is exhausted4 
,in order to  think correctly it is     
necessary to consider the whole of      
numeration1  computation1 and all       
mathematical processes whatsoever as the
  division of the unit into its         
component parts and the establishment   
of relations between these parts4       
,illustration #gc    ,illustration #gd  
,the progression and retrogression of   
numbers in groups expressed by  the     
multiplication table gives rise to what 
may be termed numerical  conjunctions4  
,these are analogous to astronomical    
conjunctions3 the  planets1 revolving   
around the sun at different rates of    
speed1 and  in widely separated orbits1 
at certain times come into line with one
  another and with the sun4 ,they are   
then said to be in conjunction4         
,similarly1 numbers1 advancing toward   
infinity singly and in groups           
7expressed by the multiplication table71
 at certain stages of their  progression

 come into relation with one another4   
,for example1 an  important conjunction 
occurs in #ab1 for of a series of twos  
it is  the sixth1 of threes the fourth1 
of fours the third1 and of sixes the    
second4 ,it stands to #h in the ratio of
 #c3b1 and to #i1 of #d3c4 ,it is       
related to #g through being the product 
of #c and #d1 of which numbers #g  is   
the sum4 ,the numbers #aa and #ac are   
not conjunctive2 #ad is so in  the      
series of twos1 and sevens2 #ae is so in
 the series of fives and  threes4 ,the  
next conjunction after #ab1 of #c and #d
 and their first  multiples1 is in #bd1 
and the next following is in #cf1 which 
numbers  are respectively the two and   
three of a series of twelves1 each end  
being but a new beginning4              
,illustration #ge    ,it will be seen   
that this discovery of numerical        
conjunctions consists  merely of        
resolving numbers into their prime      
factors1 and that a  conjunctive number 
is a common multiple2 but by naming it  

so1 to  dismiss the entire subject as   
known and exhausted1 is to miss a  sense
 of the wonder1 beauty and rhythm of it 
all3 a mental impression  analogous to  
that made upon the eye by the           
swift-glancing balls of a  juggler1 the 
evolutions of drilling troops1 or the   
intricate figures  of a dance2 for these
 things are number concrete and animate 
in time  and space4    ,illustration #gf
    ,the truths of number are of all    
truths the most interior1 abstract  and 
difficult of apprehension1 and since    
knowledge becomes clear and  definite to
 the extent that it can be made to enter
 the mind through  the channels of      
physical sense1 it is well to accustom  
oneself to  conceiving of number        
graphically1 by means of geometrical    
symbols  7,illustration #gb71 rather    
than in terms of the familiar arabic    
notation which though admirable for     
purposes of computation1 is of  too     
condensed and arbitrary a character to  
reveal the properties of  individual    

numbers4 ,to state1 for example1 that #d
 is the first square1  and #h the first 
cube1 conveys but a vague idea to most  
persons1 but if  #d be represented as a 
square enclosing four smaller squares1  
and #h  as a cube containing eight      
smaller cubes1 the idea is apprehended  
immediately and without effort4 ,the    
number #c is of course the  triangle2   
the irregular and vital beauty of the   
number #e appears  clearly in the       
heptalpha1 or five-pointed star2 the    
faultless symmetry  of #f1 its relation 
to #c and #b1 and its regular division  
of the circle1  are portrayed in the    
familiar hexagram known as the ,shield  
of ,david4  ,seven1 when represented as 
a compact group of circles reveals      
itself  as a number of singular beauty  
and perfection1 worthy of the important 
place accorded to it in all mystical    
philosophy 7,illustration #gc74 ,it  is 
a curious fact that when asked to think 
of any number less than #aj1  most      
persons will choose #g4    ,illustration

 #gg    ,every form of art1 though      
primarily a vehicle for the expression  
and  transmission of particular ideas   
and emotions1 has subsidiary offices1   
just as a musical tone has harmonics    
which render it more sweet4  ,painting  
reveals the nature of color2 music1 of  
sound--in wood1  in brass1 and in       
stretched strings2 architecture shows   
forth the  qualities of light1 and the  
strength and beauty of materials4 ,all  
of the arts1 and particularly music and 
architecture1 portray in  different     
manners and degrees the truths of       
number4 ,architecture does  this in two 
ways3 esoterically as it were in the    
form of harmonic  proportions2 and      
exoterically in the form of symbols     
which represent  numbers and groups of  
numbers4 ,the fact that a series of     
threes and  a series of fours mutually  
conjoin in #ab1 finds an architectural  
expression in the ,tuscan1 the ,doric1  
and the ,ionic orders according to      
,vignole1 for in them all the stylobate 

is four parts1 the entablature  #c1 and 
the intermediate column #ab             
7,illustration #gd74 ,the affinity      
between #d and #g1 revealed in the fact 
that they express 7very nearly7  the    
ratio between the base and the altitude 
of the right-angled  triangle which     
forms half of an equilateral1 and the   
musical interval  of the diminished     
seventh1 is architecturally suggested in
 the ,palazzo  ,giraud1 which is four   
stories in height with seven openings in
 each  story 7,illustration #ge74       
,illustration #gh    ,illustration #gi  
,illustration #hj    ,illustration #ha  
,every building is a symbol of some     
number or group of numbers1 and  other  
things being equal the more perfect the 
numbers involved the  more beautiful    
will be the building 7,illustrations    
#gf-hb74 ,the numbers  #e and #g--those 
which occur oftenest--are the most      
satisfactory because  being of small    
quantity1 they are easily grasped by the
 eye1 and being  odd1 they yield a      

center or axis1 so necessary in every   
architectural  composition4 ,next in    
value are the lowest multiples of these 
numbers  and the least common multiples 
of any two of them1 because the  eye1   
with a little assistance1 is able to    
resolve them into their  constituent    
factors4 ,it is part of the art of      
architecture to  render such assistance1
 for the eye counts always1 consciously 
or  unconsciously1 and when it is       
confronted with a number of units       
greater than it can readily resolve1 it 
is refreshed and rested if  these units 
are so grouped and arranged that they   
reveal themselves as  factors of some   
higher quantity4    ,illustration #hb   
,illustration #hc3 ,a ,,numerical       
,,analysis ,,of ,,gothic ,,tracery      
,there is a raison d'tre for string     
courses other than to mark the  position
 of a floor on the interior of a        
building1 and for quoins and  pilasters 
other than to indicate the presence of a
 transverse wall4  ,these sometimes     

serve the useful purpose of so          
subdividing a faade  that the eye       
estimates the number of its openings    
without conscious  effort and consequent
 fatigue 7,illustration #hb74 ,the      
tracery of ,gothic  windows forms       
perhaps the highest and finest          
architectural expression  of number     
7,illustration #hc74 ,just as thirst    
makes water more sweet1 so  does ,gothic
 tracery confuse the eye with its       
complexity only the more  greatly to    
gratify the sight by revealing the      
inherent simplicity in  which this      
complexity has its root4 ,sometimes1 as 
in the case of  the ,venetian ,ducal    
,palace1 the numbers involved are too   
great for  counting1 but other and      
different arithmetical truths are       
portrayed2  for example1 the            
multiplication of the first arcade by #b
 in  the second1 and this by #c in the  
cusped arches1 and by #d in the         
quatrefoils immediately above4          
,illustration #hd3 ,,numeration ,,in    

,,groups ,,expressed ,,architecturally  
,illustration #he3 ,,architectural      
,,ornament ,,considered ,,as ,,the      
,,objectification ,,of ,,number4        
,,multiplication ,,in ,,groups ,,of     
,,five2 ,,two2  ,,three2 ,,alternation  
,,of ,,three ,,and ,,seven              
,illustration #hf    ,seven is          
proverbially the perfect number4 ,it is 
of a quantity  sufficiently complex to  
stimulate the eye to resolve it1 and yet
 so  simple that it can be analyzed at a
 glance2 as a center with two equal     
sides1 it is possessed of symmetry1 and 
as the sum of an odd and even  number   
7#c and #d7 it has vitality and variety4
 ,all these properties a  work of       
architecture can variously reveal       
7,illustration #gg74 ,fifteen1  also1 is
 a number of great perfection4 ,it is   
possible to arrange the  first #i       
numbers in the form of a magic square so
 that the sum of  each line1 read       
vertically1 horizontally or diagonally1 
will be #ae4  ,thus3         #d    #i   

#b     #ae       #c    #e    #g     #ae 
#h    #a    #f     #ae      --   --   --
      #ae   #ae   #ae    ,its beauty is 
portrayed geometrically in the          
accompanying figure which  expresses it1
 being #ae triangles in three groups of 
#e 7,illustration  #hf74 ,few           
arrangements of openings in a faade     
better satisfy the eye  than three      
superimposed groups of five             
7,illustrations #gf-hj74 ,may not  one  
source of this satisfaction dwell in the
 intrinsic beauty of the  number #ae8   
,in conclusion1 it is perhaps well that 
the reader be again reminded  that these
 are the by-ways1 and not the highways  
of architecture3 that  the highest      
beauty comes always1 not from beautiful 
numbers1 nor  from likenesses to        
,nature's eternal patterns of the world1
 but from  utility1 fitness1 economy1   
and the perfect adaptation of means to  
ends4 ,but along with this truth there  
goes another3 that in every  excellent  
work of architecture1 in addition to its

 obvious and  individual beauty1 there  
dwells an esoteric and universal beauty1
  following as it does the archetypal   
pattern laid down by the ,great         
,architect for the building of that     
temple which is the world wherein  we   
dwell4          ,,vii    ,,frozen       
,,music      ,in the series of essays of
 which this is the final one1 the author
 has  undertaken to enforce the truth   
that evolution on any plane and on  any 
scale proceeds according to certain laws
 which are in reality only              
ramifications of one ubiquitous and ever
 operative law2 that this law  registers
 itself in the thing evolved1 leaving   
stamped thereon as it  were fossil      
footprints by means of which it may be  
known4 ,in the arts  the creative spirit
 of man is at its freest and finest1 and
 nowhere  among the arts is it so free  
and so fine as in music4 ,in music      
accordingly the universal law of        
becoming finds instant1 direct  and     
perfect self-expression2 music voices   

the inner nature of the  will-to-live in
 all its moods and moments2 in it form1 
content1  means and end are perfectly   
fused4 ,it is this fact which gives     
validity to the before quoted saying    
that all of the arts aspire  toward the 
condition of music4 ,all aspire to      
express the law1 but  music1 being least
 encumbered by the leaden burden of     
materiality1  expresses it most easily  
and adequately4 ,this being so there is 
nothing unreasonable in attempting to   
apply the known facts of musical        
harmony and rhythm to any other art1 and
 since these essays concern  themselves 
primarily with architecture1 the final  
aspect in which  that art will be       
presented here is as frozen             
music--ponderable form  governed by     
musical law4    ,music depends primarily
 upon the equal and regular division of 
time  into beats1 and of these beats    
into measures4 ,over this soundless and 
invisible warp is woven an infinitely   
various melodic pattern1 made  up of    

tones of different pitch and duration   
arithmetically related  and combined    
according to the laws of harmony4       
,architecture1  correspondingly1 implies
 the rhythmical division of space1 and  
obedience to laws numerical and         
geometrical4 ,a certain identity        
therefore exists between simple harmony 
in music1 and simple  proportion in     
architecture4 ,by translating the       
consonant  tone-intervals into number1  
the common denominator1 as it were1 of  
both arts1 it is possible to give these 
intervals a spatial1 and  hence an      
architectural1 expression4 ,such        
expression1 considered as  proportion   
only and divorced from ornament1 will   
prove pleasing to  the eye in the same  
way that its correlative is pleasing to 
the ear1  because in either case it is  
not alone the special organ of sense    
which is gratified1 but the inner ,self1
 in which all senses are one4           
,containing within itself the mystery of
 number1 it thrills responsive  to every

 audible or visible presentment of that 
mystery4    ,illustration #hg    ,if a  
vibrating string yielding a certain     
musical note be stopped in  its center1 
that is1 divided by half1 it will then  
sound the octave  of that note4 ,the    
numerical ratio which expresses the     
interval of  the octave is therefore    
#a3b4 ,if one-third instead of one-half 
of the  string be stopped1 and the      
remaining two-thirds struck1 it will    
yield  the musical fifth of the original
 note1 which thus corresponds to the    
ratio #b3c4 ,the length represented by  
#c3d yields the fourth2 #d3e the  major 
third2 and #e3f the minor third4 ,these 
comprise the principal  consonant       
intervals within the range of one       
octave4 ,the ratios of  inverted        
intervals1 so called1 are found by      
doubling the smaller  number of the     
original interval as given above3 #b3c1 
the fifth1 gives  #c3d1 the fourth2     
#d3e1 the major third1 gives #e3h1 the  
minor sixth2  #e3f1 the minor third1    

gives #f3aj1 or #c3e1 the major sixth4  
,illustration #hh3 ,,architecture ,,as  
,,harmony    ,of these various consonant
 intervals the octave1 fifth1 and major 
third are the most important1 in the    
sense of being the most perfect1  and   
they are expressed by numbers of the    
smallest quantity1 an odd  number and an
 even4 ,it will be noted that all the   
intervals above  given are expressed by 
the numbers #a1 #b1 #c1 #d1 #e and #f1  
except the  minor sixth 7#e3h71 and this
 is the most imperfect of all consonant 
intervals4 ,the sub-minor seventh1      
expressed by the ratio #d3g though      
included among the dissonances1 forms1  
according to ,helmholtz1 a more  perfect
 consonance with the tonic than does the
 minor sixth4    ,a natural deduction   
from these facts is that relations of   
architectural length and breadth1 height
 and width1 to be musical  should be    
capable of being expressed by ratios of 
quantitively small  numbers1 preferably 
an odd number and an even4 ,although    

generally  speaking the simpler the     
numerical ratio the more perfect the    
consonance1 yet the intervals of the    
fifth and major third 7#b3c and  #d3e71 
are considered to be more pleasing than 
the octave 7#a3b71 which  is too        
obviously a repetition of the original  
note4 ,from this it is  reasonable to   
assume 7and the assumption is borne out 
by experience71  that proportions1 the  
numerical ratios of which the eye       
resolves too  readily1 become at last   
wearisome4 ,the relation should be felt 
rather  than fathomed4 ,there should be 
a perception of identity1 and also  of  
difference4 ,as in music1 where         
dissonances are introduced to give      
value to consonances which follow them1 
so in architecture simple  ratios should
 be employed in connection with those   
more complex4    ,illustration #hi      
,harmonics are those tones which sound  
with1 and reinforce any musical  note   
when it is sounded4 ,the distinguishable
 harmonics of the tonic  yield the      

ratios #a3b1 #b3c1 #c3d1 #d3e1 and #d3g4
 ,a note and its harmonics  form a      
natural chord4 ,they may be compared to 
the widening circles  which appear in   
still water when a stone is dropped into
 it1 for when  a musical sound disturbs 
the quietude of that pool of silence    
which  we call the air1 it ripples into 
overtones1 which becoming fainter  and  
fainter1 die away into silence4 ,it     
would seem reasonable to assume  that   
the combination of numbers which express
 these overtones1 if  translated into   
terms of space1 would yield proportions 
agreeable  to the eye1 and such is the  
fact1 as the accompanying examples      
sufficiently indicate 7,illustrations   
#hg-ij74    ,the interval of the        
sub-minor seventh 7#d3g71 used in this  
way1 in  connection with the simpler    
intervals of the octave 7#a3b71 and the 
fifth 7#b3c71 is particularly pleasing  
because it is neither too  obvious nor  
too subtle4 ,this ratio of #d3g is      
important for the reason  that it       

expresses the angle of sixty degrees1   
that is1 the numbers #d  and #g         
represent 7very nearly7 the ratio       
between one-half the base and  the      
altitude of an equilateral triangle3    
also because they form part  of the     
numerical series #a1 #d1 #g1 #aj1 etc4  
,both are mystic numbers1  and in       
,gothic architecture particularly1      
proportions were frequently  determined 
by numbers to which a mystic meaning was
 attached4  ,according to ,gwilt1 the   
,gothic chapels of ,windsor and ,oxford 
are  divided longitudinally by four1 and
 transversely by seven equal parts4     
,the arcade above the roses in the faade
 of the cathedral of ,tours  shows seven
 principal units across the front of the
 nave1 and four in  each of the towers4 
,a distinguishing characteristic of the 
series of ratios which  represent the   
consonant intervals within the compass  
of an octave is  that it advances by the
 addition of #a to both terms3 #a3b1    
#b3c1  #c3d1 #d3e1 and #e3f4 ,such a    

series always approaches unity1 just as1
  represented graphically by means of   
parallelograms1 it tends toward a       
square4 ,alberti in his book presents a 
design for a tower showing his  idea for
 its general proportions4 ,it consists  
of six stories1 in a  sequence of       
orders4 ,the lowest story is a perfect  
cube and each of the  other stories is  
#aa-abths of the story below1           
diminishing practically  in the         
proportion of #h1 #g1 #f1 #e1 #d1 #c1   
allowing in each case for the  amount   
hidden by the projection of the cornice 
below2 each order being  accurate as    
regards column1 entablature1 etc4 ,it is
 of interest to  compare this with      
,ruskin's idea in his ,seven ,lamps1    
where he takes  the case of a plant     
called ,alisma ,plantago1 in which the  
various  branches diminish in the       
proportion of #g1 #f1 #e1 #d1 #c1       
respectively1  and so carry out the same
 idea2 on which ,ruskin observes that   
diminution in a building should be after

 the manner of ,nature4    ,illustration
 #ij3 ,,arcade ,,of ,,the ,,cancelleria 
,it would be a profitless task to       
formulate exact rules of  architectural 
proportion based upon the laws of       
musical harmony4 ,the  two arts are too 
different from each other for that1 and 
moreover  the last appeal must always be
 to the eye1 and not to a mathematical  
formula1 just as in music the last      
appeal is to the ear4 ,laws there  are1 
but they discover themselves to the     
artist as he proceeds1 and  are for the 
most part incommunicable4 ,rules and    
formul are useful and  valuable not as a
 substitute for inspiration1 but as a   
guide3 not as  wings1 but as a tail4 ,in
 this connection perhaps all that is    
necessary  for the architectural        
designer to bear in mind is that        
important  ratios of length and breadth1
 height and width1 to be musical should 
be expressed by quantitively small      
numbers1 and that if possible they      
should obey some simple law of numerical

 progression4 ,from this basic          
simplicity complexity will follow1 but  
it will be an ordered and  harmonious   
complexity1 like that of a tree1 or of a
 symphony4    ,illustration #ia3 ,,the  
,,palazzo ,,verzi ,,at ,,verona 7,,lower
 ,,portion ,,only74  ,a ,,composition   
,,founded ,,on ,,the ,,equal ,,and      
,,regular ,,division ,,of ,,space1 ,,as 
,,music ,,is ,,founded ,,on ,,the       
,,equal ,,and ,,regular ,,division ,,of 
,,time4    ,illustration #ib3           
,,architecture ,,as ,,rhythm4 ,a        
,,division ,,of ,,space  ,,corresponding
 ,,to #c_/d ,,and #d_/d ,,time4    ,in  
the same way that a musical composition 
implies the division of  time into equal
 and regular beats1 so a work of        
architecture should  have for its basis 
some unit of space4 ,this unit should be
 nowhere too  obvious and may be varied 
within certain limits1 just as musical  
time  is retarded or accelerated4 ,the  
underlying rhythm and symmetry will     
thus give value and distinction to such 

variation4 ,vasari tells how            
,brunelleschi4 ,bramante and ,leonardo  
da ,vinci used to work on paper  ruled  
in squares1 describing it as a truly    
ingenious thing1 and of  great utility  
in the work of design4 ,by this means   
they developed  proportions according to
 a definite scheme4 ,they set to work   
with a  division of space analogous to  
the musician's division of time4  ,the  
examples given herewith indicate how    
close a parallel may exist  between     
music and architecture in this matter of
 rhythm 7,illustrations  #ia-ic74       
,illustration #ic    ,it is a           
demonstrable fact that musical sounds   
weave invisible patterns  in the air4   
,architecture1 correspondingly1 in one  
of its aspects1  is geometric pattern   
made fixed and enduring4 ,what could be 
more  essentially musical for example   
than the sea arcade of the ,venetian    
,ducal ,palace8 ,the sand forms traced  
by sound-waves on a musically  vibrating
 steel plate might easily suggest       

architectural ornament did  not the     
differences of scale and of material    
tend to confuse the mind4  ,the         
architect should occupy himself with    
identities1 not differences4  ,if he    
will but bear in mind that architecture 
is pattern in space1  just as music is  
pattern in time1 he will come to        
perceive the  essential identity        
between1 say1 a ,greek rosette and a    
,gothic  rose-window2 an arcade and an  
egg and dart moulding 7,illustration    
#id74  ,all architectural forms and     
arrangements which give enduring        
pleasure  are in their essence musical4 
,every well composed faade makes harmony
  in three dimensions2 every good       
roof-line sings a melody against the    
sky4    ,illustration #id3              
,,architecture ,,as ,,pattern           
,,conclusion      ,in taking leave of   
the reader at the end of this excursion 
together  among the by-ways of a        
beautiful art1 the author must needs add
 a  final word or two touching upon the 

purpose and scope of these essays4      
,architecture 7like everything else7 has
 two aspects3 it may be viewed  from the
 standpoint of utility1 that is1 as     
construction2 or from the  standpoint of
 expressiveness1 that is1 as decoration4
 ,no attempt has  been made here to deal
 with its first aspect1 and of the      
second  7which is again twofold71 only  
the universal1 not the particular       
expressiveness has been sought4 ,the    
literature of architecture is rich  in  
works dealing with the utilitarian and  
constructive side of the  art3 indeed1  
it may be said that to this side that   
literature is  almost exclusively       
devoted4 ,this being so1 it has seemed  
worth while  to attempt to show the     
reverse of the medal1 even though it be 
tails  instead of heads4    ,it will be 
noted that the inductive method has not1
 in these pages1  been honored by a due 
observance4 ,it would have been easy to 
have treated the subject inductively1   
amassing facts and drawing  conclusions1

 but to have done so the author would   
have been false  to the very principle  
about which the work came into being4   
,with the  acceptance of the ,ancient   
,wisdom1 the inductive method becomes   
no longer necessary4 ,facts are not     
useful in order to establish a          
hypothesis1 they are used rather to     
elucidate a known and accepted  truth4  
,when theosophical ideas shall have     
permeated the thought of  mankind1 this 
work1 if it survives at all1 will be    
chiefly--perhaps  solely--remarkable by 
reason of the fact that it was among the
  first in which the attempt was made   
again to unify science1 art and         
religion1 as they were unified in those 
ancient times and among those  ancient  
peoples when the ,wisdom swayed the     
hearts and minds of men4